LMFDB - Embedded newform 4235.2.a.bk.1.2

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			1.2
Root			$-1.83371$ 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)

$f(q)$	$=$	$q-1.83371 q^{2} -1.24345 q^{3} +1.36250 q^{4} +1.00000 q^{5} +2.28012 q^{6} -1.00000 q^{7} +1.16899 q^{8} -1.45384 q^{9} +O(q^{10})$	\(q-1.83371 q^{2} -1.24345 q^{3} +1.36250 q^{4} +1.00000 q^{5} +2.28012 q^{6} -1.00000 q^{7} +1.16899 q^{8} -1.45384 q^{9} -1.83371 q^{10} -1.69420 q^{12} +2.32528 q^{13} +1.83371 q^{14} -1.24345 q^{15} -4.86859 q^{16} -4.59626 q^{17} +2.66592 q^{18} -7.12249 q^{19} +1.36250 q^{20} +1.24345 q^{21} -9.05919 q^{23} -1.45358 q^{24} +1.00000 q^{25} -4.26390 q^{26} +5.53811 q^{27} -1.36250 q^{28} +4.99497 q^{29} +2.28012 q^{30} -9.24132 q^{31} +6.58962 q^{32} +8.42822 q^{34} -1.00000 q^{35} -1.98086 q^{36} +7.21523 q^{37} +13.0606 q^{38} -2.89137 q^{39} +1.16899 q^{40} +7.07508 q^{41} -2.28012 q^{42} -7.35367 q^{43} -1.45384 q^{45} +16.6119 q^{46} -8.20509 q^{47} +6.05384 q^{48} +1.00000 q^{49} -1.83371 q^{50} +5.71521 q^{51} +3.16820 q^{52} -5.89627 q^{53} -10.1553 q^{54} -1.16899 q^{56} +8.85643 q^{57} -9.15934 q^{58} +8.08132 q^{59} -1.69420 q^{60} -0.0843910 q^{61} +16.9459 q^{62} +1.45384 q^{63} -2.34628 q^{64} +2.32528 q^{65} -12.3209 q^{67} -6.26241 q^{68} +11.2646 q^{69} +1.83371 q^{70} +1.50066 q^{71} -1.69952 q^{72} +16.3973 q^{73} -13.2307 q^{74} -1.24345 q^{75} -9.70439 q^{76} +5.30193 q^{78} +12.5640 q^{79} -4.86859 q^{80} -2.52483 q^{81} -12.9737 q^{82} +7.62857 q^{83} +1.69420 q^{84} -4.59626 q^{85} +13.4845 q^{86} -6.21098 q^{87} -5.73477 q^{89} +2.66592 q^{90} -2.32528 q^{91} -12.3432 q^{92} +11.4911 q^{93} +15.0458 q^{94} -7.12249 q^{95} -8.19384 q^{96} -16.7237 q^{97} -1.83371 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−1.83371	−1.29663	−0.648315	−	0.761372i	$-0.724526\pi$
$2$	−1.83371	−1.29663	−0.648315	+	0.761372i	$0.724526\pi$
$3$	−1.24345	−0.717904	−0.358952	−	0.933356i	$-0.616866\pi$
$3$	−1.24345	−0.717904	−0.358952	+	0.933356i	$0.616866\pi$
$4$	1.36250	0.681251
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	2.28012	0.930857
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	1.16899	0.413300
$9$	−1.45384	−0.484613
$10$	−1.83371	−0.579871
$11$	0	0
$11$	0	0
$12$	−1.69420	−0.489073
$13$	2.32528	0.644917	0.322459	−	0.946584i	$-0.395491\pi$
$13$	2.32528	0.644917	0.322459	+	0.946584i	$0.395491\pi$
$14$	1.83371	0.490080
$15$	−1.24345	−0.321057
$16$	−4.86859	−1.21715
$17$	−4.59626	−1.11476	−0.557379	−	0.830258i	$-0.688193\pi$
$17$	−4.59626	−1.11476	−0.557379	+	0.830258i	$0.688193\pi$
$18$	2.66592	0.628364
$19$	−7.12249	−1.63401	−0.817005	−	0.576630i	$-0.804367\pi$
$19$	−7.12249	−1.63401	−0.817005	+	0.576630i	$0.804367\pi$
$20$	1.36250	0.304665
$21$	1.24345	0.271342
$22$	0	0
$23$	−9.05919	−1.88897	−0.944486	−	0.328552i	$-0.893439\pi$
$23$	−9.05919	−1.88897	−0.944486	+	0.328552i	$0.893439\pi$
$24$	−1.45358	−0.296710
$25$	1.00000	0.200000
$26$	−4.26390	−0.836220
$27$	5.53811	1.06581
$28$	−1.36250	−0.257489
$29$	4.99497	0.927543	0.463771	−	0.885955i	$-0.346496\pi$
$29$	4.99497	0.927543	0.463771	+	0.885955i	$0.346496\pi$
$30$	2.28012	0.416292
$31$	−9.24132	−1.65979	−0.829895	−	0.557920i	$-0.811600\pi$
$31$	−9.24132	−1.65979	−0.829895	+	0.557920i	$0.811600\pi$
$32$	6.58962	1.16489
$33$	0	0
$34$	8.42822	1.44543
$35$	−1.00000	−0.169031
$36$	−1.98086	−0.330143
$37$	7.21523	1.18618	0.593088	−	0.805137i	$-0.297908\pi$
$37$	7.21523	1.18618	0.593088	+	0.805137i	$0.297908\pi$
$38$	13.0606	2.11871
$39$	−2.89137	−0.462989
$40$	1.16899	0.184833
$41$	7.07508	1.10494	0.552471	−	0.833532i	$-0.313685\pi$
$41$	7.07508	1.10494	0.552471	+	0.833532i	$0.313685\pi$
$42$	−2.28012	−0.351831
$43$	−7.35367	−1.12142	−0.560712	−	0.828011i	$-0.689473\pi$
$43$	−7.35367	−1.12142	−0.560712	+	0.828011i	$0.689473\pi$
$44$	0	0
$45$	−1.45384	−0.216726
$46$	16.6119	2.44930
$47$	−8.20509	−1.19684	−0.598418	−	0.801184i	$-0.704204\pi$
$47$	−8.20509	−1.19684	−0.598418	+	0.801184i	$0.704204\pi$
$48$	6.05384	0.873796
$49$	1.00000	0.142857
$50$	−1.83371	−0.259326
$51$	5.71521	0.800289
$52$	3.16820	0.439350
$53$	−5.89627	−0.809915	−0.404958	−	0.914335i	$-0.632714\pi$
$53$	−5.89627	−0.809915	−0.404958	+	0.914335i	$0.632714\pi$
$54$	−10.1553	−1.38196
$55$	0	0
$56$	−1.16899	−0.156213
$57$	8.85643	1.17306
$58$	−9.15934	−1.20268
$59$	8.08132	1.05210	0.526049	−	0.850454i	$-0.323673\pi$
$59$	8.08132	1.05210	0.526049	+	0.850454i	$0.323673\pi$
$60$	−1.69420	−0.218720
$61$	−0.0843910	−0.0108052	−0.00540258	−	0.999985i	$-0.501720\pi$
$61$	−0.0843910	−0.0108052	−0.00540258	+	0.999985i	$0.501720\pi$
$62$	16.9459	2.15213
$63$	1.45384	0.183167
$64$	−2.34628	−0.293285
$65$	2.32528	0.288416
$66$	0	0
$67$	−12.3209	−1.50523	−0.752616	−	0.658460i	$-0.771208\pi$
$67$	−12.3209	−1.50523	−0.752616	+	0.658460i	$0.771208\pi$
$68$	−6.26241	−0.759429
$69$	11.2646	1.35610
$70$	1.83371	0.219171
$71$	1.50066	0.178096	0.0890479	−	0.996027i	$-0.471618\pi$
$71$	1.50066	0.178096	0.0890479	+	0.996027i	$0.471618\pi$
$72$	−1.69952	−0.200291
$73$	16.3973	1.91916	0.959580	−	0.281437i	$-0.0908110\pi$
$73$	16.3973	1.91916	0.959580	+	0.281437i	$0.0908110\pi$
$74$	−13.2307	−1.53803
$75$	−1.24345	−0.143581
$76$	−9.70439	−1.11317
$77$	0	0
$78$	5.30193	0.600326
$79$	12.5640	1.41356	0.706778	−	0.707436i	$-0.250148\pi$
$79$	12.5640	1.41356	0.706778	+	0.707436i	$0.250148\pi$
$80$	−4.86859	−0.544325
$81$	−2.52483	−0.280537
$82$	−12.9737	−1.43270
$83$	7.62857	0.837344	0.418672	−	0.908138i	$-0.362496\pi$
$83$	7.62857	0.837344	0.418672	+	0.908138i	$0.362496\pi$
$84$	1.69420	0.184852
$85$	−4.59626	−0.498535
$86$	13.4845	1.45407
$87$	−6.21098	−0.665887
$88$	0	0
$89$	−5.73477	−0.607885	−0.303942	−	0.952690i	$-0.598303\pi$
$89$	−5.73477	−0.607885	−0.303942	+	0.952690i	$0.598303\pi$
$90$	2.66592	0.281013
$91$	−2.32528	−0.243756
$92$	−12.3432	−1.28686
$93$	11.4911	1.19157
$94$	15.0458	1.55185
$95$	−7.12249	−0.730752
$96$	−8.19384	−0.836281
$97$	−16.7237	−1.69804	−0.849018	−	0.528365i	$-0.822805\pi$
$97$	−16.7237	−1.69804	−0.849018	+	0.528365i	$0.822805\pi$
$98$	−1.83371	−0.185233
$99$	0	0
$100$	1.36250	0.136250
$101$	−14.4661	−1.43943	−0.719717	−	0.694267i	$-0.755729\pi$
$101$	−14.4661	−1.43943	−0.719717	+	0.694267i	$0.755729\pi$
$102$	−10.4801	−1.03768
$103$	−8.81363	−0.868433	−0.434216	−	0.900809i	$-0.642975\pi$
$103$	−8.81363	−0.868433	−0.434216	+	0.900809i	$0.642975\pi$
$104$	2.71823	0.266544
$105$	1.24345	0.121348
$106$	10.8121	1.05016
$107$	−12.9494	−1.25187	−0.625935	−	0.779875i	$-0.715282\pi$
$107$	−12.9494	−1.25187	−0.625935	+	0.779875i	$0.715282\pi$
$108$	7.54569	0.726084
$109$	11.2278	1.07543	0.537713	−	0.843128i	$-0.319289\pi$
$109$	11.2278	1.07543	0.537713	+	0.843128i	$0.319289\pi$
$110$	0	0
$111$	−8.97176	−0.851562
$112$	4.86859	0.460039
$113$	8.56605	0.805826	0.402913	−	0.915238i	$-0.367998\pi$
$113$	8.56605	0.805826	0.402913	+	0.915238i	$0.367998\pi$
$114$	−16.2402	−1.52103
$115$	−9.05919	−0.844774
$116$	6.80565	0.631889
$117$	−3.38059	−0.312535
$118$	−14.8188	−1.36418
$119$	4.59626	0.421339
$120$	−1.45358	−0.132693
$121$	0	0
$122$	0.154749	0.0140103
$123$	−8.79749	−0.793243
$124$	−12.5913	−1.13073
$125$	1.00000	0.0894427
$126$	−2.66592	−0.237499
$127$	−14.1771	−1.25802	−0.629008	−	0.777399i	$-0.716539\pi$
$127$	−14.1771	−1.25802	−0.629008	+	0.777399i	$0.716539\pi$
$128$	−8.87683	−0.784609
$129$	9.14390	0.805076
$130$	−4.26390	−0.373969
$131$	−2.33604	−0.204101	−0.102050	−	0.994779i	$-0.532540\pi$
$131$	−2.33604	−0.204101	−0.102050	+	0.994779i	$0.532540\pi$
$132$	0	0
$133$	7.12249	0.617598
$134$	22.5929	1.95173
$135$	5.53811	0.476645
$136$	−5.37298	−0.460729
$137$	4.63373	0.395886	0.197943	−	0.980214i	$-0.436574\pi$
$137$	4.63373	0.395886	0.197943	+	0.980214i	$0.436574\pi$
$138$	−20.6561	−1.75836
$139$	2.67590	0.226967	0.113484	−	0.993540i	$-0.463799\pi$
$139$	2.67590	0.226967	0.113484	+	0.993540i	$0.463799\pi$
$140$	−1.36250	−0.115152
$141$	10.2026	0.859214
$142$	−2.75178	−0.230924
$143$	0	0
$144$	7.07815	0.589846
$145$	4.99497	0.414810
$146$	−30.0679	−2.48844
$147$	−1.24345	−0.102558
$148$	9.83076	0.808084
$149$	10.8701	0.890516	0.445258	−	0.895402i	$-0.353112\pi$
$149$	10.8701	0.890516	0.445258	+	0.895402i	$0.353112\pi$
$150$	2.28012	0.186171
$151$	22.3425	1.81821	0.909103	−	0.416571i	$-0.136768\pi$
$151$	22.3425	1.81821	0.909103	+	0.416571i	$0.136768\pi$
$152$	−8.32611	−0.675337
$153$	6.68223	0.540226
$154$	0	0
$155$	−9.24132	−0.742281
$156$	−3.93949	−0.315412
$157$	−6.07383	−0.484744	−0.242372	−	0.970183i	$-0.577926\pi$
$157$	−6.07383	−0.484744	−0.242372	+	0.970183i	$0.577926\pi$
$158$	−23.0387	−1.83286
$159$	7.33170	0.581442
$160$	6.58962	0.520955
$161$	9.05919	0.713964
$162$	4.62982	0.363753
$163$	18.9147	1.48152	0.740758	−	0.671772i	$-0.234467\pi$
$163$	18.9147	1.48152	0.740758	+	0.671772i	$0.234467\pi$
$164$	9.63981	0.752743
$165$	0	0
$166$	−13.9886	−1.08573
$167$	11.3437	0.877805	0.438903	−	0.898535i	$-0.355367\pi$
$167$	11.3437	0.877805	0.438903	+	0.898535i	$0.355367\pi$
$168$	1.45358	0.112146
$169$	−7.59306	−0.584082
$170$	8.42822	0.646415
$171$	10.3550	0.791863
$172$	−10.0194	−0.763971
$173$	4.14833	0.315391	0.157696	−	0.987488i	$-0.449593\pi$
$173$	4.14833	0.315391	0.157696	+	0.987488i	$0.449593\pi$
$174$	11.3892	0.863409
$175$	−1.00000	−0.0755929
$176$	0	0
$177$	−10.0487	−0.755306
$178$	10.5159	0.788202
$179$	−6.44774	−0.481926	−0.240963	−	0.970534i	$-0.577463\pi$
$179$	−6.44774	−0.481926	−0.240963	+	0.970534i	$0.577463\pi$
$180$	−1.98086	−0.147644
$181$	−7.52216	−0.559118	−0.279559	−	0.960129i	$-0.590188\pi$
$181$	−7.52216	−0.559118	−0.279559	+	0.960129i	$0.590188\pi$
$182$	4.26390	0.316061
$183$	0.104936	0.00775707
$184$	−10.5901	−0.780712
$185$	7.21523	0.530474
$186$	−21.0714	−1.54503
$187$	0	0
$188$	−11.1795	−0.815345
$189$	−5.53811	−0.402838
$190$	13.0606	0.947515
$191$	8.06190	0.583339	0.291669	−	0.956519i	$-0.405789\pi$
$191$	8.06190	0.583339	0.291669	+	0.956519i	$0.405789\pi$
$192$	2.91748	0.210551
$193$	−2.13696	−0.153822	−0.0769109	−	0.997038i	$-0.524506\pi$
$193$	−2.13696	−0.153822	−0.0769109	+	0.997038i	$0.524506\pi$
$194$	30.6665	2.20172
$195$	−2.89137	−0.207055
$196$	1.36250	0.0973215
$197$	−21.5102	−1.53254	−0.766268	−	0.642521i	$-0.777888\pi$
$197$	−21.5102	−1.53254	−0.766268	+	0.642521i	$0.777888\pi$
$198$	0	0
$199$	10.2860	0.729156	0.364578	−	0.931173i	$-0.381213\pi$
$199$	10.2860	0.729156	0.364578	+	0.931173i	$0.381213\pi$
$200$	1.16899	0.0826600
$201$	15.3203	1.08061
$202$	26.5267	1.86641
$203$	−4.99497	−0.350578
$204$	7.78698	0.545198
$205$	7.07508	0.494145
$206$	16.1617	1.12604
$207$	13.1706	0.915420
$208$	−11.3209	−0.784960
$209$	0	0
$210$	−2.28012	−0.157344
$211$	−12.0326	−0.828355	−0.414178	−	0.910196i	$-0.635931\pi$
$211$	−12.0326	−0.828355	−0.414178	+	0.910196i	$0.635931\pi$
$212$	−8.03368	−0.551755
$213$	−1.86599	−0.127856
$214$	23.7456	1.62321
$215$	−7.35367	−0.501516
$216$	6.47400	0.440500
$217$	9.24132	0.627342
$218$	−20.5885	−1.39443
$219$	−20.3892	−1.37777
$220$	0	0
$221$	−10.6876	−0.718927
$222$	16.4516	1.10416
$223$	−20.8215	−1.39431	−0.697155	−	0.716920i	$-0.745551\pi$
$223$	−20.8215	−1.39431	−0.697155	+	0.716920i	$0.745551\pi$
$224$	−6.58962	−0.440288
$225$	−1.45384	−0.0969226
$226$	−15.7077	−1.04486
$227$	−12.3737	−0.821273	−0.410636	−	0.911799i	$-0.634693\pi$
$227$	−12.3737	−0.821273	−0.410636	+	0.911799i	$0.634693\pi$
$228$	12.0669	0.799150
$229$	19.4294	1.28393	0.641964	−	0.766735i	$-0.278120\pi$
$229$	19.4294	1.28393	0.641964	+	0.766735i	$0.278120\pi$
$230$	16.6119	1.09536
$231$	0	0
$232$	5.83907	0.383354
$233$	−12.7780	−0.837113	−0.418557	−	0.908191i	$-0.637464\pi$
$233$	−12.7780	−0.837113	−0.418557	+	0.908191i	$0.637464\pi$
$234$	6.19903	0.405243
$235$	−8.20509	−0.535241
$236$	11.0108	0.716743
$237$	−15.6226	−1.01480
$238$	−8.42822	−0.546321
$239$	15.5461	1.00559	0.502797	−	0.864405i	$-0.332304\pi$
$239$	15.5461	1.00559	0.502797	+	0.864405i	$0.332304\pi$
$240$	6.05384	0.390774
$241$	15.5339	1.00063	0.500315	−	0.865844i	$-0.333218\pi$
$241$	15.5339	1.00063	0.500315	+	0.865844i	$0.333218\pi$
$242$	0	0
$243$	−13.4748	−0.864412
$244$	−0.114983	−0.00736102
$245$	1.00000	0.0638877
$246$	16.1321	1.02854
$247$	−16.5618	−1.05380
$248$	−10.8030	−0.685991
$249$	−9.48572	−0.601133
$250$	−1.83371	−0.115974
$251$	−5.87802	−0.371017	−0.185509	−	0.982643i	$-0.559393\pi$
$251$	−5.87802	−0.371017	−0.185509	+	0.982643i	$0.559393\pi$
$252$	1.98086	0.124782
$253$	0	0
$254$	25.9968	1.63118
$255$	5.71521	0.357900
$256$	20.9701	1.31063
$257$	−9.18295	−0.572817	−0.286408	−	0.958108i	$-0.592461\pi$
$257$	−9.18295	−0.572817	−0.286408	+	0.958108i	$0.592461\pi$
$258$	−16.7673	−1.04389
$259$	−7.21523	−0.448333
$260$	3.16820	0.196483
$261$	−7.26188	−0.449499
$262$	4.28363	0.264643
$263$	14.4605	0.891675	0.445837	−	0.895114i	$-0.352906\pi$
$263$	14.4605	0.891675	0.445837	+	0.895114i	$0.352906\pi$
$264$	0	0
$265$	−5.89627	−0.362205
$266$	−13.0606	−0.800796
$267$	7.13089	0.436403
$268$	−16.7872	−1.02544
$269$	−4.14477	−0.252711	−0.126356	−	0.991985i	$-0.540328\pi$
$269$	−4.14477	−0.252711	−0.126356	+	0.991985i	$0.540328\pi$
$270$	−10.1553	−0.618032
$271$	4.84676	0.294420	0.147210	−	0.989105i	$-0.452971\pi$
$271$	4.84676	0.294420	0.147210	+	0.989105i	$0.452971\pi$
$272$	22.3773	1.35683
$273$	2.89137	0.174993
$274$	−8.49692	−0.513318
$275$	0	0
$276$	15.3481	0.923845
$277$	4.95167	0.297517	0.148759	−	0.988874i	$-0.452472\pi$
$277$	4.95167	0.297517	0.148759	+	0.988874i	$0.452472\pi$
$278$	−4.90684	−0.294293
$279$	13.4354	0.804356
$280$	−1.16899	−0.0698605
$281$	−10.0193	−0.597700	−0.298850	−	0.954300i	$-0.596603\pi$
$281$	−10.0193	−0.597700	−0.298850	+	0.954300i	$0.596603\pi$
$282$	−18.7086	−1.11408
$283$	−13.5891	−0.807788	−0.403894	−	0.914806i	$-0.632344\pi$
$283$	−13.5891	−0.807788	−0.403894	+	0.914806i	$0.632344\pi$
$284$	2.04465	0.121328
$285$	8.85643	0.524610
$286$	0	0
$287$	−7.07508	−0.417629
$288$	−9.58025	−0.564522
$289$	4.12563	0.242684
$290$	−9.15934	−0.537855
$291$	20.7950	1.21903
$292$	22.3413	1.30743
$293$	18.0311	1.05339	0.526693	−	0.850056i	$-0.323432\pi$
$293$	18.0311	1.05339	0.526693	+	0.850056i	$0.323432\pi$
$294$	2.28012	0.132980
$295$	8.08132	0.470513
$296$	8.43453	0.490247
$297$	0	0
$298$	−19.9327	−1.15467
$299$	−21.0652	−1.21823
$300$	−1.69420	−0.0978146
$301$	7.35367	0.423859
$302$	−40.9697	−2.35754
$303$	17.9879	1.03338
$304$	34.6765	1.98883
$305$	−0.0843910	−0.00483221
$306$	−12.2533	−0.700474
$307$	16.8574	0.962103	0.481052	−	0.876692i	$-0.340255\pi$
$307$	16.8574	0.962103	0.481052	+	0.876692i	$0.340255\pi$
$308$	0	0
$309$	10.9593	0.623452
$310$	16.9459	0.962464
$311$	15.4916	0.878446	0.439223	−	0.898378i	$-0.355254\pi$
$311$	15.4916	0.878446	0.439223	+	0.898378i	$0.355254\pi$
$312$	−3.37998	−0.191353
$313$	24.8387	1.40397	0.701983	−	0.712193i	$-0.252298\pi$
$313$	24.8387	1.40397	0.701983	+	0.712193i	$0.252298\pi$
$314$	11.1377	0.628534
$315$	1.45384	0.0819146
$316$	17.1184	0.962985
$317$	6.38480	0.358606	0.179303	−	0.983794i	$-0.442616\pi$
$317$	6.38480	0.358606	0.179303	+	0.983794i	$0.442616\pi$
$318$	−13.4442	−0.753915
$319$	0	0
$320$	−2.34628	−0.131161
$321$	16.1019	0.898723
$322$	−16.6119	−0.925748
$323$	32.7368	1.82153
$324$	−3.44009	−0.191116
$325$	2.32528	0.128983
$326$	−34.6842	−1.92098
$327$	−13.9611	−0.772052
$328$	8.27070	0.456673
$329$	8.20509	0.452362
$330$	0	0
$331$	3.40346	0.187071	0.0935354	−	0.995616i	$-0.470183\pi$
$331$	3.40346	0.187071	0.0935354	+	0.995616i	$0.470183\pi$
$332$	10.3939	0.570441
$333$	−10.4898	−0.574837
$334$	−20.8012	−1.13819
$335$	−12.3209	−0.673160
$336$	−6.05384	−0.330264
$337$	16.9485	0.923243	0.461621	−	0.887077i	$-0.347268\pi$
$337$	16.9485	0.923243	0.461621	+	0.887077i	$0.347268\pi$
$338$	13.9235	0.757338
$339$	−10.6514	−0.578506
$340$	−6.26241	−0.339627
$341$	0	0
$342$	−18.9880	−1.02675
$343$	−1.00000	−0.0539949
$344$	−8.59637	−0.463485
$345$	11.2646	0.606467
$346$	−7.60684	−0.408946
$347$	−24.1273	−1.29522	−0.647610	−	0.761972i	$-0.724231\pi$
$347$	−24.1273	−1.29522	−0.647610	+	0.761972i	$0.724231\pi$
$348$	−8.46247	−0.453636
$349$	−1.61779	−0.0865981	−0.0432990	−	0.999062i	$-0.513787\pi$
$349$	−1.61779	−0.0865981	−0.0432990	+	0.999062i	$0.513787\pi$
$350$	1.83371	0.0980161
$351$	12.8777	0.687360
$352$	0	0
$353$	6.33431	0.337141	0.168571	−	0.985690i	$-0.446085\pi$
$353$	6.33431	0.337141	0.168571	+	0.985690i	$0.446085\pi$
$354$	18.4264	0.979353
$355$	1.50066	0.0796468
$356$	−7.81363	−0.414122
$357$	−5.71521	−0.302481
$358$	11.8233	0.624880
$359$	19.4388	1.02594	0.512970	−	0.858407i	$-0.328545\pi$
$359$	19.4388	1.02594	0.512970	+	0.858407i	$0.328545\pi$
$360$	−1.69952	−0.0895727
$361$	31.7298	1.66999
$362$	13.7935	0.724970
$363$	0	0
$364$	−3.16820	−0.166059
$365$	16.3973	0.858274
$366$	−0.192422	−0.0100581
$367$	17.2825	0.902139	0.451069	−	0.892489i	$-0.351043\pi$
$367$	17.2825	0.902139	0.451069	+	0.892489i	$0.351043\pi$
$368$	44.1055	2.29916
$369$	−10.2860	−0.535470
$370$	−13.2307	−0.687829
$371$	5.89627	0.306119
$372$	15.6566	0.811758
$373$	11.5883	0.600021	0.300011	−	0.953936i	$-0.403010\pi$
$373$	11.5883	0.600021	0.300011	+	0.953936i	$0.403010\pi$
$374$	0	0
$375$	−1.24345	−0.0642113
$376$	−9.59167	−0.494653
$377$	11.6147	0.598188
$378$	10.1553	0.522333
$379$	28.5085	1.46438	0.732192	−	0.681099i	$-0.238498\pi$
$379$	28.5085	1.46438	0.732192	+	0.681099i	$0.238498\pi$
$380$	−9.70439	−0.497825
$381$	17.6285	0.903136
$382$	−14.7832	−0.756375
$383$	10.5272	0.537917	0.268959	−	0.963152i	$-0.413321\pi$
$383$	10.5272	0.537917	0.268959	+	0.963152i	$0.413321\pi$
$384$	11.0379	0.563274
$385$	0	0
$386$	3.91857	0.199450
$387$	10.6911	0.543457
$388$	−22.7861	−1.15679
$389$	−21.6793	−1.09918	−0.549591	−	0.835434i	$-0.685216\pi$
$389$	−21.6793	−1.09918	−0.549591	+	0.835434i	$0.685216\pi$
$390$	5.30193	0.268474
$391$	41.6384	2.10575
$392$	1.16899	0.0590429
$393$	2.90474	0.146525
$394$	39.4435	1.98713
$395$	12.5640	0.632161
$396$	0	0
$397$	−5.11795	−0.256862	−0.128431	−	0.991718i	$-0.540994\pi$
$397$	−5.11795	−0.256862	−0.128431	+	0.991718i	$0.540994\pi$
$398$	−18.8616	−0.945446
$399$	−8.85643	−0.443376
$400$	−4.86859	−0.243430
$401$	−0.933584	−0.0466210	−0.0233105	−	0.999728i	$-0.507421\pi$
$401$	−0.933584	−0.0466210	−0.0233105	+	0.999728i	$0.507421\pi$
$402$	−28.0931	−1.40116
$403$	−21.4887	−1.07043
$404$	−19.7101	−0.980616
$405$	−2.52483	−0.125460
$406$	9.15934	0.454570
$407$	0	0
$408$	6.68102	0.330760
$409$	5.76927	0.285272	0.142636	−	0.989775i	$-0.454442\pi$
$409$	5.76927	0.285272	0.142636	+	0.989775i	$0.454442\pi$
$410$	−12.9737	−0.640724
$411$	−5.76179	−0.284208
$412$	−12.0086	−0.591620
$413$	−8.08132	−0.397656
$414$	−24.1511	−1.18696
$415$	7.62857	0.374472
$416$	15.3227	0.751259
$417$	−3.32734	−0.162941
$418$	0	0
$419$	8.67071	0.423592	0.211796	−	0.977314i	$-0.432069\pi$
$419$	8.67071	0.423592	0.211796	+	0.977314i	$0.432069\pi$
$420$	1.69420	0.0826684
$421$	−9.15790	−0.446329	−0.223164	−	0.974781i	$-0.571639\pi$
$421$	−9.15790	−0.446329	−0.223164	+	0.974781i	$0.571639\pi$
$422$	22.0642	1.07407
$423$	11.9289	0.580003
$424$	−6.89268	−0.334738
$425$	−4.59626	−0.222951
$426$	3.42169	0.165782
$427$	0.0843910	0.00408397
$428$	−17.6436	−0.852837
$429$	0	0
$430$	13.4845	0.650282
$431$	−17.8714	−0.860834	−0.430417	−	0.902630i	$-0.641633\pi$
$431$	−17.8714	−0.860834	−0.430417	+	0.902630i	$0.641633\pi$
$432$	−26.9628	−1.29725
$433$	22.0284	1.05862	0.529308	−	0.848430i	$-0.322452\pi$
$433$	22.0284	1.05862	0.529308	+	0.848430i	$0.322452\pi$
$434$	−16.9459	−0.813430
$435$	−6.21098	−0.297794
$436$	15.2978	0.732634
$437$	64.5239	3.08660
$438$	37.3879	1.78646
$439$	25.0462	1.19539	0.597695	−	0.801723i	$-0.296083\pi$
$439$	25.0462	1.19539	0.597695	+	0.801723i	$0.296083\pi$
$440$	0	0
$441$	−1.45384	−0.0692305
$442$	19.5980	0.932182
$443$	35.1182	1.66852	0.834258	−	0.551374i	$-0.185896\pi$
$443$	35.1182	1.66852	0.834258	+	0.551374i	$0.185896\pi$
$444$	−12.2240	−0.580127
$445$	−5.73477	−0.271854
$446$	38.1806	1.80791
$447$	−13.5164	−0.639305
$448$	2.34628	0.110851
$449$	−9.35391	−0.441438	−0.220719	−	0.975337i	$-0.570840\pi$
$449$	−9.35391	−0.441438	−0.220719	+	0.975337i	$0.570840\pi$
$450$	2.66592	0.125673
$451$	0	0
$452$	11.6713	0.548970
$453$	−27.7817	−1.30530
$454$	22.6898	1.06489
$455$	−2.32528	−0.109011
$456$	10.3531	0.484827
$457$	−4.02606	−0.188331	−0.0941655	−	0.995557i	$-0.530018\pi$
$457$	−4.02606	−0.188331	−0.0941655	+	0.995557i	$0.530018\pi$
$458$	−35.6279	−1.66478
$459$	−25.4546	−1.18812
$460$	−12.3432	−0.575503
$461$	−18.3760	−0.855855	−0.427928	−	0.903813i	$-0.640756\pi$
$461$	−18.3760	−0.855855	−0.427928	+	0.903813i	$0.640756\pi$
$462$	0	0
$463$	−19.1804	−0.891389	−0.445694	−	0.895185i	$-0.647043\pi$
$463$	−19.1804	−0.891389	−0.445694	+	0.895185i	$0.647043\pi$
$464$	−24.3185	−1.12896
$465$	11.4911	0.532886
$466$	23.4311	1.08543
$467$	15.6548	0.724417	0.362209	−	0.932097i	$-0.382023\pi$
$467$	15.6548	0.724417	0.362209	+	0.932097i	$0.382023\pi$
$468$	−4.60606	−0.212915
$469$	12.3209	0.568924
$470$	15.0458	0.694010
$471$	7.55248	0.348000
$472$	9.44698	0.434833
$473$	0	0
$474$	28.6474	1.31582
$475$	−7.12249	−0.326802
$476$	6.26241	0.287037
$477$	8.57223	0.392496
$478$	−28.5071	−1.30388
$479$	2.73149	0.124805	0.0624026	−	0.998051i	$-0.480124\pi$
$479$	2.73149	0.124805	0.0624026	+	0.998051i	$0.480124\pi$
$480$	−8.19384	−0.373996
$481$	16.7775	0.764986
$482$	−28.4848	−1.29745
$483$	−11.2646	−0.512558
$484$	0	0
$485$	−16.7237	−0.759384
$486$	24.7090	1.12082
$487$	42.2525	1.91464	0.957322	−	0.289025i	$-0.0933309\pi$
$487$	42.2525	1.91464	0.957322	+	0.289025i	$0.0933309\pi$
$488$	−0.0986522	−0.00446578
$489$	−23.5195	−1.06359
$490$	−1.83371	−0.0828387
$491$	1.14622	0.0517281	0.0258641	−	0.999665i	$-0.491766\pi$
$491$	1.14622	0.0517281	0.0258641	+	0.999665i	$0.491766\pi$
$492$	−11.9866	−0.540397
$493$	−22.9582	−1.03398
$494$	30.3696	1.36639
$495$	0	0
$496$	44.9922	2.02021
$497$	−1.50066	−0.0673139
$498$	17.3941	0.779447
$499$	8.44273	0.377949	0.188974	−	0.981982i	$-0.439484\pi$
$499$	8.44273	0.377949	0.188974	+	0.981982i	$0.439484\pi$
$500$	1.36250	0.0609329
$501$	−14.1053	−0.630180
$502$	10.7786	0.481072
$503$	8.30509	0.370306	0.185153	−	0.982710i	$-0.440722\pi$
$503$	8.30509	0.370306	0.185153	+	0.982710i	$0.440722\pi$
$504$	1.69952	0.0757028
$505$	−14.4661	−0.643735
$506$	0	0
$507$	9.44157	0.419315
$508$	−19.3164	−0.857024
$509$	4.03562	0.178876	0.0894379	−	0.995992i	$-0.471493\pi$
$509$	4.03562	0.178876	0.0894379	+	0.995992i	$0.471493\pi$
$510$	−10.4801	−0.464064
$511$	−16.3973	−0.725374
$512$	−20.6995	−0.914798
$513$	−39.4451	−1.74155
$514$	16.8389	0.742731
$515$	−8.81363	−0.388375
$516$	12.4586	0.548458
$517$	0	0
$518$	13.2307	0.581322
$519$	−5.15823	−0.226421
$520$	2.71823	0.119202
$521$	1.07536	0.0471124	0.0235562	−	0.999723i	$-0.492501\pi$
$521$	1.07536	0.0471124	0.0235562	+	0.999723i	$0.492501\pi$
$522$	13.3162	0.582835
$523$	16.5229	0.722494	0.361247	−	0.932470i	$-0.382351\pi$
$523$	16.5229	0.722494	0.361247	+	0.932470i	$0.382351\pi$
$524$	−3.18286	−0.139044
$525$	1.24345	0.0542685
$526$	−26.5165	−1.15617
$527$	42.4755	1.85026
$528$	0	0
$529$	59.0689	2.56821
$530$	10.8121	0.469646
$531$	−11.7489	−0.509861
$532$	9.70439	0.420739
$533$	16.4516	0.712597
$534$	−13.0760	−0.565854
$535$	−12.9494	−0.559853
$536$	−14.4030	−0.622113
$537$	8.01742	0.345977
$538$	7.60032	0.327673
$539$	0	0
$540$	7.54569	0.324715
$541$	−4.07129	−0.175039	−0.0875193	−	0.996163i	$-0.527894\pi$
$541$	−4.07129	−0.175039	−0.0875193	+	0.996163i	$0.527894\pi$
$542$	−8.88756	−0.381754
$543$	9.35341	0.401393
$544$	−30.2876	−1.29857
$545$	11.2278	0.480945
$546$	−5.30193	−0.226902
$547$	19.1227	0.817629	0.408815	−	0.912617i	$-0.365942\pi$
$547$	19.1227	0.817629	0.408815	+	0.912617i	$0.365942\pi$
$548$	6.31346	0.269697
$549$	0.122691	0.00523632
$550$	0	0
$551$	−35.5766	−1.51561
$552$	13.1682	0.560477
$553$	−12.5640	−0.534274
$554$	−9.07994	−0.385770
$555$	−8.97176	−0.380830
$556$	3.64592	0.154621
$557$	10.3272	0.437580	0.218790	−	0.975772i	$-0.429789\pi$
$557$	10.3272	0.437580	0.218790	+	0.975772i	$0.429789\pi$
$558$	−24.6366	−1.04295
$559$	−17.0994	−0.723226
$560$	4.86859	0.205736
$561$	0	0
$562$	18.3725	0.774997
$563$	−26.4474	−1.11462	−0.557312	−	0.830303i	$-0.688167\pi$
$563$	−26.4474	−1.11462	−0.557312	+	0.830303i	$0.688167\pi$
$564$	13.9011	0.585340
$565$	8.56605	0.360376
$566$	24.9185	1.04740
$567$	2.52483	0.106033
$568$	1.75426	0.0736070
$569$	1.84608	0.0773917	0.0386958	−	0.999251i	$-0.487680\pi$
$569$	1.84608	0.0773917	0.0386958	+	0.999251i	$0.487680\pi$
$570$	−16.2402	−0.680225
$571$	35.7994	1.49816	0.749080	−	0.662480i	$-0.230496\pi$
$571$	35.7994	1.49816	0.749080	+	0.662480i	$0.230496\pi$
$572$	0	0
$573$	−10.0245	−0.418781
$574$	12.9737	0.541511
$575$	−9.05919	−0.377794
$576$	3.41112	0.142130
$577$	−17.2442	−0.717884	−0.358942	−	0.933360i	$-0.616862\pi$
$577$	−17.2442	−0.717884	−0.358942	+	0.933360i	$0.616862\pi$
$578$	−7.56522	−0.314672
$579$	2.65720	0.110429
$580$	6.80565	0.282589
$581$	−7.62857	−0.316486
$582$	−38.1321	−1.58063
$583$	0	0
$584$	19.1683	0.793189
$585$	−3.38059	−0.139770
$586$	−33.0638	−1.36585
$587$	−5.24042	−0.216295	−0.108148	−	0.994135i	$-0.534492\pi$
$587$	−5.24042	−0.216295	−0.108148	+	0.994135i	$0.534492\pi$
$588$	−1.69420	−0.0698675
$589$	65.8211	2.71211
$590$	−14.8188	−0.610081
$591$	26.7467	1.10021
$592$	−35.1280	−1.44375
$593$	−11.2786	−0.463155	−0.231578	−	0.972816i	$-0.574389\pi$
$593$	−11.2786	−0.463155	−0.231578	+	0.972816i	$0.574389\pi$
$594$	0	0
$595$	4.59626	0.188428
$596$	14.8106	0.606664
$597$	−12.7901	−0.523464
$598$	38.6275	1.57959
$599$	20.8163	0.850532	0.425266	−	0.905068i	$-0.360181\pi$
$599$	20.8163	0.850532	0.425266	+	0.905068i	$0.360181\pi$
$600$	−1.45358	−0.0593420
$601$	2.94066	0.119952	0.0599760	−	0.998200i	$-0.480898\pi$
$601$	2.94066	0.119952	0.0599760	+	0.998200i	$0.480898\pi$
$602$	−13.4845	−0.549588
$603$	17.9125	0.729455
$604$	30.4417	1.23865
$605$	0	0
$606$	−32.9846	−1.33991
$607$	−1.51314	−0.0614165	−0.0307082	−	0.999528i	$-0.509776\pi$
$607$	−1.51314	−0.0614165	−0.0307082	+	0.999528i	$0.509776\pi$
$608$	−46.9345	−1.90344
$609$	6.21098	0.251682
$610$	0.154749	0.00626560
$611$	−19.0792	−0.771860
$612$	9.10454	0.368029
$613$	−36.3272	−1.46724	−0.733621	−	0.679558i	$-0.762171\pi$
$613$	−36.3272	−1.46724	−0.733621	+	0.679558i	$0.762171\pi$
$614$	−30.9117	−1.24749
$615$	−8.79749	−0.354749
$616$	0	0
$617$	−12.9028	−0.519447	−0.259724	−	0.965683i	$-0.583631\pi$
$617$	−12.9028	−0.519447	−0.259724	+	0.965683i	$0.583631\pi$
$618$	−20.0962	−0.808387
$619$	28.0721	1.12831	0.564156	−	0.825668i	$-0.309202\pi$
$619$	28.0721	1.12831	0.564156	+	0.825668i	$0.309202\pi$
$620$	−12.5913	−0.505679
$621$	−50.1708	−2.01329
$622$	−28.4071	−1.13902
$623$	5.73477	0.229759
$624$	14.0769	0.563526
$625$	1.00000	0.0400000
$626$	−45.5470	−1.82043
$627$	0	0
$628$	−8.27560	−0.330232
$629$	−33.1631	−1.32230
$630$	−2.66592	−0.106213
$631$	32.6132	1.29831	0.649156	−	0.760655i	$-0.275122\pi$
$631$	32.6132	1.29831	0.649156	+	0.760655i	$0.275122\pi$
$632$	14.6871	0.584223
$633$	14.9618	0.594680
$634$	−11.7079	−0.464980
$635$	−14.1771	−0.562602
$636$	9.98945	0.396107
$637$	2.32528	0.0921311
$638$	0	0
$639$	−2.18172	−0.0863075
$640$	−8.87683	−0.350888
$641$	−23.6424	−0.933820	−0.466910	−	0.884305i	$-0.654633\pi$
$641$	−23.6424	−0.933820	−0.466910	+	0.884305i	$0.654633\pi$
$642$	−29.5263	−1.16531
$643$	1.36723	0.0539183	0.0269592	−	0.999637i	$-0.491418\pi$
$643$	1.36723	0.0539183	0.0269592	+	0.999637i	$0.491418\pi$
$644$	12.3432	0.486388
$645$	9.14390	0.360041
$646$	−60.0299	−2.36184
$647$	8.26915	0.325094	0.162547	−	0.986701i	$-0.448029\pi$
$647$	8.26915	0.325094	0.162547	+	0.986701i	$0.448029\pi$
$648$	−2.95150	−0.115946
$649$	0	0
$650$	−4.26390	−0.167244
$651$	−11.4911	−0.450371
$652$	25.7713	1.00928
$653$	−0.368310	−0.0144131	−0.00720654	−	0.999974i	$-0.502294\pi$
$653$	−0.368310	−0.0144131	−0.00720654	+	0.999974i	$0.502294\pi$
$654$	25.6007	1.00107
$655$	−2.33604	−0.0912767
$656$	−34.4457	−1.34488
$657$	−23.8391	−0.930050
$658$	−15.0458	−0.586546
$659$	23.8535	0.929200	0.464600	−	0.885521i	$-0.346198\pi$
$659$	23.8535	0.929200	0.464600	+	0.885521i	$0.346198\pi$
$660$	0	0
$661$	25.8432	1.00518	0.502592	−	0.864524i	$-0.332380\pi$
$661$	25.8432	1.00518	0.502592	+	0.864524i	$0.332380\pi$
$662$	−6.24096	−0.242562
$663$	13.2895	0.516121
$664$	8.91772	0.346074
$665$	7.12249	0.276198
$666$	19.2353	0.745351
$667$	−45.2504	−1.75210
$668$	15.4559	0.598005
$669$	25.8904	1.00098
$670$	22.5929	0.872840
$671$	0	0
$672$	8.19384	0.316084
$673$	46.3296	1.78587	0.892937	−	0.450182i	$-0.148641\pi$
$673$	46.3296	1.78587	0.892937	+	0.450182i	$0.148641\pi$
$674$	−31.0786	−1.19710
$675$	5.53811	0.213162
$676$	−10.3456	−0.397906
$677$	−34.4721	−1.32487	−0.662435	−	0.749119i	$-0.730477\pi$
$677$	−34.4721	−1.32487	−0.662435	+	0.749119i	$0.730477\pi$
$678$	19.5317	0.750109
$679$	16.7237	0.641797
$680$	−5.37298	−0.206044
$681$	15.3861	0.589595
$682$	0	0
$683$	−9.59240	−0.367043	−0.183521	−	0.983016i	$-0.558750\pi$
$683$	−9.59240	−0.367043	−0.183521	+	0.983016i	$0.558750\pi$
$684$	14.1086	0.539457
$685$	4.63373	0.177046
$686$	1.83371	0.0700115
$687$	−24.1594	−0.921738
$688$	35.8020	1.36494
$689$	−13.7105	−0.522328
$690$	−20.6561	−0.786363
$691$	5.24456	0.199512	0.0997562	−	0.995012i	$-0.468194\pi$
$691$	5.24456	0.199512	0.0997562	+	0.995012i	$0.468194\pi$
$692$	5.65210	0.214861
$693$	0	0
$694$	44.2425	1.67942
$695$	2.67590	0.101503
$696$	−7.26057	−0.275211
$697$	−32.5189	−1.23174
$698$	2.96655	0.112286
$699$	15.8887	0.600967
$700$	−1.36250	−0.0514977
$701$	5.02640	0.189844	0.0949222	−	0.995485i	$-0.469740\pi$
$701$	5.02640	0.189844	0.0949222	+	0.995485i	$0.469740\pi$
$702$	−23.6140	−0.891252
$703$	−51.3904	−1.93822
$704$	0	0
$705$	10.2026	0.384252
$706$	−11.6153	−0.437148
$707$	14.4661	0.544055
$708$	−13.6914	−0.514553
$709$	48.2644	1.81261	0.906304	−	0.422626i	$-0.138892\pi$
$709$	48.2644	1.81261	0.906304	+	0.422626i	$0.138892\pi$
$710$	−2.75178	−0.103273
$711$	−18.2660	−0.685027
$712$	−6.70389	−0.251239
$713$	83.7188	3.13530
$714$	10.4801	0.392206
$715$	0	0
$716$	−8.78505	−0.328313
$717$	−19.3308	−0.721920
$718$	−35.6451	−1.33026
$719$	−43.5336	−1.62353	−0.811765	−	0.583984i	$-0.801493\pi$
$719$	−43.5336	−1.62353	−0.811765	+	0.583984i	$0.801493\pi$
$720$	7.07815	0.263787
$721$	8.81363	0.328237
$722$	−58.1833	−2.16536
$723$	−19.3156	−0.718356
$724$	−10.2490	−0.380900
$725$	4.99497	0.185509
$726$	0	0
$727$	−3.86136	−0.143210	−0.0716049	−	0.997433i	$-0.522812\pi$
$727$	−3.86136	−0.143210	−0.0716049	+	0.997433i	$0.522812\pi$
$728$	−2.71823	−0.100744
$729$	24.3298	0.901102
$730$	−30.0679	−1.11286
$731$	33.7994	1.25012
$732$	0.142975	0.00528451
$733$	11.1704	0.412588	0.206294	−	0.978490i	$-0.433860\pi$
$733$	11.1704	0.412588	0.206294	+	0.978490i	$0.433860\pi$
$734$	−31.6911	−1.16974
$735$	−1.24345	−0.0458652
$736$	−59.6966	−2.20045
$737$	0	0
$738$	18.8616	0.694306
$739$	−34.0701	−1.25329	−0.626644	−	0.779306i	$-0.715572\pi$
$739$	−34.0701	−1.25329	−0.626644	+	0.779306i	$0.715572\pi$
$740$	9.83076	0.361386
$741$	20.5937	0.756529
$742$	−10.8121	−0.396923
$743$	−44.7290	−1.64095	−0.820473	−	0.571685i	$-0.806290\pi$
$743$	−44.7290	−1.64095	−0.820473	+	0.571685i	$0.806290\pi$
$744$	13.4330	0.492476
$745$	10.8701	0.398251
$746$	−21.2497	−0.778006
$747$	−11.0907	−0.405788
$748$	0	0
$749$	12.9494	0.473162
$750$	2.28012	0.0832584
$751$	−49.6466	−1.81163	−0.905816	−	0.423672i	$-0.860741\pi$
$751$	−49.6466	−1.81163	−0.905816	+	0.423672i	$0.860741\pi$
$752$	39.9473	1.45673
$753$	7.30901	0.266355
$754$	−21.2980	−0.775629
$755$	22.3425	0.813127
$756$	−7.54569	−0.274434
$757$	−33.7569	−1.22692	−0.613458	−	0.789727i	$-0.710222\pi$
$757$	−33.7569	−1.22692	−0.613458	+	0.789727i	$0.710222\pi$
$758$	−52.2764	−1.89876
$759$	0	0
$760$	−8.32611	−0.302020
$761$	−22.1295	−0.802194	−0.401097	−	0.916036i	$-0.631371\pi$
$761$	−22.1295	−0.802194	−0.401097	+	0.916036i	$0.631371\pi$
$762$	−32.3256	−1.17103
$763$	−11.2278	−0.406472
$764$	10.9843	0.397400
$765$	6.68223	0.241596
$766$	−19.3039	−0.697480
$767$	18.7914	0.678517
$768$	−26.0752	−0.940909
$769$	8.95697	0.322996	0.161498	−	0.986873i	$-0.448367\pi$
$769$	8.95697	0.322996	0.161498	+	0.986873i	$0.448367\pi$
$770$	0	0
$771$	11.4185	0.411228
$772$	−2.91161	−0.104791
$773$	−10.5336	−0.378868	−0.189434	−	0.981893i	$-0.560665\pi$
$773$	−10.5336	−0.378868	−0.189434	+	0.981893i	$0.560665\pi$
$774$	−19.6043	−0.704663
$775$	−9.24132	−0.331958
$776$	−19.5498	−0.701798
$777$	8.97176	0.321860
$778$	39.7535	1.42523
$779$	−50.3922	−1.80549
$780$	−3.93949	−0.141056
$781$	0	0
$782$	−76.3529	−2.73037
$783$	27.6627	0.988584
$784$	−4.86859	−0.173878
$785$	−6.07383	−0.216784
$786$	−5.32647	−0.189989
$787$	−13.7498	−0.490127	−0.245064	−	0.969507i	$-0.578809\pi$
$787$	−13.7498	−0.490127	−0.245064	+	0.969507i	$0.578809\pi$
$788$	−29.3076	−1.04404
$789$	−17.9809	−0.640137
$790$	−23.0387	−0.819679
$791$	−8.56605	−0.304574
$792$	0	0
$793$	−0.196233	−0.00696844
$794$	9.38484	0.333056
$795$	7.33170	0.260029
$796$	14.0147	0.496738
$797$	−52.4813	−1.85898	−0.929492	−	0.368842i	$-0.879754\pi$
$797$	−52.4813	−1.85898	−0.929492	+	0.368842i	$0.879754\pi$
$798$	16.2402	0.574895
$799$	37.7128	1.33418
$800$	6.58962	0.232978
$801$	8.33744	0.294589
$802$	1.71192	0.0604502
$803$	0	0
$804$	20.8740	0.736168
$805$	9.05919	0.319294
$806$	39.4041	1.38795
$807$	5.15381	0.181423
$808$	−16.9108	−0.594919
$809$	−0.805837	−0.0283317	−0.0141659	−	0.999900i	$-0.504509\pi$
$809$	−0.805837	−0.0283317	−0.0141659	+	0.999900i	$0.504509\pi$
$810$	4.62982	0.162675
$811$	11.3227	0.397594	0.198797	−	0.980041i	$-0.436296\pi$
$811$	11.3227	0.397594	0.198797	+	0.980041i	$0.436296\pi$
$812$	−6.80565	−0.238832
$813$	−6.02669	−0.211365
$814$	0	0
$815$	18.9147	0.662554
$816$	−27.8250	−0.974071
$817$	52.3764	1.83242
$818$	−10.5792	−0.369893
$819$	3.38059	0.118127
$820$	9.63981	0.336637
$821$	1.36294	0.0475670	0.0237835	−	0.999717i	$-0.492429\pi$
$821$	1.36294	0.0475670	0.0237835	+	0.999717i	$0.492429\pi$
$822$	10.5655	0.368513
$823$	16.4248	0.572533	0.286267	−	0.958150i	$-0.407586\pi$
$823$	16.4248	0.572533	0.286267	+	0.958150i	$0.407586\pi$
$824$	−10.3030	−0.358923
$825$	0	0
$826$	14.8188	0.515613
$827$	3.10583	0.108000	0.0540002	−	0.998541i	$-0.482803\pi$
$827$	3.10583	0.108000	0.0540002	+	0.998541i	$0.482803\pi$
$828$	17.9450	0.623631
$829$	−35.7350	−1.24113	−0.620564	−	0.784156i	$-0.713096\pi$
$829$	−35.7350	−1.24113	−0.620564	+	0.784156i	$0.713096\pi$
$830$	−13.9886	−0.485551
$831$	−6.15714	−0.213589
$832$	−5.45577	−0.189145
$833$	−4.59626	−0.159251
$834$	6.10139	0.211274
$835$	11.3437	0.392566
$836$	0	0
$837$	−51.1795	−1.76902
$838$	−15.8996	−0.549242
$839$	56.2174	1.94084	0.970420	−	0.241423i	$-0.0776141\pi$
$839$	56.2174	1.94084	0.970420	+	0.241423i	$0.0776141\pi$
$840$	1.45358	0.0501532
$841$	−4.05028	−0.139665
$842$	16.7929	0.578723
$843$	12.4584	0.429092
$844$	−16.3944	−0.564317
$845$	−7.59306	−0.261209
$846$	−21.8742	−0.752049
$847$	0	0
$848$	28.7065	0.985787
$849$	16.8973	0.579915
$850$	8.42822	0.289086
$851$	−65.3641	−2.24065
$852$	−2.54242	−0.0871018
$853$	34.4320	1.17893	0.589464	−	0.807795i	$-0.299339\pi$
$853$	34.4320	1.17893	0.589464	+	0.807795i	$0.299339\pi$
$854$	−0.154749	−0.00529540
$855$	10.3550	0.354132
$856$	−15.1378	−0.517398
$857$	−13.7994	−0.471380	−0.235690	−	0.971828i	$-0.575735\pi$
$857$	−13.7994	−0.471380	−0.235690	+	0.971828i	$0.575735\pi$
$858$	0	0
$859$	−35.4971	−1.21114	−0.605572	−	0.795790i	$-0.707056\pi$
$859$	−35.4971	−1.21114	−0.605572	+	0.795790i	$0.707056\pi$
$860$	−10.0194	−0.341658
$861$	8.79749	0.299818
$862$	32.7710	1.11618
$863$	7.11705	0.242267	0.121134	−	0.992636i	$-0.461347\pi$
$863$	7.11705	0.242267	0.121134	+	0.992636i	$0.461347\pi$
$864$	36.4941	1.24155
$865$	4.14833	0.141047
$866$	−40.3937	−1.37263
$867$	−5.13000	−0.174224
$868$	12.5913	0.427377
$869$	0	0
$870$	11.3892	0.386128
$871$	−28.6495	−0.970750
$872$	13.1251	0.444473
$873$	24.3136	0.822890
$874$	−118.318	−4.00218
$875$	−1.00000	−0.0338062
$876$	−27.7803	−0.938609
$877$	21.1786	0.715151	0.357576	−	0.933884i	$-0.383603\pi$
$877$	21.1786	0.715151	0.357576	+	0.933884i	$0.383603\pi$
$878$	−45.9275	−1.54998
$879$	−22.4207	−0.756230
$880$	0	0
$881$	19.3420	0.651649	0.325825	−	0.945430i	$-0.394358\pi$
$881$	19.3420	0.651649	0.325825	+	0.945430i	$0.394358\pi$
$882$	2.66592	0.0897663
$883$	53.9330	1.81499	0.907495	−	0.420063i	$-0.137992\pi$
$883$	53.9330	1.81499	0.907495	+	0.420063i	$0.137992\pi$
$884$	−14.5619	−0.489769
$885$	−10.0487	−0.337783
$886$	−64.3967	−2.16345
$887$	−50.5317	−1.69669	−0.848345	−	0.529444i	$-0.822401\pi$
$887$	−50.5317	−1.69669	−0.848345	+	0.529444i	$0.822401\pi$
$888$	−10.4879	−0.351951
$889$	14.1771	0.475486
$890$	10.5159	0.352495
$891$	0	0
$892$	−28.3693	−0.949875
$893$	58.4407	1.95564
$894$	24.7853	0.828943
$895$	−6.44774	−0.215524
$896$	8.87683	0.296554
$897$	26.1934	0.874573
$898$	17.1524	0.572382
$899$	−46.1601	−1.53953
$900$	−1.98086	−0.0660286
$901$	27.1008	0.902859
$902$	0	0
$903$	−9.14390	−0.304290
$904$	10.0136	0.333048
$905$	−7.52216	−0.250045
$906$	50.9437	1.69249
$907$	57.3368	1.90384	0.951918	−	0.306351i	$-0.0991083\pi$
$907$	57.3368	1.90384	0.951918	+	0.306351i	$0.0991083\pi$
$908$	−16.8592	−0.559492
$909$	21.0314	0.697569
$910$	4.26390	0.141347
$911$	−45.9616	−1.52277	−0.761387	−	0.648298i	$-0.775481\pi$
$911$	−45.9616	−1.52277	−0.761387	+	0.648298i	$0.775481\pi$
$912$	−43.1184	−1.42779
$913$	0	0
$914$	7.38263	0.244196
$915$	0.104936	0.00346907
$916$	26.4725	0.874677
$917$	2.33604	0.0771429
$918$	46.6765	1.54055
$919$	−40.1114	−1.32315	−0.661577	−	0.749877i	$-0.730113\pi$
$919$	−40.1114	−1.32315	−0.661577	+	0.749877i	$0.730113\pi$
$920$	−10.5901	−0.349145
$921$	−20.9613	−0.690698
$922$	33.6963	1.10973
$923$	3.48946	0.114857
$924$	0	0
$925$	7.21523	0.237235
$926$	35.1713	1.15580
$927$	12.8136	0.420854
$928$	32.9150	1.08049
$929$	38.8631	1.27506	0.637528	−	0.770427i	$-0.279957\pi$
$929$	38.8631	1.27506	0.637528	+	0.770427i	$0.279957\pi$
$930$	−21.0714	−0.690957
$931$	−7.12249	−0.233430
$932$	−17.4100	−0.570284
$933$	−19.2629	−0.630640
$934$	−28.7064	−0.939302
$935$	0	0
$936$	−3.95187	−0.129171
$937$	−5.98293	−0.195454	−0.0977270	−	0.995213i	$-0.531157\pi$
$937$	−5.98293	−0.195454	−0.0977270	+	0.995213i	$0.531157\pi$
$938$	−22.5929	−0.737685
$939$	−30.8856	−1.00791
$940$	−11.1795	−0.364633
$941$	8.16686	0.266232	0.133116	−	0.991100i	$-0.457502\pi$
$941$	8.16686	0.266232	0.133116	+	0.991100i	$0.457502\pi$
$942$	−13.8491	−0.451228
$943$	−64.0945	−2.08720
$944$	−39.3447	−1.28056
$945$	−5.53811	−0.180155
$946$	0	0
$947$	11.9721	0.389040	0.194520	−	0.980899i	$-0.437685\pi$
$947$	11.9721	0.389040	0.194520	+	0.980899i	$0.437685\pi$
$948$	−21.2858	−0.691331
$949$	38.1284	1.23770
$950$	13.0606	0.423741
$951$	−7.93916	−0.257445
$952$	5.37298	0.174139
$953$	−10.6284	−0.344289	−0.172144	−	0.985072i	$-0.555070\pi$
$953$	−10.6284	−0.344289	−0.172144	+	0.985072i	$0.555070\pi$
$954$	−15.7190	−0.508922
$955$	8.06190	0.260877
$956$	21.1816	0.685061
$957$	0	0
$958$	−5.00878	−0.161826
$959$	−4.63373	−0.149631
$960$	2.91748	0.0941612
$961$	54.4020	1.75490
$962$	−30.7650	−0.991904
$963$	18.8264	0.606673
$964$	21.1650	0.681680
$965$	−2.13696	−0.0687912
$966$	20.6561	0.664598
$967$	−20.2717	−0.651895	−0.325947	−	0.945388i	$-0.605683\pi$
$967$	−20.2717	−0.651895	−0.325947	+	0.945388i	$0.605683\pi$
$968$	0	0
$969$	−40.7065	−1.30768
$970$	30.6665	0.984641
$971$	−23.3667	−0.749872	−0.374936	−	0.927051i	$-0.622335\pi$
$971$	−23.3667	−0.749872	−0.374936	+	0.927051i	$0.622335\pi$
$972$	−18.3595	−0.588881
$973$	−2.67590	−0.0857855
$974$	−77.4789	−2.48258
$975$	−2.89137	−0.0925978
$976$	0.410865	0.0131515
$977$	24.6826	0.789668	0.394834	−	0.918753i	$-0.370802\pi$
$977$	24.6826	0.789668	0.394834	+	0.918753i	$0.370802\pi$
$978$	43.1279	1.37908
$979$	0	0
$980$	1.36250	0.0435235
$981$	−16.3234	−0.521165
$982$	−2.10184	−0.0670723
$983$	15.0462	0.479899	0.239949	−	0.970785i	$-0.422869\pi$
$983$	15.0462	0.479899	0.239949	+	0.970785i	$0.422869\pi$
$984$	−10.2842	−0.327848
$985$	−21.5102	−0.685371
$986$	42.0987	1.34070
$987$	−10.2026	−0.324752
$988$	−22.5655	−0.717903
$989$	66.6183	2.11834
$990$	0	0
$991$	−19.6338	−0.623688	−0.311844	−	0.950133i	$-0.600947\pi$
$991$	−19.6338	−0.623688	−0.311844	+	0.950133i	$0.600947\pi$
$992$	−60.8968	−1.93347
$993$	−4.23202	−0.134299
$994$	2.75178	0.0872812
$995$	10.2860	0.326089
$996$	−12.9243	−0.409522
$997$	−18.3926	−0.582501	−0.291250	−	0.956647i	$-0.594071\pi$
$997$	−18.3926	−0.582501	−0.291250	+	0.956647i	$0.594071\pi$
$998$	−15.4815	−0.490060
$999$	39.9588	1.26424

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bk.1.2	yes	10
11.10	odd	2		4235.2.a.bi.1.9	✓	10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4235.2.a.bi.1.9	✓	10	11.10	odd	2
4235.2.a.bk.1.2	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)

\(f(q)\)	\(=\)	\(q-1.83371 q^{2} -1.24345 q^{3} +1.36250 q^{4} +1.00000 q^{5} +2.28012 q^{6} -1.00000 q^{7} +1.16899 q^{8} -1.45384 q^{9} +O(q^{10})\)	\(q-1.83371 q^{2} -1.24345 q^{3} +1.36250 q^{4} +1.00000 q^{5} +2.28012 q^{6} -1.00000 q^{7} +1.16899 q^{8} -1.45384 q^{9} -1.83371 q^{10} -1.69420 q^{12} +2.32528 q^{13} +1.83371 q^{14} -1.24345 q^{15} -4.86859 q^{16} -4.59626 q^{17} +2.66592 q^{18} -7.12249 q^{19} +1.36250 q^{20} +1.24345 q^{21} -9.05919 q^{23} -1.45358 q^{24} +1.00000 q^{25} -4.26390 q^{26} +5.53811 q^{27} -1.36250 q^{28} +4.99497 q^{29} +2.28012 q^{30} -9.24132 q^{31} +6.58962 q^{32} +8.42822 q^{34} -1.00000 q^{35} -1.98086 q^{36} +7.21523 q^{37} +13.0606 q^{38} -2.89137 q^{39} +1.16899 q^{40} +7.07508 q^{41} -2.28012 q^{42} -7.35367 q^{43} -1.45384 q^{45} +16.6119 q^{46} -8.20509 q^{47} +6.05384 q^{48} +1.00000 q^{49} -1.83371 q^{50} +5.71521 q^{51} +3.16820 q^{52} -5.89627 q^{53} -10.1553 q^{54} -1.16899 q^{56} +8.85643 q^{57} -9.15934 q^{58} +8.08132 q^{59} -1.69420 q^{60} -0.0843910 q^{61} +16.9459 q^{62} +1.45384 q^{63} -2.34628 q^{64} +2.32528 q^{65} -12.3209 q^{67} -6.26241 q^{68} +11.2646 q^{69} +1.83371 q^{70} +1.50066 q^{71} -1.69952 q^{72} +16.3973 q^{73} -13.2307 q^{74} -1.24345 q^{75} -9.70439 q^{76} +5.30193 q^{78} +12.5640 q^{79} -4.86859 q^{80} -2.52483 q^{81} -12.9737 q^{82} +7.62857 q^{83} +1.69420 q^{84} -4.59626 q^{85} +13.4845 q^{86} -6.21098 q^{87} -5.73477 q^{89} +2.66592 q^{90} -2.32528 q^{91} -12.3432 q^{92} +11.4911 q^{93} +15.0458 q^{94} -7.12249 q^{95} -8.19384 q^{96} -16.7237 q^{97} -1.83371 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 2 q^{2} - 4 q^{3} + 12 q^{4} + 10 q^{5} + 8 q^{6} - 10 q^{7} + 6 q^{8} + 14 q^{9}+O(q^{10}) \) 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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