LMFDB - Embedded newform 4235.2.a.bp.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

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

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

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

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

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

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

chi := DirichletCharacter("4235.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	yes
Analytic conductor:	$33.8166452560$
Analytic rank:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 2 x^{17} - 28 x^{16} + 54 x^{15} + 317 x^{14} - 580 x^{13} - 1874 x^{12} + 3158 x^{11} + \cdots - 176 $ x^18 - 2x^17 - 28x^16 + 54x^15 + 317x^14 - 580x^13 - 1874x^12 + 3158x^11 + 6290x^10 - 9228x^9 - 12411x^8 + 14224x^7 + 14618x^6 - 10744x^5 - 9817x^4 + 3146x^3 + 3048x^2 - 16*x - 176
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 385)
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.52971$ of defining polynomial
Character	$\chi$	$=$	4235.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.52971 q^{2} +3.17620 q^{3} +4.39941 q^{4} +1.00000 q^{5} +8.03485 q^{6} +1.00000 q^{7} +6.06980 q^{8} +7.08825 q^{9} +O(q^{10})$	\(q+2.52971 q^{2} +3.17620 q^{3} +4.39941 q^{4} +1.00000 q^{5} +8.03485 q^{6} +1.00000 q^{7} +6.06980 q^{8} +7.08825 q^{9} +2.52971 q^{10} +13.9734 q^{12} -5.63769 q^{13} +2.52971 q^{14} +3.17620 q^{15} +6.55600 q^{16} -3.53328 q^{17} +17.9312 q^{18} -2.61505 q^{19} +4.39941 q^{20} +3.17620 q^{21} -8.37986 q^{23} +19.2789 q^{24} +1.00000 q^{25} -14.2617 q^{26} +12.9851 q^{27} +4.39941 q^{28} -1.44065 q^{29} +8.03485 q^{30} +7.31191 q^{31} +4.44513 q^{32} -8.93815 q^{34} +1.00000 q^{35} +31.1841 q^{36} +5.31511 q^{37} -6.61531 q^{38} -17.9064 q^{39} +6.06980 q^{40} +0.865054 q^{41} +8.03485 q^{42} -1.36344 q^{43} +7.08825 q^{45} -21.1986 q^{46} +0.122739 q^{47} +20.8232 q^{48} +1.00000 q^{49} +2.52971 q^{50} -11.2224 q^{51} -24.8025 q^{52} -1.23172 q^{53} +32.8485 q^{54} +6.06980 q^{56} -8.30593 q^{57} -3.64441 q^{58} -3.19714 q^{59} +13.9734 q^{60} +11.7896 q^{61} +18.4970 q^{62} +7.08825 q^{63} -1.86712 q^{64} -5.63769 q^{65} -5.98011 q^{67} -15.5443 q^{68} -26.6161 q^{69} +2.52971 q^{70} -0.392303 q^{71} +43.0243 q^{72} +6.72276 q^{73} +13.4457 q^{74} +3.17620 q^{75} -11.5047 q^{76} -45.2980 q^{78} -9.77438 q^{79} +6.55600 q^{80} +19.9785 q^{81} +2.18833 q^{82} +7.32744 q^{83} +13.9734 q^{84} -3.53328 q^{85} -3.44910 q^{86} -4.57578 q^{87} +6.61870 q^{89} +17.9312 q^{90} -5.63769 q^{91} -36.8665 q^{92} +23.2241 q^{93} +0.310492 q^{94} -2.61505 q^{95} +14.1186 q^{96} -5.17987 q^{97} +2.52971 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) $ 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * q^98

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	2.52971	1.78877	0.894386	−	0.447296i	$-0.147613\pi$
$2$	2.52971	1.78877	0.894386	+	0.447296i	$0.147613\pi$
$3$	3.17620	1.83378	0.916890	−	0.399140i	$-0.130691\pi$
$3$	3.17620	1.83378	0.916890	+	0.399140i	$0.130691\pi$
$4$	4.39941	2.19971
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	8.03485	3.28021
$7$	1.00000	0.377964
$7$	1.00000	0.377964
$8$	6.06980	2.14600
$9$	7.08825	2.36275
$10$	2.52971	0.799963
$11$	0	0
$11$	0	0
$12$	13.9734	4.03378
$13$	−5.63769	−1.56361	−0.781807	−	0.623521i	$-0.785702\pi$
$13$	−5.63769	−1.56361	−0.781807	+	0.623521i	$0.785702\pi$
$14$	2.52971	0.676092
$15$	3.17620	0.820091
$16$	6.55600	1.63900
$17$	−3.53328	−0.856945	−0.428473	−	0.903555i	$-0.640948\pi$
$17$	−3.53328	−0.856945	−0.428473	+	0.903555i	$0.640948\pi$
$18$	17.9312	4.22642
$19$	−2.61505	−0.599934	−0.299967	−	0.953950i	$-0.596976\pi$
$19$	−2.61505	−0.599934	−0.299967	+	0.953950i	$0.596976\pi$
$20$	4.39941	0.983738
$21$	3.17620	0.693104
$22$	0	0
$23$	−8.37986	−1.74732	−0.873661	−	0.486535i	$-0.838261\pi$
$23$	−8.37986	−1.74732	−0.873661	+	0.486535i	$0.838261\pi$
$24$	19.2789	3.93529
$25$	1.00000	0.200000
$26$	−14.2617	−2.79695
$27$	12.9851	2.49898
$28$	4.39941	0.831411
$29$	−1.44065	−0.267521	−0.133761	−	0.991014i	$-0.542705\pi$
$29$	−1.44065	−0.267521	−0.133761	+	0.991014i	$0.542705\pi$
$30$	8.03485	1.46696
$31$	7.31191	1.31326	0.656629	−	0.754214i	$-0.271982\pi$
$31$	7.31191	1.31326	0.656629	+	0.754214i	$0.271982\pi$
$32$	4.44513	0.785796
$33$	0	0
$34$	−8.93815	−1.53288
$35$	1.00000	0.169031
$36$	31.1841	5.19735
$37$	5.31511	0.873799	0.436899	−	0.899510i	$-0.356077\pi$
$37$	5.31511	0.873799	0.436899	+	0.899510i	$0.356077\pi$
$38$	−6.61531	−1.07315
$39$	−17.9064	−2.86732
$40$	6.06980	0.959720
$41$	0.865054	0.135099	0.0675494	−	0.997716i	$-0.478482\pi$
$41$	0.865054	0.135099	0.0675494	+	0.997716i	$0.478482\pi$
$42$	8.03485	1.23980
$43$	−1.36344	−0.207923	−0.103961	−	0.994581i	$-0.533152\pi$
$43$	−1.36344	−0.207923	−0.103961	+	0.994581i	$0.533152\pi$
$44$	0	0
$45$	7.08825	1.05665
$46$	−21.1986	−3.12556
$47$	0.122739	0.0179033	0.00895163	−	0.999960i	$-0.497151\pi$
$47$	0.122739	0.0179033	0.00895163	+	0.999960i	$0.497151\pi$
$48$	20.8232	3.00556
$49$	1.00000	0.142857
$50$	2.52971	0.357754
$51$	−11.2224	−1.57145
$52$	−24.8025	−3.43949
$53$	−1.23172	−0.169189	−0.0845945	−	0.996415i	$-0.526959\pi$
$53$	−1.23172	−0.169189	−0.0845945	+	0.996415i	$0.526959\pi$
$54$	32.8485	4.47011
$55$	0	0
$56$	6.06980	0.811112
$57$	−8.30593	−1.10015
$58$	−3.64441	−0.478534
$59$	−3.19714	−0.416232	−0.208116	−	0.978104i	$-0.566733\pi$
$59$	−3.19714	−0.416232	−0.208116	+	0.978104i	$0.566733\pi$
$60$	13.9734	1.80396
$61$	11.7896	1.50950	0.754751	−	0.656011i	$-0.227757\pi$
$61$	11.7896	1.50950	0.754751	+	0.656011i	$0.227757\pi$
$62$	18.4970	2.34912
$63$	7.08825	0.893035
$64$	−1.86712	−0.233389
$65$	−5.63769	−0.699269
$66$	0	0
$67$	−5.98011	−0.730586	−0.365293	−	0.930893i	$-0.619031\pi$
$67$	−5.98011	−0.730586	−0.365293	+	0.930893i	$0.619031\pi$
$68$	−15.5443	−1.88503
$69$	−26.6161	−3.20420
$70$	2.52971	0.302358
$71$	−0.392303	−0.0465578	−0.0232789	−	0.999729i	$-0.507411\pi$
$71$	−0.392303	−0.0465578	−0.0232789	+	0.999729i	$0.507411\pi$
$72$	43.0243	5.07046
$73$	6.72276	0.786840	0.393420	−	0.919359i	$-0.371292\pi$
$73$	6.72276	0.786840	0.393420	+	0.919359i	$0.371292\pi$
$74$	13.4457	1.56303
$75$	3.17620	0.366756
$76$	−11.5047	−1.31968
$77$	0	0
$78$	−45.2980	−5.12899
$79$	−9.77438	−1.09970	−0.549852	−	0.835262i	$-0.685316\pi$
$79$	−9.77438	−1.09970	−0.549852	+	0.835262i	$0.685316\pi$
$80$	6.55600	0.732983
$81$	19.9785	2.21984
$82$	2.18833	0.241661
$83$	7.32744	0.804291	0.402146	−	0.915576i	$-0.368265\pi$
$83$	7.32744	0.804291	0.402146	+	0.915576i	$0.368265\pi$
$84$	13.9734	1.52462
$85$	−3.53328	−0.383238
$86$	−3.44910	−0.371926
$87$	−4.57578	−0.490575
$88$	0	0
$89$	6.61870	0.701581	0.350791	−	0.936454i	$-0.385913\pi$
$89$	6.61870	0.701581	0.350791	+	0.936454i	$0.385913\pi$
$90$	17.9312	1.89011
$91$	−5.63769	−0.590990
$92$	−36.8665	−3.84359
$93$	23.2241	2.40822
$94$	0.310492	0.0320249
$95$	−2.61505	−0.268299
$96$	14.1186	1.44098
$97$	−5.17987	−0.525936	−0.262968	−	0.964805i	$-0.584701\pi$
$97$	−5.17987	−0.525936	−0.262968	+	0.964805i	$0.584701\pi$
$98$	2.52971	0.255539
$99$	0	0
$100$	4.39941	0.439941
$101$	−5.27517	−0.524899	−0.262450	−	0.964946i	$-0.584530\pi$
$101$	−5.27517	−0.524899	−0.262450	+	0.964946i	$0.584530\pi$
$102$	−28.3893	−2.81096
$103$	3.56945	0.351708	0.175854	−	0.984416i	$-0.443731\pi$
$103$	3.56945	0.351708	0.175854	+	0.984416i	$0.443731\pi$
$104$	−34.2197	−3.35551
$105$	3.17620	0.309965
$106$	−3.11588	−0.302641
$107$	−9.62169	−0.930164	−0.465082	−	0.885268i	$-0.653975\pi$
$107$	−9.62169	−0.930164	−0.465082	+	0.885268i	$0.653975\pi$
$108$	57.1268	5.49703
$109$	17.3052	1.65754	0.828768	−	0.559592i	$-0.189042\pi$
$109$	17.3052	1.65754	0.828768	+	0.559592i	$0.189042\pi$
$110$	0	0
$111$	16.8819	1.60235
$112$	6.55600	0.619483
$113$	−12.4595	−1.17209	−0.586047	−	0.810277i	$-0.699317\pi$
$113$	−12.4595	−1.17209	−0.586047	+	0.810277i	$0.699317\pi$
$114$	−21.0116	−1.96791
$115$	−8.37986	−0.781426
$116$	−6.33799	−0.588468
$117$	−39.9613	−3.69443
$118$	−8.08783	−0.744545
$119$	−3.53328	−0.323895
$120$	19.2789	1.75992
$121$	0	0
$122$	29.8242	2.70016
$123$	2.74759	0.247742
$124$	32.1681	2.88878
$125$	1.00000	0.0894427
$126$	17.9312	1.59744
$127$	0.309232	0.0274399	0.0137200	−	0.999906i	$-0.495633\pi$
$127$	0.309232	0.0274399	0.0137200	+	0.999906i	$0.495633\pi$
$128$	−13.6135	−1.20328
$129$	−4.33056	−0.381284
$130$	−14.2617	−1.25083
$131$	−1.36409	−0.119181	−0.0595906	−	0.998223i	$-0.518980\pi$
$131$	−1.36409	−0.119181	−0.0595906	+	0.998223i	$0.518980\pi$
$132$	0	0
$133$	−2.61505	−0.226754
$134$	−15.1279	−1.30685
$135$	12.9851	1.11758
$136$	−21.4463	−1.83900
$137$	−13.5912	−1.16117	−0.580587	−	0.814198i	$-0.697177\pi$
$137$	−13.5912	−1.16117	−0.580587	+	0.814198i	$0.697177\pi$
$138$	−67.3310	−5.73159
$139$	−2.19758	−0.186396	−0.0931980	−	0.995648i	$-0.529709\pi$
$139$	−2.19758	−0.186396	−0.0931980	+	0.995648i	$0.529709\pi$
$140$	4.39941	0.371818
$141$	0.389842	0.0328306
$142$	−0.992411	−0.0832812
$143$	0	0
$144$	46.4705	3.87254
$145$	−1.44065	−0.119639
$146$	17.0066	1.40748
$147$	3.17620	0.261969
$148$	23.3834	1.92210
$149$	2.15954	0.176916	0.0884581	−	0.996080i	$-0.471806\pi$
$149$	2.15954	0.176916	0.0884581	+	0.996080i	$0.471806\pi$
$150$	8.03485	0.656043
$151$	−17.7495	−1.44444	−0.722218	−	0.691666i	$-0.756877\pi$
$151$	−17.7495	−1.44444	−0.722218	+	0.691666i	$0.756877\pi$
$152$	−15.8729	−1.28746
$153$	−25.0447	−2.02475
$154$	0	0
$155$	7.31191	0.587306
$156$	−78.7777	−6.30727
$157$	15.0001	1.19714	0.598569	−	0.801071i	$-0.295736\pi$
$157$	15.0001	1.19714	0.598569	+	0.801071i	$0.295736\pi$
$158$	−24.7263	−1.96712
$159$	−3.91217	−0.310256
$160$	4.44513	0.351419
$161$	−8.37986	−0.660426
$162$	50.5398	3.97078
$163$	4.56712	0.357724	0.178862	−	0.983874i	$-0.442758\pi$
$163$	4.56712	0.357724	0.178862	+	0.983874i	$0.442758\pi$
$164$	3.80573	0.297178
$165$	0	0
$166$	18.5363	1.43869
$167$	12.2162	0.945316	0.472658	−	0.881246i	$-0.343295\pi$
$167$	12.2162	0.945316	0.472658	+	0.881246i	$0.343295\pi$
$168$	19.2789	1.48740
$169$	18.7835	1.44489
$170$	−8.93815	−0.685525
$171$	−18.5361	−1.41749
$172$	−5.99833	−0.457368
$173$	−23.8209	−1.81107	−0.905536	−	0.424270i	$-0.860531\pi$
$173$	−23.8209	−1.81107	−0.905536	+	0.424270i	$0.860531\pi$
$174$	−11.5754	−0.877527
$175$	1.00000	0.0755929
$176$	0	0
$177$	−10.1548	−0.763279
$178$	16.7434	1.25497
$179$	−7.62096	−0.569617	−0.284809	−	0.958584i	$-0.591930\pi$
$179$	−7.62096	−0.569617	−0.284809	+	0.958584i	$0.591930\pi$
$180$	31.1841	2.32433
$181$	5.87082	0.436375	0.218187	−	0.975907i	$-0.429986\pi$
$181$	5.87082	0.436375	0.218187	+	0.975907i	$0.429986\pi$
$182$	−14.2617	−1.05715
$183$	37.4461	2.76810
$184$	−50.8641	−3.74975
$185$	5.31511	0.390775
$186$	58.7501	4.30777
$187$	0	0
$188$	0.539977	0.0393819
$189$	12.9851	0.944527
$190$	−6.61531	−0.479925
$191$	13.4016	0.969708	0.484854	−	0.874595i	$-0.338873\pi$
$191$	13.4016	0.969708	0.484854	+	0.874595i	$0.338873\pi$
$192$	−5.93033	−0.427985
$193$	19.9470	1.43582	0.717908	−	0.696138i	$-0.245100\pi$
$193$	19.9470	1.43582	0.717908	+	0.696138i	$0.245100\pi$
$194$	−13.1035	−0.940779
$195$	−17.9064	−1.28231
$196$	4.39941	0.314244
$197$	19.1658	1.36551	0.682753	−	0.730649i	$-0.260783\pi$
$197$	19.1658	1.36551	0.682753	+	0.730649i	$0.260783\pi$
$198$	0	0
$199$	20.9482	1.48498	0.742489	−	0.669858i	$-0.233645\pi$
$199$	20.9482	1.48498	0.742489	+	0.669858i	$0.233645\pi$
$200$	6.06980	0.429200
$201$	−18.9940	−1.33973
$202$	−13.3446	−0.938925
$203$	−1.44065	−0.101114
$204$	−49.3719	−3.45673
$205$	0.865054	0.0604180
$206$	9.02965	0.629125
$207$	−59.3986	−4.12848
$208$	−36.9607	−2.56276
$209$	0	0
$210$	8.03485	0.554457
$211$	−1.32291	−0.0910731	−0.0455366	−	0.998963i	$-0.514500\pi$
$211$	−1.32291	−0.0910731	−0.0455366	+	0.998963i	$0.514500\pi$
$212$	−5.41882	−0.372166
$213$	−1.24603	−0.0853767
$214$	−24.3400	−1.66385
$215$	−1.36344	−0.0929858
$216$	78.8170	5.36282
$217$	7.31191	0.496364
$218$	43.7770	2.96496
$219$	21.3528	1.44289
$220$	0	0
$221$	19.9195	1.33993
$222$	42.7061	2.86625
$223$	−26.2249	−1.75615	−0.878073	−	0.478526i	$-0.841171\pi$
$223$	−26.2249	−1.75615	−0.878073	+	0.478526i	$0.841171\pi$
$224$	4.44513	0.297003
$225$	7.08825	0.472550
$226$	−31.5189	−2.09661
$227$	7.28891	0.483782	0.241891	−	0.970303i	$-0.422232\pi$
$227$	7.28891	0.483782	0.241891	+	0.970303i	$0.422232\pi$
$228$	−36.5412	−2.42000
$229$	28.2901	1.86946	0.934730	−	0.355359i	$-0.115641\pi$
$229$	28.2901	1.86946	0.934730	+	0.355359i	$0.115641\pi$
$230$	−21.1986	−1.39779
$231$	0	0
$232$	−8.74444	−0.574100
$233$	−15.0917	−0.988690	−0.494345	−	0.869266i	$-0.664592\pi$
$233$	−15.0917	−0.988690	−0.494345	+	0.869266i	$0.664592\pi$
$234$	−101.090	−6.60849
$235$	0.122739	0.00800658
$236$	−14.0655	−0.915589
$237$	−31.0454	−2.01661
$238$	−8.93815	−0.579374
$239$	20.6558	1.33611	0.668056	−	0.744111i	$-0.267127\pi$
$239$	20.6558	1.33611	0.668056	+	0.744111i	$0.267127\pi$
$240$	20.8232	1.34413
$241$	7.44861	0.479807	0.239904	−	0.970797i	$-0.422884\pi$
$241$	7.44861	0.479807	0.239904	+	0.970797i	$0.422884\pi$
$242$	0	0
$243$	24.5005	1.57171
$244$	51.8673	3.32046
$245$	1.00000	0.0638877
$246$	6.95058	0.443153
$247$	14.7429	0.938065
$248$	44.3818	2.81825
$249$	23.2734	1.47489
$250$	2.52971	0.159993
$251$	−3.78243	−0.238745	−0.119373	−	0.992850i	$-0.538088\pi$
$251$	−3.78243	−0.238745	−0.119373	+	0.992850i	$0.538088\pi$
$252$	31.1841	1.96442
$253$	0	0
$254$	0.782267	0.0490838
$255$	−11.2224	−0.702773
$256$	−30.7040	−1.91900
$257$	−9.98333	−0.622743	−0.311371	−	0.950288i	$-0.600788\pi$
$257$	−9.98333	−0.622743	−0.311371	+	0.950288i	$0.600788\pi$
$258$	−10.9550	−0.682031
$259$	5.31511	0.330265
$260$	−24.8025	−1.53819
$261$	−10.2117	−0.632086
$262$	−3.45075	−0.213188
$263$	6.87053	0.423655	0.211827	−	0.977307i	$-0.432059\pi$
$263$	6.87053	0.423655	0.211827	+	0.977307i	$0.432059\pi$
$264$	0	0
$265$	−1.23172	−0.0756637
$266$	−6.61531	−0.405611
$267$	21.0223	1.28655
$268$	−26.3090	−1.60707
$269$	9.69144	0.590897	0.295449	−	0.955359i	$-0.404531\pi$
$269$	9.69144	0.590897	0.295449	+	0.955359i	$0.404531\pi$
$270$	32.8485	1.99909
$271$	−0.437944	−0.0266032	−0.0133016	−	0.999912i	$-0.504234\pi$
$271$	−0.437944	−0.0266032	−0.0133016	+	0.999912i	$0.504234\pi$
$272$	−23.1641	−1.40453
$273$	−17.9064	−1.08375
$274$	−34.3817	−2.07708
$275$	0	0
$276$	−117.095	−7.04831
$277$	−17.2189	−1.03459	−0.517293	−	0.855808i	$-0.673060\pi$
$277$	−17.2189	−1.03459	−0.517293	+	0.855808i	$0.673060\pi$
$278$	−5.55922	−0.333420
$279$	51.8286	3.10290
$280$	6.06980	0.362740
$281$	13.3564	0.796775	0.398387	−	0.917217i	$-0.369570\pi$
$281$	13.3564	0.796775	0.398387	+	0.917217i	$0.369570\pi$
$282$	0.986186	0.0587265
$283$	−7.77180	−0.461986	−0.230993	−	0.972955i	$-0.574197\pi$
$283$	−7.77180	−0.461986	−0.230993	+	0.972955i	$0.574197\pi$
$284$	−1.72590	−0.102413
$285$	−8.30593	−0.492001
$286$	0	0
$287$	0.865054	0.0510625
$288$	31.5082	1.85664
$289$	−4.51596	−0.265645
$290$	−3.64441	−0.214007
$291$	−16.4523	−0.964451
$292$	29.5762	1.73082
$293$	−23.8475	−1.39319	−0.696594	−	0.717466i	$-0.745302\pi$
$293$	−23.8475	−1.39319	−0.696594	+	0.717466i	$0.745302\pi$
$294$	8.03485	0.468602
$295$	−3.19714	−0.186145
$296$	32.2617	1.87517
$297$	0	0
$298$	5.46299	0.316463
$299$	47.2431	2.73214
$300$	13.9734	0.806755
$301$	−1.36344	−0.0785873
$302$	−44.9011	−2.58377
$303$	−16.7550	−0.962550
$304$	−17.1443	−0.983292
$305$	11.7896	0.675070
$306$	−63.3558	−3.62181
$307$	10.4347	0.595540	0.297770	−	0.954638i	$-0.403757\pi$
$307$	10.4347	0.595540	0.297770	+	0.954638i	$0.403757\pi$
$308$	0	0
$309$	11.3373	0.644955
$310$	18.4970	1.05056
$311$	21.7814	1.23511	0.617555	−	0.786527i	$-0.288123\pi$
$311$	21.7814	1.23511	0.617555	+	0.786527i	$0.288123\pi$
$312$	−108.689	−6.15328
$313$	20.5817	1.16335	0.581674	−	0.813422i	$-0.302398\pi$
$313$	20.5817	1.16335	0.581674	+	0.813422i	$0.302398\pi$
$314$	37.9459	2.14141
$315$	7.08825	0.399378
$316$	−43.0015	−2.41902
$317$	−5.24021	−0.294319	−0.147160	−	0.989113i	$-0.547013\pi$
$317$	−5.24021	−0.294319	−0.147160	+	0.989113i	$0.547013\pi$
$318$	−9.89665	−0.554977
$319$	0	0
$320$	−1.86712	−0.104375
$321$	−30.5604	−1.70572
$322$	−21.1986	−1.18135
$323$	9.23970	0.514111
$324$	87.8938	4.88299
$325$	−5.63769	−0.312723
$326$	11.5535	0.639887
$327$	54.9648	3.03956
$328$	5.25071	0.289922
$329$	0.122739	0.00676680
$330$	0	0
$331$	9.90584	0.544474	0.272237	−	0.962230i	$-0.412236\pi$
$331$	9.90584	0.544474	0.272237	+	0.962230i	$0.412236\pi$
$332$	32.2364	1.76920
$333$	37.6748	2.06457
$334$	30.9033	1.69096
$335$	−5.98011	−0.326728
$336$	20.8232	1.13600
$337$	−0.320499	−0.0174587	−0.00872934	−	0.999962i	$-0.502779\pi$
$337$	−0.320499	−0.0174587	−0.00872934	+	0.999962i	$0.502779\pi$
$338$	47.5168	2.58457
$339$	−39.5740	−2.14936
$340$	−15.5443	−0.843010
$341$	0	0
$342$	−46.8910	−2.53557
$343$	1.00000	0.0539949
$344$	−8.27581	−0.446202
$345$	−26.6161	−1.43296
$346$	−60.2599	−3.23959
$347$	27.4721	1.47478	0.737389	−	0.675469i	$-0.236059\pi$
$347$	27.4721	1.47478	0.737389	+	0.675469i	$0.236059\pi$
$348$	−20.1307	−1.07912
$349$	−15.4750	−0.828358	−0.414179	−	0.910196i	$-0.635931\pi$
$349$	−15.4750	−0.828358	−0.414179	+	0.910196i	$0.635931\pi$
$350$	2.52971	0.135218
$351$	−73.2059	−3.90744
$352$	0	0
$353$	17.2939	0.920463	0.460231	−	0.887799i	$-0.347766\pi$
$353$	17.2939	0.920463	0.460231	+	0.887799i	$0.347766\pi$
$354$	−25.6886	−1.36533
$355$	−0.392303	−0.0208213
$356$	29.1184	1.54327
$357$	−11.2224	−0.593952
$358$	−19.2788	−1.01892
$359$	11.2623	0.594401	0.297200	−	0.954815i	$-0.403947\pi$
$359$	11.2623	0.594401	0.297200	+	0.954815i	$0.403947\pi$
$360$	43.0243	2.26758
$361$	−12.1615	−0.640079
$362$	14.8514	0.780575
$363$	0	0
$364$	−24.8025	−1.30000
$365$	6.72276	0.351885
$366$	94.7277	4.95149
$367$	26.5375	1.38525	0.692623	−	0.721300i	$-0.256455\pi$
$367$	26.5375	1.38525	0.692623	+	0.721300i	$0.256455\pi$
$368$	−54.9383	−2.86386
$369$	6.13172	0.319205
$370$	13.4457	0.699007
$371$	−1.23172	−0.0639475
$372$	102.172	5.29739
$373$	16.7560	0.867594	0.433797	−	0.901011i	$-0.357173\pi$
$373$	16.7560	0.867594	0.433797	+	0.901011i	$0.357173\pi$
$374$	0	0
$375$	3.17620	0.164018
$376$	0.744999	0.0384204
$377$	8.12191	0.418300
$378$	32.8485	1.68954
$379$	0.106993	0.00549586	0.00274793	−	0.999996i	$-0.499125\pi$
$379$	0.106993	0.00549586	0.00274793	+	0.999996i	$0.499125\pi$
$380$	−11.5047	−0.590178
$381$	0.982184	0.0503188
$382$	33.9022	1.73459
$383$	−19.5081	−0.996817	−0.498408	−	0.866942i	$-0.666082\pi$
$383$	−19.5081	−0.996817	−0.498408	+	0.866942i	$0.666082\pi$
$384$	−43.2393	−2.20654
$385$	0	0
$386$	50.4600	2.56835
$387$	−9.66440	−0.491269
$388$	−22.7884	−1.15690
$389$	−21.9847	−1.11467	−0.557334	−	0.830288i	$-0.688176\pi$
$389$	−21.9847	−1.11467	−0.557334	+	0.830288i	$0.688176\pi$
$390$	−45.2980	−2.29375
$391$	29.6084	1.49736
$392$	6.06980	0.306571
$393$	−4.33263	−0.218552
$394$	48.4838	2.44258
$395$	−9.77438	−0.491802
$396$	0	0
$397$	−18.5801	−0.932508	−0.466254	−	0.884651i	$-0.654397\pi$
$397$	−18.5801	−0.932508	−0.466254	+	0.884651i	$0.654397\pi$
$398$	52.9928	2.65629
$399$	−8.30593	−0.415817
$400$	6.55600	0.327800
$401$	25.6147	1.27914	0.639569	−	0.768733i	$-0.279113\pi$
$401$	25.6147	1.27914	0.639569	+	0.768733i	$0.279113\pi$
$402$	−48.0493	−2.39648
$403$	−41.2222	−2.05343
$404$	−23.2077	−1.15462
$405$	19.9785	0.992741
$406$	−3.64441	−0.180869
$407$	0	0
$408$	−68.1177	−3.37233
$409$	−10.3184	−0.510213	−0.255106	−	0.966913i	$-0.582111\pi$
$409$	−10.3184	−0.510213	−0.255106	+	0.966913i	$0.582111\pi$
$410$	2.18833	0.108074
$411$	−43.1684	−2.12934
$412$	15.7035	0.773654
$413$	−3.19714	−0.157321
$414$	−150.261	−7.38492
$415$	7.32744	0.359690
$416$	−25.0603	−1.22868
$417$	−6.97994	−0.341809
$418$	0	0
$419$	−18.7645	−0.916704	−0.458352	−	0.888771i	$-0.651560\pi$
$419$	−18.7645	−0.916704	−0.458352	+	0.888771i	$0.651560\pi$
$420$	13.9734	0.681833
$421$	34.9078	1.70130	0.850652	−	0.525730i	$-0.176208\pi$
$421$	34.9078	1.70130	0.850652	+	0.525730i	$0.176208\pi$
$422$	−3.34658	−0.162909
$423$	0.870002	0.0423009
$424$	−7.47627	−0.363080
$425$	−3.53328	−0.171389
$426$	−3.15209	−0.152719
$427$	11.7896	0.570538
$428$	−42.3298	−2.04609
$429$	0	0
$430$	−3.44910	−0.166330
$431$	39.4899	1.90216	0.951081	−	0.308942i	$-0.0999748\pi$
$431$	39.4899	1.90216	0.951081	+	0.308942i	$0.0999748\pi$
$432$	85.1303	4.09583
$433$	−35.3061	−1.69670	−0.848351	−	0.529434i	$-0.822405\pi$
$433$	−35.3061	−1.69670	−0.848351	+	0.529434i	$0.822405\pi$
$434$	18.4970	0.887883
$435$	−4.57578	−0.219392
$436$	76.1327	3.64609
$437$	21.9138	1.04828
$438$	54.0164	2.58100
$439$	2.86796	0.136880	0.0684401	−	0.997655i	$-0.478198\pi$
$439$	2.86796	0.136880	0.0684401	+	0.997655i	$0.478198\pi$
$440$	0	0
$441$	7.08825	0.337536
$442$	50.3905	2.39683
$443$	−34.3050	−1.62988	−0.814939	−	0.579547i	$-0.803230\pi$
$443$	−34.3050	−1.62988	−0.814939	+	0.579547i	$0.803230\pi$
$444$	74.2702	3.52471
$445$	6.61870	0.313757
$446$	−66.3412	−3.14135
$447$	6.85912	0.324425
$448$	−1.86712	−0.0882129
$449$	−19.4291	−0.916916	−0.458458	−	0.888716i	$-0.651598\pi$
$449$	−19.4291	−0.916916	−0.458458	+	0.888716i	$0.651598\pi$
$450$	17.9312	0.845284
$451$	0	0
$452$	−54.8146	−2.57826
$453$	−56.3761	−2.64878
$454$	18.4388	0.865376
$455$	−5.63769	−0.264299
$456$	−50.4154	−2.36092
$457$	−27.4987	−1.28634	−0.643168	−	0.765725i	$-0.722380\pi$
$457$	−27.4987	−1.28634	−0.643168	+	0.765725i	$0.722380\pi$
$458$	71.5655	3.34404
$459$	−45.8799	−2.14149
$460$	−36.8665	−1.71891
$461$	8.93876	0.416320	0.208160	−	0.978095i	$-0.433253\pi$
$461$	8.93876	0.416320	0.208160	+	0.978095i	$0.433253\pi$
$462$	0	0
$463$	−28.3671	−1.31833	−0.659165	−	0.751998i	$-0.729090\pi$
$463$	−28.3671	−1.31833	−0.659165	+	0.751998i	$0.729090\pi$
$464$	−9.44487	−0.438467
$465$	23.2241	1.07699
$466$	−38.1775	−1.76854
$467$	−20.0542	−0.927996	−0.463998	−	0.885836i	$-0.653585\pi$
$467$	−20.0542	−0.927996	−0.463998	+	0.885836i	$0.653585\pi$
$468$	−175.806	−8.12665
$469$	−5.98011	−0.276136
$470$	0.310492	0.0143220
$471$	47.6433	2.19529
$472$	−19.4060	−0.893235
$473$	0	0
$474$	−78.5357	−3.60726
$475$	−2.61505	−0.119987
$476$	−15.5443	−0.712473
$477$	−8.73070	−0.399751
$478$	52.2531	2.39000
$479$	−7.02005	−0.320754	−0.160377	−	0.987056i	$-0.551271\pi$
$479$	−7.02005	−0.320754	−0.160377	+	0.987056i	$0.551271\pi$
$480$	14.1186	0.644424
$481$	−29.9649	−1.36628
$482$	18.8428	0.858266
$483$	−26.6161	−1.21108
$484$	0	0
$485$	−5.17987	−0.235206
$486$	61.9791	2.81143
$487$	−18.5520	−0.840670	−0.420335	−	0.907369i	$-0.638088\pi$
$487$	−18.5520	−0.840670	−0.420335	+	0.907369i	$0.638088\pi$
$488$	71.5605	3.23939
$489$	14.5061	0.655988
$490$	2.52971	0.114280
$491$	−8.60028	−0.388125	−0.194063	−	0.980989i	$-0.562167\pi$
$491$	−8.60028	−0.388125	−0.194063	+	0.980989i	$0.562167\pi$
$492$	12.0878	0.544958
$493$	5.09020	0.229251
$494$	37.2951	1.67798
$495$	0	0
$496$	47.9368	2.15243
$497$	−0.392303	−0.0175972
$498$	58.8749	2.63825
$499$	−21.7420	−0.973304	−0.486652	−	0.873596i	$-0.661782\pi$
$499$	−21.7420	−0.973304	−0.486652	+	0.873596i	$0.661782\pi$
$500$	4.39941	0.196748
$501$	38.8010	1.73350
$502$	−9.56844	−0.427060
$503$	−8.62523	−0.384580	−0.192290	−	0.981338i	$-0.561591\pi$
$503$	−8.62523	−0.384580	−0.192290	+	0.981338i	$0.561591\pi$
$504$	43.0243	1.91645
$505$	−5.27517	−0.234742
$506$	0	0
$507$	59.6603	2.64961
$508$	1.36044	0.0603598
$509$	29.7295	1.31774	0.658868	−	0.752259i	$-0.271036\pi$
$509$	29.7295	1.31774	0.658868	+	0.752259i	$0.271036\pi$
$510$	−28.3893	−1.25710
$511$	6.72276	0.297397
$512$	−50.4450	−2.22937
$513$	−33.9567	−1.49923
$514$	−25.2549	−1.11394
$515$	3.56945	0.157289
$516$	−19.0519	−0.838713
$517$	0	0
$518$	13.4457	0.590769
$519$	−75.6600	−3.32111
$520$	−34.2197	−1.50063
$521$	15.4755	0.677995	0.338997	−	0.940787i	$-0.389912\pi$
$521$	15.4755	0.677995	0.338997	+	0.940787i	$0.389912\pi$
$522$	−25.8325	−1.13066
$523$	23.7764	1.03967	0.519835	−	0.854267i	$-0.325993\pi$
$523$	23.7764	1.03967	0.519835	+	0.854267i	$0.325993\pi$
$524$	−6.00120	−0.262164
$525$	3.17620	0.138621
$526$	17.3804	0.757822
$527$	−25.8350	−1.12539
$528$	0	0
$529$	47.2221	2.05313
$530$	−3.11588	−0.135345
$531$	−22.6621	−0.983453
$532$	−11.5047	−0.498792
$533$	−4.87691	−0.211242
$534$	53.1803	2.30134
$535$	−9.62169	−0.415982
$536$	−36.2981	−1.56784
$537$	−24.2057	−1.04455
$538$	24.5165	1.05698
$539$	0	0
$540$	57.1268	2.45835
$541$	−30.1370	−1.29569	−0.647846	−	0.761772i	$-0.724330\pi$
$541$	−30.1370	−1.29569	−0.647846	+	0.761772i	$0.724330\pi$
$542$	−1.10787	−0.0475870
$543$	18.6469	0.800215
$544$	−15.7059	−0.673384
$545$	17.3052	0.741273
$546$	−45.2980	−1.93858
$547$	−7.40044	−0.316420	−0.158210	−	0.987405i	$-0.550572\pi$
$547$	−7.40044	−0.316420	−0.158210	+	0.987405i	$0.550572\pi$
$548$	−59.7933	−2.55424
$549$	83.5676	3.56658
$550$	0	0
$551$	3.76736	0.160495
$552$	−161.555	−6.87622
$553$	−9.77438	−0.415649
$554$	−43.5588	−1.85064
$555$	16.8819	0.716595
$556$	−9.66804	−0.410016
$557$	6.52363	0.276415	0.138207	−	0.990403i	$-0.455866\pi$
$557$	6.52363	0.276415	0.138207	+	0.990403i	$0.455866\pi$
$558$	131.111	5.55038
$559$	7.68665	0.325111
$560$	6.55600	0.277041
$561$	0	0
$562$	33.7877	1.42525
$563$	−3.30104	−0.139122	−0.0695611	−	0.997578i	$-0.522160\pi$
$563$	−3.30104	−0.139122	−0.0695611	+	0.997578i	$0.522160\pi$
$564$	1.71508	0.0722178
$565$	−12.4595	−0.524176
$566$	−19.6604	−0.826387
$567$	19.9785	0.839019
$568$	−2.38120	−0.0999130
$569$	−15.7739	−0.661274	−0.330637	−	0.943758i	$-0.607264\pi$
$569$	−15.7739	−0.661274	−0.330637	+	0.943758i	$0.607264\pi$
$570$	−21.0116	−0.880078
$571$	−43.1359	−1.80518	−0.902591	−	0.430499i	$-0.858338\pi$
$571$	−43.1359	−1.80518	−0.902591	+	0.430499i	$0.858338\pi$
$572$	0	0
$573$	42.5663	1.77823
$574$	2.18833	0.0913393
$575$	−8.37986	−0.349464
$576$	−13.2346	−0.551441
$577$	39.7078	1.65306	0.826529	−	0.562893i	$-0.190312\pi$
$577$	39.7078	1.65306	0.826529	+	0.562893i	$0.190312\pi$
$578$	−11.4241	−0.475178
$579$	63.3556	2.63297
$580$	−6.33799	−0.263171
$581$	7.32744	0.303993
$582$	−41.6195	−1.72518
$583$	0	0
$584$	40.8058	1.68856
$585$	−39.9613	−1.65220
$586$	−60.3272	−2.49209
$587$	−19.9477	−0.823330	−0.411665	−	0.911335i	$-0.635053\pi$
$587$	−19.9477	−0.823330	−0.411665	+	0.911335i	$0.635053\pi$
$588$	13.9734	0.576254
$589$	−19.1210	−0.787868
$590$	−8.08783	−0.332971
$591$	60.8744	2.50404
$592$	34.8458	1.43216
$593$	7.85058	0.322385	0.161192	−	0.986923i	$-0.448466\pi$
$593$	7.85058	0.322385	0.161192	+	0.986923i	$0.448466\pi$
$594$	0	0
$595$	−3.53328	−0.144850
$596$	9.50069	0.389164
$597$	66.5357	2.72312
$598$	119.511	4.88717
$599$	−39.4695	−1.61268	−0.806340	−	0.591453i	$-0.798555\pi$
$599$	−39.4695	−1.61268	−0.806340	+	0.591453i	$0.798555\pi$
$600$	19.2789	0.787058
$601$	−26.0899	−1.06423	−0.532114	−	0.846673i	$-0.678602\pi$
$601$	−26.0899	−1.06423	−0.532114	+	0.846673i	$0.678602\pi$
$602$	−3.44910	−0.140575
$603$	−42.3885	−1.72619
$604$	−78.0875	−3.17733
$605$	0	0
$606$	−42.3852	−1.72178
$607$	−2.63117	−0.106796	−0.0533978	−	0.998573i	$-0.517005\pi$
$607$	−2.63117	−0.106796	−0.0533978	+	0.998573i	$0.517005\pi$
$608$	−11.6243	−0.471426
$609$	−4.57578	−0.185420
$610$	29.8242	1.20755
$611$	−0.691962	−0.0279938
$612$	−110.182	−4.45385
$613$	16.1698	0.653094	0.326547	−	0.945181i	$-0.394115\pi$
$613$	16.1698	0.653094	0.326547	+	0.945181i	$0.394115\pi$
$614$	26.3967	1.06529
$615$	2.74759	0.110793
$616$	0	0
$617$	−23.0446	−0.927740	−0.463870	−	0.885903i	$-0.653540\pi$
$617$	−23.0446	−0.927740	−0.463870	+	0.885903i	$0.653540\pi$
$618$	28.6800	1.15368
$619$	14.8265	0.595925	0.297963	−	0.954578i	$-0.403693\pi$
$619$	14.8265	0.595925	0.297963	+	0.954578i	$0.403693\pi$
$620$	32.1681	1.29190
$621$	−108.813	−4.36653
$622$	55.1006	2.20933
$623$	6.61870	0.265173
$624$	−117.394	−4.69954
$625$	1.00000	0.0400000
$626$	52.0657	2.08096
$627$	0	0
$628$	65.9916	2.63335
$629$	−18.7798	−0.748798
$630$	17.9312	0.714396
$631$	−12.1204	−0.482507	−0.241253	−	0.970462i	$-0.577559\pi$
$631$	−12.1204	−0.482507	−0.241253	+	0.970462i	$0.577559\pi$
$632$	−59.3286	−2.35996
$633$	−4.20184	−0.167008
$634$	−13.2562	−0.526470
$635$	0.309232	0.0122715
$636$	−17.2113	−0.682471
$637$	−5.63769	−0.223373
$638$	0	0
$639$	−2.78074	−0.110004
$640$	−13.6135	−0.538121
$641$	11.0282	0.435586	0.217793	−	0.975995i	$-0.430114\pi$
$641$	11.0282	0.435586	0.217793	+	0.975995i	$0.430114\pi$
$642$	−77.3088	−3.05114
$643$	10.9108	0.430281	0.215140	−	0.976583i	$-0.430979\pi$
$643$	10.9108	0.430281	0.215140	+	0.976583i	$0.430979\pi$
$644$	−36.8665	−1.45274
$645$	−4.33056	−0.170516
$646$	23.3737	0.919627
$647$	36.6002	1.43890	0.719451	−	0.694544i	$-0.244394\pi$
$647$	36.6002	1.43890	0.719451	+	0.694544i	$0.244394\pi$
$648$	121.266	4.76377
$649$	0	0
$650$	−14.2617	−0.559390
$651$	23.2241	0.910223
$652$	20.0926	0.786888
$653$	33.3733	1.30600	0.652999	−	0.757359i	$-0.273511\pi$
$653$	33.3733	1.30600	0.652999	+	0.757359i	$0.273511\pi$
$654$	139.045	5.43708
$655$	−1.36409	−0.0532995
$656$	5.67129	0.221427
$657$	47.6526	1.85911
$658$	0.310492	0.0121043
$659$	−16.5133	−0.643268	−0.321634	−	0.946864i	$-0.604232\pi$
$659$	−16.5133	−0.643268	−0.321634	+	0.946864i	$0.604232\pi$
$660$	0	0
$661$	41.8472	1.62767	0.813833	−	0.581099i	$-0.197377\pi$
$661$	41.8472	1.62767	0.813833	+	0.581099i	$0.197377\pi$
$662$	25.0589	0.973941
$663$	63.2684	2.45714
$664$	44.4761	1.72601
$665$	−2.61505	−0.101407
$666$	95.3062	3.69304
$667$	12.0724	0.467446
$668$	53.7440	2.07942
$669$	−83.2954	−3.22039
$670$	−15.1279	−0.584442
$671$	0	0
$672$	14.1186	0.544638
$673$	37.2002	1.43396	0.716982	−	0.697092i	$-0.245523\pi$
$673$	37.2002	1.43396	0.716982	+	0.697092i	$0.245523\pi$
$674$	−0.810767	−0.0312296
$675$	12.9851	0.499797
$676$	82.6365	3.17833
$677$	−31.8060	−1.22240	−0.611202	−	0.791475i	$-0.709314\pi$
$677$	−31.8060	−1.22240	−0.611202	+	0.791475i	$0.709314\pi$
$678$	−100.110	−3.84472
$679$	−5.17987	−0.198785
$680$	−21.4463	−0.822428
$681$	23.1510	0.887150
$682$	0	0
$683$	−46.9678	−1.79717	−0.898587	−	0.438796i	$-0.855405\pi$
$683$	−46.9678	−1.79717	−0.898587	+	0.438796i	$0.855405\pi$
$684$	−81.5481	−3.11807
$685$	−13.5912	−0.519293
$686$	2.52971	0.0965846
$687$	89.8549	3.42818
$688$	−8.93870	−0.340785
$689$	6.94403	0.264546
$690$	−67.3310	−2.56325
$691$	−23.5453	−0.895705	−0.447852	−	0.894108i	$-0.647811\pi$
$691$	−23.5453	−0.895705	−0.447852	+	0.894108i	$0.647811\pi$
$692$	−104.798	−3.98382
$693$	0	0
$694$	69.4962	2.63804
$695$	−2.19758	−0.0833588
$696$	−27.7741	−1.05277
$697$	−3.05648	−0.115772
$698$	−39.1472	−1.48174
$699$	−47.9342	−1.81304
$700$	4.39941	0.166282
$701$	−33.1393	−1.25165	−0.625826	−	0.779962i	$-0.715238\pi$
$701$	−33.1393	−1.25165	−0.625826	+	0.779962i	$0.715238\pi$
$702$	−185.189	−6.98953
$703$	−13.8993	−0.524222
$704$	0	0
$705$	0.389842	0.0146823
$706$	43.7485	1.64650
$707$	−5.27517	−0.198393
$708$	−44.6750	−1.67899
$709$	−38.3698	−1.44101	−0.720504	−	0.693451i	$-0.756090\pi$
$709$	−38.3698	−1.44101	−0.720504	+	0.693451i	$0.756090\pi$
$710$	−0.992411	−0.0372445
$711$	−69.2832	−2.59832
$712$	40.1742	1.50559
$713$	−61.2728	−2.29468
$714$	−28.3893	−1.06244
$715$	0	0
$716$	−33.5277	−1.25299
$717$	65.6069	2.45014
$718$	28.4903	1.06325
$719$	45.2554	1.68774	0.843870	−	0.536548i	$-0.180272\pi$
$719$	45.2554	1.68774	0.843870	+	0.536548i	$0.180272\pi$
$720$	46.4705	1.73185
$721$	3.56945	0.132933
$722$	−30.7650	−1.14496
$723$	23.6583	0.879861
$724$	25.8281	0.959896
$725$	−1.44065	−0.0535042
$726$	0	0
$727$	4.61924	0.171318	0.0856591	−	0.996325i	$-0.472700\pi$
$727$	4.61924	0.171318	0.0856591	+	0.996325i	$0.472700\pi$
$728$	−34.2197	−1.26827
$729$	17.8830	0.662332
$730$	17.0066	0.629443
$731$	4.81741	0.178178
$732$	164.741	6.08900
$733$	−3.63357	−0.134209	−0.0671045	−	0.997746i	$-0.521376\pi$
$733$	−3.63357	−0.134209	−0.0671045	+	0.997746i	$0.521376\pi$
$734$	67.1320	2.47789
$735$	3.17620	0.117156
$736$	−37.2496	−1.37304
$737$	0	0
$738$	15.5115	0.570984
$739$	11.3176	0.416325	0.208162	−	0.978094i	$-0.433252\pi$
$739$	11.3176	0.416325	0.208162	+	0.978094i	$0.433252\pi$
$740$	23.3834	0.859589
$741$	46.8263	1.72021
$742$	−3.11588	−0.114387
$743$	27.4807	1.00817	0.504084	−	0.863654i	$-0.331830\pi$
$743$	27.4807	1.00817	0.504084	+	0.863654i	$0.331830\pi$
$744$	140.966	5.16805
$745$	2.15954	0.0791193
$746$	42.3878	1.55193
$747$	51.9387	1.90034
$748$	0	0
$749$	−9.62169	−0.351569
$750$	8.03485	0.293391
$751$	−6.00075	−0.218970	−0.109485	−	0.993988i	$-0.534920\pi$
$751$	−6.00075	−0.218970	−0.109485	+	0.993988i	$0.534920\pi$
$752$	0.804674	0.0293434
$753$	−12.0138	−0.437806
$754$	20.5460	0.748243
$755$	−17.7495	−0.645971
$756$	57.1268	2.07768
$757$	−24.6226	−0.894923	−0.447461	−	0.894303i	$-0.647672\pi$
$757$	−24.6226	−0.894923	−0.447461	+	0.894303i	$0.647672\pi$
$758$	0.270661	0.00983084
$759$	0	0
$760$	−15.8729	−0.575769
$761$	−3.89989	−0.141371	−0.0706854	−	0.997499i	$-0.522519\pi$
$761$	−3.89989	−0.141371	−0.0706854	+	0.997499i	$0.522519\pi$
$762$	2.48464	0.0900089
$763$	17.3052	0.626490
$764$	58.9593	2.13307
$765$	−25.0447	−0.905494
$766$	−49.3497	−1.78308
$767$	18.0245	0.650827
$768$	−97.5219	−3.51902
$769$	−37.1018	−1.33793	−0.668963	−	0.743295i	$-0.733262\pi$
$769$	−37.1018	−1.33793	−0.668963	+	0.743295i	$0.733262\pi$
$770$	0	0
$771$	−31.7090	−1.14197
$772$	87.7550	3.15837
$773$	−34.2276	−1.23108	−0.615541	−	0.788105i	$-0.711062\pi$
$773$	−34.2276	−1.23108	−0.615541	+	0.788105i	$0.711062\pi$
$774$	−24.4481	−0.878768
$775$	7.31191	0.262651
$776$	−31.4408	−1.12866
$777$	16.8819	0.605633
$778$	−55.6148	−1.99389
$779$	−2.26216	−0.0810504
$780$	−78.7777	−2.82070
$781$	0	0
$782$	74.9004	2.67843
$783$	−18.7069	−0.668531
$784$	6.55600	0.234143
$785$	15.0001	0.535377
$786$	−10.9603	−0.390940
$787$	48.6836	1.73538	0.867691	−	0.497105i	$-0.165603\pi$
$787$	48.6836	1.73538	0.867691	+	0.497105i	$0.165603\pi$
$788$	84.3182	3.00371
$789$	21.8222	0.776890
$790$	−24.7263	−0.879722
$791$	−12.4595	−0.443010
$792$	0	0
$793$	−66.4661	−2.36028
$794$	−47.0022	−1.66804
$795$	−3.91217	−0.138751
$796$	92.1598	3.26652
$797$	37.8272	1.33991	0.669953	−	0.742403i	$-0.266314\pi$
$797$	37.8272	1.33991	0.669953	+	0.742403i	$0.266314\pi$
$798$	−21.0116	−0.743801
$799$	−0.433669	−0.0153421
$800$	4.44513	0.157159
$801$	46.9150	1.65766
$802$	64.7977	2.28809
$803$	0	0
$804$	−83.5625	−2.94702
$805$	−8.37986	−0.295351
$806$	−104.280	−3.67311
$807$	30.7819	1.08358
$808$	−32.0193	−1.12643
$809$	3.16987	0.111447	0.0557234	−	0.998446i	$-0.482253\pi$
$809$	3.16987	0.111447	0.0557234	+	0.998446i	$0.482253\pi$
$810$	50.5398	1.77579
$811$	17.1618	0.602633	0.301317	−	0.953524i	$-0.402574\pi$
$811$	17.1618	0.602633	0.301317	+	0.953524i	$0.402574\pi$
$812$	−6.33799	−0.222420
$813$	−1.39100	−0.0487844
$814$	0	0
$815$	4.56712	0.159979
$816$	−73.5740	−2.57560
$817$	3.56547	0.124740
$818$	−26.1026	−0.912655
$819$	−39.9613	−1.39636
$820$	3.80573	0.132902
$821$	30.8868	1.07796	0.538978	−	0.842320i	$-0.318810\pi$
$821$	30.8868	1.07796	0.538978	+	0.842320i	$0.318810\pi$
$822$	−109.203	−3.80890
$823$	10.7191	0.373643	0.186822	−	0.982394i	$-0.440181\pi$
$823$	10.7191	0.373643	0.186822	+	0.982394i	$0.440181\pi$
$824$	21.6658	0.754765
$825$	0	0
$826$	−8.08783	−0.281412
$827$	6.05810	0.210661	0.105330	−	0.994437i	$-0.466410\pi$
$827$	6.05810	0.210661	0.105330	+	0.994437i	$0.466410\pi$
$828$	−261.319	−9.08145
$829$	−50.0477	−1.73823	−0.869115	−	0.494610i	$-0.835311\pi$
$829$	−50.0477	−1.73823	−0.869115	+	0.494610i	$0.835311\pi$
$830$	18.5363	0.643403
$831$	−54.6908	−1.89720
$832$	10.5262	0.364931
$833$	−3.53328	−0.122421
$834$	−17.6572	−0.611419
$835$	12.2162	0.422758
$836$	0	0
$837$	94.9458	3.28181
$838$	−47.4686	−1.63977
$839$	24.3625	0.841088	0.420544	−	0.907272i	$-0.361839\pi$
$839$	24.3625	0.841088	0.420544	+	0.907272i	$0.361839\pi$
$840$	19.2789	0.665186
$841$	−26.9245	−0.928432
$842$	88.3065	3.04324
$843$	42.4225	1.46111
$844$	−5.82004	−0.200334
$845$	18.7835	0.646173
$846$	2.20085	0.0756667
$847$	0	0
$848$	−8.07512	−0.277301
$849$	−24.6848	−0.847180
$850$	−8.93815	−0.306576
$851$	−44.5399	−1.52681
$852$	−5.48181	−0.187804
$853$	16.1023	0.551332	0.275666	−	0.961253i	$-0.411102\pi$
$853$	16.1023	0.551332	0.275666	+	0.961253i	$0.411102\pi$
$854$	29.8242	1.02056
$855$	−18.5361	−0.633923
$856$	−58.4018	−1.99613
$857$	40.7596	1.39232	0.696161	−	0.717885i	$-0.254890\pi$
$857$	40.7596	1.39232	0.696161	+	0.717885i	$0.254890\pi$
$858$	0	0
$859$	14.2120	0.484907	0.242454	−	0.970163i	$-0.422048\pi$
$859$	14.2120	0.484907	0.242454	+	0.970163i	$0.422048\pi$
$860$	−5.99833	−0.204541
$861$	2.74759	0.0936375
$862$	99.8979	3.40253
$863$	−29.6152	−1.00811	−0.504057	−	0.863671i	$-0.668160\pi$
$863$	−29.6152	−1.00811	−0.504057	+	0.863671i	$0.668160\pi$
$864$	57.7205	1.96369
$865$	−23.8209	−0.809936
$866$	−89.3140	−3.03501
$867$	−14.3436	−0.487134
$868$	32.1681	1.09186
$869$	0	0
$870$	−11.5754	−0.392442
$871$	33.7140	1.14235
$872$	105.039	3.55707
$873$	−36.7162	−1.24265
$874$	55.4354	1.87513
$875$	1.00000	0.0338062
$876$	93.9399	3.17394
$877$	25.3384	0.855619	0.427809	−	0.903869i	$-0.359285\pi$
$877$	25.3384	0.855619	0.427809	+	0.903869i	$0.359285\pi$
$878$	7.25510	0.244848
$879$	−75.7445	−2.55480
$880$	0	0
$881$	22.1503	0.746261	0.373131	−	0.927779i	$-0.378284\pi$
$881$	22.1503	0.746261	0.373131	+	0.927779i	$0.378284\pi$
$882$	17.9312	0.603774
$883$	−25.1422	−0.846102	−0.423051	−	0.906106i	$-0.639041\pi$
$883$	−25.1422	−0.846102	−0.423051	+	0.906106i	$0.639041\pi$
$884$	87.6341	2.94745
$885$	−10.1548	−0.341349
$886$	−86.7815	−2.91548
$887$	3.61555	0.121398	0.0606991	−	0.998156i	$-0.480667\pi$
$887$	3.61555	0.121398	0.0606991	+	0.998156i	$0.480667\pi$
$888$	102.470	3.43865
$889$	0.309232	0.0103713
$890$	16.7434	0.561239
$891$	0	0
$892$	−115.374	−3.86301
$893$	−0.320968	−0.0107408
$894$	17.3516	0.580323
$895$	−7.62096	−0.254740
$896$	−13.6135	−0.454796
$897$	150.053	5.01014
$898$	−49.1499	−1.64015
$899$	−10.5339	−0.351324
$900$	31.1841	1.03947
$901$	4.35199	0.144986
$902$	0	0
$903$	−4.33056	−0.144112
$904$	−75.6269	−2.51531
$905$	5.87082	0.195153
$906$	−142.615	−4.73806
$907$	44.2171	1.46820	0.734102	−	0.679039i	$-0.237603\pi$
$907$	44.2171	1.46820	0.734102	+	0.679039i	$0.237603\pi$
$908$	32.0669	1.06418
$909$	−37.3917	−1.24021
$910$	−14.2617	−0.472771
$911$	9.73586	0.322563	0.161282	−	0.986908i	$-0.448437\pi$
$911$	9.73586	0.322563	0.161282	+	0.986908i	$0.448437\pi$
$912$	−54.4537	−1.80314
$913$	0	0
$914$	−69.5637	−2.30096
$915$	37.4461	1.23793
$916$	124.460	4.11226
$917$	−1.36409	−0.0450463
$918$	−116.063	−3.83064
$919$	7.77690	0.256536	0.128268	−	0.991740i	$-0.459058\pi$
$919$	7.77690	0.256536	0.128268	+	0.991740i	$0.459058\pi$
$920$	−50.8641	−1.67694
$921$	33.1427	1.09209
$922$	22.6124	0.744701
$923$	2.21168	0.0727984
$924$	0	0
$925$	5.31511	0.174760
$926$	−71.7604	−2.35819
$927$	25.3011	0.830998
$928$	−6.40386	−0.210217
$929$	50.1656	1.64588	0.822939	−	0.568129i	$-0.192333\pi$
$929$	50.1656	1.64588	0.822939	+	0.568129i	$0.192333\pi$
$930$	58.7501	1.92649
$931$	−2.61505	−0.0857049
$932$	−66.3946	−2.17483
$933$	69.1821	2.26492
$934$	−50.7311	−1.65997
$935$	0	0
$936$	−242.558	−7.92824
$937$	−34.0204	−1.11140	−0.555698	−	0.831384i	$-0.687549\pi$
$937$	−34.0204	−1.11140	−0.555698	+	0.831384i	$0.687549\pi$
$938$	−15.1279	−0.493944
$939$	65.3717	2.13332
$940$	0.539977	0.0176121
$941$	−35.3661	−1.15290	−0.576450	−	0.817132i	$-0.695563\pi$
$941$	−35.3661	−1.15290	−0.576450	+	0.817132i	$0.695563\pi$
$942$	120.524	3.92687
$943$	−7.24904	−0.236061
$944$	−20.9604	−0.682204
$945$	12.9851	0.422405
$946$	0	0
$947$	31.2795	1.01645	0.508223	−	0.861225i	$-0.330302\pi$
$947$	31.2795	1.01645	0.508223	+	0.861225i	$0.330302\pi$
$948$	−136.581	−4.43596
$949$	−37.9008	−1.23031
$950$	−6.61531	−0.214629
$951$	−16.6439	−0.539717
$952$	−21.4463	−0.695078
$953$	−21.3222	−0.690693	−0.345347	−	0.938475i	$-0.612239\pi$
$953$	−21.3222	−0.690693	−0.345347	+	0.938475i	$0.612239\pi$
$954$	−22.0861	−0.715064
$955$	13.4016	0.433667
$956$	90.8733	2.93905
$957$	0	0
$958$	−17.7587	−0.573756
$959$	−13.5912	−0.438883
$960$	−5.93033	−0.191401
$961$	22.4640	0.724644
$962$	−75.8025	−2.44397
$963$	−68.2009	−2.19774
$964$	32.7695	1.05544
$965$	19.9470	0.642116
$966$	−67.3310	−2.16634
$967$	29.0789	0.935115	0.467558	−	0.883963i	$-0.345134\pi$
$967$	29.0789	0.935115	0.467558	+	0.883963i	$0.345134\pi$
$968$	0	0
$969$	29.3471	0.942766
$970$	−13.1035	−0.420729
$971$	−52.9650	−1.69973	−0.849863	−	0.527003i	$-0.823316\pi$
$971$	−52.9650	−1.69973	−0.849863	+	0.527003i	$0.823316\pi$
$972$	107.788	3.45730
$973$	−2.19758	−0.0704511
$974$	−46.9310	−1.50377
$975$	−17.9064	−0.573465
$976$	77.2925	2.47407
$977$	22.2750	0.712642	0.356321	−	0.934364i	$-0.384031\pi$
$977$	22.2750	0.712642	0.356321	+	0.934364i	$0.384031\pi$
$978$	36.6961	1.17341
$979$	0	0
$980$	4.39941	0.140534
$981$	122.664	3.91634
$982$	−21.7562	−0.694268
$983$	−13.4526	−0.429071	−0.214535	−	0.976716i	$-0.568824\pi$
$983$	−13.4526	−0.429071	−0.214535	+	0.976716i	$0.568824\pi$
$984$	16.6773	0.531653
$985$	19.1658	0.610673
$986$	12.8767	0.410078
$987$	0.389842	0.0124088
$988$	64.8599	2.06347
$989$	11.4254	0.363308
$990$	0	0
$991$	−34.0101	−1.08037	−0.540183	−	0.841547i	$-0.681645\pi$
$991$	−34.0101	−1.08037	−0.540183	+	0.841547i	$0.681645\pi$
$992$	32.5024	1.03195
$993$	31.4629	0.998446
$994$	−0.992411	−0.0314774
$995$	20.9482	0.664103
$996$	102.389	3.24433
$997$	55.7335	1.76510	0.882549	−	0.470221i	$-0.155826\pi$
$997$	55.7335	1.76510	0.882549	+	0.470221i	$0.155826\pi$
$998$	−55.0008	−1.74102
$999$	69.0172	2.18361

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4235.2.a.bp.1.16		18
11.7	odd	10		385.2.n.f.71.2	✓	36
11.8	odd	10		385.2.n.f.141.2	yes	36
11.10	odd	2		4235.2.a.bo.1.3		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
385.2.n.f.71.2	✓	36	11.7	odd	10
385.2.n.f.141.2	yes	36	11.8	odd	10
4235.2.a.bo.1.3		18	11.10	odd	2
4235.2.a.bp.1.16		18	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q+2.52971 q^{2} +3.17620 q^{3} +4.39941 q^{4} +1.00000 q^{5} +8.03485 q^{6} +1.00000 q^{7} +6.06980 q^{8} +7.08825 q^{9} +O(q^{10})\)	\(q+2.52971 q^{2} +3.17620 q^{3} +4.39941 q^{4} +1.00000 q^{5} +8.03485 q^{6} +1.00000 q^{7} +6.06980 q^{8} +7.08825 q^{9} +2.52971 q^{10} +13.9734 q^{12} -5.63769 q^{13} +2.52971 q^{14} +3.17620 q^{15} +6.55600 q^{16} -3.53328 q^{17} +17.9312 q^{18} -2.61505 q^{19} +4.39941 q^{20} +3.17620 q^{21} -8.37986 q^{23} +19.2789 q^{24} +1.00000 q^{25} -14.2617 q^{26} +12.9851 q^{27} +4.39941 q^{28} -1.44065 q^{29} +8.03485 q^{30} +7.31191 q^{31} +4.44513 q^{32} -8.93815 q^{34} +1.00000 q^{35} +31.1841 q^{36} +5.31511 q^{37} -6.61531 q^{38} -17.9064 q^{39} +6.06980 q^{40} +0.865054 q^{41} +8.03485 q^{42} -1.36344 q^{43} +7.08825 q^{45} -21.1986 q^{46} +0.122739 q^{47} +20.8232 q^{48} +1.00000 q^{49} +2.52971 q^{50} -11.2224 q^{51} -24.8025 q^{52} -1.23172 q^{53} +32.8485 q^{54} +6.06980 q^{56} -8.30593 q^{57} -3.64441 q^{58} -3.19714 q^{59} +13.9734 q^{60} +11.7896 q^{61} +18.4970 q^{62} +7.08825 q^{63} -1.86712 q^{64} -5.63769 q^{65} -5.98011 q^{67} -15.5443 q^{68} -26.6161 q^{69} +2.52971 q^{70} -0.392303 q^{71} +43.0243 q^{72} +6.72276 q^{73} +13.4457 q^{74} +3.17620 q^{75} -11.5047 q^{76} -45.2980 q^{78} -9.77438 q^{79} +6.55600 q^{80} +19.9785 q^{81} +2.18833 q^{82} +7.32744 q^{83} +13.9734 q^{84} -3.53328 q^{85} -3.44910 q^{86} -4.57578 q^{87} +6.61870 q^{89} +17.9312 q^{90} -5.63769 q^{91} -36.8665 q^{92} +23.2241 q^{93} +0.310492 q^{94} -2.61505 q^{95} +14.1186 q^{96} -5.17987 q^{97} +2.52971 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9}+O(q^{10}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9	\( 18 q + 2 q^{2} + 5 q^{3} + 24 q^{4} + 18 q^{5} - q^{6} + 18 q^{7} + 6 q^{8} + 37 q^{9} + 2 q^{10} + 15 q^{12} + 8 q^{13} + 2 q^{14} + 5 q^{15} + 44 q^{16} - 5 q^{17} + 2 q^{18} + 15 q^{19} + 24 q^{20} + 5 q^{21} + 4 q^{23} + 8 q^{24} + 18 q^{25} + 14 q^{26} + 20 q^{27} + 24 q^{28} - 6 q^{29} - q^{30} + 22 q^{31} - 6 q^{32} + 44 q^{34} + 18 q^{35} + 83 q^{36} + 26 q^{37} - 11 q^{38} - 38 q^{39} + 6 q^{40} + 7 q^{41} - q^{42} + 10 q^{43} + 37 q^{45} - 40 q^{46} - q^{47} - 15 q^{48} + 18 q^{49} + 2 q^{50} - 11 q^{51} + 18 q^{52} + 23 q^{53} + 13 q^{54} + 6 q^{56} - 16 q^{57} + 2 q^{58} + 30 q^{59} + 15 q^{60} + 17 q^{61} + 57 q^{62} + 37 q^{63} + 64 q^{64} + 8 q^{65} + 29 q^{67} - 66 q^{68} + 54 q^{69} + 2 q^{70} - 2 q^{71} - 77 q^{72} + 3 q^{73} - 48 q^{74} + 5 q^{75} + 47 q^{76} + 10 q^{78} - 18 q^{79} + 44 q^{80} + 110 q^{81} + 56 q^{82} + 9 q^{83} + 15 q^{84} - 5 q^{85} + 25 q^{86} + 23 q^{87} + 59 q^{89} + 2 q^{90} + 8 q^{91} - 74 q^{92} + 33 q^{93} - 19 q^{94} + 15 q^{95} + 14 q^{96} + 30 q^{97} + 2 q^{98}+O(q^{100}) \) 18 * q + 2 * q^2 + 5 * q^3 + 24 * q^4 + 18 * q^5 - q^6 + 18 * q^7 + 6 * q^8 + 37 * q^9 + 2 * q^10 + 15 * q^12 + 8 * q^13 + 2 * q^14 + 5 * q^15 + 44 * q^16 - 5 * q^17 + 2 * q^18 + 15 * q^19 + 24 * q^20 + 5 * q^21 + 4 * q^23 + 8 * q^24 + 18 * q^25 + 14 * q^26 + 20 * q^27 + 24 * q^28 - 6 * q^29 - q^30 + 22 * q^31 - 6 * q^32 + 44 * q^34 + 18 * q^35 + 83 * q^36 + 26 * q^37 - 11 * q^38 - 38 * q^39 + 6 * q^40 + 7 * q^41 - q^42 + 10 * q^43 + 37 * q^45 - 40 * q^46 - q^47 - 15 * q^48 + 18 * q^49 + 2 * q^50 - 11 * q^51 + 18 * q^52 + 23 * q^53 + 13 * q^54 + 6 * q^56 - 16 * q^57 + 2 * q^58 + 30 * q^59 + 15 * q^60 + 17 * q^61 + 57 * q^62 + 37 * q^63 + 64 * q^64 + 8 * q^65 + 29 * q^67 - 66 * q^68 + 54 * q^69 + 2 * q^70 - 2 * q^71 - 77 * q^72 + 3 * q^73 - 48 * q^74 + 5 * q^75 + 47 * q^76 + 10 * q^78 - 18 * q^79 + 44 * q^80 + 110 * q^81 + 56 * q^82 + 9 * q^83 + 15 * q^84 - 5 * q^85 + 25 * q^86 + 23 * q^87 + 59 * q^89 + 2 * q^90 + 8 * q^91 - 74 * q^92 + 33 * q^93 - 19 * q^94 + 15 * q^95 + 14 * q^96 + 30 * q^97 + 2 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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