LMFDB - Embedded newform 3630.2.a.bl.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [3630,2,Mod(1,3630)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(3630, 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("3630.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	3630.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:	$28.9856959337$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{10})^+$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 1 $ x^2 - x - 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 330)
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$1.61803$ of defining polynomial
Character	$\chi$	$=$	3630.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +1.85410 q^{13} -3.61803 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.47214 q^{17} +1.00000 q^{18} +1.85410 q^{19} +1.00000 q^{20} +3.61803 q^{21} -6.38197 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.85410 q^{26} -1.00000 q^{27} -3.61803 q^{28} +2.76393 q^{29} -1.00000 q^{30} -2.76393 q^{31} +1.00000 q^{32} -2.47214 q^{34} -3.61803 q^{35} +1.00000 q^{36} -9.85410 q^{37} +1.85410 q^{38} -1.85410 q^{39} +1.00000 q^{40} +10.0902 q^{41} +3.61803 q^{42} -3.23607 q^{43} +1.00000 q^{45} -6.38197 q^{46} -12.7984 q^{47} -1.00000 q^{48} +6.09017 q^{49} +1.00000 q^{50} +2.47214 q^{51} +1.85410 q^{52} -1.90983 q^{53} -1.00000 q^{54} -3.61803 q^{56} -1.85410 q^{57} +2.76393 q^{58} +6.32624 q^{59} -1.00000 q^{60} +9.70820 q^{61} -2.76393 q^{62} -3.61803 q^{63} +1.00000 q^{64} +1.85410 q^{65} -2.29180 q^{67} -2.47214 q^{68} +6.38197 q^{69} -3.61803 q^{70} -14.1803 q^{71} +1.00000 q^{72} +2.00000 q^{73} -9.85410 q^{74} -1.00000 q^{75} +1.85410 q^{76} -1.85410 q^{78} -12.4721 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0902 q^{82} +2.47214 q^{83} +3.61803 q^{84} -2.47214 q^{85} -3.23607 q^{86} -2.76393 q^{87} -8.56231 q^{89} +1.00000 q^{90} -6.70820 q^{91} -6.38197 q^{92} +2.76393 q^{93} -12.7984 q^{94} +1.85410 q^{95} -1.00000 q^{96} -2.00000 q^{97} +6.09017 q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9	$ 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - 3 q^{13} - 5 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} - 3 q^{19} + 2 q^{20} + 5 q^{21} - 15 q^{23} - 2 q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} - 5 q^{28} + 10 q^{29} - 2 q^{30} - 10 q^{31} + 2 q^{32} + 4 q^{34} - 5 q^{35} + 2 q^{36} - 13 q^{37} - 3 q^{38} + 3 q^{39} + 2 q^{40} + 9 q^{41} + 5 q^{42} - 2 q^{43} + 2 q^{45} - 15 q^{46} - q^{47} - 2 q^{48} + q^{49} + 2 q^{50} - 4 q^{51} - 3 q^{52} - 15 q^{53} - 2 q^{54} - 5 q^{56} + 3 q^{57} + 10 q^{58} - 3 q^{59} - 2 q^{60} + 6 q^{61} - 10 q^{62} - 5 q^{63} + 2 q^{64} - 3 q^{65} - 18 q^{67} + 4 q^{68} + 15 q^{69} - 5 q^{70} - 6 q^{71} + 2 q^{72} + 4 q^{73} - 13 q^{74} - 2 q^{75} - 3 q^{76} + 3 q^{78} - 16 q^{79} + 2 q^{80} + 2 q^{81} + 9 q^{82} - 4 q^{83} + 5 q^{84} + 4 q^{85} - 2 q^{86} - 10 q^{87} + 3 q^{89} + 2 q^{90} - 15 q^{92} + 10 q^{93} - q^{94} - 3 q^{95} - 2 q^{96} - 4 q^{97} + q^{98}+O(q^{100}) $ 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - 3 * q^13 - 5 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 - 3 * q^19 + 2 * q^20 + 5 * q^21 - 15 * q^23 - 2 * q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 - 5 * q^28 + 10 * q^29 - 2 * q^30 - 10 * q^31 + 2 * q^32 + 4 * q^34 - 5 * q^35 + 2 * q^36 - 13 * q^37 - 3 * q^38 + 3 * q^39 + 2 * q^40 + 9 * q^41 + 5 * q^42 - 2 * q^43 + 2 * q^45 - 15 * q^46 - q^47 - 2 * q^48 + q^49 + 2 * q^50 - 4 * q^51 - 3 * q^52 - 15 * q^53 - 2 * q^54 - 5 * q^56 + 3 * q^57 + 10 * q^58 - 3 * q^59 - 2 * q^60 + 6 * q^61 - 10 * q^62 - 5 * q^63 + 2 * q^64 - 3 * q^65 - 18 * q^67 + 4 * q^68 + 15 * q^69 - 5 * q^70 - 6 * q^71 + 2 * q^72 + 4 * q^73 - 13 * q^74 - 2 * q^75 - 3 * q^76 + 3 * q^78 - 16 * q^79 + 2 * q^80 + 2 * q^81 + 9 * q^82 - 4 * q^83 + 5 * q^84 + 4 * q^85 - 2 * q^86 - 10 * q^87 + 3 * q^89 + 2 * q^90 - 15 * q^92 + 10 * q^93 - q^94 - 3 * q^95 - 2 * q^96 - 4 * q^97 + 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−1.00000	−0.577350
$3$	−1.00000	−0.577350
$4$	1.00000	0.500000
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−1.00000	−0.408248
$7$	−3.61803	−1.36749	−0.683744	−	0.729722i	$-0.739650\pi$
$7$	−3.61803	−1.36749	−0.683744	+	0.729722i	$0.739650\pi$
$8$	1.00000	0.353553
$9$	1.00000	0.333333
$10$	1.00000	0.316228
$11$	0	0
$11$	0	0
$12$	−1.00000	−0.288675
$13$	1.85410	0.514235	0.257118	−	0.966380i	$-0.417227\pi$
$13$	1.85410	0.514235	0.257118	+	0.966380i	$0.417227\pi$
$14$	−3.61803	−0.966960
$15$	−1.00000	−0.258199
$16$	1.00000	0.250000
$17$	−2.47214	−0.599581	−0.299791	−	0.954005i	$-0.596917\pi$
$17$	−2.47214	−0.599581	−0.299791	+	0.954005i	$0.596917\pi$
$18$	1.00000	0.235702
$19$	1.85410	0.425360	0.212680	−	0.977122i	$-0.431781\pi$
$19$	1.85410	0.425360	0.212680	+	0.977122i	$0.431781\pi$
$20$	1.00000	0.223607
$21$	3.61803	0.789520
$22$	0	0
$23$	−6.38197	−1.33073	−0.665366	−	0.746517i	$-0.731724\pi$
$23$	−6.38197	−1.33073	−0.665366	+	0.746517i	$0.731724\pi$
$24$	−1.00000	−0.204124
$25$	1.00000	0.200000
$26$	1.85410	0.363619
$27$	−1.00000	−0.192450
$28$	−3.61803	−0.683744
$29$	2.76393	0.513249	0.256625	−	0.966511i	$-0.417390\pi$
$29$	2.76393	0.513249	0.256625	+	0.966511i	$0.417390\pi$
$30$	−1.00000	−0.182574
$31$	−2.76393	−0.496417	−0.248208	−	0.968707i	$-0.579842\pi$
$31$	−2.76393	−0.496417	−0.248208	+	0.968707i	$0.579842\pi$
$32$	1.00000	0.176777
$33$	0	0
$34$	−2.47214	−0.423968
$35$	−3.61803	−0.611559
$36$	1.00000	0.166667
$37$	−9.85410	−1.62000	−0.810002	−	0.586427i	$-0.800534\pi$
$37$	−9.85410	−1.62000	−0.810002	+	0.586427i	$0.800534\pi$
$38$	1.85410	0.300775
$39$	−1.85410	−0.296894
$40$	1.00000	0.158114
$41$	10.0902	1.57582	0.787910	−	0.615791i	$-0.211163\pi$
$41$	10.0902	1.57582	0.787910	+	0.615791i	$0.211163\pi$
$42$	3.61803	0.558275
$43$	−3.23607	−0.493496	−0.246748	−	0.969080i	$-0.579362\pi$
$43$	−3.23607	−0.493496	−0.246748	+	0.969080i	$0.579362\pi$
$44$	0	0
$45$	1.00000	0.149071
$46$	−6.38197	−0.940970
$47$	−12.7984	−1.86683	−0.933417	−	0.358792i	$-0.883189\pi$
$47$	−12.7984	−1.86683	−0.933417	+	0.358792i	$0.883189\pi$
$48$	−1.00000	−0.144338
$49$	6.09017	0.870024
$50$	1.00000	0.141421
$51$	2.47214	0.346168
$52$	1.85410	0.257118
$53$	−1.90983	−0.262335	−0.131168	−	0.991360i	$-0.541873\pi$
$53$	−1.90983	−0.262335	−0.131168	+	0.991360i	$0.541873\pi$
$54$	−1.00000	−0.136083
$55$	0	0
$56$	−3.61803	−0.483480
$57$	−1.85410	−0.245582
$58$	2.76393	0.362922
$59$	6.32624	0.823606	0.411803	−	0.911273i	$-0.364899\pi$
$59$	6.32624	0.823606	0.411803	+	0.911273i	$0.364899\pi$
$60$	−1.00000	−0.129099
$61$	9.70820	1.24301	0.621504	−	0.783411i	$-0.286522\pi$
$61$	9.70820	1.24301	0.621504	+	0.783411i	$0.286522\pi$
$62$	−2.76393	−0.351020
$63$	−3.61803	−0.455829
$64$	1.00000	0.125000
$65$	1.85410	0.229973
$66$	0	0
$67$	−2.29180	−0.279987	−0.139994	−	0.990152i	$-0.544708\pi$
$67$	−2.29180	−0.279987	−0.139994	+	0.990152i	$0.544708\pi$
$68$	−2.47214	−0.299791
$69$	6.38197	0.768298
$70$	−3.61803	−0.432438
$71$	−14.1803	−1.68290	−0.841448	−	0.540338i	$-0.818297\pi$
$71$	−14.1803	−1.68290	−0.841448	+	0.540338i	$0.818297\pi$
$72$	1.00000	0.117851
$73$	2.00000	0.234082	0.117041	−	0.993127i	$-0.462659\pi$
$73$	2.00000	0.234082	0.117041	+	0.993127i	$0.462659\pi$
$74$	−9.85410	−1.14552
$75$	−1.00000	−0.115470
$76$	1.85410	0.212680
$77$	0	0
$78$	−1.85410	−0.209936
$79$	−12.4721	−1.40322	−0.701612	−	0.712559i	$-0.747536\pi$
$79$	−12.4721	−1.40322	−0.701612	+	0.712559i	$0.747536\pi$
$80$	1.00000	0.111803
$81$	1.00000	0.111111
$82$	10.0902	1.11427
$83$	2.47214	0.271352	0.135676	−	0.990753i	$-0.456679\pi$
$83$	2.47214	0.271352	0.135676	+	0.990753i	$0.456679\pi$
$84$	3.61803	0.394760
$85$	−2.47214	−0.268141
$86$	−3.23607	−0.348954
$87$	−2.76393	−0.296325
$88$	0	0
$89$	−8.56231	−0.907603	−0.453801	−	0.891103i	$-0.649932\pi$
$89$	−8.56231	−0.907603	−0.453801	+	0.891103i	$0.649932\pi$
$90$	1.00000	0.105409
$91$	−6.70820	−0.703211
$92$	−6.38197	−0.665366
$93$	2.76393	0.286606
$94$	−12.7984	−1.32005
$95$	1.85410	0.190227
$96$	−1.00000	−0.102062
$97$	−2.00000	−0.203069	−0.101535	−	0.994832i	$-0.532375\pi$
$97$	−2.00000	−0.203069	−0.101535	+	0.994832i	$0.532375\pi$
$98$	6.09017	0.615200
$99$	0	0
$100$	1.00000	0.100000
$101$	−19.4164	−1.93200	−0.966002	−	0.258533i	$-0.916761\pi$
$101$	−19.4164	−1.93200	−0.966002	+	0.258533i	$0.916761\pi$
$102$	2.47214	0.244778
$103$	1.85410	0.182690	0.0913450	−	0.995819i	$-0.470883\pi$
$103$	1.85410	0.182690	0.0913450	+	0.995819i	$0.470883\pi$
$104$	1.85410	0.181810
$105$	3.61803	0.353084
$106$	−1.90983	−0.185499
$107$	10.4721	1.01238	0.506190	−	0.862422i	$-0.331054\pi$
$107$	10.4721	1.01238	0.506190	+	0.862422i	$0.331054\pi$
$108$	−1.00000	−0.0962250
$109$	−19.4164	−1.85975	−0.929877	−	0.367870i	$-0.880087\pi$
$109$	−19.4164	−1.85975	−0.929877	+	0.367870i	$0.880087\pi$
$110$	0	0
$111$	9.85410	0.935310
$112$	−3.61803	−0.341872
$113$	−12.4721	−1.17328	−0.586640	−	0.809848i	$-0.699550\pi$
$113$	−12.4721	−1.17328	−0.586640	+	0.809848i	$0.699550\pi$
$114$	−1.85410	−0.173653
$115$	−6.38197	−0.595121
$116$	2.76393	0.256625
$117$	1.85410	0.171412
$118$	6.32624	0.582377
$119$	8.94427	0.819920
$120$	−1.00000	−0.0912871
$121$	0	0
$122$	9.70820	0.878939
$123$	−10.0902	−0.909800
$124$	−2.76393	−0.248208
$125$	1.00000	0.0894427
$126$	−3.61803	−0.322320
$127$	−9.56231	−0.848517	−0.424259	−	0.905541i	$-0.639465\pi$
$127$	−9.56231	−0.848517	−0.424259	+	0.905541i	$0.639465\pi$
$128$	1.00000	0.0883883
$129$	3.23607	0.284920
$130$	1.85410	0.162615
$131$	0	0		−	1.00000i	$-0.5\pi$
$131$	0	0			1.00000i	$0.5\pi$
$132$	0	0
$133$	−6.70820	−0.581675
$134$	−2.29180	−0.197981
$135$	−1.00000	−0.0860663
$136$	−2.47214	−0.211984
$137$	7.41641	0.633626	0.316813	−	0.948488i	$-0.397387\pi$
$137$	7.41641	0.633626	0.316813	+	0.948488i	$0.397387\pi$
$138$	6.38197	0.543269
$139$	3.79837	0.322174	0.161087	−	0.986940i	$-0.448500\pi$
$139$	3.79837	0.322174	0.161087	+	0.986940i	$0.448500\pi$
$140$	−3.61803	−0.305780
$141$	12.7984	1.07782
$142$	−14.1803	−1.18999
$143$	0	0
$144$	1.00000	0.0833333
$145$	2.76393	0.229532
$146$	2.00000	0.165521
$147$	−6.09017	−0.502309
$148$	−9.85410	−0.810002
$149$	6.47214	0.530218	0.265109	−	0.964218i	$-0.414592\pi$
$149$	6.47214	0.530218	0.265109	+	0.964218i	$0.414592\pi$
$150$	−1.00000	−0.0816497
$151$	−20.4721	−1.66600	−0.832999	−	0.553274i	$-0.813378\pi$
$151$	−20.4721	−1.66600	−0.832999	+	0.553274i	$0.813378\pi$
$152$	1.85410	0.150388
$153$	−2.47214	−0.199860
$154$	0	0
$155$	−2.76393	−0.222004
$156$	−1.85410	−0.148447
$157$	−8.85410	−0.706634	−0.353317	−	0.935504i	$-0.614946\pi$
$157$	−8.85410	−0.706634	−0.353317	+	0.935504i	$0.614946\pi$
$158$	−12.4721	−0.992230
$159$	1.90983	0.151459
$160$	1.00000	0.0790569
$161$	23.0902	1.81976
$162$	1.00000	0.0785674
$163$	23.4164	1.83411	0.917057	−	0.398755i	$-0.130558\pi$
$163$	23.4164	1.83411	0.917057	+	0.398755i	$0.130558\pi$
$164$	10.0902	0.787910
$165$	0	0
$166$	2.47214	0.191875
$167$	6.03444	0.466959	0.233480	−	0.972362i	$-0.424989\pi$
$167$	6.03444	0.466959	0.233480	+	0.972362i	$0.424989\pi$
$168$	3.61803	0.279137
$169$	−9.56231	−0.735562
$170$	−2.47214	−0.189604
$171$	1.85410	0.141787
$172$	−3.23607	−0.246748
$173$	−12.3820	−0.941383	−0.470692	−	0.882298i	$-0.655996\pi$
$173$	−12.3820	−0.941383	−0.470692	+	0.882298i	$0.655996\pi$
$174$	−2.76393	−0.209533
$175$	−3.61803	−0.273498
$176$	0	0
$177$	−6.32624	−0.475509
$178$	−8.56231	−0.641772
$179$	−0.0901699	−0.00673962	−0.00336981	−	0.999994i	$-0.501073\pi$
$179$	−0.0901699	−0.00673962	−0.00336981	+	0.999994i	$0.501073\pi$
$180$	1.00000	0.0745356
$181$	0	0		−	1.00000i	$-0.5\pi$
$181$	0	0			1.00000i	$0.5\pi$
$182$	−6.70820	−0.497245
$183$	−9.70820	−0.717651
$184$	−6.38197	−0.470485
$185$	−9.85410	−0.724488
$186$	2.76393	0.202661
$187$	0	0
$188$	−12.7984	−0.933417
$189$	3.61803	0.263173
$190$	1.85410	0.134511
$191$	16.1803	1.17077	0.585384	−	0.810756i	$-0.300944\pi$
$191$	16.1803	1.17077	0.585384	+	0.810756i	$0.300944\pi$
$192$	−1.00000	−0.0721688
$193$	11.7082	0.842775	0.421387	−	0.906881i	$-0.361543\pi$
$193$	11.7082	0.842775	0.421387	+	0.906881i	$0.361543\pi$
$194$	−2.00000	−0.143592
$195$	−1.85410	−0.132775
$196$	6.09017	0.435012
$197$	12.3820	0.882179	0.441089	−	0.897463i	$-0.354592\pi$
$197$	12.3820	0.882179	0.441089	+	0.897463i	$0.354592\pi$
$198$	0	0
$199$	−6.47214	−0.458798	−0.229399	−	0.973333i	$-0.573676\pi$
$199$	−6.47214	−0.458798	−0.229399	+	0.973333i	$0.573676\pi$
$200$	1.00000	0.0707107
$201$	2.29180	0.161651
$202$	−19.4164	−1.36613
$203$	−10.0000	−0.701862
$204$	2.47214	0.173084
$205$	10.0902	0.704728
$206$	1.85410	0.129181
$207$	−6.38197	−0.443577
$208$	1.85410	0.128559
$209$	0	0
$210$	3.61803	0.249668
$211$	5.52786	0.380554	0.190277	−	0.981730i	$-0.439061\pi$
$211$	5.52786	0.380554	0.190277	+	0.981730i	$0.439061\pi$
$212$	−1.90983	−0.131168
$213$	14.1803	0.971621
$214$	10.4721	0.715860
$215$	−3.23607	−0.220698
$216$	−1.00000	−0.0680414
$217$	10.0000	0.678844
$218$	−19.4164	−1.31505
$219$	−2.00000	−0.135147
$220$	0	0
$221$	−4.58359	−0.308326
$222$	9.85410	0.661364
$223$	−28.5623	−1.91267	−0.956337	−	0.292267i	$-0.905590\pi$
$223$	−28.5623	−1.91267	−0.956337	+	0.292267i	$0.905590\pi$
$224$	−3.61803	−0.241740
$225$	1.00000	0.0666667
$226$	−12.4721	−0.829634
$227$	2.29180	0.152112	0.0760559	−	0.997104i	$-0.475767\pi$
$227$	2.29180	0.152112	0.0760559	+	0.997104i	$0.475767\pi$
$228$	−1.85410	−0.122791
$229$	22.9443	1.51620	0.758100	−	0.652138i	$-0.226128\pi$
$229$	22.9443	1.51620	0.758100	+	0.652138i	$0.226128\pi$
$230$	−6.38197	−0.420814
$231$	0	0
$232$	2.76393	0.181461
$233$	1.23607	0.0809775	0.0404888	−	0.999180i	$-0.487109\pi$
$233$	1.23607	0.0809775	0.0404888	+	0.999180i	$0.487109\pi$
$234$	1.85410	0.121206
$235$	−12.7984	−0.834874
$236$	6.32624	0.411803
$237$	12.4721	0.810152
$238$	8.94427	0.579771
$239$	−10.1803	−0.658511	−0.329256	−	0.944241i	$-0.606798\pi$
$239$	−10.1803	−0.658511	−0.329256	+	0.944241i	$0.606798\pi$
$240$	−1.00000	−0.0645497
$241$	−14.5623	−0.938041	−0.469020	−	0.883187i	$-0.655393\pi$
$241$	−14.5623	−0.938041	−0.469020	+	0.883187i	$0.655393\pi$
$242$	0	0
$243$	−1.00000	−0.0641500
$244$	9.70820	0.621504
$245$	6.09017	0.389087
$246$	−10.0902	−0.643326
$247$	3.43769	0.218735
$248$	−2.76393	−0.175510
$249$	−2.47214	−0.156665
$250$	1.00000	0.0632456
$251$	−19.3262	−1.21986	−0.609931	−	0.792455i	$-0.708803\pi$
$251$	−19.3262	−1.21986	−0.609931	+	0.792455i	$0.708803\pi$
$252$	−3.61803	−0.227915
$253$	0	0
$254$	−9.56231	−0.599992
$255$	2.47214	0.154811
$256$	1.00000	0.0625000
$257$	−28.4721	−1.77604	−0.888022	−	0.459802i	$-0.847920\pi$
$257$	−28.4721	−1.77604	−0.888022	+	0.459802i	$0.847920\pi$
$258$	3.23607	0.201469
$259$	35.6525	2.21534
$260$	1.85410	0.114987
$261$	2.76393	0.171083
$262$	0	0
$263$	2.61803	0.161435	0.0807174	−	0.996737i	$-0.474279\pi$
$263$	2.61803	0.161435	0.0807174	+	0.996737i	$0.474279\pi$
$264$	0	0
$265$	−1.90983	−0.117320
$266$	−6.70820	−0.411306
$267$	8.56231	0.524005
$268$	−2.29180	−0.139994
$269$	27.5967	1.68260	0.841302	−	0.540566i	$-0.181790\pi$
$269$	27.5967	1.68260	0.841302	+	0.540566i	$0.181790\pi$
$270$	−1.00000	−0.0608581
$271$	−19.7082	−1.19719	−0.598594	−	0.801053i	$-0.704274\pi$
$271$	−19.7082	−1.19719	−0.598594	+	0.801053i	$0.704274\pi$
$272$	−2.47214	−0.149895
$273$	6.70820	0.405999
$274$	7.41641	0.448042
$275$	0	0
$276$	6.38197	0.384149
$277$	30.7426	1.84715	0.923573	−	0.383422i	$-0.125254\pi$
$277$	30.7426	1.84715	0.923573	+	0.383422i	$0.125254\pi$
$278$	3.79837	0.227811
$279$	−2.76393	−0.165472
$280$	−3.61803	−0.216219
$281$	9.05573	0.540219	0.270110	−	0.962830i	$-0.412940\pi$
$281$	9.05573	0.540219	0.270110	+	0.962830i	$0.412940\pi$
$282$	12.7984	0.762132
$283$	23.1246	1.37462	0.687308	−	0.726366i	$-0.258792\pi$
$283$	23.1246	1.37462	0.687308	+	0.726366i	$0.258792\pi$
$284$	−14.1803	−0.841448
$285$	−1.85410	−0.109828
$286$	0	0
$287$	−36.5066	−2.15492
$288$	1.00000	0.0589256
$289$	−10.8885	−0.640503
$290$	2.76393	0.162304
$291$	2.00000	0.117242
$292$	2.00000	0.117041
$293$	−22.0902	−1.29052	−0.645261	−	0.763962i	$-0.723251\pi$
$293$	−22.0902	−1.29052	−0.645261	+	0.763962i	$0.723251\pi$
$294$	−6.09017	−0.355186
$295$	6.32624	0.368328
$296$	−9.85410	−0.572758
$297$	0	0
$298$	6.47214	0.374921
$299$	−11.8328	−0.684309
$300$	−1.00000	−0.0577350
$301$	11.7082	0.674850
$302$	−20.4721	−1.17804
$303$	19.4164	1.11544
$304$	1.85410	0.106340
$305$	9.70820	0.555890
$306$	−2.47214	−0.141323
$307$	−26.8328	−1.53143	−0.765715	−	0.643180i	$-0.777615\pi$
$307$	−26.8328	−1.53143	−0.765715	+	0.643180i	$0.777615\pi$
$308$	0	0
$309$	−1.85410	−0.105476
$310$	−2.76393	−0.156981
$311$	−23.8885	−1.35460	−0.677298	−	0.735709i	$-0.736849\pi$
$311$	−23.8885	−1.35460	−0.677298	+	0.735709i	$0.736849\pi$
$312$	−1.85410	−0.104968
$313$	5.70820	0.322647	0.161323	−	0.986902i	$-0.448424\pi$
$313$	5.70820	0.322647	0.161323	+	0.986902i	$0.448424\pi$
$314$	−8.85410	−0.499666
$315$	−3.61803	−0.203853
$316$	−12.4721	−0.701612
$317$	−10.9098	−0.612757	−0.306379	−	0.951910i	$-0.599117\pi$
$317$	−10.9098	−0.612757	−0.306379	+	0.951910i	$0.599117\pi$
$318$	1.90983	0.107098
$319$	0	0
$320$	1.00000	0.0559017
$321$	−10.4721	−0.584498
$322$	23.0902	1.28676
$323$	−4.58359	−0.255038
$324$	1.00000	0.0555556
$325$	1.85410	0.102847
$326$	23.4164	1.29691
$327$	19.4164	1.07373
$328$	10.0902	0.557136
$329$	46.3050	2.55287
$330$	0	0
$331$	10.1459	0.557669	0.278834	−	0.960339i	$-0.410052\pi$
$331$	10.1459	0.557669	0.278834	+	0.960339i	$0.410052\pi$
$332$	2.47214	0.135676
$333$	−9.85410	−0.540001
$334$	6.03444	0.330190
$335$	−2.29180	−0.125214
$336$	3.61803	0.197380
$337$	23.4164	1.27557	0.637787	−	0.770213i	$-0.279850\pi$
$337$	23.4164	1.27557	0.637787	+	0.770213i	$0.279850\pi$
$338$	−9.56231	−0.520121
$339$	12.4721	0.677393
$340$	−2.47214	−0.134070
$341$	0	0
$342$	1.85410	0.100258
$343$	3.29180	0.177740
$344$	−3.23607	−0.174477
$345$	6.38197	0.343594
$346$	−12.3820	−0.665659
$347$	−9.70820	−0.521164	−0.260582	−	0.965452i	$-0.583914\pi$
$347$	−9.70820	−0.521164	−0.260582	+	0.965452i	$0.583914\pi$
$348$	−2.76393	−0.148162
$349$	13.4164	0.718164	0.359082	−	0.933306i	$-0.383090\pi$
$349$	13.4164	0.718164	0.359082	+	0.933306i	$0.383090\pi$
$350$	−3.61803	−0.193392
$351$	−1.85410	−0.0989646
$352$	0	0
$353$	−1.23607	−0.0657893	−0.0328946	−	0.999459i	$-0.510473\pi$
$353$	−1.23607	−0.0657893	−0.0328946	+	0.999459i	$0.510473\pi$
$354$	−6.32624	−0.336236
$355$	−14.1803	−0.752614
$356$	−8.56231	−0.453801
$357$	−8.94427	−0.473381
$358$	−0.0901699	−0.00476563
$359$	29.2361	1.54302	0.771510	−	0.636217i	$-0.219502\pi$
$359$	29.2361	1.54302	0.771510	+	0.636217i	$0.219502\pi$
$360$	1.00000	0.0527046
$361$	−15.5623	−0.819069
$362$	0	0
$363$	0	0
$364$	−6.70820	−0.351605
$365$	2.00000	0.104685
$366$	−9.70820	−0.507456
$367$	35.4164	1.84872	0.924361	−	0.381520i	$-0.124599\pi$
$367$	35.4164	1.84872	0.924361	+	0.381520i	$0.124599\pi$
$368$	−6.38197	−0.332683
$369$	10.0902	0.525273
$370$	−9.85410	−0.512290
$371$	6.90983	0.358741
$372$	2.76393	0.143303
$373$	14.4377	0.747555	0.373778	−	0.927518i	$-0.378062\pi$
$373$	14.4377	0.747555	0.373778	+	0.927518i	$0.378062\pi$
$374$	0	0
$375$	−1.00000	−0.0516398
$376$	−12.7984	−0.660026
$377$	5.12461	0.263931
$378$	3.61803	0.186092
$379$	33.5066	1.72112	0.860559	−	0.509351i	$-0.170115\pi$
$379$	33.5066	1.72112	0.860559	+	0.509351i	$0.170115\pi$
$380$	1.85410	0.0951134
$381$	9.56231	0.489892
$382$	16.1803	0.827858
$383$	−26.7426	−1.36649	−0.683243	−	0.730191i	$-0.739431\pi$
$383$	−26.7426	−1.36649	−0.683243	+	0.730191i	$0.739431\pi$
$384$	−1.00000	−0.0510310
$385$	0	0
$386$	11.7082	0.595932
$387$	−3.23607	−0.164499
$388$	−2.00000	−0.101535
$389$	6.00000	0.304212	0.152106	−	0.988364i	$-0.451394\pi$
$389$	6.00000	0.304212	0.152106	+	0.988364i	$0.451394\pi$
$390$	−1.85410	−0.0938861
$391$	15.7771	0.797882
$392$	6.09017	0.307600
$393$	0	0
$394$	12.3820	0.623794
$395$	−12.4721	−0.627541
$396$	0	0
$397$	6.74265	0.338404	0.169202	−	0.985581i	$-0.445881\pi$
$397$	6.74265	0.338404	0.169202	+	0.985581i	$0.445881\pi$
$398$	−6.47214	−0.324419
$399$	6.70820	0.335830
$400$	1.00000	0.0500000
$401$	−1.09017	−0.0544405	−0.0272202	−	0.999629i	$-0.508666\pi$
$401$	−1.09017	−0.0544405	−0.0272202	+	0.999629i	$0.508666\pi$
$402$	2.29180	0.114304
$403$	−5.12461	−0.255275
$404$	−19.4164	−0.966002
$405$	1.00000	0.0496904
$406$	−10.0000	−0.496292
$407$	0	0
$408$	2.47214	0.122389
$409$	2.43769	0.120536	0.0602681	−	0.998182i	$-0.480804\pi$
$409$	2.43769	0.120536	0.0602681	+	0.998182i	$0.480804\pi$
$410$	10.0902	0.498318
$411$	−7.41641	−0.365824
$412$	1.85410	0.0913450
$413$	−22.8885	−1.12627
$414$	−6.38197	−0.313657
$415$	2.47214	0.121352
$416$	1.85410	0.0909048
$417$	−3.79837	−0.186007
$418$	0	0
$419$	20.7984	1.01607	0.508034	−	0.861337i	$-0.330373\pi$
$419$	20.7984	1.01607	0.508034	+	0.861337i	$0.330373\pi$
$420$	3.61803	0.176542
$421$	−4.11146	−0.200380	−0.100190	−	0.994968i	$-0.531945\pi$
$421$	−4.11146	−0.200380	−0.100190	+	0.994968i	$0.531945\pi$
$422$	5.52786	0.269092
$423$	−12.7984	−0.622278
$424$	−1.90983	−0.0927495
$425$	−2.47214	−0.119916
$426$	14.1803	0.687040
$427$	−35.1246	−1.69980
$428$	10.4721	0.506190
$429$	0	0
$430$	−3.23607	−0.156057
$431$	−3.34752	−0.161245	−0.0806223	−	0.996745i	$-0.525691\pi$
$431$	−3.34752	−0.161245	−0.0806223	+	0.996745i	$0.525691\pi$
$432$	−1.00000	−0.0481125
$433$	−13.1246	−0.630729	−0.315364	−	0.948971i	$-0.602127\pi$
$433$	−13.1246	−0.630729	−0.315364	+	0.948971i	$0.602127\pi$
$434$	10.0000	0.480015
$435$	−2.76393	−0.132520
$436$	−19.4164	−0.929877
$437$	−11.8328	−0.566040
$438$	−2.00000	−0.0955637
$439$	33.7082	1.60880	0.804402	−	0.594085i	$-0.202486\pi$
$439$	33.7082	1.60880	0.804402	+	0.594085i	$0.202486\pi$
$440$	0	0
$441$	6.09017	0.290008
$442$	−4.58359	−0.218019
$443$	−0.472136	−0.0224319	−0.0112159	−	0.999937i	$-0.503570\pi$
$443$	−0.472136	−0.0224319	−0.0112159	+	0.999937i	$0.503570\pi$
$444$	9.85410	0.467655
$445$	−8.56231	−0.405892
$446$	−28.5623	−1.35246
$447$	−6.47214	−0.306122
$448$	−3.61803	−0.170936
$449$	26.9098	1.26995	0.634977	−	0.772531i	$-0.281010\pi$
$449$	26.9098	1.26995	0.634977	+	0.772531i	$0.281010\pi$
$450$	1.00000	0.0471405
$451$	0	0
$452$	−12.4721	−0.586640
$453$	20.4721	0.961865
$454$	2.29180	0.107559
$455$	−6.70820	−0.314485
$456$	−1.85410	−0.0868263
$457$	−18.8328	−0.880962	−0.440481	−	0.897762i	$-0.645192\pi$
$457$	−18.8328	−0.880962	−0.440481	+	0.897762i	$0.645192\pi$
$458$	22.9443	1.07212
$459$	2.47214	0.115389
$460$	−6.38197	−0.297561
$461$	−2.29180	−0.106740	−0.0533698	−	0.998575i	$-0.516996\pi$
$461$	−2.29180	−0.106740	−0.0533698	+	0.998575i	$0.516996\pi$
$462$	0	0
$463$	29.2705	1.36032	0.680158	−	0.733066i	$-0.261911\pi$
$463$	29.2705	1.36032	0.680158	+	0.733066i	$0.261911\pi$
$464$	2.76393	0.128312
$465$	2.76393	0.128174
$466$	1.23607	0.0572597
$467$	−18.4721	−0.854789	−0.427394	−	0.904065i	$-0.640568\pi$
$467$	−18.4721	−0.854789	−0.427394	+	0.904065i	$0.640568\pi$
$468$	1.85410	0.0857059
$469$	8.29180	0.382880
$470$	−12.7984	−0.590345
$471$	8.85410	0.407975
$472$	6.32624	0.291189
$473$	0	0
$474$	12.4721	0.572864
$475$	1.85410	0.0850720
$476$	8.94427	0.409960
$477$	−1.90983	−0.0874451
$478$	−10.1803	−0.465638
$479$	−7.23607	−0.330624	−0.165312	−	0.986241i	$-0.552863\pi$
$479$	−7.23607	−0.330624	−0.165312	+	0.986241i	$0.552863\pi$
$480$	−1.00000	−0.0456435
$481$	−18.2705	−0.833064
$482$	−14.5623	−0.663295
$483$	−23.0902	−1.05064
$484$	0	0
$485$	−2.00000	−0.0908153
$486$	−1.00000	−0.0453609
$487$	3.41641	0.154812	0.0774061	−	0.997000i	$-0.475336\pi$
$487$	3.41641	0.154812	0.0774061	+	0.997000i	$0.475336\pi$
$488$	9.70820	0.439470
$489$	−23.4164	−1.05893
$490$	6.09017	0.275126
$491$	−26.3262	−1.18809	−0.594043	−	0.804433i	$-0.702469\pi$
$491$	−26.3262	−1.18809	−0.594043	+	0.804433i	$0.702469\pi$
$492$	−10.0902	−0.454900
$493$	−6.83282	−0.307735
$494$	3.43769	0.154669
$495$	0	0
$496$	−2.76393	−0.124104
$497$	51.3050	2.30134
$498$	−2.47214	−0.110779
$499$	32.5623	1.45769	0.728845	−	0.684679i	$-0.240058\pi$
$499$	32.5623	1.45769	0.728845	+	0.684679i	$0.240058\pi$
$500$	1.00000	0.0447214
$501$	−6.03444	−0.269599
$502$	−19.3262	−0.862572
$503$	−41.4508	−1.84820	−0.924101	−	0.382148i	$-0.875184\pi$
$503$	−41.4508	−1.84820	−0.924101	+	0.382148i	$0.875184\pi$
$504$	−3.61803	−0.161160
$505$	−19.4164	−0.864019
$506$	0	0
$507$	9.56231	0.424677
$508$	−9.56231	−0.424259
$509$	−18.3607	−0.813823	−0.406911	−	0.913468i	$-0.633394\pi$
$509$	−18.3607	−0.813823	−0.406911	+	0.913468i	$0.633394\pi$
$510$	2.47214	0.109468
$511$	−7.23607	−0.320105
$512$	1.00000	0.0441942
$513$	−1.85410	−0.0818606
$514$	−28.4721	−1.25585
$515$	1.85410	0.0817015
$516$	3.23607	0.142460
$517$	0	0
$518$	35.6525	1.56648
$519$	12.3820	0.543508
$520$	1.85410	0.0813077
$521$	11.7984	0.516896	0.258448	−	0.966025i	$-0.416789\pi$
$521$	11.7984	0.516896	0.258448	+	0.966025i	$0.416789\pi$
$522$	2.76393	0.120974
$523$	19.5967	0.856906	0.428453	−	0.903564i	$-0.359059\pi$
$523$	19.5967	0.856906	0.428453	+	0.903564i	$0.359059\pi$
$524$	0	0
$525$	3.61803	0.157904
$526$	2.61803	0.114152
$527$	6.83282	0.297642
$528$	0	0
$529$	17.7295	0.770847
$530$	−1.90983	−0.0829577
$531$	6.32624	0.274535
$532$	−6.70820	−0.290838
$533$	18.7082	0.810342
$534$	8.56231	0.370527
$535$	10.4721	0.452750
$536$	−2.29180	−0.0989905
$537$	0.0901699	0.00389112
$538$	27.5967	1.18978
$539$	0	0
$540$	−1.00000	−0.0430331
$541$	11.4164	0.490830	0.245415	−	0.969418i	$-0.421076\pi$
$541$	11.4164	0.490830	0.245415	+	0.969418i	$0.421076\pi$
$542$	−19.7082	−0.846540
$543$	0	0
$544$	−2.47214	−0.105992
$545$	−19.4164	−0.831708
$546$	6.70820	0.287085
$547$	14.2918	0.611073	0.305537	−	0.952180i	$-0.401164\pi$
$547$	14.2918	0.611073	0.305537	+	0.952180i	$0.401164\pi$
$548$	7.41641	0.316813
$549$	9.70820	0.414336
$550$	0	0
$551$	5.12461	0.218316
$552$	6.38197	0.271635
$553$	45.1246	1.91889
$554$	30.7426	1.30613
$555$	9.85410	0.418283
$556$	3.79837	0.161087
$557$	3.49342	0.148021	0.0740105	−	0.997257i	$-0.476420\pi$
$557$	3.49342	0.148021	0.0740105	+	0.997257i	$0.476420\pi$
$558$	−2.76393	−0.117007
$559$	−6.00000	−0.253773
$560$	−3.61803	−0.152890
$561$	0	0
$562$	9.05573	0.381993
$563$	−26.4721	−1.11567	−0.557834	−	0.829953i	$-0.688367\pi$
$563$	−26.4721	−1.11567	−0.557834	+	0.829953i	$0.688367\pi$
$564$	12.7984	0.538909
$565$	−12.4721	−0.524707
$566$	23.1246	0.972000
$567$	−3.61803	−0.151943
$568$	−14.1803	−0.594994
$569$	13.3262	0.558665	0.279332	−	0.960194i	$-0.409887\pi$
$569$	13.3262	0.558665	0.279332	+	0.960194i	$0.409887\pi$
$570$	−1.85410	−0.0776598
$571$	−27.9787	−1.17087	−0.585436	−	0.810718i	$-0.699077\pi$
$571$	−27.9787	−1.17087	−0.585436	+	0.810718i	$0.699077\pi$
$572$	0	0
$573$	−16.1803	−0.675943
$574$	−36.5066	−1.52376
$575$	−6.38197	−0.266146
$576$	1.00000	0.0416667
$577$	−4.29180	−0.178670	−0.0893349	−	0.996002i	$-0.528474\pi$
$577$	−4.29180	−0.178670	−0.0893349	+	0.996002i	$0.528474\pi$
$578$	−10.8885	−0.452904
$579$	−11.7082	−0.486576
$580$	2.76393	0.114766
$581$	−8.94427	−0.371071
$582$	2.00000	0.0829027
$583$	0	0
$584$	2.00000	0.0827606
$585$	1.85410	0.0766577
$586$	−22.0902	−0.912537
$587$	−20.9443	−0.864463	−0.432231	−	0.901763i	$-0.642274\pi$
$587$	−20.9443	−0.864463	−0.432231	+	0.901763i	$0.642274\pi$
$588$	−6.09017	−0.251154
$589$	−5.12461	−0.211156
$590$	6.32624	0.260447
$591$	−12.3820	−0.509326
$592$	−9.85410	−0.405001
$593$	11.8885	0.488204	0.244102	−	0.969750i	$-0.421507\pi$
$593$	11.8885	0.488204	0.244102	+	0.969750i	$0.421507\pi$
$594$	0	0
$595$	8.94427	0.366679
$596$	6.47214	0.265109
$597$	6.47214	0.264887
$598$	−11.8328	−0.483880
$599$	−22.1803	−0.906264	−0.453132	−	0.891443i	$-0.649693\pi$
$599$	−22.1803	−0.906264	−0.453132	+	0.891443i	$0.649693\pi$
$600$	−1.00000	−0.0408248
$601$	6.79837	0.277311	0.138656	−	0.990341i	$-0.455722\pi$
$601$	6.79837	0.277311	0.138656	+	0.990341i	$0.455722\pi$
$602$	11.7082	0.477191
$603$	−2.29180	−0.0933292
$604$	−20.4721	−0.832999
$605$	0	0
$606$	19.4164	0.788738
$607$	3.41641	0.138668	0.0693339	−	0.997594i	$-0.477913\pi$
$607$	3.41641	0.138668	0.0693339	+	0.997594i	$0.477913\pi$
$608$	1.85410	0.0751938
$609$	10.0000	0.405220
$610$	9.70820	0.393074
$611$	−23.7295	−0.959992
$612$	−2.47214	−0.0999302
$613$	41.4164	1.67279	0.836396	−	0.548125i	$-0.184658\pi$
$613$	41.4164	1.67279	0.836396	+	0.548125i	$0.184658\pi$
$614$	−26.8328	−1.08288
$615$	−10.0902	−0.406875
$616$	0	0
$617$	−24.0000	−0.966204	−0.483102	−	0.875564i	$-0.660490\pi$
$617$	−24.0000	−0.966204	−0.483102	+	0.875564i	$0.660490\pi$
$618$	−1.85410	−0.0745829
$619$	6.43769	0.258753	0.129376	−	0.991596i	$-0.458702\pi$
$619$	6.43769	0.258753	0.129376	+	0.991596i	$0.458702\pi$
$620$	−2.76393	−0.111002
$621$	6.38197	0.256099
$622$	−23.8885	−0.957843
$623$	30.9787	1.24114
$624$	−1.85410	−0.0742235
$625$	1.00000	0.0400000
$626$	5.70820	0.228146
$627$	0	0
$628$	−8.85410	−0.353317
$629$	24.3607	0.971324
$630$	−3.61803	−0.144146
$631$	8.76393	0.348887	0.174443	−	0.984667i	$-0.444187\pi$
$631$	8.76393	0.348887	0.174443	+	0.984667i	$0.444187\pi$
$632$	−12.4721	−0.496115
$633$	−5.52786	−0.219713
$634$	−10.9098	−0.433285
$635$	−9.56231	−0.379469
$636$	1.90983	0.0757297
$637$	11.2918	0.447397
$638$	0	0
$639$	−14.1803	−0.560966
$640$	1.00000	0.0395285
$641$	−31.6312	−1.24936	−0.624678	−	0.780882i	$-0.714770\pi$
$641$	−31.6312	−1.24936	−0.624678	+	0.780882i	$0.714770\pi$
$642$	−10.4721	−0.413302
$643$	40.0000	1.57745	0.788723	−	0.614749i	$-0.210743\pi$
$643$	40.0000	1.57745	0.788723	+	0.614749i	$0.210743\pi$
$644$	23.0902	0.909880
$645$	3.23607	0.127420
$646$	−4.58359	−0.180339
$647$	−49.8885	−1.96132	−0.980661	−	0.195716i	$-0.937297\pi$
$647$	−49.8885	−1.96132	−0.980661	+	0.195716i	$0.937297\pi$
$648$	1.00000	0.0392837
$649$	0	0
$650$	1.85410	0.0727239
$651$	−10.0000	−0.391931
$652$	23.4164	0.917057
$653$	46.6869	1.82700	0.913500	−	0.406838i	$-0.133369\pi$
$653$	46.6869	1.82700	0.913500	+	0.406838i	$0.133369\pi$
$654$	19.4164	0.759242
$655$	0	0
$656$	10.0902	0.393955
$657$	2.00000	0.0780274
$658$	46.3050	1.80515
$659$	−8.67376	−0.337882	−0.168941	−	0.985626i	$-0.554035\pi$
$659$	−8.67376	−0.337882	−0.168941	+	0.985626i	$0.554035\pi$
$660$	0	0
$661$	−10.6525	−0.414333	−0.207167	−	0.978306i	$-0.566424\pi$
$661$	−10.6525	−0.414333	−0.207167	+	0.978306i	$0.566424\pi$
$662$	10.1459	0.394332
$663$	4.58359	0.178012
$664$	2.47214	0.0959375
$665$	−6.70820	−0.260133
$666$	−9.85410	−0.381839
$667$	−17.6393	−0.682997
$668$	6.03444	0.233480
$669$	28.5623	1.10428
$670$	−2.29180	−0.0885398
$671$	0	0
$672$	3.61803	0.139569
$673$	25.2361	0.972779	0.486389	−	0.873742i	$-0.338314\pi$
$673$	25.2361	0.972779	0.486389	+	0.873742i	$0.338314\pi$
$674$	23.4164	0.901966
$675$	−1.00000	−0.0384900
$676$	−9.56231	−0.367781
$677$	34.3607	1.32059	0.660294	−	0.751007i	$-0.270432\pi$
$677$	34.3607	1.32059	0.660294	+	0.751007i	$0.270432\pi$
$678$	12.4721	0.478989
$679$	7.23607	0.277695
$680$	−2.47214	−0.0948021
$681$	−2.29180	−0.0878218
$682$	0	0
$683$	−33.0132	−1.26321	−0.631607	−	0.775289i	$-0.717604\pi$
$683$	−33.0132	−1.26321	−0.631607	+	0.775289i	$0.717604\pi$
$684$	1.85410	0.0708934
$685$	7.41641	0.283366
$686$	3.29180	0.125681
$687$	−22.9443	−0.875379
$688$	−3.23607	−0.123374
$689$	−3.54102	−0.134902
$690$	6.38197	0.242957
$691$	35.7984	1.36183	0.680917	−	0.732360i	$-0.261581\pi$
$691$	35.7984	1.36183	0.680917	+	0.732360i	$0.261581\pi$
$692$	−12.3820	−0.470692
$693$	0	0
$694$	−9.70820	−0.368518
$695$	3.79837	0.144081
$696$	−2.76393	−0.104767
$697$	−24.9443	−0.944832
$698$	13.4164	0.507819
$699$	−1.23607	−0.0467524
$700$	−3.61803	−0.136749
$701$	48.0689	1.81554	0.907768	−	0.419472i	$-0.137785\pi$
$701$	48.0689	1.81554	0.907768	+	0.419472i	$0.137785\pi$
$702$	−1.85410	−0.0699786
$703$	−18.2705	−0.689085
$704$	0	0
$705$	12.7984	0.482015
$706$	−1.23607	−0.0465200
$707$	70.2492	2.64199
$708$	−6.32624	−0.237755
$709$	10.7639	0.404248	0.202124	−	0.979360i	$-0.435216\pi$
$709$	10.7639	0.404248	0.202124	+	0.979360i	$0.435216\pi$
$710$	−14.1803	−0.532179
$711$	−12.4721	−0.467742
$712$	−8.56231	−0.320886
$713$	17.6393	0.660598
$714$	−8.94427	−0.334731
$715$	0	0
$716$	−0.0901699	−0.00336981
$717$	10.1803	0.380192
$718$	29.2361	1.09108
$719$	23.5279	0.877441	0.438721	−	0.898624i	$-0.355432\pi$
$719$	23.5279	0.877441	0.438721	+	0.898624i	$0.355432\pi$
$720$	1.00000	0.0372678
$721$	−6.70820	−0.249827
$722$	−15.5623	−0.579169
$723$	14.5623	0.541578
$724$	0	0
$725$	2.76393	0.102650
$726$	0	0
$727$	49.6869	1.84279	0.921393	−	0.388632i	$-0.127052\pi$
$727$	49.6869	1.84279	0.921393	+	0.388632i	$0.127052\pi$
$728$	−6.70820	−0.248623
$729$	1.00000	0.0370370
$730$	2.00000	0.0740233
$731$	8.00000	0.295891
$732$	−9.70820	−0.358826
$733$	−37.4164	−1.38201	−0.691003	−	0.722852i	$-0.742831\pi$
$733$	−37.4164	−1.38201	−0.691003	+	0.722852i	$0.742831\pi$
$734$	35.4164	1.30724
$735$	−6.09017	−0.224639
$736$	−6.38197	−0.235242
$737$	0	0
$738$	10.0902	0.371424
$739$	−10.8541	−0.399275	−0.199637	−	0.979870i	$-0.563976\pi$
$739$	−10.8541	−0.399275	−0.199637	+	0.979870i	$0.563976\pi$
$740$	−9.85410	−0.362244
$741$	−3.43769	−0.126287
$742$	6.90983	0.253668
$743$	−10.3820	−0.380877	−0.190439	−	0.981699i	$-0.560991\pi$
$743$	−10.3820	−0.380877	−0.190439	+	0.981699i	$0.560991\pi$
$744$	2.76393	0.101331
$745$	6.47214	0.237121
$746$	14.4377	0.528602
$747$	2.47214	0.0904507
$748$	0	0
$749$	−37.8885	−1.38442
$750$	−1.00000	−0.0365148
$751$	35.4164	1.29236	0.646182	−	0.763184i	$-0.276365\pi$
$751$	35.4164	1.29236	0.646182	+	0.763184i	$0.276365\pi$
$752$	−12.7984	−0.466709
$753$	19.3262	0.704287
$754$	5.12461	0.186627
$755$	−20.4721	−0.745057
$756$	3.61803	0.131587
$757$	−19.1591	−0.696348	−0.348174	−	0.937430i	$-0.613198\pi$
$757$	−19.1591	−0.696348	−0.348174	+	0.937430i	$0.613198\pi$
$758$	33.5066	1.21701
$759$	0	0
$760$	1.85410	0.0672553
$761$	0.111456	0.00404028	0.00202014	−	0.999998i	$-0.499357\pi$
$761$	0.111456	0.00404028	0.00202014	+	0.999998i	$0.499357\pi$
$762$	9.56231	0.346406
$763$	70.2492	2.54319
$764$	16.1803	0.585384
$765$	−2.47214	−0.0893803
$766$	−26.7426	−0.966251
$767$	11.7295	0.423527
$768$	−1.00000	−0.0360844
$769$	47.0902	1.69811	0.849057	−	0.528300i	$-0.177171\pi$
$769$	47.0902	1.69811	0.849057	+	0.528300i	$0.177171\pi$
$770$	0	0
$771$	28.4721	1.02540
$772$	11.7082	0.421387
$773$	22.0902	0.794528	0.397264	−	0.917704i	$-0.369960\pi$
$773$	22.0902	0.794528	0.397264	+	0.917704i	$0.369960\pi$
$774$	−3.23607	−0.116318
$775$	−2.76393	−0.0992834
$776$	−2.00000	−0.0717958
$777$	−35.6525	−1.27903
$778$	6.00000	0.215110
$779$	18.7082	0.670291
$780$	−1.85410	−0.0663875
$781$	0	0
$782$	15.7771	0.564188
$783$	−2.76393	−0.0987749
$784$	6.09017	0.217506
$785$	−8.85410	−0.316016
$786$	0	0
$787$	19.7082	0.702522	0.351261	−	0.936278i	$-0.385753\pi$
$787$	19.7082	0.702522	0.351261	+	0.936278i	$0.385753\pi$
$788$	12.3820	0.441089
$789$	−2.61803	−0.0932045
$790$	−12.4721	−0.443739
$791$	45.1246	1.60445
$792$	0	0
$793$	18.0000	0.639199
$794$	6.74265	0.239288
$795$	1.90983	0.0677347
$796$	−6.47214	−0.229399
$797$	33.0902	1.17211	0.586057	−	0.810270i	$-0.300679\pi$
$797$	33.0902	1.17211	0.586057	+	0.810270i	$0.300679\pi$
$798$	6.70820	0.237468
$799$	31.6393	1.11932
$800$	1.00000	0.0353553
$801$	−8.56231	−0.302534
$802$	−1.09017	−0.0384952
$803$	0	0
$804$	2.29180	0.0808254
$805$	23.0902	0.813822
$806$	−5.12461	−0.180507
$807$	−27.5967	−0.971452
$808$	−19.4164	−0.683067
$809$	−25.7426	−0.905063	−0.452532	−	0.891748i	$-0.649479\pi$
$809$	−25.7426	−0.905063	−0.452532	+	0.891748i	$0.649479\pi$
$810$	1.00000	0.0351364
$811$	−28.9230	−1.01562	−0.507812	−	0.861468i	$-0.669545\pi$
$811$	−28.9230	−1.01562	−0.507812	+	0.861468i	$0.669545\pi$
$812$	−10.0000	−0.350931
$813$	19.7082	0.691197
$814$	0	0
$815$	23.4164	0.820241
$816$	2.47214	0.0865421
$817$	−6.00000	−0.209913
$818$	2.43769	0.0852320
$819$	−6.70820	−0.234404
$820$	10.0902	0.352364
$821$	−31.0132	−1.08237	−0.541183	−	0.840905i	$-0.682023\pi$
$821$	−31.0132	−1.08237	−0.541183	+	0.840905i	$0.682023\pi$
$822$	−7.41641	−0.258677
$823$	−13.8541	−0.482924	−0.241462	−	0.970410i	$-0.577627\pi$
$823$	−13.8541	−0.482924	−0.241462	+	0.970410i	$0.577627\pi$
$824$	1.85410	0.0645907
$825$	0	0
$826$	−22.8885	−0.796394
$827$	34.6525	1.20498	0.602492	−	0.798125i	$-0.294174\pi$
$827$	34.6525	1.20498	0.602492	+	0.798125i	$0.294174\pi$
$828$	−6.38197	−0.221789
$829$	−13.0557	−0.453444	−0.226722	−	0.973959i	$-0.572801\pi$
$829$	−13.0557	−0.453444	−0.226722	+	0.973959i	$0.572801\pi$
$830$	2.47214	0.0858091
$831$	−30.7426	−1.06645
$832$	1.85410	0.0642794
$833$	−15.0557	−0.521650
$834$	−3.79837	−0.131527
$835$	6.03444	0.208830
$836$	0	0
$837$	2.76393	0.0955355
$838$	20.7984	0.718468
$839$	41.4853	1.43223	0.716116	−	0.697982i	$-0.245918\pi$
$839$	41.4853	1.43223	0.716116	+	0.697982i	$0.245918\pi$
$840$	3.61803	0.124834
$841$	−21.3607	−0.736575
$842$	−4.11146	−0.141690
$843$	−9.05573	−0.311896
$844$	5.52786	0.190277
$845$	−9.56231	−0.328953
$846$	−12.7984	−0.440017
$847$	0	0
$848$	−1.90983	−0.0655838
$849$	−23.1246	−0.793635
$850$	−2.47214	−0.0847936
$851$	62.8885	2.15579
$852$	14.1803	0.485810
$853$	−33.6180	−1.15106	−0.575530	−	0.817781i	$-0.695204\pi$
$853$	−33.6180	−1.15106	−0.575530	+	0.817781i	$0.695204\pi$
$854$	−35.1246	−1.20194
$855$	1.85410	0.0634089
$856$	10.4721	0.357930
$857$	−11.5967	−0.396137	−0.198069	−	0.980188i	$-0.563467\pi$
$857$	−11.5967	−0.396137	−0.198069	+	0.980188i	$0.563467\pi$
$858$	0	0
$859$	25.5066	0.870273	0.435137	−	0.900364i	$-0.356700\pi$
$859$	25.5066	0.870273	0.435137	+	0.900364i	$0.356700\pi$
$860$	−3.23607	−0.110349
$861$	36.5066	1.24414
$862$	−3.34752	−0.114017
$863$	38.3951	1.30699	0.653493	−	0.756933i	$-0.273303\pi$
$863$	38.3951	1.30699	0.653493	+	0.756933i	$0.273303\pi$
$864$	−1.00000	−0.0340207
$865$	−12.3820	−0.420999
$866$	−13.1246	−0.445992
$867$	10.8885	0.369794
$868$	10.0000	0.339422
$869$	0	0
$870$	−2.76393	−0.0937061
$871$	−4.24922	−0.143979
$872$	−19.4164	−0.657523
$873$	−2.00000	−0.0676897
$874$	−11.8328	−0.400251
$875$	−3.61803	−0.122312
$876$	−2.00000	−0.0675737
$877$	17.8541	0.602890	0.301445	−	0.953484i	$-0.402531\pi$
$877$	17.8541	0.602890	0.301445	+	0.953484i	$0.402531\pi$
$878$	33.7082	1.13760
$879$	22.0902	0.745083
$880$	0	0
$881$	−29.5066	−0.994102	−0.497051	−	0.867721i	$-0.665584\pi$
$881$	−29.5066	−0.994102	−0.497051	+	0.867721i	$0.665584\pi$
$882$	6.09017	0.205067
$883$	−11.4164	−0.384193	−0.192096	−	0.981376i	$-0.561529\pi$
$883$	−11.4164	−0.384193	−0.192096	+	0.981376i	$0.561529\pi$
$884$	−4.58359	−0.154163
$885$	−6.32624	−0.212654
$886$	−0.472136	−0.0158617
$887$	−17.6180	−0.591556	−0.295778	−	0.955257i	$-0.595579\pi$
$887$	−17.6180	−0.591556	−0.295778	+	0.955257i	$0.595579\pi$
$888$	9.85410	0.330682
$889$	34.5967	1.16034
$890$	−8.56231	−0.287009
$891$	0	0
$892$	−28.5623	−0.956337
$893$	−23.7295	−0.794077
$894$	−6.47214	−0.216461
$895$	−0.0901699	−0.00301405
$896$	−3.61803	−0.120870
$897$	11.8328	0.395086
$898$	26.9098	0.897993
$899$	−7.63932	−0.254786
$900$	1.00000	0.0333333
$901$	4.72136	0.157291
$902$	0	0
$903$	−11.7082	−0.389625
$904$	−12.4721	−0.414817
$905$	0	0
$906$	20.4721	0.680141
$907$	−22.2492	−0.738773	−0.369387	−	0.929276i	$-0.620432\pi$
$907$	−22.2492	−0.738773	−0.369387	+	0.929276i	$0.620432\pi$
$908$	2.29180	0.0760559
$909$	−19.4164	−0.644002
$910$	−6.70820	−0.222375
$911$	35.0132	1.16004	0.580019	−	0.814603i	$-0.303045\pi$
$911$	35.0132	1.16004	0.580019	+	0.814603i	$0.303045\pi$
$912$	−1.85410	−0.0613955
$913$	0	0
$914$	−18.8328	−0.622934
$915$	−9.70820	−0.320943
$916$	22.9443	0.758100
$917$	0	0
$918$	2.47214	0.0815926
$919$	−22.6525	−0.747236	−0.373618	−	0.927583i	$-0.621883\pi$
$919$	−22.6525	−0.747236	−0.373618	+	0.927583i	$0.621883\pi$
$920$	−6.38197	−0.210407
$921$	26.8328	0.884171
$922$	−2.29180	−0.0754763
$923$	−26.2918	−0.865405
$924$	0	0
$925$	−9.85410	−0.324001
$926$	29.2705	0.961889
$927$	1.85410	0.0608967
$928$	2.76393	0.0907305
$929$	−32.5623	−1.06833	−0.534167	−	0.845379i	$-0.679375\pi$
$929$	−32.5623	−1.06833	−0.534167	+	0.845379i	$0.679375\pi$
$930$	2.76393	0.0906329
$931$	11.2918	0.370074
$932$	1.23607	0.0404888
$933$	23.8885	0.782076
$934$	−18.4721	−0.604427
$935$	0	0
$936$	1.85410	0.0606032
$937$	38.8328	1.26861	0.634306	−	0.773082i	$-0.281286\pi$
$937$	38.8328	1.26861	0.634306	+	0.773082i	$0.281286\pi$
$938$	8.29180	0.270737
$939$	−5.70820	−0.186280
$940$	−12.7984	−0.417437
$941$	35.7771	1.16630	0.583150	−	0.812365i	$-0.301820\pi$
$941$	35.7771	1.16630	0.583150	+	0.812365i	$0.301820\pi$
$942$	8.85410	0.288482
$943$	−64.3951	−2.09699
$944$	6.32624	0.205902
$945$	3.61803	0.117695
$946$	0	0
$947$	−9.05573	−0.294272	−0.147136	−	0.989116i	$-0.547005\pi$
$947$	−9.05573	−0.294272	−0.147136	+	0.989116i	$0.547005\pi$
$948$	12.4721	0.405076
$949$	3.70820	0.120373
$950$	1.85410	0.0601550
$951$	10.9098	0.353775
$952$	8.94427	0.289886
$953$	−39.0132	−1.26376	−0.631880	−	0.775066i	$-0.717716\pi$
$953$	−39.0132	−1.26376	−0.631880	+	0.775066i	$0.717716\pi$
$954$	−1.90983	−0.0618330
$955$	16.1803	0.523584
$956$	−10.1803	−0.329256
$957$	0	0
$958$	−7.23607	−0.233787
$959$	−26.8328	−0.866477
$960$	−1.00000	−0.0322749
$961$	−23.3607	−0.753570
$962$	−18.2705	−0.589065
$963$	10.4721	0.337460
$964$	−14.5623	−0.469020
$965$	11.7082	0.376900
$966$	−23.0902	−0.742914
$967$	−11.0213	−0.354421	−0.177210	−	0.984173i	$-0.556707\pi$
$967$	−11.0213	−0.354421	−0.177210	+	0.984173i	$0.556707\pi$
$968$	0	0
$969$	4.58359	0.147246
$970$	−2.00000	−0.0642161
$971$	−25.0344	−0.803393	−0.401697	−	0.915773i	$-0.631579\pi$
$971$	−25.0344	−0.803393	−0.401697	+	0.915773i	$0.631579\pi$
$972$	−1.00000	−0.0320750
$973$	−13.7426	−0.440569
$974$	3.41641	0.109469
$975$	−1.85410	−0.0593788
$976$	9.70820	0.310752
$977$	18.9443	0.606081	0.303040	−	0.952978i	$-0.401998\pi$
$977$	18.9443	0.606081	0.303040	+	0.952978i	$0.401998\pi$
$978$	−23.4164	−0.748774
$979$	0	0
$980$	6.09017	0.194543
$981$	−19.4164	−0.619918
$982$	−26.3262	−0.840104
$983$	−12.2705	−0.391368	−0.195684	−	0.980667i	$-0.562693\pi$
$983$	−12.2705	−0.391368	−0.195684	+	0.980667i	$0.562693\pi$
$984$	−10.0902	−0.321663
$985$	12.3820	0.394522
$986$	−6.83282	−0.217601
$987$	−46.3050	−1.47390
$988$	3.43769	0.109368
$989$	20.6525	0.656711
$990$	0	0
$991$	−12.0000	−0.381193	−0.190596	−	0.981669i	$-0.561042\pi$
$991$	−12.0000	−0.381193	−0.190596	+	0.981669i	$0.561042\pi$
$992$	−2.76393	−0.0877549
$993$	−10.1459	−0.321970
$994$	51.3050	1.62729
$995$	−6.47214	−0.205181
$996$	−2.47214	−0.0783326
$997$	−22.0000	−0.696747	−0.348373	−	0.937356i	$-0.613266\pi$
$997$	−22.0000	−0.696747	−0.348373	+	0.937356i	$0.613266\pi$
$998$	32.5623	1.03074
$999$	9.85410	0.311770

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	3630.2.a.bl.1.1		2
11.3	even	5		330.2.m.a.31.1	✓	4
11.4	even	5		330.2.m.a.181.1	yes	4
11.10	odd	2		3630.2.a.bf.1.2		2
33.14	odd	10		990.2.n.h.361.1		4
33.26	odd	10		990.2.n.h.181.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
330.2.m.a.31.1	✓	4	11.3	even	5
330.2.m.a.181.1	yes	4	11.4	even	5
990.2.n.h.181.1		4	33.26	odd	10
990.2.n.h.361.1		4	33.14	odd	10
3630.2.a.bf.1.2		2	11.10	odd	2
3630.2.a.bl.1.1		2	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:	\( N \)	\(=\)	\( 3630 = 2 \cdot 3 \cdot 5 \cdot 11^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	3630.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -1.00000 q^{3} +1.00000 q^{4} +1.00000 q^{5} -1.00000 q^{6} -3.61803 q^{7} +1.00000 q^{8} +1.00000 q^{9} +1.00000 q^{10} -1.00000 q^{12} +1.85410 q^{13} -3.61803 q^{14} -1.00000 q^{15} +1.00000 q^{16} -2.47214 q^{17} +1.00000 q^{18} +1.85410 q^{19} +1.00000 q^{20} +3.61803 q^{21} -6.38197 q^{23} -1.00000 q^{24} +1.00000 q^{25} +1.85410 q^{26} -1.00000 q^{27} -3.61803 q^{28} +2.76393 q^{29} -1.00000 q^{30} -2.76393 q^{31} +1.00000 q^{32} -2.47214 q^{34} -3.61803 q^{35} +1.00000 q^{36} -9.85410 q^{37} +1.85410 q^{38} -1.85410 q^{39} +1.00000 q^{40} +10.0902 q^{41} +3.61803 q^{42} -3.23607 q^{43} +1.00000 q^{45} -6.38197 q^{46} -12.7984 q^{47} -1.00000 q^{48} +6.09017 q^{49} +1.00000 q^{50} +2.47214 q^{51} +1.85410 q^{52} -1.90983 q^{53} -1.00000 q^{54} -3.61803 q^{56} -1.85410 q^{57} +2.76393 q^{58} +6.32624 q^{59} -1.00000 q^{60} +9.70820 q^{61} -2.76393 q^{62} -3.61803 q^{63} +1.00000 q^{64} +1.85410 q^{65} -2.29180 q^{67} -2.47214 q^{68} +6.38197 q^{69} -3.61803 q^{70} -14.1803 q^{71} +1.00000 q^{72} +2.00000 q^{73} -9.85410 q^{74} -1.00000 q^{75} +1.85410 q^{76} -1.85410 q^{78} -12.4721 q^{79} +1.00000 q^{80} +1.00000 q^{81} +10.0902 q^{82} +2.47214 q^{83} +3.61803 q^{84} -2.47214 q^{85} -3.23607 q^{86} -2.76393 q^{87} -8.56231 q^{89} +1.00000 q^{90} -6.70820 q^{91} -6.38197 q^{92} +2.76393 q^{93} -12.7984 q^{94} +1.85410 q^{95} -1.00000 q^{96} -2.00000 q^{97} +6.09017 q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9}+O(q^{10}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9	\( 2 q + 2 q^{2} - 2 q^{3} + 2 q^{4} + 2 q^{5} - 2 q^{6} - 5 q^{7} + 2 q^{8} + 2 q^{9} + 2 q^{10} - 2 q^{12} - 3 q^{13} - 5 q^{14} - 2 q^{15} + 2 q^{16} + 4 q^{17} + 2 q^{18} - 3 q^{19} + 2 q^{20} + 5 q^{21} - 15 q^{23} - 2 q^{24} + 2 q^{25} - 3 q^{26} - 2 q^{27} - 5 q^{28} + 10 q^{29} - 2 q^{30} - 10 q^{31} + 2 q^{32} + 4 q^{34} - 5 q^{35} + 2 q^{36} - 13 q^{37} - 3 q^{38} + 3 q^{39} + 2 q^{40} + 9 q^{41} + 5 q^{42} - 2 q^{43} + 2 q^{45} - 15 q^{46} - q^{47} - 2 q^{48} + q^{49} + 2 q^{50} - 4 q^{51} - 3 q^{52} - 15 q^{53} - 2 q^{54} - 5 q^{56} + 3 q^{57} + 10 q^{58} - 3 q^{59} - 2 q^{60} + 6 q^{61} - 10 q^{62} - 5 q^{63} + 2 q^{64} - 3 q^{65} - 18 q^{67} + 4 q^{68} + 15 q^{69} - 5 q^{70} - 6 q^{71} + 2 q^{72} + 4 q^{73} - 13 q^{74} - 2 q^{75} - 3 q^{76} + 3 q^{78} - 16 q^{79} + 2 q^{80} + 2 q^{81} + 9 q^{82} - 4 q^{83} + 5 q^{84} + 4 q^{85} - 2 q^{86} - 10 q^{87} + 3 q^{89} + 2 q^{90} - 15 q^{92} + 10 q^{93} - q^{94} - 3 q^{95} - 2 q^{96} - 4 q^{97} + q^{98}+O(q^{100}) \) 2 * q + 2 * q^2 - 2 * q^3 + 2 * q^4 + 2 * q^5 - 2 * q^6 - 5 * q^7 + 2 * q^8 + 2 * q^9 + 2 * q^10 - 2 * q^12 - 3 * q^13 - 5 * q^14 - 2 * q^15 + 2 * q^16 + 4 * q^17 + 2 * q^18 - 3 * q^19 + 2 * q^20 + 5 * q^21 - 15 * q^23 - 2 * q^24 + 2 * q^25 - 3 * q^26 - 2 * q^27 - 5 * q^28 + 10 * q^29 - 2 * q^30 - 10 * q^31 + 2 * q^32 + 4 * q^34 - 5 * q^35 + 2 * q^36 - 13 * q^37 - 3 * q^38 + 3 * q^39 + 2 * q^40 + 9 * q^41 + 5 * q^42 - 2 * q^43 + 2 * q^45 - 15 * q^46 - q^47 - 2 * q^48 + q^49 + 2 * q^50 - 4 * q^51 - 3 * q^52 - 15 * q^53 - 2 * q^54 - 5 * q^56 + 3 * q^57 + 10 * q^58 - 3 * q^59 - 2 * q^60 + 6 * q^61 - 10 * q^62 - 5 * q^63 + 2 * q^64 - 3 * q^65 - 18 * q^67 + 4 * q^68 + 15 * q^69 - 5 * q^70 - 6 * q^71 + 2 * q^72 + 4 * q^73 - 13 * q^74 - 2 * q^75 - 3 * q^76 + 3 * q^78 - 16 * q^79 + 2 * q^80 + 2 * q^81 + 9 * q^82 - 4 * q^83 + 5 * q^84 + 4 * q^85 - 2 * q^86 - 10 * q^87 + 3 * q^89 + 2 * q^90 - 15 * q^92 + 10 * q^93 - q^94 - 3 * q^95 - 2 * q^96 - 4 * q^97 + q^98

Introduction

L-functions

Modular forms

Varieties

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Groups

Database

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