LMFDB - Embedded newform 2645.2.a.h.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [2645,2,Mod(1,2645)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(2645, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([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("2645.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 2645 = 5 \cdot 23^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	2645.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:	$21.1204313346$
Analytic rank:	$1$
Dimension:	$2$
Coefficient field:	$\Q(\sqrt{13}) $
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x - 3 $ x^2 - x - 3
Coefficient ring:	$\Z[a_1, a_2]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$2.30278$ of defining polynomial
Character	$\chi$	$=$	2645.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.30278 q^{2} +1.00000 q^{3} +3.30278 q^{4} +1.00000 q^{5} -2.30278 q^{6} -4.60555 q^{7} -3.00000 q^{8} -2.00000 q^{9} +O(q^{10})$	\(q-2.30278 q^{2} +1.00000 q^{3} +3.30278 q^{4} +1.00000 q^{5} -2.30278 q^{6} -4.60555 q^{7} -3.00000 q^{8} -2.00000 q^{9} -2.30278 q^{10} +4.60555 q^{11} +3.30278 q^{12} +5.60555 q^{13} +10.6056 q^{14} +1.00000 q^{15} +0.302776 q^{16} -6.00000 q^{17} +4.60555 q^{18} -1.39445 q^{19} +3.30278 q^{20} -4.60555 q^{21} -10.6056 q^{22} -3.00000 q^{24} +1.00000 q^{25} -12.9083 q^{26} -5.00000 q^{27} -15.2111 q^{28} -3.00000 q^{29} -2.30278 q^{30} +2.39445 q^{31} +5.30278 q^{32} +4.60555 q^{33} +13.8167 q^{34} -4.60555 q^{35} -6.60555 q^{36} +4.60555 q^{37} +3.21110 q^{38} +5.60555 q^{39} -3.00000 q^{40} +3.00000 q^{41} +10.6056 q^{42} -1.39445 q^{43} +15.2111 q^{44} -2.00000 q^{45} -3.00000 q^{47} +0.302776 q^{48} +14.2111 q^{49} -2.30278 q^{50} -6.00000 q^{51} +18.5139 q^{52} -9.21110 q^{53} +11.5139 q^{54} +4.60555 q^{55} +13.8167 q^{56} -1.39445 q^{57} +6.90833 q^{58} +3.30278 q^{60} -1.39445 q^{61} -5.51388 q^{62} +9.21110 q^{63} -12.8167 q^{64} +5.60555 q^{65} -10.6056 q^{66} -13.8167 q^{67} -19.8167 q^{68} +10.6056 q^{70} +7.60555 q^{71} +6.00000 q^{72} -6.81665 q^{73} -10.6056 q^{74} +1.00000 q^{75} -4.60555 q^{76} -21.2111 q^{77} -12.9083 q^{78} +1.39445 q^{79} +0.302776 q^{80} +1.00000 q^{81} -6.90833 q^{82} -3.21110 q^{83} -15.2111 q^{84} -6.00000 q^{85} +3.21110 q^{86} -3.00000 q^{87} -13.8167 q^{88} +7.81665 q^{89} +4.60555 q^{90} -25.8167 q^{91} +2.39445 q^{93} +6.90833 q^{94} -1.39445 q^{95} +5.30278 q^{96} +4.60555 q^{97} -32.7250 q^{98} -9.21110 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) $ 2 * q - q^2 + 2 * q^3 + 3 * q^4 + 2 * q^5 - q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9	\( 2 q - q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9} - q^{10} + 2 q^{11} + 3 q^{12} + 4 q^{13} + 14 q^{14} + 2 q^{15} - 3 q^{16} - 12 q^{17} + 2 q^{18} - 10 q^{19} + 3 q^{20} - 2 q^{21} - 14 q^{22} - 6 q^{24} + 2 q^{25} - 15 q^{26} - 10 q^{27} - 16 q^{28} - 6 q^{29} - q^{30} + 12 q^{31} + 7 q^{32} + 2 q^{33} + 6 q^{34} - 2 q^{35} - 6 q^{36} + 2 q^{37} - 8 q^{38} + 4 q^{39} - 6 q^{40} + 6 q^{41} + 14 q^{42} - 10 q^{43} + 16 q^{44} - 4 q^{45} - 6 q^{47} - 3 q^{48} + 14 q^{49} - q^{50} - 12 q^{51} + 19 q^{52} - 4 q^{53} + 5 q^{54} + 2 q^{55} + 6 q^{56} - 10 q^{57} + 3 q^{58} + 3 q^{60} - 10 q^{61} + 7 q^{62} + 4 q^{63} - 4 q^{64} + 4 q^{65} - 14 q^{66} - 6 q^{67} - 18 q^{68} + 14 q^{70} + 8 q^{71} + 12 q^{72} + 8 q^{73} - 14 q^{74} + 2 q^{75} - 2 q^{76} - 28 q^{77} - 15 q^{78} + 10 q^{79} - 3 q^{80} + 2 q^{81} - 3 q^{82} + 8 q^{83} - 16 q^{84} - 12 q^{85} - 8 q^{86} - 6 q^{87} - 6 q^{88} - 6 q^{89} + 2 q^{90} - 30 q^{91} + 12 q^{93} + 3 q^{94} - 10 q^{95} + 7 q^{96} + 2 q^{97} - 33 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 + 3 * q^4 + 2 * q^5 - q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9 - q^10 + 2 * q^11 + 3 * q^12 + 4 * q^13 + 14 * q^14 + 2 * q^15 - 3 * q^16 - 12 * q^17 + 2 * q^18 - 10 * q^19 + 3 * q^20 - 2 * q^21 - 14 * q^22 - 6 * q^24 + 2 * q^25 - 15 * q^26 - 10 * q^27 - 16 * q^28 - 6 * q^29 - q^30 + 12 * q^31 + 7 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^35 - 6 * q^36 + 2 * q^37 - 8 * q^38 + 4 * q^39 - 6 * q^40 + 6 * q^41 + 14 * q^42 - 10 * q^43 + 16 * q^44 - 4 * q^45 - 6 * q^47 - 3 * q^48 + 14 * q^49 - q^50 - 12 * q^51 + 19 * q^52 - 4 * q^53 + 5 * q^54 + 2 * q^55 + 6 * q^56 - 10 * q^57 + 3 * q^58 + 3 * q^60 - 10 * q^61 + 7 * q^62 + 4 * q^63 - 4 * q^64 + 4 * q^65 - 14 * q^66 - 6 * q^67 - 18 * q^68 + 14 * q^70 + 8 * q^71 + 12 * q^72 + 8 * q^73 - 14 * q^74 + 2 * q^75 - 2 * q^76 - 28 * q^77 - 15 * q^78 + 10 * q^79 - 3 * q^80 + 2 * q^81 - 3 * q^82 + 8 * q^83 - 16 * q^84 - 12 * q^85 - 8 * q^86 - 6 * q^87 - 6 * q^88 - 6 * q^89 + 2 * q^90 - 30 * q^91 + 12 * q^93 + 3 * q^94 - 10 * q^95 + 7 * q^96 + 2 * q^97 - 33 * q^98 - 4 * q^99

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 $

$2$	−2.30278	−1.62831	−0.814154	−	0.580649i	$-0.802799\pi$
$2$	−2.30278	−1.62831	−0.814154	+	0.580649i	$0.802799\pi$
$3$	1.00000	0.577350	0.288675	−	0.957427i	$-0.406785\pi$
$3$	1.00000	0.577350	0.288675	+	0.957427i	$0.406785\pi$
$4$	3.30278	1.65139
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−2.30278	−0.940104
$7$	−4.60555	−1.74073	−0.870367	−	0.492403i	$-0.836119\pi$
$7$	−4.60555	−1.74073	−0.870367	+	0.492403i	$0.836119\pi$
$8$	−3.00000	−1.06066
$9$	−2.00000	−0.666667
$10$	−2.30278	−0.728202
$11$	4.60555	1.38863	0.694313	−	0.719673i	$-0.255708\pi$
$11$	4.60555	1.38863	0.694313	+	0.719673i	$0.255708\pi$
$12$	3.30278	0.953429
$13$	5.60555	1.55470	0.777350	−	0.629068i	$-0.216563\pi$
$13$	5.60555	1.55470	0.777350	+	0.629068i	$0.216563\pi$
$14$	10.6056	2.83445
$15$	1.00000	0.258199
$16$	0.302776	0.0756939
$17$	−6.00000	−1.45521	−0.727607	−	0.685994i	$-0.759367\pi$
$17$	−6.00000	−1.45521	−0.727607	+	0.685994i	$0.759367\pi$
$18$	4.60555	1.08554
$19$	−1.39445	−0.319908	−0.159954	−	0.987124i	$-0.551135\pi$
$19$	−1.39445	−0.319908	−0.159954	+	0.987124i	$0.551135\pi$
$20$	3.30278	0.738523
$21$	−4.60555	−1.00501
$22$	−10.6056	−2.26111
$23$	0	0
$23$	0	0
$24$	−3.00000	−0.612372
$25$	1.00000	0.200000
$26$	−12.9083	−2.53153
$27$	−5.00000	−0.962250
$28$	−15.2111	−2.87463
$29$	−3.00000	−0.557086	−0.278543	−	0.960424i	$-0.589851\pi$
$29$	−3.00000	−0.557086	−0.278543	+	0.960424i	$0.589851\pi$
$30$	−2.30278	−0.420427
$31$	2.39445	0.430056	0.215028	−	0.976608i	$-0.431016\pi$
$31$	2.39445	0.430056	0.215028	+	0.976608i	$0.431016\pi$
$32$	5.30278	0.937407
$33$	4.60555	0.801724
$34$	13.8167	2.36954
$35$	−4.60555	−0.778480
$36$	−6.60555	−1.10093
$37$	4.60555	0.757148	0.378574	−	0.925571i	$-0.376415\pi$
$37$	4.60555	0.757148	0.378574	+	0.925571i	$0.376415\pi$
$38$	3.21110	0.520910
$39$	5.60555	0.897607
$40$	−3.00000	−0.474342
$41$	3.00000	0.468521	0.234261	−	0.972174i	$-0.424733\pi$
$41$	3.00000	0.468521	0.234261	+	0.972174i	$0.424733\pi$
$42$	10.6056	1.63647
$43$	−1.39445	−0.212651	−0.106326	−	0.994331i	$-0.533909\pi$
$43$	−1.39445	−0.212651	−0.106326	+	0.994331i	$0.533909\pi$
$44$	15.2111	2.29316
$45$	−2.00000	−0.298142
$46$	0	0
$47$	−3.00000	−0.437595	−0.218797	−	0.975770i	$-0.570213\pi$
$47$	−3.00000	−0.437595	−0.218797	+	0.975770i	$0.570213\pi$
$48$	0.302776	0.0437019
$49$	14.2111	2.03016
$50$	−2.30278	−0.325662
$51$	−6.00000	−0.840168
$52$	18.5139	2.56741
$53$	−9.21110	−1.26524	−0.632621	−	0.774461i	$-0.718021\pi$
$53$	−9.21110	−1.26524	−0.632621	+	0.774461i	$0.718021\pi$
$54$	11.5139	1.56684
$55$	4.60555	0.621012
$56$	13.8167	1.84633
$57$	−1.39445	−0.184699
$58$	6.90833	0.907108
$59$	0	0		−	1.00000i	$-0.5\pi$
$59$	0	0			1.00000i	$0.5\pi$
$60$	3.30278	0.426387
$61$	−1.39445	−0.178541	−0.0892704	−	0.996007i	$-0.528454\pi$
$61$	−1.39445	−0.178541	−0.0892704	+	0.996007i	$0.528454\pi$
$62$	−5.51388	−0.700263
$63$	9.21110	1.16049
$64$	−12.8167	−1.60208
$65$	5.60555	0.695283
$66$	−10.6056	−1.30545
$67$	−13.8167	−1.68797	−0.843986	−	0.536364i	$-0.819797\pi$
$67$	−13.8167	−1.68797	−0.843986	+	0.536364i	$0.819797\pi$
$68$	−19.8167	−2.40312
$69$	0	0
$70$	10.6056	1.26761
$71$	7.60555	0.902613	0.451306	−	0.892369i	$-0.350958\pi$
$71$	7.60555	0.902613	0.451306	+	0.892369i	$0.350958\pi$
$72$	6.00000	0.707107
$73$	−6.81665	−0.797829	−0.398914	−	0.916988i	$-0.630613\pi$
$73$	−6.81665	−0.797829	−0.398914	+	0.916988i	$0.630613\pi$
$74$	−10.6056	−1.23287
$75$	1.00000	0.115470
$76$	−4.60555	−0.528293
$77$	−21.2111	−2.41723
$78$	−12.9083	−1.46158
$79$	1.39445	0.156888	0.0784439	−	0.996919i	$-0.475005\pi$
$79$	1.39445	0.156888	0.0784439	+	0.996919i	$0.475005\pi$
$80$	0.302776	0.0338513
$81$	1.00000	0.111111
$82$	−6.90833	−0.762897
$83$	−3.21110	−0.352464	−0.176232	−	0.984349i	$-0.556391\pi$
$83$	−3.21110	−0.352464	−0.176232	+	0.984349i	$0.556391\pi$
$84$	−15.2111	−1.65967
$85$	−6.00000	−0.650791
$86$	3.21110	0.346262
$87$	−3.00000	−0.321634
$88$	−13.8167	−1.47286
$89$	7.81665	0.828564	0.414282	−	0.910149i	$-0.364033\pi$
$89$	7.81665	0.828564	0.414282	+	0.910149i	$0.364033\pi$
$90$	4.60555	0.485468
$91$	−25.8167	−2.70632
$92$	0	0
$93$	2.39445	0.248293
$94$	6.90833	0.712540
$95$	−1.39445	−0.143067
$96$	5.30278	0.541212
$97$	4.60555	0.467623	0.233811	−	0.972282i	$-0.424880\pi$
$97$	4.60555	0.467623	0.233811	+	0.972282i	$0.424880\pi$
$98$	−32.7250	−3.30572
$99$	−9.21110	−0.925751
$100$	3.30278	0.330278
$101$	−12.4222	−1.23606	−0.618028	−	0.786156i	$-0.712068\pi$
$101$	−12.4222	−1.23606	−0.618028	+	0.786156i	$0.712068\pi$
$102$	13.8167	1.36805
$103$	−15.2111	−1.49879	−0.749397	−	0.662121i	$-0.769657\pi$
$103$	−15.2111	−1.49879	−0.749397	+	0.662121i	$0.769657\pi$
$104$	−16.8167	−1.64901
$105$	−4.60555	−0.449456
$106$	21.2111	2.06020
$107$	−1.39445	−0.134806	−0.0674032	−	0.997726i	$-0.521471\pi$
$107$	−1.39445	−0.134806	−0.0674032	+	0.997726i	$0.521471\pi$
$108$	−16.5139	−1.58905
$109$	−1.39445	−0.133564	−0.0667820	−	0.997768i	$-0.521273\pi$
$109$	−1.39445	−0.133564	−0.0667820	+	0.997768i	$0.521273\pi$
$110$	−10.6056	−1.01120
$111$	4.60555	0.437140
$112$	−1.39445	−0.131763
$113$	7.39445	0.695611	0.347806	−	0.937567i	$-0.386927\pi$
$113$	7.39445	0.695611	0.347806	+	0.937567i	$0.386927\pi$
$114$	3.21110	0.300747
$115$	0	0
$116$	−9.90833	−0.919965
$117$	−11.2111	−1.03647
$118$	0	0
$119$	27.6333	2.53314
$120$	−3.00000	−0.273861
$121$	10.2111	0.928282
$122$	3.21110	0.290720
$123$	3.00000	0.270501
$124$	7.90833	0.710189
$125$	1.00000	0.0894427
$126$	−21.2111	−1.88964
$127$	−14.2111	−1.26103	−0.630516	−	0.776176i	$-0.717157\pi$
$127$	−14.2111	−1.26103	−0.630516	+	0.776176i	$0.717157\pi$
$128$	18.9083	1.67128
$129$	−1.39445	−0.122774
$130$	−12.9083	−1.13214
$131$	−1.60555	−0.140278	−0.0701388	−	0.997537i	$-0.522344\pi$
$131$	−1.60555	−0.140278	−0.0701388	+	0.997537i	$0.522344\pi$
$132$	15.2111	1.32396
$133$	6.42221	0.556876
$134$	31.8167	2.74854
$135$	−5.00000	−0.430331
$136$	18.0000	1.54349
$137$	0	0		−	1.00000i	$-0.5\pi$
$137$	0	0			1.00000i	$0.5\pi$
$138$	0	0
$139$	−2.39445	−0.203094	−0.101547	−	0.994831i	$-0.532379\pi$
$139$	−2.39445	−0.203094	−0.101547	+	0.994831i	$0.532379\pi$
$140$	−15.2111	−1.28557
$141$	−3.00000	−0.252646
$142$	−17.5139	−1.46973
$143$	25.8167	2.15890
$144$	−0.605551	−0.0504626
$145$	−3.00000	−0.249136
$146$	15.6972	1.29911
$147$	14.2111	1.17211
$148$	15.2111	1.25034
$149$	−21.2111	−1.73768	−0.868841	−	0.495092i	$-0.835134\pi$
$149$	−21.2111	−1.73768	−0.868841	+	0.495092i	$0.835134\pi$
$150$	−2.30278	−0.188021
$151$	−8.39445	−0.683131	−0.341565	−	0.939858i	$-0.610957\pi$
$151$	−8.39445	−0.683131	−0.341565	+	0.939858i	$0.610957\pi$
$152$	4.18335	0.339314
$153$	12.0000	0.970143
$154$	48.8444	3.93599
$155$	2.39445	0.192327
$156$	18.5139	1.48230
$157$	−22.6056	−1.80412	−0.902060	−	0.431611i	$-0.857945\pi$
$157$	−22.6056	−1.80412	−0.902060	+	0.431611i	$0.857945\pi$
$158$	−3.21110	−0.255462
$159$	−9.21110	−0.730488
$160$	5.30278	0.419221
$161$	0	0
$162$	−2.30278	−0.180923
$163$	13.4222	1.05131	0.525654	−	0.850698i	$-0.323821\pi$
$163$	13.4222	1.05131	0.525654	+	0.850698i	$0.323821\pi$
$164$	9.90833	0.773710
$165$	4.60555	0.358542
$166$	7.39445	0.573921
$167$	12.0000	0.928588	0.464294	−	0.885681i	$-0.346308\pi$
$167$	12.0000	0.928588	0.464294	+	0.885681i	$0.346308\pi$
$168$	13.8167	1.06598
$169$	18.4222	1.41709
$170$	13.8167	1.05969
$171$	2.78890	0.213272
$172$	−4.60555	−0.351170
$173$	21.6333	1.64475	0.822375	−	0.568946i	$-0.192649\pi$
$173$	21.6333	1.64475	0.822375	+	0.568946i	$0.192649\pi$
$174$	6.90833	0.523719
$175$	−4.60555	−0.348147
$176$	1.39445	0.105111
$177$	0	0
$178$	−18.0000	−1.34916
$179$	−4.81665	−0.360014	−0.180007	−	0.983665i	$-0.557612\pi$
$179$	−4.81665	−0.360014	−0.180007	+	0.983665i	$0.557612\pi$
$180$	−6.60555	−0.492349
$181$	13.8167	1.02698	0.513492	−	0.858094i	$-0.328352\pi$
$181$	13.8167	1.02698	0.513492	+	0.858094i	$0.328352\pi$
$182$	59.4500	4.40672
$183$	−1.39445	−0.103081
$184$	0	0
$185$	4.60555	0.338607
$186$	−5.51388	−0.404297
$187$	−27.6333	−2.02075
$188$	−9.90833	−0.722639
$189$	23.0278	1.67502
$190$	3.21110	0.232958
$191$	12.4222	0.898839	0.449420	−	0.893321i	$-0.351631\pi$
$191$	12.4222	0.898839	0.449420	+	0.893321i	$0.351631\pi$
$192$	−12.8167	−0.924962
$193$	−26.8167	−1.93030	−0.965152	−	0.261688i	$-0.915721\pi$
$193$	−26.8167	−1.93030	−0.965152	+	0.261688i	$0.915721\pi$
$194$	−10.6056	−0.761434
$195$	5.60555	0.401422
$196$	46.9361	3.35258
$197$	−13.6056	−0.969355	−0.484678	−	0.874693i	$-0.661063\pi$
$197$	−13.6056	−0.969355	−0.484678	+	0.874693i	$0.661063\pi$
$198$	21.2111	1.50741
$199$	−13.8167	−0.979437	−0.489718	−	0.871881i	$-0.662900\pi$
$199$	−13.8167	−0.979437	−0.489718	+	0.871881i	$0.662900\pi$
$200$	−3.00000	−0.212132
$201$	−13.8167	−0.974552
$202$	28.6056	2.01268
$203$	13.8167	0.969739
$204$	−19.8167	−1.38744
$205$	3.00000	0.209529
$206$	35.0278	2.44050
$207$	0	0
$208$	1.69722	0.117681
$209$	−6.42221	−0.444233
$210$	10.6056	0.731853
$211$	−17.2111	−1.18486	−0.592431	−	0.805622i	$-0.701832\pi$
$211$	−17.2111	−1.18486	−0.592431	+	0.805622i	$0.701832\pi$
$212$	−30.4222	−2.08941
$213$	7.60555	0.521124
$214$	3.21110	0.219506
$215$	−1.39445	−0.0951006
$216$	15.0000	1.02062
$217$	−11.0278	−0.748613
$218$	3.21110	0.217483
$219$	−6.81665	−0.460627
$220$	15.2111	1.02553
$221$	−33.6333	−2.26242
$222$	−10.6056	−0.711798
$223$	−13.2111	−0.884681	−0.442340	−	0.896847i	$-0.645852\pi$
$223$	−13.2111	−0.884681	−0.442340	+	0.896847i	$0.645852\pi$
$224$	−24.4222	−1.63178
$225$	−2.00000	−0.133333
$226$	−17.0278	−1.13267
$227$	−16.6056	−1.10215	−0.551075	−	0.834456i	$-0.685782\pi$
$227$	−16.6056	−1.10215	−0.551075	+	0.834456i	$0.685782\pi$
$228$	−4.60555	−0.305010
$229$	−22.6056	−1.49382	−0.746908	−	0.664927i	$-0.768463\pi$
$229$	−22.6056	−1.49382	−0.746908	+	0.664927i	$0.768463\pi$
$230$	0	0
$231$	−21.2111	−1.39559
$232$	9.00000	0.590879
$233$	−4.81665	−0.315549	−0.157775	−	0.987475i	$-0.550432\pi$
$233$	−4.81665	−0.315549	−0.157775	+	0.987475i	$0.550432\pi$
$234$	25.8167	1.68769
$235$	−3.00000	−0.195698
$236$	0	0
$237$	1.39445	0.0905792
$238$	−63.6333	−4.12473
$239$	23.2389	1.50320	0.751598	−	0.659621i	$-0.229283\pi$
$239$	23.2389	1.50320	0.751598	+	0.659621i	$0.229283\pi$
$240$	0.302776	0.0195441
$241$	−3.21110	−0.206845	−0.103423	−	0.994637i	$-0.532979\pi$
$241$	−3.21110	−0.206845	−0.103423	+	0.994637i	$0.532979\pi$
$242$	−23.5139	−1.51153
$243$	16.0000	1.02640
$244$	−4.60555	−0.294840
$245$	14.2111	0.907914
$246$	−6.90833	−0.440459
$247$	−7.81665	−0.497362
$248$	−7.18335	−0.456143
$249$	−3.21110	−0.203495
$250$	−2.30278	−0.145640
$251$	−8.78890	−0.554750	−0.277375	−	0.960762i	$-0.589464\pi$
$251$	−8.78890	−0.554750	−0.277375	+	0.960762i	$0.589464\pi$
$252$	30.4222	1.91642
$253$	0	0
$254$	32.7250	2.05335
$255$	−6.00000	−0.375735
$256$	−17.9083	−1.11927
$257$	−4.81665	−0.300455	−0.150227	−	0.988651i	$-0.548001\pi$
$257$	−4.81665	−0.300455	−0.150227	+	0.988651i	$0.548001\pi$
$258$	3.21110	0.199915
$259$	−21.2111	−1.31799
$260$	18.5139	1.14818
$261$	6.00000	0.371391
$262$	3.69722	0.228415
$263$	−7.81665	−0.481996	−0.240998	−	0.970526i	$-0.577475\pi$
$263$	−7.81665	−0.481996	−0.240998	+	0.970526i	$0.577475\pi$
$264$	−13.8167	−0.850356
$265$	−9.21110	−0.565834
$266$	−14.7889	−0.906765
$267$	7.81665	0.478371
$268$	−45.6333	−2.78750
$269$	15.4222	0.940308	0.470154	−	0.882584i	$-0.344198\pi$
$269$	15.4222	0.940308	0.470154	+	0.882584i	$0.344198\pi$
$270$	11.5139	0.700712
$271$	−26.4222	−1.60503	−0.802517	−	0.596629i	$-0.796506\pi$
$271$	−26.4222	−1.60503	−0.802517	+	0.596629i	$0.796506\pi$
$272$	−1.81665	−0.110151
$273$	−25.8167	−1.56249
$274$	0	0
$275$	4.60555	0.277725
$276$	0	0
$277$	18.0278	1.08318	0.541591	−	0.840642i	$-0.317822\pi$
$277$	18.0278	1.08318	0.541591	+	0.840642i	$0.317822\pi$
$278$	5.51388	0.330700
$279$	−4.78890	−0.286704
$280$	13.8167	0.825703
$281$	1.81665	0.108372	0.0541862	−	0.998531i	$-0.482744\pi$
$281$	1.81665	0.108372	0.0541862	+	0.998531i	$0.482744\pi$
$282$	6.90833	0.411385
$283$	−8.78890	−0.522446	−0.261223	−	0.965279i	$-0.584126\pi$
$283$	−8.78890	−0.522446	−0.261223	+	0.965279i	$0.584126\pi$
$284$	25.1194	1.49056
$285$	−1.39445	−0.0826000
$286$	−59.4500	−3.51535
$287$	−13.8167	−0.815571
$288$	−10.6056	−0.624938
$289$	19.0000	1.11765
$290$	6.90833	0.405671
$291$	4.60555	0.269982
$292$	−22.5139	−1.31753
$293$	−24.8444	−1.45143	−0.725713	−	0.687998i	$-0.758490\pi$
$293$	−24.8444	−1.45143	−0.725713	+	0.687998i	$0.758490\pi$
$294$	−32.7250	−1.90856
$295$	0	0
$296$	−13.8167	−0.803077
$297$	−23.0278	−1.33621
$298$	48.8444	2.82948
$299$	0	0
$300$	3.30278	0.190686
$301$	6.42221	0.370170
$302$	19.3305	1.11235
$303$	−12.4222	−0.713637
$304$	−0.422205	−0.0242151
$305$	−1.39445	−0.0798459
$306$	−27.6333	−1.57969
$307$	16.0000	0.913168	0.456584	−	0.889680i	$-0.349073\pi$
$307$	16.0000	0.913168	0.456584	+	0.889680i	$0.349073\pi$
$308$	−70.0555	−3.99178
$309$	−15.2111	−0.865329
$310$	−5.51388	−0.313167
$311$	10.3944	0.589415	0.294708	−	0.955587i	$-0.404778\pi$
$311$	10.3944	0.589415	0.294708	+	0.955587i	$0.404778\pi$
$312$	−16.8167	−0.952056
$313$	−14.7889	−0.835918	−0.417959	−	0.908466i	$-0.637254\pi$
$313$	−14.7889	−0.835918	−0.417959	+	0.908466i	$0.637254\pi$
$314$	52.0555	2.93766
$315$	9.21110	0.518987
$316$	4.60555	0.259083
$317$	27.2111	1.52833	0.764164	−	0.645022i	$-0.223152\pi$
$317$	27.2111	1.52833	0.764164	+	0.645022i	$0.223152\pi$
$318$	21.2111	1.18946
$319$	−13.8167	−0.773584
$320$	−12.8167	−0.716473
$321$	−1.39445	−0.0778305
$322$	0	0
$323$	8.36669	0.465535
$324$	3.30278	0.183488
$325$	5.60555	0.310940
$326$	−30.9083	−1.71185
$327$	−1.39445	−0.0771132
$328$	−9.00000	−0.496942
$329$	13.8167	0.761737
$330$	−10.6056	−0.583816
$331$	8.39445	0.461401	0.230700	−	0.973025i	$-0.425898\pi$
$331$	8.39445	0.461401	0.230700	+	0.973025i	$0.425898\pi$
$332$	−10.6056	−0.582055
$333$	−9.21110	−0.504765
$334$	−27.6333	−1.51203
$335$	−13.8167	−0.754884
$336$	−1.39445	−0.0760734
$337$	4.18335	0.227881	0.113941	−	0.993488i	$-0.463653\pi$
$337$	4.18335	0.227881	0.113941	+	0.993488i	$0.463653\pi$
$338$	−42.4222	−2.30746
$339$	7.39445	0.401611
$340$	−19.8167	−1.07471
$341$	11.0278	0.597186
$342$	−6.42221	−0.347273
$343$	−33.2111	−1.79323
$344$	4.18335	0.225551
$345$	0	0
$346$	−49.8167	−2.67816
$347$	−9.21110	−0.494478	−0.247239	−	0.968955i	$-0.579523\pi$
$347$	−9.21110	−0.494478	−0.247239	+	0.968955i	$0.579523\pi$
$348$	−9.90833	−0.531142
$349$	8.63331	0.462130	0.231065	−	0.972938i	$-0.425779\pi$
$349$	8.63331	0.462130	0.231065	+	0.972938i	$0.425779\pi$
$350$	10.6056	0.566891
$351$	−28.0278	−1.49601
$352$	24.4222	1.30171
$353$	7.60555	0.404803	0.202401	−	0.979303i	$-0.435125\pi$
$353$	7.60555	0.404803	0.202401	+	0.979303i	$0.435125\pi$
$354$	0	0
$355$	7.60555	0.403661
$356$	25.8167	1.36828
$357$	27.6333	1.46251
$358$	11.0917	0.586213
$359$	−14.2389	−0.751498	−0.375749	−	0.926721i	$-0.622615\pi$
$359$	−14.2389	−0.751498	−0.375749	+	0.926721i	$0.622615\pi$
$360$	6.00000	0.316228
$361$	−17.0555	−0.897659
$362$	−31.8167	−1.67225
$363$	10.2111	0.535944
$364$	−85.2666	−4.46918
$365$	−6.81665	−0.356800
$366$	3.21110	0.167847
$367$	−18.0000	−0.939592	−0.469796	−	0.882775i	$-0.655673\pi$
$367$	−18.0000	−0.939592	−0.469796	+	0.882775i	$0.655673\pi$
$368$	0	0
$369$	−6.00000	−0.312348
$370$	−10.6056	−0.551356
$371$	42.4222	2.20245
$372$	7.90833	0.410028
$373$	−27.2111	−1.40894	−0.704469	−	0.709735i	$-0.748815\pi$
$373$	−27.2111	−1.40894	−0.704469	+	0.709735i	$0.748815\pi$
$374$	63.6333	3.29040
$375$	1.00000	0.0516398
$376$	9.00000	0.464140
$377$	−16.8167	−0.866102
$378$	−53.0278	−2.72745
$379$	−6.42221	−0.329887	−0.164943	−	0.986303i	$-0.552744\pi$
$379$	−6.42221	−0.329887	−0.164943	+	0.986303i	$0.552744\pi$
$380$	−4.60555	−0.236260
$381$	−14.2111	−0.728057
$382$	−28.6056	−1.46359
$383$	19.8167	1.01258	0.506292	−	0.862362i	$-0.331016\pi$
$383$	19.8167	1.01258	0.506292	+	0.862362i	$0.331016\pi$
$384$	18.9083	0.964912
$385$	−21.2111	−1.08102
$386$	61.7527	3.14313
$387$	2.78890	0.141768
$388$	15.2111	0.772227
$389$	−12.0000	−0.608424	−0.304212	−	0.952604i	$-0.598393\pi$
$389$	−12.0000	−0.608424	−0.304212	+	0.952604i	$0.598393\pi$
$390$	−12.9083	−0.653639
$391$	0	0
$392$	−42.6333	−2.15331
$393$	−1.60555	−0.0809893
$394$	31.3305	1.57841
$395$	1.39445	0.0701623
$396$	−30.4222	−1.52877
$397$	−6.02776	−0.302524	−0.151262	−	0.988494i	$-0.548334\pi$
$397$	−6.02776	−0.302524	−0.151262	+	0.988494i	$0.548334\pi$
$398$	31.8167	1.59482
$399$	6.42221	0.321512
$400$	0.302776	0.0151388
$401$	33.6333	1.67957	0.839784	−	0.542921i	$-0.182682\pi$
$401$	33.6333	1.67957	0.839784	+	0.542921i	$0.182682\pi$
$402$	31.8167	1.58687
$403$	13.4222	0.668608
$404$	−41.0278	−2.04121
$405$	1.00000	0.0496904
$406$	−31.8167	−1.57903
$407$	21.2111	1.05140
$408$	18.0000	0.891133
$409$	−1.42221	−0.0703235	−0.0351618	−	0.999382i	$-0.511195\pi$
$409$	−1.42221	−0.0703235	−0.0351618	+	0.999382i	$0.511195\pi$
$410$	−6.90833	−0.341178
$411$	0	0
$412$	−50.2389	−2.47509
$413$	0	0
$414$	0	0
$415$	−3.21110	−0.157627
$416$	29.7250	1.45739
$417$	−2.39445	−0.117257
$418$	14.7889	0.723349
$419$	−19.8167	−0.968107	−0.484053	−	0.875038i	$-0.660836\pi$
$419$	−19.8167	−0.968107	−0.484053	+	0.875038i	$0.660836\pi$
$420$	−15.2111	−0.742226
$421$	16.6056	0.809305	0.404653	−	0.914471i	$-0.367392\pi$
$421$	16.6056	0.809305	0.404653	+	0.914471i	$0.367392\pi$
$422$	39.6333	1.92932
$423$	6.00000	0.291730
$424$	27.6333	1.34199
$425$	−6.00000	−0.291043
$426$	−17.5139	−0.848550
$427$	6.42221	0.310792
$428$	−4.60555	−0.222618
$429$	25.8167	1.24644
$430$	3.21110	0.154853
$431$	−35.4500	−1.70756	−0.853782	−	0.520630i	$-0.825697\pi$
$431$	−35.4500	−1.70756	−0.853782	+	0.520630i	$0.825697\pi$
$432$	−1.51388	−0.0728365
$433$	−8.78890	−0.422367	−0.211184	−	0.977446i	$-0.567732\pi$
$433$	−8.78890	−0.422367	−0.211184	+	0.977446i	$0.567732\pi$
$434$	25.3944	1.21897
$435$	−3.00000	−0.143839
$436$	−4.60555	−0.220566
$437$	0	0
$438$	15.6972	0.750042
$439$	3.18335	0.151933	0.0759664	−	0.997110i	$-0.475796\pi$
$439$	3.18335	0.151933	0.0759664	+	0.997110i	$0.475796\pi$
$440$	−13.8167	−0.658683
$441$	−28.4222	−1.35344
$442$	77.4500	3.68392
$443$	−27.0000	−1.28281	−0.641404	−	0.767203i	$-0.721648\pi$
$443$	−27.0000	−1.28281	−0.641404	+	0.767203i	$0.721648\pi$
$444$	15.2111	0.721887
$445$	7.81665	0.370545
$446$	30.4222	1.44053
$447$	−21.2111	−1.00325
$448$	59.0278	2.78880
$449$	−15.2111	−0.717856	−0.358928	−	0.933365i	$-0.616858\pi$
$449$	−15.2111	−0.717856	−0.358928	+	0.933365i	$0.616858\pi$
$450$	4.60555	0.217108
$451$	13.8167	0.650601
$452$	24.4222	1.14872
$453$	−8.39445	−0.394406
$454$	38.2389	1.79464
$455$	−25.8167	−1.21030
$456$	4.18335	0.195903
$457$	18.0000	0.842004	0.421002	−	0.907060i	$-0.361678\pi$
$457$	18.0000	0.842004	0.421002	+	0.907060i	$0.361678\pi$
$458$	52.0555	2.43239
$459$	30.0000	1.40028
$460$	0	0
$461$	12.6333	0.588392	0.294196	−	0.955745i	$-0.404948\pi$
$461$	12.6333	0.588392	0.294196	+	0.955745i	$0.404948\pi$
$462$	48.8444	2.27245
$463$	−31.6333	−1.47012	−0.735062	−	0.678000i	$-0.762847\pi$
$463$	−31.6333	−1.47012	−0.735062	+	0.678000i	$0.762847\pi$
$464$	−0.908327	−0.0421680
$465$	2.39445	0.111040
$466$	11.0917	0.513812
$467$	−27.6333	−1.27872	−0.639358	−	0.768909i	$-0.720800\pi$
$467$	−27.6333	−1.27872	−0.639358	+	0.768909i	$0.720800\pi$
$468$	−37.0278	−1.71161
$469$	63.6333	2.93831
$470$	6.90833	0.318657
$471$	−22.6056	−1.04161
$472$	0	0
$473$	−6.42221	−0.295293
$474$	−3.21110	−0.147491
$475$	−1.39445	−0.0639817
$476$	91.2666	4.18320
$477$	18.4222	0.843495
$478$	−53.5139	−2.44767
$479$	−20.7889	−0.949869	−0.474934	−	0.880021i	$-0.657528\pi$
$479$	−20.7889	−0.949869	−0.474934	+	0.880021i	$0.657528\pi$
$480$	5.30278	0.242037
$481$	25.8167	1.17714
$482$	7.39445	0.336808
$483$	0	0
$484$	33.7250	1.53295
$485$	4.60555	0.209127
$486$	−36.8444	−1.67130
$487$	32.2111	1.45962	0.729812	−	0.683648i	$-0.239607\pi$
$487$	32.2111	1.45962	0.729812	+	0.683648i	$0.239607\pi$
$488$	4.18335	0.189371
$489$	13.4222	0.606973
$490$	−32.7250	−1.47836
$491$	−35.2389	−1.59031	−0.795154	−	0.606408i	$-0.792610\pi$
$491$	−35.2389	−1.59031	−0.795154	+	0.606408i	$0.792610\pi$
$492$	9.90833	0.446702
$493$	18.0000	0.810679
$494$	18.0000	0.809858
$495$	−9.21110	−0.414008
$496$	0.724981	0.0325526
$497$	−35.0278	−1.57121
$498$	7.39445	0.331353
$499$	−33.6056	−1.50439	−0.752196	−	0.658940i	$-0.771005\pi$
$499$	−33.6056	−1.50439	−0.752196	+	0.658940i	$0.771005\pi$
$500$	3.30278	0.147705
$501$	12.0000	0.536120
$502$	20.2389	0.903304
$503$	30.4222	1.35646	0.678230	−	0.734850i	$-0.262748\pi$
$503$	30.4222	1.35646	0.678230	+	0.734850i	$0.262748\pi$
$504$	−27.6333	−1.23089
$505$	−12.4222	−0.552781
$506$	0	0
$507$	18.4222	0.818159
$508$	−46.9361	−2.08245
$509$	6.21110	0.275302	0.137651	−	0.990481i	$-0.456045\pi$
$509$	6.21110	0.275302	0.137651	+	0.990481i	$0.456045\pi$
$510$	13.8167	0.611812
$511$	31.3944	1.38881
$512$	3.42221	0.151242
$513$	6.97224	0.307832
$514$	11.0917	0.489233
$515$	−15.2111	−0.670281
$516$	−4.60555	−0.202748
$517$	−13.8167	−0.607656
$518$	48.8444	2.14610
$519$	21.6333	0.949597
$520$	−16.8167	−0.737459
$521$	36.0000	1.57719	0.788594	−	0.614914i	$-0.210809\pi$
$521$	36.0000	1.57719	0.788594	+	0.614914i	$0.210809\pi$
$522$	−13.8167	−0.604739
$523$	32.2389	1.40971	0.704853	−	0.709353i	$-0.251013\pi$
$523$	32.2389	1.40971	0.704853	+	0.709353i	$0.251013\pi$
$524$	−5.30278	−0.231653
$525$	−4.60555	−0.201003
$526$	18.0000	0.784837
$527$	−14.3667	−0.625823
$528$	1.39445	0.0606856
$529$	0	0
$530$	21.2111	0.921351
$531$	0	0
$532$	21.2111	0.919618
$533$	16.8167	0.728410
$534$	−18.0000	−0.778936
$535$	−1.39445	−0.0602873
$536$	41.4500	1.79037
$537$	−4.81665	−0.207854
$538$	−35.5139	−1.53111
$539$	65.4500	2.81913
$540$	−16.5139	−0.710644
$541$	−7.00000	−0.300954	−0.150477	−	0.988614i	$-0.548081\pi$
$541$	−7.00000	−0.300954	−0.150477	+	0.988614i	$0.548081\pi$
$542$	60.8444	2.61349
$543$	13.8167	0.592929
$544$	−31.8167	−1.36413
$545$	−1.39445	−0.0597316
$546$	59.4500	2.54422
$547$	10.6333	0.454647	0.227324	−	0.973819i	$-0.427002\pi$
$547$	10.6333	0.454647	0.227324	+	0.973819i	$0.427002\pi$
$548$	0	0
$549$	2.78890	0.119027
$550$	−10.6056	−0.452222
$551$	4.18335	0.178217
$552$	0	0
$553$	−6.42221	−0.273100
$554$	−41.5139	−1.76376
$555$	4.60555	0.195495
$556$	−7.90833	−0.335388
$557$	−17.0278	−0.721489	−0.360745	−	0.932665i	$-0.617477\pi$
$557$	−17.0278	−0.721489	−0.360745	+	0.932665i	$0.617477\pi$
$558$	11.0278	0.466842
$559$	−7.81665	−0.330609
$560$	−1.39445	−0.0589262
$561$	−27.6333	−1.16668
$562$	−4.18335	−0.176464
$563$	15.6333	0.658865	0.329433	−	0.944179i	$-0.393143\pi$
$563$	15.6333	0.658865	0.329433	+	0.944179i	$0.393143\pi$
$564$	−9.90833	−0.417216
$565$	7.39445	0.311087
$566$	20.2389	0.850703
$567$	−4.60555	−0.193415
$568$	−22.8167	−0.957366
$569$	15.2111	0.637683	0.318841	−	0.947808i	$-0.396706\pi$
$569$	15.2111	0.637683	0.318841	+	0.947808i	$0.396706\pi$
$570$	3.21110	0.134498
$571$	−20.7889	−0.869988	−0.434994	−	0.900433i	$-0.643250\pi$
$571$	−20.7889	−0.869988	−0.434994	+	0.900433i	$0.643250\pi$
$572$	85.2666	3.56518
$573$	12.4222	0.518945
$574$	31.8167	1.32800
$575$	0	0
$576$	25.6333	1.06805
$577$	−24.0278	−1.00029	−0.500144	−	0.865942i	$-0.666720\pi$
$577$	−24.0278	−1.00029	−0.500144	+	0.865942i	$0.666720\pi$
$578$	−43.7527	−1.81987
$579$	−26.8167	−1.11446
$580$	−9.90833	−0.411421
$581$	14.7889	0.613547
$582$	−10.6056	−0.439614
$583$	−42.4222	−1.75695
$584$	20.4500	0.846225
$585$	−11.2111	−0.463522
$586$	57.2111	2.36337
$587$	18.2111	0.751653	0.375826	−	0.926690i	$-0.377359\pi$
$587$	18.2111	0.751653	0.375826	+	0.926690i	$0.377359\pi$
$588$	46.9361	1.93561
$589$	−3.33894	−0.137578
$590$	0	0
$591$	−13.6056	−0.559658
$592$	1.39445	0.0573115
$593$	−8.78890	−0.360917	−0.180458	−	0.983583i	$-0.557758\pi$
$593$	−8.78890	−0.360917	−0.180458	+	0.983583i	$0.557758\pi$
$594$	53.0278	2.17576
$595$	27.6333	1.13286
$596$	−70.0555	−2.86959
$597$	−13.8167	−0.565478
$598$	0	0
$599$	−12.0000	−0.490307	−0.245153	−	0.969484i	$-0.578838\pi$
$599$	−12.0000	−0.490307	−0.245153	+	0.969484i	$0.578838\pi$
$600$	−3.00000	−0.122474
$601$	8.63331	0.352160	0.176080	−	0.984376i	$-0.443658\pi$
$601$	8.63331	0.352160	0.176080	+	0.984376i	$0.443658\pi$
$602$	−14.7889	−0.602750
$603$	27.6333	1.12532
$604$	−27.7250	−1.12811
$605$	10.2111	0.415140
$606$	28.6056	1.16202
$607$	−25.2111	−1.02329	−0.511644	−	0.859198i	$-0.670963\pi$
$607$	−25.2111	−1.02329	−0.511644	+	0.859198i	$0.670963\pi$
$608$	−7.39445	−0.299884
$609$	13.8167	0.559879
$610$	3.21110	0.130014
$611$	−16.8167	−0.680329
$612$	39.6333	1.60208
$613$	−42.8444	−1.73047	−0.865235	−	0.501367i	$-0.832831\pi$
$613$	−42.8444	−1.73047	−0.865235	+	0.501367i	$0.832831\pi$
$614$	−36.8444	−1.48692
$615$	3.00000	0.120972
$616$	63.6333	2.56386
$617$	38.2389	1.53944	0.769719	−	0.638383i	$-0.220396\pi$
$617$	38.2389	1.53944	0.769719	+	0.638383i	$0.220396\pi$
$618$	35.0278	1.40902
$619$	−9.21110	−0.370225	−0.185113	−	0.982717i	$-0.559265\pi$
$619$	−9.21110	−0.370225	−0.185113	+	0.982717i	$0.559265\pi$
$620$	7.90833	0.317606
$621$	0	0
$622$	−23.9361	−0.959750
$623$	−36.0000	−1.44231
$624$	1.69722	0.0679434
$625$	1.00000	0.0400000
$626$	34.0555	1.36113
$627$	−6.42221	−0.256478
$628$	−74.6611	−2.97930
$629$	−27.6333	−1.10181
$630$	−21.2111	−0.845071
$631$	−4.18335	−0.166536	−0.0832682	−	0.996527i	$-0.526536\pi$
$631$	−4.18335	−0.166536	−0.0832682	+	0.996527i	$0.526536\pi$
$632$	−4.18335	−0.166405
$633$	−17.2111	−0.684080
$634$	−62.6611	−2.48859
$635$	−14.2111	−0.563950
$636$	−30.4222	−1.20632
$637$	79.6611	3.15629
$638$	31.8167	1.25963
$639$	−15.2111	−0.601742
$640$	18.9083	0.747417
$641$	10.6056	0.418894	0.209447	−	0.977820i	$-0.432834\pi$
$641$	10.6056	0.418894	0.209447	+	0.977820i	$0.432834\pi$
$642$	3.21110	0.126732
$643$	−30.8444	−1.21638	−0.608192	−	0.793790i	$-0.708105\pi$
$643$	−30.8444	−1.21638	−0.608192	+	0.793790i	$0.708105\pi$
$644$	0	0
$645$	−1.39445	−0.0549064
$646$	−19.2666	−0.758035
$647$	−24.2111	−0.951837	−0.475918	−	0.879489i	$-0.657884\pi$
$647$	−24.2111	−0.951837	−0.475918	+	0.879489i	$0.657884\pi$
$648$	−3.00000	−0.117851
$649$	0	0
$650$	−12.9083	−0.506306
$651$	−11.0278	−0.432212
$652$	44.3305	1.73612
$653$	29.2389	1.14420	0.572102	−	0.820182i	$-0.306128\pi$
$653$	29.2389	1.14420	0.572102	+	0.820182i	$0.306128\pi$
$654$	3.21110	0.125564
$655$	−1.60555	−0.0627341
$656$	0.908327	0.0354642
$657$	13.6333	0.531886
$658$	−31.8167	−1.24034
$659$	−21.6333	−0.842714	−0.421357	−	0.906895i	$-0.638446\pi$
$659$	−21.6333	−0.842714	−0.421357	+	0.906895i	$0.638446\pi$
$660$	15.2111	0.592091
$661$	36.8444	1.43308	0.716541	−	0.697545i	$-0.245724\pi$
$661$	36.8444	1.43308	0.716541	+	0.697545i	$0.245724\pi$
$662$	−19.3305	−0.751302
$663$	−33.6333	−1.30621
$664$	9.63331	0.373845
$665$	6.42221	0.249042
$666$	21.2111	0.821914
$667$	0	0
$668$	39.6333	1.53346
$669$	−13.2111	−0.510771
$670$	31.8167	1.22918
$671$	−6.42221	−0.247926
$672$	−24.4222	−0.942107
$673$	36.0278	1.38877	0.694384	−	0.719605i	$-0.255677\pi$
$673$	36.0278	1.38877	0.694384	+	0.719605i	$0.255677\pi$
$674$	−9.63331	−0.371061
$675$	−5.00000	−0.192450
$676$	60.8444	2.34017
$677$	39.6333	1.52323	0.761616	−	0.648029i	$-0.224406\pi$
$677$	39.6333	1.52323	0.761616	+	0.648029i	$0.224406\pi$
$678$	−17.0278	−0.653947
$679$	−21.2111	−0.814007
$680$	18.0000	0.690268
$681$	−16.6056	−0.636326
$682$	−25.3944	−0.972404
$683$	−9.00000	−0.344375	−0.172188	−	0.985064i	$-0.555084\pi$
$683$	−9.00000	−0.344375	−0.172188	+	0.985064i	$0.555084\pi$
$684$	9.21110	0.352195
$685$	0	0
$686$	76.4777	2.91993
$687$	−22.6056	−0.862456
$688$	−0.422205	−0.0160964
$689$	−51.6333	−1.96707
$690$	0	0
$691$	−14.4222	−0.548647	−0.274323	−	0.961638i	$-0.588454\pi$
$691$	−14.4222	−0.548647	−0.274323	+	0.961638i	$0.588454\pi$
$692$	71.4500	2.71612
$693$	42.4222	1.61149
$694$	21.2111	0.805162
$695$	−2.39445	−0.0908266
$696$	9.00000	0.341144
$697$	−18.0000	−0.681799
$698$	−19.8806	−0.752491
$699$	−4.81665	−0.182183
$700$	−15.2111	−0.574926
$701$	17.4500	0.659076	0.329538	−	0.944142i	$-0.393107\pi$
$701$	17.4500	0.659076	0.329538	+	0.944142i	$0.393107\pi$
$702$	64.5416	2.43597
$703$	−6.42221	−0.242218
$704$	−59.0278	−2.22469
$705$	−3.00000	−0.112987
$706$	−17.5139	−0.659144
$707$	57.2111	2.15164
$708$	0	0
$709$	40.6056	1.52497	0.762487	−	0.647004i	$-0.223978\pi$
$709$	40.6056	1.52497	0.762487	+	0.647004i	$0.223978\pi$
$710$	−17.5139	−0.657284
$711$	−2.78890	−0.104592
$712$	−23.4500	−0.878824
$713$	0	0
$714$	−63.6333	−2.38142
$715$	25.8167	0.965488
$716$	−15.9083	−0.594522
$717$	23.2389	0.867871
$718$	32.7889	1.22367
$719$	36.8444	1.37406	0.687032	−	0.726627i	$-0.258913\pi$
$719$	36.8444	1.37406	0.687032	+	0.726627i	$0.258913\pi$
$720$	−0.605551	−0.0225676
$721$	70.0555	2.60900
$722$	39.2750	1.46166
$723$	−3.21110	−0.119422
$724$	45.6333	1.69595
$725$	−3.00000	−0.111417
$726$	−23.5139	−0.872682
$727$	42.8444	1.58901	0.794506	−	0.607257i	$-0.207730\pi$
$727$	42.8444	1.58901	0.794506	+	0.607257i	$0.207730\pi$
$728$	77.4500	2.87049
$729$	13.0000	0.481481
$730$	15.6972	0.580980
$731$	8.36669	0.309453
$732$	−4.60555	−0.170226
$733$	18.0000	0.664845	0.332423	−	0.943131i	$-0.392134\pi$
$733$	18.0000	0.664845	0.332423	+	0.943131i	$0.392134\pi$
$734$	41.4500	1.52995
$735$	14.2111	0.524184
$736$	0	0
$737$	−63.6333	−2.34396
$738$	13.8167	0.508598
$739$	−27.2389	−1.00200	−0.500999	−	0.865448i	$-0.667034\pi$
$739$	−27.2389	−1.00200	−0.500999	+	0.865448i	$0.667034\pi$
$740$	15.2111	0.559171
$741$	−7.81665	−0.287152
$742$	−97.6888	−3.58627
$743$	33.6333	1.23389	0.616943	−	0.787008i	$-0.288371\pi$
$743$	33.6333	1.23389	0.616943	+	0.787008i	$0.288371\pi$
$744$	−7.18335	−0.263354
$745$	−21.2111	−0.777115
$746$	62.6611	2.29418
$747$	6.42221	0.234976
$748$	−91.2666	−3.33704
$749$	6.42221	0.234662
$750$	−2.30278	−0.0840855
$751$	41.0278	1.49712	0.748562	−	0.663065i	$-0.230745\pi$
$751$	41.0278	1.49712	0.748562	+	0.663065i	$0.230745\pi$
$752$	−0.908327	−0.0331233
$753$	−8.78890	−0.320285
$754$	38.7250	1.41028
$755$	−8.39445	−0.305505
$756$	76.0555	2.76611
$757$	31.3944	1.14105	0.570525	−	0.821280i	$-0.306740\pi$
$757$	31.3944	1.14105	0.570525	+	0.821280i	$0.306740\pi$
$758$	14.7889	0.537157
$759$	0	0
$760$	4.18335	0.151746
$761$	48.6333	1.76296	0.881478	−	0.472225i	$-0.156549\pi$
$761$	48.6333	1.76296	0.881478	+	0.472225i	$0.156549\pi$
$762$	32.7250	1.18550
$763$	6.42221	0.232499
$764$	41.0278	1.48433
$765$	12.0000	0.433861
$766$	−45.6333	−1.64880
$767$	0	0
$768$	−17.9083	−0.646211
$769$	−45.6333	−1.64558	−0.822790	−	0.568346i	$-0.807583\pi$
$769$	−45.6333	−1.64558	−0.822790	+	0.568346i	$0.807583\pi$
$770$	48.8444	1.76023
$771$	−4.81665	−0.173468
$772$	−88.5694	−3.18768
$773$	1.39445	0.0501548	0.0250774	−	0.999686i	$-0.492017\pi$
$773$	1.39445	0.0501548	0.0250774	+	0.999686i	$0.492017\pi$
$774$	−6.42221	−0.230841
$775$	2.39445	0.0860111
$776$	−13.8167	−0.495989
$777$	−21.2111	−0.760944
$778$	27.6333	0.990702
$779$	−4.18335	−0.149884
$780$	18.5139	0.662903
$781$	35.0278	1.25339
$782$	0	0
$783$	15.0000	0.536056
$784$	4.30278	0.153671
$785$	−22.6056	−0.806827
$786$	3.69722	0.131876
$787$	9.21110	0.328340	0.164170	−	0.986432i	$-0.447505\pi$
$787$	9.21110	0.328340	0.164170	+	0.986432i	$0.447505\pi$
$788$	−44.9361	−1.60078
$789$	−7.81665	−0.278280
$790$	−3.21110	−0.114246
$791$	−34.0555	−1.21087
$792$	27.6333	0.981907
$793$	−7.81665	−0.277578
$794$	13.8806	0.492603
$795$	−9.21110	−0.326684
$796$	−45.6333	−1.61743
$797$	25.3944	0.899518	0.449759	−	0.893150i	$-0.351510\pi$
$797$	25.3944	0.899518	0.449759	+	0.893150i	$0.351510\pi$
$798$	−14.7889	−0.523521
$799$	18.0000	0.636794
$800$	5.30278	0.187481
$801$	−15.6333	−0.552376
$802$	−77.4500	−2.73485
$803$	−31.3944	−1.10789
$804$	−45.6333	−1.60936
$805$	0	0
$806$	−30.9083	−1.08870
$807$	15.4222	0.542887
$808$	37.2666	1.31103
$809$	−30.8444	−1.08443	−0.542216	−	0.840239i	$-0.682414\pi$
$809$	−30.8444	−1.08443	−0.542216	+	0.840239i	$0.682414\pi$
$810$	−2.30278	−0.0809113
$811$	42.0278	1.47579	0.737897	−	0.674913i	$-0.235819\pi$
$811$	42.0278	1.47579	0.737897	+	0.674913i	$0.235819\pi$
$812$	45.6333	1.60142
$813$	−26.4222	−0.926667
$814$	−48.8444	−1.71200
$815$	13.4222	0.470159
$816$	−1.81665	−0.0635956
$817$	1.94449	0.0680290
$818$	3.27502	0.114508
$819$	51.6333	1.80421
$820$	9.90833	0.346014
$821$	−33.6333	−1.17381	−0.586905	−	0.809656i	$-0.699654\pi$
$821$	−33.6333	−1.17381	−0.586905	+	0.809656i	$0.699654\pi$
$822$	0	0
$823$	47.0555	1.64025	0.820126	−	0.572183i	$-0.193903\pi$
$823$	47.0555	1.64025	0.820126	+	0.572183i	$0.193903\pi$
$824$	45.6333	1.58971
$825$	4.60555	0.160345
$826$	0	0
$827$	33.2111	1.15486	0.577432	−	0.816439i	$-0.304055\pi$
$827$	33.2111	1.15486	0.577432	+	0.816439i	$0.304055\pi$
$828$	0	0
$829$	44.4222	1.54285	0.771423	−	0.636322i	$-0.219545\pi$
$829$	44.4222	1.54285	0.771423	+	0.636322i	$0.219545\pi$
$830$	7.39445	0.256665
$831$	18.0278	0.625376
$832$	−71.8444	−2.49076
$833$	−85.2666	−2.95431
$834$	5.51388	0.190930
$835$	12.0000	0.415277
$836$	−21.2111	−0.733601
$837$	−11.9722	−0.413821
$838$	45.6333	1.57638
$839$	−10.1833	−0.351568	−0.175784	−	0.984429i	$-0.556246\pi$
$839$	−10.1833	−0.351568	−0.175784	+	0.984429i	$0.556246\pi$
$840$	13.8167	0.476720
$841$	−20.0000	−0.689655
$842$	−38.2389	−1.31780
$843$	1.81665	0.0625689
$844$	−56.8444	−1.95667
$845$	18.4222	0.633743
$846$	−13.8167	−0.475026
$847$	−47.0278	−1.61589
$848$	−2.78890	−0.0957711
$849$	−8.78890	−0.301634
$850$	13.8167	0.473907
$851$	0	0
$852$	25.1194	0.860577
$853$	−3.57779	−0.122501	−0.0612507	−	0.998122i	$-0.519509\pi$
$853$	−3.57779	−0.122501	−0.0612507	+	0.998122i	$0.519509\pi$
$854$	−14.7889	−0.506066
$855$	2.78890	0.0953783
$856$	4.18335	0.142984
$857$	−13.1833	−0.450335	−0.225167	−	0.974320i	$-0.572293\pi$
$857$	−13.1833	−0.450335	−0.225167	+	0.974320i	$0.572293\pi$
$858$	−59.4500	−2.02959
$859$	−12.0278	−0.410382	−0.205191	−	0.978722i	$-0.565782\pi$
$859$	−12.0278	−0.410382	−0.205191	+	0.978722i	$0.565782\pi$
$860$	−4.60555	−0.157048
$861$	−13.8167	−0.470870
$862$	81.6333	2.78044
$863$	3.00000	0.102121	0.0510606	−	0.998696i	$-0.483740\pi$
$863$	3.00000	0.102121	0.0510606	+	0.998696i	$0.483740\pi$
$864$	−26.5139	−0.902020
$865$	21.6333	0.735555
$866$	20.2389	0.687744
$867$	19.0000	0.645274
$868$	−36.4222	−1.23625
$869$	6.42221	0.217858
$870$	6.90833	0.234214
$871$	−77.4500	−2.62429
$872$	4.18335	0.141666
$873$	−9.21110	−0.311749
$874$	0	0
$875$	−4.60555	−0.155696
$876$	−22.5139	−0.760673
$877$	−41.6333	−1.40586	−0.702928	−	0.711261i	$-0.748125\pi$
$877$	−41.6333	−1.40586	−0.702928	+	0.711261i	$0.748125\pi$
$878$	−7.33053	−0.247393
$879$	−24.8444	−0.837981
$880$	1.39445	0.0470069
$881$	6.00000	0.202145	0.101073	−	0.994879i	$-0.467773\pi$
$881$	6.00000	0.202145	0.101073	+	0.994879i	$0.467773\pi$
$882$	65.4500	2.20381
$883$	−34.7889	−1.17074	−0.585370	−	0.810766i	$-0.699051\pi$
$883$	−34.7889	−1.17074	−0.585370	+	0.810766i	$0.699051\pi$
$884$	−111.083	−3.73613
$885$	0	0
$886$	62.1749	2.08881
$887$	33.8444	1.13638	0.568192	−	0.822896i	$-0.307643\pi$
$887$	33.8444	1.13638	0.568192	+	0.822896i	$0.307643\pi$
$888$	−13.8167	−0.463657
$889$	65.4500	2.19512
$890$	−18.0000	−0.603361
$891$	4.60555	0.154292
$892$	−43.6333	−1.46095
$893$	4.18335	0.139990
$894$	48.8444	1.63360
$895$	−4.81665	−0.161003
$896$	−87.0833	−2.90925
$897$	0	0
$898$	35.0278	1.16889
$899$	−7.18335	−0.239578
$900$	−6.60555	−0.220185
$901$	55.2666	1.84120
$902$	−31.8167	−1.05938
$903$	6.42221	0.213718
$904$	−22.1833	−0.737807
$905$	13.8167	0.459281
$906$	19.3305	0.642214
$907$	41.0278	1.36230	0.681152	−	0.732142i	$-0.261479\pi$
$907$	41.0278	1.36230	0.681152	+	0.732142i	$0.261479\pi$
$908$	−54.8444	−1.82008
$909$	24.8444	0.824037
$910$	59.4500	1.97075
$911$	53.0278	1.75689	0.878444	−	0.477845i	$-0.158582\pi$
$911$	53.0278	1.75689	0.878444	+	0.477845i	$0.158582\pi$
$912$	−0.422205	−0.0139806
$913$	−14.7889	−0.489441
$914$	−41.4500	−1.37104
$915$	−1.39445	−0.0460991
$916$	−74.6611	−2.46687
$917$	7.39445	0.244186
$918$	−69.0833	−2.28009
$919$	38.6611	1.27531	0.637655	−	0.770322i	$-0.279904\pi$
$919$	38.6611	1.27531	0.637655	+	0.770322i	$0.279904\pi$
$920$	0	0
$921$	16.0000	0.527218
$922$	−29.0917	−0.958083
$923$	42.6333	1.40329
$924$	−70.0555	−2.30466
$925$	4.60555	0.151430
$926$	72.8444	2.39382
$927$	30.4222	0.999196
$928$	−15.9083	−0.522216
$929$	27.0000	0.885841	0.442921	−	0.896561i	$-0.353942\pi$
$929$	27.0000	0.885841	0.442921	+	0.896561i	$0.353942\pi$
$930$	−5.51388	−0.180807
$931$	−19.8167	−0.649465
$932$	−15.9083	−0.521095
$933$	10.3944	0.340299
$934$	63.6333	2.08215
$935$	−27.6333	−0.903706
$936$	33.6333	1.09934
$937$	8.23886	0.269152	0.134576	−	0.990903i	$-0.457033\pi$
$937$	8.23886	0.269152	0.134576	+	0.990903i	$0.457033\pi$
$938$	−146.533	−4.78448
$939$	−14.7889	−0.482617
$940$	−9.90833	−0.323174
$941$	2.36669	0.0771520	0.0385760	−	0.999256i	$-0.487718\pi$
$941$	2.36669	0.0771520	0.0385760	+	0.999256i	$0.487718\pi$
$942$	52.0555	1.69606
$943$	0	0
$944$	0	0
$945$	23.0278	0.749093
$946$	14.7889	0.480829
$947$	45.8444	1.48974	0.744872	−	0.667208i	$-0.232511\pi$
$947$	45.8444	1.48974	0.744872	+	0.667208i	$0.232511\pi$
$948$	4.60555	0.149581
$949$	−38.2111	−1.24038
$950$	3.21110	0.104182
$951$	27.2111	0.882380
$952$	−82.8999	−2.68680
$953$	43.2666	1.40154	0.700772	−	0.713386i	$-0.252839\pi$
$953$	43.2666	1.40154	0.700772	+	0.713386i	$0.252839\pi$
$954$	−42.4222	−1.37347
$955$	12.4222	0.401973
$956$	76.7527	2.48236
$957$	−13.8167	−0.446629
$958$	47.8722	1.54668
$959$	0	0
$960$	−12.8167	−0.413656
$961$	−25.2666	−0.815052
$962$	−59.4500	−1.91674
$963$	2.78890	0.0898710
$964$	−10.6056	−0.341582
$965$	−26.8167	−0.863259
$966$	0	0
$967$	7.84441	0.252259	0.126130	−	0.992014i	$-0.459744\pi$
$967$	7.84441	0.252259	0.126130	+	0.992014i	$0.459744\pi$
$968$	−30.6333	−0.984592
$969$	8.36669	0.268777
$970$	−10.6056	−0.340524
$971$	−39.6333	−1.27189	−0.635947	−	0.771733i	$-0.719390\pi$
$971$	−39.6333	−1.27189	−0.635947	+	0.771733i	$0.719390\pi$
$972$	52.8444	1.69499
$973$	11.0278	0.353534
$974$	−74.1749	−2.37672
$975$	5.60555	0.179521
$976$	−0.422205	−0.0135145
$977$	28.6056	0.915173	0.457586	−	0.889165i	$-0.348714\pi$
$977$	28.6056	0.915173	0.457586	+	0.889165i	$0.348714\pi$
$978$	−30.9083	−0.988339
$979$	36.0000	1.15056
$980$	46.9361	1.49932
$981$	2.78890	0.0890426
$982$	81.1472	2.58951
$983$	−2.78890	−0.0889520	−0.0444760	−	0.999010i	$-0.514162\pi$
$983$	−2.78890	−0.0889520	−0.0444760	+	0.999010i	$0.514162\pi$
$984$	−9.00000	−0.286910
$985$	−13.6056	−0.433509
$986$	−41.4500	−1.32004
$987$	13.8167	0.439789
$988$	−25.8167	−0.821337
$989$	0	0
$990$	21.2111	0.674133
$991$	37.2111	1.18205	0.591025	−	0.806653i	$-0.298724\pi$
$991$	37.2111	1.18205	0.591025	+	0.806653i	$0.298724\pi$
$992$	12.6972	0.403137
$993$	8.39445	0.266390
$994$	80.6611	2.55841
$995$	−13.8167	−0.438017
$996$	−10.6056	−0.336050
$997$	−52.4222	−1.66023	−0.830114	−	0.557594i	$-0.811725\pi$
$997$	−52.4222	−1.66023	−0.830114	+	0.557594i	$0.811725\pi$
$998$	77.3860	2.44961
$999$	−23.0278	−0.728566

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.h.1.1	yes	2
23.22	odd	2		2645.2.a.g.1.1	✓	2

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2645.2.a.g.1.1	✓	2	23.22	odd	2
2645.2.a.h.1.1	yes	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:	\( N \)	\(=\)	\( 2645 = 5 \cdot 23^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	2645.a (trivial)

\(f(q)\)	\(=\)	\(q-2.30278 q^{2} +1.00000 q^{3} +3.30278 q^{4} +1.00000 q^{5} -2.30278 q^{6} -4.60555 q^{7} -3.00000 q^{8} -2.00000 q^{9} +O(q^{10})\)	\(q-2.30278 q^{2} +1.00000 q^{3} +3.30278 q^{4} +1.00000 q^{5} -2.30278 q^{6} -4.60555 q^{7} -3.00000 q^{8} -2.00000 q^{9} -2.30278 q^{10} +4.60555 q^{11} +3.30278 q^{12} +5.60555 q^{13} +10.6056 q^{14} +1.00000 q^{15} +0.302776 q^{16} -6.00000 q^{17} +4.60555 q^{18} -1.39445 q^{19} +3.30278 q^{20} -4.60555 q^{21} -10.6056 q^{22} -3.00000 q^{24} +1.00000 q^{25} -12.9083 q^{26} -5.00000 q^{27} -15.2111 q^{28} -3.00000 q^{29} -2.30278 q^{30} +2.39445 q^{31} +5.30278 q^{32} +4.60555 q^{33} +13.8167 q^{34} -4.60555 q^{35} -6.60555 q^{36} +4.60555 q^{37} +3.21110 q^{38} +5.60555 q^{39} -3.00000 q^{40} +3.00000 q^{41} +10.6056 q^{42} -1.39445 q^{43} +15.2111 q^{44} -2.00000 q^{45} -3.00000 q^{47} +0.302776 q^{48} +14.2111 q^{49} -2.30278 q^{50} -6.00000 q^{51} +18.5139 q^{52} -9.21110 q^{53} +11.5139 q^{54} +4.60555 q^{55} +13.8167 q^{56} -1.39445 q^{57} +6.90833 q^{58} +3.30278 q^{60} -1.39445 q^{61} -5.51388 q^{62} +9.21110 q^{63} -12.8167 q^{64} +5.60555 q^{65} -10.6056 q^{66} -13.8167 q^{67} -19.8167 q^{68} +10.6056 q^{70} +7.60555 q^{71} +6.00000 q^{72} -6.81665 q^{73} -10.6056 q^{74} +1.00000 q^{75} -4.60555 q^{76} -21.2111 q^{77} -12.9083 q^{78} +1.39445 q^{79} +0.302776 q^{80} +1.00000 q^{81} -6.90833 q^{82} -3.21110 q^{83} -15.2111 q^{84} -6.00000 q^{85} +3.21110 q^{86} -3.00000 q^{87} -13.8167 q^{88} +7.81665 q^{89} +4.60555 q^{90} -25.8167 q^{91} +2.39445 q^{93} +6.90833 q^{94} -1.39445 q^{95} +5.30278 q^{96} +4.60555 q^{97} -32.7250 q^{98} -9.21110 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9}+O(q^{10}) \) 2 * q - q^2 + 2 * q^3 + 3 * q^4 + 2 * q^5 - q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9	\( 2 q - q^{2} + 2 q^{3} + 3 q^{4} + 2 q^{5} - q^{6} - 2 q^{7} - 6 q^{8} - 4 q^{9} - q^{10} + 2 q^{11} + 3 q^{12} + 4 q^{13} + 14 q^{14} + 2 q^{15} - 3 q^{16} - 12 q^{17} + 2 q^{18} - 10 q^{19} + 3 q^{20} - 2 q^{21} - 14 q^{22} - 6 q^{24} + 2 q^{25} - 15 q^{26} - 10 q^{27} - 16 q^{28} - 6 q^{29} - q^{30} + 12 q^{31} + 7 q^{32} + 2 q^{33} + 6 q^{34} - 2 q^{35} - 6 q^{36} + 2 q^{37} - 8 q^{38} + 4 q^{39} - 6 q^{40} + 6 q^{41} + 14 q^{42} - 10 q^{43} + 16 q^{44} - 4 q^{45} - 6 q^{47} - 3 q^{48} + 14 q^{49} - q^{50} - 12 q^{51} + 19 q^{52} - 4 q^{53} + 5 q^{54} + 2 q^{55} + 6 q^{56} - 10 q^{57} + 3 q^{58} + 3 q^{60} - 10 q^{61} + 7 q^{62} + 4 q^{63} - 4 q^{64} + 4 q^{65} - 14 q^{66} - 6 q^{67} - 18 q^{68} + 14 q^{70} + 8 q^{71} + 12 q^{72} + 8 q^{73} - 14 q^{74} + 2 q^{75} - 2 q^{76} - 28 q^{77} - 15 q^{78} + 10 q^{79} - 3 q^{80} + 2 q^{81} - 3 q^{82} + 8 q^{83} - 16 q^{84} - 12 q^{85} - 8 q^{86} - 6 q^{87} - 6 q^{88} - 6 q^{89} + 2 q^{90} - 30 q^{91} + 12 q^{93} + 3 q^{94} - 10 q^{95} + 7 q^{96} + 2 q^{97} - 33 q^{98} - 4 q^{99}+O(q^{100}) \) 2 * q - q^2 + 2 * q^3 + 3 * q^4 + 2 * q^5 - q^6 - 2 * q^7 - 6 * q^8 - 4 * q^9 - q^10 + 2 * q^11 + 3 * q^12 + 4 * q^13 + 14 * q^14 + 2 * q^15 - 3 * q^16 - 12 * q^17 + 2 * q^18 - 10 * q^19 + 3 * q^20 - 2 * q^21 - 14 * q^22 - 6 * q^24 + 2 * q^25 - 15 * q^26 - 10 * q^27 - 16 * q^28 - 6 * q^29 - q^30 + 12 * q^31 + 7 * q^32 + 2 * q^33 + 6 * q^34 - 2 * q^35 - 6 * q^36 + 2 * q^37 - 8 * q^38 + 4 * q^39 - 6 * q^40 + 6 * q^41 + 14 * q^42 - 10 * q^43 + 16 * q^44 - 4 * q^45 - 6 * q^47 - 3 * q^48 + 14 * q^49 - q^50 - 12 * q^51 + 19 * q^52 - 4 * q^53 + 5 * q^54 + 2 * q^55 + 6 * q^56 - 10 * q^57 + 3 * q^58 + 3 * q^60 - 10 * q^61 + 7 * q^62 + 4 * q^63 - 4 * q^64 + 4 * q^65 - 14 * q^66 - 6 * q^67 - 18 * q^68 + 14 * q^70 + 8 * q^71 + 12 * q^72 + 8 * q^73 - 14 * q^74 + 2 * q^75 - 2 * q^76 - 28 * q^77 - 15 * q^78 + 10 * q^79 - 3 * q^80 + 2 * q^81 - 3 * q^82 + 8 * q^83 - 16 * q^84 - 12 * q^85 - 8 * q^86 - 6 * q^87 - 6 * q^88 - 6 * q^89 + 2 * q^90 - 30 * q^91 + 12 * q^93 + 3 * q^94 - 10 * q^95 + 7 * q^96 + 2 * q^97 - 33 * q^98 - 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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