LMFDB - Embedded newform 2645.2.a.w.1.16

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:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} - 18 x^{14} + 88 x^{13} + 93 x^{12} - 728 x^{11} + 58 x^{10} + 2760 x^{9} - 1764 x^{8} + \cdots - 18 $ x^16 - 4x^15 - 18x^14 + 88x^13 + 93x^12 - 728x^11 + 58x^10 + 2760x^9 - 1764x^8 - 4568x^7 + 4414x^6 + 2440x^5 - 2759x^4 - 684x^3 + 558x^2 + 108*x - 18
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Root			$2.67211$ 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)

$f(q)$	$=$	$q+2.67211 q^{2} -0.174241 q^{3} +5.14016 q^{4} +1.00000 q^{5} -0.465591 q^{6} +2.95430 q^{7} +8.39086 q^{8} -2.96964 q^{9} +O(q^{10})$	\(q+2.67211 q^{2} -0.174241 q^{3} +5.14016 q^{4} +1.00000 q^{5} -0.465591 q^{6} +2.95430 q^{7} +8.39086 q^{8} -2.96964 q^{9} +2.67211 q^{10} +5.52598 q^{11} -0.895628 q^{12} -4.80156 q^{13} +7.89422 q^{14} -0.174241 q^{15} +12.1410 q^{16} -3.11097 q^{17} -7.93520 q^{18} +1.08685 q^{19} +5.14016 q^{20} -0.514761 q^{21} +14.7660 q^{22} -1.46203 q^{24} +1.00000 q^{25} -12.8303 q^{26} +1.04016 q^{27} +15.1856 q^{28} +0.195407 q^{29} -0.465591 q^{30} -5.16860 q^{31} +15.6602 q^{32} -0.962852 q^{33} -8.31286 q^{34} +2.95430 q^{35} -15.2644 q^{36} +5.69073 q^{37} +2.90419 q^{38} +0.836628 q^{39} +8.39086 q^{40} +10.5517 q^{41} -1.37550 q^{42} +0.0385385 q^{43} +28.4044 q^{44} -2.96964 q^{45} -3.52814 q^{47} -2.11545 q^{48} +1.72790 q^{49} +2.67211 q^{50} +0.542059 q^{51} -24.6808 q^{52} -4.04412 q^{53} +2.77941 q^{54} +5.52598 q^{55} +24.7891 q^{56} -0.189375 q^{57} +0.522148 q^{58} -9.23653 q^{59} -0.895628 q^{60} -8.63999 q^{61} -13.8110 q^{62} -8.77321 q^{63} +17.5640 q^{64} -4.80156 q^{65} -2.57285 q^{66} -1.65654 q^{67} -15.9909 q^{68} +7.89422 q^{70} -14.0277 q^{71} -24.9178 q^{72} +1.13928 q^{73} +15.2062 q^{74} -0.174241 q^{75} +5.58661 q^{76} +16.3254 q^{77} +2.23556 q^{78} -12.8530 q^{79} +12.1410 q^{80} +8.72768 q^{81} +28.1954 q^{82} +9.03744 q^{83} -2.64595 q^{84} -3.11097 q^{85} +0.102979 q^{86} -0.0340478 q^{87} +46.3677 q^{88} -4.47669 q^{89} -7.93520 q^{90} -14.1852 q^{91} +0.900582 q^{93} -9.42756 q^{94} +1.08685 q^{95} -2.72866 q^{96} -1.70332 q^{97} +4.61714 q^{98} -16.4102 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 4 q^{2} + 4 q^{3} + 20 q^{4} + 16 q^{5} - 12 q^{6} + 12 q^{7} + 8 q^{9}+O(q^{10}) $ 16 * q + 4 * q^2 + 4 * q^3 + 20 * q^4 + 16 * q^5 - 12 * q^6 + 12 * q^7 + 8 * q^9	\( 16 q + 4 q^{2} + 4 q^{3} + 20 q^{4} + 16 q^{5} - 12 q^{6} + 12 q^{7} + 8 q^{9} + 4 q^{10} + 16 q^{11} - 4 q^{12} + 8 q^{13} + 8 q^{14} + 4 q^{15} + 28 q^{16} - 8 q^{17} + 4 q^{18} + 32 q^{19} + 20 q^{20} + 16 q^{21} + 44 q^{22} - 28 q^{24} + 16 q^{25} - 20 q^{26} - 8 q^{27} + 52 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{31} + 4 q^{32} + 20 q^{33} + 24 q^{34} + 12 q^{35} - 4 q^{36} + 28 q^{37} - 20 q^{38} - 8 q^{39} - 4 q^{41} - 8 q^{42} + 48 q^{43} + 32 q^{44} + 8 q^{45} + 48 q^{47} + 24 q^{48} + 12 q^{49} + 4 q^{50} + 24 q^{51} + 12 q^{52} - 4 q^{53} - 44 q^{54} + 16 q^{55} + 64 q^{56} + 52 q^{57} - 28 q^{58} - 40 q^{59} - 4 q^{60} + 16 q^{61} + 4 q^{63} - 16 q^{64} + 8 q^{65} + 8 q^{66} + 68 q^{67} - 4 q^{68} + 8 q^{70} - 24 q^{71} - 12 q^{72} + 52 q^{73} + 40 q^{74} + 4 q^{75} + 24 q^{76} + 44 q^{77} + 12 q^{78} + 72 q^{79} + 28 q^{80} + 20 q^{81} - 20 q^{82} + 12 q^{83} + 32 q^{84} - 8 q^{85} - 56 q^{86} + 104 q^{88} + 48 q^{89} + 4 q^{90} + 48 q^{91} - 48 q^{93} - 60 q^{94} + 32 q^{95} - 108 q^{96} + 4 q^{97} + 8 q^{98} + 24 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 4 * q^3 + 20 * q^4 + 16 * q^5 - 12 * q^6 + 12 * q^7 + 8 * q^9 + 4 * q^10 + 16 * q^11 - 4 * q^12 + 8 * q^13 + 8 * q^14 + 4 * q^15 + 28 * q^16 - 8 * q^17 + 4 * q^18 + 32 * q^19 + 20 * q^20 + 16 * q^21 + 44 * q^22 - 28 * q^24 + 16 * q^25 - 20 * q^26 - 8 * q^27 + 52 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^31 + 4 * q^32 + 20 * q^33 + 24 * q^34 + 12 * q^35 - 4 * q^36 + 28 * q^37 - 20 * q^38 - 8 * q^39 - 4 * q^41 - 8 * q^42 + 48 * q^43 + 32 * q^44 + 8 * q^45 + 48 * q^47 + 24 * q^48 + 12 * q^49 + 4 * q^50 + 24 * q^51 + 12 * q^52 - 4 * q^53 - 44 * q^54 + 16 * q^55 + 64 * q^56 + 52 * q^57 - 28 * q^58 - 40 * q^59 - 4 * q^60 + 16 * q^61 + 4 * q^63 - 16 * q^64 + 8 * q^65 + 8 * q^66 + 68 * q^67 - 4 * q^68 + 8 * q^70 - 24 * q^71 - 12 * q^72 + 52 * q^73 + 40 * q^74 + 4 * q^75 + 24 * q^76 + 44 * q^77 + 12 * q^78 + 72 * q^79 + 28 * q^80 + 20 * q^81 - 20 * q^82 + 12 * q^83 + 32 * q^84 - 8 * q^85 - 56 * q^86 + 104 * q^88 + 48 * q^89 + 4 * q^90 + 48 * q^91 - 48 * q^93 - 60 * q^94 + 32 * q^95 - 108 * q^96 + 4 * q^97 + 8 * q^98 + 24 * 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 $

$2$	2.67211	1.88947	0.944733	−	0.327841i	$-0.106321\pi$
$2$	2.67211	1.88947	0.944733	+	0.327841i	$0.106321\pi$
$3$	−0.174241	−0.100598	−0.0502991	−	0.998734i	$-0.516017\pi$
$3$	−0.174241	−0.100598	−0.0502991	+	0.998734i	$0.516017\pi$
$4$	5.14016	2.57008
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−0.465591	−0.190077
$7$	2.95430	1.11662	0.558311	−	0.829632i	$-0.311450\pi$
$7$	2.95430	1.11662	0.558311	+	0.829632i	$0.311450\pi$
$8$	8.39086	2.96662
$9$	−2.96964	−0.989880
$10$	2.67211	0.844995
$11$	5.52598	1.66615	0.833073	−	0.553164i	$-0.186580\pi$
$11$	5.52598	1.66615	0.833073	+	0.553164i	$0.186580\pi$
$12$	−0.895628	−0.258545
$13$	−4.80156	−1.33171	−0.665856	−	0.746080i	$-0.731934\pi$
$13$	−4.80156	−1.33171	−0.665856	+	0.746080i	$0.731934\pi$
$14$	7.89422	2.10982
$15$	−0.174241	−0.0449888
$16$	12.1410	3.03524
$17$	−3.11097	−0.754522	−0.377261	−	0.926107i	$-0.623134\pi$
$17$	−3.11097	−0.754522	−0.377261	+	0.926107i	$0.623134\pi$
$18$	−7.93520	−1.87034
$19$	1.08685	0.249342	0.124671	−	0.992198i	$-0.460213\pi$
$19$	1.08685	0.249342	0.124671	+	0.992198i	$0.460213\pi$
$20$	5.14016	1.14938
$21$	−0.514761	−0.112330
$22$	14.7660	3.14812
$23$	0	0
$23$	0	0
$24$	−1.46203	−0.298436
$25$	1.00000	0.200000
$26$	−12.8303	−2.51622
$27$	1.04016	0.200178
$28$	15.1856	2.86981
$29$	0.195407	0.0362861	0.0181430	−	0.999835i	$-0.494225\pi$
$29$	0.195407	0.0362861	0.0181430	+	0.999835i	$0.494225\pi$
$30$	−0.465591	−0.0850049
$31$	−5.16860	−0.928307	−0.464154	−	0.885755i	$-0.653641\pi$
$31$	−5.16860	−0.928307	−0.464154	+	0.885755i	$0.653641\pi$
$32$	15.6602	2.76837
$33$	−0.962852	−0.167611
$34$	−8.31286	−1.42564
$35$	2.95430	0.499368
$36$	−15.2644	−2.54407
$37$	5.69073	0.935549	0.467775	−	0.883848i	$-0.345056\pi$
$37$	5.69073	0.935549	0.467775	+	0.883848i	$0.345056\pi$
$38$	2.90419	0.471122
$39$	0.836628	0.133968
$40$	8.39086	1.32671
$41$	10.5517	1.64790	0.823952	−	0.566659i	$-0.191764\pi$
$41$	10.5517	1.64790	0.823952	+	0.566659i	$0.191764\pi$
$42$	−1.37550	−0.212244
$43$	0.0385385	0.00587706	0.00293853	−	0.999996i	$-0.499065\pi$
$43$	0.0385385	0.00587706	0.00293853	+	0.999996i	$0.499065\pi$
$44$	28.4044	4.28213
$45$	−2.96964	−0.442688
$46$	0	0
$47$	−3.52814	−0.514631	−0.257316	−	0.966327i	$-0.582838\pi$
$47$	−3.52814	−0.514631	−0.257316	+	0.966327i	$0.582838\pi$
$48$	−2.11545	−0.305339
$49$	1.72790	0.246843
$50$	2.67211	0.377893
$51$	0.542059	0.0759035
$52$	−24.6808	−3.42261
$53$	−4.04412	−0.555503	−0.277751	−	0.960653i	$-0.589589\pi$
$53$	−4.04412	−0.555503	−0.277751	+	0.960653i	$0.589589\pi$
$54$	2.77941	0.378230
$55$	5.52598	0.745123
$56$	24.7891	3.31259
$57$	−0.189375	−0.0250833
$58$	0.522148	0.0685613
$59$	−9.23653	−1.20249	−0.601247	−	0.799063i	$-0.705329\pi$
$59$	−9.23653	−1.20249	−0.601247	+	0.799063i	$0.705329\pi$
$60$	−0.895628	−0.115625
$61$	−8.63999	−1.10624	−0.553119	−	0.833102i	$-0.686562\pi$
$61$	−8.63999	−1.10624	−0.553119	+	0.833102i	$0.686562\pi$
$62$	−13.8110	−1.75400
$63$	−8.77321	−1.10532
$64$	17.5640	2.19549
$65$	−4.80156	−0.595560
$66$	−2.57285	−0.316695
$67$	−1.65654	−0.202378	−0.101189	−	0.994867i	$-0.532265\pi$
$67$	−1.65654	−0.202378	−0.101189	+	0.994867i	$0.532265\pi$
$68$	−15.9909	−1.93918
$69$	0	0
$70$	7.89422	0.943539
$71$	−14.0277	−1.66479	−0.832393	−	0.554185i	$-0.813030\pi$
$71$	−14.0277	−1.66479	−0.832393	+	0.554185i	$0.813030\pi$
$72$	−24.9178	−2.93660
$73$	1.13928	0.133343	0.0666716	−	0.997775i	$-0.478762\pi$
$73$	1.13928	0.133343	0.0666716	+	0.997775i	$0.478762\pi$
$74$	15.2062	1.76769
$75$	−0.174241	−0.0201196
$76$	5.58661	0.640828
$77$	16.3254	1.86045
$78$	2.23556	0.253128
$79$	−12.8530	−1.44608	−0.723040	−	0.690806i	$-0.757256\pi$
$79$	−12.8530	−1.44608	−0.723040	+	0.690806i	$0.757256\pi$
$80$	12.1410	1.35740
$81$	8.72768	0.969742
$82$	28.1954	3.11366
$83$	9.03744	0.991987	0.495994	−	0.868326i	$-0.334804\pi$
$83$	9.03744	0.991987	0.495994	+	0.868326i	$0.334804\pi$
$84$	−2.64595	−0.288697
$85$	−3.11097	−0.337432
$86$	0.102979	0.0111045
$87$	−0.0340478	−0.00365031
$88$	46.3677	4.94281
$89$	−4.47669	−0.474528	−0.237264	−	0.971445i	$-0.576251\pi$
$89$	−4.47669	−0.474528	−0.237264	+	0.971445i	$0.576251\pi$
$90$	−7.93520	−0.836444
$91$	−14.1852	−1.48702
$92$	0	0
$93$	0.900582	0.0933860
$94$	−9.42756	−0.972379
$95$	1.08685	0.111509
$96$	−2.72866	−0.278492
$97$	−1.70332	−0.172946	−0.0864732	−	0.996254i	$-0.527560\pi$
$97$	−1.70332	−0.172946	−0.0864732	+	0.996254i	$0.527560\pi$
$98$	4.61714	0.466402
$99$	−16.4102	−1.64928
$100$	5.14016	0.514016
$101$	−1.46472	−0.145745	−0.0728727	−	0.997341i	$-0.523217\pi$
$101$	−1.46472	−0.145745	−0.0728727	+	0.997341i	$0.523217\pi$
$102$	1.44844	0.143417
$103$	−4.18627	−0.412485	−0.206243	−	0.978501i	$-0.566124\pi$
$103$	−4.18627	−0.412485	−0.206243	+	0.978501i	$0.566124\pi$
$104$	−40.2892	−3.95068
$105$	−0.514761	−0.0502355
$106$	−10.8063	−1.04960
$107$	7.03379	0.679982	0.339991	−	0.940429i	$-0.389576\pi$
$107$	7.03379	0.679982	0.339991	+	0.940429i	$0.389576\pi$
$108$	5.34658	0.514474
$109$	18.2119	1.74438	0.872191	−	0.489165i	$-0.162698\pi$
$109$	18.2119	1.74438	0.872191	+	0.489165i	$0.162698\pi$
$110$	14.7660	1.40788
$111$	−0.991558	−0.0941145
$112$	35.8681	3.38921
$113$	7.80885	0.734595	0.367297	−	0.930104i	$-0.380283\pi$
$113$	7.80885	0.734595	0.367297	+	0.930104i	$0.380283\pi$
$114$	−0.506030	−0.0473940
$115$	0	0
$116$	1.00442	0.0932582
$117$	14.2589	1.31824
$118$	−24.6810	−2.27207
$119$	−9.19076	−0.842515
$120$	−1.46203	−0.133465
$121$	19.5364	1.77604
$122$	−23.0870	−2.09020
$123$	−1.83855	−0.165776
$124$	−26.5674	−2.38583
$125$	1.00000	0.0894427
$126$	−23.4430	−2.08847
$127$	14.3072	1.26956	0.634780	−	0.772693i	$-0.281091\pi$
$127$	14.3072	1.26956	0.634780	+	0.772693i	$0.281091\pi$
$128$	15.6123	1.37995
$129$	−0.00671498	−0.000591221 0
$130$	−12.8303	−1.12529
$131$	−3.65367	−0.319223	−0.159612	−	0.987180i	$-0.551024\pi$
$131$	−3.65367	−0.319223	−0.159612	+	0.987180i	$0.551024\pi$
$132$	−4.94922	−0.430774
$133$	3.21090	0.278420
$134$	−4.42645	−0.382387
$135$	1.04016	0.0895224
$136$	−26.1037	−2.23838
$137$	21.7157	1.85530	0.927650	−	0.373450i	$-0.121825\pi$
$137$	21.7157	1.85530	0.927650	+	0.373450i	$0.121825\pi$
$138$	0	0
$139$	−0.0207896	−0.00176335	−0.000881677	−	1.00000i	$-0.500281\pi$
$139$	−0.0207896	−0.00176335	−0.000881677		1.00000i	$0.500281\pi$
$140$	15.1856	1.28342
$141$	0.614746	0.0517710
$142$	−37.4837	−3.14556
$143$	−26.5333	−2.21883
$144$	−36.0543	−3.00452
$145$	0.195407	0.0162276
$146$	3.04429	0.251947
$147$	−0.301071	−0.0248319
$148$	29.2513	2.40444
$149$	−9.16238	−0.750611	−0.375306	−	0.926901i	$-0.622462\pi$
$149$	−9.16238	−0.750611	−0.375306	+	0.926901i	$0.622462\pi$
$150$	−0.465591	−0.0380153
$151$	12.2398	0.996058	0.498029	−	0.867160i	$-0.334057\pi$
$151$	12.2398	0.996058	0.498029	+	0.867160i	$0.334057\pi$
$152$	9.11965	0.739701
$153$	9.23847	0.746886
$154$	43.6233	3.51526
$155$	−5.16860	−0.415152
$156$	4.30041	0.344308
$157$	−14.5261	−1.15931	−0.579653	−	0.814863i	$-0.696812\pi$
$157$	−14.5261	−1.15931	−0.579653	+	0.814863i	$0.696812\pi$
$158$	−34.3447	−2.73232
$159$	0.704652	0.0558825
$160$	15.6602	1.23805
$161$	0	0
$162$	23.3213	1.83230
$163$	−3.27801	−0.256753	−0.128377	−	0.991725i	$-0.540977\pi$
$163$	−3.27801	−0.256753	−0.128377	+	0.991725i	$0.540977\pi$
$164$	54.2377	4.23525
$165$	−0.962852	−0.0749580
$166$	24.1490	1.87433
$167$	21.9708	1.70015	0.850075	−	0.526662i	$-0.176557\pi$
$167$	21.9708	1.70015	0.850075	+	0.526662i	$0.176557\pi$
$168$	−4.31929	−0.333240
$169$	10.0549	0.773457
$170$	−8.31286	−0.637567
$171$	−3.22757	−0.246818
$172$	0.198094	0.0151045
$173$	−17.5850	−1.33696	−0.668482	−	0.743728i	$-0.733056\pi$
$173$	−17.5850	−1.33696	−0.668482	+	0.743728i	$0.733056\pi$
$174$	−0.0909795	−0.00689714
$175$	2.95430	0.223324
$176$	67.0907	5.05715
$177$	1.60938	0.120969
$178$	−11.9622	−0.896605
$179$	6.82793	0.510343	0.255172	−	0.966896i	$-0.417868\pi$
$179$	6.82793	0.510343	0.255172	+	0.966896i	$0.417868\pi$
$180$	−15.2644	−1.13774
$181$	−10.8714	−0.808065	−0.404032	−	0.914745i	$-0.632392\pi$
$181$	−10.8714	−0.808065	−0.404032	+	0.914745i	$0.632392\pi$
$182$	−37.9045	−2.80967
$183$	1.50544	0.111285
$184$	0	0
$185$	5.69073	0.418390
$186$	2.40645	0.176450
$187$	−17.1912	−1.25714
$188$	−18.1352	−1.32264
$189$	3.07294	0.223523
$190$	2.90419	0.210692
$191$	−1.53285	−0.110913	−0.0554567	−	0.998461i	$-0.517661\pi$
$191$	−1.53285	−0.110913	−0.0554567	+	0.998461i	$0.517661\pi$
$192$	−3.06036	−0.220863
$193$	−24.8082	−1.78573	−0.892866	−	0.450322i	$-0.851309\pi$
$193$	−24.8082	−1.78573	−0.892866	+	0.450322i	$0.851309\pi$
$194$	−4.55147	−0.326776
$195$	0.836628	0.0599122
$196$	8.88170	0.634407
$197$	−4.83078	−0.344179	−0.172090	−	0.985081i	$-0.555052\pi$
$197$	−4.83078	−0.344179	−0.172090	+	0.985081i	$0.555052\pi$
$198$	−43.8497	−3.11627
$199$	4.89688	0.347131	0.173565	−	0.984822i	$-0.444471\pi$
$199$	4.89688	0.347131	0.173565	+	0.984822i	$0.444471\pi$
$200$	8.39086	0.593323
$201$	0.288637	0.0203589
$202$	−3.91390	−0.275381
$203$	0.577290	0.0405178
$204$	2.78627	0.195078
$205$	10.5517	0.736965
$206$	−11.1862	−0.779377
$207$	0	0
$208$	−58.2955	−4.04207
$209$	6.00594	0.415439
$210$	−1.37550	−0.0949183
$211$	−20.2948	−1.39715	−0.698577	−	0.715535i	$-0.746183\pi$
$211$	−20.2948	−1.39715	−0.698577	+	0.715535i	$0.746183\pi$
$212$	−20.7874	−1.42769
$213$	2.44421	0.167474
$214$	18.7950	1.28480
$215$	0.0385385	0.00262830
$216$	8.72781	0.593852
$217$	−15.2696	−1.03657
$218$	48.6642	3.29595
$219$	−0.198510	−0.0134141
$220$	28.4044	1.91503
$221$	14.9375	1.00481
$222$	−2.64955	−0.177826
$223$	−13.8980	−0.930677	−0.465338	−	0.885133i	$-0.654067\pi$
$223$	−13.8980	−0.930677	−0.465338	+	0.885133i	$0.654067\pi$
$224$	46.2651	3.09122
$225$	−2.96964	−0.197976
$226$	20.8661	1.38799
$227$	8.80233	0.584231	0.292115	−	0.956383i	$-0.405641\pi$
$227$	8.80233	0.584231	0.292115	+	0.956383i	$0.405641\pi$
$228$	−0.973417	−0.0644661
$229$	−4.19701	−0.277346	−0.138673	−	0.990338i	$-0.544284\pi$
$229$	−4.19701	−0.277346	−0.138673	+	0.990338i	$0.544284\pi$
$230$	0	0
$231$	−2.84456	−0.187158
$232$	1.63963	0.107647
$233$	−6.40310	−0.419481	−0.209741	−	0.977757i	$-0.567262\pi$
$233$	−6.40310	−0.419481	−0.209741	+	0.977757i	$0.567262\pi$
$234$	38.1013	2.49076
$235$	−3.52814	−0.230150
$236$	−47.4773	−3.09051
$237$	2.23953	0.145473
$238$	−24.5587	−1.59190
$239$	−17.2559	−1.11619	−0.558096	−	0.829776i	$-0.688468\pi$
$239$	−17.2559	−1.11619	−0.558096	+	0.829776i	$0.688468\pi$
$240$	−2.11545	−0.136552
$241$	14.5050	0.934351	0.467176	−	0.884165i	$-0.345272\pi$
$241$	14.5050	0.934351	0.467176	+	0.884165i	$0.345272\pi$
$242$	52.2035	3.35577
$243$	−4.64119	−0.297732
$244$	−44.4110	−2.84312
$245$	1.72790	0.110392
$246$	−4.91279	−0.313228
$247$	−5.21859	−0.332051
$248$	−43.3690	−2.75393
$249$	−1.57469	−0.0997921
$250$	2.67211	0.168999
$251$	24.9515	1.57492	0.787461	−	0.616364i	$-0.211395\pi$
$251$	24.9515	1.57492	0.787461	+	0.616364i	$0.211395\pi$
$252$	−45.0958	−2.84077
$253$	0	0
$254$	38.2304	2.39879
$255$	0.542059	0.0339451
$256$	6.58987	0.411867
$257$	29.3254	1.82927	0.914634	−	0.404283i	$-0.132479\pi$
$257$	29.3254	1.82927	0.914634	+	0.404283i	$0.132479\pi$
$258$	−0.0179432	−0.00111709
$259$	16.8121	1.04465
$260$	−24.6808	−1.53064
$261$	−0.580287	−0.0359189
$262$	−9.76301	−0.603161
$263$	−6.03359	−0.372047	−0.186023	−	0.982545i	$-0.559560\pi$
$263$	−6.03359	−0.372047	−0.186023	+	0.982545i	$0.559560\pi$
$264$	−8.07916	−0.497238
$265$	−4.04412	−0.248428
$266$	8.57987	0.526065
$267$	0.780023	0.0477366
$268$	−8.51488	−0.520129
$269$	−12.5290	−0.763908	−0.381954	−	0.924181i	$-0.624749\pi$
$269$	−12.5290	−0.763908	−0.381954	+	0.924181i	$0.624749\pi$
$270$	2.77941	0.169150
$271$	−18.2033	−1.10577	−0.552887	−	0.833257i	$-0.686474\pi$
$271$	−18.2033	−1.10577	−0.552887	+	0.833257i	$0.686474\pi$
$272$	−37.7702	−2.29016
$273$	2.47165	0.149591
$274$	58.0268	3.50553
$275$	5.52598	0.333229
$276$	0	0
$277$	−8.93758	−0.537007	−0.268503	−	0.963279i	$-0.586529\pi$
$277$	−8.93758	−0.537007	−0.268503	+	0.963279i	$0.586529\pi$
$278$	−0.0555522	−0.00333180
$279$	15.3489	0.918913
$280$	24.7891	1.48143
$281$	3.37660	0.201431	0.100716	−	0.994915i	$-0.467887\pi$
$281$	3.37660	0.201431	0.100716	+	0.994915i	$0.467887\pi$
$282$	1.64267	0.0978195
$283$	−13.8988	−0.826195	−0.413098	−	0.910687i	$-0.635553\pi$
$283$	−13.8988	−0.826195	−0.413098	+	0.910687i	$0.635553\pi$
$284$	−72.1049	−4.27864
$285$	−0.189375	−0.0112176
$286$	−70.8998	−4.19240
$287$	31.1730	1.84009
$288$	−46.5053	−2.74035
$289$	−7.32184	−0.430697
$290$	0.522148	0.0306616
$291$	0.296789	0.0173981
$292$	5.85611	0.342703
$293$	−26.7797	−1.56449	−0.782243	−	0.622973i	$-0.785925\pi$
$293$	−26.7797	−1.56449	−0.782243	+	0.622973i	$0.785925\pi$
$294$	−0.804495	−0.0469191
$295$	−9.23653	−0.537772
$296$	47.7501	2.77542
$297$	5.74788	0.333526
$298$	−24.4829	−1.41825
$299$	0	0
$300$	−0.895628	−0.0517091
$301$	0.113854	0.00656245
$302$	32.7060	1.88202
$303$	0.255215	0.0146617
$304$	13.1955	0.756812
$305$	−8.63999	−0.494724
$306$	24.6862	1.41122
$307$	−3.38231	−0.193038	−0.0965192	−	0.995331i	$-0.530771\pi$
$307$	−3.38231	−0.193038	−0.0965192	+	0.995331i	$0.530771\pi$
$308$	83.9153	4.78152
$309$	0.729420	0.0414952
$310$	−13.8110	−0.784415
$311$	−23.7892	−1.34896	−0.674481	−	0.738293i	$-0.735632\pi$
$311$	−23.7892	−1.34896	−0.674481	+	0.738293i	$0.735632\pi$
$312$	7.02003	0.397431
$313$	10.6645	0.602794	0.301397	−	0.953499i	$-0.402547\pi$
$313$	10.6645	0.602794	0.301397	+	0.953499i	$0.402547\pi$
$314$	−38.8152	−2.19047
$315$	−8.77321	−0.494315
$316$	−66.0667	−3.71654
$317$	13.7983	0.774990	0.387495	−	0.921872i	$-0.373340\pi$
$317$	13.7983	0.774990	0.387495	+	0.921872i	$0.373340\pi$
$318$	1.88291	0.105588
$319$	1.07981	0.0604579
$320$	17.5640	0.981855
$321$	−1.22557	−0.0684049
$322$	0	0
$323$	−3.38118	−0.188134
$324$	44.8617	2.49232
$325$	−4.80156	−0.266342
$326$	−8.75919	−0.485127
$327$	−3.17326	−0.175482
$328$	88.5382	4.88870
$329$	−10.4232	−0.574648
$330$	−2.57285	−0.141631
$331$	−9.39475	−0.516382	−0.258191	−	0.966094i	$-0.583126\pi$
$331$	−9.39475	−0.516382	−0.258191	+	0.966094i	$0.583126\pi$
$332$	46.4539	2.54949
$333$	−16.8994	−0.926082
$334$	58.7083	3.21238
$335$	−1.65654	−0.0905064
$336$	−6.24969	−0.340949
$337$	−4.82818	−0.263008	−0.131504	−	0.991316i	$-0.541981\pi$
$337$	−4.82818	−0.263008	−0.131504	+	0.991316i	$0.541981\pi$
$338$	26.8679	1.46142
$339$	−1.36062	−0.0738989
$340$	−15.9909	−0.867229
$341$	−28.5615	−1.54669
$342$	−8.62441	−0.466355
$343$	−15.5754	−0.840991
$344$	0.323371	0.0174350
$345$	0	0
$346$	−46.9891	−2.52615
$347$	−19.8663	−1.06648	−0.533239	−	0.845965i	$-0.679025\pi$
$347$	−19.8663	−1.06648	−0.533239	+	0.845965i	$0.679025\pi$
$348$	−0.175012	−0.00938160
$349$	10.9871	0.588127	0.294064	−	0.955786i	$-0.404992\pi$
$349$	10.9871	0.588127	0.294064	+	0.955786i	$0.404992\pi$
$350$	7.89422	0.421964
$351$	−4.99437	−0.266580
$352$	86.5382	4.61250
$353$	25.0778	1.33475	0.667377	−	0.744720i	$-0.267417\pi$
$353$	25.0778	1.33475	0.667377	+	0.744720i	$0.267417\pi$
$354$	4.30045	0.228566
$355$	−14.0277	−0.744515
$356$	−23.0109	−1.21958
$357$	1.60141	0.0847554
$358$	18.2450	0.964276
$359$	0.908608	0.0479545	0.0239773	−	0.999713i	$-0.492367\pi$
$359$	0.908608	0.0479545	0.0239773	+	0.999713i	$0.492367\pi$
$360$	−24.9178	−1.31329
$361$	−17.8187	−0.937829
$362$	−29.0496	−1.52681
$363$	−3.40405	−0.178666
$364$	−72.9145	−3.82176
$365$	1.13928	0.0596329
$366$	4.02270	0.210270
$367$	−25.8707	−1.35044	−0.675221	−	0.737616i	$-0.735952\pi$
$367$	−25.8707	−1.35044	−0.675221	+	0.737616i	$0.735952\pi$
$368$	0	0
$369$	−31.3349	−1.63123
$370$	15.2062	0.790535
$371$	−11.9476	−0.620286
$372$	4.62914	0.240010
$373$	25.9616	1.34424	0.672119	−	0.740443i	$-0.265384\pi$
$373$	25.9616	1.34424	0.672119	+	0.740443i	$0.265384\pi$
$374$	−45.9367	−2.37533
$375$	−0.174241	−0.00899777
$376$	−29.6041	−1.52671
$377$	−0.938256	−0.0483226
$378$	8.21122	0.422340
$379$	24.9275	1.28044	0.640220	−	0.768191i	$-0.278843\pi$
$379$	24.9275	1.28044	0.640220	+	0.768191i	$0.278843\pi$
$380$	5.58661	0.286587
$381$	−2.49290	−0.127715
$382$	−4.09595	−0.209567
$383$	13.8241	0.706377	0.353189	−	0.935552i	$-0.385097\pi$
$383$	13.8241	0.706377	0.353189	+	0.935552i	$0.385097\pi$
$384$	−2.72031	−0.138820
$385$	16.3254	0.832020
$386$	−66.2902	−3.37408
$387$	−0.114445	−0.00581758
$388$	−8.75536	−0.444486
$389$	−7.00963	−0.355403	−0.177701	−	0.984084i	$-0.556866\pi$
$389$	−7.00963	−0.355403	−0.177701	+	0.984084i	$0.556866\pi$
$390$	2.23556	0.113202
$391$	0	0
$392$	14.4986	0.732289
$393$	0.636620	0.0321132
$394$	−12.9084	−0.650315
$395$	−12.8530	−0.646707
$396$	−84.3510	−4.23879
$397$	17.5710	0.881865	0.440933	−	0.897540i	$-0.354648\pi$
$397$	17.5710	0.881865	0.440933	+	0.897540i	$0.354648\pi$
$398$	13.0850	0.655892
$399$	−0.559470	−0.0280085
$400$	12.1410	0.607048
$401$	7.45403	0.372236	0.186118	−	0.982527i	$-0.440409\pi$
$401$	7.45403	0.372236	0.186118	+	0.982527i	$0.440409\pi$
$402$	0.771270	0.0384674
$403$	24.8173	1.23624
$404$	−7.52892	−0.374578
$405$	8.72768	0.433682
$406$	1.54258	0.0765570
$407$	31.4468	1.55876
$408$	4.54834	0.225177
$409$	32.3009	1.59718	0.798589	−	0.601877i	$-0.205580\pi$
$409$	32.3009	1.59718	0.798589	+	0.601877i	$0.205580\pi$
$410$	28.1954	1.39247
$411$	−3.78377	−0.186640
$412$	−21.5181	−1.06012
$413$	−27.2875	−1.34273
$414$	0	0
$415$	9.03744	0.443630
$416$	−75.1936	−3.68667
$417$	0.00362241	0.000177390 0
$418$	16.0485	0.784958
$419$	10.5937	0.517535	0.258768	−	0.965940i	$-0.416684\pi$
$419$	10.5937	0.517535	0.258768	+	0.965940i	$0.416684\pi$
$420$	−2.64595	−0.129109
$421$	19.5586	0.953230	0.476615	−	0.879112i	$-0.341864\pi$
$421$	19.5586	0.953230	0.476615	+	0.879112i	$0.341864\pi$
$422$	−54.2300	−2.63987
$423$	10.4773	0.509423
$424$	−33.9337	−1.64796
$425$	−3.11097	−0.150904
$426$	6.53119	0.316437
$427$	−25.5251	−1.23525
$428$	36.1548	1.74761
$429$	4.62319	0.223210
$430$	0.102979	0.00496609
$431$	10.0735	0.485221	0.242611	−	0.970124i	$-0.421996\pi$
$431$	10.0735	0.485221	0.242611	+	0.970124i	$0.421996\pi$
$432$	12.6285	0.607589
$433$	−11.5492	−0.555020	−0.277510	−	0.960723i	$-0.589509\pi$
$433$	−11.5492	−0.555020	−0.277510	+	0.960723i	$0.589509\pi$
$434$	−40.8020	−1.95856
$435$	−0.0340478	−0.00163247
$436$	93.6121	4.48321
$437$	0	0
$438$	−0.530441	−0.0253454
$439$	3.99549	0.190694	0.0953471	−	0.995444i	$-0.469604\pi$
$439$	3.99549	0.190694	0.0953471	+	0.995444i	$0.469604\pi$
$440$	46.3677	2.21049
$441$	−5.13124	−0.244345
$442$	39.9147	1.89855
$443$	12.4780	0.592849	0.296425	−	0.955056i	$-0.404206\pi$
$443$	12.4780	0.592849	0.296425	+	0.955056i	$0.404206\pi$
$444$	−5.09677	−0.241882
$445$	−4.47669	−0.212215
$446$	−37.1369	−1.75848
$447$	1.59646	0.0755101
$448$	51.8892	2.45154
$449$	3.74100	0.176549	0.0882744	−	0.996096i	$-0.471865\pi$
$449$	3.74100	0.176549	0.0882744	+	0.996096i	$0.471865\pi$
$450$	−7.93520	−0.374069
$451$	58.3087	2.74565
$452$	40.1388	1.88797
$453$	−2.13267	−0.100202
$454$	23.5208	1.10388
$455$	−14.1852	−0.665015
$456$	−1.58902	−0.0744125
$457$	22.8923	1.07085	0.535427	−	0.844581i	$-0.320151\pi$
$457$	22.8923	1.07085	0.535427	+	0.844581i	$0.320151\pi$
$458$	−11.2149	−0.524036
$459$	−3.23590	−0.151039
$460$	0	0
$461$	20.8931	0.973089	0.486544	−	0.873656i	$-0.338257\pi$
$461$	20.8931	0.973089	0.486544	+	0.873656i	$0.338257\pi$
$462$	−7.60096	−0.353629
$463$	25.9972	1.20819	0.604095	−	0.796912i	$-0.293535\pi$
$463$	25.9972	1.20819	0.604095	+	0.796912i	$0.293535\pi$
$464$	2.37242	0.110137
$465$	0.900582	0.0417635
$466$	−17.1098	−0.792596
$467$	−25.4335	−1.17692	−0.588460	−	0.808526i	$-0.700266\pi$
$467$	−25.4335	−1.17692	−0.588460	+	0.808526i	$0.700266\pi$
$468$	73.2931	3.38797
$469$	−4.89392	−0.225980
$470$	−9.42756	−0.434861
$471$	2.53104	0.116624
$472$	−77.5025	−3.56734
$473$	0.212963	0.00979204
$474$	5.98426	0.274866
$475$	1.08685	0.0498683
$476$	−47.2420	−2.16533
$477$	12.0096	0.549881
$478$	−46.1097	−2.10901
$479$	−27.0414	−1.23555	−0.617776	−	0.786354i	$-0.711966\pi$
$479$	−27.0414	−1.23555	−0.617776	+	0.786354i	$0.711966\pi$
$480$	−2.72866	−0.124546
$481$	−27.3243	−1.24588
$482$	38.7590	1.76543
$483$	0	0
$484$	100.420	4.56457
$485$	−1.70332	−0.0773439
$486$	−12.4018	−0.562555
$487$	12.9621	0.587369	0.293684	−	0.955902i	$-0.405119\pi$
$487$	12.9621	0.587369	0.293684	+	0.955902i	$0.405119\pi$
$488$	−72.4970	−3.28178
$489$	0.571163	0.0258289
$490$	4.61714	0.208581
$491$	6.80988	0.307326	0.153663	−	0.988123i	$-0.450893\pi$
$491$	6.80988	0.307326	0.153663	+	0.988123i	$0.450893\pi$
$492$	−9.45043	−0.426058
$493$	−0.607905	−0.0273786
$494$	−13.9446	−0.627399
$495$	−16.4102	−0.737582
$496$	−62.7517	−2.81764
$497$	−41.4422	−1.85894
$498$	−4.20775	−0.188554
$499$	5.57438	0.249543	0.124772	−	0.992185i	$-0.460180\pi$
$499$	5.57438	0.249543	0.124772	+	0.992185i	$0.460180\pi$
$500$	5.14016	0.229875
$501$	−3.82821	−0.171032
$502$	66.6730	2.97576
$503$	2.39629	0.106845	0.0534227	−	0.998572i	$-0.482987\pi$
$503$	2.39629	0.106845	0.0534227	+	0.998572i	$0.482987\pi$
$504$	−73.6148	−3.27906
$505$	−1.46472	−0.0651793
$506$	0	0
$507$	−1.75198	−0.0778083
$508$	73.5414	3.26287
$509$	−9.81163	−0.434893	−0.217447	−	0.976072i	$-0.569773\pi$
$509$	−9.81163	−0.434893	−0.217447	+	0.976072i	$0.569773\pi$
$510$	1.44844	0.0641381
$511$	3.36579	0.148894
$512$	−13.6158	−0.601738
$513$	1.13050	0.0499127
$514$	78.3606	3.45634
$515$	−4.18627	−0.184469
$516$	−0.0345161	−0.00151949
$517$	−19.4964	−0.857451
$518$	44.9238	1.97384
$519$	3.06403	0.134496
$520$	−40.2892	−1.76680
$521$	−4.98432	−0.218367	−0.109184	−	0.994022i	$-0.534824\pi$
$521$	−4.98432	−0.218367	−0.109184	+	0.994022i	$0.534824\pi$
$522$	−1.55059	−0.0678675
$523$	32.4420	1.41859	0.709295	−	0.704912i	$-0.249014\pi$
$523$	32.4420	1.41859	0.709295	+	0.704912i	$0.249014\pi$
$524$	−18.7805	−0.820429
$525$	−0.514761	−0.0224660
$526$	−16.1224	−0.702970
$527$	16.0794	0.700428
$528$	−11.6900	−0.508740
$529$	0	0
$530$	−10.8063	−0.469397
$531$	27.4292	1.19032
$532$	16.5045	0.715562
$533$	−50.6648	−2.19453
$534$	2.08431	0.0901968
$535$	7.03379	0.304097
$536$	−13.8998	−0.600379
$537$	−1.18971	−0.0513396
$538$	−33.4789	−1.44338
$539$	9.54834	0.411276
$540$	5.34658	0.230080
$541$	−28.9278	−1.24370	−0.621851	−	0.783136i	$-0.713619\pi$
$541$	−28.9278	−1.24370	−0.621851	+	0.783136i	$0.713619\pi$
$542$	−48.6413	−2.08932
$543$	1.89424	0.0812898
$544$	−48.7186	−2.08879
$545$	18.2119	0.780112
$546$	6.60452	0.282648
$547$	21.2221	0.907391	0.453696	−	0.891157i	$-0.350105\pi$
$547$	21.2221	0.907391	0.453696	+	0.891157i	$0.350105\pi$
$548$	111.622	4.76828
$549$	25.6577	1.09504
$550$	14.7660	0.629625
$551$	0.212379	0.00904763
$552$	0	0
$553$	−37.9718	−1.61472
$554$	−23.8822	−1.01466
$555$	−0.991558	−0.0420893
$556$	−0.106862	−0.00453197
$557$	−11.8272	−0.501136	−0.250568	−	0.968099i	$-0.580617\pi$
$557$	−11.8272	−0.501136	−0.250568	+	0.968099i	$0.580617\pi$
$558$	41.0138	1.73625
$559$	−0.185045	−0.00782655
$560$	35.8681	1.51570
$561$	2.99541	0.126466
$562$	9.02266	0.380598
$563$	5.19503	0.218945	0.109472	−	0.993990i	$-0.465084\pi$
$563$	5.19503	0.218945	0.109472	+	0.993990i	$0.465084\pi$
$564$	3.15990	0.133056
$565$	7.80885	0.328521
$566$	−37.1390	−1.56107
$567$	25.7842	1.08284
$568$	−117.705	−4.93878
$569$	−45.8948	−1.92401	−0.962004	−	0.273034i	$-0.911973\pi$
$569$	−45.8948	−1.92401	−0.962004	+	0.273034i	$0.911973\pi$
$570$	−0.506030	−0.0211953
$571$	9.31974	0.390019	0.195009	−	0.980801i	$-0.437526\pi$
$571$	9.31974	0.390019	0.195009	+	0.980801i	$0.437526\pi$
$572$	−136.386	−5.70256
$573$	0.267086	0.0111577
$574$	83.2977	3.47678
$575$	0	0
$576$	−52.1586	−2.17328
$577$	−22.1565	−0.922388	−0.461194	−	0.887299i	$-0.652579\pi$
$577$	−22.1565	−0.922388	−0.461194	+	0.887299i	$0.652579\pi$
$578$	−19.5648	−0.813787
$579$	4.32260	0.179641
$580$	1.00442	0.0417063
$581$	26.6993	1.10767
$582$	0.793052	0.0328731
$583$	−22.3477	−0.925548
$584$	9.55958	0.395578
$585$	14.2589	0.589533
$586$	−71.5583	−2.95605
$587$	−3.68617	−0.152145	−0.0760723	−	0.997102i	$-0.524238\pi$
$587$	−3.68617	−0.152145	−0.0760723	+	0.997102i	$0.524238\pi$
$588$	−1.54756	−0.0638201
$589$	−5.61751	−0.231466
$590$	−24.6810	−1.01610
$591$	0.841721	0.0346238
$592$	69.0909	2.83962
$593$	36.6339	1.50437	0.752186	−	0.658951i	$-0.228999\pi$
$593$	36.6339	1.50437	0.752186	+	0.658951i	$0.228999\pi$
$594$	15.3590	0.630186
$595$	−9.19076	−0.376784
$596$	−47.0961	−1.92913
$597$	−0.853238	−0.0349207
$598$	0	0
$599$	18.9252	0.773263	0.386631	−	0.922234i	$-0.373639\pi$
$599$	18.9252	0.773263	0.386631	+	0.922234i	$0.373639\pi$
$600$	−1.46203	−0.0596872
$601$	−11.4063	−0.465274	−0.232637	−	0.972564i	$-0.574735\pi$
$601$	−11.4063	−0.465274	−0.232637	+	0.972564i	$0.574735\pi$
$602$	0.304231	0.0123995
$603$	4.91932	0.200330
$604$	62.9144	2.55995
$605$	19.5364	0.794269
$606$	0.681962	0.0277028
$607$	29.3520	1.19136	0.595680	−	0.803222i	$-0.296882\pi$
$607$	29.3520	1.19136	0.595680	+	0.803222i	$0.296882\pi$
$608$	17.0204	0.690269
$609$	−0.100588	−0.00407602
$610$	−23.0870	−0.934765
$611$	16.9405	0.685341
$612$	47.4873	1.91956
$613$	−1.21861	−0.0492191	−0.0246095	−	0.999697i	$-0.507834\pi$
$613$	−1.21861	−0.0492191	−0.0246095	+	0.999697i	$0.507834\pi$
$614$	−9.03789	−0.364740
$615$	−1.83855	−0.0741373
$616$	136.984	5.51925
$617$	19.4208	0.781850	0.390925	−	0.920422i	$-0.372155\pi$
$617$	19.4208	0.781850	0.390925	+	0.920422i	$0.372155\pi$
$618$	1.94909	0.0784038
$619$	−1.44093	−0.0579160	−0.0289580	−	0.999581i	$-0.509219\pi$
$619$	−1.44093	−0.0579160	−0.0289580	+	0.999581i	$0.509219\pi$
$620$	−26.5674	−1.06697
$621$	0	0
$622$	−63.5673	−2.54882
$623$	−13.2255	−0.529868
$624$	10.1575	0.406624
$625$	1.00000	0.0400000
$626$	28.4968	1.13896
$627$	−1.04648	−0.0417924
$628$	−74.6664	−2.97951
$629$	−17.7037	−0.705893
$630$	−23.4430	−0.933991
$631$	39.5371	1.57395	0.786974	−	0.616986i	$-0.211646\pi$
$631$	39.5371	1.57395	0.786974	+	0.616986i	$0.211646\pi$
$632$	−107.848	−4.28997
$633$	3.53619	0.140551
$634$	36.8706	1.46432
$635$	14.3072	0.567764
$636$	3.62203	0.143623
$637$	−8.29661	−0.328724
$638$	2.88538	0.114233
$639$	41.6573	1.64794
$640$	15.6123	0.617131
$641$	−15.4201	−0.609058	−0.304529	−	0.952503i	$-0.598499\pi$
$641$	−15.4201	−0.609058	−0.304529	+	0.952503i	$0.598499\pi$
$642$	−3.27487	−0.129249
$643$	44.7240	1.76374	0.881871	−	0.471491i	$-0.156284\pi$
$643$	44.7240	1.76374	0.881871	+	0.471491i	$0.156284\pi$
$644$	0	0
$645$	−0.00671498	−0.000264402 0
$646$	−9.03487	−0.355472
$647$	29.4009	1.15587	0.577935	−	0.816083i	$-0.303859\pi$
$647$	29.4009	1.15587	0.577935	+	0.816083i	$0.303859\pi$
$648$	73.2328	2.87685
$649$	−51.0409	−2.00353
$650$	−12.8303	−0.503245
$651$	2.66059	0.104277
$652$	−16.8495	−0.659877
$653$	28.5135	1.11582	0.557910	−	0.829901i	$-0.311603\pi$
$653$	28.5135	1.11582	0.557910	+	0.829901i	$0.311603\pi$
$654$	−8.47929	−0.331567
$655$	−3.65367	−0.142761
$656$	128.108	5.00179
$657$	−3.38327	−0.131994
$658$	−27.8519	−1.08578
$659$	−38.7813	−1.51070	−0.755352	−	0.655319i	$-0.772534\pi$
$659$	−38.7813	−1.51070	−0.755352	+	0.655319i	$0.772534\pi$
$660$	−4.94922	−0.192648
$661$	21.0344	0.818145	0.409072	−	0.912502i	$-0.365852\pi$
$661$	21.0344	0.818145	0.409072	+	0.912502i	$0.365852\pi$
$662$	−25.1038	−0.975687
$663$	−2.60273	−0.101082
$664$	75.8319	2.94285
$665$	3.21090	0.124513
$666$	−45.1570	−1.74980
$667$	0	0
$668$	112.933	4.36952
$669$	2.42160	0.0936244
$670$	−4.42645	−0.171009
$671$	−47.7444	−1.84315
$672$	−8.06128	−0.310971
$673$	−23.1329	−0.891707	−0.445854	−	0.895106i	$-0.647100\pi$
$673$	−23.1329	−0.891707	−0.445854	+	0.895106i	$0.647100\pi$
$674$	−12.9014	−0.496944
$675$	1.04016	0.0400356
$676$	51.6841	1.98785
$677$	−46.3312	−1.78065	−0.890327	−	0.455322i	$-0.849524\pi$
$677$	−46.3312	−1.78065	−0.890327	+	0.455322i	$0.849524\pi$
$678$	−3.63573	−0.139629
$679$	−5.03213	−0.193116
$680$	−26.1037	−1.00103
$681$	−1.53373	−0.0587725
$682$	−76.3196	−2.92243
$683$	−11.0573	−0.423097	−0.211548	−	0.977368i	$-0.567851\pi$
$683$	−11.0573	−0.423097	−0.211548	+	0.977368i	$0.567851\pi$
$684$	−16.5902	−0.634343
$685$	21.7157	0.829716
$686$	−41.6191	−1.58902
$687$	0.731291	0.0279005
$688$	0.467894	0.0178383
$689$	19.4181	0.739770
$690$	0	0
$691$	33.0280	1.25644	0.628222	−	0.778034i	$-0.283783\pi$
$691$	33.0280	1.25644	0.628222	+	0.778034i	$0.283783\pi$
$692$	−90.3899	−3.43611
$693$	−48.4806	−1.84163
$694$	−53.0849	−2.01507
$695$	−0.0207896	−0.000788596 0
$696$	−0.285691	−0.0108291
$697$	−32.8262	−1.24338
$698$	29.3588	1.11125
$699$	1.11568	0.0421990
$700$	15.1856	0.573962
$701$	−12.5072	−0.472390	−0.236195	−	0.971706i	$-0.575900\pi$
$701$	−12.5072	−0.472390	−0.236195	+	0.971706i	$0.575900\pi$
$702$	−13.3455	−0.503693
$703$	6.18499	0.233271
$704$	97.0580	3.65801
$705$	0.614746	0.0231527
$706$	67.0105	2.52197
$707$	−4.32723	−0.162742
$708$	8.27249	0.310899
$709$	27.9335	1.04906	0.524532	−	0.851391i	$-0.324240\pi$
$709$	27.9335	1.04906	0.524532	+	0.851391i	$0.324240\pi$
$710$	−37.4837	−1.40674
$711$	38.1689	1.43145
$712$	−37.5633	−1.40774
$713$	0	0
$714$	4.27913	0.160143
$715$	−26.5333	−0.992289
$716$	35.0967	1.31162
$717$	3.00669	0.112287
$718$	2.42790	0.0906084
$719$	−47.2337	−1.76152	−0.880759	−	0.473565i	$-0.842967\pi$
$719$	−47.2337	−1.76152	−0.880759	+	0.473565i	$0.842967\pi$
$720$	−36.0543	−1.34366
$721$	−12.3675	−0.460590
$722$	−47.6136	−1.77200
$723$	−2.52737	−0.0939940
$724$	−55.8808	−2.07679
$725$	0.195407	0.00725722
$726$	−9.09599	−0.337584
$727$	−40.9027	−1.51700	−0.758499	−	0.651675i	$-0.774067\pi$
$727$	−40.9027	−1.51700	−0.758499	+	0.651675i	$0.774067\pi$
$728$	−119.026	−4.41141
$729$	−25.3744	−0.939791
$730$	3.04429	0.112674
$731$	−0.119892	−0.00443437
$732$	7.73821	0.286013
$733$	38.1358	1.40858	0.704288	−	0.709914i	$-0.251266\pi$
$733$	38.1358	1.40858	0.704288	+	0.709914i	$0.251266\pi$
$734$	−69.1294	−2.55161
$735$	−0.301071	−0.0111052
$736$	0	0
$737$	−9.15400	−0.337192
$738$	−83.7302	−3.08215
$739$	3.32548	0.122330	0.0611649	−	0.998128i	$-0.480518\pi$
$739$	3.32548	0.122330	0.0611649	+	0.998128i	$0.480518\pi$
$740$	29.2513	1.07530
$741$	0.909293	0.0334037
$742$	−31.9252	−1.17201
$743$	39.7232	1.45730	0.728652	−	0.684884i	$-0.240147\pi$
$743$	39.7232	1.45730	0.728652	+	0.684884i	$0.240147\pi$
$744$	7.55665	0.277040
$745$	−9.16238	−0.335684
$746$	69.3721	2.53989
$747$	−26.8379	−0.981948
$748$	−88.3655	−3.23096
$749$	20.7799	0.759282
$750$	−0.465591	−0.0170010
$751$	13.7323	0.501098	0.250549	−	0.968104i	$-0.419389\pi$
$751$	13.7323	0.501098	0.250549	+	0.968104i	$0.419389\pi$
$752$	−42.8350	−1.56203
$753$	−4.34757	−0.158434
$754$	−2.50712	−0.0913040
$755$	12.2398	0.445451
$756$	15.7954	0.574473
$757$	28.6125	1.03994	0.519970	−	0.854184i	$-0.325943\pi$
$757$	28.6125	1.03994	0.519970	+	0.854184i	$0.325943\pi$
$758$	66.6090	2.41935
$759$	0	0
$760$	9.11965	0.330804
$761$	−4.15741	−0.150706	−0.0753529	−	0.997157i	$-0.524008\pi$
$761$	−4.15741	−0.150706	−0.0753529	+	0.997157i	$0.524008\pi$
$762$	−6.66131	−0.241314
$763$	53.8034	1.94782
$764$	−7.87912	−0.285056
$765$	9.23847	0.334018
$766$	36.9394	1.33468
$767$	44.3497	1.60138
$768$	−1.14823	−0.0414330
$769$	8.05684	0.290537	0.145269	−	0.989392i	$-0.453595\pi$
$769$	8.05684	0.290537	0.145269	+	0.989392i	$0.453595\pi$
$770$	43.6233	1.57207
$771$	−5.10969	−0.184021
$772$	−127.518	−4.58948
$773$	−3.76498	−0.135417	−0.0677084	−	0.997705i	$-0.521569\pi$
$773$	−3.76498	−0.135417	−0.0677084	+	0.997705i	$0.521569\pi$
$774$	−0.305810	−0.0109921
$775$	−5.16860	−0.185661
$776$	−14.2923	−0.513065
$777$	−2.92936	−0.105090
$778$	−18.7305	−0.671521
$779$	11.4682	0.410891
$780$	4.30041	0.153979
$781$	−77.5170	−2.77378
$782$	0	0
$783$	0.203253	0.00726368
$784$	20.9784	0.749228
$785$	−14.5261	−0.518458
$786$	1.70112	0.0606769
$787$	−40.3029	−1.43664	−0.718321	−	0.695711i	$-0.755089\pi$
$787$	−40.3029	−1.43664	−0.718321	+	0.695711i	$0.755089\pi$
$788$	−24.8310	−0.884569
$789$	1.05130	0.0374272
$790$	−34.3447	−1.22193
$791$	23.0697	0.820264
$792$	−137.695	−4.89279
$793$	41.4854	1.47319
$794$	46.9517	1.66625
$795$	0.704652	0.0249914
$796$	25.1708	0.892154
$797$	33.6780	1.19294	0.596468	−	0.802637i	$-0.296570\pi$
$797$	33.6780	1.19294	0.596468	+	0.802637i	$0.296570\pi$
$798$	−1.49496	−0.0529212
$799$	10.9759	0.388301
$800$	15.6602	0.553673
$801$	13.2942	0.469726
$802$	19.9180	0.703328
$803$	6.29566	0.222169
$804$	1.48364	0.0523240
$805$	0	0
$806$	66.3145	2.33583
$807$	2.18307	0.0768477
$808$	−12.2903	−0.432371
$809$	50.3610	1.77060	0.885299	−	0.465022i	$-0.153954\pi$
$809$	50.3610	1.77060	0.885299	+	0.465022i	$0.153954\pi$
$810$	23.3213	0.819427
$811$	−39.1012	−1.37303	−0.686514	−	0.727117i	$-0.740860\pi$
$811$	−39.1012	−1.37303	−0.686514	+	0.727117i	$0.740860\pi$
$812$	2.96737	0.104134
$813$	3.17177	0.111239
$814$	84.0293	2.94523
$815$	−3.27801	−0.114824
$816$	6.58112	0.230385
$817$	0.0418857	0.00146540
$818$	86.3115	3.01781
$819$	42.1251	1.47197
$820$	54.2377	1.89406
$821$	−24.5276	−0.856020	−0.428010	−	0.903774i	$-0.640785\pi$
$821$	−24.5276	−0.856020	−0.428010	+	0.903774i	$0.640785\pi$
$822$	−10.1107	−0.352650
$823$	−5.14408	−0.179312	−0.0896558	−	0.995973i	$-0.528577\pi$
$823$	−5.14408	−0.179312	−0.0896558	+	0.995973i	$0.528577\pi$
$824$	−35.1264	−1.22369
$825$	−0.962852	−0.0335222
$826$	−72.9152	−2.53704
$827$	34.2601	1.19134	0.595669	−	0.803230i	$-0.296887\pi$
$827$	34.2601	1.19134	0.595669	+	0.803230i	$0.296887\pi$
$828$	0	0
$829$	−37.0732	−1.28761	−0.643803	−	0.765192i	$-0.722644\pi$
$829$	−37.0732	−1.28761	−0.643803	+	0.765192i	$0.722644\pi$
$830$	24.1490	0.838224
$831$	1.55729	0.0540219
$832$	−84.3343	−2.92377
$833$	−5.37545	−0.186248
$834$	0.00967947	0.000335173 0
$835$	21.9708	0.760330
$836$	30.8715	1.06771
$837$	−5.37615	−0.185827
$838$	28.3075	0.977865
$839$	40.5084	1.39851	0.699253	−	0.714874i	$-0.253516\pi$
$839$	40.5084	1.39851	0.699253	+	0.714874i	$0.253516\pi$
$840$	−4.31929	−0.149030
$841$	−28.9618	−0.998683
$842$	52.2628	1.80109
$843$	−0.588343	−0.0202636
$844$	−104.319	−3.59080
$845$	10.0549	0.345901
$846$	27.9965	0.962538
$847$	57.7165	1.98316
$848$	−49.0995	−1.68608
$849$	2.42173	0.0831137
$850$	−8.31286	−0.285129
$851$	0	0
$852$	12.5636	0.430423
$853$	10.2284	0.350212	0.175106	−	0.984550i	$-0.443973\pi$
$853$	10.2284	0.350212	0.175106	+	0.984550i	$0.443973\pi$
$854$	−68.2059	−2.33396
$855$	−3.22757	−0.110380
$856$	59.0195	2.01725
$857$	2.67608	0.0914131	0.0457065	−	0.998955i	$-0.485446\pi$
$857$	2.67608	0.0914131	0.0457065	+	0.998955i	$0.485446\pi$
$858$	12.3537	0.421747
$859$	15.5897	0.531915	0.265957	−	0.963985i	$-0.414312\pi$
$859$	15.5897	0.531915	0.265957	+	0.963985i	$0.414312\pi$
$860$	0.198094	0.00675495
$861$	−5.43162	−0.185109
$862$	26.9174	0.916809
$863$	0.873157	0.0297226	0.0148613	−	0.999890i	$-0.495269\pi$
$863$	0.873157	0.0297226	0.0148613	+	0.999890i	$0.495269\pi$
$864$	16.2891	0.554167
$865$	−17.5850	−0.597909
$866$	−30.8608	−1.04869
$867$	1.27577	0.0433273
$868$	−78.4882	−2.66406
$869$	−71.0256	−2.40938
$870$	−0.0909795	−0.00308450
$871$	7.95396	0.269510
$872$	152.813	5.17492
$873$	5.05826	0.171196
$874$	0	0
$875$	2.95430	0.0998736
$876$	−1.02037	−0.0344753
$877$	51.4650	1.73785	0.868925	−	0.494945i	$-0.164812\pi$
$877$	51.4650	1.73785	0.868925	+	0.494945i	$0.164812\pi$
$878$	10.6764	0.360310
$879$	4.66612	0.157384
$880$	67.0907	2.26163
$881$	43.7973	1.47557	0.737785	−	0.675036i	$-0.235872\pi$
$881$	43.7973	1.47557	0.737785	+	0.675036i	$0.235872\pi$
$882$	−13.7112	−0.461682
$883$	−11.8077	−0.397360	−0.198680	−	0.980064i	$-0.563665\pi$
$883$	−11.8077	−0.397360	−0.198680	+	0.980064i	$0.563665\pi$
$884$	76.7813	2.58243
$885$	1.60938	0.0540988
$886$	33.3426	1.12017
$887$	33.8957	1.13811	0.569053	−	0.822301i	$-0.307310\pi$
$887$	33.8957	1.13811	0.569053	+	0.822301i	$0.307310\pi$
$888$	−8.32003	−0.279202
$889$	42.2678	1.41762
$890$	−11.9622	−0.400974
$891$	48.2290	1.61573
$892$	−71.4379	−2.39192
$893$	−3.83457	−0.128319
$894$	4.26592	0.142674
$895$	6.82793	0.228232
$896$	46.1235	1.54088
$897$	0	0
$898$	9.99636	0.333583
$899$	−1.00998	−0.0336846
$900$	−15.2644	−0.508815
$901$	12.5812	0.419139
$902$	155.807	5.18781
$903$	−0.0198381	−0.000660170 0
$904$	65.5230	2.17926
$905$	−10.8714	−0.361378
$906$	−5.69873	−0.189328
$907$	50.8030	1.68689	0.843444	−	0.537218i	$-0.180525\pi$
$907$	50.8030	1.68689	0.843444	+	0.537218i	$0.180525\pi$
$908$	45.2454	1.50152
$909$	4.34970	0.144270
$910$	−37.9045	−1.25652
$911$	−0.111712	−0.00370119	−0.00185059	−	0.999998i	$-0.500589\pi$
$911$	−0.111712	−0.00370119	−0.00185059	+	0.999998i	$0.500589\pi$
$912$	−2.29919	−0.0761338
$913$	49.9407	1.65279
$914$	61.1706	2.02334
$915$	1.50544	0.0497683
$916$	−21.5733	−0.712802
$917$	−10.7941	−0.356451
$918$	−8.64667	−0.285383
$919$	44.9530	1.48286	0.741431	−	0.671029i	$-0.234147\pi$
$919$	44.9530	1.48286	0.741431	+	0.671029i	$0.234147\pi$
$920$	0	0
$921$	0.589337	0.0194193
$922$	55.8286	1.83862
$923$	67.3550	2.21702
$924$	−14.6215	−0.481012
$925$	5.69073	0.187110
$926$	69.4673	2.28284
$927$	12.4317	0.408311
$928$	3.06012	0.100453
$929$	24.5909	0.806800	0.403400	−	0.915024i	$-0.367828\pi$
$929$	24.5909	0.806800	0.403400	+	0.915024i	$0.367828\pi$
$930$	2.40645	0.0789107
$931$	1.87798	0.0615482
$932$	−32.9130	−1.07810
$933$	4.14505	0.135703
$934$	−67.9610	−2.22375
$935$	−17.1912	−0.562211
$936$	119.644	3.91070
$937$	−30.4433	−0.994539	−0.497270	−	0.867596i	$-0.665664\pi$
$937$	−30.4433	−0.994539	−0.497270	+	0.867596i	$0.665664\pi$
$938$	−13.0771	−0.426982
$939$	−1.85820	−0.0606400
$940$	−18.1352	−0.591505
$941$	−36.1828	−1.17952	−0.589762	−	0.807577i	$-0.700779\pi$
$941$	−36.1828	−1.17952	−0.589762	+	0.807577i	$0.700779\pi$
$942$	6.76321	0.220357
$943$	0	0
$944$	−112.140	−3.64986
$945$	3.07294	0.0999626
$946$	0.569059	0.0185017
$947$	−26.0262	−0.845738	−0.422869	−	0.906191i	$-0.638977\pi$
$947$	−26.0262	−0.845738	−0.422869	+	0.906191i	$0.638977\pi$
$948$	11.5115	0.373877
$949$	−5.47034	−0.177575
$950$	2.90419	0.0942245
$951$	−2.40423	−0.0779625
$952$	−77.1183	−2.49942
$953$	−23.4578	−0.759874	−0.379937	−	0.925012i	$-0.624054\pi$
$953$	−23.4578	−0.759874	−0.379937	+	0.925012i	$0.624054\pi$
$954$	32.0909	1.03898
$955$	−1.53285	−0.0496020
$956$	−88.6982	−2.86871
$957$	−0.188148	−0.00608195
$958$	−72.2575	−2.33453
$959$	64.1549	2.07167
$960$	−3.06036	−0.0987728
$961$	−4.28562	−0.138246
$962$	−73.0136	−2.35405
$963$	−20.8878	−0.673100
$964$	74.5583	2.40136
$965$	−24.8082	−0.798604
$966$	0	0
$967$	−12.3252	−0.396352	−0.198176	−	0.980166i	$-0.563502\pi$
$967$	−12.3252	−0.396352	−0.198176	+	0.980166i	$0.563502\pi$
$968$	163.928	5.26883
$969$	0.589140	0.0189259
$970$	−4.55147	−0.146139
$971$	14.9038	0.478287	0.239143	−	0.970984i	$-0.423133\pi$
$971$	14.9038	0.478287	0.239143	+	0.970984i	$0.423133\pi$
$972$	−23.8565	−0.765197
$973$	−0.0614189	−0.00196900
$974$	34.6361	1.10981
$975$	0.836628	0.0267935
$976$	−104.898	−3.35770
$977$	−30.9563	−0.990380	−0.495190	−	0.868785i	$-0.664902\pi$
$977$	−30.9563	−0.990380	−0.495190	+	0.868785i	$0.664902\pi$
$978$	1.52621	0.0488028
$979$	−24.7381	−0.790633
$980$	8.88170	0.283715
$981$	−54.0828	−1.72673
$982$	18.1967	0.580681
$983$	36.1810	1.15399	0.576997	−	0.816747i	$-0.304225\pi$
$983$	36.1810	1.15399	0.576997	+	0.816747i	$0.304225\pi$
$984$	−15.4270	−0.491794
$985$	−4.83078	−0.153922
$986$	−1.62439	−0.0517310
$987$	1.81615	0.0578085
$988$	−26.8244	−0.853399
$989$	0	0
$990$	−43.8497	−1.39364
$991$	33.0399	1.04955	0.524773	−	0.851242i	$-0.324150\pi$
$991$	33.0399	1.04955	0.524773	+	0.851242i	$0.324150\pi$
$992$	−80.9415	−2.56989
$993$	1.63695	0.0519471
$994$	−110.738	−3.51240
$995$	4.89688	0.155242
$996$	−8.09418	−0.256474
$997$	46.7877	1.48178	0.740891	−	0.671625i	$-0.234403\pi$
$997$	46.7877	1.48178	0.740891	+	0.671625i	$0.234403\pi$
$998$	14.8953	0.471504
$999$	5.91924	0.187277

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	2645.2.a.w.1.16	yes	16
23.22	odd	2		2645.2.a.v.1.16	✓	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
2645.2.a.v.1.16	✓	16	23.22	odd	2
2645.2.a.w.1.16	yes	16	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)

\(f(q)\)	\(=\)	\(q+2.67211 q^{2} -0.174241 q^{3} +5.14016 q^{4} +1.00000 q^{5} -0.465591 q^{6} +2.95430 q^{7} +8.39086 q^{8} -2.96964 q^{9} +O(q^{10})\)	\(q+2.67211 q^{2} -0.174241 q^{3} +5.14016 q^{4} +1.00000 q^{5} -0.465591 q^{6} +2.95430 q^{7} +8.39086 q^{8} -2.96964 q^{9} +2.67211 q^{10} +5.52598 q^{11} -0.895628 q^{12} -4.80156 q^{13} +7.89422 q^{14} -0.174241 q^{15} +12.1410 q^{16} -3.11097 q^{17} -7.93520 q^{18} +1.08685 q^{19} +5.14016 q^{20} -0.514761 q^{21} +14.7660 q^{22} -1.46203 q^{24} +1.00000 q^{25} -12.8303 q^{26} +1.04016 q^{27} +15.1856 q^{28} +0.195407 q^{29} -0.465591 q^{30} -5.16860 q^{31} +15.6602 q^{32} -0.962852 q^{33} -8.31286 q^{34} +2.95430 q^{35} -15.2644 q^{36} +5.69073 q^{37} +2.90419 q^{38} +0.836628 q^{39} +8.39086 q^{40} +10.5517 q^{41} -1.37550 q^{42} +0.0385385 q^{43} +28.4044 q^{44} -2.96964 q^{45} -3.52814 q^{47} -2.11545 q^{48} +1.72790 q^{49} +2.67211 q^{50} +0.542059 q^{51} -24.6808 q^{52} -4.04412 q^{53} +2.77941 q^{54} +5.52598 q^{55} +24.7891 q^{56} -0.189375 q^{57} +0.522148 q^{58} -9.23653 q^{59} -0.895628 q^{60} -8.63999 q^{61} -13.8110 q^{62} -8.77321 q^{63} +17.5640 q^{64} -4.80156 q^{65} -2.57285 q^{66} -1.65654 q^{67} -15.9909 q^{68} +7.89422 q^{70} -14.0277 q^{71} -24.9178 q^{72} +1.13928 q^{73} +15.2062 q^{74} -0.174241 q^{75} +5.58661 q^{76} +16.3254 q^{77} +2.23556 q^{78} -12.8530 q^{79} +12.1410 q^{80} +8.72768 q^{81} +28.1954 q^{82} +9.03744 q^{83} -2.64595 q^{84} -3.11097 q^{85} +0.102979 q^{86} -0.0340478 q^{87} +46.3677 q^{88} -4.47669 q^{89} -7.93520 q^{90} -14.1852 q^{91} +0.900582 q^{93} -9.42756 q^{94} +1.08685 q^{95} -2.72866 q^{96} -1.70332 q^{97} +4.61714 q^{98} -16.4102 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 4 q^{2} + 4 q^{3} + 20 q^{4} + 16 q^{5} - 12 q^{6} + 12 q^{7} + 8 q^{9}+O(q^{10}) \) 16 * q + 4 * q^2 + 4 * q^3 + 20 * q^4 + 16 * q^5 - 12 * q^6 + 12 * q^7 + 8 * q^9	\( 16 q + 4 q^{2} + 4 q^{3} + 20 q^{4} + 16 q^{5} - 12 q^{6} + 12 q^{7} + 8 q^{9} + 4 q^{10} + 16 q^{11} - 4 q^{12} + 8 q^{13} + 8 q^{14} + 4 q^{15} + 28 q^{16} - 8 q^{17} + 4 q^{18} + 32 q^{19} + 20 q^{20} + 16 q^{21} + 44 q^{22} - 28 q^{24} + 16 q^{25} - 20 q^{26} - 8 q^{27} + 52 q^{28} - 12 q^{29} - 12 q^{30} - 12 q^{31} + 4 q^{32} + 20 q^{33} + 24 q^{34} + 12 q^{35} - 4 q^{36} + 28 q^{37} - 20 q^{38} - 8 q^{39} - 4 q^{41} - 8 q^{42} + 48 q^{43} + 32 q^{44} + 8 q^{45} + 48 q^{47} + 24 q^{48} + 12 q^{49} + 4 q^{50} + 24 q^{51} + 12 q^{52} - 4 q^{53} - 44 q^{54} + 16 q^{55} + 64 q^{56} + 52 q^{57} - 28 q^{58} - 40 q^{59} - 4 q^{60} + 16 q^{61} + 4 q^{63} - 16 q^{64} + 8 q^{65} + 8 q^{66} + 68 q^{67} - 4 q^{68} + 8 q^{70} - 24 q^{71} - 12 q^{72} + 52 q^{73} + 40 q^{74} + 4 q^{75} + 24 q^{76} + 44 q^{77} + 12 q^{78} + 72 q^{79} + 28 q^{80} + 20 q^{81} - 20 q^{82} + 12 q^{83} + 32 q^{84} - 8 q^{85} - 56 q^{86} + 104 q^{88} + 48 q^{89} + 4 q^{90} + 48 q^{91} - 48 q^{93} - 60 q^{94} + 32 q^{95} - 108 q^{96} + 4 q^{97} + 8 q^{98} + 24 q^{99}+O(q^{100}) \) 16 * q + 4 * q^2 + 4 * q^3 + 20 * q^4 + 16 * q^5 - 12 * q^6 + 12 * q^7 + 8 * q^9 + 4 * q^10 + 16 * q^11 - 4 * q^12 + 8 * q^13 + 8 * q^14 + 4 * q^15 + 28 * q^16 - 8 * q^17 + 4 * q^18 + 32 * q^19 + 20 * q^20 + 16 * q^21 + 44 * q^22 - 28 * q^24 + 16 * q^25 - 20 * q^26 - 8 * q^27 + 52 * q^28 - 12 * q^29 - 12 * q^30 - 12 * q^31 + 4 * q^32 + 20 * q^33 + 24 * q^34 + 12 * q^35 - 4 * q^36 + 28 * q^37 - 20 * q^38 - 8 * q^39 - 4 * q^41 - 8 * q^42 + 48 * q^43 + 32 * q^44 + 8 * q^45 + 48 * q^47 + 24 * q^48 + 12 * q^49 + 4 * q^50 + 24 * q^51 + 12 * q^52 - 4 * q^53 - 44 * q^54 + 16 * q^55 + 64 * q^56 + 52 * q^57 - 28 * q^58 - 40 * q^59 - 4 * q^60 + 16 * q^61 + 4 * q^63 - 16 * q^64 + 8 * q^65 + 8 * q^66 + 68 * q^67 - 4 * q^68 + 8 * q^70 - 24 * q^71 - 12 * q^72 + 52 * q^73 + 40 * q^74 + 4 * q^75 + 24 * q^76 + 44 * q^77 + 12 * q^78 + 72 * q^79 + 28 * q^80 + 20 * q^81 - 20 * q^82 + 12 * q^83 + 32 * q^84 - 8 * q^85 - 56 * q^86 + 104 * q^88 + 48 * q^89 + 4 * q^90 + 48 * q^91 - 48 * q^93 - 60 * q^94 + 32 * q^95 - 108 * q^96 + 4 * q^97 + 8 * q^98 + 24 * q^99

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