LMFDB - Embedded newform 435.4.a.i.1.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,4,Mod(1,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("435.1");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	435.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:	$25.6658308525$
Analytic rank:	$0$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 2x^{6} - 37x^{5} + 55x^{4} + 336x^{3} - 227x^{2} - 824x - 166 $ x^7 - 2x^6 - 37x^5 + 55x^4 + 336x^3 - 227x^2 - 824x - 166
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.2
Root			$3.57720$ of defining polynomial
Character	$\chi$	$=$	435.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.57720 q^{2} -3.00000 q^{3} +4.79637 q^{4} +5.00000 q^{5} +10.7316 q^{6} +15.0281 q^{7} +11.4600 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q-3.57720 q^{2} -3.00000 q^{3} +4.79637 q^{4} +5.00000 q^{5} +10.7316 q^{6} +15.0281 q^{7} +11.4600 q^{8} +9.00000 q^{9} -17.8860 q^{10} +70.8260 q^{11} -14.3891 q^{12} +62.2117 q^{13} -53.7587 q^{14} -15.0000 q^{15} -79.3658 q^{16} -67.1848 q^{17} -32.1948 q^{18} +118.988 q^{19} +23.9818 q^{20} -45.0844 q^{21} -253.359 q^{22} +72.5383 q^{23} -34.3801 q^{24} +25.0000 q^{25} -222.544 q^{26} -27.0000 q^{27} +72.0804 q^{28} +29.0000 q^{29} +53.6580 q^{30} -180.227 q^{31} +192.227 q^{32} -212.478 q^{33} +240.334 q^{34} +75.1407 q^{35} +43.1673 q^{36} -47.8439 q^{37} -425.646 q^{38} -186.635 q^{39} +57.3002 q^{40} +371.956 q^{41} +161.276 q^{42} -409.069 q^{43} +339.707 q^{44} +45.0000 q^{45} -259.484 q^{46} +125.891 q^{47} +238.097 q^{48} -117.155 q^{49} -89.4300 q^{50} +201.555 q^{51} +298.390 q^{52} -215.764 q^{53} +96.5844 q^{54} +354.130 q^{55} +172.223 q^{56} -356.965 q^{57} -103.739 q^{58} +356.919 q^{59} -71.9455 q^{60} -466.115 q^{61} +644.707 q^{62} +135.253 q^{63} -52.7086 q^{64} +311.059 q^{65} +760.076 q^{66} -578.359 q^{67} -322.243 q^{68} -217.615 q^{69} -268.793 q^{70} +870.924 q^{71} +103.140 q^{72} +411.904 q^{73} +171.147 q^{74} -75.0000 q^{75} +570.712 q^{76} +1064.38 q^{77} +667.631 q^{78} +1120.23 q^{79} -396.829 q^{80} +81.0000 q^{81} -1330.56 q^{82} +1079.28 q^{83} -216.241 q^{84} -335.924 q^{85} +1463.32 q^{86} -87.0000 q^{87} +811.668 q^{88} +388.993 q^{89} -160.974 q^{90} +934.926 q^{91} +347.920 q^{92} +540.680 q^{93} -450.339 q^{94} +594.942 q^{95} -576.681 q^{96} -1528.82 q^{97} +419.088 q^{98} +637.434 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9}+O(q^{10}) $ 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19} + 110 q^{20} + 150 q^{21} + 61 q^{22} + 34 q^{23} + 99 q^{24} + 175 q^{25} - 241 q^{26} - 189 q^{27} - 57 q^{28} + 203 q^{29} + 30 q^{30} + 524 q^{31} - 6 q^{32} - 228 q^{33} + 255 q^{34} - 250 q^{35} + 198 q^{36} - 28 q^{37} + 222 q^{38} - 90 q^{39} - 165 q^{40} + 1532 q^{41} - 267 q^{42} - 464 q^{43} + 1475 q^{44} + 315 q^{45} + 72 q^{46} - 360 q^{47} - 414 q^{48} + 569 q^{49} - 50 q^{50} + 420 q^{51} - 205 q^{52} + 282 q^{53} + 54 q^{54} + 380 q^{55} + 1102 q^{56} - 270 q^{57} - 58 q^{58} + 766 q^{59} - 330 q^{60} + 1200 q^{61} + 2856 q^{62} - 450 q^{63} + 701 q^{64} + 150 q^{65} - 183 q^{66} + 1546 q^{67} + 1801 q^{68} - 102 q^{69} + 445 q^{70} + 1802 q^{71} - 297 q^{72} - 220 q^{73} + 1594 q^{74} - 525 q^{75} + 1960 q^{76} + 3222 q^{77} + 723 q^{78} + 1298 q^{79} + 690 q^{80} + 567 q^{81} + 856 q^{82} + 1652 q^{83} + 171 q^{84} - 700 q^{85} + 7628 q^{86} - 609 q^{87} + 550 q^{88} + 2846 q^{89} - 90 q^{90} - 816 q^{91} + 472 q^{92} - 1572 q^{93} + 745 q^{94} + 450 q^{95} + 18 q^{96} + 1110 q^{97} - 761 q^{98} + 684 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9 - 10 * q^10 + 76 * q^11 - 66 * q^12 + 30 * q^13 + 89 * q^14 - 105 * q^15 + 138 * q^16 - 140 * q^17 - 18 * q^18 + 90 * q^19 + 110 * q^20 + 150 * q^21 + 61 * q^22 + 34 * q^23 + 99 * q^24 + 175 * q^25 - 241 * q^26 - 189 * q^27 - 57 * q^28 + 203 * q^29 + 30 * q^30 + 524 * q^31 - 6 * q^32 - 228 * q^33 + 255 * q^34 - 250 * q^35 + 198 * q^36 - 28 * q^37 + 222 * q^38 - 90 * q^39 - 165 * q^40 + 1532 * q^41 - 267 * q^42 - 464 * q^43 + 1475 * q^44 + 315 * q^45 + 72 * q^46 - 360 * q^47 - 414 * q^48 + 569 * q^49 - 50 * q^50 + 420 * q^51 - 205 * q^52 + 282 * q^53 + 54 * q^54 + 380 * q^55 + 1102 * q^56 - 270 * q^57 - 58 * q^58 + 766 * q^59 - 330 * q^60 + 1200 * q^61 + 2856 * q^62 - 450 * q^63 + 701 * q^64 + 150 * q^65 - 183 * q^66 + 1546 * q^67 + 1801 * q^68 - 102 * q^69 + 445 * q^70 + 1802 * q^71 - 297 * q^72 - 220 * q^73 + 1594 * q^74 - 525 * q^75 + 1960 * q^76 + 3222 * q^77 + 723 * q^78 + 1298 * q^79 + 690 * q^80 + 567 * q^81 + 856 * q^82 + 1652 * q^83 + 171 * q^84 - 700 * q^85 + 7628 * q^86 - 609 * q^87 + 550 * q^88 + 2846 * q^89 - 90 * q^90 - 816 * q^91 + 472 * q^92 - 1572 * q^93 + 745 * q^94 + 450 * q^95 + 18 * q^96 + 1110 * q^97 - 761 * q^98 + 684 * 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 $

$2$	−3.57720	−1.26473	−0.632366	−	0.774670i	$-0.717916\pi$
$2$	−3.57720	−1.26473	−0.632366	+	0.774670i	$0.717916\pi$
$3$	−3.00000	−0.577350
$3$	−3.00000	−0.577350
$4$	4.79637	0.599546
$5$	5.00000	0.447214
$5$	5.00000	0.447214
$6$	10.7316	0.730193
$7$	15.0281	0.811443	0.405721	−	0.913997i	$-0.367020\pi$
$7$	15.0281	0.811443	0.405721	+	0.913997i	$0.367020\pi$
$8$	11.4600	0.506467
$9$	9.00000	0.333333
$10$	−17.8860	−0.565605
$11$	70.8260	1.94135	0.970674	−	0.240399i	$-0.0772781\pi$
$11$	70.8260	1.94135	0.970674	+	0.240399i	$0.0772781\pi$
$12$	−14.3891	−0.346148
$13$	62.2117	1.32726	0.663632	−	0.748059i	$-0.269014\pi$
$13$	62.2117	1.32726	0.663632	+	0.748059i	$0.269014\pi$
$14$	−53.7587	−1.02626
$15$	−15.0000	−0.258199
$16$	−79.3658	−1.24009
$17$	−67.1848	−0.958513	−0.479256	−	0.877675i	$-0.659094\pi$
$17$	−67.1848	−0.958513	−0.479256	+	0.877675i	$0.659094\pi$
$18$	−32.1948	−0.421577
$19$	118.988	1.43673	0.718364	−	0.695667i	$-0.244891\pi$
$19$	118.988	1.43673	0.718364	+	0.695667i	$0.244891\pi$
$20$	23.9818	0.268125
$21$	−45.0844	−0.468487
$22$	−253.359	−2.45528
$23$	72.5383	0.657621	0.328810	−	0.944396i	$-0.393352\pi$
$23$	72.5383	0.657621	0.328810	+	0.944396i	$0.393352\pi$
$24$	−34.3801	−0.292409
$25$	25.0000	0.200000
$26$	−222.544	−1.67863
$27$	−27.0000	−0.192450
$28$	72.0804	0.486497
$29$	29.0000	0.185695
$29$	29.0000	0.185695
$30$	53.6580	0.326552
$31$	−180.227	−1.04418	−0.522092	−	0.852889i	$-0.674848\pi$
$31$	−180.227	−1.04418	−0.522092	+	0.852889i	$0.674848\pi$
$32$	192.227	1.06191
$33$	−212.478	−1.12084
$34$	240.334	1.21226
$35$	75.1407	0.362888
$36$	43.1673	0.199849
$37$	−47.8439	−0.212581	−0.106290	−	0.994335i	$-0.533897\pi$
$37$	−47.8439	−0.212581	−0.106290	+	0.994335i	$0.533897\pi$
$38$	−425.646	−1.81708
$39$	−186.635	−0.766296
$40$	57.3002	0.226499
$41$	371.956	1.41682	0.708411	−	0.705800i	$-0.249412\pi$
$41$	371.956	1.41682	0.708411	+	0.705800i	$0.249412\pi$
$42$	161.276	0.592510
$43$	−409.069	−1.45075	−0.725377	−	0.688352i	$-0.758334\pi$
$43$	−409.069	−1.45075	−0.725377	+	0.688352i	$0.758334\pi$
$44$	339.707	1.16393
$45$	45.0000	0.149071
$46$	−259.484	−0.831714
$47$	125.891	0.390705	0.195353	−	0.980733i	$-0.437415\pi$
$47$	125.891	0.390705	0.195353	+	0.980733i	$0.437415\pi$
$48$	238.097	0.715967
$49$	−117.155	−0.341560
$50$	−89.4300	−0.252946
$51$	201.555	0.553398
$52$	298.390	0.795755
$53$	−215.764	−0.559198	−0.279599	−	0.960117i	$-0.590202\pi$
$53$	−215.764	−0.559198	−0.279599	+	0.960117i	$0.590202\pi$
$54$	96.5844	0.243398
$55$	354.130	0.868197
$56$	172.223	0.410969
$57$	−356.965	−0.829495
$58$	−103.739	−0.234855
$59$	356.919	0.787575	0.393788	−	0.919201i	$-0.371165\pi$
$59$	356.919	0.787575	0.393788	+	0.919201i	$0.371165\pi$
$60$	−71.9455	−0.154802
$61$	−466.115	−0.978358	−0.489179	−	0.872183i	$-0.662704\pi$
$61$	−466.115	−0.978358	−0.489179	+	0.872183i	$0.662704\pi$
$62$	644.707	1.32061
$63$	135.253	0.270481
$64$	−52.7086	−0.102946
$65$	311.059	0.593570
$66$	760.076	1.41756
$67$	−578.359	−1.05459	−0.527297	−	0.849681i	$-0.676794\pi$
$67$	−578.359	−1.05459	−0.527297	+	0.849681i	$0.676794\pi$
$68$	−322.243	−0.574672
$69$	−217.615	−0.379678
$70$	−268.793	−0.458956
$71$	870.924	1.45577	0.727885	−	0.685699i	$-0.240503\pi$
$71$	870.924	1.45577	0.727885	+	0.685699i	$0.240503\pi$
$72$	103.140	0.168822
$73$	411.904	0.660407	0.330204	−	0.943910i	$-0.392883\pi$
$73$	411.904	0.660407	0.330204	+	0.943910i	$0.392883\pi$
$74$	171.147	0.268857
$75$	−75.0000	−0.115470
$76$	570.712	0.861384
$77$	1064.38	1.57529
$78$	667.631	0.969159
$79$	1120.23	1.59538	0.797692	−	0.603065i	$-0.206054\pi$
$79$	1120.23	1.59538	0.797692	+	0.603065i	$0.206054\pi$
$80$	−396.829	−0.554585
$81$	81.0000	0.111111
$82$	−1330.56	−1.79190
$83$	1079.28	1.42730	0.713652	−	0.700501i	$-0.247040\pi$
$83$	1079.28	1.42730	0.713652	+	0.700501i	$0.247040\pi$
$84$	−216.241	−0.280879
$85$	−335.924	−0.428660
$86$	1463.32	1.83481
$87$	−87.0000	−0.107211
$88$	811.668	0.983229
$89$	388.993	0.463294	0.231647	−	0.972800i	$-0.425589\pi$
$89$	388.993	0.463294	0.231647	+	0.972800i	$0.425589\pi$
$90$	−160.974	−0.188535
$91$	934.926	1.07700
$92$	347.920	0.394274
$93$	540.680	0.602859
$94$	−450.339	−0.494137
$95$	594.942	0.642524
$96$	−576.681	−0.613097
$97$	−1528.82	−1.60029	−0.800147	−	0.599803i	$-0.795245\pi$
$97$	−1528.82	−1.60029	−0.800147	+	0.599803i	$0.795245\pi$
$98$	419.088	0.431982
$99$	637.434	0.647116
$100$	119.909	0.119909
$101$	−1425.50	−1.40439	−0.702193	−	0.711987i	$-0.747796\pi$
$101$	−1425.50	−1.40439	−0.702193	+	0.711987i	$0.747796\pi$
$102$	−721.001	−0.699899
$103$	−1595.68	−1.52648	−0.763240	−	0.646116i	$-0.776392\pi$
$103$	−1595.68	−1.52648	−0.763240	+	0.646116i	$0.776392\pi$
$104$	712.949	0.672215
$105$	−225.422	−0.209514
$106$	771.832	0.707236
$107$	−155.104	−0.140135	−0.0700675	−	0.997542i	$-0.522321\pi$
$107$	−155.104	−0.140135	−0.0700675	+	0.997542i	$0.522321\pi$
$108$	−129.502	−0.115383
$109$	1212.23	1.06524	0.532618	−	0.846356i	$-0.321208\pi$
$109$	1212.23	1.06524	0.532618	+	0.846356i	$0.321208\pi$
$110$	−1266.79	−1.09804
$111$	143.532	0.122733
$112$	−1192.72	−1.00626
$113$	−1152.01	−0.959043	−0.479521	−	0.877530i	$-0.659190\pi$
$113$	−1152.01	−0.959043	−0.479521	+	0.877530i	$0.659190\pi$
$114$	1276.94	1.04909
$115$	362.691	0.294097
$116$	139.095	0.111333
$117$	559.905	0.442421
$118$	−1276.77	−0.996072
$119$	−1009.66	−0.777778
$120$	−171.901	−0.130769
$121$	3685.32	2.76883
$122$	1667.39	1.23736
$123$	−1115.87	−0.818003
$124$	−864.434	−0.626036
$125$	125.000	0.0894427
$126$	−483.828	−0.342086
$127$	398.743	0.278604	0.139302	−	0.990250i	$-0.455514\pi$
$127$	398.743	0.278604	0.139302	+	0.990250i	$0.455514\pi$
$128$	−1349.27	−0.931715
$129$	1227.21	0.837593
$130$	−1112.72	−0.750707
$131$	−385.241	−0.256937	−0.128468	−	0.991714i	$-0.541006\pi$
$131$	−385.241	−0.256937	−0.128468	+	0.991714i	$0.541006\pi$
$132$	−1019.12	−0.671994
$133$	1788.17	1.16582
$134$	2068.90	1.33378
$135$	−135.000	−0.0860663
$136$	−769.941	−0.485455
$137$	−351.877	−0.219437	−0.109719	−	0.993963i	$-0.534995\pi$
$137$	−351.877	−0.219437	−0.109719	+	0.993963i	$0.534995\pi$
$138$	778.452	0.480190
$139$	1138.48	0.694711	0.347355	−	0.937734i	$-0.387080\pi$
$139$	1138.48	0.694711	0.347355	+	0.937734i	$0.387080\pi$
$140$	360.402	0.217568
$141$	−377.674	−0.225574
$142$	−3115.47	−1.84116
$143$	4406.21	2.57668
$144$	−714.292	−0.413364
$145$	145.000	0.0830455
$146$	−1473.46	−0.835238
$147$	351.466	0.197200
$148$	−229.477	−0.127452
$149$	1200.59	0.660107	0.330053	−	0.943962i	$-0.392933\pi$
$149$	1200.59	0.660107	0.330053	+	0.943962i	$0.392933\pi$
$150$	268.290	0.146039
$151$	−1539.35	−0.829605	−0.414802	−	0.909911i	$-0.636149\pi$
$151$	−1539.35	−0.829605	−0.414802	+	0.909911i	$0.636149\pi$
$152$	1363.61	0.727655
$153$	−604.664	−0.319504
$154$	−3807.51	−1.99232
$155$	−901.134	−0.466973
$156$	−895.171	−0.459430
$157$	223.134	0.113427	0.0567136	−	0.998390i	$-0.481938\pi$
$157$	223.134	0.113427	0.0567136	+	0.998390i	$0.481938\pi$
$158$	−4007.28	−2.01773
$159$	647.293	0.322853
$160$	961.136	0.474903
$161$	1090.11	0.533622
$162$	−289.753	−0.140526
$163$	−3114.71	−1.49671	−0.748353	−	0.663301i	$-0.769155\pi$
$163$	−3114.71	−1.49671	−0.748353	+	0.663301i	$0.769155\pi$
$164$	1784.04	0.849450
$165$	−1062.39	−0.501254
$166$	−3860.79	−1.80516
$167$	−1720.78	−0.797351	−0.398676	−	0.917092i	$-0.630530\pi$
$167$	−1720.78	−0.797351	−0.398676	+	0.917092i	$0.630530\pi$
$168$	−516.669	−0.237273
$169$	1673.30	0.761629
$170$	1201.67	0.542140
$171$	1070.90	0.478909
$172$	−1962.04	−0.869793
$173$	2438.70	1.07174	0.535870	−	0.844301i	$-0.319984\pi$
$173$	2438.70	1.07174	0.535870	+	0.844301i	$0.319984\pi$
$174$	311.216	0.135593
$175$	375.703	0.162289
$176$	−5621.16	−2.40745
$177$	−1070.76	−0.454707
$178$	−1391.50	−0.585942
$179$	−2248.00	−0.938676	−0.469338	−	0.883018i	$-0.655507\pi$
$179$	−2248.00	−0.938676	−0.469338	+	0.883018i	$0.655507\pi$
$180$	215.837	0.0893750
$181$	−2357.13	−0.967977	−0.483989	−	0.875074i	$-0.660812\pi$
$181$	−2357.13	−0.967977	−0.483989	+	0.875074i	$0.660812\pi$
$182$	−3344.42	−1.36211
$183$	1398.34	0.564855
$184$	831.292	0.333063
$185$	−239.219	−0.0950689
$186$	−1934.12	−0.762455
$187$	−4758.43	−1.86081
$188$	603.821	0.234246
$189$	−405.760	−0.156162
$190$	−2128.23	−0.812621
$191$	1922.56	0.728331	0.364166	−	0.931334i	$-0.381354\pi$
$191$	1922.56	0.728331	0.364166	+	0.931334i	$0.381354\pi$
$192$	158.126	0.0594362
$193$	1840.68	0.686504	0.343252	−	0.939243i	$-0.388472\pi$
$193$	1840.68	0.686504	0.343252	+	0.939243i	$0.388472\pi$
$194$	5468.91	2.02394
$195$	−933.176	−0.342698
$196$	−561.919	−0.204781
$197$	−2712.79	−0.981109	−0.490555	−	0.871410i	$-0.663206\pi$
$197$	−2712.79	−0.981109	−0.490555	+	0.871410i	$0.663206\pi$
$198$	−2280.23	−0.818428
$199$	224.631	0.0800185	0.0400093	−	0.999199i	$-0.487261\pi$
$199$	224.631	0.0800185	0.0400093	+	0.999199i	$0.487261\pi$
$200$	286.501	0.101293
$201$	1735.08	0.608870
$202$	5099.31	1.77617
$203$	435.816	0.150681
$204$	966.729	0.331787
$205$	1859.78	0.633622
$206$	5708.08	1.93059
$207$	652.845	0.219207
$208$	−4937.48	−1.64593
$209$	8427.48	2.78919
$210$	806.380	0.264979
$211$	−4160.10	−1.35731	−0.678656	−	0.734456i	$-0.737437\pi$
$211$	−4160.10	−1.35731	−0.678656	+	0.734456i	$0.737437\pi$
$212$	−1034.88	−0.335265
$213$	−2612.77	−0.840489
$214$	554.837	0.177233
$215$	−2045.34	−0.648797
$216$	−309.421	−0.0974696
$217$	−2708.47	−0.847295
$218$	−4336.40	−1.34724
$219$	−1235.71	−0.381286
$220$	1698.54	0.520524
$221$	−4179.68	−1.27220
$222$	−513.441	−0.155225
$223$	−1746.41	−0.524432	−0.262216	−	0.965009i	$-0.584453\pi$
$223$	−1746.41	−0.524432	−0.262216	+	0.965009i	$0.584453\pi$
$224$	2888.81	0.861683
$225$	225.000	0.0666667
$226$	4120.97	1.21293
$227$	129.508	0.0378666	0.0189333	−	0.999821i	$-0.493973\pi$
$227$	129.508	0.0378666	0.0189333	+	0.999821i	$0.493973\pi$
$228$	−1712.14	−0.497320
$229$	−682.166	−0.196851	−0.0984253	−	0.995144i	$-0.531381\pi$
$229$	−682.166	−0.196851	−0.0984253	+	0.995144i	$0.531381\pi$
$230$	−1297.42	−0.371954
$231$	−3193.15	−0.909496
$232$	332.341	0.0940486
$233$	1731.11	0.486732	0.243366	−	0.969935i	$-0.421748\pi$
$233$	1731.11	0.486732	0.243366	+	0.969935i	$0.421748\pi$
$234$	−2002.89	−0.559544
$235$	629.457	0.174729
$236$	1711.92	0.472188
$237$	−3360.68	−0.921095
$238$	3611.77	0.983681
$239$	3308.38	0.895402	0.447701	−	0.894183i	$-0.352243\pi$
$239$	3308.38	0.895402	0.447701	+	0.894183i	$0.352243\pi$
$240$	1190.49	0.320190
$241$	3586.39	0.958588	0.479294	−	0.877654i	$-0.340893\pi$
$241$	3586.39	0.958588	0.479294	+	0.877654i	$0.340893\pi$
$242$	−13183.1	−3.50183
$243$	−243.000	−0.0641500
$244$	−2235.66	−0.586571
$245$	−585.776	−0.152750
$246$	3991.68	1.03455
$247$	7402.48	1.90692
$248$	−2065.41	−0.528844
$249$	−3237.83	−0.824054
$250$	−447.150	−0.113121
$251$	−2956.22	−0.743406	−0.371703	−	0.928352i	$-0.621226\pi$
$251$	−2956.22	−0.743406	−0.371703	+	0.928352i	$0.621226\pi$
$252$	648.724	0.162166
$253$	5137.59	1.27667
$254$	−1426.39	−0.352360
$255$	1007.77	0.247487
$256$	5248.27	1.28132
$257$	2258.12	0.548084	0.274042	−	0.961718i	$-0.411639\pi$
$257$	2258.12	0.548084	0.274042	+	0.961718i	$0.411639\pi$
$258$	−4389.96	−1.05933
$259$	−719.004	−0.172497
$260$	1491.95	0.355873
$261$	261.000	0.0618984
$262$	1378.09	0.324956
$263$	2908.67	0.681963	0.340981	−	0.940070i	$-0.389241\pi$
$263$	2908.67	0.681963	0.340981	+	0.940070i	$0.389241\pi$
$264$	−2435.01	−0.567667
$265$	−1078.82	−0.250081
$266$	−6396.66	−1.47445
$267$	−1166.98	−0.267483
$268$	−2774.02	−0.632277
$269$	−297.910	−0.0675238	−0.0337619	−	0.999430i	$-0.510749\pi$
$269$	−297.910	−0.0675238	−0.0337619	+	0.999430i	$0.510749\pi$
$270$	482.922	0.108851
$271$	6993.04	1.56752	0.783758	−	0.621067i	$-0.213300\pi$
$271$	6993.04	1.56752	0.783758	+	0.621067i	$0.213300\pi$
$272$	5332.18	1.18864
$273$	−2804.78	−0.621805
$274$	1258.73	0.277529
$275$	1770.65	0.388270
$276$	−1043.76	−0.227634
$277$	5701.84	1.23679	0.618394	−	0.785868i	$-0.287784\pi$
$277$	5701.84	1.23679	0.618394	+	0.785868i	$0.287784\pi$
$278$	−4072.58	−0.878622
$279$	−1622.04	−0.348061
$280$	861.115	0.183791
$281$	−1216.34	−0.258223	−0.129112	−	0.991630i	$-0.541213\pi$
$281$	−1216.34	−0.258223	−0.129112	+	0.991630i	$0.541213\pi$
$282$	1351.02	0.285290
$283$	4096.17	0.860396	0.430198	−	0.902735i	$-0.358444\pi$
$283$	4096.17	0.860396	0.430198	+	0.902735i	$0.358444\pi$
$284$	4177.27	0.872801
$285$	−1784.83	−0.370962
$286$	−15761.9	−3.25881
$287$	5589.80	1.14967
$288$	1730.04	0.353972
$289$	−399.197	−0.0812532
$290$	−518.694	−0.105030
$291$	4586.47	0.923931
$292$	1975.64	0.395944
$293$	5854.29	1.16727	0.583637	−	0.812015i	$-0.301629\pi$
$293$	5854.29	1.16727	0.583637	+	0.812015i	$0.301629\pi$
$294$	−1257.26	−0.249405
$295$	1784.60	0.352214
$296$	−548.292	−0.107665
$297$	−1912.30	−0.373613
$298$	−4294.74	−0.834858
$299$	4512.73	0.872836
$300$	−359.728	−0.0692296
$301$	−6147.54	−1.17720
$302$	5506.56	1.04923
$303$	4276.51	0.810822
$304$	−9443.62	−1.78167
$305$	−2330.57	−0.437535
$306$	2163.00	0.404087
$307$	−2748.38	−0.510940	−0.255470	−	0.966817i	$-0.582230\pi$
$307$	−2748.38	−0.510940	−0.255470	+	0.966817i	$0.582230\pi$
$308$	5105.17	0.944461
$309$	4787.05	0.881313
$310$	3223.54	0.590595
$311$	−10289.0	−1.87600	−0.938000	−	0.346634i	$-0.887325\pi$
$311$	−10289.0	−1.87600	−0.938000	+	0.346634i	$0.887325\pi$
$312$	−2138.85	−0.388104
$313$	8540.93	1.54237	0.771185	−	0.636611i	$-0.219664\pi$
$313$	8540.93	1.54237	0.771185	+	0.636611i	$0.219664\pi$
$314$	−798.196	−0.143455
$315$	676.266	0.120963
$316$	5373.02	0.956506
$317$	−131.153	−0.0232375	−0.0116187	−	0.999933i	$-0.503698\pi$
$317$	−131.153	−0.0232375	−0.0116187	+	0.999933i	$0.503698\pi$
$318$	−2315.50	−0.408323
$319$	2053.95	0.360499
$320$	−263.543	−0.0460391
$321$	465.311	0.0809070
$322$	−3899.56	−0.674888
$323$	−7994.22	−1.37712
$324$	388.506	0.0666162
$325$	1555.29	0.265453
$326$	11142.0	1.89293
$327$	−3636.70	−0.615014
$328$	4262.63	0.717574
$329$	1891.91	0.317035
$330$	3800.38	0.633952
$331$	−7274.79	−1.20803	−0.604016	−	0.796972i	$-0.706434\pi$
$331$	−7274.79	−1.20803	−0.604016	+	0.796972i	$0.706434\pi$
$332$	5176.61	0.855734
$333$	−430.595	−0.0708602
$334$	6155.56	1.00844
$335$	−2891.79	−0.471628
$336$	3578.16	0.580966
$337$	4663.56	0.753830	0.376915	−	0.926248i	$-0.376985\pi$
$337$	4663.56	0.753830	0.376915	+	0.926248i	$0.376985\pi$
$338$	−5985.72	−0.963256
$339$	3456.03	0.553704
$340$	−1611.22	−0.257001
$341$	−12764.7	−2.02712
$342$	−3830.81	−0.605692
$343$	−6915.27	−1.08860
$344$	−4687.94	−0.734759
$345$	−1088.07	−0.169797
$346$	−8723.72	−1.35546
$347$	6050.81	0.936093	0.468046	−	0.883704i	$-0.344958\pi$
$347$	6050.81	0.936093	0.468046	+	0.883704i	$0.344958\pi$
$348$	−417.284	−0.0642781
$349$	12824.0	1.96691	0.983455	−	0.181152i	$-0.0579825\pi$
$349$	12824.0	1.96691	0.983455	+	0.181152i	$0.0579825\pi$
$350$	−1343.97	−0.205251
$351$	−1679.72	−0.255432
$352$	13614.7	2.06155
$353$	12514.5	1.88691	0.943457	−	0.331494i	$-0.107553\pi$
$353$	12514.5	1.88691	0.943457	+	0.331494i	$0.107553\pi$
$354$	3830.32	0.575082
$355$	4354.62	0.651040
$356$	1865.75	0.277766
$357$	3028.99	0.449051
$358$	8041.53	1.18717
$359$	3394.70	0.499068	0.249534	−	0.968366i	$-0.419723\pi$
$359$	3394.70	0.499068	0.249534	+	0.968366i	$0.419723\pi$
$360$	515.702	0.0754996
$361$	7299.26	1.06419
$362$	8431.92	1.22423
$363$	−11056.0	−1.59859
$364$	4484.25	0.645710
$365$	2059.52	0.295343
$366$	−5002.16	−0.714391
$367$	−9991.93	−1.42118	−0.710592	−	0.703604i	$-0.751573\pi$
$367$	−9991.93	−1.42118	−0.710592	+	0.703604i	$0.751573\pi$
$368$	−5757.06	−0.815509
$369$	3347.60	0.472274
$370$	855.735	0.120237
$371$	−3242.54	−0.453758
$372$	2593.30	0.361442
$373$	7219.40	1.00216	0.501081	−	0.865400i	$-0.332936\pi$
$373$	7219.40	1.00216	0.501081	+	0.865400i	$0.332936\pi$
$374$	17021.9	2.35342
$375$	−375.000	−0.0516398
$376$	1442.72	0.197879
$377$	1804.14	0.246467
$378$	1451.48	0.197503
$379$	10797.8	1.46345	0.731724	−	0.681601i	$-0.238716\pi$
$379$	10797.8	1.46345	0.731724	+	0.681601i	$0.238716\pi$
$380$	2853.56	0.385223
$381$	−1196.23	−0.160852
$382$	−6877.37	−0.921144
$383$	−3396.75	−0.453174	−0.226587	−	0.973991i	$-0.572757\pi$
$383$	−3396.75	−0.453174	−0.226587	+	0.973991i	$0.572757\pi$
$384$	4047.80	0.537926
$385$	5321.91	0.704493
$386$	−6584.49	−0.868243
$387$	−3681.62	−0.483585
$388$	−7332.80	−0.959450
$389$	−4927.07	−0.642192	−0.321096	−	0.947047i	$-0.604051\pi$
$389$	−4927.07	−0.642192	−0.321096	+	0.947047i	$0.604051\pi$
$390$	3338.16	0.433421
$391$	−4873.47	−0.630338
$392$	−1342.60	−0.172989
$393$	1155.72	0.148342
$394$	9704.21	1.24084
$395$	5601.13	0.713477
$396$	3057.37	0.387976
$397$	−7777.55	−0.983234	−0.491617	−	0.870812i	$-0.663594\pi$
$397$	−7777.55	−0.983234	−0.491617	+	0.870812i	$0.663594\pi$
$398$	−803.551	−0.101202
$399$	−5364.52	−0.673088
$400$	−1984.14	−0.248018
$401$	6058.22	0.754446	0.377223	−	0.926122i	$-0.376879\pi$
$401$	6058.22	0.754446	0.377223	+	0.926122i	$0.376879\pi$
$402$	−6206.71	−0.770057
$403$	−11212.2	−1.38591
$404$	−6837.24	−0.841994
$405$	405.000	0.0496904
$406$	−1559.00	−0.190571
$407$	−3388.59	−0.412693
$408$	2309.82	0.280278
$409$	−15078.2	−1.82291	−0.911454	−	0.411403i	$-0.865039\pi$
$409$	−15078.2	−1.82291	−0.911454	+	0.411403i	$0.865039\pi$
$410$	−6652.80	−0.801362
$411$	1055.63	0.126692
$412$	−7653.48	−0.915194
$413$	5363.83	0.639073
$414$	−2335.36	−0.277238
$415$	5396.39	0.638309
$416$	11958.8	1.40944
$417$	−3415.45	−0.401091
$418$	−30146.8	−3.52758
$419$	5698.22	0.664383	0.332192	−	0.943212i	$-0.392212\pi$
$419$	5698.22	0.664383	0.332192	+	0.943212i	$0.392212\pi$
$420$	−1081.21	−0.125613
$421$	846.838	0.0980341	0.0490171	−	0.998798i	$-0.484391\pi$
$421$	846.838	0.0980341	0.0490171	+	0.998798i	$0.484391\pi$
$422$	14881.5	1.71664
$423$	1133.02	0.130235
$424$	−2472.67	−0.283215
$425$	−1679.62	−0.191703
$426$	9346.41	1.06299
$427$	−7004.83	−0.793882
$428$	−743.934	−0.0840173
$429$	−13218.6	−1.48765
$430$	7316.61	0.820554
$431$	−7518.27	−0.840237	−0.420119	−	0.907469i	$-0.638012\pi$
$431$	−7518.27	−0.840237	−0.420119	+	0.907469i	$0.638012\pi$
$432$	2142.88	0.238656
$433$	12686.0	1.40797	0.703987	−	0.710213i	$-0.251401\pi$
$433$	12686.0	1.40797	0.703987	+	0.710213i	$0.251401\pi$
$434$	9688.75	1.07160
$435$	−435.000	−0.0479463
$436$	5814.31	0.638658
$437$	8631.22	0.944822
$438$	4420.39	0.482225
$439$	10530.4	1.14485	0.572424	−	0.819958i	$-0.306003\pi$
$439$	10530.4	1.14485	0.572424	+	0.819958i	$0.306003\pi$
$440$	4058.34	0.439713
$441$	−1054.40	−0.113853
$442$	14951.6	1.60899
$443$	−5199.17	−0.557608	−0.278804	−	0.960348i	$-0.589938\pi$
$443$	−5199.17	−0.557608	−0.278804	+	0.960348i	$0.589938\pi$
$444$	688.430	0.0735843
$445$	1944.96	0.207191
$446$	6247.27	0.663266
$447$	−3601.76	−0.381113
$448$	−792.112	−0.0835352
$449$	−11836.7	−1.24412	−0.622058	−	0.782971i	$-0.713703\pi$
$449$	−11836.7	−1.24412	−0.622058	+	0.782971i	$0.713703\pi$
$450$	−804.870	−0.0843154
$451$	26344.1	2.75055
$452$	−5525.46	−0.574990
$453$	4618.04	0.478973
$454$	−463.274	−0.0478911
$455$	4674.63	0.481648
$456$	−4090.84	−0.420112
$457$	404.451	0.0413992	0.0206996	−	0.999786i	$-0.493411\pi$
$457$	404.451	0.0413992	0.0206996	+	0.999786i	$0.493411\pi$
$458$	2440.24	0.248963
$459$	1813.99	0.184466
$460$	1739.60	0.176325
$461$	7072.59	0.714541	0.357270	−	0.934001i	$-0.383707\pi$
$461$	7072.59	0.714541	0.357270	+	0.934001i	$0.383707\pi$
$462$	11422.5	1.15027
$463$	−6500.22	−0.652464	−0.326232	−	0.945290i	$-0.605779\pi$
$463$	−6500.22	−0.652464	−0.326232	+	0.945290i	$0.605779\pi$
$464$	−2301.61	−0.230279
$465$	2703.40	0.269607
$466$	−6192.51	−0.615585
$467$	−8850.61	−0.876997	−0.438498	−	0.898732i	$-0.644489\pi$
$467$	−8850.61	−0.876997	−0.438498	+	0.898732i	$0.644489\pi$
$468$	2685.51	0.265252
$469$	−8691.65	−0.855742
$470$	−2251.69	−0.220985
$471$	−669.403	−0.0654872
$472$	4090.31	0.398881
$473$	−28972.7	−2.81642
$474$	12021.8	1.16494
$475$	2974.71	0.287346
$476$	−4842.71	−0.466314
$477$	−1941.88	−0.186399
$478$	−11834.7	−1.13244
$479$	−8582.91	−0.818712	−0.409356	−	0.912375i	$-0.634247\pi$
$479$	−8582.91	−0.818712	−0.409356	+	0.912375i	$0.634247\pi$
$480$	−2883.41	−0.274185
$481$	−2976.45	−0.282150
$482$	−12829.2	−1.21236
$483$	−3270.34	−0.308087
$484$	17676.1	1.66004
$485$	−7644.12	−0.715674
$486$	869.260	0.0811326
$487$	−2823.62	−0.262732	−0.131366	−	0.991334i	$-0.541936\pi$
$487$	−2823.62	−0.262732	−0.131366	+	0.991334i	$0.541936\pi$
$488$	−5341.69	−0.495506
$489$	9344.14	0.864124
$490$	2095.44	0.193188
$491$	−13116.2	−1.20555	−0.602776	−	0.797911i	$-0.705939\pi$
$491$	−13116.2	−1.20555	−0.602776	+	0.797911i	$0.705939\pi$
$492$	−5352.11	−0.490430
$493$	−1948.36	−0.177991
$494$	−26480.2	−2.41174
$495$	3187.17	0.289399
$496$	14303.8	1.29488
$497$	13088.4	1.18127
$498$	11582.4	1.04221
$499$	−16495.4	−1.47983	−0.739916	−	0.672699i	$-0.765135\pi$
$499$	−16495.4	−1.47983	−0.739916	+	0.672699i	$0.765135\pi$
$500$	599.546	0.0536250
$501$	5162.33	0.460351
$502$	10575.0	0.940209
$503$	−16677.3	−1.47834	−0.739169	−	0.673520i	$-0.764781\pi$
$503$	−16677.3	−1.47834	−0.739169	+	0.673520i	$0.764781\pi$
$504$	1550.01	0.136990
$505$	−7127.52	−0.628060
$506$	−18378.2	−1.61465
$507$	−5019.89	−0.439726
$508$	1912.52	0.167036
$509$	9386.35	0.817373	0.408686	−	0.912675i	$-0.365987\pi$
$509$	9386.35	0.817373	0.408686	+	0.912675i	$0.365987\pi$
$510$	−3605.01	−0.313005
$511$	6190.15	0.535883
$512$	−7979.98	−0.688806
$513$	−3212.69	−0.276498
$514$	−8077.75	−0.693180
$515$	−7978.42	−0.682662
$516$	5886.13	0.502175
$517$	8916.37	0.758495
$518$	2572.02	0.218162
$519$	−7316.10	−0.618769
$520$	3564.74	0.300624
$521$	−16530.2	−1.39002	−0.695009	−	0.719001i	$-0.744600\pi$
$521$	−16530.2	−1.39002	−0.695009	+	0.719001i	$0.744600\pi$
$522$	−933.649	−0.0782849
$523$	−18295.9	−1.52968	−0.764842	−	0.644217i	$-0.777183\pi$
$523$	−18295.9	−1.52968	−0.764842	+	0.644217i	$0.777183\pi$
$524$	−1847.76	−0.154045
$525$	−1127.11	−0.0936974
$526$	−10404.9	−0.862500
$527$	12108.5	1.00086
$528$	16863.5	1.38994
$529$	−6905.20	−0.567535
$530$	3859.16	0.316285
$531$	3212.27	0.262525
$532$	8576.74	0.698964
$533$	23140.0	1.88050
$534$	4174.51	0.338294
$535$	−775.518	−0.0626703
$536$	−6628.01	−0.534117
$537$	6743.99	0.541945
$538$	1065.68	0.0853994
$539$	−8297.63	−0.663088
$540$	−647.510	−0.0516007
$541$	−949.695	−0.0754724	−0.0377362	−	0.999288i	$-0.512015\pi$
$541$	−949.695	−0.0754724	−0.0377362	+	0.999288i	$0.512015\pi$
$542$	−25015.5	−1.98249
$543$	7071.38	0.558862
$544$	−12914.7	−1.01786
$545$	6061.16	0.476388
$546$	10033.3	0.786417
$547$	18017.4	1.40835	0.704177	−	0.710024i	$-0.251316\pi$
$547$	18017.4	1.40835	0.704177	+	0.710024i	$0.251316\pi$
$548$	−1687.73	−0.131563
$549$	−4195.03	−0.326119
$550$	−6333.97	−0.491057
$551$	3450.67	0.266794
$552$	−2493.87	−0.192294
$553$	16834.9	1.29456
$554$	−20396.6	−1.56420
$555$	717.658	0.0548881
$556$	5460.58	0.416511
$557$	−11387.6	−0.866263	−0.433131	−	0.901331i	$-0.642591\pi$
$557$	−11387.6	−0.866263	−0.433131	+	0.901331i	$0.642591\pi$
$558$	5802.37	0.440204
$559$	−25448.9	−1.92553
$560$	−5963.60	−0.450014
$561$	14275.3	1.07434
$562$	4351.09	0.326583
$563$	−277.822	−0.0207971	−0.0103986	−	0.999946i	$-0.503310\pi$
$563$	−277.822	−0.0207971	−0.0103986	+	0.999946i	$0.503310\pi$
$564$	−1811.46	−0.135242
$565$	−5760.04	−0.428897
$566$	−14652.8	−1.08817
$567$	1217.28	0.0901603
$568$	9980.82	0.737299
$569$	15475.5	1.14019	0.570093	−	0.821580i	$-0.306907\pi$
$569$	15475.5	1.14019	0.570093	+	0.821580i	$0.306907\pi$
$570$	6384.69	0.469167
$571$	−3245.82	−0.237887	−0.118944	−	0.992901i	$-0.537951\pi$
$571$	−3245.82	−0.237887	−0.118944	+	0.992901i	$0.537951\pi$
$572$	21133.8	1.54484
$573$	−5767.67	−0.420502
$574$	−19995.8	−1.45402
$575$	1813.46	0.131524
$576$	−474.377	−0.0343155
$577$	−23087.9	−1.66579	−0.832895	−	0.553430i	$-0.813318\pi$
$577$	−23087.9	−1.66579	−0.832895	+	0.553430i	$0.813318\pi$
$578$	1428.01	0.102764
$579$	−5522.05	−0.396353
$580$	695.473	0.0497896
$581$	16219.5	1.15818
$582$	−16406.7	−1.16852
$583$	−15281.7	−1.08560
$584$	4720.44	0.334474
$585$	2799.53	0.197857
$586$	−20942.0	−1.47629
$587$	13526.1	0.951075	0.475537	−	0.879696i	$-0.342254\pi$
$587$	13526.1	0.951075	0.475537	+	0.879696i	$0.342254\pi$
$588$	1685.76	0.118230
$589$	−21444.9	−1.50021
$590$	−6383.86	−0.445457
$591$	8138.38	0.566444
$592$	3797.17	0.263619
$593$	15964.6	1.10554	0.552770	−	0.833334i	$-0.313571\pi$
$593$	15964.6	1.10554	0.552770	+	0.833334i	$0.313571\pi$
$594$	6840.69	0.472520
$595$	−5048.31	−0.347833
$596$	5758.46	0.395764
$597$	−673.894	−0.0461987
$598$	−16142.9	−1.10390
$599$	22.9584	0.00156603	0.000783017	−	1.00000i	$-0.499751\pi$
$599$	22.9584	0.00156603	0.000783017		1.00000i	$0.499751\pi$
$600$	−859.503	−0.0584818
$601$	−7471.32	−0.507090	−0.253545	−	0.967324i	$-0.581597\pi$
$601$	−7471.32	−0.507090	−0.253545	+	0.967324i	$0.581597\pi$
$602$	21991.0	1.48885
$603$	−5205.23	−0.351531
$604$	−7383.28	−0.497386
$605$	18426.6	1.23826
$606$	−15297.9	−1.02547
$607$	23036.9	1.54042	0.770212	−	0.637788i	$-0.220151\pi$
$607$	23036.9	1.54042	0.770212	+	0.637788i	$0.220151\pi$
$608$	22872.8	1.52568
$609$	−1307.45	−0.0869958
$610$	8336.93	0.553365
$611$	7831.91	0.518569
$612$	−2900.19	−0.191557
$613$	−20040.0	−1.32040	−0.660202	−	0.751088i	$-0.729530\pi$
$613$	−20040.0	−1.32040	−0.660202	+	0.751088i	$0.729530\pi$
$614$	9831.52	0.646202
$615$	−5579.34	−0.365822
$616$	12197.9	0.797834
$617$	−27464.4	−1.79202	−0.896010	−	0.444035i	$-0.853547\pi$
$617$	−27464.4	−1.79202	−0.896010	+	0.444035i	$0.853547\pi$
$618$	−17124.2	−1.11462
$619$	3585.29	0.232803	0.116402	−	0.993202i	$-0.462864\pi$
$619$	3585.29	0.232803	0.116402	+	0.993202i	$0.462864\pi$
$620$	−4322.17	−0.279972
$621$	−1958.53	−0.126559
$622$	36805.9	2.37264
$623$	5845.83	0.375936
$624$	14812.4	0.950276
$625$	625.000	0.0400000
$626$	−30552.6	−1.95069
$627$	−25282.4	−1.61034
$628$	1070.23	0.0680048
$629$	3214.38	0.203761
$630$	−2419.14	−0.152985
$631$	−27135.3	−1.71195	−0.855973	−	0.517020i	$-0.827041\pi$
$631$	−27135.3	−1.71195	−0.855973	+	0.517020i	$0.827041\pi$
$632$	12837.8	0.808009
$633$	12480.3	0.783645
$634$	469.160	0.0293892
$635$	1993.72	0.124596
$636$	3104.65	0.193565
$637$	−7288.43	−0.453341
$638$	−7347.40	−0.455935
$639$	7838.32	0.485257
$640$	−6746.34	−0.416676
$641$	23443.5	1.44456	0.722278	−	0.691603i	$-0.243095\pi$
$641$	23443.5	1.44456	0.722278	+	0.691603i	$0.243095\pi$
$642$	−1664.51	−0.102326
$643$	−9339.29	−0.572792	−0.286396	−	0.958111i	$-0.592457\pi$
$643$	−9339.29	−0.572792	−0.286396	+	0.958111i	$0.592457\pi$
$644$	5228.59	0.319931
$645$	6136.03	0.374583
$646$	28596.9	1.74169
$647$	1103.56	0.0670562	0.0335281	−	0.999438i	$-0.489326\pi$
$647$	1103.56	0.0670562	0.0335281	+	0.999438i	$0.489326\pi$
$648$	928.263	0.0562741
$649$	25279.2	1.52896
$650$	−5563.60	−0.335726
$651$	8125.41	0.489186
$652$	−14939.3	−0.897344
$653$	−3127.51	−0.187425	−0.0937127	−	0.995599i	$-0.529874\pi$
$653$	−3127.51	−0.187425	−0.0937127	+	0.995599i	$0.529874\pi$
$654$	13009.2	0.777828
$655$	−1926.21	−0.114906
$656$	−29520.6	−1.75699
$657$	3707.14	0.220136
$658$	−6767.75	−0.400964
$659$	16004.5	0.946050	0.473025	−	0.881049i	$-0.343162\pi$
$659$	16004.5	0.946050	0.473025	+	0.881049i	$0.343162\pi$
$660$	−5095.61	−0.300525
$661$	10807.3	0.635939	0.317970	−	0.948101i	$-0.396999\pi$
$661$	10807.3	0.635939	0.317970	+	0.948101i	$0.396999\pi$
$662$	26023.4	1.52784
$663$	12539.1	0.734504
$664$	12368.6	0.722882
$665$	8940.87	0.521372
$666$	1540.32	0.0896191
$667$	2103.61	0.122117
$668$	−8253.47	−0.478049
$669$	5239.24	0.302781
$670$	10344.5	0.596483
$671$	−33013.0	−1.89933
$672$	−8666.44	−0.497493
$673$	23835.6	1.36522	0.682612	−	0.730781i	$-0.260844\pi$
$673$	23835.6	1.36522	0.682612	+	0.730781i	$0.260844\pi$
$674$	−16682.5	−0.953392
$675$	−675.000	−0.0384900
$676$	8025.75	0.456631
$677$	5081.10	0.288453	0.144227	−	0.989545i	$-0.453931\pi$
$677$	5081.10	0.288453	0.144227	+	0.989545i	$0.453931\pi$
$678$	−12362.9	−0.700286
$679$	−22975.4	−1.29855
$680$	−3849.70	−0.217102
$681$	−388.523	−0.0218623
$682$	45662.0	2.56377
$683$	7815.19	0.437833	0.218917	−	0.975744i	$-0.429748\pi$
$683$	7815.19	0.437833	0.218917	+	0.975744i	$0.429748\pi$
$684$	5136.41	0.287128
$685$	−1759.38	−0.0981352
$686$	24737.3	1.37679
$687$	2046.50	0.113652
$688$	32466.1	1.79907
$689$	−13423.1	−0.742204
$690$	3892.26	0.214748
$691$	8815.96	0.485347	0.242674	−	0.970108i	$-0.421976\pi$
$691$	8815.96	0.485347	0.242674	+	0.970108i	$0.421976\pi$
$692$	11696.9	0.642557
$693$	9579.44	0.525098
$694$	−21644.9	−1.18391
$695$	5692.41	0.310684
$696$	−997.023	−0.0542990
$697$	−24989.8	−1.35804
$698$	−45873.9	−2.48761
$699$	−5193.32	−0.281015
$700$	1802.01	0.0972994
$701$	−4100.40	−0.220927	−0.110464	−	0.993880i	$-0.535234\pi$
$701$	−4100.40	−0.220927	−0.110464	+	0.993880i	$0.535234\pi$
$702$	6008.68	0.323053
$703$	−5692.87	−0.305420
$704$	−3733.14	−0.199855
$705$	−1888.37	−0.100880
$706$	−44767.0	−2.38644
$707$	−21422.7	−1.13958
$708$	−5135.75	−0.272618
$709$	−17803.3	−0.943042	−0.471521	−	0.881855i	$-0.656295\pi$
$709$	−17803.3	−0.943042	−0.471521	+	0.881855i	$0.656295\pi$
$710$	−15577.4	−0.823391
$711$	10082.0	0.531795
$712$	4457.87	0.234643
$713$	−13073.3	−0.686677
$714$	−10835.3	−0.567928
$715$	22031.0	1.15233
$716$	−10782.2	−0.562780
$717$	−9925.13	−0.516961
$718$	−12143.5	−0.631187
$719$	−4213.37	−0.218543	−0.109271	−	0.994012i	$-0.534852\pi$
$719$	−4213.37	−0.218543	−0.109271	+	0.994012i	$0.534852\pi$
$720$	−3571.46	−0.184862
$721$	−23980.1	−1.23865
$722$	−26110.9	−1.34591
$723$	−10759.2	−0.553441
$724$	−11305.6	−0.580347
$725$	725.000	0.0371391
$726$	39549.4	2.02178
$727$	29559.3	1.50797	0.753984	−	0.656893i	$-0.228130\pi$
$727$	29559.3	1.50797	0.753984	+	0.656893i	$0.228130\pi$
$728$	10714.3	0.545464
$729$	729.000	0.0370370
$730$	−7367.32	−0.373530
$731$	27483.2	1.39057
$732$	6706.97	0.338657
$733$	23312.9	1.17474	0.587369	−	0.809319i	$-0.300164\pi$
$733$	23312.9	1.17474	0.587369	+	0.809319i	$0.300164\pi$
$734$	35743.1	1.79742
$735$	1757.33	0.0881905
$736$	13943.8	0.698337
$737$	−40962.8	−2.04733
$738$	−11975.0	−0.597300
$739$	27985.2	1.39303	0.696517	−	0.717540i	$-0.254732\pi$
$739$	27985.2	1.39303	0.696517	+	0.717540i	$0.254732\pi$
$740$	−1147.38	−0.0569982
$741$	−22207.4	−1.10096
$742$	11599.2	0.573881
$743$	−2542.48	−0.125538	−0.0627690	−	0.998028i	$-0.519993\pi$
$743$	−2542.48	−0.125538	−0.0627690	+	0.998028i	$0.519993\pi$
$744$	6196.22	0.305328
$745$	6002.94	0.295209
$746$	−25825.3	−1.26747
$747$	9713.50	0.475768
$748$	−22823.2	−1.11564
$749$	−2330.92	−0.113712
$750$	1341.45	0.0653105
$751$	33600.2	1.63261	0.816305	−	0.577622i	$-0.196019\pi$
$751$	33600.2	1.63261	0.816305	+	0.577622i	$0.196019\pi$
$752$	−9991.46	−0.484510
$753$	8868.65	0.429206
$754$	−6453.77	−0.311714
$755$	−7696.74	−0.371011
$756$	−1946.17	−0.0936264
$757$	−34022.4	−1.63351	−0.816754	−	0.576986i	$-0.804229\pi$
$757$	−34022.4	−1.63351	−0.816754	+	0.576986i	$0.804229\pi$
$758$	−38626.0	−1.85087
$759$	−15412.8	−0.737086
$760$	6818.06	0.325417
$761$	15032.8	0.716084	0.358042	−	0.933705i	$-0.383444\pi$
$761$	15032.8	0.716084	0.358042	+	0.933705i	$0.383444\pi$
$762$	4279.16	0.203435
$763$	18217.6	0.864378
$764$	9221.28	0.436668
$765$	−3023.32	−0.142887
$766$	12150.8	0.573144
$767$	22204.6	1.04532
$768$	−15744.8	−0.739768
$769$	−24042.9	−1.12745	−0.563725	−	0.825963i	$-0.690632\pi$
$769$	−24042.9	−1.12745	−0.563725	+	0.825963i	$0.690632\pi$
$770$	−19037.5	−0.890994
$771$	−6774.36	−0.316437
$772$	8828.59	0.411590
$773$	17441.1	0.811530	0.405765	−	0.913977i	$-0.367005\pi$
$773$	17441.1	0.811530	0.405765	+	0.913977i	$0.367005\pi$
$774$	13169.9	0.611605
$775$	−4505.67	−0.208837
$776$	−17520.4	−0.810496
$777$	2157.01	0.0995912
$778$	17625.1	0.812200
$779$	44258.5	2.03559
$780$	−4475.85	−0.205463
$781$	61684.0	2.82616
$782$	17433.4	0.797208
$783$	−783.000	−0.0357371
$784$	9298.12	0.423566
$785$	1115.67	0.0507262
$786$	−4134.26	−0.187613
$787$	−38211.9	−1.73076	−0.865379	−	0.501119i	$-0.832922\pi$
$787$	−38211.9	−1.73076	−0.865379	+	0.501119i	$0.832922\pi$
$788$	−13011.6	−0.588220
$789$	−8726.00	−0.393731
$790$	−20036.4	−0.902357
$791$	−17312.5	−0.778208
$792$	7305.02	0.327743
$793$	−28997.8	−1.29854
$794$	27821.8	1.24353
$795$	3236.47	0.144384
$796$	1077.41	0.0479748
$797$	18149.9	0.806655	0.403327	−	0.915056i	$-0.367854\pi$
$797$	18149.9	0.806655	0.403327	+	0.915056i	$0.367854\pi$
$798$	19190.0	0.851276
$799$	−8457.99	−0.374496
$800$	4805.68	0.212383
$801$	3500.93	0.154431
$802$	−21671.5	−0.954172
$803$	29173.5	1.28208
$804$	8322.06	0.365045
$805$	5450.57	0.238643
$806$	40108.3	1.75280
$807$	893.730	0.0389849
$808$	−16336.3	−0.711275
$809$	−339.522	−0.0147552	−0.00737759	−	0.999973i	$-0.502348\pi$
$809$	−339.522	−0.0147552	−0.00737759	+	0.999973i	$0.502348\pi$
$810$	−1448.77	−0.0628450
$811$	26295.4	1.13854	0.569270	−	0.822151i	$-0.307226\pi$
$811$	26295.4	1.13854	0.569270	+	0.822151i	$0.307226\pi$
$812$	2090.33	0.0903403
$813$	−20979.1	−0.905005
$814$	12121.7	0.521946
$815$	−15573.6	−0.669347
$816$	−15996.5	−0.686263
$817$	−48674.5	−2.08434
$818$	53937.8	2.30549
$819$	8414.33	0.359000
$820$	8920.18	0.379886
$821$	−46289.6	−1.96775	−0.983873	−	0.178867i	$-0.942757\pi$
$821$	−46289.6	−1.96775	−0.983873	+	0.178867i	$0.942757\pi$
$822$	−3776.20	−0.160231
$823$	−28099.3	−1.19013	−0.595067	−	0.803676i	$-0.702874\pi$
$823$	−28099.3	−1.19013	−0.595067	+	0.803676i	$0.702874\pi$
$824$	−18286.6	−0.773111
$825$	−5311.95	−0.224168
$826$	−19187.5	−0.808255
$827$	−38732.3	−1.62860	−0.814301	−	0.580443i	$-0.802879\pi$
$827$	−38732.3	−1.62860	−0.814301	+	0.580443i	$0.802879\pi$
$828$	3131.28	0.131425
$829$	−9334.33	−0.391067	−0.195534	−	0.980697i	$-0.562644\pi$
$829$	−9334.33	−0.391067	−0.195534	+	0.980697i	$0.562644\pi$
$830$	−19304.0	−0.807290
$831$	−17105.5	−0.714060
$832$	−3279.09	−0.136637
$833$	7871.06	0.327390
$834$	12217.7	0.507273
$835$	−8603.88	−0.356586
$836$	40421.3	1.67225
$837$	4866.12	0.200953
$838$	−20383.7	−0.840266
$839$	−40742.1	−1.67649	−0.838245	−	0.545294i	$-0.816418\pi$
$839$	−40742.1	−1.67649	−0.838245	+	0.545294i	$0.816418\pi$
$840$	−2583.34	−0.106112
$841$	841.000	0.0344828
$842$	−3029.31	−0.123987
$843$	3649.02	0.149085
$844$	−19953.4	−0.813771
$845$	8366.49	0.340611
$846$	−4053.05	−0.164712
$847$	55383.5	2.24675
$848$	17124.3	0.693457
$849$	−12288.5	−0.496750
$850$	6008.34	0.242452
$851$	−3470.51	−0.139797
$852$	−12531.8	−0.503912
$853$	−29088.9	−1.16762	−0.583812	−	0.811889i	$-0.698440\pi$
$853$	−29088.9	−1.16762	−0.583812	+	0.811889i	$0.698440\pi$
$854$	25057.7	1.00405
$855$	5354.48	0.214175
$856$	−1777.49	−0.0709737
$857$	31564.0	1.25812	0.629059	−	0.777357i	$-0.283440\pi$
$857$	31564.0	1.25812	0.629059	+	0.777357i	$0.283440\pi$
$858$	47285.6	1.88147
$859$	21654.5	0.860120	0.430060	−	0.902800i	$-0.358492\pi$
$859$	21654.5	0.860120	0.430060	+	0.902800i	$0.358492\pi$
$860$	−9810.22	−0.388983
$861$	−16769.4	−0.663763
$862$	26894.4	1.06267
$863$	2304.51	0.0908996	0.0454498	−	0.998967i	$-0.485528\pi$
$863$	2304.51	0.0908996	0.0454498	+	0.998967i	$0.485528\pi$
$864$	−5190.13	−0.204366
$865$	12193.5	0.479297
$866$	−45380.5	−1.78071
$867$	1197.59	0.0469116
$868$	−12990.8	−0.507992
$869$	79341.1	3.09720
$870$	1556.08	0.0606392
$871$	−35980.7	−1.39972
$872$	13892.2	0.539507
$873$	−13759.4	−0.533432
$874$	−30875.6	−1.19495
$875$	1878.52	0.0725777
$876$	−5926.93	−0.228599
$877$	42141.0	1.62258	0.811289	−	0.584645i	$-0.198766\pi$
$877$	42141.0	1.62258	0.811289	+	0.584645i	$0.198766\pi$
$878$	−37669.4	−1.44793
$879$	−17562.9	−0.673926
$880$	−28105.8	−1.07664
$881$	3482.39	0.133172	0.0665861	−	0.997781i	$-0.478789\pi$
$881$	3482.39	0.133172	0.0665861	+	0.997781i	$0.478789\pi$
$882$	3771.79	0.143994
$883$	28559.6	1.08846	0.544229	−	0.838937i	$-0.316822\pi$
$883$	28559.6	1.08846	0.544229	+	0.838937i	$0.316822\pi$
$884$	−20047.3	−0.762742
$885$	−5353.79	−0.203351
$886$	18598.5	0.705224
$887$	−42485.5	−1.60826	−0.804128	−	0.594456i	$-0.797367\pi$
$887$	−42485.5	−1.60826	−0.804128	+	0.594456i	$0.797367\pi$
$888$	1644.88	0.0621604
$889$	5992.37	0.226072
$890$	−6957.52	−0.262041
$891$	5736.90	0.215705
$892$	−8376.43	−0.314421
$893$	14979.6	0.561337
$894$	12884.2	0.482005
$895$	−11240.0	−0.419789
$896$	−20277.0	−0.756034
$897$	−13538.2	−0.503932
$898$	42342.3	1.57347
$899$	−5226.58	−0.193900
$900$	1079.18	0.0399697
$901$	14496.1	0.535999
$902$	−94238.2	−3.47870
$903$	18442.6	0.679659
$904$	−13202.1	−0.485724
$905$	−11785.6	−0.432893
$906$	−16519.7	−0.605772
$907$	−22359.4	−0.818559	−0.409280	−	0.912409i	$-0.634220\pi$
$907$	−22359.4	−0.818559	−0.409280	+	0.912409i	$0.634220\pi$
$908$	621.166	0.0227028
$909$	−12829.5	−0.468128
$910$	−16722.1	−0.609156
$911$	−14833.6	−0.539471	−0.269735	−	0.962934i	$-0.586936\pi$
$911$	−14833.6	−0.539471	−0.269735	+	0.962934i	$0.586936\pi$
$912$	28330.9	1.02865
$913$	76440.9	2.77089
$914$	−1446.80	−0.0523588
$915$	6991.72	0.252611
$916$	−3271.92	−0.118021
$917$	−5789.46	−0.208489
$918$	−6489.01	−0.233300
$919$	−41161.8	−1.47748	−0.738740	−	0.673991i	$-0.764579\pi$
$919$	−41161.8	−1.47748	−0.738740	+	0.673991i	$0.764579\pi$
$920$	4156.46	0.148950
$921$	8245.15	0.294991
$922$	−25300.1	−0.903702
$923$	54181.7	1.93219
$924$	−15315.5	−0.545285
$925$	−1196.10	−0.0425161
$926$	23252.6	0.825192
$927$	−14361.2	−0.508826
$928$	5574.59	0.197193
$929$	29321.8	1.03554	0.517771	−	0.855519i	$-0.326762\pi$
$929$	29321.8	1.03554	0.517771	+	0.855519i	$0.326762\pi$
$930$	−9670.61	−0.340980
$931$	−13940.1	−0.490729
$932$	8303.02	0.291818
$933$	30867.0	1.08311
$934$	31660.4	1.10917
$935$	−23792.2	−0.832178
$936$	6416.54	0.224072
$937$	−42922.5	−1.49650	−0.748249	−	0.663418i	$-0.769105\pi$
$937$	−42922.5	−1.49650	−0.748249	+	0.663418i	$0.769105\pi$
$938$	31091.8	1.08228
$939$	−25622.8	−0.890488
$940$	3019.10	0.104758
$941$	−13239.3	−0.458650	−0.229325	−	0.973350i	$-0.573652\pi$
$941$	−13239.3	−0.458650	−0.229325	+	0.973350i	$0.573652\pi$
$942$	2394.59	0.0828237
$943$	26981.0	0.931732
$944$	−28327.2	−0.976665
$945$	−2028.80	−0.0698379
$946$	103641.	3.56201
$947$	−19266.8	−0.661126	−0.330563	−	0.943784i	$-0.607239\pi$
$947$	−19266.8	−0.661126	−0.330563	+	0.943784i	$0.607239\pi$
$948$	−16119.1	−0.552239
$949$	25625.3	0.876534
$950$	−10641.1	−0.363415
$951$	393.459	0.0134162
$952$	−11570.8	−0.393919
$953$	−14816.2	−0.503615	−0.251807	−	0.967777i	$-0.581025\pi$
$953$	−14816.2	−0.503615	−0.251807	+	0.967777i	$0.581025\pi$
$954$	6946.49	0.235745
$955$	9612.78	0.325720
$956$	15868.2	0.536835
$957$	−6161.86	−0.208134
$958$	30702.8	1.03545
$959$	−5288.05	−0.178061
$960$	790.629	0.0265807
$961$	2690.68	0.0903185
$962$	10647.4	0.356845
$963$	−1395.93	−0.0467117
$964$	17201.6	0.574717
$965$	9203.41	0.307014
$966$	11698.7	0.389647
$967$	1342.65	0.0446502	0.0223251	−	0.999751i	$-0.492893\pi$
$967$	1342.65	0.0446502	0.0223251	+	0.999751i	$0.492893\pi$
$968$	42233.9	1.40232
$969$	23982.7	0.795082
$970$	27344.6	0.905135
$971$	−11211.1	−0.370526	−0.185263	−	0.982689i	$-0.559314\pi$
$971$	−11211.1	−0.370526	−0.185263	+	0.982689i	$0.559314\pi$
$972$	−1165.52	−0.0384609
$973$	17109.3	0.563718
$974$	10100.7	0.332285
$975$	−4665.88	−0.153259
$976$	36993.6	1.21325
$977$	30870.2	1.01088	0.505438	−	0.862863i	$-0.331331\pi$
$977$	30870.2	1.01088	0.505438	+	0.862863i	$0.331331\pi$
$978$	−33425.9	−1.09288
$979$	27550.8	0.899414
$980$	−2809.60	−0.0915809
$981$	10910.1	0.355079
$982$	46919.3	1.52470
$983$	28549.4	0.926332	0.463166	−	0.886272i	$-0.346713\pi$
$983$	28549.4	0.926332	0.463166	+	0.886272i	$0.346713\pi$
$984$	−12787.9	−0.414292
$985$	−13564.0	−0.438765
$986$	6969.68	0.225111
$987$	−5675.73	−0.183040
$988$	35505.0	1.14328
$989$	−29673.1	−0.954046
$990$	−11401.1	−0.366012
$991$	−20806.0	−0.666927	−0.333464	−	0.942763i	$-0.608217\pi$
$991$	−20806.0	−0.666927	−0.333464	+	0.942763i	$0.608217\pi$
$992$	−34644.5	−1.10883
$993$	21824.4	0.697458
$994$	−46819.7	−1.49399
$995$	1123.16	0.0357854
$996$	−15529.8	−0.494058
$997$	57999.9	1.84240	0.921201	−	0.389088i	$-0.127210\pi$
$997$	57999.9	1.84240	0.921201	+	0.389088i	$0.127210\pi$
$998$	59007.4	1.87159
$999$	1291.78	0.0409112

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.4.a.i.1.2	✓	7
3.2	odd	2		1305.4.a.n.1.6		7
5.4	even	2		2175.4.a.n.1.6		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.4.a.i.1.2	✓	7	1.1	even	1	trivial
1305.4.a.n.1.6		7	3.2	odd	2
2175.4.a.n.1.6		7	5.4	even	2

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:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	435.a (trivial)

\(f(q)\)	\(=\)	\(q-3.57720 q^{2} -3.00000 q^{3} +4.79637 q^{4} +5.00000 q^{5} +10.7316 q^{6} +15.0281 q^{7} +11.4600 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q-3.57720 q^{2} -3.00000 q^{3} +4.79637 q^{4} +5.00000 q^{5} +10.7316 q^{6} +15.0281 q^{7} +11.4600 q^{8} +9.00000 q^{9} -17.8860 q^{10} +70.8260 q^{11} -14.3891 q^{12} +62.2117 q^{13} -53.7587 q^{14} -15.0000 q^{15} -79.3658 q^{16} -67.1848 q^{17} -32.1948 q^{18} +118.988 q^{19} +23.9818 q^{20} -45.0844 q^{21} -253.359 q^{22} +72.5383 q^{23} -34.3801 q^{24} +25.0000 q^{25} -222.544 q^{26} -27.0000 q^{27} +72.0804 q^{28} +29.0000 q^{29} +53.6580 q^{30} -180.227 q^{31} +192.227 q^{32} -212.478 q^{33} +240.334 q^{34} +75.1407 q^{35} +43.1673 q^{36} -47.8439 q^{37} -425.646 q^{38} -186.635 q^{39} +57.3002 q^{40} +371.956 q^{41} +161.276 q^{42} -409.069 q^{43} +339.707 q^{44} +45.0000 q^{45} -259.484 q^{46} +125.891 q^{47} +238.097 q^{48} -117.155 q^{49} -89.4300 q^{50} +201.555 q^{51} +298.390 q^{52} -215.764 q^{53} +96.5844 q^{54} +354.130 q^{55} +172.223 q^{56} -356.965 q^{57} -103.739 q^{58} +356.919 q^{59} -71.9455 q^{60} -466.115 q^{61} +644.707 q^{62} +135.253 q^{63} -52.7086 q^{64} +311.059 q^{65} +760.076 q^{66} -578.359 q^{67} -322.243 q^{68} -217.615 q^{69} -268.793 q^{70} +870.924 q^{71} +103.140 q^{72} +411.904 q^{73} +171.147 q^{74} -75.0000 q^{75} +570.712 q^{76} +1064.38 q^{77} +667.631 q^{78} +1120.23 q^{79} -396.829 q^{80} +81.0000 q^{81} -1330.56 q^{82} +1079.28 q^{83} -216.241 q^{84} -335.924 q^{85} +1463.32 q^{86} -87.0000 q^{87} +811.668 q^{88} +388.993 q^{89} -160.974 q^{90} +934.926 q^{91} +347.920 q^{92} +540.680 q^{93} -450.339 q^{94} +594.942 q^{95} -576.681 q^{96} -1528.82 q^{97} +419.088 q^{98} +637.434 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9}+O(q^{10}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9	\( 7 q - 2 q^{2} - 21 q^{3} + 22 q^{4} + 35 q^{5} + 6 q^{6} - 50 q^{7} - 33 q^{8} + 63 q^{9} - 10 q^{10} + 76 q^{11} - 66 q^{12} + 30 q^{13} + 89 q^{14} - 105 q^{15} + 138 q^{16} - 140 q^{17} - 18 q^{18} + 90 q^{19} + 110 q^{20} + 150 q^{21} + 61 q^{22} + 34 q^{23} + 99 q^{24} + 175 q^{25} - 241 q^{26} - 189 q^{27} - 57 q^{28} + 203 q^{29} + 30 q^{30} + 524 q^{31} - 6 q^{32} - 228 q^{33} + 255 q^{34} - 250 q^{35} + 198 q^{36} - 28 q^{37} + 222 q^{38} - 90 q^{39} - 165 q^{40} + 1532 q^{41} - 267 q^{42} - 464 q^{43} + 1475 q^{44} + 315 q^{45} + 72 q^{46} - 360 q^{47} - 414 q^{48} + 569 q^{49} - 50 q^{50} + 420 q^{51} - 205 q^{52} + 282 q^{53} + 54 q^{54} + 380 q^{55} + 1102 q^{56} - 270 q^{57} - 58 q^{58} + 766 q^{59} - 330 q^{60} + 1200 q^{61} + 2856 q^{62} - 450 q^{63} + 701 q^{64} + 150 q^{65} - 183 q^{66} + 1546 q^{67} + 1801 q^{68} - 102 q^{69} + 445 q^{70} + 1802 q^{71} - 297 q^{72} - 220 q^{73} + 1594 q^{74} - 525 q^{75} + 1960 q^{76} + 3222 q^{77} + 723 q^{78} + 1298 q^{79} + 690 q^{80} + 567 q^{81} + 856 q^{82} + 1652 q^{83} + 171 q^{84} - 700 q^{85} + 7628 q^{86} - 609 q^{87} + 550 q^{88} + 2846 q^{89} - 90 q^{90} - 816 q^{91} + 472 q^{92} - 1572 q^{93} + 745 q^{94} + 450 q^{95} + 18 q^{96} + 1110 q^{97} - 761 q^{98} + 684 q^{99}+O(q^{100}) \) 7 * q - 2 * q^2 - 21 * q^3 + 22 * q^4 + 35 * q^5 + 6 * q^6 - 50 * q^7 - 33 * q^8 + 63 * q^9 - 10 * q^10 + 76 * q^11 - 66 * q^12 + 30 * q^13 + 89 * q^14 - 105 * q^15 + 138 * q^16 - 140 * q^17 - 18 * q^18 + 90 * q^19 + 110 * q^20 + 150 * q^21 + 61 * q^22 + 34 * q^23 + 99 * q^24 + 175 * q^25 - 241 * q^26 - 189 * q^27 - 57 * q^28 + 203 * q^29 + 30 * q^30 + 524 * q^31 - 6 * q^32 - 228 * q^33 + 255 * q^34 - 250 * q^35 + 198 * q^36 - 28 * q^37 + 222 * q^38 - 90 * q^39 - 165 * q^40 + 1532 * q^41 - 267 * q^42 - 464 * q^43 + 1475 * q^44 + 315 * q^45 + 72 * q^46 - 360 * q^47 - 414 * q^48 + 569 * q^49 - 50 * q^50 + 420 * q^51 - 205 * q^52 + 282 * q^53 + 54 * q^54 + 380 * q^55 + 1102 * q^56 - 270 * q^57 - 58 * q^58 + 766 * q^59 - 330 * q^60 + 1200 * q^61 + 2856 * q^62 - 450 * q^63 + 701 * q^64 + 150 * q^65 - 183 * q^66 + 1546 * q^67 + 1801 * q^68 - 102 * q^69 + 445 * q^70 + 1802 * q^71 - 297 * q^72 - 220 * q^73 + 1594 * q^74 - 525 * q^75 + 1960 * q^76 + 3222 * q^77 + 723 * q^78 + 1298 * q^79 + 690 * q^80 + 567 * q^81 + 856 * q^82 + 1652 * q^83 + 171 * q^84 - 700 * q^85 + 7628 * q^86 - 609 * q^87 + 550 * q^88 + 2846 * q^89 - 90 * q^90 - 816 * q^91 + 472 * q^92 - 1572 * q^93 + 745 * q^94 + 450 * q^95 + 18 * q^96 + 1110 * q^97 - 761 * q^98 + 684 * q^99

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