LMFDB - Embedded newform 503.2.a.f.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [503,2,Mod(1,503)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(503, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("503.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 503 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	503.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:	$4.01647522167$
Analytic rank:	$0$
Dimension:	$26$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Character	$\chi$	$=$	503.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.44158 q^{2} -1.65492 q^{3} +0.0781455 q^{4} +1.16845 q^{5} +2.38569 q^{6} -5.22170 q^{7} +2.77050 q^{8} -0.261242 q^{9} +O(q^{10})$	\(q-1.44158 q^{2} -1.65492 q^{3} +0.0781455 q^{4} +1.16845 q^{5} +2.38569 q^{6} -5.22170 q^{7} +2.77050 q^{8} -0.261242 q^{9} -1.68442 q^{10} -1.87602 q^{11} -0.129324 q^{12} +3.59450 q^{13} +7.52749 q^{14} -1.93370 q^{15} -4.15018 q^{16} -4.39494 q^{17} +0.376600 q^{18} -3.70486 q^{19} +0.0913094 q^{20} +8.64150 q^{21} +2.70442 q^{22} +7.20094 q^{23} -4.58496 q^{24} -3.63472 q^{25} -5.18175 q^{26} +5.39709 q^{27} -0.408052 q^{28} +5.84811 q^{29} +2.78757 q^{30} -1.35487 q^{31} +0.441808 q^{32} +3.10465 q^{33} +6.33565 q^{34} -6.10132 q^{35} -0.0204149 q^{36} +3.71544 q^{37} +5.34085 q^{38} -5.94860 q^{39} +3.23720 q^{40} -2.17811 q^{41} -12.4574 q^{42} +10.7599 q^{43} -0.146602 q^{44} -0.305249 q^{45} -10.3807 q^{46} +2.70411 q^{47} +6.86822 q^{48} +20.2662 q^{49} +5.23973 q^{50} +7.27328 q^{51} +0.280894 q^{52} +13.6672 q^{53} -7.78033 q^{54} -2.19204 q^{55} -14.4667 q^{56} +6.13125 q^{57} -8.43050 q^{58} -10.8525 q^{59} -0.151110 q^{60} +13.7302 q^{61} +1.95314 q^{62} +1.36413 q^{63} +7.66347 q^{64} +4.20000 q^{65} -4.47560 q^{66} +2.91833 q^{67} -0.343445 q^{68} -11.9170 q^{69} +8.79552 q^{70} -5.23876 q^{71} -0.723771 q^{72} -6.15254 q^{73} -5.35609 q^{74} +6.01516 q^{75} -0.289518 q^{76} +9.79599 q^{77} +8.57537 q^{78} -8.25148 q^{79} -4.84930 q^{80} -8.14803 q^{81} +3.13991 q^{82} -13.1873 q^{83} +0.675294 q^{84} -5.13529 q^{85} -15.5112 q^{86} -9.67814 q^{87} -5.19750 q^{88} -12.9803 q^{89} +0.440040 q^{90} -18.7694 q^{91} +0.562721 q^{92} +2.24219 q^{93} -3.89819 q^{94} -4.32896 q^{95} -0.731156 q^{96} +8.59794 q^{97} -29.2153 q^{98} +0.490093 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) $ 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * 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 $

$2$	−1.44158	−1.01935	−0.509675	−	0.860367i	$-0.670234\pi$
$2$	−1.44158	−1.01935	−0.509675	+	0.860367i	$0.670234\pi$
$3$	−1.65492	−0.955468	−0.477734	−	0.878504i	$-0.658542\pi$
$3$	−1.65492	−0.955468	−0.477734	+	0.878504i	$0.658542\pi$
$4$	0.0781455	0.0390727
$5$	1.16845	0.522548	0.261274	−	0.965265i	$-0.415857\pi$
$5$	1.16845	0.522548	0.261274	+	0.965265i	$0.415857\pi$
$6$	2.38569	0.973956
$7$	−5.22170	−1.97362	−0.986809	−	0.161889i	$-0.948241\pi$
$7$	−5.22170	−1.97362	−0.986809	+	0.161889i	$0.948241\pi$
$8$	2.77050	0.979520
$9$	−0.261242	−0.0870806
$10$	−1.68442	−0.532659
$11$	−1.87602	−0.565640	−0.282820	−	0.959173i	$-0.591270\pi$
$11$	−1.87602	−0.565640	−0.282820	+	0.959173i	$0.591270\pi$
$12$	−0.129324	−0.0373328
$13$	3.59450	0.996934	0.498467	−	0.866909i	$-0.333896\pi$
$13$	3.59450	0.996934	0.498467	+	0.866909i	$0.333896\pi$
$14$	7.52749	2.01181
$15$	−1.93370	−0.499278
$16$	−4.15018	−1.03755
$17$	−4.39494	−1.06593	−0.532965	−	0.846137i	$-0.678922\pi$
$17$	−4.39494	−1.06593	−0.532965	+	0.846137i	$0.678922\pi$
$18$	0.376600	0.0887655
$19$	−3.70486	−0.849954	−0.424977	−	0.905204i	$-0.639718\pi$
$19$	−3.70486	−0.849954	−0.424977	+	0.905204i	$0.639718\pi$
$20$	0.0913094	0.0204174
$21$	8.64150	1.88573
$22$	2.70442	0.576585
$23$	7.20094	1.50150	0.750750	−	0.660587i	$-0.229692\pi$
$23$	7.20094	1.50150	0.750750	+	0.660587i	$0.229692\pi$
$24$	−4.58496	−0.935901
$25$	−3.63472	−0.726943
$26$	−5.18175	−1.01622
$27$	5.39709	1.03867
$28$	−0.408052	−0.0771147
$29$	5.84811	1.08597	0.542983	−	0.839744i	$-0.317295\pi$
$29$	5.84811	1.08597	0.542983	+	0.839744i	$0.317295\pi$
$30$	2.78757	0.508939
$31$	−1.35487	−0.243341	−0.121671	−	0.992571i	$-0.538825\pi$
$31$	−1.35487	−0.243341	−0.121671	+	0.992571i	$0.538825\pi$
$32$	0.441808	0.0781013
$33$	3.10465	0.540451
$34$	6.33565	1.08656
$35$	−6.10132	−1.03131
$36$	−0.0204149	−0.00340248
$37$	3.71544	0.610814	0.305407	−	0.952222i	$-0.401207\pi$
$37$	3.71544	0.610814	0.305407	+	0.952222i	$0.401207\pi$
$38$	5.34085	0.866400
$39$	−5.94860	−0.952539
$40$	3.23720	0.511847
$41$	−2.17811	−0.340163	−0.170082	−	0.985430i	$-0.554403\pi$
$41$	−2.17811	−0.340163	−0.170082	+	0.985430i	$0.554403\pi$
$42$	−12.4574	−1.92222
$43$	10.7599	1.64087	0.820435	−	0.571740i	$-0.193731\pi$
$43$	10.7599	1.64087	0.820435	+	0.571740i	$0.193731\pi$
$44$	−0.146602	−0.0221011
$45$	−0.305249	−0.0455038
$46$	−10.3807	−1.53055
$47$	2.70411	0.394435	0.197218	−	0.980360i	$-0.436809\pi$
$47$	2.70411	0.394435	0.197218	+	0.980360i	$0.436809\pi$
$48$	6.86822	0.991342
$49$	20.2662	2.89517
$50$	5.23973	0.741009
$51$	7.27328	1.01846
$52$	0.280894	0.0389530
$53$	13.6672	1.87734	0.938668	−	0.344823i	$-0.112061\pi$
$53$	13.6672	1.87734	0.938668	+	0.344823i	$0.112061\pi$
$54$	−7.78033	−1.05877
$55$	−2.19204	−0.295574
$56$	−14.4667	−1.93320
$57$	6.13125	0.812104
$58$	−8.43050	−1.10698
$59$	−10.8525	−1.41288	−0.706439	−	0.707774i	$-0.749700\pi$
$59$	−10.8525	−1.41288	−0.706439	+	0.707774i	$0.749700\pi$
$60$	−0.151110	−0.0195082
$61$	13.7302	1.75797	0.878985	−	0.476849i	$-0.158221\pi$
$61$	13.7302	1.75797	0.878985	+	0.476849i	$0.158221\pi$
$62$	1.95314	0.248050
$63$	1.36413	0.171864
$64$	7.66347	0.957934
$65$	4.20000	0.520946
$66$	−4.47560	−0.550908
$67$	2.91833	0.356531	0.178265	−	0.983982i	$-0.442951\pi$
$67$	2.91833	0.356531	0.178265	+	0.983982i	$0.442951\pi$
$68$	−0.343445	−0.0416488
$69$	−11.9170	−1.43463
$70$	8.79552	1.05127
$71$	−5.23876	−0.621727	−0.310863	−	0.950455i	$-0.600618\pi$
$71$	−5.23876	−0.621727	−0.310863	+	0.950455i	$0.600618\pi$
$72$	−0.723771	−0.0852972
$73$	−6.15254	−0.720100	−0.360050	−	0.932933i	$-0.617240\pi$
$73$	−6.15254	−0.720100	−0.360050	+	0.932933i	$0.617240\pi$
$74$	−5.35609	−0.622633
$75$	6.01516	0.694571
$76$	−0.289518	−0.0332100
$77$	9.79599	1.11636
$78$	8.57537	0.970970
$79$	−8.25148	−0.928364	−0.464182	−	0.885740i	$-0.653652\pi$
$79$	−8.25148	−0.928364	−0.464182	+	0.885740i	$0.653652\pi$
$80$	−4.84930	−0.542168
$81$	−8.14803	−0.905336
$82$	3.13991	0.346745
$83$	−13.1873	−1.44750	−0.723749	−	0.690063i	$-0.757583\pi$
$83$	−13.1873	−1.44750	−0.723749	+	0.690063i	$0.757583\pi$
$84$	0.675294	0.0736806
$85$	−5.13529	−0.557000
$86$	−15.5112	−1.67262
$87$	−9.67814	−1.03761
$88$	−5.19750	−0.554056
$89$	−12.9803	−1.37591	−0.687957	−	0.725752i	$-0.741492\pi$
$89$	−12.9803	−1.37591	−0.687957	+	0.725752i	$0.741492\pi$
$90$	0.440040	0.0463843
$91$	−18.7694	−1.96757
$92$	0.562721	0.0586677
$93$	2.24219	0.232505
$94$	−3.89819	−0.402067
$95$	−4.32896	−0.444142
$96$	−0.731156	−0.0746233
$97$	8.59794	0.872988	0.436494	−	0.899707i	$-0.356220\pi$
$97$	8.59794	0.872988	0.436494	+	0.899707i	$0.356220\pi$
$98$	−29.2153	−2.95119
$99$	0.490093	0.0492562
$100$	−0.284037	−0.0284037
$101$	14.7250	1.46519	0.732596	−	0.680663i	$-0.238308\pi$
$101$	14.7250	1.46519	0.732596	+	0.680663i	$0.238308\pi$
$102$	−10.4850	−1.03817
$103$	17.8630	1.76010	0.880049	−	0.474883i	$-0.157510\pi$
$103$	17.8630	1.76010	0.880049	+	0.474883i	$0.157510\pi$
$104$	9.95856	0.976518
$105$	10.0972	0.985385
$106$	−19.7023	−1.91366
$107$	−4.24062	−0.409956	−0.204978	−	0.978767i	$-0.565712\pi$
$107$	−4.24062	−0.409956	−0.204978	+	0.978767i	$0.565712\pi$
$108$	0.421758	0.0405837
$109$	7.64169	0.731942	0.365971	−	0.930626i	$-0.380737\pi$
$109$	7.64169	0.731942	0.365971	+	0.930626i	$0.380737\pi$
$110$	3.15999	0.301293
$111$	−6.14875	−0.583613
$112$	21.6710	2.04772
$113$	−6.24322	−0.587313	−0.293656	−	0.955911i	$-0.594872\pi$
$113$	−6.24322	−0.587313	−0.293656	+	0.955911i	$0.594872\pi$
$114$	−8.83867	−0.827818
$115$	8.41396	0.784606
$116$	0.457003	0.0424317
$117$	−0.939033	−0.0868136
$118$	15.6448	1.44022
$119$	22.9491	2.10374
$120$	−5.35731	−0.489053
$121$	−7.48057	−0.680052
$122$	−19.7931	−1.79199
$123$	3.60459	0.325015
$124$	−0.105877	−0.00950801
$125$	−10.0893	−0.902411
$126$	−1.96649	−0.175189
$127$	−18.0174	−1.59878	−0.799392	−	0.600810i	$-0.794845\pi$
$127$	−18.0174	−1.59878	−0.799392	+	0.600810i	$0.794845\pi$
$128$	−11.9311	−1.05457
$129$	−17.8068	−1.56780
$130$	−6.05463	−0.531026
$131$	−4.17633	−0.364888	−0.182444	−	0.983216i	$-0.558401\pi$
$131$	−4.17633	−0.364888	−0.182444	+	0.983216i	$0.558401\pi$
$132$	0.242615	0.0211169
$133$	19.3457	1.67748
$134$	−4.20700	−0.363429
$135$	6.30625	0.542756
$136$	−12.1762	−1.04410
$137$	5.22839	0.446692	0.223346	−	0.974739i	$-0.428302\pi$
$137$	5.22839	0.446692	0.223346	+	0.974739i	$0.428302\pi$
$138$	17.1792	1.46239
$139$	12.6668	1.07438	0.537191	−	0.843460i	$-0.319485\pi$
$139$	12.6668	1.07438	0.537191	+	0.843460i	$0.319485\pi$
$140$	−0.476790	−0.0402961
$141$	−4.47509	−0.376870
$142$	7.55208	0.633756
$143$	−6.74333	−0.563906
$144$	1.08420	0.0903501
$145$	6.83324	0.567470
$146$	8.86936	0.734034
$147$	−33.5389	−2.76624
$148$	0.290345	0.0238662
$149$	−6.95650	−0.569898	−0.284949	−	0.958543i	$-0.591977\pi$
$149$	−6.95650	−0.569898	−0.284949	+	0.958543i	$0.591977\pi$
$150$	−8.67132	−0.708011
$151$	−4.24542	−0.345488	−0.172744	−	0.984967i	$-0.555263\pi$
$151$	−4.24542	−0.345488	−0.172744	+	0.984967i	$0.555263\pi$
$152$	−10.2643	−0.832547
$153$	1.14814	0.0928218
$154$	−14.1217	−1.13796
$155$	−1.58310	−0.127157
$156$	−0.464857	−0.0372183
$157$	12.7081	1.01421	0.507107	−	0.861883i	$-0.330715\pi$
$157$	12.7081	1.01421	0.507107	+	0.861883i	$0.330715\pi$
$158$	11.8952	0.946327
$159$	−22.6181	−1.79373
$160$	0.516232	0.0408117
$161$	−37.6012	−2.96339
$162$	11.7460	0.922854
$163$	11.2202	0.878831	0.439416	−	0.898284i	$-0.355186\pi$
$163$	11.2202	0.878831	0.439416	+	0.898284i	$0.355186\pi$
$164$	−0.170209	−0.0132911
$165$	3.62764	0.282412
$166$	19.0106	1.47551
$167$	24.3997	1.88811	0.944054	−	0.329790i	$-0.106978\pi$
$167$	24.3997	1.88811	0.944054	+	0.329790i	$0.106978\pi$
$168$	23.9413	1.84711
$169$	−0.0795839	−0.00612184
$170$	7.40291	0.567778
$171$	0.967865	0.0740145
$172$	0.840838	0.0641133
$173$	−15.7024	−1.19383	−0.596916	−	0.802304i	$-0.703607\pi$
$173$	−15.7024	−1.19383	−0.596916	+	0.802304i	$0.703607\pi$
$174$	13.9518	1.05768
$175$	18.9794	1.43471
$176$	7.78581	0.586877
$177$	17.9601	1.34996
$178$	18.7122	1.40254
$179$	13.2973	0.993889	0.496944	−	0.867782i	$-0.334455\pi$
$179$	13.2973	0.993889	0.496944	+	0.867782i	$0.334455\pi$
$180$	−0.0238538	−0.00177796
$181$	4.74072	0.352375	0.176187	−	0.984357i	$-0.443624\pi$
$181$	4.74072	0.352375	0.176187	+	0.984357i	$0.443624\pi$
$182$	27.0575	2.00564
$183$	−22.7224	−1.67968
$184$	19.9502	1.47075
$185$	4.34132	0.319180
$186$	−3.23230	−0.237003
$187$	8.24498	0.602933
$188$	0.211314	0.0154117
$189$	−28.1820	−2.04994
$190$	6.24053	0.452736
$191$	12.0868	0.874570	0.437285	−	0.899323i	$-0.355940\pi$
$191$	12.0868	0.874570	0.437285	+	0.899323i	$0.355940\pi$
$192$	−12.6824	−0.915275
$193$	16.6225	1.19652	0.598259	−	0.801303i	$-0.295860\pi$
$193$	16.6225	1.19652	0.598259	+	0.801303i	$0.295860\pi$
$194$	−12.3946	−0.889880
$195$	−6.95067	−0.497748
$196$	1.58371	0.113122
$197$	9.11878	0.649686	0.324843	−	0.945768i	$-0.394689\pi$
$197$	9.11878	0.649686	0.324843	+	0.945768i	$0.394689\pi$
$198$	−0.706508	−0.0502093
$199$	−5.97681	−0.423685	−0.211842	−	0.977304i	$-0.567946\pi$
$199$	−5.97681	−0.423685	−0.211842	+	0.977304i	$0.567946\pi$
$200$	−10.0700	−0.712056
$201$	−4.82960	−0.340654
$202$	−21.2272	−1.49354
$203$	−30.5371	−2.14328
$204$	0.568374	0.0397941
$205$	−2.54502	−0.177752
$206$	−25.7510	−1.79415
$207$	−1.88119	−0.130751
$208$	−14.9178	−1.03437
$209$	6.95038	0.480768
$210$	−14.5559	−1.00445
$211$	4.05588	0.279218	0.139609	−	0.990207i	$-0.455415\pi$
$211$	4.05588	0.279218	0.139609	+	0.990207i	$0.455415\pi$
$212$	1.06803	0.0733526
$213$	8.66973	0.594040
$214$	6.11318	0.417888
$215$	12.5724	0.857434
$216$	14.9527	1.01740
$217$	7.07471	0.480262
$218$	−11.0161	−0.746104
$219$	10.1820	0.688033
$220$	−0.171298	−0.0115489
$221$	−15.7976	−1.06266
$222$	8.86390	0.594906
$223$	−2.35562	−0.157744	−0.0788719	−	0.996885i	$-0.525132\pi$
$223$	−2.35562	−0.157744	−0.0788719	+	0.996885i	$0.525132\pi$
$224$	−2.30699	−0.154142
$225$	0.949540	0.0633026
$226$	9.00008	0.598677
$227$	6.87919	0.456588	0.228294	−	0.973592i	$-0.426685\pi$
$227$	6.87919	0.456588	0.228294	+	0.973592i	$0.426685\pi$
$228$	0.479130	0.0317311
$229$	−1.96260	−0.129692	−0.0648462	−	0.997895i	$-0.520656\pi$
$229$	−1.96260	−0.129692	−0.0648462	+	0.997895i	$0.520656\pi$
$230$	−12.1294	−0.799787
$231$	−16.2116	−1.06664
$232$	16.2022	1.06373
$233$	−16.7753	−1.09899	−0.549493	−	0.835499i	$-0.685179\pi$
$233$	−16.7753	−1.09899	−0.549493	+	0.835499i	$0.685179\pi$
$234$	1.35369	0.0884934
$235$	3.15963	0.206112
$236$	−0.848076	−0.0552050
$237$	13.6555	0.887023
$238$	−33.0829	−2.14444
$239$	4.26878	0.276124	0.138062	−	0.990424i	$-0.455913\pi$
$239$	4.26878	0.276124	0.138062	+	0.990424i	$0.455913\pi$
$240$	8.02520	0.518024
$241$	−6.02897	−0.388360	−0.194180	−	0.980966i	$-0.562205\pi$
$241$	−6.02897	−0.388360	−0.194180	+	0.980966i	$0.562205\pi$
$242$	10.7838	0.693210
$243$	−2.70695	−0.173651
$244$	1.07295	0.0686887
$245$	23.6801	1.51286
$246$	−5.19630	−0.331304
$247$	−13.3171	−0.847349
$248$	−3.75366	−0.238358
$249$	21.8240	1.38304
$250$	14.5445	0.919872
$251$	22.4540	1.41728	0.708642	−	0.705568i	$-0.249308\pi$
$251$	22.4540	1.41728	0.708642	+	0.705568i	$0.249308\pi$
$252$	0.106600	0.00671519
$253$	−13.5091	−0.849308
$254$	25.9735	1.62972
$255$	8.49849	0.532196
$256$	1.87267	0.117042
$257$	5.60541	0.349656	0.174828	−	0.984599i	$-0.444063\pi$
$257$	5.60541	0.349656	0.174828	+	0.984599i	$0.444063\pi$
$258$	25.6698	1.59813
$259$	−19.4009	−1.20551
$260$	0.328211	0.0203548
$261$	−1.52777	−0.0945665
$262$	6.02050	0.371948
$263$	1.68398	0.103839	0.0519194	−	0.998651i	$-0.483466\pi$
$263$	1.68398	0.103839	0.0519194	+	0.998651i	$0.483466\pi$
$264$	8.60145	0.529383
$265$	15.9695	0.980998
$266$	−27.8883	−1.70994
$267$	21.4814	1.31464
$268$	0.228054	0.0139306
$269$	−11.6951	−0.713063	−0.356532	−	0.934283i	$-0.616041\pi$
$269$	−11.6951	−0.713063	−0.356532	+	0.934283i	$0.616041\pi$
$270$	−9.09095	−0.553258
$271$	8.02617	0.487555	0.243778	−	0.969831i	$-0.421613\pi$
$271$	8.02617	0.487555	0.243778	+	0.969831i	$0.421613\pi$
$272$	18.2398	1.10595
$273$	31.0618	1.87995
$274$	−7.53714	−0.455335
$275$	6.81878	0.411188
$276$	−0.931258	−0.0560551
$277$	24.9879	1.50138	0.750689	−	0.660656i	$-0.229722\pi$
$277$	24.9879	1.50138	0.750689	+	0.660656i	$0.229722\pi$
$278$	−18.2602	−1.09517
$279$	0.353948	0.0211903
$280$	−16.9037	−1.01019
$281$	13.2415	0.789921	0.394961	−	0.918698i	$-0.370758\pi$
$281$	13.2415	0.789921	0.394961	+	0.918698i	$0.370758\pi$
$282$	6.45119	0.384163
$283$	−20.7184	−1.23158	−0.615791	−	0.787910i	$-0.711163\pi$
$283$	−20.7184	−1.23158	−0.615791	+	0.787910i	$0.711163\pi$
$284$	−0.409386	−0.0242926
$285$	7.16408	0.424364
$286$	9.72104	0.574817
$287$	11.3734	0.671352
$288$	−0.115419	−0.00680111
$289$	2.31552	0.136207
$290$	−9.85064	−0.578450
$291$	−14.2289	−0.834113
$292$	−0.480793	−0.0281363
$293$	6.18432	0.361292	0.180646	−	0.983548i	$-0.442181\pi$
$293$	6.18432	0.361292	0.180646	+	0.983548i	$0.442181\pi$
$294$	48.3489	2.81977
$295$	−12.6807	−0.738297
$296$	10.2936	0.598305
$297$	−10.1250	−0.587514
$298$	10.0283	0.580925
$299$	25.8838	1.49690
$300$	0.470058	0.0271388
$301$	−56.1850	−3.23845
$302$	6.12011	0.352173
$303$	−24.3687	−1.39994
$304$	15.3759	0.881867
$305$	16.0431	0.918624
$306$	−1.65514	−0.0946178
$307$	6.11954	0.349260	0.174630	−	0.984634i	$-0.444127\pi$
$307$	6.11954	0.349260	0.174630	+	0.984634i	$0.444127\pi$
$308$	0.765513	0.0436191
$309$	−29.5619	−1.68172
$310$	2.28216	0.129618
$311$	11.4142	0.647241	0.323621	−	0.946187i	$-0.395100\pi$
$311$	11.4142	0.647241	0.323621	+	0.946187i	$0.395100\pi$
$312$	−16.4806	−0.933031
$313$	32.2666	1.82382	0.911908	−	0.410394i	$-0.134609\pi$
$313$	32.2666	1.82382	0.911908	+	0.410394i	$0.134609\pi$
$314$	−18.3197	−1.03384
$315$	1.59392	0.0898071
$316$	−0.644816	−0.0362737
$317$	−16.2640	−0.913476	−0.456738	−	0.889601i	$-0.650982\pi$
$317$	−16.2640	−0.913476	−0.456738	+	0.889601i	$0.650982\pi$
$318$	32.6058	1.82844
$319$	−10.9711	−0.614266
$320$	8.95441	0.500567
$321$	7.01788	0.391700
$322$	54.2050	3.02073
$323$	16.2827	0.905992
$324$	−0.636732	−0.0353740
$325$	−13.0650	−0.724715
$326$	−16.1747	−0.895836
$327$	−12.6464	−0.699347
$328$	−6.03445	−0.333197
$329$	−14.1201	−0.778465
$330$	−5.22953	−0.287876
$331$	17.1918	0.944945	0.472473	−	0.881345i	$-0.343362\pi$
$331$	17.1918	0.944945	0.472473	+	0.881345i	$0.343362\pi$
$332$	−1.03053	−0.0565577
$333$	−0.970627	−0.0531900
$334$	−35.1741	−1.92464
$335$	3.40993	0.186304
$336$	−35.8638	−1.95653
$337$	−12.7167	−0.692724	−0.346362	−	0.938101i	$-0.612583\pi$
$337$	−12.7167	−0.692724	−0.346362	+	0.938101i	$0.612583\pi$
$338$	0.114726	0.00624029
$339$	10.3320	0.561158
$340$	−0.401299	−0.0217635
$341$	2.54175	0.137643
$342$	−1.39525	−0.0754466
$343$	−69.2720	−3.74034
$344$	29.8103	1.60727
$345$	−13.9244	−0.749666
$346$	22.6362	1.21693
$347$	11.1578	0.598982	0.299491	−	0.954099i	$-0.403183\pi$
$347$	11.1578	0.598982	0.299491	+	0.954099i	$0.403183\pi$
$348$	−0.756303	−0.0405421
$349$	−5.37351	−0.287638	−0.143819	−	0.989604i	$-0.545938\pi$
$349$	−5.37351	−0.287638	−0.143819	+	0.989604i	$0.545938\pi$
$350$	−27.3603	−1.46247
$351$	19.3998	1.03549
$352$	−0.828838	−0.0441772
$353$	−13.5118	−0.719163	−0.359582	−	0.933114i	$-0.617081\pi$
$353$	−13.5118	−0.719163	−0.359582	+	0.933114i	$0.617081\pi$
$354$	−25.8908	−1.37608
$355$	−6.12125	−0.324882
$356$	−1.01435	−0.0537607
$357$	−37.9789	−2.01006
$358$	−19.1691	−1.01312
$359$	16.0870	0.849039	0.424519	−	0.905419i	$-0.360443\pi$
$359$	16.0870	0.849039	0.424519	+	0.905419i	$0.360443\pi$
$360$	−0.845693	−0.0445719
$361$	−5.27398	−0.277578
$362$	−6.83411	−0.359193
$363$	12.3797	0.649768
$364$	−1.46674	−0.0768783
$365$	−7.18896	−0.376287
$366$	32.7560	1.71218
$367$	17.6750	0.922626	0.461313	−	0.887237i	$-0.347378\pi$
$367$	17.6750	0.922626	0.461313	+	0.887237i	$0.347378\pi$
$368$	−29.8852	−1.55787
$369$	0.569013	0.0296216
$370$	−6.25834	−0.325356
$371$	−71.3661	−3.70514
$372$	0.175217	0.00908460
$373$	8.48505	0.439339	0.219670	−	0.975574i	$-0.429502\pi$
$373$	8.48505	0.439339	0.219670	+	0.975574i	$0.429502\pi$
$374$	−11.8858	−0.614599
$375$	16.6969	0.862225
$376$	7.49175	0.386358
$377$	21.0210	1.08264
$378$	40.6265	2.08960
$379$	−9.85389	−0.506160	−0.253080	−	0.967445i	$-0.581444\pi$
$379$	−9.85389	−0.506160	−0.253080	+	0.967445i	$0.581444\pi$
$380$	−0.338289	−0.0173539
$381$	29.8173	1.52759
$382$	−17.4240	−0.891492
$383$	−10.4001	−0.531420	−0.265710	−	0.964053i	$-0.585606\pi$
$383$	−10.4001	−0.531420	−0.265710	+	0.964053i	$0.585606\pi$
$384$	19.7450	1.00761
$385$	11.4462	0.583350
$386$	−23.9627	−1.21967
$387$	−2.81094	−0.142888
$388$	0.671890	0.0341101
$389$	−1.07680	−0.0545960	−0.0272980	−	0.999627i	$-0.508690\pi$
$389$	−1.07680	−0.0545960	−0.0272980	+	0.999627i	$0.508690\pi$
$390$	10.0199	0.507379
$391$	−31.6477	−1.60049
$392$	56.1475	2.83588
$393$	6.91149	0.348639
$394$	−13.1454	−0.662257
$395$	−9.64147	−0.485115
$396$	0.0382986	0.00192458
$397$	−22.0327	−1.10579	−0.552895	−	0.833251i	$-0.686477\pi$
$397$	−22.0327	−1.10579	−0.552895	+	0.833251i	$0.686477\pi$
$398$	8.61603	0.431883
$399$	−32.0156	−1.60278
$400$	15.0847	0.754237
$401$	1.11136	0.0554988	0.0277494	−	0.999615i	$-0.491166\pi$
$401$	1.11136	0.0554988	0.0277494	+	0.999615i	$0.491166\pi$
$402$	6.96224	0.347245
$403$	−4.87006	−0.242595
$404$	1.15069	0.0572491
$405$	−9.52059	−0.473082
$406$	44.0215	2.18475
$407$	−6.97022	−0.345501
$408$	20.1506	0.997605
$409$	−12.7644	−0.631158	−0.315579	−	0.948899i	$-0.602199\pi$
$409$	−12.7644	−0.631158	−0.315579	+	0.948899i	$0.602199\pi$
$410$	3.66884	0.181191
$411$	−8.65257	−0.426800
$412$	1.39592	0.0687719
$413$	56.6686	2.78848
$414$	2.71187	0.133281
$415$	−15.4088	−0.756388
$416$	1.58808	0.0778619
$417$	−20.9625	−1.02654
$418$	−10.0195	−0.490070
$419$	2.81345	0.137446	0.0687230	−	0.997636i	$-0.478108\pi$
$419$	2.81345	0.137446	0.0687230	+	0.997636i	$0.478108\pi$
$420$	0.789050	0.0385017
$421$	0.340713	0.0166053	0.00830267	−	0.999966i	$-0.497357\pi$
$421$	0.340713	0.0166053	0.00830267	+	0.999966i	$0.497357\pi$
$422$	−5.84687	−0.284621
$423$	−0.706427	−0.0343477
$424$	37.8650	1.83889
$425$	15.9744	0.774871
$426$	−12.4981	−0.605534
$427$	−71.6949	−3.46956
$428$	−0.331385	−0.0160181
$429$	11.1597	0.538794
$430$	−18.1242	−0.874024
$431$	17.9632	0.865257	0.432629	−	0.901572i	$-0.357586\pi$
$431$	17.9632	0.865257	0.432629	+	0.901572i	$0.357586\pi$
$432$	−22.3989	−1.07767
$433$	15.4246	0.741259	0.370629	−	0.928781i	$-0.379142\pi$
$433$	15.4246	0.741259	0.370629	+	0.928781i	$0.379142\pi$
$434$	−10.1987	−0.489555
$435$	−11.3085	−0.542199
$436$	0.597164	0.0285990
$437$	−26.6785	−1.27621
$438$	−14.6781	−0.701346
$439$	6.69721	0.319640	0.159820	−	0.987146i	$-0.448909\pi$
$439$	6.69721	0.319640	0.159820	+	0.987146i	$0.448909\pi$
$440$	−6.07304	−0.289521
$441$	−5.29437	−0.252113
$442$	22.7735	1.08322
$443$	33.6219	1.59743	0.798713	−	0.601712i	$-0.205514\pi$
$443$	33.6219	1.59743	0.798713	+	0.601712i	$0.205514\pi$
$444$	−0.480497	−0.0228034
$445$	−15.1669	−0.718981
$446$	3.39580	0.160796
$447$	11.5124	0.544520
$448$	−40.0164	−1.89059
$449$	27.8142	1.31263	0.656316	−	0.754486i	$-0.272114\pi$
$449$	27.8142	1.31263	0.656316	+	0.754486i	$0.272114\pi$
$450$	−1.36883	−0.0645275
$451$	4.08616	0.192410
$452$	−0.487879	−0.0229479
$453$	7.02583	0.330102
$454$	−9.91689	−0.465423
$455$	−21.9312	−1.02815
$456$	16.9866	0.795473
$457$	−2.39554	−0.112059	−0.0560294	−	0.998429i	$-0.517844\pi$
$457$	−2.39554	−0.112059	−0.0560294	+	0.998429i	$0.517844\pi$
$458$	2.82924	0.132202
$459$	−23.7199	−1.10715
$460$	0.657513	0.0306567
$461$	−24.6862	−1.14975	−0.574876	−	0.818241i	$-0.694950\pi$
$461$	−24.6862	−1.14975	−0.574876	+	0.818241i	$0.694950\pi$
$462$	23.3702	1.08728
$463$	12.5562	0.583537	0.291769	−	0.956489i	$-0.405756\pi$
$463$	12.5562	0.583537	0.291769	+	0.956489i	$0.405756\pi$
$464$	−24.2707	−1.12674
$465$	2.61990	0.121495
$466$	24.1829	1.12025
$467$	3.68834	0.170676	0.0853380	−	0.996352i	$-0.472803\pi$
$467$	3.68834	0.170676	0.0853380	+	0.996352i	$0.472803\pi$
$468$	−0.0733812	−0.00339205
$469$	−15.2386	−0.703655
$470$	−4.55485	−0.210100
$471$	−21.0308	−0.969049
$472$	−30.0669	−1.38394
$473$	−20.1857	−0.928141
$474$	−19.6855	−0.904186
$475$	13.4661	0.617868
$476$	1.79337	0.0821989
$477$	−3.57044	−0.163479
$478$	−6.15377	−0.281467
$479$	−8.22389	−0.375759	−0.187880	−	0.982192i	$-0.560161\pi$
$479$	−8.22389	−0.375759	−0.187880	+	0.982192i	$0.560161\pi$
$480$	−0.854322	−0.0389943
$481$	13.3551	0.608942
$482$	8.69122	0.395874
$483$	62.2269	2.83142
$484$	−0.584573	−0.0265715
$485$	10.0463	0.456179
$486$	3.90227	0.177011
$487$	15.8574	0.718569	0.359284	−	0.933228i	$-0.383021\pi$
$487$	15.8574	0.718569	0.359284	+	0.933228i	$0.383021\pi$
$488$	38.0395	1.72197
$489$	−18.5685	−0.839695
$490$	−34.1367	−1.54214
$491$	−29.4948	−1.33108	−0.665541	−	0.746361i	$-0.731799\pi$
$491$	−29.4948	−1.33108	−0.665541	+	0.746361i	$0.731799\pi$
$492$	0.281683	0.0126992
$493$	−25.7021	−1.15756
$494$	19.1977	0.863744
$495$	0.572651	0.0257388
$496$	5.62294	0.252478
$497$	27.3553	1.22705
$498$	−31.4610	−1.40980
$499$	31.8227	1.42458	0.712291	−	0.701884i	$-0.247658\pi$
$499$	31.8227	1.42458	0.712291	+	0.701884i	$0.247658\pi$
$500$	−0.788431	−0.0352597
$501$	−40.3796	−1.80403
$502$	−32.3692	−1.44471
$503$	1.00000	0.0445878
$503$	1.00000	0.0445878
$504$	3.77932	0.168344
$505$	17.2055	0.765634
$506$	19.4744	0.865741
$507$	0.131705	0.00584923
$508$	−1.40798	−0.0624689
$509$	−11.5533	−0.512092	−0.256046	−	0.966665i	$-0.582420\pi$
$509$	−11.5533	−0.512092	−0.256046	+	0.966665i	$0.582420\pi$
$510$	−12.2512	−0.542493
$511$	32.1267	1.42120
$512$	21.1626	0.935264
$513$	−19.9955	−0.882823
$514$	−8.08064	−0.356422
$515$	20.8721	0.919736
$516$	−1.39152	−0.0612582
$517$	−5.07296	−0.223108
$518$	27.9679	1.22884
$519$	25.9862	1.14067
$520$	11.6361	0.510278
$521$	−27.4131	−1.20099	−0.600494	−	0.799629i	$-0.705029\pi$
$521$	−27.4131	−1.20099	−0.600494	+	0.799629i	$0.705029\pi$
$522$	2.20240	0.0963963
$523$	−9.22449	−0.403359	−0.201679	−	0.979452i	$-0.564640\pi$
$523$	−9.22449	−0.403359	−0.201679	+	0.979452i	$0.564640\pi$
$524$	−0.326361	−0.0142572
$525$	−31.4094	−1.37082
$526$	−2.42759	−0.105848
$527$	5.95456	0.259385
$528$	−12.8849	−0.560743
$529$	28.8535	1.25450
$530$	−23.0213	−0.999980
$531$	2.83513	0.123034
$532$	1.51178	0.0655439
$533$	−7.82921	−0.339121
$534$	−30.9671	−1.34008
$535$	−4.95496	−0.214222
$536$	8.08524	0.349229
$537$	−22.0060	−0.949629
$538$	16.8594	0.726860
$539$	−38.0197	−1.63762
$540$	0.492805	0.0212070
$541$	39.5153	1.69890	0.849449	−	0.527671i	$-0.176935\pi$
$541$	39.5153	1.69890	0.849449	+	0.527671i	$0.176935\pi$
$542$	−11.5703	−0.496989
$543$	−7.84551	−0.336683
$544$	−1.94172	−0.0832506
$545$	8.92896	0.382475
$546$	−44.7781	−1.91632
$547$	−18.3165	−0.783157	−0.391579	−	0.920145i	$-0.628071\pi$
$547$	−18.3165	−0.783157	−0.391579	+	0.920145i	$0.628071\pi$
$548$	0.408575	0.0174535
$549$	−3.58690	−0.153085
$550$	−9.82980	−0.419144
$551$	−21.6664	−0.923021
$552$	−33.0160	−1.40525
$553$	43.0868	1.83224
$554$	−36.0220	−1.53043
$555$	−7.18453	−0.304966
$556$	0.989852	0.0419791
$557$	1.84697	0.0782588	0.0391294	−	0.999234i	$-0.487542\pi$
$557$	1.84697	0.0782588	0.0391294	+	0.999234i	$0.487542\pi$
$558$	−0.510243	−0.0216003
$559$	38.6764	1.63584
$560$	25.3216	1.07003
$561$	−13.6448	−0.576083
$562$	−19.0886	−0.805205
$563$	−18.6098	−0.784312	−0.392156	−	0.919899i	$-0.628271\pi$
$563$	−18.6098	−0.784312	−0.392156	+	0.919899i	$0.628271\pi$
$564$	−0.349708	−0.0147254
$565$	−7.29491	−0.306899
$566$	29.8672	1.25541
$567$	42.5466	1.78679
$568$	−14.5140	−0.608994
$569$	−19.8106	−0.830503	−0.415251	−	0.909707i	$-0.636306\pi$
$569$	−19.8106	−0.830503	−0.415251	+	0.909707i	$0.636306\pi$
$570$	−10.3276	−0.432575
$571$	33.9800	1.42202	0.711008	−	0.703183i	$-0.248239\pi$
$571$	33.9800	1.42202	0.711008	+	0.703183i	$0.248239\pi$
$572$	−0.526961	−0.0220333
$573$	−20.0027	−0.835624
$574$	−16.3957	−0.684343
$575$	−26.1734	−1.09150
$576$	−2.00202	−0.0834174
$577$	12.7808	0.532073	0.266037	−	0.963963i	$-0.414286\pi$
$577$	12.7808	0.532073	0.266037	+	0.963963i	$0.414286\pi$
$578$	−3.33801	−0.138843
$579$	−27.5090	−1.14323
$580$	0.533987	0.0221726
$581$	68.8604	2.85681
$582$	20.5121	0.850252
$583$	−25.6399	−1.06190
$584$	−17.0456	−0.705353
$585$	−1.09722	−0.0453643
$586$	−8.91518	−0.368283
$587$	−29.4463	−1.21538	−0.607690	−	0.794174i	$-0.707904\pi$
$587$	−29.4463	−1.21538	−0.607690	+	0.794174i	$0.707904\pi$
$588$	−2.62091	−0.108085
$589$	5.01959	0.206829
$590$	18.2802	0.752583
$591$	−15.0908	−0.620754
$592$	−15.4197	−0.633748
$593$	−20.7161	−0.850706	−0.425353	−	0.905027i	$-0.639850\pi$
$593$	−20.7161	−0.850706	−0.425353	+	0.905027i	$0.639850\pi$
$594$	14.5960	0.598882
$595$	26.8149	1.09931
$596$	−0.543619	−0.0222675
$597$	9.89114	0.404817
$598$	−37.3134	−1.52586
$599$	33.4780	1.36787	0.683937	−	0.729541i	$-0.260266\pi$
$599$	33.4780	1.36787	0.683937	+	0.729541i	$0.260266\pi$
$600$	16.6650	0.680347
$601$	−25.6180	−1.04498	−0.522489	−	0.852646i	$-0.674997\pi$
$601$	−25.6180	−1.04498	−0.522489	+	0.852646i	$0.674997\pi$
$602$	80.9950	3.30111
$603$	−0.762389	−0.0310469
$604$	−0.331761	−0.0134992
$605$	−8.74069	−0.355360
$606$	35.1294	1.42703
$607$	31.2416	1.26806	0.634028	−	0.773310i	$-0.281400\pi$
$607$	31.2416	1.26806	0.634028	+	0.773310i	$0.281400\pi$
$608$	−1.63684	−0.0663825
$609$	50.5364	2.04784
$610$	−23.1273	−0.936399
$611$	9.71993	0.393226
$612$	0.0897222	0.00362680
$613$	40.2405	1.62530	0.812650	−	0.582752i	$-0.198024\pi$
$613$	40.2405	1.62530	0.812650	+	0.582752i	$0.198024\pi$
$614$	−8.82179	−0.356018
$615$	4.21180	0.169836
$616$	27.1398	1.09349
$617$	9.27736	0.373492	0.186746	−	0.982408i	$-0.440206\pi$
$617$	9.27736	0.373492	0.186746	+	0.982408i	$0.440206\pi$
$618$	42.6158	1.71426
$619$	7.92403	0.318494	0.159247	−	0.987239i	$-0.449093\pi$
$619$	7.92403	0.318494	0.159247	+	0.987239i	$0.449093\pi$
$620$	−0.123712	−0.00496839
$621$	38.8641	1.55956
$622$	−16.4545	−0.659765
$623$	67.7795	2.71553
$624$	24.6878	0.988303
$625$	6.38474	0.255390
$626$	−46.5148	−1.85911
$627$	−11.5023	−0.459358
$628$	0.993078	0.0396281
$629$	−16.3291	−0.651085
$630$	−2.29776	−0.0915448
$631$	−9.56630	−0.380828	−0.190414	−	0.981704i	$-0.560983\pi$
$631$	−9.56630	−0.380828	−0.190414	+	0.981704i	$0.560983\pi$
$632$	−22.8607	−0.909352
$633$	−6.71216	−0.266784
$634$	23.4458	0.931151
$635$	−21.0525	−0.835442
$636$	−1.76750	−0.0700861
$637$	72.8467	2.88629
$638$	15.8157	0.626151
$639$	1.36858	0.0541403
$640$	−13.9409	−0.551064
$641$	−28.1267	−1.11094	−0.555469	−	0.831538i	$-0.687461\pi$
$641$	−28.1267	−1.11094	−0.555469	+	0.831538i	$0.687461\pi$
$642$	−10.1168	−0.399279
$643$	3.46879	0.136796	0.0683978	−	0.997658i	$-0.478211\pi$
$643$	3.46879	0.136796	0.0683978	+	0.997658i	$0.478211\pi$
$644$	−2.93836	−0.115788
$645$	−20.8064	−0.819251
$646$	−23.4727	−0.923522
$647$	14.4099	0.566512	0.283256	−	0.959044i	$-0.408585\pi$
$647$	14.4099	0.566512	0.283256	+	0.959044i	$0.408585\pi$
$648$	−22.5741	−0.886795
$649$	20.3595	0.799180
$650$	18.8342	0.738737
$651$	−11.7081	−0.458875
$652$	0.876806	0.0343384
$653$	−17.1316	−0.670411	−0.335205	−	0.942145i	$-0.608806\pi$
$653$	−17.1316	−0.670411	−0.335205	+	0.942145i	$0.608806\pi$
$654$	18.2307	0.712879
$655$	−4.87985	−0.190671
$656$	9.03955	0.352935
$657$	1.60730	0.0627067
$658$	20.3552	0.793527
$659$	3.66347	0.142709	0.0713543	−	0.997451i	$-0.477268\pi$
$659$	3.66347	0.142709	0.0713543	+	0.997451i	$0.477268\pi$
$660$	0.283484	0.0110346
$661$	39.6530	1.54232	0.771162	−	0.636639i	$-0.219676\pi$
$661$	39.6530	1.54232	0.771162	+	0.636639i	$0.219676\pi$
$662$	−24.7833	−0.963229
$663$	26.1438	1.01534
$664$	−36.5356	−1.41785
$665$	22.6045	0.876567
$666$	1.39923	0.0542192
$667$	42.1118	1.63058
$668$	1.90673	0.0737736
$669$	3.89836	0.150719
$670$	−4.91568	−0.189909
$671$	−25.7580	−0.994378
$672$	3.81788	0.147278
$673$	34.3247	1.32312	0.661560	−	0.749892i	$-0.269895\pi$
$673$	34.3247	1.32312	0.661560	+	0.749892i	$0.269895\pi$
$674$	18.3321	0.706127
$675$	−19.6169	−0.755055
$676$	−0.00621913	−0.000239197 0
$677$	20.2805	0.779442	0.389721	−	0.920933i	$-0.372572\pi$
$677$	20.2805	0.779442	0.389721	+	0.920933i	$0.372572\pi$
$678$	−14.8944	−0.572016
$679$	−44.8959	−1.72295
$680$	−14.2273	−0.545593
$681$	−11.3845	−0.436255
$682$	−3.66413	−0.140307
$683$	24.3123	0.930283	0.465141	−	0.885236i	$-0.346003\pi$
$683$	24.3123	0.930283	0.465141	+	0.885236i	$0.346003\pi$
$684$	0.0756343	0.00289195
$685$	6.10914	0.233418
$686$	99.8610	3.81271
$687$	3.24795	0.123917
$688$	−44.6556	−1.70248
$689$	49.1267	1.87158
$690$	20.0731	0.764171
$691$	17.3936	0.661684	0.330842	−	0.943686i	$-0.392667\pi$
$691$	17.3936	0.661684	0.330842	+	0.943686i	$0.392667\pi$
$692$	−1.22707	−0.0466463
$693$	−2.55912	−0.0972130
$694$	−16.0848	−0.610571
$695$	14.8006	0.561417
$696$	−26.8133	−1.01636
$697$	9.57266	0.362590
$698$	7.74634	0.293203
$699$	27.7617	1.05005
$700$	1.48315	0.0560580
$701$	−25.2331	−0.953042	−0.476521	−	0.879163i	$-0.658102\pi$
$701$	−25.2331	−0.953042	−0.476521	+	0.879163i	$0.658102\pi$
$702$	−27.9664	−1.05552
$703$	−13.7652	−0.519164
$704$	−14.3768	−0.541845
$705$	−5.22893	−0.196933
$706$	19.4784	0.733078
$707$	−76.8896	−2.89173
$708$	1.40350	0.0527466
$709$	26.0105	0.976845	0.488422	−	0.872607i	$-0.337573\pi$
$709$	26.0105	0.976845	0.488422	+	0.872607i	$0.337573\pi$
$710$	8.82425	0.331168
$711$	2.15563	0.0808425
$712$	−35.9621	−1.34773
$713$	−9.75631	−0.365377
$714$	54.7495	2.04895
$715$	−7.87927	−0.294668
$716$	1.03913	0.0388340
$717$	−7.06448	−0.263828
$718$	−23.1906	−0.865467
$719$	−11.2045	−0.417858	−0.208929	−	0.977931i	$-0.566998\pi$
$719$	−11.2045	−0.417858	−0.208929	+	0.977931i	$0.566998\pi$
$720$	1.26684	0.0472123
$721$	−93.2755	−3.47376
$722$	7.60285	0.282949
$723$	9.97745	0.371065
$724$	0.370466	0.0137682
$725$	−21.2562	−0.789436
$726$	−17.8463	−0.662340
$727$	−37.1106	−1.37636	−0.688179	−	0.725541i	$-0.741589\pi$
$727$	−37.1106	−1.37636	−0.688179	+	0.725541i	$0.741589\pi$
$728$	−52.0007	−1.92727
$729$	28.9239	1.07125
$730$	10.3634	0.383568
$731$	−47.2892	−1.74905
$732$	−1.77565	−0.0656299
$733$	32.5163	1.20102	0.600509	−	0.799618i	$-0.294965\pi$
$733$	32.5163	1.20102	0.600509	+	0.799618i	$0.294965\pi$
$734$	−25.4799	−0.940478
$735$	−39.1886	−1.44549
$736$	3.18143	0.117269
$737$	−5.47483	−0.201668
$738$	−0.820276	−0.0301948
$739$	−25.9897	−0.956046	−0.478023	−	0.878347i	$-0.658647\pi$
$739$	−25.9897	−0.956046	−0.478023	+	0.878347i	$0.658647\pi$
$740$	0.339254	0.0124712
$741$	22.0388	0.809615
$742$	102.880	3.77683
$743$	−5.63810	−0.206842	−0.103421	−	0.994638i	$-0.532979\pi$
$743$	−5.63810	−0.206842	−0.103421	+	0.994638i	$0.532979\pi$
$744$	6.21200	0.227743
$745$	−8.12834	−0.297799
$746$	−12.2319	−0.447840
$747$	3.44508	0.126049
$748$	0.644308	0.0235582
$749$	22.1432	0.809096
$750$	−24.0699	−0.878909
$751$	48.6229	1.77428	0.887138	−	0.461504i	$-0.152690\pi$
$751$	48.6229	1.77428	0.887138	+	0.461504i	$0.152690\pi$
$752$	−11.2226	−0.409245
$753$	−37.1595	−1.35417
$754$	−30.3034	−1.10358
$755$	−4.96058	−0.180534
$756$	−2.20230	−0.0800968
$757$	−37.9095	−1.37784	−0.688922	−	0.724835i	$-0.741916\pi$
$757$	−37.9095	−1.37784	−0.688922	+	0.724835i	$0.741916\pi$
$758$	14.2051	0.515954
$759$	22.3564	0.811487
$760$	−11.9934	−0.435046
$761$	32.9830	1.19563	0.597817	−	0.801633i	$-0.296035\pi$
$761$	32.9830	1.19563	0.597817	+	0.801633i	$0.296035\pi$
$762$	−42.9840	−1.55715
$763$	−39.9026	−1.44457
$764$	0.944528	0.0341718
$765$	1.34155	0.0485039
$766$	14.9925	0.541703
$767$	−39.0094	−1.40855
$768$	−3.09911	−0.111830
$769$	15.9036	0.573499	0.286749	−	0.958006i	$-0.407425\pi$
$769$	15.9036	0.573499	0.286749	+	0.958006i	$0.407425\pi$
$770$	−16.5005	−0.594638
$771$	−9.27651	−0.334085
$772$	1.29898	0.0467512
$773$	−6.67230	−0.239986	−0.119993	−	0.992775i	$-0.538287\pi$
$773$	−6.67230	−0.239986	−0.119993	+	0.992775i	$0.538287\pi$
$774$	4.05218	0.145653
$775$	4.92455	0.176895
$776$	23.8206	0.855110
$777$	32.1069	1.15183
$778$	1.55229	0.0556524
$779$	8.06960	0.289123
$780$	−0.543163	−0.0194484
$781$	9.82800	0.351673
$782$	45.6226	1.63146
$783$	31.5628	1.12796
$784$	−84.1084	−3.00387
$785$	14.8488	0.529976
$786$	−9.96345	−0.355384
$787$	−17.7383	−0.632302	−0.316151	−	0.948709i	$-0.602391\pi$
$787$	−17.7383	−0.632302	−0.316151	+	0.948709i	$0.602391\pi$
$788$	0.712591	0.0253850
$789$	−2.78685	−0.0992146
$790$	13.8989	0.494502
$791$	32.6002	1.15913
$792$	1.35780	0.0482475
$793$	49.3531	1.75258
$794$	31.7619	1.12719
$795$	−26.4282	−0.937313
$796$	−0.467061	−0.0165545
$797$	−22.1191	−0.783497	−0.391749	−	0.920072i	$-0.628130\pi$
$797$	−22.1191	−0.783497	−0.391749	+	0.920072i	$0.628130\pi$
$798$	46.1529	1.63380
$799$	−11.8844	−0.420441
$800$	−1.60585	−0.0567752
$801$	3.39101	0.119815
$802$	−1.60212	−0.0565727
$803$	11.5423	0.407317
$804$	−0.377411	−0.0133103
$805$	−43.9352	−1.54851
$806$	7.02057	0.247289
$807$	19.3545	0.681309
$808$	40.7957	1.43519
$809$	42.0410	1.47808	0.739042	−	0.673659i	$-0.235278\pi$
$809$	42.0410	1.47808	0.739042	+	0.673659i	$0.235278\pi$
$810$	13.7247	0.482236
$811$	−18.8593	−0.662238	−0.331119	−	0.943589i	$-0.607426\pi$
$811$	−18.8593	−0.662238	−0.331119	+	0.943589i	$0.607426\pi$
$812$	−2.38633	−0.0837439
$813$	−13.2827	−0.465843
$814$	10.0481	0.352186
$815$	13.1102	0.459232
$816$	−30.1854	−1.05670
$817$	−39.8640	−1.39466
$818$	18.4008	0.643370
$819$	4.90335	0.171337
$820$	−0.198882	−0.00694525
$821$	−46.4269	−1.62031	−0.810155	−	0.586216i	$-0.800617\pi$
$821$	−46.4269	−1.62031	−0.810155	+	0.586216i	$0.800617\pi$
$822$	12.4734	0.435058
$823$	10.2034	0.355669	0.177835	−	0.984060i	$-0.443091\pi$
$823$	10.2034	0.355669	0.177835	+	0.984060i	$0.443091\pi$
$824$	49.4896	1.72405
$825$	−11.2845	−0.392877
$826$	−81.6922	−2.84244
$827$	−25.0611	−0.871461	−0.435730	−	0.900077i	$-0.643510\pi$
$827$	−25.0611	−0.871461	−0.435730	+	0.900077i	$0.643510\pi$
$828$	−0.147006	−0.00510882
$829$	−19.9198	−0.691844	−0.345922	−	0.938263i	$-0.612434\pi$
$829$	−19.9198	−0.691844	−0.345922	+	0.938263i	$0.612434\pi$
$830$	22.2130	0.771023
$831$	−41.3530	−1.43452
$832$	27.5463	0.954997
$833$	−89.0687	−3.08605
$834$	30.2191	1.04640
$835$	28.5100	0.986628
$836$	0.543141	0.0187849
$837$	−7.31234	−0.252751
$838$	−4.05580	−0.140105
$839$	52.0091	1.79555	0.897777	−	0.440451i	$-0.145182\pi$
$839$	52.0091	1.79555	0.897777	+	0.440451i	$0.145182\pi$
$840$	27.9743	0.965204
$841$	5.20033	0.179322
$842$	−0.491164	−0.0169266
$843$	−21.9136	−0.754744
$844$	0.316949	0.0109098
$845$	−0.0929901	−0.00319896
$846$	1.01837	0.0350123
$847$	39.0613	1.34216
$848$	−56.7214	−1.94782
$849$	34.2873	1.17674
$850$	−23.0283	−0.789864
$851$	26.7546	0.917137
$852$	0.677500	0.0232108
$853$	37.6780	1.29007	0.645036	−	0.764152i	$-0.276842\pi$
$853$	37.6780	1.29007	0.645036	+	0.764152i	$0.276842\pi$
$854$	103.354	3.53669
$855$	1.13091	0.0386762
$856$	−11.7486	−0.401560
$857$	−34.6052	−1.18209	−0.591045	−	0.806638i	$-0.701285\pi$
$857$	−34.6052	−1.18209	−0.591045	+	0.806638i	$0.701285\pi$
$858$	−16.0875	−0.549219
$859$	−27.9524	−0.953723	−0.476861	−	0.878978i	$-0.658226\pi$
$859$	−27.9524	−0.953723	−0.476861	+	0.878978i	$0.658226\pi$
$860$	0.982480	0.0335023
$861$	−18.8221	−0.641456
$862$	−25.8954	−0.881999
$863$	35.2339	1.19938	0.599688	−	0.800234i	$-0.295291\pi$
$863$	35.2339	1.19938	0.599688	+	0.800234i	$0.295291\pi$
$864$	2.38448	0.0811216
$865$	−18.3475	−0.623835
$866$	−22.2358	−0.755602
$867$	−3.83201	−0.130142
$868$	0.552856	0.0187652
$869$	15.4799	0.525120
$870$	16.3020	0.552690
$871$	10.4899	0.355438
$872$	21.1713	0.716952
$873$	−2.24614	−0.0760203
$874$	38.4591	1.30090
$875$	52.6831	1.78102
$876$	0.795674	0.0268833
$877$	−29.6552	−1.00139	−0.500693	−	0.865625i	$-0.666921\pi$
$877$	−29.6552	−1.00139	−0.500693	+	0.865625i	$0.666921\pi$
$878$	−9.65455	−0.325825
$879$	−10.2346	−0.345203
$880$	9.09736	0.306672
$881$	−24.3183	−0.819305	−0.409653	−	0.912242i	$-0.634350\pi$
$881$	−24.3183	−0.819305	−0.409653	+	0.912242i	$0.634350\pi$
$882$	7.63225	0.256991
$883$	25.5391	0.859458	0.429729	−	0.902958i	$-0.358609\pi$
$883$	25.5391	0.859458	0.429729	+	0.902958i	$0.358609\pi$
$884$	−1.23451	−0.0415211
$885$	20.9855	0.705419
$886$	−48.4686	−1.62834
$887$	−10.9652	−0.368177	−0.184088	−	0.982910i	$-0.558933\pi$
$887$	−10.9652	−0.368177	−0.184088	+	0.982910i	$0.558933\pi$
$888$	−17.0351	−0.571661
$889$	94.0814	3.15539
$890$	21.8643	0.732893
$891$	15.2858	0.512094
$892$	−0.184081	−0.00616348
$893$	−10.0184	−0.335252
$894$	−16.5961	−0.555056
$895$	15.5373	0.519355
$896$	62.3006	2.08132
$897$	−42.8355	−1.43024
$898$	−40.0963	−1.33803
$899$	−7.92340	−0.264260
$900$	0.0742022	0.00247341
$901$	−60.0666	−2.00111
$902$	−5.89052	−0.196133
$903$	92.9816	3.09424
$904$	−17.2969	−0.575285
$905$	5.53931	0.184133
$906$	−10.1283	−0.336490
$907$	21.4093	0.710883	0.355441	−	0.934699i	$-0.384331\pi$
$907$	21.4093	0.710883	0.355441	+	0.934699i	$0.384331\pi$
$908$	0.537578	0.0178401
$909$	−3.84679	−0.127590
$910$	31.6155	1.04804
$911$	−2.28839	−0.0758178	−0.0379089	−	0.999281i	$-0.512070\pi$
$911$	−2.28839	−0.0758178	−0.0379089	+	0.999281i	$0.512070\pi$
$912$	−25.4458	−0.842595
$913$	24.7397	0.818763
$914$	3.45336	0.114227
$915$	−26.5500	−0.877716
$916$	−0.153369	−0.00506744
$917$	21.8076	0.720149
$918$	34.1941	1.12857
$919$	−4.90496	−0.161800	−0.0808999	−	0.996722i	$-0.525779\pi$
$919$	−4.90496	−0.161800	−0.0808999	+	0.996722i	$0.525779\pi$
$920$	23.3109	0.768538
$921$	−10.1273	−0.333707
$922$	35.5871	1.17200
$923$	−18.8307	−0.619821
$924$	−1.26686	−0.0416767
$925$	−13.5046	−0.444027
$926$	−18.1008	−0.594828
$927$	−4.66657	−0.153270
$928$	2.58374	0.0848154
$929$	1.20150	0.0394200	0.0197100	−	0.999806i	$-0.493726\pi$
$929$	1.20150	0.0394200	0.0197100	+	0.999806i	$0.493726\pi$
$930$	−3.77679	−0.123846
$931$	−75.0834	−2.46076
$932$	−1.31091	−0.0429404
$933$	−18.8896	−0.618419
$934$	−5.31703	−0.173978
$935$	9.63388	0.315061
$936$	−2.60159	−0.0850357
$937$	−21.8422	−0.713554	−0.356777	−	0.934190i	$-0.616124\pi$
$937$	−21.8422	−0.713554	−0.356777	+	0.934190i	$0.616124\pi$
$938$	21.9677	0.717270
$939$	−53.3986	−1.74260
$940$	0.246911	0.00805334
$941$	−49.3887	−1.61003	−0.805013	−	0.593257i	$-0.797842\pi$
$941$	−49.3887	−1.61003	−0.805013	+	0.593257i	$0.797842\pi$
$942$	30.3176	0.987800
$943$	−15.6844	−0.510755
$944$	45.0400	1.46593
$945$	−32.9294	−1.07119
$946$	29.0993	0.946100
$947$	−5.09737	−0.165642	−0.0828211	−	0.996564i	$-0.526393\pi$
$947$	−5.09737	−0.165642	−0.0828211	+	0.996564i	$0.526393\pi$
$948$	1.06712	0.0346584
$949$	−22.1153	−0.717893
$950$	−19.4125	−0.629824
$951$	26.9156	0.872797
$952$	63.5805	2.06066
$953$	38.7086	1.25389	0.626947	−	0.779062i	$-0.284304\pi$
$953$	38.7086	1.25389	0.626947	+	0.779062i	$0.284304\pi$
$954$	5.14707	0.166643
$955$	14.1229	0.457005
$956$	0.333586	0.0107889
$957$	18.1563	0.586911
$958$	11.8554	0.383030
$959$	−27.3011	−0.881599
$960$	−14.8188	−0.478275
$961$	−29.1643	−0.940785
$962$	−19.2525	−0.620724
$963$	1.10783	0.0356992
$964$	−0.471137	−0.0151743
$965$	19.4227	0.625238
$966$	−89.7049	−2.88621
$967$	17.8409	0.573725	0.286863	−	0.957972i	$-0.407388\pi$
$967$	17.8409	0.573725	0.286863	+	0.957972i	$0.407388\pi$
$968$	−20.7249	−0.666124
$969$	−26.9465	−0.865646
$970$	−14.4825	−0.465005
$971$	8.85285	0.284101	0.142051	−	0.989859i	$-0.454630\pi$
$971$	8.85285	0.284101	0.142051	+	0.989859i	$0.454630\pi$
$972$	−0.211536	−0.00678501
$973$	−66.1422	−2.12042
$974$	−22.8597	−0.732473
$975$	21.6215	0.692442
$976$	−56.9828	−1.82397
$977$	47.4775	1.51894	0.759471	−	0.650542i	$-0.225458\pi$
$977$	47.4775	1.51894	0.759471	+	0.650542i	$0.225458\pi$
$978$	26.7679	0.855943
$979$	24.3513	0.778271
$980$	1.85049	0.0591118
$981$	−1.99633	−0.0637379
$982$	42.5190	1.35684
$983$	19.8880	0.634328	0.317164	−	0.948371i	$-0.397269\pi$
$983$	19.8880	0.634328	0.317164	+	0.948371i	$0.397269\pi$
$984$	9.98653	0.318359
$985$	10.6549	0.339492
$986$	37.0515	1.17996
$987$	23.3676	0.743798
$988$	−1.04067	−0.0331082
$989$	77.4814	2.46376
$990$	−0.825521	−0.0262368
$991$	−10.7313	−0.340890	−0.170445	−	0.985367i	$-0.554521\pi$
$991$	−10.7313	−0.340890	−0.170445	+	0.985367i	$0.554521\pi$
$992$	−0.598590	−0.0190053
$993$	−28.4510	−0.902865
$994$	−39.4347	−1.25079
$995$	−6.98362	−0.221396
$996$	1.70545	0.0540391
$997$	58.1899	1.84289	0.921447	−	0.388504i	$-0.127008\pi$
$997$	58.1899	1.84289	0.921447	+	0.388504i	$0.127008\pi$
$998$	−45.8750	−1.45215
$999$	20.0526	0.634435

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.f.1.7	✓	26
3.2	odd	2		4527.2.a.o.1.20		26
4.3	odd	2		8048.2.a.u.1.20		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.f.1.7	✓	26	1.1	even	1	trivial
4527.2.a.o.1.20		26	3.2	odd	2
8048.2.a.u.1.20		26	4.3	odd	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:	\( N \)	\(=\)	\( 503 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	503.a (trivial)

\(f(q)\)	\(=\)	\(q-1.44158 q^{2} -1.65492 q^{3} +0.0781455 q^{4} +1.16845 q^{5} +2.38569 q^{6} -5.22170 q^{7} +2.77050 q^{8} -0.261242 q^{9} +O(q^{10})\)	\(q-1.44158 q^{2} -1.65492 q^{3} +0.0781455 q^{4} +1.16845 q^{5} +2.38569 q^{6} -5.22170 q^{7} +2.77050 q^{8} -0.261242 q^{9} -1.68442 q^{10} -1.87602 q^{11} -0.129324 q^{12} +3.59450 q^{13} +7.52749 q^{14} -1.93370 q^{15} -4.15018 q^{16} -4.39494 q^{17} +0.376600 q^{18} -3.70486 q^{19} +0.0913094 q^{20} +8.64150 q^{21} +2.70442 q^{22} +7.20094 q^{23} -4.58496 q^{24} -3.63472 q^{25} -5.18175 q^{26} +5.39709 q^{27} -0.408052 q^{28} +5.84811 q^{29} +2.78757 q^{30} -1.35487 q^{31} +0.441808 q^{32} +3.10465 q^{33} +6.33565 q^{34} -6.10132 q^{35} -0.0204149 q^{36} +3.71544 q^{37} +5.34085 q^{38} -5.94860 q^{39} +3.23720 q^{40} -2.17811 q^{41} -12.4574 q^{42} +10.7599 q^{43} -0.146602 q^{44} -0.305249 q^{45} -10.3807 q^{46} +2.70411 q^{47} +6.86822 q^{48} +20.2662 q^{49} +5.23973 q^{50} +7.27328 q^{51} +0.280894 q^{52} +13.6672 q^{53} -7.78033 q^{54} -2.19204 q^{55} -14.4667 q^{56} +6.13125 q^{57} -8.43050 q^{58} -10.8525 q^{59} -0.151110 q^{60} +13.7302 q^{61} +1.95314 q^{62} +1.36413 q^{63} +7.66347 q^{64} +4.20000 q^{65} -4.47560 q^{66} +2.91833 q^{67} -0.343445 q^{68} -11.9170 q^{69} +8.79552 q^{70} -5.23876 q^{71} -0.723771 q^{72} -6.15254 q^{73} -5.35609 q^{74} +6.01516 q^{75} -0.289518 q^{76} +9.79599 q^{77} +8.57537 q^{78} -8.25148 q^{79} -4.84930 q^{80} -8.14803 q^{81} +3.13991 q^{82} -13.1873 q^{83} +0.675294 q^{84} -5.13529 q^{85} -15.5112 q^{86} -9.67814 q^{87} -5.19750 q^{88} -12.9803 q^{89} +0.440040 q^{90} -18.7694 q^{91} +0.562721 q^{92} +2.24219 q^{93} -3.89819 q^{94} -4.32896 q^{95} -0.731156 q^{96} +8.59794 q^{97} -29.2153 q^{98} +0.490093 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9} + 4 q^{10} - 17 q^{11} + 19 q^{12} + 14 q^{13} + q^{14} + 18 q^{15} + 48 q^{16} + 17 q^{17} - 10 q^{18} - 22 q^{19} - 19 q^{20} - 16 q^{21} + 38 q^{22} + 27 q^{23} - 9 q^{24} + 93 q^{25} + q^{26} + 31 q^{27} - 9 q^{28} + 13 q^{29} - 28 q^{30} + 26 q^{31} + 5 q^{32} + 6 q^{33} - 32 q^{34} - 22 q^{35} + 52 q^{36} + 55 q^{37} - 24 q^{38} - 15 q^{39} - 7 q^{40} + 24 q^{41} - 50 q^{42} + 20 q^{43} - 27 q^{44} - 8 q^{45} + 6 q^{46} - 25 q^{47} + 29 q^{48} + 65 q^{49} - 16 q^{50} + 7 q^{51} + 32 q^{52} + 30 q^{53} - 82 q^{54} + 25 q^{55} + 3 q^{56} + 9 q^{57} + 58 q^{58} - 26 q^{59} - 68 q^{60} + 15 q^{61} - 12 q^{62} - 19 q^{63} + 44 q^{64} + 20 q^{65} - 55 q^{66} - 20 q^{67} - 4 q^{68} - 27 q^{69} + 2 q^{70} - 35 q^{71} - 26 q^{72} + 38 q^{73} - 59 q^{74} + 2 q^{75} - 42 q^{76} - 6 q^{77} - 47 q^{78} + 21 q^{79} - 100 q^{80} + 70 q^{81} - 59 q^{82} - 48 q^{83} - 116 q^{84} + 6 q^{85} - 7 q^{86} - 9 q^{87} + 106 q^{88} - 5 q^{89} - 118 q^{90} - 24 q^{91} + 26 q^{92} - 8 q^{93} - 22 q^{94} + 43 q^{95} - 100 q^{96} + 142 q^{97} - 38 q^{98} - 50 q^{99}+O(q^{100}) \) 26 * q + 4 * q^2 + 4 * q^3 + 36 * q^4 + 9 * q^5 - 4 * q^6 + 11 * q^7 + 18 * q^8 + 42 * q^9 + 4 * q^10 - 17 * q^11 + 19 * q^12 + 14 * q^13 + q^14 + 18 * q^15 + 48 * q^16 + 17 * q^17 - 10 * q^18 - 22 * q^19 - 19 * q^20 - 16 * q^21 + 38 * q^22 + 27 * q^23 - 9 * q^24 + 93 * q^25 + q^26 + 31 * q^27 - 9 * q^28 + 13 * q^29 - 28 * q^30 + 26 * q^31 + 5 * q^32 + 6 * q^33 - 32 * q^34 - 22 * q^35 + 52 * q^36 + 55 * q^37 - 24 * q^38 - 15 * q^39 - 7 * q^40 + 24 * q^41 - 50 * q^42 + 20 * q^43 - 27 * q^44 - 8 * q^45 + 6 * q^46 - 25 * q^47 + 29 * q^48 + 65 * q^49 - 16 * q^50 + 7 * q^51 + 32 * q^52 + 30 * q^53 - 82 * q^54 + 25 * q^55 + 3 * q^56 + 9 * q^57 + 58 * q^58 - 26 * q^59 - 68 * q^60 + 15 * q^61 - 12 * q^62 - 19 * q^63 + 44 * q^64 + 20 * q^65 - 55 * q^66 - 20 * q^67 - 4 * q^68 - 27 * q^69 + 2 * q^70 - 35 * q^71 - 26 * q^72 + 38 * q^73 - 59 * q^74 + 2 * q^75 - 42 * q^76 - 6 * q^77 - 47 * q^78 + 21 * q^79 - 100 * q^80 + 70 * q^81 - 59 * q^82 - 48 * q^83 - 116 * q^84 + 6 * q^85 - 7 * q^86 - 9 * q^87 + 106 * q^88 - 5 * q^89 - 118 * q^90 - 24 * q^91 + 26 * q^92 - 8 * q^93 - 22 * q^94 + 43 * q^95 - 100 * q^96 + 142 * q^97 - 38 * q^98 - 50 * q^99

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