LMFDB - Embedded newform 503.2.a.f.1.3

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			1.3
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)

$f(q)$	$=$	$q-2.26823 q^{2} -1.83158 q^{3} +3.14489 q^{4} -3.37084 q^{5} +4.15444 q^{6} +3.93290 q^{7} -2.59688 q^{8} +0.354669 q^{9} +O(q^{10})$	\(q-2.26823 q^{2} -1.83158 q^{3} +3.14489 q^{4} -3.37084 q^{5} +4.15444 q^{6} +3.93290 q^{7} -2.59688 q^{8} +0.354669 q^{9} +7.64586 q^{10} -2.11174 q^{11} -5.76010 q^{12} -5.61624 q^{13} -8.92074 q^{14} +6.17395 q^{15} -0.399449 q^{16} -5.47848 q^{17} -0.804472 q^{18} -1.80948 q^{19} -10.6009 q^{20} -7.20340 q^{21} +4.78993 q^{22} +7.43669 q^{23} +4.75638 q^{24} +6.36256 q^{25} +12.7390 q^{26} +4.84512 q^{27} +12.3685 q^{28} -3.93402 q^{29} -14.0040 q^{30} -0.478732 q^{31} +6.09980 q^{32} +3.86781 q^{33} +12.4265 q^{34} -13.2572 q^{35} +1.11539 q^{36} +9.53362 q^{37} +4.10432 q^{38} +10.2866 q^{39} +8.75366 q^{40} -11.7134 q^{41} +16.3390 q^{42} -3.65517 q^{43} -6.64119 q^{44} -1.19553 q^{45} -16.8682 q^{46} +6.91537 q^{47} +0.731622 q^{48} +8.46770 q^{49} -14.4318 q^{50} +10.0343 q^{51} -17.6625 q^{52} +9.78185 q^{53} -10.9899 q^{54} +7.11834 q^{55} -10.2133 q^{56} +3.31419 q^{57} +8.92328 q^{58} +11.8964 q^{59} +19.4164 q^{60} +10.2416 q^{61} +1.08588 q^{62} +1.39488 q^{63} -13.0369 q^{64} +18.9315 q^{65} -8.77311 q^{66} -7.56365 q^{67} -17.2292 q^{68} -13.6209 q^{69} +30.0704 q^{70} -0.790385 q^{71} -0.921032 q^{72} -5.39720 q^{73} -21.6245 q^{74} -11.6535 q^{75} -5.69060 q^{76} -8.30527 q^{77} -23.3324 q^{78} +9.34890 q^{79} +1.34648 q^{80} -9.93822 q^{81} +26.5687 q^{82} -2.16404 q^{83} -22.6539 q^{84} +18.4671 q^{85} +8.29077 q^{86} +7.20545 q^{87} +5.48394 q^{88} +5.51350 q^{89} +2.71175 q^{90} -22.0881 q^{91} +23.3876 q^{92} +0.876834 q^{93} -15.6857 q^{94} +6.09945 q^{95} -11.1722 q^{96} +15.8056 q^{97} -19.2067 q^{98} -0.748969 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.26823	−1.60388	−0.801942	−	0.597402i	$-0.796200\pi$
$2$	−2.26823	−1.60388	−0.801942	+	0.597402i	$0.796200\pi$
$3$	−1.83158	−1.05746	−0.528730	−	0.848790i	$-0.677332\pi$
$3$	−1.83158	−1.05746	−0.528730	+	0.848790i	$0.677332\pi$
$4$	3.14489	1.57244
$5$	−3.37084	−1.50749	−0.753743	−	0.657170i	$-0.771754\pi$
$5$	−3.37084	−1.50749	−0.753743	+	0.657170i	$0.771754\pi$
$6$	4.15444	1.69604
$7$	3.93290	1.48650	0.743248	−	0.669016i	$-0.233284\pi$
$7$	3.93290	1.48650	0.743248	+	0.669016i	$0.233284\pi$
$8$	−2.59688	−0.918135
$9$	0.354669	0.118223
$10$	7.64586	2.41783
$11$	−2.11174	−0.636714	−0.318357	−	0.947971i	$-0.603131\pi$
$11$	−2.11174	−0.636714	−0.318357	+	0.947971i	$0.603131\pi$
$12$	−5.76010	−1.66280
$13$	−5.61624	−1.55767	−0.778833	−	0.627232i	$-0.784188\pi$
$13$	−5.61624	−1.55767	−0.778833	+	0.627232i	$0.784188\pi$
$14$	−8.92074	−2.38417
$15$	6.17395	1.59411
$16$	−0.399449	−0.0998623
$17$	−5.47848	−1.32873	−0.664364	−	0.747409i	$-0.731297\pi$
$17$	−5.47848	−1.32873	−0.664364	+	0.747409i	$0.731297\pi$
$18$	−0.804472	−0.189616
$19$	−1.80948	−0.415122	−0.207561	−	0.978222i	$-0.566553\pi$
$19$	−1.80948	−0.415122	−0.207561	+	0.978222i	$0.566553\pi$
$20$	−10.6009	−2.37044
$21$	−7.20340	−1.57191
$22$	4.78993	1.02122
$23$	7.43669	1.55066	0.775329	−	0.631558i	$-0.217584\pi$
$23$	7.43669	1.55066	0.775329	+	0.631558i	$0.217584\pi$
$24$	4.75638	0.970892
$25$	6.36256	1.27251
$26$	12.7390	2.49831
$27$	4.84512	0.932445
$28$	12.3685	2.33743
$29$	−3.93402	−0.730529	−0.365264	−	0.930904i	$-0.619021\pi$
$29$	−3.93402	−0.730529	−0.365264	+	0.930904i	$0.619021\pi$
$30$	−14.0040	−2.55676
$31$	−0.478732	−0.0859828	−0.0429914	−	0.999075i	$-0.513689\pi$
$31$	−0.478732	−0.0859828	−0.0429914	+	0.999075i	$0.513689\pi$
$32$	6.09980	1.07830
$33$	3.86781	0.673300
$34$	12.4265	2.13113
$35$	−13.2572	−2.24087
$36$	1.11539	0.185899
$37$	9.53362	1.56732	0.783659	−	0.621191i	$-0.213351\pi$
$37$	9.53362	1.56732	0.783659	+	0.621191i	$0.213351\pi$
$38$	4.10432	0.665808
$39$	10.2866	1.64717
$40$	8.75366	1.38408
$41$	−11.7134	−1.82933	−0.914663	−	0.404217i	$-0.867544\pi$
$41$	−11.7134	−1.82933	−0.914663	+	0.404217i	$0.867544\pi$
$42$	16.3390	2.52116
$43$	−3.65517	−0.557407	−0.278704	−	0.960377i	$-0.589905\pi$
$43$	−3.65517	−0.557407	−0.278704	+	0.960377i	$0.589905\pi$
$44$	−6.64119	−1.00120
$45$	−1.19553	−0.178219
$46$	−16.8682	−2.48708
$47$	6.91537	1.00871	0.504355	−	0.863496i	$-0.331730\pi$
$47$	6.91537	1.00871	0.504355	+	0.863496i	$0.331730\pi$
$48$	0.731622	0.105600
$49$	8.46770	1.20967
$50$	−14.4318	−2.04096
$51$	10.0343	1.40508
$52$	−17.6625	−2.44934
$53$	9.78185	1.34364	0.671820	−	0.740715i	$-0.265513\pi$
$53$	9.78185	1.34364	0.671820	+	0.740715i	$0.265513\pi$
$54$	−10.9899	−1.49553
$55$	7.11834	0.959837
$56$	−10.2133	−1.36480
$57$	3.31419	0.438975
$58$	8.92328	1.17168
$59$	11.8964	1.54877	0.774387	−	0.632712i	$-0.218058\pi$
$59$	11.8964	1.54877	0.774387	+	0.632712i	$0.218058\pi$
$60$	19.4164	2.50664
$61$	10.2416	1.31130	0.655650	−	0.755065i	$-0.272395\pi$
$61$	10.2416	1.31130	0.655650	+	0.755065i	$0.272395\pi$
$62$	1.08588	0.137906
$63$	1.39488	0.175738
$64$	−13.0369	−1.62961
$65$	18.9315	2.34816
$66$	−8.77311	−1.07990
$67$	−7.56365	−0.924047	−0.462024	−	0.886868i	$-0.652876\pi$
$67$	−7.56365	−0.924047	−0.462024	+	0.886868i	$0.652876\pi$
$68$	−17.2292	−2.08935
$69$	−13.6209	−1.63976
$70$	30.0704	3.59410
$71$	−0.790385	−0.0938014	−0.0469007	−	0.998900i	$-0.514934\pi$
$71$	−0.790385	−0.0938014	−0.0469007	+	0.998900i	$0.514934\pi$
$72$	−0.921032	−0.108545
$73$	−5.39720	−0.631694	−0.315847	−	0.948810i	$-0.602289\pi$
$73$	−5.39720	−0.631694	−0.315847	+	0.948810i	$0.602289\pi$
$74$	−21.6245	−2.51380
$75$	−11.6535	−1.34563
$76$	−5.69060	−0.652757
$77$	−8.30527	−0.946473
$78$	−23.3324	−2.64187
$79$	9.34890	1.05183	0.525917	−	0.850536i	$-0.323722\pi$
$79$	9.34890	1.05183	0.525917	+	0.850536i	$0.323722\pi$
$80$	1.34648	0.150541
$81$	−9.93822	−1.10425
$82$	26.5687	2.93403
$83$	−2.16404	−0.237534	−0.118767	−	0.992922i	$-0.537894\pi$
$83$	−2.16404	−0.237534	−0.118767	+	0.992922i	$0.537894\pi$
$84$	−22.6539	−2.47174
$85$	18.4671	2.00304
$86$	8.29077	0.894017
$87$	7.20545	0.772506
$88$	5.48394	0.584589
$89$	5.51350	0.584430	0.292215	−	0.956353i	$-0.405608\pi$
$89$	5.51350	0.584430	0.292215	+	0.956353i	$0.405608\pi$
$90$	2.71175	0.285843
$91$	−22.0881	−2.31546
$92$	23.3876	2.43832
$93$	0.876834	0.0909234
$94$	−15.6857	−1.61785
$95$	6.09945	0.625791
$96$	−11.1722	−1.14026
$97$	15.8056	1.60482	0.802408	−	0.596776i	$-0.203552\pi$
$97$	15.8056	1.60482	0.802408	+	0.596776i	$0.203552\pi$
$98$	−19.2067	−1.94017
$99$	−0.748969	−0.0752742
$100$	20.0096	2.00096
$101$	−1.51939	−0.151185	−0.0755925	−	0.997139i	$-0.524085\pi$
$101$	−1.51939	−0.151185	−0.0755925	+	0.997139i	$0.524085\pi$
$102$	−22.7601	−2.25358
$103$	1.30473	0.128559	0.0642793	−	0.997932i	$-0.479525\pi$
$103$	1.30473	0.128559	0.0642793	+	0.997932i	$0.479525\pi$
$104$	14.5847	1.43015
$105$	24.2815	2.36963
$106$	−22.1875	−2.15504
$107$	4.87377	0.471165	0.235583	−	0.971854i	$-0.424300\pi$
$107$	4.87377	0.471165	0.235583	+	0.971854i	$0.424300\pi$
$108$	15.2374	1.46622
$109$	−8.33181	−0.798042	−0.399021	−	0.916942i	$-0.630650\pi$
$109$	−8.33181	−0.798042	−0.399021	+	0.916942i	$0.630650\pi$
$110$	−16.1461	−1.53947
$111$	−17.4615	−1.65738
$112$	−1.57099	−0.148445
$113$	8.16044	0.767669	0.383835	−	0.923402i	$-0.374603\pi$
$113$	8.16044	0.767669	0.383835	+	0.923402i	$0.374603\pi$
$114$	−7.51737	−0.704066
$115$	−25.0679	−2.33759
$116$	−12.3721	−1.14872
$117$	−1.99191	−0.184152
$118$	−26.9838	−2.48406
$119$	−21.5463	−1.97515
$120$	−16.0330	−1.46361
$121$	−6.54055	−0.594595
$122$	−23.2303	−2.10317
$123$	21.4540	1.93444
$124$	−1.50556	−0.135203
$125$	−4.59298	−0.410809
$126$	−3.16391	−0.281863
$127$	5.40032	0.479201	0.239600	−	0.970872i	$-0.422984\pi$
$127$	5.40032	0.479201	0.239600	+	0.970872i	$0.422984\pi$
$128$	17.3711	1.53540
$129$	6.69471	0.589436
$130$	−42.9410	−3.76617
$131$	2.88204	0.251805	0.125902	−	0.992043i	$-0.459817\pi$
$131$	2.88204	0.251805	0.125902	+	0.992043i	$0.459817\pi$
$132$	12.1638	1.05873
$133$	−7.11649	−0.617078
$134$	17.1561	1.48206
$135$	−16.3321	−1.40565
$136$	14.2270	1.21995
$137$	15.2592	1.30368	0.651842	−	0.758355i	$-0.273997\pi$
$137$	15.2592	1.30368	0.651842	+	0.758355i	$0.273997\pi$
$138$	30.8953	2.62998
$139$	−18.7124	−1.58717	−0.793583	−	0.608461i	$-0.791787\pi$
$139$	−18.7124	−1.58717	−0.793583	+	0.608461i	$0.791787\pi$
$140$	−41.6923	−3.52365
$141$	−12.6660	−1.06667
$142$	1.79278	0.150447
$143$	11.8600	0.991787
$144$	−0.141672	−0.0118060
$145$	13.2609	1.10126
$146$	12.2421	1.01316
$147$	−15.5092	−1.27918
$148$	29.9822	2.46452
$149$	3.20565	0.262617	0.131309	−	0.991342i	$-0.458082\pi$
$149$	3.20565	0.262617	0.131309	+	0.991342i	$0.458082\pi$
$150$	26.4329	2.15824
$151$	16.4027	1.33484	0.667418	−	0.744684i	$-0.267400\pi$
$151$	16.4027	1.33484	0.667418	+	0.744684i	$0.267400\pi$
$152$	4.69899	0.381138
$153$	−1.94305	−0.157086
$154$	18.8383	1.51803
$155$	1.61373	0.129618
$156$	32.3501	2.59008
$157$	−10.8175	−0.863333	−0.431666	−	0.902033i	$-0.642074\pi$
$157$	−10.8175	−0.863333	−0.431666	+	0.902033i	$0.642074\pi$
$158$	−21.2055	−1.68702
$159$	−17.9162	−1.42085
$160$	−20.5615	−1.62553
$161$	29.2478	2.30505
$162$	22.5422	1.77108
$163$	1.23055	0.0963845	0.0481922	−	0.998838i	$-0.484654\pi$
$163$	1.23055	0.0963845	0.0481922	+	0.998838i	$0.484654\pi$
$164$	−36.8374	−2.87651
$165$	−13.0378	−1.01499
$166$	4.90855	0.380977
$167$	−15.4924	−1.19884	−0.599420	−	0.800435i	$-0.704602\pi$
$167$	−15.4924	−1.19884	−0.599420	+	0.800435i	$0.704602\pi$
$168$	18.7064	1.44323
$169$	18.5422	1.42632
$170$	−41.8877	−3.21264
$171$	−0.641765	−0.0490770
$172$	−11.4951	−0.876492
$173$	5.30946	0.403671	0.201836	−	0.979419i	$-0.435309\pi$
$173$	5.30946	0.403671	0.201836	+	0.979419i	$0.435309\pi$
$174$	−16.3437	−1.23901
$175$	25.0233	1.89159
$176$	0.843534	0.0635837
$177$	−21.7891	−1.63777
$178$	−12.5059	−0.937357
$179$	12.2554	0.916011	0.458006	−	0.888949i	$-0.348564\pi$
$179$	12.2554	0.916011	0.458006	+	0.888949i	$0.348564\pi$
$180$	−3.75982	−0.280240
$181$	−17.4515	−1.29716	−0.648582	−	0.761145i	$-0.724637\pi$
$181$	−17.4515	−1.29716	−0.648582	+	0.761145i	$0.724637\pi$
$182$	50.1010	3.71373
$183$	−18.7582	−1.38665
$184$	−19.3122	−1.42371
$185$	−32.1363	−2.36271
$186$	−1.98886	−0.145831
$187$	11.5691	0.846019
$188$	21.7481	1.58614
$189$	19.0554	1.38608
$190$	−13.8350	−1.00370
$191$	14.2632	1.03205	0.516024	−	0.856574i	$-0.327411\pi$
$191$	14.2632	1.03205	0.516024	+	0.856574i	$0.327411\pi$
$192$	23.8780	1.72325
$193$	15.9790	1.15019	0.575095	−	0.818086i	$-0.304965\pi$
$193$	15.9790	1.15019	0.575095	+	0.818086i	$0.304965\pi$
$194$	−35.8508	−2.57394
$195$	−34.6744	−2.48308
$196$	26.6300	1.90214
$197$	−17.2135	−1.22641	−0.613207	−	0.789922i	$-0.710121\pi$
$197$	−17.2135	−1.22641	−0.613207	+	0.789922i	$0.710121\pi$
$198$	1.69884	0.120731
$199$	11.2575	0.798020	0.399010	−	0.916947i	$-0.369354\pi$
$199$	11.2575	0.798020	0.399010	+	0.916947i	$0.369354\pi$
$200$	−16.5228	−1.16834
$201$	13.8534	0.977144
$202$	3.44634	0.242483
$203$	−15.4721	−1.08593
$204$	31.5566	2.20941
$205$	39.4840	2.75768
$206$	−2.95943	−0.206193
$207$	2.63756	0.183323
$208$	2.24340	0.155552
$209$	3.82115	0.264314
$210$	−55.0762	−3.80062
$211$	−8.48128	−0.583876	−0.291938	−	0.956437i	$-0.594300\pi$
$211$	−8.48128	−0.583876	−0.291938	+	0.956437i	$0.594300\pi$
$212$	30.7628	2.11280
$213$	1.44765	0.0991913
$214$	−11.0549	−0.755694
$215$	12.3210	0.840284
$216$	−12.5822	−0.856110
$217$	−1.88280	−0.127813
$218$	18.8985	1.27997
$219$	9.88538	0.667992
$220$	22.3864	1.50929
$221$	30.7685	2.06971
$222$	39.6069	2.65824
$223$	7.53536	0.504605	0.252302	−	0.967648i	$-0.418812\pi$
$223$	7.53536	0.504605	0.252302	+	0.967648i	$0.418812\pi$
$224$	23.9899	1.60289
$225$	2.25660	0.150440
$226$	−18.5098	−1.23125
$227$	−9.01995	−0.598675	−0.299338	−	0.954147i	$-0.596766\pi$
$227$	−9.01995	−0.598675	−0.299338	+	0.954147i	$0.596766\pi$
$228$	10.4228	0.690265
$229$	7.21274	0.476631	0.238316	−	0.971188i	$-0.423405\pi$
$229$	7.21274	0.476631	0.238316	+	0.971188i	$0.423405\pi$
$230$	56.8599	3.74923
$231$	15.2117	1.00086
$232$	10.2162	0.670724
$233$	−19.7964	−1.29691	−0.648453	−	0.761255i	$-0.724584\pi$
$233$	−19.7964	−1.29691	−0.648453	+	0.761255i	$0.724584\pi$
$234$	4.51811	0.295358
$235$	−23.3106	−1.52062
$236$	37.4128	2.43536
$237$	−17.1232	−1.11227
$238$	48.8721	3.16791
$239$	4.18739	0.270860	0.135430	−	0.990787i	$-0.456758\pi$
$239$	4.18739	0.270860	0.135430	+	0.990787i	$0.456758\pi$
$240$	−2.46618	−0.159191
$241$	−14.8640	−0.957472	−0.478736	−	0.877959i	$-0.658905\pi$
$241$	−14.8640	−0.957472	−0.478736	+	0.877959i	$0.658905\pi$
$242$	14.8355	0.953662
$243$	3.66722	0.235252
$244$	32.2086	2.06195
$245$	−28.5433	−1.82356
$246$	−48.6627	−3.10262
$247$	10.1625	0.646621
$248$	1.24321	0.0789438
$249$	3.96360	0.251183
$250$	10.4180	0.658890
$251$	−10.8820	−0.686863	−0.343431	−	0.939178i	$-0.611589\pi$
$251$	−10.8820	−0.686863	−0.343431	+	0.939178i	$0.611589\pi$
$252$	4.38673	0.276338
$253$	−15.7044	−0.987326
$254$	−12.2492	−0.768582
$255$	−33.8239	−2.11813
$256$	−13.3280	−0.833000
$257$	10.5412	0.657544	0.328772	−	0.944409i	$-0.393365\pi$
$257$	10.5412	0.657544	0.328772	+	0.944409i	$0.393365\pi$
$258$	−15.1852	−0.945388
$259$	37.4948	2.32981
$260$	59.5373	3.69235
$261$	−1.39527	−0.0863653
$262$	−6.53714	−0.403866
$263$	5.41144	0.333684	0.166842	−	0.985984i	$-0.446643\pi$
$263$	5.41144	0.333684	0.166842	+	0.985984i	$0.446643\pi$
$264$	−10.0442	−0.618180
$265$	−32.9730	−2.02552
$266$	16.1419	0.989721
$267$	−10.0984	−0.618011
$268$	−23.7869	−1.45301
$269$	1.28238	0.0781884	0.0390942	−	0.999236i	$-0.487553\pi$
$269$	1.28238	0.0781884	0.0390942	+	0.999236i	$0.487553\pi$
$270$	37.0451	2.25449
$271$	−9.79939	−0.595271	−0.297635	−	0.954680i	$-0.596198\pi$
$271$	−9.79939	−0.595271	−0.297635	+	0.954680i	$0.596198\pi$
$272$	2.18838	0.132690
$273$	40.4560	2.44851
$274$	−34.6115	−2.09096
$275$	−13.4361	−0.810227
$276$	−42.8361	−2.57843
$277$	21.5189	1.29294	0.646471	−	0.762938i	$-0.276244\pi$
$277$	21.5189	1.29294	0.646471	+	0.762938i	$0.276244\pi$
$278$	42.4442	2.54563
$279$	−0.169791	−0.0101651
$280$	34.4273	2.05742
$281$	−13.1972	−0.787279	−0.393639	−	0.919265i	$-0.628784\pi$
$281$	−13.1972	−0.787279	−0.393639	+	0.919265i	$0.628784\pi$
$282$	28.7295	1.71082
$283$	9.07246	0.539302	0.269651	−	0.962958i	$-0.413092\pi$
$283$	9.07246	0.539302	0.269651	+	0.962958i	$0.413092\pi$
$284$	−2.48567	−0.147498
$285$	−11.1716	−0.661749
$286$	−26.9014	−1.59071
$287$	−46.0676	−2.71929
$288$	2.16341	0.127480
$289$	13.0138	0.765517
$290$	−30.0789	−1.76630
$291$	−28.9492	−1.69703
$292$	−16.9736	−0.993305
$293$	15.1381	0.884378	0.442189	−	0.896922i	$-0.354202\pi$
$293$	15.1381	0.884378	0.442189	+	0.896922i	$0.354202\pi$
$294$	35.1786	2.05166
$295$	−40.1007	−2.33476
$296$	−24.7577	−1.43901
$297$	−10.2316	−0.593701
$298$	−7.27117	−0.421207
$299$	−41.7663	−2.41541
$300$	−36.6490	−2.11593
$301$	−14.3754	−0.828584
$302$	−37.2052	−2.14092
$303$	2.78288	0.159872
$304$	0.722794	0.0414551
$305$	−34.5227	−1.97676
$306$	4.40729	0.251948
$307$	30.8124	1.75855	0.879277	−	0.476310i	$-0.158026\pi$
$307$	30.8124	1.75855	0.879277	+	0.476310i	$0.158026\pi$
$308$	−26.1191	−1.48828
$309$	−2.38971	−0.135946
$310$	−3.66032	−0.207892
$311$	7.89838	0.447876	0.223938	−	0.974603i	$-0.428109\pi$
$311$	7.89838	0.447876	0.223938	+	0.974603i	$0.428109\pi$
$312$	−26.7130	−1.51232
$313$	18.0636	1.02102	0.510509	−	0.859873i	$-0.329457\pi$
$313$	18.0636	1.02102	0.510509	+	0.859873i	$0.329457\pi$
$314$	24.5367	1.38469
$315$	−4.70191	−0.264922
$316$	29.4013	1.65395
$317$	−34.8223	−1.95581	−0.977907	−	0.209041i	$-0.932966\pi$
$317$	−34.8223	−1.95581	−0.977907	+	0.209041i	$0.932966\pi$
$318$	40.6381	2.27887
$319$	8.30763	0.465138
$320$	43.9452	2.45661
$321$	−8.92668	−0.498239
$322$	−66.3408	−3.69703
$323$	9.91318	0.551584
$324$	−31.2546	−1.73637
$325$	−35.7337	−1.98215
$326$	−2.79119	−0.154590
$327$	15.2603	0.843898
$328$	30.4183	1.67957
$329$	27.1975	1.49944
$330$	29.5728	1.62793
$331$	−20.6821	−1.13679	−0.568394	−	0.822756i	$-0.692435\pi$
$331$	−20.6821	−1.13679	−0.568394	+	0.822756i	$0.692435\pi$
$332$	−6.80567	−0.373509
$333$	3.38128	0.185293
$334$	35.1404	1.92280
$335$	25.4959	1.39299
$336$	2.87739	0.156975
$337$	3.76498	0.205091	0.102546	−	0.994728i	$-0.467301\pi$
$337$	3.76498	0.205091	0.102546	+	0.994728i	$0.467301\pi$
$338$	−42.0580	−2.28765
$339$	−14.9465	−0.811780
$340$	58.0770	3.14967
$341$	1.01096	0.0547465
$342$	1.45567	0.0787138
$343$	5.77230	0.311675
$344$	9.49202	0.511775
$345$	45.9138	2.47191
$346$	−12.0431	−0.647442
$347$	−2.67191	−0.143435	−0.0717177	−	0.997425i	$-0.522848\pi$
$347$	−2.67191	−0.143435	−0.0717177	+	0.997425i	$0.522848\pi$
$348$	22.6604	1.21472
$349$	0.400544	0.0214406	0.0107203	−	0.999943i	$-0.496588\pi$
$349$	0.400544	0.0214406	0.0107203	+	0.999943i	$0.496588\pi$
$350$	−56.7588	−3.03388
$351$	−27.2114	−1.45244
$352$	−12.8812	−0.686570
$353$	7.38490	0.393059	0.196529	−	0.980498i	$-0.437033\pi$
$353$	7.38490	0.393059	0.196529	+	0.980498i	$0.437033\pi$
$354$	49.4228	2.62679
$355$	2.66426	0.141404
$356$	17.3393	0.918983
$357$	39.4637	2.08864
$358$	−27.7981	−1.46918
$359$	−27.3611	−1.44406	−0.722032	−	0.691860i	$-0.756792\pi$
$359$	−27.3611	−1.44406	−0.722032	+	0.691860i	$0.756792\pi$
$360$	3.10465	0.163629
$361$	−15.7258	−0.827674
$362$	39.5842	2.08050
$363$	11.9795	0.628761
$364$	−69.4647	−3.64094
$365$	18.1931	0.952270
$366$	42.5480	2.22402
$367$	−29.8760	−1.55951	−0.779756	−	0.626083i	$-0.784657\pi$
$367$	−29.8760	−1.55951	−0.779756	+	0.626083i	$0.784657\pi$
$368$	−2.97058	−0.154852
$369$	−4.15438	−0.216268
$370$	72.8927	3.78951
$371$	38.4710	1.99732
$372$	2.75754	0.142972
$373$	17.7128	0.917132	0.458566	−	0.888660i	$-0.348363\pi$
$373$	17.7128	0.917132	0.458566	+	0.888660i	$0.348363\pi$
$374$	−26.2415	−1.35692
$375$	8.41239	0.434414
$376$	−17.9584	−0.926132
$377$	22.0944	1.13792
$378$	−43.2221	−2.22310
$379$	6.82516	0.350585	0.175292	−	0.984516i	$-0.443913\pi$
$379$	6.82516	0.350585	0.175292	+	0.984516i	$0.443913\pi$
$380$	19.1821	0.984021
$381$	−9.89109	−0.506736
$382$	−32.3523	−1.65529
$383$	4.76750	0.243608	0.121804	−	0.992554i	$-0.461132\pi$
$383$	4.76750	0.243608	0.121804	+	0.992554i	$0.461132\pi$
$384$	−31.8165	−1.62363
$385$	27.9957	1.42679
$386$	−36.2440	−1.84477
$387$	−1.29637	−0.0658983
$388$	49.7069	2.52348
$389$	36.4042	1.84577	0.922883	−	0.385079i	$-0.125826\pi$
$389$	36.4042	1.84577	0.922883	+	0.385079i	$0.125826\pi$
$390$	78.6496	3.98258
$391$	−40.7418	−2.06040
$392$	−21.9896	−1.11064
$393$	−5.27867	−0.266274
$394$	39.0444	1.96703
$395$	−31.5137	−1.58562
$396$	−2.35542	−0.118365
$397$	−3.54486	−0.177912	−0.0889558	−	0.996036i	$-0.528353\pi$
$397$	−3.54486	−0.177912	−0.0889558	+	0.996036i	$0.528353\pi$
$398$	−25.5346	−1.27993
$399$	13.0344	0.652535
$400$	−2.54152	−0.127076
$401$	24.0284	1.19992	0.599960	−	0.800030i	$-0.295183\pi$
$401$	24.0284	1.19992	0.599960	+	0.800030i	$0.295183\pi$
$402$	−31.4228	−1.56723
$403$	2.68867	0.133932
$404$	−4.77832	−0.237730
$405$	33.5001	1.66464
$406$	35.0944	1.74170
$407$	−20.1325	−0.997933
$408$	−26.0577	−1.29005
$409$	−1.57024	−0.0776431	−0.0388216	−	0.999246i	$-0.512360\pi$
$409$	−1.57024	−0.0776431	−0.0388216	+	0.999246i	$0.512360\pi$
$410$	−89.5590	−4.42300
$411$	−27.9484	−1.37859
$412$	4.10322	0.202151
$413$	46.7872	2.30225
$414$	−5.98261	−0.294029
$415$	7.29463	0.358079
$416$	−34.2580	−1.67963
$417$	34.2732	1.67837
$418$	−8.66726	−0.423929
$419$	9.53222	0.465679	0.232840	−	0.972515i	$-0.425198\pi$
$419$	9.53222	0.465679	0.232840	+	0.972515i	$0.425198\pi$
$420$	76.3627	3.72612
$421$	27.0005	1.31593	0.657963	−	0.753051i	$-0.271418\pi$
$421$	27.0005	1.31593	0.657963	+	0.753051i	$0.271418\pi$
$422$	19.2375	0.936469
$423$	2.45267	0.119253
$424$	−25.4023	−1.23364
$425$	−34.8572	−1.69082
$426$	−3.28361	−0.159091
$427$	40.2791	1.94924
$428$	15.3275	0.740881
$429$	−21.7226	−1.04878
$430$	−27.9469	−1.34772
$431$	3.51308	0.169219	0.0846096	−	0.996414i	$-0.473036\pi$
$431$	3.51308	0.169219	0.0846096	+	0.996414i	$0.473036\pi$
$432$	−1.93538	−0.0931161
$433$	23.6273	1.13546	0.567729	−	0.823216i	$-0.307822\pi$
$433$	23.6273	1.13546	0.567729	+	0.823216i	$0.307822\pi$
$434$	4.27064	0.204997
$435$	−24.2884	−1.16454
$436$	−26.2026	−1.25488
$437$	−13.4565	−0.643713
$438$	−22.4224	−1.07138
$439$	8.52483	0.406868	0.203434	−	0.979089i	$-0.434790\pi$
$439$	8.52483	0.406868	0.203434	+	0.979089i	$0.434790\pi$
$440$	−18.4855	−0.881260
$441$	3.00323	0.143011
$442$	−69.7902	−3.31958
$443$	−16.9104	−0.803439	−0.401719	−	0.915763i	$-0.631587\pi$
$443$	−16.9104	−0.803439	−0.401719	+	0.915763i	$0.631587\pi$
$444$	−54.9146	−2.60613
$445$	−18.5851	−0.881019
$446$	−17.0920	−0.809328
$447$	−5.87139	−0.277707
$448$	−51.2727	−2.42241
$449$	−18.0009	−0.849516	−0.424758	−	0.905307i	$-0.639641\pi$
$449$	−18.0009	−0.849516	−0.424758	+	0.905307i	$0.639641\pi$
$450$	−5.11850	−0.241289
$451$	24.7357	1.16476
$452$	25.6637	1.20712
$453$	−30.0428	−1.41154
$454$	20.4594	0.960206
$455$	74.4555	3.49053
$456$	−8.60655	−0.403039
$457$	−29.5349	−1.38158	−0.690792	−	0.723054i	$-0.742738\pi$
$457$	−29.5349	−1.38158	−0.690792	+	0.723054i	$0.742738\pi$
$458$	−16.3602	−0.764461
$459$	−26.5439	−1.23896
$460$	−78.8358	−3.67574
$461$	−0.134802	−0.00627837	−0.00313918	−	0.999995i	$-0.500999\pi$
$461$	−0.134802	−0.00627837	−0.00313918	+	0.999995i	$0.500999\pi$
$462$	−34.5038	−1.60526
$463$	−22.8439	−1.06165	−0.530823	−	0.847483i	$-0.678117\pi$
$463$	−22.8439	−1.06165	−0.530823	+	0.847483i	$0.678117\pi$
$464$	1.57144	0.0729523
$465$	−2.95567	−0.137066
$466$	44.9029	2.08009
$467$	18.9868	0.878604	0.439302	−	0.898339i	$-0.355226\pi$
$467$	18.9868	0.878604	0.439302	+	0.898339i	$0.355226\pi$
$468$	−6.26432	−0.289568
$469$	−29.7471	−1.37359
$470$	52.8739	2.43889
$471$	19.8131	0.912941
$472$	−30.8934	−1.42198
$473$	7.71876	0.354909
$474$	38.8395	1.78396
$475$	−11.5129	−0.528248
$476$	−67.7608	−3.10581
$477$	3.46932	0.158849
$478$	−9.49798	−0.434427
$479$	28.5255	1.30337	0.651683	−	0.758492i	$-0.274063\pi$
$479$	28.5255	1.30337	0.651683	+	0.758492i	$0.274063\pi$
$480$	37.6599	1.71893
$481$	−53.5431	−2.44136
$482$	33.7150	1.53567
$483$	−53.5695	−2.43750
$484$	−20.5693	−0.934968
$485$	−53.2782	−2.41924
$486$	−8.31812	−0.377318
$487$	−5.48981	−0.248767	−0.124383	−	0.992234i	$-0.539695\pi$
$487$	−5.48981	−0.248767	−0.124383	+	0.992234i	$0.539695\pi$
$488$	−26.5961	−1.20395
$489$	−2.25385	−0.101923
$490$	64.7428	2.92478
$491$	6.15793	0.277904	0.138952	−	0.990299i	$-0.455627\pi$
$491$	6.15793	0.277904	0.138952	+	0.990299i	$0.455627\pi$
$492$	67.4704	3.04180
$493$	21.5525	0.970674
$494$	−23.0508	−1.03711
$495$	2.52465	0.113475
$496$	0.191229	0.00858644
$497$	−3.10850	−0.139435
$498$	−8.99038	−0.402869
$499$	8.61680	0.385741	0.192870	−	0.981224i	$-0.438220\pi$
$499$	8.61680	0.385741	0.192870	+	0.981224i	$0.438220\pi$
$500$	−14.4444	−0.645974
$501$	28.3755	1.26773
$502$	24.6828	1.10165
$503$	1.00000	0.0445878
$503$	1.00000	0.0445878
$504$	−3.62232	−0.161351
$505$	5.12162	0.227909
$506$	35.6212	1.58356
$507$	−33.9614	−1.50828
$508$	16.9834	0.753516
$509$	11.0021	0.487662	0.243831	−	0.969818i	$-0.421596\pi$
$509$	11.0021	0.487662	0.243831	+	0.969818i	$0.421596\pi$
$510$	76.7205	3.39724
$511$	−21.2266	−0.939011
$512$	−4.51120	−0.199369
$513$	−8.76714	−0.387078
$514$	−23.9100	−1.05462
$515$	−4.39803	−0.193800
$516$	21.0541	0.926856
$517$	−14.6035	−0.642260
$518$	−85.0470	−3.73675
$519$	−9.72468	−0.426866
$520$	−49.1627	−2.15593
$521$	−6.81642	−0.298633	−0.149316	−	0.988789i	$-0.547707\pi$
$521$	−6.81642	−0.298633	−0.149316	+	0.988789i	$0.547707\pi$
$522$	3.16481	0.138520
$523$	8.09278	0.353873	0.176936	−	0.984222i	$-0.443381\pi$
$523$	8.09278	0.353873	0.176936	+	0.984222i	$0.443381\pi$
$524$	9.06369	0.395949
$525$	−45.8321	−2.00028
$526$	−12.2744	−0.535190
$527$	2.62273	0.114248
$528$	−1.54500	−0.0672373
$529$	32.3044	1.40454
$530$	74.7906	3.24870
$531$	4.21927	0.183101
$532$	−22.3806	−0.970321
$533$	65.7853	2.84948
$534$	22.9055	0.991218
$535$	−16.4287	−0.710275
$536$	19.6419	0.848400
$537$	−22.4467	−0.968646
$538$	−2.90875	−0.125405
$539$	−17.8816	−0.770214
$540$	−51.3628	−2.21030
$541$	−29.6948	−1.27668	−0.638340	−	0.769754i	$-0.720379\pi$
$541$	−29.6948	−1.27668	−0.638340	+	0.769754i	$0.720379\pi$
$542$	22.2273	0.954745
$543$	31.9638	1.37170
$544$	−33.4177	−1.43277
$545$	28.0852	1.20304
$546$	−91.7638	−3.92713
$547$	−33.8277	−1.44637	−0.723184	−	0.690655i	$-0.757322\pi$
$547$	−33.8277	−1.44637	−0.723184	+	0.690655i	$0.757322\pi$
$548$	47.9886	2.04997
$549$	3.63237	0.155026
$550$	30.4762	1.29951
$551$	7.11851	0.303259
$552$	35.3717	1.50552
$553$	36.7683	1.56355
$554$	−48.8098	−2.07373
$555$	58.8601	2.49847
$556$	−58.8485	−2.49573
$557$	−21.5447	−0.912880	−0.456440	−	0.889754i	$-0.650876\pi$
$557$	−21.5447	−0.912880	−0.456440	+	0.889754i	$0.650876\pi$
$558$	0.385127	0.0163037
$559$	20.5283	0.868254
$560$	5.29557	0.223779
$561$	−21.1898	−0.894632
$562$	29.9343	1.26270
$563$	37.8548	1.59539	0.797694	−	0.603063i	$-0.206053\pi$
$563$	37.8548	1.59539	0.797694	+	0.603063i	$0.206053\pi$
$564$	−39.8332	−1.67728
$565$	−27.5075	−1.15725
$566$	−20.5785	−0.864978
$567$	−39.0860	−1.64146
$568$	2.05253	0.0861224
$569$	3.69911	0.155075	0.0775374	−	0.996989i	$-0.475294\pi$
$569$	3.69911	0.155075	0.0775374	+	0.996989i	$0.475294\pi$
$570$	25.3398	1.06137
$571$	7.20049	0.301331	0.150666	−	0.988585i	$-0.451858\pi$
$571$	7.20049	0.301331	0.150666	+	0.988585i	$0.451858\pi$
$572$	37.2985	1.55953
$573$	−26.1241	−1.09135
$574$	104.492	4.36142
$575$	47.3164	1.97323
$576$	−4.62378	−0.192657
$577$	−37.7171	−1.57018	−0.785091	−	0.619380i	$-0.787384\pi$
$577$	−37.7171	−1.57018	−0.785091	+	0.619380i	$0.787384\pi$
$578$	−29.5183	−1.22780
$579$	−29.2667	−1.21628
$580$	41.7042	1.73167
$581$	−8.51095	−0.353094
$582$	65.6635	2.72184
$583$	−20.6567	−0.855514
$584$	14.0159	0.579981
$585$	6.71439	0.277606
$586$	−34.3368	−1.41844
$587$	−20.9699	−0.865520	−0.432760	−	0.901509i	$-0.642460\pi$
$587$	−20.9699	−0.865520	−0.432760	+	0.901509i	$0.642460\pi$
$588$	−48.7748	−2.01144
$589$	0.866254	0.0356934
$590$	90.9579	3.74468
$591$	31.5279	1.29689
$592$	−3.80820	−0.156516
$593$	−18.0228	−0.740108	−0.370054	−	0.929010i	$-0.620661\pi$
$593$	−18.0228	−0.740108	−0.370054	+	0.929010i	$0.620661\pi$
$594$	23.2078	0.952227
$595$	72.6292	2.97751
$596$	10.0814	0.412951
$597$	−20.6189	−0.843875
$598$	94.7357	3.87403
$599$	7.86802	0.321478	0.160739	−	0.986997i	$-0.448612\pi$
$599$	7.86802	0.321478	0.160739	+	0.986997i	$0.448612\pi$
$600$	30.2628	1.23547
$601$	28.3808	1.15768	0.578838	−	0.815442i	$-0.303506\pi$
$601$	28.3808	1.15768	0.578838	+	0.815442i	$0.303506\pi$
$602$	32.6068	1.32895
$603$	−2.68259	−0.109244
$604$	51.5848	2.09895
$605$	22.0471	0.896344
$606$	−6.31222	−0.256417
$607$	39.6282	1.60846	0.804229	−	0.594319i	$-0.202578\pi$
$607$	39.6282	1.60846	0.804229	+	0.594319i	$0.202578\pi$
$608$	−11.0374	−0.447627
$609$	28.3383	1.14833
$610$	78.3056	3.17050
$611$	−38.8384	−1.57123
$612$	−6.11067	−0.247009
$613$	32.7060	1.32098	0.660492	−	0.750833i	$-0.270348\pi$
$613$	32.7060	1.32098	0.660492	+	0.750833i	$0.270348\pi$
$614$	−69.8897	−2.82052
$615$	−72.3179	−2.91614
$616$	21.5678	0.868990
$617$	20.0918	0.808867	0.404433	−	0.914567i	$-0.367469\pi$
$617$	20.0918	0.808867	0.404433	+	0.914567i	$0.367469\pi$
$618$	5.42042	0.218041
$619$	19.3242	0.776703	0.388352	−	0.921511i	$-0.373045\pi$
$619$	19.3242	0.776703	0.388352	+	0.921511i	$0.373045\pi$
$620$	5.07500	0.203817
$621$	36.0317	1.44590
$622$	−17.9154	−0.718341
$623$	21.6840	0.868752
$624$	−4.10896	−0.164490
$625$	−16.3306	−0.653224
$626$	−40.9726	−1.63759
$627$	−6.99872	−0.279502
$628$	−34.0199	−1.35754
$629$	−52.2298	−2.08254
$630$	10.6650	0.424905
$631$	14.8059	0.589413	0.294707	−	0.955588i	$-0.404778\pi$
$631$	14.8059	0.589413	0.294707	+	0.955588i	$0.404778\pi$
$632$	−24.2780	−0.965725
$633$	15.5341	0.617426
$634$	78.9851	3.13690
$635$	−18.2036	−0.722388
$636$	−56.3444	−2.23420
$637$	−47.5566	−1.88426
$638$	−18.8437	−0.746028
$639$	−0.280325	−0.0110895
$640$	−58.5552	−2.31460
$641$	−8.21255	−0.324376	−0.162188	−	0.986760i	$-0.551855\pi$
$641$	−8.21255	−0.324376	−0.162188	+	0.986760i	$0.551855\pi$
$642$	20.2478	0.799117
$643$	−1.52219	−0.0600294	−0.0300147	−	0.999549i	$-0.509555\pi$
$643$	−1.52219	−0.0600294	−0.0300147	+	0.999549i	$0.509555\pi$
$644$	91.9810	3.62456
$645$	−22.5668	−0.888567
$646$	−22.4854	−0.884677
$647$	−31.8698	−1.25293	−0.626466	−	0.779449i	$-0.715499\pi$
$647$	−31.8698	−1.25293	−0.626466	+	0.779449i	$0.715499\pi$
$648$	25.8083	1.01385
$649$	−25.1221	−0.986127
$650$	81.0524	3.17914
$651$	3.44850	0.135157
$652$	3.86996	0.151559
$653$	49.6475	1.94286	0.971429	−	0.237330i	$-0.0762724\pi$
$653$	49.6475	1.94286	0.971429	+	0.237330i	$0.0762724\pi$
$654$	−34.6140	−1.35352
$655$	−9.71489	−0.379592
$656$	4.67891	0.182681
$657$	−1.91422	−0.0746808
$658$	−61.6902	−2.40493
$659$	46.0929	1.79553	0.897763	−	0.440479i	$-0.145192\pi$
$659$	46.0929	1.79553	0.897763	+	0.440479i	$0.145192\pi$
$660$	−41.0024	−1.59602
$661$	−13.5125	−0.525577	−0.262788	−	0.964854i	$-0.584642\pi$
$661$	−13.5125	−0.525577	−0.262788	+	0.964854i	$0.584642\pi$
$662$	46.9117	1.82328
$663$	−56.3548	−2.18864
$664$	5.61975	0.218089
$665$	23.9885	0.930236
$666$	−7.66953	−0.297188
$667$	−29.2561	−1.13280
$668$	−48.7219	−1.88511
$669$	−13.8016	−0.533600
$670$	−57.8306	−2.23419
$671$	−21.6276	−0.834923
$672$	−43.9393	−1.69500
$673$	43.4042	1.67311	0.836554	−	0.547884i	$-0.184567\pi$
$673$	43.4042	1.67311	0.836554	+	0.547884i	$0.184567\pi$
$674$	−8.53986	−0.328943
$675$	30.8274	1.18655
$676$	58.3131	2.24281
$677$	−4.18622	−0.160890	−0.0804448	−	0.996759i	$-0.525634\pi$
$677$	−4.18622	−0.160890	−0.0804448	+	0.996759i	$0.525634\pi$
$678$	33.9021	1.30200
$679$	62.1618	2.38555
$680$	−47.9568	−1.83906
$681$	16.5207	0.633075
$682$	−2.29309	−0.0878070
$683$	9.01247	0.344853	0.172426	−	0.985022i	$-0.444839\pi$
$683$	9.01247	0.344853	0.172426	+	0.985022i	$0.444839\pi$
$684$	−2.01828	−0.0771708
$685$	−51.4364	−1.96528
$686$	−13.0929	−0.499891
$687$	−13.2107	−0.504019
$688$	1.46005	0.0556640
$689$	−54.9372	−2.09294
$690$	−104.143	−3.96466
$691$	22.1226	0.841584	0.420792	−	0.907157i	$-0.361752\pi$
$691$	22.1226	0.841584	0.420792	+	0.907157i	$0.361752\pi$
$692$	16.6977	0.634750
$693$	−2.94562	−0.111895
$694$	6.06051	0.230054
$695$	63.0766	2.39263
$696$	−18.7117	−0.709264
$697$	64.1717	2.43068
$698$	−0.908528	−0.0343883
$699$	36.2586	1.37143
$700$	78.6956	2.97441
$701$	41.5108	1.56784	0.783921	−	0.620861i	$-0.213217\pi$
$701$	41.5108	1.56784	0.783921	+	0.620861i	$0.213217\pi$
$702$	61.7218	2.32954
$703$	−17.2509	−0.650629
$704$	27.5305	1.03760
$705$	42.6951	1.60799
$706$	−16.7507	−0.630420
$707$	−5.97561	−0.224736
$708$	−68.5243	−2.57530
$709$	38.6944	1.45320	0.726599	−	0.687062i	$-0.241100\pi$
$709$	38.6944	1.45320	0.726599	+	0.687062i	$0.241100\pi$
$710$	−6.04317	−0.226796
$711$	3.31576	0.124351
$712$	−14.3179	−0.536585
$713$	−3.56018	−0.133330
$714$	−89.5130	−3.34994
$715$	−39.9783	−1.49510
$716$	38.5419	1.44038
$717$	−7.66951	−0.286423
$718$	62.0614	2.31611
$719$	39.0421	1.45603	0.728013	−	0.685564i	$-0.240444\pi$
$719$	39.0421	1.45603	0.728013	+	0.685564i	$0.240444\pi$
$720$	0.477554	0.0177974
$721$	5.13136	0.191102
$722$	35.6698	1.32749
$723$	27.2245	1.01249
$724$	−54.8832	−2.03972
$725$	−25.0304	−0.929607
$726$	−27.1723	−1.00846
$727$	37.1708	1.37859	0.689294	−	0.724482i	$-0.257921\pi$
$727$	37.1708	1.37859	0.689294	+	0.724482i	$0.257921\pi$
$728$	57.3601	2.12591
$729$	23.0979	0.855476
$730$	−41.2662	−1.52733
$731$	20.0248	0.740643
$732$	−58.9925	−2.18043
$733$	−41.0495	−1.51620	−0.758098	−	0.652141i	$-0.773871\pi$
$733$	−41.0495	−1.51620	−0.758098	+	0.652141i	$0.773871\pi$
$734$	67.7657	2.50128
$735$	52.2791	1.92834
$736$	45.3624	1.67208
$737$	15.9725	0.588354
$738$	9.42310	0.346869
$739$	4.21156	0.154925	0.0774624	−	0.996995i	$-0.475318\pi$
$739$	4.21156	0.154925	0.0774624	+	0.996995i	$0.475318\pi$
$740$	−101.065	−3.71523
$741$	−18.6133	−0.683777
$742$	−87.2613	−3.20346
$743$	−26.1836	−0.960583	−0.480292	−	0.877109i	$-0.659469\pi$
$743$	−26.1836	−0.960583	−0.480292	+	0.877109i	$0.659469\pi$
$744$	−2.27703	−0.0834800
$745$	−10.8057	−0.395891
$746$	−40.1767	−1.47097
$747$	−0.767517	−0.0280820
$748$	36.3837	1.33032
$749$	19.1680	0.700385
$750$	−19.0813	−0.696750
$751$	−13.1247	−0.478929	−0.239464	−	0.970905i	$-0.576972\pi$
$751$	−13.1247	−0.478929	−0.239464	+	0.970905i	$0.576972\pi$
$752$	−2.76234	−0.100732
$753$	19.9311	0.726330
$754$	−50.1153	−1.82509
$755$	−55.2910	−2.01225
$756$	59.9271	2.17953
$757$	−10.9227	−0.396993	−0.198496	−	0.980102i	$-0.563606\pi$
$757$	−10.9227	−0.396993	−0.198496	+	0.980102i	$0.563606\pi$
$758$	−15.4811	−0.562298
$759$	28.7637	1.04406
$760$	−15.8395	−0.574560
$761$	−49.6735	−1.80066	−0.900331	−	0.435207i	$-0.856675\pi$
$761$	−49.6735	−1.80066	−0.900331	+	0.435207i	$0.856675\pi$
$762$	22.4353	0.812746
$763$	−32.7682	−1.18629
$764$	44.8562	1.62284
$765$	6.54970	0.236805
$766$	−10.8138	−0.390719
$767$	−66.8129	−2.41247
$768$	24.4112	0.880864
$769$	13.1851	0.475467	0.237733	−	0.971330i	$-0.423596\pi$
$769$	13.1851	0.475467	0.237733	+	0.971330i	$0.423596\pi$
$770$	−63.5009	−2.28841
$771$	−19.3071	−0.695327
$772$	50.2521	1.80861
$773$	−19.8053	−0.712348	−0.356174	−	0.934420i	$-0.615919\pi$
$773$	−19.8053	−0.712348	−0.356174	+	0.934420i	$0.615919\pi$
$774$	2.94048	0.105693
$775$	−3.04596	−0.109414
$776$	−41.0452	−1.47344
$777$	−68.6745	−2.46368
$778$	−82.5733	−2.96040
$779$	21.1951	0.759394
$780$	−109.047	−3.90451
$781$	1.66909	0.0597247
$782$	92.4120	3.30465
$783$	−19.0608	−0.681178
$784$	−3.38242	−0.120801
$785$	36.4642	1.30146
$786$	11.9733	0.427072
$787$	18.8406	0.671596	0.335798	−	0.941934i	$-0.390994\pi$
$787$	18.8406	0.671596	0.335798	+	0.941934i	$0.390994\pi$
$788$	−54.1347	−1.92847
$789$	−9.91146	−0.352857
$790$	71.4804	2.54316
$791$	32.0942	1.14114
$792$	1.94498	0.0691119
$793$	−57.5192	−2.04257
$794$	8.04058	0.285350
$795$	60.3926	2.14191
$796$	35.4035	1.25484
$797$	24.7092	0.875243	0.437622	−	0.899159i	$-0.355821\pi$
$797$	24.7092	0.875243	0.437622	+	0.899159i	$0.355821\pi$
$798$	−29.5650	−1.04659
$799$	−37.8857	−1.34030
$800$	38.8104	1.37215
$801$	1.95547	0.0690930
$802$	−54.5021	−1.92453
$803$	11.3975	0.402209
$804$	43.5674	1.53650
$805$	−98.5895	−3.47482
$806$	−6.09854	−0.214812
$807$	−2.34878	−0.0826811
$808$	3.94567	0.138808
$809$	−16.8283	−0.591651	−0.295825	−	0.955242i	$-0.595595\pi$
$809$	−16.8283	−0.591651	−0.295825	+	0.955242i	$0.595595\pi$
$810$	−75.9862	−2.66988
$811$	49.0865	1.72366	0.861830	−	0.507197i	$-0.169319\pi$
$811$	49.0865	1.72366	0.861830	+	0.507197i	$0.169319\pi$
$812$	−48.6580	−1.70756
$813$	17.9483	0.629475
$814$	45.6653	1.60057
$815$	−4.14800	−0.145298
$816$	−4.00818	−0.140314
$817$	6.61393	0.231392
$818$	3.56166	0.124531
$819$	−7.83396	−0.273741
$820$	124.173	4.33630
$821$	−13.5789	−0.473906	−0.236953	−	0.971521i	$-0.576149\pi$
$821$	−13.5789	−0.473906	−0.236953	+	0.971521i	$0.576149\pi$
$822$	63.3936	2.21111
$823$	−43.7397	−1.52467	−0.762335	−	0.647183i	$-0.775947\pi$
$823$	−43.7397	−1.52467	−0.762335	+	0.647183i	$0.775947\pi$
$824$	−3.38822	−0.118034
$825$	24.6092	0.856783
$826$	−106.124	−3.69254
$827$	9.17206	0.318944	0.159472	−	0.987202i	$-0.449021\pi$
$827$	9.17206	0.318944	0.159472	+	0.987202i	$0.449021\pi$
$828$	8.29484	0.288266
$829$	−52.7235	−1.83116	−0.915581	−	0.402134i	$-0.868269\pi$
$829$	−52.7235	−1.83116	−0.915581	+	0.402134i	$0.868269\pi$
$830$	−16.5459	−0.574318
$831$	−39.4134	−1.36724
$832$	73.2183	2.53839
$833$	−46.3901	−1.60732
$834$	−77.7397	−2.69191
$835$	52.2225	1.80723
$836$	12.0171	0.415619
$837$	−2.31952	−0.0801742
$838$	−21.6213	−0.746896
$839$	34.6239	1.19535	0.597675	−	0.801738i	$-0.296091\pi$
$839$	34.6239	1.19535	0.597675	+	0.801738i	$0.296091\pi$
$840$	−63.0561	−2.17564
$841$	−13.5235	−0.466327
$842$	−61.2435	−2.11059
$843$	24.1717	0.832516
$844$	−26.6727	−0.918112
$845$	−62.5027	−2.15016
$846$	−5.56322	−0.191268
$847$	−25.7233	−0.883864
$848$	−3.90735	−0.134179
$849$	−16.6169	−0.570290
$850$	79.0643	2.71188
$851$	70.8986	2.43037
$852$	4.55270	0.155973
$853$	−1.18550	−0.0405908	−0.0202954	−	0.999794i	$-0.506461\pi$
$853$	−1.18550	−0.0405908	−0.0202954	+	0.999794i	$0.506461\pi$
$854$	−91.3624	−3.12636
$855$	2.16329	0.0739828
$856$	−12.6566	−0.432593
$857$	33.6140	1.14823	0.574116	−	0.818774i	$-0.305346\pi$
$857$	33.6140	1.14823	0.574116	+	0.818774i	$0.305346\pi$
$858$	49.2719	1.68212
$859$	2.66117	0.0907978	0.0453989	−	0.998969i	$-0.485544\pi$
$859$	2.66117	0.0907978	0.0453989	+	0.998969i	$0.485544\pi$
$860$	38.7481	1.32130
$861$	84.3763	2.87554
$862$	−7.96849	−0.271408
$863$	−7.20901	−0.245398	−0.122699	−	0.992444i	$-0.539155\pi$
$863$	−7.20901	−0.245398	−0.122699	+	0.992444i	$0.539155\pi$
$864$	29.5543	1.00546
$865$	−17.8974	−0.608528
$866$	−53.5923	−1.82114
$867$	−23.8357	−0.809504
$868$	−5.92121	−0.200979
$869$	−19.7425	−0.669717
$870$	55.0919	1.86779
$871$	42.4793	1.43936
$872$	21.6367	0.732711
$873$	5.60575	0.189726
$874$	30.5225	1.03244
$875$	−18.0637	−0.610666
$876$	31.0884	1.05038
$877$	26.7459	0.903145	0.451573	−	0.892234i	$-0.350863\pi$
$877$	26.7459	0.903145	0.451573	+	0.892234i	$0.350863\pi$
$878$	−19.3363	−0.652569
$879$	−27.7266	−0.935195
$880$	−2.84342	−0.0958516
$881$	−3.66811	−0.123582	−0.0617909	−	0.998089i	$-0.519681\pi$
$881$	−3.66811	−0.123582	−0.0617909	+	0.998089i	$0.519681\pi$
$882$	−6.81203	−0.229373
$883$	13.0489	0.439131	0.219566	−	0.975598i	$-0.429536\pi$
$883$	13.0489	0.439131	0.219566	+	0.975598i	$0.429536\pi$
$884$	96.7635	3.25451
$885$	73.4475	2.46891
$886$	38.3568	1.28862
$887$	10.9962	0.369217	0.184609	−	0.982812i	$-0.440898\pi$
$887$	10.9962	0.369217	0.184609	+	0.982812i	$0.440898\pi$
$888$	45.3455	1.52170
$889$	21.2389	0.712330
$890$	42.1554	1.41305
$891$	20.9869	0.703089
$892$	23.6979	0.793463
$893$	−12.5132	−0.418738
$894$	13.3177	0.445410
$895$	−41.3110	−1.38087
$896$	68.3188	2.28237
$897$	76.4981	2.55420
$898$	40.8303	1.36253
$899$	1.88334	0.0628129
$900$	7.09677	0.236559
$901$	−53.5897	−1.78533
$902$	−56.1063	−1.86814
$903$	26.3296	0.876195
$904$	−21.1917	−0.704824
$905$	58.8264	1.95545
$906$	68.1442	2.26394
$907$	46.6793	1.54996	0.774981	−	0.631985i	$-0.217759\pi$
$907$	46.6793	1.54996	0.774981	+	0.631985i	$0.217759\pi$
$908$	−28.3668	−0.941384
$909$	−0.538880	−0.0178735
$910$	−168.883	−5.59840
$911$	−47.9647	−1.58914	−0.794570	−	0.607172i	$-0.792304\pi$
$911$	−47.9647	−1.58914	−0.794570	+	0.607172i	$0.792304\pi$
$912$	−1.32385	−0.0438371
$913$	4.56989	0.151241
$914$	66.9920	2.21590
$915$	63.2310	2.09035
$916$	22.6833	0.749476
$917$	11.3348	0.374307
$918$	60.2079	1.98716
$919$	8.09542	0.267043	0.133522	−	0.991046i	$-0.457371\pi$
$919$	8.09542	0.267043	0.133522	+	0.991046i	$0.457371\pi$
$920$	65.0983	2.14623
$921$	−56.4352	−1.85960
$922$	0.305763	0.0100698
$923$	4.43899	0.146111
$924$	47.8392	1.57379
$925$	60.6583	1.99443
$926$	51.8153	1.70276
$927$	0.462746	0.0151986
$928$	−23.9967	−0.787731
$929$	−1.42092	−0.0466188	−0.0233094	−	0.999728i	$-0.507420\pi$
$929$	−1.42092	−0.0466188	−0.0233094	+	0.999728i	$0.507420\pi$
$930$	6.70414	0.219838
$931$	−15.3221	−0.502161
$932$	−62.2575	−2.03931
$933$	−14.4665	−0.473611
$934$	−43.0665	−1.40918
$935$	−38.9977	−1.27536
$936$	5.17274	0.169076
$937$	22.1100	0.722303	0.361152	−	0.932507i	$-0.382384\pi$
$937$	22.1100	0.722303	0.361152	+	0.932507i	$0.382384\pi$
$938$	67.4734	2.20308
$939$	−33.0849	−1.07969
$940$	−73.3093	−2.39108
$941$	24.0672	0.784570	0.392285	−	0.919844i	$-0.371685\pi$
$941$	24.0672	0.784570	0.392285	+	0.919844i	$0.371685\pi$
$942$	−44.9408	−1.46425
$943$	−87.1090	−2.83666
$944$	−4.75200	−0.154664
$945$	−64.2327	−2.08949
$946$	−17.5080	−0.569233
$947$	49.1632	1.59759	0.798794	−	0.601604i	$-0.205471\pi$
$947$	49.1632	1.59759	0.798794	+	0.601604i	$0.205471\pi$
$948$	−53.8506	−1.74899
$949$	30.3120	0.983968
$950$	26.1140	0.847249
$951$	63.7796	2.06820
$952$	55.9532	1.81345
$953$	−23.7610	−0.769694	−0.384847	−	0.922980i	$-0.625746\pi$
$953$	−23.7610	−0.769694	−0.384847	+	0.922980i	$0.625746\pi$
$954$	−7.86922	−0.254775
$955$	−48.0789	−1.55580
$956$	13.1689	0.425912
$957$	−15.2161	−0.491865
$958$	−64.7026	−2.09045
$959$	60.0130	1.93792
$960$	−80.4890	−2.59777
$961$	−30.7708	−0.992607
$962$	121.448	3.91565
$963$	1.72857	0.0557025
$964$	−46.7455	−1.50557
$965$	−53.8625	−1.73390
$966$	121.508	3.90946
$967$	2.56214	0.0823930	0.0411965	−	0.999151i	$-0.486883\pi$
$967$	2.56214	0.0823930	0.0411965	+	0.999151i	$0.486883\pi$
$968$	16.9850	0.545919
$969$	−18.1567	−0.583279
$970$	120.847	3.88018
$971$	57.5369	1.84645	0.923224	−	0.384262i	$-0.125544\pi$
$971$	57.5369	1.84645	0.923224	+	0.384262i	$0.125544\pi$
$972$	11.5330	0.369921
$973$	−73.5941	−2.35932
$974$	12.4522	0.398993
$975$	65.4489	2.09604
$976$	−4.09099	−0.130949
$977$	−24.3579	−0.779278	−0.389639	−	0.920968i	$-0.627400\pi$
$977$	−24.3579	−0.779278	−0.389639	+	0.920968i	$0.627400\pi$
$978$	5.11227	0.163472
$979$	−11.6431	−0.372114
$980$	−89.7654	−2.86745
$981$	−2.95503	−0.0943469
$982$	−13.9676	−0.445725
$983$	−35.3515	−1.12754	−0.563769	−	0.825932i	$-0.690649\pi$
$983$	−35.3515	−1.12754	−0.563769	+	0.825932i	$0.690649\pi$
$984$	−55.7134	−1.77608
$985$	58.0241	1.84880
$986$	−48.8860	−1.55685
$987$	−49.8142	−1.58560
$988$	31.9598	1.01678
$989$	−27.1823	−0.864348
$990$	−5.72651	−0.182000
$991$	33.2825	1.05725	0.528626	−	0.848855i	$-0.322707\pi$
$991$	33.2825	1.05725	0.528626	+	0.848855i	$0.322707\pi$
$992$	−2.92017	−0.0927155
$993$	37.8807	1.20211
$994$	7.05082	0.223638
$995$	−37.9471	−1.20300
$996$	12.4651	0.394972
$997$	52.2153	1.65368	0.826838	−	0.562441i	$-0.190138\pi$
$997$	52.2153	1.65368	0.826838	+	0.562441i	$0.190138\pi$
$998$	−19.5449	−0.618684
$999$	46.1916	1.46144

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	503.2.a.f.1.3	✓	26
3.2	odd	2		4527.2.a.o.1.24		26
4.3	odd	2		8048.2.a.u.1.21		26

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
503.2.a.f.1.3	✓	26	1.1	even	1	trivial
4527.2.a.o.1.24		26	3.2	odd	2
8048.2.a.u.1.21		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)

\(f(q)\)	\(=\)	\(q-2.26823 q^{2} -1.83158 q^{3} +3.14489 q^{4} -3.37084 q^{5} +4.15444 q^{6} +3.93290 q^{7} -2.59688 q^{8} +0.354669 q^{9} +O(q^{10})\)	\(q-2.26823 q^{2} -1.83158 q^{3} +3.14489 q^{4} -3.37084 q^{5} +4.15444 q^{6} +3.93290 q^{7} -2.59688 q^{8} +0.354669 q^{9} +7.64586 q^{10} -2.11174 q^{11} -5.76010 q^{12} -5.61624 q^{13} -8.92074 q^{14} +6.17395 q^{15} -0.399449 q^{16} -5.47848 q^{17} -0.804472 q^{18} -1.80948 q^{19} -10.6009 q^{20} -7.20340 q^{21} +4.78993 q^{22} +7.43669 q^{23} +4.75638 q^{24} +6.36256 q^{25} +12.7390 q^{26} +4.84512 q^{27} +12.3685 q^{28} -3.93402 q^{29} -14.0040 q^{30} -0.478732 q^{31} +6.09980 q^{32} +3.86781 q^{33} +12.4265 q^{34} -13.2572 q^{35} +1.11539 q^{36} +9.53362 q^{37} +4.10432 q^{38} +10.2866 q^{39} +8.75366 q^{40} -11.7134 q^{41} +16.3390 q^{42} -3.65517 q^{43} -6.64119 q^{44} -1.19553 q^{45} -16.8682 q^{46} +6.91537 q^{47} +0.731622 q^{48} +8.46770 q^{49} -14.4318 q^{50} +10.0343 q^{51} -17.6625 q^{52} +9.78185 q^{53} -10.9899 q^{54} +7.11834 q^{55} -10.2133 q^{56} +3.31419 q^{57} +8.92328 q^{58} +11.8964 q^{59} +19.4164 q^{60} +10.2416 q^{61} +1.08588 q^{62} +1.39488 q^{63} -13.0369 q^{64} +18.9315 q^{65} -8.77311 q^{66} -7.56365 q^{67} -17.2292 q^{68} -13.6209 q^{69} +30.0704 q^{70} -0.790385 q^{71} -0.921032 q^{72} -5.39720 q^{73} -21.6245 q^{74} -11.6535 q^{75} -5.69060 q^{76} -8.30527 q^{77} -23.3324 q^{78} +9.34890 q^{79} +1.34648 q^{80} -9.93822 q^{81} +26.5687 q^{82} -2.16404 q^{83} -22.6539 q^{84} +18.4671 q^{85} +8.29077 q^{86} +7.20545 q^{87} +5.48394 q^{88} +5.51350 q^{89} +2.71175 q^{90} -22.0881 q^{91} +23.3876 q^{92} +0.876834 q^{93} -15.6857 q^{94} +6.09945 q^{95} -11.1722 q^{96} +15.8056 q^{97} -19.2067 q^{98} -0.748969 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 26 q + 4 q^{2} + 4 q^{3} + 36 q^{4} + 9 q^{5} - 4 q^{6} + 11 q^{7} + 18 q^{8} + 42 q^{9}+O(q^{10}) \) 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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