LMFDB - Embedded newform 4027.2.a.c.1.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4027,2,Mod(1,4027)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4027, 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("4027.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4027 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4027.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:	$32.1557568940$
Analytic rank:	$0$
Dimension:	$174$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.10
Character	$\chi$	$=$	4027.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.51686 q^{2} -1.86760 q^{3} +4.33456 q^{4} -3.04693 q^{5} +4.70049 q^{6} -0.421908 q^{7} -5.87575 q^{8} +0.487938 q^{9} +O(q^{10})$	\(q-2.51686 q^{2} -1.86760 q^{3} +4.33456 q^{4} -3.04693 q^{5} +4.70049 q^{6} -0.421908 q^{7} -5.87575 q^{8} +0.487938 q^{9} +7.66868 q^{10} -0.625941 q^{11} -8.09524 q^{12} -3.42323 q^{13} +1.06188 q^{14} +5.69045 q^{15} +6.11930 q^{16} +7.89702 q^{17} -1.22807 q^{18} +8.21388 q^{19} -13.2071 q^{20} +0.787957 q^{21} +1.57540 q^{22} +7.05488 q^{23} +10.9736 q^{24} +4.28378 q^{25} +8.61578 q^{26} +4.69153 q^{27} -1.82879 q^{28} +8.83383 q^{29} -14.3220 q^{30} -9.72357 q^{31} -3.64989 q^{32} +1.16901 q^{33} -19.8757 q^{34} +1.28552 q^{35} +2.11500 q^{36} -6.32965 q^{37} -20.6731 q^{38} +6.39324 q^{39} +17.9030 q^{40} -9.06189 q^{41} -1.98317 q^{42} -1.16729 q^{43} -2.71318 q^{44} -1.48671 q^{45} -17.7561 q^{46} +3.30942 q^{47} -11.4284 q^{48} -6.82199 q^{49} -10.7816 q^{50} -14.7485 q^{51} -14.8382 q^{52} +11.6817 q^{53} -11.8079 q^{54} +1.90720 q^{55} +2.47903 q^{56} -15.3403 q^{57} -22.2335 q^{58} -6.06589 q^{59} +24.6656 q^{60} +5.01268 q^{61} +24.4728 q^{62} -0.205865 q^{63} -3.05236 q^{64} +10.4303 q^{65} -2.94222 q^{66} +2.89581 q^{67} +34.2301 q^{68} -13.1757 q^{69} -3.23548 q^{70} +12.5189 q^{71} -2.86701 q^{72} +10.7893 q^{73} +15.9308 q^{74} -8.00039 q^{75} +35.6036 q^{76} +0.264090 q^{77} -16.0909 q^{78} -0.898442 q^{79} -18.6451 q^{80} -10.2257 q^{81} +22.8075 q^{82} +8.49727 q^{83} +3.41545 q^{84} -24.0617 q^{85} +2.93789 q^{86} -16.4981 q^{87} +3.67787 q^{88} -8.17918 q^{89} +3.74184 q^{90} +1.44429 q^{91} +30.5798 q^{92} +18.1598 q^{93} -8.32932 q^{94} -25.0271 q^{95} +6.81654 q^{96} +3.27109 q^{97} +17.1700 q^{98} -0.305420 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) $ 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * 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 $

$2$	−2.51686	−1.77969	−0.889843	−	0.456267i	$-0.849186\pi$
$2$	−2.51686	−1.77969	−0.889843	+	0.456267i	$0.849186\pi$
$3$	−1.86760	−1.07826	−0.539130	−	0.842222i	$-0.681247\pi$
$3$	−1.86760	−1.07826	−0.539130	+	0.842222i	$0.681247\pi$
$4$	4.33456	2.16728
$5$	−3.04693	−1.36263	−0.681314	−	0.731991i	$-0.738591\pi$
$5$	−3.04693	−1.36263	−0.681314	+	0.731991i	$0.738591\pi$
$6$	4.70049	1.91897
$7$	−0.421908	−0.159466	−0.0797332	−	0.996816i	$-0.525407\pi$
$7$	−0.421908	−0.159466	−0.0797332	+	0.996816i	$0.525407\pi$
$8$	−5.87575	−2.07739
$9$	0.487938	0.162646
$10$	7.66868	2.42505
$11$	−0.625941	−0.188728	−0.0943641	−	0.995538i	$-0.530082\pi$
$11$	−0.625941	−0.188728	−0.0943641	+	0.995538i	$0.530082\pi$
$12$	−8.09524	−2.33689
$13$	−3.42323	−0.949434	−0.474717	−	0.880139i	$-0.657450\pi$
$13$	−3.42323	−0.949434	−0.474717	+	0.880139i	$0.657450\pi$
$14$	1.06188	0.283800
$15$	5.69045	1.46927
$16$	6.11930	1.52983
$17$	7.89702	1.91531	0.957655	−	0.287919i	$-0.0929635\pi$
$17$	7.89702	1.91531	0.957655	+	0.287919i	$0.0929635\pi$
$18$	−1.22807	−0.289459
$19$	8.21388	1.88439	0.942196	−	0.335061i	$-0.108757\pi$
$19$	8.21388	1.88439	0.942196	+	0.335061i	$0.108757\pi$
$20$	−13.2071	−2.95320
$21$	0.787957	0.171946
$22$	1.57540	0.335877
$23$	7.05488	1.47104	0.735522	−	0.677501i	$-0.236937\pi$
$23$	7.05488	1.47104	0.735522	+	0.677501i	$0.236937\pi$
$24$	10.9736	2.23997
$25$	4.28378	0.856755
$26$	8.61578	1.68969
$27$	4.69153	0.902886
$28$	−1.82879	−0.345608
$29$	8.83383	1.64040	0.820200	−	0.572076i	$-0.193862\pi$
$29$	8.83383	1.64040	0.820200	+	0.572076i	$0.193862\pi$
$30$	−14.3220	−2.61484
$31$	−9.72357	−1.74640	−0.873202	−	0.487358i	$-0.837961\pi$
$31$	−9.72357	−1.74640	−0.873202	+	0.487358i	$0.837961\pi$
$32$	−3.64989	−0.645216
$33$	1.16901	0.203498
$34$	−19.8757	−3.40865
$35$	1.28552	0.217293
$36$	2.11500	0.352500
$37$	−6.32965	−1.04059	−0.520294	−	0.853987i	$-0.674178\pi$
$37$	−6.32965	−1.04059	−0.520294	+	0.853987i	$0.674178\pi$
$38$	−20.6731	−3.35363
$39$	6.39324	1.02374
$40$	17.9030	2.83071
$41$	−9.06189	−1.41523	−0.707615	−	0.706598i	$-0.750229\pi$
$41$	−9.06189	−1.41523	−0.707615	+	0.706598i	$0.750229\pi$
$42$	−1.98317	−0.306010
$43$	−1.16729	−0.178010	−0.0890048	−	0.996031i	$-0.528369\pi$
$43$	−1.16729	−0.178010	−0.0890048	+	0.996031i	$0.528369\pi$
$44$	−2.71318	−0.409027
$45$	−1.48671	−0.221626
$46$	−17.7561	−2.61800
$47$	3.30942	0.482728	0.241364	−	0.970435i	$-0.422405\pi$
$47$	3.30942	0.482728	0.241364	+	0.970435i	$0.422405\pi$
$48$	−11.4284	−1.64955
$49$	−6.82199	−0.974570
$50$	−10.7816	−1.52475
$51$	−14.7485	−2.06520
$52$	−14.8382	−2.05769
$53$	11.6817	1.60461	0.802305	−	0.596914i	$-0.203607\pi$
$53$	11.6817	1.60461	0.802305	+	0.596914i	$0.203607\pi$
$54$	−11.8079	−1.60685
$55$	1.90720	0.257166
$56$	2.47903	0.331274
$57$	−15.3403	−2.03187
$58$	−22.2335	−2.91940
$59$	−6.06589	−0.789712	−0.394856	−	0.918743i	$-0.629205\pi$
$59$	−6.06589	−0.789712	−0.394856	+	0.918743i	$0.629205\pi$
$60$	24.6656	3.18432
$61$	5.01268	0.641808	0.320904	−	0.947112i	$-0.396013\pi$
$61$	5.01268	0.641808	0.320904	+	0.947112i	$0.396013\pi$
$62$	24.4728	3.10805
$63$	−0.205865	−0.0259366
$64$	−3.05236	−0.381545
$65$	10.4303	1.29373
$66$	−2.94222	−0.362163
$67$	2.89581	0.353780	0.176890	−	0.984231i	$-0.443396\pi$
$67$	2.89581	0.353780	0.176890	+	0.984231i	$0.443396\pi$
$68$	34.2301	4.15101
$69$	−13.1757	−1.58617
$70$	−3.23548	−0.386714
$71$	12.5189	1.48572	0.742859	−	0.669448i	$-0.233469\pi$
$71$	12.5189	1.48572	0.742859	+	0.669448i	$0.233469\pi$
$72$	−2.86701	−0.337880
$73$	10.7893	1.26279	0.631394	−	0.775462i	$-0.282483\pi$
$73$	10.7893	1.26279	0.631394	+	0.775462i	$0.282483\pi$
$74$	15.9308	1.85192
$75$	−8.00039	−0.923805
$76$	35.6036	4.08401
$77$	0.264090	0.0300958
$78$	−16.0909	−1.82193
$79$	−0.898442	−0.101083	−0.0505413	−	0.998722i	$-0.516095\pi$
$79$	−0.898442	−0.101083	−0.0505413	+	0.998722i	$0.516095\pi$
$80$	−18.6451	−2.08458
$81$	−10.2257	−1.13619
$82$	22.8075	2.51866
$83$	8.49727	0.932697	0.466349	−	0.884601i	$-0.345569\pi$
$83$	8.49727	0.932697	0.466349	+	0.884601i	$0.345569\pi$
$84$	3.41545	0.372656
$85$	−24.0617	−2.60985
$86$	2.93789	0.316801
$87$	−16.4981	−1.76878
$88$	3.67787	0.392063
$89$	−8.17918	−0.866991	−0.433496	−	0.901156i	$-0.642720\pi$
$89$	−8.17918	−0.866991	−0.433496	+	0.901156i	$0.642720\pi$
$90$	3.74184	0.394425
$91$	1.44429	0.151403
$92$	30.5798	3.18817
$93$	18.1598	1.88308
$94$	−8.32932	−0.859104
$95$	−25.0271	−2.56773
$96$	6.81654	0.695711
$97$	3.27109	0.332129	0.166064	−	0.986115i	$-0.446894\pi$
$97$	3.27109	0.332129	0.166064	+	0.986115i	$0.446894\pi$
$98$	17.1700	1.73443
$99$	−0.305420	−0.0306959
$100$	18.5683	1.85683
$101$	−11.4789	−1.14220	−0.571099	−	0.820881i	$-0.693483\pi$
$101$	−11.4789	−1.14220	−0.571099	+	0.820881i	$0.693483\pi$
$102$	37.1198	3.67541
$103$	−5.68400	−0.560061	−0.280031	−	0.959991i	$-0.590345\pi$
$103$	−5.68400	−0.560061	−0.280031	+	0.959991i	$0.590345\pi$
$104$	20.1141	1.97235
$105$	−2.40085	−0.234299
$106$	−29.4013	−2.85570
$107$	−12.0407	−1.16402	−0.582008	−	0.813183i	$-0.697733\pi$
$107$	−12.0407	−1.16402	−0.582008	+	0.813183i	$0.697733\pi$
$108$	20.3357	1.95681
$109$	−15.7749	−1.51096	−0.755480	−	0.655171i	$-0.772596\pi$
$109$	−15.7749	−1.51096	−0.755480	+	0.655171i	$0.772596\pi$
$110$	−4.80014	−0.457675
$111$	11.8213	1.12202
$112$	−2.58179	−0.243956
$113$	3.17564	0.298740	0.149370	−	0.988781i	$-0.452276\pi$
$113$	3.17564	0.298740	0.149370	+	0.988781i	$0.452276\pi$
$114$	38.6092	3.61608
$115$	−21.4957	−2.00449
$116$	38.2908	3.55521
$117$	−1.67033	−0.154422
$118$	15.2670	1.40544
$119$	−3.33182	−0.305427
$120$	−33.4357	−3.05225
$121$	−10.6082	−0.964382
$122$	−12.6162	−1.14222
$123$	16.9240	1.52599
$124$	−42.1474	−3.78495
$125$	2.18229	0.195190
$126$	0.518133	0.0461590
$127$	−0.376385	−0.0333988	−0.0166994	−	0.999861i	$-0.505316\pi$
$127$	−0.376385	−0.0333988	−0.0166994	+	0.999861i	$0.505316\pi$
$128$	14.9821	1.32425
$129$	2.18003	0.191941
$130$	−26.2517	−2.30242
$131$	−4.14153	−0.361847	−0.180924	−	0.983497i	$-0.557909\pi$
$131$	−4.14153	−0.361847	−0.180924	+	0.983497i	$0.557909\pi$
$132$	5.06714	0.441038
$133$	−3.46550	−0.300497
$134$	−7.28834	−0.629616
$135$	−14.2948	−1.23030
$136$	−46.4010	−3.97885
$137$	−10.0622	−0.859673	−0.429836	−	0.902907i	$-0.641429\pi$
$137$	−10.0622	−0.859673	−0.429836	+	0.902907i	$0.641429\pi$
$138$	33.1614	2.82288
$139$	23.2770	1.97433	0.987165	−	0.159703i	$-0.0510536\pi$
$139$	23.2770	1.97433	0.987165	+	0.159703i	$0.0510536\pi$
$140$	5.57219	0.470936
$141$	−6.18067	−0.520506
$142$	−31.5082	−2.64411
$143$	2.14274	0.179185
$144$	2.98584	0.248820
$145$	−26.9160	−2.23526
$146$	−27.1550	−2.24736
$147$	12.7408	1.05084
$148$	−27.4363	−2.25525
$149$	5.48939	0.449708	0.224854	−	0.974392i	$-0.427809\pi$
$149$	5.48939	0.449708	0.224854	+	0.974392i	$0.427809\pi$
$150$	20.1358	1.64408
$151$	−8.01850	−0.652536	−0.326268	−	0.945277i	$-0.605791\pi$
$151$	−8.01850	−0.652536	−0.326268	+	0.945277i	$0.605791\pi$
$152$	−48.2627	−3.91462
$153$	3.85326	0.311518
$154$	−0.664675	−0.0535611
$155$	29.6270	2.37970
$156$	27.7119	2.21873
$157$	9.72834	0.776406	0.388203	−	0.921574i	$-0.373096\pi$
$157$	9.72834	0.776406	0.388203	+	0.921574i	$0.373096\pi$
$158$	2.26125	0.179895
$159$	−21.8168	−1.73019
$160$	11.1210	0.879189
$161$	−2.97651	−0.234582
$162$	25.7367	2.02207
$163$	−8.54420	−0.669233	−0.334617	−	0.942354i	$-0.608607\pi$
$163$	−8.54420	−0.669233	−0.334617	+	0.942354i	$0.608607\pi$
$164$	−39.2793	−3.06720
$165$	−3.56188	−0.277292
$166$	−21.3864	−1.65991
$167$	7.00039	0.541707	0.270853	−	0.962621i	$-0.412694\pi$
$167$	7.00039	0.541707	0.270853	+	0.962621i	$0.412694\pi$
$168$	−4.62984	−0.357200
$169$	−1.28148	−0.0985754
$170$	60.5597	4.64472
$171$	4.00787	0.306489
$172$	−5.05968	−0.385797
$173$	5.13502	0.390408	0.195204	−	0.980763i	$-0.437463\pi$
$173$	5.13502	0.390408	0.195204	+	0.980763i	$0.437463\pi$
$174$	41.5233	3.14787
$175$	−1.80736	−0.136624
$176$	−3.83032	−0.288721
$177$	11.3287	0.851515
$178$	20.5858	1.54297
$179$	1.24979	0.0934137	0.0467069	−	0.998909i	$-0.485127\pi$
$179$	1.24979	0.0934137	0.0467069	+	0.998909i	$0.485127\pi$
$180$	−6.44425	−0.480326
$181$	10.7048	0.795684	0.397842	−	0.917454i	$-0.369759\pi$
$181$	10.7048	0.795684	0.397842	+	0.917454i	$0.369759\pi$
$182$	−3.63507	−0.269449
$183$	−9.36170	−0.692037
$184$	−41.4528	−3.05594
$185$	19.2860	1.41793
$186$	−45.7055	−3.35129
$187$	−4.94307	−0.361473
$188$	14.3449	1.04621
$189$	−1.97940	−0.143980
$190$	62.9896	4.56975
$191$	4.92943	0.356681	0.178340	−	0.983969i	$-0.442927\pi$
$191$	4.92943	0.356681	0.178340	+	0.983969i	$0.442927\pi$
$192$	5.70059	0.411405
$193$	7.98175	0.574539	0.287269	−	0.957850i	$-0.407253\pi$
$193$	7.98175	0.574539	0.287269	+	0.957850i	$0.407253\pi$
$194$	−8.23286	−0.591085
$195$	−19.4797	−1.39497
$196$	−29.5704	−2.11217
$197$	−8.52505	−0.607384	−0.303692	−	0.952770i	$-0.598219\pi$
$197$	−8.52505	−0.607384	−0.303692	+	0.952770i	$0.598219\pi$
$198$	0.768699	0.0546290
$199$	22.5631	1.59945	0.799726	−	0.600365i	$-0.204978\pi$
$199$	22.5631	1.59945	0.799726	+	0.600365i	$0.204978\pi$
$200$	−25.1704	−1.77982
$201$	−5.40822	−0.381467
$202$	28.8909	2.03275
$203$	−3.72707	−0.261589
$204$	−63.9283	−4.47587
$205$	27.6109	1.92843
$206$	14.3058	0.996733
$207$	3.44235	0.239260
$208$	−20.9478	−1.45247
$209$	−5.14140	−0.355638
$210$	6.04259	0.416978
$211$	−23.8634	−1.64282	−0.821412	−	0.570335i	$-0.806813\pi$
$211$	−23.8634	−1.64282	−0.821412	+	0.570335i	$0.806813\pi$
$212$	50.6352	3.47764
$213$	−23.3803	−1.60199
$214$	30.3046	2.07158
$215$	3.55664	0.242561
$216$	−27.5663	−1.87565
$217$	4.10245	0.278493
$218$	39.7031	2.68903
$219$	−20.1500	−1.36161
$220$	8.26686	0.557352
$221$	−27.0333	−1.81846
$222$	−29.7524	−1.99685
$223$	8.20803	0.549650	0.274825	−	0.961494i	$-0.411380\pi$
$223$	8.20803	0.549650	0.274825	+	0.961494i	$0.411380\pi$
$224$	1.53992	0.102890
$225$	2.09022	0.139348
$226$	−7.99264	−0.531662
$227$	−6.40227	−0.424933	−0.212467	−	0.977168i	$-0.568150\pi$
$227$	−6.40227	−0.424933	−0.212467	+	0.977168i	$0.568150\pi$
$228$	−66.4933	−4.40363
$229$	−4.87963	−0.322455	−0.161228	−	0.986917i	$-0.551545\pi$
$229$	−4.87963	−0.322455	−0.161228	+	0.986917i	$0.551545\pi$
$230$	54.1016	3.56736
$231$	−0.493214	−0.0324511
$232$	−51.9054	−3.40776
$233$	−12.1245	−0.794303	−0.397151	−	0.917753i	$-0.630001\pi$
$233$	−12.1245	−0.794303	−0.397151	+	0.917753i	$0.630001\pi$
$234$	4.20397	0.274822
$235$	−10.0836	−0.657778
$236$	−26.2930	−1.71153
$237$	1.67793	0.108993
$238$	8.38571	0.543565
$239$	−4.61414	−0.298464	−0.149232	−	0.988802i	$-0.547680\pi$
$239$	−4.61414	−0.298464	−0.149232	+	0.988802i	$0.547680\pi$
$240$	34.8216	2.24772
$241$	−8.80630	−0.567263	−0.283632	−	0.958933i	$-0.591539\pi$
$241$	−8.80630	−0.567263	−0.283632	+	0.958933i	$0.591539\pi$
$242$	26.6993	1.71630
$243$	5.02300	0.322226
$244$	21.7278	1.39098
$245$	20.7861	1.32798
$246$	−42.5953	−2.71578
$247$	−28.1180	−1.78911
$248$	57.1333	3.62797
$249$	−15.8695	−1.00569
$250$	−5.49250	−0.347376
$251$	23.7635	1.49994	0.749970	−	0.661472i	$-0.230068\pi$
$251$	23.7635	1.49994	0.749970	+	0.661472i	$0.230068\pi$
$252$	−0.892336	−0.0562119
$253$	−4.41594	−0.277628
$254$	0.947308	0.0594394
$255$	44.9376	2.81410
$256$	−31.6031	−1.97520
$257$	−11.6179	−0.724705	−0.362353	−	0.932041i	$-0.618026\pi$
$257$	−11.6179	−0.724705	−0.362353	+	0.932041i	$0.618026\pi$
$258$	−5.48681	−0.341594
$259$	2.67053	0.165939
$260$	45.2110	2.80387
$261$	4.31036	0.266805
$262$	10.4236	0.643974
$263$	9.71188	0.598860	0.299430	−	0.954118i	$-0.403203\pi$
$263$	9.71188	0.598860	0.299430	+	0.954118i	$0.403203\pi$
$264$	−6.86880	−0.422746
$265$	−35.5934	−2.18649
$266$	8.72217	0.534791
$267$	15.2755	0.934843
$268$	12.5521	0.766740
$269$	6.09983	0.371913	0.185956	−	0.982558i	$-0.440462\pi$
$269$	6.09983	0.371913	0.185956	+	0.982558i	$0.440462\pi$
$270$	35.9779	2.18954
$271$	9.59737	0.582999	0.291499	−	0.956571i	$-0.405846\pi$
$271$	9.59737	0.582999	0.291499	+	0.956571i	$0.405846\pi$
$272$	48.3243	2.93009
$273$	−2.69736	−0.163252
$274$	25.3251	1.52995
$275$	−2.68139	−0.161694
$276$	−57.1109	−3.43767
$277$	−3.05396	−0.183495	−0.0917475	−	0.995782i	$-0.529245\pi$
$277$	−3.05396	−0.183495	−0.0917475	+	0.995782i	$0.529245\pi$
$278$	−58.5849	−3.51369
$279$	−4.74450	−0.284046
$280$	−7.55343	−0.451404
$281$	−14.2595	−0.850650	−0.425325	−	0.905041i	$-0.639840\pi$
$281$	−14.2595	−0.850650	−0.425325	+	0.905041i	$0.639840\pi$
$282$	15.5559	0.926338
$283$	6.62530	0.393833	0.196917	−	0.980420i	$-0.436907\pi$
$283$	6.62530	0.393833	0.196917	+	0.980420i	$0.436907\pi$
$284$	54.2638	3.21997
$285$	46.7407	2.76868
$286$	−5.39297	−0.318893
$287$	3.82329	0.225682
$288$	−1.78092	−0.104942
$289$	45.3630	2.66841
$290$	67.7438	3.97805
$291$	−6.10910	−0.358122
$292$	46.7667	2.73681
$293$	30.7371	1.79568	0.897841	−	0.440320i	$-0.145135\pi$
$293$	30.7371	1.79568	0.897841	+	0.440320i	$0.145135\pi$
$294$	−32.0667	−1.87017
$295$	18.4823	1.07608
$296$	37.1915	2.16171
$297$	−2.93662	−0.170400
$298$	−13.8160	−0.800339
$299$	−24.1505	−1.39666
$300$	−34.6782	−2.00215
$301$	0.492488	0.0283865
$302$	20.1814	1.16131
$303$	21.4381	1.23159
$304$	50.2632	2.88279
$305$	−15.2733	−0.874546
$306$	−9.69810	−0.554403
$307$	−30.6461	−1.74907	−0.874533	−	0.484966i	$-0.838832\pi$
$307$	−30.6461	−1.74907	−0.874533	+	0.484966i	$0.838832\pi$
$308$	1.14471	0.0652261
$309$	10.6155	0.603892
$310$	−74.5669	−4.23512
$311$	−19.5707	−1.10975	−0.554877	−	0.831932i	$-0.687235\pi$
$311$	−19.5707	−1.10975	−0.554877	+	0.831932i	$0.687235\pi$
$312$	−37.5651	−2.12670
$313$	4.20795	0.237848	0.118924	−	0.992903i	$-0.462056\pi$
$313$	4.20795	0.237848	0.118924	+	0.992903i	$0.462056\pi$
$314$	−24.4848	−1.38176
$315$	0.627257	0.0353419
$316$	−3.89435	−0.219074
$317$	−11.0157	−0.618701	−0.309350	−	0.950948i	$-0.600112\pi$
$317$	−11.0157	−0.618701	−0.309350	+	0.950948i	$0.600112\pi$
$318$	54.9098	3.07919
$319$	−5.52945	−0.309590
$320$	9.30032	0.519904
$321$	22.4872	1.25511
$322$	7.49146	0.417483
$323$	64.8652	3.60920
$324$	−44.3241	−2.46245
$325$	−14.6644	−0.813432
$326$	21.5045	1.19102
$327$	29.4612	1.62921
$328$	53.2455	2.93999
$329$	−1.39627	−0.0769789
$330$	8.96475	0.493493
$331$	27.6843	1.52167	0.760833	−	0.648948i	$-0.224791\pi$
$331$	27.6843	1.52167	0.760833	+	0.648948i	$0.224791\pi$
$332$	36.8320	2.02142
$333$	−3.08848	−0.169248
$334$	−17.6190	−0.964067
$335$	−8.82333	−0.482070
$336$	4.82175	0.263048
$337$	21.6127	1.17732	0.588660	−	0.808381i	$-0.299656\pi$
$337$	21.6127	1.17732	0.588660	+	0.808381i	$0.299656\pi$
$338$	3.22530	0.175433
$339$	−5.93084	−0.322119
$340$	−104.297	−5.65629
$341$	6.08637	0.329596
$342$	−10.0872	−0.545454
$343$	5.83162	0.314878
$344$	6.85869	0.369796
$345$	40.1455	2.16136
$346$	−12.9241	−0.694804
$347$	29.6079	1.58943	0.794717	−	0.606980i	$-0.207619\pi$
$347$	29.6079	1.58943	0.794717	+	0.606980i	$0.207619\pi$
$348$	−71.5119	−3.83344
$349$	9.96564	0.533449	0.266724	−	0.963773i	$-0.414059\pi$
$349$	9.96564	0.533449	0.266724	+	0.963773i	$0.414059\pi$
$350$	4.54887	0.243147
$351$	−16.0602	−0.857230
$352$	2.28461	0.121770
$353$	−13.1278	−0.698723	−0.349362	−	0.936988i	$-0.613602\pi$
$353$	−13.1278	−0.698723	−0.349362	+	0.936988i	$0.613602\pi$
$354$	−28.5126	−1.51543
$355$	−38.1441	−2.02448
$356$	−35.4532	−1.87901
$357$	6.22252	0.329330
$358$	−3.14554	−0.166247
$359$	−30.8915	−1.63039	−0.815195	−	0.579186i	$-0.803370\pi$
$359$	−30.8915	−1.63039	−0.815195	+	0.579186i	$0.803370\pi$
$360$	8.73556	0.460405
$361$	48.4678	2.55094
$362$	−26.9425	−1.41607
$363$	19.8119	1.03985
$364$	6.26037	0.328132
$365$	−32.8741	−1.72071
$366$	23.5620	1.23161
$367$	−5.79545	−0.302520	−0.151260	−	0.988494i	$-0.548333\pi$
$367$	−5.79545	−0.302520	−0.151260	+	0.988494i	$0.548333\pi$
$368$	43.1710	2.25044
$369$	−4.42164	−0.230182
$370$	−48.5400	−2.52348
$371$	−4.92862	−0.255881
$372$	78.7146	4.08116
$373$	−30.6891	−1.58902	−0.794512	−	0.607249i	$-0.792273\pi$
$373$	−30.6891	−1.58902	−0.794512	+	0.607249i	$0.792273\pi$
$374$	12.4410	0.643308
$375$	−4.07564	−0.210465
$376$	−19.4453	−1.00282
$377$	−30.2402	−1.55745
$378$	4.98186	0.256239
$379$	0.770433	0.0395745	0.0197873	−	0.999804i	$-0.493701\pi$
$379$	0.770433	0.0395745	0.0197873	+	0.999804i	$0.493701\pi$
$380$	−108.482	−5.56498
$381$	0.702938	0.0360126
$382$	−12.4067	−0.634779
$383$	−23.9926	−1.22597	−0.612984	−	0.790096i	$-0.710031\pi$
$383$	−23.9926	−1.22597	−0.612984	+	0.790096i	$0.710031\pi$
$384$	−27.9807	−1.42788
$385$	−0.804662	−0.0410094
$386$	−20.0889	−1.02250
$387$	−0.569564	−0.0289526
$388$	14.1787	0.719817
$389$	17.3394	0.879141	0.439571	−	0.898208i	$-0.355131\pi$
$389$	17.3394	0.879141	0.439571	+	0.898208i	$0.355131\pi$
$390$	49.0277	2.48261
$391$	55.7126	2.81751
$392$	40.0844	2.02457
$393$	7.73473	0.390166
$394$	21.4563	1.08095
$395$	2.73749	0.137738
$396$	−1.32386	−0.0665266
$397$	27.9041	1.40047	0.700233	−	0.713914i	$-0.253079\pi$
$397$	27.9041	1.40047	0.700233	+	0.713914i	$0.253079\pi$
$398$	−56.7879	−2.84652
$399$	6.47218	0.324014
$400$	26.2137	1.31069
$401$	8.31671	0.415317	0.207658	−	0.978201i	$-0.433416\pi$
$401$	8.31671	0.415317	0.207658	+	0.978201i	$0.433416\pi$
$402$	13.6117	0.678891
$403$	33.2860	1.65810
$404$	−49.7562	−2.47546
$405$	31.1571	1.54821
$406$	9.38049	0.465546
$407$	3.96198	0.196388
$408$	86.6586	4.29024
$409$	12.2841	0.607411	0.303705	−	0.952766i	$-0.401776\pi$
$409$	12.2841	0.607411	0.303705	+	0.952766i	$0.401776\pi$
$410$	−69.4927	−3.43200
$411$	18.7922	0.926951
$412$	−24.6377	−1.21381
$413$	2.55925	0.125932
$414$	−8.66389	−0.425807
$415$	−25.8906	−1.27092
$416$	12.4944	0.612589
$417$	−43.4722	−2.12884
$418$	12.9402	0.632924
$419$	−14.2080	−0.694105	−0.347053	−	0.937846i	$-0.612817\pi$
$419$	−14.2080	−0.694105	−0.347053	+	0.937846i	$0.612817\pi$
$420$	−10.4066	−0.507792
$421$	3.46179	0.168717	0.0843586	−	0.996435i	$-0.473116\pi$
$421$	3.46179	0.168717	0.0843586	+	0.996435i	$0.473116\pi$
$422$	60.0607	2.92371
$423$	1.61479	0.0785138
$424$	−68.6390	−3.33341
$425$	33.8291	1.64095
$426$	58.8448	2.85104
$427$	−2.11489	−0.102347
$428$	−52.1911	−2.52275
$429$	−4.00179	−0.193208
$430$	−8.95155	−0.431682
$431$	27.1709	1.30878	0.654388	−	0.756159i	$-0.272926\pi$
$431$	27.1709	1.30878	0.654388	+	0.756159i	$0.272926\pi$
$432$	28.7089	1.38126
$433$	−1.63696	−0.0786672	−0.0393336	−	0.999226i	$-0.512524\pi$
$433$	−1.63696	−0.0786672	−0.0393336	+	0.999226i	$0.512524\pi$
$434$	−10.3253	−0.495630
$435$	50.2685	2.41019
$436$	−68.3772	−3.27468
$437$	57.9479	2.77203
$438$	50.7148	2.42324
$439$	−3.27286	−0.156205	−0.0781026	−	0.996945i	$-0.524886\pi$
$439$	−3.27286	−0.156205	−0.0781026	+	0.996945i	$0.524886\pi$
$440$	−11.2062	−0.534235
$441$	−3.32871	−0.158510
$442$	68.0390	3.23629
$443$	15.4438	0.733756	0.366878	−	0.930269i	$-0.380427\pi$
$443$	15.4438	0.733756	0.366878	+	0.930269i	$0.380427\pi$
$444$	51.2400	2.43174
$445$	24.9214	1.18139
$446$	−20.6584	−0.978205
$447$	−10.2520	−0.484903
$448$	1.28782	0.0608436
$449$	19.9001	0.939145	0.469572	−	0.882894i	$-0.344408\pi$
$449$	19.9001	0.939145	0.469572	+	0.882894i	$0.344408\pi$
$450$	−5.26078	−0.247995
$451$	5.67221	0.267094
$452$	13.7650	0.647452
$453$	14.9754	0.703604
$454$	16.1136	0.756248
$455$	−4.40065	−0.206306
$456$	90.1356	4.22099
$457$	−15.1854	−0.710345	−0.355172	−	0.934801i	$-0.615578\pi$
$457$	−15.1854	−0.710345	−0.355172	+	0.934801i	$0.615578\pi$
$458$	12.2813	0.573869
$459$	37.0491	1.72931
$460$	−93.1745	−4.34428
$461$	−22.9396	−1.06841	−0.534203	−	0.845356i	$-0.679388\pi$
$461$	−22.9396	−1.06841	−0.534203	+	0.845356i	$0.679388\pi$
$462$	1.24135	0.0577528
$463$	1.90155	0.0883726	0.0441863	−	0.999023i	$-0.485930\pi$
$463$	1.90155	0.0883726	0.0441863	+	0.999023i	$0.485930\pi$
$464$	54.0569	2.50953
$465$	−55.3315	−2.56594
$466$	30.5156	1.41361
$467$	22.3592	1.03466	0.517330	−	0.855786i	$-0.326926\pi$
$467$	22.3592	1.03466	0.517330	+	0.855786i	$0.326926\pi$
$468$	−7.24013	−0.334675
$469$	−1.22177	−0.0564160
$470$	25.3788	1.17064
$471$	−18.1687	−0.837168
$472$	35.6417	1.64054
$473$	0.730652	0.0335954
$474$	−4.22311	−0.193974
$475$	35.1864	1.61446
$476$	−14.4420	−0.661947
$477$	5.69997	0.260984
$478$	11.6131	0.531172
$479$	−28.8129	−1.31649	−0.658247	−	0.752802i	$-0.728702\pi$
$479$	−28.8129	−1.31649	−0.658247	+	0.752802i	$0.728702\pi$
$480$	−20.7695	−0.947995
$481$	21.6679	0.987969
$482$	22.1642	1.00955
$483$	5.55894	0.252941
$484$	−45.9819	−2.09009
$485$	−9.96678	−0.452568
$486$	−12.6422	−0.573461
$487$	−25.4891	−1.15502	−0.577510	−	0.816383i	$-0.695976\pi$
$487$	−25.4891	−1.15502	−0.577510	+	0.816383i	$0.695976\pi$
$488$	−29.4533	−1.33329
$489$	15.9572	0.721608
$490$	−52.3157	−2.36338
$491$	−6.17984	−0.278892	−0.139446	−	0.990230i	$-0.544532\pi$
$491$	−6.17984	−0.278892	−0.139446	+	0.990230i	$0.544532\pi$
$492$	73.3582	3.30724
$493$	69.7609	3.14187
$494$	70.7690	3.18405
$495$	0.930594	0.0418271
$496$	−59.5014	−2.67169
$497$	−5.28182	−0.236922
$498$	39.9413	1.78981
$499$	−18.2921	−0.818866	−0.409433	−	0.912340i	$-0.634273\pi$
$499$	−18.2921	−0.818866	−0.409433	+	0.912340i	$0.634273\pi$
$500$	9.45925	0.423031
$501$	−13.0739	−0.584101
$502$	−59.8093	−2.66942
$503$	17.8505	0.795915	0.397958	−	0.917404i	$-0.369719\pi$
$503$	17.8505	0.795915	0.397958	+	0.917404i	$0.369719\pi$
$504$	1.20961	0.0538805
$505$	34.9755	1.55639
$506$	11.1143	0.494090
$507$	2.39330	0.106290
$508$	−1.63147	−0.0723846
$509$	11.4984	0.509657	0.254829	−	0.966986i	$-0.417981\pi$
$509$	11.4984	0.509657	0.254829	+	0.966986i	$0.417981\pi$
$510$	−113.102	−5.00822
$511$	−4.55208	−0.201372
$512$	49.5763	2.19098
$513$	38.5357	1.70139
$514$	29.2406	1.28975
$515$	17.3188	0.763155
$516$	9.44946	0.415989
$517$	−2.07150	−0.0911043
$518$	−6.72134	−0.295319
$519$	−9.59017	−0.420962
$520$	−61.2861	−2.68758
$521$	−40.1587	−1.75939	−0.879693	−	0.475543i	$-0.842252\pi$
$521$	−40.1587	−1.75939	−0.879693	+	0.475543i	$0.842252\pi$
$522$	−10.8486	−0.474829
$523$	34.1629	1.49384	0.746920	−	0.664914i	$-0.231532\pi$
$523$	34.1629	1.49384	0.746920	+	0.664914i	$0.231532\pi$
$524$	−17.9517	−0.784224
$525$	3.37543	0.147316
$526$	−24.4434	−1.06578
$527$	−76.7872	−3.34490
$528$	7.15351	0.311317
$529$	26.7714	1.16397
$530$	89.5835	3.89126
$531$	−2.95978	−0.128444
$532$	−15.0214	−0.651262
$533$	31.0210	1.34367
$534$	−38.4461	−1.66373
$535$	36.6871	1.58612
$536$	−17.0151	−0.734939
$537$	−2.33411	−0.100724
$538$	−15.3524	−0.661888
$539$	4.27016	0.183929
$540$	−61.9615	−2.66640
$541$	32.3019	1.38877	0.694383	−	0.719606i	$-0.255678\pi$
$541$	32.3019	1.38877	0.694383	+	0.719606i	$0.255678\pi$
$542$	−24.1552	−1.03755
$543$	−19.9924	−0.857955
$544$	−28.8233	−1.23579
$545$	48.0650	2.05888
$546$	6.78887	0.290537
$547$	−29.3555	−1.25515	−0.627575	−	0.778556i	$-0.715952\pi$
$547$	−29.3555	−1.25515	−0.627575	+	0.778556i	$0.715952\pi$
$548$	−43.6153	−1.86315
$549$	2.44588	0.104388
$550$	6.74867	0.287764
$551$	72.5600	3.09116
$552$	77.4173	3.29510
$553$	0.379060	0.0161193
$554$	7.68639	0.326563
$555$	−36.0186	−1.52890
$556$	100.896	4.27893
$557$	−21.4737	−0.909868	−0.454934	−	0.890525i	$-0.650337\pi$
$557$	−21.4737	−0.909868	−0.454934	+	0.890525i	$0.650337\pi$
$558$	11.9412	0.505512
$559$	3.99589	0.169008
$560$	7.86652	0.332421
$561$	9.23168	0.389762
$562$	35.8891	1.51389
$563$	−20.5242	−0.864992	−0.432496	−	0.901636i	$-0.642367\pi$
$563$	−20.5242	−0.864992	−0.432496	+	0.901636i	$0.642367\pi$
$564$	−26.7905	−1.12808
$565$	−9.67596	−0.407071
$566$	−16.6749	−0.700900
$567$	4.31432	0.181185
$568$	−73.5578	−3.08642
$569$	14.8410	0.622165	0.311083	−	0.950383i	$-0.399308\pi$
$569$	14.8410	0.622165	0.311083	+	0.950383i	$0.399308\pi$
$570$	−117.640	−4.92738
$571$	−24.9780	−1.04530	−0.522648	−	0.852549i	$-0.675056\pi$
$571$	−24.9780	−1.04530	−0.522648	+	0.852549i	$0.675056\pi$
$572$	9.28784	0.388344
$573$	−9.20621	−0.384595
$574$	−9.62267	−0.401642
$575$	30.2215	1.26032
$576$	−1.48936	−0.0620568
$577$	15.6073	0.649740	0.324870	−	0.945759i	$-0.394680\pi$
$577$	15.6073	0.649740	0.324870	+	0.945759i	$0.394680\pi$
$578$	−114.172	−4.74893
$579$	−14.9067	−0.619502
$580$	−116.669	−4.84443
$581$	−3.58507	−0.148734
$582$	15.3757	0.637344
$583$	−7.31207	−0.302835
$584$	−63.3950	−2.62331
$585$	5.08936	0.210419
$586$	−77.3609	−3.19575
$587$	38.5200	1.58989	0.794945	−	0.606681i	$-0.207499\pi$
$587$	38.5200	1.58989	0.794945	+	0.606681i	$0.207499\pi$
$588$	55.2257	2.27747
$589$	−79.8682	−3.29091
$590$	−46.5174	−1.91509
$591$	15.9214	0.654919
$592$	−38.7330	−1.59192
$593$	−21.2432	−0.872353	−0.436176	−	0.899861i	$-0.643668\pi$
$593$	−21.2432	−0.872353	−0.436176	+	0.899861i	$0.643668\pi$
$594$	7.39105	0.303258
$595$	10.1518	0.416184
$596$	23.7941	0.974644
$597$	−42.1388	−1.72463
$598$	60.7833	2.48561
$599$	4.24263	0.173349	0.0866746	−	0.996237i	$-0.472376\pi$
$599$	4.24263	0.173349	0.0866746	+	0.996237i	$0.472376\pi$
$600$	47.0083	1.91911
$601$	−20.2350	−0.825404	−0.412702	−	0.910866i	$-0.635415\pi$
$601$	−20.2350	−0.825404	−0.412702	+	0.910866i	$0.635415\pi$
$602$	−1.23952	−0.0505191
$603$	1.41298	0.0575409
$604$	−34.7567	−1.41423
$605$	32.3224	1.31409
$606$	−53.9566	−2.19184
$607$	0.896137	0.0363731	0.0181865	−	0.999835i	$-0.494211\pi$
$607$	0.896137	0.0363731	0.0181865	+	0.999835i	$0.494211\pi$
$608$	−29.9798	−1.21584
$609$	6.96068	0.282061
$610$	38.4407	1.55642
$611$	−11.3289	−0.458318
$612$	16.7022	0.675146
$613$	35.2242	1.42269	0.711346	−	0.702842i	$-0.248086\pi$
$613$	35.2242	1.42269	0.711346	+	0.702842i	$0.248086\pi$
$614$	77.1318	3.11279
$615$	−51.5663	−2.07935
$616$	−1.55173	−0.0625208
$617$	0.444864	0.0179096	0.00895478	−	0.999960i	$-0.497150\pi$
$617$	0.444864	0.0179096	0.00895478	+	0.999960i	$0.497150\pi$
$618$	−26.7176	−1.07474
$619$	0.838571	0.0337050	0.0168525	−	0.999858i	$-0.494635\pi$
$619$	0.838571	0.0337050	0.0168525	+	0.999858i	$0.494635\pi$
$620$	128.420	5.15748
$621$	33.0982	1.32819
$622$	49.2567	1.97501
$623$	3.45086	0.138256
$624$	39.1221	1.56614
$625$	−28.0681	−1.12273
$626$	−10.5908	−0.423294
$627$	9.60209	0.383470
$628$	42.1681	1.68269
$629$	−49.9854	−1.99305
$630$	−1.57871	−0.0628975
$631$	−14.0658	−0.559951	−0.279975	−	0.960007i	$-0.590326\pi$
$631$	−14.0658	−0.559951	−0.279975	+	0.960007i	$0.590326\pi$
$632$	5.27902	0.209988
$633$	44.5674	1.77139
$634$	27.7248	1.10109
$635$	1.14682	0.0455102
$636$	−94.5665	−3.74980
$637$	23.3533	0.925290
$638$	13.9168	0.550973
$639$	6.10844	0.241646
$640$	−45.6495	−1.80445
$641$	22.6468	0.894496	0.447248	−	0.894410i	$-0.352404\pi$
$641$	22.6468	0.894496	0.447248	+	0.894410i	$0.352404\pi$
$642$	−56.5970	−2.23371
$643$	−33.4321	−1.31843	−0.659217	−	0.751952i	$-0.729112\pi$
$643$	−33.4321	−1.31843	−0.659217	+	0.751952i	$0.729112\pi$
$644$	−12.9019	−0.508405
$645$	−6.64239	−0.261544
$646$	−163.256	−6.42323
$647$	5.78670	0.227498	0.113749	−	0.993509i	$-0.463714\pi$
$647$	5.78670	0.227498	0.113749	+	0.993509i	$0.463714\pi$
$648$	60.0839	2.36032
$649$	3.79689	0.149041
$650$	36.9081	1.44765
$651$	−7.66175	−0.300288
$652$	−37.0354	−1.45042
$653$	1.82953	0.0715952	0.0357976	−	0.999359i	$-0.488603\pi$
$653$	1.82953	0.0715952	0.0357976	+	0.999359i	$0.488603\pi$
$654$	−74.1496	−2.89948
$655$	12.6189	0.493063
$656$	−55.4525	−2.16505
$657$	5.26449	0.205387
$658$	3.51421	0.136998
$659$	16.2713	0.633840	0.316920	−	0.948452i	$-0.397351\pi$
$659$	16.2713	0.633840	0.316920	+	0.948452i	$0.397351\pi$
$660$	−15.4392	−0.600970
$661$	50.6801	1.97123	0.985614	−	0.169014i	$-0.0540583\pi$
$661$	50.6801	1.97123	0.985614	+	0.169014i	$0.0540583\pi$
$662$	−69.6773	−2.70809
$663$	50.4875	1.96077
$664$	−49.9279	−1.93758
$665$	10.5591	0.409466
$666$	7.77325	0.301207
$667$	62.3216	2.41310
$668$	30.3436	1.17403
$669$	−15.3293	−0.592666
$670$	22.2070	0.857933
$671$	−3.13764	−0.121127
$672$	−2.87596	−0.110942
$673$	−34.2687	−1.32096	−0.660481	−	0.750843i	$-0.729648\pi$
$673$	−34.2687	−1.32096	−0.660481	+	0.750843i	$0.729648\pi$
$674$	−54.3961	−2.09526
$675$	20.0975	0.773552
$676$	−5.55466	−0.213641
$677$	−1.02388	−0.0393509	−0.0196754	−	0.999806i	$-0.506263\pi$
$677$	−1.02388	−0.0393509	−0.0196754	+	0.999806i	$0.506263\pi$
$678$	14.9271	0.573271
$679$	−1.38010	−0.0529634
$680$	141.380	5.42169
$681$	11.9569	0.458189
$682$	−15.3185	−0.586577
$683$	15.6370	0.598332	0.299166	−	0.954201i	$-0.403292\pi$
$683$	15.6370	0.598332	0.299166	+	0.954201i	$0.403292\pi$
$684$	17.3723	0.664248
$685$	30.6588	1.17141
$686$	−14.6773	−0.560383
$687$	9.11321	0.347691
$688$	−7.14298	−0.272324
$689$	−39.9893	−1.52347
$690$	−101.040	−3.84654
$691$	−26.4333	−1.00557	−0.502785	−	0.864411i	$-0.667691\pi$
$691$	−26.4333	−1.00557	−0.502785	+	0.864411i	$0.667691\pi$
$692$	22.2580	0.846124
$693$	0.128859	0.00489496
$694$	−74.5188	−2.82869
$695$	−70.9234	−2.69028
$696$	96.9387	3.67445
$697$	−71.5620	−2.71060
$698$	−25.0821	−0.949371
$699$	22.6437	0.856465
$700$	−7.83412	−0.296102
$701$	35.4643	1.33947	0.669735	−	0.742600i	$-0.266408\pi$
$701$	35.4643	1.33947	0.669735	+	0.742600i	$0.266408\pi$
$702$	40.4212	1.52560
$703$	−51.9910	−1.96088
$704$	1.91059	0.0720082
$705$	18.8321	0.709257
$706$	33.0408	1.24351
$707$	4.84307	0.182142
$708$	49.1048	1.84547
$709$	13.2221	0.496566	0.248283	−	0.968687i	$-0.420134\pi$
$709$	13.2221	0.496566	0.248283	+	0.968687i	$0.420134\pi$
$710$	96.0032	3.60294
$711$	−0.438384	−0.0164407
$712$	48.0589	1.80108
$713$	−68.5986	−2.56904
$714$	−15.6612	−0.586105
$715$	−6.52878	−0.244162
$716$	5.41729	0.202454
$717$	8.61738	0.321822
$718$	77.7494	2.90158
$719$	36.1837	1.34943	0.674713	−	0.738080i	$-0.264268\pi$
$719$	36.1837	1.34943	0.674713	+	0.738080i	$0.264268\pi$
$720$	−9.09765	−0.339049
$721$	2.39813	0.0893110
$722$	−121.986	−4.53987
$723$	16.4467	0.611658
$724$	46.4007	1.72447
$725$	37.8421	1.40542
$726$	−49.8637	−1.85061
$727$	21.9825	0.815286	0.407643	−	0.913141i	$-0.366351\pi$
$727$	21.9825	0.815286	0.407643	+	0.913141i	$0.366351\pi$
$728$	−8.48630	−0.314523
$729$	21.2962	0.788749
$730$	82.7394	3.06232
$731$	−9.21809	−0.340943
$732$	−40.5789	−1.49984
$733$	19.8639	0.733689	0.366845	−	0.930282i	$-0.380438\pi$
$733$	19.8639	0.733689	0.366845	+	0.930282i	$0.380438\pi$
$734$	14.5863	0.538390
$735$	−38.8202	−1.43191
$736$	−25.7495	−0.949141
$737$	−1.81261	−0.0667682
$738$	11.1286	0.409651
$739$	−5.39886	−0.198600	−0.0993002	−	0.995058i	$-0.531660\pi$
$739$	−5.39886	−0.198600	−0.0993002	+	0.995058i	$0.531660\pi$
$740$	83.5963	3.07306
$741$	52.5133	1.92912
$742$	12.4046	0.455389
$743$	−14.4042	−0.528439	−0.264220	−	0.964463i	$-0.585114\pi$
$743$	−14.4042	−0.528439	−0.264220	+	0.964463i	$0.585114\pi$
$744$	−106.702	−3.91189
$745$	−16.7258	−0.612785
$746$	77.2401	2.82796
$747$	4.14615	0.151700
$748$	−21.4260	−0.783413
$749$	5.08006	0.185621
$750$	10.2578	0.374562
$751$	3.43080	0.125192	0.0625958	−	0.998039i	$-0.480062\pi$
$751$	3.43080	0.125192	0.0625958	+	0.998039i	$0.480062\pi$
$752$	20.2513	0.738489
$753$	−44.3808	−1.61733
$754$	76.1103	2.77177
$755$	24.4318	0.889164
$756$	−8.57982	−0.312045
$757$	−53.0727	−1.92896	−0.964479	−	0.264158i	$-0.914906\pi$
$757$	−53.0727	−1.92896	−0.964479	+	0.264158i	$0.914906\pi$
$758$	−1.93907	−0.0704302
$759$	8.24721	0.299355
$760$	147.053	5.33418
$761$	8.29150	0.300567	0.150283	−	0.988643i	$-0.451981\pi$
$761$	8.29150	0.300567	0.150283	+	0.988643i	$0.451981\pi$
$762$	−1.76919	−0.0640911
$763$	6.65556	0.240947
$764$	21.3669	0.773027
$765$	−11.7406	−0.424483
$766$	60.3860	2.18184
$767$	20.7650	0.749779
$768$	59.0221	2.12978
$769$	4.76233	0.171734	0.0858670	−	0.996307i	$-0.472634\pi$
$769$	4.76233	0.171734	0.0858670	+	0.996307i	$0.472634\pi$
$770$	2.02522	0.0729838
$771$	21.6976	0.781421
$772$	34.5974	1.24519
$773$	36.9428	1.32874	0.664369	−	0.747404i	$-0.268700\pi$
$773$	36.9428	1.32874	0.664369	+	0.747404i	$0.268700\pi$
$774$	1.43351	0.0515265
$775$	−41.6536	−1.49624
$776$	−19.2201	−0.689962
$777$	−4.98749	−0.178925
$778$	−43.6407	−1.56460
$779$	−74.4333	−2.66685
$780$	−84.4361	−3.02330
$781$	−7.83607	−0.280397
$782$	−140.220	−5.01427
$783$	41.4442	1.48109
$784$	−41.7458	−1.49092
$785$	−29.6416	−1.05795
$786$	−19.4672	−0.694372
$787$	31.1118	1.10902	0.554508	−	0.832178i	$-0.312906\pi$
$787$	31.1118	1.10902	0.554508	+	0.832178i	$0.312906\pi$
$788$	−36.9523	−1.31637
$789$	−18.1379	−0.645728
$790$	−6.88986	−0.245130
$791$	−1.33983	−0.0476389
$792$	1.79457	0.0637674
$793$	−17.1596	−0.609354
$794$	−70.2306	−2.49239
$795$	66.4744	2.35760
$796$	97.8010	3.46646
$797$	−0.208018	−0.00736837	−0.00368418	−	0.999993i	$-0.501173\pi$
$797$	−0.208018	−0.00736837	−0.00368418	+	0.999993i	$0.501173\pi$
$798$	−16.2896	−0.576644
$799$	26.1345	0.924573
$800$	−15.6353	−0.552792
$801$	−3.99093	−0.141013
$802$	−20.9320	−0.739133
$803$	−6.75343	−0.238324
$804$	−23.4423	−0.826745
$805$	9.06923	0.319648
$806$	−83.7761	−2.95089
$807$	−11.3920	−0.401019
$808$	67.4475	2.37279
$809$	33.6358	1.18257	0.591286	−	0.806462i	$-0.298621\pi$
$809$	33.6358	1.18257	0.591286	+	0.806462i	$0.298621\pi$
$810$	−78.4179	−2.75532
$811$	−34.6459	−1.21658	−0.608292	−	0.793713i	$-0.708145\pi$
$811$	−34.6459	−1.21658	−0.608292	+	0.793713i	$0.708145\pi$
$812$	−16.1552	−0.566936
$813$	−17.9241	−0.628624
$814$	−9.97174	−0.349509
$815$	26.0336	0.911916
$816$	−90.2505	−3.15940
$817$	−9.58795	−0.335440
$818$	−30.9174	−1.08100
$819$	0.704725	0.0246251
$820$	119.681	4.17945
$821$	−0.845559	−0.0295102	−0.0147551	−	0.999891i	$-0.504697\pi$
$821$	−0.845559	−0.0295102	−0.0147551	+	0.999891i	$0.504697\pi$
$822$	−47.2973	−1.64968
$823$	46.0151	1.60399	0.801994	−	0.597333i	$-0.203773\pi$
$823$	46.0151	1.60399	0.801994	+	0.597333i	$0.203773\pi$
$824$	33.3978	1.16347
$825$	5.00777	0.174348
$826$	−6.44126	−0.224120
$827$	−7.07276	−0.245944	−0.122972	−	0.992410i	$-0.539243\pi$
$827$	−7.07276	−0.245944	−0.122972	+	0.992410i	$0.539243\pi$
$828$	14.9211	0.518543
$829$	−8.42234	−0.292520	−0.146260	−	0.989246i	$-0.546724\pi$
$829$	−8.42234	−0.292520	−0.146260	+	0.989246i	$0.546724\pi$
$830$	65.1629	2.26184
$831$	5.70359	0.197855
$832$	10.4489	0.362252
$833$	−53.8734	−1.86660
$834$	109.413	3.78867
$835$	−21.3297	−0.738145
$836$	−22.2857	−0.770767
$837$	−45.6184	−1.57680
$838$	35.7594	1.23529
$839$	49.5685	1.71129	0.855647	−	0.517560i	$-0.173160\pi$
$839$	49.5685	1.71129	0.855647	+	0.517560i	$0.173160\pi$
$840$	14.1068	0.486731
$841$	49.0365	1.69091
$842$	−8.71282	−0.300264
$843$	26.6311	0.917223
$844$	−103.437	−3.56046
$845$	3.90458	0.134322
$846$	−4.06419	−0.139730
$847$	4.47569	0.153786
$848$	71.4841	2.45477
$849$	−12.3734	−0.424655
$850$	−85.1429	−2.92038
$851$	−44.6549	−1.53075
$852$	−101.343	−3.47196
$853$	0.428189	0.0146609	0.00733046	−	0.999973i	$-0.497667\pi$
$853$	0.428189	0.0146609	0.00733046	+	0.999973i	$0.497667\pi$
$854$	5.32288	0.182145
$855$	−12.2117	−0.417631
$856$	70.7481	2.41812
$857$	29.4590	1.00630	0.503150	−	0.864199i	$-0.332174\pi$
$857$	29.4590	1.00630	0.503150	+	0.864199i	$0.332174\pi$
$858$	10.0719	0.343850
$859$	−17.1675	−0.585749	−0.292874	−	0.956151i	$-0.594612\pi$
$859$	−17.1675	−0.585749	−0.292874	+	0.956151i	$0.594612\pi$
$860$	15.4165	0.525697
$861$	−7.14038	−0.243344
$862$	−68.3852	−2.32921
$863$	6.55695	0.223201	0.111601	−	0.993753i	$-0.464402\pi$
$863$	6.55695	0.223201	0.111601	+	0.993753i	$0.464402\pi$
$864$	−17.1236	−0.582556
$865$	−15.6460	−0.531981
$866$	4.11999	0.140003
$867$	−84.7200	−2.87724
$868$	17.7823	0.603572
$869$	0.562371	0.0190771
$870$	−126.518	−4.28938
$871$	−9.91303	−0.335890
$872$	92.6894	3.13886
$873$	1.59609	0.0540195
$874$	−145.847	−4.93333
$875$	−0.920725	−0.0311262
$876$	−87.3416	−2.95100
$877$	45.4608	1.53510	0.767551	−	0.640988i	$-0.221475\pi$
$877$	45.4608	1.53510	0.767551	+	0.640988i	$0.221475\pi$
$878$	8.23732	0.277996
$879$	−57.4047	−1.93621
$880$	11.6707	0.393420
$881$	16.4479	0.554144	0.277072	−	0.960849i	$-0.410636\pi$
$881$	16.4479	0.554144	0.277072	+	0.960849i	$0.410636\pi$
$882$	8.37789	0.282098
$883$	−30.5636	−1.02855	−0.514274	−	0.857626i	$-0.671939\pi$
$883$	−30.5636	−1.02855	−0.514274	+	0.857626i	$0.671939\pi$
$884$	−117.178	−3.94111
$885$	−34.5177	−1.16030
$886$	−38.8697	−1.30585
$887$	−38.6474	−1.29765	−0.648826	−	0.760937i	$-0.724740\pi$
$887$	−38.6474	−1.29765	−0.648826	+	0.760937i	$0.724740\pi$
$888$	−69.4589	−2.33089
$889$	0.158800	0.00532599
$890$	−62.7235	−2.10250
$891$	6.40070	0.214431
$892$	35.5782	1.19125
$893$	27.1831	0.909649
$894$	25.8028	0.862974
$895$	−3.80802	−0.127288
$896$	−6.32108	−0.211173
$897$	45.1035	1.50596
$898$	−50.0857	−1.67138
$899$	−85.8963	−2.86480
$900$	9.06018	0.302006
$901$	92.2510	3.07333
$902$	−14.2761	−0.475343
$903$	−0.919772	−0.0306081
$904$	−18.6593	−0.620599
$905$	−32.6169	−1.08422
$906$	−37.6908	−1.25219
$907$	45.7578	1.51936	0.759682	−	0.650295i	$-0.225355\pi$
$907$	45.7578	1.51936	0.759682	+	0.650295i	$0.225355\pi$
$908$	−27.7510	−0.920950
$909$	−5.60102	−0.185774
$910$	11.0758	0.367159
$911$	−15.6700	−0.519172	−0.259586	−	0.965720i	$-0.583586\pi$
$911$	−15.6700	−0.519172	−0.259586	+	0.965720i	$0.583586\pi$
$912$	−93.8717	−3.10840
$913$	−5.31879	−0.176026
$914$	38.2196	1.26419
$915$	28.5244	0.942988
$916$	−21.1511	−0.698851
$917$	1.74735	0.0577025
$918$	−93.2473	−3.07762
$919$	6.57944	0.217036	0.108518	−	0.994095i	$-0.465390\pi$
$919$	6.57944	0.217036	0.108518	+	0.994095i	$0.465390\pi$
$920$	126.304	4.16411
$921$	57.2348	1.88595
$922$	57.7358	1.90143
$923$	−42.8550	−1.41059
$924$	−2.13787	−0.0703307
$925$	−27.1148	−0.891529
$926$	−4.78593	−0.157275
$927$	−2.77344	−0.0910918
$928$	−32.2425	−1.05841
$929$	−48.1614	−1.58012	−0.790062	−	0.613027i	$-0.789952\pi$
$929$	−48.1614	−1.58012	−0.790062	+	0.613027i	$0.789952\pi$
$930$	139.261	4.56656
$931$	−56.0350	−1.83647
$932$	−52.5544	−1.72148
$933$	36.5503	1.19660
$934$	−56.2748	−1.84137
$935$	15.0612	0.492553
$936$	9.81443	0.320795
$937$	−10.5352	−0.344170	−0.172085	−	0.985082i	$-0.555050\pi$
$937$	−10.5352	−0.344170	−0.172085	+	0.985082i	$0.555050\pi$
$938$	3.07501	0.100403
$939$	−7.85878	−0.256462
$940$	−43.7078	−1.42559
$941$	44.5616	1.45267	0.726333	−	0.687343i	$-0.241223\pi$
$941$	44.5616	1.45267	0.726333	+	0.687343i	$0.241223\pi$
$942$	45.7279	1.48990
$943$	−63.9306	−2.08187
$944$	−37.1190	−1.20812
$945$	6.03108	0.196191
$946$	−1.83895	−0.0597893
$947$	−35.0070	−1.13757	−0.568787	−	0.822485i	$-0.692587\pi$
$947$	−35.0070	−1.13757	−0.568787	+	0.822485i	$0.692587\pi$
$948$	7.27310	0.236219
$949$	−36.9341	−1.19893
$950$	−88.5591	−2.87324
$951$	20.5729	0.667121
$952$	19.5770	0.634493
$953$	45.0703	1.45997	0.729985	−	0.683464i	$-0.239527\pi$
$953$	45.0703	1.45997	0.729985	+	0.683464i	$0.239527\pi$
$954$	−14.3460	−0.464469
$955$	−15.0196	−0.486023
$956$	−20.0003	−0.646856
$957$	10.3268	0.333819
$958$	72.5178	2.34294
$959$	4.24533	0.137089
$960$	−17.3693	−0.560592
$961$	63.5477	2.04993
$962$	−54.5349	−1.75827
$963$	−5.87511	−0.189323
$964$	−38.1714	−1.22942
$965$	−24.3198	−0.782882
$966$	−13.9911	−0.450155
$967$	48.4112	1.55680	0.778400	−	0.627768i	$-0.216031\pi$
$967$	48.4112	1.55680	0.778400	+	0.627768i	$0.216031\pi$
$968$	62.3312	2.00340
$969$	−121.142	−3.89165
$970$	25.0849	0.805429
$971$	−32.8024	−1.05268	−0.526339	−	0.850275i	$-0.676436\pi$
$971$	−32.8024	−1.05268	−0.526339	+	0.850275i	$0.676436\pi$
$972$	21.7725	0.698354
$973$	−9.82077	−0.314839
$974$	64.1524	2.05557
$975$	27.3872	0.877092
$976$	30.6741	0.981855
$977$	5.16110	0.165118	0.0825592	−	0.996586i	$-0.473691\pi$
$977$	5.16110	0.165118	0.0825592	+	0.996586i	$0.473691\pi$
$978$	−40.1619	−1.28424
$979$	5.11968	0.163626
$980$	90.0988	2.87810
$981$	−7.69717	−0.245752
$982$	15.5538	0.496341
$983$	−13.9145	−0.443804	−0.221902	−	0.975069i	$-0.571227\pi$
$983$	−13.9145	−0.443804	−0.221902	+	0.975069i	$0.571227\pi$
$984$	−99.4413	−3.17007
$985$	25.9752	0.827639
$986$	−175.578	−5.59155
$987$	2.60768	0.0830033
$988$	−121.879	−3.87750
$989$	−8.23507	−0.261860
$990$	−2.34217	−0.0744391
$991$	−45.2288	−1.43674	−0.718370	−	0.695661i	$-0.755111\pi$
$991$	−45.2288	−1.43674	−0.718370	+	0.695661i	$0.755111\pi$
$992$	35.4899	1.12681
$993$	−51.7032	−1.64075
$994$	13.2936	0.421647
$995$	−68.7480	−2.17946
$996$	−68.7875	−2.17961
$997$	31.0000	0.981781	0.490891	−	0.871221i	$-0.336671\pi$
$997$	31.0000	0.981781	0.490891	+	0.871221i	$0.336671\pi$
$998$	46.0385	1.45732
$999$	−29.6957	−0.939532

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4027.2.a.c.1.10	✓	174

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4027.2.a.c.1.10	✓	174	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 4027 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4027.a (trivial)

\(f(q)\)	\(=\)	\(q-2.51686 q^{2} -1.86760 q^{3} +4.33456 q^{4} -3.04693 q^{5} +4.70049 q^{6} -0.421908 q^{7} -5.87575 q^{8} +0.487938 q^{9} +O(q^{10})\)	\(q-2.51686 q^{2} -1.86760 q^{3} +4.33456 q^{4} -3.04693 q^{5} +4.70049 q^{6} -0.421908 q^{7} -5.87575 q^{8} +0.487938 q^{9} +7.66868 q^{10} -0.625941 q^{11} -8.09524 q^{12} -3.42323 q^{13} +1.06188 q^{14} +5.69045 q^{15} +6.11930 q^{16} +7.89702 q^{17} -1.22807 q^{18} +8.21388 q^{19} -13.2071 q^{20} +0.787957 q^{21} +1.57540 q^{22} +7.05488 q^{23} +10.9736 q^{24} +4.28378 q^{25} +8.61578 q^{26} +4.69153 q^{27} -1.82879 q^{28} +8.83383 q^{29} -14.3220 q^{30} -9.72357 q^{31} -3.64989 q^{32} +1.16901 q^{33} -19.8757 q^{34} +1.28552 q^{35} +2.11500 q^{36} -6.32965 q^{37} -20.6731 q^{38} +6.39324 q^{39} +17.9030 q^{40} -9.06189 q^{41} -1.98317 q^{42} -1.16729 q^{43} -2.71318 q^{44} -1.48671 q^{45} -17.7561 q^{46} +3.30942 q^{47} -11.4284 q^{48} -6.82199 q^{49} -10.7816 q^{50} -14.7485 q^{51} -14.8382 q^{52} +11.6817 q^{53} -11.8079 q^{54} +1.90720 q^{55} +2.47903 q^{56} -15.3403 q^{57} -22.2335 q^{58} -6.06589 q^{59} +24.6656 q^{60} +5.01268 q^{61} +24.4728 q^{62} -0.205865 q^{63} -3.05236 q^{64} +10.4303 q^{65} -2.94222 q^{66} +2.89581 q^{67} +34.2301 q^{68} -13.1757 q^{69} -3.23548 q^{70} +12.5189 q^{71} -2.86701 q^{72} +10.7893 q^{73} +15.9308 q^{74} -8.00039 q^{75} +35.6036 q^{76} +0.264090 q^{77} -16.0909 q^{78} -0.898442 q^{79} -18.6451 q^{80} -10.2257 q^{81} +22.8075 q^{82} +8.49727 q^{83} +3.41545 q^{84} -24.0617 q^{85} +2.93789 q^{86} -16.4981 q^{87} +3.67787 q^{88} -8.17918 q^{89} +3.74184 q^{90} +1.44429 q^{91} +30.5798 q^{92} +18.1598 q^{93} -8.32932 q^{94} -25.0271 q^{95} +6.81654 q^{96} +3.27109 q^{97} +17.1700 q^{98} -0.305420 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9}+O(q^{10}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9	\( 174 q + 21 q^{2} + 17 q^{3} + 187 q^{4} + 72 q^{5} + 21 q^{6} + 24 q^{7} + 54 q^{8} + 197 q^{9} + 20 q^{10} + 35 q^{11} + 23 q^{12} + 91 q^{13} + 18 q^{14} + 16 q^{15} + 201 q^{16} + 148 q^{17} + 39 q^{18} + 36 q^{19} + 128 q^{20} + 57 q^{21} + 17 q^{22} + 96 q^{23} + 24 q^{24} + 226 q^{25} + 44 q^{26} + 62 q^{27} + 32 q^{28} + 122 q^{29} + 25 q^{30} + 23 q^{31} + 104 q^{32} + 91 q^{33} + 6 q^{34} + 80 q^{35} + 222 q^{36} + 71 q^{37} + 125 q^{38} + 16 q^{39} + 53 q^{40} + 97 q^{41} + 14 q^{42} + 38 q^{43} + 70 q^{44} + 185 q^{45} - 23 q^{46} + 110 q^{47} + 36 q^{48} + 210 q^{49} + 51 q^{50} + 33 q^{51} + 118 q^{52} + 214 q^{53} + 8 q^{54} + 37 q^{55} + 41 q^{56} + 76 q^{57} + 2 q^{58} + 66 q^{59} - 12 q^{60} + 114 q^{61} + 175 q^{62} + 62 q^{63} + 190 q^{64} + 128 q^{65} + 12 q^{66} - 6 q^{67} + 348 q^{68} + 115 q^{69} - 38 q^{70} + 54 q^{71} + 101 q^{72} + 107 q^{73} + 71 q^{74} - q^{75} + 31 q^{76} + 368 q^{77} - 14 q^{78} - 14 q^{79} + 205 q^{80} + 222 q^{81} + 26 q^{82} + 246 q^{83} + 41 q^{84} + 87 q^{85} + 33 q^{86} + 100 q^{87} - 6 q^{88} + 147 q^{89} + 50 q^{90} - 23 q^{91} + 189 q^{92} + 117 q^{93} + 23 q^{94} + 42 q^{95} + 38 q^{96} + 52 q^{97} + 148 q^{98} + 38 q^{99}+O(q^{100}) \) 174 * q + 21 * q^2 + 17 * q^3 + 187 * q^4 + 72 * q^5 + 21 * q^6 + 24 * q^7 + 54 * q^8 + 197 * q^9 + 20 * q^10 + 35 * q^11 + 23 * q^12 + 91 * q^13 + 18 * q^14 + 16 * q^15 + 201 * q^16 + 148 * q^17 + 39 * q^18 + 36 * q^19 + 128 * q^20 + 57 * q^21 + 17 * q^22 + 96 * q^23 + 24 * q^24 + 226 * q^25 + 44 * q^26 + 62 * q^27 + 32 * q^28 + 122 * q^29 + 25 * q^30 + 23 * q^31 + 104 * q^32 + 91 * q^33 + 6 * q^34 + 80 * q^35 + 222 * q^36 + 71 * q^37 + 125 * q^38 + 16 * q^39 + 53 * q^40 + 97 * q^41 + 14 * q^42 + 38 * q^43 + 70 * q^44 + 185 * q^45 - 23 * q^46 + 110 * q^47 + 36 * q^48 + 210 * q^49 + 51 * q^50 + 33 * q^51 + 118 * q^52 + 214 * q^53 + 8 * q^54 + 37 * q^55 + 41 * q^56 + 76 * q^57 + 2 * q^58 + 66 * q^59 - 12 * q^60 + 114 * q^61 + 175 * q^62 + 62 * q^63 + 190 * q^64 + 128 * q^65 + 12 * q^66 - 6 * q^67 + 348 * q^68 + 115 * q^69 - 38 * q^70 + 54 * q^71 + 101 * q^72 + 107 * q^73 + 71 * q^74 - q^75 + 31 * q^76 + 368 * q^77 - 14 * q^78 - 14 * q^79 + 205 * q^80 + 222 * q^81 + 26 * q^82 + 246 * q^83 + 41 * q^84 + 87 * q^85 + 33 * q^86 + 100 * q^87 - 6 * q^88 + 147 * q^89 + 50 * q^90 - 23 * q^91 + 189 * q^92 + 117 * q^93 + 23 * q^94 + 42 * q^95 + 38 * q^96 + 52 * q^97 + 148 * q^98 + 38 * q^99

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