LMFDB - Embedded newform 4034.2.a.d.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4034,2,Mod(1,4034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4034, 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("4034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4034 = 2 \cdot 2017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4034.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:	$32.2116521754$
Analytic rank:	$0$
Dimension:	$52$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Character	$\chi$	$=$	4034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} -2.86609 q^{3} +1.00000 q^{4} +4.19184 q^{5} -2.86609 q^{6} -2.33387 q^{7} +1.00000 q^{8} +5.21449 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -2.86609 q^{3} +1.00000 q^{4} +4.19184 q^{5} -2.86609 q^{6} -2.33387 q^{7} +1.00000 q^{8} +5.21449 q^{9} +4.19184 q^{10} -0.675015 q^{11} -2.86609 q^{12} -1.98527 q^{13} -2.33387 q^{14} -12.0142 q^{15} +1.00000 q^{16} -6.70776 q^{17} +5.21449 q^{18} -4.86703 q^{19} +4.19184 q^{20} +6.68908 q^{21} -0.675015 q^{22} +2.94081 q^{23} -2.86609 q^{24} +12.5715 q^{25} -1.98527 q^{26} -6.34693 q^{27} -2.33387 q^{28} +4.30484 q^{29} -12.0142 q^{30} +4.10790 q^{31} +1.00000 q^{32} +1.93466 q^{33} -6.70776 q^{34} -9.78321 q^{35} +5.21449 q^{36} +2.03177 q^{37} -4.86703 q^{38} +5.68997 q^{39} +4.19184 q^{40} +10.3862 q^{41} +6.68908 q^{42} -0.266265 q^{43} -0.675015 q^{44} +21.8583 q^{45} +2.94081 q^{46} +4.61312 q^{47} -2.86609 q^{48} -1.55306 q^{49} +12.5715 q^{50} +19.2251 q^{51} -1.98527 q^{52} +4.75749 q^{53} -6.34693 q^{54} -2.82956 q^{55} -2.33387 q^{56} +13.9494 q^{57} +4.30484 q^{58} +3.51797 q^{59} -12.0142 q^{60} +7.78117 q^{61} +4.10790 q^{62} -12.1699 q^{63} +1.00000 q^{64} -8.32194 q^{65} +1.93466 q^{66} +4.54817 q^{67} -6.70776 q^{68} -8.42865 q^{69} -9.78321 q^{70} -5.83849 q^{71} +5.21449 q^{72} +14.6370 q^{73} +2.03177 q^{74} -36.0312 q^{75} -4.86703 q^{76} +1.57540 q^{77} +5.68997 q^{78} -12.7319 q^{79} +4.19184 q^{80} +2.54743 q^{81} +10.3862 q^{82} +5.69532 q^{83} +6.68908 q^{84} -28.1179 q^{85} -0.266265 q^{86} -12.3381 q^{87} -0.675015 q^{88} +4.51471 q^{89} +21.8583 q^{90} +4.63336 q^{91} +2.94081 q^{92} -11.7736 q^{93} +4.61312 q^{94} -20.4018 q^{95} -2.86609 q^{96} -2.04866 q^{97} -1.55306 q^{98} -3.51986 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) $ 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−2.86609	−1.65474	−0.827370	−	0.561658i	$-0.810164\pi$
$3$	−2.86609	−1.65474	−0.827370	+	0.561658i	$0.810164\pi$
$4$	1.00000	0.500000
$5$	4.19184	1.87465	0.937324	−	0.348458i	$-0.113295\pi$
$5$	4.19184	1.87465	0.937324	+	0.348458i	$0.113295\pi$
$6$	−2.86609	−1.17008
$7$	−2.33387	−0.882119	−0.441060	−	0.897478i	$-0.645397\pi$
$7$	−2.33387	−0.882119	−0.441060	+	0.897478i	$0.645397\pi$
$8$	1.00000	0.353553
$9$	5.21449	1.73816
$10$	4.19184	1.32558
$11$	−0.675015	−0.203525	−0.101762	−	0.994809i	$-0.532448\pi$
$11$	−0.675015	−0.203525	−0.101762	+	0.994809i	$0.532448\pi$
$12$	−2.86609	−0.827370
$13$	−1.98527	−0.550615	−0.275307	−	0.961356i	$-0.588780\pi$
$13$	−1.98527	−0.550615	−0.275307	+	0.961356i	$0.588780\pi$
$14$	−2.33387	−0.623752
$15$	−12.0142	−3.10206
$16$	1.00000	0.250000
$17$	−6.70776	−1.62687	−0.813435	−	0.581656i	$-0.802405\pi$
$17$	−6.70776	−1.62687	−0.813435	+	0.581656i	$0.802405\pi$
$18$	5.21449	1.22907
$19$	−4.86703	−1.11657	−0.558286	−	0.829648i	$-0.688541\pi$
$19$	−4.86703	−1.11657	−0.558286	+	0.829648i	$0.688541\pi$
$20$	4.19184	0.937324
$21$	6.68908	1.45968
$22$	−0.675015	−0.143914
$23$	2.94081	0.613202	0.306601	−	0.951838i	$-0.400808\pi$
$23$	2.94081	0.613202	0.306601	+	0.951838i	$0.400808\pi$
$24$	−2.86609	−0.585039
$25$	12.5715	2.51431
$26$	−1.98527	−0.389343
$27$	−6.34693	−1.22147
$28$	−2.33387	−0.441060
$29$	4.30484	0.799389	0.399695	−	0.916648i	$-0.369116\pi$
$29$	4.30484	0.799389	0.399695	+	0.916648i	$0.369116\pi$
$30$	−12.0142	−2.19348
$31$	4.10790	0.737801	0.368900	−	0.929469i	$-0.379734\pi$
$31$	4.10790	0.737801	0.368900	+	0.929469i	$0.379734\pi$
$32$	1.00000	0.176777
$33$	1.93466	0.336781
$34$	−6.70776	−1.15037
$35$	−9.78321	−1.65366
$36$	5.21449	0.869082
$37$	2.03177	0.334021	0.167011	−	0.985955i	$-0.446589\pi$
$37$	2.03177	0.334021	0.167011	+	0.985955i	$0.446589\pi$
$38$	−4.86703	−0.789536
$39$	5.68997	0.911124
$40$	4.19184	0.662788
$41$	10.3862	1.62205	0.811026	−	0.585010i	$-0.198909\pi$
$41$	10.3862	1.62205	0.811026	+	0.585010i	$0.198909\pi$
$42$	6.68908	1.03215
$43$	−0.266265	−0.0406051	−0.0203025	−	0.999794i	$-0.506463\pi$
$43$	−0.266265	−0.0406051	−0.0203025	+	0.999794i	$0.506463\pi$
$44$	−0.675015	−0.101762
$45$	21.8583	3.25845
$46$	2.94081	0.433599
$47$	4.61312	0.672892	0.336446	−	0.941703i	$-0.390775\pi$
$47$	4.61312	0.672892	0.336446	+	0.941703i	$0.390775\pi$
$48$	−2.86609	−0.413685
$49$	−1.55306	−0.221866
$50$	12.5715	1.77788
$51$	19.2251	2.69205
$52$	−1.98527	−0.275307
$53$	4.75749	0.653491	0.326746	−	0.945112i	$-0.394048\pi$
$53$	4.75749	0.653491	0.326746	+	0.945112i	$0.394048\pi$
$54$	−6.34693	−0.863708
$55$	−2.82956	−0.381537
$56$	−2.33387	−0.311876
$57$	13.9494	1.84764
$58$	4.30484	0.565254
$59$	3.51797	0.458001	0.229001	−	0.973426i	$-0.426454\pi$
$59$	3.51797	0.458001	0.229001	+	0.973426i	$0.426454\pi$
$60$	−12.0142	−1.55103
$61$	7.78117	0.996277	0.498138	−	0.867098i	$-0.334017\pi$
$61$	7.78117	0.996277	0.498138	+	0.867098i	$0.334017\pi$
$62$	4.10790	0.521704
$63$	−12.1699	−1.53327
$64$	1.00000	0.125000
$65$	−8.32194	−1.03221
$66$	1.93466	0.238140
$67$	4.54817	0.555647	0.277824	−	0.960632i	$-0.410387\pi$
$67$	4.54817	0.555647	0.277824	+	0.960632i	$0.410387\pi$
$68$	−6.70776	−0.813435
$69$	−8.42865	−1.01469
$70$	−9.78321	−1.16932
$71$	−5.83849	−0.692902	−0.346451	−	0.938068i	$-0.612613\pi$
$71$	−5.83849	−0.692902	−0.346451	+	0.938068i	$0.612613\pi$
$72$	5.21449	0.614534
$73$	14.6370	1.71313	0.856565	−	0.516040i	$-0.172594\pi$
$73$	14.6370	1.71313	0.856565	+	0.516040i	$0.172594\pi$
$74$	2.03177	0.236189
$75$	−36.0312	−4.16052
$76$	−4.86703	−0.558286
$77$	1.57540	0.179533
$78$	5.68997	0.644262
$79$	−12.7319	−1.43245	−0.716225	−	0.697869i	$-0.754132\pi$
$79$	−12.7319	−1.43245	−0.716225	+	0.697869i	$0.754132\pi$
$80$	4.19184	0.468662
$81$	2.54743	0.283048
$82$	10.3862	1.14696
$83$	5.69532	0.625142	0.312571	−	0.949894i	$-0.398810\pi$
$83$	5.69532	0.625142	0.312571	+	0.949894i	$0.398810\pi$
$84$	6.68908	0.729839
$85$	−28.1179	−3.04981
$86$	−0.266265	−0.0287121
$87$	−12.3381	−1.32278
$88$	−0.675015	−0.0719569
$89$	4.51471	0.478558	0.239279	−	0.970951i	$-0.423089\pi$
$89$	4.51471	0.478558	0.239279	+	0.970951i	$0.423089\pi$
$90$	21.8583	2.30407
$91$	4.63336	0.485708
$92$	2.94081	0.306601
$93$	−11.7736	−1.22087
$94$	4.61312	0.475807
$95$	−20.4018	−2.09318
$96$	−2.86609	−0.292519
$97$	−2.04866	−0.208010	−0.104005	−	0.994577i	$-0.533166\pi$
$97$	−2.04866	−0.208010	−0.104005	+	0.994577i	$0.533166\pi$
$98$	−1.55306	−0.156883
$99$	−3.51986	−0.353759
$100$	12.5715	1.25715
$101$	−6.24503	−0.621404	−0.310702	−	0.950507i	$-0.600564\pi$
$101$	−6.24503	−0.621404	−0.310702	+	0.950507i	$0.600564\pi$
$102$	19.2251	1.90356
$103$	5.35319	0.527465	0.263733	−	0.964596i	$-0.415046\pi$
$103$	5.35319	0.527465	0.263733	+	0.964596i	$0.415046\pi$
$104$	−1.98527	−0.194672
$105$	28.0396	2.73638
$106$	4.75749	0.462088
$107$	−11.8267	−1.14333	−0.571665	−	0.820487i	$-0.693702\pi$
$107$	−11.8267	−1.14333	−0.571665	+	0.820487i	$0.693702\pi$
$108$	−6.34693	−0.610734
$109$	7.93604	0.760135	0.380067	−	0.924959i	$-0.375901\pi$
$109$	7.93604	0.760135	0.380067	+	0.924959i	$0.375901\pi$
$110$	−2.82956	−0.269788
$111$	−5.82325	−0.552718
$112$	−2.33387	−0.220530
$113$	0.577304	0.0543082	0.0271541	−	0.999631i	$-0.491356\pi$
$113$	0.577304	0.0543082	0.0271541	+	0.999631i	$0.491356\pi$
$114$	13.9494	1.30648
$115$	12.3274	1.14954
$116$	4.30484	0.399695
$117$	−10.3522	−0.957058
$118$	3.51797	0.323856
$119$	15.6550	1.43509
$120$	−12.0142	−1.09674
$121$	−10.5444	−0.958578
$122$	7.78117	0.704474
$123$	−29.7678	−2.68408
$124$	4.10790	0.368900
$125$	31.7387	2.83879
$126$	−12.1699	−1.08418
$127$	6.21845	0.551798	0.275899	−	0.961187i	$-0.411024\pi$
$127$	6.21845	0.551798	0.275899	+	0.961187i	$0.411024\pi$
$128$	1.00000	0.0883883
$129$	0.763141	0.0671908
$130$	−8.32194	−0.729882
$131$	21.7917	1.90395	0.951973	−	0.306182i	$-0.0990515\pi$
$131$	21.7917	1.90395	0.951973	+	0.306182i	$0.0990515\pi$
$132$	1.93466	0.168390
$133$	11.3590	0.984950
$134$	4.54817	0.392902
$135$	−26.6053	−2.28982
$136$	−6.70776	−0.575186
$137$	15.5640	1.32972	0.664860	−	0.746968i	$-0.268491\pi$
$137$	15.5640	1.32972	0.664860	+	0.746968i	$0.268491\pi$
$138$	−8.42865	−0.717494
$139$	11.2750	0.956331	0.478166	−	0.878270i	$-0.341302\pi$
$139$	11.2750	0.956331	0.478166	+	0.878270i	$0.341302\pi$
$140$	−9.78321	−0.826832
$141$	−13.2216	−1.11346
$142$	−5.83849	−0.489956
$143$	1.34009	0.112064
$144$	5.21449	0.434541
$145$	18.0452	1.49857
$146$	14.6370	1.21137
$147$	4.45121	0.367130
$148$	2.03177	0.167011
$149$	2.17011	0.177782	0.0888911	−	0.996041i	$-0.471668\pi$
$149$	2.17011	0.177782	0.0888911	+	0.996041i	$0.471668\pi$
$150$	−36.0312	−2.94193
$151$	12.5121	1.01822	0.509112	−	0.860700i	$-0.329974\pi$
$151$	12.5121	1.01822	0.509112	+	0.860700i	$0.329974\pi$
$152$	−4.86703	−0.394768
$153$	−34.9775	−2.82777
$154$	1.57540	0.126949
$155$	17.2197	1.38312
$156$	5.68997	0.455562
$157$	15.5108	1.23790	0.618948	−	0.785432i	$-0.287559\pi$
$157$	15.5108	1.23790	0.618948	+	0.785432i	$0.287559\pi$
$158$	−12.7319	−1.01290
$159$	−13.6354	−1.08136
$160$	4.19184	0.331394
$161$	−6.86347	−0.540917
$162$	2.54743	0.200145
$163$	−23.3727	−1.83069	−0.915345	−	0.402671i	$-0.868082\pi$
$163$	−23.3727	−1.83069	−0.915345	+	0.402671i	$0.868082\pi$
$164$	10.3862	0.811026
$165$	8.10978	0.631345
$166$	5.69532	0.442042
$167$	3.09247	0.239302	0.119651	−	0.992816i	$-0.461822\pi$
$167$	3.09247	0.239302	0.119651	+	0.992816i	$0.461822\pi$
$168$	6.68908	0.516074
$169$	−9.05870	−0.696823
$170$	−28.1179	−2.15654
$171$	−25.3791	−1.94079
$172$	−0.266265	−0.0203025
$173$	−10.2048	−0.775858	−0.387929	−	0.921689i	$-0.626809\pi$
$173$	−10.2048	−0.775858	−0.387929	+	0.921689i	$0.626809\pi$
$174$	−12.3381	−0.935347
$175$	−29.3403	−2.21792
$176$	−0.675015	−0.0508812
$177$	−10.0828	−0.757873
$178$	4.51471	0.338392
$179$	6.40496	0.478729	0.239365	−	0.970930i	$-0.423061\pi$
$179$	6.40496	0.478729	0.239365	+	0.970930i	$0.423061\pi$
$180$	21.8583	1.62922
$181$	10.7629	0.800001	0.400000	−	0.916515i	$-0.369010\pi$
$181$	10.7629	0.800001	0.400000	+	0.916515i	$0.369010\pi$
$182$	4.63336	0.343447
$183$	−22.3016	−1.64858
$184$	2.94081	0.216800
$185$	8.51687	0.626173
$186$	−11.7736	−0.863284
$187$	4.52784	0.331108
$188$	4.61312	0.336446
$189$	14.8129	1.07748
$190$	−20.4018	−1.48010
$191$	−6.65398	−0.481465	−0.240732	−	0.970592i	$-0.577388\pi$
$191$	−6.65398	−0.481465	−0.240732	+	0.970592i	$0.577388\pi$
$192$	−2.86609	−0.206842
$193$	−12.7410	−0.917116	−0.458558	−	0.888664i	$-0.651634\pi$
$193$	−12.7410	−0.917116	−0.458558	+	0.888664i	$0.651634\pi$
$194$	−2.04866	−0.147085
$195$	23.8514	1.70804
$196$	−1.55306	−0.110933
$197$	−10.1559	−0.723575	−0.361787	−	0.932261i	$-0.617833\pi$
$197$	−10.1559	−0.723575	−0.361787	+	0.932261i	$0.617833\pi$
$198$	−3.51986	−0.250146
$199$	15.7480	1.11635	0.558173	−	0.829724i	$-0.311502\pi$
$199$	15.7480	1.11635	0.558173	+	0.829724i	$0.311502\pi$
$200$	12.5715	0.888942
$201$	−13.0355	−0.919452
$202$	−6.24503	−0.439399
$203$	−10.0469	−0.705157
$204$	19.2251	1.34602
$205$	43.5373	3.04078
$206$	5.35319	0.372974
$207$	15.3348	1.06585
$208$	−1.98527	−0.137654
$209$	3.28532	0.227250
$210$	28.0396	1.93491
$211$	−4.05048	−0.278846	−0.139423	−	0.990233i	$-0.544525\pi$
$211$	−4.05048	−0.278846	−0.139423	+	0.990233i	$0.544525\pi$
$212$	4.75749	0.326746
$213$	16.7337	1.14657
$214$	−11.8267	−0.808457
$215$	−1.11614	−0.0761202
$216$	−6.34693	−0.431854
$217$	−9.58730	−0.650828
$218$	7.93604	0.537497
$219$	−41.9510	−2.83478
$220$	−2.82956	−0.190769
$221$	13.3167	0.895779
$222$	−5.82325	−0.390831
$223$	−8.33886	−0.558411	−0.279206	−	0.960231i	$-0.590071\pi$
$223$	−8.33886	−0.558411	−0.279206	+	0.960231i	$0.590071\pi$
$224$	−2.33387	−0.155938
$225$	65.5542	4.37028
$226$	0.577304	0.0384017
$227$	12.2350	0.812063	0.406032	−	0.913859i	$-0.366912\pi$
$227$	12.2350	0.812063	0.406032	+	0.913859i	$0.366912\pi$
$228$	13.9494	0.923818
$229$	9.58349	0.633295	0.316647	−	0.948543i	$-0.397443\pi$
$229$	9.58349	0.633295	0.316647	+	0.948543i	$0.397443\pi$
$230$	12.3274	0.812847
$231$	−4.51523	−0.297081
$232$	4.30484	0.282627
$233$	−17.5840	−1.15196	−0.575982	−	0.817462i	$-0.695380\pi$
$233$	−17.5840	−1.15196	−0.575982	+	0.817462i	$0.695380\pi$
$234$	−10.3522	−0.676742
$235$	19.3375	1.26144
$236$	3.51797	0.229001
$237$	36.4908	2.37033
$238$	15.6550	1.01476
$239$	−0.716956	−0.0463761	−0.0231880	−	0.999731i	$-0.507382\pi$
$239$	−0.716956	−0.0463761	−0.0231880	+	0.999731i	$0.507382\pi$
$240$	−12.0142	−0.775514
$241$	−16.7905	−1.08157	−0.540784	−	0.841161i	$-0.681872\pi$
$241$	−16.7905	−1.08157	−0.540784	+	0.841161i	$0.681872\pi$
$242$	−10.5444	−0.677817
$243$	11.7396	0.753097
$244$	7.78117	0.498138
$245$	−6.51018	−0.415920
$246$	−29.7678	−1.89793
$247$	9.66236	0.614801
$248$	4.10790	0.260852
$249$	−16.3233	−1.03445
$250$	31.7387	2.00733
$251$	21.6505	1.36657	0.683283	−	0.730154i	$-0.260552\pi$
$251$	21.6505	1.36657	0.683283	+	0.730154i	$0.260552\pi$
$252$	−12.1699	−0.766634
$253$	−1.98510	−0.124802
$254$	6.21845	0.390180
$255$	80.5884	5.04664
$256$	1.00000	0.0625000
$257$	22.2381	1.38718	0.693588	−	0.720372i	$-0.256029\pi$
$257$	22.2381	1.38718	0.693588	+	0.720372i	$0.256029\pi$
$258$	0.763141	0.0475111
$259$	−4.74189	−0.294647
$260$	−8.32194	−0.516105
$261$	22.4476	1.38947
$262$	21.7917	1.34629
$263$	−3.17475	−0.195763	−0.0978816	−	0.995198i	$-0.531207\pi$
$263$	−3.17475	−0.195763	−0.0978816	+	0.995198i	$0.531207\pi$
$264$	1.93466	0.119070
$265$	19.9426	1.22507
$266$	11.3590	0.696465
$267$	−12.9396	−0.791889
$268$	4.54817	0.277824
$269$	23.2201	1.41575	0.707876	−	0.706337i	$-0.249654\pi$
$269$	23.2201	1.41575	0.707876	+	0.706337i	$0.249654\pi$
$270$	−26.6053	−1.61915
$271$	16.7033	1.01465	0.507327	−	0.861754i	$-0.330634\pi$
$271$	16.7033	1.01465	0.507327	+	0.861754i	$0.330634\pi$
$272$	−6.70776	−0.406718
$273$	−13.2796	−0.803720
$274$	15.5640	0.940254
$275$	−8.48598	−0.511724
$276$	−8.42865	−0.507345
$277$	−28.9839	−1.74148	−0.870738	−	0.491747i	$-0.836358\pi$
$277$	−28.9839	−1.74148	−0.870738	+	0.491747i	$0.836358\pi$
$278$	11.2750	0.676228
$279$	21.4206	1.28242
$280$	−9.78321	−0.584658
$281$	25.5445	1.52386	0.761930	−	0.647660i	$-0.224252\pi$
$281$	25.5445	1.52386	0.761930	+	0.647660i	$0.224252\pi$
$282$	−13.2216	−0.787336
$283$	−16.5337	−0.982826	−0.491413	−	0.870927i	$-0.663519\pi$
$283$	−16.5337	−0.982826	−0.491413	+	0.870927i	$0.663519\pi$
$284$	−5.83849	−0.346451
$285$	58.4735	3.46367
$286$	1.34009	0.0792410
$287$	−24.2400	−1.43084
$288$	5.21449	0.307267
$289$	27.9940	1.64671
$290$	18.0452	1.05965
$291$	5.87166	0.344203
$292$	14.6370	0.856565
$293$	4.91877	0.287358	0.143679	−	0.989624i	$-0.454107\pi$
$293$	4.91877	0.287358	0.143679	+	0.989624i	$0.454107\pi$
$294$	4.45121	0.259600
$295$	14.7468	0.858591
$296$	2.03177	0.118094
$297$	4.28428	0.248599
$298$	2.17011	0.125711
$299$	−5.83831	−0.337638
$300$	−36.0312	−2.08026
$301$	0.621428	0.0358185
$302$	12.5121	0.719993
$303$	17.8988	1.02826
$304$	−4.86703	−0.279143
$305$	32.6174	1.86767
$306$	−34.9775	−1.99953
$307$	−27.2017	−1.55248	−0.776240	−	0.630437i	$-0.782876\pi$
$307$	−27.2017	−1.55248	−0.776240	+	0.630437i	$0.782876\pi$
$308$	1.57540	0.0897666
$309$	−15.3427	−0.872818
$310$	17.2197	0.978012
$311$	22.4381	1.27235	0.636173	−	0.771546i	$-0.280516\pi$
$311$	22.4381	1.27235	0.636173	+	0.771546i	$0.280516\pi$
$312$	5.68997	0.322131
$313$	−27.6891	−1.56508	−0.782540	−	0.622601i	$-0.786076\pi$
$313$	−27.6891	−1.56508	−0.782540	+	0.622601i	$0.786076\pi$
$314$	15.5108	0.875324
$315$	−51.0144	−2.87434
$316$	−12.7319	−0.716225
$317$	−28.5233	−1.60203	−0.801015	−	0.598644i	$-0.795706\pi$
$317$	−28.5233	−1.60203	−0.801015	+	0.598644i	$0.795706\pi$
$318$	−13.6354	−0.764636
$319$	−2.90584	−0.162696
$320$	4.19184	0.234331
$321$	33.8964	1.89191
$322$	−6.86347	−0.382486
$323$	32.6468	1.81652
$324$	2.54743	0.141524
$325$	−24.9579	−1.38441
$326$	−23.3727	−1.29449
$327$	−22.7454	−1.25783
$328$	10.3862	0.573482
$329$	−10.7664	−0.593571
$330$	8.10978	0.446428
$331$	9.85582	0.541725	0.270862	−	0.962618i	$-0.412691\pi$
$331$	9.85582	0.541725	0.270862	+	0.962618i	$0.412691\pi$
$332$	5.69532	0.312571
$333$	10.5947	0.580584
$334$	3.09247	0.169212
$335$	19.0652	1.04164
$336$	6.68908	0.364919
$337$	−19.0226	−1.03623	−0.518115	−	0.855311i	$-0.673366\pi$
$337$	−19.0226	−1.03623	−0.518115	+	0.855311i	$0.673366\pi$
$338$	−9.05870	−0.492729
$339$	−1.65461	−0.0898659
$340$	−28.1179	−1.52491
$341$	−2.77290	−0.150161
$342$	−25.3791	−1.37234
$343$	19.9617	1.07783
$344$	−0.266265	−0.0143561
$345$	−35.3316	−1.90219
$346$	−10.2048	−0.548614
$347$	0.372005	0.0199703	0.00998513	−	0.999950i	$-0.496822\pi$
$347$	0.372005	0.0199703	0.00998513	+	0.999950i	$0.496822\pi$
$348$	−12.3381	−0.661391
$349$	−22.1482	−1.18557	−0.592783	−	0.805363i	$-0.701971\pi$
$349$	−22.1482	−1.18557	−0.592783	+	0.805363i	$0.701971\pi$
$350$	−29.3403	−1.56831
$351$	12.6004	0.672558
$352$	−0.675015	−0.0359784
$353$	2.25416	0.119977	0.0599885	−	0.998199i	$-0.480894\pi$
$353$	2.25416	0.119977	0.0599885	+	0.998199i	$0.480894\pi$
$354$	−10.0828	−0.535897
$355$	−24.4740	−1.29895
$356$	4.51471	0.239279
$357$	−44.8688	−2.37471
$358$	6.40496	0.338513
$359$	29.3350	1.54824	0.774121	−	0.633037i	$-0.218192\pi$
$359$	29.3350	1.54824	0.774121	+	0.633037i	$0.218192\pi$
$360$	21.8583	1.15203
$361$	4.68795	0.246734
$362$	10.7629	0.565686
$363$	30.2211	1.58620
$364$	4.63336	0.242854
$365$	61.3559	3.21152
$366$	−22.3016	−1.16572
$367$	−18.2816	−0.954293	−0.477146	−	0.878824i	$-0.658329\pi$
$367$	−18.2816	−0.954293	−0.477146	+	0.878824i	$0.658329\pi$
$368$	2.94081	0.153301
$369$	54.1588	2.81939
$370$	8.51687	0.442771
$371$	−11.1034	−0.576457
$372$	−11.7736	−0.610434
$373$	−28.9312	−1.49800	−0.749001	−	0.662569i	$-0.769466\pi$
$373$	−28.9312	−1.49800	−0.749001	+	0.662569i	$0.769466\pi$
$374$	4.52784	0.234129
$375$	−90.9660	−4.69747
$376$	4.61312	0.237903
$377$	−8.54627	−0.440155
$378$	14.8129	0.761894
$379$	1.18879	0.0610638	0.0305319	−	0.999534i	$-0.490280\pi$
$379$	1.18879	0.0610638	0.0305319	+	0.999534i	$0.490280\pi$
$380$	−20.4018	−1.04659
$381$	−17.8226	−0.913082
$382$	−6.65398	−0.340447
$383$	−6.34725	−0.324329	−0.162165	−	0.986764i	$-0.551848\pi$
$383$	−6.34725	−0.324329	−0.162165	+	0.986764i	$0.551848\pi$
$384$	−2.86609	−0.146260
$385$	6.60381	0.336562
$386$	−12.7410	−0.648499
$387$	−1.38844	−0.0705782
$388$	−2.04866	−0.104005
$389$	26.4943	1.34331	0.671656	−	0.740863i	$-0.265583\pi$
$389$	26.4943	1.34331	0.671656	+	0.740863i	$0.265583\pi$
$390$	23.8514	1.20776
$391$	−19.7263	−0.997600
$392$	−1.55306	−0.0784414
$393$	−62.4569	−3.15054
$394$	−10.1559	−0.511645
$395$	−53.3701	−2.68534
$396$	−3.51986	−0.176880
$397$	−5.62513	−0.282317	−0.141159	−	0.989987i	$-0.545083\pi$
$397$	−5.62513	−0.282317	−0.141159	+	0.989987i	$0.545083\pi$
$398$	15.7480	0.789376
$399$	−32.5559	−1.62984
$400$	12.5715	0.628577
$401$	21.8952	1.09340	0.546698	−	0.837330i	$-0.315885\pi$
$401$	21.8952	1.09340	0.546698	+	0.837330i	$0.315885\pi$
$402$	−13.0355	−0.650151
$403$	−8.15529	−0.406244
$404$	−6.24503	−0.310702
$405$	10.6784	0.530616
$406$	−10.0469	−0.498621
$407$	−1.37148	−0.0679816
$408$	19.2251	0.951782
$409$	25.7435	1.27294	0.636468	−	0.771303i	$-0.280395\pi$
$409$	25.7435	1.27294	0.636468	+	0.771303i	$0.280395\pi$
$410$	43.5373	2.15016
$411$	−44.6078	−2.20034
$412$	5.35319	0.263733
$413$	−8.21048	−0.404012
$414$	15.3348	0.753667
$415$	23.8739	1.17192
$416$	−1.98527	−0.0973359
$417$	−32.3151	−1.58248
$418$	3.28532	0.160690
$419$	−4.25727	−0.207981	−0.103991	−	0.994578i	$-0.533161\pi$
$419$	−4.25727	−0.207981	−0.103991	+	0.994578i	$0.533161\pi$
$420$	28.0396	1.36819
$421$	−4.81894	−0.234861	−0.117430	−	0.993081i	$-0.537466\pi$
$421$	−4.81894	−0.234861	−0.117430	+	0.993081i	$0.537466\pi$
$422$	−4.05048	−0.197174
$423$	24.0550	1.16960
$424$	4.75749	0.231044
$425$	−84.3268	−4.09045
$426$	16.7337	0.810749
$427$	−18.1602	−0.878835
$428$	−11.8267	−0.571665
$429$	−3.84082	−0.185436
$430$	−1.11614	−0.0538251
$431$	3.30507	0.159200	0.0795999	−	0.996827i	$-0.474636\pi$
$431$	3.30507	0.159200	0.0795999	+	0.996827i	$0.474636\pi$
$432$	−6.34693	−0.305367
$433$	39.0239	1.87537	0.937686	−	0.347485i	$-0.112964\pi$
$433$	39.0239	1.87537	0.937686	+	0.347485i	$0.112964\pi$
$434$	−9.58730	−0.460205
$435$	−51.7193	−2.47975
$436$	7.93604	0.380067
$437$	−14.3130	−0.684685
$438$	−41.9510	−2.00449
$439$	6.52392	0.311370	0.155685	−	0.987807i	$-0.450242\pi$
$439$	6.52392	0.311370	0.155685	+	0.987807i	$0.450242\pi$
$440$	−2.82956	−0.134894
$441$	−8.09841	−0.385639
$442$	13.3167	0.633411
$443$	−21.4714	−1.02013	−0.510067	−	0.860134i	$-0.670380\pi$
$443$	−21.4714	−1.02013	−0.510067	+	0.860134i	$0.670380\pi$
$444$	−5.82325	−0.276359
$445$	18.9249	0.897128
$446$	−8.33886	−0.394856
$447$	−6.21973	−0.294183
$448$	−2.33387	−0.110265
$449$	12.1596	0.573849	0.286924	−	0.957953i	$-0.407367\pi$
$449$	12.1596	0.573849	0.286924	+	0.957953i	$0.407367\pi$
$450$	65.5542	3.09025
$451$	−7.01085	−0.330128
$452$	0.577304	0.0271541
$453$	−35.8610	−1.68490
$454$	12.2350	0.574215
$455$	19.4223	0.910532
$456$	13.9494	0.653238
$457$	−2.82134	−0.131977	−0.0659884	−	0.997820i	$-0.521020\pi$
$457$	−2.82134	−0.131977	−0.0659884	+	0.997820i	$0.521020\pi$
$458$	9.58349	0.447807
$459$	42.5737	1.98717
$460$	12.3274	0.574769
$461$	24.5352	1.14272	0.571359	−	0.820700i	$-0.306417\pi$
$461$	24.5352	1.14272	0.571359	+	0.820700i	$0.306417\pi$
$462$	−4.51523	−0.210068
$463$	22.8312	1.06105	0.530527	−	0.847668i	$-0.321994\pi$
$463$	22.8312	1.06105	0.530527	+	0.847668i	$0.321994\pi$
$464$	4.30484	0.199847
$465$	−49.3532	−2.28870
$466$	−17.5840	−0.814562
$467$	26.9331	1.24632	0.623158	−	0.782096i	$-0.285849\pi$
$467$	26.9331	1.24632	0.623158	+	0.782096i	$0.285849\pi$
$468$	−10.3522	−0.478529
$469$	−10.6148	−0.490147
$470$	19.3375	0.891970
$471$	−44.4554	−2.04839
$472$	3.51797	0.161928
$473$	0.179733	0.00826414
$474$	36.4908	1.67608
$475$	−61.1860	−2.80741
$476$	15.6550	0.717547
$477$	24.8079	1.13587
$478$	−0.716956	−0.0327928
$479$	−11.3564	−0.518889	−0.259445	−	0.965758i	$-0.583539\pi$
$479$	−11.3564	−0.518889	−0.259445	+	0.965758i	$0.583539\pi$
$480$	−12.0142	−0.548371
$481$	−4.03362	−0.183917
$482$	−16.7905	−0.764784
$483$	19.6714	0.895078
$484$	−10.5444	−0.479289
$485$	−8.58767	−0.389946
$486$	11.7396	0.532520
$487$	5.28079	0.239295	0.119648	−	0.992816i	$-0.461824\pi$
$487$	5.28079	0.239295	0.119648	+	0.992816i	$0.461824\pi$
$488$	7.78117	0.352237
$489$	66.9883	3.02931
$490$	−6.51018	−0.294100
$491$	−29.4378	−1.32851	−0.664254	−	0.747507i	$-0.731251\pi$
$491$	−29.4378	−1.32851	−0.664254	+	0.747507i	$0.731251\pi$
$492$	−29.7678	−1.34204
$493$	−28.8758	−1.30050
$494$	9.66236	0.434730
$495$	−14.7547	−0.663174
$496$	4.10790	0.184450
$497$	13.6263	0.611222
$498$	−16.3233	−0.731465
$499$	−17.5255	−0.784547	−0.392274	−	0.919849i	$-0.628311\pi$
$499$	−17.5255	−0.784547	−0.392274	+	0.919849i	$0.628311\pi$
$500$	31.7387	1.41940
$501$	−8.86330	−0.395983
$502$	21.6505	0.966308
$503$	−2.51695	−0.112225	−0.0561126	−	0.998424i	$-0.517871\pi$
$503$	−2.51695	−0.112225	−0.0561126	+	0.998424i	$0.517871\pi$
$504$	−12.1699	−0.542092
$505$	−26.1782	−1.16491
$506$	−1.98510	−0.0882482
$507$	25.9631	1.15306
$508$	6.21845	0.275899
$509$	−37.2868	−1.65271	−0.826355	−	0.563150i	$-0.809589\pi$
$509$	−37.2868	−1.65271	−0.826355	+	0.563150i	$0.809589\pi$
$510$	80.5884	3.56851
$511$	−34.1608	−1.51118
$512$	1.00000	0.0441942
$513$	30.8907	1.36386
$514$	22.2381	0.980881
$515$	22.4397	0.988812
$516$	0.763141	0.0335954
$517$	−3.11392	−0.136950
$518$	−4.74189	−0.208347
$519$	29.2480	1.28384
$520$	−8.32194	−0.364941
$521$	17.9478	0.786305	0.393153	−	0.919473i	$-0.371384\pi$
$521$	17.9478	0.786305	0.393153	+	0.919473i	$0.371384\pi$
$522$	22.4476	0.982503
$523$	35.2811	1.54273	0.771366	−	0.636391i	$-0.219574\pi$
$523$	35.2811	1.54273	0.771366	+	0.636391i	$0.219574\pi$
$524$	21.7917	0.951973
$525$	84.0921	3.67008
$526$	−3.17475	−0.138425
$527$	−27.5548	−1.20031
$528$	1.93466	0.0841951
$529$	−14.3516	−0.623983
$530$	19.9426	0.866253
$531$	18.3444	0.796081
$532$	11.3590	0.492475
$533$	−20.6194	−0.893126
$534$	−12.9396	−0.559950
$535$	−49.5757	−2.14334
$536$	4.54817	0.196451
$537$	−18.3572	−0.792172
$538$	23.2201	1.00109
$539$	1.04834	0.0451552
$540$	−26.6053	−1.14491
$541$	0.808670	0.0347674	0.0173837	−	0.999849i	$-0.494466\pi$
$541$	0.808670	0.0347674	0.0173837	+	0.999849i	$0.494466\pi$
$542$	16.7033	0.717469
$543$	−30.8475	−1.32379
$544$	−6.70776	−0.287593
$545$	33.2666	1.42499
$546$	−13.2796	−0.568316
$547$	−35.5790	−1.52125	−0.760625	−	0.649192i	$-0.775107\pi$
$547$	−35.5790	−1.52125	−0.760625	+	0.649192i	$0.775107\pi$
$548$	15.5640	0.664860
$549$	40.5748	1.73169
$550$	−8.48598	−0.361843
$551$	−20.9518	−0.892576
$552$	−8.42865	−0.358747
$553$	29.7146	1.26359
$554$	−28.9839	−1.23141
$555$	−24.4101	−1.03615
$556$	11.2750	0.478166
$557$	1.04732	0.0443764	0.0221882	−	0.999754i	$-0.492937\pi$
$557$	1.04732	0.0443764	0.0221882	+	0.999754i	$0.492937\pi$
$558$	21.4206	0.906807
$559$	0.528608	0.0223578
$560$	−9.78321	−0.413416
$561$	−12.9772	−0.547898
$562$	25.5445	1.07753
$563$	−43.1417	−1.81821	−0.909103	−	0.416572i	$-0.863232\pi$
$563$	−43.1417	−1.81821	−0.909103	+	0.416572i	$0.863232\pi$
$564$	−13.2216	−0.556731
$565$	2.41997	0.101809
$566$	−16.5337	−0.694963
$567$	−5.94538	−0.249682
$568$	−5.83849	−0.244978
$569$	−14.5268	−0.608993	−0.304497	−	0.952513i	$-0.598488\pi$
$569$	−14.5268	−0.608993	−0.304497	+	0.952513i	$0.598488\pi$
$570$	58.4735	2.44918
$571$	21.7766	0.911324	0.455662	−	0.890153i	$-0.349403\pi$
$571$	21.7766	0.911324	0.455662	+	0.890153i	$0.349403\pi$
$572$	1.34009	0.0560319
$573$	19.0709	0.796699
$574$	−24.2400	−1.01176
$575$	36.9706	1.54178
$576$	5.21449	0.217270
$577$	−45.4087	−1.89039	−0.945194	−	0.326510i	$-0.894127\pi$
$577$	−45.4087	−1.89039	−0.945194	+	0.326510i	$0.894127\pi$
$578$	27.9940	1.16440
$579$	36.5169	1.51759
$580$	18.0452	0.749287
$581$	−13.2921	−0.551450
$582$	5.87166	0.243388
$583$	−3.21138	−0.133002
$584$	14.6370	0.605683
$585$	−43.3947	−1.79415
$586$	4.91877	0.203193
$587$	0.811212	0.0334823	0.0167412	−	0.999860i	$-0.494671\pi$
$587$	0.811212	0.0334823	0.0167412	+	0.999860i	$0.494671\pi$
$588$	4.45121	0.183565
$589$	−19.9933	−0.823808
$590$	14.7468	0.607116
$591$	29.1076	1.19733
$592$	2.03177	0.0835053
$593$	9.59267	0.393924	0.196962	−	0.980411i	$-0.436892\pi$
$593$	9.59267	0.393924	0.196962	+	0.980411i	$0.436892\pi$
$594$	4.28428	0.175786
$595$	65.6234	2.69030
$596$	2.17011	0.0888911
$597$	−45.1353	−1.84726
$598$	−5.83831	−0.238746
$599$	31.6283	1.29230	0.646148	−	0.763212i	$-0.276379\pi$
$599$	31.6283	1.29230	0.646148	+	0.763212i	$0.276379\pi$
$600$	−36.0312	−1.47097
$601$	10.2853	0.419548	0.209774	−	0.977750i	$-0.432727\pi$
$601$	10.2853	0.419548	0.209774	+	0.977750i	$0.432727\pi$
$602$	0.621428	0.0253275
$603$	23.7164	0.965806
$604$	12.5121	0.509112
$605$	−44.2003	−1.79700
$606$	17.8988	0.727091
$607$	−45.4036	−1.84287	−0.921437	−	0.388528i	$-0.872984\pi$
$607$	−45.4036	−1.84287	−0.921437	+	0.388528i	$0.872984\pi$
$608$	−4.86703	−0.197384
$609$	28.7955	1.16685
$610$	32.6174	1.32064
$611$	−9.15828	−0.370504
$612$	−34.9775	−1.41388
$613$	43.7185	1.76577	0.882887	−	0.469586i	$-0.155597\pi$
$613$	43.7185	1.76577	0.882887	+	0.469586i	$0.155597\pi$
$614$	−27.2017	−1.09777
$615$	−124.782	−5.03170
$616$	1.57540	0.0634745
$617$	34.1578	1.37514	0.687571	−	0.726118i	$-0.258677\pi$
$617$	34.1578	1.37514	0.687571	+	0.726118i	$0.258677\pi$
$618$	−15.3427	−0.617175
$619$	−20.9780	−0.843177	−0.421588	−	0.906787i	$-0.638527\pi$
$619$	−20.9780	−0.843177	−0.421588	+	0.906787i	$0.638527\pi$
$620$	17.2197	0.691559
$621$	−18.6652	−0.749007
$622$	22.4381	0.899685
$623$	−10.5367	−0.422145
$624$	5.68997	0.227781
$625$	70.1859	2.80743
$626$	−27.6891	−1.10668
$627$	−9.41603	−0.376040
$628$	15.5108	0.618948
$629$	−13.6286	−0.543410
$630$	−51.0144	−2.03246
$631$	−2.19076	−0.0872129	−0.0436064	−	0.999049i	$-0.513885\pi$
$631$	−2.19076	−0.0872129	−0.0436064	+	0.999049i	$0.513885\pi$
$632$	−12.7319	−0.506448
$633$	11.6090	0.461418
$634$	−28.5233	−1.13281
$635$	26.0667	1.03443
$636$	−13.6354	−0.540679
$637$	3.08324	0.122163
$638$	−2.90584	−0.115043
$639$	−30.4448	−1.20438
$640$	4.19184	0.165697
$641$	−22.1513	−0.874925	−0.437463	−	0.899237i	$-0.644123\pi$
$641$	−22.1513	−0.874925	−0.437463	+	0.899237i	$0.644123\pi$
$642$	33.8964	1.33779
$643$	26.7731	1.05583	0.527914	−	0.849298i	$-0.322974\pi$
$643$	26.7731	1.05583	0.527914	+	0.849298i	$0.322974\pi$
$644$	−6.86347	−0.270459
$645$	3.19897	0.125959
$646$	32.6468	1.28447
$647$	−22.6579	−0.890774	−0.445387	−	0.895338i	$-0.646934\pi$
$647$	−22.6579	−0.890774	−0.445387	+	0.895338i	$0.646934\pi$
$648$	2.54743	0.100073
$649$	−2.37469	−0.0932146
$650$	−24.9579	−0.978929
$651$	27.4781	1.07695
$652$	−23.3727	−0.915345
$653$	14.8451	0.580932	0.290466	−	0.956885i	$-0.406190\pi$
$653$	14.8451	0.580932	0.290466	+	0.956885i	$0.406190\pi$
$654$	−22.7454	−0.889417
$655$	91.3472	3.56923
$656$	10.3862	0.405513
$657$	76.3244	2.97770
$658$	−10.7664	−0.419718
$659$	−17.5433	−0.683390	−0.341695	−	0.939811i	$-0.611001\pi$
$659$	−17.5433	−0.683390	−0.341695	+	0.939811i	$0.611001\pi$
$660$	8.10978	0.315673
$661$	−51.0049	−1.98386	−0.991929	−	0.126791i	$-0.959532\pi$
$661$	−51.0049	−1.98386	−0.991929	+	0.126791i	$0.959532\pi$
$662$	9.85582	0.383057
$663$	−38.1669	−1.48228
$664$	5.69532	0.221021
$665$	47.6151	1.84644
$666$	10.5947	0.410535
$667$	12.6597	0.490187
$668$	3.09247	0.119651
$669$	23.8999	0.924025
$670$	19.0652	0.736553
$671$	−5.25241	−0.202767
$672$	6.68908	0.258037
$673$	−4.87423	−0.187888	−0.0939438	−	0.995577i	$-0.529947\pi$
$673$	−4.87423	−0.187888	−0.0939438	+	0.995577i	$0.529947\pi$
$674$	−19.0226	−0.732725
$675$	−79.7907	−3.07115
$676$	−9.05870	−0.348412
$677$	5.70616	0.219305	0.109653	−	0.993970i	$-0.465026\pi$
$677$	5.70616	0.219305	0.109653	+	0.993970i	$0.465026\pi$
$678$	−1.65461	−0.0635448
$679$	4.78131	0.183490
$680$	−28.1179	−1.07827
$681$	−35.0666	−1.34375
$682$	−2.77290	−0.106180
$683$	26.2411	1.00409	0.502044	−	0.864842i	$-0.332582\pi$
$683$	26.2411	1.00409	0.502044	+	0.864842i	$0.332582\pi$
$684$	−25.3791	−0.970393
$685$	65.2417	2.49276
$686$	19.9617	0.762142
$687$	−27.4672	−1.04794
$688$	−0.266265	−0.0101513
$689$	−9.44490	−0.359822
$690$	−35.3316	−1.34505
$691$	14.9282	0.567894	0.283947	−	0.958840i	$-0.408356\pi$
$691$	14.9282	0.567894	0.283947	+	0.958840i	$0.408356\pi$
$692$	−10.2048	−0.387929
$693$	8.21489	0.312058
$694$	0.372005	0.0141211
$695$	47.2629	1.79279
$696$	−12.3381	−0.467674
$697$	−69.6682	−2.63887
$698$	−22.1482	−0.838321
$699$	50.3973	1.90620
$700$	−29.3403	−1.10896
$701$	38.7391	1.46316	0.731578	−	0.681758i	$-0.238784\pi$
$701$	38.7391	1.46316	0.731578	+	0.681758i	$0.238784\pi$
$702$	12.6004	0.475571
$703$	−9.88869	−0.372959
$704$	−0.675015	−0.0254406
$705$	−55.4229	−2.08735
$706$	2.25416	0.0848365
$707$	14.5751	0.548152
$708$	−10.0828	−0.378936
$709$	−22.6710	−0.851429	−0.425715	−	0.904858i	$-0.639977\pi$
$709$	−22.6710	−0.851429	−0.425715	+	0.904858i	$0.639977\pi$
$710$	−24.4740	−0.918495
$711$	−66.3904	−2.48983
$712$	4.51471	0.169196
$713$	12.0806	0.452421
$714$	−44.8688	−1.67917
$715$	5.61744	0.210080
$716$	6.40496	0.239365
$717$	2.05486	0.0767403
$718$	29.3350	1.09477
$719$	−31.9796	−1.19264	−0.596319	−	0.802747i	$-0.703371\pi$
$719$	−31.9796	−1.19264	−0.596319	+	0.802747i	$0.703371\pi$
$720$	21.8583	0.814611
$721$	−12.4936	−0.465287
$722$	4.68795	0.174467
$723$	48.1230	1.78971
$724$	10.7629	0.400000
$725$	54.1185	2.00991
$726$	30.2211	1.12161
$727$	−21.9154	−0.812798	−0.406399	−	0.913696i	$-0.633216\pi$
$727$	−21.9154	−0.812798	−0.406399	+	0.913696i	$0.633216\pi$
$728$	4.63336	0.171724
$729$	−41.2891	−1.52923
$730$	61.3559	2.27088
$731$	1.78604	0.0660592
$732$	−22.3016	−0.824289
$733$	−13.0679	−0.482673	−0.241336	−	0.970442i	$-0.577586\pi$
$733$	−13.0679	−0.482673	−0.241336	+	0.970442i	$0.577586\pi$
$734$	−18.2816	−0.674787
$735$	18.6588	0.688240
$736$	2.94081	0.108400
$737$	−3.07009	−0.113088
$738$	54.1588	1.99361
$739$	−41.3654	−1.52165	−0.760826	−	0.648956i	$-0.775206\pi$
$739$	−41.3654	−1.52165	−0.760826	+	0.648956i	$0.775206\pi$
$740$	8.51687	0.313086
$741$	−27.6932	−1.01734
$742$	−11.1034	−0.407617
$743$	−26.9462	−0.988560	−0.494280	−	0.869303i	$-0.664568\pi$
$743$	−26.9462	−0.988560	−0.494280	+	0.869303i	$0.664568\pi$
$744$	−11.7736	−0.431642
$745$	9.09675	0.333279
$746$	−28.9312	−1.05925
$747$	29.6982	1.08660
$748$	4.52784	0.165554
$749$	27.6020	1.00855
$750$	−90.9660	−3.32161
$751$	−19.8725	−0.725157	−0.362578	−	0.931953i	$-0.618103\pi$
$751$	−19.8725	−0.725157	−0.362578	+	0.931953i	$0.618103\pi$
$752$	4.61312	0.168223
$753$	−62.0523	−2.26131
$754$	−8.54627	−0.311237
$755$	52.4489	1.90881
$756$	14.8129	0.538740
$757$	−13.7202	−0.498668	−0.249334	−	0.968418i	$-0.580212\pi$
$757$	−13.7202	−0.498668	−0.249334	+	0.968418i	$0.580212\pi$
$758$	1.18879	0.0431786
$759$	5.68947	0.206515
$760$	−20.4018	−0.740051
$761$	−18.7184	−0.678540	−0.339270	−	0.940689i	$-0.610180\pi$
$761$	−18.7184	−0.678540	−0.339270	+	0.940689i	$0.610180\pi$
$762$	−17.8226	−0.645646
$763$	−18.5217	−0.670530
$764$	−6.65398	−0.240732
$765$	−146.620	−5.30107
$766$	−6.34725	−0.229335
$767$	−6.98412	−0.252182
$768$	−2.86609	−0.103421
$769$	13.4883	0.486400	0.243200	−	0.969976i	$-0.421803\pi$
$769$	13.4883	0.486400	0.243200	+	0.969976i	$0.421803\pi$
$770$	6.60381	0.237985
$771$	−63.7365	−2.29541
$772$	−12.7410	−0.458558
$773$	26.6255	0.957652	0.478826	−	0.877910i	$-0.341062\pi$
$773$	26.6255	0.957652	0.478826	+	0.877910i	$0.341062\pi$
$774$	−1.38844	−0.0499064
$775$	51.6426	1.85506
$776$	−2.04866	−0.0735427
$777$	13.5907	0.487564
$778$	26.4943	0.949866
$779$	−50.5499	−1.81114
$780$	23.8514	0.854019
$781$	3.94107	0.141023
$782$	−19.7263	−0.705410
$783$	−27.3226	−0.976428
$784$	−1.55306	−0.0554664
$785$	65.0188	2.32062
$786$	−62.4569	−2.22776
$787$	−18.7897	−0.669779	−0.334890	−	0.942257i	$-0.608699\pi$
$787$	−18.7897	−0.669779	−0.334890	+	0.942257i	$0.608699\pi$
$788$	−10.1559	−0.361787
$789$	9.09912	0.323937
$790$	−53.3701	−1.89882
$791$	−1.34735	−0.0479063
$792$	−3.51986	−0.125073
$793$	−15.4477	−0.548565
$794$	−5.62513	−0.199628
$795$	−57.1575	−2.02717
$796$	15.7480	0.558173
$797$	−7.13496	−0.252733	−0.126367	−	0.991984i	$-0.540332\pi$
$797$	−7.13496	−0.252733	−0.126367	+	0.991984i	$0.540332\pi$
$798$	−32.5559	−1.15247
$799$	−30.9437	−1.09471
$800$	12.5715	0.444471
$801$	23.5419	0.831812
$802$	21.8952	0.773148
$803$	−9.88019	−0.348664
$804$	−13.0355	−0.459726
$805$	−28.7706	−1.01403
$806$	−8.15529	−0.287258
$807$	−66.5509	−2.34270
$808$	−6.24503	−0.219699
$809$	−24.7847	−0.871384	−0.435692	−	0.900096i	$-0.643496\pi$
$809$	−24.7847	−0.871384	−0.435692	+	0.900096i	$0.643496\pi$
$810$	10.6784	0.375202
$811$	31.2352	1.09682	0.548408	−	0.836211i	$-0.315234\pi$
$811$	31.2352	1.09682	0.548408	+	0.836211i	$0.315234\pi$
$812$	−10.0469	−0.352578
$813$	−47.8733	−1.67899
$814$	−1.37148	−0.0480703
$815$	−97.9746	−3.43190
$816$	19.2251	0.673012
$817$	1.29592	0.0453385
$818$	25.7435	0.900102
$819$	24.1606	0.844240
$820$	43.5373	1.52039
$821$	54.8782	1.91526	0.957631	−	0.287999i	$-0.0929900\pi$
$821$	54.8782	1.91526	0.957631	+	0.287999i	$0.0929900\pi$
$822$	−44.6078	−1.55588
$823$	53.2055	1.85463	0.927314	−	0.374283i	$-0.122111\pi$
$823$	53.2055	1.85463	0.927314	+	0.374283i	$0.122111\pi$
$824$	5.35319	0.186487
$825$	24.3216	0.846770
$826$	−8.21048	−0.285679
$827$	35.9683	1.25074	0.625369	−	0.780329i	$-0.284948\pi$
$827$	35.9683	1.25074	0.625369	+	0.780329i	$0.284948\pi$
$828$	15.3348	0.532923
$829$	3.71339	0.128971	0.0644857	−	0.997919i	$-0.479459\pi$
$829$	3.71339	0.128971	0.0644857	+	0.997919i	$0.479459\pi$
$830$	23.8739	0.828674
$831$	83.0707	2.88169
$832$	−1.98527	−0.0688268
$833$	10.4175	0.360947
$834$	−32.3151	−1.11898
$835$	12.9631	0.448608
$836$	3.28532	0.113625
$837$	−26.0726	−0.901200
$838$	−4.25727	−0.147065
$839$	−1.44433	−0.0498637	−0.0249319	−	0.999689i	$-0.507937\pi$
$839$	−1.44433	−0.0498637	−0.0249319	+	0.999689i	$0.507937\pi$
$840$	28.0396	0.967457
$841$	−10.4683	−0.360977
$842$	−4.81894	−0.166072
$843$	−73.2130	−2.52159
$844$	−4.05048	−0.139423
$845$	−37.9727	−1.30630
$846$	24.0550	0.827030
$847$	24.6091	0.845580
$848$	4.75749	0.163373
$849$	47.3871	1.62632
$850$	−84.3268	−2.89239
$851$	5.97507	0.204823
$852$	16.7337	0.573286
$853$	39.2726	1.34467	0.672334	−	0.740248i	$-0.265292\pi$
$853$	39.2726	1.34467	0.672334	+	0.740248i	$0.265292\pi$
$854$	−18.1602	−0.621430
$855$	−106.385	−3.63829
$856$	−11.8267	−0.404228
$857$	−15.3486	−0.524298	−0.262149	−	0.965027i	$-0.584431\pi$
$857$	−15.3486	−0.524298	−0.262149	+	0.965027i	$0.584431\pi$
$858$	−3.84082	−0.131123
$859$	8.71946	0.297504	0.148752	−	0.988875i	$-0.452474\pi$
$859$	8.71946	0.297504	0.148752	+	0.988875i	$0.452474\pi$
$860$	−1.11614	−0.0380601
$861$	69.4742	2.36767
$862$	3.30507	0.112571
$863$	−11.9056	−0.405270	−0.202635	−	0.979254i	$-0.564951\pi$
$863$	−11.9056	−0.405270	−0.202635	+	0.979254i	$0.564951\pi$
$864$	−6.34693	−0.215927
$865$	−42.7770	−1.45446
$866$	39.0239	1.32609
$867$	−80.2335	−2.72487
$868$	−9.58730	−0.325414
$869$	8.59423	0.291539
$870$	−51.7193	−1.75345
$871$	−9.02934	−0.305948
$872$	7.93604	0.268748
$873$	−10.6827	−0.361556
$874$	−14.3130	−0.484145
$875$	−74.0739	−2.50416
$876$	−41.9510	−1.41739
$877$	11.4537	0.386764	0.193382	−	0.981123i	$-0.438054\pi$
$877$	11.4537	0.386764	0.193382	+	0.981123i	$0.438054\pi$
$878$	6.52392	0.220172
$879$	−14.0977	−0.475502
$880$	−2.82956	−0.0953844
$881$	−38.4270	−1.29464	−0.647319	−	0.762219i	$-0.724110\pi$
$881$	−38.4270	−1.29464	−0.647319	+	0.762219i	$0.724110\pi$
$882$	−8.09841	−0.272688
$883$	4.64106	0.156184	0.0780920	−	0.996946i	$-0.475117\pi$
$883$	4.64106	0.156184	0.0780920	+	0.996946i	$0.475117\pi$
$884$	13.3167	0.447889
$885$	−42.2657	−1.42074
$886$	−21.4714	−0.721344
$887$	43.4295	1.45822	0.729110	−	0.684397i	$-0.239934\pi$
$887$	43.4295	1.45822	0.729110	+	0.684397i	$0.239934\pi$
$888$	−5.82325	−0.195415
$889$	−14.5130	−0.486752
$890$	18.9249	0.634365
$891$	−1.71956	−0.0576073
$892$	−8.33886	−0.279206
$893$	−22.4522	−0.751333
$894$	−6.21973	−0.208019
$895$	26.8486	0.897449
$896$	−2.33387	−0.0779691
$897$	16.7331	0.558703
$898$	12.1596	0.405772
$899$	17.6839	0.589790
$900$	65.5542	2.18514
$901$	−31.9121	−1.06315
$902$	−7.01085	−0.233436
$903$	−1.78107	−0.0592703
$904$	0.577304	0.0192009
$905$	45.1164	1.49972
$906$	−35.8610	−1.19140
$907$	−12.1002	−0.401781	−0.200891	−	0.979614i	$-0.564384\pi$
$907$	−12.1002	−0.401781	−0.200891	+	0.979614i	$0.564384\pi$
$908$	12.2350	0.406032
$909$	−32.5647	−1.08010
$910$	19.4223	0.643843
$911$	−41.3820	−1.37105	−0.685524	−	0.728050i	$-0.740427\pi$
$911$	−41.3820	−1.37105	−0.685524	+	0.728050i	$0.740427\pi$
$912$	13.9494	0.461909
$913$	−3.84443	−0.127232
$914$	−2.82134	−0.0933217
$915$	−93.4846	−3.09051
$916$	9.58349	0.316647
$917$	−50.8589	−1.67951
$918$	42.5737	1.40514
$919$	34.6940	1.14445	0.572225	−	0.820097i	$-0.306081\pi$
$919$	34.6940	1.14445	0.572225	+	0.820097i	$0.306081\pi$
$920$	12.3274	0.406423
$921$	77.9625	2.56895
$922$	24.5352	0.808023
$923$	11.5910	0.381522
$924$	−4.51523	−0.148540
$925$	25.5425	0.839832
$926$	22.8312	0.750278
$927$	27.9141	0.916821
$928$	4.30484	0.141313
$929$	−35.0234	−1.14908	−0.574540	−	0.818476i	$-0.694819\pi$
$929$	−35.0234	−1.14908	−0.574540	+	0.818476i	$0.694819\pi$
$930$	−49.3532	−1.61835
$931$	7.55878	0.247729
$932$	−17.5840	−0.575982
$933$	−64.3096	−2.10540
$934$	26.9331	0.881279
$935$	18.9800	0.620712
$936$	−10.3522	−0.338371
$937$	−53.7612	−1.75630	−0.878151	−	0.478384i	$-0.841223\pi$
$937$	−53.7612	−1.75630	−0.878151	+	0.478384i	$0.841223\pi$
$938$	−10.6148	−0.346586
$939$	79.3595	2.58980
$940$	19.3375	0.630718
$941$	−13.5022	−0.440160	−0.220080	−	0.975482i	$-0.570632\pi$
$941$	−13.5022	−0.440160	−0.220080	+	0.975482i	$0.570632\pi$
$942$	−44.4554	−1.44843
$943$	30.5439	0.994646
$944$	3.51797	0.114500
$945$	62.0934	2.01990
$946$	0.179733	0.00584363
$947$	57.4128	1.86566	0.932832	−	0.360312i	$-0.117330\pi$
$947$	57.4128	1.86566	0.932832	+	0.360312i	$0.117330\pi$
$948$	36.4908	1.18517
$949$	−29.0584	−0.943274
$950$	−61.1860	−1.98514
$951$	81.7505	2.65094
$952$	15.6550	0.507382
$953$	−20.8615	−0.675772	−0.337886	−	0.941187i	$-0.609712\pi$
$953$	−20.8615	−0.675772	−0.337886	+	0.941187i	$0.609712\pi$
$954$	24.8079	0.803185
$955$	−27.8924	−0.902578
$956$	−0.716956	−0.0231880
$957$	8.32839	0.269219
$958$	−11.3564	−0.366910
$959$	−36.3243	−1.17297
$960$	−12.0142	−0.387757
$961$	−14.1252	−0.455650
$962$	−4.03362	−0.130049
$963$	−61.6702	−1.98730
$964$	−16.7905	−0.540784
$965$	−53.4082	−1.71927
$966$	19.6714	0.632915
$967$	−39.5217	−1.27093	−0.635465	−	0.772129i	$-0.719192\pi$
$967$	−39.5217	−1.27093	−0.635465	+	0.772129i	$0.719192\pi$
$968$	−10.5444	−0.338908
$969$	−93.5689	−3.00587
$970$	−8.58767	−0.275733
$971$	4.17106	0.133856	0.0669279	−	0.997758i	$-0.478680\pi$
$971$	4.17106	0.133856	0.0669279	+	0.997758i	$0.478680\pi$
$972$	11.7396	0.376548
$973$	−26.3143	−0.843598
$974$	5.28079	0.169207
$975$	71.5316	2.29085
$976$	7.78117	0.249069
$977$	−49.3663	−1.57937	−0.789684	−	0.613513i	$-0.789756\pi$
$977$	−49.3663	−1.57937	−0.789684	+	0.613513i	$0.789756\pi$
$978$	66.9883	2.14205
$979$	−3.04750	−0.0973984
$980$	−6.51018	−0.207960
$981$	41.3824	1.32124
$982$	−29.4378	−0.939397
$983$	−15.8263	−0.504780	−0.252390	−	0.967626i	$-0.581217\pi$
$983$	−15.8263	−0.504780	−0.252390	+	0.967626i	$0.581217\pi$
$984$	−29.7678	−0.948964
$985$	−42.5717	−1.35645
$986$	−28.8758	−0.919594
$987$	30.8575	0.982206
$988$	9.66236	0.307401
$989$	−0.783037	−0.0248991
$990$	−14.7547	−0.468935
$991$	47.4299	1.50666	0.753330	−	0.657642i	$-0.228446\pi$
$991$	47.4299	1.50666	0.753330	+	0.657642i	$0.228446\pi$
$992$	4.10790	0.130426
$993$	−28.2477	−0.896413
$994$	13.6263	0.432199
$995$	66.0132	2.09276
$996$	−16.3233	−0.517224
$997$	10.3279	0.327088	0.163544	−	0.986536i	$-0.447707\pi$
$997$	10.3279	0.327088	0.163544	+	0.986536i	$0.447707\pi$
$998$	−17.5255	−0.554759
$999$	−12.8955	−0.407996

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.d.1.4	✓	52

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.d.1.4	✓	52	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:	\( N \)	\(=\)	\( 4034 = 2 \cdot 2017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4034.a (trivial)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -2.86609 q^{3} +1.00000 q^{4} +4.19184 q^{5} -2.86609 q^{6} -2.33387 q^{7} +1.00000 q^{8} +5.21449 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -2.86609 q^{3} +1.00000 q^{4} +4.19184 q^{5} -2.86609 q^{6} -2.33387 q^{7} +1.00000 q^{8} +5.21449 q^{9} +4.19184 q^{10} -0.675015 q^{11} -2.86609 q^{12} -1.98527 q^{13} -2.33387 q^{14} -12.0142 q^{15} +1.00000 q^{16} -6.70776 q^{17} +5.21449 q^{18} -4.86703 q^{19} +4.19184 q^{20} +6.68908 q^{21} -0.675015 q^{22} +2.94081 q^{23} -2.86609 q^{24} +12.5715 q^{25} -1.98527 q^{26} -6.34693 q^{27} -2.33387 q^{28} +4.30484 q^{29} -12.0142 q^{30} +4.10790 q^{31} +1.00000 q^{32} +1.93466 q^{33} -6.70776 q^{34} -9.78321 q^{35} +5.21449 q^{36} +2.03177 q^{37} -4.86703 q^{38} +5.68997 q^{39} +4.19184 q^{40} +10.3862 q^{41} +6.68908 q^{42} -0.266265 q^{43} -0.675015 q^{44} +21.8583 q^{45} +2.94081 q^{46} +4.61312 q^{47} -2.86609 q^{48} -1.55306 q^{49} +12.5715 q^{50} +19.2251 q^{51} -1.98527 q^{52} +4.75749 q^{53} -6.34693 q^{54} -2.82956 q^{55} -2.33387 q^{56} +13.9494 q^{57} +4.30484 q^{58} +3.51797 q^{59} -12.0142 q^{60} +7.78117 q^{61} +4.10790 q^{62} -12.1699 q^{63} +1.00000 q^{64} -8.32194 q^{65} +1.93466 q^{66} +4.54817 q^{67} -6.70776 q^{68} -8.42865 q^{69} -9.78321 q^{70} -5.83849 q^{71} +5.21449 q^{72} +14.6370 q^{73} +2.03177 q^{74} -36.0312 q^{75} -4.86703 q^{76} +1.57540 q^{77} +5.68997 q^{78} -12.7319 q^{79} +4.19184 q^{80} +2.54743 q^{81} +10.3862 q^{82} +5.69532 q^{83} +6.68908 q^{84} -28.1179 q^{85} -0.266265 q^{86} -12.3381 q^{87} -0.675015 q^{88} +4.51471 q^{89} +21.8583 q^{90} +4.63336 q^{91} +2.94081 q^{92} -11.7736 q^{93} +4.61312 q^{94} -20.4018 q^{95} -2.86609 q^{96} -2.04866 q^{97} -1.55306 q^{98} -3.51986 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9}+O(q^{10}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9	\( 52 q + 52 q^{2} + 16 q^{3} + 52 q^{4} + 24 q^{5} + 16 q^{6} + 12 q^{7} + 52 q^{8} + 70 q^{9} + 24 q^{10} + 19 q^{11} + 16 q^{12} + 27 q^{13} + 12 q^{14} + 5 q^{15} + 52 q^{16} + 43 q^{17} + 70 q^{18} + 35 q^{19} + 24 q^{20} + 29 q^{21} + 19 q^{22} + 2 q^{23} + 16 q^{24} + 88 q^{25} + 27 q^{26} + 49 q^{27} + 12 q^{28} + 31 q^{29} + 5 q^{30} + 59 q^{31} + 52 q^{32} + 45 q^{33} + 43 q^{34} + 18 q^{35} + 70 q^{36} + 60 q^{37} + 35 q^{38} + 6 q^{39} + 24 q^{40} + 56 q^{41} + 29 q^{42} + 34 q^{43} + 19 q^{44} + 61 q^{45} + 2 q^{46} - 4 q^{47} + 16 q^{48} + 102 q^{49} + 88 q^{50} + 23 q^{51} + 27 q^{52} + 30 q^{53} + 49 q^{54} + 24 q^{55} + 12 q^{56} + 32 q^{57} + 31 q^{58} + 27 q^{59} + 5 q^{60} + 107 q^{61} + 59 q^{62} - 4 q^{63} + 52 q^{64} + 46 q^{65} + 45 q^{66} + 22 q^{67} + 43 q^{68} + 36 q^{69} + 18 q^{70} + 8 q^{71} + 70 q^{72} + 66 q^{73} + 60 q^{74} + 53 q^{75} + 35 q^{76} + 26 q^{77} + 6 q^{78} + 50 q^{79} + 24 q^{80} + 108 q^{81} + 56 q^{82} + 52 q^{83} + 29 q^{84} + 19 q^{85} + 34 q^{86} - 32 q^{87} + 19 q^{88} + 62 q^{89} + 61 q^{90} + 69 q^{91} + 2 q^{92} + 21 q^{93} - 4 q^{94} - 44 q^{95} + 16 q^{96} + 82 q^{97} + 102 q^{98} + 16 q^{99}+O(q^{100}) \) 52 * q + 52 * q^2 + 16 * q^3 + 52 * q^4 + 24 * q^5 + 16 * q^6 + 12 * q^7 + 52 * q^8 + 70 * q^9 + 24 * q^10 + 19 * q^11 + 16 * q^12 + 27 * q^13 + 12 * q^14 + 5 * q^15 + 52 * q^16 + 43 * q^17 + 70 * q^18 + 35 * q^19 + 24 * q^20 + 29 * q^21 + 19 * q^22 + 2 * q^23 + 16 * q^24 + 88 * q^25 + 27 * q^26 + 49 * q^27 + 12 * q^28 + 31 * q^29 + 5 * q^30 + 59 * q^31 + 52 * q^32 + 45 * q^33 + 43 * q^34 + 18 * q^35 + 70 * q^36 + 60 * q^37 + 35 * q^38 + 6 * q^39 + 24 * q^40 + 56 * q^41 + 29 * q^42 + 34 * q^43 + 19 * q^44 + 61 * q^45 + 2 * q^46 - 4 * q^47 + 16 * q^48 + 102 * q^49 + 88 * q^50 + 23 * q^51 + 27 * q^52 + 30 * q^53 + 49 * q^54 + 24 * q^55 + 12 * q^56 + 32 * q^57 + 31 * q^58 + 27 * q^59 + 5 * q^60 + 107 * q^61 + 59 * q^62 - 4 * q^63 + 52 * q^64 + 46 * q^65 + 45 * q^66 + 22 * q^67 + 43 * q^68 + 36 * q^69 + 18 * q^70 + 8 * q^71 + 70 * q^72 + 66 * q^73 + 60 * q^74 + 53 * q^75 + 35 * q^76 + 26 * q^77 + 6 * q^78 + 50 * q^79 + 24 * q^80 + 108 * q^81 + 56 * q^82 + 52 * q^83 + 29 * q^84 + 19 * q^85 + 34 * q^86 - 32 * q^87 + 19 * q^88 + 62 * q^89 + 61 * q^90 + 69 * q^91 + 2 * q^92 + 21 * q^93 - 4 * q^94 - 44 * q^95 + 16 * q^96 + 82 * q^97 + 102 * q^98 + 16 * q^99

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