LMFDB - Embedded newform 4034.2.a.a.1.20

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:	$1$
Dimension:	$33$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
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)

$f(q)$	$=$	$q+1.00000 q^{2} -0.138152 q^{3} +1.00000 q^{4} -3.80380 q^{5} -0.138152 q^{6} +3.68849 q^{7} +1.00000 q^{8} -2.98091 q^{9} +O(q^{10})$	\(q+1.00000 q^{2} -0.138152 q^{3} +1.00000 q^{4} -3.80380 q^{5} -0.138152 q^{6} +3.68849 q^{7} +1.00000 q^{8} -2.98091 q^{9} -3.80380 q^{10} +4.03674 q^{11} -0.138152 q^{12} -4.85511 q^{13} +3.68849 q^{14} +0.525503 q^{15} +1.00000 q^{16} -1.82831 q^{17} -2.98091 q^{18} -1.46334 q^{19} -3.80380 q^{20} -0.509572 q^{21} +4.03674 q^{22} +6.78550 q^{23} -0.138152 q^{24} +9.46890 q^{25} -4.85511 q^{26} +0.826276 q^{27} +3.68849 q^{28} -3.37734 q^{29} +0.525503 q^{30} -7.05545 q^{31} +1.00000 q^{32} -0.557684 q^{33} -1.82831 q^{34} -14.0303 q^{35} -2.98091 q^{36} -3.22613 q^{37} -1.46334 q^{38} +0.670743 q^{39} -3.80380 q^{40} -6.92393 q^{41} -0.509572 q^{42} +10.0300 q^{43} +4.03674 q^{44} +11.3388 q^{45} +6.78550 q^{46} +5.16480 q^{47} -0.138152 q^{48} +6.60495 q^{49} +9.46890 q^{50} +0.252584 q^{51} -4.85511 q^{52} -0.900238 q^{53} +0.826276 q^{54} -15.3549 q^{55} +3.68849 q^{56} +0.202163 q^{57} -3.37734 q^{58} -11.9050 q^{59} +0.525503 q^{60} -11.3671 q^{61} -7.05545 q^{62} -10.9951 q^{63} +1.00000 q^{64} +18.4679 q^{65} -0.557684 q^{66} -7.72296 q^{67} -1.82831 q^{68} -0.937431 q^{69} -14.0303 q^{70} -6.54530 q^{71} -2.98091 q^{72} -9.18729 q^{73} -3.22613 q^{74} -1.30815 q^{75} -1.46334 q^{76} +14.8895 q^{77} +0.670743 q^{78} +9.47457 q^{79} -3.80380 q^{80} +8.82859 q^{81} -6.92393 q^{82} -15.2040 q^{83} -0.509572 q^{84} +6.95451 q^{85} +10.0300 q^{86} +0.466586 q^{87} +4.03674 q^{88} +12.3062 q^{89} +11.3388 q^{90} -17.9080 q^{91} +6.78550 q^{92} +0.974726 q^{93} +5.16480 q^{94} +5.56625 q^{95} -0.138152 q^{96} -7.27093 q^{97} +6.60495 q^{98} -12.0332 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) $ 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * 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 $

$2$	1.00000	0.707107
$2$	1.00000	0.707107
$3$	−0.138152	−0.0797622	−0.0398811	−	0.999204i	$-0.512698\pi$
$3$	−0.138152	−0.0797622	−0.0398811	+	0.999204i	$0.512698\pi$
$4$	1.00000	0.500000
$5$	−3.80380	−1.70111	−0.850556	−	0.525885i	$-0.823734\pi$
$5$	−3.80380	−1.70111	−0.850556	+	0.525885i	$0.823734\pi$
$6$	−0.138152	−0.0564004
$7$	3.68849	1.39412	0.697059	−	0.717014i	$-0.254492\pi$
$7$	3.68849	1.39412	0.697059	+	0.717014i	$0.254492\pi$
$8$	1.00000	0.353553
$9$	−2.98091	−0.993638
$10$	−3.80380	−1.20287
$11$	4.03674	1.21712	0.608561	−	0.793507i	$-0.291747\pi$
$11$	4.03674	1.21712	0.608561	+	0.793507i	$0.291747\pi$
$12$	−0.138152	−0.0398811
$13$	−4.85511	−1.34656	−0.673282	−	0.739386i	$-0.735116\pi$
$13$	−4.85511	−1.34656	−0.673282	+	0.739386i	$0.735116\pi$
$14$	3.68849	0.985790
$15$	0.525503	0.135684
$16$	1.00000	0.250000
$17$	−1.82831	−0.443429	−0.221715	−	0.975112i	$-0.571165\pi$
$17$	−1.82831	−0.443429	−0.221715	+	0.975112i	$0.571165\pi$
$18$	−2.98091	−0.702608
$19$	−1.46334	−0.335713	−0.167856	−	0.985811i	$-0.553685\pi$
$19$	−1.46334	−0.335713	−0.167856	+	0.985811i	$0.553685\pi$
$20$	−3.80380	−0.850556
$21$	−0.509572	−0.111198
$22$	4.03674	0.860636
$23$	6.78550	1.41487	0.707437	−	0.706777i	$-0.249851\pi$
$23$	6.78550	1.41487	0.707437	+	0.706777i	$0.249851\pi$
$24$	−0.138152	−0.0282002
$25$	9.46890	1.89378
$26$	−4.85511	−0.952165
$27$	0.826276	0.159017
$28$	3.68849	0.697059
$29$	−3.37734	−0.627156	−0.313578	−	0.949562i	$-0.601528\pi$
$29$	−3.37734	−0.627156	−0.313578	+	0.949562i	$0.601528\pi$
$30$	0.525503	0.0959433
$31$	−7.05545	−1.26720	−0.633598	−	0.773662i	$-0.718423\pi$
$31$	−7.05545	−1.26720	−0.633598	+	0.773662i	$0.718423\pi$
$32$	1.00000	0.176777
$33$	−0.557684	−0.0970803
$34$	−1.82831	−0.313552
$35$	−14.0303	−2.37155
$36$	−2.98091	−0.496819
$37$	−3.22613	−0.530372	−0.265186	−	0.964197i	$-0.585433\pi$
$37$	−3.22613	−0.530372	−0.265186	+	0.964197i	$0.585433\pi$
$38$	−1.46334	−0.237385
$39$	0.670743	0.107405
$40$	−3.80380	−0.601434
$41$	−6.92393	−1.08134	−0.540668	−	0.841236i	$-0.681828\pi$
$41$	−6.92393	−1.08134	−0.540668	+	0.841236i	$0.681828\pi$
$42$	−0.509572	−0.0786287
$43$	10.0300	1.52956	0.764779	−	0.644292i	$-0.222848\pi$
$43$	10.0300	1.52956	0.764779	+	0.644292i	$0.222848\pi$
$44$	4.03674	0.608561
$45$	11.3388	1.69029
$46$	6.78550	1.00047
$47$	5.16480	0.753364	0.376682	−	0.926343i	$-0.377065\pi$
$47$	5.16480	0.753364	0.376682	+	0.926343i	$0.377065\pi$
$48$	−0.138152	−0.0199405
$49$	6.60495	0.943564
$50$	9.46890	1.33910
$51$	0.252584	0.0353689
$52$	−4.85511	−0.673282
$53$	−0.900238	−0.123657	−0.0618286	−	0.998087i	$-0.519693\pi$
$53$	−0.900238	−0.123657	−0.0618286	+	0.998087i	$0.519693\pi$
$54$	0.826276	0.112442
$55$	−15.3549	−2.07046
$56$	3.68849	0.492895
$57$	0.202163	0.0267772
$58$	−3.37734	−0.443466
$59$	−11.9050	−1.54990	−0.774951	−	0.632021i	$-0.782226\pi$
$59$	−11.9050	−1.54990	−0.774951	+	0.632021i	$0.782226\pi$
$60$	0.525503	0.0678422
$61$	−11.3671	−1.45541	−0.727705	−	0.685890i	$-0.759413\pi$
$61$	−11.3671	−1.45541	−0.727705	+	0.685890i	$0.759413\pi$
$62$	−7.05545	−0.896043
$63$	−10.9951	−1.38525
$64$	1.00000	0.125000
$65$	18.4679	2.29066
$66$	−0.557684	−0.0686462
$67$	−7.72296	−0.943510	−0.471755	−	0.881730i	$-0.656379\pi$
$67$	−7.72296	−0.943510	−0.471755	+	0.881730i	$0.656379\pi$
$68$	−1.82831	−0.221715
$69$	−0.937431	−0.112853
$70$	−14.0303	−1.67694
$71$	−6.54530	−0.776784	−0.388392	−	0.921494i	$-0.626969\pi$
$71$	−6.54530	−0.776784	−0.388392	+	0.921494i	$0.626969\pi$
$72$	−2.98091	−0.351304
$73$	−9.18729	−1.07529	−0.537645	−	0.843171i	$-0.680686\pi$
$73$	−9.18729	−1.07529	−0.537645	+	0.843171i	$0.680686\pi$
$74$	−3.22613	−0.375030
$75$	−1.30815	−0.151052
$76$	−1.46334	−0.167856
$77$	14.8895	1.69681
$78$	0.670743	0.0759467
$79$	9.47457	1.06597	0.532986	−	0.846124i	$-0.321070\pi$
$79$	9.47457	1.06597	0.532986	+	0.846124i	$0.321070\pi$
$80$	−3.80380	−0.425278
$81$	8.82859	0.980954
$82$	−6.92393	−0.764620
$83$	−15.2040	−1.66885	−0.834426	−	0.551120i	$-0.814201\pi$
$83$	−15.2040	−1.66885	−0.834426	+	0.551120i	$0.814201\pi$
$84$	−0.509572	−0.0555989
$85$	6.95451	0.754322
$86$	10.0300	1.08156
$87$	0.466586	0.0500233
$88$	4.03674	0.430318
$89$	12.3062	1.30446	0.652230	−	0.758021i	$-0.273834\pi$
$89$	12.3062	1.30446	0.652230	+	0.758021i	$0.273834\pi$
$90$	11.3388	1.19521
$91$	−17.9080	−1.87727
$92$	6.78550	0.707437
$93$	0.974726	0.101074
$94$	5.16480	0.532709
$95$	5.56625	0.571085
$96$	−0.138152	−0.0141001
$97$	−7.27093	−0.738251	−0.369126	−	0.929380i	$-0.620343\pi$
$97$	−7.27093	−0.738251	−0.369126	+	0.929380i	$0.620343\pi$
$98$	6.60495	0.667201
$99$	−12.0332	−1.20938
$100$	9.46890	0.946890
$101$	10.5961	1.05435	0.527174	−	0.849757i	$-0.323251\pi$
$101$	10.5961	1.05435	0.527174	+	0.849757i	$0.323251\pi$
$102$	0.252584	0.0250096
$103$	8.19283	0.807264	0.403632	−	0.914921i	$-0.367748\pi$
$103$	8.19283	0.807264	0.403632	+	0.914921i	$0.367748\pi$
$104$	−4.85511	−0.476082
$105$	1.93831	0.189160
$106$	−0.900238	−0.0874388
$107$	−20.2784	−1.96038	−0.980192	−	0.198048i	$-0.936540\pi$
$107$	−20.2784	−1.96038	−0.980192	+	0.198048i	$0.936540\pi$
$108$	0.826276	0.0795084
$109$	−8.81048	−0.843891	−0.421946	−	0.906621i	$-0.638653\pi$
$109$	−8.81048	−0.843891	−0.421946	+	0.906621i	$0.638653\pi$
$110$	−15.3549	−1.46404
$111$	0.445697	0.0423037
$112$	3.68849	0.348529
$113$	−13.7147	−1.29017	−0.645086	−	0.764110i	$-0.723178\pi$
$113$	−13.7147	−1.29017	−0.645086	+	0.764110i	$0.723178\pi$
$114$	0.202163	0.0189343
$115$	−25.8107	−2.40686
$116$	−3.37734	−0.313578
$117$	14.4727	1.33800
$118$	−11.9050	−1.09595
$119$	−6.74368	−0.618193
$120$	0.525503	0.0479716
$121$	5.29526	0.481387
$122$	−11.3671	−1.02913
$123$	0.956555	0.0862497
$124$	−7.05545	−0.633598
$125$	−16.9988	−1.52042
$126$	−10.9951	−0.979518
$127$	−21.0234	−1.86552	−0.932761	−	0.360495i	$-0.882608\pi$
$127$	−21.0234	−1.86552	−0.932761	+	0.360495i	$0.882608\pi$
$128$	1.00000	0.0883883
$129$	−1.38566	−0.122001
$130$	18.4679	1.61974
$131$	16.4176	1.43442	0.717208	−	0.696859i	$-0.245420\pi$
$131$	16.4176	1.43442	0.717208	+	0.696859i	$0.245420\pi$
$132$	−0.557684	−0.0485402
$133$	−5.39751	−0.468023
$134$	−7.72296	−0.667162
$135$	−3.14299	−0.270505
$136$	−1.82831	−0.156776
$137$	20.9287	1.78806	0.894029	−	0.448010i	$-0.147867\pi$
$137$	20.9287	1.78806	0.894029	+	0.448010i	$0.147867\pi$
$138$	−0.937431	−0.0797994
$139$	−10.4097	−0.882937	−0.441469	−	0.897277i	$-0.645542\pi$
$139$	−10.4097	−0.882937	−0.441469	+	0.897277i	$0.645542\pi$
$140$	−14.0303	−1.18577
$141$	−0.713528	−0.0600899
$142$	−6.54530	−0.549269
$143$	−19.5988	−1.63893
$144$	−2.98091	−0.248409
$145$	12.8467	1.06686
$146$	−9.18729	−0.760345
$147$	−0.912488	−0.0752607
$148$	−3.22613	−0.265186
$149$	−3.94529	−0.323211	−0.161605	−	0.986855i	$-0.551667\pi$
$149$	−3.94529	−0.323211	−0.161605	+	0.986855i	$0.551667\pi$
$150$	−1.30815	−0.106810
$151$	−0.295322	−0.0240330	−0.0120165	−	0.999928i	$-0.503825\pi$
$151$	−0.295322	−0.0240330	−0.0120165	+	0.999928i	$0.503825\pi$
$152$	−1.46334	−0.118692
$153$	5.45002	0.440608
$154$	14.8895	1.19983
$155$	26.8375	2.15564
$156$	0.670743	0.0537024
$157$	−14.1425	−1.12869	−0.564346	−	0.825539i	$-0.690871\pi$
$157$	−14.1425	−1.12869	−0.564346	+	0.825539i	$0.690871\pi$
$158$	9.47457	0.753756
$159$	0.124370	0.00986317
$160$	−3.80380	−0.300717
$161$	25.0282	1.97250
$162$	8.82859	0.693640
$163$	−12.1044	−0.948092	−0.474046	−	0.880500i	$-0.657207\pi$
$163$	−12.1044	−0.948092	−0.474046	+	0.880500i	$0.657207\pi$
$164$	−6.92393	−0.540668
$165$	2.12132	0.165144
$166$	−15.2040	−1.18006
$167$	6.66582	0.515817	0.257908	−	0.966169i	$-0.416967\pi$
$167$	6.66582	0.515817	0.257908	+	0.966169i	$0.416967\pi$
$168$	−0.509572	−0.0393144
$169$	10.5721	0.813236
$170$	6.95451	0.533387
$171$	4.36209	0.333577
$172$	10.0300	0.764779
$173$	−18.4517	−1.40285	−0.701427	−	0.712742i	$-0.747453\pi$
$173$	−18.4517	−1.40285	−0.701427	+	0.712742i	$0.747453\pi$
$174$	0.466586	0.0353718
$175$	34.9259	2.64015
$176$	4.03674	0.304281
$177$	1.64470	0.123624
$178$	12.3062	0.922392
$179$	19.0973	1.42740	0.713699	−	0.700453i	$-0.247019\pi$
$179$	19.0973	1.42740	0.713699	+	0.700453i	$0.247019\pi$
$180$	11.3388	0.845144
$181$	−4.89318	−0.363707	−0.181854	−	0.983326i	$-0.558210\pi$
$181$	−4.89318	−0.363707	−0.181854	+	0.983326i	$0.558210\pi$
$182$	−17.9080	−1.32743
$183$	1.57039	0.116087
$184$	6.78550	0.500233
$185$	12.2716	0.902223
$186$	0.974726	0.0714704
$187$	−7.38039	−0.539708
$188$	5.16480	0.376682
$189$	3.04771	0.221688
$190$	5.56625	0.403818
$191$	−5.83595	−0.422275	−0.211137	−	0.977456i	$-0.567717\pi$
$191$	−5.83595	−0.422275	−0.211137	+	0.977456i	$0.567717\pi$
$192$	−0.138152	−0.00997027
$193$	−12.5386	−0.902545	−0.451273	−	0.892386i	$-0.649030\pi$
$193$	−12.5386	−0.902545	−0.451273	+	0.892386i	$0.649030\pi$
$194$	−7.27093	−0.522022
$195$	−2.55137	−0.182708
$196$	6.60495	0.471782
$197$	8.62742	0.614678	0.307339	−	0.951600i	$-0.400561\pi$
$197$	8.62742	0.614678	0.307339	+	0.951600i	$0.400561\pi$
$198$	−12.0332	−0.855160
$199$	16.5608	1.17396	0.586981	−	0.809601i	$-0.300316\pi$
$199$	16.5608	1.17396	0.586981	+	0.809601i	$0.300316\pi$
$200$	9.46890	0.669552
$201$	1.06694	0.0752564
$202$	10.5961	0.745537
$203$	−12.4573	−0.874329
$204$	0.252584	0.0176844
$205$	26.3372	1.83947
$206$	8.19283	0.570822
$207$	−20.2270	−1.40587
$208$	−4.85511	−0.336641
$209$	−5.90712	−0.408604
$210$	1.93831	0.133756
$211$	−4.17720	−0.287570	−0.143785	−	0.989609i	$-0.545927\pi$
$211$	−4.17720	−0.287570	−0.143785	+	0.989609i	$0.545927\pi$
$212$	−0.900238	−0.0618286
$213$	0.904247	0.0619580
$214$	−20.2784	−1.38620
$215$	−38.1521	−2.60195
$216$	0.826276	0.0562210
$217$	−26.0240	−1.76662
$218$	−8.81048	−0.596721
$219$	1.26924	0.0857675
$220$	−15.3549	−1.03523
$221$	8.87662	0.597106
$222$	0.445697	0.0299132
$223$	1.43780	0.0962819	0.0481410	−	0.998841i	$-0.484670\pi$
$223$	1.43780	0.0962819	0.0481410	+	0.998841i	$0.484670\pi$
$224$	3.68849	0.246448
$225$	−28.2260	−1.88173
$226$	−13.7147	−0.912289
$227$	14.0106	0.929915	0.464957	−	0.885333i	$-0.346070\pi$
$227$	14.0106	0.929915	0.464957	+	0.885333i	$0.346070\pi$
$228$	0.202163	0.0133886
$229$	26.8105	1.77169	0.885845	−	0.463981i	$-0.153579\pi$
$229$	26.8105	1.77169	0.885845	+	0.463981i	$0.153579\pi$
$230$	−25.8107	−1.70191
$231$	−2.05701	−0.135341
$232$	−3.37734	−0.221733
$233$	−13.5620	−0.888474	−0.444237	−	0.895909i	$-0.646525\pi$
$233$	−13.5620	−0.888474	−0.444237	+	0.895909i	$0.646525\pi$
$234$	14.4727	0.946107
$235$	−19.6459	−1.28156
$236$	−11.9050	−0.774951
$237$	−1.30893	−0.0850243
$238$	−6.74368	−0.437128
$239$	−12.2472	−0.792206	−0.396103	−	0.918206i	$-0.629638\pi$
$239$	−12.2472	−0.792206	−0.396103	+	0.918206i	$0.629638\pi$
$240$	0.525503	0.0339211
$241$	−4.44401	−0.286264	−0.143132	−	0.989704i	$-0.545717\pi$
$241$	−4.44401	−0.286264	−0.143132	+	0.989704i	$0.545717\pi$
$242$	5.29526	0.340392
$243$	−3.69852	−0.237260
$244$	−11.3671	−0.727705
$245$	−25.1239	−1.60511
$246$	0.956555	0.0609877
$247$	7.10467	0.452059
$248$	−7.05545	−0.448022
$249$	2.10046	0.133111
$250$	−16.9988	−1.07510
$251$	−25.7564	−1.62573	−0.812863	−	0.582454i	$-0.802092\pi$
$251$	−25.7564	−1.62573	−0.812863	+	0.582454i	$0.802092\pi$
$252$	−10.9951	−0.692624
$253$	27.3913	1.72207
$254$	−21.0234	−1.31912
$255$	−0.960780	−0.0601664
$256$	1.00000	0.0625000
$257$	−14.7742	−0.921587	−0.460793	−	0.887508i	$-0.652435\pi$
$257$	−14.7742	−0.921587	−0.460793	+	0.887508i	$0.652435\pi$
$258$	−1.38566	−0.0862677
$259$	−11.8995	−0.739402
$260$	18.4679	1.14533
$261$	10.0676	0.623166
$262$	16.4176	1.01428
$263$	25.6841	1.58375	0.791875	−	0.610683i	$-0.209105\pi$
$263$	25.6841	1.58375	0.791875	+	0.610683i	$0.209105\pi$
$264$	−0.557684	−0.0343231
$265$	3.42433	0.210355
$266$	−5.39751	−0.330942
$267$	−1.70013	−0.104047
$268$	−7.72296	−0.471755
$269$	−4.09706	−0.249802	−0.124901	−	0.992169i	$-0.539861\pi$
$269$	−4.09706	−0.249802	−0.124901	+	0.992169i	$0.539861\pi$
$270$	−3.14299	−0.191276
$271$	−26.3848	−1.60276	−0.801380	−	0.598155i	$-0.795901\pi$
$271$	−26.3848	−1.60276	−0.801380	+	0.598155i	$0.795901\pi$
$272$	−1.82831	−0.110857
$273$	2.47403	0.149735
$274$	20.9287	1.26435
$275$	38.2235	2.30496
$276$	−0.937431	−0.0564267
$277$	−3.50538	−0.210618	−0.105309	−	0.994440i	$-0.533583\pi$
$277$	−3.50538	−0.210618	−0.105309	+	0.994440i	$0.533583\pi$
$278$	−10.4097	−0.624331
$279$	21.0317	1.25913
$280$	−14.0303	−0.838469
$281$	−15.1449	−0.903469	−0.451735	−	0.892152i	$-0.649195\pi$
$281$	−15.1449	−0.903469	−0.451735	+	0.892152i	$0.649195\pi$
$282$	−0.713528	−0.0424900
$283$	−18.5136	−1.10052	−0.550260	−	0.834994i	$-0.685471\pi$
$283$	−18.5136	−1.10052	−0.550260	+	0.834994i	$0.685471\pi$
$284$	−6.54530	−0.388392
$285$	−0.768989	−0.0455510
$286$	−19.5988	−1.15890
$287$	−25.5388	−1.50751
$288$	−2.98091	−0.175652
$289$	−13.6573	−0.803371
$290$	12.8467	0.754385
$291$	1.00449	0.0588845
$292$	−9.18729	−0.537645
$293$	−14.3836	−0.840300	−0.420150	−	0.907455i	$-0.638022\pi$
$293$	−14.3836	−0.840300	−0.420150	+	0.907455i	$0.638022\pi$
$294$	−0.912488	−0.0532174
$295$	45.2843	2.63656
$296$	−3.22613	−0.187515
$297$	3.33546	0.193543
$298$	−3.94529	−0.228545
$299$	−32.9443	−1.90522
$300$	−1.30815	−0.0755260
$301$	36.9955	2.13238
$302$	−0.295322	−0.0169939
$303$	−1.46387	−0.0840971
$304$	−1.46334	−0.0839282
$305$	43.2382	2.47581
$306$	5.45002	0.311557
$307$	−0.402647	−0.0229803	−0.0114902	−	0.999934i	$-0.503658\pi$
$307$	−0.402647	−0.0229803	−0.0114902	+	0.999934i	$0.503658\pi$
$308$	14.8895	0.848406
$309$	−1.13186	−0.0643891
$310$	26.8375	1.52427
$311$	−9.21844	−0.522730	−0.261365	−	0.965240i	$-0.584173\pi$
$311$	−9.21844	−0.522730	−0.261365	+	0.965240i	$0.584173\pi$
$312$	0.670743	0.0379734
$313$	27.1929	1.53703	0.768515	−	0.639831i	$-0.220996\pi$
$313$	27.1929	1.53703	0.768515	+	0.639831i	$0.220996\pi$
$314$	−14.1425	−0.798105
$315$	41.8230	2.35646
$316$	9.47457	0.532986
$317$	19.3827	1.08864	0.544321	−	0.838877i	$-0.316787\pi$
$317$	19.3827	1.08864	0.544321	+	0.838877i	$0.316787\pi$
$318$	0.124370	0.00697431
$319$	−13.6334	−0.763326
$320$	−3.80380	−0.212639
$321$	2.80150	0.156365
$322$	25.0282	1.39477
$323$	2.67543	0.148865
$324$	8.82859	0.490477
$325$	−45.9725	−2.55010
$326$	−12.1044	−0.670403
$327$	1.21719	0.0673106
$328$	−6.92393	−0.382310
$329$	19.0503	1.05028
$330$	2.12132	0.116775
$331$	−6.09791	−0.335171	−0.167586	−	0.985858i	$-0.553597\pi$
$331$	−6.09791	−0.335171	−0.167586	+	0.985858i	$0.553597\pi$
$332$	−15.2040	−0.834426
$333$	9.61682	0.526998
$334$	6.66582	0.364738
$335$	29.3766	1.60502
$336$	−0.509572	−0.0277995
$337$	−3.96818	−0.216161	−0.108080	−	0.994142i	$-0.534470\pi$
$337$	−3.96818	−0.216161	−0.108080	+	0.994142i	$0.534470\pi$
$338$	10.5721	0.575045
$339$	1.89472	0.102907
$340$	6.95451	0.377161
$341$	−28.4810	−1.54233
$342$	4.36209	0.235875
$343$	−1.45714	−0.0786782
$344$	10.0300	0.540781
$345$	3.56580	0.191976
$346$	−18.4517	−0.991967
$347$	6.28003	0.337130	0.168565	−	0.985691i	$-0.446087\pi$
$347$	6.28003	0.337130	0.168565	+	0.985691i	$0.446087\pi$
$348$	0.466586	0.0250117
$349$	32.4634	1.73773	0.868863	−	0.495052i	$-0.164851\pi$
$349$	32.4634	1.73773	0.868863	+	0.495052i	$0.164851\pi$
$350$	34.9259	1.86687
$351$	−4.01166	−0.214126
$352$	4.03674	0.215159
$353$	−18.1646	−0.966804	−0.483402	−	0.875399i	$-0.660599\pi$
$353$	−18.1646	−0.966804	−0.483402	+	0.875399i	$0.660599\pi$
$354$	1.64470	0.0874151
$355$	24.8970	1.32140
$356$	12.3062	0.652230
$357$	0.931654	0.0493084
$358$	19.0973	1.00932
$359$	8.40485	0.443591	0.221795	−	0.975093i	$-0.428808\pi$
$359$	8.40485	0.443591	0.221795	+	0.975093i	$0.428808\pi$
$360$	11.3388	0.597607
$361$	−16.8586	−0.887297
$362$	−4.89318	−0.257180
$363$	−0.731551	−0.0383965
$364$	−17.9080	−0.938635
$365$	34.9466	1.82919
$366$	1.57039	0.0820856
$367$	−20.2081	−1.05485	−0.527427	−	0.849601i	$-0.676843\pi$
$367$	−20.2081	−1.05485	−0.527427	+	0.849601i	$0.676843\pi$
$368$	6.78550	0.353718
$369$	20.6396	1.07446
$370$	12.2716	0.637968
$371$	−3.32052	−0.172393
$372$	0.974726	0.0505372
$373$	30.4508	1.57668	0.788340	−	0.615240i	$-0.210941\pi$
$373$	30.4508	1.57668	0.788340	+	0.615240i	$0.210941\pi$
$374$	−7.38039	−0.381631
$375$	2.34842	0.121272
$376$	5.16480	0.266354
$377$	16.3973	0.844506
$378$	3.04771	0.156757
$379$	23.9936	1.23247	0.616235	−	0.787562i	$-0.288657\pi$
$379$	23.9936	1.23247	0.616235	+	0.787562i	$0.288657\pi$
$380$	5.56625	0.285543
$381$	2.90442	0.148798
$382$	−5.83595	−0.298593
$383$	12.3897	0.633084	0.316542	−	0.948579i	$-0.397478\pi$
$383$	12.3897	0.633084	0.316542	+	0.948579i	$0.397478\pi$
$384$	−0.138152	−0.00705005
$385$	−56.6366	−2.88647
$386$	−12.5386	−0.638196
$387$	−29.8985	−1.51983
$388$	−7.27093	−0.369126
$389$	−0.875328	−0.0443809	−0.0221904	−	0.999754i	$-0.507064\pi$
$389$	−0.875328	−0.0443809	−0.0221904	+	0.999754i	$0.507064\pi$
$390$	−2.55137	−0.129194
$391$	−12.4060	−0.627396
$392$	6.60495	0.333600
$393$	−2.26813	−0.114412
$394$	8.62742	0.434643
$395$	−36.0394	−1.81334
$396$	−12.0332	−0.604690
$397$	13.6536	0.685254	0.342627	−	0.939472i	$-0.388683\pi$
$397$	13.6536	0.685254	0.342627	+	0.939472i	$0.388683\pi$
$398$	16.5608	0.830116
$399$	0.745677	0.0373305
$400$	9.46890	0.473445
$401$	37.4194	1.86864	0.934318	−	0.356442i	$-0.116010\pi$
$401$	37.4194	1.86864	0.934318	+	0.356442i	$0.116010\pi$
$402$	1.06694	0.0532143
$403$	34.2550	1.70636
$404$	10.5961	0.527174
$405$	−33.5822	−1.66871
$406$	−12.4573	−0.618244
$407$	−13.0230	−0.645528
$408$	0.252584	0.0125048
$409$	4.85520	0.240074	0.120037	−	0.992769i	$-0.461699\pi$
$409$	4.85520	0.240074	0.120037	+	0.992769i	$0.461699\pi$
$410$	26.3372	1.30070
$411$	−2.89134	−0.142619
$412$	8.19283	0.403632
$413$	−43.9116	−2.16075
$414$	−20.2270	−0.994102
$415$	57.8329	2.83890
$416$	−4.85511	−0.238041
$417$	1.43812	0.0704250
$418$	−5.90712	−0.288926
$419$	14.1697	0.692237	0.346118	−	0.938191i	$-0.387500\pi$
$419$	14.1697	0.692237	0.346118	+	0.938191i	$0.387500\pi$
$420$	1.93831	0.0945799
$421$	−24.9093	−1.21400	−0.607002	−	0.794700i	$-0.707628\pi$
$421$	−24.9093	−1.21400	−0.607002	+	0.794700i	$0.707628\pi$
$422$	−4.17720	−0.203343
$423$	−15.3958	−0.748571
$424$	−0.900238	−0.0437194
$425$	−17.3120	−0.839757
$426$	0.904247	0.0438109
$427$	−41.9275	−2.02901
$428$	−20.2784	−0.980192
$429$	2.70762	0.130725
$430$	−38.1521	−1.83986
$431$	28.7469	1.38469	0.692345	−	0.721566i	$-0.256577\pi$
$431$	28.7469	1.38469	0.692345	+	0.721566i	$0.256577\pi$
$432$	0.826276	0.0397542
$433$	−13.8318	−0.664715	−0.332357	−	0.943153i	$-0.607844\pi$
$433$	−13.8318	−0.664715	−0.332357	+	0.943153i	$0.607844\pi$
$434$	−26.0240	−1.24919
$435$	−1.77480	−0.0850952
$436$	−8.81048	−0.421946
$437$	−9.92948	−0.474991
$438$	1.26924	0.0606468
$439$	5.33531	0.254640	0.127320	−	0.991862i	$-0.459362\pi$
$439$	5.33531	0.254640	0.127320	+	0.991862i	$0.459362\pi$
$440$	−15.3549	−0.732018
$441$	−19.6888	−0.937561
$442$	8.87662	0.422218
$443$	−28.3833	−1.34853	−0.674265	−	0.738489i	$-0.735539\pi$
$443$	−28.3833	−1.34853	−0.674265	+	0.738489i	$0.735539\pi$
$444$	0.445697	0.0211518
$445$	−46.8105	−2.21903
$446$	1.43780	0.0680816
$447$	0.545050	0.0257800
$448$	3.68849	0.174265
$449$	29.4360	1.38917	0.694585	−	0.719411i	$-0.255588\pi$
$449$	29.4360	1.38917	0.694585	+	0.719411i	$0.255588\pi$
$450$	−28.2260	−1.33058
$451$	−27.9501	−1.31612
$452$	−13.7147	−0.645086
$453$	0.0407994	0.00191692
$454$	14.0106	0.657549
$455$	68.1185	3.19344
$456$	0.202163	0.00946717
$457$	20.2399	0.946784	0.473392	−	0.880852i	$-0.343029\pi$
$457$	20.2399	0.946784	0.473392	+	0.880852i	$0.343029\pi$
$458$	26.8105	1.25277
$459$	−1.51068	−0.0705127
$460$	−25.8107	−1.20343
$461$	38.1488	1.77677	0.888384	−	0.459101i	$-0.151829\pi$
$461$	38.1488	1.77677	0.888384	+	0.459101i	$0.151829\pi$
$462$	−2.05701	−0.0957008
$463$	−8.63491	−0.401298	−0.200649	−	0.979663i	$-0.564305\pi$
$463$	−8.63491	−0.401298	−0.200649	+	0.979663i	$0.564305\pi$
$464$	−3.37734	−0.156789
$465$	−3.70766	−0.171939
$466$	−13.5620	−0.628246
$467$	34.9770	1.61854	0.809271	−	0.587435i	$-0.199862\pi$
$467$	34.9770	1.61854	0.809271	+	0.587435i	$0.199862\pi$
$468$	14.4727	0.668999
$469$	−28.4861	−1.31536
$470$	−19.6459	−0.906197
$471$	1.95381	0.0900269
$472$	−11.9050	−0.547973
$473$	40.4884	1.86166
$474$	−1.30893	−0.0601212
$475$	−13.8562	−0.635766
$476$	−6.74368	−0.309096
$477$	2.68353	0.122870
$478$	−12.2472	−0.560174
$479$	25.9010	1.18345	0.591723	−	0.806141i	$-0.298448\pi$
$479$	25.9010	1.18345	0.591723	+	0.806141i	$0.298448\pi$
$480$	0.525503	0.0239858
$481$	15.6632	0.714181
$482$	−4.44401	−0.202419
$483$	−3.45770	−0.157331
$484$	5.29526	0.240694
$485$	27.6572	1.25585
$486$	−3.69852	−0.167768
$487$	15.5784	0.705924	0.352962	−	0.935638i	$-0.385175\pi$
$487$	15.5784	0.705924	0.352962	+	0.935638i	$0.385175\pi$
$488$	−11.3671	−0.514565
$489$	1.67225	0.0756219
$490$	−25.1239	−1.13498
$491$	25.4105	1.14676	0.573380	−	0.819289i	$-0.305632\pi$
$491$	25.4105	1.14676	0.573380	+	0.819289i	$0.305632\pi$
$492$	0.956555	0.0431248
$493$	6.17481	0.278099
$494$	7.10467	0.319654
$495$	45.7718	2.05729
$496$	−7.05545	−0.316799
$497$	−24.1423	−1.08293
$498$	2.10046	0.0941239
$499$	11.6801	0.522873	0.261436	−	0.965221i	$-0.415804\pi$
$499$	11.6801	0.522873	0.261436	+	0.965221i	$0.415804\pi$
$500$	−16.9988	−0.760209
$501$	−0.920897	−0.0411427
$502$	−25.7564	−1.14956
$503$	40.9864	1.82750	0.913748	−	0.406282i	$-0.133175\pi$
$503$	40.9864	1.82750	0.913748	+	0.406282i	$0.133175\pi$
$504$	−10.9951	−0.489759
$505$	−40.3054	−1.79356
$506$	27.3913	1.21769
$507$	−1.46055	−0.0648654
$508$	−21.0234	−0.932761
$509$	33.2415	1.47340	0.736701	−	0.676219i	$-0.236383\pi$
$509$	33.2415	1.47340	0.736701	+	0.676219i	$0.236383\pi$
$510$	−0.960780	−0.0425441
$511$	−33.8872	−1.49908
$512$	1.00000	0.0441942
$513$	−1.20912	−0.0533840
$514$	−14.7742	−0.651660
$515$	−31.1639	−1.37325
$516$	−1.38566	−0.0610004
$517$	20.8490	0.916936
$518$	−11.8995	−0.522836
$519$	2.54913	0.111895
$520$	18.4679	0.809869
$521$	4.45785	0.195302	0.0976510	−	0.995221i	$-0.468867\pi$
$521$	4.45785	0.195302	0.0976510	+	0.995221i	$0.468867\pi$
$522$	10.0676	0.440645
$523$	−7.64947	−0.334488	−0.167244	−	0.985916i	$-0.553487\pi$
$523$	−7.64947	−0.334488	−0.167244	+	0.985916i	$0.553487\pi$
$524$	16.4176	0.717208
$525$	−4.82509	−0.210584
$526$	25.6841	1.11988
$527$	12.8995	0.561912
$528$	−0.557684	−0.0242701
$529$	23.0430	1.00187
$530$	3.42433	0.148743
$531$	35.4879	1.54004
$532$	−5.39751	−0.234012
$533$	33.6164	1.45609
$534$	−1.70013	−0.0735720
$535$	77.1349	3.33483
$536$	−7.72296	−0.333581
$537$	−2.63833	−0.113852
$538$	−4.09706	−0.176637
$539$	26.6625	1.14843
$540$	−3.14299	−0.135253
$541$	−30.1445	−1.29601	−0.648006	−	0.761635i	$-0.724397\pi$
$541$	−30.1445	−1.29601	−0.648006	+	0.761635i	$0.724397\pi$
$542$	−26.3848	−1.13332
$543$	0.676003	0.0290101
$544$	−1.82831	−0.0783880
$545$	33.5133	1.43555
$546$	2.47403	0.105879
$547$	−15.9661	−0.682661	−0.341330	−	0.939943i	$-0.610877\pi$
$547$	−15.9661	−0.682661	−0.341330	+	0.939943i	$0.610877\pi$
$548$	20.9287	0.894029
$549$	33.8844	1.44615
$550$	38.2235	1.62985
$551$	4.94219	0.210544
$552$	−0.937431	−0.0398997
$553$	34.9469	1.48609
$554$	−3.50538	−0.148929
$555$	−1.69534	−0.0719632
$556$	−10.4097	−0.441469
$557$	5.17568	0.219300	0.109650	−	0.993970i	$-0.465027\pi$
$557$	5.17568	0.219300	0.109650	+	0.993970i	$0.465027\pi$
$558$	21.0317	0.890343
$559$	−48.6967	−2.05965
$560$	−14.0303	−0.592887
$561$	1.01962	0.0430483
$562$	−15.1449	−0.638849
$563$	22.0880	0.930897	0.465448	−	0.885075i	$-0.345893\pi$
$563$	22.0880	0.930897	0.465448	+	0.885075i	$0.345893\pi$
$564$	−0.713528	−0.0300450
$565$	52.1680	2.19472
$566$	−18.5136	−0.778184
$567$	32.5642	1.36757
$568$	−6.54530	−0.274635
$569$	−21.3987	−0.897082	−0.448541	−	0.893762i	$-0.648056\pi$
$569$	−21.3987	−0.897082	−0.448541	+	0.893762i	$0.648056\pi$
$570$	−0.768989	−0.0322094
$571$	−43.5949	−1.82439	−0.912195	−	0.409757i	$-0.865613\pi$
$571$	−43.5949	−1.82439	−0.912195	+	0.409757i	$0.865613\pi$
$572$	−19.5988	−0.819467
$573$	0.806249	0.0336816
$574$	−25.5388	−1.06597
$575$	64.2512	2.67946
$576$	−2.98091	−0.124205
$577$	33.6652	1.40150	0.700750	−	0.713407i	$-0.252849\pi$
$577$	33.6652	1.40150	0.700750	+	0.713407i	$0.252849\pi$
$578$	−13.6573	−0.568069
$579$	1.73223	0.0719889
$580$	12.8467	0.533431
$581$	−56.0797	−2.32658
$582$	1.00449	0.0416376
$583$	−3.63403	−0.150506
$584$	−9.18729	−0.380173
$585$	−55.0511	−2.27608
$586$	−14.3836	−0.594182
$587$	3.82693	0.157954	0.0789771	−	0.996876i	$-0.474835\pi$
$587$	3.82693	0.157954	0.0789771	+	0.996876i	$0.474835\pi$
$588$	−0.912488	−0.0376304
$589$	10.3245	0.425414
$590$	45.2843	1.86433
$591$	−1.19190	−0.0490281
$592$	−3.22613	−0.132593
$593$	3.35252	0.137672	0.0688358	−	0.997628i	$-0.478072\pi$
$593$	3.35252	0.137672	0.0688358	+	0.997628i	$0.478072\pi$
$594$	3.33546	0.136856
$595$	25.6516	1.05161
$596$	−3.94529	−0.161605
$597$	−2.28790	−0.0936377
$598$	−32.9443	−1.34719
$599$	6.73715	0.275272	0.137636	−	0.990483i	$-0.456050\pi$
$599$	6.73715	0.275272	0.137636	+	0.990483i	$0.456050\pi$
$600$	−1.30815	−0.0534049
$601$	24.7960	1.01145	0.505725	−	0.862695i	$-0.331225\pi$
$601$	24.7960	1.01145	0.505725	+	0.862695i	$0.331225\pi$
$602$	36.9955	1.50782
$603$	23.0215	0.937507
$604$	−0.295322	−0.0120165
$605$	−20.1421	−0.818893
$606$	−1.46387	−0.0594657
$607$	−22.7449	−0.923187	−0.461593	−	0.887092i	$-0.652722\pi$
$607$	−22.7449	−0.923187	−0.461593	+	0.887092i	$0.652722\pi$
$608$	−1.46334	−0.0593462
$609$	1.72100	0.0697384
$610$	43.2382	1.75067
$611$	−25.0757	−1.01445
$612$	5.45002	0.220304
$613$	−19.5172	−0.788291	−0.394145	−	0.919048i	$-0.628959\pi$
$613$	−19.5172	−0.788291	−0.394145	+	0.919048i	$0.628959\pi$
$614$	−0.402647	−0.0162495
$615$	−3.63855	−0.146720
$616$	14.8895	0.599914
$617$	−24.3823	−0.981596	−0.490798	−	0.871273i	$-0.663295\pi$
$617$	−24.3823	−0.981596	−0.490798	+	0.871273i	$0.663295\pi$
$618$	−1.13186	−0.0455300
$619$	5.59166	0.224748	0.112374	−	0.993666i	$-0.464155\pi$
$619$	5.59166	0.224748	0.112374	+	0.993666i	$0.464155\pi$
$620$	26.8375	1.07782
$621$	5.60669	0.224989
$622$	−9.21844	−0.369626
$623$	45.3915	1.81857
$624$	0.670743	0.0268512
$625$	17.3155	0.692621
$626$	27.1929	1.08684
$627$	0.816081	0.0325911
$628$	−14.1425	−0.564346
$629$	5.89835	0.235183
$630$	41.8230	1.66627
$631$	0.910863	0.0362609	0.0181304	−	0.999836i	$-0.494229\pi$
$631$	0.910863	0.0362609	0.0181304	+	0.999836i	$0.494229\pi$
$632$	9.47457	0.376878
$633$	0.577089	0.0229372
$634$	19.3827	0.769786
$635$	79.9687	3.17346
$636$	0.124370	0.00493158
$637$	−32.0677	−1.27057
$638$	−13.6334	−0.539753
$639$	19.5110	0.771842
$640$	−3.80380	−0.150358
$641$	−31.4769	−1.24326	−0.621631	−	0.783310i	$-0.713530\pi$
$641$	−31.4769	−1.24326	−0.621631	+	0.783310i	$0.713530\pi$
$642$	2.80150	0.110566
$643$	6.26177	0.246940	0.123470	−	0.992348i	$-0.460598\pi$
$643$	6.26177	0.246940	0.123470	+	0.992348i	$0.460598\pi$
$644$	25.0282	0.986250
$645$	5.27079	0.207537
$646$	2.67543	0.105263
$647$	27.6238	1.08600	0.543002	−	0.839732i	$-0.317288\pi$
$647$	27.6238	1.08600	0.543002	+	0.839732i	$0.317288\pi$
$648$	8.82859	0.346820
$649$	−48.0575	−1.88642
$650$	−45.9725	−1.80319
$651$	3.59526	0.140910
$652$	−12.1044	−0.474046
$653$	−42.2040	−1.65157	−0.825785	−	0.563985i	$-0.809268\pi$
$653$	−42.2040	−1.65157	−0.825785	+	0.563985i	$0.809268\pi$
$654$	1.21719	0.0475958
$655$	−62.4494	−2.44010
$656$	−6.92393	−0.270334
$657$	27.3865	1.06845
$658$	19.0503	0.742659
$659$	29.2343	1.13881	0.569404	−	0.822058i	$-0.307174\pi$
$659$	29.2343	1.13881	0.569404	+	0.822058i	$0.307174\pi$
$660$	2.12132	0.0825722
$661$	−48.8386	−1.89960	−0.949800	−	0.312858i	$-0.898714\pi$
$661$	−48.8386	−1.89960	−0.949800	+	0.312858i	$0.898714\pi$
$662$	−6.09791	−0.237002
$663$	−1.22632	−0.0476265
$664$	−15.2040	−0.590028
$665$	20.5310	0.796160
$666$	9.61682	0.372644
$667$	−22.9169	−0.887347
$668$	6.66582	0.257908
$669$	−0.198634	−0.00767965
$670$	29.3766	1.13492
$671$	−45.8861	−1.77141
$672$	−0.509572	−0.0196572
$673$	−16.0856	−0.620053	−0.310026	−	0.950728i	$-0.600338\pi$
$673$	−16.0856	−0.620053	−0.310026	+	0.950728i	$0.600338\pi$
$674$	−3.96818	−0.152849
$675$	7.82392	0.301143
$676$	10.5721	0.406618
$677$	40.2323	1.54625	0.773127	−	0.634251i	$-0.218691\pi$
$677$	40.2323	1.54625	0.773127	+	0.634251i	$0.218691\pi$
$678$	1.89472	0.0727661
$679$	−26.8187	−1.02921
$680$	6.95451	0.266693
$681$	−1.93559	−0.0741720
$682$	−28.4810	−1.09059
$683$	−32.0317	−1.22566	−0.612830	−	0.790215i	$-0.709969\pi$
$683$	−32.0317	−1.22566	−0.612830	+	0.790215i	$0.709969\pi$
$684$	4.36209	0.166789
$685$	−79.6085	−3.04168
$686$	−1.45714	−0.0556339
$687$	−3.70393	−0.141314
$688$	10.0300	0.382390
$689$	4.37075	0.166512
$690$	3.56580	0.135748
$691$	−40.0926	−1.52519	−0.762597	−	0.646874i	$-0.776076\pi$
$691$	−40.0926	−1.52519	−0.762597	+	0.646874i	$0.776076\pi$
$692$	−18.4517	−0.701427
$693$	−44.3842	−1.68602
$694$	6.28003	0.238387
$695$	39.5963	1.50197
$696$	0.466586	0.0176859
$697$	12.6591	0.479496
$698$	32.4634	1.22876
$699$	1.87361	0.0708666
$700$	34.9259	1.32008
$701$	−7.30361	−0.275854	−0.137927	−	0.990442i	$-0.544044\pi$
$701$	−7.30361	−0.275854	−0.137927	+	0.990442i	$0.544044\pi$
$702$	−4.01166	−0.151410
$703$	4.72092	0.178053
$704$	4.03674	0.152140
$705$	2.71412	0.102220
$706$	−18.1646	−0.683634
$707$	39.0835	1.46989
$708$	1.64470	0.0618118
$709$	18.8475	0.707834	0.353917	−	0.935277i	$-0.384850\pi$
$709$	18.8475	0.707834	0.353917	+	0.935277i	$0.384850\pi$
$710$	24.8970	0.934368
$711$	−28.2429	−1.05919
$712$	12.3062	0.461196
$713$	−47.8747	−1.79292
$714$	0.931654	0.0348663
$715$	74.5499	2.78801
$716$	19.0973	0.713699
$717$	1.69198	0.0631880
$718$	8.40485	0.313666
$719$	−22.8692	−0.852876	−0.426438	−	0.904517i	$-0.640232\pi$
$719$	−22.8692	−0.852876	−0.426438	+	0.904517i	$0.640232\pi$
$720$	11.3388	0.422572
$721$	30.2192	1.12542
$722$	−16.8586	−0.627414
$723$	0.613949	0.0228330
$724$	−4.89318	−0.181854
$725$	−31.9797	−1.18770
$726$	−0.731551	−0.0271504
$727$	27.8865	1.03425	0.517127	−	0.855909i	$-0.327002\pi$
$727$	27.8865	1.03425	0.517127	+	0.855909i	$0.327002\pi$
$728$	−17.9080	−0.663715
$729$	−25.9748	−0.962030
$730$	34.9466	1.29343
$731$	−18.3379	−0.678251
$732$	1.57039	0.0580433
$733$	−0.0122027	−0.000450718 0	−0.000225359	−	1.00000i	$-0.500072\pi$
$733$	−0.0122027	−0.000450718 0	−0.000225359		1.00000i	$0.500072\pi$
$734$	−20.2081	−0.745894
$735$	3.47092	0.128027
$736$	6.78550	0.250117
$737$	−31.1756	−1.14837
$738$	20.6396	0.759755
$739$	10.2818	0.378222	0.189111	−	0.981956i	$-0.439439\pi$
$739$	10.2818	0.378222	0.189111	+	0.981956i	$0.439439\pi$
$740$	12.2716	0.451111
$741$	−0.981525	−0.0360572
$742$	−3.32052	−0.121900
$743$	47.4330	1.74015	0.870074	−	0.492922i	$-0.164071\pi$
$743$	47.4330	1.74015	0.870074	+	0.492922i	$0.164071\pi$
$744$	0.974726	0.0357352
$745$	15.0071	0.549818
$746$	30.4508	1.11488
$747$	45.3217	1.65824
$748$	−7.38039	−0.269854
$749$	−74.7966	−2.73301
$750$	2.34842	0.0857521
$751$	−36.0786	−1.31653	−0.658264	−	0.752787i	$-0.728709\pi$
$751$	−36.0786	−1.31653	−0.658264	+	0.752787i	$0.728709\pi$
$752$	5.16480	0.188341
$753$	3.55830	0.129671
$754$	16.3973	0.597156
$755$	1.12335	0.0408828
$756$	3.04771	0.110844
$757$	5.66538	0.205912	0.102956	−	0.994686i	$-0.467170\pi$
$757$	5.66538	0.205912	0.102956	+	0.994686i	$0.467170\pi$
$758$	23.9936	0.871488
$759$	−3.78416	−0.137356
$760$	5.56625	0.201909
$761$	−25.4619	−0.922994	−0.461497	−	0.887142i	$-0.652688\pi$
$761$	−25.4619	−0.922994	−0.461497	+	0.887142i	$0.652688\pi$
$762$	2.90442	0.105216
$763$	−32.4974	−1.17648
$764$	−5.83595	−0.211137
$765$	−20.7308	−0.749523
$766$	12.3897	0.447658
$767$	57.8002	2.08704
$768$	−0.138152	−0.00498513
$769$	45.4612	1.63937	0.819686	−	0.572813i	$-0.194148\pi$
$769$	45.4612	1.63937	0.819686	+	0.572813i	$0.194148\pi$
$770$	−56.6366	−2.04104
$771$	2.04108	0.0735077
$772$	−12.5386	−0.451273
$773$	3.04001	0.109341	0.0546707	−	0.998504i	$-0.482589\pi$
$773$	3.04001	0.109341	0.0546707	+	0.998504i	$0.482589\pi$
$774$	−29.8985	−1.07468
$775$	−66.8074	−2.39979
$776$	−7.27093	−0.261011
$777$	1.64395	0.0589763
$778$	−0.875328	−0.0313820
$779$	10.1321	0.363018
$780$	−2.55137	−0.0913538
$781$	−26.4217	−0.945441
$782$	−12.4060	−0.443636
$783$	−2.79061	−0.0997284
$784$	6.60495	0.235891
$785$	53.7951	1.92003
$786$	−2.26813	−0.0809016
$787$	46.5204	1.65827	0.829136	−	0.559047i	$-0.188833\pi$
$787$	46.5204	1.65827	0.829136	+	0.559047i	$0.188833\pi$
$788$	8.62742	0.307339
$789$	−3.54832	−0.126323
$790$	−36.0394	−1.28222
$791$	−50.5865	−1.79865
$792$	−12.0332	−0.427580
$793$	55.1886	1.95980
$794$	13.6536	0.484548
$795$	−0.473078	−0.0167783
$796$	16.5608	0.586981
$797$	12.1458	0.430225	0.215113	−	0.976589i	$-0.430988\pi$
$797$	12.1458	0.430225	0.215113	+	0.976589i	$0.430988\pi$
$798$	0.745677	0.0263967
$799$	−9.44284	−0.334064
$800$	9.46890	0.334776
$801$	−36.6839	−1.29616
$802$	37.4194	1.32132
$803$	−37.0867	−1.30876
$804$	1.06694	0.0376282
$805$	−95.2024	−3.35544
$806$	34.2550	1.20658
$807$	0.566018	0.0199248
$808$	10.5961	0.372769
$809$	−31.7371	−1.11582	−0.557909	−	0.829902i	$-0.688396\pi$
$809$	−31.7371	−1.11582	−0.557909	+	0.829902i	$0.688396\pi$
$810$	−33.5822	−1.17996
$811$	3.56487	0.125179	0.0625897	−	0.998039i	$-0.480064\pi$
$811$	3.56487	0.125179	0.0625897	+	0.998039i	$0.480064\pi$
$812$	−12.4573	−0.437165
$813$	3.64511	0.127840
$814$	−13.0230	−0.456457
$815$	46.0428	1.61281
$816$	0.252584	0.00884222
$817$	−14.6773	−0.513493
$818$	4.85520	0.169758
$819$	53.3822	1.86533
$820$	26.3372	0.919736
$821$	−6.45999	−0.225455	−0.112728	−	0.993626i	$-0.535959\pi$
$821$	−6.45999	−0.225455	−0.112728	+	0.993626i	$0.535959\pi$
$822$	−2.89134	−0.100847
$823$	18.2555	0.636346	0.318173	−	0.948033i	$-0.396931\pi$
$823$	18.2555	0.636346	0.318173	+	0.948033i	$0.396931\pi$
$824$	8.19283	0.285411
$825$	−5.28065	−0.183849
$826$	−43.9116	−1.52788
$827$	38.5439	1.34030	0.670152	−	0.742224i	$-0.266229\pi$
$827$	38.5439	1.34030	0.670152	+	0.742224i	$0.266229\pi$
$828$	−20.2270	−0.702936
$829$	14.1762	0.492359	0.246179	−	0.969224i	$-0.420825\pi$
$829$	14.1762	0.492359	0.246179	+	0.969224i	$0.420825\pi$
$830$	57.8329	2.00741
$831$	0.484276	0.0167993
$832$	−4.85511	−0.168321
$833$	−12.0759	−0.418404
$834$	1.43812	0.0497980
$835$	−25.3555	−0.877462
$836$	−5.90712	−0.204302
$837$	−5.82975	−0.201506
$838$	14.1697	0.489485
$839$	−16.3938	−0.565978	−0.282989	−	0.959123i	$-0.591326\pi$
$839$	−16.3938	−0.565978	−0.282989	+	0.959123i	$0.591326\pi$
$840$	1.93831	0.0668781
$841$	−17.5936	−0.606675
$842$	−24.9093	−0.858430
$843$	2.09230	0.0720627
$844$	−4.17720	−0.143785
$845$	−40.2140	−1.38340
$846$	−15.3958	−0.529320
$847$	19.5315	0.671111
$848$	−0.900238	−0.0309143
$849$	2.55769	0.0877798
$850$	−17.3120	−0.593798
$851$	−21.8909	−0.750410
$852$	0.904247	0.0309790
$853$	−5.99178	−0.205155	−0.102577	−	0.994725i	$-0.532709\pi$
$853$	−5.99178	−0.205155	−0.102577	+	0.994725i	$0.532709\pi$
$854$	−41.9275	−1.43473
$855$	−16.5925	−0.567452
$856$	−20.2784	−0.693101
$857$	−30.6448	−1.04681	−0.523404	−	0.852085i	$-0.675338\pi$
$857$	−30.6448	−1.04681	−0.523404	+	0.852085i	$0.675338\pi$
$858$	2.70762	0.0924365
$859$	4.80058	0.163794	0.0818969	−	0.996641i	$-0.473902\pi$
$859$	4.80058	0.163794	0.0818969	+	0.996641i	$0.473902\pi$
$860$	−38.1521	−1.30097
$861$	3.52824	0.120242
$862$	28.7469	0.979124
$863$	−35.7733	−1.21774	−0.608869	−	0.793271i	$-0.708376\pi$
$863$	−35.7733	−1.21774	−0.608869	+	0.793271i	$0.708376\pi$
$864$	0.826276	0.0281105
$865$	70.1864	2.38641
$866$	−13.8318	−0.470024
$867$	1.88678	0.0640786
$868$	−26.0240	−0.883311
$869$	38.2464	1.29742
$870$	−1.77480	−0.0601714
$871$	37.4958	1.27050
$872$	−8.81048	−0.298361
$873$	21.6740	0.733554
$874$	−9.92948	−0.335870
$875$	−62.6999	−2.11964
$876$	1.26924	0.0428837
$877$	−46.2570	−1.56199	−0.780994	−	0.624539i	$-0.785287\pi$
$877$	−46.2570	−1.56199	−0.780994	+	0.624539i	$0.785287\pi$
$878$	5.33531	0.180058
$879$	1.98713	0.0670241
$880$	−15.3549	−0.517615
$881$	27.4333	0.924250	0.462125	−	0.886815i	$-0.347087\pi$
$881$	27.4333	0.924250	0.462125	+	0.886815i	$0.347087\pi$
$882$	−19.6888	−0.662956
$883$	−33.6879	−1.13369	−0.566845	−	0.823825i	$-0.691836\pi$
$883$	−33.6879	−1.13369	−0.566845	+	0.823825i	$0.691836\pi$
$884$	8.87662	0.298553
$885$	−6.25613	−0.210297
$886$	−28.3833	−0.953555
$887$	40.8202	1.37061	0.685303	−	0.728258i	$-0.259670\pi$
$887$	40.8202	1.37061	0.685303	+	0.728258i	$0.259670\pi$
$888$	0.445697	0.0149566
$889$	−77.5444	−2.60076
$890$	−46.8105	−1.56909
$891$	35.6387	1.19394
$892$	1.43780	0.0481410
$893$	−7.55786	−0.252914
$894$	0.545050	0.0182292
$895$	−72.6422	−2.42816
$896$	3.68849	0.123224
$897$	4.55133	0.151964
$898$	29.4360	0.982291
$899$	23.8287	0.794730
$900$	−28.2260	−0.940866
$901$	1.64591	0.0548332
$902$	−27.9501	−0.930636
$903$	−5.11100	−0.170084
$904$	−13.7147	−0.456144
$905$	18.6127	0.618706
$906$	0.0407994	0.00135547
$907$	−54.6811	−1.81566	−0.907829	−	0.419342i	$-0.862261\pi$
$907$	−54.6811	−1.81566	−0.907829	+	0.419342i	$0.862261\pi$
$908$	14.0106	0.464957
$909$	−31.5860	−1.04764
$910$	68.1185	2.25811
$911$	29.4604	0.976066	0.488033	−	0.872825i	$-0.337715\pi$
$911$	29.4604	0.976066	0.488033	+	0.872825i	$0.337715\pi$
$912$	0.202163	0.00669430
$913$	−61.3745	−2.03120
$914$	20.2399	0.669478
$915$	−5.97345	−0.197476
$916$	26.8105	0.885845
$917$	60.5563	1.99974
$918$	−1.51068	−0.0498600
$919$	−47.4207	−1.56426	−0.782132	−	0.623113i	$-0.785868\pi$
$919$	−47.4207	−1.56426	−0.782132	+	0.623113i	$0.785868\pi$
$920$	−25.8107	−0.850953
$921$	0.0556266	0.00183296
$922$	38.1488	1.25636
$923$	31.7781	1.04599
$924$	−2.05701	−0.0676707
$925$	−30.5479	−1.00441
$926$	−8.63491	−0.283761
$927$	−24.4221	−0.802128
$928$	−3.37734	−0.110867
$929$	−7.53172	−0.247108	−0.123554	−	0.992338i	$-0.539429\pi$
$929$	−7.53172	−0.247108	−0.123554	+	0.992338i	$0.539429\pi$
$930$	−3.70766	−0.121579
$931$	−9.66528	−0.316767
$932$	−13.5620	−0.444237
$933$	1.27355	0.0416940
$934$	34.9770	1.14448
$935$	28.0735	0.918103
$936$	14.4727	0.473054
$937$	−3.37970	−0.110410	−0.0552050	−	0.998475i	$-0.517581\pi$
$937$	−3.37970	−0.110410	−0.0552050	+	0.998475i	$0.517581\pi$
$938$	−28.4861	−0.930103
$939$	−3.75675	−0.122597
$940$	−19.6459	−0.640778
$941$	15.6785	0.511104	0.255552	−	0.966795i	$-0.417743\pi$
$941$	15.6785	0.511104	0.255552	+	0.966795i	$0.417743\pi$
$942$	1.95381	0.0636586
$943$	−46.9823	−1.52995
$944$	−11.9050	−0.387476
$945$	−11.5929	−0.377116
$946$	40.4884	1.31639
$947$	−43.5596	−1.41550	−0.707748	−	0.706465i	$-0.750289\pi$
$947$	−43.5596	−1.41550	−0.707748	+	0.706465i	$0.750289\pi$
$948$	−1.30893	−0.0425121
$949$	44.6053	1.44795
$950$	−13.8562	−0.449555
$951$	−2.67776	−0.0868325
$952$	−6.74368	−0.218564
$953$	38.6800	1.25297	0.626483	−	0.779435i	$-0.284494\pi$
$953$	38.6800	1.25297	0.626483	+	0.779435i	$0.284494\pi$
$954$	2.68353	0.0868826
$955$	22.1988	0.718336
$956$	−12.2472	−0.396103
$957$	1.88349	0.0608845
$958$	25.9010	0.836823
$959$	77.1952	2.49276
$960$	0.525503	0.0169605
$961$	18.7794	0.605788
$962$	15.6632	0.505002
$963$	60.4481	1.94791
$964$	−4.44401	−0.143132
$965$	47.6942	1.53533
$966$	−3.45770	−0.111250
$967$	−33.5122	−1.07768	−0.538840	−	0.842408i	$-0.681137\pi$
$967$	−33.5122	−1.07768	−0.538840	+	0.842408i	$0.681137\pi$
$968$	5.29526	0.170196
$969$	−0.369616	−0.0118738
$970$	27.6572	0.888018
$971$	2.69473	0.0864780	0.0432390	−	0.999065i	$-0.486232\pi$
$971$	2.69473	0.0864780	0.0432390	+	0.999065i	$0.486232\pi$
$972$	−3.69852	−0.118630
$973$	−38.3960	−1.23092
$974$	15.5784	0.499163
$975$	6.35120	0.203401
$976$	−11.3671	−0.363852
$977$	−11.5732	−0.370259	−0.185130	−	0.982714i	$-0.559270\pi$
$977$	−11.5732	−0.370259	−0.185130	+	0.982714i	$0.559270\pi$
$978$	1.67225	0.0534728
$979$	49.6771	1.58769
$980$	−25.1239	−0.802554
$981$	26.2633	0.838522
$982$	25.4105	0.810882
$983$	46.9423	1.49723	0.748614	−	0.663006i	$-0.230720\pi$
$983$	46.9423	1.49723	0.748614	+	0.663006i	$0.230720\pi$
$984$	0.956555	0.0304939
$985$	−32.8170	−1.04564
$986$	6.17481	0.196646
$987$	−2.63184	−0.0837724
$988$	7.10467	0.226030
$989$	68.0584	2.16413
$990$	45.7718	1.45472
$991$	−30.4396	−0.966945	−0.483473	−	0.875359i	$-0.660625\pi$
$991$	−30.4396	−0.966945	−0.483473	+	0.875359i	$0.660625\pi$
$992$	−7.05545	−0.224011
$993$	0.842439	0.0267340
$994$	−24.1423	−0.765746
$995$	−62.9938	−1.99704
$996$	2.10046	0.0665556
$997$	35.0191	1.10906	0.554532	−	0.832162i	$-0.312897\pi$
$997$	35.0191	1.10906	0.554532	+	0.832162i	$0.312897\pi$
$998$	11.6801	0.369727
$999$	−2.66567	−0.0843382

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.a.1.20	✓	33

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.a.1.20	✓	33	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)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} -0.138152 q^{3} +1.00000 q^{4} -3.80380 q^{5} -0.138152 q^{6} +3.68849 q^{7} +1.00000 q^{8} -2.98091 q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} -0.138152 q^{3} +1.00000 q^{4} -3.80380 q^{5} -0.138152 q^{6} +3.68849 q^{7} +1.00000 q^{8} -2.98091 q^{9} -3.80380 q^{10} +4.03674 q^{11} -0.138152 q^{12} -4.85511 q^{13} +3.68849 q^{14} +0.525503 q^{15} +1.00000 q^{16} -1.82831 q^{17} -2.98091 q^{18} -1.46334 q^{19} -3.80380 q^{20} -0.509572 q^{21} +4.03674 q^{22} +6.78550 q^{23} -0.138152 q^{24} +9.46890 q^{25} -4.85511 q^{26} +0.826276 q^{27} +3.68849 q^{28} -3.37734 q^{29} +0.525503 q^{30} -7.05545 q^{31} +1.00000 q^{32} -0.557684 q^{33} -1.82831 q^{34} -14.0303 q^{35} -2.98091 q^{36} -3.22613 q^{37} -1.46334 q^{38} +0.670743 q^{39} -3.80380 q^{40} -6.92393 q^{41} -0.509572 q^{42} +10.0300 q^{43} +4.03674 q^{44} +11.3388 q^{45} +6.78550 q^{46} +5.16480 q^{47} -0.138152 q^{48} +6.60495 q^{49} +9.46890 q^{50} +0.252584 q^{51} -4.85511 q^{52} -0.900238 q^{53} +0.826276 q^{54} -15.3549 q^{55} +3.68849 q^{56} +0.202163 q^{57} -3.37734 q^{58} -11.9050 q^{59} +0.525503 q^{60} -11.3671 q^{61} -7.05545 q^{62} -10.9951 q^{63} +1.00000 q^{64} +18.4679 q^{65} -0.557684 q^{66} -7.72296 q^{67} -1.82831 q^{68} -0.937431 q^{69} -14.0303 q^{70} -6.54530 q^{71} -2.98091 q^{72} -9.18729 q^{73} -3.22613 q^{74} -1.30815 q^{75} -1.46334 q^{76} +14.8895 q^{77} +0.670743 q^{78} +9.47457 q^{79} -3.80380 q^{80} +8.82859 q^{81} -6.92393 q^{82} -15.2040 q^{83} -0.509572 q^{84} +6.95451 q^{85} +10.0300 q^{86} +0.466586 q^{87} +4.03674 q^{88} +12.3062 q^{89} +11.3388 q^{90} -17.9080 q^{91} +6.78550 q^{92} +0.974726 q^{93} +5.16480 q^{94} +5.56625 q^{95} -0.138152 q^{96} -7.27093 q^{97} +6.60495 q^{98} -12.0332 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9}+O(q^{10}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9	\( 33 q + 33 q^{2} - 14 q^{3} + 33 q^{4} - 22 q^{5} - 14 q^{6} - 12 q^{7} + 33 q^{8} + 17 q^{9} - 22 q^{10} - 19 q^{11} - 14 q^{12} - 29 q^{13} - 12 q^{14} - 5 q^{15} + 33 q^{16} - 47 q^{17} + 17 q^{18} - 35 q^{19} - 22 q^{20} - 31 q^{21} - 19 q^{22} - 2 q^{23} - 14 q^{24} + 13 q^{25} - 29 q^{26} - 47 q^{27} - 12 q^{28} - 29 q^{29} - 5 q^{30} - 53 q^{31} + 33 q^{32} - 23 q^{33} - 47 q^{34} - 14 q^{35} + 17 q^{36} - 42 q^{37} - 35 q^{38} - 22 q^{40} - 42 q^{41} - 31 q^{42} - 26 q^{43} - 19 q^{44} - 55 q^{45} - 2 q^{46} - 14 q^{48} - 21 q^{49} + 13 q^{50} - 13 q^{51} - 29 q^{52} - 40 q^{53} - 47 q^{54} - 34 q^{55} - 12 q^{56} - 30 q^{57} - 29 q^{58} - 45 q^{59} - 5 q^{60} - 93 q^{61} - 53 q^{62} + 4 q^{63} + 33 q^{64} - 26 q^{65} - 23 q^{66} - 28 q^{67} - 47 q^{68} - 60 q^{69} - 14 q^{70} + 4 q^{71} + 17 q^{72} - 52 q^{73} - 42 q^{74} - 41 q^{75} - 35 q^{76} - 38 q^{77} - 38 q^{79} - 22 q^{80} + 25 q^{81} - 42 q^{82} - 42 q^{83} - 31 q^{84} - 21 q^{85} - 26 q^{86} + 12 q^{87} - 19 q^{88} - 58 q^{89} - 55 q^{90} - 79 q^{91} - 2 q^{92} + 25 q^{93} + 16 q^{95} - 14 q^{96} - 64 q^{97} - 21 q^{98} - 38 q^{99}+O(q^{100}) \) 33 * q + 33 * q^2 - 14 * q^3 + 33 * q^4 - 22 * q^5 - 14 * q^6 - 12 * q^7 + 33 * q^8 + 17 * q^9 - 22 * q^10 - 19 * q^11 - 14 * q^12 - 29 * q^13 - 12 * q^14 - 5 * q^15 + 33 * q^16 - 47 * q^17 + 17 * q^18 - 35 * q^19 - 22 * q^20 - 31 * q^21 - 19 * q^22 - 2 * q^23 - 14 * q^24 + 13 * q^25 - 29 * q^26 - 47 * q^27 - 12 * q^28 - 29 * q^29 - 5 * q^30 - 53 * q^31 + 33 * q^32 - 23 * q^33 - 47 * q^34 - 14 * q^35 + 17 * q^36 - 42 * q^37 - 35 * q^38 - 22 * q^40 - 42 * q^41 - 31 * q^42 - 26 * q^43 - 19 * q^44 - 55 * q^45 - 2 * q^46 - 14 * q^48 - 21 * q^49 + 13 * q^50 - 13 * q^51 - 29 * q^52 - 40 * q^53 - 47 * q^54 - 34 * q^55 - 12 * q^56 - 30 * q^57 - 29 * q^58 - 45 * q^59 - 5 * q^60 - 93 * q^61 - 53 * q^62 + 4 * q^63 + 33 * q^64 - 26 * q^65 - 23 * q^66 - 28 * q^67 - 47 * q^68 - 60 * q^69 - 14 * q^70 + 4 * q^71 + 17 * q^72 - 52 * q^73 - 42 * q^74 - 41 * q^75 - 35 * q^76 - 38 * q^77 - 38 * q^79 - 22 * q^80 + 25 * q^81 - 42 * q^82 - 42 * q^83 - 31 * q^84 - 21 * q^85 - 26 * q^86 + 12 * q^87 - 19 * q^88 - 58 * q^89 - 55 * q^90 - 79 * q^91 - 2 * q^92 + 25 * q^93 + 16 * q^95 - 14 * q^96 - 64 * q^97 - 21 * q^98 - 38 * q^99

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