LMFDB - Embedded newform 4034.2.a.c.1.11

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:	$49$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
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)

$f(q)$	$=$	$q-1.00000 q^{2} -1.82471 q^{3} +1.00000 q^{4} -3.41474 q^{5} +1.82471 q^{6} -0.804060 q^{7} -1.00000 q^{8} +0.329557 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -1.82471 q^{3} +1.00000 q^{4} -3.41474 q^{5} +1.82471 q^{6} -0.804060 q^{7} -1.00000 q^{8} +0.329557 q^{9} +3.41474 q^{10} +6.38247 q^{11} -1.82471 q^{12} +6.98000 q^{13} +0.804060 q^{14} +6.23090 q^{15} +1.00000 q^{16} -0.0923589 q^{17} -0.329557 q^{18} +0.778932 q^{19} -3.41474 q^{20} +1.46717 q^{21} -6.38247 q^{22} -9.02579 q^{23} +1.82471 q^{24} +6.66044 q^{25} -6.98000 q^{26} +4.87278 q^{27} -0.804060 q^{28} +6.55855 q^{29} -6.23090 q^{30} +7.08379 q^{31} -1.00000 q^{32} -11.6461 q^{33} +0.0923589 q^{34} +2.74565 q^{35} +0.329557 q^{36} +0.920901 q^{37} -0.778932 q^{38} -12.7365 q^{39} +3.41474 q^{40} -5.27041 q^{41} -1.46717 q^{42} +5.97274 q^{43} +6.38247 q^{44} -1.12535 q^{45} +9.02579 q^{46} +0.703113 q^{47} -1.82471 q^{48} -6.35349 q^{49} -6.66044 q^{50} +0.168528 q^{51} +6.98000 q^{52} -2.84125 q^{53} -4.87278 q^{54} -21.7945 q^{55} +0.804060 q^{56} -1.42132 q^{57} -6.55855 q^{58} +0.732250 q^{59} +6.23090 q^{60} +9.38872 q^{61} -7.08379 q^{62} -0.264984 q^{63} +1.00000 q^{64} -23.8349 q^{65} +11.6461 q^{66} -1.11408 q^{67} -0.0923589 q^{68} +16.4694 q^{69} -2.74565 q^{70} -1.33275 q^{71} -0.329557 q^{72} -14.3797 q^{73} -0.920901 q^{74} -12.1534 q^{75} +0.778932 q^{76} -5.13189 q^{77} +12.7365 q^{78} +1.37303 q^{79} -3.41474 q^{80} -9.88006 q^{81} +5.27041 q^{82} -12.4225 q^{83} +1.46717 q^{84} +0.315382 q^{85} -5.97274 q^{86} -11.9674 q^{87} -6.38247 q^{88} -0.0384635 q^{89} +1.12535 q^{90} -5.61234 q^{91} -9.02579 q^{92} -12.9258 q^{93} -0.703113 q^{94} -2.65985 q^{95} +1.82471 q^{96} +14.8476 q^{97} +6.35349 q^{98} +2.10339 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) $ 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * 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
$3$	−1.82471	−1.05350	−0.526748	−	0.850022i	$-0.676589\pi$
$3$	−1.82471	−1.05350	−0.526748	+	0.850022i	$0.676589\pi$
$4$	1.00000	0.500000
$5$	−3.41474	−1.52712	−0.763559	−	0.645738i	$-0.776550\pi$
$5$	−3.41474	−1.52712	−0.763559	+	0.645738i	$0.776550\pi$
$6$	1.82471	0.744934
$7$	−0.804060	−0.303906	−0.151953	−	0.988388i	$-0.548556\pi$
$7$	−0.804060	−0.303906	−0.151953	+	0.988388i	$0.548556\pi$
$8$	−1.00000	−0.353553
$9$	0.329557	0.109852
$10$	3.41474	1.07984
$11$	6.38247	1.92439	0.962194	−	0.272367i	$-0.0878064\pi$
$11$	6.38247	1.92439	0.962194	+	0.272367i	$0.0878064\pi$
$12$	−1.82471	−0.526748
$13$	6.98000	1.93590	0.967952	−	0.251137i	$-0.0808044\pi$
$13$	6.98000	1.93590	0.967952	+	0.251137i	$0.0808044\pi$
$14$	0.804060	0.214894
$15$	6.23090	1.60881
$16$	1.00000	0.250000
$17$	−0.0923589	−0.0224003	−0.0112002	−	0.999937i	$-0.503565\pi$
$17$	−0.0923589	−0.0224003	−0.0112002	+	0.999937i	$0.503565\pi$
$18$	−0.329557	−0.0776774
$19$	0.778932	0.178699	0.0893496	−	0.996000i	$-0.471521\pi$
$19$	0.778932	0.178699	0.0893496	+	0.996000i	$0.471521\pi$
$20$	−3.41474	−0.763559
$21$	1.46717	0.320164
$22$	−6.38247	−1.36075
$23$	−9.02579	−1.88201	−0.941004	−	0.338396i	$-0.890116\pi$
$23$	−9.02579	−1.88201	−0.941004	+	0.338396i	$0.890116\pi$
$24$	1.82471	0.372467
$25$	6.66044	1.33209
$26$	−6.98000	−1.36889
$27$	4.87278	0.937766
$28$	−0.804060	−0.151953
$29$	6.55855	1.21789	0.608946	−	0.793211i	$-0.291592\pi$
$29$	6.55855	1.21789	0.608946	+	0.793211i	$0.291592\pi$
$30$	−6.23090	−1.13760
$31$	7.08379	1.27229	0.636143	−	0.771571i	$-0.280529\pi$
$31$	7.08379	1.27229	0.636143	+	0.771571i	$0.280529\pi$
$32$	−1.00000	−0.176777
$33$	−11.6461	−2.02733
$34$	0.0923589	0.0158394
$35$	2.74565	0.464100
$36$	0.329557	0.0549262
$37$	0.920901	0.151395	0.0756976	−	0.997131i	$-0.475882\pi$
$37$	0.920901	0.151395	0.0756976	+	0.997131i	$0.475882\pi$
$38$	−0.778932	−0.126359
$39$	−12.7365	−2.03946
$40$	3.41474	0.539918
$41$	−5.27041	−0.823099	−0.411550	−	0.911387i	$-0.635012\pi$
$41$	−5.27041	−0.823099	−0.411550	+	0.911387i	$0.635012\pi$
$42$	−1.46717	−0.226390
$43$	5.97274	0.910834	0.455417	−	0.890278i	$-0.349490\pi$
$43$	5.97274	0.910834	0.455417	+	0.890278i	$0.349490\pi$
$44$	6.38247	0.962194
$45$	−1.12535	−0.167758
$46$	9.02579	1.33078
$47$	0.703113	0.102560	0.0512798	−	0.998684i	$-0.483670\pi$
$47$	0.703113	0.102560	0.0512798	+	0.998684i	$0.483670\pi$
$48$	−1.82471	−0.263374
$49$	−6.35349	−0.907641
$50$	−6.66044	−0.941928
$51$	0.168528	0.0235986
$52$	6.98000	0.967952
$53$	−2.84125	−0.390276	−0.195138	−	0.980776i	$-0.562515\pi$
$53$	−2.84125	−0.390276	−0.195138	+	0.980776i	$0.562515\pi$
$54$	−4.87278	−0.663101
$55$	−21.7945	−2.93877
$56$	0.804060	0.107447
$57$	−1.42132	−0.188259
$58$	−6.55855	−0.861180
$59$	0.732250	0.0953308	0.0476654	−	0.998863i	$-0.484822\pi$
$59$	0.732250	0.0953308	0.0476654	+	0.998863i	$0.484822\pi$
$60$	6.23090	0.804406
$61$	9.38872	1.20210	0.601051	−	0.799210i	$-0.294749\pi$
$61$	9.38872	1.20210	0.601051	+	0.799210i	$0.294749\pi$
$62$	−7.08379	−0.899642
$63$	−0.264984	−0.0333848
$64$	1.00000	0.125000
$65$	−23.8349	−2.95635
$66$	11.6461	1.43354
$67$	−1.11408	−0.136107	−0.0680535	−	0.997682i	$-0.521679\pi$
$67$	−1.11408	−0.136107	−0.0680535	+	0.997682i	$0.521679\pi$
$68$	−0.0923589	−0.0112002
$69$	16.4694	1.98269
$70$	−2.74565	−0.328168
$71$	−1.33275	−0.158168	−0.0790840	−	0.996868i	$-0.525200\pi$
$71$	−1.33275	−0.158168	−0.0790840	+	0.996868i	$0.525200\pi$
$72$	−0.329557	−0.0388387
$73$	−14.3797	−1.68301	−0.841507	−	0.540246i	$-0.818331\pi$
$73$	−14.3797	−1.68301	−0.841507	+	0.540246i	$0.818331\pi$
$74$	−0.920901	−0.107053
$75$	−12.1534	−1.40335
$76$	0.778932	0.0893496
$77$	−5.13189	−0.584833
$78$	12.7365	1.44212
$79$	1.37303	0.154478	0.0772389	−	0.997013i	$-0.475390\pi$
$79$	1.37303	0.154478	0.0772389	+	0.997013i	$0.475390\pi$
$80$	−3.41474	−0.381779
$81$	−9.88006	−1.09778
$82$	5.27041	0.582019
$83$	−12.4225	−1.36355	−0.681775	−	0.731562i	$-0.738792\pi$
$83$	−12.4225	−1.36355	−0.681775	+	0.731562i	$0.738792\pi$
$84$	1.46717	0.160082
$85$	0.315382	0.0342079
$86$	−5.97274	−0.644057
$87$	−11.9674	−1.28304
$88$	−6.38247	−0.680374
$89$	−0.0384635	−0.00407712	−0.00203856	−	0.999998i	$-0.500649\pi$
$89$	−0.0384635	−0.00407712	−0.00203856	+	0.999998i	$0.500649\pi$
$90$	1.12535	0.118623
$91$	−5.61234	−0.588333
$92$	−9.02579	−0.941004
$93$	−12.9258	−1.34035
$94$	−0.703113	−0.0725206
$95$	−2.65985	−0.272895
$96$	1.82471	0.186233
$97$	14.8476	1.50755	0.753775	−	0.657133i	$-0.228231\pi$
$97$	14.8476	1.50755	0.753775	+	0.657133i	$0.228231\pi$
$98$	6.35349	0.641799
$99$	2.10339	0.211399
$100$	6.66044	0.666044
$101$	10.3159	1.02647	0.513236	−	0.858247i	$-0.328446\pi$
$101$	10.3159	1.02647	0.513236	+	0.858247i	$0.328446\pi$
$102$	−0.168528	−0.0166868
$103$	−15.1720	−1.49494	−0.747472	−	0.664294i	$-0.768732\pi$
$103$	−15.1720	−1.49494	−0.747472	+	0.664294i	$0.768732\pi$
$104$	−6.98000	−0.684445
$105$	−5.01002	−0.488927
$106$	2.84125	0.275967
$107$	12.3740	1.19624	0.598118	−	0.801408i	$-0.295915\pi$
$107$	12.3740	1.19624	0.598118	+	0.801408i	$0.295915\pi$
$108$	4.87278	0.468883
$109$	−8.78977	−0.841908	−0.420954	−	0.907082i	$-0.638305\pi$
$109$	−8.78977	−0.841908	−0.420954	+	0.907082i	$0.638305\pi$
$110$	21.7945	2.07802
$111$	−1.68038	−0.159494
$112$	−0.804060	−0.0759765
$113$	4.12747	0.388280	0.194140	−	0.980974i	$-0.437808\pi$
$113$	4.12747	0.388280	0.194140	+	0.980974i	$0.437808\pi$
$114$	1.42132	0.133119
$115$	30.8207	2.87405
$116$	6.55855	0.608946
$117$	2.30031	0.212664
$118$	−0.732250	−0.0674091
$119$	0.0742621	0.00680759
$120$	−6.23090	−0.568801
$121$	29.7359	2.70327
$122$	−9.38872	−0.850015
$123$	9.61695	0.867131
$124$	7.08379	0.636143
$125$	−5.66997	−0.507137
$126$	0.264984	0.0236066
$127$	−10.6221	−0.942559	−0.471280	−	0.881984i	$-0.656208\pi$
$127$	−10.6221	−0.942559	−0.471280	+	0.881984i	$0.656208\pi$
$128$	−1.00000	−0.0883883
$129$	−10.8985	−0.959559
$130$	23.8349	2.09046
$131$	−10.7468	−0.938954	−0.469477	−	0.882945i	$-0.655558\pi$
$131$	−10.7468	−0.938954	−0.469477	+	0.882945i	$0.655558\pi$
$132$	−11.6461	−1.01367
$133$	−0.626308	−0.0543078
$134$	1.11408	0.0962422
$135$	−16.6393	−1.43208
$136$	0.0923589	0.00791971
$137$	−4.41181	−0.376927	−0.188463	−	0.982080i	$-0.560351\pi$
$137$	−4.41181	−0.376927	−0.188463	+	0.982080i	$0.560351\pi$
$138$	−16.4694	−1.40197
$139$	−6.99418	−0.593239	−0.296619	−	0.954996i	$-0.595859\pi$
$139$	−6.99418	−0.593239	−0.296619	+	0.954996i	$0.595859\pi$
$140$	2.74565	0.232050
$141$	−1.28298	−0.108046
$142$	1.33275	0.111842
$143$	44.5496	3.72543
$144$	0.329557	0.0274631
$145$	−22.3957	−1.85987
$146$	14.3797	1.19007
$147$	11.5933	0.956196
$148$	0.920901	0.0756976
$149$	−18.1832	−1.48963	−0.744813	−	0.667273i	$-0.767461\pi$
$149$	−18.1832	−1.48963	−0.744813	+	0.667273i	$0.767461\pi$
$150$	12.1534	0.992317
$151$	10.7468	0.874565	0.437283	−	0.899324i	$-0.355941\pi$
$151$	10.7468	0.874565	0.437283	+	0.899324i	$0.355941\pi$
$152$	−0.778932	−0.0631797
$153$	−0.0304375	−0.00246073
$154$	5.13189	0.413539
$155$	−24.1893	−1.94293
$156$	−12.7365	−1.01973
$157$	14.7206	1.17483	0.587417	−	0.809284i	$-0.300145\pi$
$157$	14.7206	1.17483	0.587417	+	0.809284i	$0.300145\pi$
$158$	−1.37303	−0.109232
$159$	5.18445	0.411154
$160$	3.41474	0.269959
$161$	7.25728	0.571954
$162$	9.88006	0.776251
$163$	20.4017	1.59798	0.798991	−	0.601343i	$-0.205368\pi$
$163$	20.4017	1.59798	0.798991	+	0.601343i	$0.205368\pi$
$164$	−5.27041	−0.411550
$165$	39.7685	3.09598
$166$	12.4225	0.964176
$167$	1.82880	0.141517	0.0707583	−	0.997493i	$-0.477458\pi$
$167$	1.82880	0.141517	0.0707583	+	0.997493i	$0.477458\pi$
$168$	−1.46717	−0.113195
$169$	35.7204	2.74772
$170$	−0.315382	−0.0241887
$171$	0.256703	0.0196305
$172$	5.97274	0.455417
$173$	15.8692	1.20652	0.603258	−	0.797546i	$-0.293869\pi$
$173$	15.8692	1.20652	0.603258	+	0.797546i	$0.293869\pi$
$174$	11.9674	0.907249
$175$	−5.35539	−0.404830
$176$	6.38247	0.481097
$177$	−1.33614	−0.100431
$178$	0.0384635	0.00288296
$179$	20.4734	1.53025	0.765127	−	0.643879i	$-0.222676\pi$
$179$	20.4734	1.53025	0.765127	+	0.643879i	$0.222676\pi$
$180$	−1.12535	−0.0838788
$181$	5.48356	0.407590	0.203795	−	0.979014i	$-0.434672\pi$
$181$	5.48356	0.407590	0.203795	+	0.979014i	$0.434672\pi$
$182$	5.61234	0.416014
$183$	−17.1317	−1.26641
$184$	9.02579	0.665390
$185$	−3.14464	−0.231198
$186$	12.9258	0.947769
$187$	−0.589478	−0.0431069
$188$	0.703113	0.0512798
$189$	−3.91800	−0.284993
$190$	2.65985	0.192966
$191$	12.9142	0.934441	0.467220	−	0.884141i	$-0.345255\pi$
$191$	12.9142	0.934441	0.467220	+	0.884141i	$0.345255\pi$
$192$	−1.82471	−0.131687
$193$	−11.9454	−0.859849	−0.429925	−	0.902865i	$-0.641460\pi$
$193$	−11.9454	−0.859849	−0.429925	+	0.902865i	$0.641460\pi$
$194$	−14.8476	−1.06600
$195$	43.4917	3.11450
$196$	−6.35349	−0.453821
$197$	−13.8507	−0.986818	−0.493409	−	0.869797i	$-0.664249\pi$
$197$	−13.8507	−0.986818	−0.493409	+	0.869797i	$0.664249\pi$
$198$	−2.10339	−0.149481
$199$	8.22331	0.582935	0.291468	−	0.956581i	$-0.405856\pi$
$199$	8.22331	0.582935	0.291468	+	0.956581i	$0.405856\pi$
$200$	−6.66044	−0.470964
$201$	2.03288	0.143388
$202$	−10.3159	−0.725826
$203$	−5.27347	−0.370125
$204$	0.168528	0.0117993
$205$	17.9971	1.25697
$206$	15.1720	1.05708
$207$	−2.97452	−0.206743
$208$	6.98000	0.483976
$209$	4.97151	0.343887
$210$	5.01002	0.345724
$211$	−17.2177	−1.18532	−0.592659	−	0.805453i	$-0.701922\pi$
$211$	−17.2177	−1.18532	−0.592659	+	0.805453i	$0.701922\pi$
$212$	−2.84125	−0.195138
$213$	2.43187	0.166629
$214$	−12.3740	−0.845866
$215$	−20.3953	−1.39095
$216$	−4.87278	−0.331550
$217$	−5.69579	−0.386656
$218$	8.78977	0.595319
$219$	26.2387	1.77305
$220$	−21.7945	−1.46938
$221$	−0.644665	−0.0433649
$222$	1.68038	0.112779
$223$	−24.2294	−1.62252	−0.811262	−	0.584683i	$-0.801219\pi$
$223$	−24.2294	−1.62252	−0.811262	+	0.584683i	$0.801219\pi$
$224$	0.804060	0.0537235
$225$	2.19500	0.146333
$226$	−4.12747	−0.274555
$227$	20.7747	1.37886	0.689432	−	0.724350i	$-0.257860\pi$
$227$	20.7747	1.37886	0.689432	+	0.724350i	$0.257860\pi$
$228$	−1.42132	−0.0941294
$229$	20.1643	1.33250	0.666249	−	0.745730i	$-0.267899\pi$
$229$	20.1643	1.33250	0.666249	+	0.745730i	$0.267899\pi$
$230$	−30.8207	−2.03226
$231$	9.36419	0.616119
$232$	−6.55855	−0.430590
$233$	−14.4658	−0.947687	−0.473843	−	0.880609i	$-0.657134\pi$
$233$	−14.4658	−0.947687	−0.473843	+	0.880609i	$0.657134\pi$
$234$	−2.30031	−0.150376
$235$	−2.40095	−0.156621
$236$	0.732250	0.0476654
$237$	−2.50538	−0.162742
$238$	−0.0742621	−0.00481370
$239$	2.22214	0.143738	0.0718690	−	0.997414i	$-0.477104\pi$
$239$	2.22214	0.143738	0.0718690	+	0.997414i	$0.477104\pi$
$240$	6.23090	0.402203
$241$	18.6114	1.19886	0.599432	−	0.800426i	$-0.295393\pi$
$241$	18.6114	1.19886	0.599432	+	0.800426i	$0.295393\pi$
$242$	−29.7359	−1.91150
$243$	3.40990	0.218745
$244$	9.38872	0.601051
$245$	21.6955	1.38607
$246$	−9.61695	−0.613154
$247$	5.43694	0.345944
$248$	−7.08379	−0.449821
$249$	22.6675	1.43649
$250$	5.66997	0.358600
$251$	−0.0811002	−0.00511900	−0.00255950	−	0.999997i	$-0.500815\pi$
$251$	−0.0811002	−0.00511900	−0.00255950	+	0.999997i	$0.500815\pi$
$252$	−0.264984	−0.0166924
$253$	−57.6068	−3.62171
$254$	10.6221	0.666490
$255$	−0.575479	−0.0360379
$256$	1.00000	0.0625000
$257$	−1.75366	−0.109390	−0.0546951	−	0.998503i	$-0.517419\pi$
$257$	−1.75366	−0.109390	−0.0546951	+	0.998503i	$0.517419\pi$
$258$	10.8985	0.678511
$259$	−0.740460	−0.0460099
$260$	−23.8349	−1.47818
$261$	2.16142	0.133788
$262$	10.7468	0.663941
$263$	30.1166	1.85707	0.928536	−	0.371244i	$-0.121069\pi$
$263$	30.1166	1.85707	0.928536	+	0.371244i	$0.121069\pi$
$264$	11.6461	0.716770
$265$	9.70213	0.595997
$266$	0.626308	0.0384014
$267$	0.0701847	0.00429523
$268$	−1.11408	−0.0680535
$269$	−6.60294	−0.402588	−0.201294	−	0.979531i	$-0.564515\pi$
$269$	−6.60294	−0.402588	−0.201294	+	0.979531i	$0.564515\pi$
$270$	16.6393	1.01263
$271$	13.0362	0.791895	0.395947	−	0.918273i	$-0.370416\pi$
$271$	13.0362	0.791895	0.395947	+	0.918273i	$0.370416\pi$
$272$	−0.0923589	−0.00560008
$273$	10.2409	0.619806
$274$	4.41181	0.266527
$275$	42.5101	2.56345
$276$	16.4694	0.991343
$277$	−19.8816	−1.19457	−0.597284	−	0.802029i	$-0.703754\pi$
$277$	−19.8816	−1.19457	−0.597284	+	0.802029i	$0.703754\pi$
$278$	6.99418	0.419483
$279$	2.33451	0.139764
$280$	−2.74565	−0.164084
$281$	−6.90385	−0.411849	−0.205925	−	0.978568i	$-0.566020\pi$
$281$	−6.90385	−0.411849	−0.205925	+	0.978568i	$0.566020\pi$
$282$	1.28298	0.0764001
$283$	5.06283	0.300954	0.150477	−	0.988614i	$-0.451919\pi$
$283$	5.06283	0.300954	0.150477	+	0.988614i	$0.451919\pi$
$284$	−1.33275	−0.0790840
$285$	4.85345	0.287493
$286$	−44.5496	−2.63427
$287$	4.23772	0.250145
$288$	−0.329557	−0.0194193
$289$	−16.9915	−0.999498
$290$	22.3957	1.31512
$291$	−27.0926	−1.58820
$292$	−14.3797	−0.841507
$293$	−17.3305	−1.01246	−0.506228	−	0.862399i	$-0.668961\pi$
$293$	−17.3305	−1.01246	−0.506228	+	0.862399i	$0.668961\pi$
$294$	−11.5933	−0.676132
$295$	−2.50044	−0.145581
$296$	−0.920901	−0.0535263
$297$	31.1004	1.80463
$298$	18.1832	1.05332
$299$	−63.0000	−3.64338
$300$	−12.1534	−0.701674
$301$	−4.80244	−0.276808
$302$	−10.7468	−0.618411
$303$	−18.8235	−1.08138
$304$	0.778932	0.0446748
$305$	−32.0600	−1.83575
$306$	0.0304375	0.00174000
$307$	−1.92769	−0.110019	−0.0550097	−	0.998486i	$-0.517519\pi$
$307$	−1.92769	−0.110019	−0.0550097	+	0.998486i	$0.517519\pi$
$308$	−5.13189	−0.292416
$309$	27.6845	1.57492
$310$	24.1893	1.37386
$311$	−22.9939	−1.30386	−0.651931	−	0.758278i	$-0.726041\pi$
$311$	−22.9939	−1.30386	−0.651931	+	0.758278i	$0.726041\pi$
$312$	12.7365	0.721060
$313$	11.4550	0.647475	0.323738	−	0.946147i	$-0.395061\pi$
$313$	11.4550	0.647475	0.323738	+	0.946147i	$0.395061\pi$
$314$	−14.7206	−0.830734
$315$	0.904850	0.0509825
$316$	1.37303	0.0772389
$317$	−7.05351	−0.396164	−0.198082	−	0.980185i	$-0.563471\pi$
$317$	−7.05351	−0.396164	−0.198082	+	0.980185i	$0.563471\pi$
$318$	−5.18445	−0.290730
$319$	41.8598	2.34370
$320$	−3.41474	−0.190890
$321$	−22.5789	−1.26023
$322$	−7.25728	−0.404432
$323$	−0.0719413	−0.00400292
$324$	−9.88006	−0.548892
$325$	46.4899	2.57879
$326$	−20.4017	−1.12994
$327$	16.0388	0.886946
$328$	5.27041	0.291009
$329$	−0.565345	−0.0311685
$330$	−39.7685	−2.18919
$331$	1.02399	0.0562835	0.0281418	−	0.999604i	$-0.491041\pi$
$331$	1.02399	0.0562835	0.0281418	+	0.999604i	$0.491041\pi$
$332$	−12.4225	−0.681775
$333$	0.303490	0.0166311
$334$	−1.82880	−0.100067
$335$	3.80431	0.207851
$336$	1.46717	0.0800409
$337$	18.2482	0.994040	0.497020	−	0.867739i	$-0.334427\pi$
$337$	18.2482	0.994040	0.497020	+	0.867739i	$0.334427\pi$
$338$	−35.7204	−1.94293
$339$	−7.53143	−0.409051
$340$	0.315382	0.0171040
$341$	45.2121	2.44837
$342$	−0.256703	−0.0138809
$343$	10.7370	0.579744
$344$	−5.97274	−0.322028
$345$	−56.2388	−3.02780
$346$	−15.8692	−0.853135
$347$	30.1214	1.61700	0.808500	−	0.588497i	$-0.200280\pi$
$347$	30.1214	1.61700	0.808500	+	0.588497i	$0.200280\pi$
$348$	−11.9674	−0.641522
$349$	30.1824	1.61562	0.807812	−	0.589440i	$-0.200652\pi$
$349$	30.1824	1.61562	0.807812	+	0.589440i	$0.200652\pi$
$350$	5.35539	0.286258
$351$	34.0120	1.81542
$352$	−6.38247	−0.340187
$353$	0.647638	0.0344703	0.0172352	−	0.999851i	$-0.494514\pi$
$353$	0.647638	0.0344703	0.0172352	+	0.999851i	$0.494514\pi$
$354$	1.33614	0.0710151
$355$	4.55098	0.241541
$356$	−0.0384635	−0.00203856
$357$	−0.135507	−0.00717177
$358$	−20.4734	−1.08205
$359$	8.75512	0.462078	0.231039	−	0.972945i	$-0.425788\pi$
$359$	8.75512	0.462078	0.231039	+	0.972945i	$0.425788\pi$
$360$	1.12535	0.0593113
$361$	−18.3933	−0.968067
$362$	−5.48356	−0.288210
$363$	−54.2594	−2.84788
$364$	−5.61234	−0.294166
$365$	49.1029	2.57016
$366$	17.1317	0.895487
$367$	−13.2017	−0.689121	−0.344561	−	0.938764i	$-0.611972\pi$
$367$	−13.2017	−0.689121	−0.344561	+	0.938764i	$0.611972\pi$
$368$	−9.02579	−0.470502
$369$	−1.73690	−0.0904194
$370$	3.14464	0.163482
$371$	2.28454	0.118607
$372$	−12.9258	−0.670174
$373$	−22.7658	−1.17877	−0.589385	−	0.807853i	$-0.700630\pi$
$373$	−22.7658	−1.17877	−0.589385	+	0.807853i	$0.700630\pi$
$374$	0.589478	0.0304812
$375$	10.3460	0.534267
$376$	−0.703113	−0.0362603
$377$	45.7787	2.35772
$378$	3.91800	0.201520
$379$	−21.3415	−1.09624	−0.548120	−	0.836400i	$-0.684656\pi$
$379$	−21.3415	−1.09624	−0.548120	+	0.836400i	$0.684656\pi$
$380$	−2.65985	−0.136447
$381$	19.3822	0.992982
$382$	−12.9142	−0.660749
$383$	−34.7556	−1.77593	−0.887964	−	0.459913i	$-0.847881\pi$
$383$	−34.7556	−1.77593	−0.887964	+	0.459913i	$0.847881\pi$
$384$	1.82471	0.0931167
$385$	17.5241	0.893109
$386$	11.9454	0.608005
$387$	1.96836	0.100057
$388$	14.8476	0.753775
$389$	6.51193	0.330168	0.165084	−	0.986280i	$-0.447211\pi$
$389$	6.51193	0.330168	0.165084	+	0.986280i	$0.447211\pi$
$390$	−43.4917	−2.20229
$391$	0.833612	0.0421576
$392$	6.35349	0.320900
$393$	19.6098	0.989184
$394$	13.8507	0.697786
$395$	−4.68854	−0.235906
$396$	2.10339	0.105699
$397$	7.17424	0.360065	0.180032	−	0.983661i	$-0.442380\pi$
$397$	7.17424	0.360065	0.180032	+	0.983661i	$0.442380\pi$
$398$	−8.22331	−0.412197
$399$	1.14283	0.0572130
$400$	6.66044	0.333022
$401$	−22.5823	−1.12771	−0.563853	−	0.825875i	$-0.690682\pi$
$401$	−22.5823	−1.12771	−0.563853	+	0.825875i	$0.690682\pi$
$402$	−2.03288	−0.101391
$403$	49.4448	2.46302
$404$	10.3159	0.513236
$405$	33.7378	1.67645
$406$	5.27347	0.261718
$407$	5.87762	0.291343
$408$	−0.168528	−0.00834338
$409$	30.7179	1.51890	0.759452	−	0.650563i	$-0.225467\pi$
$409$	30.7179	1.51890	0.759452	+	0.650563i	$0.225467\pi$
$410$	−17.9971	−0.888811
$411$	8.05027	0.397090
$412$	−15.1720	−0.747472
$413$	−0.588773	−0.0289716
$414$	2.97452	0.146189
$415$	42.4197	2.08230
$416$	−6.98000	−0.342223
$417$	12.7623	0.624974
$418$	−4.97151	−0.243165
$419$	13.0241	0.636268	0.318134	−	0.948046i	$-0.396944\pi$
$419$	13.0241	0.636268	0.318134	+	0.948046i	$0.396944\pi$
$420$	−5.01002	−0.244464
$421$	0.760677	0.0370732	0.0185366	−	0.999828i	$-0.494099\pi$
$421$	0.760677	0.0370732	0.0185366	+	0.999828i	$0.494099\pi$
$422$	17.2177	0.838147
$423$	0.231716	0.0112664
$424$	2.84125	0.137983
$425$	−0.615151	−0.0298392
$426$	−2.43187	−0.117825
$427$	−7.54910	−0.365326
$428$	12.3740	0.598118
$429$	−81.2900	−3.92472
$430$	20.3953	0.983551
$431$	28.6253	1.37883	0.689417	−	0.724365i	$-0.257867\pi$
$431$	28.6253	1.37883	0.689417	+	0.724365i	$0.257867\pi$
$432$	4.87278	0.234442
$433$	8.48735	0.407876	0.203938	−	0.978984i	$-0.434626\pi$
$433$	8.48735	0.407876	0.203938	+	0.978984i	$0.434626\pi$
$434$	5.69579	0.273407
$435$	40.8657	1.95936
$436$	−8.78977	−0.420954
$437$	−7.03048	−0.336313
$438$	−26.2387	−1.25373
$439$	8.42744	0.402220	0.201110	−	0.979569i	$-0.435545\pi$
$439$	8.42744	0.402220	0.201110	+	0.979569i	$0.435545\pi$
$440$	21.7945	1.03901
$441$	−2.09384	−0.0997066
$442$	0.644665	0.0306636
$443$	−19.6320	−0.932744	−0.466372	−	0.884589i	$-0.654439\pi$
$443$	−19.6320	−0.932744	−0.466372	+	0.884589i	$0.654439\pi$
$444$	−1.68038	−0.0797471
$445$	0.131343	0.00622625
$446$	24.2294	1.14730
$447$	33.1790	1.56931
$448$	−0.804060	−0.0379883
$449$	2.11400	0.0997657	0.0498828	−	0.998755i	$-0.484115\pi$
$449$	2.11400	0.0997657	0.0498828	+	0.998755i	$0.484115\pi$
$450$	−2.19500	−0.103473
$451$	−33.6382	−1.58396
$452$	4.12747	0.194140
$453$	−19.6098	−0.921350
$454$	−20.7747	−0.975004
$455$	19.1647	0.898453
$456$	1.42132	0.0665596
$457$	−6.34295	−0.296711	−0.148355	−	0.988934i	$-0.547398\pi$
$457$	−6.34295	−0.296711	−0.148355	+	0.988934i	$0.547398\pi$
$458$	−20.1643	−0.942218
$459$	−0.450044	−0.0210063
$460$	30.8207	1.43702
$461$	20.2715	0.944138	0.472069	−	0.881562i	$-0.343507\pi$
$461$	20.2715	0.944138	0.472069	+	0.881562i	$0.343507\pi$
$462$	−9.36419	−0.435662
$463$	31.5245	1.46507	0.732533	−	0.680731i	$-0.238338\pi$
$463$	31.5245	1.46507	0.732533	+	0.680731i	$0.238338\pi$
$464$	6.55855	0.304473
$465$	44.1384	2.04687
$466$	14.4658	0.670116
$467$	14.5170	0.671765	0.335882	−	0.941904i	$-0.390966\pi$
$467$	14.5170	0.671765	0.335882	+	0.941904i	$0.390966\pi$
$468$	2.30031	0.106332
$469$	0.895790	0.0413637
$470$	2.40095	0.110747
$471$	−26.8609	−1.23768
$472$	−0.732250	−0.0337045
$473$	38.1208	1.75280
$474$	2.50538	0.115076
$475$	5.18803	0.238043
$476$	0.0742621	0.00340380
$477$	−0.936355	−0.0428727
$478$	−2.22214	−0.101638
$479$	23.1465	1.05759	0.528795	−	0.848750i	$-0.322644\pi$
$479$	23.1465	1.05759	0.528795	+	0.848750i	$0.322644\pi$
$480$	−6.23090	−0.284400
$481$	6.42789	0.293086
$482$	−18.6114	−0.847725
$483$	−13.2424	−0.602550
$484$	29.7359	1.35163
$485$	−50.7008	−2.30221
$486$	−3.40990	−0.154676
$487$	20.6488	0.935686	0.467843	−	0.883812i	$-0.345031\pi$
$487$	20.6488	0.935686	0.467843	+	0.883812i	$0.345031\pi$
$488$	−9.38872	−0.425008
$489$	−37.2271	−1.68347
$490$	−21.6955	−0.980103
$491$	−22.1120	−0.997899	−0.498950	−	0.866631i	$-0.666281\pi$
$491$	−22.1120	−0.997899	−0.498950	+	0.866631i	$0.666281\pi$
$492$	9.61695	0.433566
$493$	−0.605741	−0.0272812
$494$	−5.43694	−0.244620
$495$	−7.18252	−0.322830
$496$	7.08379	0.318072
$497$	1.07161	0.0480682
$498$	−22.6675	−1.01575
$499$	25.5158	1.14224	0.571122	−	0.820865i	$-0.306508\pi$
$499$	25.5158	1.14224	0.571122	+	0.820865i	$0.306508\pi$
$500$	−5.66997	−0.253569
$501$	−3.33702	−0.149087
$502$	0.0811002	0.00361968
$503$	26.9571	1.20196	0.600979	−	0.799265i	$-0.294778\pi$
$503$	26.9571	1.20196	0.600979	+	0.799265i	$0.294778\pi$
$504$	0.264984	0.0118033
$505$	−35.2262	−1.56754
$506$	57.6068	2.56094
$507$	−65.1792	−2.89471
$508$	−10.6221	−0.471280
$509$	12.6664	0.561430	0.280715	−	0.959791i	$-0.409428\pi$
$509$	12.6664	0.561430	0.280715	+	0.959791i	$0.409428\pi$
$510$	0.575479	0.0254826
$511$	11.5621	0.511478
$512$	−1.00000	−0.0441942
$513$	3.79556	0.167578
$514$	1.75366	0.0773505
$515$	51.8085	2.28295
$516$	−10.8985	−0.479780
$517$	4.48760	0.197364
$518$	0.740460	0.0325339
$519$	−28.9567	−1.27106
$520$	23.8349	1.04523
$521$	−30.7310	−1.34635	−0.673175	−	0.739483i	$-0.735070\pi$
$521$	−30.7310	−1.34635	−0.673175	+	0.739483i	$0.735070\pi$
$522$	−2.16142	−0.0946027
$523$	32.5140	1.42174	0.710870	−	0.703324i	$-0.248302\pi$
$523$	32.5140	1.42174	0.710870	+	0.703324i	$0.248302\pi$
$524$	−10.7468	−0.469477
$525$	9.77202	0.426486
$526$	−30.1166	−1.31315
$527$	−0.654251	−0.0284996
$528$	−11.6461	−0.506833
$529$	58.4649	2.54195
$530$	−9.70213	−0.421434
$531$	0.241318	0.0104723
$532$	−0.626308	−0.0271539
$533$	−36.7874	−1.59344
$534$	−0.0701847	−0.00303719
$535$	−42.2538	−1.82679
$536$	1.11408	0.0481211
$537$	−37.3580	−1.61212
$538$	6.60294	0.284673
$539$	−40.5509	−1.74665
$540$	−16.6393	−0.716040
$541$	−30.9297	−1.32977	−0.664887	−	0.746944i	$-0.731520\pi$
$541$	−30.9297	−1.32977	−0.664887	+	0.746944i	$0.731520\pi$
$542$	−13.0362	−0.559954
$543$	−10.0059	−0.429394
$544$	0.0923589	0.00395986
$545$	30.0148	1.28569
$546$	−10.2409	−0.438269
$547$	−11.4706	−0.490446	−0.245223	−	0.969467i	$-0.578861\pi$
$547$	−11.4706	−0.490446	−0.245223	+	0.969467i	$0.578861\pi$
$548$	−4.41181	−0.188463
$549$	3.09412	0.132054
$550$	−42.5101	−1.81263
$551$	5.10867	0.217637
$552$	−16.4694	−0.700985
$553$	−1.10400	−0.0469467
$554$	19.8816	0.844688
$555$	5.73804	0.243566
$556$	−6.99418	−0.296619
$557$	16.7241	0.708624	0.354312	−	0.935127i	$-0.384715\pi$
$557$	16.7241	0.708624	0.354312	+	0.935127i	$0.384715\pi$
$558$	−2.33451	−0.0988279
$559$	41.6897	1.76329
$560$	2.74565	0.116025
$561$	1.07562	0.0454129
$562$	6.90385	0.291221
$563$	−18.7300	−0.789376	−0.394688	−	0.918815i	$-0.629147\pi$
$563$	−18.7300	−0.789376	−0.394688	+	0.918815i	$0.629147\pi$
$564$	−1.28298	−0.0540230
$565$	−14.0942	−0.592949
$566$	−5.06283	−0.212806
$567$	7.94416	0.333623
$568$	1.33275	0.0559208
$569$	−43.3980	−1.81934	−0.909669	−	0.415334i	$-0.863665\pi$
$569$	−43.3980	−1.81934	−0.909669	+	0.415334i	$0.863665\pi$
$570$	−4.85345	−0.203289
$571$	−35.0635	−1.46736	−0.733681	−	0.679494i	$-0.762199\pi$
$571$	−35.0635	−1.46736	−0.733681	+	0.679494i	$0.762199\pi$
$572$	44.5496	1.86271
$573$	−23.5647	−0.984429
$574$	−4.23772	−0.176879
$575$	−60.1157	−2.50700
$576$	0.329557	0.0137316
$577$	19.1682	0.797983	0.398991	−	0.916955i	$-0.369360\pi$
$577$	19.1682	0.797983	0.398991	+	0.916955i	$0.369360\pi$
$578$	16.9915	0.706752
$579$	21.7969	0.905847
$580$	−22.3957	−0.929933
$581$	9.98846	0.414391
$582$	27.0926	1.12302
$583$	−18.1342	−0.751042
$584$	14.3797	0.595036
$585$	−7.85495	−0.324762
$586$	17.3305	0.715915
$587$	−14.8656	−0.613571	−0.306785	−	0.951779i	$-0.599253\pi$
$587$	−14.8656	−0.613571	−0.306785	+	0.951779i	$0.599253\pi$
$588$	11.5933	0.478098
$589$	5.51779	0.227357
$590$	2.50044	0.102942
$591$	25.2734	1.03961
$592$	0.920901	0.0378488
$593$	−22.3115	−0.916225	−0.458113	−	0.888894i	$-0.651474\pi$
$593$	−22.3115	−0.916225	−0.458113	+	0.888894i	$0.651474\pi$
$594$	−31.1004	−1.27606
$595$	−0.253586	−0.0103960
$596$	−18.1832	−0.744813
$597$	−15.0051	−0.614120
$598$	63.0000	2.57626
$599$	−2.11300	−0.0863349	−0.0431674	−	0.999068i	$-0.513745\pi$
$599$	−2.11300	−0.0863349	−0.0431674	+	0.999068i	$0.513745\pi$
$600$	12.1534	0.496159
$601$	−0.764660	−0.0311911	−0.0155956	−	0.999878i	$-0.504964\pi$
$601$	−0.764660	−0.0311911	−0.0155956	+	0.999878i	$0.504964\pi$
$602$	4.80244	0.195733
$603$	−0.367154	−0.0149517
$604$	10.7468	0.437283
$605$	−101.540	−4.12820
$606$	18.8235	0.764654
$607$	24.8985	1.01060	0.505299	−	0.862944i	$-0.331382\pi$
$607$	24.8985	1.01060	0.505299	+	0.862944i	$0.331382\pi$
$608$	−0.778932	−0.0315899
$609$	9.62254	0.389925
$610$	32.0600	1.29807
$611$	4.90773	0.198545
$612$	−0.0304375	−0.00123036
$613$	6.76238	0.273130	0.136565	−	0.990631i	$-0.456394\pi$
$613$	6.76238	0.273130	0.136565	+	0.990631i	$0.456394\pi$
$614$	1.92769	0.0777954
$615$	−32.8394	−1.32421
$616$	5.13189	0.206770
$617$	−44.6146	−1.79612	−0.898058	−	0.439877i	$-0.855022\pi$
$617$	−44.6146	−1.79612	−0.898058	+	0.439877i	$0.855022\pi$
$618$	−27.6845	−1.11363
$619$	24.0162	0.965294	0.482647	−	0.875815i	$-0.339676\pi$
$619$	24.0162	0.965294	0.482647	+	0.875815i	$0.339676\pi$
$620$	−24.1893	−0.971465
$621$	−43.9807	−1.76488
$622$	22.9939	0.921970
$623$	0.0309270	0.00123906
$624$	−12.7365	−0.509866
$625$	−13.9407	−0.557630
$626$	−11.4550	−0.457834
$627$	−9.07155	−0.362283
$628$	14.7206	0.587417
$629$	−0.0850534	−0.00339130
$630$	−0.904850	−0.0360501
$631$	0.118885	0.00473273	0.00236636	−	0.999997i	$-0.499247\pi$
$631$	0.118885	0.00473273	0.00236636	+	0.999997i	$0.499247\pi$
$632$	−1.37303	−0.0546162
$633$	31.4174	1.24873
$634$	7.05351	0.280131
$635$	36.2717	1.43940
$636$	5.18445	0.205577
$637$	−44.3473	−1.75711
$638$	−41.8598	−1.65724
$639$	−0.439216	−0.0173751
$640$	3.41474	0.134979
$641$	17.3766	0.686335	0.343167	−	0.939274i	$-0.388500\pi$
$641$	17.3766	0.686335	0.343167	+	0.939274i	$0.388500\pi$
$642$	22.5789	0.891116
$643$	−27.6138	−1.08898	−0.544491	−	0.838767i	$-0.683277\pi$
$643$	−27.6138	−1.08898	−0.544491	+	0.838767i	$0.683277\pi$
$644$	7.25728	0.285977
$645$	37.2155	1.46536
$646$	0.0719413	0.00283049
$647$	36.4349	1.43240	0.716202	−	0.697893i	$-0.245879\pi$
$647$	36.4349	1.43240	0.716202	+	0.697893i	$0.245879\pi$
$648$	9.88006	0.388126
$649$	4.67356	0.183453
$650$	−46.4899	−1.82348
$651$	10.3932	0.407340
$652$	20.4017	0.798991
$653$	15.6018	0.610545	0.305273	−	0.952265i	$-0.401252\pi$
$653$	15.6018	0.610545	0.305273	+	0.952265i	$0.401252\pi$
$654$	−16.0388	−0.627165
$655$	36.6976	1.43389
$656$	−5.27041	−0.205775
$657$	−4.73893	−0.184883
$658$	0.565345	0.0220394
$659$	27.1612	1.05805	0.529026	−	0.848606i	$-0.322558\pi$
$659$	27.1612	1.05805	0.529026	+	0.848606i	$0.322558\pi$
$660$	39.7685	1.54799
$661$	28.9434	1.12577	0.562884	−	0.826536i	$-0.309692\pi$
$661$	28.9434	1.12577	0.562884	+	0.826536i	$0.309692\pi$
$662$	−1.02399	−0.0397985
$663$	1.17633	0.0456847
$664$	12.4225	0.482088
$665$	2.13868	0.0829344
$666$	−0.303490	−0.0117600
$667$	−59.1961	−2.29208
$668$	1.82880	0.0707583
$669$	44.2116	1.70932
$670$	−3.80431	−0.146973
$671$	59.9232	2.31331
$672$	−1.46717	−0.0565975
$673$	−17.4549	−0.672838	−0.336419	−	0.941712i	$-0.609216\pi$
$673$	−17.4549	−0.672838	−0.336419	+	0.941712i	$0.609216\pi$
$674$	−18.2482	−0.702893
$675$	32.4548	1.24919
$676$	35.7204	1.37386
$677$	−36.1128	−1.38793	−0.693965	−	0.720009i	$-0.744138\pi$
$677$	−36.1128	−1.38793	−0.693965	+	0.720009i	$0.744138\pi$
$678$	7.53143	0.289243
$679$	−11.9384	−0.458153
$680$	−0.315382	−0.0120943
$681$	−37.9077	−1.45263
$682$	−45.2121	−1.73126
$683$	−49.2535	−1.88463	−0.942316	−	0.334724i	$-0.891357\pi$
$683$	−49.2535	−1.88463	−0.942316	+	0.334724i	$0.891357\pi$
$684$	0.256703	0.00981527
$685$	15.0652	0.575611
$686$	−10.7370	−0.409941
$687$	−36.7940	−1.40378
$688$	5.97274	0.227708
$689$	−19.8319	−0.755536
$690$	56.2388	2.14097
$691$	38.3527	1.45900	0.729502	−	0.683979i	$-0.239752\pi$
$691$	38.3527	1.45900	0.729502	+	0.683979i	$0.239752\pi$
$692$	15.8692	0.603258
$693$	−1.69125	−0.0642453
$694$	−30.1214	−1.14339
$695$	23.8833	0.905945
$696$	11.9674	0.453625
$697$	0.486769	0.0184377
$698$	−30.1824	−1.14242
$699$	26.3959	0.998383
$700$	−5.35539	−0.202415
$701$	−26.2809	−0.992616	−0.496308	−	0.868146i	$-0.665311\pi$
$701$	−26.2809	−0.992616	−0.496308	+	0.868146i	$0.665311\pi$
$702$	−34.0120	−1.28370
$703$	0.717319	0.0270542
$704$	6.38247	0.240548
$705$	4.38103	0.164999
$706$	−0.647638	−0.0243742
$707$	−8.29462	−0.311951
$708$	−1.33614	−0.0502153
$709$	−12.3923	−0.465403	−0.232701	−	0.972548i	$-0.574756\pi$
$709$	−12.3923	−0.465403	−0.232701	+	0.972548i	$0.574756\pi$
$710$	−4.55098	−0.170795
$711$	0.452492	0.0169698
$712$	0.0384635	0.00144148
$713$	−63.9368	−2.39445
$714$	0.135507	0.00507121
$715$	−152.125	−5.68917
$716$	20.4734	0.765127
$717$	−4.05475	−0.151427
$718$	−8.75512	−0.326738
$719$	25.1792	0.939027	0.469513	−	0.882925i	$-0.344429\pi$
$719$	25.1792	0.939027	0.469513	+	0.882925i	$0.344429\pi$
$720$	−1.12535	−0.0419394
$721$	12.1992	0.454322
$722$	18.3933	0.684526
$723$	−33.9603	−1.26300
$724$	5.48356	0.203795
$725$	43.6828	1.62234
$726$	54.2594	2.01375
$727$	15.5597	0.577078	0.288539	−	0.957468i	$-0.406831\pi$
$727$	15.5597	0.577078	0.288539	+	0.957468i	$0.406831\pi$
$728$	5.61234	0.208007
$729$	23.4181	0.867338
$730$	−49.1029	−1.81738
$731$	−0.551636	−0.0204030
$732$	−17.1317	−0.633205
$733$	−18.8198	−0.695123	−0.347562	−	0.937657i	$-0.612990\pi$
$733$	−18.8198	−0.695123	−0.347562	+	0.937657i	$0.612990\pi$
$734$	13.2017	0.487282
$735$	−39.5879	−1.46022
$736$	9.02579	0.332695
$737$	−7.11061	−0.261923
$738$	1.73690	0.0639362
$739$	48.4103	1.78080	0.890400	−	0.455179i	$-0.150425\pi$
$739$	48.4103	1.78080	0.890400	+	0.455179i	$0.150425\pi$
$740$	−3.14464	−0.115599
$741$	−9.92083	−0.364451
$742$	−2.28454	−0.0838679
$743$	9.30154	0.341240	0.170620	−	0.985337i	$-0.445423\pi$
$743$	9.30154	0.341240	0.170620	+	0.985337i	$0.445423\pi$
$744$	12.9258	0.473884
$745$	62.0909	2.27483
$746$	22.7658	0.833516
$747$	−4.09394	−0.149789
$748$	−0.589478	−0.0215534
$749$	−9.94940	−0.363543
$750$	−10.3460	−0.377784
$751$	−35.8517	−1.30825	−0.654123	−	0.756388i	$-0.726962\pi$
$751$	−35.8517	−1.30825	−0.654123	+	0.756388i	$0.726962\pi$
$752$	0.703113	0.0256399
$753$	0.147984	0.00539284
$754$	−45.7787	−1.66716
$755$	−36.6976	−1.33556
$756$	−3.91800	−0.142496
$757$	−33.7198	−1.22557	−0.612784	−	0.790251i	$-0.709950\pi$
$757$	−33.7198	−1.22557	−0.612784	+	0.790251i	$0.709950\pi$
$758$	21.3415	0.775159
$759$	105.116	3.81546
$760$	2.65985	0.0964829
$761$	30.8384	1.11789	0.558946	−	0.829204i	$-0.311206\pi$
$761$	30.8384	1.11789	0.558946	+	0.829204i	$0.311206\pi$
$762$	−19.3822	−0.702144
$763$	7.06750	0.255861
$764$	12.9142	0.467220
$765$	0.103936	0.00375782
$766$	34.7556	1.25577
$767$	5.11110	0.184551
$768$	−1.82471	−0.0658435
$769$	−39.0998	−1.40998	−0.704988	−	0.709219i	$-0.749048\pi$
$769$	−39.0998	−1.40998	−0.704988	+	0.709219i	$0.749048\pi$
$770$	−17.5241	−0.631523
$771$	3.19991	0.115242
$772$	−11.9454	−0.429925
$773$	−17.9455	−0.645454	−0.322727	−	0.946492i	$-0.604600\pi$
$773$	−17.9455	−0.645454	−0.322727	+	0.946492i	$0.604600\pi$
$774$	−1.96836	−0.0707512
$775$	47.1812	1.69480
$776$	−14.8476	−0.532999
$777$	1.35112	0.0484712
$778$	−6.51193	−0.233464
$779$	−4.10529	−0.147087
$780$	43.4917	1.55725
$781$	−8.50622	−0.304376
$782$	−0.833612	−0.0298099
$783$	31.9584	1.14210
$784$	−6.35349	−0.226910
$785$	−50.2671	−1.79411
$786$	−19.6098	−0.699458
$787$	47.8777	1.70666	0.853328	−	0.521374i	$-0.174580\pi$
$787$	47.8777	1.70666	0.853328	+	0.521374i	$0.174580\pi$
$788$	−13.8507	−0.493409
$789$	−54.9540	−1.95642
$790$	4.68854	0.166811
$791$	−3.31873	−0.118001
$792$	−2.10339	−0.0747407
$793$	65.5333	2.32716
$794$	−7.17424	−0.254604
$795$	−17.7035	−0.627880
$796$	8.22331	0.291468
$797$	−11.2573	−0.398755	−0.199378	−	0.979923i	$-0.563892\pi$
$797$	−11.2573	−0.398755	−0.199378	+	0.979923i	$0.563892\pi$
$798$	−1.14283	−0.0404557
$799$	−0.0649388	−0.00229737
$800$	−6.66044	−0.235482
$801$	−0.0126759	−0.000447882 0
$802$	22.5823	0.797408
$803$	−91.7779	−3.23877
$804$	2.03288	0.0716941
$805$	−24.7817	−0.873440
$806$	−49.4448	−1.74162
$807$	12.0484	0.424125
$808$	−10.3159	−0.362913
$809$	0.258254	0.00907973	0.00453987	−	0.999990i	$-0.498555\pi$
$809$	0.258254	0.00907973	0.00453987	+	0.999990i	$0.498555\pi$
$810$	−33.7378	−1.18543
$811$	33.9969	1.19379	0.596897	−	0.802318i	$-0.296400\pi$
$811$	33.9969	1.19379	0.596897	+	0.802318i	$0.296400\pi$
$812$	−5.27347	−0.185062
$813$	−23.7873	−0.834257
$814$	−5.87762	−0.206011
$815$	−69.6663	−2.44031
$816$	0.168528	0.00589966
$817$	4.65236	0.162765
$818$	−30.7179	−1.07403
$819$	−1.84959	−0.0646298
$820$	17.9971	0.628485
$821$	26.5546	0.926761	0.463381	−	0.886159i	$-0.346636\pi$
$821$	26.5546	0.926761	0.463381	+	0.886159i	$0.346636\pi$
$822$	−8.05027	−0.280785
$823$	−21.6769	−0.755608	−0.377804	−	0.925886i	$-0.623321\pi$
$823$	−21.6769	−0.755608	−0.377804	+	0.925886i	$0.623321\pi$
$824$	15.1720	0.528542
$825$	−77.5684	−2.70059
$826$	0.588773	0.0204860
$827$	3.71514	0.129188	0.0645940	−	0.997912i	$-0.479425\pi$
$827$	3.71514	0.129188	0.0645940	+	0.997912i	$0.479425\pi$
$828$	−2.97452	−0.103372
$829$	11.2886	0.392070	0.196035	−	0.980597i	$-0.437193\pi$
$829$	11.2886	0.392070	0.196035	+	0.980597i	$0.437193\pi$
$830$	−42.4197	−1.47241
$831$	36.2781	1.25847
$832$	6.98000	0.241988
$833$	0.586801	0.0203315
$834$	−12.7623	−0.441924
$835$	−6.24487	−0.216112
$836$	4.97151	0.171943
$837$	34.5177	1.19311
$838$	−13.0241	−0.449909
$839$	2.62271	0.0905458	0.0452729	−	0.998975i	$-0.485584\pi$
$839$	2.62271	0.0905458	0.0452729	+	0.998975i	$0.485584\pi$
$840$	5.01002	0.172862
$841$	14.0146	0.483262
$842$	−0.760677	−0.0262147
$843$	12.5975	0.433881
$844$	−17.2177	−0.592659
$845$	−121.976	−4.19609
$846$	−0.231716	−0.00796656
$847$	−23.9095	−0.821539
$848$	−2.84125	−0.0975689
$849$	−9.23818	−0.317053
$850$	0.615151	0.0210995
$851$	−8.31186	−0.284927
$852$	2.43187	0.0833146
$853$	46.4395	1.59006	0.795030	−	0.606571i	$-0.207455\pi$
$853$	46.4395	1.59006	0.795030	+	0.606571i	$0.207455\pi$
$854$	7.54910	0.258325
$855$	−0.876573	−0.0299782
$856$	−12.3740	−0.422933
$857$	−53.2013	−1.81732	−0.908661	−	0.417534i	$-0.862894\pi$
$857$	−53.2013	−1.81732	−0.908661	+	0.417534i	$0.862894\pi$
$858$	81.2900	2.77520
$859$	−31.8015	−1.08505	−0.542527	−	0.840039i	$-0.682532\pi$
$859$	−31.8015	−1.08505	−0.542527	+	0.840039i	$0.682532\pi$
$860$	−20.3953	−0.695475
$861$	−7.73260	−0.263526
$862$	−28.6253	−0.974982
$863$	19.5244	0.664617	0.332309	−	0.943171i	$-0.392172\pi$
$863$	19.5244	0.664617	0.332309	+	0.943171i	$0.392172\pi$
$864$	−4.87278	−0.165775
$865$	−54.1893	−1.84249
$866$	−8.48735	−0.288412
$867$	31.0045	1.05297
$868$	−5.69579	−0.193328
$869$	8.76332	0.297275
$870$	−40.8657	−1.38548
$871$	−7.77630	−0.263490
$872$	8.78977	0.297659
$873$	4.89315	0.165608
$874$	7.03048	0.237809
$875$	4.55899	0.154122
$876$	26.2387	0.886524
$877$	23.8204	0.804358	0.402179	−	0.915561i	$-0.368253\pi$
$877$	23.8204	0.804358	0.402179	+	0.915561i	$0.368253\pi$
$878$	−8.42744	−0.284412
$879$	31.6230	1.06662
$880$	−21.7945	−0.734691
$881$	−25.3767	−0.854964	−0.427482	−	0.904024i	$-0.640599\pi$
$881$	−25.3767	−0.854964	−0.427482	+	0.904024i	$0.640599\pi$
$882$	2.09384	0.0705032
$883$	46.3751	1.56065	0.780324	−	0.625376i	$-0.215054\pi$
$883$	46.3751	1.56065	0.780324	+	0.625376i	$0.215054\pi$
$884$	−0.644665	−0.0216824
$885$	4.56257	0.153369
$886$	19.6320	0.659550
$887$	50.4211	1.69297	0.846487	−	0.532409i	$-0.178713\pi$
$887$	50.4211	1.69297	0.846487	+	0.532409i	$0.178713\pi$
$888$	1.68038	0.0563897
$889$	8.54080	0.286449
$890$	−0.131343	−0.00440262
$891$	−63.0592	−2.11256
$892$	−24.2294	−0.811262
$893$	0.547677	0.0183273
$894$	−33.1790	−1.10967
$895$	−69.9113	−2.33688
$896$	0.804060	0.0268618
$897$	114.957	3.83829
$898$	−2.11400	−0.0705450
$899$	46.4594	1.54951
$900$	2.19500	0.0731665
$901$	0.262415	0.00874230
$902$	33.6382	1.12003
$903$	8.76304	0.291616
$904$	−4.12747	−0.137278
$905$	−18.7249	−0.622438
$906$	19.6098	0.651493
$907$	57.3422	1.90402	0.952008	−	0.306073i	$-0.0990151\pi$
$907$	57.3422	1.90402	0.952008	+	0.306073i	$0.0990151\pi$
$908$	20.7747	0.689432
$909$	3.39969	0.112760
$910$	−19.1647	−0.635302
$911$	47.8464	1.58522	0.792611	−	0.609728i	$-0.208721\pi$
$911$	47.8464	1.58522	0.792611	+	0.609728i	$0.208721\pi$
$912$	−1.42132	−0.0470647
$913$	−79.2865	−2.62400
$914$	6.34295	0.209806
$915$	58.5002	1.93396
$916$	20.1643	0.666249
$917$	8.64109	0.285354
$918$	0.450044	0.0148537
$919$	32.3242	1.06628	0.533138	−	0.846028i	$-0.321012\pi$
$919$	32.3242	1.06628	0.533138	+	0.846028i	$0.321012\pi$
$920$	−30.8207	−1.01613
$921$	3.51748	0.115905
$922$	−20.2715	−0.667607
$923$	−9.30257	−0.306198
$924$	9.36419	0.308059
$925$	6.13361	0.201672
$926$	−31.5245	−1.03596
$927$	−5.00005	−0.164223
$928$	−6.55855	−0.215295
$929$	19.4594	0.638442	0.319221	−	0.947680i	$-0.396579\pi$
$929$	19.4594	0.638442	0.319221	+	0.947680i	$0.396579\pi$
$930$	−44.1384	−1.44735
$931$	−4.94894	−0.162195
$932$	−14.4658	−0.473843
$933$	41.9571	1.37361
$934$	−14.5170	−0.475009
$935$	2.01291	0.0658293
$936$	−2.30031	−0.0751880
$937$	−36.6518	−1.19736	−0.598681	−	0.800987i	$-0.704308\pi$
$937$	−36.6518	−1.19736	−0.598681	+	0.800987i	$0.704308\pi$
$938$	−0.895790	−0.0292486
$939$	−20.9020	−0.682112
$940$	−2.40095	−0.0783103
$941$	25.6193	0.835165	0.417583	−	0.908639i	$-0.362877\pi$
$941$	25.6193	0.835165	0.417583	+	0.908639i	$0.362877\pi$
$942$	26.8609	0.875174
$943$	47.5696	1.54908
$944$	0.732250	0.0238327
$945$	13.3790	0.435218
$946$	−38.1208	−1.23941
$947$	−12.2074	−0.396688	−0.198344	−	0.980132i	$-0.563556\pi$
$947$	−12.2074	−0.396688	−0.198344	+	0.980132i	$0.563556\pi$
$948$	−2.50538	−0.0813708
$949$	−100.370	−3.25815
$950$	−5.18803	−0.168322
$951$	12.8706	0.417357
$952$	−0.0742621	−0.00240685
$953$	35.4518	1.14840	0.574198	−	0.818716i	$-0.305314\pi$
$953$	35.4518	1.14840	0.574198	+	0.818716i	$0.305314\pi$
$954$	0.936355	0.0303156
$955$	−44.0987	−1.42700
$956$	2.22214	0.0718690
$957$	−76.3818	−2.46907
$958$	−23.1465	−0.747829
$959$	3.54736	0.114550
$960$	6.23090	0.201101
$961$	19.1801	0.618713
$962$	−6.42789	−0.207243
$963$	4.07793	0.131409
$964$	18.6114	0.599432
$965$	40.7904	1.31309
$966$	13.2424	0.426067
$967$	47.7817	1.53656	0.768278	−	0.640116i	$-0.221114\pi$
$967$	47.7817	1.53656	0.768278	+	0.640116i	$0.221114\pi$
$968$	−29.7359	−0.955749
$969$	0.131272	0.00421706
$970$	50.7008	1.62791
$971$	25.4994	0.818314	0.409157	−	0.912464i	$-0.365823\pi$
$971$	25.4994	0.818314	0.409157	+	0.912464i	$0.365823\pi$
$972$	3.40990	0.109372
$973$	5.62374	0.180289
$974$	−20.6488	−0.661630
$975$	−84.8304	−2.71675
$976$	9.38872	0.300526
$977$	−54.5273	−1.74448	−0.872242	−	0.489075i	$-0.837334\pi$
$977$	−54.5273	−1.74448	−0.872242	+	0.489075i	$0.837334\pi$
$978$	37.2271	1.19039
$979$	−0.245492	−0.00784597
$980$	21.6955	0.693037
$981$	−2.89673	−0.0924856
$982$	22.1120	0.705621
$983$	−42.5920	−1.35847	−0.679237	−	0.733919i	$-0.737689\pi$
$983$	−42.5920	−1.35847	−0.679237	+	0.733919i	$0.737689\pi$
$984$	−9.61695	−0.306577
$985$	47.2964	1.50699
$986$	0.605741	0.0192907
$987$	1.03159	0.0328359
$988$	5.43694	0.172972
$989$	−53.9087	−1.71420
$990$	7.18252	0.228276
$991$	−22.3116	−0.708752	−0.354376	−	0.935103i	$-0.615307\pi$
$991$	−22.3116	−0.708752	−0.354376	+	0.935103i	$0.615307\pi$
$992$	−7.08379	−0.224911
$993$	−1.86848	−0.0592944
$994$	−1.07161	−0.0339894
$995$	−28.0805	−0.890211
$996$	22.6675	0.718247
$997$	43.4345	1.37558	0.687792	−	0.725908i	$-0.258580\pi$
$997$	43.4345	1.37558	0.687792	+	0.725908i	$0.258580\pi$
$998$	−25.5158	−0.807689
$999$	4.48735	0.141973

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4034.2.a.c.1.11	✓	49

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4034.2.a.c.1.11	✓	49	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -1.82471 q^{3} +1.00000 q^{4} -3.41474 q^{5} +1.82471 q^{6} -0.804060 q^{7} -1.00000 q^{8} +0.329557 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -1.82471 q^{3} +1.00000 q^{4} -3.41474 q^{5} +1.82471 q^{6} -0.804060 q^{7} -1.00000 q^{8} +0.329557 q^{9} +3.41474 q^{10} +6.38247 q^{11} -1.82471 q^{12} +6.98000 q^{13} +0.804060 q^{14} +6.23090 q^{15} +1.00000 q^{16} -0.0923589 q^{17} -0.329557 q^{18} +0.778932 q^{19} -3.41474 q^{20} +1.46717 q^{21} -6.38247 q^{22} -9.02579 q^{23} +1.82471 q^{24} +6.66044 q^{25} -6.98000 q^{26} +4.87278 q^{27} -0.804060 q^{28} +6.55855 q^{29} -6.23090 q^{30} +7.08379 q^{31} -1.00000 q^{32} -11.6461 q^{33} +0.0923589 q^{34} +2.74565 q^{35} +0.329557 q^{36} +0.920901 q^{37} -0.778932 q^{38} -12.7365 q^{39} +3.41474 q^{40} -5.27041 q^{41} -1.46717 q^{42} +5.97274 q^{43} +6.38247 q^{44} -1.12535 q^{45} +9.02579 q^{46} +0.703113 q^{47} -1.82471 q^{48} -6.35349 q^{49} -6.66044 q^{50} +0.168528 q^{51} +6.98000 q^{52} -2.84125 q^{53} -4.87278 q^{54} -21.7945 q^{55} +0.804060 q^{56} -1.42132 q^{57} -6.55855 q^{58} +0.732250 q^{59} +6.23090 q^{60} +9.38872 q^{61} -7.08379 q^{62} -0.264984 q^{63} +1.00000 q^{64} -23.8349 q^{65} +11.6461 q^{66} -1.11408 q^{67} -0.0923589 q^{68} +16.4694 q^{69} -2.74565 q^{70} -1.33275 q^{71} -0.329557 q^{72} -14.3797 q^{73} -0.920901 q^{74} -12.1534 q^{75} +0.778932 q^{76} -5.13189 q^{77} +12.7365 q^{78} +1.37303 q^{79} -3.41474 q^{80} -9.88006 q^{81} +5.27041 q^{82} -12.4225 q^{83} +1.46717 q^{84} +0.315382 q^{85} -5.97274 q^{86} -11.9674 q^{87} -6.38247 q^{88} -0.0384635 q^{89} +1.12535 q^{90} -5.61234 q^{91} -9.02579 q^{92} -12.9258 q^{93} -0.703113 q^{94} -2.65985 q^{95} +1.82471 q^{96} +14.8476 q^{97} +6.35349 q^{98} +2.10339 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9}+O(q^{10}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9	\( 49 q - 49 q^{2} + 8 q^{3} + 49 q^{4} - 8 q^{5} - 8 q^{6} + 18 q^{7} - 49 q^{8} + 59 q^{9} + 8 q^{10} + q^{11} + 8 q^{12} + 9 q^{13} - 18 q^{14} + 15 q^{15} + 49 q^{16} - 27 q^{17} - 59 q^{18} + 27 q^{19} - 8 q^{20} + 13 q^{21} - q^{22} + 16 q^{23} - 8 q^{24} + 71 q^{25} - 9 q^{26} + 29 q^{27} + 18 q^{28} - 7 q^{29} - 15 q^{30} + 75 q^{31} - 49 q^{32} - 3 q^{33} + 27 q^{34} - 16 q^{35} + 59 q^{36} + 36 q^{37} - 27 q^{38} + 24 q^{39} + 8 q^{40} - 12 q^{41} - 13 q^{42} + 22 q^{43} + q^{44} + 5 q^{45} - 16 q^{46} + 26 q^{47} + 8 q^{48} + 107 q^{49} - 71 q^{50} + 35 q^{51} + 9 q^{52} - 10 q^{53} - 29 q^{54} + 76 q^{55} - 18 q^{56} - 10 q^{57} + 7 q^{58} + 9 q^{59} + 15 q^{60} + 87 q^{61} - 75 q^{62} + 68 q^{63} + 49 q^{64} - 6 q^{65} + 3 q^{66} + 46 q^{67} - 27 q^{68} + 70 q^{69} + 16 q^{70} + 40 q^{71} - 59 q^{72} + 6 q^{73} - 36 q^{74} + 69 q^{75} + 27 q^{76} - 12 q^{77} - 24 q^{78} + 76 q^{79} - 8 q^{80} + 77 q^{81} + 12 q^{82} - 32 q^{83} + 13 q^{84} + 19 q^{85} - 22 q^{86} + 36 q^{87} - q^{88} + 34 q^{89} - 5 q^{90} + 119 q^{91} + 16 q^{92} - 5 q^{93} - 26 q^{94} - 2 q^{95} - 8 q^{96} + 52 q^{97} - 107 q^{98} + 26 q^{99}+O(q^{100}) \) 49 * q - 49 * q^2 + 8 * q^3 + 49 * q^4 - 8 * q^5 - 8 * q^6 + 18 * q^7 - 49 * q^8 + 59 * q^9 + 8 * q^10 + q^11 + 8 * q^12 + 9 * q^13 - 18 * q^14 + 15 * q^15 + 49 * q^16 - 27 * q^17 - 59 * q^18 + 27 * q^19 - 8 * q^20 + 13 * q^21 - q^22 + 16 * q^23 - 8 * q^24 + 71 * q^25 - 9 * q^26 + 29 * q^27 + 18 * q^28 - 7 * q^29 - 15 * q^30 + 75 * q^31 - 49 * q^32 - 3 * q^33 + 27 * q^34 - 16 * q^35 + 59 * q^36 + 36 * q^37 - 27 * q^38 + 24 * q^39 + 8 * q^40 - 12 * q^41 - 13 * q^42 + 22 * q^43 + q^44 + 5 * q^45 - 16 * q^46 + 26 * q^47 + 8 * q^48 + 107 * q^49 - 71 * q^50 + 35 * q^51 + 9 * q^52 - 10 * q^53 - 29 * q^54 + 76 * q^55 - 18 * q^56 - 10 * q^57 + 7 * q^58 + 9 * q^59 + 15 * q^60 + 87 * q^61 - 75 * q^62 + 68 * q^63 + 49 * q^64 - 6 * q^65 + 3 * q^66 + 46 * q^67 - 27 * q^68 + 70 * q^69 + 16 * q^70 + 40 * q^71 - 59 * q^72 + 6 * q^73 - 36 * q^74 + 69 * q^75 + 27 * q^76 - 12 * q^77 - 24 * q^78 + 76 * q^79 - 8 * q^80 + 77 * q^81 + 12 * q^82 - 32 * q^83 + 13 * q^84 + 19 * q^85 - 22 * q^86 + 36 * q^87 - q^88 + 34 * q^89 - 5 * q^90 + 119 * q^91 + 16 * q^92 - 5 * q^93 - 26 * q^94 - 2 * q^95 - 8 * q^96 + 52 * q^97 - 107 * q^98 + 26 * q^99

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