LMFDB - Embedded newform 4029.2.a.j.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4029,2,Mod(1,4029)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4029, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("4029.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4029 = 3 \cdot 17 \cdot 79 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4029.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:	$32.1717269744$
Analytic rank:	$0$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4029.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.24074 q^{2} +1.00000 q^{3} -0.460556 q^{4} -3.76050 q^{5} +1.24074 q^{6} -4.20824 q^{7} -3.05292 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q+1.24074 q^{2} +1.00000 q^{3} -0.460556 q^{4} -3.76050 q^{5} +1.24074 q^{6} -4.20824 q^{7} -3.05292 q^{8} +1.00000 q^{9} -4.66581 q^{10} -4.74044 q^{11} -0.460556 q^{12} -2.41971 q^{13} -5.22135 q^{14} -3.76050 q^{15} -2.86678 q^{16} -1.00000 q^{17} +1.24074 q^{18} +2.51148 q^{19} +1.73192 q^{20} -4.20824 q^{21} -5.88166 q^{22} +1.32840 q^{23} -3.05292 q^{24} +9.14134 q^{25} -3.00224 q^{26} +1.00000 q^{27} +1.93813 q^{28} +2.31126 q^{29} -4.66581 q^{30} -3.84153 q^{31} +2.54890 q^{32} -4.74044 q^{33} -1.24074 q^{34} +15.8251 q^{35} -0.460556 q^{36} -4.08290 q^{37} +3.11611 q^{38} -2.41971 q^{39} +11.4805 q^{40} -3.53904 q^{41} -5.22135 q^{42} -0.802225 q^{43} +2.18323 q^{44} -3.76050 q^{45} +1.64820 q^{46} -2.93966 q^{47} -2.86678 q^{48} +10.7093 q^{49} +11.3421 q^{50} -1.00000 q^{51} +1.11441 q^{52} +4.31537 q^{53} +1.24074 q^{54} +17.8264 q^{55} +12.8474 q^{56} +2.51148 q^{57} +2.86768 q^{58} +8.38183 q^{59} +1.73192 q^{60} -6.40646 q^{61} -4.76635 q^{62} -4.20824 q^{63} +8.89609 q^{64} +9.09932 q^{65} -5.88166 q^{66} -3.80153 q^{67} +0.460556 q^{68} +1.32840 q^{69} +19.6349 q^{70} -13.5354 q^{71} -3.05292 q^{72} -13.6423 q^{73} -5.06583 q^{74} +9.14134 q^{75} -1.15668 q^{76} +19.9489 q^{77} -3.00224 q^{78} -1.00000 q^{79} +10.7805 q^{80} +1.00000 q^{81} -4.39103 q^{82} -0.0914253 q^{83} +1.93813 q^{84} +3.76050 q^{85} -0.995355 q^{86} +2.31126 q^{87} +14.4722 q^{88} +14.7714 q^{89} -4.66581 q^{90} +10.1827 q^{91} -0.611801 q^{92} -3.84153 q^{93} -3.64736 q^{94} -9.44443 q^{95} +2.54890 q^{96} -5.83272 q^{97} +13.2875 q^{98} -4.74044 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * 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 $

$2$	1.24074	0.877338	0.438669	−	0.898649i	$-0.355450\pi$
$2$	1.24074	0.877338	0.438669	+	0.898649i	$0.355450\pi$
$3$	1.00000	0.577350
$3$	1.00000	0.577350
$4$	−0.460556	−0.230278
$5$	−3.76050	−1.68175	−0.840873	−	0.541233i	$-0.817958\pi$
$5$	−3.76050	−1.68175	−0.840873	+	0.541233i	$0.817958\pi$
$6$	1.24074	0.506531
$7$	−4.20824	−1.59057	−0.795283	−	0.606238i	$-0.792678\pi$
$7$	−4.20824	−1.59057	−0.795283	+	0.606238i	$0.792678\pi$
$8$	−3.05292	−1.07937
$9$	1.00000	0.333333
$10$	−4.66581	−1.47546
$11$	−4.74044	−1.42930	−0.714648	−	0.699485i	$-0.753413\pi$
$11$	−4.74044	−1.42930	−0.714648	+	0.699485i	$0.753413\pi$
$12$	−0.460556	−0.132951
$13$	−2.41971	−0.671107	−0.335554	−	0.942021i	$-0.608923\pi$
$13$	−2.41971	−0.671107	−0.335554	+	0.942021i	$0.608923\pi$
$14$	−5.22135	−1.39546
$15$	−3.76050	−0.970956
$16$	−2.86678	−0.716694
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	1.24074	0.292446
$19$	2.51148	0.576174	0.288087	−	0.957604i	$-0.406981\pi$
$19$	2.51148	0.576174	0.288087	+	0.957604i	$0.406981\pi$
$20$	1.73192	0.387269
$21$	−4.20824	−0.918314
$22$	−5.88166	−1.25398
$23$	1.32840	0.276990	0.138495	−	0.990363i	$-0.455774\pi$
$23$	1.32840	0.276990	0.138495	+	0.990363i	$0.455774\pi$
$24$	−3.05292	−0.623174
$25$	9.14134	1.82827
$26$	−3.00224	−0.588788
$27$	1.00000	0.192450
$28$	1.93813	0.366272
$29$	2.31126	0.429190	0.214595	−	0.976703i	$-0.431157\pi$
$29$	2.31126	0.429190	0.214595	+	0.976703i	$0.431157\pi$
$30$	−4.66581	−0.851857
$31$	−3.84153	−0.689959	−0.344979	−	0.938610i	$-0.612114\pi$
$31$	−3.84153	−0.689959	−0.344979	+	0.938610i	$0.612114\pi$
$32$	2.54890	0.450586
$33$	−4.74044	−0.825204
$34$	−1.24074	−0.212786
$35$	15.8251	2.67493
$36$	−0.460556	−0.0767593
$37$	−4.08290	−0.671225	−0.335612	−	0.942000i	$-0.608943\pi$
$37$	−4.08290	−0.671225	−0.335612	+	0.942000i	$0.608943\pi$
$38$	3.11611	0.505499
$39$	−2.41971	−0.387464
$40$	11.4805	1.81523
$41$	−3.53904	−0.552704	−0.276352	−	0.961056i	$-0.589126\pi$
$41$	−3.53904	−0.552704	−0.276352	+	0.961056i	$0.589126\pi$
$42$	−5.22135	−0.805672
$43$	−0.802225	−0.122338	−0.0611691	−	0.998127i	$-0.519483\pi$
$43$	−0.802225	−0.122338	−0.0611691	+	0.998127i	$0.519483\pi$
$44$	2.18323	0.329135
$45$	−3.76050	−0.560582
$46$	1.64820	0.243014
$47$	−2.93966	−0.428793	−0.214396	−	0.976747i	$-0.568778\pi$
$47$	−2.93966	−0.428793	−0.214396	+	0.976747i	$0.568778\pi$
$48$	−2.86678	−0.413784
$49$	10.7093	1.52990
$50$	11.3421	1.60401
$51$	−1.00000	−0.140028
$52$	1.11441	0.154541
$53$	4.31537	0.592761	0.296381	−	0.955070i	$-0.404220\pi$
$53$	4.31537	0.592761	0.296381	+	0.955070i	$0.404220\pi$
$54$	1.24074	0.168844
$55$	17.8264	2.40371
$56$	12.8474	1.71681
$57$	2.51148	0.332654
$58$	2.86768	0.376545
$59$	8.38183	1.09122	0.545611	−	0.838039i	$-0.316298\pi$
$59$	8.38183	1.09122	0.545611	+	0.838039i	$0.316298\pi$
$60$	1.73192	0.223590
$61$	−6.40646	−0.820263	−0.410132	−	0.912026i	$-0.634517\pi$
$61$	−6.40646	−0.820263	−0.410132	+	0.912026i	$0.634517\pi$
$62$	−4.76635	−0.605327
$63$	−4.20824	−0.530189
$64$	8.89609	1.11201
$65$	9.09932	1.12863
$66$	−5.88166	−0.723983
$67$	−3.80153	−0.464431	−0.232216	−	0.972664i	$-0.574598\pi$
$67$	−3.80153	−0.464431	−0.232216	+	0.972664i	$0.574598\pi$
$68$	0.460556	0.0558506
$69$	1.32840	0.159920
$70$	19.6349	2.34682
$71$	−13.5354	−1.60635	−0.803177	−	0.595741i	$-0.796859\pi$
$71$	−13.5354	−1.60635	−0.803177	+	0.595741i	$0.796859\pi$
$72$	−3.05292	−0.359790
$73$	−13.6423	−1.59672	−0.798358	−	0.602183i	$-0.794298\pi$
$73$	−13.6423	−1.59672	−0.798358	+	0.602183i	$0.794298\pi$
$74$	−5.06583	−0.588891
$75$	9.14134	1.05555
$76$	−1.15668	−0.132680
$77$	19.9489	2.27339
$78$	−3.00224	−0.339937
$79$	−1.00000	−0.112509
$79$	−1.00000	−0.112509
$80$	10.7805	1.20530
$81$	1.00000	0.111111
$82$	−4.39103	−0.484909
$83$	−0.0914253	−0.0100352	−0.00501761	−	0.999987i	$-0.501597\pi$
$83$	−0.0914253	−0.0100352	−0.00501761	+	0.999987i	$0.501597\pi$
$84$	1.93813	0.211467
$85$	3.76050	0.407883
$86$	−0.995355	−0.107332
$87$	2.31126	0.247793
$88$	14.4722	1.54274
$89$	14.7714	1.56577	0.782884	−	0.622168i	$-0.213748\pi$
$89$	14.7714	1.56577	0.782884	+	0.622168i	$0.213748\pi$
$90$	−4.66581	−0.491820
$91$	10.1827	1.06744
$92$	−0.611801	−0.0637846
$93$	−3.84153	−0.398348
$94$	−3.64736	−0.376196
$95$	−9.44443	−0.968978
$96$	2.54890	0.260146
$97$	−5.83272	−0.592223	−0.296111	−	0.955153i	$-0.595690\pi$
$97$	−5.83272	−0.592223	−0.296111	+	0.955153i	$0.595690\pi$
$98$	13.2875	1.34224
$99$	−4.74044	−0.476432
$100$	−4.21010	−0.421010
$101$	−3.02549	−0.301048	−0.150524	−	0.988606i	$-0.548096\pi$
$101$	−3.02549	−0.301048	−0.150524	+	0.988606i	$0.548096\pi$
$102$	−1.24074	−0.122852
$103$	10.6453	1.04892	0.524458	−	0.851436i	$-0.324268\pi$
$103$	10.6453	1.04892	0.524458	+	0.851436i	$0.324268\pi$
$104$	7.38718	0.724373
$105$	15.8251	1.54437
$106$	5.35426	0.520052
$107$	9.81953	0.949290	0.474645	−	0.880177i	$-0.342576\pi$
$107$	9.81953	0.949290	0.474645	+	0.880177i	$0.342576\pi$
$108$	−0.460556	−0.0443170
$109$	2.73349	0.261821	0.130911	−	0.991394i	$-0.458210\pi$
$109$	2.73349	0.261821	0.130911	+	0.991394i	$0.458210\pi$
$110$	22.1180	2.10887
$111$	−4.08290	−0.387532
$112$	12.0641	1.13995
$113$	14.0751	1.32407	0.662035	−	0.749473i	$-0.269693\pi$
$113$	14.0751	1.32407	0.662035	+	0.749473i	$0.269693\pi$
$114$	3.11611	0.291850
$115$	−4.99543	−0.465826
$116$	−1.06446	−0.0988330
$117$	−2.41971	−0.223702
$118$	10.3997	0.957370
$119$	4.20824	0.385769
$120$	11.4805	1.04802
$121$	11.4717	1.04288
$122$	−7.94877	−0.719648
$123$	−3.53904	−0.319104
$124$	1.76924	0.158882
$125$	−15.5735	−1.39294
$126$	−5.22135	−0.465155
$127$	−16.2568	−1.44256	−0.721279	−	0.692645i	$-0.756445\pi$
$127$	−16.2568	−1.44256	−0.721279	+	0.692645i	$0.756445\pi$
$128$	5.93996	0.525023
$129$	−0.802225	−0.0706319
$130$	11.2899	0.990192
$131$	12.9852	1.13452	0.567262	−	0.823537i	$-0.308003\pi$
$131$	12.9852	1.13452	0.567262	+	0.823537i	$0.308003\pi$
$132$	2.18323	0.190026
$133$	−10.5689	−0.916443
$134$	−4.71673	−0.407463
$135$	−3.76050	−0.323652
$136$	3.05292	0.261786
$137$	−4.87532	−0.416527	−0.208263	−	0.978073i	$-0.566781\pi$
$137$	−4.87532	−0.416527	−0.208263	+	0.978073i	$0.566781\pi$
$138$	1.64820	0.140304
$139$	9.37460	0.795143	0.397571	−	0.917571i	$-0.369853\pi$
$139$	9.37460	0.795143	0.397571	+	0.917571i	$0.369853\pi$
$140$	−7.28833	−0.615977
$141$	−2.93966	−0.247564
$142$	−16.7939	−1.40932
$143$	11.4705	0.959210
$144$	−2.86678	−0.238898
$145$	−8.69149	−0.721789
$146$	−16.9267	−1.40086
$147$	10.7093	0.883289
$148$	1.88040	0.154568
$149$	−18.9847	−1.55529	−0.777645	−	0.628703i	$-0.783586\pi$
$149$	−18.9847	−1.55529	−0.777645	+	0.628703i	$0.783586\pi$
$150$	11.3421	0.926075
$151$	0.289962	0.0235968	0.0117984	−	0.999930i	$-0.496244\pi$
$151$	0.289962	0.0235968	0.0117984	+	0.999930i	$0.496244\pi$
$152$	−7.66736	−0.621905
$153$	−1.00000	−0.0808452
$154$	24.7515	1.99453
$155$	14.4461	1.16033
$156$	1.11441	0.0892243
$157$	−13.4571	−1.07399	−0.536997	−	0.843584i	$-0.680442\pi$
$157$	−13.4571	−1.07399	−0.536997	+	0.843584i	$0.680442\pi$
$158$	−1.24074	−0.0987083
$159$	4.31537	0.342231
$160$	−9.58514	−0.757772
$161$	−5.59022	−0.440571
$162$	1.24074	0.0974820
$163$	−16.3732	−1.28245	−0.641223	−	0.767355i	$-0.721573\pi$
$163$	−16.3732	−1.28245	−0.641223	+	0.767355i	$0.721573\pi$
$164$	1.62992	0.127276
$165$	17.8264	1.38778
$166$	−0.113435	−0.00880429
$167$	−16.9644	−1.31274	−0.656371	−	0.754438i	$-0.727909\pi$
$167$	−16.9644	−1.31274	−0.656371	+	0.754438i	$0.727909\pi$
$168$	12.8474	0.991200
$169$	−7.14500	−0.549615
$170$	4.66581	0.357851
$171$	2.51148	0.192058
$172$	0.369469	0.0281718
$173$	−8.64112	−0.656972	−0.328486	−	0.944509i	$-0.606538\pi$
$173$	−8.64112	−0.656972	−0.328486	+	0.944509i	$0.606538\pi$
$174$	2.86768	0.217398
$175$	−38.4690	−2.90798
$176$	13.5898	1.02437
$177$	8.38183	0.630017
$178$	18.3276	1.37371
$179$	−14.9731	−1.11914	−0.559572	−	0.828782i	$-0.689034\pi$
$179$	−14.9731	−1.11914	−0.559572	+	0.828782i	$0.689034\pi$
$180$	1.73192	0.129090
$181$	13.1478	0.977272	0.488636	−	0.872488i	$-0.337495\pi$
$181$	13.1478	0.977272	0.488636	+	0.872488i	$0.337495\pi$
$182$	12.6342	0.936506
$183$	−6.40646	−0.473579
$184$	−4.05549	−0.298974
$185$	15.3537	1.12883
$186$	−4.76635	−0.349486
$187$	4.74044	0.346655
$188$	1.35387	0.0987415
$189$	−4.20824	−0.306105
$190$	−11.7181	−0.850121
$191$	1.51173	0.109385	0.0546926	−	0.998503i	$-0.482582\pi$
$191$	1.51173	0.109385	0.0546926	+	0.998503i	$0.482582\pi$
$192$	8.89609	0.642020
$193$	26.3888	1.89951	0.949754	−	0.312999i	$-0.101334\pi$
$193$	26.3888	1.89951	0.949754	+	0.312999i	$0.101334\pi$
$194$	−7.23691	−0.519580
$195$	9.09932	0.651616
$196$	−4.93223	−0.352302
$197$	−2.21772	−0.158006	−0.0790031	−	0.996874i	$-0.525174\pi$
$197$	−2.21772	−0.158006	−0.0790031	+	0.996874i	$0.525174\pi$
$198$	−5.88166	−0.417992
$199$	10.4208	0.738712	0.369356	−	0.929288i	$-0.379578\pi$
$199$	10.4208	0.738712	0.369356	+	0.929288i	$0.379578\pi$
$200$	−27.9078	−1.97338
$201$	−3.80153	−0.268140
$202$	−3.75386	−0.264121
$203$	−9.72635	−0.682656
$204$	0.460556	0.0322453
$205$	13.3085	0.929508
$206$	13.2081	0.920254
$207$	1.32840	0.0923300
$208$	6.93677	0.480979
$209$	−11.9055	−0.823523
$210$	19.6349	1.35494
$211$	−14.4327	−0.993589	−0.496794	−	0.867868i	$-0.665490\pi$
$211$	−14.4327	−0.993589	−0.496794	+	0.867868i	$0.665490\pi$
$212$	−1.98747	−0.136500
$213$	−13.5354	−0.927429
$214$	12.1835	0.832848
$215$	3.01676	0.205742
$216$	−3.05292	−0.207725
$217$	16.1661	1.09743
$218$	3.39156	0.229706
$219$	−13.6423	−0.921865
$220$	−8.21005	−0.553521
$221$	2.41971	0.162767
$222$	−5.06583	−0.339996
$223$	−5.33411	−0.357198	−0.178599	−	0.983922i	$-0.557157\pi$
$223$	−5.33411	−0.357198	−0.178599	+	0.983922i	$0.557157\pi$
$224$	−10.7264	−0.716688
$225$	9.14134	0.609423
$226$	17.4635	1.16166
$227$	22.8295	1.51525	0.757624	−	0.652692i	$-0.226360\pi$
$227$	22.8295	1.51525	0.757624	+	0.652692i	$0.226360\pi$
$228$	−1.15668	−0.0766029
$229$	−9.29747	−0.614394	−0.307197	−	0.951646i	$-0.599391\pi$
$229$	−9.29747	−0.614394	−0.307197	+	0.951646i	$0.599391\pi$
$230$	−6.19805	−0.408687
$231$	19.9489	1.31254
$232$	−7.05609	−0.463255
$233$	−6.62285	−0.433877	−0.216939	−	0.976185i	$-0.569607\pi$
$233$	−6.62285	−0.433877	−0.216939	+	0.976185i	$0.569607\pi$
$234$	−3.00224	−0.196263
$235$	11.0546	0.721120
$236$	−3.86030	−0.251284
$237$	−1.00000	−0.0649570
$238$	5.22135	0.338450
$239$	23.1751	1.49907	0.749537	−	0.661963i	$-0.230276\pi$
$239$	23.1751	1.49907	0.749537	+	0.661963i	$0.230276\pi$
$240$	10.7805	0.695879
$241$	−16.2794	−1.04865	−0.524324	−	0.851519i	$-0.675682\pi$
$241$	−16.2794	−1.04865	−0.524324	+	0.851519i	$0.675682\pi$
$242$	14.2335	0.914962
$243$	1.00000	0.0641500
$244$	2.95053	0.188888
$245$	−40.2723	−2.57291
$246$	−4.39103	−0.279962
$247$	−6.07707	−0.386675
$248$	11.7279	0.744720
$249$	−0.0914253	−0.00579384
$250$	−19.3227	−1.22208
$251$	9.61100	0.606641	0.303320	−	0.952889i	$-0.401905\pi$
$251$	9.61100	0.606641	0.303320	+	0.952889i	$0.401905\pi$
$252$	1.93813	0.122091
$253$	−6.29718	−0.395900
$254$	−20.1705	−1.26561
$255$	3.76050	0.235491
$256$	−10.4222	−0.651388
$257$	6.32461	0.394518	0.197259	−	0.980351i	$-0.436796\pi$
$257$	6.32461	0.394518	0.197259	+	0.980351i	$0.436796\pi$
$258$	−0.995355	−0.0619681
$259$	17.1818	1.06763
$260$	−4.19074	−0.259899
$261$	2.31126	0.143063
$262$	16.1113	0.995361
$263$	14.7986	0.912519	0.456260	−	0.889847i	$-0.349189\pi$
$263$	14.7986	0.912519	0.456260	+	0.889847i	$0.349189\pi$
$264$	14.4722	0.890700
$265$	−16.2279	−0.996874
$266$	−13.1133	−0.804031
$267$	14.7714	0.903997
$268$	1.75082	0.106948
$269$	31.6988	1.93271	0.966354	−	0.257215i	$-0.0828050\pi$
$269$	31.6988	1.93271	0.966354	+	0.257215i	$0.0828050\pi$
$270$	−4.66581	−0.283952
$271$	24.4889	1.48759	0.743796	−	0.668407i	$-0.233023\pi$
$271$	24.4889	1.48759	0.743796	+	0.668407i	$0.233023\pi$
$272$	2.86678	0.173824
$273$	10.1827	0.616287
$274$	−6.04902	−0.365435
$275$	−43.3339	−2.61313
$276$	−0.611801	−0.0368261
$277$	−24.1538	−1.45126	−0.725631	−	0.688085i	$-0.758452\pi$
$277$	−24.1538	−1.45126	−0.725631	+	0.688085i	$0.758452\pi$
$278$	11.6315	0.697609
$279$	−3.84153	−0.229986
$280$	−48.3127	−2.88724
$281$	−3.54768	−0.211637	−0.105818	−	0.994385i	$-0.533746\pi$
$281$	−3.54768	−0.211637	−0.105818	+	0.994385i	$0.533746\pi$
$282$	−3.64736	−0.217197
$283$	−10.4617	−0.621882	−0.310941	−	0.950429i	$-0.600644\pi$
$283$	−10.4617	−0.621882	−0.310941	+	0.950429i	$0.600644\pi$
$284$	6.23379	0.369908
$285$	−9.44443	−0.559440
$286$	14.2319	0.841552
$287$	14.8931	0.879113
$288$	2.54890	0.150195
$289$	1.00000	0.0588235
$290$	−10.7839	−0.633253
$291$	−5.83272	−0.341920
$292$	6.28306	0.367688
$293$	−10.9532	−0.639890	−0.319945	−	0.947436i	$-0.603664\pi$
$293$	−10.9532	−0.639890	−0.319945	+	0.947436i	$0.603664\pi$
$294$	13.2875	0.774943
$295$	−31.5199	−1.83516
$296$	12.4648	0.724499
$297$	−4.74044	−0.275068
$298$	−23.5552	−1.36452
$299$	−3.21434	−0.185890
$300$	−4.21010	−0.243070
$301$	3.37596	0.194587
$302$	0.359768	0.0207023
$303$	−3.02549	−0.173810
$304$	−7.19987	−0.412941
$305$	24.0915	1.37947
$306$	−1.24074	−0.0709286
$307$	11.0880	0.632824	0.316412	−	0.948622i	$-0.397522\pi$
$307$	11.0880	0.632824	0.316412	+	0.948622i	$0.397522\pi$
$308$	−9.18758	−0.523511
$309$	10.6453	0.605592
$310$	17.9238	1.01801
$311$	−18.1067	−1.02674	−0.513368	−	0.858169i	$-0.671602\pi$
$311$	−18.1067	−1.02674	−0.513368	+	0.858169i	$0.671602\pi$
$312$	7.38718	0.418217
$313$	−4.62019	−0.261148	−0.130574	−	0.991439i	$-0.541682\pi$
$313$	−4.62019	−0.261148	−0.130574	+	0.991439i	$0.541682\pi$
$314$	−16.6968	−0.942257
$315$	15.8251	0.891643
$316$	0.460556	0.0259083
$317$	1.84505	0.103628	0.0518141	−	0.998657i	$-0.483500\pi$
$317$	1.84505	0.103628	0.0518141	+	0.998657i	$0.483500\pi$
$318$	5.35426	0.300252
$319$	−10.9564	−0.613440
$320$	−33.4537	−1.87012
$321$	9.81953	0.548073
$322$	−6.93603	−0.386530
$323$	−2.51148	−0.139743
$324$	−0.460556	−0.0255864
$325$	−22.1194	−1.22696
$326$	−20.3149	−1.12514
$327$	2.73349	0.151162
$328$	10.8044	0.596572
$329$	12.3708	0.682023
$330$	22.1180	1.21755
$331$	−28.5265	−1.56796	−0.783978	−	0.620788i	$-0.786813\pi$
$331$	−28.5265	−1.56796	−0.783978	+	0.620788i	$0.786813\pi$
$332$	0.0421064	0.00231089
$333$	−4.08290	−0.223742
$334$	−21.0484	−1.15172
$335$	14.2957	0.781055
$336$	12.0641	0.658150
$337$	31.7599	1.73007	0.865036	−	0.501710i	$-0.167295\pi$
$337$	31.7599	1.73007	0.865036	+	0.501710i	$0.167295\pi$
$338$	−8.86511	−0.482198
$339$	14.0751	0.764452
$340$	−1.73192	−0.0939264
$341$	18.2105	0.986154
$342$	3.11611	0.168500
$343$	−15.6097	−0.842844
$344$	2.44913	0.132048
$345$	−4.99543	−0.268945
$346$	−10.7214	−0.576387
$347$	13.9952	0.751302	0.375651	−	0.926761i	$-0.377419\pi$
$347$	13.9952	0.751302	0.375651	+	0.926761i	$0.377419\pi$
$348$	−1.06446	−0.0570613
$349$	7.66884	0.410503	0.205252	−	0.978709i	$-0.434199\pi$
$349$	7.66884	0.410503	0.205252	+	0.978709i	$0.434199\pi$
$350$	−47.7301	−2.55128
$351$	−2.41971	−0.129155
$352$	−12.0829	−0.644021
$353$	−6.47234	−0.344488	−0.172244	−	0.985054i	$-0.555102\pi$
$353$	−6.47234	−0.344488	−0.172244	+	0.985054i	$0.555102\pi$
$354$	10.3997	0.552738
$355$	50.8997	2.70148
$356$	−6.80306	−0.360562
$357$	4.20824	0.222724
$358$	−18.5778	−0.981867
$359$	10.0122	0.528422	0.264211	−	0.964465i	$-0.414888\pi$
$359$	10.0122	0.528422	0.264211	+	0.964465i	$0.414888\pi$
$360$	11.4805	0.605075
$361$	−12.6924	−0.668023
$362$	16.3131	0.857398
$363$	11.4717	0.602109
$364$	−4.68972	−0.245808
$365$	51.3020	2.68527
$366$	−7.94877	−0.415489
$367$	30.2682	1.57999	0.789993	−	0.613116i	$-0.210084\pi$
$367$	30.2682	1.57999	0.789993	+	0.613116i	$0.210084\pi$
$368$	−3.80822	−0.198517
$369$	−3.53904	−0.184235
$370$	19.0500	0.990365
$371$	−18.1601	−0.942826
$372$	1.76924	0.0917306
$373$	28.1386	1.45696	0.728480	−	0.685067i	$-0.240227\pi$
$373$	28.1386	1.45696	0.728480	+	0.685067i	$0.240227\pi$
$374$	5.88166	0.304134
$375$	−15.5735	−0.804212
$376$	8.97453	0.462826
$377$	−5.59258	−0.288033
$378$	−5.22135	−0.268557
$379$	27.9896	1.43773	0.718864	−	0.695150i	$-0.244662\pi$
$379$	27.9896	1.43773	0.718864	+	0.695150i	$0.244662\pi$
$380$	4.34969	0.223134
$381$	−16.2568	−0.832861
$382$	1.87567	0.0959677
$383$	−0.919955	−0.0470075	−0.0235038	−	0.999724i	$-0.507482\pi$
$383$	−0.919955	−0.0470075	−0.0235038	+	0.999724i	$0.507482\pi$
$384$	5.93996	0.303122
$385$	−75.0178	−3.82326
$386$	32.7417	1.66651
$387$	−0.802225	−0.0407794
$388$	2.68629	0.136376
$389$	−24.7345	−1.25409	−0.627045	−	0.778983i	$-0.715736\pi$
$389$	−24.7345	−1.25409	−0.627045	+	0.778983i	$0.715736\pi$
$390$	11.2899	0.571687
$391$	−1.32840	−0.0671799
$392$	−32.6947	−1.65133
$393$	12.9852	0.655018
$394$	−2.75162	−0.138625
$395$	3.76050	0.189211
$396$	2.18323	0.109712
$397$	−36.5377	−1.83377	−0.916887	−	0.399148i	$-0.869306\pi$
$397$	−36.5377	−1.83377	−0.916887	+	0.399148i	$0.869306\pi$
$398$	12.9296	0.648100
$399$	−10.5689	−0.529109
$400$	−26.2062	−1.31031
$401$	14.4616	0.722179	0.361090	−	0.932531i	$-0.382405\pi$
$401$	14.4616	0.722179	0.361090	+	0.932531i	$0.382405\pi$
$402$	−4.71673	−0.235249
$403$	9.29539	0.463036
$404$	1.39341	0.0693246
$405$	−3.76050	−0.186861
$406$	−12.0679	−0.598920
$407$	19.3547	0.959378
$408$	3.05292	0.151142
$409$	5.63398	0.278582	0.139291	−	0.990251i	$-0.455518\pi$
$409$	5.63398	0.278582	0.139291	+	0.990251i	$0.455518\pi$
$410$	16.5125	0.815493
$411$	−4.87532	−0.240482
$412$	−4.90277	−0.241542
$413$	−35.2728	−1.73566
$414$	1.64820	0.0810046
$415$	0.343805	0.0168767
$416$	−6.16761	−0.302392
$417$	9.37460	0.459076
$418$	−14.7717	−0.722508
$419$	−28.8348	−1.40867	−0.704336	−	0.709867i	$-0.748755\pi$
$419$	−28.8348	−1.40867	−0.704336	+	0.709867i	$0.748755\pi$
$420$	−7.28833	−0.355634
$421$	−3.21149	−0.156518	−0.0782591	−	0.996933i	$-0.524936\pi$
$421$	−3.21149	−0.156518	−0.0782591	+	0.996933i	$0.524936\pi$
$422$	−17.9073	−0.871713
$423$	−2.93966	−0.142931
$424$	−13.1745	−0.639809
$425$	−9.14134	−0.443420
$426$	−16.7939	−0.813669
$427$	26.9599	1.30468
$428$	−4.52244	−0.218600
$429$	11.4705	0.553800
$430$	3.74303	0.180505
$431$	12.7046	0.611958	0.305979	−	0.952038i	$-0.401016\pi$
$431$	12.7046	0.611958	0.305979	+	0.952038i	$0.401016\pi$
$432$	−2.86678	−0.137928
$433$	−15.5912	−0.749265	−0.374632	−	0.927173i	$-0.622231\pi$
$433$	−15.5912	−0.749265	−0.374632	+	0.927173i	$0.622231\pi$
$434$	20.0580	0.962813
$435$	−8.69149	−0.416725
$436$	−1.25892	−0.0602916
$437$	3.33625	0.159594
$438$	−16.9267	−0.808787
$439$	−18.1791	−0.867642	−0.433821	−	0.900999i	$-0.642835\pi$
$439$	−18.1791	−0.867642	−0.433821	+	0.900999i	$0.642835\pi$
$440$	−54.4225	−2.59449
$441$	10.7093	0.509967
$442$	3.00224	0.142802
$443$	13.7103	0.651394	0.325697	−	0.945474i	$-0.394401\pi$
$443$	13.7103	0.651394	0.325697	+	0.945474i	$0.394401\pi$
$444$	1.88040	0.0892399
$445$	−55.5479	−2.63322
$446$	−6.61826	−0.313384
$447$	−18.9847	−0.897947
$448$	−37.4369	−1.76873
$449$	−21.2161	−1.00125	−0.500625	−	0.865665i	$-0.666896\pi$
$449$	−21.2161	−1.00125	−0.500625	+	0.865665i	$0.666896\pi$
$450$	11.3421	0.534670
$451$	16.7766	0.789978
$452$	−6.48235	−0.304904
$453$	0.289962	0.0136236
$454$	28.3256	1.32938
$455$	−38.2921	−1.79516
$456$	−7.66736	−0.359057
$457$	−24.2236	−1.13313	−0.566567	−	0.824016i	$-0.691729\pi$
$457$	−24.2236	−1.13313	−0.566567	+	0.824016i	$0.691729\pi$
$458$	−11.5358	−0.539031
$459$	−1.00000	−0.0466760
$460$	2.30067	0.107269
$461$	7.42222	0.345687	0.172844	−	0.984949i	$-0.444704\pi$
$461$	7.42222	0.345687	0.172844	+	0.984949i	$0.444704\pi$
$462$	24.7515	1.15154
$463$	−16.1407	−0.750124	−0.375062	−	0.927000i	$-0.622379\pi$
$463$	−16.1407	−0.750124	−0.375062	+	0.927000i	$0.622379\pi$
$464$	−6.62587	−0.307598
$465$	14.4461	0.669920
$466$	−8.21726	−0.380657
$467$	−26.5407	−1.22816	−0.614078	−	0.789245i	$-0.710472\pi$
$467$	−26.5407	−1.22816	−0.614078	+	0.789245i	$0.710472\pi$
$468$	1.11441	0.0515137
$469$	15.9978	0.738709
$470$	13.7159	0.632666
$471$	−13.4571	−0.620071
$472$	−25.5891	−1.17783
$473$	3.80289	0.174857
$474$	−1.24074	−0.0569892
$475$	22.9583	1.05340
$476$	−1.93813	−0.0888340
$477$	4.31537	0.197587
$478$	28.7544	1.31519
$479$	21.2275	0.969909	0.484955	−	0.874539i	$-0.338836\pi$
$479$	21.2275	0.969909	0.484955	+	0.874539i	$0.338836\pi$
$480$	−9.58514	−0.437500
$481$	9.87944	0.450464
$482$	−20.1986	−0.920020
$483$	−5.59022	−0.254364
$484$	−5.28337	−0.240153
$485$	21.9339	0.995968
$486$	1.24074	0.0562813
$487$	6.72318	0.304656	0.152328	−	0.988330i	$-0.451323\pi$
$487$	6.72318	0.304656	0.152328	+	0.988330i	$0.451323\pi$
$488$	19.5584	0.885367
$489$	−16.3732	−0.740420
$490$	−49.9676	−2.25731
$491$	−5.79055	−0.261324	−0.130662	−	0.991427i	$-0.541710\pi$
$491$	−5.79055	−0.261324	−0.130662	+	0.991427i	$0.541710\pi$
$492$	1.62992	0.0734826
$493$	−2.31126	−0.104094
$494$	−7.54008	−0.339244
$495$	17.8264	0.801237
$496$	11.0128	0.494489
$497$	56.9602	2.55501
$498$	−0.113435	−0.00508316
$499$	13.2182	0.591729	0.295864	−	0.955230i	$-0.404392\pi$
$499$	13.2182	0.591729	0.295864	+	0.955230i	$0.404392\pi$
$500$	7.17246	0.320762
$501$	−16.9644	−0.757912
$502$	11.9248	0.532229
$503$	16.3115	0.727295	0.363648	−	0.931537i	$-0.381531\pi$
$503$	16.3115	0.727295	0.363648	+	0.931537i	$0.381531\pi$
$504$	12.8474	0.572270
$505$	11.3774	0.506286
$506$	−7.81318	−0.347338
$507$	−7.14500	−0.317320
$508$	7.48716	0.332189
$509$	27.5761	1.22229	0.611145	−	0.791519i	$-0.290709\pi$
$509$	27.5761	1.22229	0.611145	+	0.791519i	$0.290709\pi$
$510$	4.66581	0.206606
$511$	57.4103	2.53968
$512$	−24.8112	−1.09651
$513$	2.51148	0.110885
$514$	7.84722	0.346126
$515$	−40.0317	−1.76401
$516$	0.369469	0.0162650
$517$	13.9352	0.612871
$518$	21.3183	0.936670
$519$	−8.64112	−0.379303
$520$	−27.7795	−1.21821
$521$	−30.7571	−1.34749	−0.673747	−	0.738962i	$-0.735316\pi$
$521$	−30.7571	−1.34749	−0.673747	+	0.738962i	$0.735316\pi$
$522$	2.86768	0.125515
$523$	19.0353	0.832357	0.416179	−	0.909283i	$-0.363369\pi$
$523$	19.0353	0.832357	0.416179	+	0.909283i	$0.363369\pi$
$524$	−5.98041	−0.261256
$525$	−38.4690	−1.67892
$526$	18.3612	0.800588
$527$	3.84153	0.167340
$528$	13.5898	0.591419
$529$	−21.2354	−0.923277
$530$	−20.1347	−0.874595
$531$	8.38183	0.363741
$532$	4.86758	0.211037
$533$	8.56344	0.370924
$534$	18.3276	0.793111
$535$	−36.9263	−1.59646
$536$	11.6058	0.501293
$537$	−14.9731	−0.646138
$538$	39.3300	1.69564
$539$	−50.7668	−2.18668
$540$	1.73192	0.0745299
$541$	18.7217	0.804907	0.402454	−	0.915440i	$-0.368157\pi$
$541$	18.7217	0.804907	0.402454	+	0.915440i	$0.368157\pi$
$542$	30.3844	1.30512
$543$	13.1478	0.564228
$544$	−2.54890	−0.109283
$545$	−10.2793	−0.440316
$546$	12.6342	0.540692
$547$	15.4737	0.661609	0.330804	−	0.943699i	$-0.392680\pi$
$547$	15.4737	0.661609	0.330804	+	0.943699i	$0.392680\pi$
$548$	2.24536	0.0959169
$549$	−6.40646	−0.273421
$550$	−53.7663	−2.29260
$551$	5.80470	0.247288
$552$	−4.05549	−0.172613
$553$	4.20824	0.178953
$554$	−29.9687	−1.27325
$555$	15.3537	0.651730
$556$	−4.31752	−0.183104
$557$	43.5723	1.84622	0.923108	−	0.384540i	$-0.125640\pi$
$557$	43.5723	1.84622	0.923108	+	0.384540i	$0.125640\pi$
$558$	−4.76635	−0.201776
$559$	1.94115	0.0821020
$560$	−45.3670	−1.91711
$561$	4.74044	0.200141
$562$	−4.40176	−0.185677
$563$	−22.3513	−0.941993	−0.470997	−	0.882135i	$-0.656106\pi$
$563$	−22.3513	−0.941993	−0.470997	+	0.882135i	$0.656106\pi$
$564$	1.35387	0.0570084
$565$	−52.9292	−2.22675
$566$	−12.9803	−0.545601
$567$	−4.20824	−0.176730
$568$	41.3224	1.73385
$569$	−0.786821	−0.0329853	−0.0164926	−	0.999864i	$-0.505250\pi$
$569$	−0.786821	−0.0329853	−0.0164926	+	0.999864i	$0.505250\pi$
$570$	−11.7181	−0.490818
$571$	44.9626	1.88163	0.940814	−	0.338925i	$-0.110063\pi$
$571$	44.9626	1.88163	0.940814	+	0.338925i	$0.110063\pi$
$572$	−5.28280	−0.220885
$573$	1.51173	0.0631535
$574$	18.4785	0.771280
$575$	12.1433	0.506412
$576$	8.89609	0.370670
$577$	29.5066	1.22837	0.614187	−	0.789160i	$-0.289484\pi$
$577$	29.5066	1.22837	0.614187	+	0.789160i	$0.289484\pi$
$578$	1.24074	0.0516081
$579$	26.3888	1.09668
$580$	4.00291	0.166212
$581$	0.384740	0.0159617
$582$	−7.23691	−0.299980
$583$	−20.4567	−0.847231
$584$	41.6490	1.72345
$585$	9.09932	0.376211
$586$	−13.5901	−0.561400
$587$	36.8601	1.52138	0.760689	−	0.649117i	$-0.224861\pi$
$587$	36.8601	1.52138	0.760689	+	0.649117i	$0.224861\pi$
$588$	−4.93223	−0.203402
$589$	−9.64793	−0.397536
$590$	−39.1081	−1.61005
$591$	−2.21772	−0.0912249
$592$	11.7048	0.481063
$593$	27.8519	1.14374	0.571871	−	0.820343i	$-0.306218\pi$
$593$	27.8519	1.14374	0.571871	+	0.820343i	$0.306218\pi$
$594$	−5.88166	−0.241328
$595$	−15.8251	−0.648765
$596$	8.74353	0.358149
$597$	10.4208	0.426495
$598$	−3.98817	−0.163088
$599$	6.87737	0.281002	0.140501	−	0.990081i	$-0.455129\pi$
$599$	6.87737	0.281002	0.140501	+	0.990081i	$0.455129\pi$
$600$	−27.9078	−1.13933
$601$	−41.7942	−1.70482	−0.852411	−	0.522872i	$-0.824861\pi$
$601$	−41.7942	−1.70482	−0.852411	+	0.522872i	$0.824861\pi$
$602$	4.18870	0.170719
$603$	−3.80153	−0.154810
$604$	−0.133544	−0.00543381
$605$	−43.1394	−1.75387
$606$	−3.75386	−0.152490
$607$	−11.7603	−0.477337	−0.238669	−	0.971101i	$-0.576711\pi$
$607$	−11.7603	−0.477337	−0.238669	+	0.971101i	$0.576711\pi$
$608$	6.40153	0.259616
$609$	−9.72635	−0.394132
$610$	29.8913	1.21027
$611$	7.11312	0.287766
$612$	0.460556	0.0186169
$613$	−10.3534	−0.418172	−0.209086	−	0.977897i	$-0.567049\pi$
$613$	−10.3534	−0.418172	−0.209086	+	0.977897i	$0.567049\pi$
$614$	13.7573	0.555201
$615$	13.3085	0.536652
$616$	−60.9024	−2.45383
$617$	27.9124	1.12371	0.561856	−	0.827235i	$-0.310088\pi$
$617$	27.9124	1.12371	0.561856	+	0.827235i	$0.310088\pi$
$618$	13.2081	0.531309
$619$	0.618023	0.0248404	0.0124202	−	0.999923i	$-0.496046\pi$
$619$	0.618023	0.0248404	0.0124202	+	0.999923i	$0.496046\pi$
$620$	−6.65321	−0.267199
$621$	1.32840	0.0533067
$622$	−22.4657	−0.900794
$623$	−62.1618	−2.49046
$624$	6.93677	0.277693
$625$	12.8574	0.514296
$626$	−5.73247	−0.229115
$627$	−11.9055	−0.475461
$628$	6.19775	0.247317
$629$	4.08290	0.162796
$630$	19.6349	0.782272
$631$	31.1855	1.24147	0.620737	−	0.784019i	$-0.286833\pi$
$631$	31.1855	1.24147	0.620737	+	0.784019i	$0.286833\pi$
$632$	3.05292	0.121439
$633$	−14.4327	−0.573649
$634$	2.28923	0.0909170
$635$	61.1336	2.42601
$636$	−1.98747	−0.0788082
$637$	−25.9134	−1.02673
$638$	−13.5941	−0.538194
$639$	−13.5354	−0.535451
$640$	−22.3372	−0.882955
$641$	30.3329	1.19808	0.599039	−	0.800720i	$-0.295549\pi$
$641$	30.3329	1.19808	0.599039	+	0.800720i	$0.295549\pi$
$642$	12.1835	0.480845
$643$	27.1203	1.06952	0.534760	−	0.845004i	$-0.320402\pi$
$643$	27.1203	1.06952	0.534760	+	0.845004i	$0.320402\pi$
$644$	2.57461	0.101454
$645$	3.01676	0.118785
$646$	−3.11611	−0.122602
$647$	−14.3143	−0.562754	−0.281377	−	0.959597i	$-0.590791\pi$
$647$	−14.3143	−0.562754	−0.281377	+	0.959597i	$0.590791\pi$
$648$	−3.05292	−0.119930
$649$	−39.7335	−1.55968
$650$	−27.4445	−1.07646
$651$	16.1661	0.633599
$652$	7.54076	0.295319
$653$	−42.7346	−1.67233	−0.836167	−	0.548475i	$-0.815209\pi$
$653$	−42.7346	−1.67233	−0.836167	+	0.548475i	$0.815209\pi$
$654$	3.39156	0.132621
$655$	−48.8309	−1.90798
$656$	10.1456	0.396120
$657$	−13.6423	−0.532239
$658$	15.3490	0.598365
$659$	−1.48143	−0.0577085	−0.0288542	−	0.999584i	$-0.509186\pi$
$659$	−1.48143	−0.0577085	−0.0288542	+	0.999584i	$0.509186\pi$
$660$	−8.21005	−0.319576
$661$	40.8545	1.58905	0.794527	−	0.607229i	$-0.207719\pi$
$661$	40.8545	1.58905	0.794527	+	0.607229i	$0.207719\pi$
$662$	−35.3940	−1.37563
$663$	2.41971	0.0939738
$664$	0.279114	0.0108317
$665$	39.7445	1.54122
$666$	−5.06583	−0.196297
$667$	3.07027	0.118881
$668$	7.81303	0.302295
$669$	−5.33411	−0.206228
$670$	17.7372	0.685250
$671$	30.3694	1.17240
$672$	−10.7264	−0.413780
$673$	−32.1363	−1.23876	−0.619382	−	0.785090i	$-0.712617\pi$
$673$	−32.1363	−1.23876	−0.619382	+	0.785090i	$0.712617\pi$
$674$	39.4059	1.51786
$675$	9.14134	0.351850
$676$	3.29067	0.126564
$677$	23.9947	0.922190	0.461095	−	0.887351i	$-0.347457\pi$
$677$	23.9947	0.922190	0.461095	+	0.887351i	$0.347457\pi$
$678$	17.4635	0.670683
$679$	24.5455	0.941970
$680$	−11.4805	−0.440257
$681$	22.8295	0.874828
$682$	22.5946	0.865191
$683$	−35.3644	−1.35318	−0.676591	−	0.736359i	$-0.736543\pi$
$683$	−35.3644	−1.35318	−0.676591	+	0.736359i	$0.736543\pi$
$684$	−1.15668	−0.0442267
$685$	18.3336	0.700492
$686$	−19.3676	−0.739459
$687$	−9.29747	−0.354721
$688$	2.29980	0.0876790
$689$	−10.4419	−0.397806
$690$	−6.19805	−0.235956
$691$	−0.408907	−0.0155556	−0.00777779	−	0.999970i	$-0.502476\pi$
$691$	−0.408907	−0.0155556	−0.00777779	+	0.999970i	$0.502476\pi$
$692$	3.97972	0.151286
$693$	19.9489	0.757796
$694$	17.3645	0.659146
$695$	−35.2531	−1.33723
$696$	−7.05609	−0.267460
$697$	3.53904	0.134051
$698$	9.51506	0.360150
$699$	−6.62285	−0.250499
$700$	17.7171	0.669644
$701$	16.6331	0.628222	0.314111	−	0.949386i	$-0.398294\pi$
$701$	16.6331	0.628222	0.314111	+	0.949386i	$0.398294\pi$
$702$	−3.00224	−0.113312
$703$	−10.2541	−0.386742
$704$	−42.1713	−1.58939
$705$	11.0546	0.416339
$706$	−8.03051	−0.302232
$707$	12.7320	0.478837
$708$	−3.86030	−0.145079
$709$	−11.1262	−0.417854	−0.208927	−	0.977931i	$-0.566997\pi$
$709$	−11.1262	−0.417854	−0.208927	+	0.977931i	$0.566997\pi$
$710$	63.1535	2.37011
$711$	−1.00000	−0.0375029
$712$	−45.0960	−1.69004
$713$	−5.10307	−0.191112
$714$	5.22135	0.195404
$715$	−43.1347	−1.61315
$716$	6.89595	0.257714
$717$	23.1751	0.865490
$718$	12.4225	0.463605
$719$	3.65479	0.136301	0.0681503	−	0.997675i	$-0.478290\pi$
$719$	3.65479	0.136301	0.0681503	+	0.997675i	$0.478290\pi$
$720$	10.7805	0.401766
$721$	−44.7981	−1.66837
$722$	−15.7481	−0.586082
$723$	−16.2794	−0.605438
$724$	−6.05531	−0.225044
$725$	21.1280	0.784675
$726$	14.2335	0.528254
$727$	−52.9491	−1.96377	−0.981887	−	0.189467i	$-0.939324\pi$
$727$	−52.9491	−1.96377	−0.981887	+	0.189467i	$0.939324\pi$
$728$	−31.0871	−1.15216
$729$	1.00000	0.0370370
$730$	63.6526	2.35589
$731$	0.802225	0.0296714
$732$	2.95053	0.109055
$733$	18.9107	0.698483	0.349242	−	0.937033i	$-0.386439\pi$
$733$	18.9107	0.698483	0.349242	+	0.937033i	$0.386439\pi$
$734$	37.5550	1.38618
$735$	−40.2723	−1.48547
$736$	3.38595	0.124808
$737$	18.0209	0.663809
$738$	−4.39103	−0.161636
$739$	−35.3773	−1.30137	−0.650687	−	0.759346i	$-0.725519\pi$
$739$	−35.3773	−1.30137	−0.650687	+	0.759346i	$0.725519\pi$
$740$	−7.07125	−0.259944
$741$	−6.07707	−0.223247
$742$	−22.5321	−0.827178
$743$	−21.3290	−0.782484	−0.391242	−	0.920288i	$-0.627954\pi$
$743$	−21.3290	−0.782484	−0.391242	+	0.920288i	$0.627954\pi$
$744$	11.7279	0.429964
$745$	71.3921	2.61560
$746$	34.9127	1.27825
$747$	−0.0914253	−0.00334508
$748$	−2.18323	−0.0798269
$749$	−41.3230	−1.50991
$750$	−19.3227	−0.705566
$751$	34.8694	1.27240	0.636201	−	0.771523i	$-0.280505\pi$
$751$	34.8694	1.27240	0.636201	+	0.771523i	$0.280505\pi$
$752$	8.42734	0.307313
$753$	9.61100	0.350244
$754$	−6.93896	−0.252702
$755$	−1.09040	−0.0396837
$756$	1.93813	0.0704891
$757$	18.3441	0.666729	0.333365	−	0.942798i	$-0.391816\pi$
$757$	18.3441	0.666729	0.333365	+	0.942798i	$0.391816\pi$
$758$	34.7279	1.26137
$759$	−6.29718	−0.228573
$760$	28.8331	1.04589
$761$	13.8647	0.502594	0.251297	−	0.967910i	$-0.419143\pi$
$761$	13.8647	0.502594	0.251297	+	0.967910i	$0.419143\pi$
$762$	−20.1705	−0.730701
$763$	−11.5032	−0.416444
$764$	−0.696237	−0.0251890
$765$	3.76050	0.135961
$766$	−1.14143	−0.0412415
$767$	−20.2816	−0.732327
$768$	−10.4222	−0.376079
$769$	−26.2024	−0.944881	−0.472441	−	0.881362i	$-0.656627\pi$
$769$	−26.2024	−0.944881	−0.472441	+	0.881362i	$0.656627\pi$
$770$	−93.0779	−3.35429
$771$	6.32461	0.227775
$772$	−12.1535	−0.437414
$773$	32.6310	1.17365	0.586827	−	0.809712i	$-0.300377\pi$
$773$	32.6310	1.17365	0.586827	+	0.809712i	$0.300377\pi$
$774$	−0.995355	−0.0357773
$775$	−35.1167	−1.26143
$776$	17.8068	0.639228
$777$	17.1818	0.616395
$778$	−30.6892	−1.10026
$779$	−8.88823	−0.318454
$780$	−4.19074	−0.150053
$781$	64.1636	2.29595
$782$	−1.64820	−0.0589395
$783$	2.31126	0.0825977
$784$	−30.7012	−1.09647
$785$	50.6055	1.80619
$786$	16.1113	0.574672
$787$	−15.6643	−0.558372	−0.279186	−	0.960237i	$-0.590065\pi$
$787$	−15.6643	−0.558372	−0.279186	+	0.960237i	$0.590065\pi$
$788$	1.02138	0.0363853
$789$	14.7986	0.526843
$790$	4.66581	0.166002
$791$	−59.2313	−2.10602
$792$	14.4722	0.514246
$793$	15.5018	0.550485
$794$	−45.3339	−1.60884
$795$	−16.2279	−0.575545
$796$	−4.79936	−0.170109
$797$	32.1096	1.13738	0.568690	−	0.822552i	$-0.307450\pi$
$797$	32.1096	1.13738	0.568690	+	0.822552i	$0.307450\pi$
$798$	−13.1133	−0.464207
$799$	2.93966	0.103998
$800$	23.3004	0.823793
$801$	14.7714	0.521923
$802$	17.9432	0.633596
$803$	64.6707	2.28218
$804$	1.75082	0.0617466
$805$	21.0220	0.740928
$806$	11.5332	0.406239
$807$	31.6988	1.11585
$808$	9.23658	0.324942
$809$	53.6043	1.88463	0.942314	−	0.334731i	$-0.108645\pi$
$809$	53.6043	1.88463	0.942314	+	0.334731i	$0.108645\pi$
$810$	−4.66581	−0.163940
$811$	14.5310	0.510254	0.255127	−	0.966908i	$-0.417883\pi$
$811$	14.5310	0.510254	0.255127	+	0.966908i	$0.417883\pi$
$812$	4.47952	0.157200
$813$	24.4889	0.858862
$814$	24.0142	0.841699
$815$	61.5713	2.15675
$816$	2.86678	0.100357
$817$	−2.01477	−0.0704880
$818$	6.99032	0.244411
$819$	10.1827	0.355814
$820$	−6.12932	−0.214045
$821$	26.1915	0.914089	0.457044	−	0.889444i	$-0.348908\pi$
$821$	26.1915	0.914089	0.457044	+	0.889444i	$0.348908\pi$
$822$	−6.04902	−0.210984
$823$	1.83518	0.0639703	0.0319852	−	0.999488i	$-0.489817\pi$
$823$	1.83518	0.0639703	0.0319852	+	0.999488i	$0.489817\pi$
$824$	−32.4993	−1.13217
$825$	−43.3339	−1.50869
$826$	−43.7645	−1.52276
$827$	−12.8490	−0.446803	−0.223401	−	0.974727i	$-0.571716\pi$
$827$	−12.8490	−0.446803	−0.223401	+	0.974727i	$0.571716\pi$
$828$	−0.611801	−0.0212615
$829$	7.88581	0.273885	0.136943	−	0.990579i	$-0.456272\pi$
$829$	7.88581	0.273885	0.136943	+	0.990579i	$0.456272\pi$
$830$	0.426573	0.0148066
$831$	−24.1538	−0.837886
$832$	−21.5260	−0.746279
$833$	−10.7093	−0.371056
$834$	11.6315	0.402765
$835$	63.7944	2.20770
$836$	5.48316	0.189639
$837$	−3.84153	−0.132783
$838$	−35.7766	−1.23588
$839$	−29.7908	−1.02849	−0.514247	−	0.857642i	$-0.671929\pi$
$839$	−29.7908	−1.02849	−0.514247	+	0.857642i	$0.671929\pi$
$840$	−48.3127	−1.66695
$841$	−23.6581	−0.815796
$842$	−3.98463	−0.137319
$843$	−3.54768	−0.122188
$844$	6.64707	0.228801
$845$	26.8687	0.924313
$846$	−3.64736	−0.125399
$847$	−48.2758	−1.65878
$848$	−12.3712	−0.424829
$849$	−10.4617	−0.359044
$850$	−11.3421	−0.389029
$851$	−5.42371	−0.185922
$852$	6.23379	0.213566
$853$	−18.2496	−0.624856	−0.312428	−	0.949941i	$-0.601142\pi$
$853$	−18.2496	−0.624856	−0.312428	+	0.949941i	$0.601142\pi$
$854$	33.4504	1.14465
$855$	−9.44443	−0.322993
$856$	−29.9782	−1.02463
$857$	48.3068	1.65013	0.825064	−	0.565039i	$-0.191139\pi$
$857$	48.3068	1.65013	0.825064	+	0.565039i	$0.191139\pi$
$858$	14.2319	0.485870
$859$	33.3642	1.13837	0.569187	−	0.822208i	$-0.307258\pi$
$859$	33.3642	1.13837	0.569187	+	0.822208i	$0.307258\pi$
$860$	−1.38939	−0.0473777
$861$	14.8931	0.507556
$862$	15.7631	0.536894
$863$	−24.1573	−0.822324	−0.411162	−	0.911562i	$-0.634877\pi$
$863$	−24.1573	−0.822324	−0.411162	+	0.911562i	$0.634877\pi$
$864$	2.54890	0.0867154
$865$	32.4949	1.10486
$866$	−19.3447	−0.657359
$867$	1.00000	0.0339618
$868$	−7.44538	−0.252713
$869$	4.74044	0.160808
$870$	−10.7839	−0.365609
$871$	9.19862	0.311683
$872$	−8.34513	−0.282602
$873$	−5.83272	−0.197408
$874$	4.13943	0.140018
$875$	65.5371	2.21556
$876$	6.28306	0.212285
$877$	−50.0267	−1.68928	−0.844640	−	0.535334i	$-0.820186\pi$
$877$	−50.0267	−1.68928	−0.844640	+	0.535334i	$0.820186\pi$
$878$	−22.5556	−0.761215
$879$	−10.9532	−0.369441
$880$	−51.1043	−1.72273
$881$	8.03603	0.270741	0.135370	−	0.990795i	$-0.456778\pi$
$881$	8.03603	0.270741	0.135370	+	0.990795i	$0.456778\pi$
$882$	13.2875	0.447414
$883$	−7.30744	−0.245915	−0.122957	−	0.992412i	$-0.539238\pi$
$883$	−7.30744	−0.245915	−0.122957	+	0.992412i	$0.539238\pi$
$884$	−1.11441	−0.0374817
$885$	−31.5199	−1.05953
$886$	17.0109	0.571493
$887$	−8.72947	−0.293107	−0.146553	−	0.989203i	$-0.546818\pi$
$887$	−8.72947	−0.293107	−0.146553	+	0.989203i	$0.546818\pi$
$888$	12.4648	0.418290
$889$	68.4126	2.29448
$890$	−68.9207	−2.31023
$891$	−4.74044	−0.158811
$892$	2.45665	0.0822548
$893$	−7.38290	−0.247059
$894$	−23.5552	−0.787803
$895$	56.3064	1.88211
$896$	−24.9968	−0.835084
$897$	−3.21434	−0.107324
$898$	−26.3237	−0.878434
$899$	−8.87877	−0.296124
$900$	−4.21010	−0.140337
$901$	−4.31537	−0.143766
$902$	20.8154	0.693078
$903$	3.37596	0.112345
$904$	−42.9700	−1.42916
$905$	−49.4424	−1.64352
$906$	0.359768	0.0119525
$907$	−22.3240	−0.741256	−0.370628	−	0.928781i	$-0.620857\pi$
$907$	−22.3240	−0.741256	−0.370628	+	0.928781i	$0.620857\pi$
$908$	−10.5143	−0.348928
$909$	−3.02549	−0.100349
$910$	−47.5107	−1.57497
$911$	49.6127	1.64374	0.821871	−	0.569674i	$-0.192931\pi$
$911$	49.6127	1.64374	0.821871	+	0.569674i	$0.192931\pi$
$912$	−7.19987	−0.238411
$913$	0.433396	0.0143433
$914$	−30.0553	−0.994141
$915$	24.0915	0.796440
$916$	4.28200	0.141481
$917$	−54.6450	−1.80454
$918$	−1.24074	−0.0409506
$919$	−17.4277	−0.574886	−0.287443	−	0.957798i	$-0.592805\pi$
$919$	−17.4277	−0.574886	−0.287443	+	0.957798i	$0.592805\pi$
$920$	15.2506	0.502799
$921$	11.0880	0.365361
$922$	9.20907	0.303284
$923$	32.7517	1.07804
$924$	−9.18758	−0.302249
$925$	−37.3232	−1.22718
$926$	−20.0265	−0.658112
$927$	10.6453	0.349639
$928$	5.89118	0.193387
$929$	20.7056	0.679330	0.339665	−	0.940547i	$-0.389686\pi$
$929$	20.7056	0.679330	0.339665	+	0.940547i	$0.389686\pi$
$930$	17.9238	0.587746
$931$	26.8963	0.881490
$932$	3.05019	0.0999123
$933$	−18.1067	−0.592786
$934$	−32.9302	−1.07751
$935$	−17.8264	−0.582985
$936$	7.38718	0.241458
$937$	−39.4585	−1.28905	−0.644527	−	0.764581i	$-0.722946\pi$
$937$	−39.4585	−1.28905	−0.644527	+	0.764581i	$0.722946\pi$
$938$	19.8491	0.648097
$939$	−4.62019	−0.150774
$940$	−5.09124	−0.166058
$941$	−31.2805	−1.01972	−0.509858	−	0.860259i	$-0.670302\pi$
$941$	−31.2805	−1.01972	−0.509858	+	0.860259i	$0.670302\pi$
$942$	−16.6968	−0.544012
$943$	−4.70124	−0.153094
$944$	−24.0289	−0.782072
$945$	15.8251	0.514790
$946$	4.71842	0.153409
$947$	−9.09376	−0.295507	−0.147754	−	0.989024i	$-0.547204\pi$
$947$	−9.09376	−0.295507	−0.147754	+	0.989024i	$0.547204\pi$
$948$	0.460556	0.0149582
$949$	33.0106	1.07157
$950$	28.4854	0.924188
$951$	1.84505	0.0598298
$952$	−12.8474	−0.416387
$953$	16.2314	0.525786	0.262893	−	0.964825i	$-0.415323\pi$
$953$	16.2314	0.525786	0.262893	+	0.964825i	$0.415323\pi$
$954$	5.35426	0.173351
$955$	−5.68487	−0.183958
$956$	−10.6734	−0.345203
$957$	−10.9564	−0.354170
$958$	26.3379	0.850938
$959$	20.5165	0.662514
$960$	−33.4537	−1.07971
$961$	−16.2427	−0.523957
$962$	12.2579	0.395209
$963$	9.81953	0.316430
$964$	7.49757	0.241481
$965$	−99.2350	−3.19449
$966$	−6.93603	−0.223163
$967$	30.8501	0.992072	0.496036	−	0.868302i	$-0.334788\pi$
$967$	30.8501	0.992072	0.496036	+	0.868302i	$0.334788\pi$
$968$	−35.0222	−1.12566
$969$	−2.51148	−0.0806805
$970$	27.2144	0.873801
$971$	−8.11318	−0.260364	−0.130182	−	0.991490i	$-0.541556\pi$
$971$	−8.11318	−0.260364	−0.130182	+	0.991490i	$0.541556\pi$
$972$	−0.460556	−0.0147723
$973$	−39.4506	−1.26473
$974$	8.34174	0.267287
$975$	−22.1194	−0.708388
$976$	18.3659	0.587878
$977$	27.0071	0.864034	0.432017	−	0.901865i	$-0.357802\pi$
$977$	27.0071	0.864034	0.432017	+	0.901865i	$0.357802\pi$
$978$	−20.3149	−0.649599
$979$	−70.0230	−2.23794
$980$	18.5477	0.592483
$981$	2.73349	0.0872737
$982$	−7.18459	−0.229269
$983$	−46.2064	−1.47375	−0.736877	−	0.676027i	$-0.763700\pi$
$983$	−46.2064	−1.47375	−0.736877	+	0.676027i	$0.763700\pi$
$984$	10.8044	0.344431
$985$	8.33974	0.265726
$986$	−2.86768	−0.0913256
$987$	12.3708	0.393766
$988$	2.79883	0.0890426
$989$	−1.06567	−0.0338864
$990$	22.1180	0.702956
$991$	51.7921	1.64523	0.822616	−	0.568598i	$-0.192514\pi$
$991$	51.7921	1.64523	0.822616	+	0.568598i	$0.192514\pi$
$992$	−9.79167	−0.310886
$993$	−28.5265	−0.905260
$994$	70.6729	2.24161
$995$	−39.1874	−1.24232
$996$	0.0421064	0.00133419
$997$	−7.18921	−0.227685	−0.113842	−	0.993499i	$-0.536316\pi$
$997$	−7.18921	−0.227685	−0.113842	+	0.993499i	$0.536316\pi$
$998$	16.4004	0.519146
$999$	−4.08290	−0.129177

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4029.2.a.j.1.17	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4029.2.a.j.1.17	✓	25	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:	\( N \)	\(=\)	\( 4029 = 3 \cdot 17 \cdot 79 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4029.a (trivial)

\(f(q)\)	\(=\)	\(q+1.24074 q^{2} +1.00000 q^{3} -0.460556 q^{4} -3.76050 q^{5} +1.24074 q^{6} -4.20824 q^{7} -3.05292 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q+1.24074 q^{2} +1.00000 q^{3} -0.460556 q^{4} -3.76050 q^{5} +1.24074 q^{6} -4.20824 q^{7} -3.05292 q^{8} +1.00000 q^{9} -4.66581 q^{10} -4.74044 q^{11} -0.460556 q^{12} -2.41971 q^{13} -5.22135 q^{14} -3.76050 q^{15} -2.86678 q^{16} -1.00000 q^{17} +1.24074 q^{18} +2.51148 q^{19} +1.73192 q^{20} -4.20824 q^{21} -5.88166 q^{22} +1.32840 q^{23} -3.05292 q^{24} +9.14134 q^{25} -3.00224 q^{26} +1.00000 q^{27} +1.93813 q^{28} +2.31126 q^{29} -4.66581 q^{30} -3.84153 q^{31} +2.54890 q^{32} -4.74044 q^{33} -1.24074 q^{34} +15.8251 q^{35} -0.460556 q^{36} -4.08290 q^{37} +3.11611 q^{38} -2.41971 q^{39} +11.4805 q^{40} -3.53904 q^{41} -5.22135 q^{42} -0.802225 q^{43} +2.18323 q^{44} -3.76050 q^{45} +1.64820 q^{46} -2.93966 q^{47} -2.86678 q^{48} +10.7093 q^{49} +11.3421 q^{50} -1.00000 q^{51} +1.11441 q^{52} +4.31537 q^{53} +1.24074 q^{54} +17.8264 q^{55} +12.8474 q^{56} +2.51148 q^{57} +2.86768 q^{58} +8.38183 q^{59} +1.73192 q^{60} -6.40646 q^{61} -4.76635 q^{62} -4.20824 q^{63} +8.89609 q^{64} +9.09932 q^{65} -5.88166 q^{66} -3.80153 q^{67} +0.460556 q^{68} +1.32840 q^{69} +19.6349 q^{70} -13.5354 q^{71} -3.05292 q^{72} -13.6423 q^{73} -5.06583 q^{74} +9.14134 q^{75} -1.15668 q^{76} +19.9489 q^{77} -3.00224 q^{78} -1.00000 q^{79} +10.7805 q^{80} +1.00000 q^{81} -4.39103 q^{82} -0.0914253 q^{83} +1.93813 q^{84} +3.76050 q^{85} -0.995355 q^{86} +2.31126 q^{87} +14.4722 q^{88} +14.7714 q^{89} -4.66581 q^{90} +10.1827 q^{91} -0.611801 q^{92} -3.84153 q^{93} -3.64736 q^{94} -9.44443 q^{95} +2.54890 q^{96} -5.83272 q^{97} +13.2875 q^{98} -4.74044 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9	\( 25 q + 6 q^{2} + 25 q^{3} + 26 q^{4} + 6 q^{5} + 6 q^{6} + 4 q^{7} + 18 q^{8} + 25 q^{9} + 13 q^{10} + 19 q^{11} + 26 q^{12} + 17 q^{14} + 6 q^{15} + 16 q^{16} - 25 q^{17} + 6 q^{18} + 25 q^{19} + 32 q^{20} + 4 q^{21} - 7 q^{22} + 8 q^{23} + 18 q^{24} + 15 q^{25} + 20 q^{26} + 25 q^{27} + 9 q^{28} + 21 q^{29} + 13 q^{30} + 4 q^{31} + 27 q^{32} + 19 q^{33} - 6 q^{34} + 50 q^{35} + 26 q^{36} - 8 q^{37} + 31 q^{38} + 52 q^{40} + 40 q^{41} + 17 q^{42} + 21 q^{43} + 34 q^{44} + 6 q^{45} + 29 q^{46} + 43 q^{47} + 16 q^{48} + 21 q^{49} + 13 q^{50} - 25 q^{51} + 3 q^{52} + 44 q^{53} + 6 q^{54} + 13 q^{55} + 38 q^{56} + 25 q^{57} - 5 q^{58} + 45 q^{59} + 32 q^{60} + 22 q^{61} + 4 q^{62} + 4 q^{63} + 26 q^{64} + 43 q^{65} - 7 q^{66} + 8 q^{67} - 26 q^{68} + 8 q^{69} + 29 q^{70} + 9 q^{71} + 18 q^{72} - 7 q^{73} + 18 q^{74} + 15 q^{75} + 33 q^{76} + 20 q^{77} + 20 q^{78} - 25 q^{79} + 42 q^{80} + 25 q^{81} - 43 q^{82} + 41 q^{83} + 9 q^{84} - 6 q^{85} - 12 q^{86} + 21 q^{87} - 43 q^{88} + 68 q^{89} + 13 q^{90} + 10 q^{91} + 2 q^{92} + 4 q^{93} - 17 q^{94} + 8 q^{95} + 27 q^{96} + 15 q^{97} + 11 q^{98} + 19 q^{99}+O(q^{100}) \) 25 * q + 6 * q^2 + 25 * q^3 + 26 * q^4 + 6 * q^5 + 6 * q^6 + 4 * q^7 + 18 * q^8 + 25 * q^9 + 13 * q^10 + 19 * q^11 + 26 * q^12 + 17 * q^14 + 6 * q^15 + 16 * q^16 - 25 * q^17 + 6 * q^18 + 25 * q^19 + 32 * q^20 + 4 * q^21 - 7 * q^22 + 8 * q^23 + 18 * q^24 + 15 * q^25 + 20 * q^26 + 25 * q^27 + 9 * q^28 + 21 * q^29 + 13 * q^30 + 4 * q^31 + 27 * q^32 + 19 * q^33 - 6 * q^34 + 50 * q^35 + 26 * q^36 - 8 * q^37 + 31 * q^38 + 52 * q^40 + 40 * q^41 + 17 * q^42 + 21 * q^43 + 34 * q^44 + 6 * q^45 + 29 * q^46 + 43 * q^47 + 16 * q^48 + 21 * q^49 + 13 * q^50 - 25 * q^51 + 3 * q^52 + 44 * q^53 + 6 * q^54 + 13 * q^55 + 38 * q^56 + 25 * q^57 - 5 * q^58 + 45 * q^59 + 32 * q^60 + 22 * q^61 + 4 * q^62 + 4 * q^63 + 26 * q^64 + 43 * q^65 - 7 * q^66 + 8 * q^67 - 26 * q^68 + 8 * q^69 + 29 * q^70 + 9 * q^71 + 18 * q^72 - 7 * q^73 + 18 * q^74 + 15 * q^75 + 33 * q^76 + 20 * q^77 + 20 * q^78 - 25 * q^79 + 42 * q^80 + 25 * q^81 - 43 * q^82 + 41 * q^83 + 9 * q^84 - 6 * q^85 - 12 * q^86 + 21 * q^87 - 43 * q^88 + 68 * q^89 + 13 * q^90 + 10 * q^91 + 2 * q^92 + 4 * q^93 - 17 * q^94 + 8 * q^95 + 27 * q^96 + 15 * q^97 + 11 * q^98 + 19 * q^99

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