LMFDB - Embedded newform 4019.2.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4019,2,Mod(1,4019)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4019, 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("4019.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4019 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4019.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:	$32.0918765724$
Analytic rank:	$1$
Dimension:	$149$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Character	$\chi$	$=$	4019.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.78495 q^{2} +3.42897 q^{3} +5.75594 q^{4} +1.05066 q^{5} -9.54951 q^{6} -0.902468 q^{7} -10.4601 q^{8} +8.75783 q^{9} +O(q^{10})$	\(q-2.78495 q^{2} +3.42897 q^{3} +5.75594 q^{4} +1.05066 q^{5} -9.54951 q^{6} -0.902468 q^{7} -10.4601 q^{8} +8.75783 q^{9} -2.92604 q^{10} -4.12162 q^{11} +19.7370 q^{12} -4.50545 q^{13} +2.51333 q^{14} +3.60269 q^{15} +17.6190 q^{16} +1.95561 q^{17} -24.3901 q^{18} -4.11181 q^{19} +6.04755 q^{20} -3.09454 q^{21} +11.4785 q^{22} +0.762025 q^{23} -35.8674 q^{24} -3.89611 q^{25} +12.5475 q^{26} +19.7434 q^{27} -5.19456 q^{28} -6.98278 q^{29} -10.0333 q^{30} -10.2246 q^{31} -28.1478 q^{32} -14.1329 q^{33} -5.44627 q^{34} -0.948189 q^{35} +50.4096 q^{36} -5.24778 q^{37} +11.4512 q^{38} -15.4491 q^{39} -10.9900 q^{40} +4.02700 q^{41} +8.61813 q^{42} +0.710767 q^{43} -23.7238 q^{44} +9.20151 q^{45} -2.12220 q^{46} -3.36177 q^{47} +60.4150 q^{48} -6.18555 q^{49} +10.8505 q^{50} +6.70572 q^{51} -25.9331 q^{52} -3.20873 q^{53} -54.9844 q^{54} -4.33043 q^{55} +9.43992 q^{56} -14.0993 q^{57} +19.4467 q^{58} +10.5570 q^{59} +20.7369 q^{60} -14.9315 q^{61} +28.4749 q^{62} -7.90366 q^{63} +43.1521 q^{64} -4.73371 q^{65} +39.3594 q^{66} -14.7135 q^{67} +11.2564 q^{68} +2.61296 q^{69} +2.64066 q^{70} +1.33234 q^{71} -91.6079 q^{72} +12.3888 q^{73} +14.6148 q^{74} -13.3596 q^{75} -23.6673 q^{76} +3.71963 q^{77} +43.0248 q^{78} +12.1945 q^{79} +18.5116 q^{80} +41.4261 q^{81} -11.2150 q^{82} +2.25210 q^{83} -17.8120 q^{84} +2.05468 q^{85} -1.97945 q^{86} -23.9437 q^{87} +43.1126 q^{88} +5.89601 q^{89} -25.6258 q^{90} +4.06603 q^{91} +4.38617 q^{92} -35.0597 q^{93} +9.36236 q^{94} -4.32012 q^{95} -96.5179 q^{96} +10.1379 q^{97} +17.2264 q^{98} -36.0964 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) $ 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

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

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

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

$2$	−2.78495	−1.96926	−0.984628	−	0.174663i	$-0.944116\pi$
$2$	−2.78495	−1.96926	−0.984628	+	0.174663i	$0.944116\pi$
$3$	3.42897	1.97972	0.989858	−	0.142059i	$-0.0453724\pi$
$3$	3.42897	1.97972	0.989858	+	0.142059i	$0.0453724\pi$
$4$	5.75594	2.87797
$5$	1.05066	0.469870	0.234935	−	0.972011i	$-0.424512\pi$
$5$	1.05066	0.469870	0.234935	+	0.972011i	$0.424512\pi$
$6$	−9.54951	−3.89857
$7$	−0.902468	−0.341101	−0.170550	−	0.985349i	$-0.554555\pi$
$7$	−0.902468	−0.341101	−0.170550	+	0.985349i	$0.554555\pi$
$8$	−10.4601	−3.69821
$9$	8.75783	2.91928
$10$	−2.92604	−0.925295
$11$	−4.12162	−1.24271	−0.621357	−	0.783527i	$-0.713419\pi$
$11$	−4.12162	−1.24271	−0.621357	+	0.783527i	$0.713419\pi$
$12$	19.7370	5.69757
$13$	−4.50545	−1.24959	−0.624794	−	0.780790i	$-0.714817\pi$
$13$	−4.50545	−1.24959	−0.624794	+	0.780790i	$0.714817\pi$
$14$	2.51333	0.671715
$15$	3.60269	0.930209
$16$	17.6190	4.40475
$17$	1.95561	0.474305	0.237152	−	0.971472i	$-0.423786\pi$
$17$	1.95561	0.474305	0.237152	+	0.971472i	$0.423786\pi$
$18$	−24.3901	−5.74880
$19$	−4.11181	−0.943314	−0.471657	−	0.881782i	$-0.656344\pi$
$19$	−4.11181	−0.943314	−0.471657	+	0.881782i	$0.656344\pi$
$20$	6.04755	1.35227
$21$	−3.09454	−0.675283
$22$	11.4785	2.44722
$23$	0.762025	0.158893	0.0794466	−	0.996839i	$-0.474685\pi$
$23$	0.762025	0.158893	0.0794466	+	0.996839i	$0.474685\pi$
$24$	−35.8674	−7.32140
$25$	−3.89611	−0.779222
$26$	12.5475	2.46076
$27$	19.7434	3.79962
$28$	−5.19456	−0.981679
$29$	−6.98278	−1.29667	−0.648335	−	0.761356i	$-0.724534\pi$
$29$	−6.98278	−1.29667	−0.648335	+	0.761356i	$0.724534\pi$
$30$	−10.0333	−1.83182
$31$	−10.2246	−1.83638	−0.918192	−	0.396136i	$-0.870351\pi$
$31$	−10.2246	−1.83638	−0.918192	+	0.396136i	$0.870351\pi$
$32$	−28.1478	−4.97587
$33$	−14.1329	−2.46022
$34$	−5.44627	−0.934028
$35$	−0.948189	−0.160273
$36$	50.4096	8.40159
$37$	−5.24778	−0.862730	−0.431365	−	0.902178i	$-0.641968\pi$
$37$	−5.24778	−0.862730	−0.431365	+	0.902178i	$0.641968\pi$
$38$	11.4512	1.85763
$39$	−15.4491	−2.47383
$40$	−10.9900	−1.73768
$41$	4.02700	0.628912	0.314456	−	0.949272i	$-0.398178\pi$
$41$	4.02700	0.628912	0.314456	+	0.949272i	$0.398178\pi$
$42$	8.61813	1.32981
$43$	0.710767	0.108391	0.0541954	−	0.998530i	$-0.482741\pi$
$43$	0.710767	0.108391	0.0541954	+	0.998530i	$0.482741\pi$
$44$	−23.7238	−3.57650
$45$	9.20151	1.37168
$46$	−2.12220	−0.312901
$47$	−3.36177	−0.490365	−0.245182	−	0.969477i	$-0.578848\pi$
$47$	−3.36177	−0.490365	−0.245182	+	0.969477i	$0.578848\pi$
$48$	60.4150	8.72015
$49$	−6.18555	−0.883650
$50$	10.8505	1.53449
$51$	6.70572	0.938989
$52$	−25.9331	−3.59628
$53$	−3.20873	−0.440754	−0.220377	−	0.975415i	$-0.570729\pi$
$53$	−3.20873	−0.440754	−0.220377	+	0.975415i	$0.570729\pi$
$54$	−54.9844	−7.48243
$55$	−4.33043	−0.583915
$56$	9.43992	1.26146
$57$	−14.0993	−1.86749
$58$	19.4467	2.55347
$59$	10.5570	1.37441	0.687203	−	0.726465i	$-0.258838\pi$
$59$	10.5570	1.37441	0.687203	+	0.726465i	$0.258838\pi$
$60$	20.7369	2.67712
$61$	−14.9315	−1.91179	−0.955894	−	0.293711i	$-0.905110\pi$
$61$	−14.9315	−1.91179	−0.955894	+	0.293711i	$0.905110\pi$
$62$	28.4749	3.61631
$63$	−7.90366	−0.995768
$64$	43.1521	5.39402
$65$	−4.73371	−0.587144
$66$	39.3594	4.84481
$67$	−14.7135	−1.79754	−0.898771	−	0.438418i	$-0.855539\pi$
$67$	−14.7135	−1.79754	−0.898771	+	0.438418i	$0.855539\pi$
$68$	11.2564	1.36504
$69$	2.61296	0.314563
$70$	2.64066	0.315619
$71$	1.33234	0.158119	0.0790597	−	0.996870i	$-0.474808\pi$
$71$	1.33234	0.158119	0.0790597	+	0.996870i	$0.474808\pi$
$72$	−91.6079	−10.7961
$73$	12.3888	1.45000	0.724998	−	0.688751i	$-0.241841\pi$
$73$	12.3888	1.45000	0.724998	+	0.688751i	$0.241841\pi$
$74$	14.6148	1.69894
$75$	−13.3596	−1.54264
$76$	−23.6673	−2.71483
$77$	3.71963	0.423891
$78$	43.0248	4.87160
$79$	12.1945	1.37199	0.685994	−	0.727608i	$-0.259368\pi$
$79$	12.1945	1.37199	0.685994	+	0.727608i	$0.259368\pi$
$80$	18.5116	2.06966
$81$	41.4261	4.60290
$82$	−11.2150	−1.23849
$83$	2.25210	0.247200	0.123600	−	0.992332i	$-0.460556\pi$
$83$	2.25210	0.247200	0.123600	+	0.992332i	$0.460556\pi$
$84$	−17.8120	−1.94345
$85$	2.05468	0.222862
$86$	−1.97945	−0.213449
$87$	−23.9437	−2.56704
$88$	43.1126	4.59582
$89$	5.89601	0.624976	0.312488	−	0.949922i	$-0.398838\pi$
$89$	5.89601	0.624976	0.312488	+	0.949922i	$0.398838\pi$
$90$	−25.6258	−2.70119
$91$	4.06603	0.426236
$92$	4.38617	0.457290
$93$	−35.0597	−3.63552
$94$	9.36236	0.965654
$95$	−4.32012	−0.443235
$96$	−96.5179	−9.85081
$97$	10.1379	1.02934	0.514671	−	0.857388i	$-0.327914\pi$
$97$	10.1379	1.02934	0.514671	+	0.857388i	$0.327914\pi$
$98$	17.2264	1.74013
$99$	−36.0964	−3.62783
$100$	−22.4258	−2.24258
$101$	−13.4791	−1.34122	−0.670610	−	0.741810i	$-0.733967\pi$
$101$	−13.4791	−1.34122	−0.670610	+	0.741810i	$0.733967\pi$
$102$	−18.6751	−1.84911
$103$	1.79463	0.176830	0.0884151	−	0.996084i	$-0.471820\pi$
$103$	1.79463	0.176830	0.0884151	+	0.996084i	$0.471820\pi$
$104$	47.1275	4.62123
$105$	−3.25131	−0.317295
$106$	8.93616	0.867957
$107$	−2.77495	−0.268265	−0.134132	−	0.990963i	$-0.542825\pi$
$107$	−2.77495	−0.268265	−0.134132	+	0.990963i	$0.542825\pi$
$108$	113.642	10.9352
$109$	0.929961	0.0890741	0.0445371	−	0.999008i	$-0.485819\pi$
$109$	0.929961	0.0890741	0.0445371	+	0.999008i	$0.485819\pi$
$110$	12.0600	1.14988
$111$	−17.9945	−1.70796
$112$	−15.9006	−1.50246
$113$	3.80980	0.358396	0.179198	−	0.983813i	$-0.442650\pi$
$113$	3.80980	0.358396	0.179198	+	0.983813i	$0.442650\pi$
$114$	39.2657	3.67757
$115$	0.800630	0.0746591
$116$	−40.1925	−3.73178
$117$	−39.4580	−3.64789
$118$	−29.4008	−2.70656
$119$	−1.76488	−0.161786
$120$	−37.6845	−3.44011
$121$	5.98775	0.544340
$122$	41.5836	3.76480
$123$	13.8085	1.24507
$124$	−58.8519	−5.28506
$125$	−9.34680	−0.836003
$126$	22.0113	1.96092
$127$	−15.7246	−1.39533	−0.697667	−	0.716422i	$-0.745778\pi$
$127$	−15.7246	−1.39533	−0.697667	+	0.716422i	$0.745778\pi$
$128$	−63.8810	−5.64633
$129$	2.43720	0.214583
$130$	13.1831	1.15624
$131$	8.26868	0.722438	0.361219	−	0.932481i	$-0.382361\pi$
$131$	8.26868	0.722438	0.361219	+	0.932481i	$0.382361\pi$
$132$	−81.3482	−7.08045
$133$	3.71078	0.321765
$134$	40.9764	3.53982
$135$	20.7437	1.78533
$136$	−20.4559	−1.75408
$137$	6.98486	0.596757	0.298378	−	0.954448i	$-0.403554\pi$
$137$	6.98486	0.596757	0.298378	+	0.954448i	$0.403554\pi$
$138$	−7.27696	−0.619456
$139$	−6.38655	−0.541700	−0.270850	−	0.962622i	$-0.587305\pi$
$139$	−6.38655	−0.541700	−0.270850	+	0.962622i	$0.587305\pi$
$140$	−5.45772	−0.461262
$141$	−11.5274	−0.970783
$142$	−3.71049	−0.311378
$143$	18.5698	1.55288
$144$	154.304	12.8587
$145$	−7.33653	−0.609266
$146$	−34.5021	−2.85542
$147$	−21.2101	−1.74938
$148$	−30.2059	−2.48291
$149$	6.74832	0.552844	0.276422	−	0.961036i	$-0.410851\pi$
$149$	6.74832	0.552844	0.276422	+	0.961036i	$0.410851\pi$
$150$	37.2059	3.03785
$151$	−5.34088	−0.434635	−0.217317	−	0.976101i	$-0.569731\pi$
$151$	−5.34088	−0.434635	−0.217317	+	0.976101i	$0.569731\pi$
$152$	43.0100	3.48857
$153$	17.1269	1.38463
$154$	−10.3590	−0.834751
$155$	−10.7425	−0.862862
$156$	−88.9239	−7.11961
$157$	−16.2670	−1.29825	−0.649125	−	0.760682i	$-0.724865\pi$
$157$	−16.2670	−1.29825	−0.649125	+	0.760682i	$0.724865\pi$
$158$	−33.9610	−2.70179
$159$	−11.0027	−0.872567
$160$	−29.5738	−2.33801
$161$	−0.687703	−0.0541986
$162$	−115.370	−9.06429
$163$	−13.2917	−1.04108	−0.520542	−	0.853836i	$-0.674270\pi$
$163$	−13.2917	−1.04108	−0.520542	+	0.853836i	$0.674270\pi$
$164$	23.1792	1.80999
$165$	−14.8489	−1.15599
$166$	−6.27199	−0.486801
$167$	−20.1529	−1.55948	−0.779740	−	0.626103i	$-0.784649\pi$
$167$	−20.1529	−1.55948	−0.779740	+	0.626103i	$0.784649\pi$
$168$	32.3692	2.49734
$169$	7.29911	0.561470
$170$	−5.72219	−0.438872
$171$	−36.0105	−2.75379
$172$	4.09113	0.311946
$173$	12.4029	0.942975	0.471487	−	0.881873i	$-0.343717\pi$
$173$	12.4029	0.942975	0.471487	+	0.881873i	$0.343717\pi$
$174$	66.6821	5.05515
$175$	3.51612	0.265793
$176$	−72.6188	−5.47385
$177$	36.1997	2.72094
$178$	−16.4201	−1.23074
$179$	5.76836	0.431148	0.215574	−	0.976488i	$-0.430838\pi$
$179$	5.76836	0.431148	0.215574	+	0.976488i	$0.430838\pi$
$180$	52.9634	3.94766
$181$	6.41616	0.476909	0.238455	−	0.971154i	$-0.423359\pi$
$181$	6.41616	0.476909	0.238455	+	0.971154i	$0.423359\pi$
$182$	−11.3237	−0.839367
$183$	−51.1998	−3.78480
$184$	−7.97086	−0.587620
$185$	−5.51364	−0.405371
$186$	97.6394	7.15927
$187$	−8.06028	−0.589426
$188$	−19.3502	−1.41126
$189$	−17.8178	−1.29606
$190$	12.0313	0.872843
$191$	11.5123	0.832998	0.416499	−	0.909136i	$-0.363257\pi$
$191$	11.5123	0.832998	0.416499	+	0.909136i	$0.363257\pi$
$192$	147.967	10.6786
$193$	3.30624	0.237988	0.118994	−	0.992895i	$-0.462033\pi$
$193$	3.30624	0.237988	0.118994	+	0.992895i	$0.462033\pi$
$194$	−28.2334	−2.02704
$195$	−16.2317	−1.16238
$196$	−35.6037	−2.54312
$197$	9.47711	0.675216	0.337608	−	0.941287i	$-0.390382\pi$
$197$	9.47711	0.675216	0.337608	+	0.941287i	$0.390382\pi$
$198$	100.527	7.14413
$199$	11.3295	0.803125	0.401562	−	0.915832i	$-0.368467\pi$
$199$	11.3295	0.803125	0.401562	+	0.915832i	$0.368467\pi$
$200$	40.7537	2.88172
$201$	−50.4522	−3.55862
$202$	37.5386	2.64120
$203$	6.30173	0.442295
$204$	38.5978	2.70238
$205$	4.23102	0.295507
$206$	−4.99795	−0.348224
$207$	6.67368	0.463853
$208$	−79.3815	−5.50412
$209$	16.9473	1.17227
$210$	9.05473	0.624836
$211$	6.13870	0.422606	0.211303	−	0.977421i	$-0.432229\pi$
$211$	6.13870	0.422606	0.211303	+	0.977421i	$0.432229\pi$
$212$	−18.4693	−1.26848
$213$	4.56854	0.313031
$214$	7.72810	0.528282
$215$	0.746775	0.0509296
$216$	−206.518	−14.0518
$217$	9.22734	0.626392
$218$	−2.58989	−0.175410
$219$	42.4807	2.87058
$220$	−24.9257	−1.68049
$221$	−8.81090	−0.592686
$222$	50.1137	3.36341
$223$	22.9352	1.53586	0.767928	−	0.640536i	$-0.221288\pi$
$223$	22.9352	1.53586	0.767928	+	0.640536i	$0.221288\pi$
$224$	25.4025	1.69727
$225$	−34.1215	−2.27476
$226$	−10.6101	−0.705773
$227$	−9.07468	−0.602308	−0.301154	−	0.953576i	$-0.597372\pi$
$227$	−9.07468	−0.602308	−0.301154	+	0.953576i	$0.597372\pi$
$228$	−81.1546	−5.37459
$229$	−29.9224	−1.97733	−0.988665	−	0.150136i	$-0.952029\pi$
$229$	−29.9224	−1.97733	−0.988665	+	0.150136i	$0.952029\pi$
$230$	−2.22971	−0.147023
$231$	12.7545	0.839184
$232$	73.0406	4.79535
$233$	9.59513	0.628598	0.314299	−	0.949324i	$-0.398231\pi$
$233$	9.59513	0.628598	0.314299	+	0.949324i	$0.398231\pi$
$234$	109.889	7.18364
$235$	−3.53208	−0.230408
$236$	60.7656	3.95550
$237$	41.8145	2.71615
$238$	4.91509	0.318598
$239$	2.77301	0.179371	0.0896856	−	0.995970i	$-0.471414\pi$
$239$	2.77301	0.179371	0.0896856	+	0.995970i	$0.471414\pi$
$240$	63.4757	4.09734
$241$	11.7895	0.759431	0.379715	−	0.925103i	$-0.376022\pi$
$241$	11.7895	0.759431	0.379715	+	0.925103i	$0.376022\pi$
$242$	−16.6756	−1.07195
$243$	82.8185	5.31281
$244$	−85.9451	−5.50207
$245$	−6.49892	−0.415201
$246$	−38.4559	−2.45186
$247$	18.5256	1.17875
$248$	106.950	6.79133
$249$	7.72239	0.489387
$250$	26.0304	1.64630
$251$	2.12899	0.134381	0.0671904	−	0.997740i	$-0.478597\pi$
$251$	2.12899	0.134381	0.0671904	+	0.997740i	$0.478597\pi$
$252$	−45.4930	−2.86579
$253$	−3.14078	−0.197459
$254$	43.7922	2.74777
$255$	7.04545	0.441203
$256$	91.6010	5.72506
$257$	−6.46770	−0.403444	−0.201722	−	0.979443i	$-0.564654\pi$
$257$	−6.46770	−0.403444	−0.201722	+	0.979443i	$0.564654\pi$
$258$	−6.78747	−0.422569
$259$	4.73596	0.294278
$260$	−27.2469	−1.68978
$261$	−61.1540	−3.78534
$262$	−23.0278	−1.42266
$263$	23.0970	1.42422	0.712112	−	0.702065i	$-0.247739\pi$
$263$	23.0970	1.42422	0.712112	+	0.702065i	$0.247739\pi$
$264$	147.832	9.09841
$265$	−3.37129	−0.207097
$266$	−10.3343	−0.633638
$267$	20.2173	1.23728
$268$	−84.6902	−5.17328
$269$	10.9195	0.665775	0.332888	−	0.942966i	$-0.391977\pi$
$269$	10.9195	0.665775	0.332888	+	0.942966i	$0.391977\pi$
$270$	−57.7700	−3.51577
$271$	11.8238	0.718244	0.359122	−	0.933291i	$-0.383076\pi$
$271$	11.8238	0.718244	0.359122	+	0.933291i	$0.383076\pi$
$272$	34.4559	2.08919
$273$	13.9423	0.843826
$274$	−19.4525	−1.17517
$275$	16.0583	0.968351
$276$	15.0400	0.905304
$277$	18.1594	1.09109	0.545546	−	0.838081i	$-0.316322\pi$
$277$	18.1594	1.09109	0.545546	+	0.838081i	$0.316322\pi$
$278$	17.7862	1.06675
$279$	−89.5449	−5.36091
$280$	9.91816	0.592723
$281$	−32.4766	−1.93739	−0.968695	−	0.248256i	$-0.920143\pi$
$281$	−32.4766	−1.93739	−0.968695	+	0.248256i	$0.920143\pi$
$282$	32.1032	1.91172
$283$	−1.11424	−0.0662348	−0.0331174	−	0.999451i	$-0.510544\pi$
$283$	−1.11424	−0.0662348	−0.0331174	+	0.999451i	$0.510544\pi$
$284$	7.66886	0.455063
$285$	−14.8136	−0.877479
$286$	−51.7158	−3.05802
$287$	−3.63424	−0.214523
$288$	−246.513	−14.5259
$289$	−13.1756	−0.775035
$290$	20.4319	1.19980
$291$	34.7624	2.03781
$292$	71.3091	4.17305
$293$	21.1905	1.23796	0.618981	−	0.785406i	$-0.287546\pi$
$293$	21.1905	1.23796	0.618981	+	0.785406i	$0.287546\pi$
$294$	59.0690	3.44497
$295$	11.0919	0.645793
$296$	54.8924	3.19055
$297$	−81.3749	−4.72185
$298$	−18.7937	−1.08869
$299$	−3.43327	−0.198551
$300$	−76.8973	−4.43967
$301$	−0.641444	−0.0369722
$302$	14.8741	0.855907
$303$	−46.2194	−2.65523
$304$	−72.4459	−4.15506
$305$	−15.6880	−0.898292
$306$	−47.6975	−2.72669
$307$	−0.302684	−0.0172751	−0.00863753	−	0.999963i	$-0.502749\pi$
$307$	−0.302684	−0.0172751	−0.00863753	+	0.999963i	$0.502749\pi$
$308$	21.4100	1.21995
$309$	6.15373	0.350074
$310$	29.9174	1.69920
$311$	−25.6457	−1.45423	−0.727116	−	0.686515i	$-0.759140\pi$
$311$	−25.6457	−1.45423	−0.727116	+	0.686515i	$0.759140\pi$
$312$	161.599	9.14873
$313$	−16.0221	−0.905625	−0.452812	−	0.891606i	$-0.649579\pi$
$313$	−16.0221	−0.905625	−0.452812	+	0.891606i	$0.649579\pi$
$314$	45.3028	2.55659
$315$	−8.30408	−0.467882
$316$	70.1908	3.94854
$317$	13.5819	0.762834	0.381417	−	0.924403i	$-0.375436\pi$
$317$	13.5819	0.762834	0.381417	+	0.924403i	$0.375436\pi$
$318$	30.6418	1.71831
$319$	28.7803	1.61139
$320$	45.3383	2.53449
$321$	−9.51523	−0.531088
$322$	1.91522	0.106731
$323$	−8.04109	−0.447418
$324$	238.446	13.2470
$325$	17.5537	0.973706
$326$	37.0166	2.05016
$327$	3.18881	0.176341
$328$	−42.1229	−2.32585
$329$	3.03389	0.167264
$330$	41.3534	2.27643
$331$	−6.35356	−0.349223	−0.174612	−	0.984637i	$-0.555867\pi$
$331$	−6.35356	−0.349223	−0.174612	+	0.984637i	$0.555867\pi$
$332$	12.9630	0.711436
$333$	−45.9592	−2.51855
$334$	56.1249	3.07102
$335$	−15.4589	−0.844612
$336$	−54.5226	−2.97445
$337$	23.0198	1.25397	0.626985	−	0.779032i	$-0.284289\pi$
$337$	23.0198	1.25397	0.626985	+	0.779032i	$0.284289\pi$
$338$	−20.3276	−1.10568
$339$	13.0637	0.709522
$340$	11.8266	0.641389
$341$	42.1417	2.28210
$342$	100.288	5.42293
$343$	11.8995	0.642515
$344$	−7.43470	−0.400852
$345$	2.74534	0.147804
$346$	−34.5414	−1.85696
$347$	−18.6535	−1.00137	−0.500686	−	0.865629i	$-0.666919\pi$
$347$	−18.6535	−1.00137	−0.500686	+	0.865629i	$0.666919\pi$
$348$	−137.819	−7.38786
$349$	2.56336	0.137214	0.0686068	−	0.997644i	$-0.478145\pi$
$349$	2.56336	0.137214	0.0686068	+	0.997644i	$0.478145\pi$
$350$	−9.79221	−0.523415
$351$	−88.9531	−4.74796
$352$	116.014	6.18359
$353$	−6.02120	−0.320476	−0.160238	−	0.987078i	$-0.551226\pi$
$353$	−6.02120	−0.320476	−0.160238	+	0.987078i	$0.551226\pi$
$354$	−100.814	−5.35822
$355$	1.39984	0.0742956
$356$	33.9371	1.79866
$357$	−6.05170	−0.320290
$358$	−16.0646	−0.849040
$359$	−0.0145844	−0.000769735 0	−0.000384868	−	1.00000i	$-0.500123\pi$
$359$	−0.0145844	−0.000769735 0	−0.000384868		1.00000i	$0.500123\pi$
$360$	−96.2489	−5.07276
$361$	−2.09302	−0.110159
$362$	−17.8687	−0.939157
$363$	20.5318	1.07764
$364$	23.4038	1.22669
$365$	13.0164	0.681310
$366$	142.589	7.45324
$367$	13.1099	0.684333	0.342166	−	0.939639i	$-0.388839\pi$
$367$	13.1099	0.684333	0.342166	+	0.939639i	$0.388839\pi$
$368$	13.4261	0.699884
$369$	35.2678	1.83597
$370$	15.3552	0.798279
$371$	2.89578	0.150341
$372$	−201.801	−10.4629
$373$	9.17620	0.475126	0.237563	−	0.971372i	$-0.423651\pi$
$373$	9.17620	0.475126	0.237563	+	0.971372i	$0.423651\pi$
$374$	22.4475	1.16073
$375$	−32.0499	−1.65505
$376$	35.1645	1.81347
$377$	31.4606	1.62030
$378$	49.6217	2.55227
$379$	9.35455	0.480511	0.240255	−	0.970710i	$-0.422769\pi$
$379$	9.35455	0.480511	0.240255	+	0.970710i	$0.422769\pi$
$380$	−24.8664	−1.27562
$381$	−53.9192	−2.76236
$382$	−32.0611	−1.64039
$383$	14.9017	0.761439	0.380720	−	0.924690i	$-0.375676\pi$
$383$	14.9017	0.761439	0.380720	+	0.924690i	$0.375676\pi$
$384$	−219.046	−11.1781
$385$	3.90807	0.199174
$386$	−9.20771	−0.468660
$387$	6.22477	0.316423
$388$	58.3529	2.96242
$389$	−23.2741	−1.18004	−0.590022	−	0.807387i	$-0.700881\pi$
$389$	−23.2741	−1.18004	−0.590022	+	0.807387i	$0.700881\pi$
$390$	45.2046	2.28902
$391$	1.49022	0.0753638
$392$	64.7015	3.26792
$393$	28.3530	1.43022
$394$	−26.3933	−1.32967
$395$	12.8123	0.644656
$396$	−207.769	−10.4408
$397$	−20.9034	−1.04911	−0.524557	−	0.851375i	$-0.675769\pi$
$397$	−20.9034	−1.04911	−0.524557	+	0.851375i	$0.675769\pi$
$398$	−31.5520	−1.58156
$399$	12.7241	0.637004
$400$	−68.6455	−3.43228
$401$	19.9197	0.994744	0.497372	−	0.867537i	$-0.334298\pi$
$401$	19.9197	0.994744	0.497372	+	0.867537i	$0.334298\pi$
$402$	140.507	7.00784
$403$	46.0662	2.29472
$404$	−77.5849	−3.85999
$405$	43.5248	2.16276
$406$	−17.5500	−0.870992
$407$	21.6293	1.07213
$408$	−70.1426	−3.47258
$409$	−4.72219	−0.233497	−0.116749	−	0.993161i	$-0.537247\pi$
$409$	−4.72219	−0.233497	−0.116749	+	0.993161i	$0.537247\pi$
$410$	−11.7832	−0.581929
$411$	23.9509	1.18141
$412$	10.3298	0.508912
$413$	−9.52738	−0.468812
$414$	−18.5859	−0.913445
$415$	2.36620	0.116152
$416$	126.818	6.21779
$417$	−21.8993	−1.07241
$418$	−47.1974	−2.30850
$419$	−32.5508	−1.59021	−0.795105	−	0.606472i	$-0.792584\pi$
$419$	−32.5508	−1.59021	−0.795105	+	0.606472i	$0.792584\pi$
$420$	−18.7144	−0.913167
$421$	−3.70476	−0.180559	−0.0902795	−	0.995916i	$-0.528776\pi$
$421$	−3.70476	−0.180559	−0.0902795	+	0.995916i	$0.528776\pi$
$422$	−17.0960	−0.832219
$423$	−29.4418	−1.43151
$424$	33.5637	1.63000
$425$	−7.61927	−0.369589
$426$	−12.7232	−0.616439
$427$	13.4752	0.652113
$428$	−15.9725	−0.772058
$429$	63.6751	3.07426
$430$	−2.07973	−0.100294
$431$	1.20700	0.0581392	0.0290696	−	0.999577i	$-0.490746\pi$
$431$	1.20700	0.0581392	0.0290696	+	0.999577i	$0.490746\pi$
$432$	347.859	16.7364
$433$	10.6589	0.512233	0.256117	−	0.966646i	$-0.417557\pi$
$433$	10.6589	0.512233	0.256117	+	0.966646i	$0.417557\pi$
$434$	−25.6977	−1.23353
$435$	−25.1568	−1.20617
$436$	5.35280	0.256353
$437$	−3.13330	−0.149886
$438$	−118.307	−5.65291
$439$	9.72924	0.464351	0.232176	−	0.972674i	$-0.425416\pi$
$439$	9.72924	0.464351	0.232176	+	0.972674i	$0.425416\pi$
$440$	45.2967	2.15944
$441$	−54.1720	−2.57962
$442$	24.5379	1.16715
$443$	−2.90737	−0.138133	−0.0690666	−	0.997612i	$-0.522002\pi$
$443$	−2.90737	−0.138133	−0.0690666	+	0.997612i	$0.522002\pi$
$444$	−103.575	−4.91546
$445$	6.19472	0.293658
$446$	−63.8734	−3.02449
$447$	23.1398	1.09447
$448$	−38.9434	−1.83990
$449$	−21.6684	−1.02260	−0.511298	−	0.859403i	$-0.670835\pi$
$449$	−21.6684	−1.02260	−0.511298	+	0.859403i	$0.670835\pi$
$450$	95.0266	4.47960
$451$	−16.5978	−0.781559
$452$	21.9290	1.03145
$453$	−18.3137	−0.860453
$454$	25.2725	1.18610
$455$	4.27202	0.200275
$456$	147.480	6.90638
$457$	−41.0155	−1.91863	−0.959313	−	0.282346i	$-0.908887\pi$
$457$	−41.0155	−1.91863	−0.959313	+	0.282346i	$0.908887\pi$
$458$	83.3325	3.89387
$459$	38.6104	1.80218
$460$	4.60838	0.214867
$461$	−21.3847	−0.995985	−0.497992	−	0.867181i	$-0.665929\pi$
$461$	−21.3847	−0.995985	−0.497992	+	0.867181i	$0.665929\pi$
$462$	−35.5206	−1.65257
$463$	37.5534	1.74526	0.872628	−	0.488386i	$-0.162414\pi$
$463$	37.5534	1.74526	0.872628	+	0.488386i	$0.162414\pi$
$464$	−123.029	−5.71150
$465$	−36.8359	−1.70822
$466$	−26.7219	−1.23787
$467$	−14.0795	−0.651519	−0.325760	−	0.945453i	$-0.605620\pi$
$467$	−14.0795	−0.651519	−0.325760	+	0.945453i	$0.605620\pi$
$468$	−227.118	−10.4985
$469$	13.2785	0.613144
$470$	9.83667	0.453732
$471$	−55.7791	−2.57017
$472$	−110.428	−5.08284
$473$	−2.92951	−0.134699
$474$	−116.451	−5.34879
$475$	16.0201	0.735051
$476$	−10.1585	−0.465615
$477$	−28.1015	−1.28668
$478$	−7.72270	−0.353228
$479$	−18.2999	−0.836145	−0.418073	−	0.908414i	$-0.637294\pi$
$479$	−18.2999	−0.836145	−0.418073	+	0.908414i	$0.637294\pi$
$480$	−101.408	−4.62860
$481$	23.6436	1.07806
$482$	−32.8333	−1.49551
$483$	−2.35811	−0.107298
$484$	34.4651	1.56660
$485$	10.6514	0.483657
$486$	−230.645	−10.4623
$487$	−2.72839	−0.123635	−0.0618177	−	0.998087i	$-0.519690\pi$
$487$	−2.72839	−0.123635	−0.0618177	+	0.998087i	$0.519690\pi$
$488$	156.186	7.07019
$489$	−45.5767	−2.06105
$490$	18.0992	0.817637
$491$	−27.7523	−1.25244	−0.626222	−	0.779644i	$-0.715400\pi$
$491$	−27.7523	−1.25244	−0.626222	+	0.779644i	$0.715400\pi$
$492$	79.4808	3.58327
$493$	−13.6556	−0.615016
$494$	−51.5928	−2.32127
$495$	−37.9251	−1.70461
$496$	−180.146	−8.08881
$497$	−1.20239	−0.0539347
$498$	−21.5065	−0.963728
$499$	−19.9843	−0.894619	−0.447310	−	0.894379i	$-0.647618\pi$
$499$	−19.9843	−0.894619	−0.447310	+	0.894379i	$0.647618\pi$
$500$	−53.7996	−2.40599
$501$	−69.1038	−3.08733
$502$	−5.92913	−0.264630
$503$	−4.07091	−0.181513	−0.0907564	−	0.995873i	$-0.528928\pi$
$503$	−4.07091	−0.181513	−0.0907564	+	0.995873i	$0.528928\pi$
$504$	82.6732	3.68256
$505$	−14.1620	−0.630199
$506$	8.74690	0.388847
$507$	25.0284	1.11155
$508$	−90.5100	−4.01573
$509$	−6.72291	−0.297988	−0.148994	−	0.988838i	$-0.547603\pi$
$509$	−6.72291	−0.297988	−0.148994	+	0.988838i	$0.547603\pi$
$510$	−19.6212	−0.868842
$511$	−11.1805	−0.494595
$512$	−127.342	−5.62778
$513$	−81.1812	−3.58424
$514$	18.0122	0.794485
$515$	1.88555	0.0830872
$516$	14.0284	0.617564
$517$	13.8559	0.609384
$518$	−13.1894	−0.579509
$519$	42.5291	1.86682
$520$	49.5151	2.17138
$521$	11.1017	0.486372	0.243186	−	0.969980i	$-0.421807\pi$
$521$	11.1017	0.486372	0.243186	+	0.969980i	$0.421807\pi$
$522$	170.311	7.45430
$523$	25.2234	1.10294	0.551472	−	0.834194i	$-0.314066\pi$
$523$	25.2234	1.10294	0.551472	+	0.834194i	$0.314066\pi$
$524$	47.5940	2.07915
$525$	12.0567	0.526196
$526$	−64.3241	−2.80466
$527$	−19.9952	−0.871006
$528$	−249.008	−10.8367
$529$	−22.4193	−0.974753
$530$	9.38888	0.407827
$531$	92.4566	4.01227
$532$	21.3590	0.926031
$533$	−18.1435	−0.785881
$534$	−56.3040	−2.43651
$535$	−2.91554	−0.126050
$536$	153.905	6.64768
$537$	19.7795	0.853550
$538$	−30.4103	−1.31108
$539$	25.4945	1.09813
$540$	119.399	5.13813
$541$	−21.1973	−0.911341	−0.455670	−	0.890149i	$-0.650600\pi$
$541$	−21.1973	−0.911341	−0.455670	+	0.890149i	$0.650600\pi$
$542$	−32.9286	−1.41441
$543$	22.0008	0.944145
$544$	−55.0460	−2.36008
$545$	0.977074	0.0418533
$546$	−38.8286	−1.66171
$547$	7.99605	0.341886	0.170943	−	0.985281i	$-0.445319\pi$
$547$	7.99605	0.341886	0.170943	+	0.985281i	$0.445319\pi$
$548$	40.2045	1.71745
$549$	−130.768	−5.58104
$550$	−44.7215	−1.90693
$551$	28.7118	1.22317
$552$	−27.3318	−1.16332
$553$	−11.0051	−0.467986
$554$	−50.5730	−2.14864
$555$	−18.9061	−0.802519
$556$	−36.7606	−1.55900
$557$	9.72535	0.412076	0.206038	−	0.978544i	$-0.433943\pi$
$557$	9.72535	0.412076	0.206038	+	0.978544i	$0.433943\pi$
$558$	249.378	10.5570
$559$	−3.20233	−0.135444
$560$	−16.7061	−0.705963
$561$	−27.6384	−1.16690
$562$	90.4456	3.81522
$563$	41.9846	1.76944	0.884720	−	0.466124i	$-0.154350\pi$
$563$	41.9846	1.76944	0.884720	+	0.466124i	$0.154350\pi$
$564$	−66.3511	−2.79389
$565$	4.00281	0.168399
$566$	3.10311	0.130433
$567$	−37.3857	−1.57005
$568$	−13.9364	−0.584758
$569$	−44.6005	−1.86975	−0.934875	−	0.354977i	$-0.884489\pi$
$569$	−44.6005	−1.86975	−0.934875	+	0.354977i	$0.884489\pi$
$570$	41.2550	1.72798
$571$	−12.4744	−0.522039	−0.261019	−	0.965334i	$-0.584059\pi$
$571$	−12.4744	−0.522039	−0.261019	+	0.965334i	$0.584059\pi$
$572$	106.886	4.46915
$573$	39.4752	1.64910
$574$	10.1212	0.422450
$575$	−2.96893	−0.123813
$576$	377.919	15.7466
$577$	34.3698	1.43083	0.715417	−	0.698698i	$-0.246237\pi$
$577$	34.3698	1.43083	0.715417	+	0.698698i	$0.246237\pi$
$578$	36.6934	1.52624
$579$	11.3370	0.471149
$580$	−42.2287	−1.75345
$581$	−2.03245	−0.0843203
$582$	−96.8115	−4.01296
$583$	13.2252	0.547731
$584$	−129.588	−5.36239
$585$	−41.4570	−1.71404
$586$	−59.0144	−2.43786
$587$	4.61482	0.190474	0.0952371	−	0.995455i	$-0.469639\pi$
$587$	4.61482	0.190474	0.0952371	+	0.995455i	$0.469639\pi$
$588$	−122.084	−5.03466
$589$	42.0414	1.73229
$590$	−30.8903	−1.27173
$591$	32.4967	1.33674
$592$	−92.4606	−3.80011
$593$	36.6807	1.50630	0.753148	−	0.657851i	$-0.228534\pi$
$593$	36.6807	1.50630	0.753148	+	0.657851i	$0.228534\pi$
$594$	226.625	9.29853
$595$	−1.85429	−0.0760183
$596$	38.8430	1.59107
$597$	38.8484	1.58996
$598$	9.56147	0.390998
$599$	36.8013	1.50366	0.751831	−	0.659356i	$-0.229171\pi$
$599$	36.8013	1.50366	0.751831	+	0.659356i	$0.229171\pi$
$600$	139.743	5.70500
$601$	−4.42498	−0.180499	−0.0902494	−	0.995919i	$-0.528766\pi$
$601$	−4.42498	−0.180499	−0.0902494	+	0.995919i	$0.528766\pi$
$602$	1.78639	0.0728078
$603$	−128.859	−5.24752
$604$	−30.7418	−1.25087
$605$	6.29109	0.255769
$606$	128.719	5.22884
$607$	−38.6898	−1.57037	−0.785186	−	0.619261i	$-0.787432\pi$
$607$	−38.6898	−1.57037	−0.785186	+	0.619261i	$0.787432\pi$
$608$	115.738	4.69381
$609$	21.6085	0.875619
$610$	43.6903	1.76897
$611$	15.1463	0.612754
$612$	98.5814	3.98492
$613$	34.4204	1.39023	0.695114	−	0.718899i	$-0.255354\pi$
$613$	34.4204	1.39023	0.695114	+	0.718899i	$0.255354\pi$
$614$	0.842959	0.0340190
$615$	14.5080	0.585020
$616$	−38.9077	−1.56764
$617$	−23.9266	−0.963250	−0.481625	−	0.876377i	$-0.659953\pi$
$617$	−23.9266	−0.963250	−0.481625	+	0.876377i	$0.659953\pi$
$618$	−17.1378	−0.689385
$619$	4.49839	0.180805	0.0904027	−	0.995905i	$-0.471185\pi$
$619$	4.49839	0.180805	0.0904027	+	0.995905i	$0.471185\pi$
$620$	−61.8335	−2.48329
$621$	15.0450	0.603734
$622$	71.4219	2.86376
$623$	−5.32097	−0.213180
$624$	−272.197	−10.8966
$625$	9.66023	0.386409
$626$	44.6208	1.78341
$627$	58.1118	2.32076
$628$	−93.6321	−3.73633
$629$	−10.2626	−0.409197
$630$	23.1264	0.921379
$631$	20.1490	0.802117	0.401059	−	0.916052i	$-0.368642\pi$
$631$	20.1490	0.802117	0.401059	+	0.916052i	$0.368642\pi$
$632$	−127.556	−5.07389
$633$	21.0494	0.836640
$634$	−37.8248	−1.50222
$635$	−16.5212	−0.655626
$636$	−63.3306	−2.51122
$637$	27.8687	1.10420
$638$	−80.1518	−3.17324
$639$	11.6684	0.461594
$640$	−67.1173	−2.65304
$641$	−37.9167	−1.49762	−0.748809	−	0.662786i	$-0.769374\pi$
$641$	−37.9167	−1.49762	−0.748809	+	0.662786i	$0.769374\pi$
$642$	26.4994	1.04585
$643$	−8.48708	−0.334698	−0.167349	−	0.985898i	$-0.553521\pi$
$643$	−8.48708	−0.334698	−0.167349	+	0.985898i	$0.553521\pi$
$644$	−3.95838	−0.155982
$645$	2.56067	0.100826
$646$	22.3940	0.881081
$647$	−4.25344	−0.167220	−0.0836099	−	0.996499i	$-0.526645\pi$
$647$	−4.25344	−0.167220	−0.0836099	+	0.996499i	$0.526645\pi$
$648$	−433.322	−17.0225
$649$	−43.5120	−1.70800
$650$	−48.8863	−1.91748
$651$	31.6402	1.24008
$652$	−76.5061	−2.99621
$653$	−0.964816	−0.0377562	−0.0188781	−	0.999822i	$-0.506009\pi$
$653$	−0.964816	−0.0377562	−0.0188781	+	0.999822i	$0.506009\pi$
$654$	−8.88067	−0.347262
$655$	8.68758	0.339452
$656$	70.9517	2.77020
$657$	108.499	4.23294
$658$	−8.44923	−0.329385
$659$	11.4362	0.445492	0.222746	−	0.974877i	$-0.428498\pi$
$659$	11.4362	0.445492	0.222746	+	0.974877i	$0.428498\pi$
$660$	−85.4694	−3.32689
$661$	−26.7488	−1.04041	−0.520205	−	0.854042i	$-0.674144\pi$
$661$	−26.7488	−1.04041	−0.520205	+	0.854042i	$0.674144\pi$
$662$	17.6943	0.687710
$663$	−30.2123	−1.17335
$664$	−23.5572	−0.914198
$665$	3.89877	0.151188
$666$	127.994	4.95966
$667$	−5.32105	−0.206032
$668$	−115.999	−4.48814
$669$	78.6442	3.04056
$670$	43.0523	1.66326
$671$	61.5422	2.37581
$672$	87.1043	3.36012
$673$	−25.0835	−0.966897	−0.483448	−	0.875373i	$-0.660616\pi$
$673$	−25.0835	−0.966897	−0.483448	+	0.875373i	$0.660616\pi$
$674$	−64.1090	−2.46939
$675$	−76.9226	−2.96075
$676$	42.0132	1.61589
$677$	−2.37133	−0.0911375	−0.0455688	−	0.998961i	$-0.514510\pi$
$677$	−2.37133	−0.0911375	−0.0455688	+	0.998961i	$0.514510\pi$
$678$	−36.3817	−1.39723
$679$	−9.14909	−0.351110
$680$	−21.4922	−0.824189
$681$	−31.1168	−1.19240
$682$	−117.363	−4.49404
$683$	35.3008	1.35075	0.675374	−	0.737476i	$-0.263982\pi$
$683$	35.3008	1.35075	0.675374	+	0.737476i	$0.263982\pi$
$684$	−207.275	−7.92534
$685$	7.33873	0.280398
$686$	−33.1396	−1.26528
$687$	−102.603	−3.91455
$688$	12.5230	0.477435
$689$	14.4568	0.550760
$690$	−7.64562	−0.291064
$691$	−30.9102	−1.17588	−0.587939	−	0.808905i	$-0.700061\pi$
$691$	−30.9102	−1.17588	−0.587939	+	0.808905i	$0.700061\pi$
$692$	71.3904	2.71385
$693$	32.5759	1.23746
$694$	51.9490	1.97196
$695$	−6.71010	−0.254529
$696$	250.454	9.49343
$697$	7.87525	0.298296
$698$	−7.13883	−0.270209
$699$	32.9014	1.24445
$700$	20.2386	0.764946
$701$	−3.41204	−0.128871	−0.0644355	−	0.997922i	$-0.520525\pi$
$701$	−3.41204	−0.128871	−0.0644355	+	0.997922i	$0.520525\pi$
$702$	247.730	9.34996
$703$	21.5779	0.813825
$704$	−177.857	−6.70323
$705$	−12.1114	−0.456142
$706$	16.7687	0.631100
$707$	12.1644	0.457491
$708$	208.363	7.83077
$709$	24.5044	0.920281	0.460140	−	0.887846i	$-0.347799\pi$
$709$	24.5044	0.920281	0.460140	+	0.887846i	$0.347799\pi$
$710$	−3.89847	−0.146307
$711$	106.797	4.00521
$712$	−61.6730	−2.31129
$713$	−7.79136	−0.291789
$714$	16.8537	0.630733
$715$	19.5105	0.729653
$716$	33.2024	1.24083
$717$	9.50857	0.355104
$718$	0.0406168	0.00151581
$719$	53.5553	1.99727	0.998637	−	0.0521892i	$-0.0166199\pi$
$719$	53.5553	1.99727	0.998637	+	0.0521892i	$0.0166199\pi$
$720$	162.121	6.04191
$721$	−1.61960	−0.0603169
$722$	5.82896	0.216931
$723$	40.4260	1.50346
$724$	36.9310	1.37253
$725$	27.2057	1.01039
$726$	−57.1800	−2.12215
$727$	5.81248	0.215573	0.107786	−	0.994174i	$-0.465624\pi$
$727$	5.81248	0.215573	0.107786	+	0.994174i	$0.465624\pi$
$728$	−42.5311	−1.57631
$729$	159.704	5.91496
$730$	−36.2500	−1.34167
$731$	1.38998	0.0514103
$732$	−294.703	−10.8925
$733$	−39.2452	−1.44956	−0.724778	−	0.688983i	$-0.758058\pi$
$733$	−39.2452	−1.44956	−0.724778	+	0.688983i	$0.758058\pi$
$734$	−36.5105	−1.34763
$735$	−22.2846	−0.821980
$736$	−21.4493	−0.790632
$737$	60.6435	2.23383
$738$	−98.2191	−3.61549
$739$	7.94417	0.292231	0.146115	−	0.989268i	$-0.453323\pi$
$739$	7.94417	0.292231	0.146115	+	0.989268i	$0.453323\pi$
$740$	−31.7362	−1.16665
$741$	63.5236	2.33360
$742$	−8.06460	−0.296061
$743$	14.3060	0.524838	0.262419	−	0.964954i	$-0.415480\pi$
$743$	14.3060	0.524838	0.262419	+	0.964954i	$0.415480\pi$
$744$	366.728	13.4449
$745$	7.09020	0.259765
$746$	−25.5553	−0.935644
$747$	19.7235	0.721646
$748$	−46.3945	−1.69635
$749$	2.50431	0.0915054
$750$	89.2573	3.25922
$751$	−39.8439	−1.45393	−0.726963	−	0.686677i	$-0.759069\pi$
$751$	−39.8439	−1.45393	−0.726963	+	0.686677i	$0.759069\pi$
$752$	−59.2310	−2.15993
$753$	7.30025	0.266036
$754$	−87.6161	−3.19079
$755$	−5.61146	−0.204222
$756$	−102.558	−3.73001
$757$	−27.2789	−0.991468	−0.495734	−	0.868474i	$-0.665101\pi$
$757$	−27.2789	−0.991468	−0.495734	+	0.868474i	$0.665101\pi$
$758$	−26.0519	−0.946249
$759$	−10.7696	−0.390913
$760$	45.1889	1.63917
$761$	−6.33374	−0.229598	−0.114799	−	0.993389i	$-0.536622\pi$
$761$	−6.33374	−0.229598	−0.114799	+	0.993389i	$0.536622\pi$
$762$	150.162	5.43980
$763$	−0.839260	−0.0303833
$764$	66.2639	2.39734
$765$	17.9946	0.650595
$766$	−41.5004	−1.49947
$767$	−47.5642	−1.71744
$768$	314.097	11.3340
$769$	−33.3449	−1.20245	−0.601224	−	0.799080i	$-0.705320\pi$
$769$	−33.3449	−1.20245	−0.601224	+	0.799080i	$0.705320\pi$
$770$	−10.8838	−0.392224
$771$	−22.1775	−0.798705
$772$	19.0305	0.684924
$773$	−9.76328	−0.351161	−0.175580	−	0.984465i	$-0.556180\pi$
$773$	−9.76328	−0.351161	−0.175580	+	0.984465i	$0.556180\pi$
$774$	−17.3357	−0.623118
$775$	39.8360	1.43095
$776$	−106.043	−3.80672
$777$	16.2394	0.582587
$778$	64.8172	2.32381
$779$	−16.5583	−0.593262
$780$	−93.4289	−3.34529
$781$	−5.49139	−0.196497
$782$	−4.15019	−0.148411
$783$	−137.864	−4.92685
$784$	−108.983	−3.89226
$785$	−17.0911	−0.610009
$786$	−78.9618	−2.81647
$787$	−1.26759	−0.0451846	−0.0225923	−	0.999745i	$-0.507192\pi$
$787$	−1.26759	−0.0451846	−0.0225923	+	0.999745i	$0.507192\pi$
$788$	54.5497	1.94325
$789$	79.1991	2.81956
$790$	−35.6815	−1.26949
$791$	−3.43822	−0.122249
$792$	377.573	13.4165
$793$	67.2734	2.38895
$794$	58.2150	2.06597
$795$	−11.5601	−0.409993
$796$	65.2118	2.31137
$797$	43.8883	1.55460	0.777302	−	0.629127i	$-0.216588\pi$
$797$	43.8883	1.55460	0.777302	+	0.629127i	$0.216588\pi$
$798$	−35.4361	−1.25442
$799$	−6.57431	−0.232582
$800$	109.667	3.87731
$801$	51.6363	1.82448
$802$	−55.4754	−1.95891
$803$	−51.0618	−1.80193
$804$	−290.400	−10.2416
$805$	−0.722543	−0.0254663
$806$	−128.292	−4.51890
$807$	37.4427	1.31805
$808$	140.993	4.96011
$809$	22.3272	0.784983	0.392492	−	0.919756i	$-0.371613\pi$
$809$	22.3272	0.784983	0.392492	+	0.919756i	$0.371613\pi$
$810$	−121.214	−4.25904
$811$	−13.3423	−0.468511	−0.234255	−	0.972175i	$-0.575265\pi$
$811$	−13.3423	−0.468511	−0.234255	+	0.972175i	$0.575265\pi$
$812$	36.2724	1.27291
$813$	40.5434	1.42192
$814$	−60.2366	−2.11129
$815$	−13.9651	−0.489174
$816$	118.148	4.13601
$817$	−2.92254	−0.102247
$818$	13.1511	0.459816
$819$	35.6096	1.24430
$820$	24.3535	0.850461
$821$	−28.6676	−1.00051	−0.500253	−	0.865879i	$-0.666760\pi$
$821$	−28.6676	−1.00051	−0.500253	+	0.865879i	$0.666760\pi$
$822$	−66.7020	−2.32650
$823$	3.86258	0.134641	0.0673205	−	0.997731i	$-0.478555\pi$
$823$	3.86258	0.134641	0.0673205	+	0.997731i	$0.478555\pi$
$824$	−18.7720	−0.653955
$825$	55.0634	1.91706
$826$	26.5333	0.923210
$827$	33.4560	1.16338	0.581690	−	0.813411i	$-0.302392\pi$
$827$	33.4560	1.16338	0.581690	+	0.813411i	$0.302392\pi$
$828$	38.4133	1.33496
$829$	−48.7489	−1.69312	−0.846560	−	0.532293i	$-0.821331\pi$
$829$	−48.7489	−1.69312	−0.846560	+	0.532293i	$0.821331\pi$
$830$	−6.58974	−0.228733
$831$	62.2680	2.16005
$832$	−194.420	−6.74030
$833$	−12.0965	−0.419120
$834$	60.9884	2.11185
$835$	−21.1739	−0.732753
$836$	97.5478	3.37376
$837$	−201.868	−6.97757
$838$	90.6523	3.13153
$839$	2.67966	0.0925120	0.0462560	−	0.998930i	$-0.485271\pi$
$839$	2.67966	0.0925120	0.0462560	+	0.998930i	$0.485271\pi$
$840$	34.0091	1.17342
$841$	19.7592	0.681351
$842$	10.3176	0.355567
$843$	−111.361	−3.83548
$844$	35.3340	1.21625
$845$	7.66889	0.263818
$846$	81.9940	2.81901
$847$	−5.40375	−0.185675
$848$	−56.5347	−1.94141
$849$	−3.82070	−0.131126
$850$	21.2193	0.727815
$851$	−3.99894	−0.137082
$852$	26.2963	0.900896
$853$	−13.2267	−0.452872	−0.226436	−	0.974026i	$-0.572707\pi$
$853$	−13.2267	−0.452872	−0.226436	+	0.974026i	$0.572707\pi$
$854$	−37.5279	−1.28418
$855$	−37.8349	−1.29393
$856$	29.0263	0.992099
$857$	−22.9797	−0.784970	−0.392485	−	0.919758i	$-0.628385\pi$
$857$	−22.9797	−0.784970	−0.392485	+	0.919758i	$0.628385\pi$
$858$	−177.332	−6.05402
$859$	−8.48226	−0.289411	−0.144705	−	0.989475i	$-0.546223\pi$
$859$	−8.48226	−0.289411	−0.144705	+	0.989475i	$0.546223\pi$
$860$	4.29839	0.146574
$861$	−12.4617	−0.424694
$862$	−3.36144	−0.114491
$863$	−6.20551	−0.211238	−0.105619	−	0.994407i	$-0.533682\pi$
$863$	−6.20551	−0.211238	−0.105619	+	0.994407i	$0.533682\pi$
$864$	−555.733	−18.9064
$865$	13.0312	0.443076
$866$	−29.6844	−1.00872
$867$	−45.1787	−1.53435
$868$	53.1120	1.80274
$869$	−50.2610	−1.70499
$870$	70.0603	2.37527
$871$	66.2911	2.24619
$872$	−9.72749	−0.329415
$873$	88.7856	3.00494
$874$	8.72608	0.295164
$875$	8.43519	0.285162
$876$	244.517	8.26145
$877$	0.866805	0.0292699	0.0146350	−	0.999893i	$-0.495341\pi$
$877$	0.866805	0.0292699	0.0146350	+	0.999893i	$0.495341\pi$
$878$	−27.0954	−0.914427
$879$	72.6615	2.45081
$880$	−76.2977	−2.57200
$881$	50.1041	1.68805	0.844026	−	0.536303i	$-0.180180\pi$
$881$	50.1041	1.68805	0.844026	+	0.536303i	$0.180180\pi$
$882$	150.866	5.07993
$883$	−29.9926	−1.00933	−0.504666	−	0.863315i	$-0.668384\pi$
$883$	−29.9926	−1.00933	−0.504666	+	0.863315i	$0.668384\pi$
$884$	−50.7151	−1.70573
$885$	38.0336	1.27849
$886$	8.09687	0.272020
$887$	36.8943	1.23879	0.619394	−	0.785080i	$-0.287378\pi$
$887$	36.8943	1.23879	0.619394	+	0.785080i	$0.287378\pi$
$888$	188.224	6.31639
$889$	14.1910	0.475950
$890$	−17.2520	−0.578287
$891$	−170.743	−5.72009
$892$	132.014	4.42015
$893$	13.8230	0.462568
$894$	−64.4431	−2.15530
$895$	6.06060	0.202583
$896$	57.6506	1.92597
$897$	−11.7726	−0.393074
$898$	60.3455	2.01376
$899$	71.3958	2.38118
$900$	−196.401	−6.54671
$901$	−6.27503	−0.209052
$902$	46.2240	1.53909
$903$	−2.19949	−0.0731945
$904$	−39.8509	−1.32542
$905$	6.74121	0.224085
$906$	51.0028	1.69445
$907$	−33.5309	−1.11337	−0.556687	−	0.830722i	$-0.687928\pi$
$907$	−33.5309	−1.11337	−0.556687	+	0.830722i	$0.687928\pi$
$908$	−52.2333	−1.73342
$909$	−118.048	−3.91539
$910$	−11.8974	−0.394394
$911$	−28.6629	−0.949643	−0.474822	−	0.880082i	$-0.657487\pi$
$911$	−28.6629	−0.949643	−0.474822	+	0.880082i	$0.657487\pi$
$912$	−248.415	−8.22584
$913$	−9.28231	−0.307200
$914$	114.226	3.77827
$915$	−53.7937	−1.77836
$916$	−172.232	−5.69070
$917$	−7.46222	−0.246424
$918$	−107.528	−3.54895
$919$	5.98047	0.197278	0.0986388	−	0.995123i	$-0.468551\pi$
$919$	5.98047	0.197278	0.0986388	+	0.995123i	$0.468551\pi$
$920$	−8.37468	−0.276105
$921$	−1.03789	−0.0341997
$922$	59.5553	1.96135
$923$	−6.00278	−0.197584
$924$	73.4142	2.41515
$925$	20.4459	0.672258
$926$	−104.584	−3.43686
$927$	15.7171	0.516216
$928$	196.550	6.45206
$929$	33.7320	1.10671	0.553356	−	0.832945i	$-0.313347\pi$
$929$	33.7320	1.10671	0.553356	+	0.832945i	$0.313347\pi$
$930$	102.586	3.36393
$931$	25.4338	0.833559
$932$	55.2290	1.80909
$933$	−87.9382	−2.87897
$934$	39.2106	1.28301
$935$	−8.46862	−0.276954
$936$	412.735	13.4907
$937$	24.4862	0.799928	0.399964	−	0.916531i	$-0.369023\pi$
$937$	24.4862	0.799928	0.399964	+	0.916531i	$0.369023\pi$
$938$	−36.9799	−1.20744
$939$	−54.9394	−1.79288
$940$	−20.3305	−0.663107
$941$	10.3742	0.338190	0.169095	−	0.985600i	$-0.445916\pi$
$941$	10.3742	0.338190	0.169095	+	0.985600i	$0.445916\pi$
$942$	155.342	5.06132
$943$	3.06868	0.0999298
$944$	186.004	6.05392
$945$	−18.7205	−0.608978
$946$	8.15854	0.265257
$947$	12.8892	0.418842	0.209421	−	0.977826i	$-0.432842\pi$
$947$	12.8892	0.418842	0.209421	+	0.977826i	$0.432842\pi$
$948$	240.682	7.81699
$949$	−55.8171	−1.81190
$950$	−44.6151	−1.44750
$951$	46.5718	1.51019
$952$	18.4608	0.598318
$953$	−41.5929	−1.34733	−0.673663	−	0.739039i	$-0.735280\pi$
$953$	−41.5929	−1.34733	−0.673663	+	0.739039i	$0.735280\pi$
$954$	78.2614	2.53381
$955$	12.0955	0.391401
$956$	15.9613	0.516225
$957$	98.6869	3.19010
$958$	50.9644	1.64658
$959$	−6.30362	−0.203554
$960$	155.464	5.01757
$961$	73.5415	2.37231
$962$	−65.8463	−2.12297
$963$	−24.3026	−0.783139
$964$	67.8599	2.18562
$965$	3.47374	0.111824
$966$	6.56722	0.211297
$967$	−36.2948	−1.16716	−0.583581	−	0.812055i	$-0.698349\pi$
$967$	−36.2948	−1.16716	−0.583581	+	0.812055i	$0.698349\pi$
$968$	−62.6325	−2.01308
$969$	−27.5727	−0.885761
$970$	−29.6637	−0.952445
$971$	41.5808	1.33439	0.667195	−	0.744883i	$-0.267495\pi$
$971$	41.5808	1.33439	0.667195	+	0.744883i	$0.267495\pi$
$972$	476.699	15.2901
$973$	5.76366	0.184774
$974$	7.59844	0.243470
$975$	60.1912	1.92766
$976$	−263.079	−8.42095
$977$	−29.4193	−0.941208	−0.470604	−	0.882344i	$-0.655964\pi$
$977$	−29.4193	−0.941208	−0.470604	+	0.882344i	$0.655964\pi$
$978$	126.929	4.05874
$979$	−24.3011	−0.776667
$980$	−37.4074	−1.19494
$981$	8.14444	0.260032
$982$	77.2888	2.46639
$983$	0.0471544	0.00150399	0.000751996	−	1.00000i	$-0.499761\pi$
$983$	0.0471544	0.00150399	0.000751996		1.00000i	$0.499761\pi$
$984$	−144.438	−4.60452
$985$	9.95723	0.317264
$986$	38.0301	1.21113
$987$	10.4031	0.331135
$988$	106.632	3.39242
$989$	0.541622	0.0172226
$990$	105.620	3.35681
$991$	−55.9549	−1.77746	−0.888732	−	0.458427i	$-0.848413\pi$
$991$	−55.9549	−1.77746	−0.888732	+	0.458427i	$0.848413\pi$
$992$	287.798	9.13761
$993$	−21.7862	−0.691363
$994$	3.34860	0.106211
$995$	11.9034	0.377364
$996$	44.4496	1.40844
$997$	−17.8305	−0.564696	−0.282348	−	0.959312i	$-0.591113\pi$
$997$	−17.8305	−0.564696	−0.282348	+	0.959312i	$0.591113\pi$
$998$	55.6552	1.76173
$999$	−103.609	−3.27805

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.1	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.1	✓	149	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:	\( N \)	\(=\)	\( 4019 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4019.a (trivial)

\(f(q)\)	\(=\)	\(q-2.78495 q^{2} +3.42897 q^{3} +5.75594 q^{4} +1.05066 q^{5} -9.54951 q^{6} -0.902468 q^{7} -10.4601 q^{8} +8.75783 q^{9} +O(q^{10})\)	\(q-2.78495 q^{2} +3.42897 q^{3} +5.75594 q^{4} +1.05066 q^{5} -9.54951 q^{6} -0.902468 q^{7} -10.4601 q^{8} +8.75783 q^{9} -2.92604 q^{10} -4.12162 q^{11} +19.7370 q^{12} -4.50545 q^{13} +2.51333 q^{14} +3.60269 q^{15} +17.6190 q^{16} +1.95561 q^{17} -24.3901 q^{18} -4.11181 q^{19} +6.04755 q^{20} -3.09454 q^{21} +11.4785 q^{22} +0.762025 q^{23} -35.8674 q^{24} -3.89611 q^{25} +12.5475 q^{26} +19.7434 q^{27} -5.19456 q^{28} -6.98278 q^{29} -10.0333 q^{30} -10.2246 q^{31} -28.1478 q^{32} -14.1329 q^{33} -5.44627 q^{34} -0.948189 q^{35} +50.4096 q^{36} -5.24778 q^{37} +11.4512 q^{38} -15.4491 q^{39} -10.9900 q^{40} +4.02700 q^{41} +8.61813 q^{42} +0.710767 q^{43} -23.7238 q^{44} +9.20151 q^{45} -2.12220 q^{46} -3.36177 q^{47} +60.4150 q^{48} -6.18555 q^{49} +10.8505 q^{50} +6.70572 q^{51} -25.9331 q^{52} -3.20873 q^{53} -54.9844 q^{54} -4.33043 q^{55} +9.43992 q^{56} -14.0993 q^{57} +19.4467 q^{58} +10.5570 q^{59} +20.7369 q^{60} -14.9315 q^{61} +28.4749 q^{62} -7.90366 q^{63} +43.1521 q^{64} -4.73371 q^{65} +39.3594 q^{66} -14.7135 q^{67} +11.2564 q^{68} +2.61296 q^{69} +2.64066 q^{70} +1.33234 q^{71} -91.6079 q^{72} +12.3888 q^{73} +14.6148 q^{74} -13.3596 q^{75} -23.6673 q^{76} +3.71963 q^{77} +43.0248 q^{78} +12.1945 q^{79} +18.5116 q^{80} +41.4261 q^{81} -11.2150 q^{82} +2.25210 q^{83} -17.8120 q^{84} +2.05468 q^{85} -1.97945 q^{86} -23.9437 q^{87} +43.1126 q^{88} +5.89601 q^{89} -25.6258 q^{90} +4.06603 q^{91} +4.38617 q^{92} -35.0597 q^{93} +9.36236 q^{94} -4.32012 q^{95} -96.5179 q^{96} +10.1379 q^{97} +17.2264 q^{98} -36.0964 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9} - 58 q^{10} - 33 q^{11} - 33 q^{12} - 107 q^{13} - 28 q^{14} - 24 q^{15} + 74 q^{16} - 39 q^{17} - 33 q^{18} - 93 q^{19} - 63 q^{20} - 113 q^{21} - 38 q^{22} - 11 q^{23} - 130 q^{24} + 85 q^{25} - 33 q^{26} - 30 q^{27} - 94 q^{28} - 85 q^{29} - 16 q^{30} - 129 q^{31} - 35 q^{32} - 64 q^{33} - 78 q^{34} - 27 q^{35} + 79 q^{36} - 135 q^{37} - 11 q^{38} - 73 q^{39} - 146 q^{40} - 101 q^{41} + 4 q^{42} - 55 q^{43} - 82 q^{44} - 168 q^{45} - 113 q^{46} - 40 q^{47} - 65 q^{48} + 27 q^{49} - 5 q^{50} - 49 q^{51} - 177 q^{52} - 32 q^{53} - 155 q^{54} - 128 q^{55} - 44 q^{56} - 47 q^{57} - 46 q^{58} - 53 q^{59} - 11 q^{60} - 347 q^{61} - 11 q^{62} - 73 q^{63} + q^{64} - 31 q^{65} - 37 q^{66} - 40 q^{67} - 80 q^{68} - 175 q^{69} - 61 q^{70} - 31 q^{71} - 68 q^{72} - 193 q^{73} - 33 q^{74} - 56 q^{75} - 248 q^{76} - 84 q^{77} + 40 q^{78} - 111 q^{79} - 54 q^{80} + 49 q^{81} - 74 q^{82} - 24 q^{83} - 159 q^{84} - 258 q^{85} - q^{86} - 66 q^{87} - 97 q^{88} - 76 q^{89} - 75 q^{90} - 134 q^{91} + 31 q^{92} - 97 q^{93} - 111 q^{94} - 14 q^{95} - 216 q^{96} - 140 q^{97} - 13 q^{98} - 116 q^{99}+O(q^{100}) \) 149 * q - 8 * q^2 - 12 * q^3 + 124 * q^4 - 36 * q^5 - 45 * q^6 - 32 * q^7 - 21 * q^8 + 115 * q^9 - 58 * q^10 - 33 * q^11 - 33 * q^12 - 107 * q^13 - 28 * q^14 - 24 * q^15 + 74 * q^16 - 39 * q^17 - 33 * q^18 - 93 * q^19 - 63 * q^20 - 113 * q^21 - 38 * q^22 - 11 * q^23 - 130 * q^24 + 85 * q^25 - 33 * q^26 - 30 * q^27 - 94 * q^28 - 85 * q^29 - 16 * q^30 - 129 * q^31 - 35 * q^32 - 64 * q^33 - 78 * q^34 - 27 * q^35 + 79 * q^36 - 135 * q^37 - 11 * q^38 - 73 * q^39 - 146 * q^40 - 101 * q^41 + 4 * q^42 - 55 * q^43 - 82 * q^44 - 168 * q^45 - 113 * q^46 - 40 * q^47 - 65 * q^48 + 27 * q^49 - 5 * q^50 - 49 * q^51 - 177 * q^52 - 32 * q^53 - 155 * q^54 - 128 * q^55 - 44 * q^56 - 47 * q^57 - 46 * q^58 - 53 * q^59 - 11 * q^60 - 347 * q^61 - 11 * q^62 - 73 * q^63 + q^64 - 31 * q^65 - 37 * q^66 - 40 * q^67 - 80 * q^68 - 175 * q^69 - 61 * q^70 - 31 * q^71 - 68 * q^72 - 193 * q^73 - 33 * q^74 - 56 * q^75 - 248 * q^76 - 84 * q^77 + 40 * q^78 - 111 * q^79 - 54 * q^80 + 49 * q^81 - 74 * q^82 - 24 * q^83 - 159 * q^84 - 258 * q^85 - q^86 - 66 * q^87 - 97 * q^88 - 76 * q^89 - 75 * q^90 - 134 * q^91 + 31 * q^92 - 97 * q^93 - 111 * q^94 - 14 * q^95 - 216 * q^96 - 140 * q^97 - 13 * q^98 - 116 * q^99

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