LMFDB - Embedded newform 4019.2.a.a.1.14

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			1.14
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)

$f(q)$	$=$	$q-2.40917 q^{2} -3.09144 q^{3} +3.80411 q^{4} -1.16894 q^{5} +7.44782 q^{6} +2.97947 q^{7} -4.34641 q^{8} +6.55703 q^{9} +O(q^{10})$	\(q-2.40917 q^{2} -3.09144 q^{3} +3.80411 q^{4} -1.16894 q^{5} +7.44782 q^{6} +2.97947 q^{7} -4.34641 q^{8} +6.55703 q^{9} +2.81617 q^{10} +0.140001 q^{11} -11.7602 q^{12} -0.561088 q^{13} -7.17805 q^{14} +3.61370 q^{15} +2.86303 q^{16} +5.44713 q^{17} -15.7970 q^{18} +1.19275 q^{19} -4.44677 q^{20} -9.21086 q^{21} -0.337285 q^{22} +8.28516 q^{23} +13.4367 q^{24} -3.63359 q^{25} +1.35176 q^{26} -10.9964 q^{27} +11.3342 q^{28} +5.56771 q^{29} -8.70604 q^{30} -2.18489 q^{31} +1.79529 q^{32} -0.432804 q^{33} -13.1231 q^{34} -3.48281 q^{35} +24.9437 q^{36} -2.29101 q^{37} -2.87355 q^{38} +1.73457 q^{39} +5.08068 q^{40} -4.76180 q^{41} +22.1905 q^{42} -11.6811 q^{43} +0.532577 q^{44} -7.66476 q^{45} -19.9604 q^{46} -8.00197 q^{47} -8.85090 q^{48} +1.87723 q^{49} +8.75393 q^{50} -16.8395 q^{51} -2.13444 q^{52} +6.30714 q^{53} +26.4921 q^{54} -0.163652 q^{55} -12.9500 q^{56} -3.68733 q^{57} -13.4136 q^{58} -12.6031 q^{59} +13.7469 q^{60} -14.5362 q^{61} +5.26376 q^{62} +19.5365 q^{63} -10.0512 q^{64} +0.655877 q^{65} +1.04270 q^{66} +13.9171 q^{67} +20.7215 q^{68} -25.6131 q^{69} +8.39069 q^{70} +3.20244 q^{71} -28.4995 q^{72} -15.3975 q^{73} +5.51945 q^{74} +11.2330 q^{75} +4.53737 q^{76} +0.417127 q^{77} -4.17889 q^{78} +8.90517 q^{79} -3.34670 q^{80} +14.3235 q^{81} +11.4720 q^{82} -12.7261 q^{83} -35.0391 q^{84} -6.36735 q^{85} +28.1418 q^{86} -17.2123 q^{87} -0.608500 q^{88} -3.10902 q^{89} +18.4657 q^{90} -1.67174 q^{91} +31.5177 q^{92} +6.75445 q^{93} +19.2781 q^{94} -1.39426 q^{95} -5.55003 q^{96} +9.06266 q^{97} -4.52257 q^{98} +0.917987 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.40917	−1.70354	−0.851771	−	0.523914i	$-0.824471\pi$
$2$	−2.40917	−1.70354	−0.851771	+	0.523914i	$0.824471\pi$
$3$	−3.09144	−1.78485	−0.892423	−	0.451199i	$-0.850996\pi$
$3$	−3.09144	−1.78485	−0.892423	+	0.451199i	$0.850996\pi$
$4$	3.80411	1.90205
$5$	−1.16894	−0.522765	−0.261382	−	0.965235i	$-0.584178\pi$
$5$	−1.16894	−0.522765	−0.261382	+	0.965235i	$0.584178\pi$
$6$	7.44782	3.04056
$7$	2.97947	1.12613	0.563066	−	0.826412i	$-0.309621\pi$
$7$	2.97947	1.12613	0.563066	+	0.826412i	$0.309621\pi$
$8$	−4.34641	−1.53669
$9$	6.55703	2.18568
$10$	2.81617	0.890551
$11$	0.140001	0.0422117	0.0211059	−	0.999777i	$-0.493281\pi$
$11$	0.140001	0.0422117	0.0211059	+	0.999777i	$0.493281\pi$
$12$	−11.7602	−3.39488
$13$	−0.561088	−0.155618	−0.0778090	−	0.996968i	$-0.524792\pi$
$13$	−0.561088	−0.155618	−0.0778090	+	0.996968i	$0.524792\pi$
$14$	−7.17805	−1.91841
$15$	3.61370	0.933055
$16$	2.86303	0.715758
$17$	5.44713	1.32112	0.660561	−	0.750772i	$-0.270318\pi$
$17$	5.44713	1.32112	0.660561	+	0.750772i	$0.270318\pi$
$18$	−15.7970	−3.72339
$19$	1.19275	0.273637	0.136818	−	0.990596i	$-0.456312\pi$
$19$	1.19275	0.273637	0.136818	+	0.990596i	$0.456312\pi$
$20$	−4.44677	−0.994327
$21$	−9.21086	−2.00997
$22$	−0.337285	−0.0719095
$23$	8.28516	1.72758	0.863788	−	0.503856i	$-0.168086\pi$
$23$	8.28516	1.72758	0.863788	+	0.503856i	$0.168086\pi$
$24$	13.4367	2.74275
$25$	−3.63359	−0.726717
$26$	1.35176	0.265102
$27$	−10.9964	−2.11625
$28$	11.3342	2.14197
$29$	5.56771	1.03390	0.516949	−	0.856016i	$-0.327068\pi$
$29$	5.56771	1.03390	0.516949	+	0.856016i	$0.327068\pi$
$30$	−8.70604	−1.58950
$31$	−2.18489	−0.392417	−0.196208	−	0.980562i	$-0.562863\pi$
$31$	−2.18489	−0.392417	−0.196208	+	0.980562i	$0.562863\pi$
$32$	1.79529	0.317365
$33$	−0.432804	−0.0753415
$34$	−13.1231	−2.25059
$35$	−3.48281	−0.588703
$36$	24.9437	4.15728
$37$	−2.29101	−0.376641	−0.188320	−	0.982108i	$-0.560304\pi$
$37$	−2.29101	−0.376641	−0.188320	+	0.982108i	$0.560304\pi$
$38$	−2.87355	−0.466152
$39$	1.73457	0.277754
$40$	5.08068	0.803326
$41$	−4.76180	−0.743668	−0.371834	−	0.928299i	$-0.621271\pi$
$41$	−4.76180	−0.743668	−0.371834	+	0.928299i	$0.621271\pi$
$42$	22.1905	3.42408
$43$	−11.6811	−1.78135	−0.890676	−	0.454638i	$-0.849769\pi$
$43$	−11.6811	−1.78135	−0.890676	+	0.454638i	$0.849769\pi$
$44$	0.532577	0.0802891
$45$	−7.66476	−1.14259
$46$	−19.9604	−2.94300
$47$	−8.00197	−1.16721	−0.583604	−	0.812039i	$-0.698358\pi$
$47$	−8.00197	−1.16721	−0.583604	+	0.812039i	$0.698358\pi$
$48$	−8.85090	−1.27752
$49$	1.87723	0.268176
$50$	8.75393	1.23799
$51$	−16.8395	−2.35800
$52$	−2.13444	−0.295994
$53$	6.30714	0.866352	0.433176	−	0.901309i	$-0.357393\pi$
$53$	6.30714	0.866352	0.433176	+	0.901309i	$0.357393\pi$
$54$	26.4921	3.60512
$55$	−0.163652	−0.0220668
$56$	−12.9500	−1.73052
$57$	−3.68733	−0.488399
$58$	−13.4136	−1.76129
$59$	−12.6031	−1.64078	−0.820390	−	0.571804i	$-0.806244\pi$
$59$	−12.6031	−1.64078	−0.820390	+	0.571804i	$0.806244\pi$
$60$	13.7469	1.77472
$61$	−14.5362	−1.86117	−0.930587	−	0.366070i	$-0.880703\pi$
$61$	−14.5362	−1.86117	−0.930587	+	0.366070i	$0.880703\pi$
$62$	5.26376	0.668499
$63$	19.5365	2.46136
$64$	−10.0512	−1.25640
$65$	0.655877	0.0813515
$66$	1.04270	0.128347
$67$	13.9171	1.70024	0.850122	−	0.526586i	$-0.176528\pi$
$67$	13.9171	1.70024	0.850122	+	0.526586i	$0.176528\pi$
$68$	20.7215	2.51285
$69$	−25.6131	−3.08346
$70$	8.39069	1.00288
$71$	3.20244	0.380059	0.190030	−	0.981778i	$-0.439142\pi$
$71$	3.20244	0.380059	0.190030	+	0.981778i	$0.439142\pi$
$72$	−28.4995	−3.35870
$73$	−15.3975	−1.80214	−0.901068	−	0.433678i	$-0.857216\pi$
$73$	−15.3975	−1.80214	−0.901068	+	0.433678i	$0.857216\pi$
$74$	5.51945	0.641623
$75$	11.2330	1.29708
$76$	4.53737	0.520472
$77$	0.417127	0.0475360
$78$	−4.17889	−0.473166
$79$	8.90517	1.00191	0.500955	−	0.865473i	$-0.332982\pi$
$79$	8.90517	1.00191	0.500955	+	0.865473i	$0.332982\pi$
$80$	−3.34670	−0.374173
$81$	14.3235	1.59150
$82$	11.4720	1.26687
$83$	−12.7261	−1.39687	−0.698437	−	0.715672i	$-0.746121\pi$
$83$	−12.7261	−1.39687	−0.698437	+	0.715672i	$0.746121\pi$
$84$	−35.0391	−3.82308
$85$	−6.36735	−0.690636
$86$	28.1418	3.03461
$87$	−17.2123	−1.84535
$88$	−0.608500	−0.0648663
$89$	−3.10902	−0.329555	−0.164778	−	0.986331i	$-0.552691\pi$
$89$	−3.10902	−0.329555	−0.164778	+	0.986331i	$0.552691\pi$
$90$	18.4657	1.94646
$91$	−1.67174	−0.175246
$92$	31.5177	3.28594
$93$	6.75445	0.700404
$94$	19.2781	1.98839
$95$	−1.39426	−0.143048
$96$	−5.55003	−0.566447
$97$	9.06266	0.920174	0.460087	−	0.887874i	$-0.347818\pi$
$97$	9.06266	0.920174	0.460087	+	0.887874i	$0.347818\pi$
$98$	−4.52257	−0.456848
$99$	0.917987	0.0922612
$100$	−13.8226	−1.38226
$101$	−14.9260	−1.48519	−0.742597	−	0.669738i	$-0.766406\pi$
$101$	−14.9260	−1.48519	−0.742597	+	0.669738i	$0.766406\pi$
$102$	40.5692	4.01695
$103$	−2.48496	−0.244850	−0.122425	−	0.992478i	$-0.539067\pi$
$103$	−2.48496	−0.244850	−0.122425	+	0.992478i	$0.539067\pi$
$104$	2.43872	0.239136
$105$	10.7669	1.05074
$106$	−15.1950	−1.47587
$107$	19.3052	1.86630	0.933150	−	0.359486i	$-0.117048\pi$
$107$	19.3052	1.86630	0.933150	+	0.359486i	$0.117048\pi$
$108$	−41.8314	−4.02522
$109$	9.16229	0.877588	0.438794	−	0.898588i	$-0.355406\pi$
$109$	9.16229	0.877588	0.438794	+	0.898588i	$0.355406\pi$
$110$	0.394265	0.0375917
$111$	7.08255	0.672245
$112$	8.53031	0.806039
$113$	9.78388	0.920390	0.460195	−	0.887818i	$-0.347780\pi$
$113$	9.78388	0.920390	0.460195	+	0.887818i	$0.347780\pi$
$114$	8.88342	0.832009
$115$	−9.68483	−0.903115
$116$	21.1802	1.96653
$117$	−3.67907	−0.340130
$118$	30.3630	2.79514
$119$	16.2295	1.48776
$120$	−15.7066	−1.43381
$121$	−10.9804	−0.998218
$122$	35.0203	3.17059
$123$	14.7208	1.32733
$124$	−8.31154	−0.746399
$125$	10.0921	0.902667
$126$	−47.0667	−4.19303
$127$	−5.54737	−0.492249	−0.246125	−	0.969238i	$-0.579157\pi$
$127$	−5.54737	−0.492249	−0.246125	+	0.969238i	$0.579157\pi$
$128$	20.6245	1.82297
$129$	36.1115	3.17944
$130$	−1.58012	−0.138586
$131$	5.70829	0.498736	0.249368	−	0.968409i	$-0.419777\pi$
$131$	5.70829	0.498736	0.249368	+	0.968409i	$0.419777\pi$
$132$	−1.64643	−0.143304
$133$	3.55377	0.308151
$134$	−33.5287	−2.89644
$135$	12.8541	1.10630
$136$	−23.6755	−2.03015
$137$	7.57947	0.647558	0.323779	−	0.946133i	$-0.395047\pi$
$137$	7.57947	0.647558	0.323779	+	0.946133i	$0.395047\pi$
$138$	61.7064	5.25280
$139$	−6.21002	−0.526727	−0.263363	−	0.964697i	$-0.584832\pi$
$139$	−6.21002	−0.526727	−0.263363	+	0.964697i	$0.584832\pi$
$140$	−13.2490	−1.11974
$141$	24.7376	2.08329
$142$	−7.71522	−0.647447
$143$	−0.0785527	−0.00656890
$144$	18.7730	1.56442
$145$	−6.50830	−0.540485
$146$	37.0951	3.07001
$147$	−5.80335	−0.478652
$148$	−8.71527	−0.716391
$149$	−0.0935781	−0.00766621	−0.00383311	−	0.999993i	$-0.501220\pi$
$149$	−0.0935781	−0.00766621	−0.00383311	+	0.999993i	$0.501220\pi$
$150$	−27.0623	−2.20963
$151$	−20.3783	−1.65836	−0.829181	−	0.558980i	$-0.811193\pi$
$151$	−20.3783	−1.65836	−0.829181	+	0.558980i	$0.811193\pi$
$152$	−5.18420	−0.420494
$153$	35.7170	2.88755
$154$	−1.00493	−0.0809796
$155$	2.55399	0.205142
$156$	6.59851	0.528303
$157$	22.0692	1.76132	0.880658	−	0.473752i	$-0.157101\pi$
$157$	22.0692	1.76132	0.880658	+	0.473752i	$0.157101\pi$
$158$	−21.4541	−1.70679
$159$	−19.4982	−1.54631
$160$	−2.09858	−0.165907
$161$	24.6854	1.94548
$162$	−34.5079	−2.71120
$163$	−10.4483	−0.818374	−0.409187	−	0.912450i	$-0.634188\pi$
$163$	−10.4483	−0.818374	−0.409187	+	0.912450i	$0.634188\pi$
$164$	−18.1144	−1.41450
$165$	0.505921	0.0393859
$166$	30.6594	2.37963
$167$	19.4382	1.50417	0.752085	−	0.659066i	$-0.229048\pi$
$167$	19.4382	1.50417	0.752085	+	0.659066i	$0.229048\pi$
$168$	40.0342	3.08870
$169$	−12.6852	−0.975783
$170$	15.3400	1.17653
$171$	7.82093	0.598081
$172$	−44.4362	−3.38823
$173$	−12.7468	−0.969121	−0.484561	−	0.874758i	$-0.661021\pi$
$173$	−12.7468	−0.969121	−0.484561	+	0.874758i	$0.661021\pi$
$174$	41.4673	3.14363
$175$	−10.8262	−0.818380
$176$	0.400826	0.0302134
$177$	38.9617	2.92854
$178$	7.49016	0.561411
$179$	−23.1894	−1.73325	−0.866627	−	0.498957i	$-0.833717\pi$
$179$	−23.1894	−1.73325	−0.866627	+	0.498957i	$0.833717\pi$
$180$	−29.1576	−2.17328
$181$	−5.61933	−0.417682	−0.208841	−	0.977950i	$-0.566969\pi$
$181$	−5.61933	−0.417682	−0.208841	+	0.977950i	$0.566969\pi$
$182$	4.02752	0.298540
$183$	44.9380	3.32191
$184$	−36.0107	−2.65474
$185$	2.67805	0.196894
$186$	−16.2726	−1.19317
$187$	0.762601	0.0557669
$188$	−30.4404	−2.22009
$189$	−32.7633	−2.38318
$190$	3.35900	0.243688
$191$	−5.87880	−0.425375	−0.212687	−	0.977120i	$-0.568222\pi$
$191$	−5.87880	−0.425375	−0.212687	+	0.977120i	$0.568222\pi$
$192$	31.0728	2.24248
$193$	−18.7758	−1.35151	−0.675757	−	0.737124i	$-0.736183\pi$
$193$	−18.7758	−1.35151	−0.675757	+	0.737124i	$0.736183\pi$
$194$	−21.8335	−1.56755
$195$	−2.02761	−0.145200
$196$	7.14118	0.510085
$197$	−23.4362	−1.66976	−0.834879	−	0.550433i	$-0.814463\pi$
$197$	−23.4362	−1.66976	−0.834879	+	0.550433i	$0.814463\pi$
$198$	−2.21159	−0.157171
$199$	12.6502	0.896746	0.448373	−	0.893847i	$-0.352004\pi$
$199$	12.6502	0.896746	0.448373	+	0.893847i	$0.352004\pi$
$200$	15.7931	1.11674
$201$	−43.0239	−3.03467
$202$	35.9594	2.53009
$203$	16.5888	1.16431
$204$	−64.0593	−4.48505
$205$	5.56624	0.388763
$206$	5.98669	0.417113
$207$	54.3260	3.77592
$208$	−1.60641	−0.111385
$209$	0.166986	0.0115507
$210$	−25.9394	−1.78999
$211$	−0.0853785	−0.00587770	−0.00293885	−	0.999996i	$-0.500935\pi$
$211$	−0.0853785	−0.00587770	−0.00293885	+	0.999996i	$0.500935\pi$
$212$	23.9930	1.64785
$213$	−9.90015	−0.678347
$214$	−46.5095	−3.17932
$215$	13.6545	0.931228
$216$	47.7947	3.25202
$217$	−6.50980	−0.441914
$218$	−22.0735	−1.49501
$219$	47.6004	3.21654
$220$	−0.622550	−0.0419723
$221$	−3.05632	−0.205590
$222$	−17.0631	−1.14520
$223$	10.6605	0.713877	0.356938	−	0.934128i	$-0.383821\pi$
$223$	10.6605	0.713877	0.356938	+	0.934128i	$0.383821\pi$
$224$	5.34900	0.357395
$225$	−23.8255	−1.58837
$226$	−23.5710	−1.56792
$227$	−9.76908	−0.648397	−0.324198	−	0.945989i	$-0.605095\pi$
$227$	−9.76908	−0.648397	−0.324198	+	0.945989i	$0.605095\pi$
$228$	−14.0270	−0.928963
$229$	−6.29747	−0.416148	−0.208074	−	0.978113i	$-0.566720\pi$
$229$	−6.29747	−0.416148	−0.208074	+	0.978113i	$0.566720\pi$
$230$	23.3324	1.53849
$231$	−1.28953	−0.0848445
$232$	−24.1996	−1.58878
$233$	−4.75857	−0.311744	−0.155872	−	0.987777i	$-0.549819\pi$
$233$	−4.75857	−0.311744	−0.155872	+	0.987777i	$0.549819\pi$
$234$	8.86352	0.579426
$235$	9.35380	0.610175
$236$	−47.9435	−3.12085
$237$	−27.5298	−1.78825
$238$	−39.0998	−2.53446
$239$	27.1950	1.75910	0.879548	−	0.475810i	$-0.157845\pi$
$239$	27.1950	1.75910	0.879548	+	0.475810i	$0.157845\pi$
$240$	10.3462	0.667841
$241$	7.69410	0.495621	0.247810	−	0.968809i	$-0.420289\pi$
$241$	7.69410	0.495621	0.247810	+	0.968809i	$0.420289\pi$
$242$	26.4537	1.70051
$243$	−11.2914	−0.724342
$244$	−55.2974	−3.54006
$245$	−2.19436	−0.140193
$246$	−35.4650	−2.26117
$247$	−0.669241	−0.0425828
$248$	9.49641	0.603023
$249$	39.3421	2.49320
$250$	−24.3137	−1.53773
$251$	17.7046	1.11750	0.558751	−	0.829336i	$-0.311281\pi$
$251$	17.7046	1.11750	0.558751	+	0.829336i	$0.311281\pi$
$252$	74.3188	4.68165
$253$	1.15993	0.0729240
$254$	13.3646	0.838567
$255$	19.6843	1.23268
$256$	−29.5856	−1.84910
$257$	8.22502	0.513063	0.256531	−	0.966536i	$-0.417420\pi$
$257$	8.22502	0.513063	0.256531	+	0.966536i	$0.417420\pi$
$258$	−86.9988	−5.41631
$259$	−6.82601	−0.424147
$260$	2.49503	0.154735
$261$	36.5076	2.25977
$262$	−13.7523	−0.849617
$263$	9.06455	0.558944	0.279472	−	0.960154i	$-0.409841\pi$
$263$	9.06455	0.558944	0.279472	+	0.960154i	$0.409841\pi$
$264$	1.88114	0.115776
$265$	−7.37265	−0.452898
$266$	−8.56165	−0.524949
$267$	9.61136	0.588206
$268$	52.9421	3.23396
$269$	−8.66728	−0.528454	−0.264227	−	0.964461i	$-0.585117\pi$
$269$	−8.66728	−0.528454	−0.264227	+	0.964461i	$0.585117\pi$
$270$	−30.9676	−1.88463
$271$	−8.92651	−0.542247	−0.271123	−	0.962545i	$-0.587395\pi$
$271$	−8.92651	−0.542247	−0.271123	+	0.962545i	$0.587395\pi$
$272$	15.5953	0.945604
$273$	5.16811	0.312788
$274$	−18.2602	−1.10314
$275$	−0.508704	−0.0306760
$276$	−97.4351	−5.86490
$277$	13.0327	0.783058	0.391529	−	0.920166i	$-0.371946\pi$
$277$	13.0327	0.783058	0.391529	+	0.920166i	$0.371946\pi$
$278$	14.9610	0.897301
$279$	−14.3264	−0.857697
$280$	15.1377	0.904652
$281$	−13.1287	−0.783195	−0.391598	−	0.920137i	$-0.628077\pi$
$281$	−13.1287	−0.783195	−0.391598	+	0.920137i	$0.628077\pi$
$282$	−59.5972	−3.54896
$283$	−21.0993	−1.25422	−0.627112	−	0.778929i	$-0.715763\pi$
$283$	−21.0993	−1.25422	−0.627112	+	0.778929i	$0.715763\pi$
$284$	12.1824	0.722893
$285$	4.31026	0.255318
$286$	0.189247	0.0111904
$287$	−14.1876	−0.837469
$288$	11.7717	0.693657
$289$	12.6712	0.745365
$290$	15.6796	0.920739
$291$	−28.0167	−1.64237
$292$	−58.5736	−3.42776
$293$	−25.7499	−1.50432	−0.752162	−	0.658978i	$-0.770989\pi$
$293$	−25.7499	−1.50432	−0.752162	+	0.658978i	$0.770989\pi$
$294$	13.9813	0.815404
$295$	14.7322	0.857742
$296$	9.95769	0.578779
$297$	−1.53950	−0.0893306
$298$	0.225446	0.0130597
$299$	−4.64871	−0.268842
$300$	42.7317	2.46711
$301$	−34.8035	−2.00604
$302$	49.0948	2.82509
$303$	46.1430	2.65084
$304$	3.41489	0.195858
$305$	16.9919	0.972956
$306$	−86.0483	−4.91906
$307$	−20.2011	−1.15294	−0.576470	−	0.817119i	$-0.695570\pi$
$307$	−20.2011	−1.15294	−0.576470	+	0.817119i	$0.695570\pi$
$308$	1.58680	0.0904161
$309$	7.68211	0.437020
$310$	−6.15301	−0.349468
$311$	−8.01805	−0.454662	−0.227331	−	0.973818i	$-0.573000\pi$
$311$	−8.01805	−0.454662	−0.227331	+	0.973818i	$0.573000\pi$
$312$	−7.53917	−0.426821
$313$	−12.8682	−0.727352	−0.363676	−	0.931526i	$-0.618478\pi$
$313$	−12.8682	−0.727352	−0.363676	+	0.931526i	$0.618478\pi$
$314$	−53.1686	−3.00048
$315$	−22.8369	−1.28671
$316$	33.8762	1.90569
$317$	−7.95612	−0.446860	−0.223430	−	0.974720i	$-0.571725\pi$
$317$	−7.95612	−0.446860	−0.223430	+	0.974720i	$0.571725\pi$
$318$	46.9744	2.63420
$319$	0.779482	0.0436426
$320$	11.7492	0.656803
$321$	−59.6808	−3.33106
$322$	−59.4713	−3.31421
$323$	6.49709	0.361508
$324$	54.4883	3.02713
$325$	2.03876	0.113090
$326$	25.1718	1.39414
$327$	−28.3247	−1.56636
$328$	20.6967	1.14279
$329$	−23.8416	−1.31443
$330$	−1.21885	−0.0670955
$331$	−23.7197	−1.30375	−0.651876	−	0.758325i	$-0.726018\pi$
$331$	−23.7197	−1.30375	−0.651876	+	0.758325i	$0.726018\pi$
$332$	−48.4116	−2.65693
$333$	−15.0223	−0.823214
$334$	−46.8299	−2.56242
$335$	−16.2682	−0.888827
$336$	−26.3710	−1.43865
$337$	4.09980	0.223330	0.111665	−	0.993746i	$-0.464382\pi$
$337$	4.09980	0.223330	0.111665	+	0.993746i	$0.464382\pi$
$338$	30.5608	1.66229
$339$	−30.2463	−1.64275
$340$	−24.2221	−1.31363
$341$	−0.305885	−0.0165646
$342$	−18.8420	−1.01886
$343$	−15.2631	−0.824132
$344$	50.7709	2.73738
$345$	29.9401	1.61192
$346$	30.7092	1.65094
$347$	17.5720	0.943315	0.471658	−	0.881782i	$-0.343656\pi$
$347$	17.5720	0.943315	0.471658	+	0.881782i	$0.343656\pi$
$348$	−65.4773	−3.50995
$349$	25.3345	1.35612	0.678062	−	0.735005i	$-0.262820\pi$
$349$	25.3345	1.35612	0.678062	+	0.735005i	$0.262820\pi$
$350$	26.0821	1.39414
$351$	6.16993	0.329326
$352$	0.251341	0.0133965
$353$	10.6378	0.566194	0.283097	−	0.959091i	$-0.408638\pi$
$353$	10.6378	0.566194	0.283097	+	0.959091i	$0.408638\pi$
$354$	−93.8654	−4.98889
$355$	−3.74345	−0.198682
$356$	−11.8271	−0.626832
$357$	−50.1727	−2.65542
$358$	55.8671	2.95267
$359$	−8.34432	−0.440396	−0.220198	−	0.975455i	$-0.570670\pi$
$359$	−8.34432	−0.440396	−0.220198	+	0.975455i	$0.570670\pi$
$360$	33.3142	1.75581
$361$	−17.5773	−0.925123
$362$	13.5379	0.711539
$363$	33.9453	1.78167
$364$	−6.35950	−0.333328
$365$	17.9987	0.942093
$366$	−108.263	−5.65901
$367$	21.6582	1.13055	0.565274	−	0.824904i	$-0.308771\pi$
$367$	21.6582	1.13055	0.565274	+	0.824904i	$0.308771\pi$
$368$	23.7207	1.23653
$369$	−31.2232	−1.62542
$370$	−6.45189	−0.335418
$371$	18.7919	0.975628
$372$	25.6947	1.33221
$373$	17.4260	0.902284	0.451142	−	0.892452i	$-0.351017\pi$
$373$	17.4260	0.902284	0.451142	+	0.892452i	$0.351017\pi$
$374$	−1.83724	−0.0950012
$375$	−31.1992	−1.61112
$376$	34.7798	1.79363
$377$	−3.12398	−0.160893
$378$	78.9324	4.05985
$379$	11.5970	0.595696	0.297848	−	0.954613i	$-0.403731\pi$
$379$	11.5970	0.595696	0.297848	+	0.954613i	$0.403731\pi$
$380$	−5.30390	−0.272084
$381$	17.1494	0.878590
$382$	14.1630	0.724644
$383$	5.72162	0.292361	0.146180	−	0.989258i	$-0.453302\pi$
$383$	5.72162	0.292361	0.146180	+	0.989258i	$0.453302\pi$
$384$	−63.7596	−3.25372
$385$	−0.487595	−0.0248502
$386$	45.2342	2.30236
$387$	−76.5934	−3.89346
$388$	34.4753	1.75022
$389$	1.49287	0.0756914	0.0378457	−	0.999284i	$-0.487950\pi$
$389$	1.49287	0.0756914	0.0378457	+	0.999284i	$0.487950\pi$
$390$	4.88486	0.247354
$391$	45.1303	2.28234
$392$	−8.15921	−0.412102
$393$	−17.6469	−0.890166
$394$	56.4618	2.84450
$395$	−10.4096	−0.523763
$396$	3.49212	0.175486
$397$	22.1439	1.11137	0.555685	−	0.831393i	$-0.312456\pi$
$397$	22.1439	1.11137	0.555685	+	0.831393i	$0.312456\pi$
$398$	−30.4764	−1.52764
$399$	−10.9863	−0.550003
$400$	−10.4031	−0.520153
$401$	23.6457	1.18081	0.590405	−	0.807107i	$-0.298968\pi$
$401$	23.6457	1.18081	0.590405	+	0.807107i	$0.298968\pi$
$402$	103.652	5.16969
$403$	1.22591	0.0610671
$404$	−56.7802	−2.82492
$405$	−16.7433	−0.831983
$406$	−39.9653	−1.98344
$407$	−0.320743	−0.0158987
$408$	73.1914	3.62351
$409$	28.8307	1.42559	0.712794	−	0.701374i	$-0.247430\pi$
$409$	28.8307	1.42559	0.712794	+	0.701374i	$0.247430\pi$
$410$	−13.4100	−0.662274
$411$	−23.4315	−1.15579
$412$	−9.45306	−0.465719
$413$	−37.5504	−1.84774
$414$	−130.881	−6.43244
$415$	14.8760	0.730236
$416$	−1.00731	−0.0493876
$417$	19.1979	0.940127
$418$	−0.402299	−0.0196771
$419$	−0.666179	−0.0325450	−0.0162725	−	0.999868i	$-0.505180\pi$
$419$	−0.666179	−0.0325450	−0.0162725	+	0.999868i	$0.505180\pi$
$420$	40.9585	1.99857
$421$	−7.16000	−0.348957	−0.174479	−	0.984661i	$-0.555824\pi$
$421$	−7.16000	−0.348957	−0.174479	+	0.984661i	$0.555824\pi$
$422$	0.205692	0.0100129
$423$	−52.4691	−2.55114
$424$	−27.4134	−1.33131
$425$	−19.7926	−0.960082
$426$	23.8512	1.15559
$427$	−43.3102	−2.09593
$428$	73.4390	3.54981
$429$	0.242841	0.0117245
$430$	−32.8960	−1.58639
$431$	30.3682	1.46278	0.731392	−	0.681957i	$-0.238871\pi$
$431$	30.3682	1.46278	0.731392	+	0.681957i	$0.238871\pi$
$432$	−31.4829	−1.51472
$433$	−7.18941	−0.345501	−0.172750	−	0.984966i	$-0.555265\pi$
$433$	−7.18941	−0.345501	−0.172750	+	0.984966i	$0.555265\pi$
$434$	15.6832	0.752818
$435$	20.1201	0.964683
$436$	34.8543	1.66922
$437$	9.88216	0.472728
$438$	−114.678	−5.47950
$439$	2.26038	0.107882	0.0539411	−	0.998544i	$-0.482822\pi$
$439$	2.26038	0.107882	0.0539411	+	0.998544i	$0.482822\pi$
$440$	0.711298	0.0339098
$441$	12.3090	0.586145
$442$	7.36320	0.350232
$443$	−27.5099	−1.30704	−0.653518	−	0.756911i	$-0.726708\pi$
$443$	−27.5099	−1.30704	−0.653518	+	0.756911i	$0.726708\pi$
$444$	26.9428	1.27865
$445$	3.63425	0.172280
$446$	−25.6829	−1.21612
$447$	0.289291	0.0136830
$448$	−29.9473	−1.41488
$449$	−38.2726	−1.80619	−0.903097	−	0.429436i	$-0.858712\pi$
$449$	−38.2726	−1.80619	−0.903097	+	0.429436i	$0.858712\pi$
$450$	57.3998	2.70585
$451$	−0.666654	−0.0313915
$452$	37.2189	1.75063
$453$	62.9984	2.95992
$454$	23.5354	1.10457
$455$	1.95416	0.0916127
$456$	16.0267	0.750518
$457$	−36.9275	−1.72739	−0.863697	−	0.504011i	$-0.831857\pi$
$457$	−36.9275	−1.72739	−0.863697	+	0.504011i	$0.831857\pi$
$458$	15.1717	0.708926
$459$	−59.8986	−2.79583
$460$	−36.8422	−1.71778
$461$	−36.0716	−1.68002	−0.840011	−	0.542569i	$-0.817452\pi$
$461$	−36.0716	−1.68002	−0.840011	+	0.542569i	$0.817452\pi$
$462$	3.10669	0.144536
$463$	28.0339	1.30284	0.651422	−	0.758715i	$-0.274173\pi$
$463$	28.0339	1.30284	0.651422	+	0.758715i	$0.274173\pi$
$464$	15.9405	0.740020
$465$	−7.89553	−0.366146
$466$	11.4642	0.531069
$467$	−32.8548	−1.52034	−0.760170	−	0.649724i	$-0.774884\pi$
$467$	−32.8548	−1.52034	−0.760170	+	0.649724i	$0.774884\pi$
$468$	−13.9956	−0.646947
$469$	41.4655	1.91470
$470$	−22.5349	−1.03946
$471$	−68.2258	−3.14368
$472$	54.7781	2.52137
$473$	−1.63536	−0.0751940
$474$	66.3241	3.04637
$475$	−4.33398	−0.198856
$476$	61.7390	2.82980
$477$	41.3561	1.89356
$478$	−65.5173	−2.99669
$479$	27.3955	1.25173	0.625865	−	0.779931i	$-0.284746\pi$
$479$	27.3955	1.25173	0.625865	+	0.779931i	$0.284746\pi$
$480$	6.48763	0.296119
$481$	1.28546	0.0586120
$482$	−18.5364	−0.844310
$483$	−76.3135	−3.47238
$484$	−41.7706	−1.89867
$485$	−10.5937	−0.481034
$486$	27.2028	1.23395
$487$	14.5506	0.659352	0.329676	−	0.944094i	$-0.393061\pi$
$487$	14.5506	0.659352	0.329676	+	0.944094i	$0.393061\pi$
$488$	63.1805	2.86004
$489$	32.3004	1.46067
$490$	5.28660	0.238824
$491$	−16.0124	−0.722631	−0.361316	−	0.932444i	$-0.617672\pi$
$491$	−16.0124	−0.722631	−0.361316	+	0.932444i	$0.617672\pi$
$492$	55.9997	2.52466
$493$	30.3280	1.36591
$494$	1.61232	0.0725415
$495$	−1.07307	−0.0482309
$496$	−6.25539	−0.280876
$497$	9.54155	0.427997
$498$	−94.7819	−4.24728
$499$	−40.3930	−1.80824	−0.904119	−	0.427281i	$-0.859472\pi$
$499$	−40.3930	−1.80824	−0.904119	+	0.427281i	$0.859472\pi$
$500$	38.3915	1.71692
$501$	−60.0920	−2.68471
$502$	−42.6533	−1.90371
$503$	−6.99763	−0.312009	−0.156005	−	0.987756i	$-0.549861\pi$
$503$	−6.99763	−0.312009	−0.156005	+	0.987756i	$0.549861\pi$
$504$	−84.9135	−3.78235
$505$	17.4476	0.776407
$506$	−2.79446	−0.124229
$507$	39.2155	1.74162
$508$	−21.1028	−0.936285
$509$	−29.5107	−1.30804	−0.654019	−	0.756478i	$-0.726918\pi$
$509$	−29.5107	−1.30804	−0.654019	+	0.756478i	$0.726918\pi$
$510$	−47.4229	−2.09992
$511$	−45.8762	−2.02944
$512$	30.0278	1.32705
$513$	−13.1160	−0.579084
$514$	−19.8155	−0.874024
$515$	2.90476	0.127999
$516$	137.372	6.04747
$517$	−1.12028	−0.0492698
$518$	16.4450	0.722553
$519$	39.4060	1.72973
$520$	−2.85071	−0.125012
$521$	−28.3330	−1.24129	−0.620645	−	0.784092i	$-0.713129\pi$
$521$	−28.3330	−1.24129	−0.620645	+	0.784092i	$0.713129\pi$
$522$	−87.9532	−3.84961
$523$	20.6044	0.900968	0.450484	−	0.892785i	$-0.351251\pi$
$523$	20.6044	0.900968	0.450484	+	0.892785i	$0.351251\pi$
$524$	21.7150	0.948623
$525$	33.4684	1.46068
$526$	−21.8380	−0.952184
$527$	−11.9014	−0.518431
$528$	−1.23913	−0.0539263
$529$	45.6439	1.98452
$530$	17.7620	0.771531
$531$	−82.6387	−3.58621
$532$	13.5189	0.586121
$533$	2.67179	0.115728
$534$	−23.1554	−1.00203
$535$	−22.5665	−0.975636
$536$	−60.4894	−2.61274
$537$	71.6886	3.09359
$538$	20.8810	0.900243
$539$	0.262813	0.0113202
$540$	48.8982	2.10424
$541$	−19.4076	−0.834396	−0.417198	−	0.908816i	$-0.636988\pi$
$541$	−19.4076	−0.834396	−0.417198	+	0.908816i	$0.636988\pi$
$542$	21.5055	0.923740
$543$	17.3719	0.745498
$544$	9.77915	0.419278
$545$	−10.7101	−0.458772
$546$	−12.4509	−0.532847
$547$	−7.83758	−0.335111	−0.167555	−	0.985863i	$-0.553587\pi$
$547$	−7.83758	−0.335111	−0.167555	+	0.985863i	$0.553587\pi$
$548$	28.8331	1.23169
$549$	−95.3145	−4.06792
$550$	1.22556	0.0522578
$551$	6.64091	0.282912
$552$	111.325	4.73831
$553$	26.5327	1.12828
$554$	−31.3980	−1.33397
$555$	−8.27905	−0.351426
$556$	−23.6236	−1.00186
$557$	−25.2671	−1.07060	−0.535302	−	0.844661i	$-0.679802\pi$
$557$	−25.2671	−1.07060	−0.535302	+	0.844661i	$0.679802\pi$
$558$	34.5147	1.46112
$559$	6.55413	0.277210
$560$	−9.97140	−0.421368
$561$	−2.35754	−0.0995353
$562$	31.6294	1.33421
$563$	32.6743	1.37706	0.688528	−	0.725210i	$-0.258257\pi$
$563$	32.6743	1.37706	0.688528	+	0.725210i	$0.258257\pi$
$564$	94.1047	3.96252
$565$	−11.4367	−0.481147
$566$	50.8318	2.13662
$567$	42.6765	1.79225
$568$	−13.9191	−0.584032
$569$	34.5990	1.45046	0.725232	−	0.688505i	$-0.241733\pi$
$569$	34.5990	1.45046	0.725232	+	0.688505i	$0.241733\pi$
$570$	−10.3842	−0.434945
$571$	27.7653	1.16194	0.580972	−	0.813924i	$-0.302673\pi$
$571$	27.7653	1.16194	0.580972	+	0.813924i	$0.302673\pi$
$572$	−0.298823	−0.0124944
$573$	18.1740	0.759229
$574$	34.1804	1.42666
$575$	−30.1048	−1.25546
$576$	−65.9061	−2.74609
$577$	−16.5939	−0.690811	−0.345406	−	0.938453i	$-0.612259\pi$
$577$	−16.5939	−0.690811	−0.345406	+	0.938453i	$0.612259\pi$
$578$	−30.5271	−1.26976
$579$	58.0445	2.41225
$580$	−24.7583	−1.02803
$581$	−37.9171	−1.57306
$582$	67.4971	2.79784
$583$	0.883002	0.0365702
$584$	66.9237	2.76932
$585$	4.30061	0.177808
$586$	62.0359	2.56268
$587$	−13.9850	−0.577222	−0.288611	−	0.957446i	$-0.593193\pi$
$587$	−13.9850	−0.577222	−0.288611	+	0.957446i	$0.593193\pi$
$588$	−22.0766	−0.910423
$589$	−2.60603	−0.107380
$590$	−35.4924	−1.46120
$591$	72.4517	2.98026
$592$	−6.55925	−0.269583
$593$	−35.3577	−1.45197	−0.725984	−	0.687711i	$-0.758616\pi$
$593$	−35.3577	−1.45197	−0.725984	+	0.687711i	$0.758616\pi$
$594$	3.70891	0.152178
$595$	−18.9713	−0.777748
$596$	−0.355981	−0.0145816
$597$	−39.1073	−1.60055
$598$	11.1995	0.457983
$599$	−28.7764	−1.17577	−0.587885	−	0.808944i	$-0.700039\pi$
$599$	−28.7764	−1.17577	−0.587885	+	0.808944i	$0.700039\pi$
$600$	−48.8234	−1.99321
$601$	−30.6466	−1.25010	−0.625050	−	0.780585i	$-0.714921\pi$
$601$	−30.6466	−1.25010	−0.625050	+	0.780585i	$0.714921\pi$
$602$	83.8476	3.41737
$603$	91.2548	3.71618
$604$	−77.5213	−3.15430
$605$	12.8354	0.521833
$606$	−111.166	−4.51582
$607$	−9.75679	−0.396016	−0.198008	−	0.980200i	$-0.563447\pi$
$607$	−9.75679	−0.396016	−0.198008	+	0.980200i	$0.563447\pi$
$608$	2.14134	0.0868426
$609$	−51.2834	−2.07811
$610$	−40.9365	−1.65747
$611$	4.48981	0.181638
$612$	135.871	5.49227
$613$	2.51984	0.101775	0.0508877	−	0.998704i	$-0.483795\pi$
$613$	2.51984	0.101775	0.0508877	+	0.998704i	$0.483795\pi$
$614$	48.6680	1.96408
$615$	−17.2077	−0.693883
$616$	−1.81301	−0.0730481
$617$	0.0972877	0.00391665	0.00195833	−	0.999998i	$-0.499377\pi$
$617$	0.0972877	0.00391665	0.00195833	+	0.999998i	$0.499377\pi$
$618$	−18.5075	−0.744482
$619$	−6.68900	−0.268854	−0.134427	−	0.990924i	$-0.542919\pi$
$619$	−6.68900	−0.268854	−0.134427	+	0.990924i	$0.542919\pi$
$620$	9.71567	0.390191
$621$	−91.1066	−3.65598
$622$	19.3169	0.774536
$623$	−9.26322	−0.371123
$624$	4.96614	0.198805
$625$	6.37087	0.254835
$626$	31.0016	1.23907
$627$	−0.516229	−0.0206162
$628$	83.9538	3.35012
$629$	−12.4795	−0.497588
$630$	55.0180	2.19197
$631$	11.8235	0.470687	0.235344	−	0.971912i	$-0.424378\pi$
$631$	11.8235	0.470687	0.235344	+	0.971912i	$0.424378\pi$
$632$	−38.7055	−1.53962
$633$	0.263943	0.0104908
$634$	19.1677	0.761245
$635$	6.48453	0.257331
$636$	−74.1732	−2.94116
$637$	−1.05329	−0.0417329
$638$	−1.87791	−0.0743470
$639$	20.9985	0.830686
$640$	−24.1088	−0.952984
$641$	8.66958	0.342428	0.171214	−	0.985234i	$-0.445231\pi$
$641$	8.66958	0.342428	0.171214	+	0.985234i	$0.445231\pi$
$642$	143.781	5.67460
$643$	−44.8715	−1.76956	−0.884780	−	0.466008i	$-0.845692\pi$
$643$	−44.8715	−1.76956	−0.884780	+	0.466008i	$0.845692\pi$
$644$	93.9059	3.70041
$645$	−42.2121	−1.66210
$646$	−15.6526	−0.615843
$647$	43.9430	1.72758	0.863789	−	0.503855i	$-0.168085\pi$
$647$	43.9430	1.72758	0.863789	+	0.503855i	$0.168085\pi$
$648$	−62.2560	−2.44565
$649$	−1.76444	−0.0692602
$650$	−4.91173	−0.192654
$651$	20.1247	0.788748
$652$	−39.7465	−1.55659
$653$	17.7844	0.695959	0.347979	−	0.937502i	$-0.386868\pi$
$653$	17.7844	0.695959	0.347979	+	0.937502i	$0.386868\pi$
$654$	68.2391	2.66836
$655$	−6.67263	−0.260721
$656$	−13.6332	−0.532286
$657$	−100.962	−3.93889
$658$	57.4385	2.23919
$659$	26.7232	1.04099	0.520494	−	0.853865i	$-0.325748\pi$
$659$	26.7232	1.04099	0.520494	+	0.853865i	$0.325748\pi$
$660$	1.92458	0.0749141
$661$	−47.2199	−1.83664	−0.918321	−	0.395836i	$-0.870455\pi$
$661$	−47.2199	−1.83664	−0.918321	+	0.395836i	$0.870455\pi$
$662$	57.1448	2.22100
$663$	9.44844	0.366947
$664$	55.3129	2.14656
$665$	−4.15414	−0.161091
$666$	36.1912	1.40238
$667$	46.1294	1.78614
$668$	73.9449	2.86101
$669$	−32.9562	−1.27416
$670$	39.1929	1.51415
$671$	−2.03508	−0.0785634
$672$	−16.5361	−0.637895
$673$	0.137359	0.00529482	0.00264741	−	0.999996i	$-0.499157\pi$
$673$	0.137359	0.00529482	0.00264741	+	0.999996i	$0.499157\pi$
$674$	−9.87712	−0.380452
$675$	39.9562	1.53792
$676$	−48.2558	−1.85599
$677$	−15.0185	−0.577206	−0.288603	−	0.957449i	$-0.593191\pi$
$677$	−15.0185	−0.577206	−0.288603	+	0.957449i	$0.593191\pi$
$678$	72.8686	2.79850
$679$	27.0019	1.03624
$680$	27.6751	1.06129
$681$	30.2006	1.15729
$682$	0.736930	0.0282185
$683$	16.4445	0.629232	0.314616	−	0.949219i	$-0.398124\pi$
$683$	16.4445	0.629232	0.314616	+	0.949219i	$0.398124\pi$
$684$	29.7517	1.13758
$685$	−8.85992	−0.338520
$686$	36.7715	1.40394
$687$	19.4683	0.742761
$688$	−33.4434	−1.27502
$689$	−3.53886	−0.134820
$690$	−72.1309	−2.74598
$691$	27.1107	1.03134	0.515671	−	0.856787i	$-0.327543\pi$
$691$	27.1107	1.03134	0.515671	+	0.856787i	$0.327543\pi$
$692$	−48.4902	−1.84332
$693$	2.73511	0.103898
$694$	−42.3340	−1.60698
$695$	7.25912	0.275354
$696$	74.8116	2.83573
$697$	−25.9381	−0.982476
$698$	−61.0351	−2.31021
$699$	14.7108	0.556415
$700$	−41.1839	−1.55660
$701$	12.6456	0.477617	0.238809	−	0.971067i	$-0.423243\pi$
$701$	12.6456	0.477617	0.238809	+	0.971067i	$0.423243\pi$
$702$	−14.8644	−0.561021
$703$	−2.73262	−0.103063
$704$	−1.40718	−0.0530349
$705$	−28.9168	−1.08907
$706$	−25.6283	−0.964535
$707$	−44.4716	−1.67253
$708$	148.215	5.57025
$709$	24.2567	0.910978	0.455489	−	0.890241i	$-0.349464\pi$
$709$	24.2567	0.910978	0.455489	+	0.890241i	$0.349464\pi$
$710$	9.01861	0.338462
$711$	58.3914	2.18985
$712$	13.5131	0.506424
$713$	−18.1021	−0.677930
$714$	120.875	4.52362
$715$	0.0918231	0.00343399
$716$	−88.2148	−3.29674
$717$	−84.0717	−3.13972
$718$	20.1029	0.750233
$719$	−31.0740	−1.15887	−0.579433	−	0.815020i	$-0.696726\pi$
$719$	−31.0740	−1.15887	−0.579433	+	0.815020i	$0.696726\pi$
$720$	−21.9444	−0.817821
$721$	−7.40386	−0.275734
$722$	42.3468	1.57599
$723$	−23.7859	−0.884607
$724$	−21.3766	−0.794454
$725$	−20.2307	−0.751351
$726$	−81.7801	−3.03514
$727$	42.3511	1.57072	0.785359	−	0.619041i	$-0.212479\pi$
$727$	42.3511	1.57072	0.785359	+	0.619041i	$0.212479\pi$
$728$	7.26609	0.269299
$729$	−8.06400	−0.298667
$730$	−43.3619	−1.60489
$731$	−63.6285	−2.35339
$732$	170.949	6.31846
$733$	−1.33990	−0.0494905	−0.0247453	−	0.999694i	$-0.507877\pi$
$733$	−1.33990	−0.0494905	−0.0247453	+	0.999694i	$0.507877\pi$
$734$	−52.1782	−1.92593
$735$	6.78375	0.250222
$736$	14.8742	0.548272
$737$	1.94840	0.0717702
$738$	75.2222	2.76897
$739$	−25.9730	−0.955434	−0.477717	−	0.878514i	$-0.658536\pi$
$739$	−25.9730	−0.955434	−0.477717	+	0.878514i	$0.658536\pi$
$740$	10.1876	0.374504
$741$	2.06892	0.0760037
$742$	−45.2730	−1.66202
$743$	29.2607	1.07347	0.536736	−	0.843751i	$-0.319657\pi$
$743$	29.2607	1.07347	0.536736	+	0.843751i	$0.319657\pi$
$744$	−29.3576	−1.07630
$745$	0.109387	0.00400763
$746$	−41.9822	−1.53708
$747$	−83.4455	−3.05311
$748$	2.90102	0.106072
$749$	57.5191	2.10170
$750$	75.1643	2.74461
$751$	−19.8835	−0.725561	−0.362780	−	0.931875i	$-0.618173\pi$
$751$	−19.8835	−0.725561	−0.362780	+	0.931875i	$0.618173\pi$
$752$	−22.9099	−0.835438
$753$	−54.7327	−1.99457
$754$	7.52620	0.274088
$755$	23.8210	0.866934
$756$	−124.635	−4.53294
$757$	−17.0281	−0.618896	−0.309448	−	0.950916i	$-0.600144\pi$
$757$	−17.0281	−0.618896	−0.309448	+	0.950916i	$0.600144\pi$
$758$	−27.9391	−1.01479
$759$	−3.58585	−0.130158
$760$	6.06001	0.219820
$761$	−37.9114	−1.37429	−0.687144	−	0.726521i	$-0.741136\pi$
$761$	−37.9114	−1.37429	−0.687144	+	0.726521i	$0.741136\pi$
$762$	−41.3158	−1.49671
$763$	27.2987	0.988281
$764$	−22.3636	−0.809087
$765$	−41.7509	−1.50951
$766$	−13.7844	−0.498049
$767$	7.07144	0.255335
$768$	91.4623	3.30036
$769$	22.7389	0.819984	0.409992	−	0.912089i	$-0.365531\pi$
$769$	22.7389	0.819984	0.409992	+	0.912089i	$0.365531\pi$
$770$	1.17470	0.0423333
$771$	−25.4272	−0.915738
$772$	−71.4254	−2.57066
$773$	22.9707	0.826199	0.413100	−	0.910686i	$-0.364446\pi$
$773$	22.9707	0.826199	0.413100	+	0.910686i	$0.364446\pi$
$774$	184.527	6.63267
$775$	7.93897	0.285176
$776$	−39.3900	−1.41402
$777$	21.1022	0.757038
$778$	−3.59657	−0.128943
$779$	−5.67966	−0.203495
$780$	−7.71324	−0.276178
$781$	0.448343	0.0160430
$782$	−108.727	−3.88806
$783$	−61.2245	−2.18799
$784$	5.37456	0.191949
$785$	−25.7975	−0.920754
$786$	42.5143	1.51644
$787$	23.5818	0.840600	0.420300	−	0.907385i	$-0.361925\pi$
$787$	23.5818	0.840600	0.420300	+	0.907385i	$0.361925\pi$
$788$	−89.1538	−3.17597
$789$	−28.0225	−0.997629
$790$	25.0785	0.892252
$791$	29.1507	1.03648
$792$	−3.98995	−0.141777
$793$	8.15611	0.289632
$794$	−53.3485	−1.89327
$795$	22.7921	0.808354
$796$	48.1226	1.70566
$797$	−26.7648	−0.948059	−0.474029	−	0.880509i	$-0.657201\pi$
$797$	−26.7648	−0.948059	−0.474029	+	0.880509i	$0.657201\pi$
$798$	26.4679	0.936953
$799$	−43.5878	−1.54202
$800$	−6.52333	−0.230634
$801$	−20.3859	−0.720301
$802$	−56.9666	−2.01156
$803$	−2.15565	−0.0760713
$804$	−163.668	−5.77211
$805$	−28.8557	−1.01703
$806$	−2.95344	−0.104030
$807$	26.7944	0.943209
$808$	64.8746	2.28228
$809$	−0.0704379	−0.00247646	−0.00123823	−	0.999999i	$-0.500394\pi$
$809$	−0.0704379	−0.00247646	−0.00123823	+	0.999999i	$0.500394\pi$
$810$	40.3376	1.41732
$811$	40.1428	1.40961	0.704803	−	0.709403i	$-0.251036\pi$
$811$	40.1428	1.40961	0.704803	+	0.709403i	$0.251036\pi$
$812$	63.1057	2.21457
$813$	27.5958	0.967827
$814$	0.772726	0.0270840
$815$	12.2134	0.427817
$816$	−48.2120	−1.68776
$817$	−13.9327	−0.487443
$818$	−69.4582	−2.42855
$819$	−10.9617	−0.383032
$820$	21.1746	0.739449
$821$	−34.8955	−1.21786	−0.608930	−	0.793224i	$-0.708401\pi$
$821$	−34.8955	−1.21786	−0.608930	+	0.793224i	$0.708401\pi$
$822$	56.4505	1.96894
$823$	−1.81198	−0.0631616	−0.0315808	−	0.999501i	$-0.510054\pi$
$823$	−1.81198	−0.0631616	−0.0315808	+	0.999501i	$0.510054\pi$
$824$	10.8007	0.376259
$825$	1.57263	0.0547519
$826$	90.4655	3.14770
$827$	0.754898	0.0262504	0.0131252	−	0.999914i	$-0.495822\pi$
$827$	0.754898	0.0262504	0.0131252	+	0.999914i	$0.495822\pi$
$828$	206.662	7.18201
$829$	13.1153	0.455513	0.227757	−	0.973718i	$-0.426861\pi$
$829$	13.1153	0.455513	0.227757	+	0.973718i	$0.426861\pi$
$830$	−35.8389	−1.24399
$831$	−40.2898	−1.39764
$832$	5.63962	0.195519
$833$	10.2255	0.354293
$834$	−46.2511	−1.60155
$835$	−22.7220	−0.786327
$836$	0.635234	0.0219700
$837$	24.0258	0.830452
$838$	1.60494	0.0554417
$839$	33.7368	1.16472	0.582362	−	0.812930i	$-0.302129\pi$
$839$	33.7368	1.16472	0.582362	+	0.812930i	$0.302129\pi$
$840$	−46.7974	−1.61467
$841$	1.99939	0.0689445
$842$	17.2497	0.594463
$843$	40.5868	1.39788
$844$	−0.324789	−0.0111797
$845$	14.8282	0.510105
$846$	126.407	4.34597
$847$	−32.7157	−1.12413
$848$	18.0575	0.620098
$849$	65.2273	2.23860
$850$	47.6838	1.63554
$851$	−18.9814	−0.650675
$852$	−37.6613	−1.29025
$853$	−21.7972	−0.746323	−0.373161	−	0.927766i	$-0.621726\pi$
$853$	−21.7972	−0.746323	−0.373161	+	0.927766i	$0.621726\pi$
$854$	104.342	3.57050
$855$	−9.14217	−0.312656
$856$	−83.9082	−2.86792
$857$	39.3213	1.34319	0.671595	−	0.740918i	$-0.265609\pi$
$857$	39.3213	1.34319	0.671595	+	0.740918i	$0.265609\pi$
$858$	−0.585046	−0.0199731
$859$	−48.7515	−1.66338	−0.831690	−	0.555240i	$-0.812626\pi$
$859$	−48.7515	−1.66338	−0.831690	+	0.555240i	$0.812626\pi$
$860$	51.9432	1.77125
$861$	43.8602	1.49475
$862$	−73.1622	−2.49191
$863$	5.00141	0.170250	0.0851250	−	0.996370i	$-0.472871\pi$
$863$	5.00141	0.170250	0.0851250	+	0.996370i	$0.472871\pi$
$864$	−19.7416	−0.671623
$865$	14.9002	0.506622
$866$	17.3205	0.588575
$867$	−39.1723	−1.33036
$868$	−24.7640	−0.840544
$869$	1.24673	0.0422923
$870$	−48.4727	−1.64338
$871$	−7.80872	−0.264588
$872$	−39.8231	−1.34858
$873$	59.4241	2.01120
$874$	−23.8078	−0.805312
$875$	30.0691	1.01652
$876$	181.077	6.11803
$877$	−30.9055	−1.04360	−0.521802	−	0.853067i	$-0.674740\pi$
$877$	−30.9055	−1.04360	−0.521802	+	0.853067i	$0.674740\pi$
$878$	−5.44565	−0.183782
$879$	79.6044	2.68499
$880$	−0.468540	−0.0157945
$881$	39.6284	1.33511	0.667557	−	0.744559i	$-0.267340\pi$
$881$	39.6284	1.33511	0.667557	+	0.744559i	$0.267340\pi$
$882$	−29.6546	−0.998522
$883$	13.7415	0.462439	0.231219	−	0.972902i	$-0.425729\pi$
$883$	13.7415	0.462439	0.231219	+	0.972902i	$0.425729\pi$
$884$	−11.6266	−0.391044
$885$	−45.5438	−1.53094
$886$	66.2762	2.22659
$887$	10.1107	0.339486	0.169743	−	0.985488i	$-0.445706\pi$
$887$	10.1107	0.339486	0.169743	+	0.985488i	$0.445706\pi$
$888$	−30.7837	−1.03303
$889$	−16.5282	−0.554338
$890$	−8.75553	−0.293486
$891$	2.00530	0.0671802
$892$	40.5535	1.35783
$893$	−9.54439	−0.319391
$894$	−0.696953	−0.0233096
$895$	27.1069	0.906084
$896$	61.4501	2.05291
$897$	14.3712	0.479841
$898$	92.2052	3.07693
$899$	−12.1648	−0.405719
$900$	−90.6349	−3.02116
$901$	34.3558	1.14456
$902$	1.60608	0.0534768
$903$	107.593	3.58047
$904$	−42.5247	−1.41435
$905$	6.56865	0.218349
$906$	−151.774	−5.04235
$907$	5.34422	0.177452	0.0887260	−	0.996056i	$-0.471720\pi$
$907$	5.34422	0.177452	0.0887260	+	0.996056i	$0.471720\pi$
$908$	−37.1627	−1.23329
$909$	−97.8704	−3.24616
$910$	−4.70792	−0.156066
$911$	25.6661	0.850355	0.425178	−	0.905110i	$-0.360212\pi$
$911$	25.6661	0.850355	0.425178	+	0.905110i	$0.360212\pi$
$912$	−10.5570	−0.349576
$913$	−1.78166	−0.0589644
$914$	88.9646	2.94269
$915$	−52.5297	−1.73658
$916$	−23.9563	−0.791537
$917$	17.0077	0.561643
$918$	144.306	4.76281
$919$	−20.1944	−0.666150	−0.333075	−	0.942900i	$-0.608086\pi$
$919$	−20.1944	−0.666150	−0.333075	+	0.942900i	$0.608086\pi$
$920$	42.0943	1.38781
$921$	62.4507	2.05782
$922$	86.9027	2.86199
$923$	−1.79685	−0.0591440
$924$	−4.90549	−0.161379
$925$	8.32460	0.273711
$926$	−67.5384	−2.21945
$927$	−16.2940	−0.535164
$928$	9.99563	0.328123
$929$	26.1780	0.858872	0.429436	−	0.903097i	$-0.358712\pi$
$929$	26.1780	0.858872	0.429436	+	0.903097i	$0.358712\pi$
$930$	19.0217	0.623746
$931$	2.23907	0.0733827
$932$	−18.1021	−0.592954
$933$	24.7874	0.811502
$934$	79.1529	2.58996
$935$	−0.891432	−0.0291530
$936$	15.9908	0.522674
$937$	18.0478	0.589595	0.294798	−	0.955560i	$-0.404748\pi$
$937$	18.0478	0.589595	0.294798	+	0.955560i	$0.404748\pi$
$938$	−99.8976	−3.26177
$939$	39.7812	1.29821
$940$	35.5829	1.16059
$941$	30.0237	0.978745	0.489373	−	0.872075i	$-0.337226\pi$
$941$	30.0237	0.978745	0.489373	+	0.872075i	$0.337226\pi$
$942$	164.368	5.35539
$943$	−39.4523	−1.28474
$944$	−36.0830	−1.17440
$945$	38.2982	1.24584
$946$	3.93987	0.128096
$947$	27.7672	0.902312	0.451156	−	0.892445i	$-0.351012\pi$
$947$	27.7672	0.902312	0.451156	+	0.892445i	$0.351012\pi$
$948$	−104.726	−3.40136
$949$	8.63933	0.280445
$950$	10.4413	0.338760
$951$	24.5959	0.797577
$952$	−70.5403	−2.28622
$953$	−44.8387	−1.45247	−0.726234	−	0.687448i	$-0.758731\pi$
$953$	−44.8387	−1.45247	−0.726234	+	0.687448i	$0.758731\pi$
$954$	−99.6339	−3.22577
$955$	6.87195	0.222371
$956$	103.453	3.34590
$957$	−2.40973	−0.0778954
$958$	−66.0004	−2.13237
$959$	22.5828	0.729236
$960$	−36.3221	−1.17229
$961$	−26.2263	−0.846009
$962$	−3.09690	−0.0998480
$963$	126.585	4.07913
$964$	29.2692	0.942698
$965$	21.9478	0.706524
$966$	183.852	5.91535
$967$	2.19376	0.0705466	0.0352733	−	0.999378i	$-0.488770\pi$
$967$	2.19376	0.0705466	0.0352733	+	0.999378i	$0.488770\pi$
$968$	47.7253	1.53395
$969$	−20.0854	−0.645236
$970$	25.5220	0.819462
$971$	6.79935	0.218202	0.109101	−	0.994031i	$-0.465203\pi$
$971$	6.79935	0.218202	0.109101	+	0.994031i	$0.465203\pi$
$972$	−42.9536	−1.37774
$973$	−18.5026	−0.593165
$974$	−35.0550	−1.12323
$975$	−6.30272	−0.201849
$976$	−41.6177	−1.33215
$977$	−23.2704	−0.744485	−0.372243	−	0.928135i	$-0.621411\pi$
$977$	−23.2704	−0.744485	−0.372243	+	0.928135i	$0.621411\pi$
$978$	−77.8171	−2.48832
$979$	−0.435264	−0.0139111
$980$	−8.34760	−0.266654
$981$	60.0774	1.91812
$982$	38.5767	1.23103
$983$	−10.1638	−0.324176	−0.162088	−	0.986776i	$-0.551823\pi$
$983$	−10.1638	−0.324176	−0.162088	+	0.986776i	$0.551823\pi$
$984$	−63.9828	−2.03970
$985$	27.3954	0.872891
$986$	−73.0654	−2.32688
$987$	73.7050	2.34606
$988$	−2.54587	−0.0809948
$989$	−96.7799	−3.07742
$990$	2.58521	0.0821634
$991$	−3.13496	−0.0995854	−0.0497927	−	0.998760i	$-0.515856\pi$
$991$	−3.13496	−0.0995854	−0.0497927	+	0.998760i	$0.515856\pi$
$992$	−3.92249	−0.124539
$993$	73.3281	2.32700
$994$	−22.9872	−0.729111
$995$	−14.7872	−0.468787
$996$	149.662	4.74221
$997$	24.1616	0.765204	0.382602	−	0.923913i	$-0.375028\pi$
$997$	24.1616	0.765204	0.382602	+	0.923913i	$0.375028\pi$
$998$	97.3136	3.08041
$999$	25.1928	0.797066

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4019.2.a.a.1.14	✓	149

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4019.2.a.a.1.14	✓	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)

\(f(q)\)	\(=\)	\(q-2.40917 q^{2} -3.09144 q^{3} +3.80411 q^{4} -1.16894 q^{5} +7.44782 q^{6} +2.97947 q^{7} -4.34641 q^{8} +6.55703 q^{9} +O(q^{10})\)	\(q-2.40917 q^{2} -3.09144 q^{3} +3.80411 q^{4} -1.16894 q^{5} +7.44782 q^{6} +2.97947 q^{7} -4.34641 q^{8} +6.55703 q^{9} +2.81617 q^{10} +0.140001 q^{11} -11.7602 q^{12} -0.561088 q^{13} -7.17805 q^{14} +3.61370 q^{15} +2.86303 q^{16} +5.44713 q^{17} -15.7970 q^{18} +1.19275 q^{19} -4.44677 q^{20} -9.21086 q^{21} -0.337285 q^{22} +8.28516 q^{23} +13.4367 q^{24} -3.63359 q^{25} +1.35176 q^{26} -10.9964 q^{27} +11.3342 q^{28} +5.56771 q^{29} -8.70604 q^{30} -2.18489 q^{31} +1.79529 q^{32} -0.432804 q^{33} -13.1231 q^{34} -3.48281 q^{35} +24.9437 q^{36} -2.29101 q^{37} -2.87355 q^{38} +1.73457 q^{39} +5.08068 q^{40} -4.76180 q^{41} +22.1905 q^{42} -11.6811 q^{43} +0.532577 q^{44} -7.66476 q^{45} -19.9604 q^{46} -8.00197 q^{47} -8.85090 q^{48} +1.87723 q^{49} +8.75393 q^{50} -16.8395 q^{51} -2.13444 q^{52} +6.30714 q^{53} +26.4921 q^{54} -0.163652 q^{55} -12.9500 q^{56} -3.68733 q^{57} -13.4136 q^{58} -12.6031 q^{59} +13.7469 q^{60} -14.5362 q^{61} +5.26376 q^{62} +19.5365 q^{63} -10.0512 q^{64} +0.655877 q^{65} +1.04270 q^{66} +13.9171 q^{67} +20.7215 q^{68} -25.6131 q^{69} +8.39069 q^{70} +3.20244 q^{71} -28.4995 q^{72} -15.3975 q^{73} +5.51945 q^{74} +11.2330 q^{75} +4.53737 q^{76} +0.417127 q^{77} -4.17889 q^{78} +8.90517 q^{79} -3.34670 q^{80} +14.3235 q^{81} +11.4720 q^{82} -12.7261 q^{83} -35.0391 q^{84} -6.36735 q^{85} +28.1418 q^{86} -17.2123 q^{87} -0.608500 q^{88} -3.10902 q^{89} +18.4657 q^{90} -1.67174 q^{91} +31.5177 q^{92} +6.75445 q^{93} +19.2781 q^{94} -1.39426 q^{95} -5.55003 q^{96} +9.06266 q^{97} -4.52257 q^{98} +0.917987 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 149 q - 8 q^{2} - 12 q^{3} + 124 q^{4} - 36 q^{5} - 45 q^{6} - 32 q^{7} - 21 q^{8} + 115 q^{9}+O(q^{10}) \) 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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