LMFDB - Embedded newform 4013.2.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4013,2,Mod(1,4013)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4013, 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("4013.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4013 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4013.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:	$32.0439663311$
Analytic rank:	$1$
Dimension:	$157$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Character	$\chi$	$=$	4013.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.65659 q^{2} +1.81764 q^{3} +5.05746 q^{4} +3.63888 q^{5} -4.82872 q^{6} -3.82226 q^{7} -8.12240 q^{8} +0.303819 q^{9} +O(q^{10})$	\(q-2.65659 q^{2} +1.81764 q^{3} +5.05746 q^{4} +3.63888 q^{5} -4.82872 q^{6} -3.82226 q^{7} -8.12240 q^{8} +0.303819 q^{9} -9.66700 q^{10} -1.82954 q^{11} +9.19264 q^{12} +1.82046 q^{13} +10.1542 q^{14} +6.61417 q^{15} +11.4630 q^{16} +3.46432 q^{17} -0.807123 q^{18} -6.12645 q^{19} +18.4035 q^{20} -6.94749 q^{21} +4.86033 q^{22} -8.79988 q^{23} -14.7636 q^{24} +8.24143 q^{25} -4.83620 q^{26} -4.90069 q^{27} -19.3309 q^{28} -1.07726 q^{29} -17.5711 q^{30} +3.82481 q^{31} -14.2075 q^{32} -3.32544 q^{33} -9.20326 q^{34} -13.9087 q^{35} +1.53655 q^{36} +3.37318 q^{37} +16.2755 q^{38} +3.30894 q^{39} -29.5564 q^{40} +3.83431 q^{41} +18.4566 q^{42} -0.675093 q^{43} -9.25281 q^{44} +1.10556 q^{45} +23.3777 q^{46} -5.00527 q^{47} +20.8355 q^{48} +7.60966 q^{49} -21.8941 q^{50} +6.29689 q^{51} +9.20688 q^{52} -0.258715 q^{53} +13.0191 q^{54} -6.65747 q^{55} +31.0459 q^{56} -11.1357 q^{57} +2.86184 q^{58} +14.7746 q^{59} +33.4509 q^{60} -8.96929 q^{61} -10.1609 q^{62} -1.16128 q^{63} +14.8177 q^{64} +6.62442 q^{65} +8.83433 q^{66} +7.89978 q^{67} +17.5206 q^{68} -15.9950 q^{69} +36.9498 q^{70} +1.76640 q^{71} -2.46774 q^{72} -12.5002 q^{73} -8.96116 q^{74} +14.9800 q^{75} -30.9843 q^{76} +6.99297 q^{77} -8.79048 q^{78} -1.92666 q^{79} +41.7123 q^{80} -9.81915 q^{81} -10.1862 q^{82} -9.27109 q^{83} -35.1366 q^{84} +12.6062 q^{85} +1.79344 q^{86} -1.95808 q^{87} +14.8602 q^{88} -12.2455 q^{89} -2.93702 q^{90} -6.95825 q^{91} -44.5050 q^{92} +6.95214 q^{93} +13.2969 q^{94} -22.2934 q^{95} -25.8242 q^{96} +8.92767 q^{97} -20.2157 q^{98} -0.555849 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) $ 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * 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 $

$2$	−2.65659	−1.87849	−0.939245	−	0.343246i	$-0.888473\pi$
$2$	−2.65659	−1.87849	−0.939245	+	0.343246i	$0.888473\pi$
$3$	1.81764	1.04942	0.524708	−	0.851282i	$-0.324175\pi$
$3$	1.81764	1.04942	0.524708	+	0.851282i	$0.324175\pi$
$4$	5.05746	2.52873
$5$	3.63888	1.62736	0.813678	−	0.581316i	$-0.197462\pi$
$5$	3.63888	1.62736	0.813678	+	0.581316i	$0.197462\pi$
$6$	−4.82872	−1.97132
$7$	−3.82226	−1.44468	−0.722339	−	0.691539i	$-0.756933\pi$
$7$	−3.82226	−1.44468	−0.722339	+	0.691539i	$0.756933\pi$
$8$	−8.12240	−2.87170
$9$	0.303819	0.101273
$10$	−9.66700	−3.05697
$11$	−1.82954	−0.551627	−0.275813	−	0.961211i	$-0.588947\pi$
$11$	−1.82954	−0.551627	−0.275813	+	0.961211i	$0.588947\pi$
$12$	9.19264	2.65369
$13$	1.82046	0.504904	0.252452	−	0.967609i	$-0.418763\pi$
$13$	1.82046	0.504904	0.252452	+	0.967609i	$0.418763\pi$
$14$	10.1542	2.71381
$15$	6.61417	1.70777
$16$	11.4630	2.86574
$17$	3.46432	0.840220	0.420110	−	0.907473i	$-0.361991\pi$
$17$	3.46432	0.840220	0.420110	+	0.907473i	$0.361991\pi$
$18$	−0.807123	−0.190241
$19$	−6.12645	−1.40550	−0.702752	−	0.711435i	$-0.748046\pi$
$19$	−6.12645	−1.40550	−0.702752	+	0.711435i	$0.748046\pi$
$20$	18.4035	4.11514
$21$	−6.94749	−1.51607
$22$	4.86033	1.03623
$23$	−8.79988	−1.83490	−0.917451	−	0.397849i	$-0.869757\pi$
$23$	−8.79988	−1.83490	−0.917451	+	0.397849i	$0.869757\pi$
$24$	−14.7636	−3.01361
$25$	8.24143	1.64829
$26$	−4.83620	−0.948457
$27$	−4.90069	−0.943138
$28$	−19.3309	−3.65320
$29$	−1.07726	−0.200043	−0.100021	−	0.994985i	$-0.531891\pi$
$29$	−1.07726	−0.200043	−0.100021	+	0.994985i	$0.531891\pi$
$30$	−17.5711	−3.20804
$31$	3.82481	0.686957	0.343478	−	0.939161i	$-0.388395\pi$
$31$	3.82481	0.686957	0.343478	+	0.939161i	$0.388395\pi$
$32$	−14.2075	−2.51156
$33$	−3.32544	−0.578885
$34$	−9.20326	−1.57835
$35$	−13.9087	−2.35100
$36$	1.53655	0.256092
$37$	3.37318	0.554548	0.277274	−	0.960791i	$-0.410569\pi$
$37$	3.37318	0.554548	0.277274	+	0.960791i	$0.410569\pi$
$38$	16.2755	2.64023
$39$	3.30894	0.529854
$40$	−29.5564	−4.67328
$41$	3.83431	0.598819	0.299409	−	0.954125i	$-0.403210\pi$
$41$	3.83431	0.598819	0.299409	+	0.954125i	$0.403210\pi$
$42$	18.4566	2.84792
$43$	−0.675093	−0.102951	−0.0514754	−	0.998674i	$-0.516392\pi$
$43$	−0.675093	−0.102951	−0.0514754	+	0.998674i	$0.516392\pi$
$44$	−9.25281	−1.39491
$45$	1.10556	0.164807
$46$	23.3777	3.44685
$47$	−5.00527	−0.730094	−0.365047	−	0.930989i	$-0.618947\pi$
$47$	−5.00527	−0.730094	−0.365047	+	0.930989i	$0.618947\pi$
$48$	20.8355	3.00735
$49$	7.60966	1.08709
$50$	−21.8941	−3.09629
$51$	6.29689	0.881740
$52$	9.20688	1.27676
$53$	−0.258715	−0.0355372	−0.0177686	−	0.999842i	$-0.505656\pi$
$53$	−0.258715	−0.0355372	−0.0177686	+	0.999842i	$0.505656\pi$
$54$	13.0191	1.77168
$55$	−6.65747	−0.897693
$56$	31.0459	4.14868
$57$	−11.1357	−1.47496
$58$	2.86184	0.375778
$59$	14.7746	1.92349	0.961746	−	0.273943i	$-0.0883279\pi$
$59$	14.7746	1.92349	0.961746	+	0.273943i	$0.0883279\pi$
$60$	33.4509	4.31849
$61$	−8.96929	−1.14840	−0.574200	−	0.818715i	$-0.694687\pi$
$61$	−8.96929	−1.14840	−0.574200	+	0.818715i	$0.694687\pi$
$62$	−10.1609	−1.29044
$63$	−1.16128	−0.146307
$64$	14.8177	1.85221
$65$	6.62442	0.821658
$66$	8.83433	1.08743
$67$	7.89978	0.965111	0.482556	−	0.875865i	$-0.339709\pi$
$67$	7.89978	0.965111	0.482556	+	0.875865i	$0.339709\pi$
$68$	17.5206	2.12469
$69$	−15.9950	−1.92557
$70$	36.9498	4.41634
$71$	1.76640	0.209633	0.104817	−	0.994492i	$-0.466574\pi$
$71$	1.76640	0.209633	0.104817	+	0.994492i	$0.466574\pi$
$72$	−2.46774	−0.290826
$73$	−12.5002	−1.46303	−0.731517	−	0.681823i	$-0.761187\pi$
$73$	−12.5002	−1.46303	−0.731517	+	0.681823i	$0.761187\pi$
$74$	−8.96116	−1.04171
$75$	14.9800	1.72974
$76$	−30.9843	−3.55414
$77$	6.99297	0.796923
$78$	−8.79048	−0.995325
$79$	−1.92666	−0.216766	−0.108383	−	0.994109i	$-0.534567\pi$
$79$	−1.92666	−0.216766	−0.108383	+	0.994109i	$0.534567\pi$
$80$	41.7123	4.66358
$81$	−9.81915	−1.09102
$82$	−10.1862	−1.12488
$83$	−9.27109	−1.01763	−0.508817	−	0.860875i	$-0.669917\pi$
$83$	−9.27109	−1.01763	−0.508817	+	0.860875i	$0.669917\pi$
$84$	−35.1366	−3.83372
$85$	12.6062	1.36734
$86$	1.79344	0.193392
$87$	−1.95808	−0.209928
$88$	14.8602	1.58411
$89$	−12.2455	−1.29802	−0.649012	−	0.760778i	$-0.724817\pi$
$89$	−12.2455	−1.29802	−0.649012	+	0.760778i	$0.724817\pi$
$90$	−2.93702	−0.309589
$91$	−6.95825	−0.729423
$92$	−44.5050	−4.63997
$93$	6.95214	0.720903
$94$	13.2969	1.37148
$95$	−22.2934	−2.28726
$96$	−25.8242	−2.63567
$97$	8.92767	0.906467	0.453234	−	0.891392i	$-0.350270\pi$
$97$	8.92767	0.906467	0.453234	+	0.891392i	$0.350270\pi$
$98$	−20.2157	−2.04210
$99$	−0.555849	−0.0558649
$100$	41.6807	4.16807
$101$	2.69883	0.268544	0.134272	−	0.990945i	$-0.457130\pi$
$101$	2.69883	0.268544	0.134272	+	0.990945i	$0.457130\pi$
$102$	−16.7282	−1.65634
$103$	8.59514	0.846905	0.423452	−	0.905918i	$-0.360818\pi$
$103$	8.59514	0.846905	0.423452	+	0.905918i	$0.360818\pi$
$104$	−14.7865	−1.44993
$105$	−25.2811	−2.46718
$106$	0.687299	0.0667563
$107$	−18.2411	−1.76343	−0.881716	−	0.471781i	$-0.843611\pi$
$107$	−18.2411	−1.76343	−0.881716	+	0.471781i	$0.843611\pi$
$108$	−24.7850	−2.38494
$109$	−8.55222	−0.819154	−0.409577	−	0.912275i	$-0.634324\pi$
$109$	−8.55222	−0.819154	−0.409577	+	0.912275i	$0.634324\pi$
$110$	17.6861	1.68631
$111$	6.13124	0.581951
$112$	−43.8144	−4.14007
$113$	−11.4009	−1.07251	−0.536254	−	0.844057i	$-0.680161\pi$
$113$	−11.4009	−1.07251	−0.536254	+	0.844057i	$0.680161\pi$
$114$	29.5829	2.77070
$115$	−32.0217	−2.98604
$116$	−5.44821	−0.505854
$117$	0.553090	0.0511332
$118$	−39.2501	−3.61326
$119$	−13.2415	−1.21385
$120$	−53.7230	−4.90421
$121$	−7.65279	−0.695708
$122$	23.8277	2.15726
$123$	6.96940	0.628410
$124$	19.3438	1.73713
$125$	11.7952	1.05499
$126$	3.08503	0.274836
$127$	−12.7453	−1.13096	−0.565481	−	0.824761i	$-0.691309\pi$
$127$	−12.7453	−1.13096	−0.565481	+	0.824761i	$0.691309\pi$
$128$	−10.9493	−0.967792
$129$	−1.22708	−0.108038
$130$	−17.5983	−1.54348
$131$	13.4295	1.17334	0.586670	−	0.809826i	$-0.300439\pi$
$131$	13.4295	1.17334	0.586670	+	0.809826i	$0.300439\pi$
$132$	−16.8183	−1.46384
$133$	23.4169	2.03050
$134$	−20.9864	−1.81295
$135$	−17.8330	−1.53482
$136$	−28.1386	−2.41286
$137$	−13.7871	−1.17791	−0.588954	−	0.808166i	$-0.700460\pi$
$137$	−13.7871	−1.17791	−0.588954	+	0.808166i	$0.700460\pi$
$138$	42.4922	3.61718
$139$	−1.95154	−0.165528	−0.0827638	−	0.996569i	$-0.526375\pi$
$139$	−1.95154	−0.165528	−0.0827638	+	0.996569i	$0.526375\pi$
$140$	−70.3428	−5.94505
$141$	−9.09779	−0.766172
$142$	−4.69260	−0.393794
$143$	−3.33059	−0.278518
$144$	3.48267	0.290222
$145$	−3.92003	−0.325541
$146$	33.2078	2.74830
$147$	13.8316	1.14081
$148$	17.0597	1.40230
$149$	19.9083	1.63095	0.815474	−	0.578794i	$-0.196476\pi$
$149$	19.9083	1.63095	0.815474	+	0.578794i	$0.196476\pi$
$150$	−39.7956	−3.24930
$151$	−22.9422	−1.86701	−0.933503	−	0.358568i	$-0.883265\pi$
$151$	−22.9422	−1.86701	−0.933503	+	0.358568i	$0.883265\pi$
$152$	49.7615	4.03619
$153$	1.05253	0.0850917
$154$	−18.5774	−1.49701
$155$	13.9180	1.11792
$156$	16.7348	1.33986
$157$	−14.9381	−1.19219	−0.596095	−	0.802914i	$-0.703282\pi$
$157$	−14.9381	−1.19219	−0.596095	+	0.802914i	$0.703282\pi$
$158$	5.11834	0.407194
$159$	−0.470251	−0.0372933
$160$	−51.6995	−4.08720
$161$	33.6354	2.65084
$162$	26.0854	2.04947
$163$	−15.2541	−1.19479	−0.597397	−	0.801946i	$-0.703798\pi$
$163$	−15.2541	−1.19479	−0.597397	+	0.801946i	$0.703798\pi$
$164$	19.3919	1.51425
$165$	−12.1009	−0.942053
$166$	24.6295	1.91162
$167$	−17.0852	−1.32209	−0.661044	−	0.750347i	$-0.729886\pi$
$167$	−17.0852	−1.32209	−0.661044	+	0.750347i	$0.729886\pi$
$168$	56.4303	4.35369
$169$	−9.68594	−0.745072
$170$	−33.4895	−2.56853
$171$	−1.86133	−0.142340
$172$	−3.41425	−0.260334
$173$	−2.32630	−0.176865	−0.0884326	−	0.996082i	$-0.528186\pi$
$173$	−2.32630	−0.176865	−0.0884326	+	0.996082i	$0.528186\pi$
$174$	5.20180	0.394348
$175$	−31.5009	−2.38124
$176$	−20.9719	−1.58082
$177$	26.8550	2.01854
$178$	32.5313	2.43833
$179$	−15.7631	−1.17819	−0.589096	−	0.808063i	$-0.700516\pi$
$179$	−15.7631	−1.17819	−0.589096	+	0.808063i	$0.700516\pi$
$180$	5.59133	0.416753
$181$	7.58953	0.564125	0.282063	−	0.959396i	$-0.408981\pi$
$181$	7.58953	0.564125	0.282063	+	0.959396i	$0.408981\pi$
$182$	18.4852	1.37021
$183$	−16.3030	−1.20515
$184$	71.4762	5.26929
$185$	12.2746	0.902447
$186$	−18.4690	−1.35421
$187$	−6.33810	−0.463488
$188$	−25.3140	−1.84621
$189$	18.7317	1.36253
$190$	59.2244	4.29659
$191$	−7.37870	−0.533904	−0.266952	−	0.963710i	$-0.586017\pi$
$191$	−7.37870	−0.533904	−0.266952	+	0.963710i	$0.586017\pi$
$192$	26.9332	1.94373
$193$	20.1744	1.45219	0.726093	−	0.687597i	$-0.241334\pi$
$193$	20.1744	1.45219	0.726093	+	0.687597i	$0.241334\pi$
$194$	−23.7171	−1.70279
$195$	12.0408	0.862261
$196$	38.4855	2.74896
$197$	0.887273	0.0632156	0.0316078	−	0.999500i	$-0.489937\pi$
$197$	0.887273	0.0632156	0.0316078	+	0.999500i	$0.489937\pi$
$198$	1.47666	0.104942
$199$	−1.65144	−0.117068	−0.0585338	−	0.998285i	$-0.518643\pi$
$199$	−1.65144	−0.117068	−0.0585338	+	0.998285i	$0.518643\pi$
$200$	−66.9402	−4.73339
$201$	14.3590	1.01280
$202$	−7.16968	−0.504457
$203$	4.11758	0.288997
$204$	31.8462	2.22968
$205$	13.9526	0.974491
$206$	−22.8338	−1.59090
$207$	−2.67357	−0.185826
$208$	20.8678	1.44692
$209$	11.2086	0.775314
$210$	67.1614	4.63458
$211$	−25.0364	−1.72357	−0.861787	−	0.507270i	$-0.830655\pi$
$211$	−25.0364	−1.72357	−0.861787	+	0.507270i	$0.830655\pi$
$212$	−1.30844	−0.0898640
$213$	3.21068	0.219992
$214$	48.4590	3.31259
$215$	−2.45658	−0.167537
$216$	39.8054	2.70841
$217$	−14.6194	−0.992431
$218$	22.7197	1.53877
$219$	−22.7208	−1.53533
$220$	−33.6698	−2.27002
$221$	6.30664	0.424230
$222$	−16.2882	−1.09319
$223$	5.85415	0.392023	0.196011	−	0.980602i	$-0.437201\pi$
$223$	5.85415	0.392023	0.196011	+	0.980602i	$0.437201\pi$
$224$	54.3049	3.62840
$225$	2.50391	0.166927
$226$	30.2875	2.01470
$227$	17.9797	1.19335	0.596676	−	0.802482i	$-0.296488\pi$
$227$	17.9797	1.19335	0.596676	+	0.802482i	$0.296488\pi$
$228$	−56.3183	−3.72977
$229$	−18.3642	−1.21354	−0.606771	−	0.794876i	$-0.707536\pi$
$229$	−18.3642	−1.21354	−0.606771	+	0.794876i	$0.707536\pi$
$230$	85.0684	5.60925
$231$	12.7107	0.836303
$232$	8.74996	0.574463
$233$	12.8103	0.839231	0.419616	−	0.907702i	$-0.362165\pi$
$233$	12.8103	0.839231	0.419616	+	0.907702i	$0.362165\pi$
$234$	−1.46933	−0.0960532
$235$	−18.2136	−1.18812
$236$	74.7220	4.86399
$237$	−3.50198	−0.227478
$238$	35.1772	2.28020
$239$	16.9467	1.09619	0.548095	−	0.836416i	$-0.315353\pi$
$239$	16.9467	1.09619	0.548095	+	0.836416i	$0.315353\pi$
$240$	75.8180	4.89403
$241$	−6.73433	−0.433796	−0.216898	−	0.976194i	$-0.569594\pi$
$241$	−6.73433	−0.433796	−0.216898	+	0.976194i	$0.569594\pi$
$242$	20.3303	1.30688
$243$	−3.14563	−0.201792
$244$	−45.3618	−2.90399
$245$	27.6906	1.76909
$246$	−18.5148	−1.18046
$247$	−11.1529	−0.709644
$248$	−31.0667	−1.97273
$249$	−16.8515	−1.06792
$250$	−31.3349	−1.98179
$251$	−7.42606	−0.468729	−0.234364	−	0.972149i	$-0.575301\pi$
$251$	−7.42606	−0.468729	−0.234364	+	0.972149i	$0.575301\pi$
$252$	−5.87310	−0.369971
$253$	16.0997	1.01218
$254$	33.8590	2.12450
$255$	22.9136	1.43491
$256$	−0.547490	−0.0342181
$257$	2.73318	0.170491	0.0852457	−	0.996360i	$-0.472832\pi$
$257$	2.73318	0.170491	0.0852457	+	0.996360i	$0.472832\pi$
$258$	3.25984	0.202949
$259$	−12.8932	−0.801143
$260$	33.5027	2.07775
$261$	−0.327293	−0.0202589
$262$	−35.6766	−2.20411
$263$	19.7083	1.21527	0.607633	−	0.794218i	$-0.292119\pi$
$263$	19.7083	1.21527	0.607633	+	0.794218i	$0.292119\pi$
$264$	27.0106	1.66239
$265$	−0.941432	−0.0578317
$266$	−62.2090	−3.81428
$267$	−22.2580	−1.36217
$268$	39.9528	2.44050
$269$	28.3104	1.72611	0.863056	−	0.505107i	$-0.168547\pi$
$269$	28.3104	1.72611	0.863056	+	0.505107i	$0.168547\pi$
$270$	47.3749	2.88315
$271$	−2.11507	−0.128481	−0.0642406	−	0.997934i	$-0.520463\pi$
$271$	−2.11507	−0.128481	−0.0642406	+	0.997934i	$0.520463\pi$
$272$	39.7113	2.40785
$273$	−12.6476	−0.765468
$274$	36.6266	2.21269
$275$	−15.0780	−0.909239
$276$	−80.8942	−4.86926
$277$	−24.1283	−1.44973	−0.724865	−	0.688891i	$-0.758098\pi$
$277$	−24.1283	−1.44973	−0.724865	+	0.688891i	$0.758098\pi$
$278$	5.18444	0.310942
$279$	1.16205	0.0695702
$280$	112.972	6.75138
$281$	−13.8299	−0.825025	−0.412513	−	0.910952i	$-0.635349\pi$
$281$	−13.8299	−0.825025	−0.412513	+	0.910952i	$0.635349\pi$
$282$	24.1691	1.43925
$283$	−15.1655	−0.901498	−0.450749	−	0.892651i	$-0.648843\pi$
$283$	−15.1655	−0.901498	−0.450749	+	0.892651i	$0.648843\pi$
$284$	8.93349	0.530105
$285$	−40.5214	−2.40028
$286$	8.84801	0.523194
$287$	−14.6557	−0.865100
$288$	−4.31652	−0.254354
$289$	−4.99851	−0.294030
$290$	10.4139	0.611525
$291$	16.2273	0.951261
$292$	−63.2191	−3.69962
$293$	−0.869846	−0.0508169	−0.0254085	−	0.999677i	$-0.508089\pi$
$293$	−0.869846	−0.0508169	−0.0254085	+	0.999677i	$0.508089\pi$
$294$	−36.7449	−2.14301
$295$	53.7630	3.13021
$296$	−27.3983	−1.59250
$297$	8.96600	0.520260
$298$	−52.8880	−3.06372
$299$	−16.0198	−0.926449
$300$	75.7605	4.37404
$301$	2.58038	0.148731
$302$	60.9479	3.50716
$303$	4.90551	0.281814
$304$	−70.2272	−4.02781
$305$	−32.6382	−1.86886
$306$	−2.79613	−0.159844
$307$	−27.9772	−1.59674	−0.798372	−	0.602165i	$-0.794305\pi$
$307$	−27.9772	−1.59674	−0.798372	+	0.602165i	$0.794305\pi$
$308$	35.3666	2.01520
$309$	15.6229	0.888755
$310$	−36.9745	−2.10001
$311$	−3.58289	−0.203167	−0.101584	−	0.994827i	$-0.532391\pi$
$311$	−3.58289	−0.203167	−0.101584	+	0.994827i	$0.532391\pi$
$312$	−26.8765	−1.52158
$313$	−5.49429	−0.310555	−0.155278	−	0.987871i	$-0.549627\pi$
$313$	−5.49429	−0.310555	−0.155278	+	0.987871i	$0.549627\pi$
$314$	39.6844	2.23952
$315$	−4.22574	−0.238094
$316$	−9.74401	−0.548143
$317$	−16.3892	−0.920512	−0.460256	−	0.887786i	$-0.652242\pi$
$317$	−16.3892	−0.920512	−0.460256	+	0.887786i	$0.652242\pi$
$318$	1.24926	0.0700551
$319$	1.97089	0.110349
$320$	53.9196	3.01420
$321$	−33.1557	−1.85057
$322$	−89.3554	−4.97958
$323$	−21.2240	−1.18093
$324$	−49.6599	−2.75889
$325$	15.0032	0.832226
$326$	40.5239	2.24441
$327$	−15.5449	−0.859633
$328$	−31.1438	−1.71963
$329$	19.1314	1.05475
$330$	32.1471	1.76964
$331$	5.40124	0.296879	0.148439	−	0.988921i	$-0.452575\pi$
$331$	5.40124	0.296879	0.148439	+	0.988921i	$0.452575\pi$
$332$	−46.8881	−2.57332
$333$	1.02484	0.0561608
$334$	45.3882	2.48353
$335$	28.7463	1.57058
$336$	−79.6388	−4.34465
$337$	19.6290	1.06926	0.534629	−	0.845087i	$-0.320451\pi$
$337$	19.6290	1.06926	0.534629	+	0.845087i	$0.320451\pi$
$338$	25.7315	1.39961
$339$	−20.7228	−1.12551
$340$	63.7554	3.45762
$341$	−6.99764	−0.378943
$342$	4.94480	0.267384
$343$	−2.33027	−0.125823
$344$	5.48338	0.295644
$345$	−58.2040	−3.13360
$346$	6.18001	0.332240
$347$	16.0512	0.861673	0.430837	−	0.902430i	$-0.358218\pi$
$347$	16.0512	0.861673	0.430837	+	0.902430i	$0.358218\pi$
$348$	−9.90289	−0.530851
$349$	1.76857	0.0946692	0.0473346	−	0.998879i	$-0.484927\pi$
$349$	1.76857	0.0946692	0.0473346	+	0.998879i	$0.484927\pi$
$350$	83.6849	4.47314
$351$	−8.92149	−0.476194
$352$	25.9932	1.38544
$353$	24.5983	1.30923	0.654617	−	0.755961i	$-0.272830\pi$
$353$	24.5983	1.30923	0.654617	+	0.755961i	$0.272830\pi$
$354$	−71.3426	−3.79181
$355$	6.42772	0.341148
$356$	−61.9312	−3.28235
$357$	−24.0683	−1.27383
$358$	41.8762	2.21322
$359$	3.82660	0.201960	0.100980	−	0.994888i	$-0.467802\pi$
$359$	3.82660	0.201960	0.100980	+	0.994888i	$0.467802\pi$
$360$	−8.97981	−0.473278
$361$	18.5334	0.975443
$362$	−20.1622	−1.05970
$363$	−13.9100	−0.730087
$364$	−35.1911	−1.84451
$365$	−45.4866	−2.38088
$366$	43.3102	2.26386
$367$	19.8638	1.03688	0.518442	−	0.855113i	$-0.326512\pi$
$367$	19.8638	1.03688	0.518442	+	0.855113i	$0.326512\pi$
$368$	−100.873	−5.25835
$369$	1.16494	0.0606442
$370$	−32.6086	−1.69524
$371$	0.988875	0.0513398
$372$	35.1601	1.82297
$373$	15.7330	0.814626	0.407313	−	0.913289i	$-0.366466\pi$
$373$	15.7330	0.814626	0.407313	+	0.913289i	$0.366466\pi$
$374$	16.8377	0.870658
$375$	21.4394	1.10713
$376$	40.6548	2.09661
$377$	−1.96111	−0.101002
$378$	−49.7624	−2.55950
$379$	27.8684	1.43150	0.715751	−	0.698356i	$-0.246085\pi$
$379$	27.8684	1.43150	0.715751	+	0.698356i	$0.246085\pi$
$380$	−112.748	−5.78385
$381$	−23.1664	−1.18685
$382$	19.6022	1.00293
$383$	9.52067	0.486483	0.243242	−	0.969966i	$-0.421789\pi$
$383$	9.52067	0.486483	0.243242	+	0.969966i	$0.421789\pi$
$384$	−19.9019	−1.01562
$385$	25.4466	1.29688
$386$	−53.5951	−2.72792
$387$	−0.205106	−0.0104261
$388$	45.1513	2.29221
$389$	9.59180	0.486324	0.243162	−	0.969986i	$-0.421815\pi$
$389$	9.59180	0.486324	0.243162	+	0.969986i	$0.421815\pi$
$390$	−31.9875	−1.61975
$391$	−30.4856	−1.54172
$392$	−61.8087	−3.12181
$393$	24.4100	1.23132
$394$	−2.35712	−0.118750
$395$	−7.01089	−0.352756
$396$	−2.81118	−0.141267
$397$	−35.8299	−1.79825	−0.899124	−	0.437693i	$-0.855796\pi$
$397$	−35.8299	−1.79825	−0.899124	+	0.437693i	$0.855796\pi$
$398$	4.38720	0.219910
$399$	42.5635	2.13084
$400$	94.4712	4.72356
$401$	25.6326	1.28003	0.640014	−	0.768363i	$-0.278928\pi$
$401$	25.6326	1.28003	0.640014	+	0.768363i	$0.278928\pi$
$402$	−38.1458	−1.90254
$403$	6.96290	0.346847
$404$	13.6492	0.679074
$405$	−35.7307	−1.77547
$406$	−10.9387	−0.542879
$407$	−6.17137	−0.305903
$408$	−51.1458	−2.53210
$409$	35.1661	1.73885	0.869425	−	0.494065i	$-0.164489\pi$
$409$	35.1661	1.73885	0.869425	+	0.494065i	$0.164489\pi$
$410$	−37.0663	−1.83057
$411$	−25.0599	−1.23612
$412$	43.4696	2.14159
$413$	−56.4724	−2.77883
$414$	7.10258	0.349073
$415$	−33.7364	−1.65605
$416$	−25.8642	−1.26810
$417$	−3.54720	−0.173707
$418$	−29.7766	−1.45642
$419$	−7.42614	−0.362791	−0.181395	−	0.983410i	$-0.558061\pi$
$419$	−7.42614	−0.362791	−0.181395	+	0.983410i	$0.558061\pi$
$420$	−127.858	−6.23883
$421$	24.3592	1.18719	0.593597	−	0.804763i	$-0.297708\pi$
$421$	24.3592	1.18719	0.593597	+	0.804763i	$0.297708\pi$
$422$	66.5113	3.23772
$423$	−1.52070	−0.0739389
$424$	2.10139	0.102052
$425$	28.5509	1.38492
$426$	−8.52946	−0.413254
$427$	34.2830	1.65907
$428$	−92.2534	−4.45924
$429$	−6.05382	−0.292281
$430$	6.52612	0.314718
$431$	8.88554	0.428002	0.214001	−	0.976833i	$-0.431350\pi$
$431$	8.88554	0.428002	0.214001	+	0.976833i	$0.431350\pi$
$432$	−56.1764	−2.70279
$433$	−25.8203	−1.24085	−0.620423	−	0.784267i	$-0.713039\pi$
$433$	−25.8203	−1.24085	−0.620423	+	0.784267i	$0.713039\pi$
$434$	38.8378	1.86427
$435$	−7.12521	−0.341627
$436$	−43.2525	−2.07142
$437$	53.9121	2.57896
$438$	60.3599	2.88411
$439$	−1.73458	−0.0827871	−0.0413935	−	0.999143i	$-0.513180\pi$
$439$	−1.73458	−0.0827871	−0.0413935	+	0.999143i	$0.513180\pi$
$440$	54.0746	2.57791
$441$	2.31196	0.110093
$442$	−16.7541	−0.796913
$443$	−6.82997	−0.324502	−0.162251	−	0.986750i	$-0.551875\pi$
$443$	−6.82997	−0.324502	−0.162251	+	0.986750i	$0.551875\pi$
$444$	31.0085	1.47160
$445$	−44.5600	−2.11235
$446$	−15.5521	−0.736412
$447$	36.1861	1.71154
$448$	−56.6369	−2.67584
$449$	32.1364	1.51661	0.758305	−	0.651900i	$-0.226028\pi$
$449$	32.1364	1.51661	0.758305	+	0.651900i	$0.226028\pi$
$450$	−6.65185	−0.313571
$451$	−7.01502	−0.330324
$452$	−57.6596	−2.71208
$453$	−41.7006	−1.95927
$454$	−47.7646	−2.24170
$455$	−25.3202	−1.18703
$456$	90.4485	4.23564
$457$	−10.5525	−0.493625	−0.246812	−	0.969063i	$-0.579383\pi$
$457$	−10.5525	−0.493625	−0.246812	+	0.969063i	$0.579383\pi$
$458$	48.7862	2.27963
$459$	−16.9775	−0.792444
$460$	−161.948	−7.55088
$461$	20.1109	0.936658	0.468329	−	0.883554i	$-0.344856\pi$
$461$	20.1109	0.936658	0.468329	+	0.883554i	$0.344856\pi$
$462$	−33.7671	−1.57099
$463$	3.91189	0.181801	0.0909004	−	0.995860i	$-0.471025\pi$
$463$	3.91189	0.181801	0.0909004	+	0.995860i	$0.471025\pi$
$464$	−12.3486	−0.573270
$465$	25.2980	1.17317
$466$	−34.0317	−1.57649
$467$	20.0542	0.927997	0.463999	−	0.885836i	$-0.346414\pi$
$467$	20.0542	0.927997	0.463999	+	0.885836i	$0.346414\pi$
$468$	2.79723	0.129302
$469$	−30.1950	−1.39427
$470$	48.3860	2.23188
$471$	−27.1521	−1.25110
$472$	−120.005	−5.52370
$473$	1.23511	0.0567903
$474$	9.30331	0.427315
$475$	−50.4908	−2.31667
$476$	−66.9684	−3.06949
$477$	−0.0786026	−0.00359896
$478$	−45.0204	−2.05918
$479$	−5.87190	−0.268294	−0.134147	−	0.990961i	$-0.542829\pi$
$479$	−5.87190	−0.268294	−0.134147	+	0.990961i	$0.542829\pi$
$480$	−93.9711	−4.28917
$481$	6.14073	0.279993
$482$	17.8903	0.814882
$483$	61.1371	2.78184
$484$	−38.7037	−1.75926
$485$	32.4867	1.47514
$486$	8.35663	0.379065
$487$	18.3347	0.830823	0.415412	−	0.909634i	$-0.363638\pi$
$487$	18.3347	0.830823	0.415412	+	0.909634i	$0.363638\pi$
$488$	72.8522	3.29786
$489$	−27.7265	−1.25384
$490$	−73.5625	−3.32322
$491$	−2.06411	−0.0931520	−0.0465760	−	0.998915i	$-0.514831\pi$
$491$	−2.06411	−0.0931520	−0.0465760	+	0.998915i	$0.514831\pi$
$492$	35.2474	1.58908
$493$	−3.73198	−0.168080
$494$	29.6288	1.33306
$495$	−2.02267	−0.0909121
$496$	43.8436	1.96864
$497$	−6.75164	−0.302852
$498$	44.7675	2.00608
$499$	16.7899	0.751619	0.375810	−	0.926697i	$-0.377365\pi$
$499$	16.7899	0.751619	0.375810	+	0.926697i	$0.377365\pi$
$500$	59.6536	2.66779
$501$	−31.0547	−1.38742
$502$	19.7280	0.880503
$503$	−34.7233	−1.54824	−0.774118	−	0.633042i	$-0.781806\pi$
$503$	−34.7233	−1.54824	−0.774118	+	0.633042i	$0.781806\pi$
$504$	9.43235	0.420150
$505$	9.82072	0.437016
$506$	−42.7703	−1.90137
$507$	−17.6056	−0.781891
$508$	−64.4588	−2.85990
$509$	37.0908	1.64402	0.822009	−	0.569474i	$-0.192853\pi$
$509$	37.0908	1.64402	0.822009	+	0.569474i	$0.192853\pi$
$510$	−60.8720	−2.69546
$511$	47.7789	2.11361
$512$	23.3531	1.03207
$513$	30.0238	1.32558
$514$	−7.26094	−0.320266
$515$	31.2767	1.37822
$516$	−6.20589	−0.273199
$517$	9.15734	0.402739
$518$	34.2519	1.50494
$519$	−4.22837	−0.185605
$520$	−53.8062	−2.35956
$521$	32.2341	1.41220	0.706101	−	0.708111i	$-0.250452\pi$
$521$	32.2341	1.41220	0.706101	+	0.708111i	$0.250452\pi$
$522$	0.869483	0.0380562
$523$	−25.8972	−1.13241	−0.566203	−	0.824266i	$-0.691588\pi$
$523$	−25.8972	−1.13241	−0.566203	+	0.824266i	$0.691588\pi$
$524$	67.9190	2.96706
$525$	−57.2573	−2.49891
$526$	−52.3568	−2.28287
$527$	13.2504	0.577195
$528$	−38.1194	−1.65893
$529$	54.4379	2.36687
$530$	2.50100	0.108636
$531$	4.48882	0.194798
$532$	118.430	5.13459
$533$	6.98019	0.302346
$534$	59.1303	2.55882
$535$	−66.3770	−2.86973
$536$	−64.1651	−2.77151
$537$	−28.6517	−1.23641
$538$	−75.2089	−3.24249
$539$	−13.9222	−0.599670
$540$	−90.1897	−3.88115
$541$	−19.8991	−0.855528	−0.427764	−	0.903890i	$-0.640699\pi$
$541$	−19.8991	−0.855528	−0.427764	+	0.903890i	$0.640699\pi$
$542$	5.61886	0.241351
$543$	13.7950	0.592002
$544$	−49.2194	−2.11026
$545$	−31.1205	−1.33306
$546$	33.5995	1.43792
$547$	3.72607	0.159315	0.0796577	−	0.996822i	$-0.474617\pi$
$547$	3.72607	0.159315	0.0796577	+	0.996822i	$0.474617\pi$
$548$	−69.7275	−2.97861
$549$	−2.72504	−0.116302
$550$	40.0561	1.70800
$551$	6.59980	0.281161
$552$	129.918	5.52968
$553$	7.36420	0.313158
$554$	64.0990	2.72331
$555$	22.3108	0.947042
$556$	−9.86984	−0.418575
$557$	−9.06028	−0.383896	−0.191948	−	0.981405i	$-0.561481\pi$
$557$	−9.06028	−0.383896	−0.191948	+	0.981405i	$0.561481\pi$
$558$	−3.08709	−0.130687
$559$	−1.22898	−0.0519802
$560$	−159.435	−6.73736
$561$	−11.5204	−0.486391
$562$	36.7405	1.54980
$563$	18.2671	0.769868	0.384934	−	0.922944i	$-0.374224\pi$
$563$	18.2671	0.769868	0.384934	+	0.922944i	$0.374224\pi$
$564$	−46.0117	−1.93744
$565$	−41.4865	−1.74535
$566$	40.2886	1.69346
$567$	37.5313	1.57617
$568$	−14.3474	−0.602004
$569$	−43.5867	−1.82725	−0.913625	−	0.406557i	$-0.866729\pi$
$569$	−43.5867	−1.82725	−0.913625	+	0.406557i	$0.866729\pi$
$570$	107.649	4.50891
$571$	−23.7799	−0.995157	−0.497579	−	0.867419i	$-0.665777\pi$
$571$	−23.7799	−0.995157	−0.497579	+	0.867419i	$0.665777\pi$
$572$	−16.8443	−0.704297
$573$	−13.4118	−0.560287
$574$	38.9342	1.62508
$575$	−72.5236	−3.02444
$576$	4.50189	0.187579
$577$	12.7574	0.531099	0.265550	−	0.964097i	$-0.414447\pi$
$577$	12.7574	0.531099	0.265550	+	0.964097i	$0.414447\pi$
$578$	13.2790	0.552332
$579$	36.6698	1.52395
$580$	−19.8254	−0.823204
$581$	35.4365	1.47015
$582$	−43.1092	−1.78694
$583$	0.473329	0.0196033
$584$	101.531	4.20140
$585$	2.01263	0.0832118
$586$	2.31082	0.0954591
$587$	−31.7140	−1.30898	−0.654489	−	0.756072i	$-0.727116\pi$
$587$	−31.7140	−1.30898	−0.654489	+	0.756072i	$0.727116\pi$
$588$	69.9528	2.88481
$589$	−23.4325	−0.965521
$590$	−142.826	−5.88006
$591$	1.61274	0.0663394
$592$	38.6666	1.58919
$593$	7.48273	0.307279	0.153639	−	0.988127i	$-0.450901\pi$
$593$	7.48273	0.307279	0.153639	+	0.988127i	$0.450901\pi$
$594$	−23.8190	−0.977304
$595$	−48.1843	−1.97536
$596$	100.685	4.12422
$597$	−3.00173	−0.122852
$598$	42.5580	1.74033
$599$	25.1618	1.02808	0.514042	−	0.857765i	$-0.328148\pi$
$599$	25.1618	1.02808	0.514042	+	0.857765i	$0.328148\pi$
$600$	−121.673	−4.96729
$601$	7.36133	0.300275	0.150137	−	0.988665i	$-0.452028\pi$
$601$	7.36133	0.300275	0.150137	+	0.988665i	$0.452028\pi$
$602$	−6.85500	−0.279389
$603$	2.40010	0.0977398
$604$	−116.029	−4.72115
$605$	−27.8476	−1.13216
$606$	−13.0319	−0.529385
$607$	−5.07874	−0.206140	−0.103070	−	0.994674i	$-0.532867\pi$
$607$	−5.07874	−0.206140	−0.103070	+	0.994674i	$0.532867\pi$
$608$	87.0418	3.53001
$609$	7.48428	0.303278
$610$	86.7061	3.51063
$611$	−9.11188	−0.368627
$612$	5.32311	0.215174
$613$	−38.0848	−1.53823	−0.769115	−	0.639111i	$-0.779303\pi$
$613$	−38.0848	−1.53823	−0.769115	+	0.639111i	$0.779303\pi$
$614$	74.3239	2.99947
$615$	25.3608	1.02265
$616$	−56.7997	−2.28852
$617$	−28.9701	−1.16629	−0.583147	−	0.812367i	$-0.698179\pi$
$617$	−28.9701	−1.16629	−0.583147	+	0.812367i	$0.698179\pi$
$618$	−41.5036	−1.66952
$619$	41.8316	1.68136	0.840678	−	0.541536i	$-0.182157\pi$
$619$	41.8316	1.68136	0.840678	+	0.541536i	$0.182157\pi$
$620$	70.3898	2.82692
$621$	43.1255	1.73057
$622$	9.51827	0.381648
$623$	46.8056	1.87523
$624$	37.9302	1.51842
$625$	1.71406	0.0685623
$626$	14.5960	0.583375
$627$	20.3732	0.813626
$628$	−75.5488	−3.01473
$629$	11.6858	0.465943
$630$	11.2261	0.447257
$631$	4.31448	0.171757	0.0858784	−	0.996306i	$-0.472630\pi$
$631$	4.31448	0.171757	0.0858784	+	0.996306i	$0.472630\pi$
$632$	15.6491	0.622488
$633$	−45.5071	−1.80875
$634$	43.5395	1.72917
$635$	−46.3786	−1.84048
$636$	−2.37827	−0.0943046
$637$	13.8530	0.548878
$638$	−5.23585	−0.207289
$639$	0.536667	0.0212302
$640$	−39.8432	−1.57494
$641$	38.4757	1.51970	0.759850	−	0.650098i	$-0.225272\pi$
$641$	38.4757	1.51970	0.759850	+	0.650098i	$0.225272\pi$
$642$	88.0811	3.47628
$643$	−2.99314	−0.118038	−0.0590191	−	0.998257i	$-0.518797\pi$
$643$	−2.99314	−0.118038	−0.0590191	+	0.998257i	$0.518797\pi$
$644$	170.110	6.70326
$645$	−4.46518	−0.175816
$646$	56.3833	2.21837
$647$	−25.2812	−0.993906	−0.496953	−	0.867777i	$-0.665548\pi$
$647$	−25.2812	−0.993906	−0.496953	+	0.867777i	$0.665548\pi$
$648$	79.7551	3.13308
$649$	−27.0307	−1.06105
$650$	−39.8572	−1.56333
$651$	−26.5729	−1.04147
$652$	−77.1470	−3.02131
$653$	−2.82812	−0.110673	−0.0553365	−	0.998468i	$-0.517623\pi$
$653$	−2.82812	−0.110673	−0.0553365	+	0.998468i	$0.517623\pi$
$654$	41.2963	1.61481
$655$	48.8682	1.90944
$656$	43.9525	1.71606
$657$	−3.79779	−0.148166
$658$	−50.8244	−1.98134
$659$	29.9648	1.16726	0.583631	−	0.812019i	$-0.301632\pi$
$659$	29.9648	1.16726	0.583631	+	0.812019i	$0.301632\pi$
$660$	−61.1997	−2.38219
$661$	32.5600	1.26644	0.633219	−	0.773972i	$-0.281733\pi$
$661$	32.5600	1.26644	0.633219	+	0.773972i	$0.281733\pi$
$662$	−14.3489	−0.557684
$663$	11.4632	0.445194
$664$	75.3035	2.92234
$665$	85.2112	3.30435
$666$	−2.72257	−0.105498
$667$	9.47979	0.367059
$668$	−86.4074	−3.34320
$669$	10.6407	0.411395
$670$	−76.3671	−2.95032
$671$	16.4097	0.633488
$672$	98.7067	3.80770
$673$	−33.8821	−1.30606	−0.653029	−	0.757333i	$-0.726502\pi$
$673$	−33.8821	−1.30606	−0.653029	+	0.757333i	$0.726502\pi$
$674$	−52.1460	−2.00859
$675$	−40.3887	−1.55456
$676$	−48.9862	−1.88409
$677$	14.9647	0.575139	0.287569	−	0.957760i	$-0.407153\pi$
$677$	14.9647	0.575139	0.287569	+	0.957760i	$0.407153\pi$
$678$	55.0518	2.11425
$679$	−34.1239	−1.30955
$680$	−102.393	−3.92659
$681$	32.6806	1.25232
$682$	18.5898	0.711842
$683$	−0.998782	−0.0382173	−0.0191087	−	0.999817i	$-0.506083\pi$
$683$	−0.998782	−0.0382173	−0.0191087	+	0.999817i	$0.506083\pi$
$684$	−9.41362	−0.359939
$685$	−50.1695	−1.91688
$686$	6.19056	0.236357
$687$	−33.3796	−1.27351
$688$	−7.73856	−0.295030
$689$	−0.470979	−0.0179429
$690$	154.624	5.88643
$691$	−0.664574	−0.0252816	−0.0126408	−	0.999920i	$-0.504024\pi$
$691$	−0.664574	−0.0252816	−0.0126408	+	0.999920i	$0.504024\pi$
$692$	−11.7652	−0.447244
$693$	2.12460	0.0807068
$694$	−42.6414	−1.61865
$695$	−7.10143	−0.269372
$696$	15.9043	0.602851
$697$	13.2833	0.503140
$698$	−4.69835	−0.177835
$699$	23.2846	0.880703
$700$	−159.314	−6.02152
$701$	36.8849	1.39312	0.696562	−	0.717497i	$-0.254712\pi$
$701$	36.8849	1.39312	0.696562	+	0.717497i	$0.254712\pi$
$702$	23.7007	0.894526
$703$	−20.6657	−0.779420
$704$	−27.1095	−1.02173
$705$	−33.1058	−1.24683
$706$	−65.3474	−2.45938
$707$	−10.3156	−0.387959
$708$	135.818	5.10435
$709$	−0.889967	−0.0334234	−0.0167117	−	0.999860i	$-0.505320\pi$
$709$	−0.889967	−0.0334234	−0.0167117	+	0.999860i	$0.505320\pi$
$710$	−17.0758	−0.640843
$711$	−0.585357	−0.0219526
$712$	99.4631	3.72754
$713$	−33.6579	−1.26050
$714$	63.9396	2.39288
$715$	−12.1196	−0.453248
$716$	−79.7214	−2.97933
$717$	30.8030	1.15036
$718$	−10.1657	−0.379381
$719$	45.6163	1.70120	0.850601	−	0.525812i	$-0.176239\pi$
$719$	45.6163	1.70120	0.850601	+	0.525812i	$0.176239\pi$
$720$	12.6730	0.472295
$721$	−32.8529	−1.22350
$722$	−49.2357	−1.83236
$723$	−12.2406	−0.455233
$724$	38.3837	1.42652
$725$	−8.87819	−0.329728
$726$	36.9532	1.37146
$727$	−16.9541	−0.628793	−0.314397	−	0.949292i	$-0.601802\pi$
$727$	−16.9541	−0.628793	−0.314397	+	0.949292i	$0.601802\pi$
$728$	56.5177	2.09469
$729$	23.7398	0.879253
$730$	120.839	4.47246
$731$	−2.33874	−0.0865013
$732$	−82.4515	−3.04750
$733$	43.5897	1.61002	0.805010	−	0.593261i	$-0.202160\pi$
$733$	43.5897	1.61002	0.805010	+	0.593261i	$0.202160\pi$
$734$	−52.7700	−1.94778
$735$	50.3316	1.85651
$736$	125.025	4.60847
$737$	−14.4529	−0.532381
$738$	−3.09476	−0.113920
$739$	−9.12385	−0.335626	−0.167813	−	0.985819i	$-0.553671\pi$
$739$	−9.12385	−0.335626	−0.167813	+	0.985819i	$0.553671\pi$
$740$	62.0783	2.28204
$741$	−20.2720	−0.744712
$742$	−2.62703	−0.0964414
$743$	32.0364	1.17530	0.587650	−	0.809115i	$-0.300053\pi$
$743$	32.0364	1.17530	0.587650	+	0.809115i	$0.300053\pi$
$744$	−56.4680	−2.07022
$745$	72.4437	2.65413
$746$	−41.7962	−1.53027
$747$	−2.81674	−0.103059
$748$	−32.0547	−1.17203
$749$	69.7221	2.54759
$750$	−56.9557	−2.07973
$751$	−36.1632	−1.31962	−0.659808	−	0.751435i	$-0.729362\pi$
$751$	−36.1632	−1.31962	−0.659808	+	0.751435i	$0.729362\pi$
$752$	−57.3752	−2.09226
$753$	−13.4979	−0.491891
$754$	5.20986	0.189732
$755$	−83.4837	−3.03828
$756$	94.7347	3.44547
$757$	−47.0287	−1.70929	−0.854644	−	0.519214i	$-0.826225\pi$
$757$	−47.0287	−1.70929	−0.854644	+	0.519214i	$0.826225\pi$
$758$	−74.0347	−2.68906
$759$	29.2635	1.06220
$760$	181.076	6.56832
$761$	−27.9800	−1.01427	−0.507137	−	0.861865i	$-0.669296\pi$
$761$	−27.9800	−1.01427	−0.507137	+	0.861865i	$0.669296\pi$
$762$	61.5435	2.22949
$763$	32.6888	1.18341
$764$	−37.3175	−1.35010
$765$	3.83002	0.138475
$766$	−25.2925	−0.913854
$767$	26.8966	0.971178
$768$	−0.995140	−0.0359090
$769$	−21.1417	−0.762388	−0.381194	−	0.924495i	$-0.624487\pi$
$769$	−21.1417	−0.762388	−0.381194	+	0.924495i	$0.624487\pi$
$770$	−67.6010	−2.43617
$771$	4.96795	0.178916
$772$	102.031	3.67218
$773$	3.35653	0.120726	0.0603631	−	0.998176i	$-0.480774\pi$
$773$	3.35653	0.120726	0.0603631	+	0.998176i	$0.480774\pi$
$774$	0.544883	0.0195854
$775$	31.5219	1.13230
$776$	−72.5141	−2.60310
$777$	−23.4352	−0.840732
$778$	−25.4815	−0.913554
$779$	−23.4907	−0.841642
$780$	60.8959	2.18042
$781$	−3.23170	−0.115639
$782$	80.9876	2.89611
$783$	5.27933	0.188668
$784$	87.2291	3.11533
$785$	−54.3579	−1.94012
$786$	−64.8472	−2.31302
$787$	16.8614	0.601044	0.300522	−	0.953775i	$-0.402839\pi$
$787$	16.8614	0.601044	0.300522	+	0.953775i	$0.402839\pi$
$788$	4.48734	0.159855
$789$	35.8226	1.27532
$790$	18.6250	0.662649
$791$	43.5772	1.54943
$792$	4.51483	0.160427
$793$	−16.3282	−0.579832
$794$	95.1851	3.37799
$795$	−1.71119	−0.0606895
$796$	−8.35209	−0.296032
$797$	−14.8708	−0.526751	−0.263376	−	0.964693i	$-0.584836\pi$
$797$	−14.8708	−0.526751	−0.263376	+	0.964693i	$0.584836\pi$
$798$	−113.074	−4.00276
$799$	−17.3399	−0.613440
$800$	−117.090	−4.13977
$801$	−3.72043	−0.131455
$802$	−68.0951	−2.40452
$803$	22.8695	0.807049
$804$	72.6198	2.56110
$805$	122.395	4.31386
$806$	−18.4976	−0.651549
$807$	51.4581	1.81141
$808$	−21.9210	−0.771178
$809$	42.7734	1.50383	0.751917	−	0.659258i	$-0.229130\pi$
$809$	42.7734	1.50383	0.751917	+	0.659258i	$0.229130\pi$
$810$	94.9217	3.33521
$811$	−5.40204	−0.189691	−0.0948456	−	0.995492i	$-0.530236\pi$
$811$	−5.40204	−0.189691	−0.0948456	+	0.995492i	$0.530236\pi$
$812$	20.8245	0.730796
$813$	−3.84443	−0.134830
$814$	16.3948	0.574637
$815$	−55.5079	−1.94436
$816$	72.1809	2.52684
$817$	4.13593	0.144698
$818$	−93.4217	−3.26641
$819$	−2.11405	−0.0738709
$820$	70.5646	2.46422
$821$	−32.2369	−1.12507	−0.562537	−	0.826772i	$-0.690175\pi$
$821$	−32.2369	−1.12507	−0.562537	+	0.826772i	$0.690175\pi$
$822$	66.5739	2.32203
$823$	−44.9599	−1.56721	−0.783603	−	0.621262i	$-0.786620\pi$
$823$	−44.9599	−1.56721	−0.783603	+	0.621262i	$0.786620\pi$
$824$	−69.8132	−2.43206
$825$	−27.4064	−0.954169
$826$	150.024	5.22000
$827$	9.64565	0.335412	0.167706	−	0.985837i	$-0.446364\pi$
$827$	9.64565	0.335412	0.167706	+	0.985837i	$0.446364\pi$
$828$	−13.5215	−0.469904
$829$	−17.2470	−0.599013	−0.299506	−	0.954094i	$-0.596822\pi$
$829$	−17.2470	−0.599013	−0.299506	+	0.954094i	$0.596822\pi$
$830$	89.6236	3.11088
$831$	−43.8566	−1.52137
$832$	26.9749	0.935186
$833$	26.3623	0.913398
$834$	9.42346	0.326308
$835$	−62.1708	−2.15151
$836$	56.6869	1.96056
$837$	−18.7442	−0.647895
$838$	19.7282	0.681499
$839$	−43.7963	−1.51202	−0.756009	−	0.654561i	$-0.772853\pi$
$839$	−43.7963	−1.51202	−0.756009	+	0.654561i	$0.772853\pi$
$840$	205.343	7.08501
$841$	−27.8395	−0.959983
$842$	−64.7122	−2.23013
$843$	−25.1379	−0.865794
$844$	−126.620	−4.35845
$845$	−35.2460	−1.21250
$846$	4.03987	0.138894
$847$	29.2509	1.00507
$848$	−2.96564	−0.101840
$849$	−27.5655	−0.946046
$850$	−75.8481	−2.60157
$851$	−29.6836	−1.01754
$852$	16.2379	0.556301
$853$	−48.4916	−1.66032	−0.830161	−	0.557523i	$-0.811752\pi$
$853$	−48.4916	−1.66032	−0.830161	+	0.557523i	$0.811752\pi$
$854$	−91.0757	−3.11655
$855$	−6.77317	−0.231638
$856$	148.161	5.06405
$857$	−22.9042	−0.782393	−0.391197	−	0.920307i	$-0.627939\pi$
$857$	−22.9042	−0.782393	−0.391197	+	0.920307i	$0.627939\pi$
$858$	16.0825	0.549048
$859$	−7.57407	−0.258424	−0.129212	−	0.991617i	$-0.541245\pi$
$859$	−7.57407	−0.258424	−0.129212	+	0.991617i	$0.541245\pi$
$860$	−12.4241	−0.423657
$861$	−26.6388	−0.907849
$862$	−23.6052	−0.803997
$863$	40.1274	1.36595	0.682976	−	0.730441i	$-0.260685\pi$
$863$	40.1274	1.36595	0.682976	+	0.730441i	$0.260685\pi$
$864$	69.6267	2.36875
$865$	−8.46511	−0.287823
$866$	68.5940	2.33092
$867$	−9.08549	−0.308559
$868$	−73.9371	−2.50959
$869$	3.52490	0.119574
$870$	18.9287	0.641744
$871$	14.3812	0.487288
$872$	69.4646	2.35237
$873$	2.71240	0.0918008
$874$	−143.222	−4.84456
$875$	−45.0842	−1.52413
$876$	−114.910	−3.88244
$877$	5.21679	0.176159	0.0880793	−	0.996113i	$-0.471927\pi$
$877$	5.21679	0.176159	0.0880793	+	0.996113i	$0.471927\pi$
$878$	4.60807	0.155515
$879$	−1.58107	−0.0533281
$880$	−76.3142	−2.57255
$881$	−52.6938	−1.77530	−0.887650	−	0.460519i	$-0.847663\pi$
$881$	−52.6938	−1.77530	−0.887650	+	0.460519i	$0.847663\pi$
$882$	−6.14193	−0.206809
$883$	39.9245	1.34356	0.671782	−	0.740748i	$-0.265529\pi$
$883$	39.9245	1.34356	0.671782	+	0.740748i	$0.265529\pi$
$884$	31.8955	1.07276
$885$	97.7219	3.28489
$886$	18.1444	0.609573
$887$	−43.8669	−1.47290	−0.736452	−	0.676489i	$-0.763500\pi$
$887$	−43.8669	−1.47290	−0.736452	+	0.676489i	$0.763500\pi$
$888$	−49.8004	−1.67119
$889$	48.7158	1.63388
$890$	118.378	3.96802
$891$	17.9645	0.601834
$892$	29.6071	0.991319
$893$	30.6646	1.02615
$894$	−96.1314	−3.21512
$895$	−57.3602	−1.91734
$896$	41.8511	1.39815
$897$	−29.1182	−0.972230
$898$	−85.3731	−2.84894
$899$	−4.12033	−0.137421
$900$	12.6634	0.422113
$901$	−0.896270	−0.0298591
$902$	18.6360	0.620511
$903$	4.69020	0.156080
$904$	92.6028	3.07992
$905$	27.6174	0.918032
$906$	110.781	3.68046
$907$	2.51771	0.0835993	0.0417997	−	0.999126i	$-0.486691\pi$
$907$	2.51771	0.0835993	0.0417997	+	0.999126i	$0.486691\pi$
$908$	90.9314	3.01766
$909$	0.819957	0.0271963
$910$	67.2654	2.22983
$911$	−29.2071	−0.967674	−0.483837	−	0.875158i	$-0.660757\pi$
$911$	−29.2071	−0.967674	−0.483837	+	0.875158i	$0.660757\pi$
$912$	−127.648	−4.22684
$913$	16.9618	0.561354
$914$	28.0336	0.927269
$915$	−59.3245	−1.96121
$916$	−92.8763	−3.06872
$917$	−51.3309	−1.69510
$918$	45.1023	1.48860
$919$	−3.73887	−0.123334	−0.0616669	−	0.998097i	$-0.519642\pi$
$919$	−3.73887	−0.123334	−0.0616669	+	0.998097i	$0.519642\pi$
$920$	260.093	8.57501
$921$	−50.8525	−1.67565
$922$	−53.4264	−1.75950
$923$	3.21565	0.105845
$924$	64.2838	2.11478
$925$	27.7999	0.914054
$926$	−10.3923	−0.341511
$927$	2.61137	0.0857687
$928$	15.3053	0.502419
$929$	−9.31122	−0.305491	−0.152746	−	0.988266i	$-0.548812\pi$
$929$	−9.31122	−0.305491	−0.152746	+	0.988266i	$0.548812\pi$
$930$	−67.2063	−2.20378
$931$	−46.6202	−1.52792
$932$	64.7876	2.12219
$933$	−6.51242	−0.213207
$934$	−53.2757	−1.74323
$935$	−23.0636	−0.754260
$936$	−4.49242	−0.146839
$937$	55.0753	1.79923	0.899616	−	0.436681i	$-0.143846\pi$
$937$	55.0753	1.79923	0.899616	+	0.436681i	$0.143846\pi$
$938$	80.2156	2.61913
$939$	−9.98664	−0.325902
$940$	−92.1144	−3.00444
$941$	51.1941	1.66888	0.834441	−	0.551098i	$-0.185791\pi$
$941$	51.1941	1.66888	0.834441	+	0.551098i	$0.185791\pi$
$942$	72.1320	2.35019
$943$	−33.7415	−1.09877
$944$	169.361	5.51222
$945$	68.1624	2.21732
$946$	−3.28117	−0.106680
$947$	−29.4732	−0.957751	−0.478875	−	0.877883i	$-0.658955\pi$
$947$	−29.4732	−0.957751	−0.478875	+	0.877883i	$0.658955\pi$
$948$	−17.7111	−0.575230
$949$	−22.7560	−0.738691
$950$	134.133	4.35185
$951$	−29.7898	−0.965999
$952$	107.553	3.48581
$953$	7.97063	0.258194	0.129097	−	0.991632i	$-0.458792\pi$
$953$	7.97063	0.258194	0.129097	+	0.991632i	$0.458792\pi$
$954$	0.208815	0.00676062
$955$	−26.8502	−0.868852
$956$	85.7071	2.77197
$957$	3.58238	0.115802
$958$	15.5992	0.503987
$959$	52.6977	1.70170
$960$	98.0065	3.16315
$961$	−16.3708	−0.528091
$962$	−16.3134	−0.525965
$963$	−5.54199	−0.178588
$964$	−34.0586	−1.09695
$965$	73.4122	2.36322
$966$	−162.416	−5.22565
$967$	51.9442	1.67041	0.835206	−	0.549937i	$-0.185348\pi$
$967$	51.9442	1.67041	0.835206	+	0.549937i	$0.185348\pi$
$968$	62.1590	1.99787
$969$	−38.5776	−1.23929
$970$	−86.3038	−2.77105
$971$	−24.1691	−0.775624	−0.387812	−	0.921739i	$-0.626769\pi$
$971$	−24.1691	−0.775624	−0.387812	+	0.921739i	$0.626769\pi$
$972$	−15.9089	−0.510277
$973$	7.45930	0.239134
$974$	−48.7077	−1.56069
$975$	27.2704	0.873351
$976$	−102.815	−3.29101
$977$	14.0539	0.449624	0.224812	−	0.974402i	$-0.427823\pi$
$977$	14.0539	0.449624	0.224812	+	0.974402i	$0.427823\pi$
$978$	73.6579	2.35532
$979$	22.4037	0.716024
$980$	140.044	4.47354
$981$	−2.59833	−0.0829583
$982$	5.48349	0.174985
$983$	−25.2306	−0.804732	−0.402366	−	0.915479i	$-0.631812\pi$
$983$	−25.2306	−0.804732	−0.402366	+	0.915479i	$0.631812\pi$
$984$	−56.6082	−1.80460
$985$	3.22868	0.102874
$986$	9.91433	0.315737
$987$	34.7741	1.10687
$988$	−56.4055	−1.79450
$989$	5.94074	0.188904
$990$	5.37339	0.170778
$991$	−3.46536	−0.110081	−0.0550404	−	0.998484i	$-0.517529\pi$
$991$	−3.46536	−0.110081	−0.0550404	+	0.998484i	$0.517529\pi$
$992$	−54.3412	−1.72533
$993$	9.81752	0.311549
$994$	17.9363	0.568906
$995$	−6.00939	−0.190510
$996$	−85.2258	−2.70048
$997$	63.0582	1.99707	0.998536	−	0.0540835i	$-0.0172237\pi$
$997$	63.0582	1.99707	0.998536	+	0.0540835i	$0.0172237\pi$
$998$	−44.6038	−1.41191
$999$	−16.5309	−0.523015

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4013.2.a.b.1.5	✓	157

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4013.2.a.b.1.5	✓	157	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:	\( N \)	\(=\)	\( 4013 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4013.a (trivial)

\(f(q)\)	\(=\)	\(q-2.65659 q^{2} +1.81764 q^{3} +5.05746 q^{4} +3.63888 q^{5} -4.82872 q^{6} -3.82226 q^{7} -8.12240 q^{8} +0.303819 q^{9} +O(q^{10})\)	\(q-2.65659 q^{2} +1.81764 q^{3} +5.05746 q^{4} +3.63888 q^{5} -4.82872 q^{6} -3.82226 q^{7} -8.12240 q^{8} +0.303819 q^{9} -9.66700 q^{10} -1.82954 q^{11} +9.19264 q^{12} +1.82046 q^{13} +10.1542 q^{14} +6.61417 q^{15} +11.4630 q^{16} +3.46432 q^{17} -0.807123 q^{18} -6.12645 q^{19} +18.4035 q^{20} -6.94749 q^{21} +4.86033 q^{22} -8.79988 q^{23} -14.7636 q^{24} +8.24143 q^{25} -4.83620 q^{26} -4.90069 q^{27} -19.3309 q^{28} -1.07726 q^{29} -17.5711 q^{30} +3.82481 q^{31} -14.2075 q^{32} -3.32544 q^{33} -9.20326 q^{34} -13.9087 q^{35} +1.53655 q^{36} +3.37318 q^{37} +16.2755 q^{38} +3.30894 q^{39} -29.5564 q^{40} +3.83431 q^{41} +18.4566 q^{42} -0.675093 q^{43} -9.25281 q^{44} +1.10556 q^{45} +23.3777 q^{46} -5.00527 q^{47} +20.8355 q^{48} +7.60966 q^{49} -21.8941 q^{50} +6.29689 q^{51} +9.20688 q^{52} -0.258715 q^{53} +13.0191 q^{54} -6.65747 q^{55} +31.0459 q^{56} -11.1357 q^{57} +2.86184 q^{58} +14.7746 q^{59} +33.4509 q^{60} -8.96929 q^{61} -10.1609 q^{62} -1.16128 q^{63} +14.8177 q^{64} +6.62442 q^{65} +8.83433 q^{66} +7.89978 q^{67} +17.5206 q^{68} -15.9950 q^{69} +36.9498 q^{70} +1.76640 q^{71} -2.46774 q^{72} -12.5002 q^{73} -8.96116 q^{74} +14.9800 q^{75} -30.9843 q^{76} +6.99297 q^{77} -8.79048 q^{78} -1.92666 q^{79} +41.7123 q^{80} -9.81915 q^{81} -10.1862 q^{82} -9.27109 q^{83} -35.1366 q^{84} +12.6062 q^{85} +1.79344 q^{86} -1.95808 q^{87} +14.8602 q^{88} -12.2455 q^{89} -2.93702 q^{90} -6.95825 q^{91} -44.5050 q^{92} +6.95214 q^{93} +13.2969 q^{94} -22.2934 q^{95} -25.8242 q^{96} +8.92767 q^{97} -20.2157 q^{98} -0.555849 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9}+O(q^{10}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9	\( 157 q - 15 q^{2} - 51 q^{3} + 137 q^{4} - 13 q^{5} - 15 q^{6} - 49 q^{7} - 42 q^{8} + 144 q^{9} - 61 q^{10} - 27 q^{11} - 93 q^{12} - 97 q^{13} - 12 q^{14} - 36 q^{15} + 105 q^{16} - 45 q^{17} - 68 q^{18} - 128 q^{19} - 30 q^{20} - 26 q^{21} - 68 q^{22} - 41 q^{23} - 40 q^{24} + 102 q^{25} - 5 q^{26} - 189 q^{27} - 115 q^{28} - 26 q^{29} - 12 q^{30} - 88 q^{31} - 89 q^{32} - 52 q^{33} - 61 q^{34} - 87 q^{35} + 110 q^{36} - 62 q^{37} - 37 q^{38} - 20 q^{39} - 161 q^{40} - 34 q^{41} - 53 q^{42} - 254 q^{43} - 19 q^{44} - 46 q^{45} - 52 q^{46} - 76 q^{47} - 162 q^{48} + 96 q^{49} - 54 q^{50} - 76 q^{51} - 259 q^{52} - 48 q^{53} - 12 q^{54} - 194 q^{55} - 10 q^{56} - 30 q^{57} - 52 q^{58} - 64 q^{59} - 31 q^{60} - 107 q^{61} - 51 q^{62} - 106 q^{63} + 54 q^{64} - 17 q^{65} - 13 q^{66} - 193 q^{67} - 118 q^{68} - 55 q^{69} - 86 q^{70} - 11 q^{71} - 172 q^{72} - 173 q^{73} - 11 q^{74} - 209 q^{75} - 213 q^{76} - 84 q^{77} - 30 q^{78} - 111 q^{79} - 6 q^{80} + 157 q^{81} - 117 q^{82} - 154 q^{83} - 6 q^{84} - 91 q^{85} + 28 q^{86} - 165 q^{87} - 165 q^{88} - 32 q^{89} - 103 q^{90} - 200 q^{91} - 86 q^{92} - 39 q^{93} - 118 q^{94} - 22 q^{95} - 28 q^{96} - 151 q^{97} - 38 q^{98} - 91 q^{99}+O(q^{100}) \) 157 * q - 15 * q^2 - 51 * q^3 + 137 * q^4 - 13 * q^5 - 15 * q^6 - 49 * q^7 - 42 * q^8 + 144 * q^9 - 61 * q^10 - 27 * q^11 - 93 * q^12 - 97 * q^13 - 12 * q^14 - 36 * q^15 + 105 * q^16 - 45 * q^17 - 68 * q^18 - 128 * q^19 - 30 * q^20 - 26 * q^21 - 68 * q^22 - 41 * q^23 - 40 * q^24 + 102 * q^25 - 5 * q^26 - 189 * q^27 - 115 * q^28 - 26 * q^29 - 12 * q^30 - 88 * q^31 - 89 * q^32 - 52 * q^33 - 61 * q^34 - 87 * q^35 + 110 * q^36 - 62 * q^37 - 37 * q^38 - 20 * q^39 - 161 * q^40 - 34 * q^41 - 53 * q^42 - 254 * q^43 - 19 * q^44 - 46 * q^45 - 52 * q^46 - 76 * q^47 - 162 * q^48 + 96 * q^49 - 54 * q^50 - 76 * q^51 - 259 * q^52 - 48 * q^53 - 12 * q^54 - 194 * q^55 - 10 * q^56 - 30 * q^57 - 52 * q^58 - 64 * q^59 - 31 * q^60 - 107 * q^61 - 51 * q^62 - 106 * q^63 + 54 * q^64 - 17 * q^65 - 13 * q^66 - 193 * q^67 - 118 * q^68 - 55 * q^69 - 86 * q^70 - 11 * q^71 - 172 * q^72 - 173 * q^73 - 11 * q^74 - 209 * q^75 - 213 * q^76 - 84 * q^77 - 30 * q^78 - 111 * q^79 - 6 * q^80 + 157 * q^81 - 117 * q^82 - 154 * q^83 - 6 * q^84 - 91 * q^85 + 28 * q^86 - 165 * q^87 - 165 * q^88 - 32 * q^89 - 103 * q^90 - 200 * q^91 - 86 * q^92 - 39 * q^93 - 118 * q^94 - 22 * q^95 - 28 * q^96 - 151 * q^97 - 38 * q^98 - 91 * q^99

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