LMFDB - Embedded newform 8023.2.a.c.1.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8023,2,Mod(1,8023)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8023, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("8023.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8023 = 71 \cdot 113 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8023.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:	$64.0639775417$
Analytic rank:	$1$
Dimension:	$158$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.20
Character	$\chi$	$=$	8023.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.36619 q^{2} -2.12839 q^{3} +3.59886 q^{4} +0.442767 q^{5} +5.03618 q^{6} -4.08071 q^{7} -3.78320 q^{8} +1.53005 q^{9} +O(q^{10})$	\(q-2.36619 q^{2} -2.12839 q^{3} +3.59886 q^{4} +0.442767 q^{5} +5.03618 q^{6} -4.08071 q^{7} -3.78320 q^{8} +1.53005 q^{9} -1.04767 q^{10} +6.07255 q^{11} -7.65978 q^{12} -2.05816 q^{13} +9.65574 q^{14} -0.942382 q^{15} +1.75406 q^{16} -7.35382 q^{17} -3.62039 q^{18} -7.65712 q^{19} +1.59346 q^{20} +8.68535 q^{21} -14.3688 q^{22} +3.46771 q^{23} +8.05214 q^{24} -4.80396 q^{25} +4.87000 q^{26} +3.12863 q^{27} -14.6859 q^{28} +1.30887 q^{29} +2.22986 q^{30} +2.51535 q^{31} +3.41596 q^{32} -12.9248 q^{33} +17.4005 q^{34} -1.80681 q^{35} +5.50644 q^{36} +8.78489 q^{37} +18.1182 q^{38} +4.38058 q^{39} -1.67508 q^{40} +1.66699 q^{41} -20.5512 q^{42} -12.6010 q^{43} +21.8542 q^{44} +0.677457 q^{45} -8.20527 q^{46} +0.421122 q^{47} -3.73333 q^{48} +9.65220 q^{49} +11.3671 q^{50} +15.6518 q^{51} -7.40703 q^{52} +11.6200 q^{53} -7.40293 q^{54} +2.68873 q^{55} +15.4382 q^{56} +16.2973 q^{57} -3.09703 q^{58} +12.7502 q^{59} -3.39150 q^{60} -3.33656 q^{61} -5.95179 q^{62} -6.24370 q^{63} -11.5909 q^{64} -0.911287 q^{65} +30.5824 q^{66} -10.2681 q^{67} -26.4653 q^{68} -7.38065 q^{69} +4.27525 q^{70} -1.00000 q^{71} -5.78850 q^{72} -8.36381 q^{73} -20.7867 q^{74} +10.2247 q^{75} -27.5569 q^{76} -24.7803 q^{77} -10.3653 q^{78} +6.19979 q^{79} +0.776642 q^{80} -11.2491 q^{81} -3.94441 q^{82} -5.89730 q^{83} +31.2573 q^{84} -3.25603 q^{85} +29.8163 q^{86} -2.78578 q^{87} -22.9737 q^{88} +10.3247 q^{89} -1.60299 q^{90} +8.39877 q^{91} +12.4798 q^{92} -5.35364 q^{93} -0.996455 q^{94} -3.39032 q^{95} -7.27050 q^{96} +12.9648 q^{97} -22.8390 q^{98} +9.29131 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) $ 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * 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 $

$2$	−2.36619	−1.67315	−0.836575	−	0.547853i	$-0.815445\pi$
$2$	−2.36619	−1.67315	−0.836575	+	0.547853i	$0.815445\pi$
$3$	−2.12839	−1.22883	−0.614414	−	0.788984i	$-0.710607\pi$
$3$	−2.12839	−1.22883	−0.614414	+	0.788984i	$0.710607\pi$
$4$	3.59886	1.79943
$5$	0.442767	0.198012	0.0990058	−	0.995087i	$-0.468434\pi$
$5$	0.442767	0.198012	0.0990058	+	0.995087i	$0.468434\pi$
$6$	5.03618	2.05601
$7$	−4.08071	−1.54236	−0.771182	−	0.636615i	$-0.780334\pi$
$7$	−4.08071	−1.54236	−0.771182	+	0.636615i	$0.780334\pi$
$8$	−3.78320	−1.33756
$9$	1.53005	0.510017
$10$	−1.04767	−0.331303
$11$	6.07255	1.83094	0.915471	−	0.402384i	$-0.131818\pi$
$11$	6.07255	1.83094	0.915471	+	0.402384i	$0.131818\pi$
$12$	−7.65978	−2.21119
$13$	−2.05816	−0.570831	−0.285416	−	0.958404i	$-0.592132\pi$
$13$	−2.05816	−0.570831	−0.285416	+	0.958404i	$0.592132\pi$
$14$	9.65574	2.58061
$15$	−0.942382	−0.243322
$16$	1.75406	0.438516
$17$	−7.35382	−1.78356	−0.891781	−	0.452467i	$-0.850544\pi$
$17$	−7.35382	−1.78356	−0.891781	+	0.452467i	$0.850544\pi$
$18$	−3.62039	−0.853335
$19$	−7.65712	−1.75666	−0.878332	−	0.478052i	$-0.841343\pi$
$19$	−7.65712	−1.75666	−0.878332	+	0.478052i	$0.841343\pi$
$20$	1.59346	0.356308
$21$	8.68535	1.89530
$22$	−14.3688	−3.06344
$23$	3.46771	0.723068	0.361534	−	0.932359i	$-0.382253\pi$
$23$	3.46771	0.723068	0.361534	+	0.932359i	$0.382253\pi$
$24$	8.05214	1.64364
$25$	−4.80396	−0.960791
$26$	4.87000	0.955086
$27$	3.12863	0.602104
$28$	−14.6859	−2.77537
$29$	1.30887	0.243051	0.121525	−	0.992588i	$-0.461221\pi$
$29$	1.30887	0.243051	0.121525	+	0.992588i	$0.461221\pi$
$30$	2.22986	0.407114
$31$	2.51535	0.451770	0.225885	−	0.974154i	$-0.427473\pi$
$31$	2.51535	0.451770	0.225885	+	0.974154i	$0.427473\pi$
$32$	3.41596	0.603862
$33$	−12.9248	−2.24991
$34$	17.4005	2.98417
$35$	−1.80681	−0.305406
$36$	5.50644	0.917740
$37$	8.78489	1.44423	0.722114	−	0.691774i	$-0.243171\pi$
$37$	8.78489	1.44423	0.722114	+	0.691774i	$0.243171\pi$
$38$	18.1182	2.93916
$39$	4.38058	0.701453
$40$	−1.67508	−0.264853
$41$	1.66699	0.260340	0.130170	−	0.991492i	$-0.458448\pi$
$41$	1.66699	0.260340	0.130170	+	0.991492i	$0.458448\pi$
$42$	−20.5512	−3.17112
$43$	−12.6010	−1.92163	−0.960814	−	0.277193i	$-0.910596\pi$
$43$	−12.6010	−1.92163	−0.960814	+	0.277193i	$0.910596\pi$
$44$	21.8542	3.29465
$45$	0.677457	0.100989
$46$	−8.20527	−1.20980
$47$	0.421122	0.0614270	0.0307135	−	0.999528i	$-0.490222\pi$
$47$	0.421122	0.0614270	0.0307135	+	0.999528i	$0.490222\pi$
$48$	−3.73333	−0.538860
$49$	9.65220	1.37889
$50$	11.3671	1.60755
$51$	15.6518	2.19169
$52$	−7.40703	−1.02717
$53$	11.6200	1.59612	0.798062	−	0.602576i	$-0.205859\pi$
$53$	11.6200	1.59612	0.798062	+	0.602576i	$0.205859\pi$
$54$	−7.40293	−1.00741
$55$	2.68873	0.362548
$56$	15.4382	2.06301
$57$	16.2973	2.15864
$58$	−3.09703	−0.406660
$59$	12.7502	1.65994	0.829970	−	0.557808i	$-0.188357\pi$
$59$	12.7502	1.65994	0.829970	+	0.557808i	$0.188357\pi$
$60$	−3.39150	−0.437841
$61$	−3.33656	−0.427203	−0.213601	−	0.976921i	$-0.568519\pi$
$61$	−3.33656	−0.427203	−0.213601	+	0.976921i	$0.568519\pi$
$62$	−5.95179	−0.755878
$63$	−6.24370	−0.786632
$64$	−11.5909	−1.44887
$65$	−0.911287	−0.113031
$66$	30.5824	3.76444
$67$	−10.2681	−1.25444	−0.627222	−	0.778840i	$-0.715808\pi$
$67$	−10.2681	−1.25444	−0.627222	+	0.778840i	$0.715808\pi$
$68$	−26.4653	−3.20939
$69$	−7.38065	−0.888526
$70$	4.27525	0.510990
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−5.78850	−0.682181
$73$	−8.36381	−0.978910	−0.489455	−	0.872029i	$-0.662804\pi$
$73$	−8.36381	−0.978910	−0.489455	+	0.872029i	$0.662804\pi$
$74$	−20.7867	−2.41641
$75$	10.2247	1.18065
$76$	−27.5569	−3.16099
$77$	−24.7803	−2.82398
$78$	−10.3653	−1.17364
$79$	6.19979	0.697531	0.348766	−	0.937210i	$-0.386601\pi$
$79$	6.19979	0.697531	0.348766	+	0.937210i	$0.386601\pi$
$80$	0.776642	0.0868312
$81$	−11.2491	−1.24990
$82$	−3.94441	−0.435588
$83$	−5.89730	−0.647313	−0.323657	−	0.946175i	$-0.604912\pi$
$83$	−5.89730	−0.647313	−0.323657	+	0.946175i	$0.604912\pi$
$84$	31.2573	3.41046
$85$	−3.25603	−0.353166
$86$	29.8163	3.21517
$87$	−2.78578	−0.298667
$88$	−22.9737	−2.44900
$89$	10.3247	1.09442	0.547210	−	0.836995i	$-0.315690\pi$
$89$	10.3247	1.09442	0.547210	+	0.836995i	$0.315690\pi$
$90$	−1.60299	−0.168970
$91$	8.39877	0.880430
$92$	12.4798	1.30111
$93$	−5.35364	−0.555147
$94$	−0.996455	−0.102777
$95$	−3.39032	−0.347840
$96$	−7.27050	−0.742042
$97$	12.9648	1.31638	0.658189	−	0.752852i	$-0.271323\pi$
$97$	12.9648	1.31638	0.658189	+	0.752852i	$0.271323\pi$
$98$	−22.8390	−2.30708
$99$	9.29131	0.933812
$100$	−17.2888	−1.72888
$101$	−13.2816	−1.32157	−0.660783	−	0.750577i	$-0.729776\pi$
$101$	−13.2816	−1.32157	−0.660783	+	0.750577i	$0.729776\pi$
$102$	−37.0352	−3.66703
$103$	−8.06131	−0.794305	−0.397152	−	0.917753i	$-0.630002\pi$
$103$	−8.06131	−0.794305	−0.397152	+	0.917753i	$0.630002\pi$
$104$	7.78645	0.763524
$105$	3.84559	0.375291
$106$	−27.4950	−2.67055
$107$	8.88851	0.859285	0.429642	−	0.902999i	$-0.358640\pi$
$107$	8.88851	0.859285	0.429642	+	0.902999i	$0.358640\pi$
$108$	11.2595	1.08344
$109$	10.0984	0.967253	0.483627	−	0.875274i	$-0.339319\pi$
$109$	10.0984	0.967253	0.483627	+	0.875274i	$0.339319\pi$
$110$	−6.36204	−0.606596
$111$	−18.6977	−1.77471
$112$	−7.15783	−0.676351
$113$	−1.00000	−0.0940721
$113$	−1.00000	−0.0940721
$114$	−38.5626	−3.61172
$115$	1.53539	0.143176
$116$	4.71043	0.437352
$117$	−3.14909	−0.291134
$118$	−30.1695	−2.77733
$119$	30.0088	2.75090
$120$	3.56522	0.325459
$121$	25.8758	2.35235
$122$	7.89493	0.714774
$123$	−3.54801	−0.319913
$124$	9.05238	0.812927
$125$	−4.34087	−0.388259
$126$	14.7738	1.31615
$127$	−6.65856	−0.590852	−0.295426	−	0.955366i	$-0.595462\pi$
$127$	−6.65856	−0.590852	−0.295426	+	0.955366i	$0.595462\pi$
$128$	20.5944	1.82031
$129$	26.8198	2.36135
$130$	2.15628	0.189118
$131$	9.11938	0.796764	0.398382	−	0.917220i	$-0.369572\pi$
$131$	9.11938	0.796764	0.398382	+	0.917220i	$0.369572\pi$
$132$	−46.5144	−4.04856
$133$	31.2465	2.70941
$134$	24.2962	2.09887
$135$	1.38525	0.119224
$136$	27.8210	2.38563
$137$	5.12922	0.438219	0.219109	−	0.975700i	$-0.429685\pi$
$137$	5.12922	0.438219	0.219109	+	0.975700i	$0.429685\pi$
$138$	17.4640	1.48664
$139$	3.16049	0.268069	0.134034	−	0.990977i	$-0.457207\pi$
$139$	3.16049	0.268069	0.134034	+	0.990977i	$0.457207\pi$
$140$	−6.50244	−0.549556
$141$	−0.896313	−0.0754832
$142$	2.36619	0.198566
$143$	−12.4983	−1.04516
$144$	2.68381	0.223651
$145$	0.579524	0.0481268
$146$	19.7904	1.63786
$147$	−20.5437	−1.69441
$148$	31.6156	2.59879
$149$	17.2508	1.41324	0.706620	−	0.707593i	$-0.250219\pi$
$149$	17.2508	1.41324	0.706620	+	0.707593i	$0.250219\pi$
$150$	−24.1936	−1.97540
$151$	−13.1367	−1.06905	−0.534526	−	0.845152i	$-0.679510\pi$
$151$	−13.1367	−1.06905	−0.534526	+	0.845152i	$0.679510\pi$
$152$	28.9684	2.34965
$153$	−11.2517	−0.909648
$154$	58.6349	4.72494
$155$	1.11371	0.0894556
$156$	15.7651	1.26222
$157$	−13.5724	−1.08319	−0.541597	−	0.840639i	$-0.682180\pi$
$157$	−13.5724	−1.08319	−0.541597	+	0.840639i	$0.682180\pi$
$158$	−14.6699	−1.16707
$159$	−24.7318	−1.96136
$160$	1.51247	0.119572
$161$	−14.1507	−1.11523
$162$	26.6175	2.09127
$163$	12.6027	0.987120	0.493560	−	0.869712i	$-0.335695\pi$
$163$	12.6027	0.987120	0.493560	+	0.869712i	$0.335695\pi$
$164$	5.99926	0.468463
$165$	−5.72266	−0.445508
$166$	13.9541	1.08305
$167$	0.771686	0.0597149	0.0298574	−	0.999554i	$-0.490495\pi$
$167$	0.771686	0.0597149	0.0298574	+	0.999554i	$0.490495\pi$
$168$	−32.8585	−2.53508
$169$	−8.76397	−0.674151
$170$	7.70439	0.590899
$171$	−11.7158	−0.895929
$172$	−45.3491	−3.45783
$173$	−12.5847	−0.956796	−0.478398	−	0.878143i	$-0.658782\pi$
$173$	−12.5847	−0.956796	−0.478398	+	0.878143i	$0.658782\pi$
$174$	6.59170	0.499715
$175$	19.6036	1.48189
$176$	10.6516	0.802897
$177$	−27.1375	−2.03978
$178$	−24.4303	−1.83113
$179$	2.97475	0.222343	0.111172	−	0.993801i	$-0.464540\pi$
$179$	2.97475	0.222343	0.111172	+	0.993801i	$0.464540\pi$
$180$	2.43807	0.181723
$181$	−14.3982	−1.07021	−0.535106	−	0.844785i	$-0.679728\pi$
$181$	−14.3982	−1.07021	−0.535106	+	0.844785i	$0.679728\pi$
$182$	−19.8731	−1.47309
$183$	7.10150	0.524958
$184$	−13.1191	−0.967150
$185$	3.88966	0.285974
$186$	12.6677	0.928844
$187$	−44.6564	−3.26560
$188$	1.51556	0.110534
$189$	−12.7670	−0.928664
$190$	8.02215	0.581988
$191$	−17.7644	−1.28539	−0.642695	−	0.766122i	$-0.722184\pi$
$191$	−17.7644	−1.28539	−0.642695	+	0.766122i	$0.722184\pi$
$192$	24.6700	1.78041
$193$	−4.14988	−0.298715	−0.149358	−	0.988783i	$-0.547721\pi$
$193$	−4.14988	−0.298715	−0.149358	+	0.988783i	$0.547721\pi$
$194$	−30.6773	−2.20250
$195$	1.93958	0.138896
$196$	34.7369	2.48121
$197$	19.1210	1.36231	0.681157	−	0.732138i	$-0.261477\pi$
$197$	19.1210	1.36231	0.681157	+	0.732138i	$0.261477\pi$
$198$	−21.9850	−1.56241
$199$	8.73906	0.619496	0.309748	−	0.950819i	$-0.399755\pi$
$199$	8.73906	0.619496	0.309748	+	0.950819i	$0.399755\pi$
$200$	18.1743	1.28512
$201$	21.8545	1.54150
$202$	31.4268	2.21118
$203$	−5.34111	−0.374873
$204$	56.3286	3.94379
$205$	0.738088	0.0515503
$206$	19.0746	1.32899
$207$	5.30578	0.368777
$208$	−3.61015	−0.250319
$209$	−46.4982	−3.21635
$210$	−9.09940	−0.627918
$211$	9.50402	0.654284	0.327142	−	0.944975i	$-0.393915\pi$
$211$	9.50402	0.654284	0.327142	+	0.944975i	$0.393915\pi$
$212$	41.8186	2.87211
$213$	2.12839	0.145835
$214$	−21.0319	−1.43771
$215$	−5.57929	−0.380505
$216$	−11.8362	−0.805353
$217$	−10.2644	−0.696793
$218$	−23.8948	−1.61836
$219$	17.8015	1.20291
$220$	9.67634	0.652379
$221$	15.1353	1.01811
$222$	44.2423	2.96935
$223$	22.6442	1.51637	0.758185	−	0.652039i	$-0.226086\pi$
$223$	22.6442	1.51637	0.758185	+	0.652039i	$0.226086\pi$
$224$	−13.9395	−0.931374
$225$	−7.35030	−0.490020
$226$	2.36619	0.157397
$227$	23.4338	1.55536	0.777679	−	0.628661i	$-0.216397\pi$
$227$	23.4338	1.55536	0.777679	+	0.628661i	$0.216397\pi$
$228$	58.6518	3.88431
$229$	−10.4501	−0.690562	−0.345281	−	0.938499i	$-0.612216\pi$
$229$	−10.4501	−0.690562	−0.345281	+	0.938499i	$0.612216\pi$
$230$	−3.63302	−0.239555
$231$	52.7422	3.47018
$232$	−4.95171	−0.325096
$233$	−0.628158	−0.0411520	−0.0205760	−	0.999788i	$-0.506550\pi$
$233$	−0.628158	−0.0411520	−0.0205760	+	0.999788i	$0.506550\pi$
$234$	7.45136	0.487110
$235$	0.186459	0.0121633
$236$	45.8863	2.98694
$237$	−13.1956	−0.857146
$238$	−71.0065	−4.60267
$239$	12.5760	0.813475	0.406737	−	0.913545i	$-0.366666\pi$
$239$	12.5760	0.813475	0.406737	+	0.913545i	$0.366666\pi$
$240$	−1.65300	−0.106701
$241$	12.6444	0.814499	0.407250	−	0.913317i	$-0.366488\pi$
$241$	12.6444	0.814499	0.407250	+	0.913317i	$0.366488\pi$
$242$	−61.2271	−3.93583
$243$	14.5566	0.933807
$244$	−12.0078	−0.768721
$245$	4.27368	0.273035
$246$	8.39526	0.535262
$247$	15.7596	1.00276
$248$	−9.51607	−0.604271
$249$	12.5518	0.795436
$250$	10.2713	0.649616
$251$	24.1268	1.52287	0.761434	−	0.648243i	$-0.224496\pi$
$251$	24.1268	1.52287	0.761434	+	0.648243i	$0.224496\pi$
$252$	−22.4702	−1.41549
$253$	21.0579	1.32390
$254$	15.7554	0.988584
$255$	6.93011	0.433980
$256$	−25.5485	−1.59678
$257$	−2.28458	−0.142508	−0.0712542	−	0.997458i	$-0.522700\pi$
$257$	−2.28458	−0.142508	−0.0712542	+	0.997458i	$0.522700\pi$
$258$	−63.4607	−3.95089
$259$	−35.8486	−2.22752
$260$	−3.27959	−0.203392
$261$	2.00264	0.123960
$262$	−21.5782	−1.33311
$263$	−6.37142	−0.392879	−0.196439	−	0.980516i	$-0.562938\pi$
$263$	−6.37142	−0.392879	−0.196439	+	0.980516i	$0.562938\pi$
$264$	48.8970	3.00940
$265$	5.14493	0.316051
$266$	−73.9352	−4.53325
$267$	−21.9751	−1.34485
$268$	−36.9533	−2.25728
$269$	−14.6742	−0.894701	−0.447351	−	0.894359i	$-0.647632\pi$
$269$	−14.6742	−0.894701	−0.447351	+	0.894359i	$0.647632\pi$
$270$	−3.27777	−0.199479
$271$	−4.61315	−0.280229	−0.140115	−	0.990135i	$-0.544747\pi$
$271$	−4.61315	−0.280229	−0.140115	+	0.990135i	$0.544747\pi$
$272$	−12.8991	−0.782120
$273$	−17.8759	−1.08190
$274$	−12.1367	−0.733205
$275$	−29.1723	−1.75915
$276$	−26.5619	−1.59884
$277$	31.6588	1.90219	0.951095	−	0.308898i	$-0.0999603\pi$
$277$	31.6588	1.90219	0.951095	+	0.308898i	$0.0999603\pi$
$278$	−7.47831	−0.448519
$279$	3.84861	0.230410
$280$	6.83551	0.408500
$281$	4.80563	0.286680	0.143340	−	0.989674i	$-0.454216\pi$
$281$	4.80563	0.286680	0.143340	+	0.989674i	$0.454216\pi$
$282$	2.12085	0.126295
$283$	−20.3995	−1.21262	−0.606311	−	0.795228i	$-0.707351\pi$
$283$	−20.3995	−1.21262	−0.606311	+	0.795228i	$0.707351\pi$
$284$	−3.59886	−0.213553
$285$	7.21593	0.427435
$286$	29.5733	1.74871
$287$	−6.80250	−0.401539
$288$	5.22659	0.307980
$289$	37.0786	2.18110
$290$	−1.37126	−0.0805234
$291$	−27.5942	−1.61760
$292$	−30.1002	−1.76148
$293$	12.9704	0.757740	0.378870	−	0.925450i	$-0.376313\pi$
$293$	12.9704	0.757740	0.378870	+	0.925450i	$0.376313\pi$
$294$	48.6102	2.83501
$295$	5.64539	0.328687
$296$	−33.2350	−1.93175
$297$	18.9987	1.10242
$298$	−40.8186	−2.36456
$299$	−7.13712	−0.412750
$300$	36.7973	2.12449
$301$	51.4209	2.96385
$302$	31.0840	1.78868
$303$	28.2684	1.62398
$304$	−13.4311	−0.770325
$305$	−1.47732	−0.0845910
$306$	26.6237	1.52198
$307$	20.9522	1.19580	0.597902	−	0.801569i	$-0.296001\pi$
$307$	20.9522	1.19580	0.597902	+	0.801569i	$0.296001\pi$
$308$	−89.1808	−5.08155
$309$	17.1576	0.976064
$310$	−2.63526	−0.149673
$311$	−2.33388	−0.132342	−0.0661711	−	0.997808i	$-0.521078\pi$
$311$	−2.33388	−0.132342	−0.0661711	+	0.997808i	$0.521078\pi$
$312$	−16.5726	−0.938239
$313$	−21.6269	−1.22242	−0.611212	−	0.791467i	$-0.709318\pi$
$313$	−21.6269	−1.22242	−0.611212	+	0.791467i	$0.709318\pi$
$314$	32.1148	1.81234
$315$	−2.76451	−0.155762
$316$	22.3122	1.25516
$317$	−33.5458	−1.88412	−0.942061	−	0.335442i	$-0.891114\pi$
$317$	−33.5458	−1.88412	−0.942061	+	0.335442i	$0.891114\pi$
$318$	58.5202	3.28165
$319$	7.94816	0.445012
$320$	−5.13209	−0.286892
$321$	−18.9182	−1.05591
$322$	33.4833	1.86595
$323$	56.3090	3.13312
$324$	−40.4839	−2.24911
$325$	9.88732	0.548450
$326$	−29.8204	−1.65160
$327$	−21.4934	−1.18859
$328$	−6.30656	−0.348221
$329$	−1.71848	−0.0947428
$330$	13.5409	0.745402
$331$	35.2081	1.93521	0.967605	−	0.252467i	$-0.0812420\pi$
$331$	35.2081	1.93521	0.967605	+	0.252467i	$0.0812420\pi$
$332$	−21.2236	−1.16479
$333$	13.4413	0.736581
$334$	−1.82596	−0.0999119
$335$	−4.54637	−0.248395
$336$	15.2347	0.831119
$337$	8.92467	0.486157	0.243079	−	0.970007i	$-0.421843\pi$
$337$	8.92467	0.486157	0.243079	+	0.970007i	$0.421843\pi$
$338$	20.7372	1.12796
$339$	2.12839	0.115598
$340$	−11.7180	−0.635497
$341$	15.2746	0.827164
$342$	27.7218	1.49902
$343$	−10.8229	−0.584380
$344$	47.6720	2.57030
$345$	−3.26791	−0.175938
$346$	29.7778	1.60086
$347$	−16.0283	−0.860445	−0.430223	−	0.902723i	$-0.641565\pi$
$347$	−16.0283	−0.860445	−0.430223	+	0.902723i	$0.641565\pi$
$348$	−10.0256	−0.537431
$349$	−12.4523	−0.666559	−0.333279	−	0.942828i	$-0.608155\pi$
$349$	−12.4523	−0.666559	−0.333279	+	0.942828i	$0.608155\pi$
$350$	−46.3858	−2.47942
$351$	−6.43922	−0.343700
$352$	20.7436	1.10564
$353$	3.79464	0.201968	0.100984	−	0.994888i	$-0.467801\pi$
$353$	3.79464	0.201968	0.100984	+	0.994888i	$0.467801\pi$
$354$	64.2125	3.41286
$355$	−0.442767	−0.0234996
$356$	37.1573	1.96933
$357$	−63.8705	−3.38038
$358$	−7.03883	−0.372013
$359$	32.8685	1.73473	0.867366	−	0.497671i	$-0.165811\pi$
$359$	32.8685	1.73473	0.867366	+	0.497671i	$0.165811\pi$
$360$	−2.56296	−0.135080
$361$	39.6315	2.08587
$362$	34.0690	1.79062
$363$	−55.0739	−2.89063
$364$	30.2260	1.58427
$365$	−3.70322	−0.193835
$366$	−16.8035	−0.878334
$367$	5.35795	0.279683	0.139841	−	0.990174i	$-0.455341\pi$
$367$	5.35795	0.279683	0.139841	+	0.990174i	$0.455341\pi$
$368$	6.08259	0.317077
$369$	2.55058	0.132778
$370$	−9.20369	−0.478477
$371$	−47.4177	−2.46180
$372$	−19.2670	−0.998948
$373$	−21.9639	−1.13725	−0.568623	−	0.822598i	$-0.692524\pi$
$373$	−21.9639	−1.13725	−0.568623	+	0.822598i	$0.692524\pi$
$374$	105.666	5.46384
$375$	9.23907	0.477104
$376$	−1.59319	−0.0821625
$377$	−2.69386	−0.138741
$378$	30.2092	1.55379
$379$	2.02462	0.103998	0.0519989	−	0.998647i	$-0.483441\pi$
$379$	2.02462	0.103998	0.0519989	+	0.998647i	$0.483441\pi$
$380$	−12.2013	−0.625913
$381$	14.1720	0.726055
$382$	42.0341	2.15065
$383$	−5.91063	−0.302019	−0.151010	−	0.988532i	$-0.548252\pi$
$383$	−5.91063	−0.302019	−0.151010	+	0.988532i	$0.548252\pi$
$384$	−43.8330	−2.23685
$385$	−10.9719	−0.559180
$386$	9.81942	0.499795
$387$	−19.2801	−0.980064
$388$	46.6586	2.36873
$389$	−32.5830	−1.65202	−0.826011	−	0.563653i	$-0.809395\pi$
$389$	−32.5830	−1.65202	−0.826011	+	0.563653i	$0.809395\pi$
$390$	−4.58941	−0.232394
$391$	−25.5009	−1.28964
$392$	−36.5162	−1.84435
$393$	−19.4096	−0.979086
$394$	−45.2439	−2.27935
$395$	2.74507	0.138119
$396$	33.4381	1.68033
$397$	−7.99867	−0.401442	−0.200721	−	0.979648i	$-0.564328\pi$
$397$	−7.99867	−0.401442	−0.200721	+	0.979648i	$0.564328\pi$
$398$	−20.6783	−1.03651
$399$	−66.5048	−3.32940
$400$	−8.42645	−0.421322
$401$	−17.5912	−0.878463	−0.439232	−	0.898374i	$-0.644749\pi$
$401$	−17.5912	−0.878463	−0.439232	+	0.898374i	$0.644749\pi$
$402$	−51.7119	−2.57915
$403$	−5.17699	−0.257884
$404$	−47.7985	−2.37807
$405$	−4.98073	−0.247495
$406$	12.6381	0.627218
$407$	53.3467	2.64430
$408$	−59.2140	−2.93153
$409$	−12.6318	−0.624602	−0.312301	−	0.949983i	$-0.601100\pi$
$409$	−12.6318	−0.624602	−0.312301	+	0.949983i	$0.601100\pi$
$410$	−1.74646	−0.0862514
$411$	−10.9170	−0.538495
$412$	−29.0115	−1.42930
$413$	−52.0301	−2.56023
$414$	−12.5545	−0.617019
$415$	−2.61113	−0.128176
$416$	−7.03060	−0.344703
$417$	−6.72675	−0.329410
$418$	110.024	5.38143
$419$	9.63409	0.470656	0.235328	−	0.971916i	$-0.424384\pi$
$419$	9.63409	0.470656	0.235328	+	0.971916i	$0.424384\pi$
$420$	13.8397	0.675310
$421$	17.1770	0.837157	0.418578	−	0.908181i	$-0.362529\pi$
$421$	17.1770	0.837157	0.418578	+	0.908181i	$0.362529\pi$
$422$	−22.4883	−1.09471
$423$	0.644339	0.0313288
$424$	−43.9606	−2.13492
$425$	35.3274	1.71363
$426$	−5.03618	−0.244004
$427$	13.6155	0.658902
$428$	31.9885	1.54622
$429$	26.6013	1.28432
$430$	13.2017	0.636641
$431$	10.8666	0.523423	0.261712	−	0.965146i	$-0.415713\pi$
$431$	10.8666	0.523423	0.261712	+	0.965146i	$0.415713\pi$
$432$	5.48781	0.264032
$433$	14.6337	0.703250	0.351625	−	0.936141i	$-0.385629\pi$
$433$	14.6337	0.703250	0.351625	+	0.936141i	$0.385629\pi$
$434$	24.2875	1.16584
$435$	−1.23345	−0.0591396
$436$	36.3428	1.74050
$437$	−26.5527	−1.27019
$438$	−42.1217	−2.01265
$439$	17.7050	0.845012	0.422506	−	0.906360i	$-0.361150\pi$
$439$	17.7050	0.845012	0.422506	+	0.906360i	$0.361150\pi$
$440$	−10.1720	−0.484931
$441$	14.7684	0.703256
$442$	−35.8131	−1.70346
$443$	16.7633	0.796449	0.398225	−	0.917288i	$-0.369626\pi$
$443$	16.7633	0.796449	0.398225	+	0.917288i	$0.369626\pi$
$444$	−67.2904	−3.19346
$445$	4.57146	0.216708
$446$	−53.5806	−2.53711
$447$	−36.7164	−1.73663
$448$	47.2993	2.23468
$449$	13.5333	0.638677	0.319339	−	0.947641i	$-0.396539\pi$
$449$	13.5333	0.638677	0.319339	+	0.947641i	$0.396539\pi$
$450$	17.3922	0.819877
$451$	10.1229	0.476667
$452$	−3.59886	−0.169276
$453$	27.9601	1.31368
$454$	−55.4489	−2.60235
$455$	3.71870	0.174335
$456$	−61.6562	−2.88732
$457$	−37.9060	−1.77317	−0.886585	−	0.462567i	$-0.846929\pi$
$457$	−37.9060	−1.77317	−0.886585	+	0.462567i	$0.846929\pi$
$458$	24.7269	1.15541
$459$	−23.0073	−1.07389
$460$	5.52565	0.257635
$461$	−0.753289	−0.0350841	−0.0175421	−	0.999846i	$-0.505584\pi$
$461$	−0.753289	−0.0350841	−0.0175421	+	0.999846i	$0.505584\pi$
$462$	−124.798	−5.80613
$463$	27.9872	1.30067	0.650337	−	0.759645i	$-0.274627\pi$
$463$	27.9872	1.30067	0.650337	+	0.759645i	$0.274627\pi$
$464$	2.29584	0.106582
$465$	−2.37042	−0.109925
$466$	1.48634	0.0688534
$467$	35.1515	1.62662	0.813310	−	0.581831i	$-0.197664\pi$
$467$	35.1515	1.62662	0.813310	+	0.581831i	$0.197664\pi$
$468$	−11.3331	−0.523875
$469$	41.9010	1.93481
$470$	−0.441198	−0.0203509
$471$	28.8873	1.33106
$472$	−48.2368	−2.22028
$473$	−76.5199	−3.51839
$474$	31.2233	1.43413
$475$	36.7845	1.68779
$476$	107.997	4.95005
$477$	17.7791	0.814050
$478$	−29.7572	−1.36106
$479$	−4.71072	−0.215238	−0.107619	−	0.994192i	$-0.534323\pi$
$479$	−4.71072	−0.215238	−0.107619	+	0.994192i	$0.534323\pi$
$480$	−3.21914	−0.146933
$481$	−18.0807	−0.824411
$482$	−29.9191	−1.36278
$483$	30.1183	1.37043
$484$	93.1234	4.23288
$485$	5.74040	0.260658
$486$	−34.4437	−1.56240
$487$	40.4490	1.83292	0.916459	−	0.400129i	$-0.131035\pi$
$487$	40.4490	1.83292	0.916459	+	0.400129i	$0.131035\pi$
$488$	12.6229	0.571411
$489$	−26.8235	−1.21300
$490$	−10.1123	−0.456829
$491$	−18.8191	−0.849293	−0.424647	−	0.905359i	$-0.639602\pi$
$491$	−18.8191	−0.849293	−0.424647	+	0.905359i	$0.639602\pi$
$492$	−12.7688	−0.575661
$493$	−9.62517	−0.433496
$494$	−37.2902	−1.67777
$495$	4.11389	0.184906
$496$	4.41208	0.198108
$497$	4.08071	0.183045
$498$	−29.6999	−1.33088
$499$	−39.0292	−1.74719	−0.873593	−	0.486657i	$-0.838216\pi$
$499$	−39.0292	−1.74719	−0.873593	+	0.486657i	$0.838216\pi$
$500$	−15.6222	−0.698645
$501$	−1.64245	−0.0733793
$502$	−57.0885	−2.54799
$503$	−16.8751	−0.752423	−0.376212	−	0.926534i	$-0.622773\pi$
$503$	−16.8751	−0.752423	−0.376212	+	0.926534i	$0.622773\pi$
$504$	23.6212	1.05217
$505$	−5.88065	−0.261685
$506$	−49.8269	−2.21508
$507$	18.6532	0.828416
$508$	−23.9632	−1.06320
$509$	9.70641	0.430229	0.215115	−	0.976589i	$-0.430988\pi$
$509$	9.70641	0.430229	0.215115	+	0.976589i	$0.430988\pi$
$510$	−16.3980	−0.726114
$511$	34.1303	1.50984
$512$	19.2638	0.851346
$513$	−23.9563	−1.05769
$514$	5.40576	0.238438
$515$	−3.56929	−0.157282
$516$	96.5206	4.24908
$517$	2.55728	0.112469
$518$	84.8247	3.72698
$519$	26.7852	1.17574
$520$	3.44758	0.151187
$521$	30.8855	1.35312	0.676559	−	0.736389i	$-0.263471\pi$
$521$	30.8855	1.35312	0.676559	+	0.736389i	$0.263471\pi$
$522$	−4.73862	−0.207404
$523$	−34.9363	−1.52766	−0.763828	−	0.645420i	$-0.776682\pi$
$523$	−34.9363	−1.52766	−0.763828	+	0.645420i	$0.776682\pi$
$524$	32.8194	1.43372
$525$	−41.7241	−1.82099
$526$	15.0760	0.657345
$527$	−18.4974	−0.805759
$528$	−22.6708	−0.986622
$529$	−10.9750	−0.477172
$530$	−12.1739	−0.528800
$531$	19.5085	0.846598
$532$	112.452	4.87540
$533$	−3.43093	−0.148610
$534$	51.9972	2.25014
$535$	3.93554	0.170148
$536$	38.8462	1.67790
$537$	−6.33143	−0.273221
$538$	34.7219	1.49697
$539$	58.6135	2.52466
$540$	4.98533	0.214534
$541$	−26.3746	−1.13393	−0.566965	−	0.823742i	$-0.691883\pi$
$541$	−26.3746	−1.13393	−0.566965	+	0.823742i	$0.691883\pi$
$542$	10.9156	0.468865
$543$	30.6451	1.31511
$544$	−25.1203	−1.07703
$545$	4.47125	0.191527
$546$	42.2977	1.81017
$547$	−26.8385	−1.14753	−0.573766	−	0.819019i	$-0.694518\pi$
$547$	−26.8385	−1.14753	−0.573766	+	0.819019i	$0.694518\pi$
$548$	18.4593	0.788543
$549$	−5.10511	−0.217881
$550$	69.0271	2.94333
$551$	−10.0222	−0.426958
$552$	27.9225	1.18846
$553$	−25.2996	−1.07585
$554$	−74.9106	−3.18265
$555$	−8.27873	−0.351412
$556$	11.3741	0.482371
$557$	11.2130	0.475109	0.237554	−	0.971374i	$-0.423654\pi$
$557$	11.2130	0.475109	0.237554	+	0.971374i	$0.423654\pi$
$558$	−9.10655	−0.385511
$559$	25.9348	1.09693
$560$	−3.16925	−0.133925
$561$	95.0463	4.01286
$562$	−11.3710	−0.479658
$563$	−29.7705	−1.25468	−0.627338	−	0.778747i	$-0.715856\pi$
$563$	−29.7705	−1.25468	−0.627338	+	0.778747i	$0.715856\pi$
$564$	−3.22570	−0.135827
$565$	−0.442767	−0.0186274
$566$	48.2690	2.02890
$567$	45.9043	1.92780
$568$	3.78320	0.158740
$569$	−7.74289	−0.324599	−0.162299	−	0.986742i	$-0.551891\pi$
$569$	−7.74289	−0.324599	−0.162299	+	0.986742i	$0.551891\pi$
$570$	−17.0743	−0.715163
$571$	−13.2941	−0.556343	−0.278171	−	0.960531i	$-0.589728\pi$
$571$	−13.2941	−0.556343	−0.278171	+	0.960531i	$0.589728\pi$
$572$	−44.9796	−1.88069
$573$	37.8097	1.57952
$574$	16.0960	0.671835
$575$	−16.6587	−0.694718
$576$	−17.7347	−0.738947
$577$	15.7063	0.653860	0.326930	−	0.945049i	$-0.393986\pi$
$577$	15.7063	0.653860	0.326930	+	0.945049i	$0.393986\pi$
$578$	−87.7351	−3.64930
$579$	8.83258	0.367069
$580$	2.08562	0.0866008
$581$	24.0652	0.998393
$582$	65.2932	2.70649
$583$	70.5627	2.92241
$584$	31.6420	1.30935
$585$	−1.39432	−0.0576479
$586$	−30.6905	−1.26781
$587$	39.8682	1.64554	0.822768	−	0.568377i	$-0.192428\pi$
$587$	39.8682	1.64554	0.822768	+	0.568377i	$0.192428\pi$
$588$	−73.9338	−3.04898
$589$	−19.2603	−0.793607
$590$	−13.3581	−0.549943
$591$	−40.6969	−1.67405
$592$	15.4093	0.633317
$593$	−16.1606	−0.663636	−0.331818	−	0.943343i	$-0.607662\pi$
$593$	−16.1606	−0.663636	−0.331818	+	0.943343i	$0.607662\pi$
$594$	−44.9546	−1.84451
$595$	13.2869	0.544710
$596$	62.0831	2.54302
$597$	−18.6001	−0.761253
$598$	16.8878	0.690593
$599$	−9.69394	−0.396084	−0.198042	−	0.980194i	$-0.563458\pi$
$599$	−9.69394	−0.396084	−0.198042	+	0.980194i	$0.563458\pi$
$600$	−38.6821	−1.57919
$601$	27.1552	1.10768	0.553841	−	0.832622i	$-0.313161\pi$
$601$	27.1552	1.10768	0.553841	+	0.832622i	$0.313161\pi$
$602$	−121.672	−4.95897
$603$	−15.7107	−0.639788
$604$	−47.2772	−1.92368
$605$	11.4570	0.465792
$606$	−66.8885	−2.71716
$607$	15.5194	0.629912	0.314956	−	0.949106i	$-0.398010\pi$
$607$	15.5194	0.629912	0.314956	+	0.949106i	$0.398010\pi$
$608$	−26.1564	−1.06078
$609$	11.3680	0.460654
$610$	3.49562	0.141533
$611$	−0.866738	−0.0350645
$612$	−40.4933	−1.63685
$613$	40.0318	1.61687	0.808435	−	0.588585i	$-0.200315\pi$
$613$	40.0318	1.61687	0.808435	+	0.588585i	$0.200315\pi$
$614$	−49.5769	−2.00076
$615$	−1.57094	−0.0633465
$616$	93.7489	3.77725
$617$	9.15416	0.368533	0.184266	−	0.982876i	$-0.441009\pi$
$617$	9.15416	0.368533	0.184266	+	0.982876i	$0.441009\pi$
$618$	−40.5982	−1.63310
$619$	−22.7056	−0.912617	−0.456308	−	0.889822i	$-0.650829\pi$
$619$	−22.7056	−0.912617	−0.456308	+	0.889822i	$0.650829\pi$
$620$	4.00810	0.160969
$621$	10.8492	0.435363
$622$	5.52240	0.221428
$623$	−42.1323	−1.68799
$624$	7.68381	0.307598
$625$	22.0978	0.883912
$626$	51.1734	2.04530
$627$	98.9664	3.95234
$628$	−48.8450	−1.94913
$629$	−64.6025	−2.57587
$630$	6.54135	0.260613
$631$	3.81869	0.152020	0.0760099	−	0.997107i	$-0.475782\pi$
$631$	3.81869	0.152020	0.0760099	+	0.997107i	$0.475782\pi$
$632$	−23.4551	−0.932993
$633$	−20.2283	−0.804002
$634$	79.3758	3.15242
$635$	−2.94819	−0.116996
$636$	−89.0063	−3.52933
$637$	−19.8658	−0.787112
$638$	−18.8069	−0.744571
$639$	−1.53005	−0.0605279
$640$	9.11855	0.360442
$641$	29.3557	1.15948	0.579740	−	0.814801i	$-0.303154\pi$
$641$	29.3557	1.15948	0.579740	+	0.814801i	$0.303154\pi$
$642$	44.7641	1.76670
$643$	−29.3639	−1.15800	−0.578999	−	0.815329i	$-0.696556\pi$
$643$	−29.3639	−1.15800	−0.578999	+	0.815329i	$0.696556\pi$
$644$	−50.9265	−2.00678
$645$	11.8749	0.467575
$646$	−133.238	−5.24218
$647$	35.3270	1.38885	0.694423	−	0.719567i	$-0.255660\pi$
$647$	35.3270	1.38885	0.694423	+	0.719567i	$0.255660\pi$
$648$	42.5576	1.67182
$649$	77.4265	3.03925
$650$	−23.3953	−0.917639
$651$	21.8467	0.856239
$652$	45.3553	1.77625
$653$	−45.1762	−1.76788	−0.883940	−	0.467601i	$-0.845119\pi$
$653$	−45.1762	−1.76788	−0.883940	+	0.467601i	$0.845119\pi$
$654$	50.8575	1.98868
$655$	4.03776	0.157768
$656$	2.92401	0.114163
$657$	−12.7971	−0.499261
$658$	4.06625	0.158519
$659$	6.73244	0.262259	0.131129	−	0.991365i	$-0.458140\pi$
$659$	6.73244	0.262259	0.131129	+	0.991365i	$0.458140\pi$
$660$	−20.5950	−0.801661
$661$	−30.5092	−1.18667	−0.593336	−	0.804955i	$-0.702189\pi$
$661$	−30.5092	−1.18667	−0.593336	+	0.804955i	$0.702189\pi$
$662$	−83.3090	−3.23790
$663$	−32.2140	−1.25109
$664$	22.3107	0.865823
$665$	13.8349	0.536495
$666$	−31.8048	−1.23241
$667$	4.53878	0.175742
$668$	2.77719	0.107453
$669$	−48.1958	−1.86336
$670$	10.7576	0.415601
$671$	−20.2614	−0.782183
$672$	29.6688	1.14450
$673$	−44.9978	−1.73454	−0.867268	−	0.497841i	$-0.834126\pi$
$673$	−44.9978	−1.73454	−0.867268	+	0.497841i	$0.834126\pi$
$674$	−21.1175	−0.813414
$675$	−15.0298	−0.578497
$676$	−31.5403	−1.21309
$677$	−31.0734	−1.19425	−0.597125	−	0.802149i	$-0.703690\pi$
$677$	−31.0734	−1.19425	−0.597125	+	0.802149i	$0.703690\pi$
$678$	−5.03618	−0.193413
$679$	−52.9057	−2.03033
$680$	12.3182	0.472382
$681$	−49.8764	−1.91127
$682$	−36.1425	−1.38397
$683$	15.9081	0.608708	0.304354	−	0.952559i	$-0.401559\pi$
$683$	15.9081	0.608708	0.304354	+	0.952559i	$0.401559\pi$
$684$	−42.1635	−1.61216
$685$	2.27105	0.0867723
$686$	25.6090	0.977756
$687$	22.2419	0.848582
$688$	−22.1029	−0.842665
$689$	−23.9157	−0.911117
$690$	7.73250	0.294371
$691$	−5.80557	−0.220854	−0.110427	−	0.993884i	$-0.535222\pi$
$691$	−5.80557	−0.220854	−0.110427	+	0.993884i	$0.535222\pi$
$692$	−45.2905	−1.72169
$693$	−37.9152	−1.44028
$694$	37.9261	1.43965
$695$	1.39936	0.0530807
$696$	10.5392	0.399487
$697$	−12.2587	−0.464333
$698$	29.4646	1.11525
$699$	1.33697	0.0505687
$700$	70.5504	2.66656
$701$	−13.4768	−0.509012	−0.254506	−	0.967071i	$-0.581913\pi$
$701$	−13.4768	−0.509012	−0.254506	+	0.967071i	$0.581913\pi$
$702$	15.2364	0.575062
$703$	−67.2670	−2.53702
$704$	−70.3865	−2.65279
$705$	−0.396858	−0.0149465
$706$	−8.97884	−0.337923
$707$	54.1983	2.03834
$708$	−97.6641	−3.67044
$709$	−14.4289	−0.541887	−0.270943	−	0.962595i	$-0.587336\pi$
$709$	−14.4289	−0.541887	−0.270943	+	0.962595i	$0.587336\pi$
$710$	1.04767	0.0393184
$711$	9.48600	0.355753
$712$	−39.0606	−1.46386
$713$	8.72250	0.326660
$714$	151.130	5.65589
$715$	−5.53383	−0.206954
$716$	10.7057	0.400091
$717$	−26.7667	−0.999620
$718$	−77.7731	−2.90246
$719$	−49.9060	−1.86118	−0.930590	−	0.366064i	$-0.880705\pi$
$719$	−49.9060	−1.86118	−0.930590	+	0.366064i	$0.880705\pi$
$720$	1.18830	0.0442854
$721$	32.8959	1.22511
$722$	−93.7756	−3.48997
$723$	−26.9123	−1.00088
$724$	−51.8172	−1.92577
$725$	−6.28775	−0.233521
$726$	130.315	4.83646
$727$	−12.2743	−0.455229	−0.227615	−	0.973751i	$-0.573093\pi$
$727$	−12.2743	−0.455229	−0.227615	+	0.973751i	$0.573093\pi$
$728$	−31.7742	−1.17763
$729$	2.76513	0.102412
$730$	8.76253	0.324316
$731$	92.6652	3.42735
$732$	25.5573	0.944625
$733$	−24.4649	−0.903633	−0.451817	−	0.892111i	$-0.649224\pi$
$733$	−24.4649	−0.903633	−0.451817	+	0.892111i	$0.649224\pi$
$734$	−12.6779	−0.467951
$735$	−9.09606	−0.335513
$736$	11.8456	0.436633
$737$	−62.3534	−2.29682
$738$	−6.03516	−0.222157
$739$	−21.2934	−0.783289	−0.391645	−	0.920117i	$-0.628094\pi$
$739$	−21.2934	−0.783289	−0.391645	+	0.920117i	$0.628094\pi$
$740$	13.9983	0.514589
$741$	−33.5426	−1.23222
$742$	112.199	4.11896
$743$	−29.2966	−1.07479	−0.537394	−	0.843331i	$-0.680591\pi$
$743$	−29.2966	−1.07479	−0.537394	+	0.843331i	$0.680591\pi$
$744$	20.2539	0.742545
$745$	7.63808	0.279838
$746$	51.9707	1.90278
$747$	−9.02318	−0.330141
$748$	−160.712	−5.87621
$749$	−36.2714	−1.32533
$750$	−21.8614	−0.798266
$751$	−13.5655	−0.495011	−0.247505	−	0.968887i	$-0.579611\pi$
$751$	−13.5655	−0.495011	−0.247505	+	0.968887i	$0.579611\pi$
$752$	0.738675	0.0269367
$753$	−51.3512	−1.87134
$754$	6.37419	0.232134
$755$	−5.81651	−0.211685
$756$	−45.9467	−1.67107
$757$	14.8883	0.541125	0.270563	−	0.962702i	$-0.412790\pi$
$757$	14.8883	0.541125	0.270563	+	0.962702i	$0.412790\pi$
$758$	−4.79064	−0.174004
$759$	−44.8194	−1.62684
$760$	12.8263	0.465258
$761$	−20.8990	−0.757589	−0.378795	−	0.925481i	$-0.623661\pi$
$761$	−20.8990	−0.757589	−0.378795	+	0.925481i	$0.623661\pi$
$762$	−33.5337	−1.21480
$763$	−41.2087	−1.49186
$764$	−63.9317	−2.31297
$765$	−4.98189	−0.180121
$766$	13.9857	0.505323
$767$	−26.2421	−0.947546
$768$	54.3772	1.96217
$769$	−28.2988	−1.02048	−0.510241	−	0.860031i	$-0.670444\pi$
$769$	−28.2988	−1.02048	−0.510241	+	0.860031i	$0.670444\pi$
$770$	25.9616	0.935592
$771$	4.86249	0.175118
$772$	−14.9348	−0.537517
$773$	−29.1467	−1.04833	−0.524166	−	0.851616i	$-0.675623\pi$
$773$	−29.1467	−1.04833	−0.524166	+	0.851616i	$0.675623\pi$
$774$	45.6204	1.63979
$775$	−12.0836	−0.434056
$776$	−49.0486	−1.76074
$777$	76.2999	2.73724
$778$	77.0976	2.76408
$779$	−12.7643	−0.457330
$780$	6.98026	0.249933
$781$	−6.07255	−0.217293
$782$	60.3401	2.15776
$783$	4.09496	0.146342
$784$	16.9306	0.604663
$785$	−6.00940	−0.214485
$786$	45.9269	1.63816
$787$	17.5048	0.623978	0.311989	−	0.950086i	$-0.399005\pi$
$787$	17.5048	0.623978	0.311989	+	0.950086i	$0.399005\pi$
$788$	68.8137	2.45139
$789$	13.5609	0.482780
$790$	−6.49535	−0.231094
$791$	4.08071	0.145093
$792$	−35.1509	−1.24903
$793$	6.86718	0.243861
$794$	18.9264	0.671672
$795$	−10.9504	−0.388372
$796$	31.4506	1.11474
$797$	11.2022	0.396801	0.198401	−	0.980121i	$-0.436425\pi$
$797$	11.2022	0.396801	0.198401	+	0.980121i	$0.436425\pi$
$798$	157.363	5.57059
$799$	−3.09686	−0.109559
$800$	−16.4101	−0.580185
$801$	15.7974	0.558173
$802$	41.6242	1.46980
$803$	−50.7896	−1.79233
$804$	78.6512	2.77381
$805$	−6.26548	−0.220829
$806$	12.2497	0.431479
$807$	31.2324	1.09943
$808$	50.2469	1.76768
$809$	28.3606	0.997106	0.498553	−	0.866859i	$-0.333865\pi$
$809$	28.3606	0.997106	0.498553	+	0.866859i	$0.333865\pi$
$810$	11.7854	0.414095
$811$	43.2481	1.51865	0.759323	−	0.650714i	$-0.225530\pi$
$811$	43.2481	1.51865	0.759323	+	0.650714i	$0.225530\pi$
$812$	−19.2219	−0.674557
$813$	9.81859	0.344353
$814$	−126.228	−4.42430
$815$	5.58006	0.195461
$816$	27.4543	0.961091
$817$	96.4871	3.37566
$818$	29.8892	1.04505
$819$	12.8505	0.449034
$820$	2.65628	0.0927612
$821$	−41.6063	−1.45207	−0.726036	−	0.687657i	$-0.758639\pi$
$821$	−41.6063	−1.45207	−0.726036	+	0.687657i	$0.758639\pi$
$822$	25.8317	0.900983
$823$	17.8613	0.622606	0.311303	−	0.950311i	$-0.399235\pi$
$823$	17.8613	0.622606	0.311303	+	0.950311i	$0.399235\pi$
$824$	30.4976	1.06243
$825$	62.0900	2.16170
$826$	123.113	4.28365
$827$	−36.9493	−1.28485	−0.642427	−	0.766347i	$-0.722072\pi$
$827$	−36.9493	−1.28485	−0.642427	+	0.766347i	$0.722072\pi$
$828$	19.0947	0.663588
$829$	−2.88194	−0.100094	−0.0500469	−	0.998747i	$-0.515937\pi$
$829$	−2.88194	−0.100094	−0.0500469	+	0.998747i	$0.515937\pi$
$830$	6.17844	0.214457
$831$	−67.3822	−2.33746
$832$	23.8560	0.827059
$833$	−70.9805	−2.45933
$834$	15.9168	0.551153
$835$	0.341678	0.0118242
$836$	−167.340	−5.78759
$837$	7.86958	0.272012
$838$	−22.7961	−0.787478
$839$	−50.3066	−1.73678	−0.868388	−	0.495885i	$-0.834844\pi$
$839$	−50.3066	−1.73678	−0.868388	+	0.495885i	$0.834844\pi$
$840$	−14.5486	−0.501976
$841$	−27.2869	−0.940926
$842$	−40.6441	−1.40069
$843$	−10.2283	−0.352280
$844$	34.2036	1.17734
$845$	−3.88040	−0.133490
$846$	−1.52463	−0.0524178
$847$	−105.592	−3.62818
$848$	20.3821	0.699925
$849$	43.4180	1.49010
$850$	−83.5914	−2.86716
$851$	30.4635	1.04428
$852$	7.65978	0.262420
$853$	1.14137	0.0390797	0.0195399	−	0.999809i	$-0.493780\pi$
$853$	1.14137	0.0390797	0.0195399	+	0.999809i	$0.493780\pi$
$854$	−32.2169	−1.10244
$855$	−5.18737	−0.177404
$856$	−33.6270	−1.14935
$857$	22.3373	0.763028	0.381514	−	0.924363i	$-0.375403\pi$
$857$	22.3373	0.763028	0.381514	+	0.924363i	$0.375403\pi$
$858$	−62.9436	−2.14886
$859$	−46.2928	−1.57949	−0.789745	−	0.613435i	$-0.789787\pi$
$859$	−46.2928	−1.57949	−0.789745	+	0.613435i	$0.789787\pi$
$860$	−20.0791	−0.684691
$861$	14.4784	0.493422
$862$	−25.7123	−0.875766
$863$	30.6372	1.04290	0.521451	−	0.853281i	$-0.325391\pi$
$863$	30.6372	1.04290	0.521451	+	0.853281i	$0.325391\pi$
$864$	10.6873	0.363588
$865$	−5.57209	−0.189457
$866$	−34.6261	−1.17664
$867$	−78.9178	−2.68019
$868$	−36.9401	−1.25383
$869$	37.6485	1.27714
$870$	2.91859	0.0989494
$871$	21.1334	0.716077
$872$	−38.2044	−1.29376
$873$	19.8369	0.671376
$874$	62.8287	2.12521
$875$	17.7138	0.598837
$876$	64.0649	2.16455
$877$	30.4664	1.02878	0.514388	−	0.857558i	$-0.328019\pi$
$877$	30.4664	1.02878	0.514388	+	0.857558i	$0.328019\pi$
$878$	−41.8934	−1.41383
$879$	−27.6061	−0.931131
$880$	4.71619	0.158983
$881$	39.1199	1.31798	0.658991	−	0.752151i	$-0.270983\pi$
$881$	39.1199	1.31798	0.658991	+	0.752151i	$0.270983\pi$
$882$	−34.9448	−1.17665
$883$	−49.0245	−1.64981	−0.824903	−	0.565275i	$-0.808770\pi$
$883$	−49.0245	−1.64981	−0.824903	+	0.565275i	$0.808770\pi$
$884$	54.4700	1.83202
$885$	−12.0156	−0.403900
$886$	−39.6652	−1.33258
$887$	−2.47273	−0.0830260	−0.0415130	−	0.999138i	$-0.513218\pi$
$887$	−2.47273	−0.0830260	−0.0415130	+	0.999138i	$0.513218\pi$
$888$	70.7372	2.37378
$889$	27.1717	0.911309
$890$	−10.8169	−0.362584
$891$	−68.3107	−2.28849
$892$	81.4934	2.72860
$893$	−3.22458	−0.107907
$894$	86.8781	2.90564
$895$	1.31712	0.0440265
$896$	−84.0400	−2.80758
$897$	15.1906	0.507199
$898$	−32.0224	−1.06860
$899$	3.29226	0.109803
$900$	−26.4527	−0.881756
$901$	−85.4510	−2.84679
$902$	−23.9526	−0.797536
$903$	−109.444	−3.64206
$904$	3.78320	0.125827
$905$	−6.37506	−0.211914
$906$	−66.1589	−2.19798
$907$	−8.09294	−0.268722	−0.134361	−	0.990932i	$-0.542898\pi$
$907$	−8.09294	−0.268722	−0.134361	+	0.990932i	$0.542898\pi$
$908$	84.3351	2.79876
$909$	−20.3215	−0.674022
$910$	−8.79915	−0.291689
$911$	40.8838	1.35454	0.677271	−	0.735734i	$-0.263162\pi$
$911$	40.8838	1.35454	0.677271	+	0.735734i	$0.263162\pi$
$912$	28.5866	0.946596
$913$	−35.8117	−1.18519
$914$	89.6929	2.96678
$915$	3.14431	0.103948
$916$	−37.6084	−1.24262
$917$	−37.2136	−1.22890
$918$	54.4398	1.79678
$919$	8.89358	0.293372	0.146686	−	0.989183i	$-0.453139\pi$
$919$	8.89358	0.293372	0.146686	+	0.989183i	$0.453139\pi$
$920$	−5.80869	−0.191507
$921$	−44.5945	−1.46944
$922$	1.78242	0.0587010
$923$	2.05816	0.0677452
$924$	189.812	6.24435
$925$	−42.2023	−1.38760
$926$	−66.2230	−2.17622
$927$	−12.3342	−0.405109
$928$	4.47104	0.146769
$929$	−40.2545	−1.32071	−0.660354	−	0.750955i	$-0.729594\pi$
$929$	−40.2545	−1.32071	−0.660354	+	0.750955i	$0.729594\pi$
$930$	5.60886	0.183922
$931$	−73.9081	−2.42224
$932$	−2.26065	−0.0740501
$933$	4.96741	0.162626
$934$	−83.1752	−2.72158
$935$	−19.7724	−0.646626
$936$	11.9137	0.389410
$937$	−39.6863	−1.29650	−0.648248	−	0.761430i	$-0.724498\pi$
$937$	−39.6863	−1.29650	−0.648248	+	0.761430i	$0.724498\pi$
$938$	−99.1459	−3.23723
$939$	46.0305	1.50215
$940$	0.671040	0.0218869
$941$	34.2656	1.11703	0.558514	−	0.829495i	$-0.311372\pi$
$941$	34.2656	1.11703	0.558514	+	0.829495i	$0.311372\pi$
$942$	−68.3529	−2.22706
$943$	5.78064	0.188244
$944$	22.3647	0.727910
$945$	−5.65282	−0.183886
$946$	181.061	5.88679
$947$	−36.4741	−1.18525	−0.592625	−	0.805478i	$-0.701908\pi$
$947$	−36.4741	−1.18525	−0.592625	+	0.805478i	$0.701908\pi$
$948$	−47.4890	−1.54237
$949$	17.2141	0.558793
$950$	−87.0391	−2.82392
$951$	71.3987	2.31526
$952$	−113.529	−3.67951
$953$	−12.0291	−0.389660	−0.194830	−	0.980837i	$-0.562415\pi$
$953$	−12.0291	−0.389660	−0.194830	+	0.980837i	$0.562415\pi$
$954$	−42.0688	−1.36203
$955$	−7.86551	−0.254522
$956$	45.2593	1.46379
$957$	−16.9168	−0.546843
$958$	11.1465	0.360126
$959$	−20.9309	−0.675893
$960$	10.9231	0.352541
$961$	−24.6730	−0.795904
$962$	42.7825	1.37936
$963$	13.5999	0.438250
$964$	45.5055	1.46563
$965$	−1.83743	−0.0591490
$966$	−71.2657	−2.29293
$967$	−13.0230	−0.418790	−0.209395	−	0.977831i	$-0.567150\pi$
$967$	−13.0230	−0.418790	−0.209395	+	0.977831i	$0.567150\pi$
$968$	−97.8935	−3.14642
$969$	−119.848	−3.85006
$970$	−13.5829	−0.436120
$971$	8.32769	0.267248	0.133624	−	0.991032i	$-0.457338\pi$
$971$	8.32769	0.267248	0.133624	+	0.991032i	$0.457338\pi$
$972$	52.3872	1.68032
$973$	−12.8970	−0.413460
$974$	−95.7100	−3.06674
$975$	−21.0441	−0.673950
$976$	−5.85254	−0.187335
$977$	21.2680	0.680424	0.340212	−	0.940349i	$-0.389501\pi$
$977$	21.2680	0.680424	0.340212	+	0.940349i	$0.389501\pi$
$978$	63.4695	2.02953
$979$	62.6974	2.00382
$980$	15.3804	0.491308
$981$	15.4511	0.493316
$982$	44.5295	1.42099
$983$	−36.4184	−1.16157	−0.580783	−	0.814058i	$-0.697253\pi$
$983$	−36.4184	−1.16157	−0.580783	+	0.814058i	$0.697253\pi$
$984$	13.4228	0.427904
$985$	8.46614	0.269754
$986$	22.7750	0.725304
$987$	3.65759	0.116423
$988$	56.7165	1.80439
$989$	−43.6965	−1.38947
$990$	−9.73424	−0.309375
$991$	−9.99182	−0.317401	−0.158700	−	0.987327i	$-0.550730\pi$
$991$	−9.99182	−0.317401	−0.158700	+	0.987327i	$0.550730\pi$
$992$	8.59232	0.272806
$993$	−74.9366	−2.37804
$994$	−9.65574	−0.306261
$995$	3.86937	0.122667
$996$	45.1721	1.43133
$997$	−7.06723	−0.223821	−0.111911	−	0.993718i	$-0.535697\pi$
$997$	−7.06723	−0.223821	−0.111911	+	0.993718i	$0.535697\pi$
$998$	92.3505	2.92330
$999$	27.4846	0.869576

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8023.2.a.c.1.20	✓	158

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8023.2.a.c.1.20	✓	158	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:	\( N \)	\(=\)	\( 8023 = 71 \cdot 113 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8023.a (trivial)

\(f(q)\)	\(=\)	\(q-2.36619 q^{2} -2.12839 q^{3} +3.59886 q^{4} +0.442767 q^{5} +5.03618 q^{6} -4.08071 q^{7} -3.78320 q^{8} +1.53005 q^{9} +O(q^{10})\)	\(q-2.36619 q^{2} -2.12839 q^{3} +3.59886 q^{4} +0.442767 q^{5} +5.03618 q^{6} -4.08071 q^{7} -3.78320 q^{8} +1.53005 q^{9} -1.04767 q^{10} +6.07255 q^{11} -7.65978 q^{12} -2.05816 q^{13} +9.65574 q^{14} -0.942382 q^{15} +1.75406 q^{16} -7.35382 q^{17} -3.62039 q^{18} -7.65712 q^{19} +1.59346 q^{20} +8.68535 q^{21} -14.3688 q^{22} +3.46771 q^{23} +8.05214 q^{24} -4.80396 q^{25} +4.87000 q^{26} +3.12863 q^{27} -14.6859 q^{28} +1.30887 q^{29} +2.22986 q^{30} +2.51535 q^{31} +3.41596 q^{32} -12.9248 q^{33} +17.4005 q^{34} -1.80681 q^{35} +5.50644 q^{36} +8.78489 q^{37} +18.1182 q^{38} +4.38058 q^{39} -1.67508 q^{40} +1.66699 q^{41} -20.5512 q^{42} -12.6010 q^{43} +21.8542 q^{44} +0.677457 q^{45} -8.20527 q^{46} +0.421122 q^{47} -3.73333 q^{48} +9.65220 q^{49} +11.3671 q^{50} +15.6518 q^{51} -7.40703 q^{52} +11.6200 q^{53} -7.40293 q^{54} +2.68873 q^{55} +15.4382 q^{56} +16.2973 q^{57} -3.09703 q^{58} +12.7502 q^{59} -3.39150 q^{60} -3.33656 q^{61} -5.95179 q^{62} -6.24370 q^{63} -11.5909 q^{64} -0.911287 q^{65} +30.5824 q^{66} -10.2681 q^{67} -26.4653 q^{68} -7.38065 q^{69} +4.27525 q^{70} -1.00000 q^{71} -5.78850 q^{72} -8.36381 q^{73} -20.7867 q^{74} +10.2247 q^{75} -27.5569 q^{76} -24.7803 q^{77} -10.3653 q^{78} +6.19979 q^{79} +0.776642 q^{80} -11.2491 q^{81} -3.94441 q^{82} -5.89730 q^{83} +31.2573 q^{84} -3.25603 q^{85} +29.8163 q^{86} -2.78578 q^{87} -22.9737 q^{88} +10.3247 q^{89} -1.60299 q^{90} +8.39877 q^{91} +12.4798 q^{92} -5.35364 q^{93} -0.996455 q^{94} -3.39032 q^{95} -7.27050 q^{96} +12.9648 q^{97} -22.8390 q^{98} +9.29131 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9}+O(q^{10}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9	\( 158 q - 24 q^{2} - 23 q^{3} + 158 q^{4} - 31 q^{5} - 17 q^{6} - 2 q^{7} - 69 q^{8} + 135 q^{9} - 10 q^{10} - 10 q^{11} - 46 q^{12} - 28 q^{13} - 27 q^{14} - 41 q^{15} + 150 q^{16} - 137 q^{17} - 67 q^{18} - 42 q^{19} - 66 q^{20} - 46 q^{21} - 8 q^{22} - 26 q^{23} - 48 q^{24} + 129 q^{25} - 67 q^{26} - 89 q^{27} - 21 q^{28} - 79 q^{29} - 11 q^{30} + 7 q^{31} - 147 q^{32} - 112 q^{33} - 28 q^{34} - 53 q^{35} + 141 q^{36} - 60 q^{37} - 53 q^{38} - 3 q^{39} - 48 q^{40} - 128 q^{41} + 32 q^{42} - 63 q^{43} - 88 q^{45} - 2 q^{46} - 92 q^{47} - 131 q^{48} + 122 q^{49} - 116 q^{50} - 12 q^{51} - 89 q^{52} - 94 q^{53} - 71 q^{54} - 12 q^{55} - 104 q^{56} - 93 q^{57} - 65 q^{58} - 54 q^{59} - 12 q^{60} + 17 q^{61} - 97 q^{62} - 28 q^{63} + 163 q^{64} - 163 q^{65} - 65 q^{66} - 35 q^{67} - 217 q^{68} - 46 q^{69} - 79 q^{70} - 158 q^{71} - 99 q^{72} - 165 q^{73} - 94 q^{75} - 93 q^{76} - 140 q^{77} + 25 q^{78} - 61 q^{79} - 134 q^{80} + 114 q^{81} + 10 q^{82} - 158 q^{83} - 160 q^{84} + 23 q^{85} - 122 q^{86} - 71 q^{87} - 14 q^{88} - 251 q^{89} - 6 q^{90} - 57 q^{91} - 58 q^{92} - 52 q^{93} - 64 q^{94} - 84 q^{95} - 98 q^{96} - 48 q^{97} - 84 q^{98} + 85 q^{99}+O(q^{100}) \) 158 * q - 24 * q^2 - 23 * q^3 + 158 * q^4 - 31 * q^5 - 17 * q^6 - 2 * q^7 - 69 * q^8 + 135 * q^9 - 10 * q^10 - 10 * q^11 - 46 * q^12 - 28 * q^13 - 27 * q^14 - 41 * q^15 + 150 * q^16 - 137 * q^17 - 67 * q^18 - 42 * q^19 - 66 * q^20 - 46 * q^21 - 8 * q^22 - 26 * q^23 - 48 * q^24 + 129 * q^25 - 67 * q^26 - 89 * q^27 - 21 * q^28 - 79 * q^29 - 11 * q^30 + 7 * q^31 - 147 * q^32 - 112 * q^33 - 28 * q^34 - 53 * q^35 + 141 * q^36 - 60 * q^37 - 53 * q^38 - 3 * q^39 - 48 * q^40 - 128 * q^41 + 32 * q^42 - 63 * q^43 - 88 * q^45 - 2 * q^46 - 92 * q^47 - 131 * q^48 + 122 * q^49 - 116 * q^50 - 12 * q^51 - 89 * q^52 - 94 * q^53 - 71 * q^54 - 12 * q^55 - 104 * q^56 - 93 * q^57 - 65 * q^58 - 54 * q^59 - 12 * q^60 + 17 * q^61 - 97 * q^62 - 28 * q^63 + 163 * q^64 - 163 * q^65 - 65 * q^66 - 35 * q^67 - 217 * q^68 - 46 * q^69 - 79 * q^70 - 158 * q^71 - 99 * q^72 - 165 * q^73 - 94 * q^75 - 93 * q^76 - 140 * q^77 + 25 * q^78 - 61 * q^79 - 134 * q^80 + 114 * q^81 + 10 * q^82 - 158 * q^83 - 160 * q^84 + 23 * q^85 - 122 * q^86 - 71 * q^87 - 14 * q^88 - 251 * q^89 - 6 * q^90 - 57 * q^91 - 58 * q^92 - 52 * q^93 - 64 * q^94 - 84 * q^95 - 98 * q^96 - 48 * q^97 - 84 * q^98 + 85 * q^99

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