LMFDB - Embedded newform 5077.2.a.b.1.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [5077,2,Mod(1,5077)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(5077, 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("5077.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 5077 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	5077.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:	$40.5400491062$
Analytic rank:	$1$
Dimension:	$205$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.11
Character	$\chi$	$=$	5077.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.63322 q^{2} -3.42055 q^{3} +4.93387 q^{4} +2.45426 q^{5} +9.00708 q^{6} +4.09681 q^{7} -7.72553 q^{8} +8.70017 q^{9} +O(q^{10})$	\(q-2.63322 q^{2} -3.42055 q^{3} +4.93387 q^{4} +2.45426 q^{5} +9.00708 q^{6} +4.09681 q^{7} -7.72553 q^{8} +8.70017 q^{9} -6.46261 q^{10} -6.19096 q^{11} -16.8765 q^{12} -0.0874215 q^{13} -10.7878 q^{14} -8.39492 q^{15} +10.4753 q^{16} +5.79065 q^{17} -22.9095 q^{18} -3.80985 q^{19} +12.1090 q^{20} -14.0133 q^{21} +16.3022 q^{22} +3.09654 q^{23} +26.4256 q^{24} +1.02339 q^{25} +0.230200 q^{26} -19.4977 q^{27} +20.2131 q^{28} +1.90023 q^{29} +22.1057 q^{30} +9.16959 q^{31} -12.1328 q^{32} +21.1765 q^{33} -15.2481 q^{34} +10.0546 q^{35} +42.9255 q^{36} -3.39619 q^{37} +10.0322 q^{38} +0.299030 q^{39} -18.9605 q^{40} -2.11845 q^{41} +36.9002 q^{42} +0.506772 q^{43} -30.5454 q^{44} +21.3525 q^{45} -8.15389 q^{46} -11.2833 q^{47} -35.8314 q^{48} +9.78383 q^{49} -2.69481 q^{50} -19.8072 q^{51} -0.431326 q^{52} -5.12632 q^{53} +51.3418 q^{54} -15.1942 q^{55} -31.6500 q^{56} +13.0318 q^{57} -5.00373 q^{58} -1.93217 q^{59} -41.4194 q^{60} +5.69236 q^{61} -24.1456 q^{62} +35.6429 q^{63} +10.9978 q^{64} -0.214555 q^{65} -55.7625 q^{66} -8.02430 q^{67} +28.5703 q^{68} -10.5919 q^{69} -26.4761 q^{70} +4.99122 q^{71} -67.2134 q^{72} -3.59822 q^{73} +8.94292 q^{74} -3.50055 q^{75} -18.7973 q^{76} -25.3632 q^{77} -0.787412 q^{78} +1.73880 q^{79} +25.7092 q^{80} +40.5924 q^{81} +5.57835 q^{82} -16.3936 q^{83} -69.1400 q^{84} +14.2118 q^{85} -1.33444 q^{86} -6.49983 q^{87} +47.8285 q^{88} -12.1054 q^{89} -56.2258 q^{90} -0.358149 q^{91} +15.2779 q^{92} -31.3651 q^{93} +29.7114 q^{94} -9.35036 q^{95} +41.5009 q^{96} -13.5164 q^{97} -25.7630 q^{98} -53.8624 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) $ 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * 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 $

$2$	−2.63322	−1.86197	−0.930985	−	0.365057i	$-0.881050\pi$
$2$	−2.63322	−1.86197	−0.930985	+	0.365057i	$0.881050\pi$
$3$	−3.42055	−1.97486	−0.987428	−	0.158070i	$-0.949473\pi$
$3$	−3.42055	−1.97486	−0.987428	+	0.158070i	$0.949473\pi$
$4$	4.93387	2.46693
$5$	2.45426	1.09758	0.548789	−	0.835961i	$-0.315089\pi$
$5$	2.45426	1.09758	0.548789	+	0.835961i	$0.315089\pi$
$6$	9.00708	3.67712
$7$	4.09681	1.54845	0.774224	−	0.632912i	$-0.218141\pi$
$7$	4.09681	1.54845	0.774224	+	0.632912i	$0.218141\pi$
$8$	−7.72553	−2.73139
$9$	8.70017	2.90006
$10$	−6.46261	−2.04366
$11$	−6.19096	−1.86665	−0.933323	−	0.359039i	$-0.883105\pi$
$11$	−6.19096	−1.86665	−0.933323	+	0.359039i	$0.883105\pi$
$12$	−16.8765	−4.87184
$13$	−0.0874215	−0.0242464	−0.0121232	−	0.999927i	$-0.503859\pi$
$13$	−0.0874215	−0.0242464	−0.0121232	+	0.999927i	$0.503859\pi$
$14$	−10.7878	−2.88316
$15$	−8.39492	−2.16756
$16$	10.4753	2.61883
$17$	5.79065	1.40444	0.702220	−	0.711960i	$-0.252192\pi$
$17$	5.79065	1.40444	0.702220	+	0.711960i	$0.252192\pi$
$18$	−22.9095	−5.39982
$19$	−3.80985	−0.874039	−0.437020	−	0.899452i	$-0.643966\pi$
$19$	−3.80985	−0.874039	−0.437020	+	0.899452i	$0.643966\pi$
$20$	12.1090	2.70765
$21$	−14.0133	−3.05796
$22$	16.3022	3.47564
$23$	3.09654	0.645674	0.322837	−	0.946455i	$-0.395363\pi$
$23$	3.09654	0.645674	0.322837	+	0.946455i	$0.395363\pi$
$24$	26.4256	5.39410
$25$	1.02339	0.204678
$26$	0.230200	0.0451460
$27$	−19.4977	−3.75234
$28$	20.2131	3.81992
$29$	1.90023	0.352864	0.176432	−	0.984313i	$-0.443545\pi$
$29$	1.90023	0.352864	0.176432	+	0.984313i	$0.443545\pi$
$30$	22.1057	4.03593
$31$	9.16959	1.64691	0.823454	−	0.567383i	$-0.192044\pi$
$31$	9.16959	1.64691	0.823454	+	0.567383i	$0.192044\pi$
$32$	−12.1328	−2.14480
$33$	21.1765	3.68636
$34$	−15.2481	−2.61503
$35$	10.0546	1.69954
$36$	42.9255	7.15425
$37$	−3.39619	−0.558330	−0.279165	−	0.960243i	$-0.590058\pi$
$37$	−3.39619	−0.558330	−0.279165	+	0.960243i	$0.590058\pi$
$38$	10.0322	1.62744
$39$	0.299030	0.0478831
$40$	−18.9605	−2.99791
$41$	−2.11845	−0.330846	−0.165423	−	0.986223i	$-0.552899\pi$
$41$	−2.11845	−0.330846	−0.165423	+	0.986223i	$0.552899\pi$
$42$	36.9002	5.69383
$43$	0.506772	0.0772820	0.0386410	−	0.999253i	$-0.487697\pi$
$43$	0.506772	0.0772820	0.0386410	+	0.999253i	$0.487697\pi$
$44$	−30.5454	−4.60489
$45$	21.3525	3.18304
$46$	−8.15389	−1.20223
$47$	−11.2833	−1.64584	−0.822918	−	0.568160i	$-0.807655\pi$
$47$	−11.2833	−1.64584	−0.822918	+	0.568160i	$0.807655\pi$
$48$	−35.8314	−5.17181
$49$	9.78383	1.39769
$50$	−2.69481	−0.381104
$51$	−19.8072	−2.77357
$52$	−0.431326	−0.0598142
$53$	−5.12632	−0.704154	−0.352077	−	0.935971i	$-0.614525\pi$
$53$	−5.12632	−0.704154	−0.352077	+	0.935971i	$0.614525\pi$
$54$	51.3418	6.98674
$55$	−15.1942	−2.04879
$56$	−31.6500	−4.22941
$57$	13.0318	1.72610
$58$	−5.00373	−0.657022
$59$	−1.93217	−0.251547	−0.125774	−	0.992059i	$-0.540141\pi$
$59$	−1.93217	−0.251547	−0.125774	+	0.992059i	$0.540141\pi$
$60$	−41.4194	−5.34722
$61$	5.69236	0.728832	0.364416	−	0.931236i	$-0.381269\pi$
$61$	5.69236	0.728832	0.364416	+	0.931236i	$0.381269\pi$
$62$	−24.1456	−3.06649
$63$	35.6429	4.49058
$64$	10.9978	1.37472
$65$	−0.214555	−0.0266123
$66$	−55.7625	−6.86389
$67$	−8.02430	−0.980324	−0.490162	−	0.871631i	$-0.663062\pi$
$67$	−8.02430	−0.980324	−0.490162	+	0.871631i	$0.663062\pi$
$68$	28.5703	3.46466
$69$	−10.5919	−1.27511
$70$	−26.4761	−3.16450
$71$	4.99122	0.592349	0.296175	−	0.955134i	$-0.404289\pi$
$71$	4.99122	0.592349	0.296175	+	0.955134i	$0.404289\pi$
$72$	−67.2134	−7.92118
$73$	−3.59822	−0.421140	−0.210570	−	0.977579i	$-0.567532\pi$
$73$	−3.59822	−0.421140	−0.210570	+	0.977579i	$0.567532\pi$
$74$	8.94292	1.03959
$75$	−3.50055	−0.404209
$76$	−18.7973	−2.15620
$77$	−25.3632	−2.89040
$78$	−0.787412	−0.0891568
$79$	1.73880	0.195631	0.0978154	−	0.995205i	$-0.468815\pi$
$79$	1.73880	0.195631	0.0978154	+	0.995205i	$0.468815\pi$
$80$	25.7092	2.87437
$81$	40.5924	4.51027
$82$	5.57835	0.616025
$83$	−16.3936	−1.79943	−0.899715	−	0.436478i	$-0.856226\pi$
$83$	−16.3936	−1.79943	−0.899715	+	0.436478i	$0.856226\pi$
$84$	−69.1400	−7.54379
$85$	14.2118	1.54148
$86$	−1.33444	−0.143897
$87$	−6.49983	−0.696855
$88$	47.8285	5.09853
$89$	−12.1054	−1.28317	−0.641583	−	0.767054i	$-0.721722\pi$
$89$	−12.1054	−1.28317	−0.641583	+	0.767054i	$0.721722\pi$
$90$	−56.2258	−5.92672
$91$	−0.358149	−0.0375442
$92$	15.2779	1.59284
$93$	−31.3651	−3.25240
$94$	29.7114	3.06450
$95$	−9.35036	−0.959326
$96$	41.5009	4.23567
$97$	−13.5164	−1.37238	−0.686189	−	0.727423i	$-0.740718\pi$
$97$	−13.5164	−1.37238	−0.686189	+	0.727423i	$0.740718\pi$
$98$	−25.7630	−2.60246
$99$	−53.8624	−5.41337
$100$	5.04926	0.504926
$101$	4.19796	0.417712	0.208856	−	0.977946i	$-0.433026\pi$
$101$	4.19796	0.417712	0.208856	+	0.977946i	$0.433026\pi$
$102$	52.1569	5.16430
$103$	−6.34450	−0.625142	−0.312571	−	0.949894i	$-0.601190\pi$
$103$	−6.34450	−0.625142	−0.312571	+	0.949894i	$0.601190\pi$
$104$	0.675378	0.0662262
$105$	−34.3924	−3.35635
$106$	13.4988	1.31111
$107$	−1.82577	−0.176504	−0.0882521	−	0.996098i	$-0.528128\pi$
$107$	−1.82577	−0.176504	−0.0882521	+	0.996098i	$0.528128\pi$
$108$	−96.1991	−9.25676
$109$	−8.45566	−0.809905	−0.404953	−	0.914338i	$-0.632712\pi$
$109$	−8.45566	−0.809905	−0.404953	+	0.914338i	$0.632712\pi$
$110$	40.0098	3.81478
$111$	11.6168	1.10262
$112$	42.9154	4.05512
$113$	−1.56365	−0.147096	−0.0735479	−	0.997292i	$-0.523432\pi$
$113$	−1.56365	−0.147096	−0.0735479	+	0.997292i	$0.523432\pi$
$114$	−34.3156	−3.21395
$115$	7.59972	0.708677
$116$	9.37548	0.870491
$117$	−0.760581	−0.0703158
$118$	5.08784	0.468374
$119$	23.7232	2.17470
$120$	64.8552	5.92044
$121$	27.3280	2.48437
$122$	−14.9893	−1.35706
$123$	7.24626	0.653373
$124$	45.2416	4.06281
$125$	−9.75964	−0.872928
$126$	−93.8557	−8.36133
$127$	−4.10300	−0.364083	−0.182041	−	0.983291i	$-0.558270\pi$
$127$	−4.10300	−0.364083	−0.182041	+	0.983291i	$0.558270\pi$
$128$	−4.69393	−0.414889
$129$	−1.73344	−0.152621
$130$	0.564971	0.0495513
$131$	−17.0151	−1.48662	−0.743310	−	0.668947i	$-0.766745\pi$
$131$	−17.0151	−1.48662	−0.743310	+	0.668947i	$0.766745\pi$
$132$	104.482	9.09400
$133$	−15.6082	−1.35340
$134$	21.1298	1.82533
$135$	−47.8524	−4.11848
$136$	−44.7359	−3.83607
$137$	3.82807	0.327054	0.163527	−	0.986539i	$-0.447713\pi$
$137$	3.82807	0.327054	0.163527	+	0.986539i	$0.447713\pi$
$138$	27.8908	2.37422
$139$	10.2725	0.871298	0.435649	−	0.900117i	$-0.356519\pi$
$139$	10.2725	0.871298	0.435649	+	0.900117i	$0.356519\pi$
$140$	49.6082	4.19266
$141$	38.5950	3.25029
$142$	−13.1430	−1.10294
$143$	0.541223	0.0452593
$144$	91.1371	7.59475
$145$	4.66365	0.387295
$146$	9.47491	0.784149
$147$	−33.4661	−2.76024
$148$	−16.7563	−1.37736
$149$	−15.8436	−1.29796	−0.648978	−	0.760807i	$-0.724803\pi$
$149$	−15.8436	−1.29796	−0.648978	+	0.760807i	$0.724803\pi$
$150$	9.21773	0.752625
$151$	12.2241	0.994781	0.497390	−	0.867527i	$-0.334292\pi$
$151$	12.2241	0.994781	0.497390	+	0.867527i	$0.334292\pi$
$152$	29.4331	2.38734
$153$	50.3796	4.07295
$154$	66.7869	5.38184
$155$	22.5046	1.80761
$156$	1.47537	0.118124
$157$	3.96042	0.316076	0.158038	−	0.987433i	$-0.449483\pi$
$157$	3.96042	0.316076	0.158038	+	0.987433i	$0.449483\pi$
$158$	−4.57866	−0.364259
$159$	17.5348	1.39060
$160$	−29.7771	−2.35408
$161$	12.6859	0.999792
$162$	−106.889	−8.39798
$163$	14.1522	1.10849	0.554243	−	0.832355i	$-0.313008\pi$
$163$	14.1522	1.10849	0.554243	+	0.832355i	$0.313008\pi$
$164$	−10.4521	−0.816175
$165$	51.9726	4.04606
$166$	43.1680	3.35049
$167$	−25.5702	−1.97868	−0.989339	−	0.145627i	$-0.953480\pi$
$167$	−25.5702	−1.97868	−0.989339	+	0.145627i	$0.953480\pi$
$168$	108.260	8.35248
$169$	−12.9924	−0.999412
$170$	−37.4228	−2.87019
$171$	−33.1463	−2.53476
$172$	2.50035	0.190650
$173$	7.97196	0.606097	0.303049	−	0.952975i	$-0.401996\pi$
$173$	7.97196	0.606097	0.303049	+	0.952975i	$0.401996\pi$
$174$	17.1155	1.29752
$175$	4.19262	0.316932
$176$	−64.8523	−4.88843
$177$	6.60909	0.496769
$178$	31.8761	2.38922
$179$	−13.8454	−1.03485	−0.517426	−	0.855728i	$-0.673110\pi$
$179$	−13.8454	−1.03485	−0.517426	+	0.855728i	$0.673110\pi$
$180$	105.350	7.85234
$181$	20.0188	1.48799	0.743993	−	0.668187i	$-0.232929\pi$
$181$	20.0188	1.48799	0.743993	+	0.668187i	$0.232929\pi$
$182$	0.943086	0.0699062
$183$	−19.4710	−1.43934
$184$	−23.9224	−1.76359
$185$	−8.33512	−0.612811
$186$	82.5912	6.05588
$187$	−35.8497	−2.62159
$188$	−55.6702	−4.06017
$189$	−79.8783	−5.81029
$190$	24.6216	1.78624
$191$	−22.2598	−1.61066	−0.805331	−	0.592826i	$-0.798012\pi$
$191$	−22.2598	−1.61066	−0.805331	+	0.592826i	$0.798012\pi$
$192$	−37.6184	−2.71487
$193$	−20.3766	−1.46674	−0.733370	−	0.679829i	$-0.762054\pi$
$193$	−20.3766	−1.46674	−0.733370	+	0.679829i	$0.762054\pi$
$194$	35.5916	2.55533
$195$	0.733896	0.0525554
$196$	48.2721	3.44801
$197$	−6.70730	−0.477875	−0.238938	−	0.971035i	$-0.576799\pi$
$197$	−6.70730	−0.477875	−0.238938	+	0.971035i	$0.576799\pi$
$198$	141.832	10.0795
$199$	16.1582	1.14543	0.572713	−	0.819756i	$-0.305891\pi$
$199$	16.1582	1.14543	0.572713	+	0.819756i	$0.305891\pi$
$200$	−7.90622	−0.559054
$201$	27.4475	1.93600
$202$	−11.0542	−0.777768
$203$	7.78487	0.546391
$204$	−97.7262	−6.84221
$205$	−5.19922	−0.363129
$206$	16.7065	1.16400
$207$	26.9404	1.87249
$208$	−0.915768	−0.0634971
$209$	23.5866	1.63152
$210$	90.5628	6.24943
$211$	4.28067	0.294693	0.147347	−	0.989085i	$-0.452927\pi$
$211$	4.28067	0.294693	0.147347	+	0.989085i	$0.452927\pi$
$212$	−25.2926	−1.73710
$213$	−17.0727	−1.16980
$214$	4.80767	0.328646
$215$	1.24375	0.0848231
$216$	150.630	10.2491
$217$	37.5660	2.55015
$218$	22.2656	1.50802
$219$	12.3079	0.831690
$220$	−74.9663	−5.05423
$221$	−0.506227	−0.0340525
$222$	−30.5897	−2.05305
$223$	0.874432	0.0585563	0.0292781	−	0.999571i	$-0.490679\pi$
$223$	0.874432	0.0585563	0.0292781	+	0.999571i	$0.490679\pi$
$224$	−49.7058	−3.32111
$225$	8.90364	0.593576
$226$	4.11744	0.273888
$227$	−18.5795	−1.23316	−0.616582	−	0.787291i	$-0.711483\pi$
$227$	−18.5795	−1.23316	−0.616582	+	0.787291i	$0.711483\pi$
$228$	64.2971	4.25818
$229$	15.0608	0.995243	0.497622	−	0.867394i	$-0.334207\pi$
$229$	15.0608	0.995243	0.497622	+	0.867394i	$0.334207\pi$
$230$	−20.0118	−1.31954
$231$	86.7560	5.70813
$232$	−14.6803	−0.963808
$233$	−4.68875	−0.307170	−0.153585	−	0.988135i	$-0.549082\pi$
$233$	−4.68875	−0.307170	−0.153585	+	0.988135i	$0.549082\pi$
$234$	2.00278	0.130926
$235$	−27.6921	−1.80643
$236$	−9.53308	−0.620551
$237$	−5.94767	−0.386343
$238$	−62.4685	−4.04923
$239$	12.0715	0.780843	0.390422	−	0.920636i	$-0.372329\pi$
$239$	12.0715	0.780843	0.390422	+	0.920636i	$0.372329\pi$
$240$	−87.9395	−5.67647
$241$	9.16444	0.590333	0.295167	−	0.955446i	$-0.404625\pi$
$241$	9.16444	0.590333	0.295167	+	0.955446i	$0.404625\pi$
$242$	−71.9608	−4.62581
$243$	−80.3552	−5.15479
$244$	28.0854	1.79798
$245$	24.0120	1.53407
$246$	−19.0810	−1.21656
$247$	0.333063	0.0211923
$248$	−70.8400	−4.49834
$249$	56.0751	3.55361
$250$	25.6993	1.62537
$251$	−0.0940097	−0.00593384	−0.00296692	−	0.999996i	$-0.500944\pi$
$251$	−0.0940097	−0.00593384	−0.00296692	+	0.999996i	$0.500944\pi$
$252$	175.857	11.0780
$253$	−19.1706	−1.20524
$254$	10.8041	0.677911
$255$	−48.6121	−3.04421
$256$	−9.63534	−0.602209
$257$	1.65069	0.102967	0.0514835	−	0.998674i	$-0.483605\pi$
$257$	1.65069	0.102967	0.0514835	+	0.998674i	$0.483605\pi$
$258$	4.56454	0.284176
$259$	−13.9135	−0.864544
$260$	−1.05859	−0.0656507
$261$	16.5323	1.02332
$262$	44.8047	2.76804
$263$	−25.3443	−1.56280	−0.781399	−	0.624032i	$-0.785493\pi$
$263$	−25.3443	−1.56280	−0.781399	+	0.624032i	$0.785493\pi$
$264$	−163.600	−10.0689
$265$	−12.5813	−0.772864
$266$	41.0999	2.52000
$267$	41.4070	2.53407
$268$	−39.5908	−2.41839
$269$	1.91413	0.116706	0.0583532	−	0.998296i	$-0.481415\pi$
$269$	1.91413	0.116706	0.0583532	+	0.998296i	$0.481415\pi$
$270$	126.006	7.66849
$271$	−26.4171	−1.60472	−0.802362	−	0.596838i	$-0.796424\pi$
$271$	−26.4171	−1.60472	−0.802362	+	0.596838i	$0.796424\pi$
$272$	60.6590	3.67799
$273$	1.22507	0.0741444
$274$	−10.0802	−0.608965
$275$	−6.33576	−0.382060
$276$	−52.2590	−3.14562
$277$	−7.94525	−0.477384	−0.238692	−	0.971095i	$-0.576719\pi$
$277$	−7.94525	−0.477384	−0.238692	+	0.971095i	$0.576719\pi$
$278$	−27.0497	−1.62233
$279$	79.7770	4.77612
$280$	−77.6774	−4.64211
$281$	−6.51558	−0.388687	−0.194343	−	0.980934i	$-0.562258\pi$
$281$	−6.51558	−0.388687	−0.194343	+	0.980934i	$0.562258\pi$
$282$	−101.629	−6.05194
$283$	−0.0941076	−0.00559412	−0.00279706	−	0.999996i	$-0.500890\pi$
$283$	−0.0941076	−0.00559412	−0.00279706	+	0.999996i	$0.500890\pi$
$284$	24.6260	1.46129
$285$	31.9834	1.89453
$286$	−1.42516	−0.0842716
$287$	−8.67887	−0.512298
$288$	−105.557	−6.22003
$289$	16.5317	0.972451
$290$	−12.2804	−0.721132
$291$	46.2334	2.71025
$292$	−17.7531	−1.03892
$293$	24.6282	1.43879	0.719396	−	0.694600i	$-0.244419\pi$
$293$	24.6282	1.43879	0.719396	+	0.694600i	$0.244419\pi$
$294$	88.1237	5.13948
$295$	−4.74205	−0.276093
$296$	26.2374	1.52502
$297$	120.710	7.00428
$298$	41.7197	2.41675
$299$	−0.270704	−0.0156552
$300$	−17.2713	−0.997156
$301$	2.07615	0.119667
$302$	−32.1887	−1.85225
$303$	−14.3593	−0.824922
$304$	−39.9094	−2.28896
$305$	13.9705	0.799950
$306$	−132.661	−7.58372
$307$	7.12166	0.406455	0.203227	−	0.979132i	$-0.434857\pi$
$307$	7.12166	0.406455	0.203227	+	0.979132i	$0.434857\pi$
$308$	−125.139	−7.13043
$309$	21.7017	1.23457
$310$	−59.2595	−3.36572
$311$	5.27773	0.299273	0.149636	−	0.988741i	$-0.452190\pi$
$311$	5.27773	0.299273	0.149636	+	0.988741i	$0.452190\pi$
$312$	−2.31016	−0.130787
$313$	15.9343	0.900662	0.450331	−	0.892862i	$-0.351306\pi$
$313$	15.9343	0.900662	0.450331	+	0.892862i	$0.351306\pi$
$314$	−10.4287	−0.588524
$315$	87.4769	4.92877
$316$	8.57903	0.482608
$317$	29.6977	1.66799	0.833994	−	0.551774i	$-0.186049\pi$
$317$	29.6977	1.66799	0.833994	+	0.551774i	$0.186049\pi$
$318$	−46.1732	−2.58926
$319$	−11.7642	−0.658671
$320$	26.9913	1.50886
$321$	6.24515	0.348570
$322$	−33.4049	−1.86158
$323$	−22.0615	−1.22754
$324$	200.278	11.1265
$325$	−0.0894661	−0.00496268
$326$	−37.2659	−2.06397
$327$	28.9230	1.59945
$328$	16.3661	0.903669
$329$	−46.2254	−2.54849
$330$	−136.856	−7.53365
$331$	−17.0215	−0.935589	−0.467794	−	0.883837i	$-0.654951\pi$
$331$	−17.0215	−0.935589	−0.467794	+	0.883837i	$0.654951\pi$
$332$	−80.8838	−4.43908
$333$	−29.5474	−1.61919
$334$	67.3320	3.68424
$335$	−19.6937	−1.07598
$336$	−146.794	−8.00828
$337$	−6.07798	−0.331089	−0.165544	−	0.986202i	$-0.552938\pi$
$337$	−6.07798	−0.331089	−0.165544	+	0.986202i	$0.552938\pi$
$338$	34.2118	1.86088
$339$	5.34854	0.290493
$340$	70.1190	3.80274
$341$	−56.7686	−3.07419
$342$	87.2817	4.71965
$343$	11.4048	0.615801
$344$	−3.91509	−0.211087
$345$	−25.9952	−1.39954
$346$	−20.9920	−1.12853
$347$	30.8814	1.65780	0.828899	−	0.559398i	$-0.188968\pi$
$347$	30.8814	1.65780	0.828899	+	0.559398i	$0.188968\pi$
$348$	−32.0693	−1.71909
$349$	19.6207	1.05027	0.525136	−	0.851019i	$-0.324015\pi$
$349$	19.6207	1.05027	0.525136	+	0.851019i	$0.324015\pi$
$350$	−11.0401	−0.590119
$351$	1.70452	0.0909804
$352$	75.1138	4.00358
$353$	−1.15842	−0.0616567	−0.0308283	−	0.999525i	$-0.509815\pi$
$353$	−1.15842	−0.0616567	−0.0308283	+	0.999525i	$0.509815\pi$
$354$	−17.4032	−0.924970
$355$	12.2498	0.650150
$356$	−59.7262	−3.16548
$357$	−81.1464	−4.29472
$358$	36.4580	1.92686
$359$	10.7572	0.567744	0.283872	−	0.958862i	$-0.408381\pi$
$359$	10.7572	0.567744	0.283872	+	0.958862i	$0.408381\pi$
$360$	−164.959	−8.69411
$361$	−4.48505	−0.236055
$362$	−52.7140	−2.77059
$363$	−93.4769	−4.90626
$364$	−1.76706	−0.0926191
$365$	−8.83096	−0.462234
$366$	51.2715	2.68000
$367$	24.2501	1.26584	0.632921	−	0.774216i	$-0.281856\pi$
$367$	24.2501	1.26584	0.632921	+	0.774216i	$0.281856\pi$
$368$	32.4373	1.69091
$369$	−18.4308	−0.959472
$370$	21.9483	1.14104
$371$	−21.0015	−1.09035
$372$	−154.751	−8.02347
$373$	−32.6872	−1.69248	−0.846239	−	0.532803i	$-0.821139\pi$
$373$	−32.6872	−1.69248	−0.846239	+	0.532803i	$0.821139\pi$
$374$	94.4003	4.88133
$375$	33.3833	1.72391
$376$	87.1694	4.49542
$377$	−0.166121	−0.00855565
$378$	210.338	10.8186
$379$	2.80420	0.144042	0.0720210	−	0.997403i	$-0.477055\pi$
$379$	2.80420	0.144042	0.0720210	+	0.997403i	$0.477055\pi$
$380$	−46.1334	−2.36660
$381$	14.0345	0.719011
$382$	58.6150	2.99900
$383$	−37.8301	−1.93303	−0.966514	−	0.256614i	$-0.917393\pi$
$383$	−37.8301	−1.93303	−0.966514	+	0.256614i	$0.917393\pi$
$384$	16.0558	0.819345
$385$	−62.2478	−3.17244
$386$	53.6562	2.73103
$387$	4.40900	0.224122
$388$	−66.6879	−3.38557
$389$	25.7098	1.30354	0.651769	−	0.758418i	$-0.274027\pi$
$389$	25.7098	1.30354	0.651769	+	0.758418i	$0.274027\pi$
$390$	−1.93251	−0.0978566
$391$	17.9310	0.906810
$392$	−75.5853	−3.81763
$393$	58.2012	2.93586
$394$	17.6618	0.889789
$395$	4.26748	0.214720
$396$	−265.750	−13.3544
$397$	−11.5589	−0.580124	−0.290062	−	0.957008i	$-0.593676\pi$
$397$	−11.5589	−0.580124	−0.290062	+	0.957008i	$0.593676\pi$
$398$	−42.5482	−2.13275
$399$	53.3887	2.67278
$400$	10.7203	0.536016
$401$	20.7531	1.03636	0.518180	−	0.855272i	$-0.326610\pi$
$401$	20.7531	1.03636	0.518180	+	0.855272i	$0.326610\pi$
$402$	−72.2754	−3.60477
$403$	−0.801619	−0.0399315
$404$	20.7122	1.03047
$405$	99.6242	4.95037
$406$	−20.4993	−1.01736
$407$	21.0257	1.04220
$408$	153.021	7.57569
$409$	−36.0310	−1.78162	−0.890809	−	0.454378i	$-0.849861\pi$
$409$	−36.0310	−1.78162	−0.890809	+	0.454378i	$0.849861\pi$
$410$	13.6907	0.676136
$411$	−13.0941	−0.645884
$412$	−31.3029	−1.54219
$413$	−7.91573	−0.389508
$414$	−70.9402	−3.48652
$415$	−40.2341	−1.97501
$416$	1.06067	0.0520035
$417$	−35.1375	−1.72069
$418$	−62.1089	−3.03785
$419$	−5.71509	−0.279200	−0.139600	−	0.990208i	$-0.544582\pi$
$419$	−5.71509	−0.279200	−0.139600	+	0.990208i	$0.544582\pi$
$420$	−169.687	−8.27990
$421$	5.00308	0.243835	0.121918	−	0.992540i	$-0.461096\pi$
$421$	5.00308	0.243835	0.121918	+	0.992540i	$0.461096\pi$
$422$	−11.2720	−0.548710
$423$	−98.1664	−4.77302
$424$	39.6036	1.92332
$425$	5.92608	0.287457
$426$	44.9563	2.17814
$427$	23.3205	1.12856
$428$	−9.00813	−0.435424
$429$	−1.85128	−0.0893807
$430$	−3.27507	−0.157938
$431$	−35.9211	−1.73026	−0.865130	−	0.501549i	$-0.832764\pi$
$431$	−35.9211	−1.73026	−0.865130	+	0.501549i	$0.832764\pi$
$432$	−204.245	−9.82673
$433$	−30.4867	−1.46510	−0.732548	−	0.680715i	$-0.761669\pi$
$433$	−30.4867	−1.46510	−0.732548	+	0.680715i	$0.761669\pi$
$434$	−98.9198	−4.74830
$435$	−15.9523	−0.764852
$436$	−41.7191	−1.99798
$437$	−11.7974	−0.564344
$438$	−32.4094	−1.54858
$439$	−2.03966	−0.0973476	−0.0486738	−	0.998815i	$-0.515499\pi$
$439$	−2.03966	−0.0973476	−0.0486738	+	0.998815i	$0.515499\pi$
$440$	117.384	5.59604
$441$	85.1209	4.05338
$442$	1.33301	0.0634048
$443$	22.2136	1.05540	0.527699	−	0.849432i	$-0.323055\pi$
$443$	22.2136	1.05540	0.527699	+	0.849432i	$0.323055\pi$
$444$	57.3159	2.72009
$445$	−29.7097	−1.40837
$446$	−2.30258	−0.109030
$447$	54.1937	2.56327
$448$	45.0557	2.12868
$449$	30.6226	1.44517	0.722584	−	0.691283i	$-0.242954\pi$
$449$	30.6226	1.44517	0.722584	+	0.691283i	$0.242954\pi$
$450$	−23.4453	−1.10522
$451$	13.1152	0.617572
$452$	−7.71484	−0.362876
$453$	−41.8130	−1.96455
$454$	48.9239	2.29611
$455$	−0.878990	−0.0412077
$456$	−100.677	−4.71465
$457$	−18.8520	−0.881858	−0.440929	−	0.897542i	$-0.645351\pi$
$457$	−18.8520	−0.881858	−0.440929	+	0.897542i	$0.645351\pi$
$458$	−39.6584	−1.85311
$459$	−112.904	−5.26993
$460$	37.4960	1.74826
$461$	21.3421	0.993999	0.497000	−	0.867751i	$-0.334435\pi$
$461$	21.3421	0.993999	0.497000	+	0.867751i	$0.334435\pi$
$462$	−228.448	−10.6284
$463$	31.8606	1.48069	0.740343	−	0.672230i	$-0.234663\pi$
$463$	31.8606	1.48069	0.740343	+	0.672230i	$0.234663\pi$
$464$	19.9055	0.924090
$465$	−76.9780	−3.56977
$466$	12.3465	0.571942
$467$	−13.2492	−0.613102	−0.306551	−	0.951854i	$-0.599175\pi$
$467$	−13.2492	−0.613102	−0.306551	+	0.951854i	$0.599175\pi$
$468$	−3.75261	−0.173464
$469$	−32.8740	−1.51798
$470$	72.9195	3.36353
$471$	−13.5468	−0.624204
$472$	14.9271	0.687073
$473$	−3.13741	−0.144258
$474$	15.6615	0.719359
$475$	−3.89895	−0.178896
$476$	117.047	5.36485
$477$	−44.5998	−2.04209
$478$	−31.7871	−1.45391
$479$	19.5536	0.893428	0.446714	−	0.894677i	$-0.352594\pi$
$479$	19.5536	0.893428	0.446714	+	0.894677i	$0.352594\pi$
$480$	101.854	4.64897
$481$	0.296900	0.0135375
$482$	−24.1320	−1.09918
$483$	−43.3929	−1.97445
$484$	134.833	6.12877
$485$	−33.1726	−1.50629
$486$	211.593	9.59806
$487$	0.00935702	0.000424007 0	0.000212004	−	1.00000i	$-0.499933\pi$
$487$	0.00935702	0.000424007 0	0.000212004		1.00000i	$0.499933\pi$
$488$	−43.9765	−1.99072
$489$	−48.4083	−2.18910
$490$	−63.2291	−2.85640
$491$	34.5118	1.55749	0.778747	−	0.627338i	$-0.215855\pi$
$491$	34.5118	1.55749	0.778747	+	0.627338i	$0.215855\pi$
$492$	35.7521	1.61183
$493$	11.0036	0.495576
$494$	−0.877029	−0.0394594
$495$	−132.192	−5.94160
$496$	96.0545	4.31297
$497$	20.4481	0.917222
$498$	−147.658	−6.61673
$499$	−29.2623	−1.30996	−0.654981	−	0.755645i	$-0.727323\pi$
$499$	−29.2623	−1.30996	−0.654981	+	0.755645i	$0.727323\pi$
$500$	−48.1528	−2.15346
$501$	87.4641	3.90761
$502$	0.247549	0.0110486
$503$	39.0691	1.74200	0.871002	−	0.491279i	$-0.163470\pi$
$503$	39.0691	1.74200	0.871002	+	0.491279i	$0.163470\pi$
$504$	−275.360	−12.2655
$505$	10.3029	0.458472
$506$	50.4804	2.24413
$507$	44.4410	1.97369
$508$	−20.2437	−0.898168
$509$	13.7684	0.610273	0.305136	−	0.952309i	$-0.401298\pi$
$509$	13.7684	0.610273	0.305136	+	0.952309i	$0.401298\pi$
$510$	128.006	5.66822
$511$	−14.7412	−0.652112
$512$	34.7599	1.53618
$513$	74.2833	3.27969
$514$	−4.34663	−0.191721
$515$	−15.5711	−0.686143
$516$	−8.55257	−0.376506
$517$	69.8544	3.07219
$518$	36.6374	1.60976
$519$	−27.2685	−1.19695
$520$	1.65755	0.0726884
$521$	−13.8296	−0.605888	−0.302944	−	0.953008i	$-0.597970\pi$
$521$	−13.8296	−0.605888	−0.302944	+	0.953008i	$0.597970\pi$
$522$	−43.5333	−1.90540
$523$	26.5288	1.16003	0.580013	−	0.814608i	$-0.303048\pi$
$523$	26.5288	1.16003	0.580013	+	0.814608i	$0.303048\pi$
$524$	−83.9505	−3.66739
$525$	−14.3411	−0.625896
$526$	66.7372	2.90988
$527$	53.0979	2.31298
$528$	221.831	9.65394
$529$	−13.4114	−0.583105
$530$	33.1294	1.43905
$531$	−16.8102	−0.729501
$532$	−77.0089	−3.33876
$533$	0.185198	0.00802181
$534$	−109.034	−4.71836
$535$	−4.48092	−0.193727
$536$	61.9920	2.67765
$537$	47.3588	2.04368
$538$	−5.04032	−0.217304
$539$	−60.5713	−2.60899
$540$	−236.098	−10.1600
$541$	−20.2908	−0.872371	−0.436185	−	0.899857i	$-0.643671\pi$
$541$	−20.2908	−0.872371	−0.436185	+	0.899857i	$0.643671\pi$
$542$	69.5621	2.98795
$543$	−68.4754	−2.93856
$544$	−70.2569	−3.01224
$545$	−20.7524	−0.888934
$546$	−3.22587	−0.138055
$547$	−6.72815	−0.287675	−0.143837	−	0.989601i	$-0.545944\pi$
$547$	−6.72815	−0.287675	−0.143837	+	0.989601i	$0.545944\pi$
$548$	18.8872	0.806821
$549$	49.5245	2.11365
$550$	16.6835	0.711385
$551$	−7.23958	−0.308417
$552$	81.8279	3.48283
$553$	7.12355	0.302924
$554$	20.9216	0.888875
$555$	28.5107	1.21021
$556$	50.6829	2.14944
$557$	14.2685	0.604577	0.302288	−	0.953217i	$-0.402249\pi$
$557$	14.2685	0.604577	0.302288	+	0.953217i	$0.402249\pi$
$558$	−210.071	−8.89300
$559$	−0.0443028	−0.00187381
$560$	105.325	4.45081
$561$	122.626	5.17726
$562$	17.1570	0.723724
$563$	12.6054	0.531254	0.265627	−	0.964076i	$-0.414421\pi$
$563$	12.6054	0.531254	0.265627	+	0.964076i	$0.414421\pi$
$564$	190.423	8.01825
$565$	−3.83760	−0.161449
$566$	0.247806	0.0104161
$567$	166.299	6.98391
$568$	−38.5599	−1.61794
$569$	−20.7748	−0.870925	−0.435462	−	0.900207i	$-0.643415\pi$
$569$	−20.7748	−0.870925	−0.435462	+	0.900207i	$0.643415\pi$
$570$	−84.2194	−3.52756
$571$	−18.6075	−0.778700	−0.389350	−	0.921090i	$-0.627300\pi$
$571$	−18.6075	−0.778700	−0.389350	+	0.921090i	$0.627300\pi$
$572$	2.67032	0.111652
$573$	76.1407	3.18082
$574$	22.8534	0.953883
$575$	3.16896	0.132155
$576$	95.6823	3.98676
$577$	23.4004	0.974173	0.487086	−	0.873354i	$-0.338060\pi$
$577$	23.4004	0.974173	0.487086	+	0.873354i	$0.338060\pi$
$578$	−43.5316	−1.81068
$579$	69.6992	2.89660
$580$	23.0099	0.955432
$581$	−67.1614	−2.78632
$582$	−121.743	−5.04640
$583$	31.7369	1.31441
$584$	27.7982	1.15030
$585$	−1.86666	−0.0771770
$586$	−64.8515	−2.67899
$587$	16.3806	0.676101	0.338051	−	0.941128i	$-0.390232\pi$
$587$	16.3806	0.676101	0.338051	+	0.941128i	$0.390232\pi$
$588$	−165.117	−6.80932
$589$	−34.9348	−1.43946
$590$	12.4869	0.514077
$591$	22.9426	0.943734
$592$	−35.5762	−1.46217
$593$	−40.1695	−1.64956	−0.824781	−	0.565453i	$-0.808702\pi$
$593$	−40.1695	−1.64956	−0.824781	+	0.565453i	$0.808702\pi$
$594$	−317.855	−13.0418
$595$	58.2229	2.38690
$596$	−78.1701	−3.20197
$597$	−55.2700	−2.26205
$598$	0.712825	0.0291496
$599$	34.5538	1.41183	0.705915	−	0.708297i	$-0.250536\pi$
$599$	34.5538	1.41183	0.705915	+	0.708297i	$0.250536\pi$
$600$	27.0436	1.10405
$601$	−6.85703	−0.279704	−0.139852	−	0.990172i	$-0.544663\pi$
$601$	−6.85703	−0.279704	−0.139852	+	0.990172i	$0.544663\pi$
$602$	−5.46696	−0.222817
$603$	−69.8127	−2.84299
$604$	60.3120	2.45406
$605$	67.0700	2.72678
$606$	37.8113	1.53598
$607$	31.9929	1.29855	0.649276	−	0.760553i	$-0.275072\pi$
$607$	31.9929	1.29855	0.649276	+	0.760553i	$0.275072\pi$
$608$	46.2242	1.87464
$609$	−26.6285	−1.07904
$610$	−36.7875	−1.48948
$611$	0.986401	0.0399055
$612$	248.567	10.0477
$613$	−2.54659	−0.102856	−0.0514279	−	0.998677i	$-0.516377\pi$
$613$	−2.54659	−0.102856	−0.0514279	+	0.998677i	$0.516377\pi$
$614$	−18.7529	−0.756807
$615$	17.7842	0.717128
$616$	195.944	7.89481
$617$	−42.3867	−1.70642	−0.853212	−	0.521565i	$-0.825348\pi$
$617$	−42.3867	−1.70642	−0.853212	+	0.521565i	$0.825348\pi$
$618$	−57.1454	−2.29873
$619$	−47.3611	−1.90360	−0.951802	−	0.306715i	$-0.900770\pi$
$619$	−47.3611	−1.90360	−0.951802	+	0.306715i	$0.900770\pi$
$620$	111.035	4.45925
$621$	−60.3755	−2.42278
$622$	−13.8974	−0.557237
$623$	−49.5933	−1.98691
$624$	3.13243	0.125398
$625$	−29.0696	−1.16278
$626$	−41.9587	−1.67701
$627$	−80.6793	−3.22202
$628$	19.5402	0.779738
$629$	−19.6661	−0.784141
$630$	−230.346	−9.17722
$631$	43.7953	1.74346	0.871732	−	0.489983i	$-0.162997\pi$
$631$	43.7953	1.74346	0.871732	+	0.489983i	$0.162997\pi$
$632$	−13.4332	−0.534344
$633$	−14.6422	−0.581977
$634$	−78.2006	−3.10574
$635$	−10.0698	−0.399609
$636$	86.5146	3.43053
$637$	−0.855317	−0.0338889
$638$	30.9779	1.22643
$639$	43.4245	1.71785
$640$	−11.5201	−0.455373
$641$	13.5253	0.534217	0.267109	−	0.963666i	$-0.413932\pi$
$641$	13.5253	0.534217	0.267109	+	0.963666i	$0.413932\pi$
$642$	−16.4449	−0.649028
$643$	7.35406	0.290016	0.145008	−	0.989430i	$-0.453679\pi$
$643$	7.35406	0.290016	0.145008	+	0.989430i	$0.453679\pi$
$644$	62.5908	2.46642
$645$	−4.25431	−0.167513
$646$	58.0929	2.28564
$647$	−16.8562	−0.662684	−0.331342	−	0.943511i	$-0.607501\pi$
$647$	−16.8562	−0.662684	−0.331342	+	0.943511i	$0.607501\pi$
$648$	−313.598	−12.3193
$649$	11.9620	0.469549
$650$	0.235584	0.00924037
$651$	−128.497	−5.03618
$652$	69.8251	2.73456
$653$	−26.6801	−1.04407	−0.522036	−	0.852923i	$-0.674828\pi$
$653$	−26.6801	−1.04407	−0.522036	+	0.852923i	$0.674828\pi$
$654$	−76.1608	−2.97812
$655$	−41.7596	−1.63168
$656$	−22.1914	−0.866430
$657$	−31.3051	−1.22133
$658$	121.722	4.74521
$659$	23.0246	0.896910	0.448455	−	0.893805i	$-0.351974\pi$
$659$	23.0246	0.896910	0.448455	+	0.893805i	$0.351974\pi$
$660$	256.426	9.98137
$661$	−17.8026	−0.692442	−0.346221	−	0.938153i	$-0.612535\pi$
$661$	−17.8026	−0.692442	−0.346221	+	0.938153i	$0.612535\pi$
$662$	44.8215	1.74204
$663$	1.73158	0.0672489
$664$	126.649	4.91494
$665$	−38.3066	−1.48547
$666$	77.8049	3.01488
$667$	5.88414	0.227835
$668$	−126.160	−4.88127
$669$	−2.99104	−0.115640
$670$	51.8579	2.00345
$671$	−35.2412	−1.36047
$672$	170.021	6.55871
$673$	4.72810	0.182255	0.0911274	−	0.995839i	$-0.470953\pi$
$673$	4.72810	0.182255	0.0911274	+	0.995839i	$0.470953\pi$
$674$	16.0047	0.616478
$675$	−19.9537	−0.768019
$676$	−64.1026	−2.46548
$677$	44.1300	1.69605	0.848027	−	0.529953i	$-0.177790\pi$
$677$	44.1300	1.69605	0.848027	+	0.529953i	$0.177790\pi$
$678$	−14.0839	−0.540889
$679$	−55.3739	−2.12506
$680$	−109.793	−4.21039
$681$	63.5521	2.43532
$682$	149.484	5.72406
$683$	−19.2462	−0.736434	−0.368217	−	0.929740i	$-0.620032\pi$
$683$	−19.2462	−0.736434	−0.368217	+	0.929740i	$0.620032\pi$
$684$	−163.540	−6.25309
$685$	9.39507	0.358967
$686$	−30.0314	−1.14660
$687$	−51.5161	−1.96546
$688$	5.30860	0.202389
$689$	0.448151	0.0170732
$690$	68.4512	2.60589
$691$	−14.6391	−0.556897	−0.278449	−	0.960451i	$-0.589820\pi$
$691$	−14.6391	−0.556897	−0.278449	+	0.960451i	$0.589820\pi$
$692$	39.3326	1.49520
$693$	−220.664	−8.38233
$694$	−81.3176	−3.08677
$695$	25.2113	0.956318
$696$	50.2146	1.90338
$697$	−12.2672	−0.464653
$698$	−51.6657	−1.95557
$699$	16.0381	0.606617
$700$	20.6858	0.781852
$701$	10.8908	0.411339	0.205669	−	0.978622i	$-0.434063\pi$
$701$	10.8908	0.411339	0.205669	+	0.978622i	$0.434063\pi$
$702$	−4.48838	−0.169403
$703$	12.9390	0.488002
$704$	−68.0867	−2.56611
$705$	94.7222	3.56745
$706$	3.05039	0.114803
$707$	17.1982	0.646806
$708$	32.6084	1.22550
$709$	30.5788	1.14841	0.574206	−	0.818711i	$-0.305311\pi$
$709$	30.5788	1.14841	0.574206	+	0.818711i	$0.305311\pi$
$710$	−32.2564	−1.21056
$711$	15.1279	0.567340
$712$	93.5203	3.50482
$713$	28.3940	1.06337
$714$	213.677	7.99664
$715$	1.32830	0.0496757
$716$	−68.3113	−2.55291
$717$	−41.2913	−1.54205
$718$	−28.3262	−1.05712
$719$	19.9626	0.744480	0.372240	−	0.928137i	$-0.378590\pi$
$719$	19.9626	0.744480	0.372240	+	0.928137i	$0.378590\pi$
$720$	223.674	8.33584
$721$	−25.9922	−0.968000
$722$	11.8101	0.439528
$723$	−31.3474	−1.16582
$724$	98.7702	3.67077
$725$	1.94467	0.0722233
$726$	246.146	9.13532
$727$	14.9383	0.554030	0.277015	−	0.960866i	$-0.410655\pi$
$727$	14.9383	0.554030	0.277015	+	0.960866i	$0.410655\pi$
$728$	2.76689	0.102548
$729$	153.082	5.66970
$730$	23.2539	0.860665
$731$	2.93454	0.108538
$732$	−96.0674	−3.55075
$733$	5.95609	0.219993	0.109997	−	0.993932i	$-0.464916\pi$
$733$	5.95609	0.219993	0.109997	+	0.993932i	$0.464916\pi$
$734$	−63.8558	−2.35696
$735$	−82.1344	−3.02957
$736$	−37.5698	−1.38484
$737$	49.6781	1.82992
$738$	48.5326	1.78651
$739$	−8.47654	−0.311814	−0.155907	−	0.987772i	$-0.549830\pi$
$739$	−8.47654	−0.311814	−0.155907	+	0.987772i	$0.549830\pi$
$740$	−41.1244	−1.51176
$741$	−1.13926	−0.0418517
$742$	55.3018	2.03019
$743$	3.26456	0.119765	0.0598826	−	0.998205i	$-0.480927\pi$
$743$	3.26456	0.119765	0.0598826	+	0.998205i	$0.480927\pi$
$744$	242.312	8.88358
$745$	−38.8842	−1.42461
$746$	86.0727	3.15135
$747$	−142.627	−5.21845
$748$	−176.878	−6.46729
$749$	−7.47984	−0.273308
$750$	−87.9058	−3.20987
$751$	13.0462	0.476063	0.238032	−	0.971257i	$-0.423498\pi$
$751$	13.0462	0.476063	0.238032	+	0.971257i	$0.423498\pi$
$752$	−118.196	−4.31017
$753$	0.321565	0.0117185
$754$	0.437433	0.0159304
$755$	30.0010	1.09185
$756$	−394.109	−14.3336
$757$	−29.2075	−1.06157	−0.530783	−	0.847508i	$-0.678102\pi$
$757$	−29.2075	−1.06157	−0.530783	+	0.847508i	$0.678102\pi$
$758$	−7.38409	−0.268202
$759$	65.5739	2.38018
$760$	72.2365	2.62029
$761$	−22.4545	−0.813973	−0.406987	−	0.913434i	$-0.633420\pi$
$761$	−22.4545	−0.813973	−0.406987	+	0.913434i	$0.633420\pi$
$762$	−36.9561	−1.33878
$763$	−34.6412	−1.25410
$764$	−109.827	−3.97340
$765$	123.645	4.47038
$766$	99.6151	3.59924
$767$	0.168913	0.00609910
$768$	32.9582	1.18928
$769$	−26.1651	−0.943539	−0.471769	−	0.881722i	$-0.656385\pi$
$769$	−26.1651	−0.943539	−0.471769	+	0.881722i	$0.656385\pi$
$770$	163.912	5.90699
$771$	−5.64625	−0.203345
$772$	−100.536	−3.61835
$773$	−32.5569	−1.17099	−0.585495	−	0.810676i	$-0.699100\pi$
$773$	−32.5569	−1.17099	−0.585495	+	0.810676i	$0.699100\pi$
$774$	−11.6099	−0.417309
$775$	9.38405	0.337085
$776$	104.421	3.74850
$777$	47.5919	1.70735
$778$	−67.6996	−2.42715
$779$	8.07097	0.289172
$780$	3.62095	0.129651
$781$	−30.9005	−1.10571
$782$	−47.2164	−1.68845
$783$	−37.0501	−1.32406
$784$	102.489	3.66031
$785$	9.71989	0.346918
$786$	−153.257	−5.46649
$787$	28.3593	1.01090	0.505449	−	0.862856i	$-0.331327\pi$
$787$	28.3593	1.01090	0.505449	+	0.862856i	$0.331327\pi$
$788$	−33.0929	−1.17889
$789$	86.6915	3.08630
$790$	−11.2372	−0.399802
$791$	−6.40597	−0.227770
$792$	416.116	14.7860
$793$	−0.497634	−0.0176715
$794$	30.4372	1.08017
$795$	43.0350	1.52630
$796$	79.7225	2.82569
$797$	2.75951	0.0977470	0.0488735	−	0.998805i	$-0.484437\pi$
$797$	2.75951	0.0977470	0.0488735	+	0.998805i	$0.484437\pi$
$798$	−140.584	−4.97663
$799$	−65.3376	−2.31148
$800$	−12.4166	−0.438992
$801$	−105.319	−3.72125
$802$	−54.6475	−1.92967
$803$	22.2764	0.786118
$804$	135.422	4.77598
$805$	31.1346	1.09735
$806$	2.11084	0.0743513
$807$	−6.54737	−0.230478
$808$	−32.4315	−1.14094
$809$	28.9287	1.01708	0.508540	−	0.861038i	$-0.330185\pi$
$809$	28.9287	1.01708	0.508540	+	0.861038i	$0.330185\pi$
$810$	−262.333	−9.21744
$811$	−45.3744	−1.59331	−0.796656	−	0.604433i	$-0.793400\pi$
$811$	−45.3744	−1.59331	−0.796656	+	0.604433i	$0.793400\pi$
$812$	38.4095	1.34791
$813$	90.3610	3.16910
$814$	−55.3653	−1.94055
$815$	34.7332	1.21665
$816$	−207.487	−7.26350
$817$	−1.93073	−0.0675476
$818$	94.8777	3.31732
$819$	−3.11595	−0.108880
$820$	−25.6523	−0.895816
$821$	−3.41711	−0.119258	−0.0596289	−	0.998221i	$-0.518992\pi$
$821$	−3.41711	−0.119258	−0.0596289	+	0.998221i	$0.518992\pi$
$822$	34.4797	1.20262
$823$	−37.6386	−1.31200	−0.656000	−	0.754761i	$-0.727753\pi$
$823$	−37.6386	−1.31200	−0.656000	+	0.754761i	$0.727753\pi$
$824$	49.0147	1.70751
$825$	21.6718	0.754514
$826$	20.8439	0.725252
$827$	−28.8666	−1.00379	−0.501895	−	0.864929i	$-0.667364\pi$
$827$	−28.8666	−1.00379	−0.501895	+	0.864929i	$0.667364\pi$
$828$	132.921	4.61931
$829$	24.1380	0.838348	0.419174	−	0.907906i	$-0.362320\pi$
$829$	24.1380	0.838348	0.419174	+	0.907906i	$0.362320\pi$
$830$	105.945	3.67742
$831$	27.1771	0.942764
$832$	−0.961440	−0.0333319
$833$	56.6547	1.96297
$834$	92.5248	3.20387
$835$	−62.7558	−2.17175
$836$	116.373	4.02486
$837$	−178.786	−6.17975
$838$	15.0491	0.519863
$839$	24.8102	0.856544	0.428272	−	0.903650i	$-0.359123\pi$
$839$	24.8102	0.856544	0.428272	+	0.903650i	$0.359123\pi$
$840$	265.699	9.16750
$841$	−25.3891	−0.875487
$842$	−13.1742	−0.454014
$843$	22.2869	0.767601
$844$	21.1203	0.726989
$845$	−31.8866	−1.09693
$846$	258.494	8.88721
$847$	111.958	3.84691
$848$	−53.6999	−1.84406
$849$	0.321900	0.0110476
$850$	−15.6047	−0.535237
$851$	−10.5164	−0.360499
$852$	−84.2346	−2.88583
$853$	15.3299	0.524887	0.262443	−	0.964947i	$-0.415472\pi$
$853$	15.3299	0.524887	0.262443	+	0.964947i	$0.415472\pi$
$854$	−61.4081	−2.10134
$855$	−81.3497	−2.78210
$856$	14.1051	0.482102
$857$	15.0240	0.513209	0.256604	−	0.966517i	$-0.417396\pi$
$857$	15.0240	0.513209	0.256604	+	0.966517i	$0.417396\pi$
$858$	4.87484	0.166424
$859$	−11.0081	−0.375590	−0.187795	−	0.982208i	$-0.560134\pi$
$859$	−11.0081	−0.375590	−0.187795	+	0.982208i	$0.560134\pi$
$860$	6.13650	0.209253
$861$	29.6865	1.01171
$862$	94.5883	3.22169
$863$	−38.4655	−1.30938	−0.654691	−	0.755897i	$-0.727201\pi$
$863$	−38.4655	−1.30938	−0.654691	+	0.755897i	$0.727201\pi$
$864$	236.562	8.04800
$865$	19.5653	0.665239
$866$	80.2783	2.72797
$867$	−56.5474	−1.92045
$868$	185.346	6.29105
$869$	−10.7649	−0.365173
$870$	42.0059	1.42413
$871$	0.701496	0.0237693
$872$	65.3245	2.21217
$873$	−117.595	−3.97997
$874$	31.0651	1.05079
$875$	−39.9833	−1.35168
$876$	60.7255	2.05172
$877$	22.4174	0.756983	0.378491	−	0.925605i	$-0.376443\pi$
$877$	22.4174	0.756983	0.378491	+	0.925605i	$0.376443\pi$
$878$	5.37088	0.181258
$879$	−84.2419	−2.84141
$880$	−159.164	−5.36543
$881$	−25.2099	−0.849342	−0.424671	−	0.905348i	$-0.639610\pi$
$881$	−25.2099	−0.849342	−0.424671	+	0.905348i	$0.639610\pi$
$882$	−224.142	−7.54727
$883$	9.30758	0.313225	0.156613	−	0.987660i	$-0.449943\pi$
$883$	9.30758	0.313225	0.156613	+	0.987660i	$0.449943\pi$
$884$	−2.49766	−0.0840054
$885$	16.2204	0.545243
$886$	−58.4933	−1.96512
$887$	−1.06149	−0.0356413	−0.0178207	−	0.999841i	$-0.505673\pi$
$887$	−1.06149	−0.0356413	−0.0178207	+	0.999841i	$0.505673\pi$
$888$	−89.7462	−3.01169
$889$	−16.8092	−0.563763
$890$	78.2322	2.62235
$891$	−251.306	−8.41907
$892$	4.31433	0.144455
$893$	42.9876	1.43853
$894$	−142.704	−4.77274
$895$	−33.9801	−1.13583
$896$	−19.2301	−0.642433
$897$	0.925958	0.0309168
$898$	−80.6361	−2.69086
$899$	17.4243	0.581134
$900$	43.9294	1.46431
$901$	−29.6848	−0.988942
$902$	−34.5353	−1.14990
$903$	−7.10157	−0.236325
$904$	12.0800	0.401776
$905$	49.1314	1.63318
$906$	110.103	3.65793
$907$	15.0982	0.501326	0.250663	−	0.968074i	$-0.419351\pi$
$907$	15.0982	0.501326	0.250663	+	0.968074i	$0.419351\pi$
$908$	−91.6687	−3.04213
$909$	36.5229	1.21139
$910$	2.31458	0.0767275
$911$	−4.08206	−0.135245	−0.0676223	−	0.997711i	$-0.521541\pi$
$911$	−4.08206	−0.135245	−0.0676223	+	0.997711i	$0.521541\pi$
$912$	136.512	4.52037
$913$	101.492	3.35890
$914$	49.6414	1.64199
$915$	−47.7869	−1.57979
$916$	74.3078	2.45520
$917$	−69.7078	−2.30195
$918$	297.303	9.81245
$919$	−55.1985	−1.82083	−0.910416	−	0.413694i	$-0.864238\pi$
$919$	−55.1985	−1.82083	−0.910416	+	0.413694i	$0.864238\pi$
$920$	−58.7119	−1.93567
$921$	−24.3600	−0.802690
$922$	−56.1985	−1.85080
$923$	−0.436340	−0.0143623
$924$	428.043	14.0816
$925$	−3.47562	−0.114278
$926$	−83.8960	−2.75699
$927$	−55.1982	−1.81295
$928$	−23.0551	−0.756821
$929$	1.45161	0.0476257	0.0238128	−	0.999716i	$-0.492419\pi$
$929$	1.45161	0.0476257	0.0238128	+	0.999716i	$0.492419\pi$
$930$	202.700	6.64680
$931$	−37.2749	−1.22164
$932$	−23.1337	−0.757768
$933$	−18.0527	−0.591020
$934$	34.8882	1.14158
$935$	−87.9845	−2.87740
$936$	5.87590	0.192060
$937$	−23.9375	−0.782003	−0.391001	−	0.920390i	$-0.627871\pi$
$937$	−23.9375	−0.782003	−0.391001	+	0.920390i	$0.627871\pi$
$938$	86.5646	2.82643
$939$	−54.5042	−1.77868
$940$	−136.629	−4.45635
$941$	−8.88908	−0.289776	−0.144888	−	0.989448i	$-0.546282\pi$
$941$	−8.88908	−0.289776	−0.144888	+	0.989448i	$0.546282\pi$
$942$	35.6718	1.16225
$943$	−6.55987	−0.213619
$944$	−20.2401	−0.658760
$945$	−196.042	−6.37725
$946$	8.26150	0.268604
$947$	−54.4330	−1.76883	−0.884417	−	0.466697i	$-0.845444\pi$
$947$	−54.4330	−1.76883	−0.884417	+	0.466697i	$0.845444\pi$
$948$	−29.3450	−0.953082
$949$	0.314562	0.0102111
$950$	10.2668	0.333100
$951$	−101.582	−3.29404
$952$	−183.274	−5.93995
$953$	−26.2253	−0.849521	−0.424760	−	0.905306i	$-0.639642\pi$
$953$	−26.2253	−0.849521	−0.424760	+	0.905306i	$0.639642\pi$
$954$	117.441	3.80231
$955$	−54.6313	−1.76783
$956$	59.5594	1.92629
$957$	40.2402	1.30078
$958$	−51.4891	−1.66354
$959$	15.6829	0.506426
$960$	−92.3252	−2.97978
$961$	53.0814	1.71230
$962$	−0.781804	−0.0252064
$963$	−15.8845	−0.511872
$964$	45.2161	1.45631
$965$	−50.0095	−1.60986
$966$	114.263	3.67636
$967$	−38.6470	−1.24280	−0.621402	−	0.783492i	$-0.713436\pi$
$967$	−38.6470	−1.24280	−0.621402	+	0.783492i	$0.713436\pi$
$968$	−211.124	−6.78577
$969$	75.4625	2.42421
$970$	87.3510	2.80467
$971$	0.0790352	0.00253636	0.00126818	−	0.999999i	$-0.499596\pi$
$971$	0.0790352	0.00253636	0.00126818	+	0.999999i	$0.499596\pi$
$972$	−396.462	−12.7165
$973$	42.0843	1.34916
$974$	−0.0246391	−0.000789489 0
$975$	0.306023	0.00980059
$976$	59.6293	1.90869
$977$	−20.2057	−0.646437	−0.323219	−	0.946324i	$-0.604765\pi$
$977$	−20.2057	−0.646437	−0.323219	+	0.946324i	$0.604765\pi$
$978$	127.470	4.07604
$979$	74.9438	2.39521
$980$	118.472	3.78446
$981$	−73.5656	−2.34877
$982$	−90.8772	−2.90001
$983$	−23.0611	−0.735535	−0.367768	−	0.929918i	$-0.619878\pi$
$983$	−23.0611	−0.735535	−0.367768	+	0.929918i	$0.619878\pi$
$984$	−55.9812	−1.78462
$985$	−16.4614	−0.524505
$986$	−28.9749	−0.922747
$987$	158.116	5.03290
$988$	1.64329	0.0522799
$989$	1.56924	0.0498990
$990$	348.092	11.0631
$991$	−3.85834	−0.122564	−0.0612821	−	0.998120i	$-0.519519\pi$
$991$	−3.85834	−0.122564	−0.0612821	+	0.998120i	$0.519519\pi$
$992$	−111.253	−3.53228
$993$	58.2230	1.84765
$994$	−53.8444	−1.70784
$995$	39.6564	1.25719
$996$	276.667	8.76653
$997$	23.2253	0.735552	0.367776	−	0.929915i	$-0.380119\pi$
$997$	23.2253	0.735552	0.367776	+	0.929915i	$0.380119\pi$
$998$	77.0543	2.43911
$999$	66.2179	2.09504

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	5077.2.a.b.1.11	✓	205

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
5077.2.a.b.1.11	✓	205	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:	\( N \)	\(=\)	\( 5077 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	5077.a (trivial)

\(f(q)\)	\(=\)	\(q-2.63322 q^{2} -3.42055 q^{3} +4.93387 q^{4} +2.45426 q^{5} +9.00708 q^{6} +4.09681 q^{7} -7.72553 q^{8} +8.70017 q^{9} +O(q^{10})\)	\(q-2.63322 q^{2} -3.42055 q^{3} +4.93387 q^{4} +2.45426 q^{5} +9.00708 q^{6} +4.09681 q^{7} -7.72553 q^{8} +8.70017 q^{9} -6.46261 q^{10} -6.19096 q^{11} -16.8765 q^{12} -0.0874215 q^{13} -10.7878 q^{14} -8.39492 q^{15} +10.4753 q^{16} +5.79065 q^{17} -22.9095 q^{18} -3.80985 q^{19} +12.1090 q^{20} -14.0133 q^{21} +16.3022 q^{22} +3.09654 q^{23} +26.4256 q^{24} +1.02339 q^{25} +0.230200 q^{26} -19.4977 q^{27} +20.2131 q^{28} +1.90023 q^{29} +22.1057 q^{30} +9.16959 q^{31} -12.1328 q^{32} +21.1765 q^{33} -15.2481 q^{34} +10.0546 q^{35} +42.9255 q^{36} -3.39619 q^{37} +10.0322 q^{38} +0.299030 q^{39} -18.9605 q^{40} -2.11845 q^{41} +36.9002 q^{42} +0.506772 q^{43} -30.5454 q^{44} +21.3525 q^{45} -8.15389 q^{46} -11.2833 q^{47} -35.8314 q^{48} +9.78383 q^{49} -2.69481 q^{50} -19.8072 q^{51} -0.431326 q^{52} -5.12632 q^{53} +51.3418 q^{54} -15.1942 q^{55} -31.6500 q^{56} +13.0318 q^{57} -5.00373 q^{58} -1.93217 q^{59} -41.4194 q^{60} +5.69236 q^{61} -24.1456 q^{62} +35.6429 q^{63} +10.9978 q^{64} -0.214555 q^{65} -55.7625 q^{66} -8.02430 q^{67} +28.5703 q^{68} -10.5919 q^{69} -26.4761 q^{70} +4.99122 q^{71} -67.2134 q^{72} -3.59822 q^{73} +8.94292 q^{74} -3.50055 q^{75} -18.7973 q^{76} -25.3632 q^{77} -0.787412 q^{78} +1.73880 q^{79} +25.7092 q^{80} +40.5924 q^{81} +5.57835 q^{82} -16.3936 q^{83} -69.1400 q^{84} +14.2118 q^{85} -1.33444 q^{86} -6.49983 q^{87} +47.8285 q^{88} -12.1054 q^{89} -56.2258 q^{90} -0.358149 q^{91} +15.2779 q^{92} -31.3651 q^{93} +29.7114 q^{94} -9.35036 q^{95} +41.5009 q^{96} -13.5164 q^{97} -25.7630 q^{98} -53.8624 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9}+O(q^{10}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9	\( 205 q - 25 q^{2} - 59 q^{3} + 195 q^{4} - 44 q^{5} - 26 q^{6} - 30 q^{7} - 75 q^{8} + 186 q^{9} - 28 q^{10} - 83 q^{11} - 108 q^{12} - 36 q^{13} - 67 q^{14} - 63 q^{15} + 187 q^{16} - 72 q^{17} - 57 q^{18} - 47 q^{19} - 132 q^{20} - 35 q^{21} - 40 q^{22} - 97 q^{23} - 49 q^{24} + 175 q^{25} - 78 q^{26} - 227 q^{27} - 59 q^{28} - 46 q^{29} + 30 q^{30} - 77 q^{31} - 175 q^{32} - 74 q^{33} - 28 q^{34} - 171 q^{35} + 171 q^{36} - 52 q^{37} - 144 q^{38} - 54 q^{39} - 49 q^{40} - 107 q^{41} + 7 q^{42} - 58 q^{43} - 139 q^{44} - 89 q^{45} - 33 q^{46} - 255 q^{47} - 202 q^{48} + 171 q^{49} - 74 q^{50} - 63 q^{51} - 90 q^{52} - 82 q^{53} - 51 q^{54} - 70 q^{55} - 180 q^{56} - 70 q^{57} - 50 q^{58} - 289 q^{59} - 105 q^{60} - 20 q^{61} - 143 q^{62} - 119 q^{63} + 201 q^{64} - 92 q^{65} - 3 q^{66} - 138 q^{67} - 177 q^{68} - 67 q^{69} + 4 q^{70} - 141 q^{71} - 138 q^{72} - 71 q^{73} - 26 q^{74} - 251 q^{75} - 42 q^{76} - 149 q^{77} - 6 q^{78} - 47 q^{79} - 294 q^{80} + 193 q^{81} - 70 q^{82} - 329 q^{83} - 40 q^{84} - 45 q^{85} - 83 q^{86} - 139 q^{87} - 45 q^{88} - 163 q^{89} - 116 q^{90} - 141 q^{91} - 204 q^{92} - 91 q^{93} - 8 q^{94} - 173 q^{95} - 53 q^{96} - 147 q^{97} - 156 q^{98} - 157 q^{99}+O(q^{100}) \) 205 * q - 25 * q^2 - 59 * q^3 + 195 * q^4 - 44 * q^5 - 26 * q^6 - 30 * q^7 - 75 * q^8 + 186 * q^9 - 28 * q^10 - 83 * q^11 - 108 * q^12 - 36 * q^13 - 67 * q^14 - 63 * q^15 + 187 * q^16 - 72 * q^17 - 57 * q^18 - 47 * q^19 - 132 * q^20 - 35 * q^21 - 40 * q^22 - 97 * q^23 - 49 * q^24 + 175 * q^25 - 78 * q^26 - 227 * q^27 - 59 * q^28 - 46 * q^29 + 30 * q^30 - 77 * q^31 - 175 * q^32 - 74 * q^33 - 28 * q^34 - 171 * q^35 + 171 * q^36 - 52 * q^37 - 144 * q^38 - 54 * q^39 - 49 * q^40 - 107 * q^41 + 7 * q^42 - 58 * q^43 - 139 * q^44 - 89 * q^45 - 33 * q^46 - 255 * q^47 - 202 * q^48 + 171 * q^49 - 74 * q^50 - 63 * q^51 - 90 * q^52 - 82 * q^53 - 51 * q^54 - 70 * q^55 - 180 * q^56 - 70 * q^57 - 50 * q^58 - 289 * q^59 - 105 * q^60 - 20 * q^61 - 143 * q^62 - 119 * q^63 + 201 * q^64 - 92 * q^65 - 3 * q^66 - 138 * q^67 - 177 * q^68 - 67 * q^69 + 4 * q^70 - 141 * q^71 - 138 * q^72 - 71 * q^73 - 26 * q^74 - 251 * q^75 - 42 * q^76 - 149 * q^77 - 6 * q^78 - 47 * q^79 - 294 * q^80 + 193 * q^81 - 70 * q^82 - 329 * q^83 - 40 * q^84 - 45 * q^85 - 83 * q^86 - 139 * q^87 - 45 * q^88 - 163 * q^89 - 116 * q^90 - 141 * q^91 - 204 * q^92 - 91 * q^93 - 8 * q^94 - 173 * q^95 - 53 * q^96 - 147 * q^97 - 156 * q^98 - 157 * q^99

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