LMFDB - Embedded newform 4007.2.a.b.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [4007,2,Mod(1,4007)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(4007, 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("4007.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 4007 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	4007.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:	$31.9960560899$
Analytic rank:	$0$
Dimension:	$195$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	4007.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.43669 q^{2} +0.943453 q^{3} +3.93744 q^{4} -0.444210 q^{5} -2.29890 q^{6} -0.206330 q^{7} -4.72093 q^{8} -2.10990 q^{9} +O(q^{10})$	\(q-2.43669 q^{2} +0.943453 q^{3} +3.93744 q^{4} -0.444210 q^{5} -2.29890 q^{6} -0.206330 q^{7} -4.72093 q^{8} -2.10990 q^{9} +1.08240 q^{10} -2.85720 q^{11} +3.71479 q^{12} -3.30403 q^{13} +0.502762 q^{14} -0.419091 q^{15} +3.62855 q^{16} -5.32386 q^{17} +5.14115 q^{18} +4.50135 q^{19} -1.74905 q^{20} -0.194663 q^{21} +6.96210 q^{22} -6.02478 q^{23} -4.45398 q^{24} -4.80268 q^{25} +8.05089 q^{26} -4.82095 q^{27} -0.812413 q^{28} -6.23481 q^{29} +1.02119 q^{30} +7.04978 q^{31} +0.600225 q^{32} -2.69563 q^{33} +12.9726 q^{34} +0.0916540 q^{35} -8.30759 q^{36} +10.0941 q^{37} -10.9684 q^{38} -3.11720 q^{39} +2.09708 q^{40} -5.01777 q^{41} +0.474333 q^{42} -8.16236 q^{43} -11.2500 q^{44} +0.937236 q^{45} +14.6805 q^{46} -0.798320 q^{47} +3.42337 q^{48} -6.95743 q^{49} +11.7026 q^{50} -5.02281 q^{51} -13.0094 q^{52} +9.70532 q^{53} +11.7471 q^{54} +1.26920 q^{55} +0.974072 q^{56} +4.24681 q^{57} +15.1923 q^{58} -1.81877 q^{59} -1.65015 q^{60} -1.01437 q^{61} -17.1781 q^{62} +0.435336 q^{63} -8.71966 q^{64} +1.46768 q^{65} +6.56841 q^{66} +7.51481 q^{67} -20.9624 q^{68} -5.68410 q^{69} -0.223332 q^{70} +6.82149 q^{71} +9.96067 q^{72} +15.0059 q^{73} -24.5963 q^{74} -4.53110 q^{75} +17.7238 q^{76} +0.589527 q^{77} +7.59564 q^{78} -6.91531 q^{79} -1.61184 q^{80} +1.78135 q^{81} +12.2267 q^{82} +14.9487 q^{83} -0.766474 q^{84} +2.36491 q^{85} +19.8891 q^{86} -5.88225 q^{87} +13.4886 q^{88} -15.9849 q^{89} -2.28375 q^{90} +0.681722 q^{91} -23.7222 q^{92} +6.65113 q^{93} +1.94525 q^{94} -1.99954 q^{95} +0.566285 q^{96} -0.296533 q^{97} +16.9531 q^{98} +6.02839 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) $ 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * 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 $

$2$	−2.43669	−1.72300	−0.861499	−	0.507760i	$-0.830474\pi$
$2$	−2.43669	−1.72300	−0.861499	+	0.507760i	$0.830474\pi$
$3$	0.943453	0.544703	0.272352	−	0.962198i	$-0.412199\pi$
$3$	0.943453	0.544703	0.272352	+	0.962198i	$0.412199\pi$
$4$	3.93744	1.96872
$5$	−0.444210	−0.198657	−0.0993283	−	0.995055i	$-0.531669\pi$
$5$	−0.444210	−0.198657	−0.0993283	+	0.995055i	$0.531669\pi$
$6$	−2.29890	−0.938522
$7$	−0.206330	−0.0779856	−0.0389928	−	0.999239i	$-0.512415\pi$
$7$	−0.206330	−0.0779856	−0.0389928	+	0.999239i	$0.512415\pi$
$8$	−4.72093	−1.66910
$9$	−2.10990	−0.703299
$10$	1.08240	0.342285
$11$	−2.85720	−0.861478	−0.430739	−	0.902477i	$-0.641747\pi$
$11$	−2.85720	−0.861478	−0.430739	+	0.902477i	$0.641747\pi$
$12$	3.71479	1.07237
$13$	−3.30403	−0.916374	−0.458187	−	0.888856i	$-0.651501\pi$
$13$	−3.30403	−0.916374	−0.458187	+	0.888856i	$0.651501\pi$
$14$	0.502762	0.134369
$15$	−0.419091	−0.108209
$16$	3.62855	0.907138
$17$	−5.32386	−1.29123	−0.645613	−	0.763665i	$-0.723398\pi$
$17$	−5.32386	−1.29123	−0.645613	+	0.763665i	$0.723398\pi$
$18$	5.14115	1.21178
$19$	4.50135	1.03268	0.516340	−	0.856384i	$-0.327294\pi$
$19$	4.50135	1.03268	0.516340	+	0.856384i	$0.327294\pi$
$20$	−1.74905	−0.391099
$21$	−0.194663	−0.0424790
$22$	6.96210	1.48432
$23$	−6.02478	−1.25625	−0.628127	−	0.778111i	$-0.716178\pi$
$23$	−6.02478	−1.25625	−0.628127	+	0.778111i	$0.716178\pi$
$24$	−4.45398	−0.909165
$25$	−4.80268	−0.960536
$26$	8.05089	1.57891
$27$	−4.82095	−0.927792
$28$	−0.812413	−0.153532
$29$	−6.23481	−1.15778	−0.578888	−	0.815407i	$-0.696513\pi$
$29$	−6.23481	−1.15778	−0.578888	+	0.815407i	$0.696513\pi$
$30$	1.02119	0.186444
$31$	7.04978	1.26618	0.633089	−	0.774079i	$-0.281787\pi$
$31$	7.04978	1.26618	0.633089	+	0.774079i	$0.281787\pi$
$32$	0.600225	0.106106
$33$	−2.69563	−0.469250
$34$	12.9726	2.22478
$35$	0.0916540	0.0154924
$36$	−8.30759	−1.38460
$37$	10.0941	1.65947	0.829734	−	0.558160i	$-0.188492\pi$
$37$	10.0941	1.65947	0.829734	+	0.558160i	$0.188492\pi$
$38$	−10.9684	−1.77930
$39$	−3.11720	−0.499152
$40$	2.09708	0.331578
$41$	−5.01777	−0.783644	−0.391822	−	0.920041i	$-0.628155\pi$
$41$	−5.01777	−0.783644	−0.391822	+	0.920041i	$0.628155\pi$
$42$	0.474333	0.0731912
$43$	−8.16236	−1.24475	−0.622374	−	0.782720i	$-0.713832\pi$
$43$	−8.16236	−1.24475	−0.622374	+	0.782720i	$0.713832\pi$
$44$	−11.2500	−1.69601
$45$	0.937236	0.139715
$46$	14.6805	2.16452
$47$	−0.798320	−0.116447	−0.0582234	−	0.998304i	$-0.518544\pi$
$47$	−0.798320	−0.116447	−0.0582234	+	0.998304i	$0.518544\pi$
$48$	3.42337	0.494121
$49$	−6.95743	−0.993918
$50$	11.7026	1.65500
$51$	−5.02281	−0.703334
$52$	−13.0094	−1.80408
$53$	9.70532	1.33313	0.666564	−	0.745448i	$-0.267764\pi$
$53$	9.70532	1.33313	0.666564	+	0.745448i	$0.267764\pi$
$54$	11.7471	1.59858
$55$	1.26920	0.171138
$56$	0.974072	0.130166
$57$	4.24681	0.562504
$58$	15.1923	1.99484
$59$	−1.81877	−0.236784	−0.118392	−	0.992967i	$-0.537774\pi$
$59$	−1.81877	−0.236784	−0.118392	+	0.992967i	$0.537774\pi$
$60$	−1.65015	−0.213033
$61$	−1.01437	−0.129876	−0.0649382	−	0.997889i	$-0.520685\pi$
$61$	−1.01437	−0.129876	−0.0649382	+	0.997889i	$0.520685\pi$
$62$	−17.1781	−2.18162
$63$	0.435336	0.0548471
$64$	−8.71966	−1.08996
$65$	1.46768	0.182044
$66$	6.56841	0.808516
$67$	7.51481	0.918081	0.459040	−	0.888415i	$-0.348193\pi$
$67$	7.51481	0.918081	0.459040	+	0.888415i	$0.348193\pi$
$68$	−20.9624	−2.54206
$69$	−5.68410	−0.684285
$70$	−0.223332	−0.0266933
$71$	6.82149	0.809562	0.404781	−	0.914414i	$-0.367348\pi$
$71$	6.82149	0.809562	0.404781	+	0.914414i	$0.367348\pi$
$72$	9.96067	1.17388
$73$	15.0059	1.75630	0.878152	−	0.478382i	$-0.158777\pi$
$73$	15.0059	1.75630	0.878152	+	0.478382i	$0.158777\pi$
$74$	−24.5963	−2.85926
$75$	−4.53110	−0.523207
$76$	17.7238	2.03306
$77$	0.589527	0.0671828
$78$	7.59564	0.860037
$79$	−6.91531	−0.778033	−0.389017	−	0.921231i	$-0.627185\pi$
$79$	−6.91531	−0.778033	−0.389017	+	0.921231i	$0.627185\pi$
$80$	−1.61184	−0.180209
$81$	1.78135	0.197927
$82$	12.2267	1.35022
$83$	14.9487	1.64083	0.820416	−	0.571768i	$-0.193742\pi$
$83$	14.9487	1.64083	0.820416	+	0.571768i	$0.193742\pi$
$84$	−0.766474	−0.0836292
$85$	2.36491	0.256511
$86$	19.8891	2.14470
$87$	−5.88225	−0.630644
$88$	13.4886	1.43789
$89$	−15.9849	−1.69440	−0.847199	−	0.531275i	$-0.821713\pi$
$89$	−15.9849	−1.69440	−0.847199	+	0.531275i	$0.821713\pi$
$90$	−2.28375	−0.240728
$91$	0.681722	0.0714639
$92$	−23.7222	−2.47321
$93$	6.65113	0.689691
$94$	1.94525	0.200638
$95$	−1.99954	−0.205149
$96$	0.566285	0.0577962
$97$	−0.296533	−0.0301084	−0.0150542	−	0.999887i	$-0.504792\pi$
$97$	−0.296533	−0.0301084	−0.0150542	+	0.999887i	$0.504792\pi$
$98$	16.9531	1.71252
$99$	6.02839	0.605876
$100$	−18.9103	−1.89103
$101$	15.9886	1.59093	0.795464	−	0.606000i	$-0.207227\pi$
$101$	15.9886	1.59093	0.795464	+	0.606000i	$0.207227\pi$
$102$	12.2390	1.21184
$103$	0.571849	0.0563460	0.0281730	−	0.999603i	$-0.491031\pi$
$103$	0.571849	0.0563460	0.0281730	+	0.999603i	$0.491031\pi$
$104$	15.5981	1.52952
$105$	0.0864713	0.00843873
$106$	−23.6488	−2.29698
$107$	19.5118	1.88627	0.943137	−	0.332404i	$-0.107860\pi$
$107$	19.5118	1.88627	0.943137	+	0.332404i	$0.107860\pi$
$108$	−18.9822	−1.82656
$109$	10.8189	1.03626	0.518131	−	0.855301i	$-0.326628\pi$
$109$	10.8189	1.03626	0.518131	+	0.855301i	$0.326628\pi$
$110$	−3.09263	−0.294871
$111$	9.52335	0.903917
$112$	−0.748680	−0.0707436
$113$	−17.9614	−1.68966	−0.844832	−	0.535031i	$-0.820300\pi$
$113$	−17.9614	−1.68966	−0.844832	+	0.535031i	$0.820300\pi$
$114$	−10.3481	−0.969193
$115$	2.67627	0.249563
$116$	−24.5492	−2.27934
$117$	6.97116	0.644484
$118$	4.43178	0.407978
$119$	1.09847	0.100697
$120$	1.97850	0.180612
$121$	−2.83641	−0.257856
$122$	2.47169	0.223777
$123$	−4.73403	−0.426853
$124$	27.7581	2.49275
$125$	4.35445	0.389473
$126$	−1.06078	−0.0945015
$127$	5.50319	0.488329	0.244165	−	0.969734i	$-0.421486\pi$
$127$	5.50319	0.488329	0.244165	+	0.969734i	$0.421486\pi$
$128$	20.0466	1.77189
$129$	−7.70080	−0.678018
$130$	−3.57628	−0.313661
$131$	11.1233	0.971844	0.485922	−	0.874002i	$-0.338484\pi$
$131$	11.1233	0.971844	0.485922	+	0.874002i	$0.338484\pi$
$132$	−10.6139	−0.923821
$133$	−0.928765	−0.0805341
$134$	−18.3112	−1.58185
$135$	2.14151	0.184312
$136$	25.1336	2.15519
$137$	4.69862	0.401430	0.200715	−	0.979650i	$-0.435673\pi$
$137$	4.69862	0.401430	0.200715	+	0.979650i	$0.435673\pi$
$138$	13.8504	1.17902
$139$	16.1910	1.37330	0.686650	−	0.726988i	$-0.259080\pi$
$139$	16.1910	1.37330	0.686650	+	0.726988i	$0.259080\pi$
$140$	0.360882	0.0305001
$141$	−0.753177	−0.0634290
$142$	−16.6218	−1.39487
$143$	9.44028	0.789436
$144$	−7.65586	−0.637989
$145$	2.76956	0.230000
$146$	−36.5646	−3.02611
$147$	−6.56401	−0.541390
$148$	39.7451	3.26703
$149$	9.05194	0.741564	0.370782	−	0.928720i	$-0.379090\pi$
$149$	9.05194	0.741564	0.370782	+	0.928720i	$0.379090\pi$
$150$	11.0409	0.901484
$151$	−17.4551	−1.42047	−0.710237	−	0.703963i	$-0.751412\pi$
$151$	−17.4551	−1.42047	−0.710237	+	0.703963i	$0.751412\pi$
$152$	−21.2506	−1.72365
$153$	11.2328	0.908117
$154$	−1.43649	−0.115756
$155$	−3.13158	−0.251535
$156$	−12.2738	−0.982690
$157$	2.80097	0.223542	0.111771	−	0.993734i	$-0.464348\pi$
$157$	2.80097	0.223542	0.111771	+	0.993734i	$0.464348\pi$
$158$	16.8504	1.34055
$159$	9.15652	0.726159
$160$	−0.266626	−0.0210786
$161$	1.24310	0.0979697
$162$	−4.34058	−0.341028
$163$	−6.47262	−0.506975	−0.253487	−	0.967339i	$-0.581578\pi$
$163$	−6.47262	−0.506975	−0.253487	+	0.967339i	$0.581578\pi$
$164$	−19.7572	−1.54277
$165$	1.19743	0.0932196
$166$	−36.4253	−2.82715
$167$	16.8018	1.30016	0.650082	−	0.759864i	$-0.274735\pi$
$167$	16.8018	1.30016	0.650082	+	0.759864i	$0.274735\pi$
$168$	0.918991	0.0709017
$169$	−2.08337	−0.160259
$170$	−5.76254	−0.441967
$171$	−9.49737	−0.726282
$172$	−32.1388	−2.45056
$173$	−10.4916	−0.797665	−0.398832	−	0.917024i	$-0.630584\pi$
$173$	−10.4916	−0.797665	−0.398832	+	0.917024i	$0.630584\pi$
$174$	14.3332	1.08660
$175$	0.990938	0.0749079
$176$	−10.3675	−0.781479
$177$	−1.71593	−0.128977
$178$	38.9502	2.91944
$179$	−9.03145	−0.675042	−0.337521	−	0.941318i	$-0.609588\pi$
$179$	−9.03145	−0.675042	−0.337521	+	0.941318i	$0.609588\pi$
$180$	3.69031	0.275060
$181$	10.5606	0.784960	0.392480	−	0.919760i	$-0.371617\pi$
$181$	10.5606	0.784960	0.392480	+	0.919760i	$0.371617\pi$
$182$	−1.66114	−0.123132
$183$	−0.957007	−0.0707440
$184$	28.4426	2.09682
$185$	−4.48392	−0.329664
$186$	−16.2067	−1.18833
$187$	15.2113	1.11236
$188$	−3.14333	−0.229251
$189$	0.994708	0.0723544
$190$	4.87226	0.353471
$191$	−13.8642	−1.00318	−0.501588	−	0.865107i	$-0.667251\pi$
$191$	−13.8642	−1.00318	−0.501588	+	0.865107i	$0.667251\pi$
$192$	−8.22659	−0.593703
$193$	−13.9176	−1.00181	−0.500904	−	0.865503i	$-0.666999\pi$
$193$	−13.9176	−1.00181	−0.500904	+	0.865503i	$0.666999\pi$
$194$	0.722558	0.0518766
$195$	1.38469	0.0991598
$196$	−27.3945	−1.95675
$197$	−16.3415	−1.16428	−0.582142	−	0.813087i	$-0.697785\pi$
$197$	−16.3415	−1.16428	−0.582142	+	0.813087i	$0.697785\pi$
$198$	−14.6893	−1.04392
$199$	25.5369	1.81027	0.905133	−	0.425129i	$-0.139771\pi$
$199$	25.5369	1.81027	0.905133	+	0.425129i	$0.139771\pi$
$200$	22.6731	1.60323
$201$	7.08988	0.500081
$202$	−38.9593	−2.74117
$203$	1.28643	0.0902898
$204$	−19.7770	−1.38467
$205$	2.22894	0.155676
$206$	−1.39342	−0.0970840
$207$	12.7117	0.883522
$208$	−11.9888	−0.831277
$209$	−12.8612	−0.889631
$210$	−0.210703	−0.0145399
$211$	1.09358	0.0752852	0.0376426	−	0.999291i	$-0.488015\pi$
$211$	1.09358	0.0752852	0.0376426	+	0.999291i	$0.488015\pi$
$212$	38.2141	2.62456
$213$	6.43575	0.440971
$214$	−47.5441	−3.25004
$215$	3.62580	0.247277
$216$	22.7594	1.54858
$217$	−1.45458	−0.0987435
$218$	−26.3623	−1.78548
$219$	14.1573	0.956664
$220$	4.99738	0.336923
$221$	17.5902	1.18325
$222$	−23.2054	−1.55745
$223$	10.9182	0.731138	0.365569	−	0.930784i	$-0.380874\pi$
$223$	10.9182	0.731138	0.365569	+	0.930784i	$0.380874\pi$
$224$	−0.123845	−0.00827473
$225$	10.1331	0.675543
$226$	43.7662	2.91129
$227$	8.69007	0.576780	0.288390	−	0.957513i	$-0.406880\pi$
$227$	8.69007	0.576780	0.288390	+	0.957513i	$0.406880\pi$
$228$	16.7216	1.10741
$229$	−18.5801	−1.22781	−0.613903	−	0.789382i	$-0.710401\pi$
$229$	−18.5801	−1.22781	−0.613903	+	0.789382i	$0.710401\pi$
$230$	−6.52122	−0.429997
$231$	0.556191	0.0365947
$232$	29.4341	1.93244
$233$	−6.99115	−0.458005	−0.229003	−	0.973426i	$-0.573546\pi$
$233$	−6.99115	−0.458005	−0.229003	+	0.973426i	$0.573546\pi$
$234$	−16.9865	−1.11044
$235$	0.354621	0.0231329
$236$	−7.16130	−0.466161
$237$	−6.52427	−0.423797
$238$	−2.67664	−0.173501
$239$	−0.839791	−0.0543216	−0.0271608	−	0.999631i	$-0.508647\pi$
$239$	−0.839791	−0.0543216	−0.0271608	+	0.999631i	$0.508647\pi$
$240$	−1.52069	−0.0981603
$241$	−12.6686	−0.816057	−0.408028	−	0.912969i	$-0.633784\pi$
$241$	−12.6686	−0.816057	−0.408028	+	0.912969i	$0.633784\pi$
$242$	6.91145	0.444285
$243$	16.1435	1.03560
$244$	−3.99401	−0.255690
$245$	3.09056	0.197448
$246$	11.5353	0.735467
$247$	−14.8726	−0.946321
$248$	−33.2815	−2.11338
$249$	14.1034	0.893766
$250$	−10.6104	−0.671062
$251$	−15.1046	−0.953395	−0.476697	−	0.879068i	$-0.658166\pi$
$251$	−15.1046	−0.953395	−0.476697	+	0.879068i	$0.658166\pi$
$252$	1.71411	0.107979
$253$	17.2140	1.08224
$254$	−13.4096	−0.841390
$255$	2.23118	0.139722
$256$	−31.4080	−1.96300
$257$	−25.9772	−1.62041	−0.810206	−	0.586145i	$-0.800645\pi$
$257$	−25.9772	−1.62041	−0.810206	+	0.586145i	$0.800645\pi$
$258$	18.7644	1.16822
$259$	−2.08273	−0.129414
$260$	5.77892	0.358393
$261$	13.1548	0.814262
$262$	−27.1039	−1.67448
$263$	−9.89932	−0.610418	−0.305209	−	0.952285i	$-0.598726\pi$
$263$	−9.89932	−0.610418	−0.305209	+	0.952285i	$0.598726\pi$
$264$	12.7259	0.783225
$265$	−4.31120	−0.264835
$266$	2.26311	0.138760
$267$	−15.0810	−0.922944
$268$	29.5891	1.80744
$269$	5.23291	0.319056	0.159528	−	0.987193i	$-0.449003\pi$
$269$	5.23291	0.319056	0.159528	+	0.987193i	$0.449003\pi$
$270$	−5.21819	−0.317569
$271$	1.20373	0.0731214	0.0365607	−	0.999331i	$-0.488360\pi$
$271$	1.20373	0.0731214	0.0365607	+	0.999331i	$0.488360\pi$
$272$	−19.3179	−1.17132
$273$	0.643173	0.0389266
$274$	−11.4491	−0.691664
$275$	13.7222	0.827480
$276$	−22.3808	−1.34717
$277$	−6.02108	−0.361771	−0.180886	−	0.983504i	$-0.557896\pi$
$277$	−6.02108	−0.361771	−0.180886	+	0.983504i	$0.557896\pi$
$278$	−39.4523	−2.36619
$279$	−14.8743	−0.890501
$280$	−0.432692	−0.0258583
$281$	−25.6984	−1.53304	−0.766519	−	0.642221i	$-0.778013\pi$
$281$	−25.6984	−1.53304	−0.766519	+	0.642221i	$0.778013\pi$
$282$	1.83526	0.109288
$283$	5.92126	0.351982	0.175991	−	0.984392i	$-0.443687\pi$
$283$	5.92126	0.351982	0.175991	+	0.984392i	$0.443687\pi$
$284$	26.8592	1.59380
$285$	−1.88648	−0.111745
$286$	−23.0030	−1.36020
$287$	1.03532	0.0611129
$288$	−1.26641	−0.0746241
$289$	11.3435	0.667263
$290$	−6.74856	−0.396289
$291$	−0.279765	−0.0164001
$292$	59.0847	3.45767
$293$	−28.1254	−1.64310	−0.821552	−	0.570133i	$-0.806891\pi$
$293$	−28.1254	−1.64310	−0.821552	+	0.570133i	$0.806891\pi$
$294$	15.9944	0.932814
$295$	0.807916	0.0470387
$296$	−47.6538	−2.76982
$297$	13.7744	0.799272
$298$	−22.0567	−1.27771
$299$	19.9061	1.15120
$300$	−17.8409	−1.03005
$301$	1.68414	0.0970723
$302$	42.5325	2.44747
$303$	15.0845	0.866584
$304$	16.3334	0.936783
$305$	0.450592	0.0258008
$306$	−27.3708	−1.56468
$307$	13.3635	0.762693	0.381346	−	0.924432i	$-0.375461\pi$
$307$	13.3635	0.762693	0.381346	+	0.924432i	$0.375461\pi$
$308$	2.32123	0.132264
$309$	0.539513	0.0306918
$310$	7.63068	0.433393
$311$	−28.5445	−1.61861	−0.809305	−	0.587388i	$-0.800156\pi$
$311$	−28.5445	−1.61861	−0.809305	+	0.587388i	$0.800156\pi$
$312$	14.7161	0.833135
$313$	−3.26045	−0.184291	−0.0921457	−	0.995746i	$-0.529373\pi$
$313$	−3.26045	−0.184291	−0.0921457	+	0.995746i	$0.529373\pi$
$314$	−6.82510	−0.385162
$315$	−0.193380	−0.0108957
$316$	−27.2286	−1.53173
$317$	18.8697	1.05983	0.529914	−	0.848051i	$-0.322224\pi$
$317$	18.8697	1.05983	0.529914	+	0.848051i	$0.322224\pi$
$318$	−22.3116	−1.25117
$319$	17.8141	0.997398
$320$	3.87336	0.216527
$321$	18.4084	1.02746
$322$	−3.02903	−0.168801
$323$	−23.9645	−1.33342
$324$	7.01395	0.389664
$325$	15.8682	0.880210
$326$	15.7717	0.873516
$327$	10.2071	0.564455
$328$	23.6885	1.30798
$329$	0.164718	0.00908117
$330$	−2.91775	−0.160617
$331$	9.73348	0.535001	0.267500	−	0.963558i	$-0.413802\pi$
$331$	9.73348	0.535001	0.267500	+	0.963558i	$0.413802\pi$
$332$	58.8595	3.23034
$333$	−21.2976	−1.16710
$334$	−40.9408	−2.24018
$335$	−3.33815	−0.182383
$336$	−0.706345	−0.0385343
$337$	10.1134	0.550913	0.275457	−	0.961314i	$-0.411171\pi$
$337$	10.1134	0.550913	0.275457	+	0.961314i	$0.411171\pi$
$338$	5.07652	0.276126
$339$	−16.9457	−0.920365
$340$	9.31169	0.504997
$341$	−20.1426	−1.09078
$342$	23.1421	1.25138
$343$	2.87984	0.155497
$344$	38.5339	2.07761
$345$	2.52493	0.135938
$346$	25.5648	1.37437
$347$	10.4124	0.558969	0.279484	−	0.960150i	$-0.409837\pi$
$347$	10.4124	0.558969	0.279484	+	0.960150i	$0.409837\pi$
$348$	−23.1610	−1.24156
$349$	−0.267493	−0.0143185	−0.00715927	−	0.999974i	$-0.502279\pi$
$349$	−0.267493	−0.0143185	−0.00715927	+	0.999974i	$0.502279\pi$
$350$	−2.41461	−0.129066
$351$	15.9286	0.850204
$352$	−1.71496	−0.0914079
$353$	4.97166	0.264615	0.132307	−	0.991209i	$-0.457761\pi$
$353$	4.97166	0.264615	0.132307	+	0.991209i	$0.457761\pi$
$354$	4.18117	0.222227
$355$	−3.03017	−0.160825
$356$	−62.9397	−3.33580
$357$	1.03636	0.0548499
$358$	22.0068	1.16310
$359$	33.0745	1.74561	0.872803	−	0.488072i	$-0.162300\pi$
$359$	33.0745	1.74561	0.872803	+	0.488072i	$0.162300\pi$
$360$	−4.42463	−0.233198
$361$	1.26213	0.0664280
$362$	−25.7328	−1.35248
$363$	−2.67602	−0.140455
$364$	2.68424	0.140692
$365$	−6.66575	−0.348901
$366$	2.33193	0.121892
$367$	23.0467	1.20303	0.601513	−	0.798863i	$-0.294565\pi$
$367$	23.0467	1.20303	0.601513	+	0.798863i	$0.294565\pi$
$368$	−21.8612	−1.13960
$369$	10.5870	0.551135
$370$	10.9259	0.568011
$371$	−2.00250	−0.103965
$372$	26.1884	1.35781
$373$	32.7754	1.69705	0.848524	−	0.529157i	$-0.177492\pi$
$373$	32.7754	1.69705	0.848524	+	0.529157i	$0.177492\pi$
$374$	−37.0652	−1.91660
$375$	4.10822	0.212147
$376$	3.76881	0.194362
$377$	20.6000	1.06096
$378$	−2.42379	−0.124666
$379$	15.5186	0.797136	0.398568	−	0.917139i	$-0.369507\pi$
$379$	15.5186	0.797136	0.398568	+	0.917139i	$0.369507\pi$
$380$	−7.87308	−0.403880
$381$	5.19200	0.265994
$382$	33.7826	1.72847
$383$	12.1108	0.618834	0.309417	−	0.950926i	$-0.399866\pi$
$383$	12.1108	0.618834	0.309417	+	0.950926i	$0.399866\pi$
$384$	18.9131	0.965153
$385$	−0.261874	−0.0133463
$386$	33.9127	1.72611
$387$	17.2217	0.875429
$388$	−1.16758	−0.0592749
$389$	7.16013	0.363033	0.181517	−	0.983388i	$-0.441899\pi$
$389$	7.16013	0.363033	0.181517	+	0.983388i	$0.441899\pi$
$390$	−3.37406	−0.170852
$391$	32.0751	1.62211
$392$	32.8455	1.65895
$393$	10.4943	0.529366
$394$	39.8191	2.00606
$395$	3.07185	0.154562
$396$	23.7364	1.19280
$397$	−21.0615	−1.05705	−0.528524	−	0.848918i	$-0.677254\pi$
$397$	−21.0615	−1.05705	−0.528524	+	0.848918i	$0.677254\pi$
$398$	−62.2255	−3.11908
$399$	−0.876246	−0.0438672
$400$	−17.4268	−0.871338
$401$	12.4048	0.619467	0.309733	−	0.950823i	$-0.399760\pi$
$401$	12.4048	0.619467	0.309733	+	0.950823i	$0.399760\pi$
$402$	−17.2758	−0.861639
$403$	−23.2927	−1.16029
$404$	62.9543	3.13209
$405$	−0.791292	−0.0393196
$406$	−3.13463	−0.155569
$407$	−28.8410	−1.42959
$408$	23.7124	1.17394
$409$	12.1275	0.599664	0.299832	−	0.953992i	$-0.403069\pi$
$409$	12.1275	0.599664	0.299832	+	0.953992i	$0.403069\pi$
$410$	−5.43123	−0.268229
$411$	4.43293	0.218660
$412$	2.25162	0.110929
$413$	0.375268	0.0184657
$414$	−30.9743	−1.52231
$415$	−6.64035	−0.325962
$416$	−1.98316	−0.0972326
$417$	15.2754	0.748041
$418$	31.3388	1.53283
$419$	1.16401	0.0568655	0.0284327	−	0.999596i	$-0.490948\pi$
$419$	1.16401	0.0568655	0.0284327	+	0.999596i	$0.490948\pi$
$420$	0.340475	0.0166135
$421$	7.87057	0.383588	0.191794	−	0.981435i	$-0.438569\pi$
$421$	7.87057	0.383588	0.191794	+	0.981435i	$0.438569\pi$
$422$	−2.66471	−0.129716
$423$	1.68437	0.0818969
$424$	−45.8181	−2.22513
$425$	25.5688	1.24027
$426$	−15.6819	−0.759791
$427$	0.209295	0.0101285
$428$	76.8264	3.71354
$429$	8.90646	0.430008
$430$	−8.83493	−0.426058
$431$	−32.0793	−1.54521	−0.772603	−	0.634889i	$-0.781046\pi$
$431$	−32.0793	−1.54521	−0.772603	+	0.634889i	$0.781046\pi$
$432$	−17.4931	−0.841635
$433$	−12.8974	−0.619809	−0.309904	−	0.950768i	$-0.600297\pi$
$433$	−12.8974	−0.619809	−0.309904	+	0.950768i	$0.600297\pi$
$434$	3.54436	0.170135
$435$	2.61296	0.125282
$436$	42.5988	2.04011
$437$	−27.1196	−1.29731
$438$	−34.4970	−1.64833
$439$	−12.4910	−0.596161	−0.298081	−	0.954541i	$-0.596346\pi$
$439$	−12.4910	−0.596161	−0.298081	+	0.954541i	$0.596346\pi$
$440$	−5.99179	−0.285647
$441$	14.6794	0.699021
$442$	−42.8618	−2.03873
$443$	−8.46734	−0.402295	−0.201148	−	0.979561i	$-0.564467\pi$
$443$	−8.46734	−0.402295	−0.201148	+	0.979561i	$0.564467\pi$
$444$	37.4976	1.77956
$445$	7.10066	0.336604
$446$	−26.6043	−1.25975
$447$	8.54009	0.403932
$448$	1.79913	0.0850010
$449$	−18.8409	−0.889157	−0.444579	−	0.895740i	$-0.646647\pi$
$449$	−18.8409	−0.889157	−0.444579	+	0.895740i	$0.646647\pi$
$450$	−24.6913	−1.16396
$451$	14.3368	0.675092
$452$	−70.7218	−3.32648
$453$	−16.4680	−0.773736
$454$	−21.1750	−0.993791
$455$	−0.302828	−0.0141968
$456$	−20.0489	−0.938876
$457$	−3.42887	−0.160396	−0.0801979	−	0.996779i	$-0.525555\pi$
$457$	−3.42887	−0.160396	−0.0801979	+	0.996779i	$0.525555\pi$
$458$	45.2738	2.11550
$459$	25.6661	1.19799
$460$	10.5376	0.491320
$461$	−29.2414	−1.36191	−0.680954	−	0.732326i	$-0.738435\pi$
$461$	−29.2414	−1.36191	−0.680954	+	0.732326i	$0.738435\pi$
$462$	−1.35526	−0.0630526
$463$	29.4819	1.37014	0.685071	−	0.728477i	$-0.259771\pi$
$463$	29.4819	1.37014	0.685071	+	0.728477i	$0.259771\pi$
$464$	−22.6233	−1.05026
$465$	−2.95450	−0.137012
$466$	17.0352	0.789142
$467$	1.89137	0.0875222	0.0437611	−	0.999042i	$-0.486066\pi$
$467$	1.89137	0.0875222	0.0437611	+	0.999042i	$0.486066\pi$
$468$	27.4485	1.26881
$469$	−1.55053	−0.0715970
$470$	−0.864101	−0.0398580
$471$	2.64259	0.121764
$472$	8.58630	0.395216
$473$	23.3215	1.07232
$474$	15.8976	0.730201
$475$	−21.6185	−0.991926
$476$	4.32517	0.198244
$477$	−20.4772	−0.937587
$478$	2.04631	0.0935960
$479$	39.8861	1.82244	0.911222	−	0.411916i	$-0.135140\pi$
$479$	39.8861	1.82244	0.911222	+	0.411916i	$0.135140\pi$
$480$	−0.251549	−0.0114816
$481$	−33.3514	−1.52069
$482$	30.8694	1.40606
$483$	1.17280	0.0533644
$484$	−11.1682	−0.507646
$485$	0.131723	0.00598123
$486$	−39.3366	−1.78434
$487$	−10.0975	−0.457561	−0.228781	−	0.973478i	$-0.573474\pi$
$487$	−10.0975	−0.457561	−0.228781	+	0.973478i	$0.573474\pi$
$488$	4.78875	0.216777
$489$	−6.10661	−0.276151
$490$	−7.53072	−0.340203
$491$	−11.6956	−0.527815	−0.263907	−	0.964548i	$-0.585011\pi$
$491$	−11.6956	−0.527815	−0.263907	+	0.964548i	$0.585011\pi$
$492$	−18.6400	−0.840354
$493$	33.1933	1.49495
$494$	36.2399	1.63051
$495$	−2.67787	−0.120361
$496$	25.5805	1.14860
$497$	−1.40748	−0.0631341
$498$	−34.3655	−1.53996
$499$	−23.4823	−1.05121	−0.525605	−	0.850729i	$-0.676161\pi$
$499$	−23.4823	−1.05121	−0.525605	+	0.850729i	$0.676161\pi$
$500$	17.1454	0.766764
$501$	15.8517	0.708203
$502$	36.8052	1.64270
$503$	26.0473	1.16139	0.580695	−	0.814121i	$-0.302781\pi$
$503$	26.0473	1.16139	0.580695	+	0.814121i	$0.302781\pi$
$504$	−2.05519	−0.0915454
$505$	−7.10231	−0.316049
$506$	−41.9451	−1.86469
$507$	−1.96556	−0.0872937
$508$	21.6685	0.961384
$509$	24.8477	1.10135	0.550677	−	0.834718i	$-0.314369\pi$
$509$	24.8477	1.10135	0.550677	+	0.834718i	$0.314369\pi$
$510$	−5.43669	−0.240741
$511$	−3.09617	−0.136966
$512$	36.4382	1.61036
$513$	−21.7008	−0.958112
$514$	63.2982	2.79197
$515$	−0.254021	−0.0111935
$516$	−30.3214	−1.33483
$517$	2.28096	0.100316
$518$	5.07496	0.222981
$519$	−9.89837	−0.434490
$520$	−6.92883	−0.303849
$521$	20.4338	0.895221	0.447610	−	0.894229i	$-0.352275\pi$
$521$	20.4338	0.895221	0.447610	+	0.894229i	$0.352275\pi$
$522$	−32.0541	−1.40297
$523$	15.4833	0.677036	0.338518	−	0.940960i	$-0.390074\pi$
$523$	15.4833	0.677036	0.338518	+	0.940960i	$0.390074\pi$
$524$	43.7972	1.91329
$525$	0.934904	0.0408026
$526$	24.1215	1.05175
$527$	−37.5320	−1.63492
$528$	−9.78124	−0.425674
$529$	13.2980	0.578174
$530$	10.5050	0.456310
$531$	3.83742	0.166530
$532$	−3.65696	−0.158549
$533$	16.5789	0.718110
$534$	36.7477	1.59023
$535$	−8.66732	−0.374721
$536$	−35.4769	−1.53237
$537$	−8.52075	−0.367698
$538$	−12.7510	−0.549733
$539$	19.8788	0.856239
$540$	8.43208	0.362859
$541$	44.6969	1.92167	0.960834	−	0.277125i	$-0.0893815\pi$
$541$	44.6969	1.92167	0.960834	+	0.277125i	$0.0893815\pi$
$542$	−2.93311	−0.125988
$543$	9.96340	0.427570
$544$	−3.19552	−0.137007
$545$	−4.80586	−0.205860
$546$	−1.56721	−0.0670705
$547$	−17.6931	−0.756504	−0.378252	−	0.925703i	$-0.623475\pi$
$547$	−17.6931	−0.756504	−0.378252	+	0.925703i	$0.623475\pi$
$548$	18.5005	0.790304
$549$	2.14021	0.0913418
$550$	−33.4367	−1.42575
$551$	−28.0651	−1.19561
$552$	26.8343	1.14214
$553$	1.42684	0.0606754
$554$	14.6715	0.623331
$555$	−4.23037	−0.179569
$556$	63.7510	2.70364
$557$	5.29535	0.224371	0.112186	−	0.993687i	$-0.464215\pi$
$557$	5.29535	0.224371	0.112186	+	0.993687i	$0.464215\pi$
$558$	36.2440	1.53433
$559$	26.9687	1.14065
$560$	0.332571	0.0140537
$561$	14.3512	0.605907
$562$	62.6190	2.64142
$563$	−1.93502	−0.0815513	−0.0407757	−	0.999168i	$-0.512983\pi$
$563$	−1.93502	−0.0815513	−0.0407757	+	0.999168i	$0.512983\pi$
$564$	−2.96559	−0.124874
$565$	7.97862	0.335663
$566$	−14.4282	−0.606464
$567$	−0.367546	−0.0154355
$568$	−32.2038	−1.35124
$569$	29.4464	1.23446	0.617229	−	0.786783i	$-0.288255\pi$
$569$	29.4464	1.23446	0.617229	+	0.786783i	$0.288255\pi$
$570$	4.59675	0.192537
$571$	−46.4791	−1.94509	−0.972546	−	0.232712i	$-0.925240\pi$
$571$	−46.4791	−1.94509	−0.972546	+	0.232712i	$0.925240\pi$
$572$	37.1705	1.55418
$573$	−13.0802	−0.546433
$574$	−2.52274	−0.105297
$575$	28.9351	1.20668
$576$	18.3976	0.766566
$577$	29.2599	1.21811	0.609053	−	0.793129i	$-0.291550\pi$
$577$	29.2599	1.21811	0.609053	+	0.793129i	$0.291550\pi$
$578$	−27.6405	−1.14969
$579$	−13.1306	−0.545688
$580$	10.9050	0.452805
$581$	−3.08437	−0.127961
$582$	0.681700	0.0282574
$583$	−27.7300	−1.14846
$584$	−70.8417	−2.93145
$585$	−3.09666	−0.128031
$586$	68.5328	2.83106
$587$	46.0135	1.89918	0.949589	−	0.313497i	$-0.101500\pi$
$587$	46.0135	1.89918	0.949589	+	0.313497i	$0.101500\pi$
$588$	−25.8454	−1.06585
$589$	31.7335	1.30756
$590$	−1.96864	−0.0810476
$591$	−15.4174	−0.634189
$592$	36.6271	1.50536
$593$	12.4547	0.511453	0.255727	−	0.966749i	$-0.417685\pi$
$593$	12.4547	0.511453	0.255727	+	0.966749i	$0.417685\pi$
$594$	−33.5639	−1.37714
$595$	−0.487953	−0.0200041
$596$	35.6415	1.45993
$597$	24.0929	0.986057
$598$	−48.5049	−1.98351
$599$	38.6410	1.57883	0.789415	−	0.613860i	$-0.210384\pi$
$599$	38.6410	1.57883	0.789415	+	0.613860i	$0.210384\pi$
$600$	21.3910	0.873285
$601$	14.9942	0.611627	0.305813	−	0.952091i	$-0.401072\pi$
$601$	14.9942	0.611627	0.305813	+	0.952091i	$0.401072\pi$
$602$	−4.10373	−0.167255
$603$	−15.8555	−0.645685
$604$	−68.7283	−2.79651
$605$	1.25996	0.0512248
$606$	−36.7563	−1.49312
$607$	−15.5033	−0.629260	−0.314630	−	0.949214i	$-0.601881\pi$
$607$	−15.5033	−0.629260	−0.314630	+	0.949214i	$0.601881\pi$
$608$	2.70182	0.109573
$609$	1.21369	0.0491811
$610$	−1.09795	−0.0444547
$611$	2.63767	0.106709
$612$	44.2284	1.78783
$613$	36.5479	1.47616	0.738079	−	0.674715i	$-0.235733\pi$
$613$	36.5479	1.47616	0.738079	+	0.674715i	$0.235733\pi$
$614$	−32.5625	−1.31412
$615$	2.10290	0.0847972
$616$	−2.78312	−0.112135
$617$	2.01752	0.0812222	0.0406111	−	0.999175i	$-0.487070\pi$
$617$	2.01752	0.0812222	0.0406111	+	0.999175i	$0.487070\pi$
$618$	−1.31462	−0.0528819
$619$	−7.93885	−0.319089	−0.159545	−	0.987191i	$-0.551003\pi$
$619$	−7.93885	−0.319089	−0.159545	+	0.987191i	$0.551003\pi$
$620$	−12.3304	−0.495201
$621$	29.0452	1.16554
$622$	69.5540	2.78886
$623$	3.29818	0.132139
$624$	−11.3109	−0.452799
$625$	22.0791	0.883164
$626$	7.94469	0.317534
$627$	−12.1340	−0.484585
$628$	11.0287	0.440092
$629$	−53.7398	−2.14275
$630$	0.471207	0.0187733
$631$	6.05721	0.241134	0.120567	−	0.992705i	$-0.461529\pi$
$631$	6.05721	0.241134	0.120567	+	0.992705i	$0.461529\pi$
$632$	32.6467	1.29862
$633$	1.03174	0.0410081
$634$	−45.9796	−1.82608
$635$	−2.44457	−0.0970099
$636$	36.0532	1.42960
$637$	22.9876	0.910801
$638$	−43.4074	−1.71851
$639$	−14.3926	−0.569363
$640$	−8.90491	−0.351997
$641$	−46.6817	−1.84382	−0.921908	−	0.387408i	$-0.873370\pi$
$641$	−46.6817	−1.84382	−0.921908	+	0.387408i	$0.873370\pi$
$642$	−44.8556	−1.77031
$643$	5.10969	0.201507	0.100753	−	0.994911i	$-0.467875\pi$
$643$	5.10969	0.201507	0.100753	+	0.994911i	$0.467875\pi$
$644$	4.89461	0.192875
$645$	3.42077	0.134693
$646$	58.3941	2.29748
$647$	−48.1652	−1.89357	−0.946786	−	0.321865i	$-0.895690\pi$
$647$	−48.1652	−1.89357	−0.946786	+	0.321865i	$0.895690\pi$
$648$	−8.40962	−0.330361
$649$	5.19659	0.203984
$650$	−38.6658	−1.51660
$651$	−1.37233	−0.0537859
$652$	−25.4855	−0.998091
$653$	−22.4910	−0.880142	−0.440071	−	0.897963i	$-0.645047\pi$
$653$	−22.4910	−0.880142	−0.440071	+	0.897963i	$0.645047\pi$
$654$	−24.8716	−0.972555
$655$	−4.94106	−0.193063
$656$	−18.2072	−0.710873
$657$	−31.6608	−1.23521
$658$	−0.401365	−0.0156468
$659$	−27.5411	−1.07285	−0.536425	−	0.843948i	$-0.680225\pi$
$659$	−27.5411	−1.07285	−0.536425	+	0.843948i	$0.680225\pi$
$660$	4.71480	0.183523
$661$	−47.6588	−1.85371	−0.926856	−	0.375416i	$-0.877500\pi$
$661$	−47.6588	−1.85371	−0.926856	+	0.375416i	$0.877500\pi$
$662$	−23.7174	−0.921804
$663$	16.5955	0.644517
$664$	−70.5717	−2.73871
$665$	0.412566	0.0159986
$666$	51.8955	2.01091
$667$	37.5634	1.45446
$668$	66.1561	2.55966
$669$	10.3008	0.398253
$670$	8.13403	0.314245
$671$	2.89825	0.111886
$672$	−0.116842	−0.00450727
$673$	37.0130	1.42675	0.713373	−	0.700785i	$-0.247167\pi$
$673$	37.0130	1.42675	0.713373	+	0.700785i	$0.247167\pi$
$674$	−24.6432	−0.949222
$675$	23.1535	0.891177
$676$	−8.20314	−0.315505
$677$	39.7422	1.52741	0.763707	−	0.645562i	$-0.223377\pi$
$677$	39.7422	1.52741	0.763707	+	0.645562i	$0.223377\pi$
$678$	41.2914	1.58579
$679$	0.0611838	0.00234802
$680$	−11.1646	−0.428142
$681$	8.19867	0.314174
$682$	49.0812	1.87942
$683$	8.42119	0.322228	0.161114	−	0.986936i	$-0.448491\pi$
$683$	8.42119	0.322228	0.161114	+	0.986936i	$0.448491\pi$
$684$	−37.3953	−1.42985
$685$	−2.08717	−0.0797468
$686$	−7.01727	−0.267921
$687$	−17.5294	−0.668789
$688$	−29.6175	−1.12916
$689$	−32.0667	−1.22164
$690$	−6.15247	−0.234221
$691$	43.6599	1.66090	0.830451	−	0.557092i	$-0.188083\pi$
$691$	43.6599	1.66090	0.830451	+	0.557092i	$0.188083\pi$
$692$	−41.3102	−1.57038
$693$	−1.24384	−0.0472496
$694$	−25.3718	−0.963101
$695$	−7.19219	−0.272815
$696$	27.7697	1.05261
$697$	26.7139	1.01186
$698$	0.651795	0.0246708
$699$	−6.59582	−0.249477
$700$	3.90176	0.147473
$701$	41.3009	1.55991	0.779956	−	0.625834i	$-0.215241\pi$
$701$	41.3009	1.55991	0.779956	+	0.625834i	$0.215241\pi$
$702$	−38.8129	−1.46490
$703$	45.4373	1.71370
$704$	24.9138	0.938974
$705$	0.334569	0.0126006
$706$	−12.1144	−0.455931
$707$	−3.29894	−0.124069
$708$	−6.75636	−0.253919
$709$	2.36426	0.0887915	0.0443957	−	0.999014i	$-0.485864\pi$
$709$	2.36426	0.0887915	0.0443957	+	0.999014i	$0.485864\pi$
$710$	7.38358	0.277101
$711$	14.5906	0.547190
$712$	75.4637	2.82812
$713$	−42.4734	−1.59064
$714$	−2.52528	−0.0945063
$715$	−4.19346	−0.156827
$716$	−35.5608	−1.32897
$717$	−0.792304	−0.0295891
$718$	−80.5922	−3.00768
$719$	−36.1757	−1.34913	−0.674563	−	0.738217i	$-0.735668\pi$
$719$	−36.1757	−1.34913	−0.674563	+	0.738217i	$0.735668\pi$
$720$	3.40081	0.126741
$721$	−0.117990	−0.00439417
$722$	−3.07542	−0.114455
$723$	−11.9522	−0.444509
$724$	41.5816	1.54537
$725$	29.9438	1.11208
$726$	6.52063	0.242003
$727$	32.6402	1.21056	0.605279	−	0.796013i	$-0.293062\pi$
$727$	32.6402	1.21056	0.605279	+	0.796013i	$0.293062\pi$
$728$	−3.21836	−0.119281
$729$	9.88656	0.366169
$730$	16.2423	0.601156
$731$	43.4552	1.60725
$732$	−3.76816	−0.139275
$733$	43.3307	1.60045	0.800227	−	0.599697i	$-0.204712\pi$
$733$	43.3307	1.60045	0.800227	+	0.599697i	$0.204712\pi$
$734$	−56.1575	−2.07281
$735$	2.91580	0.107551
$736$	−3.61623	−0.133296
$737$	−21.4713	−0.790906
$738$	−25.7971	−0.949605
$739$	41.6176	1.53093	0.765464	−	0.643478i	$-0.222509\pi$
$739$	41.6176	1.53093	0.765464	+	0.643478i	$0.222509\pi$
$740$	−17.6552	−0.649016
$741$	−14.0316	−0.515464
$742$	4.87947	0.179131
$743$	−51.3754	−1.88478	−0.942391	−	0.334513i	$-0.891428\pi$
$743$	−51.3754	−1.88478	−0.942391	+	0.334513i	$0.891428\pi$
$744$	−31.3996	−1.15116
$745$	−4.02096	−0.147317
$746$	−79.8635	−2.92401
$747$	−31.5402	−1.15399
$748$	59.8937	2.18993
$749$	−4.02587	−0.147102
$750$	−10.0104	−0.365529
$751$	−17.4109	−0.635333	−0.317667	−	0.948202i	$-0.602899\pi$
$751$	−17.4109	−0.635333	−0.317667	+	0.948202i	$0.602899\pi$
$752$	−2.89674	−0.105633
$753$	−14.2505	−0.519317
$754$	−50.1958	−1.82802
$755$	7.75371	0.282186
$756$	3.91660	0.142445
$757$	−28.6587	−1.04162	−0.520809	−	0.853673i	$-0.674369\pi$
$757$	−28.6587	−1.04162	−0.520809	+	0.853673i	$0.674369\pi$
$758$	−37.8139	−1.37346
$759$	16.2406	0.589497
$760$	9.43970	0.342414
$761$	41.7633	1.51392	0.756958	−	0.653463i	$-0.226685\pi$
$761$	41.7633	1.51392	0.756958	+	0.653463i	$0.226685\pi$
$762$	−12.6513	−0.458308
$763$	−2.23227	−0.0808135
$764$	−54.5893	−1.97497
$765$	−4.98971	−0.180404
$766$	−29.5103	−1.06625
$767$	6.00928	0.216983
$768$	−29.6320	−1.06925
$769$	−12.1426	−0.437872	−0.218936	−	0.975739i	$-0.570259\pi$
$769$	−12.1426	−0.437872	−0.218936	+	0.975739i	$0.570259\pi$
$770$	0.638104	0.0229957
$771$	−24.5083	−0.882643
$772$	−54.7996	−1.97228
$773$	27.5737	0.991757	0.495879	−	0.868392i	$-0.334846\pi$
$773$	27.5737	0.991757	0.495879	+	0.868392i	$0.334846\pi$
$774$	−41.9639	−1.50836
$775$	−33.8578	−1.21621
$776$	1.39991	0.0502539
$777$	−1.96496	−0.0704925
$778$	−17.4470	−0.625505
$779$	−22.5867	−0.809253
$780$	5.45214	0.195218
$781$	−19.4903	−0.697419
$782$	−78.1569	−2.79489
$783$	30.0577	1.07417
$784$	−25.2454	−0.901621
$785$	−1.24422	−0.0444081
$786$	−25.5713	−0.912097
$787$	−20.8428	−0.742965	−0.371482	−	0.928440i	$-0.621150\pi$
$787$	−20.8428	−0.742965	−0.371482	+	0.928440i	$0.621150\pi$
$788$	−64.3436	−2.29215
$789$	−9.33954	−0.332497
$790$	−7.48513	−0.266309
$791$	3.70598	0.131769
$792$	−28.4596	−1.01127
$793$	3.35150	0.119015
$794$	51.3203	1.82129
$795$	−4.06741	−0.144256
$796$	100.550	3.56391
$797$	54.8495	1.94287	0.971435	−	0.237308i	$-0.0762649\pi$
$797$	54.8495	1.94287	0.971435	+	0.237308i	$0.0762649\pi$
$798$	2.13514	0.0755830
$799$	4.25014	0.150359
$800$	−2.88269	−0.101918
$801$	33.7265	1.19167
$802$	−30.2266	−1.06734
$803$	−42.8747	−1.51302
$804$	27.9160	0.984520
$805$	−0.552195	−0.0194623
$806$	56.7570	1.99918
$807$	4.93701	0.173791
$808$	−75.4813	−2.65542
$809$	12.0379	0.423229	0.211615	−	0.977353i	$-0.432128\pi$
$809$	12.0379	0.423229	0.211615	+	0.977353i	$0.432128\pi$
$810$	1.92813	0.0677476
$811$	3.88870	0.136551	0.0682754	−	0.997667i	$-0.478250\pi$
$811$	3.88870	0.136551	0.0682754	+	0.997667i	$0.478250\pi$
$812$	5.06525	0.177755
$813$	1.13566	0.0398295
$814$	70.2764	2.46319
$815$	2.87520	0.100714
$816$	−18.2255	−0.638021
$817$	−36.7416	−1.28543
$818$	−29.5508	−1.03322
$819$	−1.43836	−0.0502605
$820$	8.77632	0.306482
$821$	−35.0722	−1.22403	−0.612014	−	0.790847i	$-0.709640\pi$
$821$	−35.0722	−1.22403	−0.612014	+	0.790847i	$0.709640\pi$
$822$	−10.8017	−0.376751
$823$	−20.9837	−0.731446	−0.365723	−	0.930724i	$-0.619178\pi$
$823$	−20.9837	−0.731446	−0.365723	+	0.930724i	$0.619178\pi$
$824$	−2.69966	−0.0940472
$825$	12.9463	0.450731
$826$	−0.914410	−0.0318164
$827$	−18.4445	−0.641378	−0.320689	−	0.947185i	$-0.603914\pi$
$827$	−18.4445	−0.641378	−0.320689	+	0.947185i	$0.603914\pi$
$828$	50.0514	1.73941
$829$	−28.2735	−0.981981	−0.490990	−	0.871165i	$-0.663365\pi$
$829$	−28.2735	−0.981981	−0.490990	+	0.871165i	$0.663365\pi$
$830$	16.1805	0.561632
$831$	−5.68061	−0.197058
$832$	28.8100	0.998809
$833$	37.0404	1.28337
$834$	−37.2214	−1.28887
$835$	−7.46353	−0.258286
$836$	−50.6404	−1.75143
$837$	−33.9866	−1.17475
$838$	−2.83632	−0.0979790
$839$	18.1669	0.627189	0.313595	−	0.949557i	$-0.398467\pi$
$839$	18.1669	0.627189	0.313595	+	0.949557i	$0.398467\pi$
$840$	−0.408225	−0.0140851
$841$	9.87288	0.340444
$842$	−19.1781	−0.660921
$843$	−24.2453	−0.835051
$844$	4.30591	0.148216
$845$	0.925453	0.0318365
$846$	−4.10428	−0.141108
$847$	0.585238	0.0201090
$848$	35.2162	1.20933
$849$	5.58643	0.191726
$850$	−62.3031	−2.13698
$851$	−60.8150	−2.08471
$852$	25.3404	0.868148
$853$	−26.8865	−0.920576	−0.460288	−	0.887770i	$-0.652254\pi$
$853$	−26.8865	−0.920576	−0.460288	+	0.887770i	$0.652254\pi$
$854$	−0.509985	−0.0174513
$855$	4.21883	0.144281
$856$	−92.1137	−3.14838
$857$	3.90201	0.133290	0.0666451	−	0.997777i	$-0.478770\pi$
$857$	3.90201	0.133290	0.0666451	+	0.997777i	$0.478770\pi$
$858$	−21.7023	−0.740903
$859$	−30.1762	−1.02960	−0.514800	−	0.857310i	$-0.672134\pi$
$859$	−30.1762	−1.02960	−0.514800	+	0.857310i	$0.672134\pi$
$860$	14.2764	0.486820
$861$	0.976774	0.0332884
$862$	78.1672	2.66239
$863$	23.5041	0.800090	0.400045	−	0.916496i	$-0.368995\pi$
$863$	23.5041	0.800090	0.400045	+	0.916496i	$0.368995\pi$
$864$	−2.89366	−0.0984442
$865$	4.66049	0.158461
$866$	31.4269	1.06793
$867$	10.7020	0.363460
$868$	−5.72733	−0.194398
$869$	19.7584	0.670259
$870$	−6.36695	−0.215860
$871$	−24.8292	−0.841305
$872$	−51.0753	−1.72963
$873$	0.625654	0.0211752
$874$	66.0821	2.23526
$875$	−0.898454	−0.0303733
$876$	55.7436	1.88340
$877$	−26.3045	−0.888239	−0.444120	−	0.895967i	$-0.646484\pi$
$877$	−26.3045	−0.888239	−0.444120	+	0.895967i	$0.646484\pi$
$878$	30.4366	1.02718
$879$	−26.5350	−0.895004
$880$	4.60534	0.155246
$881$	6.46060	0.217663	0.108832	−	0.994060i	$-0.465289\pi$
$881$	6.46060	0.217663	0.108832	+	0.994060i	$0.465289\pi$
$882$	−35.7692	−1.20441
$883$	9.83010	0.330809	0.165405	−	0.986226i	$-0.447107\pi$
$883$	9.83010	0.330809	0.165405	+	0.986226i	$0.447107\pi$
$884$	69.2604	2.32948
$885$	0.762231	0.0256221
$886$	20.6322	0.693154
$887$	−31.3299	−1.05196	−0.525978	−	0.850498i	$-0.676300\pi$
$887$	−31.3299	−1.05196	−0.525978	+	0.850498i	$0.676300\pi$
$888$	−44.9591	−1.50873
$889$	−1.13548	−0.0380826
$890$	−17.3021	−0.579967
$891$	−5.08966	−0.170510
$892$	42.9898	1.43941
$893$	−3.59351	−0.120252
$894$	−20.8095	−0.695974
$895$	4.01186	0.134102
$896$	−4.13623	−0.138182
$897$	18.7805	0.627061
$898$	45.9094	1.53202
$899$	−43.9540	−1.46595
$900$	39.8987	1.32996
$901$	−51.6697	−1.72137
$902$	−34.9342	−1.16318
$903$	1.58891	0.0528756
$904$	84.7944	2.82022
$905$	−4.69111	−0.155938
$906$	40.1274	1.33315
$907$	24.6141	0.817297	0.408649	−	0.912692i	$-0.366000\pi$
$907$	24.6141	0.817297	0.408649	+	0.912692i	$0.366000\pi$
$908$	34.2166	1.13552
$909$	−33.7344	−1.11890
$910$	0.737896	0.0244610
$911$	5.66981	0.187849	0.0939246	−	0.995579i	$-0.470059\pi$
$911$	5.66981	0.187849	0.0939246	+	0.995579i	$0.470059\pi$
$912$	15.4098	0.510268
$913$	−42.7114	−1.41354
$914$	8.35508	0.276362
$915$	0.425112	0.0140538
$916$	−73.1579	−2.41720
$917$	−2.29507	−0.0757898
$918$	−62.5401	−2.06413
$919$	23.0316	0.759743	0.379871	−	0.925039i	$-0.375968\pi$
$919$	23.0316	0.759743	0.379871	+	0.925039i	$0.375968\pi$
$920$	−12.6345	−0.416546
$921$	12.6078	0.415441
$922$	71.2522	2.34656
$923$	−22.5384	−0.741861
$924$	2.18997	0.0720447
$925$	−48.4789	−1.59398
$926$	−71.8382	−2.36075
$927$	−1.20654	−0.0396281
$928$	−3.74229	−0.122847
$929$	−40.3276	−1.32311	−0.661553	−	0.749898i	$-0.730102\pi$
$929$	−40.3276	−1.32311	−0.661553	+	0.749898i	$0.730102\pi$
$930$	7.19919	0.236071
$931$	−31.3178	−1.02640
$932$	−27.5272	−0.901684
$933$	−26.9304	−0.881662
$934$	−4.60868	−0.150800
$935$	−6.75702	−0.220978
$936$	−32.9104	−1.07571
$937$	−27.9680	−0.913674	−0.456837	−	0.889550i	$-0.651018\pi$
$937$	−27.9680	−0.913674	−0.456837	+	0.889550i	$0.651018\pi$
$938$	3.77817	0.123361
$939$	−3.07608	−0.100384
$940$	1.39630	0.0455423
$941$	−35.2069	−1.14771	−0.573856	−	0.818956i	$-0.694553\pi$
$941$	−35.2069	−1.14771	−0.573856	+	0.818956i	$0.694553\pi$
$942$	−6.43916	−0.209799
$943$	30.2310	0.984455
$944$	−6.59950	−0.214796
$945$	−0.441859	−0.0143737
$946$	−56.8271	−1.84761
$947$	38.0145	1.23531	0.617653	−	0.786451i	$-0.288084\pi$
$947$	38.0145	1.23531	0.617653	+	0.786451i	$0.288084\pi$
$948$	−25.6889	−0.834338
$949$	−49.5799	−1.60943
$950$	52.6776	1.70909
$951$	17.8027	0.577292
$952$	−5.18582	−0.168073
$953$	−56.7180	−1.83728	−0.918639	−	0.395099i	$-0.870710\pi$
$953$	−56.7180	−1.83728	−0.918639	+	0.395099i	$0.870710\pi$
$954$	49.8965	1.61546
$955$	6.15859	0.199287
$956$	−3.30663	−0.106944
$957$	16.8068	0.543286
$958$	−97.1900	−3.14007
$959$	−0.969469	−0.0313058
$960$	3.65433	0.117943
$961$	18.6993	0.603204
$962$	81.2669	2.62015
$963$	−41.1678	−1.32661
$964$	−49.8819	−1.60659
$965$	6.18232	0.199016
$966$	−2.85775	−0.0919467
$967$	2.97278	0.0955983	0.0477991	−	0.998857i	$-0.484779\pi$
$967$	2.97278	0.0955983	0.0477991	+	0.998857i	$0.484779\pi$
$968$	13.3905	0.430388
$969$	−22.6094	−0.726319
$970$	−0.320967	−0.0103056
$971$	−9.83219	−0.315530	−0.157765	−	0.987477i	$-0.550429\pi$
$971$	−9.83219	−0.315530	−0.157765	+	0.987477i	$0.550429\pi$
$972$	63.5639	2.03881
$973$	−3.34069	−0.107098
$974$	24.6044	0.788377
$975$	14.9709	0.479453
$976$	−3.68068	−0.117816
$977$	−49.9299	−1.59740	−0.798700	−	0.601729i	$-0.794479\pi$
$977$	−49.9299	−1.59740	−0.798700	+	0.601729i	$0.794479\pi$
$978$	14.8799	0.475807
$979$	45.6721	1.45969
$980$	12.1689	0.388721
$981$	−22.8267	−0.728802
$982$	28.4985	0.909423
$983$	−5.74578	−0.183262	−0.0916309	−	0.995793i	$-0.529208\pi$
$983$	−5.74578	−0.183262	−0.0916309	+	0.995793i	$0.529208\pi$
$984$	22.3490	0.712461
$985$	7.25905	0.231293
$986$	−80.8816	−2.57579
$987$	0.155403	0.00494654
$988$	−58.5600	−1.86304
$989$	49.1764	1.56372
$990$	6.52513	0.207382
$991$	−47.4922	−1.50864	−0.754319	−	0.656508i	$-0.772033\pi$
$991$	−47.4922	−1.50864	−0.754319	+	0.656508i	$0.772033\pi$
$992$	4.23145	0.134349
$993$	9.18309	0.291416
$994$	3.42959	0.108780
$995$	−11.3438	−0.359621
$996$	55.5312	1.75957
$997$	−38.8196	−1.22943	−0.614714	−	0.788750i	$-0.710729\pi$
$997$	−38.8196	−1.22943	−0.614714	+	0.788750i	$0.710729\pi$
$998$	57.2189	1.81123
$999$	−48.6633	−1.53964

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	4007.2.a.b.1.17	✓	195

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
4007.2.a.b.1.17	✓	195	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:	\( N \)	\(=\)	\( 4007 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	4007.a (trivial)

\(f(q)\)	\(=\)	\(q-2.43669 q^{2} +0.943453 q^{3} +3.93744 q^{4} -0.444210 q^{5} -2.29890 q^{6} -0.206330 q^{7} -4.72093 q^{8} -2.10990 q^{9} +O(q^{10})\)	\(q-2.43669 q^{2} +0.943453 q^{3} +3.93744 q^{4} -0.444210 q^{5} -2.29890 q^{6} -0.206330 q^{7} -4.72093 q^{8} -2.10990 q^{9} +1.08240 q^{10} -2.85720 q^{11} +3.71479 q^{12} -3.30403 q^{13} +0.502762 q^{14} -0.419091 q^{15} +3.62855 q^{16} -5.32386 q^{17} +5.14115 q^{18} +4.50135 q^{19} -1.74905 q^{20} -0.194663 q^{21} +6.96210 q^{22} -6.02478 q^{23} -4.45398 q^{24} -4.80268 q^{25} +8.05089 q^{26} -4.82095 q^{27} -0.812413 q^{28} -6.23481 q^{29} +1.02119 q^{30} +7.04978 q^{31} +0.600225 q^{32} -2.69563 q^{33} +12.9726 q^{34} +0.0916540 q^{35} -8.30759 q^{36} +10.0941 q^{37} -10.9684 q^{38} -3.11720 q^{39} +2.09708 q^{40} -5.01777 q^{41} +0.474333 q^{42} -8.16236 q^{43} -11.2500 q^{44} +0.937236 q^{45} +14.6805 q^{46} -0.798320 q^{47} +3.42337 q^{48} -6.95743 q^{49} +11.7026 q^{50} -5.02281 q^{51} -13.0094 q^{52} +9.70532 q^{53} +11.7471 q^{54} +1.26920 q^{55} +0.974072 q^{56} +4.24681 q^{57} +15.1923 q^{58} -1.81877 q^{59} -1.65015 q^{60} -1.01437 q^{61} -17.1781 q^{62} +0.435336 q^{63} -8.71966 q^{64} +1.46768 q^{65} +6.56841 q^{66} +7.51481 q^{67} -20.9624 q^{68} -5.68410 q^{69} -0.223332 q^{70} +6.82149 q^{71} +9.96067 q^{72} +15.0059 q^{73} -24.5963 q^{74} -4.53110 q^{75} +17.7238 q^{76} +0.589527 q^{77} +7.59564 q^{78} -6.91531 q^{79} -1.61184 q^{80} +1.78135 q^{81} +12.2267 q^{82} +14.9487 q^{83} -0.766474 q^{84} +2.36491 q^{85} +19.8891 q^{86} -5.88225 q^{87} +13.4886 q^{88} -15.9849 q^{89} -2.28375 q^{90} +0.681722 q^{91} -23.7222 q^{92} +6.65113 q^{93} +1.94525 q^{94} -1.99954 q^{95} +0.566285 q^{96} -0.296533 q^{97} +16.9531 q^{98} +6.02839 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9}+O(q^{10}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9	\( 195 q + 14 q^{2} + 22 q^{3} + 220 q^{4} + 14 q^{5} + 13 q^{6} + 48 q^{7} + 39 q^{8} + 245 q^{9} + 40 q^{10} + 13 q^{11} + 57 q^{12} + 97 q^{13} + 9 q^{14} + 23 q^{15} + 270 q^{16} + 66 q^{17} + 60 q^{18} + 33 q^{19} + 24 q^{20} + 27 q^{21} + 127 q^{22} + 42 q^{23} + 33 q^{24} + 357 q^{25} + 8 q^{26} + 79 q^{27} + 131 q^{28} + 57 q^{29} + 51 q^{30} + 41 q^{31} + 67 q^{32} + 74 q^{33} + 26 q^{34} + 14 q^{35} + 279 q^{36} + 133 q^{37} + 7 q^{38} + 28 q^{39} + 97 q^{40} + 64 q^{41} - q^{42} + 123 q^{43} + 21 q^{44} + 40 q^{45} + 84 q^{46} + 14 q^{47} + 122 q^{48} + 335 q^{49} + 35 q^{50} + 37 q^{51} + 220 q^{52} + 83 q^{53} + 21 q^{54} + 47 q^{55} + q^{56} + 235 q^{57} + 138 q^{58} + 18 q^{59} - 4 q^{60} + 81 q^{61} + 39 q^{62} + 102 q^{63} + 343 q^{64} + 165 q^{65} - 54 q^{66} + 147 q^{67} + 74 q^{68} - 2 q^{69} + 13 q^{70} + 31 q^{71} + 112 q^{72} + 300 q^{73} + 5 q^{74} + 84 q^{75} + 64 q^{76} + 67 q^{77} + 61 q^{78} + 144 q^{79} - 8 q^{80} + 359 q^{81} + 85 q^{82} + 26 q^{83} + 12 q^{84} + 201 q^{85} - 2 q^{86} + 80 q^{87} + 347 q^{88} + 29 q^{89} + 62 q^{90} + 70 q^{91} + 79 q^{92} + 76 q^{93} + 72 q^{94} + 71 q^{95} + 31 q^{96} + 264 q^{97} + 30 q^{98} + 19 q^{99}+O(q^{100}) \) 195 * q + 14 * q^2 + 22 * q^3 + 220 * q^4 + 14 * q^5 + 13 * q^6 + 48 * q^7 + 39 * q^8 + 245 * q^9 + 40 * q^10 + 13 * q^11 + 57 * q^12 + 97 * q^13 + 9 * q^14 + 23 * q^15 + 270 * q^16 + 66 * q^17 + 60 * q^18 + 33 * q^19 + 24 * q^20 + 27 * q^21 + 127 * q^22 + 42 * q^23 + 33 * q^24 + 357 * q^25 + 8 * q^26 + 79 * q^27 + 131 * q^28 + 57 * q^29 + 51 * q^30 + 41 * q^31 + 67 * q^32 + 74 * q^33 + 26 * q^34 + 14 * q^35 + 279 * q^36 + 133 * q^37 + 7 * q^38 + 28 * q^39 + 97 * q^40 + 64 * q^41 - q^42 + 123 * q^43 + 21 * q^44 + 40 * q^45 + 84 * q^46 + 14 * q^47 + 122 * q^48 + 335 * q^49 + 35 * q^50 + 37 * q^51 + 220 * q^52 + 83 * q^53 + 21 * q^54 + 47 * q^55 + q^56 + 235 * q^57 + 138 * q^58 + 18 * q^59 - 4 * q^60 + 81 * q^61 + 39 * q^62 + 102 * q^63 + 343 * q^64 + 165 * q^65 - 54 * q^66 + 147 * q^67 + 74 * q^68 - 2 * q^69 + 13 * q^70 + 31 * q^71 + 112 * q^72 + 300 * q^73 + 5 * q^74 + 84 * q^75 + 64 * q^76 + 67 * q^77 + 61 * q^78 + 144 * q^79 - 8 * q^80 + 359 * q^81 + 85 * q^82 + 26 * q^83 + 12 * q^84 + 201 * q^85 - 2 * q^86 + 80 * q^87 + 347 * q^88 + 29 * q^89 + 62 * q^90 + 70 * q^91 + 79 * q^92 + 76 * q^93 + 72 * q^94 + 71 * q^95 + 31 * q^96 + 264 * q^97 + 30 * q^98 + 19 * q^99

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