LMFDB - Embedded newform 8017.2.a.a.1.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [8017,2,Mod(1,8017)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(8017, 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("8017.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 8017 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	8017.a (trivial)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	yes
Analytic conductor:	$64.0160673005$
Analytic rank:	$1$
Dimension:	$327$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.16
Character	$\chi$	$=$	8017.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.60838 q^{2} +2.59159 q^{3} +4.80367 q^{4} -3.67050 q^{5} -6.75986 q^{6} +1.01472 q^{7} -7.31304 q^{8} +3.71634 q^{9} +O(q^{10})$	\(q-2.60838 q^{2} +2.59159 q^{3} +4.80367 q^{4} -3.67050 q^{5} -6.75986 q^{6} +1.01472 q^{7} -7.31304 q^{8} +3.71634 q^{9} +9.57408 q^{10} -1.01048 q^{11} +12.4491 q^{12} +5.35346 q^{13} -2.64679 q^{14} -9.51244 q^{15} +9.46788 q^{16} +0.358672 q^{17} -9.69364 q^{18} +2.66572 q^{19} -17.6319 q^{20} +2.62975 q^{21} +2.63571 q^{22} -5.07124 q^{23} -18.9524 q^{24} +8.47259 q^{25} -13.9639 q^{26} +1.85645 q^{27} +4.87439 q^{28} -4.87822 q^{29} +24.8121 q^{30} -5.56394 q^{31} -10.0698 q^{32} -2.61874 q^{33} -0.935553 q^{34} -3.72455 q^{35} +17.8520 q^{36} -4.45833 q^{37} -6.95322 q^{38} +13.8740 q^{39} +26.8425 q^{40} +6.67984 q^{41} -6.85939 q^{42} +5.63708 q^{43} -4.85400 q^{44} -13.6408 q^{45} +13.2278 q^{46} +3.27720 q^{47} +24.5369 q^{48} -5.97034 q^{49} -22.0998 q^{50} +0.929530 q^{51} +25.7162 q^{52} -9.42527 q^{53} -4.84234 q^{54} +3.70896 q^{55} -7.42071 q^{56} +6.90845 q^{57} +12.7243 q^{58} +10.8440 q^{59} -45.6946 q^{60} -12.0300 q^{61} +14.5129 q^{62} +3.77105 q^{63} +7.33013 q^{64} -19.6499 q^{65} +6.83069 q^{66} +3.31724 q^{67} +1.72294 q^{68} -13.1426 q^{69} +9.71504 q^{70} -7.24140 q^{71} -27.1777 q^{72} +3.08954 q^{73} +11.6290 q^{74} +21.9575 q^{75} +12.8052 q^{76} -1.02536 q^{77} -36.1887 q^{78} -1.15382 q^{79} -34.7519 q^{80} -6.33785 q^{81} -17.4236 q^{82} +4.03702 q^{83} +12.6324 q^{84} -1.31650 q^{85} -14.7037 q^{86} -12.6423 q^{87} +7.38967 q^{88} -1.27577 q^{89} +35.5805 q^{90} +5.43228 q^{91} -24.3606 q^{92} -14.4195 q^{93} -8.54819 q^{94} -9.78454 q^{95} -26.0968 q^{96} +2.69528 q^{97} +15.5729 q^{98} -3.75528 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) $ 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * 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 $

$2$	−2.60838	−1.84441	−0.922203	−	0.386706i	$-0.873613\pi$
$2$	−2.60838	−1.84441	−0.922203	+	0.386706i	$0.873613\pi$
$3$	2.59159	1.49626	0.748128	−	0.663555i	$-0.230953\pi$
$3$	2.59159	1.49626	0.748128	+	0.663555i	$0.230953\pi$
$4$	4.80367	2.40183
$5$	−3.67050	−1.64150	−0.820749	−	0.571288i	$-0.806444\pi$
$5$	−3.67050	−1.64150	−0.820749	+	0.571288i	$0.806444\pi$
$6$	−6.75986	−2.75970
$7$	1.01472	0.383529	0.191765	−	0.981441i	$-0.438579\pi$
$7$	1.01472	0.383529	0.191765	+	0.981441i	$0.438579\pi$
$8$	−7.31304	−2.58555
$9$	3.71634	1.23878
$10$	9.57408	3.02759
$11$	−1.01048	−0.304671	−0.152335	−	0.988329i	$-0.548679\pi$
$11$	−1.01048	−0.304671	−0.152335	+	0.988329i	$0.548679\pi$
$12$	12.4491	3.59376
$13$	5.35346	1.48478	0.742392	−	0.669966i	$-0.233691\pi$
$13$	5.35346	1.48478	0.742392	+	0.669966i	$0.233691\pi$
$14$	−2.64679	−0.707384
$15$	−9.51244	−2.45610
$16$	9.46788	2.36697
$17$	0.358672	0.0869906	0.0434953	−	0.999054i	$-0.486151\pi$
$17$	0.358672	0.0869906	0.0434953	+	0.999054i	$0.486151\pi$
$18$	−9.69364	−2.28481
$19$	2.66572	0.611558	0.305779	−	0.952102i	$-0.401083\pi$
$19$	2.66572	0.611558	0.305779	+	0.952102i	$0.401083\pi$
$20$	−17.6319	−3.94261
$21$	2.62975	0.573858
$22$	2.63571	0.561936
$23$	−5.07124	−1.05743	−0.528714	−	0.848800i	$-0.677325\pi$
$23$	−5.07124	−1.05743	−0.528714	+	0.848800i	$0.677325\pi$
$24$	−18.9524	−3.86864
$25$	8.47259	1.69452
$26$	−13.9639	−2.73854
$27$	1.85645	0.357275
$28$	4.87439	0.921174
$29$	−4.87822	−0.905862	−0.452931	−	0.891545i	$-0.649622\pi$
$29$	−4.87822	−0.905862	−0.452931	+	0.891545i	$0.649622\pi$
$30$	24.8121	4.53005
$31$	−5.56394	−0.999313	−0.499657	−	0.866224i	$-0.666540\pi$
$31$	−5.56394	−0.999313	−0.499657	+	0.866224i	$0.666540\pi$
$32$	−10.0698	−1.78011
$33$	−2.61874	−0.455865
$34$	−0.935553	−0.160446
$35$	−3.72455	−0.629563
$36$	17.8520	2.97534
$37$	−4.45833	−0.732945	−0.366472	−	0.930429i	$-0.619435\pi$
$37$	−4.45833	−0.732945	−0.366472	+	0.930429i	$0.619435\pi$
$38$	−6.95322	−1.12796
$39$	13.8740	2.22161
$40$	26.8425	4.24418
$41$	6.67984	1.04322	0.521608	−	0.853185i	$-0.325332\pi$
$41$	6.67984	1.04322	0.521608	+	0.853185i	$0.325332\pi$
$42$	−6.85939	−1.05843
$43$	5.63708	0.859647	0.429823	−	0.902913i	$-0.358576\pi$
$43$	5.63708	0.859647	0.429823	+	0.902913i	$0.358576\pi$
$44$	−4.85400	−0.731768
$45$	−13.6408	−2.03345
$46$	13.2278	1.95033
$47$	3.27720	0.478029	0.239014	−	0.971016i	$-0.423176\pi$
$47$	3.27720	0.478029	0.239014	+	0.971016i	$0.423176\pi$
$48$	24.5369	3.54159
$49$	−5.97034	−0.852905
$50$	−22.0998	−3.12538
$51$	0.929530	0.130160
$52$	25.7162	3.56620
$53$	−9.42527	−1.29466	−0.647330	−	0.762210i	$-0.724114\pi$
$53$	−9.42527	−1.29466	−0.647330	+	0.762210i	$0.724114\pi$
$54$	−4.84234	−0.658959
$55$	3.70896	0.500116
$56$	−7.42071	−0.991635
$57$	6.90845	0.915047
$58$	12.7243	1.67078
$59$	10.8440	1.41176	0.705882	−	0.708329i	$-0.250551\pi$
$59$	10.8440	1.41176	0.705882	+	0.708329i	$0.250551\pi$
$60$	−45.6946	−5.89915
$61$	−12.0300	−1.54028	−0.770139	−	0.637876i	$-0.779813\pi$
$61$	−12.0300	−1.54028	−0.770139	+	0.637876i	$0.779813\pi$
$62$	14.5129	1.84314
$63$	3.77105	0.475108
$64$	7.33013	0.916266
$65$	−19.6499	−2.43727
$66$	6.83069	0.840800
$67$	3.31724	0.405266	0.202633	−	0.979255i	$-0.435050\pi$
$67$	3.31724	0.405266	0.202633	+	0.979255i	$0.435050\pi$
$68$	1.72294	0.208937
$69$	−13.1426	−1.58218
$70$	9.71504	1.16117
$71$	−7.24140	−0.859396	−0.429698	−	0.902973i	$-0.641380\pi$
$71$	−7.24140	−0.859396	−0.429698	+	0.902973i	$0.641380\pi$
$72$	−27.1777	−3.20293
$73$	3.08954	0.361604	0.180802	−	0.983520i	$-0.442131\pi$
$73$	3.08954	0.361604	0.180802	+	0.983520i	$0.442131\pi$
$74$	11.6290	1.35185
$75$	21.9575	2.53543
$76$	12.8052	1.46886
$77$	−1.02536	−0.116850
$78$	−36.1887	−4.09756
$79$	−1.15382	−0.129815	−0.0649074	−	0.997891i	$-0.520675\pi$
$79$	−1.15382	−0.129815	−0.0649074	+	0.997891i	$0.520675\pi$
$80$	−34.7519	−3.88538
$81$	−6.33785	−0.704205
$82$	−17.4236	−1.92411
$83$	4.03702	0.443121	0.221560	−	0.975147i	$-0.428885\pi$
$83$	4.03702	0.443121	0.221560	+	0.975147i	$0.428885\pi$
$84$	12.6324	1.37831
$85$	−1.31650	−0.142795
$86$	−14.7037	−1.58554
$87$	−12.6423	−1.35540
$88$	7.38967	0.787741
$89$	−1.27577	−0.135231	−0.0676156	−	0.997711i	$-0.521539\pi$
$89$	−1.27577	−0.135231	−0.0676156	+	0.997711i	$0.521539\pi$
$90$	35.5805	3.75052
$91$	5.43228	0.569458
$92$	−24.3606	−2.53976
$93$	−14.4195	−1.49523
$94$	−8.54819	−0.881679
$95$	−9.78454	−1.00387
$96$	−26.0968	−2.66349
$97$	2.69528	0.273664	0.136832	−	0.990594i	$-0.456308\pi$
$97$	2.69528	0.273664	0.136832	+	0.990594i	$0.456308\pi$
$98$	15.5729	1.57310
$99$	−3.75528	−0.377420
$100$	40.6995	4.06995
$101$	−6.13892	−0.610846	−0.305423	−	0.952217i	$-0.598798\pi$
$101$	−6.13892	−0.610846	−0.305423	+	0.952217i	$0.598798\pi$
$102$	−2.42457	−0.240068
$103$	−4.13926	−0.407854	−0.203927	−	0.978986i	$-0.565370\pi$
$103$	−4.13926	−0.407854	−0.203927	+	0.978986i	$0.565370\pi$
$104$	−39.1501	−3.83898
$105$	−9.65249	−0.941987
$106$	24.5847	2.38788
$107$	7.43501	0.718770	0.359385	−	0.933189i	$-0.382987\pi$
$107$	7.43501	0.718770	0.359385	+	0.933189i	$0.382987\pi$
$108$	8.91778	0.858114
$109$	−6.33378	−0.606666	−0.303333	−	0.952885i	$-0.598099\pi$
$109$	−6.33378	−0.606666	−0.303333	+	0.952885i	$0.598099\pi$
$110$	−9.67440	−0.922418
$111$	−11.5542	−1.09667
$112$	9.60728	0.907803
$113$	−7.14940	−0.672559	−0.336279	−	0.941762i	$-0.609169\pi$
$113$	−7.14940	−0.672559	−0.336279	+	0.941762i	$0.609169\pi$
$114$	−18.0199	−1.68772
$115$	18.6140	1.73577
$116$	−23.4333	−2.17573
$117$	19.8953	1.83932
$118$	−28.2852	−2.60387
$119$	0.363952	0.0333635
$120$	69.5648	6.35037
$121$	−9.97893	−0.907176
$122$	31.3788	2.84090
$123$	17.3114	1.56092
$124$	−26.7273	−2.40018
$125$	−12.7462	−1.14005
$126$	−9.83636	−0.876293
$127$	−7.95155	−0.705586	−0.352793	−	0.935701i	$-0.614768\pi$
$127$	−7.95155	−0.705586	−0.352793	+	0.935701i	$0.614768\pi$
$128$	1.01980	0.0901388
$129$	14.6090	1.28625
$130$	51.2545	4.49531
$131$	−0.796515	−0.0695919	−0.0347959	−	0.999394i	$-0.511078\pi$
$131$	−0.796515	−0.0695919	−0.0347959	+	0.999394i	$0.511078\pi$
$132$	−12.5796	−1.09491
$133$	2.70497	0.234551
$134$	−8.65264	−0.747474
$135$	−6.81412	−0.586466
$136$	−2.62298	−0.224919
$137$	−19.8605	−1.69680	−0.848400	−	0.529356i	$-0.822434\pi$
$137$	−19.8605	−1.69680	−0.848400	+	0.529356i	$0.822434\pi$
$138$	34.2809	2.91818
$139$	14.1037	1.19626	0.598130	−	0.801399i	$-0.295911\pi$
$139$	14.1037	1.19626	0.598130	+	0.801399i	$0.295911\pi$
$140$	−17.8915	−1.51211
$141$	8.49315	0.715253
$142$	18.8884	1.58508
$143$	−5.40956	−0.452370
$144$	35.1859	2.93215
$145$	17.9055	1.48697
$146$	−8.05872	−0.666944
$147$	−15.4727	−1.27616
$148$	−21.4163	−1.76041
$149$	3.82217	0.313124	0.156562	−	0.987668i	$-0.449959\pi$
$149$	3.82217	0.313124	0.156562	+	0.987668i	$0.449959\pi$
$150$	−57.2735	−4.67636
$151$	−6.24490	−0.508203	−0.254102	−	0.967178i	$-0.581780\pi$
$151$	−6.24490	−0.508203	−0.254102	+	0.967178i	$0.581780\pi$
$152$	−19.4945	−1.58121
$153$	1.33294	0.107762
$154$	2.67452	0.215519
$155$	20.4225	1.64037
$156$	66.6460	5.33595
$157$	−13.6673	−1.09077	−0.545385	−	0.838186i	$-0.683617\pi$
$157$	−13.6673	−1.09077	−0.545385	+	0.838186i	$0.683617\pi$
$158$	3.00961	0.239431
$159$	−24.4264	−1.93714
$160$	36.9612	2.92204
$161$	−5.14591	−0.405555
$162$	16.5315	1.29884
$163$	15.7913	1.23687	0.618436	−	0.785835i	$-0.287766\pi$
$163$	15.7913	1.23687	0.618436	+	0.785835i	$0.287766\pi$
$164$	32.0877	2.50563
$165$	9.61211	0.748302
$166$	−10.5301	−0.817294
$167$	18.1640	1.40557	0.702785	−	0.711402i	$-0.251940\pi$
$167$	18.1640	1.40557	0.702785	+	0.711402i	$0.251940\pi$
$168$	−19.2314	−1.48374
$169$	15.6596	1.20458
$170$	3.43395	0.263372
$171$	9.90672	0.757586
$172$	27.0787	2.06473
$173$	−7.80055	−0.593065	−0.296532	−	0.955023i	$-0.595830\pi$
$173$	−7.80055	−0.593065	−0.296532	+	0.955023i	$0.595830\pi$
$174$	32.9761	2.49991
$175$	8.59734	0.649898
$176$	−9.56709	−0.721146
$177$	28.1031	2.11236
$178$	3.32769	0.249421
$179$	7.55670	0.564815	0.282407	−	0.959295i	$-0.408867\pi$
$179$	7.55670	0.564815	0.282407	+	0.959295i	$0.408867\pi$
$180$	−65.5260	−4.88402
$181$	−7.48171	−0.556111	−0.278056	−	0.960565i	$-0.589690\pi$
$181$	−7.48171	−0.556111	−0.278056	+	0.960565i	$0.589690\pi$
$182$	−14.1695	−1.05031
$183$	−31.1767	−2.30465
$184$	37.0862	2.73403
$185$	16.3643	1.20313
$186$	37.6115	2.75781
$187$	−0.362430	−0.0265035
$188$	15.7426	1.14814
$189$	1.88379	0.137025
$190$	25.5218	1.85155
$191$	−0.612265	−0.0443019	−0.0221510	−	0.999755i	$-0.507051\pi$
$191$	−0.612265	−0.0443019	−0.0221510	+	0.999755i	$0.507051\pi$
$192$	18.9967	1.37097
$193$	2.10759	0.151708	0.0758539	−	0.997119i	$-0.475832\pi$
$193$	2.10759	0.151708	0.0758539	+	0.997119i	$0.475832\pi$
$194$	−7.03032	−0.504748
$195$	−50.9245	−3.64678
$196$	−28.6795	−2.04854
$197$	16.0270	1.14187	0.570937	−	0.820994i	$-0.306580\pi$
$197$	16.0270	1.14187	0.570937	+	0.820994i	$0.306580\pi$
$198$	9.79521	0.696115
$199$	24.3954	1.72934	0.864672	−	0.502337i	$-0.167526\pi$
$199$	24.3954	1.72934	0.864672	+	0.502337i	$0.167526\pi$
$200$	−61.9604	−4.38126
$201$	8.59693	0.606381
$202$	16.0127	1.12665
$203$	−4.95004	−0.347425
$204$	4.46515	0.312623
$205$	−24.5184	−1.71244
$206$	10.7968	0.752248
$207$	−18.8465	−1.30992
$208$	50.6860	3.51444
$209$	−2.69365	−0.186324
$210$	25.1774	1.73741
$211$	2.40788	0.165766	0.0828828	−	0.996559i	$-0.473587\pi$
$211$	2.40788	0.165766	0.0828828	+	0.996559i	$0.473587\pi$
$212$	−45.2758	−3.10956
$213$	−18.7667	−1.28588
$214$	−19.3934	−1.32570
$215$	−20.6909	−1.41111
$216$	−13.5763	−0.923751
$217$	−5.64586	−0.383266
$218$	16.5209	1.11894
$219$	8.00683	0.541051
$220$	17.8166	1.20120
$221$	1.92013	0.129162
$222$	30.1377	2.02271
$223$	9.13857	0.611964	0.305982	−	0.952037i	$-0.401015\pi$
$223$	9.13857	0.611964	0.305982	+	0.952037i	$0.401015\pi$
$224$	−10.2181	−0.682723
$225$	31.4870	2.09913
$226$	18.6484	1.24047
$227$	−0.766020	−0.0508425	−0.0254213	−	0.999677i	$-0.508093\pi$
$227$	−0.766020	−0.0508425	−0.0254213	+	0.999677i	$0.508093\pi$
$228$	33.1859	2.19779
$229$	−19.0414	−1.25829	−0.629145	−	0.777288i	$-0.716595\pi$
$229$	−19.0414	−1.25829	−0.629145	+	0.777288i	$0.716595\pi$
$230$	−48.5525	−3.20146
$231$	−2.65730	−0.174838
$232$	35.6746	2.34215
$233$	−7.24175	−0.474423	−0.237211	−	0.971458i	$-0.576233\pi$
$233$	−7.24175	−0.474423	−0.237211	+	0.971458i	$0.576233\pi$
$234$	−51.8945	−3.39245
$235$	−12.0290	−0.784683
$236$	52.0908	3.39082
$237$	−2.99023	−0.194236
$238$	−0.949328	−0.0615358
$239$	9.54675	0.617528	0.308764	−	0.951139i	$-0.400085\pi$
$239$	9.54675	0.617528	0.308764	+	0.951139i	$0.400085\pi$
$240$	−90.0627	−5.81352
$241$	10.8009	0.695747	0.347874	−	0.937541i	$-0.386904\pi$
$241$	10.8009	0.695747	0.347874	+	0.937541i	$0.386904\pi$
$242$	26.0289	1.67320
$243$	−21.9945	−1.41095
$244$	−57.7879	−3.69949
$245$	21.9141	1.40004
$246$	−45.1548	−2.87896
$247$	14.2708	0.908031
$248$	40.6893	2.58378
$249$	10.4623	0.663021
$250$	33.2469	2.10272
$251$	−11.5984	−0.732084	−0.366042	−	0.930598i	$-0.619287\pi$
$251$	−11.5984	−0.732084	−0.366042	+	0.930598i	$0.619287\pi$
$252$	18.1149	1.14113
$253$	5.12438	0.322167
$254$	20.7407	1.30139
$255$	−3.41184	−0.213658
$256$	−17.3203	−1.08252
$257$	−15.9993	−0.998010	−0.499005	−	0.866599i	$-0.666301\pi$
$257$	−15.9993	−0.998010	−0.499005	+	0.866599i	$0.666301\pi$
$258$	−38.1059	−2.37237
$259$	−4.52397	−0.281106
$260$	−94.3916	−5.85392
$261$	−18.1291	−1.12216
$262$	2.07762	0.128356
$263$	16.9381	1.04445	0.522225	−	0.852808i	$-0.325102\pi$
$263$	16.9381	1.04445	0.522225	+	0.852808i	$0.325102\pi$
$264$	19.1510	1.17866
$265$	34.5955	2.12518
$266$	−7.05560	−0.432607
$267$	−3.30627	−0.202340
$268$	15.9349	0.973381
$269$	−8.93147	−0.544561	−0.272281	−	0.962218i	$-0.587778\pi$
$269$	−8.93147	−0.544561	−0.272281	+	0.962218i	$0.587778\pi$
$270$	17.7738	1.08168
$271$	−2.70301	−0.164196	−0.0820982	−	0.996624i	$-0.526162\pi$
$271$	−2.70301	−0.164196	−0.0820982	+	0.996624i	$0.526162\pi$
$272$	3.39586	0.205904
$273$	14.0782	0.852054
$274$	51.8039	3.12959
$275$	−8.56137	−0.516270
$276$	−63.1326	−3.80014
$277$	−7.06713	−0.424623	−0.212311	−	0.977202i	$-0.568099\pi$
$277$	−7.06713	−0.424623	−0.212311	+	0.977202i	$0.568099\pi$
$278$	−36.7879	−2.20639
$279$	−20.6775	−1.23793
$280$	27.2378	1.62777
$281$	−11.3172	−0.675127	−0.337563	−	0.941303i	$-0.609603\pi$
$281$	−11.3172	−0.675127	−0.337563	+	0.941303i	$0.609603\pi$
$282$	−22.1534	−1.31922
$283$	−12.0142	−0.714168	−0.357084	−	0.934072i	$-0.616229\pi$
$283$	−12.0142	−0.714168	−0.357084	+	0.934072i	$0.616229\pi$
$284$	−34.7853	−2.06413
$285$	−25.3575	−1.50205
$286$	14.1102	0.834353
$287$	6.77819	0.400104
$288$	−37.4228	−2.20516
$289$	−16.8714	−0.992433
$290$	−46.7045	−2.74258
$291$	6.98506	0.409471
$292$	14.8411	0.868512
$293$	−17.5570	−1.02569	−0.512845	−	0.858481i	$-0.671409\pi$
$293$	−17.5570	−1.02569	−0.512845	+	0.858481i	$0.671409\pi$
$294$	40.3586	2.35376
$295$	−39.8028	−2.31741
$296$	32.6039	1.89507
$297$	−1.87591	−0.108851
$298$	−9.96967	−0.577528
$299$	−27.1487	−1.57005
$300$	105.476	6.08968
$301$	5.72008	0.329700
$302$	16.2891	0.937333
$303$	−15.9096	−0.913981
$304$	25.2387	1.44754
$305$	44.1560	2.52837
$306$	−3.47683	−0.198757
$307$	−22.9549	−1.31010	−0.655052	−	0.755584i	$-0.727353\pi$
$307$	−22.9549	−1.31010	−0.655052	+	0.755584i	$0.727353\pi$
$308$	−4.92547	−0.280655
$309$	−10.7273	−0.610253
$310$	−53.2696	−3.02551
$311$	−4.27993	−0.242692	−0.121346	−	0.992610i	$-0.538721\pi$
$311$	−4.27993	−0.242692	−0.121346	+	0.992610i	$0.538721\pi$
$312$	−101.461	−5.74410
$313$	−31.4925	−1.78006	−0.890031	−	0.455900i	$-0.849317\pi$
$313$	−31.4925	−1.78006	−0.890031	+	0.455900i	$0.849317\pi$
$314$	35.6496	2.01182
$315$	−13.8417	−0.779890
$316$	−5.54257	−0.311794
$317$	−8.33146	−0.467941	−0.233971	−	0.972244i	$-0.575172\pi$
$317$	−8.33146	−0.467941	−0.233971	+	0.972244i	$0.575172\pi$
$318$	63.7135	3.57287
$319$	4.92933	0.275990
$320$	−26.9053	−1.50405
$321$	19.2685	1.07546
$322$	13.4225	0.748007
$323$	0.956118	0.0531998
$324$	−30.4449	−1.69138
$325$	45.3577	2.51599
$326$	−41.1899	−2.28130
$327$	−16.4146	−0.907727
$328$	−48.8499	−2.69729
$329$	3.32545	0.183338
$330$	−25.0721	−1.38017
$331$	−10.5046	−0.577383	−0.288691	−	0.957422i	$-0.593220\pi$
$331$	−10.5046	−0.577383	−0.288691	+	0.957422i	$0.593220\pi$
$332$	19.3925	1.06430
$333$	−16.5687	−0.907957
$334$	−47.3786	−2.59244
$335$	−12.1759	−0.665243
$336$	24.8981	1.35830
$337$	6.17187	0.336203	0.168101	−	0.985770i	$-0.446236\pi$
$337$	6.17187	0.336203	0.168101	+	0.985770i	$0.446236\pi$
$338$	−40.8461	−2.22174
$339$	−18.5283	−1.00632
$340$	−6.32405	−0.342970
$341$	5.62224	0.304461
$342$	−25.8405	−1.39730
$343$	−13.1613	−0.710644
$344$	−41.2242	−2.22266
$345$	48.2399	2.59715
$346$	20.3468	1.09385
$347$	1.41606	0.0760179	0.0380089	−	0.999277i	$-0.487898\pi$
$347$	1.41606	0.0760179	0.0380089	+	0.999277i	$0.487898\pi$
$348$	−60.7296	−3.25545
$349$	−11.8648	−0.635110	−0.317555	−	0.948240i	$-0.602862\pi$
$349$	−11.8648	−0.635110	−0.317555	+	0.948240i	$0.602862\pi$
$350$	−22.4252	−1.19867
$351$	9.93845	0.530475
$352$	10.1753	0.542346
$353$	2.96981	0.158067	0.0790334	−	0.996872i	$-0.474817\pi$
$353$	2.96981	0.158067	0.0790334	+	0.996872i	$0.474817\pi$
$354$	−73.3037	−3.89605
$355$	26.5796	1.41070
$356$	−6.12836	−0.324803
$357$	0.943215	0.0499203
$358$	−19.7108	−1.04175
$359$	−16.2959	−0.860063	−0.430031	−	0.902814i	$-0.641498\pi$
$359$	−16.2959	−0.860063	−0.430031	+	0.902814i	$0.641498\pi$
$360$	99.7559	5.25760
$361$	−11.8939	−0.625996
$362$	19.5152	1.02570
$363$	−25.8613	−1.35737
$364$	26.0949	1.36774
$365$	−11.3402	−0.593572
$366$	81.3209	4.25071
$367$	26.4726	1.38186	0.690929	−	0.722923i	$-0.257202\pi$
$367$	26.4726	1.38186	0.690929	+	0.722923i	$0.257202\pi$
$368$	−48.0139	−2.50290
$369$	24.8245	1.29231
$370$	−42.6844	−2.21906
$371$	−9.56404	−0.496540
$372$	−69.2663	−3.59129
$373$	4.00062	0.207144	0.103572	−	0.994622i	$-0.466973\pi$
$373$	4.00062	0.207144	0.103572	+	0.994622i	$0.466973\pi$
$374$	0.945356	0.0488832
$375$	−33.0328	−1.70581
$376$	−23.9663	−1.23597
$377$	−26.1154	−1.34501
$378$	−4.91364	−0.252730
$379$	−10.0716	−0.517345	−0.258672	−	0.965965i	$-0.583285\pi$
$379$	−10.0716	−0.517345	−0.258672	+	0.965965i	$0.583285\pi$
$380$	−47.0017	−2.41113
$381$	−20.6071	−1.05574
$382$	1.59702	0.0817107
$383$	−31.4731	−1.60820	−0.804100	−	0.594494i	$-0.797352\pi$
$383$	−31.4731	−1.60820	−0.804100	+	0.594494i	$0.797352\pi$
$384$	2.64291	0.134871
$385$	3.76357	0.191809
$386$	−5.49741	−0.279811
$387$	20.9493	1.06491
$388$	12.9472	0.657296
$389$	29.7438	1.50807	0.754035	−	0.656834i	$-0.228105\pi$
$389$	29.7438	1.50807	0.754035	+	0.656834i	$0.228105\pi$
$390$	132.831	6.72614
$391$	−1.81891	−0.0919863
$392$	43.6613	2.20523
$393$	−2.06424	−0.104127
$394$	−41.8045	−2.10608
$395$	4.23510	0.213091
$396$	−18.0391	−0.906499
$397$	−28.0274	−1.40666	−0.703329	−	0.710865i	$-0.748304\pi$
$397$	−28.0274	−1.40666	−0.703329	+	0.710865i	$0.748304\pi$
$398$	−63.6326	−3.18961
$399$	7.01017	0.350947
$400$	80.2175	4.01088
$401$	18.7791	0.937782	0.468891	−	0.883256i	$-0.344654\pi$
$401$	18.7791	0.937782	0.468891	+	0.883256i	$0.344654\pi$
$402$	−22.4241	−1.11841
$403$	−29.7863	−1.48376
$404$	−29.4893	−1.46715
$405$	23.2631	1.15595
$406$	12.9116	0.640793
$407$	4.50504	0.223307
$408$	−6.79769	−0.336536
$409$	34.2160	1.69187	0.845937	−	0.533284i	$-0.179042\pi$
$409$	34.2160	1.69187	0.845937	+	0.533284i	$0.179042\pi$
$410$	63.9533	3.15843
$411$	−51.4704	−2.53885
$412$	−19.8836	−0.979597
$413$	11.0036	0.541453
$414$	49.1588	2.41602
$415$	−14.8179	−0.727382
$416$	−53.9083	−2.64307
$417$	36.5510	1.78991
$418$	7.02608	0.343657
$419$	16.8279	0.822098	0.411049	−	0.911613i	$-0.365163\pi$
$419$	16.8279	0.822098	0.411049	+	0.911613i	$0.365163\pi$
$420$	−46.3674	−2.26250
$421$	−24.8118	−1.20925	−0.604626	−	0.796509i	$-0.706678\pi$
$421$	−24.8118	−1.20925	−0.604626	+	0.796509i	$0.706678\pi$
$422$	−6.28068	−0.305739
$423$	12.1792	0.592172
$424$	68.9274	3.34741
$425$	3.03888	0.147407
$426$	48.9509	2.37168
$427$	−12.2071	−0.590742
$428$	35.7153	1.72637
$429$	−14.0193	−0.676861
$430$	53.9699	2.60266
$431$	22.8193	1.09917	0.549584	−	0.835438i	$-0.314786\pi$
$431$	22.8193	1.09917	0.549584	+	0.835438i	$0.314786\pi$
$432$	17.5767	0.845659
$433$	1.73687	0.0834689	0.0417344	−	0.999129i	$-0.486712\pi$
$433$	1.73687	0.0834689	0.0417344	+	0.999129i	$0.486712\pi$
$434$	14.7266	0.706898
$435$	46.4037	2.22489
$436$	−30.4254	−1.45711
$437$	−13.5185	−0.646679
$438$	−20.8849	−0.997919
$439$	37.4771	1.78868	0.894341	−	0.447385i	$-0.147645\pi$
$439$	37.4771	1.78868	0.894341	+	0.447385i	$0.147645\pi$
$440$	−27.1238	−1.29308
$441$	−22.1878	−1.05656
$442$	−5.00845	−0.238228
$443$	−12.8349	−0.609804	−0.304902	−	0.952384i	$-0.598624\pi$
$443$	−12.8349	−0.609804	−0.304902	+	0.952384i	$0.598624\pi$
$444$	−55.5023	−2.63402
$445$	4.68271	0.221982
$446$	−23.8369	−1.12871
$447$	9.90548	0.468513
$448$	7.43805	0.351415
$449$	−0.231681	−0.0109337	−0.00546684	−	0.999985i	$-0.501740\pi$
$449$	−0.231681	−0.0109337	−0.00546684	+	0.999985i	$0.501740\pi$
$450$	−82.1302	−3.87166
$451$	−6.74983	−0.317837
$452$	−34.3433	−1.61537
$453$	−16.1842	−0.760401
$454$	1.99807	0.0937743
$455$	−19.9392	−0.934765
$456$	−50.5218	−2.36590
$457$	29.1431	1.36326	0.681628	−	0.731699i	$-0.261272\pi$
$457$	29.1431	1.36326	0.681628	+	0.731699i	$0.261272\pi$
$458$	49.6673	2.32080
$459$	0.665857	0.0310795
$460$	89.4155	4.16902
$461$	20.5425	0.956759	0.478379	−	0.878153i	$-0.341224\pi$
$461$	20.5425	0.956759	0.478379	+	0.878153i	$0.341224\pi$
$462$	6.93126	0.322471
$463$	6.95988	0.323453	0.161727	−	0.986836i	$-0.448294\pi$
$463$	6.95988	0.323453	0.161727	+	0.986836i	$0.448294\pi$
$464$	−46.1864	−2.14415
$465$	52.9266	2.45441
$466$	18.8893	0.875029
$467$	−22.9677	−1.06282	−0.531409	−	0.847115i	$-0.678337\pi$
$467$	−22.9677	−1.06282	−0.531409	+	0.847115i	$0.678337\pi$
$468$	95.5703	4.41774
$469$	3.36608	0.155431
$470$	31.3762	1.44727
$471$	−35.4201	−1.63207
$472$	−79.3024	−3.65019
$473$	−5.69614	−0.261909
$474$	7.79966	0.358250
$475$	22.5856	1.03630
$476$	1.74831	0.0801335
$477$	−35.0275	−1.60380
$478$	−24.9016	−1.13897
$479$	−37.5648	−1.71638	−0.858190	−	0.513332i	$-0.828411\pi$
$479$	−37.5648	−1.71638	−0.858190	+	0.513332i	$0.828411\pi$
$480$	95.7883	4.37212
$481$	−23.8675	−1.08826
$482$	−28.1729	−1.28324
$483$	−13.3361	−0.606813
$484$	−47.9355	−2.17889
$485$	−9.89303	−0.449219
$486$	57.3700	2.60236
$487$	−18.1005	−0.820210	−0.410105	−	0.912038i	$-0.634508\pi$
$487$	−18.1005	−0.820210	−0.410105	+	0.912038i	$0.634508\pi$
$488$	87.9756	3.98247
$489$	40.9247	1.85068
$490$	−57.1605	−2.58225
$491$	−1.56429	−0.0705952	−0.0352976	−	0.999377i	$-0.511238\pi$
$491$	−1.56429	−0.0705952	−0.0352976	+	0.999377i	$0.511238\pi$
$492$	83.1582	3.74906
$493$	−1.74968	−0.0788015
$494$	−37.2238	−1.67478
$495$	13.7838	0.619534
$496$	−52.6788	−2.36535
$497$	−7.34802	−0.329604
$498$	−27.2897	−1.22288
$499$	−30.4306	−1.36226	−0.681129	−	0.732163i	$-0.738511\pi$
$499$	−30.4306	−1.36226	−0.681129	+	0.732163i	$0.738511\pi$
$500$	−61.2283	−2.73821
$501$	47.0735	2.10309
$502$	30.2531	1.35026
$503$	12.7126	0.566825	0.283412	−	0.958998i	$-0.408533\pi$
$503$	12.7126	0.566825	0.283412	+	0.958998i	$0.408533\pi$
$504$	−27.5779	−1.22842
$505$	22.5329	1.00270
$506$	−13.3664	−0.594207
$507$	40.5831	1.80236
$508$	−38.1966	−1.69470
$509$	−0.00930885	−0.000412607 0	−0.000206304	−	1.00000i	$-0.500066\pi$
$509$	−0.00930885	−0.000412607 0	−0.000206304		1.00000i	$0.500066\pi$
$510$	8.89939	0.394072
$511$	3.13503	0.138686
$512$	43.1384	1.90646
$513$	4.94879	0.218494
$514$	41.7324	1.84074
$515$	15.1932	0.669492
$516$	70.1768	3.08936
$517$	−3.31154	−0.145641
$518$	11.8003	0.518473
$519$	−20.2158	−0.887376
$520$	143.700	6.30168
$521$	−10.9228	−0.478539	−0.239269	−	0.970953i	$-0.576908\pi$
$521$	−10.9228	−0.478539	−0.239269	+	0.970953i	$0.576908\pi$
$522$	47.2877	2.06973
$523$	−39.9436	−1.74661	−0.873305	−	0.487173i	$-0.838028\pi$
$523$	−39.9436	−1.74661	−0.873305	+	0.487173i	$0.838028\pi$
$524$	−3.82619	−0.167148
$525$	22.2808	0.972412
$526$	−44.1812	−1.92639
$527$	−1.99563	−0.0869309
$528$	−24.7940	−1.07902
$529$	2.71751	0.118153
$530$	−90.2383	−3.91970
$531$	40.2998	1.74886
$532$	12.9938	0.563351
$533$	35.7603	1.54895
$534$	8.62401	0.373198
$535$	−27.2902	−1.17986
$536$	−24.2591	−1.04783
$537$	19.5839	0.845107
$538$	23.2967	1.00439
$539$	6.03289	0.259855
$540$	−32.7327	−1.40859
$541$	−30.0520	−1.29203	−0.646017	−	0.763323i	$-0.723567\pi$
$541$	−30.0520	−1.29203	−0.646017	+	0.763323i	$0.723567\pi$
$542$	7.05050	0.302845
$543$	−19.3895	−0.832084
$544$	−3.61175	−0.154852
$545$	23.2481	0.995841
$546$	−36.7215	−1.57153
$547$	−7.89910	−0.337741	−0.168870	−	0.985638i	$-0.554012\pi$
$547$	−7.89910	−0.337741	−0.168870	+	0.985638i	$0.554012\pi$
$548$	−95.4034	−4.07543
$549$	−44.7074	−1.90807
$550$	22.3313	0.952211
$551$	−13.0040	−0.553988
$552$	96.1122	4.09081
$553$	−1.17081	−0.0497878
$554$	18.4338	0.783177
$555$	42.4096	1.80019
$556$	67.7495	2.87322
$557$	22.7876	0.965542	0.482771	−	0.875747i	$-0.339630\pi$
$557$	22.7876	0.965542	0.482771	+	0.875747i	$0.339630\pi$
$558$	53.9348	2.28324
$559$	30.1779	1.27639
$560$	−35.2636	−1.49016
$561$	−0.939269	−0.0396560
$562$	29.5196	1.24521
$563$	9.59030	0.404183	0.202091	−	0.979367i	$-0.435226\pi$
$563$	9.59030	0.404183	0.202091	+	0.979367i	$0.435226\pi$
$564$	40.7983	1.71792
$565$	26.2419	1.10400
$566$	31.3376	1.31722
$567$	−6.43116	−0.270083
$568$	52.9567	2.22201
$569$	−7.39003	−0.309806	−0.154903	−	0.987930i	$-0.549507\pi$
$569$	−7.39003	−0.309806	−0.154903	+	0.987930i	$0.549507\pi$
$570$	66.1421	2.77039
$571$	−30.0154	−1.25610	−0.628052	−	0.778171i	$-0.716148\pi$
$571$	−30.0154	−1.25610	−0.628052	+	0.778171i	$0.716148\pi$
$572$	−25.9857	−1.08652
$573$	−1.58674	−0.0662870
$574$	−17.6801	−0.737954
$575$	−42.9666	−1.79183
$576$	27.2412	1.13505
$577$	31.1738	1.29778	0.648890	−	0.760882i	$-0.275233\pi$
$577$	31.1738	1.29778	0.648890	+	0.760882i	$0.275233\pi$
$578$	44.0070	1.83045
$579$	5.46201	0.226993
$580$	86.0121	3.57146
$581$	4.09646	0.169950
$582$	−18.2197	−0.755231
$583$	9.52402	0.394445
$584$	−22.5940	−0.934945
$585$	−73.0257	−3.01924
$586$	45.7954	1.89179
$587$	24.8306	1.02487	0.512433	−	0.858727i	$-0.328744\pi$
$587$	24.8306	1.02487	0.512433	+	0.858727i	$0.328744\pi$
$588$	−74.3255	−3.06513
$589$	−14.8319	−0.611138
$590$	103.821	4.27424
$591$	41.5353	1.70853
$592$	−42.2109	−1.73486
$593$	33.8746	1.39106	0.695531	−	0.718496i	$-0.255169\pi$
$593$	33.8746	1.39106	0.695531	+	0.718496i	$0.255169\pi$
$594$	4.89308	0.200766
$595$	−1.33589	−0.0547661
$596$	18.3604	0.752072
$597$	63.2229	2.58754
$598$	70.8143	2.89581
$599$	−38.8067	−1.58560	−0.792799	−	0.609484i	$-0.791377\pi$
$599$	−38.8067	−1.58560	−0.792799	+	0.609484i	$0.791377\pi$
$600$	−160.576	−6.55549
$601$	−7.87625	−0.321279	−0.160640	−	0.987013i	$-0.551356\pi$
$601$	−7.87625	−0.321279	−0.160640	+	0.987013i	$0.551356\pi$
$602$	−14.9202	−0.608100
$603$	12.3280	0.502035
$604$	−29.9984	−1.22062
$605$	36.6277	1.48913
$606$	41.4983	1.68575
$607$	39.7604	1.61383	0.806913	−	0.590671i	$-0.201137\pi$
$607$	39.7604	1.61383	0.806913	+	0.590671i	$0.201137\pi$
$608$	−26.8433	−1.08864
$609$	−12.8285	−0.519836
$610$	−115.176	−4.66333
$611$	17.5444	0.709769
$612$	6.40302	0.258827
$613$	−39.0900	−1.57883	−0.789414	−	0.613861i	$-0.789616\pi$
$613$	−39.0900	−1.57883	−0.789414	+	0.613861i	$0.789616\pi$
$614$	59.8751	2.41636
$615$	−63.5416	−2.56224
$616$	7.49847	0.302122
$617$	−24.8074	−0.998709	−0.499355	−	0.866398i	$-0.666430\pi$
$617$	−24.8074	−0.998709	−0.499355	+	0.866398i	$0.666430\pi$
$618$	27.9809	1.12555
$619$	−36.1258	−1.45202	−0.726010	−	0.687684i	$-0.758627\pi$
$619$	−36.1258	−1.45202	−0.726010	+	0.687684i	$0.758627\pi$
$620$	98.1027	3.93990
$621$	−9.41453	−0.377792
$622$	11.1637	0.447623
$623$	−1.29455	−0.0518651
$624$	131.357	5.25850
$625$	4.42184	0.176874
$626$	82.1446	3.28316
$627$	−6.98084	−0.278788
$628$	−65.6532	−2.61985
$629$	−1.59908	−0.0637593
$630$	36.1044	1.43843
$631$	−26.6604	−1.06133	−0.530667	−	0.847581i	$-0.678058\pi$
$631$	−26.6604	−1.06133	−0.530667	+	0.847581i	$0.678058\pi$
$632$	8.43793	0.335643
$633$	6.24025	0.248028
$634$	21.7316	0.863074
$635$	29.1862	1.15822
$636$	−117.336	−4.65269
$637$	−31.9620	−1.26638
$638$	−12.8576	−0.509037
$639$	−26.9115	−1.06460
$640$	−3.74319	−0.147963
$641$	−8.61135	−0.340128	−0.170064	−	0.985433i	$-0.554397\pi$
$641$	−8.61135	−0.340128	−0.170064	+	0.985433i	$0.554397\pi$
$642$	−50.2597	−1.98359
$643$	−26.5058	−1.04529	−0.522643	−	0.852552i	$-0.675054\pi$
$643$	−26.5058	−1.04529	−0.522643	+	0.852552i	$0.675054\pi$
$644$	−24.7192	−0.974074
$645$	−53.6224	−2.11138
$646$	−2.49392	−0.0981221
$647$	14.1828	0.557582	0.278791	−	0.960352i	$-0.410066\pi$
$647$	14.1828	0.557582	0.278791	+	0.960352i	$0.410066\pi$
$648$	46.3489	1.82076
$649$	−10.9576	−0.430123
$650$	−118.310	−4.64051
$651$	−14.6318	−0.573464
$652$	75.8563	2.97076
$653$	8.94121	0.349897	0.174948	−	0.984578i	$-0.444024\pi$
$653$	8.94121	0.349897	0.174948	+	0.984578i	$0.444024\pi$
$654$	42.8155	1.67422
$655$	2.92361	0.114235
$656$	63.2440	2.46926
$657$	11.4818	0.447947
$658$	−8.67405	−0.338150
$659$	−12.8580	−0.500875	−0.250438	−	0.968133i	$-0.580574\pi$
$659$	−12.8580	−0.500875	−0.250438	+	0.968133i	$0.580574\pi$
$660$	46.1734	1.79730
$661$	26.5195	1.03149	0.515744	−	0.856743i	$-0.327515\pi$
$661$	26.5195	1.03149	0.515744	+	0.856743i	$0.327515\pi$
$662$	27.3999	1.06493
$663$	4.97620	0.193260
$664$	−29.5229	−1.14571
$665$	−9.92860	−0.385014
$666$	43.2174	1.67464
$667$	24.7386	0.957884
$668$	87.2536	3.37594
$669$	23.6834	0.915654
$670$	31.7595	1.22698
$671$	12.1560	0.469278
$672$	−26.4810	−1.02153
$673$	−45.8652	−1.76798	−0.883988	−	0.467510i	$-0.845151\pi$
$673$	−45.8652	−1.76798	−0.883988	+	0.467510i	$0.845151\pi$
$674$	−16.0986	−0.620095
$675$	15.7290	0.605408
$676$	75.2233	2.89320
$677$	−17.9373	−0.689388	−0.344694	−	0.938715i	$-0.612017\pi$
$677$	−17.9373	−0.689388	−0.344694	+	0.938715i	$0.612017\pi$
$678$	48.3290	1.85606
$679$	2.73496	0.104958
$680$	9.62765	0.369204
$681$	−1.98521	−0.0760734
$682$	−14.6650	−0.561550
$683$	−18.7894	−0.718957	−0.359478	−	0.933153i	$-0.617045\pi$
$683$	−18.7894	−0.718957	−0.359478	+	0.933153i	$0.617045\pi$
$684$	47.5886	1.81959
$685$	72.8981	2.78529
$686$	34.3297	1.31072
$687$	−49.3475	−1.88272
$688$	53.3712	2.03476
$689$	−50.4578	−1.92229
$690$	−125.828	−4.79020
$691$	24.8177	0.944109	0.472054	−	0.881569i	$-0.343513\pi$
$691$	24.8177	0.944109	0.472054	+	0.881569i	$0.343513\pi$
$692$	−37.4712	−1.42444
$693$	−3.81057	−0.144751
$694$	−3.69362	−0.140208
$695$	−51.7677	−1.96366
$696$	92.4540	3.50446
$697$	2.39587	0.0907500
$698$	30.9481	1.17140
$699$	−18.7677	−0.709858
$700$	41.2987	1.56095
$701$	−19.1974	−0.725075	−0.362538	−	0.931969i	$-0.618090\pi$
$701$	−19.1974	−0.725075	−0.362538	+	0.931969i	$0.618090\pi$
$702$	−25.9233	−0.978412
$703$	−11.8847	−0.448238
$704$	−7.40693	−0.279159
$705$	−31.1741	−1.17409
$706$	−7.74640	−0.291539
$707$	−6.22931	−0.234277
$708$	134.998	5.07353
$709$	−53.0520	−1.99241	−0.996205	−	0.0870359i	$-0.972261\pi$
$709$	−53.0520	−1.99241	−0.996205	+	0.0870359i	$0.972261\pi$
$710$	−69.3298	−2.60190
$711$	−4.28798	−0.160812
$712$	9.32974	0.349647
$713$	28.2161	1.05670
$714$	−2.46027	−0.0920732
$715$	19.8558	0.742564
$716$	36.2999	1.35659
$717$	24.7413	0.923979
$718$	42.5059	1.58631
$719$	23.8300	0.888711	0.444355	−	0.895851i	$-0.353433\pi$
$719$	23.8300	0.888711	0.444355	+	0.895851i	$0.353433\pi$
$720$	−129.150	−4.81313
$721$	−4.20021	−0.156424
$722$	31.0239	1.15459
$723$	27.9915	1.04102
$724$	−35.9397	−1.33569
$725$	−41.3311	−1.53500
$726$	67.4562	2.50353
$727$	23.6255	0.876221	0.438111	−	0.898921i	$-0.355648\pi$
$727$	23.6255	0.876221	0.438111	+	0.898921i	$0.355648\pi$
$728$	−39.7265	−1.47236
$729$	−37.9871	−1.40693
$730$	29.5795	1.09479
$731$	2.02186	0.0747812
$732$	−149.763	−5.53539
$733$	25.0275	0.924410	0.462205	−	0.886773i	$-0.347058\pi$
$733$	25.0275	0.924410	0.462205	+	0.886773i	$0.347058\pi$
$734$	−69.0507	−2.54871
$735$	56.7925	2.09482
$736$	51.0664	1.88233
$737$	−3.35200	−0.123473
$738$	−64.7519	−2.38355
$739$	−16.7614	−0.616578	−0.308289	−	0.951293i	$-0.599756\pi$
$739$	−16.7614	−0.616578	−0.308289	+	0.951293i	$0.599756\pi$
$740$	78.6087	2.88971
$741$	36.9841	1.35865
$742$	24.9467	0.915822
$743$	−29.6545	−1.08792	−0.543960	−	0.839111i	$-0.683076\pi$
$743$	−29.6545	−1.08792	−0.543960	+	0.839111i	$0.683076\pi$
$744$	105.450	3.86599
$745$	−14.0293	−0.513993
$746$	−10.4352	−0.382058
$747$	15.0029	0.548929
$748$	−1.74099	−0.0636570
$749$	7.54448	0.275669
$750$	86.1622	3.14620
$751$	−17.4148	−0.635476	−0.317738	−	0.948179i	$-0.602923\pi$
$751$	−17.4148	−0.635476	−0.317738	+	0.948179i	$0.602923\pi$
$752$	31.0281	1.13148
$753$	−30.0583	−1.09538
$754$	68.1189	2.48074
$755$	22.9219	0.834215
$756$	9.04908	0.329112
$757$	−16.3751	−0.595163	−0.297582	−	0.954696i	$-0.596180\pi$
$757$	−16.3751	−0.595163	−0.297582	+	0.954696i	$0.596180\pi$
$758$	26.2707	0.954194
$759$	13.2803	0.482044
$760$	71.5547	2.59556
$761$	−10.9558	−0.397147	−0.198573	−	0.980086i	$-0.563631\pi$
$761$	−10.9558	−0.397147	−0.198573	+	0.980086i	$0.563631\pi$
$762$	53.7514	1.94721
$763$	−6.42703	−0.232674
$764$	−2.94112	−0.106406
$765$	−4.89258	−0.176891
$766$	82.0939	2.96617
$767$	58.0528	2.09616
$768$	−44.8871	−1.61972
$769$	−8.92406	−0.321810	−0.160905	−	0.986970i	$-0.551441\pi$
$769$	−8.92406	−0.321810	−0.160905	+	0.986970i	$0.551441\pi$
$770$	−9.81684	−0.353774
$771$	−41.4637	−1.49328
$772$	10.1242	0.364377
$773$	24.1610	0.869010	0.434505	−	0.900669i	$-0.356923\pi$
$773$	24.1610	0.869010	0.434505	+	0.900669i	$0.356923\pi$
$774$	−54.6438	−1.96413
$775$	−47.1410	−1.69335
$776$	−19.7107	−0.707572
$777$	−11.7243	−0.420606
$778$	−77.5833	−2.78149
$779$	17.8066	0.637987
$780$	−244.624	−8.75895
$781$	7.31728	0.261833
$782$	4.74442	0.169660
$783$	−9.05618	−0.323642
$784$	−56.5265	−2.01880
$785$	50.1659	1.79050
$786$	5.38433	0.192053
$787$	−33.6852	−1.20075	−0.600375	−	0.799719i	$-0.704982\pi$
$787$	−33.6852	−1.20075	−0.600375	+	0.799719i	$0.704982\pi$
$788$	76.9882	2.74259
$789$	43.8967	1.56276
$790$	−11.0468	−0.393026
$791$	−7.25466	−0.257946
$792$	27.4625	0.975837
$793$	−64.4019	−2.28698
$794$	73.1063	2.59445
$795$	89.6572	3.17981
$796$	117.187	4.15360
$797$	15.9443	0.564778	0.282389	−	0.959300i	$-0.408873\pi$
$797$	15.9443	0.564778	0.282389	+	0.959300i	$0.408873\pi$
$798$	−18.2852	−0.647290
$799$	1.17544	0.0415840
$800$	−85.3173	−3.01642
$801$	−4.74118	−0.167522
$802$	−48.9830	−1.72965
$803$	−3.12192	−0.110170
$804$	41.2968	1.45643
$805$	18.8881	0.665717
$806$	77.6942	2.73666
$807$	−23.1467	−0.814803
$808$	44.8942	1.57937
$809$	34.2049	1.20258	0.601291	−	0.799030i	$-0.294653\pi$
$809$	34.2049	1.20258	0.601291	+	0.799030i	$0.294653\pi$
$810$	−60.6791	−2.13205
$811$	41.9828	1.47422	0.737108	−	0.675775i	$-0.236191\pi$
$811$	41.9828	1.47422	0.737108	+	0.675775i	$0.236191\pi$
$812$	−23.7784	−0.834457
$813$	−7.00510	−0.245680
$814$	−11.7509	−0.411868
$815$	−57.9621	−2.03032
$816$	8.80068	0.308085
$817$	15.0269	0.525724
$818$	−89.2485	−3.12050
$819$	20.1882	0.705433
$820$	−117.778	−4.11299
$821$	−54.2096	−1.89193	−0.945963	−	0.324274i	$-0.894880\pi$
$821$	−54.2096	−1.89193	−0.945963	+	0.324274i	$0.894880\pi$
$822$	134.254	4.68266
$823$	29.2689	1.02025	0.510124	−	0.860101i	$-0.329599\pi$
$823$	29.2689	1.02025	0.510124	+	0.860101i	$0.329599\pi$
$824$	30.2706	1.05453
$825$	−22.1875	−0.772471
$826$	−28.7017	−0.998659
$827$	17.3924	0.604792	0.302396	−	0.953182i	$-0.402213\pi$
$827$	17.3924	0.604792	0.302396	+	0.953182i	$0.402213\pi$
$828$	−90.5321	−3.14621
$829$	23.9383	0.831413	0.415707	−	0.909499i	$-0.363534\pi$
$829$	23.9383	0.831413	0.415707	+	0.909499i	$0.363534\pi$
$830$	38.6508	1.34159
$831$	−18.3151	−0.635344
$832$	39.2416	1.36046
$833$	−2.14139	−0.0741948
$834$	−95.3391	−3.30132
$835$	−66.6709	−2.30724
$836$	−12.9394	−0.447519
$837$	−10.3292	−0.357029
$838$	−43.8937	−1.51628
$839$	22.8781	0.789841	0.394921	−	0.918715i	$-0.370772\pi$
$839$	22.8781	0.789841	0.394921	+	0.918715i	$0.370772\pi$
$840$	70.5891	2.43555
$841$	−5.20298	−0.179413
$842$	64.7187	2.23035
$843$	−29.3295	−1.01016
$844$	11.5667	0.398141
$845$	−57.4784	−1.97732
$846$	−31.7680	−1.09221
$847$	−10.1259	−0.347929
$848$	−89.2373	−3.06442
$849$	−31.1358	−1.06858
$850$	−7.92656	−0.271879
$851$	22.6093	0.775036
$852$	−90.1492	−3.08846
$853$	6.40602	0.219338	0.109669	−	0.993968i	$-0.465021\pi$
$853$	6.40602	0.219338	0.109669	+	0.993968i	$0.465021\pi$
$854$	31.8408	1.08957
$855$	−36.3626	−1.24358
$856$	−54.3726	−1.85842
$857$	−24.5425	−0.838355	−0.419178	−	0.907904i	$-0.637682\pi$
$857$	−24.5425	−0.838355	−0.419178	+	0.907904i	$0.637682\pi$
$858$	36.5678	1.24841
$859$	39.7032	1.35465	0.677327	−	0.735682i	$-0.263138\pi$
$859$	39.7032	1.35465	0.677327	+	0.735682i	$0.263138\pi$
$860$	−99.3923	−3.38925
$861$	17.5663	0.598657
$862$	−59.5216	−2.02731
$863$	7.01888	0.238925	0.119463	−	0.992839i	$-0.461883\pi$
$863$	7.01888	0.238925	0.119463	+	0.992839i	$0.461883\pi$
$864$	−18.6941	−0.635986
$865$	28.6319	0.973515
$866$	−4.53044	−0.153951
$867$	−43.7236	−1.48493
$868$	−27.1208	−0.920541
$869$	1.16591	0.0395508
$870$	−121.039	−4.10360
$871$	17.7587	0.601732
$872$	46.3192	1.56856
$873$	10.0166	0.339009
$874$	35.2615	1.19274
$875$	−12.9338	−0.437243
$876$	38.4621	1.29952
$877$	−34.0128	−1.14853	−0.574265	−	0.818670i	$-0.694712\pi$
$877$	−34.0128	−1.14853	−0.574265	+	0.818670i	$0.694712\pi$
$878$	−97.7546	−3.29906
$879$	−45.5005	−1.53470
$880$	35.1160	1.18376
$881$	−15.4387	−0.520142	−0.260071	−	0.965590i	$-0.583746\pi$
$881$	−15.4387	−0.520142	−0.260071	+	0.965590i	$0.583746\pi$
$882$	57.8743	1.94873
$883$	5.07109	0.170656	0.0853279	−	0.996353i	$-0.472806\pi$
$883$	5.07109	0.170656	0.0853279	+	0.996353i	$0.472806\pi$
$884$	9.22369	0.310226
$885$	−103.153	−3.46743
$886$	33.4783	1.12473
$887$	−41.3307	−1.38775	−0.693875	−	0.720096i	$-0.744098\pi$
$887$	−41.3307	−1.38775	−0.693875	+	0.720096i	$0.744098\pi$
$888$	84.4960	2.83550
$889$	−8.06862	−0.270613
$890$	−12.2143	−0.409424
$891$	6.40426	0.214551
$892$	43.8987	1.46984
$893$	8.73610	0.292342
$894$	−25.8373	−0.864129
$895$	−27.7369	−0.927142
$896$	1.03482	0.0345709
$897$	−70.3583	−2.34920
$898$	0.604312	0.0201662
$899$	27.1421	0.905240
$900$	151.253	5.04177
$901$	−3.38057	−0.112623
$902$	17.6062	0.586221
$903$	14.8241	0.493315
$904$	52.2839	1.73894
$905$	27.4616	0.912856
$906$	42.2147	1.40249
$907$	58.0434	1.92730	0.963650	−	0.267169i	$-0.0860881\pi$
$907$	58.0434	1.92730	0.963650	+	0.267169i	$0.0860881\pi$
$908$	−3.67971	−0.122115
$909$	−22.8143	−0.756703
$910$	52.0091	1.72409
$911$	−22.5945	−0.748591	−0.374295	−	0.927310i	$-0.622115\pi$
$911$	−22.5945	−0.748591	−0.374295	+	0.927310i	$0.622115\pi$
$912$	65.4085	2.16589
$913$	−4.07932	−0.135006
$914$	−76.0163	−2.51440
$915$	114.434	3.78308
$916$	−91.4685	−3.02220
$917$	−0.808243	−0.0266905
$918$	−1.73681	−0.0573233
$919$	18.1867	0.599925	0.299963	−	0.953951i	$-0.403026\pi$
$919$	18.1867	0.599925	0.299963	+	0.953951i	$0.403026\pi$
$920$	−136.125	−4.48791
$921$	−59.4896	−1.96025
$922$	−53.5827	−1.76465
$923$	−38.7666	−1.27602
$924$	−12.7648	−0.419931
$925$	−37.7736	−1.24199
$926$	−18.1540	−0.596579
$927$	−15.3829	−0.505241
$928$	49.1227	1.61253
$929$	−12.6809	−0.416046	−0.208023	−	0.978124i	$-0.566703\pi$
$929$	−12.6809	−0.416046	−0.208023	+	0.978124i	$0.566703\pi$
$930$	−138.053	−4.52694
$931$	−15.9152	−0.521601
$932$	−34.7870	−1.13949
$933$	−11.0918	−0.363130
$934$	59.9086	1.96027
$935$	1.33030	0.0435054
$936$	−145.495	−4.75565
$937$	−37.8751	−1.23733	−0.618664	−	0.785656i	$-0.712326\pi$
$937$	−37.8751	−1.23733	−0.618664	+	0.785656i	$0.712326\pi$
$938$	−8.78004	−0.286678
$939$	−81.6157	−2.66343
$940$	−57.7832	−1.88468
$941$	17.9925	0.586537	0.293269	−	0.956030i	$-0.405257\pi$
$941$	17.9925	0.586537	0.293269	+	0.956030i	$0.405257\pi$
$942$	92.3891	3.01020
$943$	−33.8751	−1.10312
$944$	102.669	3.34160
$945$	−6.91444	−0.224927
$946$	14.8577	0.483067
$947$	7.86007	0.255418	0.127709	−	0.991812i	$-0.459238\pi$
$947$	7.86007	0.255418	0.127709	+	0.991812i	$0.459238\pi$
$948$	−14.3641	−0.466523
$949$	16.5398	0.536903
$950$	−58.9118	−1.91135
$951$	−21.5917	−0.700160
$952$	−2.66160	−0.0862629
$953$	−36.1381	−1.17063	−0.585314	−	0.810807i	$-0.699029\pi$
$953$	−36.1381	−1.17063	−0.585314	+	0.810807i	$0.699029\pi$
$954$	91.3651	2.95805
$955$	2.24732	0.0727215
$956$	45.8594	1.48320
$957$	12.7748	0.412951
$958$	97.9835	3.16570
$959$	−20.1529	−0.650773
$960$	−69.7274	−2.25044
$961$	−0.0425551	−0.00137275
$962$	62.2556	2.00720
$963$	27.6310	0.890397
$964$	51.8839	1.67107
$965$	−7.73592	−0.249028
$966$	34.7856	1.11921
$967$	−8.94963	−0.287801	−0.143900	−	0.989592i	$-0.545964\pi$
$967$	−8.94963	−0.287801	−0.143900	+	0.989592i	$0.545964\pi$
$968$	72.9764	2.34555
$969$	2.47787	0.0796005
$970$	25.8048	0.828543
$971$	50.0652	1.60667	0.803335	−	0.595528i	$-0.203057\pi$
$971$	50.0652	1.60667	0.803335	+	0.595528i	$0.203057\pi$
$972$	−105.654	−3.38886
$973$	14.3114	0.458801
$974$	47.2129	1.51280
$975$	117.549	3.76457
$976$	−113.898	−3.64580
$977$	−7.06573	−0.226053	−0.113026	−	0.993592i	$-0.536054\pi$
$977$	−7.06573	−0.226053	−0.113026	+	0.993592i	$0.536054\pi$
$978$	−106.747	−3.41340
$979$	1.28914	0.0412009
$980$	105.268	3.36267
$981$	−23.5385	−0.751525
$982$	4.08026	0.130206
$983$	−21.2299	−0.677130	−0.338565	−	0.940943i	$-0.609942\pi$
$983$	−21.2299	−0.677130	−0.338565	+	0.940943i	$0.609942\pi$
$984$	−126.599	−4.03583
$985$	−58.8270	−1.87438
$986$	4.56383	0.145342
$987$	8.61820	0.274320
$988$	68.5523	2.18094
$989$	−28.5870	−0.909014
$990$	−35.9533	−1.14267
$991$	−9.14180	−0.290399	−0.145199	−	0.989402i	$-0.546382\pi$
$991$	−9.14180	−0.290399	−0.145199	+	0.989402i	$0.546382\pi$
$992$	56.0278	1.77888
$993$	−27.2235	−0.863912
$994$	19.1665	0.607923
$995$	−89.5434	−2.83872
$996$	50.2574	1.59247
$997$	−13.0496	−0.413285	−0.206643	−	0.978416i	$-0.566254\pi$
$997$	−13.0496	−0.413285	−0.206643	+	0.978416i	$0.566254\pi$
$998$	79.3746	2.51256
$999$	−8.27668	−0.261863

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.16	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.16	✓	327	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:	\( N \)	\(=\)	\( 8017 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	8017.a (trivial)

\(f(q)\)	\(=\)	\(q-2.60838 q^{2} +2.59159 q^{3} +4.80367 q^{4} -3.67050 q^{5} -6.75986 q^{6} +1.01472 q^{7} -7.31304 q^{8} +3.71634 q^{9} +O(q^{10})\)	\(q-2.60838 q^{2} +2.59159 q^{3} +4.80367 q^{4} -3.67050 q^{5} -6.75986 q^{6} +1.01472 q^{7} -7.31304 q^{8} +3.71634 q^{9} +9.57408 q^{10} -1.01048 q^{11} +12.4491 q^{12} +5.35346 q^{13} -2.64679 q^{14} -9.51244 q^{15} +9.46788 q^{16} +0.358672 q^{17} -9.69364 q^{18} +2.66572 q^{19} -17.6319 q^{20} +2.62975 q^{21} +2.63571 q^{22} -5.07124 q^{23} -18.9524 q^{24} +8.47259 q^{25} -13.9639 q^{26} +1.85645 q^{27} +4.87439 q^{28} -4.87822 q^{29} +24.8121 q^{30} -5.56394 q^{31} -10.0698 q^{32} -2.61874 q^{33} -0.935553 q^{34} -3.72455 q^{35} +17.8520 q^{36} -4.45833 q^{37} -6.95322 q^{38} +13.8740 q^{39} +26.8425 q^{40} +6.67984 q^{41} -6.85939 q^{42} +5.63708 q^{43} -4.85400 q^{44} -13.6408 q^{45} +13.2278 q^{46} +3.27720 q^{47} +24.5369 q^{48} -5.97034 q^{49} -22.0998 q^{50} +0.929530 q^{51} +25.7162 q^{52} -9.42527 q^{53} -4.84234 q^{54} +3.70896 q^{55} -7.42071 q^{56} +6.90845 q^{57} +12.7243 q^{58} +10.8440 q^{59} -45.6946 q^{60} -12.0300 q^{61} +14.5129 q^{62} +3.77105 q^{63} +7.33013 q^{64} -19.6499 q^{65} +6.83069 q^{66} +3.31724 q^{67} +1.72294 q^{68} -13.1426 q^{69} +9.71504 q^{70} -7.24140 q^{71} -27.1777 q^{72} +3.08954 q^{73} +11.6290 q^{74} +21.9575 q^{75} +12.8052 q^{76} -1.02536 q^{77} -36.1887 q^{78} -1.15382 q^{79} -34.7519 q^{80} -6.33785 q^{81} -17.4236 q^{82} +4.03702 q^{83} +12.6324 q^{84} -1.31650 q^{85} -14.7037 q^{86} -12.6423 q^{87} +7.38967 q^{88} -1.27577 q^{89} +35.5805 q^{90} +5.43228 q^{91} -24.3606 q^{92} -14.4195 q^{93} -8.54819 q^{94} -9.78454 q^{95} -26.0968 q^{96} +2.69528 q^{97} +15.5729 q^{98} -3.75528 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9} - 48 q^{10} - 70 q^{11} - 120 q^{12} - 53 q^{13} - 52 q^{14} - 77 q^{15} + 295 q^{16} - 164 q^{17} - 58 q^{18} - 47 q^{19} - 153 q^{20} - 39 q^{21} - 68 q^{22} - 256 q^{23} - 107 q^{24} + 288 q^{25} - 95 q^{26} - 189 q^{27} - 167 q^{28} - 99 q^{29} - 81 q^{30} - 71 q^{31} - 146 q^{32} - 95 q^{33} - 40 q^{34} - 192 q^{35} + 261 q^{36} - 54 q^{37} - 179 q^{38} - 115 q^{39} - 121 q^{40} - 111 q^{41} - 62 q^{42} - 110 q^{43} - 157 q^{44} - 137 q^{45} - 11 q^{46} - 324 q^{47} - 236 q^{48} + 296 q^{49} - 73 q^{50} - 88 q^{51} - 138 q^{52} - 170 q^{53} - 127 q^{54} - 151 q^{55} - 151 q^{56} - 106 q^{57} - 81 q^{58} - 123 q^{59} - 83 q^{60} - 62 q^{61} - 287 q^{62} - 400 q^{63} + 263 q^{64} - 143 q^{65} - 64 q^{66} - 95 q^{67} - 442 q^{68} - 22 q^{69} - 26 q^{70} - 210 q^{71} - 129 q^{72} - 121 q^{73} - 159 q^{74} - 194 q^{75} - 86 q^{76} - 178 q^{77} - 68 q^{78} - 145 q^{79} - 338 q^{80} + 259 q^{81} - 103 q^{82} - 418 q^{83} - 102 q^{84} - 40 q^{85} - 89 q^{86} - 372 q^{87} - 186 q^{88} - 100 q^{89} - 150 q^{90} - 69 q^{91} - 458 q^{92} - 81 q^{93} - 46 q^{94} - 377 q^{95} - 190 q^{96} - 87 q^{97} - 147 q^{98} - 171 q^{99}+O(q^{100}) \) 327 * q - 23 * q^2 - 48 * q^3 + 315 * q^4 - 55 * q^5 - 38 * q^6 - 87 * q^7 - 69 * q^8 + 303 * q^9 - 48 * q^10 - 70 * q^11 - 120 * q^12 - 53 * q^13 - 52 * q^14 - 77 * q^15 + 295 * q^16 - 164 * q^17 - 58 * q^18 - 47 * q^19 - 153 * q^20 - 39 * q^21 - 68 * q^22 - 256 * q^23 - 107 * q^24 + 288 * q^25 - 95 * q^26 - 189 * q^27 - 167 * q^28 - 99 * q^29 - 81 * q^30 - 71 * q^31 - 146 * q^32 - 95 * q^33 - 40 * q^34 - 192 * q^35 + 261 * q^36 - 54 * q^37 - 179 * q^38 - 115 * q^39 - 121 * q^40 - 111 * q^41 - 62 * q^42 - 110 * q^43 - 157 * q^44 - 137 * q^45 - 11 * q^46 - 324 * q^47 - 236 * q^48 + 296 * q^49 - 73 * q^50 - 88 * q^51 - 138 * q^52 - 170 * q^53 - 127 * q^54 - 151 * q^55 - 151 * q^56 - 106 * q^57 - 81 * q^58 - 123 * q^59 - 83 * q^60 - 62 * q^61 - 287 * q^62 - 400 * q^63 + 263 * q^64 - 143 * q^65 - 64 * q^66 - 95 * q^67 - 442 * q^68 - 22 * q^69 - 26 * q^70 - 210 * q^71 - 129 * q^72 - 121 * q^73 - 159 * q^74 - 194 * q^75 - 86 * q^76 - 178 * q^77 - 68 * q^78 - 145 * q^79 - 338 * q^80 + 259 * q^81 - 103 * q^82 - 418 * q^83 - 102 * q^84 - 40 * q^85 - 89 * q^86 - 372 * q^87 - 186 * q^88 - 100 * q^89 - 150 * q^90 - 69 * q^91 - 458 * q^92 - 81 * q^93 - 46 * q^94 - 377 * q^95 - 190 * q^96 - 87 * q^97 - 147 * q^98 - 171 * q^99

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