LMFDB - Embedded newform 8017.2.a.a.1.4

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			1.4
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)

$f(q)$	$=$	$q-2.76749 q^{2} +2.84439 q^{3} +5.65899 q^{4} -0.717749 q^{5} -7.87182 q^{6} -1.28590 q^{7} -10.1262 q^{8} +5.09057 q^{9} +O(q^{10})$	\(q-2.76749 q^{2} +2.84439 q^{3} +5.65899 q^{4} -0.717749 q^{5} -7.87182 q^{6} -1.28590 q^{7} -10.1262 q^{8} +5.09057 q^{9} +1.98636 q^{10} +5.40602 q^{11} +16.0964 q^{12} -4.14764 q^{13} +3.55872 q^{14} -2.04156 q^{15} +16.7062 q^{16} +3.10244 q^{17} -14.0881 q^{18} +0.741106 q^{19} -4.06174 q^{20} -3.65761 q^{21} -14.9611 q^{22} -2.73356 q^{23} -28.8029 q^{24} -4.48484 q^{25} +11.4786 q^{26} +5.94641 q^{27} -7.27690 q^{28} -8.22070 q^{29} +5.65000 q^{30} +4.49784 q^{31} -25.9818 q^{32} +15.3769 q^{33} -8.58598 q^{34} +0.922955 q^{35} +28.8075 q^{36} +0.940453 q^{37} -2.05100 q^{38} -11.7975 q^{39} +7.26808 q^{40} +4.07542 q^{41} +10.1224 q^{42} +0.422141 q^{43} +30.5926 q^{44} -3.65376 q^{45} +7.56509 q^{46} -10.3625 q^{47} +47.5190 q^{48} -5.34646 q^{49} +12.4117 q^{50} +8.82457 q^{51} -23.4715 q^{52} -10.1988 q^{53} -16.4566 q^{54} -3.88017 q^{55} +13.0213 q^{56} +2.10800 q^{57} +22.7507 q^{58} +0.327670 q^{59} -11.5532 q^{60} +1.87631 q^{61} -12.4477 q^{62} -6.54597 q^{63} +38.4918 q^{64} +2.97697 q^{65} -42.5553 q^{66} -5.45030 q^{67} +17.5567 q^{68} -7.77531 q^{69} -2.55427 q^{70} -1.02627 q^{71} -51.5482 q^{72} -15.8318 q^{73} -2.60269 q^{74} -12.7566 q^{75} +4.19391 q^{76} -6.95161 q^{77} +32.6495 q^{78} -16.9936 q^{79} -11.9909 q^{80} +1.64221 q^{81} -11.2787 q^{82} -3.72875 q^{83} -20.6984 q^{84} -2.22678 q^{85} -1.16827 q^{86} -23.3829 q^{87} -54.7425 q^{88} -12.3663 q^{89} +10.1117 q^{90} +5.33346 q^{91} -15.4692 q^{92} +12.7936 q^{93} +28.6782 q^{94} -0.531929 q^{95} -73.9024 q^{96} +16.4635 q^{97} +14.7963 q^{98} +27.5197 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−2.76749	−1.95691	−0.978455	−	0.206461i	$-0.933805\pi$
$2$	−2.76749	−1.95691	−0.978455	+	0.206461i	$0.933805\pi$
$3$	2.84439	1.64221	0.821106	−	0.570776i	$-0.193358\pi$
$3$	2.84439	1.64221	0.821106	+	0.570776i	$0.193358\pi$
$4$	5.65899	2.82950
$5$	−0.717749	−0.320987	−0.160494	−	0.987037i	$-0.551309\pi$
$5$	−0.717749	−0.320987	−0.160494	+	0.987037i	$0.551309\pi$
$6$	−7.87182	−3.21366
$7$	−1.28590	−0.486025	−0.243012	−	0.970023i	$-0.578136\pi$
$7$	−1.28590	−0.486025	−0.243012	+	0.970023i	$0.578136\pi$
$8$	−10.1262	−3.58016
$9$	5.09057	1.69686
$10$	1.98636	0.628143
$11$	5.40602	1.62998	0.814989	−	0.579477i	$-0.196743\pi$
$11$	5.40602	1.62998	0.814989	+	0.579477i	$0.196743\pi$
$12$	16.0964	4.64663
$13$	−4.14764	−1.15035	−0.575175	−	0.818031i	$-0.695066\pi$
$13$	−4.14764	−1.15035	−0.575175	+	0.818031i	$0.695066\pi$
$14$	3.55872	0.951107
$15$	−2.04156	−0.527129
$16$	16.7062	4.17655
$17$	3.10244	0.752453	0.376227	−	0.926528i	$-0.377221\pi$
$17$	3.10244	0.752453	0.376227	+	0.926528i	$0.377221\pi$
$18$	−14.0881	−3.32060
$19$	0.741106	0.170021	0.0850107	−	0.996380i	$-0.472908\pi$
$19$	0.741106	0.170021	0.0850107	+	0.996380i	$0.472908\pi$
$20$	−4.06174	−0.908232
$21$	−3.65761	−0.798156
$22$	−14.9611	−3.18972
$23$	−2.73356	−0.569986	−0.284993	−	0.958530i	$-0.591991\pi$
$23$	−2.73356	−0.569986	−0.284993	+	0.958530i	$0.591991\pi$
$24$	−28.8029	−5.87937
$25$	−4.48484	−0.896967
$26$	11.4786	2.25113
$27$	5.94641	1.14439
$28$	−7.27690	−1.37521
$29$	−8.22070	−1.52655	−0.763273	−	0.646077i	$-0.776409\pi$
$29$	−8.22070	−1.52655	−0.763273	+	0.646077i	$0.776409\pi$
$30$	5.65000	1.03154
$31$	4.49784	0.807835	0.403918	−	0.914795i	$-0.367648\pi$
$31$	4.49784	0.807835	0.403918	+	0.914795i	$0.367648\pi$
$32$	−25.9818	−4.59297
$33$	15.3769	2.67677
$34$	−8.58598	−1.47248
$35$	0.922955	0.156008
$36$	28.8075	4.80125
$37$	0.940453	0.154609	0.0773047	−	0.997008i	$-0.475369\pi$
$37$	0.940453	0.154609	0.0773047	+	0.997008i	$0.475369\pi$
$38$	−2.05100	−0.332717
$39$	−11.7975	−1.88912
$40$	7.26808	1.14919
$41$	4.07542	0.636474	0.318237	−	0.948011i	$-0.396909\pi$
$41$	4.07542	0.636474	0.318237	+	0.948011i	$0.396909\pi$
$42$	10.1224	1.56192
$43$	0.422141	0.0643759	0.0321879	−	0.999482i	$-0.489752\pi$
$43$	0.422141	0.0643759	0.0321879	+	0.999482i	$0.489752\pi$
$44$	30.5926	4.61201
$45$	−3.65376	−0.544670
$46$	7.56509	1.11541
$47$	−10.3625	−1.51153	−0.755765	−	0.654843i	$-0.772735\pi$
$47$	−10.3625	−1.51153	−0.755765	+	0.654843i	$0.772735\pi$
$48$	47.5190	6.85877
$49$	−5.34646	−0.763780
$50$	12.4117	1.75528
$51$	8.82457	1.23569
$52$	−23.4715	−3.25491
$53$	−10.1988	−1.40091	−0.700456	−	0.713696i	$-0.747020\pi$
$53$	−10.1988	−1.40091	−0.700456	+	0.713696i	$0.747020\pi$
$54$	−16.4566	−2.23946
$55$	−3.88017	−0.523202
$56$	13.0213	1.74005
$57$	2.10800	0.279211
$58$	22.7507	2.98731
$59$	0.327670	0.0426590	0.0213295	−	0.999773i	$-0.493210\pi$
$59$	0.327670	0.0426590	0.0213295	+	0.999773i	$0.493210\pi$
$60$	−11.5532	−1.49151
$61$	1.87631	0.240236	0.120118	−	0.992760i	$-0.461673\pi$
$61$	1.87631	0.240236	0.120118	+	0.992760i	$0.461673\pi$
$62$	−12.4477	−1.58086
$63$	−6.54597	−0.824715
$64$	38.4918	4.81148
$65$	2.97697	0.369248
$66$	−42.5553	−5.23819
$67$	−5.45030	−0.665860	−0.332930	−	0.942952i	$-0.608037\pi$
$67$	−5.45030	−0.665860	−0.332930	+	0.942952i	$0.608037\pi$
$68$	17.5567	2.12906
$69$	−7.77531	−0.936038
$70$	−2.55427	−0.305293
$71$	−1.02627	−0.121796	−0.0608979	−	0.998144i	$-0.519396\pi$
$71$	−1.02627	−0.121796	−0.0608979	+	0.998144i	$0.519396\pi$
$72$	−51.5482	−6.07502
$73$	−15.8318	−1.85297	−0.926483	−	0.376335i	$-0.877184\pi$
$73$	−15.8318	−1.85297	−0.926483	+	0.376335i	$0.877184\pi$
$74$	−2.60269	−0.302557
$75$	−12.7566	−1.47301
$76$	4.19391	0.481075
$77$	−6.95161	−0.792210
$78$	32.6495	3.69683
$79$	−16.9936	−1.91193	−0.955966	−	0.293478i	$-0.905187\pi$
$79$	−16.9936	−1.91193	−0.955966	+	0.293478i	$0.905187\pi$
$80$	−11.9909	−1.34062
$81$	1.64221	0.182467
$82$	−11.2787	−1.24552
$83$	−3.72875	−0.409283	−0.204642	−	0.978837i	$-0.565603\pi$
$83$	−3.72875	−0.409283	−0.204642	+	0.978837i	$0.565603\pi$
$84$	−20.6984	−2.25838
$85$	−2.22678	−0.241528
$86$	−1.16827	−0.125978
$87$	−23.3829	−2.50691
$88$	−54.7425	−5.83557
$89$	−12.3663	−1.31083	−0.655413	−	0.755271i	$-0.727505\pi$
$89$	−12.3663	−1.31083	−0.655413	+	0.755271i	$0.727505\pi$
$90$	10.1117	1.06587
$91$	5.33346	0.559098
$92$	−15.4692	−1.61277
$93$	12.7936	1.32664
$94$	28.6782	2.95793
$95$	−0.531929	−0.0545747
$96$	−73.9024	−7.54263
$97$	16.4635	1.67162	0.835809	−	0.549021i	$-0.184999\pi$
$97$	16.4635	1.67162	0.835809	+	0.549021i	$0.184999\pi$
$98$	14.7963	1.49465
$99$	27.5197	2.76584
$100$	−25.3796	−2.53796
$101$	2.65495	0.264177	0.132089	−	0.991238i	$-0.457832\pi$
$101$	2.65495	0.264177	0.132089	+	0.991238i	$0.457832\pi$
$102$	−24.4219	−2.41813
$103$	13.3275	1.31320	0.656600	−	0.754239i	$-0.271994\pi$
$103$	13.3275	1.31320	0.656600	+	0.754239i	$0.271994\pi$
$104$	41.9999	4.11843
$105$	2.62525	0.256198
$106$	28.2250	2.74146
$107$	−15.8620	−1.53343	−0.766717	−	0.641985i	$-0.778111\pi$
$107$	−15.8620	−1.53343	−0.766717	+	0.641985i	$0.778111\pi$
$108$	33.6507	3.23804
$109$	2.52936	0.242269	0.121134	−	0.992636i	$-0.461347\pi$
$109$	2.52936	0.242269	0.121134	+	0.992636i	$0.461347\pi$
$110$	10.7383	1.02386
$111$	2.67502	0.253901
$112$	−21.4825	−2.02991
$113$	8.69391	0.817854	0.408927	−	0.912567i	$-0.365903\pi$
$113$	8.69391	0.817854	0.408927	+	0.912567i	$0.365903\pi$
$114$	−5.83386	−0.546391
$115$	1.96201	0.182958
$116$	−46.5208	−4.31935
$117$	−21.1139	−1.95198
$118$	−0.906822	−0.0834797
$119$	−3.98944	−0.365711
$120$	20.6733	1.88720
$121$	18.2251	1.65683
$122$	−5.19266	−0.470121
$123$	11.5921	1.04522
$124$	25.4532	2.28577
$125$	6.80774	0.608902
$126$	18.1159	1.61389
$127$	−10.2795	−0.912154	−0.456077	−	0.889940i	$-0.650746\pi$
$127$	−10.2795	−0.912154	−0.456077	+	0.889940i	$0.650746\pi$
$128$	−54.5622	−4.82266
$129$	1.20073	0.105719
$130$	−8.23873	−0.722584
$131$	6.07475	0.530753	0.265377	−	0.964145i	$-0.414504\pi$
$131$	6.07475	0.530753	0.265377	+	0.964145i	$0.414504\pi$
$132$	87.0175	7.57390
$133$	−0.952990	−0.0826347
$134$	15.0836	1.30303
$135$	−4.26803	−0.367334
$136$	−31.4160	−2.69390
$137$	2.84322	0.242913	0.121456	−	0.992597i	$-0.461244\pi$
$137$	2.84322	0.242913	0.121456	+	0.992597i	$0.461244\pi$
$138$	21.5181	1.83174
$139$	13.3248	1.13020	0.565098	−	0.825024i	$-0.308838\pi$
$139$	13.3248	1.13020	0.565098	+	0.825024i	$0.308838\pi$
$140$	5.22299	0.441424
$141$	−29.4751	−2.48225
$142$	2.84019	0.238344
$143$	−22.4223	−1.87504
$144$	85.0441	7.08701
$145$	5.90040	0.490002
$146$	43.8142	3.62609
$147$	−15.2074	−1.25429
$148$	5.32201	0.437467
$149$	−20.1288	−1.64902	−0.824508	−	0.565850i	$-0.808548\pi$
$149$	−20.1288	−1.64902	−0.824508	+	0.565850i	$0.808548\pi$
$150$	35.3038	2.88255
$151$	−3.23684	−0.263410	−0.131705	−	0.991289i	$-0.542045\pi$
$151$	−3.23684	−0.263410	−0.131705	+	0.991289i	$0.542045\pi$
$152$	−7.50460	−0.608703
$153$	15.7932	1.27681
$154$	19.2385	1.55028
$155$	−3.22832	−0.259305
$156$	−66.7621	−5.34525
$157$	−8.82461	−0.704281	−0.352140	−	0.935947i	$-0.614546\pi$
$157$	−8.82461	−0.704281	−0.352140	+	0.935947i	$0.614546\pi$
$158$	47.0296	3.74148
$159$	−29.0094	−2.30059
$160$	18.6484	1.47429
$161$	3.51509	0.277028
$162$	−4.54479	−0.357072
$163$	18.8945	1.47993	0.739965	−	0.672646i	$-0.234842\pi$
$163$	18.8945	1.47993	0.739965	+	0.672646i	$0.234842\pi$
$164$	23.0628	1.80090
$165$	−11.0367	−0.859208
$166$	10.3193	0.800930
$167$	−6.60769	−0.511319	−0.255659	−	0.966767i	$-0.582293\pi$
$167$	−6.60769	−0.511319	−0.255659	+	0.966767i	$0.582293\pi$
$168$	37.0377	2.85752
$169$	4.20294	0.323303
$170$	6.16258	0.472648
$171$	3.77265	0.288502
$172$	2.38889	0.182151
$173$	−17.7797	−1.35176	−0.675882	−	0.737010i	$-0.736237\pi$
$173$	−17.7797	−1.35176	−0.675882	+	0.737010i	$0.736237\pi$
$174$	64.7119	4.90580
$175$	5.76706	0.435948
$176$	90.3141	6.80768
$177$	0.932022	0.0700550
$178$	34.2236	2.56517
$179$	13.8521	1.03535	0.517676	−	0.855577i	$-0.326797\pi$
$179$	13.8521	1.03535	0.517676	+	0.855577i	$0.326797\pi$
$180$	−20.6766	−1.54114
$181$	23.4636	1.74403	0.872016	−	0.489477i	$-0.162812\pi$
$181$	23.4636	1.74403	0.872016	+	0.489477i	$0.162812\pi$
$182$	−14.7603	−1.09411
$183$	5.33695	0.394519
$184$	27.6806	2.04064
$185$	−0.675009	−0.0496277
$186$	−35.4062	−2.59611
$187$	16.7719	1.22648
$188$	−58.6415	−4.27687
$189$	−7.64649	−0.556201
$190$	1.47211	0.106798
$191$	3.61373	0.261481	0.130740	−	0.991417i	$-0.458265\pi$
$191$	3.61373	0.261481	0.130740	+	0.991417i	$0.458265\pi$
$192$	109.486	7.90147
$193$	7.81541	0.562565	0.281283	−	0.959625i	$-0.409240\pi$
$193$	7.81541	0.562565	0.281283	+	0.959625i	$0.409240\pi$
$194$	−45.5626	−3.27120
$195$	8.46767	0.606382
$196$	−30.2556	−2.16111
$197$	−13.1476	−0.936727	−0.468364	−	0.883536i	$-0.655156\pi$
$197$	−13.1476	−0.936727	−0.468364	+	0.883536i	$0.655156\pi$
$198$	−76.1606	−5.41250
$199$	1.22325	0.0867139	0.0433569	−	0.999060i	$-0.486195\pi$
$199$	1.22325	0.0867139	0.0433569	+	0.999060i	$0.486195\pi$
$200$	45.4144	3.21128
$201$	−15.5028	−1.09348
$202$	−7.34754	−0.516971
$203$	10.5710	0.741939
$204$	49.9382	3.49637
$205$	−2.92513	−0.204300
$206$	−36.8838	−2.56981
$207$	−13.9154	−0.967185
$208$	−69.2913	−4.80449
$209$	4.00644	0.277131
$210$	−7.26534	−0.501356
$211$	−2.24843	−0.154788	−0.0773942	−	0.997001i	$-0.524660\pi$
$211$	−2.24843	−0.154788	−0.0773942	+	0.997001i	$0.524660\pi$
$212$	−57.7149	−3.96387
$213$	−2.91912	−0.200015
$214$	43.8978	3.00079
$215$	−0.302991	−0.0206638
$216$	−60.2146	−4.09708
$217$	−5.78377	−0.392628
$218$	−6.99998	−0.474098
$219$	−45.0317	−3.04296
$220$	−21.9578	−1.48040
$221$	−12.8678	−0.865584
$222$	−7.40308	−0.496862
$223$	14.3480	0.960816	0.480408	−	0.877045i	$-0.340489\pi$
$223$	14.3480	0.960816	0.480408	+	0.877045i	$0.340489\pi$
$224$	33.4100	2.23230
$225$	−22.8304	−1.52203
$226$	−24.0603	−1.60047
$227$	20.6592	1.37120	0.685600	−	0.727979i	$-0.259540\pi$
$227$	20.6592	1.37120	0.685600	+	0.727979i	$0.259540\pi$
$228$	11.9291	0.790027
$229$	25.5365	1.68750	0.843749	−	0.536737i	$-0.180343\pi$
$229$	25.5365	1.68750	0.843749	+	0.536737i	$0.180343\pi$
$230$	−5.42984	−0.358033
$231$	−19.7731	−1.30098
$232$	83.2445	5.46527
$233$	−10.2044	−0.668513	−0.334256	−	0.942482i	$-0.608485\pi$
$233$	−10.2044	−0.668513	−0.334256	+	0.942482i	$0.608485\pi$
$234$	58.4324	3.81985
$235$	7.43770	0.485182
$236$	1.85428	0.120703
$237$	−48.3365	−3.13980
$238$	11.0407	0.715664
$239$	−16.8980	−1.09304	−0.546520	−	0.837446i	$-0.684048\pi$
$239$	−16.8980	−1.09304	−0.546520	+	0.837446i	$0.684048\pi$
$240$	−34.1067	−2.20158
$241$	−5.00085	−0.322133	−0.161067	−	0.986944i	$-0.551493\pi$
$241$	−5.00085	−0.322133	−0.161067	+	0.986944i	$0.551493\pi$
$242$	−50.4377	−3.24226
$243$	−13.1681	−0.844737
$244$	10.6180	0.679748
$245$	3.83742	0.245164
$246$	−32.0810	−2.04541
$247$	−3.07384	−0.195584
$248$	−45.5460	−2.89218
$249$	−10.6060	−0.672129
$250$	−18.8403	−1.19157
$251$	−26.3820	−1.66522	−0.832609	−	0.553861i	$-0.813154\pi$
$251$	−26.3820	−1.66522	−0.832609	+	0.553861i	$0.813154\pi$
$252$	−37.0436	−2.33353
$253$	−14.7777	−0.929065
$254$	28.4483	1.78500
$255$	−6.33383	−0.396640
$256$	74.0165	4.62603
$257$	30.6373	1.91110	0.955552	−	0.294822i	$-0.0952605\pi$
$257$	30.6373	1.91110	0.955552	+	0.294822i	$0.0952605\pi$
$258$	−3.32302	−0.206882
$259$	−1.20933	−0.0751441
$260$	16.8466	1.04478
$261$	−41.8480	−2.59033
$262$	−16.8118	−1.03864
$263$	12.3879	0.763871	0.381935	−	0.924189i	$-0.375258\pi$
$263$	12.3879	0.763871	0.381935	+	0.924189i	$0.375258\pi$
$264$	−155.709	−9.58324
$265$	7.32018	0.449675
$266$	2.63739	0.161709
$267$	−35.1746	−2.15265
$268$	−30.8432	−1.88405
$269$	−8.95171	−0.545795	−0.272898	−	0.962043i	$-0.587982\pi$
$269$	−8.95171	−0.545795	−0.272898	+	0.962043i	$0.587982\pi$
$270$	11.8117	0.718839
$271$	9.40697	0.571433	0.285716	−	0.958314i	$-0.407768\pi$
$271$	9.40697	0.571433	0.285716	+	0.958314i	$0.407768\pi$
$272$	51.8300	3.14266
$273$	15.1705	0.918158
$274$	−7.86858	−0.475358
$275$	−24.2451	−1.46204
$276$	−44.0004	−2.64851
$277$	−3.01603	−0.181216	−0.0906078	−	0.995887i	$-0.528881\pi$
$277$	−3.01603	−0.181216	−0.0906078	+	0.995887i	$0.528881\pi$
$278$	−36.8763	−2.21169
$279$	22.8966	1.37078
$280$	−9.34604	−0.558533
$281$	−12.7735	−0.762003	−0.381002	−	0.924574i	$-0.624421\pi$
$281$	−12.7735	−0.762003	−0.381002	+	0.924574i	$0.624421\pi$
$282$	81.5720	4.85754
$283$	−9.21145	−0.547564	−0.273782	−	0.961792i	$-0.588275\pi$
$283$	−9.21145	−0.547564	−0.273782	+	0.961792i	$0.588275\pi$
$284$	−5.80765	−0.344621
$285$	−1.51301	−0.0896232
$286$	62.0533	3.66929
$287$	−5.24059	−0.309342
$288$	−132.262	−7.79362
$289$	−7.37484	−0.433814
$290$	−16.3293	−0.958889
$291$	46.8287	2.74515
$292$	−89.5918	−5.24296
$293$	−18.9821	−1.10895	−0.554474	−	0.832201i	$-0.687081\pi$
$293$	−18.9821	−1.10895	−0.554474	+	0.832201i	$0.687081\pi$
$294$	42.0864	2.45453
$295$	−0.235185	−0.0136930
$296$	−9.52322	−0.553526
$297$	32.1464	1.86532
$298$	55.7062	3.22698
$299$	11.3378	0.655683
$300$	−72.1897	−4.16787
$301$	−0.542831	−0.0312883
$302$	8.95791	0.515470
$303$	7.55172	0.433835
$304$	12.3811	0.710103
$305$	−1.34672	−0.0771128
$306$	−43.7075	−2.49859
$307$	27.6372	1.57734	0.788668	−	0.614819i	$-0.210771\pi$
$307$	27.6372	1.57734	0.788668	+	0.614819i	$0.210771\pi$
$308$	−39.3391	−2.24155
$309$	37.9087	2.15655
$310$	8.93433	0.507436
$311$	16.4343	0.931902	0.465951	−	0.884810i	$-0.345712\pi$
$311$	16.4343	0.931902	0.465951	+	0.884810i	$0.345712\pi$
$312$	119.464	6.76333
$313$	−27.2798	−1.54195	−0.770974	−	0.636867i	$-0.780230\pi$
$313$	−27.2798	−1.54195	−0.770974	+	0.636867i	$0.780230\pi$
$314$	24.4220	1.37821
$315$	4.69837	0.264723
$316$	−96.1667	−5.40980
$317$	−17.2141	−0.966842	−0.483421	−	0.875388i	$-0.660606\pi$
$317$	−17.2141	−0.966842	−0.483421	+	0.875388i	$0.660606\pi$
$318$	80.2831	4.50205
$319$	−44.4413	−2.48823
$320$	−27.6275	−1.54442
$321$	−45.1177	−2.51822
$322$	−9.72796	−0.542118
$323$	2.29924	0.127933
$324$	9.29323	0.516291
$325$	18.6015	1.03183
$326$	−52.2902	−2.89609
$327$	7.19450	0.397857
$328$	−41.2686	−2.27868
$329$	13.3252	0.734642
$330$	30.5440	1.68139
$331$	−10.8394	−0.595788	−0.297894	−	0.954599i	$-0.596284\pi$
$331$	−10.8394	−0.595788	−0.297894	+	0.954599i	$0.596284\pi$
$332$	−21.1009	−1.15806
$333$	4.78744	0.262350
$334$	18.2867	1.00060
$335$	3.91195	0.213733
$336$	−61.1047	−3.33354
$337$	2.87065	0.156374	0.0781872	−	0.996939i	$-0.475087\pi$
$337$	2.87065	0.156374	0.0781872	+	0.996939i	$0.475087\pi$
$338$	−11.6316	−0.632675
$339$	24.7289	1.34309
$340$	−12.6013	−0.683402
$341$	24.3154	1.31675
$342$	−10.4408	−0.564573
$343$	15.8763	0.857241
$344$	−4.27469	−0.230476
$345$	5.58073	0.300456
$346$	49.2051	2.64528
$347$	−20.6698	−1.10962	−0.554808	−	0.831979i	$-0.687208\pi$
$347$	−20.6698	−1.10962	−0.554808	+	0.831979i	$0.687208\pi$
$348$	−132.324	−7.09329
$349$	12.5001	0.669112	0.334556	−	0.942376i	$-0.391414\pi$
$349$	12.5001	0.669112	0.334556	+	0.942376i	$0.391414\pi$
$350$	−15.9603	−0.853112
$351$	−24.6636	−1.31644
$352$	−140.458	−7.48644
$353$	7.22198	0.384387	0.192194	−	0.981357i	$-0.438440\pi$
$353$	7.22198	0.384387	0.192194	+	0.981357i	$0.438440\pi$
$354$	−2.57936	−0.137091
$355$	0.736605	0.0390949
$356$	−69.9808	−3.70898
$357$	−11.3475	−0.600575
$358$	−38.3354	−2.02609
$359$	17.9087	0.945184	0.472592	−	0.881281i	$-0.343318\pi$
$359$	17.9087	0.945184	0.472592	+	0.881281i	$0.343318\pi$
$360$	36.9987	1.95000
$361$	−18.4508	−0.971093
$362$	−64.9351	−3.41291
$363$	51.8393	2.72086
$364$	30.1820	1.58197
$365$	11.3632	0.594779
$366$	−14.7700	−0.772038
$367$	−24.6280	−1.28557	−0.642786	−	0.766046i	$-0.722221\pi$
$367$	−24.6280	−1.28557	−0.642786	+	0.766046i	$0.722221\pi$
$368$	−45.6673	−2.38057
$369$	20.7462	1.08001
$370$	1.86808	0.0971169
$371$	13.1146	0.680878
$372$	72.3989	3.75371
$373$	−3.92518	−0.203238	−0.101619	−	0.994823i	$-0.532402\pi$
$373$	−3.92518	−0.203238	−0.101619	+	0.994823i	$0.532402\pi$
$374$	−46.4160	−2.40011
$375$	19.3639	0.999946
$376$	104.933	5.41152
$377$	34.0965	1.75606
$378$	21.1616	1.08843
$379$	10.3032	0.529240	0.264620	−	0.964353i	$-0.414753\pi$
$379$	10.3032	0.529240	0.264620	+	0.964353i	$0.414753\pi$
$380$	−3.01018	−0.154419
$381$	−29.2388	−1.49795
$382$	−10.0010	−0.511694
$383$	8.71067	0.445095	0.222547	−	0.974922i	$-0.428563\pi$
$383$	8.71067	0.445095	0.222547	+	0.974922i	$0.428563\pi$
$384$	−155.196	−7.91983
$385$	4.98952	0.254289
$386$	−21.6290	−1.10089
$387$	2.14894	0.109237
$388$	93.1669	4.72983
$389$	−36.0026	−1.82540	−0.912701	−	0.408628i	$-0.866007\pi$
$389$	−36.0026	−1.82540	−0.912701	+	0.408628i	$0.866007\pi$
$390$	−23.4342	−1.18664
$391$	−8.48071	−0.428888
$392$	54.1394	2.73445
$393$	17.2790	0.871609
$394$	36.3858	1.83309
$395$	12.1972	0.613706
$396$	155.734	7.82593
$397$	−23.4716	−1.17801	−0.589004	−	0.808130i	$-0.700480\pi$
$397$	−23.4716	−1.17801	−0.589004	+	0.808130i	$0.700480\pi$
$398$	−3.38533	−0.169691
$399$	−2.71068	−0.135704
$400$	−74.9245	−3.74623
$401$	−13.4757	−0.672943	−0.336471	−	0.941694i	$-0.609234\pi$
$401$	−13.4757	−0.672943	−0.336471	+	0.941694i	$0.609234\pi$
$402$	42.9038	2.13985
$403$	−18.6554	−0.929292
$404$	15.0243	0.747488
$405$	−1.17869	−0.0585697
$406$	−29.2551	−1.45191
$407$	5.08411	0.252010
$408$	−89.3595	−4.42395
$409$	3.19922	0.158191	0.0790956	−	0.996867i	$-0.474797\pi$
$409$	3.19922	0.158191	0.0790956	+	0.996867i	$0.474797\pi$
$410$	8.09527	0.399797
$411$	8.08723	0.398914
$412$	75.4204	3.71569
$413$	−0.421351	−0.0207333
$414$	38.5106	1.89269
$415$	2.67631	0.131375
$416$	107.763	5.28352
$417$	37.9010	1.85602
$418$	−11.0878	−0.542320
$419$	−32.4717	−1.58635	−0.793174	−	0.608995i	$-0.791573\pi$
$419$	−32.4717	−1.58635	−0.793174	+	0.608995i	$0.791573\pi$
$420$	14.8562	0.724911
$421$	23.8558	1.16266	0.581331	−	0.813667i	$-0.302532\pi$
$421$	23.8558	1.16266	0.581331	+	0.813667i	$0.302532\pi$
$422$	6.22251	0.302907
$423$	−52.7512	−2.56485
$424$	103.275	5.01548
$425$	−13.9140	−0.674926
$426$	8.07862	0.391410
$427$	−2.41274	−0.116761
$428$	−89.7627	−4.33884
$429$	−63.7777	−3.07922
$430$	0.838525	0.0404373
$431$	17.9134	0.862859	0.431430	−	0.902147i	$-0.358009\pi$
$431$	17.9134	0.862859	0.431430	+	0.902147i	$0.358009\pi$
$432$	99.3418	4.77959
$433$	−20.8749	−1.00318	−0.501592	−	0.865104i	$-0.667252\pi$
$433$	−20.8749	−1.00318	−0.501592	+	0.865104i	$0.667252\pi$
$434$	16.0065	0.768338
$435$	16.7831	0.804686
$436$	14.3136	0.685498
$437$	−2.02586	−0.0969099
$438$	124.625	5.95480
$439$	−21.1702	−1.01040	−0.505199	−	0.863003i	$-0.668581\pi$
$439$	−21.1702	−1.01040	−0.505199	+	0.863003i	$0.668581\pi$
$440$	39.2914	1.87315
$441$	−27.2165	−1.29603
$442$	35.6116	1.69387
$443$	−22.6987	−1.07845	−0.539224	−	0.842162i	$-0.681282\pi$
$443$	−22.6987	−1.07845	−0.539224	+	0.842162i	$0.681282\pi$
$444$	15.1379	0.718413
$445$	8.87591	0.420759
$446$	−39.7081	−1.88023
$447$	−57.2543	−2.70803
$448$	−49.4967	−2.33850
$449$	1.80748	0.0853002	0.0426501	−	0.999090i	$-0.486420\pi$
$449$	1.80748	0.0853002	0.0426501	+	0.999090i	$0.486420\pi$
$450$	63.1828	2.97847
$451$	22.0318	1.03744
$452$	49.1987	2.31411
$453$	−9.20684	−0.432575
$454$	−57.1741	−2.68331
$455$	−3.82809	−0.179464
$456$	−21.3460	−0.999620
$457$	−9.32771	−0.436332	−0.218166	−	0.975912i	$-0.570007\pi$
$457$	−9.32771	−0.436332	−0.218166	+	0.975912i	$0.570007\pi$
$458$	−70.6719	−3.30228
$459$	18.4484	0.861098
$460$	11.1030	0.517680
$461$	27.6353	1.28710	0.643552	−	0.765402i	$-0.277460\pi$
$461$	27.6353	1.28710	0.643552	+	0.765402i	$0.277460\pi$
$462$	54.7219	2.54589
$463$	−9.45391	−0.439360	−0.219680	−	0.975572i	$-0.570501\pi$
$463$	−9.45391	−0.439360	−0.219680	+	0.975572i	$0.570501\pi$
$464$	−137.337	−6.37569
$465$	−9.18261	−0.425833
$466$	28.2406	1.30822
$467$	32.3027	1.49479	0.747395	−	0.664380i	$-0.231304\pi$
$467$	32.3027	1.49479	0.747395	+	0.664380i	$0.231304\pi$
$468$	−119.483	−5.52311
$469$	7.00855	0.323625
$470$	−20.5837	−0.949458
$471$	−25.1007	−1.15658
$472$	−3.31805	−0.152726
$473$	2.28210	0.104931
$474$	133.771	6.14430
$475$	−3.32374	−0.152504
$476$	−22.5762	−1.03478
$477$	−51.9177	−2.37715
$478$	46.7650	2.13898
$479$	19.6952	0.899896	0.449948	−	0.893055i	$-0.351442\pi$
$479$	19.6952	0.899896	0.449948	+	0.893055i	$0.351442\pi$
$480$	53.0434	2.42109
$481$	−3.90066	−0.177855
$482$	13.8398	0.630386
$483$	9.99828	0.454938
$484$	103.136	4.68798
$485$	−11.8167	−0.536568
$486$	36.4427	1.65307
$487$	39.0175	1.76805	0.884026	−	0.467437i	$-0.154823\pi$
$487$	39.0175	1.76805	0.884026	+	0.467437i	$0.154823\pi$
$488$	−18.9999	−0.860084
$489$	53.7433	2.43036
$490$	−10.6200	−0.479763
$491$	7.44121	0.335817	0.167909	−	0.985803i	$-0.446299\pi$
$491$	7.44121	0.335817	0.167909	+	0.985803i	$0.446299\pi$
$492$	65.5996	2.95746
$493$	−25.5043	−1.14865
$494$	8.50683	0.382740
$495$	−19.7523	−0.887799
$496$	75.1417	3.37396
$497$	1.31968	0.0591958
$498$	29.3520	1.31530
$499$	−0.901824	−0.0403712	−0.0201856	−	0.999796i	$-0.506426\pi$
$499$	−0.901824	−0.0403712	−0.0201856	+	0.999796i	$0.506426\pi$
$500$	38.5249	1.72289
$501$	−18.7949	−0.839693
$502$	73.0119	3.25868
$503$	−5.01103	−0.223431	−0.111715	−	0.993740i	$-0.535634\pi$
$503$	−5.01103	−0.223431	−0.111715	+	0.993740i	$0.535634\pi$
$504$	66.2859	2.95261
$505$	−1.90559	−0.0847975
$506$	40.8970	1.81810
$507$	11.9548	0.530932
$508$	−58.1713	−2.58094
$509$	−11.4035	−0.505451	−0.252726	−	0.967538i	$-0.581327\pi$
$509$	−11.4035	−0.505451	−0.252726	+	0.967538i	$0.581327\pi$
$510$	17.5288	0.776188
$511$	20.3581	0.900588
$512$	−95.7154	−4.23007
$513$	4.40692	0.194570
$514$	−84.7884	−3.73986
$515$	−9.56583	−0.421521
$516$	6.79494	0.299131
$517$	−56.0201	−2.46376
$518$	3.34680	0.147050
$519$	−50.5724	−2.21988
$520$	−30.1454	−1.32196
$521$	−6.12877	−0.268506	−0.134253	−	0.990947i	$-0.542864\pi$
$521$	−6.12877	−0.268506	−0.134253	+	0.990947i	$0.542864\pi$
$522$	115.814	5.06904
$523$	−7.33746	−0.320845	−0.160422	−	0.987048i	$-0.551286\pi$
$523$	−7.33746	−0.320845	−0.160422	+	0.987048i	$0.551286\pi$
$524$	34.3770	1.50176
$525$	16.4038	0.715919
$526$	−34.2834	−1.49483
$527$	13.9543	0.607858
$528$	256.889	11.1796
$529$	−15.5277	−0.675116
$530$	−20.2585	−0.879973
$531$	1.66803	0.0723862
$532$	−5.39296	−0.233814
$533$	−16.9034	−0.732167
$534$	97.3454	4.21255
$535$	11.3849	0.492213
$536$	55.1909	2.38388
$537$	39.4007	1.70027
$538$	24.7738	1.06807
$539$	−28.9031	−1.24494
$540$	−24.1527	−1.03937
$541$	16.8597	0.724855	0.362428	−	0.932012i	$-0.381948\pi$
$541$	16.8597	0.724855	0.362428	+	0.932012i	$0.381948\pi$
$542$	−26.0337	−1.11824
$543$	66.7396	2.86407
$544$	−80.6070	−3.45600
$545$	−1.81545	−0.0777652
$546$	−41.9841	−1.79675
$547$	38.2204	1.63419	0.817094	−	0.576504i	$-0.195584\pi$
$547$	38.2204	1.63419	0.817094	+	0.576504i	$0.195584\pi$
$548$	16.0898	0.687320
$549$	9.55147	0.407647
$550$	67.0981	2.86107
$551$	−6.09241	−0.259545
$552$	78.7345	3.35116
$553$	21.8521	0.929247
$554$	8.34682	0.354622
$555$	−1.91999	−0.0814991
$556$	75.4050	3.19788
$557$	−36.1450	−1.53151	−0.765757	−	0.643130i	$-0.777635\pi$
$557$	−36.1450	−1.53151	−0.765757	+	0.643130i	$0.777635\pi$
$558$	−63.3659	−2.68249
$559$	−1.75089	−0.0740547
$560$	15.4191	0.651574
$561$	47.7058	2.01414
$562$	35.3505	1.49117
$563$	−41.3506	−1.74272	−0.871360	−	0.490645i	$-0.836761\pi$
$563$	−41.3506	−1.74272	−0.871360	+	0.490645i	$0.836761\pi$
$564$	−166.799	−7.02352
$565$	−6.24005	−0.262521
$566$	25.4926	1.07153
$567$	−2.11172	−0.0886837
$568$	10.3922	0.436048
$569$	40.1421	1.68284	0.841421	−	0.540380i	$-0.181719\pi$
$569$	40.1421	1.68284	0.841421	+	0.540380i	$0.181719\pi$
$570$	4.18725	0.175385
$571$	−22.4509	−0.939541	−0.469770	−	0.882789i	$-0.655663\pi$
$571$	−22.4509	−0.939541	−0.469770	+	0.882789i	$0.655663\pi$
$572$	−126.887	−5.30543
$573$	10.2789	0.429406
$574$	14.5033	0.605355
$575$	12.2596	0.511259
$576$	195.945	8.16440
$577$	−1.65566	−0.0689262	−0.0344631	−	0.999406i	$-0.510972\pi$
$577$	−1.65566	−0.0689262	−0.0344631	+	0.999406i	$0.510972\pi$
$578$	20.4098	0.848935
$579$	22.2301	0.923851
$580$	33.3903	1.38646
$581$	4.79480	0.198922
$582$	−129.598	−5.37201
$583$	−55.1349	−2.28345
$584$	160.316	6.63391
$585$	15.1545	0.626560
$586$	52.5329	2.17011
$587$	−26.0277	−1.07428	−0.537138	−	0.843494i	$-0.680495\pi$
$587$	−26.0277	−1.07428	−0.537138	+	0.843494i	$0.680495\pi$
$588$	−86.0587	−3.54900
$589$	3.33337	0.137349
$590$	0.650871	0.0267959
$591$	−37.3969	−1.53830
$592$	15.7114	0.645734
$593$	−32.6405	−1.34038	−0.670192	−	0.742188i	$-0.733788\pi$
$593$	−32.6405	−1.34038	−0.670192	+	0.742188i	$0.733788\pi$
$594$	−88.9648	−3.65027
$595$	2.86342	0.117389
$596$	−113.909	−4.66588
$597$	3.47940	0.142403
$598$	−31.3773	−1.28311
$599$	31.1612	1.27321	0.636606	−	0.771189i	$-0.280338\pi$
$599$	31.1612	1.27321	0.636606	+	0.771189i	$0.280338\pi$
$600$	129.176	5.27360
$601$	−12.6671	−0.516702	−0.258351	−	0.966051i	$-0.583179\pi$
$601$	−12.6671	−0.516702	−0.258351	+	0.966051i	$0.583179\pi$
$602$	1.50228	0.0612283
$603$	−27.7451	−1.12987
$604$	−18.3172	−0.745318
$605$	−13.0810	−0.531820
$606$	−20.8993	−0.848975
$607$	5.31072	0.215555	0.107778	−	0.994175i	$-0.465627\pi$
$607$	5.31072	0.215555	0.107778	+	0.994175i	$0.465627\pi$
$608$	−19.2553	−0.780904
$609$	30.0681	1.21842
$610$	3.72703	0.150903
$611$	42.9801	1.73879
$612$	89.3737	3.61272
$613$	21.3807	0.863557	0.431778	−	0.901980i	$-0.357886\pi$
$613$	21.3807	0.863557	0.431778	+	0.901980i	$0.357886\pi$
$614$	−76.4855	−3.08670
$615$	−8.32022	−0.335504
$616$	70.3935	2.83623
$617$	7.74474	0.311792	0.155896	−	0.987774i	$-0.450174\pi$
$617$	7.74474	0.311792	0.155896	+	0.987774i	$0.450174\pi$
$618$	−104.912	−4.22018
$619$	25.0012	1.00488	0.502442	−	0.864611i	$-0.332435\pi$
$619$	25.0012	1.00488	0.502442	+	0.864611i	$0.332435\pi$
$620$	−18.2690	−0.733702
$621$	−16.2549	−0.652285
$622$	−45.4817	−1.82365
$623$	15.9018	0.637094
$624$	−197.092	−7.88999
$625$	17.5379	0.701517
$626$	75.4966	3.01745
$627$	11.3959	0.455108
$628$	−49.9384	−1.99276
$629$	2.91770	0.116336
$630$	−13.0027	−0.518039
$631$	11.7799	0.468949	0.234474	−	0.972122i	$-0.424663\pi$
$631$	11.7799	0.468949	0.234474	+	0.972122i	$0.424663\pi$
$632$	172.081	6.84502
$633$	−6.39542	−0.254195
$634$	47.6399	1.89202
$635$	7.37807	0.292790
$636$	−164.164	−6.50952
$637$	22.1752	0.878613
$638$	122.991	4.86925
$639$	−5.22430	−0.206670
$640$	39.1620	1.54801
$641$	−14.2824	−0.564123	−0.282061	−	0.959396i	$-0.591018\pi$
$641$	−14.2824	−0.564123	−0.282061	+	0.959396i	$0.591018\pi$
$642$	124.863	4.92793
$643$	39.9331	1.57481	0.787403	−	0.616439i	$-0.211425\pi$
$643$	39.9331	1.57481	0.787403	+	0.616439i	$0.211425\pi$
$644$	19.8918	0.783848
$645$	−0.861826	−0.0339344
$646$	−6.36312	−0.250354
$647$	−30.8643	−1.21340	−0.606700	−	0.794931i	$-0.707507\pi$
$647$	−30.8643	−1.21340	−0.606700	+	0.794931i	$0.707507\pi$
$648$	−16.6293	−0.653262
$649$	1.77139	0.0695331
$650$	−51.4794	−2.01919
$651$	−16.4513	−0.644778
$652$	106.924	4.18745
$653$	19.3083	0.755591	0.377796	−	0.925889i	$-0.376682\pi$
$653$	19.3083	0.755591	0.377796	+	0.925889i	$0.376682\pi$
$654$	−19.9107	−0.778569
$655$	−4.36015	−0.170365
$656$	68.0848	2.65826
$657$	−80.5927	−3.14422
$658$	−36.8773	−1.43763
$659$	−2.57604	−0.100348	−0.0501742	−	0.998740i	$-0.515978\pi$
$659$	−2.57604	−0.100348	−0.0501742	+	0.998740i	$0.515978\pi$
$660$	−62.4567	−2.43113
$661$	28.4855	1.10796	0.553979	−	0.832531i	$-0.313109\pi$
$661$	28.4855	1.10796	0.553979	+	0.832531i	$0.313109\pi$
$662$	29.9980	1.16590
$663$	−36.6012	−1.42147
$664$	37.7581	1.46530
$665$	0.684008	0.0265247
$666$	−13.2492	−0.513396
$667$	22.4718	0.870110
$668$	−37.3929	−1.44677
$669$	40.8115	1.57786
$670$	−10.8263	−0.418256
$671$	10.1434	0.391580
$672$	95.0311	3.66591
$673$	−3.08742	−0.119011	−0.0595057	−	0.998228i	$-0.518952\pi$
$673$	−3.08742	−0.119011	−0.0595057	+	0.998228i	$0.518952\pi$
$674$	−7.94450	−0.306011
$675$	−26.6687	−1.02648
$676$	23.7844	0.914785
$677$	−16.2570	−0.624807	−0.312403	−	0.949950i	$-0.601134\pi$
$677$	−16.2570	−0.624807	−0.312403	+	0.949950i	$0.601134\pi$
$678$	−68.4369	−2.62830
$679$	−21.1705	−0.812448
$680$	22.5488	0.864708
$681$	58.7629	2.25180
$682$	−67.2926	−2.57677
$683$	−14.2447	−0.545059	−0.272529	−	0.962147i	$-0.587860\pi$
$683$	−14.2447	−0.545059	−0.272529	+	0.962147i	$0.587860\pi$
$684$	21.3494	0.816315
$685$	−2.04072	−0.0779719
$686$	−43.9375	−1.67754
$687$	72.6358	2.77123
$688$	7.05237	0.268869
$689$	42.3009	1.61154
$690$	−15.4446	−0.587966
$691$	19.9792	0.760045	0.380022	−	0.924977i	$-0.375916\pi$
$691$	19.9792	0.760045	0.380022	+	0.924977i	$0.375916\pi$
$692$	−100.615	−3.82481
$693$	−35.3877	−1.34427
$694$	57.2036	2.17142
$695$	−9.56388	−0.362779
$696$	236.780	8.97513
$697$	12.6438	0.478917
$698$	−34.5937	−1.30939
$699$	−29.0253	−1.09784
$700$	32.6357	1.23351
$701$	18.5183	0.699427	0.349713	−	0.936857i	$-0.386279\pi$
$701$	18.5183	0.699427	0.349713	+	0.936857i	$0.386279\pi$
$702$	68.2562	2.57616
$703$	0.696975	0.0262869
$704$	208.088	7.84260
$705$	21.1557	0.796771
$706$	−19.9867	−0.752211
$707$	−3.41400	−0.128397
$708$	5.27430	0.198220
$709$	7.18868	0.269976	0.134988	−	0.990847i	$-0.456900\pi$
$709$	7.18868	0.269976	0.134988	+	0.990847i	$0.456900\pi$
$710$	−2.03855	−0.0765053
$711$	−86.5072	−3.24428
$712$	125.224	4.69296
$713$	−12.2951	−0.460455
$714$	31.4041	1.17527
$715$	16.0936	0.601865
$716$	78.3887	2.92952
$717$	−48.0645	−1.79500
$718$	−49.5621	−1.84964
$719$	−23.5046	−0.876574	−0.438287	−	0.898835i	$-0.644415\pi$
$719$	−23.5046	−0.876574	−0.438287	+	0.898835i	$0.644415\pi$
$720$	−61.0403	−2.27484
$721$	−17.1379	−0.638248
$722$	51.0623	1.90034
$723$	−14.2244	−0.529011
$724$	132.780	4.93473
$725$	36.8685	1.36926
$726$	−143.465	−5.32447
$727$	16.1529	0.599077	0.299539	−	0.954084i	$-0.403167\pi$
$727$	16.1529	0.599077	0.299539	+	0.954084i	$0.403167\pi$
$728$	−54.0077	−2.00166
$729$	−42.3820	−1.56970
$730$	−31.4476	−1.16393
$731$	1.30967	0.0484398
$732$	30.2018	1.11629
$733$	−17.0144	−0.628440	−0.314220	−	0.949350i	$-0.601743\pi$
$733$	−17.0144	−0.628440	−0.314220	+	0.949350i	$0.601743\pi$
$734$	68.1577	2.51575
$735$	10.9151	0.402610
$736$	71.0227	2.61793
$737$	−29.4645	−1.08534
$738$	−57.4149	−2.11347
$739$	−34.7598	−1.27866	−0.639329	−	0.768933i	$-0.720788\pi$
$739$	−34.7598	−1.27866	−0.639329	+	0.768933i	$0.720788\pi$
$740$	−3.81987	−0.140421
$741$	−8.74322	−0.321190
$742$	−36.2946	−1.33242
$743$	45.7429	1.67815	0.839073	−	0.544020i	$-0.183098\pi$
$743$	45.7429	1.67815	0.839073	+	0.544020i	$0.183098\pi$
$744$	−129.551	−4.74956
$745$	14.4474	0.529313
$746$	10.8629	0.397718
$747$	−18.9814	−0.694495
$748$	94.9119	3.47032
$749$	20.3969	0.745287
$750$	−53.5893	−1.95680
$751$	−3.14990	−0.114941	−0.0574707	−	0.998347i	$-0.518304\pi$
$751$	−3.14990	−0.114941	−0.0574707	+	0.998347i	$0.518304\pi$
$752$	−173.118	−6.31298
$753$	−75.0408	−2.73464
$754$	−94.3617	−3.43645
$755$	2.32324	0.0845513
$756$	−43.2714	−1.57377
$757$	−20.5132	−0.745566	−0.372783	−	0.927919i	$-0.621596\pi$
$757$	−20.5132	−0.745566	−0.372783	+	0.927919i	$0.621596\pi$
$758$	−28.5140	−1.03567
$759$	−42.0335	−1.52572
$760$	5.38642	0.195386
$761$	−34.1997	−1.23974	−0.619869	−	0.784706i	$-0.712814\pi$
$761$	−34.1997	−1.23974	−0.619869	+	0.784706i	$0.712814\pi$
$762$	80.9181	2.93135
$763$	−3.25251	−0.117749
$764$	20.4501	0.739858
$765$	−11.3356	−0.409838
$766$	−24.1067	−0.871010
$767$	−1.35906	−0.0490727
$768$	210.532	7.59692
$769$	−41.0620	−1.48073	−0.740366	−	0.672203i	$-0.765348\pi$
$769$	−41.0620	−1.48073	−0.740366	+	0.672203i	$0.765348\pi$
$770$	−13.8084	−0.497621
$771$	87.1446	3.13844
$772$	44.2273	1.59178
$773$	13.4236	0.482812	0.241406	−	0.970424i	$-0.422392\pi$
$773$	13.4236	0.482812	0.241406	+	0.970424i	$0.422392\pi$
$774$	−5.94716	−0.213766
$775$	−20.1721	−0.724601
$776$	−166.713	−5.98465
$777$	−3.43981	−0.123402
$778$	99.6366	3.57215
$779$	3.02032	0.108214
$780$	47.9185	1.71576
$781$	−5.54804	−0.198525
$782$	23.4703	0.839295
$783$	−48.8836	−1.74696
$784$	−89.3190	−3.18996
$785$	6.33386	0.226065
$786$	−47.8194	−1.70566
$787$	42.4678	1.51381	0.756907	−	0.653523i	$-0.226710\pi$
$787$	42.4678	1.51381	0.756907	+	0.653523i	$0.226710\pi$
$788$	−74.4021	−2.65046
$789$	35.2361	1.25444
$790$	−33.7555	−1.20097
$791$	−11.1795	−0.397498
$792$	−278.671	−9.90214
$793$	−7.78225	−0.276356
$794$	64.9575	2.30526
$795$	20.8215	0.738461
$796$	6.92236	0.245357
$797$	−29.3082	−1.03815	−0.519074	−	0.854729i	$-0.673723\pi$
$797$	−29.3082	−1.03815	−0.519074	+	0.854729i	$0.673723\pi$
$798$	7.50177	0.265560
$799$	−32.1492	−1.13736
$800$	116.524	4.11974
$801$	−62.9516	−2.22428
$802$	37.2937	1.31689
$803$	−85.5868	−3.02029
$804$	−87.7302	−3.09401
$805$	−2.52295	−0.0889223
$806$	51.6286	1.81854
$807$	−25.4622	−0.896311
$808$	−26.8846	−0.945796
$809$	−34.8943	−1.22682	−0.613410	−	0.789765i	$-0.710203\pi$
$809$	−34.8943	−1.22682	−0.613410	+	0.789765i	$0.710203\pi$
$810$	3.26202	0.114616
$811$	10.0651	0.353433	0.176716	−	0.984262i	$-0.443452\pi$
$811$	10.0651	0.353433	0.176716	+	0.984262i	$0.443452\pi$
$812$	59.8212	2.09931
$813$	26.7571	0.938413
$814$	−14.0702	−0.493161
$815$	−13.5615	−0.475039
$816$	147.425	5.16091
$817$	0.312851	0.0109453
$818$	−8.85380	−0.309566
$819$	27.1504	0.948710
$820$	−16.5533	−0.578066
$821$	−53.9074	−1.88138	−0.940691	−	0.339264i	$-0.889822\pi$
$821$	−53.9074	−1.88138	−0.940691	+	0.339264i	$0.889822\pi$
$822$	−22.3813	−0.780638
$823$	−40.1713	−1.40028	−0.700142	−	0.714004i	$-0.746880\pi$
$823$	−40.1713	−1.40028	−0.700142	+	0.714004i	$0.746880\pi$
$824$	−134.957	−4.70146
$825$	−68.9627	−2.40097
$826$	1.16608	0.0405732
$827$	−18.6014	−0.646833	−0.323416	−	0.946257i	$-0.604831\pi$
$827$	−18.6014	−0.646833	−0.323416	+	0.946257i	$0.604831\pi$
$828$	−78.7470	−2.73665
$829$	−27.9498	−0.970737	−0.485369	−	0.874310i	$-0.661315\pi$
$829$	−27.9498	−0.970737	−0.485369	+	0.874310i	$0.661315\pi$
$830$	−7.40664	−0.257088
$831$	−8.57877	−0.297594
$832$	−159.650	−5.53488
$833$	−16.5871	−0.574709
$834$	−104.891	−3.63206
$835$	4.74267	0.164127
$836$	22.6724	0.784141
$837$	26.7460	0.924476
$838$	89.8651	3.10434
$839$	42.5914	1.47042	0.735208	−	0.677841i	$-0.237084\pi$
$839$	42.5914	1.47042	0.735208	+	0.677841i	$0.237084\pi$
$840$	−26.5838	−0.917229
$841$	38.5799	1.33034
$842$	−66.0207	−2.27522
$843$	−36.3329	−1.25137
$844$	−12.7239	−0.437973
$845$	−3.01666	−0.103776
$846$	145.988	5.01918
$847$	−23.4357	−0.805259
$848$	−170.383	−5.85097
$849$	−26.2010	−0.899215
$850$	38.5067	1.32077
$851$	−2.57078	−0.0881253
$852$	−16.5193	−0.565940
$853$	−7.68931	−0.263277	−0.131639	−	0.991298i	$-0.542024\pi$
$853$	−7.68931	−0.263277	−0.131639	+	0.991298i	$0.542024\pi$
$854$	6.67724	0.228491
$855$	−2.70782	−0.0926055
$856$	160.622	5.48993
$857$	9.13512	0.312050	0.156025	−	0.987753i	$-0.450132\pi$
$857$	9.13512	0.312050	0.156025	+	0.987753i	$0.450132\pi$
$858$	176.504	6.02575
$859$	22.2014	0.757503	0.378751	−	0.925498i	$-0.376354\pi$
$859$	22.2014	0.757503	0.378751	+	0.925498i	$0.376354\pi$
$860$	−1.71463	−0.0584682
$861$	−14.9063	−0.508005
$862$	−49.5752	−1.68854
$863$	17.9246	0.610161	0.305080	−	0.952327i	$-0.401317\pi$
$863$	17.9246	0.610161	0.305080	+	0.952327i	$0.401317\pi$
$864$	−154.498	−5.25613
$865$	12.7614	0.433899
$866$	57.7711	1.96314
$867$	−20.9769	−0.712414
$868$	−32.7303	−1.11094
$869$	−91.8679	−3.11641
$870$	−46.4469	−1.57470
$871$	22.6059	0.765972
$872$	−25.6128	−0.867360
$873$	83.8087	2.83650
$874$	5.60654	0.189644
$875$	−8.75408	−0.295942
$876$	−254.834	−8.61005
$877$	−40.7125	−1.37476	−0.687381	−	0.726297i	$-0.741240\pi$
$877$	−40.7125	−1.37476	−0.687381	+	0.726297i	$0.741240\pi$
$878$	58.5882	1.97726
$879$	−53.9927	−1.82113
$880$	−64.8229	−2.18518
$881$	49.8609	1.67986	0.839929	−	0.542696i	$-0.182597\pi$
$881$	49.8609	1.67986	0.839929	+	0.542696i	$0.182597\pi$
$882$	75.3214	2.53620
$883$	3.97972	0.133928	0.0669642	−	0.997755i	$-0.478669\pi$
$883$	3.97972	0.133928	0.0669642	+	0.997755i	$0.478669\pi$
$884$	−72.8189	−2.44917
$885$	−0.668958	−0.0224868
$886$	62.8184	2.11042
$887$	50.5537	1.69743	0.848713	−	0.528854i	$-0.177378\pi$
$887$	50.5537	1.69743	0.848713	+	0.528854i	$0.177378\pi$
$888$	−27.0878	−0.909007
$889$	13.2184	0.443330
$890$	−24.5640	−0.823386
$891$	8.87781	0.297418
$892$	81.1955	2.71863
$893$	−7.67974	−0.256993
$894$	158.450	5.29938
$895$	−9.94231	−0.332335
$896$	70.1616	2.34393
$897$	32.2492	1.07677
$898$	−5.00217	−0.166925
$899$	−36.9753	−1.23320
$900$	−129.197	−4.30656
$901$	−31.6412	−1.05412
$902$	−60.9728	−2.03017
$903$	−1.54403	−0.0513820
$904$	−88.0364	−2.92805
$905$	−16.8410	−0.559812
$906$	25.4798	0.846510
$907$	−51.4349	−1.70787	−0.853933	−	0.520382i	$-0.825789\pi$
$907$	−51.4349	−1.70787	−0.853933	+	0.520382i	$0.825789\pi$
$908$	116.910	3.87980
$909$	13.5152	0.448271
$910$	10.5942	0.351194
$911$	−25.8495	−0.856432	−0.428216	−	0.903676i	$-0.640858\pi$
$911$	−25.8495	−0.856432	−0.428216	+	0.903676i	$0.640858\pi$
$912$	35.2166	1.16614
$913$	−20.1577	−0.667122
$914$	25.8143	0.853862
$915$	−3.83060	−0.126636
$916$	144.511	4.77477
$917$	−7.81153	−0.257959
$918$	−51.0557	−1.68509
$919$	5.98532	0.197437	0.0987187	−	0.995115i	$-0.468526\pi$
$919$	5.98532	0.197437	0.0987187	+	0.995115i	$0.468526\pi$
$920$	−19.8677	−0.655020
$921$	78.6110	2.59032
$922$	−76.4804	−2.51875
$923$	4.25660	0.140108
$924$	−111.896	−3.68110
$925$	−4.21778	−0.138680
$926$	26.1636	0.859789
$927$	67.8447	2.22831
$928$	213.588	7.01138
$929$	−50.8556	−1.66852	−0.834259	−	0.551373i	$-0.814104\pi$
$929$	−50.8556	−1.66852	−0.834259	+	0.551373i	$0.814104\pi$
$930$	25.4128	0.833317
$931$	−3.96229	−0.129859
$932$	−57.7466	−1.89155
$933$	46.7455	1.53038
$934$	−89.3973	−2.92517
$935$	−12.0380	−0.393685
$936$	213.804	6.98839
$937$	−25.3411	−0.827858	−0.413929	−	0.910309i	$-0.635844\pi$
$937$	−25.3411	−0.827858	−0.413929	+	0.910309i	$0.635844\pi$
$938$	−19.3961	−0.633304
$939$	−77.5946	−2.53220
$940$	42.0899	1.37282
$941$	−6.60978	−0.215473	−0.107736	−	0.994179i	$-0.534360\pi$
$941$	−6.60978	−0.215473	−0.107736	+	0.994179i	$0.534360\pi$
$942$	69.4658	2.26332
$943$	−11.1404	−0.362781
$944$	5.47411	0.178167
$945$	5.48827	0.178533
$946$	−6.31569	−0.205341
$947$	−0.498788	−0.0162084	−0.00810422	−	0.999967i	$-0.502580\pi$
$947$	−0.498788	−0.0162084	−0.00810422	+	0.999967i	$0.502580\pi$
$948$	−273.536	−8.88404
$949$	65.6645	2.13156
$950$	9.19841	0.298436
$951$	−48.9637	−1.58776
$952$	40.3979	1.30930
$953$	23.5147	0.761717	0.380858	−	0.924633i	$-0.375629\pi$
$953$	23.5147	0.761717	0.380858	+	0.924633i	$0.375629\pi$
$954$	143.682	4.65186
$955$	−2.59376	−0.0839319
$956$	−95.6256	−3.09275
$957$	−126.408	−4.08621
$958$	−54.5062	−1.76102
$959$	−3.65610	−0.118062
$960$	−78.5835	−2.53627
$961$	−10.7695	−0.347403
$962$	10.7950	0.348046
$963$	−80.7465	−2.60202
$964$	−28.2998	−0.911475
$965$	−5.60950	−0.180576
$966$	−27.6701	−0.890272
$967$	16.9129	0.543881	0.271940	−	0.962314i	$-0.412335\pi$
$967$	16.9129	0.543881	0.271940	+	0.962314i	$0.412335\pi$
$968$	−184.551	−5.93170
$969$	6.53995	0.210093
$970$	32.7025	1.05001
$971$	36.4463	1.16962	0.584809	−	0.811171i	$-0.301169\pi$
$971$	36.4463	1.16962	0.584809	+	0.811171i	$0.301169\pi$
$972$	−74.5184	−2.39018
$973$	−17.1344	−0.549304
$974$	−107.981	−3.45992
$975$	52.9100	1.69448
$976$	31.3459	1.00336
$977$	24.6003	0.787035	0.393517	−	0.919317i	$-0.371258\pi$
$977$	24.6003	0.787035	0.393517	+	0.919317i	$0.371258\pi$
$978$	−148.734	−4.75599
$979$	−66.8525	−2.13662
$980$	21.7159	0.693689
$981$	12.8759	0.411096
$982$	−20.5935	−0.657164
$983$	14.3044	0.456238	0.228119	−	0.973633i	$-0.426742\pi$
$983$	14.3044	0.456238	0.228119	+	0.973633i	$0.426742\pi$
$984$	−117.384	−3.74207
$985$	9.43668	0.300678
$986$	70.5827	2.24781
$987$	37.9021	1.20644
$988$	−17.3949	−0.553404
$989$	−1.15395	−0.0366934
$990$	54.6642	1.73734
$991$	15.1821	0.482274	0.241137	−	0.970491i	$-0.422480\pi$
$991$	15.1821	0.482274	0.241137	+	0.970491i	$0.422480\pi$
$992$	−116.862	−3.71036
$993$	−30.8316	−0.978410
$994$	−3.65221	−0.115841
$995$	−0.877987	−0.0278341
$996$	−60.0194	−1.90179
$997$	32.6924	1.03538	0.517689	−	0.855569i	$-0.326793\pi$
$997$	32.6924	1.03538	0.517689	+	0.855569i	$0.326793\pi$
$998$	2.49579	0.0790028
$999$	5.59232	0.176933

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	8017.2.a.a.1.4	✓	327

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
8017.2.a.a.1.4	✓	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)

\(f(q)\)	\(=\)	\(q-2.76749 q^{2} +2.84439 q^{3} +5.65899 q^{4} -0.717749 q^{5} -7.87182 q^{6} -1.28590 q^{7} -10.1262 q^{8} +5.09057 q^{9} +O(q^{10})\)	\(q-2.76749 q^{2} +2.84439 q^{3} +5.65899 q^{4} -0.717749 q^{5} -7.87182 q^{6} -1.28590 q^{7} -10.1262 q^{8} +5.09057 q^{9} +1.98636 q^{10} +5.40602 q^{11} +16.0964 q^{12} -4.14764 q^{13} +3.55872 q^{14} -2.04156 q^{15} +16.7062 q^{16} +3.10244 q^{17} -14.0881 q^{18} +0.741106 q^{19} -4.06174 q^{20} -3.65761 q^{21} -14.9611 q^{22} -2.73356 q^{23} -28.8029 q^{24} -4.48484 q^{25} +11.4786 q^{26} +5.94641 q^{27} -7.27690 q^{28} -8.22070 q^{29} +5.65000 q^{30} +4.49784 q^{31} -25.9818 q^{32} +15.3769 q^{33} -8.58598 q^{34} +0.922955 q^{35} +28.8075 q^{36} +0.940453 q^{37} -2.05100 q^{38} -11.7975 q^{39} +7.26808 q^{40} +4.07542 q^{41} +10.1224 q^{42} +0.422141 q^{43} +30.5926 q^{44} -3.65376 q^{45} +7.56509 q^{46} -10.3625 q^{47} +47.5190 q^{48} -5.34646 q^{49} +12.4117 q^{50} +8.82457 q^{51} -23.4715 q^{52} -10.1988 q^{53} -16.4566 q^{54} -3.88017 q^{55} +13.0213 q^{56} +2.10800 q^{57} +22.7507 q^{58} +0.327670 q^{59} -11.5532 q^{60} +1.87631 q^{61} -12.4477 q^{62} -6.54597 q^{63} +38.4918 q^{64} +2.97697 q^{65} -42.5553 q^{66} -5.45030 q^{67} +17.5567 q^{68} -7.77531 q^{69} -2.55427 q^{70} -1.02627 q^{71} -51.5482 q^{72} -15.8318 q^{73} -2.60269 q^{74} -12.7566 q^{75} +4.19391 q^{76} -6.95161 q^{77} +32.6495 q^{78} -16.9936 q^{79} -11.9909 q^{80} +1.64221 q^{81} -11.2787 q^{82} -3.72875 q^{83} -20.6984 q^{84} -2.22678 q^{85} -1.16827 q^{86} -23.3829 q^{87} -54.7425 q^{88} -12.3663 q^{89} +10.1117 q^{90} +5.33346 q^{91} -15.4692 q^{92} +12.7936 q^{93} +28.6782 q^{94} -0.531929 q^{95} -73.9024 q^{96} +16.4635 q^{97} +14.7963 q^{98} +27.5197 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 327 q - 23 q^{2} - 48 q^{3} + 315 q^{4} - 55 q^{5} - 38 q^{6} - 87 q^{7} - 69 q^{8} + 303 q^{9}+O(q^{10}) \) 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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