LMFDB - Embedded newform 6001.2.a.a.1.17

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6001,2,Mod(1,6001)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6001, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("6001.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6001 = 17 \cdot 353 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6001.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:	$47.9182262530$
Analytic rank:	$1$
Dimension:	$113$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.17
Character	$\chi$	$=$	6001.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.18121 q^{2} +0.0139647 q^{3} +2.75766 q^{4} -0.236603 q^{5} -0.0304599 q^{6} +2.78463 q^{7} -1.65261 q^{8} -2.99980 q^{9} +O(q^{10})$	\(q-2.18121 q^{2} +0.0139647 q^{3} +2.75766 q^{4} -0.236603 q^{5} -0.0304599 q^{6} +2.78463 q^{7} -1.65261 q^{8} -2.99980 q^{9} +0.516079 q^{10} -5.66454 q^{11} +0.0385099 q^{12} +4.89548 q^{13} -6.07386 q^{14} -0.00330409 q^{15} -1.91063 q^{16} -1.00000 q^{17} +6.54319 q^{18} +6.12718 q^{19} -0.652470 q^{20} +0.0388866 q^{21} +12.3555 q^{22} -0.0978372 q^{23} -0.0230782 q^{24} -4.94402 q^{25} -10.6780 q^{26} -0.0837856 q^{27} +7.67907 q^{28} +2.61417 q^{29} +0.00720690 q^{30} -5.19135 q^{31} +7.47271 q^{32} -0.0791037 q^{33} +2.18121 q^{34} -0.658852 q^{35} -8.27244 q^{36} -4.53283 q^{37} -13.3646 q^{38} +0.0683639 q^{39} +0.391012 q^{40} -1.67928 q^{41} -0.0848197 q^{42} +6.00110 q^{43} -15.6209 q^{44} +0.709762 q^{45} +0.213403 q^{46} -1.79980 q^{47} -0.0266815 q^{48} +0.754186 q^{49} +10.7839 q^{50} -0.0139647 q^{51} +13.5001 q^{52} +0.426460 q^{53} +0.182754 q^{54} +1.34024 q^{55} -4.60192 q^{56} +0.0855643 q^{57} -5.70205 q^{58} +9.44480 q^{59} -0.00911155 q^{60} +8.22973 q^{61} +11.3234 q^{62} -8.35336 q^{63} -12.4782 q^{64} -1.15828 q^{65} +0.172541 q^{66} -3.84988 q^{67} -2.75766 q^{68} -0.00136627 q^{69} +1.43709 q^{70} -0.400465 q^{71} +4.95751 q^{72} +4.44739 q^{73} +9.88704 q^{74} -0.0690418 q^{75} +16.8967 q^{76} -15.7737 q^{77} -0.149116 q^{78} +11.8782 q^{79} +0.452061 q^{80} +8.99824 q^{81} +3.66285 q^{82} -16.5780 q^{83} +0.107236 q^{84} +0.236603 q^{85} -13.0896 q^{86} +0.0365062 q^{87} +9.36128 q^{88} -1.90879 q^{89} -1.54814 q^{90} +13.6321 q^{91} -0.269802 q^{92} -0.0724957 q^{93} +3.92573 q^{94} -1.44971 q^{95} +0.104354 q^{96} -7.79531 q^{97} -1.64504 q^{98} +16.9925 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) $ 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * 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 $

$2$	−2.18121	−1.54235	−0.771173	−	0.636626i	$-0.780330\pi$
$2$	−2.18121	−1.54235	−0.771173	+	0.636626i	$0.780330\pi$
$3$	0.0139647	0.00806253	0.00403127	−	0.999992i	$-0.498717\pi$
$3$	0.0139647	0.00806253	0.00403127	+	0.999992i	$0.498717\pi$
$4$	2.75766	1.37883
$5$	−0.236603	−0.105812	−0.0529060	−	0.998599i	$-0.516848\pi$
$5$	−0.236603	−0.105812	−0.0529060	+	0.998599i	$0.516848\pi$
$6$	−0.0304599	−0.0124352
$7$	2.78463	1.05249	0.526246	−	0.850332i	$-0.323599\pi$
$7$	2.78463	1.05249	0.526246	+	0.850332i	$0.323599\pi$
$8$	−1.65261	−0.584286
$9$	−2.99980	−0.999935
$10$	0.516079	0.163199
$11$	−5.66454	−1.70792	−0.853961	−	0.520337i	$-0.825806\pi$
$11$	−5.66454	−1.70792	−0.853961	+	0.520337i	$0.825806\pi$
$12$	0.0385099	0.0111169
$13$	4.89548	1.35776	0.678880	−	0.734249i	$-0.262465\pi$
$13$	4.89548	1.35776	0.678880	+	0.734249i	$0.262465\pi$
$14$	−6.07386	−1.62331
$15$	−0.00330409	−0.000853112 0
$16$	−1.91063	−0.477658
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	6.54319	1.54225
$19$	6.12718	1.40567	0.702836	−	0.711352i	$-0.251917\pi$
$19$	6.12718	1.40567	0.702836	+	0.711352i	$0.251917\pi$
$20$	−0.652470	−0.145897
$21$	0.0388866	0.00848576
$22$	12.3555	2.63421
$23$	−0.0978372	−0.0204005	−0.0102002	−	0.999948i	$-0.503247\pi$
$23$	−0.0978372	−0.0204005	−0.0102002	+	0.999948i	$0.503247\pi$
$24$	−0.0230782	−0.00471083
$25$	−4.94402	−0.988804
$26$	−10.6780	−2.09414
$27$	−0.0837856	−0.0161245
$28$	7.67907	1.45121
$29$	2.61417	0.485440	0.242720	−	0.970096i	$-0.421960\pi$
$29$	2.61417	0.485440	0.242720	+	0.970096i	$0.421960\pi$
$30$	0.00720690	0.00131579
$31$	−5.19135	−0.932394	−0.466197	−	0.884681i	$-0.654376\pi$
$31$	−5.19135	−0.932394	−0.466197	+	0.884681i	$0.654376\pi$
$32$	7.47271	1.32100
$33$	−0.0791037	−0.0137702
$34$	2.18121	0.374074
$35$	−0.658852	−0.111366
$36$	−8.27244	−1.37874
$37$	−4.53283	−0.745193	−0.372596	−	0.927994i	$-0.621532\pi$
$37$	−4.53283	−0.745193	−0.372596	+	0.927994i	$0.621532\pi$
$38$	−13.3646	−2.16803
$39$	0.0683639	0.0109470
$40$	0.391012	0.0618245
$41$	−1.67928	−0.262259	−0.131130	−	0.991365i	$-0.541860\pi$
$41$	−1.67928	−0.262259	−0.131130	+	0.991365i	$0.541860\pi$
$42$	−0.0848197	−0.0130880
$43$	6.00110	0.915160	0.457580	−	0.889169i	$-0.348716\pi$
$43$	6.00110	0.915160	0.457580	+	0.889169i	$0.348716\pi$
$44$	−15.6209	−2.35493
$45$	0.709762	0.105805
$46$	0.213403	0.0314646
$47$	−1.79980	−0.262527	−0.131264	−	0.991347i	$-0.541903\pi$
$47$	−1.79980	−0.262527	−0.131264	+	0.991347i	$0.541903\pi$
$48$	−0.0266815	−0.00385114
$49$	0.754186	0.107741
$50$	10.7839	1.52508
$51$	−0.0139647	−0.00195545
$52$	13.5001	1.87212
$53$	0.426460	0.0585787	0.0292894	−	0.999571i	$-0.490676\pi$
$53$	0.426460	0.0585787	0.0292894	+	0.999571i	$0.490676\pi$
$54$	0.182754	0.0248696
$55$	1.34024	0.180719
$56$	−4.60192	−0.614957
$57$	0.0855643	0.0113333
$58$	−5.70205	−0.748716
$59$	9.44480	1.22961	0.614804	−	0.788680i	$-0.289235\pi$
$59$	9.44480	1.22961	0.614804	+	0.788680i	$0.289235\pi$
$60$	−0.00911155	−0.00117630
$61$	8.22973	1.05371	0.526855	−	0.849955i	$-0.323371\pi$
$61$	8.22973	1.05371	0.526855	+	0.849955i	$0.323371\pi$
$62$	11.3234	1.43807
$63$	−8.35336	−1.05242
$64$	−12.4782	−1.55978
$65$	−1.15828	−0.143667
$66$	0.172541	0.0212384
$67$	−3.84988	−0.470338	−0.235169	−	0.971955i	$-0.575564\pi$
$67$	−3.84988	−0.470338	−0.235169	+	0.971955i	$0.575564\pi$
$68$	−2.75766	−0.334415
$69$	−0.00136627	−0.000164480 0
$70$	1.43709	0.171765
$71$	−0.400465	−0.0475264	−0.0237632	−	0.999718i	$-0.507565\pi$
$71$	−0.400465	−0.0475264	−0.0237632	+	0.999718i	$0.507565\pi$
$72$	4.95751	0.584248
$73$	4.44739	0.520527	0.260264	−	0.965538i	$-0.416190\pi$
$73$	4.44739	0.520527	0.260264	+	0.965538i	$0.416190\pi$
$74$	9.88704	1.14934
$75$	−0.0690418	−0.00797226
$76$	16.8967	1.93818
$77$	−15.7737	−1.79758
$78$	−0.149116	−0.0168840
$79$	11.8782	1.33640	0.668201	−	0.743980i	$-0.267064\pi$
$79$	11.8782	1.33640	0.668201	+	0.743980i	$0.267064\pi$
$80$	0.452061	0.0505420
$81$	8.99824	0.999805
$82$	3.66285	0.404494
$83$	−16.5780	−1.81968	−0.909838	−	0.414964i	$-0.863794\pi$
$83$	−16.5780	−1.81968	−0.909838	+	0.414964i	$0.863794\pi$
$84$	0.107236	0.0117004
$85$	0.236603	0.0256632
$86$	−13.0896	−1.41149
$87$	0.0365062	0.00391388
$88$	9.36128	0.997915
$89$	−1.90879	−0.202331	−0.101166	−	0.994870i	$-0.532257\pi$
$89$	−1.90879	−0.202331	−0.101166	+	0.994870i	$0.532257\pi$
$90$	−1.54814	−0.163188
$91$	13.6321	1.42903
$92$	−0.269802	−0.0281288
$93$	−0.0724957	−0.00751746
$94$	3.92573	0.404908
$95$	−1.44971	−0.148737
$96$	0.104354	0.0106506
$97$	−7.79531	−0.791494	−0.395747	−	0.918360i	$-0.629514\pi$
$97$	−7.79531	−0.791494	−0.395747	+	0.918360i	$0.629514\pi$
$98$	−1.64504	−0.166174
$99$	16.9925	1.70781
$100$	−13.6339	−1.36339
$101$	0.952146	0.0947421	0.0473710	−	0.998877i	$-0.484916\pi$
$101$	0.952146	0.0947421	0.0473710	+	0.998877i	$0.484916\pi$
$102$	0.0304599	0.00301598
$103$	13.2739	1.30791	0.653956	−	0.756533i	$-0.273108\pi$
$103$	13.2739	1.30791	0.653956	+	0.756533i	$0.273108\pi$
$104$	−8.09032	−0.793321
$105$	−0.00920068	−0.000897895 0
$106$	−0.930197	−0.0903487
$107$	−12.7926	−1.23671	−0.618354	−	0.785900i	$-0.712200\pi$
$107$	−12.7926	−1.23671	−0.618354	+	0.785900i	$0.712200\pi$
$108$	−0.231052	−0.0222330
$109$	−19.3938	−1.85759	−0.928793	−	0.370600i	$-0.879152\pi$
$109$	−19.3938	−1.85759	−0.928793	+	0.370600i	$0.879152\pi$
$110$	−2.92335	−0.278730
$111$	−0.0632997	−0.00600814
$112$	−5.32042	−0.502732
$113$	−1.68194	−0.158224	−0.0791118	−	0.996866i	$-0.525208\pi$
$113$	−1.68194	−0.158224	−0.0791118	+	0.996866i	$0.525208\pi$
$114$	−0.186633	−0.0174798
$115$	0.0231486	0.00215861
$116$	7.20900	0.669339
$117$	−14.6855	−1.35767
$118$	−20.6011	−1.89648
$119$	−2.78463	−0.255267
$120$	0.00546038	0.000498462 0
$121$	21.0870	1.91700
$122$	−17.9507	−1.62518
$123$	−0.0234506	−0.00211447
$124$	−14.3160	−1.28561
$125$	2.35278	0.210439
$126$	18.2204	1.62320
$127$	1.04483	0.0927136	0.0463568	−	0.998925i	$-0.485239\pi$
$127$	1.04483	0.0927136	0.0463568	+	0.998925i	$0.485239\pi$
$128$	12.2722	1.08472
$129$	0.0838037	0.00737851
$130$	2.52645	0.221585
$131$	−8.35504	−0.729983	−0.364992	−	0.931011i	$-0.618928\pi$
$131$	−8.35504	−0.729983	−0.364992	+	0.931011i	$0.618928\pi$
$132$	−0.218141	−0.0189867
$133$	17.0620	1.47946
$134$	8.39738	0.725423
$135$	0.0198239	0.00170617
$136$	1.65261	0.141710
$137$	−22.2126	−1.89775	−0.948874	−	0.315654i	$-0.897776\pi$
$137$	−22.2126	−1.89775	−0.948874	+	0.315654i	$0.897776\pi$
$138$	0.00298011	0.000253684 0
$139$	−14.1827	−1.20296	−0.601479	−	0.798889i	$-0.705422\pi$
$139$	−14.1827	−1.20296	−0.601479	+	0.798889i	$0.705422\pi$
$140$	−1.81689	−0.153555
$141$	−0.0251337	−0.00211664
$142$	0.873496	0.0733022
$143$	−27.7306	−2.31895
$144$	5.73153	0.477627
$145$	−0.618521	−0.0513654
$146$	−9.70067	−0.802833
$147$	0.0105320	0.000868665 0
$148$	−12.5000	−1.02749
$149$	−4.34874	−0.356263	−0.178131	−	0.984007i	$-0.557005\pi$
$149$	−4.34874	−0.356263	−0.178131	+	0.984007i	$0.557005\pi$
$150$	0.150594	0.0122960
$151$	−10.2906	−0.837435	−0.418717	−	0.908117i	$-0.637520\pi$
$151$	−10.2906	−0.837435	−0.418717	+	0.908117i	$0.637520\pi$
$152$	−10.1258	−0.821314
$153$	2.99980	0.242520
$154$	34.4056	2.77248
$155$	1.22829	0.0986584
$156$	0.188524	0.0150940
$157$	−24.4283	−1.94959	−0.974796	−	0.223096i	$-0.928383\pi$
$157$	−24.4283	−1.94959	−0.974796	+	0.223096i	$0.928383\pi$
$158$	−25.9088	−2.06120
$159$	0.00595539	0.000472293 0
$160$	−1.76806	−0.139778
$161$	−0.272441	−0.0214714
$162$	−19.6270	−1.54204
$163$	18.0880	1.41676	0.708380	−	0.705831i	$-0.249426\pi$
$163$	18.0880	1.41676	0.708380	+	0.705831i	$0.249426\pi$
$164$	−4.63087	−0.361611
$165$	0.0187161	0.00145705
$166$	36.1601	2.80657
$167$	−8.90292	−0.688928	−0.344464	−	0.938799i	$-0.611939\pi$
$167$	−8.90292	−0.688928	−0.344464	+	0.938799i	$0.611939\pi$
$168$	−0.0642645	−0.00495811
$169$	10.9657	0.843514
$170$	−0.516079	−0.0395815
$171$	−18.3803	−1.40558
$172$	16.5490	1.26185
$173$	10.4391	0.793672	0.396836	−	0.917890i	$-0.370108\pi$
$173$	10.4391	0.793672	0.396836	+	0.917890i	$0.370108\pi$
$174$	−0.0796276	−0.00603655
$175$	−13.7673	−1.04071
$176$	10.8229	0.815803
$177$	0.131894	0.00991376
$178$	4.16346	0.312065
$179$	−7.44349	−0.556353	−0.278176	−	0.960530i	$-0.589730\pi$
$179$	−7.44349	−0.556353	−0.278176	+	0.960530i	$0.589730\pi$
$180$	1.95728	0.145887
$181$	21.5322	1.60047	0.800236	−	0.599685i	$-0.204707\pi$
$181$	21.5322	1.60047	0.800236	+	0.599685i	$0.204707\pi$
$182$	−29.7344	−2.20406
$183$	0.114926	0.00849557
$184$	0.161687	0.0119197
$185$	1.07248	0.0788503
$186$	0.158128	0.0115945
$187$	5.66454	0.414232
$188$	−4.96323	−0.361980
$189$	−0.233312	−0.0169710
$190$	3.16211	0.229404
$191$	26.8064	1.93965	0.969823	−	0.243810i	$-0.0783973\pi$
$191$	26.8064	1.93965	0.969823	+	0.243810i	$0.0783973\pi$
$192$	−0.174255	−0.0125758
$193$	23.2383	1.67273	0.836366	−	0.548172i	$-0.184676\pi$
$193$	23.2383	1.67273	0.836366	+	0.548172i	$0.184676\pi$
$194$	17.0032	1.22076
$195$	−0.0161751	−0.00115832
$196$	2.07979	0.148556
$197$	−21.9696	−1.56527	−0.782636	−	0.622479i	$-0.786125\pi$
$197$	−21.9696	−1.56527	−0.782636	+	0.622479i	$0.786125\pi$
$198$	−37.0642	−2.63403
$199$	−20.4389	−1.44888	−0.724438	−	0.689340i	$-0.757900\pi$
$199$	−20.4389	−1.44888	−0.724438	+	0.689340i	$0.757900\pi$
$200$	8.17054	0.577744
$201$	−0.0537625	−0.00379211
$202$	−2.07683	−0.146125
$203$	7.27952	0.510922
$204$	−0.0385099	−0.00269623
$205$	0.397322	0.0277501
$206$	−28.9530	−2.01725
$207$	0.293493	0.0203991
$208$	−9.35346	−0.648546
$209$	−34.7076	−2.40078
$210$	0.0200686	0.00138486
$211$	16.8800	1.16207	0.581033	−	0.813880i	$-0.302649\pi$
$211$	16.8800	1.16207	0.581033	+	0.813880i	$0.302649\pi$
$212$	1.17603	0.0807701
$213$	−0.00559238	−0.000383183 0
$214$	27.9033	1.90743
$215$	−1.41988	−0.0968348
$216$	0.138465	0.00942135
$217$	−14.4560	−0.981338
$218$	42.3018	2.86504
$219$	0.0621065	0.00419677
$220$	3.69594	0.249180
$221$	−4.89548	−0.329305
$222$	0.138070	0.00926663
$223$	1.82424	0.122160	0.0610799	−	0.998133i	$-0.480546\pi$
$223$	1.82424	0.122160	0.0610799	+	0.998133i	$0.480546\pi$
$224$	20.8088	1.39034
$225$	14.8311	0.988740
$226$	3.66866	0.244036
$227$	23.7571	1.57681	0.788406	−	0.615156i	$-0.210907\pi$
$227$	23.7571	1.57681	0.788406	+	0.615156i	$0.210907\pi$
$228$	0.235957	0.0156267
$229$	−0.899324	−0.0594290	−0.0297145	−	0.999558i	$-0.509460\pi$
$229$	−0.899324	−0.0594290	−0.0297145	+	0.999558i	$0.509460\pi$
$230$	−0.0504918	−0.00332933
$231$	−0.220275	−0.0144930
$232$	−4.32021	−0.283636
$233$	24.1405	1.58150	0.790749	−	0.612141i	$-0.209692\pi$
$233$	24.1405	1.58150	0.790749	+	0.612141i	$0.209692\pi$
$234$	32.0320	2.09400
$235$	0.425837	0.0277785
$236$	26.0456	1.69542
$237$	0.165876	0.0107748
$238$	6.07386	0.393710
$239$	8.45644	0.547002	0.273501	−	0.961872i	$-0.411818\pi$
$239$	8.45644	0.547002	0.273501	+	0.961872i	$0.411818\pi$
$240$	0.00631291	0.000407496 0
$241$	15.6352	1.00715	0.503575	−	0.863952i	$-0.332018\pi$
$241$	15.6352	1.00715	0.503575	+	0.863952i	$0.332018\pi$
$242$	−45.9950	−2.95667
$243$	0.377015	0.0241855
$244$	22.6948	1.45289
$245$	−0.178443	−0.0114003
$246$	0.0511507	0.00326125
$247$	29.9955	1.90857
$248$	8.57928	0.544785
$249$	−0.231508	−0.0146712
$250$	−5.13190	−0.324570
$251$	−14.3074	−0.903074	−0.451537	−	0.892252i	$-0.649124\pi$
$251$	−14.3074	−0.903074	−0.451537	+	0.892252i	$0.649124\pi$
$252$	−23.0357	−1.45111
$253$	0.554203	0.0348424
$254$	−2.27899	−0.142996
$255$	0.00330409	0.000206910 0
$256$	−1.81172	−0.113233
$257$	−11.1563	−0.695912	−0.347956	−	0.937511i	$-0.613124\pi$
$257$	−11.1563	−0.695912	−0.347956	+	0.937511i	$0.613124\pi$
$258$	−0.182793	−0.0113802
$259$	−12.6223	−0.784310
$260$	−3.19415	−0.198093
$261$	−7.84201	−0.485409
$262$	18.2241	1.12589
$263$	−6.74471	−0.415897	−0.207948	−	0.978140i	$-0.566679\pi$
$263$	−6.74471	−0.415897	−0.207948	+	0.978140i	$0.566679\pi$
$264$	0.130728	0.00804573
$265$	−0.100902	−0.00619833
$266$	−37.2156	−2.28184
$267$	−0.0266557	−0.00163130
$268$	−10.6167	−0.648516
$269$	−3.45962	−0.210937	−0.105468	−	0.994423i	$-0.533634\pi$
$269$	−3.45962	−0.210937	−0.105468	+	0.994423i	$0.533634\pi$
$270$	−0.0432400	−0.00263150
$271$	12.5859	0.764542	0.382271	−	0.924050i	$-0.375142\pi$
$271$	12.5859	0.764542	0.382271	+	0.924050i	$0.375142\pi$
$272$	1.91063	0.115849
$273$	0.190369	0.0115216
$274$	48.4502	2.92698
$275$	28.0056	1.68880
$276$	−0.00376771	−0.000226789 0
$277$	−17.6037	−1.05770	−0.528851	−	0.848715i	$-0.677377\pi$
$277$	−17.6037	−1.05770	−0.528851	+	0.848715i	$0.677377\pi$
$278$	30.9353	1.85538
$279$	15.5730	0.932333
$280$	1.08883	0.0650698
$281$	−6.35606	−0.379171	−0.189585	−	0.981864i	$-0.560714\pi$
$281$	−6.35606	−0.379171	−0.189585	+	0.981864i	$0.560714\pi$
$282$	0.0548217	0.00326458
$283$	−4.62251	−0.274780	−0.137390	−	0.990517i	$-0.543871\pi$
$283$	−4.62251	−0.274780	−0.137390	+	0.990517i	$0.543871\pi$
$284$	−1.10435	−0.0655309
$285$	−0.0202448	−0.00119920
$286$	60.4862	3.57662
$287$	−4.67617	−0.276026
$288$	−22.4167	−1.32091
$289$	1.00000	0.0588235
$290$	1.34912	0.0792231
$291$	−0.108859	−0.00638145
$292$	12.2644	0.717719
$293$	11.1440	0.651040	0.325520	−	0.945535i	$-0.394461\pi$
$293$	11.1440	0.651040	0.325520	+	0.945535i	$0.394461\pi$
$294$	−0.0229725	−0.00133978
$295$	−2.23467	−0.130107
$296$	7.49100	0.435406
$297$	0.474607	0.0275395
$298$	9.48550	0.549480
$299$	−0.478960	−0.0276990
$300$	−0.190394	−0.0109924
$301$	16.7109	0.963199
$302$	22.4459	1.29161
$303$	0.0132964	0.000763861 0
$304$	−11.7068	−0.671431
$305$	−1.94718	−0.111495
$306$	−6.54319	−0.374049
$307$	−21.1329	−1.20612	−0.603060	−	0.797696i	$-0.706052\pi$
$307$	−21.1329	−1.20612	−0.603060	+	0.797696i	$0.706052\pi$
$308$	−43.4984	−2.47855
$309$	0.185366	0.0105451
$310$	−2.67915	−0.152165
$311$	4.16065	0.235929	0.117964	−	0.993018i	$-0.462363\pi$
$311$	4.16065	0.235929	0.117964	+	0.993018i	$0.462363\pi$
$312$	−0.112979	−0.00639618
$313$	−5.53361	−0.312778	−0.156389	−	0.987696i	$-0.549985\pi$
$313$	−5.53361	−0.312778	−0.156389	+	0.987696i	$0.549985\pi$
$314$	53.2832	3.00695
$315$	1.97643	0.111359
$316$	32.7561	1.84267
$317$	0.486623	0.0273315	0.0136657	−	0.999907i	$-0.495650\pi$
$317$	0.486623	0.0273315	0.0136657	+	0.999907i	$0.495650\pi$
$318$	−0.0129899	−0.000728439 0
$319$	−14.8081	−0.829094
$320$	2.95239	0.165043
$321$	−0.178645	−0.00997100
$322$	0.594250	0.0331162
$323$	−6.12718	−0.340925
$324$	24.8141	1.37856
$325$	−24.2033	−1.34256
$326$	−39.4536	−2.18513
$327$	−0.270828	−0.0149768
$328$	2.77519	0.153234
$329$	−5.01178	−0.276308
$330$	−0.0408238	−0.00224727
$331$	−26.7772	−1.47181	−0.735903	−	0.677087i	$-0.763242\pi$
$331$	−26.7772	−1.47181	−0.735903	+	0.677087i	$0.763242\pi$
$332$	−45.7166	−2.50902
$333$	13.5976	0.745144
$334$	19.4191	1.06257
$335$	0.910892	0.0497674
$336$	−0.0742981	−0.00405329
$337$	−11.7837	−0.641901	−0.320950	−	0.947096i	$-0.604002\pi$
$337$	−11.7837	−0.641901	−0.320950	+	0.947096i	$0.604002\pi$
$338$	−23.9184	−1.30099
$339$	−0.0234878	−0.00127568
$340$	0.652470	0.0353851
$341$	29.4066	1.59246
$342$	40.0913	2.16789
$343$	−17.3923	−0.939096
$344$	−9.91749	−0.534715
$345$	0.000323263 0	1.74039e−5 0
$346$	−22.7699	−1.22412
$347$	−26.3068	−1.41222	−0.706111	−	0.708101i	$-0.749552\pi$
$347$	−26.3068	−1.41222	−0.706111	+	0.708101i	$0.749552\pi$
$348$	0.100672	0.00539657
$349$	−2.05948	−0.110241	−0.0551206	−	0.998480i	$-0.517554\pi$
$349$	−2.05948	−0.110241	−0.0551206	+	0.998480i	$0.517554\pi$
$350$	30.0293	1.60513
$351$	−0.410170	−0.0218933
$352$	−42.3294	−2.25617
$353$	−1.00000	−0.0532246
$353$	−1.00000	−0.0532246
$354$	−0.287688	−0.0152904
$355$	0.0947511	0.00502886
$356$	−5.26379	−0.278980
$357$	−0.0388866	−0.00205810
$358$	16.2358	0.858088
$359$	−33.2043	−1.75245	−0.876227	−	0.481898i	$-0.839947\pi$
$359$	−33.2043	−1.75245	−0.876227	+	0.481898i	$0.839947\pi$
$360$	−1.17296	−0.0618204
$361$	18.5423	0.975912
$362$	−46.9661	−2.46848
$363$	0.294474	0.0154559
$364$	37.5927	1.97039
$365$	−1.05226	−0.0550780
$366$	−0.250677	−0.0131031
$367$	−2.02566	−0.105738	−0.0528692	−	0.998601i	$-0.516837\pi$
$367$	−2.02566	−0.105738	−0.0528692	+	0.998601i	$0.516837\pi$
$368$	0.186931	0.00974446
$369$	5.03750	0.262242
$370$	−2.33930	−0.121614
$371$	1.18753	0.0616537
$372$	−0.199919	−0.0103653
$373$	−17.0074	−0.880610	−0.440305	−	0.897848i	$-0.645130\pi$
$373$	−17.0074	−0.880610	−0.440305	+	0.897848i	$0.645130\pi$
$374$	−12.3555	−0.638889
$375$	0.0328559	0.00169667
$376$	2.97436	0.153391
$377$	12.7976	0.659112
$378$	0.508902	0.0261751
$379$	−28.2999	−1.45367	−0.726834	−	0.686813i	$-0.759009\pi$
$379$	−28.2999	−1.45367	−0.726834	+	0.686813i	$0.759009\pi$
$380$	−3.99780	−0.205083
$381$	0.0145907	0.000747506 0
$382$	−58.4704	−2.99160
$383$	−12.5405	−0.640788	−0.320394	−	0.947284i	$-0.603815\pi$
$383$	−12.5405	−0.640788	−0.320394	+	0.947284i	$0.603815\pi$
$384$	0.171378	0.00874559
$385$	3.73209	0.190205
$386$	−50.6876	−2.57993
$387$	−18.0021	−0.915100
$388$	−21.4968	−1.09134
$389$	−22.2421	−1.12772	−0.563860	−	0.825870i	$-0.690684\pi$
$389$	−22.2421	−1.12772	−0.563860	+	0.825870i	$0.690684\pi$
$390$	0.0352812	0.00178653
$391$	0.0978372	0.00494784
$392$	−1.24638	−0.0629515
$393$	−0.116676	−0.00588552
$394$	47.9203	2.41419
$395$	−2.81042	−0.141407
$396$	46.8595	2.35478
$397$	21.0139	1.05466	0.527328	−	0.849662i	$-0.323194\pi$
$397$	21.0139	1.05466	0.527328	+	0.849662i	$0.323194\pi$
$398$	44.5814	2.23467
$399$	0.238265	0.0119282
$400$	9.44621	0.472311
$401$	−9.45476	−0.472148	−0.236074	−	0.971735i	$-0.575861\pi$
$401$	−9.45476	−0.472148	−0.236074	+	0.971735i	$0.575861\pi$
$402$	0.117267	0.00584875
$403$	−25.4141	−1.26597
$404$	2.62569	0.130633
$405$	−2.12901	−0.105791
$406$	−15.8781	−0.788018
$407$	25.6764	1.27273
$408$	0.0230782	0.00114254
$409$	−5.34721	−0.264403	−0.132201	−	0.991223i	$-0.542205\pi$
$409$	−5.34721	−0.264403	−0.132201	+	0.991223i	$0.542205\pi$
$410$	−0.866640	−0.0428003
$411$	−0.310192	−0.0153007
$412$	36.6048	1.80339
$413$	26.3003	1.29415
$414$	−0.640168	−0.0314625
$415$	3.92241	0.192543
$416$	36.5825	1.79360
$417$	−0.198057	−0.00969889
$418$	75.7045	3.70283
$419$	−7.67143	−0.374774	−0.187387	−	0.982286i	$-0.560002\pi$
$419$	−7.67143	−0.374774	−0.187387	+	0.982286i	$0.560002\pi$
$420$	−0.0253723	−0.00123804
$421$	30.9376	1.50781	0.753904	−	0.656985i	$-0.228168\pi$
$421$	30.9376	1.50781	0.753904	+	0.656985i	$0.228168\pi$
$422$	−36.8187	−1.79231
$423$	5.39904	0.262510
$424$	−0.704772	−0.0342268
$425$	4.94402	0.239820
$426$	0.0121981	0.000591001 0
$427$	22.9168	1.10902
$428$	−35.2776	−1.70521
$429$	−0.387250	−0.0186966
$430$	3.09705	0.149353
$431$	0.762389	0.0367230	0.0183615	−	0.999831i	$-0.494155\pi$
$431$	0.762389	0.0367230	0.0183615	+	0.999831i	$0.494155\pi$
$432$	0.160084	0.00770202
$433$	−9.95407	−0.478362	−0.239181	−	0.970975i	$-0.576879\pi$
$433$	−9.95407	−0.478362	−0.239181	+	0.970975i	$0.576879\pi$
$434$	31.5315	1.51356
$435$	−0.00863747	−0.000414135 0
$436$	−53.4814	−2.56129
$437$	−0.599466	−0.0286764
$438$	−0.135467	−0.00647287
$439$	17.6779	0.843718	0.421859	−	0.906661i	$-0.361378\pi$
$439$	17.6779	0.843718	0.421859	+	0.906661i	$0.361378\pi$
$440$	−2.21490	−0.105591
$441$	−2.26241	−0.107734
$442$	10.6780	0.507903
$443$	11.3613	0.539790	0.269895	−	0.962890i	$-0.413011\pi$
$443$	11.3613	0.539790	0.269895	+	0.962890i	$0.413011\pi$
$444$	−0.174559	−0.00828420
$445$	0.451625	0.0214091
$446$	−3.97903	−0.188413
$447$	−0.0607289	−0.00287238
$448$	−34.7473	−1.64166
$449$	31.2258	1.47364	0.736818	−	0.676091i	$-0.236327\pi$
$449$	31.2258	1.47364	0.736818	+	0.676091i	$0.236327\pi$
$450$	−32.3497	−1.52498
$451$	9.51233	0.447918
$452$	−4.63822	−0.218164
$453$	−0.143705	−0.00675185
$454$	−51.8190	−2.43199
$455$	−3.22539	−0.151209
$456$	−0.141405	−0.00662187
$457$	−15.0644	−0.704681	−0.352340	−	0.935872i	$-0.614614\pi$
$457$	−15.0644	−0.704681	−0.352340	+	0.935872i	$0.614614\pi$
$458$	1.96161	0.0916601
$459$	0.0837856	0.00391078
$460$	0.0638358	0.00297636
$461$	−23.6852	−1.10313	−0.551565	−	0.834132i	$-0.685969\pi$
$461$	−23.6852	−1.10313	−0.551565	+	0.834132i	$0.685969\pi$
$462$	0.480465	0.0223532
$463$	−21.9846	−1.02171	−0.510854	−	0.859667i	$-0.670671\pi$
$463$	−21.9846	−1.02171	−0.510854	+	0.859667i	$0.670671\pi$
$464$	−4.99473	−0.231875
$465$	0.0171527	0.000795437 0
$466$	−52.6554	−2.43922
$467$	−18.0037	−0.833112	−0.416556	−	0.909110i	$-0.636763\pi$
$467$	−18.0037	−0.833112	−0.416556	+	0.909110i	$0.636763\pi$
$468$	−40.4975	−1.87200
$469$	−10.7205	−0.495027
$470$	−0.928838	−0.0428441
$471$	−0.341135	−0.0157187
$472$	−15.6086	−0.718443
$473$	−33.9935	−1.56302
$474$	−0.361809	−0.0166185
$475$	−30.2929	−1.38993
$476$	−7.67907	−0.351970
$477$	−1.27930	−0.0585749
$478$	−18.4452	−0.843666
$479$	28.6005	1.30679	0.653396	−	0.757017i	$-0.273344\pi$
$479$	28.6005	1.30679	0.653396	+	0.757017i	$0.273344\pi$
$480$	−0.0246905	−0.00112696
$481$	−22.1904	−1.01179
$482$	−34.1035	−1.55337
$483$	−0.00380456	−0.000173113 0
$484$	58.1507	2.64321
$485$	1.84439	0.0837495
$486$	−0.822347	−0.0373024
$487$	33.8607	1.53438	0.767188	−	0.641422i	$-0.221655\pi$
$487$	33.8607	1.53438	0.767188	+	0.641422i	$0.221655\pi$
$488$	−13.6005	−0.615668
$489$	0.252594	0.0114227
$490$	0.389220	0.0175832
$491$	−13.2322	−0.597161	−0.298580	−	0.954385i	$-0.596513\pi$
$491$	−13.2322	−0.597161	−0.298580	+	0.954385i	$0.596513\pi$
$492$	−0.0646689	−0.00291550
$493$	−2.61417	−0.117737
$494$	−65.4263	−2.94367
$495$	−4.02047	−0.180707
$496$	9.91877	0.445366
$497$	−1.11515	−0.0500212
$498$	0.504966	0.0226281
$499$	28.8426	1.29117	0.645586	−	0.763687i	$-0.276613\pi$
$499$	28.8426	1.29117	0.645586	+	0.763687i	$0.276613\pi$
$500$	6.48817	0.290160
$501$	−0.124327	−0.00555451
$502$	31.2073	1.39285
$503$	−4.17259	−0.186046	−0.0930232	−	0.995664i	$-0.529653\pi$
$503$	−4.17259	−0.186046	−0.0930232	+	0.995664i	$0.529653\pi$
$504$	13.8049	0.614917
$505$	−0.225280	−0.0100248
$506$	−1.20883	−0.0537391
$507$	0.153133	0.00680086
$508$	2.88128	0.127836
$509$	5.03476	0.223162	0.111581	−	0.993755i	$-0.464409\pi$
$509$	5.03476	0.223162	0.111581	+	0.993755i	$0.464409\pi$
$510$	−0.00720690	−0.000319127 0
$511$	12.3843	0.547851
$512$	−20.5927	−0.910076
$513$	−0.513369	−0.0226658
$514$	24.3342	1.07334
$515$	−3.14063	−0.138393
$516$	0.231102	0.0101737
$517$	10.1950	0.448376
$518$	27.5318	1.20968
$519$	0.145779	0.00639900
$520$	1.91419	0.0839428
$521$	1.12780	0.0494098	0.0247049	−	0.999695i	$-0.492135\pi$
$521$	1.12780	0.0494098	0.0247049	+	0.999695i	$0.492135\pi$
$522$	17.1050	0.748668
$523$	−10.7089	−0.468267	−0.234133	−	0.972204i	$-0.575225\pi$
$523$	−10.7089	−0.468267	−0.234133	+	0.972204i	$0.575225\pi$
$524$	−23.0404	−1.00652
$525$	−0.192256	−0.00839075
$526$	14.7116	0.641457
$527$	5.19135	0.226139
$528$	0.151138	0.00657744
$529$	−22.9904	−0.999584
$530$	0.220087	0.00955997
$531$	−28.3326	−1.22953
$532$	47.0511	2.03992
$533$	−8.22086	−0.356085
$534$	0.0581416	0.00251603
$535$	3.02676	0.130858
$536$	6.36235	0.274812
$537$	−0.103946	−0.00448561
$538$	7.54615	0.325338
$539$	−4.27212	−0.184013
$540$	0.0546676	0.00235252
$541$	−36.7597	−1.58042	−0.790211	−	0.612835i	$-0.790029\pi$
$541$	−36.7597	−1.58042	−0.790211	+	0.612835i	$0.790029\pi$
$542$	−27.4525	−1.17919
$543$	0.300690	0.0129039
$544$	−7.47271	−0.320390
$545$	4.58862	0.196555
$546$	−0.415233	−0.0177703
$547$	−18.4845	−0.790340	−0.395170	−	0.918608i	$-0.629314\pi$
$547$	−18.4845	−0.790340	−0.395170	+	0.918608i	$0.629314\pi$
$548$	−61.2547	−2.61667
$549$	−24.6876	−1.05364
$550$	−61.0859	−2.60471
$551$	16.0175	0.682369
$552$	0.00225791	9.61031e−5 0
$553$	33.0765	1.40655
$554$	38.3972	1.63134
$555$	0.0149769	0.000635733 0
$556$	−39.1110	−1.65867
$557$	6.35504	0.269271	0.134636	−	0.990895i	$-0.457014\pi$
$557$	6.35504	0.269271	0.134636	+	0.990895i	$0.457014\pi$
$558$	−33.9680	−1.43798
$559$	29.3783	1.24257
$560$	1.25882	0.0531951
$561$	0.0791037	0.00333976
$562$	13.8639	0.584812
$563$	43.6912	1.84136	0.920682	−	0.390314i	$-0.127633\pi$
$563$	43.6912	1.84136	0.920682	+	0.390314i	$0.127633\pi$
$564$	−0.0693100	−0.00291848
$565$	0.397952	0.0167420
$566$	10.0826	0.423805
$567$	25.0568	1.05229
$568$	0.661813	0.0277690
$569$	−37.7757	−1.58364	−0.791819	−	0.610755i	$-0.790866\pi$
$569$	−37.7757	−1.58364	−0.791819	+	0.610755i	$0.790866\pi$
$570$	0.0441580	0.00184957
$571$	−29.3777	−1.22942	−0.614710	−	0.788753i	$-0.710727\pi$
$571$	−29.3777	−1.22942	−0.614710	+	0.788753i	$0.710727\pi$
$572$	−76.4716	−3.19744
$573$	0.374344	0.0156385
$574$	10.1997	0.425727
$575$	0.483709	0.0201721
$576$	37.4323	1.55968
$577$	−41.9271	−1.74545	−0.872723	−	0.488216i	$-0.837648\pi$
$577$	−41.9271	−1.74545	−0.872723	+	0.488216i	$0.837648\pi$
$578$	−2.18121	−0.0907262
$579$	0.324517	0.0134865
$580$	−1.70567	−0.0708241
$581$	−46.1638	−1.91520
$582$	0.237445	0.00984240
$583$	−2.41570	−0.100048
$584$	−7.34980	−0.304137
$585$	3.47462	0.143658
$586$	−24.3074	−1.00413
$587$	38.8925	1.60526	0.802632	−	0.596474i	$-0.203432\pi$
$587$	38.8925	1.60526	0.802632	+	0.596474i	$0.203432\pi$
$588$	0.0290437	0.00119774
$589$	−31.8083	−1.31064
$590$	4.87427	0.200670
$591$	−0.306800	−0.0126201
$592$	8.66058	0.355948
$593$	−35.5013	−1.45786	−0.728931	−	0.684587i	$-0.759983\pi$
$593$	−35.5013	−1.45786	−0.728931	+	0.684587i	$0.759983\pi$
$594$	−1.03521	−0.0424754
$595$	0.658852	0.0270103
$596$	−11.9923	−0.491226
$597$	−0.285423	−0.0116816
$598$	1.04471	0.0427214
$599$	−30.9110	−1.26299	−0.631494	−	0.775380i	$-0.717558\pi$
$599$	−30.9110	−1.26299	−0.631494	+	0.775380i	$0.717558\pi$
$600$	0.114099	0.00465808
$601$	−27.9168	−1.13875	−0.569375	−	0.822078i	$-0.692815\pi$
$601$	−27.9168	−1.13875	−0.569375	+	0.822078i	$0.692815\pi$
$602$	−36.4499	−1.48559
$603$	11.5489	0.470307
$604$	−28.3779	−1.15468
$605$	−4.98924	−0.202841
$606$	−0.0290023	−0.00117814
$607$	21.0643	0.854974	0.427487	−	0.904021i	$-0.359399\pi$
$607$	21.0643	0.854974	0.427487	+	0.904021i	$0.359399\pi$
$608$	45.7866	1.85689
$609$	0.101656	0.00411933
$610$	4.24719	0.171964
$611$	−8.81086	−0.356449
$612$	8.27244	0.334394
$613$	−30.3754	−1.22685	−0.613425	−	0.789753i	$-0.710209\pi$
$613$	−30.3754	−1.22685	−0.613425	+	0.789753i	$0.710209\pi$
$614$	46.0953	1.86025
$615$	0.00554848	0.000223736 0
$616$	26.0677	1.05030
$617$	30.6892	1.23550	0.617750	−	0.786374i	$-0.288044\pi$
$617$	30.6892	1.23550	0.617750	+	0.786374i	$0.288044\pi$
$618$	−0.404321	−0.0162642
$619$	−6.43322	−0.258573	−0.129287	−	0.991607i	$-0.541269\pi$
$619$	−6.43322	−0.258573	−0.129287	+	0.991607i	$0.541269\pi$
$620$	3.38720	0.136033
$621$	0.00819735	0.000328948 0
$622$	−9.07523	−0.363883
$623$	−5.31528	−0.212952
$624$	−0.130618	−0.00522892
$625$	24.1634	0.966537
$626$	12.0699	0.482412
$627$	−0.484682	−0.0193563
$628$	−67.3650	−2.68816
$629$	4.53283	0.180736
$630$	−4.31100	−0.171754
$631$	−25.8309	−1.02831	−0.514155	−	0.857697i	$-0.671894\pi$
$631$	−25.8309	−1.02831	−0.514155	+	0.857697i	$0.671894\pi$
$632$	−19.6301	−0.780842
$633$	0.235724	0.00936919
$634$	−1.06143	−0.0421546
$635$	−0.247209	−0.00981021
$636$	0.0164229	0.000651212 0
$637$	3.69210	0.146286
$638$	32.2995	1.27875
$639$	1.20132	0.0475233
$640$	−2.90364	−0.114776
$641$	−29.6927	−1.17279	−0.586395	−	0.810025i	$-0.699453\pi$
$641$	−29.6927	−1.17279	−0.586395	+	0.810025i	$0.699453\pi$
$642$	0.389662	0.0153787
$643$	−28.1602	−1.11053	−0.555265	−	0.831674i	$-0.687383\pi$
$643$	−28.1602	−1.11053	−0.555265	+	0.831674i	$0.687383\pi$
$644$	−0.751299	−0.0296053
$645$	−0.0198282	−0.000780734 0
$646$	13.3646	0.525825
$647$	−9.08415	−0.357135	−0.178567	−	0.983928i	$-0.557146\pi$
$647$	−9.08415	−0.357135	−0.178567	+	0.983928i	$0.557146\pi$
$648$	−14.8706	−0.584172
$649$	−53.5004	−2.10008
$650$	52.7924	2.07069
$651$	−0.201874	−0.00791207
$652$	49.8805	1.95347
$653$	−1.25147	−0.0489737	−0.0244869	−	0.999700i	$-0.507795\pi$
$653$	−1.25147	−0.0489737	−0.0244869	+	0.999700i	$0.507795\pi$
$654$	0.590732	0.0230995
$655$	1.97683	0.0772410
$656$	3.20848	0.125270
$657$	−13.3413	−0.520494
$658$	10.9317	0.426163
$659$	−9.65702	−0.376184	−0.188092	−	0.982151i	$-0.560230\pi$
$659$	−9.65702	−0.376184	−0.188092	+	0.982151i	$0.560230\pi$
$660$	0.0516127	0.00200902
$661$	28.5909	1.11206	0.556028	−	0.831164i	$-0.312325\pi$
$661$	28.5909	1.11206	0.556028	+	0.831164i	$0.312325\pi$
$662$	58.4065	2.27003
$663$	−0.0683639	−0.00265504
$664$	27.3970	1.06321
$665$	−4.03690	−0.156544
$666$	−29.6592	−1.14927
$667$	−0.255764	−0.00990321
$668$	−24.5512	−0.949915
$669$	0.0254749	0.000984918 0
$670$	−1.98684	−0.0767585
$671$	−46.6176	−1.79965
$672$	0.290588	0.0112097
$673$	22.9124	0.883210	0.441605	−	0.897210i	$-0.354409\pi$
$673$	22.9124	0.883210	0.441605	+	0.897210i	$0.354409\pi$
$674$	25.7027	0.990033
$675$	0.414238	0.0159440
$676$	30.2396	1.16306
$677$	43.5410	1.67342	0.836709	−	0.547648i	$-0.184477\pi$
$677$	43.5410	1.67342	0.836709	+	0.547648i	$0.184477\pi$
$678$	0.0512318	0.00196755
$679$	−21.7071	−0.833042
$680$	−0.391012	−0.0149946
$681$	0.331761	0.0127131
$682$	−64.1418	−2.45612
$683$	−19.6023	−0.750061	−0.375030	−	0.927013i	$-0.622368\pi$
$683$	−19.6023	−0.750061	−0.375030	+	0.927013i	$0.622368\pi$
$684$	−50.6867	−1.93806
$685$	5.25556	0.200804
$686$	37.9362	1.44841
$687$	−0.0125588	−0.000479148 0
$688$	−11.4659	−0.437134
$689$	2.08772	0.0795359
$690$	−0.000705103 0	−2.68428e−5 0
$691$	−15.5760	−0.592540	−0.296270	−	0.955104i	$-0.595743\pi$
$691$	−15.5760	−0.592540	−0.296270	+	0.955104i	$0.595743\pi$
$692$	28.7875	1.09434
$693$	47.3179	1.79746
$694$	57.3805	2.17813
$695$	3.35566	0.127287
$696$	−0.0603306	−0.00228682
$697$	1.67928	0.0636072
$698$	4.49214	0.170030
$699$	0.337115	0.0127509
$700$	−37.9655	−1.43496
$701$	15.0191	0.567262	0.283631	−	0.958934i	$-0.408461\pi$
$701$	15.0191	0.567262	0.283631	+	0.958934i	$0.408461\pi$
$702$	0.894666	0.0337670
$703$	−27.7735	−1.04750
$704$	70.6835	2.66398
$705$	0.00594669	0.000223965 0
$706$	2.18121	0.0820908
$707$	2.65138	0.0997153
$708$	0.363719	0.0136694
$709$	17.2014	0.646013	0.323006	−	0.946397i	$-0.395306\pi$
$709$	17.2014	0.646013	0.323006	+	0.946397i	$0.395306\pi$
$710$	−0.206672	−0.00775625
$711$	−35.6323	−1.33632
$712$	3.15449	0.118219
$713$	0.507907	0.0190213
$714$	0.0848197	0.00317430
$715$	6.56114	0.245373
$716$	−20.5266	−0.767115
$717$	0.118092	0.00441022
$718$	72.4254	2.70289
$719$	−18.6173	−0.694309	−0.347155	−	0.937808i	$-0.612852\pi$
$719$	−18.6173	−0.694309	−0.347155	+	0.937808i	$0.612852\pi$
$720$	−1.35610	−0.0505387
$721$	36.9628	1.37657
$722$	−40.4446	−1.50519
$723$	0.218341	0.00812018
$724$	59.3783	2.20678
$725$	−12.9245	−0.480005
$726$	−0.642308	−0.0238383
$727$	28.1468	1.04391	0.521954	−	0.852974i	$-0.325203\pi$
$727$	28.1468	1.04391	0.521954	+	0.852974i	$0.325203\pi$
$728$	−22.5286	−0.834964
$729$	−26.9895	−0.999610
$730$	2.29520	0.0849493
$731$	−6.00110	−0.221959
$732$	0.316926	0.0117139
$733$	18.8824	0.697437	0.348718	−	0.937228i	$-0.386617\pi$
$733$	18.8824	0.697437	0.348718	+	0.937228i	$0.386617\pi$
$734$	4.41837	0.163085
$735$	−0.00249190	−9.19151e−5 0
$736$	−0.731109	−0.0269490
$737$	21.8078	0.803300
$738$	−10.9878	−0.404468
$739$	−44.8838	−1.65108	−0.825538	−	0.564346i	$-0.809128\pi$
$739$	−44.8838	−1.65108	−0.825538	+	0.564346i	$0.809128\pi$
$740$	2.95753	0.108721
$741$	0.418878	0.0153879
$742$	−2.59026	−0.0950913
$743$	−1.37361	−0.0503927	−0.0251963	−	0.999683i	$-0.508021\pi$
$743$	−1.37361	−0.0503927	−0.0251963	+	0.999683i	$0.508021\pi$
$744$	0.119807	0.00439235
$745$	1.02892	0.0376969
$746$	37.0966	1.35820
$747$	49.7309	1.81956
$748$	15.6209	0.571155
$749$	−35.6227	−1.30163
$750$	−0.0716656	−0.00261686
$751$	−10.6431	−0.388371	−0.194186	−	0.980965i	$-0.562206\pi$
$751$	−10.6431	−0.388371	−0.194186	+	0.980965i	$0.562206\pi$
$752$	3.43875	0.125398
$753$	−0.199798	−0.00728106
$754$	−27.9143	−1.01658
$755$	2.43478	0.0886106
$756$	−0.643395	−0.0234001
$757$	−19.9738	−0.725959	−0.362979	−	0.931797i	$-0.618240\pi$
$757$	−19.9738	−0.725959	−0.362979	+	0.931797i	$0.618240\pi$
$758$	61.7279	2.24206
$759$	0.00773928	0.000280918 0
$760$	2.39580	0.0869049
$761$	−40.4768	−1.46728	−0.733642	−	0.679536i	$-0.762181\pi$
$761$	−40.4768	−1.46728	−0.733642	+	0.679536i	$0.762181\pi$
$762$	−0.0318254	−0.00115291
$763$	−54.0045	−1.95509
$764$	73.9230	2.67444
$765$	−0.709762	−0.0256615
$766$	27.3534	0.988317
$767$	46.2368	1.66951
$768$	−0.0253002	−0.000912943 0
$769$	−36.9411	−1.33213	−0.666065	−	0.745894i	$-0.732023\pi$
$769$	−36.9411	−1.33213	−0.666065	+	0.745894i	$0.732023\pi$
$770$	−8.14046	−0.293362
$771$	−0.155795	−0.00561082
$772$	64.0834	2.30641
$773$	−12.2586	−0.440910	−0.220455	−	0.975397i	$-0.570754\pi$
$773$	−12.2586	−0.440910	−0.220455	+	0.975397i	$0.570754\pi$
$774$	39.2664	1.41140
$775$	25.6661	0.921955
$776$	12.8826	0.462459
$777$	−0.176266	−0.00632352
$778$	48.5147	1.73934
$779$	−10.2892	−0.368650
$780$	−0.0446054	−0.00159713
$781$	2.26845	0.0811714
$782$	−0.213403	−0.00763128
$783$	−0.219030	−0.00782750
$784$	−1.44097	−0.0514634
$785$	5.77981	0.206290
$786$	0.254494	0.00907750
$787$	31.9408	1.13857	0.569283	−	0.822141i	$-0.307221\pi$
$787$	31.9408	1.13857	0.569283	+	0.822141i	$0.307221\pi$
$788$	−60.5848	−2.15824
$789$	−0.0941880	−0.00335318
$790$	6.13010	0.218099
$791$	−4.68359	−0.166529
$792$	−28.0820	−0.997850
$793$	40.2885	1.43069
$794$	−45.8356	−1.62664
$795$	−0.00140906	−4.99743e−5 0
$796$	−56.3635	−1.99775
$797$	−41.4683	−1.46888	−0.734442	−	0.678672i	$-0.762556\pi$
$797$	−41.4683	−1.46888	−0.734442	+	0.678672i	$0.762556\pi$
$798$	−0.519706	−0.0183974
$799$	1.79980	0.0636722
$800$	−36.9452	−1.30621
$801$	5.72600	0.202318
$802$	20.6228	0.728215
$803$	−25.1924	−0.889020
$804$	−0.148259	−0.00522868
$805$	0.0644603	0.00227193
$806$	55.4335	1.95256
$807$	−0.0483127	−0.00170069
$808$	−1.57353	−0.0553565
$809$	41.8984	1.47307	0.736535	−	0.676399i	$-0.236461\pi$
$809$	41.8984	1.47307	0.736535	+	0.676399i	$0.236461\pi$
$810$	4.64381	0.163167
$811$	−46.6179	−1.63697	−0.818487	−	0.574525i	$-0.805187\pi$
$811$	−46.6179	−1.63697	−0.818487	+	0.574525i	$0.805187\pi$
$812$	20.0744	0.704475
$813$	0.175759	0.00616414
$814$	−56.0055	−1.96299
$815$	−4.27967	−0.149910
$816$	0.0266815	0.000934038 0
$817$	36.7698	1.28641
$818$	11.6634	0.407800
$819$	−40.8937	−1.42894
$820$	1.09568	0.0382627
$821$	20.0625	0.700187	0.350093	−	0.936715i	$-0.386150\pi$
$821$	20.0625	0.700187	0.350093	+	0.936715i	$0.386150\pi$
$822$	0.676593	0.0235989
$823$	−44.0229	−1.53454	−0.767271	−	0.641323i	$-0.778386\pi$
$823$	−44.0229	−1.53454	−0.767271	+	0.641323i	$0.778386\pi$
$824$	−21.9365	−0.764195
$825$	0.391090	0.0136160
$826$	−57.3664	−1.99603
$827$	−51.1236	−1.77774	−0.888870	−	0.458159i	$-0.848509\pi$
$827$	−51.1236	−1.77774	−0.888870	+	0.458159i	$0.848509\pi$
$828$	0.809353	0.0281270
$829$	−3.99014	−0.138583	−0.0692916	−	0.997596i	$-0.522074\pi$
$829$	−3.99014	−0.138583	−0.0692916	+	0.997596i	$0.522074\pi$
$830$	−8.55558	−0.296968
$831$	−0.245830	−0.00852776
$832$	−61.0870	−2.11781
$833$	−0.754186	−0.0261310
$834$	0.432003	0.0149590
$835$	2.10645	0.0728969
$836$	−95.7118	−3.31026
$837$	0.434960	0.0150344
$838$	16.7330	0.578030
$839$	53.2980	1.84005	0.920025	−	0.391859i	$-0.128168\pi$
$839$	53.2980	1.84005	0.920025	+	0.391859i	$0.128168\pi$
$840$	0.0152051	0.000524627 0
$841$	−22.1661	−0.764348
$842$	−67.4814	−2.32556
$843$	−0.0887606	−0.00305708
$844$	46.5492	1.60229
$845$	−2.59451	−0.0892539
$846$	−11.7764	−0.404882
$847$	58.7195	2.01763
$848$	−0.814808	−0.0279806
$849$	−0.0645521	−0.00221542
$850$	−10.7839	−0.369886
$851$	0.443480	0.0152023
$852$	−0.0154219	−0.000528345 0
$853$	31.4696	1.07750	0.538748	−	0.842467i	$-0.318897\pi$
$853$	31.4696	1.07750	0.538748	+	0.842467i	$0.318897\pi$
$854$	−49.9862	−1.71049
$855$	4.34884	0.148727
$856$	21.1412	0.722591
$857$	4.42923	0.151300	0.0756499	−	0.997134i	$-0.475897\pi$
$857$	4.42923	0.151300	0.0756499	+	0.997134i	$0.475897\pi$
$858$	0.844672	0.0288366
$859$	−24.4884	−0.835533	−0.417767	−	0.908554i	$-0.637187\pi$
$859$	−24.4884	−0.835533	−0.417767	+	0.908554i	$0.637187\pi$
$860$	−3.91554	−0.133519
$861$	−0.0653014	−0.00222547
$862$	−1.66293	−0.0566395
$863$	38.4806	1.30989	0.654947	−	0.755675i	$-0.272691\pi$
$863$	38.4806	1.30989	0.654947	+	0.755675i	$0.272691\pi$
$864$	−0.626105	−0.0213005
$865$	−2.46992	−0.0839800
$866$	21.7119	0.737799
$867$	0.0139647	0.000474267 0
$868$	−39.8648	−1.35310
$869$	−67.2846	−2.28247
$870$	0.0188401	0.000638739 0
$871$	−18.8470	−0.638606
$872$	32.0503	1.08536
$873$	23.3844	0.791443
$874$	1.30756	0.0442289
$875$	6.55164	0.221486
$876$	0.171269	0.00578663
$877$	−39.1642	−1.32248	−0.661240	−	0.750174i	$-0.729970\pi$
$877$	−39.1642	−1.32248	−0.661240	+	0.750174i	$0.729970\pi$
$878$	−38.5590	−1.30130
$879$	0.155623	0.00524903
$880$	−2.56072	−0.0863218
$881$	−11.3651	−0.382900	−0.191450	−	0.981502i	$-0.561319\pi$
$881$	−11.3651	−0.382900	−0.191450	+	0.981502i	$0.561319\pi$
$882$	4.93479	0.166163
$883$	−44.5454	−1.49907	−0.749536	−	0.661963i	$-0.769724\pi$
$883$	−44.5454	−1.49907	−0.749536	+	0.661963i	$0.769724\pi$
$884$	−13.5001	−0.454056
$885$	−0.0312065	−0.00104899
$886$	−24.7813	−0.832543
$887$	−22.5535	−0.757271	−0.378636	−	0.925546i	$-0.623607\pi$
$887$	−22.5535	−0.757271	−0.378636	+	0.925546i	$0.623607\pi$
$888$	0.104610	0.00351047
$889$	2.90947	0.0975804
$890$	−0.985087	−0.0330202
$891$	−50.9709	−1.70759
$892$	5.03062	0.168438
$893$	−11.0277	−0.369027
$894$	0.132462	0.00443020
$895$	1.76115	0.0588687
$896$	34.1736	1.14166
$897$	−0.00668854	−0.000223324 0
$898$	−68.1099	−2.27286
$899$	−13.5711	−0.452621
$900$	40.8991	1.36330
$901$	−0.426460	−0.0142074
$902$	−20.7483	−0.690844
$903$	0.233363	0.00776582
$904$	2.77959	0.0924479
$905$	−5.09457	−0.169349
$906$	0.313450	0.0104137
$907$	−2.75533	−0.0914892	−0.0457446	−	0.998953i	$-0.514566\pi$
$907$	−2.75533	−0.0914892	−0.0457446	+	0.998953i	$0.514566\pi$
$908$	65.5139	2.17415
$909$	−2.85625	−0.0947359
$910$	7.03525	0.233216
$911$	−35.7433	−1.18423	−0.592114	−	0.805854i	$-0.701706\pi$
$911$	−35.7433	−1.18423	−0.592114	+	0.805854i	$0.701706\pi$
$912$	−0.163482	−0.00541343
$913$	93.9069	3.10786
$914$	32.8585	1.08686
$915$	−0.0271918	−0.000898933 0
$916$	−2.48003	−0.0819425
$917$	−23.2657	−0.768302
$918$	−0.182754	−0.00603177
$919$	−10.4386	−0.344337	−0.172168	−	0.985068i	$-0.555077\pi$
$919$	−10.4386	−0.344337	−0.172168	+	0.985068i	$0.555077\pi$
$920$	−0.0382556	−0.00126125
$921$	−0.295115	−0.00972438
$922$	51.6623	1.70141
$923$	−1.96047	−0.0645295
$924$	−0.607443	−0.0199834
$925$	22.4104	0.736849
$926$	47.9528	1.57583
$927$	−39.8190	−1.30783
$928$	19.5350	0.641267
$929$	9.22618	0.302701	0.151351	−	0.988480i	$-0.451638\pi$
$929$	9.22618	0.302701	0.151351	+	0.988480i	$0.451638\pi$
$930$	−0.0374135	−0.00122684
$931$	4.62104	0.151448
$932$	66.5713	2.18062
$933$	0.0581022	0.00190218
$934$	39.2698	1.28495
$935$	−1.34024	−0.0438307
$936$	24.2694	0.793269
$937$	−8.12207	−0.265336	−0.132668	−	0.991161i	$-0.542354\pi$
$937$	−8.12207	−0.265336	−0.132668	+	0.991161i	$0.542354\pi$
$938$	23.3836	0.763503
$939$	−0.0772753	−0.00252178
$940$	1.17431	0.0383019
$941$	−0.911222	−0.0297050	−0.0148525	−	0.999890i	$-0.504728\pi$
$941$	−0.911222	−0.0297050	−0.0148525	+	0.999890i	$0.504728\pi$
$942$	0.744085	0.0242436
$943$	0.164296	0.00535021
$944$	−18.0456	−0.587333
$945$	0.0552023	0.00179573
$946$	74.1468	2.41072
$947$	−58.2294	−1.89220	−0.946101	−	0.323873i	$-0.895015\pi$
$947$	−58.2294	−1.89220	−0.946101	+	0.323873i	$0.895015\pi$
$948$	0.457429	0.0148566
$949$	21.7721	0.706752
$950$	66.0750	2.14376
$951$	0.00679556	0.000220361 0
$952$	4.60192	0.149149
$953$	−50.9839	−1.65153	−0.825766	−	0.564013i	$-0.809257\pi$
$953$	−50.9839	−1.65153	−0.825766	+	0.564013i	$0.809257\pi$
$954$	2.79041	0.0903428
$955$	−6.34248	−0.205238
$956$	23.3200	0.754222
$957$	−0.206791	−0.00668460
$958$	−62.3836	−2.01552
$959$	−61.8539	−1.99737
$960$	0.0412293	0.00133067
$961$	−4.04988	−0.130641
$962$	48.4017	1.56053
$963$	38.3753	1.23663
$964$	43.1165	1.38869
$965$	−5.49825	−0.176995
$966$	0.00829853	0.000267001 0
$967$	−48.0953	−1.54664	−0.773320	−	0.634015i	$-0.781406\pi$
$967$	−48.0953	−1.54664	−0.773320	+	0.634015i	$0.781406\pi$
$968$	−34.8486	−1.12008
$969$	−0.0855643	−0.00274872
$970$	−4.02300	−0.129171
$971$	20.4804	0.657247	0.328624	−	0.944461i	$-0.393415\pi$
$971$	20.4804	0.657247	0.328624	+	0.944461i	$0.393415\pi$
$972$	1.03968	0.0333477
$973$	−39.4935	−1.26610
$974$	−73.8572	−2.36654
$975$	−0.337993	−0.0108244
$976$	−15.7240	−0.503313
$977$	−57.8840	−1.85187	−0.925937	−	0.377678i	$-0.876723\pi$
$977$	−57.8840	−1.85187	−0.925937	+	0.377678i	$0.876723\pi$
$978$	−0.550959	−0.0176177
$979$	10.8124	0.345566
$980$	−0.492084	−0.0157190
$981$	58.1775	1.85746
$982$	28.8621	0.921028
$983$	23.4871	0.749123	0.374561	−	0.927202i	$-0.377793\pi$
$983$	23.4871	0.749123	0.374561	+	0.927202i	$0.377793\pi$
$984$	0.0387548	0.00123546
$985$	5.19808	0.165625
$986$	5.70205	0.181590
$987$	−0.0699880	−0.00222774
$988$	82.7173	2.63159
$989$	−0.587131	−0.0186697
$990$	8.76948	0.278712
$991$	39.7572	1.26293	0.631464	−	0.775405i	$-0.282454\pi$
$991$	39.7572	1.26293	0.631464	+	0.775405i	$0.282454\pi$
$992$	−38.7934	−1.23169
$993$	−0.373936	−0.0118665
$994$	2.43237	0.0771500
$995$	4.83590	0.153308
$996$	−0.638419	−0.0202291
$997$	37.9721	1.20259	0.601295	−	0.799027i	$-0.294652\pi$
$997$	37.9721	1.20259	0.601295	+	0.799027i	$0.294652\pi$
$998$	−62.9117	−1.99143
$999$	0.379786	0.0120159

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.a.1.17	✓	113

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.a.1.17	✓	113	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:	\( N \)	\(=\)	\( 6001 = 17 \cdot 353 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6001.a (trivial)

\(f(q)\)	\(=\)	\(q-2.18121 q^{2} +0.0139647 q^{3} +2.75766 q^{4} -0.236603 q^{5} -0.0304599 q^{6} +2.78463 q^{7} -1.65261 q^{8} -2.99980 q^{9} +O(q^{10})\)	\(q-2.18121 q^{2} +0.0139647 q^{3} +2.75766 q^{4} -0.236603 q^{5} -0.0304599 q^{6} +2.78463 q^{7} -1.65261 q^{8} -2.99980 q^{9} +0.516079 q^{10} -5.66454 q^{11} +0.0385099 q^{12} +4.89548 q^{13} -6.07386 q^{14} -0.00330409 q^{15} -1.91063 q^{16} -1.00000 q^{17} +6.54319 q^{18} +6.12718 q^{19} -0.652470 q^{20} +0.0388866 q^{21} +12.3555 q^{22} -0.0978372 q^{23} -0.0230782 q^{24} -4.94402 q^{25} -10.6780 q^{26} -0.0837856 q^{27} +7.67907 q^{28} +2.61417 q^{29} +0.00720690 q^{30} -5.19135 q^{31} +7.47271 q^{32} -0.0791037 q^{33} +2.18121 q^{34} -0.658852 q^{35} -8.27244 q^{36} -4.53283 q^{37} -13.3646 q^{38} +0.0683639 q^{39} +0.391012 q^{40} -1.67928 q^{41} -0.0848197 q^{42} +6.00110 q^{43} -15.6209 q^{44} +0.709762 q^{45} +0.213403 q^{46} -1.79980 q^{47} -0.0266815 q^{48} +0.754186 q^{49} +10.7839 q^{50} -0.0139647 q^{51} +13.5001 q^{52} +0.426460 q^{53} +0.182754 q^{54} +1.34024 q^{55} -4.60192 q^{56} +0.0855643 q^{57} -5.70205 q^{58} +9.44480 q^{59} -0.00911155 q^{60} +8.22973 q^{61} +11.3234 q^{62} -8.35336 q^{63} -12.4782 q^{64} -1.15828 q^{65} +0.172541 q^{66} -3.84988 q^{67} -2.75766 q^{68} -0.00136627 q^{69} +1.43709 q^{70} -0.400465 q^{71} +4.95751 q^{72} +4.44739 q^{73} +9.88704 q^{74} -0.0690418 q^{75} +16.8967 q^{76} -15.7737 q^{77} -0.149116 q^{78} +11.8782 q^{79} +0.452061 q^{80} +8.99824 q^{81} +3.66285 q^{82} -16.5780 q^{83} +0.107236 q^{84} +0.236603 q^{85} -13.0896 q^{86} +0.0365062 q^{87} +9.36128 q^{88} -1.90879 q^{89} -1.54814 q^{90} +13.6321 q^{91} -0.269802 q^{92} -0.0724957 q^{93} +3.92573 q^{94} -1.44971 q^{95} +0.104354 q^{96} -7.79531 q^{97} -1.64504 q^{98} +16.9925 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9}+O(q^{10}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9	\( 113 q - 11 q^{2} - 11 q^{3} + 103 q^{4} - 19 q^{5} - 13 q^{6} + 11 q^{7} - 36 q^{8} + 94 q^{9} - 5 q^{10} - 40 q^{11} - 19 q^{12} - 18 q^{13} - 48 q^{14} - 63 q^{15} + 79 q^{16} - 113 q^{17} - 32 q^{18} - 46 q^{19} - 56 q^{20} - 46 q^{21} + 14 q^{22} - 35 q^{23} - 42 q^{24} + 88 q^{25} - 89 q^{26} - 41 q^{27} + 20 q^{28} - 51 q^{29} - 18 q^{30} - 57 q^{31} - 93 q^{32} - 40 q^{33} + 11 q^{34} - 69 q^{35} + 18 q^{36} + 16 q^{37} - 74 q^{38} - 51 q^{39} + 2 q^{40} - 87 q^{41} - 23 q^{42} - 32 q^{43} - 110 q^{44} - 17 q^{45} - 17 q^{46} - 161 q^{47} - 36 q^{48} + 56 q^{49} - 69 q^{50} + 11 q^{51} - 49 q^{52} - 48 q^{53} - 38 q^{54} - 79 q^{55} - 171 q^{56} + 20 q^{57} + 13 q^{58} - 174 q^{59} - 146 q^{60} - 34 q^{61} - 34 q^{62} - 14 q^{63} + 62 q^{64} - 22 q^{65} - 60 q^{66} - 50 q^{67} - 103 q^{68} - 59 q^{69} - 58 q^{70} - 189 q^{71} - 123 q^{72} - 4 q^{73} - 24 q^{74} - 106 q^{75} - 92 q^{76} - 78 q^{77} - 42 q^{78} + 8 q^{79} - 150 q^{80} + 13 q^{81} + 6 q^{82} - 109 q^{83} - 114 q^{84} + 19 q^{85} - 116 q^{86} - 106 q^{87} + 54 q^{88} - 170 q^{89} - q^{90} - 43 q^{91} - 94 q^{92} - 69 q^{93} - 35 q^{94} - 78 q^{95} - 44 q^{96} - 3 q^{97} - 68 q^{98} - 119 q^{99}+O(q^{100}) \) 113 * q - 11 * q^2 - 11 * q^3 + 103 * q^4 - 19 * q^5 - 13 * q^6 + 11 * q^7 - 36 * q^8 + 94 * q^9 - 5 * q^10 - 40 * q^11 - 19 * q^12 - 18 * q^13 - 48 * q^14 - 63 * q^15 + 79 * q^16 - 113 * q^17 - 32 * q^18 - 46 * q^19 - 56 * q^20 - 46 * q^21 + 14 * q^22 - 35 * q^23 - 42 * q^24 + 88 * q^25 - 89 * q^26 - 41 * q^27 + 20 * q^28 - 51 * q^29 - 18 * q^30 - 57 * q^31 - 93 * q^32 - 40 * q^33 + 11 * q^34 - 69 * q^35 + 18 * q^36 + 16 * q^37 - 74 * q^38 - 51 * q^39 + 2 * q^40 - 87 * q^41 - 23 * q^42 - 32 * q^43 - 110 * q^44 - 17 * q^45 - 17 * q^46 - 161 * q^47 - 36 * q^48 + 56 * q^49 - 69 * q^50 + 11 * q^51 - 49 * q^52 - 48 * q^53 - 38 * q^54 - 79 * q^55 - 171 * q^56 + 20 * q^57 + 13 * q^58 - 174 * q^59 - 146 * q^60 - 34 * q^61 - 34 * q^62 - 14 * q^63 + 62 * q^64 - 22 * q^65 - 60 * q^66 - 50 * q^67 - 103 * q^68 - 59 * q^69 - 58 * q^70 - 189 * q^71 - 123 * q^72 - 4 * q^73 - 24 * q^74 - 106 * q^75 - 92 * q^76 - 78 * q^77 - 42 * q^78 + 8 * q^79 - 150 * q^80 + 13 * q^81 + 6 * q^82 - 109 * q^83 - 114 * q^84 + 19 * q^85 - 116 * q^86 - 106 * q^87 + 54 * q^88 - 170 * q^89 - q^90 - 43 * q^91 - 94 * q^92 - 69 * q^93 - 35 * q^94 - 78 * q^95 - 44 * q^96 - 3 * q^97 - 68 * q^98 - 119 * q^99

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