LMFDB - Embedded newform 6001.2.a.b.1.9

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:	$114$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.9
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)

$f(q)$	$=$	$q-2.39336 q^{2} +0.882221 q^{3} +3.72817 q^{4} +0.123030 q^{5} -2.11147 q^{6} -1.77301 q^{7} -4.13613 q^{8} -2.22169 q^{9} +O(q^{10})$	\(q-2.39336 q^{2} +0.882221 q^{3} +3.72817 q^{4} +0.123030 q^{5} -2.11147 q^{6} -1.77301 q^{7} -4.13613 q^{8} -2.22169 q^{9} -0.294456 q^{10} +1.33826 q^{11} +3.28907 q^{12} +1.60065 q^{13} +4.24346 q^{14} +0.108540 q^{15} +2.44290 q^{16} +1.00000 q^{17} +5.31729 q^{18} +5.76795 q^{19} +0.458678 q^{20} -1.56419 q^{21} -3.20294 q^{22} +3.19803 q^{23} -3.64898 q^{24} -4.98486 q^{25} -3.83093 q^{26} -4.60668 q^{27} -6.61009 q^{28} -1.74173 q^{29} -0.259775 q^{30} +1.64454 q^{31} +2.42552 q^{32} +1.18064 q^{33} -2.39336 q^{34} -0.218135 q^{35} -8.28282 q^{36} +5.32254 q^{37} -13.8048 q^{38} +1.41213 q^{39} -0.508869 q^{40} -6.97762 q^{41} +3.74367 q^{42} -5.34754 q^{43} +4.98926 q^{44} -0.273335 q^{45} -7.65404 q^{46} -9.93182 q^{47} +2.15518 q^{48} -3.85642 q^{49} +11.9306 q^{50} +0.882221 q^{51} +5.96750 q^{52} -12.9838 q^{53} +11.0254 q^{54} +0.164647 q^{55} +7.33341 q^{56} +5.08861 q^{57} +4.16859 q^{58} +4.56078 q^{59} +0.404655 q^{60} +2.77929 q^{61} -3.93598 q^{62} +3.93908 q^{63} -10.6909 q^{64} +0.196929 q^{65} -2.82570 q^{66} +13.4500 q^{67} +3.72817 q^{68} +2.82137 q^{69} +0.522074 q^{70} +8.33793 q^{71} +9.18917 q^{72} -3.50164 q^{73} -12.7387 q^{74} -4.39775 q^{75} +21.5039 q^{76} -2.37275 q^{77} -3.37973 q^{78} -15.4312 q^{79} +0.300551 q^{80} +2.60095 q^{81} +16.7000 q^{82} +8.57409 q^{83} -5.83156 q^{84} +0.123030 q^{85} +12.7986 q^{86} -1.53659 q^{87} -5.53521 q^{88} -2.14066 q^{89} +0.654188 q^{90} -2.83798 q^{91} +11.9228 q^{92} +1.45085 q^{93} +23.7704 q^{94} +0.709633 q^{95} +2.13984 q^{96} +9.16315 q^{97} +9.22980 q^{98} -2.97319 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) $ 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * 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 $

$2$	−2.39336	−1.69236	−0.846180	−	0.532897i	$-0.821103\pi$
$2$	−2.39336	−1.69236	−0.846180	+	0.532897i	$0.821103\pi$
$3$	0.882221	0.509351	0.254675	−	0.967027i	$-0.418031\pi$
$3$	0.882221	0.509351	0.254675	+	0.967027i	$0.418031\pi$
$4$	3.72817	1.86408
$5$	0.123030	0.0550208	0.0275104	−	0.999622i	$-0.491242\pi$
$5$	0.123030	0.0550208	0.0275104	+	0.999622i	$0.491242\pi$
$6$	−2.11147	−0.862005
$7$	−1.77301	−0.670136	−0.335068	−	0.942194i	$-0.608759\pi$
$7$	−1.77301	−0.670136	−0.335068	+	0.942194i	$0.608759\pi$
$8$	−4.13613	−1.46234
$9$	−2.22169	−0.740562
$10$	−0.294456	−0.0931151
$11$	1.33826	0.403500	0.201750	−	0.979437i	$-0.435337\pi$
$11$	1.33826	0.403500	0.201750	+	0.979437i	$0.435337\pi$
$12$	3.28907	0.949472
$13$	1.60065	0.443941	0.221970	−	0.975053i	$-0.428751\pi$
$13$	1.60065	0.443941	0.221970	+	0.975053i	$0.428751\pi$
$14$	4.24346	1.13411
$15$	0.108540	0.0280249
$16$	2.44290	0.610725
$17$	1.00000	0.242536
$17$	1.00000	0.242536
$18$	5.31729	1.25330
$19$	5.76795	1.32326	0.661629	−	0.749831i	$-0.269865\pi$
$19$	5.76795	1.32326	0.661629	+	0.749831i	$0.269865\pi$
$20$	0.458678	0.102563
$21$	−1.56419	−0.341334
$22$	−3.20294	−0.682868
$23$	3.19803	0.666836	0.333418	−	0.942779i	$-0.391798\pi$
$23$	3.19803	0.666836	0.333418	+	0.942779i	$0.391798\pi$
$24$	−3.64898	−0.744844
$25$	−4.98486	−0.996973
$26$	−3.83093	−0.751308
$27$	−4.60668	−0.886556
$28$	−6.61009	−1.24919
$29$	−1.74173	−0.323432	−0.161716	−	0.986837i	$-0.551703\pi$
$29$	−1.74173	−0.323432	−0.161716	+	0.986837i	$0.551703\pi$
$30$	−0.259775	−0.0474282
$31$	1.64454	0.295369	0.147684	−	0.989035i	$-0.452818\pi$
$31$	1.64454	0.295369	0.147684	+	0.989035i	$0.452818\pi$
$32$	2.42552	0.428775
$33$	1.18064	0.205523
$34$	−2.39336	−0.410458
$35$	−0.218135	−0.0368715
$36$	−8.28282	−1.38047
$37$	5.32254	0.875020	0.437510	−	0.899214i	$-0.355861\pi$
$37$	5.32254	0.875020	0.437510	+	0.899214i	$0.355861\pi$
$38$	−13.8048	−2.23943
$39$	1.41213	0.226121
$40$	−0.508869	−0.0804593
$41$	−6.97762	−1.08972	−0.544861	−	0.838527i	$-0.683417\pi$
$41$	−6.97762	−1.08972	−0.544861	+	0.838527i	$0.683417\pi$
$42$	3.74367	0.577661
$43$	−5.34754	−0.815493	−0.407746	−	0.913095i	$-0.633685\pi$
$43$	−5.34754	−0.815493	−0.407746	+	0.913095i	$0.633685\pi$
$44$	4.98926	0.752159
$45$	−0.273335	−0.0407463
$46$	−7.65404	−1.12853
$47$	−9.93182	−1.44870	−0.724352	−	0.689430i	$-0.757861\pi$
$47$	−9.93182	−1.44870	−0.724352	+	0.689430i	$0.757861\pi$
$48$	2.15518	0.311073
$49$	−3.85642	−0.550917
$50$	11.9306	1.68724
$51$	0.882221	0.123536
$52$	5.96750	0.827543
$53$	−12.9838	−1.78346	−0.891729	−	0.452571i	$-0.850507\pi$
$53$	−12.9838	−1.78346	−0.891729	+	0.452571i	$0.850507\pi$
$54$	11.0254	1.50037
$55$	0.164647	0.0222009
$56$	7.33341	0.979968
$57$	5.08861	0.674003
$58$	4.16859	0.547363
$59$	4.56078	0.593763	0.296881	−	0.954914i	$-0.404053\pi$
$59$	4.56078	0.593763	0.296881	+	0.954914i	$0.404053\pi$
$60$	0.404655	0.0522408
$61$	2.77929	0.355852	0.177926	−	0.984044i	$-0.443061\pi$
$61$	2.77929	0.355852	0.177926	+	0.984044i	$0.443061\pi$
$62$	−3.93598	−0.499870
$63$	3.93908	0.496278
$64$	−10.6909	−1.33637
$65$	0.196929	0.0244260
$66$	−2.82570	−0.347819
$67$	13.4500	1.64317	0.821587	−	0.570083i	$-0.193089\pi$
$67$	13.4500	1.64317	0.821587	+	0.570083i	$0.193089\pi$
$68$	3.72817	0.452107
$69$	2.82137	0.339653
$70$	0.522074	0.0623998
$71$	8.33793	0.989530	0.494765	−	0.869027i	$-0.335254\pi$
$71$	8.33793	0.989530	0.494765	+	0.869027i	$0.335254\pi$
$72$	9.18917	1.08295
$73$	−3.50164	−0.409836	−0.204918	−	0.978779i	$-0.565693\pi$
$73$	−3.50164	−0.409836	−0.204918	+	0.978779i	$0.565693\pi$
$74$	−12.7387	−1.48085
$75$	−4.39775	−0.507809
$76$	21.5039	2.46667
$77$	−2.37275	−0.270400
$78$	−3.37973	−0.382679
$79$	−15.4312	−1.73615	−0.868075	−	0.496434i	$-0.834643\pi$
$79$	−15.4312	−1.73615	−0.868075	+	0.496434i	$0.834643\pi$
$80$	0.300551	0.0336026
$81$	2.60095	0.288994
$82$	16.7000	1.84420
$83$	8.57409	0.941129	0.470564	−	0.882366i	$-0.344050\pi$
$83$	8.57409	0.941129	0.470564	+	0.882366i	$0.344050\pi$
$84$	−5.83156	−0.636276
$85$	0.123030	0.0133445
$86$	12.7986	1.38011
$87$	−1.53659	−0.164740
$88$	−5.53521	−0.590055
$89$	−2.14066	−0.226910	−0.113455	−	0.993543i	$-0.536192\pi$
$89$	−2.14066	−0.226910	−0.113455	+	0.993543i	$0.536192\pi$
$90$	0.654188	0.0689575
$91$	−2.83798	−0.297501
$92$	11.9228	1.24304
$93$	1.45085	0.150446
$94$	23.7704	2.45173
$95$	0.709633	0.0728068
$96$	2.13984	0.218397
$97$	9.16315	0.930377	0.465188	−	0.885212i	$-0.345987\pi$
$97$	9.16315	0.930377	0.465188	+	0.885212i	$0.345987\pi$
$98$	9.22980	0.932351
$99$	−2.97319	−0.298817
$100$	−18.5844	−1.85844
$101$	15.3396	1.52634	0.763172	−	0.646195i	$-0.223641\pi$
$101$	15.3396	1.52634	0.763172	+	0.646195i	$0.223641\pi$
$102$	−2.11147	−0.209067
$103$	1.98584	0.195671	0.0978353	−	0.995203i	$-0.468808\pi$
$103$	1.98584	0.195671	0.0978353	+	0.995203i	$0.468808\pi$
$104$	−6.62049	−0.649193
$105$	−0.192443	−0.0187805
$106$	31.0748	3.01825
$107$	−15.6668	−1.51457	−0.757284	−	0.653086i	$-0.773474\pi$
$107$	−15.6668	−1.51457	−0.757284	+	0.653086i	$0.773474\pi$
$108$	−17.1745	−1.65262
$109$	−9.18696	−0.879952	−0.439976	−	0.898010i	$-0.645013\pi$
$109$	−9.18696	−0.879952	−0.439976	+	0.898010i	$0.645013\pi$
$110$	−0.394058	−0.0375720
$111$	4.69565	0.445692
$112$	−4.33130	−0.409269
$113$	7.03963	0.662233	0.331117	−	0.943590i	$-0.392575\pi$
$113$	7.03963	0.662233	0.331117	+	0.943590i	$0.392575\pi$
$114$	−12.1789	−1.14066
$115$	0.393455	0.0366899
$116$	−6.49348	−0.602904
$117$	−3.55614	−0.328766
$118$	−10.9156	−1.00486
$119$	−1.77301	−0.162532
$120$	−0.448935	−0.0409820
$121$	−9.20906	−0.837187
$122$	−6.65184	−0.602229
$123$	−6.15580	−0.555050
$124$	6.13113	0.550592
$125$	−1.22844	−0.109875
$126$	−9.42763	−0.839880
$127$	19.3547	1.71746	0.858728	−	0.512432i	$-0.171255\pi$
$127$	19.3547	1.71746	0.858728	+	0.512432i	$0.171255\pi$
$128$	20.7362	1.83284
$129$	−4.71772	−0.415372
$130$	−0.471321	−0.0413376
$131$	−1.90329	−0.166291	−0.0831454	−	0.996537i	$-0.526497\pi$
$131$	−1.90329	−0.166291	−0.0831454	+	0.996537i	$0.526497\pi$
$132$	4.40163	0.383112
$133$	−10.2267	−0.886764
$134$	−32.1906	−2.78084
$135$	−0.566762	−0.0487791
$136$	−4.13613	−0.354670
$137$	5.40409	0.461702	0.230851	−	0.972989i	$-0.425849\pi$
$137$	5.40409	0.461702	0.230851	+	0.972989i	$0.425849\pi$
$138$	−6.75256	−0.574816
$139$	14.0663	1.19309	0.596545	−	0.802579i	$-0.296540\pi$
$139$	14.0663	1.19309	0.596545	+	0.802579i	$0.296540\pi$
$140$	−0.813242	−0.0687315
$141$	−8.76206	−0.737898
$142$	−19.9557	−1.67464
$143$	2.14209	0.179130
$144$	−5.42736	−0.452280
$145$	−0.214286	−0.0177955
$146$	8.38068	0.693590
$147$	−3.40222	−0.280610
$148$	19.8433	1.63111
$149$	0.755096	0.0618598	0.0309299	−	0.999522i	$-0.490153\pi$
$149$	0.755096	0.0618598	0.0309299	+	0.999522i	$0.490153\pi$
$150$	10.5254	0.859395
$151$	1.46087	0.118884	0.0594419	−	0.998232i	$-0.481068\pi$
$151$	1.46087	0.118884	0.0594419	+	0.998232i	$0.481068\pi$
$152$	−23.8570	−1.93506
$153$	−2.22169	−0.179613
$154$	5.67885	0.457615
$155$	0.202329	0.0162514
$156$	5.26465	0.421509
$157$	−8.91025	−0.711116	−0.355558	−	0.934654i	$-0.615709\pi$
$157$	−8.91025	−0.711116	−0.355558	+	0.934654i	$0.615709\pi$
$158$	36.9325	2.93819
$159$	−11.4546	−0.908405
$160$	0.298412	0.0235915
$161$	−5.67016	−0.446871
$162$	−6.22500	−0.489082
$163$	20.4245	1.59977	0.799886	−	0.600152i	$-0.204893\pi$
$163$	20.4245	1.59977	0.799886	+	0.600152i	$0.204893\pi$
$164$	−26.0137	−2.03133
$165$	0.145255	0.0113081
$166$	−20.5209	−1.59273
$167$	−8.85599	−0.685297	−0.342649	−	0.939464i	$-0.611324\pi$
$167$	−8.85599	−0.685297	−0.342649	+	0.939464i	$0.611324\pi$
$168$	6.46969	0.499147
$169$	−10.4379	−0.802917
$170$	−0.294456	−0.0225837
$171$	−12.8146	−0.979955
$172$	−19.9365	−1.52015
$173$	−11.5527	−0.878332	−0.439166	−	0.898406i	$-0.644726\pi$
$173$	−11.5527	−0.878332	−0.439166	+	0.898406i	$0.644726\pi$
$174$	3.67762	0.278800
$175$	8.83823	0.668108
$176$	3.26923	0.246428
$177$	4.02361	0.302433
$178$	5.12337	0.384013
$179$	−19.9777	−1.49320	−0.746600	−	0.665273i	$-0.768315\pi$
$179$	−19.9777	−1.49320	−0.746600	+	0.665273i	$0.768315\pi$
$180$	−1.01904	−0.0759546
$181$	−5.00580	−0.372078	−0.186039	−	0.982542i	$-0.559565\pi$
$181$	−5.00580	−0.372078	−0.186039	+	0.982542i	$0.559565\pi$
$182$	6.79230	0.503479
$183$	2.45195	0.181253
$184$	−13.2275	−0.975142
$185$	0.654833	0.0481443
$186$	−3.47241	−0.254609
$187$	1.33826	0.0978632
$188$	−37.0275	−2.70051
$189$	8.16771	0.594114
$190$	−1.69841	−0.123215
$191$	−8.04155	−0.581866	−0.290933	−	0.956743i	$-0.593966\pi$
$191$	−8.04155	−0.581866	−0.290933	+	0.956743i	$0.593966\pi$
$192$	−9.43176	−0.680679
$193$	−1.37559	−0.0990169	−0.0495084	−	0.998774i	$-0.515765\pi$
$193$	−1.37559	−0.0990169	−0.0495084	+	0.998774i	$0.515765\pi$
$194$	−21.9307	−1.57453
$195$	0.173735	0.0124414
$196$	−14.3774	−1.02696
$197$	−22.8788	−1.63005	−0.815024	−	0.579427i	$-0.803276\pi$
$197$	−22.8788	−1.63005	−0.815024	+	0.579427i	$0.803276\pi$
$198$	7.11592	0.505706
$199$	0.0299027	0.00211974	0.00105987	−	0.999999i	$-0.499663\pi$
$199$	0.0299027	0.00211974	0.00105987	+	0.999999i	$0.499663\pi$
$200$	20.6180	1.45791
$201$	11.8658	0.836952
$202$	−36.7131	−2.58313
$203$	3.08812	0.216743
$204$	3.28907	0.230281
$205$	−0.858459	−0.0599574
$206$	−4.75283	−0.331145
$207$	−7.10503	−0.493834
$208$	3.91023	0.271126
$209$	7.71902	0.533935
$210$	0.460585	0.0317834
$211$	−22.8389	−1.57230	−0.786148	−	0.618039i	$-0.787928\pi$
$211$	−22.8389	−1.57230	−0.786148	+	0.618039i	$0.787928\pi$
$212$	−48.4057	−3.32451
$213$	7.35590	0.504018
$214$	37.4963	2.56319
$215$	−0.657910	−0.0448691
$216$	19.0538	1.29645
$217$	−2.91580	−0.197937
$218$	21.9877	1.48920
$219$	−3.08922	−0.208750
$220$	0.613830	0.0413844
$221$	1.60065	0.107671
$222$	−11.2384	−0.754271
$223$	−3.93567	−0.263552	−0.131776	−	0.991280i	$-0.542068\pi$
$223$	−3.93567	−0.263552	−0.131776	+	0.991280i	$0.542068\pi$
$224$	−4.30047	−0.287338
$225$	11.0748	0.738320
$226$	−16.8484	−1.12074
$227$	23.1926	1.53935	0.769674	−	0.638437i	$-0.220419\pi$
$227$	23.1926	1.53935	0.769674	+	0.638437i	$0.220419\pi$
$228$	18.9712	1.25640
$229$	8.96577	0.592475	0.296237	−	0.955114i	$-0.404268\pi$
$229$	8.96577	0.592475	0.296237	+	0.955114i	$0.404268\pi$
$230$	−0.941680	−0.0620925
$231$	−2.09329	−0.137729
$232$	7.20403	0.472968
$233$	−27.1240	−1.77695	−0.888477	−	0.458920i	$-0.848236\pi$
$233$	−27.1240	−1.77695	−0.888477	+	0.458920i	$0.848236\pi$
$234$	8.51113	0.556390
$235$	−1.22191	−0.0797089
$236$	17.0033	1.10682
$237$	−13.6138	−0.884309
$238$	4.24346	0.275063
$239$	−5.21028	−0.337025	−0.168513	−	0.985700i	$-0.553896\pi$
$239$	−5.21028	−0.337025	−0.168513	+	0.985700i	$0.553896\pi$
$240$	0.265152	0.0171155
$241$	0.981420	0.0632188	0.0316094	−	0.999500i	$-0.489937\pi$
$241$	0.981420	0.0632188	0.0316094	+	0.999500i	$0.489937\pi$
$242$	22.0406	1.41682
$243$	16.1147	1.03376
$244$	10.3617	0.663337
$245$	−0.474457	−0.0303119
$246$	14.7330	0.939345
$247$	9.23248	0.587448
$248$	−6.80204	−0.431930
$249$	7.56424	0.479364
$250$	2.94010	0.185948
$251$	−7.63378	−0.481840	−0.240920	−	0.970545i	$-0.577449\pi$
$251$	−7.63378	−0.481840	−0.240920	+	0.970545i	$0.577449\pi$
$252$	14.6856	0.925103
$253$	4.27980	0.269069
$254$	−46.3229	−2.90655
$255$	0.108540	0.00679704
$256$	−28.2473	−1.76546
$257$	−17.6713	−1.10230	−0.551152	−	0.834405i	$-0.685812\pi$
$257$	−17.6713	−1.10230	−0.551152	+	0.834405i	$0.685812\pi$
$258$	11.2912	0.702959
$259$	−9.43693	−0.586382
$260$	0.734183	0.0455321
$261$	3.86958	0.239521
$262$	4.55525	0.281424
$263$	2.88392	0.177830	0.0889151	−	0.996039i	$-0.471660\pi$
$263$	2.88392	0.177830	0.0889151	+	0.996039i	$0.471660\pi$
$264$	−4.88328	−0.300545
$265$	−1.59740	−0.0981273
$266$	24.4761	1.50072
$267$	−1.88854	−0.115577
$268$	50.1437	3.06301
$269$	11.6444	0.709972	0.354986	−	0.934872i	$-0.384486\pi$
$269$	11.6444	0.709972	0.354986	+	0.934872i	$0.384486\pi$
$270$	1.35646	0.0825518
$271$	−10.9744	−0.666648	−0.333324	−	0.942812i	$-0.608170\pi$
$271$	−10.9744	−0.666648	−0.333324	+	0.942812i	$0.608170\pi$
$272$	2.44290	0.148123
$273$	−2.50372	−0.151532
$274$	−12.9339	−0.781367
$275$	−6.67104	−0.402279
$276$	10.5186	0.633143
$277$	12.4385	0.747354	0.373677	−	0.927559i	$-0.378097\pi$
$277$	12.4385	0.747354	0.373677	+	0.927559i	$0.378097\pi$
$278$	−33.6658	−2.01914
$279$	−3.65366	−0.218739
$280$	0.902232	0.0539187
$281$	−27.1118	−1.61735	−0.808676	−	0.588254i	$-0.799816\pi$
$281$	−27.1118	−1.61735	−0.808676	+	0.588254i	$0.799816\pi$
$282$	20.9708	1.24879
$283$	−4.89908	−0.291220	−0.145610	−	0.989342i	$-0.546514\pi$
$283$	−4.89908	−0.291220	−0.145610	+	0.989342i	$0.546514\pi$
$284$	31.0852	1.84457
$285$	0.626053	0.0370842
$286$	−5.12678	−0.303153
$287$	12.3714	0.730262
$288$	−5.38874	−0.317534
$289$	1.00000	0.0588235
$290$	0.512864	0.0301164
$291$	8.08392	0.473888
$292$	−13.0547	−0.763968
$293$	−13.0381	−0.761695	−0.380848	−	0.924638i	$-0.624368\pi$
$293$	−13.0381	−0.761695	−0.380848	+	0.924638i	$0.624368\pi$
$294$	8.14272	0.474893
$295$	0.561114	0.0326693
$296$	−22.0147	−1.27958
$297$	−6.16494	−0.357726
$298$	−1.80721	−0.104689
$299$	5.11894	0.296036
$300$	−16.3956	−0.946598
$301$	9.48127	0.546491
$302$	−3.49638	−0.201194
$303$	13.5329	0.777445
$304$	14.0905	0.808147
$305$	0.341937	0.0195793
$306$	5.31729	0.303969
$307$	−12.9970	−0.741779	−0.370889	−	0.928677i	$-0.620947\pi$
$307$	−12.9970	−0.741779	−0.370889	+	0.928677i	$0.620947\pi$
$308$	−8.84602	−0.504049
$309$	1.75195	0.0996649
$310$	−0.484245	−0.0275033
$311$	24.7999	1.40627	0.703135	−	0.711056i	$-0.251783\pi$
$311$	24.7999	1.40627	0.703135	+	0.711056i	$0.251783\pi$
$312$	−5.84074	−0.330667
$313$	27.0158	1.52702	0.763511	−	0.645794i	$-0.223474\pi$
$313$	27.0158	1.52702	0.763511	+	0.645794i	$0.223474\pi$
$314$	21.3254	1.20346
$315$	0.484626	0.0273056
$316$	−57.5302	−3.23633
$317$	−1.28434	−0.0721359	−0.0360680	−	0.999349i	$-0.511483\pi$
$317$	−1.28434	−0.0721359	−0.0360680	+	0.999349i	$0.511483\pi$
$318$	27.4149	1.53735
$319$	−2.33089	−0.130505
$320$	−1.31531	−0.0735280
$321$	−13.8216	−0.771446
$322$	13.5707	0.756267
$323$	5.76795	0.320937
$324$	9.69676	0.538709
$325$	−7.97903	−0.442597
$326$	−48.8832	−2.70739
$327$	−8.10493	−0.448204
$328$	28.8603	1.59354
$329$	17.6093	0.970830
$330$	−0.347647	−0.0191373
$331$	13.5904	0.746996	0.373498	−	0.927631i	$-0.378158\pi$
$331$	13.5904	0.746996	0.373498	+	0.927631i	$0.378158\pi$
$332$	31.9656	1.75434
$333$	−11.8250	−0.648006
$334$	21.1956	1.15977
$335$	1.65475	0.0904088
$336$	−3.82116	−0.208461
$337$	−27.0928	−1.47584	−0.737921	−	0.674887i	$-0.764192\pi$
$337$	−27.0928	−1.47584	−0.737921	+	0.674887i	$0.764192\pi$
$338$	24.9817	1.35882
$339$	6.21051	0.337309
$340$	0.458678	0.0248753
$341$	2.20082	0.119181
$342$	30.6699	1.65844
$343$	19.2486	1.03933
$344$	22.1181	1.19253
$345$	0.347115	0.0186880
$346$	27.6496	1.48645
$347$	−12.7237	−0.683044	−0.341522	−	0.939874i	$-0.610942\pi$
$347$	−12.7237	−0.683044	−0.341522	+	0.939874i	$0.610942\pi$
$348$	−5.72868	−0.307090
$349$	10.8860	0.582712	0.291356	−	0.956615i	$-0.405894\pi$
$349$	10.8860	0.582712	0.291356	+	0.956615i	$0.405894\pi$
$350$	−21.1531	−1.13068
$351$	−7.37369	−0.393578
$352$	3.24597	0.173011
$353$	1.00000	0.0532246
$353$	1.00000	0.0532246
$354$	−9.62995	−0.511826
$355$	1.02582	0.0544448
$356$	−7.98075	−0.422979
$357$	−1.56419	−0.0827857
$358$	47.8137	2.52703
$359$	−26.3020	−1.38817	−0.694084	−	0.719894i	$-0.744190\pi$
$359$	−26.3020	−1.38817	−0.694084	+	0.719894i	$0.744190\pi$
$360$	1.13055	0.0595851
$361$	14.2693	0.751014
$362$	11.9807	0.629690
$363$	−8.12443	−0.426422
$364$	−10.5805	−0.554566
$365$	−0.430808	−0.0225495
$366$	−5.86839	−0.306746
$367$	−14.6838	−0.766489	−0.383245	−	0.923647i	$-0.625193\pi$
$367$	−14.6838	−0.766489	−0.383245	+	0.923647i	$0.625193\pi$
$368$	7.81248	0.407254
$369$	15.5021	0.807006
$370$	−1.56725	−0.0814775
$371$	23.0204	1.19516
$372$	5.40901	0.280444
$373$	11.8096	0.611476	0.305738	−	0.952116i	$-0.401097\pi$
$373$	11.8096	0.611476	0.305738	+	0.952116i	$0.401097\pi$
$374$	−3.20294	−0.165620
$375$	−1.08376	−0.0559650
$376$	41.0792	2.11850
$377$	−2.78791	−0.143585
$378$	−19.5483	−1.00545
$379$	−0.242188	−0.0124404	−0.00622019	−	0.999981i	$-0.501980\pi$
$379$	−0.242188	−0.0124404	−0.00622019	+	0.999981i	$0.501980\pi$
$380$	2.64563	0.135718
$381$	17.0752	0.874787
$382$	19.2463	0.984728
$383$	−11.2947	−0.577131	−0.288565	−	0.957460i	$-0.593178\pi$
$383$	−11.2947	−0.577131	−0.288565	+	0.957460i	$0.593178\pi$
$384$	18.2939	0.933558
$385$	−0.291921	−0.0148777
$386$	3.29227	0.167572
$387$	11.8806	0.603923
$388$	34.1618	1.73430
$389$	−7.25377	−0.367781	−0.183890	−	0.982947i	$-0.558869\pi$
$389$	−7.25377	−0.367781	−0.183890	+	0.982947i	$0.558869\pi$
$390$	−0.415809	−0.0210553
$391$	3.19803	0.161732
$392$	15.9506	0.805629
$393$	−1.67912	−0.0847003
$394$	54.7572	2.75863
$395$	−1.89851	−0.0955244
$396$	−11.0846	−0.557020
$397$	−30.2885	−1.52014	−0.760068	−	0.649843i	$-0.774834\pi$
$397$	−30.2885	−1.52014	−0.760068	+	0.649843i	$0.774834\pi$
$398$	−0.0715679	−0.00358737
$399$	−9.02218	−0.451674
$400$	−12.1775	−0.608876
$401$	−34.4278	−1.71924	−0.859622	−	0.510930i	$-0.829301\pi$
$401$	−34.4278	−1.71924	−0.859622	+	0.510930i	$0.829301\pi$
$402$	−28.3992	−1.41642
$403$	2.63234	0.131126
$404$	57.1885	2.84523
$405$	0.319995	0.0159007
$406$	−7.39098	−0.366808
$407$	7.12293	0.353071
$408$	−3.64898	−0.180651
$409$	25.4054	1.25622	0.628108	−	0.778126i	$-0.283830\pi$
$409$	25.4054	1.25622	0.628108	+	0.778126i	$0.283830\pi$
$410$	2.05460	0.101469
$411$	4.76760	0.235168
$412$	7.40354	0.364746
$413$	−8.08632	−0.397902
$414$	17.0049	0.835744
$415$	1.05487	0.0517817
$416$	3.88240	0.190351
$417$	12.4096	0.607702
$418$	−18.4744	−0.903611
$419$	1.53694	0.0750843	0.0375421	−	0.999295i	$-0.488047\pi$
$419$	1.53694	0.0750843	0.0375421	+	0.999295i	$0.488047\pi$
$420$	−0.717459	−0.0350084
$421$	−14.0713	−0.685793	−0.342897	−	0.939373i	$-0.611408\pi$
$421$	−14.0713	−0.685793	−0.342897	+	0.939373i	$0.611408\pi$
$422$	54.6617	2.66089
$423$	22.0654	1.07286
$424$	53.7025	2.60802
$425$	−4.98486	−0.241801
$426$	−17.6053	−0.852980
$427$	−4.92772	−0.238469
$428$	−58.4085	−2.82328
$429$	1.88979	0.0912401
$430$	1.57461	0.0759347
$431$	−24.5700	−1.18349	−0.591747	−	0.806124i	$-0.701562\pi$
$431$	−24.5700	−1.18349	−0.591747	+	0.806124i	$0.701562\pi$
$432$	−11.2537	−0.541442
$433$	−1.27391	−0.0612200	−0.0306100	−	0.999531i	$-0.509745\pi$
$433$	−1.27391	−0.0612200	−0.0306100	+	0.999531i	$0.509745\pi$
$434$	6.97855	0.334981
$435$	−0.189048	−0.00906414
$436$	−34.2505	−1.64030
$437$	18.4461	0.882397
$438$	7.39361	0.353280
$439$	24.6898	1.17838	0.589190	−	0.807995i	$-0.299447\pi$
$439$	24.6898	1.17838	0.589190	+	0.807995i	$0.299447\pi$
$440$	−0.680999	−0.0324653
$441$	8.56776	0.407988
$442$	−3.83093	−0.182219
$443$	4.09156	0.194396	0.0971979	−	0.995265i	$-0.469012\pi$
$443$	4.09156	0.194396	0.0971979	+	0.995265i	$0.469012\pi$
$444$	17.5062	0.830807
$445$	−0.263366	−0.0124848
$446$	9.41948	0.446025
$447$	0.666161	0.0315083
$448$	18.9552	0.895548
$449$	3.25229	0.153485	0.0767426	−	0.997051i	$-0.475548\pi$
$449$	3.25229	0.153485	0.0767426	+	0.997051i	$0.475548\pi$
$450$	−26.5060	−1.24950
$451$	−9.33787	−0.439703
$452$	26.2449	1.23446
$453$	1.28881	0.0605535
$454$	−55.5083	−2.60513
$455$	−0.349157	−0.0163687
$456$	−21.0471	−0.985622
$457$	33.9759	1.58933	0.794664	−	0.607050i	$-0.207647\pi$
$457$	33.9759	1.58933	0.794664	+	0.607050i	$0.207647\pi$
$458$	−21.4583	−1.00268
$459$	−4.60668	−0.215021
$460$	1.46687	0.0683930
$461$	−38.8339	−1.80867	−0.904337	−	0.426819i	$-0.859634\pi$
$461$	−38.8339	−1.80867	−0.904337	+	0.426819i	$0.859634\pi$
$462$	5.01000	0.233086
$463$	8.43322	0.391925	0.195963	−	0.980611i	$-0.437217\pi$
$463$	8.43322	0.391925	0.195963	+	0.980611i	$0.437217\pi$
$464$	−4.25488	−0.197528
$465$	0.178499	0.00827767
$466$	64.9176	3.00725
$467$	−24.4175	−1.12991	−0.564954	−	0.825122i	$-0.691106\pi$
$467$	−24.4175	−1.12991	−0.564954	+	0.825122i	$0.691106\pi$
$468$	−13.2579	−0.612847
$469$	−23.8470	−1.10115
$470$	2.92448	0.134896
$471$	−7.86081	−0.362207
$472$	−18.8639	−0.868284
$473$	−7.15640	−0.329052
$474$	32.5826	1.49657
$475$	−28.7525	−1.31925
$476$	−6.61009	−0.302973
$477$	28.8458	1.32076
$478$	12.4701	0.570368
$479$	23.3105	1.06509	0.532543	−	0.846403i	$-0.321237\pi$
$479$	23.3105	1.06509	0.532543	+	0.846403i	$0.321237\pi$
$480$	0.263265	0.0120164
$481$	8.51952	0.388457
$482$	−2.34889	−0.106989
$483$	−5.00234	−0.227614
$484$	−34.3329	−1.56059
$485$	1.12735	0.0511901
$486$	−38.5682	−1.74949
$487$	−30.5097	−1.38252	−0.691262	−	0.722604i	$-0.742945\pi$
$487$	−30.5097	−1.38252	−0.691262	+	0.722604i	$0.742945\pi$
$488$	−11.4955	−0.520377
$489$	18.0190	0.814845
$490$	1.13555	0.0512987
$491$	−24.5234	−1.10672	−0.553362	−	0.832941i	$-0.686655\pi$
$491$	−24.5234	−1.10672	−0.553362	+	0.832941i	$0.686655\pi$
$492$	−22.9499	−1.03466
$493$	−1.74173	−0.0784437
$494$	−22.0966	−0.994174
$495$	−0.365793	−0.0164412
$496$	4.01745	0.180389
$497$	−14.7833	−0.663120
$498$	−18.1040	−0.811257
$499$	−10.2987	−0.461034	−0.230517	−	0.973068i	$-0.574042\pi$
$499$	−10.2987	−0.461034	−0.230517	+	0.973068i	$0.574042\pi$
$500$	−4.57983	−0.204816
$501$	−7.81294	−0.349057
$502$	18.2704	0.815447
$503$	−21.5652	−0.961544	−0.480772	−	0.876846i	$-0.659644\pi$
$503$	−21.5652	−0.961544	−0.480772	+	0.876846i	$0.659644\pi$
$504$	−16.2925	−0.725727
$505$	1.88723	0.0839808
$506$	−10.2431	−0.455361
$507$	−9.20855	−0.408966
$508$	72.1577	3.20148
$509$	−37.7273	−1.67223	−0.836116	−	0.548553i	$-0.815179\pi$
$509$	−37.7273	−1.67223	−0.836116	+	0.548553i	$0.815179\pi$
$510$	−0.259775	−0.0115030
$511$	6.20846	0.274646
$512$	26.1336	1.15495
$513$	−26.5711	−1.17314
$514$	42.2937	1.86550
$515$	0.244318	0.0107660
$516$	−17.5884	−0.774288
$517$	−13.2913	−0.584553
$518$	22.5860	0.992370
$519$	−10.1920	−0.447379
$520$	−0.814522	−0.0357191
$521$	−3.26730	−0.143143	−0.0715714	−	0.997435i	$-0.522801\pi$
$521$	−3.26730	−0.143143	−0.0715714	+	0.997435i	$0.522801\pi$
$522$	−9.26131	−0.405356
$523$	32.2982	1.41230	0.706150	−	0.708063i	$-0.250431\pi$
$523$	32.2982	1.41230	0.706150	+	0.708063i	$0.250431\pi$
$524$	−7.09577	−0.309980
$525$	7.79728	0.340301
$526$	−6.90226	−0.300953
$527$	1.64454	0.0716374
$528$	2.88419	0.125518
$529$	−12.7726	−0.555329
$530$	3.82314	0.166067
$531$	−10.1326	−0.439718
$532$	−38.1267	−1.65300
$533$	−11.1687	−0.483772
$534$	4.51995	0.195597
$535$	−1.92749	−0.0833327
$536$	−55.6307	−2.40288
$537$	−17.6247	−0.760563
$538$	−27.8693	−1.20153
$539$	−5.16089	−0.222295
$540$	−2.11298	−0.0909283
$541$	−9.21622	−0.396236	−0.198118	−	0.980178i	$-0.563483\pi$
$541$	−9.21622	−0.396236	−0.198118	+	0.980178i	$0.563483\pi$
$542$	26.2657	1.12821
$543$	−4.41622	−0.189518
$544$	2.42552	0.103993
$545$	−1.13028	−0.0484157
$546$	5.99231	0.256447
$547$	3.74196	0.159995	0.0799973	−	0.996795i	$-0.474509\pi$
$547$	3.74196	0.159995	0.0799973	+	0.996795i	$0.474509\pi$
$548$	20.1473	0.860652
$549$	−6.17471	−0.263530
$550$	15.9662	0.680801
$551$	−10.0462	−0.427984
$552$	−11.6696	−0.496689
$553$	27.3598	1.16346
$554$	−29.7697	−1.26479
$555$	0.577708	0.0245223
$556$	52.4417	2.22402
$557$	−37.3328	−1.58184	−0.790921	−	0.611919i	$-0.790398\pi$
$557$	−37.3328	−1.58184	−0.790921	+	0.611919i	$0.790398\pi$
$558$	8.74451	0.370185
$559$	−8.55955	−0.362030
$560$	−0.532881	−0.0225183
$561$	1.18064	0.0498467
$562$	64.8882	2.73714
$563$	−18.8935	−0.796267	−0.398133	−	0.917328i	$-0.630342\pi$
$563$	−18.8935	−0.796267	−0.398133	+	0.917328i	$0.630342\pi$
$564$	−32.6664	−1.37550
$565$	0.866089	0.0364366
$566$	11.7253	0.492849
$567$	−4.61151	−0.193665
$568$	−34.4867	−1.44703
$569$	14.2499	0.597386	0.298693	−	0.954349i	$-0.403449\pi$
$569$	14.2499	0.597386	0.298693	+	0.954349i	$0.403449\pi$
$570$	−1.49837	−0.0627598
$571$	−32.9788	−1.38012	−0.690060	−	0.723752i	$-0.742416\pi$
$571$	−32.9788	−1.38012	−0.690060	+	0.723752i	$0.742416\pi$
$572$	7.98606	0.333914
$573$	−7.09443	−0.296374
$574$	−29.6092	−1.23587
$575$	−15.9418	−0.664818
$576$	23.7519	0.989662
$577$	−38.1539	−1.58837	−0.794183	−	0.607679i	$-0.792101\pi$
$577$	−38.1539	−1.58837	−0.794183	+	0.607679i	$0.792101\pi$
$578$	−2.39336	−0.0995506
$579$	−1.21357	−0.0504343
$580$	−0.798894	−0.0331723
$581$	−15.2020	−0.630685
$582$	−19.3477	−0.801989
$583$	−17.3756	−0.719626
$584$	14.4832	0.599320
$585$	−0.437514	−0.0180890
$586$	31.2049	1.28906
$587$	−9.98957	−0.412314	−0.206157	−	0.978519i	$-0.566096\pi$
$587$	−9.98957	−0.412314	−0.206157	+	0.978519i	$0.566096\pi$
$588$	−12.6840	−0.523081
$589$	9.48564	0.390849
$590$	−1.34295	−0.0552883
$591$	−20.1842	−0.830266
$592$	13.0024	0.534396
$593$	−28.0243	−1.15082	−0.575409	−	0.817866i	$-0.695157\pi$
$593$	−28.0243	−1.15082	−0.575409	+	0.817866i	$0.695157\pi$
$594$	14.7549	0.605401
$595$	−0.218135	−0.00894264
$596$	2.81512	0.115312
$597$	0.0263808	0.00107969
$598$	−12.2515	−0.500999
$599$	−7.66024	−0.312989	−0.156494	−	0.987679i	$-0.550019\pi$
$599$	−7.66024	−0.312989	−0.156494	+	0.987679i	$0.550019\pi$
$600$	18.1897	0.742590
$601$	−9.01507	−0.367732	−0.183866	−	0.982951i	$-0.558861\pi$
$601$	−9.01507	−0.367732	−0.183866	+	0.982951i	$0.558861\pi$
$602$	−22.6921	−0.924860
$603$	−29.8816	−1.21687
$604$	5.44636	0.221609
$605$	−1.13299	−0.0460628
$606$	−32.3891	−1.31572
$607$	27.0189	1.09666	0.548331	−	0.836261i	$-0.315263\pi$
$607$	27.0189	1.09666	0.548331	+	0.836261i	$0.315263\pi$
$608$	13.9903	0.567380
$609$	2.72440	0.110398
$610$	−0.818378	−0.0331352
$611$	−15.8974	−0.643139
$612$	−8.28282	−0.334813
$613$	23.6707	0.956049	0.478025	−	0.878346i	$-0.341353\pi$
$613$	23.6707	0.956049	0.478025	+	0.878346i	$0.341353\pi$
$614$	31.1065	1.25536
$615$	−0.757351	−0.0305393
$616$	9.81401	0.395418
$617$	2.68488	0.108089	0.0540447	−	0.998539i	$-0.482789\pi$
$617$	2.68488	0.108089	0.0540447	+	0.998539i	$0.482789\pi$
$618$	−4.19304	−0.168669
$619$	−22.6814	−0.911643	−0.455822	−	0.890071i	$-0.650655\pi$
$619$	−22.6814	−0.911643	−0.455822	+	0.890071i	$0.650655\pi$
$620$	0.754315	0.0302940
$621$	−14.7323	−0.591188
$622$	−59.3550	−2.37992
$623$	3.79542	0.152060
$624$	3.44969	0.138098
$625$	24.7732	0.990927
$626$	−64.6585	−2.58427
$627$	6.80988	0.271960
$628$	−33.2189	−1.32558
$629$	5.32254	0.212223
$630$	−1.15989	−0.0462109
$631$	3.17988	0.126589	0.0632946	−	0.997995i	$-0.479839\pi$
$631$	3.17988	0.126589	0.0632946	+	0.997995i	$0.479839\pi$
$632$	63.8255	2.53884
$633$	−20.1490	−0.800850
$634$	3.07390	0.122080
$635$	2.38122	0.0944959
$636$	−42.7045	−1.69334
$637$	−6.17278	−0.244575
$638$	5.57866	0.220861
$639$	−18.5243	−0.732808
$640$	2.55118	0.100844
$641$	7.35204	0.290388	0.145194	−	0.989403i	$-0.453619\pi$
$641$	7.35204	0.290388	0.145194	+	0.989403i	$0.453619\pi$
$642$	33.0800	1.30556
$643$	15.3946	0.607103	0.303551	−	0.952815i	$-0.401828\pi$
$643$	15.3946	0.607103	0.303551	+	0.952815i	$0.401828\pi$
$644$	−21.1393	−0.833005
$645$	−0.580422	−0.0228541
$646$	−13.8048	−0.543142
$647$	−0.189022	−0.00743123	−0.00371561	−	0.999993i	$-0.501183\pi$
$647$	−0.189022	−0.00743123	−0.00371561	+	0.999993i	$0.501183\pi$
$648$	−10.7578	−0.422608
$649$	6.10350	0.239583
$650$	19.0967	0.749033
$651$	−2.57238	−0.100819
$652$	76.1461	2.98211
$653$	−31.4016	−1.22884	−0.614420	−	0.788979i	$-0.710610\pi$
$653$	−31.4016	−1.22884	−0.614420	+	0.788979i	$0.710610\pi$
$654$	19.3980	0.758522
$655$	−0.234162	−0.00914946
$656$	−17.0456	−0.665520
$657$	7.77954	0.303509
$658$	−42.1453	−1.64299
$659$	−2.28881	−0.0891595	−0.0445798	−	0.999006i	$-0.514195\pi$
$659$	−2.28881	−0.0891595	−0.0445798	+	0.999006i	$0.514195\pi$
$660$	0.541534	0.0210792
$661$	20.6718	0.804039	0.402019	−	0.915631i	$-0.368308\pi$
$661$	20.6718	0.804039	0.402019	+	0.915631i	$0.368308\pi$
$662$	−32.5267	−1.26419
$663$	1.41213	0.0548425
$664$	−35.4635	−1.37625
$665$	−1.25819	−0.0487905
$666$	28.3015	1.09666
$667$	−5.57012	−0.215676
$668$	−33.0166	−1.27745
$669$	−3.47213	−0.134240
$670$	−3.96042	−0.153004
$671$	3.71941	0.143586
$672$	−3.79397	−0.146356
$673$	43.9699	1.69491	0.847457	−	0.530865i	$-0.178133\pi$
$673$	43.9699	1.69491	0.847457	+	0.530865i	$0.178133\pi$
$674$	64.8429	2.49766
$675$	22.9637	0.883872
$676$	−38.9143	−1.49670
$677$	42.3937	1.62932	0.814661	−	0.579937i	$-0.196923\pi$
$677$	42.3937	1.62932	0.814661	+	0.579937i	$0.196923\pi$
$678$	−14.8640	−0.570848
$679$	−16.2464	−0.623479
$680$	−0.508869	−0.0195142
$681$	20.4610	0.784068
$682$	−5.26736	−0.201698
$683$	−23.9217	−0.915337	−0.457668	−	0.889123i	$-0.651315\pi$
$683$	−23.9217	−0.915337	−0.457668	+	0.889123i	$0.651315\pi$
$684$	−47.7749	−1.82672
$685$	0.664867	0.0254032
$686$	−46.0688	−1.75891
$687$	7.90979	0.301777
$688$	−13.0635	−0.498042
$689$	−20.7825	−0.791749
$690$	−0.830770	−0.0316269
$691$	−27.4096	−1.04271	−0.521355	−	0.853340i	$-0.674573\pi$
$691$	−27.4096	−1.04271	−0.521355	+	0.853340i	$0.674573\pi$
$692$	−43.0702	−1.63728
$693$	5.27151	0.200248
$694$	30.4524	1.15596
$695$	1.73059	0.0656449
$696$	6.35555	0.240906
$697$	−6.97762	−0.264296
$698$	−26.0540	−0.986158
$699$	−23.9294	−0.905093
$700$	32.9504	1.24541
$701$	−16.2080	−0.612169	−0.306084	−	0.952004i	$-0.599019\pi$
$701$	−16.2080	−0.612169	−0.306084	+	0.952004i	$0.599019\pi$
$702$	17.6479	0.666077
$703$	30.7001	1.15788
$704$	−14.3072	−0.539224
$705$	−1.07800	−0.0405998
$706$	−2.39336	−0.0900753
$707$	−27.1973	−1.02286
$708$	15.0007	0.563761
$709$	−32.7594	−1.23030	−0.615152	−	0.788408i	$-0.710905\pi$
$709$	−32.7594	−1.23030	−0.615152	+	0.788408i	$0.710905\pi$
$710$	−2.45515	−0.0921402
$711$	34.2833	1.28573
$712$	8.85405	0.331819
$713$	5.25930	0.196962
$714$	3.74367	0.140103
$715$	0.263542	0.00985590
$716$	−74.4801	−2.78345
$717$	−4.59662	−0.171664
$718$	62.9502	2.34928
$719$	−13.3415	−0.497553	−0.248777	−	0.968561i	$-0.580029\pi$
$719$	−13.3415	−0.497553	−0.248777	+	0.968561i	$0.580029\pi$
$720$	−0.667729	−0.0248848
$721$	−3.52092	−0.131126
$722$	−34.1515	−1.27099
$723$	0.865830	0.0322005
$724$	−18.6625	−0.693585
$725$	8.68230	0.322453
$726$	19.4447	0.721660
$727$	−43.6640	−1.61941	−0.809704	−	0.586838i	$-0.800372\pi$
$727$	−43.6640	−1.61941	−0.809704	+	0.586838i	$0.800372\pi$
$728$	11.7382	0.435048
$729$	6.41385	0.237550
$730$	1.03108	0.0381619
$731$	−5.34754	−0.197786
$732$	9.14128	0.337871
$733$	21.4406	0.791925	0.395962	−	0.918267i	$-0.370411\pi$
$733$	21.4406	0.791925	0.395962	+	0.918267i	$0.370411\pi$
$734$	35.1437	1.29718
$735$	−0.418576	−0.0154394
$736$	7.75688	0.285923
$737$	17.9995	0.663021
$738$	−37.1020	−1.36575
$739$	41.9140	1.54183	0.770916	−	0.636937i	$-0.219799\pi$
$739$	41.9140	1.54183	0.770916	+	0.636937i	$0.219799\pi$
$740$	2.44133	0.0897450
$741$	8.14509	0.299217
$742$	−55.0961	−2.02264
$743$	40.4103	1.48251	0.741254	−	0.671224i	$-0.234231\pi$
$743$	40.4103	1.48251	0.741254	+	0.671224i	$0.234231\pi$
$744$	−6.00090	−0.220004
$745$	0.0928997	0.00340358
$746$	−28.2645	−1.03484
$747$	−19.0489	−0.696964
$748$	4.98926	0.182425
$749$	27.7775	1.01497
$750$	2.59382	0.0947129
$751$	18.8097	0.686376	0.343188	−	0.939267i	$-0.388493\pi$
$751$	18.8097	0.686376	0.343188	+	0.939267i	$0.388493\pi$
$752$	−24.2624	−0.884760
$753$	−6.73468	−0.245426
$754$	6.67246	0.242997
$755$	0.179731	0.00654108
$756$	30.4506	1.10748
$757$	33.5789	1.22045	0.610223	−	0.792230i	$-0.291080\pi$
$757$	33.5789	1.22045	0.610223	+	0.792230i	$0.291080\pi$
$758$	0.579643	0.0210536
$759$	3.77573	0.137050
$760$	−2.93513	−0.106468
$761$	43.6170	1.58112	0.790558	−	0.612387i	$-0.209791\pi$
$761$	43.6170	1.58112	0.790558	+	0.612387i	$0.209791\pi$
$762$	−40.8670	−1.48046
$763$	16.2886	0.589688
$764$	−29.9803	−1.08465
$765$	−0.273335	−0.00988244
$766$	27.0322	0.976714
$767$	7.30021	0.263595
$768$	−24.9204	−0.899237
$769$	−35.7241	−1.28824	−0.644121	−	0.764923i	$-0.722777\pi$
$769$	−35.7241	−1.28824	−0.644121	+	0.764923i	$0.722777\pi$
$770$	0.698671	0.0251783
$771$	−15.5900	−0.561459
$772$	−5.12842	−0.184576
$773$	33.7598	1.21425	0.607127	−	0.794605i	$-0.292322\pi$
$773$	33.7598	1.21425	0.607127	+	0.794605i	$0.292322\pi$
$774$	−28.4344	−1.02206
$775$	−8.19782	−0.294474
$776$	−37.8999	−1.36053
$777$	−8.32546	−0.298674
$778$	17.3609	0.622417
$779$	−40.2466	−1.44198
$780$	0.647712	0.0231918
$781$	11.1583	0.399276
$782$	−7.65404	−0.273708
$783$	8.02361	0.286741
$784$	−9.42085	−0.336459
$785$	−1.09623	−0.0391262
$786$	4.01873	0.143344
$787$	0.0813139	0.00289853	0.00144926	−	0.999999i	$-0.499539\pi$
$787$	0.0813139	0.00289853	0.00144926	+	0.999999i	$0.499539\pi$
$788$	−85.2960	−3.03855
$789$	2.54426	0.0905779
$790$	4.54381	0.161662
$791$	−12.4814	−0.443786
$792$	12.2975	0.436973
$793$	4.44867	0.157977
$794$	72.4913	2.57262
$795$	−1.40926	−0.0499812
$796$	0.111482	0.00395138
$797$	−18.7502	−0.664167	−0.332083	−	0.943250i	$-0.607752\pi$
$797$	−18.7502	−0.664167	−0.332083	+	0.943250i	$0.607752\pi$
$798$	21.5933	0.764395
$799$	−9.93182	−0.351362
$800$	−12.0909	−0.427477
$801$	4.75588	0.168041
$802$	82.3982	2.90958
$803$	−4.68610	−0.165369
$804$	44.2378	1.56015
$805$	−0.697602	−0.0245872
$806$	−6.30013	−0.221913
$807$	10.2729	0.361625
$808$	−63.4464	−2.23204
$809$	6.47016	0.227479	0.113739	−	0.993511i	$-0.463717\pi$
$809$	6.47016	0.227479	0.113739	+	0.993511i	$0.463717\pi$
$810$	−0.765864	−0.0269097
$811$	16.8686	0.592336	0.296168	−	0.955136i	$-0.404291\pi$
$811$	16.8686	0.592336	0.296168	+	0.955136i	$0.404291\pi$
$812$	11.5130	0.404028
$813$	−9.68185	−0.339557
$814$	−17.0477	−0.597523
$815$	2.51284	0.0880208
$816$	2.15518	0.0754463
$817$	−30.8444	−1.07911
$818$	−60.8042	−2.12597
$819$	6.30509	0.220318
$820$	−3.20048	−0.111766
$821$	−4.27083	−0.149053	−0.0745266	−	0.997219i	$-0.523745\pi$
$821$	−4.27083	−0.149053	−0.0745266	+	0.997219i	$0.523745\pi$
$822$	−11.4106	−0.397990
$823$	18.9157	0.659361	0.329680	−	0.944093i	$-0.393059\pi$
$823$	18.9157	0.659361	0.329680	+	0.944093i	$0.393059\pi$
$824$	−8.21368	−0.286137
$825$	−5.88533	−0.204901
$826$	19.3535	0.673393
$827$	−16.6223	−0.578012	−0.289006	−	0.957327i	$-0.593325\pi$
$827$	−16.6223	−0.578012	−0.289006	+	0.957327i	$0.593325\pi$
$828$	−26.4887	−0.920547
$829$	−46.5733	−1.61756	−0.808779	−	0.588113i	$-0.799871\pi$
$829$	−46.5733	−1.61756	−0.808779	+	0.588113i	$0.799871\pi$
$830$	−2.52469	−0.0876333
$831$	10.9735	0.380665
$832$	−17.1124	−0.593267
$833$	−3.85642	−0.133617
$834$	−29.7007	−1.02845
$835$	−1.08956	−0.0377056
$836$	28.7778	0.995301
$837$	−7.57588	−0.261861
$838$	−3.67844	−0.127070
$839$	−22.3118	−0.770290	−0.385145	−	0.922856i	$-0.625849\pi$
$839$	−22.3118	−0.770290	−0.385145	+	0.922856i	$0.625849\pi$
$840$	0.795968	0.0274635
$841$	−25.9664	−0.895392
$842$	33.6777	1.16061
$843$	−23.9186	−0.823799
$844$	−85.1473	−2.93089
$845$	−1.28418	−0.0441772
$846$	−52.8104	−1.81566
$847$	16.3278	0.561030
$848$	−31.7180	−1.08920
$849$	−4.32207	−0.148333
$850$	11.9306	0.409215
$851$	17.0217	0.583495
$852$	27.4240	0.939531
$853$	−47.9888	−1.64310	−0.821552	−	0.570133i	$-0.806892\pi$
$853$	−47.9888	−1.64310	−0.821552	+	0.570133i	$0.806892\pi$
$854$	11.7938	0.403576
$855$	−1.57658	−0.0539180
$856$	64.7999	2.21481
$857$	−12.6109	−0.430779	−0.215389	−	0.976528i	$-0.569102\pi$
$857$	−12.6109	−0.430779	−0.215389	+	0.976528i	$0.569102\pi$
$858$	−4.52295	−0.154411
$859$	−43.2642	−1.47616	−0.738078	−	0.674715i	$-0.764267\pi$
$859$	−43.2642	−1.47616	−0.738078	+	0.674715i	$0.764267\pi$
$860$	−2.45280	−0.0836397
$861$	10.9143	0.371959
$862$	58.8048	2.00290
$863$	−2.35486	−0.0801605	−0.0400803	−	0.999196i	$-0.512761\pi$
$863$	−2.35486	−0.0801605	−0.0400803	+	0.999196i	$0.512761\pi$
$864$	−11.1736	−0.380133
$865$	−1.42133	−0.0483266
$866$	3.04892	0.103606
$867$	0.882221	0.0299618
$868$	−10.8706	−0.368972
$869$	−20.6510	−0.700537
$870$	0.452459	0.0153398
$871$	21.5287	0.729472
$872$	37.9984	1.28679
$873$	−20.3576	−0.689002
$874$	−44.1482	−1.49333
$875$	2.17804	0.0736313
$876$	−11.5171	−0.389128
$877$	46.4181	1.56743	0.783714	−	0.621122i	$-0.213323\pi$
$877$	46.4181	1.56743	0.783714	+	0.621122i	$0.213323\pi$
$878$	−59.0915	−1.99424
$879$	−11.5025	−0.387970
$880$	0.402215	0.0135587
$881$	−14.8706	−0.501002	−0.250501	−	0.968116i	$-0.580595\pi$
$881$	−14.8706	−0.501002	−0.250501	+	0.968116i	$0.580595\pi$
$882$	−20.5057	−0.690463
$883$	−5.33774	−0.179629	−0.0898146	−	0.995959i	$-0.528627\pi$
$883$	−5.33774	−0.179629	−0.0898146	+	0.995959i	$0.528627\pi$
$884$	5.96750	0.200709
$885$	0.495027	0.0166401
$886$	−9.79257	−0.328988
$887$	9.26697	0.311154	0.155577	−	0.987824i	$-0.450276\pi$
$887$	9.26697	0.311154	0.155577	+	0.987824i	$0.450276\pi$
$888$	−19.4218	−0.651753
$889$	−34.3162	−1.15093
$890$	0.630330	0.0211287
$891$	3.48074	0.116609
$892$	−14.6729	−0.491283
$893$	−57.2862	−1.91701
$894$	−1.59436	−0.0533235
$895$	−2.45786	−0.0821571
$896$	−36.7656	−1.22825
$897$	4.51603	0.150786
$898$	−7.78390	−0.259752
$899$	−2.86435	−0.0955316
$900$	41.2887	1.37629
$901$	−12.9838	−0.432552
$902$	22.3489	0.744136
$903$	8.36458	0.278356
$904$	−29.1168	−0.968411
$905$	−0.615865	−0.0204720
$906$	−3.08458	−0.102478
$907$	−19.7093	−0.654437	−0.327218	−	0.944949i	$-0.606111\pi$
$907$	−19.7093	−0.654437	−0.327218	+	0.944949i	$0.606111\pi$
$908$	86.4660	2.86947
$909$	−34.0797	−1.13035
$910$	0.835659	0.0277018
$911$	17.8572	0.591635	0.295817	−	0.955245i	$-0.404408\pi$
$911$	17.8572	0.591635	0.295817	+	0.955245i	$0.404408\pi$
$912$	12.4310	0.411630
$913$	11.4744	0.379746
$914$	−81.3166	−2.68972
$915$	0.301664	0.00997271
$916$	33.4259	1.10442
$917$	3.37455	0.111438
$918$	11.0254	0.363894
$919$	24.6958	0.814638	0.407319	−	0.913286i	$-0.366464\pi$
$919$	24.6958	0.814638	0.407319	+	0.913286i	$0.366464\pi$
$920$	−1.62738	−0.0536531
$921$	−11.4662	−0.377826
$922$	92.9434	3.06093
$923$	13.3461	0.439293
$924$	−7.80415	−0.256738
$925$	−26.5321	−0.872371
$926$	−20.1837	−0.663279
$927$	−4.41191	−0.144906
$928$	−4.22460	−0.138679
$929$	−4.14132	−0.135872	−0.0679362	−	0.997690i	$-0.521641\pi$
$929$	−4.14132	−0.135872	−0.0679362	+	0.997690i	$0.521641\pi$
$930$	−0.427211	−0.0140088
$931$	−22.2436	−0.729006
$932$	−101.123	−3.31239
$933$	21.8790	0.716285
$934$	58.4399	1.91221
$935$	0.164647	0.00538452
$936$	14.7087	0.480768
$937$	−29.3178	−0.957772	−0.478886	−	0.877877i	$-0.658959\pi$
$937$	−29.3178	−0.957772	−0.478886	+	0.877877i	$0.658959\pi$
$938$	57.0744	1.86354
$939$	23.8339	0.777790
$940$	−4.55550	−0.148584
$941$	10.0712	0.328312	0.164156	−	0.986434i	$-0.447510\pi$
$941$	10.0712	0.328312	0.164156	+	0.986434i	$0.447510\pi$
$942$	18.8138	0.612985
$943$	−22.3147	−0.726666
$944$	11.1415	0.362626
$945$	1.00488	0.0326886
$946$	17.1278	0.556874
$947$	−4.87194	−0.158317	−0.0791583	−	0.996862i	$-0.525223\pi$
$947$	−4.87194	−0.158317	−0.0791583	+	0.996862i	$0.525223\pi$
$948$	−50.7544	−1.64843
$949$	−5.60490	−0.181943
$950$	68.8149	2.23265
$951$	−1.13308	−0.0367425
$952$	7.33341	0.237677
$953$	56.7348	1.83782	0.918911	−	0.394466i	$-0.129070\pi$
$953$	56.7348	1.83782	0.918911	+	0.394466i	$0.129070\pi$
$954$	−69.0385	−2.23520
$955$	−0.989355	−0.0320148
$956$	−19.4248	−0.628243
$957$	−2.05636	−0.0664727
$958$	−55.7905	−1.80251
$959$	−9.58152	−0.309403
$960$	−1.16039	−0.0374515
$961$	−28.2955	−0.912757
$962$	−20.3903	−0.657409
$963$	34.8067	1.12163
$964$	3.65890	0.117845
$965$	−0.169239	−0.00544799
$966$	11.9724	0.385205
$967$	−1.71951	−0.0552958	−0.0276479	−	0.999618i	$-0.508802\pi$
$967$	−1.71951	−0.0552958	−0.0276479	+	0.999618i	$0.508802\pi$
$968$	38.0898	1.22425
$969$	5.08861	0.163470
$970$	−2.69814	−0.0866321
$971$	−38.9313	−1.24937	−0.624683	−	0.780878i	$-0.714772\pi$
$971$	−38.9313	−1.24937	−0.624683	+	0.780878i	$0.714772\pi$
$972$	60.0781	1.92701
$973$	−24.9398	−0.799534
$974$	73.0206	2.33973
$975$	−7.03927	−0.225437
$976$	6.78953	0.217327
$977$	−3.21251	−0.102777	−0.0513886	−	0.998679i	$-0.516365\pi$
$977$	−3.21251	−0.102777	−0.0513886	+	0.998679i	$0.516365\pi$
$978$	−43.1258	−1.37901
$979$	−2.86476	−0.0915581
$980$	−1.76885	−0.0565040
$981$	20.4105	0.651659
$982$	58.6932	1.87298
$983$	8.65240	0.275969	0.137984	−	0.990434i	$-0.455938\pi$
$983$	8.65240	0.275969	0.137984	+	0.990434i	$0.455938\pi$
$984$	25.4612	0.811673
$985$	−2.81479	−0.0896866
$986$	4.16859	0.132755
$987$	15.5353	0.494493
$988$	34.4202	1.09505
$989$	−17.1016	−0.543800
$990$	0.875474	0.0278244
$991$	−21.1868	−0.673022	−0.336511	−	0.941680i	$-0.609247\pi$
$991$	−21.1868	−0.673022	−0.336511	+	0.941680i	$0.609247\pi$
$992$	3.98886	0.126647
$993$	11.9897	0.380483
$994$	35.3817	1.12224
$995$	0.00367894	0.000116630 0
$996$	28.2008	0.893576
$997$	42.9369	1.35983	0.679913	−	0.733293i	$-0.262017\pi$
$997$	42.9369	1.35983	0.679913	+	0.733293i	$0.262017\pi$
$998$	24.6485	0.780235
$999$	−24.5192	−0.775754

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6001.2.a.b.1.9	✓	114

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6001.2.a.b.1.9	✓	114	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)

\(f(q)\)	\(=\)	\(q-2.39336 q^{2} +0.882221 q^{3} +3.72817 q^{4} +0.123030 q^{5} -2.11147 q^{6} -1.77301 q^{7} -4.13613 q^{8} -2.22169 q^{9} +O(q^{10})\)	\(q-2.39336 q^{2} +0.882221 q^{3} +3.72817 q^{4} +0.123030 q^{5} -2.11147 q^{6} -1.77301 q^{7} -4.13613 q^{8} -2.22169 q^{9} -0.294456 q^{10} +1.33826 q^{11} +3.28907 q^{12} +1.60065 q^{13} +4.24346 q^{14} +0.108540 q^{15} +2.44290 q^{16} +1.00000 q^{17} +5.31729 q^{18} +5.76795 q^{19} +0.458678 q^{20} -1.56419 q^{21} -3.20294 q^{22} +3.19803 q^{23} -3.64898 q^{24} -4.98486 q^{25} -3.83093 q^{26} -4.60668 q^{27} -6.61009 q^{28} -1.74173 q^{29} -0.259775 q^{30} +1.64454 q^{31} +2.42552 q^{32} +1.18064 q^{33} -2.39336 q^{34} -0.218135 q^{35} -8.28282 q^{36} +5.32254 q^{37} -13.8048 q^{38} +1.41213 q^{39} -0.508869 q^{40} -6.97762 q^{41} +3.74367 q^{42} -5.34754 q^{43} +4.98926 q^{44} -0.273335 q^{45} -7.65404 q^{46} -9.93182 q^{47} +2.15518 q^{48} -3.85642 q^{49} +11.9306 q^{50} +0.882221 q^{51} +5.96750 q^{52} -12.9838 q^{53} +11.0254 q^{54} +0.164647 q^{55} +7.33341 q^{56} +5.08861 q^{57} +4.16859 q^{58} +4.56078 q^{59} +0.404655 q^{60} +2.77929 q^{61} -3.93598 q^{62} +3.93908 q^{63} -10.6909 q^{64} +0.196929 q^{65} -2.82570 q^{66} +13.4500 q^{67} +3.72817 q^{68} +2.82137 q^{69} +0.522074 q^{70} +8.33793 q^{71} +9.18917 q^{72} -3.50164 q^{73} -12.7387 q^{74} -4.39775 q^{75} +21.5039 q^{76} -2.37275 q^{77} -3.37973 q^{78} -15.4312 q^{79} +0.300551 q^{80} +2.60095 q^{81} +16.7000 q^{82} +8.57409 q^{83} -5.83156 q^{84} +0.123030 q^{85} +12.7986 q^{86} -1.53659 q^{87} -5.53521 q^{88} -2.14066 q^{89} +0.654188 q^{90} -2.83798 q^{91} +11.9228 q^{92} +1.45085 q^{93} +23.7704 q^{94} +0.709633 q^{95} +2.13984 q^{96} +9.16315 q^{97} +9.22980 q^{98} -2.97319 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9}+O(q^{10}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9	\( 114 q - 8 q^{2} - 23 q^{3} + 110 q^{4} - 27 q^{5} - 23 q^{6} - 53 q^{7} - 21 q^{8} + 107 q^{9} - 19 q^{10} - 52 q^{11} - 49 q^{12} - 12 q^{13} - 40 q^{14} - 39 q^{15} + 110 q^{16} + 114 q^{17} - 21 q^{18} - 30 q^{19} - 88 q^{20} - 30 q^{21} - 36 q^{22} - 77 q^{23} - 72 q^{24} + 119 q^{25} - 79 q^{26} - 77 q^{27} - 92 q^{28} - 65 q^{29} - 10 q^{30} - 131 q^{31} - 30 q^{32} - 12 q^{33} - 8 q^{34} - 33 q^{35} + 109 q^{36} - 54 q^{37} - 14 q^{38} - 83 q^{39} - 42 q^{40} - 99 q^{41} + 29 q^{42} + 4 q^{43} - 98 q^{44} - 73 q^{45} - 35 q^{46} - 113 q^{47} - 86 q^{48} + 101 q^{49} - 44 q^{50} - 23 q^{51} - 3 q^{52} - 18 q^{53} - 78 q^{54} - 63 q^{55} - 117 q^{56} - 64 q^{57} - 31 q^{58} - 134 q^{59} - 6 q^{60} - 30 q^{61} - 30 q^{62} - 154 q^{63} + 117 q^{64} - 66 q^{65} - 12 q^{66} - 34 q^{67} + 110 q^{68} - 35 q^{69} + 18 q^{70} - 233 q^{71} + 16 q^{72} - 56 q^{73} - 64 q^{74} - 100 q^{75} - 64 q^{76} - 6 q^{77} + 50 q^{78} - 154 q^{79} - 128 q^{80} + 118 q^{81} + 2 q^{82} - 53 q^{83} - 6 q^{84} - 27 q^{85} - 52 q^{86} - 22 q^{87} - 52 q^{88} - 118 q^{89} - 5 q^{90} - 95 q^{91} - 102 q^{92} + 47 q^{93} - 3 q^{94} - 158 q^{95} - 144 q^{96} - 57 q^{97} + 3 q^{98} - 131 q^{99}+O(q^{100}) \) 114 * q - 8 * q^2 - 23 * q^3 + 110 * q^4 - 27 * q^5 - 23 * q^6 - 53 * q^7 - 21 * q^8 + 107 * q^9 - 19 * q^10 - 52 * q^11 - 49 * q^12 - 12 * q^13 - 40 * q^14 - 39 * q^15 + 110 * q^16 + 114 * q^17 - 21 * q^18 - 30 * q^19 - 88 * q^20 - 30 * q^21 - 36 * q^22 - 77 * q^23 - 72 * q^24 + 119 * q^25 - 79 * q^26 - 77 * q^27 - 92 * q^28 - 65 * q^29 - 10 * q^30 - 131 * q^31 - 30 * q^32 - 12 * q^33 - 8 * q^34 - 33 * q^35 + 109 * q^36 - 54 * q^37 - 14 * q^38 - 83 * q^39 - 42 * q^40 - 99 * q^41 + 29 * q^42 + 4 * q^43 - 98 * q^44 - 73 * q^45 - 35 * q^46 - 113 * q^47 - 86 * q^48 + 101 * q^49 - 44 * q^50 - 23 * q^51 - 3 * q^52 - 18 * q^53 - 78 * q^54 - 63 * q^55 - 117 * q^56 - 64 * q^57 - 31 * q^58 - 134 * q^59 - 6 * q^60 - 30 * q^61 - 30 * q^62 - 154 * q^63 + 117 * q^64 - 66 * q^65 - 12 * q^66 - 34 * q^67 + 110 * q^68 - 35 * q^69 + 18 * q^70 - 233 * q^71 + 16 * q^72 - 56 * q^73 - 64 * q^74 - 100 * q^75 - 64 * q^76 - 6 * q^77 + 50 * q^78 - 154 * q^79 - 128 * q^80 + 118 * q^81 + 2 * q^82 - 53 * q^83 - 6 * q^84 - 27 * q^85 - 52 * q^86 - 22 * q^87 - 52 * q^88 - 118 * q^89 - 5 * q^90 - 95 * q^91 - 102 * q^92 + 47 * q^93 - 3 * q^94 - 158 * q^95 - 144 * q^96 - 57 * q^97 + 3 * q^98 - 131 * q^99

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