LMFDB - Embedded newform 6034.2.a.o.1.13

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6034,2,Mod(1,6034)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6034, 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("6034.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6034 = 2 \cdot 7 \cdot 431 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6034.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:	$48.1817325796$
Analytic rank:	$1$
Dimension:	$25$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.13
Character	$\chi$	$=$	6034.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.00000 q^{2} -0.286451 q^{3} +1.00000 q^{4} +3.05880 q^{5} +0.286451 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.91795 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.286451 q^{3} +1.00000 q^{4} +3.05880 q^{5} +0.286451 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.91795 q^{9} -3.05880 q^{10} -1.07589 q^{11} -0.286451 q^{12} +0.416492 q^{13} +1.00000 q^{14} -0.876199 q^{15} +1.00000 q^{16} +3.47026 q^{17} +2.91795 q^{18} -8.09796 q^{19} +3.05880 q^{20} +0.286451 q^{21} +1.07589 q^{22} +1.29844 q^{23} +0.286451 q^{24} +4.35628 q^{25} -0.416492 q^{26} +1.69520 q^{27} -1.00000 q^{28} +3.37542 q^{29} +0.876199 q^{30} +0.387252 q^{31} -1.00000 q^{32} +0.308190 q^{33} -3.47026 q^{34} -3.05880 q^{35} -2.91795 q^{36} -10.4404 q^{37} +8.09796 q^{38} -0.119305 q^{39} -3.05880 q^{40} +9.90838 q^{41} -0.286451 q^{42} -1.60411 q^{43} -1.07589 q^{44} -8.92542 q^{45} -1.29844 q^{46} +0.853391 q^{47} -0.286451 q^{48} +1.00000 q^{49} -4.35628 q^{50} -0.994060 q^{51} +0.416492 q^{52} +13.2340 q^{53} -1.69520 q^{54} -3.29093 q^{55} +1.00000 q^{56} +2.31967 q^{57} -3.37542 q^{58} -3.69246 q^{59} -0.876199 q^{60} +2.58602 q^{61} -0.387252 q^{62} +2.91795 q^{63} +1.00000 q^{64} +1.27397 q^{65} -0.308190 q^{66} -7.58109 q^{67} +3.47026 q^{68} -0.371940 q^{69} +3.05880 q^{70} +10.5968 q^{71} +2.91795 q^{72} -1.99205 q^{73} +10.4404 q^{74} -1.24786 q^{75} -8.09796 q^{76} +1.07589 q^{77} +0.119305 q^{78} -13.5915 q^{79} +3.05880 q^{80} +8.26824 q^{81} -9.90838 q^{82} -5.26114 q^{83} +0.286451 q^{84} +10.6148 q^{85} +1.60411 q^{86} -0.966893 q^{87} +1.07589 q^{88} -9.10243 q^{89} +8.92542 q^{90} -0.416492 q^{91} +1.29844 q^{92} -0.110929 q^{93} -0.853391 q^{94} -24.7701 q^{95} +0.286451 q^{96} -6.49101 q^{97} -1.00000 q^{98} +3.13939 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) $ 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * 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 $

$2$	−1.00000	−0.707107
$2$	−1.00000	−0.707107
$3$	−0.286451	−0.165383	−0.0826914	−	0.996575i	$-0.526352\pi$
$3$	−0.286451	−0.165383	−0.0826914	+	0.996575i	$0.526352\pi$
$4$	1.00000	0.500000
$5$	3.05880	1.36794	0.683969	−	0.729511i	$-0.260252\pi$
$5$	3.05880	1.36794	0.683969	+	0.729511i	$0.260252\pi$
$6$	0.286451	0.116943
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.91795	−0.972649
$10$	−3.05880	−0.967278
$11$	−1.07589	−0.324393	−0.162196	−	0.986758i	$-0.551858\pi$
$11$	−1.07589	−0.324393	−0.162196	+	0.986758i	$0.551858\pi$
$12$	−0.286451	−0.0826914
$13$	0.416492	0.115514	0.0577570	−	0.998331i	$-0.481605\pi$
$13$	0.416492	0.115514	0.0577570	+	0.998331i	$0.481605\pi$
$14$	1.00000	0.267261
$15$	−0.876199	−0.226234
$16$	1.00000	0.250000
$17$	3.47026	0.841661	0.420830	−	0.907139i	$-0.361739\pi$
$17$	3.47026	0.841661	0.420830	+	0.907139i	$0.361739\pi$
$18$	2.91795	0.687766
$19$	−8.09796	−1.85780	−0.928900	−	0.370330i	$-0.879245\pi$
$19$	−8.09796	−1.85780	−0.928900	+	0.370330i	$0.879245\pi$
$20$	3.05880	0.683969
$21$	0.286451	0.0625088
$22$	1.07589	0.229380
$23$	1.29844	0.270744	0.135372	−	0.990795i	$-0.456777\pi$
$23$	1.29844	0.270744	0.135372	+	0.990795i	$0.456777\pi$
$24$	0.286451	0.0584717
$25$	4.35628	0.871255
$26$	−0.416492	−0.0816807
$27$	1.69520	0.326242
$28$	−1.00000	−0.188982
$29$	3.37542	0.626799	0.313399	−	0.949621i	$-0.398532\pi$
$29$	3.37542	0.626799	0.313399	+	0.949621i	$0.398532\pi$
$30$	0.876199	0.159971
$31$	0.387252	0.0695525	0.0347762	−	0.999395i	$-0.488928\pi$
$31$	0.387252	0.0695525	0.0347762	+	0.999395i	$0.488928\pi$
$32$	−1.00000	−0.176777
$33$	0.308190	0.0536490
$34$	−3.47026	−0.595144
$35$	−3.05880	−0.517032
$36$	−2.91795	−0.486324
$37$	−10.4404	−1.71639	−0.858194	−	0.513326i	$-0.828413\pi$
$37$	−10.4404	−1.71639	−0.858194	+	0.513326i	$0.828413\pi$
$38$	8.09796	1.31366
$39$	−0.119305	−0.0191040
$40$	−3.05880	−0.483639
$41$	9.90838	1.54743	0.773715	−	0.633534i	$-0.218396\pi$
$41$	9.90838	1.54743	0.773715	+	0.633534i	$0.218396\pi$
$42$	−0.286451	−0.0442004
$43$	−1.60411	−0.244625	−0.122313	−	0.992492i	$-0.539031\pi$
$43$	−1.60411	−0.244625	−0.122313	+	0.992492i	$0.539031\pi$
$44$	−1.07589	−0.162196
$45$	−8.92542	−1.33052
$46$	−1.29844	−0.191445
$47$	0.853391	0.124480	0.0622400	−	0.998061i	$-0.480176\pi$
$47$	0.853391	0.124480	0.0622400	+	0.998061i	$0.480176\pi$
$48$	−0.286451	−0.0413457
$49$	1.00000	0.142857
$50$	−4.35628	−0.616071
$51$	−0.994060	−0.139196
$52$	0.416492	0.0577570
$53$	13.2340	1.81783	0.908917	−	0.416977i	$-0.136910\pi$
$53$	13.2340	1.81783	0.908917	+	0.416977i	$0.136910\pi$
$54$	−1.69520	−0.230688
$55$	−3.29093	−0.443750
$56$	1.00000	0.133631
$57$	2.31967	0.307248
$58$	−3.37542	−0.443214
$59$	−3.69246	−0.480717	−0.240358	−	0.970684i	$-0.577265\pi$
$59$	−3.69246	−0.480717	−0.240358	+	0.970684i	$0.577265\pi$
$60$	−0.876199	−0.113117
$61$	2.58602	0.331105	0.165553	−	0.986201i	$-0.447059\pi$
$61$	2.58602	0.331105	0.165553	+	0.986201i	$0.447059\pi$
$62$	−0.387252	−0.0491810
$63$	2.91795	0.367627
$64$	1.00000	0.125000
$65$	1.27397	0.158016
$66$	−0.308190	−0.0379356
$67$	−7.58109	−0.926177	−0.463089	−	0.886312i	$-0.653259\pi$
$67$	−7.58109	−0.926177	−0.463089	+	0.886312i	$0.653259\pi$
$68$	3.47026	0.420830
$69$	−0.371940	−0.0447763
$70$	3.05880	0.365597
$71$	10.5968	1.25760	0.628802	−	0.777565i	$-0.283546\pi$
$71$	10.5968	1.25760	0.628802	+	0.777565i	$0.283546\pi$
$72$	2.91795	0.343883
$73$	−1.99205	−0.233152	−0.116576	−	0.993182i	$-0.537192\pi$
$73$	−1.99205	−0.233152	−0.116576	+	0.993182i	$0.537192\pi$
$74$	10.4404	1.21367
$75$	−1.24786	−0.144091
$76$	−8.09796	−0.928900
$77$	1.07589	0.122609
$78$	0.119305	0.0135086
$79$	−13.5915	−1.52916	−0.764579	−	0.644530i	$-0.777053\pi$
$79$	−13.5915	−1.52916	−0.764579	+	0.644530i	$0.777053\pi$
$80$	3.05880	0.341985
$81$	8.26824	0.918694
$82$	−9.90838	−1.09420
$83$	−5.26114	−0.577486	−0.288743	−	0.957407i	$-0.593237\pi$
$83$	−5.26114	−0.577486	−0.288743	+	0.957407i	$0.593237\pi$
$84$	0.286451	0.0312544
$85$	10.6148	1.15134
$86$	1.60411	0.172976
$87$	−0.966893	−0.103662
$88$	1.07589	0.114690
$89$	−9.10243	−0.964855	−0.482428	−	0.875936i	$-0.660245\pi$
$89$	−9.10243	−0.964855	−0.482428	+	0.875936i	$0.660245\pi$
$90$	8.92542	0.940822
$91$	−0.416492	−0.0436602
$92$	1.29844	0.135372
$93$	−0.110929	−0.0115028
$94$	−0.853391	−0.0880206
$95$	−24.7701	−2.54136
$96$	0.286451	0.0292358
$97$	−6.49101	−0.659062	−0.329531	−	0.944145i	$-0.606891\pi$
$97$	−6.49101	−0.659062	−0.329531	+	0.944145i	$0.606891\pi$
$98$	−1.00000	−0.101015
$99$	3.13939	0.315520
$100$	4.35628	0.435628
$101$	−4.76321	−0.473958	−0.236979	−	0.971515i	$-0.576157\pi$
$101$	−4.76321	−0.473958	−0.236979	+	0.971515i	$0.576157\pi$
$102$	0.994060	0.0984266
$103$	4.98646	0.491331	0.245665	−	0.969355i	$-0.420994\pi$
$103$	4.98646	0.491331	0.245665	+	0.969355i	$0.420994\pi$
$104$	−0.416492	−0.0408404
$105$	0.876199	0.0855082
$106$	−13.2340	−1.28540
$107$	−5.52059	−0.533696	−0.266848	−	0.963739i	$-0.585982\pi$
$107$	−5.52059	−0.533696	−0.266848	+	0.963739i	$0.585982\pi$
$108$	1.69520	0.163121
$109$	7.88728	0.755464	0.377732	−	0.925915i	$-0.376704\pi$
$109$	7.88728	0.755464	0.377732	+	0.925915i	$0.376704\pi$
$110$	3.29093	0.313778
$111$	2.99066	0.283861
$112$	−1.00000	−0.0944911
$113$	−14.2035	−1.33615	−0.668076	−	0.744093i	$-0.732882\pi$
$113$	−14.2035	−1.33615	−0.668076	+	0.744093i	$0.732882\pi$
$114$	−2.31967	−0.217257
$115$	3.97167	0.370361
$116$	3.37542	0.313399
$117$	−1.21530	−0.112355
$118$	3.69246	0.339918
$119$	−3.47026	−0.318118
$120$	0.876199	0.0799856
$121$	−9.84246	−0.894769
$122$	−2.58602	−0.234127
$123$	−2.83827	−0.255918
$124$	0.387252	0.0347762
$125$	−1.96902	−0.176115
$126$	−2.91795	−0.259951
$127$	−21.4168	−1.90043	−0.950216	−	0.311592i	$-0.899138\pi$
$127$	−21.4168	−1.90043	−0.950216	+	0.311592i	$0.899138\pi$
$128$	−1.00000	−0.0883883
$129$	0.459501	0.0404568
$130$	−1.27397	−0.111734
$131$	−2.80376	−0.244966	−0.122483	−	0.992471i	$-0.539086\pi$
$131$	−2.80376	−0.244966	−0.122483	+	0.992471i	$0.539086\pi$
$132$	0.308190	0.0268245
$133$	8.09796	0.702183
$134$	7.58109	0.654906
$135$	5.18530	0.446279
$136$	−3.47026	−0.297572
$137$	−7.91913	−0.676577	−0.338289	−	0.941042i	$-0.609848\pi$
$137$	−7.91913	−0.676577	−0.338289	+	0.941042i	$0.609848\pi$
$138$	0.371940	0.0316617
$139$	−2.30618	−0.195608	−0.0978038	−	0.995206i	$-0.531182\pi$
$139$	−2.30618	−0.195608	−0.0978038	+	0.995206i	$0.531182\pi$
$140$	−3.05880	−0.258516
$141$	−0.244455	−0.0205868
$142$	−10.5968	−0.889260
$143$	−0.448099	−0.0374719
$144$	−2.91795	−0.243162
$145$	10.3247	0.857422
$146$	1.99205	0.164864
$147$	−0.286451	−0.0236261
$148$	−10.4404	−0.858194
$149$	−9.67711	−0.792780	−0.396390	−	0.918082i	$-0.629737\pi$
$149$	−9.67711	−0.792780	−0.396390	+	0.918082i	$0.629737\pi$
$150$	1.24786	0.101887
$151$	−15.3631	−1.25023	−0.625114	−	0.780533i	$-0.714948\pi$
$151$	−15.3631	−1.25023	−0.625114	+	0.780533i	$0.714948\pi$
$152$	8.09796	0.656832
$153$	−10.1260	−0.818640
$154$	−1.07589	−0.0866977
$155$	1.18453	0.0951435
$156$	−0.119305	−0.00955202
$157$	−23.1186	−1.84507	−0.922534	−	0.385916i	$-0.873885\pi$
$157$	−23.1186	−1.84507	−0.922534	+	0.385916i	$0.873885\pi$
$158$	13.5915	1.08128
$159$	−3.79091	−0.300639
$160$	−3.05880	−0.241820
$161$	−1.29844	−0.102331
$162$	−8.26824	−0.649615
$163$	−4.99733	−0.391421	−0.195711	−	0.980662i	$-0.562701\pi$
$163$	−4.99733	−0.391421	−0.195711	+	0.980662i	$0.562701\pi$
$164$	9.90838	0.773715
$165$	0.942693	0.0733886
$166$	5.26114	0.408344
$167$	3.75457	0.290538	0.145269	−	0.989392i	$-0.453595\pi$
$167$	3.75457	0.290538	0.145269	+	0.989392i	$0.453595\pi$
$168$	−0.286451	−0.0221002
$169$	−12.8265	−0.986657
$170$	−10.6148	−0.814120
$171$	23.6294	1.80699
$172$	−1.60411	−0.122313
$173$	3.90866	0.297170	0.148585	−	0.988900i	$-0.452528\pi$
$173$	3.90866	0.297170	0.148585	+	0.988900i	$0.452528\pi$
$174$	0.966893	0.0732999
$175$	−4.35628	−0.329304
$176$	−1.07589	−0.0810982
$177$	1.05771	0.0795023
$178$	9.10243	0.682256
$179$	−2.77765	−0.207611	−0.103806	−	0.994598i	$-0.533102\pi$
$179$	−2.77765	−0.207611	−0.103806	+	0.994598i	$0.533102\pi$
$180$	−8.92542	−0.665262
$181$	13.1330	0.976171	0.488085	−	0.872796i	$-0.337695\pi$
$181$	13.1330	0.976171	0.488085	+	0.872796i	$0.337695\pi$
$182$	0.416492	0.0308724
$183$	−0.740768	−0.0547591
$184$	−1.29844	−0.0957223
$185$	−31.9351	−2.34791
$186$	0.110929	0.00813370
$187$	−3.73361	−0.273029
$188$	0.853391	0.0622400
$189$	−1.69520	−0.123308
$190$	24.7701	1.79701
$191$	2.51499	0.181978	0.0909890	−	0.995852i	$-0.470997\pi$
$191$	2.51499	0.181978	0.0909890	+	0.995852i	$0.470997\pi$
$192$	−0.286451	−0.0206729
$193$	12.1068	0.871470	0.435735	−	0.900075i	$-0.356489\pi$
$193$	12.1068	0.871470	0.435735	+	0.900075i	$0.356489\pi$
$194$	6.49101	0.466027
$195$	−0.364929	−0.0261331
$196$	1.00000	0.0714286
$197$	14.4249	1.02773	0.513865	−	0.857871i	$-0.328213\pi$
$197$	14.4249	1.02773	0.513865	+	0.857871i	$0.328213\pi$
$198$	−3.13939	−0.223107
$199$	4.95485	0.351240	0.175620	−	0.984458i	$-0.443807\pi$
$199$	4.95485	0.351240	0.175620	+	0.984458i	$0.443807\pi$
$200$	−4.35628	−0.308035
$201$	2.17161	0.153174
$202$	4.76321	0.335139
$203$	−3.37542	−0.236908
$204$	−0.994060	−0.0695981
$205$	30.3078	2.11679
$206$	−4.98646	−0.347423
$207$	−3.78878	−0.263338
$208$	0.416492	0.0288785
$209$	8.71252	0.602657
$210$	−0.876199	−0.0604635
$211$	0.345353	0.0237751	0.0118875	−	0.999929i	$-0.496216\pi$
$211$	0.345353	0.0237751	0.0118875	+	0.999929i	$0.496216\pi$
$212$	13.2340	0.908917
$213$	−3.03546	−0.207986
$214$	5.52059	0.377380
$215$	−4.90667	−0.334632
$216$	−1.69520	−0.115344
$217$	−0.387252	−0.0262884
$218$	−7.88728	−0.534194
$219$	0.570627	0.0385594
$220$	−3.29093	−0.221875
$221$	1.44533	0.0972236
$222$	−2.99066	−0.200720
$223$	5.00342	0.335054	0.167527	−	0.985868i	$-0.446422\pi$
$223$	5.00342	0.335054	0.167527	+	0.985868i	$0.446422\pi$
$224$	1.00000	0.0668153
$225$	−12.7114	−0.847425
$226$	14.2035	0.944802
$227$	−7.44151	−0.493910	−0.246955	−	0.969027i	$-0.579430\pi$
$227$	−7.44151	−0.493910	−0.246955	+	0.969027i	$0.579430\pi$
$228$	2.31967	0.153624
$229$	−12.3159	−0.813859	−0.406929	−	0.913460i	$-0.633400\pi$
$229$	−12.3159	−0.813859	−0.406929	+	0.913460i	$0.633400\pi$
$230$	−3.97167	−0.261884
$231$	−0.308190	−0.0202774
$232$	−3.37542	−0.221607
$233$	−2.04594	−0.134034	−0.0670170	−	0.997752i	$-0.521348\pi$
$233$	−2.04594	−0.134034	−0.0670170	+	0.997752i	$0.521348\pi$
$234$	1.21530	0.0794466
$235$	2.61036	0.170281
$236$	−3.69246	−0.240358
$237$	3.89329	0.252896
$238$	3.47026	0.224943
$239$	−23.9796	−1.55111	−0.775555	−	0.631280i	$-0.782530\pi$
$239$	−23.9796	−1.55111	−0.775555	+	0.631280i	$0.782530\pi$
$240$	−0.876199	−0.0565584
$241$	8.15301	0.525181	0.262591	−	0.964907i	$-0.415423\pi$
$241$	8.15301	0.525181	0.262591	+	0.964907i	$0.415423\pi$
$242$	9.84246	0.632697
$243$	−7.45406	−0.478178
$244$	2.58602	0.165553
$245$	3.05880	0.195420
$246$	2.83827	0.180962
$247$	−3.37273	−0.214602
$248$	−0.387252	−0.0245905
$249$	1.50706	0.0955062
$250$	1.96902	0.124532
$251$	−28.9868	−1.82963	−0.914816	−	0.403871i	$-0.867665\pi$
$251$	−28.9868	−1.82963	−0.914816	+	0.403871i	$0.867665\pi$
$252$	2.91795	0.183813
$253$	−1.39698	−0.0878273
$254$	21.4168	1.34381
$255$	−3.04063	−0.190412
$256$	1.00000	0.0625000
$257$	21.1043	1.31645	0.658225	−	0.752821i	$-0.271308\pi$
$257$	21.1043	1.31645	0.658225	+	0.752821i	$0.271308\pi$
$258$	−0.459501	−0.0286073
$259$	10.4404	0.648733
$260$	1.27397	0.0790080
$261$	−9.84928	−0.609655
$262$	2.80376	0.173217
$263$	19.2074	1.18438	0.592189	−	0.805799i	$-0.298264\pi$
$263$	19.2074	1.18438	0.592189	+	0.805799i	$0.298264\pi$
$264$	−0.308190	−0.0189678
$265$	40.4803	2.48669
$266$	−8.09796	−0.496518
$267$	2.60740	0.159570
$268$	−7.58109	−0.463089
$269$	15.0382	0.916895	0.458448	−	0.888721i	$-0.348406\pi$
$269$	15.0382	0.916895	0.458448	+	0.888721i	$0.348406\pi$
$270$	−5.18530	−0.315567
$271$	5.69918	0.346200	0.173100	−	0.984904i	$-0.444622\pi$
$271$	5.69918	0.346200	0.173100	+	0.984904i	$0.444622\pi$
$272$	3.47026	0.210415
$273$	0.119305	0.00722065
$274$	7.91913	0.478412
$275$	−4.68687	−0.282629
$276$	−0.371940	−0.0223882
$277$	−28.6892	−1.72377	−0.861885	−	0.507104i	$-0.830716\pi$
$277$	−28.6892	−1.72377	−0.861885	+	0.507104i	$0.830716\pi$
$278$	2.30618	0.138315
$279$	−1.12998	−0.0676501
$280$	3.05880	0.182798
$281$	−1.30453	−0.0778219	−0.0389109	−	0.999243i	$-0.512389\pi$
$281$	−1.30453	−0.0778219	−0.0389109	+	0.999243i	$0.512389\pi$
$282$	0.244455	0.0145571
$283$	24.0796	1.43138	0.715691	−	0.698417i	$-0.246112\pi$
$283$	24.0796	1.43138	0.715691	+	0.698417i	$0.246112\pi$
$284$	10.5968	0.628802
$285$	7.09543	0.420297
$286$	0.448099	0.0264967
$287$	−9.90838	−0.584873
$288$	2.91795	0.171942
$289$	−4.95733	−0.291608
$290$	−10.3247	−0.606289
$291$	1.85936	0.108998
$292$	−1.99205	−0.116576
$293$	−3.77811	−0.220719	−0.110360	−	0.993892i	$-0.535200\pi$
$293$	−3.77811	−0.220719	−0.110360	+	0.993892i	$0.535200\pi$
$294$	0.286451	0.0167062
$295$	−11.2945	−0.657591
$296$	10.4404	0.606834
$297$	−1.82385	−0.105831
$298$	9.67711	0.560580
$299$	0.540790	0.0312747
$300$	−1.24786	−0.0720453
$301$	1.60411	0.0924596
$302$	15.3631	0.884045
$303$	1.36443	0.0783844
$304$	−8.09796	−0.464450
$305$	7.91011	0.452932
$306$	10.1260	0.578866
$307$	−14.8451	−0.847255	−0.423628	−	0.905836i	$-0.639244\pi$
$307$	−14.8451	−0.847255	−0.423628	+	0.905836i	$0.639244\pi$
$308$	1.07589	0.0613045
$309$	−1.42838	−0.0812576
$310$	−1.18453	−0.0672766
$311$	−17.5369	−0.994425	−0.497212	−	0.867629i	$-0.665643\pi$
$311$	−17.5369	−0.994425	−0.497212	+	0.867629i	$0.665643\pi$
$312$	0.119305	0.00675430
$313$	−33.3496	−1.88503	−0.942516	−	0.334161i	$-0.891547\pi$
$313$	−33.3496	−1.88503	−0.942516	+	0.334161i	$0.891547\pi$
$314$	23.1186	1.30466
$315$	8.92542	0.502890
$316$	−13.5915	−0.764579
$317$	13.6333	0.765720	0.382860	−	0.923806i	$-0.374939\pi$
$317$	13.6333	0.765720	0.382860	+	0.923806i	$0.374939\pi$
$318$	3.79091	0.212584
$319$	−3.63157	−0.203329
$320$	3.05880	0.170992
$321$	1.58138	0.0882641
$322$	1.29844	0.0723593
$323$	−28.1020	−1.56364
$324$	8.26824	0.459347
$325$	1.81435	0.100642
$326$	4.99733	0.276777
$327$	−2.25932	−0.124941
$328$	−9.90838	−0.547099
$329$	−0.853391	−0.0470490
$330$	−0.942693	−0.0518935
$331$	22.3646	1.22927	0.614636	−	0.788811i	$-0.289303\pi$
$331$	22.3646	1.22927	0.614636	+	0.788811i	$0.289303\pi$
$332$	−5.26114	−0.288743
$333$	30.4644	1.66944
$334$	−3.75457	−0.205441
$335$	−23.1891	−1.26695
$336$	0.286451	0.0156272
$337$	−19.8409	−1.08080	−0.540402	−	0.841407i	$-0.681728\pi$
$337$	−19.8409	−1.08080	−0.540402	+	0.841407i	$0.681728\pi$
$338$	12.8265	0.697672
$339$	4.06861	0.220977
$340$	10.6148	0.575670
$341$	−0.416640	−0.0225623
$342$	−23.6294	−1.27773
$343$	−1.00000	−0.0539949
$344$	1.60411	0.0864881
$345$	−1.13769	−0.0612513
$346$	−3.90866	−0.210131
$347$	11.5510	0.620090	0.310045	−	0.950722i	$-0.399656\pi$
$347$	11.5510	0.620090	0.310045	+	0.950722i	$0.399656\pi$
$348$	−0.966893	−0.0518309
$349$	27.6792	1.48163	0.740817	−	0.671707i	$-0.234438\pi$
$349$	27.6792	1.48163	0.740817	+	0.671707i	$0.234438\pi$
$350$	4.35628	0.232853
$351$	0.706038	0.0376855
$352$	1.07589	0.0573451
$353$	−19.6168	−1.04409	−0.522047	−	0.852917i	$-0.674832\pi$
$353$	−19.6168	−1.04409	−0.522047	+	0.852917i	$0.674832\pi$
$354$	−1.05771	−0.0562166
$355$	32.4134	1.72033
$356$	−9.10243	−0.482428
$357$	0.994060	0.0526112
$358$	2.77765	0.146803
$359$	12.9115	0.681442	0.340721	−	0.940165i	$-0.389329\pi$
$359$	12.9115	0.681442	0.340721	+	0.940165i	$0.389329\pi$
$360$	8.92542	0.470411
$361$	46.5770	2.45142
$362$	−13.1330	−0.690257
$363$	2.81939	0.147979
$364$	−0.416492	−0.0218301
$365$	−6.09330	−0.318938
$366$	0.740768	0.0387206
$367$	−23.5445	−1.22901	−0.614506	−	0.788912i	$-0.710645\pi$
$367$	−23.5445	−1.22901	−0.614506	+	0.788912i	$0.710645\pi$
$368$	1.29844	0.0676859
$369$	−28.9121	−1.50511
$370$	31.9351	1.66022
$371$	−13.2340	−0.687077
$372$	−0.110929	−0.00575139
$373$	20.0320	1.03722	0.518608	−	0.855012i	$-0.326450\pi$
$373$	20.0320	1.03722	0.518608	+	0.855012i	$0.326450\pi$
$374$	3.73361	0.193060
$375$	0.564030	0.0291264
$376$	−0.853391	−0.0440103
$377$	1.40583	0.0724040
$378$	1.69520	0.0871919
$379$	−15.7223	−0.807603	−0.403801	−	0.914847i	$-0.632311\pi$
$379$	−15.7223	−0.807603	−0.403801	+	0.914847i	$0.632311\pi$
$380$	−24.7701	−1.27068
$381$	6.13487	0.314299
$382$	−2.51499	−0.128678
$383$	−16.2889	−0.832325	−0.416163	−	0.909290i	$-0.636625\pi$
$383$	−16.2889	−0.832325	−0.416163	+	0.909290i	$0.636625\pi$
$384$	0.286451	0.0146179
$385$	3.29093	0.167722
$386$	−12.1068	−0.616222
$387$	4.68072	0.237934
$388$	−6.49101	−0.329531
$389$	−0.887499	−0.0449980	−0.0224990	−	0.999747i	$-0.507162\pi$
$389$	−0.887499	−0.0449980	−0.0224990	+	0.999747i	$0.507162\pi$
$390$	0.364929	0.0184789
$391$	4.50592	0.227874
$392$	−1.00000	−0.0505076
$393$	0.803142	0.0405131
$394$	−14.4249	−0.726714
$395$	−41.5736	−2.09179
$396$	3.13939	0.157760
$397$	28.2413	1.41739	0.708694	−	0.705516i	$-0.249285\pi$
$397$	28.2413	1.41739	0.708694	+	0.705516i	$0.249285\pi$
$398$	−4.95485	−0.248364
$399$	−2.31967	−0.116129
$400$	4.35628	0.217814
$401$	−29.0416	−1.45027	−0.725134	−	0.688608i	$-0.758222\pi$
$401$	−29.0416	−1.45027	−0.725134	+	0.688608i	$0.758222\pi$
$402$	−2.17161	−0.108310
$403$	0.161287	0.00803428
$404$	−4.76321	−0.236979
$405$	25.2909	1.25672
$406$	3.37542	0.167519
$407$	11.2327	0.556784
$408$	0.994060	0.0492133
$409$	0.814422	0.0402706	0.0201353	−	0.999797i	$-0.493590\pi$
$409$	0.814422	0.0402706	0.0201353	+	0.999797i	$0.493590\pi$
$410$	−30.3078	−1.49680
$411$	2.26845	0.111894
$412$	4.98646	0.245665
$413$	3.69246	0.181694
$414$	3.78878	0.186208
$415$	−16.0928	−0.789965
$416$	−0.416492	−0.0204202
$417$	0.660609	0.0323501
$418$	−8.71252	−0.426143
$419$	40.2300	1.96536	0.982682	−	0.185299i	$-0.0593254\pi$
$419$	40.2300	1.96536	0.982682	+	0.185299i	$0.0593254\pi$
$420$	0.876199	0.0427541
$421$	−32.4405	−1.58105	−0.790527	−	0.612427i	$-0.790193\pi$
$421$	−32.4405	−1.58105	−0.790527	+	0.612427i	$0.790193\pi$
$422$	−0.345353	−0.0168115
$423$	−2.49015	−0.121075
$424$	−13.2340	−0.642701
$425$	15.1174	0.733301
$426$	3.03546	0.147068
$427$	−2.58602	−0.125146
$428$	−5.52059	−0.266848
$429$	0.128359	0.00619721
$430$	4.90667	0.236621
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	1.69520	0.0815606
$433$	25.6969	1.23491	0.617457	−	0.786605i	$-0.288163\pi$
$433$	25.6969	1.23491	0.617457	+	0.786605i	$0.288163\pi$
$434$	0.387252	0.0185887
$435$	−2.95753	−0.141803
$436$	7.88728	0.377732
$437$	−10.5147	−0.502988
$438$	−0.570627	−0.0272656
$439$	14.2842	0.681746	0.340873	−	0.940109i	$-0.389277\pi$
$439$	14.2842	0.681746	0.340873	+	0.940109i	$0.389277\pi$
$440$	3.29093	0.156889
$441$	−2.91795	−0.138950
$442$	−1.44533	−0.0687475
$443$	8.08876	0.384309	0.192154	−	0.981365i	$-0.438453\pi$
$443$	8.08876	0.384309	0.192154	+	0.981365i	$0.438453\pi$
$444$	2.99066	0.141930
$445$	−27.8425	−1.31986
$446$	−5.00342	−0.236919
$447$	2.77202	0.131112
$448$	−1.00000	−0.0472456
$449$	−32.9585	−1.55541	−0.777704	−	0.628631i	$-0.783616\pi$
$449$	−32.9585	−1.55541	−0.777704	+	0.628631i	$0.783616\pi$
$450$	12.7114	0.599220
$451$	−10.6603	−0.501975
$452$	−14.2035	−0.668076
$453$	4.40077	0.206766
$454$	7.44151	0.349247
$455$	−1.27397	−0.0597244
$456$	−2.31967	−0.108629
$457$	−19.3212	−0.903809	−0.451904	−	0.892066i	$-0.649255\pi$
$457$	−19.3212	−0.903809	−0.451904	+	0.892066i	$0.649255\pi$
$458$	12.3159	0.575485
$459$	5.88279	0.274585
$460$	3.97167	0.185180
$461$	14.7296	0.686027	0.343014	−	0.939330i	$-0.388552\pi$
$461$	14.7296	0.686027	0.343014	+	0.939330i	$0.388552\pi$
$462$	0.308190	0.0143383
$463$	−28.4223	−1.32089	−0.660447	−	0.750872i	$-0.729633\pi$
$463$	−28.4223	−1.32089	−0.660447	+	0.750872i	$0.729633\pi$
$464$	3.37542	0.156700
$465$	−0.339309	−0.0157351
$466$	2.04594	0.0947763
$467$	36.1698	1.67374	0.836870	−	0.547402i	$-0.184383\pi$
$467$	36.1698	1.67374	0.836870	+	0.547402i	$0.184383\pi$
$468$	−1.21530	−0.0561773
$469$	7.58109	0.350062
$470$	−2.61036	−0.120407
$471$	6.62237	0.305143
$472$	3.69246	0.169959
$473$	1.72585	0.0793547
$474$	−3.89329	−0.178825
$475$	−35.2770	−1.61862
$476$	−3.47026	−0.159059
$477$	−38.6162	−1.76811
$478$	23.9796	1.09680
$479$	23.2517	1.06240	0.531198	−	0.847248i	$-0.321742\pi$
$479$	23.2517	1.06240	0.531198	+	0.847248i	$0.321742\pi$
$480$	0.876199	0.0399928
$481$	−4.34833	−0.198267
$482$	−8.15301	−0.371359
$483$	0.371940	0.0169239
$484$	−9.84246	−0.447385
$485$	−19.8547	−0.901556
$486$	7.45406	0.338123
$487$	−11.5654	−0.524078	−0.262039	−	0.965057i	$-0.584395\pi$
$487$	−11.5654	−0.524078	−0.262039	+	0.965057i	$0.584395\pi$
$488$	−2.58602	−0.117063
$489$	1.43149	0.0647343
$490$	−3.05880	−0.138183
$491$	4.61509	0.208276	0.104138	−	0.994563i	$-0.466792\pi$
$491$	4.61509	0.208276	0.104138	+	0.994563i	$0.466792\pi$
$492$	−2.83827	−0.127959
$493$	11.7136	0.527552
$494$	3.37273	0.151747
$495$	9.60277	0.431612
$496$	0.387252	0.0173881
$497$	−10.5968	−0.475330
$498$	−1.50706	−0.0675331
$499$	−15.7245	−0.703924	−0.351962	−	0.936014i	$-0.614485\pi$
$499$	−15.7245	−0.703924	−0.351962	+	0.936014i	$0.614485\pi$
$500$	−1.96902	−0.0880574
$501$	−1.07550	−0.0480499
$502$	28.9868	1.29375
$503$	19.5914	0.873539	0.436770	−	0.899573i	$-0.356122\pi$
$503$	19.5914	0.873539	0.436770	+	0.899573i	$0.356122\pi$
$504$	−2.91795	−0.129976
$505$	−14.5697	−0.648345
$506$	1.39698	0.0621033
$507$	3.67418	0.163176
$508$	−21.4168	−0.950216
$509$	29.7079	1.31678	0.658389	−	0.752678i	$-0.271238\pi$
$509$	29.7079	1.31678	0.658389	+	0.752678i	$0.271238\pi$
$510$	3.04063	0.134641
$511$	1.99205	0.0881233
$512$	−1.00000	−0.0441942
$513$	−13.7277	−0.606093
$514$	−21.1043	−0.930870
$515$	15.2526	0.672110
$516$	0.459501	0.0202284
$517$	−0.918155	−0.0403804
$518$	−10.4404	−0.458724
$519$	−1.11964	−0.0491467
$520$	−1.27397	−0.0558671
$521$	6.18305	0.270884	0.135442	−	0.990785i	$-0.456755\pi$
$521$	6.18305	0.270884	0.135442	+	0.990785i	$0.456755\pi$
$522$	9.84928	0.431091
$523$	−2.69087	−0.117664	−0.0588319	−	0.998268i	$-0.518738\pi$
$523$	−2.69087	−0.117664	−0.0588319	+	0.998268i	$0.518738\pi$
$524$	−2.80376	−0.122483
$525$	1.24786	0.0544612
$526$	−19.2074	−0.837482
$527$	1.34386	0.0585396
$528$	0.308190	0.0134123
$529$	−21.3141	−0.926698
$530$	−40.4803	−1.75835
$531$	10.7744	0.467568
$532$	8.09796	0.351091
$533$	4.12676	0.178750
$534$	−2.60740	−0.112833
$535$	−16.8864	−0.730063
$536$	7.58109	0.327453
$537$	0.795661	0.0343353
$538$	−15.0382	−0.648343
$539$	−1.07589	−0.0463418
$540$	5.18530	0.223140
$541$	−37.8511	−1.62735	−0.813673	−	0.581323i	$-0.802535\pi$
$541$	−37.8511	−1.62735	−0.813673	+	0.581323i	$0.802535\pi$
$542$	−5.69918	−0.244801
$543$	−3.76198	−0.161442
$544$	−3.47026	−0.148786
$545$	24.1256	1.03343
$546$	−0.119305	−0.00510577
$547$	−25.7732	−1.10198	−0.550990	−	0.834512i	$-0.685750\pi$
$547$	−25.7732	−1.10198	−0.550990	+	0.834512i	$0.685750\pi$
$548$	−7.91913	−0.338289
$549$	−7.54585	−0.322049
$550$	4.68687	0.199849
$551$	−27.3340	−1.16447
$552$	0.371940	0.0158308
$553$	13.5915	0.577967
$554$	28.6892	1.21889
$555$	9.14784	0.388304
$556$	−2.30618	−0.0978038
$557$	34.3705	1.45632	0.728162	−	0.685405i	$-0.240375\pi$
$557$	34.3705	1.45632	0.728162	+	0.685405i	$0.240375\pi$
$558$	1.12998	0.0478358
$559$	−0.668100	−0.0282576
$560$	−3.05880	−0.129258
$561$	1.06950	0.0451543
$562$	1.30453	0.0550284
$563$	−42.8852	−1.80740	−0.903698	−	0.428171i	$-0.859158\pi$
$563$	−42.8852	−1.80740	−0.903698	+	0.428171i	$0.859158\pi$
$564$	−0.244455	−0.0102934
$565$	−43.4457	−1.82777
$566$	−24.0796	−1.01214
$567$	−8.26824	−0.347234
$568$	−10.5968	−0.444630
$569$	−19.6419	−0.823433	−0.411716	−	0.911312i	$-0.635071\pi$
$569$	−19.6419	−0.823433	−0.411716	+	0.911312i	$0.635071\pi$
$570$	−7.09543	−0.297195
$571$	36.2923	1.51878	0.759392	−	0.650634i	$-0.225497\pi$
$571$	36.2923	1.51878	0.759392	+	0.650634i	$0.225497\pi$
$572$	−0.448099	−0.0187360
$573$	−0.720421	−0.0300960
$574$	9.90838	0.413568
$575$	5.65637	0.235887
$576$	−2.91795	−0.121581
$577$	20.5266	0.854532	0.427266	−	0.904126i	$-0.359477\pi$
$577$	20.5266	0.854532	0.427266	+	0.904126i	$0.359477\pi$
$578$	4.95733	0.206198
$579$	−3.46802	−0.144126
$580$	10.3247	0.428711
$581$	5.26114	0.218269
$582$	−1.85936	−0.0770729
$583$	−14.2384	−0.589693
$584$	1.99205	0.0824318
$585$	−3.71736	−0.153694
$586$	3.77811	0.156072
$587$	−17.8656	−0.737394	−0.368697	−	0.929550i	$-0.620196\pi$
$587$	−17.8656	−0.737394	−0.368697	+	0.929550i	$0.620196\pi$
$588$	−0.286451	−0.0118131
$589$	−3.13595	−0.129215
$590$	11.2945	0.464987
$591$	−4.13202	−0.169969
$592$	−10.4404	−0.429097
$593$	28.0917	1.15359	0.576795	−	0.816889i	$-0.304303\pi$
$593$	28.0917	1.15359	0.576795	+	0.816889i	$0.304303\pi$
$594$	1.82385	0.0748336
$595$	−10.6148	−0.435166
$596$	−9.67711	−0.396390
$597$	−1.41933	−0.0580891
$598$	−0.540790	−0.0221145
$599$	−20.8665	−0.852581	−0.426291	−	0.904586i	$-0.640180\pi$
$599$	−20.8665	−0.852581	−0.426291	+	0.904586i	$0.640180\pi$
$600$	1.24786	0.0509437
$601$	−32.0496	−1.30733	−0.653665	−	0.756784i	$-0.726769\pi$
$601$	−32.0496	−1.30733	−0.653665	+	0.756784i	$0.726769\pi$
$602$	−1.60411	−0.0653788
$603$	22.1212	0.900845
$604$	−15.3631	−0.625114
$605$	−30.1062	−1.22399
$606$	−1.36443	−0.0554262
$607$	7.09938	0.288155	0.144077	−	0.989566i	$-0.453979\pi$
$607$	7.09938	0.288155	0.144077	+	0.989566i	$0.453979\pi$
$608$	8.09796	0.328416
$609$	0.966893	0.0391805
$610$	−7.91011	−0.320271
$611$	0.355430	0.0143792
$612$	−10.1260	−0.409320
$613$	−0.904461	−0.0365308	−0.0182654	−	0.999833i	$-0.505814\pi$
$613$	−0.904461	−0.0365308	−0.0182654	+	0.999833i	$0.505814\pi$
$614$	14.8451	0.599100
$615$	−8.68171	−0.350080
$616$	−1.07589	−0.0433488
$617$	−1.74101	−0.0700905	−0.0350452	−	0.999386i	$-0.511158\pi$
$617$	−1.74101	−0.0700905	−0.0350452	+	0.999386i	$0.511158\pi$
$618$	1.42838	0.0574578
$619$	−25.2913	−1.01654	−0.508271	−	0.861197i	$-0.669715\pi$
$619$	−25.2913	−1.01654	−0.508271	+	0.861197i	$0.669715\pi$
$620$	1.18453	0.0475717
$621$	2.20112	0.0883280
$622$	17.5369	0.703165
$623$	9.10243	0.364681
$624$	−0.119305	−0.00477601
$625$	−27.8042	−1.11217
$626$	33.3496	1.33292
$627$	−2.49571	−0.0996692
$628$	−23.1186	−0.922534
$629$	−36.2308	−1.44462
$630$	−8.92542	−0.355597
$631$	12.7434	0.507307	0.253654	−	0.967295i	$-0.418368\pi$
$631$	12.7434	0.507307	0.253654	+	0.967295i	$0.418368\pi$
$632$	13.5915	0.540639
$633$	−0.0989269	−0.00393199
$634$	−13.6333	−0.541446
$635$	−65.5097	−2.59967
$636$	−3.79091	−0.150319
$637$	0.416492	0.0165020
$638$	3.63157	0.143775
$639$	−30.9208	−1.22321
$640$	−3.05880	−0.120910
$641$	−41.5854	−1.64252	−0.821262	−	0.570552i	$-0.806729\pi$
$641$	−41.5854	−1.64252	−0.821262	+	0.570552i	$0.806729\pi$
$642$	−1.58138	−0.0624121
$643$	−24.8552	−0.980194	−0.490097	−	0.871668i	$-0.663039\pi$
$643$	−24.8552	−0.980194	−0.490097	+	0.871668i	$0.663039\pi$
$644$	−1.29844	−0.0511657
$645$	1.40552	0.0553424
$646$	28.1020	1.10566
$647$	−38.8928	−1.52903	−0.764516	−	0.644605i	$-0.777022\pi$
$647$	−38.8928	−1.52903	−0.764516	+	0.644605i	$0.777022\pi$
$648$	−8.26824	−0.324807
$649$	3.97267	0.155941
$650$	−1.81435	−0.0711648
$651$	0.110929	0.00434764
$652$	−4.99733	−0.195711
$653$	24.1054	0.943317	0.471658	−	0.881781i	$-0.343656\pi$
$653$	24.1054	0.943317	0.471658	+	0.881781i	$0.343656\pi$
$654$	2.25932	0.0883465
$655$	−8.57615	−0.335098
$656$	9.90838	0.386857
$657$	5.81270	0.226775
$658$	0.853391	0.0332687
$659$	−14.1241	−0.550198	−0.275099	−	0.961416i	$-0.588711\pi$
$659$	−14.1241	−0.550198	−0.275099	+	0.961416i	$0.588711\pi$
$660$	0.942693	0.0366943
$661$	31.1222	1.21051	0.605256	−	0.796031i	$-0.293071\pi$
$661$	31.1222	1.21051	0.605256	+	0.796031i	$0.293071\pi$
$662$	−22.3646	−0.869227
$663$	−0.414018	−0.0160791
$664$	5.26114	0.204172
$665$	24.7701	0.960542
$666$	−30.4644	−1.18047
$667$	4.38278	0.169702
$668$	3.75457	0.145269
$669$	−1.43324	−0.0554121
$670$	23.1891	0.895871
$671$	−2.78227	−0.107408
$672$	−0.286451	−0.0110501
$673$	4.62757	0.178380	0.0891899	−	0.996015i	$-0.471572\pi$
$673$	4.62757	0.178380	0.0891899	+	0.996015i	$0.471572\pi$
$674$	19.8409	0.764243
$675$	7.38478	0.284240
$676$	−12.8265	−0.493328
$677$	−46.0440	−1.76961	−0.884807	−	0.465958i	$-0.845710\pi$
$677$	−46.0440	−1.76961	−0.884807	+	0.465958i	$0.845710\pi$
$678$	−4.06861	−0.156254
$679$	6.49101	0.249102
$680$	−10.6148	−0.407060
$681$	2.13163	0.0816843
$682$	0.416640	0.0159540
$683$	−28.5833	−1.09371	−0.546854	−	0.837228i	$-0.684175\pi$
$683$	−28.5833	−1.09371	−0.546854	+	0.837228i	$0.684175\pi$
$684$	23.6294	0.903493
$685$	−24.2231	−0.925516
$686$	1.00000	0.0381802
$687$	3.52791	0.134598
$688$	−1.60411	−0.0611563
$689$	5.51186	0.209985
$690$	1.13769	0.0433112
$691$	−39.0515	−1.48559	−0.742794	−	0.669520i	$-0.766500\pi$
$691$	−39.0515	−1.48559	−0.742794	+	0.669520i	$0.766500\pi$
$692$	3.90866	0.148585
$693$	−3.13939	−0.119255
$694$	−11.5510	−0.438470
$695$	−7.05415	−0.267579
$696$	0.966893	0.0366500
$697$	34.3846	1.30241
$698$	−27.6792	−1.04767
$699$	0.586063	0.0221669
$700$	−4.35628	−0.164652
$701$	−17.3962	−0.657045	−0.328522	−	0.944496i	$-0.606551\pi$
$701$	−17.3962	−0.657045	−0.328522	+	0.944496i	$0.606551\pi$
$702$	−0.706038	−0.0266477
$703$	84.5458	3.18870
$704$	−1.07589	−0.0405491
$705$	−0.747741	−0.0281615
$706$	19.6168	0.738286
$707$	4.76321	0.179139
$708$	1.05771	0.0397512
$709$	19.8968	0.747239	0.373619	−	0.927582i	$-0.378117\pi$
$709$	19.8968	0.747239	0.373619	+	0.927582i	$0.378117\pi$
$710$	−32.4134	−1.21645
$711$	39.6591	1.48733
$712$	9.10243	0.341128
$713$	0.502823	0.0188309
$714$	−0.994060	−0.0372018
$715$	−1.37065	−0.0512593
$716$	−2.77765	−0.103806
$717$	6.86898	0.256527
$718$	−12.9115	−0.481852
$719$	−43.3731	−1.61754	−0.808771	−	0.588123i	$-0.799867\pi$
$719$	−43.3731	−1.61754	−0.808771	+	0.588123i	$0.799867\pi$
$720$	−8.92542	−0.332631
$721$	−4.98646	−0.185705
$722$	−46.5770	−1.73342
$723$	−2.33544	−0.0868560
$724$	13.1330	0.488085
$725$	14.7042	0.546102
$726$	−2.81939	−0.104637
$727$	35.0265	1.29906	0.649530	−	0.760336i	$-0.274966\pi$
$727$	35.0265	1.29906	0.649530	+	0.760336i	$0.274966\pi$
$728$	0.416492	0.0154362
$729$	−22.6695	−0.839611
$730$	6.09330	0.225523
$731$	−5.56669	−0.205891
$732$	−0.740768	−0.0273796
$733$	−39.7092	−1.46669	−0.733346	−	0.679855i	$-0.762043\pi$
$733$	−39.7092	−1.46669	−0.733346	+	0.679855i	$0.762043\pi$
$734$	23.5445	0.869043
$735$	−0.876199	−0.0323191
$736$	−1.29844	−0.0478612
$737$	8.15641	0.300445
$738$	28.9121	1.06427
$739$	29.0280	1.06781	0.533907	−	0.845543i	$-0.320723\pi$
$739$	29.0280	1.06781	0.533907	+	0.845543i	$0.320723\pi$
$740$	−31.9351	−1.17396
$741$	0.966125	0.0354915
$742$	13.2340	0.485837
$743$	27.0789	0.993428	0.496714	−	0.867914i	$-0.334540\pi$
$743$	27.0789	0.993428	0.496714	+	0.867914i	$0.334540\pi$
$744$	0.110929	0.00406685
$745$	−29.6004	−1.08447
$746$	−20.0320	−0.733422
$747$	15.3517	0.561690
$748$	−3.73361	−0.136514
$749$	5.52059	0.201718
$750$	−0.564030	−0.0205955
$751$	5.23406	0.190994	0.0954968	−	0.995430i	$-0.469556\pi$
$751$	5.23406	0.190994	0.0954968	+	0.995430i	$0.469556\pi$
$752$	0.853391	0.0311200
$753$	8.30332	0.302590
$754$	−1.40583	−0.0511974
$755$	−46.9926	−1.71024
$756$	−1.69520	−0.0616540
$757$	−3.60830	−0.131146	−0.0655730	−	0.997848i	$-0.520888\pi$
$757$	−3.60830	−0.131146	−0.0655730	+	0.997848i	$0.520888\pi$
$758$	15.7223	0.571061
$759$	0.400167	0.0145251
$760$	24.7701	0.898505
$761$	−27.6372	−1.00185	−0.500923	−	0.865492i	$-0.667006\pi$
$761$	−27.6372	−1.00185	−0.500923	+	0.865492i	$0.667006\pi$
$762$	−6.13487	−0.222243
$763$	−7.88728	−0.285539
$764$	2.51499	0.0909890
$765$	−30.9735	−1.11985
$766$	16.2889	0.588543
$767$	−1.53788	−0.0555295
$768$	−0.286451	−0.0103364
$769$	23.8726	0.860867	0.430434	−	0.902622i	$-0.358361\pi$
$769$	23.8726	0.860867	0.430434	+	0.902622i	$0.358361\pi$
$770$	−3.29093	−0.118597
$771$	−6.04536	−0.217718
$772$	12.1068	0.435735
$773$	−5.90869	−0.212521	−0.106260	−	0.994338i	$-0.533888\pi$
$773$	−5.90869	−0.212521	−0.106260	+	0.994338i	$0.533888\pi$
$774$	−4.68072	−0.168245
$775$	1.68698	0.0605980
$776$	6.49101	0.233014
$777$	−2.99066	−0.107289
$778$	0.887499	0.0318184
$779$	−80.2377	−2.87482
$780$	−0.364929	−0.0130666
$781$	−11.4009	−0.407958
$782$	−4.50592	−0.161131
$783$	5.72202	0.204488
$784$	1.00000	0.0357143
$785$	−70.7153	−2.52394
$786$	−0.803142	−0.0286471
$787$	14.4190	0.513981	0.256990	−	0.966414i	$-0.417269\pi$
$787$	14.4190	0.513981	0.256990	+	0.966414i	$0.417269\pi$
$788$	14.4249	0.513865
$789$	−5.50199	−0.195876
$790$	41.5736	1.47912
$791$	14.2035	0.505018
$792$	−3.13939	−0.111553
$793$	1.07705	0.0382473
$794$	−28.2413	−1.00224
$795$	−11.5956	−0.411255
$796$	4.95485	0.175620
$797$	40.4801	1.43388	0.716940	−	0.697135i	$-0.245542\pi$
$797$	40.4801	1.43388	0.716940	+	0.697135i	$0.245542\pi$
$798$	2.31967	0.0821156
$799$	2.96149	0.104770
$800$	−4.35628	−0.154018
$801$	26.5604	0.938465
$802$	29.0416	1.02549
$803$	2.14323	0.0756329
$804$	2.17161	0.0765869
$805$	−3.97167	−0.139983
$806$	−0.161287	−0.00568110
$807$	−4.30771	−0.151639
$808$	4.76321	0.167569
$809$	43.7749	1.53904	0.769522	−	0.638620i	$-0.220494\pi$
$809$	43.7749	1.53904	0.769522	+	0.638620i	$0.220494\pi$
$810$	−25.2909	−0.888633
$811$	−29.8346	−1.04763	−0.523817	−	0.851831i	$-0.675493\pi$
$811$	−29.8346	−1.04763	−0.523817	+	0.851831i	$0.675493\pi$
$812$	−3.37542	−0.118454
$813$	−1.63254	−0.0572556
$814$	−11.2327	−0.393706
$815$	−15.2858	−0.535440
$816$	−0.994060	−0.0347991
$817$	12.9901	0.454465
$818$	−0.814422	−0.0284756
$819$	1.21530	0.0424660
$820$	30.3078	1.05839
$821$	44.8888	1.56663	0.783314	−	0.621626i	$-0.213527\pi$
$821$	44.8888	1.56663	0.783314	+	0.621626i	$0.213527\pi$
$822$	−2.26845	−0.0791212
$823$	3.03809	0.105901	0.0529505	−	0.998597i	$-0.483137\pi$
$823$	3.03809	0.105901	0.0529505	+	0.998597i	$0.483137\pi$
$824$	−4.98646	−0.173712
$825$	1.34256	0.0467420
$826$	−3.69246	−0.128477
$827$	32.9719	1.14654	0.573272	−	0.819365i	$-0.305674\pi$
$827$	32.9719	1.14654	0.573272	+	0.819365i	$0.305674\pi$
$828$	−3.78878	−0.131669
$829$	42.4241	1.47345	0.736724	−	0.676193i	$-0.236372\pi$
$829$	42.4241	1.47345	0.736724	+	0.676193i	$0.236372\pi$
$830$	16.0928	0.558589
$831$	8.21808	0.285082
$832$	0.416492	0.0144393
$833$	3.47026	0.120237
$834$	−0.660609	−0.0228750
$835$	11.4845	0.397438
$836$	8.71252	0.301329
$837$	0.656471	0.0226910
$838$	−40.2300	−1.38972
$839$	18.6407	0.643547	0.321774	−	0.946817i	$-0.395721\pi$
$839$	18.6407	0.643547	0.321774	+	0.946817i	$0.395721\pi$
$840$	−0.876199	−0.0302317
$841$	−17.6066	−0.607123
$842$	32.4405	1.11797
$843$	0.373685	0.0128704
$844$	0.345353	0.0118875
$845$	−39.2338	−1.34969
$846$	2.49015	0.0856131
$847$	9.84246	0.338191
$848$	13.2340	0.454459
$849$	−6.89763	−0.236726
$850$	−15.1174	−0.518522
$851$	−13.5562	−0.464701
$852$	−3.03546	−0.103993
$853$	−41.5222	−1.42169	−0.710847	−	0.703347i	$-0.751688\pi$
$853$	−41.5222	−1.42169	−0.710847	+	0.703347i	$0.751688\pi$
$854$	2.58602	0.0884916
$855$	72.2777	2.47185
$856$	5.52059	0.188690
$857$	14.0734	0.480739	0.240369	−	0.970681i	$-0.422731\pi$
$857$	14.0734	0.480739	0.240369	+	0.970681i	$0.422731\pi$
$858$	−0.128359	−0.00438209
$859$	13.1079	0.447235	0.223618	−	0.974677i	$-0.428213\pi$
$859$	13.1079	0.447235	0.223618	+	0.974677i	$0.428213\pi$
$860$	−4.90667	−0.167316
$861$	2.83827	0.0967280
$862$	1.00000	0.0340601
$863$	14.9210	0.507918	0.253959	−	0.967215i	$-0.418267\pi$
$863$	14.9210	0.507918	0.253959	+	0.967215i	$0.418267\pi$
$864$	−1.69520	−0.0576720
$865$	11.9558	0.406510
$866$	−25.6969	−0.873216
$867$	1.42003	0.0482269
$868$	−0.387252	−0.0131442
$869$	14.6229	0.496048
$870$	2.95753	0.100270
$871$	−3.15746	−0.106986
$872$	−7.88728	−0.267097
$873$	18.9404	0.641036
$874$	10.5147	0.355666
$875$	1.96902	0.0665651
$876$	0.570627	0.0192797
$877$	41.8695	1.41383	0.706917	−	0.707297i	$-0.250085\pi$
$877$	41.8695	1.41383	0.706917	+	0.707297i	$0.250085\pi$
$878$	−14.2842	−0.482067
$879$	1.08224	0.0365032
$880$	−3.29093	−0.110937
$881$	22.0867	0.744118	0.372059	−	0.928209i	$-0.378652\pi$
$881$	22.0867	0.744118	0.372059	+	0.928209i	$0.378652\pi$
$882$	2.91795	0.0982523
$883$	3.01690	0.101527	0.0507633	−	0.998711i	$-0.483835\pi$
$883$	3.01690	0.101527	0.0507633	+	0.998711i	$0.483835\pi$
$884$	1.44533	0.0486118
$885$	3.23532	0.108754
$886$	−8.08876	−0.271747
$887$	−31.2262	−1.04847	−0.524237	−	0.851572i	$-0.675650\pi$
$887$	−31.2262	−1.04847	−0.524237	+	0.851572i	$0.675650\pi$
$888$	−2.99066	−0.100360
$889$	21.4168	0.718296
$890$	27.8425	0.933284
$891$	−8.89572	−0.298018
$892$	5.00342	0.167527
$893$	−6.91073	−0.231259
$894$	−2.77202	−0.0927103
$895$	−8.49628	−0.283999
$896$	1.00000	0.0334077
$897$	−0.154910	−0.00517229
$898$	32.9585	1.09984
$899$	1.30714	0.0435954
$900$	−12.7114	−0.423713
$901$	45.9255	1.53000
$902$	10.6603	0.354950
$903$	−0.459501	−0.0152912
$904$	14.2035	0.472401
$905$	40.1714	1.33534
$906$	−4.40077	−0.146206
$907$	5.05441	0.167829	0.0839145	−	0.996473i	$-0.473258\pi$
$907$	5.05441	0.167829	0.0839145	+	0.996473i	$0.473258\pi$
$908$	−7.44151	−0.246955
$909$	13.8988	0.460994
$910$	1.27397	0.0422316
$911$	57.1830	1.89456	0.947278	−	0.320413i	$-0.103822\pi$
$911$	57.1830	1.89456	0.947278	+	0.320413i	$0.103822\pi$
$912$	2.31967	0.0768121
$913$	5.66041	0.187332
$914$	19.3212	0.639089
$915$	−2.26586	−0.0749071
$916$	−12.3159	−0.406929
$917$	2.80376	0.0925884
$918$	−5.88279	−0.194161
$919$	8.60516	0.283858	0.141929	−	0.989877i	$-0.454669\pi$
$919$	8.60516	0.283858	0.141929	+	0.989877i	$0.454669\pi$
$920$	−3.97167	−0.130942
$921$	4.25241	0.140122
$922$	−14.7296	−0.485095
$923$	4.41346	0.145271
$924$	−0.308190	−0.0101387
$925$	−45.4812	−1.49541
$926$	28.4223	0.934014
$927$	−14.5502	−0.477892
$928$	−3.37542	−0.110803
$929$	−0.867667	−0.0284672	−0.0142336	−	0.999899i	$-0.504531\pi$
$929$	−0.867667	−0.0284672	−0.0142336	+	0.999899i	$0.504531\pi$
$930$	0.339309	0.0111264
$931$	−8.09796	−0.265400
$932$	−2.04594	−0.0670170
$933$	5.02346	0.164461
$934$	−36.1698	−1.18351
$935$	−11.4204	−0.373486
$936$	1.21530	0.0397233
$937$	32.0973	1.04857	0.524286	−	0.851542i	$-0.324332\pi$
$937$	32.0973	1.04857	0.524286	+	0.851542i	$0.324332\pi$
$938$	−7.58109	−0.247531
$939$	9.55305	0.311752
$940$	2.61036	0.0851404
$941$	−20.6961	−0.674674	−0.337337	−	0.941384i	$-0.609526\pi$
$941$	−20.6961	−0.674674	−0.337337	+	0.941384i	$0.609526\pi$
$942$	−6.62237	−0.215768
$943$	12.8654	0.418957
$944$	−3.69246	−0.120179
$945$	−5.18530	−0.168678
$946$	−1.72585	−0.0561122
$947$	−24.7579	−0.804523	−0.402261	−	0.915525i	$-0.631776\pi$
$947$	−24.7579	−0.804523	−0.402261	+	0.915525i	$0.631776\pi$
$948$	3.89329	0.126448
$949$	−0.829674	−0.0269323
$950$	35.2770	1.14454
$951$	−3.90527	−0.126637
$952$	3.47026	0.112472
$953$	44.7558	1.44978	0.724891	−	0.688863i	$-0.241890\pi$
$953$	44.7558	1.44978	0.724891	+	0.688863i	$0.241890\pi$
$954$	38.6162	1.25025
$955$	7.69285	0.248935
$956$	−23.9796	−0.775555
$957$	1.04027	0.0336271
$958$	−23.2517	−0.751227
$959$	7.91913	0.255722
$960$	−0.876199	−0.0282792
$961$	−30.8500	−0.995162
$962$	4.34833	0.140196
$963$	16.1088	0.519098
$964$	8.15301	0.262591
$965$	37.0325	1.19212
$966$	−0.371940	−0.0119670
$967$	31.0517	0.998556	0.499278	−	0.866442i	$-0.333599\pi$
$967$	31.0517	0.998556	0.499278	+	0.866442i	$0.333599\pi$
$968$	9.84246	0.316349
$969$	8.04986	0.258599
$970$	19.8547	0.637496
$971$	−20.4649	−0.656749	−0.328374	−	0.944548i	$-0.606501\pi$
$971$	−20.4649	−0.656749	−0.328374	+	0.944548i	$0.606501\pi$
$972$	−7.45406	−0.239089
$973$	2.30618	0.0739327
$974$	11.5654	0.370579
$975$	−0.519724	−0.0166445
$976$	2.58602	0.0827763
$977$	13.0157	0.416408	0.208204	−	0.978085i	$-0.433238\pi$
$977$	13.0157	0.416408	0.208204	+	0.978085i	$0.433238\pi$
$978$	−1.43149	−0.0457741
$979$	9.79321	0.312992
$980$	3.05880	0.0977099
$981$	−23.0147	−0.734801
$982$	−4.61509	−0.147274
$983$	−16.4723	−0.525384	−0.262692	−	0.964880i	$-0.584610\pi$
$983$	−16.4723	−0.525384	−0.262692	+	0.964880i	$0.584610\pi$
$984$	2.83827	0.0904808
$985$	44.1228	1.40587
$986$	−11.7136	−0.373035
$987$	0.244455	0.00778110
$988$	−3.37273	−0.107301
$989$	−2.08285	−0.0662307
$990$	−9.60277	−0.305196
$991$	31.2755	0.993498	0.496749	−	0.867894i	$-0.334527\pi$
$991$	31.2755	0.993498	0.496749	+	0.867894i	$0.334527\pi$
$992$	−0.387252	−0.0122953
$993$	−6.40639	−0.203300
$994$	10.5968	0.336109
$995$	15.1559	0.480475
$996$	1.50706	0.0477531
$997$	17.5605	0.556145	0.278073	−	0.960560i	$-0.410304\pi$
$997$	17.5605	0.556145	0.278073	+	0.960560i	$0.410304\pi$
$998$	15.7245	0.497750
$999$	−17.6986	−0.559958

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.13	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.13	✓	25	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:	\( N \)	\(=\)	\( 6034 = 2 \cdot 7 \cdot 431 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6034.a (trivial)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.286451 q^{3} +1.00000 q^{4} +3.05880 q^{5} +0.286451 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.91795 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.286451 q^{3} +1.00000 q^{4} +3.05880 q^{5} +0.286451 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.91795 q^{9} -3.05880 q^{10} -1.07589 q^{11} -0.286451 q^{12} +0.416492 q^{13} +1.00000 q^{14} -0.876199 q^{15} +1.00000 q^{16} +3.47026 q^{17} +2.91795 q^{18} -8.09796 q^{19} +3.05880 q^{20} +0.286451 q^{21} +1.07589 q^{22} +1.29844 q^{23} +0.286451 q^{24} +4.35628 q^{25} -0.416492 q^{26} +1.69520 q^{27} -1.00000 q^{28} +3.37542 q^{29} +0.876199 q^{30} +0.387252 q^{31} -1.00000 q^{32} +0.308190 q^{33} -3.47026 q^{34} -3.05880 q^{35} -2.91795 q^{36} -10.4404 q^{37} +8.09796 q^{38} -0.119305 q^{39} -3.05880 q^{40} +9.90838 q^{41} -0.286451 q^{42} -1.60411 q^{43} -1.07589 q^{44} -8.92542 q^{45} -1.29844 q^{46} +0.853391 q^{47} -0.286451 q^{48} +1.00000 q^{49} -4.35628 q^{50} -0.994060 q^{51} +0.416492 q^{52} +13.2340 q^{53} -1.69520 q^{54} -3.29093 q^{55} +1.00000 q^{56} +2.31967 q^{57} -3.37542 q^{58} -3.69246 q^{59} -0.876199 q^{60} +2.58602 q^{61} -0.387252 q^{62} +2.91795 q^{63} +1.00000 q^{64} +1.27397 q^{65} -0.308190 q^{66} -7.58109 q^{67} +3.47026 q^{68} -0.371940 q^{69} +3.05880 q^{70} +10.5968 q^{71} +2.91795 q^{72} -1.99205 q^{73} +10.4404 q^{74} -1.24786 q^{75} -8.09796 q^{76} +1.07589 q^{77} +0.119305 q^{78} -13.5915 q^{79} +3.05880 q^{80} +8.26824 q^{81} -9.90838 q^{82} -5.26114 q^{83} +0.286451 q^{84} +10.6148 q^{85} +1.60411 q^{86} -0.966893 q^{87} +1.07589 q^{88} -9.10243 q^{89} +8.92542 q^{90} -0.416492 q^{91} +1.29844 q^{92} -0.110929 q^{93} -0.853391 q^{94} -24.7701 q^{95} +0.286451 q^{96} -6.49101 q^{97} -1.00000 q^{98} +3.13939 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9} - 13 q^{11} - 4 q^{12} + 17 q^{13} + 25 q^{14} - 18 q^{15} + 25 q^{16} - 4 q^{17} - 25 q^{18} - 9 q^{19} + 4 q^{21} + 13 q^{22} - 14 q^{23} + 4 q^{24} + 23 q^{25} - 17 q^{26} - 7 q^{27} - 25 q^{28} - 4 q^{29} + 18 q^{30} - 15 q^{31} - 25 q^{32} - 15 q^{33} + 4 q^{34} + 25 q^{36} + 13 q^{37} + 9 q^{38} - 31 q^{39} - 31 q^{41} - 4 q^{42} + 29 q^{43} - 13 q^{44} + 10 q^{45} + 14 q^{46} - 31 q^{47} - 4 q^{48} + 25 q^{49} - 23 q^{50} - 9 q^{51} + 17 q^{52} + 23 q^{53} + 7 q^{54} - 48 q^{55} + 25 q^{56} + 32 q^{57} + 4 q^{58} - 50 q^{59} - 18 q^{60} - 2 q^{61} + 15 q^{62} - 25 q^{63} + 25 q^{64} - 4 q^{65} + 15 q^{66} - 8 q^{67} - 4 q^{68} - 57 q^{69} - 61 q^{71} - 25 q^{72} + 31 q^{73} - 13 q^{74} - 21 q^{75} - 9 q^{76} + 13 q^{77} + 31 q^{78} - 10 q^{79} + 61 q^{81} + 31 q^{82} - 47 q^{83} + 4 q^{84} + 2 q^{85} - 29 q^{86} + 17 q^{87} + 13 q^{88} - 44 q^{89} - 10 q^{90} - 17 q^{91} - 14 q^{92} - 13 q^{93} + 31 q^{94} - 7 q^{95} + 4 q^{96} + 10 q^{97} - 25 q^{98} - 47 q^{99}+O(q^{100}) \) 25 * q - 25 * q^2 - 4 * q^3 + 25 * q^4 + 4 * q^6 - 25 * q^7 - 25 * q^8 + 25 * q^9 - 13 * q^11 - 4 * q^12 + 17 * q^13 + 25 * q^14 - 18 * q^15 + 25 * q^16 - 4 * q^17 - 25 * q^18 - 9 * q^19 + 4 * q^21 + 13 * q^22 - 14 * q^23 + 4 * q^24 + 23 * q^25 - 17 * q^26 - 7 * q^27 - 25 * q^28 - 4 * q^29 + 18 * q^30 - 15 * q^31 - 25 * q^32 - 15 * q^33 + 4 * q^34 + 25 * q^36 + 13 * q^37 + 9 * q^38 - 31 * q^39 - 31 * q^41 - 4 * q^42 + 29 * q^43 - 13 * q^44 + 10 * q^45 + 14 * q^46 - 31 * q^47 - 4 * q^48 + 25 * q^49 - 23 * q^50 - 9 * q^51 + 17 * q^52 + 23 * q^53 + 7 * q^54 - 48 * q^55 + 25 * q^56 + 32 * q^57 + 4 * q^58 - 50 * q^59 - 18 * q^60 - 2 * q^61 + 15 * q^62 - 25 * q^63 + 25 * q^64 - 4 * q^65 + 15 * q^66 - 8 * q^67 - 4 * q^68 - 57 * q^69 - 61 * q^71 - 25 * q^72 + 31 * q^73 - 13 * q^74 - 21 * q^75 - 9 * q^76 + 13 * q^77 + 31 * q^78 - 10 * q^79 + 61 * q^81 + 31 * q^82 - 47 * q^83 + 4 * q^84 + 2 * q^85 - 29 * q^86 + 17 * q^87 + 13 * q^88 - 44 * q^89 - 10 * q^90 - 17 * q^91 - 14 * q^92 - 13 * q^93 + 31 * q^94 - 7 * q^95 + 4 * q^96 + 10 * q^97 - 25 * q^98 - 47 * q^99

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