LMFDB - Embedded newform 6034.2.a.o.1.12

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			1.12
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)

$f(q)$	$=$	$q-1.00000 q^{2} -0.642803 q^{3} +1.00000 q^{4} -0.120045 q^{5} +0.642803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.58680 q^{9} +O(q^{10})$	\(q-1.00000 q^{2} -0.642803 q^{3} +1.00000 q^{4} -0.120045 q^{5} +0.642803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.58680 q^{9} +0.120045 q^{10} -0.587191 q^{11} -0.642803 q^{12} +3.04657 q^{13} +1.00000 q^{14} +0.0771656 q^{15} +1.00000 q^{16} +4.23963 q^{17} +2.58680 q^{18} +1.22801 q^{19} -0.120045 q^{20} +0.642803 q^{21} +0.587191 q^{22} +1.34791 q^{23} +0.642803 q^{24} -4.98559 q^{25} -3.04657 q^{26} +3.59121 q^{27} -1.00000 q^{28} -5.89329 q^{29} -0.0771656 q^{30} +0.347369 q^{31} -1.00000 q^{32} +0.377448 q^{33} -4.23963 q^{34} +0.120045 q^{35} -2.58680 q^{36} -0.751815 q^{37} -1.22801 q^{38} -1.95834 q^{39} +0.120045 q^{40} -2.04831 q^{41} -0.642803 q^{42} -5.41187 q^{43} -0.587191 q^{44} +0.310534 q^{45} -1.34791 q^{46} +1.40847 q^{47} -0.642803 q^{48} +1.00000 q^{49} +4.98559 q^{50} -2.72525 q^{51} +3.04657 q^{52} -9.56168 q^{53} -3.59121 q^{54} +0.0704897 q^{55} +1.00000 q^{56} -0.789369 q^{57} +5.89329 q^{58} +8.10850 q^{59} +0.0771656 q^{60} +10.0800 q^{61} -0.347369 q^{62} +2.58680 q^{63} +1.00000 q^{64} -0.365727 q^{65} -0.377448 q^{66} +0.0479050 q^{67} +4.23963 q^{68} -0.866441 q^{69} -0.120045 q^{70} +8.03477 q^{71} +2.58680 q^{72} +3.29812 q^{73} +0.751815 q^{74} +3.20475 q^{75} +1.22801 q^{76} +0.587191 q^{77} +1.95834 q^{78} -9.69152 q^{79} -0.120045 q^{80} +5.45197 q^{81} +2.04831 q^{82} +10.5785 q^{83} +0.642803 q^{84} -0.508948 q^{85} +5.41187 q^{86} +3.78823 q^{87} +0.587191 q^{88} +8.57123 q^{89} -0.310534 q^{90} -3.04657 q^{91} +1.34791 q^{92} -0.223290 q^{93} -1.40847 q^{94} -0.147417 q^{95} +0.642803 q^{96} +7.55383 q^{97} -1.00000 q^{98} +1.51895 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−0.642803	−0.371123	−0.185561	−	0.982633i	$-0.559410\pi$
$3$	−0.642803	−0.371123	−0.185561	+	0.982633i	$0.559410\pi$
$4$	1.00000	0.500000
$5$	−0.120045	−0.0536860	−0.0268430	−	0.999640i	$-0.508545\pi$
$5$	−0.120045	−0.0536860	−0.0268430	+	0.999640i	$0.508545\pi$
$6$	0.642803	0.262423
$7$	−1.00000	−0.377964
$7$	−1.00000	−0.377964
$8$	−1.00000	−0.353553
$9$	−2.58680	−0.862268
$10$	0.120045	0.0379617
$11$	−0.587191	−0.177045	−0.0885224	−	0.996074i	$-0.528214\pi$
$11$	−0.587191	−0.177045	−0.0885224	+	0.996074i	$0.528214\pi$
$12$	−0.642803	−0.185561
$13$	3.04657	0.844967	0.422483	−	0.906371i	$-0.361159\pi$
$13$	3.04657	0.844967	0.422483	+	0.906371i	$0.361159\pi$
$14$	1.00000	0.267261
$15$	0.0771656	0.0199241
$16$	1.00000	0.250000
$17$	4.23963	1.02826	0.514131	−	0.857712i	$-0.328115\pi$
$17$	4.23963	1.02826	0.514131	+	0.857712i	$0.328115\pi$
$18$	2.58680	0.609716
$19$	1.22801	0.281725	0.140862	−	0.990029i	$-0.455012\pi$
$19$	1.22801	0.281725	0.140862	+	0.990029i	$0.455012\pi$
$20$	−0.120045	−0.0268430
$21$	0.642803	0.140271
$22$	0.587191	0.125190
$23$	1.34791	0.281059	0.140529	−	0.990077i	$-0.455120\pi$
$23$	1.34791	0.281059	0.140529	+	0.990077i	$0.455120\pi$
$24$	0.642803	0.131212
$25$	−4.98559	−0.997118
$26$	−3.04657	−0.597482
$27$	3.59121	0.691130
$28$	−1.00000	−0.188982
$29$	−5.89329	−1.09436	−0.547178	−	0.837016i	$-0.684298\pi$
$29$	−5.89329	−1.09436	−0.547178	+	0.837016i	$0.684298\pi$
$30$	−0.0771656	−0.0140884
$31$	0.347369	0.0623893	0.0311947	−	0.999513i	$-0.490069\pi$
$31$	0.347369	0.0623893	0.0311947	+	0.999513i	$0.490069\pi$
$32$	−1.00000	−0.176777
$33$	0.377448	0.0657053
$34$	−4.23963	−0.727091
$35$	0.120045	0.0202914
$36$	−2.58680	−0.431134
$37$	−0.751815	−0.123598	−0.0617988	−	0.998089i	$-0.519684\pi$
$37$	−0.751815	−0.123598	−0.0617988	+	0.998089i	$0.519684\pi$
$38$	−1.22801	−0.199210
$39$	−1.95834	−0.313586
$40$	0.120045	0.0189809
$41$	−2.04831	−0.319892	−0.159946	−	0.987126i	$-0.551132\pi$
$41$	−2.04831	−0.319892	−0.159946	+	0.987126i	$0.551132\pi$
$42$	−0.642803	−0.0991867
$43$	−5.41187	−0.825303	−0.412651	−	0.910889i	$-0.635397\pi$
$43$	−5.41187	−0.825303	−0.412651	+	0.910889i	$0.635397\pi$
$44$	−0.587191	−0.0885224
$45$	0.310534	0.0462917
$46$	−1.34791	−0.198738
$47$	1.40847	0.205446	0.102723	−	0.994710i	$-0.467244\pi$
$47$	1.40847	0.205446	0.102723	+	0.994710i	$0.467244\pi$
$48$	−0.642803	−0.0927806
$49$	1.00000	0.142857
$50$	4.98559	0.705069
$51$	−2.72525	−0.381611
$52$	3.04657	0.422483
$53$	−9.56168	−1.31340	−0.656699	−	0.754153i	$-0.728048\pi$
$53$	−9.56168	−1.31340	−0.656699	+	0.754153i	$0.728048\pi$
$54$	−3.59121	−0.488702
$55$	0.0704897	0.00950483
$56$	1.00000	0.133631
$57$	−0.789369	−0.104554
$58$	5.89329	0.773827
$59$	8.10850	1.05564	0.527819	−	0.849357i	$-0.323010\pi$
$59$	8.10850	1.05564	0.527819	+	0.849357i	$0.323010\pi$
$60$	0.0771656	0.00996204
$61$	10.0800	1.29062	0.645309	−	0.763922i	$-0.276729\pi$
$61$	10.0800	1.29062	0.645309	+	0.763922i	$0.276729\pi$
$62$	−0.347369	−0.0441159
$63$	2.58680	0.325907
$64$	1.00000	0.125000
$65$	−0.365727	−0.0453628
$66$	−0.377448	−0.0464607
$67$	0.0479050	0.00585253	0.00292626	−	0.999996i	$-0.499069\pi$
$67$	0.0479050	0.00585253	0.00292626	+	0.999996i	$0.499069\pi$
$68$	4.23963	0.514131
$69$	−0.866441	−0.104307
$70$	−0.120045	−0.0143482
$71$	8.03477	0.953552	0.476776	−	0.879025i	$-0.341805\pi$
$71$	8.03477	0.953552	0.476776	+	0.879025i	$0.341805\pi$
$72$	2.58680	0.304858
$73$	3.29812	0.386016	0.193008	−	0.981197i	$-0.438176\pi$
$73$	3.29812	0.386016	0.193008	+	0.981197i	$0.438176\pi$
$74$	0.751815	0.0873968
$75$	3.20475	0.370053
$76$	1.22801	0.140862
$77$	0.587191	0.0669167
$78$	1.95834	0.221739
$79$	−9.69152	−1.09038	−0.545191	−	0.838312i	$-0.683543\pi$
$79$	−9.69152	−1.09038	−0.545191	+	0.838312i	$0.683543\pi$
$80$	−0.120045	−0.0134215
$81$	5.45197	0.605774
$82$	2.04831	0.226198
$83$	10.5785	1.16114	0.580568	−	0.814212i	$-0.302830\pi$
$83$	10.5785	1.16114	0.580568	+	0.814212i	$0.302830\pi$
$84$	0.642803	0.0701356
$85$	−0.508948	−0.0552032
$86$	5.41187	0.583577
$87$	3.78823	0.406141
$88$	0.587191	0.0625948
$89$	8.57123	0.908548	0.454274	−	0.890862i	$-0.349899\pi$
$89$	8.57123	0.908548	0.454274	+	0.890862i	$0.349899\pi$
$90$	−0.310534	−0.0327332
$91$	−3.04657	−0.319367
$92$	1.34791	0.140529
$93$	−0.223290	−0.0231541
$94$	−1.40847	−0.145272
$95$	−0.147417	−0.0151247
$96$	0.642803	0.0656058
$97$	7.55383	0.766975	0.383487	−	0.923546i	$-0.374723\pi$
$97$	7.55383	0.766975	0.383487	+	0.923546i	$0.374723\pi$
$98$	−1.00000	−0.101015
$99$	1.51895	0.152660
$100$	−4.98559	−0.498559
$101$	−7.70365	−0.766542	−0.383271	−	0.923636i	$-0.625202\pi$
$101$	−7.70365	−0.766542	−0.383271	+	0.923636i	$0.625202\pi$
$102$	2.72525	0.269840
$103$	−10.4983	−1.03443	−0.517213	−	0.855856i	$-0.673031\pi$
$103$	−10.4983	−1.03443	−0.517213	+	0.855856i	$0.673031\pi$
$104$	−3.04657	−0.298741
$105$	−0.0771656	−0.00753059
$106$	9.56168	0.928712
$107$	−13.5895	−1.31375	−0.656873	−	0.754001i	$-0.728121\pi$
$107$	−13.5895	−1.31375	−0.656873	+	0.754001i	$0.728121\pi$
$108$	3.59121	0.345565
$109$	9.75411	0.934274	0.467137	−	0.884185i	$-0.345285\pi$
$109$	9.75411	0.934274	0.467137	+	0.884185i	$0.345285\pi$
$110$	−0.0704897	−0.00672093
$111$	0.483269	0.0458699
$112$	−1.00000	−0.0944911
$113$	3.61651	0.340213	0.170106	−	0.985426i	$-0.445589\pi$
$113$	3.61651	0.340213	0.170106	+	0.985426i	$0.445589\pi$
$114$	0.789369	0.0739311
$115$	−0.161810	−0.0150889
$116$	−5.89329	−0.547178
$117$	−7.88088	−0.728588
$118$	−8.10850	−0.746448
$119$	−4.23963	−0.388646
$120$	−0.0771656	−0.00704422
$121$	−10.6552	−0.968655
$122$	−10.0800	−0.912604
$123$	1.31666	0.118719
$124$	0.347369	0.0311947
$125$	1.19872	0.107217
$126$	−2.58680	−0.230451
$127$	1.62844	0.144501	0.0722505	−	0.997387i	$-0.476982\pi$
$127$	1.62844	0.144501	0.0722505	+	0.997387i	$0.476982\pi$
$128$	−1.00000	−0.0883883
$129$	3.47877	0.306288
$130$	0.365727	0.0320764
$131$	−7.36727	−0.643681	−0.321841	−	0.946794i	$-0.604302\pi$
$131$	−7.36727	−0.643681	−0.321841	+	0.946794i	$0.604302\pi$
$132$	0.377448	0.0328527
$133$	−1.22801	−0.106482
$134$	−0.0479050	−0.00413836
$135$	−0.431109	−0.0371040
$136$	−4.23963	−0.363545
$137$	−21.4838	−1.83549	−0.917744	−	0.397173i	$-0.869991\pi$
$137$	−21.4838	−1.83549	−0.917744	+	0.397173i	$0.869991\pi$
$138$	0.866441	0.0737563
$139$	14.7936	1.25478	0.627388	−	0.778707i	$-0.284124\pi$
$139$	14.7936	1.25478	0.627388	+	0.778707i	$0.284124\pi$
$140$	0.120045	0.0101457
$141$	−0.905368	−0.0762457
$142$	−8.03477	−0.674263
$143$	−1.78892	−0.149597
$144$	−2.58680	−0.215567
$145$	0.707463	0.0587516
$146$	−3.29812	−0.272954
$147$	−0.642803	−0.0530175
$148$	−0.751815	−0.0617988
$149$	9.52393	0.780231	0.390116	−	0.920766i	$-0.372435\pi$
$149$	9.52393	0.780231	0.390116	+	0.920766i	$0.372435\pi$
$150$	−3.20475	−0.261667
$151$	9.02759	0.734655	0.367327	−	0.930092i	$-0.380273\pi$
$151$	9.02759	0.734655	0.367327	+	0.930092i	$0.380273\pi$
$152$	−1.22801	−0.0996048
$153$	−10.9671	−0.886637
$154$	−0.587191	−0.0473172
$155$	−0.0417001	−0.00334943
$156$	−1.95834	−0.156793
$157$	6.01529	0.480072	0.240036	−	0.970764i	$-0.422841\pi$
$157$	6.01529	0.480072	0.240036	+	0.970764i	$0.422841\pi$
$158$	9.69152	0.771016
$159$	6.14627	0.487431
$160$	0.120045	0.00949043
$161$	−1.34791	−0.106230
$162$	−5.45197	−0.428347
$163$	−0.894134	−0.0700340	−0.0350170	−	0.999387i	$-0.511149\pi$
$163$	−0.894134	−0.0700340	−0.0350170	+	0.999387i	$0.511149\pi$
$164$	−2.04831	−0.159946
$165$	−0.0453110	−0.00352745
$166$	−10.5785	−0.821048
$167$	−20.5478	−1.59004	−0.795018	−	0.606586i	$-0.792539\pi$
$167$	−20.5478	−1.59004	−0.795018	+	0.606586i	$0.792539\pi$
$168$	−0.642803	−0.0495933
$169$	−3.71841	−0.286031
$170$	0.508948	0.0390346
$171$	−3.17662	−0.242922
$172$	−5.41187	−0.412651
$173$	−9.57340	−0.727852	−0.363926	−	0.931428i	$-0.618564\pi$
$173$	−9.57340	−0.727852	−0.363926	+	0.931428i	$0.618564\pi$
$174$	−3.78823	−0.287185
$175$	4.98559	0.376875
$176$	−0.587191	−0.0442612
$177$	−5.21217	−0.391771
$178$	−8.57123	−0.642441
$179$	3.29028	0.245927	0.122963	−	0.992411i	$-0.460760\pi$
$179$	3.29028	0.245927	0.122963	+	0.992411i	$0.460760\pi$
$180$	0.310534	0.0231458
$181$	6.24094	0.463885	0.231943	−	0.972729i	$-0.425492\pi$
$181$	6.24094	0.463885	0.231943	+	0.972729i	$0.425492\pi$
$182$	3.04657	0.225827
$183$	−6.47948	−0.478977
$184$	−1.34791	−0.0993692
$185$	0.0902520	0.00663546
$186$	0.223290	0.0163724
$187$	−2.48947	−0.182048
$188$	1.40847	0.102723
$189$	−3.59121	−0.261222
$190$	0.147417	0.0106948
$191$	−21.3354	−1.54378	−0.771888	−	0.635758i	$-0.780688\pi$
$191$	−21.3354	−1.54378	−0.771888	+	0.635758i	$0.780688\pi$
$192$	−0.642803	−0.0463903
$193$	25.9170	1.86555	0.932774	−	0.360461i	$-0.117381\pi$
$193$	25.9170	1.86555	0.932774	+	0.360461i	$0.117381\pi$
$194$	−7.55383	−0.542333
$195$	0.235090	0.0168352
$196$	1.00000	0.0714286
$197$	−19.3789	−1.38069	−0.690344	−	0.723481i	$-0.742541\pi$
$197$	−19.3789	−1.38069	−0.690344	+	0.723481i	$0.742541\pi$
$198$	−1.51895	−0.107947
$199$	10.1177	0.717224	0.358612	−	0.933487i	$-0.383250\pi$
$199$	10.1177	0.717224	0.358612	+	0.933487i	$0.383250\pi$
$200$	4.98559	0.352534
$201$	−0.0307935	−0.00217201
$202$	7.70365	0.542027
$203$	5.89329	0.413628
$204$	−2.72525	−0.190805
$205$	0.245890	0.0171737
$206$	10.4983	0.731450
$207$	−3.48678	−0.242348
$208$	3.04657	0.211242
$209$	−0.721077	−0.0498779
$210$	0.0771656	0.00532493
$211$	−28.6731	−1.97394	−0.986970	−	0.160904i	$-0.948559\pi$
$211$	−28.6731	−1.97394	−0.986970	+	0.160904i	$0.948559\pi$
$212$	−9.56168	−0.656699
$213$	−5.16478	−0.353885
$214$	13.5895	0.928959
$215$	0.649671	0.0443072
$216$	−3.59121	−0.244351
$217$	−0.347369	−0.0235810
$218$	−9.75411	−0.660632
$219$	−2.12004	−0.143259
$220$	0.0704897	0.00475241
$221$	12.9163	0.868847
$222$	−0.483269	−0.0324349
$223$	−18.0627	−1.20957	−0.604784	−	0.796390i	$-0.706740\pi$
$223$	−18.0627	−1.20957	−0.604784	+	0.796390i	$0.706740\pi$
$224$	1.00000	0.0668153
$225$	12.8967	0.859783
$226$	−3.61651	−0.240567
$227$	−9.99480	−0.663378	−0.331689	−	0.943389i	$-0.607618\pi$
$227$	−9.99480	−0.663378	−0.331689	+	0.943389i	$0.607618\pi$
$228$	−0.789369	−0.0522772
$229$	−21.3932	−1.41370	−0.706851	−	0.707362i	$-0.749885\pi$
$229$	−21.3932	−1.41370	−0.706851	+	0.707362i	$0.749885\pi$
$230$	0.161810	0.0106695
$231$	−0.377448	−0.0248343
$232$	5.89329	0.386914
$233$	−17.8641	−1.17032	−0.585159	−	0.810919i	$-0.698968\pi$
$233$	−17.8641	−1.17032	−0.585159	+	0.810919i	$0.698968\pi$
$234$	7.88088	0.515189
$235$	−0.169080	−0.0110296
$236$	8.10850	0.527819
$237$	6.22974	0.404665
$238$	4.23963	0.274814
$239$	−0.346855	−0.0224362	−0.0112181	−	0.999937i	$-0.503571\pi$
$239$	−0.346855	−0.0224362	−0.0112181	+	0.999937i	$0.503571\pi$
$240$	0.0771656	0.00498102
$241$	17.1778	1.10652	0.553260	−	0.833009i	$-0.313384\pi$
$241$	17.1778	1.10652	0.553260	+	0.833009i	$0.313384\pi$
$242$	10.6552	0.684943
$243$	−14.2782	−0.915946
$244$	10.0800	0.645309
$245$	−0.120045	−0.00766942
$246$	−1.31666	−0.0839472
$247$	3.74122	0.238048
$248$	−0.347369	−0.0220580
$249$	−6.79987	−0.430924
$250$	−1.19872	−0.0758140
$251$	3.65298	0.230574	0.115287	−	0.993332i	$-0.463221\pi$
$251$	3.65298	0.230574	0.115287	+	0.993332i	$0.463221\pi$
$252$	2.58680	0.162953
$253$	−0.791481	−0.0497600
$254$	−1.62844	−0.102178
$255$	0.327154	0.0204872
$256$	1.00000	0.0625000
$257$	7.15975	0.446613	0.223307	−	0.974748i	$-0.428315\pi$
$257$	7.15975	0.446613	0.223307	+	0.974748i	$0.428315\pi$
$258$	−3.47877	−0.216579
$259$	0.751815	0.0467155
$260$	−0.365727	−0.0226814
$261$	15.2448	0.943629
$262$	7.36727	0.455151
$263$	17.7471	1.09433	0.547166	−	0.837024i	$-0.315707\pi$
$263$	17.7471	1.09433	0.547166	+	0.837024i	$0.315707\pi$
$264$	−0.377448	−0.0232303
$265$	1.14784	0.0705110
$266$	1.22801	0.0752941
$267$	−5.50961	−0.337183
$268$	0.0479050	0.00292626
$269$	−24.1717	−1.47377	−0.736887	−	0.676016i	$-0.763705\pi$
$269$	−24.1717	−1.47377	−0.736887	+	0.676016i	$0.763705\pi$
$270$	0.431109	0.0262365
$271$	−21.0843	−1.28078	−0.640389	−	0.768050i	$-0.721227\pi$
$271$	−21.0843	−1.28078	−0.640389	+	0.768050i	$0.721227\pi$
$272$	4.23963	0.257065
$273$	1.95834	0.118524
$274$	21.4838	1.29789
$275$	2.92750	0.176535
$276$	−0.866441	−0.0521536
$277$	5.88459	0.353571	0.176785	−	0.984249i	$-0.443430\pi$
$277$	5.88459	0.353571	0.176785	+	0.984249i	$0.443430\pi$
$278$	−14.7936	−0.887260
$279$	−0.898576	−0.0537963
$280$	−0.120045	−0.00717409
$281$	−0.242027	−0.0144381	−0.00721906	−	0.999974i	$-0.502298\pi$
$281$	−0.242027	−0.0144381	−0.00721906	+	0.999974i	$0.502298\pi$
$282$	0.905368	0.0539139
$283$	−20.3070	−1.20713	−0.603563	−	0.797315i	$-0.706253\pi$
$283$	−20.3070	−1.20713	−0.603563	+	0.797315i	$0.706253\pi$
$284$	8.03477	0.476776
$285$	0.0947601	0.00561311
$286$	1.78892	0.105781
$287$	2.04831	0.120908
$288$	2.58680	0.152429
$289$	0.974465	0.0573215
$290$	−0.707463	−0.0415437
$291$	−4.85562	−0.284642
$292$	3.29812	0.193008
$293$	22.2804	1.30163	0.650817	−	0.759234i	$-0.274426\pi$
$293$	22.2804	1.30163	0.650817	+	0.759234i	$0.274426\pi$
$294$	0.642803	0.0374890
$295$	−0.973389	−0.0566729
$296$	0.751815	0.0436984
$297$	−2.10873	−0.122361
$298$	−9.52393	−0.551707
$299$	4.10650	0.237485
$300$	3.20475	0.185026
$301$	5.41187	0.311935
$302$	−9.02759	−0.519479
$303$	4.95193	0.284481
$304$	1.22801	0.0704312
$305$	−1.21006	−0.0692880
$306$	10.9671	0.626947
$307$	4.86564	0.277697	0.138848	−	0.990314i	$-0.455660\pi$
$307$	4.86564	0.277697	0.138848	+	0.990314i	$0.455660\pi$
$308$	0.587191	0.0334583
$309$	6.74833	0.383899
$310$	0.0417001	0.00236841
$311$	−8.62575	−0.489121	−0.244561	−	0.969634i	$-0.578644\pi$
$311$	−8.62575	−0.489121	−0.244561	+	0.969634i	$0.578644\pi$
$312$	1.95834	0.110869
$313$	4.17015	0.235711	0.117856	−	0.993031i	$-0.462398\pi$
$313$	4.17015	0.235711	0.117856	+	0.993031i	$0.462398\pi$
$314$	−6.01529	−0.339462
$315$	−0.310534	−0.0174966
$316$	−9.69152	−0.545191
$317$	−12.7693	−0.717196	−0.358598	−	0.933492i	$-0.616745\pi$
$317$	−12.7693	−0.717196	−0.358598	+	0.933492i	$0.616745\pi$
$318$	−6.14627	−0.344666
$319$	3.46049	0.193750
$320$	−0.120045	−0.00671075
$321$	8.73537	0.487561
$322$	1.34791	0.0751161
$323$	5.20631	0.289687
$324$	5.45197	0.302887
$325$	−15.1889	−0.842531
$326$	0.894134	0.0495215
$327$	−6.26997	−0.346730
$328$	2.04831	0.113099
$329$	−1.40847	−0.0776514
$330$	0.0453110	0.00249429
$331$	−31.4888	−1.73078	−0.865390	−	0.501098i	$-0.832929\pi$
$331$	−31.4888	−1.73078	−0.865390	+	0.501098i	$0.832929\pi$
$332$	10.5785	0.580568
$333$	1.94480	0.106574
$334$	20.5478	1.12433
$335$	−0.00575078	−0.000314199 0
$336$	0.642803	0.0350678
$337$	−18.0696	−0.984311	−0.492156	−	0.870507i	$-0.663791\pi$
$337$	−18.0696	−0.984311	−0.492156	+	0.870507i	$0.663791\pi$
$338$	3.71841	0.202255
$339$	−2.32471	−0.126261
$340$	−0.508948	−0.0276016
$341$	−0.203972	−0.0110457
$342$	3.17662	0.171772
$343$	−1.00000	−0.0539949
$344$	5.41187	0.291789
$345$	0.104012	0.00559983
$346$	9.57340	0.514669
$347$	−9.92555	−0.532831	−0.266416	−	0.963858i	$-0.585839\pi$
$347$	−9.92555	−0.532831	−0.266416	+	0.963858i	$0.585839\pi$
$348$	3.78823	0.203070
$349$	30.8329	1.65045	0.825223	−	0.564806i	$-0.191049\pi$
$349$	30.8329	1.65045	0.825223	+	0.564806i	$0.191049\pi$
$350$	−4.98559	−0.266491
$351$	10.9409	0.583981
$352$	0.587191	0.0312974
$353$	35.4920	1.88905	0.944525	−	0.328441i	$-0.106523\pi$
$353$	35.4920	1.88905	0.944525	+	0.328441i	$0.106523\pi$
$354$	5.21217	0.277024
$355$	−0.964538	−0.0511924
$356$	8.57123	0.454274
$357$	2.72525	0.144235
$358$	−3.29028	−0.173897
$359$	−11.9635	−0.631409	−0.315705	−	0.948857i	$-0.602241\pi$
$359$	−11.9635	−0.631409	−0.315705	+	0.948857i	$0.602241\pi$
$360$	−0.310534	−0.0163666
$361$	−17.4920	−0.920631
$362$	−6.24094	−0.328016
$363$	6.84920	0.359490
$364$	−3.04657	−0.159684
$365$	−0.395924	−0.0207236
$366$	6.47948	0.338688
$367$	−5.71718	−0.298435	−0.149217	−	0.988804i	$-0.547675\pi$
$367$	−5.71718	−0.298435	−0.149217	+	0.988804i	$0.547675\pi$
$368$	1.34791	0.0702647
$369$	5.29858	0.275833
$370$	−0.0902520	−0.00469198
$371$	9.56168	0.496417
$372$	−0.223290	−0.0115770
$373$	19.7339	1.02178	0.510891	−	0.859646i	$-0.329316\pi$
$373$	19.7339	1.02178	0.510891	+	0.859646i	$0.329316\pi$
$374$	2.48947	0.128728
$375$	−0.770544	−0.0397907
$376$	−1.40847	−0.0726362
$377$	−17.9543	−0.924695
$378$	3.59121	0.184712
$379$	−10.2972	−0.528934	−0.264467	−	0.964395i	$-0.585196\pi$
$379$	−10.2972	−0.528934	−0.264467	+	0.964395i	$0.585196\pi$
$380$	−0.147417	−0.00756233
$381$	−1.04677	−0.0536276
$382$	21.3354	1.09161
$383$	−19.4910	−0.995945	−0.497973	−	0.867193i	$-0.665922\pi$
$383$	−19.4910	−0.995945	−0.497973	+	0.867193i	$0.665922\pi$
$384$	0.642803	0.0328029
$385$	−0.0704897	−0.00359249
$386$	−25.9170	−1.31914
$387$	13.9995	0.711632
$388$	7.55383	0.383487
$389$	0.712481	0.0361242	0.0180621	−	0.999837i	$-0.494250\pi$
$389$	0.712481	0.0361242	0.0180621	+	0.999837i	$0.494250\pi$
$390$	−0.235090	−0.0119043
$391$	5.71464	0.289002
$392$	−1.00000	−0.0505076
$393$	4.73570	0.238885
$394$	19.3789	0.976294
$395$	1.16342	0.0585382
$396$	1.51895	0.0763301
$397$	15.1454	0.760124	0.380062	−	0.924961i	$-0.375903\pi$
$397$	15.1454	0.760124	0.380062	+	0.924961i	$0.375903\pi$
$398$	−10.1177	−0.507154
$399$	0.789369	0.0395179
$400$	−4.98559	−0.249279
$401$	5.94122	0.296691	0.148345	−	0.988936i	$-0.452605\pi$
$401$	5.94122	0.296691	0.148345	+	0.988936i	$0.452605\pi$
$402$	0.0307935	0.00153584
$403$	1.05828	0.0527169
$404$	−7.70365	−0.383271
$405$	−0.654484	−0.0325216
$406$	−5.89329	−0.292479
$407$	0.441460	0.0218823
$408$	2.72525	0.134920
$409$	−14.9971	−0.741558	−0.370779	−	0.928721i	$-0.620909\pi$
$409$	−14.9971	−0.741558	−0.370779	+	0.928721i	$0.620909\pi$
$410$	−0.245890	−0.0121437
$411$	13.8099	0.681191
$412$	−10.4983	−0.517213
$413$	−8.10850	−0.398993
$414$	3.48678	0.171366
$415$	−1.26990	−0.0623367
$416$	−3.04657	−0.149370
$417$	−9.50936	−0.465675
$418$	0.721077	0.0352690
$419$	−10.1199	−0.494389	−0.247194	−	0.968966i	$-0.579509\pi$
$419$	−10.1199	−0.494389	−0.247194	+	0.968966i	$0.579509\pi$
$420$	−0.0771656	−0.00376530
$421$	−11.1236	−0.542130	−0.271065	−	0.962561i	$-0.587376\pi$
$421$	−11.1236	−0.542130	−0.271065	+	0.962561i	$0.587376\pi$
$422$	28.6731	1.39579
$423$	−3.64343	−0.177150
$424$	9.56168	0.464356
$425$	−21.1371	−1.02530
$426$	5.16478	0.250234
$427$	−10.0800	−0.487807
$428$	−13.5895	−0.656873
$429$	1.14992	0.0555188
$430$	−0.649671	−0.0313299
$431$	−1.00000	−0.0481683
$431$	−1.00000	−0.0481683
$432$	3.59121	0.172782
$433$	−12.4696	−0.599250	−0.299625	−	0.954057i	$-0.596862\pi$
$433$	−12.4696	−0.599250	−0.299625	+	0.954057i	$0.596862\pi$
$434$	0.347369	0.0166743
$435$	−0.454759	−0.0218040
$436$	9.75411	0.467137
$437$	1.65525	0.0791812
$438$	2.12004	0.101300
$439$	−30.2819	−1.44527	−0.722637	−	0.691228i	$-0.757070\pi$
$439$	−30.2819	−1.44527	−0.722637	+	0.691228i	$0.757070\pi$
$440$	−0.0704897	−0.00336046
$441$	−2.58680	−0.123181
$442$	−12.9163	−0.614367
$443$	−22.8955	−1.08780	−0.543899	−	0.839151i	$-0.683052\pi$
$443$	−22.8955	−1.08780	−0.543899	+	0.839151i	$0.683052\pi$
$444$	0.483269	0.0229349
$445$	−1.02894	−0.0487763
$446$	18.0627	0.855293
$447$	−6.12201	−0.289561
$448$	−1.00000	−0.0472456
$449$	−23.8358	−1.12488	−0.562440	−	0.826838i	$-0.690137\pi$
$449$	−23.8358	−1.12488	−0.562440	+	0.826838i	$0.690137\pi$
$450$	−12.8967	−0.607958
$451$	1.20275	0.0566353
$452$	3.61651	0.170106
$453$	−5.80296	−0.272647
$454$	9.99480	0.469079
$455$	0.365727	0.0171455
$456$	0.789369	0.0369656
$457$	4.30683	0.201465	0.100733	−	0.994914i	$-0.467881\pi$
$457$	4.30683	0.201465	0.100733	+	0.994914i	$0.467881\pi$
$458$	21.3932	0.999639
$459$	15.2254	0.710662
$460$	−0.161810	−0.00754445
$461$	−12.1622	−0.566449	−0.283224	−	0.959054i	$-0.591404\pi$
$461$	−12.1622	−0.566449	−0.283224	+	0.959054i	$0.591404\pi$
$462$	0.377448	0.0175605
$463$	18.4344	0.856720	0.428360	−	0.903608i	$-0.359092\pi$
$463$	18.4344	0.856720	0.428360	+	0.903608i	$0.359092\pi$
$464$	−5.89329	−0.273589
$465$	0.0268049	0.00124305
$466$	17.8641	0.827540
$467$	−12.9063	−0.597235	−0.298617	−	0.954373i	$-0.596525\pi$
$467$	−12.9063	−0.597235	−0.298617	+	0.954373i	$0.596525\pi$
$468$	−7.88088	−0.364294
$469$	−0.0479050	−0.00221205
$470$	0.169080	0.00779909
$471$	−3.86665	−0.178166
$472$	−8.10850	−0.373224
$473$	3.17780	0.146116
$474$	−6.22974	−0.286141
$475$	−6.12235	−0.280913
$476$	−4.23963	−0.194323
$477$	24.7342	1.13250
$478$	0.346855	0.0158648
$479$	−33.7619	−1.54262	−0.771310	−	0.636460i	$-0.780398\pi$
$479$	−33.7619	−1.54262	−0.771310	+	0.636460i	$0.780398\pi$
$480$	−0.0771656	−0.00352211
$481$	−2.29046	−0.104436
$482$	−17.1778	−0.782428
$483$	0.866441	0.0394244
$484$	−10.6552	−0.484328
$485$	−0.906802	−0.0411758
$486$	14.2782	0.647672
$487$	−2.36101	−0.106987	−0.0534937	−	0.998568i	$-0.517036\pi$
$487$	−2.36101	−0.106987	−0.0534937	+	0.998568i	$0.517036\pi$
$488$	−10.0800	−0.456302
$489$	0.574752	0.0259912
$490$	0.120045	0.00542310
$491$	7.08683	0.319824	0.159912	−	0.987131i	$-0.448879\pi$
$491$	7.08683	0.319824	0.159912	+	0.987131i	$0.448879\pi$
$492$	1.31666	0.0593596
$493$	−24.9854	−1.12528
$494$	−3.74122	−0.168325
$495$	−0.182343	−0.00819571
$496$	0.347369	0.0155973
$497$	−8.03477	−0.360409
$498$	6.79987	0.304709
$499$	33.6334	1.50564	0.752818	−	0.658229i	$-0.228694\pi$
$499$	33.6334	1.50564	0.752818	+	0.658229i	$0.228694\pi$
$500$	1.19872	0.0536086
$501$	13.2082	0.590098
$502$	−3.65298	−0.163041
$503$	4.10687	0.183116	0.0915582	−	0.995800i	$-0.470815\pi$
$503$	4.10687	0.183116	0.0915582	+	0.995800i	$0.470815\pi$
$504$	−2.58680	−0.115225
$505$	0.924788	0.0411525
$506$	0.791481	0.0351856
$507$	2.39020	0.106153
$508$	1.62844	0.0722505
$509$	−20.6264	−0.914251	−0.457125	−	0.889402i	$-0.651121\pi$
$509$	−20.6264	−0.914251	−0.457125	+	0.889402i	$0.651121\pi$
$510$	−0.327154	−0.0144866
$511$	−3.29812	−0.145900
$512$	−1.00000	−0.0441942
$513$	4.41005	0.194708
$514$	−7.15975	−0.315803
$515$	1.26027	0.0555342
$516$	3.47877	0.153144
$517$	−0.827041	−0.0363732
$518$	−0.751815	−0.0330329
$519$	6.15381	0.270122
$520$	0.365727	0.0160382
$521$	−11.7787	−0.516036	−0.258018	−	0.966140i	$-0.583069\pi$
$521$	−11.7787	−0.516036	−0.258018	+	0.966140i	$0.583069\pi$
$522$	−15.2448	−0.667247
$523$	−8.35537	−0.365355	−0.182677	−	0.983173i	$-0.558476\pi$
$523$	−8.35537	−0.365355	−0.182677	+	0.983173i	$0.558476\pi$
$524$	−7.36727	−0.321841
$525$	−3.20475	−0.139867
$526$	−17.7471	−0.773809
$527$	1.47272	0.0641525
$528$	0.377448	0.0164263
$529$	−21.1831	−0.921006
$530$	−1.14784	−0.0498588
$531$	−20.9751	−0.910242
$532$	−1.22801	−0.0532410
$533$	−6.24032	−0.270298
$534$	5.50961	0.238424
$535$	1.63136	0.0705297
$536$	−0.0479050	−0.00206918
$537$	−2.11500	−0.0912690
$538$	24.1717	1.04212
$539$	−0.587191	−0.0252921
$540$	−0.431109	−0.0185520
$541$	−34.8630	−1.49888	−0.749438	−	0.662074i	$-0.769676\pi$
$541$	−34.8630	−1.49888	−0.749438	+	0.662074i	$0.769676\pi$
$542$	21.0843	0.905647
$543$	−4.01169	−0.172158
$544$	−4.23963	−0.181773
$545$	−1.17094	−0.0501574
$546$	−1.95834	−0.0838094
$547$	−25.9880	−1.11117	−0.555584	−	0.831461i	$-0.687505\pi$
$547$	−25.9880	−1.11117	−0.555584	+	0.831461i	$0.687505\pi$
$548$	−21.4838	−0.917744
$549$	−26.0751	−1.11286
$550$	−2.92750	−0.124829
$551$	−7.23702	−0.308308
$552$	0.866441	0.0368782
$553$	9.69152	0.412125
$554$	−5.88459	−0.250012
$555$	−0.0580143	−0.00246257
$556$	14.7936	0.627388
$557$	−3.18754	−0.135060	−0.0675302	−	0.997717i	$-0.521512\pi$
$557$	−3.18754	−0.135060	−0.0675302	+	0.997717i	$0.521512\pi$
$558$	0.898576	0.0380398
$559$	−16.4876	−0.697353
$560$	0.120045	0.00507285
$561$	1.60024	0.0675623
$562$	0.242027	0.0102093
$563$	−3.00991	−0.126853	−0.0634263	−	0.997987i	$-0.520203\pi$
$563$	−3.00991	−0.126853	−0.0634263	+	0.997987i	$0.520203\pi$
$564$	−0.905368	−0.0381229
$565$	−0.434146	−0.0182647
$566$	20.3070	0.853567
$567$	−5.45197	−0.228961
$568$	−8.03477	−0.337132
$569$	−42.9315	−1.79978	−0.899891	−	0.436115i	$-0.856354\pi$
$569$	−42.9315	−1.79978	−0.899891	+	0.436115i	$0.856354\pi$
$570$	−0.0947601	−0.00396906
$571$	7.82292	0.327379	0.163689	−	0.986512i	$-0.447661\pi$
$571$	7.82292	0.327379	0.163689	+	0.986512i	$0.447661\pi$
$572$	−1.78892	−0.0747985
$573$	13.7145	0.572930
$574$	−2.04831	−0.0854948
$575$	−6.72013	−0.280249
$576$	−2.58680	−0.107784
$577$	33.6217	1.39969	0.699845	−	0.714294i	$-0.253252\pi$
$577$	33.6217	1.39969	0.699845	+	0.714294i	$0.253252\pi$
$578$	−0.974465	−0.0405324
$579$	−16.6595	−0.692347
$580$	0.707463	0.0293758
$581$	−10.5785	−0.438868
$582$	4.85562	0.201272
$583$	5.61453	0.232530
$584$	−3.29812	−0.136477
$585$	0.946064	0.0391149
$586$	−22.2804	−0.920395
$587$	−15.3325	−0.632840	−0.316420	−	0.948619i	$-0.602481\pi$
$587$	−15.3325	−0.632840	−0.316420	+	0.948619i	$0.602481\pi$
$588$	−0.642803	−0.0265088
$589$	0.426573	0.0175766
$590$	0.973389	0.0400738
$591$	12.4568	0.512405
$592$	−0.751815	−0.0308994
$593$	−5.63653	−0.231464	−0.115732	−	0.993280i	$-0.536921\pi$
$593$	−5.63653	−0.231464	−0.115732	+	0.993280i	$0.536921\pi$
$594$	2.10873	0.0865223
$595$	0.508948	0.0208648
$596$	9.52393	0.390116
$597$	−6.50368	−0.266178
$598$	−4.10650	−0.167927
$599$	4.62114	0.188815	0.0944073	−	0.995534i	$-0.469904\pi$
$599$	4.62114	0.188815	0.0944073	+	0.995534i	$0.469904\pi$
$600$	−3.20475	−0.130833
$601$	26.5126	1.08147	0.540735	−	0.841193i	$-0.318146\pi$
$601$	26.5126	1.08147	0.540735	+	0.841193i	$0.318146\pi$
$602$	−5.41187	−0.220571
$603$	−0.123921	−0.00504645
$604$	9.02759	0.367327
$605$	1.27911	0.0520032
$606$	−4.95193	−0.201158
$607$	45.5966	1.85071	0.925354	−	0.379104i	$-0.123768\pi$
$607$	45.5966	1.85071	0.925354	+	0.379104i	$0.123768\pi$
$608$	−1.22801	−0.0498024
$609$	−3.78823	−0.153507
$610$	1.21006	0.0489940
$611$	4.29100	0.173595
$612$	−10.9671	−0.443318
$613$	15.5244	0.627025	0.313513	−	0.949584i	$-0.398494\pi$
$613$	15.5244	0.627025	0.313513	+	0.949584i	$0.398494\pi$
$614$	−4.86564	−0.196361
$615$	−0.158059	−0.00637356
$616$	−0.587191	−0.0236586
$617$	14.6524	0.589885	0.294942	−	0.955515i	$-0.404700\pi$
$617$	14.6524	0.589885	0.294942	+	0.955515i	$0.404700\pi$
$618$	−6.74833	−0.271458
$619$	−44.6110	−1.79307	−0.896533	−	0.442976i	$-0.853923\pi$
$619$	−44.6110	−1.79307	−0.896533	+	0.442976i	$0.853923\pi$
$620$	−0.0417001	−0.00167472
$621$	4.84063	0.194248
$622$	8.62575	0.345861
$623$	−8.57123	−0.343399
$624$	−1.95834	−0.0783965
$625$	24.7840	0.991362
$626$	−4.17015	−0.166673
$627$	0.463511	0.0185108
$628$	6.01529	0.240036
$629$	−3.18742	−0.127091
$630$	0.310534	0.0123720
$631$	0.0168006	0.000668820 0	0.000334410	−	1.00000i	$-0.499894\pi$
$631$	0.0168006	0.000668820 0	0.000334410		1.00000i	$0.499894\pi$
$632$	9.69152	0.385508
$633$	18.4312	0.732574
$634$	12.7693	0.507134
$635$	−0.195487	−0.00775767
$636$	6.14627	0.243716
$637$	3.04657	0.120710
$638$	−3.46049	−0.137002
$639$	−20.7844	−0.822217
$640$	0.120045	0.00474521
$641$	32.6865	1.29104	0.645520	−	0.763743i	$-0.276641\pi$
$641$	32.6865	1.29104	0.645520	+	0.763743i	$0.276641\pi$
$642$	−8.73537	−0.344758
$643$	13.3739	0.527417	0.263708	−	0.964602i	$-0.415054\pi$
$643$	13.3739	0.527417	0.263708	+	0.964602i	$0.415054\pi$
$644$	−1.34791	−0.0531151
$645$	−0.417610	−0.0164434
$646$	−5.20631	−0.204839
$647$	−32.1818	−1.26520	−0.632598	−	0.774480i	$-0.718012\pi$
$647$	−32.1818	−1.26520	−0.632598	+	0.774480i	$0.718012\pi$
$648$	−5.45197	−0.214174
$649$	−4.76124	−0.186895
$650$	15.1889	0.595760
$651$	0.223290	0.00875142
$652$	−0.894134	−0.0350170
$653$	−48.7323	−1.90704	−0.953521	−	0.301327i	$-0.902570\pi$
$653$	−48.7323	−1.90704	−0.953521	+	0.301327i	$0.902570\pi$
$654$	6.26997	0.245175
$655$	0.884407	0.0345567
$656$	−2.04831	−0.0799731
$657$	−8.53159	−0.332849
$658$	1.40847	0.0549078
$659$	−45.1570	−1.75907	−0.879534	−	0.475836i	$-0.842146\pi$
$659$	−45.1570	−1.75907	−0.879534	+	0.475836i	$0.842146\pi$
$660$	−0.0453110	−0.00176373
$661$	9.91925	0.385814	0.192907	−	0.981217i	$-0.438208\pi$
$661$	9.91925	0.385814	0.192907	+	0.981217i	$0.438208\pi$
$662$	31.4888	1.22385
$663$	−8.30266	−0.322449
$664$	−10.5785	−0.410524
$665$	0.147417	0.00571659
$666$	−1.94480	−0.0753594
$667$	−7.94363	−0.307579
$668$	−20.5478	−0.795018
$669$	11.6108	0.448898
$670$	0.00575078	0.000222172 0
$671$	−5.91892	−0.228497
$672$	−0.642803	−0.0247967
$673$	11.1999	0.431724	0.215862	−	0.976424i	$-0.430744\pi$
$673$	11.1999	0.431724	0.215862	+	0.976424i	$0.430744\pi$
$674$	18.0696	0.696013
$675$	−17.9043	−0.689138
$676$	−3.71841	−0.143016
$677$	−22.2347	−0.854548	−0.427274	−	0.904122i	$-0.640526\pi$
$677$	−22.2347	−0.854548	−0.427274	+	0.904122i	$0.640526\pi$
$678$	2.32471	0.0892798
$679$	−7.55383	−0.289889
$680$	0.508948	0.0195173
$681$	6.42469	0.246195
$682$	0.203972	0.00781050
$683$	10.0016	0.382700	0.191350	−	0.981522i	$-0.438713\pi$
$683$	10.0016	0.382700	0.191350	+	0.981522i	$0.438713\pi$
$684$	−3.17662	−0.121461
$685$	2.57904	0.0985399
$686$	1.00000	0.0381802
$687$	13.7516	0.524657
$688$	−5.41187	−0.206326
$689$	−29.1303	−1.10978
$690$	−0.104012	−0.00395968
$691$	20.9956	0.798709	0.399354	−	0.916797i	$-0.369234\pi$
$691$	20.9956	0.798709	0.399354	+	0.916797i	$0.369234\pi$
$692$	−9.57340	−0.363926
$693$	−1.51895	−0.0577001
$694$	9.92555	0.376769
$695$	−1.77590	−0.0673638
$696$	−3.78823	−0.143592
$697$	−8.68408	−0.328933
$698$	−30.8329	−1.16704
$699$	11.4831	0.434331
$700$	4.98559	0.188438
$701$	−32.5488	−1.22935	−0.614676	−	0.788780i	$-0.710713\pi$
$701$	−32.5488	−1.22935	−0.614676	+	0.788780i	$0.710713\pi$
$702$	−10.9409	−0.412937
$703$	−0.923237	−0.0348205
$704$	−0.587191	−0.0221306
$705$	0.108685	0.00409333
$706$	−35.4920	−1.33576
$707$	7.70365	0.289726
$708$	−5.21217	−0.195885
$709$	12.8443	0.482376	0.241188	−	0.970478i	$-0.422463\pi$
$709$	12.8443	0.482376	0.241188	+	0.970478i	$0.422463\pi$
$710$	0.964538	0.0361985
$711$	25.0701	0.940201
$712$	−8.57123	−0.321220
$713$	0.468222	0.0175351
$714$	−2.72525	−0.101990
$715$	0.214752	0.00803126
$716$	3.29028	0.122963
$717$	0.222960	0.00832658
$718$	11.9635	0.446474
$719$	34.5840	1.28976	0.644882	−	0.764282i	$-0.276906\pi$
$719$	34.5840	1.28976	0.644882	+	0.764282i	$0.276906\pi$
$720$	0.310534	0.0115729
$721$	10.4983	0.390977
$722$	17.4920	0.650985
$723$	−11.0420	−0.410655
$724$	6.24094	0.231943
$725$	29.3815	1.09120
$726$	−6.84920	−0.254198
$727$	−5.51382	−0.204496	−0.102248	−	0.994759i	$-0.532604\pi$
$727$	−5.51382	−0.204496	−0.102248	+	0.994759i	$0.532604\pi$
$728$	3.04657	0.112913
$729$	−7.17784	−0.265846
$730$	0.395924	0.0146538
$731$	−22.9443	−0.848627
$732$	−6.47948	−0.239489
$733$	28.1994	1.04157	0.520784	−	0.853689i	$-0.325640\pi$
$733$	28.1994	1.04157	0.520784	+	0.853689i	$0.325640\pi$
$734$	5.71718	0.211025
$735$	0.0771656	0.00284630
$736$	−1.34791	−0.0496846
$737$	−0.0281294	−0.00103616
$738$	−5.29858	−0.195043
$739$	−33.9662	−1.24947	−0.624734	−	0.780838i	$-0.714793\pi$
$739$	−33.9662	−1.24947	−0.624734	+	0.780838i	$0.714793\pi$
$740$	0.0902520	0.00331773
$741$	−2.40487	−0.0883450
$742$	−9.56168	−0.351020
$743$	18.1422	0.665574	0.332787	−	0.943002i	$-0.392011\pi$
$743$	18.1422	0.665574	0.332787	+	0.943002i	$0.392011\pi$
$744$	0.223290	0.00818621
$745$	−1.14331	−0.0418875
$746$	−19.7339	−0.722509
$747$	−27.3644	−1.00121
$748$	−2.48947	−0.0910242
$749$	13.5895	0.496549
$750$	0.770544	0.0281363
$751$	23.8607	0.870691	0.435346	−	0.900263i	$-0.356626\pi$
$751$	23.8607	0.870691	0.435346	+	0.900263i	$0.356626\pi$
$752$	1.40847	0.0513616
$753$	−2.34815	−0.0855712
$754$	17.9543	0.653858
$755$	−1.08372	−0.0394407
$756$	−3.59121	−0.130611
$757$	5.26836	0.191482	0.0957410	−	0.995406i	$-0.469478\pi$
$757$	5.26836	0.191482	0.0957410	+	0.995406i	$0.469478\pi$
$758$	10.2972	0.374013
$759$	0.508767	0.0184671
$760$	0.147417	0.00534738
$761$	−8.25697	−0.299315	−0.149657	−	0.988738i	$-0.547817\pi$
$761$	−8.25697	−0.299315	−0.149657	+	0.988738i	$0.547817\pi$
$762$	1.04677	0.0379204
$763$	−9.75411	−0.353122
$764$	−21.3354	−0.771888
$765$	1.31655	0.0476000
$766$	19.4910	0.704240
$767$	24.7031	0.891978
$768$	−0.642803	−0.0231952
$769$	−8.47549	−0.305634	−0.152817	−	0.988255i	$-0.548834\pi$
$769$	−8.47549	−0.305634	−0.152817	+	0.988255i	$0.548834\pi$
$770$	0.0704897	0.00254027
$771$	−4.60231	−0.165748
$772$	25.9170	0.932774
$773$	45.1663	1.62452	0.812260	−	0.583295i	$-0.198237\pi$
$773$	45.1663	1.62452	0.812260	+	0.583295i	$0.198237\pi$
$774$	−13.9995	−0.503200
$775$	−1.73184	−0.0622095
$776$	−7.55383	−0.271167
$777$	−0.483269	−0.0173372
$778$	−0.712481	−0.0255437
$779$	−2.51535	−0.0901216
$780$	0.235090	0.00841759
$781$	−4.71795	−0.168821
$782$	−5.71464	−0.204355
$783$	−21.1641	−0.756342
$784$	1.00000	0.0357143
$785$	−0.722108	−0.0257732
$786$	−4.73570	−0.168917
$787$	−19.4472	−0.693216	−0.346608	−	0.938010i	$-0.612667\pi$
$787$	−19.4472	−0.693216	−0.346608	+	0.938010i	$0.612667\pi$
$788$	−19.3789	−0.690344
$789$	−11.4079	−0.406131
$790$	−1.16342	−0.0413927
$791$	−3.61651	−0.128588
$792$	−1.51895	−0.0539735
$793$	30.7096	1.09053
$794$	−15.1454	−0.537489
$795$	−0.737832	−0.0261682
$796$	10.1177	0.358612
$797$	−3.79604	−0.134463	−0.0672314	−	0.997737i	$-0.521417\pi$
$797$	−3.79604	−0.134463	−0.0672314	+	0.997737i	$0.521417\pi$
$798$	−0.789369	−0.0279433
$799$	5.97139	0.211253
$800$	4.98559	0.176267
$801$	−22.1721	−0.783412
$802$	−5.94122	−0.209792
$803$	−1.93663	−0.0683421
$804$	−0.0307935	−0.00108600
$805$	0.161810	0.00570307
$806$	−1.05828	−0.0372765
$807$	15.5376	0.546951
$808$	7.70365	0.271013
$809$	31.4493	1.10570	0.552849	−	0.833281i	$-0.313541\pi$
$809$	31.4493	1.10570	0.552849	+	0.833281i	$0.313541\pi$
$810$	0.654484	0.0229962
$811$	−15.5107	−0.544653	−0.272327	−	0.962205i	$-0.587793\pi$
$811$	−15.5107	−0.544653	−0.272327	+	0.962205i	$0.587793\pi$
$812$	5.89329	0.206814
$813$	13.5530	0.475326
$814$	−0.441460	−0.0154731
$815$	0.107337	0.00375984
$816$	−2.72525	−0.0954027
$817$	−6.64583	−0.232508
$818$	14.9971	0.524361
$819$	7.88088	0.275380
$820$	0.245890	0.00858686
$821$	−18.5503	−0.647410	−0.323705	−	0.946158i	$-0.604928\pi$
$821$	−18.5503	−0.647410	−0.323705	+	0.946158i	$0.604928\pi$
$822$	−13.8099	−0.481675
$823$	22.9629	0.800437	0.400218	−	0.916420i	$-0.368934\pi$
$823$	22.9629	0.800437	0.400218	+	0.916420i	$0.368934\pi$
$824$	10.4983	0.365725
$825$	−1.88180	−0.0655160
$826$	8.10850	0.282131
$827$	1.21210	0.0421489	0.0210745	−	0.999778i	$-0.493291\pi$
$827$	1.21210	0.0421489	0.0210745	+	0.999778i	$0.493291\pi$
$828$	−3.48678	−0.121174
$829$	30.3146	1.05287	0.526435	−	0.850215i	$-0.323528\pi$
$829$	30.3146	1.05287	0.526435	+	0.850215i	$0.323528\pi$
$830$	1.26990	0.0440787
$831$	−3.78263	−0.131218
$832$	3.04657	0.105621
$833$	4.23963	0.146894
$834$	9.50936	0.329282
$835$	2.46667	0.0853626
$836$	−0.721077	−0.0249390
$837$	1.24748	0.0431191
$838$	10.1199	0.349586
$839$	−11.1159	−0.383764	−0.191882	−	0.981418i	$-0.561459\pi$
$839$	−11.1159	−0.383764	−0.191882	+	0.981418i	$0.561459\pi$
$840$	0.0771656	0.00266247
$841$	5.73090	0.197617
$842$	11.1236	0.383344
$843$	0.155576	0.00535831
$844$	−28.6731	−0.986970
$845$	0.446378	0.0153559
$846$	3.64343	0.125264
$847$	10.6552	0.366117
$848$	−9.56168	−0.328349
$849$	13.0534	0.447992
$850$	21.1371	0.724995
$851$	−1.01338	−0.0347382
$852$	−5.16478	−0.176942
$853$	−0.0703622	−0.00240915	−0.00120458	−	0.999999i	$-0.500383\pi$
$853$	−0.0703622	−0.00240915	−0.00120458	+	0.999999i	$0.500383\pi$
$854$	10.0800	0.344932
$855$	0.381339	0.0130415
$856$	13.5895	0.464479
$857$	12.8136	0.437704	0.218852	−	0.975758i	$-0.429769\pi$
$857$	12.8136	0.437704	0.218852	+	0.975758i	$0.429769\pi$
$858$	−1.14992	−0.0392577
$859$	23.0811	0.787516	0.393758	−	0.919214i	$-0.371175\pi$
$859$	23.0811	0.787516	0.393758	+	0.919214i	$0.371175\pi$
$860$	0.649671	0.0221536
$861$	−1.31666	−0.0448716
$862$	1.00000	0.0340601
$863$	18.4569	0.628282	0.314141	−	0.949376i	$-0.398284\pi$
$863$	18.4569	0.628282	0.314141	+	0.949376i	$0.398284\pi$
$864$	−3.59121	−0.122176
$865$	1.14924	0.0390755
$866$	12.4696	0.423734
$867$	−0.626389	−0.0212733
$868$	−0.347369	−0.0117905
$869$	5.69078	0.193046
$870$	0.454759	0.0154178
$871$	0.145946	0.00494519
$872$	−9.75411	−0.330316
$873$	−19.5403	−0.661338
$874$	−1.65525	−0.0559896
$875$	−1.19872	−0.0405243
$876$	−2.12004	−0.0716296
$877$	−40.4492	−1.36587	−0.682936	−	0.730479i	$-0.739297\pi$
$877$	−40.4492	−1.36587	−0.682936	+	0.730479i	$0.739297\pi$
$878$	30.2819	1.02196
$879$	−14.3219	−0.483066
$880$	0.0704897	0.00237621
$881$	17.8731	0.602159	0.301080	−	0.953599i	$-0.402653\pi$
$881$	17.8731	0.602159	0.301080	+	0.953599i	$0.402653\pi$
$882$	2.58680	0.0871022
$883$	9.45921	0.318328	0.159164	−	0.987252i	$-0.449120\pi$
$883$	9.45921	0.318328	0.159164	+	0.987252i	$0.449120\pi$
$884$	12.9163	0.434423
$885$	0.625697	0.0210326
$886$	22.8955	0.769189
$887$	−34.0636	−1.14374	−0.571872	−	0.820343i	$-0.693783\pi$
$887$	−34.0636	−1.14374	−0.571872	+	0.820343i	$0.693783\pi$
$888$	−0.483269	−0.0162175
$889$	−1.62844	−0.0546162
$890$	1.02894	0.0344900
$891$	−3.20135	−0.107249
$892$	−18.0627	−0.604784
$893$	1.72961	0.0578793
$894$	6.12201	0.204751
$895$	−0.394983	−0.0132028
$896$	1.00000	0.0334077
$897$	−2.63967	−0.0881361
$898$	23.8358	0.795410
$899$	−2.04715	−0.0682762
$900$	12.8967	0.429891
$901$	−40.5380	−1.35052
$902$	−1.20275	−0.0400472
$903$	−3.47877	−0.115766
$904$	−3.61651	−0.120283
$905$	−0.749196	−0.0249041
$906$	5.80296	0.192791
$907$	14.6992	0.488080	0.244040	−	0.969765i	$-0.421527\pi$
$907$	14.6992	0.488080	0.244040	+	0.969765i	$0.421527\pi$
$908$	−9.99480	−0.331689
$909$	19.9278	0.660965
$910$	−0.365727	−0.0121237
$911$	−22.2955	−0.738683	−0.369342	−	0.929294i	$-0.620417\pi$
$911$	−22.2955	−0.738683	−0.369342	+	0.929294i	$0.620417\pi$
$912$	−0.789369	−0.0261386
$913$	−6.21158	−0.205573
$914$	−4.30683	−0.142457
$915$	0.777832	0.0257143
$916$	−21.3932	−0.706851
$917$	7.36727	0.243289
$918$	−15.2254	−0.502514
$919$	17.1843	0.566857	0.283429	−	0.958993i	$-0.408528\pi$
$919$	17.1843	0.566857	0.283429	+	0.958993i	$0.408528\pi$
$920$	0.161810	0.00533473
$921$	−3.12765	−0.103060
$922$	12.1622	0.400540
$923$	24.4785	0.805720
$924$	−0.377448	−0.0124171
$925$	3.74824	0.123241
$926$	−18.4344	−0.605792
$927$	27.1570	0.891953
$928$	5.89329	0.193457
$929$	−45.7037	−1.49949	−0.749745	−	0.661727i	$-0.769824\pi$
$929$	−45.7037	−1.49949	−0.749745	+	0.661727i	$0.769824\pi$
$930$	−0.0268049	−0.000878969 0
$931$	1.22801	0.0402464
$932$	−17.8641	−0.585159
$933$	5.54466	0.181524
$934$	12.9063	0.422309
$935$	0.298850	0.00977344
$936$	7.88088	0.257595
$937$	−26.6791	−0.871569	−0.435785	−	0.900051i	$-0.643529\pi$
$937$	−26.6791	−0.871569	−0.435785	+	0.900051i	$0.643529\pi$
$938$	0.0479050	0.00156415
$939$	−2.68059	−0.0874777
$940$	−0.169080	−0.00551479
$941$	13.8437	0.451290	0.225645	−	0.974210i	$-0.427551\pi$
$941$	13.8437	0.451290	0.225645	+	0.974210i	$0.427551\pi$
$942$	3.86665	0.125982
$943$	−2.76094	−0.0899085
$944$	8.10850	0.263909
$945$	0.431109	0.0140240
$946$	−3.17780	−0.103319
$947$	54.9782	1.78655	0.893275	−	0.449511i	$-0.148402\pi$
$947$	54.9782	1.78655	0.893275	+	0.449511i	$0.148402\pi$
$948$	6.22974	0.202333
$949$	10.0480	0.326170
$950$	6.12235	0.198635
$951$	8.20815	0.266168
$952$	4.23963	0.137407
$953$	−30.9925	−1.00394	−0.501972	−	0.864884i	$-0.667392\pi$
$953$	−30.9925	−1.00394	−0.501972	+	0.864884i	$0.667392\pi$
$954$	−24.7342	−0.800799
$955$	2.56122	0.0828791
$956$	−0.346855	−0.0112181
$957$	−2.22441	−0.0719051
$958$	33.7619	1.09080
$959$	21.4838	0.693749
$960$	0.0771656	0.00249051
$961$	−30.8793	−0.996108
$962$	2.29046	0.0738473
$963$	35.1534	1.13280
$964$	17.1778	0.553260
$965$	−3.11122	−0.100154
$966$	−0.866441	−0.0278773
$967$	−5.81874	−0.187118	−0.0935590	−	0.995614i	$-0.529824\pi$
$967$	−5.81874	−0.187118	−0.0935590	+	0.995614i	$0.529824\pi$
$968$	10.6552	0.342471
$969$	−3.34663	−0.107509
$970$	0.906802	0.0291157
$971$	39.9785	1.28297	0.641485	−	0.767135i	$-0.278319\pi$
$971$	39.9785	1.28297	0.641485	+	0.767135i	$0.278319\pi$
$972$	−14.2782	−0.457973
$973$	−14.7936	−0.474260
$974$	2.36101	0.0756515
$975$	9.76350	0.312682
$976$	10.0800	0.322654
$977$	19.4490	0.622230	0.311115	−	0.950372i	$-0.399298\pi$
$977$	19.4490	0.622230	0.311115	+	0.950372i	$0.399298\pi$
$978$	−0.574752	−0.0183785
$979$	−5.03295	−0.160854
$980$	−0.120045	−0.00383471
$981$	−25.2320	−0.805595
$982$	−7.08683	−0.226150
$983$	−18.1767	−0.579746	−0.289873	−	0.957065i	$-0.593613\pi$
$983$	−18.1767	−0.579746	−0.289873	+	0.957065i	$0.593613\pi$
$984$	−1.31666	−0.0419736
$985$	2.32635	0.0741236
$986$	24.9854	0.795697
$987$	0.905368	0.0288182
$988$	3.74122	0.119024
$989$	−7.29472	−0.231958
$990$	0.182343	0.00579524
$991$	−48.8617	−1.55214	−0.776071	−	0.630645i	$-0.782790\pi$
$991$	−48.8617	−1.55214	−0.776071	+	0.630645i	$0.782790\pi$
$992$	−0.347369	−0.0110290
$993$	20.2411	0.642332
$994$	8.03477	0.254847
$995$	−1.21458	−0.0385049
$996$	−6.79987	−0.215462
$997$	10.8122	0.342426	0.171213	−	0.985234i	$-0.445231\pi$
$997$	10.8122	0.342426	0.171213	+	0.985234i	$0.445231\pi$
$998$	−33.6334	−1.06465
$999$	−2.69993	−0.0854220

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6034.2.a.o.1.12	✓	25

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6034.2.a.o.1.12	✓	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)

\(f(q)\)	\(=\)	\(q-1.00000 q^{2} -0.642803 q^{3} +1.00000 q^{4} -0.120045 q^{5} +0.642803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.58680 q^{9} +O(q^{10})\)	\(q-1.00000 q^{2} -0.642803 q^{3} +1.00000 q^{4} -0.120045 q^{5} +0.642803 q^{6} -1.00000 q^{7} -1.00000 q^{8} -2.58680 q^{9} +0.120045 q^{10} -0.587191 q^{11} -0.642803 q^{12} +3.04657 q^{13} +1.00000 q^{14} +0.0771656 q^{15} +1.00000 q^{16} +4.23963 q^{17} +2.58680 q^{18} +1.22801 q^{19} -0.120045 q^{20} +0.642803 q^{21} +0.587191 q^{22} +1.34791 q^{23} +0.642803 q^{24} -4.98559 q^{25} -3.04657 q^{26} +3.59121 q^{27} -1.00000 q^{28} -5.89329 q^{29} -0.0771656 q^{30} +0.347369 q^{31} -1.00000 q^{32} +0.377448 q^{33} -4.23963 q^{34} +0.120045 q^{35} -2.58680 q^{36} -0.751815 q^{37} -1.22801 q^{38} -1.95834 q^{39} +0.120045 q^{40} -2.04831 q^{41} -0.642803 q^{42} -5.41187 q^{43} -0.587191 q^{44} +0.310534 q^{45} -1.34791 q^{46} +1.40847 q^{47} -0.642803 q^{48} +1.00000 q^{49} +4.98559 q^{50} -2.72525 q^{51} +3.04657 q^{52} -9.56168 q^{53} -3.59121 q^{54} +0.0704897 q^{55} +1.00000 q^{56} -0.789369 q^{57} +5.89329 q^{58} +8.10850 q^{59} +0.0771656 q^{60} +10.0800 q^{61} -0.347369 q^{62} +2.58680 q^{63} +1.00000 q^{64} -0.365727 q^{65} -0.377448 q^{66} +0.0479050 q^{67} +4.23963 q^{68} -0.866441 q^{69} -0.120045 q^{70} +8.03477 q^{71} +2.58680 q^{72} +3.29812 q^{73} +0.751815 q^{74} +3.20475 q^{75} +1.22801 q^{76} +0.587191 q^{77} +1.95834 q^{78} -9.69152 q^{79} -0.120045 q^{80} +5.45197 q^{81} +2.04831 q^{82} +10.5785 q^{83} +0.642803 q^{84} -0.508948 q^{85} +5.41187 q^{86} +3.78823 q^{87} +0.587191 q^{88} +8.57123 q^{89} -0.310534 q^{90} -3.04657 q^{91} +1.34791 q^{92} -0.223290 q^{93} -1.40847 q^{94} -0.147417 q^{95} +0.642803 q^{96} +7.55383 q^{97} -1.00000 q^{98} +1.51895 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 25 q - 25 q^{2} - 4 q^{3} + 25 q^{4} + 4 q^{6} - 25 q^{7} - 25 q^{8} + 25 q^{9}+O(q^{10}) \) 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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