LMFDB - Embedded newform 6035.2.a.h.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [6035,2,Mod(1,6035)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(6035, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 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("6035.1");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 6035 = 5 \cdot 17 \cdot 71 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	6035.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:	$48.1897176198$
Analytic rank:	$0$
Dimension:	$59$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Character	$\chi$	$=$	6035.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.69345 q^{2} +3.39811 q^{3} +5.25470 q^{4} +1.00000 q^{5} -9.15266 q^{6} -4.44179 q^{7} -8.76637 q^{8} +8.54717 q^{9} +O(q^{10})$	\(q-2.69345 q^{2} +3.39811 q^{3} +5.25470 q^{4} +1.00000 q^{5} -9.15266 q^{6} -4.44179 q^{7} -8.76637 q^{8} +8.54717 q^{9} -2.69345 q^{10} -4.95320 q^{11} +17.8560 q^{12} +5.86554 q^{13} +11.9638 q^{14} +3.39811 q^{15} +13.1024 q^{16} -1.00000 q^{17} -23.0214 q^{18} +4.19249 q^{19} +5.25470 q^{20} -15.0937 q^{21} +13.3412 q^{22} -1.68508 q^{23} -29.7891 q^{24} +1.00000 q^{25} -15.7986 q^{26} +18.8499 q^{27} -23.3403 q^{28} -4.59613 q^{29} -9.15266 q^{30} -0.781463 q^{31} -17.7581 q^{32} -16.8315 q^{33} +2.69345 q^{34} -4.44179 q^{35} +44.9128 q^{36} +7.00045 q^{37} -11.2923 q^{38} +19.9318 q^{39} -8.76637 q^{40} -3.70176 q^{41} +40.6542 q^{42} -3.91347 q^{43} -26.0276 q^{44} +8.54717 q^{45} +4.53869 q^{46} -2.47862 q^{47} +44.5236 q^{48} +12.7295 q^{49} -2.69345 q^{50} -3.39811 q^{51} +30.8217 q^{52} +10.7103 q^{53} -50.7714 q^{54} -4.95320 q^{55} +38.9384 q^{56} +14.2465 q^{57} +12.3795 q^{58} +2.52154 q^{59} +17.8560 q^{60} +9.77896 q^{61} +2.10483 q^{62} -37.9647 q^{63} +21.6256 q^{64} +5.86554 q^{65} +45.3350 q^{66} -8.28934 q^{67} -5.25470 q^{68} -5.72610 q^{69} +11.9638 q^{70} -1.00000 q^{71} -74.9277 q^{72} +2.99507 q^{73} -18.8554 q^{74} +3.39811 q^{75} +22.0303 q^{76} +22.0011 q^{77} -53.6853 q^{78} +13.5110 q^{79} +13.1024 q^{80} +38.4126 q^{81} +9.97052 q^{82} +2.10229 q^{83} -79.3128 q^{84} -1.00000 q^{85} +10.5408 q^{86} -15.6182 q^{87} +43.4216 q^{88} +17.5463 q^{89} -23.0214 q^{90} -26.0535 q^{91} -8.85459 q^{92} -2.65550 q^{93} +6.67604 q^{94} +4.19249 q^{95} -60.3439 q^{96} +0.0532706 q^{97} -34.2863 q^{98} -42.3358 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) $ 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−2.69345	−1.90456	−0.952280	−	0.305226i	$-0.901268\pi$
$2$	−2.69345	−1.90456	−0.952280	+	0.305226i	$0.901268\pi$
$3$	3.39811	1.96190	0.980951	−	0.194257i	$-0.0622295\pi$
$3$	3.39811	1.96190	0.980951	+	0.194257i	$0.0622295\pi$
$4$	5.25470	2.62735
$5$	1.00000	0.447214
$5$	1.00000	0.447214
$6$	−9.15266	−3.73656
$7$	−4.44179	−1.67884	−0.839419	−	0.543484i	$-0.817105\pi$
$7$	−4.44179	−1.67884	−0.839419	+	0.543484i	$0.817105\pi$
$8$	−8.76637	−3.09938
$9$	8.54717	2.84906
$10$	−2.69345	−0.851745
$11$	−4.95320	−1.49345	−0.746723	−	0.665135i	$-0.768374\pi$
$11$	−4.95320	−1.49345	−0.746723	+	0.665135i	$0.768374\pi$
$12$	17.8560	5.15460
$13$	5.86554	1.62681	0.813405	−	0.581698i	$-0.197612\pi$
$13$	5.86554	1.62681	0.813405	+	0.581698i	$0.197612\pi$
$14$	11.9638	3.19745
$15$	3.39811	0.877389
$16$	13.1024	3.27561
$17$	−1.00000	−0.242536
$17$	−1.00000	−0.242536
$18$	−23.0214	−5.42620
$19$	4.19249	0.961823	0.480911	−	0.876769i	$-0.340306\pi$
$19$	4.19249	0.961823	0.480911	+	0.876769i	$0.340306\pi$
$20$	5.25470	1.17499
$21$	−15.0937	−3.29372
$22$	13.3412	2.84436
$23$	−1.68508	−0.351364	−0.175682	−	0.984447i	$-0.556213\pi$
$23$	−1.68508	−0.351364	−0.175682	+	0.984447i	$0.556213\pi$
$24$	−29.7891	−6.08068
$25$	1.00000	0.200000
$26$	−15.7986	−3.09836
$27$	18.8499	3.62767
$28$	−23.3403	−4.41089
$29$	−4.59613	−0.853480	−0.426740	−	0.904374i	$-0.640338\pi$
$29$	−4.59613	−0.853480	−0.426740	+	0.904374i	$0.640338\pi$
$30$	−9.15266	−1.67104
$31$	−0.781463	−0.140355	−0.0701774	−	0.997535i	$-0.522357\pi$
$31$	−0.781463	−0.140355	−0.0701774	+	0.997535i	$0.522357\pi$
$32$	−17.7581	−3.13921
$33$	−16.8315	−2.92999
$34$	2.69345	0.461924
$35$	−4.44179	−0.750799
$36$	44.9128	7.48546
$37$	7.00045	1.15087	0.575433	−	0.817849i	$-0.304834\pi$
$37$	7.00045	1.15087	0.575433	+	0.817849i	$0.304834\pi$
$38$	−11.2923	−1.83185
$39$	19.9318	3.19164
$40$	−8.76637	−1.38609
$41$	−3.70176	−0.578118	−0.289059	−	0.957311i	$-0.593342\pi$
$41$	−3.70176	−0.578118	−0.289059	+	0.957311i	$0.593342\pi$
$42$	40.6542	6.27308
$43$	−3.91347	−0.596799	−0.298399	−	0.954441i	$-0.596453\pi$
$43$	−3.91347	−0.596799	−0.298399	+	0.954441i	$0.596453\pi$
$44$	−26.0276	−3.92380
$45$	8.54717	1.27414
$46$	4.53869	0.669193
$47$	−2.47862	−0.361543	−0.180772	−	0.983525i	$-0.557859\pi$
$47$	−2.47862	−0.361543	−0.180772	+	0.983525i	$0.557859\pi$
$48$	44.5236	6.42642
$49$	12.7295	1.81850
$50$	−2.69345	−0.380912
$51$	−3.39811	−0.475831
$52$	30.8217	4.27419
$53$	10.7103	1.47117	0.735587	−	0.677430i	$-0.236906\pi$
$53$	10.7103	1.47117	0.735587	+	0.677430i	$0.236906\pi$
$54$	−50.7714	−6.90911
$55$	−4.95320	−0.667889
$56$	38.9384	5.20336
$57$	14.2465	1.88700
$58$	12.3795	1.62550
$59$	2.52154	0.328276	0.164138	−	0.986437i	$-0.447516\pi$
$59$	2.52154	0.328276	0.164138	+	0.986437i	$0.447516\pi$
$60$	17.8560	2.30521
$61$	9.77896	1.25207	0.626034	−	0.779796i	$-0.284677\pi$
$61$	9.77896	1.25207	0.626034	+	0.779796i	$0.284677\pi$
$62$	2.10483	0.267314
$63$	−37.9647	−4.78311
$64$	21.6256	2.70321
$65$	5.86554	0.727531
$66$	45.3350	5.58035
$67$	−8.28934	−1.01270	−0.506352	−	0.862327i	$-0.669006\pi$
$67$	−8.28934	−1.01270	−0.506352	+	0.862327i	$0.669006\pi$
$68$	−5.25470	−0.637225
$69$	−5.72610	−0.689341
$70$	11.9638	1.42994
$71$	−1.00000	−0.118678
$71$	−1.00000	−0.118678
$72$	−74.9277	−8.83031
$73$	2.99507	0.350546	0.175273	−	0.984520i	$-0.443919\pi$
$73$	2.99507	0.350546	0.175273	+	0.984520i	$0.443919\pi$
$74$	−18.8554	−2.19189
$75$	3.39811	0.392380
$76$	22.0303	2.52704
$77$	22.0011	2.50725
$78$	−53.6853	−6.07867
$79$	13.5110	1.52011	0.760054	−	0.649860i	$-0.225172\pi$
$79$	13.5110	1.52011	0.760054	+	0.649860i	$0.225172\pi$
$80$	13.1024	1.46490
$81$	38.4126	4.26807
$82$	9.97052	1.10106
$83$	2.10229	0.230756	0.115378	−	0.993322i	$-0.463192\pi$
$83$	2.10229	0.230756	0.115378	+	0.993322i	$0.463192\pi$
$84$	−79.3128	−8.65374
$85$	−1.00000	−0.108465
$86$	10.5408	1.13664
$87$	−15.6182	−1.67444
$88$	43.4216	4.62876
$89$	17.5463	1.85990	0.929950	−	0.367686i	$-0.119850\pi$
$89$	17.5463	1.85990	0.929950	+	0.367686i	$0.119850\pi$
$90$	−23.0214	−2.42667
$91$	−26.0535	−2.73115
$92$	−8.85459	−0.923155
$93$	−2.65550	−0.275362
$94$	6.67604	0.688581
$95$	4.19249	0.430140
$96$	−60.3439	−6.15882
$97$	0.0532706	0.00540881	0.00270441	−	0.999996i	$-0.499139\pi$
$97$	0.0532706	0.00540881	0.00270441	+	0.999996i	$0.499139\pi$
$98$	−34.2863	−3.46344
$99$	−42.3358	−4.25491
$100$	5.25470	0.525470
$101$	−4.77914	−0.475542	−0.237771	−	0.971321i	$-0.576417\pi$
$101$	−4.77914	−0.475542	−0.237771	+	0.971321i	$0.576417\pi$
$102$	9.15266	0.906249
$103$	6.94259	0.684074	0.342037	−	0.939687i	$-0.388883\pi$
$103$	6.94259	0.684074	0.342037	+	0.939687i	$0.388883\pi$
$104$	−51.4196	−5.04210
$105$	−15.0937	−1.47299
$106$	−28.8477	−2.80194
$107$	−4.61299	−0.445955	−0.222977	−	0.974824i	$-0.571578\pi$
$107$	−4.61299	−0.445955	−0.222977	+	0.974824i	$0.571578\pi$
$108$	99.0506	9.53115
$109$	−10.1430	−0.971526	−0.485763	−	0.874091i	$-0.661458\pi$
$109$	−10.1430	−0.971526	−0.485763	+	0.874091i	$0.661458\pi$
$110$	13.3412	1.27203
$111$	23.7883	2.25789
$112$	−58.1983	−5.49922
$113$	−13.2865	−1.24989	−0.624945	−	0.780669i	$-0.714878\pi$
$113$	−13.2865	−1.24989	−0.624945	+	0.780669i	$0.714878\pi$
$114$	−38.3724	−3.59391
$115$	−1.68508	−0.157135
$116$	−24.1513	−2.24239
$117$	50.1338	4.63487
$118$	−6.79164	−0.625221
$119$	4.44179	0.407178
$120$	−29.7891	−2.71936
$121$	13.5342	1.23038
$122$	−26.3392	−2.38464
$123$	−12.5790	−1.13421
$124$	−4.10635	−0.368761
$125$	1.00000	0.0894427
$126$	102.256	9.10971
$127$	−17.6960	−1.57026	−0.785132	−	0.619329i	$-0.787405\pi$
$127$	−17.6960	−1.57026	−0.785132	+	0.619329i	$0.787405\pi$
$128$	−22.7316	−2.00921
$129$	−13.2984	−1.17086
$130$	−15.7986	−1.38563
$131$	16.0849	1.40534	0.702672	−	0.711514i	$-0.251990\pi$
$131$	16.0849	1.40534	0.702672	+	0.711514i	$0.251990\pi$
$132$	−88.4446	−7.69811
$133$	−18.6222	−1.61475
$134$	22.3270	1.92876
$135$	18.8499	1.62234
$136$	8.76637	0.751710
$137$	−4.09582	−0.349930	−0.174965	−	0.984575i	$-0.555981\pi$
$137$	−4.09582	−0.349930	−0.174965	+	0.984575i	$0.555981\pi$
$138$	15.4230	1.31289
$139$	4.96444	0.421079	0.210539	−	0.977585i	$-0.432478\pi$
$139$	4.96444	0.421079	0.210539	+	0.977585i	$0.432478\pi$
$140$	−23.3403	−1.97261
$141$	−8.42262	−0.709312
$142$	2.69345	0.226030
$143$	−29.0532	−2.42955
$144$	111.989	9.33240
$145$	−4.59613	−0.381688
$146$	−8.06708	−0.667636
$147$	43.2563	3.56772
$148$	36.7852	3.02373
$149$	15.7381	1.28931	0.644657	−	0.764472i	$-0.277000\pi$
$149$	15.7381	1.28931	0.644657	+	0.764472i	$0.277000\pi$
$150$	−9.15266	−0.747312
$151$	6.51682	0.530331	0.265166	−	0.964203i	$-0.414573\pi$
$151$	6.51682	0.530331	0.265166	+	0.964203i	$0.414573\pi$
$152$	−36.7529	−2.98106
$153$	−8.54717	−0.690998
$154$	−59.2589	−4.77522
$155$	−0.781463	−0.0627686
$156$	104.735	8.38555
$157$	15.1313	1.20761	0.603804	−	0.797133i	$-0.293651\pi$
$157$	15.1313	1.20761	0.603804	+	0.797133i	$0.293651\pi$
$158$	−36.3913	−2.89514
$159$	36.3949	2.88630
$160$	−17.7581	−1.40390
$161$	7.48478	0.589883
$162$	−103.463	−8.12880
$163$	−15.4669	−1.21146	−0.605731	−	0.795669i	$-0.707119\pi$
$163$	−15.4669	−1.21146	−0.605731	+	0.795669i	$0.707119\pi$
$164$	−19.4516	−1.51892
$165$	−16.8315	−1.31033
$166$	−5.66241	−0.439489
$167$	5.10566	0.395088	0.197544	−	0.980294i	$-0.436703\pi$
$167$	5.10566	0.395088	0.197544	+	0.980294i	$0.436703\pi$
$168$	132.317	10.2085
$169$	21.4046	1.64651
$170$	2.69345	0.206579
$171$	35.8339	2.74029
$172$	−20.5641	−1.56800
$173$	6.09028	0.463035	0.231518	−	0.972831i	$-0.425631\pi$
$173$	6.09028	0.463035	0.231518	+	0.972831i	$0.425631\pi$
$174$	42.0668	3.18908
$175$	−4.44179	−0.335768
$176$	−64.8990	−4.89194
$177$	8.56846	0.644045
$178$	−47.2600	−3.54229
$179$	22.6704	1.69446	0.847232	−	0.531223i	$-0.178267\pi$
$179$	22.6704	1.69446	0.847232	+	0.531223i	$0.178267\pi$
$180$	44.9128	3.34760
$181$	18.1039	1.34566	0.672828	−	0.739799i	$-0.265079\pi$
$181$	18.1039	1.34566	0.672828	+	0.739799i	$0.265079\pi$
$182$	70.1739	5.20164
$183$	33.2300	2.45643
$184$	14.7721	1.08901
$185$	7.00045	0.514683
$186$	7.15247	0.524444
$187$	4.95320	0.362214
$188$	−13.0244	−0.949900
$189$	−83.7274	−6.09027
$190$	−11.2923	−0.819228
$191$	10.2157	0.739181	0.369590	−	0.929195i	$-0.379498\pi$
$191$	10.2157	0.739181	0.369590	+	0.929195i	$0.379498\pi$
$192$	73.4864	5.30342
$193$	17.4516	1.25619	0.628096	−	0.778136i	$-0.283834\pi$
$193$	17.4516	1.25619	0.628096	+	0.778136i	$0.283834\pi$
$194$	−0.143482	−0.0103014
$195$	19.9318	1.42734
$196$	66.8896	4.77783
$197$	−18.8582	−1.34359	−0.671796	−	0.740736i	$-0.734477\pi$
$197$	−18.8582	−1.34359	−0.671796	+	0.740736i	$0.734477\pi$
$198$	114.030	8.10373
$199$	−20.1943	−1.43154	−0.715768	−	0.698338i	$-0.753923\pi$
$199$	−20.1943	−1.43154	−0.715768	+	0.698338i	$0.753923\pi$
$200$	−8.76637	−0.619876
$201$	−28.1681	−1.98683
$202$	12.8724	0.905698
$203$	20.4151	1.43286
$204$	−17.8560	−1.25017
$205$	−3.70176	−0.258542
$206$	−18.6996	−1.30286
$207$	−14.4027	−1.00106
$208$	76.8529	5.32879
$209$	−20.7662	−1.43643
$210$	40.6542	2.80541
$211$	−1.22282	−0.0841821	−0.0420911	−	0.999114i	$-0.513402\pi$
$211$	−1.22282	−0.0841821	−0.0420911	+	0.999114i	$0.513402\pi$
$212$	56.2794	3.86529
$213$	−3.39811	−0.232835
$214$	12.4249	0.849347
$215$	−3.91347	−0.266897
$216$	−165.245	−11.2435
$217$	3.47109	0.235633
$218$	27.3198	1.85033
$219$	10.1776	0.687737
$220$	−26.0276	−1.75478
$221$	−5.86554	−0.394559
$222$	−64.0727	−4.30028
$223$	−19.6851	−1.31821	−0.659105	−	0.752051i	$-0.729065\pi$
$223$	−19.6851	−1.31821	−0.659105	+	0.752051i	$0.729065\pi$
$224$	78.8776	5.27023
$225$	8.54717	0.569811
$226$	35.7866	2.38049
$227$	11.7792	0.781812	0.390906	−	0.920431i	$-0.372162\pi$
$227$	11.7792	0.781812	0.390906	+	0.920431i	$0.372162\pi$
$228$	74.8613	4.95781
$229$	28.9912	1.91579	0.957895	−	0.287118i	$-0.0926973\pi$
$229$	28.9912	1.91579	0.957895	+	0.287118i	$0.0926973\pi$
$230$	4.53869	0.299272
$231$	74.7621	4.91899
$232$	40.2914	2.64526
$233$	−19.3002	−1.26440	−0.632199	−	0.774806i	$-0.717847\pi$
$233$	−19.3002	−1.26440	−0.632199	+	0.774806i	$0.717847\pi$
$234$	−135.033	−8.82739
$235$	−2.47862	−0.161687
$236$	13.2499	0.862495
$237$	45.9120	2.98230
$238$	−11.9638	−0.775495
$239$	20.3655	1.31733	0.658666	−	0.752436i	$-0.271121\pi$
$239$	20.3655	1.31733	0.658666	+	0.752436i	$0.271121\pi$
$240$	44.5236	2.87398
$241$	2.68967	0.173257	0.0866284	−	0.996241i	$-0.472391\pi$
$241$	2.68967	0.173257	0.0866284	+	0.996241i	$0.472391\pi$
$242$	−36.4537	−2.34333
$243$	73.9807	4.74587
$244$	51.3855	3.28962
$245$	12.7295	0.813258
$246$	33.8810	2.16017
$247$	24.5912	1.56470
$248$	6.85059	0.435013
$249$	7.14381	0.452721
$250$	−2.69345	−0.170349
$251$	−5.13120	−0.323878	−0.161939	−	0.986801i	$-0.551775\pi$
$251$	−5.13120	−0.323878	−0.161939	+	0.986801i	$0.551775\pi$
$252$	−199.493	−12.5669
$253$	8.34655	0.524743
$254$	47.6633	2.99066
$255$	−3.39811	−0.212798
$256$	17.9752	1.12345
$257$	−6.18666	−0.385913	−0.192957	−	0.981207i	$-0.561808\pi$
$257$	−6.18666	−0.385913	−0.192957	+	0.981207i	$0.561808\pi$
$258$	35.8187	2.22997
$259$	−31.0945	−1.93212
$260$	30.8217	1.91148
$261$	−39.2839	−2.43161
$262$	−43.3239	−2.67656
$263$	−2.94697	−0.181718	−0.0908589	−	0.995864i	$-0.528961\pi$
$263$	−2.94697	−0.181718	−0.0908589	+	0.995864i	$0.528961\pi$
$264$	147.551	9.08117
$265$	10.7103	0.657929
$266$	50.1579	3.07538
$267$	59.6242	3.64894
$268$	−43.5580	−2.66073
$269$	−6.83395	−0.416673	−0.208337	−	0.978057i	$-0.566805\pi$
$269$	−6.83395	−0.416673	−0.208337	+	0.978057i	$0.566805\pi$
$270$	−50.7714	−3.08985
$271$	−22.6944	−1.37859	−0.689293	−	0.724482i	$-0.742079\pi$
$271$	−22.6944	−1.37859	−0.689293	+	0.724482i	$0.742079\pi$
$272$	−13.1024	−0.794452
$273$	−88.5328	−5.35825
$274$	11.0319	0.666462
$275$	−4.95320	−0.298689
$276$	−30.0889	−1.81114
$277$	−19.8656	−1.19361	−0.596806	−	0.802386i	$-0.703564\pi$
$277$	−19.8656	−1.19361	−0.596806	+	0.802386i	$0.703564\pi$
$278$	−13.3715	−0.801969
$279$	−6.67930	−0.399879
$280$	38.9384	2.32701
$281$	0.842715	0.0502722	0.0251361	−	0.999684i	$-0.491998\pi$
$281$	0.842715	0.0502722	0.0251361	+	0.999684i	$0.491998\pi$
$282$	22.6859	1.35093
$283$	17.6306	1.04803	0.524014	−	0.851709i	$-0.324434\pi$
$283$	17.6306	1.04803	0.524014	+	0.851709i	$0.324434\pi$
$284$	−5.25470	−0.311809
$285$	14.2465	0.843893
$286$	78.2535	4.62723
$287$	16.4424	0.970567
$288$	−151.781	−8.94379
$289$	1.00000	0.0588235
$290$	12.3795	0.726948
$291$	0.181020	0.0106116
$292$	15.7382	0.921007
$293$	5.97305	0.348949	0.174475	−	0.984662i	$-0.444177\pi$
$293$	5.97305	0.348949	0.174475	+	0.984662i	$0.444177\pi$
$294$	−116.509	−6.79493
$295$	2.52154	0.146809
$296$	−61.3685	−3.56697
$297$	−93.3674	−5.41773
$298$	−42.3898	−2.45557
$299$	−9.88392	−0.571602
$300$	17.8560	1.03092
$301$	17.3828	1.00193
$302$	−17.5528	−1.01005
$303$	−16.2400	−0.932966
$304$	54.9318	3.15055
$305$	9.77896	0.559942
$306$	23.0214	1.31605
$307$	−0.985050	−0.0562197	−0.0281099	−	0.999605i	$-0.508949\pi$
$307$	−0.985050	−0.0562197	−0.0281099	+	0.999605i	$0.508949\pi$
$308$	115.609	6.58743
$309$	23.5917	1.34209
$310$	2.10483	0.119547
$311$	15.0265	0.852073	0.426037	−	0.904706i	$-0.359909\pi$
$311$	15.0265	0.852073	0.426037	+	0.904706i	$0.359909\pi$
$312$	−174.729	−9.89211
$313$	−15.2712	−0.863181	−0.431591	−	0.902070i	$-0.642047\pi$
$313$	−15.2712	−0.863181	−0.431591	+	0.902070i	$0.642047\pi$
$314$	−40.7554	−2.29996
$315$	−37.9647	−2.13907
$316$	70.9963	3.99385
$317$	−12.2207	−0.686382	−0.343191	−	0.939266i	$-0.611508\pi$
$317$	−12.2207	−0.686382	−0.343191	+	0.939266i	$0.611508\pi$
$318$	−98.0279	−5.49713
$319$	22.7656	1.27463
$320$	21.6256	1.20891
$321$	−15.6755	−0.874919
$322$	−20.1599	−1.12347
$323$	−4.19249	−0.233276
$324$	201.847	11.2137
$325$	5.86554	0.325362
$326$	41.6594	2.30730
$327$	−34.4672	−1.90604
$328$	32.4510	1.79181
$329$	11.0095	0.606973
$330$	45.3350	2.49561
$331$	−1.81614	−0.0998242	−0.0499121	−	0.998754i	$-0.515894\pi$
$331$	−1.81614	−0.0998242	−0.0499121	+	0.998754i	$0.515894\pi$
$332$	11.0469	0.606276
$333$	59.8340	3.27888
$334$	−13.7519	−0.752469
$335$	−8.28934	−0.452895
$336$	−197.764	−10.7889
$337$	27.1226	1.47746	0.738731	−	0.674000i	$-0.235425\pi$
$337$	27.1226	1.47746	0.738731	+	0.674000i	$0.235425\pi$
$338$	−57.6523	−3.13587
$339$	−45.1490	−2.45216
$340$	−5.25470	−0.284976
$341$	3.87074	0.209612
$342$	−96.5170	−5.21904
$343$	−25.4492	−1.37413
$344$	34.3070	1.84971
$345$	−5.72610	−0.308283
$346$	−16.4039	−0.881879
$347$	−3.98043	−0.213681	−0.106840	−	0.994276i	$-0.534073\pi$
$347$	−3.98043	−0.213681	−0.106840	+	0.994276i	$0.534073\pi$
$348$	−82.0688	−4.39935
$349$	−10.1530	−0.543477	−0.271739	−	0.962371i	$-0.587599\pi$
$349$	−10.1530	−0.543477	−0.271739	+	0.962371i	$0.587599\pi$
$350$	11.9638	0.639490
$351$	110.565	5.90153
$352$	87.9592	4.68824
$353$	−4.38021	−0.233135	−0.116568	−	0.993183i	$-0.537189\pi$
$353$	−4.38021	−0.233135	−0.116568	+	0.993183i	$0.537189\pi$
$354$	−23.0788	−1.22662
$355$	−1.00000	−0.0530745
$356$	92.2003	4.88660
$357$	15.0937	0.798843
$358$	−61.0617	−3.22721
$359$	10.3359	0.545506	0.272753	−	0.962084i	$-0.412066\pi$
$359$	10.3359	0.545506	0.272753	+	0.962084i	$0.412066\pi$
$360$	−74.9277	−3.94904
$361$	−1.42304	−0.0748969
$362$	−48.7622	−2.56288
$363$	45.9907	2.41388
$364$	−136.903	−7.17568
$365$	2.99507	0.156769
$366$	−89.5035	−4.67843
$367$	1.61188	0.0841397	0.0420699	−	0.999115i	$-0.486605\pi$
$367$	1.61188	0.0841397	0.0420699	+	0.999115i	$0.486605\pi$
$368$	−22.0787	−1.15093
$369$	−31.6396	−1.64709
$370$	−18.8554	−0.980244
$371$	−47.5730	−2.46987
$372$	−13.9538	−0.723473
$373$	17.4109	0.901504	0.450752	−	0.892649i	$-0.351156\pi$
$373$	17.4109	0.901504	0.450752	+	0.892649i	$0.351156\pi$
$374$	−13.3412	−0.689858
$375$	3.39811	0.175478
$376$	21.7285	1.12056
$377$	−26.9588	−1.38845
$378$	225.516	11.5993
$379$	10.0716	0.517344	0.258672	−	0.965965i	$-0.416715\pi$
$379$	10.0716	0.517344	0.258672	+	0.965965i	$0.416715\pi$
$380$	22.0303	1.13013
$381$	−60.1329	−3.08070
$382$	−27.5155	−1.40781
$383$	29.4299	1.50380	0.751900	−	0.659277i	$-0.229138\pi$
$383$	29.4299	1.50380	0.751900	+	0.659277i	$0.229138\pi$
$384$	−77.2445	−3.94187
$385$	22.0011	1.12128
$386$	−47.0050	−2.39249
$387$	−33.4491	−1.70031
$388$	0.279921	0.0142108
$389$	14.2036	0.720150	0.360075	−	0.932923i	$-0.382751\pi$
$389$	14.2036	0.720150	0.360075	+	0.932923i	$0.382751\pi$
$390$	−53.6853	−2.71846
$391$	1.68508	0.0852183
$392$	−111.592	−5.63622
$393$	54.6583	2.75715
$394$	50.7938	2.55895
$395$	13.5110	0.679813
$396$	−222.462	−11.1791
$397$	21.8662	1.09743	0.548715	−	0.836009i	$-0.315117\pi$
$397$	21.8662	1.09743	0.548715	+	0.836009i	$0.315117\pi$
$398$	54.3924	2.72645
$399$	−63.2802	−3.16797
$400$	13.1024	0.655122
$401$	−10.4710	−0.522896	−0.261448	−	0.965217i	$-0.584200\pi$
$401$	−10.4710	−0.522896	−0.261448	+	0.965217i	$0.584200\pi$
$402$	75.8695	3.78403
$403$	−4.58371	−0.228331
$404$	−25.1129	−1.24941
$405$	38.4126	1.90874
$406$	−54.9870	−2.72896
$407$	−34.6746	−1.71876
$408$	29.7891	1.47478
$409$	−24.9695	−1.23466	−0.617330	−	0.786704i	$-0.711786\pi$
$409$	−24.9695	−1.23466	−0.617330	+	0.786704i	$0.711786\pi$
$410$	9.97052	0.492409
$411$	−13.9181	−0.686528
$412$	36.4812	1.79730
$413$	−11.2001	−0.551122
$414$	38.7930	1.90657
$415$	2.10229	0.103197
$416$	−104.161	−5.10690
$417$	16.8697	0.826115
$418$	55.9329	2.73577
$419$	−19.6890	−0.961872	−0.480936	−	0.876756i	$-0.659703\pi$
$419$	−19.6890	−0.961872	−0.480936	+	0.876756i	$0.659703\pi$
$420$	−79.3128	−3.87007
$421$	−10.8842	−0.530464	−0.265232	−	0.964185i	$-0.585449\pi$
$421$	−10.8842	−0.530464	−0.265232	+	0.964185i	$0.585449\pi$
$422$	3.29360	0.160330
$423$	−21.1852	−1.03006
$424$	−93.8906	−4.55973
$425$	−1.00000	−0.0485071
$426$	9.15266	0.443448
$427$	−43.4361	−2.10202
$428$	−24.2399	−1.17168
$429$	−98.7261	−4.76654
$430$	10.5408	0.508321
$431$	20.4532	0.985197	0.492599	−	0.870257i	$-0.336047\pi$
$431$	20.4532	0.985197	0.492599	+	0.870257i	$0.336047\pi$
$432$	246.980	11.8828
$433$	5.78435	0.277978	0.138989	−	0.990294i	$-0.455615\pi$
$433$	5.78435	0.277978	0.138989	+	0.990294i	$0.455615\pi$
$434$	−9.34923	−0.448777
$435$	−15.6182	−0.748834
$436$	−53.2985	−2.55254
$437$	−7.06469	−0.337950
$438$	−27.4128	−1.30984
$439$	2.35946	0.112611	0.0563054	−	0.998414i	$-0.482068\pi$
$439$	2.35946	0.112611	0.0563054	+	0.998414i	$0.482068\pi$
$440$	43.4216	2.07004
$441$	108.801	5.18101
$442$	15.7986	0.751462
$443$	6.95226	0.330312	0.165156	−	0.986267i	$-0.447187\pi$
$443$	6.95226	0.330312	0.165156	+	0.986267i	$0.447187\pi$
$444$	125.000	5.93225
$445$	17.5463	0.831773
$446$	53.0208	2.51061
$447$	53.4797	2.52951
$448$	−96.0566	−4.53825
$449$	18.9676	0.895136	0.447568	−	0.894250i	$-0.352290\pi$
$449$	18.9676	0.895136	0.447568	+	0.894250i	$0.352290\pi$
$450$	−23.0214	−1.08524
$451$	18.3356	0.863388
$452$	−69.8165	−3.28389
$453$	22.1449	1.04046
$454$	−31.7267	−1.48901
$455$	−26.0535	−1.22141
$456$	−124.891	−5.84854
$457$	13.0352	0.609762	0.304881	−	0.952391i	$-0.401383\pi$
$457$	13.0352	0.609762	0.304881	+	0.952391i	$0.401383\pi$
$458$	−78.0864	−3.64874
$459$	−18.8499	−0.879839
$460$	−8.85459	−0.412847
$461$	28.9137	1.34664	0.673322	−	0.739350i	$-0.264867\pi$
$461$	28.9137	1.34664	0.673322	+	0.739350i	$0.264867\pi$
$462$	−201.368	−9.36850
$463$	22.7658	1.05802	0.529009	−	0.848616i	$-0.322564\pi$
$463$	22.7658	1.05802	0.529009	+	0.848616i	$0.322564\pi$
$464$	−60.2205	−2.79567
$465$	−2.65550	−0.123146
$466$	51.9842	2.40812
$467$	−38.7460	−1.79295	−0.896476	−	0.443092i	$-0.853882\pi$
$467$	−38.7460	−1.79295	−0.896476	+	0.443092i	$0.853882\pi$
$468$	263.438	12.1774
$469$	36.8195	1.70017
$470$	6.67604	0.307943
$471$	51.4178	2.36921
$472$	−22.1047	−1.01745
$473$	19.3842	0.891287
$474$	−123.662	−5.67997
$475$	4.19249	0.192365
$476$	23.3403	1.06980
$477$	91.5429	4.19146
$478$	−54.8534	−2.50894
$479$	3.32515	0.151930	0.0759649	−	0.997110i	$-0.475796\pi$
$479$	3.32515	0.151930	0.0759649	+	0.997110i	$0.475796\pi$
$480$	−60.3439	−2.75431
$481$	41.0614	1.87224
$482$	−7.24450	−0.329978
$483$	25.4341	1.15729
$484$	71.1180	3.23264
$485$	0.0532706	0.00241889
$486$	−199.264	−9.03879
$487$	−16.5593	−0.750375	−0.375188	−	0.926949i	$-0.622422\pi$
$487$	−16.5593	−0.750375	−0.375188	+	0.926949i	$0.622422\pi$
$488$	−85.7260	−3.88064
$489$	−52.5583	−2.37677
$490$	−34.2863	−1.54890
$491$	−12.4716	−0.562838	−0.281419	−	0.959585i	$-0.590805\pi$
$491$	−12.4716	−0.562838	−0.281419	+	0.959585i	$0.590805\pi$
$492$	−66.0988	−2.97996
$493$	4.59613	0.206999
$494$	−66.2353	−2.98007
$495$	−42.3358	−1.90285
$496$	−10.2391	−0.459748
$497$	4.44179	0.199241
$498$	−19.2415	−0.862233
$499$	14.9422	0.668904	0.334452	−	0.942413i	$-0.391449\pi$
$499$	14.9422	0.668904	0.334452	+	0.942413i	$0.391449\pi$
$500$	5.25470	0.234997
$501$	17.3496	0.775124
$502$	13.8206	0.616846
$503$	−6.90651	−0.307946	−0.153973	−	0.988075i	$-0.549207\pi$
$503$	−6.90651	−0.307946	−0.153973	+	0.988075i	$0.549207\pi$
$504$	332.813	14.8247
$505$	−4.77914	−0.212669
$506$	−22.4810	−0.999404
$507$	72.7353	3.23029
$508$	−92.9869	−4.12563
$509$	−3.74452	−0.165973	−0.0829865	−	0.996551i	$-0.526446\pi$
$509$	−3.74452	−0.165973	−0.0829865	+	0.996551i	$0.526446\pi$
$510$	9.15266	0.405287
$511$	−13.3035	−0.588511
$512$	−2.95214	−0.130467
$513$	79.0281	3.48917
$514$	16.6635	0.734994
$515$	6.94259	0.305927
$516$	−69.8792	−3.07626
$517$	12.2771	0.539945
$518$	83.7516	3.67984
$519$	20.6955	0.908430
$520$	−51.4196	−2.25490
$521$	10.2494	0.449033	0.224516	−	0.974470i	$-0.427920\pi$
$521$	10.2494	0.449033	0.224516	+	0.974470i	$0.427920\pi$
$522$	105.809	4.63116
$523$	11.5294	0.504146	0.252073	−	0.967708i	$-0.418888\pi$
$523$	11.5294	0.504146	0.252073	+	0.967708i	$0.418888\pi$
$524$	84.5212	3.69233
$525$	−15.0937	−0.658743
$526$	7.93752	0.346092
$527$	0.781463	0.0340411
$528$	−220.534	−9.59751
$529$	−20.1605	−0.876543
$530$	−28.8477	−1.25307
$531$	21.5520	0.935277
$532$	−97.8537	−4.24250
$533$	−21.7128	−0.940488
$534$	−160.595	−6.94962
$535$	−4.61299	−0.199437
$536$	72.6674	3.13876
$537$	77.0365	3.32437
$538$	18.4069	0.793580
$539$	−63.0517	−2.71583
$540$	99.0506	4.26246
$541$	−7.14760	−0.307299	−0.153650	−	0.988125i	$-0.549103\pi$
$541$	−7.14760	−0.307299	−0.153650	+	0.988125i	$0.549103\pi$
$542$	61.1263	2.62560
$543$	61.5193	2.64004
$544$	17.7581	0.761370
$545$	−10.1430	−0.434480
$546$	238.459	10.2051
$547$	40.9132	1.74932	0.874661	−	0.484735i	$-0.161084\pi$
$547$	40.9132	1.74932	0.874661	+	0.484735i	$0.161084\pi$
$548$	−21.5223	−0.919387
$549$	83.5825	3.56721
$550$	13.3412	0.568871
$551$	−19.2692	−0.820897
$552$	50.1971	2.13653
$553$	−60.0131	−2.55202
$554$	53.5072	2.27330
$555$	23.7883	1.00976
$556$	26.0866	1.10632
$557$	−38.4269	−1.62820	−0.814100	−	0.580724i	$-0.802769\pi$
$557$	−38.4269	−1.62820	−0.814100	+	0.580724i	$0.802769\pi$
$558$	17.9904	0.761594
$559$	−22.9546	−0.970878
$560$	−58.1983	−2.45933
$561$	16.8315	0.710628
$562$	−2.26981	−0.0957463
$563$	−30.5844	−1.28898	−0.644490	−	0.764613i	$-0.722930\pi$
$563$	−30.5844	−1.28898	−0.644490	+	0.764613i	$0.722930\pi$
$564$	−44.2583	−1.86361
$565$	−13.2865	−0.558967
$566$	−47.4871	−1.99603
$567$	−170.621	−7.16540
$568$	8.76637	0.367829
$569$	−5.28964	−0.221753	−0.110877	−	0.993834i	$-0.535366\pi$
$569$	−5.28964	−0.221753	−0.110877	+	0.993834i	$0.535366\pi$
$570$	−38.3724	−1.60724
$571$	−42.3074	−1.77051	−0.885255	−	0.465106i	$-0.846016\pi$
$571$	−42.3074	−1.77051	−0.885255	+	0.465106i	$0.846016\pi$
$572$	−152.666	−6.38328
$573$	34.7140	1.45020
$574$	−44.2870	−1.84850
$575$	−1.68508	−0.0702728
$576$	184.838	7.70159
$577$	26.4886	1.10273	0.551367	−	0.834263i	$-0.314106\pi$
$577$	26.4886	1.10273	0.551367	+	0.834263i	$0.314106\pi$
$578$	−2.69345	−0.112033
$579$	59.3024	2.46453
$580$	−24.1513	−1.00283
$581$	−9.33792	−0.387402
$582$	−0.487568	−0.0202103
$583$	−53.0503	−2.19712
$584$	−26.2559	−1.08648
$585$	50.1338	2.07278
$586$	−16.0881	−0.664594
$587$	−8.25116	−0.340562	−0.170281	−	0.985396i	$-0.554467\pi$
$587$	−8.25116	−0.340562	−0.170281	+	0.985396i	$0.554467\pi$
$588$	227.298	9.37363
$589$	−3.27627	−0.134997
$590$	−6.79164	−0.279607
$591$	−64.0824	−2.63600
$592$	91.7229	3.76979
$593$	35.0076	1.43759	0.718795	−	0.695222i	$-0.244694\pi$
$593$	35.0076	1.43759	0.718795	+	0.695222i	$0.244694\pi$
$594$	251.481	10.3184
$595$	4.44179	0.182096
$596$	82.6988	3.38747
$597$	−68.6225	−2.80853
$598$	26.6219	1.08865
$599$	−20.0518	−0.819294	−0.409647	−	0.912244i	$-0.634348\pi$
$599$	−20.0518	−0.819294	−0.409647	+	0.912244i	$0.634348\pi$
$600$	−29.7891	−1.21614
$601$	−21.7385	−0.886732	−0.443366	−	0.896341i	$-0.646216\pi$
$601$	−21.7385	−0.886732	−0.443366	+	0.896341i	$0.646216\pi$
$602$	−46.8198	−1.90823
$603$	−70.8504	−2.88525
$604$	34.2439	1.39336
$605$	13.5342	0.550243
$606$	43.7418	1.77689
$607$	33.8417	1.37359	0.686795	−	0.726851i	$-0.259017\pi$
$607$	33.8417	1.37359	0.686795	+	0.726851i	$0.259017\pi$
$608$	−74.4505	−3.01936
$609$	69.3727	2.81112
$610$	−26.3392	−1.06644
$611$	−14.5384	−0.588162
$612$	−44.9128	−1.81549
$613$	3.70549	0.149663	0.0748317	−	0.997196i	$-0.476158\pi$
$613$	3.70549	0.149663	0.0748317	+	0.997196i	$0.476158\pi$
$614$	2.65319	0.107074
$615$	−12.5790	−0.507234
$616$	−192.870	−7.77094
$617$	−15.9900	−0.643731	−0.321866	−	0.946785i	$-0.604310\pi$
$617$	−15.9900	−0.643731	−0.321866	+	0.946785i	$0.604310\pi$
$618$	−63.5432	−2.55608
$619$	−23.7520	−0.954673	−0.477336	−	0.878721i	$-0.658398\pi$
$619$	−23.7520	−0.954673	−0.477336	+	0.878721i	$0.658398\pi$
$620$	−4.10635	−0.164915
$621$	−31.7637	−1.27463
$622$	−40.4731	−1.62282
$623$	−77.9368	−3.12247
$624$	261.155	10.4546
$625$	1.00000	0.0400000
$626$	41.1324	1.64398
$627$	−70.5660	−2.81813
$628$	79.5103	3.17281
$629$	−7.00045	−0.279126
$630$	102.256	4.07399
$631$	−22.9583	−0.913956	−0.456978	−	0.889478i	$-0.651068\pi$
$631$	−22.9583	−0.913956	−0.456978	+	0.889478i	$0.651068\pi$
$632$	−118.443	−4.71139
$633$	−4.15527	−0.165157
$634$	32.9158	1.30726
$635$	−17.6960	−0.702243
$636$	191.244	7.58331
$637$	74.6654	2.95835
$638$	−61.3180	−2.42760
$639$	−8.54717	−0.338121
$640$	−22.7316	−0.898545
$641$	9.13929	0.360980	0.180490	−	0.983577i	$-0.442232\pi$
$641$	9.13929	0.360980	0.180490	+	0.983577i	$0.442232\pi$
$642$	42.2211	1.66634
$643$	10.0190	0.395110	0.197555	−	0.980292i	$-0.436700\pi$
$643$	10.0190	0.395110	0.197555	+	0.980292i	$0.436700\pi$
$644$	39.3302	1.54983
$645$	−13.2984	−0.523625
$646$	11.2923	0.444289
$647$	−39.5278	−1.55400	−0.776998	−	0.629503i	$-0.783259\pi$
$647$	−39.5278	−1.55400	−0.776998	+	0.629503i	$0.783259\pi$
$648$	−336.740	−13.2284
$649$	−12.4897	−0.490262
$650$	−15.7986	−0.619671
$651$	11.7952	0.462289
$652$	−81.2739	−3.18293
$653$	−21.2834	−0.832882	−0.416441	−	0.909163i	$-0.636723\pi$
$653$	−21.2834	−0.832882	−0.416441	+	0.909163i	$0.636723\pi$
$654$	92.8357	3.63016
$655$	16.0849	0.628489
$656$	−48.5021	−1.89369
$657$	25.5994	0.998726
$658$	−29.6536	−1.15602
$659$	12.2627	0.477686	0.238843	−	0.971058i	$-0.423232\pi$
$659$	12.2627	0.477686	0.238843	+	0.971058i	$0.423232\pi$
$660$	−88.4446	−3.44270
$661$	11.5661	0.449870	0.224935	−	0.974374i	$-0.427783\pi$
$661$	11.5661	0.449870	0.224935	+	0.974374i	$0.427783\pi$
$662$	4.89170	0.190121
$663$	−19.9318	−0.774086
$664$	−18.4294	−0.715201
$665$	−18.6222	−0.722136
$666$	−161.160	−6.24483
$667$	7.74486	0.299882
$668$	26.8287	1.03803
$669$	−66.8921	−2.58620
$670$	22.3270	0.862565
$671$	−48.4372	−1.86990
$672$	268.035	10.3397
$673$	−50.3289	−1.94004	−0.970019	−	0.243030i	$-0.921859\pi$
$673$	−50.3289	−1.94004	−0.970019	+	0.243030i	$0.921859\pi$
$674$	−73.0535	−2.81392
$675$	18.8499	0.725534
$676$	112.475	4.32595
$677$	−2.07785	−0.0798581	−0.0399291	−	0.999203i	$-0.512713\pi$
$677$	−2.07785	−0.0798581	−0.0399291	+	0.999203i	$0.512713\pi$
$678$	121.607	4.67028
$679$	−0.236617	−0.00908052
$680$	8.76637	0.336175
$681$	40.0270	1.53384
$682$	−10.4257	−0.399219
$683$	−24.8475	−0.950765	−0.475382	−	0.879779i	$-0.657690\pi$
$683$	−24.8475	−0.950765	−0.475382	+	0.879779i	$0.657690\pi$
$684$	188.296	7.19969
$685$	−4.09582	−0.156493
$686$	68.5463	2.61711
$687$	98.5153	3.75859
$688$	−51.2760	−1.95488
$689$	62.8218	2.39332
$690$	15.4230	0.587143
$691$	18.6408	0.709130	0.354565	−	0.935031i	$-0.384629\pi$
$691$	18.6408	0.709130	0.354565	+	0.935031i	$0.384629\pi$
$692$	32.0026	1.21656
$693$	188.047	7.14331
$694$	10.7211	0.406968
$695$	4.96444	0.188312
$696$	136.915	5.18974
$697$	3.70176	0.140214
$698$	27.3466	1.03508
$699$	−65.5842	−2.48062
$700$	−23.3403	−0.882179
$701$	5.85074	0.220979	0.110490	−	0.993877i	$-0.464758\pi$
$701$	5.85074	0.220979	0.110490	+	0.993877i	$0.464758\pi$
$702$	−297.802	−11.2398
$703$	29.3493	1.10693
$704$	−107.116	−4.03709
$705$	−8.42262	−0.317214
$706$	11.7979	0.444020
$707$	21.2279	0.798358
$708$	45.0247	1.69213
$709$	21.1525	0.794401	0.397200	−	0.917732i	$-0.369982\pi$
$709$	21.1525	0.794401	0.397200	+	0.917732i	$0.369982\pi$
$710$	2.69345	0.101084
$711$	115.481	4.33088
$712$	−153.817	−5.76454
$713$	1.31683	0.0493156
$714$	−40.6542	−1.52145
$715$	−29.0532	−1.08653
$716$	119.126	4.45195
$717$	69.2041	2.58448
$718$	−27.8392	−1.03895
$719$	−3.47328	−0.129531	−0.0647657	−	0.997900i	$-0.520630\pi$
$719$	−3.47328	−0.129531	−0.0647657	+	0.997900i	$0.520630\pi$
$720$	111.989	4.17357
$721$	−30.8375	−1.14845
$722$	3.83289	0.142646
$723$	9.13980	0.339913
$724$	95.1307	3.53551
$725$	−4.59613	−0.170696
$726$	−123.874	−4.59739
$727$	26.7277	0.991274	0.495637	−	0.868530i	$-0.334935\pi$
$727$	26.7277	0.991274	0.495637	+	0.868530i	$0.334935\pi$
$728$	228.395	8.46488
$729$	136.157	5.04285
$730$	−8.06708	−0.298576
$731$	3.91347	0.144745
$732$	174.614	6.45391
$733$	−11.8864	−0.439034	−0.219517	−	0.975609i	$-0.570448\pi$
$733$	−11.8864	−0.439034	−0.219517	+	0.975609i	$0.570448\pi$
$734$	−4.34154	−0.160249
$735$	43.2563	1.59553
$736$	29.9238	1.10301
$737$	41.0587	1.51242
$738$	85.2198	3.13698
$739$	19.0931	0.702353	0.351176	−	0.936309i	$-0.385782\pi$
$739$	19.0931	0.702353	0.351176	+	0.936309i	$0.385782\pi$
$740$	36.7852	1.35225
$741$	83.5638	3.06979
$742$	128.136	4.70401
$743$	−8.24047	−0.302314	−0.151157	−	0.988510i	$-0.548300\pi$
$743$	−8.24047	−0.302314	−0.151157	+	0.988510i	$0.548300\pi$
$744$	23.2791	0.853453
$745$	15.7381	0.576598
$746$	−46.8955	−1.71697
$747$	17.9686	0.657437
$748$	26.0276	0.951662
$749$	20.4899	0.748686
$750$	−9.15266	−0.334208
$751$	13.1381	0.479415	0.239707	−	0.970845i	$-0.422949\pi$
$751$	13.1381	0.479415	0.239707	+	0.970845i	$0.422949\pi$
$752$	−32.4759	−1.18427
$753$	−17.4364	−0.635418
$754$	72.6123	2.64439
$755$	6.51682	0.237171
$756$	−439.962	−16.0013
$757$	26.7399	0.971880	0.485940	−	0.873992i	$-0.338477\pi$
$757$	26.7399	0.971880	0.485940	+	0.873992i	$0.338477\pi$
$758$	−27.1274	−0.985312
$759$	28.3625	1.02949
$760$	−36.7529	−1.33317
$761$	−36.4537	−1.32145	−0.660724	−	0.750629i	$-0.729750\pi$
$761$	−36.4537	−1.32145	−0.660724	+	0.750629i	$0.729750\pi$
$762$	161.965	5.86738
$763$	45.0532	1.63104
$764$	53.6803	1.94208
$765$	−8.54717	−0.309024
$766$	−79.2682	−2.86408
$767$	14.7902	0.534042
$768$	61.0817	2.20409
$769$	37.2908	1.34474	0.672370	−	0.740215i	$-0.265276\pi$
$769$	37.2908	1.34474	0.672370	+	0.740215i	$0.265276\pi$
$770$	−59.2589	−2.13554
$771$	−21.0230	−0.757123
$772$	91.7027	3.30045
$773$	53.3617	1.91929	0.959644	−	0.281218i	$-0.0907383\pi$
$773$	53.3617	1.91929	0.959644	+	0.281218i	$0.0907383\pi$
$774$	90.0937	3.23835
$775$	−0.781463	−0.0280710
$776$	−0.466990	−0.0167640
$777$	−105.663	−3.79063
$778$	−38.2567	−1.37157
$779$	−15.5196	−0.556047
$780$	104.735	3.75013
$781$	4.95320	0.177239
$782$	−4.53869	−0.162303
$783$	−86.6367	−3.09614
$784$	166.787	5.95669
$785$	15.1313	0.540059
$786$	−147.220	−5.25115
$787$	−31.2030	−1.11227	−0.556133	−	0.831093i	$-0.687716\pi$
$787$	−31.2030	−1.11227	−0.556133	+	0.831093i	$0.687716\pi$
$788$	−99.0942	−3.53009
$789$	−10.0141	−0.356512
$790$	−36.3913	−1.29474
$791$	59.0159	2.09836
$792$	371.132	13.1876
$793$	57.3589	2.03688
$794$	−58.8955	−2.09012
$795$	36.3949	1.29079
$796$	−106.115	−3.76114
$797$	−45.8184	−1.62297	−0.811486	−	0.584372i	$-0.801341\pi$
$797$	−45.8184	−1.62297	−0.811486	+	0.584372i	$0.801341\pi$
$798$	170.442	6.03359
$799$	2.47862	0.0876871
$800$	−17.7581	−0.627842
$801$	149.971	5.29896
$802$	28.2031	0.995888
$803$	−14.8352	−0.523522
$804$	−148.015	−5.22008
$805$	7.48478	0.263804
$806$	12.3460	0.434869
$807$	−23.2225	−0.817472
$808$	41.8957	1.47389
$809$	−43.1269	−1.51626	−0.758131	−	0.652103i	$-0.773887\pi$
$809$	−43.1269	−1.51626	−0.758131	+	0.652103i	$0.773887\pi$
$810$	−103.463	−3.63531
$811$	−40.5337	−1.42333	−0.711666	−	0.702518i	$-0.752059\pi$
$811$	−40.5337	−1.42333	−0.711666	+	0.702518i	$0.752059\pi$
$812$	107.275	3.76461
$813$	−77.1181	−2.70465
$814$	93.3944	3.27347
$815$	−15.4669	−0.541782
$816$	−44.5236	−1.55864
$817$	−16.4072	−0.574015
$818$	67.2541	2.35148
$819$	−222.684	−7.78120
$820$	−19.4516	−0.679280
$821$	52.3216	1.82604	0.913018	−	0.407918i	$-0.133745\pi$
$821$	52.3216	1.82604	0.913018	+	0.407918i	$0.133745\pi$
$822$	37.4877	1.30753
$823$	6.41943	0.223767	0.111884	−	0.993721i	$-0.464312\pi$
$823$	6.41943	0.223767	0.111884	+	0.993721i	$0.464312\pi$
$824$	−60.8613	−2.12021
$825$	−16.8315	−0.585999
$826$	30.1670	1.04965
$827$	21.4812	0.746974	0.373487	−	0.927635i	$-0.378162\pi$
$827$	21.4812	0.746974	0.373487	+	0.927635i	$0.378162\pi$
$828$	−75.6817	−2.63012
$829$	−0.852311	−0.0296020	−0.0148010	−	0.999890i	$-0.504711\pi$
$829$	−0.852311	−0.0296020	−0.0148010	+	0.999890i	$0.504711\pi$
$830$	−5.66241	−0.196545
$831$	−67.5057	−2.34175
$832$	126.846	4.39760
$833$	−12.7295	−0.441051
$834$	−45.4379	−1.57338
$835$	5.10566	0.176689
$836$	−109.120	−3.77400
$837$	−14.7305	−0.509161
$838$	53.0315	1.83194
$839$	−38.3262	−1.32317	−0.661583	−	0.749872i	$-0.730115\pi$
$839$	−38.3262	−1.32317	−0.661583	+	0.749872i	$0.730115\pi$
$840$	132.317	4.56537
$841$	−7.87557	−0.271571
$842$	29.3161	1.01030
$843$	2.86364	0.0986290
$844$	−6.42553	−0.221176
$845$	21.4046	0.736341
$846$	57.0612	1.96181
$847$	−60.1160	−2.06561
$848$	140.331	4.81899
$849$	59.9107	2.05613
$850$	2.69345	0.0923847
$851$	−11.7963	−0.404373
$852$	−17.8560	−0.611738
$853$	30.7079	1.05142	0.525709	−	0.850664i	$-0.323800\pi$
$853$	30.7079	1.05142	0.525709	+	0.850664i	$0.323800\pi$
$854$	116.993	4.00342
$855$	35.8339	1.22549
$856$	40.4392	1.38218
$857$	29.3418	1.00230	0.501149	−	0.865361i	$-0.332911\pi$
$857$	29.3418	1.00230	0.501149	+	0.865361i	$0.332911\pi$
$858$	265.914	9.07816
$859$	−27.8247	−0.949368	−0.474684	−	0.880156i	$-0.657438\pi$
$859$	−27.8247	−0.949368	−0.474684	+	0.880156i	$0.657438\pi$
$860$	−20.5641	−0.701230
$861$	55.8733	1.90416
$862$	−55.0898	−1.87637
$863$	0.572395	0.0194846	0.00974228	−	0.999953i	$-0.496899\pi$
$863$	0.572395	0.0194846	0.00974228	+	0.999953i	$0.496899\pi$
$864$	−334.738	−11.3880
$865$	6.09028	0.207076
$866$	−15.5799	−0.529426
$867$	3.39811	0.115406
$868$	18.2395	0.619090
$869$	−66.9228	−2.27020
$870$	42.0668	1.42620
$871$	−48.6215	−1.64748
$872$	88.9176	3.01113
$873$	0.455313	0.0154100
$874$	19.0284	0.643646
$875$	−4.44179	−0.150160
$876$	53.4801	1.80692
$877$	−29.8636	−1.00842	−0.504211	−	0.863580i	$-0.668217\pi$
$877$	−29.8636	−1.00842	−0.504211	+	0.863580i	$0.668217\pi$
$878$	−6.35509	−0.214474
$879$	20.2971	0.684604
$880$	−64.8990	−2.18774
$881$	44.3489	1.49415	0.747077	−	0.664738i	$-0.231457\pi$
$881$	44.3489	1.49415	0.747077	+	0.664738i	$0.231457\pi$
$882$	−293.051	−9.86754
$883$	−43.4668	−1.46278	−0.731388	−	0.681962i	$-0.761127\pi$
$883$	−43.4668	−1.46278	−0.731388	+	0.681962i	$0.761127\pi$
$884$	−30.8217	−1.03664
$885$	8.56846	0.288026
$886$	−18.7256	−0.629098
$887$	38.4739	1.29183	0.645913	−	0.763411i	$-0.276477\pi$
$887$	38.4739	1.29183	0.645913	+	0.763411i	$0.276477\pi$
$888$	−208.537	−6.99805
$889$	78.6018	2.63622
$890$	−47.2600	−1.58416
$891$	−190.265	−6.37413
$892$	−103.439	−3.46339
$893$	−10.3916	−0.347741
$894$	−144.045	−4.81759
$895$	22.6704	0.757788
$896$	100.969	3.37313
$897$	−33.5867	−1.12143
$898$	−51.0884	−1.70484
$899$	3.59171	0.119790
$900$	44.9128	1.49709
$901$	−10.7103	−0.356812
$902$	−49.3860	−1.64437
$903$	59.0688	1.96569
$904$	116.474	3.87388
$905$	18.1039	0.601796
$906$	−59.6463	−1.98161
$907$	16.2069	0.538140	0.269070	−	0.963121i	$-0.413284\pi$
$907$	16.2069	0.538140	0.269070	+	0.963121i	$0.413284\pi$
$908$	61.8960	2.05409
$909$	−40.8481	−1.35485
$910$	70.1739	2.32624
$911$	−25.4253	−0.842377	−0.421189	−	0.906973i	$-0.638387\pi$
$911$	−25.4253	−0.842377	−0.421189	+	0.906973i	$0.638387\pi$
$912$	186.664	6.18108
$913$	−10.4130	−0.344622
$914$	−35.1097	−1.16133
$915$	33.2300	1.09855
$916$	152.340	5.03345
$917$	−71.4457	−2.35935
$918$	50.7714	1.67571
$919$	55.9681	1.84622	0.923108	−	0.384540i	$-0.125640\pi$
$919$	55.9681	1.84622	0.923108	+	0.384540i	$0.125640\pi$
$920$	14.7721	0.487020
$921$	−3.34731	−0.110298
$922$	−77.8776	−2.56476
$923$	−5.86554	−0.193067
$924$	392.852	12.9239
$925$	7.00045	0.230173
$926$	−61.3187	−2.01506
$927$	59.3395	1.94897
$928$	81.6184	2.67925
$929$	−18.6288	−0.611191	−0.305596	−	0.952161i	$-0.598856\pi$
$929$	−18.6288	−0.611191	−0.305596	+	0.952161i	$0.598856\pi$
$930$	7.15247	0.234539
$931$	53.3683	1.74907
$932$	−101.417	−3.32201
$933$	51.0617	1.67168
$934$	104.361	3.41478
$935$	4.95320	0.161987
$936$	−439.492	−14.3652
$937$	25.1425	0.821369	0.410684	−	0.911778i	$-0.365290\pi$
$937$	25.1425	0.821369	0.410684	+	0.911778i	$0.365290\pi$
$938$	−99.1716	−3.23807
$939$	−51.8934	−1.69348
$940$	−13.0244	−0.424808
$941$	5.48746	0.178886	0.0894430	−	0.995992i	$-0.471491\pi$
$941$	5.48746	0.178886	0.0894430	+	0.995992i	$0.471491\pi$
$942$	−138.492	−4.51230
$943$	6.23777	0.203130
$944$	33.0383	1.07530
$945$	−83.7274	−2.72365
$946$	−52.2105	−1.69751
$947$	−55.6019	−1.80682	−0.903409	−	0.428779i	$-0.858944\pi$
$947$	−55.6019	−1.80682	−0.903409	+	0.428779i	$0.858944\pi$
$948$	241.253	7.83555
$949$	17.5677	0.570272
$950$	−11.2923	−0.366370
$951$	−41.5272	−1.34661
$952$	−38.9384	−1.26200
$953$	−31.5179	−1.02096	−0.510482	−	0.859888i	$-0.670533\pi$
$953$	−31.5179	−1.02096	−0.510482	+	0.859888i	$0.670533\pi$
$954$	−246.567	−7.98289
$955$	10.2157	0.330572
$956$	107.014	3.46109
$957$	77.3599	2.50069
$958$	−8.95613	−0.289359
$959$	18.1928	0.587475
$960$	73.4864	2.37176
$961$	−30.3893	−0.980301
$962$	−110.597	−3.56579
$963$	−39.4280	−1.27055
$964$	14.1334	0.455206
$965$	17.4516	0.561786
$966$	−68.5057	−2.20413
$967$	1.28073	0.0411855	0.0205928	−	0.999788i	$-0.493445\pi$
$967$	1.28073	0.0411855	0.0205928	+	0.999788i	$0.493445\pi$
$968$	−118.646	−3.81342
$969$	−14.2465	−0.457665
$970$	−0.143482	−0.00460693
$971$	−50.3461	−1.61568	−0.807842	−	0.589400i	$-0.799364\pi$
$971$	−50.3461	−1.61568	−0.807842	+	0.589400i	$0.799364\pi$
$972$	388.746	12.4690
$973$	−22.0510	−0.706923
$974$	44.6018	1.42913
$975$	19.9318	0.638328
$976$	128.128	4.10128
$977$	−53.3534	−1.70693	−0.853463	−	0.521153i	$-0.825502\pi$
$977$	−53.3534	−1.70693	−0.853463	+	0.521153i	$0.825502\pi$
$978$	141.563	4.52670
$979$	−86.9101	−2.77766
$980$	66.8896	2.13671
$981$	−86.6942	−2.76793
$982$	33.5918	1.07196
$983$	−13.1088	−0.418105	−0.209053	−	0.977904i	$-0.567038\pi$
$983$	−13.1088	−0.418105	−0.209053	+	0.977904i	$0.567038\pi$
$984$	110.272	3.51535
$985$	−18.8582	−0.600873
$986$	−12.3795	−0.394243
$987$	37.4115	1.19082
$988$	129.219	4.11102
$989$	6.59452	0.209694
$990$	114.030	3.62410
$991$	−12.3114	−0.391084	−0.195542	−	0.980695i	$-0.562647\pi$
$991$	−12.3114	−0.391084	−0.195542	+	0.980695i	$0.562647\pi$
$992$	13.8773	0.440604
$993$	−6.17146	−0.195845
$994$	−11.9638	−0.379467
$995$	−20.1943	−0.640203
$996$	37.5385	1.18945
$997$	10.6155	0.336197	0.168098	−	0.985770i	$-0.446237\pi$
$997$	10.6155	0.336197	0.168098	+	0.985770i	$0.446237\pi$
$998$	−40.2461	−1.27397
$999$	131.958	4.17496

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	6035.2.a.h.1.3	✓	59

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
6035.2.a.h.1.3	✓	59	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:	\( N \)	\(=\)	\( 6035 = 5 \cdot 17 \cdot 71 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	6035.a (trivial)

\(f(q)\)	\(=\)	\(q-2.69345 q^{2} +3.39811 q^{3} +5.25470 q^{4} +1.00000 q^{5} -9.15266 q^{6} -4.44179 q^{7} -8.76637 q^{8} +8.54717 q^{9} +O(q^{10})\)	\(q-2.69345 q^{2} +3.39811 q^{3} +5.25470 q^{4} +1.00000 q^{5} -9.15266 q^{6} -4.44179 q^{7} -8.76637 q^{8} +8.54717 q^{9} -2.69345 q^{10} -4.95320 q^{11} +17.8560 q^{12} +5.86554 q^{13} +11.9638 q^{14} +3.39811 q^{15} +13.1024 q^{16} -1.00000 q^{17} -23.0214 q^{18} +4.19249 q^{19} +5.25470 q^{20} -15.0937 q^{21} +13.3412 q^{22} -1.68508 q^{23} -29.7891 q^{24} +1.00000 q^{25} -15.7986 q^{26} +18.8499 q^{27} -23.3403 q^{28} -4.59613 q^{29} -9.15266 q^{30} -0.781463 q^{31} -17.7581 q^{32} -16.8315 q^{33} +2.69345 q^{34} -4.44179 q^{35} +44.9128 q^{36} +7.00045 q^{37} -11.2923 q^{38} +19.9318 q^{39} -8.76637 q^{40} -3.70176 q^{41} +40.6542 q^{42} -3.91347 q^{43} -26.0276 q^{44} +8.54717 q^{45} +4.53869 q^{46} -2.47862 q^{47} +44.5236 q^{48} +12.7295 q^{49} -2.69345 q^{50} -3.39811 q^{51} +30.8217 q^{52} +10.7103 q^{53} -50.7714 q^{54} -4.95320 q^{55} +38.9384 q^{56} +14.2465 q^{57} +12.3795 q^{58} +2.52154 q^{59} +17.8560 q^{60} +9.77896 q^{61} +2.10483 q^{62} -37.9647 q^{63} +21.6256 q^{64} +5.86554 q^{65} +45.3350 q^{66} -8.28934 q^{67} -5.25470 q^{68} -5.72610 q^{69} +11.9638 q^{70} -1.00000 q^{71} -74.9277 q^{72} +2.99507 q^{73} -18.8554 q^{74} +3.39811 q^{75} +22.0303 q^{76} +22.0011 q^{77} -53.6853 q^{78} +13.5110 q^{79} +13.1024 q^{80} +38.4126 q^{81} +9.97052 q^{82} +2.10229 q^{83} -79.3128 q^{84} -1.00000 q^{85} +10.5408 q^{86} -15.6182 q^{87} +43.4216 q^{88} +17.5463 q^{89} -23.0214 q^{90} -26.0535 q^{91} -8.85459 q^{92} -2.65550 q^{93} +6.67604 q^{94} +4.19249 q^{95} -60.3439 q^{96} +0.0532706 q^{97} -34.2863 q^{98} -42.3358 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9}+O(q^{10}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9	\( 59 q + 2 q^{2} + 6 q^{3} + 76 q^{4} + 59 q^{5} + 14 q^{6} + 9 q^{7} + 6 q^{8} + 97 q^{9} + 2 q^{10} + 6 q^{11} + 16 q^{12} + 25 q^{13} + 8 q^{14} + 6 q^{15} + 114 q^{16} - 59 q^{17} + 3 q^{18} + 35 q^{19} + 76 q^{20} + 41 q^{21} + 13 q^{22} - 2 q^{23} + 35 q^{24} + 59 q^{25} + 10 q^{26} + 27 q^{27} + 28 q^{28} + 10 q^{29} + 14 q^{30} + 15 q^{31} + 19 q^{32} - 3 q^{33} - 2 q^{34} + 9 q^{35} + 160 q^{36} + 56 q^{37} + 17 q^{38} + 25 q^{39} + 6 q^{40} + 47 q^{41} + 46 q^{42} + 27 q^{43} + 39 q^{44} + 97 q^{45} + 4 q^{46} - 8 q^{47} + 58 q^{48} + 174 q^{49} + 2 q^{50} - 6 q^{51} + 13 q^{52} + 17 q^{53} + 48 q^{54} + 6 q^{55} + 33 q^{56} + 6 q^{57} + 32 q^{58} + 30 q^{59} + 16 q^{60} + 85 q^{61} - 3 q^{62} + 14 q^{63} + 168 q^{64} + 25 q^{65} + 87 q^{66} + 21 q^{67} - 76 q^{68} + 111 q^{69} + 8 q^{70} - 59 q^{71} - 52 q^{72} + 41 q^{73} + 11 q^{74} + 6 q^{75} + 118 q^{76} + 55 q^{77} - 54 q^{78} + 43 q^{79} + 114 q^{80} + 207 q^{81} + 45 q^{82} + 10 q^{83} + 62 q^{84} - 59 q^{85} + 19 q^{86} + 8 q^{87} + 35 q^{88} + 86 q^{89} + 3 q^{90} + 47 q^{91} - 98 q^{92} + 41 q^{93} + 30 q^{94} + 35 q^{95} + 69 q^{96} + 72 q^{97} + 14 q^{98} + 25 q^{99}+O(q^{100}) \) 59 * q + 2 * q^2 + 6 * q^3 + 76 * q^4 + 59 * q^5 + 14 * q^6 + 9 * q^7 + 6 * q^8 + 97 * q^9 + 2 * q^10 + 6 * q^11 + 16 * q^12 + 25 * q^13 + 8 * q^14 + 6 * q^15 + 114 * q^16 - 59 * q^17 + 3 * q^18 + 35 * q^19 + 76 * q^20 + 41 * q^21 + 13 * q^22 - 2 * q^23 + 35 * q^24 + 59 * q^25 + 10 * q^26 + 27 * q^27 + 28 * q^28 + 10 * q^29 + 14 * q^30 + 15 * q^31 + 19 * q^32 - 3 * q^33 - 2 * q^34 + 9 * q^35 + 160 * q^36 + 56 * q^37 + 17 * q^38 + 25 * q^39 + 6 * q^40 + 47 * q^41 + 46 * q^42 + 27 * q^43 + 39 * q^44 + 97 * q^45 + 4 * q^46 - 8 * q^47 + 58 * q^48 + 174 * q^49 + 2 * q^50 - 6 * q^51 + 13 * q^52 + 17 * q^53 + 48 * q^54 + 6 * q^55 + 33 * q^56 + 6 * q^57 + 32 * q^58 + 30 * q^59 + 16 * q^60 + 85 * q^61 - 3 * q^62 + 14 * q^63 + 168 * q^64 + 25 * q^65 + 87 * q^66 + 21 * q^67 - 76 * q^68 + 111 * q^69 + 8 * q^70 - 59 * q^71 - 52 * q^72 + 41 * q^73 + 11 * q^74 + 6 * q^75 + 118 * q^76 + 55 * q^77 - 54 * q^78 + 43 * q^79 + 114 * q^80 + 207 * q^81 + 45 * q^82 + 10 * q^83 + 62 * q^84 - 59 * q^85 + 19 * q^86 + 8 * q^87 + 35 * q^88 + 86 * q^89 + 3 * q^90 + 47 * q^91 - 98 * q^92 + 41 * q^93 + 30 * q^94 + 35 * q^95 + 69 * q^96 + 72 * q^97 + 14 * q^98 + 25 * q^99

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