LMFDB - Embedded newform 177.10.a.d.1.21

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,10,Mod(1,177)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(177, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	177.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:	$91.1613430010$
Analytic rank:	$0$
Dimension:	$22$
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.21
Character	$\chi$	$=$	177.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+42.2698 q^{2} +81.0000 q^{3} +1274.73 q^{4} -60.0153 q^{5} +3423.85 q^{6} +8826.78 q^{7} +32240.5 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+42.2698 q^{2} +81.0000 q^{3} +1274.73 q^{4} -60.0153 q^{5} +3423.85 q^{6} +8826.78 q^{7} +32240.5 q^{8} +6561.00 q^{9} -2536.83 q^{10} +16200.8 q^{11} +103253. q^{12} +123272. q^{13} +373106. q^{14} -4861.24 q^{15} +710136. q^{16} -165876. q^{17} +277332. q^{18} -692496. q^{19} -76503.4 q^{20} +714969. q^{21} +684803. q^{22} -387376. q^{23} +2.61148e6 q^{24} -1.94952e6 q^{25} +5.21069e6 q^{26} +531441. q^{27} +1.12518e7 q^{28} -1.66452e6 q^{29} -205483. q^{30} -1.05783e6 q^{31} +1.35101e7 q^{32} +1.31226e6 q^{33} -7.01153e6 q^{34} -529742. q^{35} +8.36352e6 q^{36} +5.42244e6 q^{37} -2.92717e7 q^{38} +9.98505e6 q^{39} -1.93492e6 q^{40} -2.48157e7 q^{41} +3.02216e7 q^{42} +1.30273e7 q^{43} +2.06516e7 q^{44} -393760. q^{45} -1.63743e7 q^{46} +2.22102e7 q^{47} +5.75210e7 q^{48} +3.75584e7 q^{49} -8.24059e7 q^{50} -1.34359e7 q^{51} +1.57139e8 q^{52} +9.05128e7 q^{53} +2.24639e7 q^{54} -972293. q^{55} +2.84580e8 q^{56} -5.60922e7 q^{57} -7.03589e7 q^{58} -1.21174e7 q^{59} -6.19678e6 q^{60} +5.78319e7 q^{61} -4.47143e7 q^{62} +5.79125e7 q^{63} +2.07481e8 q^{64} -7.39822e6 q^{65} +5.54690e7 q^{66} -2.31519e8 q^{67} -2.11447e8 q^{68} -3.13775e7 q^{69} -2.23920e7 q^{70} +1.74344e7 q^{71} +2.11530e8 q^{72} +1.14788e8 q^{73} +2.29205e8 q^{74} -1.57911e8 q^{75} -8.82748e8 q^{76} +1.43001e8 q^{77} +4.22066e8 q^{78} -1.84489e8 q^{79} -4.26190e7 q^{80} +4.30467e7 q^{81} -1.04895e9 q^{82} +5.49192e8 q^{83} +9.11394e8 q^{84} +9.95509e6 q^{85} +5.50661e8 q^{86} -1.34826e8 q^{87} +5.22321e8 q^{88} +1.64838e8 q^{89} -1.66442e7 q^{90} +1.08810e9 q^{91} -4.93801e8 q^{92} -8.56843e7 q^{93} +9.38821e8 q^{94} +4.15604e7 q^{95} +1.09432e9 q^{96} -1.37978e9 q^{97} +1.58758e9 q^{98} +1.06293e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) $ 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * 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 $

$2$	42.2698	1.86808	0.934039	−	0.357172i	$-0.116259\pi$
$2$	42.2698	1.86808	0.934039	+	0.357172i	$0.116259\pi$
$3$	81.0000	0.577350
$3$	81.0000	0.577350
$4$	1274.73	2.48971
$5$	−60.0153	−0.0429434	−0.0214717	−	0.999769i	$-0.506835\pi$
$5$	−60.0153	−0.0429434	−0.0214717	+	0.999769i	$0.506835\pi$
$6$	3423.85	1.07853
$7$	8826.78	1.38951	0.694754	−	0.719247i	$-0.255513\pi$
$7$	8826.78	1.38951	0.694754	+	0.719247i	$0.255513\pi$
$8$	32240.5	2.78290
$9$	6561.00	0.333333
$10$	−2536.83	−0.0802217
$11$	16200.8	0.333633	0.166816	−	0.985988i	$-0.446651\pi$
$11$	16200.8	0.333633	0.166816	+	0.985988i	$0.446651\pi$
$12$	103253.	1.43744
$13$	123272.	1.19707	0.598536	−	0.801096i	$-0.295749\pi$
$13$	123272.	1.19707	0.598536	+	0.801096i	$0.295749\pi$
$14$	373106.	2.59571
$15$	−4861.24	−0.0247934
$16$	710136.	2.70896
$17$	−165876.	−0.481685	−0.240842	−	0.970564i	$-0.577424\pi$
$17$	−165876.	−0.481685	−0.240842	+	0.970564i	$0.577424\pi$
$18$	277332.	0.622692
$19$	−692496.	−1.21906	−0.609532	−	0.792762i	$-0.708643\pi$
$19$	−692496.	−1.21906	−0.609532	+	0.792762i	$0.708643\pi$
$20$	−76503.4	−0.106917
$21$	714969.	0.802233
$22$	684803.	0.623251
$23$	−387376.	−0.288641	−0.144320	−	0.989531i	$-0.546100\pi$
$23$	−387376.	−0.288641	−0.144320	+	0.989531i	$0.546100\pi$
$24$	2.61148e6	1.60671
$25$	−1.94952e6	−0.998156
$26$	5.21069e6	2.23622
$27$	531441.	0.192450
$28$	1.12518e7	3.45947
$29$	−1.66452e6	−0.437017	−0.218509	−	0.975835i	$-0.570119\pi$
$29$	−1.66452e6	−0.437017	−0.218509	+	0.975835i	$0.570119\pi$
$30$	−205483.	−0.0463160
$31$	−1.05783e6	−0.205726	−0.102863	−	0.994696i	$-0.532800\pi$
$31$	−1.05783e6	−0.205726	−0.102863	+	0.994696i	$0.532800\pi$
$32$	1.35101e7	2.27764
$33$	1.31226e6	0.192623
$34$	−7.01153e6	−0.899825
$35$	−529742.	−0.0596702
$36$	8.36352e6	0.829904
$37$	5.42244e6	0.475650	0.237825	−	0.971308i	$-0.423566\pi$
$37$	5.42244e6	0.475650	0.237825	+	0.971308i	$0.423566\pi$
$38$	−2.92717e7	−2.27730
$39$	9.98505e6	0.691130
$40$	−1.93492e6	−0.119507
$41$	−2.48157e7	−1.37151	−0.685755	−	0.727832i	$-0.740528\pi$
$41$	−2.48157e7	−1.37151	−0.685755	+	0.727832i	$0.740528\pi$
$42$	3.02216e7	1.49863
$43$	1.30273e7	0.581094	0.290547	−	0.956861i	$-0.406163\pi$
$43$	1.30273e7	0.581094	0.290547	+	0.956861i	$0.406163\pi$
$44$	2.06516e7	0.830649
$45$	−393760.	−0.0143145
$46$	−1.63743e7	−0.539203
$47$	2.22102e7	0.663915	0.331958	−	0.943294i	$-0.392291\pi$
$47$	2.22102e7	0.663915	0.331958	+	0.943294i	$0.392291\pi$
$48$	5.75210e7	1.56402
$49$	3.75584e7	0.930732
$50$	−8.24059e7	−1.86463
$51$	−1.34359e7	−0.278101
$52$	1.57139e8	2.98036
$53$	9.05128e7	1.57568	0.787841	−	0.615879i	$-0.211199\pi$
$53$	9.05128e7	1.57568	0.787841	+	0.615879i	$0.211199\pi$
$54$	2.24639e7	0.359512
$55$	−972293.	−0.0143273
$56$	2.84580e8	3.86686
$57$	−5.60922e7	−0.703827
$58$	−7.03589e7	−0.816382
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−6.19678e6	−0.0617284
$61$	5.78319e7	0.534790	0.267395	−	0.963587i	$-0.413837\pi$
$61$	5.78319e7	0.534790	0.267395	+	0.963587i	$0.413837\pi$
$62$	−4.47143e7	−0.384312
$63$	5.79125e7	0.463169
$64$	2.07481e8	1.54585
$65$	−7.39822e6	−0.0514064
$66$	5.54690e7	0.359834
$67$	−2.31519e8	−1.40362	−0.701810	−	0.712364i	$-0.747624\pi$
$67$	−2.31519e8	−1.40362	−0.701810	+	0.712364i	$0.747624\pi$
$68$	−2.11447e8	−1.19926
$69$	−3.13775e7	−0.166647
$70$	−2.23920e7	−0.111469
$71$	1.74344e7	0.0814227	0.0407114	−	0.999171i	$-0.487038\pi$
$71$	1.74344e7	0.0814227	0.0407114	+	0.999171i	$0.487038\pi$
$72$	2.11530e8	0.927633
$73$	1.14788e8	0.473092	0.236546	−	0.971620i	$-0.423985\pi$
$73$	1.14788e8	0.473092	0.236546	+	0.971620i	$0.423985\pi$
$74$	2.29205e8	0.888551
$75$	−1.57911e8	−0.576286
$76$	−8.82748e8	−3.03512
$77$	1.43001e8	0.463585
$78$	4.22066e8	1.29108
$79$	−1.84489e8	−0.532905	−0.266452	−	0.963848i	$-0.585852\pi$
$79$	−1.84489e8	−0.532905	−0.266452	+	0.963848i	$0.585852\pi$
$80$	−4.26190e7	−0.116332
$81$	4.30467e7	0.111111
$82$	−1.04895e9	−2.56209
$83$	5.49192e8	1.27020	0.635101	−	0.772429i	$-0.280959\pi$
$83$	5.49192e8	1.27020	0.635101	+	0.772429i	$0.280959\pi$
$84$	9.11394e8	1.99733
$85$	9.95509e6	0.0206852
$86$	5.50661e8	1.08553
$87$	−1.34826e8	−0.252312
$88$	5.22321e8	0.928465
$89$	1.64838e8	0.278485	0.139242	−	0.990258i	$-0.455533\pi$
$89$	1.64838e8	0.278485	0.139242	+	0.990258i	$0.455533\pi$
$90$	−1.66442e7	−0.0267406
$91$	1.08810e9	1.66334
$92$	−4.93801e8	−0.718632
$93$	−8.56843e7	−0.118776
$94$	9.38821e8	1.24025
$95$	4.15604e7	0.0523508
$96$	1.09432e9	1.31500
$97$	−1.37978e9	−1.58248	−0.791239	−	0.611507i	$-0.790564\pi$
$97$	−1.37978e9	−1.58248	−0.791239	+	0.611507i	$0.790564\pi$
$98$	1.58758e9	1.73868
$99$	1.06293e8	0.111211
$100$	−2.48512e9	−2.48512
$101$	7.27601e8	0.695740	0.347870	−	0.937543i	$-0.386905\pi$
$101$	7.27601e8	0.695740	0.347870	+	0.937543i	$0.386905\pi$
$102$	−5.67934e8	−0.519514
$103$	2.84037e8	0.248661	0.124330	−	0.992241i	$-0.460322\pi$
$103$	2.84037e8	0.248661	0.124330	+	0.992241i	$0.460322\pi$
$104$	3.97436e9	3.33133
$105$	−4.29091e7	−0.0344506
$106$	3.82595e9	2.94350
$107$	7.20470e8	0.531360	0.265680	−	0.964061i	$-0.414404\pi$
$107$	7.20470e8	0.531360	0.265680	+	0.964061i	$0.414404\pi$
$108$	6.77445e8	0.479145
$109$	−2.76564e9	−1.87662	−0.938312	−	0.345790i	$-0.887611\pi$
$109$	−2.76564e9	−1.87662	−0.938312	+	0.345790i	$0.887611\pi$
$110$	−4.10986e7	−0.0267646
$111$	4.39218e8	0.274617
$112$	6.26822e9	3.76411
$113$	−1.41911e9	−0.818773	−0.409386	−	0.912361i	$-0.634257\pi$
$113$	−1.41911e9	−0.818773	−0.409386	+	0.912361i	$0.634257\pi$
$114$	−2.37100e9	−1.31480
$115$	2.32485e7	0.0123952
$116$	−2.12182e9	−1.08805
$117$	8.08789e8	0.399024
$118$	−5.12198e8	−0.243203
$119$	−1.46415e9	−0.669305
$120$	−1.56729e8	−0.0689975
$121$	−2.09548e9	−0.888689
$122$	2.44454e9	0.999029
$123$	−2.01007e9	−0.791842
$124$	−1.34845e9	−0.512198
$125$	2.34219e8	0.0858077
$126$	2.44795e9	0.865236
$127$	−4.50001e9	−1.53496	−0.767479	−	0.641074i	$-0.778489\pi$
$127$	−4.50001e9	−1.53496	−0.767479	+	0.641074i	$0.778489\pi$
$128$	1.85297e9	0.610130
$129$	1.05521e9	0.335495
$130$	−3.12721e8	−0.0960311
$131$	−2.56225e8	−0.0760151	−0.0380076	−	0.999277i	$-0.512101\pi$
$131$	−2.56225e8	−0.0760151	−0.0380076	+	0.999277i	$0.512101\pi$
$132$	1.67278e9	0.479576
$133$	−6.11251e9	−1.69390
$134$	−9.78624e9	−2.62207
$135$	−3.18946e7	−0.00826447
$136$	−5.34793e9	−1.34048
$137$	7.23263e9	1.75410	0.877048	−	0.480402i	$-0.159509\pi$
$137$	7.23263e9	1.75410	0.877048	+	0.480402i	$0.159509\pi$
$138$	−1.32632e9	−0.311309
$139$	6.75360e9	1.53451	0.767253	−	0.641344i	$-0.221623\pi$
$139$	6.75360e9	1.53451	0.767253	+	0.641344i	$0.221623\pi$
$140$	−6.75279e8	−0.148562
$141$	1.79903e9	0.383312
$142$	7.36950e8	0.152104
$143$	1.99710e9	0.399382
$144$	4.65920e9	0.902985
$145$	9.98967e7	0.0187670
$146$	4.85208e9	0.883772
$147$	3.04223e9	0.537359
$148$	6.91217e9	1.18423
$149$	−8.62282e9	−1.43321	−0.716607	−	0.697477i	$-0.754306\pi$
$149$	−8.62282e9	−1.43321	−0.716607	+	0.697477i	$0.754306\pi$
$150$	−6.67488e9	−1.07655
$151$	−4.09088e9	−0.640355	−0.320178	−	0.947358i	$-0.603743\pi$
$151$	−4.09088e9	−0.640355	−0.320178	+	0.947358i	$0.603743\pi$
$152$	−2.23265e10	−3.39253
$153$	−1.08831e9	−0.160562
$154$	6.04460e9	0.866013
$155$	6.34860e7	0.00883457
$156$	1.27283e10	1.72071
$157$	−3.74731e9	−0.492234	−0.246117	−	0.969240i	$-0.579155\pi$
$157$	−3.74731e9	−0.492234	−0.246117	+	0.969240i	$0.579155\pi$
$158$	−7.79833e9	−0.995507
$159$	7.33154e9	0.909720
$160$	−8.10815e8	−0.0978097
$161$	−3.41928e9	−0.401068
$162$	1.81957e9	0.207564
$163$	1.62523e9	0.180332	0.0901658	−	0.995927i	$-0.471260\pi$
$163$	1.62523e9	0.180332	0.0901658	+	0.995927i	$0.471260\pi$
$164$	−3.16334e10	−3.41467
$165$	−7.87558e7	−0.00827189
$166$	2.32142e10	2.37283
$167$	−8.68516e9	−0.864080	−0.432040	−	0.901854i	$-0.642206\pi$
$167$	−8.68516e9	−0.864080	−0.432040	+	0.901854i	$0.642206\pi$
$168$	2.30510e10	2.23253
$169$	4.59154e9	0.432980
$170$	4.20799e8	0.0386416
$171$	−4.54347e9	−0.406355
$172$	1.66063e10	1.44676
$173$	−5.57213e9	−0.472948	−0.236474	−	0.971638i	$-0.575992\pi$
$173$	−5.57213e9	−0.472948	−0.236474	+	0.971638i	$0.575992\pi$
$174$	−5.69907e9	−0.471338
$175$	−1.72080e10	−1.38695
$176$	1.15048e10	0.903796
$177$	−9.81506e8	−0.0751646
$178$	6.96765e9	0.520231
$179$	2.83494e9	0.206398	0.103199	−	0.994661i	$-0.467092\pi$
$179$	2.83494e9	0.206398	0.103199	+	0.994661i	$0.467092\pi$
$180$	−5.01939e8	−0.0356389
$181$	−6.81693e8	−0.0472101	−0.0236051	−	0.999721i	$-0.507514\pi$
$181$	−6.81693e8	−0.0472101	−0.0236051	+	0.999721i	$0.507514\pi$
$182$	4.59936e10	3.10725
$183$	4.68439e9	0.308761
$184$	−1.24892e10	−0.803257
$185$	−3.25430e8	−0.0204260
$186$	−3.62186e9	−0.221882
$187$	−2.68732e9	−0.160706
$188$	2.83121e10	1.65296
$189$	4.69091e9	0.267411
$190$	1.75675e9	0.0977953
$191$	3.50450e9	0.190535	0.0952676	−	0.995452i	$-0.469629\pi$
$191$	3.50450e9	0.190535	0.0952676	+	0.995452i	$0.469629\pi$
$192$	1.68059e10	0.892498
$193$	3.04202e10	1.57817	0.789085	−	0.614285i	$-0.210555\pi$
$193$	3.04202e10	1.57817	0.789085	+	0.614285i	$0.210555\pi$
$194$	−5.83231e10	−2.95619
$195$	−5.99256e8	−0.0296795
$196$	4.78769e10	2.31726
$197$	2.76245e10	1.30676	0.653380	−	0.757030i	$-0.273350\pi$
$197$	2.76245e10	1.30676	0.653380	+	0.757030i	$0.273350\pi$
$198$	4.49299e9	0.207750
$199$	1.23928e10	0.560185	0.280093	−	0.959973i	$-0.409635\pi$
$199$	1.23928e10	0.560185	0.280093	+	0.959973i	$0.409635\pi$
$200$	−6.28537e10	−2.77777
$201$	−1.87530e10	−0.810380
$202$	3.07555e10	1.29970
$203$	−1.46924e10	−0.607239
$204$	−1.71272e10	−0.692391
$205$	1.48932e9	0.0588974
$206$	1.20062e10	0.464517
$207$	−2.54157e9	−0.0962135
$208$	8.75401e10	3.24281
$209$	−1.12190e10	−0.406719
$210$	−1.81376e9	−0.0643564
$211$	2.58153e10	0.896615	0.448308	−	0.893879i	$-0.352027\pi$
$211$	2.58153e10	0.896615	0.448308	+	0.893879i	$0.352027\pi$
$212$	1.15380e11	3.92299
$213$	1.41219e9	0.0470094
$214$	3.04541e10	0.992621
$215$	−7.81837e8	−0.0249542
$216$	1.71339e10	0.535569
$217$	−9.33724e9	−0.285858
$218$	−1.16903e11	−3.50568
$219$	9.29786e9	0.273140
$220$	−1.23941e9	−0.0356709
$221$	−2.04479e10	−0.576611
$222$	1.85656e10	0.513005
$223$	−2.78289e9	−0.0753572	−0.0376786	−	0.999290i	$-0.511996\pi$
$223$	−2.78289e9	−0.0753572	−0.0376786	+	0.999290i	$0.511996\pi$
$224$	1.19251e11	3.16480
$225$	−1.27908e10	−0.332719
$226$	−5.99855e10	−1.52953
$227$	−2.66911e10	−0.667191	−0.333595	−	0.942716i	$-0.608262\pi$
$227$	−2.66911e10	−0.667191	−0.333595	+	0.942716i	$0.608262\pi$
$228$	−7.15026e10	−1.75233
$229$	−2.17020e10	−0.521482	−0.260741	−	0.965409i	$-0.583967\pi$
$229$	−2.17020e10	−0.521482	−0.260741	+	0.965409i	$0.583967\pi$
$230$	9.82707e8	0.0231552
$231$	1.15830e10	0.267651
$232$	−5.36650e10	−1.21617
$233$	8.26830e10	1.83787	0.918935	−	0.394409i	$-0.129051\pi$
$233$	8.26830e10	1.83787	0.918935	+	0.394409i	$0.129051\pi$
$234$	3.41873e10	0.745407
$235$	−1.33295e9	−0.0285108
$236$	−1.54464e10	−0.324133
$237$	−1.49436e10	−0.307673
$238$	−6.18892e10	−1.25031
$239$	−4.38699e10	−0.869713	−0.434857	−	0.900500i	$-0.643201\pi$
$239$	−4.38699e10	−0.869713	−0.434857	+	0.900500i	$0.643201\pi$
$240$	−3.45214e9	−0.0671642
$241$	2.06071e10	0.393495	0.196748	−	0.980454i	$-0.436962\pi$
$241$	2.06071e10	0.393495	0.196748	+	0.980454i	$0.436962\pi$
$242$	−8.85756e10	−1.66014
$243$	3.48678e9	0.0641500
$244$	7.37202e10	1.33147
$245$	−2.25408e9	−0.0399688
$246$	−8.49652e10	−1.47922
$247$	−8.53656e10	−1.45931
$248$	−3.41050e10	−0.572514
$249$	4.44845e10	0.733351
$250$	9.90036e9	0.160295
$251$	4.19417e10	0.666983	0.333492	−	0.942753i	$-0.391773\pi$
$251$	4.19417e10	0.666983	0.333492	+	0.942753i	$0.391773\pi$
$252$	7.38229e10	1.15316
$253$	−6.27579e9	−0.0962999
$254$	−1.90214e11	−2.86742
$255$	8.06362e8	0.0119426
$256$	−2.79057e10	−0.406081
$257$	−1.08931e11	−1.55759	−0.778796	−	0.627277i	$-0.784169\pi$
$257$	−1.08931e11	−1.55759	−0.778796	+	0.627277i	$0.784169\pi$
$258$	4.46035e10	0.626730
$259$	4.78627e10	0.660919
$260$	−9.43075e9	−0.127987
$261$	−1.09209e10	−0.145672
$262$	−1.08306e10	−0.142002
$263$	−1.51234e11	−1.94916	−0.974581	−	0.224037i	$-0.928076\pi$
$263$	−1.51234e11	−1.94916	−0.974581	+	0.224037i	$0.928076\pi$
$264$	4.23080e10	0.536050
$265$	−5.43215e9	−0.0676652
$266$	−2.58374e11	−3.16433
$267$	1.33518e10	0.160783
$268$	−2.95124e11	−3.49461
$269$	−4.01575e10	−0.467607	−0.233804	−	0.972284i	$-0.575117\pi$
$269$	−4.01575e10	−0.467607	−0.233804	+	0.972284i	$0.575117\pi$
$270$	−1.34818e9	−0.0154387
$271$	−3.70127e10	−0.416859	−0.208429	−	0.978037i	$-0.566835\pi$
$271$	−3.70127e10	−0.416859	−0.208429	+	0.978037i	$0.566835\pi$
$272$	−1.17794e11	−1.30486
$273$	8.81358e10	0.960330
$274$	3.05721e11	3.27679
$275$	−3.15838e10	−0.333017
$276$	−3.99979e10	−0.414902
$277$	8.72178e10	0.890115	0.445057	−	0.895502i	$-0.353183\pi$
$277$	8.72178e10	0.890115	0.445057	+	0.895502i	$0.353183\pi$
$278$	2.85473e11	2.86658
$279$	−6.94043e9	−0.0685753
$280$	−1.70791e10	−0.166056
$281$	−8.67326e10	−0.829859	−0.414929	−	0.909854i	$-0.636194\pi$
$281$	−8.67326e10	−0.829859	−0.414929	+	0.909854i	$0.636194\pi$
$282$	7.60445e10	0.716056
$283$	3.51750e10	0.325983	0.162992	−	0.986627i	$-0.447886\pi$
$283$	3.51750e10	0.325983	0.162992	+	0.986627i	$0.447886\pi$
$284$	2.22243e10	0.202719
$285$	3.36639e9	0.0302247
$286$	8.44171e10	0.746077
$287$	−2.19043e11	−1.90572
$288$	8.86400e10	0.759213
$289$	−9.10731e10	−0.767980
$290$	4.22261e9	0.0350582
$291$	−1.11762e11	−0.913644
$292$	1.46325e11	1.17786
$293$	1.83113e11	1.45149	0.725746	−	0.687963i	$-0.241495\pi$
$293$	1.83113e11	1.45149	0.725746	+	0.687963i	$0.241495\pi$
$294$	1.28594e11	1.00383
$295$	7.27227e8	0.00559076
$296$	1.74822e11	1.32368
$297$	8.60975e9	0.0642076
$298$	−3.64484e11	−2.67735
$299$	−4.77527e10	−0.345523
$300$	−2.01295e11	−1.43479
$301$	1.14989e11	0.807434
$302$	−1.72921e11	−1.19623
$303$	5.89357e10	0.401686
$304$	−4.91767e11	−3.30239
$305$	−3.47080e9	−0.0229657
$306$	−4.60027e10	−0.299942
$307$	−1.30126e11	−0.836068	−0.418034	−	0.908431i	$-0.637281\pi$
$307$	−1.30126e11	−0.836068	−0.418034	+	0.908431i	$0.637281\pi$
$308$	1.82287e11	1.15419
$309$	2.30070e10	0.143564
$310$	2.68354e9	0.0165037
$311$	2.36559e11	1.43390	0.716948	−	0.697127i	$-0.245538\pi$
$311$	2.36559e11	1.43390	0.716948	+	0.697127i	$0.245538\pi$
$312$	3.21923e11	1.92334
$313$	−2.09703e11	−1.23497	−0.617483	−	0.786584i	$-0.711848\pi$
$313$	−2.09703e11	−1.23497	−0.617483	+	0.786584i	$0.711848\pi$
$314$	−1.58398e11	−0.919531
$315$	−3.47563e9	−0.0198901
$316$	−2.35175e11	−1.32678
$317$	2.01816e11	1.12251	0.561253	−	0.827645i	$-0.310320\pi$
$317$	2.01816e11	1.12251	0.561253	+	0.827645i	$0.310320\pi$
$318$	3.09902e11	1.69943
$319$	−2.69665e10	−0.145803
$320$	−1.24520e10	−0.0663842
$321$	5.83581e10	0.306781
$322$	−1.44532e11	−0.749227
$323$	1.14868e11	0.587205
$324$	5.48731e10	0.276635
$325$	−2.40322e11	−1.19486
$326$	6.86983e10	0.336873
$327$	−2.24017e11	−1.08347
$328$	−8.00071e11	−3.81677
$329$	1.96045e11	0.922516
$330$	−3.32899e9	−0.0154525
$331$	−3.32010e11	−1.52029	−0.760144	−	0.649755i	$-0.774871\pi$
$331$	−3.32010e11	−1.52029	−0.760144	+	0.649755i	$0.774871\pi$
$332$	7.00073e11	3.16244
$333$	3.55767e10	0.158550
$334$	−3.67120e11	−1.61417
$335$	1.38947e10	0.0602763
$336$	5.07725e11	2.17321
$337$	−5.50980e10	−0.232703	−0.116351	−	0.993208i	$-0.537120\pi$
$337$	−5.50980e10	−0.232703	−0.116351	+	0.993208i	$0.537120\pi$
$338$	1.94083e11	0.808841
$339$	−1.14948e11	−0.472719
$340$	1.26901e10	0.0515002
$341$	−1.71377e10	−0.0686368
$342$	−1.92051e11	−0.759102
$343$	−2.46726e10	−0.0962481
$344$	4.20007e11	1.61712
$345$	1.88313e9	0.00715638
$346$	−2.35533e11	−0.883504
$347$	−3.11529e11	−1.15349	−0.576747	−	0.816923i	$-0.695678\pi$
$347$	−3.11529e11	−1.15349	−0.576747	+	0.816923i	$0.695678\pi$
$348$	−1.71867e11	−0.628184
$349$	−3.19139e11	−1.15150	−0.575751	−	0.817625i	$-0.695290\pi$
$349$	−3.19139e11	−1.15150	−0.575751	+	0.817625i	$0.695290\pi$
$350$	−7.27378e11	−2.59092
$351$	6.55119e10	0.230377
$352$	2.18875e11	0.759895
$353$	−1.33725e11	−0.458382	−0.229191	−	0.973382i	$-0.573608\pi$
$353$	−1.33725e11	−0.458382	−0.229191	+	0.973382i	$0.573608\pi$
$354$	−4.14880e10	−0.140413
$355$	−1.04633e9	−0.00349657
$356$	2.10124e11	0.693347
$357$	−1.18596e11	−0.386423
$358$	1.19832e11	0.385567
$359$	−1.61952e11	−0.514590	−0.257295	−	0.966333i	$-0.582831\pi$
$359$	−1.61952e11	−0.514590	−0.257295	+	0.966333i	$0.582831\pi$
$360$	−1.26950e10	−0.0398357
$361$	1.56864e11	0.486116
$362$	−2.88150e10	−0.0881921
$363$	−1.69734e11	−0.513085
$364$	1.38703e12	4.14124
$365$	−6.88906e9	−0.0203162
$366$	1.98008e11	0.576790
$367$	−2.17085e11	−0.624643	−0.312322	−	0.949976i	$-0.601107\pi$
$367$	−2.17085e11	−0.624643	−0.312322	+	0.949976i	$0.601107\pi$
$368$	−2.75090e11	−0.781914
$369$	−1.62816e11	−0.457170
$370$	−1.37558e10	−0.0381574
$371$	7.98936e11	2.18942
$372$	−1.09225e11	−0.295718
$373$	−3.00669e11	−0.804265	−0.402132	−	0.915581i	$-0.631731\pi$
$373$	−3.00669e11	−0.804265	−0.402132	+	0.915581i	$0.631731\pi$
$374$	−1.13592e11	−0.300211
$375$	1.89717e10	0.0495411
$376$	7.16070e11	1.84761
$377$	−2.05189e11	−0.523141
$378$	1.98284e11	0.499544
$379$	3.67439e11	0.914763	0.457381	−	0.889271i	$-0.348787\pi$
$379$	3.67439e11	0.914763	0.457381	+	0.889271i	$0.348787\pi$
$380$	5.29784e10	0.130338
$381$	−3.64501e11	−0.886209
$382$	1.48134e11	0.355935
$383$	3.85840e11	0.916247	0.458124	−	0.888888i	$-0.348522\pi$
$383$	3.85840e11	0.916247	0.458124	+	0.888888i	$0.348522\pi$
$384$	1.50090e11	0.352259
$385$	−8.58222e9	−0.0199079
$386$	1.28585e12	2.94814
$387$	8.54721e10	0.193698
$388$	−1.75885e12	−3.93992
$389$	4.01764e11	0.889606	0.444803	−	0.895628i	$-0.353274\pi$
$389$	4.01764e11	0.889606	0.444803	+	0.895628i	$0.353274\pi$
$390$	−2.53304e10	−0.0554436
$391$	6.42563e10	0.139034
$392$	1.21090e12	2.59013
$393$	−2.07542e10	−0.0438874
$394$	1.16768e12	2.44113
$395$	1.10722e10	0.0228848
$396$	1.35495e11	0.276883
$397$	1.01154e11	0.204374	0.102187	−	0.994765i	$-0.467416\pi$
$397$	1.01154e11	0.204374	0.102187	+	0.994765i	$0.467416\pi$
$398$	5.23842e11	1.04647
$399$	−4.95113e11	−0.977973
$400$	−1.38443e12	−2.70396
$401$	2.50446e11	0.483687	0.241844	−	0.970315i	$-0.422248\pi$
$401$	2.50446e11	0.483687	0.241844	+	0.970315i	$0.422248\pi$
$402$	−7.92685e11	−1.51385
$403$	−1.30401e11	−0.246269
$404$	9.27497e11	1.73219
$405$	−2.58346e9	−0.00477149
$406$	−6.21043e11	−1.13437
$407$	8.78478e10	0.158692
$408$	−4.33182e11	−0.773926
$409$	1.11159e12	1.96421	0.982106	−	0.188329i	$-0.0603070\pi$
$409$	1.11159e12	1.96421	0.982106	+	0.188329i	$0.0603070\pi$
$410$	6.29532e10	0.110025
$411$	5.85843e11	1.01273
$412$	3.62071e11	0.619094
$413$	−1.06957e11	−0.180899
$414$	−1.07432e11	−0.179734
$415$	−3.29599e10	−0.0545468
$416$	1.66543e12	2.72650
$417$	5.47042e11	0.885948
$418$	−4.74223e11	−0.759783
$419$	1.33843e11	0.212145	0.106072	−	0.994358i	$-0.466173\pi$
$419$	1.33843e11	0.212145	0.106072	+	0.994358i	$0.466173\pi$
$420$	−5.46976e10	−0.0857722
$421$	1.05335e12	1.63419	0.817095	−	0.576504i	$-0.195583\pi$
$421$	1.05335e12	1.63419	0.817095	+	0.576504i	$0.195583\pi$
$422$	1.09121e12	1.67495
$423$	1.45721e11	0.221305
$424$	2.91818e12	4.38496
$425$	3.23379e11	0.480797
$426$	5.96929e10	0.0878172
$427$	5.10470e11	0.743095
$428$	9.18406e11	1.32293
$429$	1.61765e11	0.230583
$430$	−3.30481e10	−0.0466163
$431$	−1.21469e12	−1.69558	−0.847792	−	0.530330i	$-0.822068\pi$
$431$	−1.21469e12	−1.69558	−0.847792	+	0.530330i	$0.822068\pi$
$432$	3.77396e11	0.521339
$433$	−4.80989e11	−0.657567	−0.328783	−	0.944405i	$-0.606639\pi$
$433$	−4.80989e11	−0.657567	−0.328783	+	0.944405i	$0.606639\pi$
$434$	−3.94683e11	−0.534004
$435$	8.09163e9	0.0108351
$436$	−3.52546e12	−4.67225
$437$	2.68256e11	0.351871
$438$	3.93018e11	0.510246
$439$	6.73221e11	0.865101	0.432551	−	0.901610i	$-0.357614\pi$
$439$	6.73221e11	0.865101	0.432551	+	0.901610i	$0.357614\pi$
$440$	−3.13473e10	−0.0398715
$441$	2.46421e11	0.310244
$442$	−8.64327e11	−1.07715
$443$	−1.33274e12	−1.64411	−0.822054	−	0.569410i	$-0.807172\pi$
$443$	−1.33274e12	−1.64411	−0.822054	+	0.569410i	$0.807172\pi$
$444$	5.59886e11	0.683716
$445$	−9.89278e9	−0.0119591
$446$	−1.17632e11	−0.140773
$447$	−6.98448e11	−0.827466
$448$	1.83139e12	2.14797
$449$	9.05955e11	1.05196	0.525979	−	0.850498i	$-0.323699\pi$
$449$	9.05955e11	1.05196	0.525979	+	0.850498i	$0.323699\pi$
$450$	−5.40665e11	−0.621544
$451$	−4.02033e11	−0.457581
$452$	−1.80899e12	−2.03851
$453$	−3.31362e11	−0.369709
$454$	−1.12823e12	−1.24636
$455$	−6.53024e10	−0.0714296
$456$	−1.80844e12	−1.95868
$457$	1.69512e12	1.81793	0.908965	−	0.416872i	$-0.136874\pi$
$457$	1.69512e12	1.81793	0.908965	+	0.416872i	$0.136874\pi$
$458$	−9.17337e11	−0.974168
$459$	−8.81532e10	−0.0927003
$460$	2.96356e10	0.0308605
$461$	1.26008e12	1.29940	0.649702	−	0.760189i	$-0.274894\pi$
$461$	1.26008e12	1.29940	0.649702	+	0.760189i	$0.274894\pi$
$462$	4.89613e11	0.499993
$463$	5.71530e11	0.577996	0.288998	−	0.957330i	$-0.406678\pi$
$463$	5.71530e11	0.577996	0.288998	+	0.957330i	$0.406678\pi$
$464$	−1.18204e12	−1.18386
$465$	5.14237e9	0.00510064
$466$	3.49499e12	3.43328
$467$	1.03056e12	1.00264	0.501322	−	0.865261i	$-0.332847\pi$
$467$	1.03056e12	1.00264	0.501322	+	0.865261i	$0.332847\pi$
$468$	1.03099e12	0.993455
$469$	−2.04356e12	−1.95034
$470$	−5.63436e10	−0.0532604
$471$	−3.03532e11	−0.284191
$472$	−3.90670e11	−0.362302
$473$	2.11052e11	0.193872
$474$	−6.31664e11	−0.574756
$475$	1.35004e12	1.21682
$476$	−1.86640e12	−1.66638
$477$	5.93854e11	0.525227
$478$	−1.85437e12	−1.62469
$479$	−1.20661e12	−1.04727	−0.523634	−	0.851943i	$-0.675424\pi$
$479$	−1.20661e12	−1.04727	−0.523634	+	0.851943i	$0.675424\pi$
$480$	−6.56760e10	−0.0564704
$481$	6.68437e11	0.569387
$482$	8.71056e11	0.735079
$483$	−2.76962e11	−0.231557
$484$	−2.67118e12	−2.21258
$485$	8.28080e10	0.0679571
$486$	1.47386e11	0.119837
$487$	−1.26332e12	−1.01773	−0.508867	−	0.860845i	$-0.669935\pi$
$487$	−1.26332e12	−1.01773	−0.508867	+	0.860845i	$0.669935\pi$
$488$	1.86453e12	1.48827
$489$	1.31644e11	0.104115
$490$	−9.52793e10	−0.0746649
$491$	−7.81392e11	−0.606740	−0.303370	−	0.952873i	$-0.598112\pi$
$491$	−7.81392e11	−0.606740	−0.303370	+	0.952873i	$0.598112\pi$
$492$	−2.56230e12	−1.97146
$493$	2.76104e11	0.210505
$494$	−3.60838e12	−2.72610
$495$	−6.37922e9	−0.00477578
$496$	−7.51205e11	−0.557302
$497$	1.53890e11	0.113137
$498$	1.88035e12	1.36996
$499$	2.09499e12	1.51262	0.756309	−	0.654215i	$-0.227001\pi$
$499$	2.09499e12	1.51262	0.756309	+	0.654215i	$0.227001\pi$
$500$	2.98566e11	0.213636
$501$	−7.03498e11	−0.498877
$502$	1.77287e12	1.24598
$503$	−7.43670e11	−0.517993	−0.258997	−	0.965878i	$-0.583392\pi$
$503$	−7.43670e11	−0.517993	−0.258997	+	0.965878i	$0.583392\pi$
$504$	1.86713e12	1.28895
$505$	−4.36672e10	−0.0298775
$506$	−2.65276e11	−0.179896
$507$	3.71915e11	0.249981
$508$	−5.73631e12	−3.82161
$509$	2.21983e12	1.46585	0.732926	−	0.680308i	$-0.238154\pi$
$509$	2.21983e12	1.46585	0.732926	+	0.680308i	$0.238154\pi$
$510$	3.40847e10	0.0223097
$511$	1.01321e12	0.657364
$512$	−2.12829e12	−1.36872
$513$	−3.68021e11	−0.234609
$514$	−4.60450e12	−2.90970
$515$	−1.70465e10	−0.0106783
$516$	1.34511e12	0.835285
$517$	3.59823e11	0.221504
$518$	2.02315e12	1.23465
$519$	−4.51343e11	−0.273057
$520$	−2.38522e11	−0.143059
$521$	8.40218e9	0.00499600	0.00249800	−	0.999997i	$-0.499205\pi$
$521$	8.40218e9	0.00499600	0.00249800	+	0.999997i	$0.499205\pi$
$522$	−4.61625e11	−0.272127
$523$	2.60435e12	1.52209	0.761047	−	0.648697i	$-0.224686\pi$
$523$	2.60435e12	1.52209	0.761047	+	0.648697i	$0.224686\pi$
$524$	−3.26618e11	−0.189256
$525$	−1.39385e12	−0.800753
$526$	−6.39261e12	−3.64118
$527$	1.75469e11	0.0990950
$528$	9.31885e11	0.521807
$529$	−1.65109e12	−0.916687
$530$	−2.29616e11	−0.126404
$531$	−7.95020e10	−0.0433963
$532$	−7.79182e12	−4.21732
$533$	−3.05909e12	−1.64180
$534$	5.64379e11	0.300355
$535$	−4.32392e10	−0.0228184
$536$	−7.46429e12	−3.90613
$537$	2.29630e11	0.119164
$538$	−1.69745e12	−0.873526
$539$	6.08475e11	0.310523
$540$	−4.06571e10	−0.0205761
$541$	8.34995e11	0.419079	0.209540	−	0.977800i	$-0.432803\pi$
$541$	8.34995e11	0.419079	0.209540	+	0.977800i	$0.432803\pi$
$542$	−1.56452e12	−0.778724
$543$	−5.52171e10	−0.0272568
$544$	−2.24101e12	−1.09710
$545$	1.65981e11	0.0805887
$546$	3.72548e12	1.79397
$547$	−6.95891e11	−0.332352	−0.166176	−	0.986096i	$-0.553142\pi$
$547$	−6.95891e11	−0.332352	−0.166176	+	0.986096i	$0.553142\pi$
$548$	9.21967e12	4.36720
$549$	3.79435e11	0.178263
$550$	−1.33504e12	−0.622102
$551$	1.15268e12	0.532752
$552$	−1.01163e12	−0.463761
$553$	−1.62845e12	−0.740476
$554$	3.68667e12	1.66280
$555$	−2.63598e10	−0.0117930
$556$	8.60904e12	3.82048
$557$	1.76865e12	0.778562	0.389281	−	0.921119i	$-0.372724\pi$
$557$	1.76865e12	0.778562	0.389281	+	0.921119i	$0.372724\pi$
$558$	−2.93370e11	−0.128104
$559$	1.60590e12	0.695611
$560$	−3.76189e11	−0.161644
$561$	−2.17673e11	−0.0927835
$562$	−3.66617e12	−1.55024
$563$	2.10069e12	0.881201	0.440600	−	0.897703i	$-0.354766\pi$
$563$	2.10069e12	0.881201	0.440600	+	0.897703i	$0.354766\pi$
$564$	2.29328e12	0.954336
$565$	8.51683e10	0.0351609
$566$	1.48684e12	0.608962
$567$	3.79964e11	0.154390
$568$	5.62096e11	0.226591
$569$	1.35737e12	0.542867	0.271434	−	0.962457i	$-0.412502\pi$
$569$	1.35737e12	0.542867	0.271434	+	0.962457i	$0.412502\pi$
$570$	1.42296e11	0.0564621
$571$	3.13960e12	1.23598	0.617991	−	0.786185i	$-0.287947\pi$
$571$	3.13960e12	1.23598	0.617991	+	0.786185i	$0.287947\pi$
$572$	2.54577e12	0.994347
$573$	2.83864e11	0.110006
$574$	−9.25888e12	−3.56004
$575$	7.55198e11	0.288108
$576$	1.36128e12	0.515284
$577$	2.09516e12	0.786913	0.393456	−	0.919343i	$-0.371279\pi$
$577$	2.09516e12	0.786913	0.393456	+	0.919343i	$0.371279\pi$
$578$	−3.84964e12	−1.43465
$579$	2.46403e12	0.911156
$580$	1.27342e11	0.0467245
$581$	4.84759e12	1.76496
$582$	−4.72417e12	−1.70676
$583$	1.46638e12	0.525699
$584$	3.70084e12	1.31657
$585$	−4.85397e10	−0.0171355
$586$	7.74014e12	2.71150
$587$	4.64609e12	1.61516	0.807581	−	0.589757i	$-0.200776\pi$
$587$	4.64609e12	1.61516	0.807581	+	0.589757i	$0.200776\pi$
$588$	3.87803e12	1.33787
$589$	7.32545e11	0.250793
$590$	3.07397e10	0.0104440
$591$	2.23758e12	0.754458
$592$	3.85067e12	1.28851
$593$	4.34209e12	1.44196	0.720979	−	0.692957i	$-0.243693\pi$
$593$	4.34209e12	1.44196	0.720979	+	0.692957i	$0.243693\pi$
$594$	3.63932e11	0.119945
$595$	8.78713e10	0.0287423
$596$	−1.09918e13	−3.56829
$597$	1.00382e12	0.323423
$598$	−2.01849e12	−0.645464
$599$	4.84567e12	1.53792	0.768958	−	0.639299i	$-0.220775\pi$
$599$	4.84567e12	1.53792	0.768958	+	0.639299i	$0.220775\pi$
$600$	−5.09115e12	−1.60374
$601$	−2.85729e12	−0.893344	−0.446672	−	0.894698i	$-0.647391\pi$
$601$	−2.85729e12	−0.893344	−0.446672	+	0.894698i	$0.647391\pi$
$602$	4.86056e12	1.50835
$603$	−1.51899e12	−0.467873
$604$	−5.21478e12	−1.59430
$605$	1.25761e11	0.0381634
$606$	2.49120e12	0.750380
$607$	−6.02059e11	−0.180007	−0.0900036	−	0.995941i	$-0.528688\pi$
$607$	−6.02059e11	−0.180007	−0.0900036	+	0.995941i	$0.528688\pi$
$608$	−9.35572e12	−2.77659
$609$	−1.19008e12	−0.350589
$610$	−1.46710e11	−0.0429017
$611$	2.73790e12	0.794754
$612$	−1.38731e12	−0.399752
$613$	−3.72672e12	−1.06599	−0.532997	−	0.846117i	$-0.678934\pi$
$613$	−3.72672e12	−1.06599	−0.532997	+	0.846117i	$0.678934\pi$
$614$	−5.50040e12	−1.56184
$615$	1.20635e11	0.0340044
$616$	4.61041e12	1.29011
$617$	−5.71905e12	−1.58869	−0.794347	−	0.607464i	$-0.792187\pi$
$617$	−5.71905e12	−1.58869	−0.794347	+	0.607464i	$0.792187\pi$
$618$	9.72500e11	0.268189
$619$	−2.32367e12	−0.636159	−0.318080	−	0.948064i	$-0.603038\pi$
$619$	−2.32367e12	−0.636159	−0.318080	+	0.948064i	$0.603038\pi$
$620$	8.09277e10	0.0219955
$621$	−2.05867e11	−0.0555489
$622$	9.99929e12	2.67863
$623$	1.45499e12	0.386957
$624$	7.09075e12	1.87224
$625$	3.79361e12	0.994471
$626$	−8.86410e12	−2.30701
$627$	−9.08737e11	−0.234820
$628$	−4.77682e12	−1.22552
$629$	−8.99453e11	−0.229113
$630$	−1.46914e11	−0.0371562
$631$	−4.04352e12	−1.01538	−0.507689	−	0.861541i	$-0.669500\pi$
$631$	−4.04352e12	−1.01538	−0.507689	+	0.861541i	$0.669500\pi$
$632$	−5.94804e12	−1.48302
$633$	2.09104e12	0.517661
$634$	8.53070e12	2.09693
$635$	2.70069e11	0.0659164
$636$	9.34575e12	2.26494
$637$	4.62991e12	1.11415
$638$	−1.13987e12	−0.272371
$639$	1.14387e11	0.0271409
$640$	−1.11206e11	−0.0262011
$641$	8.23067e11	0.192563	0.0962817	−	0.995354i	$-0.469305\pi$
$641$	8.23067e11	0.192563	0.0962817	+	0.995354i	$0.469305\pi$
$642$	2.46678e12	0.573090
$643$	2.70737e12	0.624594	0.312297	−	0.949985i	$-0.398902\pi$
$643$	2.70737e12	0.624594	0.312297	+	0.949985i	$0.398902\pi$
$644$	−4.35867e12	−0.998545
$645$	−6.33288e10	−0.0144073
$646$	4.85546e12	1.09694
$647$	5.65228e12	1.26810	0.634051	−	0.773291i	$-0.281391\pi$
$647$	5.65228e12	1.26810	0.634051	+	0.773291i	$0.281391\pi$
$648$	1.38785e12	0.309211
$649$	−1.96311e11	−0.0434353
$650$	−1.01584e13	−2.23210
$651$	−7.56317e11	−0.165040
$652$	2.07174e12	0.448974
$653$	−5.64503e11	−0.121495	−0.0607473	−	0.998153i	$-0.519348\pi$
$653$	−5.64503e11	−0.121495	−0.0607473	+	0.998153i	$0.519348\pi$
$654$	−9.46915e12	−2.02400
$655$	1.53774e10	0.00326435
$656$	−1.76225e13	−3.71536
$657$	7.53127e11	0.157697
$658$	8.28677e12	1.72333
$659$	8.34085e11	0.172276	0.0861382	−	0.996283i	$-0.472547\pi$
$659$	8.34085e11	0.172276	0.0861382	+	0.996283i	$0.472547\pi$
$660$	−1.00393e11	−0.0205946
$661$	−4.09602e12	−0.834555	−0.417278	−	0.908779i	$-0.637016\pi$
$661$	−4.09602e12	−0.834555	−0.417278	+	0.908779i	$0.637016\pi$
$662$	−1.40340e13	−2.84001
$663$	−1.65628e12	−0.332907
$664$	1.77062e13	3.53484
$665$	3.66844e11	0.0727418
$666$	1.50382e12	0.296184
$667$	6.44796e11	0.126141
$668$	−1.10713e13	−2.15131
$669$	−2.25414e11	−0.0435075
$670$	5.87324e11	0.112601
$671$	9.36921e11	0.178423
$672$	9.65933e12	1.82720
$673$	6.26288e12	1.17681	0.588405	−	0.808566i	$-0.299756\pi$
$673$	6.26288e12	1.17681	0.588405	+	0.808566i	$0.299756\pi$
$674$	−2.32898e12	−0.434707
$675$	−1.03606e12	−0.192095
$676$	5.85299e12	1.07800
$677$	5.43978e11	0.0995250	0.0497625	−	0.998761i	$-0.484154\pi$
$677$	5.43978e11	0.0995250	0.0497625	+	0.998761i	$0.484154\pi$
$678$	−4.85882e12	−0.883075
$679$	−1.21790e13	−2.19887
$680$	3.20957e11	0.0575648
$681$	−2.16198e12	−0.385203
$682$	−7.24406e11	−0.128219
$683$	−7.39909e12	−1.30102	−0.650512	−	0.759496i	$-0.725446\pi$
$683$	−7.39909e12	−1.30102	−0.650512	+	0.759496i	$0.725446\pi$
$684$	−5.79171e12	−1.01171
$685$	−4.34068e11	−0.0753269
$686$	−1.04291e12	−0.179799
$687$	−1.75786e12	−0.301078
$688$	9.25116e12	1.57416
$689$	1.11577e13	1.88620
$690$	7.95993e10	0.0133687
$691$	−4.12021e12	−0.687493	−0.343746	−	0.939063i	$-0.611696\pi$
$691$	−4.12021e12	−0.687493	−0.343746	+	0.939063i	$0.611696\pi$
$692$	−7.10298e12	−1.17751
$693$	9.38227e11	0.154528
$694$	−1.31682e13	−2.15482
$695$	−4.05319e11	−0.0658970
$696$	−4.34687e12	−0.702158
$697$	4.11632e12	0.660636
$698$	−1.34899e13	−2.15110
$699$	6.69733e12	1.06109
$700$	−2.19356e13	−3.45310
$701$	−1.38815e12	−0.217123	−0.108561	−	0.994090i	$-0.534624\pi$
$701$	−1.38815e12	−0.217123	−0.108561	+	0.994090i	$0.534624\pi$
$702$	2.76917e12	0.430361
$703$	−3.75502e12	−0.579847
$704$	3.36135e12	0.515746
$705$	−1.07969e11	−0.0164607
$706$	−5.65253e12	−0.856292
$707$	6.42237e12	0.966737
$708$	−1.25116e12	−0.187138
$709$	−6.66867e12	−0.991131	−0.495565	−	0.868571i	$-0.665039\pi$
$709$	−6.66867e12	−0.991131	−0.495565	+	0.868571i	$0.665039\pi$
$710$	−4.42282e10	−0.00653186
$711$	−1.21044e12	−0.177635
$712$	5.31445e12	0.774994
$713$	4.09778e11	0.0593808
$714$	−5.01303e12	−0.721869
$715$	−1.19857e11	−0.0171508
$716$	3.61379e12	0.513871
$717$	−3.55346e12	−0.502129
$718$	−6.84568e12	−0.961294
$719$	−1.00413e12	−0.140123	−0.0700616	−	0.997543i	$-0.522320\pi$
$719$	−1.00413e12	−0.140123	−0.0700616	+	0.997543i	$0.522320\pi$
$720$	−2.79623e11	−0.0387773
$721$	2.50713e12	0.345516
$722$	6.63059e12	0.908102
$723$	1.66917e12	0.227185
$724$	−8.68976e11	−0.117540
$725$	3.24502e12	0.436211
$726$	−7.17462e12	−0.958482
$727$	1.41169e13	1.87428	0.937139	−	0.348958i	$-0.113464\pi$
$727$	1.41169e13	1.87428	0.937139	+	0.348958i	$0.113464\pi$
$728$	3.50808e13	4.62891
$729$	2.82430e11	0.0370370
$730$	−2.91199e11	−0.0379522
$731$	−2.16091e12	−0.279904
$732$	5.97134e12	0.768727
$733$	7.89551e12	1.01021	0.505106	−	0.863057i	$-0.331453\pi$
$733$	7.89551e12	1.01021	0.505106	+	0.863057i	$0.331453\pi$
$734$	−9.17612e12	−1.16688
$735$	−1.82580e11	−0.0230760
$736$	−5.23350e12	−0.657419
$737$	−3.75078e12	−0.468293
$738$	−6.88218e12	−0.854029
$739$	5.28001e12	0.651231	0.325615	−	0.945502i	$-0.394429\pi$
$739$	5.28001e12	0.651231	0.325615	+	0.945502i	$0.394429\pi$
$740$	−4.14836e11	−0.0508550
$741$	−6.91461e12	−0.842531
$742$	3.37708e13	4.09001
$743$	7.69938e12	0.926843	0.463422	−	0.886138i	$-0.346622\pi$
$743$	7.69938e12	0.926843	0.463422	+	0.886138i	$0.346622\pi$
$744$	−2.76251e12	−0.330541
$745$	5.17501e11	0.0615471
$746$	−1.27092e13	−1.50243
$747$	3.60325e12	0.423401
$748$	−3.42561e12	−0.400111
$749$	6.35943e12	0.738329
$750$	8.01929e11	0.0925466
$751$	−1.35739e13	−1.55713	−0.778563	−	0.627566i	$-0.784051\pi$
$751$	−1.35739e13	−1.55713	−0.778563	+	0.627566i	$0.784051\pi$
$752$	1.57723e13	1.79852
$753$	3.39728e12	0.385083
$754$	−8.67330e12	−0.977267
$755$	2.45516e11	0.0274991
$756$	5.97966e12	0.665776
$757$	−9.32404e12	−1.03198	−0.515992	−	0.856594i	$-0.672577\pi$
$757$	−9.32404e12	−1.03198	−0.515992	+	0.856594i	$0.672577\pi$
$758$	1.55315e13	1.70885
$759$	−5.08339e11	−0.0555988
$760$	1.33993e12	0.145687
$761$	−6.42108e12	−0.694028	−0.347014	−	0.937860i	$-0.612804\pi$
$761$	−6.42108e12	−0.694028	−0.347014	+	0.937860i	$0.612804\pi$
$762$	−1.54074e13	−1.65551
$763$	−2.44117e13	−2.60758
$764$	4.46729e12	0.474378
$765$	6.53153e10	0.00689507
$766$	1.63094e13	1.71162
$767$	−1.49373e12	−0.155845
$768$	−2.26036e12	−0.234451
$769$	−5.58942e12	−0.576366	−0.288183	−	0.957575i	$-0.593051\pi$
$769$	−5.58942e12	−0.576366	−0.288183	+	0.957575i	$0.593051\pi$
$770$	−3.62768e11	−0.0371896
$771$	−8.82344e12	−0.899276
$772$	3.87776e13	3.92919
$773$	8.17454e12	0.823485	0.411742	−	0.911300i	$-0.364920\pi$
$773$	8.17454e12	0.823485	0.411742	+	0.911300i	$0.364920\pi$
$774$	3.61288e12	0.361843
$775$	2.06227e12	0.205346
$776$	−4.44849e13	−4.40388
$777$	3.87688e12	0.381582
$778$	1.69825e13	1.66185
$779$	1.71848e13	1.67196
$780$	−7.63891e11	−0.0738934
$781$	2.82451e11	0.0271653
$782$	2.71610e12	0.259726
$783$	−8.84595e11	−0.0841040
$784$	2.66716e13	2.52131
$785$	2.24896e11	0.0211382
$786$	−8.77275e11	−0.0819850
$787$	−3.35172e12	−0.311445	−0.155723	−	0.987801i	$-0.549771\pi$
$787$	−3.35172e12	−0.311445	−0.155723	+	0.987801i	$0.549771\pi$
$788$	3.52138e13	3.25346
$789$	−1.22499e13	−1.12535
$790$	4.68019e11	0.0427505
$791$	−1.25262e13	−1.13769
$792$	3.42695e12	0.309488
$793$	7.12907e12	0.640182
$794$	4.27575e12	0.381786
$795$	−4.40004e11	−0.0390665
$796$	1.57975e13	1.39470
$797$	−1.48041e13	−1.29963	−0.649817	−	0.760091i	$-0.725154\pi$
$797$	−1.48041e13	−1.29963	−0.649817	+	0.760091i	$0.725154\pi$
$798$	−2.09283e13	−1.82693
$799$	−3.68414e12	−0.319798
$800$	−2.63383e13	−2.27344
$801$	1.08150e12	0.0928282
$802$	1.05863e13	0.903565
$803$	1.85966e12	0.157839
$804$	−2.39051e13	−2.01761
$805$	2.05209e11	0.0172233
$806$	−5.51203e12	−0.460049
$807$	−3.25276e12	−0.269973
$808$	2.34582e13	1.93617
$809$	1.05150e13	0.863058	0.431529	−	0.902099i	$-0.357974\pi$
$809$	1.05150e13	0.863058	0.431529	+	0.902099i	$0.357974\pi$
$810$	−1.09202e11	−0.00891352
$811$	−2.07754e13	−1.68638	−0.843191	−	0.537615i	$-0.819326\pi$
$811$	−2.07754e13	−1.68638	−0.843191	+	0.537615i	$0.819326\pi$
$812$	−1.87288e13	−1.51185
$813$	−2.99803e12	−0.240673
$814$	3.71330e12	0.296449
$815$	−9.75389e10	−0.00774406
$816$	−9.54135e12	−0.753363
$817$	−9.02136e12	−0.708390
$818$	4.69865e13	3.66930
$819$	7.13900e12	0.554447
$820$	1.89849e12	0.146637
$821$	7.67497e12	0.589566	0.294783	−	0.955564i	$-0.404753\pi$
$821$	7.67497e12	0.589566	0.294783	+	0.955564i	$0.404753\pi$
$822$	2.47634e13	1.89185
$823$	−9.08768e12	−0.690484	−0.345242	−	0.938514i	$-0.612203\pi$
$823$	−9.08768e12	−0.690484	−0.345242	+	0.938514i	$0.612203\pi$
$824$	9.15750e12	0.691997
$825$	−2.55829e12	−0.192268
$826$	−4.52106e12	−0.337932
$827$	−1.56022e13	−1.15988	−0.579938	−	0.814660i	$-0.696923\pi$
$827$	−1.56022e13	−1.15988	−0.579938	+	0.814660i	$0.696923\pi$
$828$	−3.23983e12	−0.239544
$829$	2.64563e13	1.94551	0.972754	−	0.231840i	$-0.0744747\pi$
$829$	2.64563e13	1.94551	0.972754	+	0.231840i	$0.0744747\pi$
$830$	−1.39321e12	−0.101898
$831$	7.06464e12	0.513908
$832$	2.55766e13	1.85049
$833$	−6.23003e12	−0.448320
$834$	2.31233e13	1.65502
$835$	5.21243e11	0.0371066
$836$	−1.43012e13	−1.01261
$837$	−5.62175e11	−0.0395920
$838$	5.65750e12	0.396302
$839$	8.86025e12	0.617329	0.308665	−	0.951171i	$-0.400118\pi$
$839$	8.86025e12	0.617329	0.308665	+	0.951171i	$0.400118\pi$
$840$	−1.38341e12	−0.0958726
$841$	−1.17365e13	−0.809016
$842$	4.45248e13	3.05279
$843$	−7.02534e12	−0.479119
$844$	3.29076e13	2.23231
$845$	−2.75563e11	−0.0185937
$846$	6.15961e12	0.413415
$847$	−1.84964e13	−1.23484
$848$	6.42764e13	4.26845
$849$	2.84918e12	0.188207
$850$	1.36691e13	0.898165
$851$	−2.10052e12	−0.137292
$852$	1.80016e12	0.117040
$853$	−1.33799e13	−0.865332	−0.432666	−	0.901554i	$-0.642427\pi$
$853$	−1.33799e13	−0.865332	−0.432666	+	0.901554i	$0.642427\pi$
$854$	2.15774e13	1.38816
$855$	2.72678e11	0.0174503
$856$	2.32283e13	1.47872
$857$	−7.75808e12	−0.491293	−0.245646	−	0.969360i	$-0.579000\pi$
$857$	−7.75808e12	−0.491293	−0.245646	+	0.969360i	$0.579000\pi$
$858$	6.83779e12	0.430748
$859$	−1.43176e13	−0.897222	−0.448611	−	0.893727i	$-0.648081\pi$
$859$	−1.43176e13	−0.897222	−0.448611	+	0.893727i	$0.648081\pi$
$860$	−9.96633e11	−0.0621287
$861$	−1.77425e13	−1.10027
$862$	−5.13448e13	−3.16748
$863$	6.99759e12	0.429437	0.214719	−	0.976676i	$-0.431117\pi$
$863$	6.99759e12	0.429437	0.214719	+	0.976676i	$0.431117\pi$
$864$	7.17984e12	0.438332
$865$	3.34413e11	0.0203100
$866$	−2.03313e13	−1.22839
$867$	−7.37692e12	−0.443393
$868$	−1.19025e13	−0.711703
$869$	−2.98887e12	−0.177794
$870$	3.42031e11	0.0202409
$871$	−2.85398e13	−1.68023
$872$	−8.91659e13	−5.22245
$873$	−9.05275e12	−0.527493
$874$	1.13391e13	0.657323
$875$	2.06739e12	0.119230
$876$	1.18523e13	0.680039
$877$	3.15194e13	1.79920	0.899600	−	0.436714i	$-0.143858\pi$
$877$	3.15194e13	1.79920	0.899600	+	0.436714i	$0.143858\pi$
$878$	2.84569e13	1.61608
$879$	1.48321e13	0.838019
$880$	−6.90461e11	−0.0388121
$881$	−1.72449e13	−0.964424	−0.482212	−	0.876055i	$-0.660166\pi$
$881$	−1.72449e13	−0.964424	−0.482212	+	0.876055i	$0.660166\pi$
$882$	1.04161e13	0.579560
$883$	−1.01246e13	−0.560472	−0.280236	−	0.959931i	$-0.590413\pi$
$883$	−1.01246e13	−0.560472	−0.280236	+	0.959931i	$0.590413\pi$
$884$	−2.60656e13	−1.43560
$885$	5.89054e10	0.00322783
$886$	−5.63348e13	−3.07132
$887$	−1.50249e12	−0.0814995	−0.0407497	−	0.999169i	$-0.512975\pi$
$887$	−1.50249e12	−0.0814995	−0.0407497	+	0.999169i	$0.512975\pi$
$888$	1.41606e13	0.764230
$889$	−3.97206e13	−2.13284
$890$	−4.18165e11	−0.0223405
$891$	6.97390e11	0.0370703
$892$	−3.54745e12	−0.187618
$893$	−1.53805e13	−0.809355
$894$	−2.95232e13	−1.54577
$895$	−1.70140e11	−0.00886343
$896$	1.63557e13	0.847781
$897$	−3.86797e12	−0.199488
$898$	3.82945e13	1.96514
$899$	1.76078e12	0.0899057
$900$	−1.63049e13	−0.828374
$901$	−1.50139e13	−0.758982
$902$	−1.69938e13	−0.854796
$903$	9.31411e12	0.466172
$904$	−4.57529e13	−2.27856
$905$	4.09120e10	0.00202736
$906$	−1.40066e13	−0.690645
$907$	2.46747e13	1.21065	0.605326	−	0.795977i	$-0.293043\pi$
$907$	2.46747e13	1.21065	0.605326	+	0.795977i	$0.293043\pi$
$908$	−3.40240e13	−1.66111
$909$	4.77379e12	0.231913
$910$	−2.76032e12	−0.133436
$911$	−2.96700e13	−1.42720	−0.713599	−	0.700554i	$-0.752936\pi$
$911$	−2.96700e13	−1.42720	−0.713599	+	0.700554i	$0.752936\pi$
$912$	−3.98331e13	−1.90663
$913$	8.89733e12	0.423781
$914$	7.16523e13	3.39603
$915$	−2.81135e11	−0.0132593
$916$	−2.76642e13	−1.29834
$917$	−2.26164e12	−0.105624
$918$	−3.72622e12	−0.173171
$919$	−6.41468e11	−0.0296658	−0.0148329	−	0.999890i	$-0.504722\pi$
$919$	−6.41468e11	−0.0296658	−0.0148329	+	0.999890i	$0.504722\pi$
$920$	7.49543e11	0.0344946
$921$	−1.05402e13	−0.482704
$922$	5.32633e13	2.42739
$923$	2.14918e12	0.0974688
$924$	1.47653e13	0.666374
$925$	−1.05712e13	−0.474773
$926$	2.41584e13	1.07974
$927$	1.86357e12	0.0828869
$928$	−2.24879e13	−0.995367
$929$	2.78508e13	1.22678	0.613391	−	0.789779i	$-0.289805\pi$
$929$	2.78508e13	1.22678	0.613391	+	0.789779i	$0.289805\pi$
$930$	2.17367e11	0.00952840
$931$	−2.60091e13	−1.13462
$932$	1.05399e14	4.57577
$933$	1.91613e13	0.827860
$934$	4.35614e13	1.87302
$935$	1.61280e11	0.00690126
$936$	2.60758e13	1.11044
$937$	2.19926e13	0.932071	0.466035	−	0.884766i	$-0.345682\pi$
$937$	2.19926e13	0.932071	0.466035	+	0.884766i	$0.345682\pi$
$938$	−8.63810e13	−3.64339
$939$	−1.69859e13	−0.713008
$940$	−1.69916e12	−0.0709837
$941$	3.39798e13	1.41276	0.706378	−	0.707835i	$-0.250328\pi$
$941$	3.39798e13	1.41276	0.706378	+	0.707835i	$0.250328\pi$
$942$	−1.28302e13	−0.530892
$943$	9.61300e12	0.395874
$944$	−8.60498e12	−0.352676
$945$	−2.81526e11	−0.0114835
$946$	8.92113e12	0.362168
$947$	3.01777e13	1.21930	0.609650	−	0.792671i	$-0.291310\pi$
$947$	3.01777e13	1.21930	0.609650	+	0.792671i	$0.291310\pi$
$948$	−1.90492e13	−0.766017
$949$	1.41502e13	0.566324
$950$	5.70658e13	2.27311
$951$	1.63471e13	0.648079
$952$	−4.72050e13	−1.86261
$953$	8.09006e12	0.317712	0.158856	−	0.987302i	$-0.449219\pi$
$953$	8.09006e12	0.317712	0.158856	+	0.987302i	$0.449219\pi$
$954$	2.51021e13	0.981165
$955$	−2.10323e11	−0.00818224
$956$	−5.59224e13	−2.16534
$957$	−2.18429e12	−0.0841795
$958$	−5.10032e13	−1.95638
$959$	6.38408e13	2.43733
$960$	−1.00861e12	−0.0383269
$961$	−2.53206e13	−0.957677
$962$	2.82547e13	1.06366
$963$	4.72700e12	0.177120
$964$	2.62685e13	0.979690
$965$	−1.82567e12	−0.0677720
$966$	−1.17071e13	−0.432566
$967$	1.06043e13	0.389998	0.194999	−	0.980803i	$-0.437530\pi$
$967$	1.06043e13	0.389998	0.194999	+	0.980803i	$0.437530\pi$
$968$	−6.75595e13	−2.47313
$969$	9.30434e12	0.339023
$970$	3.50028e12	0.126949
$971$	3.83413e13	1.38414	0.692071	−	0.721830i	$-0.256699\pi$
$971$	3.83413e13	1.38414	0.692071	+	0.721830i	$0.256699\pi$
$972$	4.44472e12	0.159715
$973$	5.96125e13	2.13221
$974$	−5.34003e13	−1.90120
$975$	−1.94661e13	−0.689855
$976$	4.10685e13	1.44872
$977$	1.97686e12	0.0694145	0.0347073	−	0.999398i	$-0.488950\pi$
$977$	1.97686e12	0.0694145	0.0347073	+	0.999398i	$0.488950\pi$
$978$	5.56456e12	0.194494
$979$	2.67050e12	0.0929116
$980$	−2.87335e12	−0.0995109
$981$	−1.81454e13	−0.625541
$982$	−3.30293e13	−1.13344
$983$	5.58570e12	0.190804	0.0954019	−	0.995439i	$-0.469586\pi$
$983$	5.58570e12	0.190804	0.0954019	+	0.995439i	$0.469586\pi$
$984$	−6.48058e13	−2.20361
$985$	−1.65789e12	−0.0561168
$986$	1.16708e13	0.393239
$987$	1.58796e13	0.532615
$988$	−1.08818e14	−3.63325
$989$	−5.04646e12	−0.167727
$990$	−2.69648e11	−0.00892152
$991$	−4.45379e10	−0.00146689	−0.000733447	−	1.00000i	$-0.500233\pi$
$991$	−4.45379e10	−0.00146689	−0.000733447		1.00000i	$0.500233\pi$
$992$	−1.42915e13	−0.468569
$993$	−2.68928e13	−0.877738
$994$	6.50489e12	0.211350
$995$	−7.43759e11	−0.0240563
$996$	5.67059e13	1.82583
$997$	−5.30115e13	−1.69919	−0.849595	−	0.527436i	$-0.823154\pi$
$997$	−5.30115e13	−1.69919	−0.849595	+	0.527436i	$0.823154\pi$
$998$	8.85547e13	2.82569
$999$	2.88171e12	0.0915389

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.d.1.21	✓	22

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.d.1.21	✓	22	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:	\( N \)	\(=\)	\( 177 = 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q+42.2698 q^{2} +81.0000 q^{3} +1274.73 q^{4} -60.0153 q^{5} +3423.85 q^{6} +8826.78 q^{7} +32240.5 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+42.2698 q^{2} +81.0000 q^{3} +1274.73 q^{4} -60.0153 q^{5} +3423.85 q^{6} +8826.78 q^{7} +32240.5 q^{8} +6561.00 q^{9} -2536.83 q^{10} +16200.8 q^{11} +103253. q^{12} +123272. q^{13} +373106. q^{14} -4861.24 q^{15} +710136. q^{16} -165876. q^{17} +277332. q^{18} -692496. q^{19} -76503.4 q^{20} +714969. q^{21} +684803. q^{22} -387376. q^{23} +2.61148e6 q^{24} -1.94952e6 q^{25} +5.21069e6 q^{26} +531441. q^{27} +1.12518e7 q^{28} -1.66452e6 q^{29} -205483. q^{30} -1.05783e6 q^{31} +1.35101e7 q^{32} +1.31226e6 q^{33} -7.01153e6 q^{34} -529742. q^{35} +8.36352e6 q^{36} +5.42244e6 q^{37} -2.92717e7 q^{38} +9.98505e6 q^{39} -1.93492e6 q^{40} -2.48157e7 q^{41} +3.02216e7 q^{42} +1.30273e7 q^{43} +2.06516e7 q^{44} -393760. q^{45} -1.63743e7 q^{46} +2.22102e7 q^{47} +5.75210e7 q^{48} +3.75584e7 q^{49} -8.24059e7 q^{50} -1.34359e7 q^{51} +1.57139e8 q^{52} +9.05128e7 q^{53} +2.24639e7 q^{54} -972293. q^{55} +2.84580e8 q^{56} -5.60922e7 q^{57} -7.03589e7 q^{58} -1.21174e7 q^{59} -6.19678e6 q^{60} +5.78319e7 q^{61} -4.47143e7 q^{62} +5.79125e7 q^{63} +2.07481e8 q^{64} -7.39822e6 q^{65} +5.54690e7 q^{66} -2.31519e8 q^{67} -2.11447e8 q^{68} -3.13775e7 q^{69} -2.23920e7 q^{70} +1.74344e7 q^{71} +2.11530e8 q^{72} +1.14788e8 q^{73} +2.29205e8 q^{74} -1.57911e8 q^{75} -8.82748e8 q^{76} +1.43001e8 q^{77} +4.22066e8 q^{78} -1.84489e8 q^{79} -4.26190e7 q^{80} +4.30467e7 q^{81} -1.04895e9 q^{82} +5.49192e8 q^{83} +9.11394e8 q^{84} +9.95509e6 q^{85} +5.50661e8 q^{86} -1.34826e8 q^{87} +5.22321e8 q^{88} +1.64838e8 q^{89} -1.66442e7 q^{90} +1.08810e9 q^{91} -4.93801e8 q^{92} -8.56843e7 q^{93} +9.38821e8 q^{94} +4.15604e7 q^{95} +1.09432e9 q^{96} -1.37978e9 q^{97} +1.58758e9 q^{98} +1.06293e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9}+O(q^{10}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9	\( 22 q + 46 q^{2} + 1782 q^{3} + 5974 q^{4} + 5786 q^{5} + 3726 q^{6} + 7641 q^{7} + 61395 q^{8} + 144342 q^{9} + 45337 q^{10} + 111769 q^{11} + 483894 q^{12} + 189121 q^{13} + 251053 q^{14} + 468666 q^{15} + 2311074 q^{16} + 1113841 q^{17} + 301806 q^{18} + 476068 q^{19} - 42495 q^{20} + 618921 q^{21} - 2252022 q^{22} + 7103062 q^{23} + 4972995 q^{24} + 10628442 q^{25} + 6871048 q^{26} + 11691702 q^{27} + 8112650 q^{28} + 15279316 q^{29} + 3672297 q^{30} + 17610338 q^{31} + 32378276 q^{32} + 9053289 q^{33} + 29339436 q^{34} + 7134904 q^{35} + 39195414 q^{36} + 21961411 q^{37} + 65195131 q^{38} + 15318801 q^{39} + 75185084 q^{40} + 52781575 q^{41} + 20335293 q^{42} + 76191313 q^{43} + 61127768 q^{44} + 37961946 q^{45} + 290208769 q^{46} + 160572396 q^{47} + 187196994 q^{48} + 156292703 q^{49} + 169504821 q^{50} + 90221121 q^{51} + 65465920 q^{52} - 8762038 q^{53} + 24446286 q^{54} + 147125140 q^{55} + 9671794 q^{56} + 38561508 q^{57} - 37665424 q^{58} - 266581942 q^{59} - 3442095 q^{60} + 120750754 q^{61} - 152465186 q^{62} + 50132601 q^{63} - 40658803 q^{64} + 331055798 q^{65} - 182413782 q^{66} + 41371828 q^{67} + 145606631 q^{68} + 575348022 q^{69} - 920887614 q^{70} + 261018751 q^{71} + 402812595 q^{72} + 178388 q^{73} - 303908734 q^{74} + 860903802 q^{75} - 94541144 q^{76} + 299640561 q^{77} + 556554888 q^{78} - 905381353 q^{79} + 939128289 q^{80} + 947027862 q^{81} - 551739753 q^{82} + 1173257869 q^{83} + 657124650 q^{84} - 1546633210 q^{85} + 1384869460 q^{86} + 1237624596 q^{87} + 189740713 q^{88} + 898004974 q^{89} + 297456057 q^{90} + 591272339 q^{91} + 4328210270 q^{92} + 1426437378 q^{93} + 122568068 q^{94} + 2487967134 q^{95} + 2622640356 q^{96} + 3175709684 q^{97} + 5095778404 q^{98} + 733316409 q^{99}+O(q^{100}) \) 22 * q + 46 * q^2 + 1782 * q^3 + 5974 * q^4 + 5786 * q^5 + 3726 * q^6 + 7641 * q^7 + 61395 * q^8 + 144342 * q^9 + 45337 * q^10 + 111769 * q^11 + 483894 * q^12 + 189121 * q^13 + 251053 * q^14 + 468666 * q^15 + 2311074 * q^16 + 1113841 * q^17 + 301806 * q^18 + 476068 * q^19 - 42495 * q^20 + 618921 * q^21 - 2252022 * q^22 + 7103062 * q^23 + 4972995 * q^24 + 10628442 * q^25 + 6871048 * q^26 + 11691702 * q^27 + 8112650 * q^28 + 15279316 * q^29 + 3672297 * q^30 + 17610338 * q^31 + 32378276 * q^32 + 9053289 * q^33 + 29339436 * q^34 + 7134904 * q^35 + 39195414 * q^36 + 21961411 * q^37 + 65195131 * q^38 + 15318801 * q^39 + 75185084 * q^40 + 52781575 * q^41 + 20335293 * q^42 + 76191313 * q^43 + 61127768 * q^44 + 37961946 * q^45 + 290208769 * q^46 + 160572396 * q^47 + 187196994 * q^48 + 156292703 * q^49 + 169504821 * q^50 + 90221121 * q^51 + 65465920 * q^52 - 8762038 * q^53 + 24446286 * q^54 + 147125140 * q^55 + 9671794 * q^56 + 38561508 * q^57 - 37665424 * q^58 - 266581942 * q^59 - 3442095 * q^60 + 120750754 * q^61 - 152465186 * q^62 + 50132601 * q^63 - 40658803 * q^64 + 331055798 * q^65 - 182413782 * q^66 + 41371828 * q^67 + 145606631 * q^68 + 575348022 * q^69 - 920887614 * q^70 + 261018751 * q^71 + 402812595 * q^72 + 178388 * q^73 - 303908734 * q^74 + 860903802 * q^75 - 94541144 * q^76 + 299640561 * q^77 + 556554888 * q^78 - 905381353 * q^79 + 939128289 * q^80 + 947027862 * q^81 - 551739753 * q^82 + 1173257869 * q^83 + 657124650 * q^84 - 1546633210 * q^85 + 1384869460 * q^86 + 1237624596 * q^87 + 189740713 * q^88 + 898004974 * q^89 + 297456057 * q^90 + 591272339 * q^91 + 4328210270 * q^92 + 1426437378 * q^93 + 122568068 * q^94 + 2487967134 * q^95 + 2622640356 * q^96 + 3175709684 * q^97 + 5095778404 * q^98 + 733316409 * q^99

Introduction

L-functions

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