LMFDB - Embedded newform 177.10.a.b.1.6

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:	$1$
Dimension:	$21$
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.6
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)

$f(q)$	$=$	$q-23.3610 q^{2} -81.0000 q^{3} +33.7344 q^{4} +477.585 q^{5} +1892.24 q^{6} +1570.96 q^{7} +11172.7 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q-23.3610 q^{2} -81.0000 q^{3} +33.7344 q^{4} +477.585 q^{5} +1892.24 q^{6} +1570.96 q^{7} +11172.7 q^{8} +6561.00 q^{9} -11156.8 q^{10} -48168.1 q^{11} -2732.48 q^{12} +60042.1 q^{13} -36699.1 q^{14} -38684.4 q^{15} -278278. q^{16} +65961.2 q^{17} -153271. q^{18} -314381. q^{19} +16111.0 q^{20} -127248. q^{21} +1.12525e6 q^{22} -1.21197e6 q^{23} -904992. q^{24} -1.72504e6 q^{25} -1.40264e6 q^{26} -531441. q^{27} +52995.3 q^{28} +5.11139e6 q^{29} +903704. q^{30} +2.37877e6 q^{31} +780396. q^{32} +3.90161e6 q^{33} -1.54092e6 q^{34} +750267. q^{35} +221331. q^{36} +1.04291e6 q^{37} +7.34424e6 q^{38} -4.86341e6 q^{39} +5.33593e6 q^{40} -9.06456e6 q^{41} +2.97263e6 q^{42} +3.58131e7 q^{43} -1.62492e6 q^{44} +3.13343e6 q^{45} +2.83128e7 q^{46} +3.00013e7 q^{47} +2.25405e7 q^{48} -3.78857e7 q^{49} +4.02985e7 q^{50} -5.34286e6 q^{51} +2.02548e6 q^{52} -2.45832e7 q^{53} +1.24150e7 q^{54} -2.30043e7 q^{55} +1.75519e7 q^{56} +2.54649e7 q^{57} -1.19407e8 q^{58} -1.21174e7 q^{59} -1.30499e6 q^{60} +6.49807e7 q^{61} -5.55703e7 q^{62} +1.03071e7 q^{63} +1.24248e8 q^{64} +2.86752e7 q^{65} -9.11454e7 q^{66} +2.82563e8 q^{67} +2.22516e6 q^{68} +9.81696e7 q^{69} -1.75269e7 q^{70} -6.33502e7 q^{71} +7.33044e7 q^{72} +3.82696e8 q^{73} -2.43634e7 q^{74} +1.39728e8 q^{75} -1.06054e7 q^{76} -7.56701e7 q^{77} +1.13614e8 q^{78} -5.56447e8 q^{79} -1.32901e8 q^{80} +4.30467e7 q^{81} +2.11757e8 q^{82} +4.81897e7 q^{83} -4.29262e6 q^{84} +3.15021e7 q^{85} -8.36627e8 q^{86} -4.14023e8 q^{87} -5.38169e8 q^{88} +1.06126e9 q^{89} -7.32000e7 q^{90} +9.43237e7 q^{91} -4.08850e7 q^{92} -1.92680e8 q^{93} -7.00858e8 q^{94} -1.50144e8 q^{95} -6.32120e7 q^{96} +1.41946e6 q^{97} +8.85046e8 q^{98} -3.16031e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) $ 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * 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 $

$2$	−23.3610	−1.03242	−0.516209	−	0.856463i	$-0.672657\pi$
$2$	−23.3610	−1.03242	−0.516209	+	0.856463i	$0.672657\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	33.7344	0.0658874
$5$	477.585	0.341732	0.170866	−	0.985294i	$-0.445343\pi$
$5$	477.585	0.341732	0.170866	+	0.985294i	$0.445343\pi$
$6$	1892.24	0.596067
$7$	1570.96	0.247300	0.123650	−	0.992326i	$-0.460540\pi$
$7$	1570.96	0.247300	0.123650	+	0.992326i	$0.460540\pi$
$8$	11172.7	0.964395
$9$	6561.00	0.333333
$10$	−11156.8	−0.352810
$11$	−48168.1	−0.991955	−0.495978	−	0.868335i	$-0.665190\pi$
$11$	−48168.1	−0.991955	−0.495978	+	0.868335i	$0.665190\pi$
$12$	−2732.48	−0.0380401
$13$	60042.1	0.583057	0.291528	−	0.956562i	$-0.405836\pi$
$13$	60042.1	0.583057	0.291528	+	0.956562i	$0.405836\pi$
$14$	−36699.1	−0.255317
$15$	−38684.4	−0.197299
$16$	−278278.	−1.06155
$17$	65961.2	0.191544	0.0957720	−	0.995403i	$-0.469468\pi$
$17$	65961.2	0.191544	0.0957720	+	0.995403i	$0.469468\pi$
$18$	−153271.	−0.344139
$19$	−314381.	−0.553433	−0.276716	−	0.960952i	$-0.589246\pi$
$19$	−314381.	−0.553433	−0.276716	+	0.960952i	$0.589246\pi$
$20$	16111.0	0.0225158
$21$	−127248.	−0.142779
$22$	1.12525e6	1.02411
$23$	−1.21197e6	−0.903060	−0.451530	−	0.892256i	$-0.649122\pi$
$23$	−1.21197e6	−0.903060	−0.451530	+	0.892256i	$0.649122\pi$
$24$	−904992.	−0.556794
$25$	−1.72504e6	−0.883219
$26$	−1.40264e6	−0.601958
$27$	−531441.	−0.192450
$28$	52995.3	0.0162939
$29$	5.11139e6	1.34199	0.670993	−	0.741464i	$-0.265868\pi$
$29$	5.11139e6	1.34199	0.670993	+	0.741464i	$0.265868\pi$
$30$	903704.	0.203695
$31$	2.37877e6	0.462620	0.231310	−	0.972880i	$-0.425699\pi$
$31$	2.37877e6	0.462620	0.231310	+	0.972880i	$0.425699\pi$
$32$	780396.	0.131565
$33$	3.90161e6	0.572706
$34$	−1.54092e6	−0.197753
$35$	750267.	0.0845102
$36$	221331.	0.0219625
$37$	1.04291e6	0.0914830	0.0457415	−	0.998953i	$-0.485435\pi$
$37$	1.04291e6	0.0914830	0.0457415	+	0.998953i	$0.485435\pi$
$38$	7.34424e6	0.571374
$39$	−4.86341e6	−0.336628
$40$	5.33593e6	0.329565
$41$	−9.06456e6	−0.500979	−0.250490	−	0.968119i	$-0.580592\pi$
$41$	−9.06456e6	−0.500979	−0.250490	+	0.968119i	$0.580592\pi$
$42$	2.97263e6	0.147407
$43$	3.58131e7	1.59747	0.798736	−	0.601681i	$-0.205502\pi$
$43$	3.58131e7	1.59747	0.798736	+	0.601681i	$0.205502\pi$
$44$	−1.62492e6	−0.0653574
$45$	3.13343e6	0.113911
$46$	2.83128e7	0.932336
$47$	3.00013e7	0.896808	0.448404	−	0.893831i	$-0.351993\pi$
$47$	3.00013e7	0.896808	0.448404	+	0.893831i	$0.351993\pi$
$48$	2.25405e7	0.612884
$49$	−3.78857e7	−0.938843
$50$	4.02985e7	0.911852
$51$	−5.34286e6	−0.110588
$52$	2.02548e6	0.0384161
$53$	−2.45832e7	−0.427954	−0.213977	−	0.976839i	$-0.568642\pi$
$53$	−2.45832e7	−0.427954	−0.213977	+	0.976839i	$0.568642\pi$
$54$	1.24150e7	0.198689
$55$	−2.30043e7	−0.338983
$56$	1.75519e7	0.238495
$57$	2.54649e7	0.319525
$58$	−1.19407e8	−1.38549
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−1.30499e6	−0.0129995
$61$	6.49807e7	0.600897	0.300448	−	0.953798i	$-0.402864\pi$
$61$	6.49807e7	0.600897	0.300448	+	0.953798i	$0.402864\pi$
$62$	−5.55703e7	−0.477618
$63$	1.03071e7	0.0824333
$64$	1.24248e8	0.925716
$65$	2.86752e7	0.199249
$66$	−9.11454e7	−0.591272
$67$	2.82563e8	1.71309	0.856543	−	0.516076i	$-0.172608\pi$
$67$	2.82563e8	1.71309	0.856543	+	0.516076i	$0.172608\pi$
$68$	2.22516e6	0.0126203
$69$	9.81696e7	0.521382
$70$	−1.75269e7	−0.0872499
$71$	−6.33502e7	−0.295860	−0.147930	−	0.988998i	$-0.547261\pi$
$71$	−6.33502e7	−0.295860	−0.147930	+	0.988998i	$0.547261\pi$
$72$	7.33044e7	0.321465
$73$	3.82696e8	1.57725	0.788626	−	0.614873i	$-0.210793\pi$
$73$	3.82696e8	1.57725	0.788626	+	0.614873i	$0.210793\pi$
$74$	−2.43634e7	−0.0944487
$75$	1.39728e8	0.509927
$76$	−1.06054e7	−0.0364643
$77$	−7.56701e7	−0.245310
$78$	1.13614e8	0.347541
$79$	−5.56447e8	−1.60732	−0.803660	−	0.595089i	$-0.797117\pi$
$79$	−5.56447e8	−1.60732	−0.803660	+	0.595089i	$0.797117\pi$
$80$	−1.32901e8	−0.362764
$81$	4.30467e7	0.111111
$82$	2.11757e8	0.517220
$83$	4.81897e7	0.111456	0.0557279	−	0.998446i	$-0.482252\pi$
$83$	4.81897e7	0.111456	0.0557279	+	0.998446i	$0.482252\pi$
$84$	−4.29262e6	−0.00940731
$85$	3.15021e7	0.0654567
$86$	−8.36627e8	−1.64926
$87$	−4.14023e8	−0.774796
$88$	−5.38169e8	−0.956637
$89$	1.06126e9	1.79294	0.896471	−	0.443103i	$-0.146122\pi$
$89$	1.06126e9	1.79294	0.896471	+	0.443103i	$0.146122\pi$
$90$	−7.32000e7	−0.117603
$91$	9.43237e7	0.144190
$92$	−4.08850e7	−0.0595003
$93$	−1.92680e8	−0.267094
$94$	−7.00858e8	−0.925880
$95$	−1.50144e8	−0.189126
$96$	−6.32120e7	−0.0759590
$97$	1.41946e6	0.00162799	0.000813994	−	1.00000i	$-0.499741\pi$
$97$	1.41946e6	0.00162799	0.000813994		1.00000i	$0.499741\pi$
$98$	8.85046e8	0.969278
$99$	−3.16031e8	−0.330652
$100$	−5.81930e7	−0.0581930
$101$	−1.20629e9	−1.15347	−0.576736	−	0.816931i	$-0.695674\pi$
$101$	−1.20629e9	−1.15347	−0.576736	+	0.816931i	$0.695674\pi$
$102$	1.24814e8	0.114173
$103$	−1.98483e9	−1.73762	−0.868811	−	0.495144i	$-0.835115\pi$
$103$	−1.98483e9	−1.73762	−0.868811	+	0.495144i	$0.835115\pi$
$104$	6.70835e8	0.562297
$105$	−6.07716e7	−0.0487920
$106$	5.74287e8	0.441827
$107$	−1.19300e9	−0.879859	−0.439930	−	0.898032i	$-0.644997\pi$
$107$	−1.19300e9	−0.879859	−0.439930	+	0.898032i	$0.644997\pi$
$108$	−1.79278e7	−0.0126800
$109$	−1.66774e9	−1.13164	−0.565821	−	0.824528i	$-0.691441\pi$
$109$	−1.66774e9	−1.13164	−0.565821	+	0.824528i	$0.691441\pi$
$110$	5.37403e8	0.349972
$111$	−8.44760e7	−0.0528177
$112$	−4.37163e8	−0.262520
$113$	2.96330e9	1.70971	0.854857	−	0.518864i	$-0.173645\pi$
$113$	2.96330e9	1.70971	0.854857	+	0.518864i	$0.173645\pi$
$114$	−5.94883e8	−0.329883
$115$	−5.78819e8	−0.308605
$116$	1.72429e8	0.0884200
$117$	3.93936e8	0.194352
$118$	2.83073e8	0.134409
$119$	1.03622e8	0.0473688
$120$	−4.32211e8	−0.190274
$121$	−3.77854e7	−0.0160247
$122$	−1.51801e9	−0.620377
$123$	7.34230e8	0.289240
$124$	8.02463e7	0.0304809
$125$	−1.75663e9	−0.643556
$126$	−2.40783e8	−0.0851056
$127$	−1.29615e9	−0.442120	−0.221060	−	0.975260i	$-0.570952\pi$
$127$	−1.29615e9	−0.442120	−0.221060	+	0.975260i	$0.570952\pi$
$128$	−3.30210e9	−1.08729
$129$	−2.90086e9	−0.922301
$130$	−6.69880e8	−0.205708
$131$	1.95690e9	0.580562	0.290281	−	0.956941i	$-0.406251\pi$
$131$	1.95690e9	0.580562	0.290281	+	0.956941i	$0.406251\pi$
$132$	1.31618e8	0.0377341
$133$	−4.93880e8	−0.136864
$134$	−6.60095e9	−1.76862
$135$	−2.53808e8	−0.0657663
$136$	7.36968e8	0.184724
$137$	1.14427e9	0.277515	0.138757	−	0.990326i	$-0.455689\pi$
$137$	1.14427e9	0.277515	0.138757	+	0.990326i	$0.455689\pi$
$138$	−2.29334e9	−0.538284
$139$	−8.49846e9	−1.93096	−0.965481	−	0.260474i	$-0.916121\pi$
$139$	−8.49846e9	−1.93096	−0.965481	+	0.260474i	$0.916121\pi$
$140$	2.53098e7	0.00556816
$141$	−2.43010e9	−0.517772
$142$	1.47992e9	0.305451
$143$	−2.89211e9	−0.578366
$144$	−1.82578e9	−0.353849
$145$	2.44112e9	0.458600
$146$	−8.94014e9	−1.62838
$147$	3.06874e9	0.542041
$148$	3.51820e7	0.00602758
$149$	2.92284e9	0.485811	0.242905	−	0.970050i	$-0.421900\pi$
$149$	2.92284e9	0.485811	0.242905	+	0.970050i	$0.421900\pi$
$150$	−3.26418e9	−0.526458
$151$	1.67412e9	0.262054	0.131027	−	0.991379i	$-0.458173\pi$
$151$	1.67412e9	0.262054	0.131027	+	0.991379i	$0.458173\pi$
$152$	−3.51250e9	−0.533728
$153$	4.32772e8	0.0638480
$154$	1.76773e9	0.253263
$155$	1.13606e9	0.158092
$156$	−1.64064e8	−0.0221795
$157$	−7.62113e9	−1.00108	−0.500542	−	0.865712i	$-0.666866\pi$
$157$	−7.62113e9	−1.00108	−0.500542	+	0.865712i	$0.666866\pi$
$158$	1.29991e10	1.65943
$159$	1.99124e9	0.247079
$160$	3.72705e8	0.0449599
$161$	−1.90396e9	−0.223327
$162$	−1.00561e9	−0.114713
$163$	−1.78418e10	−1.97968	−0.989839	−	0.142193i	$-0.954585\pi$
$163$	−1.78418e10	−1.97968	−0.989839	+	0.142193i	$0.954585\pi$
$164$	−3.05787e8	−0.0330082
$165$	1.86335e9	0.195712
$166$	−1.12576e9	−0.115069
$167$	1.14867e10	1.14280	0.571400	−	0.820672i	$-0.306400\pi$
$167$	1.14867e10	1.14280	0.571400	+	0.820672i	$0.306400\pi$
$168$	−1.42171e9	−0.137695
$169$	−6.99945e9	−0.660045
$170$	−7.35919e8	−0.0675787
$171$	−2.06265e9	−0.184478
$172$	1.20813e9	0.105253
$173$	−8.09192e9	−0.686822	−0.343411	−	0.939185i	$-0.611582\pi$
$173$	−8.09192e9	−0.686822	−0.343411	+	0.939185i	$0.611582\pi$
$174$	9.67197e9	0.799914
$175$	−2.70996e9	−0.218420
$176$	1.34041e10	1.05301
$177$	9.81506e8	0.0751646
$178$	−2.47920e10	−1.85107
$179$	−1.44994e10	−1.05563	−0.527814	−	0.849360i	$-0.676988\pi$
$179$	−1.44994e10	−1.05563	−0.527814	+	0.849360i	$0.676988\pi$
$180$	1.05704e8	0.00750528
$181$	1.31916e10	0.913574	0.456787	−	0.889576i	$-0.349000\pi$
$181$	1.31916e10	0.913574	0.456787	+	0.889576i	$0.349000\pi$
$182$	−2.20349e9	−0.148864
$183$	−5.26343e9	−0.346928
$184$	−1.35410e10	−0.870907
$185$	4.98079e8	0.0312627
$186$	4.50120e9	0.275753
$187$	−3.17722e9	−0.190003
$188$	1.01207e9	0.0590883
$189$	−8.34872e8	−0.0475929
$190$	3.50750e9	0.195257
$191$	1.40593e10	0.764387	0.382193	−	0.924082i	$-0.375169\pi$
$191$	1.40593e10	0.764387	0.382193	+	0.924082i	$0.375169\pi$
$192$	−1.00641e10	−0.534463
$193$	2.42504e10	1.25809	0.629044	−	0.777369i	$-0.283446\pi$
$193$	2.42504e10	1.25809	0.629044	+	0.777369i	$0.283446\pi$
$194$	−3.31600e7	−0.00168076
$195$	−2.32269e9	−0.115036
$196$	−1.27805e9	−0.0618579
$197$	2.25575e10	1.06707	0.533536	−	0.845777i	$-0.320863\pi$
$197$	2.25575e10	1.06707	0.533536	+	0.845777i	$0.320863\pi$
$198$	7.38278e9	0.341371
$199$	−2.75426e10	−1.24499	−0.622495	−	0.782624i	$-0.713881\pi$
$199$	−2.75426e10	−1.24499	−0.622495	+	0.782624i	$0.713881\pi$
$200$	−1.92734e10	−0.851772
$201$	−2.28876e10	−0.989050
$202$	2.81802e10	1.19087
$203$	8.02979e9	0.331873
$204$	−1.80238e8	−0.00728636
$205$	−4.32910e9	−0.171201
$206$	4.63675e10	1.79395
$207$	−7.95174e9	−0.301020
$208$	−1.67084e10	−0.618941
$209$	1.51431e10	0.548981
$210$	1.41968e9	0.0503738
$211$	−3.44676e10	−1.19713	−0.598563	−	0.801076i	$-0.704261\pi$
$211$	−3.44676e10	−1.19713	−0.598563	+	0.801076i	$0.704261\pi$
$212$	−8.29298e8	−0.0281968
$213$	5.13137e9	0.170815
$214$	2.78696e10	0.908383
$215$	1.71038e10	0.545907
$216$	−5.93765e9	−0.185598
$217$	3.73695e9	0.114406
$218$	3.89600e10	1.16833
$219$	−3.09984e10	−0.910627
$220$	−7.76037e8	−0.0223347
$221$	3.96045e9	0.111681
$222$	1.97344e9	0.0545300
$223$	1.69066e10	0.457808	0.228904	−	0.973449i	$-0.426486\pi$
$223$	1.69066e10	0.457808	0.228904	+	0.973449i	$0.426486\pi$
$224$	1.22597e9	0.0325360
$225$	−1.13180e10	−0.294406
$226$	−6.92256e10	−1.76514
$227$	1.99018e10	0.497482	0.248741	−	0.968570i	$-0.419983\pi$
$227$	1.99018e10	0.497482	0.248741	+	0.968570i	$0.419983\pi$
$228$	8.59041e8	0.0210527
$229$	1.05069e10	0.252473	0.126236	−	0.992000i	$-0.459710\pi$
$229$	1.05069e10	0.252473	0.126236	+	0.992000i	$0.459710\pi$
$230$	1.35218e10	0.318609
$231$	6.12928e9	0.141630
$232$	5.71083e10	1.29420
$233$	3.44694e10	0.766183	0.383092	−	0.923710i	$-0.374859\pi$
$233$	3.44694e10	0.766183	0.383092	+	0.923710i	$0.374859\pi$
$234$	−9.20272e9	−0.200653
$235$	1.43282e10	0.306468
$236$	−4.08771e8	−0.00857781
$237$	4.50722e10	0.927986
$238$	−2.42072e9	−0.0489044
$239$	2.73381e10	0.541974	0.270987	−	0.962583i	$-0.412650\pi$
$239$	2.73381e10	0.541974	0.270987	+	0.962583i	$0.412650\pi$
$240$	1.07650e10	0.209442
$241$	−5.47074e9	−0.104465	−0.0522323	−	0.998635i	$-0.516634\pi$
$241$	−5.47074e9	−0.104465	−0.0522323	+	0.998635i	$0.516634\pi$
$242$	8.82703e8	0.0165442
$243$	−3.48678e9	−0.0641500
$244$	2.19208e9	0.0395915
$245$	−1.80936e10	−0.320833
$246$	−1.71523e10	−0.298617
$247$	−1.88761e10	−0.322683
$248$	2.65774e10	0.446149
$249$	−3.90336e9	−0.0643490
$250$	4.10367e10	0.664419
$251$	−4.37703e10	−0.696062	−0.348031	−	0.937483i	$-0.613150\pi$
$251$	−4.37703e10	−0.696062	−0.348031	+	0.937483i	$0.613150\pi$
$252$	3.47702e8	0.00543132
$253$	5.83783e10	0.895795
$254$	3.02794e10	0.456453
$255$	−2.55167e9	−0.0377914
$256$	1.35256e10	0.196823
$257$	6.50898e10	0.930709	0.465355	−	0.885124i	$-0.345927\pi$
$257$	6.50898e10	0.930709	0.465355	+	0.885124i	$0.345927\pi$
$258$	6.77668e10	0.952201
$259$	1.63837e9	0.0226237
$260$	9.67339e8	0.0131280
$261$	3.35358e10	0.447329
$262$	−4.57152e10	−0.599383
$263$	1.08038e11	1.39243	0.696215	−	0.717833i	$-0.254866\pi$
$263$	1.08038e11	1.39243	0.696215	+	0.717833i	$0.254866\pi$
$264$	4.35917e10	0.552314
$265$	−1.17406e10	−0.146245
$266$	1.15375e10	0.141301
$267$	−8.59619e10	−1.03516
$268$	9.53209e9	0.112871
$269$	−1.42805e11	−1.66287	−0.831437	−	0.555619i	$-0.812481\pi$
$269$	−1.42805e11	−1.66287	−0.831437	+	0.555619i	$0.812481\pi$
$270$	5.92920e9	0.0678984
$271$	−8.54937e10	−0.962880	−0.481440	−	0.876479i	$-0.659886\pi$
$271$	−8.54937e10	−0.962880	−0.481440	+	0.876479i	$0.659886\pi$
$272$	−1.83556e10	−0.203333
$273$	−7.64022e9	−0.0832480
$274$	−2.67313e10	−0.286511
$275$	8.30917e10	0.876114
$276$	3.31169e9	0.0343525
$277$	−9.85414e10	−1.00568	−0.502840	−	0.864380i	$-0.667711\pi$
$277$	−9.85414e10	−1.00568	−0.502840	+	0.864380i	$0.667711\pi$
$278$	1.98532e11	1.99356
$279$	1.56071e10	0.154207
$280$	8.38254e9	0.0815012
$281$	−9.83292e10	−0.940815	−0.470407	−	0.882449i	$-0.655893\pi$
$281$	−9.83292e10	−0.940815	−0.470407	+	0.882449i	$0.655893\pi$
$282$	5.67695e10	0.534557
$283$	1.36212e11	1.26234	0.631168	−	0.775646i	$-0.282576\pi$
$283$	1.36212e11	1.26234	0.631168	+	0.775646i	$0.282576\pi$
$284$	−2.13708e9	−0.0194934
$285$	1.21616e10	0.109192
$286$	6.75625e10	0.597116
$287$	−1.42401e10	−0.123892
$288$	5.12018e9	0.0438550
$289$	−1.14237e11	−0.963311
$290$	−5.70270e10	−0.473467
$291$	−1.14976e8	−0.000939919 0
$292$	1.29100e10	0.103921
$293$	2.49642e10	0.197885	0.0989425	−	0.995093i	$-0.468454\pi$
$293$	2.49642e10	0.197885	0.0989425	+	0.995093i	$0.468454\pi$
$294$	−7.16887e10	−0.559613
$295$	−5.78707e9	−0.0444897
$296$	1.16522e10	0.0882257
$297$	2.55985e10	0.190902
$298$	−6.82804e10	−0.501560
$299$	−7.27692e10	−0.526535
$300$	4.71364e9	0.0335978
$301$	5.62609e10	0.395055
$302$	−3.91091e10	−0.270549
$303$	9.77098e10	0.665957
$304$	8.74853e10	0.587495
$305$	3.10338e10	0.205346
$306$	−1.01100e10	−0.0659178
$307$	−8.15988e10	−0.524277	−0.262139	−	0.965030i	$-0.584428\pi$
$307$	−8.15988e10	−0.524277	−0.262139	+	0.965030i	$0.584428\pi$
$308$	−2.55268e9	−0.0161629
$309$	1.60771e11	1.00322
$310$	−2.65395e10	−0.163217
$311$	−8.66559e10	−0.525263	−0.262631	−	0.964896i	$-0.584590\pi$
$311$	−8.66559e10	−0.525263	−0.262631	+	0.964896i	$0.584590\pi$
$312$	−5.43376e10	−0.324642
$313$	−2.95540e11	−1.74047	−0.870236	−	0.492636i	$-0.836034\pi$
$313$	−2.95540e11	−1.74047	−0.870236	+	0.492636i	$0.836034\pi$
$314$	1.78037e11	1.03354
$315$	4.92250e9	0.0281701
$316$	−1.87714e10	−0.105902
$317$	−3.28835e11	−1.82899	−0.914495	−	0.404597i	$-0.867412\pi$
$317$	−3.28835e11	−1.82899	−0.914495	+	0.404597i	$0.867412\pi$
$318$	−4.65172e10	−0.255089
$319$	−2.46206e11	−1.33119
$320$	5.93387e10	0.316347
$321$	9.66329e10	0.507987
$322$	4.44782e10	0.230567
$323$	−2.07369e10	−0.106007
$324$	1.45215e9	0.00732082
$325$	−1.03575e11	−0.514967
$326$	4.16802e11	2.04386
$327$	1.35087e11	0.653354
$328$	−1.01276e11	−0.483142
$329$	4.71308e10	0.221780
$330$	−4.35297e10	−0.202056
$331$	1.82900e10	0.0837504	0.0418752	−	0.999123i	$-0.486667\pi$
$331$	1.82900e10	0.0837504	0.0418752	+	0.999123i	$0.486667\pi$
$332$	1.62565e9	0.00734353
$333$	6.84255e9	0.0304943
$334$	−2.68340e11	−1.17985
$335$	1.34948e11	0.585416
$336$	3.54102e10	0.151566
$337$	3.39078e11	1.43207	0.716037	−	0.698062i	$-0.245954\pi$
$337$	3.39078e11	1.43207	0.716037	+	0.698062i	$0.245954\pi$
$338$	1.63514e11	0.681443
$339$	−2.40028e11	−0.987104
$340$	1.06270e9	0.00431277
$341$	−1.14581e11	−0.458899
$342$	4.81856e10	0.190458
$343$	−1.22911e11	−0.479475
$344$	4.00130e11	1.54059
$345$	4.68843e10	0.178173
$346$	1.89035e11	0.709087
$347$	−4.74641e11	−1.75745	−0.878724	−	0.477330i	$-0.841605\pi$
$347$	−4.74641e11	−1.75745	−0.878724	+	0.477330i	$0.841605\pi$
$348$	−1.39668e10	−0.0510493
$349$	2.47333e11	0.892417	0.446209	−	0.894929i	$-0.352774\pi$
$349$	2.47333e11	0.892417	0.446209	+	0.894929i	$0.352774\pi$
$350$	6.33074e10	0.225501
$351$	−3.19088e10	−0.112209
$352$	−3.75901e10	−0.130506
$353$	−1.91987e11	−0.658090	−0.329045	−	0.944314i	$-0.606727\pi$
$353$	−1.91987e11	−0.658090	−0.329045	+	0.944314i	$0.606727\pi$
$354$	−2.29289e10	−0.0776013
$355$	−3.02551e10	−0.101105
$356$	3.58009e10	0.118132
$357$	−8.39341e9	−0.0273484
$358$	3.38719e11	1.08985
$359$	−3.99067e9	−0.0126800	−0.00634002	−	0.999980i	$-0.502018\pi$
$359$	−3.99067e9	−0.0126800	−0.00634002	+	0.999980i	$0.502018\pi$
$360$	3.50091e10	0.109855
$361$	−2.23852e11	−0.693712
$362$	−3.08168e11	−0.943190
$363$	3.06062e9	0.00925186
$364$	3.18195e9	0.00950029
$365$	1.82770e11	0.538997
$366$	1.22959e11	0.358175
$367$	−5.84621e11	−1.68220	−0.841098	−	0.540882i	$-0.818090\pi$
$367$	−5.84621e11	−1.68220	−0.841098	+	0.540882i	$0.818090\pi$
$368$	3.37265e11	0.958640
$369$	−5.94726e10	−0.166993
$370$	−1.16356e10	−0.0322761
$371$	−3.86192e10	−0.105833
$372$	−6.49995e9	−0.0175981
$373$	−5.84664e11	−1.56393	−0.781964	−	0.623323i	$-0.785782\pi$
$373$	−5.84664e11	−1.56393	−0.781964	+	0.623323i	$0.785782\pi$
$374$	7.42230e10	0.196163
$375$	1.42287e11	0.371557
$376$	3.35196e11	0.864877
$377$	3.06899e11	0.782454
$378$	1.95034e10	0.0491358
$379$	1.81625e11	0.452168	0.226084	−	0.974108i	$-0.427408\pi$
$379$	1.81625e11	0.452168	0.226084	+	0.974108i	$0.427408\pi$
$380$	−5.06500e9	−0.0124610
$381$	1.04988e11	0.255258
$382$	−3.28438e11	−0.789167
$383$	6.89118e11	1.63644	0.818218	−	0.574908i	$-0.194962\pi$
$383$	6.89118e11	1.63644	0.818218	+	0.574908i	$0.194962\pi$
$384$	2.67470e11	0.627748
$385$	−3.61389e10	−0.0838304
$386$	−5.66513e11	−1.29887
$387$	2.34970e11	0.532491
$388$	4.78847e7	0.000107264 0
$389$	−4.98090e11	−1.10290	−0.551449	−	0.834209i	$-0.685925\pi$
$389$	−4.98090e11	−1.10290	−0.551449	+	0.834209i	$0.685925\pi$
$390$	5.42603e10	0.118766
$391$	−7.99430e10	−0.172976
$392$	−4.23287e11	−0.905415
$393$	−1.58509e11	−0.335188
$394$	−5.26966e11	−1.10166
$395$	−2.65751e11	−0.549272
$396$	−1.06611e10	−0.0217858
$397$	−2.97522e11	−0.601122	−0.300561	−	0.953763i	$-0.597174\pi$
$397$	−2.97522e11	−0.601122	−0.300561	+	0.953763i	$0.597174\pi$
$398$	6.43421e11	1.28535
$399$	4.00043e10	0.0790184
$400$	4.80040e11	0.937578
$401$	−4.84900e11	−0.936489	−0.468244	−	0.883599i	$-0.655113\pi$
$401$	−4.84900e11	−0.936489	−0.468244	+	0.883599i	$0.655113\pi$
$402$	5.34677e11	1.02111
$403$	1.42826e11	0.269734
$404$	−4.06936e10	−0.0759993
$405$	2.05585e10	0.0379702
$406$	−1.87584e11	−0.342632
$407$	−5.02351e10	−0.0907470
$408$	−5.96944e10	−0.106650
$409$	4.31529e11	0.762527	0.381264	−	0.924466i	$-0.375489\pi$
$409$	4.31529e11	0.762527	0.381264	+	0.924466i	$0.375489\pi$
$410$	1.01132e11	0.176751
$411$	−9.26859e10	−0.160223
$412$	−6.69569e10	−0.114487
$413$	−1.90359e10	−0.0321957
$414$	1.85760e11	0.310779
$415$	2.30147e10	0.0380880
$416$	4.68566e10	0.0767098
$417$	6.88375e11	1.11484
$418$	−3.53758e11	−0.566778
$419$	−4.45084e11	−0.705471	−0.352736	−	0.935723i	$-0.614748\pi$
$419$	−4.45084e11	−0.705471	−0.352736	+	0.935723i	$0.614748\pi$
$420$	−2.05009e9	−0.00321478
$421$	−2.91834e11	−0.452758	−0.226379	−	0.974039i	$-0.572689\pi$
$421$	−2.91834e11	−0.452758	−0.226379	+	0.974039i	$0.572689\pi$
$422$	8.05196e11	1.23593
$423$	1.96838e11	0.298936
$424$	−2.74662e11	−0.412716
$425$	−1.13786e11	−0.169175
$426$	−1.19874e11	−0.176352
$427$	1.02082e11	0.148602
$428$	−4.02451e10	−0.0579716
$429$	2.34261e11	0.333920
$430$	−3.99561e11	−0.563605
$431$	−6.26106e11	−0.873978	−0.436989	−	0.899467i	$-0.643955\pi$
$431$	−6.26106e11	−0.873978	−0.436989	+	0.899467i	$0.643955\pi$
$432$	1.47888e11	0.204295
$433$	−6.10341e11	−0.834405	−0.417203	−	0.908813i	$-0.636989\pi$
$433$	−6.10341e11	−0.834405	−0.417203	+	0.908813i	$0.636989\pi$
$434$	−8.72987e10	−0.118115
$435$	−1.97731e11	−0.264773
$436$	−5.62601e10	−0.0745609
$437$	3.81020e11	0.499783
$438$	7.24152e11	0.940148
$439$	7.33210e11	0.942190	0.471095	−	0.882083i	$-0.343859\pi$
$439$	7.33210e11	0.942190	0.471095	+	0.882083i	$0.343859\pi$
$440$	−2.57022e11	−0.326913
$441$	−2.48568e11	−0.312948
$442$	−9.25199e10	−0.115301
$443$	−8.62779e11	−1.06435	−0.532173	−	0.846636i	$-0.678624\pi$
$443$	−8.62779e11	−1.06435	−0.532173	+	0.846636i	$0.678624\pi$
$444$	−2.84974e9	−0.00348002
$445$	5.06841e11	0.612705
$446$	−3.94954e11	−0.472650
$447$	−2.36750e11	−0.280483
$448$	1.95188e11	0.228929
$449$	−3.21480e11	−0.373289	−0.186645	−	0.982427i	$-0.559761\pi$
$449$	−3.21480e11	−0.373289	−0.186645	+	0.982427i	$0.559761\pi$
$450$	2.64399e11	0.303951
$451$	4.36622e11	0.496949
$452$	9.99652e10	0.112649
$453$	−1.35604e11	−0.151297
$454$	−4.64926e11	−0.513609
$455$	4.50476e10	0.0492742
$456$	2.84512e11	0.308148
$457$	−1.73149e12	−1.85693	−0.928467	−	0.371415i	$-0.878873\pi$
$457$	−1.73149e12	−1.85693	−0.928467	+	0.371415i	$0.878873\pi$
$458$	−2.45451e11	−0.260658
$459$	−3.50545e10	−0.0368627
$460$	−1.95261e10	−0.0203332
$461$	7.85929e11	0.810455	0.405228	−	0.914216i	$-0.367192\pi$
$461$	7.85929e11	0.810455	0.405228	+	0.914216i	$0.367192\pi$
$462$	−1.43186e11	−0.146221
$463$	−7.57858e11	−0.766431	−0.383216	−	0.923659i	$-0.625183\pi$
$463$	−7.57858e11	−0.766431	−0.383216	+	0.923659i	$0.625183\pi$
$464$	−1.42239e12	−1.42458
$465$	−9.20212e10	−0.0912745
$466$	−8.05239e11	−0.791022
$467$	−2.11064e11	−0.205347	−0.102674	−	0.994715i	$-0.532740\pi$
$467$	−2.11064e11	−0.205347	−0.102674	+	0.994715i	$0.532740\pi$
$468$	1.32892e10	0.0128054
$469$	4.43895e11	0.423646
$470$	−3.34719e11	−0.316403
$471$	6.17311e11	0.577976
$472$	−1.35384e11	−0.125554
$473$	−1.72505e12	−1.58462
$474$	−1.05293e12	−0.958070
$475$	5.42319e11	0.488803
$476$	3.49564e9	0.00312101
$477$	−1.61290e11	−0.142651
$478$	−6.38645e11	−0.559543
$479$	−1.00601e12	−0.873158	−0.436579	−	0.899666i	$-0.643810\pi$
$479$	−1.00601e12	−0.873158	−0.436579	+	0.899666i	$0.643810\pi$
$480$	−3.01891e10	−0.0259576
$481$	6.26187e10	0.0533397
$482$	1.27802e11	0.107851
$483$	1.54220e11	0.128938
$484$	−1.27467e9	−0.00105583
$485$	6.77914e8	0.000556335 0
$486$	8.14546e10	0.0662297
$487$	−1.83444e12	−1.47783	−0.738914	−	0.673800i	$-0.764661\pi$
$487$	−1.83444e12	−1.47783	−0.738914	+	0.673800i	$0.764661\pi$
$488$	7.26012e11	0.579502
$489$	1.44519e12	1.14297
$490$	4.22685e11	0.331233
$491$	1.51402e11	0.117562	0.0587808	−	0.998271i	$-0.481279\pi$
$491$	1.51402e11	0.117562	0.0587808	+	0.998271i	$0.481279\pi$
$492$	2.47688e10	0.0190573
$493$	3.37154e11	0.257049
$494$	4.40963e11	0.333144
$495$	−1.50931e11	−0.112994
$496$	−6.61959e11	−0.491093
$497$	−9.95206e10	−0.0731660
$498$	9.11863e10	0.0664351
$499$	−1.06835e12	−0.771366	−0.385683	−	0.922631i	$-0.626034\pi$
$499$	−1.06835e12	−0.771366	−0.385683	+	0.922631i	$0.626034\pi$
$500$	−5.92590e10	−0.0424023
$501$	−9.30421e11	−0.659796
$502$	1.02252e12	0.718627
$503$	5.89639e11	0.410705	0.205353	−	0.978688i	$-0.434166\pi$
$503$	5.89639e11	0.410705	0.205353	+	0.978688i	$0.434166\pi$
$504$	1.15158e11	0.0794982
$505$	−5.76108e11	−0.394178
$506$	−1.36377e12	−0.924836
$507$	5.66955e11	0.381077
$508$	−4.37249e10	−0.0291301
$509$	1.50529e12	0.994009	0.497005	−	0.867748i	$-0.334433\pi$
$509$	1.50529e12	0.994009	0.497005	+	0.867748i	$0.334433\pi$
$510$	5.96094e10	0.0390166
$511$	6.01200e11	0.390054
$512$	1.37471e12	0.884088
$513$	1.67075e11	0.106508
$514$	−1.52056e12	−0.960881
$515$	−9.47924e11	−0.593801
$516$	−9.78586e10	−0.0607680
$517$	−1.44510e12	−0.889593
$518$	−3.82740e10	−0.0233571
$519$	6.55445e11	0.396537
$520$	3.20381e11	0.192155
$521$	1.04958e12	0.624088	0.312044	−	0.950068i	$-0.398986\pi$
$521$	1.04958e12	0.624088	0.312044	+	0.950068i	$0.398986\pi$
$522$	−7.83429e11	−0.461830
$523$	−2.30838e12	−1.34912	−0.674558	−	0.738222i	$-0.735666\pi$
$523$	−2.30838e12	−1.34912	−0.674558	+	0.738222i	$0.735666\pi$
$524$	6.60149e10	0.0382518
$525$	2.19507e11	0.126105
$526$	−2.52386e12	−1.43757
$527$	1.56907e11	0.0886121
$528$	−1.08573e12	−0.607954
$529$	−3.32280e11	−0.184482
$530$	2.74271e11	0.150986
$531$	−7.95020e10	−0.0433963
$532$	−1.66607e10	−0.00901761
$533$	−5.44255e11	−0.292099
$534$	2.00815e12	1.06871
$535$	−5.69758e11	−0.300676
$536$	3.15701e12	1.65209
$537$	1.17445e12	0.609467
$538$	3.33607e12	1.71678
$539$	1.82488e12	0.931290
$540$	−8.56206e9	−0.00433317
$541$	1.72825e12	0.867399	0.433699	−	0.901058i	$-0.357208\pi$
$541$	1.72825e12	0.867399	0.433699	+	0.901058i	$0.357208\pi$
$542$	1.99722e12	0.994095
$543$	−1.06852e12	−0.527452
$544$	5.14758e10	0.0252005
$545$	−7.96487e11	−0.386718
$546$	1.78483e11	0.0859468
$547$	−1.36998e12	−0.654292	−0.327146	−	0.944974i	$-0.606087\pi$
$547$	−1.36998e12	−0.654292	−0.327146	+	0.944974i	$0.606087\pi$
$548$	3.86012e10	0.0182847
$549$	4.26338e11	0.200299
$550$	−1.94110e12	−0.904516
$551$	−1.60692e12	−0.742699
$552$	1.09682e12	0.502818
$553$	−8.74156e11	−0.397490
$554$	2.30202e12	1.03828
$555$	−4.03444e10	−0.0180495
$556$	−2.86690e11	−0.127226
$557$	2.50228e12	1.10151	0.550753	−	0.834668i	$-0.314341\pi$
$557$	2.50228e12	1.10151	0.550753	+	0.834668i	$0.314341\pi$
$558$	−3.64597e11	−0.159206
$559$	2.15029e12	0.931417
$560$	−2.08783e11	−0.0897115
$561$	2.57355e11	0.109698
$562$	2.29706e12	0.971314
$563$	−1.45935e12	−0.612167	−0.306084	−	0.952005i	$-0.599019\pi$
$563$	−1.45935e12	−0.612167	−0.306084	+	0.952005i	$0.599019\pi$
$564$	−8.19780e10	−0.0341147
$565$	1.41523e12	0.584264
$566$	−3.18203e12	−1.30326
$567$	6.76247e10	0.0274778
$568$	−7.07796e11	−0.285325
$569$	3.11112e12	1.24426	0.622131	−	0.782913i	$-0.286267\pi$
$569$	3.11112e12	1.24426	0.622131	+	0.782913i	$0.286267\pi$
$570$	−2.84107e11	−0.112732
$571$	4.63281e12	1.82382	0.911909	−	0.410391i	$-0.134608\pi$
$571$	4.63281e12	1.82382	0.911909	+	0.410391i	$0.134608\pi$
$572$	−9.75635e10	−0.0381070
$573$	−1.13880e12	−0.441319
$574$	3.32661e11	0.127908
$575$	2.09069e12	0.797600
$576$	8.15188e11	0.308572
$577$	3.67714e12	1.38108	0.690540	−	0.723294i	$-0.257373\pi$
$577$	3.67714e12	1.38108	0.690540	+	0.723294i	$0.257373\pi$
$578$	2.66869e12	0.994540
$579$	−1.96428e12	−0.726358
$580$	8.23497e10	0.0302159
$581$	7.57040e10	0.0275630
$582$	2.68596e9	0.000970390 0
$583$	1.18412e12	0.424511
$584$	4.27576e12	1.52109
$585$	1.88138e11	0.0664163
$586$	−5.83187e11	−0.204300
$587$	3.18227e12	1.10628	0.553141	−	0.833088i	$-0.313429\pi$
$587$	3.18227e12	1.10628	0.553141	+	0.833088i	$0.313429\pi$
$588$	1.03522e11	0.0357137
$589$	−7.47840e11	−0.256029
$590$	1.35191e11	0.0459320
$591$	−1.82716e12	−0.616075
$592$	−2.90220e11	−0.0971134
$593$	−1.13721e12	−0.377654	−0.188827	−	0.982010i	$-0.560469\pi$
$593$	−1.13721e12	−0.377654	−0.188827	+	0.982010i	$0.560469\pi$
$594$	−5.98005e11	−0.197091
$595$	4.94885e10	0.0161874
$596$	9.86002e10	0.0320088
$597$	2.23095e12	0.718795
$598$	1.69996e12	0.543605
$599$	8.18505e8	0.000259777 0	0.000129888	−	1.00000i	$-0.499959\pi$
$599$	8.18505e8	0.000259777 0	0.000129888		1.00000i	$0.499959\pi$
$600$	1.56115e12	0.491771
$601$	−8.21445e11	−0.256828	−0.128414	−	0.991721i	$-0.540989\pi$
$601$	−8.21445e11	−0.256828	−0.128414	+	0.991721i	$0.540989\pi$
$602$	−1.31431e12	−0.407862
$603$	1.85390e12	0.571028
$604$	5.64754e10	0.0172661
$605$	−1.80457e10	−0.00547615
$606$	−2.28260e12	−0.687547
$607$	−1.81063e12	−0.541353	−0.270676	−	0.962670i	$-0.587247\pi$
$607$	−1.81063e12	−0.541353	−0.270676	+	0.962670i	$0.587247\pi$
$608$	−2.45342e11	−0.0728123
$609$	−6.50413e11	−0.191607
$610$	−7.24979e11	−0.212003
$611$	1.80134e12	0.522889
$612$	1.45993e10	0.00420678
$613$	1.14483e12	0.327468	0.163734	−	0.986505i	$-0.447646\pi$
$613$	1.14483e12	0.327468	0.163734	+	0.986505i	$0.447646\pi$
$614$	1.90623e12	0.541273
$615$	3.50657e11	0.0988427
$616$	−8.45442e11	−0.236576
$617$	−1.58187e12	−0.439428	−0.219714	−	0.975564i	$-0.570512\pi$
$617$	−1.58187e12	−0.439428	−0.219714	+	0.975564i	$0.570512\pi$
$618$	−3.75577e12	−1.03574
$619$	−1.91787e12	−0.525062	−0.262531	−	0.964924i	$-0.584557\pi$
$619$	−1.91787e12	−0.525062	−0.262531	+	0.964924i	$0.584557\pi$
$620$	3.83244e10	0.0104163
$621$	6.44091e11	0.173794
$622$	2.02437e12	0.542291
$623$	1.66719e12	0.443394
$624$	1.35338e12	0.357346
$625$	2.53027e12	0.663296
$626$	6.90410e12	1.79689
$627$	−1.22659e12	−0.316954
$628$	−2.57094e11	−0.0659589
$629$	6.87918e10	0.0175230
$630$	−1.14994e11	−0.0290833
$631$	−3.98851e12	−1.00156	−0.500782	−	0.865573i	$-0.666954\pi$
$631$	−3.98851e12	−1.00156	−0.500782	+	0.865573i	$0.666954\pi$
$632$	−6.21704e12	−1.55009
$633$	2.79187e12	0.691161
$634$	7.68190e12	1.88828
$635$	−6.19024e11	−0.151086
$636$	6.71732e10	0.0162794
$637$	−2.27474e12	−0.547398
$638$	5.75160e12	1.37435
$639$	−4.15641e11	−0.0986198
$640$	−1.57704e12	−0.371562
$641$	4.30645e12	1.00753	0.503765	−	0.863841i	$-0.331948\pi$
$641$	4.30645e12	1.00753	0.503765	+	0.863841i	$0.331948\pi$
$642$	−2.25744e12	−0.524455
$643$	−2.93311e12	−0.676674	−0.338337	−	0.941025i	$-0.609864\pi$
$643$	−2.93311e12	−0.676674	−0.338337	+	0.941025i	$0.609864\pi$
$644$	−6.42288e10	−0.0147144
$645$	−1.38541e12	−0.315180
$646$	4.84435e11	0.109443
$647$	1.29709e12	0.291006	0.145503	−	0.989358i	$-0.453520\pi$
$647$	1.29709e12	0.291006	0.145503	+	0.989358i	$0.453520\pi$
$648$	4.80950e11	0.107155
$649$	5.83670e11	0.129142
$650$	2.41961e12	0.531661
$651$	−3.02693e11	−0.0660523
$652$	−6.01882e11	−0.130436
$653$	4.63066e12	0.996630	0.498315	−	0.866996i	$-0.333952\pi$
$653$	4.63066e12	0.996630	0.498315	+	0.866996i	$0.333952\pi$
$654$	−3.15576e12	−0.674534
$655$	9.34588e11	0.198397
$656$	2.52247e12	0.531812
$657$	2.51087e12	0.525751
$658$	−1.10102e12	−0.228970
$659$	3.08986e11	0.0638196	0.0319098	−	0.999491i	$-0.489841\pi$
$659$	3.08986e11	0.0638196	0.0319098	+	0.999491i	$0.489841\pi$
$660$	6.28590e10	0.0128949
$661$	5.48364e12	1.11728	0.558640	−	0.829410i	$-0.311323\pi$
$661$	5.48364e12	1.11728	0.558640	+	0.829410i	$0.311323\pi$
$662$	−4.27271e11	−0.0864654
$663$	−3.20796e11	−0.0644790
$664$	5.38411e11	0.107487
$665$	−2.35870e11	−0.0467708
$666$	−1.59849e11	−0.0314829
$667$	−6.19485e12	−1.21189
$668$	3.87496e11	0.0752962
$669$	−1.36943e12	−0.264316
$670$	−3.15251e12	−0.604394
$671$	−3.12999e12	−0.596063
$672$	−9.93036e10	−0.0187846
$673$	−4.26313e12	−0.801053	−0.400526	−	0.916285i	$-0.631173\pi$
$673$	−4.26313e12	−0.801053	−0.400526	+	0.916285i	$0.631173\pi$
$674$	−7.92120e12	−1.47850
$675$	9.16756e11	0.169976
$676$	−2.36122e11	−0.0434887
$677$	3.55841e11	0.0651038	0.0325519	−	0.999470i	$-0.489637\pi$
$677$	3.55841e11	0.0651038	0.0325519	+	0.999470i	$0.489637\pi$
$678$	5.60728e12	1.01910
$679$	2.22992e9	0.000402601 0
$680$	3.51965e11	0.0631261
$681$	−1.61205e12	−0.287221
$682$	2.67671e12	0.473775
$683$	−5.38485e12	−0.946849	−0.473424	−	0.880834i	$-0.656982\pi$
$683$	−5.38485e12	−0.946849	−0.473424	+	0.880834i	$0.656982\pi$
$684$	−6.95823e10	−0.0121548
$685$	5.46487e11	0.0948357
$686$	2.87131e12	0.495019
$687$	−8.51058e11	−0.145765
$688$	−9.96599e12	−1.69579
$689$	−1.47603e12	−0.249521
$690$	−1.09526e12	−0.183949
$691$	2.56126e12	0.427369	0.213684	−	0.976903i	$-0.431454\pi$
$691$	2.56126e12	0.427369	0.213684	+	0.976903i	$0.431454\pi$
$692$	−2.72976e11	−0.0452529
$693$	−4.96471e11	−0.0817701
$694$	1.10881e13	1.81442
$695$	−4.05874e12	−0.659871
$696$	−4.62577e12	−0.747209
$697$	−5.97910e11	−0.0959595
$698$	−5.77794e12	−0.921348
$699$	−2.79203e12	−0.442356
$700$	−9.14189e10	−0.0143911
$701$	−6.38644e12	−0.998914	−0.499457	−	0.866339i	$-0.666467\pi$
$701$	−6.38644e12	−0.998914	−0.499457	+	0.866339i	$0.666467\pi$
$702$	7.45421e11	0.115847
$703$	−3.27872e11	−0.0506297
$704$	−5.98476e12	−0.918269
$705$	−1.16058e12	−0.176939
$706$	4.48500e12	0.679425
$707$	−1.89504e12	−0.285253
$708$	3.31105e10	0.00495240
$709$	4.71903e12	0.701367	0.350683	−	0.936494i	$-0.385949\pi$
$709$	4.71903e12	0.701367	0.350683	+	0.936494i	$0.385949\pi$
$710$	7.06788e11	0.104382
$711$	−3.65085e12	−0.535773
$712$	1.18572e13	1.72910
$713$	−2.88300e12	−0.417774
$714$	1.96078e11	0.0282350
$715$	−1.38123e12	−0.197646
$716$	−4.89127e11	−0.0695526
$717$	−2.21439e12	−0.312909
$718$	9.32259e10	0.0130911
$719$	−8.71884e12	−1.21669	−0.608343	−	0.793674i	$-0.708166\pi$
$719$	−8.71884e12	−1.21669	−0.608343	+	0.793674i	$0.708166\pi$
$720$	−8.71966e11	−0.120921
$721$	−3.11808e12	−0.429714
$722$	5.22940e12	0.716201
$723$	4.43130e11	0.0603127
$724$	4.45010e11	0.0601930
$725$	−8.81734e12	−1.18527
$726$	−7.14990e10	−0.00955179
$727$	−1.17664e13	−1.56220	−0.781101	−	0.624405i	$-0.785342\pi$
$727$	−1.17664e13	−1.56220	−0.781101	+	0.624405i	$0.785342\pi$
$728$	1.05385e12	0.139056
$729$	2.82430e11	0.0370370
$730$	−4.26968e12	−0.556471
$731$	2.36227e12	0.305986
$732$	−1.77559e11	−0.0228582
$733$	−1.13764e12	−0.145559	−0.0727794	−	0.997348i	$-0.523187\pi$
$733$	−1.13764e12	−0.145559	−0.0727794	+	0.997348i	$0.523187\pi$
$734$	1.36573e13	1.73673
$735$	1.46558e12	0.185233
$736$	−9.45816e11	−0.118811
$737$	−1.36105e13	−1.69930
$738$	1.38934e12	0.172407
$739$	9.77524e12	1.20567	0.602834	−	0.797867i	$-0.294038\pi$
$739$	9.77524e12	1.20567	0.602834	+	0.797867i	$0.294038\pi$
$740$	1.68024e10	0.00205982
$741$	1.52896e12	0.186301
$742$	9.02181e11	0.109264
$743$	6.06927e11	0.0730612	0.0365306	−	0.999333i	$-0.488369\pi$
$743$	6.06927e11	0.0730612	0.0365306	+	0.999333i	$0.488369\pi$
$744$	−2.15277e12	−0.257584
$745$	1.39590e12	0.166017
$746$	1.36583e13	1.61463
$747$	3.16172e11	0.0371519
$748$	−1.07182e11	−0.0125188
$749$	−1.87415e12	−0.217589
$750$	−3.32397e12	−0.383603
$751$	−3.40247e12	−0.390315	−0.195157	−	0.980772i	$-0.562522\pi$
$751$	−3.40247e12	−0.390315	−0.195157	+	0.980772i	$0.562522\pi$
$752$	−8.34869e12	−0.952003
$753$	3.54540e12	0.401872
$754$	−7.16944e12	−0.807820
$755$	7.99535e11	0.0895522
$756$	−2.81639e10	−0.00313577
$757$	6.46608e11	0.0715665	0.0357832	−	0.999360i	$-0.488607\pi$
$757$	6.46608e11	0.0715665	0.0357832	+	0.999360i	$0.488607\pi$
$758$	−4.24294e12	−0.466827
$759$	−4.72864e12	−0.517188
$760$	−1.67752e12	−0.182392
$761$	−1.30326e13	−1.40864	−0.704320	−	0.709882i	$-0.748748\pi$
$761$	−1.30326e13	−1.40864	−0.704320	+	0.709882i	$0.748748\pi$
$762$	−2.45263e12	−0.263533
$763$	−2.61995e12	−0.279855
$764$	4.74281e11	0.0503635
$765$	2.06685e11	0.0218189
$766$	−1.60985e13	−1.68949
$767$	−7.27552e11	−0.0759075
$768$	−1.09557e12	−0.113636
$769$	−3.31464e11	−0.0341797	−0.0170898	−	0.999854i	$-0.505440\pi$
$769$	−3.31464e11	−0.0341797	−0.0170898	+	0.999854i	$0.505440\pi$
$770$	8.44239e11	0.0865480
$771$	−5.27228e12	−0.537345
$772$	8.18072e11	0.0828922
$773$	−1.11690e13	−1.12514	−0.562568	−	0.826751i	$-0.690187\pi$
$773$	−1.11690e13	−1.12514	−0.562568	+	0.826751i	$0.690187\pi$
$774$	−5.48911e12	−0.549753
$775$	−4.10347e12	−0.408595
$776$	1.58593e10	0.00157002
$777$	−1.32708e11	−0.0130618
$778$	1.16359e13	1.13865
$779$	2.84973e12	0.277258
$780$	−7.83545e10	−0.00757946
$781$	3.05146e12	0.293479
$782$	1.86755e12	0.178583
$783$	−2.71640e12	−0.258265
$784$	1.05428e13	0.996625
$785$	−3.63973e12	−0.342102
$786$	3.70293e12	0.346054
$787$	−1.36913e13	−1.27221	−0.636105	−	0.771602i	$-0.719456\pi$
$787$	−1.36913e13	−1.27221	−0.636105	+	0.771602i	$0.719456\pi$
$788$	7.60964e11	0.0703066
$789$	−8.75104e12	−0.803920
$790$	6.20819e12	0.567079
$791$	4.65523e12	0.422812
$792$	−3.53093e12	−0.318879
$793$	3.90157e12	0.350357
$794$	6.95041e12	0.620609
$795$	9.50985e11	0.0844349
$796$	−9.29132e11	−0.0820292
$797$	1.16938e13	1.02658	0.513290	−	0.858215i	$-0.328427\pi$
$797$	1.16938e13	1.02658	0.513290	+	0.858215i	$0.328427\pi$
$798$	−9.34538e11	−0.0815800
$799$	1.97892e12	0.171778
$800$	−1.34621e12	−0.116201
$801$	6.96292e12	0.597647
$802$	1.13277e13	0.966848
$803$	−1.84337e13	−1.56456
$804$	−7.72099e11	−0.0651660
$805$	−9.09301e11	−0.0763179
$806$	−3.33656e12	−0.278478
$807$	1.15672e13	0.960061
$808$	−1.34776e13	−1.11240
$809$	2.55564e12	0.209765	0.104882	−	0.994485i	$-0.466553\pi$
$809$	2.55564e12	0.209765	0.104882	+	0.994485i	$0.466553\pi$
$810$	−4.80265e11	−0.0392011
$811$	9.70911e12	0.788107	0.394054	−	0.919087i	$-0.371072\pi$
$811$	9.70911e12	0.788107	0.394054	+	0.919087i	$0.371072\pi$
$812$	2.70880e11	0.0218663
$813$	6.92499e12	0.555919
$814$	1.17354e12	0.0936889
$815$	−8.52098e12	−0.676519
$816$	1.48680e12	0.117394
$817$	−1.12589e13	−0.884094
$818$	−1.00809e13	−0.787247
$819$	6.18858e11	0.0480633
$820$	−1.46039e11	−0.0112800
$821$	−8.51723e12	−0.654265	−0.327133	−	0.944978i	$-0.606082\pi$
$821$	−8.51723e12	−0.654265	−0.327133	+	0.944978i	$0.606082\pi$
$822$	2.16523e12	0.165417
$823$	1.00520e13	0.763750	0.381875	−	0.924214i	$-0.375278\pi$
$823$	1.00520e13	0.763750	0.381875	+	0.924214i	$0.375278\pi$
$824$	−2.21760e13	−1.67575
$825$	−6.73043e12	−0.505825
$826$	4.44696e11	0.0332394
$827$	−8.59417e11	−0.0638895	−0.0319447	−	0.999490i	$-0.510170\pi$
$827$	−8.59417e11	−0.0638895	−0.0319447	+	0.999490i	$0.510170\pi$
$828$	−2.68247e11	−0.0198334
$829$	1.45843e13	1.07248	0.536242	−	0.844064i	$-0.319844\pi$
$829$	1.45843e13	1.07248	0.536242	+	0.844064i	$0.319844\pi$
$830$	−5.37644e11	−0.0393227
$831$	7.98185e12	0.580630
$832$	7.46008e12	0.539745
$833$	−2.49899e12	−0.179830
$834$	−1.60811e13	−1.15098
$835$	5.48586e12	0.390531
$836$	5.10844e11	0.0361709
$837$	−1.26418e12	−0.0890313
$838$	1.03976e13	0.728341
$839$	1.28668e13	0.896484	0.448242	−	0.893912i	$-0.352050\pi$
$839$	1.28668e13	0.896484	0.448242	+	0.893912i	$0.352050\pi$
$840$	−6.78985e11	−0.0470548
$841$	1.16192e13	0.800927
$842$	6.81752e12	0.467436
$843$	7.96467e12	0.543180
$844$	−1.16274e12	−0.0788755
$845$	−3.34283e12	−0.225558
$846$	−4.59833e12	−0.308627
$847$	−5.93593e10	−0.00396291
$848$	6.84096e12	0.454293
$849$	−1.10331e13	−0.728810
$850$	2.65814e12	0.174660
$851$	−1.26398e12	−0.0826147
$852$	1.73103e11	0.0112545
$853$	9.19067e12	0.594397	0.297198	−	0.954816i	$-0.403948\pi$
$853$	9.19067e12	0.594397	0.297198	+	0.954816i	$0.403948\pi$
$854$	−2.38473e12	−0.153419
$855$	−9.85092e11	−0.0630419
$856$	−1.33291e13	−0.848532
$857$	6.56735e12	0.415888	0.207944	−	0.978141i	$-0.433323\pi$
$857$	6.56735e12	0.415888	0.207944	+	0.978141i	$0.433323\pi$
$858$	−5.47256e12	−0.344745
$859$	−1.15305e13	−0.722566	−0.361283	−	0.932456i	$-0.617661\pi$
$859$	−1.15305e13	−0.722566	−0.361283	+	0.932456i	$0.617661\pi$
$860$	5.76985e11	0.0359684
$861$	1.15345e12	0.0715291
$862$	1.46264e13	0.902311
$863$	−3.57238e12	−0.219235	−0.109617	−	0.993974i	$-0.534963\pi$
$863$	−3.57238e12	−0.219235	−0.109617	+	0.993974i	$0.534963\pi$
$864$	−4.14734e11	−0.0253197
$865$	−3.86458e12	−0.234709
$866$	1.42582e13	0.861455
$867$	9.25320e12	0.556168
$868$	1.26064e11	0.00753791
$869$	2.68030e13	1.59439
$870$	4.61918e12	0.273356
$871$	1.69657e13	0.998825
$872$	−1.86332e13	−1.09135
$873$	9.31309e9	0.000542663 0
$874$	−8.90100e12	−0.515985
$875$	−2.75960e12	−0.159151
$876$	−1.04571e12	−0.0599988
$877$	3.20992e13	1.83230	0.916149	−	0.400837i	$-0.131281\pi$
$877$	3.20992e13	1.83230	0.916149	+	0.400837i	$0.131281\pi$
$878$	−1.71285e13	−0.972734
$879$	−2.02210e12	−0.114249
$880$	6.40160e12	0.359846
$881$	−2.72871e13	−1.52604	−0.763020	−	0.646375i	$-0.776284\pi$
$881$	−2.72871e13	−1.52604	−0.763020	+	0.646375i	$0.776284\pi$
$882$	5.80679e12	0.323093
$883$	−5.72818e12	−0.317098	−0.158549	−	0.987351i	$-0.550682\pi$
$883$	−5.72818e12	−0.317098	−0.158549	+	0.987351i	$0.550682\pi$
$884$	1.33603e11	0.00735837
$885$	4.68753e11	0.0256861
$886$	2.01554e13	1.09885
$887$	9.01105e12	0.488787	0.244393	−	0.969676i	$-0.421411\pi$
$887$	9.01105e12	0.488787	0.244393	+	0.969676i	$0.421411\pi$
$888$	−9.43828e11	−0.0509371
$889$	−2.03621e12	−0.109336
$890$	−1.18403e13	−0.632568
$891$	−2.07348e12	−0.110217
$892$	5.70333e11	0.0301638
$893$	−9.43183e12	−0.496323
$894$	5.53071e12	0.289576
$895$	−6.92468e12	−0.360742
$896$	−5.18747e12	−0.268887
$897$	5.89431e12	0.303995
$898$	7.51009e12	0.385391
$899$	1.21588e13	0.620830
$900$	−3.81805e11	−0.0193977
$901$	−1.62154e12	−0.0819720
$902$	−1.01999e13	−0.513059
$903$	−4.55713e12	−0.228085
$904$	3.31082e13	1.64884
$905$	6.30011e12	0.312197
$906$	3.16784e12	0.156202
$907$	−1.01989e12	−0.0500402	−0.0250201	−	0.999687i	$-0.507965\pi$
$907$	−1.01989e12	−0.0500402	−0.0250201	+	0.999687i	$0.507965\pi$
$908$	6.71376e11	0.0327778
$909$	−7.91450e12	−0.384491
$910$	−1.05235e12	−0.0508716
$911$	−1.10786e13	−0.532909	−0.266455	−	0.963847i	$-0.585852\pi$
$911$	−1.10786e13	−0.532909	−0.266455	+	0.963847i	$0.585852\pi$
$912$	−7.08631e12	−0.339190
$913$	−2.32120e12	−0.110559
$914$	4.04492e13	1.91713
$915$	−2.51374e12	−0.118556
$916$	3.54443e11	0.0166348
$917$	3.07422e12	0.143573
$918$	8.18907e11	0.0380577
$919$	−1.02036e13	−0.471881	−0.235941	−	0.971767i	$-0.575817\pi$
$919$	−1.02036e13	−0.471881	−0.235941	+	0.971767i	$0.575817\pi$
$920$	−6.46699e12	−0.297617
$921$	6.60950e12	0.302692
$922$	−1.83601e13	−0.836729
$923$	−3.80368e12	−0.172503
$924$	2.06767e11	0.00933164
$925$	−1.79906e12	−0.0807995
$926$	1.77043e13	0.791278
$927$	−1.30225e13	−0.579207
$928$	3.98891e12	0.176558
$929$	−3.80349e13	−1.67537	−0.837686	−	0.546152i	$-0.816092\pi$
$929$	−3.80349e13	−1.67537	−0.837686	+	0.546152i	$0.816092\pi$
$930$	2.14970e12	0.0942335
$931$	1.19105e13	0.519587
$932$	1.16280e12	0.0504818
$933$	7.01913e12	0.303260
$934$	4.93066e12	0.212004
$935$	−1.51739e12	−0.0649301
$936$	4.40135e12	0.187432
$937$	3.02627e13	1.28256	0.641282	−	0.767305i	$-0.278403\pi$
$937$	3.02627e13	1.28256	0.641282	+	0.767305i	$0.278403\pi$
$938$	−1.03698e13	−0.437379
$939$	2.39387e13	1.00486
$940$	4.83351e11	0.0201924
$941$	1.55023e12	0.0644531	0.0322266	−	0.999481i	$-0.489740\pi$
$941$	1.55023e12	0.0644531	0.0322266	+	0.999481i	$0.489740\pi$
$942$	−1.44210e13	−0.596713
$943$	1.09860e13	0.452414
$944$	3.37199e12	0.138202
$945$	−3.98722e11	−0.0162640
$946$	4.02987e13	1.63599
$947$	−3.90879e13	−1.57931	−0.789654	−	0.613552i	$-0.789740\pi$
$947$	−3.90879e13	−1.57931	−0.789654	+	0.613552i	$0.789740\pi$
$948$	1.52048e12	0.0611426
$949$	2.29779e13	0.919627
$950$	−1.26691e13	−0.504649
$951$	2.66356e13	1.05597
$952$	1.15775e12	0.0456822
$953$	−2.78189e13	−1.09250	−0.546251	−	0.837622i	$-0.683945\pi$
$953$	−2.78189e13	−1.09250	−0.546251	+	0.837622i	$0.683945\pi$
$954$	3.76790e12	0.147276
$955$	6.71450e12	0.261215
$956$	9.22234e11	0.0357092
$957$	1.99427e13	0.768563
$958$	2.35014e13	0.901464
$959$	1.79760e12	0.0686294
$960$	−4.80644e12	−0.182643
$961$	−2.07811e13	−0.785982
$962$	−1.46283e12	−0.0550689
$963$	−7.82727e12	−0.293286
$964$	−1.84552e11	−0.00688291
$965$	1.15816e13	0.429929
$966$	−3.60274e12	−0.133118
$967$	3.01952e12	0.111050	0.0555250	−	0.998457i	$-0.482317\pi$
$967$	3.01952e12	0.111050	0.0555250	+	0.998457i	$0.482317\pi$
$968$	−4.22167e11	−0.0154541
$969$	1.67969e12	0.0612030
$970$	−1.58367e10	−0.000574371 0
$971$	4.22227e13	1.52426	0.762130	−	0.647424i	$-0.224154\pi$
$971$	4.22227e13	1.52426	0.762130	+	0.647424i	$0.224154\pi$
$972$	−1.17624e11	−0.00422668
$973$	−1.33507e13	−0.477526
$974$	4.28543e13	1.52574
$975$	8.38956e12	0.297316
$976$	−1.80827e13	−0.637880
$977$	2.06518e12	0.0725159	0.0362579	−	0.999342i	$-0.488456\pi$
$977$	2.06518e12	0.0725159	0.0362579	+	0.999342i	$0.488456\pi$
$978$	−3.37609e13	−1.18002
$979$	−5.11188e13	−1.77852
$980$	−6.10377e11	−0.0211388
$981$	−1.09420e13	−0.377214
$982$	−3.53690e12	−0.121373
$983$	−2.25904e13	−0.771674	−0.385837	−	0.922567i	$-0.626087\pi$
$983$	−2.25904e13	−0.771674	−0.385837	+	0.922567i	$0.626087\pi$
$984$	8.20336e12	0.278942
$985$	1.07731e13	0.364653
$986$	−7.87623e12	−0.265382
$987$	−3.81759e12	−0.128045
$988$	−6.36773e11	−0.0212607
$989$	−4.34044e13	−1.44261
$990$	3.52590e12	0.116657
$991$	5.55935e12	0.183102	0.0915509	−	0.995800i	$-0.470818\pi$
$991$	5.55935e12	0.183102	0.0915509	+	0.995800i	$0.470818\pi$
$992$	1.85638e12	0.0608646
$993$	−1.48149e12	−0.0483533
$994$	2.32490e12	0.0755379
$995$	−1.31539e13	−0.425453
$996$	−1.31677e11	−0.00423979
$997$	2.57742e13	0.826145	0.413073	−	0.910698i	$-0.364456\pi$
$997$	2.57742e13	0.826145	0.413073	+	0.910698i	$0.364456\pi$
$998$	2.49576e13	0.796372
$999$	−5.54247e11	−0.0176059

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.6	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.6	✓	21	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)

\(f(q)\)	\(=\)	\(q-23.3610 q^{2} -81.0000 q^{3} +33.7344 q^{4} +477.585 q^{5} +1892.24 q^{6} +1570.96 q^{7} +11172.7 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q-23.3610 q^{2} -81.0000 q^{3} +33.7344 q^{4} +477.585 q^{5} +1892.24 q^{6} +1570.96 q^{7} +11172.7 q^{8} +6561.00 q^{9} -11156.8 q^{10} -48168.1 q^{11} -2732.48 q^{12} +60042.1 q^{13} -36699.1 q^{14} -38684.4 q^{15} -278278. q^{16} +65961.2 q^{17} -153271. q^{18} -314381. q^{19} +16111.0 q^{20} -127248. q^{21} +1.12525e6 q^{22} -1.21197e6 q^{23} -904992. q^{24} -1.72504e6 q^{25} -1.40264e6 q^{26} -531441. q^{27} +52995.3 q^{28} +5.11139e6 q^{29} +903704. q^{30} +2.37877e6 q^{31} +780396. q^{32} +3.90161e6 q^{33} -1.54092e6 q^{34} +750267. q^{35} +221331. q^{36} +1.04291e6 q^{37} +7.34424e6 q^{38} -4.86341e6 q^{39} +5.33593e6 q^{40} -9.06456e6 q^{41} +2.97263e6 q^{42} +3.58131e7 q^{43} -1.62492e6 q^{44} +3.13343e6 q^{45} +2.83128e7 q^{46} +3.00013e7 q^{47} +2.25405e7 q^{48} -3.78857e7 q^{49} +4.02985e7 q^{50} -5.34286e6 q^{51} +2.02548e6 q^{52} -2.45832e7 q^{53} +1.24150e7 q^{54} -2.30043e7 q^{55} +1.75519e7 q^{56} +2.54649e7 q^{57} -1.19407e8 q^{58} -1.21174e7 q^{59} -1.30499e6 q^{60} +6.49807e7 q^{61} -5.55703e7 q^{62} +1.03071e7 q^{63} +1.24248e8 q^{64} +2.86752e7 q^{65} -9.11454e7 q^{66} +2.82563e8 q^{67} +2.22516e6 q^{68} +9.81696e7 q^{69} -1.75269e7 q^{70} -6.33502e7 q^{71} +7.33044e7 q^{72} +3.82696e8 q^{73} -2.43634e7 q^{74} +1.39728e8 q^{75} -1.06054e7 q^{76} -7.56701e7 q^{77} +1.13614e8 q^{78} -5.56447e8 q^{79} -1.32901e8 q^{80} +4.30467e7 q^{81} +2.11757e8 q^{82} +4.81897e7 q^{83} -4.29262e6 q^{84} +3.15021e7 q^{85} -8.36627e8 q^{86} -4.14023e8 q^{87} -5.38169e8 q^{88} +1.06126e9 q^{89} -7.32000e7 q^{90} +9.43237e7 q^{91} -4.08850e7 q^{92} -1.92680e8 q^{93} -7.00858e8 q^{94} -1.50144e8 q^{95} -6.32120e7 q^{96} +1.41946e6 q^{97} +8.85046e8 q^{98} -3.16031e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9} - 31559 q^{10} - 38751 q^{11} - 400950 q^{12} - 58915 q^{13} + 3453 q^{14} - 166698 q^{15} + 1655714 q^{16} - 64233 q^{17} + 131220 q^{18} - 1937236 q^{19} - 1065507 q^{20} + 1390527 q^{21} - 5386882 q^{22} - 1838574 q^{23} + 231093 q^{24} + 4565755 q^{25} - 839702 q^{26} - 11160261 q^{27} - 4471034 q^{28} + 15658544 q^{29} + 2556279 q^{30} - 14282802 q^{31} - 2205286 q^{32} + 3138831 q^{33} + 19005532 q^{34} - 8633300 q^{35} + 32476950 q^{36} + 7531195 q^{37} + 26649773 q^{38} + 4772115 q^{39} + 17775672 q^{40} + 18338245 q^{41} - 279693 q^{42} - 22480305 q^{43} - 80230922 q^{44} + 13502538 q^{45} - 83894107 q^{46} - 110397260 q^{47} - 134112834 q^{48} + 130653638 q^{49} + 65575693 q^{50} + 5202873 q^{51} + 177908014 q^{52} + 145498338 q^{53} - 10628820 q^{54} + 86448944 q^{55} + 354387888 q^{56} + 156916116 q^{57} + 115508368 q^{58} - 254464581 q^{59} + 86306067 q^{60} + 287595506 q^{61} + 819899030 q^{62} - 112632687 q^{63} + 822446413 q^{64} + 77238206 q^{65} + 436337442 q^{66} - 392860610 q^{67} + 167325073 q^{68} + 148924494 q^{69} - 424902116 q^{70} - 248960491 q^{71} - 18718533 q^{72} - 758406074 q^{73} - 923266846 q^{74} - 369826155 q^{75} - 2312747568 q^{76} - 878126795 q^{77} + 68015862 q^{78} - 1925801029 q^{79} - 1898919861 q^{80} + 903981141 q^{81} - 3249102191 q^{82} - 1650336307 q^{83} + 362153754 q^{84} - 2342480762 q^{85} - 3609864952 q^{86} - 1268342064 q^{87} - 5987792887 q^{88} - 574997526 q^{89} - 207058599 q^{90} - 4481387117 q^{91} - 5317166770 q^{92} + 1156906962 q^{93} - 5360726568 q^{94} - 2789231462 q^{95} + 178628166 q^{96} - 4651540898 q^{97} - 5566652976 q^{98} - 254245311 q^{99}+O(q^{100}) \) 21 * q + 20 * q^2 - 1701 * q^3 + 4950 * q^4 + 2058 * q^5 - 1620 * q^6 - 17167 * q^7 - 2853 * q^8 + 137781 * q^9 - 31559 * q^10 - 38751 * q^11 - 400950 * q^12 - 58915 * q^13 + 3453 * q^14 - 166698 * q^15 + 1655714 * q^16 - 64233 * q^17 + 131220 * q^18 - 1937236 * q^19 - 1065507 * q^20 + 1390527 * q^21 - 5386882 * q^22 - 1838574 * q^23 + 231093 * q^24 + 4565755 * q^25 - 839702 * q^26 - 11160261 * q^27 - 4471034 * q^28 + 15658544 * q^29 + 2556279 * q^30 - 14282802 * q^31 - 2205286 * q^32 + 3138831 * q^33 + 19005532 * q^34 - 8633300 * q^35 + 32476950 * q^36 + 7531195 * q^37 + 26649773 * q^38 + 4772115 * q^39 + 17775672 * q^40 + 18338245 * q^41 - 279693 * q^42 - 22480305 * q^43 - 80230922 * q^44 + 13502538 * q^45 - 83894107 * q^46 - 110397260 * q^47 - 134112834 * q^48 + 130653638 * q^49 + 65575693 * q^50 + 5202873 * q^51 + 177908014 * q^52 + 145498338 * q^53 - 10628820 * q^54 + 86448944 * q^55 + 354387888 * q^56 + 156916116 * q^57 + 115508368 * q^58 - 254464581 * q^59 + 86306067 * q^60 + 287595506 * q^61 + 819899030 * q^62 - 112632687 * q^63 + 822446413 * q^64 + 77238206 * q^65 + 436337442 * q^66 - 392860610 * q^67 + 167325073 * q^68 + 148924494 * q^69 - 424902116 * q^70 - 248960491 * q^71 - 18718533 * q^72 - 758406074 * q^73 - 923266846 * q^74 - 369826155 * q^75 - 2312747568 * q^76 - 878126795 * q^77 + 68015862 * q^78 - 1925801029 * q^79 - 1898919861 * q^80 + 903981141 * q^81 - 3249102191 * q^82 - 1650336307 * q^83 + 362153754 * q^84 - 2342480762 * q^85 - 3609864952 * q^86 - 1268342064 * q^87 - 5987792887 * q^88 - 574997526 * q^89 - 207058599 * q^90 - 4481387117 * q^91 - 5317166770 * q^92 + 1156906962 * q^93 - 5360726568 * q^94 - 2789231462 * q^95 + 178628166 * q^96 - 4651540898 * q^97 - 5566652976 * q^98 - 254245311 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more