LMFDB - Embedded newform 177.10.a.b.1.16

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			1.16
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)

$f(q)$	$=$	$q+24.6766 q^{2} -81.0000 q^{3} +96.9337 q^{4} +1351.78 q^{5} -1998.80 q^{6} -4831.46 q^{7} -10242.4 q^{8} +6561.00 q^{9} +O(q^{10})$	\(q+24.6766 q^{2} -81.0000 q^{3} +96.9337 q^{4} +1351.78 q^{5} -1998.80 q^{6} -4831.46 q^{7} -10242.4 q^{8} +6561.00 q^{9} +33357.2 q^{10} +17390.2 q^{11} -7851.63 q^{12} +156345. q^{13} -119224. q^{14} -109494. q^{15} -302378. q^{16} -358347. q^{17} +161903. q^{18} +77701.9 q^{19} +131033. q^{20} +391349. q^{21} +429131. q^{22} +1.04074e6 q^{23} +829636. q^{24} -125828. q^{25} +3.85805e6 q^{26} -531441. q^{27} -468332. q^{28} +4.51161e6 q^{29} -2.70193e6 q^{30} -9.81810e6 q^{31} -2.21753e6 q^{32} -1.40861e6 q^{33} -8.84278e6 q^{34} -6.53106e6 q^{35} +635982. q^{36} +5.36151e6 q^{37} +1.91742e6 q^{38} -1.26639e7 q^{39} -1.38455e7 q^{40} -1.59041e7 q^{41} +9.65715e6 q^{42} -1.04717e7 q^{43} +1.68570e6 q^{44} +8.86900e6 q^{45} +2.56819e7 q^{46} -2.40460e7 q^{47} +2.44926e7 q^{48} -1.70106e7 q^{49} -3.10500e6 q^{50} +2.90261e7 q^{51} +1.51551e7 q^{52} +2.96704e7 q^{53} -1.31141e7 q^{54} +2.35077e7 q^{55} +4.94859e7 q^{56} -6.29385e6 q^{57} +1.11331e8 q^{58} -1.21174e7 q^{59} -1.06136e7 q^{60} -1.50242e8 q^{61} -2.42277e8 q^{62} -3.16992e7 q^{63} +1.00096e8 q^{64} +2.11343e8 q^{65} -3.47596e7 q^{66} -1.05311e8 q^{67} -3.47359e7 q^{68} -8.43000e7 q^{69} -1.61164e8 q^{70} -4.08704e8 q^{71} -6.72005e7 q^{72} +3.83910e8 q^{73} +1.32304e8 q^{74} +1.01921e7 q^{75} +7.53193e6 q^{76} -8.40202e7 q^{77} -3.12502e8 q^{78} +2.66685e8 q^{79} -4.08747e8 q^{80} +4.30467e7 q^{81} -3.92459e8 q^{82} -7.10929e8 q^{83} +3.79349e7 q^{84} -4.84405e8 q^{85} -2.58406e8 q^{86} -3.65441e8 q^{87} -1.78118e8 q^{88} -9.56287e8 q^{89} +2.18857e8 q^{90} -7.55373e8 q^{91} +1.00883e8 q^{92} +7.95266e8 q^{93} -5.93373e8 q^{94} +1.05035e8 q^{95} +1.79620e8 q^{96} +8.46910e8 q^{97} -4.19762e8 q^{98} +1.14097e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	24.6766	1.09056	0.545281	−	0.838254i	$-0.316423\pi$
$2$	24.6766	1.09056	0.545281	+	0.838254i	$0.316423\pi$
$3$	−81.0000	−0.577350
$3$	−81.0000	−0.577350
$4$	96.9337	0.189324
$5$	1351.78	0.967252	0.483626	−	0.875275i	$-0.339320\pi$
$5$	1351.78	0.967252	0.483626	+	0.875275i	$0.339320\pi$
$6$	−1998.80	−0.629636
$7$	−4831.46	−0.760567	−0.380284	−	0.924870i	$-0.624174\pi$
$7$	−4831.46	−0.760567	−0.380284	+	0.924870i	$0.624174\pi$
$8$	−10242.4	−0.884092
$9$	6561.00	0.333333
$10$	33357.2	1.05485
$11$	17390.2	0.358128	0.179064	−	0.983837i	$-0.442693\pi$
$11$	17390.2	0.358128	0.179064	+	0.983837i	$0.442693\pi$
$12$	−7851.63	−0.109306
$13$	156345.	1.51823	0.759115	−	0.650956i	$-0.225632\pi$
$13$	156345.	1.51823	0.759115	+	0.650956i	$0.225632\pi$
$14$	−119224.	−0.829445
$15$	−109494.	−0.558443
$16$	−302378.	−1.15348
$17$	−358347.	−1.04060	−0.520300	−	0.853984i	$-0.674180\pi$
$17$	−358347.	−1.04060	−0.520300	+	0.853984i	$0.674180\pi$
$18$	161903.	0.363520
$19$	77701.9	0.136786	0.0683928	−	0.997658i	$-0.478213\pi$
$19$	77701.9	0.136786	0.0683928	+	0.997658i	$0.478213\pi$
$20$	131033.	0.183124
$21$	391349.	0.439114
$22$	429131.	0.390560
$23$	1.04074e6	0.775474	0.387737	−	0.921770i	$-0.373257\pi$
$23$	1.04074e6	0.775474	0.387737	+	0.921770i	$0.373257\pi$
$24$	829636.	0.510431
$25$	−125828.	−0.0644239
$26$	3.85805e6	1.65572
$27$	−531441.	−0.192450
$28$	−468332.	−0.143993
$29$	4.51161e6	1.18452	0.592258	−	0.805749i	$-0.298237\pi$
$29$	4.51161e6	1.18452	0.592258	+	0.805749i	$0.298237\pi$
$30$	−2.70193e6	−0.609016
$31$	−9.81810e6	−1.90941	−0.954707	−	0.297549i	$-0.903831\pi$
$31$	−9.81810e6	−1.90941	−0.954707	+	0.297549i	$0.903831\pi$
$32$	−2.21753e6	−0.373848
$33$	−1.40861e6	−0.206765
$34$	−8.84278e6	−1.13484
$35$	−6.53106e6	−0.735660
$36$	635982.	0.0631079
$37$	5.36151e6	0.470305	0.235153	−	0.971958i	$-0.424441\pi$
$37$	5.36151e6	0.470305	0.235153	+	0.971958i	$0.424441\pi$
$38$	1.91742e6	0.149173
$39$	−1.26639e7	−0.876551
$40$	−1.38455e7	−0.855140
$41$	−1.59041e7	−0.878986	−0.439493	−	0.898246i	$-0.644842\pi$
$41$	−1.59041e7	−0.878986	−0.439493	+	0.898246i	$0.644842\pi$
$42$	9.65715e6	0.478880
$43$	−1.04717e7	−0.467099	−0.233550	−	0.972345i	$-0.575034\pi$
$43$	−1.04717e7	−0.467099	−0.233550	+	0.972345i	$0.575034\pi$
$44$	1.68570e6	0.0678020
$45$	8.86900e6	0.322417
$46$	2.56819e7	0.845702
$47$	−2.40460e7	−0.718790	−0.359395	−	0.933185i	$-0.617017\pi$
$47$	−2.40460e7	−0.718790	−0.359395	+	0.933185i	$0.617017\pi$
$48$	2.44926e7	0.665962
$49$	−1.70106e7	−0.421537
$50$	−3.10500e6	−0.0702582
$51$	2.90261e7	0.600790
$52$	1.51551e7	0.287437
$53$	2.96704e7	0.516514	0.258257	−	0.966076i	$-0.416852\pi$
$53$	2.96704e7	0.516514	0.258257	+	0.966076i	$0.416852\pi$
$54$	−1.31141e7	−0.209879
$55$	2.35077e7	0.346400
$56$	4.94859e7	0.672412
$57$	−6.29385e6	−0.0789732
$58$	1.11331e8	1.29179
$59$	−1.21174e7	−0.130189
$59$	−1.21174e7	−0.130189
$60$	−1.06136e7	−0.105726
$61$	−1.50242e8	−1.38934	−0.694668	−	0.719330i	$-0.744449\pi$
$61$	−1.50242e8	−1.38934	−0.694668	+	0.719330i	$0.744449\pi$
$62$	−2.42277e8	−2.08233
$63$	−3.16992e7	−0.253522
$64$	1.00096e8	0.745776
$65$	2.11343e8	1.46851
$66$	−3.47596e7	−0.225490
$67$	−1.05311e8	−0.638462	−0.319231	−	0.947677i	$-0.603425\pi$
$67$	−1.05311e8	−0.638462	−0.319231	+	0.947677i	$0.603425\pi$
$68$	−3.47359e7	−0.197010
$69$	−8.43000e7	−0.447720
$70$	−1.61164e8	−0.802282
$71$	−4.08704e8	−1.90874	−0.954370	−	0.298626i	$-0.903472\pi$
$71$	−4.08704e8	−1.90874	−0.954370	+	0.298626i	$0.903472\pi$
$72$	−6.72005e7	−0.294697
$73$	3.83910e8	1.58225	0.791127	−	0.611652i	$-0.209495\pi$
$73$	3.83910e8	1.58225	0.791127	+	0.611652i	$0.209495\pi$
$74$	1.32304e8	0.512896
$75$	1.01921e7	0.0371951
$76$	7.53193e6	0.0258967
$77$	−8.40202e7	−0.272380
$78$	−3.12502e8	−0.955932
$79$	2.66685e8	0.770329	0.385164	−	0.922848i	$-0.374145\pi$
$79$	2.66685e8	0.770329	0.385164	+	0.922848i	$0.374145\pi$
$80$	−4.08747e8	−1.11571
$81$	4.30467e7	0.111111
$82$	−3.92459e8	−0.958588
$83$	−7.10929e8	−1.64428	−0.822138	−	0.569288i	$-0.807219\pi$
$83$	−7.10929e8	−1.64428	−0.822138	+	0.569288i	$0.807219\pi$
$84$	3.79349e7	0.0831346
$85$	−4.84405e8	−1.00652
$86$	−2.58406e8	−0.509400
$87$	−3.65441e8	−0.683880
$88$	−1.78118e8	−0.316618
$89$	−9.56287e8	−1.61560	−0.807799	−	0.589459i	$-0.799341\pi$
$89$	−9.56287e8	−1.61560	−0.807799	+	0.589459i	$0.799341\pi$
$90$	2.18857e8	0.351616
$91$	−7.55373e8	−1.15472
$92$	1.00883e8	0.146816
$93$	7.95266e8	1.10240
$94$	−5.93373e8	−0.783885
$95$	1.05035e8	0.132306
$96$	1.79620e8	0.215841
$97$	8.46910e8	0.971324	0.485662	−	0.874147i	$-0.338579\pi$
$97$	8.46910e8	0.971324	0.485662	+	0.874147i	$0.338579\pi$
$98$	−4.19762e8	−0.459712
$99$	1.14097e8	0.119376
$100$	−1.21970e7	−0.0121970
$101$	−1.06321e9	−1.01665	−0.508327	−	0.861164i	$-0.669736\pi$
$101$	−1.06321e9	−1.01665	−0.508327	+	0.861164i	$0.669736\pi$
$102$	7.16265e8	0.655199
$103$	−2.15338e9	−1.88518	−0.942591	−	0.333948i	$-0.891619\pi$
$103$	−2.15338e9	−1.88518	−0.942591	+	0.333948i	$0.891619\pi$
$104$	−1.60135e9	−1.34226
$105$	5.29016e8	0.424734
$106$	7.32165e8	0.563290
$107$	2.51024e9	1.85135	0.925675	−	0.378319i	$-0.123498\pi$
$107$	2.51024e9	1.85135	0.925675	+	0.378319i	$0.123498\pi$
$108$	−5.15145e7	−0.0364353
$109$	−8.42739e8	−0.571839	−0.285919	−	0.958254i	$-0.592299\pi$
$109$	−8.42739e8	−0.571839	−0.285919	+	0.958254i	$0.592299\pi$
$110$	5.80089e8	0.377770
$111$	−4.34283e8	−0.271531
$112$	1.46093e9	0.877299
$113$	−9.11969e8	−0.526171	−0.263085	−	0.964773i	$-0.584740\pi$
$113$	−9.11969e8	−0.526171	−0.263085	+	0.964773i	$0.584740\pi$
$114$	−1.55311e8	−0.0861251
$115$	1.40685e9	0.750079
$116$	4.37327e8	0.224257
$117$	1.02578e9	0.506077
$118$	−2.99015e8	−0.141979
$119$	1.73134e9	0.791446
$120$	1.12148e9	0.493715
$121$	−2.05553e9	−0.871745
$122$	−3.70746e9	−1.51516
$123$	1.28823e9	0.507483
$124$	−9.51705e8	−0.361497
$125$	−2.81028e9	−1.02957
$126$	−7.82229e8	−0.276482
$127$	−4.28296e9	−1.46092	−0.730461	−	0.682954i	$-0.760695\pi$
$127$	−4.28296e9	−1.46092	−0.730461	+	0.682954i	$0.760695\pi$
$128$	3.60541e9	1.18716
$129$	8.48208e8	0.269680
$130$	5.21522e9	1.60150
$131$	−3.46692e8	−0.102854	−0.0514272	−	0.998677i	$-0.516377\pi$
$131$	−3.46692e8	−0.102854	−0.0514272	+	0.998677i	$0.516377\pi$
$132$	−1.36541e8	−0.0391455
$133$	−3.75414e8	−0.104035
$134$	−2.59870e9	−0.696282
$135$	−7.18389e8	−0.186148
$136$	3.67034e9	0.919986
$137$	−6.09826e9	−1.47898	−0.739492	−	0.673165i	$-0.764934\pi$
$137$	−6.09826e9	−1.47898	−0.739492	+	0.673165i	$0.764934\pi$
$138$	−2.08024e9	−0.488266
$139$	1.61338e9	0.366581	0.183291	−	0.983059i	$-0.441325\pi$
$139$	1.61338e9	0.366581	0.183291	+	0.983059i	$0.441325\pi$
$140$	−6.33079e8	−0.139278
$141$	1.94773e9	0.414994
$142$	−1.00854e10	−2.08160
$143$	2.71887e9	0.543720
$144$	−1.98390e9	−0.384493
$145$	6.09869e9	1.14572
$146$	9.47358e9	1.72554
$147$	1.37786e9	0.243375
$148$	5.19711e8	0.0890398
$149$	8.58258e9	1.42653	0.713263	−	0.700897i	$-0.247217\pi$
$149$	8.58258e9	1.42653	0.713263	+	0.700897i	$0.247217\pi$
$150$	2.51505e8	0.0405636
$151$	2.61006e9	0.408558	0.204279	−	0.978913i	$-0.434515\pi$
$151$	2.61006e9	0.408558	0.204279	+	0.978913i	$0.434515\pi$
$152$	−7.95855e8	−0.120931
$153$	−2.35111e9	−0.346866
$154$	−2.07333e9	−0.297047
$155$	−1.32719e10	−1.84688
$156$	−1.22756e9	−0.165952
$157$	−7.15014e9	−0.939218	−0.469609	−	0.882875i	$-0.655605\pi$
$157$	−7.15014e9	−0.939218	−0.469609	+	0.882875i	$0.655605\pi$
$158$	6.58086e9	0.840090
$159$	−2.40330e9	−0.298210
$160$	−2.99761e9	−0.361606
$161$	−5.02830e9	−0.589800
$162$	1.06225e9	0.121173
$163$	1.40975e10	1.56422	0.782112	−	0.623138i	$-0.214142\pi$
$163$	1.40975e10	1.56422	0.782112	+	0.623138i	$0.214142\pi$
$164$	−1.54164e9	−0.166413
$165$	−1.90412e9	−0.199994
$166$	−1.75433e10	−1.79318
$167$	3.55226e9	0.353412	0.176706	−	0.984264i	$-0.443456\pi$
$167$	3.55226e9	0.353412	0.176706	+	0.984264i	$0.443456\pi$
$168$	−4.00836e9	−0.388217
$169$	1.38391e10	1.30502
$170$	−1.19534e10	−1.09767
$171$	5.09802e8	0.0455952
$172$	−1.01506e9	−0.0884329
$173$	1.07116e10	0.909177	0.454589	−	0.890702i	$-0.349786\pi$
$173$	1.07116e10	0.909177	0.454589	+	0.890702i	$0.349786\pi$
$174$	−9.01782e9	−0.745813
$175$	6.07933e8	0.0489987
$176$	−5.25842e9	−0.413093
$177$	9.81506e8	0.0751646
$178$	−2.35979e10	−1.76191
$179$	−2.47669e10	−1.80315	−0.901576	−	0.432621i	$-0.857589\pi$
$179$	−2.47669e10	−1.80315	−0.901576	+	0.432621i	$0.857589\pi$
$180$	8.59705e8	0.0610412
$181$	−4.03191e9	−0.279227	−0.139613	−	0.990206i	$-0.544586\pi$
$181$	−4.03191e9	−0.279227	−0.139613	+	0.990206i	$0.544586\pi$
$182$	−1.86400e10	−1.25929
$183$	1.21696e10	0.802134
$184$	−1.06597e10	−0.685591
$185$	7.24756e9	0.454903
$186$	1.96245e10	1.20223
$187$	−6.23173e9	−0.372667
$188$	−2.33087e9	−0.136084
$189$	2.56764e9	0.146371
$190$	2.59192e9	0.144288
$191$	−3.18277e10	−1.73043	−0.865216	−	0.501399i	$-0.832819\pi$
$191$	−3.18277e10	−1.73043	−0.865216	+	0.501399i	$0.832819\pi$
$192$	−8.10780e9	−0.430574
$193$	2.72496e10	1.41368	0.706842	−	0.707371i	$-0.250119\pi$
$193$	2.72496e10	1.41368	0.706842	+	0.707371i	$0.250119\pi$
$194$	2.08988e10	1.05929
$195$	−1.71188e10	−0.847846
$196$	−1.64890e9	−0.0798070
$197$	3.38740e10	1.60239	0.801196	−	0.598402i	$-0.204198\pi$
$197$	3.38740e10	1.60239	0.801196	+	0.598402i	$0.204198\pi$
$198$	2.81553e9	0.130187
$199$	1.53426e10	0.693520	0.346760	−	0.937954i	$-0.387282\pi$
$199$	1.53426e10	0.693520	0.346760	+	0.937954i	$0.387282\pi$
$200$	1.28878e9	0.0569566
$201$	8.53015e9	0.368616
$202$	−2.62364e10	−1.10872
$203$	−2.17977e10	−0.900904
$204$	2.81361e9	0.113744
$205$	−2.14988e10	−0.850201
$206$	−5.31381e10	−2.05591
$207$	6.82830e9	0.258491
$208$	−4.72752e10	−1.75125
$209$	1.35125e9	0.0489867
$210$	1.30543e10	0.463198
$211$	3.28168e10	1.13979	0.569895	−	0.821717i	$-0.306984\pi$
$211$	3.28168e10	1.13979	0.569895	+	0.821717i	$0.306984\pi$
$212$	2.87606e9	0.0977883
$213$	3.31051e10	1.10201
$214$	6.19442e10	2.01901
$215$	−1.41554e10	−0.451803
$216$	5.44324e9	0.170144
$217$	4.74358e10	1.45224
$218$	−2.07959e10	−0.623625
$219$	−3.10967e10	−0.913514
$220$	2.27868e9	0.0655816
$221$	−5.60256e10	−1.57987
$222$	−1.07166e10	−0.296121
$223$	4.00825e10	1.08538	0.542692	−	0.839932i	$-0.317405\pi$
$223$	4.00825e10	1.08538	0.542692	+	0.839932i	$0.317405\pi$
$224$	1.07139e10	0.284337
$225$	−8.25557e8	−0.0214746
$226$	−2.25043e10	−0.573822
$227$	−4.05197e10	−1.01286	−0.506430	−	0.862281i	$-0.669035\pi$
$227$	−4.05197e10	−1.01286	−0.506430	+	0.862281i	$0.669035\pi$
$228$	−6.10086e8	−0.0149515
$229$	−7.76259e9	−0.186529	−0.0932646	−	0.995641i	$-0.529730\pi$
$229$	−7.76259e9	−0.186529	−0.0932646	+	0.995641i	$0.529730\pi$
$230$	3.47162e10	0.818007
$231$	6.80564e9	0.157259
$232$	−4.62098e10	−1.04722
$233$	−1.73507e10	−0.385670	−0.192835	−	0.981231i	$-0.561768\pi$
$233$	−1.73507e10	−0.385670	−0.192835	+	0.981231i	$0.561768\pi$
$234$	2.53127e10	0.551908
$235$	−3.25048e10	−0.695251
$236$	−1.17458e9	−0.0246478
$237$	−2.16015e10	−0.444749
$238$	4.27236e10	0.863120
$239$	3.29921e10	0.654063	0.327032	−	0.945013i	$-0.393952\pi$
$239$	3.29921e10	0.654063	0.327032	+	0.945013i	$0.393952\pi$
$240$	3.31085e10	0.644153
$241$	8.91189e8	0.0170174	0.00850870	−	0.999964i	$-0.497292\pi$
$241$	8.91189e8	0.0170174	0.00850870	+	0.999964i	$0.497292\pi$
$242$	−5.07234e10	−0.950691
$243$	−3.48678e9	−0.0641500
$244$	−1.45635e10	−0.263034
$245$	−2.29945e10	−0.407733
$246$	3.17892e10	0.553441
$247$	1.21483e10	0.207672
$248$	1.00561e11	1.68810
$249$	5.75853e10	0.949323
$250$	−6.93480e10	−1.12280
$251$	−9.43867e10	−1.50099	−0.750497	−	0.660874i	$-0.770186\pi$
$251$	−9.43867e10	−1.50099	−0.750497	+	0.660874i	$0.770186\pi$
$252$	−3.07272e9	−0.0479978
$253$	1.80987e10	0.277719
$254$	−1.05689e11	−1.59323
$255$	3.92368e10	0.581116
$256$	3.77199e10	0.548897
$257$	1.22809e11	1.75603	0.878014	−	0.478635i	$-0.158868\pi$
$257$	1.22809e11	1.75603	0.878014	+	0.478635i	$0.158868\pi$
$258$	2.09309e10	0.294102
$259$	−2.59040e10	−0.357699
$260$	2.04862e10	0.278024
$261$	2.96007e10	0.394838
$262$	−8.55517e9	−0.112169
$263$	5.70567e10	0.735369	0.367685	−	0.929951i	$-0.380151\pi$
$263$	5.70567e10	0.735369	0.367685	+	0.929951i	$0.380151\pi$
$264$	1.44275e10	0.182799
$265$	4.01077e10	0.499599
$266$	−9.26393e9	−0.113456
$267$	7.74592e10	0.932766
$268$	−1.02081e10	−0.120876
$269$	9.42735e10	1.09775	0.548876	−	0.835904i	$-0.315056\pi$
$269$	9.42735e10	1.09775	0.548876	+	0.835904i	$0.315056\pi$
$270$	−1.77274e10	−0.203005
$271$	1.72655e11	1.94454	0.972272	−	0.233855i	$-0.0751340\pi$
$271$	1.72655e11	1.94454	0.972272	+	0.233855i	$0.0751340\pi$
$272$	1.08356e11	1.20031
$273$	6.11852e10	0.666676
$274$	−1.50484e11	−1.61292
$275$	−2.18817e9	−0.0230720
$276$	−8.17151e9	−0.0847640
$277$	3.21674e10	0.328289	0.164145	−	0.986436i	$-0.447514\pi$
$277$	3.21674e10	0.328289	0.164145	+	0.986436i	$0.447514\pi$
$278$	3.98127e10	0.399779
$279$	−6.44166e10	−0.636471
$280$	6.68938e10	0.650391
$281$	8.73319e10	0.835593	0.417796	−	0.908541i	$-0.362803\pi$
$281$	8.73319e10	0.835593	0.417796	+	0.908541i	$0.362803\pi$
$282$	4.80632e10	0.452576
$283$	−4.86603e10	−0.450958	−0.225479	−	0.974248i	$-0.572395\pi$
$283$	−4.86603e10	−0.450958	−0.225479	+	0.974248i	$0.572395\pi$
$284$	−3.96172e10	−0.361370
$285$	−8.50787e9	−0.0763869
$286$	6.70923e10	0.592960
$287$	7.68401e10	0.668528
$288$	−1.45492e10	−0.124616
$289$	9.82464e9	0.0828469
$290$	1.50495e11	1.24948
$291$	−6.85997e10	−0.560794
$292$	3.72138e10	0.299558
$293$	8.55239e10	0.677927	0.338964	−	0.940800i	$-0.389924\pi$
$293$	8.55239e10	0.677927	0.338964	+	0.940800i	$0.389924\pi$
$294$	3.40008e10	0.265415
$295$	−1.63800e10	−0.125925
$296$	−5.49149e10	−0.415793
$297$	−9.24187e9	−0.0689217
$298$	2.11789e11	1.55571
$299$	1.62714e11	1.17735
$300$	9.87953e8	0.00704192
$301$	5.05937e10	0.355260
$302$	6.44073e10	0.445557
$303$	8.61202e10	0.586966
$304$	−2.34953e10	−0.157779
$305$	−2.03094e11	−1.34384
$306$	−5.80175e10	−0.378279
$307$	−6.14259e10	−0.394665	−0.197333	−	0.980337i	$-0.563228\pi$
$307$	−6.14259e10	−0.394665	−0.197333	+	0.980337i	$0.563228\pi$
$308$	−8.14439e9	−0.0515680
$309$	1.74424e11	1.08841
$310$	−3.27504e11	−2.01414
$311$	4.98435e10	0.302125	0.151062	−	0.988524i	$-0.451731\pi$
$311$	4.98435e10	0.302125	0.151062	+	0.988524i	$0.451731\pi$
$312$	1.29709e11	0.774952
$313$	7.67771e9	0.0452150	0.0226075	−	0.999744i	$-0.492803\pi$
$313$	7.67771e9	0.0452150	0.0226075	+	0.999744i	$0.492803\pi$
$314$	−1.76441e11	−1.02427
$315$	−4.28503e10	−0.245220
$316$	2.58507e10	0.145841
$317$	−8.79590e10	−0.489230	−0.244615	−	0.969620i	$-0.578662\pi$
$317$	−8.79590e10	−0.489230	−0.244615	+	0.969620i	$0.578662\pi$
$318$	−5.93053e10	−0.325216
$319$	7.84579e10	0.424208
$320$	1.35308e11	0.721353
$321$	−2.03330e11	−1.06888
$322$	−1.24081e11	−0.643213
$323$	−2.78442e10	−0.142339
$324$	4.17268e9	0.0210360
$325$	−1.96725e10	−0.0978103
$326$	3.47879e11	1.70588
$327$	6.82618e10	0.330151
$328$	1.62896e11	0.777104
$329$	1.16177e11	0.546689
$330$	−4.69872e10	−0.218106
$331$	−7.39306e10	−0.338531	−0.169265	−	0.985571i	$-0.554139\pi$
$331$	−7.39306e10	−0.338531	−0.169265	+	0.985571i	$0.554139\pi$
$332$	−6.89130e10	−0.311300
$333$	3.51769e10	0.156768
$334$	8.76577e10	0.385417
$335$	−1.42356e11	−0.617554
$336$	−1.18335e11	−0.506509
$337$	−1.54529e11	−0.652642	−0.326321	−	0.945259i	$-0.605809\pi$
$337$	−1.54529e11	−0.652642	−0.326321	+	0.945259i	$0.605809\pi$
$338$	3.41503e11	1.42321
$339$	7.38695e10	0.303785
$340$	−4.69551e10	−0.190558
$341$	−1.70739e11	−0.683814
$342$	1.25802e10	0.0497243
$343$	2.77153e11	1.08117
$344$	1.07256e11	0.412959
$345$	−1.13955e11	−0.433058
$346$	2.64327e11	0.991513
$347$	−1.37596e11	−0.509476	−0.254738	−	0.967010i	$-0.581989\pi$
$347$	−1.37596e11	−0.509476	−0.254738	+	0.967010i	$0.581989\pi$
$348$	−3.54235e10	−0.129475
$349$	−2.44352e11	−0.881660	−0.440830	−	0.897591i	$-0.645316\pi$
$349$	−2.44352e11	−0.881660	−0.440830	+	0.897591i	$0.645316\pi$
$350$	1.50017e10	0.0534361
$351$	−8.30879e10	−0.292184
$352$	−3.85634e10	−0.133885
$353$	−2.00711e11	−0.687996	−0.343998	−	0.938970i	$-0.611781\pi$
$353$	−2.00711e11	−0.687996	−0.343998	+	0.938970i	$0.611781\pi$
$354$	2.42202e10	0.0819716
$355$	−5.52477e11	−1.84623
$356$	−9.26964e10	−0.305871
$357$	−1.40239e11	−0.456941
$358$	−6.11161e11	−1.96645
$359$	−2.19071e11	−0.696082	−0.348041	−	0.937479i	$-0.613153\pi$
$359$	−2.19071e11	−0.696082	−0.348041	+	0.937479i	$0.613153\pi$
$360$	−9.08400e10	−0.285047
$361$	−3.16650e11	−0.981290
$362$	−9.94937e10	−0.304514
$363$	1.66498e11	0.503302
$364$	−7.32211e10	−0.218615
$365$	5.18960e11	1.53044
$366$	3.00304e11	0.874776
$367$	−3.57591e11	−1.02894	−0.514470	−	0.857509i	$-0.672011\pi$
$367$	−3.57591e11	−1.02894	−0.514470	+	0.857509i	$0.672011\pi$
$368$	−3.14697e11	−0.894494
$369$	−1.04347e11	−0.292995
$370$	1.78845e11	0.496100
$371$	−1.43352e11	−0.392844
$372$	7.70881e10	0.208710
$373$	−5.54118e11	−1.48222	−0.741109	−	0.671384i	$-0.765700\pi$
$373$	−5.54118e11	−1.48222	−0.741109	+	0.671384i	$0.765700\pi$
$374$	−1.53778e11	−0.406417
$375$	2.27632e11	0.594420
$376$	2.46289e11	0.635477
$377$	7.05366e11	1.79837
$378$	6.33605e10	0.159627
$379$	−1.51950e11	−0.378290	−0.189145	−	0.981949i	$-0.560572\pi$
$379$	−1.51950e11	−0.378290	−0.189145	+	0.981949i	$0.560572\pi$
$380$	1.01815e10	0.0250487
$381$	3.46920e11	0.843464
$382$	−7.85398e11	−1.88714
$383$	−4.27773e11	−1.01582	−0.507912	−	0.861409i	$-0.669583\pi$
$383$	−4.27773e11	−1.01582	−0.507912	+	0.861409i	$0.669583\pi$
$384$	−2.92038e11	−0.685408
$385$	−1.13576e11	−0.263460
$386$	6.72427e11	1.54171
$387$	−6.87048e10	−0.155700
$388$	8.20940e10	0.183895
$389$	4.50463e11	0.997438	0.498719	−	0.866764i	$-0.333804\pi$
$389$	4.50463e11	0.997438	0.498719	+	0.866764i	$0.333804\pi$
$390$	−4.22433e11	−0.924627
$391$	−3.72946e11	−0.806958
$392$	1.74229e11	0.372678
$393$	2.80820e10	0.0593830
$394$	8.35895e11	1.74751
$395$	3.60498e11	0.745102
$396$	1.10599e10	0.0226007
$397$	−7.26579e11	−1.46800	−0.734000	−	0.679150i	$-0.762349\pi$
$397$	−7.26579e11	−1.46800	−0.734000	+	0.679150i	$0.762349\pi$
$398$	3.78602e11	0.756326
$399$	3.04085e10	0.0600644
$400$	3.80476e10	0.0743116
$401$	5.60206e11	1.08193	0.540964	−	0.841046i	$-0.318060\pi$
$401$	5.60206e11	1.08193	0.540964	+	0.841046i	$0.318060\pi$
$402$	2.10495e11	0.401999
$403$	−1.53501e12	−2.89893
$404$	−1.03061e11	−0.192477
$405$	5.81895e10	0.107472
$406$	−5.37893e11	−0.982490
$407$	9.32379e10	0.168429
$408$	−2.97297e11	−0.531154
$409$	6.91262e11	1.22148	0.610742	−	0.791829i	$-0.290871\pi$
$409$	6.91262e11	1.22148	0.610742	+	0.791829i	$0.290871\pi$
$410$	−5.30516e11	−0.927196
$411$	4.93959e11	0.853892
$412$	−2.08735e11	−0.356910
$413$	5.85446e10	0.0990174
$414$	1.68499e11	0.281901
$415$	−9.61017e11	−1.59043
$416$	−3.46700e11	−0.567588
$417$	−1.30684e11	−0.211646
$418$	3.33443e10	0.0534230
$419$	−2.75312e11	−0.436377	−0.218188	−	0.975907i	$-0.570015\pi$
$419$	−2.75312e11	−0.436377	−0.218188	+	0.975907i	$0.570015\pi$
$420$	5.12794e10	0.0804121
$421$	4.44239e11	0.689203	0.344602	−	0.938749i	$-0.388014\pi$
$421$	4.44239e11	0.689203	0.344602	+	0.938749i	$0.388014\pi$
$422$	8.09806e11	1.24301
$423$	−1.57766e11	−0.239597
$424$	−3.03897e11	−0.456646
$425$	4.50900e10	0.0670394
$426$	8.16920e11	1.20181
$427$	7.25889e11	1.05668
$428$	2.43327e11	0.350504
$429$	−2.20228e11	−0.313917
$430$	−3.49307e11	−0.492718
$431$	−1.10048e12	−1.53616	−0.768079	−	0.640355i	$-0.778787\pi$
$431$	−1.10048e12	−1.53616	−0.768079	+	0.640355i	$0.778787\pi$
$432$	1.60696e11	0.221987
$433$	−2.93842e11	−0.401715	−0.200857	−	0.979620i	$-0.564373\pi$
$433$	−2.93842e11	−0.401715	−0.200857	+	0.979620i	$0.564373\pi$
$434$	1.17055e12	1.58375
$435$	−4.93994e11	−0.661484
$436$	−8.16897e10	−0.108263
$437$	8.08675e10	0.106074
$438$	−7.67360e11	−0.996243
$439$	9.85425e11	1.26629	0.633145	−	0.774033i	$-0.281764\pi$
$439$	9.85425e11	1.26629	0.633145	+	0.774033i	$0.281764\pi$
$440$	−2.40775e11	−0.306249
$441$	−1.11606e11	−0.140512
$442$	−1.38252e12	−1.72294
$443$	−4.56768e11	−0.563480	−0.281740	−	0.959491i	$-0.590912\pi$
$443$	−4.56768e11	−0.563480	−0.281740	+	0.959491i	$0.590912\pi$
$444$	−4.20966e10	−0.0514072
$445$	−1.29269e12	−1.56269
$446$	9.89100e11	1.18368
$447$	−6.95189e11	−0.823605
$448$	−4.83612e11	−0.567212
$449$	−1.09455e12	−1.27095	−0.635475	−	0.772121i	$-0.719196\pi$
$449$	−1.09455e12	−1.27095	−0.635475	+	0.772121i	$0.719196\pi$
$450$	−2.03719e10	−0.0234194
$451$	−2.76576e11	−0.314789
$452$	−8.84005e10	−0.0996166
$453$	−2.11415e11	−0.235881
$454$	−9.99887e11	−1.10459
$455$	−1.02110e12	−1.11690
$456$	6.44642e10	0.0698196
$457$	8.18364e11	0.877654	0.438827	−	0.898571i	$-0.355394\pi$
$457$	8.18364e11	0.877654	0.438827	+	0.898571i	$0.355394\pi$
$458$	−1.91554e11	−0.203421
$459$	1.90440e11	0.200263
$460$	1.36371e11	0.142008
$461$	5.03039e11	0.518738	0.259369	−	0.965778i	$-0.416485\pi$
$461$	5.03039e11	0.518738	0.259369	+	0.965778i	$0.416485\pi$
$462$	1.67940e11	0.171500
$463$	1.69189e12	1.71103	0.855515	−	0.517779i	$-0.173241\pi$
$463$	1.69189e12	1.71103	0.855515	+	0.517779i	$0.173241\pi$
$464$	−1.36421e12	−1.36631
$465$	1.07502e12	1.06630
$466$	−4.28156e11	−0.420597
$467$	7.40656e9	0.00720594	0.00360297	−	0.999994i	$-0.498853\pi$
$467$	7.40656e9	0.00720594	0.00360297	+	0.999994i	$0.498853\pi$
$468$	9.94323e10	0.0958123
$469$	5.08804e11	0.485593
$470$	−8.02107e11	−0.758214
$471$	5.79162e11	0.542258
$472$	1.24111e11	0.115099
$473$	−1.82105e11	−0.167281
$474$	−5.33050e11	−0.485026
$475$	−9.77706e9	−0.00881225
$476$	1.67825e11	0.149839
$477$	1.94668e11	0.172171
$478$	8.14133e11	0.713296
$479$	8.74214e11	0.758766	0.379383	−	0.925240i	$-0.376136\pi$
$479$	8.74214e11	0.758766	0.379383	+	0.925240i	$0.376136\pi$
$480$	2.42806e11	0.208773
$481$	8.38244e11	0.714032
$482$	2.19915e10	0.0185585
$483$	4.07293e11	0.340521
$484$	−1.99250e11	−0.165042
$485$	1.14483e12	0.939515
$486$	−8.60419e10	−0.0699595
$487$	−1.11634e12	−0.899325	−0.449663	−	0.893198i	$-0.648456\pi$
$487$	−1.11634e12	−0.899325	−0.449663	+	0.893198i	$0.648456\pi$
$488$	1.53884e12	1.22830
$489$	−1.14190e12	−0.903105
$490$	−5.67425e11	−0.444658
$491$	−1.09081e11	−0.0846998	−0.0423499	−	0.999103i	$-0.513484\pi$
$491$	−1.09081e11	−0.0846998	−0.0423499	+	0.999103i	$0.513484\pi$
$492$	1.24873e11	0.0960784
$493$	−1.61672e12	−1.23261
$494$	2.99778e11	0.226479
$495$	1.54234e11	0.115467
$496$	2.96878e12	2.20247
$497$	1.97464e12	1.45173
$498$	1.42101e12	1.03530
$499$	3.25184e11	0.234788	0.117394	−	0.993085i	$-0.462546\pi$
$499$	3.25184e11	0.234788	0.117394	+	0.993085i	$0.462546\pi$
$500$	−2.72411e11	−0.194921
$501$	−2.87733e11	−0.204042
$502$	−2.32914e12	−1.63693
$503$	−3.82998e11	−0.266772	−0.133386	−	0.991064i	$-0.542585\pi$
$503$	−3.82998e11	−0.266772	−0.133386	+	0.991064i	$0.542585\pi$
$504$	3.24677e11	0.224137
$505$	−1.43722e12	−0.983361
$506$	4.46614e11	0.302869
$507$	−1.12097e12	−0.753457
$508$	−4.15163e11	−0.276587
$509$	2.38906e12	1.57760	0.788800	−	0.614650i	$-0.210703\pi$
$509$	2.38906e12	1.57760	0.788800	+	0.614650i	$0.210703\pi$
$510$	9.68229e11	0.633742
$511$	−1.85485e12	−1.20341
$512$	−9.15172e11	−0.588556
$513$	−4.12939e10	−0.0263244
$514$	3.03051e12	1.91506
$515$	−2.91089e12	−1.82345
$516$	8.22199e10	0.0510568
$517$	−4.18165e11	−0.257419
$518$	−6.39221e11	−0.390092
$519$	−8.67643e11	−0.524914
$520$	−2.16466e12	−1.29830
$521$	5.93917e11	0.353147	0.176574	−	0.984287i	$-0.443499\pi$
$521$	5.93917e11	0.353147	0.176574	+	0.984287i	$0.443499\pi$
$522$	7.30444e11	0.430595
$523$	−2.71554e12	−1.58708	−0.793539	−	0.608519i	$-0.791764\pi$
$523$	−2.71554e12	−1.58708	−0.793539	+	0.608519i	$0.791764\pi$
$524$	−3.36061e10	−0.0194727
$525$	−4.92426e10	−0.0282894
$526$	1.40796e12	0.801965
$527$	3.51829e12	1.98693
$528$	4.25932e11	0.238499
$529$	−7.18011e11	−0.398639
$530$	9.89722e11	0.544844
$531$	−7.95020e10	−0.0433963
$532$	−3.63902e10	−0.0196962
$533$	−2.48652e12	−1.33450
$534$	1.91143e12	1.01724
$535$	3.39328e12	1.79072
$536$	1.07863e12	0.564459
$537$	2.00612e12	1.04105
$538$	2.32635e12	1.19717
$539$	−2.95817e11	−0.150964
$540$	−6.96361e10	−0.0352421
$541$	1.08823e12	0.546177	0.273089	−	0.961989i	$-0.411955\pi$
$541$	1.08823e12	0.546177	0.273089	+	0.961989i	$0.411955\pi$
$542$	4.26054e12	2.12064
$543$	3.26584e11	0.161212
$544$	7.94647e11	0.389026
$545$	−1.13919e12	−0.553112
$546$	1.50984e12	0.727051
$547$	−1.59236e12	−0.760496	−0.380248	−	0.924885i	$-0.624161\pi$
$547$	−1.59236e12	−0.760496	−0.380248	+	0.924885i	$0.624161\pi$
$548$	−5.91127e11	−0.280007
$549$	−9.85738e11	−0.463112
$550$	−5.39966e10	−0.0251614
$551$	3.50561e11	0.162025
$552$	8.63436e11	0.395826
$553$	−1.28848e12	−0.585887
$554$	7.93781e11	0.358020
$555$	−5.87053e11	−0.262639
$556$	1.56391e11	0.0694025
$557$	2.18678e12	0.962623	0.481312	−	0.876550i	$-0.340161\pi$
$557$	2.18678e12	0.962623	0.481312	+	0.876550i	$0.340161\pi$
$558$	−1.58958e12	−0.694111
$559$	−1.63719e12	−0.709164
$560$	1.97485e12	0.848569
$561$	5.04770e11	0.215160
$562$	2.15505e12	0.911265
$563$	−1.61621e12	−0.677971	−0.338985	−	0.940792i	$-0.610084\pi$
$563$	−1.61621e12	−0.677971	−0.338985	+	0.940792i	$0.610084\pi$
$564$	1.88800e11	0.0785681
$565$	−1.23278e12	−0.508940
$566$	−1.20077e12	−0.491797
$567$	−2.07979e11	−0.0845075
$568$	4.18612e12	1.68750
$569$	−1.93492e12	−0.773851	−0.386926	−	0.922111i	$-0.626463\pi$
$569$	−1.93492e12	−0.773851	−0.386926	+	0.922111i	$0.626463\pi$
$570$	−2.09945e11	−0.0833046
$571$	−6.69506e11	−0.263567	−0.131784	−	0.991278i	$-0.542070\pi$
$571$	−6.69506e11	−0.263567	−0.131784	+	0.991278i	$0.542070\pi$
$572$	2.63550e11	0.102939
$573$	2.57804e12	0.999066
$574$	1.89615e12	0.729070
$575$	−1.30954e11	−0.0499591
$576$	6.56732e11	0.248592
$577$	−4.52091e12	−1.69799	−0.848995	−	0.528402i	$-0.822792\pi$
$577$	−4.52091e12	−1.69799	−0.848995	+	0.528402i	$0.822792\pi$
$578$	2.42438e11	0.0903496
$579$	−2.20722e12	−0.816191
$580$	5.91168e11	0.216913
$581$	3.43483e12	1.25058
$582$	−1.69281e12	−0.611580
$583$	5.15975e11	0.184978
$584$	−3.93216e12	−1.39886
$585$	1.38662e12	0.489504
$586$	2.11044e12	0.739321
$587$	−2.49172e12	−0.866219	−0.433109	−	0.901341i	$-0.642584\pi$
$587$	−2.49172e12	−0.866219	−0.433109	+	0.901341i	$0.642584\pi$
$588$	1.33561e11	0.0460766
$589$	−7.62885e11	−0.261180
$590$	−4.04201e11	−0.137329
$591$	−2.74380e12	−0.925141
$592$	−1.62120e12	−0.542488
$593$	6.67397e11	0.221635	0.110817	−	0.993841i	$-0.464653\pi$
$593$	6.67397e11	0.221635	0.110817	+	0.993841i	$0.464653\pi$
$594$	−2.28058e11	−0.0751633
$595$	2.34038e12	0.765527
$596$	8.31941e11	0.270075
$597$	−1.24275e12	−0.400404
$598$	4.01523e12	1.28397
$599$	−1.52637e12	−0.484440	−0.242220	−	0.970221i	$-0.577876\pi$
$599$	−1.52637e12	−0.484440	−0.242220	+	0.970221i	$0.577876\pi$
$600$	−1.04391e11	−0.0328839
$601$	1.37907e11	0.0431174	0.0215587	−	0.999768i	$-0.493137\pi$
$601$	1.37907e11	0.0431174	0.0215587	+	0.999768i	$0.493137\pi$
$602$	1.24848e12	0.387433
$603$	−6.90942e11	−0.212821
$604$	2.53002e11	0.0773496
$605$	−2.77861e12	−0.843197
$606$	2.12515e12	0.640122
$607$	4.01371e12	1.20004	0.600021	−	0.799984i	$-0.295159\pi$
$607$	4.01371e12	1.20004	0.600021	+	0.799984i	$0.295159\pi$
$608$	−1.72307e11	−0.0511371
$609$	1.76561e12	0.520137
$610$	−5.01166e12	−1.46554
$611$	−3.75946e12	−1.09129
$612$	−2.27902e11	−0.0656700
$613$	−4.46430e11	−0.127697	−0.0638486	−	0.997960i	$-0.520337\pi$
$613$	−4.46430e11	−0.127697	−0.0638486	+	0.997960i	$0.520337\pi$
$614$	−1.51578e12	−0.430407
$615$	1.74140e12	0.490864
$616$	8.60570e11	0.240809
$617$	−1.66078e12	−0.461349	−0.230674	−	0.973031i	$-0.574093\pi$
$617$	−1.66078e12	−0.461349	−0.230674	+	0.973031i	$0.574093\pi$
$618$	4.30419e12	1.18698
$619$	−2.53835e12	−0.694933	−0.347467	−	0.937692i	$-0.612958\pi$
$619$	−2.53835e12	−0.694933	−0.347467	+	0.937692i	$0.612958\pi$
$620$	−1.28649e12	−0.349659
$621$	−5.53093e11	−0.149240
$622$	1.22997e12	0.329486
$623$	4.62027e12	1.22877
$624$	3.82929e12	1.01108
$625$	−3.55311e12	−0.931426
$626$	1.89460e11	0.0493097
$627$	−1.09451e11	−0.0282825
$628$	−6.93090e11	−0.177816
$629$	−1.92128e12	−0.489399
$630$	−1.05740e12	−0.267427
$631$	−3.44715e12	−0.865621	−0.432811	−	0.901485i	$-0.642478\pi$
$631$	−3.44715e12	−0.865621	−0.432811	+	0.901485i	$0.642478\pi$
$632$	−2.73150e12	−0.681041
$633$	−2.65816e12	−0.658058
$634$	−2.17053e12	−0.533536
$635$	−5.78960e12	−1.41308
$636$	−2.32961e11	−0.0564581
$637$	−2.65951e12	−0.639991
$638$	1.93607e12	0.462624
$639$	−2.68151e12	−0.636247
$640$	4.87371e12	1.14828
$641$	6.73195e12	1.57500	0.787498	−	0.616317i	$-0.211376\pi$
$641$	6.73195e12	1.57500	0.787498	+	0.616317i	$0.211376\pi$
$642$	−5.01748e12	−1.16568
$643$	2.98977e12	0.689745	0.344873	−	0.938649i	$-0.387922\pi$
$643$	2.98977e12	0.689745	0.344873	+	0.938649i	$0.387922\pi$
$644$	−4.87412e11	−0.111663
$645$	1.14659e12	0.260848
$646$	−6.87100e11	−0.155229
$647$	2.00400e12	0.449601	0.224801	−	0.974405i	$-0.427827\pi$
$647$	2.00400e12	0.449601	0.224801	+	0.974405i	$0.427827\pi$
$648$	−4.40903e11	−0.0982325
$649$	−2.10724e11	−0.0466243
$650$	−4.85450e11	−0.106668
$651$	−3.84230e12	−0.838449
$652$	1.36653e12	0.296144
$653$	−8.37262e11	−0.180199	−0.0900994	−	0.995933i	$-0.528718\pi$
$653$	−8.37262e11	−0.180199	−0.0900994	+	0.995933i	$0.528718\pi$
$654$	1.68447e12	0.360050
$655$	−4.68649e11	−0.0994860
$656$	4.80905e12	1.01389
$657$	2.51883e12	0.527418
$658$	2.86686e12	0.596197
$659$	5.14455e12	1.06258	0.531291	−	0.847189i	$-0.321707\pi$
$659$	5.14455e12	1.06258	0.531291	+	0.847189i	$0.321707\pi$
$660$	−1.84573e11	−0.0378636
$661$	7.96290e12	1.62243	0.811213	−	0.584751i	$-0.198808\pi$
$661$	7.96290e12	1.62243	0.811213	+	0.584751i	$0.198808\pi$
$662$	−1.82435e12	−0.369188
$663$	4.53807e12	0.912138
$664$	7.28163e12	1.45369
$665$	−5.07475e11	−0.100628
$666$	8.68045e11	0.170965
$667$	4.69542e12	0.918561
$668$	3.44334e11	0.0669091
$669$	−3.24668e12	−0.626646
$670$	−3.51286e12	−0.673480
$671$	−2.61274e12	−0.497560
$672$	−8.67829e11	−0.164162
$673$	−3.95241e12	−0.742667	−0.371334	−	0.928499i	$-0.621099\pi$
$673$	−3.95241e12	−0.742667	−0.371334	+	0.928499i	$0.621099\pi$
$674$	−3.81324e12	−0.711746
$675$	6.68701e10	0.0123984
$676$	1.34148e12	0.247072
$677$	−8.30975e12	−1.52033	−0.760166	−	0.649728i	$-0.774883\pi$
$677$	−8.30975e12	−1.52033	−0.760166	+	0.649728i	$0.774883\pi$
$678$	1.82285e12	0.331296
$679$	−4.09181e12	−0.738757
$680$	4.96147e12	0.889858
$681$	3.28209e12	0.584775
$682$	−4.21325e12	−0.745741
$683$	−2.21459e12	−0.389403	−0.194701	−	0.980863i	$-0.562374\pi$
$683$	−2.21459e12	−0.389403	−0.194701	+	0.980863i	$0.562374\pi$
$684$	4.94170e10	0.00863224
$685$	−8.24348e12	−1.43055
$686$	6.83919e12	1.17909
$687$	6.28770e11	0.107693
$688$	3.16641e12	0.538790
$689$	4.63881e12	0.784188
$690$	−2.81201e12	−0.472277
$691$	−3.30602e12	−0.551638	−0.275819	−	0.961210i	$-0.588949\pi$
$691$	−3.30602e12	−0.551638	−0.275819	+	0.961210i	$0.588949\pi$
$692$	1.03832e12	0.172129
$693$	−5.51257e11	−0.0907934
$694$	−3.39540e12	−0.555615
$695$	2.18093e12	0.354576
$696$	3.74299e12	0.604613
$697$	5.69919e12	0.914672
$698$	−6.02977e12	−0.961505
$699$	1.40541e12	0.222667
$700$	5.89292e10	0.00927661
$701$	−1.50916e12	−0.236050	−0.118025	−	0.993011i	$-0.537656\pi$
$701$	−1.50916e12	−0.236050	−0.118025	+	0.993011i	$0.537656\pi$
$702$	−2.05033e12	−0.318644
$703$	4.16600e11	0.0643309
$704$	1.74070e12	0.267083
$705$	2.63289e12	0.401404
$706$	−4.95287e12	−0.750301
$707$	5.13687e12	0.773234
$708$	9.51410e10	0.0142304
$709$	4.19952e12	0.624154	0.312077	−	0.950057i	$-0.398975\pi$
$709$	4.19952e12	0.624154	0.312077	+	0.950057i	$0.398975\pi$
$710$	−1.36332e13	−2.01343
$711$	1.74972e12	0.256776
$712$	9.79469e12	1.42834
$713$	−1.02181e13	−1.48070
$714$	−3.46061e12	−0.498323
$715$	3.67530e12	0.525915
$716$	−2.40074e12	−0.341379
$717$	−2.67236e12	−0.377624
$718$	−5.40593e12	−0.759120
$719$	2.56575e12	0.358042	0.179021	−	0.983845i	$-0.442707\pi$
$719$	2.56575e12	0.358042	0.179021	+	0.983845i	$0.442707\pi$
$720$	−2.68179e12	−0.371902
$721$	1.04040e13	1.43381
$722$	−7.81384e12	−1.07016
$723$	−7.21863e10	−0.00982500
$724$	−3.90828e11	−0.0528642
$725$	−5.67686e11	−0.0763111
$726$	4.10860e12	0.548882
$727$	−3.93388e12	−0.522296	−0.261148	−	0.965299i	$-0.584101\pi$
$727$	−3.93388e12	−0.522296	−0.261148	+	0.965299i	$0.584101\pi$
$728$	7.73685e12	1.02088
$729$	2.82430e11	0.0370370
$730$	1.28061e13	1.66904
$731$	3.75250e12	0.486063
$732$	1.17964e12	0.151863
$733$	5.34623e12	0.684037	0.342019	−	0.939693i	$-0.388889\pi$
$733$	5.34623e12	0.684037	0.342019	+	0.939693i	$0.388889\pi$
$734$	−8.82413e12	−1.12212
$735$	1.86255e12	0.235405
$736$	−2.30788e12	−0.289910
$737$	−1.83137e12	−0.228651
$738$	−2.57492e12	−0.319529
$739$	2.20679e12	0.272183	0.136091	−	0.990696i	$-0.456546\pi$
$739$	2.20679e12	0.272183	0.136091	+	0.990696i	$0.456546\pi$
$740$	7.02533e11	0.0861239
$741$	−9.84009e11	−0.119899
$742$	−3.53743e12	−0.428420
$743$	1.61454e12	0.194356	0.0971782	−	0.995267i	$-0.469018\pi$
$743$	1.61454e12	0.194356	0.0971782	+	0.995267i	$0.469018\pi$
$744$	−8.14545e12	−0.974623
$745$	1.16017e13	1.37981
$746$	−1.36737e13	−1.61645
$747$	−4.66441e12	−0.548092
$748$	−6.04064e11	−0.0705547
$749$	−1.21281e13	−1.40808
$750$	5.61719e12	0.648252
$751$	−3.76703e12	−0.432135	−0.216067	−	0.976378i	$-0.569323\pi$
$751$	−3.76703e12	−0.432135	−0.216067	+	0.976378i	$0.569323\pi$
$752$	7.27098e12	0.829111
$753$	7.64532e12	0.866599
$754$	1.74060e13	1.96123
$755$	3.52821e12	0.395178
$756$	2.48891e11	0.0277115
$757$	−1.18381e13	−1.31024	−0.655122	−	0.755523i	$-0.727383\pi$
$757$	−1.18381e13	−1.31024	−0.655122	+	0.755523i	$0.727383\pi$
$758$	−3.74962e12	−0.412549
$759$	−1.46600e12	−0.160341
$760$	−1.07582e12	−0.116971
$761$	5.32000e12	0.575017	0.287509	−	0.957778i	$-0.407173\pi$
$761$	5.32000e12	0.575017	0.287509	+	0.957778i	$0.407173\pi$
$762$	8.56079e12	0.919849
$763$	4.07166e12	0.434922
$764$	−3.08517e12	−0.327612
$765$	−3.17818e12	−0.335507
$766$	−1.05560e13	−1.10782
$767$	−1.89448e12	−0.197657
$768$	−3.05532e12	−0.316906
$769$	−5.58489e12	−0.575898	−0.287949	−	0.957646i	$-0.592973\pi$
$769$	−5.58489e12	−0.575898	−0.287949	+	0.957646i	$0.592973\pi$
$770$	−2.80268e12	−0.287319
$771$	−9.94754e12	−1.01384
$772$	2.64141e12	0.267644
$773$	−2.34571e12	−0.236301	−0.118151	−	0.992996i	$-0.537697\pi$
$773$	−2.34571e12	−0.236301	−0.118151	+	0.992996i	$0.537697\pi$
$774$	−1.69540e12	−0.169800
$775$	1.23539e12	0.123012
$776$	−8.67440e12	−0.858740
$777$	2.09822e12	0.206517
$778$	1.11159e13	1.08777
$779$	−1.23578e12	−0.120233
$780$	−1.65939e12	−0.160517
$781$	−7.10746e12	−0.683573
$782$	−9.20304e12	−0.880037
$783$	−2.39766e12	−0.227960
$784$	5.14362e12	0.486235
$785$	−9.66539e12	−0.908460
$786$	6.92968e11	0.0647608
$787$	1.63539e13	1.51962	0.759812	−	0.650143i	$-0.225291\pi$
$787$	1.63539e13	1.51962	0.759812	+	0.650143i	$0.225291\pi$
$788$	3.28353e12	0.303371
$789$	−4.62159e12	−0.424566
$790$	8.89585e12	0.812579
$791$	4.40614e12	0.400188
$792$	−1.16863e12	−0.105539
$793$	−2.34895e13	−2.10933
$794$	−1.79295e13	−1.60094
$795$	−3.24873e12	−0.288444
$796$	1.48721e12	0.131300
$797$	7.98493e12	0.700985	0.350493	−	0.936565i	$-0.386014\pi$
$797$	7.98493e12	0.700985	0.350493	+	0.936565i	$0.386014\pi$
$798$	7.50378e11	0.0655039
$799$	8.61681e12	0.747973
$800$	2.79028e11	0.0240848
$801$	−6.27420e12	−0.538532
$802$	1.38240e13	1.17991
$803$	6.67627e12	0.566649
$804$	8.26859e11	0.0697877
$805$	−6.79714e12	−0.570486
$806$	−3.78787e13	−3.16146
$807$	−7.63615e12	−0.633788
$808$	1.08899e13	0.898817
$809$	8.18221e12	0.671587	0.335794	−	0.941936i	$-0.390996\pi$
$809$	8.18221e12	0.671587	0.335794	+	0.941936i	$0.390996\pi$
$810$	1.43592e12	0.117205
$811$	−1.08175e13	−0.878077	−0.439038	−	0.898468i	$-0.644681\pi$
$811$	−1.08175e13	−0.878077	−0.439038	+	0.898468i	$0.644681\pi$
$812$	−2.11293e12	−0.170562
$813$	−1.39851e13	−1.12268
$814$	2.30079e12	0.183682
$815$	1.90567e13	1.51300
$816$	−8.77685e12	−0.693000
$817$	−8.13671e11	−0.0638924
$818$	1.70580e13	1.33210
$819$	−4.95601e12	−0.384906
$820$	−2.08396e12	−0.160963
$821$	2.25816e13	1.73464	0.867322	−	0.497747i	$-0.165839\pi$
$821$	2.25816e13	1.73464	0.867322	+	0.497747i	$0.165839\pi$
$822$	1.21892e13	0.931221
$823$	−1.26241e13	−0.959184	−0.479592	−	0.877492i	$-0.659215\pi$
$823$	−1.26241e13	−0.959184	−0.479592	+	0.877492i	$0.659215\pi$
$824$	2.20558e13	1.66668
$825$	1.77242e11	0.0133206
$826$	1.44468e12	0.107985
$827$	−1.97443e13	−1.46780	−0.733901	−	0.679256i	$-0.762303\pi$
$827$	−1.97443e13	−1.46780	−0.733901	+	0.679256i	$0.762303\pi$
$828$	6.61892e11	0.0489385
$829$	−6.92065e12	−0.508922	−0.254461	−	0.967083i	$-0.581898\pi$
$829$	−6.92065e12	−0.508922	−0.254461	+	0.967083i	$0.581898\pi$
$830$	−2.37146e13	−1.73446
$831$	−2.60556e12	−0.189538
$832$	1.56495e13	1.13226
$833$	6.09568e12	0.438652
$834$	−3.22483e12	−0.230813
$835$	4.80186e12	0.341838
$836$	1.30982e11	0.00927433
$837$	5.21774e12	0.367467
$838$	−6.79376e12	−0.475896
$839$	−1.15417e13	−0.804155	−0.402077	−	0.915606i	$-0.631712\pi$
$839$	−1.15417e13	−0.804155	−0.402077	+	0.915606i	$0.631712\pi$
$840$	−5.41840e12	−0.375504
$841$	5.84749e12	0.403077
$842$	1.09623e13	0.751618
$843$	−7.07389e12	−0.482430
$844$	3.18105e12	0.215789
$845$	1.87074e13	1.26229
$846$	−3.89312e12	−0.261295
$847$	9.93121e12	0.663020
$848$	−8.97168e12	−0.595789
$849$	3.94148e12	0.260361
$850$	1.11267e12	0.0731106
$851$	5.57995e12	0.364710
$852$	3.20900e12	0.208637
$853$	4.10642e11	0.0265579	0.0132789	−	0.999912i	$-0.495773\pi$
$853$	4.10642e11	0.0265579	0.0132789	+	0.999912i	$0.495773\pi$
$854$	1.79125e13	1.15238
$855$	6.89138e11	0.0441020
$856$	−2.57110e13	−1.63676
$857$	8.38710e12	0.531126	0.265563	−	0.964093i	$-0.414442\pi$
$857$	8.38710e12	0.531126	0.265563	+	0.964093i	$0.414442\pi$
$858$	−5.43448e12	−0.342346
$859$	−2.68616e13	−1.68330	−0.841651	−	0.540022i	$-0.818416\pi$
$859$	−2.68616e13	−1.68330	−0.841651	+	0.540022i	$0.818416\pi$
$860$	−1.37213e12	−0.0855369
$861$	−6.22405e12	−0.385975
$862$	−2.71562e13	−1.67527
$863$	1.97692e13	1.21322	0.606610	−	0.795000i	$-0.292529\pi$
$863$	1.97692e13	1.21322	0.606610	+	0.795000i	$0.292529\pi$
$864$	1.17849e12	0.0719472
$865$	1.44797e13	0.879403
$866$	−7.25101e12	−0.438095
$867$	−7.95796e11	−0.0478317
$868$	4.59813e12	0.274943
$869$	4.63770e12	0.275876
$870$	−1.21901e13	−0.721389
$871$	−1.64647e13	−0.969333
$872$	8.63168e12	0.505558
$873$	5.55657e12	0.323775
$874$	1.99553e12	0.115680
$875$	1.35778e13	0.783054
$876$	−3.01431e12	−0.172950
$877$	9.19482e12	0.524862	0.262431	−	0.964951i	$-0.415476\pi$
$877$	9.19482e12	0.524862	0.262431	+	0.964951i	$0.415476\pi$
$878$	2.43169e13	1.38097
$879$	−6.92743e12	−0.391401
$880$	−7.10820e12	−0.399565
$881$	8.80242e12	0.492278	0.246139	−	0.969235i	$-0.420838\pi$
$881$	8.80242e12	0.492278	0.246139	+	0.969235i	$0.420838\pi$
$882$	−2.75406e12	−0.153237
$883$	1.54523e13	0.855400	0.427700	−	0.903921i	$-0.359324\pi$
$883$	1.54523e13	0.855400	0.427700	+	0.903921i	$0.359324\pi$
$884$	−5.43077e12	−0.299107
$885$	1.32678e12	0.0727031
$886$	−1.12715e13	−0.614510
$887$	2.05990e13	1.11735	0.558676	−	0.829386i	$-0.311309\pi$
$887$	2.05990e13	1.11735	0.558676	+	0.829386i	$0.311309\pi$
$888$	4.44810e12	0.240058
$889$	2.06930e13	1.11113
$890$	−3.18990e13	−1.70421
$891$	7.48592e11	0.0397920
$892$	3.88535e12	0.205489
$893$	−1.86842e12	−0.0983201
$894$	−1.71549e13	−0.898192
$895$	−3.34792e13	−1.74410
$896$	−1.74194e13	−0.902917
$897$	−1.31799e13	−0.679743
$898$	−2.70099e13	−1.38605
$899$	−4.42955e13	−2.26173
$900$	−8.00242e10	−0.00406565
$901$	−1.06323e13	−0.537484
$902$	−6.82494e12	−0.343297
$903$	−4.09809e12	−0.205110
$904$	9.34076e12	0.465184
$905$	−5.45023e12	−0.270083
$906$	−5.21699e12	−0.257243
$907$	2.40214e13	1.17860	0.589299	−	0.807915i	$-0.299404\pi$
$907$	2.40214e13	1.17860	0.589299	+	0.807915i	$0.299404\pi$
$908$	−3.92772e12	−0.191758
$909$	−6.97573e12	−0.338885
$910$	−2.51971e13	−1.21805
$911$	5.73966e12	0.276092	0.138046	−	0.990426i	$-0.455918\pi$
$911$	5.73966e12	0.276092	0.138046	+	0.990426i	$0.455918\pi$
$912$	1.90312e12	0.0910940
$913$	−1.23632e13	−0.588861
$914$	2.01944e13	0.957136
$915$	1.64506e13	0.775865
$916$	−7.52456e11	−0.0353144
$917$	1.67503e12	0.0782276
$918$	4.69941e12	0.218400
$919$	2.83891e13	1.31290	0.656451	−	0.754368i	$-0.272057\pi$
$919$	2.83891e13	1.31290	0.656451	+	0.754368i	$0.272057\pi$
$920$	−1.44095e13	−0.663139
$921$	4.97550e12	0.227860
$922$	1.24133e13	0.565715
$923$	−6.38987e13	−2.89791
$924$	6.59695e11	0.0297728
$925$	−6.74628e11	−0.0302989
$926$	4.17500e13	1.86598
$927$	−1.41283e13	−0.628394
$928$	−1.00047e13	−0.442829
$929$	−1.44672e13	−0.637257	−0.318628	−	0.947880i	$-0.603222\pi$
$929$	−1.44672e13	−0.637257	−0.318628	+	0.947880i	$0.603222\pi$
$930$	2.65279e13	1.16286
$931$	−1.32175e12	−0.0576602
$932$	−1.68187e12	−0.0730164
$933$	−4.03732e12	−0.174432
$934$	1.82769e11	0.00785852
$935$	−8.42390e12	−0.360463
$936$	−1.05064e13	−0.447419
$937$	−1.94080e13	−0.822531	−0.411266	−	0.911515i	$-0.634913\pi$
$937$	−1.94080e13	−0.822531	−0.411266	+	0.911515i	$0.634913\pi$
$938$	1.25555e13	0.529569
$939$	−6.21894e11	−0.0261049
$940$	−3.15081e12	−0.131627
$941$	2.21587e13	0.921279	0.460640	−	0.887587i	$-0.347620\pi$
$941$	2.21587e13	0.921279	0.460640	+	0.887587i	$0.347620\pi$
$942$	1.42917e13	0.591365
$943$	−1.65521e13	−0.681631
$944$	3.66402e12	0.150170
$945$	3.47087e12	0.141578
$946$	−4.49373e12	−0.182430
$947$	2.08532e13	0.842552	0.421276	−	0.906932i	$-0.361582\pi$
$947$	2.08532e13	0.842552	0.421276	+	0.906932i	$0.361582\pi$
$948$	−2.09391e12	−0.0842016
$949$	6.00222e13	2.40223
$950$	−2.41264e11	−0.00961030
$951$	7.12468e12	0.282457
$952$	−1.77331e13	−0.699711
$953$	−6.20564e12	−0.243707	−0.121854	−	0.992548i	$-0.538884\pi$
$953$	−6.20564e12	−0.243707	−0.121854	+	0.992548i	$0.538884\pi$
$954$	4.80373e12	0.187763
$955$	−4.30239e13	−1.67376
$956$	3.19805e12	0.123830
$957$	−6.35509e12	−0.244916
$958$	2.15726e13	0.827481
$959$	2.94635e13	1.12487
$960$	−1.09599e13	−0.416473
$961$	6.99555e13	2.64586
$962$	2.06850e13	0.778695
$963$	1.64697e13	0.617117
$964$	8.63862e10	0.00322180
$965$	3.68354e13	1.36739
$966$	1.00506e13	0.371359
$967$	−4.63676e13	−1.70528	−0.852639	−	0.522501i	$-0.824999\pi$
$967$	−4.63676e13	−1.70528	−0.852639	+	0.522501i	$0.824999\pi$
$968$	2.10536e13	0.770703
$969$	2.25538e12	0.0821794
$970$	2.82505e13	1.02460
$971$	4.99705e13	1.80396	0.901980	−	0.431778i	$-0.142114\pi$
$971$	4.99705e13	1.80396	0.901980	+	0.431778i	$0.142114\pi$
$972$	−3.37987e11	−0.0121451
$973$	−7.79499e12	−0.278810
$974$	−2.75475e13	−0.980769
$975$	1.59347e12	0.0564708
$976$	4.54299e13	1.60257
$977$	4.70947e13	1.65366	0.826830	−	0.562452i	$-0.190142\pi$
$977$	4.70947e13	1.65366	0.826830	+	0.562452i	$0.190142\pi$
$978$	−2.81782e13	−0.984891
$979$	−1.66300e13	−0.578590
$980$	−2.22894e12	−0.0771934
$981$	−5.52921e12	−0.190613
$982$	−2.69175e12	−0.0923703
$983$	2.86405e13	0.978340	0.489170	−	0.872189i	$-0.337300\pi$
$983$	2.86405e13	0.978340	0.489170	+	0.872189i	$0.337300\pi$
$984$	−1.31946e13	−0.448661
$985$	4.57901e13	1.54992
$986$	−3.98952e13	−1.34423
$987$	−9.41037e12	−0.315631
$988$	1.17758e12	0.0393172
$989$	−1.08983e13	−0.362223
$990$	3.80596e12	0.125923
$991$	5.61009e13	1.84773	0.923866	−	0.382717i	$-0.125012\pi$
$991$	5.61009e13	1.84773	0.923866	+	0.382717i	$0.125012\pi$
$992$	2.17720e13	0.713831
$993$	5.98838e12	0.195451
$994$	4.87274e13	1.58320
$995$	2.07397e13	0.670808
$996$	5.58195e12	0.179729
$997$	7.32678e12	0.234847	0.117423	−	0.993082i	$-0.462537\pi$
$997$	7.32678e12	0.234847	0.117423	+	0.993082i	$0.462537\pi$
$998$	8.02442e12	0.256051
$999$	−2.84933e12	−0.0905102

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.10.a.b.1.16	✓	21

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.10.a.b.1.16	✓	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)

\(f(q)\)	\(=\)	\(q+24.6766 q^{2} -81.0000 q^{3} +96.9337 q^{4} +1351.78 q^{5} -1998.80 q^{6} -4831.46 q^{7} -10242.4 q^{8} +6561.00 q^{9} +O(q^{10})\)	\(q+24.6766 q^{2} -81.0000 q^{3} +96.9337 q^{4} +1351.78 q^{5} -1998.80 q^{6} -4831.46 q^{7} -10242.4 q^{8} +6561.00 q^{9} +33357.2 q^{10} +17390.2 q^{11} -7851.63 q^{12} +156345. q^{13} -119224. q^{14} -109494. q^{15} -302378. q^{16} -358347. q^{17} +161903. q^{18} +77701.9 q^{19} +131033. q^{20} +391349. q^{21} +429131. q^{22} +1.04074e6 q^{23} +829636. q^{24} -125828. q^{25} +3.85805e6 q^{26} -531441. q^{27} -468332. q^{28} +4.51161e6 q^{29} -2.70193e6 q^{30} -9.81810e6 q^{31} -2.21753e6 q^{32} -1.40861e6 q^{33} -8.84278e6 q^{34} -6.53106e6 q^{35} +635982. q^{36} +5.36151e6 q^{37} +1.91742e6 q^{38} -1.26639e7 q^{39} -1.38455e7 q^{40} -1.59041e7 q^{41} +9.65715e6 q^{42} -1.04717e7 q^{43} +1.68570e6 q^{44} +8.86900e6 q^{45} +2.56819e7 q^{46} -2.40460e7 q^{47} +2.44926e7 q^{48} -1.70106e7 q^{49} -3.10500e6 q^{50} +2.90261e7 q^{51} +1.51551e7 q^{52} +2.96704e7 q^{53} -1.31141e7 q^{54} +2.35077e7 q^{55} +4.94859e7 q^{56} -6.29385e6 q^{57} +1.11331e8 q^{58} -1.21174e7 q^{59} -1.06136e7 q^{60} -1.50242e8 q^{61} -2.42277e8 q^{62} -3.16992e7 q^{63} +1.00096e8 q^{64} +2.11343e8 q^{65} -3.47596e7 q^{66} -1.05311e8 q^{67} -3.47359e7 q^{68} -8.43000e7 q^{69} -1.61164e8 q^{70} -4.08704e8 q^{71} -6.72005e7 q^{72} +3.83910e8 q^{73} +1.32304e8 q^{74} +1.01921e7 q^{75} +7.53193e6 q^{76} -8.40202e7 q^{77} -3.12502e8 q^{78} +2.66685e8 q^{79} -4.08747e8 q^{80} +4.30467e7 q^{81} -3.92459e8 q^{82} -7.10929e8 q^{83} +3.79349e7 q^{84} -4.84405e8 q^{85} -2.58406e8 q^{86} -3.65441e8 q^{87} -1.78118e8 q^{88} -9.56287e8 q^{89} +2.18857e8 q^{90} -7.55373e8 q^{91} +1.00883e8 q^{92} +7.95266e8 q^{93} -5.93373e8 q^{94} +1.05035e8 q^{95} +1.79620e8 q^{96} +8.46910e8 q^{97} -4.19762e8 q^{98} +1.14097e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 21 q + 20 q^{2} - 1701 q^{3} + 4950 q^{4} + 2058 q^{5} - 1620 q^{6} - 17167 q^{7} - 2853 q^{8} + 137781 q^{9}+O(q^{10}) \) 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

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