LMFDB - Embedded newform 177.8.a.b.1.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [177,8,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, 8, names="a")

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

chi := DirichletCharacter("177.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 177 = 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
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:	$55.2921495107$
Analytic rank:	$1$
Dimension:	$17$
Coefficient field:	$\mathbb{Q}[x]/(x^{17} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} + \cdots - 58\!\cdots\!76 $ x^17 - 2x^16 - 1639x^15 + 1625x^14 + 1070274x^13 - 274939x^12 - 357079564x^11 - 89298188x^10 + 64650816672x^9 + 33122051904x^8 - 6210397064704x^7 - 2735256748800x^6 + 288860762071040x^5 - 34502173230080x^4 - 5633463408885760x^3 + 4719471961341952x^2 + 37636623107620864x - 58321181718347776
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	multiple of $ 2^{10}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.7
Root			$-4.85375$ of defining polynomial
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)

$f(q)$	$=$	$q-6.85375 q^{2} +27.0000 q^{3} -81.0262 q^{4} -190.727 q^{5} -185.051 q^{6} -799.288 q^{7} +1432.61 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-6.85375 q^{2} +27.0000 q^{3} -81.0262 q^{4} -190.727 q^{5} -185.051 q^{6} -799.288 q^{7} +1432.61 q^{8} +729.000 q^{9} +1307.20 q^{10} +972.348 q^{11} -2187.71 q^{12} -1278.77 q^{13} +5478.12 q^{14} -5149.64 q^{15} +552.586 q^{16} +36467.5 q^{17} -4996.38 q^{18} +1900.72 q^{19} +15453.9 q^{20} -21580.8 q^{21} -6664.23 q^{22} +80181.7 q^{23} +38680.5 q^{24} -41748.1 q^{25} +8764.35 q^{26} +19683.0 q^{27} +64763.2 q^{28} -201337. q^{29} +35294.3 q^{30} +106900. q^{31} -187162. q^{32} +26253.4 q^{33} -249939. q^{34} +152446. q^{35} -59068.1 q^{36} -246438. q^{37} -13027.1 q^{38} -34526.7 q^{39} -273238. q^{40} -348348. q^{41} +147909. q^{42} +303791. q^{43} -78785.6 q^{44} -139040. q^{45} -549545. q^{46} +1.12223e6 q^{47} +14919.8 q^{48} -184682. q^{49} +286131. q^{50} +984622. q^{51} +103614. q^{52} +534787. q^{53} -134902. q^{54} -185453. q^{55} -1.14507e6 q^{56} +51319.5 q^{57} +1.37991e6 q^{58} -205379. q^{59} +417255. q^{60} -2.14348e6 q^{61} -732666. q^{62} -582681. q^{63} +1.21203e6 q^{64} +243896. q^{65} -179934. q^{66} -158432. q^{67} -2.95482e6 q^{68} +2.16491e6 q^{69} -1.04483e6 q^{70} -3.94945e6 q^{71} +1.04437e6 q^{72} +3.25842e6 q^{73} +1.68903e6 q^{74} -1.12720e6 q^{75} -154008. q^{76} -777186. q^{77} +236637. q^{78} -5.28930e6 q^{79} -105393. q^{80} +531441. q^{81} +2.38749e6 q^{82} -3.63337e6 q^{83} +1.74861e6 q^{84} -6.95534e6 q^{85} -2.08211e6 q^{86} -5.43609e6 q^{87} +1.39300e6 q^{88} -1.34439e6 q^{89} +952946. q^{90} +1.02210e6 q^{91} -6.49682e6 q^{92} +2.88630e6 q^{93} -7.69146e6 q^{94} -362519. q^{95} -5.05336e6 q^{96} +2.79048e6 q^{97} +1.26576e6 q^{98} +708842. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) $ 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * 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 $

$2$	−6.85375	−0.605791	−0.302896	−	0.953024i	$-0.597953\pi$
$2$	−6.85375	−0.605791	−0.302896	+	0.953024i	$0.597953\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	−81.0262	−0.633017
$5$	−190.727	−0.682367	−0.341183	−	0.939997i	$-0.610828\pi$
$5$	−190.727	−0.682367	−0.341183	+	0.939997i	$0.610828\pi$
$6$	−185.051	−0.349754
$7$	−799.288	−0.880765	−0.440383	−	0.897810i	$-0.645157\pi$
$7$	−799.288	−0.880765	−0.440383	+	0.897810i	$0.645157\pi$
$8$	1432.61	0.989267
$9$	729.000	0.333333
$10$	1307.20	0.413372
$11$	972.348	0.220266	0.110133	−	0.993917i	$-0.464872\pi$
$11$	972.348	0.220266	0.110133	+	0.993917i	$0.464872\pi$
$12$	−2187.71	−0.365472
$13$	−1278.77	−0.161432	−0.0807161	−	0.996737i	$-0.525721\pi$
$13$	−1278.77	−0.161432	−0.0807161	+	0.996737i	$0.525721\pi$
$14$	5478.12	0.533560
$15$	−5149.64	−0.393965
$16$	552.586	0.0337272
$17$	36467.5	1.80026	0.900128	−	0.435625i	$-0.143473\pi$
$17$	36467.5	1.80026	0.900128	+	0.435625i	$0.143473\pi$
$18$	−4996.38	−0.201930
$19$	1900.72	0.0635742	0.0317871	−	0.999495i	$-0.489880\pi$
$19$	1900.72	0.0635742	0.0317871	+	0.999495i	$0.489880\pi$
$20$	15453.9	0.431950
$21$	−21580.8	−0.508510
$22$	−6664.23	−0.133435
$23$	80181.7	1.37413	0.687065	−	0.726596i	$-0.258899\pi$
$23$	80181.7	1.37413	0.687065	+	0.726596i	$0.258899\pi$
$24$	38680.5	0.571154
$25$	−41748.1	−0.534376
$26$	8764.35	0.0977942
$27$	19683.0	0.192450
$28$	64763.2	0.557539
$29$	−201337.	−1.53296	−0.766479	−	0.642270i	$-0.777993\pi$
$29$	−201337.	−1.53296	−0.766479	+	0.642270i	$0.777993\pi$
$30$	35294.3	0.238660
$31$	106900.	0.644484	0.322242	−	0.946657i	$-0.395564\pi$
$31$	106900.	0.644484	0.322242	+	0.946657i	$0.395564\pi$
$32$	−187162.	−1.00970
$33$	26253.4	0.127171
$34$	−249939.	−1.09058
$35$	152446.	0.601005
$36$	−59068.1	−0.211006
$37$	−246438.	−0.799838	−0.399919	−	0.916550i	$-0.630962\pi$
$37$	−246438.	−0.799838	−0.399919	+	0.916550i	$0.630962\pi$
$38$	−13027.1	−0.0385127
$39$	−34526.7	−0.0932029
$40$	−273238.	−0.675043
$41$	−348348.	−0.789350	−0.394675	−	0.918821i	$-0.629143\pi$
$41$	−348348.	−0.789350	−0.394675	+	0.918821i	$0.629143\pi$
$42$	147909.	0.308051
$43$	303791.	0.582687	0.291343	−	0.956619i	$-0.405898\pi$
$43$	303791.	0.582687	0.291343	+	0.956619i	$0.405898\pi$
$44$	−78785.6	−0.139432
$45$	−139040.	−0.227456
$46$	−549545.	−0.832436
$47$	1.12223e6	1.57666	0.788330	−	0.615252i	$-0.210946\pi$
$47$	1.12223e6	1.57666	0.788330	+	0.615252i	$0.210946\pi$
$48$	14919.8	0.0194724
$49$	−184682.	−0.224253
$50$	286131.	0.323720
$51$	984622.	1.03938
$52$	103614.	0.102189
$53$	534787.	0.493418	0.246709	−	0.969090i	$-0.420651\pi$
$53$	534787.	0.493418	0.246709	+	0.969090i	$0.420651\pi$
$54$	−134902.	−0.116585
$55$	−185453.	−0.150302
$56$	−1.14507e6	−0.871312
$57$	51319.5	0.0367046
$58$	1.37991e6	0.928652
$59$	−205379.	−0.130189
$59$	−205379.	−0.130189
$60$	417255.	0.249386
$61$	−2.14348e6	−1.20911	−0.604555	−	0.796564i	$-0.706649\pi$
$61$	−2.14348e6	−1.20911	−0.604555	+	0.796564i	$0.706649\pi$
$62$	−732666.	−0.390423
$63$	−582681.	−0.293588
$64$	1.21203e6	0.577940
$65$	243896.	0.110156
$66$	−179934.	−0.0770389
$67$	−158432.	−0.0643548	−0.0321774	−	0.999482i	$-0.510244\pi$
$67$	−158432.	−0.0643548	−0.0321774	+	0.999482i	$0.510244\pi$
$68$	−2.95482e6	−1.13959
$69$	2.16491e6	0.793355
$70$	−1.04483e6	−0.364084
$71$	−3.94945e6	−1.30958	−0.654790	−	0.755811i	$-0.727243\pi$
$71$	−3.94945e6	−1.30958	−0.654790	+	0.755811i	$0.727243\pi$
$72$	1.04437e6	0.329756
$73$	3.25842e6	0.980342	0.490171	−	0.871626i	$-0.336934\pi$
$73$	3.25842e6	0.980342	0.490171	+	0.871626i	$0.336934\pi$
$74$	1.68903e6	0.484535
$75$	−1.12720e6	−0.308522
$76$	−154008.	−0.0402435
$77$	−777186.	−0.194003
$78$	236637.	0.0564615
$79$	−5.28930e6	−1.20699	−0.603494	−	0.797367i	$-0.706225\pi$
$79$	−5.28930e6	−1.20699	−0.603494	+	0.797367i	$0.706225\pi$
$80$	−105393.	−0.0230143
$81$	531441.	0.111111
$82$	2.38749e6	0.478181
$83$	−3.63337e6	−0.697487	−0.348744	−	0.937218i	$-0.613392\pi$
$83$	−3.63337e6	−0.697487	−0.348744	+	0.937218i	$0.613392\pi$
$84$	1.74861e6	0.321895
$85$	−6.95534e6	−1.22844
$86$	−2.08211e6	−0.352987
$87$	−5.43609e6	−0.885053
$88$	1.39300e6	0.217902
$89$	−1.34439e6	−0.202143	−0.101072	−	0.994879i	$-0.532227\pi$
$89$	−1.34439e6	−0.202143	−0.101072	+	0.994879i	$0.532227\pi$
$90$	952946.	0.137791
$91$	1.02210e6	0.142184
$92$	−6.49682e6	−0.869848
$93$	2.88630e6	0.372093
$94$	−7.69146e6	−0.955128
$95$	−362519.	−0.0433809
$96$	−5.05336e6	−0.582950
$97$	2.79048e6	0.310441	0.155220	−	0.987880i	$-0.450391\pi$
$97$	2.79048e6	0.310441	0.155220	+	0.987880i	$0.450391\pi$
$98$	1.26576e6	0.135850
$99$	708842.	0.0734220
$100$	3.38269e6	0.338269
$101$	−1.43415e7	−1.38506	−0.692532	−	0.721387i	$-0.743505\pi$
$101$	−1.43415e7	−1.38506	−0.692532	+	0.721387i	$0.743505\pi$
$102$	−6.74835e6	−0.629647
$103$	1.62771e6	0.146773	0.0733867	−	0.997304i	$-0.476619\pi$
$103$	1.62771e6	0.146773	0.0733867	+	0.997304i	$0.476619\pi$
$104$	−1.83198e6	−0.159700
$105$	4.11604e6	0.346990
$106$	−3.66529e6	−0.298908
$107$	−7.86386e6	−0.620572	−0.310286	−	0.950643i	$-0.600425\pi$
$107$	−7.86386e6	−0.620572	−0.310286	+	0.950643i	$0.600425\pi$
$108$	−1.59484e6	−0.121824
$109$	2.63958e6	0.195228	0.0976141	−	0.995224i	$-0.468879\pi$
$109$	2.63958e6	0.195228	0.0976141	+	0.995224i	$0.468879\pi$
$110$	1.27105e6	0.0910518
$111$	−6.65383e6	−0.461787
$112$	−441675.	−0.0297057
$113$	−2.91448e7	−1.90015	−0.950074	−	0.312026i	$-0.898992\pi$
$113$	−2.91448e7	−1.90015	−0.950074	+	0.312026i	$0.898992\pi$
$114$	−351731.	−0.0222353
$115$	−1.52928e7	−0.937661
$116$	1.63135e7	0.970388
$117$	−932222.	−0.0538107
$118$	1.40762e6	0.0788673
$119$	−2.91480e7	−1.58560
$120$	−7.37743e6	−0.389736
$121$	−1.85417e7	−0.951483
$122$	1.46909e7	0.732468
$123$	−9.40539e6	−0.455731
$124$	−8.66170e6	−0.407969
$125$	2.28631e7	1.04701
$126$	3.99355e6	0.177853
$127$	−3.71615e7	−1.60983	−0.804915	−	0.593390i	$-0.797789\pi$
$127$	−3.71615e7	−1.60983	−0.804915	+	0.593390i	$0.797789\pi$
$128$	1.56498e7	0.659588
$129$	8.20235e6	0.336414
$130$	−1.67160e6	−0.0667315
$131$	1.50104e7	0.583369	0.291684	−	0.956515i	$-0.405784\pi$
$131$	1.50104e7	0.583369	0.291684	+	0.956515i	$0.405784\pi$
$132$	−2.12721e6	−0.0805011
$133$	−1.51922e6	−0.0559939
$134$	1.08585e6	0.0389856
$135$	−3.75409e6	−0.131322
$136$	5.22437e7	1.78094
$137$	1.75306e7	0.582470	0.291235	−	0.956652i	$-0.405934\pi$
$137$	1.75306e7	0.582470	0.291235	+	0.956652i	$0.405934\pi$
$138$	−1.48377e7	−0.480607
$139$	−1.16871e7	−0.369110	−0.184555	−	0.982822i	$-0.559084\pi$
$139$	−1.16871e7	−0.369110	−0.184555	+	0.982822i	$0.559084\pi$
$140$	−1.23521e7	−0.380446
$141$	3.03001e7	0.910286
$142$	2.70685e7	0.793332
$143$	−1.24341e6	−0.0355580
$144$	402835.	0.0112424
$145$	3.84004e7	1.04604
$146$	−2.23324e7	−0.593883
$147$	−4.98641e6	−0.129472
$148$	1.99679e7	0.506311
$149$	−6.76391e7	−1.67512	−0.837559	−	0.546346i	$-0.816018\pi$
$149$	−6.76391e7	−1.67512	−0.837559	+	0.546346i	$0.816018\pi$
$150$	7.72553e6	0.186900
$151$	4.31830e7	1.02069	0.510345	−	0.859970i	$-0.329518\pi$
$151$	4.31830e7	1.02069	0.510345	+	0.859970i	$0.329518\pi$
$152$	2.72300e6	0.0628919
$153$	2.65848e7	0.600085
$154$	5.32664e6	0.117525
$155$	−2.03888e7	−0.439775
$156$	2.79757e6	0.0589990
$157$	4.62920e7	0.954679	0.477340	−	0.878719i	$-0.341601\pi$
$157$	4.62920e7	0.954679	0.477340	+	0.878719i	$0.341601\pi$
$158$	3.62515e7	0.731183
$159$	1.44392e7	0.284875
$160$	3.56968e7	0.688985
$161$	−6.40883e7	−1.21029
$162$	−3.64236e6	−0.0673101
$163$	7.22501e7	1.30672	0.653359	−	0.757048i	$-0.273359\pi$
$163$	7.22501e7	1.30672	0.653359	+	0.757048i	$0.273359\pi$
$164$	2.82253e7	0.499672
$165$	−5.00724e6	−0.0867770
$166$	2.49022e7	0.422532
$167$	3.24667e7	0.539425	0.269713	−	0.962941i	$-0.413071\pi$
$167$	3.24667e7	0.539425	0.269713	+	0.962941i	$0.413071\pi$
$168$	−3.09169e7	−0.503052
$169$	−6.11133e7	−0.973940
$170$	4.76702e7	0.744175
$171$	1.38563e6	0.0211914
$172$	−2.46150e7	−0.368851
$173$	1.31381e7	0.192918	0.0964589	−	0.995337i	$-0.469248\pi$
$173$	1.31381e7	0.192918	0.0964589	+	0.995337i	$0.469248\pi$
$174$	3.72576e7	0.536158
$175$	3.33687e7	0.470659
$176$	537306.	0.00742895
$177$	−5.54523e6	−0.0751646
$178$	9.21409e6	0.122457
$179$	−1.99708e7	−0.260261	−0.130131	−	0.991497i	$-0.541540\pi$
$179$	−1.99708e7	−0.260261	−0.130131	+	0.991497i	$0.541540\pi$
$180$	1.12659e7	0.143983
$181$	9.38499e7	1.17641	0.588205	−	0.808712i	$-0.299835\pi$
$181$	9.38499e7	1.17641	0.588205	+	0.808712i	$0.299835\pi$
$182$	−7.00524e6	−0.0861337
$183$	−5.78740e7	−0.698080
$184$	1.14869e8	1.35938
$185$	4.70025e7	0.545783
$186$	−1.97820e7	−0.225411
$187$	3.54591e7	0.396535
$188$	−9.09298e7	−0.998053
$189$	−1.57324e7	−0.169503
$190$	2.48462e6	0.0262798
$191$	−7.50591e7	−0.779447	−0.389724	−	0.920932i	$-0.627429\pi$
$191$	−7.50591e7	−0.779447	−0.389724	+	0.920932i	$0.627429\pi$
$192$	3.27247e7	0.333674
$193$	−7.13691e7	−0.714594	−0.357297	−	0.933991i	$-0.616302\pi$
$193$	−7.13691e7	−0.714594	−0.357297	+	0.933991i	$0.616302\pi$
$194$	−1.91253e7	−0.188062
$195$	6.58519e6	0.0635985
$196$	1.49641e7	0.141956
$197$	−1.40656e8	−1.31077	−0.655384	−	0.755296i	$-0.727493\pi$
$197$	−1.40656e8	−1.31077	−0.655384	+	0.755296i	$0.727493\pi$
$198$	−4.85822e6	−0.0444784
$199$	2.79140e7	0.251094	0.125547	−	0.992088i	$-0.459931\pi$
$199$	2.79140e7	0.251094	0.125547	+	0.992088i	$0.459931\pi$
$200$	−5.98088e7	−0.528640
$201$	−4.27767e6	−0.0371553
$202$	9.82931e7	0.839060
$203$	1.60926e8	1.35018
$204$	−7.97801e7	−0.657944
$205$	6.64394e7	0.538626
$206$	−1.11559e7	−0.0889140
$207$	5.84525e7	0.458043
$208$	−706629.	−0.00544465
$209$	1.84816e6	0.0140032
$210$	−2.82103e7	−0.210204
$211$	1.66531e8	1.22041	0.610207	−	0.792242i	$-0.291086\pi$
$211$	1.66531e8	1.22041	0.610207	+	0.792242i	$0.291086\pi$
$212$	−4.33317e7	−0.312342
$213$	−1.06635e8	−0.756087
$214$	5.38969e7	0.375937
$215$	−5.79412e7	−0.397606
$216$	2.81981e7	0.190385
$217$	−8.54439e7	−0.567639
$218$	−1.80910e7	−0.118268
$219$	8.79775e7	0.566001
$220$	1.50266e7	0.0951438
$221$	−4.66334e7	−0.290619
$222$	4.56037e7	0.279746
$223$	8.94297e6	0.0540026	0.0270013	−	0.999635i	$-0.491404\pi$
$223$	8.94297e6	0.0540026	0.0270013	+	0.999635i	$0.491404\pi$
$224$	1.49596e8	0.889308
$225$	−3.04344e7	−0.178125
$226$	1.99751e8	1.15109
$227$	−6.88172e7	−0.390487	−0.195243	−	0.980755i	$-0.562550\pi$
$227$	−6.88172e7	−0.390487	−0.195243	+	0.980755i	$0.562550\pi$
$228$	−4.15822e6	−0.0232346
$229$	1.97507e8	1.08682	0.543411	−	0.839467i	$-0.317132\pi$
$229$	1.97507e8	1.08682	0.543411	+	0.839467i	$0.317132\pi$
$230$	1.04813e8	0.568027
$231$	−2.09840e7	−0.112007
$232$	−2.88438e8	−1.51651
$233$	2.46365e8	1.27595	0.637973	−	0.770058i	$-0.279773\pi$
$233$	2.46365e8	1.27595	0.637973	+	0.770058i	$0.279773\pi$
$234$	6.38921e6	0.0325981
$235$	−2.14039e8	−1.07586
$236$	1.66411e7	0.0824118
$237$	−1.42811e8	−0.696855
$238$	1.99773e8	0.960545
$239$	−3.78259e8	−1.79224	−0.896120	−	0.443812i	$-0.853626\pi$
$239$	−3.78259e8	−1.79224	−0.896120	+	0.443812i	$0.853626\pi$
$240$	−2.84562e6	−0.0132873
$241$	−2.71983e8	−1.25165	−0.625824	−	0.779964i	$-0.715237\pi$
$241$	−2.71983e8	−1.25165	−0.625824	+	0.779964i	$0.715237\pi$
$242$	1.27080e8	0.576400
$243$	1.43489e7	0.0641500
$244$	1.73678e8	0.765387
$245$	3.52239e7	0.153023
$246$	6.44622e7	0.276078
$247$	−2.43058e6	−0.0102629
$248$	1.53146e8	0.637567
$249$	−9.81010e7	−0.402695
$250$	−1.56698e8	−0.634268
$251$	1.67816e8	0.669847	0.334923	−	0.942245i	$-0.391290\pi$
$251$	1.67816e8	0.669847	0.334923	+	0.942245i	$0.391290\pi$
$252$	4.72124e7	0.185846
$253$	7.79645e7	0.302674
$254$	2.54695e8	0.975221
$255$	−1.87794e8	−0.709237
$256$	−2.62399e8	−0.977513
$257$	−3.77370e8	−1.38676	−0.693381	−	0.720571i	$-0.743880\pi$
$257$	−3.77370e8	−1.38676	−0.693381	+	0.720571i	$0.743880\pi$
$258$	−5.62169e7	−0.203797
$259$	1.96975e8	0.704470
$260$	−1.97619e7	−0.0697305
$261$	−1.46775e8	−0.510986
$262$	−1.02878e8	−0.353400
$263$	−2.37395e8	−0.804686	−0.402343	−	0.915489i	$-0.631804\pi$
$263$	−2.37395e8	−0.804686	−0.402343	+	0.915489i	$0.631804\pi$
$264$	3.76109e7	0.125806
$265$	−1.01998e8	−0.336692
$266$	1.04124e7	0.0339206
$267$	−3.62985e7	−0.116707
$268$	1.28371e7	0.0407377
$269$	2.56851e8	0.804542	0.402271	−	0.915521i	$-0.368221\pi$
$269$	2.56851e8	0.804542	0.402271	+	0.915521i	$0.368221\pi$
$270$	2.57296e7	0.0795535
$271$	−2.99436e8	−0.913927	−0.456964	−	0.889485i	$-0.651063\pi$
$271$	−2.99436e8	−0.913927	−0.456964	+	0.889485i	$0.651063\pi$
$272$	2.01514e7	0.0607176
$273$	2.75968e7	0.0820898
$274$	−1.20150e8	−0.352855
$275$	−4.05937e7	−0.117705
$276$	−1.75414e8	−0.502207
$277$	−1.07342e8	−0.303453	−0.151727	−	0.988422i	$-0.548483\pi$
$277$	−1.07342e8	−0.303453	−0.151727	+	0.988422i	$0.548483\pi$
$278$	8.01006e7	0.223604
$279$	7.79302e7	0.214828
$280$	2.18396e8	0.594555
$281$	1.26999e8	0.341451	0.170726	−	0.985319i	$-0.445389\pi$
$281$	1.26999e8	0.341451	0.170726	+	0.985319i	$0.445389\pi$
$282$	−2.07669e8	−0.551443
$283$	6.79420e8	1.78191	0.890955	−	0.454091i	$-0.150036\pi$
$283$	6.79420e8	1.78191	0.890955	+	0.454091i	$0.150036\pi$
$284$	3.20009e8	0.828986
$285$	−9.78802e6	−0.0250460
$286$	8.52200e6	0.0215407
$287$	2.78430e8	0.695232
$288$	−1.36441e8	−0.336566
$289$	9.19537e8	2.24092
$290$	−2.63187e8	−0.633682
$291$	7.53431e7	0.179233
$292$	−2.64018e8	−0.620573
$293$	3.54246e8	0.822752	0.411376	−	0.911466i	$-0.365048\pi$
$293$	3.54246e8	0.822752	0.411376	+	0.911466i	$0.365048\pi$
$294$	3.41756e7	0.0784333
$295$	3.91714e7	0.0888366
$296$	−3.53051e8	−0.791254
$297$	1.91387e7	0.0423902
$298$	4.63581e8	1.01477
$299$	−1.02534e8	−0.221829
$300$	9.13325e7	0.195300
$301$	−2.42816e8	−0.513210
$302$	−2.95966e8	−0.618325
$303$	−3.87221e8	−0.799667
$304$	1.05031e6	0.00214418
$305$	4.08821e8	0.825056
$306$	−1.82205e8	−0.363527
$307$	−4.47178e8	−0.882056	−0.441028	−	0.897493i	$-0.645386\pi$
$307$	−4.47178e8	−0.882056	−0.441028	+	0.897493i	$0.645386\pi$
$308$	6.29724e7	0.122807
$309$	4.39482e7	0.0847396
$310$	1.39739e8	0.266412
$311$	−1.03177e9	−1.94501	−0.972506	−	0.232879i	$-0.925185\pi$
$311$	−1.03177e9	−1.94501	−0.972506	+	0.232879i	$0.925185\pi$
$312$	−4.94634e7	−0.0922026
$313$	−1.47667e8	−0.272194	−0.136097	−	0.990695i	$-0.543456\pi$
$313$	−1.47667e8	−0.272194	−0.136097	+	0.990695i	$0.543456\pi$
$314$	−3.17274e8	−0.578336
$315$	1.11133e8	0.200335
$316$	4.28571e8	0.764044
$317$	−8.08129e8	−1.42486	−0.712431	−	0.701742i	$-0.752406\pi$
$317$	−8.08129e8	−1.42486	−0.712431	+	0.701742i	$0.752406\pi$
$318$	−9.89629e7	−0.172575
$319$	−1.95769e8	−0.337658
$320$	−2.31167e8	−0.394367
$321$	−2.12324e8	−0.358288
$322$	4.39245e8	0.733181
$323$	6.93145e7	0.114450
$324$	−4.30606e7	−0.0703352
$325$	5.33861e7	0.0862654
$326$	−4.95184e8	−0.791599
$327$	7.12687e7	0.112715
$328$	−4.99047e8	−0.780878
$329$	−8.96983e8	−1.38867
$330$	3.43184e7	0.0525688
$331$	−1.71934e8	−0.260594	−0.130297	−	0.991475i	$-0.541593\pi$
$331$	−1.71934e8	−0.260594	−0.130297	+	0.991475i	$0.541593\pi$
$332$	2.94398e8	0.441521
$333$	−1.79654e8	−0.266613
$334$	−2.22519e8	−0.326779
$335$	3.02173e7	0.0439136
$336$	−1.19252e7	−0.0171506
$337$	2.64986e8	0.377154	0.188577	−	0.982058i	$-0.439613\pi$
$337$	2.64986e8	0.377154	0.188577	+	0.982058i	$0.439613\pi$
$338$	4.18855e8	0.590004
$339$	−7.86911e8	−1.09705
$340$	5.63565e8	0.777620
$341$	1.03944e8	0.141958
$342$	−9.49673e6	−0.0128376
$343$	8.05862e8	1.07828
$344$	4.35215e8	0.576433
$345$	−4.12907e8	−0.541359
$346$	−9.00455e7	−0.116868
$347$	5.14421e8	0.660945	0.330473	−	0.943816i	$-0.392792\pi$
$347$	5.14421e8	0.660945	0.330473	+	0.943816i	$0.392792\pi$
$348$	4.40466e8	0.560254
$349$	−6.09218e7	−0.0767157	−0.0383578	−	0.999264i	$-0.512213\pi$
$349$	−6.09218e7	−0.0767157	−0.0383578	+	0.999264i	$0.512213\pi$
$350$	−2.28701e8	−0.285121
$351$	−2.51700e7	−0.0310676
$352$	−1.81986e8	−0.222402
$353$	−1.90611e8	−0.230641	−0.115320	−	0.993328i	$-0.536789\pi$
$353$	−1.90611e8	−0.230641	−0.115320	+	0.993328i	$0.536789\pi$
$354$	3.80056e7	0.0455341
$355$	7.53268e8	0.893614
$356$	1.08931e8	0.127960
$357$	−7.86996e8	−0.915448
$358$	1.36875e8	0.157664
$359$	−1.39955e9	−1.59646	−0.798229	−	0.602354i	$-0.794230\pi$
$359$	−1.39955e9	−1.59646	−0.798229	+	0.602354i	$0.794230\pi$
$360$	−1.99191e8	−0.225014
$361$	−8.90259e8	−0.995958
$362$	−6.43224e8	−0.712659
$363$	−5.00626e8	−0.549339
$364$	−8.28171e7	−0.0900047
$365$	−6.21471e8	−0.668953
$366$	3.96654e8	0.422891
$367$	−1.50266e9	−1.58683	−0.793413	−	0.608684i	$-0.791698\pi$
$367$	−1.50266e9	−1.58683	−0.793413	+	0.608684i	$0.791698\pi$
$368$	4.43073e7	0.0463455
$369$	−2.53946e8	−0.263117
$370$	−3.22143e8	−0.330631
$371$	−4.27449e8	−0.434585
$372$	−2.33866e8	−0.235541
$373$	8.89561e7	0.0887554	0.0443777	−	0.999015i	$-0.485869\pi$
$373$	8.89561e7	0.0887554	0.0443777	+	0.999015i	$0.485869\pi$
$374$	−2.43027e8	−0.240218
$375$	6.17303e8	0.604490
$376$	1.60772e9	1.55974
$377$	2.57463e8	0.247469
$378$	1.07826e8	0.102684
$379$	−7.27075e8	−0.686028	−0.343014	−	0.939330i	$-0.611448\pi$
$379$	−7.27075e8	−0.686028	−0.343014	+	0.939330i	$0.611448\pi$
$380$	2.93736e7	0.0274608
$381$	−1.00336e9	−0.929436
$382$	5.14436e8	0.472182
$383$	2.06745e9	1.88036	0.940178	−	0.340683i	$-0.110658\pi$
$383$	2.06745e9	1.88036	0.940178	+	0.340683i	$0.110658\pi$
$384$	4.22544e8	0.380813
$385$	1.48231e8	0.132381
$386$	4.89145e8	0.432895
$387$	2.21464e8	0.194229
$388$	−2.26102e8	−0.196514
$389$	−8.24531e7	−0.0710205	−0.0355102	−	0.999369i	$-0.511306\pi$
$389$	−8.24531e7	−0.0710205	−0.0355102	+	0.999369i	$0.511306\pi$
$390$	−4.51332e7	−0.0385274
$391$	2.92402e9	2.47379
$392$	−2.64578e8	−0.221846
$393$	4.05281e8	0.336808
$394$	9.64019e8	0.794051
$395$	1.00881e9	0.823609
$396$	−5.74347e7	−0.0464774
$397$	2.60792e8	0.209183	0.104592	−	0.994515i	$-0.466646\pi$
$397$	2.60792e8	0.209183	0.104592	+	0.994515i	$0.466646\pi$
$398$	−1.91316e8	−0.152111
$399$	−4.10190e7	−0.0323281
$400$	−2.30694e7	−0.0180230
$401$	−5.57165e8	−0.431498	−0.215749	−	0.976449i	$-0.569219\pi$
$401$	−5.57165e8	−0.431498	−0.215749	+	0.976449i	$0.569219\pi$
$402$	2.93180e7	0.0225084
$403$	−1.36700e8	−0.104040
$404$	1.16204e9	0.876769
$405$	−1.01360e8	−0.0758185
$406$	−1.10295e9	−0.817925
$407$	−2.39624e8	−0.176177
$408$	1.41058e9	1.02822
$409$	−1.59001e9	−1.14913	−0.574564	−	0.818460i	$-0.694828\pi$
$409$	−1.59001e9	−1.14913	−0.574564	+	0.818460i	$0.694828\pi$
$410$	−4.55359e8	−0.326295
$411$	4.73325e8	0.336289
$412$	−1.31887e8	−0.0929100
$413$	1.64157e8	0.114666
$414$	−4.00618e8	−0.277479
$415$	6.92983e8	0.475942
$416$	2.39336e8	0.162998
$417$	−3.15552e8	−0.213106
$418$	−1.26668e7	−0.00848303
$419$	5.88021e8	0.390520	0.195260	−	0.980751i	$-0.437445\pi$
$419$	5.88021e8	0.390520	0.195260	+	0.980751i	$0.437445\pi$
$420$	−3.33507e8	−0.219651
$421$	−7.50924e8	−0.490466	−0.245233	−	0.969464i	$-0.578864\pi$
$421$	−7.50924e8	−0.490466	−0.245233	+	0.969464i	$0.578864\pi$
$422$	−1.14136e9	−0.739316
$423$	8.18104e8	0.525554
$424$	7.66142e8	0.488123
$425$	−1.52245e9	−0.962013
$426$	7.30850e8	0.458031
$427$	1.71326e9	1.06494
$428$	6.37178e8	0.392833
$429$	−3.35720e7	−0.0205294
$430$	3.97114e8	0.240866
$431$	−2.36435e9	−1.42247	−0.711233	−	0.702957i	$-0.751863\pi$
$431$	−2.36435e9	−1.42247	−0.711233	+	0.702957i	$0.751863\pi$
$432$	1.08766e7	0.00649080
$433$	6.97398e7	0.0412832	0.0206416	−	0.999787i	$-0.493429\pi$
$433$	6.97398e7	0.0412832	0.0206416	+	0.999787i	$0.493429\pi$
$434$	5.85611e8	0.343871
$435$	1.03681e9	0.603931
$436$	−2.13875e8	−0.123583
$437$	1.52403e8	0.0873592
$438$	−6.02975e8	−0.342878
$439$	−2.54774e9	−1.43724	−0.718620	−	0.695403i	$-0.755226\pi$
$439$	−2.54774e9	−1.43724	−0.718620	+	0.695403i	$0.755226\pi$
$440$	−2.65683e8	−0.148689
$441$	−1.34633e8	−0.0747510
$442$	3.19614e8	0.176055
$443$	1.15431e9	0.630825	0.315412	−	0.948955i	$-0.397857\pi$
$443$	1.15431e9	0.630825	0.315412	+	0.948955i	$0.397857\pi$
$444$	5.39135e8	0.292319
$445$	2.56411e8	0.137936
$446$	−6.12929e7	−0.0327143
$447$	−1.82625e9	−0.967130
$448$	−9.68759e8	−0.509029
$449$	5.55994e8	0.289873	0.144937	−	0.989441i	$-0.453702\pi$
$449$	5.55994e8	0.289873	0.144937	+	0.989441i	$0.453702\pi$
$450$	2.08589e8	0.107907
$451$	−3.38715e8	−0.173867
$452$	2.36150e9	1.20283
$453$	1.16594e9	0.589296
$454$	4.71655e8	0.236554
$455$	−1.94943e8	−0.0970215
$456$	7.35209e7	0.0363106
$457$	3.93559e8	0.192887	0.0964435	−	0.995338i	$-0.469253\pi$
$457$	3.93559e8	0.192887	0.0964435	+	0.995338i	$0.469253\pi$
$458$	−1.35366e9	−0.658388
$459$	7.17789e8	0.346460
$460$	1.23912e9	0.593555
$461$	−2.99382e9	−1.42322	−0.711611	−	0.702574i	$-0.752034\pi$
$461$	−2.99382e9	−1.42322	−0.711611	+	0.702574i	$0.752034\pi$
$462$	1.43819e8	0.0678531
$463$	−1.18369e9	−0.554248	−0.277124	−	0.960834i	$-0.589381\pi$
$463$	−1.18369e9	−0.554248	−0.277124	+	0.960834i	$0.589381\pi$
$464$	−1.11256e8	−0.0517023
$465$	−5.50497e8	−0.253904
$466$	−1.68852e9	−0.772957
$467$	3.15650e9	1.43416	0.717079	−	0.696992i	$-0.245479\pi$
$467$	3.15650e9	1.43416	0.717079	+	0.696992i	$0.245479\pi$
$468$	7.55343e7	0.0340631
$469$	1.26633e8	0.0566815
$470$	1.46697e9	0.651747
$471$	1.24988e9	0.551184
$472$	−2.94228e8	−0.128792
$473$	2.95390e8	0.128346
$474$	9.78791e8	0.422149
$475$	−7.93515e7	−0.0339725
$476$	2.36175e9	1.00371
$477$	3.89860e8	0.164473
$478$	2.59249e9	1.08572
$479$	2.27050e9	0.943945	0.471972	−	0.881613i	$-0.343542\pi$
$479$	2.27050e9	0.943945	0.471972	+	0.881613i	$0.343542\pi$
$480$	9.63815e8	0.397786
$481$	3.15137e8	0.129120
$482$	1.86410e9	0.758238
$483$	−1.73038e9	−0.698759
$484$	1.50236e9	0.602305
$485$	−5.32222e8	−0.211834
$486$	−9.83438e7	−0.0388615
$487$	2.04995e8	0.0804252	0.0402126	−	0.999191i	$-0.487196\pi$
$487$	2.04995e8	0.0804252	0.0402126	+	0.999191i	$0.487196\pi$
$488$	−3.07078e9	−1.19613
$489$	1.95075e9	0.754434
$490$	−2.41416e8	−0.0926999
$491$	1.08333e9	0.413023	0.206512	−	0.978444i	$-0.433789\pi$
$491$	1.08333e9	0.413023	0.206512	+	0.978444i	$0.433789\pi$
$492$	7.62083e8	0.288486
$493$	−7.34224e9	−2.75972
$494$	1.66586e7	0.00621718
$495$	−1.35195e8	−0.0501007
$496$	5.90715e7	0.0217366
$497$	3.15675e9	1.15343
$498$	6.72360e8	0.243949
$499$	1.23774e9	0.445942	0.222971	−	0.974825i	$-0.428425\pi$
$499$	1.23774e9	0.445942	0.222971	+	0.974825i	$0.428425\pi$
$500$	−1.85251e9	−0.662773
$501$	8.76602e8	0.311437
$502$	−1.15017e9	−0.405787
$503$	3.42069e9	1.19847	0.599234	−	0.800574i	$-0.295472\pi$
$503$	3.42069e9	1.19847	0.599234	+	0.800574i	$0.295472\pi$
$504$	−8.34756e8	−0.290437
$505$	2.73532e9	0.945122
$506$	−5.34349e8	−0.183357
$507$	−1.65006e9	−0.562304
$508$	3.01105e9	1.01905
$509$	−3.62806e9	−1.21944	−0.609722	−	0.792616i	$-0.708719\pi$
$509$	−3.62806e9	−1.21944	−0.609722	+	0.792616i	$0.708719\pi$
$510$	1.28709e9	0.429650
$511$	−2.60442e9	−0.863451
$512$	−2.04753e8	−0.0674195
$513$	3.74119e7	0.0122349
$514$	2.58640e9	0.840088
$515$	−3.10449e8	−0.100153
$516$	−6.64605e8	−0.212956
$517$	1.09120e9	0.347285
$518$	−1.35002e9	−0.426762
$519$	3.54730e8	0.111381
$520$	3.49408e8	0.108974
$521$	−1.36162e9	−0.421817	−0.210909	−	0.977506i	$-0.567642\pi$
$521$	−1.36162e9	−0.421817	−0.210909	+	0.977506i	$0.567642\pi$
$522$	1.00596e9	0.309551
$523$	1.07415e9	0.328329	0.164165	−	0.986433i	$-0.447507\pi$
$523$	1.07415e9	0.328329	0.164165	+	0.986433i	$0.447507\pi$
$524$	−1.21624e9	−0.369282
$525$	9.00956e8	0.271735
$526$	1.62705e9	0.487472
$527$	3.89838e9	1.16024
$528$	1.45073e7	0.00428911
$529$	3.02428e9	0.888234
$530$	6.99072e8	0.203965
$531$	−1.49721e8	−0.0433963
$532$	1.23097e8	0.0354451
$533$	4.45456e8	0.127426
$534$	2.48780e8	0.0707004
$535$	1.49985e9	0.423458
$536$	−2.26972e8	−0.0636642
$537$	−5.39211e8	−0.150262
$538$	−1.76039e9	−0.487385
$539$	−1.79575e8	−0.0493953
$540$	3.04179e8	0.0831288
$541$	−6.13348e9	−1.66539	−0.832696	−	0.553730i	$-0.813204\pi$
$541$	−6.13348e9	−1.66539	−0.832696	+	0.553730i	$0.813204\pi$
$542$	2.05226e9	0.553649
$543$	2.53395e9	0.679201
$544$	−6.82531e9	−1.81772
$545$	−5.03440e8	−0.133217
$546$	−1.89141e8	−0.0497293
$547$	−6.39180e9	−1.66981	−0.834906	−	0.550392i	$-0.814478\pi$
$547$	−6.39180e9	−1.66981	−0.834906	+	0.550392i	$0.814478\pi$
$548$	−1.42043e9	−0.368713
$549$	−1.56260e9	−0.403036
$550$	2.78219e8	0.0713045
$551$	−3.82685e8	−0.0974565
$552$	3.10147e9	0.784840
$553$	4.22767e9	1.06307
$554$	7.35697e8	0.183829
$555$	1.26907e9	0.315108
$556$	9.46963e8	0.233653
$557$	5.20568e9	1.27639	0.638197	−	0.769873i	$-0.279681\pi$
$557$	5.20568e9	1.27639	0.638197	+	0.769873i	$0.279681\pi$
$558$	−5.34114e8	−0.130141
$559$	−3.88478e8	−0.0940643
$560$	8.42396e7	0.0202702
$561$	9.57395e8	0.228940
$562$	−8.70420e8	−0.206848
$563$	3.32429e9	0.785089	0.392545	−	0.919733i	$-0.371595\pi$
$563$	3.32429e9	0.785089	0.392545	+	0.919733i	$0.371595\pi$
$564$	−2.45510e9	−0.576226
$565$	5.55872e9	1.29660
$566$	−4.65657e9	−1.07947
$567$	−4.24774e8	−0.0978628
$568$	−5.65803e9	−1.29553
$569$	1.61858e9	0.368333	0.184166	−	0.982895i	$-0.441041\pi$
$569$	1.61858e9	0.368333	0.184166	+	0.982895i	$0.441041\pi$
$570$	6.70846e7	0.0151726
$571$	−6.26853e8	−0.140909	−0.0704546	−	0.997515i	$-0.522445\pi$
$571$	−6.26853e8	−0.140909	−0.0704546	+	0.997515i	$0.522445\pi$
$572$	1.00749e8	0.0225088
$573$	−2.02660e9	−0.450014
$574$	−1.90829e9	−0.421165
$575$	−3.34743e9	−0.734302
$576$	8.83568e8	0.192647
$577$	2.33845e9	0.506772	0.253386	−	0.967365i	$-0.418456\pi$
$577$	2.33845e9	0.506772	0.253386	+	0.967365i	$0.418456\pi$
$578$	−6.30228e9	−1.35753
$579$	−1.92696e9	−0.412571
$580$	−3.11144e9	−0.662161
$581$	2.90411e9	0.614323
$582$	−5.16382e8	−0.108578
$583$	5.19999e8	0.108683
$584$	4.66806e9	0.969820
$585$	1.77800e8	0.0367186
$586$	−2.42791e9	−0.498416
$587$	−5.68734e9	−1.16058	−0.580291	−	0.814409i	$-0.697061\pi$
$587$	−5.68734e9	−1.16058	−0.580291	+	0.814409i	$0.697061\pi$
$588$	4.04030e8	0.0819583
$589$	2.03187e8	0.0409725
$590$	−2.68471e8	−0.0538164
$591$	−3.79770e9	−0.756772
$592$	−1.36178e8	−0.0269763
$593$	−6.92748e9	−1.36422	−0.682109	−	0.731250i	$-0.738937\pi$
$593$	−6.92748e9	−1.36422	−0.682109	+	0.731250i	$0.738937\pi$
$594$	−1.31172e8	−0.0256796
$595$	5.55932e9	1.08196
$596$	5.48053e9	1.06038
$597$	7.53679e8	0.144969
$598$	7.02741e8	0.134382
$599$	1.04577e7	0.00198812	0.000994062	−	1.00000i	$-0.499684\pi$
$599$	1.04577e7	0.00198812	0.000994062		1.00000i	$0.499684\pi$
$600$	−1.61484e9	−0.305211
$601$	5.50968e9	1.03530	0.517649	−	0.855593i	$-0.326807\pi$
$601$	5.50968e9	1.03530	0.517649	+	0.855593i	$0.326807\pi$
$602$	1.66420e9	0.310898
$603$	−1.15497e8	−0.0214516
$604$	−3.49896e9	−0.646114
$605$	3.53641e9	0.649260
$606$	2.65391e9	0.484432
$607$	−1.08515e10	−1.96939	−0.984693	−	0.174298i	$-0.944234\pi$
$607$	−1.08515e10	−1.96939	−0.984693	+	0.174298i	$0.944234\pi$
$608$	−3.55742e8	−0.0641908
$609$	4.34500e9	0.779524
$610$	−2.80195e9	−0.499812
$611$	−1.43507e9	−0.254524
$612$	−2.15406e9	−0.379864
$613$	−5.00263e9	−0.877177	−0.438588	−	0.898688i	$-0.644521\pi$
$613$	−5.00263e9	−0.877177	−0.438588	+	0.898688i	$0.644521\pi$
$614$	3.06485e9	0.534342
$615$	1.79386e9	0.310976
$616$	−1.11341e9	−0.191920
$617$	1.47593e9	0.252970	0.126485	−	0.991969i	$-0.459630\pi$
$617$	1.47593e9	0.252970	0.126485	+	0.991969i	$0.459630\pi$
$618$	−3.01210e8	−0.0513345
$619$	−9.36559e9	−1.58715	−0.793575	−	0.608472i	$-0.791783\pi$
$619$	−9.36559e9	−1.58715	−0.793575	+	0.608472i	$0.791783\pi$
$620$	1.65202e9	0.278385
$621$	1.57822e9	0.264452
$622$	7.07150e9	1.17827
$623$	1.07455e9	0.178041
$624$	−1.90790e7	−0.00314347
$625$	−1.09904e9	−0.180067
$626$	1.01207e9	0.164893
$627$	4.99004e7	0.00808477
$628$	−3.75087e9	−0.604328
$629$	−8.98698e9	−1.43991
$630$	−7.61679e8	−0.121361
$631$	−1.19966e10	−1.90088	−0.950438	−	0.310914i	$-0.899365\pi$
$631$	−1.19966e10	−1.90088	−0.950438	+	0.310914i	$0.899365\pi$
$632$	−7.57751e9	−1.19403
$633$	4.49634e9	0.704606
$634$	5.53871e9	0.863170
$635$	7.08771e9	1.09849
$636$	−1.16996e9	−0.180331
$637$	2.36165e8	0.0362016
$638$	1.34175e9	0.204551
$639$	−2.87915e9	−0.436527
$640$	−2.98484e9	−0.450081
$641$	−1.25626e10	−1.88398	−0.941989	−	0.335644i	$-0.891046\pi$
$641$	−1.25626e10	−1.88398	−0.941989	+	0.335644i	$0.891046\pi$
$642$	1.45522e9	0.217047
$643$	−4.11211e9	−0.609995	−0.304997	−	0.952353i	$-0.598656\pi$
$643$	−4.11211e9	−0.609995	−0.304997	+	0.952353i	$0.598656\pi$
$644$	5.19283e9	0.766131
$645$	−1.56441e9	−0.229558
$646$	−4.75064e8	−0.0693327
$647$	−8.36038e9	−1.21356	−0.606780	−	0.794870i	$-0.707539\pi$
$647$	−8.36038e9	−1.21356	−0.606780	+	0.794870i	$0.707539\pi$
$648$	7.61349e8	0.109919
$649$	−1.99700e8	−0.0286762
$650$	−3.65895e8	−0.0522588
$651$	−2.30699e9	−0.327727
$652$	−5.85415e9	−0.827175
$653$	5.92578e8	0.0832817	0.0416409	−	0.999133i	$-0.486741\pi$
$653$	5.92578e8	0.0832817	0.0416409	+	0.999133i	$0.486741\pi$
$654$	−4.88458e8	−0.0682818
$655$	−2.86290e9	−0.398072
$656$	−1.92492e8	−0.0266225
$657$	2.37539e9	0.326781
$658$	6.14769e9	0.841243
$659$	3.61916e9	0.492617	0.246308	−	0.969192i	$-0.420782\pi$
$659$	3.61916e9	0.492617	0.246308	+	0.969192i	$0.420782\pi$
$660$	4.05717e8	0.0549313
$661$	1.49686e9	0.201593	0.100797	−	0.994907i	$-0.467861\pi$
$661$	1.49686e9	0.201593	0.100797	+	0.994907i	$0.467861\pi$
$662$	1.17839e9	0.157866
$663$	−1.25910e9	−0.167789
$664$	−5.20521e9	−0.690002
$665$	2.89757e8	0.0382084
$666$	1.23130e9	0.161512
$667$	−1.61435e10	−2.10648
$668$	−2.63066e9	−0.341465
$669$	2.41460e8	0.0311784
$670$	−2.07102e8	−0.0266025
$671$	−2.08421e9	−0.266326
$672$	4.03909e9	0.513442
$673$	1.55009e10	1.96022	0.980109	−	0.198461i	$-0.0635943\pi$
$673$	1.55009e10	1.96022	0.980109	+	0.198461i	$0.0635943\pi$
$674$	−1.81615e9	−0.228476
$675$	−8.21728e8	−0.102841
$676$	4.95177e9	0.616520
$677$	−7.97429e9	−0.987715	−0.493857	−	0.869543i	$-0.664414\pi$
$677$	−7.97429e9	−0.987715	−0.493857	+	0.869543i	$0.664414\pi$
$678$	5.39329e9	0.664584
$679$	−2.23040e9	−0.273425
$680$	−9.96431e9	−1.21525
$681$	−1.85806e9	−0.225448
$682$	−7.12407e8	−0.0859969
$683$	7.37364e9	0.885542	0.442771	−	0.896635i	$-0.353995\pi$
$683$	7.37364e9	0.885542	0.442771	+	0.896635i	$0.353995\pi$
$684$	−1.12272e8	−0.0134145
$685$	−3.34356e9	−0.397458
$686$	−5.52317e9	−0.653212
$687$	5.33269e9	0.627477
$688$	1.67871e8	0.0196524
$689$	−6.83868e8	−0.0796535
$690$	2.82996e9	0.327951
$691$	5.70889e9	0.658232	0.329116	−	0.944290i	$-0.393249\pi$
$691$	5.70889e9	0.658232	0.329116	+	0.944290i	$0.393249\pi$
$692$	−1.06453e9	−0.122120
$693$	−5.66569e8	−0.0646675
$694$	−3.52571e9	−0.400395
$695$	2.22905e9	0.251868
$696$	−7.78781e9	−0.875555
$697$	−1.27034e10	−1.42103
$698$	4.17543e8	0.0464737
$699$	6.65184e9	0.736668
$700$	−2.70374e9	−0.297935
$701$	1.23928e10	1.35880	0.679402	−	0.733767i	$-0.262239\pi$
$701$	1.23928e10	1.35880	0.679402	+	0.733767i	$0.262239\pi$
$702$	1.72509e8	0.0188205
$703$	−4.68410e8	−0.0508491
$704$	1.17851e9	0.127300
$705$	−5.77906e9	−0.621149
$706$	1.30640e9	0.139720
$707$	1.14630e10	1.21992
$708$	4.49309e8	0.0475805
$709$	1.39979e10	1.47504	0.737518	−	0.675328i	$-0.235998\pi$
$709$	1.39979e10	1.47504	0.737518	+	0.675328i	$0.235998\pi$
$710$	−5.16271e9	−0.541344
$711$	−3.85590e9	−0.402330
$712$	−1.92599e9	−0.199974
$713$	8.57143e9	0.885605
$714$	5.39387e9	0.554571
$715$	2.37152e8	0.0242636
$716$	1.61815e9	0.164750
$717$	−1.02130e10	−1.03475
$718$	9.59215e9	0.967120
$719$	7.66012e9	0.768572	0.384286	−	0.923214i	$-0.374448\pi$
$719$	7.66012e9	0.768572	0.384286	+	0.923214i	$0.374448\pi$
$720$	−7.68317e7	−0.00767144
$721$	−1.30101e9	−0.129273
$722$	6.10161e9	0.603343
$723$	−7.34354e9	−0.722639
$724$	−7.60430e9	−0.744688
$725$	8.40543e9	0.819175
$726$	3.43116e9	0.332785
$727$	1.02618e10	0.990493	0.495247	−	0.868752i	$-0.335078\pi$
$727$	1.02618e10	0.990493	0.495247	+	0.868752i	$0.335078\pi$
$728$	1.46428e9	0.140658
$729$	3.87420e8	0.0370370
$730$	4.25940e9	0.405246
$731$	1.10785e10	1.04899
$732$	4.68931e9	0.441896
$733$	−1.67714e10	−1.57292	−0.786459	−	0.617643i	$-0.788088\pi$
$733$	−1.67714e10	−1.57292	−0.786459	+	0.617643i	$0.788088\pi$
$734$	1.02988e10	0.961285
$735$	9.51045e8	0.0883477
$736$	−1.50069e10	−1.38746
$737$	−1.54051e8	−0.0141752
$738$	1.74048e9	0.159394
$739$	5.49527e9	0.500880	0.250440	−	0.968132i	$-0.419425\pi$
$739$	5.49527e9	0.500880	0.250440	+	0.968132i	$0.419425\pi$
$740$	−3.80843e9	−0.345490
$741$	−6.56257e7	−0.00592530
$742$	2.92962e9	0.263268
$743$	−1.77986e9	−0.159193	−0.0795966	−	0.996827i	$-0.525363\pi$
$743$	−1.77986e9	−0.159193	−0.0795966	+	0.996827i	$0.525363\pi$
$744$	4.13495e9	0.368100
$745$	1.29006e10	1.14305
$746$	−6.09683e8	−0.0537673
$747$	−2.64873e9	−0.232496
$748$	−2.87311e9	−0.251013
$749$	6.28548e9	0.546578
$750$	−4.23084e9	−0.366195
$751$	−7.12062e9	−0.613448	−0.306724	−	0.951798i	$-0.599233\pi$
$751$	−7.12062e9	−0.613448	−0.306724	+	0.951798i	$0.599233\pi$
$752$	6.20127e8	0.0531763
$753$	4.53103e9	0.386736
$754$	−1.76459e9	−0.149914
$755$	−8.23619e9	−0.696485
$756$	1.27473e9	0.107298
$757$	6.43143e9	0.538855	0.269428	−	0.963021i	$-0.413166\pi$
$757$	6.43143e9	0.538855	0.269428	+	0.963021i	$0.413166\pi$
$758$	4.98319e9	0.415590
$759$	2.10504e9	0.174749
$760$	−5.19350e8	−0.0429153
$761$	1.46912e10	1.20840	0.604202	−	0.796831i	$-0.293492\pi$
$761$	1.46912e10	1.20840	0.604202	+	0.796831i	$0.293492\pi$
$762$	6.87678e9	0.563044
$763$	−2.10979e9	−0.171950
$764$	6.08175e9	0.493403
$765$	−5.07044e9	−0.409478
$766$	−1.41698e10	−1.13910
$767$	2.62632e8	0.0210167
$768$	−7.08477e9	−0.564367
$769$	1.24049e10	0.983677	0.491838	−	0.870687i	$-0.336325\pi$
$769$	1.24049e10	0.983677	0.491838	+	0.870687i	$0.336325\pi$
$770$	−1.01594e9	−0.0801952
$771$	−1.01890e10	−0.800647
$772$	5.78276e9	0.452350
$773$	−2.65186e9	−0.206501	−0.103250	−	0.994655i	$-0.532924\pi$
$773$	−2.65186e9	−0.206501	−0.103250	+	0.994655i	$0.532924\pi$
$774$	−1.51786e9	−0.117662
$775$	−4.46287e9	−0.344396
$776$	3.99768e9	0.307109
$777$	5.31833e9	0.406726
$778$	5.65113e8	0.0430236
$779$	−6.62112e8	−0.0501823
$780$	−5.33573e8	−0.0402590
$781$	−3.84024e9	−0.288456
$782$	−2.00405e10	−1.49860
$783$	−3.96291e9	−0.295018
$784$	−1.02053e8	−0.00756342
$785$	−8.82916e9	−0.651441
$786$	−2.77770e9	−0.204036
$787$	−4.05957e9	−0.296871	−0.148436	−	0.988922i	$-0.547424\pi$
$787$	−4.05957e9	−0.296871	−0.148436	+	0.988922i	$0.547424\pi$
$788$	1.13968e10	0.829738
$789$	−6.40967e9	−0.464586
$790$	−6.91415e9	−0.498935
$791$	2.32951e10	1.67358
$792$	1.01550e9	0.0726340
$793$	2.74102e9	0.195189
$794$	−1.78740e9	−0.126721
$795$	−2.75396e9	−0.194389
$796$	−2.26177e9	−0.158947
$797$	2.36833e10	1.65706	0.828530	−	0.559944i	$-0.189177\pi$
$797$	2.36833e10	1.65706	0.828530	+	0.559944i	$0.189177\pi$
$798$	2.81134e8	0.0195841
$799$	4.09248e10	2.83839
$800$	7.81364e9	0.539558
$801$	−9.80058e8	−0.0673811
$802$	3.81867e9	0.261398
$803$	3.16832e9	0.215936
$804$	3.46603e8	0.0235199
$805$	1.22234e10	0.825859
$806$	9.36910e8	0.0630268
$807$	6.93499e9	0.464503
$808$	−2.05458e10	−1.37020
$809$	−9.66394e9	−0.641704	−0.320852	−	0.947129i	$-0.603969\pi$
$809$	−9.66394e9	−0.641704	−0.320852	+	0.947129i	$0.603969\pi$
$810$	6.94698e8	0.0459302
$811$	1.27359e10	0.838413	0.419207	−	0.907891i	$-0.362308\pi$
$811$	1.27359e10	0.838413	0.419207	+	0.907891i	$0.362308\pi$
$812$	−1.30392e10	−0.854684
$813$	−8.08477e9	−0.527656
$814$	1.64232e9	0.106727
$815$	−1.37801e10	−0.891661
$816$	5.44088e8	0.0350553
$817$	5.77422e8	0.0370438
$818$	1.08975e10	0.696132
$819$	7.45113e8	0.0473946
$820$	−5.38333e9	−0.340959
$821$	1.18429e10	0.746893	0.373446	−	0.927652i	$-0.378176\pi$
$821$	1.18429e10	0.746893	0.373446	+	0.927652i	$0.378176\pi$
$822$	−3.24405e9	−0.203721
$823$	1.12076e10	0.700829	0.350415	−	0.936595i	$-0.386041\pi$
$823$	1.12076e10	0.700829	0.350415	+	0.936595i	$0.386041\pi$
$824$	2.33188e9	0.145198
$825$	−1.09603e9	−0.0679569
$826$	−1.12509e9	−0.0694636
$827$	−1.69838e10	−1.04416	−0.522078	−	0.852898i	$-0.674843\pi$
$827$	−1.69838e10	−1.04416	−0.522078	+	0.852898i	$0.674843\pi$
$828$	−4.73618e9	−0.289949
$829$	−4.59293e9	−0.279994	−0.139997	−	0.990152i	$-0.544709\pi$
$829$	−4.59293e9	−0.279994	−0.139997	+	0.990152i	$0.544709\pi$
$830$	−4.74953e9	−0.288322
$831$	−2.89824e9	−0.175199
$832$	−1.54990e9	−0.0932980
$833$	−6.73488e9	−0.403713
$834$	2.16272e9	0.129098
$835$	−6.19230e9	−0.368086
$836$	−1.49749e8	−0.00886428
$837$	2.10411e9	0.124031
$838$	−4.03015e9	−0.236574
$839$	−2.30945e10	−1.35002	−0.675012	−	0.737806i	$-0.735862\pi$
$839$	−2.30945e10	−1.35002	−0.675012	+	0.737806i	$0.735862\pi$
$840$	5.89669e9	0.343266
$841$	2.32866e10	1.34996
$842$	5.14664e9	0.297120
$843$	3.42898e9	0.197137
$844$	−1.34934e10	−0.772542
$845$	1.16560e10	0.664584
$846$	−5.60708e9	−0.318376
$847$	1.48202e10	0.838033
$848$	2.95516e8	0.0166416
$849$	1.83443e10	1.02879
$850$	1.04345e10	0.582779
$851$	−1.97598e10	−1.09908
$852$	8.64023e9	0.478616
$853$	2.22496e10	1.22744	0.613721	−	0.789523i	$-0.289672\pi$
$853$	2.22496e10	1.22744	0.613721	+	0.789523i	$0.289672\pi$
$854$	−1.17422e10	−0.645132
$855$	−2.64277e8	−0.0144603
$856$	−1.12659e10	−0.613912
$857$	1.07105e10	0.581270	0.290635	−	0.956834i	$-0.406133\pi$
$857$	1.07105e10	0.581270	0.290635	+	0.956834i	$0.406133\pi$
$858$	2.30094e8	0.0124365
$859$	3.19391e10	1.71928	0.859639	−	0.510902i	$-0.170688\pi$
$859$	3.19391e10	1.71928	0.859639	+	0.510902i	$0.170688\pi$
$860$	4.69475e9	0.251691
$861$	7.51761e9	0.401392
$862$	1.62047e10	0.861717
$863$	2.90663e10	1.53940	0.769700	−	0.638406i	$-0.220406\pi$
$863$	2.90663e10	1.53940	0.769700	+	0.638406i	$0.220406\pi$
$864$	−3.68390e9	−0.194317
$865$	−2.50580e9	−0.131641
$866$	−4.77979e8	−0.0250090
$867$	2.48275e10	1.29380
$868$	6.92319e9	0.359325
$869$	−5.14304e9	−0.265858
$870$	−7.10604e9	−0.365856
$871$	2.02598e8	0.0103889
$872$	3.78150e9	0.193133
$873$	2.03426e9	0.103480
$874$	−1.04453e9	−0.0529215
$875$	−1.82742e10	−0.922167
$876$	−7.12848e9	−0.358288
$877$	−1.87443e9	−0.0938364	−0.0469182	−	0.998899i	$-0.514940\pi$
$877$	−1.87443e9	−0.0938364	−0.0469182	+	0.998899i	$0.514940\pi$
$878$	1.74616e10	0.870668
$879$	9.56465e9	0.475016
$880$	−1.02479e8	−0.00506927
$881$	−3.84330e10	−1.89360	−0.946802	−	0.321818i	$-0.895706\pi$
$881$	−3.84330e10	−1.89360	−0.946802	+	0.321818i	$0.895706\pi$
$882$	9.22741e8	0.0452835
$883$	1.17045e10	0.572125	0.286063	−	0.958211i	$-0.407653\pi$
$883$	1.17045e10	0.572125	0.286063	+	0.958211i	$0.407653\pi$
$884$	3.77853e9	0.183967
$885$	1.05763e9	0.0512898
$886$	−7.91134e9	−0.382148
$887$	3.09354e9	0.148841	0.0744205	−	0.997227i	$-0.476289\pi$
$887$	3.09354e9	0.148841	0.0744205	+	0.997227i	$0.476289\pi$
$888$	−9.53236e9	−0.456831
$889$	2.97027e10	1.41788
$890$	−1.75738e9	−0.0835604
$891$	5.16746e8	0.0244740
$892$	−7.24615e8	−0.0341846
$893$	2.13304e9	0.100235
$894$	1.25167e10	0.585879
$895$	3.80897e9	0.177594
$896$	−1.25087e10	−0.580942
$897$	−2.76841e9	−0.128073
$898$	−3.81064e9	−0.175603
$899$	−2.15229e10	−0.987967
$900$	2.46598e9	0.112756
$901$	1.95023e10	0.888279
$902$	2.32147e9	0.105327
$903$	−6.55604e9	−0.296302
$904$	−4.17533e10	−1.87975
$905$	−1.78997e10	−0.802744
$906$	−7.99107e9	−0.356990
$907$	−5.95597e9	−0.265050	−0.132525	−	0.991180i	$-0.542308\pi$
$907$	−5.95597e9	−0.265050	−0.132525	+	0.991180i	$0.542308\pi$
$908$	5.57599e9	0.247185
$909$	−1.04550e10	−0.461688
$910$	1.33609e9	0.0587748
$911$	−4.08258e10	−1.78904	−0.894521	−	0.447026i	$-0.852483\pi$
$911$	−4.08258e10	−1.78904	−0.894521	+	0.447026i	$0.852483\pi$
$912$	2.83584e7	0.00123794
$913$	−3.53290e9	−0.153633
$914$	−2.69735e9	−0.116849
$915$	1.10382e10	0.476346
$916$	−1.60032e10	−0.687977
$917$	−1.19976e10	−0.513811
$918$	−4.91954e9	−0.209882
$919$	−1.12519e10	−0.478214	−0.239107	−	0.970993i	$-0.576855\pi$
$919$	−1.12519e10	−0.478214	−0.239107	+	0.970993i	$0.576855\pi$
$920$	−2.19087e10	−0.927598
$921$	−1.20738e10	−0.509255
$922$	2.05189e10	0.862176
$923$	5.05043e9	0.211408
$924$	1.70025e9	0.0709026
$925$	1.02883e10	0.427414
$926$	8.11271e9	0.335759
$927$	1.18660e9	0.0489244
$928$	3.76825e10	1.54783
$929$	1.44429e10	0.591018	0.295509	−	0.955340i	$-0.404511\pi$
$929$	1.44429e10	0.591018	0.295509	+	0.955340i	$0.404511\pi$
$930$	3.77297e9	0.153813
$931$	−3.51029e8	−0.0142567
$932$	−1.99620e10	−0.807696
$933$	−2.78578e10	−1.12295
$934$	−2.16339e10	−0.868801
$935$	−6.76301e9	−0.270582
$936$	−1.33551e9	−0.0532332
$937$	2.43718e10	0.967829	0.483915	−	0.875115i	$-0.339215\pi$
$937$	2.43718e10	0.967829	0.483915	+	0.875115i	$0.339215\pi$
$938$	−8.67909e8	−0.0343372
$939$	−3.98702e9	−0.157151
$940$	1.73428e10	0.681038
$941$	−1.04613e10	−0.409280	−0.204640	−	0.978837i	$-0.565602\pi$
$941$	−1.04613e10	−0.409280	−0.204640	+	0.978837i	$0.565602\pi$
$942$	−8.56639e9	−0.333903
$943$	−2.79311e10	−1.08467
$944$	−1.13490e8	−0.00439090
$945$	3.00060e9	0.115663
$946$	−2.02453e9	−0.0777509
$947$	−6.80097e9	−0.260223	−0.130112	−	0.991499i	$-0.541534\pi$
$947$	−6.80097e9	−0.260223	−0.130112	+	0.991499i	$0.541534\pi$
$948$	1.15714e10	0.441121
$949$	−4.16677e9	−0.158259
$950$	5.43855e8	0.0205802
$951$	−2.18195e10	−0.822645
$952$	−4.17578e10	−1.56859
$953$	−9.17306e8	−0.0343312	−0.0171656	−	0.999853i	$-0.505464\pi$
$953$	−9.17306e8	−0.0343312	−0.0171656	+	0.999853i	$0.505464\pi$
$954$	−2.67200e9	−0.0996362
$955$	1.43158e10	0.531869
$956$	3.06488e10	1.13452
$957$	−5.28577e9	−0.194947
$958$	−1.55614e10	−0.571833
$959$	−1.40120e10	−0.513019
$960$	−6.24150e9	−0.227688
$961$	−1.60850e10	−0.584640
$962$	−2.15987e9	−0.0782195
$963$	−5.73275e9	−0.206857
$964$	2.20377e10	0.792314
$965$	1.36120e10	0.487615
$966$	1.18596e10	0.423302
$967$	−3.69970e10	−1.31575	−0.657875	−	0.753127i	$-0.728544\pi$
$967$	−3.69970e10	−1.31575	−0.657875	+	0.753127i	$0.728544\pi$
$968$	−2.65631e10	−0.941271
$969$	1.87149e9	0.0660776
$970$	3.64771e9	0.128327
$971$	−1.31210e10	−0.459937	−0.229968	−	0.973198i	$-0.573862\pi$
$971$	−1.31210e10	−0.459937	−0.229968	+	0.973198i	$0.573862\pi$
$972$	−1.16264e9	−0.0406080
$973$	9.34138e9	0.325099
$974$	−1.40498e9	−0.0487209
$975$	1.44142e9	0.0498053
$976$	−1.18446e9	−0.0407798
$977$	−3.90962e10	−1.34123	−0.670615	−	0.741806i	$-0.733970\pi$
$977$	−3.90962e10	−1.34123	−0.670615	+	0.741806i	$0.733970\pi$
$978$	−1.33700e10	−0.457030
$979$	−1.30721e9	−0.0445253
$980$	−2.85406e9	−0.0968660
$981$	1.92426e9	0.0650760
$982$	−7.42485e9	−0.250206
$983$	−3.75059e10	−1.25940	−0.629699	−	0.776840i	$-0.716822\pi$
$983$	−3.75059e10	−1.25940	−0.629699	+	0.776840i	$0.716822\pi$
$984$	−1.34743e10	−0.450840
$985$	2.68269e10	0.894424
$986$	5.03219e10	1.67181
$987$	−2.42185e10	−0.801748
$988$	1.96941e8	0.00649660
$989$	2.43585e10	0.800688
$990$	9.26596e8	0.0303506
$991$	5.39247e10	1.76007	0.880036	−	0.474907i	$-0.157518\pi$
$991$	5.39247e10	1.76007	0.880036	+	0.474907i	$0.157518\pi$
$992$	−2.00076e10	−0.650735
$993$	−4.64223e9	−0.150454
$994$	−2.16355e10	−0.698739
$995$	−5.32397e9	−0.171338
$996$	7.94875e9	0.254912
$997$	2.01581e10	0.644192	0.322096	−	0.946707i	$-0.395613\pi$
$997$	2.01581e10	0.644192	0.322096	+	0.946707i	$0.395613\pi$
$998$	−8.48317e9	−0.270148
$999$	−4.85064e9	−0.153929

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.b.1.7	✓	17
3.2	odd	2		531.8.a.d.1.11		17

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.b.1.7	✓	17	1.1	even	1	trivial
531.8.a.d.1.11		17	3.2	odd	2

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:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	177.a (trivial)

\(f(q)\)	\(=\)	\(q-6.85375 q^{2} +27.0000 q^{3} -81.0262 q^{4} -190.727 q^{5} -185.051 q^{6} -799.288 q^{7} +1432.61 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-6.85375 q^{2} +27.0000 q^{3} -81.0262 q^{4} -190.727 q^{5} -185.051 q^{6} -799.288 q^{7} +1432.61 q^{8} +729.000 q^{9} +1307.20 q^{10} +972.348 q^{11} -2187.71 q^{12} -1278.77 q^{13} +5478.12 q^{14} -5149.64 q^{15} +552.586 q^{16} +36467.5 q^{17} -4996.38 q^{18} +1900.72 q^{19} +15453.9 q^{20} -21580.8 q^{21} -6664.23 q^{22} +80181.7 q^{23} +38680.5 q^{24} -41748.1 q^{25} +8764.35 q^{26} +19683.0 q^{27} +64763.2 q^{28} -201337. q^{29} +35294.3 q^{30} +106900. q^{31} -187162. q^{32} +26253.4 q^{33} -249939. q^{34} +152446. q^{35} -59068.1 q^{36} -246438. q^{37} -13027.1 q^{38} -34526.7 q^{39} -273238. q^{40} -348348. q^{41} +147909. q^{42} +303791. q^{43} -78785.6 q^{44} -139040. q^{45} -549545. q^{46} +1.12223e6 q^{47} +14919.8 q^{48} -184682. q^{49} +286131. q^{50} +984622. q^{51} +103614. q^{52} +534787. q^{53} -134902. q^{54} -185453. q^{55} -1.14507e6 q^{56} +51319.5 q^{57} +1.37991e6 q^{58} -205379. q^{59} +417255. q^{60} -2.14348e6 q^{61} -732666. q^{62} -582681. q^{63} +1.21203e6 q^{64} +243896. q^{65} -179934. q^{66} -158432. q^{67} -2.95482e6 q^{68} +2.16491e6 q^{69} -1.04483e6 q^{70} -3.94945e6 q^{71} +1.04437e6 q^{72} +3.25842e6 q^{73} +1.68903e6 q^{74} -1.12720e6 q^{75} -154008. q^{76} -777186. q^{77} +236637. q^{78} -5.28930e6 q^{79} -105393. q^{80} +531441. q^{81} +2.38749e6 q^{82} -3.63337e6 q^{83} +1.74861e6 q^{84} -6.95534e6 q^{85} -2.08211e6 q^{86} -5.43609e6 q^{87} +1.39300e6 q^{88} -1.34439e6 q^{89} +952946. q^{90} +1.02210e6 q^{91} -6.49682e6 q^{92} +2.88630e6 q^{93} -7.69146e6 q^{94} -362519. q^{95} -5.05336e6 q^{96} +2.79048e6 q^{97} +1.26576e6 q^{98} +708842. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9}+O(q^{10}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9	\( 17 q - 32 q^{2} + 459 q^{3} + 1166 q^{4} - 1072 q^{5} - 864 q^{6} - 2407 q^{7} - 6645 q^{8} + 12393 q^{9} - 6391 q^{10} - 8888 q^{11} + 31482 q^{12} - 12702 q^{13} - 17555 q^{14} - 28944 q^{15} + 139226 q^{16} - 36167 q^{17} - 23328 q^{18} - 71037 q^{19} - 274883 q^{20} - 64989 q^{21} - 325182 q^{22} - 269995 q^{23} - 179415 q^{24} + 97329 q^{25} - 336906 q^{26} + 334611 q^{27} - 901362 q^{28} - 543825 q^{29} - 172557 q^{30} - 633109 q^{31} - 837062 q^{32} - 239976 q^{33} - 529288 q^{34} - 287621 q^{35} + 850014 q^{36} - 867607 q^{37} - 1727169 q^{38} - 342954 q^{39} - 815662 q^{40} - 1428939 q^{41} - 473985 q^{42} - 477060 q^{43} - 1667926 q^{44} - 781488 q^{45} + 5305549 q^{46} - 1217849 q^{47} + 3759102 q^{48} + 4350738 q^{49} + 4561369 q^{50} - 976509 q^{51} + 4175994 q^{52} - 3487068 q^{53} - 629856 q^{54} - 960484 q^{55} - 5363196 q^{56} - 1917999 q^{57} - 3082906 q^{58} - 3491443 q^{59} - 7421841 q^{60} + 998917 q^{61} - 5742614 q^{62} - 1754703 q^{63} + 17531621 q^{64} - 6075816 q^{65} - 8779914 q^{66} - 356026 q^{67} - 16149231 q^{68} - 7289865 q^{69} - 548798 q^{70} - 12879428 q^{71} - 4844205 q^{72} - 6176157 q^{73} - 5971906 q^{74} + 2627883 q^{75} - 17624580 q^{76} + 239687 q^{77} - 9096462 q^{78} - 18886490 q^{79} - 70463349 q^{80} + 9034497 q^{81} - 19351611 q^{82} - 22824893 q^{83} - 24336774 q^{84} - 7973079 q^{85} - 27502196 q^{86} - 14683275 q^{87} - 62527651 q^{88} - 30609647 q^{89} - 4659039 q^{90} - 36301521 q^{91} - 41388548 q^{92} - 17093943 q^{93} + 1010176 q^{94} - 29303629 q^{95} - 22600674 q^{96} - 26249806 q^{97} - 93110852 q^{98} - 6479352 q^{99}+O(q^{100}) \) 17 * q - 32 * q^2 + 459 * q^3 + 1166 * q^4 - 1072 * q^5 - 864 * q^6 - 2407 * q^7 - 6645 * q^8 + 12393 * q^9 - 6391 * q^10 - 8888 * q^11 + 31482 * q^12 - 12702 * q^13 - 17555 * q^14 - 28944 * q^15 + 139226 * q^16 - 36167 * q^17 - 23328 * q^18 - 71037 * q^19 - 274883 * q^20 - 64989 * q^21 - 325182 * q^22 - 269995 * q^23 - 179415 * q^24 + 97329 * q^25 - 336906 * q^26 + 334611 * q^27 - 901362 * q^28 - 543825 * q^29 - 172557 * q^30 - 633109 * q^31 - 837062 * q^32 - 239976 * q^33 - 529288 * q^34 - 287621 * q^35 + 850014 * q^36 - 867607 * q^37 - 1727169 * q^38 - 342954 * q^39 - 815662 * q^40 - 1428939 * q^41 - 473985 * q^42 - 477060 * q^43 - 1667926 * q^44 - 781488 * q^45 + 5305549 * q^46 - 1217849 * q^47 + 3759102 * q^48 + 4350738 * q^49 + 4561369 * q^50 - 976509 * q^51 + 4175994 * q^52 - 3487068 * q^53 - 629856 * q^54 - 960484 * q^55 - 5363196 * q^56 - 1917999 * q^57 - 3082906 * q^58 - 3491443 * q^59 - 7421841 * q^60 + 998917 * q^61 - 5742614 * q^62 - 1754703 * q^63 + 17531621 * q^64 - 6075816 * q^65 - 8779914 * q^66 - 356026 * q^67 - 16149231 * q^68 - 7289865 * q^69 - 548798 * q^70 - 12879428 * q^71 - 4844205 * q^72 - 6176157 * q^73 - 5971906 * q^74 + 2627883 * q^75 - 17624580 * q^76 + 239687 * q^77 - 9096462 * q^78 - 18886490 * q^79 - 70463349 * q^80 + 9034497 * q^81 - 19351611 * q^82 - 22824893 * q^83 - 24336774 * q^84 - 7973079 * q^85 - 27502196 * q^86 - 14683275 * q^87 - 62527651 * q^88 - 30609647 * q^89 - 4659039 * q^90 - 36301521 * q^91 - 41388548 * q^92 - 17093943 * q^93 + 1010176 * q^94 - 29303629 * q^95 - 22600674 * q^96 - 26249806 * q^97 - 93110852 * q^98 - 6479352 * q^99

Introduction

L-functions

Modular forms

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