LMFDB - Embedded newform 177.8.a.d.1.14

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:	$0$
Dimension:	$18$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 6 x^{17} - 1798 x^{16} + 11087 x^{15} + 1326765 x^{14} - 8403720 x^{13} - 518334228 x^{12} + \cdots + 51\!\cdots\!48 $ x^18 - 6x^17 - 1798x^16 + 11087x^15 + 1326765x^14 - 8403720x^13 - 518334228x^12 + 3375594921x^11 + 115310342333x^10 - 774932111214x^9 - 14600047830166x^8 + 102185027148481x^7 + 988557475638619x^6 - 7379206238519716x^5 - 30152342836849520x^4 + 260578770749067175x^3 + 182609347488069978x^2 - 3481290425710753600*x + 5164646074739714048
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{5} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.14
Root			$13.6971$ 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)

$f(q)$	$=$	$q+14.6971 q^{2} +27.0000 q^{3} +88.0043 q^{4} +457.882 q^{5} +396.821 q^{6} +1576.42 q^{7} -587.821 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+14.6971 q^{2} +27.0000 q^{3} +88.0043 q^{4} +457.882 q^{5} +396.821 q^{6} +1576.42 q^{7} -587.821 q^{8} +729.000 q^{9} +6729.53 q^{10} +6841.63 q^{11} +2376.11 q^{12} +4116.85 q^{13} +23168.8 q^{14} +12362.8 q^{15} -19903.8 q^{16} -34857.5 q^{17} +10714.2 q^{18} -30826.5 q^{19} +40295.5 q^{20} +42563.4 q^{21} +100552. q^{22} -51444.0 q^{23} -15871.2 q^{24} +131531. q^{25} +60505.7 q^{26} +19683.0 q^{27} +138732. q^{28} +106767. q^{29} +181697. q^{30} -236039. q^{31} -217287. q^{32} +184724. q^{33} -512304. q^{34} +721815. q^{35} +64155.1 q^{36} -320825. q^{37} -453059. q^{38} +111155. q^{39} -269152. q^{40} -227909. q^{41} +625558. q^{42} +156061. q^{43} +602092. q^{44} +333796. q^{45} -756076. q^{46} +902640. q^{47} -537402. q^{48} +1.66156e6 q^{49} +1.93312e6 q^{50} -941152. q^{51} +362300. q^{52} -1.28791e6 q^{53} +289283. q^{54} +3.13266e6 q^{55} -926654. q^{56} -832315. q^{57} +1.56916e6 q^{58} +205379. q^{59} +1.08798e6 q^{60} +719101. q^{61} -3.46908e6 q^{62} +1.14921e6 q^{63} -645794. q^{64} +1.88503e6 q^{65} +2.71490e6 q^{66} -2.73492e6 q^{67} -3.06761e6 q^{68} -1.38899e6 q^{69} +1.06086e7 q^{70} +2.81839e6 q^{71} -428521. q^{72} -880677. q^{73} -4.71519e6 q^{74} +3.55133e6 q^{75} -2.71286e6 q^{76} +1.07853e7 q^{77} +1.63365e6 q^{78} +2.91979e6 q^{79} -9.11359e6 q^{80} +531441. q^{81} -3.34960e6 q^{82} -6.61990e6 q^{83} +3.74576e6 q^{84} -1.59606e7 q^{85} +2.29364e6 q^{86} +2.88271e6 q^{87} -4.02165e6 q^{88} -6.36510e6 q^{89} +4.90583e6 q^{90} +6.48989e6 q^{91} -4.52729e6 q^{92} -6.37305e6 q^{93} +1.32662e7 q^{94} -1.41149e7 q^{95} -5.86674e6 q^{96} +1.73556e7 q^{97} +2.44201e7 q^{98} +4.98755e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) $ 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * 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 $

$2$	14.6971	1.29905	0.649525	−	0.760340i	$-0.274968\pi$
$2$	14.6971	1.29905	0.649525	+	0.760340i	$0.274968\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	88.0043	0.687533
$5$	457.882	1.63817	0.819084	−	0.573674i	$-0.194482\pi$
$5$	457.882	1.63817	0.819084	+	0.573674i	$0.194482\pi$
$6$	396.821	0.750007
$7$	1576.42	1.73712	0.868559	−	0.495585i	$-0.165046\pi$
$7$	1576.42	1.73712	0.868559	+	0.495585i	$0.165046\pi$
$8$	−587.821	−0.405910
$9$	729.000	0.333333
$10$	6729.53	2.12806
$11$	6841.63	1.54983	0.774917	−	0.632064i	$-0.217792\pi$
$11$	6841.63	1.54983	0.774917	+	0.632064i	$0.217792\pi$
$12$	2376.11	0.396947
$13$	4116.85	0.519713	0.259856	−	0.965647i	$-0.416325\pi$
$13$	4116.85	0.519713	0.259856	+	0.965647i	$0.416325\pi$
$14$	23168.8	2.25661
$15$	12362.8	0.945797
$16$	−19903.8	−1.21483
$17$	−34857.5	−1.72078	−0.860389	−	0.509637i	$-0.829780\pi$
$17$	−34857.5	−1.72078	−0.860389	+	0.509637i	$0.829780\pi$
$18$	10714.2	0.433017
$19$	−30826.5	−1.03107	−0.515533	−	0.856870i	$-0.672406\pi$
$19$	−30826.5	−1.03107	−0.515533	+	0.856870i	$0.672406\pi$
$20$	40295.5	1.12629
$21$	42563.4	1.00293
$22$	100552.	2.01331
$23$	−51444.0	−0.881632	−0.440816	−	0.897598i	$-0.645311\pi$
$23$	−51444.0	−0.881632	−0.440816	+	0.897598i	$0.645311\pi$
$24$	−15871.2	−0.234352
$25$	131531.	1.68359
$26$	60505.7	0.675133
$27$	19683.0	0.192450
$28$	138732.	1.19433
$29$	106767.	0.812913	0.406457	−	0.913670i	$-0.366764\pi$
$29$	106767.	0.812913	0.406457	+	0.913670i	$0.366764\pi$
$30$	181697.	1.22864
$31$	−236039.	−1.42304	−0.711521	−	0.702665i	$-0.751993\pi$
$31$	−236039.	−1.42304	−0.711521	+	0.702665i	$0.751993\pi$
$32$	−217287.	−1.17222
$33$	184724.	0.894797
$34$	−512304.	−2.23538
$35$	721815.	2.84569
$36$	64155.1	0.229178
$37$	−320825.	−1.04127	−0.520633	−	0.853781i	$-0.674304\pi$
$37$	−320825.	−1.04127	−0.520633	+	0.853781i	$0.674304\pi$
$38$	−453059.	−1.33941
$39$	111155.	0.300056
$40$	−269152.	−0.664949
$41$	−227909.	−0.516439	−0.258219	−	0.966086i	$-0.583136\pi$
$41$	−227909.	−0.516439	−0.258219	+	0.966086i	$0.583136\pi$
$42$	625558.	1.30285
$43$	156061.	0.299333	0.149667	−	0.988737i	$-0.452180\pi$
$43$	156061.	0.299333	0.149667	+	0.988737i	$0.452180\pi$
$44$	602092.	1.06556
$45$	333796.	0.546056
$46$	−756076.	−1.14528
$47$	902640.	1.26815	0.634077	−	0.773270i	$-0.281380\pi$
$47$	902640.	1.26815	0.634077	+	0.773270i	$0.281380\pi$
$48$	−537402.	−0.701383
$49$	1.66156e6	2.01758
$50$	1.93312e6	2.18707
$51$	−941152.	−0.993492
$52$	362300.	0.357320
$53$	−1.28791e6	−1.18829	−0.594143	−	0.804360i	$-0.702509\pi$
$53$	−1.28791e6	−1.18829	−0.594143	+	0.804360i	$0.702509\pi$
$54$	289283.	0.250002
$55$	3.13266e6	2.53889
$56$	−926654.	−0.705114
$57$	−832315.	−0.595286
$58$	1.56916e6	1.05602
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	1.08798e6	0.650267
$61$	719101.	0.405635	0.202818	−	0.979217i	$-0.434990\pi$
$61$	719101.	0.405635	0.202818	+	0.979217i	$0.434990\pi$
$62$	−3.46908e6	−1.84860
$63$	1.14921e6	0.579039
$64$	−645794.	−0.307939
$65$	1.88503e6	0.851377
$66$	2.71490e6	1.16239
$67$	−2.73492e6	−1.11092	−0.555460	−	0.831544i	$-0.687458\pi$
$67$	−2.73492e6	−1.11092	−0.555460	+	0.831544i	$0.687458\pi$
$68$	−3.06761e6	−1.18309
$69$	−1.38899e6	−0.509010
$70$	1.06086e7	3.69670
$71$	2.81839e6	0.934538	0.467269	−	0.884115i	$-0.345238\pi$
$71$	2.81839e6	0.934538	0.467269	+	0.884115i	$0.345238\pi$
$72$	−428521.	−0.135303
$73$	−880677.	−0.264964	−0.132482	−	0.991185i	$-0.542295\pi$
$73$	−880677.	−0.264964	−0.132482	+	0.991185i	$0.542295\pi$
$74$	−4.71519e6	−1.35266
$75$	3.55133e6	0.972023
$76$	−2.71286e6	−0.708892
$77$	1.07853e7	2.69224
$78$	1.63365e6	0.389788
$79$	2.91979e6	0.666281	0.333140	−	0.942877i	$-0.391892\pi$
$79$	2.91979e6	0.666281	0.333140	+	0.942877i	$0.391892\pi$
$80$	−9.11359e6	−1.99010
$81$	531441.	0.111111
$82$	−3.34960e6	−0.670880
$83$	−6.61990e6	−1.27080	−0.635402	−	0.772182i	$-0.719165\pi$
$83$	−6.61990e6	−1.27080	−0.635402	+	0.772182i	$0.719165\pi$
$84$	3.74576e6	0.689545
$85$	−1.59606e7	−2.81892
$86$	2.29364e6	0.388849
$87$	2.88271e6	0.469336
$88$	−4.02165e6	−0.629093
$89$	−6.36510e6	−0.957062	−0.478531	−	0.878071i	$-0.658831\pi$
$89$	−6.36510e6	−0.957062	−0.478531	+	0.878071i	$0.658831\pi$
$90$	4.90583e6	0.709354
$91$	6.48989e6	0.902803
$92$	−4.52729e6	−0.606151
$93$	−6.37305e6	−0.821593
$94$	1.32662e7	1.64740
$95$	−1.41149e7	−1.68906
$96$	−5.86674e6	−0.676780
$97$	1.73556e7	1.93081	0.965403	−	0.260764i	$-0.0839744\pi$
$97$	1.73556e7	1.93081	0.965403	+	0.260764i	$0.0839744\pi$
$98$	2.44201e7	2.62094
$99$	4.98755e6	0.516611
$100$	1.15753e7	1.15753
$101$	1.48075e7	1.43007	0.715036	−	0.699087i	$-0.246410\pi$
$101$	1.48075e7	1.43007	0.715036	+	0.699087i	$0.246410\pi$
$102$	−1.38322e7	−1.29060
$103$	8.68688e6	0.783310	0.391655	−	0.920112i	$-0.371903\pi$
$103$	8.68688e6	0.783310	0.391655	+	0.920112i	$0.371903\pi$
$104$	−2.41997e6	−0.210957
$105$	1.94890e7	1.64296
$106$	−1.89286e7	−1.54364
$107$	−1.01246e7	−0.798974	−0.399487	−	0.916739i	$-0.630812\pi$
$107$	−1.01246e7	−0.798974	−0.399487	+	0.916739i	$0.630812\pi$
$108$	1.73219e6	0.132316
$109$	−4.44690e6	−0.328900	−0.164450	−	0.986385i	$-0.552585\pi$
$109$	−4.44690e6	−0.328900	−0.164450	+	0.986385i	$0.552585\pi$
$110$	4.60409e7	3.29814
$111$	−8.66227e6	−0.601175
$112$	−3.13768e7	−2.11031
$113$	−2.11640e6	−0.137982	−0.0689910	−	0.997617i	$-0.521978\pi$
$113$	−2.11640e6	−0.137982	−0.0689910	+	0.997617i	$0.521978\pi$
$114$	−1.22326e7	−0.773307
$115$	−2.35553e7	−1.44426
$116$	9.39595e6	0.558905
$117$	3.00118e6	0.173238
$118$	3.01847e6	0.169122
$119$	−5.49501e7	−2.98920
$120$	−7.26712e6	−0.383909
$121$	2.73207e7	1.40198
$122$	1.05687e7	0.526941
$123$	−6.15356e6	−0.298166
$124$	−2.07724e7	−0.978388
$125$	2.44535e7	1.11984
$126$	1.68901e7	0.752202
$127$	1.43195e7	0.620317	0.310159	−	0.950685i	$-0.399618\pi$
$127$	1.43195e7	0.620317	0.310159	+	0.950685i	$0.399618\pi$
$128$	1.83214e7	0.772189
$129$	4.21365e6	0.172820
$130$	2.77045e7	1.10598
$131$	−4.80639e7	−1.86797	−0.933985	−	0.357312i	$-0.883693\pi$
$131$	−4.80639e7	−1.86797	−0.933985	+	0.357312i	$0.883693\pi$
$132$	1.62565e7	0.615202
$133$	−4.85956e7	−1.79108
$134$	−4.01953e7	−1.44314
$135$	9.01249e6	0.315266
$136$	2.04900e7	0.698482
$137$	−1.81664e7	−0.603598	−0.301799	−	0.953372i	$-0.597587\pi$
$137$	−1.81664e7	−0.603598	−0.301799	+	0.953372i	$0.597587\pi$
$138$	−2.04141e7	−0.661230
$139$	2.63273e7	0.831484	0.415742	−	0.909483i	$-0.363522\pi$
$139$	2.63273e7	0.831484	0.415742	+	0.909483i	$0.363522\pi$
$140$	6.35228e7	1.95651
$141$	2.43713e7	0.732170
$142$	4.14221e7	1.21401
$143$	2.81659e7	0.805468
$144$	−1.45099e7	−0.404944
$145$	4.88867e7	1.33169
$146$	−1.29434e7	−0.344201
$147$	4.48622e7	1.16485
$148$	−2.82339e7	−0.715905
$149$	6.64472e7	1.64560	0.822801	−	0.568329i	$-0.192410\pi$
$149$	6.64472e7	1.64560	0.822801	+	0.568329i	$0.192410\pi$
$150$	5.21942e7	1.26271
$151$	−6.98756e7	−1.65160	−0.825802	−	0.563960i	$-0.809277\pi$
$151$	−6.98756e7	−1.65160	−0.825802	+	0.563960i	$0.809277\pi$
$152$	1.81205e7	0.418520
$153$	−2.54111e7	−0.573593
$154$	1.58512e8	3.49736
$155$	−1.08078e8	−2.33118
$156$	9.78211e6	0.206299
$157$	−2.65494e7	−0.547528	−0.273764	−	0.961797i	$-0.588269\pi$
$157$	−2.65494e7	−0.547528	−0.273764	+	0.961797i	$0.588269\pi$
$158$	4.29124e7	0.865533
$159$	−3.47736e7	−0.686057
$160$	−9.94916e7	−1.92029
$161$	−8.10974e7	−1.53150
$162$	7.81063e6	0.144339
$163$	5.75891e7	1.04156	0.520779	−	0.853691i	$-0.325642\pi$
$163$	5.75891e7	1.04156	0.520779	+	0.853691i	$0.325642\pi$
$164$	−2.00570e7	−0.355069
$165$	8.45817e7	1.46583
$166$	−9.72933e7	−1.65084
$167$	4.98500e6	0.0828242	0.0414121	−	0.999142i	$-0.486814\pi$
$167$	4.98500e6	0.0828242	0.0414121	+	0.999142i	$0.486814\pi$
$168$	−2.50197e7	−0.407098
$169$	−4.58001e7	−0.729899
$170$	−2.34574e8	−3.66193
$171$	−2.24725e7	−0.343689
$172$	1.37340e7	0.205801
$173$	8.44843e7	1.24055	0.620276	−	0.784384i	$-0.287021\pi$
$173$	8.44843e7	1.24055	0.620276	+	0.784384i	$0.287021\pi$
$174$	4.23674e7	0.609691
$175$	2.07348e8	2.92460
$176$	−1.36174e8	−1.88279
$177$	5.54523e6	0.0751646
$178$	−9.35484e7	−1.24327
$179$	−7.90602e6	−0.103032	−0.0515160	−	0.998672i	$-0.516405\pi$
$179$	−7.90602e6	−0.103032	−0.0515160	+	0.998672i	$0.516405\pi$
$180$	2.93755e7	0.375432
$181$	4.23307e7	0.530616	0.265308	−	0.964164i	$-0.414526\pi$
$181$	4.23307e7	0.530616	0.265308	+	0.964164i	$0.414526\pi$
$182$	9.53825e7	1.17279
$183$	1.94157e7	0.234194
$184$	3.02398e7	0.357863
$185$	−1.46900e8	−1.70577
$186$	−9.36652e7	−1.06729
$187$	−2.38482e8	−2.66692
$188$	7.94362e7	0.871899
$189$	3.10287e7	0.334309
$190$	−2.07448e8	−2.19417
$191$	−8.15774e7	−0.847136	−0.423568	−	0.905864i	$-0.639223\pi$
$191$	−8.15774e7	−0.847136	−0.423568	+	0.905864i	$0.639223\pi$
$192$	−1.74365e7	−0.177789
$193$	3.34817e7	0.335240	0.167620	−	0.985852i	$-0.446392\pi$
$193$	3.34817e7	0.335240	0.167620	+	0.985852i	$0.446392\pi$
$194$	2.55077e8	2.50821
$195$	5.08958e7	0.491543
$196$	1.46225e8	1.38715
$197$	−5.69368e7	−0.530593	−0.265296	−	0.964167i	$-0.585470\pi$
$197$	−5.69368e7	−0.530593	−0.265296	+	0.964167i	$0.585470\pi$
$198$	7.33024e7	0.671104
$199$	3.68438e7	0.331420	0.165710	−	0.986175i	$-0.447008\pi$
$199$	3.68438e7	0.331420	0.165710	+	0.986175i	$0.447008\pi$
$200$	−7.73165e7	−0.683388
$201$	−7.38428e7	−0.641389
$202$	2.17628e8	1.85774
$203$	1.68310e8	1.41213
$204$	−8.28254e7	−0.683059
$205$	−1.04356e8	−0.846013
$206$	1.27672e8	1.01756
$207$	−3.75027e7	−0.293877
$208$	−8.19410e7	−0.631363
$209$	−2.10903e8	−1.59798
$210$	2.86432e8	2.13429
$211$	6.42783e6	0.0471059	0.0235530	−	0.999723i	$-0.492502\pi$
$211$	6.42783e6	0.0471059	0.0235530	+	0.999723i	$0.492502\pi$
$212$	−1.13342e8	−0.816986
$213$	7.60965e7	0.539556
$214$	−1.48801e8	−1.03791
$215$	7.14575e7	0.490358
$216$	−1.15701e7	−0.0781175
$217$	−3.72097e8	−2.47199
$218$	−6.53564e7	−0.427258
$219$	−2.37783e7	−0.152977
$220$	2.75687e8	1.74557
$221$	−1.43503e8	−0.894311
$222$	−1.27310e8	−0.780957
$223$	−5.93351e7	−0.358298	−0.179149	−	0.983822i	$-0.557334\pi$
$223$	−5.93351e7	−0.358298	−0.179149	+	0.983822i	$0.557334\pi$
$224$	−3.42536e8	−2.03628
$225$	9.58859e7	0.561198
$226$	−3.11049e7	−0.179246
$227$	2.49947e8	1.41827	0.709134	−	0.705074i	$-0.249086\pi$
$227$	2.49947e8	1.41827	0.709134	+	0.705074i	$0.249086\pi$
$228$	−7.32473e7	−0.409279
$229$	−1.83888e8	−1.01188	−0.505941	−	0.862568i	$-0.668855\pi$
$229$	−1.83888e8	−1.01188	−0.505941	+	0.862568i	$0.668855\pi$
$230$	−3.46194e8	−1.87617
$231$	2.91203e8	1.55437
$232$	−6.27599e7	−0.329970
$233$	−1.34216e8	−0.695120	−0.347560	−	0.937658i	$-0.612990\pi$
$233$	−1.34216e8	−0.695120	−0.347560	+	0.937658i	$0.612990\pi$
$234$	4.41087e7	0.225044
$235$	4.13303e8	2.07745
$236$	1.80742e7	0.0895092
$237$	7.88344e7	0.384677
$238$	−8.07607e8	−3.88312
$239$	−3.79885e8	−1.79994	−0.899972	−	0.435947i	$-0.856413\pi$
$239$	−3.79885e8	−1.79994	−0.899972	+	0.435947i	$0.856413\pi$
$240$	−2.46067e8	−1.14898
$241$	−2.48361e7	−0.114294	−0.0571470	−	0.998366i	$-0.518200\pi$
$241$	−2.48361e7	−0.114294	−0.0571470	+	0.998366i	$0.518200\pi$
$242$	4.01534e8	1.82125
$243$	1.43489e7	0.0641500
$244$	6.32840e7	0.278888
$245$	7.60800e8	3.30514
$246$	−9.04393e7	−0.387333
$247$	−1.26908e8	−0.535858
$248$	1.38749e8	0.577627
$249$	−1.78737e8	−0.733699
$250$	3.59395e8	1.45473
$251$	−2.30663e8	−0.920705	−0.460352	−	0.887736i	$-0.652277\pi$
$251$	−2.30663e8	−0.920705	−0.460352	+	0.887736i	$0.652277\pi$
$252$	1.01136e8	0.398109
$253$	−3.51960e8	−1.36638
$254$	2.10454e8	0.805824
$255$	−4.30937e8	−1.62751
$256$	3.51933e8	1.31105
$257$	2.98007e8	1.09512	0.547558	−	0.836768i	$-0.315558\pi$
$257$	2.98007e8	1.09512	0.547558	+	0.836768i	$0.315558\pi$
$258$	6.19283e7	0.224502
$259$	−5.05755e8	−1.80880
$260$	1.65891e8	0.585350
$261$	7.78332e7	0.270971
$262$	−7.06400e8	−2.42659
$263$	2.77082e8	0.939211	0.469605	−	0.882876i	$-0.344396\pi$
$263$	2.77082e8	0.939211	0.469605	+	0.882876i	$0.344396\pi$
$264$	−1.08585e8	−0.363207
$265$	−5.89712e8	−1.94661
$266$	−7.14213e8	−2.32671
$267$	−1.71858e8	−0.552560
$268$	−2.40684e8	−0.763794
$269$	2.71094e8	0.849155	0.424577	−	0.905392i	$-0.360423\pi$
$269$	2.71094e8	0.849155	0.424577	+	0.905392i	$0.360423\pi$
$270$	1.32457e8	0.409546
$271$	−4.89470e8	−1.49394	−0.746970	−	0.664858i	$-0.768492\pi$
$271$	−4.89470e8	−1.49394	−0.746970	+	0.664858i	$0.768492\pi$
$272$	6.93797e8	2.09046
$273$	1.75227e8	0.521233
$274$	−2.66994e8	−0.784104
$275$	8.99884e8	2.60929
$276$	−1.22237e8	−0.349961
$277$	−2.76753e8	−0.782371	−0.391186	−	0.920312i	$-0.627935\pi$
$277$	−2.76753e8	−0.782371	−0.391186	+	0.920312i	$0.627935\pi$
$278$	3.86934e8	1.08014
$279$	−1.72072e8	−0.474347
$280$	−4.24298e8	−1.15510
$281$	3.28075e8	0.882065	0.441032	−	0.897491i	$-0.354612\pi$
$281$	3.28075e8	0.882065	0.441032	+	0.897491i	$0.354612\pi$
$282$	3.58187e8	0.951126
$283$	2.47479e8	0.649061	0.324531	−	0.945875i	$-0.394794\pi$
$283$	2.47479e8	0.649061	0.324531	+	0.945875i	$0.394794\pi$
$284$	2.48030e8	0.642526
$285$	−3.81102e8	−0.975179
$286$	4.13957e8	1.04634
$287$	−3.59282e8	−0.897115
$288$	−1.58402e8	−0.390739
$289$	8.04706e8	1.96108
$290$	7.18492e8	1.72993
$291$	4.68601e8	1.11475
$292$	−7.75033e7	−0.182171
$293$	3.73118e8	0.866582	0.433291	−	0.901254i	$-0.357352\pi$
$293$	3.73118e8	0.866582	0.433291	+	0.901254i	$0.357352\pi$
$294$	6.59344e8	1.51320
$295$	9.40393e7	0.213271
$296$	1.88587e8	0.422661
$297$	1.34664e8	0.298266
$298$	9.76581e8	2.13772
$299$	−2.11787e8	−0.458195
$300$	3.12532e8	0.668298
$301$	2.46018e8	0.519977
$302$	−1.02697e9	−2.14552
$303$	3.99804e8	0.825653
$304$	6.13564e8	1.25257
$305$	3.29263e8	0.664498
$306$	−3.73469e8	−0.745126
$307$	−5.11504e8	−1.00894	−0.504469	−	0.863430i	$-0.668312\pi$
$307$	−5.11504e8	−1.00894	−0.504469	+	0.863430i	$0.668312\pi$
$308$	9.49151e8	1.85101
$309$	2.34546e8	0.452244
$310$	−1.58843e9	−3.02832
$311$	6.07087e6	0.0114443	0.00572215	−	0.999984i	$-0.498179\pi$
$311$	6.07087e6	0.0114443	0.00572215	+	0.999984i	$0.498179\pi$
$312$	−6.53392e7	−0.121796
$313$	9.00976e6	0.0166076	0.00830382	−	0.999966i	$-0.497357\pi$
$313$	9.00976e6	0.0166076	0.00830382	+	0.999966i	$0.497357\pi$
$314$	−3.90199e8	−0.711266
$315$	5.26203e8	0.948564
$316$	2.56954e8	0.458090
$317$	1.54129e8	0.271755	0.135878	−	0.990726i	$-0.456615\pi$
$317$	1.54129e8	0.271755	0.135878	+	0.990726i	$0.456615\pi$
$318$	−5.11071e8	−0.891223
$319$	7.30460e8	1.25988
$320$	−2.95698e8	−0.504455
$321$	−2.73363e8	−0.461288
$322$	−1.19190e9	−1.98949
$323$	1.07453e9	1.77424
$324$	4.67691e7	0.0763926
$325$	5.41492e8	0.874985
$326$	8.46391e8	1.35304
$327$	−1.20066e8	−0.189891
$328$	1.33970e8	0.209628
$329$	1.42294e9	2.20294
$330$	1.24310e9	1.90418
$331$	6.66857e8	1.01073	0.505365	−	0.862906i	$-0.331358\pi$
$331$	6.66857e8	1.01073	0.505365	+	0.862906i	$0.331358\pi$
$332$	−5.82580e8	−0.873719
$333$	−2.33881e8	−0.347089
$334$	7.32649e7	0.107593
$335$	−1.25227e9	−1.81987
$336$	−8.47173e8	−1.21839
$337$	7.12103e8	1.01353	0.506767	−	0.862083i	$-0.330840\pi$
$337$	7.12103e8	1.01353	0.506767	+	0.862083i	$0.330840\pi$
$338$	−6.73127e8	−0.948176
$339$	−5.71427e7	−0.0796640
$340$	−1.40460e9	−1.93810
$341$	−1.61489e9	−2.20548
$342$	−3.30280e8	−0.446469
$343$	1.32108e9	1.76766
$344$	−9.17359e7	−0.121502
$345$	−6.35992e8	−0.833844
$346$	1.24167e9	1.61154
$347$	6.85187e8	0.880351	0.440175	−	0.897912i	$-0.354916\pi$
$347$	6.85187e8	0.880351	0.440175	+	0.897912i	$0.354916\pi$
$348$	2.53691e8	0.322684
$349$	−4.10968e8	−0.517511	−0.258755	−	0.965943i	$-0.583312\pi$
$349$	−4.10968e8	−0.517511	−0.258755	+	0.965943i	$0.583312\pi$
$350$	3.04741e9	3.79921
$351$	8.10320e7	0.100019
$352$	−1.48659e9	−1.81674
$353$	7.36899e8	0.891654	0.445827	−	0.895119i	$-0.352910\pi$
$353$	7.36899e8	0.891654	0.445827	+	0.895119i	$0.352910\pi$
$354$	8.14988e7	0.0976426
$355$	1.29049e9	1.53093
$356$	−5.60156e8	−0.658012
$357$	−1.48365e9	−1.72581
$358$	−1.16195e8	−0.133844
$359$	1.53809e9	1.75449	0.877246	−	0.480041i	$-0.159378\pi$
$359$	1.53809e9	1.75449	0.877246	+	0.480041i	$0.159378\pi$
$360$	−1.96212e8	−0.221650
$361$	5.64007e7	0.0630971
$362$	6.22138e8	0.689298
$363$	7.37658e8	0.809435
$364$	5.71138e8	0.620707
$365$	−4.03246e8	−0.434055
$366$	2.85355e8	0.304229
$367$	−9.99795e8	−1.05580	−0.527898	−	0.849308i	$-0.677020\pi$
$367$	−9.99795e8	−1.05580	−0.527898	+	0.849308i	$0.677020\pi$
$368$	1.02393e9	1.07103
$369$	−1.66146e8	−0.172146
$370$	−2.15900e9	−2.21588
$371$	−2.03029e9	−2.06419
$372$	−5.60855e8	−0.564873
$373$	−9.19979e8	−0.917903	−0.458952	−	0.888461i	$-0.651775\pi$
$373$	−9.19979e8	−0.917903	−0.458952	+	0.888461i	$0.651775\pi$
$374$	−3.50499e9	−3.46446
$375$	6.60245e8	0.646540
$376$	−5.30591e8	−0.514757
$377$	4.39544e8	0.422481
$378$	4.56032e8	0.434284
$379$	1.21564e9	1.14701	0.573505	−	0.819202i	$-0.305583\pi$
$379$	1.21564e9	1.14701	0.573505	+	0.819202i	$0.305583\pi$
$380$	−1.24217e9	−1.16128
$381$	3.86626e8	0.358140
$382$	−1.19895e9	−1.10047
$383$	3.85577e8	0.350683	0.175342	−	0.984508i	$-0.443897\pi$
$383$	3.85577e8	0.350683	0.175342	+	0.984508i	$0.443897\pi$
$384$	4.94678e8	0.445824
$385$	4.93839e9	4.41035
$386$	4.92083e8	0.435494
$387$	1.13768e8	0.0997777
$388$	1.52737e9	1.32749
$389$	−1.39089e9	−1.19804	−0.599019	−	0.800735i	$-0.704443\pi$
$389$	−1.39089e9	−1.19804	−0.599019	+	0.800735i	$0.704443\pi$
$390$	7.48020e8	0.638539
$391$	1.79321e9	1.51709
$392$	−9.76702e8	−0.818957
$393$	−1.29773e9	−1.07847
$394$	−8.36805e8	−0.689267
$395$	1.33692e9	1.09148
$396$	4.38925e8	0.355187
$397$	−1.34669e8	−0.108019	−0.0540096	−	0.998540i	$-0.517200\pi$
$397$	−1.34669e8	−0.108019	−0.0540096	+	0.998540i	$0.517200\pi$
$398$	5.41497e8	0.430532
$399$	−1.31208e9	−1.03408
$400$	−2.61796e9	−2.04528
$401$	7.92234e8	0.613547	0.306774	−	0.951782i	$-0.400751\pi$
$401$	7.92234e8	0.613547	0.306774	+	0.951782i	$0.400751\pi$
$402$	−1.08527e9	−0.833197
$403$	−9.71737e8	−0.739573
$404$	1.30313e9	0.983223
$405$	2.43337e8	0.182019
$406$	2.47367e9	1.83442
$407$	−2.19496e9	−1.61379
$408$	5.53229e8	0.403269
$409$	−1.98450e9	−1.43424	−0.717118	−	0.696952i	$-0.754539\pi$
$409$	−1.98450e9	−1.43424	−0.717118	+	0.696952i	$0.754539\pi$
$410$	−1.53372e9	−1.09901
$411$	−4.90494e8	−0.348487
$412$	7.64482e8	0.538551
$413$	3.23764e8	0.226154
$414$	−5.51180e8	−0.381761
$415$	−3.03113e9	−2.08179
$416$	−8.94537e8	−0.609216
$417$	7.10836e8	0.480058
$418$	−3.09966e9	−2.07586
$419$	1.12010e9	0.743886	0.371943	−	0.928256i	$-0.378692\pi$
$419$	1.12010e9	0.743886	0.371943	+	0.928256i	$0.378692\pi$
$420$	1.71512e9	1.12959
$421$	1.60154e9	1.04605	0.523024	−	0.852318i	$-0.324804\pi$
$421$	1.60154e9	1.04605	0.523024	+	0.852318i	$0.324804\pi$
$422$	9.44703e7	0.0611930
$423$	6.58025e8	0.422718
$424$	7.57062e8	0.482337
$425$	−4.58483e9	−2.89709
$426$	1.11840e9	0.700910
$427$	1.13361e9	0.704636
$428$	−8.91004e8	−0.549321
$429$	7.60481e8	0.465037
$430$	1.05022e9	0.637000
$431$	−1.42222e9	−0.855648	−0.427824	−	0.903862i	$-0.640720\pi$
$431$	−1.42222e9	−0.855648	−0.427824	+	0.903862i	$0.640720\pi$
$432$	−3.91766e8	−0.233794
$433$	1.13304e9	0.670713	0.335356	−	0.942091i	$-0.391143\pi$
$433$	1.13304e9	0.670713	0.335356	+	0.942091i	$0.391143\pi$
$434$	−5.46874e9	−3.21124
$435$	1.31994e9	0.768851
$436$	−3.91346e8	−0.226130
$437$	1.58584e9	0.909020
$438$	−3.49471e8	−0.198725
$439$	−1.92938e9	−1.08841	−0.544204	−	0.838953i	$-0.683168\pi$
$439$	−1.92938e9	−1.08841	−0.544204	+	0.838953i	$0.683168\pi$
$440$	−1.84144e9	−1.03056
$441$	1.21128e9	0.672527
$442$	−2.10908e9	−1.16175
$443$	−8.33711e7	−0.0455620	−0.0227810	−	0.999740i	$-0.507252\pi$
$443$	−8.33711e7	−0.0455620	−0.0227810	+	0.999740i	$0.507252\pi$
$444$	−7.62316e8	−0.413328
$445$	−2.91446e9	−1.56783
$446$	−8.72053e8	−0.465448
$447$	1.79408e9	0.950089
$448$	−1.01804e9	−0.534926
$449$	2.88898e9	1.50620	0.753099	−	0.657907i	$-0.228558\pi$
$449$	2.88898e9	1.50620	0.753099	+	0.657907i	$0.228558\pi$
$450$	1.40924e9	0.729025
$451$	−1.55927e9	−0.800394
$452$	−1.86252e8	−0.0948673
$453$	−1.88664e9	−0.953554
$454$	3.67350e9	1.84240
$455$	2.97160e9	1.47894
$456$	4.89252e8	0.241633
$457$	−2.23596e9	−1.09587	−0.547933	−	0.836522i	$-0.684585\pi$
$457$	−2.23596e9	−1.09587	−0.547933	+	0.836522i	$0.684585\pi$
$458$	−2.70262e9	−1.31449
$459$	−6.86100e8	−0.331164
$460$	−2.07296e9	−0.992977
$461$	−1.26440e9	−0.601077	−0.300539	−	0.953770i	$-0.597166\pi$
$461$	−1.26440e9	−0.601077	−0.300539	+	0.953770i	$0.597166\pi$
$462$	4.27983e9	2.01920
$463$	2.39212e9	1.12008	0.560041	−	0.828465i	$-0.310785\pi$
$463$	2.39212e9	1.12008	0.560041	+	0.828465i	$0.310785\pi$
$464$	−2.12507e9	−0.987553
$465$	−2.91810e9	−1.34591
$466$	−1.97259e9	−0.902996
$467$	5.83299e8	0.265022	0.132511	−	0.991182i	$-0.457696\pi$
$467$	5.83299e8	0.265022	0.132511	+	0.991182i	$0.457696\pi$
$468$	2.64117e8	0.119107
$469$	−4.31138e9	−1.92980
$470$	6.07434e9	2.69871
$471$	−7.16834e8	−0.316115
$472$	−1.20726e8	−0.0528450
$473$	1.06771e9	0.463916
$474$	1.15864e9	0.499715
$475$	−4.05463e9	−1.73590
$476$	−4.83585e9	−2.05517
$477$	−9.38888e8	−0.396095
$478$	−5.58320e9	−2.33822
$479$	3.79366e9	1.57719	0.788595	−	0.614913i	$-0.210809\pi$
$479$	3.79366e9	1.57719	0.788595	+	0.614913i	$0.210809\pi$
$480$	−2.68627e9	−1.10868
$481$	−1.32079e9	−0.541159
$482$	−3.65018e8	−0.148474
$483$	−2.18963e9	−0.884211
$484$	2.40434e9	0.963909
$485$	7.94681e9	3.16298
$486$	2.10887e8	0.0833342
$487$	−2.39967e9	−0.941455	−0.470728	−	0.882279i	$-0.656009\pi$
$487$	−2.39967e9	−0.941455	−0.470728	+	0.882279i	$0.656009\pi$
$488$	−4.22703e8	−0.164651
$489$	1.55491e9	0.601344
$490$	1.11815e10	4.29354
$491$	4.01253e9	1.52979	0.764897	−	0.644152i	$-0.222790\pi$
$491$	4.01253e9	1.52979	0.764897	+	0.644152i	$0.222790\pi$
$492$	−5.41539e8	−0.204999
$493$	−3.72163e9	−1.39884
$494$	−1.86518e9	−0.696107
$495$	2.28371e9	0.846295
$496$	4.69807e9	1.72876
$497$	4.44297e9	1.62340
$498$	−2.62692e9	−0.953112
$499$	2.58807e9	0.932445	0.466223	−	0.884667i	$-0.345615\pi$
$499$	2.58807e9	0.932445	0.466223	+	0.884667i	$0.345615\pi$
$500$	2.15201e9	0.769928
$501$	1.34595e8	0.0478186
$502$	−3.39008e9	−1.19604
$503$	−5.50700e9	−1.92942	−0.964712	−	0.263309i	$-0.915186\pi$
$503$	−5.50700e9	−1.92942	−0.964712	+	0.263309i	$0.915186\pi$
$504$	−6.75531e8	−0.235038
$505$	6.78010e9	2.34270
$506$	−5.17279e9	−1.77500
$507$	−1.23660e9	−0.421407
$508$	1.26017e9	0.426489
$509$	1.30017e9	0.437007	0.218503	−	0.975836i	$-0.429883\pi$
$509$	1.30017e9	0.437007	0.218503	+	0.975836i	$0.429883\pi$
$510$	−6.33351e9	−2.11421
$511$	−1.38832e9	−0.460273
$512$	2.82725e9	0.930934
$513$	−6.06758e8	−0.198429
$514$	4.37983e9	1.42261
$515$	3.97756e9	1.28319
$516$	3.70819e8	0.118820
$517$	6.17553e9	1.96543
$518$	−7.43313e9	−2.34973
$519$	2.28108e9	0.716233
$520$	−1.10806e9	−0.345582
$521$	−4.64043e9	−1.43756	−0.718780	−	0.695238i	$-0.755299\pi$
$521$	−4.64043e9	−1.43756	−0.718780	+	0.695238i	$0.755299\pi$
$522$	1.14392e9	0.352005
$523$	6.14798e9	1.87922	0.939608	−	0.342254i	$-0.111190\pi$
$523$	6.14798e9	1.87922	0.939608	+	0.342254i	$0.111190\pi$
$524$	−4.22983e9	−1.28429
$525$	5.59840e9	1.68852
$526$	4.07230e9	1.22008
$527$	8.22772e9	2.44874
$528$	−3.67671e9	−1.08703
$529$	−7.58342e8	−0.222726
$530$	−8.66704e9	−2.52875
$531$	1.49721e8	0.0433963
$532$	−4.27662e9	−1.23143
$533$	−9.38269e8	−0.268400
$534$	−2.52581e9	−0.717804
$535$	−4.63585e9	−1.30885
$536$	1.60764e9	0.450933
$537$	−2.13463e8	−0.0594856
$538$	3.98429e9	1.10310
$539$	1.13678e10	3.12691
$540$	7.93137e8	0.216756
$541$	−1.05096e9	−0.285362	−0.142681	−	0.989769i	$-0.545572\pi$
$541$	−1.05096e9	−0.285362	−0.142681	+	0.989769i	$0.545572\pi$
$542$	−7.19377e9	−1.94070
$543$	1.14293e9	0.306351
$544$	7.57407e9	2.01713
$545$	−2.03615e9	−0.538794
$546$	2.57533e9	0.677109
$547$	5.58405e9	1.45879	0.729396	−	0.684092i	$-0.239801\pi$
$547$	5.58405e9	1.45879	0.729396	+	0.684092i	$0.239801\pi$
$548$	−1.59872e9	−0.414994
$549$	5.24225e8	0.135212
$550$	1.32257e10	3.38960
$551$	−3.29125e9	−0.838167
$552$	8.16476e8	0.206612
$553$	4.60283e9	1.15741
$554$	−4.06746e9	−1.01634
$555$	−3.96629e9	−0.984826
$556$	2.31691e9	0.571673
$557$	−2.32229e7	−0.00569408	−0.00284704	−	0.999996i	$-0.500906\pi$
$557$	−2.32229e7	−0.00569408	−0.00284704	+	0.999996i	$0.500906\pi$
$558$	−2.52896e9	−0.616201
$559$	6.42480e8	0.155567
$560$	−1.43669e10	−3.45703
$561$	−6.43901e9	−1.53975
$562$	4.82174e9	1.14585
$563$	4.34065e9	1.02512	0.512561	−	0.858651i	$-0.328697\pi$
$563$	4.34065e9	1.02512	0.512561	+	0.858651i	$0.328697\pi$
$564$	2.14478e9	0.503391
$565$	−9.69060e8	−0.226038
$566$	3.63722e9	0.843163
$567$	8.37775e8	0.193013
$568$	−1.65671e9	−0.379338
$569$	−1.25447e9	−0.285474	−0.142737	−	0.989761i	$-0.545590\pi$
$569$	−1.25447e9	−0.285474	−0.142737	+	0.989761i	$0.545590\pi$
$570$	−5.60109e9	−1.26681
$571$	−7.73775e9	−1.73936	−0.869678	−	0.493620i	$-0.835673\pi$
$571$	−7.73775e9	−1.73936	−0.869678	+	0.493620i	$0.835673\pi$
$572$	2.47872e9	0.553786
$573$	−2.20259e9	−0.489094
$574$	−5.28039e9	−1.16540
$575$	−6.76646e9	−1.48431
$576$	−4.70784e8	−0.102646
$577$	6.30012e9	1.36532	0.682658	−	0.730738i	$-0.260824\pi$
$577$	6.30012e9	1.36532	0.682658	+	0.730738i	$0.260824\pi$
$578$	1.18268e10	2.54754
$579$	9.04005e8	0.193551
$580$	4.30224e9	0.915580
$581$	−1.04358e10	−2.20754
$582$	6.88707e9	1.44812
$583$	−8.81142e9	−1.84164
$584$	5.17680e8	0.107551
$585$	1.37419e9	0.283792
$586$	5.48375e9	1.12573
$587$	−2.77083e9	−0.565426	−0.282713	−	0.959204i	$-0.591234\pi$
$587$	−2.77083e9	−0.565426	−0.282713	+	0.959204i	$0.591234\pi$
$588$	3.94807e9	0.800873
$589$	7.27625e9	1.46725
$590$	1.38210e9	0.277050
$591$	−1.53729e9	−0.306338
$592$	6.38563e9	1.26496
$593$	−5.31671e9	−1.04701	−0.523506	−	0.852022i	$-0.675376\pi$
$593$	−5.31671e9	−1.04701	−0.523506	+	0.852022i	$0.675376\pi$
$594$	1.97916e9	0.387462
$595$	−2.51607e10	−4.89680
$596$	5.84764e9	1.13141
$597$	9.94783e8	0.191346
$598$	−3.11265e9	−0.595219
$599$	−5.08449e9	−0.966616	−0.483308	−	0.875450i	$-0.660565\pi$
$599$	−5.08449e9	−0.966616	−0.483308	+	0.875450i	$0.660565\pi$
$600$	−2.08755e9	−0.394554
$601$	−5.61219e9	−1.05456	−0.527280	−	0.849691i	$-0.676788\pi$
$601$	−5.61219e9	−1.05456	−0.527280	+	0.849691i	$0.676788\pi$
$602$	3.61575e9	0.675477
$603$	−1.99375e9	−0.370306
$604$	−6.14935e9	−1.13553
$605$	1.25096e10	2.29668
$606$	5.87595e9	1.07257
$607$	6.49781e9	1.17925	0.589626	−	0.807677i	$-0.299275\pi$
$607$	6.49781e9	1.17925	0.589626	+	0.807677i	$0.299275\pi$
$608$	6.69819e9	1.20863
$609$	4.54437e9	0.815292
$610$	4.83921e9	0.863217
$611$	3.71604e9	0.659076
$612$	−2.23629e9	−0.394364
$613$	3.54849e9	0.622203	0.311102	−	0.950377i	$-0.399302\pi$
$613$	3.54849e9	0.622203	0.311102	+	0.950377i	$0.399302\pi$
$614$	−7.51762e9	−1.31066
$615$	−2.81760e9	−0.488446
$616$	−6.33982e9	−1.09281
$617$	−8.10427e9	−1.38904	−0.694522	−	0.719472i	$-0.744384\pi$
$617$	−8.10427e9	−1.38904	−0.694522	+	0.719472i	$0.744384\pi$
$618$	3.44714e9	0.587488
$619$	−4.62805e9	−0.784298	−0.392149	−	0.919902i	$-0.628268\pi$
$619$	−4.62805e9	−0.784298	−0.392149	+	0.919902i	$0.628268\pi$
$620$	−9.51131e9	−1.60276
$621$	−1.01257e9	−0.169670
$622$	8.92240e7	0.0148667
$623$	−1.00341e10	−1.66253
$624$	−2.21241e9	−0.364518
$625$	9.20980e8	0.150893
$626$	1.32417e8	0.0215742
$627$	−5.69439e9	−0.922594
$628$	−2.33646e9	−0.376443
$629$	1.11831e10	1.79179
$630$	7.73365e9	1.23223
$631$	−2.22522e9	−0.352590	−0.176295	−	0.984337i	$-0.556411\pi$
$631$	−2.22522e9	−0.352590	−0.176295	+	0.984337i	$0.556411\pi$
$632$	−1.71632e9	−0.270450
$633$	1.73551e8	0.0271966
$634$	2.26525e9	0.353024
$635$	6.55663e9	1.01618
$636$	−3.06023e9	−0.471687
$637$	6.84041e9	1.04856
$638$	1.07356e10	1.63665
$639$	2.05461e9	0.311513
$640$	8.38904e9	1.26498
$641$	−3.74794e9	−0.562069	−0.281034	−	0.959698i	$-0.590677\pi$
$641$	−3.74794e9	−0.562069	−0.281034	+	0.959698i	$0.590677\pi$
$642$	−4.01764e9	−0.599237
$643$	−6.50343e9	−0.964726	−0.482363	−	0.875971i	$-0.660221\pi$
$643$	−6.50343e9	−0.964726	−0.482363	+	0.875971i	$0.660221\pi$
$644$	−7.13692e9	−1.05296
$645$	1.92935e9	0.283108
$646$	1.57925e10	2.30482
$647$	−4.25390e9	−0.617479	−0.308740	−	0.951147i	$-0.599907\pi$
$647$	−4.25390e9	−0.617479	−0.308740	+	0.951147i	$0.599907\pi$
$648$	−3.12392e8	−0.0451011
$649$	1.40513e9	0.201771
$650$	7.95836e9	1.13665
$651$	−1.00466e10	−1.42721
$652$	5.06808e9	0.716106
$653$	3.65504e9	0.513684	0.256842	−	0.966453i	$-0.417318\pi$
$653$	3.65504e9	0.513684	0.256842	+	0.966453i	$0.417318\pi$
$654$	−1.76462e9	−0.246678
$655$	−2.20076e10	−3.06005
$656$	4.53626e9	0.627386
$657$	−6.42013e8	−0.0883212
$658$	2.09131e10	2.86173
$659$	−9.45163e9	−1.28649	−0.643247	−	0.765659i	$-0.722413\pi$
$659$	−9.45163e9	−1.28649	−0.643247	+	0.765659i	$0.722413\pi$
$660$	7.44355e9	1.00780
$661$	−4.38475e9	−0.590527	−0.295264	−	0.955416i	$-0.595407\pi$
$661$	−4.38475e9	−0.590527	−0.295264	+	0.955416i	$0.595407\pi$
$662$	9.80086e9	1.31299
$663$	−3.87458e9	−0.516330
$664$	3.89132e9	0.515832
$665$	−2.22510e10	−2.93410
$666$	−3.43737e9	−0.450886
$667$	−5.49252e9	−0.716690
$668$	4.38701e8	0.0569444
$669$	−1.60205e9	−0.206864
$670$	−1.84047e10	−2.36411
$671$	4.91982e9	0.628667
$672$	−9.24846e9	−1.17565
$673$	−1.06771e10	−1.35020	−0.675102	−	0.737724i	$-0.735900\pi$
$673$	−1.06771e10	−1.35020	−0.675102	+	0.737724i	$0.735900\pi$
$674$	1.04658e10	1.31663
$675$	2.58892e9	0.324008
$676$	−4.03060e9	−0.501830
$677$	5.43224e8	0.0672851	0.0336426	−	0.999434i	$-0.489289\pi$
$677$	5.43224e8	0.0672851	0.0336426	+	0.999434i	$0.489289\pi$
$678$	−8.39832e8	−0.103488
$679$	2.73597e10	3.35404
$680$	9.38198e9	1.14423
$681$	6.74858e9	0.818837
$682$	−2.37342e10	−2.86503
$683$	−9.65996e8	−0.116012	−0.0580060	−	0.998316i	$-0.518474\pi$
$683$	−9.65996e8	−0.116012	−0.0580060	+	0.998316i	$0.518474\pi$
$684$	−1.97768e9	−0.236297
$685$	−8.31808e9	−0.988794
$686$	1.94160e10	2.29628
$687$	−4.96498e9	−0.584210
$688$	−3.10621e9	−0.363639
$689$	−5.30214e9	−0.617567
$690$	−9.34723e9	−1.08321
$691$	−6.65558e9	−0.767384	−0.383692	−	0.923461i	$-0.625348\pi$
$691$	−6.65558e9	−0.767384	−0.383692	+	0.923461i	$0.625348\pi$
$692$	7.43498e9	0.852920
$693$	7.86248e9	0.897415
$694$	1.00702e10	1.14362
$695$	1.20548e10	1.36211
$696$	−1.69452e9	−0.190508
$697$	7.94435e9	0.888677
$698$	−6.04004e9	−0.672273
$699$	−3.62384e9	−0.401328
$700$	1.82475e10	2.01076
$701$	−7.59130e9	−0.832345	−0.416172	−	0.909286i	$-0.636629\pi$
$701$	−7.59130e9	−0.832345	−0.416172	+	0.909286i	$0.636629\pi$
$702$	1.19093e9	0.129929
$703$	9.88990e9	1.07361
$704$	−4.41828e9	−0.477254
$705$	1.11592e10	1.19942
$706$	1.08303e10	1.15830
$707$	2.33429e10	2.48421
$708$	4.88004e8	0.0516782
$709$	−7.76529e9	−0.818268	−0.409134	−	0.912474i	$-0.634169\pi$
$709$	−7.76529e9	−0.818268	−0.409134	+	0.912474i	$0.634169\pi$
$710$	1.89664e10	1.98876
$711$	2.12853e9	0.222094
$712$	3.74154e9	0.388481
$713$	1.21428e10	1.25460
$714$	−2.18054e10	−2.24192
$715$	1.28967e10	1.31949
$716$	−6.95763e8	−0.0708380
$717$	−1.02569e10	−1.03920
$718$	2.26054e10	2.27917
$719$	2.04713e9	0.205398	0.102699	−	0.994713i	$-0.467252\pi$
$719$	2.04713e9	0.205398	0.102699	+	0.994713i	$0.467252\pi$
$720$	−6.64380e9	−0.663366
$721$	1.36942e10	1.36070
$722$	8.28926e8	0.0819664
$723$	−6.70574e8	−0.0659876
$724$	3.72528e9	0.364816
$725$	1.40431e10	1.36862
$726$	1.08414e10	1.05150
$727$	−7.27546e9	−0.702247	−0.351124	−	0.936329i	$-0.614200\pi$
$727$	−7.27546e9	−0.702247	−0.351124	+	0.936329i	$0.614200\pi$
$728$	−3.81490e9	−0.366457
$729$	3.87420e8	0.0370370
$730$	−5.92654e9	−0.563860
$731$	−5.43990e9	−0.515086
$732$	1.70867e9	0.161016
$733$	1.92809e9	0.180827	0.0904135	−	0.995904i	$-0.471181\pi$
$733$	1.92809e9	0.180827	0.0904135	+	0.995904i	$0.471181\pi$
$734$	−1.46941e10	−1.37153
$735$	2.05416e10	1.90822
$736$	1.11781e10	1.03346
$737$	−1.87113e10	−1.72174
$738$	−2.44186e9	−0.223627
$739$	−1.32836e9	−0.121077	−0.0605385	−	0.998166i	$-0.519282\pi$
$739$	−1.32836e9	−0.121077	−0.0605385	+	0.998166i	$0.519282\pi$
$740$	−1.29278e10	−1.17277
$741$	−3.42652e9	−0.309378
$742$	−2.98394e10	−2.68149
$743$	2.02673e10	1.81273	0.906367	−	0.422490i	$-0.138844\pi$
$743$	2.02673e10	1.81273	0.906367	+	0.422490i	$0.138844\pi$
$744$	3.74621e9	0.333493
$745$	3.04250e10	2.69577
$746$	−1.35210e10	−1.19240
$747$	−4.82591e9	−0.423601
$748$	−2.09874e10	−1.83360
$749$	−1.59606e10	−1.38791
$750$	9.70367e9	0.839889
$751$	−7.01982e9	−0.604764	−0.302382	−	0.953187i	$-0.597782\pi$
$751$	−7.01982e9	−0.604764	−0.302382	+	0.953187i	$0.597782\pi$
$752$	−1.79660e10	−1.54059
$753$	−6.22791e9	−0.531569
$754$	6.46001e9	0.548825
$755$	−3.19947e10	−2.70560
$756$	2.73066e9	0.229848
$757$	−1.56061e10	−1.30755	−0.653774	−	0.756690i	$-0.726815\pi$
$757$	−1.56061e10	−1.30755	−0.653774	+	0.756690i	$0.726815\pi$
$758$	1.78664e10	1.49003
$759$	−9.50293e9	−0.788881
$760$	8.29703e9	0.685606
$761$	1.06411e8	0.00875264	0.00437632	−	0.999990i	$-0.498607\pi$
$761$	1.06411e8	0.00875264	0.00437632	+	0.999990i	$0.498607\pi$
$762$	5.68227e9	0.465243
$763$	−7.01018e9	−0.571339
$764$	−7.17916e9	−0.582434
$765$	−1.16353e10	−0.939641
$766$	5.66685e9	0.455556
$767$	8.45515e8	0.0676608
$768$	9.50219e9	0.756936
$769$	1.40421e9	0.111350	0.0556750	−	0.998449i	$-0.482269\pi$
$769$	1.40421e9	0.111350	0.0556750	+	0.998449i	$0.482269\pi$
$770$	7.25799e10	5.72926
$771$	8.04618e9	0.632266
$772$	2.94653e9	0.230489
$773$	1.70826e10	1.33022	0.665112	−	0.746744i	$-0.268384\pi$
$773$	1.70826e10	1.33022	0.665112	+	0.746744i	$0.268384\pi$
$774$	1.67206e9	0.129616
$775$	−3.10464e10	−2.39582
$776$	−1.02020e10	−0.783734
$777$	−1.36554e10	−1.04431
$778$	−2.04421e10	−1.55631
$779$	7.02565e9	0.532483
$780$	4.47905e9	0.337952
$781$	1.92824e10	1.44838
$782$	2.63549e10	1.97078
$783$	2.10150e9	0.156445
$784$	−3.30714e10	−2.45102
$785$	−1.21565e10	−0.896942
$786$	−1.90728e10	−1.40099
$787$	−9.46350e9	−0.692054	−0.346027	−	0.938224i	$-0.612470\pi$
$787$	−9.46350e9	−0.692054	−0.346027	+	0.938224i	$0.612470\pi$
$788$	−5.01068e9	−0.364800
$789$	7.48121e9	0.542254
$790$	1.96488e10	1.41789
$791$	−3.33634e9	−0.239691
$792$	−2.93178e9	−0.209698
$793$	2.96043e9	0.210814
$794$	−1.97924e9	−0.140322
$795$	−1.59222e10	−1.12388
$796$	3.24241e9	0.227862
$797$	−1.05899e10	−0.740949	−0.370474	−	0.928843i	$-0.620805\pi$
$797$	−1.05899e10	−0.740949	−0.370474	+	0.928843i	$0.620805\pi$
$798$	−1.92838e10	−1.34333
$799$	−3.14638e10	−2.18221
$800$	−2.85799e10	−1.97354
$801$	−4.64016e9	−0.319021
$802$	1.16435e10	0.797029
$803$	−6.02526e9	−0.410650
$804$	−6.49848e9	−0.440977
$805$	−3.71330e10	−2.50885
$806$	−1.42817e10	−0.960743
$807$	7.31954e9	0.490260
$808$	−8.70418e9	−0.580481
$809$	1.90523e10	1.26511	0.632555	−	0.774516i	$-0.282006\pi$
$809$	1.90523e10	1.26511	0.632555	+	0.774516i	$0.282006\pi$
$810$	3.57635e9	0.236451
$811$	1.62908e10	1.07243	0.536217	−	0.844080i	$-0.319853\pi$
$811$	1.62908e10	1.07243	0.536217	+	0.844080i	$0.319853\pi$
$812$	1.48120e10	0.970884
$813$	−1.32157e10	−0.862527
$814$	−3.22595e10	−2.09639
$815$	2.63690e10	1.70625
$816$	1.87325e10	1.20693
$817$	−4.81081e9	−0.308632
$818$	−2.91664e10	−1.86314
$819$	4.73113e9	0.300934
$820$	−9.18374e9	−0.581662
$821$	1.60953e9	0.101508	0.0507539	−	0.998711i	$-0.483838\pi$
$821$	1.60953e9	0.101508	0.0507539	+	0.998711i	$0.483838\pi$
$822$	−7.20883e9	−0.452703
$823$	−1.20942e10	−0.756272	−0.378136	−	0.925750i	$-0.623435\pi$
$823$	−1.20942e10	−0.756272	−0.378136	+	0.925750i	$0.623435\pi$
$824$	−5.10633e9	−0.317953
$825$	2.42969e10	1.50647
$826$	4.75839e9	0.293785
$827$	9.39665e9	0.577702	0.288851	−	0.957374i	$-0.406727\pi$
$827$	9.39665e9	0.577702	0.288851	+	0.957374i	$0.406727\pi$
$828$	−3.30039e9	−0.202050
$829$	1.58388e10	0.965563	0.482781	−	0.875741i	$-0.339627\pi$
$829$	1.58388e10	0.965563	0.482781	+	0.875741i	$0.339627\pi$
$830$	−4.45488e10	−2.70435
$831$	−7.47232e9	−0.451702
$832$	−2.65864e9	−0.160040
$833$	−5.79180e10	−3.47181
$834$	1.04472e10	0.623619
$835$	2.28254e9	0.135680
$836$	−1.85604e10	−1.09866
$837$	−4.64595e9	−0.273864
$838$	1.64622e10	0.966346
$839$	3.24355e10	1.89607	0.948034	−	0.318170i	$-0.103068\pi$
$839$	3.24355e10	1.89607	0.948034	+	0.318170i	$0.103068\pi$
$840$	−1.14560e10	−0.666895
$841$	−5.85067e9	−0.339172
$842$	2.35380e10	1.35887
$843$	8.85801e9	0.509260
$844$	5.65676e8	0.0323869
$845$	−2.09710e10	−1.19570
$846$	9.67105e9	0.549133
$847$	4.30689e10	2.43541
$848$	2.56343e10	1.44357
$849$	6.68193e9	0.374736
$850$	−6.73837e10	−3.76347
$851$	1.65045e10	0.918013
$852$	6.69682e9	0.370962
$853$	4.28375e9	0.236321	0.118161	−	0.992995i	$-0.462300\pi$
$853$	4.28375e9	0.236321	0.118161	+	0.992995i	$0.462300\pi$
$854$	1.66607e10	0.915358
$855$	−1.02898e10	−0.563020
$856$	5.95142e9	0.324312
$857$	−2.60684e9	−0.141475	−0.0707377	−	0.997495i	$-0.522535\pi$
$857$	−2.60684e9	−0.141475	−0.0707377	+	0.997495i	$0.522535\pi$
$858$	1.11768e10	0.604107
$859$	7.87750e8	0.0424046	0.0212023	−	0.999775i	$-0.493251\pi$
$859$	7.87750e8	0.0424046	0.0212023	+	0.999775i	$0.493251\pi$
$860$	6.28856e9	0.337137
$861$	−9.70060e9	−0.517950
$862$	−2.09024e10	−1.11153
$863$	−1.69537e10	−0.897896	−0.448948	−	0.893558i	$-0.648201\pi$
$863$	−1.69537e10	−0.897896	−0.448948	+	0.893558i	$0.648201\pi$
$864$	−4.27685e9	−0.225593
$865$	3.86838e10	2.03223
$866$	1.66523e10	0.871290
$867$	2.17271e10	1.13223
$868$	−3.27461e10	−1.69958
$869$	1.99761e10	1.03262
$870$	1.93993e10	0.998776
$871$	−1.12592e10	−0.577359
$872$	2.61398e9	0.133504
$873$	1.26522e10	0.643602
$874$	2.33072e10	1.18086
$875$	3.85491e10	1.94530
$876$	−2.09259e9	−0.105177
$877$	−1.67825e10	−0.840153	−0.420076	−	0.907489i	$-0.637997\pi$
$877$	−1.67825e10	−0.840153	−0.420076	+	0.907489i	$0.637997\pi$
$878$	−2.83562e10	−1.41390
$879$	1.00742e10	0.500321
$880$	−6.23517e10	−3.08432
$881$	3.74442e10	1.84488	0.922442	−	0.386135i	$-0.126190\pi$
$881$	3.74442e10	1.84488	0.922442	+	0.386135i	$0.126190\pi$
$882$	1.78023e10	0.873647
$883$	2.15204e10	1.05193	0.525967	−	0.850505i	$-0.323703\pi$
$883$	2.15204e10	1.05193	0.525967	+	0.850505i	$0.323703\pi$
$884$	−1.26289e10	−0.614868
$885$	2.53906e9	0.123132
$886$	−1.22531e9	−0.0591873
$887$	−1.11581e10	−0.536857	−0.268429	−	0.963300i	$-0.586504\pi$
$887$	−1.11581e10	−0.536857	−0.268429	+	0.963300i	$0.586504\pi$
$888$	5.09186e9	0.244023
$889$	2.25735e10	1.07756
$890$	−4.28341e10	−2.03669
$891$	3.63592e9	0.172204
$892$	−5.22174e9	−0.246342
$893$	−2.78252e10	−1.30755
$894$	2.63677e10	1.23421
$895$	−3.62002e9	−0.168784
$896$	2.88823e10	1.34138
$897$	−5.71825e9	−0.264539
$898$	4.24596e10	1.95663
$899$	−2.52012e10	−1.15681
$900$	8.43837e9	0.385842
$901$	4.48934e10	2.04478
$902$	−2.29167e10	−1.03975
$903$	6.64249e9	0.300209
$904$	1.24406e9	0.0560083
$905$	1.93825e10	0.869238
$906$	−2.77281e10	−1.23872
$907$	7.89855e9	0.351497	0.175749	−	0.984435i	$-0.443765\pi$
$907$	7.89855e9	0.351497	0.175749	+	0.984435i	$0.443765\pi$
$908$	2.19964e10	0.975106
$909$	1.07947e10	0.476691
$910$	4.36739e10	1.92122
$911$	1.68370e10	0.737821	0.368911	−	0.929465i	$-0.379731\pi$
$911$	1.68370e10	0.737821	0.368911	+	0.929465i	$0.379731\pi$
$912$	1.65662e10	0.723172
$913$	−4.52909e10	−1.96953
$914$	−3.28621e10	−1.42359
$915$	8.89011e9	0.383648
$916$	−1.61829e10	−0.695702
$917$	−7.57691e10	−3.24489
$918$	−1.00837e10	−0.430199
$919$	2.78362e10	1.18306	0.591529	−	0.806284i	$-0.298525\pi$
$919$	2.78362e10	1.18306	0.591529	+	0.806284i	$0.298525\pi$
$920$	1.38463e10	0.586240
$921$	−1.38106e10	−0.582511
$922$	−1.85830e10	−0.780830
$923$	1.16029e10	0.485691
$924$	2.56271e10	1.06868
$925$	−4.21983e10	−1.75307
$926$	3.51572e10	1.45504
$927$	6.33273e9	0.261103
$928$	−2.31991e10	−0.952911
$929$	2.25578e10	0.923083	0.461542	−	0.887119i	$-0.347296\pi$
$929$	2.25578e10	0.923083	0.461542	+	0.887119i	$0.347296\pi$
$930$	−4.28876e10	−1.74840
$931$	−5.12202e10	−2.08026
$932$	−1.18116e10	−0.477918
$933$	1.63913e8	0.00660737
$934$	8.57279e9	0.344277
$935$	−1.09197e11	−4.36886
$936$	−1.76416e9	−0.0703189
$937$	−2.56679e10	−1.01930	−0.509649	−	0.860382i	$-0.670225\pi$
$937$	−2.56679e10	−1.01930	−0.509649	+	0.860382i	$0.670225\pi$
$938$	−6.33648e10	−2.50691
$939$	2.43263e8	0.00958842
$940$	3.63724e10	1.42832
$941$	7.37013e9	0.288344	0.144172	−	0.989553i	$-0.453948\pi$
$941$	7.37013e9	0.288344	0.144172	+	0.989553i	$0.453948\pi$
$942$	−1.05354e10	−0.410650
$943$	1.17246e10	0.455309
$944$	−4.08782e9	−0.158158
$945$	1.42075e10	0.547654
$946$	1.56922e10	0.602651
$947$	4.90023e10	1.87496	0.937479	−	0.348042i	$-0.113153\pi$
$947$	4.90023e10	1.87496	0.937479	+	0.348042i	$0.113153\pi$
$948$	6.93776e9	0.264478
$949$	−3.62561e9	−0.137705
$950$	−5.95912e10	−2.25502
$951$	4.16149e9	0.156898
$952$	3.23008e10	1.21335
$953$	−2.07767e10	−0.777590	−0.388795	−	0.921324i	$-0.627109\pi$
$953$	−2.07767e10	−0.777590	−0.388795	+	0.921324i	$0.627109\pi$
$954$	−1.37989e10	−0.514548
$955$	−3.73528e10	−1.38775
$956$	−3.34315e10	−1.23752
$957$	1.97224e10	0.727392
$958$	5.57557e10	2.04885
$959$	−2.86380e10	−1.04852
$960$	−7.98383e9	−0.291247
$961$	2.82017e10	1.02505
$962$	−1.94117e10	−0.702993
$963$	−7.38080e9	−0.266325
$964$	−2.18568e9	−0.0785809
$965$	1.53306e10	0.549180
$966$	−3.21812e10	−1.14864
$967$	−1.99822e10	−0.710642	−0.355321	−	0.934744i	$-0.615628\pi$
$967$	−1.99822e10	−0.710642	−0.355321	+	0.934744i	$0.615628\pi$
$968$	−1.60597e10	−0.569079
$969$	2.90124e10	1.02436
$970$	1.16795e11	4.10888
$971$	−1.36752e9	−0.0479365	−0.0239683	−	0.999713i	$-0.507630\pi$
$971$	−1.36752e9	−0.0479365	−0.0239683	+	0.999713i	$0.507630\pi$
$972$	1.26276e9	0.0441053
$973$	4.15029e10	1.44439
$974$	−3.52681e10	−1.22300
$975$	1.46203e10	0.505173
$976$	−1.43128e10	−0.492778
$977$	−2.85359e10	−0.978951	−0.489475	−	0.872017i	$-0.662812\pi$
$977$	−2.85359e10	−0.978951	−0.489475	+	0.872017i	$0.662812\pi$
$978$	2.28526e10	0.781176
$979$	−4.35476e10	−1.48329
$980$	6.69536e10	2.27239
$981$	−3.24179e9	−0.109633
$982$	5.89725e10	1.98728
$983$	1.22389e10	0.410965	0.205483	−	0.978661i	$-0.434124\pi$
$983$	1.22389e10	0.410965	0.205483	+	0.978661i	$0.434124\pi$
$984$	3.61719e9	0.121029
$985$	−2.60703e10	−0.869200
$986$	−5.46971e10	−1.81717
$987$	3.84195e10	1.27187
$988$	−1.11684e10	−0.368420
$989$	−8.02840e9	−0.263902
$990$	3.35638e10	1.09938
$991$	−3.67813e10	−1.20052	−0.600260	−	0.799805i	$-0.704936\pi$
$991$	−3.67813e10	−1.20052	−0.600260	+	0.799805i	$0.704936\pi$
$992$	5.12881e10	1.66811
$993$	1.80052e10	0.583545
$994$	6.52987e10	2.10888
$995$	1.68701e10	0.542922
$996$	−1.57296e10	−0.504442
$997$	−6.04917e10	−1.93314	−0.966569	−	0.256405i	$-0.917462\pi$
$997$	−6.04917e10	−1.93314	−0.966569	+	0.256405i	$0.917462\pi$
$998$	3.80370e10	1.21129
$999$	−6.31479e9	−0.200392

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.d.1.14	✓	18
3.2	odd	2		531.8.a.e.1.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.14	✓	18	1.1	even	1	trivial
531.8.a.e.1.5		18	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)

\(f(q)\)	\(=\)	\(q+14.6971 q^{2} +27.0000 q^{3} +88.0043 q^{4} +457.882 q^{5} +396.821 q^{6} +1576.42 q^{7} -587.821 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+14.6971 q^{2} +27.0000 q^{3} +88.0043 q^{4} +457.882 q^{5} +396.821 q^{6} +1576.42 q^{7} -587.821 q^{8} +729.000 q^{9} +6729.53 q^{10} +6841.63 q^{11} +2376.11 q^{12} +4116.85 q^{13} +23168.8 q^{14} +12362.8 q^{15} -19903.8 q^{16} -34857.5 q^{17} +10714.2 q^{18} -30826.5 q^{19} +40295.5 q^{20} +42563.4 q^{21} +100552. q^{22} -51444.0 q^{23} -15871.2 q^{24} +131531. q^{25} +60505.7 q^{26} +19683.0 q^{27} +138732. q^{28} +106767. q^{29} +181697. q^{30} -236039. q^{31} -217287. q^{32} +184724. q^{33} -512304. q^{34} +721815. q^{35} +64155.1 q^{36} -320825. q^{37} -453059. q^{38} +111155. q^{39} -269152. q^{40} -227909. q^{41} +625558. q^{42} +156061. q^{43} +602092. q^{44} +333796. q^{45} -756076. q^{46} +902640. q^{47} -537402. q^{48} +1.66156e6 q^{49} +1.93312e6 q^{50} -941152. q^{51} +362300. q^{52} -1.28791e6 q^{53} +289283. q^{54} +3.13266e6 q^{55} -926654. q^{56} -832315. q^{57} +1.56916e6 q^{58} +205379. q^{59} +1.08798e6 q^{60} +719101. q^{61} -3.46908e6 q^{62} +1.14921e6 q^{63} -645794. q^{64} +1.88503e6 q^{65} +2.71490e6 q^{66} -2.73492e6 q^{67} -3.06761e6 q^{68} -1.38899e6 q^{69} +1.06086e7 q^{70} +2.81839e6 q^{71} -428521. q^{72} -880677. q^{73} -4.71519e6 q^{74} +3.55133e6 q^{75} -2.71286e6 q^{76} +1.07853e7 q^{77} +1.63365e6 q^{78} +2.91979e6 q^{79} -9.11359e6 q^{80} +531441. q^{81} -3.34960e6 q^{82} -6.61990e6 q^{83} +3.74576e6 q^{84} -1.59606e7 q^{85} +2.29364e6 q^{86} +2.88271e6 q^{87} -4.02165e6 q^{88} -6.36510e6 q^{89} +4.90583e6 q^{90} +6.48989e6 q^{91} -4.52729e6 q^{92} -6.37305e6 q^{93} +1.32662e7 q^{94} -1.41149e7 q^{95} -5.86674e6 q^{96} +1.73556e7 q^{97} +2.44201e7 q^{98} +4.98755e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9} + 3609 q^{10} + 15070 q^{11} + 36666 q^{12} + 13662 q^{13} + 20861 q^{14} + 18306 q^{15} + 60482 q^{16} + 71919 q^{17} + 17496 q^{18} + 56231 q^{19} + 143053 q^{20} + 83187 q^{21} + 274198 q^{22} + 150029 q^{23} + 110889 q^{24} + 399672 q^{25} + 182846 q^{26} + 354294 q^{27} + 434150 q^{28} + 591285 q^{29} + 97443 q^{30} + 426733 q^{31} + 1205630 q^{32} + 406890 q^{33} + 403548 q^{34} + 912879 q^{35} + 989982 q^{36} + 7703 q^{37} - 417859 q^{38} + 368874 q^{39} + 618020 q^{40} + 770959 q^{41} + 563247 q^{42} + 793050 q^{43} + 2591274 q^{44} + 494262 q^{45} - 4068019 q^{46} + 1410373 q^{47} + 1633014 q^{48} + 1637427 q^{49} + 1021549 q^{50} + 1941813 q^{51} - 3749190 q^{52} + 1037934 q^{53} + 472392 q^{54} + 331974 q^{55} - 391748 q^{56} + 1518237 q^{57} + 653724 q^{58} + 3696822 q^{59} + 3862431 q^{60} - 1374623 q^{61} + 5251718 q^{62} + 2246049 q^{63} + 5077197 q^{64} + 3257170 q^{65} + 7403346 q^{66} - 2436904 q^{67} + 14119909 q^{68} + 4050783 q^{69} + 5185580 q^{70} + 14289172 q^{71} + 2994003 q^{72} + 5482515 q^{73} + 14934154 q^{74} + 10791144 q^{75} + 3822912 q^{76} + 23157109 q^{77} + 4936842 q^{78} + 19786414 q^{79} + 31978143 q^{80} + 9565938 q^{81} + 9749509 q^{82} + 30227337 q^{83} + 11722050 q^{84} + 9946981 q^{85} + 44295864 q^{86} + 15964695 q^{87} + 39970897 q^{88} + 31061677 q^{89} + 2630961 q^{90} + 26377785 q^{91} + 4719698 q^{92} + 11521791 q^{93} + 44488296 q^{94} + 15534599 q^{95} + 32552010 q^{96} + 12084118 q^{97} + 42274744 q^{98} + 10986030 q^{99}+O(q^{100}) \) 18 * q + 24 * q^2 + 486 * q^3 + 1358 * q^4 + 678 * q^5 + 648 * q^6 + 3081 * q^7 + 4107 * q^8 + 13122 * q^9 + 3609 * q^10 + 15070 * q^11 + 36666 * q^12 + 13662 * q^13 + 20861 * q^14 + 18306 * q^15 + 60482 * q^16 + 71919 * q^17 + 17496 * q^18 + 56231 * q^19 + 143053 * q^20 + 83187 * q^21 + 274198 * q^22 + 150029 * q^23 + 110889 * q^24 + 399672 * q^25 + 182846 * q^26 + 354294 * q^27 + 434150 * q^28 + 591285 * q^29 + 97443 * q^30 + 426733 * q^31 + 1205630 * q^32 + 406890 * q^33 + 403548 * q^34 + 912879 * q^35 + 989982 * q^36 + 7703 * q^37 - 417859 * q^38 + 368874 * q^39 + 618020 * q^40 + 770959 * q^41 + 563247 * q^42 + 793050 * q^43 + 2591274 * q^44 + 494262 * q^45 - 4068019 * q^46 + 1410373 * q^47 + 1633014 * q^48 + 1637427 * q^49 + 1021549 * q^50 + 1941813 * q^51 - 3749190 * q^52 + 1037934 * q^53 + 472392 * q^54 + 331974 * q^55 - 391748 * q^56 + 1518237 * q^57 + 653724 * q^58 + 3696822 * q^59 + 3862431 * q^60 - 1374623 * q^61 + 5251718 * q^62 + 2246049 * q^63 + 5077197 * q^64 + 3257170 * q^65 + 7403346 * q^66 - 2436904 * q^67 + 14119909 * q^68 + 4050783 * q^69 + 5185580 * q^70 + 14289172 * q^71 + 2994003 * q^72 + 5482515 * q^73 + 14934154 * q^74 + 10791144 * q^75 + 3822912 * q^76 + 23157109 * q^77 + 4936842 * q^78 + 19786414 * q^79 + 31978143 * q^80 + 9565938 * q^81 + 9749509 * q^82 + 30227337 * q^83 + 11722050 * q^84 + 9946981 * q^85 + 44295864 * q^86 + 15964695 * q^87 + 39970897 * q^88 + 31061677 * q^89 + 2630961 * q^90 + 26377785 * q^91 + 4719698 * q^92 + 11521791 * q^93 + 44488296 * q^94 + 15534599 * q^95 + 32552010 * q^96 + 12084118 * q^97 + 42274744 * q^98 + 10986030 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more