LMFDB - Embedded newform 177.8.a.d.1.4

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			1.4
Root			$-16.0158$ 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)

$f(q)$	$=$	$q-15.0158 q^{2} +27.0000 q^{3} +97.4757 q^{4} +6.55078 q^{5} -405.428 q^{6} +1466.16 q^{7} +458.348 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-15.0158 q^{2} +27.0000 q^{3} +97.4757 q^{4} +6.55078 q^{5} -405.428 q^{6} +1466.16 q^{7} +458.348 q^{8} +729.000 q^{9} -98.3656 q^{10} +4599.84 q^{11} +2631.84 q^{12} +15226.3 q^{13} -22015.6 q^{14} +176.871 q^{15} -19359.4 q^{16} +38992.1 q^{17} -10946.6 q^{18} -499.547 q^{19} +638.542 q^{20} +39586.2 q^{21} -69070.4 q^{22} +58259.9 q^{23} +12375.4 q^{24} -78082.1 q^{25} -228636. q^{26} +19683.0 q^{27} +142915. q^{28} +211255. q^{29} -2655.87 q^{30} +61846.8 q^{31} +232029. q^{32} +124196. q^{33} -585500. q^{34} +9604.48 q^{35} +71059.8 q^{36} -62940.4 q^{37} +7501.12 q^{38} +411110. q^{39} +3002.54 q^{40} -619876. q^{41} -594421. q^{42} -356192. q^{43} +448372. q^{44} +4775.52 q^{45} -874822. q^{46} -953515. q^{47} -522703. q^{48} +1.32607e6 q^{49} +1.17247e6 q^{50} +1.05279e6 q^{51} +1.48419e6 q^{52} -1.97760e6 q^{53} -295557. q^{54} +30132.5 q^{55} +672010. q^{56} -13487.8 q^{57} -3.17218e6 q^{58} +205379. q^{59} +17240.6 q^{60} -2.98506e6 q^{61} -928683. q^{62} +1.06883e6 q^{63} -1.00611e6 q^{64} +99744.2 q^{65} -1.86490e6 q^{66} -1.04862e6 q^{67} +3.80078e6 q^{68} +1.57302e6 q^{69} -144219. q^{70} +4.10180e6 q^{71} +334136. q^{72} -260342. q^{73} +945104. q^{74} -2.10822e6 q^{75} -48693.7 q^{76} +6.74408e6 q^{77} -6.17317e6 q^{78} -1.33466e6 q^{79} -126819. q^{80} +531441. q^{81} +9.30797e6 q^{82} +8.30823e6 q^{83} +3.85870e6 q^{84} +255429. q^{85} +5.34852e6 q^{86} +5.70389e6 q^{87} +2.10832e6 q^{88} +3.49331e6 q^{89} -71708.5 q^{90} +2.23242e7 q^{91} +5.67893e6 q^{92} +1.66986e6 q^{93} +1.43178e7 q^{94} -3272.42 q^{95} +6.26478e6 q^{96} -1.00211e7 q^{97} -1.99121e7 q^{98} +3.35328e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−15.0158	−1.32723	−0.663613	−	0.748076i	$-0.730978\pi$
$2$	−15.0158	−1.32723	−0.663613	+	0.748076i	$0.730978\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	97.4757	0.761529
$5$	6.55078	0.0234368	0.0117184	−	0.999931i	$-0.496270\pi$
$5$	6.55078	0.0234368	0.0117184	+	0.999931i	$0.496270\pi$
$6$	−405.428	−0.766274
$7$	1466.16	1.61561	0.807807	−	0.589448i	$-0.200655\pi$
$7$	1466.16	1.61561	0.807807	+	0.589448i	$0.200655\pi$
$8$	458.348	0.316505
$9$	729.000	0.333333
$10$	−98.3656	−0.0311059
$11$	4599.84	1.04200	0.521000	−	0.853556i	$-0.325559\pi$
$11$	4599.84	1.04200	0.521000	+	0.853556i	$0.325559\pi$
$12$	2631.84	0.439669
$13$	15226.3	1.92217	0.961087	−	0.276246i	$-0.0890903\pi$
$13$	15226.3	1.92217	0.961087	+	0.276246i	$0.0890903\pi$
$14$	−22015.6	−2.14428
$15$	176.871	0.0135312
$16$	−19359.4	−1.18160
$17$	38992.1	1.92489	0.962444	−	0.271481i	$-0.0875133\pi$
$17$	38992.1	1.92489	0.962444	+	0.271481i	$0.0875133\pi$
$18$	−10946.6	−0.442409
$19$	−499.547	−0.0167085	−0.00835427	−	0.999965i	$-0.502659\pi$
$19$	−499.547	−0.0167085	−0.00835427	+	0.999965i	$0.502659\pi$
$20$	638.542	0.0178478
$21$	39586.2	0.932775
$22$	−69070.4	−1.38297
$23$	58259.9	0.998441	0.499220	−	0.866475i	$-0.333620\pi$
$23$	58259.9	0.998441	0.499220	+	0.866475i	$0.333620\pi$
$24$	12375.4	0.182734
$25$	−78082.1	−0.999451
$26$	−228636.	−2.55116
$27$	19683.0	0.192450
$28$	142915.	1.23034
$29$	211255.	1.60848	0.804238	−	0.594307i	$-0.202574\pi$
$29$	211255.	1.60848	0.804238	+	0.594307i	$0.202574\pi$
$30$	−2655.87	−0.0179590
$31$	61846.8	0.372865	0.186432	−	0.982468i	$-0.440307\pi$
$31$	61846.8	0.372865	0.186432	+	0.982468i	$0.440307\pi$
$32$	232029.	1.25175
$33$	124196.	0.601599
$34$	−585500.	−2.55476
$35$	9604.48	0.0378648
$36$	71059.8	0.253843
$37$	−62940.4	−0.204279	−0.102139	−	0.994770i	$-0.532569\pi$
$37$	−62940.4	−0.204279	−0.102139	+	0.994770i	$0.532569\pi$
$38$	7501.12	0.0221760
$39$	411110.	1.10977
$40$	3002.54	0.00741785
$41$	−619876.	−1.40463	−0.702314	−	0.711867i	$-0.747850\pi$
$41$	−619876.	−1.40463	−0.702314	+	0.711867i	$0.747850\pi$
$42$	−594421.	−1.23800
$43$	−356192.	−0.683194	−0.341597	−	0.939846i	$-0.610968\pi$
$43$	−356192.	−0.683194	−0.341597	+	0.939846i	$0.610968\pi$
$44$	448372.	0.793514
$45$	4775.52	0.00781226
$46$	−874822.	−1.32516
$47$	−953515.	−1.33963	−0.669815	−	0.742528i	$-0.733627\pi$
$47$	−953515.	−1.33963	−0.669815	+	0.742528i	$0.733627\pi$
$48$	−522703.	−0.682199
$49$	1.32607e6	1.61021
$50$	1.17247e6	1.32650
$51$	1.05279e6	1.11133
$52$	1.48419e6	1.46379
$53$	−1.97760e6	−1.82462	−0.912310	−	0.409501i	$-0.865703\pi$
$53$	−1.97760e6	−1.82462	−0.912310	+	0.409501i	$0.865703\pi$
$54$	−295557.	−0.255425
$55$	30132.5	0.0244211
$56$	672010.	0.511349
$57$	−13487.8	−0.00964668
$58$	−3.17218e6	−2.13481
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	17240.6	0.0103044
$61$	−2.98506e6	−1.68383	−0.841917	−	0.539607i	$-0.818573\pi$
$61$	−2.98506e6	−1.68383	−0.841917	+	0.539607i	$0.818573\pi$
$62$	−928683.	−0.494876
$63$	1.06883e6	0.538538
$64$	−1.00611e6	−0.479751
$65$	99744.2	0.0450496
$66$	−1.86490e6	−0.798458
$67$	−1.04862e6	−0.425948	−0.212974	−	0.977058i	$-0.568315\pi$
$67$	−1.04862e6	−0.425948	−0.212974	+	0.977058i	$0.568315\pi$
$68$	3.80078e6	1.46586
$69$	1.57302e6	0.576450
$70$	−144219.	−0.0502551
$71$	4.10180e6	1.36010	0.680049	−	0.733166i	$-0.261958\pi$
$71$	4.10180e6	1.36010	0.680049	+	0.733166i	$0.261958\pi$
$72$	334136.	0.105502
$73$	−260342.	−0.0783273	−0.0391637	−	0.999233i	$-0.512469\pi$
$73$	−260342.	−0.0783273	−0.0391637	+	0.999233i	$0.512469\pi$
$74$	945104.	0.271124
$75$	−2.10822e6	−0.577033
$76$	−48693.7	−0.0127240
$77$	6.74408e6	1.68347
$78$	−6.17317e6	−1.47291
$79$	−1.33466e6	−0.304562	−0.152281	−	0.988337i	$-0.548662\pi$
$79$	−1.33466e6	−0.304562	−0.152281	+	0.988337i	$0.548662\pi$
$80$	−126819.	−0.0276930
$81$	531441.	0.111111
$82$	9.30797e6	1.86426
$83$	8.30823e6	1.59491	0.797454	−	0.603380i	$-0.206180\pi$
$83$	8.30823e6	1.59491	0.797454	+	0.603380i	$0.206180\pi$
$84$	3.85870e6	0.710335
$85$	255429.	0.0451132
$86$	5.34852e6	0.906753
$87$	5.70389e6	0.928654
$88$	2.10832e6	0.329798
$89$	3.49331e6	0.525257	0.262628	−	0.964897i	$-0.415411\pi$
$89$	3.49331e6	0.525257	0.262628	+	0.964897i	$0.415411\pi$
$90$	−71708.5	−0.0103686
$91$	2.23242e7	3.10549
$92$	5.67893e6	0.760342
$93$	1.66986e6	0.215274
$94$	1.43178e7	1.77799
$95$	−3272.42	−0.000391594 0
$96$	6.26478e6	0.722698
$97$	−1.00211e7	−1.11484	−0.557420	−	0.830230i	$-0.688209\pi$
$97$	−1.00211e7	−1.11484	−0.557420	+	0.830230i	$0.688209\pi$
$98$	−1.99121e7	−2.13711
$99$	3.35328e6	0.347334
$100$	−7.61111e6	−0.761111
$101$	9.44535e6	0.912206	0.456103	−	0.889927i	$-0.349245\pi$
$101$	9.44535e6	0.912206	0.456103	+	0.889927i	$0.349245\pi$
$102$	−1.58085e7	−1.47499
$103$	−4.07761e6	−0.367684	−0.183842	−	0.982956i	$-0.558854\pi$
$103$	−4.07761e6	−0.367684	−0.183842	+	0.982956i	$0.558854\pi$
$104$	6.97894e6	0.608377
$105$	259321.	0.0218612
$106$	2.96953e7	2.42168
$107$	−2.17048e7	−1.71282	−0.856410	−	0.516296i	$-0.827310\pi$
$107$	−2.17048e7	−1.71282	−0.856410	+	0.516296i	$0.827310\pi$
$108$	1.91861e6	0.146556
$109$	−4.43849e6	−0.328278	−0.164139	−	0.986437i	$-0.552485\pi$
$109$	−4.43849e6	−0.328278	−0.164139	+	0.986437i	$0.552485\pi$
$110$	−452465.	−0.0324124
$111$	−1.69939e6	−0.117941
$112$	−2.83839e7	−1.90901
$113$	7.13404e6	0.465116	0.232558	−	0.972583i	$-0.425290\pi$
$113$	7.13404e6	0.465116	0.232558	+	0.972583i	$0.425290\pi$
$114$	202530.	0.0128033
$115$	381648.	0.0234002
$116$	2.05923e7	1.22490
$117$	1.11000e7	0.640725
$118$	−3.08394e6	−0.172790
$119$	5.71686e7	3.10987
$120$	81068.5	0.00428270
$121$	1.67132e6	0.0857652
$122$	4.48233e7	2.23483
$123$	−1.67367e7	−0.810963
$124$	6.02857e6	0.283948
$125$	−1.02328e6	−0.0468607
$126$	−1.60494e7	−0.714761
$127$	−1.23488e7	−0.534948	−0.267474	−	0.963565i	$-0.586189\pi$
$127$	−1.23488e7	−0.534948	−0.267474	+	0.963565i	$0.586189\pi$
$128$	−1.45921e7	−0.615010
$129$	−9.61718e6	−0.394442
$130$	−1.49774e6	−0.0597910
$131$	−1.76969e7	−0.687779	−0.343889	−	0.939010i	$-0.611744\pi$
$131$	−1.76969e7	−0.687779	−0.343889	+	0.939010i	$0.611744\pi$
$132$	1.21061e7	0.458135
$133$	−732414.	−0.0269945
$134$	1.57459e7	0.565329
$135$	128939.	0.00451041
$136$	1.78719e7	0.609236
$137$	−2.34535e6	−0.0779265	−0.0389632	−	0.999241i	$-0.512406\pi$
$137$	−2.34535e6	−0.0779265	−0.0389632	+	0.999241i	$0.512406\pi$
$138$	−2.36202e7	−0.765079
$139$	−1.84954e7	−0.584134	−0.292067	−	0.956398i	$-0.594343\pi$
$139$	−1.84954e7	−0.584134	−0.292067	+	0.956398i	$0.594343\pi$
$140$	936203.	0.0288351
$141$	−2.57449e7	−0.773436
$142$	−6.15920e7	−1.80516
$143$	7.00385e7	2.00291
$144$	−1.41130e7	−0.393868
$145$	1.38389e6	0.0376975
$146$	3.90925e6	0.103958
$147$	3.58040e7	0.929653
$148$	−6.13516e6	−0.155564
$149$	−1.87066e7	−0.463278	−0.231639	−	0.972802i	$-0.574409\pi$
$149$	−1.87066e7	−0.463278	−0.231639	+	0.972802i	$0.574409\pi$
$150$	3.16567e7	0.765853
$151$	−3.23257e7	−0.764062	−0.382031	−	0.924150i	$-0.624775\pi$
$151$	−3.23257e7	−0.764062	−0.382031	+	0.924150i	$0.624775\pi$
$152$	−228966.	−0.00528833
$153$	2.84252e7	0.641629
$154$	−1.01268e8	−2.23435
$155$	405145.	0.00873876
$156$	4.00733e7	0.845120
$157$	−5.46991e7	−1.12806	−0.564029	−	0.825755i	$-0.690749\pi$
$157$	−5.46991e7	−1.12806	−0.564029	+	0.825755i	$0.690749\pi$
$158$	2.00411e7	0.404223
$159$	−5.33951e7	−1.05344
$160$	1.51997e6	0.0293370
$161$	8.54182e7	1.61309
$162$	−7.98004e6	−0.147470
$163$	−4.22142e7	−0.763487	−0.381744	−	0.924268i	$-0.624676\pi$
$163$	−4.22142e7	−0.763487	−0.381744	+	0.924268i	$0.624676\pi$
$164$	−6.04229e7	−1.06967
$165$	813578.	0.0140996
$166$	−1.24755e8	−2.11680
$167$	−8.74223e6	−0.145250	−0.0726248	−	0.997359i	$-0.523138\pi$
$167$	−8.74223e6	−0.145250	−0.0726248	+	0.997359i	$0.523138\pi$
$168$	1.81443e7	0.295228
$169$	1.69092e8	2.69475
$170$	−3.83548e6	−0.0598754
$171$	−364169.	−0.00556951
$172$	−3.47201e7	−0.520272
$173$	4.41610e7	0.648451	0.324225	−	0.945980i	$-0.394896\pi$
$173$	4.41610e7	0.648451	0.324225	+	0.945980i	$0.394896\pi$
$174$	−8.56488e7	−1.23253
$175$	−1.14481e8	−1.61473
$176$	−8.90500e7	−1.23123
$177$	5.54523e6	0.0751646
$178$	−5.24550e7	−0.697135
$179$	−3.77776e7	−0.492322	−0.246161	−	0.969229i	$-0.579169\pi$
$179$	−3.77776e7	−0.492322	−0.246161	+	0.969229i	$0.579169\pi$
$180$	465497.	0.00594927
$181$	1.26649e8	1.58755	0.793774	−	0.608213i	$-0.208113\pi$
$181$	1.26649e8	1.58755	0.793774	+	0.608213i	$0.208113\pi$
$182$	−3.35216e8	−4.12169
$183$	−8.05967e7	−0.972162
$184$	2.67033e7	0.316011
$185$	−412309.	−0.00478764
$186$	−2.50744e7	−0.285717
$187$	1.79357e8	2.00573
$188$	−9.29445e7	−1.02017
$189$	2.88584e7	0.310925
$190$	49138.2	0.000519734 0
$191$	−2.15055e7	−0.223323	−0.111661	−	0.993746i	$-0.535617\pi$
$191$	−2.15055e7	−0.223323	−0.111661	+	0.993746i	$0.535617\pi$
$192$	−2.71650e7	−0.276985
$193$	2.18519e7	0.218796	0.109398	−	0.993998i	$-0.465108\pi$
$193$	2.18519e7	0.218796	0.109398	+	0.993998i	$0.465108\pi$
$194$	1.50475e8	1.47965
$195$	2.69309e6	0.0260094
$196$	1.29260e8	1.22622
$197$	−8.73312e7	−0.813837	−0.406919	−	0.913464i	$-0.633397\pi$
$197$	−8.73312e7	−0.813837	−0.406919	+	0.913464i	$0.633397\pi$
$198$	−5.03524e7	−0.460990
$199$	−2.03499e8	−1.83053	−0.915266	−	0.402850i	$-0.868020\pi$
$199$	−2.03499e8	−1.83053	−0.915266	+	0.402850i	$0.868020\pi$
$200$	−3.57888e7	−0.316331
$201$	−2.83127e7	−0.245921
$202$	−1.41830e8	−1.21070
$203$	3.09734e8	2.59868
$204$	1.02621e8	0.846314
$205$	−4.06067e6	−0.0329200
$206$	6.12288e7	0.488000
$207$	4.24715e7	0.332814
$208$	−2.94772e8	−2.27125
$209$	−2.29783e6	−0.0174103
$210$	−3.89392e6	−0.0290148
$211$	−7.64544e7	−0.560291	−0.280146	−	0.959958i	$-0.590383\pi$
$211$	−7.64544e7	−0.560291	−0.280146	+	0.959958i	$0.590383\pi$
$212$	−1.92768e8	−1.38950
$213$	1.10749e8	0.785253
$214$	3.25915e8	2.27330
$215$	−2.33333e6	−0.0160119
$216$	9.02166e6	0.0609114
$217$	9.06772e7	0.602406
$218$	6.66477e7	0.435700
$219$	−7.02922e6	−0.0452223
$220$	2.93719e6	0.0185974
$221$	5.93706e8	3.69997
$222$	2.55178e7	0.156534
$223$	−5.24257e7	−0.316575	−0.158288	−	0.987393i	$-0.550597\pi$
$223$	−5.24257e7	−0.316575	−0.158288	+	0.987393i	$0.550597\pi$
$224$	3.40191e8	2.02234
$225$	−5.69218e7	−0.333150
$226$	−1.07124e8	−0.617314
$227$	3.76491e6	0.0213631	0.0106816	−	0.999943i	$-0.496600\pi$
$227$	3.76491e6	0.0213631	0.0106816	+	0.999943i	$0.496600\pi$
$228$	−1.31473e6	−0.00734623
$229$	−1.48786e8	−0.818723	−0.409362	−	0.912372i	$-0.634249\pi$
$229$	−1.48786e8	−0.818723	−0.409362	+	0.912372i	$0.634249\pi$
$230$	−5.73077e6	−0.0310574
$231$	1.82090e8	0.971952
$232$	9.68284e7	0.509090
$233$	1.35403e8	0.701265	0.350632	−	0.936513i	$-0.385967\pi$
$233$	1.35403e8	0.701265	0.350632	+	0.936513i	$0.385967\pi$
$234$	−1.66676e8	−0.850387
$235$	−6.24627e6	−0.0313966
$236$	2.00195e7	0.0991427
$237$	−3.60358e7	−0.175839
$238$	−8.58434e8	−4.12751
$239$	−3.35966e8	−1.59185	−0.795926	−	0.605394i	$-0.793016\pi$
$239$	−3.35966e8	−1.59185	−0.795926	+	0.605394i	$0.793016\pi$
$240$	−3.42411e6	−0.0159885
$241$	−2.48239e8	−1.14238	−0.571189	−	0.820818i	$-0.693518\pi$
$241$	−2.48239e8	−1.14238	−0.571189	+	0.820818i	$0.693518\pi$
$242$	−2.50963e7	−0.113830
$243$	1.43489e7	0.0641500
$244$	−2.90971e8	−1.28229
$245$	8.68682e6	0.0377381
$246$	2.51315e8	1.07633
$247$	−7.60625e6	−0.0321167
$248$	2.83474e7	0.118014
$249$	2.24322e8	0.920820
$250$	1.53654e7	0.0621948
$251$	9.71369e7	0.387727	0.193864	−	0.981028i	$-0.437898\pi$
$251$	9.71369e7	0.387727	0.193864	+	0.981028i	$0.437898\pi$
$252$	1.04185e8	0.410112
$253$	2.67986e8	1.04038
$254$	1.85428e8	0.709997
$255$	6.89658e6	0.0260461
$256$	3.47895e8	1.29601
$257$	5.01702e6	0.0184366	0.00921829	−	0.999958i	$-0.497066\pi$
$257$	5.01702e6	0.0184366	0.00921829	+	0.999958i	$0.497066\pi$
$258$	1.44410e8	0.523514
$259$	−9.22806e7	−0.330036
$260$	9.72264e6	0.0343066
$261$	1.54005e8	0.536159
$262$	2.65735e8	0.912838
$263$	−3.81564e8	−1.29337	−0.646685	−	0.762757i	$-0.723845\pi$
$263$	−3.81564e8	−1.29337	−0.646685	+	0.762757i	$0.723845\pi$
$264$	5.69248e7	0.190409
$265$	−1.29548e7	−0.0427632
$266$	1.09978e7	0.0358278
$267$	9.43193e7	0.303257
$268$	−1.02215e8	−0.324372
$269$	−2.82835e8	−0.885931	−0.442965	−	0.896539i	$-0.646074\pi$
$269$	−2.82835e8	−0.885931	−0.442965	+	0.896539i	$0.646074\pi$
$270$	−1.93613e6	−0.00598634
$271$	2.76884e7	0.0845095	0.0422547	−	0.999107i	$-0.486546\pi$
$271$	2.76884e7	0.0845095	0.0422547	+	0.999107i	$0.486546\pi$
$272$	−7.54863e8	−2.27445
$273$	6.02752e8	1.79296
$274$	3.52174e7	0.103426
$275$	−3.59165e8	−1.04143
$276$	1.53331e8	0.438983
$277$	1.63786e7	0.0463018	0.0231509	−	0.999732i	$-0.492630\pi$
$277$	1.63786e7	0.0463018	0.0231509	+	0.999732i	$0.492630\pi$
$278$	2.77725e8	0.775278
$279$	4.50863e7	0.124288
$280$	4.40219e6	0.0119844
$281$	−1.44402e8	−0.388240	−0.194120	−	0.980978i	$-0.562185\pi$
$281$	−1.44402e8	−0.388240	−0.194120	+	0.980978i	$0.562185\pi$
$282$	3.86582e8	1.02652
$283$	1.29642e8	0.340011	0.170005	−	0.985443i	$-0.445622\pi$
$283$	1.29642e8	0.340011	0.170005	+	0.985443i	$0.445622\pi$
$284$	3.99826e8	1.03575
$285$	−88355.3	−0.000226087 0
$286$	−1.05169e9	−2.65831
$287$	−9.08836e8	−2.26934
$288$	1.69149e8	0.417250
$289$	1.11005e9	2.70519
$290$	−2.07802e7	−0.0500331
$291$	−2.70569e8	−0.643654
$292$	−2.53770e7	−0.0596486
$293$	−5.48210e8	−1.27324	−0.636620	−	0.771178i	$-0.719668\pi$
$293$	−5.48210e8	−1.27324	−0.636620	+	0.771178i	$0.719668\pi$
$294$	−5.37628e8	−1.23386
$295$	1.34539e6	0.00305121
$296$	−2.88486e7	−0.0646553
$297$	9.05386e7	0.200533
$298$	2.80895e8	0.614875
$299$	8.87083e8	1.91918
$300$	−2.05500e8	−0.439428
$301$	−5.22233e8	−1.10378
$302$	4.85398e8	1.01408
$303$	2.55024e8	0.526663
$304$	9.67091e6	0.0197428
$305$	−1.95545e7	−0.0394637
$306$	−4.26829e8	−0.851587
$307$	7.57326e8	1.49382	0.746910	−	0.664925i	$-0.231536\pi$
$307$	7.57326e8	1.49382	0.746910	+	0.664925i	$0.231536\pi$
$308$	6.57384e8	1.28201
$309$	−1.10095e8	−0.212283
$310$	−6.08360e6	−0.0115983
$311$	3.48341e8	0.656665	0.328332	−	0.944562i	$-0.393513\pi$
$311$	3.48341e8	0.656665	0.328332	+	0.944562i	$0.393513\pi$
$312$	1.88431e8	0.351247
$313$	−7.49639e8	−1.38180	−0.690902	−	0.722948i	$-0.742787\pi$
$313$	−7.49639e8	−1.38180	−0.690902	+	0.722948i	$0.742787\pi$
$314$	8.21354e8	1.49719
$315$	7.00166e6	0.0126216
$316$	−1.30097e8	−0.231933
$317$	7.39103e7	0.130316	0.0651580	−	0.997875i	$-0.479245\pi$
$317$	7.39103e7	0.130316	0.0651580	+	0.997875i	$0.479245\pi$
$318$	8.01773e8	1.39816
$319$	9.71740e8	1.67603
$320$	−6.59082e6	−0.0112438
$321$	−5.86029e8	−0.988897
$322$	−1.28263e9	−2.14094
$323$	−1.94784e7	−0.0321621
$324$	5.18026e7	0.0846144
$325$	−1.18890e9	−1.92112
$326$	6.33882e8	1.01332
$327$	−1.19839e8	−0.189532
$328$	−2.84119e8	−0.444572
$329$	−1.39800e9	−2.16432
$330$	−1.22166e7	−0.0187133
$331$	−6.07136e8	−0.920212	−0.460106	−	0.887864i	$-0.652189\pi$
$331$	−6.07136e8	−0.920212	−0.460106	+	0.887864i	$0.652189\pi$
$332$	8.09851e8	1.21457
$333$	−4.58836e7	−0.0680930
$334$	1.31272e8	0.192779
$335$	−6.86928e6	−0.00998285
$336$	−7.66365e8	−1.10217
$337$	1.21856e9	1.73437	0.867186	−	0.497985i	$-0.165926\pi$
$337$	1.21856e9	1.73437	0.867186	+	0.497985i	$0.165926\pi$
$338$	−2.53906e9	−3.57655
$339$	1.92619e8	0.268535
$340$	2.48981e7	0.0343550
$341$	2.84485e8	0.388526
$342$	5.46831e6	0.00739200
$343$	7.36790e8	0.985858
$344$	−1.63260e8	−0.216234
$345$	1.03045e7	0.0135101
$346$	−6.63114e8	−0.860641
$347$	8.27617e8	1.06335	0.531675	−	0.846948i	$-0.321563\pi$
$347$	8.27617e8	1.06335	0.531675	+	0.846948i	$0.321563\pi$
$348$	5.55991e8	0.707197
$349$	−9.88709e8	−1.24503	−0.622515	−	0.782608i	$-0.713889\pi$
$349$	−9.88709e8	−1.24503	−0.622515	+	0.782608i	$0.713889\pi$
$350$	1.71902e9	2.14311
$351$	2.99699e8	0.369923
$352$	1.06730e9	1.30432
$353$	2.48535e7	0.0300730	0.0150365	−	0.999887i	$-0.495214\pi$
$353$	2.48535e7	0.0300730	0.0150365	+	0.999887i	$0.495214\pi$
$354$	−8.32664e7	−0.0997604
$355$	2.68700e7	0.0318763
$356$	3.40513e8	0.399998
$357$	1.54355e9	1.79549
$358$	5.67263e8	0.653423
$359$	6.66922e8	0.760755	0.380377	−	0.924831i	$-0.375794\pi$
$359$	6.66922e8	0.760755	0.380377	+	0.924831i	$0.375794\pi$
$360$	2.18885e6	0.00247262
$361$	−8.93622e8	−0.999721
$362$	−1.90174e9	−2.10703
$363$	4.51257e7	0.0495166
$364$	2.17606e9	2.36492
$365$	−1.70544e6	−0.00183574
$366$	1.21023e9	1.29028
$367$	4.68476e8	0.494716	0.247358	−	0.968924i	$-0.420438\pi$
$367$	4.68476e8	0.494716	0.247358	+	0.968924i	$0.420438\pi$
$368$	−1.12788e9	−1.17976
$369$	−4.51890e8	−0.468209
$370$	6.19117e6	0.00635429
$371$	−2.89947e9	−2.94788
$372$	1.62771e8	0.163937
$373$	5.89698e8	0.588368	0.294184	−	0.955749i	$-0.404952\pi$
$373$	5.89698e8	0.588368	0.294184	+	0.955749i	$0.404952\pi$
$374$	−2.69320e9	−2.66206
$375$	−2.76285e7	−0.0270550
$376$	−4.37041e8	−0.423999
$377$	3.21664e9	3.09177
$378$	−4.33333e8	−0.412668
$379$	7.55066e8	0.712439	0.356220	−	0.934402i	$-0.384066\pi$
$379$	7.55066e8	0.712439	0.356220	+	0.934402i	$0.384066\pi$
$380$	−318982.	−0.000298211 0
$381$	−3.33418e8	−0.308853
$382$	3.22924e8	0.296400
$383$	−5.16218e8	−0.469502	−0.234751	−	0.972056i	$-0.575427\pi$
$383$	−5.16218e8	−0.469502	−0.234751	+	0.972056i	$0.575427\pi$
$384$	−3.93986e8	−0.355076
$385$	4.41790e7	0.0394551
$386$	−3.28125e8	−0.290392
$387$	−2.59664e8	−0.227731
$388$	−9.76811e8	−0.848984
$389$	2.02594e9	1.74503	0.872514	−	0.488589i	$-0.162488\pi$
$389$	2.02594e9	1.74503	0.872514	+	0.488589i	$0.162488\pi$
$390$	−4.04391e7	−0.0345203
$391$	2.27168e9	1.92189
$392$	6.07803e8	0.509638
$393$	−4.77817e8	−0.397089
$394$	1.31135e9	1.08015
$395$	−8.74307e6	−0.00713796
$396$	3.26863e8	0.264505
$397$	1.11905e9	0.897601	0.448801	−	0.893632i	$-0.351851\pi$
$397$	1.11905e9	0.897601	0.448801	+	0.893632i	$0.351851\pi$
$398$	3.05572e9	2.42953
$399$	−1.97752e7	−0.0155853
$400$	1.51162e9	1.18095
$401$	−2.75487e8	−0.213352	−0.106676	−	0.994294i	$-0.534021\pi$
$401$	−2.75487e8	−0.213352	−0.106676	+	0.994294i	$0.534021\pi$
$402$	4.25140e8	0.326393
$403$	9.41699e8	0.716711
$404$	9.20692e8	0.694672
$405$	3.48135e6	0.00260409
$406$	−4.65091e9	−3.44903
$407$	−2.89516e8	−0.212859
$408$	4.82543e8	0.351743
$409$	−7.49535e8	−0.541702	−0.270851	−	0.962621i	$-0.587305\pi$
$409$	−7.49535e8	−0.541702	−0.270851	+	0.962621i	$0.587305\pi$
$410$	6.09745e7	0.0436923
$411$	−6.33244e7	−0.0449909
$412$	−3.97468e8	−0.280002
$413$	3.01118e8	0.210335
$414$	−6.37745e8	−0.441719
$415$	5.44254e7	0.0373795
$416$	3.53294e9	2.40608
$417$	−4.99377e8	−0.337250
$418$	3.45039e7	0.0231074
$419$	2.09732e9	1.39289	0.696445	−	0.717611i	$-0.254764\pi$
$419$	2.09732e9	1.39289	0.696445	+	0.717611i	$0.254764\pi$
$420$	2.52775e7	0.0166480
$421$	8.22045e8	0.536919	0.268459	−	0.963291i	$-0.413486\pi$
$421$	8.22045e8	0.536919	0.268459	+	0.963291i	$0.413486\pi$
$422$	1.14803e9	0.743633
$423$	−6.95112e8	−0.446543
$424$	−9.06427e8	−0.577501
$425$	−3.04458e9	−1.92383
$426$	−1.66298e9	−1.04221
$427$	−4.37657e9	−2.72042
$428$	−2.11569e9	−1.30436
$429$	1.89104e9	1.15638
$430$	3.50370e7	0.0212514
$431$	−9.73123e8	−0.585460	−0.292730	−	0.956195i	$-0.594564\pi$
$431$	−9.73123e8	−0.585460	−0.292730	+	0.956195i	$0.594564\pi$
$432$	−3.81051e8	−0.227400
$433$	2.68877e9	1.59165	0.795823	−	0.605529i	$-0.207039\pi$
$433$	2.68877e9	1.59165	0.795823	+	0.605529i	$0.207039\pi$
$434$	−1.36160e9	−0.799528
$435$	3.73650e7	0.0217647
$436$	−4.32645e8	−0.249994
$437$	−2.91035e7	−0.0166825
$438$	1.05550e8	0.0600202
$439$	2.20359e9	1.24309	0.621547	−	0.783377i	$-0.286504\pi$
$439$	2.20359e9	1.24309	0.621547	+	0.783377i	$0.286504\pi$
$440$	1.38112e7	0.00772941
$441$	9.66708e8	0.536736
$442$	−8.91499e9	−4.91070
$443$	−1.04965e9	−0.573630	−0.286815	−	0.957986i	$-0.592597\pi$
$443$	−1.04965e9	−0.573630	−0.286815	+	0.957986i	$0.592597\pi$
$444$	−1.65649e8	−0.0898151
$445$	2.28839e7	0.0123103
$446$	7.87216e8	0.420167
$447$	−5.05077e8	−0.267474
$448$	−1.47512e9	−0.775093
$449$	−2.02286e9	−1.05464	−0.527320	−	0.849667i	$-0.676803\pi$
$449$	−2.02286e9	−1.05464	−0.527320	+	0.849667i	$0.676803\pi$
$450$	8.54730e8	0.442166
$451$	−2.85133e9	−1.46362
$452$	6.95396e8	0.354199
$453$	−8.72794e8	−0.441131
$454$	−5.65334e7	−0.0283537
$455$	1.46241e8	0.0727827
$456$	−6.18208e6	−0.00305322
$457$	−3.01761e9	−1.47896	−0.739480	−	0.673178i	$-0.764929\pi$
$457$	−3.01761e9	−1.47896	−0.739480	+	0.673178i	$0.764929\pi$
$458$	2.23414e9	1.08663
$459$	7.67482e8	0.370445
$460$	3.72014e7	0.0178200
$461$	3.13368e9	1.48971	0.744854	−	0.667228i	$-0.232519\pi$
$461$	3.13368e9	1.48971	0.744854	+	0.667228i	$0.232519\pi$
$462$	−2.73424e9	−1.29000
$463$	−2.30769e9	−1.08055	−0.540275	−	0.841489i	$-0.681680\pi$
$463$	−2.30769e9	−1.08055	−0.540275	+	0.841489i	$0.681680\pi$
$464$	−4.08977e9	−1.90058
$465$	1.09389e7	0.00504532
$466$	−2.03319e9	−0.930737
$467$	−3.23147e9	−1.46822	−0.734110	−	0.679030i	$-0.762400\pi$
$467$	−3.23147e9	−1.46822	−0.734110	+	0.679030i	$0.762400\pi$
$468$	1.08198e9	0.487931
$469$	−1.53744e9	−0.688167
$470$	9.37930e7	0.0416704
$471$	−1.47688e9	−0.651285
$472$	9.41350e7	0.0412054
$473$	−1.63842e9	−0.711889
$474$	5.41109e8	0.233378
$475$	3.90056e7	0.0166994
$476$	5.57255e9	2.36826
$477$	−1.44167e9	−0.608206
$478$	5.04482e9	2.11275
$479$	3.12158e9	1.29778	0.648888	−	0.760884i	$-0.275234\pi$
$479$	3.12158e9	1.29778	0.648888	+	0.760884i	$0.275234\pi$
$480$	4.10392e7	0.0169377
$481$	−9.58350e8	−0.392660
$482$	3.72752e9	1.51619
$483$	2.30629e9	0.931320
$484$	1.62913e8	0.0653127
$485$	−6.56458e7	−0.0261283
$486$	−2.15461e8	−0.0851416
$487$	−1.98211e9	−0.777636	−0.388818	−	0.921315i	$-0.627116\pi$
$487$	−1.98211e9	−0.777636	−0.388818	+	0.921315i	$0.627116\pi$
$488$	−1.36820e9	−0.532941
$489$	−1.13978e9	−0.440800
$490$	−1.30440e8	−0.0500870
$491$	2.49858e9	0.952594	0.476297	−	0.879285i	$-0.341979\pi$
$491$	2.49858e9	0.952594	0.476297	+	0.879285i	$0.341979\pi$
$492$	−1.63142e9	−0.617572
$493$	8.23729e9	3.09614
$494$	1.14214e8	0.0426261
$495$	2.19666e7	0.00814038
$496$	−1.19732e9	−0.440578
$497$	6.01389e9	2.19739
$498$	−3.36839e9	−1.22214
$499$	4.80008e9	1.72940	0.864702	−	0.502285i	$-0.167507\pi$
$499$	4.80008e9	1.72940	0.864702	+	0.502285i	$0.167507\pi$
$500$	−9.97448e7	−0.0356858
$501$	−2.36040e8	−0.0838599
$502$	−1.45859e9	−0.514602
$503$	−3.37167e9	−1.18129	−0.590645	−	0.806931i	$-0.701127\pi$
$503$	−3.37167e9	−1.18129	−0.590645	+	0.806931i	$0.701127\pi$
$504$	4.89895e8	0.170450
$505$	6.18744e7	0.0213792
$506$	−4.02404e9	−1.38081
$507$	4.56548e9	1.55582
$508$	−1.20371e9	−0.407379
$509$	−2.96439e9	−0.996376	−0.498188	−	0.867069i	$-0.666001\pi$
$509$	−2.96439e9	−0.996376	−0.498188	+	0.867069i	$0.666001\pi$
$510$	−1.03558e8	−0.0345691
$511$	−3.81702e8	−0.126547
$512$	−3.35615e9	−1.10509
$513$	−9.83257e6	−0.00321556
$514$	−7.53349e7	−0.0244695
$515$	−2.67115e7	−0.00861734
$516$	−9.37441e8	−0.300379
$517$	−4.38601e9	−1.39590
$518$	1.38567e9	0.438032
$519$	1.19235e9	0.374383
$520$	4.57175e7	0.0142584
$521$	−2.91409e9	−0.902757	−0.451378	−	0.892333i	$-0.649067\pi$
$521$	−2.91409e9	−0.902757	−0.451378	+	0.892333i	$0.649067\pi$
$522$	−2.31252e9	−0.711604
$523$	−4.99881e9	−1.52796	−0.763978	−	0.645243i	$-0.776756\pi$
$523$	−4.99881e9	−1.52796	−0.763978	+	0.645243i	$0.776756\pi$
$524$	−1.72502e9	−0.523763
$525$	−3.09098e9	−0.932262
$526$	5.72951e9	1.71659
$527$	2.41154e9	0.717723
$528$	−2.40435e9	−0.710851
$529$	−1.06102e7	−0.00311622
$530$	1.94527e8	0.0567565
$531$	1.49721e8	0.0433963
$532$	−7.13926e7	−0.0205571
$533$	−9.43842e9	−2.69994
$534$	−1.41628e9	−0.402491
$535$	−1.42183e8	−0.0401430
$536$	−4.80633e8	−0.134814
$537$	−1.02000e9	−0.284242
$538$	4.24700e9	1.17583
$539$	6.09972e9	1.67784
$540$	1.25684e7	0.00343481
$541$	−1.32516e9	−0.359813	−0.179906	−	0.983684i	$-0.557580\pi$
$541$	−1.32516e9	−0.359813	−0.179906	+	0.983684i	$0.557580\pi$
$542$	−4.15765e8	−0.112163
$543$	3.41952e9	0.916571
$544$	9.04730e9	2.40948
$545$	−2.90756e7	−0.00769379
$546$	−9.05084e9	−2.37966
$547$	1.49203e9	0.389782	0.194891	−	0.980825i	$-0.437565\pi$
$547$	1.49203e9	0.389782	0.194891	+	0.980825i	$0.437565\pi$
$548$	−2.28614e8	−0.0593433
$549$	−2.17611e9	−0.561278
$550$	5.39316e9	1.38221
$551$	−1.05532e8	−0.0268753
$552$	7.20989e8	0.182449
$553$	−1.95682e9	−0.492055
$554$	−2.45939e8	−0.0614530
$555$	−1.11323e7	−0.00276415
$556$	−1.80286e9	−0.444835
$557$	−1.87638e9	−0.460074	−0.230037	−	0.973182i	$-0.573885\pi$
$557$	−1.87638e9	−0.460074	−0.230037	+	0.973182i	$0.573885\pi$
$558$	−6.77010e8	−0.164959
$559$	−5.42348e9	−1.31322
$560$	−1.85937e8	−0.0447411
$561$	4.84265e9	1.15801
$562$	2.16831e9	0.515282
$563$	−2.13285e9	−0.503711	−0.251855	−	0.967765i	$-0.581041\pi$
$563$	−2.13285e9	−0.503711	−0.251855	+	0.967765i	$0.581041\pi$
$564$	−2.50950e9	−0.588994
$565$	4.67336e7	0.0109008
$566$	−1.94668e9	−0.451271
$567$	7.79176e8	0.179513
$568$	1.88005e9	0.430478
$569$	−1.42082e9	−0.323331	−0.161666	−	0.986846i	$-0.551687\pi$
$569$	−1.42082e9	−0.323331	−0.161666	+	0.986846i	$0.551687\pi$
$570$	1.32673e6	0.000300069 0
$571$	1.63133e9	0.366703	0.183352	−	0.983047i	$-0.441305\pi$
$571$	1.63133e9	0.366703	0.183352	+	0.983047i	$0.441305\pi$
$572$	6.82705e9	1.52527
$573$	−5.80649e8	−0.128936
$574$	1.36469e10	3.01192
$575$	−4.54905e9	−0.997892
$576$	−7.33455e8	−0.159917
$577$	7.83244e9	1.69739	0.848695	−	0.528882i	$-0.177389\pi$
$577$	7.83244e9	1.69739	0.848695	+	0.528882i	$0.177389\pi$
$578$	−1.66683e10	−3.59040
$579$	5.90002e8	0.126322
$580$	1.34895e8	0.0287078
$581$	1.21812e10	2.57675
$582$	4.06282e9	0.854274
$583$	−9.09662e9	−1.90125
$584$	−1.19327e8	−0.0247910
$585$	7.27135e7	0.0150165
$586$	8.23184e9	1.68988
$587$	5.25336e9	1.07202	0.536011	−	0.844211i	$-0.319931\pi$
$587$	5.25336e9	1.07202	0.536011	+	0.844211i	$0.319931\pi$
$588$	3.49002e9	0.707958
$589$	−3.08954e7	−0.00623003
$590$	−2.02022e7	−0.00404965
$591$	−2.35794e9	−0.469869
$592$	1.21849e9	0.241377
$593$	3.96594e9	0.781007	0.390503	−	0.920601i	$-0.372301\pi$
$593$	3.96594e9	0.781007	0.390503	+	0.920601i	$0.372301\pi$
$594$	−1.35951e9	−0.266153
$595$	3.74499e8	0.0728855
$596$	−1.82344e9	−0.352800
$597$	−5.49448e9	−1.05686
$598$	−1.33203e10	−2.54718
$599$	4.82067e9	0.916461	0.458230	−	0.888833i	$-0.348483\pi$
$599$	4.82067e9	0.916461	0.458230	+	0.888833i	$0.348483\pi$
$600$	−9.66296e8	−0.182634
$601$	1.29063e9	0.242516	0.121258	−	0.992621i	$-0.461307\pi$
$601$	1.29063e9	0.242516	0.121258	+	0.992621i	$0.461307\pi$
$602$	7.84177e9	1.46496
$603$	−7.64444e8	−0.141983
$604$	−3.15097e9	−0.581855
$605$	1.09485e7	0.00201006
$606$	−3.82941e9	−0.699000
$607$	7.37737e9	1.33888	0.669440	−	0.742866i	$-0.266534\pi$
$607$	7.37737e9	1.33888	0.669440	+	0.742866i	$0.266534\pi$
$608$	−1.15909e8	−0.0209149
$609$	8.36281e9	1.50035
$610$	2.93627e8	0.0523772
$611$	−1.45185e10	−2.57500
$612$	2.77077e9	0.488619
$613$	−8.76333e9	−1.53659	−0.768294	−	0.640097i	$-0.778894\pi$
$613$	−8.76333e9	−1.53659	−0.768294	+	0.640097i	$0.778894\pi$
$614$	−1.13719e10	−1.98264
$615$	−1.09638e8	−0.0190064
$616$	3.09114e9	0.532826
$617$	9.05070e9	1.55126	0.775629	−	0.631189i	$-0.217433\pi$
$617$	9.05070e9	1.55126	0.775629	+	0.631189i	$0.217433\pi$
$618$	1.65318e9	0.281747
$619$	7.25987e9	1.23030	0.615151	−	0.788409i	$-0.289095\pi$
$619$	7.25987e9	1.23030	0.615151	+	0.788409i	$0.289095\pi$
$620$	3.94918e7	0.00665482
$621$	1.14673e9	0.192150
$622$	−5.23064e9	−0.871543
$623$	5.12174e9	0.848612
$624$	−7.95884e9	−1.31130
$625$	6.09346e9	0.998352
$626$	1.12565e10	1.83397
$627$	−6.20415e7	−0.0100518
$628$	−5.33184e9	−0.859049
$629$	−2.45418e9	−0.393214
$630$	−1.05136e8	−0.0167517
$631$	6.82668e9	1.08170	0.540850	−	0.841119i	$-0.318103\pi$
$631$	6.82668e9	1.08170	0.540850	+	0.841119i	$0.318103\pi$
$632$	−6.11739e8	−0.0963954
$633$	−2.06427e9	−0.323484
$634$	−1.10983e9	−0.172959
$635$	−8.08943e7	−0.0125375
$636$	−5.20473e9	−0.802229
$637$	2.01912e10	3.09510
$638$	−1.45915e10	−2.22448
$639$	2.99021e9	0.453366
$640$	−9.55896e7	−0.0144139
$641$	2.79576e9	0.419273	0.209637	−	0.977779i	$-0.432772\pi$
$641$	2.79576e9	0.419273	0.209637	+	0.977779i	$0.432772\pi$
$642$	8.79972e9	1.31249
$643$	−2.72738e9	−0.404583	−0.202292	−	0.979325i	$-0.564839\pi$
$643$	−2.72738e9	−0.404583	−0.202292	+	0.979325i	$0.564839\pi$
$644$	8.32620e9	1.22842
$645$	−6.30000e7	−0.00924446
$646$	2.92484e8	0.0426863
$647$	−4.23656e9	−0.614962	−0.307481	−	0.951554i	$-0.599486\pi$
$647$	−4.23656e9	−0.614962	−0.307481	+	0.951554i	$0.599486\pi$
$648$	2.43585e8	0.0351672
$649$	9.44710e8	0.135657
$650$	1.78524e10	2.54976
$651$	2.44828e9	0.347799
$652$	−4.11486e9	−0.581418
$653$	−5.22693e9	−0.734599	−0.367300	−	0.930103i	$-0.619718\pi$
$653$	−5.22693e9	−0.734599	−0.367300	+	0.930103i	$0.619718\pi$
$654$	1.79949e9	0.251551
$655$	−1.15929e8	−0.0161193
$656$	1.20004e10	1.65971
$657$	−1.89789e8	−0.0261091
$658$	2.09922e10	2.87255
$659$	3.27514e9	0.445791	0.222896	−	0.974842i	$-0.428449\pi$
$659$	3.27514e9	0.445791	0.222896	+	0.974842i	$0.428449\pi$
$660$	7.93041e7	0.0107372
$661$	1.03921e10	1.39958	0.699788	−	0.714351i	$-0.253278\pi$
$661$	1.03921e10	1.39958	0.699788	+	0.714351i	$0.253278\pi$
$662$	9.11666e9	1.22133
$663$	1.60300e10	2.13618
$664$	3.80806e9	0.504796
$665$	−4.79788e6	−0.000632665 0
$666$	6.88981e8	0.0903748
$667$	1.23077e10	1.60597
$668$	−8.52156e8	−0.110612
$669$	−1.41549e9	−0.182775
$670$	1.03148e8	0.0132495
$671$	−1.37308e10	−1.75456
$672$	9.18516e9	1.16760
$673$	1.08020e10	1.36601	0.683003	−	0.730416i	$-0.260674\pi$
$673$	1.08020e10	1.36601	0.683003	+	0.730416i	$0.260674\pi$
$674$	−1.82977e10	−2.30190
$675$	−1.53689e9	−0.192344
$676$	1.64823e10	2.05213
$677$	1.40245e8	0.0173711	0.00868555	−	0.999962i	$-0.497235\pi$
$677$	1.40245e8	0.0173711	0.00868555	+	0.999962i	$0.497235\pi$
$678$	−2.89234e9	−0.356406
$679$	−1.46925e10	−1.80115
$680$	1.17075e8	0.0142785
$681$	1.01653e8	0.0123340
$682$	−4.27179e9	−0.515661
$683$	−5.38006e9	−0.646122	−0.323061	−	0.946378i	$-0.604712\pi$
$683$	−5.38006e9	−0.646122	−0.323061	+	0.946378i	$0.604712\pi$
$684$	−3.54977e7	−0.00424135
$685$	−1.53639e7	−0.00182635
$686$	−1.10635e10	−1.30846
$687$	−4.01721e9	−0.472690
$688$	6.89565e9	0.807264
$689$	−3.01115e10	−3.50724
$690$	−1.54731e8	−0.0179310
$691$	−8.51475e9	−0.981745	−0.490873	−	0.871231i	$-0.663322\pi$
$691$	−8.51475e9	−0.981745	−0.490873	+	0.871231i	$0.663322\pi$
$692$	4.30462e9	0.493814
$693$	4.91644e9	0.561157
$694$	−1.24274e10	−1.41131
$695$	−1.21160e8	−0.0136902
$696$	2.61437e9	0.293923
$697$	−2.41703e10	−2.70375
$698$	1.48463e10	1.65244
$699$	3.65588e9	0.404875
$700$	−1.11591e10	−1.22966
$701$	1.29311e10	1.41782	0.708911	−	0.705298i	$-0.249187\pi$
$701$	1.29311e10	1.41782	0.708911	+	0.705298i	$0.249187\pi$
$702$	−4.50024e9	−0.490971
$703$	3.14417e7	0.00341320
$704$	−4.62795e9	−0.499901
$705$	−1.68649e8	−0.0181269
$706$	−3.73197e8	−0.0399137
$707$	1.38484e10	1.47377
$708$	5.40526e8	0.0572400
$709$	5.39507e9	0.568506	0.284253	−	0.958749i	$-0.408254\pi$
$709$	5.39507e9	0.568506	0.284253	+	0.958749i	$0.408254\pi$
$710$	−4.03476e8	−0.0423071
$711$	−9.72968e8	−0.101521
$712$	1.60115e9	0.166246
$713$	3.60319e9	0.372284
$714$	−2.31777e10	−2.38302
$715$	4.58807e8	0.0469417
$716$	−3.68240e9	−0.374918
$717$	−9.07108e9	−0.919056
$718$	−1.00144e10	−1.00969
$719$	−8.62160e9	−0.865041	−0.432521	−	0.901624i	$-0.642376\pi$
$719$	−8.62160e9	−0.865041	−0.432521	+	0.901624i	$0.642376\pi$
$720$	−9.24511e7	−0.00923099
$721$	−5.97842e9	−0.594036
$722$	1.34185e10	1.32686
$723$	−6.70245e9	−0.659553
$724$	1.23452e10	1.20896
$725$	−1.64953e10	−1.60759
$726$	−6.77601e8	−0.0657197
$727$	−7.76855e9	−0.749841	−0.374921	−	0.927057i	$-0.622330\pi$
$727$	−7.76855e9	−0.749841	−0.374921	+	0.927057i	$0.622330\pi$
$728$	1.02322e10	0.982902
$729$	3.87420e8	0.0370370
$730$	2.56086e7	0.00243644
$731$	−1.38887e10	−1.31507
$732$	−7.85622e9	−0.740330
$733$	−2.43007e9	−0.227906	−0.113953	−	0.993486i	$-0.536351\pi$
$733$	−2.43007e9	−0.227906	−0.113953	+	0.993486i	$0.536351\pi$
$734$	−7.03456e9	−0.656600
$735$	2.34544e8	0.0217881
$736$	1.35180e10	1.24980
$737$	−4.82348e9	−0.443838
$738$	6.78551e9	0.621420
$739$	−7.09023e9	−0.646256	−0.323128	−	0.946355i	$-0.604734\pi$
$739$	−7.09023e9	−0.646256	−0.323128	+	0.946355i	$0.604734\pi$
$740$	−4.01901e7	−0.00364593
$741$	−2.05369e8	−0.0185426
$742$	4.35380e10	3.91250
$743$	6.11412e9	0.546857	0.273428	−	0.961892i	$-0.411842\pi$
$743$	6.11412e9	0.546857	0.273428	+	0.961892i	$0.411842\pi$
$744$	7.65379e8	0.0681351
$745$	−1.22543e8	−0.0108578
$746$	−8.85482e9	−0.780897
$747$	6.05670e9	0.531636
$748$	1.74830e10	1.52743
$749$	−3.18226e10	−2.76726
$750$	4.14866e8	0.0359082
$751$	1.01871e10	0.877629	0.438815	−	0.898578i	$-0.355398\pi$
$751$	1.01871e10	0.877629	0.438815	+	0.898578i	$0.355398\pi$
$752$	1.84594e10	1.58291
$753$	2.62270e9	0.223854
$754$	−4.83005e10	−4.10348
$755$	−2.11759e8	−0.0179072
$756$	2.81299e9	0.236778
$757$	2.04917e10	1.71689	0.858446	−	0.512903i	$-0.171430\pi$
$757$	2.04917e10	1.71689	0.858446	+	0.512903i	$0.171430\pi$
$758$	−1.13380e10	−0.945568
$759$	7.23562e9	0.600661
$760$	−1.49991e6	−0.000123941 0
$761$	4.69491e9	0.386172	0.193086	−	0.981182i	$-0.438150\pi$
$761$	4.69491e9	0.386172	0.193086	+	0.981182i	$0.438150\pi$
$762$	5.00655e9	0.409917
$763$	−6.50752e9	−0.530371
$764$	−2.09627e9	−0.170067
$765$	1.86208e8	0.0150377
$766$	7.75145e9	0.623135
$767$	3.12716e9	0.250246
$768$	9.39316e9	0.748251
$769$	1.90779e10	1.51282	0.756412	−	0.654095i	$-0.226951\pi$
$769$	1.90779e10	1.51282	0.756412	+	0.654095i	$0.226951\pi$
$770$	−6.63386e8	−0.0523659
$771$	1.35460e8	0.0106444
$772$	2.13003e9	0.166619
$773$	−1.43599e10	−1.11821	−0.559105	−	0.829097i	$-0.688855\pi$
$773$	−1.43599e10	−1.11821	−0.559105	+	0.829097i	$0.688855\pi$
$774$	3.89907e9	0.302251
$775$	−4.82913e9	−0.372660
$776$	−4.59313e9	−0.352852
$777$	−2.49158e9	−0.190546
$778$	−3.04212e10	−2.31605
$779$	3.09657e8	0.0234693
$780$	2.62511e8	0.0198069
$781$	1.88676e10	1.41722
$782$	−3.41111e10	−2.55078
$783$	4.15814e9	0.309551
$784$	−2.56720e10	−1.90262
$785$	−3.58322e8	−0.0264381
$786$	7.17483e9	0.527027
$787$	−4.56113e9	−0.333550	−0.166775	−	0.985995i	$-0.553335\pi$
$787$	−4.56113e9	−0.333550	−0.166775	+	0.985995i	$0.553335\pi$
$788$	−8.51267e9	−0.619761
$789$	−1.03022e10	−0.746727
$790$	1.31285e8	0.00947369
$791$	1.04596e10	0.751447
$792$	1.53697e9	0.109933
$793$	−4.54515e10	−3.23662
$794$	−1.68035e10	−1.19132
$795$	−3.49780e8	−0.0246894
$796$	−1.98363e10	−1.39400
$797$	1.19252e10	0.834374	0.417187	−	0.908821i	$-0.363016\pi$
$797$	1.19252e10	0.834374	0.417187	+	0.908821i	$0.363016\pi$
$798$	2.96941e8	0.0206852
$799$	−3.71795e10	−2.57864
$800$	−1.81173e10	−1.25106
$801$	2.54662e9	0.175086
$802$	4.13667e9	0.283166
$803$	−1.19753e9	−0.0816171
$804$	−2.75980e9	−0.187276
$805$	5.59556e8	0.0378057
$806$	−1.41404e10	−0.951238
$807$	−7.63654e9	−0.511492
$808$	4.32925e9	0.288718
$809$	−1.14473e10	−0.760121	−0.380061	−	0.924962i	$-0.624097\pi$
$809$	−1.14473e10	−0.760121	−0.380061	+	0.924962i	$0.624097\pi$
$810$	−5.22755e7	−0.00345621
$811$	−1.28875e10	−0.848389	−0.424195	−	0.905571i	$-0.639443\pi$
$811$	−1.28875e10	−0.848389	−0.424195	+	0.905571i	$0.639443\pi$
$812$	3.01915e10	1.97897
$813$	7.47587e8	0.0487916
$814$	4.34732e9	0.282512
$815$	−2.76536e8	−0.0178937
$816$	−2.03813e10	−1.31316
$817$	1.77934e8	0.0114152
$818$	1.12549e10	0.718961
$819$	1.62743e10	1.03516
$820$	−3.95817e8	−0.0250695
$821$	−1.25024e10	−0.788481	−0.394240	−	0.919007i	$-0.628992\pi$
$821$	−1.25024e10	−0.788481	−0.394240	+	0.919007i	$0.628992\pi$
$822$	9.50869e8	0.0597131
$823$	1.32497e10	0.828528	0.414264	−	0.910157i	$-0.364039\pi$
$823$	1.32497e10	0.828528	0.414264	+	0.910157i	$0.364039\pi$
$824$	−1.86896e9	−0.116374
$825$	−9.69745e9	−0.601269
$826$	−4.52154e9	−0.279162
$827$	3.06111e9	0.188196	0.0940980	−	0.995563i	$-0.470003\pi$
$827$	3.06111e9	0.188196	0.0940980	+	0.995563i	$0.470003\pi$
$828$	4.13994e9	0.253447
$829$	−1.74744e10	−1.06527	−0.532637	−	0.846344i	$-0.678799\pi$
$829$	−1.74744e10	−1.06527	−0.532637	+	0.846344i	$0.678799\pi$
$830$	−8.17244e8	−0.0496111
$831$	4.42223e8	0.0267324
$832$	−1.53194e10	−0.922166
$833$	5.17064e10	3.09947
$834$	7.49856e9	0.447607
$835$	−5.72685e7	−0.00340418
$836$	−2.23983e8	−0.0132585
$837$	1.21733e9	0.0717579
$838$	−3.14931e10	−1.84868
$839$	−3.10592e9	−0.181562	−0.0907808	−	0.995871i	$-0.528936\pi$
$839$	−3.10592e9	−0.181562	−0.0907808	+	0.995871i	$0.528936\pi$
$840$	1.18859e8	0.00691919
$841$	2.73789e10	1.58720
$842$	−1.23437e10	−0.712612
$843$	−3.89885e9	−0.224150
$844$	−7.45245e9	−0.426678
$845$	1.10768e9	0.0631564
$846$	1.04377e10	0.592664
$847$	2.45042e9	0.138563
$848$	3.82850e10	2.15597
$849$	3.50033e9	0.196305
$850$	4.57170e10	2.55336
$851$	−3.66690e9	−0.203960
$852$	1.07953e10	0.597993
$853$	1.91007e10	1.05372	0.526862	−	0.849951i	$-0.323368\pi$
$853$	1.91007e10	1.05372	0.526862	+	0.849951i	$0.323368\pi$
$854$	6.57180e10	3.61062
$855$	−2.38559e6	−0.000130531 0
$856$	−9.94833e9	−0.542116
$857$	3.07421e9	0.166840	0.0834202	−	0.996514i	$-0.473416\pi$
$857$	3.07421e9	0.166840	0.0834202	+	0.996514i	$0.473416\pi$
$858$	−2.83956e10	−1.53478
$859$	−7.57219e9	−0.407610	−0.203805	−	0.979011i	$-0.565331\pi$
$859$	−7.57219e9	−0.407610	−0.203805	+	0.979011i	$0.565331\pi$
$860$	−2.27443e8	−0.0121935
$861$	−2.45386e10	−1.31020
$862$	1.46123e10	0.777038
$863$	6.48477e9	0.343445	0.171722	−	0.985145i	$-0.445067\pi$
$863$	6.48477e9	0.343445	0.171722	+	0.985145i	$0.445067\pi$
$864$	4.56703e9	0.240899
$865$	2.89289e8	0.0151976
$866$	−4.03742e10	−2.11247
$867$	2.99712e10	1.56184
$868$	8.83883e9	0.458749
$869$	−6.13922e9	−0.317354
$870$	−5.61067e8	−0.0288866
$871$	−1.59666e10	−0.818746
$872$	−2.03437e9	−0.103902
$873$	−7.30536e9	−0.371614
$874$	4.37014e8	0.0221414
$875$	−1.50029e9	−0.0757088
$876$	−6.85178e8	−0.0344381
$877$	−7.00447e9	−0.350652	−0.175326	−	0.984510i	$-0.556098\pi$
$877$	−7.00447e9	−0.350652	−0.175326	+	0.984510i	$0.556098\pi$
$878$	−3.30887e10	−1.64987
$879$	−1.48017e10	−0.735106
$880$	−5.83347e8	−0.0288561
$881$	−1.76566e10	−0.869944	−0.434972	−	0.900444i	$-0.643242\pi$
$881$	−1.76566e10	−0.869944	−0.434972	+	0.900444i	$0.643242\pi$
$882$	−1.45159e10	−0.712369
$883$	−1.27783e10	−0.624610	−0.312305	−	0.949982i	$-0.601101\pi$
$883$	−1.27783e10	−0.624610	−0.312305	+	0.949982i	$0.601101\pi$
$884$	5.78719e10	2.81763
$885$	3.63256e7	0.00176162
$886$	1.57614e10	0.761337
$887$	3.30434e10	1.58983	0.794917	−	0.606719i	$-0.207515\pi$
$887$	3.30434e10	1.58983	0.794917	+	0.606719i	$0.207515\pi$
$888$	−7.78912e8	−0.0373287
$889$	−1.81053e10	−0.864270
$890$	−3.43621e8	−0.0163386
$891$	2.44454e9	0.115778
$892$	−5.11023e9	−0.241081
$893$	4.76325e8	0.0223833
$894$	7.58416e9	0.354998
$895$	−2.47473e8	−0.0115384
$896$	−2.13943e10	−0.993619
$897$	2.39512e10	1.10804
$898$	3.03750e10	1.39975
$899$	1.30655e10	0.599744
$900$	−5.54850e9	−0.253704
$901$	−7.71107e10	−3.51219
$902$	4.28151e10	1.94256
$903$	−1.41003e10	−0.637266
$904$	3.26987e9	0.147211
$905$	8.29650e8	0.0372070
$906$	1.31057e10	0.585481
$907$	−1.42333e10	−0.633401	−0.316701	−	0.948526i	$-0.602575\pi$
$907$	−1.42333e10	−0.633401	−0.316701	+	0.948526i	$0.602575\pi$
$908$	3.66988e8	0.0162686
$909$	6.88566e9	0.304069
$910$	−2.19593e9	−0.0965991
$911$	8.60227e9	0.376963	0.188482	−	0.982077i	$-0.439643\pi$
$911$	8.60227e9	0.376963	0.188482	+	0.982077i	$0.439643\pi$
$912$	2.61115e8	0.0113985
$913$	3.82165e10	1.66189
$914$	4.53120e10	1.96292
$915$	−5.27971e8	−0.0227844
$916$	−1.45030e10	−0.623482
$917$	−2.59465e10	−1.11118
$918$	−1.15244e10	−0.491664
$919$	2.07267e10	0.880898	0.440449	−	0.897778i	$-0.354819\pi$
$919$	2.07267e10	0.880898	0.440449	+	0.897778i	$0.354819\pi$
$920$	1.74927e8	0.00740629
$921$	2.04478e10	0.862458
$922$	−4.70548e10	−1.97718
$923$	6.24553e10	2.61435
$924$	1.77494e10	0.740170
$925$	4.91452e9	0.204167
$926$	3.46520e10	1.43413
$927$	−2.97258e9	−0.122561
$928$	4.90174e10	2.01341
$929$	−4.14549e10	−1.69637	−0.848186	−	0.529699i	$-0.822305\pi$
$929$	−4.14549e10	−1.69637	−0.848186	+	0.529699i	$0.822305\pi$
$930$	−1.64257e8	−0.00669629
$931$	−6.62436e8	−0.0269042
$932$	1.31985e10	0.534034
$933$	9.40522e9	0.379126
$934$	4.85233e10	1.94866
$935$	1.17493e9	0.0470080
$936$	5.08765e9	0.202792
$937$	−2.37792e10	−0.944296	−0.472148	−	0.881519i	$-0.656521\pi$
$937$	−2.37792e10	−0.944296	−0.472148	+	0.881519i	$0.656521\pi$
$938$	2.30860e10	0.913353
$939$	−2.02402e10	−0.797785
$940$	−6.08859e8	−0.0239094
$941$	−1.90527e10	−0.745407	−0.372703	−	0.927951i	$-0.621569\pi$
$941$	−1.90527e10	−0.745407	−0.372703	+	0.927951i	$0.621569\pi$
$942$	2.21766e10	0.864402
$943$	−3.61139e10	−1.40244
$944$	−3.97601e9	−0.153832
$945$	1.89045e8	0.00728708
$946$	2.46023e10	0.944838
$947$	2.17206e10	0.831089	0.415544	−	0.909573i	$-0.363591\pi$
$947$	2.17206e10	0.831089	0.415544	+	0.909573i	$0.363591\pi$
$948$	−3.51262e9	−0.133907
$949$	−3.96404e9	−0.150559
$950$	−5.85703e8	−0.0221638
$951$	1.99558e9	0.0752379
$952$	2.62031e10	0.984290
$953$	−2.72331e9	−0.101923	−0.0509614	−	0.998701i	$-0.516229\pi$
$953$	−2.72331e9	−0.101923	−0.0509614	+	0.998701i	$0.516229\pi$
$954$	2.16479e10	0.807227
$955$	−1.40878e8	−0.00523397
$956$	−3.27485e10	−1.21224
$957$	2.62370e10	0.967658
$958$	−4.68732e10	−1.72244
$959$	−3.43865e9	−0.125899
$960$	−1.77952e8	−0.00649163
$961$	−2.36876e10	−0.860972
$962$	1.43904e10	0.521148
$963$	−1.58228e10	−0.570940
$964$	−2.41973e10	−0.869955
$965$	1.43147e8	0.00512787
$966$	−3.46309e10	−1.23607
$967$	−1.19767e10	−0.425935	−0.212967	−	0.977059i	$-0.568313\pi$
$967$	−1.19767e10	−0.425935	−0.212967	+	0.977059i	$0.568313\pi$
$968$	7.66047e8	0.0271451
$969$	−5.25916e8	−0.0185688
$970$	9.85728e8	0.0346781
$971$	4.20855e9	0.147525	0.0737625	−	0.997276i	$-0.476499\pi$
$971$	4.20855e9	0.147525	0.0737625	+	0.997276i	$0.476499\pi$
$972$	1.39867e9	0.0488521
$973$	−2.71172e10	−0.943735
$974$	2.97631e10	1.03210
$975$	−3.21003e10	−1.10916
$976$	5.77890e10	1.98962
$977$	3.92707e10	1.34722	0.673608	−	0.739089i	$-0.264744\pi$
$977$	3.92707e10	1.34722	0.673608	+	0.739089i	$0.264744\pi$
$978$	1.71148e10	0.585041
$979$	1.60686e10	0.547318
$980$	8.46754e8	0.0287386
$981$	−3.23566e9	−0.109426
$982$	−3.75183e10	−1.26431
$983$	2.85690e10	0.959308	0.479654	−	0.877458i	$-0.340762\pi$
$983$	2.85690e10	0.959308	0.479654	+	0.877458i	$0.340762\pi$
$984$	−7.67121e9	−0.256673
$985$	−5.72087e8	−0.0190737
$986$	−1.23690e11	−4.10927
$987$	−3.77461e10	−1.24957
$988$	−7.41424e8	−0.0244578
$989$	−2.07517e10	−0.682129
$990$	−3.29847e8	−0.0108041
$991$	2.53806e10	0.828408	0.414204	−	0.910184i	$-0.364060\pi$
$991$	2.53806e10	0.828408	0.414204	+	0.910184i	$0.364060\pi$
$992$	1.43503e10	0.466733
$993$	−1.63927e10	−0.531285
$994$	−9.03036e10	−2.91644
$995$	−1.33308e9	−0.0429018
$996$	2.18660e10	0.701231
$997$	9.36748e9	0.299357	0.149679	−	0.988735i	$-0.452176\pi$
$997$	9.36748e9	0.299357	0.149679	+	0.988735i	$0.452176\pi$
$998$	−7.20773e10	−2.29531
$999$	−1.23886e9	−0.0393135

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	177.8.a.d.1.4	✓	18
3.2	odd	2		531.8.a.e.1.15		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
177.8.a.d.1.4	✓	18	1.1	even	1	trivial
531.8.a.e.1.15		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)

\(f(q)\)	\(=\)	\(q-15.0158 q^{2} +27.0000 q^{3} +97.4757 q^{4} +6.55078 q^{5} -405.428 q^{6} +1466.16 q^{7} +458.348 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-15.0158 q^{2} +27.0000 q^{3} +97.4757 q^{4} +6.55078 q^{5} -405.428 q^{6} +1466.16 q^{7} +458.348 q^{8} +729.000 q^{9} -98.3656 q^{10} +4599.84 q^{11} +2631.84 q^{12} +15226.3 q^{13} -22015.6 q^{14} +176.871 q^{15} -19359.4 q^{16} +38992.1 q^{17} -10946.6 q^{18} -499.547 q^{19} +638.542 q^{20} +39586.2 q^{21} -69070.4 q^{22} +58259.9 q^{23} +12375.4 q^{24} -78082.1 q^{25} -228636. q^{26} +19683.0 q^{27} +142915. q^{28} +211255. q^{29} -2655.87 q^{30} +61846.8 q^{31} +232029. q^{32} +124196. q^{33} -585500. q^{34} +9604.48 q^{35} +71059.8 q^{36} -62940.4 q^{37} +7501.12 q^{38} +411110. q^{39} +3002.54 q^{40} -619876. q^{41} -594421. q^{42} -356192. q^{43} +448372. q^{44} +4775.52 q^{45} -874822. q^{46} -953515. q^{47} -522703. q^{48} +1.32607e6 q^{49} +1.17247e6 q^{50} +1.05279e6 q^{51} +1.48419e6 q^{52} -1.97760e6 q^{53} -295557. q^{54} +30132.5 q^{55} +672010. q^{56} -13487.8 q^{57} -3.17218e6 q^{58} +205379. q^{59} +17240.6 q^{60} -2.98506e6 q^{61} -928683. q^{62} +1.06883e6 q^{63} -1.00611e6 q^{64} +99744.2 q^{65} -1.86490e6 q^{66} -1.04862e6 q^{67} +3.80078e6 q^{68} +1.57302e6 q^{69} -144219. q^{70} +4.10180e6 q^{71} +334136. q^{72} -260342. q^{73} +945104. q^{74} -2.10822e6 q^{75} -48693.7 q^{76} +6.74408e6 q^{77} -6.17317e6 q^{78} -1.33466e6 q^{79} -126819. q^{80} +531441. q^{81} +9.30797e6 q^{82} +8.30823e6 q^{83} +3.85870e6 q^{84} +255429. q^{85} +5.34852e6 q^{86} +5.70389e6 q^{87} +2.10832e6 q^{88} +3.49331e6 q^{89} -71708.5 q^{90} +2.23242e7 q^{91} +5.67893e6 q^{92} +1.66986e6 q^{93} +1.43178e7 q^{94} -3272.42 q^{95} +6.26478e6 q^{96} -1.00211e7 q^{97} -1.99121e7 q^{98} +3.35328e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q + 24 q^{2} + 486 q^{3} + 1358 q^{4} + 678 q^{5} + 648 q^{6} + 3081 q^{7} + 4107 q^{8} + 13122 q^{9}+O(q^{10}) \) 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

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