LMFDB - Embedded newform 354.8.a.e.1.4

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [354,8,Mod(1,354)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(354, 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("354.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 354 = 2 \cdot 3 \cdot 59 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	354.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:	$110.584299021$
Analytic rank:	$1$
Dimension:	$9$
Coefficient field:	$\mathbb{Q}[x]/(x^{9} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{9} - 4 x^{8} - 260588 x^{7} - 2627755 x^{6} + 16696953355 x^{5} + 808091684078 x^{4} + \cdots + 15\!\cdots\!00 $ x^9 - 4x^8 - 260588x^7 - 2627755x^6 + 16696953355x^5 + 808091684078x^4 - 191825159847522x^3 - 12153827093891319x^2 + 237398587398357570x + 15300107670464479800
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{4}\cdot 3^{5}\cdot 5\cdot 7 $
Twist minimal:	yes
Fricke sign:	$-1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.4
Root			$401.344$ of defining polynomial
Character	$\chi$	$=$	354.1

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -140.027 q^{5} +216.000 q^{6} -1605.75 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -140.027 q^{5} +216.000 q^{6} -1605.75 q^{7} -512.000 q^{8} +729.000 q^{9} +1120.22 q^{10} -916.249 q^{11} -1728.00 q^{12} -14697.3 q^{13} +12846.0 q^{14} +3780.73 q^{15} +4096.00 q^{16} +27651.8 q^{17} -5832.00 q^{18} +25042.0 q^{19} -8961.74 q^{20} +43355.4 q^{21} +7329.99 q^{22} +76405.0 q^{23} +13824.0 q^{24} -58517.4 q^{25} +117579. q^{26} -19683.0 q^{27} -102768. q^{28} +51926.9 q^{29} -30245.9 q^{30} -118252. q^{31} -32768.0 q^{32} +24738.7 q^{33} -221214. q^{34} +224849. q^{35} +46656.0 q^{36} +213929. q^{37} -200336. q^{38} +396828. q^{39} +71693.9 q^{40} -193644. q^{41} -346843. q^{42} +436441. q^{43} -58639.9 q^{44} -102080. q^{45} -611240. q^{46} +586009. q^{47} -110592. q^{48} +1.75491e6 q^{49} +468139. q^{50} -746597. q^{51} -940628. q^{52} -486065. q^{53} +157464. q^{54} +128300. q^{55} +822147. q^{56} -676133. q^{57} -415415. q^{58} +205379. q^{59} +241967. q^{60} -2.30409e6 q^{61} +946017. q^{62} -1.17060e6 q^{63} +262144. q^{64} +2.05802e6 q^{65} -197910. q^{66} +2.01540e6 q^{67} +1.76971e6 q^{68} -2.06294e6 q^{69} -1.79879e6 q^{70} -319421. q^{71} -373248. q^{72} +3.49861e6 q^{73} -1.71143e6 q^{74} +1.57997e6 q^{75} +1.60269e6 q^{76} +1.47127e6 q^{77} -3.17462e6 q^{78} -2.66598e6 q^{79} -573551. q^{80} +531441. q^{81} +1.54915e6 q^{82} -755869. q^{83} +2.77474e6 q^{84} -3.87200e6 q^{85} -3.49153e6 q^{86} -1.40203e6 q^{87} +469119. q^{88} +1.17456e6 q^{89} +816639. q^{90} +2.36003e7 q^{91} +4.88992e6 q^{92} +3.19281e6 q^{93} -4.68807e6 q^{94} -3.50656e6 q^{95} +884736. q^{96} +1.72581e7 q^{97} -1.40392e7 q^{98} -667945. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) $ 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * 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 $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−27.0000	−0.577350
$3$	−27.0000	−0.577350
$4$	64.0000	0.500000
$5$	−140.027	−0.500976	−0.250488	−	0.968120i	$-0.580591\pi$
$5$	−140.027	−0.500976	−0.250488	+	0.968120i	$0.580591\pi$
$6$	216.000	0.408248
$7$	−1605.75	−1.76944	−0.884721	−	0.466122i	$-0.845651\pi$
$7$	−1605.75	−1.76944	−0.884721	+	0.466122i	$0.845651\pi$
$8$	−512.000	−0.353553
$9$	729.000	0.333333
$10$	1120.22	0.354244
$11$	−916.249	−0.207558	−0.103779	−	0.994600i	$-0.533093\pi$
$11$	−916.249	−0.207558	−0.103779	+	0.994600i	$0.533093\pi$
$12$	−1728.00	−0.288675
$13$	−14697.3	−1.85539	−0.927697	−	0.373333i	$-0.878215\pi$
$13$	−14697.3	−1.85539	−0.927697	+	0.373333i	$0.878215\pi$
$14$	12846.0	1.25118
$15$	3780.73	0.289239
$16$	4096.00	0.250000
$17$	27651.8	1.36506	0.682530	−	0.730858i	$-0.260880\pi$
$17$	27651.8	1.36506	0.682530	+	0.730858i	$0.260880\pi$
$18$	−5832.00	−0.235702
$19$	25042.0	0.837589	0.418794	−	0.908081i	$-0.362453\pi$
$19$	25042.0	0.837589	0.418794	+	0.908081i	$0.362453\pi$
$20$	−8961.74	−0.250488
$21$	43355.4	1.02159
$22$	7329.99	0.146765
$23$	76405.0	1.30941	0.654703	−	0.755886i	$-0.272794\pi$
$23$	76405.0	1.30941	0.654703	+	0.755886i	$0.272794\pi$
$24$	13824.0	0.204124
$25$	−58517.4	−0.749023
$26$	117579.	1.31196
$27$	−19683.0	−0.192450
$28$	−102768.	−0.884721
$29$	51926.9	0.395366	0.197683	−	0.980266i	$-0.436658\pi$
$29$	51926.9	0.395366	0.197683	+	0.980266i	$0.436658\pi$
$30$	−30245.9	−0.204523
$31$	−118252.	−0.712924	−0.356462	−	0.934310i	$-0.616017\pi$
$31$	−118252.	−0.712924	−0.356462	+	0.934310i	$0.616017\pi$
$32$	−32768.0	−0.176777
$33$	24738.7	0.119834
$34$	−221214.	−0.965243
$35$	224849.	0.886448
$36$	46656.0	0.166667
$37$	213929.	0.694327	0.347163	−	0.937805i	$-0.387145\pi$
$37$	213929.	0.694327	0.347163	+	0.937805i	$0.387145\pi$
$38$	−200336.	−0.592265
$39$	396828.	1.07121
$40$	71693.9	0.177122
$41$	−193644.	−0.438794	−0.219397	−	0.975636i	$-0.570409\pi$
$41$	−193644.	−0.438794	−0.219397	+	0.975636i	$0.570409\pi$
$42$	−346843.	−0.722371
$43$	436441.	0.837117	0.418558	−	0.908190i	$-0.362535\pi$
$43$	436441.	0.837117	0.418558	+	0.908190i	$0.362535\pi$
$44$	−58639.9	−0.103779
$45$	−102080.	−0.166992
$46$	−611240.	−0.925890
$47$	586009.	0.823307	0.411654	−	0.911340i	$-0.364951\pi$
$47$	586009.	0.823307	0.411654	+	0.911340i	$0.364951\pi$
$48$	−110592.	−0.144338
$49$	1.75491e6	2.13092
$50$	468139.	0.529639
$51$	−746597.	−0.788117
$52$	−940628.	−0.927697
$53$	−486065.	−0.448465	−0.224233	−	0.974536i	$-0.571988\pi$
$53$	−486065.	−0.448465	−0.224233	+	0.974536i	$0.571988\pi$
$54$	157464.	0.136083
$55$	128300.	0.103982
$56$	822147.	0.625592
$57$	−676133.	−0.483582
$58$	−415415.	−0.279566
$59$	205379.	0.130189
$59$	205379.	0.130189
$60$	241967.	0.144619
$61$	−2.30409e6	−1.29971	−0.649853	−	0.760060i	$-0.725170\pi$
$61$	−2.30409e6	−1.29971	−0.649853	+	0.760060i	$0.725170\pi$
$62$	946017.	0.504113
$63$	−1.17060e6	−0.589814
$64$	262144.	0.125000
$65$	2.05802e6	0.929509
$66$	−197910.	−0.0847351
$67$	2.01540e6	0.818654	0.409327	−	0.912388i	$-0.365764\pi$
$67$	2.01540e6	0.818654	0.409327	+	0.912388i	$0.365764\pi$
$68$	1.76971e6	0.682530
$69$	−2.06294e6	−0.755986
$70$	−1.79879e6	−0.626814
$71$	−319421.	−0.105915	−0.0529576	−	0.998597i	$-0.516865\pi$
$71$	−319421.	−0.105915	−0.0529576	+	0.998597i	$0.516865\pi$
$72$	−373248.	−0.117851
$73$	3.49861e6	1.05260	0.526302	−	0.850298i	$-0.323578\pi$
$73$	3.49861e6	1.05260	0.526302	+	0.850298i	$0.323578\pi$
$74$	−1.71143e6	−0.490963
$75$	1.57997e6	0.432448
$76$	1.60269e6	0.418794
$77$	1.47127e6	0.367261
$78$	−3.17462e6	−0.757462
$79$	−2.66598e6	−0.608363	−0.304181	−	0.952614i	$-0.598383\pi$
$79$	−2.66598e6	−0.608363	−0.304181	+	0.952614i	$0.598383\pi$
$80$	−573551.	−0.125244
$81$	531441.	0.111111
$82$	1.54915e6	0.310275
$83$	−755869.	−0.145102	−0.0725509	−	0.997365i	$-0.523114\pi$
$83$	−755869.	−0.145102	−0.0725509	+	0.997365i	$0.523114\pi$
$84$	2.77474e6	0.510794
$85$	−3.87200e6	−0.683862
$86$	−3.49153e6	−0.591931
$87$	−1.40203e6	−0.228265
$88$	469119.	0.0733827
$89$	1.17456e6	0.176607	0.0883037	−	0.996094i	$-0.471855\pi$
$89$	1.17456e6	0.176607	0.0883037	+	0.996094i	$0.471855\pi$
$90$	816639.	0.118081
$91$	2.36003e7	3.28301
$92$	4.88992e6	0.654703
$93$	3.19281e6	0.411607
$94$	−4.68807e6	−0.582166
$95$	−3.50656e6	−0.419612
$96$	884736.	0.102062
$97$	1.72581e7	1.91995	0.959977	−	0.280080i	$-0.0903609\pi$
$97$	1.72581e7	1.91995	0.959977	+	0.280080i	$0.0903609\pi$
$98$	−1.40392e7	−1.50679
$99$	−667945.	−0.0691859
$100$	−3.74511e6	−0.374511
$101$	1.16071e7	1.12098	0.560490	−	0.828161i	$-0.310613\pi$
$101$	1.16071e7	1.12098	0.560490	+	0.828161i	$0.310613\pi$
$102$	5.97278e6	0.557283
$103$	4.27703e6	0.385667	0.192833	−	0.981232i	$-0.438232\pi$
$103$	4.27703e6	0.385667	0.192833	+	0.981232i	$0.438232\pi$
$104$	7.52503e6	0.655981
$105$	−6.07093e6	−0.511791
$106$	3.88852e6	0.317113
$107$	1.27910e7	1.00939	0.504696	−	0.863297i	$-0.331605\pi$
$107$	1.27910e7	1.00939	0.504696	+	0.863297i	$0.331605\pi$
$108$	−1.25971e6	−0.0962250
$109$	1.91379e6	0.141547	0.0707736	−	0.997492i	$-0.477453\pi$
$109$	1.91379e6	0.141547	0.0707736	+	0.997492i	$0.477453\pi$
$110$	−1.02640e6	−0.0735261
$111$	−5.77609e6	−0.400870
$112$	−6.57717e6	−0.442360
$113$	−1.83091e7	−1.19369	−0.596846	−	0.802356i	$-0.703580\pi$
$113$	−1.83091e7	−1.19369	−0.596846	+	0.802356i	$0.703580\pi$
$114$	5.40907e6	0.341944
$115$	−1.06988e7	−0.655982
$116$	3.32332e6	0.197683
$117$	−1.07143e7	−0.618465
$118$	−1.64303e6	−0.0920575
$119$	−4.44019e7	−2.41539
$120$	−1.93574e6	−0.102261
$121$	−1.86477e7	−0.956920
$122$	1.84327e7	0.919031
$123$	5.22840e6	0.253338
$124$	−7.56814e6	−0.356462
$125$	1.91336e7	0.876219
$126$	9.36476e6	0.417061
$127$	1.24600e7	0.539764	0.269882	−	0.962893i	$-0.413015\pi$
$127$	1.24600e7	0.539764	0.269882	+	0.962893i	$0.413015\pi$
$128$	−2.09715e6	−0.0883883
$129$	−1.17839e7	−0.483310
$130$	−1.64642e7	−0.657262
$131$	−3.29601e7	−1.28097	−0.640485	−	0.767971i	$-0.721266\pi$
$131$	−3.29601e7	−1.28097	−0.640485	+	0.767971i	$0.721266\pi$
$132$	1.58328e6	0.0599168
$133$	−4.02113e7	−1.48206
$134$	−1.61232e7	−0.578876
$135$	2.75616e6	0.0964130
$136$	−1.41577e7	−0.482621
$137$	−5.09640e7	−1.69333	−0.846664	−	0.532127i	$-0.821393\pi$
$137$	−5.09640e7	−1.69333	−0.846664	+	0.532127i	$0.821393\pi$
$138$	1.65035e7	0.534563
$139$	−2.71027e7	−0.855973	−0.427987	−	0.903785i	$-0.640777\pi$
$139$	−2.71027e7	−0.855973	−0.427987	+	0.903785i	$0.640777\pi$
$140$	1.43904e7	0.443224
$141$	−1.58222e7	−0.475337
$142$	2.55536e6	0.0748934
$143$	1.34664e7	0.385102
$144$	2.98598e6	0.0833333
$145$	−7.27118e6	−0.198069
$146$	−2.79888e7	−0.744303
$147$	−4.73825e7	−1.23029
$148$	1.36915e7	0.347163
$149$	5.26301e7	1.30341	0.651707	−	0.758471i	$-0.274053\pi$
$149$	5.26301e7	1.30341	0.651707	+	0.758471i	$0.274053\pi$
$150$	−1.26398e7	−0.305787
$151$	−4.44996e7	−1.05181	−0.525905	−	0.850543i	$-0.676273\pi$
$151$	−4.44996e7	−1.05181	−0.525905	+	0.850543i	$0.676273\pi$
$152$	−1.28215e7	−0.296132
$153$	2.01581e7	0.455020
$154$	−1.17702e7	−0.259693
$155$	1.65585e7	0.357158
$156$	2.53970e7	0.535606
$157$	6.80166e7	1.40270	0.701352	−	0.712815i	$-0.252580\pi$
$157$	6.80166e7	1.40270	0.701352	+	0.712815i	$0.252580\pi$
$158$	2.13279e7	0.430178
$159$	1.31238e7	0.258921
$160$	4.58841e6	0.0885610
$161$	−1.22688e8	−2.31692
$162$	−4.25153e6	−0.0785674
$163$	−5.55304e7	−1.00432	−0.502162	−	0.864773i	$-0.667462\pi$
$163$	−5.55304e7	−1.00432	−0.502162	+	0.864773i	$0.667462\pi$
$164$	−1.23932e7	−0.219397
$165$	−3.46409e6	−0.0600338
$166$	6.04695e6	0.102603
$167$	−8.36141e6	−0.138922	−0.0694611	−	0.997585i	$-0.522128\pi$
$167$	−8.36141e6	−0.138922	−0.0694611	+	0.997585i	$0.522128\pi$
$168$	−2.21980e7	−0.361186
$169$	1.53263e8	2.44249
$170$	3.09760e7	0.483564
$171$	1.82556e7	0.279196
$172$	2.79322e7	0.418558
$173$	−1.91521e7	−0.281226	−0.140613	−	0.990065i	$-0.544907\pi$
$173$	−1.91521e7	−0.281226	−0.140613	+	0.990065i	$0.544907\pi$
$174$	1.12162e7	0.161407
$175$	9.39646e7	1.32535
$176$	−3.75295e6	−0.0518894
$177$	−5.54523e6	−0.0751646
$178$	−9.39645e6	−0.124880
$179$	−1.33016e8	−1.73348	−0.866741	−	0.498759i	$-0.833789\pi$
$179$	−1.33016e8	−1.73348	−0.866741	+	0.498759i	$0.833789\pi$
$180$	−6.53311e6	−0.0834961
$181$	−1.46491e8	−1.83627	−0.918133	−	0.396271i	$-0.870304\pi$
$181$	−1.46491e8	−1.83627	−0.918133	+	0.396271i	$0.870304\pi$
$182$	−1.88802e8	−2.32144
$183$	6.22104e7	0.750386
$184$	−3.91194e7	−0.462945
$185$	−2.99559e7	−0.347841
$186$	−2.55425e7	−0.291050
$187$	−2.53359e7	−0.283329
$188$	3.75046e7	0.411654
$189$	3.16061e7	0.340529
$190$	2.80525e7	0.296711
$191$	−1.19542e8	−1.24137	−0.620687	−	0.784058i	$-0.713146\pi$
$191$	−1.19542e8	−1.24137	−0.620687	+	0.784058i	$0.713146\pi$
$192$	−7.07789e6	−0.0721688
$193$	1.04733e8	1.04866	0.524329	−	0.851516i	$-0.324316\pi$
$193$	1.04733e8	1.04866	0.524329	+	0.851516i	$0.324316\pi$
$194$	−1.38064e8	−1.35761
$195$	−5.55666e7	−0.536652
$196$	1.12314e8	1.06546
$197$	4.89121e7	0.455810	0.227905	−	0.973683i	$-0.426812\pi$
$197$	4.89121e7	0.455810	0.227905	+	0.973683i	$0.426812\pi$
$198$	5.34356e6	0.0489218
$199$	−1.30414e8	−1.17311	−0.586554	−	0.809910i	$-0.699516\pi$
$199$	−1.30414e8	−1.17311	−0.586554	+	0.809910i	$0.699516\pi$
$200$	2.99609e7	0.264819
$201$	−5.44159e7	−0.472650
$202$	−9.28566e7	−0.792653
$203$	−8.33819e7	−0.699577
$204$	−4.77822e7	−0.394059
$205$	2.71155e7	0.219826
$206$	−3.42162e7	−0.272708
$207$	5.56993e7	0.436469
$208$	−6.02002e7	−0.463849
$209$	−2.29447e7	−0.173848
$210$	4.85675e7	0.361891
$211$	4.61326e7	0.338080	0.169040	−	0.985609i	$-0.445933\pi$
$211$	4.61326e7	0.338080	0.169040	+	0.985609i	$0.445933\pi$
$212$	−3.11082e7	−0.224233
$213$	8.62436e6	0.0611502
$214$	−1.02328e8	−0.713748
$215$	−6.11136e7	−0.419376
$216$	1.00777e7	0.0680414
$217$	1.89884e8	1.26148
$218$	−1.53103e7	−0.100089
$219$	−9.44624e7	−0.607721
$220$	8.21118e6	0.0519908
$221$	−4.06407e8	−2.53272
$222$	4.62087e7	0.283458
$223$	−2.87841e8	−1.73815	−0.869073	−	0.494684i	$-0.835284\pi$
$223$	−2.87841e8	−1.73815	−0.869073	+	0.494684i	$0.835284\pi$
$224$	5.26174e7	0.312796
$225$	−4.26592e7	−0.249674
$226$	1.46473e8	0.844068
$227$	−2.66612e8	−1.51283	−0.756414	−	0.654093i	$-0.773051\pi$
$227$	−2.66612e8	−1.51283	−0.756414	+	0.654093i	$0.773051\pi$
$228$	−4.32725e7	−0.241791
$229$	2.54159e8	1.39856	0.699279	−	0.714849i	$-0.253504\pi$
$229$	2.54159e8	1.39856	0.699279	+	0.714849i	$0.253504\pi$
$230$	8.55903e7	0.463849
$231$	−3.97243e7	−0.212038
$232$	−2.65866e7	−0.139783
$233$	3.45773e7	0.179079	0.0895396	−	0.995983i	$-0.471460\pi$
$233$	3.45773e7	0.179079	0.0895396	+	0.995983i	$0.471460\pi$
$234$	8.57147e7	0.437321
$235$	−8.20572e7	−0.412458
$236$	1.31443e7	0.0650945
$237$	7.19816e7	0.351239
$238$	3.55216e8	1.70794
$239$	3.78210e8	1.79201	0.896005	−	0.444043i	$-0.146456\pi$
$239$	3.78210e8	1.79201	0.896005	+	0.444043i	$0.146456\pi$
$240$	1.54859e7	0.0723097
$241$	−2.67466e8	−1.23086	−0.615430	−	0.788192i	$-0.711018\pi$
$241$	−2.67466e8	−1.23086	−0.615430	+	0.788192i	$0.711018\pi$
$242$	1.49181e8	0.676644
$243$	−1.43489e7	−0.0641500
$244$	−1.47462e8	−0.649853
$245$	−2.45735e8	−1.06754
$246$	−4.18272e7	−0.179137
$247$	−3.68050e8	−1.55406
$248$	6.05451e7	0.252057
$249$	2.04085e7	0.0837746
$250$	−1.53069e8	−0.619581
$251$	4.13453e8	1.65032	0.825161	−	0.564898i	$-0.191085\pi$
$251$	4.13453e8	1.65032	0.825161	+	0.564898i	$0.191085\pi$
$252$	−7.49181e7	−0.294907
$253$	−7.00060e7	−0.271778
$254$	−9.96798e7	−0.381671
$255$	1.04544e8	0.394828
$256$	1.67772e7	0.0625000
$257$	7.73795e7	0.284354	0.142177	−	0.989841i	$-0.454590\pi$
$257$	7.73795e7	0.284354	0.142177	+	0.989841i	$0.454590\pi$
$258$	9.42713e7	0.341752
$259$	−3.43518e8	−1.22857
$260$	1.31714e8	0.464755
$261$	3.78547e7	0.131789
$262$	2.63681e8	0.905782
$263$	2.34007e7	0.0793203	0.0396602	−	0.999213i	$-0.487372\pi$
$263$	2.34007e7	0.0793203	0.0396602	+	0.999213i	$0.487372\pi$
$264$	−1.26662e7	−0.0423675
$265$	6.80623e7	0.224670
$266$	3.21690e8	1.04798
$267$	−3.17130e7	−0.101964
$268$	1.28986e8	0.409327
$269$	−1.07554e8	−0.336896	−0.168448	−	0.985711i	$-0.553875\pi$
$269$	−1.07554e8	−0.336896	−0.168448	+	0.985711i	$0.553875\pi$
$270$	−2.20492e7	−0.0681743
$271$	−4.46638e8	−1.36321	−0.681606	−	0.731720i	$-0.738718\pi$
$271$	−4.46638e8	−1.36321	−0.681606	+	0.731720i	$0.738718\pi$
$272$	1.13262e8	0.341265
$273$	−6.37208e8	−1.89545
$274$	4.07712e8	1.19736
$275$	5.36165e7	0.155465
$276$	−1.32028e8	−0.377993
$277$	2.74335e8	0.775536	0.387768	−	0.921757i	$-0.373246\pi$
$277$	2.74335e8	0.775536	0.387768	+	0.921757i	$0.373246\pi$
$278$	2.16821e8	0.605264
$279$	−8.62058e7	−0.237641
$280$	−1.15123e8	−0.313407
$281$	3.94116e8	1.05962	0.529812	−	0.848115i	$-0.322262\pi$
$281$	3.94116e8	1.05962	0.529812	+	0.848115i	$0.322262\pi$
$282$	1.26578e8	0.336114
$283$	2.70402e8	0.709182	0.354591	−	0.935022i	$-0.384620\pi$
$283$	2.70402e8	0.709182	0.354591	+	0.935022i	$0.384620\pi$
$284$	−2.04429e7	−0.0529576
$285$	9.46770e7	0.242263
$286$	−1.07731e8	−0.272308
$287$	3.10945e8	0.776421
$288$	−2.38879e7	−0.0589256
$289$	3.54281e8	0.863386
$290$	5.81694e7	0.140056
$291$	−4.65967e8	−1.10849
$292$	2.23911e8	0.526302
$293$	9.95252e7	0.231151	0.115576	−	0.993299i	$-0.463129\pi$
$293$	9.95252e7	0.231151	0.115576	+	0.993299i	$0.463129\pi$
$294$	3.79060e8	0.869945
$295$	−2.87586e7	−0.0652216
$296$	−1.09532e8	−0.245482
$297$	1.80345e7	0.0399445
$298$	−4.21041e8	−0.921653
$299$	−1.12295e9	−2.42947
$300$	1.01118e8	0.216224
$301$	−7.00818e8	−1.48123
$302$	3.55997e8	0.743742
$303$	−3.13391e8	−0.647199
$304$	1.02572e8	0.209397
$305$	3.22635e8	0.651122
$306$	−1.61265e8	−0.321748
$307$	7.94593e8	1.56733	0.783665	−	0.621183i	$-0.213348\pi$
$307$	7.94593e8	1.56733	0.783665	+	0.621183i	$0.213348\pi$
$308$	9.41613e7	0.183631
$309$	−1.15480e8	−0.222665
$310$	−1.32468e8	−0.252549
$311$	−7.02591e8	−1.32447	−0.662234	−	0.749297i	$-0.730391\pi$
$311$	−7.02591e8	−1.32447	−0.662234	+	0.749297i	$0.730391\pi$
$312$	−2.03176e8	−0.378731
$313$	5.12724e8	0.945102	0.472551	−	0.881303i	$-0.343333\pi$
$313$	5.12724e8	0.945102	0.472551	+	0.881303i	$0.343333\pi$
$314$	−5.44133e8	−0.991862
$315$	1.63915e8	0.295483
$316$	−1.70623e8	−0.304181
$317$	7.15241e8	1.26109	0.630543	−	0.776154i	$-0.282832\pi$
$317$	7.15241e8	1.26109	0.630543	+	0.776154i	$0.282832\pi$
$318$	−1.04990e8	−0.183085
$319$	−4.75779e7	−0.0820613
$320$	−3.67073e7	−0.0626221
$321$	−3.45356e8	−0.582773
$322$	9.81502e8	1.63831
$323$	6.92454e8	1.14336
$324$	3.40122e7	0.0555556
$325$	8.60049e8	1.38973
$326$	4.44243e8	0.710165
$327$	−5.16723e7	−0.0817223
$328$	9.91459e7	0.155137
$329$	−9.40987e8	−1.45679
$330$	2.77127e7	0.0424503
$331$	1.48313e8	0.224792	0.112396	−	0.993664i	$-0.464148\pi$
$331$	1.48313e8	0.224792	0.112396	+	0.993664i	$0.464148\pi$
$332$	−4.83756e7	−0.0725509
$333$	1.55954e8	0.231442
$334$	6.68913e7	0.0982329
$335$	−2.82211e8	−0.410126
$336$	1.77584e8	0.255397
$337$	6.34670e8	0.903323	0.451662	−	0.892189i	$-0.350831\pi$
$337$	6.34670e8	0.903323	0.451662	+	0.892189i	$0.350831\pi$
$338$	−1.22610e9	−1.72710
$339$	4.94346e8	0.689179
$340$	−2.47808e8	−0.341931
$341$	1.08348e8	0.147973
$342$	−1.46045e8	−0.197422
$343$	−1.49554e9	−2.00110
$344$	−2.23458e8	−0.295966
$345$	2.88867e8	0.378731
$346$	1.53217e8	0.198857
$347$	1.76916e8	0.227307	0.113653	−	0.993520i	$-0.463745\pi$
$347$	1.76916e8	0.227307	0.113653	+	0.993520i	$0.463745\pi$
$348$	−8.97297e7	−0.114132
$349$	−6.69158e8	−0.842635	−0.421318	−	0.906913i	$-0.638432\pi$
$349$	−6.69158e8	−0.842635	−0.421318	+	0.906913i	$0.638432\pi$
$350$	−7.51717e8	−0.937165
$351$	2.89287e8	0.357071
$352$	3.00236e7	0.0366914
$353$	−5.59888e8	−0.677469	−0.338734	−	0.940882i	$-0.609999\pi$
$353$	−5.59888e8	−0.677469	−0.338734	+	0.940882i	$0.609999\pi$
$354$	4.43619e7	0.0531494
$355$	4.47276e7	0.0530611
$356$	7.51716e7	0.0883037
$357$	1.19885e9	1.39453
$358$	1.06413e9	1.22576
$359$	−3.10105e8	−0.353735	−0.176867	−	0.984235i	$-0.556596\pi$
$359$	−3.10105e8	−0.353735	−0.176867	+	0.984235i	$0.556596\pi$
$360$	5.22649e7	0.0590406
$361$	−2.66771e8	−0.298445
$362$	1.17193e9	1.29844
$363$	5.03487e8	0.552478
$364$	1.51042e9	1.64151
$365$	−4.89900e8	−0.527330
$366$	−4.97684e8	−0.530603
$367$	−2.58546e7	−0.0273027	−0.0136514	−	0.999907i	$-0.504346\pi$
$367$	−2.58546e7	−0.0273027	−0.0136514	+	0.999907i	$0.504346\pi$
$368$	3.12955e8	0.327352
$369$	−1.41167e8	−0.146265
$370$	2.39647e8	0.245961
$371$	7.80501e8	0.793533
$372$	2.04340e8	0.205803
$373$	−2.81757e8	−0.281121	−0.140561	−	0.990072i	$-0.544891\pi$
$373$	−2.81757e8	−0.281121	−0.140561	+	0.990072i	$0.544891\pi$
$374$	2.02687e8	0.200344
$375$	−5.16609e8	−0.505885
$376$	−3.00037e8	−0.291083
$377$	−7.63186e8	−0.733560
$378$	−2.52849e8	−0.240790
$379$	8.49522e8	0.801562	0.400781	−	0.916174i	$-0.368739\pi$
$379$	8.49522e8	0.801562	0.400781	+	0.916174i	$0.368739\pi$
$380$	−2.24420e8	−0.209806
$381$	−3.36419e8	−0.311633
$382$	9.56334e8	0.877784
$383$	2.37538e8	0.216041	0.108021	−	0.994149i	$-0.465549\pi$
$383$	2.37538e8	0.216041	0.108021	+	0.994149i	$0.465549\pi$
$384$	5.66231e7	0.0510310
$385$	−2.06018e8	−0.183989
$386$	−8.37866e8	−0.741513
$387$	3.18166e8	0.279039
$388$	1.10452e9	0.959977
$389$	−1.85579e9	−1.59847	−0.799237	−	0.601017i	$-0.794763\pi$
$389$	−1.85579e9	−1.59847	−0.799237	+	0.601017i	$0.794763\pi$
$390$	4.44533e8	0.379471
$391$	2.11273e9	1.78742
$392$	−8.98512e8	−0.753395
$393$	8.89922e8	0.739568
$394$	−3.91297e8	−0.322307
$395$	3.73310e8	0.304776
$396$	−4.27485e7	−0.0345930
$397$	−1.36430e9	−1.09431	−0.547157	−	0.837030i	$-0.684290\pi$
$397$	−1.36430e9	−1.09431	−0.547157	+	0.837030i	$0.684290\pi$
$398$	1.04331e9	0.829512
$399$	1.08570e9	0.855670
$400$	−2.39687e8	−0.187256
$401$	−2.02978e9	−1.57197	−0.785985	−	0.618246i	$-0.787844\pi$
$401$	−2.02978e9	−1.57197	−0.785985	+	0.618246i	$0.787844\pi$
$402$	4.35327e8	0.334214
$403$	1.73799e9	1.32275
$404$	7.42853e8	0.560490
$405$	−7.44162e7	−0.0556641
$406$	6.67055e8	0.494676
$407$	−1.96012e8	−0.144113
$408$	3.82258e8	0.278642
$409$	1.13164e9	0.817857	0.408928	−	0.912567i	$-0.365903\pi$
$409$	1.13164e9	0.817857	0.408928	+	0.912567i	$0.365903\pi$
$410$	−2.16924e8	−0.155440
$411$	1.37603e9	0.977644
$412$	2.73730e8	0.192833
$413$	−3.29788e8	−0.230362
$414$	−4.45594e8	−0.308630
$415$	1.05842e8	0.0726926
$416$	4.81602e8	0.327991
$417$	7.31772e8	0.494196
$418$	1.83557e8	0.122929
$419$	1.85604e9	1.23264	0.616322	−	0.787494i	$-0.288622\pi$
$419$	1.85604e9	1.23264	0.616322	+	0.787494i	$0.288622\pi$
$420$	−3.88540e8	−0.255896
$421$	2.30720e9	1.50695	0.753473	−	0.657479i	$-0.228377\pi$
$421$	2.30720e9	1.50695	0.753473	+	0.657479i	$0.228377\pi$
$422$	−3.69061e8	−0.239059
$423$	4.27201e8	0.274436
$424$	2.48865e8	0.158556
$425$	−1.61811e9	−1.02246
$426$	−6.89948e7	−0.0432397
$427$	3.69980e9	2.29975
$428$	8.18621e8	0.504696
$429$	−3.63593e8	−0.222338
$430$	4.88909e8	0.296544
$431$	7.44082e8	0.447662	0.223831	−	0.974628i	$-0.428144\pi$
$431$	7.44082e8	0.447662	0.223831	+	0.974628i	$0.428144\pi$
$432$	−8.06216e7	−0.0481125
$433$	−9.75926e8	−0.577709	−0.288855	−	0.957373i	$-0.593274\pi$
$433$	−9.75926e8	−0.577709	−0.288855	+	0.957373i	$0.593274\pi$
$434$	−1.51907e9	−0.891999
$435$	1.96322e8	0.114355
$436$	1.22482e8	0.0707736
$437$	1.91333e9	1.09674
$438$	7.55699e8	0.429724
$439$	−4.91428e8	−0.277226	−0.138613	−	0.990347i	$-0.544264\pi$
$439$	−4.91428e8	−0.277226	−0.138613	+	0.990347i	$0.544264\pi$
$440$	−6.56895e7	−0.0367630
$441$	1.27933e9	0.710307
$442$	3.25125e9	1.79091
$443$	−1.78548e9	−0.975757	−0.487878	−	0.872912i	$-0.662229\pi$
$443$	−1.78548e9	−0.975757	−0.487878	+	0.872912i	$0.662229\pi$
$444$	−3.69670e8	−0.200435
$445$	−1.64470e8	−0.0884761
$446$	2.30273e9	1.22905
$447$	−1.42101e9	−0.752527
$448$	−4.20939e8	−0.221180
$449$	3.29358e9	1.71714	0.858570	−	0.512697i	$-0.171354\pi$
$449$	3.29358e9	1.71714	0.858570	+	0.512697i	$0.171354\pi$
$450$	3.41273e8	0.176546
$451$	1.77426e8	0.0910752
$452$	−1.17178e9	−0.596846
$453$	1.20149e9	0.607262
$454$	2.13290e9	1.06973
$455$	−3.30468e9	−1.64471
$456$	3.46180e8	0.170972
$457$	−1.81915e9	−0.891581	−0.445790	−	0.895137i	$-0.647077\pi$
$457$	−1.81915e9	−0.891581	−0.445790	+	0.895137i	$0.647077\pi$
$458$	−2.03327e9	−0.988930
$459$	−5.44269e8	−0.262706
$460$	−6.84722e8	−0.327991
$461$	−5.89601e8	−0.280288	−0.140144	−	0.990131i	$-0.544757\pi$
$461$	−5.89601e8	−0.280288	−0.140144	+	0.990131i	$0.544757\pi$
$462$	3.17794e8	0.149934
$463$	−9.75842e8	−0.456926	−0.228463	−	0.973553i	$-0.573370\pi$
$463$	−9.75842e8	−0.456926	−0.228463	+	0.973553i	$0.573370\pi$
$464$	2.12693e8	0.0988415
$465$	−4.47080e8	−0.206205
$466$	−2.76618e8	−0.126628
$467$	2.76788e9	1.25759	0.628794	−	0.777572i	$-0.283549\pi$
$467$	2.76788e9	1.25759	0.628794	+	0.777572i	$0.283549\pi$
$468$	−6.85718e8	−0.309232
$469$	−3.23624e9	−1.44856
$470$	6.56458e8	0.291652
$471$	−1.83645e9	−0.809852
$472$	−1.05154e8	−0.0460287
$473$	−3.99889e8	−0.173750
$474$	−5.75853e8	−0.248363
$475$	−1.46539e9	−0.627373
$476$	−2.84172e9	−1.20770
$477$	−3.54341e8	−0.149488
$478$	−3.02568e9	−1.26714
$479$	−1.86156e9	−0.773933	−0.386966	−	0.922094i	$-0.626477\pi$
$479$	−1.86156e9	−0.773933	−0.386966	+	0.922094i	$0.626477\pi$
$480$	−1.23887e8	−0.0511307
$481$	−3.14418e9	−1.28825
$482$	2.13973e9	0.870349
$483$	3.31257e9	1.33767
$484$	−1.19345e9	−0.478460
$485$	−2.41660e9	−0.961852
$486$	1.14791e8	0.0453609
$487$	2.75659e9	1.08149	0.540744	−	0.841187i	$-0.318143\pi$
$487$	2.75659e9	1.08149	0.540744	+	0.841187i	$0.318143\pi$
$488$	1.17969e9	0.459515
$489$	1.49932e9	0.579847
$490$	1.96588e9	0.754866
$491$	−4.39248e9	−1.67465	−0.837325	−	0.546705i	$-0.815882\pi$
$491$	−4.39248e9	−1.67465	−0.837325	+	0.546705i	$0.815882\pi$
$492$	3.34617e8	0.126669
$493$	1.43587e9	0.539698
$494$	2.94440e9	1.09889
$495$	9.35305e7	0.0346605
$496$	−4.84361e8	−0.178231
$497$	5.12911e8	0.187411
$498$	−1.63268e8	−0.0592376
$499$	−1.62510e9	−0.585501	−0.292750	−	0.956189i	$-0.594570\pi$
$499$	−1.62510e9	−0.585501	−0.292750	+	0.956189i	$0.594570\pi$
$500$	1.22455e9	0.438110
$501$	2.25758e8	0.0802068
$502$	−3.30763e9	−1.16695
$503$	−4.56621e9	−1.59981	−0.799904	−	0.600128i	$-0.795116\pi$
$503$	−4.56621e9	−1.59981	−0.799904	+	0.600128i	$0.795116\pi$
$504$	5.99345e8	0.208531
$505$	−1.62531e9	−0.561585
$506$	5.60048e8	0.192176
$507$	−4.13809e9	−1.41017
$508$	7.97439e8	0.269882
$509$	−4.67834e9	−1.57246	−0.786230	−	0.617934i	$-0.787970\pi$
$509$	−4.67834e9	−1.57246	−0.786230	+	0.617934i	$0.787970\pi$
$510$	−8.36351e8	−0.279186
$511$	−5.61790e9	−1.86252
$512$	−1.34218e8	−0.0441942
$513$	−4.92901e8	−0.161194
$514$	−6.19036e8	−0.201069
$515$	−5.98901e8	−0.193210
$516$	−7.54170e8	−0.241655
$517$	−5.36930e8	−0.170884
$518$	2.74814e9	0.868730
$519$	5.17108e8	0.162366
$520$	−1.05371e9	−0.328631
$521$	1.42656e9	0.441934	0.220967	−	0.975281i	$-0.429079\pi$
$521$	1.42656e9	0.441934	0.220967	+	0.975281i	$0.429079\pi$
$522$	−3.02838e8	−0.0931887
$523$	5.06615e9	1.54854	0.774269	−	0.632857i	$-0.218118\pi$
$523$	5.06615e9	1.54854	0.774269	+	0.632857i	$0.218118\pi$
$524$	−2.10944e9	−0.640485
$525$	−2.53704e9	−0.765192
$526$	−1.87206e8	−0.0560879
$527$	−3.26988e9	−0.973183
$528$	1.01330e8	0.0299584
$529$	2.43290e9	0.714546
$530$	−5.44498e8	−0.158866
$531$	1.49721e8	0.0433963
$532$	−2.57352e9	−0.741032
$533$	2.84605e9	0.814137
$534$	2.53704e8	0.0720996
$535$	−1.79108e9	−0.505682
$536$	−1.03189e9	−0.289438
$537$	3.59144e9	1.00083
$538$	8.60436e8	0.238221
$539$	−1.60793e9	−0.442289
$540$	1.76394e8	0.0482065
$541$	5.11110e9	1.38779	0.693895	−	0.720076i	$-0.255893\pi$
$541$	5.11110e9	1.38779	0.693895	+	0.720076i	$0.255893\pi$
$542$	3.57311e9	0.963936
$543$	3.95526e9	1.06017
$544$	−9.06093e8	−0.241311
$545$	−2.67982e8	−0.0709118
$546$	5.09766e9	1.34028
$547$	−3.17406e9	−0.829200	−0.414600	−	0.910004i	$-0.636078\pi$
$547$	−3.17406e9	−0.829200	−0.414600	+	0.910004i	$0.636078\pi$
$548$	−3.26169e9	−0.846664
$549$	−1.67968e9	−0.433235
$550$	−4.28932e8	−0.109931
$551$	1.30035e9	0.331154
$552$	1.05622e9	0.267282
$553$	4.28092e9	1.07646
$554$	−2.19468e9	−0.548386
$555$	8.08809e8	0.200826
$556$	−1.73457e9	−0.427987
$557$	−1.92812e9	−0.472761	−0.236380	−	0.971661i	$-0.575961\pi$
$557$	−1.92812e9	−0.472761	−0.236380	+	0.971661i	$0.575961\pi$
$558$	6.89647e8	0.168038
$559$	−6.41451e9	−1.55318
$560$	9.20983e8	0.221612
$561$	6.84069e8	0.163580
$562$	−3.15293e9	−0.749268
$563$	2.79414e9	0.659885	0.329942	−	0.944001i	$-0.392971\pi$
$563$	2.79414e9	0.659885	0.329942	+	0.944001i	$0.392971\pi$
$564$	−1.01262e9	−0.237668
$565$	2.56377e9	0.598012
$566$	−2.16322e9	−0.501467
$567$	−8.53364e8	−0.196605
$568$	1.63543e8	0.0374467
$569$	4.20797e9	0.957591	0.478795	−	0.877926i	$-0.341074\pi$
$569$	4.20797e9	0.957591	0.478795	+	0.877926i	$0.341074\pi$
$570$	−7.57416e8	−0.171306
$571$	2.13455e9	0.479822	0.239911	−	0.970795i	$-0.422882\pi$
$571$	2.13455e9	0.479822	0.239911	+	0.970795i	$0.422882\pi$
$572$	8.61849e8	0.192551
$573$	3.22763e9	0.716708
$574$	−2.48756e9	−0.549013
$575$	−4.47102e9	−0.980775
$576$	1.91103e8	0.0416667
$577$	1.01024e9	0.218933	0.109466	−	0.993990i	$-0.465086\pi$
$577$	1.01024e9	0.218933	0.109466	+	0.993990i	$0.465086\pi$
$578$	−2.83425e9	−0.610506
$579$	−2.82780e9	−0.605443
$580$	−4.65355e8	−0.0990345
$581$	1.21374e9	0.256749
$582$	3.72774e9	0.783818
$583$	4.45356e8	0.0930824
$584$	−1.79129e9	−0.372152
$585$	1.50030e9	0.309836
$586$	−7.96202e8	−0.163449
$587$	−4.42069e9	−0.902103	−0.451052	−	0.892498i	$-0.648951\pi$
$587$	−4.42069e9	−0.902103	−0.451052	+	0.892498i	$0.648951\pi$
$588$	−3.03248e9	−0.615144
$589$	−2.96127e9	−0.597137
$590$	2.30069e8	0.0461186
$591$	−1.32063e9	−0.263162
$592$	8.76254e8	0.173582
$593$	2.46202e9	0.484842	0.242421	−	0.970171i	$-0.422058\pi$
$593$	2.46202e9	0.484842	0.242421	+	0.970171i	$0.422058\pi$
$594$	−1.44276e8	−0.0282450
$595$	6.21748e9	1.21005
$596$	3.36833e9	0.651707
$597$	3.52117e9	0.677294
$598$	8.98359e9	1.71789
$599$	−5.98539e9	−1.13789	−0.568943	−	0.822377i	$-0.692647\pi$
$599$	−5.98539e9	−1.13789	−0.568943	+	0.822377i	$0.692647\pi$
$600$	−8.08944e8	−0.152894
$601$	−4.36567e9	−0.820334	−0.410167	−	0.912011i	$-0.634530\pi$
$601$	−4.36567e9	−0.820334	−0.410167	+	0.912011i	$0.634530\pi$
$602$	5.60654e9	1.04739
$603$	1.46923e9	0.272885
$604$	−2.84798e9	−0.525905
$605$	2.61118e9	0.479394
$606$	2.50713e9	0.457638
$607$	4.84358e9	0.879034	0.439517	−	0.898234i	$-0.355150\pi$
$607$	4.84358e9	0.879034	0.439517	+	0.898234i	$0.355150\pi$
$608$	−8.20575e8	−0.148066
$609$	2.25131e9	0.403901
$610$	−2.58108e9	−0.460413
$611$	−8.61276e9	−1.52756
$612$	1.29012e9	0.227510
$613$	−4.37718e9	−0.767507	−0.383754	−	0.923435i	$-0.625369\pi$
$613$	−4.37718e9	−0.767507	−0.383754	+	0.923435i	$0.625369\pi$
$614$	−6.35675e9	−1.10827
$615$	−7.32117e8	−0.126916
$616$	−7.53291e8	−0.129846
$617$	9.28111e9	1.59075	0.795375	−	0.606118i	$-0.207274\pi$
$617$	9.28111e9	1.59075	0.795375	+	0.606118i	$0.207274\pi$
$618$	9.23839e8	0.157448
$619$	2.72022e9	0.460984	0.230492	−	0.973074i	$-0.425966\pi$
$619$	2.72022e9	0.460984	0.230492	+	0.973074i	$0.425966\pi$
$620$	1.05974e9	0.178579
$621$	−1.50388e9	−0.251995
$622$	5.62073e9	0.936540
$623$	−1.88605e9	−0.312496
$624$	1.62541e9	0.267803
$625$	1.89244e9	0.310057
$626$	−4.10179e9	−0.668288
$627$	6.19506e8	0.100371
$628$	4.35306e9	0.701352
$629$	5.91552e9	0.947797
$630$	−1.31132e9	−0.208938
$631$	9.34304e9	1.48042	0.740211	−	0.672375i	$-0.234726\pi$
$631$	9.34304e9	1.48042	0.740211	+	0.672375i	$0.234726\pi$
$632$	1.36498e9	0.215089
$633$	−1.24558e9	−0.195190
$634$	−5.72192e9	−0.891722
$635$	−1.74474e9	−0.270409
$636$	8.39920e8	0.129461
$637$	−2.57924e10	−3.95370
$638$	3.80624e8	0.0580261
$639$	−2.32858e8	−0.0353051
$640$	2.93658e8	0.0442805
$641$	3.93151e9	0.589598	0.294799	−	0.955559i	$-0.404747\pi$
$641$	3.93151e9	0.589598	0.294799	+	0.955559i	$0.404747\pi$
$642$	2.76285e9	0.412083
$643$	3.02539e9	0.448790	0.224395	−	0.974498i	$-0.427959\pi$
$643$	3.02539e9	0.448790	0.224395	+	0.974498i	$0.427959\pi$
$644$	−7.85202e9	−1.15846
$645$	1.65007e9	0.242127
$646$	−5.53964e9	−0.808477
$647$	−5.92595e9	−0.860187	−0.430094	−	0.902784i	$-0.641519\pi$
$647$	−5.92595e9	−0.860187	−0.430094	+	0.902784i	$0.641519\pi$
$648$	−2.72098e8	−0.0392837
$649$	−1.88178e8	−0.0270217
$650$	−6.88039e9	−0.982689
$651$	−5.12687e9	−0.728314
$652$	−3.55394e9	−0.502162
$653$	−4.56263e9	−0.641237	−0.320619	−	0.947208i	$-0.603891\pi$
$653$	−4.56263e9	−0.641237	−0.320619	+	0.947208i	$0.603891\pi$
$654$	4.13378e8	0.0577864
$655$	4.61531e9	0.641735
$656$	−7.93167e8	−0.109699
$657$	2.55048e9	0.350868
$658$	7.52790e9	1.03011
$659$	−3.55446e9	−0.483810	−0.241905	−	0.970300i	$-0.577772\pi$
$659$	−3.55446e9	−0.483810	−0.241905	+	0.970300i	$0.577772\pi$
$660$	−2.21702e8	−0.0300169
$661$	1.53925e9	0.207302	0.103651	−	0.994614i	$-0.466947\pi$
$661$	1.53925e9	0.207302	0.103651	+	0.994614i	$0.466947\pi$
$662$	−1.18650e9	−0.158952
$663$	1.09730e10	1.46227
$664$	3.87005e8	0.0513013
$665$	5.63067e9	0.742479
$666$	−1.24763e9	−0.163654
$667$	3.96748e9	0.517695
$668$	−5.35130e8	−0.0694611
$669$	7.77171e9	1.00352
$670$	2.25769e9	0.290003
$671$	2.11112e9	0.269764
$672$	−1.42067e9	−0.180593
$673$	5.79332e9	0.732613	0.366306	−	0.930494i	$-0.380622\pi$
$673$	5.79332e9	0.732613	0.366306	+	0.930494i	$0.380622\pi$
$674$	−5.07736e9	−0.638746
$675$	1.15180e9	0.144149
$676$	9.80881e9	1.22124
$677$	3.22923e9	0.399980	0.199990	−	0.979798i	$-0.435909\pi$
$677$	3.22923e9	0.399980	0.199990	+	0.979798i	$0.435909\pi$
$678$	−3.95477e9	−0.487323
$679$	−2.77122e10	−3.39724
$680$	1.98246e9	0.241782
$681$	7.19853e9	0.873432
$682$	−8.66787e8	−0.104633
$683$	−1.13529e10	−1.36344	−0.681719	−	0.731614i	$-0.738767\pi$
$683$	−1.13529e10	−1.36344	−0.681719	+	0.731614i	$0.738767\pi$
$684$	1.16836e9	0.139598
$685$	7.13634e9	0.848318
$686$	1.19643e10	1.41499
$687$	−6.86228e9	−0.807458
$688$	1.78766e9	0.209279
$689$	7.14385e9	0.832080
$690$	−2.31094e9	−0.267804
$691$	−4.30643e9	−0.496529	−0.248264	−	0.968692i	$-0.579860\pi$
$691$	−4.30643e9	−0.496529	−0.248264	+	0.968692i	$0.579860\pi$
$692$	−1.22574e9	−0.140613
$693$	1.07256e9	0.122420
$694$	−1.41532e9	−0.160730
$695$	3.79511e9	0.428822
$696$	7.17837e8	0.0807037
$697$	−5.35460e9	−0.598980
$698$	5.35326e9	0.595833
$699$	−9.33587e8	−0.103391
$700$	6.01373e9	0.662676
$701$	8.91114e9	0.977058	0.488529	−	0.872548i	$-0.337534\pi$
$701$	8.91114e9	0.977058	0.488529	+	0.872548i	$0.337534\pi$
$702$	−2.31430e9	−0.252487
$703$	5.35721e9	0.581560
$704$	−2.40189e8	−0.0259447
$705$	2.21554e9	0.238132
$706$	4.47910e9	0.479043
$707$	−1.86381e10	−1.98351
$708$	−3.54895e8	−0.0375823
$709$	−1.01390e10	−1.06839	−0.534197	−	0.845360i	$-0.679386\pi$
$709$	−1.01390e10	−1.06839	−0.534197	+	0.845360i	$0.679386\pi$
$710$	−3.57821e8	−0.0375198
$711$	−1.94350e9	−0.202788
$712$	−6.01373e8	−0.0624401
$713$	−9.03506e9	−0.933507
$714$	−9.59082e9	−0.986080
$715$	−1.88566e9	−0.192927
$716$	−8.51304e9	−0.866741
$717$	−1.02117e10	−1.03462
$718$	2.48084e9	0.250128
$719$	−1.22723e10	−1.23133	−0.615664	−	0.788008i	$-0.711112\pi$
$719$	−1.22723e10	−1.23133	−0.615664	+	0.788008i	$0.711112\pi$
$720$	−4.18119e8	−0.0417480
$721$	−6.86786e9	−0.682414
$722$	2.13417e9	0.211032
$723$	7.22158e9	0.710637
$724$	−9.37542e9	−0.918133
$725$	−3.03863e9	−0.296138
$726$	−4.02789e9	−0.390661
$727$	−1.43966e10	−1.38960	−0.694799	−	0.719204i	$-0.744507\pi$
$727$	−1.43966e10	−1.38960	−0.694799	+	0.719204i	$0.744507\pi$
$728$	−1.20833e10	−1.16072
$729$	3.87420e8	0.0370370
$730$	3.91920e9	0.372878
$731$	1.20684e10	1.14271
$732$	3.98147e9	0.375193
$733$	−8.02758e9	−0.752872	−0.376436	−	0.926443i	$-0.622850\pi$
$733$	−8.02758e9	−0.752872	−0.376436	+	0.926443i	$0.622850\pi$
$734$	2.06837e8	0.0193060
$735$	6.63483e9	0.616346
$736$	−2.50364e9	−0.231473
$737$	−1.84661e9	−0.169918
$738$	1.12933e9	0.103425
$739$	1.79415e10	1.63532	0.817660	−	0.575702i	$-0.195271\pi$
$739$	1.79415e10	1.63532	0.817660	+	0.575702i	$0.195271\pi$
$740$	−1.91718e9	−0.173921
$741$	9.93735e9	0.897236
$742$	−6.24401e9	−0.561112
$743$	1.49566e9	0.133774	0.0668870	−	0.997761i	$-0.478693\pi$
$743$	1.49566e9	0.133774	0.0668870	+	0.997761i	$0.478693\pi$
$744$	−1.63472e9	−0.145525
$745$	−7.36965e9	−0.652980
$746$	2.25406e9	0.198783
$747$	−5.51028e8	−0.0483673
$748$	−1.62150e9	−0.141664
$749$	−2.05391e10	−1.78606
$750$	4.13287e9	0.357715
$751$	−8.15641e9	−0.702683	−0.351341	−	0.936247i	$-0.614274\pi$
$751$	−8.15641e9	−0.702683	−0.351341	+	0.936247i	$0.614274\pi$
$752$	2.40029e9	0.205827
$753$	−1.11632e10	−0.952813
$754$	6.10549e9	0.518705
$755$	6.23116e9	0.526932
$756$	2.02279e9	0.170265
$757$	9.61977e9	0.805989	0.402994	−	0.915202i	$-0.367969\pi$
$757$	9.61977e9	0.805989	0.402994	+	0.915202i	$0.367969\pi$
$758$	−6.79617e9	−0.566790
$759$	1.89016e9	0.156911
$760$	1.79536e9	0.148355
$761$	1.27660e8	0.0105005	0.00525024	−	0.999986i	$-0.498329\pi$
$761$	1.27660e8	0.0105005	0.00525024	+	0.999986i	$0.498329\pi$
$762$	2.69136e9	0.220358
$763$	−3.07307e9	−0.250459
$764$	−7.65067e9	−0.620687
$765$	−2.82269e9	−0.227954
$766$	−1.90030e9	−0.152764
$767$	−3.01852e9	−0.241552
$768$	−4.52985e8	−0.0360844
$769$	−2.12417e10	−1.68441	−0.842204	−	0.539159i	$-0.818742\pi$
$769$	−2.12417e10	−1.68441	−0.842204	+	0.539159i	$0.818742\pi$
$770$	1.64814e9	0.130100
$771$	−2.08925e9	−0.164172
$772$	6.70293e9	0.524329
$773$	1.94186e10	1.51213	0.756065	−	0.654496i	$-0.227119\pi$
$773$	1.94186e10	1.51213	0.756065	+	0.654496i	$0.227119\pi$
$774$	−2.54532e9	−0.197310
$775$	6.91981e9	0.533996
$776$	−8.83612e9	−0.678806
$777$	9.27498e9	0.709315
$778$	1.48463e10	1.13029
$779$	−4.84923e9	−0.367529
$780$	−3.55627e9	−0.268326
$781$	2.92669e8	0.0219835
$782$	−1.69019e10	−1.26390
$783$	−1.02208e9	−0.0760882
$784$	7.18810e9	0.532731
$785$	−9.52418e9	−0.702722
$786$	−7.11938e9	−0.522953
$787$	1.04836e10	0.766655	0.383327	−	0.923613i	$-0.374778\pi$
$787$	1.04836e10	0.766655	0.383327	+	0.923613i	$0.374778\pi$
$788$	3.13037e9	0.227905
$789$	−6.31820e8	−0.0457956
$790$	−2.98648e9	−0.215509
$791$	2.93999e10	2.11217
$792$	3.41988e8	0.0244609
$793$	3.38639e10	2.41147
$794$	1.09144e10	0.773796
$795$	−1.83768e9	−0.129714
$796$	−8.34648e9	−0.586554
$797$	−1.99022e10	−1.39251	−0.696253	−	0.717797i	$-0.745151\pi$
$797$	−1.99022e10	−1.39251	−0.696253	+	0.717797i	$0.745151\pi$
$798$	−8.68564e9	−0.605050
$799$	1.62042e10	1.12386
$800$	1.91750e9	0.132410
$801$	8.56251e8	0.0588691
$802$	1.62383e10	1.11155
$803$	−3.20559e9	−0.218476
$804$	−3.48262e9	−0.236325
$805$	1.71796e10	1.16072
$806$	−1.39039e10	−0.935329
$807$	2.90397e9	0.194507
$808$	−5.94282e9	−0.396327
$809$	2.23323e10	1.48291	0.741454	−	0.671004i	$-0.234137\pi$
$809$	2.23323e10	1.48291	0.741454	+	0.671004i	$0.234137\pi$
$810$	5.95329e8	0.0393604
$811$	−7.25165e9	−0.477379	−0.238690	−	0.971096i	$-0.576718\pi$
$811$	−7.25165e9	−0.477379	−0.238690	+	0.971096i	$0.576718\pi$
$812$	−5.33644e9	−0.349788
$813$	1.20592e10	0.787051
$814$	1.56810e9	0.101903
$815$	7.77576e9	0.503143
$816$	−3.05806e9	−0.197029
$817$	1.09293e10	0.701160
$818$	−9.05313e9	−0.578312
$819$	1.72046e10	1.09434
$820$	1.73539e9	0.109913
$821$	1.53841e10	0.970220	0.485110	−	0.874453i	$-0.338780\pi$
$821$	1.53841e10	0.970220	0.485110	+	0.874453i	$0.338780\pi$
$822$	−1.10082e10	−0.691299
$823$	−1.07821e10	−0.674223	−0.337112	−	0.941465i	$-0.609450\pi$
$823$	−1.07821e10	−0.674223	−0.337112	+	0.941465i	$0.609450\pi$
$824$	−2.18984e9	−0.136354
$825$	−1.44764e9	−0.0897580
$826$	2.63831e9	0.162890
$827$	−2.21587e10	−1.36231	−0.681153	−	0.732141i	$-0.738521\pi$
$827$	−2.21587e10	−1.36231	−0.681153	+	0.732141i	$0.738521\pi$
$828$	3.56475e9	0.218234
$829$	2.59964e10	1.58479	0.792396	−	0.610008i	$-0.208834\pi$
$829$	2.59964e10	1.58479	0.792396	+	0.610008i	$0.208834\pi$
$830$	−8.46737e8	−0.0514015
$831$	−7.40704e9	−0.447756
$832$	−3.85281e9	−0.231924
$833$	4.85262e10	2.90883
$834$	−5.85417e9	−0.349450
$835$	1.17082e9	0.0695968
$836$	−1.46846e9	−0.0869240
$837$	2.32756e9	0.137202
$838$	−1.48483e10	−0.871611
$839$	3.25455e10	1.90250	0.951249	−	0.308424i	$-0.0998015\pi$
$839$	3.25455e10	1.90250	0.951249	+	0.308424i	$0.0998015\pi$
$840$	3.10832e9	0.180946
$841$	−1.45535e10	−0.843686
$842$	−1.84576e10	−1.06557
$843$	−1.06411e10	−0.611775
$844$	2.95249e9	0.169040
$845$	−2.14609e10	−1.22363
$846$	−3.41761e9	−0.194055
$847$	2.99436e10	1.69321
$848$	−1.99092e9	−0.112116
$849$	−7.30086e9	−0.409446
$850$	1.29449e10	0.722988
$851$	1.63453e10	0.909156
$852$	5.51959e8	0.0305751
$853$	−1.88337e10	−1.03900	−0.519498	−	0.854472i	$-0.673881\pi$
$853$	−1.88337e10	−1.03900	−0.519498	+	0.854472i	$0.673881\pi$
$854$	−2.95984e10	−1.62617
$855$	−2.55628e9	−0.139871
$856$	−6.54897e9	−0.356874
$857$	6.63057e8	0.0359847	0.0179923	−	0.999838i	$-0.494273\pi$
$857$	6.63057e8	0.0359847	0.0179923	+	0.999838i	$0.494273\pi$
$858$	2.90874e9	0.157217
$859$	−1.92938e8	−0.0103859	−0.00519293	−	0.999987i	$-0.501653\pi$
$859$	−1.92938e8	−0.0103859	−0.00519293	+	0.999987i	$0.501653\pi$
$860$	−3.91127e9	−0.209688
$861$	−8.39552e9	−0.448267
$862$	−5.95266e9	−0.316545
$863$	−1.46927e10	−0.778149	−0.389074	−	0.921206i	$-0.627205\pi$
$863$	−1.46927e10	−0.778149	−0.389074	+	0.921206i	$0.627205\pi$
$864$	6.44973e8	0.0340207
$865$	2.68182e9	0.140888
$866$	7.80741e9	0.408502
$867$	−9.56558e9	−0.498476
$868$	1.21526e10	0.630738
$869$	2.44270e9	0.126270
$870$	−1.57057e9	−0.0808614
$871$	−2.96210e10	−1.51893
$872$	−9.79860e8	−0.0500445
$873$	1.25811e10	0.639984
$874$	−1.53067e10	−0.775516
$875$	−3.07240e10	−1.55042
$876$	−6.04559e9	−0.303861
$877$	9.83360e9	0.492282	0.246141	−	0.969234i	$-0.420837\pi$
$877$	9.83360e9	0.492282	0.246141	+	0.969234i	$0.420837\pi$
$878$	3.93142e9	0.196028
$879$	−2.68718e9	−0.133455
$880$	5.25516e8	0.0259954
$881$	3.77019e8	0.0185758	0.00928789	−	0.999957i	$-0.497044\pi$
$881$	3.77019e8	0.0185758	0.00928789	+	0.999957i	$0.497044\pi$
$882$	−1.02346e10	−0.502263
$883$	−2.03172e10	−0.993119	−0.496559	−	0.868003i	$-0.665403\pi$
$883$	−2.03172e10	−0.993119	−0.496559	+	0.868003i	$0.665403\pi$
$884$	−2.60100e10	−1.26636
$885$	7.76483e8	0.0376557
$886$	1.42838e10	0.689964
$887$	−1.70213e10	−0.818957	−0.409479	−	0.912320i	$-0.634289\pi$
$887$	−1.70213e10	−0.818957	−0.409479	+	0.912320i	$0.634289\pi$
$888$	2.95736e9	0.141729
$889$	−2.00077e10	−0.955081
$890$	1.31576e9	0.0625621
$891$	−4.86932e8	−0.0230620
$892$	−1.84218e10	−0.869073
$893$	1.46748e10	0.689593
$894$	1.13681e10	0.532117
$895$	1.86259e10	0.868433
$896$	3.36751e9	0.156398
$897$	3.03196e10	1.40265
$898$	−2.63486e10	−1.21420
$899$	−6.14047e9	−0.281866
$900$	−2.73019e9	−0.124837
$901$	−1.34405e10	−0.612181
$902$	−1.41941e9	−0.0643999
$903$	1.89221e10	0.855188
$904$	9.37426e9	0.422034
$905$	2.05127e10	0.919927
$906$	−9.61192e9	−0.429399
$907$	−3.80757e9	−0.169443	−0.0847213	−	0.996405i	$-0.527000\pi$
$907$	−3.80757e9	−0.169443	−0.0847213	+	0.996405i	$0.527000\pi$
$908$	−1.70632e10	−0.756414
$909$	8.46156e9	0.373660
$910$	2.64375e10	1.16299
$911$	3.55939e10	1.55977	0.779886	−	0.625922i	$-0.215277\pi$
$911$	3.55939e10	1.55977	0.779886	+	0.625922i	$0.215277\pi$
$912$	−2.76944e9	−0.120896
$913$	6.92564e8	0.0301170
$914$	1.45532e10	0.630443
$915$	−8.71115e9	−0.375926
$916$	1.62662e10	0.699279
$917$	5.29258e10	2.26660
$918$	4.35416e9	0.185761
$919$	−8.14861e9	−0.346321	−0.173161	−	0.984894i	$-0.555398\pi$
$919$	−8.14861e9	−0.346321	−0.173161	+	0.984894i	$0.555398\pi$
$920$	5.47778e9	0.231925
$921$	−2.14540e10	−0.904899
$922$	4.71681e9	0.198194
$923$	4.69463e9	0.196515
$924$	−2.54236e9	−0.106019
$925$	−1.25186e10	−0.520066
$926$	7.80674e9	0.323096
$927$	3.11796e9	0.128556
$928$	−1.70154e9	−0.0698915
$929$	−8.95877e9	−0.366601	−0.183300	−	0.983057i	$-0.558678\pi$
$929$	−8.95877e9	−0.366601	−0.183300	+	0.983057i	$0.558678\pi$
$930$	3.57664e9	0.145809
$931$	4.39463e10	1.78484
$932$	2.21295e9	0.0895396
$933$	1.89700e10	0.764682
$934$	−2.21430e10	−0.889248
$935$	3.54771e9	0.141941
$936$	5.48574e9	0.218660
$937$	−9.46385e9	−0.375820	−0.187910	−	0.982186i	$-0.560171\pi$
$937$	−9.46385e9	−0.375820	−0.187910	+	0.982186i	$0.560171\pi$
$938$	2.58900e10	1.02429
$939$	−1.38436e10	−0.545655
$940$	−5.25166e9	−0.206229
$941$	2.26318e8	0.00885434	0.00442717	−	0.999990i	$-0.498591\pi$
$941$	2.26318e8	0.00885434	0.00442717	+	0.999990i	$0.498591\pi$
$942$	1.46916e10	0.572652
$943$	−1.47954e10	−0.574560
$944$	8.41232e8	0.0325472
$945$	−4.42571e9	−0.170597
$946$	3.19911e9	0.122860
$947$	1.48480e9	0.0568122	0.0284061	−	0.999596i	$-0.490957\pi$
$947$	1.48480e9	0.0568122	0.0284061	+	0.999596i	$0.490957\pi$
$948$	4.60682e9	0.175619
$949$	−5.14201e10	−1.95300
$950$	1.17231e10	0.443620
$951$	−1.93115e10	−0.728088
$952$	2.27338e10	0.853970
$953$	1.72190e10	0.644441	0.322220	−	0.946665i	$-0.395571\pi$
$953$	1.72190e10	0.644441	0.322220	+	0.946665i	$0.395571\pi$
$954$	2.83473e9	0.105704
$955$	1.67391e10	0.621900
$956$	2.42055e10	0.896005
$957$	1.28460e9	0.0473781
$958$	1.48925e10	0.547253
$959$	8.18357e10	2.99625
$960$	9.91097e8	0.0361549
$961$	−1.35290e10	−0.491740
$962$	2.51535e10	0.910930
$963$	9.32461e9	0.336464
$964$	−1.71178e10	−0.615430
$965$	−1.46655e10	−0.525353
$966$	−2.65006e10	−0.945878
$967$	2.35774e10	0.838499	0.419250	−	0.907871i	$-0.362293\pi$
$967$	2.35774e10	0.838499	0.419250	+	0.907871i	$0.362293\pi$
$968$	9.54760e9	0.338322
$969$	−1.86963e10	−0.660118
$970$	1.93328e10	0.680132
$971$	1.15655e10	0.405411	0.202706	−	0.979240i	$-0.435027\pi$
$971$	1.15655e10	0.405411	0.202706	+	0.979240i	$0.435027\pi$
$972$	−9.18330e8	−0.0320750
$973$	4.35202e10	1.51459
$974$	−2.20527e10	−0.764727
$975$	−2.32213e10	−0.802362
$976$	−9.43755e9	−0.324926
$977$	3.58570e10	1.23011	0.615054	−	0.788485i	$-0.289134\pi$
$977$	3.58570e10	1.23011	0.615054	+	0.788485i	$0.289134\pi$
$978$	−1.19946e10	−0.410014
$979$	−1.07619e9	−0.0366562
$980$	−1.57270e10	−0.533771
$981$	1.39515e9	0.0471824
$982$	3.51398e10	1.18416
$983$	−3.69123e10	−1.23946	−0.619732	−	0.784814i	$-0.712759\pi$
$983$	−3.69123e10	−1.23946	−0.619732	+	0.784814i	$0.712759\pi$
$984$	−2.67694e9	−0.0895685
$985$	−6.84902e9	−0.228350
$986$	−1.14870e10	−0.381624
$987$	2.54067e10	0.841080
$988$	−2.35552e10	−0.777029
$989$	3.33463e10	1.09613
$990$	−7.48244e8	−0.0245087
$991$	3.17001e10	1.03467	0.517336	−	0.855782i	$-0.326924\pi$
$991$	3.17001e10	1.03467	0.517336	+	0.855782i	$0.326924\pi$
$992$	3.87489e9	0.126028
$993$	−4.00444e9	−0.129783
$994$	−4.10329e9	−0.132520
$995$	1.82615e10	0.587699
$996$	1.30614e9	0.0418873
$997$	−3.06165e10	−0.978413	−0.489206	−	0.872168i	$-0.662714\pi$
$997$	−3.06165e10	−0.978413	−0.489206	+	0.872168i	$0.662714\pi$
$998$	1.30008e10	0.414012
$999$	−4.21077e9	−0.133623

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	354.8.a.e.1.4	✓	9

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
354.8.a.e.1.4	✓	9	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 354 = 2 \cdot 3 \cdot 59 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	354.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -140.027 q^{5} +216.000 q^{6} -1605.75 q^{7} -512.000 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -27.0000 q^{3} +64.0000 q^{4} -140.027 q^{5} +216.000 q^{6} -1605.75 q^{7} -512.000 q^{8} +729.000 q^{9} +1120.22 q^{10} -916.249 q^{11} -1728.00 q^{12} -14697.3 q^{13} +12846.0 q^{14} +3780.73 q^{15} +4096.00 q^{16} +27651.8 q^{17} -5832.00 q^{18} +25042.0 q^{19} -8961.74 q^{20} +43355.4 q^{21} +7329.99 q^{22} +76405.0 q^{23} +13824.0 q^{24} -58517.4 q^{25} +117579. q^{26} -19683.0 q^{27} -102768. q^{28} +51926.9 q^{29} -30245.9 q^{30} -118252. q^{31} -32768.0 q^{32} +24738.7 q^{33} -221214. q^{34} +224849. q^{35} +46656.0 q^{36} +213929. q^{37} -200336. q^{38} +396828. q^{39} +71693.9 q^{40} -193644. q^{41} -346843. q^{42} +436441. q^{43} -58639.9 q^{44} -102080. q^{45} -611240. q^{46} +586009. q^{47} -110592. q^{48} +1.75491e6 q^{49} +468139. q^{50} -746597. q^{51} -940628. q^{52} -486065. q^{53} +157464. q^{54} +128300. q^{55} +822147. q^{56} -676133. q^{57} -415415. q^{58} +205379. q^{59} +241967. q^{60} -2.30409e6 q^{61} +946017. q^{62} -1.17060e6 q^{63} +262144. q^{64} +2.05802e6 q^{65} -197910. q^{66} +2.01540e6 q^{67} +1.76971e6 q^{68} -2.06294e6 q^{69} -1.79879e6 q^{70} -319421. q^{71} -373248. q^{72} +3.49861e6 q^{73} -1.71143e6 q^{74} +1.57997e6 q^{75} +1.60269e6 q^{76} +1.47127e6 q^{77} -3.17462e6 q^{78} -2.66598e6 q^{79} -573551. q^{80} +531441. q^{81} +1.54915e6 q^{82} -755869. q^{83} +2.77474e6 q^{84} -3.87200e6 q^{85} -3.49153e6 q^{86} -1.40203e6 q^{87} +469119. q^{88} +1.17456e6 q^{89} +816639. q^{90} +2.36003e7 q^{91} +4.88992e6 q^{92} +3.19281e6 q^{93} -4.68807e6 q^{94} -3.50656e6 q^{95} +884736. q^{96} +1.72581e7 q^{97} -1.40392e7 q^{98} -667945. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9}+O(q^{10}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9	\( 9 q - 72 q^{2} - 243 q^{3} + 576 q^{4} - 230 q^{5} + 1944 q^{6} - 340 q^{7} - 4608 q^{8} + 6561 q^{9} + 1840 q^{10} - 5472 q^{11} - 15552 q^{12} + 3144 q^{13} + 2720 q^{14} + 6210 q^{15} + 36864 q^{16} - 3662 q^{17} - 52488 q^{18} + 692 q^{19} - 14720 q^{20} + 9180 q^{21} + 43776 q^{22} - 92046 q^{23} + 124416 q^{24} + 74731 q^{25} - 25152 q^{26} - 177147 q^{27} - 21760 q^{28} - 41060 q^{29} - 49680 q^{30} - 324504 q^{31} - 294912 q^{32} + 147744 q^{33} + 29296 q^{34} - 415602 q^{35} + 419904 q^{36} + 338612 q^{37} - 5536 q^{38} - 84888 q^{39} + 117760 q^{40} - 104312 q^{41} - 73440 q^{42} + 1000602 q^{43} - 350208 q^{44} - 167670 q^{45} + 736368 q^{46} - 365148 q^{47} - 995328 q^{48} + 2307505 q^{49} - 597848 q^{50} + 98874 q^{51} + 201216 q^{52} + 2017498 q^{53} + 1417176 q^{54} + 1120520 q^{55} + 174080 q^{56} - 18684 q^{57} + 328480 q^{58} + 1848411 q^{59} + 397440 q^{60} + 5102340 q^{61} + 2596032 q^{62} - 247860 q^{63} + 2359296 q^{64} + 7512810 q^{65} - 1181952 q^{66} + 10920464 q^{67} - 234368 q^{68} + 2485242 q^{69} + 3324816 q^{70} + 3607024 q^{71} - 3359232 q^{72} + 12949418 q^{73} - 2708896 q^{74} - 2017737 q^{75} + 44288 q^{76} + 7127994 q^{77} + 679104 q^{78} + 7489472 q^{79} - 942080 q^{80} + 4782969 q^{81} + 834496 q^{82} + 2760502 q^{83} + 587520 q^{84} + 11815354 q^{85} - 8004816 q^{86} + 1108620 q^{87} + 2801664 q^{88} - 9948196 q^{89} + 1341360 q^{90} + 19400656 q^{91} - 5890944 q^{92} + 8761608 q^{93} + 2921184 q^{94} + 24045208 q^{95} + 7962624 q^{96} + 38157642 q^{97} - 18460040 q^{98} - 3989088 q^{99}+O(q^{100}) \) 9 * q - 72 * q^2 - 243 * q^3 + 576 * q^4 - 230 * q^5 + 1944 * q^6 - 340 * q^7 - 4608 * q^8 + 6561 * q^9 + 1840 * q^10 - 5472 * q^11 - 15552 * q^12 + 3144 * q^13 + 2720 * q^14 + 6210 * q^15 + 36864 * q^16 - 3662 * q^17 - 52488 * q^18 + 692 * q^19 - 14720 * q^20 + 9180 * q^21 + 43776 * q^22 - 92046 * q^23 + 124416 * q^24 + 74731 * q^25 - 25152 * q^26 - 177147 * q^27 - 21760 * q^28 - 41060 * q^29 - 49680 * q^30 - 324504 * q^31 - 294912 * q^32 + 147744 * q^33 + 29296 * q^34 - 415602 * q^35 + 419904 * q^36 + 338612 * q^37 - 5536 * q^38 - 84888 * q^39 + 117760 * q^40 - 104312 * q^41 - 73440 * q^42 + 1000602 * q^43 - 350208 * q^44 - 167670 * q^45 + 736368 * q^46 - 365148 * q^47 - 995328 * q^48 + 2307505 * q^49 - 597848 * q^50 + 98874 * q^51 + 201216 * q^52 + 2017498 * q^53 + 1417176 * q^54 + 1120520 * q^55 + 174080 * q^56 - 18684 * q^57 + 328480 * q^58 + 1848411 * q^59 + 397440 * q^60 + 5102340 * q^61 + 2596032 * q^62 - 247860 * q^63 + 2359296 * q^64 + 7512810 * q^65 - 1181952 * q^66 + 10920464 * q^67 - 234368 * q^68 + 2485242 * q^69 + 3324816 * q^70 + 3607024 * q^71 - 3359232 * q^72 + 12949418 * q^73 - 2708896 * q^74 - 2017737 * q^75 + 44288 * q^76 + 7127994 * q^77 + 679104 * q^78 + 7489472 * q^79 - 942080 * q^80 + 4782969 * q^81 + 834496 * q^82 + 2760502 * q^83 + 587520 * q^84 + 11815354 * q^85 - 8004816 * q^86 + 1108620 * q^87 + 2801664 * q^88 - 9948196 * q^89 + 1341360 * q^90 + 19400656 * q^91 - 5890944 * q^92 + 8761608 * q^93 + 2921184 * q^94 + 24045208 * q^95 + 7962624 * q^96 + 38157642 * q^97 - 18460040 * q^98 - 3989088 * q^99

Introduction

L-functions

Modular forms

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