LMFDB - Embedded newform 33.8.a.e.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [33,8,Mod(1,33)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(33, 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("33.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 33 = 3 \cdot 11 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	33.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:	$10.3087058410$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\mathbb{Q}[x]/(x^{4} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} - 510x^{2} - 1544x + 28880 $ x^4 - x^3 - 510x^2 - 1544x + 28880
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$-11.0316$ of defining polynomial
Character	$\chi$	$=$	33.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+15.0316 q^{2} +27.0000 q^{3} +97.9505 q^{4} +367.278 q^{5} +405.855 q^{6} -91.9512 q^{7} -451.694 q^{8} +729.000 q^{9} +O(q^{10})$	\(q+15.0316 q^{2} +27.0000 q^{3} +97.9505 q^{4} +367.278 q^{5} +405.855 q^{6} -91.9512 q^{7} -451.694 q^{8} +729.000 q^{9} +5520.80 q^{10} +1331.00 q^{11} +2644.66 q^{12} +5118.56 q^{13} -1382.18 q^{14} +9916.51 q^{15} -19327.4 q^{16} -8838.56 q^{17} +10958.1 q^{18} +13319.2 q^{19} +35975.1 q^{20} -2482.68 q^{21} +20007.1 q^{22} -70727.0 q^{23} -12195.7 q^{24} +56768.3 q^{25} +76940.4 q^{26} +19683.0 q^{27} -9006.66 q^{28} -123137. q^{29} +149062. q^{30} +116235. q^{31} -232705. q^{32} +35937.0 q^{33} -132858. q^{34} -33771.7 q^{35} +71405.9 q^{36} -445173. q^{37} +200209. q^{38} +138201. q^{39} -165897. q^{40} -586341. q^{41} -37318.8 q^{42} -470214. q^{43} +130372. q^{44} +267746. q^{45} -1.06314e6 q^{46} +818322. q^{47} -521839. q^{48} -815088. q^{49} +853322. q^{50} -238641. q^{51} +501366. q^{52} +2.08896e6 q^{53} +295868. q^{54} +488847. q^{55} +41533.8 q^{56} +359617. q^{57} -1.85096e6 q^{58} +1.96982e6 q^{59} +971327. q^{60} +1.31411e6 q^{61} +1.74721e6 q^{62} -67032.4 q^{63} -1.02404e6 q^{64} +1.87994e6 q^{65} +540192. q^{66} +2.43094e6 q^{67} -865741. q^{68} -1.90963e6 q^{69} -507644. q^{70} -2.63282e6 q^{71} -329285. q^{72} -576963. q^{73} -6.69169e6 q^{74} +1.53275e6 q^{75} +1.30462e6 q^{76} -122387. q^{77} +2.07739e6 q^{78} -1.00612e6 q^{79} -7.09852e6 q^{80} +531441. q^{81} -8.81367e6 q^{82} +8.42647e6 q^{83} -243180. q^{84} -3.24621e6 q^{85} -7.06809e6 q^{86} -3.32470e6 q^{87} -601204. q^{88} +3.80212e6 q^{89} +4.02466e6 q^{90} -470658. q^{91} -6.92775e6 q^{92} +3.13835e6 q^{93} +1.23007e7 q^{94} +4.89184e6 q^{95} -6.28305e6 q^{96} +1.53023e7 q^{97} -1.22521e7 q^{98} +970299. q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 15 q^{2} + 108 q^{3} + 565 q^{4} + 306 q^{5} + 405 q^{6} + 890 q^{7} + 2457 q^{8} + 2916 q^{9}+O(q^{10}) $ 4 * q + 15 * q^2 + 108 * q^3 + 565 * q^4 + 306 * q^5 + 405 * q^6 + 890 * q^7 + 2457 * q^8 + 2916 * q^9	\( 4 q + 15 q^{2} + 108 q^{3} + 565 q^{4} + 306 q^{5} + 405 q^{6} + 890 q^{7} + 2457 q^{8} + 2916 q^{9} - 8946 q^{10} + 5324 q^{11} + 15255 q^{12} - 1822 q^{13} + 35340 q^{14} + 8262 q^{15} + 65041 q^{16} + 32856 q^{17} + 10935 q^{18} - 12784 q^{19} - 4002 q^{20} + 24030 q^{21} + 19965 q^{22} + 114858 q^{23} + 66339 q^{24} + 72856 q^{25} - 221466 q^{26} + 78732 q^{27} + 10112 q^{28} - 104952 q^{29} - 241542 q^{30} - 24976 q^{31} + 337761 q^{32} + 143748 q^{33} - 741690 q^{34} - 722856 q^{35} + 411885 q^{36} - 498856 q^{37} - 897156 q^{38} - 49194 q^{39} - 2676930 q^{40} + 734556 q^{41} + 954180 q^{42} - 201916 q^{43} + 752015 q^{44} + 223074 q^{45} - 3068508 q^{46} + 1995894 q^{47} + 1756107 q^{48} - 771024 q^{49} + 1632129 q^{50} + 887112 q^{51} - 4412266 q^{52} + 929970 q^{53} + 295245 q^{54} + 407286 q^{55} + 7224888 q^{56} - 345168 q^{57} + 2864322 q^{58} + 1353156 q^{59} - 108054 q^{60} + 3998774 q^{61} - 3783264 q^{62} + 648810 q^{63} + 1480129 q^{64} + 6612108 q^{65} + 539055 q^{66} + 1722008 q^{67} + 1596906 q^{68} + 3101166 q^{69} - 2751024 q^{70} + 5571858 q^{71} + 1791153 q^{72} + 5600528 q^{73} - 10907838 q^{74} + 1967112 q^{75} - 19634884 q^{76} + 1184590 q^{77} - 5979582 q^{78} - 7710226 q^{79} - 24073794 q^{80} + 2125764 q^{81} - 11230842 q^{82} + 3431856 q^{83} + 273024 q^{84} + 5909484 q^{85} - 25687140 q^{86} - 2833704 q^{87} + 3270267 q^{88} + 4611528 q^{89} - 6521634 q^{90} - 9032696 q^{91} + 13608576 q^{92} - 674352 q^{93} - 3497436 q^{94} + 21828000 q^{95} + 9119547 q^{96} + 1401692 q^{97} - 7230081 q^{98} + 3881196 q^{99}+O(q^{100}) \) 4 * q + 15 * q^2 + 108 * q^3 + 565 * q^4 + 306 * q^5 + 405 * q^6 + 890 * q^7 + 2457 * q^8 + 2916 * q^9 - 8946 * q^10 + 5324 * q^11 + 15255 * q^12 - 1822 * q^13 + 35340 * q^14 + 8262 * q^15 + 65041 * q^16 + 32856 * q^17 + 10935 * q^18 - 12784 * q^19 - 4002 * q^20 + 24030 * q^21 + 19965 * q^22 + 114858 * q^23 + 66339 * q^24 + 72856 * q^25 - 221466 * q^26 + 78732 * q^27 + 10112 * q^28 - 104952 * q^29 - 241542 * q^30 - 24976 * q^31 + 337761 * q^32 + 143748 * q^33 - 741690 * q^34 - 722856 * q^35 + 411885 * q^36 - 498856 * q^37 - 897156 * q^38 - 49194 * q^39 - 2676930 * q^40 + 734556 * q^41 + 954180 * q^42 - 201916 * q^43 + 752015 * q^44 + 223074 * q^45 - 3068508 * q^46 + 1995894 * q^47 + 1756107 * q^48 - 771024 * q^49 + 1632129 * q^50 + 887112 * q^51 - 4412266 * q^52 + 929970 * q^53 + 295245 * q^54 + 407286 * q^55 + 7224888 * q^56 - 345168 * q^57 + 2864322 * q^58 + 1353156 * q^59 - 108054 * q^60 + 3998774 * q^61 - 3783264 * q^62 + 648810 * q^63 + 1480129 * q^64 + 6612108 * q^65 + 539055 * q^66 + 1722008 * q^67 + 1596906 * q^68 + 3101166 * q^69 - 2751024 * q^70 + 5571858 * q^71 + 1791153 * q^72 + 5600528 * q^73 - 10907838 * q^74 + 1967112 * q^75 - 19634884 * q^76 + 1184590 * q^77 - 5979582 * q^78 - 7710226 * q^79 - 24073794 * q^80 + 2125764 * q^81 - 11230842 * q^82 + 3431856 * q^83 + 273024 * q^84 + 5909484 * q^85 - 25687140 * q^86 - 2833704 * q^87 + 3270267 * q^88 + 4611528 * q^89 - 6521634 * q^90 - 9032696 * q^91 + 13608576 * q^92 - 674352 * q^93 - 3497436 * q^94 + 21828000 * q^95 + 9119547 * q^96 + 1401692 * q^97 - 7230081 * q^98 + 3881196 * 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 $

$2$	15.0316	1.32862	0.664311	−	0.747456i	$-0.268725\pi$
$2$	15.0316	1.32862	0.664311	+	0.747456i	$0.268725\pi$
$3$	27.0000	0.577350
$3$	27.0000	0.577350
$4$	97.9505	0.765238
$5$	367.278	1.31401	0.657007	−	0.753884i	$-0.271822\pi$
$5$	367.278	1.31401	0.657007	+	0.753884i	$0.271822\pi$
$6$	405.855	0.767081
$7$	−91.9512	−0.101324	−0.0506622	−	0.998716i	$-0.516133\pi$
$7$	−91.9512	−0.101324	−0.0506622	+	0.998716i	$0.516133\pi$
$8$	−451.694	−0.311910
$9$	729.000	0.333333
$10$	5520.80	1.74583
$11$	1331.00	0.301511
$11$	1331.00	0.301511
$12$	2644.66	0.441811
$13$	5118.56	0.646169	0.323084	−	0.946370i	$-0.395280\pi$
$13$	5118.56	0.646169	0.323084	+	0.946370i	$0.395280\pi$
$14$	−1382.18	−0.134622
$15$	9916.51	0.758647
$16$	−19327.4	−1.17965
$17$	−8838.56	−0.436325	−0.218163	−	0.975912i	$-0.570006\pi$
$17$	−8838.56	−0.436325	−0.218163	+	0.975912i	$0.570006\pi$
$18$	10958.1	0.442874
$19$	13319.2	0.445491	0.222746	−	0.974877i	$-0.428498\pi$
$19$	13319.2	0.445491	0.222746	+	0.974877i	$0.428498\pi$
$20$	35975.1	1.00553
$21$	−2482.68	−0.0584997
$22$	20007.1	0.400595
$23$	−70727.0	−1.21210	−0.606049	−	0.795427i	$-0.707247\pi$
$23$	−70727.0	−1.21210	−0.606049	+	0.795427i	$0.707247\pi$
$24$	−12195.7	−0.180081
$25$	56768.3	0.726635
$26$	76940.4	0.858515
$27$	19683.0	0.192450
$28$	−9006.66	−0.0775373
$29$	−123137.	−0.937554	−0.468777	−	0.883317i	$-0.655305\pi$
$29$	−123137.	−0.937554	−0.468777	+	0.883317i	$0.655305\pi$
$30$	149062.	1.00796
$31$	116235.	0.700764	0.350382	−	0.936607i	$-0.386052\pi$
$31$	116235.	0.700764	0.350382	+	0.936607i	$0.386052\pi$
$32$	−232705.	−1.25540
$33$	35937.0	0.174078
$34$	−132858.	−0.579712
$35$	−33771.7	−0.133142
$36$	71405.9	0.255079
$37$	−445173.	−1.44485	−0.722426	−	0.691449i	$-0.756973\pi$
$37$	−445173.	−1.44485	−0.722426	+	0.691449i	$0.756973\pi$
$38$	200209.	0.591890
$39$	138201.	0.373066
$40$	−165897.	−0.409854
$41$	−586341.	−1.32864	−0.664319	−	0.747449i	$-0.731278\pi$
$41$	−586341.	−1.32864	−0.664319	+	0.747449i	$0.731278\pi$
$42$	−37318.8	−0.0777240
$43$	−470214.	−0.901895	−0.450947	−	0.892550i	$-0.648914\pi$
$43$	−470214.	−0.901895	−0.450947	+	0.892550i	$0.648914\pi$
$44$	130372.	0.230728
$45$	267746.	0.438005
$46$	−1.06314e6	−1.61042
$47$	818322.	1.14969	0.574846	−	0.818261i	$-0.305062\pi$
$47$	818322.	1.14969	0.574846	+	0.818261i	$0.305062\pi$
$48$	−521839.	−0.681070
$49$	−815088.	−0.989733
$50$	853322.	0.965423
$51$	−238641.	−0.251912
$52$	501366.	0.494473
$53$	2.08896e6	1.92737	0.963684	−	0.267046i	$-0.0860475\pi$
$53$	2.08896e6	1.92737	0.963684	+	0.267046i	$0.0860475\pi$
$54$	295868.	0.255694
$55$	488847.	0.396190
$56$	41533.8	0.0316041
$57$	359617.	0.257204
$58$	−1.85096e6	−1.24566
$59$	1.96982e6	1.24866	0.624331	−	0.781160i	$-0.285372\pi$
$59$	1.96982e6	1.24866	0.624331	+	0.781160i	$0.285372\pi$
$60$	971327.	0.580546
$61$	1.31411e6	0.741270	0.370635	−	0.928779i	$-0.379140\pi$
$61$	1.31411e6	0.741270	0.370635	+	0.928779i	$0.379140\pi$
$62$	1.74721e6	0.931051
$63$	−67032.4	−0.0337748
$64$	−1.02404e6	−0.488302
$65$	1.87994e6	0.849076
$66$	540192.	0.231284
$67$	2.43094e6	0.987445	0.493723	−	0.869619i	$-0.335636\pi$
$67$	2.43094e6	0.987445	0.493723	+	0.869619i	$0.335636\pi$
$68$	−865741.	−0.333893
$69$	−1.90963e6	−0.699806
$70$	−507644.	−0.176895
$71$	−2.63282e6	−0.873006	−0.436503	−	0.899703i	$-0.643783\pi$
$71$	−2.63282e6	−0.873006	−0.436503	+	0.899703i	$0.643783\pi$
$72$	−329285.	−0.103970
$73$	−576963.	−0.173587	−0.0867937	−	0.996226i	$-0.527662\pi$
$73$	−576963.	−0.173587	−0.0867937	+	0.996226i	$0.527662\pi$
$74$	−6.69169e6	−1.91966
$75$	1.53275e6	0.419523
$76$	1.30462e6	0.340907
$77$	−122387.	−0.0305505
$78$	2.07739e6	0.495664
$79$	−1.00612e6	−0.229590	−0.114795	−	0.993389i	$-0.536621\pi$
$79$	−1.00612e6	−0.229590	−0.114795	+	0.993389i	$0.536621\pi$
$80$	−7.09852e6	−1.55008
$81$	531441.	0.111111
$82$	−8.81367e6	−1.76526
$83$	8.42647e6	1.61760	0.808802	−	0.588081i	$-0.200116\pi$
$83$	8.42647e6	1.61760	0.808802	+	0.588081i	$0.200116\pi$
$84$	−243180.	−0.0447662
$85$	−3.24621e6	−0.573338
$86$	−7.06809e6	−1.19828
$87$	−3.32470e6	−0.541297
$88$	−601204.	−0.0940443
$89$	3.80212e6	0.571691	0.285845	−	0.958276i	$-0.407726\pi$
$89$	3.80212e6	0.571691	0.285845	+	0.958276i	$0.407726\pi$
$90$	4.02466e6	0.581943
$91$	−470658.	−0.0654727
$92$	−6.92775e6	−0.927544
$93$	3.13835e6	0.404586
$94$	1.23007e7	1.52751
$95$	4.89184e6	0.585382
$96$	−6.28305e6	−0.724804
$97$	1.53023e7	1.70238	0.851191	−	0.524856i	$-0.175881\pi$
$97$	1.53023e7	1.70238	0.851191	+	0.524856i	$0.175881\pi$
$98$	−1.22521e7	−1.31498
$99$	970299.	0.100504
$100$	5.56049e6	0.556049
$101$	1.30361e7	1.25899	0.629494	−	0.777005i	$-0.283262\pi$
$101$	1.30361e7	1.25899	0.629494	+	0.777005i	$0.283262\pi$
$102$	−3.58717e6	−0.334697
$103$	−4.86462e6	−0.438650	−0.219325	−	0.975652i	$-0.570386\pi$
$103$	−4.86462e6	−0.438650	−0.219325	+	0.975652i	$0.570386\pi$
$104$	−2.31202e6	−0.201546
$105$	−911835.	−0.0768694
$106$	3.14005e7	2.56074
$107$	−1.22653e7	−0.967909	−0.483954	−	0.875093i	$-0.660800\pi$
$107$	−1.22653e7	−0.967909	−0.483954	+	0.875093i	$0.660800\pi$
$108$	1.92796e6	0.147270
$109$	−1.54745e7	−1.14452	−0.572262	−	0.820071i	$-0.693934\pi$
$109$	−1.54745e7	−1.14452	−0.572262	+	0.820071i	$0.693934\pi$
$110$	7.34818e6	0.526387
$111$	−1.20197e7	−0.834185
$112$	1.77717e6	0.119527
$113$	−1.56100e7	−1.01772	−0.508861	−	0.860849i	$-0.669933\pi$
$113$	−1.56100e7	−1.01772	−0.508861	+	0.860849i	$0.669933\pi$
$114$	5.40564e6	0.341728
$115$	−2.59765e7	−1.59272
$116$	−1.20613e7	−0.717452
$117$	3.73143e6	0.215390
$118$	2.96097e7	1.65900
$119$	812716.	0.0442104
$120$	−4.47923e6	−0.236629
$121$	1.77156e6	0.0909091
$122$	1.97532e7	0.984868
$123$	−1.58312e7	−0.767090
$124$	1.13853e7	0.536251
$125$	−7.84384e6	−0.359206
$126$	−1.00761e6	−0.0448740
$127$	−873608.	−0.0378446	−0.0189223	−	0.999821i	$-0.506024\pi$
$127$	−873608.	−0.0378446	−0.0189223	+	0.999821i	$0.506024\pi$
$128$	1.43932e7	0.606629
$129$	−1.26958e7	−0.520709
$130$	2.82585e7	1.12810
$131$	3.74565e7	1.45572	0.727861	−	0.685725i	$-0.240515\pi$
$131$	3.74565e7	1.45572	0.727861	+	0.685725i	$0.240515\pi$
$132$	3.52005e6	0.133211
$133$	−1.22471e6	−0.0451391
$134$	3.65411e7	1.31194
$135$	7.22914e6	0.252882
$136$	3.99232e6	0.136094
$137$	3.94359e6	0.131030	0.0655149	−	0.997852i	$-0.479131\pi$
$137$	3.94359e6	0.131030	0.0655149	+	0.997852i	$0.479131\pi$
$138$	−2.87049e7	−0.929777
$139$	1.38786e6	0.0438321	0.0219161	−	0.999760i	$-0.493023\pi$
$139$	1.38786e6	0.0438321	0.0219161	+	0.999760i	$0.493023\pi$
$140$	−3.30795e6	−0.101885
$141$	2.20947e7	0.663776
$142$	−3.95756e7	−1.15989
$143$	6.81280e6	0.194827
$144$	−1.40896e7	−0.393216
$145$	−4.52256e7	−1.23196
$146$	−8.67271e6	−0.230632
$147$	−2.20074e7	−0.571423
$148$	−4.36050e7	−1.10566
$149$	−4.82972e7	−1.19611	−0.598053	−	0.801457i	$-0.704059\pi$
$149$	−4.82972e7	−1.19611	−0.598053	+	0.801457i	$0.704059\pi$
$150$	2.30397e7	0.557387
$151$	−5.21333e7	−1.23224	−0.616121	−	0.787652i	$-0.711297\pi$
$151$	−5.21333e7	−1.23224	−0.616121	+	0.787652i	$0.711297\pi$
$152$	−6.01618e6	−0.138953
$153$	−6.44331e6	−0.145442
$154$	−1.83968e6	−0.0405900
$155$	4.26907e7	0.920814
$156$	1.35369e7	0.285484
$157$	6.04356e7	1.24636	0.623181	−	0.782078i	$-0.285840\pi$
$157$	6.04356e7	1.24636	0.623181	+	0.782078i	$0.285840\pi$
$158$	−1.51236e7	−0.305039
$159$	5.64019e7	1.11277
$160$	−8.54676e7	−1.64961
$161$	6.50343e6	0.122815
$162$	7.98843e6	0.147625
$163$	1.19287e7	0.215743	0.107872	−	0.994165i	$-0.465596\pi$
$163$	1.19287e7	0.215743	0.107872	+	0.994165i	$0.465596\pi$
$164$	−5.74324e7	−1.01672
$165$	1.31989e7	0.228741
$166$	1.26664e8	2.14919
$167$	−5.74301e7	−0.954183	−0.477091	−	0.878854i	$-0.658309\pi$
$167$	−5.74301e7	−0.954183	−0.477091	+	0.878854i	$0.658309\pi$
$168$	1.12141e6	0.0182466
$169$	−3.65489e7	−0.582466
$170$	−4.87959e7	−0.761750
$171$	9.70966e6	0.148497
$172$	−4.60577e7	−0.690164
$173$	−8.60605e7	−1.26369	−0.631847	−	0.775093i	$-0.717703\pi$
$173$	−8.60605e7	−1.26369	−0.631847	+	0.775093i	$0.717703\pi$
$174$	−4.99758e7	−0.719179
$175$	−5.21992e6	−0.0736258
$176$	−2.57247e7	−0.355677
$177$	5.31852e7	0.720916
$178$	5.71522e7	0.759561
$179$	1.27863e8	1.66632	0.833161	−	0.553031i	$-0.186529\pi$
$179$	1.27863e8	1.66632	0.833161	+	0.553031i	$0.186529\pi$
$180$	2.62258e7	0.335178
$181$	6.33489e6	0.0794080	0.0397040	−	0.999211i	$-0.487358\pi$
$181$	6.33489e6	0.0794080	0.0397040	+	0.999211i	$0.487358\pi$
$182$	−7.07476e6	−0.0869885
$183$	3.54809e7	0.427972
$184$	3.19469e7	0.378065
$185$	−1.63503e8	−1.89856
$186$	4.71746e7	0.537543
$187$	−1.17641e7	−0.131557
$188$	8.01551e7	0.879789
$189$	−1.80987e6	−0.0194999
$190$	7.35324e7	0.777752
$191$	1.68610e8	1.75092	0.875460	−	0.483291i	$-0.160559\pi$
$191$	1.68610e8	1.75092	0.875460	+	0.483291i	$0.160559\pi$
$192$	−2.76492e7	−0.281921
$193$	−1.62754e8	−1.62960	−0.814800	−	0.579742i	$-0.803153\pi$
$193$	−1.62754e8	−1.62960	−0.814800	+	0.579742i	$0.803153\pi$
$194$	2.30020e8	2.26182
$195$	5.07583e7	0.490214
$196$	−7.98383e7	−0.757382
$197$	1.64384e8	1.53189	0.765944	−	0.642908i	$-0.222272\pi$
$197$	1.64384e8	1.53189	0.765944	+	0.642908i	$0.222272\pi$
$198$	1.45852e7	0.133532
$199$	8.15883e7	0.733909	0.366955	−	0.930239i	$-0.380400\pi$
$199$	8.15883e7	0.733909	0.366955	+	0.930239i	$0.380400\pi$
$200$	−2.56419e7	−0.226645
$201$	6.56355e7	0.570102
$202$	1.95954e8	1.67272
$203$	1.13226e7	0.0949971
$204$	−2.33750e7	−0.192773
$205$	−2.15350e8	−1.74585
$206$	−7.31233e7	−0.582801
$207$	−5.15600e7	−0.404033
$208$	−9.89283e7	−0.762252
$209$	1.77278e7	0.134321
$210$	−1.37064e7	−0.102130
$211$	1.73181e8	1.26914	0.634571	−	0.772864i	$-0.281177\pi$
$211$	1.73181e8	1.26914	0.634571	+	0.772864i	$0.281177\pi$
$212$	2.04615e8	1.47490
$213$	−7.10861e7	−0.504030
$214$	−1.84367e8	−1.28599
$215$	−1.72699e8	−1.18510
$216$	−8.89069e6	−0.0600271
$217$	−1.06880e7	−0.0710045
$218$	−2.32608e8	−1.52064
$219$	−1.55780e7	−0.100221
$220$	4.78828e7	0.303180
$221$	−4.52407e7	−0.281940
$222$	−1.80676e8	−1.10832
$223$	−1.55928e8	−0.941582	−0.470791	−	0.882245i	$-0.656031\pi$
$223$	−1.55928e8	−0.941582	−0.470791	+	0.882245i	$0.656031\pi$
$224$	2.13975e7	0.127202
$225$	4.13841e7	0.242212
$226$	−2.34644e8	−1.35217
$227$	1.35680e8	0.769882	0.384941	−	0.922941i	$-0.374222\pi$
$227$	1.35680e8	0.769882	0.384941	+	0.922941i	$0.374222\pi$
$228$	3.52247e7	0.196823
$229$	5.12748e7	0.282150	0.141075	−	0.989999i	$-0.454944\pi$
$229$	5.12748e7	0.282150	0.141075	+	0.989999i	$0.454944\pi$
$230$	−3.90470e8	−2.11612
$231$	−3.30445e6	−0.0176383
$232$	5.56203e7	0.292432
$233$	−1.22312e8	−0.633465	−0.316733	−	0.948515i	$-0.602586\pi$
$233$	−1.22312e8	−0.633465	−0.316733	+	0.948515i	$0.602586\pi$
$234$	5.60896e7	0.286172
$235$	3.00552e8	1.51071
$236$	1.92945e8	0.955524
$237$	−2.71652e7	−0.132554
$238$	1.22165e7	0.0587389
$239$	2.92687e8	1.38679	0.693396	−	0.720557i	$-0.256114\pi$
$239$	2.92687e8	1.38679	0.693396	+	0.720557i	$0.256114\pi$
$240$	−1.91660e8	−0.894937
$241$	−2.62795e8	−1.20937	−0.604684	−	0.796466i	$-0.706700\pi$
$241$	−2.62795e8	−1.20937	−0.604684	+	0.796466i	$0.706700\pi$
$242$	2.66295e7	0.120784
$243$	1.43489e7	0.0641500
$244$	1.28717e8	0.567248
$245$	−2.99364e8	−1.30052
$246$	−2.37969e8	−1.01917
$247$	6.81749e7	0.287863
$248$	−5.25027e7	−0.218575
$249$	2.27515e8	0.933924
$250$	−1.17906e8	−0.477249
$251$	1.48087e8	0.591096	0.295548	−	0.955328i	$-0.404498\pi$
$251$	1.48087e8	0.591096	0.295548	+	0.955328i	$0.404498\pi$
$252$	−6.56586e6	−0.0258458
$253$	−9.41377e7	−0.365462
$254$	−1.31318e7	−0.0502812
$255$	−8.76477e7	−0.331017
$256$	3.47432e8	1.29428
$257$	−1.32655e8	−0.487480	−0.243740	−	0.969841i	$-0.578374\pi$
$257$	−1.32655e8	−0.487480	−0.243740	+	0.969841i	$0.578374\pi$
$258$	−1.90838e8	−0.691826
$259$	4.09342e7	0.146399
$260$	1.84141e8	0.649745
$261$	−8.97670e7	−0.312518
$262$	5.63034e8	1.93410
$263$	−2.18061e8	−0.739149	−0.369575	−	0.929201i	$-0.620497\pi$
$263$	−2.18061e8	−0.739149	−0.369575	+	0.929201i	$0.620497\pi$
$264$	−1.62325e7	−0.0542965
$265$	7.67230e8	2.53259
$266$	−1.84094e7	−0.0599729
$267$	1.02657e8	0.330066
$268$	2.38112e8	0.755631
$269$	1.38257e8	0.433065	0.216532	−	0.976275i	$-0.430525\pi$
$269$	1.38257e8	0.433065	0.216532	+	0.976275i	$0.430525\pi$
$270$	1.08666e8	0.335985
$271$	−4.82337e8	−1.47217	−0.736086	−	0.676888i	$-0.763328\pi$
$271$	−4.82337e8	−1.47217	−0.736086	+	0.676888i	$0.763328\pi$
$272$	1.70826e8	0.514710
$273$	−1.27078e7	−0.0378007
$274$	5.92787e7	0.174089
$275$	7.55587e7	0.219089
$276$	−1.87049e8	−0.535518
$277$	1.12004e8	0.316631	0.158316	−	0.987389i	$-0.449394\pi$
$277$	1.12004e8	0.316631	0.158316	+	0.987389i	$0.449394\pi$
$278$	2.08618e7	0.0582364
$279$	8.47355e7	0.233588
$280$	1.52544e7	0.0415282
$281$	−2.64955e8	−0.712360	−0.356180	−	0.934417i	$-0.615921\pi$
$281$	−2.64955e8	−0.712360	−0.356180	+	0.934417i	$0.615921\pi$
$282$	3.32120e8	0.881907
$283$	−3.02507e8	−0.793384	−0.396692	−	0.917952i	$-0.629842\pi$
$283$	−3.02507e8	−0.793384	−0.396692	+	0.917952i	$0.629842\pi$
$284$	−2.57886e8	−0.668057
$285$	1.32080e8	0.337970
$286$	1.02408e8	0.258852
$287$	5.39147e7	0.134623
$288$	−1.69642e8	−0.418466
$289$	−3.32219e8	−0.809620
$290$	−6.79816e8	−1.63681
$291$	4.13163e8	0.982871
$292$	−5.65138e7	−0.132836
$293$	3.85014e8	0.894210	0.447105	−	0.894481i	$-0.352455\pi$
$293$	3.85014e8	0.894210	0.447105	+	0.894481i	$0.352455\pi$
$294$	−3.30807e8	−0.759205
$295$	7.23473e8	1.64076
$296$	2.01082e8	0.450663
$297$	2.61981e7	0.0580259
$298$	−7.25986e8	−1.58917
$299$	−3.62021e8	−0.783221
$300$	1.50133e8	0.321035
$301$	4.32367e7	0.0913840
$302$	−7.83649e8	−1.63718
$303$	3.51974e8	0.726878
$304$	−2.57424e8	−0.525523
$305$	4.82643e8	0.974040
$306$	−9.68536e7	−0.193237
$307$	6.36045e8	1.25460	0.627298	−	0.778780i	$-0.284161\pi$
$307$	6.36045e8	1.25460	0.627298	+	0.778780i	$0.284161\pi$
$308$	−1.19879e7	−0.0233784
$309$	−1.31345e8	−0.253255
$310$	6.41711e8	1.22341
$311$	−1.01932e9	−1.92153	−0.960766	−	0.277360i	$-0.910541\pi$
$311$	−1.01932e9	−1.92153	−0.960766	+	0.277360i	$0.910541\pi$
$312$	−6.24246e7	−0.116363
$313$	−9.69295e8	−1.78670	−0.893348	−	0.449365i	$-0.851650\pi$
$313$	−9.69295e8	−1.78670	−0.893348	+	0.449365i	$0.851650\pi$
$314$	9.08447e8	1.65594
$315$	−2.46195e7	−0.0443806
$316$	−9.85497e7	−0.175691
$317$	4.71892e8	0.832023	0.416012	−	0.909359i	$-0.363428\pi$
$317$	4.71892e8	0.832023	0.416012	+	0.909359i	$0.363428\pi$
$318$	8.47814e8	1.47845
$319$	−1.63896e8	−0.282683
$320$	−3.76109e8	−0.641636
$321$	−3.31163e8	−0.558822
$322$	9.77573e7	0.163175
$323$	−1.17722e8	−0.194379
$324$	5.20549e7	0.0850265
$325$	2.90572e8	0.469529
$326$	1.79308e8	0.286641
$327$	−4.17813e8	−0.660792
$328$	2.64846e8	0.414415
$329$	−7.52457e7	−0.116492
$330$	1.98401e8	0.303910
$331$	3.19142e8	0.483711	0.241856	−	0.970312i	$-0.422244\pi$
$331$	3.19142e8	0.483711	0.241856	+	0.970312i	$0.422244\pi$
$332$	8.25377e8	1.23785
$333$	−3.24531e8	−0.481617
$334$	−8.63268e8	−1.26775
$335$	8.92833e8	1.29752
$336$	4.79837e7	0.0690091
$337$	−4.45647e8	−0.634287	−0.317144	−	0.948378i	$-0.602724\pi$
$337$	−4.45647e8	−0.634287	−0.317144	+	0.948378i	$0.602724\pi$
$338$	−5.49390e8	−0.773877
$339$	−4.21470e8	−0.587582
$340$	−3.17968e8	−0.438740
$341$	1.54709e8	0.211288
$342$	1.45952e8	0.197297
$343$	1.50674e8	0.201609
$344$	2.12393e8	0.281310
$345$	−7.01366e8	−0.919555
$346$	−1.29363e9	−1.67897
$347$	6.40262e8	0.822630	0.411315	−	0.911493i	$-0.365070\pi$
$347$	6.40262e8	0.822630	0.411315	+	0.911493i	$0.365070\pi$
$348$	−3.25656e8	−0.414221
$349$	−1.44158e9	−1.81530	−0.907651	−	0.419725i	$-0.862127\pi$
$349$	−1.44158e9	−1.81530	−0.907651	+	0.419725i	$0.862127\pi$
$350$	−7.84639e7	−0.0978210
$351$	1.00749e8	0.124355
$352$	−3.09731e8	−0.378517
$353$	−5.37426e8	−0.650290	−0.325145	−	0.945664i	$-0.605413\pi$
$353$	−5.37426e8	−0.650290	−0.325145	+	0.945664i	$0.605413\pi$
$354$	7.99462e8	0.957825
$355$	−9.66978e8	−1.14714
$356$	3.72420e8	0.437479
$357$	2.19433e7	0.0255249
$358$	1.92199e9	2.21391
$359$	1.03148e9	1.17660	0.588302	−	0.808641i	$-0.299797\pi$
$359$	1.03148e9	1.17660	0.588302	+	0.808641i	$0.299797\pi$
$360$	−1.20939e8	−0.136618
$361$	−7.16472e8	−0.801538
$362$	9.52239e7	0.105503
$363$	4.78321e7	0.0524864
$364$	−4.61011e7	−0.0501022
$365$	−2.11906e8	−0.228096
$366$	5.33336e8	0.568614
$367$	−2.80377e8	−0.296082	−0.148041	−	0.988981i	$-0.547297\pi$
$367$	−2.80377e8	−0.296082	−0.148041	+	0.988981i	$0.547297\pi$
$368$	1.36697e9	1.42985
$369$	−4.27443e8	−0.442879
$370$	−2.45771e9	−2.52246
$371$	−1.92082e8	−0.195289
$372$	3.07403e8	0.309605
$373$	−2.55292e8	−0.254716	−0.127358	−	0.991857i	$-0.540650\pi$
$373$	−2.55292e8	−0.254716	−0.127358	+	0.991857i	$0.540650\pi$
$374$	−1.76834e8	−0.174790
$375$	−2.11784e8	−0.207388
$376$	−3.69631e8	−0.358601
$377$	−6.30285e8	−0.605818
$378$	−2.72054e7	−0.0259080
$379$	9.45832e7	0.0892435	0.0446218	−	0.999004i	$-0.485792\pi$
$379$	9.45832e7	0.0892435	0.0446218	+	0.999004i	$0.485792\pi$
$380$	4.79158e8	0.447957
$381$	−2.35874e7	−0.0218496
$382$	2.53448e9	2.32631
$383$	3.60129e8	0.327538	0.163769	−	0.986499i	$-0.447635\pi$
$383$	3.60129e8	0.327538	0.163769	+	0.986499i	$0.447635\pi$
$384$	3.88617e8	0.350238
$385$	−4.49501e7	−0.0401438
$386$	−2.44646e9	−2.16512
$387$	−3.42786e8	−0.300632
$388$	1.49887e9	1.30273
$389$	9.18457e8	0.791107	0.395553	−	0.918443i	$-0.370553\pi$
$389$	9.18457e8	0.791107	0.395553	+	0.918443i	$0.370553\pi$
$390$	7.62981e8	0.651309
$391$	6.25125e8	0.528869
$392$	3.68170e8	0.308708
$393$	1.01133e9	0.840461
$394$	2.47096e9	2.03530
$395$	−3.69525e8	−0.301685
$396$	9.50413e7	0.0769093
$397$	8.33128e8	0.668259	0.334130	−	0.942527i	$-0.391558\pi$
$397$	8.33128e8	0.668259	0.334130	+	0.942527i	$0.391558\pi$
$398$	1.22641e9	0.975088
$399$	−3.30672e7	−0.0260611
$400$	−1.09718e9	−0.857174
$401$	1.29459e9	1.00260	0.501301	−	0.865273i	$-0.332855\pi$
$401$	1.29459e9	1.00260	0.501301	+	0.865273i	$0.332855\pi$
$402$	9.86610e8	0.757450
$403$	5.94957e8	0.452812
$404$	1.27689e9	0.963426
$405$	1.95187e8	0.146002
$406$	1.70197e8	0.126215
$407$	−5.92526e8	−0.435639
$408$	1.07793e8	0.0785740
$409$	−2.18443e9	−1.57873	−0.789364	−	0.613925i	$-0.789590\pi$
$409$	−2.18443e9	−1.57873	−0.789364	+	0.613925i	$0.789590\pi$
$410$	−3.23707e9	−2.31958
$411$	1.06477e8	0.0756501
$412$	−4.76492e8	−0.335672
$413$	−1.81128e8	−0.126520
$414$	−7.75032e8	−0.536807
$415$	3.09486e9	2.12556
$416$	−1.19112e9	−0.811199
$417$	3.74721e7	0.0253065
$418$	2.66478e8	0.178461
$419$	−4.94882e8	−0.328664	−0.164332	−	0.986405i	$-0.552547\pi$
$419$	−4.94882e8	−0.328664	−0.164332	+	0.986405i	$0.552547\pi$
$420$	−8.93147e7	−0.0588234
$421$	−3.37073e8	−0.220159	−0.110079	−	0.993923i	$-0.535111\pi$
$421$	−3.37073e8	−0.220159	−0.110079	+	0.993923i	$0.535111\pi$
$422$	2.60319e9	1.68621
$423$	5.96557e8	0.383231
$424$	−9.43570e8	−0.601165
$425$	−5.01750e8	−0.317049
$426$	−1.06854e9	−0.669666
$427$	−1.20834e8	−0.0751087
$428$	−1.20139e9	−0.740681
$429$	1.83946e8	0.112484
$430$	−2.59596e9	−1.57456
$431$	−2.13731e9	−1.28587	−0.642934	−	0.765922i	$-0.722283\pi$
$431$	−2.13731e9	−1.28587	−0.642934	+	0.765922i	$0.722283\pi$
$432$	−3.80421e8	−0.227023
$433$	3.01414e9	1.78425	0.892125	−	0.451789i	$-0.149214\pi$
$433$	3.01414e9	1.78425	0.892125	+	0.451789i	$0.149214\pi$
$434$	−1.60658e8	−0.0943382
$435$	−1.22109e9	−0.711272
$436$	−1.51574e9	−0.875834
$437$	−9.42024e8	−0.539979
$438$	−2.34163e8	−0.133156
$439$	2.34406e9	1.32234	0.661170	−	0.750236i	$-0.270060\pi$
$439$	2.34406e9	1.32234	0.661170	+	0.750236i	$0.270060\pi$
$440$	−2.20809e8	−0.123576
$441$	−5.94199e8	−0.329911
$442$	−6.80042e8	−0.374592
$443$	−1.66669e9	−0.910837	−0.455418	−	0.890278i	$-0.650510\pi$
$443$	−1.66669e9	−0.910837	−0.455418	+	0.890278i	$0.650510\pi$
$444$	−1.17733e9	−0.638350
$445$	1.39644e9	0.751210
$446$	−2.34386e9	−1.25101
$447$	−1.30402e9	−0.690572
$448$	9.41620e7	0.0494769
$449$	−1.67459e9	−0.873067	−0.436533	−	0.899688i	$-0.643794\pi$
$449$	−1.67459e9	−0.873067	−0.436533	+	0.899688i	$0.643794\pi$
$450$	6.22072e8	0.321808
$451$	−7.80420e8	−0.400599
$452$	−1.52901e9	−0.778799
$453$	−1.40760e9	−0.711435
$454$	2.03949e9	1.02288
$455$	−1.72862e8	−0.0860321
$456$	−1.62437e8	−0.0802246
$457$	1.90338e9	0.932866	0.466433	−	0.884556i	$-0.345539\pi$
$457$	1.90338e9	0.932866	0.466433	+	0.884556i	$0.345539\pi$
$458$	7.70744e8	0.374870
$459$	−1.73969e8	−0.0839708
$460$	−2.54441e9	−1.21881
$461$	−9.64789e8	−0.458647	−0.229324	−	0.973350i	$-0.573651\pi$
$461$	−9.64789e8	−0.458647	−0.229324	+	0.973350i	$0.573651\pi$
$462$	−4.96713e7	−0.0234347
$463$	−2.59795e8	−0.121646	−0.0608229	−	0.998149i	$-0.519372\pi$
$463$	−2.59795e8	−0.121646	−0.0608229	+	0.998149i	$0.519372\pi$
$464$	2.37992e9	1.10598
$465$	1.15265e9	0.531632
$466$	−1.83855e9	−0.841637
$467$	1.25810e9	0.571620	0.285810	−	0.958286i	$-0.407737\pi$
$467$	1.25810e9	0.571620	0.285810	+	0.958286i	$0.407737\pi$
$468$	3.65495e8	0.164824
$469$	−2.23528e8	−0.100052
$470$	4.51779e9	2.00717
$471$	1.63176e9	0.719588
$472$	−8.89756e8	−0.389470
$473$	−6.25855e8	−0.271932
$474$	−4.08337e8	−0.176114
$475$	7.56106e8	0.323709
$476$	7.96059e7	0.0338315
$477$	1.52285e9	0.642456
$478$	4.39957e9	1.84252
$479$	2.45751e9	1.02169	0.510847	−	0.859672i	$-0.329332\pi$
$479$	2.45751e9	1.02169	0.510847	+	0.859672i	$0.329332\pi$
$480$	−2.30763e9	−0.952404
$481$	−2.27865e9	−0.933618
$482$	−3.95025e9	−1.60679
$483$	1.75593e8	0.0709074
$484$	1.73525e8	0.0695671
$485$	5.62022e9	2.23695
$486$	2.15688e8	0.0852312
$487$	4.00331e9	1.57061	0.785305	−	0.619109i	$-0.212506\pi$
$487$	4.00331e9	1.57061	0.785305	+	0.619109i	$0.212506\pi$
$488$	−5.93574e8	−0.231209
$489$	3.22075e8	0.124559
$490$	−4.49994e9	−1.72791
$491$	−4.80277e9	−1.83108	−0.915539	−	0.402230i	$-0.868235\pi$
$491$	−4.80277e9	−1.83108	−0.915539	+	0.402230i	$0.868235\pi$
$492$	−1.55067e9	−0.587006
$493$	1.08836e9	0.409078
$494$	1.02478e9	0.382461
$495$	3.56370e8	0.132063
$496$	−2.24652e9	−0.826655
$497$	2.42091e8	0.0884568
$498$	3.41992e9	1.24083
$499$	1.56779e8	0.0564855	0.0282427	−	0.999601i	$-0.491009\pi$
$499$	1.56779e8	0.0564855	0.0282427	+	0.999601i	$0.491009\pi$
$500$	−7.68308e8	−0.274878
$501$	−1.55061e9	−0.550898
$502$	2.22599e9	0.785343
$503$	3.38644e9	1.18647	0.593233	−	0.805031i	$-0.297851\pi$
$503$	3.38644e9	1.18647	0.593233	+	0.805031i	$0.297851\pi$
$504$	3.02781e7	0.0105347
$505$	4.78787e9	1.65433
$506$	−1.41504e9	−0.485560
$507$	−9.86819e8	−0.336287
$508$	−8.55704e7	−0.0289601
$509$	3.74614e9	1.25913	0.629567	−	0.776946i	$-0.283232\pi$
$509$	3.74614e9	1.25913	0.629567	+	0.776946i	$0.283232\pi$
$510$	−1.31749e9	−0.439796
$511$	5.30524e7	0.0175886
$512$	3.38014e9	1.11298
$513$	2.62161e8	0.0857348
$514$	−1.99402e9	−0.647677
$515$	−1.78667e9	−0.576393
$516$	−1.24356e9	−0.398467
$517$	1.08919e9	0.346645
$518$	6.15309e8	0.194509
$519$	−2.32363e9	−0.729595
$520$	−8.49155e8	−0.264835
$521$	1.73449e9	0.537328	0.268664	−	0.963234i	$-0.413418\pi$
$521$	1.73449e9	0.537328	0.268664	+	0.963234i	$0.413418\pi$
$522$	−1.34935e9	−0.415218
$523$	−4.28089e7	−0.0130851	−0.00654256	−	0.999979i	$-0.502083\pi$
$523$	−4.28089e7	−0.0130851	−0.00654256	+	0.999979i	$0.502083\pi$
$524$	3.66889e9	1.11397
$525$	−1.40938e8	−0.0425079
$526$	−3.27781e9	−0.982050
$527$	−1.02735e9	−0.305761
$528$	−6.94567e8	−0.205350
$529$	1.59749e9	0.469183
$530$	1.15327e10	3.36486
$531$	1.43600e9	0.416221
$532$	−1.19961e8	−0.0345422
$533$	−3.00122e9	−0.858525
$534$	1.54311e9	0.438533
$535$	−4.50477e9	−1.27185
$536$	−1.09804e9	−0.307994
$537$	3.45230e9	0.962051
$538$	2.07822e9	0.575379
$539$	−1.08488e9	−0.298416
$540$	7.08098e8	0.193515
$541$	−4.18440e9	−1.13617	−0.568085	−	0.822970i	$-0.692315\pi$
$541$	−4.18440e9	−1.13617	−0.568085	+	0.822970i	$0.692315\pi$
$542$	−7.25033e9	−1.95596
$543$	1.71042e8	0.0458462
$544$	2.05678e9	0.547762
$545$	−5.68346e9	−1.50392
$546$	−1.91019e8	−0.0502228
$547$	−3.60517e9	−0.941825	−0.470913	−	0.882180i	$-0.656075\pi$
$547$	−3.60517e9	−0.941825	−0.470913	+	0.882180i	$0.656075\pi$
$548$	3.86277e8	0.100269
$549$	9.57984e8	0.247090
$550$	1.13577e9	0.291086
$551$	−1.64008e9	−0.417672
$552$	8.62568e8	0.218276
$553$	9.25137e7	0.0232631
$554$	1.68360e9	0.420683
$555$	−4.41457e9	−1.09613
$556$	1.35941e8	0.0335420
$557$	3.16535e9	0.776120	0.388060	−	0.921634i	$-0.373145\pi$
$557$	3.16535e9	0.776120	0.388060	+	0.921634i	$0.373145\pi$
$558$	1.27371e9	0.310350
$559$	−2.40682e9	−0.582777
$560$	6.52717e8	0.157061
$561$	−3.17631e8	−0.0759545
$562$	−3.98270e9	−0.946457
$563$	−3.44458e9	−0.813499	−0.406750	−	0.913540i	$-0.633338\pi$
$563$	−3.44458e9	−0.813499	−0.406750	+	0.913540i	$0.633338\pi$
$564$	2.16419e9	0.507946
$565$	−5.73322e9	−1.33730
$566$	−4.54719e9	−1.05411
$567$	−4.88666e7	−0.0112583
$568$	1.18923e9	0.272299
$569$	−2.13767e8	−0.0486460	−0.0243230	−	0.999704i	$-0.507743\pi$
$569$	−2.13767e8	−0.0486460	−0.0243230	+	0.999704i	$0.507743\pi$
$570$	1.98537e9	0.449035
$571$	1.69649e9	0.381350	0.190675	−	0.981653i	$-0.438932\pi$
$571$	1.69649e9	0.381350	0.190675	+	0.981653i	$0.438932\pi$
$572$	6.67318e8	0.149089
$573$	4.55247e9	1.01089
$574$	8.10427e8	0.178864
$575$	−4.01506e9	−0.880753
$576$	−7.46527e8	−0.162767
$577$	−1.59938e9	−0.346607	−0.173304	−	0.984868i	$-0.555444\pi$
$577$	−1.59938e9	−0.346607	−0.173304	+	0.984868i	$0.555444\pi$
$578$	−4.99379e9	−1.07568
$579$	−4.39436e9	−0.940850
$580$	−4.42987e9	−0.942743
$581$	−7.74824e8	−0.163903
$582$	6.21053e9	1.30586
$583$	2.78041e9	0.581123
$584$	2.60611e8	0.0541436
$585$	1.37047e9	0.283025
$586$	5.78739e9	1.18807
$587$	2.17523e9	0.443886	0.221943	−	0.975060i	$-0.428760\pi$
$587$	2.17523e9	0.443886	0.221943	+	0.975060i	$0.428760\pi$
$588$	−2.15563e9	−0.437275
$589$	1.54815e9	0.312184
$590$	1.08750e10	2.17995
$591$	4.43836e9	0.884435
$592$	8.60403e9	1.70442
$593$	−8.69992e9	−1.71326	−0.856632	−	0.515929i	$-0.827447\pi$
$593$	−8.69992e9	−1.71326	−0.856632	+	0.515929i	$0.827447\pi$
$594$	3.93800e8	0.0770945
$595$	2.98493e8	0.0580931
$596$	−4.73073e9	−0.915306
$597$	2.20288e9	0.423723
$598$	−5.44177e9	−1.04060
$599$	−1.16124e9	−0.220764	−0.110382	−	0.993889i	$-0.535207\pi$
$599$	−1.16124e9	−0.220764	−0.110382	+	0.993889i	$0.535207\pi$
$600$	−6.92331e8	−0.130853
$601$	8.37192e9	1.57313	0.786564	−	0.617508i	$-0.211858\pi$
$601$	8.37192e9	1.57313	0.786564	+	0.617508i	$0.211858\pi$
$602$	6.49919e8	0.121415
$603$	1.77216e9	0.329148
$604$	−5.10648e9	−0.942958
$605$	6.50656e8	0.119456
$606$	5.29075e9	0.965746
$607$	−4.65984e9	−0.845688	−0.422844	−	0.906202i	$-0.638968\pi$
$607$	−4.65984e9	−0.845688	−0.422844	+	0.906202i	$0.638968\pi$
$608$	−3.09944e9	−0.559269
$609$	3.05710e8	0.0548466
$610$	7.25492e9	1.29413
$611$	4.18863e9	0.742896
$612$	−6.31125e8	−0.111298
$613$	−3.82596e9	−0.670855	−0.335428	−	0.942066i	$-0.608881\pi$
$613$	−3.82596e9	−0.670855	−0.335428	+	0.942066i	$0.608881\pi$
$614$	9.56081e9	1.66688
$615$	−5.81446e9	−1.00797
$616$	5.52814e7	0.00952899
$617$	3.15185e9	0.540216	0.270108	−	0.962830i	$-0.412941\pi$
$617$	3.15185e9	0.540216	0.270108	+	0.962830i	$0.412941\pi$
$618$	−1.97433e9	−0.336480
$619$	−1.11183e10	−1.88417	−0.942086	−	0.335372i	$-0.891138\pi$
$619$	−1.11183e10	−1.88417	−0.942086	+	0.335372i	$0.891138\pi$
$620$	4.18157e9	0.704642
$621$	−1.39212e9	−0.233269
$622$	−1.53220e10	−2.55299
$623$	−3.49610e8	−0.0579262
$624$	−2.67106e9	−0.440087
$625$	−7.31590e9	−1.19864
$626$	−1.45701e10	−2.37385
$627$	4.78650e8	0.0775500
$628$	5.91970e9	0.953764
$629$	3.93469e9	0.630425
$630$	−3.70072e8	−0.0589651
$631$	−3.74087e9	−0.592748	−0.296374	−	0.955072i	$-0.595778\pi$
$631$	−3.74087e9	−0.592748	−0.296374	+	0.955072i	$0.595778\pi$
$632$	4.54457e8	0.0716115
$633$	4.67587e9	0.732740
$634$	7.09332e9	1.10545
$635$	−3.20857e8	−0.0497283
$636$	5.52460e9	0.851531
$637$	−4.17208e9	−0.639535
$638$	−2.46362e9	−0.375579
$639$	−1.91933e9	−0.291002
$640$	5.28632e9	0.797120
$641$	−1.30668e9	−0.195959	−0.0979796	−	0.995188i	$-0.531238\pi$
$641$	−1.30668e9	−0.195959	−0.0979796	+	0.995188i	$0.531238\pi$
$642$	−4.97792e9	−0.742464
$643$	5.01887e9	0.744504	0.372252	−	0.928132i	$-0.378586\pi$
$643$	5.01887e9	0.744504	0.372252	+	0.928132i	$0.378586\pi$
$644$	6.37014e8	0.0939829
$645$	−4.66288e9	−0.684220
$646$	−1.76956e9	−0.258256
$647$	6.91469e9	1.00371	0.501855	−	0.864952i	$-0.332651\pi$
$647$	6.91469e9	1.00371	0.501855	+	0.864952i	$0.332651\pi$
$648$	−2.40049e8	−0.0346566
$649$	2.62183e9	0.376486
$650$	4.36778e9	0.623827
$651$	−2.88575e8	−0.0409945
$652$	1.16842e9	0.165095
$653$	7.49431e9	1.05326	0.526630	−	0.850094i	$-0.323455\pi$
$653$	7.49431e9	1.05326	0.526630	+	0.850094i	$0.323455\pi$
$654$	−6.28041e9	−0.877943
$655$	1.37570e10	1.91284
$656$	1.13324e10	1.56733
$657$	−4.20606e8	−0.0578625
$658$	−1.13107e9	−0.154774
$659$	−4.01111e9	−0.545966	−0.272983	−	0.962019i	$-0.588010\pi$
$659$	−4.01111e9	−0.545966	−0.272983	+	0.962019i	$0.588010\pi$
$660$	1.29284e9	0.175041
$661$	4.43123e9	0.596786	0.298393	−	0.954443i	$-0.403549\pi$
$661$	4.43123e9	0.596786	0.298393	+	0.954443i	$0.403549\pi$
$662$	4.79723e9	0.642670
$663$	−1.22150e9	−0.162778
$664$	−3.80618e9	−0.504547
$665$	−4.49810e8	−0.0593135
$666$	−4.87824e9	−0.639887
$667$	8.70913e9	1.13641
$668$	−5.62530e9	−0.730177
$669$	−4.21007e9	−0.543622
$670$	1.34208e10	1.72391
$671$	1.74908e9	0.223501
$672$	5.77733e8	0.0734404
$673$	−1.09178e9	−0.138064	−0.0690322	−	0.997614i	$-0.521991\pi$
$673$	−1.09178e9	−0.138064	−0.0690322	+	0.997614i	$0.521991\pi$
$674$	−6.69880e9	−0.842728
$675$	1.11737e9	0.139841
$676$	−3.57998e9	−0.445725
$677$	1.13823e10	1.40984	0.704919	−	0.709288i	$-0.250983\pi$
$677$	1.13823e10	1.40984	0.704919	+	0.709288i	$0.250983\pi$
$678$	−6.33540e9	−0.780674
$679$	−1.40707e9	−0.172493
$680$	1.46629e9	0.178830
$681$	3.66335e9	0.444492
$682$	2.32553e9	0.280722
$683$	−7.14821e9	−0.858470	−0.429235	−	0.903193i	$-0.641217\pi$
$683$	−7.14821e9	−0.858470	−0.429235	+	0.903193i	$0.641217\pi$
$684$	9.51066e8	0.113636
$685$	1.44840e9	0.172175
$686$	2.26488e9	0.267862
$687$	1.38442e9	0.162899
$688$	9.08800e9	1.06392
$689$	1.06925e10	1.24541
$690$	−1.05427e10	−1.22174
$691$	−7.94882e9	−0.916494	−0.458247	−	0.888825i	$-0.651522\pi$
$691$	−7.94882e9	−0.916494	−0.458247	+	0.888825i	$0.651522\pi$
$692$	−8.42966e9	−0.967028
$693$	−8.92201e7	−0.0101835
$694$	9.62419e9	1.09296
$695$	5.09729e8	0.0575961
$696$	1.50175e9	0.168836
$697$	5.18241e9	0.579718
$698$	−2.16693e10	−2.41185
$699$	−3.30242e9	−0.365731
$700$	−5.11293e8	−0.0563413
$701$	1.42083e10	1.55786	0.778932	−	0.627109i	$-0.215762\pi$
$701$	1.42083e10	1.55786	0.778932	+	0.627109i	$0.215762\pi$
$702$	1.51442e9	0.165221
$703$	−5.92933e9	−0.643668
$704$	−1.36300e9	−0.147229
$705$	8.11490e9	0.872211
$706$	−8.07839e9	−0.863990
$707$	−1.19868e9	−0.127566
$708$	5.20952e9	0.551672
$709$	−1.72520e10	−1.81793	−0.908967	−	0.416868i	$-0.863128\pi$
$709$	−1.72520e10	−1.81793	−0.908967	+	0.416868i	$0.863128\pi$
$710$	−1.45353e10	−1.52412
$711$	−7.33459e8	−0.0765301
$712$	−1.71739e9	−0.178316
$713$	−8.22097e9	−0.849395
$714$	3.29844e8	0.0339129
$715$	2.50219e9	0.256006
$716$	1.25242e10	1.27513
$717$	7.90255e9	0.800664
$718$	1.55049e10	1.56326
$719$	6.01848e9	0.603859	0.301929	−	0.953330i	$-0.402369\pi$
$719$	6.01848e9	0.603859	0.301929	+	0.953330i	$0.402369\pi$
$720$	−5.17482e9	−0.516692
$721$	4.47307e8	0.0444460
$722$	−1.07698e10	−1.06494
$723$	−7.09548e9	−0.698229
$724$	6.20506e8	0.0607661
$725$	−6.99029e9	−0.681259
$726$	7.18996e8	0.0697346
$727$	−6.27113e9	−0.605306	−0.302653	−	0.953101i	$-0.597872\pi$
$727$	−6.27113e9	−0.605306	−0.302653	+	0.953101i	$0.597872\pi$
$728$	2.12593e8	0.0204216
$729$	3.87420e8	0.0370370
$730$	−3.18530e9	−0.303054
$731$	4.15601e9	0.393519
$732$	3.47537e9	0.327501
$733$	1.07976e9	0.101266	0.0506328	−	0.998717i	$-0.483876\pi$
$733$	1.07976e9	0.101266	0.0506328	+	0.998717i	$0.483876\pi$
$734$	−4.21453e9	−0.393381
$735$	−8.08283e9	−0.750858
$736$	1.64586e10	1.52167
$737$	3.23559e9	0.297726
$738$	−6.42517e9	−0.588420
$739$	−2.74991e9	−0.250647	−0.125324	−	0.992116i	$-0.539997\pi$
$739$	−2.74991e9	−0.250647	−0.125324	+	0.992116i	$0.539997\pi$
$740$	−1.60152e10	−1.45285
$741$	1.84072e9	0.166197
$742$	−2.88731e9	−0.259466
$743$	−1.45368e10	−1.30019	−0.650096	−	0.759852i	$-0.725271\pi$
$743$	−1.45368e10	−1.30019	−0.650096	+	0.759852i	$0.725271\pi$
$744$	−1.41757e9	−0.126194
$745$	−1.77385e10	−1.57170
$746$	−3.83746e9	−0.338422
$747$	6.14290e9	0.539202
$748$	−1.15230e9	−0.100672
$749$	1.12781e9	0.0980728
$750$	−3.18346e9	−0.275540
$751$	1.24242e10	1.07035	0.535177	−	0.844740i	$-0.320245\pi$
$751$	1.24242e10	1.07035	0.535177	+	0.844740i	$0.320245\pi$
$752$	−1.58160e10	−1.35623
$753$	3.99834e9	0.341269
$754$	−9.47423e9	−0.804904
$755$	−1.91474e10	−1.61918
$756$	−1.77278e8	−0.0149221
$757$	−6.60390e9	−0.553305	−0.276653	−	0.960970i	$-0.589225\pi$
$757$	−6.60390e9	−0.553305	−0.276653	+	0.960970i	$0.589225\pi$
$758$	1.42174e9	0.118571
$759$	−2.54172e9	−0.210999
$760$	−2.20961e9	−0.182586
$761$	7.65346e9	0.629523	0.314762	−	0.949171i	$-0.398075\pi$
$761$	7.65346e9	0.629523	0.314762	+	0.949171i	$0.398075\pi$
$762$	−3.54558e8	−0.0290299
$763$	1.42290e9	0.115968
$764$	1.65154e10	1.33987
$765$	−2.36649e9	−0.191113
$766$	5.41333e9	0.435175
$767$	1.00827e10	0.806847
$768$	9.38065e9	0.747255
$769$	−7.34905e9	−0.582759	−0.291380	−	0.956607i	$-0.594114\pi$
$769$	−7.34905e9	−0.582759	−0.291380	+	0.956607i	$0.594114\pi$
$770$	−6.75674e8	−0.0533359
$771$	−3.58168e9	−0.281447
$772$	−1.59418e10	−1.24703
$773$	2.99068e9	0.232885	0.116443	−	0.993197i	$-0.462851\pi$
$773$	2.99068e9	0.232885	0.116443	+	0.993197i	$0.462851\pi$
$774$	−5.15264e9	−0.399426
$775$	6.59848e9	0.509199
$776$	−6.91197e9	−0.530990
$777$	1.10522e9	0.0845233
$778$	1.38059e10	1.05108
$779$	−7.80957e9	−0.591896
$780$	4.97180e9	0.375131
$781$	−3.50428e9	−0.263221
$782$	9.39666e9	0.702668
$783$	−2.42371e9	−0.180432
$784$	1.57535e10	1.16754
$785$	2.21967e10	1.63774
$786$	1.52019e10	1.11666
$787$	2.40705e10	1.76025	0.880125	−	0.474742i	$-0.157459\pi$
$787$	2.40705e10	1.76025	0.880125	+	0.474742i	$0.157459\pi$
$788$	1.61015e10	1.17226
$789$	−5.88764e9	−0.426748
$790$	−5.55457e9	−0.400826
$791$	1.43536e9	0.103120
$792$	−4.38278e8	−0.0313481
$793$	6.72634e9	0.478986
$794$	1.25233e10	0.887865
$795$	2.07152e10	1.46219
$796$	7.99162e9	0.561615
$797$	4.33730e9	0.303470	0.151735	−	0.988421i	$-0.451514\pi$
$797$	4.33730e9	0.303470	0.151735	+	0.988421i	$0.451514\pi$
$798$	−4.97055e8	−0.0346253
$799$	−7.23279e9	−0.501640
$800$	−1.32103e10	−0.912216
$801$	2.77175e9	0.190564
$802$	1.94599e10	1.33208
$803$	−7.67938e8	−0.0523386
$804$	6.42903e9	0.436264
$805$	2.38857e9	0.161381
$806$	8.94319e9	0.601616
$807$	3.73293e9	0.250030
$808$	−5.88831e9	−0.392691
$809$	−7.50051e7	−0.00498048	−0.00249024	−	0.999997i	$-0.500793\pi$
$809$	−7.50051e7	−0.00498048	−0.00249024	+	0.999997i	$0.500793\pi$
$810$	2.93398e9	0.193981
$811$	1.60048e10	1.05361	0.526803	−	0.849988i	$-0.323391\pi$
$811$	1.60048e10	1.05361	0.526803	+	0.849988i	$0.323391\pi$
$812$	1.10906e9	0.0726954
$813$	−1.30231e10	−0.849959
$814$	−8.90664e9	−0.578800
$815$	4.38115e9	0.283490
$816$	4.61230e9	0.297168
$817$	−6.26285e9	−0.401786
$818$	−3.28356e10	−2.09753
$819$	−3.43109e8	−0.0218242
$820$	−2.10937e10	−1.33599
$821$	−9.00415e9	−0.567860	−0.283930	−	0.958845i	$-0.591638\pi$
$821$	−9.00415e9	−0.567860	−0.283930	+	0.958845i	$0.591638\pi$
$822$	1.60052e9	0.100510
$823$	1.74879e10	1.09355	0.546776	−	0.837279i	$-0.315855\pi$
$823$	1.74879e10	1.09355	0.546776	+	0.837279i	$0.315855\pi$
$824$	2.19732e9	0.136819
$825$	2.04008e9	0.126491
$826$	−2.72265e9	−0.168097
$827$	−9.24503e9	−0.568381	−0.284190	−	0.958768i	$-0.591725\pi$
$827$	−9.24503e9	−0.568381	−0.284190	+	0.958768i	$0.591725\pi$
$828$	−5.05033e9	−0.309181
$829$	−8.34392e9	−0.508662	−0.254331	−	0.967117i	$-0.581855\pi$
$829$	−8.34392e9	−0.508662	−0.254331	+	0.967117i	$0.581855\pi$
$830$	4.65208e10	2.82406
$831$	3.02410e9	0.182807
$832$	−5.24163e9	−0.315525
$833$	7.20420e9	0.431846
$834$	5.63268e8	0.0336228
$835$	−2.10928e10	−1.25381
$836$	1.73645e9	0.102787
$837$	2.28786e9	0.134862
$838$	−7.43889e9	−0.436671
$839$	3.52733e9	0.206195	0.103098	−	0.994671i	$-0.467125\pi$
$839$	3.52733e9	0.206195	0.103098	+	0.994671i	$0.467125\pi$
$840$	4.11870e8	0.0239763
$841$	−2.08711e9	−0.120993
$842$	−5.06676e9	−0.292508
$843$	−7.15377e9	−0.411281
$844$	1.69631e10	0.971197
$845$	−1.34236e10	−0.765368
$846$	8.96723e9	0.509169
$847$	−1.62897e8	−0.00921131
$848$	−4.03741e10	−2.27362
$849$	−8.16770e9	−0.458061
$850$	−7.54214e9	−0.421239
$851$	3.14858e10	1.75130
$852$	−6.96292e9	−0.385703
$853$	−3.29500e10	−1.81775	−0.908875	−	0.417069i	$-0.863057\pi$
$853$	−3.29500e10	−1.81775	−0.908875	+	0.417069i	$0.863057\pi$
$854$	−1.81633e9	−0.0997912
$855$	3.56615e9	0.195127
$856$	5.54015e9	0.301900
$857$	1.15453e10	0.626576	0.313288	−	0.949658i	$-0.398570\pi$
$857$	1.15453e10	0.626576	0.313288	+	0.949658i	$0.398570\pi$
$858$	2.76501e9	0.149448
$859$	−1.10119e10	−0.592773	−0.296386	−	0.955068i	$-0.595782\pi$
$859$	−1.10119e10	−0.592773	−0.296386	+	0.955068i	$0.595782\pi$
$860$	−1.69160e10	−0.906886
$861$	1.45570e9	0.0777249
$862$	−3.21272e10	−1.70843
$863$	−4.86919e9	−0.257881	−0.128940	−	0.991652i	$-0.541158\pi$
$863$	−4.86919e9	−0.257881	−0.128940	+	0.991652i	$0.541158\pi$
$864$	−4.58034e9	−0.241601
$865$	−3.16081e10	−1.66051
$866$	4.53075e10	2.37060
$867$	−8.96990e9	−0.467435
$868$	−1.04689e9	−0.0543354
$869$	−1.33914e9	−0.0692241
$870$	−1.83550e10	−0.945012
$871$	1.24429e10	0.638057
$872$	6.98975e9	0.356988
$873$	1.11554e10	0.567461
$874$	−1.41602e10	−0.717429
$875$	7.21250e8	0.0363963
$876$	−1.52587e9	−0.0766927
$877$	2.78944e9	0.139643	0.0698214	−	0.997560i	$-0.477757\pi$
$877$	2.78944e9	0.139643	0.0698214	+	0.997560i	$0.477757\pi$
$878$	3.52351e10	1.75689
$879$	1.03954e10	0.516272
$880$	−9.44813e9	−0.467365
$881$	−2.69844e10	−1.32953	−0.664763	−	0.747054i	$-0.731467\pi$
$881$	−2.69844e10	−1.32953	−0.664763	+	0.747054i	$0.731467\pi$
$882$	−8.93179e9	−0.438327
$883$	−8.92756e9	−0.436386	−0.218193	−	0.975906i	$-0.570016\pi$
$883$	−8.92756e9	−0.436386	−0.218193	+	0.975906i	$0.570016\pi$
$884$	−4.43135e9	−0.215751
$885$	1.95338e10	0.947294
$886$	−2.50530e10	−1.21016
$887$	2.24812e10	1.08165	0.540824	−	0.841136i	$-0.318112\pi$
$887$	2.24812e10	1.08165	0.540824	+	0.841136i	$0.318112\pi$
$888$	5.42921e9	0.260191
$889$	8.03293e7	0.00383458
$890$	2.09908e10	0.998074
$891$	7.07348e8	0.0335013
$892$	−1.52733e10	−0.720534
$893$	1.08994e10	0.512178
$894$	−1.96016e10	−0.917510
$895$	4.69613e10	2.18957
$896$	−1.32347e9	−0.0614664
$897$	−9.77456e9	−0.452193
$898$	−2.51719e10	−1.15998
$899$	−1.43129e10	−0.657004
$900$	4.05360e9	0.185350
$901$	−1.84634e10	−0.840959
$902$	−1.17310e10	−0.532246
$903$	1.16739e9	0.0527606
$904$	7.05095e9	0.317437
$905$	2.32667e9	0.104343
$906$	−2.11585e10	−0.945229
$907$	3.82511e9	0.170223	0.0851115	−	0.996371i	$-0.472875\pi$
$907$	3.82511e9	0.170223	0.0851115	+	0.996371i	$0.472875\pi$
$908$	1.32899e10	0.589144
$909$	9.50330e9	0.419663
$910$	−2.59841e9	−0.114304
$911$	−2.83658e10	−1.24303	−0.621514	−	0.783403i	$-0.713482\pi$
$911$	−2.83658e10	−1.24303	−0.621514	+	0.783403i	$0.713482\pi$
$912$	−6.95045e9	−0.303411
$913$	1.12156e10	0.487726
$914$	2.86110e10	1.23943
$915$	1.30314e10	0.562362
$916$	5.02239e9	0.215912
$917$	−3.44417e9	−0.147500
$918$	−2.61505e9	−0.111566
$919$	4.26088e10	1.81090	0.905450	−	0.424452i	$-0.139533\pi$
$919$	4.26088e10	1.81090	0.905450	+	0.424452i	$0.139533\pi$
$920$	1.17334e10	0.496784
$921$	1.71732e10	0.724341
$922$	−1.45024e10	−0.609369
$923$	−1.34762e10	−0.564109
$924$	−3.23672e8	−0.0134975
$925$	−2.52718e10	−1.04988
$926$	−3.90514e9	−0.161621
$927$	−3.54631e9	−0.146217
$928$	2.86547e10	1.17700
$929$	−1.62785e10	−0.666131	−0.333065	−	0.942904i	$-0.608083\pi$
$929$	−1.62785e10	−0.666131	−0.333065	+	0.942904i	$0.608083\pi$
$930$	1.73262e10	0.706339
$931$	−1.08563e10	−0.440917
$932$	−1.19805e10	−0.484752
$933$	−2.75215e10	−1.10940
$934$	1.89114e10	0.759467
$935$	−4.32071e9	−0.172868
$936$	−1.68546e9	−0.0671821
$937$	1.42832e10	0.567202	0.283601	−	0.958942i	$-0.408471\pi$
$937$	1.42832e10	0.567202	0.283601	+	0.958942i	$0.408471\pi$
$938$	−3.36000e9	−0.132932
$939$	−2.61710e10	−1.03155
$940$	2.94392e10	1.15606
$941$	2.28343e10	0.893356	0.446678	−	0.894695i	$-0.352607\pi$
$941$	2.28343e10	0.893356	0.446678	+	0.894695i	$0.352607\pi$
$942$	2.45281e10	0.956060
$943$	4.14702e10	1.61044
$944$	−3.80715e10	−1.47298
$945$	−6.64728e8	−0.0256231
$946$	−9.40763e9	−0.361294
$947$	−3.56818e10	−1.36528	−0.682641	−	0.730754i	$-0.739169\pi$
$947$	−3.56818e10	−1.36528	−0.682641	+	0.730754i	$0.739169\pi$
$948$	−2.66084e9	−0.101435
$949$	−2.95322e9	−0.112167
$950$	1.13655e10	0.430088
$951$	1.27411e10	0.480369
$952$	−3.67099e8	−0.0137897
$953$	−3.09703e10	−1.15910	−0.579549	−	0.814937i	$-0.696771\pi$
$953$	−3.09703e10	−1.15910	−0.579549	+	0.814937i	$0.696771\pi$
$954$	2.28910e10	0.853581
$955$	6.19267e10	2.30073
$956$	2.86689e10	1.06123
$957$	−4.42518e9	−0.163207
$958$	3.69404e10	1.35744
$959$	−3.62618e8	−0.0132765
$960$	−1.01549e10	−0.370449
$961$	−1.40020e10	−0.508930
$962$	−3.42518e10	−1.24043
$963$	−8.94139e9	−0.322636
$964$	−2.57409e10	−0.925454
$965$	−5.97760e10	−2.14132
$966$	2.63945e9	0.0942092
$967$	−2.33295e10	−0.829683	−0.414841	−	0.909894i	$-0.636163\pi$
$967$	−2.33295e10	−0.829683	−0.414841	+	0.909894i	$0.636163\pi$
$968$	−8.00203e8	−0.0283554
$969$	−3.17850e9	−0.112225
$970$	8.44812e10	2.97207
$971$	3.59204e9	0.125914	0.0629571	−	0.998016i	$-0.479947\pi$
$971$	3.59204e9	0.125914	0.0629571	+	0.998016i	$0.479947\pi$
$972$	1.40548e9	0.0490901
$973$	−1.27615e8	−0.00444127
$974$	6.01764e10	2.08675
$975$	7.84545e9	0.271083
$976$	−2.53982e10	−0.874438
$977$	−4.27678e10	−1.46719	−0.733594	−	0.679588i	$-0.762158\pi$
$977$	−4.27678e10	−1.46719	−0.733594	+	0.679588i	$0.762158\pi$
$978$	4.84132e9	0.165492
$979$	5.06062e9	0.172371
$980$	−2.93229e10	−0.995211
$981$	−1.12809e10	−0.381508
$982$	−7.21936e10	−2.43281
$983$	−5.36514e10	−1.80154	−0.900769	−	0.434298i	$-0.856997\pi$
$983$	−5.36514e10	−1.80154	−0.900769	+	0.434298i	$0.856997\pi$
$984$	7.15086e9	0.239263
$985$	6.03745e10	2.01292
$986$	1.63598e10	0.543511
$987$	−2.03163e9	−0.0672567
$988$	6.67776e9	0.220283
$989$	3.32568e10	1.09319
$990$	5.35683e9	0.175462
$991$	2.06830e10	0.675081	0.337541	−	0.941311i	$-0.390405\pi$
$991$	2.06830e10	0.675081	0.337541	+	0.941311i	$0.390405\pi$
$992$	−2.70486e10	−0.879738
$993$	8.61684e9	0.279271
$994$	3.63903e9	0.117526
$995$	2.99656e10	0.964367
$996$	2.22852e10	0.714675
$997$	−2.42215e10	−0.774049	−0.387025	−	0.922069i	$-0.626497\pi$
$997$	−2.42215e10	−0.774049	−0.387025	+	0.922069i	$0.626497\pi$
$998$	2.35665e9	0.0750479
$999$	−8.76235e9	−0.278062

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	33.8.a.e.1.3	✓	4
3.2	odd	2		99.8.a.f.1.2		4
4.3	odd	2		528.8.a.r.1.4		4
11.10	odd	2		363.8.a.f.1.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
33.8.a.e.1.3	✓	4	1.1	even	1	trivial
99.8.a.f.1.2		4	3.2	odd	2
363.8.a.f.1.2		4	11.10	odd	2
528.8.a.r.1.4		4	4.3	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:	\( N \)	\(=\)	\( 33 = 3 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	33.a (trivial)

\(f(q)\)	\(=\)	\(q+15.0316 q^{2} +27.0000 q^{3} +97.9505 q^{4} +367.278 q^{5} +405.855 q^{6} -91.9512 q^{7} -451.694 q^{8} +729.000 q^{9} +O(q^{10})\)	\(q+15.0316 q^{2} +27.0000 q^{3} +97.9505 q^{4} +367.278 q^{5} +405.855 q^{6} -91.9512 q^{7} -451.694 q^{8} +729.000 q^{9} +5520.80 q^{10} +1331.00 q^{11} +2644.66 q^{12} +5118.56 q^{13} -1382.18 q^{14} +9916.51 q^{15} -19327.4 q^{16} -8838.56 q^{17} +10958.1 q^{18} +13319.2 q^{19} +35975.1 q^{20} -2482.68 q^{21} +20007.1 q^{22} -70727.0 q^{23} -12195.7 q^{24} +56768.3 q^{25} +76940.4 q^{26} +19683.0 q^{27} -9006.66 q^{28} -123137. q^{29} +149062. q^{30} +116235. q^{31} -232705. q^{32} +35937.0 q^{33} -132858. q^{34} -33771.7 q^{35} +71405.9 q^{36} -445173. q^{37} +200209. q^{38} +138201. q^{39} -165897. q^{40} -586341. q^{41} -37318.8 q^{42} -470214. q^{43} +130372. q^{44} +267746. q^{45} -1.06314e6 q^{46} +818322. q^{47} -521839. q^{48} -815088. q^{49} +853322. q^{50} -238641. q^{51} +501366. q^{52} +2.08896e6 q^{53} +295868. q^{54} +488847. q^{55} +41533.8 q^{56} +359617. q^{57} -1.85096e6 q^{58} +1.96982e6 q^{59} +971327. q^{60} +1.31411e6 q^{61} +1.74721e6 q^{62} -67032.4 q^{63} -1.02404e6 q^{64} +1.87994e6 q^{65} +540192. q^{66} +2.43094e6 q^{67} -865741. q^{68} -1.90963e6 q^{69} -507644. q^{70} -2.63282e6 q^{71} -329285. q^{72} -576963. q^{73} -6.69169e6 q^{74} +1.53275e6 q^{75} +1.30462e6 q^{76} -122387. q^{77} +2.07739e6 q^{78} -1.00612e6 q^{79} -7.09852e6 q^{80} +531441. q^{81} -8.81367e6 q^{82} +8.42647e6 q^{83} -243180. q^{84} -3.24621e6 q^{85} -7.06809e6 q^{86} -3.32470e6 q^{87} -601204. q^{88} +3.80212e6 q^{89} +4.02466e6 q^{90} -470658. q^{91} -6.92775e6 q^{92} +3.13835e6 q^{93} +1.23007e7 q^{94} +4.89184e6 q^{95} -6.28305e6 q^{96} +1.53023e7 q^{97} -1.22521e7 q^{98} +970299. q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 15 q^{2} + 108 q^{3} + 565 q^{4} + 306 q^{5} + 405 q^{6} + 890 q^{7} + 2457 q^{8} + 2916 q^{9}+O(q^{10}) \) 4 * q + 15 * q^2 + 108 * q^3 + 565 * q^4 + 306 * q^5 + 405 * q^6 + 890 * q^7 + 2457 * q^8 + 2916 * q^9	\( 4 q + 15 q^{2} + 108 q^{3} + 565 q^{4} + 306 q^{5} + 405 q^{6} + 890 q^{7} + 2457 q^{8} + 2916 q^{9} - 8946 q^{10} + 5324 q^{11} + 15255 q^{12} - 1822 q^{13} + 35340 q^{14} + 8262 q^{15} + 65041 q^{16} + 32856 q^{17} + 10935 q^{18} - 12784 q^{19} - 4002 q^{20} + 24030 q^{21} + 19965 q^{22} + 114858 q^{23} + 66339 q^{24} + 72856 q^{25} - 221466 q^{26} + 78732 q^{27} + 10112 q^{28} - 104952 q^{29} - 241542 q^{30} - 24976 q^{31} + 337761 q^{32} + 143748 q^{33} - 741690 q^{34} - 722856 q^{35} + 411885 q^{36} - 498856 q^{37} - 897156 q^{38} - 49194 q^{39} - 2676930 q^{40} + 734556 q^{41} + 954180 q^{42} - 201916 q^{43} + 752015 q^{44} + 223074 q^{45} - 3068508 q^{46} + 1995894 q^{47} + 1756107 q^{48} - 771024 q^{49} + 1632129 q^{50} + 887112 q^{51} - 4412266 q^{52} + 929970 q^{53} + 295245 q^{54} + 407286 q^{55} + 7224888 q^{56} - 345168 q^{57} + 2864322 q^{58} + 1353156 q^{59} - 108054 q^{60} + 3998774 q^{61} - 3783264 q^{62} + 648810 q^{63} + 1480129 q^{64} + 6612108 q^{65} + 539055 q^{66} + 1722008 q^{67} + 1596906 q^{68} + 3101166 q^{69} - 2751024 q^{70} + 5571858 q^{71} + 1791153 q^{72} + 5600528 q^{73} - 10907838 q^{74} + 1967112 q^{75} - 19634884 q^{76} + 1184590 q^{77} - 5979582 q^{78} - 7710226 q^{79} - 24073794 q^{80} + 2125764 q^{81} - 11230842 q^{82} + 3431856 q^{83} + 273024 q^{84} + 5909484 q^{85} - 25687140 q^{86} - 2833704 q^{87} + 3270267 q^{88} + 4611528 q^{89} - 6521634 q^{90} - 9032696 q^{91} + 13608576 q^{92} - 674352 q^{93} - 3497436 q^{94} + 21828000 q^{95} + 9119547 q^{96} + 1401692 q^{97} - 7230081 q^{98} + 3881196 q^{99}+O(q^{100}) \) 4 * q + 15 * q^2 + 108 * q^3 + 565 * q^4 + 306 * q^5 + 405 * q^6 + 890 * q^7 + 2457 * q^8 + 2916 * q^9 - 8946 * q^10 + 5324 * q^11 + 15255 * q^12 - 1822 * q^13 + 35340 * q^14 + 8262 * q^15 + 65041 * q^16 + 32856 * q^17 + 10935 * q^18 - 12784 * q^19 - 4002 * q^20 + 24030 * q^21 + 19965 * q^22 + 114858 * q^23 + 66339 * q^24 + 72856 * q^25 - 221466 * q^26 + 78732 * q^27 + 10112 * q^28 - 104952 * q^29 - 241542 * q^30 - 24976 * q^31 + 337761 * q^32 + 143748 * q^33 - 741690 * q^34 - 722856 * q^35 + 411885 * q^36 - 498856 * q^37 - 897156 * q^38 - 49194 * q^39 - 2676930 * q^40 + 734556 * q^41 + 954180 * q^42 - 201916 * q^43 + 752015 * q^44 + 223074 * q^45 - 3068508 * q^46 + 1995894 * q^47 + 1756107 * q^48 - 771024 * q^49 + 1632129 * q^50 + 887112 * q^51 - 4412266 * q^52 + 929970 * q^53 + 295245 * q^54 + 407286 * q^55 + 7224888 * q^56 - 345168 * q^57 + 2864322 * q^58 + 1353156 * q^59 - 108054 * q^60 + 3998774 * q^61 - 3783264 * q^62 + 648810 * q^63 + 1480129 * q^64 + 6612108 * q^65 + 539055 * q^66 + 1722008 * q^67 + 1596906 * q^68 + 3101166 * q^69 - 2751024 * q^70 + 5571858 * q^71 + 1791153 * q^72 + 5600528 * q^73 - 10907838 * q^74 + 1967112 * q^75 - 19634884 * q^76 + 1184590 * q^77 - 5979582 * q^78 - 7710226 * q^79 - 24073794 * q^80 + 2125764 * q^81 - 11230842 * q^82 + 3431856 * q^83 + 273024 * q^84 + 5909484 * q^85 - 25687140 * q^86 - 2833704 * q^87 + 3270267 * q^88 + 4611528 * q^89 - 6521634 * q^90 - 9032696 * q^91 + 13608576 * q^92 - 674352 * q^93 - 3497436 * q^94 + 21828000 * q^95 + 9119547 * q^96 + 1401692 * q^97 - 7230081 * q^98 + 3881196 * q^99

Introduction

L-functions

Modular forms

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