LMFDB - Embedded newform 23.10.a.a.1.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,10,Mod(1,23)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(23, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0]))

N = Newforms(chi, 10, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 10);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 10 $
Character orbit:	$[\chi]$	$=$	23.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:	$11.8458242318$
Analytic rank:	$1$
Dimension:	$7$
Coefficient field:	$\mathbb{Q}[x]/(x^{7} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{7} - 640x^{5} - 1455x^{4} + 114552x^{3} + 321544x^{2} - 5741296x - 13379024 $ x^7 - 640x^5 - 1455x^4 + 114552x^3 + 321544x^2 - 5741296*x - 13379024
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.1
Root			$-15.4224$ of defining polynomial
Character	$\chi$	$=$	23.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-30.8448 q^{2} +107.347 q^{3} +439.399 q^{4} -1512.00 q^{5} -3311.09 q^{6} +8168.19 q^{7} +2239.35 q^{8} -8159.64 q^{9} +O(q^{10})$	\(q-30.8448 q^{2} +107.347 q^{3} +439.399 q^{4} -1512.00 q^{5} -3311.09 q^{6} +8168.19 q^{7} +2239.35 q^{8} -8159.64 q^{9} +46637.2 q^{10} +62526.2 q^{11} +47168.2 q^{12} -169909. q^{13} -251946. q^{14} -162308. q^{15} -294045. q^{16} +66901.0 q^{17} +251682. q^{18} -1.01209e6 q^{19} -664371. q^{20} +876830. q^{21} -1.92860e6 q^{22} -279841. q^{23} +240388. q^{24} +333012. q^{25} +5.24081e6 q^{26} -2.98882e6 q^{27} +3.58910e6 q^{28} +691764. q^{29} +5.00636e6 q^{30} -8.24019e6 q^{31} +7.92319e6 q^{32} +6.71199e6 q^{33} -2.06355e6 q^{34} -1.23503e7 q^{35} -3.58534e6 q^{36} +1.38524e6 q^{37} +3.12176e7 q^{38} -1.82393e7 q^{39} -3.38590e6 q^{40} -1.44333e7 q^{41} -2.70456e7 q^{42} +2.03285e7 q^{43} +2.74740e7 q^{44} +1.23374e7 q^{45} +8.63163e6 q^{46} +3.20230e7 q^{47} -3.15648e7 q^{48} +2.63657e7 q^{49} -1.02717e7 q^{50} +7.18162e6 q^{51} -7.46581e7 q^{52} -2.49649e7 q^{53} +9.21895e7 q^{54} -9.45394e7 q^{55} +1.82915e7 q^{56} -1.08644e8 q^{57} -2.13373e7 q^{58} -1.58169e8 q^{59} -7.13181e7 q^{60} +6.31285e7 q^{61} +2.54167e8 q^{62} -6.66494e7 q^{63} -9.38380e7 q^{64} +2.56903e8 q^{65} -2.07030e8 q^{66} +6.21501e7 q^{67} +2.93962e7 q^{68} -3.00401e7 q^{69} +3.80941e8 q^{70} -2.56532e8 q^{71} -1.82723e7 q^{72} -2.04068e8 q^{73} -4.27273e7 q^{74} +3.57478e7 q^{75} -4.44710e8 q^{76} +5.10725e8 q^{77} +5.62585e8 q^{78} +3.28718e8 q^{79} +4.44595e8 q^{80} -1.60235e8 q^{81} +4.45191e8 q^{82} +4.83853e7 q^{83} +3.85278e8 q^{84} -1.01154e8 q^{85} -6.27027e8 q^{86} +7.42587e7 q^{87} +1.40018e8 q^{88} +3.83007e8 q^{89} -3.80543e8 q^{90} -1.38785e9 q^{91} -1.22962e8 q^{92} -8.84559e8 q^{93} -9.87743e8 q^{94} +1.53027e9 q^{95} +8.50530e8 q^{96} -1.30917e9 q^{97} -8.13243e8 q^{98} -5.10191e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9}+O(q^{10}) $ 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9} - 60820 q^{10} - 78484 q^{11} - 343492 q^{12} - 296769 q^{13} - 711120 q^{14} - 237870 q^{15} - 253440 q^{16} - 1128820 q^{17} - 499874 q^{18} - 1301252 q^{19} - 3482704 q^{20} - 108908 q^{21} - 1562088 q^{22} - 1958887 q^{23} - 4606464 q^{24} - 1320899 q^{25} + 692230 q^{26} + 2977921 q^{27} - 8371144 q^{28} + 2813849 q^{29} + 25535196 q^{30} + 7334751 q^{31} + 26028800 q^{32} + 646330 q^{33} + 14981564 q^{34} + 23410104 q^{35} + 40211900 q^{36} - 13324320 q^{37} + 37578632 q^{38} + 6304533 q^{39} - 45307920 q^{40} - 15691573 q^{41} + 124523248 q^{42} - 46474818 q^{43} + 43428040 q^{44} - 72736710 q^{45} + 8232227 q^{47} - 163054384 q^{48} + 29219031 q^{49} + 50366304 q^{50} - 136344764 q^{51} - 100922292 q^{52} - 53545400 q^{53} - 26171642 q^{54} - 181608484 q^{55} - 420111696 q^{56} - 218913370 q^{57} - 39304854 q^{58} - 341275144 q^{59} + 420822384 q^{60} - 277157656 q^{61} + 464777594 q^{62} - 574619276 q^{63} + 340566208 q^{64} + 106659278 q^{65} + 258025876 q^{66} + 89654580 q^{67} + 62700400 q^{68} + 24905849 q^{69} + 1187910040 q^{70} - 286098961 q^{71} + 1446323640 q^{72} - 637495039 q^{73} + 189880036 q^{74} - 160733159 q^{75} + 228563936 q^{76} + 511682536 q^{77} + 1199383686 q^{78} + 274469546 q^{79} - 345318560 q^{80} - 237775217 q^{81} - 570256066 q^{82} + 1164579762 q^{83} + 3447171416 q^{84} - 18639492 q^{85} + 415245796 q^{86} - 595368433 q^{87} + 103329440 q^{88} - 504153000 q^{89} - 1414126968 q^{90} - 1692320156 q^{91} - 429835776 q^{92} - 2753858687 q^{93} - 2214048622 q^{94} + 162962164 q^{95} - 3332565856 q^{96} - 3519929016 q^{97} + 2474592568 q^{98} - 1883749262 q^{99}+O(q^{100}) \) 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9 - 60820 * q^10 - 78484 * q^11 - 343492 * q^12 - 296769 * q^13 - 711120 * q^14 - 237870 * q^15 - 253440 * q^16 - 1128820 * q^17 - 499874 * q^18 - 1301252 * q^19 - 3482704 * q^20 - 108908 * q^21 - 1562088 * q^22 - 1958887 * q^23 - 4606464 * q^24 - 1320899 * q^25 + 692230 * q^26 + 2977921 * q^27 - 8371144 * q^28 + 2813849 * q^29 + 25535196 * q^30 + 7334751 * q^31 + 26028800 * q^32 + 646330 * q^33 + 14981564 * q^34 + 23410104 * q^35 + 40211900 * q^36 - 13324320 * q^37 + 37578632 * q^38 + 6304533 * q^39 - 45307920 * q^40 - 15691573 * q^41 + 124523248 * q^42 - 46474818 * q^43 + 43428040 * q^44 - 72736710 * q^45 + 8232227 * q^47 - 163054384 * q^48 + 29219031 * q^49 + 50366304 * q^50 - 136344764 * q^51 - 100922292 * q^52 - 53545400 * q^53 - 26171642 * q^54 - 181608484 * q^55 - 420111696 * q^56 - 218913370 * q^57 - 39304854 * q^58 - 341275144 * q^59 + 420822384 * q^60 - 277157656 * q^61 + 464777594 * q^62 - 574619276 * q^63 + 340566208 * q^64 + 106659278 * q^65 + 258025876 * q^66 + 89654580 * q^67 + 62700400 * q^68 + 24905849 * q^69 + 1187910040 * q^70 - 286098961 * q^71 + 1446323640 * q^72 - 637495039 * q^73 + 189880036 * q^74 - 160733159 * q^75 + 228563936 * q^76 + 511682536 * q^77 + 1199383686 * q^78 + 274469546 * q^79 - 345318560 * q^80 - 237775217 * q^81 - 570256066 * q^82 + 1164579762 * q^83 + 3447171416 * q^84 - 18639492 * q^85 + 415245796 * q^86 - 595368433 * q^87 + 103329440 * q^88 - 504153000 * q^89 - 1414126968 * q^90 - 1692320156 * q^91 - 429835776 * q^92 - 2753858687 * q^93 - 2214048622 * q^94 + 162962164 * q^95 - 3332565856 * q^96 - 3519929016 * q^97 + 2474592568 * q^98 - 1883749262 * 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 $

$2$	−30.8448	−1.36316	−0.681579	−	0.731744i	$-0.738707\pi$
$2$	−30.8448	−1.36316	−0.681579	+	0.731744i	$0.738707\pi$
$3$	107.347	0.765145	0.382573	−	0.923925i	$-0.375038\pi$
$3$	107.347	0.765145	0.382573	+	0.923925i	$0.375038\pi$
$4$	439.399	0.858202
$5$	−1512.00	−1.08190	−0.540949	−	0.841056i	$-0.681935\pi$
$5$	−1512.00	−1.08190	−0.540949	+	0.841056i	$0.681935\pi$
$6$	−3311.09	−1.04301
$7$	8168.19	1.28583	0.642916	−	0.765936i	$-0.277724\pi$
$7$	8168.19	1.28583	0.642916	+	0.765936i	$0.277724\pi$
$8$	2239.35	0.193294
$9$	−8159.64	−0.414552
$10$	46637.2	1.47480
$11$	62526.2	1.28764	0.643820	−	0.765177i	$-0.277348\pi$
$11$	62526.2	1.28764	0.643820	+	0.765177i	$0.277348\pi$
$12$	47168.2	0.656649
$13$	−169909.	−1.64996	−0.824978	−	0.565165i	$-0.808812\pi$
$13$	−169909.	−1.64996	−0.824978	+	0.565165i	$0.808812\pi$
$14$	−251946.	−1.75279
$15$	−162308.	−0.827809
$16$	−294045.	−1.12169
$17$	66901.0	0.194273	0.0971365	−	0.995271i	$-0.469032\pi$
$17$	66901.0	0.194273	0.0971365	+	0.995271i	$0.469032\pi$
$18$	251682.	0.565101
$19$	−1.01209e6	−1.78167	−0.890833	−	0.454331i	$-0.849878\pi$
$19$	−1.01209e6	−1.78167	−0.890833	+	0.454331i	$0.849878\pi$
$20$	−664371.	−0.928486
$21$	876830.	0.983849
$22$	−1.92860e6	−1.75526
$23$	−279841.	−0.208514
$23$	−279841.	−0.208514
$24$	240388.	0.147898
$25$	333012.	0.170502
$26$	5.24081e6	2.24915
$27$	−2.98882e6	−1.08234
$28$	3.58910e6	1.10350
$29$	691764.	0.181621	0.0908107	−	0.995868i	$-0.471054\pi$
$29$	691764.	0.181621	0.0908107	+	0.995868i	$0.471054\pi$
$30$	5.00636e6	1.12843
$31$	−8.24019e6	−1.60254	−0.801271	−	0.598301i	$-0.795843\pi$
$31$	−8.24019e6	−1.60254	−0.801271	+	0.598301i	$0.795843\pi$
$32$	7.92319e6	1.33575
$33$	6.71199e6	0.985233
$34$	−2.06355e6	−0.264825
$35$	−1.23503e7	−1.39114
$36$	−3.58534e6	−0.355770
$37$	1.38524e6	0.121511	0.0607556	−	0.998153i	$-0.480649\pi$
$37$	1.38524e6	0.121511	0.0607556	+	0.998153i	$0.480649\pi$
$38$	3.12176e7	2.42869
$39$	−1.82393e7	−1.26246
$40$	−3.38590e6	−0.209124
$41$	−1.44333e7	−0.797696	−0.398848	−	0.917017i	$-0.630590\pi$
$41$	−1.44333e7	−0.797696	−0.398848	+	0.917017i	$0.630590\pi$
$42$	−2.70456e7	−1.34114
$43$	2.03285e7	0.906770	0.453385	−	0.891315i	$-0.350216\pi$
$43$	2.03285e7	0.906770	0.453385	+	0.891315i	$0.350216\pi$
$44$	2.74740e7	1.10506
$45$	1.23374e7	0.448503
$46$	8.63163e6	0.284238
$47$	3.20230e7	0.957243	0.478621	−	0.878021i	$-0.341137\pi$
$47$	3.20230e7	0.957243	0.478621	+	0.878021i	$0.341137\pi$
$48$	−3.15648e7	−0.858257
$49$	2.63657e7	0.653366
$50$	−1.02717e7	−0.232421
$51$	7.18162e6	0.148647
$52$	−7.46581e7	−1.41599
$53$	−2.49649e7	−0.434599	−0.217300	−	0.976105i	$-0.569725\pi$
$53$	−2.49649e7	−0.434599	−0.217300	+	0.976105i	$0.569725\pi$
$54$	9.21895e7	1.47540
$55$	−9.45394e7	−1.39310
$56$	1.82915e7	0.248543
$57$	−1.08644e8	−1.36323
$58$	−2.13373e7	−0.247579
$59$	−1.58169e8	−1.69937	−0.849684	−	0.527292i	$-0.823207\pi$
$59$	−1.58169e8	−1.69937	−0.849684	+	0.527292i	$0.823207\pi$
$60$	−7.13181e7	−0.710427
$61$	6.31285e7	0.583769	0.291885	−	0.956454i	$-0.405718\pi$
$61$	6.31285e7	0.583769	0.291885	+	0.956454i	$0.405718\pi$
$62$	2.54167e8	2.18452
$63$	−6.66494e7	−0.533045
$64$	−9.38380e7	−0.699148
$65$	2.56903e8	1.78508
$66$	−2.07030e8	−1.34303
$67$	6.21501e7	0.376795	0.188397	−	0.982093i	$-0.439671\pi$
$67$	6.21501e7	0.376795	0.188397	+	0.982093i	$0.439671\pi$
$68$	2.93962e7	0.166725
$69$	−3.00401e7	−0.159544
$70$	3.80941e8	1.89634
$71$	−2.56532e8	−1.19806	−0.599031	−	0.800726i	$-0.704447\pi$
$71$	−2.56532e8	−1.19806	−0.599031	+	0.800726i	$0.704447\pi$
$72$	−1.82723e7	−0.0801304
$73$	−2.04068e8	−0.841049	−0.420524	−	0.907281i	$-0.638154\pi$
$73$	−2.04068e8	−0.841049	−0.420524	+	0.907281i	$0.638154\pi$
$74$	−4.27273e7	−0.165639
$75$	3.57478e7	0.130459
$76$	−4.44710e8	−1.52903
$77$	5.10725e8	1.65569
$78$	5.62585e8	1.72093
$79$	3.28718e8	0.949513	0.474757	−	0.880117i	$-0.342536\pi$
$79$	3.28718e8	0.949513	0.474757	+	0.880117i	$0.342536\pi$
$80$	4.44595e8	1.21356
$81$	−1.60235e8	−0.413594
$82$	4.45191e8	1.08739
$83$	4.83853e7	0.111908	0.0559541	−	0.998433i	$-0.482180\pi$
$83$	4.83853e7	0.111908	0.0559541	+	0.998433i	$0.482180\pi$
$84$	3.85278e8	0.844341
$85$	−1.01154e8	−0.210183
$86$	−6.27027e8	−1.23607
$87$	7.42587e7	0.138967
$88$	1.40018e8	0.248893
$89$	3.83007e8	0.647071	0.323536	−	0.946216i	$-0.395128\pi$
$89$	3.83007e8	0.647071	0.323536	+	0.946216i	$0.395128\pi$
$90$	−3.80543e8	−0.611381
$91$	−1.38785e9	−2.12157
$92$	−1.22962e8	−0.178947
$93$	−8.84559e8	−1.22618
$94$	−9.87743e8	−1.30487
$95$	1.53027e9	1.92758
$96$	8.50530e8	1.02204
$97$	−1.30917e9	−1.50150	−0.750749	−	0.660588i	$-0.770307\pi$
$97$	−1.30917e9	−1.50150	−0.750749	+	0.660588i	$0.770307\pi$
$98$	−8.13243e8	−0.890642
$99$	−5.10191e8	−0.533795
$100$	1.46325e8	0.146325
$101$	7.12991e8	0.681770	0.340885	−	0.940105i	$-0.389273\pi$
$101$	7.12991e8	0.681770	0.340885	+	0.940105i	$0.389273\pi$
$102$	−2.21515e8	−0.202630
$103$	−1.75194e9	−1.53374	−0.766868	−	0.641804i	$-0.778186\pi$
$103$	−1.75194e9	−1.53374	−0.766868	+	0.641804i	$0.778186\pi$
$104$	−3.80487e8	−0.318926
$105$	−1.32576e9	−1.06442
$106$	7.70038e8	0.592428
$107$	7.39811e8	0.545625	0.272812	−	0.962067i	$-0.412046\pi$
$107$	7.39811e8	0.545625	0.272812	+	0.962067i	$0.412046\pi$
$108$	−1.31329e9	−0.928865
$109$	1.38272e9	0.938241	0.469121	−	0.883134i	$-0.344571\pi$
$109$	1.38272e9	0.938241	0.469121	+	0.883134i	$0.344571\pi$
$110$	2.91605e9	1.89901
$111$	1.48701e8	0.0929737
$112$	−2.40181e9	−1.44231
$113$	−1.52520e9	−0.879980	−0.439990	−	0.898003i	$-0.645018\pi$
$113$	−1.52520e9	−0.879980	−0.439990	+	0.898003i	$0.645018\pi$
$114$	3.35111e9	1.85830
$115$	4.23119e8	0.225591
$116$	3.03960e8	0.155868
$117$	1.38640e9	0.683993
$118$	4.87869e9	2.31651
$119$	5.46460e8	0.249803
$120$	−3.63466e8	−0.160010
$121$	1.55157e9	0.658019
$122$	−1.94718e9	−0.795770
$123$	−1.54937e9	−0.610353
$124$	−3.62073e9	−1.37530
$125$	2.44961e9	0.897432
$126$	2.05579e9	0.726625
$127$	9.65570e8	0.329357	0.164679	−	0.986347i	$-0.447341\pi$
$127$	9.65570e8	0.329357	0.164679	+	0.986347i	$0.447341\pi$
$128$	−1.16226e9	−0.382701
$129$	2.18220e9	0.693811
$130$	−7.92410e9	−2.43335
$131$	1.94940e9	0.578337	0.289168	−	0.957278i	$-0.406621\pi$
$131$	1.94940e9	0.578337	0.289168	+	0.957278i	$0.406621\pi$
$132$	2.94924e9	0.845528
$133$	−8.26691e9	−2.29092
$134$	−1.91700e9	−0.513631
$135$	4.51909e9	1.17098
$136$	1.49815e8	0.0375517
$137$	3.52100e9	0.853933	0.426966	−	0.904268i	$-0.359582\pi$
$137$	3.52100e9	0.853933	0.426966	+	0.904268i	$0.359582\pi$
$138$	9.26579e8	0.217484
$139$	−3.49722e9	−0.794615	−0.397307	−	0.917686i	$-0.630055\pi$
$139$	−3.49722e9	−0.794615	−0.397307	+	0.917686i	$0.630055\pi$
$140$	−5.42670e9	−1.19388
$141$	3.43757e9	0.732430
$142$	7.91267e9	1.63315
$143$	−1.06238e10	−2.12455
$144$	2.39930e9	0.465000
$145$	−1.04595e9	−0.196496
$146$	6.29442e9	1.14648
$147$	2.83027e9	0.499920
$148$	6.08672e8	0.104281
$149$	5.96700e9	0.991785	0.495893	−	0.868384i	$-0.334841\pi$
$149$	5.96700e9	0.991785	0.495893	+	0.868384i	$0.334841\pi$
$150$	−1.10263e9	−0.177836
$151$	8.99763e9	1.40842	0.704210	−	0.709992i	$-0.251301\pi$
$151$	8.99763e9	1.40842	0.704210	+	0.709992i	$0.251301\pi$
$152$	−2.26642e9	−0.344385
$153$	−5.45888e8	−0.0805364
$154$	−1.57532e10	−2.25697
$155$	1.24591e10	1.73379
$156$	−8.01431e9	−1.08344
$157$	2.13347e9	0.280246	0.140123	−	0.990134i	$-0.455250\pi$
$157$	2.13347e9	0.280246	0.140123	+	0.990134i	$0.455250\pi$
$158$	−1.01392e10	−1.29434
$159$	−2.67991e9	−0.332532
$160$	−1.19798e10	−1.44514
$161$	−2.28579e9	−0.268115
$162$	4.94240e9	0.563794
$163$	1.19012e10	1.32052	0.660260	−	0.751037i	$-0.270446\pi$
$163$	1.19012e10	1.32052	0.660260	+	0.751037i	$0.270446\pi$
$164$	−6.34197e9	−0.684584
$165$	−1.01485e10	−1.06592
$166$	−1.49243e9	−0.152549
$167$	−1.32685e10	−1.32007	−0.660036	−	0.751234i	$-0.729459\pi$
$167$	−1.32685e10	−1.32007	−0.660036	+	0.751234i	$0.729459\pi$
$168$	1.96353e9	0.190172
$169$	1.82647e10	1.72235
$170$	3.12008e9	0.286513
$171$	8.25826e9	0.738594
$172$	8.93232e9	0.778191
$173$	−1.98416e10	−1.68411	−0.842055	−	0.539392i	$-0.818654\pi$
$173$	−1.98416e10	−1.68411	−0.842055	+	0.539392i	$0.818654\pi$
$174$	−2.29049e9	−0.189434
$175$	2.72010e9	0.219237
$176$	−1.83855e10	−1.44434
$177$	−1.69790e10	−1.30026
$178$	−1.18138e10	−0.882061
$179$	3.98356e9	0.290023	0.145012	−	0.989430i	$-0.453678\pi$
$179$	3.98356e9	0.290023	0.145012	+	0.989430i	$0.453678\pi$
$180$	5.42102e9	0.384906
$181$	7.20984e9	0.499312	0.249656	−	0.968335i	$-0.419682\pi$
$181$	7.20984e9	0.499312	0.249656	+	0.968335i	$0.419682\pi$
$182$	4.28080e10	2.89203
$183$	6.77665e9	0.446668
$184$	−6.26663e8	−0.0403045
$185$	−2.09448e9	−0.131463
$186$	2.72840e10	1.67148
$187$	4.18306e9	0.250154
$188$	1.40709e10	0.821507
$189$	−2.44133e10	−1.39171
$190$	−4.72009e10	−2.62760
$191$	−4.03655e9	−0.219463	−0.109731	−	0.993961i	$-0.534999\pi$
$191$	−4.03655e9	−0.219463	−0.109731	+	0.993961i	$0.534999\pi$
$192$	−1.00732e10	−0.534950
$193$	−4.56100e9	−0.236621	−0.118310	−	0.992977i	$-0.537748\pi$
$193$	−4.56100e9	−0.236621	−0.118310	+	0.992977i	$0.537748\pi$
$194$	4.03811e10	2.04678
$195$	2.75777e10	1.36585
$196$	1.15851e10	0.560720
$197$	2.56978e10	1.21562	0.607810	−	0.794082i	$-0.292048\pi$
$197$	2.56978e10	1.21562	0.607810	+	0.794082i	$0.292048\pi$
$198$	1.57367e10	0.727647
$199$	−2.13186e10	−0.963652	−0.481826	−	0.876267i	$-0.660026\pi$
$199$	−2.13186e10	−0.963652	−0.481826	+	0.876267i	$0.660026\pi$
$200$	7.45730e8	0.0329569
$201$	6.67162e9	0.288303
$202$	−2.19920e10	−0.929361
$203$	5.65046e9	0.233535
$204$	3.15560e9	0.127569
$205$	2.18231e10	0.863025
$206$	5.40381e10	2.09073
$207$	2.28340e9	0.0864402
$208$	4.99610e10	1.85074
$209$	−6.32819e10	−2.29415
$210$	4.08929e10	1.45098
$211$	−2.89183e10	−1.00439	−0.502194	−	0.864755i	$-0.667474\pi$
$211$	−2.89183e10	−1.00439	−0.502194	+	0.864755i	$0.667474\pi$
$212$	−1.09696e10	−0.372974
$213$	−2.75379e10	−0.916691
$214$	−2.28193e10	−0.743773
$215$	−3.07366e10	−0.981032
$216$	−6.69303e9	−0.209209
$217$	−6.73074e10	−2.06060
$218$	−4.26496e10	−1.27897
$219$	−2.19060e10	−0.643525
$220$	−4.15406e10	−1.19556
$221$	−1.13671e10	−0.320542
$222$	−4.58664e9	−0.126738
$223$	−5.09347e10	−1.37925	−0.689623	−	0.724169i	$-0.742224\pi$
$223$	−5.09347e10	−1.37925	−0.689623	+	0.724169i	$0.742224\pi$
$224$	6.47181e10	1.71755
$225$	−2.71725e9	−0.0706820
$226$	4.70443e10	1.19955
$227$	5.52689e10	1.38154	0.690771	−	0.723074i	$-0.257271\pi$
$227$	5.52689e10	1.38154	0.690771	+	0.723074i	$0.257271\pi$
$228$	−4.77382e10	−1.16993
$229$	3.51572e10	0.844802	0.422401	−	0.906409i	$-0.361187\pi$
$229$	3.51572e10	0.844802	0.422401	+	0.906409i	$0.361187\pi$
$230$	−1.30510e10	−0.307517
$231$	5.48248e10	1.26684
$232$	1.54910e9	0.0351062
$233$	−9.27636e9	−0.206194	−0.103097	−	0.994671i	$-0.532875\pi$
$233$	−9.27636e9	−0.206194	−0.103097	+	0.994671i	$0.532875\pi$
$234$	−4.27631e10	−0.932391
$235$	−4.84187e10	−1.03564
$236$	−6.94993e10	−1.45840
$237$	3.52868e10	0.726516
$238$	−1.68554e10	−0.340521
$239$	6.01062e10	1.19159	0.595797	−	0.803135i	$-0.296836\pi$
$239$	6.01062e10	1.19159	0.595797	+	0.803135i	$0.296836\pi$
$240$	4.77259e10	0.928546
$241$	−5.94000e10	−1.13425	−0.567127	−	0.823631i	$-0.691945\pi$
$241$	−5.94000e10	−1.13425	−0.567127	+	0.823631i	$0.691945\pi$
$242$	−4.78579e10	−0.896984
$243$	4.16283e10	0.765879
$244$	2.77386e10	0.500992
$245$	−3.98648e10	−0.706875
$246$	4.77898e10	0.832008
$247$	1.71963e11	2.93967
$248$	−1.84527e10	−0.309761
$249$	5.19401e9	0.0856260
$250$	−7.55576e10	−1.22334
$251$	5.13306e9	0.0816290	0.0408145	−	0.999167i	$-0.487005\pi$
$251$	5.13306e9	0.0816290	0.0408145	+	0.999167i	$0.487005\pi$
$252$	−2.92857e10	−0.457460
$253$	−1.74974e10	−0.268492
$254$	−2.97828e10	−0.448966
$255$	−1.08586e10	−0.160821
$256$	8.38948e10	1.22083
$257$	5.34931e10	0.764890	0.382445	−	0.923978i	$-0.375082\pi$
$257$	5.34931e10	0.764890	0.382445	+	0.923978i	$0.375082\pi$
$258$	−6.73095e10	−0.945774
$259$	1.13149e10	0.156243
$260$	1.12883e11	1.53196
$261$	−5.64454e9	−0.0752916
$262$	−6.01289e10	−0.788365
$263$	−3.09318e10	−0.398662	−0.199331	−	0.979932i	$-0.563877\pi$
$263$	−3.09318e10	−0.398662	−0.199331	+	0.979932i	$0.563877\pi$
$264$	1.50305e10	0.190439
$265$	3.77469e10	0.470192
$266$	2.54991e11	3.12289
$267$	4.11147e10	0.495104
$268$	2.73087e10	0.323366
$269$	2.97228e10	0.346102	0.173051	−	0.984913i	$-0.444637\pi$
$269$	2.97228e10	0.346102	0.173051	+	0.984913i	$0.444637\pi$
$270$	−1.39390e11	−1.59623
$271$	1.03974e11	1.17101	0.585506	−	0.810668i	$-0.300896\pi$
$271$	1.03974e11	1.17101	0.585506	+	0.810668i	$0.300896\pi$
$272$	−1.96719e10	−0.217914
$273$	−1.48982e11	−1.62331
$274$	−1.08604e11	−1.16405
$275$	2.08219e10	0.219545
$276$	−1.31996e10	−0.136921
$277$	5.29947e10	0.540846	0.270423	−	0.962742i	$-0.412836\pi$
$277$	5.29947e10	0.540846	0.270423	+	0.962742i	$0.412836\pi$
$278$	1.07871e11	1.08319
$279$	6.72370e10	0.664338
$280$	−2.76566e10	−0.268898
$281$	−9.52085e10	−0.910956	−0.455478	−	0.890247i	$-0.650532\pi$
$281$	−9.52085e10	−0.910956	−0.455478	+	0.890247i	$0.650532\pi$
$282$	−1.06031e11	−0.998418
$283$	−2.15252e11	−1.99484	−0.997421	−	0.0717716i	$-0.977135\pi$
$283$	−2.15252e11	−1.99484	−0.997421	+	0.0717716i	$0.977135\pi$
$284$	−1.12720e11	−1.02818
$285$	1.64270e11	1.47488
$286$	3.27688e11	2.89610
$287$	−1.17894e11	−1.02570
$288$	−6.46504e10	−0.553738
$289$	−1.14112e11	−0.962258
$290$	3.22619e10	0.267855
$291$	−1.40536e11	−1.14886
$292$	−8.96671e10	−0.721789
$293$	5.00648e10	0.396852	0.198426	−	0.980116i	$-0.436417\pi$
$293$	5.00648e10	0.396852	0.198426	+	0.980116i	$0.436417\pi$
$294$	−8.72991e10	−0.681470
$295$	2.39151e11	1.83854
$296$	3.10203e9	0.0234873
$297$	−1.86880e11	−1.39366
$298$	−1.84051e11	−1.35196
$299$	4.75476e10	0.344040
$300$	1.57075e10	0.111960
$301$	1.66047e11	1.16595
$302$	−2.77530e11	−1.91990
$303$	7.65374e10	0.521653
$304$	2.97599e11	1.99848
$305$	−9.54501e10	−0.631578
$306$	1.68378e10	0.109784
$307$	1.06334e11	0.683203	0.341602	−	0.939845i	$-0.389031\pi$
$307$	1.06334e11	0.683203	0.341602	+	0.939845i	$0.389031\pi$
$308$	2.24412e11	1.42092
$309$	−1.88065e11	−1.17353
$310$	−3.84299e11	−2.36343
$311$	3.14691e10	0.190749	0.0953747	−	0.995441i	$-0.469595\pi$
$311$	3.14691e10	0.190749	0.0953747	+	0.995441i	$0.469595\pi$
$312$	−4.08441e10	−0.244025
$313$	2.55558e11	1.50501	0.752507	−	0.658584i	$-0.228844\pi$
$313$	2.55558e11	1.50501	0.752507	+	0.658584i	$0.228844\pi$
$314$	−6.58065e10	−0.382019
$315$	1.00774e11	0.576700
$316$	1.44438e11	0.814874
$317$	−1.86544e11	−1.03756	−0.518781	−	0.854907i	$-0.673614\pi$
$317$	−1.86544e11	−1.03756	−0.518781	+	0.854907i	$0.673614\pi$
$318$	8.26612e10	0.453294
$319$	4.32533e10	0.233863
$320$	1.41883e11	0.756406
$321$	7.94165e10	0.417482
$322$	7.05048e10	0.365483
$323$	−6.77096e10	−0.346130
$324$	−7.04070e10	−0.354947
$325$	−5.65818e10	−0.281321
$326$	−3.67088e11	−1.80008
$327$	1.48431e11	0.717891
$328$	−3.23212e10	−0.154190
$329$	2.61570e11	1.23085
$330$	3.13029e11	1.45302
$331$	−1.47374e11	−0.674829	−0.337414	−	0.941356i	$-0.609552\pi$
$331$	−1.47374e11	−0.674829	−0.337414	+	0.941356i	$0.609552\pi$
$332$	2.12605e10	0.0960398
$333$	−1.13030e10	−0.0503728
$334$	4.09264e11	1.79947
$335$	−9.39708e10	−0.407653
$336$	−2.57827e11	−1.10358
$337$	−2.59383e11	−1.09549	−0.547744	−	0.836646i	$-0.684513\pi$
$337$	−2.59383e11	−1.09549	−0.547744	+	0.836646i	$0.684513\pi$
$338$	−5.63370e11	−2.34784
$339$	−1.63725e11	−0.673313
$340$	−4.44471e10	−0.180380
$341$	−5.15228e11	−2.06350
$342$	−2.54724e11	−1.00682
$343$	−1.14256e11	−0.445713
$344$	4.55227e10	0.175273
$345$	4.54205e10	0.172610
$346$	6.12011e11	2.29571
$347$	−3.73463e11	−1.38282	−0.691409	−	0.722464i	$-0.743010\pi$
$347$	−3.73463e11	−1.38282	−0.691409	+	0.722464i	$0.743010\pi$
$348$	3.26292e10	0.119261
$349$	1.64303e11	0.592831	0.296416	−	0.955059i	$-0.404209\pi$
$349$	1.64303e11	0.592831	0.296416	+	0.955059i	$0.404209\pi$
$350$	−8.39009e10	−0.298855
$351$	5.07829e11	1.78581
$352$	4.95407e11	1.71997
$353$	−4.50663e10	−0.154478	−0.0772389	−	0.997013i	$-0.524610\pi$
$353$	−4.50663e10	−0.154478	−0.0772389	+	0.997013i	$0.524610\pi$
$354$	5.23712e11	1.77247
$355$	3.87876e11	1.29618
$356$	1.68293e11	0.555318
$357$	5.86608e10	0.191135
$358$	−1.22872e11	−0.395348
$359$	1.52508e11	0.484583	0.242292	−	0.970203i	$-0.422101\pi$
$359$	1.52508e11	0.484583	0.242292	+	0.970203i	$0.422101\pi$
$360$	2.76277e10	0.0866928
$361$	7.01631e11	2.17433
$362$	−2.22386e11	−0.680642
$363$	1.66557e11	0.503480
$364$	−6.09821e11	−1.82073
$365$	3.08550e11	0.909928
$366$	−2.09024e11	−0.608880
$367$	1.05863e10	0.0304611	0.0152306	−	0.999884i	$-0.495152\pi$
$367$	1.05863e10	0.0304611	0.0152306	+	0.999884i	$0.495152\pi$
$368$	8.22858e10	0.233889
$369$	1.17770e11	0.330687
$370$	6.46036e10	0.179204
$371$	−2.03918e11	−0.558822
$372$	−3.88675e11	−1.05231
$373$	−5.10153e11	−1.36462	−0.682308	−	0.731065i	$-0.739024\pi$
$373$	−5.10153e11	−1.36462	−0.682308	+	0.731065i	$0.739024\pi$
$374$	−1.29026e11	−0.340999
$375$	2.62958e11	0.686666
$376$	7.17109e10	0.185029
$377$	−1.17537e11	−0.299667
$378$	7.53021e11	1.89712
$379$	−4.38707e11	−1.09219	−0.546096	−	0.837723i	$-0.683886\pi$
$379$	−4.38707e11	−1.09219	−0.546096	+	0.837723i	$0.683886\pi$
$380$	6.72400e11	1.65425
$381$	1.03651e11	0.252006
$382$	1.24506e11	0.299162
$383$	6.57734e11	1.56191	0.780954	−	0.624588i	$-0.214733\pi$
$383$	6.57734e11	1.56191	0.780954	+	0.624588i	$0.214733\pi$
$384$	−1.24765e11	−0.292822
$385$	−7.72216e11	−1.79129
$386$	1.40683e11	0.322551
$387$	−1.65873e11	−0.375904
$388$	−5.75250e11	−1.28859
$389$	−7.13273e9	−0.0157937	−0.00789683	−	0.999969i	$-0.502514\pi$
$389$	−7.13273e9	−0.0157937	−0.00789683	+	0.999969i	$0.502514\pi$
$390$	−8.50628e11	−1.86187
$391$	−1.87216e10	−0.0405087
$392$	5.90421e10	0.126292
$393$	2.09262e11	0.442512
$394$	−7.92643e11	−1.65708
$395$	−4.97020e11	−1.02728
$396$	−2.24177e11	−0.458104
$397$	−3.45715e11	−0.698491	−0.349245	−	0.937031i	$-0.613562\pi$
$397$	−3.45715e11	−0.698491	−0.349245	+	0.937031i	$0.613562\pi$
$398$	6.57567e11	1.31361
$399$	−8.87427e11	−1.75289
$400$	−9.79203e10	−0.191251
$401$	−3.99254e11	−0.771081	−0.385541	−	0.922691i	$-0.625985\pi$
$401$	−3.99254e11	−0.771081	−0.385541	+	0.922691i	$0.625985\pi$
$402$	−2.05785e11	−0.393003
$403$	1.40009e12	2.64412
$404$	3.13288e11	0.585096
$405$	2.42274e11	0.447466
$406$	−1.74287e11	−0.318345
$407$	8.66136e10	0.156463
$408$	1.60822e10	0.0287325
$409$	1.29944e11	0.229616	0.114808	−	0.993388i	$-0.463375\pi$
$409$	1.29944e11	0.229616	0.114808	+	0.993388i	$0.463375\pi$
$410$	−6.73127e11	−1.17644
$411$	3.77969e11	0.653383
$412$	−7.69800e11	−1.31626
$413$	−1.29195e12	−2.18510
$414$	−7.04310e10	−0.117832
$415$	−7.31584e10	−0.121073
$416$	−1.34622e12	−2.20393
$417$	−3.75416e11	−0.607996
$418$	1.95191e12	3.12729
$419$	3.73452e11	0.591932	0.295966	−	0.955198i	$-0.404358\pi$
$419$	3.73452e11	0.591932	0.295966	+	0.955198i	$0.404358\pi$
$420$	−5.82540e11	−0.913490
$421$	−1.45691e11	−0.226028	−0.113014	−	0.993593i	$-0.536050\pi$
$421$	−1.45691e11	−0.226028	−0.113014	+	0.993593i	$0.536050\pi$
$422$	8.91977e11	1.36914
$423$	−2.61296e11	−0.396827
$424$	−5.59053e10	−0.0840053
$425$	2.22788e10	0.0331239
$426$	8.49401e11	1.24960
$427$	5.15645e11	0.750629
$428$	3.25073e11	0.468256
$429$	−1.14043e12	−1.62559
$430$	9.48064e11	1.33730
$431$	5.80632e11	0.810500	0.405250	−	0.914206i	$-0.367185\pi$
$431$	5.80632e11	0.810500	0.405250	+	0.914206i	$0.367185\pi$
$432$	8.78847e11	1.21405
$433$	−6.08311e11	−0.831630	−0.415815	−	0.909449i	$-0.636504\pi$
$433$	−6.08311e11	−0.831630	−0.415815	+	0.909449i	$0.636504\pi$
$434$	2.07608e12	2.80893
$435$	−1.12279e11	−0.150348
$436$	6.07566e11	0.805200
$437$	2.83223e11	0.371503
$438$	6.75686e11	0.877226
$439$	−5.82957e11	−0.749112	−0.374556	−	0.927204i	$-0.622205\pi$
$439$	−5.82957e11	−0.749112	−0.374556	+	0.927204i	$0.622205\pi$
$440$	−2.11707e11	−0.269276
$441$	−2.15134e11	−0.270855
$442$	3.50616e11	0.436949
$443$	−1.00231e12	−1.23647	−0.618236	−	0.785993i	$-0.712152\pi$
$443$	−1.00231e12	−1.23647	−0.618236	+	0.785993i	$0.712152\pi$
$444$	6.53391e10	0.0797902
$445$	−5.79106e11	−0.700065
$446$	1.57107e12	1.88013
$447$	6.40539e11	0.758860
$448$	−7.66486e11	−0.898987
$449$	1.20795e12	1.40262	0.701310	−	0.712856i	$-0.252599\pi$
$449$	1.20795e12	1.40262	0.701310	+	0.712856i	$0.252599\pi$
$450$	8.38130e10	0.0963508
$451$	−9.02457e11	−1.02715
$452$	−6.70170e11	−0.755201
$453$	9.65868e11	1.07765
$454$	−1.70475e12	−1.88326
$455$	2.09843e12	2.29532
$456$	−2.43293e11	−0.263504
$457$	−7.50878e11	−0.805280	−0.402640	−	0.915359i	$-0.631907\pi$
$457$	−7.50878e11	−0.805280	−0.402640	+	0.915359i	$0.631907\pi$
$458$	−1.08442e12	−1.15160
$459$	−1.99955e11	−0.210269
$460$	1.85918e11	0.193603
$461$	−2.16766e11	−0.223531	−0.111765	−	0.993735i	$-0.535651\pi$
$461$	−2.16766e11	−0.223531	−0.111765	+	0.993735i	$0.535651\pi$
$462$	−1.69106e12	−1.72691
$463$	4.99175e11	0.504822	0.252411	−	0.967620i	$-0.418776\pi$
$463$	4.99175e11	0.504822	0.252411	+	0.967620i	$0.418776\pi$
$464$	−2.03409e11	−0.203723
$465$	1.33745e12	1.32660
$466$	2.86127e11	0.281075
$467$	−1.29887e12	−1.26369	−0.631844	−	0.775096i	$-0.717702\pi$
$467$	−1.29887e12	−1.26369	−0.631844	+	0.775096i	$0.717702\pi$
$468$	6.09183e11	0.587004
$469$	5.07653e11	0.484495
$470$	1.49346e12	1.41174
$471$	2.29022e11	0.214429
$472$	−3.54196e11	−0.328477
$473$	1.27106e12	1.16759
$474$	−1.08841e12	−0.990356
$475$	−3.37036e11	−0.303778
$476$	2.40114e11	0.214381
$477$	2.03705e11	0.180164
$478$	−1.85396e12	−1.62433
$479$	−1.45321e12	−1.26130	−0.630651	−	0.776067i	$-0.717212\pi$
$479$	−1.45321e12	−1.26130	−0.630651	+	0.776067i	$0.717212\pi$
$480$	−1.28600e12	−1.10575
$481$	−2.35365e11	−0.200488
$482$	1.83218e12	1.54617
$483$	−2.45373e11	−0.205147
$484$	6.81761e11	0.564713
$485$	1.97947e12	1.62447
$486$	−1.28401e12	−1.04401
$487$	−1.98895e12	−1.60230	−0.801151	−	0.598462i	$-0.795779\pi$
$487$	−1.98895e12	−1.60230	−0.801151	+	0.598462i	$0.795779\pi$
$488$	1.41367e11	0.112839
$489$	1.27755e12	1.01039
$490$	1.22962e12	0.963583
$491$	−1.28668e11	−0.0999091	−0.0499545	−	0.998751i	$-0.515908\pi$
$491$	−1.28668e11	−0.0999091	−0.0499545	+	0.998751i	$0.515908\pi$
$492$	−6.80791e11	−0.523806
$493$	4.62797e10	0.0352841
$494$	−5.30416e12	−4.00724
$495$	7.71407e11	0.577511
$496$	2.42298e12	1.79756
$497$	−2.09540e12	−1.54051
$498$	−1.60208e11	−0.116722
$499$	−1.92929e12	−1.39298	−0.696489	−	0.717567i	$-0.745256\pi$
$499$	−1.92929e12	−1.39298	−0.696489	+	0.717567i	$0.745256\pi$
$500$	1.07636e12	0.770177
$501$	−1.42433e12	−1.01005
$502$	−1.58328e11	−0.111273
$503$	−1.02855e12	−0.716426	−0.358213	−	0.933640i	$-0.616614\pi$
$503$	−1.02855e12	−0.716426	−0.358213	+	0.933640i	$0.616614\pi$
$504$	−1.49252e11	−0.103034
$505$	−1.07804e12	−0.737605
$506$	5.39703e11	0.365997
$507$	1.96066e12	1.31785
$508$	4.24271e11	0.282655
$509$	2.42776e12	1.60316	0.801579	−	0.597889i	$-0.203994\pi$
$509$	2.42776e12	1.60316	0.801579	+	0.597889i	$0.203994\pi$
$510$	3.34931e11	0.219224
$511$	−1.66686e12	−1.08145
$512$	−1.99264e12	−1.28148
$513$	3.02495e12	1.92837
$514$	−1.64998e12	−1.04267
$515$	2.64892e12	1.65935
$516$	9.58858e11	0.595430
$517$	2.00228e12	1.23258
$518$	−3.49005e11	−0.212984
$519$	−2.12994e12	−1.28859
$520$	5.75296e11	0.345045
$521$	2.25865e12	1.34301	0.671505	−	0.741000i	$-0.265648\pi$
$521$	2.25865e12	1.34301	0.671505	+	0.741000i	$0.265648\pi$
$522$	1.74105e11	0.102634
$523$	5.02701e11	0.293800	0.146900	−	0.989151i	$-0.453070\pi$
$523$	5.02701e11	0.293800	0.146900	+	0.989151i	$0.453070\pi$
$524$	8.56566e11	0.496330
$525$	2.91995e11	0.167748
$526$	9.54085e11	0.543439
$527$	−5.51277e11	−0.311331
$528$	−1.97363e12	−1.10513
$529$	7.83110e10	0.0434783
$530$	−1.16430e12	−0.640946
$531$	1.29060e12	0.704477
$532$	−3.63247e12	−1.96608
$533$	2.45235e12	1.31616
$534$	−1.26817e12	−0.674905
$535$	−1.11859e12	−0.590310
$536$	1.39176e11	0.0728321
$537$	4.27623e11	0.221910
$538$	−9.16791e11	−0.471792
$539$	1.64854e12	0.841301
$540$	1.98569e12	1.00494
$541$	−2.34334e12	−1.17611	−0.588054	−	0.808822i	$-0.700106\pi$
$541$	−2.34334e12	−1.17611	−0.588054	+	0.808822i	$0.700106\pi$
$542$	−3.20704e12	−1.59627
$543$	7.73954e11	0.382046
$544$	5.30069e11	0.259500
$545$	−2.09067e12	−1.01508
$546$	4.59530e12	2.21283
$547$	1.20584e11	0.0575901	0.0287951	−	0.999585i	$-0.490833\pi$
$547$	1.20584e11	0.0575901	0.0287951	+	0.999585i	$0.490833\pi$
$548$	1.54713e12	0.732847
$549$	−5.15105e11	−0.242003
$550$	−6.42248e11	−0.299275
$551$	−7.00125e11	−0.323589
$552$	−6.72703e10	−0.0308388
$553$	2.68503e12	1.22092
$554$	−1.63461e12	−0.737259
$555$	−2.24835e11	−0.100588
$556$	−1.53668e12	−0.681940
$557$	1.16218e12	0.511594	0.255797	−	0.966730i	$-0.417662\pi$
$557$	1.16218e12	0.511594	0.255797	+	0.966730i	$0.417662\pi$
$558$	−2.07391e12	−0.905598
$559$	−3.45400e12	−1.49613
$560$	3.63153e12	1.56043
$561$	4.49039e11	0.191404
$562$	2.93668e12	1.24178
$563$	−1.59915e12	−0.670814	−0.335407	−	0.942073i	$-0.608874\pi$
$563$	−1.59915e12	−0.670814	−0.335407	+	0.942073i	$0.608874\pi$
$564$	1.51047e12	0.628573
$565$	2.30609e12	0.952048
$566$	6.63940e12	2.71929
$567$	−1.30883e12	−0.531812
$568$	−5.74466e11	−0.231578
$569$	−3.16764e12	−1.26686	−0.633432	−	0.773798i	$-0.718354\pi$
$569$	−3.16764e12	−1.26686	−0.633432	+	0.773798i	$0.718354\pi$
$570$	−5.06687e12	−2.01049
$571$	1.10661e12	0.435646	0.217823	−	0.975988i	$-0.430105\pi$
$571$	1.10661e12	0.435646	0.217823	+	0.975988i	$0.430105\pi$
$572$	−4.66808e12	−1.82329
$573$	−4.33311e11	−0.167921
$574$	3.63640e12	1.39820
$575$	−9.31903e10	−0.0355521
$576$	7.65684e11	0.289833
$577$	2.78776e12	1.04704	0.523522	−	0.852012i	$-0.324618\pi$
$577$	2.78776e12	1.04704	0.523522	+	0.852012i	$0.324618\pi$
$578$	3.51976e12	1.31171
$579$	−4.89610e11	−0.181049
$580$	−4.59588e11	−0.168633
$581$	3.95220e11	0.143895
$582$	4.33479e12	1.56608
$583$	−1.56096e12	−0.559608
$584$	−4.56979e11	−0.162569
$585$	−2.09623e12	−0.740011
$586$	−1.54424e12	−0.540972
$587$	−4.17897e12	−1.45277	−0.726387	−	0.687286i	$-0.758802\pi$
$587$	−4.17897e12	−1.45277	−0.726387	+	0.687286i	$0.758802\pi$
$588$	1.24362e12	0.429032
$589$	8.33978e12	2.85520
$590$	−7.37656e12	−2.50622
$591$	2.75858e12	0.930127
$592$	−4.07322e11	−0.136298
$593$	−9.14891e11	−0.303825	−0.151912	−	0.988394i	$-0.548543\pi$
$593$	−9.14891e11	−0.303825	−0.151912	+	0.988394i	$0.548543\pi$
$594$	5.76426e12	1.89978
$595$	−8.26246e11	−0.270261
$596$	2.62189e12	0.851152
$597$	−2.28849e12	−0.737334
$598$	−1.46659e12	−0.468981
$599$	8.46317e11	0.268604	0.134302	−	0.990940i	$-0.457121\pi$
$599$	8.46317e11	0.268604	0.134302	+	0.990940i	$0.457121\pi$
$600$	8.00519e10	0.0252169
$601$	−2.78743e12	−0.871504	−0.435752	−	0.900067i	$-0.643517\pi$
$601$	−2.78743e12	−0.871504	−0.435752	+	0.900067i	$0.643517\pi$
$602$	−5.12168e12	−1.58938
$603$	−5.07122e11	−0.156201
$604$	3.95355e12	1.20871
$605$	−2.34598e12	−0.711909
$606$	−2.36078e12	−0.711096
$607$	2.71231e12	0.810942	0.405471	−	0.914108i	$-0.367107\pi$
$607$	2.71231e12	0.810942	0.405471	+	0.914108i	$0.367107\pi$
$608$	−8.01895e12	−2.37986
$609$	6.06559e11	0.178688
$610$	2.94414e12	0.860941
$611$	−5.44101e12	−1.57941
$612$	−2.39863e11	−0.0691164
$613$	−3.09012e12	−0.883900	−0.441950	−	0.897040i	$-0.645713\pi$
$613$	−3.09012e12	−0.883900	−0.441950	+	0.897040i	$0.645713\pi$
$614$	−3.27985e12	−0.931314
$615$	2.34264e12	0.660340
$616$	1.14369e12	0.320035
$617$	2.36828e12	0.657884	0.328942	−	0.944350i	$-0.393308\pi$
$617$	2.36828e12	0.657884	0.328942	+	0.944350i	$0.393308\pi$
$618$	5.80082e12	1.59971
$619$	1.79919e12	0.492571	0.246285	−	0.969197i	$-0.420790\pi$
$619$	1.79919e12	0.492571	0.246285	+	0.969197i	$0.420790\pi$
$620$	5.47454e12	1.48794
$621$	8.36395e11	0.225683
$622$	−9.70658e11	−0.260022
$623$	3.12848e12	0.832026
$624$	5.36316e12	1.41609
$625$	−4.35421e12	−1.14143
$626$	−7.88264e12	−2.05157
$627$	−6.79312e12	−1.75536
$628$	9.37447e11	0.240507
$629$	9.26737e10	0.0236063
$630$	−3.10834e12	−0.786134
$631$	9.02196e11	0.226553	0.113276	−	0.993564i	$-0.463865\pi$
$631$	9.02196e11	0.226553	0.113276	+	0.993564i	$0.463865\pi$
$632$	7.36114e11	0.183535
$633$	−3.10429e12	−0.768503
$634$	5.75390e12	1.41436
$635$	−1.45994e12	−0.356331
$636$	−1.17755e12	−0.285379
$637$	−4.47978e12	−1.07803
$638$	−1.33414e12	−0.318792
$639$	2.09321e12	0.496659
$640$	1.75734e12	0.414043
$641$	−1.82621e12	−0.427257	−0.213628	−	0.976915i	$-0.568528\pi$
$641$	−1.82621e12	−0.427257	−0.213628	+	0.976915i	$0.568528\pi$
$642$	−2.44958e12	−0.569094
$643$	9.49494e11	0.219050	0.109525	−	0.993984i	$-0.465067\pi$
$643$	9.49494e11	0.219050	0.109525	+	0.993984i	$0.465067\pi$
$644$	−1.00438e12	−0.230096
$645$	−3.29948e12	−0.750632
$646$	2.08849e12	0.471830
$647$	6.67470e12	1.49749	0.748743	−	0.662861i	$-0.230658\pi$
$647$	6.67470e12	1.49749	0.748743	+	0.662861i	$0.230658\pi$
$648$	−3.58822e11	−0.0799450
$649$	−9.88970e12	−2.18818
$650$	1.74525e12	0.383485
$651$	−7.22524e12	−1.57666
$652$	5.22936e12	1.13327
$653$	−7.39612e11	−0.159182	−0.0795911	−	0.996828i	$-0.525361\pi$
$653$	−7.39612e11	−0.159182	−0.0795911	+	0.996828i	$0.525361\pi$
$654$	−4.57831e12	−0.978600
$655$	−2.94749e12	−0.625701
$656$	4.24403e12	0.894768
$657$	1.66512e12	0.348659
$658$	−8.06807e12	−1.67785
$659$	8.86589e11	0.183121	0.0915604	−	0.995800i	$-0.470815\pi$
$659$	8.86589e11	0.183121	0.0915604	+	0.995800i	$0.470815\pi$
$660$	−4.45925e12	−0.914775
$661$	7.25610e12	1.47842	0.739208	−	0.673477i	$-0.235200\pi$
$661$	7.25610e12	1.47842	0.739208	+	0.673477i	$0.235200\pi$
$662$	4.54570e12	0.919899
$663$	−1.22022e12	−0.245261
$664$	1.08352e11	0.0216311
$665$	1.24995e13	2.47855
$666$	3.48639e11	0.0686661
$667$	−1.93584e11	−0.0378707
$668$	−5.83017e12	−1.13289
$669$	−5.46768e12	−1.05532
$670$	2.89851e12	0.555696
$671$	3.94718e12	0.751685
$672$	6.94729e12	1.31418
$673$	−1.58003e12	−0.296891	−0.148446	−	0.988921i	$-0.547427\pi$
$673$	−1.58003e12	−0.296891	−0.148446	+	0.988921i	$0.547427\pi$
$674$	8.00062e12	1.49332
$675$	−9.95312e11	−0.184541
$676$	8.02550e12	1.47813
$677$	8.13932e12	1.48915	0.744576	−	0.667537i	$-0.232652\pi$
$677$	8.13932e12	1.48915	0.744576	+	0.667537i	$0.232652\pi$
$678$	5.05007e12	0.917832
$679$	−1.06936e13	−1.93067
$680$	−2.26520e11	−0.0406271
$681$	5.93294e12	1.05708
$682$	1.58921e13	2.81288
$683$	3.15353e12	0.554502	0.277251	−	0.960798i	$-0.410577\pi$
$683$	3.15353e12	0.554502	0.277251	+	0.960798i	$0.410577\pi$
$684$	3.62867e12	0.633863
$685$	−5.32375e12	−0.923868
$686$	3.52420e12	0.607578
$687$	3.77402e12	0.646397
$688$	−5.97749e12	−1.01712
$689$	4.24178e12	0.717070
$690$	−1.40098e12	−0.235295
$691$	5.23590e12	0.873655	0.436827	−	0.899545i	$-0.356102\pi$
$691$	5.23590e12	0.873655	0.436827	+	0.899545i	$0.356102\pi$
$692$	−8.71841e12	−1.44531
$693$	−4.16733e12	−0.686371
$694$	1.15194e13	1.88500
$695$	5.28779e12	0.859692
$696$	1.66291e11	0.0268614
$697$	−9.65600e11	−0.154971
$698$	−5.06789e12	−0.808123
$699$	−9.95789e11	−0.157768
$700$	1.19521e12	0.188150
$701$	8.92354e12	1.39575	0.697873	−	0.716222i	$-0.254130\pi$
$701$	8.92354e12	1.39575	0.697873	+	0.716222i	$0.254130\pi$
$702$	−1.56639e13	−2.43434
$703$	−1.40198e12	−0.216492
$704$	−5.86733e12	−0.900251
$705$	−5.19760e12	−0.792414
$706$	1.39006e12	0.210578
$707$	5.82385e12	0.876643
$708$	−7.46054e12	−1.11589
$709$	−2.37434e12	−0.352887	−0.176444	−	0.984311i	$-0.556459\pi$
$709$	−2.37434e12	−0.352887	−0.176444	+	0.984311i	$0.556459\pi$
$710$	−1.19639e13	−1.76690
$711$	−2.68222e12	−0.393623
$712$	8.57689e11	0.125075
$713$	2.30594e12	0.334153
$714$	−1.80938e12	−0.260548
$715$	1.60631e13	2.29855
$716$	1.75037e12	0.248899
$717$	6.45221e12	0.911743
$718$	−4.70408e12	−0.660564
$719$	−7.91166e12	−1.10405	−0.552024	−	0.833828i	$-0.686144\pi$
$719$	−7.91166e12	−1.10405	−0.552024	+	0.833828i	$0.686144\pi$
$720$	−3.62773e12	−0.503082
$721$	−1.43101e13	−1.97213
$722$	−2.16416e13	−2.96396
$723$	−6.37641e12	−0.867869
$724$	3.16800e12	0.428510
$725$	2.30365e11	0.0309668
$726$	−5.13740e12	−0.686324
$727$	−1.14801e13	−1.52420	−0.762099	−	0.647461i	$-0.775831\pi$
$727$	−1.14801e13	−1.52420	−0.762099	+	0.647461i	$0.775831\pi$
$728$	−3.10789e12	−0.410085
$729$	7.62257e12	0.999603
$730$	−9.51714e12	−1.24038
$731$	1.36000e12	0.176161
$732$	2.97765e12	0.383331
$733$	1.54057e13	1.97112	0.985558	−	0.169339i	$-0.0541631\pi$
$733$	1.54057e13	1.97112	0.985558	+	0.169339i	$0.0541631\pi$
$734$	−3.26531e11	−0.0415234
$735$	−4.27937e12	−0.540862
$736$	−2.21723e12	−0.278523
$737$	3.88601e12	0.485177
$738$	−3.63259e12	−0.450778
$739$	2.54989e12	0.314501	0.157250	−	0.987559i	$-0.449737\pi$
$739$	2.54989e12	0.314501	0.157250	+	0.987559i	$0.449737\pi$
$740$	−9.20311e11	−0.112821
$741$	1.84597e13	2.24928
$742$	6.28981e12	0.761763
$743$	−1.61842e13	−1.94824	−0.974120	−	0.226032i	$-0.927425\pi$
$743$	−1.61842e13	−1.94824	−0.974120	+	0.226032i	$0.927425\pi$
$744$	−1.98084e12	−0.237012
$745$	−9.02209e12	−1.07301
$746$	1.57355e13	1.86019
$747$	−3.94806e11	−0.0463918
$748$	1.83803e12	0.214682
$749$	6.04292e12	0.701582
$750$	−8.11087e12	−0.936034
$751$	5.37330e12	0.616399	0.308199	−	0.951322i	$-0.400274\pi$
$751$	5.37330e12	0.616399	0.308199	+	0.951322i	$0.400274\pi$
$752$	−9.41620e12	−1.07373
$753$	5.51018e11	0.0624580
$754$	3.62541e12	0.408494
$755$	−1.36044e13	−1.52377
$756$	−1.07272e13	−1.19436
$757$	5.30798e12	0.587487	0.293743	−	0.955884i	$-0.405099\pi$
$757$	5.30798e12	0.587487	0.293743	+	0.955884i	$0.405099\pi$
$758$	1.35318e13	1.48883
$759$	−1.87829e12	−0.205435
$760$	3.42682e12	0.372589
$761$	−9.39388e11	−0.101535	−0.0507673	−	0.998711i	$-0.516167\pi$
$761$	−9.39388e11	−0.101535	−0.0507673	+	0.998711i	$0.516167\pi$
$762$	−3.19709e12	−0.343524
$763$	1.12943e13	1.20642
$764$	−1.77366e12	−0.188343
$765$	8.25381e11	0.0871321
$766$	−2.02876e13	−2.12913
$767$	2.68744e13	2.80388
$768$	9.00585e12	0.934112
$769$	−1.71874e13	−1.77232	−0.886161	−	0.463378i	$-0.846637\pi$
$769$	−1.71874e13	−1.77232	−0.886161	+	0.463378i	$0.846637\pi$
$770$	2.38188e13	2.44181
$771$	5.74232e12	0.585252
$772$	−2.00410e12	−0.203068
$773$	−1.21415e13	−1.22310	−0.611552	−	0.791205i	$-0.709454\pi$
$773$	−1.21415e13	−1.22310	−0.611552	+	0.791205i	$0.709454\pi$
$774$	5.11632e12	0.512416
$775$	−2.74408e12	−0.273237
$776$	−2.93170e12	−0.290230
$777$	1.21462e12	0.119549
$778$	2.20007e11	0.0215293
$779$	1.46077e13	1.42123
$780$	1.21176e13	1.17217
$781$	−1.60400e13	−1.54267
$782$	5.77465e11	0.0552198
$783$	−2.06756e12	−0.196576
$784$	−7.75269e12	−0.732875
$785$	−3.22581e12	−0.303197
$786$	−6.45465e12	−0.603214
$787$	8.09739e12	0.752417	0.376209	−	0.926535i	$-0.377228\pi$
$787$	8.09739e12	0.752417	0.376209	+	0.926535i	$0.377228\pi$
$788$	1.12916e13	1.04325
$789$	−3.32044e12	−0.305034
$790$	1.53305e13	1.40034
$791$	−1.24581e13	−1.13151
$792$	−1.14250e12	−0.103179
$793$	−1.07261e13	−0.963193
$794$	1.06635e13	0.952154
$795$	4.05202e12	0.359765
$796$	−9.36738e12	−0.827007
$797$	8.81800e12	0.774119	0.387059	−	0.922055i	$-0.373491\pi$
$797$	8.81800e12	0.774119	0.387059	+	0.922055i	$0.373491\pi$
$798$	2.73725e13	2.38947
$799$	2.14237e12	0.185966
$800$	2.63851e12	0.227748
$801$	−3.12520e12	−0.268245
$802$	1.23149e13	1.05111
$803$	−1.27596e13	−1.08297
$804$	2.93150e12	0.247422
$805$	3.45611e12	0.290073
$806$	−4.31853e13	−3.60436
$807$	3.19065e12	0.264818
$808$	1.59664e12	0.131782
$809$	−2.08358e13	−1.71018	−0.855090	−	0.518480i	$-0.826498\pi$
$809$	−2.08358e13	−1.71018	−0.855090	+	0.518480i	$0.826498\pi$
$810$	−7.47290e12	−0.609967
$811$	1.73688e13	1.40986	0.704932	−	0.709275i	$-0.250978\pi$
$811$	1.73688e13	1.40986	0.704932	+	0.709275i	$0.250978\pi$
$812$	2.48281e12	0.200420
$813$	1.11612e13	0.895994
$814$	−2.67157e12	−0.213284
$815$	−1.79945e13	−1.42867
$816$	−2.11172e12	−0.166736
$817$	−2.05742e13	−1.61556
$818$	−4.00810e12	−0.313003
$819$	1.13244e13	0.879501
$820$	9.58904e12	0.740649
$821$	6.70150e12	0.514788	0.257394	−	0.966307i	$-0.417136\pi$
$821$	6.70150e12	0.514788	0.257394	+	0.966307i	$0.417136\pi$
$822$	−1.16584e13	−0.890664
$823$	9.98866e12	0.758941	0.379471	−	0.925204i	$-0.376106\pi$
$823$	9.98866e12	0.758941	0.379471	+	0.925204i	$0.376106\pi$
$824$	−3.92320e12	−0.296462
$825$	2.23517e12	0.167984
$826$	3.98500e13	2.97864
$827$	−7.64587e12	−0.568398	−0.284199	−	0.958765i	$-0.591728\pi$
$827$	−7.64587e12	−0.568398	−0.284199	+	0.958765i	$0.591728\pi$
$828$	1.00332e12	0.0741831
$829$	−1.19275e13	−0.877108	−0.438554	−	0.898705i	$-0.644509\pi$
$829$	−1.19275e13	−0.877108	−0.438554	+	0.898705i	$0.644509\pi$
$830$	2.25655e12	0.165042
$831$	5.68882e12	0.413826
$832$	1.59440e13	1.15356
$833$	1.76389e12	0.126931
$834$	1.15796e13	0.828795
$835$	2.00619e13	1.42818
$836$	−2.78060e13	−1.96884
$837$	2.46285e13	1.73449
$838$	−1.15190e13	−0.806897
$839$	2.39442e13	1.66829	0.834146	−	0.551544i	$-0.185961\pi$
$839$	2.39442e13	1.66829	0.834146	+	0.551544i	$0.185961\pi$
$840$	−2.96885e12	−0.205746
$841$	−1.40286e13	−0.967014
$842$	4.49379e12	0.308112
$843$	−1.02203e13	−0.697014
$844$	−1.27067e13	−0.861967
$845$	−2.76162e13	−1.86341
$846$	8.05962e12	0.540939
$847$	1.26736e13	0.846103
$848$	7.34081e12	0.487487
$849$	−2.31067e13	−1.52634
$850$	−6.87185e11	−0.0451532
$851$	−3.87646e11	−0.0253368
$852$	−1.21001e13	−0.786706
$853$	−2.34362e12	−0.151571	−0.0757857	−	0.997124i	$-0.524146\pi$
$853$	−2.34362e12	−0.151571	−0.0757857	+	0.997124i	$0.524146\pi$
$854$	−1.59050e13	−1.02323
$855$	−1.24865e13	−0.799083
$856$	1.65670e12	0.105466
$857$	1.81747e13	1.15094	0.575470	−	0.817823i	$-0.304819\pi$
$857$	1.81747e13	1.15094	0.575470	+	0.817823i	$0.304819\pi$
$858$	3.51763e13	2.21594
$859$	−1.91864e13	−1.20233	−0.601167	−	0.799124i	$-0.705297\pi$
$859$	−1.91864e13	−1.20233	−0.601167	+	0.799124i	$0.705297\pi$
$860$	−1.35057e13	−0.841923
$861$	−1.26555e13	−0.784812
$862$	−1.79094e13	−1.10484
$863$	1.51363e13	0.928903	0.464451	−	0.885599i	$-0.346252\pi$
$863$	1.51363e13	0.928903	0.464451	+	0.885599i	$0.346252\pi$
$864$	−2.36810e13	−1.44573
$865$	3.00005e13	1.82203
$866$	1.87632e13	1.13364
$867$	−1.22496e13	−0.736267
$868$	−2.95748e13	−1.76841
$869$	2.05534e13	1.22263
$870$	3.46322e12	0.204948
$871$	−1.05599e13	−0.621695
$872$	3.09640e12	0.181356
$873$	1.06824e13	0.622449
$874$	−8.73595e12	−0.506418
$875$	2.00089e13	1.15395
$876$	−9.62549e12	−0.552274
$877$	−9.89360e12	−0.564750	−0.282375	−	0.959304i	$-0.591122\pi$
$877$	−9.89360e12	−0.564750	−0.282375	+	0.959304i	$0.591122\pi$
$878$	1.79812e13	1.02116
$879$	5.37431e12	0.303649
$880$	2.77988e13	1.56262
$881$	−2.94153e13	−1.64506	−0.822530	−	0.568722i	$-0.807438\pi$
$881$	−2.94153e13	−1.64506	−0.822530	+	0.568722i	$0.807438\pi$
$882$	6.63577e12	0.369218
$883$	−1.40370e13	−0.777055	−0.388528	−	0.921437i	$-0.627016\pi$
$883$	−1.40370e13	−0.777055	−0.388528	+	0.921437i	$0.627016\pi$
$884$	−4.99470e12	−0.275090
$885$	2.56721e13	1.40675
$886$	3.09159e13	1.68551
$887$	−2.09569e12	−0.113677	−0.0568383	−	0.998383i	$-0.518102\pi$
$887$	−2.09569e12	−0.113677	−0.0568383	+	0.998383i	$0.518102\pi$
$888$	3.32994e11	0.0179712
$889$	7.88696e12	0.423498
$890$	1.78624e13	0.954299
$891$	−1.00189e13	−0.532560
$892$	−2.23807e13	−1.18367
$893$	−3.24101e13	−1.70549
$894$	−1.97573e13	−1.03445
$895$	−6.02314e12	−0.313776
$896$	−9.49358e12	−0.492089
$897$	5.10409e12	0.263240
$898$	−3.72589e13	−1.91199
$899$	−5.70026e12	−0.291056
$900$	−1.19396e12	−0.0606594
$901$	−1.67018e12	−0.0844309
$902$	2.78361e13	1.40016
$903$	1.78246e13	0.892125
$904$	−3.41545e12	−0.170095
$905$	−1.09013e13	−0.540204
$906$	−2.97920e13	−1.46900
$907$	9.84838e12	0.483206	0.241603	−	0.970375i	$-0.422327\pi$
$907$	9.84838e12	0.483206	0.241603	+	0.970375i	$0.422327\pi$
$908$	2.42851e13	1.18564
$909$	−5.81775e12	−0.282630
$910$	−6.47255e13	−3.12888
$911$	−3.56054e13	−1.71271	−0.856353	−	0.516390i	$-0.827275\pi$
$911$	−3.56054e13	−1.71271	−0.856353	+	0.516390i	$0.827275\pi$
$912$	3.19463e13	1.52913
$913$	3.02535e12	0.144098
$914$	2.31607e13	1.09772
$915$	−1.02463e13	−0.483249
$916$	1.54481e13	0.725011
$917$	1.59231e13	0.743644
$918$	6.16757e12	0.286630
$919$	−3.47352e13	−1.60639	−0.803193	−	0.595718i	$-0.796867\pi$
$919$	−3.47352e13	−1.60639	−0.803193	+	0.595718i	$0.796867\pi$
$920$	9.47513e11	0.0436053
$921$	1.14146e13	0.522750
$922$	6.68610e12	0.304708
$923$	4.35872e13	1.97675
$924$	2.40900e13	1.08721
$925$	4.61300e11	0.0207179
$926$	−1.53969e13	−0.688153
$927$	1.42952e13	0.635814
$928$	5.48098e12	0.242601
$929$	−5.99190e12	−0.263933	−0.131966	−	0.991254i	$-0.542129\pi$
$929$	−5.99190e12	−0.263933	−0.131966	+	0.991254i	$0.542129\pi$
$930$	−4.12534e13	−1.80836
$931$	−2.66843e13	−1.16408
$932$	−4.07603e12	−0.176956
$933$	3.37812e12	0.145951
$934$	4.00633e13	1.72261
$935$	−6.32478e12	−0.270641
$936$	3.10464e12	0.132212
$937$	−1.54163e13	−0.653360	−0.326680	−	0.945135i	$-0.605930\pi$
$937$	−1.54163e13	−0.653360	−0.326680	+	0.945135i	$0.605930\pi$
$938$	−1.56584e13	−0.660444
$939$	2.74334e13	1.15155
$940$	−2.12752e13	−0.888787
$941$	−2.81560e13	−1.17062	−0.585312	−	0.810808i	$-0.699028\pi$
$941$	−2.81560e13	−1.17062	−0.585312	+	0.810808i	$0.699028\pi$
$942$	−7.06413e12	−0.292300
$943$	4.03902e12	0.166331
$944$	4.65088e13	1.90617
$945$	3.69128e13	1.50568
$946$	−3.92056e13	−1.59162
$947$	4.97515e12	0.201016	0.100508	−	0.994936i	$-0.467953\pi$
$947$	4.97515e12	0.201016	0.100508	+	0.994936i	$0.467953\pi$
$948$	1.55050e13	0.623497
$949$	3.46730e13	1.38769
$950$	1.03958e13	0.414097
$951$	−2.00249e13	−0.793886
$952$	1.22372e12	0.0482853
$953$	−1.00003e13	−0.392731	−0.196365	−	0.980531i	$-0.562914\pi$
$953$	−1.00003e13	−0.392731	−0.196365	+	0.980531i	$0.562914\pi$
$954$	−6.28323e12	−0.245593
$955$	6.10326e12	0.237436
$956$	2.64106e13	1.02263
$957$	4.64311e12	0.178939
$958$	4.48240e13	1.71935
$959$	2.87602e13	1.09801
$960$	1.52307e13	0.578761
$961$	4.14611e13	1.56814
$962$	7.25977e12	0.273297
$963$	−6.03659e12	−0.226190
$964$	−2.61003e13	−0.973418
$965$	6.89623e12	0.255999
$966$	7.56847e12	0.279648
$967$	7.42410e12	0.273039	0.136520	−	0.990637i	$-0.456408\pi$
$967$	7.42410e12	0.273039	0.136520	+	0.990637i	$0.456408\pi$
$968$	3.47452e12	0.127191
$969$	−7.26841e12	−0.264839
$970$	−6.10562e13	−2.21440
$971$	−1.79014e13	−0.646251	−0.323125	−	0.946356i	$-0.604734\pi$
$971$	−1.79014e13	−0.646251	−0.323125	+	0.946356i	$0.604734\pi$
$972$	1.82914e13	0.657279
$973$	−2.85660e13	−1.02174
$974$	6.13488e13	2.18419
$975$	−6.07388e12	−0.215251
$976$	−1.85626e13	−0.654809
$977$	−1.62509e13	−0.570625	−0.285313	−	0.958435i	$-0.592097\pi$
$977$	−1.62509e13	−0.570625	−0.285313	+	0.958435i	$0.592097\pi$
$978$	−3.94058e13	−1.37732
$979$	2.39480e13	0.833196
$980$	−1.75166e13	−0.606641
$981$	−1.12825e13	−0.388950
$982$	3.96874e12	0.136192
$983$	4.85899e12	0.165980	0.0829899	−	0.996550i	$-0.473553\pi$
$983$	4.85899e12	0.165980	0.0829899	+	0.996550i	$0.473553\pi$
$984$	−3.46958e12	−0.117977
$985$	−3.88550e13	−1.31518
$986$	−1.42749e12	−0.0480979
$987$	2.80788e13	0.941782
$988$	7.55604e13	2.52283
$989$	−5.68875e12	−0.189075
$990$	−2.37939e13	−0.787239
$991$	3.95531e13	1.30271	0.651356	−	0.758772i	$-0.274200\pi$
$991$	3.95531e13	1.30271	0.651356	+	0.758772i	$0.274200\pi$
$992$	−6.52886e13	−2.14060
$993$	−1.58201e13	−0.516342
$994$	6.46322e13	2.09995
$995$	3.22337e13	1.04257
$996$	2.28224e12	0.0734844
$997$	−2.76871e13	−0.887460	−0.443730	−	0.896161i	$-0.646345\pi$
$997$	−2.76871e13	−0.887460	−0.443730	+	0.896161i	$0.646345\pi$
$998$	5.95084e13	1.89885
$999$	−4.14023e12	−0.131516

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.10.a.a.1.1	✓	7
3.2	odd	2		207.10.a.b.1.7		7
4.3	odd	2		368.10.a.f.1.2		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.10.a.a.1.1	✓	7	1.1	even	1	trivial
207.10.a.b.1.7		7	3.2	odd	2
368.10.a.f.1.2		7	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:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 10 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q-30.8448 q^{2} +107.347 q^{3} +439.399 q^{4} -1512.00 q^{5} -3311.09 q^{6} +8168.19 q^{7} +2239.35 q^{8} -8159.64 q^{9} +O(q^{10})\)	\(q-30.8448 q^{2} +107.347 q^{3} +439.399 q^{4} -1512.00 q^{5} -3311.09 q^{6} +8168.19 q^{7} +2239.35 q^{8} -8159.64 q^{9} +46637.2 q^{10} +62526.2 q^{11} +47168.2 q^{12} -169909. q^{13} -251946. q^{14} -162308. q^{15} -294045. q^{16} +66901.0 q^{17} +251682. q^{18} -1.01209e6 q^{19} -664371. q^{20} +876830. q^{21} -1.92860e6 q^{22} -279841. q^{23} +240388. q^{24} +333012. q^{25} +5.24081e6 q^{26} -2.98882e6 q^{27} +3.58910e6 q^{28} +691764. q^{29} +5.00636e6 q^{30} -8.24019e6 q^{31} +7.92319e6 q^{32} +6.71199e6 q^{33} -2.06355e6 q^{34} -1.23503e7 q^{35} -3.58534e6 q^{36} +1.38524e6 q^{37} +3.12176e7 q^{38} -1.82393e7 q^{39} -3.38590e6 q^{40} -1.44333e7 q^{41} -2.70456e7 q^{42} +2.03285e7 q^{43} +2.74740e7 q^{44} +1.23374e7 q^{45} +8.63163e6 q^{46} +3.20230e7 q^{47} -3.15648e7 q^{48} +2.63657e7 q^{49} -1.02717e7 q^{50} +7.18162e6 q^{51} -7.46581e7 q^{52} -2.49649e7 q^{53} +9.21895e7 q^{54} -9.45394e7 q^{55} +1.82915e7 q^{56} -1.08644e8 q^{57} -2.13373e7 q^{58} -1.58169e8 q^{59} -7.13181e7 q^{60} +6.31285e7 q^{61} +2.54167e8 q^{62} -6.66494e7 q^{63} -9.38380e7 q^{64} +2.56903e8 q^{65} -2.07030e8 q^{66} +6.21501e7 q^{67} +2.93962e7 q^{68} -3.00401e7 q^{69} +3.80941e8 q^{70} -2.56532e8 q^{71} -1.82723e7 q^{72} -2.04068e8 q^{73} -4.27273e7 q^{74} +3.57478e7 q^{75} -4.44710e8 q^{76} +5.10725e8 q^{77} +5.62585e8 q^{78} +3.28718e8 q^{79} +4.44595e8 q^{80} -1.60235e8 q^{81} +4.45191e8 q^{82} +4.83853e7 q^{83} +3.85278e8 q^{84} -1.01154e8 q^{85} -6.27027e8 q^{86} +7.42587e7 q^{87} +1.40018e8 q^{88} +3.83007e8 q^{89} -3.80543e8 q^{90} -1.38785e9 q^{91} -1.22962e8 q^{92} -8.84559e8 q^{93} -9.87743e8 q^{94} +1.53027e9 q^{95} +8.50530e8 q^{96} -1.30917e9 q^{97} -8.13243e8 q^{98} -5.10191e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9}+O(q^{10}) \) 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9} - 60820 q^{10} - 78484 q^{11} - 343492 q^{12} - 296769 q^{13} - 711120 q^{14} - 237870 q^{15} - 253440 q^{16} - 1128820 q^{17} - 499874 q^{18} - 1301252 q^{19} - 3482704 q^{20} - 108908 q^{21} - 1562088 q^{22} - 1958887 q^{23} - 4606464 q^{24} - 1320899 q^{25} + 692230 q^{26} + 2977921 q^{27} - 8371144 q^{28} + 2813849 q^{29} + 25535196 q^{30} + 7334751 q^{31} + 26028800 q^{32} + 646330 q^{33} + 14981564 q^{34} + 23410104 q^{35} + 40211900 q^{36} - 13324320 q^{37} + 37578632 q^{38} + 6304533 q^{39} - 45307920 q^{40} - 15691573 q^{41} + 124523248 q^{42} - 46474818 q^{43} + 43428040 q^{44} - 72736710 q^{45} + 8232227 q^{47} - 163054384 q^{48} + 29219031 q^{49} + 50366304 q^{50} - 136344764 q^{51} - 100922292 q^{52} - 53545400 q^{53} - 26171642 q^{54} - 181608484 q^{55} - 420111696 q^{56} - 218913370 q^{57} - 39304854 q^{58} - 341275144 q^{59} + 420822384 q^{60} - 277157656 q^{61} + 464777594 q^{62} - 574619276 q^{63} + 340566208 q^{64} + 106659278 q^{65} + 258025876 q^{66} + 89654580 q^{67} + 62700400 q^{68} + 24905849 q^{69} + 1187910040 q^{70} - 286098961 q^{71} + 1446323640 q^{72} - 637495039 q^{73} + 189880036 q^{74} - 160733159 q^{75} + 228563936 q^{76} + 511682536 q^{77} + 1199383686 q^{78} + 274469546 q^{79} - 345318560 q^{80} - 237775217 q^{81} - 570256066 q^{82} + 1164579762 q^{83} + 3447171416 q^{84} - 18639492 q^{85} + 415245796 q^{86} - 595368433 q^{87} + 103329440 q^{88} - 504153000 q^{89} - 1414126968 q^{90} - 1692320156 q^{91} - 429835776 q^{92} - 2753858687 q^{93} - 2214048622 q^{94} + 162962164 q^{95} - 3332565856 q^{96} - 3519929016 q^{97} + 2474592568 q^{98} - 1883749262 q^{99}+O(q^{100}) \) 7 * q - 89 * q^3 + 1536 * q^4 - 2388 * q^5 - 12518 * q^6 - 9896 * q^7 + 34920 * q^8 + 33064 * q^9 - 60820 * q^10 - 78484 * q^11 - 343492 * q^12 - 296769 * q^13 - 711120 * q^14 - 237870 * q^15 - 253440 * q^16 - 1128820 * q^17 - 499874 * q^18 - 1301252 * q^19 - 3482704 * q^20 - 108908 * q^21 - 1562088 * q^22 - 1958887 * q^23 - 4606464 * q^24 - 1320899 * q^25 + 692230 * q^26 + 2977921 * q^27 - 8371144 * q^28 + 2813849 * q^29 + 25535196 * q^30 + 7334751 * q^31 + 26028800 * q^32 + 646330 * q^33 + 14981564 * q^34 + 23410104 * q^35 + 40211900 * q^36 - 13324320 * q^37 + 37578632 * q^38 + 6304533 * q^39 - 45307920 * q^40 - 15691573 * q^41 + 124523248 * q^42 - 46474818 * q^43 + 43428040 * q^44 - 72736710 * q^45 + 8232227 * q^47 - 163054384 * q^48 + 29219031 * q^49 + 50366304 * q^50 - 136344764 * q^51 - 100922292 * q^52 - 53545400 * q^53 - 26171642 * q^54 - 181608484 * q^55 - 420111696 * q^56 - 218913370 * q^57 - 39304854 * q^58 - 341275144 * q^59 + 420822384 * q^60 - 277157656 * q^61 + 464777594 * q^62 - 574619276 * q^63 + 340566208 * q^64 + 106659278 * q^65 + 258025876 * q^66 + 89654580 * q^67 + 62700400 * q^68 + 24905849 * q^69 + 1187910040 * q^70 - 286098961 * q^71 + 1446323640 * q^72 - 637495039 * q^73 + 189880036 * q^74 - 160733159 * q^75 + 228563936 * q^76 + 511682536 * q^77 + 1199383686 * q^78 + 274469546 * q^79 - 345318560 * q^80 - 237775217 * q^81 - 570256066 * q^82 + 1164579762 * q^83 + 3447171416 * q^84 - 18639492 * q^85 + 415245796 * q^86 - 595368433 * q^87 + 103329440 * q^88 - 504153000 * q^89 - 1414126968 * q^90 - 1692320156 * q^91 - 429835776 * q^92 - 2753858687 * q^93 - 2214048622 * q^94 + 162962164 * q^95 - 3332565856 * q^96 - 3519929016 * q^97 + 2474592568 * q^98 - 1883749262 * q^99

Introduction

L-functions

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