LMFDB - Embedded newform 23.10.a.a.1.4

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			1.4
Root			$-2.27545$ 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)

$f(q)$	$=$	$q-4.55091 q^{2} -23.1179 q^{3} -491.289 q^{4} +2146.10 q^{5} +105.207 q^{6} +615.663 q^{7} +4565.88 q^{8} -19148.6 q^{9} +O(q^{10})$	\(q-4.55091 q^{2} -23.1179 q^{3} -491.289 q^{4} +2146.10 q^{5} +105.207 q^{6} +615.663 q^{7} +4565.88 q^{8} -19148.6 q^{9} -9766.68 q^{10} -29031.0 q^{11} +11357.6 q^{12} -63714.3 q^{13} -2801.82 q^{14} -49613.2 q^{15} +230761. q^{16} -491541. q^{17} +87143.4 q^{18} -896238. q^{19} -1.05435e6 q^{20} -14232.8 q^{21} +132117. q^{22} -279841. q^{23} -105553. q^{24} +2.65260e6 q^{25} +289958. q^{26} +897703. q^{27} -302468. q^{28} -2.26300e6 q^{29} +225785. q^{30} +2.40246e6 q^{31} -3.38790e6 q^{32} +671135. q^{33} +2.23696e6 q^{34} +1.32127e6 q^{35} +9.40748e6 q^{36} +1.26269e7 q^{37} +4.07870e6 q^{38} +1.47294e6 q^{39} +9.79881e6 q^{40} -2.03845e7 q^{41} +64772.2 q^{42} +1.79238e7 q^{43} +1.42626e7 q^{44} -4.10946e7 q^{45} +1.27353e6 q^{46} -2.27631e7 q^{47} -5.33471e6 q^{48} -3.99746e7 q^{49} -1.20717e7 q^{50} +1.13634e7 q^{51} +3.13021e7 q^{52} +4.23878e7 q^{53} -4.08536e6 q^{54} -6.23033e7 q^{55} +2.81104e6 q^{56} +2.07191e7 q^{57} +1.02987e7 q^{58} -2.02688e7 q^{59} +2.43744e7 q^{60} -2.08303e8 q^{61} -1.09334e7 q^{62} -1.17891e7 q^{63} -1.02732e8 q^{64} -1.36737e8 q^{65} -3.05427e6 q^{66} +2.23315e8 q^{67} +2.41489e8 q^{68} +6.46933e6 q^{69} -6.01298e6 q^{70} +3.89416e8 q^{71} -8.74300e7 q^{72} -7.74476e7 q^{73} -5.74638e7 q^{74} -6.13225e7 q^{75} +4.40312e8 q^{76} -1.78733e7 q^{77} -6.70321e6 q^{78} -3.24490e8 q^{79} +4.95236e8 q^{80} +3.56148e8 q^{81} +9.27678e7 q^{82} +6.16169e7 q^{83} +6.99243e6 q^{84} -1.05489e9 q^{85} -8.15697e7 q^{86} +5.23158e7 q^{87} -1.32552e8 q^{88} +5.49858e8 q^{89} +1.87018e8 q^{90} -3.92265e7 q^{91} +1.37483e8 q^{92} -5.55397e7 q^{93} +1.03593e8 q^{94} -1.92341e9 q^{95} +7.83211e7 q^{96} -1.84163e7 q^{97} +1.81921e8 q^{98} +5.55902e8 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $

$2$	−4.55091	−0.201124	−0.100562	−	0.994931i	$-0.532064\pi$
$2$	−4.55091	−0.201124	−0.100562	+	0.994931i	$0.532064\pi$
$3$	−23.1179	−0.164779	−0.0823896	−	0.996600i	$-0.526255\pi$
$3$	−23.1179	−0.164779	−0.0823896	+	0.996600i	$0.526255\pi$
$4$	−491.289	−0.959549
$5$	2146.10	1.53562	0.767810	−	0.640677i	$-0.221346\pi$
$5$	2146.10	1.53562	0.767810	+	0.640677i	$0.221346\pi$
$6$	105.207	0.0331410
$7$	615.663	0.0969174	0.0484587	−	0.998825i	$-0.484569\pi$
$7$	615.663	0.0969174	0.0484587	+	0.998825i	$0.484569\pi$
$8$	4565.88	0.394112
$9$	−19148.6	−0.972848
$10$	−9766.68	−0.308850
$11$	−29031.0	−0.597854	−0.298927	−	0.954276i	$-0.596629\pi$
$11$	−29031.0	−0.597854	−0.298927	+	0.954276i	$0.596629\pi$
$12$	11357.6	0.158114
$13$	−63714.3	−0.618717	−0.309358	−	0.950946i	$-0.600114\pi$
$13$	−63714.3	−0.618717	−0.309358	+	0.950946i	$0.600114\pi$
$14$	−2801.82	−0.0194924
$15$	−49613.2	−0.253038
$16$	230761.	0.880284
$17$	−491541.	−1.42738	−0.713690	−	0.700462i	$-0.752977\pi$
$17$	−491541.	−1.42738	−0.713690	+	0.700462i	$0.752977\pi$
$18$	87143.4	0.195663
$19$	−896238.	−1.57773	−0.788864	−	0.614568i	$-0.789330\pi$
$19$	−896238.	−1.57773	−0.788864	+	0.614568i	$0.789330\pi$
$20$	−1.05435e6	−1.47350
$21$	−14232.8	−0.0159700
$22$	132117.	0.120242
$23$	−279841.	−0.208514
$23$	−279841.	−0.208514
$24$	−105553.	−0.0649414
$25$	2.65260e6	1.35813
$26$	289958.	0.124439
$27$	897703.	0.325084
$28$	−302468.	−0.0929970
$29$	−2.26300e6	−0.594148	−0.297074	−	0.954855i	$-0.596011\pi$
$29$	−2.26300e6	−0.594148	−0.297074	+	0.954855i	$0.596011\pi$
$30$	225785.	0.0508920
$31$	2.40246e6	0.467228	0.233614	−	0.972329i	$-0.424945\pi$
$31$	2.40246e6	0.467228	0.233614	+	0.972329i	$0.424945\pi$
$32$	−3.38790e6	−0.571158
$33$	671135.	0.0985138
$34$	2.23696e6	0.287080
$35$	1.32127e6	0.148828
$36$	9.40748e6	0.933495
$37$	1.26269e7	1.10761	0.553807	−	0.832645i	$-0.313175\pi$
$37$	1.26269e7	1.10761	0.553807	+	0.832645i	$0.313175\pi$
$38$	4.07870e6	0.317318
$39$	1.47294e6	0.101952
$40$	9.79881e6	0.605206
$41$	−2.03845e7	−1.12661	−0.563303	−	0.826251i	$-0.690469\pi$
$41$	−2.03845e7	−1.12661	−0.563303	+	0.826251i	$0.690469\pi$
$42$	64772.2	0.00321194
$43$	1.79238e7	0.799508	0.399754	−	0.916622i	$-0.369096\pi$
$43$	1.79238e7	0.799508	0.399754	+	0.916622i	$0.369096\pi$
$44$	1.42626e7	0.573670
$45$	−4.10946e7	−1.49393
$46$	1.27353e6	0.0419372
$47$	−2.27631e7	−0.680440	−0.340220	−	0.940346i	$-0.610502\pi$
$47$	−2.27631e7	−0.680440	−0.340220	+	0.940346i	$0.610502\pi$
$48$	−5.33471e6	−0.145052
$49$	−3.99746e7	−0.990607
$50$	−1.20717e7	−0.273152
$51$	1.13634e7	0.235202
$52$	3.13021e7	0.593689
$53$	4.23878e7	0.737903	0.368952	−	0.929449i	$-0.379717\pi$
$53$	4.23878e7	0.737903	0.368952	+	0.929449i	$0.379717\pi$
$54$	−4.08536e6	−0.0653821
$55$	−6.23033e7	−0.918077
$56$	2.81104e6	0.0381963
$57$	2.07191e7	0.259977
$58$	1.02987e7	0.119497
$59$	−2.02688e7	−0.217768	−0.108884	−	0.994054i	$-0.534728\pi$
$59$	−2.02688e7	−0.217768	−0.108884	+	0.994054i	$0.534728\pi$
$60$	2.43744e7	0.242803
$61$	−2.08303e8	−1.92625	−0.963124	−	0.269058i	$-0.913288\pi$
$61$	−2.08303e8	−1.92625	−0.963124	+	0.269058i	$0.913288\pi$
$62$	−1.09334e7	−0.0939705
$63$	−1.17891e7	−0.0942858
$64$	−1.02732e8	−0.765411
$65$	−1.36737e8	−0.950114
$66$	−3.05427e6	−0.0198135
$67$	2.23315e8	1.35388	0.676940	−	0.736038i	$-0.263305\pi$
$67$	2.23315e8	1.35388	0.676940	+	0.736038i	$0.263305\pi$
$68$	2.41489e8	1.36964
$69$	6.46933e6	0.0343588
$70$	−6.01298e6	−0.0299329
$71$	3.89416e8	1.81866	0.909330	−	0.416077i	$-0.136595\pi$
$71$	3.89416e8	1.81866	0.909330	+	0.416077i	$0.136595\pi$
$72$	−8.74300e7	−0.383411
$73$	−7.74476e7	−0.319194	−0.159597	−	0.987182i	$-0.551020\pi$
$73$	−7.74476e7	−0.319194	−0.159597	+	0.987182i	$0.551020\pi$
$74$	−5.74638e7	−0.222767
$75$	−6.13225e7	−0.223792
$76$	4.40312e8	1.51391
$77$	−1.78733e7	−0.0579424
$78$	−6.70321e6	−0.0205049
$79$	−3.24490e8	−0.937300	−0.468650	−	0.883384i	$-0.655260\pi$
$79$	−3.24490e8	−0.937300	−0.468650	+	0.883384i	$0.655260\pi$
$80$	4.95236e8	1.35178
$81$	3.56148e8	0.919281
$82$	9.27678e7	0.226587
$83$	6.16169e7	0.142511	0.0712555	−	0.997458i	$-0.477299\pi$
$83$	6.16169e7	0.142511	0.0712555	+	0.997458i	$0.477299\pi$
$84$	6.99243e6	0.0153240
$85$	−1.05489e9	−2.19191
$86$	−8.15697e7	−0.160800
$87$	5.23158e7	0.0979031
$88$	−1.32552e8	−0.235621
$89$	5.49858e8	0.928957	0.464479	−	0.885584i	$-0.346242\pi$
$89$	5.49858e8	0.928957	0.464479	+	0.885584i	$0.346242\pi$
$90$	1.87018e8	0.300464
$91$	−3.92265e7	−0.0599644
$92$	1.37483e8	0.200080
$93$	−5.55397e7	−0.0769893
$94$	1.03593e8	0.136853
$95$	−1.92341e9	−2.42279
$96$	7.83211e7	0.0941148
$97$	−1.84163e7	−0.0211218	−0.0105609	−	0.999944i	$-0.503362\pi$
$97$	−1.84163e7	−0.0211218	−0.0105609	+	0.999944i	$0.503362\pi$
$98$	1.81921e8	0.199234
$99$	5.55902e8	0.581621
$100$	−1.30319e9	−1.30319
$101$	−3.88822e8	−0.371796	−0.185898	−	0.982569i	$-0.559519\pi$
$101$	−3.88822e8	−0.371796	−0.185898	+	0.982569i	$0.559519\pi$
$102$	−5.17137e7	−0.0473048
$103$	1.25516e9	1.09883	0.549417	−	0.835548i	$-0.314850\pi$
$103$	1.25516e9	1.09883	0.549417	+	0.835548i	$0.314850\pi$
$104$	−2.90912e8	−0.243843
$105$	−3.05450e7	−0.0245238
$106$	−1.92903e8	−0.148410
$107$	−2.18268e9	−1.60977	−0.804883	−	0.593433i	$-0.797772\pi$
$107$	−2.18268e9	−1.60977	−0.804883	+	0.593433i	$0.797772\pi$
$108$	−4.41032e8	−0.311934
$109$	9.27511e8	0.629361	0.314681	−	0.949198i	$-0.398103\pi$
$109$	9.27511e8	0.629361	0.314681	+	0.949198i	$0.398103\pi$
$110$	2.83537e8	0.184647
$111$	−2.91907e8	−0.182512
$112$	1.42071e8	0.0853148
$113$	1.72967e9	0.997951	0.498975	−	0.866616i	$-0.333710\pi$
$113$	1.72967e9	0.997951	0.498975	+	0.866616i	$0.333710\pi$
$114$	−9.42908e7	−0.0522874
$115$	−6.00565e8	−0.320199
$116$	1.11179e9	0.570114
$117$	1.22004e9	0.601917
$118$	9.22415e7	0.0437983
$119$	−3.02623e8	−0.138338
$120$	−2.26528e8	−0.0997253
$121$	−1.51515e9	−0.642571
$122$	9.47970e8	0.387414
$123$	4.71245e8	0.185641
$124$	−1.18030e9	−0.448328
$125$	1.50114e9	0.549954
$126$	5.36509e7	0.0189631
$127$	9.83420e8	0.335446	0.167723	−	0.985834i	$-0.446359\pi$
$127$	9.83420e8	0.335446	0.167723	+	0.985834i	$0.446359\pi$
$128$	2.20213e9	0.725100
$129$	−4.14361e8	−0.131742
$130$	6.22277e8	0.191090
$131$	4.77581e9	1.41686	0.708429	−	0.705782i	$-0.249404\pi$
$131$	4.77581e9	1.41686	0.708429	+	0.705782i	$0.249404\pi$
$132$	−3.29721e8	−0.0945288
$133$	−5.51780e8	−0.152909
$134$	−1.01628e9	−0.272297
$135$	1.92656e9	0.499206
$136$	−2.24432e9	−0.562547
$137$	3.92967e9	0.953044	0.476522	−	0.879162i	$-0.341897\pi$
$137$	3.92967e9	0.953044	0.476522	+	0.879162i	$0.341897\pi$
$138$	−2.94413e7	−0.00691037
$139$	−7.17630e8	−0.163055	−0.0815275	−	0.996671i	$-0.525980\pi$
$139$	−7.17630e8	−0.163055	−0.0815275	+	0.996671i	$0.525980\pi$
$140$	−6.49126e8	−0.142808
$141$	5.26233e8	0.112122
$142$	−1.77220e9	−0.365775
$143$	1.84969e9	0.369902
$144$	−4.41875e9	−0.856383
$145$	−4.85662e9	−0.912386
$146$	3.52457e8	0.0641975
$147$	9.24127e8	0.163231
$148$	−6.20345e9	−1.06281
$149$	−9.09927e9	−1.51241	−0.756203	−	0.654337i	$-0.772948\pi$
$149$	−9.09927e9	−1.51241	−0.756203	+	0.654337i	$0.772948\pi$
$150$	2.79073e8	0.0450098
$151$	5.17721e9	0.810400	0.405200	−	0.914228i	$-0.367202\pi$
$151$	5.17721e9	0.810400	0.405200	+	0.914228i	$0.367202\pi$
$152$	−4.09211e9	−0.621801
$153$	9.41230e9	1.38862
$154$	8.13397e7	0.0116536
$155$	5.15591e9	0.717484
$156$	−7.23639e8	−0.0978276
$157$	2.57953e8	0.0338838	0.0169419	−	0.999856i	$-0.494607\pi$
$157$	2.57953e8	0.0338838	0.0169419	+	0.999856i	$0.494607\pi$
$158$	1.47672e9	0.188513
$159$	−9.79915e8	−0.121591
$160$	−7.27076e9	−0.877082
$161$	−1.72288e8	−0.0202087
$162$	−1.62080e9	−0.184889
$163$	−1.39493e10	−1.54777	−0.773886	−	0.633325i	$-0.781690\pi$
$163$	−1.39493e10	−1.54777	−0.773886	+	0.633325i	$0.781690\pi$
$164$	1.00147e10	1.08103
$165$	1.44032e9	0.151280
$166$	−2.80413e8	−0.0286623
$167$	−5.90588e9	−0.587571	−0.293785	−	0.955871i	$-0.594915\pi$
$167$	−5.90588e9	−0.587571	−0.293785	+	0.955871i	$0.594915\pi$
$168$	−6.49853e7	−0.00629395
$169$	−6.54499e9	−0.617190
$170$	4.80072e9	0.440846
$171$	1.71617e10	1.53489
$172$	−8.80579e9	−0.767168
$173$	−1.86979e10	−1.58703	−0.793513	−	0.608553i	$-0.791750\pi$
$173$	−1.86979e10	−1.58703	−0.793513	+	0.608553i	$0.791750\pi$
$174$	−2.38085e8	−0.0196906
$175$	1.63311e9	0.131627
$176$	−6.69923e9	−0.526281
$177$	4.68572e8	0.0358836
$178$	−2.50235e9	−0.186835
$179$	1.04617e10	0.761665	0.380833	−	0.924644i	$-0.375637\pi$
$179$	1.04617e10	0.761665	0.380833	+	0.924644i	$0.375637\pi$
$180$	2.01894e10	1.43350
$181$	−2.04280e10	−1.41472	−0.707362	−	0.706851i	$-0.750115\pi$
$181$	−2.04280e10	−1.41472	−0.707362	+	0.706851i	$0.750115\pi$
$182$	1.78516e8	0.0120603
$183$	4.81553e9	0.317405
$184$	−1.27772e9	−0.0821780
$185$	2.70985e10	1.70087
$186$	2.52756e8	0.0154844
$187$	1.42699e10	0.853364
$188$	1.11832e10	0.652916
$189$	5.52682e8	0.0315063
$190$	8.75327e9	0.487281
$191$	−9.63397e9	−0.523787	−0.261894	−	0.965097i	$-0.584347\pi$
$191$	−9.63397e9	−0.523787	−0.261894	+	0.965097i	$0.584347\pi$
$192$	2.37494e9	0.126124
$193$	1.97416e10	1.02418	0.512088	−	0.858933i	$-0.328872\pi$
$193$	1.97416e10	1.02418	0.512088	+	0.858933i	$0.328872\pi$
$194$	8.38111e7	0.00424809
$195$	3.16107e9	0.156559
$196$	1.96391e10	0.950536
$197$	−2.69330e10	−1.27405	−0.637025	−	0.770843i	$-0.719835\pi$
$197$	−2.69330e10	−1.27405	−0.637025	+	0.770843i	$0.719835\pi$
$198$	−2.52986e9	−0.116978
$199$	2.57417e9	0.116358	0.0581792	−	0.998306i	$-0.481471\pi$
$199$	2.57417e9	0.116358	0.0581792	+	0.998306i	$0.481471\pi$
$200$	1.21114e10	0.535255
$201$	−5.16256e9	−0.223091
$202$	1.76949e9	0.0747769
$203$	−1.39325e9	−0.0575832
$204$	−5.58271e9	−0.225688
$205$	−4.37470e10	−1.73004
$206$	−5.71212e9	−0.221001
$207$	5.35855e9	0.202853
$208$	−1.47028e10	−0.544646
$209$	2.60187e10	0.943250
$210$	1.39007e8	0.00493232
$211$	−2.21424e10	−0.769048	−0.384524	−	0.923115i	$-0.625634\pi$
$211$	−2.21424e10	−0.769048	−0.384524	+	0.923115i	$0.625634\pi$
$212$	−2.08247e10	−0.708054
$213$	−9.00247e9	−0.299677
$214$	9.93317e9	0.323762
$215$	3.84663e10	1.22774
$216$	4.09880e9	0.128119
$217$	1.47910e9	0.0452825
$218$	−4.22102e9	−0.126579
$219$	1.79042e9	0.0525966
$220$	3.06089e10	0.880940
$221$	3.13182e10	0.883144
$222$	1.32844e9	0.0367074
$223$	−5.65545e10	−1.53142	−0.765711	−	0.643185i	$-0.777613\pi$
$223$	−5.65545e10	−1.53142	−0.765711	+	0.643185i	$0.777613\pi$
$224$	−2.08580e9	−0.0553551
$225$	−5.07935e10	−1.32126
$226$	−7.87155e9	−0.200711
$227$	−3.17256e9	−0.0793037	−0.0396519	−	0.999214i	$-0.512625\pi$
$227$	−3.17256e9	−0.0793037	−0.0396519	+	0.999214i	$0.512625\pi$
$228$	−1.01791e10	−0.249460
$229$	4.75590e8	0.0114281	0.00571403	−	0.999984i	$-0.498181\pi$
$229$	4.75590e8	0.0114281	0.00571403	+	0.999984i	$0.498181\pi$
$230$	2.73312e9	0.0643996
$231$	4.13193e8	0.00954770
$232$	−1.03326e10	−0.234161
$233$	−5.33681e10	−1.18626	−0.593131	−	0.805106i	$-0.702108\pi$
$233$	−5.33681e10	−1.18626	−0.593131	+	0.805106i	$0.702108\pi$
$234$	−5.55228e9	−0.121060
$235$	−4.88517e10	−1.04490
$236$	9.95785e9	0.208959
$237$	7.50151e9	0.154448
$238$	1.37721e9	0.0278230
$239$	7.71276e9	0.152904	0.0764521	−	0.997073i	$-0.475641\pi$
$239$	7.71276e9	0.152904	0.0764521	+	0.997073i	$0.475641\pi$
$240$	−1.14488e10	−0.222746
$241$	−1.82011e10	−0.347552	−0.173776	−	0.984785i	$-0.555597\pi$
$241$	−1.82011e10	−0.347552	−0.173776	+	0.984785i	$0.555597\pi$
$242$	6.89530e9	0.129236
$243$	−2.59029e10	−0.476562
$244$	1.02337e11	1.84833
$245$	−8.57892e10	−1.52120
$246$	−2.14459e9	−0.0373368
$247$	5.71032e10	0.976166
$248$	1.09693e10	0.184140
$249$	−1.42445e9	−0.0234828
$250$	−6.83156e9	−0.110609
$251$	9.78883e10	1.55668	0.778339	−	0.627844i	$-0.216062\pi$
$251$	9.78883e10	1.55668	0.778339	+	0.627844i	$0.216062\pi$
$252$	5.79184e9	0.0904719
$253$	8.12406e9	0.124661
$254$	−4.47545e9	−0.0674661
$255$	2.43869e10	0.361182
$256$	4.25769e10	0.619576
$257$	−2.50832e10	−0.358661	−0.179331	−	0.983789i	$-0.557393\pi$
$257$	−2.50832e10	−0.358661	−0.179331	+	0.983789i	$0.557393\pi$
$258$	1.88572e9	0.0264965
$259$	7.77390e9	0.107347
$260$	6.71774e10	0.911681
$261$	4.33333e10	0.578015
$262$	−2.17343e10	−0.284964
$263$	1.52881e11	1.97039	0.985195	−	0.171438i	$-0.0548412\pi$
$263$	1.52881e11	1.97039	0.985195	+	0.171438i	$0.0548412\pi$
$264$	3.06432e9	0.0388254
$265$	9.09682e10	1.13314
$266$	2.51110e9	0.0307537
$267$	−1.27116e10	−0.153073
$268$	−1.09712e11	−1.29912
$269$	−5.76344e10	−0.671115	−0.335557	−	0.942020i	$-0.608925\pi$
$269$	−5.76344e10	−0.671115	−0.335557	+	0.942020i	$0.608925\pi$
$270$	−8.76758e9	−0.100402
$271$	−4.13527e10	−0.465738	−0.232869	−	0.972508i	$-0.574811\pi$
$271$	−4.13527e10	−0.465738	−0.232869	+	0.972508i	$0.574811\pi$
$272$	−1.13429e11	−1.25650
$273$	9.06833e8	0.00988088
$274$	−1.78835e10	−0.191680
$275$	−7.70076e10	−0.811964
$276$	−3.17831e9	−0.0329690
$277$	3.96279e10	0.404428	0.202214	−	0.979341i	$-0.435186\pi$
$277$	3.96279e10	0.404428	0.202214	+	0.979341i	$0.435186\pi$
$278$	3.26587e9	0.0327942
$279$	−4.60036e10	−0.454541
$280$	6.03276e9	0.0586550
$281$	9.33731e10	0.893394	0.446697	−	0.894685i	$-0.352600\pi$
$281$	9.33731e10	0.893394	0.446697	+	0.894685i	$0.352600\pi$
$282$	−2.39484e9	−0.0225505
$283$	1.49276e11	1.38341	0.691707	−	0.722178i	$-0.256859\pi$
$283$	1.49276e11	1.38341	0.691707	+	0.722178i	$0.256859\pi$
$284$	−1.91316e11	−1.74509
$285$	4.44652e10	0.399226
$286$	−8.41777e9	−0.0743960
$287$	−1.25499e10	−0.109188
$288$	6.48735e10	0.555649
$289$	1.23025e11	1.03741
$290$	2.21020e10	0.183502
$291$	4.25747e8	0.00348043
$292$	3.80492e10	0.306283
$293$	−8.39012e10	−0.665065	−0.332533	−	0.943092i	$-0.607903\pi$
$293$	−8.39012e10	−0.665065	−0.332533	+	0.943092i	$0.607903\pi$
$294$	−4.20562e9	−0.0328297
$295$	−4.34988e10	−0.334409
$296$	5.76528e10	0.436523
$297$	−2.60612e10	−0.194353
$298$	4.14099e10	0.304181
$299$	1.78299e10	0.129011
$300$	3.01271e10	0.214739
$301$	1.10350e10	0.0774862
$302$	−2.35610e10	−0.162991
$303$	8.98874e9	0.0612642
$304$	−2.06817e11	−1.38885
$305$	−4.47039e11	−2.95799
$306$	−4.28345e10	−0.279285
$307$	1.08226e11	0.695357	0.347679	−	0.937614i	$-0.386970\pi$
$307$	1.08226e11	0.695357	0.347679	+	0.937614i	$0.386970\pi$
$308$	8.78096e9	0.0555986
$309$	−2.90167e10	−0.181065
$310$	−2.34641e10	−0.144303
$311$	8.56748e10	0.519316	0.259658	−	0.965701i	$-0.416390\pi$
$311$	8.56748e10	0.519316	0.259658	+	0.965701i	$0.416390\pi$
$312$	6.72526e9	0.0401803
$313$	−2.41265e11	−1.42084	−0.710418	−	0.703780i	$-0.751494\pi$
$313$	−2.41265e11	−1.42084	−0.710418	+	0.703780i	$0.751494\pi$
$314$	−1.17392e9	−0.00681483
$315$	−2.53004e10	−0.144787
$316$	1.59418e11	0.899386
$317$	−6.60254e10	−0.367235	−0.183618	−	0.982998i	$-0.558781\pi$
$317$	−6.60254e10	−0.367235	−0.183618	+	0.982998i	$0.558781\pi$
$318$	4.45950e9	0.0244548
$319$	6.56973e10	0.355213
$320$	−2.20472e11	−1.17538
$321$	5.04589e10	0.265256
$322$	7.84065e8	0.00406444
$323$	4.40538e11	2.25202
$324$	−1.74972e11	−0.882095
$325$	−1.69009e11	−0.840298
$326$	6.34818e10	0.311293
$327$	−2.14421e10	−0.103706
$328$	−9.30729e10	−0.444008
$329$	−1.40144e10	−0.0659465
$330$	−6.55476e9	−0.0304260
$331$	3.23911e11	1.48320	0.741599	−	0.670843i	$-0.234068\pi$
$331$	3.23911e11	1.48320	0.741599	+	0.670843i	$0.234068\pi$
$332$	−3.02717e10	−0.136746
$333$	−2.41787e11	−1.07754
$334$	2.68771e10	0.118174
$335$	4.79254e11	2.07905
$336$	−3.28438e9	−0.0140581
$337$	−4.63717e10	−0.195848	−0.0979238	−	0.995194i	$-0.531220\pi$
$337$	−4.63717e10	−0.195848	−0.0979238	+	0.995194i	$0.531220\pi$
$338$	2.97856e10	0.124131
$339$	−3.99862e10	−0.164441
$340$	5.18258e11	2.10325
$341$	−6.97458e10	−0.279334
$342$	−7.81012e10	−0.308703
$343$	−4.94551e10	−0.192924
$344$	8.18380e10	0.315096
$345$	1.38838e10	0.0527621
$346$	8.50922e10	0.319189
$347$	−2.83656e11	−1.05029	−0.525145	−	0.851013i	$-0.675989\pi$
$347$	−2.83656e11	−1.05029	−0.525145	+	0.851013i	$0.675989\pi$
$348$	−2.57022e10	−0.0939429
$349$	−4.64002e10	−0.167419	−0.0837096	−	0.996490i	$-0.526677\pi$
$349$	−4.64002e10	−0.167419	−0.0837096	+	0.996490i	$0.526677\pi$
$350$	−7.43212e9	−0.0264732
$351$	−5.71965e10	−0.201135
$352$	9.83542e10	0.341469
$353$	−1.07258e11	−0.367658	−0.183829	−	0.982958i	$-0.558849\pi$
$353$	−1.07258e11	−0.367658	−0.183829	+	0.982958i	$0.558849\pi$
$354$	−2.13243e9	−0.00721704
$355$	8.35724e11	2.79277
$356$	−2.70139e11	−0.891380
$357$	6.99601e9	0.0227952
$358$	−4.76103e10	−0.153189
$359$	−1.83222e11	−0.582174	−0.291087	−	0.956697i	$-0.594017\pi$
$359$	−1.83222e11	−0.582174	−0.291087	+	0.956697i	$0.594017\pi$
$360$	−1.87633e11	−0.588773
$361$	4.80555e11	1.48923
$362$	9.29659e10	0.284534
$363$	3.50270e10	0.105882
$364$	1.92716e10	0.0575388
$365$	−1.66210e11	−0.490161
$366$	−2.19150e10	−0.0638377
$367$	−4.14618e11	−1.19303	−0.596515	−	0.802602i	$-0.703448\pi$
$367$	−4.14618e11	−1.19303	−0.596515	+	0.802602i	$0.703448\pi$
$368$	−6.45764e10	−0.183552
$369$	3.90333e11	1.09602
$370$	−1.23323e11	−0.342086
$371$	2.60966e10	0.0715156
$372$	2.72861e10	0.0738751
$373$	3.78599e11	1.01272	0.506361	−	0.862322i	$-0.330990\pi$
$373$	3.78599e11	1.01272	0.506361	+	0.862322i	$0.330990\pi$
$374$	−6.49411e10	−0.171632
$375$	−3.47032e10	−0.0906210
$376$	−1.03933e11	−0.268170
$377$	1.44186e11	0.367609
$378$	−2.51521e9	−0.00633666
$379$	−6.40826e11	−1.59538	−0.797689	−	0.603070i	$-0.793944\pi$
$379$	−6.40826e11	−1.59538	−0.797689	+	0.603070i	$0.793944\pi$
$380$	9.44952e11	2.32479
$381$	−2.27346e10	−0.0552744
$382$	4.38433e10	0.105346
$383$	−1.28786e11	−0.305826	−0.152913	−	0.988240i	$-0.548866\pi$
$383$	−1.28786e11	−0.305826	−0.152913	+	0.988240i	$0.548866\pi$
$384$	−5.09085e10	−0.119481
$385$	−3.83578e10	−0.0889776
$386$	−8.98423e10	−0.205986
$387$	−3.43216e11	−0.777800
$388$	9.04775e9	0.0202674
$389$	−5.72428e11	−1.26750	−0.633750	−	0.773538i	$-0.718485\pi$
$389$	−5.72428e11	−1.26750	−0.633750	+	0.773538i	$0.718485\pi$
$390$	−1.43857e10	−0.0314877
$391$	1.37553e11	0.297629
$392$	−1.82519e11	−0.390410
$393$	−1.10407e11	−0.233469
$394$	1.22569e11	0.256241
$395$	−6.96386e11	−1.43934
$396$	−2.73109e11	−0.558094
$397$	−9.05368e11	−1.82923	−0.914614	−	0.404328i	$-0.867505\pi$
$397$	−9.05368e11	−1.82923	−0.914614	+	0.404328i	$0.867505\pi$
$398$	−1.17148e10	−0.0234024
$399$	1.27560e10	0.0251963
$400$	6.12117e11	1.19554
$401$	4.34574e11	0.839293	0.419646	−	0.907688i	$-0.362154\pi$
$401$	4.34574e11	0.839293	0.419646	+	0.907688i	$0.362154\pi$
$402$	2.34943e10	0.0448689
$403$	−1.53071e11	−0.289081
$404$	1.91024e11	0.356756
$405$	7.64328e11	1.41167
$406$	6.34054e9	0.0115813
$407$	−3.66571e11	−0.662191
$408$	5.18838e10	0.0926960
$409$	−7.88295e11	−1.39294	−0.696472	−	0.717584i	$-0.745248\pi$
$409$	−7.88295e11	−1.39294	−0.696472	+	0.717584i	$0.745248\pi$
$410$	1.99089e11	0.347952
$411$	−9.08455e10	−0.157042
$412$	−6.16647e11	−1.05439
$413$	−1.24787e10	−0.0211055
$414$	−2.43863e10	−0.0407985
$415$	1.32236e11	0.218843
$416$	2.15858e11	0.353385
$417$	1.65901e10	0.0268681
$418$	−1.18409e11	−0.189710
$419$	−4.37142e11	−0.692882	−0.346441	−	0.938072i	$-0.612610\pi$
$419$	−4.37142e11	−0.692882	−0.346441	+	0.938072i	$0.612610\pi$
$420$	1.50064e10	0.0235318
$421$	1.12912e12	1.75175	0.875873	−	0.482543i	$-0.160287\pi$
$421$	1.12912e12	1.75175	0.875873	+	0.482543i	$0.160287\pi$
$422$	1.00768e11	0.154674
$423$	4.35880e11	0.661965
$424$	1.93537e11	0.290816
$425$	−1.30386e12	−1.93857
$426$	4.09694e10	0.0602721
$427$	−1.28245e11	−0.186687
$428$	1.07233e12	1.54465
$429$	−4.27609e10	−0.0609521
$430$	−1.75056e11	−0.246928
$431$	1.54261e11	0.215331	0.107666	−	0.994187i	$-0.465662\pi$
$431$	1.54261e11	0.215331	0.107666	+	0.994187i	$0.465662\pi$
$432$	2.07155e11	0.286166
$433$	−9.92086e11	−1.35629	−0.678147	−	0.734926i	$-0.737217\pi$
$433$	−9.92086e11	−1.35629	−0.678147	+	0.734926i	$0.737217\pi$
$434$	−6.73127e9	−0.00910737
$435$	1.12275e11	0.150342
$436$	−4.55676e11	−0.603903
$437$	2.50804e11	0.328979
$438$	−8.14805e9	−0.0105784
$439$	5.20320e11	0.668622	0.334311	−	0.942463i	$-0.391496\pi$
$439$	5.20320e11	0.668622	0.334311	+	0.942463i	$0.391496\pi$
$440$	−2.84469e11	−0.361825
$441$	7.65456e11	0.963710
$442$	−1.42526e11	−0.177621
$443$	7.69893e11	0.949759	0.474880	−	0.880051i	$-0.342492\pi$
$443$	7.69893e11	0.949759	0.474880	+	0.880051i	$0.342492\pi$
$444$	1.43411e11	0.175129
$445$	1.18005e12	1.42653
$446$	2.57374e11	0.308005
$447$	2.10356e11	0.249213
$448$	−6.32481e10	−0.0741816
$449$	1.50679e12	1.74962	0.874811	−	0.484464i	$-0.160985\pi$
$449$	1.50679e12	1.74962	0.874811	+	0.484464i	$0.160985\pi$
$450$	2.31157e11	0.265736
$451$	5.91781e11	0.673545
$452$	−8.49766e11	−0.957583
$453$	−1.19686e11	−0.133537
$454$	1.44380e10	0.0159499
$455$	−8.41838e10	−0.0920825
$456$	9.46009e10	0.102460
$457$	−1.68606e12	−1.80821	−0.904107	−	0.427307i	$-0.859462\pi$
$457$	−1.68606e12	−1.80821	−0.904107	+	0.427307i	$0.859462\pi$
$458$	−2.16437e9	−0.00229845
$459$	−4.41258e11	−0.464019
$460$	2.95051e11	0.307247
$461$	1.64162e12	1.69285	0.846424	−	0.532509i	$-0.178751\pi$
$461$	1.64162e12	1.69285	0.846424	+	0.532509i	$0.178751\pi$
$462$	−1.88040e9	−0.00192027
$463$	−1.15754e12	−1.17064	−0.585320	−	0.810803i	$-0.699031\pi$
$463$	−1.15754e12	−1.17064	−0.585320	+	0.810803i	$0.699031\pi$
$464$	−5.22214e11	−0.523019
$465$	−1.19194e11	−0.118226
$466$	2.42873e11	0.238585
$467$	1.68807e12	1.64235	0.821174	−	0.570677i	$-0.193319\pi$
$467$	1.68807e12	1.64235	0.821174	+	0.570677i	$0.193319\pi$
$468$	−5.99391e11	−0.577569
$469$	1.37486e11	0.131215
$470$	2.22320e11	0.210154
$471$	−5.96332e9	−0.00558334
$472$	−9.25449e10	−0.0858249
$473$	−5.20347e11	−0.477989
$474$	−3.41387e10	−0.0310631
$475$	−2.37736e12	−2.14276
$476$	1.48676e11	0.132742
$477$	−8.11665e11	−0.717867
$478$	−3.51001e10	−0.0307527
$479$	9.89355e11	0.858702	0.429351	−	0.903138i	$-0.358742\pi$
$479$	9.89355e11	0.858702	0.429351	+	0.903138i	$0.358742\pi$
$480$	1.68085e11	0.144525
$481$	−8.04513e11	−0.685299
$482$	8.28314e10	0.0699010
$483$	3.98292e9	0.00332997
$484$	7.44376e11	0.616579
$485$	−3.95232e10	−0.0324351
$486$	1.17882e11	0.0958480
$487$	−1.22675e12	−0.988268	−0.494134	−	0.869386i	$-0.664515\pi$
$487$	−1.22675e12	−0.988268	−0.494134	+	0.869386i	$0.664515\pi$
$488$	−9.51088e11	−0.759157
$489$	3.22477e11	0.255040
$490$	3.90419e11	0.305949
$491$	−2.67109e11	−0.207406	−0.103703	−	0.994608i	$-0.533069\pi$
$491$	−2.67109e11	−0.207406	−0.103703	+	0.994608i	$0.533069\pi$
$492$	−2.31518e11	−0.178132
$493$	1.11236e12	0.848074
$494$	−2.59871e11	−0.196330
$495$	1.19302e12	0.893149
$496$	5.54394e11	0.411293
$497$	2.39749e11	0.176260
$498$	6.48255e9	0.00472296
$499$	−2.11426e12	−1.52653	−0.763267	−	0.646084i	$-0.776406\pi$
$499$	−2.11426e12	−1.52653	−0.763267	+	0.646084i	$0.776406\pi$
$500$	−7.37494e11	−0.527708
$501$	1.36531e11	0.0968194
$502$	−4.45481e11	−0.313085
$503$	1.58631e11	0.110493	0.0552463	−	0.998473i	$-0.482406\pi$
$503$	1.58631e11	0.110493	0.0552463	+	0.998473i	$0.482406\pi$
$504$	−5.38274e10	−0.0371592
$505$	−8.34449e11	−0.570938
$506$	−3.69719e10	−0.0250723
$507$	1.51306e11	0.101700
$508$	−4.83144e11	−0.321877
$509$	−4.93414e11	−0.325823	−0.162911	−	0.986641i	$-0.552089\pi$
$509$	−4.93414e11	−0.325823	−0.162911	+	0.986641i	$0.552089\pi$
$510$	−1.10983e11	−0.0726422
$511$	−4.76816e10	−0.0309355
$512$	−1.32125e12	−0.849711
$513$	−8.04556e11	−0.512894
$514$	1.14152e11	0.0721353
$515$	2.69370e12	1.68739
$516$	2.03571e11	0.126413
$517$	6.60834e11	0.406804
$518$	−3.53783e10	−0.0215900
$519$	4.32255e11	0.261509
$520$	−6.24324e11	−0.374451
$521$	−3.87333e11	−0.230311	−0.115156	−	0.993347i	$-0.536737\pi$
$521$	−3.87333e11	−0.230311	−0.115156	+	0.993347i	$0.536737\pi$
$522$	−1.97206e11	−0.116253
$523$	2.37846e12	1.39008	0.695038	−	0.718973i	$-0.255388\pi$
$523$	2.37846e12	1.39008	0.695038	+	0.718973i	$0.255388\pi$
$524$	−2.34631e12	−1.35955
$525$	−3.77540e10	−0.0216893
$526$	−6.95747e11	−0.396292
$527$	−1.18091e12	−0.666911
$528$	1.54872e11	0.0867201
$529$	7.83110e10	0.0434783
$530$	−4.13988e11	−0.227901
$531$	3.88119e11	0.211855
$532$	2.71084e11	0.146724
$533$	1.29878e12	0.697049
$534$	5.78491e10	0.0307865
$535$	−4.68424e12	−2.47199
$536$	1.01963e12	0.533580
$537$	−2.41853e11	−0.125507
$538$	2.62289e11	0.134977
$539$	1.16050e12	0.592238
$540$	−9.46496e11	−0.479013
$541$	1.80744e12	0.907144	0.453572	−	0.891220i	$-0.350149\pi$
$541$	1.80744e12	0.907144	0.453572	+	0.891220i	$0.350149\pi$
$542$	1.88192e11	0.0936710
$543$	4.72251e11	0.233117
$544$	1.66529e12	0.815259
$545$	1.99053e12	0.966460
$546$	−4.12691e9	−0.00198728
$547$	3.42334e12	1.63496	0.817479	−	0.575958i	$-0.195371\pi$
$547$	3.42334e12	1.63496	0.817479	+	0.575958i	$0.195371\pi$
$548$	−1.93060e12	−0.914493
$549$	3.98871e12	1.87395
$550$	3.50455e11	0.163305
$551$	2.02819e12	0.937404
$552$	2.95382e10	0.0135412
$553$	−1.99776e11	−0.0908407
$554$	−1.80343e11	−0.0813401
$555$	−6.26459e11	−0.280269
$556$	3.52564e11	0.156459
$557$	4.31494e11	0.189944	0.0949722	−	0.995480i	$-0.469724\pi$
$557$	4.31494e11	0.189944	0.0949722	+	0.995480i	$0.469724\pi$
$558$	2.09358e11	0.0914190
$559$	−1.14200e12	−0.494669
$560$	3.04898e11	0.131011
$561$	−3.29890e11	−0.140617
$562$	−4.24932e11	−0.179683
$563$	−3.36352e12	−1.41093	−0.705467	−	0.708743i	$-0.749262\pi$
$563$	−3.36352e12	−1.41093	−0.705467	+	0.708743i	$0.749262\pi$
$564$	−2.58533e11	−0.107587
$565$	3.71203e12	1.53247
$566$	−6.79343e11	−0.278237
$567$	2.19267e11	0.0890943
$568$	1.77803e12	0.716755
$569$	−1.16637e12	−0.466477	−0.233239	−	0.972420i	$-0.574932\pi$
$569$	−1.16637e12	−0.466477	−0.233239	+	0.972420i	$0.574932\pi$
$570$	−2.02357e11	−0.0802937
$571$	−2.66787e12	−1.05027	−0.525136	−	0.851018i	$-0.675986\pi$
$571$	−2.66787e12	−1.05027	−0.525136	+	0.851018i	$0.675986\pi$
$572$	−9.08732e11	−0.354939
$573$	2.22717e11	0.0863092
$574$	5.71137e10	0.0219602
$575$	−7.42306e11	−0.283190
$576$	1.96716e12	0.744628
$577$	−4.00791e12	−1.50531	−0.752656	−	0.658414i	$-0.771227\pi$
$577$	−4.00791e12	−1.50531	−0.752656	+	0.658414i	$0.771227\pi$
$578$	−5.59874e11	−0.208648
$579$	−4.56384e11	−0.168763
$580$	2.38601e12	0.875479
$581$	3.79352e10	0.0138118
$582$	−1.93753e9	−0.000699997 0
$583$	−1.23056e12	−0.441158
$584$	−3.53616e11	−0.125798
$585$	2.61832e12	0.924316
$586$	3.81827e11	0.133760
$587$	−3.22964e12	−1.12275	−0.561374	−	0.827562i	$-0.689727\pi$
$587$	−3.22964e12	−1.12275	−0.561374	+	0.827562i	$0.689727\pi$
$588$	−4.54014e11	−0.156629
$589$	−2.15318e12	−0.737158
$590$	1.97959e11	0.0672576
$591$	6.22633e11	0.209937
$592$	2.91379e12	0.975015
$593$	3.60741e12	1.19798	0.598990	−	0.800757i	$-0.295569\pi$
$593$	3.60741e12	1.19798	0.598990	+	0.800757i	$0.295569\pi$
$594$	1.18602e11	0.0390889
$595$	−6.49459e11	−0.212435
$596$	4.47037e12	1.45123
$597$	−5.95093e10	−0.0191734
$598$	−8.11421e10	−0.0259472
$599$	1.79812e12	0.570687	0.285343	−	0.958425i	$-0.407892\pi$
$599$	1.79812e12	0.570687	0.285343	+	0.958425i	$0.407892\pi$
$600$	−2.79991e11	−0.0881989
$601$	4.12221e12	1.28883	0.644414	−	0.764677i	$-0.277101\pi$
$601$	4.12221e12	1.28883	0.644414	+	0.764677i	$0.277101\pi$
$602$	−5.02194e10	−0.0155843
$603$	−4.27615e12	−1.31712
$604$	−2.54351e12	−0.777619
$605$	−3.25165e12	−0.986745
$606$	−4.09069e10	−0.0123217
$607$	−5.05467e12	−1.51128	−0.755638	−	0.654989i	$-0.772673\pi$
$607$	−5.05467e12	−1.51128	−0.755638	+	0.654989i	$0.772673\pi$
$608$	3.03637e12	0.901131
$609$	3.22089e10	0.00948851
$610$	2.03443e12	0.594921
$611$	1.45033e12	0.421000
$612$	−4.62416e12	−1.33245
$613$	−2.20307e12	−0.630168	−0.315084	−	0.949064i	$-0.602033\pi$
$613$	−2.20307e12	−0.630168	−0.315084	+	0.949064i	$0.602033\pi$
$614$	−4.92526e11	−0.139853
$615$	1.01134e12	0.285074
$616$	−8.16073e10	−0.0228358
$617$	1.71317e12	0.475901	0.237950	−	0.971277i	$-0.423524\pi$
$617$	1.71317e12	0.475901	0.237950	+	0.971277i	$0.423524\pi$
$618$	1.32052e11	0.0364164
$619$	−4.93702e12	−1.35163	−0.675813	−	0.737073i	$-0.736207\pi$
$619$	−4.93702e12	−1.35163	−0.675813	+	0.737073i	$0.736207\pi$
$620$	−2.53304e12	−0.688462
$621$	−2.51214e11	−0.0677847
$622$	−3.89898e11	−0.104447
$623$	3.38527e11	0.0900321
$624$	3.39897e11	0.0897464
$625$	−1.95927e12	−0.513610
$626$	1.09797e12	0.285764
$627$	−6.01497e11	−0.155428
$628$	−1.26729e11	−0.0325132
$629$	−6.20663e12	−1.58099
$630$	1.15140e11	0.0291201
$631$	−5.77328e12	−1.44974	−0.724871	−	0.688885i	$-0.758101\pi$
$631$	−5.77328e12	−1.44974	−0.724871	+	0.688885i	$0.758101\pi$
$632$	−1.48158e12	−0.369401
$633$	5.11885e11	0.126723
$634$	3.00475e11	0.0738597
$635$	2.11051e12	0.515117
$636$	4.81422e11	0.116673
$637$	2.54695e12	0.612905
$638$	−2.98982e11	−0.0714418
$639$	−7.45676e12	−1.76928
$640$	4.72598e12	1.11348
$641$	1.52940e12	0.357816	0.178908	−	0.983866i	$-0.442744\pi$
$641$	1.52940e12	0.357816	0.178908	+	0.983866i	$0.442744\pi$
$642$	−2.29634e11	−0.0533492
$643$	2.83985e12	0.655158	0.327579	−	0.944824i	$-0.393767\pi$
$643$	2.83985e12	0.655158	0.327579	+	0.944824i	$0.393767\pi$
$644$	8.46431e10	0.0193912
$645$	−8.89258e11	−0.202306
$646$	−2.00485e12	−0.452934
$647$	5.39114e11	0.120952	0.0604758	−	0.998170i	$-0.480738\pi$
$647$	5.39114e11	0.120952	0.0604758	+	0.998170i	$0.480738\pi$
$648$	1.62613e12	0.362299
$649$	5.88424e11	0.130193
$650$	7.69142e11	0.169004
$651$	−3.41937e10	−0.00746160
$652$	6.85312e12	1.48516
$653$	2.82563e12	0.608143	0.304072	−	0.952649i	$-0.401654\pi$
$653$	2.82563e12	0.608143	0.304072	+	0.952649i	$0.401654\pi$
$654$	9.75810e10	0.0208576
$655$	1.02494e13	2.17576
$656$	−4.70394e12	−0.991733
$657$	1.48301e12	0.310527
$658$	6.37781e10	0.0132634
$659$	2.75067e12	0.568138	0.284069	−	0.958804i	$-0.408315\pi$
$659$	2.75067e12	0.568138	0.284069	+	0.958804i	$0.408315\pi$
$660$	−7.07613e11	−0.145160
$661$	1.38168e12	0.281515	0.140757	−	0.990044i	$-0.455046\pi$
$661$	1.38168e12	0.281515	0.140757	+	0.990044i	$0.455046\pi$
$662$	−1.47409e12	−0.298306
$663$	−7.24010e11	−0.145524
$664$	2.81335e11	0.0561653
$665$	−1.18417e12	−0.234811
$666$	1.10035e12	0.216719
$667$	6.33281e11	0.123888
$668$	2.90149e12	0.563803
$669$	1.30742e12	0.252346
$670$	−2.18104e12	−0.418146
$671$	6.04726e12	1.15161
$672$	4.82194e10	0.00912136
$673$	5.52153e12	1.03751	0.518754	−	0.854923i	$-0.326396\pi$
$673$	5.52153e12	1.03751	0.518754	+	0.854923i	$0.326396\pi$
$674$	2.11033e11	0.0393896
$675$	2.38125e12	0.441507
$676$	3.21548e12	0.592224
$677$	−7.80588e12	−1.42815	−0.714074	−	0.700071i	$-0.753152\pi$
$677$	−7.80588e12	−1.42815	−0.714074	+	0.700071i	$0.753152\pi$
$678$	1.81973e11	0.0330731
$679$	−1.13383e10	−0.00204707
$680$	−4.81652e12	−0.863859
$681$	7.33429e10	0.0130676
$682$	3.17407e11	0.0561806
$683$	−7.03238e12	−1.23654	−0.618271	−	0.785965i	$-0.712167\pi$
$683$	−7.03238e12	−1.23654	−0.618271	+	0.785965i	$0.712167\pi$
$684$	−8.43134e12	−1.47280
$685$	8.43344e12	1.46351
$686$	2.25065e11	0.0388017
$687$	−1.09946e10	−0.00188311
$688$	4.13613e12	0.703794
$689$	−2.70071e12	−0.456553
$690$	−6.31839e10	−0.0106117
$691$	−1.15771e13	−1.93174	−0.965869	−	0.259032i	$-0.916596\pi$
$691$	−1.15771e13	−1.93174	−0.965869	+	0.259032i	$0.916596\pi$
$692$	9.18605e12	1.52283
$693$	3.42248e11	0.0563691
$694$	1.29089e12	0.211238
$695$	−1.54010e12	−0.250391
$696$	2.38868e11	0.0385848
$697$	1.00198e13	1.60809
$698$	2.11163e11	0.0336720
$699$	1.23376e12	0.195471
$700$	−8.02328e11	−0.126302
$701$	−3.30617e12	−0.517123	−0.258561	−	0.965995i	$-0.583248\pi$
$701$	−3.30617e12	−0.517123	−0.258561	+	0.965995i	$0.583248\pi$
$702$	2.60296e11	0.0404530
$703$	−1.13167e13	−1.74751
$704$	2.98240e12	0.457604
$705$	1.12935e12	0.172177
$706$	4.88122e11	0.0739448
$707$	−2.39383e11	−0.0360335
$708$	−2.30204e11	−0.0344321
$709$	3.17988e12	0.472610	0.236305	−	0.971679i	$-0.424064\pi$
$709$	3.17988e12	0.472610	0.236305	+	0.971679i	$0.424064\pi$
$710$	−3.80330e12	−0.561692
$711$	6.21351e12	0.911851
$712$	2.51059e12	0.366113
$713$	−6.72307e11	−0.0974237
$714$	−3.18382e10	−0.00458465
$715$	3.96961e12	0.568029
$716$	−5.13973e12	−0.730856
$717$	−1.78303e11	−0.0251954
$718$	8.33827e11	0.117089
$719$	1.03326e13	1.44189	0.720944	−	0.692994i	$-0.243709\pi$
$719$	1.03326e13	1.44189	0.720944	+	0.692994i	$0.243709\pi$
$720$	−9.48305e12	−1.31508
$721$	7.72756e11	0.106496
$722$	−2.18696e12	−0.299518
$723$	4.20770e11	0.0572694
$724$	1.00360e13	1.35750
$725$	−6.00285e12	−0.806931
$726$	−1.59405e11	−0.0212954
$727$	1.21606e13	1.61454	0.807271	−	0.590181i	$-0.200944\pi$
$727$	1.21606e13	1.61454	0.807271	+	0.590181i	$0.200944\pi$
$728$	−1.79103e11	−0.0236327
$729$	−6.41125e12	−0.840753
$730$	7.56406e11	0.0985830
$731$	−8.81030e12	−1.14120
$732$	−2.36582e12	−0.304566
$733$	−9.83401e12	−1.25824	−0.629119	−	0.777309i	$-0.716584\pi$
$733$	−9.83401e12	−1.25824	−0.629119	+	0.777309i	$0.716584\pi$
$734$	1.88689e12	0.239946
$735$	1.98326e12	0.250661
$736$	9.48074e11	0.119095
$737$	−6.48304e12	−0.809423
$738$	−1.77637e12	−0.220435
$739$	1.11044e13	1.36960	0.684801	−	0.728730i	$-0.259889\pi$
$739$	1.11044e13	1.36960	0.684801	+	0.728730i	$0.259889\pi$
$740$	−1.33132e13	−1.63207
$741$	−1.32010e12	−0.160852
$742$	−1.18763e11	−0.0143835
$743$	−7.01241e12	−0.844146	−0.422073	−	0.906562i	$-0.638697\pi$
$743$	−7.01241e12	−0.844146	−0.422073	+	0.906562i	$0.638697\pi$
$744$	−2.53588e11	−0.0303424
$745$	−1.95279e13	−2.32248
$746$	−1.72297e12	−0.203682
$747$	−1.17988e12	−0.138642
$748$	−7.01066e12	−0.818845
$749$	−1.34379e12	−0.156014
$750$	1.57931e11	0.0182260
$751$	−3.87793e12	−0.444857	−0.222428	−	0.974949i	$-0.571398\pi$
$751$	−3.87793e12	−0.444857	−0.222428	+	0.974949i	$0.571398\pi$
$752$	−5.25283e12	−0.598981
$753$	−2.26297e12	−0.256508
$754$	−6.56176e11	−0.0739349
$755$	1.11108e13	1.24447
$756$	−2.71527e11	−0.0302318
$757$	3.18066e12	0.352035	0.176018	−	0.984387i	$-0.443678\pi$
$757$	3.18066e12	0.352035	0.176018	+	0.984387i	$0.443678\pi$
$758$	2.91634e12	0.320868
$759$	−1.87811e11	−0.0205415
$760$	−8.78206e12	−0.954851
$761$	1.23066e13	1.33017	0.665086	−	0.746767i	$-0.268395\pi$
$761$	1.23066e13	1.33017	0.665086	+	0.746767i	$0.268395\pi$
$762$	1.03463e11	0.0111170
$763$	5.71034e11	0.0609960
$764$	4.73306e12	0.502600
$765$	2.01997e13	2.13240
$766$	5.86094e11	0.0615089
$767$	1.29141e12	0.134737
$768$	−9.84288e11	−0.102093
$769$	−3.39782e12	−0.350374	−0.175187	−	0.984535i	$-0.556053\pi$
$769$	−3.39782e12	−0.350374	−0.175187	+	0.984535i	$0.556053\pi$
$770$	1.74563e11	0.0178955
$771$	5.79871e11	0.0590999
$772$	−9.69885e12	−0.982748
$773$	−4.22407e12	−0.425523	−0.212762	−	0.977104i	$-0.568246\pi$
$773$	−4.22407e12	−0.425523	−0.212762	+	0.977104i	$0.568246\pi$
$774$	1.56194e12	0.156434
$775$	6.37276e12	0.634556
$776$	−8.40868e10	−0.00832434
$777$	−1.79716e11	−0.0176885
$778$	2.60507e12	0.254924
$779$	1.82693e13	1.77748
$780$	−1.55300e12	−0.150226
$781$	−1.13051e13	−1.08729
$782$	−6.25992e11	−0.0598603
$783$	−2.03151e12	−0.193148
$784$	−9.22458e12	−0.872016
$785$	5.53592e11	0.0520327
$786$	5.02450e11	0.0469561
$787$	6.64075e12	0.617064	0.308532	−	0.951214i	$-0.400162\pi$
$787$	6.64075e12	0.617064	0.308532	+	0.951214i	$0.400162\pi$
$788$	1.32319e13	1.22251
$789$	−3.53428e12	−0.324679
$790$	3.16919e12	0.289485
$791$	1.06489e12	0.0967187
$792$	2.53818e12	0.229223
$793$	1.32719e13	1.19180
$794$	4.12025e12	0.367901
$795$	−2.10299e12	−0.186718
$796$	−1.26466e12	−0.111652
$797$	1.72875e13	1.51765	0.758824	−	0.651296i	$-0.225774\pi$
$797$	1.72875e13	1.51765	0.758824	+	0.651296i	$0.225774\pi$
$798$	−5.80513e10	−0.00506756
$799$	1.11890e13	0.971247
$800$	−8.98675e12	−0.775707
$801$	−1.05290e13	−0.903734
$802$	−1.97770e12	−0.168802
$803$	2.24838e12	0.190831
$804$	2.53631e12	0.214067
$805$	−3.69746e11	−0.0310329
$806$	6.96612e11	0.0581411
$807$	1.33239e12	0.110586
$808$	−1.77531e12	−0.146529
$809$	−2.79948e12	−0.229778	−0.114889	−	0.993378i	$-0.536651\pi$
$809$	−2.79948e12	−0.229778	−0.114889	+	0.993378i	$0.536651\pi$
$810$	−3.47839e12	−0.283920
$811$	−1.32107e13	−1.07234	−0.536169	−	0.844111i	$-0.680129\pi$
$811$	−1.32107e13	−1.07234	−0.536169	+	0.844111i	$0.680129\pi$
$812$	6.84487e11	0.0552539
$813$	9.55986e11	0.0767439
$814$	1.66823e12	0.133182
$815$	−2.99364e13	−2.37679
$816$	2.62223e12	0.207045
$817$	−1.60640e13	−1.26141
$818$	3.58746e12	0.280154
$819$	7.51131e11	0.0583362
$820$	2.14924e13	1.66006
$821$	2.19469e13	1.68589	0.842945	−	0.538000i	$-0.180820\pi$
$821$	2.19469e13	1.68589	0.842945	+	0.538000i	$0.180820\pi$
$822$	4.13430e11	0.0315848
$823$	1.05046e13	0.798145	0.399072	−	0.916919i	$-0.369332\pi$
$823$	1.05046e13	0.798145	0.399072	+	0.916919i	$0.369332\pi$
$824$	5.73091e12	0.433063
$825$	1.78025e12	0.133795
$826$	5.67896e10	0.00424482
$827$	1.03403e13	0.768701	0.384350	−	0.923187i	$-0.374425\pi$
$827$	1.03403e13	0.768701	0.384350	+	0.923187i	$0.374425\pi$
$828$	−2.63260e12	−0.194647
$829$	−1.37587e13	−1.01177	−0.505886	−	0.862600i	$-0.668834\pi$
$829$	−1.37587e13	−1.01177	−0.505886	+	0.862600i	$0.668834\pi$
$830$	−6.01793e11	−0.0440145
$831$	−9.16112e11	−0.0666414
$832$	6.54548e12	0.473572
$833$	1.96491e13	1.41397
$834$	−7.54999e10	−0.00540380
$835$	−1.26746e13	−0.902286
$836$	−1.27827e13	−0.905095
$837$	2.15670e12	0.151888
$838$	1.98939e12	0.139355
$839$	3.00763e12	0.209554	0.104777	−	0.994496i	$-0.466587\pi$
$839$	3.00763e12	0.209554	0.104777	+	0.994496i	$0.466587\pi$
$840$	−1.39465e11	−0.00966512
$841$	−9.38596e12	−0.646988
$842$	−5.13852e12	−0.352317
$843$	−2.15859e12	−0.147213
$844$	1.08783e13	0.737939
$845$	−1.40462e13	−0.947770
$846$	−1.98365e12	−0.133137
$847$	−9.32820e11	−0.0622763
$848$	9.78146e12	0.649564
$849$	−3.45095e12	−0.227958
$850$	5.93376e12	0.389892
$851$	−3.53352e12	−0.230953
$852$	4.42282e12	0.287555
$853$	−5.44419e12	−0.352097	−0.176049	−	0.984381i	$-0.556332\pi$
$853$	−5.44419e12	−0.352097	−0.176049	+	0.984381i	$0.556332\pi$
$854$	5.83630e11	0.0375471
$855$	3.68306e13	2.35701
$856$	−9.96585e12	−0.634428
$857$	7.53309e12	0.477045	0.238523	−	0.971137i	$-0.423337\pi$
$857$	7.53309e12	0.477045	0.238523	+	0.971137i	$0.423337\pi$
$858$	1.94601e11	0.0122589
$859$	1.26295e13	0.791438	0.395719	−	0.918372i	$-0.370495\pi$
$859$	1.26295e13	0.791438	0.395719	+	0.918372i	$0.370495\pi$
$860$	−1.88981e13	−1.17808
$861$	2.90128e11	0.0179918
$862$	−7.02026e11	−0.0433082
$863$	−2.79666e13	−1.71629	−0.858146	−	0.513406i	$-0.828383\pi$
$863$	−2.79666e13	−1.71629	−0.858146	+	0.513406i	$0.828383\pi$
$864$	−3.04133e12	−0.185674
$865$	−4.01274e13	−2.43707
$866$	4.51489e12	0.272783
$867$	−2.84407e12	−0.170944
$868$	−7.26668e11	−0.0434508
$869$	9.42026e12	0.560369
$870$	−5.10952e11	−0.0302374
$871$	−1.42283e13	−0.837668
$872$	4.23490e12	0.248039
$873$	3.52647e11	0.0205483
$874$	−1.14139e12	−0.0661655
$875$	9.24196e11	0.0533001
$876$	−8.79616e11	−0.0504690
$877$	6.48053e12	0.369924	0.184962	−	0.982746i	$-0.440784\pi$
$877$	6.48053e12	0.369924	0.184962	+	0.982746i	$0.440784\pi$
$878$	−2.36793e12	−0.134476
$879$	1.93962e12	0.109589
$880$	−1.43772e13	−0.808168
$881$	−1.95933e13	−1.09576	−0.547880	−	0.836557i	$-0.684565\pi$
$881$	−1.95933e13	−1.09576	−0.547880	+	0.836557i	$0.684565\pi$
$882$	−3.48352e12	−0.193825
$883$	−1.35104e13	−0.747904	−0.373952	−	0.927448i	$-0.621997\pi$
$883$	−1.35104e13	−0.747904	−0.373952	+	0.927448i	$0.621997\pi$
$884$	−1.53863e13	−0.847420
$885$	1.00560e12	0.0551036
$886$	−3.50371e12	−0.191019
$887$	3.10954e13	1.68671	0.843354	−	0.537358i	$-0.180578\pi$
$887$	3.10954e13	1.68671	0.843354	+	0.537358i	$0.180578\pi$
$888$	−1.33281e12	−0.0719299
$889$	6.05455e11	0.0325105
$890$	−5.37029e12	−0.286908
$891$	−1.03393e13	−0.549595
$892$	2.77846e13	1.46948
$893$	2.04011e13	1.07355
$894$	−9.57310e11	−0.0501226
$895$	2.24518e13	1.16963
$896$	1.35577e12	0.0702748
$897$	−4.12189e11	−0.0212584
$898$	−6.85727e12	−0.351890
$899$	−5.43678e12	−0.277602
$900$	2.49543e13	1.26781
$901$	−2.08353e13	−1.05327
$902$	−2.69314e12	−0.135466
$903$	−2.55107e11	−0.0127681
$904$	7.89744e12	0.393304
$905$	−4.38404e13	−2.17248
$906$	5.44680e11	0.0268575
$907$	−9.77696e11	−0.0479702	−0.0239851	−	0.999712i	$-0.507635\pi$
$907$	−9.77696e11	−0.0479702	−0.0239851	+	0.999712i	$0.507635\pi$
$908$	1.55865e12	0.0760959
$909$	7.44538e12	0.361701
$910$	3.83113e11	0.0185200
$911$	−2.87604e13	−1.38345	−0.691724	−	0.722162i	$-0.743148\pi$
$911$	−2.87604e13	−1.38345	−0.691724	+	0.722162i	$0.743148\pi$
$912$	4.78117e12	0.228853
$913$	−1.78880e12	−0.0852008
$914$	7.67310e12	0.363674
$915$	1.03346e13	0.487414
$916$	−2.33652e11	−0.0109658
$917$	2.94029e12	0.137318
$918$	2.00812e12	0.0933251
$919$	−1.21835e13	−0.563446	−0.281723	−	0.959496i	$-0.590906\pi$
$919$	−1.21835e13	−0.563446	−0.281723	+	0.959496i	$0.590906\pi$
$920$	−2.74211e12	−0.126194
$921$	−2.50195e12	−0.114580
$922$	−7.47085e12	−0.340472
$923$	−2.48114e13	−1.12523
$924$	−2.02997e11	−0.00916149
$925$	3.34941e13	1.50428
$926$	5.26788e12	0.235443
$927$	−2.40345e13	−1.06900
$928$	7.66684e12	0.339352
$929$	−3.41272e12	−0.150325	−0.0751624	−	0.997171i	$-0.523948\pi$
$929$	−3.41272e12	−0.150325	−0.0751624	+	0.997171i	$0.523948\pi$
$930$	5.42439e11	0.0237781
$931$	3.58267e13	1.56291
$932$	2.62192e13	1.13828
$933$	−1.98062e12	−0.0855724
$934$	−7.68227e12	−0.330315
$935$	3.06246e13	1.31044
$936$	5.57054e12	0.237223
$937$	−3.00286e13	−1.27264	−0.636322	−	0.771423i	$-0.719545\pi$
$937$	−3.00286e13	−1.27264	−0.636322	+	0.771423i	$0.719545\pi$
$938$	−6.25688e11	−0.0263903
$939$	5.57752e12	0.234124
$940$	2.40003e13	1.00263
$941$	1.32633e12	0.0551442	0.0275721	−	0.999620i	$-0.491222\pi$
$941$	1.32633e12	0.0551442	0.0275721	+	0.999620i	$0.491222\pi$
$942$	2.71385e10	0.00112294
$943$	5.70441e12	0.234913
$944$	−4.67725e12	−0.191698
$945$	1.18611e12	0.0483817
$946$	2.36805e12	0.0961349
$947$	1.40224e13	0.566561	0.283281	−	0.959037i	$-0.408577\pi$
$947$	1.40224e13	0.566561	0.283281	+	0.959037i	$0.408577\pi$
$948$	−3.68541e12	−0.148200
$949$	4.93452e12	0.197491
$950$	1.08192e13	0.430960
$951$	1.52637e12	0.0605127
$952$	−1.38174e12	−0.0545206
$953$	1.12886e13	0.443327	0.221663	−	0.975123i	$-0.428851\pi$
$953$	1.12886e13	0.443327	0.221663	+	0.975123i	$0.428851\pi$
$954$	3.69381e12	0.144380
$955$	−2.06754e13	−0.804339
$956$	−3.78920e12	−0.146719
$957$	−1.51878e12	−0.0585318
$958$	−4.50246e12	−0.172705
$959$	2.41935e12	0.0923665
$960$	5.09684e12	0.193678
$961$	−2.06678e13	−0.781698
$962$	3.66126e12	0.137830
$963$	4.17952e13	1.56606
$964$	8.94199e12	0.333494
$965$	4.23674e13	1.57275
$966$	−1.81259e10	−0.000669735 0
$967$	−6.49322e12	−0.238804	−0.119402	−	0.992846i	$-0.538098\pi$
$967$	−6.49322e12	−0.238804	−0.119402	+	0.992846i	$0.538098\pi$
$968$	−6.91798e12	−0.253245
$969$	−1.01843e13	−0.371085
$970$	1.79867e11	0.00652346
$971$	7.85147e12	0.283442	0.141721	−	0.989907i	$-0.454736\pi$
$971$	7.85147e12	0.283442	0.141721	+	0.989907i	$0.454736\pi$
$972$	1.27258e13	0.457285
$973$	−4.41818e11	−0.0158029
$974$	5.58281e12	0.198764
$975$	3.90712e12	0.138464
$976$	−4.80684e13	−1.69565
$977$	−9.39015e12	−0.329721	−0.164861	−	0.986317i	$-0.552717\pi$
$977$	−9.39015e12	−0.329721	−0.164861	+	0.986317i	$0.552717\pi$
$978$	−1.46756e12	−0.0512947
$979$	−1.59629e13	−0.555380
$980$	4.21473e13	1.45966
$981$	−1.77605e13	−0.612273
$982$	1.21559e12	0.0417143
$983$	5.44981e13	1.86162	0.930810	−	0.365504i	$-0.119103\pi$
$983$	5.44981e13	1.86162	0.930810	+	0.365504i	$0.119103\pi$
$984$	2.15165e12	0.0731633
$985$	−5.78007e13	−1.95646
$986$	−5.06225e12	−0.170568
$987$	3.23982e11	0.0108666
$988$	−2.80542e13	−0.936680
$989$	−5.01582e12	−0.166709
$990$	−5.42932e12	−0.179633
$991$	9.66649e12	0.318374	0.159187	−	0.987248i	$-0.449113\pi$
$991$	9.66649e12	0.318374	0.159187	+	0.987248i	$0.449113\pi$
$992$	−8.13930e12	−0.266861
$993$	−7.48812e12	−0.244400
$994$	−1.09108e12	−0.0354500
$995$	5.52441e12	0.178682
$996$	6.99818e11	0.0225329
$997$	5.43361e13	1.74165	0.870824	−	0.491594i	$-0.163586\pi$
$997$	5.43361e13	1.74165	0.870824	+	0.491594i	$0.163586\pi$
$998$	9.62181e12	0.307022
$999$	1.13352e13	0.360068

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.10.a.a.1.4	✓	7
3.2	odd	2		207.10.a.b.1.4		7
4.3	odd	2		368.10.a.f.1.4		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.10.a.a.1.4	✓	7	1.1	even	1	trivial
207.10.a.b.1.4		7	3.2	odd	2
368.10.a.f.1.4		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)

\(f(q)\)	\(=\)	\(q-4.55091 q^{2} -23.1179 q^{3} -491.289 q^{4} +2146.10 q^{5} +105.207 q^{6} +615.663 q^{7} +4565.88 q^{8} -19148.6 q^{9} +O(q^{10})\)	\(q-4.55091 q^{2} -23.1179 q^{3} -491.289 q^{4} +2146.10 q^{5} +105.207 q^{6} +615.663 q^{7} +4565.88 q^{8} -19148.6 q^{9} -9766.68 q^{10} -29031.0 q^{11} +11357.6 q^{12} -63714.3 q^{13} -2801.82 q^{14} -49613.2 q^{15} +230761. q^{16} -491541. q^{17} +87143.4 q^{18} -896238. q^{19} -1.05435e6 q^{20} -14232.8 q^{21} +132117. q^{22} -279841. q^{23} -105553. q^{24} +2.65260e6 q^{25} +289958. q^{26} +897703. q^{27} -302468. q^{28} -2.26300e6 q^{29} +225785. q^{30} +2.40246e6 q^{31} -3.38790e6 q^{32} +671135. q^{33} +2.23696e6 q^{34} +1.32127e6 q^{35} +9.40748e6 q^{36} +1.26269e7 q^{37} +4.07870e6 q^{38} +1.47294e6 q^{39} +9.79881e6 q^{40} -2.03845e7 q^{41} +64772.2 q^{42} +1.79238e7 q^{43} +1.42626e7 q^{44} -4.10946e7 q^{45} +1.27353e6 q^{46} -2.27631e7 q^{47} -5.33471e6 q^{48} -3.99746e7 q^{49} -1.20717e7 q^{50} +1.13634e7 q^{51} +3.13021e7 q^{52} +4.23878e7 q^{53} -4.08536e6 q^{54} -6.23033e7 q^{55} +2.81104e6 q^{56} +2.07191e7 q^{57} +1.02987e7 q^{58} -2.02688e7 q^{59} +2.43744e7 q^{60} -2.08303e8 q^{61} -1.09334e7 q^{62} -1.17891e7 q^{63} -1.02732e8 q^{64} -1.36737e8 q^{65} -3.05427e6 q^{66} +2.23315e8 q^{67} +2.41489e8 q^{68} +6.46933e6 q^{69} -6.01298e6 q^{70} +3.89416e8 q^{71} -8.74300e7 q^{72} -7.74476e7 q^{73} -5.74638e7 q^{74} -6.13225e7 q^{75} +4.40312e8 q^{76} -1.78733e7 q^{77} -6.70321e6 q^{78} -3.24490e8 q^{79} +4.95236e8 q^{80} +3.56148e8 q^{81} +9.27678e7 q^{82} +6.16169e7 q^{83} +6.99243e6 q^{84} -1.05489e9 q^{85} -8.15697e7 q^{86} +5.23158e7 q^{87} -1.32552e8 q^{88} +5.49858e8 q^{89} +1.87018e8 q^{90} -3.92265e7 q^{91} +1.37483e8 q^{92} -5.55397e7 q^{93} +1.03593e8 q^{94} -1.92341e9 q^{95} +7.83211e7 q^{96} -1.84163e7 q^{97} +1.81921e8 q^{98} +5.55902e8 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 7 q - 89 q^{3} + 1536 q^{4} - 2388 q^{5} - 12518 q^{6} - 9896 q^{7} + 34920 q^{8} + 33064 q^{9}+O(q^{10}) \) 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

Modular forms

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