LMFDB - Embedded newform 23.12.a.b.1.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [23,12,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, 12, names="a")

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

chi := DirichletCharacter("23.1");

S:= CuspForms(chi, 12);

N := Newforms(S);

Level:	$ N $	$=$	$ 23 $
Weight:	$ k $	$=$	$ 12 $
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:	$17.6718931529$
Analytic rank:	$0$
Dimension:	$11$
Coefficient field:	$\mathbb{Q}[x]/(x^{11} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{11} - x^{10} - 16849 x^{9} - 2148 x^{8} + 97176782 x^{7} + 169360278 x^{6} - 226650696110 x^{5} + \cdots - 51\!\cdots\!56 $ x^11 - x^10 - 16849x^9 - 2148x^8 + 97176782x^7 + 169360278x^6 - 226650696110x^5 - 940430954112x^4 + 180101325169073x^3 + 1690347715497299x^2 - 9620508603737857*x - 51108001263703556
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2^{11}\cdot 3^{2} $
Twist minimal:	yes
Fricke sign:	$1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.5
Root			$6.40598$ 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)

$f(q)$	$=$	$q-3.40598 q^{2} +746.589 q^{3} -2036.40 q^{4} -11427.6 q^{5} -2542.87 q^{6} +38639.7 q^{7} +13911.4 q^{8} +380248. q^{9} +O(q^{10})$	\(q-3.40598 q^{2} +746.589 q^{3} -2036.40 q^{4} -11427.6 q^{5} -2542.87 q^{6} +38639.7 q^{7} +13911.4 q^{8} +380248. q^{9} +38922.2 q^{10} +733395. q^{11} -1.52035e6 q^{12} +1.73764e6 q^{13} -131606. q^{14} -8.53172e6 q^{15} +4.12316e6 q^{16} -709414. q^{17} -1.29512e6 q^{18} +4.74056e6 q^{19} +2.32712e7 q^{20} +2.88480e7 q^{21} -2.49793e6 q^{22} -6.43634e6 q^{23} +1.03861e7 q^{24} +8.17622e7 q^{25} -5.91837e6 q^{26} +1.51633e8 q^{27} -7.86859e7 q^{28} -4.78519e7 q^{29} +2.90589e7 q^{30} -2.42404e8 q^{31} -4.25339e7 q^{32} +5.47544e8 q^{33} +2.41625e6 q^{34} -4.41560e8 q^{35} -7.74336e8 q^{36} +5.88015e8 q^{37} -1.61463e7 q^{38} +1.29730e9 q^{39} -1.58974e8 q^{40} +1.50605e8 q^{41} -9.82557e7 q^{42} +1.52912e9 q^{43} -1.49348e9 q^{44} -4.34532e9 q^{45} +2.19221e7 q^{46} -1.47296e9 q^{47} +3.07831e9 q^{48} -4.84298e8 q^{49} -2.78480e8 q^{50} -5.29640e8 q^{51} -3.53853e9 q^{52} -8.04916e8 q^{53} -5.16458e8 q^{54} -8.38095e9 q^{55} +5.37532e8 q^{56} +3.53925e9 q^{57} +1.62983e8 q^{58} +8.78112e9 q^{59} +1.73740e10 q^{60} +2.87455e9 q^{61} +8.25624e8 q^{62} +1.46927e10 q^{63} -8.29937e9 q^{64} -1.98571e10 q^{65} -1.86493e9 q^{66} +1.69684e9 q^{67} +1.44465e9 q^{68} -4.80530e9 q^{69} +1.50394e9 q^{70} -3.27860e8 q^{71} +5.28977e9 q^{72} -1.74989e10 q^{73} -2.00277e9 q^{74} +6.10427e10 q^{75} -9.65367e9 q^{76} +2.83382e10 q^{77} -4.41858e9 q^{78} -2.59473e10 q^{79} -4.71179e10 q^{80} +4.58475e10 q^{81} -5.12958e8 q^{82} +5.05896e10 q^{83} -5.87460e10 q^{84} +8.10690e9 q^{85} -5.20816e9 q^{86} -3.57257e10 q^{87} +1.02025e10 q^{88} -4.36408e10 q^{89} +1.48001e10 q^{90} +6.71419e10 q^{91} +1.31070e10 q^{92} -1.80976e11 q^{93} +5.01689e9 q^{94} -5.41733e10 q^{95} -3.17554e10 q^{96} -4.61895e10 q^{97} +1.64951e9 q^{98} +2.78872e11 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9}+O(q^{10}) $ 11 * q + 32 * q^2 - 20 * q^3 + 11264 * q^4 + 1034 * q^5 - 22385 * q^6 + 159584 * q^7 + 115497 * q^8 + 611943 * q^9	\( 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9} - 627650 q^{10} - 771396 q^{11} - 1720771 q^{12} + 3433434 q^{13} + 4585896 q^{14} + 5551840 q^{15} + 18802384 q^{16} + 29035398 q^{17} + 26169127 q^{18} + 21398428 q^{19} + 72466260 q^{20} + 61896432 q^{21} + 100463524 q^{22} - 70799773 q^{23} + 161844076 q^{24} + 233562509 q^{25} + 328796191 q^{26} + 356379712 q^{27} + 499445210 q^{28} + 226699042 q^{29} + 510413234 q^{30} + 251932328 q^{31} + 806116648 q^{32} + 221442992 q^{33} + 325378622 q^{34} - 355232072 q^{35} - 1034240009 q^{36} + 573876170 q^{37} - 770782036 q^{38} - 1199522184 q^{39} - 1009699226 q^{40} - 1733596378 q^{41} - 6499506824 q^{42} + 647370308 q^{43} - 4662321170 q^{44} - 5023123422 q^{45} - 205962976 q^{46} - 5436527248 q^{47} - 4050950401 q^{48} + 4356386219 q^{49} - 10296502416 q^{50} - 1050918064 q^{51} - 5616607137 q^{52} - 3387203910 q^{53} - 21748294807 q^{54} - 10571441512 q^{55} + 635842210 q^{56} - 4678697728 q^{57} + 1991171353 q^{58} + 15113662084 q^{59} + 19934836476 q^{60} + 23895772578 q^{61} + 7557529251 q^{62} + 56666471160 q^{63} + 32993181147 q^{64} + 3660035708 q^{65} + 33342886858 q^{66} + 46806014468 q^{67} + 40754169364 q^{68} + 128726860 q^{69} - 12274756860 q^{70} + 45541532768 q^{71} + 12763980783 q^{72} + 63786612542 q^{73} - 41720765910 q^{74} + 88573702476 q^{75} + 5581739704 q^{76} + 19147126968 q^{77} - 111443125499 q^{78} + 21847812496 q^{79} - 67715736674 q^{80} + 122793712411 q^{81} - 30216129401 q^{82} + 40153340788 q^{83} - 221098994762 q^{84} + 116854272412 q^{85} - 47307463306 q^{86} - 5595049008 q^{87} - 263050721364 q^{88} + 37300228382 q^{89} - 419483354956 q^{90} + 109416811256 q^{91} - 72498967552 q^{92} - 224700035960 q^{93} - 378035850441 q^{94} - 255722421456 q^{95} - 96864379937 q^{96} - 243602730 q^{97} - 514347061348 q^{98} + 97029276404 q^{99}+O(q^{100}) \) 11 * q + 32 * q^2 - 20 * q^3 + 11264 * q^4 + 1034 * q^5 - 22385 * q^6 + 159584 * q^7 + 115497 * q^8 + 611943 * q^9 - 627650 * q^10 - 771396 * q^11 - 1720771 * q^12 + 3433434 * q^13 + 4585896 * q^14 + 5551840 * q^15 + 18802384 * q^16 + 29035398 * q^17 + 26169127 * q^18 + 21398428 * q^19 + 72466260 * q^20 + 61896432 * q^21 + 100463524 * q^22 - 70799773 * q^23 + 161844076 * q^24 + 233562509 * q^25 + 328796191 * q^26 + 356379712 * q^27 + 499445210 * q^28 + 226699042 * q^29 + 510413234 * q^30 + 251932328 * q^31 + 806116648 * q^32 + 221442992 * q^33 + 325378622 * q^34 - 355232072 * q^35 - 1034240009 * q^36 + 573876170 * q^37 - 770782036 * q^38 - 1199522184 * q^39 - 1009699226 * q^40 - 1733596378 * q^41 - 6499506824 * q^42 + 647370308 * q^43 - 4662321170 * q^44 - 5023123422 * q^45 - 205962976 * q^46 - 5436527248 * q^47 - 4050950401 * q^48 + 4356386219 * q^49 - 10296502416 * q^50 - 1050918064 * q^51 - 5616607137 * q^52 - 3387203910 * q^53 - 21748294807 * q^54 - 10571441512 * q^55 + 635842210 * q^56 - 4678697728 * q^57 + 1991171353 * q^58 + 15113662084 * q^59 + 19934836476 * q^60 + 23895772578 * q^61 + 7557529251 * q^62 + 56666471160 * q^63 + 32993181147 * q^64 + 3660035708 * q^65 + 33342886858 * q^66 + 46806014468 * q^67 + 40754169364 * q^68 + 128726860 * q^69 - 12274756860 * q^70 + 45541532768 * q^71 + 12763980783 * q^72 + 63786612542 * q^73 - 41720765910 * q^74 + 88573702476 * q^75 + 5581739704 * q^76 + 19147126968 * q^77 - 111443125499 * q^78 + 21847812496 * q^79 - 67715736674 * q^80 + 122793712411 * q^81 - 30216129401 * q^82 + 40153340788 * q^83 - 221098994762 * q^84 + 116854272412 * q^85 - 47307463306 * q^86 - 5595049008 * q^87 - 263050721364 * q^88 + 37300228382 * q^89 - 419483354956 * q^90 + 109416811256 * q^91 - 72498967552 * q^92 - 224700035960 * q^93 - 378035850441 * q^94 - 255722421456 * q^95 - 96864379937 * q^96 - 243602730 * q^97 - 514347061348 * q^98 + 97029276404 * 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 $

$2$	−3.40598	−0.0752623	−0.0376311	−	0.999292i	$-0.511981\pi$
$2$	−3.40598	−0.0752623	−0.0376311	+	0.999292i	$0.511981\pi$
$3$	746.589	1.77384	0.886920	−	0.461923i	$-0.152840\pi$
$3$	746.589	1.77384	0.886920	+	0.461923i	$0.152840\pi$
$4$	−2036.40	−0.994336
$5$	−11427.6	−1.63539	−0.817693	−	0.575654i	$-0.804747\pi$
$5$	−11427.6	−1.63539	−0.817693	+	0.575654i	$0.804747\pi$
$6$	−2542.87	−0.133503
$7$	38639.7	0.868950	0.434475	−	0.900684i	$-0.356934\pi$
$7$	38639.7	0.868950	0.434475	+	0.900684i	$0.356934\pi$
$8$	13911.4	0.150098
$9$	380248.	2.14651
$10$	38922.2	0.123083
$11$	733395.	1.37302	0.686512	−	0.727119i	$-0.259141\pi$
$11$	733395.	1.37302	0.686512	+	0.727119i	$0.259141\pi$
$12$	−1.52035e6	−1.76379
$13$	1.73764e6	1.29799	0.648995	−	0.760793i	$-0.275190\pi$
$13$	1.73764e6	1.29799	0.648995	+	0.760793i	$0.275190\pi$
$14$	−131606.	−0.0653992
$15$	−8.53172e6	−2.90091
$16$	4.12316e6	0.983039
$17$	−709414.	−0.121180	−0.0605899	−	0.998163i	$-0.519298\pi$
$17$	−709414.	−0.121180	−0.0605899	+	0.998163i	$0.519298\pi$
$18$	−1.29512e6	−0.161551
$19$	4.74056e6	0.439223	0.219611	−	0.975587i	$-0.429521\pi$
$19$	4.74056e6	0.439223	0.219611	+	0.975587i	$0.429521\pi$
$20$	2.32712e7	1.62612
$21$	2.88480e7	1.54138
$22$	−2.49793e6	−0.103337
$23$	−6.43634e6	−0.208514
$23$	−6.43634e6	−0.208514
$24$	1.03861e7	0.266250
$25$	8.17622e7	1.67449
$26$	−5.91837e6	−0.0976896
$27$	1.51633e8	2.03372
$28$	−7.86859e7	−0.864028
$29$	−4.78519e7	−0.433221	−0.216611	−	0.976258i	$-0.569500\pi$
$29$	−4.78519e7	−0.433221	−0.216611	+	0.976258i	$0.569500\pi$
$30$	2.90589e7	0.218329
$31$	−2.42404e8	−1.52072	−0.760362	−	0.649499i	$-0.774979\pi$
$31$	−2.42404e8	−1.52072	−0.760362	+	0.649499i	$0.774979\pi$
$32$	−4.25339e7	−0.224084
$33$	5.47544e8	2.43552
$34$	2.41625e6	0.00912027
$35$	−4.41560e8	−1.42107
$36$	−7.74336e8	−2.13435
$37$	5.88015e8	1.39405	0.697026	−	0.717046i	$-0.254506\pi$
$37$	5.88015e8	1.39405	0.697026	+	0.717046i	$0.254506\pi$
$38$	−1.61463e7	−0.0330569
$39$	1.29730e9	2.30243
$40$	−1.58974e8	−0.245469
$41$	1.50605e8	0.203015	0.101508	−	0.994835i	$-0.467633\pi$
$41$	1.50605e8	0.203015	0.101508	+	0.994835i	$0.467633\pi$
$42$	−9.82557e7	−0.116008
$43$	1.52912e9	1.58623	0.793113	−	0.609074i	$-0.208459\pi$
$43$	1.52912e9	1.58623	0.793113	+	0.609074i	$0.208459\pi$
$44$	−1.49348e9	−1.36525
$45$	−4.34532e9	−3.51037
$46$	2.19221e7	0.0156933
$47$	−1.47296e9	−0.936816	−0.468408	−	0.883512i	$-0.655172\pi$
$47$	−1.47296e9	−0.936816	−0.468408	+	0.883512i	$0.655172\pi$
$48$	3.07831e9	1.74375
$49$	−4.84298e8	−0.244925
$50$	−2.78480e8	−0.126026
$51$	−5.29640e8	−0.214954
$52$	−3.53853e9	−1.29064
$53$	−8.04916e8	−0.264383	−0.132191	−	0.991224i	$-0.542201\pi$
$53$	−8.04916e8	−0.264383	−0.132191	+	0.991224i	$0.542201\pi$
$54$	−5.16458e8	−0.153063
$55$	−8.38095e9	−2.24542
$56$	5.37532e8	0.130428
$57$	3.53925e9	0.779111
$58$	1.62983e8	0.0326052
$59$	8.78112e9	1.59906	0.799528	−	0.600628i	$-0.205083\pi$
$59$	8.78112e9	1.59906	0.799528	+	0.600628i	$0.205083\pi$
$60$	1.73740e10	2.88448
$61$	2.87455e9	0.435769	0.217884	−	0.975975i	$-0.430084\pi$
$61$	2.87455e9	0.435769	0.217884	+	0.975975i	$0.430084\pi$
$62$	8.25624e8	0.114453
$63$	1.46927e10	1.86521
$64$	−8.29937e9	−0.966174
$65$	−1.98571e10	−2.12271
$66$	−1.86493e9	−0.183303
$67$	1.69684e9	0.153543	0.0767714	−	0.997049i	$-0.475539\pi$
$67$	1.69684e9	0.153543	0.0767714	+	0.997049i	$0.475539\pi$
$68$	1.44465e9	0.120493
$69$	−4.80530e9	−0.369871
$70$	1.50394e9	0.106953
$71$	−3.27860e8	−0.0215659	−0.0107830	−	0.999942i	$-0.503432\pi$
$71$	−3.27860e8	−0.0215659	−0.0107830	+	0.999942i	$0.503432\pi$
$72$	5.28977e9	0.322187
$73$	−1.74989e10	−0.987951	−0.493975	−	0.869476i	$-0.664457\pi$
$73$	−1.74989e10	−0.987951	−0.493975	+	0.869476i	$0.664457\pi$
$74$	−2.00277e9	−0.104920
$75$	6.10427e10	2.97028
$76$	−9.65367e9	−0.436735
$77$	2.83382e10	1.19309
$78$	−4.41858e9	−0.173286
$79$	−2.59473e10	−0.948729	−0.474365	−	0.880328i	$-0.657322\pi$
$79$	−2.59473e10	−0.948729	−0.474365	+	0.880328i	$0.657322\pi$
$80$	−4.71179e10	−1.60765
$81$	4.58475e10	1.46099
$82$	−5.12958e8	−0.0152794
$83$	5.05896e10	1.40972	0.704858	−	0.709348i	$-0.251011\pi$
$83$	5.05896e10	1.40972	0.704858	+	0.709348i	$0.251011\pi$
$84$	−5.87460e10	−1.53265
$85$	8.10690e9	0.198176
$86$	−5.20816e9	−0.119383
$87$	−3.57257e10	−0.768466
$88$	1.02025e10	0.206088
$89$	−4.36408e10	−0.828414	−0.414207	−	0.910183i	$-0.635941\pi$
$89$	−4.36408e10	−0.828414	−0.414207	+	0.910183i	$0.635941\pi$
$90$	1.48001e10	0.264199
$91$	6.71419e10	1.12789
$92$	1.31070e10	0.207333
$93$	−1.80976e11	−2.69752
$94$	5.01689e9	0.0705069
$95$	−5.41733e10	−0.718299
$96$	−3.17554e10	−0.397489
$97$	−4.61895e10	−0.546133	−0.273067	−	0.961995i	$-0.588038\pi$
$97$	−4.61895e10	−0.546133	−0.273067	+	0.961995i	$0.588038\pi$
$98$	1.64951e9	0.0184336
$99$	2.78872e11	2.94721
$100$	−1.66500e11	−1.66500
$101$	3.21537e10	0.304413	0.152207	−	0.988349i	$-0.451362\pi$
$101$	3.21537e10	0.304413	0.152207	+	0.988349i	$0.451362\pi$
$102$	1.80395e9	0.0161779
$103$	1.40964e11	1.19813	0.599063	−	0.800702i	$-0.295540\pi$
$103$	1.40964e11	1.19813	0.599063	+	0.800702i	$0.295540\pi$
$104$	2.41730e10	0.194826
$105$	−3.29664e11	−2.52075
$106$	2.74153e9	0.0198980
$107$	−1.00790e11	−0.694714	−0.347357	−	0.937733i	$-0.612921\pi$
$107$	−1.00790e11	−0.694714	−0.347357	+	0.937733i	$0.612921\pi$
$108$	−3.08785e11	−2.02220
$109$	4.39398e10	0.273535	0.136767	−	0.990603i	$-0.456329\pi$
$109$	4.39398e10	0.273535	0.136767	+	0.990603i	$0.456329\pi$
$110$	2.85454e10	0.168996
$111$	4.39005e11	2.47283
$112$	1.59318e11	0.854212
$113$	−1.22375e11	−0.624829	−0.312415	−	0.949946i	$-0.601138\pi$
$113$	−1.22375e11	−0.624829	−0.312415	+	0.949946i	$0.601138\pi$
$114$	−1.20546e10	−0.0586377
$115$	7.35520e10	0.341002
$116$	9.74455e10	0.430768
$117$	6.60733e11	2.78614
$118$	−2.99083e10	−0.120349
$119$	−2.74116e10	−0.105299
$120$	−1.18688e11	−0.435422
$121$	2.52556e11	0.885194
$122$	−9.79067e9	−0.0327969
$123$	1.12440e11	0.360116
$124$	4.93631e11	1.51211
$125$	−3.76358e11	−1.10305
$126$	−5.00430e10	−0.140380
$127$	−4.70567e11	−1.26387	−0.631933	−	0.775023i	$-0.717738\pi$
$127$	−4.70567e11	−1.26387	−0.631933	+	0.775023i	$0.717738\pi$
$128$	1.15377e11	0.296800
$129$	1.14162e12	2.81371
$130$	6.76328e10	0.159760
$131$	−5.32414e11	−1.20575	−0.602875	−	0.797836i	$-0.705978\pi$
$131$	−5.32414e11	−1.20575	−0.602875	+	0.797836i	$0.705978\pi$
$132$	−1.11502e12	−2.42173
$133$	1.83174e11	0.381663
$134$	−5.77940e9	−0.0115560
$135$	−1.73280e12	−3.32592
$136$	−9.86893e9	−0.0181889
$137$	−7.73603e11	−1.36948	−0.684739	−	0.728788i	$-0.740084\pi$
$137$	−7.73603e11	−1.36948	−0.684739	+	0.728788i	$0.740084\pi$
$138$	1.63668e10	0.0278374
$139$	1.14461e12	1.87101	0.935505	−	0.353312i	$-0.114945\pi$
$139$	1.14461e12	1.87101	0.935505	+	0.353312i	$0.114945\pi$
$140$	8.99192e11	1.41302
$141$	−1.09970e12	−1.66176
$142$	1.11669e9	0.00162310
$143$	1.27438e12	1.78217
$144$	1.56782e12	2.11010
$145$	5.46833e11	0.708485
$146$	5.96010e10	0.0743554
$147$	−3.61571e11	−0.434459
$148$	−1.19743e12	−1.38616
$149$	−5.83682e11	−0.651107	−0.325553	−	0.945524i	$-0.605551\pi$
$149$	−5.83682e11	−0.651107	−0.325553	+	0.945524i	$0.605551\pi$
$150$	−2.07910e11	−0.223550
$151$	−6.20502e11	−0.643236	−0.321618	−	0.946870i	$-0.604227\pi$
$151$	−6.20502e11	−0.643236	−0.321618	+	0.946870i	$0.604227\pi$
$152$	6.59478e10	0.0659266
$153$	−2.69753e11	−0.260114
$154$	−9.65193e10	−0.0897946
$155$	2.77010e12	2.48697
$156$	−2.64182e12	−2.28938
$157$	3.62794e11	0.303537	0.151768	−	0.988416i	$-0.451503\pi$
$157$	3.62794e11	0.303537	0.151768	+	0.988416i	$0.451503\pi$
$158$	8.83759e10	0.0714035
$159$	−6.00941e11	−0.468973
$160$	4.86061e11	0.366464
$161$	−2.48699e11	−0.181189
$162$	−1.56156e11	−0.109958
$163$	8.93884e11	0.608485	0.304242	−	0.952595i	$-0.401597\pi$
$163$	8.93884e11	0.608485	0.304242	+	0.952595i	$0.401597\pi$
$164$	−3.06692e11	−0.201865
$165$	−6.25712e12	−3.98302
$166$	−1.72307e11	−0.106098
$167$	−1.04510e12	−0.622613	−0.311307	−	0.950310i	$-0.600767\pi$
$167$	−1.04510e12	−0.622613	−0.311307	+	0.950310i	$0.600767\pi$
$168$	4.01316e11	0.231358
$169$	1.22723e12	0.684776
$170$	−2.76120e10	−0.0149152
$171$	1.80259e12	0.942795
$172$	−3.11390e12	−1.57724
$173$	−2.50501e12	−1.22901	−0.614505	−	0.788913i	$-0.710644\pi$
$173$	−2.50501e12	−1.22901	−0.614505	+	0.788913i	$0.710644\pi$
$174$	1.21681e11	0.0578365
$175$	3.15927e12	1.45505
$176$	3.02391e12	1.34974
$177$	6.55588e12	2.83647
$178$	1.48640e11	0.0623483
$179$	−5.99853e11	−0.243980	−0.121990	−	0.992531i	$-0.538928\pi$
$179$	−5.99853e11	−0.243980	−0.121990	+	0.992531i	$0.538928\pi$
$180$	8.84881e12	3.49049
$181$	−9.41872e11	−0.360379	−0.180190	−	0.983632i	$-0.557671\pi$
$181$	−9.41872e11	−0.360379	−0.180190	+	0.983632i	$0.557671\pi$
$182$	−2.28684e11	−0.0848874
$183$	2.14611e12	0.772984
$184$	−8.95385e10	−0.0312976
$185$	−6.71961e12	−2.27981
$186$	6.16401e11	0.203022
$187$	−5.20280e11	−0.166383
$188$	2.99954e12	0.931509
$189$	5.85904e12	1.76720
$190$	1.84513e11	0.0540608
$191$	2.95177e12	0.840232	0.420116	−	0.907470i	$-0.361989\pi$
$191$	2.95177e12	0.840232	0.420116	+	0.907470i	$0.361989\pi$
$192$	−6.19622e12	−1.71384
$193$	3.27339e12	0.879897	0.439949	−	0.898023i	$-0.354997\pi$
$193$	3.27339e12	0.879897	0.439949	+	0.898023i	$0.354997\pi$
$194$	1.57321e11	0.0411032
$195$	−1.48251e13	−3.76536
$196$	9.86223e11	0.243538
$197$	−5.79465e12	−1.39143	−0.695717	−	0.718316i	$-0.744913\pi$
$197$	−5.79465e12	−1.39143	−0.695717	+	0.718316i	$0.744913\pi$
$198$	−9.49832e11	−0.221814
$199$	7.04126e12	1.59940	0.799702	−	0.600397i	$-0.204991\pi$
$199$	7.04126e12	1.59940	0.799702	+	0.600397i	$0.204991\pi$
$200$	1.13743e12	0.251338
$201$	1.26684e12	0.272360
$202$	−1.09515e11	−0.0229108
$203$	−1.84898e12	−0.376448
$204$	1.07856e12	0.213736
$205$	−1.72106e12	−0.332008
$206$	−4.80120e11	−0.0901737
$207$	−2.44740e12	−0.447578
$208$	7.16457e12	1.27597
$209$	3.47670e12	0.603063
$210$	1.12283e12	0.189717
$211$	−8.03073e12	−1.32191	−0.660955	−	0.750426i	$-0.729848\pi$
$211$	−8.03073e12	−1.32191	−0.660955	+	0.750426i	$0.729848\pi$
$212$	1.63913e12	0.262885
$213$	−2.44777e11	−0.0382545
$214$	3.43289e11	0.0522858
$215$	−1.74742e13	−2.59409
$216$	2.10942e12	0.305258
$217$	−9.36643e12	−1.32143
$218$	−1.49658e11	−0.0205868
$219$	−1.30645e13	−1.75247
$220$	1.70670e13	2.23271
$221$	−1.23270e12	−0.157290
$222$	−1.49524e12	−0.186111
$223$	−2.51033e12	−0.304828	−0.152414	−	0.988317i	$-0.548705\pi$
$223$	−2.51033e12	−0.304828	−0.152414	+	0.988317i	$0.548705\pi$
$224$	−1.64350e12	−0.194718
$225$	3.10899e13	3.59431
$226$	4.16807e11	0.0470261
$227$	−1.30649e13	−1.43867	−0.719337	−	0.694661i	$-0.755554\pi$
$227$	−1.30649e13	−1.43867	−0.719337	+	0.694661i	$0.755554\pi$
$228$	−7.20732e12	−0.774698
$229$	9.89792e12	1.03860	0.519301	−	0.854592i	$-0.326192\pi$
$229$	9.89792e12	1.03860	0.519301	+	0.854592i	$0.326192\pi$
$230$	−2.50517e11	−0.0256646
$231$	2.11570e13	2.11635
$232$	−6.65686e11	−0.0650258
$233$	−1.09341e13	−1.04310	−0.521551	−	0.853220i	$-0.674646\pi$
$233$	−1.09341e13	−1.04310	−0.521551	+	0.853220i	$0.674646\pi$
$234$	−2.25044e12	−0.209692
$235$	1.68325e13	1.53206
$236$	−1.78819e13	−1.59000
$237$	−1.93719e13	−1.68289
$238$	9.33633e10	0.00792506
$239$	4.53008e12	0.375766	0.187883	−	0.982191i	$-0.439837\pi$
$239$	4.53008e12	0.375766	0.187883	+	0.982191i	$0.439837\pi$
$240$	−3.51777e13	−2.85171
$241$	8.66864e12	0.686842	0.343421	−	0.939182i	$-0.388414\pi$
$241$	8.66864e12	0.686842	0.343421	+	0.939182i	$0.388414\pi$
$242$	−8.60202e11	−0.0666217
$243$	7.36793e12	0.557842
$244$	−5.85373e12	−0.433300
$245$	5.53436e12	0.400548
$246$	−3.82969e11	−0.0271032
$247$	8.23738e12	0.570106
$248$	−3.37218e12	−0.228258
$249$	3.77696e13	2.50061
$250$	1.28187e12	0.0830181
$251$	−1.34324e13	−0.851039	−0.425520	−	0.904949i	$-0.639909\pi$
$251$	−1.34324e13	−0.851039	−0.425520	+	0.904949i	$0.639909\pi$
$252$	−2.99201e13	−1.85464
$253$	−4.72038e12	−0.286295
$254$	1.60274e12	0.0951214
$255$	6.05252e12	0.351532
$256$	1.66041e13	0.943836
$257$	8.27418e12	0.460355	0.230178	−	0.973149i	$-0.426069\pi$
$257$	8.27418e12	0.460355	0.230178	+	0.973149i	$0.426069\pi$
$258$	−3.88835e12	−0.211766
$259$	2.27208e13	1.21136
$260$	4.04369e13	2.11069
$261$	−1.81956e13	−0.929914
$262$	1.81339e12	0.0907474
$263$	2.33836e13	1.14592	0.572960	−	0.819583i	$-0.305795\pi$
$263$	2.33836e13	1.14592	0.572960	+	0.819583i	$0.305795\pi$
$264$	7.61710e12	0.365568
$265$	9.19826e12	0.432368
$266$	−6.23887e11	−0.0287248
$267$	−3.25817e13	−1.46947
$268$	−3.45544e12	−0.152673
$269$	2.53875e13	1.09896	0.549480	−	0.835507i	$-0.314826\pi$
$269$	2.53875e13	1.09896	0.549480	+	0.835507i	$0.314826\pi$
$270$	5.90188e12	0.250317
$271$	−3.31427e13	−1.37739	−0.688695	−	0.725051i	$-0.741816\pi$
$271$	−3.31427e13	−1.37739	−0.688695	+	0.725051i	$0.741816\pi$
$272$	−2.92503e12	−0.119125
$273$	5.01274e13	2.00069
$274$	2.63488e12	0.103070
$275$	5.99639e13	2.29911
$276$	9.78551e12	0.367776
$277$	−1.45213e12	−0.0535017	−0.0267509	−	0.999642i	$-0.508516\pi$
$277$	−1.45213e12	−0.0535017	−0.0267509	+	0.999642i	$0.508516\pi$
$278$	−3.89852e12	−0.140817
$279$	−9.21736e13	−3.26425
$280$	−6.14271e12	−0.213300
$281$	−2.65287e13	−0.903297	−0.451649	−	0.892196i	$-0.649164\pi$
$281$	−2.65287e13	−0.903297	−0.451649	+	0.892196i	$0.649164\pi$
$282$	3.74555e12	0.125068
$283$	6.43460e12	0.210715	0.105358	−	0.994434i	$-0.466401\pi$
$283$	6.43460e12	0.210715	0.105358	+	0.994434i	$0.466401\pi$
$284$	6.67654e11	0.0214437
$285$	−4.04451e13	−1.27415
$286$	−4.34050e12	−0.134130
$287$	5.81934e12	0.176410
$288$	−1.61734e13	−0.480998
$289$	−3.37686e13	−0.985315
$290$	−1.86250e12	−0.0533222
$291$	−3.44845e13	−0.968753
$292$	3.56348e13	0.982354
$293$	−3.34082e13	−0.903818	−0.451909	−	0.892064i	$-0.649257\pi$
$293$	−3.34082e13	−0.903818	−0.451909	+	0.892064i	$0.649257\pi$
$294$	1.23150e12	0.0326983
$295$	−1.00347e14	−2.61508
$296$	8.18011e12	0.209245
$297$	1.11207e14	2.79235
$298$	1.98801e12	0.0490038
$299$	−1.11840e13	−0.270649
$300$	−1.24307e14	−2.95345
$301$	5.90848e13	1.37835
$302$	2.11342e12	0.0484114
$303$	2.40056e13	0.539980
$304$	1.95461e13	0.431773
$305$	−3.28492e13	−0.712650
$306$	9.18773e11	0.0195767
$307$	7.44288e13	1.55769	0.778843	−	0.627219i	$-0.215807\pi$
$307$	7.44288e13	1.55769	0.778843	+	0.627219i	$0.215807\pi$
$308$	−5.77078e13	−1.18633
$309$	1.05242e14	2.12529
$310$	−9.43491e12	−0.187175
$311$	6.21991e13	1.21228	0.606138	−	0.795359i	$-0.292718\pi$
$311$	6.21991e13	1.21228	0.606138	+	0.795359i	$0.292718\pi$
$312$	1.80473e13	0.345590
$313$	3.13579e13	0.590001	0.295000	−	0.955497i	$-0.404680\pi$
$313$	3.13579e13	0.590001	0.295000	+	0.955497i	$0.404680\pi$
$314$	−1.23567e12	−0.0228449
$315$	−1.67902e14	−3.05034
$316$	5.28390e13	0.943355
$317$	−8.40197e13	−1.47420	−0.737098	−	0.675786i	$-0.763804\pi$
$317$	−8.40197e13	−1.47420	−0.737098	+	0.675786i	$0.763804\pi$
$318$	2.04679e12	0.0352959
$319$	−3.50943e13	−0.594823
$320$	9.48420e13	1.58007
$321$	−7.52486e13	−1.23231
$322$	8.47063e11	0.0136367
$323$	−3.36302e12	−0.0532250
$324$	−9.33637e13	−1.45272
$325$	1.42073e14	2.17347
$326$	−3.04455e12	−0.0457959
$327$	3.28050e13	0.485207
$328$	2.09513e12	0.0304722
$329$	−5.69150e13	−0.814046
$330$	2.13116e13	0.299771
$331$	3.42160e12	0.0473343	0.0236671	−	0.999720i	$-0.492466\pi$
$331$	3.42160e12	0.0473343	0.0236671	+	0.999720i	$0.492466\pi$
$332$	−1.03021e14	−1.40173
$333$	2.23591e14	2.99235
$334$	3.55960e12	0.0468593
$335$	−1.93908e13	−0.251102
$336$	1.18945e14	1.51524
$337$	7.02030e13	0.879814	0.439907	−	0.898043i	$-0.355011\pi$
$337$	7.02030e13	0.879814	0.439907	+	0.898043i	$0.355011\pi$
$338$	−4.17992e12	−0.0515378
$339$	−9.13638e13	−1.10835
$340$	−1.65089e13	−0.197053
$341$	−1.77778e14	−2.08799
$342$	−6.13958e12	−0.0709569
$343$	−9.51165e13	−1.08178
$344$	2.12722e13	0.238090
$345$	5.49131e13	0.604882
$346$	8.53200e12	0.0924980
$347$	2.27504e13	0.242759	0.121380	−	0.992606i	$-0.461268\pi$
$347$	2.27504e13	0.242759	0.121380	+	0.992606i	$0.461268\pi$
$348$	7.27517e13	0.764113
$349$	−6.44822e13	−0.666654	−0.333327	−	0.942811i	$-0.608171\pi$
$349$	−6.44822e13	−0.666654	−0.333327	+	0.942811i	$0.608171\pi$
$350$	−1.07604e13	−0.109510
$351$	2.63483e14	2.63975
$352$	−3.11942e13	−0.307673
$353$	1.54701e14	1.50222	0.751109	−	0.660178i	$-0.229519\pi$
$353$	1.54701e14	1.50222	0.751109	+	0.660178i	$0.229519\pi$
$354$	−2.23292e13	−0.213479
$355$	3.74666e12	0.0352686
$356$	8.88700e13	0.823721
$357$	−2.04652e13	−0.186784
$358$	2.04309e12	0.0183625
$359$	−1.37447e14	−1.21651	−0.608256	−	0.793741i	$-0.708131\pi$
$359$	−1.37447e14	−1.21651	−0.608256	+	0.793741i	$0.708131\pi$
$360$	−6.04495e13	−0.526901
$361$	−9.40174e13	−0.807083
$362$	3.20800e12	0.0271230
$363$	1.88556e14	1.57019
$364$	−1.36728e14	−1.12150
$365$	1.99971e14	1.61568
$366$	−7.30960e12	−0.0581765
$367$	−1.59170e14	−1.24795	−0.623976	−	0.781443i	$-0.714484\pi$
$367$	−1.59170e14	−1.24795	−0.623976	+	0.781443i	$0.714484\pi$
$368$	−2.65381e13	−0.204978
$369$	5.72672e13	0.435774
$370$	2.28869e13	0.171584
$371$	−3.11017e13	−0.229735
$372$	3.68540e14	2.68224
$373$	−1.59555e14	−1.14423	−0.572114	−	0.820174i	$-0.693876\pi$
$373$	−1.59555e14	−1.14423	−0.572114	+	0.820174i	$0.693876\pi$
$374$	1.77207e12	0.0125224
$375$	−2.80984e14	−1.95664
$376$	−2.04910e13	−0.140614
$377$	−8.31493e13	−0.562317
$378$	−1.99558e13	−0.133004
$379$	2.04722e14	1.34477	0.672385	−	0.740201i	$-0.265270\pi$
$379$	2.04722e14	1.34477	0.672385	+	0.740201i	$0.265270\pi$
$380$	1.10318e14	0.714230
$381$	−3.51320e14	−2.24190
$382$	−1.00537e13	−0.0632377
$383$	−1.04542e14	−0.648184	−0.324092	−	0.946026i	$-0.605059\pi$
$383$	−1.04542e14	−0.648184	−0.324092	+	0.946026i	$0.605059\pi$
$384$	8.61392e13	0.526477
$385$	−3.23838e14	−1.95116
$386$	−1.11491e13	−0.0662231
$387$	5.81445e14	3.40485
$388$	9.40602e13	0.543040
$389$	−1.06575e14	−0.606642	−0.303321	−	0.952888i	$-0.598095\pi$
$389$	−1.06575e14	−0.606642	−0.303321	+	0.952888i	$0.598095\pi$
$390$	5.04939e13	0.283389
$391$	4.56603e12	0.0252678
$392$	−6.73725e12	−0.0367629
$393$	−3.97494e14	−2.13881
$394$	1.97365e13	0.104722
$395$	2.96515e14	1.55154
$396$	−5.67894e14	−2.93051
$397$	−1.81328e14	−0.922821	−0.461410	−	0.887187i	$-0.652656\pi$
$397$	−1.81328e14	−0.922821	−0.461410	+	0.887187i	$0.652656\pi$
$398$	−2.39824e13	−0.120375
$399$	1.36756e14	0.677009
$400$	3.37119e14	1.64609
$401$	1.47543e13	0.0710600	0.0355300	−	0.999369i	$-0.488688\pi$
$401$	1.47543e13	0.0710600	0.0355300	+	0.999369i	$0.488688\pi$
$402$	−4.31484e12	−0.0204985
$403$	−4.21211e14	−1.97388
$404$	−6.54778e13	−0.302689
$405$	−5.23927e14	−2.38929
$406$	6.29761e12	0.0283323
$407$	4.31247e14	1.91407
$408$	−7.36803e12	−0.0322642
$409$	−3.32742e13	−0.143757	−0.0718787	−	0.997413i	$-0.522899\pi$
$409$	−3.32742e13	−0.143757	−0.0718787	+	0.997413i	$0.522899\pi$
$410$	5.86189e12	0.0249877
$411$	−5.77564e14	−2.42924
$412$	−2.87058e14	−1.19134
$413$	3.39300e14	1.38950
$414$	8.33581e12	0.0336857
$415$	−5.78118e14	−2.30543
$416$	−7.39086e13	−0.290859
$417$	8.54553e14	3.31887
$418$	−1.18416e13	−0.0453879
$419$	2.58241e14	0.976897	0.488448	−	0.872593i	$-0.337563\pi$
$419$	2.58241e14	0.976897	0.488448	+	0.872593i	$0.337563\pi$
$420$	6.71327e14	2.50647
$421$	1.51417e14	0.557985	0.278993	−	0.960293i	$-0.409999\pi$
$421$	1.51417e14	0.557985	0.278993	+	0.960293i	$0.409999\pi$
$422$	2.73525e13	0.0994899
$423$	−5.60091e14	−2.01088
$424$	−1.11975e13	−0.0396834
$425$	−5.80032e13	−0.202914
$426$	8.33705e11	0.00287912
$427$	1.11072e14	0.378661
$428$	2.05248e14	0.690779
$429$	9.51434e14	3.16128
$430$	5.95168e13	0.195237
$431$	3.23325e14	1.04716	0.523581	−	0.851976i	$-0.324596\pi$
$431$	3.23325e14	1.04716	0.523581	+	0.851976i	$0.324596\pi$
$432$	6.25206e14	1.99923
$433$	−2.70764e13	−0.0854885	−0.0427442	−	0.999086i	$-0.513610\pi$
$433$	−2.70764e13	−0.0854885	−0.0427442	+	0.999086i	$0.513610\pi$
$434$	3.19019e13	0.0994541
$435$	4.08259e14	1.25674
$436$	−8.94790e13	−0.271985
$437$	−3.05119e13	−0.0915843
$438$	4.44974e13	0.131895
$439$	−4.57316e13	−0.133863	−0.0669317	−	0.997758i	$-0.521321\pi$
$439$	−4.57316e13	−0.133863	−0.0669317	+	0.997758i	$0.521321\pi$
$440$	−1.16591e14	−0.337034
$441$	−1.84153e14	−0.525735
$442$	4.19857e12	0.0118380
$443$	−4.00490e14	−1.11525	−0.557624	−	0.830094i	$-0.688287\pi$
$443$	−4.00490e14	−1.11525	−0.557624	+	0.830094i	$0.688287\pi$
$444$	−8.93990e14	−2.45882
$445$	4.98710e14	1.35478
$446$	8.55015e12	0.0229420
$447$	−4.35771e14	−1.15496
$448$	−3.20685e14	−0.839557
$449$	1.98585e14	0.513560	0.256780	−	0.966470i	$-0.417338\pi$
$449$	1.98585e14	0.513560	0.256780	+	0.966470i	$0.417338\pi$
$450$	−1.05892e14	−0.270516
$451$	1.10453e14	0.278745
$452$	2.49205e14	0.621290
$453$	−4.63260e14	−1.14100
$454$	4.44987e13	0.108278
$455$	−7.67272e14	−1.84453
$456$	4.92359e13	0.116943
$457$	2.08158e14	0.488489	0.244244	−	0.969714i	$-0.421460\pi$
$457$	2.08158e14	0.488489	0.244244	+	0.969714i	$0.421460\pi$
$458$	−3.37121e13	−0.0781675
$459$	−1.07570e14	−0.246446
$460$	−1.49781e14	−0.339070
$461$	−3.48515e14	−0.779591	−0.389795	−	0.920901i	$-0.627454\pi$
$461$	−3.48515e14	−0.779591	−0.389795	+	0.920901i	$0.627454\pi$
$462$	−7.20602e13	−0.159281
$463$	6.08052e13	0.132814	0.0664072	−	0.997793i	$-0.478846\pi$
$463$	6.08052e13	0.132814	0.0664072	+	0.997793i	$0.478846\pi$
$464$	−1.97301e14	−0.425874
$465$	2.06812e15	4.41149
$466$	3.72415e13	0.0785062
$467$	−2.45301e14	−0.511041	−0.255521	−	0.966804i	$-0.582247\pi$
$467$	−2.45301e14	−0.511041	−0.255521	+	0.966804i	$0.582247\pi$
$468$	−1.34552e15	−2.77036
$469$	6.55654e13	0.133421
$470$	−5.73311e13	−0.115306
$471$	2.70858e14	0.538426
$472$	1.22158e14	0.240016
$473$	1.12145e15	2.17793
$474$	6.59804e13	0.126658
$475$	3.87598e14	0.735474
$476$	5.58209e13	0.104703
$477$	−3.06067e14	−0.567500
$478$	−1.54294e13	−0.0282810
$479$	−3.99312e14	−0.723548	−0.361774	−	0.932266i	$-0.617829\pi$
$479$	−3.99312e14	−0.723548	−0.361774	+	0.932266i	$0.617829\pi$
$480$	3.62888e14	0.650048
$481$	1.02176e15	1.80946
$482$	−2.95252e13	−0.0516933
$483$	−1.85676e14	−0.321400
$484$	−5.14305e14	−0.880180
$485$	5.27835e14	0.893139
$486$	−2.50950e13	−0.0419844
$487$	−6.77061e14	−1.12000	−0.560001	−	0.828492i	$-0.689199\pi$
$487$	−6.77061e14	−1.12000	−0.560001	+	0.828492i	$0.689199\pi$
$488$	3.99890e13	0.0654081
$489$	6.67364e14	1.07935
$490$	−1.88499e13	−0.0301461
$491$	−6.05027e12	−0.00956812	−0.00478406	−	0.999989i	$-0.501523\pi$
$491$	−6.05027e12	−0.00956812	−0.00478406	+	0.999989i	$0.501523\pi$
$492$	−2.28973e14	−0.358077
$493$	3.39468e13	0.0524977
$494$	−2.80564e13	−0.0429075
$495$	−3.18684e15	−4.81982
$496$	−9.99472e14	−1.49493
$497$	−1.26684e13	−0.0187397
$498$	−1.28643e14	−0.188202
$499$	1.12702e15	1.63072	0.815359	−	0.578955i	$-0.196539\pi$
$499$	1.12702e15	1.63072	0.815359	+	0.578955i	$0.196539\pi$
$500$	7.66414e14	1.09680
$501$	−7.80262e14	−1.10442
$502$	4.57507e13	0.0640511
$503$	4.16027e14	0.576100	0.288050	−	0.957615i	$-0.406993\pi$
$503$	4.16027e14	0.576100	0.288050	+	0.957615i	$0.406993\pi$
$504$	2.04395e14	0.279965
$505$	−3.67440e14	−0.497833
$506$	1.60775e13	0.0215472
$507$	9.16234e14	1.21468
$508$	9.58262e14	1.25671
$509$	−9.10667e14	−1.18144	−0.590720	−	0.806876i	$-0.701156\pi$
$509$	−9.10667e14	−1.18144	−0.590720	+	0.806876i	$0.701156\pi$
$510$	−2.06148e13	−0.0264571
$511$	−6.76153e14	−0.858480
$512$	−2.92846e14	−0.367836
$513$	7.18823e14	0.893257
$514$	−2.81817e13	−0.0346474
$515$	−1.61088e15	−1.95940
$516$	−2.32480e15	−2.79777
$517$	−1.08026e15	−1.28627
$518$	−7.73865e13	−0.0911699
$519$	−1.87021e15	−2.18007
$520$	−2.76239e14	−0.318616
$521$	−3.96936e14	−0.453016	−0.226508	−	0.974009i	$-0.572731\pi$
$521$	−3.96936e14	−0.453016	−0.226508	+	0.974009i	$0.572731\pi$
$522$	6.19738e13	0.0699874
$523$	3.86216e14	0.431589	0.215795	−	0.976439i	$-0.430766\pi$
$523$	3.86216e14	0.431589	0.215795	+	0.976439i	$0.430766\pi$
$524$	1.08421e15	1.19892
$525$	2.35867e15	2.58102
$526$	−7.96441e13	−0.0862446
$527$	1.71965e14	0.184281
$528$	2.25761e15	2.39422
$529$	4.14265e13	0.0434783
$530$	−3.13291e13	−0.0325410
$531$	3.33900e15	3.43239
$532$	−3.73015e14	−0.379501
$533$	2.61697e14	0.263511
$534$	1.10973e14	0.110596
$535$	1.15179e15	1.13613
$536$	2.36054e13	0.0230465
$537$	−4.47844e14	−0.432781
$538$	−8.64693e13	−0.0827103
$539$	−3.55181e14	−0.336288
$540$	3.52867e15	3.30708
$541$	−1.01828e15	−0.944676	−0.472338	−	0.881417i	$-0.656590\pi$
$541$	−1.01828e15	−0.944676	−0.472338	+	0.881417i	$0.656590\pi$
$542$	1.12883e14	0.103665
$543$	−7.03191e14	−0.639255
$544$	3.01742e13	0.0271545
$545$	−5.02127e14	−0.447335
$546$	−1.70733e14	−0.150577
$547$	7.81050e13	0.0681944	0.0340972	−	0.999419i	$-0.489144\pi$
$547$	7.81050e13	0.0681944	0.0340972	+	0.999419i	$0.489144\pi$
$548$	1.57537e15	1.36172
$549$	1.09304e15	0.935381
$550$	−2.04236e14	−0.173037
$551$	−2.26845e14	−0.190281
$552$	−6.68484e13	−0.0555170
$553$	−1.00259e15	−0.824399
$554$	4.94594e12	0.00402666
$555$	−5.01678e15	−4.04403
$556$	−2.33088e15	−1.86041
$557$	1.84121e15	1.45512	0.727560	−	0.686044i	$-0.240654\pi$
$557$	1.84121e15	1.45512	0.727560	+	0.686044i	$0.240654\pi$
$558$	3.13941e14	0.245675
$559$	2.65706e15	2.05891
$560$	−1.82062e15	−1.39697
$561$	−3.88435e14	−0.295137
$562$	9.03562e13	0.0679842
$563$	2.34103e15	1.74426	0.872128	−	0.489278i	$-0.162740\pi$
$563$	2.34103e15	1.74426	0.872128	+	0.489278i	$0.162740\pi$
$564$	2.23943e15	1.65235
$565$	1.39845e15	1.02184
$566$	−2.19161e13	−0.0158589
$567$	1.77153e15	1.26953
$568$	−4.56099e12	−0.00323700
$569$	−2.39686e15	−1.68471	−0.842354	−	0.538924i	$-0.818831\pi$
$569$	−2.39686e15	−1.68471	−0.842354	+	0.538924i	$0.818831\pi$
$570$	1.37755e14	0.0958952
$571$	1.22775e15	0.846471	0.423235	−	0.906020i	$-0.360894\pi$
$571$	1.22775e15	0.846471	0.423235	+	0.906020i	$0.360894\pi$
$572$	−2.59514e15	−1.77207
$573$	2.20376e15	1.49044
$574$	−1.98206e13	−0.0132770
$575$	−5.26249e14	−0.349155
$576$	−3.15582e15	−2.07390
$577$	−6.83822e14	−0.445119	−0.222560	−	0.974919i	$-0.571441\pi$
$577$	−6.83822e14	−0.445119	−0.222560	+	0.974919i	$0.571441\pi$
$578$	1.15015e14	0.0741571
$579$	2.44387e15	1.56080
$580$	−1.11357e15	−0.704471
$581$	1.95477e15	1.22497
$582$	1.17454e14	0.0729106
$583$	−5.90321e14	−0.363004
$584$	−2.43434e14	−0.148290
$585$	−7.55060e15	−4.55642
$586$	1.13788e14	0.0680234
$587$	−1.42590e15	−0.844461	−0.422231	−	0.906488i	$-0.638753\pi$
$587$	−1.42590e15	−0.844461	−0.422231	+	0.906488i	$0.638753\pi$
$588$	7.36303e14	0.431998
$589$	−1.14913e15	−0.667937
$590$	3.41781e14	0.196817
$591$	−4.32622e15	−2.46818
$592$	2.42448e15	1.37041
$593$	−9.37196e14	−0.524843	−0.262422	−	0.964953i	$-0.584521\pi$
$593$	−9.37196e14	−0.524843	−0.262422	+	0.964953i	$0.584521\pi$
$594$	−3.78767e14	−0.210159
$595$	3.13249e14	0.172205
$596$	1.18861e15	0.647419
$597$	5.25692e15	2.83709
$598$	3.80926e13	0.0203697
$599$	2.85937e15	1.51503	0.757517	−	0.652815i	$-0.226412\pi$
$599$	2.85937e15	1.51503	0.757517	+	0.652815i	$0.226412\pi$
$600$	8.49189e14	0.445833
$601$	2.74015e15	1.42549	0.712746	−	0.701422i	$-0.247451\pi$
$601$	2.74015e15	1.42549	0.712746	+	0.701422i	$0.247451\pi$
$602$	−2.01242e14	−0.103738
$603$	6.45219e14	0.329581
$604$	1.26359e15	0.639592
$605$	−2.88611e15	−1.44763
$606$	−8.17626e13	−0.0406401
$607$	−1.14990e15	−0.566399	−0.283200	−	0.959061i	$-0.591396\pi$
$607$	−1.14990e15	−0.566399	−0.283200	+	0.959061i	$0.591396\pi$
$608$	−2.01635e14	−0.0984228
$609$	−1.38043e15	−0.667758
$610$	1.11884e14	0.0536357
$611$	−2.55948e15	−1.21598
$612$	5.49325e14	0.258640
$613$	−1.99514e14	−0.0930981	−0.0465490	−	0.998916i	$-0.514822\pi$
$613$	−1.99514e14	−0.0930981	−0.0465490	+	0.998916i	$0.514822\pi$
$614$	−2.53503e14	−0.117235
$615$	−1.28492e15	−0.588930
$616$	3.94223e14	0.179081
$617$	−1.00397e15	−0.452015	−0.226007	−	0.974126i	$-0.572567\pi$
$617$	−1.00397e15	−0.452015	−0.226007	+	0.974126i	$0.572567\pi$
$618$	−3.58452e14	−0.159954
$619$	1.06184e15	0.469636	0.234818	−	0.972039i	$-0.424551\pi$
$619$	1.06184e15	0.469636	0.234818	+	0.972039i	$0.424551\pi$
$620$	−5.64103e15	−2.47289
$621$	−9.75959e14	−0.424061
$622$	−2.11849e14	−0.0912387
$623$	−1.68627e15	−0.719850
$624$	5.34899e15	2.26337
$625$	3.08574e14	0.129425
$626$	−1.06804e14	−0.0444048
$627$	2.59567e15	1.06974
$628$	−7.38793e14	−0.301818
$629$	−4.17146e14	−0.168931
$630$	5.71871e14	0.229575
$631$	2.55864e15	1.01823	0.509117	−	0.860697i	$-0.329972\pi$
$631$	2.55864e15	1.01823	0.509117	+	0.860697i	$0.329972\pi$
$632$	−3.60962e14	−0.142403
$633$	−5.99565e15	−2.34486
$634$	2.86170e14	0.110951
$635$	5.37745e15	2.06691
$636$	1.22376e15	0.466316
$637$	−8.41534e14	−0.317911
$638$	1.19531e14	0.0447678
$639$	−1.24668e14	−0.0462914
$640$	−1.31848e15	−0.485383
$641$	3.37864e15	1.23317	0.616585	−	0.787289i	$-0.288516\pi$
$641$	3.37864e15	1.23317	0.616585	+	0.787289i	$0.288516\pi$
$642$	2.56295e14	0.0927466
$643$	1.64184e14	0.0589076	0.0294538	−	0.999566i	$-0.490623\pi$
$643$	1.64184e14	0.0589076	0.0294538	+	0.999566i	$0.490623\pi$
$644$	5.06450e14	0.180162
$645$	−1.30460e16	−4.60151
$646$	1.14544e13	0.00400583
$647$	1.72552e15	0.598337	0.299168	−	0.954200i	$-0.403291\pi$
$647$	1.72552e15	0.598337	0.299168	+	0.954200i	$0.403291\pi$
$648$	6.37802e14	0.219292
$649$	6.44003e15	2.19554
$650$	−4.83898e14	−0.163580
$651$	−6.99287e15	−2.34401
$652$	−1.82031e15	−0.605038
$653$	−2.89274e15	−0.953426	−0.476713	−	0.879059i	$-0.658172\pi$
$653$	−2.89274e15	−0.953426	−0.476713	+	0.879059i	$0.658172\pi$
$654$	−1.11733e14	−0.0365178
$655$	6.08421e15	1.97187
$656$	6.20969e14	0.199572
$657$	−6.65392e15	−2.12064
$658$	1.93851e14	0.0612670
$659$	1.71243e15	0.536713	0.268356	−	0.963320i	$-0.413520\pi$
$659$	1.71243e15	0.536713	0.268356	+	0.963320i	$0.413520\pi$
$660$	1.27420e16	3.96046
$661$	1.08631e15	0.334846	0.167423	−	0.985885i	$-0.446456\pi$
$661$	1.08631e15	0.334846	0.167423	+	0.985885i	$0.446456\pi$
$662$	−1.16539e13	−0.00356248
$663$	−9.20323e14	−0.279008
$664$	7.03772e14	0.211596
$665$	−2.09324e15	−0.624166
$666$	−7.61548e14	−0.225211
$667$	3.07991e14	0.0903329
$668$	2.12825e15	0.619087
$669$	−1.87419e15	−0.540716
$670$	6.60448e13	0.0188985
$671$	2.10818e15	0.598321
$672$	−1.22702e15	−0.345398
$673$	−8.60090e14	−0.240138	−0.120069	−	0.992766i	$-0.538312\pi$
$673$	−8.60090e14	−0.240138	−0.120069	+	0.992766i	$0.538312\pi$
$674$	−2.39110e14	−0.0662168
$675$	1.23978e16	3.40545
$676$	−2.49913e15	−0.680897
$677$	5.84415e15	1.57937	0.789684	−	0.613514i	$-0.210244\pi$
$677$	5.84415e15	1.57937	0.789684	+	0.613514i	$0.210244\pi$
$678$	3.11184e14	0.0834168
$679$	−1.78475e15	−0.474563
$680$	1.12778e14	0.0297459
$681$	−9.75408e15	−2.55198
$682$	6.05508e14	0.157147
$683$	2.76434e15	0.711668	0.355834	−	0.934549i	$-0.384197\pi$
$683$	2.76434e15	0.711668	0.355834	+	0.934549i	$0.384197\pi$
$684$	−3.67079e15	−0.937455
$685$	8.84044e15	2.23963
$686$	3.23965e14	0.0814171
$687$	7.38968e15	1.84231
$688$	6.30482e15	1.55932
$689$	−1.39865e15	−0.343166
$690$	−1.87033e14	−0.0455248
$691$	1.48977e15	0.359742	0.179871	−	0.983690i	$-0.442432\pi$
$691$	1.48977e15	0.359742	0.179871	+	0.983690i	$0.442432\pi$
$692$	5.10119e15	1.22205
$693$	1.07755e16	2.56098
$694$	−7.74873e13	−0.0182706
$695$	−1.30802e16	−3.05983
$696$	−4.96994e14	−0.115345
$697$	−1.06841e14	−0.0246014
$698$	2.19625e14	0.0501739
$699$	−8.16330e15	−1.85030
$700$	−6.43353e15	−1.44681
$701$	−3.80793e15	−0.849649	−0.424825	−	0.905276i	$-0.639664\pi$
$701$	−3.80793e15	−0.849649	−0.424825	+	0.905276i	$0.639664\pi$
$702$	−8.97417e14	−0.198674
$703$	2.78752e15	0.612299
$704$	−6.08671e15	−1.32658
$705$	1.25669e16	2.71762
$706$	−5.26910e14	−0.113060
$707$	1.24241e15	0.264520
$708$	−1.33504e16	−2.82040
$709$	1.99020e15	0.417198	0.208599	−	0.978001i	$-0.433110\pi$
$709$	1.99020e15	0.417198	0.208599	+	0.978001i	$0.433110\pi$
$710$	−1.27610e13	−0.00265439
$711$	−9.86638e15	−2.03646
$712$	−6.07104e14	−0.124343
$713$	1.56020e15	0.317093
$714$	6.97040e13	0.0140578
$715$	−1.45631e16	−2.91454
$716$	1.22154e15	0.242598
$717$	3.38210e15	0.666548
$718$	4.68143e14	0.0915575
$719$	8.35578e15	1.62173	0.810864	−	0.585234i	$-0.198997\pi$
$719$	8.35578e15	1.62173	0.810864	+	0.585234i	$0.198997\pi$
$720$	−1.79165e16	−3.45083
$721$	5.44680e15	1.04111
$722$	3.20221e14	0.0607429
$723$	6.47191e15	1.21835
$724$	1.91803e15	0.358338
$725$	−3.91247e15	−0.725425
$726$	−6.42217e14	−0.118176
$727$	2.77103e14	0.0506060	0.0253030	−	0.999680i	$-0.491945\pi$
$727$	2.77103e14	0.0506060	0.0253030	+	0.999680i	$0.491945\pi$
$728$	9.34037e14	0.169294
$729$	−2.62093e15	−0.471469
$730$	−6.81097e14	−0.121600
$731$	−1.08478e15	−0.192219
$732$	−4.37033e15	−0.768605
$733$	−1.08401e16	−1.89218	−0.946092	−	0.323898i	$-0.895006\pi$
$733$	−1.08401e16	−1.89218	−0.946092	+	0.323898i	$0.895006\pi$
$734$	5.42130e14	0.0939237
$735$	4.13189e15	0.710508
$736$	2.73763e14	0.0467247
$737$	1.24445e15	0.210818
$738$	−1.95051e14	−0.0327973
$739$	−1.11338e15	−0.185822	−0.0929112	−	0.995674i	$-0.529617\pi$
$739$	−1.11338e15	−0.185822	−0.0929112	+	0.995674i	$0.529617\pi$
$740$	1.36838e16	2.26690
$741$	6.14993e15	1.01128
$742$	1.05932e14	0.0172904
$743$	−4.81885e15	−0.780737	−0.390369	−	0.920659i	$-0.627652\pi$
$743$	−4.81885e15	−0.780737	−0.390369	+	0.920659i	$0.627652\pi$
$744$	−2.51763e15	−0.404893
$745$	6.67010e15	1.06481
$746$	5.43442e14	0.0861172
$747$	1.92366e16	3.02597
$748$	1.05950e15	0.165440
$749$	−3.89449e15	−0.603672
$750$	9.57027e14	0.147261
$751$	−1.68330e15	−0.257124	−0.128562	−	0.991701i	$-0.541036\pi$
$751$	−1.68330e15	−0.257124	−0.128562	+	0.991701i	$0.541036\pi$
$752$	−6.07327e15	−0.920926
$753$	−1.00285e16	−1.50961
$754$	2.83205e14	0.0423212
$755$	7.09086e15	1.05194
$756$	−1.19314e16	−1.75719
$757$	−5.28281e15	−0.772392	−0.386196	−	0.922417i	$-0.626211\pi$
$757$	−5.28281e15	−0.772392	−0.386196	+	0.922417i	$0.626211\pi$
$758$	−6.97278e14	−0.101210
$759$	−3.52418e15	−0.507842
$760$	−7.53625e14	−0.107815
$761$	−1.04670e16	−1.48664	−0.743321	−	0.668935i	$-0.766751\pi$
$761$	−1.04670e16	−1.48664	−0.743321	+	0.668935i	$0.766751\pi$
$762$	1.19659e15	0.168730
$763$	1.69782e15	0.237688
$764$	−6.01098e15	−0.835472
$765$	3.08263e15	0.425386
$766$	3.56069e14	0.0487838
$767$	1.52584e16	2.07556
$768$	1.23965e16	1.67421
$769$	−8.05151e15	−1.07965	−0.539824	−	0.841778i	$-0.681509\pi$
$769$	−8.05151e15	−1.07965	−0.539824	+	0.841778i	$0.681509\pi$
$770$	1.10299e15	0.146849
$771$	6.17741e15	0.816596
$772$	−6.66592e15	−0.874913
$773$	−7.55732e15	−0.984874	−0.492437	−	0.870348i	$-0.663894\pi$
$773$	−7.55732e15	−0.984874	−0.492437	+	0.870348i	$0.663894\pi$
$774$	−1.98039e15	−0.256257
$775$	−1.98195e16	−2.54644
$776$	−6.42560e14	−0.0819736
$777$	1.69631e16	2.14876
$778$	3.62993e14	0.0456573
$779$	7.13952e14	0.0891689
$780$	3.01897e16	3.74403
$781$	−2.40451e14	−0.0296105
$782$	−1.55518e13	−0.00190171
$783$	−7.25590e15	−0.881053
$784$	−1.99684e15	−0.240771
$785$	−4.14586e15	−0.496400
$786$	1.35386e15	0.160971
$787$	7.66393e15	0.904879	0.452440	−	0.891795i	$-0.350554\pi$
$787$	7.66393e15	0.904879	0.452440	+	0.891795i	$0.350554\pi$
$788$	1.18002e16	1.38355
$789$	1.74579e16	2.03268
$790$	−1.00993e15	−0.116772
$791$	−4.72854e15	−0.542946
$792$	3.87949e15	0.442371
$793$	4.99493e15	0.565623
$794$	6.17600e14	0.0694536
$795$	6.86732e15	0.766952
$796$	−1.43388e16	−1.59034
$797$	−7.27260e15	−0.801068	−0.400534	−	0.916282i	$-0.631175\pi$
$797$	−7.27260e15	−0.801068	−0.400534	+	0.916282i	$0.631175\pi$
$798$	−4.65787e14	−0.0509532
$799$	1.04494e15	0.113523
$800$	−3.47767e15	−0.375226
$801$	−1.65943e16	−1.77820
$802$	−5.02529e13	−0.00534814
$803$	−1.28336e16	−1.35648
$804$	−2.57979e15	−0.270818
$805$	2.84203e15	0.296314
$806$	1.43464e15	0.148559
$807$	1.89540e16	1.94938
$808$	4.47303e14	0.0456919
$809$	1.51920e15	0.154134	0.0770669	−	0.997026i	$-0.475444\pi$
$809$	1.51920e15	0.154134	0.0770669	+	0.997026i	$0.475444\pi$
$810$	1.78449e15	0.179823
$811$	−1.98293e16	−1.98469	−0.992347	−	0.123484i	$-0.960593\pi$
$811$	−1.98293e16	−1.98469	−0.992347	+	0.123484i	$0.960593\pi$
$812$	3.76527e15	0.374316
$813$	−2.47440e16	−2.44327
$814$	−1.46882e15	−0.144057
$815$	−1.02150e16	−0.995108
$816$	−2.18379e15	−0.211308
$817$	7.24889e15	0.696707
$818$	1.13331e14	0.0108195
$819$	2.55305e16	2.42102
$820$	3.50476e15	0.330128
$821$	1.54939e16	1.44968	0.724840	−	0.688917i	$-0.241914\pi$
$821$	1.54939e16	1.44968	0.724840	+	0.688917i	$0.241914\pi$
$822$	1.96717e15	0.182830
$823$	2.32481e14	0.0214629	0.0107314	−	0.999942i	$-0.496584\pi$
$823$	2.32481e14	0.0214629	0.0107314	+	0.999942i	$0.496584\pi$
$824$	1.96100e15	0.179837
$825$	4.47684e16	4.07826
$826$	−1.15565e15	−0.104577
$827$	8.75795e15	0.787267	0.393634	−	0.919267i	$-0.371218\pi$
$827$	8.75795e15	0.787267	0.393634	+	0.919267i	$0.371218\pi$
$828$	4.98389e15	0.445043
$829$	−5.50257e15	−0.488108	−0.244054	−	0.969762i	$-0.578477\pi$
$829$	−5.50257e15	−0.488108	−0.244054	+	0.969762i	$0.578477\pi$
$830$	1.96906e15	0.173512
$831$	−1.08415e15	−0.0949035
$832$	−1.44213e16	−1.25408
$833$	3.43567e14	0.0296800
$834$	−2.91059e15	−0.249786
$835$	1.19430e16	1.01821
$836$	−7.07995e15	−0.599647
$837$	−3.67564e16	−3.09273
$838$	−8.79566e14	−0.0735235
$839$	1.11178e16	0.923269	0.461635	−	0.887070i	$-0.347263\pi$
$839$	1.11178e16	0.923269	0.461635	+	0.887070i	$0.347263\pi$
$840$	−4.58608e15	−0.378360
$841$	−9.91071e15	−0.812319
$842$	−5.15723e14	−0.0419953
$843$	−1.98060e16	−1.60230
$844$	1.63538e16	1.31442
$845$	−1.40243e16	−1.11987
$846$	1.90766e15	0.151344
$847$	9.75870e15	0.769190
$848$	−3.31880e15	−0.259898
$849$	4.80400e15	0.373776
$850$	1.97558e14	0.0152718
$851$	−3.78467e15	−0.290680
$852$	4.98463e14	0.0380378
$853$	1.21838e16	0.923767	0.461883	−	0.886941i	$-0.347174\pi$
$853$	1.21838e16	0.923767	0.461883	+	0.886941i	$0.347174\pi$
$854$	−3.78309e14	−0.0284989
$855$	−2.05993e16	−1.54183
$856$	−1.40213e15	−0.104275
$857$	1.27752e16	0.944004	0.472002	−	0.881597i	$-0.343531\pi$
$857$	1.27752e16	0.944004	0.472002	+	0.881597i	$0.343531\pi$
$858$	−3.24057e15	−0.237925
$859$	−9.70965e15	−0.708339	−0.354169	−	0.935181i	$-0.615236\pi$
$859$	−9.70965e15	−0.708339	−0.354169	+	0.935181i	$0.615236\pi$
$860$	3.55844e16	2.57940
$861$	4.34465e15	0.312923
$862$	−1.10124e15	−0.0788118
$863$	−7.09145e15	−0.504285	−0.252142	−	0.967690i	$-0.581135\pi$
$863$	−7.09145e15	−0.504285	−0.252142	+	0.967690i	$0.581135\pi$
$864$	−6.44953e15	−0.455725
$865$	2.86262e16	2.00991
$866$	9.22217e13	0.00643406
$867$	−2.52113e16	−1.74779
$868$	1.90738e16	1.31395
$869$	−1.90296e16	−1.30263
$870$	−1.39052e15	−0.0945850
$871$	2.94849e15	0.199297
$872$	6.11264e14	0.0410571
$873$	−1.75634e16	−1.17228
$874$	1.03923e14	0.00689284
$875$	−1.45424e16	−0.958496
$876$	2.66045e16	1.74254
$877$	−6.56811e15	−0.427507	−0.213753	−	0.976888i	$-0.568569\pi$
$877$	−6.56811e15	−0.427507	−0.213753	+	0.976888i	$0.568569\pi$
$878$	1.55761e14	0.0100749
$879$	−2.49422e16	−1.60323
$880$	−3.45560e16	−2.20734
$881$	5.51518e15	0.350100	0.175050	−	0.984560i	$-0.443991\pi$
$881$	5.51518e15	0.350100	0.175050	+	0.984560i	$0.443991\pi$
$882$	6.27222e14	0.0395680
$883$	−3.04798e16	−1.91086	−0.955428	−	0.295223i	$-0.904606\pi$
$883$	−3.04798e16	−1.91086	−0.955428	+	0.295223i	$0.904606\pi$
$884$	2.51028e15	0.156399
$885$	−7.49181e16	−4.63873
$886$	1.36406e15	0.0839361
$887$	3.26397e16	1.99603	0.998014	−	0.0629986i	$-0.0200664\pi$
$887$	3.26397e16	1.99603	0.998014	+	0.0629986i	$0.0200664\pi$
$888$	6.10718e15	0.371167
$889$	−1.81826e16	−1.09824
$890$	−1.69860e15	−0.101964
$891$	3.36243e16	2.00598
$892$	5.11204e15	0.303101
$893$	−6.98268e15	−0.411471
$894$	1.48423e15	0.0869249
$895$	6.85489e15	0.399001
$896$	4.45814e15	0.257905
$897$	−8.34988e15	−0.480089
$898$	−6.76377e14	−0.0386517
$899$	1.15995e16	0.658810
$900$	−6.33114e16	−3.57395
$901$	5.71018e14	0.0320379
$902$	−3.76201e14	−0.0209790
$903$	4.41121e16	2.44498
$904$	−1.70241e15	−0.0937858
$905$	1.07633e16	0.589359
$906$	1.57786e15	0.0858741
$907$	−2.47855e16	−1.34078	−0.670391	−	0.742008i	$-0.733874\pi$
$907$	−2.47855e16	−1.34078	−0.670391	+	0.742008i	$0.733874\pi$
$908$	2.66053e16	1.43053
$909$	1.22264e16	0.653425
$910$	2.61331e15	0.138824
$911$	2.42456e15	0.128021	0.0640106	−	0.997949i	$-0.479611\pi$
$911$	2.42456e15	0.128021	0.0640106	+	0.997949i	$0.479611\pi$
$912$	1.45929e16	0.765896
$913$	3.71022e16	1.93557
$914$	−7.08983e14	−0.0367648
$915$	−2.45249e16	−1.26413
$916$	−2.01561e16	−1.03272
$917$	−2.05723e16	−1.04774
$918$	3.66382e14	0.0185481
$919$	3.23071e16	1.62579	0.812893	−	0.582413i	$-0.197891\pi$
$919$	3.23071e16	1.62579	0.812893	+	0.582413i	$0.197891\pi$
$920$	1.02321e15	0.0511838
$921$	5.55677e16	2.76308
$922$	1.18704e15	0.0586738
$923$	−5.69702e14	−0.0279923
$924$	−4.30840e16	−2.10436
$925$	4.80774e16	2.33433
$926$	−2.07101e14	−0.00999592
$927$	5.36011e16	2.57179
$928$	2.03533e15	0.0970780
$929$	5.18206e15	0.245706	0.122853	−	0.992425i	$-0.460796\pi$
$929$	5.18206e15	0.245706	0.122853	+	0.992425i	$0.460796\pi$
$930$	−7.04399e15	−0.332019
$931$	−2.29584e15	−0.107577
$932$	2.22663e16	1.03719
$933$	4.64371e16	2.15038
$934$	8.35490e14	0.0384621
$935$	5.94556e15	0.272100
$936$	9.19171e15	0.418195
$937$	−3.02877e16	−1.36993	−0.684964	−	0.728577i	$-0.740182\pi$
$937$	−3.02877e16	−1.36993	−0.684964	+	0.728577i	$0.740182\pi$
$938$	−2.23315e14	−0.0100416
$939$	2.34114e16	1.04657
$940$	−3.42776e16	−1.52338
$941$	−1.14006e16	−0.503714	−0.251857	−	0.967764i	$-0.581041\pi$
$941$	−1.14006e16	−0.503714	−0.251857	+	0.967764i	$0.581041\pi$
$942$	−9.22536e14	−0.0405232
$943$	−9.69346e14	−0.0423316
$944$	3.62060e16	1.57193
$945$	−6.69549e16	−2.89006
$946$	−3.81964e15	−0.163916
$947$	2.25353e16	0.961475	0.480738	−	0.876865i	$-0.340369\pi$
$947$	2.25353e16	0.961475	0.480738	+	0.876865i	$0.340369\pi$
$948$	3.94490e16	1.67336
$949$	−3.04068e16	−1.28235
$950$	−1.32015e15	−0.0553534
$951$	−6.27282e16	−2.61499
$952$	−3.81333e14	−0.0158052
$953$	9.77340e15	0.402749	0.201375	−	0.979514i	$-0.435459\pi$
$953$	9.77340e15	0.402749	0.201375	+	0.979514i	$0.435459\pi$
$954$	1.04246e15	0.0427113
$955$	−3.37317e16	−1.37410
$956$	−9.22504e15	−0.373637
$957$	−2.62010e16	−1.05512
$958$	1.36005e15	0.0544559
$959$	−2.98918e16	−1.19001
$960$	7.08079e16	2.80279
$961$	3.33512e16	1.31260
$962$	−3.48009e15	−0.136184
$963$	−3.83251e16	−1.49121
$964$	−1.76528e16	−0.682952
$965$	−3.74070e16	−1.43897
$966$	6.32408e14	0.0241893
$967$	−1.33606e16	−0.508136	−0.254068	−	0.967186i	$-0.581769\pi$
$967$	−1.33606e16	−0.508136	−0.254068	+	0.967186i	$0.581769\pi$
$968$	3.51341e15	0.132866
$969$	−2.51079e15	−0.0944126
$970$	−1.79780e15	−0.0672197
$971$	1.34904e15	0.0501557	0.0250778	−	0.999686i	$-0.492017\pi$
$971$	1.34904e15	0.0501557	0.0250778	+	0.999686i	$0.492017\pi$
$972$	−1.50040e16	−0.554682
$973$	4.42274e16	1.62582
$974$	2.30606e15	0.0842939
$975$	1.06070e17	3.85539
$976$	1.18522e16	0.428377
$977$	−4.06412e16	−1.46065	−0.730325	−	0.683099i	$-0.760632\pi$
$977$	−4.06412e16	−1.46065	−0.730325	+	0.683099i	$0.760632\pi$
$978$	−2.27303e15	−0.0812347
$979$	−3.20059e16	−1.13743
$980$	−1.12702e16	−0.398279
$981$	1.67080e16	0.587145
$982$	2.06071e13	0.000720118 0
$983$	−3.43151e16	−1.19245	−0.596226	−	0.802816i	$-0.703334\pi$
$983$	−3.43151e16	−1.19245	−0.596226	+	0.802816i	$0.703334\pi$
$984$	1.56420e15	0.0540528
$985$	6.62190e16	2.27553
$986$	−1.15622e14	−0.00395110
$987$	−4.24921e16	−1.44399
$988$	−1.67746e16	−0.566877
$989$	−9.84195e15	−0.330751
$990$	1.08543e16	0.362751
$991$	4.96389e16	1.64975	0.824873	−	0.565319i	$-0.191247\pi$
$991$	4.96389e16	1.64975	0.824873	+	0.565319i	$0.191247\pi$
$992$	1.03104e16	0.340770
$993$	2.55453e15	0.0839634
$994$	4.31484e13	0.00141039
$995$	−8.04648e16	−2.61564
$996$	−7.69140e16	−2.48645
$997$	3.52940e16	1.13469	0.567346	−	0.823480i	$-0.307970\pi$
$997$	3.52940e16	1.13469	0.567346	+	0.823480i	$0.307970\pi$
$998$	−3.83861e15	−0.122732
$999$	8.91623e16	2.83512

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	23.12.a.b.1.5	✓	11
3.2	odd	2		207.12.a.d.1.7		11

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
23.12.a.b.1.5	✓	11	1.1	even	1	trivial
207.12.a.d.1.7		11	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 23 \)
Weight:	\( k \)	\(=\)	\( 12 \)
Character orbit:	\([\chi]\)	\(=\)	23.a (trivial)

\(f(q)\)	\(=\)	\(q-3.40598 q^{2} +746.589 q^{3} -2036.40 q^{4} -11427.6 q^{5} -2542.87 q^{6} +38639.7 q^{7} +13911.4 q^{8} +380248. q^{9} +O(q^{10})\)	\(q-3.40598 q^{2} +746.589 q^{3} -2036.40 q^{4} -11427.6 q^{5} -2542.87 q^{6} +38639.7 q^{7} +13911.4 q^{8} +380248. q^{9} +38922.2 q^{10} +733395. q^{11} -1.52035e6 q^{12} +1.73764e6 q^{13} -131606. q^{14} -8.53172e6 q^{15} +4.12316e6 q^{16} -709414. q^{17} -1.29512e6 q^{18} +4.74056e6 q^{19} +2.32712e7 q^{20} +2.88480e7 q^{21} -2.49793e6 q^{22} -6.43634e6 q^{23} +1.03861e7 q^{24} +8.17622e7 q^{25} -5.91837e6 q^{26} +1.51633e8 q^{27} -7.86859e7 q^{28} -4.78519e7 q^{29} +2.90589e7 q^{30} -2.42404e8 q^{31} -4.25339e7 q^{32} +5.47544e8 q^{33} +2.41625e6 q^{34} -4.41560e8 q^{35} -7.74336e8 q^{36} +5.88015e8 q^{37} -1.61463e7 q^{38} +1.29730e9 q^{39} -1.58974e8 q^{40} +1.50605e8 q^{41} -9.82557e7 q^{42} +1.52912e9 q^{43} -1.49348e9 q^{44} -4.34532e9 q^{45} +2.19221e7 q^{46} -1.47296e9 q^{47} +3.07831e9 q^{48} -4.84298e8 q^{49} -2.78480e8 q^{50} -5.29640e8 q^{51} -3.53853e9 q^{52} -8.04916e8 q^{53} -5.16458e8 q^{54} -8.38095e9 q^{55} +5.37532e8 q^{56} +3.53925e9 q^{57} +1.62983e8 q^{58} +8.78112e9 q^{59} +1.73740e10 q^{60} +2.87455e9 q^{61} +8.25624e8 q^{62} +1.46927e10 q^{63} -8.29937e9 q^{64} -1.98571e10 q^{65} -1.86493e9 q^{66} +1.69684e9 q^{67} +1.44465e9 q^{68} -4.80530e9 q^{69} +1.50394e9 q^{70} -3.27860e8 q^{71} +5.28977e9 q^{72} -1.74989e10 q^{73} -2.00277e9 q^{74} +6.10427e10 q^{75} -9.65367e9 q^{76} +2.83382e10 q^{77} -4.41858e9 q^{78} -2.59473e10 q^{79} -4.71179e10 q^{80} +4.58475e10 q^{81} -5.12958e8 q^{82} +5.05896e10 q^{83} -5.87460e10 q^{84} +8.10690e9 q^{85} -5.20816e9 q^{86} -3.57257e10 q^{87} +1.02025e10 q^{88} -4.36408e10 q^{89} +1.48001e10 q^{90} +6.71419e10 q^{91} +1.31070e10 q^{92} -1.80976e11 q^{93} +5.01689e9 q^{94} -5.41733e10 q^{95} -3.17554e10 q^{96} -4.61895e10 q^{97} +1.64951e9 q^{98} +2.78872e11 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9}+O(q^{10}) \) 11 * q + 32 * q^2 - 20 * q^3 + 11264 * q^4 + 1034 * q^5 - 22385 * q^6 + 159584 * q^7 + 115497 * q^8 + 611943 * q^9	\( 11 q + 32 q^{2} - 20 q^{3} + 11264 q^{4} + 1034 q^{5} - 22385 q^{6} + 159584 q^{7} + 115497 q^{8} + 611943 q^{9} - 627650 q^{10} - 771396 q^{11} - 1720771 q^{12} + 3433434 q^{13} + 4585896 q^{14} + 5551840 q^{15} + 18802384 q^{16} + 29035398 q^{17} + 26169127 q^{18} + 21398428 q^{19} + 72466260 q^{20} + 61896432 q^{21} + 100463524 q^{22} - 70799773 q^{23} + 161844076 q^{24} + 233562509 q^{25} + 328796191 q^{26} + 356379712 q^{27} + 499445210 q^{28} + 226699042 q^{29} + 510413234 q^{30} + 251932328 q^{31} + 806116648 q^{32} + 221442992 q^{33} + 325378622 q^{34} - 355232072 q^{35} - 1034240009 q^{36} + 573876170 q^{37} - 770782036 q^{38} - 1199522184 q^{39} - 1009699226 q^{40} - 1733596378 q^{41} - 6499506824 q^{42} + 647370308 q^{43} - 4662321170 q^{44} - 5023123422 q^{45} - 205962976 q^{46} - 5436527248 q^{47} - 4050950401 q^{48} + 4356386219 q^{49} - 10296502416 q^{50} - 1050918064 q^{51} - 5616607137 q^{52} - 3387203910 q^{53} - 21748294807 q^{54} - 10571441512 q^{55} + 635842210 q^{56} - 4678697728 q^{57} + 1991171353 q^{58} + 15113662084 q^{59} + 19934836476 q^{60} + 23895772578 q^{61} + 7557529251 q^{62} + 56666471160 q^{63} + 32993181147 q^{64} + 3660035708 q^{65} + 33342886858 q^{66} + 46806014468 q^{67} + 40754169364 q^{68} + 128726860 q^{69} - 12274756860 q^{70} + 45541532768 q^{71} + 12763980783 q^{72} + 63786612542 q^{73} - 41720765910 q^{74} + 88573702476 q^{75} + 5581739704 q^{76} + 19147126968 q^{77} - 111443125499 q^{78} + 21847812496 q^{79} - 67715736674 q^{80} + 122793712411 q^{81} - 30216129401 q^{82} + 40153340788 q^{83} - 221098994762 q^{84} + 116854272412 q^{85} - 47307463306 q^{86} - 5595049008 q^{87} - 263050721364 q^{88} + 37300228382 q^{89} - 419483354956 q^{90} + 109416811256 q^{91} - 72498967552 q^{92} - 224700035960 q^{93} - 378035850441 q^{94} - 255722421456 q^{95} - 96864379937 q^{96} - 243602730 q^{97} - 514347061348 q^{98} + 97029276404 q^{99}+O(q^{100}) \) 11 * q + 32 * q^2 - 20 * q^3 + 11264 * q^4 + 1034 * q^5 - 22385 * q^6 + 159584 * q^7 + 115497 * q^8 + 611943 * q^9 - 627650 * q^10 - 771396 * q^11 - 1720771 * q^12 + 3433434 * q^13 + 4585896 * q^14 + 5551840 * q^15 + 18802384 * q^16 + 29035398 * q^17 + 26169127 * q^18 + 21398428 * q^19 + 72466260 * q^20 + 61896432 * q^21 + 100463524 * q^22 - 70799773 * q^23 + 161844076 * q^24 + 233562509 * q^25 + 328796191 * q^26 + 356379712 * q^27 + 499445210 * q^28 + 226699042 * q^29 + 510413234 * q^30 + 251932328 * q^31 + 806116648 * q^32 + 221442992 * q^33 + 325378622 * q^34 - 355232072 * q^35 - 1034240009 * q^36 + 573876170 * q^37 - 770782036 * q^38 - 1199522184 * q^39 - 1009699226 * q^40 - 1733596378 * q^41 - 6499506824 * q^42 + 647370308 * q^43 - 4662321170 * q^44 - 5023123422 * q^45 - 205962976 * q^46 - 5436527248 * q^47 - 4050950401 * q^48 + 4356386219 * q^49 - 10296502416 * q^50 - 1050918064 * q^51 - 5616607137 * q^52 - 3387203910 * q^53 - 21748294807 * q^54 - 10571441512 * q^55 + 635842210 * q^56 - 4678697728 * q^57 + 1991171353 * q^58 + 15113662084 * q^59 + 19934836476 * q^60 + 23895772578 * q^61 + 7557529251 * q^62 + 56666471160 * q^63 + 32993181147 * q^64 + 3660035708 * q^65 + 33342886858 * q^66 + 46806014468 * q^67 + 40754169364 * q^68 + 128726860 * q^69 - 12274756860 * q^70 + 45541532768 * q^71 + 12763980783 * q^72 + 63786612542 * q^73 - 41720765910 * q^74 + 88573702476 * q^75 + 5581739704 * q^76 + 19147126968 * q^77 - 111443125499 * q^78 + 21847812496 * q^79 - 67715736674 * q^80 + 122793712411 * q^81 - 30216129401 * q^82 + 40153340788 * q^83 - 221098994762 * q^84 + 116854272412 * q^85 - 47307463306 * q^86 - 5595049008 * q^87 - 263050721364 * q^88 + 37300228382 * q^89 - 419483354956 * q^90 + 109416811256 * q^91 - 72498967552 * q^92 - 224700035960 * q^93 - 378035850441 * q^94 - 255722421456 * q^95 - 96864379937 * q^96 - 243602730 * q^97 - 514347061348 * q^98 + 97029276404 * q^99

Introduction

L-functions

Modular forms

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Database

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