LMFDB - Embedded newform 74.8.a.c.1.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,8,Mod(1,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(2))

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

N = Newforms(chi, 8, names="a")

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

chi := DirichletCharacter("74.1");

S:= CuspForms(chi, 8);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 8 $
Character orbit:	$[\chi]$	$=$	74.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:	$23.1164918858$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	$\mathbb{Q}[x]/(x^{6} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} - 10621x^{4} + 102052x^{3} + 31004503x^{2} - 305547358x - 22608804936 $ x^6 - 2x^5 - 10621x^4 + 102052x^3 + 31004503x^2 - 305547358*x - 22608804936
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{3} $
Twist minimal:	yes
Fricke sign:	$+1$
Sato-Tate group:	$\mathrm{SU}(2)$

Embedding invariants

Embedding label			1.3
Root			$44.6523$ of defining polynomial
Character	$\chi$	$=$	74.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-8.00000 q^{2} -39.6523 q^{3} +64.0000 q^{4} -332.745 q^{5} +317.219 q^{6} -135.814 q^{7} -512.000 q^{8} -614.693 q^{9} +O(q^{10})$	\(q-8.00000 q^{2} -39.6523 q^{3} +64.0000 q^{4} -332.745 q^{5} +317.219 q^{6} -135.814 q^{7} -512.000 q^{8} -614.693 q^{9} +2661.96 q^{10} -6182.84 q^{11} -2537.75 q^{12} -9398.11 q^{13} +1086.51 q^{14} +13194.1 q^{15} +4096.00 q^{16} -4302.47 q^{17} +4917.54 q^{18} -15806.0 q^{19} -21295.7 q^{20} +5385.34 q^{21} +49462.7 q^{22} -104800. q^{23} +20302.0 q^{24} +32594.0 q^{25} +75184.9 q^{26} +111094. q^{27} -8692.09 q^{28} +93937.7 q^{29} -105553. q^{30} +118220. q^{31} -32768.0 q^{32} +245164. q^{33} +34419.8 q^{34} +45191.4 q^{35} -39340.3 q^{36} -50653.0 q^{37} +126448. q^{38} +372657. q^{39} +170365. q^{40} +578567. q^{41} -43082.7 q^{42} +1.01884e6 q^{43} -395702. q^{44} +204536. q^{45} +838403. q^{46} -1.05076e6 q^{47} -162416. q^{48} -805098. q^{49} -260752. q^{50} +170603. q^{51} -601479. q^{52} -230063. q^{53} -888749. q^{54} +2.05731e6 q^{55} +69536.7 q^{56} +626743. q^{57} -751502. q^{58} -2.22169e6 q^{59} +844422. q^{60} +1.26320e6 q^{61} -945760. q^{62} +83483.9 q^{63} +262144. q^{64} +3.12717e6 q^{65} -1.96131e6 q^{66} +1.31032e6 q^{67} -275358. q^{68} +4.15558e6 q^{69} -361531. q^{70} -2.73160e6 q^{71} +314723. q^{72} -5.21783e6 q^{73} +405224. q^{74} -1.29243e6 q^{75} -1.01158e6 q^{76} +839716. q^{77} -2.98126e6 q^{78} -2.42990e6 q^{79} -1.36292e6 q^{80} -3.06079e6 q^{81} -4.62853e6 q^{82} +1.69149e6 q^{83} +344662. q^{84} +1.43162e6 q^{85} -8.15075e6 q^{86} -3.72485e6 q^{87} +3.16561e6 q^{88} -5.89988e6 q^{89} -1.63629e6 q^{90} +1.27639e6 q^{91} -6.70723e6 q^{92} -4.68770e6 q^{93} +8.40610e6 q^{94} +5.25935e6 q^{95} +1.29933e6 q^{96} -6.48918e6 q^{97} +6.44078e6 q^{98} +3.80055e6 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9}+O(q^{10}) $ 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9} + 112 q^{10} + 2956 q^{11} + 1792 q^{12} + 2394 q^{13} + 7840 q^{14} - 28820 q^{15} + 24576 q^{16} - 45108 q^{17} - 66032 q^{18} + 11764 q^{19} - 896 q^{20} - 135378 q^{21} - 23648 q^{22} + 21052 q^{23} - 14336 q^{24} + 194744 q^{25} - 19152 q^{26} + 439240 q^{27} - 62720 q^{28} + 288454 q^{29} + 230560 q^{30} + 578868 q^{31} - 196608 q^{32} + 980174 q^{33} + 360864 q^{34} + 1243052 q^{35} + 528256 q^{36} - 303918 q^{37} - 94112 q^{38} + 1735296 q^{39} + 7168 q^{40} + 1176840 q^{41} + 1083024 q^{42} + 2669236 q^{43} + 189184 q^{44} + 2560692 q^{45} - 168416 q^{46} - 131044 q^{47} + 114688 q^{48} + 2460856 q^{49} - 1557952 q^{50} + 2899732 q^{51} + 153216 q^{52} + 983190 q^{53} - 3513920 q^{54} - 1200168 q^{55} + 501760 q^{56} - 163216 q^{57} - 2307632 q^{58} - 1215568 q^{59} - 1844480 q^{60} + 3136358 q^{61} - 4630944 q^{62} - 1444880 q^{63} + 1572864 q^{64} - 1302836 q^{65} - 7841392 q^{66} + 2179276 q^{67} - 2886912 q^{68} - 929514 q^{69} - 9944416 q^{70} + 325164 q^{71} - 4226048 q^{72} + 5011444 q^{73} + 2431344 q^{74} - 9374520 q^{75} + 752896 q^{76} - 26500426 q^{77} - 13882368 q^{78} + 3173032 q^{79} - 57344 q^{80} - 2565226 q^{81} - 9414720 q^{82} - 22567048 q^{83} - 8664192 q^{84} + 1486476 q^{85} - 21353888 q^{86} - 157228 q^{87} - 1513472 q^{88} + 26836996 q^{89} - 20485536 q^{90} + 17942380 q^{91} + 1347328 q^{92} + 16734948 q^{93} + 1048352 q^{94} - 4252048 q^{95} - 917504 q^{96} + 295792 q^{97} - 19686848 q^{98} + 25990712 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9 + 112 * q^10 + 2956 * q^11 + 1792 * q^12 + 2394 * q^13 + 7840 * q^14 - 28820 * q^15 + 24576 * q^16 - 45108 * q^17 - 66032 * q^18 + 11764 * q^19 - 896 * q^20 - 135378 * q^21 - 23648 * q^22 + 21052 * q^23 - 14336 * q^24 + 194744 * q^25 - 19152 * q^26 + 439240 * q^27 - 62720 * q^28 + 288454 * q^29 + 230560 * q^30 + 578868 * q^31 - 196608 * q^32 + 980174 * q^33 + 360864 * q^34 + 1243052 * q^35 + 528256 * q^36 - 303918 * q^37 - 94112 * q^38 + 1735296 * q^39 + 7168 * q^40 + 1176840 * q^41 + 1083024 * q^42 + 2669236 * q^43 + 189184 * q^44 + 2560692 * q^45 - 168416 * q^46 - 131044 * q^47 + 114688 * q^48 + 2460856 * q^49 - 1557952 * q^50 + 2899732 * q^51 + 153216 * q^52 + 983190 * q^53 - 3513920 * q^54 - 1200168 * q^55 + 501760 * q^56 - 163216 * q^57 - 2307632 * q^58 - 1215568 * q^59 - 1844480 * q^60 + 3136358 * q^61 - 4630944 * q^62 - 1444880 * q^63 + 1572864 * q^64 - 1302836 * q^65 - 7841392 * q^66 + 2179276 * q^67 - 2886912 * q^68 - 929514 * q^69 - 9944416 * q^70 + 325164 * q^71 - 4226048 * q^72 + 5011444 * q^73 + 2431344 * q^74 - 9374520 * q^75 + 752896 * q^76 - 26500426 * q^77 - 13882368 * q^78 + 3173032 * q^79 - 57344 * q^80 - 2565226 * q^81 - 9414720 * q^82 - 22567048 * q^83 - 8664192 * q^84 + 1486476 * q^85 - 21353888 * q^86 - 157228 * q^87 - 1513472 * q^88 + 26836996 * q^89 - 20485536 * q^90 + 17942380 * q^91 + 1347328 * q^92 + 16734948 * q^93 + 1048352 * q^94 - 4252048 * q^95 - 917504 * q^96 + 295792 * q^97 - 19686848 * q^98 + 25990712 * q^99

Display 100 coefficients 10 coefficients

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$	$a_n / n^{(k-1)/2}$	$ \alpha_n $			$ \theta_n $
$p$	$a_p$	$a_p / p^{(k-1)/2}$	$ \alpha_p$			$ \theta_p $

$2$	−8.00000	−0.707107
$2$	−8.00000	−0.707107
$3$	−39.6523	−0.847899	−0.423950	−	0.905686i	$-0.639357\pi$
$3$	−39.6523	−0.847899	−0.423950	+	0.905686i	$0.639357\pi$
$4$	64.0000	0.500000
$5$	−332.745	−1.19046	−0.595232	−	0.803554i	$-0.702940\pi$
$5$	−332.745	−1.19046	−0.595232	+	0.803554i	$0.702940\pi$
$6$	317.219	0.599555
$7$	−135.814	−0.149658	−0.0748292	−	0.997196i	$-0.523841\pi$
$7$	−135.814	−0.149658	−0.0748292	+	0.997196i	$0.523841\pi$
$8$	−512.000	−0.353553
$9$	−614.693	−0.281067
$10$	2661.96	0.841785
$11$	−6182.84	−1.40060	−0.700299	−	0.713849i	$-0.746950\pi$
$11$	−6182.84	−1.40060	−0.700299	+	0.713849i	$0.746950\pi$
$12$	−2537.75	−0.423950
$13$	−9398.11	−1.18642	−0.593211	−	0.805047i	$-0.702140\pi$
$13$	−9398.11	−1.18642	−0.593211	+	0.805047i	$0.702140\pi$
$14$	1086.51	0.105825
$15$	13194.1	1.00939
$16$	4096.00	0.250000
$17$	−4302.47	−0.212396	−0.106198	−	0.994345i	$-0.533868\pi$
$17$	−4302.47	−0.212396	−0.106198	+	0.994345i	$0.533868\pi$
$18$	4917.54	0.198744
$19$	−15806.0	−0.528668	−0.264334	−	0.964431i	$-0.585152\pi$
$19$	−15806.0	−0.528668	−0.264334	+	0.964431i	$0.585152\pi$
$20$	−21295.7	−0.595232
$21$	5385.34	0.126895
$22$	49462.7	0.990373
$23$	−104800.	−1.79604	−0.898019	−	0.439956i	$-0.854994\pi$
$23$	−104800.	−1.79604	−0.898019	+	0.439956i	$0.854994\pi$
$24$	20302.0	0.299778
$25$	32594.0	0.417203
$26$	75184.9	0.838927
$27$	111094.	1.08622
$28$	−8692.09	−0.0748292
$29$	93937.7	0.715232	0.357616	−	0.933869i	$-0.383590\pi$
$29$	93937.7	0.715232	0.357616	+	0.933869i	$0.383590\pi$
$30$	−105553.	−0.713749
$31$	118220.	0.712730	0.356365	−	0.934347i	$-0.384016\pi$
$31$	118220.	0.712730	0.356365	+	0.934347i	$0.384016\pi$
$32$	−32768.0	−0.176777
$33$	245164.	1.18757
$34$	34419.8	0.150187
$35$	45191.4	0.178163
$36$	−39340.3	−0.140533
$37$	−50653.0	−0.164399
$37$	−50653.0	−0.164399
$38$	126448.	0.373825
$39$	372657.	1.00597
$40$	170365.	0.420892
$41$	578567.	1.31102	0.655511	−	0.755186i	$-0.272453\pi$
$41$	578567.	1.31102	0.655511	+	0.755186i	$0.272453\pi$
$42$	−43082.7	−0.0897285
$43$	1.01884e6	1.95420	0.977098	−	0.212789i	$-0.0682547\pi$
$43$	1.01884e6	1.95420	0.977098	+	0.212789i	$0.0682547\pi$
$44$	−395702.	−0.700299
$45$	204536.	0.334599
$46$	838403.	1.26999
$47$	−1.05076e6	−1.47626	−0.738129	−	0.674660i	$-0.764290\pi$
$47$	−1.05076e6	−1.47626	−0.738129	+	0.674660i	$0.764290\pi$
$48$	−162416.	−0.211975
$49$	−805098.	−0.977602
$50$	−260752.	−0.295007
$51$	170603.	0.180091
$52$	−601479.	−0.593211
$53$	−230063.	−0.212266	−0.106133	−	0.994352i	$-0.533847\pi$
$53$	−230063.	−0.212266	−0.106133	+	0.994352i	$0.533847\pi$
$54$	−888749.	−0.768070
$55$	2.05731e6	1.66736
$56$	69536.7	0.0529123
$57$	626743.	0.448257
$58$	−751502.	−0.505746
$59$	−2.22169e6	−1.40832	−0.704160	−	0.710041i	$-0.748676\pi$
$59$	−2.22169e6	−1.40832	−0.704160	+	0.710041i	$0.748676\pi$
$60$	844422.	0.504697
$61$	1.26320e6	0.712552	0.356276	−	0.934381i	$-0.384046\pi$
$61$	1.26320e6	0.712552	0.356276	+	0.934381i	$0.384046\pi$
$62$	−945760.	−0.503976
$63$	83483.9	0.0420640
$64$	262144.	0.125000
$65$	3.12717e6	1.41239
$66$	−1.96131e6	−0.839736
$67$	1.31032e6	0.532251	0.266126	−	0.963938i	$-0.414256\pi$
$67$	1.31032e6	0.532251	0.266126	+	0.963938i	$0.414256\pi$
$68$	−275358.	−0.106198
$69$	4.15558e6	1.52286
$70$	−361531.	−0.125980
$71$	−2.73160e6	−0.905759	−0.452880	−	0.891572i	$-0.649603\pi$
$71$	−2.73160e6	−0.905759	−0.452880	+	0.891572i	$0.649603\pi$
$72$	314723.	0.0993721
$73$	−5.21783e6	−1.56986	−0.784929	−	0.619586i	$-0.787300\pi$
$73$	−5.21783e6	−1.56986	−0.784929	+	0.619586i	$0.787300\pi$
$74$	405224.	0.116248
$75$	−1.29243e6	−0.353746
$76$	−1.01158e6	−0.264334
$77$	839716.	0.209611
$78$	−2.98126e6	−0.711325
$79$	−2.42990e6	−0.554489	−0.277244	−	0.960799i	$-0.589421\pi$
$79$	−2.42990e6	−0.554489	−0.277244	+	0.960799i	$0.589421\pi$
$80$	−1.36292e6	−0.297616
$81$	−3.06079e6	−0.639935
$82$	−4.62853e6	−0.927032
$83$	1.69149e6	0.324711	0.162355	−	0.986732i	$-0.448091\pi$
$83$	1.69149e6	0.324711	0.162355	+	0.986732i	$0.448091\pi$
$84$	344662.	0.0634477
$85$	1.43162e6	0.252850
$86$	−8.15075e6	−1.38183
$87$	−3.72485e6	−0.606445
$88$	3.16561e6	0.495186
$89$	−5.89988e6	−0.887111	−0.443556	−	0.896247i	$-0.646283\pi$
$89$	−5.89988e6	−0.887111	−0.443556	+	0.896247i	$0.646283\pi$
$90$	−1.63629e6	−0.236598
$91$	1.27639e6	0.177558
$92$	−6.70723e6	−0.898019
$93$	−4.68770e6	−0.604323
$94$	8.40610e6	1.04387
$95$	5.25935e6	0.629360
$96$	1.29933e6	0.149889
$97$	−6.48918e6	−0.721920	−0.360960	−	0.932581i	$-0.617551\pi$
$97$	−6.48918e6	−0.721920	−0.360960	+	0.932581i	$0.617551\pi$
$98$	6.44078e6	0.691269
$99$	3.80055e6	0.393661
$100$	2.08601e6	0.208601
$101$	−1.25596e6	−0.121297	−0.0606486	−	0.998159i	$-0.519317\pi$
$101$	−1.25596e6	−0.121297	−0.0606486	+	0.998159i	$0.519317\pi$
$102$	−1.36482e6	−0.127343
$103$	1.44149e7	1.29981	0.649907	−	0.760013i	$-0.274808\pi$
$103$	1.44149e7	1.29981	0.649907	+	0.760013i	$0.274808\pi$
$104$	4.81183e6	0.419463
$105$	−1.79194e6	−0.151064
$106$	1.84050e6	0.150095
$107$	1.52113e7	1.20039	0.600196	−	0.799853i	$-0.295089\pi$
$107$	1.52113e7	1.20039	0.600196	+	0.799853i	$0.295089\pi$
$108$	7.10999e6	0.543108
$109$	2.45775e6	0.181780	0.0908899	−	0.995861i	$-0.471029\pi$
$109$	2.45775e6	0.181780	0.0908899	+	0.995861i	$0.471029\pi$
$110$	−1.64585e7	−1.17900
$111$	2.00851e6	0.139394
$112$	−556294.	−0.0374146
$113$	−1.87115e7	−1.21993	−0.609965	−	0.792429i	$-0.708816\pi$
$113$	−1.87115e7	−1.21993	−0.609965	+	0.792429i	$0.708816\pi$
$114$	−5.01394e6	−0.316966
$115$	3.48718e7	2.13812
$116$	6.01202e6	0.357616
$117$	5.77695e6	0.333463
$118$	1.77735e7	0.995833
$119$	584336.	0.0317869
$120$	−6.75538e6	−0.356874
$121$	1.87403e7	0.961676
$122$	−1.01056e7	−0.503851
$123$	−2.29415e7	−1.11161
$124$	7.56608e6	0.356365
$125$	1.51502e7	0.693799
$126$	−667871.	−0.0297437
$127$	−1.52790e7	−0.661883	−0.330941	−	0.943651i	$-0.607366\pi$
$127$	−1.52790e7	−0.661883	−0.330941	+	0.943651i	$0.607366\pi$
$128$	−2.09715e6	−0.0883883
$129$	−4.03995e7	−1.65696
$130$	−2.50174e7	−0.998711
$131$	4.60838e6	0.179101	0.0895507	−	0.995982i	$-0.471457\pi$
$131$	4.60838e6	0.179101	0.0895507	+	0.995982i	$0.471457\pi$
$132$	1.56905e7	0.593783
$133$	2.14667e6	0.0791197
$134$	−1.04826e7	−0.376359
$135$	−3.69658e7	−1.29310
$136$	2.20287e6	0.0750934
$137$	−1.29302e7	−0.429618	−0.214809	−	0.976656i	$-0.568913\pi$
$137$	−1.29302e7	−0.429618	−0.214809	+	0.976656i	$0.568913\pi$
$138$	−3.32446e7	−1.07682
$139$	4.06836e7	1.28489	0.642447	−	0.766330i	$-0.277919\pi$
$139$	4.06836e7	1.28489	0.642447	+	0.766330i	$0.277919\pi$
$140$	2.89225e6	0.0890814
$141$	4.16652e7	1.25172
$142$	2.18528e7	0.640469
$143$	5.81070e7	1.66170
$144$	−2.51778e6	−0.0702667
$145$	−3.12573e7	−0.851458
$146$	4.17427e7	1.11006
$147$	3.19240e7	0.828908
$148$	−3.24179e6	−0.0821995
$149$	1.71235e7	0.424072	0.212036	−	0.977262i	$-0.431991\pi$
$149$	1.71235e7	0.424072	0.212036	+	0.977262i	$0.431991\pi$
$150$	1.03394e7	0.250136
$151$	1.14400e7	0.270401	0.135201	−	0.990818i	$-0.456832\pi$
$151$	1.14400e7	0.270401	0.135201	+	0.990818i	$0.456832\pi$
$152$	8.09265e6	0.186912
$153$	2.64470e6	0.0596975
$154$	−6.71773e6	−0.148218
$155$	−3.93371e7	−0.848479
$156$	2.38501e7	0.502983
$157$	−5.14403e7	−1.06085	−0.530425	−	0.847732i	$-0.677968\pi$
$157$	−5.14403e7	−1.06085	−0.530425	+	0.847732i	$0.677968\pi$
$158$	1.94392e7	0.392083
$159$	9.12252e6	0.179980
$160$	1.09034e7	0.210446
$161$	1.42334e7	0.268792
$162$	2.44863e7	0.452502
$163$	−1.13404e7	−0.205103	−0.102551	−	0.994728i	$-0.532701\pi$
$163$	−1.13404e7	−0.205103	−0.102551	+	0.994728i	$0.532701\pi$
$164$	3.70283e7	0.655511
$165$	−8.15770e7	−1.41375
$166$	−1.35319e7	−0.229605
$167$	−5.75704e7	−0.956515	−0.478258	−	0.878220i	$-0.658731\pi$
$167$	−5.75704e7	−0.956515	−0.478258	+	0.878220i	$0.658731\pi$
$168$	−2.75729e6	−0.0448643
$169$	2.55760e7	0.407596
$170$	−1.14530e7	−0.178792
$171$	9.71581e6	0.148591
$172$	6.52060e7	0.977098
$173$	−7.49139e7	−1.10002	−0.550011	−	0.835158i	$-0.685376\pi$
$173$	−7.49139e7	−1.10002	−0.550011	+	0.835158i	$0.685376\pi$
$174$	2.97988e7	0.428821
$175$	−4.42671e6	−0.0624379
$176$	−2.53249e7	−0.350150
$177$	8.80952e7	1.19411
$178$	4.71990e7	0.627282
$179$	−7.29134e7	−0.950215	−0.475107	−	0.879928i	$-0.657591\pi$
$179$	−7.29134e7	−0.950215	−0.475107	+	0.879928i	$0.657591\pi$
$180$	1.30903e7	0.167300
$181$	−9.81117e7	−1.22983	−0.614916	−	0.788592i	$-0.710810\pi$
$181$	−9.81117e7	−1.22983	−0.614916	+	0.788592i	$0.710810\pi$
$182$	−1.02112e7	−0.125552
$183$	−5.00887e7	−0.604173
$184$	5.36578e7	0.634995
$185$	1.68545e7	0.195711
$186$	3.75016e7	0.427321
$187$	2.66015e7	0.297482
$188$	−6.72488e7	−0.738129
$189$	−1.50881e7	−0.162561
$190$	−4.20748e7	−0.445025
$191$	1.74491e8	1.81199	0.905995	−	0.423287i	$-0.139124\pi$
$191$	1.74491e8	1.81199	0.905995	+	0.423287i	$0.139124\pi$
$192$	−1.03946e7	−0.105987
$193$	−1.65444e7	−0.165653	−0.0828266	−	0.996564i	$-0.526395\pi$
$193$	−1.65444e7	−0.165653	−0.0828266	+	0.996564i	$0.526395\pi$
$194$	5.19135e7	0.510474
$195$	−1.24000e8	−1.19757
$196$	−5.15262e7	−0.488801
$197$	−9.87434e7	−0.920187	−0.460094	−	0.887870i	$-0.652184\pi$
$197$	−9.87434e7	−0.920187	−0.460094	+	0.887870i	$0.652184\pi$
$198$	−3.04044e7	−0.278361
$199$	−1.03751e8	−0.933273	−0.466636	−	0.884449i	$-0.654534\pi$
$199$	−1.03751e8	−0.933273	−0.466636	+	0.884449i	$0.654534\pi$
$200$	−1.66881e7	−0.147503
$201$	−5.19574e7	−0.451296
$202$	1.00477e7	0.0857700
$203$	−1.27581e7	−0.107041
$204$	1.09186e7	0.0900454
$205$	−1.92515e8	−1.56072
$206$	−1.15319e8	−0.919108
$207$	6.44201e7	0.504806
$208$	−3.84947e7	−0.296605
$209$	9.77257e7	0.740452
$210$	1.43355e7	0.106819
$211$	1.83610e8	1.34558	0.672789	−	0.739835i	$-0.265096\pi$
$211$	1.83610e8	1.34558	0.672789	+	0.739835i	$0.265096\pi$
$212$	−1.47240e7	−0.106133
$213$	1.08314e8	0.767993
$214$	−1.21690e8	−0.848806
$215$	−3.39015e8	−2.32640
$216$	−5.68799e7	−0.384035
$217$	−1.60559e7	−0.106666
$218$	−1.96620e7	−0.128538
$219$	2.06899e8	1.33108
$220$	1.31668e8	0.833680
$221$	4.04351e7	0.251992
$222$	−1.60681e7	−0.0985663
$223$	−9.64274e7	−0.582282	−0.291141	−	0.956680i	$-0.594035\pi$
$223$	−9.64274e7	−0.582282	−0.291141	+	0.956680i	$0.594035\pi$
$224$	4.45035e6	0.0264561
$225$	−2.00353e7	−0.117262
$226$	1.49692e8	0.862620
$227$	−2.90044e8	−1.64578	−0.822892	−	0.568197i	$-0.807641\pi$
$227$	−2.90044e8	−1.64578	−0.822892	+	0.568197i	$0.807641\pi$
$228$	4.01116e7	0.224129
$229$	2.84731e8	1.56679	0.783396	−	0.621523i	$-0.213486\pi$
$229$	2.84731e8	1.56679	0.783396	+	0.621523i	$0.213486\pi$
$230$	−2.78974e8	−1.51188
$231$	−3.32967e7	−0.177729
$232$	−4.80961e7	−0.252873
$233$	−3.55271e8	−1.83998	−0.919991	−	0.391940i	$-0.871804\pi$
$233$	−3.55271e8	−1.83998	−0.919991	+	0.391940i	$0.871804\pi$
$234$	−4.62156e7	−0.235794
$235$	3.49636e8	1.75743
$236$	−1.42188e8	−0.704160
$237$	9.63510e7	0.470151
$238$	−4.67469e6	−0.0224767
$239$	9.85614e7	0.466997	0.233498	−	0.972357i	$-0.424983\pi$
$239$	9.85614e7	0.466997	0.233498	+	0.972357i	$0.424983\pi$
$240$	5.40430e7	0.252348
$241$	2.63867e8	1.21430	0.607148	−	0.794589i	$-0.292313\pi$
$241$	2.63867e8	1.21430	0.607148	+	0.794589i	$0.292313\pi$
$242$	−1.49923e8	−0.680007
$243$	−1.21594e8	−0.543615
$244$	8.08446e7	0.356276
$245$	2.67892e8	1.16380
$246$	1.83532e8	0.786030
$247$	1.48546e8	0.627223
$248$	−6.05287e7	−0.251988
$249$	−6.70716e7	−0.275322
$250$	−1.21202e8	−0.490590
$251$	2.74241e8	1.09465	0.547324	−	0.836921i	$-0.315647\pi$
$251$	2.74241e8	1.09465	0.547324	+	0.836921i	$0.315647\pi$
$252$	5.34297e6	0.0210320
$253$	6.47964e8	2.51553
$254$	1.22232e8	0.468022
$255$	−5.67673e7	−0.214391
$256$	1.67772e7	0.0625000
$257$	−1.03836e7	−0.0381577	−0.0190789	−	0.999818i	$-0.506073\pi$
$257$	−1.03836e7	−0.0381577	−0.0190789	+	0.999818i	$0.506073\pi$
$258$	3.23196e8	1.17165
$259$	6.87938e6	0.0246037
$260$	2.00139e8	0.706195
$261$	−5.77428e7	−0.201028
$262$	−3.68671e7	−0.126644
$263$	−1.51247e7	−0.0512673	−0.0256336	−	0.999671i	$-0.508160\pi$
$263$	−1.51247e7	−0.0512673	−0.0256336	+	0.999671i	$0.508160\pi$
$264$	−1.25524e8	−0.419868
$265$	7.65521e7	0.252695
$266$	−1.71734e7	−0.0559461
$267$	2.33944e8	0.752181
$268$	8.38607e7	0.266126
$269$	2.20262e7	0.0689933	0.0344966	−	0.999405i	$-0.489017\pi$
$269$	2.20262e7	0.0689933	0.0344966	+	0.999405i	$0.489017\pi$
$270$	2.95726e8	0.914360
$271$	3.98102e8	1.21507	0.607536	−	0.794292i	$-0.292158\pi$
$271$	3.98102e8	1.21507	0.607536	+	0.794292i	$0.292158\pi$
$272$	−1.76229e7	−0.0530991
$273$	−5.06120e7	−0.150551
$274$	1.03441e8	0.303785
$275$	−2.01523e8	−0.584333
$276$	2.65957e8	0.761430
$277$	−6.59305e8	−1.86383	−0.931917	−	0.362671i	$-0.881865\pi$
$277$	−6.59305e8	−1.86383	−0.931917	+	0.362671i	$0.881865\pi$
$278$	−3.25469e8	−0.908557
$279$	−7.26690e7	−0.200325
$280$	−2.31380e7	−0.0629901
$281$	1.53543e8	0.412816	0.206408	−	0.978466i	$-0.433823\pi$
$281$	1.53543e8	0.412816	0.206408	+	0.978466i	$0.433823\pi$
$282$	−3.33322e8	−0.885098
$283$	2.92491e8	0.767113	0.383557	−	0.923517i	$-0.374699\pi$
$283$	2.92491e8	0.767113	0.383557	+	0.923517i	$0.374699\pi$
$284$	−1.74822e8	−0.452880
$285$	−2.08545e8	−0.533634
$286$	−4.64856e8	−1.17500
$287$	−7.85774e7	−0.196205
$288$	2.01423e7	0.0496860
$289$	−3.91827e8	−0.954888
$290$	2.50058e8	0.602072
$291$	2.57311e8	0.612115
$292$	−3.33941e8	−0.784929
$293$	2.60323e8	0.604610	0.302305	−	0.953211i	$-0.402244\pi$
$293$	2.60323e8	0.604610	0.302305	+	0.953211i	$0.402244\pi$
$294$	−2.55392e8	−0.586127
$295$	7.39256e8	1.67655
$296$	2.59343e7	0.0581238
$297$	−6.86874e8	−1.52135
$298$	−1.36988e8	−0.299864
$299$	9.84926e8	2.13086
$300$	−8.27153e7	−0.176873
$301$	−1.38373e8	−0.292462
$302$	−9.15203e7	−0.191202
$303$	4.98017e7	0.102848
$304$	−6.47412e7	−0.132167
$305$	−4.20322e8	−0.848267
$306$	−2.11576e7	−0.0422125
$307$	5.91427e8	1.16659	0.583293	−	0.812262i	$-0.301764\pi$
$307$	5.91427e8	1.16659	0.583293	+	0.812262i	$0.301764\pi$
$308$	5.37418e7	0.104806
$309$	−5.71584e8	−1.10211
$310$	3.14697e8	0.599965
$311$	7.28404e7	0.137313	0.0686564	−	0.997640i	$-0.478129\pi$
$311$	7.28404e7	0.137313	0.0686564	+	0.997640i	$0.478129\pi$
$312$	−1.90800e8	−0.355663
$313$	2.94761e8	0.543332	0.271666	−	0.962392i	$-0.412425\pi$
$313$	2.94761e8	0.543332	0.271666	+	0.962392i	$0.412425\pi$
$314$	4.11522e8	0.750135
$315$	−2.77788e7	−0.0500756
$316$	−1.55513e8	−0.277244
$317$	−1.03976e9	−1.83326	−0.916632	−	0.399733i	$-0.869103\pi$
$317$	−1.03976e9	−1.83326	−0.916632	+	0.399733i	$0.869103\pi$
$318$	−7.29801e7	−0.127265
$319$	−5.80802e8	−1.00175
$320$	−8.72270e7	−0.148808
$321$	−6.03164e8	−1.01781
$322$	−1.13867e8	−0.190065
$323$	6.80047e7	0.112287
$324$	−1.95890e8	−0.319967
$325$	−3.06322e8	−0.494978
$326$	9.07232e7	0.145030
$327$	−9.74557e7	−0.154131
$328$	−2.96226e8	−0.463516
$329$	1.42708e8	0.220934
$330$	6.52616e8	0.999675
$331$	−6.20361e8	−0.940257	−0.470129	−	0.882598i	$-0.655792\pi$
$331$	−6.20361e8	−0.940257	−0.470129	+	0.882598i	$0.655792\pi$
$332$	1.08256e8	0.162355
$333$	3.11360e7	0.0462071
$334$	4.60564e8	0.676358
$335$	−4.36003e8	−0.633626
$336$	2.20584e7	0.0317238
$337$	5.85781e8	0.833741	0.416870	−	0.908966i	$-0.363127\pi$
$337$	5.85781e8	0.833741	0.416870	+	0.908966i	$0.363127\pi$
$338$	−2.04608e8	−0.288214
$339$	7.41956e8	1.03438
$340$	9.16240e7	0.126425
$341$	−7.30936e8	−0.998249
$342$	−7.77265e7	−0.105070
$343$	2.21192e8	0.295965
$344$	−5.21648e8	−0.690913
$345$	−1.38275e9	−1.81291
$346$	5.99311e8	0.777832
$347$	1.17427e9	1.50874	0.754370	−	0.656449i	$-0.227942\pi$
$347$	1.17427e9	1.50874	0.754370	+	0.656449i	$0.227942\pi$
$348$	−2.38390e8	−0.303223
$349$	1.11586e9	1.40514	0.702571	−	0.711614i	$-0.252035\pi$
$349$	1.11586e9	1.40514	0.702571	+	0.711614i	$0.252035\pi$
$350$	3.54137e7	0.0441503
$351$	−1.04407e9	−1.28871
$352$	2.02599e8	0.247593
$353$	−1.20291e9	−1.45553	−0.727766	−	0.685826i	$-0.759441\pi$
$353$	−1.20291e9	−1.45553	−0.727766	+	0.685826i	$0.759441\pi$
$354$	−7.04762e8	−0.844366
$355$	9.08925e8	1.07827
$356$	−3.77592e8	−0.443556
$357$	−2.31703e7	−0.0269521
$358$	5.83307e8	0.671903
$359$	−3.19392e8	−0.364329	−0.182164	−	0.983268i	$-0.558310\pi$
$359$	−3.19392e8	−0.364329	−0.182164	+	0.983268i	$0.558310\pi$
$360$	−1.04722e8	−0.118299
$361$	−6.44043e8	−0.720510
$362$	7.84894e8	0.869623
$363$	−7.43098e8	−0.815404
$364$	8.16893e7	0.0887790
$365$	1.73621e9	1.86886
$366$	4.00710e8	0.427215
$367$	1.16632e9	1.23165	0.615824	−	0.787883i	$-0.288823\pi$
$367$	1.16632e9	1.23165	0.615824	+	0.787883i	$0.288823\pi$
$368$	−4.29263e8	−0.449010
$369$	−3.55641e8	−0.368484
$370$	−1.34836e8	−0.138389
$371$	3.12457e7	0.0317674
$372$	−3.00013e8	−0.302162
$373$	−5.33726e8	−0.532522	−0.266261	−	0.963901i	$-0.585788\pi$
$373$	−5.33726e8	−0.532522	−0.266261	+	0.963901i	$0.585788\pi$
$374$	−2.12812e8	−0.210352
$375$	−6.00741e8	−0.588272
$376$	5.37991e8	0.521936
$377$	−8.82838e8	−0.848567
$378$	1.20705e8	0.114948
$379$	−3.14085e8	−0.296354	−0.148177	−	0.988961i	$-0.547340\pi$
$379$	−3.14085e8	−0.296354	−0.148177	+	0.988961i	$0.547340\pi$
$380$	3.36598e8	0.314680
$381$	6.05847e8	0.561210
$382$	−1.39593e9	−1.28127
$383$	−2.41300e8	−0.219464	−0.109732	−	0.993961i	$-0.534999\pi$
$383$	−2.41300e8	−0.219464	−0.109732	+	0.993961i	$0.534999\pi$
$384$	8.31570e7	0.0749444
$385$	−2.79411e8	−0.249535
$386$	1.32355e8	0.117134
$387$	−6.26276e8	−0.549259
$388$	−4.15308e8	−0.360960
$389$	2.65354e7	0.0228561	0.0114280	−	0.999935i	$-0.496362\pi$
$389$	2.65354e7	0.0228561	0.0114280	+	0.999935i	$0.496362\pi$
$390$	9.91997e8	0.846807
$391$	4.50901e8	0.381472
$392$	4.12210e8	0.345635
$393$	−1.82733e8	−0.151860
$394$	7.89947e8	0.650671
$395$	8.08535e8	0.660099
$396$	2.43235e8	0.196831
$397$	−7.61463e8	−0.610776	−0.305388	−	0.952228i	$-0.598786\pi$
$397$	−7.61463e8	−0.610776	−0.305388	+	0.952228i	$0.598786\pi$
$398$	8.30012e8	0.659923
$399$	−8.51205e7	−0.0670855
$400$	1.33505e8	0.104301
$401$	5.43529e8	0.420937	0.210469	−	0.977601i	$-0.432501\pi$
$401$	5.43529e8	0.420937	0.210469	+	0.977601i	$0.432501\pi$
$402$	4.15659e8	0.319114
$403$	−1.11105e9	−0.845598
$404$	−8.03814e7	−0.0606486
$405$	1.01846e9	0.761819
$406$	1.02064e8	0.0756891
$407$	3.13179e8	0.230257
$408$	−8.73488e7	−0.0636717
$409$	1.86062e9	1.34470	0.672352	−	0.740232i	$-0.265284\pi$
$409$	1.86062e9	1.34470	0.672352	+	0.740232i	$0.265284\pi$
$410$	1.54012e9	1.10360
$411$	5.12711e8	0.364272
$412$	9.22554e8	0.649907
$413$	3.01737e8	0.210767
$414$	−5.15360e8	−0.356952
$415$	−5.62835e8	−0.386556
$416$	3.07957e8	0.209732
$417$	−1.61320e9	−1.08946
$418$	−7.81806e8	−0.523578
$419$	−6.51525e8	−0.432695	−0.216347	−	0.976316i	$-0.569414\pi$
$419$	−6.51525e8	−0.432695	−0.216347	+	0.976316i	$0.569414\pi$
$420$	−1.14684e8	−0.0755321
$421$	−4.61099e8	−0.301167	−0.150583	−	0.988597i	$-0.548115\pi$
$421$	−4.61099e8	−0.301167	−0.150583	+	0.988597i	$0.548115\pi$
$422$	−1.46888e9	−0.951467
$423$	6.45896e8	0.414927
$424$	1.17792e8	0.0750474
$425$	−1.40235e8	−0.0886123
$426$	−8.66514e8	−0.543053
$427$	−1.71560e8	−0.106639
$428$	9.73523e8	0.600196
$429$	−2.30408e9	−1.40895
$430$	2.71212e9	1.64501
$431$	2.00760e9	1.20783	0.603916	−	0.797048i	$-0.293606\pi$
$431$	2.00760e9	1.20783	0.603916	+	0.797048i	$0.293606\pi$
$432$	4.55040e8	0.271554
$433$	1.05358e8	0.0623679	0.0311840	−	0.999514i	$-0.490072\pi$
$433$	1.05358e8	0.0623679	0.0311840	+	0.999514i	$0.490072\pi$
$434$	1.28447e8	0.0754243
$435$	1.23942e9	0.721950
$436$	1.57296e8	0.0908899
$437$	1.65647e9	0.949508
$438$	−1.65519e9	−0.941216
$439$	1.80594e9	1.01877	0.509386	−	0.860538i	$-0.329873\pi$
$439$	1.80594e9	1.01877	0.509386	+	0.860538i	$0.329873\pi$
$440$	−1.05334e9	−0.589501
$441$	4.94888e8	0.274771
$442$	−3.23481e8	−0.178185
$443$	−1.16679e9	−0.637647	−0.318823	−	0.947814i	$-0.603288\pi$
$443$	−1.16679e9	−0.637647	−0.318823	+	0.947814i	$0.603288\pi$
$444$	1.28545e8	0.0696969
$445$	1.96315e9	1.05607
$446$	7.71420e8	0.411736
$447$	−6.78985e8	−0.359570
$448$	−3.56028e7	−0.0187073
$449$	3.32318e8	0.173257	0.0866287	−	0.996241i	$-0.472391\pi$
$449$	3.32318e8	0.173257	0.0866287	+	0.996241i	$0.472391\pi$
$450$	1.60282e8	0.0829166
$451$	−3.57718e9	−1.83621
$452$	−1.19754e9	−0.609965
$453$	−4.53624e8	−0.229273
$454$	2.32035e9	1.16375
$455$	−4.24714e8	−0.211376
$456$	−3.20892e8	−0.158483
$457$	−2.10552e9	−1.03194	−0.515969	−	0.856608i	$-0.672568\pi$
$457$	−2.10552e9	−1.03194	−0.515969	+	0.856608i	$0.672568\pi$
$458$	−2.27785e9	−1.10789
$459$	−4.77978e8	−0.230708
$460$	2.23179e9	1.06906
$461$	3.02900e9	1.43995	0.719973	−	0.694002i	$-0.244154\pi$
$461$	3.02900e9	1.43995	0.719973	+	0.694002i	$0.244154\pi$
$462$	2.66374e8	0.125674
$463$	−1.38922e9	−0.650487	−0.325244	−	0.945630i	$-0.605446\pi$
$463$	−1.38922e9	−0.650487	−0.325244	+	0.945630i	$0.605446\pi$
$464$	3.84769e8	0.178808
$465$	1.55981e9	0.719425
$466$	2.84216e9	1.30106
$467$	3.43946e9	1.56272	0.781361	−	0.624079i	$-0.214526\pi$
$467$	3.43946e9	1.56272	0.781361	+	0.624079i	$0.214526\pi$
$468$	3.69725e8	0.166732
$469$	−1.77960e8	−0.0796559
$470$	−2.79709e9	−1.24269
$471$	2.03973e9	0.899495
$472$	1.13751e9	0.497917
$473$	−6.29935e9	−2.73704
$474$	−7.70808e8	−0.332447
$475$	−5.15179e8	−0.220562
$476$	3.73975e7	0.0158935
$477$	1.41418e8	0.0596609
$478$	−7.88491e8	−0.330217
$479$	1.69344e8	0.0704038	0.0352019	−	0.999380i	$-0.488793\pi$
$479$	1.69344e8	0.0704038	0.0352019	+	0.999380i	$0.488793\pi$
$480$	−4.32344e8	−0.178437
$481$	4.76043e8	0.195046
$482$	−2.11093e9	−0.858637
$483$	−5.64386e8	−0.227909
$484$	1.19938e9	0.480838
$485$	2.15924e9	0.859419
$486$	9.72755e8	0.384394
$487$	2.18619e9	0.857700	0.428850	−	0.903376i	$-0.358919\pi$
$487$	2.18619e9	0.857700	0.428850	+	0.903376i	$0.358919\pi$
$488$	−6.46757e8	−0.251925
$489$	4.49673e8	0.173907
$490$	−2.14313e9	−0.822931
$491$	1.74859e9	0.666658	0.333329	−	0.942811i	$-0.391828\pi$
$491$	1.74859e9	0.666658	0.333329	+	0.942811i	$0.391828\pi$
$492$	−1.46826e9	−0.555807
$493$	−4.04165e8	−0.151913
$494$	−1.18837e9	−0.443514
$495$	−1.26461e9	−0.468639
$496$	4.84229e8	0.178183
$497$	3.70989e8	0.135555
$498$	5.36573e8	0.194682
$499$	−3.48601e9	−1.25596	−0.627981	−	0.778229i	$-0.716119\pi$
$499$	−3.48601e9	−1.25596	−0.627981	+	0.778229i	$0.716119\pi$
$500$	9.69613e8	0.346899
$501$	2.28280e9	0.811029
$502$	−2.19393e9	−0.774033
$503$	3.19726e9	1.12019	0.560093	−	0.828430i	$-0.310765\pi$
$503$	3.19726e9	1.12019	0.560093	+	0.828430i	$0.310765\pi$
$504$	−4.27437e7	−0.0148719
$505$	4.17913e8	0.144400
$506$	−5.18371e9	−1.77875
$507$	−1.01415e9	−0.345600
$508$	−9.77854e8	−0.330941
$509$	−4.50646e9	−1.51469	−0.757345	−	0.653015i	$-0.773504\pi$
$509$	−4.50646e9	−1.51469	−0.757345	+	0.653015i	$0.773504\pi$
$510$	4.54138e8	0.151598
$511$	7.08655e8	0.234942
$512$	−1.34218e8	−0.0441942
$513$	−1.75594e9	−0.574248
$514$	8.30689e7	0.0269816
$515$	−4.79648e9	−1.54738
$516$	−2.58557e9	−0.828481
$517$	6.49670e9	2.06764
$518$	−5.50351e7	−0.0173974
$519$	2.97051e9	0.932707
$520$	−1.60111e9	−0.499356
$521$	−1.28857e9	−0.399185	−0.199593	−	0.979879i	$-0.563962\pi$
$521$	−1.28857e9	−0.399185	−0.199593	+	0.979879i	$0.563962\pi$
$522$	4.61943e8	0.142148
$523$	5.00338e8	0.152935	0.0764676	−	0.997072i	$-0.475636\pi$
$523$	5.00338e8	0.152935	0.0764676	+	0.997072i	$0.475636\pi$
$524$	2.94936e8	0.0895507
$525$	1.75530e8	0.0529411
$526$	1.20997e8	0.0362514
$527$	−5.08639e8	−0.151381
$528$	1.00419e9	0.296892
$529$	7.57830e9	2.22575
$530$	−6.12417e8	−0.178682
$531$	1.36566e9	0.395832
$532$	1.37387e8	0.0395598
$533$	−5.43743e9	−1.55542
$534$	−1.87155e9	−0.531872
$535$	−5.06148e9	−1.42902
$536$	−6.70886e8	−0.188179
$537$	2.89119e9	0.805687
$538$	−1.76210e8	−0.0487856
$539$	4.97779e9	1.36923
$540$	−2.36581e9	−0.646550
$541$	−9.71999e7	−0.0263922	−0.0131961	−	0.999913i	$-0.504201\pi$
$541$	−9.71999e7	−0.0263922	−0.0131961	+	0.999913i	$0.504201\pi$
$542$	−3.18482e9	−0.859186
$543$	3.89036e9	1.04277
$544$	1.40983e8	0.0375467
$545$	−8.17804e8	−0.216402
$546$	4.04896e8	0.106456
$547$	−5.01201e9	−1.30935	−0.654676	−	0.755910i	$-0.727195\pi$
$547$	−5.01201e9	−1.30935	−0.654676	+	0.755910i	$0.727195\pi$
$548$	−8.27530e8	−0.214809
$549$	−7.76478e8	−0.200275
$550$	1.61219e9	0.413186
$551$	−1.48478e9	−0.378121
$552$	−2.12766e9	−0.538412
$553$	3.30014e8	0.0829840
$554$	5.27444e9	1.31793
$555$	−6.68321e8	−0.165943
$556$	2.60375e9	0.642447
$557$	4.42995e9	1.08619	0.543095	−	0.839671i	$-0.317252\pi$
$557$	4.42995e9	1.08619	0.543095	+	0.839671i	$0.317252\pi$
$558$	5.81352e8	0.141651
$559$	−9.57521e9	−2.31850
$560$	1.85104e8	0.0445407
$561$	−1.05481e9	−0.252235
$562$	−1.22834e9	−0.291905
$563$	−3.38013e9	−0.798277	−0.399139	−	0.916891i	$-0.630691\pi$
$563$	−3.38013e9	−0.798277	−0.399139	+	0.916891i	$0.630691\pi$
$564$	2.66657e9	0.625859
$565$	6.22616e9	1.45228
$566$	−2.33992e9	−0.542431
$567$	4.15698e8	0.0957717
$568$	1.39858e9	0.320234
$569$	4.53131e9	1.03117	0.515585	−	0.856838i	$-0.327575\pi$
$569$	4.53131e9	1.03117	0.515585	+	0.856838i	$0.327575\pi$
$570$	1.66836e9	0.377336
$571$	−5.25584e9	−1.18145	−0.590726	−	0.806872i	$-0.701159\pi$
$571$	−5.25584e9	−1.18145	−0.590726	+	0.806872i	$0.701159\pi$
$572$	3.71885e9	0.830850
$573$	−6.91897e9	−1.53639
$574$	6.28619e8	0.138738
$575$	−3.41586e9	−0.749312
$576$	−1.61138e8	−0.0351333
$577$	3.46461e9	0.750825	0.375412	−	0.926858i	$-0.377501\pi$
$577$	3.46461e9	0.750825	0.375412	+	0.926858i	$0.377501\pi$
$578$	3.13462e9	0.675208
$579$	6.56023e8	0.140457
$580$	−2.00047e9	−0.425729
$581$	−2.29728e8	−0.0485957
$582$	−2.05849e9	−0.432831
$583$	1.42244e9	0.297299
$584$	2.67153e9	0.555028
$585$	−1.92225e9	−0.396976
$586$	−2.08258e9	−0.427524
$587$	3.03352e9	0.619032	0.309516	−	0.950894i	$-0.399833\pi$
$587$	3.03352e9	0.619032	0.309516	+	0.950894i	$0.399833\pi$
$588$	2.04314e9	0.414454
$589$	−1.86858e9	−0.376798
$590$	−5.91404e9	−1.18550
$591$	3.91541e9	0.780226
$592$	−2.07475e8	−0.0410997
$593$	−2.64373e9	−0.520626	−0.260313	−	0.965524i	$-0.583826\pi$
$593$	−2.64373e9	−0.520626	−0.260313	+	0.965524i	$0.583826\pi$
$594$	5.49499e9	1.07576
$595$	−1.94435e8	−0.0378411
$596$	1.09590e9	0.212036
$597$	4.11399e9	0.791321
$598$	−7.87941e9	−1.50674
$599$	−6.93679e9	−1.31876	−0.659378	−	0.751811i	$-0.729180\pi$
$599$	−6.93679e9	−1.31876	−0.659378	+	0.751811i	$0.729180\pi$
$600$	6.61722e8	0.125068
$601$	2.91911e9	0.548517	0.274259	−	0.961656i	$-0.411568\pi$
$601$	2.91911e9	0.548517	0.274259	+	0.961656i	$0.411568\pi$
$602$	1.10699e9	0.206802
$603$	−8.05447e8	−0.149598
$604$	7.32163e8	0.135201
$605$	−6.23575e9	−1.14484
$606$	−3.98413e8	−0.0727244
$607$	3.49174e8	0.0633696	0.0316848	−	0.999498i	$-0.489913\pi$
$607$	3.49174e8	0.0633696	0.0316848	+	0.999498i	$0.489913\pi$
$608$	5.17930e8	0.0934562
$609$	5.05887e8	0.0907596
$610$	3.36258e9	0.599816
$611$	9.87519e9	1.75146
$612$	1.69261e8	0.0298488
$613$	−6.10495e9	−1.07046	−0.535230	−	0.844706i	$-0.679775\pi$
$613$	−6.10495e9	−1.07046	−0.535230	+	0.844706i	$0.679775\pi$
$614$	−4.73142e9	−0.824901
$615$	7.63366e9	1.32334
$616$	−4.29935e8	−0.0741088
$617$	8.55646e9	1.46655	0.733273	−	0.679934i	$-0.237992\pi$
$617$	8.55646e9	1.46655	0.733273	+	0.679934i	$0.237992\pi$
$618$	4.57268e9	0.779311
$619$	2.81893e9	0.477713	0.238857	−	0.971055i	$-0.423227\pi$
$619$	2.81893e9	0.477713	0.238857	+	0.971055i	$0.423227\pi$
$620$	−2.51757e9	−0.424240
$621$	−1.16427e10	−1.95088
$622$	−5.82723e8	−0.0970948
$623$	8.01286e8	0.132764
$624$	1.52640e9	0.251491
$625$	−7.58755e9	−1.24314
$626$	−2.35809e9	−0.384194
$627$	−3.87505e9	−0.627829
$628$	−3.29218e9	−0.530425
$629$	2.17933e8	0.0349177
$630$	2.22230e8	0.0354088
$631$	−1.12195e10	−1.77776	−0.888879	−	0.458142i	$-0.848515\pi$
$631$	−1.12195e10	−1.77776	−0.888879	+	0.458142i	$0.848515\pi$
$632$	1.24411e9	0.196041
$633$	−7.28058e9	−1.14091
$634$	8.31806e9	1.29631
$635$	5.08399e9	0.787947
$636$	5.83841e8	0.0899901
$637$	7.56640e9	1.15985
$638$	4.64642e9	0.708346
$639$	1.67909e9	0.254579
$640$	6.97816e8	0.105223
$641$	5.81709e9	0.872374	0.436187	−	0.899856i	$-0.356329\pi$
$641$	5.81709e9	0.872374	0.436187	+	0.899856i	$0.356329\pi$
$642$	4.82531e9	0.719702
$643$	7.46250e9	1.10700	0.553498	−	0.832850i	$-0.313293\pi$
$643$	7.46250e9	1.10700	0.553498	+	0.832850i	$0.313293\pi$
$644$	9.10935e8	0.134396
$645$	1.34427e10	1.97255
$646$	−5.44038e8	−0.0793990
$647$	9.73439e9	1.41300	0.706502	−	0.707711i	$-0.250272\pi$
$647$	9.73439e9	1.41300	0.706502	+	0.707711i	$0.250272\pi$
$648$	1.56712e9	0.226251
$649$	1.37364e10	1.97249
$650$	2.45057e9	0.350002
$651$	6.36655e8	0.0904421
$652$	−7.25786e8	−0.102551
$653$	1.29780e10	1.82395	0.911974	−	0.410247i	$-0.134558\pi$
$653$	1.29780e10	1.82395	0.911974	+	0.410247i	$0.134558\pi$
$654$	7.79645e8	0.108987
$655$	−1.53341e9	−0.213214
$656$	2.36981e9	0.327755
$657$	3.20736e9	0.441234
$658$	−1.14167e9	−0.156224
$659$	−4.90320e9	−0.667391	−0.333696	−	0.942681i	$-0.608296\pi$
$659$	−4.90320e9	−0.667391	−0.333696	+	0.942681i	$0.608296\pi$
$660$	−5.22093e9	−0.706877
$661$	−6.10485e9	−0.822185	−0.411093	−	0.911594i	$-0.634853\pi$
$661$	−6.10485e9	−0.822185	−0.411093	+	0.911594i	$0.634853\pi$
$662$	4.96289e9	0.664862
$663$	−1.60335e9	−0.213663
$664$	−8.66044e8	−0.114803
$665$	−7.14293e8	−0.0941891
$666$	−2.49088e8	−0.0326733
$667$	−9.84472e9	−1.28458
$668$	−3.68451e9	−0.478258
$669$	3.82357e9	0.493717
$670$	3.48803e9	0.448041
$671$	−7.81015e9	−0.997999
$672$	−1.76467e8	−0.0224321
$673$	−9.24214e9	−1.16875	−0.584373	−	0.811485i	$-0.698659\pi$
$673$	−9.24214e9	−1.16875	−0.584373	+	0.811485i	$0.698659\pi$
$674$	−4.68625e9	−0.589544
$675$	3.62098e9	0.453172
$676$	1.63687e9	0.203798
$677$	8.75032e9	1.08384	0.541918	−	0.840432i	$-0.317698\pi$
$677$	8.75032e9	1.08384	0.541918	+	0.840432i	$0.317698\pi$
$678$	−5.93564e9	−0.731415
$679$	8.81322e8	0.108041
$680$	−7.32992e8	−0.0893960
$681$	1.15009e10	1.39546
$682$	5.84748e9	0.705868
$683$	1.70705e9	0.205009	0.102505	−	0.994733i	$-0.467314\pi$
$683$	1.70705e9	0.205009	0.102505	+	0.994733i	$0.467314\pi$
$684$	6.21812e8	0.0742955
$685$	4.30244e9	0.511444
$686$	−1.76954e9	−0.209279
$687$	−1.12903e10	−1.32848
$688$	4.17319e9	0.488549
$689$	2.16215e9	0.251837
$690$	1.10620e10	1.28192
$691$	2.24664e9	0.259036	0.129518	−	0.991577i	$-0.458657\pi$
$691$	2.24664e9	0.259036	0.129518	+	0.991577i	$0.458657\pi$
$692$	−4.79449e9	−0.550011
$693$	−5.16167e8	−0.0589148
$694$	−9.39415e9	−1.06684
$695$	−1.35372e10	−1.52962
$696$	1.90712e9	0.214411
$697$	−2.48927e9	−0.278456
$698$	−8.92687e9	−0.993585
$699$	1.40873e10	1.56012
$700$	−2.83310e8	−0.0312190
$701$	−9.30412e8	−0.102015	−0.0510073	−	0.998698i	$-0.516243\pi$
$701$	−9.30412e8	−0.102015	−0.0510073	+	0.998698i	$0.516243\pi$
$702$	8.35257e9	0.911255
$703$	8.00619e8	0.0869125
$704$	−1.62079e9	−0.175075
$705$	−1.38639e10	−1.49012
$706$	9.62328e9	1.02922
$707$	1.70577e8	0.0181531
$708$	5.63809e9	0.597057
$709$	−9.04625e9	−0.953250	−0.476625	−	0.879107i	$-0.658140\pi$
$709$	−9.04625e9	−0.953250	−0.476625	+	0.879107i	$0.658140\pi$
$710$	−7.27140e9	−0.762454
$711$	1.49364e9	0.155848
$712$	3.02074e9	0.313641
$713$	−1.23895e10	−1.28009
$714$	1.85362e8	0.0190580
$715$	−1.93348e10	−1.97819
$716$	−4.66646e9	−0.475107
$717$	−3.90819e9	−0.395966
$718$	2.55514e9	0.257619
$719$	−8.12286e9	−0.815001	−0.407500	−	0.913205i	$-0.633599\pi$
$719$	−8.12286e9	−0.815001	−0.407500	+	0.913205i	$0.633599\pi$
$720$	8.37778e8	0.0836499
$721$	−1.95775e9	−0.194528
$722$	5.15235e9	0.509477
$723$	−1.04629e10	−1.02960
$724$	−6.27915e9	−0.614916
$725$	3.06180e9	0.298397
$726$	5.94478e9	0.576578
$727$	−1.76633e10	−1.70491	−0.852456	−	0.522799i	$-0.824888\pi$
$727$	−1.76633e10	−1.70491	−0.852456	+	0.522799i	$0.824888\pi$
$728$	−6.53514e8	−0.0627762
$729$	1.15154e10	1.10087
$730$	−1.38896e10	−1.32148
$731$	−4.38355e9	−0.415064
$732$	−3.20568e9	−0.302086
$733$	−1.65936e10	−1.55624	−0.778122	−	0.628113i	$-0.783828\pi$
$733$	−1.65936e10	−1.55624	−0.778122	+	0.628113i	$0.783828\pi$
$734$	−9.33057e9	−0.870907
$735$	−1.06225e10	−0.986785
$736$	3.43410e9	0.317498
$737$	−8.10152e9	−0.745470
$738$	2.84513e9	0.260558
$739$	4.26353e9	0.388610	0.194305	−	0.980941i	$-0.437755\pi$
$739$	4.26353e9	0.388610	0.194305	+	0.980941i	$0.437755\pi$
$740$	1.07869e9	0.0978555
$741$	−5.89020e9	−0.531822
$742$	−2.49966e8	−0.0224629
$743$	3.50446e7	0.00313445	0.00156722	−	0.999999i	$-0.499501\pi$
$743$	3.50446e7	0.00313445	0.00156722	+	0.999999i	$0.499501\pi$
$744$	2.40010e9	0.213661
$745$	−5.69774e9	−0.504842
$746$	4.26981e9	0.376550
$747$	−1.03975e9	−0.0912654
$748$	1.70250e9	0.148741
$749$	−2.06591e9	−0.179649
$750$	4.80593e9	0.415971
$751$	4.69640e9	0.404600	0.202300	−	0.979324i	$-0.435158\pi$
$751$	4.69640e9	0.404600	0.202300	+	0.979324i	$0.435158\pi$
$752$	−4.30393e9	−0.369064
$753$	−1.08743e10	−0.928151
$754$	7.06270e9	0.600027
$755$	−3.80661e9	−0.321902
$756$	−9.65636e8	−0.0812807
$757$	6.98128e9	0.584924	0.292462	−	0.956277i	$-0.405526\pi$
$757$	6.98128e9	0.584924	0.292462	+	0.956277i	$0.405526\pi$
$758$	2.51268e9	0.209554
$759$	−2.56933e10	−2.13291
$760$	−2.69279e9	−0.222512
$761$	1.35602e10	1.11537	0.557687	−	0.830051i	$-0.311689\pi$
$761$	1.35602e10	1.11537	0.557687	+	0.830051i	$0.311689\pi$
$762$	−4.84677e9	−0.396835
$763$	−3.33797e8	−0.0272049
$764$	1.11674e10	0.905995
$765$	−8.80009e8	−0.0710677
$766$	1.93040e9	0.155184
$767$	2.08797e10	1.67086
$768$	−6.65256e8	−0.0529937
$769$	7.68820e9	0.609653	0.304826	−	0.952408i	$-0.401402\pi$
$769$	7.68820e9	0.609653	0.304826	+	0.952408i	$0.401402\pi$
$770$	2.23529e9	0.176448
$771$	4.11734e8	0.0323539
$772$	−1.05884e9	−0.0828266
$773$	1.21761e10	0.948156	0.474078	−	0.880483i	$-0.342782\pi$
$773$	1.21761e10	0.948156	0.474078	+	0.880483i	$0.342782\pi$
$774$	5.01021e9	0.388385
$775$	3.85326e9	0.297353
$776$	3.32246e9	0.255237
$777$	−2.72784e8	−0.0208615
$778$	−2.12283e8	−0.0161617
$779$	−9.14480e9	−0.693095
$780$	−7.93598e9	−0.598783
$781$	1.68890e10	1.26861
$782$	−3.60721e9	−0.269741
$783$	1.04359e10	0.776896
$784$	−3.29768e9	−0.244401
$785$	1.71165e10	1.26290
$786$	1.46186e9	0.107381
$787$	2.47203e10	1.80777	0.903884	−	0.427778i	$-0.140703\pi$
$787$	2.47203e10	1.80777	0.903884	+	0.427778i	$0.140703\pi$
$788$	−6.31958e9	−0.460094
$789$	5.99728e8	0.0434695
$790$	−6.46828e9	−0.466760
$791$	2.54129e9	0.182573
$792$	−1.94588e9	−0.139180
$793$	−1.18717e10	−0.845387
$794$	6.09170e9	0.431884
$795$	−3.03547e9	−0.214260
$796$	−6.64009e9	−0.466636
$797$	−4.06997e9	−0.284765	−0.142383	−	0.989812i	$-0.545476\pi$
$797$	−4.06997e9	−0.284765	−0.142383	+	0.989812i	$0.545476\pi$
$798$	6.80964e8	0.0474366
$799$	4.52088e9	0.313552
$800$	−1.06804e9	−0.0737517
$801$	3.62661e9	0.249337
$802$	−4.34823e9	−0.297648
$803$	3.22610e10	2.19874
$804$	−3.32527e9	−0.225648
$805$	−4.73607e9	−0.319987
$806$	8.88836e9	0.597928
$807$	−8.73391e8	−0.0584994
$808$	6.43051e8	0.0428850
$809$	1.98136e10	1.31566	0.657831	−	0.753166i	$-0.271474\pi$
$809$	1.98136e10	1.31566	0.657831	+	0.753166i	$0.271474\pi$
$810$	−8.14769e9	−0.538687
$811$	−1.60671e10	−1.05771	−0.528854	−	0.848713i	$-0.677378\pi$
$811$	−1.60671e10	−1.05771	−0.528854	+	0.848713i	$0.677378\pi$
$812$	−8.16516e8	−0.0535203
$813$	−1.57857e10	−1.03026
$814$	−2.50544e9	−0.162816
$815$	3.77346e9	0.244167
$816$	6.98790e8	0.0450227
$817$	−1.61038e10	−1.03312
$818$	−1.48850e10	−0.950849
$819$	−7.84591e8	−0.0499056
$820$	−1.23210e10	−0.780361
$821$	−4.94372e9	−0.311783	−0.155892	−	0.987774i	$-0.549825\pi$
$821$	−4.94372e9	−0.311783	−0.155892	+	0.987774i	$0.549825\pi$
$822$	−4.10169e9	−0.257580
$823$	−2.16097e10	−1.35129	−0.675647	−	0.737225i	$-0.736136\pi$
$823$	−2.16097e10	−1.35129	−0.675647	+	0.737225i	$0.736136\pi$
$824$	−7.38043e9	−0.459554
$825$	7.99087e9	0.495456
$826$	−2.41389e9	−0.149035
$827$	3.17672e10	1.95303	0.976517	−	0.215439i	$-0.0691182\pi$
$827$	3.17672e10	1.95303	0.976517	+	0.215439i	$0.0691182\pi$
$828$	4.12288e9	0.252403
$829$	−1.56227e10	−0.952391	−0.476196	−	0.879339i	$-0.657985\pi$
$829$	−1.56227e10	−0.952391	−0.476196	+	0.879339i	$0.657985\pi$
$830$	4.50268e9	0.273337
$831$	2.61430e10	1.58034
$832$	−2.46366e9	−0.148303
$833$	3.46391e9	0.207639
$834$	1.29056e10	0.770365
$835$	1.91563e10	1.13870
$836$	6.25444e9	0.370226
$837$	1.31335e10	0.774179
$838$	5.21220e9	0.305962
$839$	−1.62058e10	−0.947334	−0.473667	−	0.880704i	$-0.657070\pi$
$839$	−1.62058e10	−0.947334	−0.473667	+	0.880704i	$0.657070\pi$
$840$	9.17475e8	0.0534093
$841$	−8.42558e9	−0.488443
$842$	3.68879e9	0.212957
$843$	−6.08832e9	−0.350026
$844$	1.17511e10	0.672789
$845$	−8.51028e9	−0.485228
$846$	−5.16717e9	−0.293398
$847$	−2.54520e9	−0.143923
$848$	−9.42336e8	−0.0530665
$849$	−1.15979e10	−0.650435
$850$	1.12188e9	0.0626584
$851$	5.30846e9	0.295267
$852$	6.93212e9	0.383996
$853$	1.28784e10	0.710459	0.355229	−	0.934779i	$-0.384403\pi$
$853$	1.28784e10	0.710459	0.355229	+	0.934779i	$0.384403\pi$
$854$	1.37248e9	0.0754055
$855$	−3.23288e9	−0.176892
$856$	−7.78819e9	−0.424403
$857$	2.80045e10	1.51983	0.759914	−	0.650023i	$-0.225241\pi$
$857$	2.80045e10	1.51983	0.759914	+	0.650023i	$0.225241\pi$
$858$	1.84326e10	0.996281
$859$	3.67599e10	1.97878	0.989390	−	0.145281i	$-0.0464085\pi$
$859$	3.67599e10	1.97878	0.989390	+	0.145281i	$0.0464085\pi$
$860$	−2.16970e10	−1.16320
$861$	3.11578e9	0.166362
$862$	−1.60608e10	−0.854067
$863$	−2.41181e10	−1.27734	−0.638668	−	0.769483i	$-0.720514\pi$
$863$	−2.41181e10	−1.27734	−0.638668	+	0.769483i	$0.720514\pi$
$864$	−3.64032e9	−0.192018
$865$	2.49272e10	1.30953
$866$	−8.42867e8	−0.0441008
$867$	1.55369e10	0.809649
$868$	−1.02758e9	−0.0533330
$869$	1.50237e10	0.776616
$870$	−9.91539e9	−0.510496
$871$	−1.23146e10	−0.631474
$872$	−1.25837e9	−0.0642689
$873$	3.98885e9	0.202908
$874$	−1.32518e10	−0.671404
$875$	−2.05761e9	−0.103833
$876$	1.32416e10	0.665540
$877$	−1.05101e10	−0.526150	−0.263075	−	0.964775i	$-0.584737\pi$
$877$	−1.05101e10	−0.526150	−0.263075	+	0.964775i	$0.584737\pi$
$878$	−1.44475e10	−0.720380
$879$	−1.03224e10	−0.512648
$880$	8.42673e9	0.416840
$881$	2.45876e10	1.21143	0.605717	−	0.795680i	$-0.292886\pi$
$881$	2.45876e10	1.21143	0.605717	+	0.795680i	$0.292886\pi$
$882$	−3.95910e9	−0.194293
$883$	−2.90742e10	−1.42117	−0.710583	−	0.703613i	$-0.751569\pi$
$883$	−2.90742e10	−1.42117	−0.710583	+	0.703613i	$0.751569\pi$
$884$	2.58785e9	0.125996
$885$	−2.93132e10	−1.42155
$886$	9.33433e9	0.450884
$887$	2.62983e10	1.26530	0.632652	−	0.774436i	$-0.281966\pi$
$887$	2.62983e10	1.26530	0.632652	+	0.774436i	$0.281966\pi$
$888$	−1.02836e9	−0.0492832
$889$	2.07510e9	0.0990563
$890$	−1.57052e10	−0.746757
$891$	1.89244e10	0.896292
$892$	−6.17136e9	−0.291141
$893$	1.66083e10	0.780451
$894$	5.43188e9	0.254255
$895$	2.42615e10	1.13120
$896$	2.84823e8	0.0132281
$897$	−3.90546e10	−1.80675
$898$	−2.65854e9	−0.122511
$899$	1.11053e10	0.509768
$900$	−1.28226e9	−0.0586309
$901$	9.89838e8	0.0450845
$902$	2.86175e10	1.29840
$903$	5.48682e9	0.247978
$904$	9.58030e9	0.431310
$905$	3.26461e10	1.46407
$906$	3.62899e9	0.162120
$907$	4.46329e9	0.198623	0.0993115	−	0.995056i	$-0.468336\pi$
$907$	4.46329e9	0.198623	0.0993115	+	0.995056i	$0.468336\pi$
$908$	−1.85628e10	−0.822892
$909$	7.72029e8	0.0340926
$910$	3.39771e9	0.149466
$911$	−2.83469e10	−1.24220	−0.621100	−	0.783731i	$-0.713314\pi$
$911$	−2.83469e10	−1.24220	−0.621100	+	0.783731i	$0.713314\pi$
$912$	2.56714e9	0.112064
$913$	−1.04582e10	−0.454789
$914$	1.68442e10	0.729690
$915$	1.66667e10	0.719245
$916$	1.82228e10	0.783396
$917$	−6.25883e8	−0.0268040
$918$	3.82382e9	0.163135
$919$	−1.72914e10	−0.734896	−0.367448	−	0.930044i	$-0.619768\pi$
$919$	−1.72914e10	−0.734896	−0.367448	+	0.930044i	$0.619768\pi$
$920$	−1.78543e10	−0.755939
$921$	−2.34515e10	−0.989148
$922$	−2.42320e10	−1.01820
$923$	2.56719e10	1.07461
$924$	−2.13099e9	−0.0888647
$925$	−1.65098e9	−0.0685877
$926$	1.11138e10	0.459964
$927$	−8.86074e9	−0.365335
$928$	−3.07815e9	−0.126436
$929$	−7.21679e9	−0.295317	−0.147659	−	0.989038i	$-0.547174\pi$
$929$	−7.21679e9	−0.295317	−0.147659	+	0.989038i	$0.547174\pi$
$930$	−1.24785e10	−0.508710
$931$	1.27253e10	0.516827
$932$	−2.27373e10	−0.919991
$933$	−2.88829e9	−0.116427
$934$	−2.75157e10	−1.10501
$935$	−8.85151e9	−0.354141
$936$	−2.95780e9	−0.117897
$937$	−1.50607e10	−0.598078	−0.299039	−	0.954241i	$-0.596666\pi$
$937$	−1.50607e10	−0.598078	−0.299039	+	0.954241i	$0.596666\pi$
$938$	1.42368e9	0.0563252
$939$	−1.16880e10	−0.460691
$940$	2.23767e10	0.878715
$941$	−1.89579e10	−0.741695	−0.370848	−	0.928694i	$-0.620933\pi$
$941$	−1.89579e10	−0.741695	−0.370848	+	0.928694i	$0.620933\pi$
$942$	−1.63178e10	−0.636039
$943$	−6.06340e10	−2.35464
$944$	−9.10005e9	−0.352080
$945$	5.02047e9	0.193523
$946$	5.03948e10	1.93538
$947$	−4.51533e10	−1.72769	−0.863843	−	0.503760i	$-0.831949\pi$
$947$	−4.51533e10	−1.72769	−0.863843	+	0.503760i	$0.831949\pi$
$948$	6.16647e9	0.235075
$949$	4.90378e10	1.86251
$950$	4.12143e9	0.155961
$951$	4.12288e10	1.55442
$952$	−2.99180e8	−0.0112384
$953$	3.57354e10	1.33744	0.668718	−	0.743516i	$-0.266843\pi$
$953$	3.57354e10	1.33744	0.668718	+	0.743516i	$0.266843\pi$
$954$	−1.13134e9	−0.0421866
$955$	−5.80609e10	−2.15711
$956$	6.30793e9	0.233498
$957$	2.30302e10	0.849386
$958$	−1.35475e9	−0.0497830
$959$	1.75610e9	0.0642959
$960$	3.45875e9	0.126174
$961$	−1.35366e10	−0.492016
$962$	−3.80834e9	−0.137919
$963$	−9.35028e9	−0.337390
$964$	1.68875e10	0.607148
$965$	5.50505e9	0.197204
$966$	4.51509e9	0.161156
$967$	−3.28651e10	−1.16881	−0.584403	−	0.811464i	$-0.698671\pi$
$967$	−3.28651e10	−1.16881	−0.584403	+	0.811464i	$0.698671\pi$
$968$	−9.59505e9	−0.340004
$969$	−2.69655e9	−0.0952082
$970$	−1.72739e10	−0.607701
$971$	1.23913e10	0.434361	0.217181	−	0.976131i	$-0.430314\pi$
$971$	1.23913e10	0.434361	0.217181	+	0.976131i	$0.430314\pi$
$972$	−7.78204e9	−0.271808
$973$	−5.52540e9	−0.192295
$974$	−1.74895e10	−0.606486
$975$	1.21464e10	0.419692
$976$	5.17406e9	0.178138
$977$	2.14546e10	0.736021	0.368010	−	0.929822i	$-0.380039\pi$
$977$	2.14546e10	0.736021	0.368010	+	0.929822i	$0.380039\pi$
$978$	−3.59739e9	−0.122971
$979$	3.64780e10	1.24249
$980$	1.71451e10	0.581900
$981$	−1.51076e9	−0.0510922
$982$	−1.39887e10	−0.471398
$983$	−8.92113e9	−0.299559	−0.149780	−	0.988719i	$-0.547856\pi$
$983$	−8.92113e9	−0.299559	−0.149780	+	0.988719i	$0.547856\pi$
$984$	1.17461e10	0.393015
$985$	3.28563e10	1.09545
$986$	3.23332e9	0.107419
$987$	−5.65872e9	−0.187330
$988$	9.50696e9	0.313612
$989$	−1.06775e11	−3.50981
$990$	1.01169e10	0.331378
$991$	2.80580e10	0.915798	0.457899	−	0.889004i	$-0.348602\pi$
$991$	2.80580e10	0.915798	0.457899	+	0.889004i	$0.348602\pi$
$992$	−3.87383e9	−0.125994
$993$	2.45988e10	0.797243
$994$	−2.96792e9	−0.0958516
$995$	3.45227e10	1.11103
$996$	−4.29258e9	−0.137661
$997$	1.99813e10	0.638544	0.319272	−	0.947663i	$-0.396562\pi$
$997$	1.99813e10	0.638544	0.319272	+	0.947663i	$0.396562\pi$
$998$	2.78881e10	0.888099
$999$	−5.62723e9	−0.178573

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.8.a.c.1.3	✓	6
4.3	odd	2		592.8.a.c.1.4		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.8.a.c.1.3	✓	6	1.1	even	1	trivial
592.8.a.c.1.4		6	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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 8 \)
Character orbit:	\([\chi]\)	\(=\)	74.a (trivial)

\(f(q)\)	\(=\)	\(q-8.00000 q^{2} -39.6523 q^{3} +64.0000 q^{4} -332.745 q^{5} +317.219 q^{6} -135.814 q^{7} -512.000 q^{8} -614.693 q^{9} +O(q^{10})\)	\(q-8.00000 q^{2} -39.6523 q^{3} +64.0000 q^{4} -332.745 q^{5} +317.219 q^{6} -135.814 q^{7} -512.000 q^{8} -614.693 q^{9} +2661.96 q^{10} -6182.84 q^{11} -2537.75 q^{12} -9398.11 q^{13} +1086.51 q^{14} +13194.1 q^{15} +4096.00 q^{16} -4302.47 q^{17} +4917.54 q^{18} -15806.0 q^{19} -21295.7 q^{20} +5385.34 q^{21} +49462.7 q^{22} -104800. q^{23} +20302.0 q^{24} +32594.0 q^{25} +75184.9 q^{26} +111094. q^{27} -8692.09 q^{28} +93937.7 q^{29} -105553. q^{30} +118220. q^{31} -32768.0 q^{32} +245164. q^{33} +34419.8 q^{34} +45191.4 q^{35} -39340.3 q^{36} -50653.0 q^{37} +126448. q^{38} +372657. q^{39} +170365. q^{40} +578567. q^{41} -43082.7 q^{42} +1.01884e6 q^{43} -395702. q^{44} +204536. q^{45} +838403. q^{46} -1.05076e6 q^{47} -162416. q^{48} -805098. q^{49} -260752. q^{50} +170603. q^{51} -601479. q^{52} -230063. q^{53} -888749. q^{54} +2.05731e6 q^{55} +69536.7 q^{56} +626743. q^{57} -751502. q^{58} -2.22169e6 q^{59} +844422. q^{60} +1.26320e6 q^{61} -945760. q^{62} +83483.9 q^{63} +262144. q^{64} +3.12717e6 q^{65} -1.96131e6 q^{66} +1.31032e6 q^{67} -275358. q^{68} +4.15558e6 q^{69} -361531. q^{70} -2.73160e6 q^{71} +314723. q^{72} -5.21783e6 q^{73} +405224. q^{74} -1.29243e6 q^{75} -1.01158e6 q^{76} +839716. q^{77} -2.98126e6 q^{78} -2.42990e6 q^{79} -1.36292e6 q^{80} -3.06079e6 q^{81} -4.62853e6 q^{82} +1.69149e6 q^{83} +344662. q^{84} +1.43162e6 q^{85} -8.15075e6 q^{86} -3.72485e6 q^{87} +3.16561e6 q^{88} -5.89988e6 q^{89} -1.63629e6 q^{90} +1.27639e6 q^{91} -6.70723e6 q^{92} -4.68770e6 q^{93} +8.40610e6 q^{94} +5.25935e6 q^{95} +1.29933e6 q^{96} -6.48918e6 q^{97} +6.44078e6 q^{98} +3.80055e6 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9}+O(q^{10}) \) 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9	\( 6 q - 48 q^{2} + 28 q^{3} + 384 q^{4} - 14 q^{5} - 224 q^{6} - 980 q^{7} - 3072 q^{8} + 8254 q^{9} + 112 q^{10} + 2956 q^{11} + 1792 q^{12} + 2394 q^{13} + 7840 q^{14} - 28820 q^{15} + 24576 q^{16} - 45108 q^{17} - 66032 q^{18} + 11764 q^{19} - 896 q^{20} - 135378 q^{21} - 23648 q^{22} + 21052 q^{23} - 14336 q^{24} + 194744 q^{25} - 19152 q^{26} + 439240 q^{27} - 62720 q^{28} + 288454 q^{29} + 230560 q^{30} + 578868 q^{31} - 196608 q^{32} + 980174 q^{33} + 360864 q^{34} + 1243052 q^{35} + 528256 q^{36} - 303918 q^{37} - 94112 q^{38} + 1735296 q^{39} + 7168 q^{40} + 1176840 q^{41} + 1083024 q^{42} + 2669236 q^{43} + 189184 q^{44} + 2560692 q^{45} - 168416 q^{46} - 131044 q^{47} + 114688 q^{48} + 2460856 q^{49} - 1557952 q^{50} + 2899732 q^{51} + 153216 q^{52} + 983190 q^{53} - 3513920 q^{54} - 1200168 q^{55} + 501760 q^{56} - 163216 q^{57} - 2307632 q^{58} - 1215568 q^{59} - 1844480 q^{60} + 3136358 q^{61} - 4630944 q^{62} - 1444880 q^{63} + 1572864 q^{64} - 1302836 q^{65} - 7841392 q^{66} + 2179276 q^{67} - 2886912 q^{68} - 929514 q^{69} - 9944416 q^{70} + 325164 q^{71} - 4226048 q^{72} + 5011444 q^{73} + 2431344 q^{74} - 9374520 q^{75} + 752896 q^{76} - 26500426 q^{77} - 13882368 q^{78} + 3173032 q^{79} - 57344 q^{80} - 2565226 q^{81} - 9414720 q^{82} - 22567048 q^{83} - 8664192 q^{84} + 1486476 q^{85} - 21353888 q^{86} - 157228 q^{87} - 1513472 q^{88} + 26836996 q^{89} - 20485536 q^{90} + 17942380 q^{91} + 1347328 q^{92} + 16734948 q^{93} + 1048352 q^{94} - 4252048 q^{95} - 917504 q^{96} + 295792 q^{97} - 19686848 q^{98} + 25990712 q^{99}+O(q^{100}) \) 6 * q - 48 * q^2 + 28 * q^3 + 384 * q^4 - 14 * q^5 - 224 * q^6 - 980 * q^7 - 3072 * q^8 + 8254 * q^9 + 112 * q^10 + 2956 * q^11 + 1792 * q^12 + 2394 * q^13 + 7840 * q^14 - 28820 * q^15 + 24576 * q^16 - 45108 * q^17 - 66032 * q^18 + 11764 * q^19 - 896 * q^20 - 135378 * q^21 - 23648 * q^22 + 21052 * q^23 - 14336 * q^24 + 194744 * q^25 - 19152 * q^26 + 439240 * q^27 - 62720 * q^28 + 288454 * q^29 + 230560 * q^30 + 578868 * q^31 - 196608 * q^32 + 980174 * q^33 + 360864 * q^34 + 1243052 * q^35 + 528256 * q^36 - 303918 * q^37 - 94112 * q^38 + 1735296 * q^39 + 7168 * q^40 + 1176840 * q^41 + 1083024 * q^42 + 2669236 * q^43 + 189184 * q^44 + 2560692 * q^45 - 168416 * q^46 - 131044 * q^47 + 114688 * q^48 + 2460856 * q^49 - 1557952 * q^50 + 2899732 * q^51 + 153216 * q^52 + 983190 * q^53 - 3513920 * q^54 - 1200168 * q^55 + 501760 * q^56 - 163216 * q^57 - 2307632 * q^58 - 1215568 * q^59 - 1844480 * q^60 + 3136358 * q^61 - 4630944 * q^62 - 1444880 * q^63 + 1572864 * q^64 - 1302836 * q^65 - 7841392 * q^66 + 2179276 * q^67 - 2886912 * q^68 - 929514 * q^69 - 9944416 * q^70 + 325164 * q^71 - 4226048 * q^72 + 5011444 * q^73 + 2431344 * q^74 - 9374520 * q^75 + 752896 * q^76 - 26500426 * q^77 - 13882368 * q^78 + 3173032 * q^79 - 57344 * q^80 - 2565226 * q^81 - 9414720 * q^82 - 22567048 * q^83 - 8664192 * q^84 + 1486476 * q^85 - 21353888 * q^86 - 157228 * q^87 - 1513472 * q^88 + 26836996 * q^89 - 20485536 * q^90 + 17942380 * q^91 + 1347328 * q^92 + 16734948 * q^93 + 1048352 * q^94 - 4252048 * q^95 - 917504 * q^96 + 295792 * q^97 - 19686848 * q^98 + 25990712 * q^99

Introduction

L-functions

Modular forms

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