LMFDB - Embedded newform 74.4.b.a.73.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,Mod(73,74)]

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([1]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("74.73");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	74.b (of order $2$, degree $1$, minimal)

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:	no
Analytic conductor:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$10$
Coefficient field:	$\mathbb{Q}[x]/(x^{10} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{10} + 212x^{8} + 15052x^{6} + 392769x^{4} + 2690496x^{2} + 2985984 $ x^10 + 212x^8 + 15052x^6 + 392769x^4 + 2690496x^2 + 2985984
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			73.8
Root			$-1.17028i$ of defining polynomial
Character	$\chi$	$=$	74.73
Dual form			74.4.b.a.73.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+2.00000i q^{2} -0.170276 q^{3} -4.00000 q^{4} -19.7476i q^{5} -0.340553i q^{6} -28.6201 q^{7} -8.00000i q^{8} -26.9710 q^{9} +O(q^{10})$	\(q+2.00000i q^{2} -0.170276 q^{3} -4.00000 q^{4} -19.7476i q^{5} -0.340553i q^{6} -28.6201 q^{7} -8.00000i q^{8} -26.9710 q^{9} +39.4952 q^{10} +45.4455 q^{11} +0.681105 q^{12} -57.5276i q^{13} -57.2402i q^{14} +3.36255i q^{15} +16.0000 q^{16} +9.56000i q^{17} -53.9420i q^{18} +97.1528i q^{19} +78.9904i q^{20} +4.87332 q^{21} +90.8910i q^{22} -115.914i q^{23} +1.36221i q^{24} -264.968 q^{25} +115.055 q^{26} +9.18998 q^{27} +114.480 q^{28} +18.2882i q^{29} -6.72510 q^{30} -21.3577i q^{31} +32.0000i q^{32} -7.73829 q^{33} -19.1200 q^{34} +565.178i q^{35} +107.884 q^{36} +(224.910 + 8.26479i) q^{37} -194.306 q^{38} +9.79559i q^{39} -157.981 q^{40} -374.560 q^{41} +9.74664i q^{42} -421.210i q^{43} -181.782 q^{44} +532.613i q^{45} +231.828 q^{46} -39.8125 q^{47} -2.72442 q^{48} +476.109 q^{49} -529.936i q^{50} -1.62784i q^{51} +230.110i q^{52} +414.315 q^{53} +18.3800i q^{54} -897.439i q^{55} +228.961i q^{56} -16.5428i q^{57} -36.5764 q^{58} -17.8364i q^{59} -13.4502i q^{60} -529.023i q^{61} +42.7154 q^{62} +771.912 q^{63} -64.0000 q^{64} -1136.03 q^{65} -15.4766i q^{66} +948.756 q^{67} -38.2400i q^{68} +19.7374i q^{69} -1130.36 q^{70} -181.544 q^{71} +215.768i q^{72} -413.381 q^{73} +(-16.5296 + 449.821i) q^{74} +45.1178 q^{75} -388.611i q^{76} -1300.65 q^{77} -19.5912 q^{78} -445.581i q^{79} -315.962i q^{80} +726.652 q^{81} -749.120i q^{82} +725.662 q^{83} -19.4933 q^{84} +188.787 q^{85} +842.420 q^{86} -3.11405i q^{87} -363.564i q^{88} +500.083i q^{89} -1065.23 q^{90} +1646.44i q^{91} +463.655i q^{92} +3.63671i q^{93} -79.6249i q^{94} +1918.54 q^{95} -5.44884i q^{96} -226.552i q^{97} +952.218i q^{98} -1225.71 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9}+O(q^{10}) $ 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9	$ 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9} + 76 q^{10} - 50 q^{11} - 56 q^{12} + 160 q^{16} - 312 q^{21} - 700 q^{25} + 492 q^{26} + 848 q^{27} + 16 q^{28} - 240 q^{30} - 508 q^{33} - 568 q^{34} - 688 q^{36} + 82 q^{37} + 336 q^{38} - 304 q^{40} - 1194 q^{41} + 200 q^{44} + 60 q^{46} + 464 q^{47} + 224 q^{48} + 2382 q^{49} - 692 q^{53} + 1108 q^{58} - 1700 q^{62} + 2300 q^{63} - 640 q^{64} + 604 q^{65} + 1114 q^{67} + 1880 q^{70} - 1460 q^{71} + 2082 q^{73} + 968 q^{74} - 5160 q^{75} - 6096 q^{77} + 1004 q^{78} + 4978 q^{81} - 1364 q^{83} + 1248 q^{84} + 104 q^{85} + 1400 q^{86} - 2600 q^{90} + 5084 q^{95} + 508 q^{99}+O(q^{100}) $ 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9 + 76 * q^10 - 50 * q^11 - 56 * q^12 + 160 * q^16 - 312 * q^21 - 700 * q^25 + 492 * q^26 + 848 * q^27 + 16 * q^28 - 240 * q^30 - 508 * q^33 - 568 * q^34 - 688 * q^36 + 82 * q^37 + 336 * q^38 - 304 * q^40 - 1194 * q^41 + 200 * q^44 + 60 * q^46 + 464 * q^47 + 224 * q^48 + 2382 * q^49 - 692 * q^53 + 1108 * q^58 - 1700 * q^62 + 2300 * q^63 - 640 * q^64 + 604 * q^65 + 1114 * q^67 + 1880 * q^70 - 1460 * q^71 + 2082 * q^73 + 968 * q^74 - 5160 * q^75 - 6096 * q^77 + 1004 * q^78 + 4978 * q^81 - 1364 * q^83 + 1248 * q^84 + 104 * q^85 + 1400 * q^86 - 2600 * q^90 + 5084 * q^95 + 508 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$-1$

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 $

$2$			2.00000i			0.707107i
$2$			2.00000i			0.707107i
$3$	−0.170276			−0.0327697			−0.0163848	−	0.999866i	$-0.505216\pi$
$3$	−0.170276			−0.0327697			−0.0163848	+	0.999866i	$0.505216\pi$
$4$	−4.00000			−0.500000
$5$		−	19.7476i		−	1.76628i	−0.469110	−	0.883140i	$-0.655425\pi$
$5$		−	19.7476i		−	1.76628i	0.469110	−	0.883140i	$-0.344575\pi$
$6$		−	0.340553i		−	0.0231717i
$7$	−28.6201			−1.54534			−0.772670	−	0.634809i	$-0.781079\pi$
$7$	−28.6201			−1.54534			−0.772670	+	0.634809i	$0.781079\pi$
$8$		−	8.00000i		−	0.353553i
$9$	−26.9710			−0.998926
$10$	39.4952			1.24895
$11$	45.4455			1.24567			0.622833	−	0.782355i	$-0.285982\pi$
$11$	45.4455			1.24567			0.622833	+	0.782355i	$0.285982\pi$
$12$	0.681105			0.0163848
$13$		−	57.5276i		−	1.22733i	−0.789567	−	0.613665i	$-0.789695\pi$
$13$		−	57.5276i		−	1.22733i	0.789567	−	0.613665i	$-0.210305\pi$
$14$		−	57.2402i		−	1.09272i
$15$			3.36255i			0.0578804i
$16$	16.0000			0.250000
$17$			9.56000i			0.136391i	0.997672	+	0.0681953i	$0.0217241\pi$
$17$			9.56000i			0.136391i	−0.997672	+	0.0681953i	$0.978276\pi$
$18$		−	53.9420i		−	0.706347i
$19$			97.1528i			1.17307i	0.809923	+	0.586536i	$0.199509\pi$
$19$			97.1528i			1.17307i	−0.809923	+	0.586536i	$0.800491\pi$
$20$			78.9904i			0.883140i
$21$	4.87332			0.0506403
$22$			90.8910i			0.880819i
$23$		−	115.914i		−	1.05086i	−0.850838	−	0.525428i	$-0.823905\pi$
$23$		−	115.914i		−	1.05086i	0.850838	−	0.525428i	$-0.176095\pi$
$24$			1.36221i			0.0115858i
$25$	−264.968			−2.11974
$26$	115.055			0.867853
$27$	9.18998			0.0655042
$28$	114.480			0.772670
$29$			18.2882i			0.117105i	0.998284	+	0.0585523i	$0.0186485\pi$
$29$			18.2882i			0.117105i	−0.998284	+	0.0585523i	$0.981352\pi$
$30$	−6.72510			−0.0409277
$31$		−	21.3577i		−	0.123740i	−0.998084	−	0.0618702i	$-0.980294\pi$
$31$		−	21.3577i		−	0.123740i	0.998084	−	0.0618702i	$-0.0197065\pi$
$32$			32.0000i			0.176777i
$33$	−7.73829			−0.0408201
$34$	−19.1200			−0.0964428
$35$			565.178i			2.72950i
$36$	107.884			0.499463
$37$	224.910	+	8.26479i	0.999326	+	0.0367222i
$37$	224.910	+	8.26479i	0.999326	+	0.0367222i
$38$	−194.306			−0.829488
$39$			9.79559i			0.0402192i
$40$	−157.981			−0.624474
$41$	−374.560			−1.42674			−0.713371	−	0.700787i	$-0.752833\pi$
$41$	−374.560			−1.42674			−0.713371	+	0.700787i	$0.752833\pi$
$42$			9.74664i			0.0358081i
$43$		−	421.210i		−	1.49381i	−0.664929	−	0.746906i	$-0.731538\pi$
$43$		−	421.210i		−	1.49381i	0.664929	−	0.746906i	$-0.268462\pi$
$44$	−181.782			−0.622833
$45$			532.613i			1.76438i
$46$	231.828			0.743068
$47$	−39.8125			−0.123558			−0.0617792	−	0.998090i	$-0.519677\pi$
$47$	−39.8125			−0.123558			−0.0617792	+	0.998090i	$0.519677\pi$
$48$	−2.72442			−0.00819242
$49$	476.109			1.38807
$50$		−	529.936i		−	1.49889i
$51$		−	1.62784i		−	0.00446948i
$52$			230.110i			0.613665i
$53$	414.315			1.07378			0.536892	−	0.843651i	$-0.319598\pi$
$53$	414.315			1.07378			0.536892	+	0.843651i	$0.319598\pi$
$54$			18.3800i			0.0463185i
$55$		−	897.439i		−	2.20019i
$56$			228.961i			0.546360i
$57$		−	16.5428i		−	0.0384412i
$58$	−36.5764			−0.0828055
$59$		−	17.8364i		−	0.0393577i	−0.999806	−	0.0196789i	$-0.993736\pi$
$59$		−	17.8364i		−	0.0393577i	0.999806	−	0.0196789i	$-0.00626438\pi$
$60$		−	13.4502i		−	0.0289402i
$61$		−	529.023i		−	1.11040i	−0.831717	−	0.555200i	$-0.812642\pi$
$61$		−	529.023i		−	1.11040i	0.831717	−	0.555200i	$-0.187358\pi$
$62$	42.7154			0.0874977
$63$	771.912			1.54368
$64$	−64.0000			−0.125000
$65$	−1136.03			−2.16781
$66$		−	15.4766i		−	0.0288642i
$67$	948.756			1.72999			0.864993	−	0.501784i	$-0.167323\pi$
$67$	948.756			1.72999			0.864993	+	0.501784i	$0.167323\pi$
$68$		−	38.2400i		−	0.0681953i
$69$			19.7374i			0.0344362i
$70$	−1130.36			−1.93005
$71$	−181.544			−0.303455			−0.151727	−	0.988422i	$-0.548484\pi$
$71$	−181.544			−0.303455			−0.151727	+	0.988422i	$0.548484\pi$
$72$			215.768i			0.353174i
$73$	−413.381			−0.662775			−0.331388	−	0.943495i	$-0.607517\pi$
$73$	−413.381			−0.662775			−0.331388	+	0.943495i	$0.607517\pi$
$74$	−16.5296	+	449.821i	−0.0259666	+	0.706630i
$75$	45.1178			0.0694634
$76$		−	388.611i		−	0.586536i
$77$	−1300.65			−1.92498
$78$	−19.5912			−0.0284393
$79$		−	445.581i		−	0.634579i	−0.948329	−	0.317290i	$-0.897227\pi$
$79$		−	445.581i		−	0.634579i	0.948329	−	0.317290i	$-0.102773\pi$
$80$		−	315.962i		−	0.441570i
$81$	726.652			0.996780
$82$		−	749.120i		−	1.00886i
$83$	725.662			0.959660			0.479830	−	0.877362i	$-0.340698\pi$
$83$	725.662			0.959660			0.479830	+	0.877362i	$0.340698\pi$
$84$	−19.4933			−0.0253201
$85$	188.787			0.240904
$86$	842.420			1.05629
$87$		−	3.11405i		−	0.00383748i
$88$		−	363.564i		−	0.440409i
$89$			500.083i			0.595603i	0.954628	+	0.297802i	$0.0962534\pi$
$89$			500.083i			0.595603i	−0.954628	+	0.297802i	$0.903747\pi$
$90$	−1065.23			−1.24761
$91$			1646.44i			1.89664i
$92$			463.655i			0.525428i
$93$			3.63671i			0.00405494i
$94$		−	79.6249i		−	0.0873690i
$95$	1918.54			2.07197
$96$		−	5.44884i		−	0.00579292i
$97$		−	226.552i		−	0.237142i	−0.992946	−	0.118571i	$-0.962169\pi$
$97$		−	226.552i		−	0.237142i	0.992946	−	0.118571i	$-0.0378314\pi$
$98$			952.218i			0.981516i
$99$	−1225.71			−1.24433
$100$	1059.87			1.05987
$101$	−1343.44			−1.32354			−0.661768	−	0.749709i	$-0.730194\pi$
$101$	−1343.44			−1.32354			−0.661768	+	0.749709i	$0.730194\pi$
$102$	3.25568			0.00316040
$103$			1734.63i			1.65940i	0.558208	+	0.829701i	$0.311489\pi$
$103$			1734.63i			1.65940i	−0.558208	+	0.829701i	$0.688511\pi$
$104$	−460.221			−0.433926
$105$		−	96.2364i		−	0.0894449i
$106$			828.630i			0.759280i
$107$	745.556			0.673604			0.336802	−	0.941576i	$-0.390655\pi$
$107$	745.556			0.673604			0.336802	+	0.941576i	$0.390655\pi$
$108$	−36.7599			−0.0327521
$109$		−	2052.80i		−	1.80388i	−0.431865	−	0.901938i	$-0.642144\pi$
$109$		−	2052.80i		−	1.80388i	0.431865	−	0.901938i	$-0.357856\pi$
$110$	1794.88			1.55577
$111$	−38.2969	−	1.40730i	−0.0327476	−	0.00120338i
$112$	−457.921			−0.386335
$113$		−	599.467i		−	0.499054i	−0.968368	−	0.249527i	$-0.919725\pi$
$113$		−	599.467i		−	0.499054i	0.968368	−	0.249527i	$-0.0802751\pi$
$114$	33.0856			0.0271821
$115$	−2289.02			−1.85611
$116$		−	73.1528i		−	0.0585523i
$117$			1551.58i			1.22601i
$118$	35.6729			0.0278301
$119$		−	273.608i		−	0.210770i
$120$	26.9004			0.0204638
$121$	734.291			0.551684
$122$	1058.05			0.785172
$123$	63.7787			0.0467539
$124$			85.4307i			0.0618702i
$125$			2764.03i			1.97778i
$126$			1543.82i			1.09155i
$127$	502.239			0.350917			0.175459	−	0.984487i	$-0.443859\pi$
$127$	502.239			0.350917			0.175459	+	0.984487i	$0.443859\pi$
$128$		−	128.000i		−	0.0883883i
$129$			71.7221i			0.0489518i
$130$		−	2272.06i		−	1.53287i
$131$			232.744i			0.155228i	0.996983	+	0.0776142i	$0.0247302\pi$
$131$			232.744i			0.155228i	−0.996983	+	0.0776142i	$0.975270\pi$
$132$	30.9532			0.0204100
$133$		−	2780.52i		−	1.81280i
$134$			1897.51i			1.22328i
$135$		−	181.480i		−	0.115699i
$136$	76.4800			0.0482214
$137$	352.156			0.219611			0.109805	−	0.993953i	$-0.464977\pi$
$137$	352.156			0.219611			0.109805	+	0.993953i	$0.464977\pi$
$138$	−39.4747			−0.0243501
$139$	−1499.31			−0.914890			−0.457445	−	0.889238i	$-0.651235\pi$
$139$	−1499.31			−0.914890			−0.457445	+	0.889238i	$0.651235\pi$
$140$		−	2260.71i		−	1.36475i
$141$	6.77912			0.00404897
$142$		−	363.088i		−	0.214575i
$143$		−	2614.37i		−	1.52884i
$144$	−431.536			−0.249732
$145$	361.148			0.206840
$146$		−	826.762i		−	0.468653i
$147$	−81.0701			−0.0454867
$148$	−899.642	−	33.0592i	−0.499663	−	0.0183611i
$149$	−2279.38			−1.25325			−0.626625	−	0.779321i	$-0.715564\pi$
$149$	−2279.38			−1.25325			−0.626625	+	0.779321i	$0.715564\pi$
$150$			90.2356i			0.0491180i
$151$	−438.134			−0.236125			−0.118062	−	0.993006i	$-0.537668\pi$
$151$	−438.134			−0.236125			−0.118062	+	0.993006i	$0.537668\pi$
$152$	777.222			0.414744
$153$		−	257.843i		−	0.136244i
$154$		−	2601.31i		−	1.36116i
$155$	−421.763			−0.218560
$156$		−	39.1823i		−	0.0201096i
$157$	−2910.04			−1.47928			−0.739639	−	0.673004i	$-0.765004\pi$
$157$	−2910.04			−1.47928			−0.739639	+	0.673004i	$0.765004\pi$
$158$	891.162			0.448715
$159$	−70.5480			−0.0351876
$160$	631.923			0.312237
$161$			3317.46i			1.62393i
$162$			1453.30i			0.704830i
$163$		−	666.259i		−	0.320156i	−0.987104	−	0.160078i	$-0.948825\pi$
$163$		−	666.259i		−	0.320156i	0.987104	−	0.160078i	$-0.0511746\pi$
$164$	1498.24			0.713371
$165$			152.813i			0.0720997i
$166$			1451.32i			0.678582i
$167$		−	1168.68i		−	0.541527i	−0.962646	−	0.270763i	$-0.912724\pi$
$167$		−	1168.68i		−	0.541527i	0.962646	−	0.270763i	$-0.0872761\pi$
$168$		−	38.9866i		−	0.0179040i
$169$	−1112.42			−0.506338
$170$			377.574i			0.170345i
$171$		−	2620.31i		−	1.17181i
$172$			1684.84i			0.746906i
$173$	1797.12			0.789784			0.394892	−	0.918728i	$-0.370782\pi$
$173$	1797.12			0.789784			0.394892	+	0.918728i	$0.370782\pi$
$174$	6.22810			0.00271351
$175$	7583.41			3.27572
$176$	727.128			0.311417
$177$			3.03712i			0.00128974i
$178$	−1000.17			−0.421155
$179$		−	1477.63i		−	0.617001i	−0.951224	−	0.308501i	$-0.900173\pi$
$179$		−	1477.63i		−	0.617001i	0.951224	−	0.308501i	$-0.0998272\pi$
$180$		−	2130.45i		−	0.882192i
$181$	2680.08			1.10060			0.550300	−	0.834967i	$-0.314513\pi$
$181$	2680.08			1.10060			0.550300	+	0.834967i	$0.314513\pi$
$182$	−3292.89			−1.34113
$183$			90.0800i			0.0363875i
$184$	−927.310			−0.371534
$185$	163.210	−	4441.44i	0.0648618	−	1.76509i
$186$	−7.27341			−0.00286727
$187$			434.459i			0.169897i
$188$	159.250			0.0617792
$189$	−263.018			−0.101226
$190$			3837.07i			1.46511i
$191$			3001.18i			1.13695i	0.822700	+	0.568476i	$0.192467\pi$
$191$			3001.18i			1.13695i	−0.822700	+	0.568476i	$0.807533\pi$
$192$	10.8977			0.00409621
$193$		−	3097.39i		−	1.15521i	−0.816317	−	0.577604i	$-0.803988\pi$
$193$		−	3097.39i		−	1.15521i	0.816317	−	0.577604i	$-0.196012\pi$
$194$	453.103			0.167685
$195$	193.439			0.0710384
$196$	−1904.44			−0.694036
$197$	1220.89			0.441548			0.220774	−	0.975325i	$-0.429142\pi$
$197$	1220.89			0.441548			0.220774	+	0.975325i	$0.429142\pi$
$198$		−	2451.42i		−	0.879873i
$199$			2379.67i			0.847691i	0.905735	+	0.423845i	$0.139320\pi$
$199$			2379.67i			0.847691i	−0.905735	+	0.423845i	$0.860680\pi$
$200$			2119.74i			0.749443i
$201$	−161.551			−0.0566911
$202$		−	2686.88i		−	0.935881i
$203$		−	523.410i		−	0.180966i
$204$			6.51137i			0.00223474i
$205$			7396.66i			2.52003i
$206$	−3469.27			−1.17337
$207$			3126.31i			1.04973i
$208$		−	920.441i		−	0.306832i
$209$			4415.16i			1.46126i
$210$	192.473			0.0632471
$211$	−1113.02			−0.363146			−0.181573	−	0.983377i	$-0.558119\pi$
$211$	−1113.02			−0.363146			−0.181573	+	0.983377i	$0.558119\pi$
$212$	−1657.26			−0.536892
$213$	30.9126			0.00994412
$214$			1491.11i			0.476310i
$215$	−8317.89			−2.63849
$216$		−	73.5199i		−	0.0231592i
$217$			611.259i			0.191221i
$218$	4105.60			1.27553
$219$	70.3890			0.0217189
$220$			3589.76i			1.10010i
$221$	549.964			0.167396
$222$	2.81460	−	76.5938i	0.000850916	−	0.0231560i
$223$	−2470.83			−0.741970			−0.370985	−	0.928639i	$-0.620980\pi$
$223$	−2470.83			−0.741970			−0.370985	+	0.928639i	$0.620980\pi$
$224$		−	915.843i		−	0.273180i
$225$	7146.46			2.11747
$226$	1198.93			0.352884
$227$		−	3430.62i		−	1.00308i	−0.865136	−	0.501538i	$-0.832768\pi$
$227$		−	3430.62i		−	1.00308i	0.865136	−	0.501538i	$-0.167232\pi$
$228$			66.1713i			0.0192206i
$229$	5225.02			1.50777			0.753884	−	0.657008i	$-0.228178\pi$
$229$	5225.02			1.50777			0.753884	+	0.657008i	$0.228178\pi$
$230$		−	4578.04i		−	1.31247i
$231$	221.470			0.0630809
$232$	146.306			0.0414028
$233$	−2261.52			−0.635869			−0.317934	−	0.948113i	$-0.602989\pi$
$233$	−2261.52			−0.635869			−0.317934	+	0.948113i	$0.602989\pi$
$234$	−3103.15			−0.866921
$235$			786.201i			0.218239i
$236$			71.3457i			0.0196789i
$237$			75.8719i			0.0207950i
$238$	547.216			0.149037
$239$			5365.09i			1.45204i	0.687671	+	0.726022i	$0.258633\pi$
$239$			5365.09i			1.45204i	−0.687671	+	0.726022i	$0.741367\pi$
$240$			53.8008i			0.0144701i
$241$			2190.85i			0.585580i	0.956177	+	0.292790i	$0.0945837\pi$
$241$			2190.85i			0.585580i	−0.956177	+	0.292790i	$0.905416\pi$
$242$			1468.58i			0.390099i
$243$	−371.861			−0.0981683
$244$			2116.09i			0.555200i
$245$		−	9402.01i		−	2.45172i
$246$			127.557i			0.0330600i
$247$	5588.97			1.43975
$248$	−170.861			−0.0437488
$249$	−123.563			−0.0314478
$250$	−5528.07			−1.39850
$251$			531.797i			0.133732i	0.997762	+	0.0668660i	$0.0213000\pi$
$251$			531.797i			0.133732i	−0.997762	+	0.0668660i	$0.978700\pi$
$252$	−3087.65			−0.771840
$253$		−	5267.76i		−	1.30902i
$254$			1004.48i			0.248136i
$255$	−32.1460			−0.00789435
$256$	256.000			0.0625000
$257$			6162.25i			1.49568i	0.663877	+	0.747842i	$0.268910\pi$
$257$			6162.25i			1.49568i	−0.663877	+	0.747842i	$0.731090\pi$
$258$	−143.444			−0.0346141
$259$	−6436.95	−	236.539i	−1.54430	−	0.0567483i
$260$	4544.13			1.08390
$261$		−	493.251i		−	0.116979i
$262$	−465.488			−0.109763
$263$	3158.31			0.740492			0.370246	−	0.928934i	$-0.379273\pi$
$263$	3158.31			0.740492			0.370246	+	0.928934i	$0.379273\pi$
$264$			61.9063i			0.0144321i
$265$		−	8181.73i		−	1.89660i
$266$	5561.04			1.28184
$267$		−	85.1523i		−	0.0195177i
$268$	−3795.03			−0.864993
$269$	6483.52			1.46954			0.734771	−	0.678315i	$-0.237290\pi$
$269$	6483.52			1.46954			0.734771	+	0.678315i	$0.237290\pi$
$270$	362.960			0.0818114
$271$	−4808.08			−1.07775			−0.538875	−	0.842386i	$-0.681150\pi$
$271$	−4808.08			−1.07775			−0.538875	+	0.842386i	$0.681150\pi$
$272$			152.960i			0.0340977i
$273$		−	280.350i		−	0.0621523i
$274$			704.311i			0.155288i
$275$	−12041.6			−2.64049
$276$		−	78.9495i		−	0.0172181i
$277$		−	7697.02i		−	1.66956i	−0.550581	−	0.834782i	$-0.685594\pi$
$277$		−	7697.02i		−	1.66956i	0.550581	−	0.834782i	$-0.314406\pi$
$278$		−	2998.62i		−	0.646925i
$279$			576.038i			0.123608i
$280$	4521.43			0.965024
$281$		−	2190.90i		−	0.465117i	−0.972582	−	0.232559i	$-0.925290\pi$
$281$		−	2190.90i		−	0.465117i	0.972582	−	0.232559i	$-0.0747098\pi$
$282$			13.5582i			0.00286305i
$283$		−	496.119i		−	0.104209i	−0.998642	−	0.0521046i	$-0.983407\pi$
$283$		−	496.119i		−	0.104209i	0.998642	−	0.0521046i	$-0.0165929\pi$
$284$	726.175			0.151727
$285$	−326.681			−0.0678980
$286$	5228.74			1.08105
$287$	10719.9			2.20480
$288$		−	863.072i		−	0.176587i
$289$	4821.61			0.981398
$290$			722.297i			0.146258i
$291$			38.5764i			0.00777109i
$292$	1653.52			0.331388
$293$	−1221.98			−0.243648			−0.121824	−	0.992552i	$-0.538874\pi$
$293$	−1221.98			−0.243648			−0.121824	+	0.992552i	$0.538874\pi$
$294$		−	162.140i		−	0.0321640i
$295$	−352.227			−0.0695167
$296$	66.1183	−	1799.28i	0.0129833	−	0.353315i
$297$	417.643			0.0815963
$298$		−	4558.76i		−	0.886181i
$299$	−6668.24			−1.28975
$300$	−180.471			−0.0347317
$301$			12055.1i			2.30845i
$302$		−	876.268i		−	0.166965i
$303$	228.756			0.0433719
$304$			1554.44i			0.293268i
$305$	−10446.9			−1.96128
$306$	515.686			0.0963392
$307$	585.942			0.108930			0.0544650	−	0.998516i	$-0.482655\pi$
$307$	585.942			0.108930			0.0544650	+	0.998516i	$0.482655\pi$
$308$	5202.61			0.962488
$309$		−	295.367i		−	0.0543781i
$310$		−	843.526i		−	0.154545i
$311$			2055.13i			0.374714i	0.982292	+	0.187357i	$0.0599921\pi$
$311$			2055.13i			0.374714i	−0.982292	+	0.187357i	$0.940008\pi$
$312$	78.3647			0.0142196
$313$			867.512i			0.156660i	0.996927	+	0.0783302i	$0.0249588\pi$
$313$			867.512i			0.156660i	−0.996927	+	0.0783302i	$0.975041\pi$
$314$		−	5820.08i		−	1.04601i
$315$		−	15243.4i		−	2.72657i
$316$			1782.32i			0.317290i
$317$	−1820.21			−0.322501			−0.161251	−	0.986913i	$-0.551553\pi$
$317$	−1820.21			−0.322501			−0.161251	+	0.986913i	$0.551553\pi$
$318$		−	141.096i		−	0.0248814i
$319$			831.116i			0.145873i
$320$			1263.85i			0.220785i
$321$	−126.950			−0.0220738
$322$	−6634.92			−1.14829
$323$	−928.781			−0.159996
$324$	−2906.61			−0.498390
$325$			15243.0i			2.60162i
$326$	1332.52			0.226385
$327$			349.543i			0.0591125i
$328$			2996.48i			0.504430i
$329$	1139.44			0.190940
$330$	−305.625			−0.0509822
$331$			10292.9i			1.70921i	0.519279	+	0.854605i	$0.326200\pi$
$331$			10292.9i			1.70921i	−0.519279	+	0.854605i	$0.673800\pi$
$332$	−2902.65			−0.479830
$333$	−6066.06	−	222.910i	−0.998252	−	0.0366828i
$334$	2337.35			0.382917
$335$		−	18735.7i		−	3.05564i
$336$	77.9731			0.0126601
$337$	−4054.38			−0.655360			−0.327680	−	0.944789i	$-0.606267\pi$
$337$	−4054.38			−0.655360			−0.327680	+	0.944789i	$0.606267\pi$
$338$		−	2224.85i		−	0.358035i
$339$			102.075i			0.0163538i
$340$	−755.149			−0.120452
$341$		−	970.610i		−	0.154139i
$342$	5240.62			0.828597
$343$	−3809.59			−0.599704
$344$	−3369.68			−0.528143
$345$	389.766			0.0608240
$346$			3594.24i			0.558461i
$347$			9355.53i			1.44735i	0.690140	+	0.723676i	$0.257549\pi$
$347$			9355.53i			1.44735i	−0.690140	+	0.723676i	$0.742451\pi$
$348$			12.4562i			0.00191874i
$349$	4597.36			0.705131			0.352566	−	0.935787i	$-0.385309\pi$
$349$	4597.36			0.705131			0.352566	+	0.935787i	$0.385309\pi$
$350$			15166.8i			2.31629i
$351$		−	528.678i		−	0.0803952i
$352$			1454.26i			0.220205i
$353$		−	8333.71i		−	1.25654i	−0.777996	−	0.628270i	$-0.783763\pi$
$353$		−	8333.71i		−	1.25654i	0.777996	−	0.628270i	$-0.216237\pi$
$354$	−6.07424			−0.000911984
$355$			3585.06i			0.535986i
$356$		−	2000.33i		−	0.297802i
$357$			46.5890i			0.00690686i
$358$	2955.26			0.436286
$359$	6949.38			1.02165			0.510827	−	0.859683i	$-0.329339\pi$
$359$	6949.38			1.02165			0.510827	+	0.859683i	$0.329339\pi$
$360$	4260.90			0.623804
$361$	−2579.67			−0.376100
$362$			5360.15i			0.778241i
$363$	−125.032			−0.0180785
$364$		−	6585.78i		−	0.948320i
$365$			8163.29i			1.17065i
$366$	−180.160			−0.0257298
$367$	2722.95			0.387294			0.193647	−	0.981071i	$-0.437968\pi$
$367$	2722.95			0.387294			0.193647	+	0.981071i	$0.437968\pi$
$368$		−	1854.62i		−	0.262714i
$369$	10102.3			1.42521
$370$	8882.89	+	326.420i	1.24811	+	0.0458642i
$371$	−11857.7			−1.65936
$372$		−	14.5468i		−	0.00202747i
$373$	10157.6			1.41002			0.705012	−	0.709195i	$-0.250941\pi$
$373$	10157.6			1.41002			0.705012	+	0.709195i	$0.250941\pi$
$374$	−868.918			−0.120135
$375$		−	470.650i		−	0.0648113i
$376$			318.500i			0.0436845i
$377$	1052.08			0.143726
$378$		−	526.036i		−	0.0715777i
$379$	7928.20			1.07452			0.537262	−	0.843416i	$-0.319459\pi$
$379$	7928.20			1.07452			0.537262	+	0.843416i	$0.319459\pi$
$380$	−7674.14			−1.03599
$381$	−85.5194			−0.0114995
$382$	−6002.37			−0.803947
$383$		−	2794.38i		−	0.372810i	−0.982473	−	0.186405i	$-0.940316\pi$
$383$		−	2794.38i		−	0.372810i	0.982473	−	0.186405i	$-0.0596836\pi$
$384$			21.7954i			0.00289646i
$385$			25684.8i			3.40005i
$386$	6194.78			0.816855
$387$			11360.5i			1.49221i
$388$			906.206i			0.118571i
$389$		−	10763.0i		−	1.40285i	−0.712744	−	0.701424i	$-0.752548\pi$
$389$		−	10763.0i		−	1.40285i	0.712744	−	0.701424i	$-0.247452\pi$
$390$			386.879i			0.0502317i
$391$	1108.14			0.143327
$392$		−	3808.87i		−	0.490758i
$393$		−	39.6308i		−	0.00508679i
$394$			2441.78i			0.312222i
$395$	−8799.16			−1.12084
$396$	4902.84			0.622164
$397$	−10037.4			−1.26893			−0.634464	−	0.772952i	$-0.718779\pi$
$397$	−10037.4			−1.26893			−0.634464	+	0.772952i	$0.718779\pi$
$398$	−4759.34			−0.599408
$399$			473.457i			0.0594047i
$400$	−4239.49			−0.529936
$401$			4176.34i			0.520091i	0.965596	+	0.260045i	$0.0837375\pi$
$401$			4176.34i			0.520091i	−0.965596	+	0.260045i	$0.916262\pi$
$402$		−	323.101i		−	0.0400867i
$403$	−1228.66			−0.151870
$404$	5373.75			0.661768
$405$		−	14349.6i		−	1.76059i
$406$	1046.82			0.127963
$407$	10221.2	+	375.597i	1.24483	+	0.0457437i
$408$	−13.0227			−0.00158020
$409$		−	10903.5i		−	1.31820i	−0.752055	−	0.659101i	$-0.770937\pi$
$409$		−	10903.5i		−	1.31820i	0.752055	−	0.659101i	$-0.229063\pi$
$410$	−14793.3			−1.78193
$411$	−59.9638			−0.00719658
$412$		−	6938.53i		−	0.829701i
$413$			510.480i			0.0608210i
$414$	−6252.62			−0.742270
$415$		−	14330.1i		−	1.69503i
$416$	1840.88			0.216963
$417$	255.297			0.0299807
$418$	−8830.31			−1.03326
$419$	13052.8			1.52188			0.760942	−	0.648820i	$-0.224737\pi$
$419$	13052.8			1.52188			0.760942	+	0.648820i	$0.224737\pi$
$420$			384.946i			0.0447225i
$421$		−	7106.23i		−	0.822652i	−0.911488	−	0.411326i	$-0.865066\pi$
$421$		−	7106.23i		−	0.822652i	0.911488	−	0.411326i	$-0.134934\pi$
$422$		−	2226.05i		−	0.256783i
$423$	1073.78			0.123426
$424$		−	3314.52i		−	0.379640i
$425$		−	2533.10i		−	0.289113i
$426$			61.8252i			0.00703155i
$427$			15140.7i			1.71595i
$428$	−2982.22			−0.336802
$429$			445.165i			0.0500997i
$430$		−	16635.8i		−	1.86570i
$431$			7928.71i			0.886108i	0.896495	+	0.443054i	$0.146105\pi$
$431$			7928.71i			0.886108i	−0.896495	+	0.443054i	$0.853895\pi$
$432$	147.040			0.0163760
$433$	7673.86			0.851691			0.425846	−	0.904796i	$-0.359977\pi$
$433$	7673.86			0.851691			0.425846	+	0.904796i	$0.359977\pi$
$434$	−1222.52			−0.135214
$435$	−61.4950			−0.00677807
$436$			8211.20i			0.901938i
$437$	11261.4			1.23273
$438$			140.778i			0.0153576i
$439$		−	10371.9i		−	1.12762i	−0.825905	−	0.563809i	$-0.809335\pi$
$439$		−	10371.9i		−	1.12762i	0.825905	−	0.563809i	$-0.190665\pi$
$440$	−7179.52			−0.777886
$441$	−12841.1			−1.38658
$442$			1099.93i			0.118367i
$443$	−12883.2			−1.38171			−0.690856	−	0.722993i	$-0.742766\pi$
$443$	−12883.2			−1.38171			−0.690856	+	0.722993i	$0.742766\pi$
$444$	153.188	+	5.62919i	0.0163738	+	0.000601688i
$445$	9875.44			1.05200
$446$		−	4941.67i		−	0.524652i
$447$	388.125			0.0410686
$448$	1831.69			0.193167
$449$		−	2056.54i		−	0.216156i	−0.994142	−	0.108078i	$-0.965530\pi$
$449$		−	2056.54i		−	0.216156i	0.994142	−	0.108078i	$-0.0344697\pi$
$450$			14292.9i			1.49728i
$451$	−17022.1			−1.77724
$452$			2397.87i			0.249527i
$453$	74.6038			0.00773774
$454$	6861.24			0.709282
$455$	32513.3			3.35000
$456$	−132.343			−0.0135910
$457$		−	3486.79i		−	0.356904i	−0.983949	−	0.178452i	$-0.942891\pi$
$457$		−	3486.79i		−	0.356904i	0.983949	−	0.178452i	$-0.0571090\pi$
$458$			10450.0i			1.06615i
$459$			87.8563i			0.00893416i
$460$	9156.08			0.928053
$461$			4930.71i			0.498147i	0.968485	+	0.249074i	$0.0801261\pi$
$461$			4930.71i			0.498147i	−0.968485	+	0.249074i	$0.919874\pi$
$462$			442.941i			0.0446049i
$463$		−	6495.55i		−	0.651996i	−0.945371	−	0.325998i	$-0.894300\pi$
$463$		−	6495.55i		−	0.651996i	0.945371	−	0.325998i	$-0.105700\pi$
$464$			292.611i			0.0292762i
$465$	71.8163			0.00716215
$466$		−	4523.05i		−	0.449627i
$467$			6187.37i			0.613100i	0.951855	+	0.306550i	$0.0991746\pi$
$467$			6187.37i			0.613100i	−0.951855	+	0.306550i	$0.900825\pi$
$468$		−	6206.31i		−	0.613006i
$469$	−27153.5			−2.67341
$470$	−1572.40			−0.154318
$471$	495.511			0.0484755
$472$	−142.691			−0.0139151
$473$		−	19142.1i		−	1.86079i
$474$	−151.744			−0.0147043
$475$		−	25742.4i		−	2.48661i
$476$			1094.43i			0.105385i
$477$	−11174.5			−1.07263
$478$	−10730.2			−1.02675
$479$			9123.83i			0.870310i	0.900356	+	0.435155i	$0.143306\pi$
$479$			9123.83i			0.870310i	−0.900356	+	0.435155i	$0.856694\pi$
$480$	−107.602			−0.0102319
$481$	475.453	−	12938.6i	0.0450703	−	1.22650i
$482$	−4381.69			−0.414067
$483$		−	564.885i		−	0.0532157i
$484$	−2937.17			−0.275842
$485$	−4473.85			−0.418860
$486$		−	743.722i		−	0.0694155i
$487$		−	16735.5i		−	1.55720i	−0.627519	−	0.778601i	$-0.715929\pi$
$487$		−	16735.5i		−	1.55720i	0.627519	−	0.778601i	$-0.284071\pi$
$488$	−4232.18			−0.392586
$489$			113.448i			0.0104914i
$490$	18804.0			1.73363
$491$	1651.79			0.151821			0.0759106	−	0.997115i	$-0.475814\pi$
$491$	1651.79			0.151821			0.0759106	+	0.997115i	$0.475814\pi$
$492$	−255.115			−0.0233769
$493$	−174.835			−0.0159720
$494$			11177.9i			1.01805i
$495$			24204.8i			2.19783i
$496$		−	341.723i		−	0.0309351i
$497$	5195.80			0.468940
$498$		−	247.126i		−	0.0222369i
$499$			9784.49i			0.877783i	0.898540	+	0.438892i	$0.144629\pi$
$499$			9784.49i			0.877783i	−0.898540	+	0.438892i	$0.855371\pi$
$500$		−	11056.1i		−	0.988891i
$501$			198.998i			0.0177457i
$502$	−1063.59			−0.0945628
$503$			9074.26i			0.804377i	0.915557	+	0.402188i	$0.131750\pi$
$503$			9074.26i			0.804377i	−0.915557	+	0.402188i	$0.868250\pi$
$504$		−	6175.30i		−	0.545773i
$505$			26529.7i			2.33773i
$506$	10535.5			0.925614
$507$	189.419			0.0165925
$508$	−2008.96			−0.175459
$509$	−3241.45			−0.282269			−0.141134	−	0.989990i	$-0.545075\pi$
$509$	−3241.45			−0.282269			−0.141134	+	0.989990i	$0.545075\pi$
$510$		−	64.2920i		−	0.00558215i
$511$	11831.0			1.02421
$512$			512.000i			0.0441942i
$513$			892.833i			0.0768412i
$514$	−12324.5			−1.05761
$515$	34254.9			2.93097
$516$		−	286.888i		−	0.0244759i
$517$	−1809.30			−0.153913
$518$	473.078	−	12873.9i	0.0401271	−	1.09198i
$519$	−306.007			−0.0258810
$520$			9088.26i			0.766436i
$521$	1975.39			0.166110			0.0830550	−	0.996545i	$-0.473532\pi$
$521$	1975.39			0.166110			0.0830550	+	0.996545i	$0.473532\pi$
$522$	986.503			0.0827166
$523$			14711.2i			1.22997i	0.788539	+	0.614985i	$0.210838\pi$
$523$			14711.2i			1.22997i	−0.788539	+	0.614985i	$0.789162\pi$
$524$		−	930.975i		−	0.0776142i
$525$	−1291.27			−0.107344
$526$			6316.61i			0.523607i
$527$	204.179			0.0168770
$528$	−123.813			−0.0102050
$529$	−1269.01			−0.104299
$530$	16363.5			1.34110
$531$			481.066i			0.0393154i
$532$			11122.1i			0.906398i
$533$			21547.5i			1.75108i
$534$	170.305			0.0138011
$535$		−	14722.9i		−	1.18977i
$536$		−	7590.05i		−	0.611642i
$537$			251.605i			0.0202189i
$538$			12967.0i			1.03912i
$539$	21637.0			1.72907
$540$			725.921i			0.0578494i
$541$		−	17460.0i		−	1.38755i	−0.720192	−	0.693774i	$-0.755946\pi$
$541$		−	17460.0i		−	1.38755i	0.720192	−	0.693774i	$-0.244054\pi$
$542$		−	9616.16i		−	0.762084i
$543$	−456.353			−0.0360663
$544$	−305.920			−0.0241107
$545$	−40537.9			−3.18615
$546$	560.701			0.0439483
$547$		−	2932.00i		−	0.229183i	−0.993413	−	0.114592i	$-0.963444\pi$
$547$		−	2932.00i		−	0.229183i	0.993413	−	0.114592i	$-0.0365559\pi$
$548$	−1408.62			−0.109805
$549$			14268.3i			1.10921i
$550$		−	24083.2i		−	1.86711i
$551$	−1776.75			−0.137372
$552$	157.899			0.0121750
$553$			12752.6i			0.980640i
$554$	15394.0			1.18056
$555$	−27.7908	+	756.272i	−0.00212550	+	0.0578414i
$556$	5997.23			0.457445
$557$			8807.15i			0.669966i	0.942224	+	0.334983i	$0.108731\pi$
$557$			8807.15i			0.669966i	−0.942224	+	0.334983i	$0.891269\pi$
$558$	−1152.08			−0.0874037
$559$	−24231.2			−1.83340
$560$			9042.85i			0.682375i
$561$		−	73.9780i		−	0.00556748i
$562$	4381.79			0.328888
$563$		−	22783.9i		−	1.70555i	−0.522276	−	0.852776i	$-0.674917\pi$
$563$		−	22783.9i		−	1.70555i	0.522276	−	0.852776i	$-0.325083\pi$
$564$	−27.1165			−0.00202449
$565$	−11838.0			−0.881469
$566$	992.238			0.0736871
$567$	−20796.8			−1.54036
$568$			1452.35i			0.107287i
$569$			16900.7i			1.24519i	0.782544	+	0.622595i	$0.213922\pi$
$569$			16900.7i			1.24519i	−0.782544	+	0.622595i	$0.786078\pi$
$570$		−	653.362i		−	0.0480111i
$571$	−17807.4			−1.30511			−0.652553	−	0.757743i	$-0.726302\pi$
$571$	−17807.4			−1.30511			−0.652553	+	0.757743i	$0.726302\pi$
$572$			10457.5i			0.764421i
$573$		−	511.030i		−	0.0372576i
$574$			21439.9i			1.55903i
$575$			30713.5i			2.22755i
$576$	1726.14			0.124866
$577$		−	14593.5i		−	1.05292i	−0.850200	−	0.526460i	$-0.823519\pi$
$577$		−	14593.5i		−	1.05292i	0.850200	−	0.526460i	$-0.176481\pi$
$578$			9643.21i			0.693953i
$579$			527.412i			0.0378558i
$580$	−1444.59			−0.103420
$581$	−20768.5			−1.48300
$582$	−77.1527			−0.00549499
$583$	18828.7			1.33758
$584$			3307.05i			0.234326i
$585$	30639.9			2.16548
$586$		−	2443.96i		−	0.172285i
$587$		−	19644.7i		−	1.38130i	−0.723190	−	0.690649i	$-0.757325\pi$
$587$		−	19644.7i		−	1.38130i	0.723190	−	0.690649i	$-0.242675\pi$
$588$	324.280			0.0227434
$589$	2074.96			0.145157
$590$		−	704.454i		−	0.0491558i
$591$	−207.889			−0.0144694
$592$	3598.57	+	132.237i	0.249831	+	0.00918056i
$593$	−7555.29			−0.523202			−0.261601	−	0.965176i	$-0.584250\pi$
$593$	−7555.29			−0.523202			−0.261601	+	0.965176i	$0.584250\pi$
$594$			835.286i			0.0576973i
$595$	−5403.10			−0.372278
$596$	9117.52			0.626625
$597$		−	405.202i		−	0.0277786i
$598$		−	13336.5i		−	0.911989i
$599$	863.101			0.0588737			0.0294368	−	0.999567i	$-0.490629\pi$
$599$	863.101			0.0588737			0.0294368	+	0.999567i	$0.490629\pi$
$600$		−	360.942i		−	0.0245590i
$601$	191.541			0.0130002			0.00650010	−	0.999979i	$-0.497931\pi$
$601$	191.541			0.0130002			0.00650010	+	0.999979i	$0.497931\pi$
$602$	−24110.1			−1.63232
$603$	−25588.9			−1.72813
$604$	1752.54			0.118062
$605$		−	14500.5i		−	0.974428i
$606$			457.511i			0.0306685i
$607$		−	16095.9i		−	1.07630i	−0.842849	−	0.538150i	$-0.819123\pi$
$607$		−	16095.9i		−	1.07630i	0.842849	−	0.538150i	$-0.180877\pi$
$608$	−3108.89			−0.207372
$609$			89.1243i			0.00593021i
$610$		−	20893.9i		−	1.38683i
$611$			2290.32i			0.151647i
$612$			1031.37i			0.0681221i
$613$	11780.5			0.776200			0.388100	−	0.921617i	$-0.373132\pi$
$613$	11780.5			0.776200			0.388100	+	0.921617i	$0.373132\pi$
$614$			1171.88i			0.0770251i
$615$		−	1259.48i		−	0.0825805i
$616$			10405.2i			0.680582i
$617$	10495.4			0.684813			0.342406	−	0.939552i	$-0.388758\pi$
$617$	10495.4			0.684813			0.342406	+	0.939552i	$0.388758\pi$
$618$	590.734			0.0384511
$619$	14647.6			0.951111			0.475555	−	0.879686i	$-0.342247\pi$
$619$	14647.6			0.951111			0.475555	+	0.879686i	$0.342247\pi$
$620$	1687.05			0.109280
$621$		−	1065.25i		−	0.0688355i
$622$	−4110.27			−0.264963
$623$		−	14312.4i		−	0.920409i
$624$			156.729i			0.0100548i
$625$	21462.1			1.37357
$626$	−1735.02			−0.110776
$627$		−	751.796i		−	0.0478849i
$628$	11640.2			0.739639
$629$	−79.0114	+	2150.14i	−0.00500857	+	0.136299i
$630$	30486.8			1.92798
$631$			10225.1i			0.645093i	0.946554	+	0.322546i	$0.104539\pi$
$631$			10225.1i			0.645093i	−0.946554	+	0.322546i	$0.895461\pi$
$632$	−3564.65			−0.224358
$633$	189.522			0.0119002
$634$		−	3640.41i		−	0.228043i
$635$		−	9918.02i		−	0.619818i
$636$	282.192			0.0175938
$637$		−	27389.4i		−	1.70362i
$638$	−1662.23			−0.103148
$639$	4896.42			0.303129
$640$	−2527.69			−0.156119
$641$	885.374			0.0545557			0.0272778	−	0.999628i	$-0.491316\pi$
$641$	885.374			0.0545557			0.0272778	+	0.999628i	$0.491316\pi$
$642$		−	253.901i		−	0.0156085i
$643$		−	22739.0i		−	1.39461i	−0.716773	−	0.697307i	$-0.754381\pi$
$643$		−	22739.0i		−	1.39461i	0.716773	−	0.697307i	$-0.245619\pi$
$644$		−	13269.8i		−	0.811965i
$645$	1416.34			0.0864626
$646$		−	1857.56i		−	0.113134i
$647$			20461.1i			1.24329i	0.783300	+	0.621644i	$0.213535\pi$
$647$			20461.1i			1.24329i	−0.783300	+	0.621644i	$0.786465\pi$
$648$		−	5813.22i		−	0.352415i
$649$		−	810.585i		−	0.0490266i
$650$	−30485.9			−1.83963
$651$		−	104.083i		−	0.00626625i
$652$			2665.04i			0.160078i
$653$			23158.6i			1.38785i	0.720047	+	0.693925i	$0.244120\pi$
$653$			23158.6i			1.38785i	−0.720047	+	0.693925i	$0.755880\pi$
$654$	−699.086			−0.0417988
$655$	4596.13			0.274177
$656$	−5992.96			−0.356686
$657$	11149.3			0.662064
$658$			2278.87i			0.135015i
$659$	−3371.50			−0.199294			−0.0996472	−	0.995023i	$-0.531771\pi$
$659$	−3371.50			−0.199294			−0.0996472	+	0.995023i	$0.531771\pi$
$660$		−	611.251i		−	0.0360499i
$661$			20921.3i			1.23108i	0.788106	+	0.615539i	$0.211062\pi$
$661$			20921.3i			1.23108i	−0.788106	+	0.615539i	$0.788938\pi$
$662$	−20585.8			−1.20859
$663$	−93.6458			−0.00548552
$664$		−	5805.30i		−	0.339291i
$665$	−54908.6			−3.20190
$666$	445.819	−	12132.1i	0.0259387	−	0.705871i
$667$	2119.86			0.123060
$668$			4674.71i			0.270763i
$669$	420.724			0.0243141
$670$	37471.3			2.16066
$671$		−	24041.7i		−	1.38319i
$672$			155.946i			0.00895202i
$673$	−794.186			−0.0454883			−0.0227441	−	0.999741i	$-0.507240\pi$
$673$	−794.186			−0.0454883			−0.0227441	+	0.999741i	$0.507240\pi$
$674$		−	8108.76i		−	0.463409i
$675$	−2435.05			−0.138852
$676$	4449.69			0.253169
$677$	19293.8			1.09530			0.547652	−	0.836706i	$-0.315522\pi$
$677$	19293.8			1.09530			0.547652	+	0.836706i	$0.315522\pi$
$678$	−204.150			−0.0115639
$679$			6483.92i			0.366466i
$680$		−	1510.30i		−	0.0851724i
$681$			584.153i			0.0328705i
$682$	1941.22			0.108993
$683$			13677.1i			0.766234i	0.923700	+	0.383117i	$0.125149\pi$
$683$			13677.1i			0.766234i	−0.923700	+	0.383117i	$0.874851\pi$
$684$			10481.2i			0.585907i
$685$		−	6954.23i		−	0.387894i
$686$		−	7619.18i		−	0.424055i
$687$	−889.696			−0.0494091
$688$		−	6739.36i		−	0.373453i
$689$		−	23834.5i		−	1.31789i
$690$			779.532i			0.0430091i
$691$	11698.2			0.644024			0.322012	−	0.946736i	$-0.395641\pi$
$691$	11698.2			0.644024			0.322012	+	0.946736i	$0.395641\pi$
$692$	−7188.48			−0.394892
$693$	35079.9			1.92291
$694$	−18711.1			−1.02343
$695$			29607.8i			1.61595i
$696$	−24.9124			−0.00135676
$697$		−	3580.79i		−	0.194594i
$698$			9194.71i			0.498603i
$699$	385.084			0.0208372
$700$	−30333.6			−1.63786
$701$		−	23282.6i		−	1.25445i	−0.778837	−	0.627226i	$-0.784190\pi$
$701$		−	23282.6i		−	1.25445i	0.778837	−	0.627226i	$-0.215810\pi$
$702$	1057.36			0.0568480
$703$	−802.948	+	21850.7i	−0.0430779	+	1.17228i
$704$	−2908.51			−0.155708
$705$		−	133.871i		−	0.00715162i
$706$	16667.4			0.888508
$707$	38449.3			2.04531
$708$		−	12.1485i		−	0.000644870i
$709$		−	7788.65i		−	0.412565i	−0.978492	−	0.206283i	$-0.933863\pi$
$709$		−	7788.65i		−	0.412565i	0.978492	−	0.206283i	$-0.0661366\pi$
$710$	−7170.11			−0.378999
$711$			12017.8i			0.633898i
$712$	4000.66			0.210578
$713$	−2475.65			−0.130033
$714$	−93.1779			−0.00488389
$715$	−51627.5			−2.70036
$716$			5910.52i			0.308501i
$717$		−	913.547i		−	0.0475830i
$718$			13898.8i			0.722419i
$719$	11457.2			0.594272			0.297136	−	0.954835i	$-0.403969\pi$
$719$	11457.2			0.594272			0.297136	+	0.954835i	$0.403969\pi$
$720$			8521.81i			0.441096i
$721$		−	49645.3i		−	2.56434i
$722$		−	5159.34i		−	0.265943i
$723$		−	373.049i		−	0.0191893i
$724$	−10720.3			−0.550300
$725$		−	4845.79i		−	0.248232i
$726$		−	250.065i		−	0.0127834i
$727$		−	22414.2i		−	1.14346i	−0.820441	−	0.571731i	$-0.806272\pi$
$727$		−	22414.2i		−	1.14346i	0.820441	−	0.571731i	$-0.193728\pi$
$728$	13171.6			0.670564
$729$	−19556.3			−0.993563
$730$	−16326.6			−0.827772
$731$	4026.77			0.203742
$732$		−	360.320i		−	0.0181937i
$733$	−8780.12			−0.442430			−0.221215	−	0.975225i	$-0.571002\pi$
$733$	−8780.12			−0.442430			−0.221215	+	0.975225i	$0.571002\pi$
$734$			5445.91i			0.273858i
$735$			1600.94i			0.0803423i
$736$	3709.24			0.185767
$737$	43116.7			2.15498
$738$			20204.5i			1.00778i
$739$	27297.7			1.35881			0.679405	−	0.733764i	$-0.262238\pi$
$739$	27297.7			1.35881			0.679405	+	0.733764i	$0.262238\pi$
$740$	−652.839	+	17765.8i	−0.0324309	+	0.882544i
$741$	−951.669			−0.0471801
$742$		−	23715.5i		−	1.17334i
$743$	27342.1			1.35004			0.675022	−	0.737797i	$-0.264134\pi$
$743$	27342.1			1.35004			0.675022	+	0.737797i	$0.264134\pi$
$744$	29.0937			0.00143364
$745$			45012.3i			2.21359i
$746$			20315.1i			0.997038i
$747$	−19571.8			−0.958629
$748$		−	1737.84i		−	0.0849486i
$749$	−21337.9			−1.04095
$750$	941.299			0.0458285
$751$	−18354.1			−0.891809			−0.445905	−	0.895080i	$-0.647118\pi$
$751$	−18354.1			−0.891809			−0.445905	+	0.895080i	$0.647118\pi$
$752$	−636.999			−0.0308896
$753$		−	90.5524i		−	0.00438236i
$754$			2104.15i			0.101630i
$755$			8652.10i			0.417062i
$756$	1052.07			0.0506131
$757$			28973.8i			1.39111i	0.718474	+	0.695554i	$0.244841\pi$
$757$			28973.8i			1.39111i	−0.718474	+	0.695554i	$0.755159\pi$
$758$			15856.4i			0.759803i
$759$			896.974i			0.0428961i
$760$		−	15348.3i		−	0.732554i
$761$	−25560.9			−1.21759			−0.608793	−	0.793329i	$-0.708346\pi$
$761$	−25560.9			−1.21759			−0.608793	+	0.793329i	$0.708346\pi$
$762$		−	171.039i		−	0.00813134i
$763$			58751.3i			2.78760i
$764$		−	12004.7i		−	0.568476i
$765$	−5091.78			−0.240645
$766$	5588.76			0.263616
$767$	−1026.09			−0.0483049
$768$	−43.5907			−0.00204811
$769$			5429.73i			0.254618i	0.991863	+	0.127309i	$0.0406339\pi$
$769$			5429.73i			0.254618i	−0.991863	+	0.127309i	$0.959366\pi$
$770$	−51369.6			−2.40420
$771$		−	1049.29i		−	0.0490131i
$772$			12389.6i			0.577604i
$773$	28802.3			1.34016			0.670081	−	0.742288i	$-0.266259\pi$
$773$	28802.3			1.34016			0.670081	+	0.742288i	$0.266259\pi$
$774$	−22720.9			−1.05515
$775$			5659.10i			0.262298i
$776$	−1812.41			−0.0838425
$777$	1096.06	+	40.2770i	0.0506061	+	0.00185962i
$778$	21526.1			0.991963
$779$		−	36389.5i		−	1.67367i
$780$	−773.758			−0.0355192
$781$	−8250.35			−0.378003
$782$			2216.27i			0.101347i
$783$			168.068i			0.00767085i
$784$	7617.74			0.347018
$785$			57466.4i			2.61282i
$786$	79.2615			0.00359690
$787$	1078.24			0.0488375			0.0244187	−	0.999702i	$-0.492227\pi$
$787$	1078.24			0.0488375			0.0244187	+	0.999702i	$0.492227\pi$
$788$	−4883.57			−0.220774
$789$	−537.785			−0.0242657
$790$		−	17598.3i		−	0.792557i
$791$			17156.8i			0.771208i
$792$			9805.68i			0.439937i
$793$	−30433.4			−1.36283
$794$		−	20074.9i		−	0.897268i
$795$			1393.16i			0.0621511i
$796$		−	9518.69i		−	0.423845i
$797$		−	26951.2i		−	1.19782i	−0.800817	−	0.598909i	$-0.795601\pi$
$797$		−	26951.2i		−	1.19782i	0.800817	−	0.598909i	$-0.204399\pi$
$798$	−946.914			−0.0420055
$799$		−	380.607i		−	0.0168522i
$800$		−	8478.98i		−	0.374721i
$801$		−	13487.7i		−	0.594964i
$802$	−8352.68			−0.367760
$803$	−18786.3			−0.825597
$804$	646.203			0.0283455
$805$	65511.9			2.86831
$806$		−	2457.31i		−	0.107388i
$807$	−1103.99			−0.0481564
$808$			10747.5i			0.467941i
$809$		−	14227.9i		−	0.618326i	−0.951009	−	0.309163i	$-0.899951\pi$
$809$		−	14227.9i		−	0.618326i	0.951009	−	0.309163i	$-0.100049\pi$
$810$	28699.3			1.24493
$811$	15281.1			0.661642			0.330821	−	0.943693i	$-0.392674\pi$
$811$	15281.1			0.661642			0.330821	+	0.943693i	$0.392674\pi$
$812$			2093.64i			0.0904832i
$813$	818.702			0.0353175
$814$	−751.195	+	20442.3i	−0.0323457	+	0.880225i
$815$	−13157.0			−0.565485
$816$		−	26.0455i		−	0.00111737i
$817$	40921.8			1.75235
$818$	21807.0			0.932109
$819$		−	44406.3i		−	1.89460i
$820$		−	29586.6i		−	1.26001i
$821$	40307.9			1.71347			0.856733	−	0.515760i	$-0.172490\pi$
$821$	40307.9			1.71347			0.856733	+	0.515760i	$0.172490\pi$
$822$		−	119.928i		−	0.00508875i
$823$	−34170.4			−1.44727			−0.723637	−	0.690181i	$-0.757531\pi$
$823$	−34170.4			−1.44727			−0.723637	+	0.690181i	$0.757531\pi$
$824$	13877.1			0.586687
$825$	2050.40			0.0865282
$826$	−1020.96			−0.0430069
$827$			16438.5i			0.691202i	0.938382	+	0.345601i	$0.112325\pi$
$827$			16438.5i			0.691202i	−0.938382	+	0.345601i	$0.887675\pi$
$828$		−	12505.2i		−	0.524864i
$829$			1725.02i			0.0722707i	0.999347	+	0.0361354i	$0.0115047\pi$
$829$			1725.02i			0.0722707i	−0.999347	+	0.0361354i	$0.988495\pi$
$830$	28660.2			1.19857
$831$			1310.62i			0.0547111i
$832$			3681.77i			0.153416i
$833$			4551.60i			0.189320i
$834$			510.593i			0.0211995i
$835$	−23078.6			−0.956488
$836$		−	17660.6i		−	0.730628i
$837$		−	196.277i		−	0.00810552i
$838$			26105.5i			1.07613i
$839$	−12599.9			−0.518471			−0.259235	−	0.965814i	$-0.583471\pi$
$839$	−12599.9			−0.518471			−0.259235	+	0.965814i	$0.583471\pi$
$840$	−769.892			−0.0316236
$841$	24054.5			0.986286
$842$	14212.5			0.581703
$843$			373.058i			0.0152417i
$844$	4452.10			0.181573
$845$			21967.7i			0.894334i
$846$			2147.56i			0.0872752i
$847$	−21015.5			−0.852539
$848$	6629.04			0.268446
$849$			84.4773i			0.00341491i
$850$	5066.19			0.204434
$851$	958.003	−	26070.2i	0.0385898	−	1.05015i
$852$	−123.650			−0.00497206
$853$			12248.3i			0.491644i	0.969315	+	0.245822i	$0.0790578\pi$
$853$			12248.3i			0.491644i	−0.969315	+	0.245822i	$0.920942\pi$
$854$	−30281.3			−1.21336
$855$	−51744.8			−2.06975
$856$		−	5964.45i		−	0.238155i
$857$			45763.1i			1.82408i	0.410099	+	0.912041i	$0.365494\pi$
$857$			45763.1i			1.82408i	−0.410099	+	0.912041i	$0.634506\pi$
$858$	−890.330			−0.0354258
$859$			16767.3i			0.665998i	0.942927	+	0.332999i	$0.108061\pi$
$859$			16767.3i			0.665998i	−0.942927	+	0.332999i	$0.891939\pi$
$860$	33271.6			1.31925
$861$	−1825.35			−0.0722506
$862$	−15857.4			−0.626573
$863$	14337.5			0.565533			0.282767	−	0.959189i	$-0.408748\pi$
$863$	14337.5			0.565533			0.282767	+	0.959189i	$0.408748\pi$
$864$			294.079i			0.0115796i
$865$		−	35488.8i		−	1.39498i
$866$			15347.7i			0.602237i
$867$	−821.005			−0.0321601
$868$		−	2445.03i		−	0.0956104i
$869$		−	20249.6i		−	0.790474i
$870$		−	122.990i		−	0.00479282i
$871$		−	54579.7i		−	2.12326i
$872$	−16422.4			−0.637767
$873$			6110.32i			0.236888i
$874$			22522.7i			0.871673i
$875$		−	79106.9i		−	3.05634i
$876$	−281.556			−0.0108595
$877$	−38199.4			−1.47081			−0.735405	−	0.677628i	$-0.763008\pi$
$877$	−38199.4			−1.47081			−0.735405	+	0.677628i	$0.763008\pi$
$878$	20743.8			0.797346
$879$	208.074			0.00798426
$880$		−	14359.0i		−	0.550049i
$881$	−11175.1			−0.427354			−0.213677	−	0.976904i	$-0.568544\pi$
$881$	−11175.1			−0.427354			−0.213677	+	0.976904i	$0.568544\pi$
$882$		−	25682.3i		−	0.980462i
$883$			24538.0i			0.935186i	0.883944	+	0.467593i	$0.154879\pi$
$883$			24538.0i			0.935186i	−0.883944	+	0.467593i	$0.845121\pi$
$884$	−2199.86			−0.0836981
$885$	59.9759			0.00227804
$886$		−	25766.3i		−	0.977017i
$887$	−44044.3			−1.66726			−0.833631	−	0.552322i	$-0.813742\pi$
$887$	−44044.3			−1.66726			−0.833631	+	0.552322i	$0.813742\pi$
$888$	−11.2584	+	306.375i	−0.000425458	+	0.0115780i
$889$	−14374.1			−0.542286
$890$			19750.9i			0.743878i
$891$	33023.1			1.24165
$892$	9883.33			0.370985
$893$		−	3867.89i		−	0.144943i
$894$			776.249i			0.0290399i
$895$	−29179.7			−1.08980
$896$			3663.37i			0.136590i
$897$	1135.44			0.0422646
$898$	4113.08			0.152846
$899$	390.594			0.0144906
$900$	−28585.8			−1.05873
$901$			3960.85i			0.146454i
$902$		−	34044.1i		−	1.25670i
$903$		−	2052.69i		−	0.0756471i
$904$	−4795.73			−0.176442
$905$		−	52925.1i		−	1.94397i
$906$			149.208i			0.00547141i
$907$			2427.89i			0.0888829i	0.999012	+	0.0444414i	$0.0141508\pi$
$907$			2427.89i			0.0888829i	−0.999012	+	0.0444414i	$0.985849\pi$
$908$			13722.5i			0.501538i
$909$	36233.9			1.32211
$910$			65026.7i			2.36881i
$911$		−	36764.7i		−	1.33707i	−0.743681	−	0.668534i	$-0.766922\pi$
$911$		−	36764.7i		−	1.33707i	0.743681	−	0.668534i	$-0.233078\pi$
$912$		−	264.685i		−	0.00961031i
$913$	32978.1			1.19542
$914$	6973.58			0.252369
$915$	1778.87			0.0642705
$916$	−20900.1			−0.753884
$917$		−	6661.15i		−	0.239881i
$918$	−175.713			−0.00631740
$919$			33872.6i			1.21584i	0.793999	+	0.607919i	$0.207996\pi$
$919$			33872.6i			1.21584i	−0.793999	+	0.607919i	$0.792004\pi$
$920$			18312.2i			0.656233i
$921$	−99.7721			−0.00356960
$922$	−9861.42			−0.352243
$923$			10443.8i			0.372439i
$924$	−885.882			−0.0315404
$925$	−59594.1	−	2189.91i	−2.11831	−	0.0778418i
$926$	12991.1			0.461031
$927$		−	46784.8i		−	1.65762i
$928$	−585.223			−0.0207014
$929$	−7850.45			−0.277250			−0.138625	−	0.990345i	$-0.544268\pi$
$929$	−7850.45			−0.277250			−0.138625	+	0.990345i	$0.544268\pi$
$930$			143.633i			0.00506441i
$931$			46255.3i			1.62831i
$932$	9046.10			0.317934
$933$		−	349.941i		−	0.0122793i
$934$	−12374.7			−0.433527
$935$	8579.52			0.300086
$936$	12412.6			0.433461
$937$	18844.3			0.657007			0.328503	−	0.944503i	$-0.393456\pi$
$937$	18844.3			0.657007			0.328503	+	0.944503i	$0.393456\pi$
$938$		−	54307.0i		−	1.89039i
$939$		−	147.717i		−	0.00513371i
$940$		−	3144.80i		−	0.109119i
$941$	−14147.2			−0.490103			−0.245052	−	0.969510i	$-0.578805\pi$
$941$	−14147.2			−0.490103			−0.245052	+	0.969510i	$0.578805\pi$
$942$			991.022i			0.0342773i
$943$			43416.7i			1.49930i
$944$		−	285.383i		−	0.00983943i
$945$			5193.98i			0.178794i
$946$	38284.2			1.31578
$947$			37830.8i			1.29814i	0.760730	+	0.649068i	$0.224841\pi$
$947$			37830.8i			1.29814i	−0.760730	+	0.649068i	$0.775159\pi$
$948$		−	303.487i		−	0.0103975i
$949$			23780.8i			0.813444i
$950$	51484.8			1.75830
$951$	309.938			0.0105683
$952$	−2188.86			−0.0745184
$953$	−16506.8			−0.561078			−0.280539	−	0.959843i	$-0.590513\pi$
$953$	−16506.8			−0.561078			−0.280539	+	0.959843i	$0.590513\pi$
$954$		−	22349.0i		−	0.758465i
$955$	59266.2			2.00818
$956$		−	21460.3i		−	0.726022i
$957$		−	141.519i		−	0.00478022i
$958$	−18247.7			−0.615402
$959$	−10078.7			−0.339373
$960$		−	215.203i		−	0.00723506i
$961$	29334.8			0.984688
$962$	25877.1	+	950.907i	0.867268	+	0.0318695i
$963$	−20108.4			−0.672880
$964$		−	8763.38i		−	0.292790i
$965$	−61166.1			−2.04042
$966$	1129.77			0.0376292
$967$		−	29769.3i		−	0.989984i	−0.868897	−	0.494992i	$-0.835171\pi$
$967$		−	29769.3i		−	0.989984i	0.868897	−	0.494992i	$-0.164829\pi$
$968$		−	5874.33i		−	0.195050i
$969$	158.149			0.00524302
$970$		−	8947.70i		−	0.296179i
$971$	−53829.6			−1.77907			−0.889533	−	0.456871i	$-0.848970\pi$
$971$	−53829.6			−1.77907			−0.889533	+	0.456871i	$0.848970\pi$
$972$	1487.44			0.0490842
$973$	42910.3			1.41381
$974$	33471.0			1.10111
$975$		−	2595.52i		−	0.0852544i
$976$		−	8464.36i		−	0.277600i
$977$		−	54436.1i		−	1.78256i	−0.453450	−	0.891282i	$-0.649807\pi$
$977$		−	54436.1i		−	1.78256i	0.453450	−	0.891282i	$-0.350193\pi$
$978$	−226.896			−0.00741855
$979$			22726.5i			0.741923i
$980$			37608.1i			1.22586i
$981$			55366.1i			1.80194i
$982$			3303.58i			0.107354i
$983$	14101.9			0.457558			0.228779	−	0.973478i	$-0.426527\pi$
$983$	14101.9			0.457558			0.228779	+	0.973478i	$0.426527\pi$
$984$		−	510.229i		−	0.0165300i
$985$		−	24109.7i		−	0.779897i
$986$		−	349.671i		−	0.0112939i
$987$	−194.019			−0.00625703
$988$	−22355.9			−0.719873
$989$	−48824.1			−1.56978
$990$	−48409.7			−1.55410
$991$		−	22799.7i		−	0.730833i	−0.930844	−	0.365416i	$-0.880927\pi$
$991$		−	22799.7i		−	0.730833i	0.930844	−	0.365416i	$-0.119073\pi$
$992$	683.446			0.0218744
$993$		−	1752.63i		−	0.0560102i
$994$			10391.6i			0.331591i
$995$	46992.8			1.49726
$996$	494.252			0.0157239
$997$			23339.7i			0.741401i	0.928753	+	0.370700i	$0.120882\pi$
$997$			23339.7i			0.741401i	−0.928753	+	0.370700i	$0.879118\pi$
$998$	−19569.0			−0.620687
$999$	2066.92	+	75.9533i	0.0654600	+	0.00240546i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.b.a.73.8	yes	10
3.2	odd	2		666.4.c.d.73.5		10
4.3	odd	2		592.4.g.d.369.5		10
37.36	even	2	inner	74.4.b.a.73.3	✓	10
111.110	odd	2		666.4.c.d.73.6		10
148.147	odd	2		592.4.g.d.369.6		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.b.a.73.3	✓	10	37.36	even	2	inner
74.4.b.a.73.8	yes	10	1.1	even	1	trivial
592.4.g.d.369.5		10	4.3	odd	2
592.4.g.d.369.6		10	148.147	odd	2
666.4.c.d.73.5		10	3.2	odd	2
666.4.c.d.73.6		10	111.110	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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.b (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+2.00000i q^{2} -0.170276 q^{3} -4.00000 q^{4} -19.7476i q^{5} -0.340553i q^{6} -28.6201 q^{7} -8.00000i q^{8} -26.9710 q^{9} +O(q^{10})\)	\(q+2.00000i q^{2} -0.170276 q^{3} -4.00000 q^{4} -19.7476i q^{5} -0.340553i q^{6} -28.6201 q^{7} -8.00000i q^{8} -26.9710 q^{9} +39.4952 q^{10} +45.4455 q^{11} +0.681105 q^{12} -57.5276i q^{13} -57.2402i q^{14} +3.36255i q^{15} +16.0000 q^{16} +9.56000i q^{17} -53.9420i q^{18} +97.1528i q^{19} +78.9904i q^{20} +4.87332 q^{21} +90.8910i q^{22} -115.914i q^{23} +1.36221i q^{24} -264.968 q^{25} +115.055 q^{26} +9.18998 q^{27} +114.480 q^{28} +18.2882i q^{29} -6.72510 q^{30} -21.3577i q^{31} +32.0000i q^{32} -7.73829 q^{33} -19.1200 q^{34} +565.178i q^{35} +107.884 q^{36} +(224.910 + 8.26479i) q^{37} -194.306 q^{38} +9.79559i q^{39} -157.981 q^{40} -374.560 q^{41} +9.74664i q^{42} -421.210i q^{43} -181.782 q^{44} +532.613i q^{45} +231.828 q^{46} -39.8125 q^{47} -2.72442 q^{48} +476.109 q^{49} -529.936i q^{50} -1.62784i q^{51} +230.110i q^{52} +414.315 q^{53} +18.3800i q^{54} -897.439i q^{55} +228.961i q^{56} -16.5428i q^{57} -36.5764 q^{58} -17.8364i q^{59} -13.4502i q^{60} -529.023i q^{61} +42.7154 q^{62} +771.912 q^{63} -64.0000 q^{64} -1136.03 q^{65} -15.4766i q^{66} +948.756 q^{67} -38.2400i q^{68} +19.7374i q^{69} -1130.36 q^{70} -181.544 q^{71} +215.768i q^{72} -413.381 q^{73} +(-16.5296 + 449.821i) q^{74} +45.1178 q^{75} -388.611i q^{76} -1300.65 q^{77} -19.5912 q^{78} -445.581i q^{79} -315.962i q^{80} +726.652 q^{81} -749.120i q^{82} +725.662 q^{83} -19.4933 q^{84} +188.787 q^{85} +842.420 q^{86} -3.11405i q^{87} -363.564i q^{88} +500.083i q^{89} -1065.23 q^{90} +1646.44i q^{91} +463.655i q^{92} +3.63671i q^{93} -79.6249i q^{94} +1918.54 q^{95} -5.44884i q^{96} -226.552i q^{97} +952.218i q^{98} -1225.71 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9}+O(q^{10}) \) 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9	\( 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9} + 76 q^{10} - 50 q^{11} - 56 q^{12} + 160 q^{16} - 312 q^{21} - 700 q^{25} + 492 q^{26} + 848 q^{27} + 16 q^{28} - 240 q^{30} - 508 q^{33} - 568 q^{34} - 688 q^{36} + 82 q^{37} + 336 q^{38} - 304 q^{40} - 1194 q^{41} + 200 q^{44} + 60 q^{46} + 464 q^{47} + 224 q^{48} + 2382 q^{49} - 692 q^{53} + 1108 q^{58} - 1700 q^{62} + 2300 q^{63} - 640 q^{64} + 604 q^{65} + 1114 q^{67} + 1880 q^{70} - 1460 q^{71} + 2082 q^{73} + 968 q^{74} - 5160 q^{75} - 6096 q^{77} + 1004 q^{78} + 4978 q^{81} - 1364 q^{83} + 1248 q^{84} + 104 q^{85} + 1400 q^{86} - 2600 q^{90} + 5084 q^{95} + 508 q^{99}+O(q^{100}) \) 10 * q + 14 * q^3 - 40 * q^4 - 4 * q^7 + 172 * q^9 + 76 * q^10 - 50 * q^11 - 56 * q^12 + 160 * q^16 - 312 * q^21 - 700 * q^25 + 492 * q^26 + 848 * q^27 + 16 * q^28 - 240 * q^30 - 508 * q^33 - 568 * q^34 - 688 * q^36 + 82 * q^37 + 336 * q^38 - 304 * q^40 - 1194 * q^41 + 200 * q^44 + 60 * q^46 + 464 * q^47 + 224 * q^48 + 2382 * q^49 - 692 * q^53 + 1108 * q^58 - 1700 * q^62 + 2300 * q^63 - 640 * q^64 + 604 * q^65 + 1114 * q^67 + 1880 * q^70 - 1460 * q^71 + 2082 * q^73 + 968 * q^74 - 5160 * q^75 - 6096 * q^77 + 1004 * q^78 + 4978 * q^81 - 1364 * q^83 + 1248 * q^84 + 104 * q^85 + 1400 * q^86 - 2600 * q^90 + 5084 * q^95 + 508 * q^99

Introduction

L-functions

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