LMFDB - Embedded newform 74.4.b.a.73.2

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			73.2
Root			$2.87017i$ of defining polynomial
Character	$\chi$	$=$	74.73
Dual form			74.4.b.a.73.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000i q^{2} -1.87017 q^{3} -4.00000 q^{4} -8.73820i q^{5} +3.74034i q^{6} -6.27788 q^{7} +8.00000i q^{8} -23.5025 q^{9} +O(q^{10})$	\(q-2.00000i q^{2} -1.87017 q^{3} -4.00000 q^{4} -8.73820i q^{5} +3.74034i q^{6} -6.27788 q^{7} +8.00000i q^{8} -23.5025 q^{9} -17.4764 q^{10} -45.9424 q^{11} +7.48068 q^{12} -7.07441i q^{13} +12.5558i q^{14} +16.3419i q^{15} +16.0000 q^{16} -36.5208i q^{17} +47.0049i q^{18} +20.9149i q^{19} +34.9528i q^{20} +11.7407 q^{21} +91.8849i q^{22} -89.2425i q^{23} -14.9614i q^{24} +48.6438 q^{25} -14.1488 q^{26} +94.4482 q^{27} +25.1115 q^{28} -223.519i q^{29} +32.6838 q^{30} +18.0335i q^{31} -32.0000i q^{32} +85.9201 q^{33} -73.0415 q^{34} +54.8573i q^{35} +94.0099 q^{36} +(27.9412 - 223.321i) q^{37} +41.8299 q^{38} +13.2303i q^{39} +69.9056 q^{40} +101.923 q^{41} -23.4814i q^{42} +255.483i q^{43} +183.770 q^{44} +205.369i q^{45} -178.485 q^{46} +288.961 q^{47} -29.9227 q^{48} -303.588 q^{49} -97.2877i q^{50} +68.3000i q^{51} +28.2976i q^{52} -368.204 q^{53} -188.896i q^{54} +401.454i q^{55} -50.2230i q^{56} -39.1145i q^{57} -447.038 q^{58} +211.424i q^{59} -65.3677i q^{60} -178.069i q^{61} +36.0670 q^{62} +147.546 q^{63} -64.0000 q^{64} -61.8176 q^{65} -171.840i q^{66} -773.700 q^{67} +146.083i q^{68} +166.899i q^{69} +109.715 q^{70} +288.933 q^{71} -188.020i q^{72} -442.850 q^{73} +(-446.642 - 55.8824i) q^{74} -90.9722 q^{75} -83.6598i q^{76} +288.421 q^{77} +26.4607 q^{78} +299.069i q^{79} -139.811i q^{80} +457.933 q^{81} -203.846i q^{82} -490.299 q^{83} -46.9628 q^{84} -319.126 q^{85} +510.965 q^{86} +418.019i q^{87} -367.540i q^{88} -1442.74i q^{89} +410.739 q^{90} +44.4122i q^{91} +356.970i q^{92} -33.7257i q^{93} -577.922i q^{94} +182.759 q^{95} +59.8454i q^{96} +306.817i q^{97} +607.177i q^{98} +1079.76 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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
$3$	−1.87017			−0.359914			−0.179957	−	0.983674i	$-0.557596\pi$
$3$	−1.87017			−0.359914			−0.179957	+	0.983674i	$0.557596\pi$
$4$	−4.00000			−0.500000
$5$		−	8.73820i		−	0.781568i	−0.920482	−	0.390784i	$-0.872204\pi$
$5$		−	8.73820i		−	0.781568i	0.920482	−	0.390784i	$-0.127796\pi$
$6$			3.74034i			0.254498i
$7$	−6.27788			−0.338973			−0.169487	−	0.985532i	$-0.554211\pi$
$7$	−6.27788			−0.338973			−0.169487	+	0.985532i	$0.554211\pi$
$8$			8.00000i			0.353553i
$9$	−23.5025			−0.870462
$10$	−17.4764			−0.552652
$11$	−45.9424			−1.25929			−0.629644	−	0.776884i	$-0.716799\pi$
$11$	−45.9424			−1.25929			−0.629644	+	0.776884i	$0.716799\pi$
$12$	7.48068			0.179957
$13$		−	7.07441i		−	0.150930i	−0.997148	−	0.0754649i	$-0.975956\pi$
$13$		−	7.07441i		−	0.150930i	0.997148	−	0.0754649i	$-0.0240441\pi$
$14$			12.5558i			0.239690i
$15$			16.3419i			0.281298i
$16$	16.0000			0.250000
$17$		−	36.5208i		−	0.521034i	−0.965469	−	0.260517i	$-0.916107\pi$
$17$		−	36.5208i		−	0.521034i	0.965469	−	0.260517i	$-0.0838931\pi$
$18$			47.0049i			0.615509i
$19$			20.9149i			0.252538i	0.991996	+	0.126269i	$0.0403002\pi$
$19$			20.9149i			0.252538i	−0.991996	+	0.126269i	$0.959700\pi$
$20$			34.9528i			0.390784i
$21$	11.7407			0.122001
$22$			91.8849i			0.890451i
$23$		−	89.2425i		−	0.809059i	−0.914525	−	0.404529i	$-0.867435\pi$
$23$		−	89.2425i		−	0.809059i	0.914525	−	0.404529i	$-0.132565\pi$
$24$		−	14.9614i		−	0.127249i
$25$	48.6438			0.389151
$26$	−14.1488			−0.106723
$27$	94.4482			0.673206
$28$	25.1115			0.169487
$29$		−	223.519i		−	1.43126i	−0.698481	−	0.715629i	$-0.746140\pi$
$29$		−	223.519i		−	1.43126i	0.698481	−	0.715629i	$-0.253860\pi$
$30$	32.6838			0.198907
$31$			18.0335i			0.104481i	0.998635	+	0.0522406i	$0.0166363\pi$
$31$			18.0335i			0.104481i	−0.998635	+	0.0522406i	$0.983364\pi$
$32$		−	32.0000i		−	0.176777i
$33$	85.9201			0.453236
$34$	−73.0415			−0.368427
$35$			54.8573i			0.264931i
$36$	94.0099			0.435231
$37$	27.9412	−	223.321i	0.124149	−	0.992264i
$37$	27.9412	−	223.321i	0.124149	−	0.992264i
$38$	41.8299			0.178571
$39$			13.2303i			0.0543218i
$40$	69.9056			0.276326
$41$	101.923			0.388237			0.194119	−	0.980978i	$-0.437815\pi$
$41$	101.923			0.388237			0.194119	+	0.980978i	$0.437815\pi$
$42$		−	23.4814i		−	0.0862680i
$43$			255.483i			0.906064i	0.891494	+	0.453032i	$0.149658\pi$
$43$			255.483i			0.906064i	−0.891494	+	0.453032i	$0.850342\pi$
$44$	183.770			0.629644
$45$			205.369i			0.680325i
$46$	−178.485			−0.572091
$47$	288.961			0.896793			0.448397	−	0.893835i	$-0.351995\pi$
$47$	288.961			0.896793			0.448397	+	0.893835i	$0.351995\pi$
$48$	−29.9227			−0.0899786
$49$	−303.588			−0.885097
$50$		−	97.2877i		−	0.275171i
$51$			68.3000i			0.187528i
$52$			28.2976i			0.0754649i
$53$	−368.204			−0.954279			−0.477139	−	0.878828i	$-0.658326\pi$
$53$	−368.204			−0.954279			−0.477139	+	0.878828i	$0.658326\pi$
$54$		−	188.896i		−	0.476028i
$55$			401.454i			0.984220i
$56$		−	50.2230i		−	0.119845i
$57$		−	39.1145i		−	0.0908919i
$58$	−447.038			−1.01205
$59$			211.424i			0.466527i	0.972414	+	0.233263i	$0.0749404\pi$
$59$			211.424i			0.466527i	−0.972414	+	0.233263i	$0.925060\pi$
$60$		−	65.3677i		−	0.140649i
$61$		−	178.069i		−	0.373760i	−0.982383	−	0.186880i	$-0.940162\pi$
$61$		−	178.069i		−	0.373760i	0.982383	−	0.186880i	$-0.0598376\pi$
$62$	36.0670			0.0738793
$63$	147.546			0.295063
$64$	−64.0000			−0.125000
$65$	−61.8176			−0.117962
$66$		−	171.840i		−	0.320486i
$67$	−773.700			−1.41078			−0.705392	−	0.708818i	$-0.749229\pi$
$67$	−773.700			−1.41078			−0.705392	+	0.708818i	$0.749229\pi$
$68$			146.083i			0.260517i
$69$			166.899i			0.291192i
$70$	109.715			0.187334
$71$	288.933			0.482958			0.241479	−	0.970406i	$-0.422367\pi$
$71$	288.933			0.482958			0.241479	+	0.970406i	$0.422367\pi$
$72$		−	188.020i		−	0.307755i
$73$	−442.850			−0.710023			−0.355012	−	0.934862i	$-0.615523\pi$
$73$	−442.850			−0.710023			−0.355012	+	0.934862i	$0.615523\pi$
$74$	−446.642	−	55.8824i	−0.701636	−	0.0877865i
$75$	−90.9722			−0.140061
$76$		−	83.6598i		−	0.126269i
$77$	288.421			0.426865
$78$	26.4607			0.0384113
$79$			299.069i			0.425923i	0.977061	+	0.212961i	$0.0683109\pi$
$79$			299.069i			0.425923i	−0.977061	+	0.212961i	$0.931689\pi$
$80$		−	139.811i		−	0.195392i
$81$	457.933			0.628165
$82$		−	203.846i		−	0.274525i
$83$	−490.299			−0.648401			−0.324201	−	0.945988i	$-0.605095\pi$
$83$	−490.299			−0.648401			−0.324201	+	0.945988i	$0.605095\pi$
$84$	−46.9628			−0.0610007
$85$	−319.126			−0.407224
$86$	510.965			0.640684
$87$			418.019i			0.515130i
$88$		−	367.540i		−	0.445225i
$89$		−	1442.74i		−	1.71832i	−0.511711	−	0.859158i	$-0.670988\pi$
$89$		−	1442.74i		−	1.71832i	0.511711	−	0.859158i	$-0.329012\pi$
$90$	410.739			0.481063
$91$			44.4122i			0.0511612i
$92$			356.970i			0.404529i
$93$		−	33.7257i		−	0.0376042i
$94$		−	577.922i		−	0.634129i
$95$	182.759			0.197375
$96$			59.8454i			0.0636245i
$97$			306.817i			0.321160i	0.987023	+	0.160580i	$0.0513365\pi$
$97$			306.817i			0.321160i	−0.987023	+	0.160580i	$0.948664\pi$
$98$			607.177i			0.625858i
$99$	1079.76			1.09616
$100$	−194.575			−0.194575
$101$	1246.42			1.22796			0.613978	−	0.789323i	$-0.289568\pi$
$101$	1246.42			1.22796			0.613978	+	0.789323i	$0.289568\pi$
$102$	136.600			0.132602
$103$			1243.91i			1.18996i	0.803740	+	0.594981i	$0.202841\pi$
$103$			1243.91i			1.18996i	−0.803740	+	0.594981i	$0.797159\pi$
$104$	56.5952			0.0533617
$105$		−	102.593i		−	0.0953524i
$106$			736.409i			0.674777i
$107$	1236.67			1.11733			0.558663	−	0.829395i	$-0.311315\pi$
$107$	1236.67			1.11733			0.558663	+	0.829395i	$0.311315\pi$
$108$	−377.793			−0.336603
$109$		−	995.377i		−	0.874677i	−0.899297	−	0.437339i	$-0.855921\pi$
$109$		−	995.377i		−	0.874677i	0.899297	−	0.437339i	$-0.144079\pi$
$110$	802.909			0.695948
$111$	−52.2548	+	417.648i	−0.0446829	+	0.357130i
$112$	−100.446			−0.0847434
$113$			125.320i			0.104329i	0.998639	+	0.0521643i	$0.0166119\pi$
$113$			125.320i			0.104329i	−0.998639	+	0.0521643i	$0.983388\pi$
$114$	−78.2290			−0.0642703
$115$	−779.819			−0.632335
$116$			894.077i			0.715629i
$117$			166.266i			0.131379i
$118$	422.848			0.329884
$119$			229.273i			0.176617i
$120$	−130.735			−0.0994537
$121$	779.708			0.585806
$122$	−356.138			−0.264289
$123$	−190.614			−0.139732
$124$		−	72.1341i		−	0.0522406i
$125$		−	1517.33i		−	1.08572i
$126$		−	295.091i		−	0.208641i
$127$	−578.771			−0.404390			−0.202195	−	0.979345i	$-0.564808\pi$
$127$	−578.771			−0.404390			−0.202195	+	0.979345i	$0.564808\pi$
$128$			128.000i			0.0883883i
$129$		−	477.796i		−	0.326105i
$130$			123.635i			0.0834117i
$131$		−	2166.85i		−	1.44518i	−0.691276	−	0.722590i	$-0.742951\pi$
$131$		−	2166.85i		−	1.44518i	0.691276	−	0.722590i	$-0.257049\pi$
$132$	−343.681			−0.226618
$133$		−	131.301i		−	0.0856036i
$134$			1547.40i			0.997574i
$135$		−	825.307i		−	0.526156i
$136$	292.166			0.184213
$137$	246.075			0.153457			0.0767285	−	0.997052i	$-0.475553\pi$
$137$	246.075			0.153457			0.0767285	+	0.997052i	$0.475553\pi$
$138$	333.797			0.205904
$139$	−1790.47			−1.09256			−0.546280	−	0.837602i	$-0.683957\pi$
$139$	−1790.47			−1.09256			−0.546280	+	0.837602i	$0.683957\pi$
$140$		−	219.429i		−	0.132465i
$141$	−540.406			−0.322769
$142$		−	577.866i		−	0.341503i
$143$			325.015i			0.190064i
$144$	−376.039			−0.217615
$145$	−1953.16			−1.11863
$146$			885.701i			0.502062i
$147$	567.761			0.318559
$148$	−111.765	+	893.284i	−0.0620744	+	0.496132i
$149$	−1863.40			−1.02453			−0.512266	−	0.858827i	$-0.671194\pi$
$149$	−1863.40			−1.02453			−0.512266	+	0.858827i	$0.671194\pi$
$150$			181.944i			0.0990380i
$151$	38.9881			0.0210119			0.0105060	−	0.999945i	$-0.496656\pi$
$151$	38.9881			0.0210119			0.0105060	+	0.999945i	$0.496656\pi$
$152$	−167.320			−0.0892856
$153$			858.328i			0.453541i
$154$		−	576.842i		−	0.301839i
$155$	157.580			0.0816592
$156$		−	52.9214i		−	0.0271609i
$157$	−661.549			−0.336289			−0.168144	−	0.985762i	$-0.553777\pi$
$157$	−661.549			−0.336289			−0.168144	+	0.985762i	$0.553777\pi$
$158$	598.138			0.301173
$159$	688.605			0.343458
$160$	−279.622			−0.138163
$161$			560.253i			0.274249i
$162$		−	915.865i		−	0.444180i
$163$		−	2383.89i		−	1.14552i	−0.819722	−	0.572762i	$-0.805872\pi$
$163$		−	2383.89i		−	1.14552i	0.819722	−	0.572762i	$-0.194128\pi$
$164$	−407.693			−0.194119
$165$		−	750.787i		−	0.354235i
$166$			980.598i			0.458489i
$167$			3656.59i			1.69435i	0.531317	+	0.847173i	$0.321697\pi$
$167$			3656.59i			1.69435i	−0.531317	+	0.847173i	$0.678303\pi$
$168$			93.9255i			0.0431340i
$169$	2146.95			0.977220
$170$			638.251i			0.287951i
$171$		−	491.553i		−	0.219824i
$172$		−	1021.93i		−	0.453032i
$173$	−2064.46			−0.907272			−0.453636	−	0.891187i	$-0.649873\pi$
$173$	−2064.46			−0.907272			−0.453636	+	0.891187i	$0.649873\pi$
$174$	836.037			0.364252
$175$	−305.380			−0.131912
$176$	−735.079			−0.314822
$177$		−	395.399i		−	0.167910i
$178$	−2885.48			−1.21503
$179$			488.495i			0.203977i	0.994786	+	0.101988i	$0.0325204\pi$
$179$			488.495i			0.203977i	−0.994786	+	0.101988i	$0.967480\pi$
$180$		−	821.477i		−	0.340163i
$181$	1105.36			0.453928			0.226964	−	0.973903i	$-0.427120\pi$
$181$	1105.36			0.453928			0.226964	+	0.973903i	$0.427120\pi$
$182$	88.8245			0.0361764
$183$			333.019i			0.134522i
$184$	713.940			0.286045
$185$	−1951.42	−	244.156i	−0.775522	−	0.0970308i
$186$	−67.4515			−0.0265902
$187$			1677.85i			0.656132i
$188$	−1155.84			−0.448397
$189$	−592.934			−0.228199
$190$		−	365.518i		−	0.139566i
$191$			1125.40i			0.426339i	0.977015	+	0.213170i	$0.0683787\pi$
$191$			1125.40i			0.426339i	−0.977015	+	0.213170i	$0.931621\pi$
$192$	119.691			0.0449893
$193$			4847.67i			1.80799i	0.427538	+	0.903997i	$0.359381\pi$
$193$			4847.67i			1.80799i	−0.427538	+	0.903997i	$0.640619\pi$
$194$	613.634			0.227095
$195$	115.609			0.0424562
$196$	1214.35			0.442548
$197$	4044.59			1.46277			0.731383	−	0.681966i	$-0.238875\pi$
$197$	4044.59			1.46277			0.731383	+	0.681966i	$0.238875\pi$
$198$		−	2159.52i		−	0.775103i
$199$		−	2113.72i		−	0.752954i	−0.926426	−	0.376477i	$-0.877135\pi$
$199$		−	2113.72i		−	0.752954i	0.926426	−	0.376477i	$-0.122865\pi$
$200$			389.151i			0.137586i
$201$	1446.95			0.507761
$202$		−	2492.84i		−	0.868296i
$203$			1403.23i			0.485158i
$204$		−	273.200i		−	0.0937639i
$205$		−	890.625i		−	0.303434i
$206$	2487.82			0.841431
$207$			2097.42i			0.704255i
$208$		−	113.190i		−	0.0377324i
$209$		−	960.883i		−	0.318018i
$210$	−205.185			−0.0674244
$211$	4772.63			1.55716			0.778582	−	0.627543i	$-0.215939\pi$
$211$	4772.63			1.55716			0.778582	+	0.627543i	$0.215939\pi$
$212$	1472.82			0.477139
$213$	−540.354			−0.173824
$214$		−	2473.35i		−	0.790068i
$215$	2232.46			0.708151
$216$			755.585i			0.238014i
$217$		−	113.212i		−	0.0354163i
$218$	−1990.75			−0.618490
$219$	828.205			0.255548
$220$		−	1605.82i		−	0.492110i
$221$	−258.363			−0.0786396
$222$	835.296	+	104.510i	0.252529	+	0.0315956i
$223$	−3261.86			−0.979509			−0.489755	−	0.871860i	$-0.662914\pi$
$223$	−3261.86			−0.979509			−0.489755	+	0.871860i	$0.662914\pi$
$224$			200.892i			0.0599226i
$225$	−1143.25			−0.338741
$226$	250.640			0.0737715
$227$		−	5394.04i		−	1.57716i	−0.614933	−	0.788579i	$-0.710817\pi$
$227$		−	5394.04i		−	1.57716i	0.614933	−	0.788579i	$-0.289183\pi$
$228$			156.458i			0.0454460i
$229$	4511.25			1.30180			0.650899	−	0.759165i	$-0.274392\pi$
$229$	4511.25			1.30180			0.650899	+	0.759165i	$0.274392\pi$
$230$			1559.64i			0.447128i
$231$	−539.396			−0.153635
$232$	1788.15			0.506026
$233$	885.087			0.248858			0.124429	−	0.992228i	$-0.460290\pi$
$233$	885.087			0.248858			0.124429	+	0.992228i	$0.460290\pi$
$234$	332.532			0.0928987
$235$		−	2525.00i		−	0.700905i
$236$		−	845.697i		−	0.233263i
$237$		−	559.310i		−	0.153296i
$238$	458.546			0.124887
$239$		−	1540.92i		−	0.417046i	−0.978017	−	0.208523i	$-0.933134\pi$
$239$		−	1540.92i		−	0.417046i	0.978017	−	0.208523i	$-0.0668656\pi$
$240$			261.471i			0.0703244i
$241$			4755.42i			1.27105i	0.772080	+	0.635526i	$0.219217\pi$
$241$			4755.42i			1.27105i	−0.772080	+	0.635526i	$0.780783\pi$
$242$		−	1559.42i		−	0.414227i
$243$	−3406.51			−0.899292
$244$			712.276i			0.186880i
$245$			2652.82i			0.691764i
$246$			381.227i			0.0988055i
$247$	147.961			0.0381155
$248$	−144.268			−0.0369397
$249$	916.942			0.233369
$250$	−3034.67			−0.767717
$251$		−	6967.34i		−	1.75209i	−0.482230	−	0.876045i	$-0.660173\pi$
$251$		−	6967.34i		−	1.75209i	0.482230	−	0.876045i	$-0.339827\pi$
$252$	−590.182			−0.147532
$253$			4100.02i			1.01884i
$254$			1157.54i			0.285947i
$255$	596.819			0.146566
$256$	256.000			0.0625000
$257$		−	984.235i		−	0.238891i	−0.992841	−	0.119445i	$-0.961888\pi$
$257$		−	984.235i		−	0.238891i	0.992841	−	0.119445i	$-0.0381116\pi$
$258$	−955.591			−0.230591
$259$	−175.412	+	1401.98i	−0.0420832	+	0.336351i
$260$	247.270			0.0589810
$261$			5253.25i			1.24585i
$262$	−4333.70			−1.02190
$263$	−8132.02			−1.90662			−0.953311	−	0.301990i	$-0.902349\pi$
$263$	−8132.02			−1.90662			−0.953311	+	0.301990i	$0.902349\pi$
$264$			687.361i			0.160243i
$265$			3217.44i			0.745834i
$266$	−262.603			−0.0605309
$267$			2698.17i			0.618446i
$268$	3094.80			0.705392
$269$	−1868.25			−0.423454			−0.211727	−	0.977329i	$-0.567909\pi$
$269$	−1868.25			−0.423454			−0.211727	+	0.977329i	$0.567909\pi$
$270$	−1650.61			−0.372049
$271$	3090.37			0.692718			0.346359	−	0.938102i	$-0.387418\pi$
$271$	3090.37			0.692718			0.346359	+	0.938102i	$0.387418\pi$
$272$		−	584.332i		−	0.130259i
$273$		−	83.0584i		−	0.0184136i
$274$		−	492.150i		−	0.108510i
$275$	−2234.82			−0.490053
$276$		−	667.594i		−	0.145596i
$277$			4404.15i			0.955307i	0.878548	+	0.477653i	$0.158513\pi$
$277$			4404.15i			0.955307i	−0.878548	+	0.477653i	$0.841487\pi$
$278$			3580.95i			0.772557i
$279$		−	423.832i		−	0.0909468i
$280$	−438.859			−0.0936672
$281$		−	4499.08i		−	0.955134i	−0.878595	−	0.477567i	$-0.841519\pi$
$281$		−	4499.08i		−	0.955134i	0.878595	−	0.477567i	$-0.158481\pi$
$282$			1080.81i			0.228232i
$283$		−	8853.51i		−	1.85967i	−0.367978	−	0.929835i	$-0.619950\pi$
$283$		−	8853.51i		−	1.85967i	0.367978	−	0.929835i	$-0.380050\pi$
$284$	−1155.73			−0.241479
$285$	−341.790			−0.0710383
$286$	650.031			0.134396
$287$	−639.861			−0.131602
$288$			752.079i			0.153877i
$289$	3579.23			0.728523
$290$			3906.31i			0.790988i
$291$		−	573.800i		−	0.115590i
$292$	1771.40			0.355012
$293$	−6280.65			−1.25228			−0.626142	−	0.779709i	$-0.715367\pi$
$293$	−6280.65			−1.25228			−0.626142	+	0.779709i	$0.715367\pi$
$294$		−	1135.52i		−	0.225255i
$295$	1847.47			0.364623
$296$	1786.57	+	223.530i	0.350818	+	0.0438932i
$297$	−4339.18			−0.847760
$298$			3726.79i			0.724454i
$299$	−631.338			−0.122111
$300$	363.889			0.0700305
$301$		−	1603.89i		−	0.307132i
$302$		−	77.9761i		−	0.0148577i
$303$	−2331.02			−0.441959
$304$			334.639i			0.0631344i
$305$	−1556.00			−0.292119
$306$	1716.66			0.320702
$307$	342.320			0.0636392			0.0318196	−	0.999494i	$-0.489870\pi$
$307$	342.320			0.0636392			0.0318196	+	0.999494i	$0.489870\pi$
$308$	−1153.68			−0.213433
$309$		−	2326.32i		−	0.428285i
$310$		−	315.161i		−	0.0577417i
$311$		−	6764.69i		−	1.23341i	−0.787195	−	0.616704i	$-0.788467\pi$
$311$		−	6764.69i		−	1.23341i	0.787195	−	0.616704i	$-0.211533\pi$
$312$	−105.843			−0.0192057
$313$		−	5987.39i		−	1.08124i	−0.841268	−	0.540619i	$-0.818190\pi$
$313$		−	5987.39i		−	1.08124i	0.841268	−	0.540619i	$-0.181810\pi$
$314$			1323.10i			0.237792i
$315$		−	1289.28i		−	0.230612i
$316$		−	1196.28i		−	0.212961i
$317$	5976.00			1.05882			0.529409	−	0.848367i	$-0.322414\pi$
$317$	5976.00			1.05882			0.529409	+	0.848367i	$0.322414\pi$
$318$		−	1377.21i		−	0.242862i
$319$			10269.0i			1.80237i
$320$			559.245i			0.0976961i
$321$	−2312.79			−0.402141
$322$	1120.51			0.193924
$323$	763.829			0.131581
$324$	−1831.73			−0.314083
$325$		−	344.126i		−	0.0587344i
$326$	−4767.77			−0.810008
$327$			1861.52i			0.314809i
$328$			815.385i			0.137263i
$329$	−1814.06			−0.303989
$330$	−1501.57			−0.250482
$331$		−	9434.78i		−	1.56672i	−0.621571	−	0.783358i	$-0.713505\pi$
$331$		−	9434.78i		−	1.56672i	0.621571	−	0.783358i	$-0.286495\pi$
$332$	1961.20			0.324201
$333$	−656.687	+	5248.60i	−0.108067	+	0.863727i
$334$	7313.19			1.19808
$335$			6760.74i			1.10262i
$336$	187.851			0.0305003
$337$	3085.57			0.498759			0.249379	−	0.968406i	$-0.419773\pi$
$337$	3085.57			0.498759			0.249379	+	0.968406i	$0.419773\pi$
$338$		−	4293.91i		−	0.690999i
$339$		−	234.370i		−	0.0375493i
$340$	1276.50			0.203612
$341$		−	828.504i		−	0.131572i
$342$	−983.105			−0.155439
$343$	4059.20			0.638998
$344$	−2043.86			−0.320342
$345$	1458.39			0.227586
$346$			4128.92i			0.641538i
$347$		−	4522.97i		−	0.699729i	−0.936800	−	0.349864i	$-0.886228\pi$
$347$		−	4522.97i		−	0.699729i	0.936800	−	0.349864i	$-0.113772\pi$
$348$		−	1672.07i		−	0.257565i
$349$	−4204.60			−0.644891			−0.322446	−	0.946588i	$-0.604505\pi$
$349$	−4204.60			−0.644891			−0.322446	+	0.946588i	$0.604505\pi$
$350$			610.760i			0.0932757i
$351$		−	668.165i		−	0.101607i
$352$			1470.16i			0.222613i
$353$		−	10537.1i		−	1.58876i	−0.607421	−	0.794380i	$-0.707796\pi$
$353$		−	10537.1i		−	1.58876i	0.607421	−	0.794380i	$-0.292204\pi$
$354$	−790.798			−0.118730
$355$		−	2524.75i		−	0.377465i
$356$			5770.96i			0.859158i
$357$		−	428.779i		−	0.0635669i
$358$	976.989			0.144233
$359$	10147.5			1.49182			0.745912	−	0.666044i	$-0.232014\pi$
$359$	10147.5			1.49182			0.745912	+	0.666044i	$0.232014\pi$
$360$	−1642.95			−0.240531
$361$	6421.57			0.936225
$362$		−	2210.72i		−	0.320975i
$363$	−1458.19			−0.210840
$364$		−	177.649i		−	0.0255806i
$365$			3869.71i			0.554932i
$366$	666.038			0.0951212
$367$	9150.26			1.30147			0.650735	−	0.759305i	$-0.274461\pi$
$367$	9150.26			1.30147			0.650735	+	0.759305i	$0.274461\pi$
$368$		−	1427.88i		−	0.202265i
$369$	−2395.45			−0.337946
$370$	−488.312	+	3902.85i	−0.0686112	+	0.548377i
$371$	2311.54			0.323475
$372$			134.903i			0.0188021i
$373$	7820.47			1.08560			0.542800	−	0.839862i	$-0.317364\pi$
$373$	7820.47			1.08560			0.542800	+	0.839862i	$0.317364\pi$
$374$	3355.71			0.463956
$375$			2837.67i			0.390765i
$376$			2311.69i			0.317064i
$377$	−1581.27			−0.216019
$378$			1185.87i			0.161361i
$379$	−5064.36			−0.686382			−0.343191	−	0.939266i	$-0.611508\pi$
$379$	−5064.36			−0.686382			−0.343191	+	0.939266i	$0.611508\pi$
$380$	−731.036			−0.0986877
$381$	1082.40			0.145546
$382$	2250.79			0.301467
$383$			4294.32i			0.572923i	0.958092	+	0.286461i	$0.0924790\pi$
$383$			4294.32i			0.572923i	−0.958092	+	0.286461i	$0.907521\pi$
$384$		−	239.382i		−	0.0318122i
$385$		−	2520.28i		−	0.333624i
$386$	9695.34			1.27845
$387$		−	6004.47i		−	0.788694i
$388$		−	1227.27i		−	0.160580i
$389$			10770.2i			1.40379i	0.712282	+	0.701894i	$0.247662\pi$
$389$			10770.2i			1.40379i	−0.712282	+	0.701894i	$0.752338\pi$
$390$		−	231.219i		−	0.0300211i
$391$	−3259.20			−0.421547
$392$		−	2428.71i		−	0.312929i
$393$			4052.38i			0.520141i
$394$		−	8089.18i		−	1.03433i
$395$	2613.33			0.332888
$396$	−4319.04			−0.548081
$397$	−1626.31			−0.205597			−0.102798	−	0.994702i	$-0.532780\pi$
$397$	−1626.31			−0.205597			−0.102798	+	0.994702i	$0.532780\pi$
$398$	−4227.45			−0.532419
$399$			245.556i			0.0308099i
$400$	778.301			0.0972877
$401$			10284.5i			1.28076i	0.768058	+	0.640380i	$0.221223\pi$
$401$			10284.5i			1.28076i	−0.768058	+	0.640380i	$0.778777\pi$
$402$		−	2893.90i		−	0.359041i
$403$	127.576			0.0157693
$404$	−4985.69			−0.613978
$405$		−	4001.51i		−	0.490954i
$406$	2806.45			0.343059
$407$	−1283.69	+	10259.9i	−0.156339	+	1.24955i
$408$	−546.400			−0.0663011
$409$			10496.9i			1.26904i	0.772906	+	0.634521i	$0.218802\pi$
$409$			10496.9i			1.26904i	−0.772906	+	0.634521i	$0.781198\pi$
$410$	−1781.25			−0.214560
$411$	−460.202			−0.0552314
$412$		−	4975.64i		−	0.594981i
$413$		−	1327.29i		−	0.158140i
$414$	4194.84			0.497983
$415$			4284.33i			0.506770i
$416$	−226.381			−0.0266809
$417$	3348.49			0.393228
$418$	−1921.77			−0.224872
$419$	−13966.8			−1.62846			−0.814229	−	0.580543i	$-0.802840\pi$
$419$	−13966.8			−1.62846			−0.814229	+	0.580543i	$0.802840\pi$
$420$			410.370i			0.0476762i
$421$		−	14668.4i		−	1.69808i	−0.528325	−	0.849042i	$-0.677180\pi$
$421$		−	14668.4i		−	1.69808i	0.528325	−	0.849042i	$-0.322820\pi$
$422$		−	9545.27i		−	1.10108i
$423$	−6791.30			−0.780624
$424$		−	2945.64i		−	0.337388i
$425$		−	1776.51i		−	0.202761i
$426$			1080.71i			0.122912i
$427$			1117.89i			0.126695i
$428$	−4946.70			−0.558663
$429$		−	607.834i		−	0.0684068i
$430$		−	4464.92i		−	0.500738i
$431$			4129.49i			0.461509i	0.973012	+	0.230755i	$0.0741195\pi$
$431$			4129.49i			0.461509i	−0.973012	+	0.230755i	$0.925881\pi$
$432$	1511.17			0.168301
$433$	−15674.1			−1.73960			−0.869800	−	0.493405i	$-0.835752\pi$
$433$	−15674.1			−1.73960			−0.869800	+	0.493405i	$0.835752\pi$
$434$	−226.424			−0.0250431
$435$	3652.73			0.402609
$436$			3981.51i			0.437339i
$437$	1866.50			0.204318
$438$		−	1656.41i		−	0.180699i
$439$		−	2593.27i		−	0.281936i	−0.990014	−	0.140968i	$-0.954978\pi$
$439$		−	2593.27i		−	0.281936i	0.990014	−	0.140968i	$-0.0450215\pi$
$440$	−3211.63			−0.347974
$441$	7135.07			0.770443
$442$			516.725i			0.0556066i
$443$	−2017.47			−0.216372			−0.108186	−	0.994131i	$-0.534504\pi$
$443$	−2017.47			−0.216372			−0.108186	+	0.994131i	$0.534504\pi$
$444$	209.019	−	1670.59i	0.0223415	−	0.178565i
$445$	−12606.9			−1.34298
$446$			6523.73i			0.692618i
$447$	3484.87			0.368744
$448$	401.784			0.0423717
$449$		−	1798.88i		−	0.189074i	−0.995521	−	0.0945371i	$-0.969863\pi$
$449$		−	1798.88i		−	0.189074i	0.995521	−	0.0945371i	$-0.0301371\pi$
$450$			2286.50i			0.239526i
$451$	−4682.60			−0.488902
$452$		−	501.281i		−	0.0521643i
$453$	−72.9143			−0.00756250
$454$	−10788.1			−1.11522
$455$	388.083			0.0399860
$456$	312.916			0.0321351
$457$			31.1851i			0.00319207i	0.999999	+	0.00159604i	$0.000508035\pi$
$457$			31.1851i			0.00319207i	−0.999999	+	0.00159604i	$0.999492\pi$
$458$		−	9022.49i		−	0.920510i
$459$		−	3449.32i		−	0.350763i
$460$	3119.28			0.316167
$461$		−	15370.9i		−	1.55291i	−0.630170	−	0.776457i	$-0.717015\pi$
$461$		−	15370.9i		−	1.55291i	0.630170	−	0.776457i	$-0.282985\pi$
$462$			1078.79i			0.108636i
$463$			8931.38i			0.896493i	0.893910	+	0.448247i	$0.147951\pi$
$463$			8931.38i			0.896493i	−0.893910	+	0.448247i	$0.852049\pi$
$464$		−	3576.31i		−	0.357814i
$465$	−294.702			−0.0293903
$466$		−	1770.17i		−	0.175969i
$467$			15136.0i			1.49981i	0.661546	+	0.749905i	$0.269901\pi$
$467$			15136.0i			1.49981i	−0.661546	+	0.749905i	$0.730099\pi$
$468$		−	665.064i		−	0.0656893i
$469$	4857.19			0.478218
$470$	−5050.00			−0.495615
$471$	1237.21			0.121035
$472$	−1691.39			−0.164942
$473$		−	11737.5i		−	1.14099i
$474$	−1118.62			−0.108396
$475$			1017.38i			0.0982752i
$476$		−	917.091i		−	0.0883084i
$477$	8653.71			0.830663
$478$	−3081.85			−0.294896
$479$			15028.5i			1.43355i	0.697306	+	0.716773i	$0.254382\pi$
$479$			15028.5i			1.43355i	−0.697306	+	0.716773i	$0.745618\pi$
$480$	522.941			0.0497269
$481$	−1579.86	−	197.668i	−0.149762	−	0.0187378i
$482$	9510.83			0.898769
$483$		−	1047.77i		−	0.0987063i
$484$	−3118.83			−0.292903
$485$	2681.03			0.251009
$486$			6813.02i			0.635895i
$487$			5633.70i			0.524204i	0.965040	+	0.262102i	$0.0844156\pi$
$487$			5633.70i			0.524204i	−0.965040	+	0.262102i	$0.915584\pi$
$488$	1424.55			0.132144
$489$			4458.27i			0.412290i
$490$	5305.63			0.489151
$491$	−5099.54			−0.468715			−0.234357	−	0.972151i	$-0.575299\pi$
$491$	−5099.54			−0.468715			−0.234357	+	0.972151i	$0.575299\pi$
$492$	762.454			0.0698661
$493$	−8163.09			−0.745734
$494$		−	295.922i		−	0.0269517i
$495$		−	9435.17i		−	0.856726i
$496$			288.536i			0.0261203i
$497$	−1813.89			−0.163710
$498$		−	1833.88i		−	0.165017i
$499$			13694.2i			1.22853i	0.789100	+	0.614265i	$0.210548\pi$
$499$			13694.2i			1.22853i	−0.789100	+	0.614265i	$0.789452\pi$
$500$			6069.34i			0.542858i
$501$		−	6838.45i		−	0.609819i
$502$	−13934.7			−1.23891
$503$			9835.95i			0.871895i	0.899972	+	0.435948i	$0.143587\pi$
$503$			9835.95i			0.871895i	−0.899972	+	0.435948i	$0.856413\pi$
$504$			1180.36i			0.104321i
$505$		−	10891.5i		−	0.959732i
$506$	8200.04			0.720427
$507$	−4015.17			−0.351715
$508$	2315.08			0.202195
$509$	7496.16			0.652773			0.326386	−	0.945236i	$-0.394169\pi$
$509$	7496.16			0.652773			0.326386	+	0.945236i	$0.394169\pi$
$510$		−	1193.64i		−	0.103638i
$511$	2780.16			0.240679
$512$		−	512.000i		−	0.0441942i
$513$			1975.38i			0.170010i
$514$	−1968.47			−0.168921
$515$	10869.5			0.930037
$516$			1911.18i			0.163053i
$517$	−13275.6			−1.12932
$518$	2803.96	+	350.823i	0.237836	+	0.0297573i
$519$	3860.89			0.326540
$520$		−	494.541i		−	0.0417059i
$521$	13799.0			1.16035			0.580176	−	0.814491i	$-0.302984\pi$
$521$	13799.0			1.16035			0.580176	+	0.814491i	$0.302984\pi$
$522$	10506.5			0.880953
$523$		−	11834.4i		−	0.989449i	−0.869050	−	0.494725i	$-0.835269\pi$
$523$		−	11834.4i		−	0.989449i	0.869050	−	0.494725i	$-0.164731\pi$
$524$			8667.41i			0.722590i
$525$	571.112			0.0474769
$526$			16264.0i			1.34819i
$527$	658.598			0.0544383
$528$	1374.72			0.113309
$529$	4202.77			0.345424
$530$	6434.89			0.527384
$531$		−	4968.99i		−	0.406094i
$532$			525.206i			0.0428018i
$533$		−	721.046i		−	0.0585966i
$534$	5396.33			0.437307
$535$		−	10806.3i		−	0.873266i
$536$		−	6189.60i		−	0.498787i
$537$		−	913.568i		−	0.0734141i
$538$			3736.49i			0.299427i
$539$	13947.6			1.11459
$540$			3301.23i			0.263078i
$541$		−	5681.42i		−	0.451504i	−0.974185	−	0.225752i	$-0.927516\pi$
$541$		−	5681.42i		−	0.451504i	0.974185	−	0.225752i	$-0.0724839\pi$
$542$		−	6180.74i		−	0.489825i
$543$	−2067.21			−0.163375
$544$	−1168.66			−0.0921067
$545$	−8697.80			−0.683620
$546$	−166.117			−0.0130204
$547$		−	8915.76i		−	0.696911i	−0.937325	−	0.348456i	$-0.886706\pi$
$547$		−	8915.76i		−	0.696911i	0.937325	−	0.348456i	$-0.113294\pi$
$548$	−984.300			−0.0767285
$549$			4185.06i			0.325344i
$550$			4469.63i			0.346520i
$551$	4674.89			0.361446
$552$	−1335.19			−0.102952
$553$		−	1877.52i		−	0.144377i
$554$	8808.31			0.675504
$555$	3649.49	+	456.613i	0.279121	+	0.0349228i
$556$	7161.89			0.546280
$557$			2620.20i			0.199320i	0.995022	+	0.0996601i	$0.0317755\pi$
$557$			2620.20i			0.199320i	−0.995022	+	0.0996601i	$0.968224\pi$
$558$	−847.664			−0.0643091
$559$	1807.39			0.136752
$560$			877.718i			0.0662327i
$561$		−	3137.87i		−	0.236151i
$562$	−8998.16			−0.675382
$563$			7257.22i			0.543260i	0.962402	+	0.271630i	$0.0875627\pi$
$563$			7257.22i			0.543260i	−0.962402	+	0.271630i	$0.912437\pi$
$564$	2161.62			0.161384
$565$	1095.07			0.0815399
$566$	−17707.0			−1.31498
$567$	−2874.84			−0.212931
$568$			2311.46i			0.170752i
$569$		−	15143.3i		−	1.11571i	−0.829937	−	0.557857i	$-0.811624\pi$
$569$		−	15143.3i		−	1.11571i	0.829937	−	0.557857i	$-0.188376\pi$
$570$			683.580i			0.0502316i
$571$	−4983.09			−0.365211			−0.182606	−	0.983186i	$-0.558453\pi$
$571$	−4983.09			−0.365211			−0.182606	+	0.983186i	$0.558453\pi$
$572$		−	1300.06i		−	0.0950320i
$573$		−	2104.68i		−	0.153446i
$574$			1279.72i			0.0930568i
$575$		−	4341.10i		−	0.314846i
$576$	1504.16			0.108808
$577$			11019.6i			0.795064i	0.917588	+	0.397532i	$0.130133\pi$
$577$			11019.6i			0.795064i	−0.917588	+	0.397532i	$0.869867\pi$
$578$		−	7158.47i		−	0.515144i
$579$		−	9065.97i		−	0.650723i
$580$	7812.62			0.559313
$581$	3078.04			0.219791
$582$	−1147.60			−0.0817346
$583$	16916.2			1.20171
$584$		−	3542.80i		−	0.251031i
$585$	1452.87			0.102681
$586$			12561.3i			0.885499i
$587$			4192.24i			0.294774i	0.989079	+	0.147387i	$0.0470862\pi$
$587$			4192.24i			0.294774i	−0.989079	+	0.147387i	$0.952914\pi$
$588$	−2271.05			−0.159280
$589$	−377.170			−0.0263854
$590$		−	3694.93i		−	0.257827i
$591$	−7564.07			−0.526471
$592$	447.059	−	3573.14i	0.0310372	−	0.248066i
$593$	24493.9			1.69619			0.848096	−	0.529843i	$-0.177749\pi$
$593$	24493.9			1.69619			0.848096	+	0.529843i	$0.177749\pi$
$594$			8678.36i			0.599457i
$595$	2003.43			0.138038
$596$	7453.58			0.512266
$597$			3953.02i			0.270999i
$598$			1262.68i			0.0863456i
$599$	−21942.7			−1.49675			−0.748375	−	0.663276i	$-0.769166\pi$
$599$	−21942.7			−1.49675			−0.748375	+	0.663276i	$0.769166\pi$
$600$		−	727.778i		−	0.0495190i
$601$	−13605.6			−0.923431			−0.461716	−	0.887028i	$-0.652766\pi$
$601$	−13605.6			−0.923431			−0.461716	+	0.887028i	$0.652766\pi$
$602$	−3207.78			−0.217175
$603$	18183.9			1.22803
$604$	−155.952			−0.0105060
$605$		−	6813.24i		−	0.457847i
$606$			4662.04i			0.312512i
$607$		−	20734.3i		−	1.38646i	−0.720716	−	0.693230i	$-0.756187\pi$
$607$		−	20734.3i		−	1.38646i	0.720716	−	0.693230i	$-0.243813\pi$
$608$	669.278			0.0446428
$609$		−	2624.27i		−	0.174615i
$610$			3112.00i			0.206560i
$611$		−	2044.23i		−	0.135353i
$612$		−	3433.31i		−	0.226770i
$613$	2234.92			0.147255			0.0736276	−	0.997286i	$-0.476542\pi$
$613$	2234.92			0.147255			0.0736276	+	0.997286i	$0.476542\pi$
$614$		−	684.640i		−	0.0449997i
$615$			1665.62i			0.109210i
$616$			2307.37i			0.150920i
$617$	−19756.7			−1.28910			−0.644549	−	0.764563i	$-0.722955\pi$
$617$	−19756.7			−1.28910			−0.644549	+	0.764563i	$0.722955\pi$
$618$	−4652.65			−0.302843
$619$	−10351.1			−0.672126			−0.336063	−	0.941840i	$-0.609095\pi$
$619$	−10351.1			−0.672126			−0.336063	+	0.941840i	$0.609095\pi$
$620$	−630.322			−0.0408296
$621$		−	8428.79i		−	0.544663i
$622$	−13529.4			−0.872152
$623$			9057.34i			0.582463i
$624$			211.685i			0.0135804i
$625$	−7178.30			−0.459411
$626$	−11974.8			−0.764551
$627$			1797.01i			0.114459i
$628$	2646.19			0.168144
$629$	−8155.85	−	1020.43i	−0.517003	−	0.0646858i
$630$	−2578.57			−0.163068
$631$		−	1177.94i		−	0.0743157i	−0.999309	−	0.0371579i	$-0.988170\pi$
$631$		−	1177.94i		−	0.0743157i	0.999309	−	0.0371579i	$-0.0118304\pi$
$632$	−2392.55			−0.150586
$633$	−8925.63			−0.560446
$634$		−	11952.0i		−	0.748698i
$635$			5057.41i			0.316059i
$636$	−2754.42			−0.171729
$637$			2147.71i			0.133587i
$638$	20538.0			1.27446
$639$	−6790.64			−0.420397
$640$	1118.49			0.0690815
$641$	−13272.7			−0.817846			−0.408923	−	0.912569i	$-0.634096\pi$
$641$	−13272.7			−0.817846			−0.408923	+	0.912569i	$0.634096\pi$
$642$			4625.58i			0.284357i
$643$			9376.58i			0.575079i	0.957769	+	0.287540i	$0.0928373\pi$
$643$			9376.58i			0.575079i	−0.957769	+	0.287540i	$0.907163\pi$
$644$		−	2241.01i		−	0.137125i
$645$	−4175.08			−0.254874
$646$		−	1527.66i		−	0.0930417i
$647$			21920.0i			1.33194i	0.745979	+	0.665969i	$0.231982\pi$
$647$			21920.0i			1.33194i	−0.745979	+	0.665969i	$0.768018\pi$
$648$			3663.46i			0.222090i
$649$		−	9713.34i		−	0.587492i
$650$	−688.253			−0.0415315
$651$			211.726i			0.0127468i
$652$			9535.54i			0.572762i
$653$			6180.33i			0.370375i	0.982703	+	0.185188i	$0.0592893\pi$
$653$			6180.33i			0.370375i	−0.982703	+	0.185188i	$0.940711\pi$
$654$	3723.05			0.222603
$655$	−18934.4			−1.12951
$656$	1630.77			0.0970593
$657$	10408.1			0.618048
$658$			3628.12i			0.214953i
$659$	29103.0			1.72032			0.860160	−	0.510024i	$-0.170363\pi$
$659$	29103.0			1.72032			0.860160	+	0.510024i	$0.170363\pi$
$660$			3003.15i			0.177117i
$661$			26810.6i			1.57763i	0.614632	+	0.788814i	$0.289305\pi$
$661$			26810.6i			1.57763i	−0.614632	+	0.788814i	$0.710695\pi$
$662$	−18869.6			−1.10783
$663$	483.182			0.0283035
$664$		−	3922.39i		−	0.229244i
$665$	−1147.34			−0.0669051
$666$	10497.2	+	1313.37i	0.610748	+	0.0764148i
$667$	−19947.4			−1.15797
$668$		−	14626.4i		−	0.847173i
$669$	6100.24			0.352539
$670$	13521.5			0.779673
$671$			8180.92i			0.470672i
$672$		−	375.702i		−	0.0215670i
$673$	16289.8			0.933024			0.466512	−	0.884515i	$-0.345510\pi$
$673$	16289.8			0.933024			0.466512	+	0.884515i	$0.345510\pi$
$674$		−	6171.14i		−	0.352676i
$675$	4594.32			0.261979
$676$	−8587.81			−0.488610
$677$	−7534.90			−0.427754			−0.213877	−	0.976861i	$-0.568609\pi$
$677$	−7534.90			−0.427754			−0.213877	+	0.976861i	$0.568609\pi$
$678$	−468.740			−0.0265514
$679$		−	1926.16i		−	0.108865i
$680$		−	2553.01i		−	0.143975i
$681$			10087.8i			0.567642i
$682$	−1657.01			−0.0930353
$683$			3653.86i			0.204701i	0.994748	+	0.102351i	$0.0326364\pi$
$683$			3653.86i			0.204701i	−0.994748	+	0.102351i	$0.967364\pi$
$684$			1966.21i			0.109912i
$685$		−	2150.25i		−	0.119937i
$686$		−	8118.40i		−	0.451840i
$687$	−8436.79			−0.468535
$688$			4087.72i			0.226516i
$689$			2604.83i			0.144029i
$690$		−	2916.79i		−	0.160928i
$691$	−26991.0			−1.48594			−0.742971	−	0.669324i	$-0.766584\pi$
$691$	−26991.0			−1.48594			−0.742971	+	0.669324i	$0.766584\pi$
$692$	8257.84			0.453636
$693$	−6778.60			−0.371570
$694$	−9045.94			−0.494783
$695$			15645.5i			0.853911i
$696$	−3344.15			−0.182126
$697$		−	3722.31i		−	0.202285i
$698$			8409.20i			0.456007i
$699$	−1655.26			−0.0895677
$700$	1221.52			0.0659559
$701$		−	32419.9i		−	1.74677i	−0.487034	−	0.873383i	$-0.661921\pi$
$701$		−	32419.9i		−	1.74677i	0.487034	−	0.873383i	$-0.338079\pi$
$702$	−1336.33			−0.0718469
$703$	4670.75	+	584.389i	0.250584	+	0.0313523i
$704$	2940.32			0.157411
$705$			4722.18i			0.252266i
$706$	−21074.2			−1.12342
$707$	−7824.88			−0.416245
$708$			1581.60i			0.0839548i
$709$			20045.2i			1.06180i	0.847435	+	0.530898i	$0.178145\pi$
$709$			20045.2i			1.06180i	−0.847435	+	0.530898i	$0.821855\pi$
$710$	−5049.51			−0.266908
$711$		−	7028.86i		−	0.370750i
$712$	11541.9			0.607516
$713$	1609.36			0.0845314
$714$	−857.558			−0.0449486
$715$	2840.05			0.148548
$716$		−	1953.98i		−	0.101988i
$717$			2881.79i			0.150101i
$718$		−	20295.0i		−	1.05488i
$719$	16795.3			0.871154			0.435577	−	0.900151i	$-0.356544\pi$
$719$	16795.3			0.871154			0.435577	+	0.900151i	$0.356544\pi$
$720$			3285.91i			0.170081i
$721$		−	7809.12i		−	0.403366i
$722$		−	12843.1i		−	0.662011i
$723$		−	8893.44i		−	0.457470i
$724$	−4421.45			−0.226964
$725$		−	10872.8i		−	0.556975i
$726$			2916.37i			0.149086i
$727$		−	20085.1i		−	1.02464i	−0.858794	−	0.512320i	$-0.828786\pi$
$727$		−	20085.1i		−	1.02464i	0.858794	−	0.512320i	$-0.171214\pi$
$728$	−355.298			−0.0180882
$729$	−5993.42			−0.304497
$730$	7739.43			0.392396
$731$	9330.42			0.472090
$732$		−	1332.08i		−	0.0672609i
$733$	38652.8			1.94771			0.973855	−	0.227169i	$-0.0729469\pi$
$733$	38652.8			1.94771			0.973855	+	0.227169i	$0.0729469\pi$
$734$		−	18300.5i		−	0.920279i
$735$		−	4961.21i		−	0.248976i
$736$	−2855.76			−0.143023
$737$	35545.7			1.77658
$738$			4790.89i			0.238964i
$739$	−3386.40			−0.168567			−0.0842833	−	0.996442i	$-0.526860\pi$
$739$	−3386.40			−0.168567			−0.0842833	+	0.996442i	$0.526860\pi$
$740$	7805.70	+	976.624i	0.387761	+	0.0485154i
$741$	−276.712			−0.0137183
$742$		−	4623.08i		−	0.228731i
$743$	1966.71			0.0971087			0.0485543	−	0.998821i	$-0.484539\pi$
$743$	1966.71			0.0971087			0.0485543	+	0.998821i	$0.484539\pi$
$744$	269.806			0.0132951
$745$			16282.7i			0.800742i
$746$		−	15640.9i		−	0.767635i
$747$	11523.2			0.564408
$748$		−	6711.41i		−	0.328066i
$749$	−7763.69			−0.378744
$750$	5675.35			0.276312
$751$	16335.8			0.793743			0.396872	−	0.917874i	$-0.370096\pi$
$751$	16335.8			0.793743			0.396872	+	0.917874i	$0.370096\pi$
$752$	4623.38			0.224198
$753$			13030.1i			0.630602i
$754$			3162.53i			0.152749i
$755$		−	340.686i		−	0.0164223i
$756$	2371.74			0.114099
$757$			29147.0i			1.39943i	0.714424	+	0.699713i	$0.246689\pi$
$757$			29147.0i			1.39943i	−0.714424	+	0.699713i	$0.753311\pi$
$758$			10128.7i			0.485345i
$759$		−	7667.73i		−	0.366694i
$760$			1462.07i			0.0697828i
$761$	12.7672			0.000608163			0.000304082	−	1.00000i	$-0.499903\pi$
$761$	12.7672			0.000608163			0.000304082		1.00000i	$0.499903\pi$
$762$		−	2164.80i		−	0.102916i
$763$			6248.85i			0.296492i
$764$		−	4501.58i		−	0.213170i
$765$	7500.24			0.354473
$766$	8588.63			0.405117
$767$	1495.70			0.0704128
$768$	−478.763			−0.0224946
$769$			5385.01i			0.252521i	0.991997	+	0.126260i	$0.0402975\pi$
$769$			5385.01i			0.252521i	−0.991997	+	0.126260i	$0.959703\pi$
$770$	−5040.56			−0.235908
$771$			1840.69i			0.0859802i
$772$		−	19390.7i		−	0.903997i
$773$	3151.53			0.146640			0.0733199	−	0.997308i	$-0.476641\pi$
$773$	3151.53			0.146640			0.0733199	+	0.997308i	$0.476641\pi$
$774$	−12008.9			−0.557691
$775$			877.219i			0.0406589i
$776$	−2454.54			−0.113547
$777$	328.049	−	2621.94i	0.0151463	−	0.121058i
$778$	21540.5			0.992628
$779$			2131.72i			0.0980445i
$780$	−462.437			−0.0212281
$781$	−13274.3			−0.608184
$782$			6518.41i			0.298079i
$783$		−	21111.0i		−	0.963531i
$784$	−4857.41			−0.221274
$785$			5780.74i			0.262833i
$786$	8104.76			0.367795
$787$	−10073.3			−0.456259			−0.228130	−	0.973631i	$-0.573261\pi$
$787$	−10073.3			−0.456259			−0.228130	+	0.973631i	$0.573261\pi$
$788$	−16178.4			−0.731383
$789$	15208.3			0.686221
$790$		−	5226.65i		−	0.235387i
$791$		−	786.745i		−	0.0353646i
$792$			8638.08i			0.387552i
$793$	−1259.73			−0.0564116
$794$			3252.61i			0.145379i
$795$		−	6017.17i		−	0.268436i
$796$			8454.90i			0.376477i
$797$			13803.8i			0.613496i	0.951791	+	0.306748i	$0.0992408\pi$
$797$			13803.8i			0.613496i	−0.951791	+	0.306748i	$0.900759\pi$
$798$	491.112			0.0217859
$799$		−	10553.1i		−	0.467260i
$800$		−	1556.60i		−	0.0687928i
$801$			33907.9i			1.49573i
$802$	20569.1			0.905635
$803$	20345.6			0.894124
$804$	−5787.80			−0.253880
$805$	4895.61			0.214345
$806$		−	255.153i		−	0.0111506i
$807$	3493.94			0.152407
$808$			9971.37i			0.434148i
$809$		−	12667.4i		−	0.550508i	−0.961372	−	0.275254i	$-0.911238\pi$
$809$		−	12667.4i		−	0.550508i	0.961372	−	0.275254i	$-0.0887619\pi$
$810$	−8003.01			−0.347157
$811$	10487.0			0.454067			0.227033	−	0.973887i	$-0.427097\pi$
$811$	10487.0			0.454067			0.227033	+	0.973887i	$0.427097\pi$
$812$		−	5612.90i		−	0.242579i
$813$	−5779.51			−0.249319
$814$	20519.8	+	2567.38i	0.883562	+	0.110548i
$815$	−20830.9			−0.895305
$816$			1092.80i			0.0468819i
$817$	−5343.40			−0.228815
$818$	20993.8			0.897348
$819$		−	1043.80i		−	0.0445339i
$820$			3562.50i			0.151717i
$821$	−25286.0			−1.07489			−0.537446	−	0.843298i	$-0.680611\pi$
$821$	−25286.0			−1.07489			−0.537446	+	0.843298i	$0.680611\pi$
$822$			920.404i			0.0390545i
$823$	−2212.67			−0.0937166			−0.0468583	−	0.998902i	$-0.514921\pi$
$823$	−2212.67			−0.0937166			−0.0468583	+	0.998902i	$0.514921\pi$
$824$	−9951.29			−0.420715
$825$	4179.49			0.176377
$826$	−2654.59			−0.111822
$827$		−	4040.96i		−	0.169913i	−0.996385	−	0.0849565i	$-0.972925\pi$
$827$		−	4040.96i		−	0.169913i	0.996385	−	0.0849565i	$-0.0270751\pi$
$828$		−	8389.68i		−	0.352127i
$829$		−	15299.6i		−	0.640984i	−0.947251	−	0.320492i	$-0.896152\pi$
$829$		−	15299.6i		−	0.640984i	0.947251	−	0.320492i	$-0.103848\pi$
$830$	8568.66			0.358340
$831$		−	8236.51i		−	0.343829i
$832$			452.762i			0.0188662i
$833$			11087.3i			0.461166i
$834$		−	6696.98i		−	0.278054i
$835$	31952.1			1.32425
$836$			3843.53i			0.159009i
$837$			1703.23i			0.0703373i
$838$			27933.7i			1.15149i
$839$	−37634.2			−1.54860			−0.774300	−	0.632819i	$-0.781898\pi$
$839$	−37634.2			−1.54860			−0.774300	+	0.632819i	$0.781898\pi$
$840$	820.740			0.0337122
$841$	−25571.8			−1.04850
$842$	−29336.8			−1.20073
$843$			8414.04i			0.343766i
$844$	−19090.5			−0.778582
$845$		−	18760.5i		−	0.763764i
$846$			13582.6i			0.551985i
$847$	−4894.91			−0.198573
$848$	−5891.27			−0.238570
$849$			16557.6i			0.669322i
$850$	−3553.02			−0.143374
$851$	−19929.7	−	2493.54i	−0.802800	−	0.100444i
$852$	2161.41			0.0869118
$853$		−	9983.08i		−	0.400720i	−0.979722	−	0.200360i	$-0.935789\pi$
$853$		−	9983.08i		−	0.400720i	0.979722	−	0.200360i	$-0.0642112\pi$
$854$	2235.79			0.0895868
$855$	−4295.29			−0.171808
$856$			9893.39i			0.395034i
$857$		−	7908.22i		−	0.315215i	−0.987502	−	0.157608i	$-0.949622\pi$
$857$		−	7908.22i		−	0.315215i	0.987502	−	0.157608i	$-0.0503782\pi$
$858$	−1215.67			−0.0483709
$859$		−	10680.9i		−	0.424246i	−0.977243	−	0.212123i	$-0.931962\pi$
$859$		−	10680.9i		−	0.424246i	0.977243	−	0.212123i	$-0.0680377\pi$
$860$	−8929.83			−0.354075
$861$	1196.65			0.0473655
$862$	8258.98			0.326336
$863$	4915.39			0.193884			0.0969419	−	0.995290i	$-0.469094\pi$
$863$	4915.39			0.193884			0.0969419	+	0.995290i	$0.469094\pi$
$864$		−	3022.34i		−	0.119007i
$865$			18039.7i			0.709095i
$866$			31348.1i			1.23008i
$867$	−6693.77			−0.262206
$868$			452.849i			0.0177082i
$869$		−	13740.0i		−	0.536359i
$870$		−	7305.46i		−	0.284688i
$871$			5473.47i			0.212929i
$872$	7963.02			0.309245
$873$		−	7210.95i		−	0.279558i
$874$		−	3733.00i		−	0.144475i
$875$			9525.64i			0.368029i
$876$	−3312.82			−0.127774
$877$	9370.66			0.360804			0.180402	−	0.983593i	$-0.442260\pi$
$877$	9370.66			0.360804			0.180402	+	0.983593i	$0.442260\pi$
$878$	−5186.54			−0.199359
$879$	11745.9			0.450715
$880$			6423.27i			0.246055i
$881$	−6522.53			−0.249432			−0.124716	−	0.992192i	$-0.539802\pi$
$881$	−6522.53			−0.249432			−0.124716	+	0.992192i	$0.539802\pi$
$882$		−	14270.1i		−	0.544786i
$883$		−	43376.2i		−	1.65314i	−0.562831	−	0.826572i	$-0.690288\pi$
$883$		−	43376.2i		−	1.65314i	0.562831	−	0.826572i	$-0.309712\pi$
$884$	1033.45			0.0393198
$885$	−3455.08			−0.131233
$886$			4034.94i			0.152998i
$887$	1357.12			0.0513728			0.0256864	−	0.999670i	$-0.491823\pi$
$887$	1357.12			0.0513728			0.0256864	+	0.999670i	$0.491823\pi$
$888$	−3341.19	−	418.038i	−0.126264	−	0.0157978i
$889$	3633.45			0.137078
$890$			25213.9i			0.949631i
$891$	−21038.5			−0.791041
$892$	13047.5			0.489755
$893$			6043.60i			0.226474i
$894$		−	6969.73i		−	0.260741i
$895$	4268.56			0.159422
$896$		−	803.568i		−	0.0299613i
$897$	1180.71			0.0439495
$898$	−3597.76			−0.133696
$899$	4030.84			0.149539
$900$	4573.00			0.169370
$901$			13447.1i			0.497212i
$902$			9365.20i			0.345706i
$903$			2999.54i			0.110541i
$904$	−1002.56			−0.0368857
$905$		−	9658.88i		−	0.354776i
$906$			145.829i			0.00534749i
$907$			11877.1i			0.434809i	0.976082	+	0.217405i	$0.0697591\pi$
$907$			11877.1i			0.434809i	−0.976082	+	0.217405i	$0.930241\pi$
$908$			21576.2i			0.788579i
$909$	−29294.0			−1.06889
$910$		−	776.166i		−	0.0282744i
$911$		−	39948.6i		−	1.45286i	−0.687239	−	0.726431i	$-0.741178\pi$
$911$		−	39948.6i		−	1.45286i	0.687239	−	0.726431i	$-0.258822\pi$
$912$		−	625.832i		−	0.0227230i
$913$	22525.5			0.816524
$914$	62.3702			0.00225714
$915$	2909.99			0.105138
$916$	−18045.0			−0.650899
$917$			13603.2i			0.489878i
$918$	−6898.64			−0.248027
$919$		−	50764.6i		−	1.82216i	−0.412224	−	0.911082i	$-0.635248\pi$
$919$		−	50764.6i		−	1.82216i	0.412224	−	0.911082i	$-0.364752\pi$
$920$		−	6238.55i		−	0.223564i
$921$	−640.196			−0.0229047
$922$	−30741.8			−1.09808
$923$		−	2044.03i		−	0.0728928i
$924$	2157.58			0.0768174
$925$	1359.17	−	10863.2i	0.0483126	−	0.386140i
$926$	17862.8			0.633916
$927$		−	29235.0i		−	1.03582i
$928$	−7152.61			−0.253013
$929$	−50708.1			−1.79083			−0.895415	−	0.445233i	$-0.853121\pi$
$929$	−50708.1			−1.79083			−0.895415	+	0.445233i	$0.853121\pi$
$930$			589.404i			0.0207821i
$931$		−	6349.53i		−	0.223520i
$932$	−3540.35			−0.124429
$933$			12651.1i			0.443921i
$934$	30272.0			1.06053
$935$	14661.4			0.512812
$936$	−1330.13			−0.0464494
$937$	−22350.4			−0.779249			−0.389625	−	0.920974i	$-0.627395\pi$
$937$	−22350.4			−0.779249			−0.389625	+	0.920974i	$0.627395\pi$
$938$		−	9714.38i		−	0.338151i
$939$			11197.4i			0.389153i
$940$			10100.0i			0.350453i
$941$	−36996.6			−1.28167			−0.640836	−	0.767678i	$-0.721412\pi$
$941$	−36996.6			−1.28167			−0.640836	+	0.767678i	$0.721412\pi$
$942$		−	2474.42i		−	0.0855847i
$943$		−	9095.88i		−	0.314107i
$944$			3382.79i			0.116632i
$945$			5181.18i			0.178353i
$946$	−23475.0			−0.806805
$947$			31668.7i			1.08669i	0.839509	+	0.543345i	$0.182842\pi$
$947$			31668.7i			1.08669i	−0.839509	+	0.543345i	$0.817158\pi$
$948$			2237.24i			0.0766479i
$949$			3132.90i			0.107164i
$950$	2034.77			0.0694911
$951$	−11176.1			−0.381084
$952$	−1834.18			−0.0624435
$953$	15779.9			0.536370			0.268185	−	0.963367i	$-0.413576\pi$
$953$	15779.9			0.536370			0.268185	+	0.963367i	$0.413576\pi$
$954$		−	17307.4i		−	0.587367i
$955$	9833.93			0.333213
$956$			6163.69i			0.208523i
$957$		−	19204.8i		−	0.648697i
$958$	30057.0			1.01367
$959$	−1544.83			−0.0520178
$960$		−	1045.88i		−	0.0351622i
$961$	29465.8			0.989084
$962$	−395.335	+	3159.73i	−0.0132496	+	0.105898i
$963$	−29064.9			−0.972589
$964$		−	19021.7i		−	0.635526i
$965$	42359.9			1.41307
$966$	−2095.54			−0.0697959
$967$		−	45543.7i		−	1.51457i	−0.653087	−	0.757283i	$-0.726526\pi$
$967$		−	45543.7i		−	1.51457i	0.653087	−	0.757283i	$-0.273474\pi$
$968$			6237.66i			0.207114i
$969$	−1428.49			−0.0473578
$970$		−	5362.06i		−	0.177490i
$971$	−33760.6			−1.11579			−0.557894	−	0.829912i	$-0.688390\pi$
$971$	−33760.6			−1.11579			−0.557894	+	0.829912i	$0.688390\pi$
$972$	13626.0			0.449646
$973$	11240.4			0.370349
$974$	11267.4			0.370668
$975$			643.574i			0.0211394i
$976$		−	2849.10i		−	0.0934401i
$977$			28323.2i			0.927471i	0.885974	+	0.463736i	$0.153491\pi$
$977$			28323.2i			0.927471i	−0.885974	+	0.463736i	$0.846509\pi$
$978$	8916.54			0.291533
$979$			66283.0i			2.16385i
$980$		−	10611.3i		−	0.345882i
$981$			23393.8i			0.761373i
$982$			10199.1i			0.331431i
$983$	35611.5			1.15547			0.577737	−	0.816223i	$-0.303936\pi$
$983$	35611.5			1.15547			0.577737	+	0.816223i	$0.303936\pi$
$984$		−	1524.91i		−	0.0494028i
$985$		−	35342.4i		−	1.14325i
$986$			16326.2i			0.527314i
$987$	3392.60			0.109410
$988$	−591.843			−0.0190577
$989$	22799.9			0.733059
$990$	−18870.3			−0.605796
$991$		−	3498.83i		−	0.112153i	−0.998426	−	0.0560767i	$-0.982141\pi$
$991$		−	3498.83i		−	0.112153i	0.998426	−	0.0560767i	$-0.0178591\pi$
$992$	577.072			0.0184698
$993$			17644.6i			0.563883i
$994$			3627.77i			0.115760i
$995$	−18470.1			−0.588485
$996$	−3667.77			−0.116684
$997$			46736.3i			1.48461i	0.670064	+	0.742304i	$0.266267\pi$
$997$			46736.3i			1.48461i	−0.670064	+	0.742304i	$0.733733\pi$
$998$	27388.4			0.868702
$999$	2639.00	−	21092.3i	0.0835777	−	0.667998i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.b.a.73.2	✓	10
3.2	odd	2		666.4.c.d.73.9		10
4.3	odd	2		592.4.g.d.369.7		10
37.36	even	2	inner	74.4.b.a.73.7	yes	10
111.110	odd	2		666.4.c.d.73.2		10
148.147	odd	2		592.4.g.d.369.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.b.a.73.2	✓	10	1.1	even	1	trivial
74.4.b.a.73.7	yes	10	37.36	even	2	inner
592.4.g.d.369.7		10	4.3	odd	2
592.4.g.d.369.8		10	148.147	odd	2
666.4.c.d.73.2		10	111.110	odd	2
666.4.c.d.73.9		10	3.2	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

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

\(f(q)\)	\(=\)	\(q-2.00000i q^{2} -1.87017 q^{3} -4.00000 q^{4} -8.73820i q^{5} +3.74034i q^{6} -6.27788 q^{7} +8.00000i q^{8} -23.5025 q^{9} +O(q^{10})\)	\(q-2.00000i q^{2} -1.87017 q^{3} -4.00000 q^{4} -8.73820i q^{5} +3.74034i q^{6} -6.27788 q^{7} +8.00000i q^{8} -23.5025 q^{9} -17.4764 q^{10} -45.9424 q^{11} +7.48068 q^{12} -7.07441i q^{13} +12.5558i q^{14} +16.3419i q^{15} +16.0000 q^{16} -36.5208i q^{17} +47.0049i q^{18} +20.9149i q^{19} +34.9528i q^{20} +11.7407 q^{21} +91.8849i q^{22} -89.2425i q^{23} -14.9614i q^{24} +48.6438 q^{25} -14.1488 q^{26} +94.4482 q^{27} +25.1115 q^{28} -223.519i q^{29} +32.6838 q^{30} +18.0335i q^{31} -32.0000i q^{32} +85.9201 q^{33} -73.0415 q^{34} +54.8573i q^{35} +94.0099 q^{36} +(27.9412 - 223.321i) q^{37} +41.8299 q^{38} +13.2303i q^{39} +69.9056 q^{40} +101.923 q^{41} -23.4814i q^{42} +255.483i q^{43} +183.770 q^{44} +205.369i q^{45} -178.485 q^{46} +288.961 q^{47} -29.9227 q^{48} -303.588 q^{49} -97.2877i q^{50} +68.3000i q^{51} +28.2976i q^{52} -368.204 q^{53} -188.896i q^{54} +401.454i q^{55} -50.2230i q^{56} -39.1145i q^{57} -447.038 q^{58} +211.424i q^{59} -65.3677i q^{60} -178.069i q^{61} +36.0670 q^{62} +147.546 q^{63} -64.0000 q^{64} -61.8176 q^{65} -171.840i q^{66} -773.700 q^{67} +146.083i q^{68} +166.899i q^{69} +109.715 q^{70} +288.933 q^{71} -188.020i q^{72} -442.850 q^{73} +(-446.642 - 55.8824i) q^{74} -90.9722 q^{75} -83.6598i q^{76} +288.421 q^{77} +26.4607 q^{78} +299.069i q^{79} -139.811i q^{80} +457.933 q^{81} -203.846i q^{82} -490.299 q^{83} -46.9628 q^{84} -319.126 q^{85} +510.965 q^{86} +418.019i q^{87} -367.540i q^{88} -1442.74i q^{89} +410.739 q^{90} +44.4122i q^{91} +356.970i q^{92} -33.7257i q^{93} -577.922i q^{94} +182.759 q^{95} +59.8454i q^{96} +306.817i q^{97} +607.177i q^{98} +1079.76 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 10 q + 14 q^{3} - 40 q^{4} - 4 q^{7} + 172 q^{9}+O(q^{10}) \) 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

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