LMFDB - Embedded newform 245.4.e.l.116.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [245,4,Mod(116,245)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(245, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("245.116");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 245 = 5 \cdot 7^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	245.e (of order $3$, degree $2$, not 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:	$14.4554679514$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{2}, \sqrt{-3})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 2x^{2} + 4 $ x^4 + 2*x^2 + 4
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 35)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			116.1
Root			$0.707107 - 1.22474i$ of defining polynomial
Character	$\chi$	$=$	245.116
Dual form			245.4.e.l.226.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.792893 + 1.37333i) q^{2} +(-2.62132 + 4.54026i) q^{3} +(2.74264 - 4.75039i) q^{4} +(2.50000 + 4.33013i) q^{5} -8.31371 q^{6} +21.3848 q^{8} +(-0.242641 - 0.420266i) q^{9} +O(q^{10})$	\(q+(0.792893 + 1.37333i) q^{2} +(-2.62132 + 4.54026i) q^{3} +(2.74264 - 4.75039i) q^{4} +(2.50000 + 4.33013i) q^{5} -8.31371 q^{6} +21.3848 q^{8} +(-0.242641 - 0.420266i) q^{9} +(-3.96447 + 6.86666i) q^{10} +(-14.0711 + 24.3718i) q^{11} +(14.3787 + 24.9046i) q^{12} +3.85786 q^{13} -26.2132 q^{15} +(-4.98528 - 8.63476i) q^{16} +(19.1838 - 33.2273i) q^{17} +(0.384776 - 0.666452i) q^{18} +(58.3848 + 101.125i) q^{19} +27.4264 q^{20} -44.6274 q^{22} +(88.2315 + 152.821i) q^{23} +(-56.0563 + 97.0924i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(3.05887 + 5.29813i) q^{26} -139.007 q^{27} -209.853 q^{29} +(-20.7843 - 35.9994i) q^{30} +(-103.711 + 179.632i) q^{31} +(93.4447 - 161.851i) q^{32} +(-73.7696 - 127.773i) q^{33} +60.8427 q^{34} -2.66190 q^{36} +(7.83348 + 13.5680i) q^{37} +(-92.5858 + 160.363i) q^{38} +(-10.1127 + 17.5157i) q^{39} +(53.4619 + 92.5988i) q^{40} +10.5736 q^{41} -325.929 q^{43} +(77.1838 + 133.686i) q^{44} +(1.21320 - 2.10133i) q^{45} +(-139.916 + 242.342i) q^{46} +(-94.2548 - 163.254i) q^{47} +52.2721 q^{48} -39.6447 q^{50} +(100.574 + 174.199i) q^{51} +(10.5807 - 18.3264i) q^{52} +(137.591 - 238.314i) q^{53} +(-110.218 - 190.903i) q^{54} -140.711 q^{55} -612.181 q^{57} +(-166.391 - 288.197i) q^{58} +(21.9096 - 37.9485i) q^{59} +(-71.8934 + 124.523i) q^{60} +(427.551 + 740.540i) q^{61} -328.926 q^{62} +216.602 q^{64} +(9.64466 + 16.7050i) q^{65} +(116.983 - 202.620i) q^{66} +(272.710 - 472.347i) q^{67} +(-105.228 - 182.261i) q^{68} -925.132 q^{69} +1026.97 q^{71} +(-5.18882 - 8.98729i) q^{72} +(-126.439 + 218.998i) q^{73} +(-12.4222 + 21.5159i) q^{74} +(-65.5330 - 113.507i) q^{75} +640.514 q^{76} -32.0732 q^{78} +(461.321 + 799.031i) q^{79} +(24.9264 - 43.1738i) q^{80} +(370.934 - 642.476i) q^{81} +(8.38373 + 14.5210i) q^{82} +960.071 q^{83} +191.838 q^{85} +(-258.427 - 447.608i) q^{86} +(550.091 - 952.786i) q^{87} +(-300.907 + 521.186i) q^{88} +(-66.6026 - 115.359i) q^{89} +3.84776 q^{90} +967.949 q^{92} +(-543.718 - 941.747i) q^{93} +(149.468 - 258.886i) q^{94} +(-291.924 + 505.627i) q^{95} +(489.897 + 848.526i) q^{96} +1021.11 q^{97} +13.6569 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 6 q^{2} - 2 q^{3} - 6 q^{4} + 10 q^{5} + 12 q^{6} + 12 q^{8} + 16 q^{9}+O(q^{10}) $ 4 * q + 6 * q^2 - 2 * q^3 - 6 * q^4 + 10 * q^5 + 12 * q^6 + 12 * q^8 + 16 * q^9	\( 4 q + 6 q^{2} - 2 q^{3} - 6 q^{4} + 10 q^{5} + 12 q^{6} + 12 q^{8} + 16 q^{9} - 30 q^{10} - 28 q^{11} + 66 q^{12} + 72 q^{13} - 20 q^{15} + 14 q^{16} - 76 q^{17} - 72 q^{18} + 160 q^{19} - 60 q^{20} - 88 q^{22} + 22 q^{23} - 162 q^{24} - 50 q^{25} + 148 q^{26} + 4 q^{27} - 500 q^{29} + 30 q^{30} - 132 q^{31} - 42 q^{32} - 148 q^{33} - 888 q^{34} - 384 q^{36} + 416 q^{37} - 376 q^{38} + 84 q^{39} + 30 q^{40} + 212 q^{41} - 1332 q^{43} + 156 q^{44} - 80 q^{45} + 402 q^{46} - 196 q^{47} + 260 q^{48} - 300 q^{50} + 572 q^{51} - 348 q^{52} + 952 q^{53} + 402 q^{54} - 280 q^{55} - 944 q^{57} - 510 q^{58} + 840 q^{59} - 330 q^{60} + 98 q^{61} + 8 q^{62} - 1204 q^{64} + 180 q^{65} + 236 q^{66} + 1286 q^{67} - 1524 q^{68} - 2852 q^{69} + 2128 q^{71} - 264 q^{72} - 172 q^{73} - 1792 q^{74} - 50 q^{75} + 288 q^{76} + 856 q^{78} + 1240 q^{79} - 70 q^{80} + 754 q^{81} + 438 q^{82} + 3812 q^{83} - 760 q^{85} - 2018 q^{86} + 970 q^{87} - 604 q^{88} + 650 q^{89} - 720 q^{90} + 5484 q^{92} - 1332 q^{93} + 332 q^{94} - 800 q^{95} + 1722 q^{96} + 1256 q^{97} + 32 q^{99}+O(q^{100}) \) 4 * q + 6 * q^2 - 2 * q^3 - 6 * q^4 + 10 * q^5 + 12 * q^6 + 12 * q^8 + 16 * q^9 - 30 * q^10 - 28 * q^11 + 66 * q^12 + 72 * q^13 - 20 * q^15 + 14 * q^16 - 76 * q^17 - 72 * q^18 + 160 * q^19 - 60 * q^20 - 88 * q^22 + 22 * q^23 - 162 * q^24 - 50 * q^25 + 148 * q^26 + 4 * q^27 - 500 * q^29 + 30 * q^30 - 132 * q^31 - 42 * q^32 - 148 * q^33 - 888 * q^34 - 384 * q^36 + 416 * q^37 - 376 * q^38 + 84 * q^39 + 30 * q^40 + 212 * q^41 - 1332 * q^43 + 156 * q^44 - 80 * q^45 + 402 * q^46 - 196 * q^47 + 260 * q^48 - 300 * q^50 + 572 * q^51 - 348 * q^52 + 952 * q^53 + 402 * q^54 - 280 * q^55 - 944 * q^57 - 510 * q^58 + 840 * q^59 - 330 * q^60 + 98 * q^61 + 8 * q^62 - 1204 * q^64 + 180 * q^65 + 236 * q^66 + 1286 * q^67 - 1524 * q^68 - 2852 * q^69 + 2128 * q^71 - 264 * q^72 - 172 * q^73 - 1792 * q^74 - 50 * q^75 + 288 * q^76 + 856 * q^78 + 1240 * q^79 - 70 * q^80 + 754 * q^81 + 438 * q^82 + 3812 * q^83 - 760 * q^85 - 2018 * q^86 + 970 * q^87 - 604 * q^88 + 650 * q^89 - 720 * q^90 + 5484 * q^92 - 1332 * q^93 + 332 * q^94 - 800 * q^95 + 1722 * q^96 + 1256 * q^97 + 32 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/245\mathbb{Z}\right)^\times$.

$n$	$101$	$197$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$

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 $

$2$	0.792893	+	1.37333i	0.280330	+	0.485546i	0.971466	−	0.237179i	$-0.0762227\pi$
$2$	0.792893	+	1.37333i	0.280330	+	0.485546i	−0.691136	+	0.722725i	$0.742889\pi$
$3$	−2.62132	+	4.54026i	−0.504473	+	0.873773i	0.495513	+	0.868600i	$0.334980\pi$
$3$	−2.62132	+	4.54026i	−0.504473	+	0.873773i	−0.999987	+	0.00517309i	$0.998353\pi$
$4$	2.74264	−	4.75039i	0.342830	−	0.593799i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$5$	2.50000	+	4.33013i	0.223607	+	0.387298i
$6$	−8.31371			−0.565676
$7$		0			0
$7$		0			0
$8$	21.3848			0.945083
$9$	−0.242641	−	0.420266i	−0.00898669	−	0.0155654i
$10$	−3.96447	+	6.86666i	−0.125367	+	0.217143i
$11$	−14.0711	+	24.3718i	−0.385690	+	0.668034i	−0.991865	−	0.127297i	$-0.959370\pi$
$11$	−14.0711	+	24.3718i	−0.385690	+	0.668034i	0.606175	+	0.795331i	$0.292703\pi$
$12$	14.3787	+	24.9046i	0.345897	+	0.599112i
$13$	3.85786			0.0823061			0.0411530	−	0.999153i	$-0.486897\pi$
$13$	3.85786			0.0823061			0.0411530	+	0.999153i	$0.486897\pi$
$14$		0			0
$15$	−26.2132			−0.451215
$16$	−4.98528	−	8.63476i	−0.0778950	−	0.134918i
$17$	19.1838	−	33.2273i	0.273691	−	0.474047i	−0.696113	−	0.717932i	$-0.745089\pi$
$17$	19.1838	−	33.2273i	0.273691	−	0.474047i	0.969804	+	0.243885i	$0.0784221\pi$
$18$	0.384776	−	0.666452i	0.00503848	−	0.00872690i
$19$	58.3848	+	101.125i	0.704968	+	1.22104i	0.966703	+	0.255900i	$0.0823719\pi$
$19$	58.3848	+	101.125i	0.704968	+	1.22104i	−0.261735	+	0.965140i	$0.584295\pi$
$20$	27.4264			0.306637
$21$		0			0
$22$	−44.6274			−0.432482
$23$	88.2315	+	152.821i	0.799893	+	1.38546i	0.919685	+	0.392656i	$0.128444\pi$
$23$	88.2315	+	152.821i	0.799893	+	1.38546i	−0.119792	+	0.992799i	$0.538223\pi$
$24$	−56.0563	+	97.0924i	−0.476769	+	0.825788i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	3.05887	+	5.29813i	0.0230729	+	0.0399634i
$27$	−139.007			−0.990812
$28$		0			0
$29$	−209.853			−1.34375			−0.671874	−	0.740666i	$-0.734510\pi$
$29$	−209.853			−1.34375			−0.671874	+	0.740666i	$0.734510\pi$
$30$	−20.7843	−	35.9994i	−0.126489	−	0.219085i
$31$	−103.711	+	179.632i	−0.600871	+	1.04074i	0.391819	+	0.920042i	$0.371846\pi$
$31$	−103.711	+	179.632i	−0.600871	+	1.04074i	−0.992690	+	0.120696i	$0.961487\pi$
$32$	93.4447	−	161.851i	0.516214	−	0.894109i
$33$	−73.7696	−	127.773i	−0.389140	−	0.674011i
$34$	60.8427			0.306895
$35$		0			0
$36$	−2.66190			−0.0123236
$37$	7.83348	+	13.5680i	0.0348058	+	0.0602855i	0.882904	−	0.469554i	$-0.155585\pi$
$37$	7.83348	+	13.5680i	0.0348058	+	0.0602855i	−0.848098	+	0.529840i	$0.822252\pi$
$38$	−92.5858	+	160.363i	−0.395247	+	0.684588i
$39$	−10.1127	+	17.5157i	−0.0415212	+	0.0719169i
$40$	53.4619	+	92.5988i	0.211327	+	0.366029i
$41$	10.5736			0.0402760			0.0201380	−	0.999797i	$-0.493589\pi$
$41$	10.5736			0.0402760			0.0201380	+	0.999797i	$0.493589\pi$
$42$		0			0
$43$	−325.929			−1.15590			−0.577950	−	0.816072i	$-0.696147\pi$
$43$	−325.929			−1.15590			−0.577950	+	0.816072i	$0.696147\pi$
$44$	77.1838	+	133.686i	0.264452	+	0.458044i
$45$	1.21320	−	2.10133i	0.00401897	−	0.00696106i
$46$	−139.916	+	242.342i	−0.448468	+	0.776770i
$47$	−94.2548	−	163.254i	−0.292521	−	0.506661i	0.681884	−	0.731460i	$-0.261161\pi$
$47$	−94.2548	−	163.254i	−0.292521	−	0.506661i	−0.974405	+	0.224799i	$0.927827\pi$
$48$	52.2721			0.157184
$49$		0			0
$50$	−39.6447			−0.112132
$51$	100.574	+	174.199i	0.276140	+	0.478288i
$52$	10.5807	−	18.3264i	0.0282170	−	0.0488733i
$53$	137.591	−	238.314i	0.356595	−	0.617641i	−0.630794	−	0.775950i	$-0.717271\pi$
$53$	137.591	−	238.314i	0.356595	−	0.617641i	0.987390	+	0.158309i	$0.0506041\pi$
$54$	−110.218	−	190.903i	−0.277755	−	0.481085i
$55$	−140.711			−0.344971
$56$		0			0
$57$	−612.181			−1.42255
$58$	−166.391	−	288.197i	−0.376693	−	0.652451i
$59$	21.9096	−	37.9485i	0.0483455	−	0.0837369i	−0.840840	−	0.541284i	$-0.817938\pi$
$59$	21.9096	−	37.9485i	0.0483455	−	0.0837369i	0.889186	+	0.457547i	$0.151272\pi$
$60$	−71.8934	+	124.523i	−0.154690	+	0.267931i
$61$	427.551	+	740.540i	0.897414	+	1.55437i	0.830788	+	0.556589i	$0.187890\pi$
$61$	427.551	+	740.540i	0.897414	+	1.55437i	0.0666267	+	0.997778i	$0.478776\pi$
$62$	−328.926			−0.673768
$63$		0			0
$64$	216.602			0.423051
$65$	9.64466	+	16.7050i	0.0184042	+	0.0318770i
$66$	116.983	−	202.620i	0.218175	−	0.377891i
$67$	272.710	−	472.347i	0.497265	−	0.861289i	−0.502730	−	0.864444i	$-0.667671\pi$
$67$	272.710	−	472.347i	0.497265	−	0.861289i	0.999995	+	0.00315473i	$0.00100418\pi$
$68$	−105.228	−	182.261i	−0.187659	−	0.325035i
$69$	−925.132			−1.61410
$70$		0			0
$71$	1026.97			1.71661			0.858306	−	0.513138i	$-0.171517\pi$
$71$	1026.97			1.71661			0.858306	+	0.513138i	$0.171517\pi$
$72$	−5.18882	−	8.98729i	−0.00849317	−	0.0147106i
$73$	−126.439	+	218.998i	−0.202719	+	0.351120i	−0.949404	−	0.314058i	$-0.898311\pi$
$73$	−126.439	+	218.998i	−0.202719	+	0.351120i	0.746684	+	0.665179i	$0.231645\pi$
$74$	−12.4222	+	21.5159i	−0.0195142	+	0.0337997i
$75$	−65.5330	−	113.507i	−0.100895	−	0.174755i
$76$	640.514			0.966737
$77$		0			0
$78$	−32.0732			−0.0465586
$79$	461.321	+	799.031i	0.656996	+	1.13795i	0.981390	+	0.192028i	$0.0615063\pi$
$79$	461.321	+	799.031i	0.656996	+	1.13795i	−0.324394	+	0.945922i	$0.605160\pi$
$80$	24.9264	−	43.1738i	0.0348357	−	0.0603372i
$81$	370.934	−	642.476i	0.508825	−	0.881311i
$82$	8.38373	+	14.5210i	0.0112906	+	0.0195559i
$83$	960.071			1.26966			0.634828	−	0.772653i	$-0.281071\pi$
$83$	960.071			1.26966			0.634828	+	0.772653i	$0.281071\pi$
$84$		0			0
$85$	191.838			0.244797
$86$	−258.427	−	447.608i	−0.324034	−	0.561243i
$87$	550.091	−	952.786i	0.677885	−	1.17413i
$88$	−300.907	+	521.186i	−0.364509	+	0.631347i
$89$	−66.6026	−	115.359i	−0.0793243	−	0.137394i	0.823634	−	0.567121i	$-0.191943\pi$
$89$	−66.6026	−	115.359i	−0.0793243	−	0.137394i	−0.902959	+	0.429728i	$0.858610\pi$
$90$	3.84776			0.00450655
$91$		0			0
$92$	967.949			1.09691
$93$	−543.718	−	941.747i	−0.606246	−	1.05005i
$94$	149.468	−	258.886i	0.164005	−	0.284065i
$95$	−291.924	+	505.627i	−0.315271	+	0.546066i
$96$	489.897	+	848.526i	0.520832	+	0.902108i
$97$	1021.11			1.06884			0.534421	−	0.845218i	$-0.320530\pi$
$97$	1021.11			1.06884			0.534421	+	0.845218i	$0.320530\pi$
$98$		0			0
$99$	13.6569			0.0138643
$100$	68.5660	+	118.760i	0.0685660	+	0.118760i
$101$	481.779	−	834.466i	0.474642	−	0.822104i	−0.524936	−	0.851141i	$-0.675911\pi$
$101$	481.779	−	834.466i	0.474642	−	0.822104i	0.999578	+	0.0290376i	$0.00924427\pi$
$102$	−159.488	+	276.242i	−0.154820	+	0.268157i
$103$	−899.150	−	1557.37i	−0.860155	−	1.48983i	−0.871779	−	0.489899i	$-0.837034\pi$
$103$	−899.150	−	1557.37i	−0.860155	−	1.48983i	0.0116248	−	0.999932i	$-0.496300\pi$
$104$	82.4996			0.0777860
$105$		0			0
$106$	436.379			0.399858
$107$	−139.501	−	241.624i	−0.126038	−	0.218305i	0.796100	−	0.605165i	$-0.206893\pi$
$107$	−139.501	−	241.624i	−0.126038	−	0.218305i	−0.922138	+	0.386860i	$0.873560\pi$
$108$	−381.247	+	660.339i	−0.339680	+	0.588344i
$109$	−390.537	+	676.429i	−0.343180	+	0.594405i	−0.985021	−	0.172432i	$-0.944837\pi$
$109$	−390.537	+	676.429i	−0.343180	+	0.594405i	0.641841	+	0.766837i	$0.278171\pi$
$110$	−111.569	−	193.242i	−0.0967058	−	0.167499i
$111$	−82.1362			−0.0702345
$112$		0			0
$113$	−587.239			−0.488874			−0.244437	−	0.969665i	$-0.578603\pi$
$113$	−587.239			−0.488874			−0.244437	+	0.969665i	$0.578603\pi$
$114$	−485.394	−	840.727i	−0.398783	−	0.690713i
$115$	−441.157	+	764.107i	−0.357723	+	0.619594i
$116$	−575.551	+	996.883i	−0.460677	+	0.797916i
$117$	−0.936075	−	1.62133i	−0.000739659	−	0.00128113i
$118$	69.4879			0.0542108
$119$		0			0
$120$	−560.563			−0.426435
$121$	269.510	+	466.805i	0.202487	+	0.350718i
$122$	−678.004	+	1174.34i	−0.503145	+	0.871472i
$123$	−27.7168	+	48.0069i	−0.0203182	+	0.0351921i
$124$	568.882	+	985.333i	0.411993	+	0.713593i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	1559.62			1.08972			0.544860	−	0.838527i	$-0.316583\pi$
$127$	1559.62			1.08972			0.544860	+	0.838527i	$0.316583\pi$
$128$	−575.815	−	997.341i	−0.397620	−	0.688698i
$129$	854.364	−	1479.80i	0.583121	−	1.00999i
$130$	−15.2944	+	26.4906i	−0.0103185	+	0.0178722i
$131$	−826.823	−	1432.10i	−0.551449	−	0.955138i	−0.998170	−	0.0604645i	$-0.980742\pi$
$131$	−826.823	−	1432.10i	−0.551449	−	0.955138i	0.446721	−	0.894673i	$-0.352592\pi$
$132$	−809.294			−0.533636
$133$		0			0
$134$	864.918			0.557594
$135$	−347.518	−	601.919i	−0.221552	−	0.383740i
$136$	410.241	−	710.557i	0.258661	−	0.448013i
$137$	148.329	−	256.913i	0.0925007	−	0.160216i	−0.816062	−	0.577964i	$-0.803847\pi$
$137$	148.329	−	256.913i	0.0925007	−	0.160216i	0.908563	+	0.417748i	$0.137181\pi$
$138$	−733.531	−	1270.51i	−0.452480	−	0.783719i
$139$	−237.868			−0.145149			−0.0725745	−	0.997363i	$-0.523121\pi$
$139$	−237.868			−0.145149			−0.0725745	+	0.997363i	$0.523121\pi$
$140$		0			0
$141$	988.288			0.590276
$142$	814.281	+	1410.38i	0.481218	+	0.833494i
$143$	−54.2843	+	94.0231i	−0.0317446	+	0.0549833i
$144$	−2.41926	+	4.19029i	−0.00140004	+	0.00242494i
$145$	−524.632	−	908.689i	−0.300471	−	0.520431i
$146$	−401.009			−0.227313
$147$		0			0
$148$	85.9377			0.0477299
$149$	−1368.56	−	2370.41i	−0.752459	−	1.30330i	−0.946628	−	0.322329i	$-0.895534\pi$
$149$	−1368.56	−	2370.41i	−0.752459	−	1.30330i	0.194169	−	0.980968i	$-0.437799\pi$
$150$	103.921	−	179.997i	0.0565676	−	0.0979780i
$151$	1781.82	−	3086.21i	0.960283	−	1.66326i	0.238495	−	0.971144i	$-0.423346\pi$
$151$	1781.82	−	3086.21i	0.960283	−	1.66326i	0.721788	−	0.692114i	$-0.243321\pi$
$152$	1248.55	+	2162.54i	0.666253	+	1.15398i
$153$	−18.6190			−0.00983831
$154$		0			0
$155$	−1037.11			−0.537435
$156$	55.4710	+	96.0786i	0.0284694	+	0.0493105i
$157$	624.539	−	1081.73i	0.317475	−	0.549884i	−0.662485	−	0.749075i	$-0.730498\pi$
$157$	624.539	−	1081.73i	0.317475	−	0.549884i	0.979961	+	0.199191i	$0.0638316\pi$
$158$	−731.556	+	1267.09i	−0.368351	+	0.638003i
$159$	721.339	+	1249.40i	0.359786	+	0.623167i
$160$	934.447			0.461716
$161$		0			0
$162$	1176.44			0.570556
$163$	982.318	+	1701.42i	0.472031	+	0.817582i	0.999488	−	0.0320000i	$-0.0101876\pi$
$163$	982.318	+	1701.42i	0.472031	+	0.817582i	−0.527457	+	0.849582i	$0.676854\pi$
$164$	28.9996	−	50.2287i	0.0138078	−	0.0239159i
$165$	368.848	−	638.863i	0.174029	−	0.301427i
$166$	761.234	+	1318.50i	0.355923	+	0.616477i
$167$	939.402			0.435288			0.217644	−	0.976028i	$-0.430163\pi$
$167$	939.402			0.435288			0.217644	+	0.976028i	$0.430163\pi$
$168$		0			0
$169$	−2182.12			−0.993226
$170$	152.107	+	263.457i	0.0686239	+	0.118860i
$171$	28.3330	−	49.0743i	0.0126707	−	0.0219462i
$172$	−893.906	+	1548.29i	−0.396277	+	0.686372i
$173$	−1351.22	−	2340.38i	−0.593821	−	1.02853i	−0.993712	−	0.111966i	$-0.964285\pi$
$173$	−1351.22	−	2340.38i	−0.593821	−	1.02853i	0.399891	−	0.916563i	$-0.369048\pi$
$174$	1744.66			0.760126
$175$		0			0
$176$	280.593			0.120173
$177$	114.864	+	198.951i	0.0487781	+	0.0844861i
$178$	105.617	−	182.935i	0.0444740	−	0.0770312i
$179$	717.024	−	1241.92i	0.299402	−	0.518579i	−0.676597	−	0.736353i	$-0.736546\pi$
$179$	717.024	−	1241.92i	0.299402	−	0.518579i	0.975999	+	0.217774i	$0.0698796\pi$
$180$	−6.65476	−	11.5264i	−0.00275565	−	0.00477292i
$181$	−2711.21			−1.11339			−0.556693	−	0.830718i	$-0.687930\pi$
$181$	−2711.21			−1.11339			−0.556693	+	0.830718i	$0.687930\pi$
$182$		0			0
$183$	−4482.99			−1.81089
$184$	1886.81	+	3268.05i	0.755965	+	1.30937i
$185$	−39.1674	+	67.8399i	−0.0155656	+	0.0269605i
$186$	862.220	−	1493.41i	0.339898	−	0.588721i
$187$	539.872	+	935.086i	0.211120	+	0.365670i
$188$	−1034.03			−0.401140
$189$		0			0
$190$	−925.858			−0.353520
$191$	1747.30	+	3026.41i	0.661938	+	1.14651i	0.980106	+	0.198476i	$0.0635992\pi$
$191$	1747.30	+	3026.41i	0.661938	+	1.14651i	−0.318168	+	0.948034i	$0.603067\pi$
$192$	−567.784	+	983.430i	−0.213418	+	0.369651i
$193$	814.881	−	1411.41i	0.303919	−	0.526403i	−0.673101	−	0.739551i	$-0.735038\pi$
$193$	814.881	−	1411.41i	0.303919	−	0.526403i	0.977020	+	0.213147i	$0.0683714\pi$
$194$	809.629	+	1402.32i	0.299629	+	0.518972i
$195$	−101.127			−0.0371377
$196$		0			0
$197$	693.696			0.250882			0.125441	−	0.992101i	$-0.459965\pi$
$197$	693.696			0.250882			0.125441	+	0.992101i	$0.459965\pi$
$198$	10.8284	+	18.7554i	0.00388658	+	0.00673175i
$199$	−1902.81	+	3295.76i	−0.677821	+	1.17402i	0.297815	+	0.954624i	$0.403742\pi$
$199$	−1902.81	+	3295.76i	−0.677821	+	1.17402i	−0.975636	+	0.219397i	$0.929591\pi$
$200$	−267.310	+	462.994i	−0.0945083	+	0.163693i
$201$	1429.72	+	2476.35i	0.501714	+	0.868995i
$202$	1528.00			0.532226
$203$		0			0
$204$	1103.35			0.378676
$205$	26.4340	+	45.7850i	0.00900600	+	0.0155988i
$206$	1425.86	−	2469.66i	0.482254	−	0.835289i
$207$	42.8171	−	74.1614i	0.0143768	−	0.0249013i
$208$	−19.2325	−	33.3117i	−0.00641123	−	0.0111046i
$209$	−3286.14			−1.08760
$210$		0			0
$211$	−627.239			−0.204649			−0.102324	−	0.994751i	$-0.532628\pi$
$211$	−627.239			−0.204649			−0.102324	+	0.994751i	$0.532628\pi$
$212$	−754.724	−	1307.22i	−0.244503	−	0.423492i
$213$	−2692.03	+	4662.73i	−0.865985	+	1.49993i
$214$	221.220	−	383.164i	0.0706648	−	0.122395i
$215$	−814.822	−	1411.31i	−0.258467	−	0.447678i
$216$	−2972.64			−0.936400
$217$		0			0
$218$	−1238.62			−0.384815
$219$	−662.872	−	1148.13i	−0.204533	−	0.354262i
$220$	−385.919	+	668.431i	−0.118267	+	0.204844i
$221$	74.0084	−	128.186i	0.0225264	−	0.0390169i
$222$	−65.1253	−	112.800i	−0.0196888	−	0.0341021i
$223$	2000.99			0.600878			0.300439	−	0.953801i	$-0.402867\pi$
$223$	2000.99			0.600878			0.300439	+	0.953801i	$0.402867\pi$
$224$		0			0
$225$	12.1320			0.00359468
$226$	−465.618	−	806.473i	−0.137046	−	0.237371i
$227$	−796.121	+	1378.92i	−0.232777	+	0.403182i	−0.958624	−	0.284674i	$-0.908115\pi$
$227$	−796.121	+	1378.92i	−0.232777	+	0.403182i	0.725847	+	0.687856i	$0.241448\pi$
$228$	−1678.99	+	2908.10i	−0.487693	+	0.844709i
$229$	−1962.58	−	3399.29i	−0.566336	−	0.980923i	−0.996924	−	0.0783742i	$-0.975027\pi$
$229$	−1962.58	−	3399.29i	−0.566336	−	0.980923i	0.430588	−	0.902549i	$-0.358306\pi$
$230$	−1399.16			−0.401122
$231$		0			0
$232$	−4487.66			−1.26995
$233$	−1084.88	−	1879.06i	−0.305032	−	0.528331i	0.672236	−	0.740337i	$-0.265334\pi$
$233$	−1084.88	−	1879.06i	−0.305032	−	0.528331i	−0.977269	+	0.212005i	$0.932001\pi$
$234$	1.48441	−	2.57108i	0.000414698	−	0.000718277i
$235$	471.274	−	816.271i	0.130819	−	0.226586i
$236$	−120.180	−	208.158i	−0.0331486	−	0.0574151i
$237$	−4837.08			−1.32575
$238$		0			0
$239$	1057.70			0.286262			0.143131	−	0.989704i	$-0.454283\pi$
$239$	1057.70			0.286262			0.143131	+	0.989704i	$0.454283\pi$
$240$	130.680	+	226.345i	0.0351474	+	0.0608770i
$241$	1199.62	−	2077.80i	0.320640	−	0.555365i	−0.659980	−	0.751283i	$-0.729435\pi$
$241$	1199.62	−	2077.80i	0.320640	−	0.555365i	0.980620	+	0.195918i	$0.0627686\pi$
$242$	−427.385	+	740.253i	−0.113526	+	0.196633i
$243$	68.0749	+	117.909i	0.0179712	+	0.0311271i
$244$	4690.47			1.23064
$245$		0			0
$246$	−87.9058			−0.0227832
$247$	225.241	+	390.128i	0.0580231	+	0.100499i
$248$	−2217.83	+	3841.39i	−0.567872	+	0.983584i
$249$	−2516.65	+	4358.97i	−0.640508	+	1.10939i
$250$	−99.1117	−	171.666i	−0.0250735	−	0.0434286i
$251$	3812.95			0.958848			0.479424	−	0.877583i	$-0.340846\pi$
$251$	3812.95			0.958848			0.479424	+	0.877583i	$0.340846\pi$
$252$		0			0
$253$	−4966.05			−1.23404
$254$	1236.62	+	2141.88i	0.305481	+	0.529109i
$255$	−502.868	+	870.993i	−0.123493	+	0.213897i
$256$	1779.53	−	3082.23i	0.434455	−	0.752499i
$257$	1745.08	+	3022.57i	0.423561	+	0.733629i	0.996285	−	0.0861194i	$-0.0274466\pi$
$257$	1745.08	+	3022.57i	0.423561	+	0.733629i	−0.572724	+	0.819748i	$0.694113\pi$
$258$	2709.68			0.653865
$259$		0			0
$260$	105.807			0.0252381
$261$	50.9188	+	88.1940i	0.0120758	+	0.0209160i
$262$	1311.16	−	2271.00i	0.309175	−	0.535508i
$263$	−3562.28	+	6170.05i	−0.835207	+	1.44662i	0.0586547	+	0.998278i	$0.481319\pi$
$263$	−3562.28	+	6170.05i	−0.835207	+	1.44662i	−0.893862	+	0.448343i	$0.852014\pi$
$264$	−1577.55	−	2732.39i	−0.367770	−	0.636996i
$265$	1375.91			0.318949
$266$		0			0
$267$	698.347			0.160068
$268$	−1495.89	−	2590.96i	−0.340955	−	0.590552i
$269$	−213.971	+	370.609i	−0.0484984	+	0.0840017i	−0.889256	−	0.457411i	$-0.848777\pi$
$269$	−213.971	+	370.609i	−0.0484984	+	0.0840017i	0.840757	+	0.541412i	$0.182110\pi$
$270$	551.089	−	954.514i	0.124216	−	0.215148i
$271$	4094.29	+	7091.52i	0.917751	+	1.58959i	0.802824	+	0.596217i	$0.203330\pi$
$271$	4094.29	+	7091.52i	0.917751	+	1.58959i	0.114927	+	0.993374i	$0.463337\pi$
$272$	−382.546			−0.0852767
$273$		0			0
$274$	470.436			0.103723
$275$	−351.777	−	609.295i	−0.0771379	−	0.133607i
$276$	−2537.30	+	4394.74i	−0.553362	+	0.958450i
$277$	2084.98	−	3611.29i	0.452254	−	0.783326i	−0.546272	−	0.837608i	$-0.683954\pi$
$277$	2084.98	−	3611.29i	0.452254	−	0.783326i	0.998526	+	0.0542815i	$0.0172868\pi$
$278$	−188.604	−	326.672i	−0.0406896	−	0.0704765i
$279$	100.658			0.0215994
$280$		0			0
$281$	1284.60			0.272714			0.136357	−	0.990660i	$-0.456461\pi$
$281$	1284.60			0.272714			0.136357	+	0.990660i	$0.456461\pi$
$282$	783.607	+	1357.25i	0.165472	+	0.286606i
$283$	2394.67	−	4147.70i	0.502998	−	0.871219i	−0.496996	−	0.867753i	$-0.665563\pi$
$283$	2394.67	−	4147.70i	0.502998	−	0.871219i	0.999994	−	0.00346581i	$-0.00110320\pi$
$284$	2816.62	−	4878.53i	0.588506	−	1.01932i
$285$	−1530.45	−	2650.82i	−0.318092	−	0.550951i
$286$	−172.167			−0.0355959
$287$		0			0
$288$	−90.6939			−0.0185562
$289$	1720.47	+	2979.93i	0.350186	+	0.606541i
$290$	831.954	−	1440.99i	0.168462	−	0.291785i
$291$	−2676.65	+	4636.09i	−0.539202	+	0.933926i
$292$	693.551	+	1201.27i	0.138997	+	0.240749i
$293$	−6983.27			−1.39238			−0.696189	−	0.717858i	$-0.745123\pi$
$293$	−6983.27			−1.39238			−0.696189	+	0.717858i	$0.745123\pi$
$294$		0			0
$295$	219.096			0.0432416
$296$	167.517	+	290.148i	0.0328944	+	0.0569747i
$297$	1955.98	−	3387.85i	0.382146	−	0.661897i
$298$	2170.24	−	3758.96i	0.421874	−	0.730707i
$299$	340.385	+	589.564i	0.0658361	+	0.114031i
$300$	−718.934			−0.138359
$301$		0			0
$302$	5651.18			1.07678
$303$	2525.80	+	4374.81i	0.478888	+	0.829459i
$304$	582.129	−	1008.28i	0.109827	−	0.190226i
$305$	−2137.75	+	3702.70i	−0.401336	+	0.695134i
$306$	−14.7629	−	25.5701i	−0.00275797	−	0.00477695i
$307$	2069.43			0.384719			0.192359	−	0.981325i	$-0.438386\pi$
$307$	2069.43			0.384719			0.192359	+	0.981325i	$0.438386\pi$
$308$		0			0
$309$	9427.84			1.73570
$310$	−822.315	−	1424.29i	−0.150659	−	0.260949i
$311$	1060.98	−	1837.67i	0.193449	−	0.335064i	−0.752942	−	0.658087i	$-0.771366\pi$
$311$	1060.98	−	1837.67i	0.193449	−	0.335064i	0.946391	+	0.323023i	$0.104699\pi$
$312$	−216.258	+	374.569i	−0.0392410	+	0.0679674i
$313$	764.398	+	1323.98i	0.138039	+	0.239091i	0.926754	−	0.375668i	$-0.122587\pi$
$313$	764.398	+	1323.98i	0.138039	+	0.239091i	−0.788715	+	0.614759i	$0.789253\pi$
$314$	1980.77			0.355992
$315$		0			0
$316$	5060.95			0.900951
$317$	−2571.22	−	4453.49i	−0.455565	−	0.789062i	0.543155	−	0.839632i	$-0.317230\pi$
$317$	−2571.22	−	4453.49i	−0.455565	−	0.789062i	−0.998721	+	0.0505699i	$0.983896\pi$
$318$	−1143.89	+	1981.28i	−0.201718	+	0.349385i
$319$	2952.85	−	5114.49i	0.518270	−	0.897669i
$320$	541.505	+	937.915i	0.0945971	+	0.163847i
$321$	1462.71			0.254332
$322$		0			0
$323$	4480.16			0.771773
$324$	−2034.67	−	3524.16i	−0.348881	−	0.604280i
$325$	−48.2233	+	83.5252i	−0.00823061	+	0.0142558i
$326$	−1557.75	+	2698.10i	−0.264649	+	0.458386i
$327$	−2047.44	−	3546.28i	−0.346250	−	0.599723i
$328$	226.114			0.0380642
$329$		0			0
$330$	1169.83			0.195142
$331$	2887.02	+	5000.47i	0.479411	+	0.830364i	0.999721	−	0.0236134i	$-0.00751706\pi$
$331$	2887.02	+	5000.47i	0.479411	+	0.830364i	−0.520310	+	0.853977i	$0.674184\pi$
$332$	2633.13	−	4560.71i	0.435276	−	0.753921i
$333$	3.80144	−	6.58429i	0.000625579	−	0.00108353i
$334$	744.845	+	1290.11i	0.122024	+	0.211352i
$335$	2727.10			0.444768
$336$		0			0
$337$	−484.761			−0.0783579			−0.0391790	−	0.999232i	$-0.512474\pi$
$337$	−484.761			−0.0783579			−0.0391790	+	0.999232i	$0.512474\pi$
$338$	−1730.19	−	2996.77i	−0.278431	−	0.482257i
$339$	1539.34	−	2666.22i	0.246624	−	0.427165i
$340$	526.142	−	911.304i	0.0839237	−	0.145360i
$341$	−2918.64	−	5055.23i	−0.463499	−	0.802804i
$342$	89.8603			0.0142079
$343$		0			0
$344$	−6969.92			−1.09242
$345$	−2312.83	−	4005.94i	−0.360923	−	0.625138i
$346$	2142.74	−	3711.34i	0.332932	−	0.576655i
$347$	3899.11	−	6753.45i	0.603213	−	1.04480i	−0.389118	−	0.921188i	$-0.627220\pi$
$347$	3899.11	−	6753.45i	0.603213	−	1.04480i	0.992331	−	0.123608i	$-0.0394465\pi$
$348$	−3017.41	−	5226.30i	−0.464799	−	0.805055i
$349$	662.157			0.101560			0.0507800	−	0.998710i	$-0.483829\pi$
$349$	662.157			0.101560			0.0507800	+	0.998710i	$0.483829\pi$
$350$		0			0
$351$	−536.271			−0.0815499
$352$	2629.73	+	4554.83i	0.398197	+	0.689697i
$353$	3313.07	−	5738.40i	0.499538	−	0.865225i	−0.500462	−	0.865759i	$-0.666836\pi$
$353$	3313.07	−	5738.40i	0.499538	−	0.865225i	1.00000		0.000533475i	$0.000169810\pi$
$354$	−182.150	+	315.493i	−0.0273479	+	0.0473680i
$355$	2567.44	+	4446.93i	0.383846	+	0.664841i
$356$	−730.668			−0.108779
$357$		0			0
$358$	2274.10			0.335725
$359$	−5199.03	−	9004.98i	−0.764329	−	1.32386i	−0.940601	−	0.339515i	$-0.889737\pi$
$359$	−5199.03	−	9004.98i	−0.764329	−	1.32386i	0.176272	−	0.984342i	$-0.443596\pi$
$360$	25.9441	−	44.9365i	0.00379826	−	0.00657878i
$361$	−3388.06	+	5868.30i	−0.493959	+	0.855562i
$362$	−2149.70	−	3723.39i	−0.312116	−	0.540600i
$363$	−2825.89			−0.408597
$364$		0			0
$365$	−1264.39			−0.181318
$366$	−3554.53	−	6156.63i	−0.507646	−	0.879269i
$367$	1123.15	−	1945.36i	0.159750	−	0.276694i	−0.775029	−	0.631926i	$-0.782265\pi$
$367$	1123.15	−	1945.36i	0.159750	−	0.276694i	0.934778	+	0.355232i	$0.115598\pi$
$368$	879.718	−	1523.72i	0.124615	−	0.215840i
$369$	−2.56558	−	4.44372i	−0.000361948	−	0.000626913i
$370$	−124.222			−0.0174541
$371$		0			0
$372$	−5964.89			−0.831358
$373$	−96.0126	−	166.299i	−0.0133280	−	0.0230848i	0.859284	−	0.511498i	$-0.170909\pi$
$373$	−96.0126	−	166.299i	−0.0133280	−	0.0230848i	−0.872612	+	0.488413i	$0.837576\pi$
$374$	−856.122	+	1482.85i	−0.118366	+	0.205017i
$375$	327.665	−	567.533i	0.0451215	−	0.0781527i
$376$	−2015.62	−	3491.15i	−0.276456	−	0.478836i
$377$	−809.584			−0.110599
$378$		0			0
$379$	−4565.76			−0.618805			−0.309403	−	0.950931i	$-0.600129\pi$
$379$	−4565.76			−0.618805			−0.309403	+	0.950931i	$0.600129\pi$
$380$	1601.28	+	2773.51i	0.216169	+	0.374415i
$381$	−4088.28	+	7081.10i	−0.549734	+	0.952168i
$382$	−2770.84	+	4799.24i	−0.371122	+	0.642803i
$383$	693.535	+	1201.24i	0.0925273	+	0.160262i	0.908574	−	0.417724i	$-0.137172\pi$
$383$	693.535	+	1201.24i	0.0925273	+	0.160262i	−0.816047	+	0.577986i	$0.803839\pi$
$384$	6037.58			0.802355
$385$		0			0
$386$	2584.45			0.340791
$387$	79.0836	+	136.977i	0.0103877	+	0.0179921i
$388$	2800.53	−	4850.66i	0.366431	−	0.634678i
$389$	−2291.50	+	3969.00i	−0.298673	+	0.517317i	−0.975833	−	0.218519i	$-0.929877\pi$
$389$	−2291.50	+	3969.00i	−0.298673	+	0.517317i	0.677160	+	0.735836i	$0.263211\pi$
$390$	−80.1829	−	138.881i	−0.0104108	−	0.0180321i
$391$	6770.45			0.875694
$392$		0			0
$393$	8669.47			1.11277
$394$	550.026	+	952.674i	0.0703298	+	0.121815i
$395$	−2306.60	+	3995.16i	−0.293817	+	0.508907i
$396$	37.4558	−	64.8754i	0.00475310	−	0.00823261i
$397$	−4480.53	−	7760.50i	−0.566426	−	0.981079i	−0.996915	−	0.0784836i	$-0.974992\pi$
$397$	−4480.53	−	7760.50i	−0.566426	−	0.981079i	0.430489	−	0.902596i	$-0.358341\pi$
$398$	−6034.89			−0.760054
$399$		0			0
$400$	249.264			0.0311580
$401$	−5814.64	−	10071.2i	−0.724113	−	1.25420i	−0.959338	−	0.282259i	$-0.908916\pi$
$401$	−5814.64	−	10071.2i	−0.724113	−	1.25420i	0.235225	−	0.971941i	$-0.424417\pi$
$402$	−2267.23	+	3926.95i	−0.281291	+	0.487211i
$403$	−400.102	+	692.997i	−0.0494553	+	0.0856591i
$404$	−2642.69	−	4577.28i	−0.325443	−	0.563684i
$405$	3709.34			0.455107
$406$		0			0
$407$	−440.902			−0.0536970
$408$	2150.74	+	3725.20i	0.260975	+	0.452021i
$409$	2160.07	−	3741.34i	0.261145	−	0.452317i	−0.705401	−	0.708808i	$-0.749233\pi$
$409$	2160.07	−	3741.34i	0.261145	−	0.452317i	0.966546	+	0.256491i	$0.0825665\pi$
$410$	−41.9187	+	72.6052i	−0.00504930	+	0.00874565i
$411$	777.635	+	1346.90i	0.0933282	+	0.161649i
$412$	−9864.19			−1.17955
$413$		0			0
$414$	135.798			0.0161210
$415$	2400.18	+	4157.23i	0.283904	+	0.491736i
$416$	360.497	−	624.399i	0.0424875	−	0.0735906i
$417$	623.528	−	1079.98i	0.0732238	−	0.126827i
$418$	−2605.56	−	4512.97i	−0.304886	−	0.528077i
$419$	−7824.02			−0.912240			−0.456120	−	0.889918i	$-0.650761\pi$
$419$	−7824.02			−0.912240			−0.456120	+	0.889918i	$0.650761\pi$
$420$		0			0
$421$	6944.28			0.803904			0.401952	−	0.915661i	$-0.368332\pi$
$421$	6944.28			0.803904			0.401952	+	0.915661i	$0.368332\pi$
$422$	−497.333	−	861.407i	−0.0573692	−	0.0993664i
$423$	−45.7401	+	79.2242i	−0.00525759	+	0.00910641i
$424$	2942.35	−	5096.30i	0.337012	−	0.583722i
$425$	479.594	+	830.681i	0.0547382	+	0.0948093i
$426$	−8537.97			−0.971047
$427$		0			0
$428$	−1530.41			−0.172839
$429$	−284.593	−	492.929i	−0.0320286	−	0.0554752i
$430$	1292.13	−	2238.04i	0.144912	−	0.250995i
$431$	−1628.68	+	2820.96i	−0.182020	+	0.315268i	−0.942568	−	0.334013i	$-0.891597\pi$
$431$	−1628.68	+	2820.96i	−0.182020	+	0.315268i	0.760548	+	0.649282i	$0.224930\pi$
$432$	692.990	+	1200.29i	0.0771794	+	0.133679i
$433$	16857.1			1.87090			0.935449	−	0.353461i	$-0.114995\pi$
$433$	16857.1			1.87090			0.935449	+	0.353461i	$0.114995\pi$
$434$		0			0
$435$	5500.91			0.606319
$436$	2142.20	+	3710.40i	0.235305	+	0.407560i
$437$	−10302.8	+	17844.9i	−1.12780	+	1.95340i
$438$	1051.17	−	1820.69i	0.114674	−	0.198620i
$439$	3976.51	+	6887.52i	0.432320	+	0.748800i	0.997073	−	0.0764599i	$-0.0243617\pi$
$439$	3976.51	+	6887.52i	0.432320	+	0.748800i	−0.564753	+	0.825260i	$0.691028\pi$
$440$	−3009.07			−0.326026
$441$		0			0
$442$	234.723			0.0252593
$443$	4854.88	+	8408.90i	0.520683	+	0.901849i	0.999711	+	0.0240492i	$0.00765584\pi$
$443$	4854.88	+	8408.90i	0.520683	+	0.901849i	−0.479028	+	0.877800i	$0.659011\pi$
$444$	−225.270	+	390.179i	−0.0240785	+	0.0417052i
$445$	333.013	−	576.795i	0.0354749	−	0.0614443i
$446$	1586.57	+	2748.02i	0.168444	+	0.291754i
$447$	14349.7			1.51838
$448$		0			0
$449$	−11758.3			−1.23588			−0.617938	−	0.786227i	$-0.712032\pi$
$449$	−11758.3			−1.23588			−0.617938	+	0.786227i	$0.712032\pi$
$450$	9.61941	+	16.6613i	0.00100770	+	0.00174538i
$451$	−148.782	+	257.698i	−0.0155341	+	0.0269058i
$452$	−1610.59	+	2789.62i	−0.167601	+	0.290293i
$453$	9341.46	+	16179.9i	0.968874	+	1.67814i
$454$	−2524.96			−0.261018
$455$		0			0
$456$	−13091.3			−1.34443
$457$	−1375.09	−	2381.72i	−0.140753	−	0.243791i	0.787028	−	0.616918i	$-0.211619\pi$
$457$	−1375.09	−	2381.72i	−0.140753	−	0.243791i	−0.927780	+	0.373127i	$0.878286\pi$
$458$	3112.23	−	5390.55i	0.317522	−	0.549964i
$459$	−2666.68	+	4618.83i	−0.271176	+	0.469691i
$460$	2419.87	+	4191.34i	0.245276	+	0.424831i
$461$	3041.43			0.307275			0.153637	−	0.988127i	$-0.450901\pi$
$461$	3041.43			0.307275			0.153637	+	0.988127i	$0.450901\pi$
$462$		0			0
$463$	5422.89			0.544327			0.272163	−	0.962251i	$-0.412261\pi$
$463$	5422.89			0.544327			0.272163	+	0.962251i	$0.412261\pi$
$464$	1046.18	+	1812.03i	0.104671	+	0.181296i
$465$	2718.59	−	4708.73i	0.271122	−	0.469596i
$466$	1720.38	−	2979.79i	0.171019	−	0.296214i
$467$	−2773.80	−	4804.36i	−0.274853	−	0.476059i	0.695245	−	0.718772i	$-0.255296\pi$
$467$	−2773.80	−	4804.36i	−0.274853	−	0.476059i	−0.970098	+	0.242714i	$0.921962\pi$
$468$	−10.2693			−0.00101431
$469$		0			0
$470$	1494.68			0.146690
$471$	3274.23	+	5671.14i	0.320316	+	0.554803i
$472$	468.532	−	811.521i	0.0456905	−	0.0791383i
$473$	4586.17	−	7943.48i	0.445819	−	0.772181i
$474$	−3835.29	−	6642.91i	−0.371647	−	0.643711i
$475$	−2919.24			−0.281987
$476$		0			0
$477$	−133.541			−0.0128185
$478$	838.640	+	1452.57i	0.0802479	+	0.138993i
$479$	564.275	−	977.353i	0.0538254	−	0.0932284i	−0.837857	−	0.545889i	$-0.816192\pi$
$479$	564.275	−	977.353i	0.0538254	−	0.0932284i	0.891683	+	0.452661i	$0.149525\pi$
$480$	−2449.48	+	4242.63i	−0.232923	+	0.403435i
$481$	30.2205	+	52.3434i	0.00286473	+	0.00496186i
$482$	3804.68			0.359540
$483$		0			0
$484$	2956.68			0.277674
$485$	2552.77	+	4421.52i	0.239000	+	0.413961i
$486$	−107.952	+	186.979i	−0.0100757	+	0.0174517i
$487$	−2403.09	+	4162.27i	−0.223602	+	0.387291i	−0.955899	−	0.293695i	$-0.905115\pi$
$487$	−2403.09	+	4162.27i	−0.223602	+	0.387291i	0.732297	+	0.680986i	$0.238448\pi$
$488$	9143.08	+	15836.3i	0.848131	+	1.46901i
$489$	−10299.9			−0.952508
$490$		0			0
$491$	−12452.1			−1.14451			−0.572255	−	0.820076i	$-0.693931\pi$
$491$	−12452.1			−1.14451			−0.572255	+	0.820076i	$0.693931\pi$
$492$	152.034	+	263.331i	0.0139314	+	0.0241298i
$493$	−4025.77	+	6972.83i	−0.367772	+	0.636999i
$494$	−357.183	+	618.660i	−0.0325313	+	0.0563458i
$495$	34.1421	+	59.1359i	0.00310015	+	0.00536962i
$496$	2068.11			0.187219
$497$		0			0
$498$	−7981.75			−0.718214
$499$	5898.68	+	10216.8i	0.529180	+	0.916567i	0.999421	+	0.0340289i	$0.0108338\pi$
$499$	5898.68	+	10216.8i	0.529180	+	0.916567i	−0.470240	+	0.882538i	$0.655833\pi$
$500$	−342.830	+	593.799i	−0.0306637	+	0.0531110i
$501$	−2462.47	+	4265.13i	−0.219591	+	0.380343i
$502$	3023.26	+	5236.44i	0.268794	+	0.465565i
$503$	−2900.55			−0.257116			−0.128558	−	0.991702i	$-0.541035\pi$
$503$	−2900.55			−0.257116			−0.128558	+	0.991702i	$0.541035\pi$
$504$		0			0
$505$	4817.79			0.424533
$506$	−3937.54	−	6820.03i	−0.345939	−	0.599184i
$507$	5720.03	−	9907.38i	0.501056	−	0.867854i
$508$	4277.49	−	7408.83i	0.373588	−	0.647074i
$509$	4743.42	+	8215.85i	0.413062	+	0.715444i	0.995223	−	0.0976294i	$-0.0311260\pi$
$509$	4743.42	+	8215.85i	0.413062	+	0.715444i	−0.582161	+	0.813074i	$0.697793\pi$
$510$	−1594.88			−0.138476
$511$		0			0
$512$	−3569.14			−0.308076
$513$	−8115.90	−	14057.2i	−0.698491	−	1.20982i
$514$	−2767.33	+	4793.15i	−0.237474	+	0.411317i
$515$	4495.75	−	7786.87i	0.384673	−	0.666273i
$516$	−4686.43	−	8117.13i	−0.399823	−	0.692513i
$517$	5305.06			0.451289
$518$		0			0
$519$	14167.9			1.19827
$520$	206.249	+	357.234i	0.0173935	+	0.0301264i
$521$	−10176.5	+	17626.2i	−0.855740	+	1.48219i	0.0202163	+	0.999796i	$0.493565\pi$
$521$	−10176.5	+	17626.2i	−0.855740	+	1.48219i	−0.875957	+	0.482390i	$0.839769\pi$
$522$	−80.7464	+	139.857i	−0.00677045	+	0.0117268i
$523$	4614.44	+	7992.45i	0.385804	+	0.668232i	0.991880	−	0.127174i	$-0.0405907\pi$
$523$	4614.44	+	7992.45i	0.385804	+	0.668232i	−0.606076	+	0.795407i	$0.707257\pi$
$524$	−9070.71			−0.756213
$525$		0			0
$526$	−11298.0			−0.936535
$527$	3979.12	+	6892.04i	0.328906	+	0.569681i
$528$	−735.524	+	1273.96i	−0.0606242	+	0.105004i
$529$	−9486.09	+	16430.4i	−0.779658	+	1.35041i
$530$	1090.95	+	1889.58i	0.0894109	+	0.154864i
$531$	−21.2646			−0.00173787
$532$		0			0
$533$	40.7915			0.00331496
$534$	553.715	+	959.062i	0.0448719	+	0.0777203i
$535$	697.507	−	1208.12i	0.0563661	−	0.0976290i
$536$	5831.83	−	10101.0i	0.469957	−	0.813989i
$537$	3759.10	+	6510.95i	0.302080	+	0.523219i
$538$	−678.626			−0.0543822
$539$		0			0
$540$	−3812.47			−0.303819
$541$	348.637	+	603.857i	0.0277062	+	0.0479886i	0.879546	−	0.475814i	$-0.157846\pi$
$541$	348.637	+	603.857i	0.0277062	+	0.0479886i	−0.851840	+	0.523802i	$0.824513\pi$
$542$	−6492.67	+	11245.6i	−0.514546	+	0.891220i
$543$	7106.96	−	12309.6i	0.561674	−	0.972847i
$544$	−3585.24	−	6209.82i	−0.282566	−	0.489419i
$545$	−3905.37			−0.306950
$546$		0			0
$547$	−8032.62			−0.627879			−0.313940	−	0.949443i	$-0.601649\pi$
$547$	−8032.62			−0.627879			−0.313940	+	0.949443i	$0.601649\pi$
$548$	−813.626	−	1409.24i	−0.0634240	−	0.109854i
$549$	207.482	−	359.370i	0.0161296	−	0.0279372i
$550$	557.843	−	966.212i	0.0432482	−	0.0749080i
$551$	−12252.2	−	21221.4i	−0.947299	−	1.64077i
$552$	−19783.7			−1.52546
$553$		0			0
$554$	6612.66			0.507121
$555$	−205.341	−	355.660i	−0.0157049	−	0.0272017i
$556$	−652.386	+	1129.97i	−0.0497614	+	0.0861893i
$557$	−6793.37	+	11766.5i	−0.516776	+	0.895083i	0.483034	+	0.875602i	$0.339535\pi$
$557$	−6793.37	+	11766.5i	−0.516776	+	0.895083i	−0.999810	+	0.0194814i	$0.993798\pi$
$558$	79.8108	+	138.236i	0.00605495	+	0.0104875i
$559$	−1257.39			−0.0951376
$560$		0			0
$561$	−5660.71			−0.426017
$562$	1018.55	+	1764.18i	0.0764500	+	0.132415i
$563$	8607.90	−	14909.3i	0.644369	−	1.11608i	−0.340078	−	0.940397i	$-0.610453\pi$
$563$	8607.90	−	14909.3i	0.644369	−	1.11608i	0.984447	−	0.175683i	$-0.0562133\pi$
$564$	2710.52	−	4694.76i	0.202364	−	0.350505i
$565$	−1468.10	−	2542.82i	−0.109316	−	0.189340i
$566$	7594.88			0.564022
$567$		0			0
$568$	21961.6			1.62234
$569$	9220.75	+	15970.8i	0.679357	+	1.17668i	0.975175	+	0.221437i	$0.0710746\pi$
$569$	9220.75	+	15970.8i	0.679357	+	1.17668i	−0.295818	+	0.955244i	$0.595592\pi$
$570$	2426.97	−	4203.64i	0.178341	−	0.308896i
$571$	5390.17	−	9336.04i	0.395046	−	0.684240i	−0.598061	−	0.801451i	$-0.704062\pi$
$571$	5390.17	−	9336.04i	0.395046	−	0.684240i	0.993107	+	0.117210i	$0.0373952\pi$
$572$	297.765	+	515.743i	0.0217660	+	0.0376998i
$573$	−18320.9			−1.33572
$574$		0			0
$575$	−4411.57			−0.319957
$576$	−52.5565	−	91.0305i	−0.00380183	−	0.00658496i
$577$	−6481.49	+	11226.3i	−0.467640	+	0.809975i	−0.999316	−	0.0369719i	$-0.988229\pi$
$577$	−6481.49	+	11226.3i	−0.467640	+	0.809975i	0.531677	+	0.846947i	$0.321562\pi$
$578$	−2728.29	+	4725.54i	−0.196336	+	0.340063i
$579$	4272.13	+	7399.54i	0.306638	+	0.531113i
$580$	−5755.51			−0.412042
$581$		0			0
$582$	−8489.18			−0.604619
$583$	3872.10	+	6706.67i	0.275070	+	0.476436i
$584$	−2703.86	+	4683.22i	−0.191587	+	0.331838i
$585$	4.68037	−	8.10665i	0.000330786	−	0.000572938i
$586$	−5536.99	−	9590.34i	−0.390326	−	0.676064i
$587$	16181.8			1.13781			0.568905	−	0.822403i	$-0.307367\pi$
$587$	16181.8			1.13781			0.568905	+	0.822403i	$0.307367\pi$
$588$		0			0
$589$	−24220.5			−1.69438
$590$	173.720	+	300.891i	0.0121219	+	0.0209958i
$591$	−1818.40	+	3149.56i	−0.126563	+	0.219214i
$592$	78.1042	−	135.280i	0.00542240	−	0.00939188i
$593$	373.815	+	647.467i	0.0258866	+	0.0448369i	0.878678	−	0.477414i	$-0.158426\pi$
$593$	373.815	+	647.467i	0.0258866	+	0.0448369i	−0.852792	+	0.522251i	$0.825092\pi$
$594$	6203.53			0.428508
$595$		0			0
$596$	−15013.8			−1.03186
$597$	−9975.73	−	17278.5i	−0.683885	−	1.18452i
$598$	−539.778	+	934.923i	−0.0369117	+	0.0639329i
$599$	−1924.93	+	3334.08i	−0.131303	+	0.227424i	−0.924179	−	0.381959i	$-0.875249\pi$
$599$	−1924.93	+	3334.08i	−0.131303	+	0.227424i	0.792876	+	0.609383i	$0.208583\pi$
$600$	−1401.41	−	2427.31i	−0.0953538	−	0.165158i
$601$	−1808.82			−0.122768			−0.0613838	−	0.998114i	$-0.519551\pi$
$601$	−1808.82			−0.122768			−0.0613838	+	0.998114i	$0.519551\pi$
$602$		0			0
$603$	−264.682			−0.0178751
$604$	−9773.80	−	16928.7i	−0.658427	−	1.14043i
$605$	−1347.55	+	2334.03i	−0.0905549	+	0.156846i
$606$	−4005.37	+	6937.51i	−0.268494	+	0.465045i
$607$	268.046	+	464.270i	0.0179237	+	0.0310447i	0.874848	−	0.484397i	$-0.160961\pi$
$607$	268.046	+	464.270i	0.0179237	+	0.0310447i	−0.856924	+	0.515442i	$0.827628\pi$
$608$	21823.0			1.45566
$609$		0			0
$610$	−6780.04			−0.450026
$611$	−363.622	−	629.812i	−0.0240762	−	0.0417013i
$612$	−51.0654	+	88.4478i	−0.00337287	+	0.00584198i
$613$	−7367.99	+	12761.7i	−0.485465	+	0.840851i	−0.999861	−	0.0167026i	$-0.994683\pi$
$613$	−7367.99	+	12761.7i	−0.485465	+	0.840851i	0.514395	+	0.857553i	$0.328016\pi$
$614$	1640.84	+	2842.01i	0.107848	+	0.186799i
$615$	−277.168			−0.0181731
$616$		0			0
$617$	9604.91			0.626709			0.313354	−	0.949636i	$-0.398547\pi$
$617$	9604.91			0.626709			0.313354	+	0.949636i	$0.398547\pi$
$618$	7475.27	+	12947.6i	0.486569	+	0.842762i
$619$	−4297.11	+	7442.81i	−0.279023	+	0.483283i	−0.971142	−	0.238501i	$-0.923344\pi$
$619$	−4297.11	+	7442.81i	−0.279023	+	0.483283i	0.692119	+	0.721783i	$0.256677\pi$
$620$	−2844.41	+	4926.66i	−0.184249	+	0.319128i
$621$	−12264.8	−	21243.3i	−0.792544	−	1.37273i
$622$	3364.98			0.216918
$623$		0			0
$624$	201.659			0.0129372
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−1212.17	+	2099.54i	−0.0773932	+	0.134049i
$627$	8614.04	−	14920.0i	0.548663	−	0.950312i
$628$	−3425.77	−	5933.61i	−0.217680	−	0.377033i
$629$	601.102			0.0381042
$630$		0			0
$631$	−14803.3			−0.933933			−0.466966	−	0.884275i	$-0.654653\pi$
$631$	−14803.3			−0.933933			−0.466966	+	0.884275i	$0.654653\pi$
$632$	9865.24	+	17087.1i	0.620915	+	1.07546i
$633$	1644.19	−	2847.83i	0.103240	−	0.178817i
$634$	4077.41	−	7062.28i	0.255417	−	0.442396i
$635$	3899.06	+	6753.37i	0.243669	+	0.422046i
$636$	7913.50			0.493381
$637$		0			0
$638$	9365.19			0.581146
$639$	−249.186	−	431.603i	−0.0154267	−	0.0267198i
$640$	2879.08	−	4986.71i	0.177821	−	0.307995i
$641$	4645.16	−	8045.65i	0.286229	−	0.495763i	−0.686678	−	0.726962i	$-0.740932\pi$
$641$	4645.16	−	8045.65i	0.286229	−	0.495763i	0.972906	+	0.231199i	$0.0742649\pi$
$642$	1159.77	+	2008.79i	0.0712970	+	0.123490i
$643$	1861.78			0.114186			0.0570928	−	0.998369i	$-0.481817\pi$
$643$	1861.78			0.114186			0.0570928	+	0.998369i	$0.481817\pi$
$644$		0			0
$645$	8543.64			0.521559
$646$	3552.29	+	6152.74i	0.216351	+	0.374731i
$647$	14763.7	−	25571.5i	0.897095	−	1.55381i	0.0659057	−	0.997826i	$-0.479006\pi$
$647$	14763.7	−	25571.5i	0.897095	−	1.55381i	0.831190	−	0.555989i	$-0.187660\pi$
$648$	7932.33	−	13739.2i	0.480882	−	0.832912i
$649$	616.583	+	1067.95i	0.0372927	+	0.0645929i
$650$	−152.944			−0.00922915
$651$		0			0
$652$	10776.6			0.647306
$653$	−2596.28	−	4496.88i	−0.155590	−	0.269489i	0.777684	−	0.628656i	$-0.216394\pi$
$653$	−2596.28	−	4496.88i	−0.155590	−	0.269489i	−0.933274	+	0.359166i	$0.883061\pi$
$654$	3246.81	−	5623.64i	0.194129	−	0.336241i
$655$	4134.11	−	7160.49i	0.246615	−	0.427151i
$656$	−52.7123	−	91.3004i	−0.00313730	−	0.00543397i
$657$	122.717			0.00728711
$658$		0			0
$659$	−11740.1			−0.693976			−0.346988	−	0.937870i	$-0.612795\pi$
$659$	−11740.1			−0.693976			−0.346988	+	0.937870i	$0.612795\pi$
$660$	−2023.23	−	3504.34i	−0.119325	−	0.206676i
$661$	4396.25	−	7614.53i	0.258690	−	0.448065i	−0.707201	−	0.707013i	$-0.750042\pi$
$661$	4396.25	−	7614.53i	0.258690	−	0.448065i	0.965891	+	0.258948i	$0.0833757\pi$
$662$	−4578.20	+	7929.67i	−0.268787	+	0.465552i
$663$	387.999	+	672.034i	0.0227280	+	0.0393660i
$664$	20530.9			1.19993
$665$		0			0
$666$	12.0565			0.000701474
$667$	−18515.6	−	32070.0i	−1.07485	−	1.86170i
$668$	2576.44	−	4462.53i	0.149230	−	0.258474i
$669$	−5245.22	+	9084.99i	−0.303127	+	0.525032i
$670$	2162.30	+	3745.21i	0.124682	+	0.215955i
$671$	−24064.4			−1.38449
$672$		0			0
$673$	30366.5			1.73929			0.869646	−	0.493676i	$-0.164347\pi$
$673$	30366.5			1.73929			0.869646	+	0.493676i	$0.164347\pi$
$674$	−384.364	−	665.738i	−0.0219661	−	0.0380464i
$675$	1737.59	−	3009.59i	0.0990812	−	0.171614i
$676$	−5984.76	+	10365.9i	−0.340508	+	0.589777i
$677$	−8708.45	−	15083.5i	−0.494377	−	0.856286i	0.505602	−	0.862767i	$-0.331270\pi$
$677$	−8708.45	−	15083.5i	−0.494377	−	0.856286i	−0.999979	+	0.00648104i	$0.997937\pi$
$678$	4882.13			0.276544
$679$		0			0
$680$	4102.41			0.231353
$681$	−4173.78	−	7229.19i	−0.234860	−	0.406789i
$682$	4628.34	−	8016.52i	0.259866	−	0.450100i
$683$	−4414.16	+	7645.55i	−0.247296	+	0.428329i	−0.962775	−	0.270305i	$-0.912875\pi$
$683$	−4414.16	+	7645.55i	−0.247296	+	0.428329i	0.715479	+	0.698635i	$0.246209\pi$
$684$	−155.415	−	269.186i	−0.00868776	−	0.0150476i
$685$	1483.29			0.0827351
$686$		0			0
$687$	20578.2			1.14281
$688$	1624.85	+	2814.32i	0.0900388	+	0.155952i
$689$	530.807	−	919.384i	0.0293500	−	0.0508356i
$690$	3667.65	−	6352.56i	0.202355	−	0.350490i
$691$	5315.51	+	9206.74i	0.292636	+	0.506861i	0.974432	−	0.224681i	$-0.0721342\pi$
$691$	5315.51	+	9206.74i	0.292636	+	0.506861i	−0.681796	+	0.731542i	$0.738801\pi$
$692$	−14823.6			−0.814319
$693$		0			0
$694$	12366.3			0.676395
$695$	−594.670	−	1030.00i	−0.0324563	−	0.0562159i
$696$	11763.6	−	20375.1i	0.640657	−	1.10965i
$697$	202.841	−	351.332i	0.0110232	−	0.0190927i
$698$	525.020	+	909.361i	0.0284703	+	0.0493121i
$699$	11375.2			0.615523
$700$		0			0
$701$	30120.7			1.62289			0.811443	−	0.584431i	$-0.198682\pi$
$701$	30120.7			1.62289			0.811443	+	0.584431i	$0.198682\pi$
$702$	−425.205	−	736.477i	−0.0228609	−	0.0395962i
$703$	−914.712	+	1584.33i	−0.0490740	+	0.0849986i
$704$	−3047.82	+	5278.99i	−0.163166	+	0.282613i
$705$	2470.72	+	4279.41i	0.131990	+	0.228613i
$706$	10507.6			0.560142
$707$		0			0
$708$	1260.12			0.0668904
$709$	−2207.47	−	3823.45i	−0.116930	−	0.202529i	0.801620	−	0.597834i	$-0.203972\pi$
$709$	−2207.47	−	3823.45i	−0.116930	−	0.202529i	−0.918550	+	0.395306i	$0.870639\pi$
$710$	−4071.41	+	7051.88i	−0.215207	+	0.372750i
$711$	223.870	−	387.755i	0.0118084	−	0.0204528i
$712$	−1424.28	−	2466.93i	−0.0749680	−	0.129848i
$713$	−36602.2			−1.92253
$714$		0			0
$715$	−542.843			−0.0283932
$716$	−3933.08	−	6812.30i	−0.205288	−	0.355569i
$717$	−2772.56	+	4802.21i	−0.144412	+	0.250128i
$718$	8244.54	−	14280.0i	0.428529	−	0.742234i
$719$	8567.98	+	14840.2i	0.444411	+	0.769743i	0.998011	−	0.0630401i	$-0.0200796\pi$
$719$	8567.98	+	14840.2i	0.444411	+	0.769743i	−0.553600	+	0.832783i	$0.686746\pi$
$720$	−24.1926			−0.00125223
$721$		0			0
$722$	−10745.5			−0.553886
$723$	6289.18	+	10893.2i	0.323509	+	0.560334i
$724$	−7435.88	+	12879.3i	−0.381702	+	0.661128i
$725$	2623.16	−	4543.45i	0.134375	−	0.232744i
$726$	−2240.63	−	3880.88i	−0.114542	−	0.198393i
$727$	3271.77			0.166909			0.0834546	−	0.996512i	$-0.473405\pi$
$727$	3271.77			0.166909			0.0834546	+	0.996512i	$0.473405\pi$
$728$		0			0
$729$	19316.6			0.981386
$730$	−1002.52	−	1736.42i	−0.0508288	−	0.0880381i
$731$	−6252.54	+	10829.7i	−0.316359	+	0.547951i
$732$	−12295.2	+	21296.0i	−0.620826	+	1.07530i
$733$	2234.92	+	3870.99i	0.112618	+	0.195059i	0.916825	−	0.399290i	$-0.130743\pi$
$733$	2234.92	+	3870.99i	0.112618	+	0.195059i	−0.804207	+	0.594349i	$0.797410\pi$
$734$	3562.16			0.179130
$735$		0			0
$736$	32979.1			1.65166
$737$	7674.63	+	13292.9i	0.383580	+	0.664381i
$738$	4.06847	−	7.04679i	0.000202930	−	0.000351485i
$739$	1237.60	−	2143.58i	0.0616046	−	0.106702i	−0.833578	−	0.552401i	$-0.813712\pi$
$739$	1237.60	−	2143.58i	0.0616046	−	0.106702i	0.895183	+	0.445699i	$0.147045\pi$
$740$	214.844	+	372.121i	0.0106727	+	0.0184857i
$741$	−2361.71			−0.117084
$742$		0			0
$743$	9240.48			0.456259			0.228129	−	0.973631i	$-0.426739\pi$
$743$	9240.48			0.456259			0.228129	+	0.973631i	$0.426739\pi$
$744$	−11627.3	−	20139.0i	−0.572953	−	0.992383i
$745$	6842.78	−	11852.0i	0.336510	−	0.582852i
$746$	152.255	−	263.714i	0.00747248	−	0.0129427i
$747$	−232.952	−	403.485i	−0.0114100	−	0.0197627i
$748$	5922.70			0.289513
$749$		0			0
$750$	1039.21			0.0505956
$751$	−2526.23	−	4375.57i	−0.122748	−	0.212605i	0.798103	−	0.602522i	$-0.205837\pi$
$751$	−2526.23	−	4375.57i	−0.122748	−	0.212605i	−0.920850	+	0.389916i	$0.872504\pi$
$752$	−939.774	+	1627.74i	−0.0455718	+	0.0789327i
$753$	−9994.95	+	17311.8i	−0.483713	+	0.837816i
$754$	−641.913	−	1111.83i	−0.0310041	−	0.0537007i
$755$	17818.2			0.858903
$756$		0			0
$757$	−37779.2			−1.81388			−0.906942	−	0.421256i	$-0.861589\pi$
$757$	−37779.2			−1.81388			−0.906942	+	0.421256i	$0.861589\pi$
$758$	−3620.16	−	6270.30i	−0.173470	−	0.300458i
$759$	13017.6	−	22547.1i	0.622541	−	1.07827i
$760$	−6242.73	+	10812.7i	−0.297957	+	0.516077i
$761$	3751.35	+	6497.52i	0.178694	+	0.309507i	0.941434	−	0.337199i	$-0.109479\pi$
$761$	3751.35	+	6497.52i	0.178694	+	0.309507i	−0.762739	+	0.646706i	$0.776146\pi$
$762$	−12966.3			−0.616428
$763$		0			0
$764$	19168.9			0.907729
$765$	−46.5476	−	80.6228i	−0.00219991	−	0.00381036i
$766$	−1099.80	+	1904.91i	−0.0518764	+	0.0898525i
$767$	84.5243	−	146.400i	0.00397913	−	0.00689206i
$768$	9329.43	+	16159.0i	0.438342	+	0.759231i
$769$	−24209.4			−1.13526			−0.567628	−	0.823285i	$-0.692139\pi$
$769$	−24209.4			−1.13526			−0.567628	+	0.823285i	$0.692139\pi$
$770$		0			0
$771$	−18297.7			−0.854701
$772$	−4469.85	−	7742.01i	−0.208385	−	0.360934i
$773$	3760.50	−	6513.37i	0.174975	−	0.303065i	−0.765178	−	0.643819i	$-0.777349\pi$
$773$	3760.50	−	6513.37i	0.174975	−	0.303065i	0.940153	+	0.340754i	$0.110682\pi$
$774$	−125.410	+	217.216i	−0.00582398	+	0.0100874i
$775$	−2592.77	−	4490.80i	−0.120174	−	0.208148i
$776$	21836.1			1.01014
$777$		0			0
$778$	−7267.67			−0.334908
$779$	617.337	+	1069.26i	0.0283933	+	0.0491787i
$780$	−277.355	+	480.393i	−0.0127319	+	0.0220523i
$781$	−14450.6	+	25029.2i	−0.662080	+	1.14676i
$782$	5368.24	+	9298.07i	0.245483	+	0.425190i
$783$	29171.0			1.33140
$784$		0			0
$785$	6245.39			0.283959
$786$	6873.96	+	11906.1i	0.311942	+	0.540299i
$787$	−8060.68	+	13961.5i	−0.365098	+	0.632368i	−0.988792	−	0.149300i	$-0.952298\pi$
$787$	−8060.68	+	13961.5i	−0.365098	+	0.632368i	0.623694	+	0.781669i	$0.285631\pi$
$788$	1902.56	−	3295.33i	0.0860099	−	0.148974i
$789$	−18675.7	−	32347.3i	−0.842679	−	1.45956i
$790$	−7315.56			−0.329463
$791$		0			0
$792$	292.049			0.0131029
$793$	1649.43	+	2856.90i	0.0738627	+	0.127934i
$794$	7105.16	−	12306.5i	0.317573	−	0.550052i
$795$	−3606.70	+	6246.98i	−0.160901	+	0.278689i
$796$	10437.4	+	18078.2i	0.464755	+	0.804979i
$797$	32223.0			1.43212			0.716058	−	0.698041i	$-0.245944\pi$
$797$	32223.0			1.43212			0.716058	+	0.698041i	$0.245944\pi$
$798$		0			0
$799$	−7232.65			−0.320241
$800$	2336.12	+	4046.27i	0.103243	+	0.178822i
$801$	−32.3210	+	55.9816i	−0.00142573	+	0.00246943i
$802$	9220.77	−	15970.9i	0.405981	−	0.703180i
$803$	−3558.25	−	6163.07i	−0.156374	−	0.270847i
$804$	15684.8			0.688011
$805$		0			0
$806$	−1268.95			−0.0554552
$807$	−1121.77	−	1942.97i	−0.0489323	−	0.0847532i
$808$	10302.7	−	17844.9i	0.448576	−	0.776956i
$809$	12272.2	−	21256.0i	0.533334	−	0.923761i	−0.465908	−	0.884833i	$-0.654272\pi$
$809$	12272.2	−	21256.0i	0.533334	−	0.923761i	0.999242	−	0.0389282i	$-0.0123944\pi$
$810$	2941.11	+	5094.15i	0.127580	+	0.220975i
$811$	−18783.9			−0.813308			−0.406654	−	0.913582i	$-0.633305\pi$
$811$	−18783.9			−0.813308			−0.406654	+	0.913582i	$0.633305\pi$
$812$		0			0
$813$	−42929.8			−1.85192
$814$	−349.588	−	605.504i	−0.0150529	−	0.0260724i
$815$	−4911.59	+	8507.12i	−0.211099	+	0.365634i
$816$	1002.78	−	1736.86i	0.0430198	−	0.0745125i
$817$	−19029.3	−	32959.7i	−0.814872	−	1.41140i
$818$	6850.80			0.292827
$819$		0			0
$820$	289.996			0.0123501
$821$	−9042.53	−	15662.1i	−0.384393	−	0.665788i	0.607292	−	0.794479i	$-0.292256\pi$
$821$	−9042.53	−	15662.1i	−0.384393	−	0.665788i	−0.991685	+	0.128691i	$0.958923\pi$
$822$	−1233.16	+	2135.90i	−0.0523254	+	0.0906303i
$823$	−3717.59	+	6439.06i	−0.157457	+	0.272723i	−0.933951	−	0.357401i	$-0.883663\pi$
$823$	−3717.59	+	6439.06i	−0.157457	+	0.272723i	0.776494	+	0.630125i	$0.216996\pi$
$824$	−19228.1	−	33304.1i	−0.812917	−	1.40801i
$825$	3688.48			0.155656
$826$		0			0
$827$	26487.2			1.11373			0.556863	−	0.830604i	$-0.312005\pi$
$827$	26487.2			1.11373			0.556863	+	0.830604i	$0.312005\pi$
$828$	−234.864	−	406.796i	−0.00985759	−	0.0170738i
$829$	−9688.53	+	16781.0i	−0.405906	+	0.703051i	−0.994427	−	0.105432i	$-0.966377\pi$
$829$	−9688.53	+	16781.0i	−0.405906	+	0.703051i	0.588520	+	0.808483i	$0.299711\pi$
$830$	−3806.17	+	6592.48i	−0.159174	+	0.275697i
$831$	10930.8	+	18932.7i	0.456300	+	0.790334i
$832$	835.622			0.0348197
$833$		0			0
$834$	1977.56			0.0821073
$835$	2348.50	+	4067.73i	0.0973333	+	0.168586i
$836$	−9012.71	+	15610.5i	−0.372860	+	0.645813i
$837$	14416.5	−	24970.2i	0.595350	−	1.03118i
$838$	−6203.61	−	10745.0i	−0.255728	−	0.442934i
$839$	4645.97			0.191176			0.0955880	−	0.995421i	$-0.469527\pi$
$839$	4645.97			0.191176			0.0955880	+	0.995421i	$0.469527\pi$
$840$		0			0
$841$	19649.2			0.805658
$842$	5506.07	+	9536.80i	0.225358	+	0.390332i
$843$	−3367.35	+	5832.41i	−0.137577	+	0.238291i
$844$	−1720.29	+	2979.63i	−0.0701598	+	0.121520i
$845$	−5455.29	−	9448.84i	−0.222092	−	0.384675i
$846$	−145.068			−0.00589544
$847$		0			0
$848$	−2743.72			−0.111108
$849$	12554.4	+	21744.9i	0.507499	+	0.879013i
$850$	−760.534	+	1317.28i	−0.0306895	+	0.0531558i
$851$	−1382.32	+	2394.25i	−0.0556819	+	0.0964438i
$852$	14766.5	+	25576.4i	0.593772	+	1.02844i
$853$	−32566.5			−1.30722			−0.653609	−	0.756833i	$-0.726746\pi$
$853$	−32566.5			−1.30722			−0.653609	+	0.756833i	$0.726746\pi$
$854$		0			0
$855$	283.330			0.0113330
$856$	−2983.21	−	5167.07i	−0.119117	−	0.206316i
$857$	67.4706	−	116.862i	0.00268932	−	0.00465805i	−0.864678	−	0.502327i	$-0.832477\pi$
$857$	67.4706	−	116.862i	0.00268932	−	0.00465805i	0.867367	+	0.497669i	$0.165811\pi$
$858$	451.304	−	781.681i	0.0179572	−	0.0311027i
$859$	−5190.45	−	8990.13i	−0.206165	−	0.357089i	0.744338	−	0.667803i	$-0.232765\pi$
$859$	−5190.45	−	8990.13i	−0.206165	−	0.357089i	−0.950503	+	0.310714i	$0.899432\pi$
$860$	−8939.06			−0.354441
$861$		0			0
$862$	−5165.48			−0.204103
$863$	−12674.6	−	21953.1i	−0.499941	−	0.865924i	0.500059	−	0.865992i	$-0.333312\pi$
$863$	−12674.6	−	21953.1i	−0.499941	−	0.865924i	−1.00000		6.76895e-5i	$0.999978\pi$
$864$	−12989.5	+	22498.4i	−0.511471	+	0.885894i
$865$	6756.08	−	11701.9i	0.265565	−	0.459972i
$866$	13365.9	+	23150.3i	0.524469	+	0.908407i
$867$	−18039.6			−0.706639
$868$		0			0
$869$	−25965.1			−1.01359
$870$	4361.64	+	7554.58i	0.169969	+	0.294396i
$871$	1052.08	−	1822.25i	0.0409280	−	0.0708893i
$872$	−8351.54	+	14465.3i	−0.324333	+	0.561762i
$873$	−247.762	−	429.136i	−0.00960536	−	0.0166370i
$874$	−32675.9			−1.26462
$875$		0			0
$876$	−7272.08			−0.280480
$877$	11259.7	+	19502.3i	0.433537	+	0.750909i	0.997175	−	0.0751134i	$-0.0239319\pi$
$877$	11259.7	+	19502.3i	0.433537	+	0.750909i	−0.563638	+	0.826022i	$0.690599\pi$
$878$	−6305.90	+	10922.1i	−0.242385	+	0.419823i
$879$	18305.4	−	31705.9i	0.702418	−	1.21662i
$880$	701.482	+	1215.00i	0.0268716	+	0.0465429i
$881$	12419.9			0.474958			0.237479	−	0.971393i	$-0.423679\pi$
$881$	12419.9			0.474958			0.237479	+	0.971393i	$0.423679\pi$
$882$		0			0
$883$	−46011.8			−1.75359			−0.876794	−	0.480866i	$-0.840322\pi$
$883$	−46011.8			−1.75359			−0.876794	+	0.480866i	$0.840322\pi$
$884$	−405.957	−	703.138i	−0.0154455	−	0.0267524i
$885$	−574.321	+	994.753i	−0.0218142	+	0.0377833i
$886$	−7698.81	+	13334.7i	−0.291926	+	0.505631i
$887$	−14043.3	−	24323.8i	−0.531600	−	0.920759i	−0.999320	−	0.0368816i	$-0.988258\pi$
$887$	−14043.3	−	24323.8i	−0.531600	−	0.920759i	0.467719	−	0.883877i	$-0.345076\pi$
$888$	−1756.46			−0.0663774
$889$		0			0
$890$	1056.17			0.0397787
$891$	10438.9	+	18080.6i	0.392497	+	0.679825i
$892$	5487.98	−	9505.47i	0.205999	−	0.356801i
$893$	11006.1	−	19063.1i	0.412436	−	0.714359i
$894$	11377.8	+	19706.9i	0.425648	+	0.737244i
$895$	7170.24			0.267793
$896$		0			0
$897$	−3569.03			−0.132850
$898$	−9323.08	−	16148.0i	−0.346453	−	0.600075i
$899$	21764.0	−	37696.3i	0.807419	−	1.39849i
$900$	33.2738	−	57.6319i	0.00123236	−	0.00213452i
$901$	−5279.02	−	9143.53i	−0.195194	−	0.338086i
$902$	−471.872			−0.0174187
$903$		0			0
$904$	−12558.0			−0.462026
$905$	−6778.03	−	11739.9i	−0.248961	−	0.431213i
$906$	−14813.6	+	25657.8i	−0.543209	+	0.940866i
$907$	15229.4	−	26378.1i	0.557534	−	0.965677i	−0.440168	−	0.897916i	$-0.645081\pi$
$907$	15229.4	−	26378.1i	0.557534	−	0.965677i	0.997702	−	0.0677613i	$-0.0215856\pi$
$908$	4366.95	+	7563.78i	0.159606	+	0.276446i
$909$	−467.597			−0.0170618
$910$		0			0
$911$	−26850.4			−0.976502			−0.488251	−	0.872703i	$-0.662365\pi$
$911$	−26850.4			−0.976502			−0.488251	+	0.872703i	$0.662365\pi$
$912$	3051.89	+	5286.03i	0.110810	+	0.191928i
$913$	−13509.2	+	23398.7i	−0.489693	+	0.848174i
$914$	2180.60	−	3776.91i	0.0789144	−	0.136684i
$915$	−11207.5	−	19411.9i	−0.404927	−	0.701353i
$916$	−21530.6			−0.776628
$917$		0			0
$918$	−8457.57			−0.304076
$919$	19047.9	+	32992.0i	0.683714	+	1.18423i	0.973839	+	0.227238i	$0.0729697\pi$
$919$	19047.9	+	32992.0i	0.683714	+	1.18423i	−0.290125	+	0.956989i	$0.593697\pi$
$920$	−9434.05	+	16340.3i	−0.338078	+	0.585568i
$921$	−5424.64	+	9395.76i	−0.194080	+	0.336157i
$922$	2411.53	+	4176.89i	0.0861383	+	0.149196i
$923$	3961.93			0.141288
$924$		0			0
$925$	−391.674			−0.0139223
$926$	4299.78	+	7447.43i	0.152591	+	0.264296i
$927$	−436.341	+	755.765i	−0.0154599	+	0.0267773i
$928$	−19609.6	+	33964.9i	−0.693661	+	1.20146i
$929$	18177.5	+	31484.4i	0.641964	+	1.11191i	0.984994	+	0.172590i	$0.0552135\pi$
$929$	18177.5	+	31484.4i	0.641964	+	1.11191i	−0.343030	+	0.939325i	$0.611453\pi$
$930$	8622.20			0.304014
$931$		0			0
$932$	−11901.7			−0.418297
$933$	5562.34	+	9634.25i	0.195180	+	0.338061i
$934$	4398.65	−	7618.69i	0.154099	−	0.266907i
$935$	−2699.36	+	4675.43i	−0.0944155	+	0.163533i
$936$	−20.0178	−	34.6718i	−0.000699039	−	0.00121077i
$937$	−37878.5			−1.32064			−0.660318	−	0.750986i	$-0.729579\pi$
$937$	−37878.5			−1.32064			−0.660318	+	0.750986i	$0.729579\pi$
$938$		0			0
$939$	−8014.93			−0.278549
$940$	−2585.07	−	4477.48i	−0.0896976	−	0.155361i
$941$	27062.8	−	46874.1i	0.937536	−	1.62386i	0.167489	−	0.985874i	$-0.446434\pi$
$941$	27062.8	−	46874.1i	0.937536	−	1.62386i	0.770047	−	0.637987i	$-0.220233\pi$
$942$	−5192.24	+	8993.22i	−0.179588	+	0.311056i
$943$	932.924	+	1615.87i	0.0322165	+	0.0558007i
$944$	−436.902			−0.0150635
$945$		0			0
$946$	14545.4			0.499906
$947$	19172.9	+	33208.5i	0.657906	+	1.13953i	0.981157	+	0.193213i	$0.0618908\pi$
$947$	19172.9	+	33208.5i	0.657906	+	1.13953i	−0.323251	+	0.946313i	$0.604776\pi$
$948$	−13266.4	+	22978.0i	−0.454506	+	0.787227i
$949$	−487.783	+	844.865i	−0.0166850	+	0.0288993i
$950$	−2314.64	−	4009.08i	−0.0790495	−	0.136918i
$951$	26960.0			0.919282
$952$		0			0
$953$	−15096.4			−0.513137			−0.256569	−	0.966526i	$-0.582592\pi$
$953$	−15096.4			−0.513137			−0.256569	+	0.966526i	$0.582592\pi$
$954$	−105.883	−	183.395i	−0.00359340	−	0.00622395i
$955$	−8736.50	+	15132.1i	−0.296028	+	0.512735i
$956$	2900.88	−	5024.47i	0.0981393	−	0.169982i
$957$	15480.7	+	26813.4i	0.522906	+	0.905701i
$958$	1789.64			0.0603556
$959$		0			0
$960$	−5677.84			−0.190887
$961$	−6616.31	−	11459.8i	−0.222091	−	0.384673i
$962$	−47.9233	+	83.0055i	−0.00160614	+	0.00278192i
$963$	−67.6975	+	117.255i	−0.00226534	+	0.00392368i
$964$	−6580.25	−	11397.3i	−0.219850	−	0.380792i
$965$	8148.81			0.271833
$966$		0			0
$967$	6917.06			0.230029			0.115014	−	0.993364i	$-0.463309\pi$
$967$	6917.06			0.230029			0.115014	+	0.993364i	$0.463309\pi$
$968$	5763.41	+	9982.52i	0.191367	+	0.331457i
$969$	−11743.9	+	20341.1i	−0.389339	+	0.674355i
$970$	−4048.14	+	7011.59i	−0.133998	+	0.232091i
$971$	19758.8	+	34223.3i	0.653029	+	1.13108i	0.982384	+	0.186874i	$0.0598355\pi$
$971$	19758.8	+	34223.3i	0.653029	+	1.13108i	−0.329355	+	0.944206i	$0.606831\pi$
$972$	746.820			0.0246443
$973$		0			0
$974$	−7621.57			−0.250730
$975$	−252.817	−	437.893i	−0.00830424	−	0.0143834i
$976$	4262.92	−	7383.60i	0.139808	−	0.242155i
$977$	19429.2	−	33652.4i	0.636229	−	1.10198i	−0.350024	−	0.936741i	$-0.613827\pi$
$977$	19429.2	−	33652.4i	0.636229	−	1.10198i	0.986253	−	0.165240i	$-0.0528400\pi$
$978$	−8166.70	−	14145.1i	−0.267017	−	0.462487i
$979$	3748.68			0.122378
$980$		0			0
$981$	379.040			0.0123362
$982$	−9873.16	−	17100.8i	−0.320840	−	0.555712i
$983$	−255.115	+	441.872i	−0.00827762	+	0.0143373i	−0.870135	−	0.492814i	$-0.835968\pi$
$983$	−255.115	+	441.872i	−0.00827762	+	0.0143373i	0.861857	+	0.507151i	$0.169302\pi$
$984$	−592.717	+	1026.62i	−0.0192024	+	0.0332595i
$985$	1734.24	+	3003.79i	0.0560989	+	0.0971662i
$986$	−12768.0			−0.412390
$987$		0			0
$988$	2471.02			0.0795683
$989$	−28757.2	−	49808.9i	−0.924596	−	1.60145i
$990$	−54.1421	+	93.7769i	−0.00173813	+	0.00301053i
$991$	18111.4	−	31369.9i	0.580553	−	1.00555i	−0.414861	−	0.909885i	$-0.636170\pi$
$991$	18111.4	−	31369.9i	0.580553	−	1.00555i	0.995414	−	0.0956623i	$-0.0304969\pi$
$992$	19382.4	+	33571.3i	0.620355	+	1.07449i
$993$	−30271.2			−0.967400
$994$		0			0
$995$	−19028.1			−0.606262
$996$	13804.6	+	23910.2i	0.439171	+	0.760666i
$997$	−10428.0	+	18061.9i	−0.331253	+	0.573747i	−0.982758	−	0.184898i	$-0.940805\pi$
$997$	−10428.0	+	18061.9i	−0.331253	+	0.573747i	0.651505	+	0.758644i	$0.274138\pi$
$998$	−9354.04	+	16201.7i	−0.296690	+	0.513883i
$999$	−1088.91	−	1886.05i	−0.0344861	−	0.0597316i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.l.116.1		4
7.2	even	3	inner	245.4.e.l.226.1		4
7.3	odd	6		245.4.a.g.1.2		2
7.4	even	3		245.4.a.h.1.2		2
7.5	odd	6		35.4.e.b.16.1	yes	4
7.6	odd	2		35.4.e.b.11.1	✓	4
21.5	even	6		315.4.j.c.226.2		4
21.11	odd	6		2205.4.a.bg.1.1		2
21.17	even	6		2205.4.a.bf.1.1		2
21.20	even	2		315.4.j.c.46.2		4
28.19	even	6		560.4.q.i.401.1		4
28.27	even	2		560.4.q.i.81.1		4
35.4	even	6		1225.4.a.v.1.1		2
35.12	even	12		175.4.k.c.149.3		8
35.13	even	4		175.4.k.c.74.3		8
35.19	odd	6		175.4.e.c.51.2		4
35.24	odd	6		1225.4.a.x.1.1		2
35.27	even	4		175.4.k.c.74.2		8
35.33	even	12		175.4.k.c.149.2		8
35.34	odd	2		175.4.e.c.151.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.b.11.1	✓	4	7.6	odd	2
35.4.e.b.16.1	yes	4	7.5	odd	6
175.4.e.c.51.2		4	35.19	odd	6
175.4.e.c.151.2		4	35.34	odd	2
175.4.k.c.74.2		8	35.27	even	4
175.4.k.c.74.3		8	35.13	even	4
175.4.k.c.149.2		8	35.33	even	12
175.4.k.c.149.3		8	35.12	even	12
245.4.a.g.1.2		2	7.3	odd	6
245.4.a.h.1.2		2	7.4	even	3
245.4.e.l.116.1		4	1.1	even	1	trivial
245.4.e.l.226.1		4	7.2	even	3	inner
315.4.j.c.46.2		4	21.20	even	2
315.4.j.c.226.2		4	21.5	even	6
560.4.q.i.81.1		4	28.27	even	2
560.4.q.i.401.1		4	28.19	even	6
1225.4.a.v.1.1		2	35.4	even	6
1225.4.a.x.1.1		2	35.24	odd	6
2205.4.a.bf.1.1		2	21.17	even	6
2205.4.a.bg.1.1		2	21.11	odd	6

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:	\( N \)	\(=\)	\( 245 = 5 \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	245.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.792893 + 1.37333i) q^{2} +(-2.62132 + 4.54026i) q^{3} +(2.74264 - 4.75039i) q^{4} +(2.50000 + 4.33013i) q^{5} -8.31371 q^{6} +21.3848 q^{8} +(-0.242641 - 0.420266i) q^{9} +O(q^{10})\)	\(q+(0.792893 + 1.37333i) q^{2} +(-2.62132 + 4.54026i) q^{3} +(2.74264 - 4.75039i) q^{4} +(2.50000 + 4.33013i) q^{5} -8.31371 q^{6} +21.3848 q^{8} +(-0.242641 - 0.420266i) q^{9} +(-3.96447 + 6.86666i) q^{10} +(-14.0711 + 24.3718i) q^{11} +(14.3787 + 24.9046i) q^{12} +3.85786 q^{13} -26.2132 q^{15} +(-4.98528 - 8.63476i) q^{16} +(19.1838 - 33.2273i) q^{17} +(0.384776 - 0.666452i) q^{18} +(58.3848 + 101.125i) q^{19} +27.4264 q^{20} -44.6274 q^{22} +(88.2315 + 152.821i) q^{23} +(-56.0563 + 97.0924i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(3.05887 + 5.29813i) q^{26} -139.007 q^{27} -209.853 q^{29} +(-20.7843 - 35.9994i) q^{30} +(-103.711 + 179.632i) q^{31} +(93.4447 - 161.851i) q^{32} +(-73.7696 - 127.773i) q^{33} +60.8427 q^{34} -2.66190 q^{36} +(7.83348 + 13.5680i) q^{37} +(-92.5858 + 160.363i) q^{38} +(-10.1127 + 17.5157i) q^{39} +(53.4619 + 92.5988i) q^{40} +10.5736 q^{41} -325.929 q^{43} +(77.1838 + 133.686i) q^{44} +(1.21320 - 2.10133i) q^{45} +(-139.916 + 242.342i) q^{46} +(-94.2548 - 163.254i) q^{47} +52.2721 q^{48} -39.6447 q^{50} +(100.574 + 174.199i) q^{51} +(10.5807 - 18.3264i) q^{52} +(137.591 - 238.314i) q^{53} +(-110.218 - 190.903i) q^{54} -140.711 q^{55} -612.181 q^{57} +(-166.391 - 288.197i) q^{58} +(21.9096 - 37.9485i) q^{59} +(-71.8934 + 124.523i) q^{60} +(427.551 + 740.540i) q^{61} -328.926 q^{62} +216.602 q^{64} +(9.64466 + 16.7050i) q^{65} +(116.983 - 202.620i) q^{66} +(272.710 - 472.347i) q^{67} +(-105.228 - 182.261i) q^{68} -925.132 q^{69} +1026.97 q^{71} +(-5.18882 - 8.98729i) q^{72} +(-126.439 + 218.998i) q^{73} +(-12.4222 + 21.5159i) q^{74} +(-65.5330 - 113.507i) q^{75} +640.514 q^{76} -32.0732 q^{78} +(461.321 + 799.031i) q^{79} +(24.9264 - 43.1738i) q^{80} +(370.934 - 642.476i) q^{81} +(8.38373 + 14.5210i) q^{82} +960.071 q^{83} +191.838 q^{85} +(-258.427 - 447.608i) q^{86} +(550.091 - 952.786i) q^{87} +(-300.907 + 521.186i) q^{88} +(-66.6026 - 115.359i) q^{89} +3.84776 q^{90} +967.949 q^{92} +(-543.718 - 941.747i) q^{93} +(149.468 - 258.886i) q^{94} +(-291.924 + 505.627i) q^{95} +(489.897 + 848.526i) q^{96} +1021.11 q^{97} +13.6569 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 6 q^{2} - 2 q^{3} - 6 q^{4} + 10 q^{5} + 12 q^{6} + 12 q^{8} + 16 q^{9}+O(q^{10}) \) 4 * q + 6 * q^2 - 2 * q^3 - 6 * q^4 + 10 * q^5 + 12 * q^6 + 12 * q^8 + 16 * q^9	\( 4 q + 6 q^{2} - 2 q^{3} - 6 q^{4} + 10 q^{5} + 12 q^{6} + 12 q^{8} + 16 q^{9} - 30 q^{10} - 28 q^{11} + 66 q^{12} + 72 q^{13} - 20 q^{15} + 14 q^{16} - 76 q^{17} - 72 q^{18} + 160 q^{19} - 60 q^{20} - 88 q^{22} + 22 q^{23} - 162 q^{24} - 50 q^{25} + 148 q^{26} + 4 q^{27} - 500 q^{29} + 30 q^{30} - 132 q^{31} - 42 q^{32} - 148 q^{33} - 888 q^{34} - 384 q^{36} + 416 q^{37} - 376 q^{38} + 84 q^{39} + 30 q^{40} + 212 q^{41} - 1332 q^{43} + 156 q^{44} - 80 q^{45} + 402 q^{46} - 196 q^{47} + 260 q^{48} - 300 q^{50} + 572 q^{51} - 348 q^{52} + 952 q^{53} + 402 q^{54} - 280 q^{55} - 944 q^{57} - 510 q^{58} + 840 q^{59} - 330 q^{60} + 98 q^{61} + 8 q^{62} - 1204 q^{64} + 180 q^{65} + 236 q^{66} + 1286 q^{67} - 1524 q^{68} - 2852 q^{69} + 2128 q^{71} - 264 q^{72} - 172 q^{73} - 1792 q^{74} - 50 q^{75} + 288 q^{76} + 856 q^{78} + 1240 q^{79} - 70 q^{80} + 754 q^{81} + 438 q^{82} + 3812 q^{83} - 760 q^{85} - 2018 q^{86} + 970 q^{87} - 604 q^{88} + 650 q^{89} - 720 q^{90} + 5484 q^{92} - 1332 q^{93} + 332 q^{94} - 800 q^{95} + 1722 q^{96} + 1256 q^{97} + 32 q^{99}+O(q^{100}) \) 4 * q + 6 * q^2 - 2 * q^3 - 6 * q^4 + 10 * q^5 + 12 * q^6 + 12 * q^8 + 16 * q^9 - 30 * q^10 - 28 * q^11 + 66 * q^12 + 72 * q^13 - 20 * q^15 + 14 * q^16 - 76 * q^17 - 72 * q^18 + 160 * q^19 - 60 * q^20 - 88 * q^22 + 22 * q^23 - 162 * q^24 - 50 * q^25 + 148 * q^26 + 4 * q^27 - 500 * q^29 + 30 * q^30 - 132 * q^31 - 42 * q^32 - 148 * q^33 - 888 * q^34 - 384 * q^36 + 416 * q^37 - 376 * q^38 + 84 * q^39 + 30 * q^40 + 212 * q^41 - 1332 * q^43 + 156 * q^44 - 80 * q^45 + 402 * q^46 - 196 * q^47 + 260 * q^48 - 300 * q^50 + 572 * q^51 - 348 * q^52 + 952 * q^53 + 402 * q^54 - 280 * q^55 - 944 * q^57 - 510 * q^58 + 840 * q^59 - 330 * q^60 + 98 * q^61 + 8 * q^62 - 1204 * q^64 + 180 * q^65 + 236 * q^66 + 1286 * q^67 - 1524 * q^68 - 2852 * q^69 + 2128 * q^71 - 264 * q^72 - 172 * q^73 - 1792 * q^74 - 50 * q^75 + 288 * q^76 + 856 * q^78 + 1240 * q^79 - 70 * q^80 + 754 * q^81 + 438 * q^82 + 3812 * q^83 - 760 * q^85 - 2018 * q^86 + 970 * q^87 - 604 * q^88 + 650 * q^89 - 720 * q^90 + 5484 * q^92 - 1332 * q^93 + 332 * q^94 - 800 * q^95 + 1722 * q^96 + 1256 * q^97 + 32 * q^99

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