LMFDB - Embedded newform 245.4.e.n.226.3

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:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.5567659200.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 17x^{4} - 28x^{3} + 289x^{2} - 238x + 196 $ x^6 + 17x^4 - 28x^3 + 289x^2 - 238x + 196
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			226.3
Root			$1.81228 + 3.13896i$ of defining polynomial
Character	$\chi$	$=$	245.226
Dual form			245.4.e.n.116.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.31228 - 4.00499i) q^{2} +(-4.19330 - 7.26300i) q^{3} +(-6.69330 - 11.5931i) q^{4} +(2.50000 - 4.33013i) q^{5} -38.7844 q^{6} -24.9107 q^{8} +(-21.6675 + 37.5292i) q^{9} +(-11.5614 - 20.0250i) q^{10} +(15.0558 + 26.0775i) q^{11} +(-56.1340 + 97.2269i) q^{12} -88.9295 q^{13} -41.9330 q^{15} +(-4.05409 + 7.02189i) q^{16} +(-2.36850 - 4.10236i) q^{17} +(100.203 + 173.556i) q^{18} +(62.4089 - 108.095i) q^{19} -66.9330 q^{20} +139.253 q^{22} +(-10.1340 + 17.5526i) q^{23} +(104.458 + 180.926i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-205.630 + 356.162i) q^{26} +136.995 q^{27} +134.088 q^{29} +(-96.9609 + 167.941i) q^{30} +(-1.01883 - 1.76467i) q^{31} +(-80.8942 - 140.113i) q^{32} +(126.267 - 218.701i) q^{33} -21.9065 q^{34} +580.108 q^{36} +(70.5687 - 122.229i) q^{37} +(-288.614 - 499.894i) q^{38} +(372.908 + 645.895i) q^{39} +(-62.2766 + 107.866i) q^{40} -95.2784 q^{41} -298.646 q^{43} +(201.546 - 349.088i) q^{44} +(108.337 + 187.646i) q^{45} +(46.8653 + 81.1730i) q^{46} +(-64.5268 + 111.764i) q^{47} +68.0000 q^{48} -115.614 q^{50} +(-19.8636 + 34.4048i) q^{51} +(595.232 + 1030.97i) q^{52} +(-194.214 - 336.389i) q^{53} +(316.771 - 548.663i) q^{54} +150.558 q^{55} -1046.80 q^{57} +(310.049 - 537.020i) q^{58} +(419.250 + 726.163i) q^{59} +(280.670 + 486.135i) q^{60} +(194.711 - 337.250i) q^{61} -9.42333 q^{62} -813.067 q^{64} +(-222.324 + 385.076i) q^{65} +(-583.931 - 1011.40i) q^{66} +(-348.897 - 604.307i) q^{67} +(-31.7061 + 54.9166i) q^{68} +169.979 q^{69} -523.450 q^{71} +(539.752 - 934.877i) q^{72} +(33.2342 + 57.5633i) q^{73} +(-326.350 - 565.254i) q^{74} +(-104.832 + 181.575i) q^{75} -1670.89 q^{76} +3449.07 q^{78} +(263.491 - 456.380i) q^{79} +(20.2704 + 35.1094i) q^{80} +(10.5618 + 18.2936i) q^{81} +(-220.311 + 381.589i) q^{82} -70.0265 q^{83} -23.6850 q^{85} +(-690.554 + 1196.07i) q^{86} +(-562.270 - 973.880i) q^{87} +(-375.051 - 649.607i) q^{88} +(-4.63963 + 8.03607i) q^{89} +1002.03 q^{90} +271.319 q^{92} +(-8.54456 + 14.7996i) q^{93} +(298.408 + 516.858i) q^{94} +(-312.045 - 540.477i) q^{95} +(-678.427 + 1175.07i) q^{96} +4.19493 q^{97} -1304.89 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 2 q^{3} - 13 q^{4} + 15 q^{5} - 48 q^{6} - 30 q^{8} - 81 q^{9} - 15 q^{10} + 74 q^{11} - 152 q^{12} - 88 q^{13} + 20 q^{15} + 79 q^{16} - 52 q^{17} + 411 q^{18} + 168 q^{19} - 130 q^{20}+ \cdots - 6976 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 2 * q^3 - 13 * q^4 + 15 * q^5 - 48 * q^6 - 30 * q^8 - 81 * q^9 - 15 * q^10 + 74 * q^11 - 152 * q^12 - 88 * q^13 + 20 * q^15 + 79 * q^16 - 52 * q^17 + 411 * q^18 + 168 * q^19 - 130 * q^20 + 368 * q^22 + 124 * q^23 + 420 * q^24 - 75 * q^25 - 446 * q^26 - 340 * q^27 + 664 * q^29 - 120 * q^30 + 320 * q^31 + 183 * q^32 - 106 * q^33 - 1164 * q^34 + 362 * q^36 + 54 * q^37 - 460 * q^38 + 982 * q^39 - 75 * q^40 - 724 * q^41 - 32 * q^43 + 264 * q^44 + 405 * q^45 + 336 * q^46 - 730 * q^47 + 408 * q^48 - 150 * q^50 + 1178 * q^51 + 1202 * q^52 - 110 * q^53 - 180 * q^54 + 740 * q^55 - 1912 * q^57 - 450 * q^58 - 180 * q^59 + 760 * q^60 + 1222 * q^61 - 928 * q^62 - 782 * q^64 - 220 * q^65 - 532 * q^66 - 204 * q^67 + 918 * q^68 + 1432 * q^69 - 272 * q^71 - 765 * q^72 + 310 * q^73 - 502 * q^74 + 50 * q^75 - 3592 * q^76 + 7576 * q^78 + 1034 * q^79 - 395 * q^80 - 2283 * q^81 - 6 * q^82 + 3320 * q^83 - 520 * q^85 - 764 * q^86 - 1574 * q^87 + 20 * q^88 + 242 * q^89 + 4110 * q^90 + 192 * q^92 - 1376 * q^93 - 1108 * q^94 - 840 * q^95 - 3156 * q^96 - 200 * q^97 - 6976 * q^99

Character values

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

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

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 $

$2$	2.31228	−	4.00499i	0.817515	−	1.41598i	−0.0899925	−	0.995942i	$-0.528684\pi$
$2$	2.31228	−	4.00499i	0.817515	−	1.41598i	0.907508	−	0.420035i	$-0.137982\pi$
$3$	−4.19330	−	7.26300i	−0.807001	−	1.39777i	−0.914932	−	0.403608i	$-0.867756\pi$
$3$	−4.19330	−	7.26300i	−0.807001	−	1.39777i	0.107932	−	0.994158i	$-0.465577\pi$
$4$	−6.69330	−	11.5931i	−0.836662	−	1.44914i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	−38.7844			−2.63894
$7$		0			0
$7$		0			0
$8$	−24.9107			−1.10091
$9$	−21.6675	+	37.5292i	−0.802500	+	1.38997i
$10$	−11.5614	−	20.0250i	−0.365604	−	0.633245i
$11$	15.0558	+	26.0775i	0.412682	+	0.714786i	0.995182	−	0.0980443i	$-0.0312587\pi$
$11$	15.0558	+	26.0775i	0.412682	+	0.714786i	−0.582500	+	0.812831i	$0.697925\pi$
$12$	−56.1340	+	97.2269i	−1.35037	+	2.33892i
$13$	−88.9295			−1.89728			−0.948639	−	0.316362i	$-0.897539\pi$
$13$	−88.9295			−1.89728			−0.948639	+	0.316362i	$0.897539\pi$
$14$		0			0
$15$	−41.9330			−0.721803
$16$	−4.05409	+	7.02189i	−0.0633451	+	0.109717i
$17$	−2.36850	−	4.10236i	−0.0337909	−	0.0585275i	0.848635	−	0.528978i	$-0.177425\pi$
$17$	−2.36850	−	4.10236i	−0.0337909	−	0.0585275i	−0.882426	+	0.470451i	$0.844091\pi$
$18$	100.203	+	173.556i	1.31211	+	2.27264i
$19$	62.4089	−	108.095i	0.753557	−	1.30520i	−0.192531	−	0.981291i	$-0.561670\pi$
$19$	62.4089	−	108.095i	0.753557	−	1.30520i	0.946088	−	0.323909i	$-0.104997\pi$
$20$	−66.9330			−0.748333
$21$		0			0
$22$	139.253			1.34950
$23$	−10.1340	+	17.5526i	−0.0918731	+	0.159129i	−0.908299	−	0.418321i	$-0.862619\pi$
$23$	−10.1340	+	17.5526i	−0.0918731	+	0.159129i	0.816426	+	0.577450i	$0.195952\pi$
$24$	104.458	+	180.926i	0.888432	+	1.53881i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	−205.630	+	356.162i	−1.55105	+	2.68650i
$27$	136.995			0.976470
$28$		0			0
$29$	134.088			0.858603			0.429301	−	0.903161i	$-0.358760\pi$
$29$	134.088			0.858603			0.429301	+	0.903161i	$0.358760\pi$
$30$	−96.9609	+	167.941i	−0.590085	+	1.02206i
$31$	−1.01883	−	1.76467i	−0.00590284	−	0.0102240i	0.863059	−	0.505103i	$-0.168546\pi$
$31$	−1.01883	−	1.76467i	−0.00590284	−	0.0102240i	−0.868962	+	0.494879i	$0.835212\pi$
$32$	−80.8942	−	140.113i	−0.446882	−	0.774022i
$33$	126.267	−	218.701i	0.666069	−	1.15367i
$34$	−21.9065			−0.110498
$35$		0			0
$36$	580.108			2.68568
$37$	70.5687	−	122.229i	0.313552	−	0.543088i	−0.665577	−	0.746329i	$-0.731814\pi$
$37$	70.5687	−	122.229i	0.313552	−	0.543088i	0.979129	+	0.203242i	$0.0651477\pi$
$38$	−288.614	−	499.894i	−1.23209	−	2.13404i
$39$	372.908	+	645.895i	1.53110	+	2.65195i
$40$	−62.2766	+	107.866i	−0.246170	+	0.426379i
$41$	−95.2784			−0.362927			−0.181463	−	0.983398i	$-0.558083\pi$
$41$	−95.2784			−0.362927			−0.181463	+	0.983398i	$0.558083\pi$
$42$		0			0
$43$	−298.646			−1.05914			−0.529571	−	0.848266i	$-0.677647\pi$
$43$	−298.646			−1.05914			−0.529571	+	0.848266i	$0.677647\pi$
$44$	201.546	−	349.088i	0.690551	−	1.19607i
$45$	108.337	+	187.646i	0.358889	+	0.621614i
$46$	46.8653	+	81.1730i	0.150215	+	0.260181i
$47$	−64.5268	+	111.764i	−0.200260	+	0.346860i	−0.948612	−	0.316442i	$-0.897512\pi$
$47$	−64.5268	+	111.764i	−0.200260	+	0.346860i	0.748352	+	0.663301i	$0.230845\pi$
$48$	68.0000			0.204478
$49$		0			0
$50$	−115.614			−0.327006
$51$	−19.8636	+	34.4048i	−0.0545385	+	0.0944635i
$52$	595.232	+	1030.97i	1.58738	+	2.74942i
$53$	−194.214	−	336.389i	−0.503347	−	0.871823i	−0.999993	−	0.00386911i	$-0.998768\pi$
$53$	−194.214	−	336.389i	−0.503347	−	0.871823i	0.496646	−	0.867953i	$-0.334565\pi$
$54$	316.771	−	548.663i	0.798279	−	1.38266i
$55$	150.558			0.369114
$56$		0			0
$57$	−1046.80			−2.43248
$58$	310.049	−	537.020i	0.701921	−	1.21576i
$59$	419.250	+	726.163i	0.925114	+	1.60235i	0.791377	+	0.611329i	$0.209365\pi$
$59$	419.250	+	726.163i	0.925114	+	1.60235i	0.133738	+	0.991017i	$0.457302\pi$
$60$	280.670	+	486.135i	0.603905	+	1.04599i
$61$	194.711	−	337.250i	0.408692	−	0.707875i	−0.586051	−	0.810274i	$-0.699318\pi$
$61$	194.711	−	337.250i	0.408692	−	0.707875i	0.994743	+	0.102399i	$0.0326517\pi$
$62$	−9.42333			−0.0193027
$63$		0			0
$64$	−813.067			−1.58802
$65$	−222.324	+	385.076i	−0.424244	+	0.734812i
$66$	−583.931	−	1011.40i	−1.08904	−	1.88628i
$67$	−348.897	−	604.307i	−0.636187	−	1.10191i	−0.986262	−	0.165187i	$-0.947177\pi$
$67$	−348.897	−	604.307i	−0.636187	−	1.10191i	0.350075	−	0.936722i	$-0.386156\pi$
$68$	−31.7061	+	54.9166i	−0.0565431	+	0.0979355i
$69$	169.979			0.296567
$70$		0			0
$71$	−523.450			−0.874959			−0.437479	−	0.899228i	$-0.644129\pi$
$71$	−523.450			−0.874959			−0.437479	+	0.899228i	$0.644129\pi$
$72$	539.752	−	934.877i	0.883477	−	1.53023i
$73$	33.2342	+	57.5633i	0.0532845	+	0.0922915i	0.891437	−	0.453144i	$-0.149698\pi$
$73$	33.2342	+	57.5633i	0.0532845	+	0.0922915i	−0.838153	+	0.545435i	$0.816364\pi$
$74$	−326.350	−	565.254i	−0.512667	−	0.887965i
$75$	−104.832	+	181.575i	−0.161400	+	0.279553i
$76$	−1670.89			−2.52189
$77$		0			0
$78$	3449.07			5.00680
$79$	263.491	−	456.380i	0.375254	−	0.649959i	−0.615111	−	0.788440i	$-0.710889\pi$
$79$	263.491	−	456.380i	0.375254	−	0.649959i	0.990365	+	0.138482i	$0.0442222\pi$
$80$	20.2704	+	35.1094i	0.0283288	+	0.0490669i
$81$	10.5618	+	18.2936i	0.0144881	+	0.0250941i
$82$	−220.311	+	381.589i	−0.296698	+	0.513896i
$83$	−70.0265			−0.0926074			−0.0463037	−	0.998927i	$-0.514744\pi$
$83$	−70.0265			−0.0926074			−0.0463037	+	0.998927i	$0.514744\pi$
$84$		0			0
$85$	−23.6850			−0.0302235
$86$	−690.554	+	1196.07i	−0.865864	+	1.49972i
$87$	−562.270	−	973.880i	−0.692893	−	1.20013i
$88$	−375.051	−	649.607i	−0.454324	−	0.786913i
$89$	−4.63963	+	8.03607i	−0.00552584	+	0.00957103i	−0.868775	−	0.495207i	$-0.835092\pi$
$89$	−4.63963	+	8.03607i	−0.00552584	+	0.00957103i	0.863249	+	0.504778i	$0.168426\pi$
$90$	1002.03			1.17359
$91$		0			0
$92$	271.319			0.307467
$93$	−8.54456	+	14.7996i	−0.00952720	+	0.0165016i
$94$	298.408	+	516.858i	0.327431	+	0.567126i
$95$	−312.045	−	540.477i	−0.337001	−	0.583703i
$96$	−678.427	+	1175.07i	−0.721268	+	1.24927i
$97$	4.19493			0.00439104			0.00219552	−	0.999998i	$-0.499301\pi$
$97$	4.19493			0.00439104			0.00219552	+	0.999998i	$0.499301\pi$
$98$		0			0
$99$	−1304.89			−1.32471
$100$	−167.332	+	289.828i	−0.167332	+	0.289828i
$101$	−432.922	−	749.843i	−0.426508	−	0.738734i	0.570052	−	0.821609i	$-0.306923\pi$
$101$	−432.922	−	749.843i	−0.426508	−	0.738734i	−0.996560	+	0.0828749i	$0.973590\pi$
$102$	91.8606	+	159.107i	0.0891721	+	0.154451i
$103$	−583.058	+	1009.89i	−0.557771	+	0.966088i	0.439911	+	0.898042i	$0.355010\pi$
$103$	−583.058	+	1009.89i	−0.557771	+	0.966088i	−0.997682	+	0.0680469i	$0.978323\pi$
$104$	2215.29			2.08872
$105$		0			0
$106$	−1796.31			−1.64598
$107$	−28.4826	+	49.3333i	−0.0257338	+	0.0445722i	−0.878606	−	0.477548i	$-0.841526\pi$
$107$	−28.4826	+	49.3333i	−0.0257338	+	0.0445722i	0.852872	+	0.522121i	$0.174859\pi$
$108$	−916.948	−	1588.20i	−0.816975	−	1.41504i
$109$	679.445	+	1176.83i	0.597055	+	1.03413i	0.993253	+	0.115965i	$0.0369959\pi$
$109$	679.445	+	1176.83i	0.597055	+	1.03413i	−0.396198	+	0.918165i	$0.629671\pi$
$110$	348.133	−	602.985i	0.301756	−	0.522657i
$111$	−1183.66			−1.01215
$112$		0			0
$113$	436.038			0.363000			0.181500	−	0.983391i	$-0.441905\pi$
$113$	436.038			0.363000			0.181500	+	0.983391i	$0.441905\pi$
$114$	−2420.49	+	4192.41i	−1.98859	+	3.44434i
$115$	50.6699	+	87.7629i	0.0410869	+	0.0711646i
$116$	−897.490	−	1554.50i	−0.718361	−	1.24424i
$117$	1926.88	−	3337.45i	1.52256	−	2.63716i
$118$	3877.70			3.02518
$119$		0			0
$120$	1044.58			0.794637
$121$	212.144	−	367.444i	0.159387	−	0.276066i
$122$	−900.454	−	1559.63i	−0.668224	−	1.15740i
$123$	399.531	+	692.008i	0.292882	+	0.507286i
$124$	−13.6387	+	23.6230i	−0.00987737	+	0.0171081i
$125$	−125.000			−0.0894427
$126$		0			0
$127$	1186.69			0.829144			0.414572	−	0.910017i	$-0.363931\pi$
$127$	1186.69			0.829144			0.414572	+	0.910017i	$0.363931\pi$
$128$	−1232.89	+	2135.42i	−0.851349	+	1.47458i
$129$	1252.31	+	2169.07i	0.854728	+	1.48043i
$130$	1028.15	+	1780.81i	0.693652	+	1.20144i
$131$	517.278	−	895.952i	0.344999	−	0.597555i	−0.640355	−	0.768079i	$-0.721213\pi$
$131$	517.278	−	895.952i	0.344999	−	0.597555i	0.985354	+	0.170524i	$0.0545460\pi$
$132$	−3380.57			−2.22910
$133$		0			0
$134$	−3226.99			−2.08037
$135$	342.487	−	593.205i	0.218345	−	0.378185i
$136$	59.0008	+	102.192i	0.0372006	+	0.0644333i
$137$	−323.109	−	559.642i	−0.201497	−	0.349003i	0.747514	−	0.664246i	$-0.231247\pi$
$137$	−323.109	−	559.642i	−0.201497	−	0.349003i	−0.949011	+	0.315243i	$0.897914\pi$
$138$	393.040	−	680.765i	0.242448	−	0.419932i
$139$	−506.484			−0.309061			−0.154530	−	0.987988i	$-0.549386\pi$
$139$	−506.484			−0.309061			−0.154530	+	0.987988i	$0.549386\pi$
$140$		0			0
$141$	1082.32			0.646439
$142$	−1210.36	+	2096.41i	−0.715292	+	1.23892i
$143$	−1338.91	−	2319.06i	−0.782972	−	1.35615i
$144$	−175.684	−	304.293i	−0.101669	−	0.176096i
$145$	335.220	−	580.617i	0.191989	−	0.332535i
$146$	307.387			0.174244
$147$		0			0
$148$	−1889.35			−1.04935
$149$	914.058	−	1583.19i	0.502567	−	0.870472i	−0.497428	−	0.867505i	$-0.665722\pi$
$149$	914.058	−	1583.19i	0.502567	−	0.870472i	0.999996	−	0.00296704i	$-0.000944438\pi$
$150$	484.804	+	839.706i	0.263894	+	0.457078i
$151$	−1487.58	−	2576.57i	−0.801708	−	1.38860i	−0.918491	−	0.395441i	$-0.870592\pi$
$151$	−1487.58	−	2576.57i	−0.801708	−	1.38860i	0.116783	−	0.993157i	$-0.462742\pi$
$152$	−1554.65	+	2692.73i	−0.829596	+	1.43690i
$153$	205.278			0.108469
$154$		0			0
$155$	−10.1883			−0.00527966
$156$	4991.97	−	8646.34i	2.56203	−	4.43757i
$157$	−1065.87	−	1846.14i	−0.541820	−	0.938459i	−0.998800	−	0.0489821i	$-0.984402\pi$
$157$	−1065.87	−	1846.14i	−0.541820	−	0.938459i	0.456980	−	0.889477i	$-0.348931\pi$
$158$	−1218.53	−	2110.56i	−0.613551	−	1.06270i
$159$	−1628.80	+	2821.16i	−0.812403	+	1.40712i
$160$	−808.942			−0.399703
$161$		0			0
$162$	97.6876			0.0473769
$163$	296.969	−	514.366i	0.142702	−	0.247167i	−0.785811	−	0.618466i	$-0.787754\pi$
$163$	296.969	−	514.366i	0.142702	−	0.247167i	0.928513	+	0.371299i	$0.121088\pi$
$164$	637.727	+	1104.58i	0.303647	+	0.525932i
$165$	−631.336	−	1093.51i	−0.297875	−	0.515935i
$166$	−161.921	+	280.456i	−0.0757079	+	0.131130i
$167$	2936.30			1.36059			0.680293	−	0.732941i	$-0.261853\pi$
$167$	2936.30			1.36059			0.680293	+	0.732941i	$0.261853\pi$
$168$		0			0
$169$	5711.45			2.59966
$170$	−54.7663	+	94.8581i	−0.0247081	+	0.0427958i
$171$	2704.49	+	4684.31i	1.20946	+	2.09484i
$172$	1998.93	+	3462.24i	0.886144	+	1.53485i
$173$	1173.65	−	2032.83i	0.515788	−	0.893371i	−0.484044	−	0.875044i	$-0.660833\pi$
$173$	1173.65	−	2032.83i	0.515788	−	0.893371i	0.999832	−	0.0183273i	$-0.00583410\pi$
$174$	−5200.51			−2.26580
$175$		0			0
$176$	−244.151			−0.104566
$177$	3516.08	−	6090.04i	1.49314	−	2.58619i
$178$	21.4562	+	37.1633i	0.00903491	+	0.0156489i
$179$	−1518.28	−	2629.74i	−0.633975	−	1.09808i	−0.986731	−	0.162362i	$-0.948089\pi$
$179$	−1518.28	−	2629.74i	−0.633975	−	1.09808i	0.352756	−	0.935715i	$-0.385244\pi$
$180$	1450.27	−	2511.94i	0.600537	−	1.04016i
$181$	899.776			0.369502			0.184751	−	0.982785i	$-0.440852\pi$
$181$	899.776			0.369502			0.184751	+	0.982785i	$0.440852\pi$
$182$		0			0
$183$	−3265.93			−1.31926
$184$	252.444	−	437.246i	0.101144	−	0.175186i
$185$	−352.844	−	611.143i	−0.140225	−	0.242876i
$186$	39.5148	+	68.4417i	0.0155773	+	0.0269806i
$187$	71.3194	−	123.529i	0.0278898	−	0.0483065i
$188$	1727.59			0.670199
$189$		0			0
$190$	−2886.14			−1.10201
$191$	−208.084	+	360.412i	−0.0788294	+	0.136537i	−0.902745	−	0.430176i	$-0.858452\pi$
$191$	−208.084	+	360.412i	−0.0788294	+	0.136537i	0.823916	+	0.566712i	$0.191785\pi$
$192$	3409.43	+	5905.31i	1.28153	+	2.21968i
$193$	2590.52	+	4486.92i	0.966166	+	1.67345i	0.706450	+	0.707763i	$0.250296\pi$
$193$	2590.52	+	4486.92i	0.966166	+	1.67345i	0.259716	+	0.965685i	$0.416371\pi$
$194$	9.69986	−	16.8007i	0.00358974	−	0.00621761i
$195$	3729.08			1.36946
$196$		0			0
$197$	1452.34			0.525255			0.262627	−	0.964897i	$-0.415411\pi$
$197$	1452.34			0.525255			0.262627	+	0.964897i	$0.415411\pi$
$198$	−3017.27	+	5226.07i	−1.08297	+	1.87576i
$199$	−638.616	−	1106.12i	−0.227489	−	0.394023i	0.729574	−	0.683902i	$-0.239718\pi$
$199$	−638.616	−	1106.12i	−0.227489	−	0.394023i	−0.957063	+	0.289879i	$0.906385\pi$
$200$	311.383	+	539.332i	0.110091	+	0.190683i
$201$	−2926.06	+	5068.08i	−1.02681	+	1.77848i
$202$	−4004.15			−1.39471
$203$		0			0
$204$	531.813			0.182521
$205$	−238.196	+	412.568i	−0.0811528	+	0.140561i
$206$	2696.39	+	4670.29i	0.911973	+	1.57958i
$207$	−439.156	−	760.640i	−0.147456	−	0.255402i
$208$	360.528	−	624.453i	0.120183	−	0.208164i
$209$	3758.47			1.24392
$210$		0			0
$211$	−3259.09			−1.06334			−0.531670	−	0.846951i	$-0.678436\pi$
$211$	−3259.09			−1.06334			−0.531670	+	0.846951i	$0.678436\pi$
$212$	−2599.87	+	4503.10i	−0.842263	+	1.45884i
$213$	2194.98	+	3801.82i	0.706092	+	1.22299i
$214$	131.720	+	228.145i	0.0420755	+	0.0728770i
$215$	−746.615	+	1293.18i	−0.236831	+	0.410204i
$216$	−3412.63			−1.07500
$217$		0			0
$218$	6284.27			1.95241
$219$	278.722	−	482.760i	0.0860012	−	0.148959i
$220$	−1007.73	−	1745.44i	−0.308824	−	0.534899i
$221$	210.629	+	364.820i	0.0641107	+	0.111043i
$222$	−2736.96	+	4740.56i	−0.827445	+	1.43318i
$223$	−4373.35			−1.31328			−0.656639	−	0.754205i	$-0.728023\pi$
$223$	−4373.35			−1.31328			−0.656639	+	0.754205i	$0.728023\pi$
$224$		0			0
$225$	1083.37			0.321000
$226$	1008.24	−	1746.33i	0.296758	−	0.514000i
$227$	−30.5573	−	52.9267i	−0.00893461	−	0.0154752i	0.861524	−	0.507718i	$-0.169511\pi$
$227$	−30.5573	−	52.9267i	−0.00893461	−	0.0154752i	−0.870458	+	0.492242i	$0.836177\pi$
$228$	7006.52	+	12135.7i	2.03517	+	3.52501i
$229$	1509.71	−	2614.89i	0.435651	−	0.754570i	−0.561697	−	0.827343i	$-0.689851\pi$
$229$	1509.71	−	2614.89i	0.435651	−	0.754570i	0.997349	+	0.0727728i	$0.0231848\pi$
$230$	468.653			0.134357
$231$		0			0
$232$	−3340.22			−0.945241
$233$	1765.58	−	3058.08i	0.496426	−	0.859834i	−0.503566	−	0.863957i	$-0.667979\pi$
$233$	1765.58	−	3058.08i	0.496426	−	0.859834i	0.999992	+	0.00412242i	$0.00131221\pi$
$234$	−8910.98	−	15434.3i	−2.48944	−	4.31184i
$235$	322.634	+	558.819i	0.0895588	+	0.155120i
$236$	5612.34	−	9720.85i	1.54802	−	2.68124i
$237$	−4419.58			−1.21132
$238$		0			0
$239$	2282.62			0.617785			0.308893	−	0.951097i	$-0.400042\pi$
$239$	2282.62			0.617785			0.308893	+	0.951097i	$0.400042\pi$
$240$	170.000	−	294.449i	0.0457227	−	0.0791941i
$241$	−1107.84	−	1918.83i	−0.296109	−	0.512875i	0.679134	−	0.734015i	$-0.262356\pi$
$241$	−1107.84	−	1918.83i	−0.296109	−	0.512875i	−0.975242	+	0.221140i	$0.929022\pi$
$242$	−981.073	−	1699.27i	−0.260602	−	0.451377i
$243$	1938.01	−	3356.73i	0.511619	−	0.886150i
$244$	−5213.04			−1.36775
$245$		0			0
$246$	3695.31			0.957742
$247$	−5549.99	+	9612.87i	−1.42971	+	2.47633i
$248$	25.3798	+	43.9592i	0.00649848	+	0.0112557i
$249$	293.642	+	508.603i	0.0747342	+	0.129443i
$250$	−289.035	+	500.624i	−0.0731208	+	0.126649i
$251$	3082.55			0.775174			0.387587	−	0.921833i	$-0.373309\pi$
$251$	3082.55			0.775174			0.387587	+	0.921833i	$0.373309\pi$
$252$		0			0
$253$	−610.302			−0.151658
$254$	2743.95	−	4752.66i	0.677838	−	1.17405i
$255$	99.3181	+	172.024i	0.0243904	+	0.0422453i
$256$	2449.29	+	4242.30i	0.597972	+	1.03572i
$257$	−3016.20	+	5224.21i	−0.732083	+	1.26801i	0.223908	+	0.974610i	$0.428118\pi$
$257$	−3016.20	+	5224.21i	−0.732083	+	1.26801i	−0.955991	+	0.293395i	$0.905215\pi$
$258$	11582.8			2.79501
$259$		0			0
$260$	5952.32			1.41980
$261$	−2905.35	+	5032.21i	−0.689029	+	1.19343i
$262$	−2392.19	−	4143.39i	−0.564083	−	0.977021i
$263$	−2961.91	−	5130.17i	−0.694445	−	1.20281i	−0.970368	−	0.241634i	$-0.922317\pi$
$263$	−2961.91	−	5130.17i	−0.694445	−	1.20281i	0.275923	−	0.961180i	$-0.411017\pi$
$264$	−3145.40	+	5447.99i	−0.733280	+	1.27008i
$265$	−1942.14			−0.450207
$266$		0			0
$267$	77.8213			0.0178374
$268$	−4670.54	+	8089.62i	−1.06455	+	1.84385i
$269$	1626.40	+	2817.00i	0.368637	+	0.638497i	0.989353	−	0.145538i	$-0.0464914\pi$
$269$	1626.40	+	2817.00i	0.368637	+	0.638497i	−0.620716	+	0.784035i	$0.713158\pi$
$270$	−1583.85	−	2743.32i	−0.357001	−	0.618344i
$271$	−3123.13	+	5409.42i	−0.700061	+	1.21254i	0.268383	+	0.963312i	$0.413511\pi$
$271$	−3123.13	+	5409.42i	−0.700061	+	1.21254i	−0.968444	+	0.249230i	$0.919823\pi$
$272$	38.4084			0.00856195
$273$		0			0
$274$	−2988.48			−0.658907
$275$	376.396	−	651.937i	0.0825364	−	0.142957i
$276$	−1137.72	−	1970.59i	−0.248126	−	0.429767i
$277$	786.084	+	1361.54i	0.170510	+	0.295332i	0.938598	−	0.345012i	$-0.112125\pi$
$277$	786.084	+	1361.54i	0.170510	+	0.295332i	−0.768088	+	0.640344i	$0.778792\pi$
$278$	−1171.13	+	2028.47i	−0.252662	+	0.437623i
$279$	88.3024			0.0189481
$280$		0			0
$281$	−7846.03			−1.66567			−0.832837	−	0.553518i	$-0.813285\pi$
$281$	−7846.03			−1.66567			−0.832837	+	0.553518i	$0.813285\pi$
$282$	2502.63	−	4334.68i	0.528473	−	0.915343i
$283$	3132.79	+	5426.15i	0.658039	+	1.13976i	0.981123	+	0.193386i	$0.0619470\pi$
$283$	3132.79	+	5426.15i	0.658039	+	1.13976i	−0.323084	+	0.946370i	$0.604720\pi$
$284$	3503.61	+	6068.42i	0.732045	+	1.26794i
$285$	−2616.99	+	4532.76i	−0.543920	+	0.942097i
$286$	−12383.7			−2.56037
$287$		0			0
$288$	7011.10			1.43449
$289$	2445.28	−	4235.35i	0.497716	−	0.862070i
$290$	−1550.24	−	2685.10i	−0.313909	−	0.543706i
$291$	−17.5906	−	30.4678i	−0.00354357	−	0.00613764i
$292$	444.893	−	770.577i	0.0891623	−	0.154434i
$293$	7264.99			1.44855			0.724276	−	0.689511i	$-0.242174\pi$
$293$	7264.99			1.44855			0.724276	+	0.689511i	$0.242174\pi$
$294$		0			0
$295$	4192.50			0.827448
$296$	−1757.91	+	3044.79i	−0.345191	+	0.597889i
$297$	2062.57	+	3572.48i	0.402972	+	0.697967i
$298$	−4227.12	−	7321.59i	−0.821713	−	1.42325i
$299$	901.210	−	1560.94i	0.174309	−	0.301912i
$300$	2806.70			0.540149
$301$		0			0
$302$	−13758.9			−2.62163
$303$	−3630.74	+	6288.63i	−0.688385	+	1.19232i
$304$	506.023	+	876.457i	0.0954684	+	0.165356i
$305$	−973.556	−	1686.25i	−0.182773	−	0.316571i
$306$	474.660	−	822.135i	0.0886748	−	0.153589i
$307$	−1328.32			−0.246943			−0.123471	−	0.992348i	$-0.539403\pi$
$307$	−1328.32			−0.246943			−0.123471	+	0.992348i	$0.539403\pi$
$308$		0			0
$309$	9779.75			1.80049
$310$	−23.5583	+	40.8042i	−0.00431621	+	0.00747589i
$311$	2434.34	+	4216.40i	0.443855	+	0.768779i	0.997972	−	0.0636600i	$-0.0202773\pi$
$311$	2434.34	+	4216.40i	0.443855	+	0.768779i	−0.554117	+	0.832439i	$0.686944\pi$
$312$	−9289.38	−	16089.7i	−1.68560	−	2.91955i
$313$	3866.69	−	6697.31i	0.698270	−	1.20944i	−0.270796	−	0.962637i	$-0.587287\pi$
$313$	3866.69	−	6697.31i	0.698270	−	1.20944i	0.969066	−	0.246802i	$-0.0793798\pi$
$314$	−9858.37			−1.77178
$315$		0			0
$316$	−7054.49			−1.25584
$317$	4087.51	−	7079.78i	0.724220	−	1.25439i	−0.235075	−	0.971977i	$-0.575534\pi$
$317$	4087.51	−	7079.78i	0.724220	−	1.25439i	0.959294	−	0.282408i	$-0.0911331\pi$
$318$	7532.48	+	13046.6i	1.32830	+	2.30069i
$319$	2018.80	+	3496.67i	0.354330	+	0.613718i
$320$	−2032.67	+	3520.68i	−0.355092	+	0.615038i
$321$	477.744			0.0830688
$322$		0			0
$323$	−591.261			−0.101853
$324$	141.387	−	244.889i	0.0242433	−	0.0419906i
$325$	1111.62	+	1925.38i	0.189728	+	0.328618i
$326$	−1373.35	−	2378.72i	−0.233322	−	0.404126i
$327$	5698.23	−	9869.62i	0.963647	−	1.66909i
$328$	2373.45			0.399548
$329$		0			0
$330$	−5839.31			−0.974070
$331$	1020.38	−	1767.35i	0.169442	−	0.293482i	−0.768782	−	0.639511i	$-0.779137\pi$
$331$	1020.38	−	1767.35i	0.169442	−	0.293482i	0.938224	+	0.346029i	$0.112470\pi$
$332$	468.709	+	811.827i	0.0774811	+	0.134201i
$333$	3058.09	+	5296.77i	0.503251	+	0.871656i
$334$	6789.56	−	11759.9i	1.11230	−	1.92656i
$335$	−3488.97			−0.569023
$336$		0			0
$337$	7349.73			1.18803			0.594013	−	0.804455i	$-0.297543\pi$
$337$	7349.73			1.18803			0.594013	+	0.804455i	$0.297543\pi$
$338$	13206.5	−	22874.3i	2.12526	−	3.68106i
$339$	−1828.44	−	3166.94i	−0.292941	−	0.507389i
$340$	158.531	+	274.583i	0.0252868	+	0.0437981i
$341$	30.6788	−	53.1373i	0.00487200	−	0.00843855i
$342$	25014.2			3.95500
$343$		0			0
$344$	7439.47			1.16602
$345$	424.948	−	736.032i	0.0663143	−	0.114860i
$346$	−5427.64	−	9400.95i	−0.843329	−	1.46069i
$347$	6034.96	+	10452.9i	0.933642	+	1.61712i	0.777037	+	0.629454i	$0.216722\pi$
$347$	6034.96	+	10452.9i	0.933642	+	1.61712i	0.156605	+	0.987661i	$0.449945\pi$
$348$	−7526.88	+	13036.9i	−1.15943	+	2.00820i
$349$	4484.96			0.687892			0.343946	−	0.938989i	$-0.388236\pi$
$349$	4484.96			0.687892			0.343946	+	0.938989i	$0.388236\pi$
$350$		0			0
$351$	−12182.9			−1.85263
$352$	2435.86	−	4219.03i	0.368840	−	0.638850i
$353$	−6381.24	−	11052.6i	−0.962151	−	1.66649i	−0.717082	−	0.696989i	$-0.754523\pi$
$353$	−6381.24	−	11052.6i	−0.962151	−	1.66649i	−0.245069	−	0.969506i	$-0.578811\pi$
$354$	−16260.4	−	28163.8i	−2.44132	−	4.22849i
$355$	−1308.62	+	2266.60i	−0.195647	+	0.338870i
$356$	124.218			0.0184930
$357$		0			0
$358$	−14042.8			−2.07314
$359$	1209.71	−	2095.28i	0.177844	−	0.308036i	−0.763298	−	0.646047i	$-0.776421\pi$
$359$	1209.71	−	2095.28i	0.177844	−	0.308036i	0.941142	+	0.338011i	$0.109754\pi$
$360$	−2698.76	−	4674.39i	−0.395103	−	0.684338i
$361$	−4360.25	−	7552.17i	−0.635697	−	1.10106i
$362$	2080.54	−	3603.60i	0.302073	−	0.523207i
$363$	−3558.33			−0.514501
$364$		0			0
$365$	332.342			0.0476591
$366$	−7551.75	+	13080.0i	−1.07851	+	1.86804i
$367$	−3564.87	−	6174.54i	−0.507043	−	0.878224i	−0.999967	−	0.00815152i	$-0.997405\pi$
$367$	−3564.87	−	6174.54i	−0.507043	−	0.878224i	0.492924	−	0.870072i	$-0.335928\pi$
$368$	−82.1681	−	142.319i	−0.0116394	−	0.0201601i
$369$	2064.44	−	3575.72i	0.291248	−	0.504457i
$370$	−3263.50			−0.458543
$371$		0			0
$372$	228.765			0.0318842
$373$	−5798.46	+	10043.2i	−0.804914	+	1.39415i	0.111435	+	0.993772i	$0.464455\pi$
$373$	−5798.46	+	10043.2i	−0.804914	+	1.39415i	−0.916349	+	0.400380i	$0.868878\pi$
$374$	−329.821	−	571.267i	−0.0456006	−	0.0789826i
$375$	524.162	+	907.876i	0.0721803	+	0.125020i
$376$	1607.41	−	2784.11i	0.220467	−	0.381860i
$377$	−11924.4			−1.62901
$378$		0			0
$379$	−12770.8			−1.73085			−0.865424	−	0.501040i	$-0.832951\pi$
$379$	−12770.8			−1.73085			−0.865424	+	0.501040i	$0.832951\pi$
$380$	−4177.21	+	7235.15i	−0.563912	+	0.976724i
$381$	−4976.12	−	8618.90i	−0.669120	−	1.15895i
$382$	962.297	+	1666.75i	0.128888	+	0.223241i
$383$	3735.05	−	6469.30i	0.498308	−	0.863096i	−0.501690	−	0.865048i	$-0.667288\pi$
$383$	3735.05	−	6469.30i	0.498308	−	0.863096i	0.999998	+	0.00195209i	$0.000621369\pi$
$384$	20679.4			2.74816
$385$		0			0
$386$	23960.1			3.15942
$387$	6470.91	−	11207.9i	0.849961	−	1.47218i
$388$	−28.0779	−	48.6324i	−0.00367381	−	0.00636323i
$389$	−4374.89	−	7577.53i	−0.570220	−	0.987650i	−0.996543	−	0.0830789i	$-0.973525\pi$
$389$	−4374.89	−	7577.53i	−0.570220	−	0.987650i	0.426323	−	0.904571i	$-0.359809\pi$
$390$	8622.68	−	14934.9i	1.11956	−	1.93913i
$391$	96.0092			0.0124179
$392$		0			0
$393$	−8676.41			−1.11366
$394$	3358.23	−	5816.62i	0.429404	−	0.743749i
$395$	−1317.45	−	2281.90i	−0.167819	−	0.290670i
$396$	8734.01	+	15127.7i	1.10833	+	1.91969i
$397$	2687.63	−	4655.11i	0.339769	−	0.588496i	−0.644621	−	0.764503i	$-0.722985\pi$
$397$	2687.63	−	4655.11i	0.339769	−	0.588496i	0.984389	+	0.176006i	$0.0563179\pi$
$398$	−5906.65			−0.743903
$399$		0			0
$400$	202.704			0.0253381
$401$	−3680.67	+	6375.10i	−0.458363	+	0.793909i	−0.998875	−	0.0474281i	$-0.984897\pi$
$401$	−3680.67	+	6375.10i	−0.458363	+	0.793909i	0.540511	+	0.841337i	$0.318231\pi$
$402$	13531.7	+	23437.7i	1.67886	+	2.90787i
$403$	90.6045	+	156.932i	0.0111993	+	0.0193978i
$404$	−5795.35	+	10037.8i	−0.713687	+	1.23614i
$405$	105.618			0.0129585
$406$		0			0
$407$	4249.88			0.517589
$408$	494.816	−	857.046i	0.0600418	−	0.103995i
$409$	−1306.23	−	2262.45i	−0.157919	−	0.273523i	0.776199	−	0.630488i	$-0.217145\pi$
$409$	−1306.23	−	2262.45i	−0.157919	−	0.273523i	−0.934118	+	0.356964i	$0.883812\pi$
$410$	1101.55	+	1907.95i	0.132687	+	0.229821i
$411$	−2709.79	+	4693.49i	−0.325216	+	0.563291i
$412$	15610.3			1.86667
$413$		0			0
$414$	−4061.81			−0.482191
$415$	−175.066	+	303.224i	−0.0207076	+	0.0358667i
$416$	7193.88	+	12460.2i	0.847859	+	1.46853i
$417$	2123.84	+	3678.60i	0.249412	+	0.431995i
$418$	8690.65	−	15052.6i	1.01692	−	1.76136i
$419$	−4398.21			−0.512808			−0.256404	−	0.966570i	$-0.582538\pi$
$419$	−4398.21			−0.512808			−0.256404	+	0.966570i	$0.582538\pi$
$420$		0			0
$421$	9723.32			1.12562			0.562810	−	0.826587i	$-0.309720\pi$
$421$	9723.32			1.12562			0.562810	+	0.826587i	$0.309720\pi$
$422$	−7535.93	+	13052.6i	−0.869297	+	1.50567i
$423$	−2796.27	−	4843.28i	−0.321417	−	0.556710i
$424$	4838.01	+	8379.67i	0.554138	+	0.959795i
$425$	−59.2124	+	102.559i	−0.00675817	+	0.0117055i
$426$	20301.7			2.30896
$427$		0			0
$428$	762.570			0.0861220
$429$	−11228.9	+	19449.0i	−1.26372	+	2.18882i
$430$	3452.77	+	5980.37i	0.387226	+	0.670696i
$431$	7157.27	+	12396.7i	0.799892	+	1.38545i	0.919686	+	0.392655i	$0.128443\pi$
$431$	7157.27	+	12396.7i	0.799892	+	1.38545i	−0.119794	+	0.992799i	$0.538223\pi$
$432$	−555.390	+	961.963i	−0.0618546	+	0.107135i
$433$	2373.62			0.263438			0.131719	−	0.991287i	$-0.457950\pi$
$433$	2373.62			0.263438			0.131719	+	0.991287i	$0.457950\pi$
$434$		0			0
$435$	−5622.70			−0.619742
$436$	9095.45	−	15753.8i	0.999067	−	1.73043i
$437$	1264.90	+	2190.87i	0.138463	+	0.239825i
$438$	−1288.97	−	2232.56i	−0.140615	−	0.243552i
$439$	−4766.73	+	8256.22i	−0.518231	+	0.897603i	0.481544	+	0.876422i	$0.340076\pi$
$439$	−4766.73	+	8256.22i	−0.518231	+	0.897603i	−0.999776	+	0.0211814i	$0.993257\pi$
$440$	−3750.51			−0.406360
$441$		0			0
$442$	1948.14			0.209646
$443$	−3323.97	+	5757.29i	−0.356493	+	0.617465i	−0.987372	−	0.158416i	$-0.949361\pi$
$443$	−3323.97	+	5757.29i	−0.356493	+	0.617465i	0.630879	+	0.775881i	$0.282694\pi$
$444$	7922.60	+	13722.4i	0.846825	+	1.46674i
$445$	23.1981	+	40.1803i	0.00247123	+	0.00428029i
$446$	−10112.4	+	17515.2i	−1.07363	+	1.85957i
$447$	−15331.7			−1.62229
$448$		0			0
$449$	−768.256			−0.0807489			−0.0403744	−	0.999185i	$-0.512855\pi$
$449$	−768.256			−0.0807489			−0.0403744	+	0.999185i	$0.512855\pi$
$450$	2505.07	−	4338.90i	0.262422	−	0.454529i
$451$	−1434.50	−	2484.62i	−0.149773	−	0.259415i
$452$	−2918.53	−	5055.04i	−0.303708	−	0.526038i
$453$	−12475.8	+	21608.7i	−1.29396	+	2.24120i
$454$	−282.628			−0.0292167
$455$		0			0
$456$	26076.4			2.67794
$457$	1661.75	−	2878.23i	0.170095	−	0.294613i	−0.768358	−	0.640020i	$-0.778926\pi$
$457$	1661.75	−	2878.23i	0.170095	−	0.294613i	0.938453	+	0.345407i	$0.112259\pi$
$458$	−6981.73	−	12092.7i	−0.712303	−	1.23374i
$459$	−324.472	−	562.002i	−0.0329958	−	0.0571503i
$460$	678.298	−	1174.85i	0.0687517	−	0.119081i
$461$	18840.7			1.90347			0.951733	−	0.306926i	$-0.0993004\pi$
$461$	18840.7			1.90347			0.951733	+	0.306926i	$0.0993004\pi$
$462$		0			0
$463$	−10759.1			−1.07995			−0.539977	−	0.841679i	$-0.681567\pi$
$463$	−10759.1			−1.07995			−0.539977	+	0.841679i	$0.681567\pi$
$464$	−543.604	+	941.549i	−0.0543883	+	0.0942033i
$465$	42.7228	+	73.9980i	0.00426069	+	0.00737973i
$466$	−8165.05	−	14142.3i	−0.811671	−	1.40586i
$467$	3720.85	−	6444.71i	0.368695	−	0.638598i	−0.620667	−	0.784074i	$-0.713138\pi$
$467$	3720.85	−	6444.71i	0.368695	−	0.638598i	0.989362	+	0.145476i	$0.0464714\pi$
$468$	−51588.7			−5.09549
$469$		0			0
$470$	2984.08			0.292863
$471$	−8939.02	+	15482.8i	−0.874497	+	1.51467i
$472$	−10443.8	−	18089.2i	−1.01846	−	1.76403i
$473$	−4496.36	−	7787.93i	−0.437089	−	0.757060i
$474$	−10219.3	+	17700.4i	−0.990273	+	1.71520i
$475$	−3120.45			−0.301423
$476$		0			0
$477$	16832.6			1.61574
$478$	5278.07	−	9141.88i	0.505049	−	0.874770i
$479$	2845.99	+	4929.39i	0.271475	+	0.470208i	0.969240	−	0.246119i	$-0.0791553\pi$
$479$	2845.99	+	4929.39i	0.271475	+	0.470208i	−0.697765	+	0.716327i	$0.745822\pi$
$480$	3392.14	+	5875.35i	0.322561	+	0.558692i
$481$	−6275.64	+	10869.7i	−0.594895	+	1.03039i
$482$	−10246.5			−0.968293
$483$		0			0
$484$	−5679.77			−0.533412
$485$	10.4873	−	18.1646i	0.000981866	−	0.00170064i
$486$	−8962.45	−	15523.4i	−0.836512	−	1.44888i
$487$	1010.12	+	1749.59i	0.0939899	+	0.162795i	0.909187	−	0.416389i	$-0.136705\pi$
$487$	1010.12	+	1749.59i	0.0939899	+	0.162795i	−0.815197	+	0.579184i	$0.803371\pi$
$488$	−4850.38	+	8401.11i	−0.449931	+	0.779304i
$489$	−4981.12			−0.460642
$490$		0			0
$491$	7636.02			0.701851			0.350925	−	0.936403i	$-0.385867\pi$
$491$	7636.02			0.701851			0.350925	+	0.936403i	$0.385867\pi$
$492$	5348.36	−	9263.63i	0.490086	−	0.848855i
$493$	−317.587	−	550.076i	−0.0290129	−	0.0502519i
$494$	25666.3	+	44455.3i	2.33761	+	4.04887i
$495$	−3262.22	+	5650.33i	−0.296214	+	0.513058i
$496$	16.5218			0.00149567
$497$		0			0
$498$	2715.93			0.244385
$499$	−3142.28	+	5442.59i	−0.281900	+	0.488264i	−0.971853	−	0.235590i	$-0.924298\pi$
$499$	−3142.28	+	5442.59i	−0.281900	+	0.488264i	0.689953	+	0.723854i	$0.257631\pi$
$500$	836.662	+	1449.14i	0.0748333	+	0.129615i
$501$	−12312.8	−	21326.4i	−1.09799	−	1.90178i
$502$	7127.72	−	12345.6i	0.633716	−	1.09763i
$503$	−11310.9			−1.00264			−0.501319	−	0.865262i	$-0.667152\pi$
$503$	−11310.9			−1.00264			−0.501319	+	0.865262i	$0.667152\pi$
$504$		0			0
$505$	−4329.22			−0.381481
$506$	−1411.19	+	2444.25i	−0.123982	+	0.214744i
$507$	−23949.8	−	41482.3i	−2.09793	−	3.63372i
$508$	−7942.84	−	13757.4i	−0.693713	−	1.20155i
$509$	5356.37	−	9277.50i	0.466438	−	0.807894i	−0.532827	−	0.846224i	$-0.678870\pi$
$509$	5356.37	−	9277.50i	0.466438	−	0.807894i	0.999265	+	0.0383299i	$0.0122038\pi$
$510$	918.606			0.0797580
$511$		0			0
$512$	2927.65			0.252705
$513$	8549.70	−	14808.5i	0.735826	−	1.27449i
$514$	13948.6	+	24159.7i	1.19698	+	2.07323i
$515$	2915.29	+	5049.43i	0.249443	+	0.432048i
$516$	16764.2	−	29036.4i	1.43024	−	2.47724i
$517$	−3886.02			−0.330574
$518$		0			0
$519$	−19685.9			−1.66496
$520$	5538.23	−	9592.50i	0.467053	−	0.808959i
$521$	8860.95	+	15347.6i	0.745116	+	1.29058i	0.950141	+	0.311821i	$0.100939\pi$
$521$	8860.95	+	15347.6i	0.745116	+	1.29058i	−0.205025	+	0.978757i	$0.565728\pi$
$522$	13436.0	+	23271.8i	1.12658	+	1.95130i
$523$	118.597	−	205.415i	0.00991562	−	0.0171744i	−0.861025	−	0.508563i	$-0.830177\pi$
$523$	118.597	−	205.415i	0.00991562	−	0.0171744i	0.870941	+	0.491388i	$0.163510\pi$
$524$	−13849.2			−1.15459
$525$		0			0
$526$	−27395.0			−2.27088
$527$	−4.82621	+	8.35925i	−0.000398924	+	0.000690957i
$528$	1023.80	+	1773.27i	0.0843845	+	0.146158i
$529$	5878.10	+	10181.2i	0.483119	+	0.836786i
$530$	−4490.78	+	7778.27i	−0.368051	+	0.637484i
$531$	−36336.4			−2.96962
$532$		0			0
$533$	8473.06			0.688572
$534$	179.945	−	311.674i	0.0145824	−	0.0252574i
$535$	142.413	+	246.667i	0.0115085	+	0.0199333i
$536$	8691.26	+	15053.7i	0.700383	+	1.21310i
$537$	−12733.2	+	22054.5i	−1.02324	+	1.77230i
$538$	15042.8			1.20546
$539$		0			0
$540$	−9169.48			−0.730725
$541$	2676.47	−	4635.78i	0.212699	−	0.368406i	−0.739859	−	0.672762i	$-0.765108\pi$
$541$	2676.47	−	4635.78i	0.212699	−	0.368406i	0.952558	+	0.304356i	$0.0984412\pi$
$542$	14443.1	+	25016.2i	1.14462	+	1.98254i
$543$	−3773.03	−	6535.08i	−0.298188	−	0.516477i
$544$	−383.195	+	663.714i	−0.0302010	+	0.0523098i
$545$	6794.45			0.534022
$546$		0			0
$547$	−192.162			−0.0150206			−0.00751030	−	0.999972i	$-0.502391\pi$
$547$	−192.162			−0.0150206			−0.00751030	+	0.999972i	$0.502391\pi$
$548$	−4325.33	+	7491.70i	−0.337170	+	0.583995i
$549$	8437.81	+	14614.7i	0.655950	+	1.13614i
$550$	−1740.67	−	3014.92i	−0.134950	−	0.233740i
$551$	8368.27	−	14494.3i	0.647006	−	1.12065i
$552$	−4234.29			−0.326492
$553$		0			0
$554$	7270.60			0.557578
$555$	−2959.16	+	5125.41i	−0.226323	+	0.392003i
$556$	3390.05	+	5871.74i	0.258579	+	0.447873i
$557$	2425.31	+	4200.76i	0.184495	+	0.319554i	0.943406	−	0.331640i	$-0.107602\pi$
$557$	2425.31	+	4200.76i	0.184495	+	0.319554i	−0.758911	+	0.651194i	$0.774268\pi$
$558$	204.180	−	353.650i	0.0154904	−	0.0268301i
$559$	26558.4			2.00949
$560$		0			0
$561$	−1196.25			−0.0900283
$562$	−18142.2	+	31423.3i	−1.36171	+	2.35856i
$563$	4849.56	+	8399.68i	0.363027	+	0.628782i	0.988458	−	0.151498i	$-0.0484098\pi$
$563$	4849.56	+	8399.68i	0.363027	+	0.628782i	−0.625430	+	0.780280i	$0.715076\pi$
$564$	−7244.29	−	12547.5i	−0.540851	−	0.936781i
$565$	1090.09	−	1888.10i	0.0811692	−	0.140589i
$566$	28975.6			2.15183
$567$		0			0
$568$	13039.5			0.963247
$569$	−1554.76	+	2692.93i	−0.114550	+	0.198407i	−0.917600	−	0.397505i	$-0.869876\pi$
$569$	−1554.76	+	2692.93i	−0.114550	+	0.198407i	0.803050	+	0.595912i	$0.203209\pi$
$570$	12102.4	+	20962.1i	0.889326	+	1.54036i
$571$	7238.12	+	12536.8i	0.530483	+	0.918824i	0.999367	+	0.0355645i	$0.0113229\pi$
$571$	7238.12	+	12536.8i	0.530483	+	0.918824i	−0.468884	+	0.883260i	$0.655344\pi$
$572$	−17923.4	+	31044.3i	−1.31017	+	2.26928i
$573$	3490.23			0.254461
$574$		0			0
$575$	506.699			0.0367492
$576$	17617.1	−	30513.7i	1.27439	−	2.20730i
$577$	−1104.11	−	1912.38i	−0.0796617	−	0.137978i	0.823442	−	0.567400i	$-0.192051\pi$
$577$	−1104.11	−	1912.38i	−0.0796617	−	0.137978i	−0.903104	+	0.429422i	$0.858717\pi$
$578$	−11308.4	−	19586.6i	−0.813781	−	1.40951i
$579$	21725.7	−	37630.0i	1.55939	−	2.70095i
$580$	−8974.90			−0.642521
$581$		0			0
$582$	−162.698			−0.0115877
$583$	5848.12	−	10129.2i	0.415445	−	0.719571i
$584$	−827.886	−	1433.94i	−0.0586612	−	0.101604i
$585$	−9634.40	−	16687.3i	−0.680912	−	1.17937i
$586$	16798.7	−	29096.2i	1.18421	−	2.05112i
$587$	23988.7			1.68675			0.843374	−	0.537327i	$-0.180566\pi$
$587$	23988.7			1.68675			0.843374	+	0.537327i	$0.180566\pi$
$588$		0			0
$589$	−254.338			−0.0177925
$590$	9694.25	−	16790.9i	0.676451	−	1.17165i
$591$	−6090.11	−	10548.4i	−0.423881	−	0.734183i
$592$	572.184	+	991.051i	0.0397240	+	0.0688040i
$593$	−7934.68	+	13743.3i	−0.549474	+	0.951717i	0.448837	+	0.893614i	$0.351839\pi$
$593$	−7934.68	+	13743.3i	−0.549474	+	0.951717i	−0.998311	+	0.0581031i	$0.981495\pi$
$594$	19077.0			1.31774
$595$		0			0
$596$	−24472.2			−1.68192
$597$	−5355.82	+	9276.55i	−0.367168	+	0.635953i
$598$	−4167.70	−	7218.67i	−0.285000	−	0.493635i
$599$	7618.32	+	13195.3i	0.519660	+	0.900077i	0.999739	+	0.0228519i	$0.00727462\pi$
$599$	7618.32	+	13195.3i	0.519660	+	0.900077i	−0.480079	+	0.877225i	$0.659392\pi$
$600$	2611.45	−	4523.16i	0.177686	−	0.307762i
$601$	−12258.8			−0.832026			−0.416013	−	0.909359i	$-0.636573\pi$
$601$	−12258.8			−0.832026			−0.416013	+	0.909359i	$0.636573\pi$
$602$		0			0
$603$	30238.9			2.04216
$604$	−19913.7	+	34491.5i	−1.34152	+	2.32358i
$605$	−1060.72	−	1837.22i	−0.0712800	−	0.123461i
$606$	16790.6	+	29082.2i	1.12553	+	1.94948i
$607$	11743.6	−	20340.5i	0.785269	−	1.36013i	−0.143569	−	0.989640i	$-0.545858\pi$
$607$	11743.6	−	20340.5i	0.785269	−	1.36013i	0.928838	−	0.370486i	$-0.120809\pi$
$608$	−20194.1			−1.34700
$609$		0			0
$610$	−9004.54			−0.597678
$611$	5738.34	−	9939.09i	0.379948	−	0.658089i
$612$	−1373.98	−	2379.81i	−0.0907516	−	0.157186i
$613$	11152.6	+	19316.9i	0.734830	+	1.27276i	0.954798	+	0.297256i	$0.0960715\pi$
$613$	11152.6	+	19316.9i	0.734830	+	1.27276i	−0.219968	+	0.975507i	$0.570595\pi$
$614$	−3071.46	+	5319.92i	−0.201879	+	0.349666i
$615$	3995.31			0.261962
$616$		0			0
$617$	3285.91			0.214402			0.107201	−	0.994237i	$-0.465811\pi$
$617$	3285.91			0.214402			0.107201	+	0.994237i	$0.465811\pi$
$618$	22613.5	−	39167.8i	1.47193	−	2.54945i
$619$	−5806.54	−	10057.2i	−0.377035	−	0.653043i	0.613595	−	0.789621i	$-0.289723\pi$
$619$	−5806.54	−	10057.2i	−0.377035	−	0.653043i	−0.990629	+	0.136578i	$0.956390\pi$
$620$	68.1937	+	118.115i	0.00441730	+	0.00765098i
$621$	−1388.30	+	2404.61i	−0.0897113	+	0.155385i
$622$	22515.5			1.45143
$623$		0			0
$624$	−6047.21			−0.387952
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−17881.8	−	30972.1i	−1.14169	−	1.97747i
$627$	−15760.4	−	27297.8i	−1.00384	−	1.73871i
$628$	−14268.4	+	24713.5i	−0.906640	+	1.57035i
$629$	−668.567			−0.0423808
$630$		0			0
$631$	6890.91			0.434743			0.217372	−	0.976089i	$-0.430252\pi$
$631$	6890.91			0.434743			0.217372	+	0.976089i	$0.430252\pi$
$632$	−6563.73	+	11368.7i	−0.413119	+	0.715543i
$633$	13666.3	+	23670.8i	0.858117	+	1.48630i
$634$	−18903.0	−	32740.9i	−1.18412	−	2.05096i
$635$	2966.71	−	5138.50i	0.185402	−	0.321126i
$636$	43608.1			2.71883
$637$		0			0
$638$	18672.2			1.15868
$639$	11341.8	−	19644.7i	0.702154	−	1.21617i
$640$	6164.43	+	10677.1i	0.380735	+	0.659452i
$641$	−9384.63	−	16254.7i	−0.578269	−	1.00159i	−0.995678	−	0.0928728i	$-0.970395\pi$
$641$	−9384.63	−	16254.7i	−0.578269	−	1.00159i	0.417409	−	0.908719i	$-0.362938\pi$
$642$	1104.68	−	1913.36i	0.0679100	−	0.117624i
$643$	3142.30			0.192722			0.0963609	−	0.995346i	$-0.469280\pi$
$643$	3142.30			0.192722			0.0963609	+	0.995346i	$0.469280\pi$
$644$		0			0
$645$	12523.1			0.764492
$646$	−1367.16	+	2368.00i	−0.0832667	+	0.144222i
$647$	9519.07	+	16487.5i	0.578413	+	1.00184i	0.995662	+	0.0930486i	$0.0296612\pi$
$647$	9519.07	+	16487.5i	0.578413	+	1.00184i	−0.417248	+	0.908793i	$0.637005\pi$
$648$	−263.102	−	455.706i	−0.0159500	−	0.0276262i
$649$	−12624.3	+	21866.0i	−0.763557	+	1.32252i
$650$	10281.5			0.620421
$651$		0			0
$652$	−7950.82			−0.477574
$653$	10269.3	−	17787.0i	0.615420	−	1.06594i	−0.374890	−	0.927069i	$-0.622320\pi$
$653$	10269.3	−	17787.0i	0.615420	−	1.06594i	0.990311	−	0.138870i	$-0.0443471\pi$
$654$	−26351.8	−	45642.7i	−1.57559	−	2.72901i
$655$	−2586.39	−	4479.76i	−0.154288	−	0.267235i
$656$	386.267	−	669.034i	0.0229896	−	0.0398192i
$657$	−2880.41			−0.171043
$658$		0			0
$659$	−937.046			−0.0553902			−0.0276951	−	0.999616i	$-0.508817\pi$
$659$	−937.046			−0.0553902			−0.0276951	+	0.999616i	$0.508817\pi$
$660$	−8451.44	+	14638.3i	−0.498442	+	0.863327i
$661$	10558.3	+	18287.4i	0.621283	+	1.07609i	0.989247	+	0.146254i	$0.0467218\pi$
$661$	10558.3	+	18287.4i	0.621283	+	1.07609i	−0.367964	+	0.929840i	$0.619945\pi$
$662$	−4718.82	−	8173.24i	−0.277043	−	0.479852i
$663$	1766.46	−	3059.60i	0.103475	−	0.179223i
$664$	1744.41			0.101952
$665$		0			0
$666$	28284.7			1.64566
$667$	−1358.84	+	2353.59i	−0.0788825	+	0.136628i
$668$	−19653.5	−	34040.9i	−1.13835	−	1.97168i
$669$	18338.8	+	31763.7i	1.05982	+	1.83566i
$670$	−8067.48	+	13973.3i	−0.465185	+	0.805725i
$671$	11726.2			0.674640
$672$		0			0
$673$	13825.9			0.791903			0.395952	−	0.918271i	$-0.370415\pi$
$673$	13825.9			0.791903			0.395952	+	0.918271i	$0.370415\pi$
$674$	16994.6	−	29435.6i	0.971230	−	1.68222i
$675$	−1712.44	−	2966.03i	−0.0976470	−	0.169130i
$676$	−38228.5	−	66213.6i	−2.17504	−	3.76728i
$677$	−8464.20	+	14660.4i	−0.480510	+	0.832269i	−0.999750	−	0.0223602i	$-0.992882\pi$
$677$	−8464.20	+	14660.4i	−0.480510	+	0.832269i	0.519240	+	0.854629i	$0.326215\pi$
$678$	−16911.4			−0.957935
$679$		0			0
$680$	590.008			0.0332732
$681$	−256.271	+	443.875i	−0.0144205	+	0.0249770i
$682$	−141.876	−	245.737i	−0.00796586	−	0.0137973i
$683$	6908.65	+	11966.1i	0.387045	+	0.670382i	0.992051	−	0.125839i	$-0.0401623\pi$
$683$	6908.65	+	11966.1i	0.387045	+	0.670382i	−0.605005	+	0.796222i	$0.706829\pi$
$684$	36203.9	−	62707.0i	2.02382	−	3.50535i
$685$	−3231.09			−0.180224
$686$		0			0
$687$	−25322.6			−1.40628
$688$	1210.74	−	2097.06i	0.0670915	−	0.116206i
$689$	17271.4	+	29914.9i	0.954989	+	1.65409i
$690$	−1965.20	−	3403.83i	−0.108426	−	0.187799i
$691$	−11835.8	+	20500.2i	−0.651600	+	1.12860i	0.331134	+	0.943584i	$0.392569\pi$
$691$	−11835.8	+	20500.2i	−0.651600	+	1.12860i	−0.982735	+	0.185021i	$0.940765\pi$
$692$	−31422.5			−1.72616
$693$		0			0
$694$	55818.2			3.05307
$695$	−1266.21	+	2193.14i	−0.0691081	+	0.119699i
$696$	14006.5	+	24260.0i	0.762810	+	1.32123i
$697$	225.667	+	390.866i	0.0122636	+	0.0212412i
$698$	10370.5	−	17962.2i	0.562362	−	0.974040i
$699$	−29614.5			−1.60246
$700$		0			0
$701$	−17009.7			−0.916472			−0.458236	−	0.888831i	$-0.651519\pi$
$701$	−17009.7			−0.916472			−0.458236	+	0.888831i	$0.651519\pi$
$702$	−28170.3	+	48792.3i	−1.51456	+	2.62329i
$703$	−8808.23	−	15256.3i	−0.472559	−	0.818496i
$704$	−12241.4	−	21202.7i	−0.655348	−	1.13510i
$705$	2705.80	−	4686.59i	0.144548	−	0.250365i
$706$	−59020.9			−3.14629
$707$		0			0
$708$	−94136.8			−4.99700
$709$	−11019.5	+	19086.2i	−0.583701	+	1.01100i	0.411335	+	0.911484i	$0.365063\pi$
$709$	−11019.5	+	19086.2i	−0.583701	+	1.01100i	−0.995036	+	0.0995158i	$0.968271\pi$
$710$	6051.82	+	10482.1i	0.319888	+	0.554063i
$711$	11418.4	+	19777.2i	0.602282	+	1.04318i
$712$	115.576	−	200.184i	0.00608343	−	0.0105368i
$713$	41.2994			0.00216925
$714$		0			0
$715$	−13389.1			−0.700312
$716$	−20324.6	+	35203.2i	−1.06085	+	1.83744i
$717$	−9571.72	−	16578.7i	−0.498553	−	0.863519i
$718$	−5594.39	−	9689.77i	−0.290781	−	0.503648i
$719$	3643.72	−	6311.11i	0.188996	−	0.327350i	−0.755920	−	0.654664i	$-0.772810\pi$
$719$	3643.72	−	6311.11i	0.188996	−	0.327350i	0.944916	+	0.327314i	$0.106143\pi$
$720$	−1756.84			−0.0909354
$721$		0			0
$722$	−40328.5			−2.07877
$723$	−9290.99	+	16092.5i	−0.477919	+	0.827781i
$724$	−6022.47	−	10431.2i	−0.309148	−	0.535461i
$725$	−1676.10	−	2903.09i	−0.0858603	−	0.148714i
$726$	−8227.86	+	14251.1i	−0.420612	+	0.728522i
$727$	29676.7			1.51396			0.756980	−	0.653438i	$-0.226674\pi$
$727$	29676.7			1.51396			0.756980	+	0.653438i	$0.226674\pi$
$728$		0			0
$729$	−31936.3			−1.62253
$730$	768.468	−	1331.03i	0.0389620	−	0.0674842i
$731$	707.342	+	1225.15i	0.0357893	+	0.0619889i
$732$	21859.8	+	37862.3i	1.10377	+	1.91179i
$733$	11555.9	−	20015.4i	0.582300	−	1.00857i	−0.412906	−	0.910774i	$-0.635486\pi$
$733$	11555.9	−	20015.4i	0.582300	−	1.00857i	0.995206	−	0.0977999i	$-0.0311805\pi$
$734$	−32971.9			−1.65806
$735$		0			0
$736$	3279.12			0.164226
$737$	10505.9	−	18196.7i	0.525086	−	0.909476i
$738$	−9547.16	−	16536.2i	−0.476200	−	0.824803i
$739$	15585.7	+	26995.2i	0.775818	+	1.34376i	0.934334	+	0.356399i	$0.115996\pi$
$739$	15585.7	+	26995.2i	0.775818	+	1.34376i	−0.158516	+	0.987356i	$0.550671\pi$
$740$	−4723.37	+	8181.12i	−0.234641	+	0.406411i
$741$	93091.1			4.61510
$742$		0			0
$743$	−31324.4			−1.54668			−0.773338	−	0.633993i	$-0.781415\pi$
$743$	−31324.4			−1.54668			−0.773338	+	0.633993i	$0.781415\pi$
$744$	212.851	−	368.668i	0.0104885	−	0.0181667i
$745$	−4570.29	−	7915.97i	−0.224755	−	0.389287i
$746$	26815.4	+	46445.6i	1.31606	+	2.27948i
$747$	1517.30	−	2628.04i	0.0743174	−	0.128722i
$748$	−1909.45			−0.0933373
$749$		0			0
$750$	4848.04			0.236034
$751$	−2016.10	+	3491.99i	−0.0979608	+	0.169673i	−0.910840	−	0.412759i	$-0.864565\pi$
$751$	−2016.10	+	3491.99i	−0.0979608	+	0.169673i	0.812880	+	0.582432i	$0.197899\pi$
$752$	−523.195	−	906.200i	−0.0253709	−	0.0439438i
$753$	−12926.0	−	22388.5i	−0.625566	−	1.08351i
$754$	−27572.5	+	47756.9i	−1.33174	+	2.30664i
$755$	−14875.8			−0.717069
$756$		0			0
$757$	34263.7			1.64509			0.822546	−	0.568699i	$-0.192553\pi$
$757$	34263.7			1.64509			0.822546	+	0.568699i	$0.192553\pi$
$758$	−29529.7	+	51146.9i	−1.41499	+	2.45084i
$759$	2559.18	+	4432.63i	0.122388	+	0.211982i
$760$	7773.24	+	13463.6i	0.371006	+	0.642602i
$761$	3632.94	−	6292.44i	0.173054	−	0.299738i	−0.766432	−	0.642325i	$-0.777970\pi$
$761$	3632.94	−	6292.44i	0.173054	−	0.299738i	0.939486	+	0.342587i	$0.111303\pi$
$762$	−46024.8			−2.18806
$763$		0			0
$764$	5571.07			0.263814
$765$	513.194	−	888.878i	0.0242543	−	0.0420097i
$766$	−17273.0	−	29917.7i	−0.814750	−	1.41119i
$767$	−37283.7	−	64577.3i	−1.75520	−	3.04009i
$768$	20541.2	−	35578.4i	0.965127	−	1.67165i
$769$	−38116.2			−1.78739			−0.893695	−	0.448674i	$-0.851896\pi$
$769$	−38116.2			−1.78739			−0.893695	+	0.448674i	$0.851896\pi$
$770$		0			0
$771$	50591.3			2.36317
$772$	34678.3	−	60064.6i	1.61671	−	2.80022i
$773$	8079.11	+	13993.4i	0.375919	+	0.651111i	0.990464	−	0.137771i	$-0.0439937\pi$
$773$	8079.11	+	13993.4i	0.375919	+	0.651111i	−0.614545	+	0.788882i	$0.710660\pi$
$774$	−29925.1	−	51831.9i	−1.38971	−	2.40705i

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+(2.31228 - 4.00499i) q^{2} +(-4.19330 - 7.26300i) q^{3} +(-6.69330 - 11.5931i) q^{4} +(2.50000 - 4.33013i) q^{5} -38.7844 q^{6} -24.9107 q^{8} +(-21.6675 + 37.5292i) q^{9} +(-11.5614 - 20.0250i) q^{10} +(15.0558 + 26.0775i) q^{11} +(-56.1340 + 97.2269i) q^{12} -88.9295 q^{13} -41.9330 q^{15} +(-4.05409 + 7.02189i) q^{16} +(-2.36850 - 4.10236i) q^{17} +(100.203 + 173.556i) q^{18} +(62.4089 - 108.095i) q^{19} -66.9330 q^{20} +139.253 q^{22} +(-10.1340 + 17.5526i) q^{23} +(104.458 + 180.926i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(-205.630 + 356.162i) q^{26} +136.995 q^{27} +134.088 q^{29} +(-96.9609 + 167.941i) q^{30} +(-1.01883 - 1.76467i) q^{31} +(-80.8942 - 140.113i) q^{32} +(126.267 - 218.701i) q^{33} -21.9065 q^{34} +580.108 q^{36} +(70.5687 - 122.229i) q^{37} +(-288.614 - 499.894i) q^{38} +(372.908 + 645.895i) q^{39} +(-62.2766 + 107.866i) q^{40} -95.2784 q^{41} -298.646 q^{43} +(201.546 - 349.088i) q^{44} +(108.337 + 187.646i) q^{45} +(46.8653 + 81.1730i) q^{46} +(-64.5268 + 111.764i) q^{47} +68.0000 q^{48} -115.614 q^{50} +(-19.8636 + 34.4048i) q^{51} +(595.232 + 1030.97i) q^{52} +(-194.214 - 336.389i) q^{53} +(316.771 - 548.663i) q^{54} +150.558 q^{55} -1046.80 q^{57} +(310.049 - 537.020i) q^{58} +(419.250 + 726.163i) q^{59} +(280.670 + 486.135i) q^{60} +(194.711 - 337.250i) q^{61} -9.42333 q^{62} -813.067 q^{64} +(-222.324 + 385.076i) q^{65} +(-583.931 - 1011.40i) q^{66} +(-348.897 - 604.307i) q^{67} +(-31.7061 + 54.9166i) q^{68} +169.979 q^{69} -523.450 q^{71} +(539.752 - 934.877i) q^{72} +(33.2342 + 57.5633i) q^{73} +(-326.350 - 565.254i) q^{74} +(-104.832 + 181.575i) q^{75} -1670.89 q^{76} +3449.07 q^{78} +(263.491 - 456.380i) q^{79} +(20.2704 + 35.1094i) q^{80} +(10.5618 + 18.2936i) q^{81} +(-220.311 + 381.589i) q^{82} -70.0265 q^{83} -23.6850 q^{85} +(-690.554 + 1196.07i) q^{86} +(-562.270 - 973.880i) q^{87} +(-375.051 - 649.607i) q^{88} +(-4.63963 + 8.03607i) q^{89} +1002.03 q^{90} +271.319 q^{92} +(-8.54456 + 14.7996i) q^{93} +(298.408 + 516.858i) q^{94} +(-312.045 - 540.477i) q^{95} +(-678.427 + 1175.07i) q^{96} +4.19493 q^{97} -1304.89 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 2 q^{3} - 13 q^{4} + 15 q^{5} - 48 q^{6} - 30 q^{8} - 81 q^{9} - 15 q^{10} + 74 q^{11} - 152 q^{12} - 88 q^{13} + 20 q^{15} + 79 q^{16} - 52 q^{17} + 411 q^{18} + 168 q^{19} - 130 q^{20}+ \cdots - 6976 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 2 * q^3 - 13 * q^4 + 15 * q^5 - 48 * q^6 - 30 * q^8 - 81 * q^9 - 15 * q^10 + 74 * q^11 - 152 * q^12 - 88 * q^13 + 20 * q^15 + 79 * q^16 - 52 * q^17 + 411 * q^18 + 168 * q^19 - 130 * q^20 + 368 * q^22 + 124 * q^23 + 420 * q^24 - 75 * q^25 - 446 * q^26 - 340 * q^27 + 664 * q^29 - 120 * q^30 + 320 * q^31 + 183 * q^32 - 106 * q^33 - 1164 * q^34 + 362 * q^36 + 54 * q^37 - 460 * q^38 + 982 * q^39 - 75 * q^40 - 724 * q^41 - 32 * q^43 + 264 * q^44 + 405 * q^45 + 336 * q^46 - 730 * q^47 + 408 * q^48 - 150 * q^50 + 1178 * q^51 + 1202 * q^52 - 110 * q^53 - 180 * q^54 + 740 * q^55 - 1912 * q^57 - 450 * q^58 - 180 * q^59 + 760 * q^60 + 1222 * q^61 - 928 * q^62 - 782 * q^64 - 220 * q^65 - 532 * q^66 - 204 * q^67 + 918 * q^68 + 1432 * q^69 - 272 * q^71 - 765 * q^72 + 310 * q^73 - 502 * q^74 + 50 * q^75 - 3592 * q^76 + 7576 * q^78 + 1034 * q^79 - 395 * q^80 - 2283 * q^81 - 6 * q^82 + 3320 * q^83 - 520 * q^85 - 764 * q^86 - 1574 * q^87 + 20 * q^88 + 242 * q^89 + 4110 * q^90 + 192 * q^92 - 1376 * q^93 - 1108 * q^94 - 840 * q^95 - 3156 * q^96 - 200 * q^97 - 6976 * q^99

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