LMFDB - Embedded newform 245.4.e.m.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.m.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	$0.132244\pi$
$3$	4.19330	+	7.26300i	0.807001	+	1.39777i	−0.107932	+	0.994158i	$0.534423\pi$
$4$	−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	$-0.102461\pi$
$13$	88.9295			1.89728			0.948639	+	0.316362i	$0.102461\pi$
$14$		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	0.882426	−	0.470451i	$-0.155909\pi$
$17$	2.36850	+	4.10236i	0.0337909	+	0.0585275i	−0.848635	+	0.528978i	$0.822575\pi$
$18$	100.203	+	173.556i	1.31211	+	2.27264i
$19$	−62.4089	+	108.095i	−0.753557	+	1.30520i	0.192531	+	0.981291i	$0.438330\pi$
$19$	−62.4089	+	108.095i	−0.753557	+	1.30520i	−0.946088	+	0.323909i	$0.895003\pi$
$20$	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	0.868962	−	0.494879i	$-0.164788\pi$
$31$	1.01883	+	1.76467i	0.00590284	+	0.0102240i	−0.863059	+	0.505103i	$0.831454\pi$
$32$	−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	$-0.441917\pi$
$41$	95.2784			0.362927			0.181463	+	0.983398i	$0.441917\pi$
$42$		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	−0.748352	−	0.663301i	$-0.769155\pi$
$47$	64.5268	−	111.764i	0.200260	−	0.346860i	0.948612	+	0.316442i	$0.102488\pi$
$48$	−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	$-0.790635\pi$
$59$	−419.250	−	726.163i	−0.925114	−	1.60235i	−0.133738	−	0.991017i	$-0.542698\pi$
$60$	280.670	+	486.135i	0.603905	+	1.04599i
$61$	−194.711	+	337.250i	−0.408692	+	0.707875i	−0.994743	−	0.102399i	$-0.967348\pi$
$61$	−194.711	+	337.250i	−0.408692	+	0.707875i	0.586051	+	0.810274i	$0.300682\pi$
$62$	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	0.838153	−	0.545435i	$-0.183636\pi$
$73$	−33.2342	−	57.5633i	−0.0532845	−	0.0922915i	−0.891437	+	0.453144i	$0.850302\pi$
$74$	−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	$-0.485256\pi$
$83$	70.0265			0.0926074			0.0463037	+	0.998927i	$0.485256\pi$
$84$		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	−0.863249	−	0.504778i	$-0.831574\pi$
$89$	4.63963	−	8.03607i	0.00552584	−	0.00957103i	0.868775	+	0.495207i	$0.164908\pi$
$90$	−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	$-0.500699\pi$
$97$	−4.19493			−0.00439104			−0.00219552	+	0.999998i	$0.500699\pi$
$98$		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	0.996560	−	0.0828749i	$-0.0264102\pi$
$101$	432.922	+	749.843i	0.426508	+	0.738734i	−0.570052	+	0.821609i	$0.693077\pi$
$102$	91.8606	+	159.107i	0.0891721	+	0.154451i
$103$	583.058	−	1009.89i	0.557771	−	0.966088i	−0.439911	−	0.898042i	$-0.644990\pi$
$103$	583.058	−	1009.89i	0.557771	−	0.966088i	0.997682	−	0.0680469i	$-0.0216768\pi$
$104$	−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	−0.985354	−	0.170524i	$-0.945454\pi$
$131$	−517.278	+	895.952i	−0.344999	+	0.597555i	0.640355	+	0.768079i	$0.278787\pi$
$132$	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	$-0.450614\pi$
$139$	506.484			0.309061			0.154530	+	0.987988i	$0.450614\pi$
$140$		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	$0.0155977\pi$
$157$	1065.87	+	1846.14i	0.541820	+	0.938459i	−0.456980	+	0.889477i	$0.651069\pi$
$158$	−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	$-0.738147\pi$
$167$	−2936.30			−1.36059			−0.680293	+	0.732941i	$0.738147\pi$
$168$		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	$0.339167\pi$
$173$	−1173.65	+	2032.83i	−0.515788	+	0.893371i	−0.999832	+	0.0183273i	$0.994166\pi$
$174$	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	$-0.559148\pi$
$181$	−899.776			−0.369502			−0.184751	+	0.982785i	$0.559148\pi$
$182$		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	0.957063	−	0.289879i	$-0.0936151\pi$
$199$	638.616	+	1106.12i	0.227489	+	0.394023i	−0.729574	+	0.683902i	$0.760282\pi$
$200$	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	$-0.271977\pi$
$223$	4373.35			1.31328			0.656639	+	0.754205i	$0.271977\pi$
$224$		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	0.870458	−	0.492242i	$-0.163823\pi$
$227$	30.5573	+	52.9267i	0.00893461	+	0.0154752i	−0.861524	+	0.507718i	$0.830489\pi$
$228$	7006.52	+	12135.7i	2.03517	+	3.52501i
$229$	−1509.71	+	2614.89i	−0.435651	+	0.754570i	−0.997349	−	0.0727728i	$-0.976815\pi$
$229$	−1509.71	+	2614.89i	−0.435651	+	0.754570i	0.561697	+	0.827343i	$0.310149\pi$
$230$	−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	0.975242	−	0.221140i	$-0.0709777\pi$
$241$	1107.84	+	1918.83i	0.296109	+	0.512875i	−0.679134	+	0.734015i	$0.737644\pi$
$242$	−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	$-0.626691\pi$
$251$	−3082.55			−0.775174			−0.387587	+	0.921833i	$0.626691\pi$
$252$		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	$-0.571882\pi$
$257$	3016.20	−	5224.21i	0.732083	−	1.26801i	0.955991	−	0.293395i	$-0.0947851\pi$
$258$	−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	0.620716	−	0.784035i	$-0.286842\pi$
$269$	−1626.40	−	2817.00i	−0.368637	−	0.638497i	−0.989353	+	0.145538i	$0.953509\pi$
$270$	−1583.85	−	2743.32i	−0.357001	−	0.618344i
$271$	3123.13	−	5409.42i	0.700061	−	1.21254i	−0.268383	−	0.963312i	$-0.586489\pi$
$271$	3123.13	−	5409.42i	0.700061	−	1.21254i	0.968444	−	0.249230i	$-0.0801774\pi$
$272$	−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	$-0.938053\pi$
$283$	−3132.79	−	5426.15i	−0.658039	−	1.13976i	0.323084	−	0.946370i	$-0.395280\pi$
$284$	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	$-0.757826\pi$
$293$	−7264.99			−1.44855			−0.724276	+	0.689511i	$0.757826\pi$
$294$		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	$-0.460597\pi$
$307$	1328.32			0.246943			0.123471	+	0.992348i	$0.460597\pi$
$308$		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	0.554117	−	0.832439i	$-0.313056\pi$
$311$	−2434.34	−	4216.40i	−0.443855	−	0.768779i	−0.997972	+	0.0636600i	$0.979723\pi$
$312$	−9289.38	−	16089.7i	−1.68560	−	2.91955i
$313$	−3866.69	+	6697.31i	−0.698270	+	1.20944i	0.270796	+	0.962637i	$0.412713\pi$
$313$	−3866.69	+	6697.31i	−0.698270	+	1.20944i	−0.969066	+	0.246802i	$0.920620\pi$
$314$	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	$-0.611764\pi$
$349$	−4484.96			−0.687892			−0.343946	+	0.938989i	$0.611764\pi$
$350$		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	$0.245477\pi$
$353$	6381.24	+	11052.6i	0.962151	+	1.66649i	0.245069	+	0.969506i	$0.421189\pi$
$354$	−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	$0.00259474\pi$
$367$	3564.87	+	6174.54i	0.507043	+	0.878224i	−0.492924	+	0.870072i	$0.664072\pi$
$368$	−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	−0.999998	−	0.00195209i	$-0.999379\pi$
$383$	−3735.05	+	6469.30i	−0.498308	+	0.863096i	0.501690	+	0.865048i	$0.332712\pi$
$384$	−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	−0.984389	−	0.176006i	$-0.943682\pi$
$397$	−2687.63	+	4655.11i	−0.339769	+	0.588496i	0.644621	+	0.764503i	$0.277015\pi$
$398$	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	0.934118	−	0.356964i	$-0.116188\pi$
$409$	1306.23	+	2262.45i	0.157919	+	0.273523i	−0.776199	+	0.630488i	$0.782855\pi$
$410$	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	$-0.417462\pi$
$419$	4398.21			0.512808			0.256404	+	0.966570i	$0.417462\pi$
$420$		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	$-0.542050\pi$
$433$	−2373.62			−0.263438			−0.131719	+	0.991287i	$0.542050\pi$
$434$		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	$-0.659924\pi$
$439$	4766.73	−	8256.22i	0.518231	−	0.897603i	0.999776	−	0.0211814i	$-0.00674276\pi$
$440$	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	$-0.900700\pi$
$461$	−18840.7			−1.90347			−0.951733	+	0.306926i	$0.900700\pi$
$462$		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	−0.989362	−	0.145476i	$-0.953529\pi$
$467$	−3720.85	+	6444.71i	−0.368695	+	0.638598i	0.620667	+	0.784074i	$0.286862\pi$
$468$	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	0.697765	−	0.716327i	$-0.254178\pi$
$479$	−2845.99	−	4929.39i	−0.271475	−	0.470208i	−0.969240	+	0.246119i	$0.920845\pi$
$480$	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	$-0.332848\pi$
$503$	11310.9			1.00264			0.501319	+	0.865262i	$0.332848\pi$
$504$		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	−0.999265	−	0.0383299i	$-0.987796\pi$
$509$	−5356.37	+	9277.50i	−0.466438	+	0.807894i	0.532827	+	0.846224i	$0.321130\pi$
$510$	−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	$-0.899061\pi$
$521$	−8860.95	−	15347.6i	−0.745116	−	1.29058i	0.205025	−	0.978757i	$-0.434272\pi$
$522$	13436.0	+	23271.8i	1.12658	+	1.95130i
$523$	−118.597	+	205.415i	−0.00991562	+	0.0171744i	−0.870941	−	0.491388i	$-0.836490\pi$
$523$	−118.597	+	205.415i	−0.00991562	+	0.0171744i	0.861025	+	0.508563i	$0.169823\pi$
$524$	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	0.625430	−	0.780280i	$-0.284924\pi$
$563$	−4849.56	−	8399.68i	−0.363027	−	0.628782i	−0.988458	+	0.151498i	$0.951590\pi$
$564$	−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	0.903104	−	0.429422i	$-0.141283\pi$
$577$	1104.11	+	1912.38i	0.0796617	+	0.137978i	−0.823442	+	0.567400i	$0.807949\pi$
$578$	−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	$-0.819434\pi$
$587$	−23988.7			−1.68675			−0.843374	+	0.537327i	$0.819434\pi$
$588$		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	$-0.648161\pi$
$593$	7934.68	−	13743.3i	0.549474	−	0.951717i	0.998311	−	0.0581031i	$-0.0185052\pi$
$594$	−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	$-0.363427\pi$
$601$	12258.8			0.832026			0.416013	+	0.909359i	$0.363427\pi$
$602$		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	$0.454142\pi$
$607$	−11743.6	+	20340.5i	−0.785269	+	1.36013i	−0.928838	+	0.370486i	$0.879191\pi$
$608$	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	0.990629	−	0.136578i	$-0.0436104\pi$
$619$	5806.54	+	10057.2i	0.377035	+	0.653043i	−0.613595	+	0.789621i	$0.710277\pi$
$620$	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	$-0.530720\pi$
$643$	−3142.30			−0.192722			−0.0963609	+	0.995346i	$0.530720\pi$
$644$		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	$-0.970339\pi$
$647$	−9519.07	−	16487.5i	−0.578413	−	1.00184i	0.417248	−	0.908793i	$-0.362995\pi$
$648$	−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	$-0.953278\pi$
$661$	−10558.3	−	18287.4i	−0.621283	−	1.07609i	0.367964	−	0.929840i	$-0.380055\pi$
$662$	−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	−0.519240	−	0.854629i	$-0.673785\pi$
$677$	8464.20	−	14660.4i	0.480510	−	0.832269i	0.999750	+	0.0223602i	$0.00711808\pi$
$678$	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	$-0.607431\pi$
$691$	11835.8	−	20500.2i	0.651600	−	1.12860i	0.982735	−	0.185021i	$-0.0592353\pi$
$692$	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	−0.944916	−	0.327314i	$-0.893857\pi$
$719$	−3643.72	+	6311.11i	−0.188996	+	0.327350i	0.755920	+	0.654664i	$0.227190\pi$
$720$	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	$-0.773326\pi$
$727$	−29676.7			−1.51396			−0.756980	+	0.653438i	$0.773326\pi$
$728$		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	$0.364514\pi$
$733$	−11555.9	+	20015.4i	−0.582300	+	1.00857i	−0.995206	+	0.0977999i	$0.968819\pi$
$734$	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	−0.939486	−	0.342587i	$-0.888697\pi$
$761$	−3632.94	+	6292.44i	−0.173054	+	0.299738i	0.766432	+	0.642325i	$0.222030\pi$
$762$	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	$-0.148104\pi$
$769$	38116.2			1.78739			0.893695	+	0.448674i	$0.148104\pi$
$770$		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	0.614545	−	0.788882i	$-0.289340\pi$
$773$	−8079.11	−	13993.4i	−0.375919	−	0.651111i	−0.990464	+	0.137771i	$0.956006\pi$
$774$	−29925.1	−	51831.9i	−1.38971	−	2.40705i
$775$	25.4709	−	44.1168i	0.00118057	−	0.00204480i
$776$	104.498			0.00483412
$777$		0			0
$778$	−40463.9			−1.86465
$779$	−5946.22	+	10299.2i	−0.273486	+	0.473692i
$780$	24959.8	+	43231.7i	1.14578	+	1.98454i
$781$	−7880.97	−	13650.2i	−0.361080	−	0.625409i
$782$	−222.000	+	384.516i	−0.0101518	+	0.0175835i
$783$	−18369.3			−0.838400
$784$		0			0
$785$	−10658.7			−0.484618
$786$	−20062.3	+	34748.9i	−0.910431	+	1.57691i
$787$	−2546.24	−	4410.22i	−0.115329	−	0.199755i	0.802582	−	0.596541i	$-0.203459\pi$
$787$	−2546.24	−	4410.22i	−0.115329	−	0.199755i	−0.917911	+	0.396786i	$0.870126\pi$
$788$	−9720.97	−	16837.2i	−0.439461	−	0.761169i
$789$	24840.3	−	43024.7i	1.12083	−	1.94134i
$790$	12185.3			0.548777
$791$		0			0
$792$	32505.6			1.45838
$793$	−17315.6	+	29991.4i	−0.775402	+	1.34304i
$794$	12429.1	+	21527.8i	0.555532	+	0.962209i
$795$	8143.99	+	14105.8i	0.363317	+	0.629284i
$796$	8548.90	−	14807.1i	0.380663	−	0.659328i
$797$	−34666.2			−1.54070			−0.770350	−	0.637621i	$-0.779919\pi$
$797$	−34666.2			−1.54070			−0.770350	+	0.637621i	$0.779919\pi$
$798$		0			0
$799$	611.326			0.0270678
$800$	−2022.36	+	3502.82i	−0.0893764	+	0.154804i
$801$	201.058	+	348.243i	0.00886896	+	0.0153615i
$802$	17021.5	+	29482.1i	0.749438	+	1.29806i
$803$	1000.74	−	1733.33i	0.0439791	−	0.0761741i
$804$	−78339.9			−3.43636
$805$		0			0
$806$	838.012			0.0366225
$807$	13639.9	−	23625.1i	0.594980	−	1.03054i
$808$	−10784.4	−	18679.1i	−0.469545	−	0.813277i
$809$	−7563.10	−	13099.7i	−0.328683	−	0.569295i	0.653568	−	0.756868i	$-0.273271\pi$
$809$	−7563.10	−	13099.7i	−0.328683	−	0.569295i	−0.982251	+	0.187573i	$0.939938\pi$
$810$	−244.219	+	423.000i	−0.0105938	+	0.0183490i
$811$	29416.5			1.27368			0.636840	−	0.770996i	$-0.280241\pi$
$811$	29416.5			1.27368			0.636840	+	0.770996i	$0.280241\pi$
$812$		0			0
$813$	52384.9			2.25980
$814$	9826.93	−	17020.7i	0.423137	−	0.732895i
$815$	1484.85	+	2571.83i	0.0638183	+	0.110537i
$816$	−161.058	−	278.960i	−0.00690950	−	0.0119676i
$817$	18638.2	−	32282.3i	0.798124	−	1.38239i
$818$	12081.5			0.516404
$819$		0			0
$820$	6377.27			0.271590
$821$	7667.19	−	13280.0i	0.325928	−	0.564524i	−0.655772	−	0.754959i	$-0.727657\pi$
$821$	7667.19	−	13280.0i	0.325928	−	0.564524i	0.981700	+	0.190435i	$0.0609900\pi$
$822$	−12531.6	−	21705.3i	−0.531739	−	0.920998i
$823$	5501.84	+	9529.46i	0.233028	+	0.403616i	0.958698	−	0.284427i	$-0.0918033\pi$
$823$	5501.84	+	9529.46i	0.233028	+	0.403616i	−0.725670	+	0.688043i	$0.758470\pi$
$824$	−14524.4	+	25156.9i	−0.614054	+	1.06357i
$825$	6313.36			0.266428
$826$		0			0
$827$	−3261.59			−0.137142			−0.0685711	−	0.997646i	$-0.521844\pi$
$827$	−3261.59			−0.137142			−0.0685711	+	0.997646i	$0.521844\pi$
$828$	−5878.80	+	10182.4i	−0.246742	+	0.427370i
$829$	−2581.65	−	4471.55i	−0.108160	−	0.187338i	0.806865	−	0.590736i	$-0.201162\pi$
$829$	−2581.65	−	4471.55i	−0.108160	−	0.187338i	−0.915025	+	0.403398i	$0.867829\pi$
$830$	809.606	+	1402.28i	0.0338576	+	0.0586431i
$831$	−6592.57	+	11418.7i	−0.275203	+	0.476666i
$832$	−72305.6			−3.01292
$833$		0			0
$834$	19643.7			0.815593
$835$	7340.75	−	12714.6i	0.304236	−	0.526952i
$836$	25156.6	+	43572.5i	1.04074	+	1.80261i
$837$	−139.575	−	241.751i	−0.00576395	−	0.00998345i
$838$	10169.9	−	17614.8i	0.419228	−	0.726125i
$839$	−5641.70			−0.232149			−0.116075	−	0.993241i	$-0.537031\pi$
$839$	−5641.70			−0.232149			−0.116075	+	0.993241i	$0.537031\pi$
$840$		0			0
$841$	−6409.46			−0.262801
$842$	22483.1	−	38941.8i	0.920211	−	1.59385i
$843$	−32900.7	−	56985.7i	−1.34420	−	2.32822i
$844$	21814.1	+	37783.0i	0.889657	+	1.54093i
$845$	−14278.6	+	24731.3i	−0.581302	+	1.00684i
$846$	25863.0			1.05105
$847$		0			0
$848$	3149.45			0.127538
$849$	26273.4	−	45506.9i	1.06207	−	1.83957i
$850$	−273.832	−	474.290i	−0.0110498	−	0.0191389i
$851$	1430.28	+	2477.32i	0.0576140	+	0.0997903i
$852$	−29383.3	+	50893.4i	−1.18152	+	2.04645i
$853$	−7799.52			−0.313072			−0.156536	−	0.987672i	$-0.550033\pi$
$853$	−7799.52			−0.313072			−0.156536	+	0.987672i	$0.550033\pi$
$854$		0			0
$855$	27044.9			1.08177
$856$	709.520	−	1228.93i	0.0283305	−	0.0490699i
$857$	10770.0	+	18654.2i	0.429284	+	0.743542i	0.996810	−	0.0798140i	$-0.0254327\pi$
$857$	10770.0	+	18654.2i	0.429284	+	0.743542i	−0.567526	+	0.823356i	$0.692099\pi$
$858$	51928.7	+	89943.1i	2.06622	+	3.57879i
$859$	−2223.99	+	3852.06i	−0.0883370	+	0.153004i	−0.906808	−	0.421543i	$-0.861489\pi$
$859$	−2223.99	+	3852.06i	−0.0883370	+	0.153004i	0.818471	+	0.574547i	$0.194822\pi$
$860$	−19989.3			−0.792591
$861$		0			0
$862$	66198.5			2.61569
$863$	4712.60	−	8162.47i	0.185885	−	0.321963i	−0.757989	−	0.652267i	$-0.773818\pi$
$863$	4712.60	−	8162.47i	0.185885	−	0.321963i	0.943874	+	0.330304i	$0.107151\pi$
$864$	11082.1	+	19194.8i	0.436367	+	0.755809i
$865$	−5868.27	−	10164.1i	−0.230667	−	0.399528i
$866$	−5488.48	+	9506.32i	−0.215365	+	0.373023i
$867$	41015.2			1.60663
$868$		0			0
$869$	15868.3			0.619442
$870$	−13001.3	+	22518.9i	−0.506649	+	0.877541i
$871$	−31027.2	−	53740.8i	−1.20702	−	2.09063i
$872$	−16925.4	−	29315.7i	−0.657301	−	1.13848i
$873$	90.8936	−	157.432i	0.00352381	−	0.00610341i
$874$	−11699.2			−0.452783
$875$		0			0
$876$	−7462.27			−0.287816
$877$	−11173.0	+	19352.3i	−0.430201	+	0.745131i	−0.996890	−	0.0788011i	$-0.974891\pi$
$877$	−11173.0	+	19352.3i	−0.430201	+	0.745131i	0.566689	+	0.823932i	$0.308224\pi$
$878$	−22044.1	−	38181.4i	−0.847324	−	1.46761i
$879$	−30464.3	−	52765.7i	−1.16898	−	2.02474i
$880$	610.377	−	1057.20i	0.0233816	−	0.0404981i
$881$	12074.9			0.461762			0.230881	−	0.972982i	$-0.425839\pi$
$881$	12074.9			0.461762			0.230881	+	0.972982i	$0.425839\pi$
$882$		0			0
$883$	−30499.6			−1.16239			−0.581196	−	0.813764i	$-0.697415\pi$
$883$	−30499.6			−1.16239			−0.581196	+	0.813764i	$0.697415\pi$
$884$	2819.61	−	4883.70i	0.107278	−	0.185811i
$885$	17580.4	+	30450.2i	0.667751	+	1.15658i
$886$	15371.9	+	26624.9i	0.582878	+	1.00957i
$887$	−11672.1	+	20216.6i	−0.441838	+	0.765285i	−0.997826	−	0.0659050i	$-0.979007\pi$
$887$	−11672.1	+	20216.6i	−0.441838	+	0.765285i	0.555988	+	0.831190i	$0.312340\pi$
$888$	−29485.8			−1.11428
$889$		0			0
$890$	214.562			0.00808107
$891$	−318.034	+	550.851i	−0.0119580	+	0.0207118i
$892$	−29272.1	−	50700.8i	−1.09877	−	1.90313i
$893$	8054.10	+	13950.1i	0.301814	+	0.522758i
$894$	35451.1	−	61403.2i	1.32625	−	2.29712i
$895$	15182.8			0.567044
$896$		0			0
$897$	−15116.2			−0.562669
$898$	−1776.42	+	3076.86i	−0.0660134	+	0.114339i
$899$	136.613	+	236.621i	0.00506820	+	0.00877838i
$900$	−7251.35	−	12559.7i	−0.268568	−	0.465174i
$901$	919.992	−	1593.47i	0.0340171	−	0.0589193i
$902$	13267.8			0.489768
$903$		0			0
$904$	−10862.0			−0.399629
$905$	2249.44	−	3896.15i	0.0826231	−	0.143107i
$906$	−57695.0	−	99930.7i	−2.11566	−	3.66443i
$907$	7546.25	+	13070.5i	0.276262	+	0.478499i	0.970453	−	0.241292i	$-0.0775711\pi$
$907$	7546.25	+	13070.5i	0.276262	+	0.478499i	−0.694191	+	0.719791i	$0.744238\pi$
$908$	409.058	−	708.509i	0.0149505	−	0.0258950i
$909$	−37521.3			−1.36909
$910$		0			0
$911$	−15207.8			−0.553081			−0.276541	−	0.961002i	$-0.589188\pi$
$911$	−15207.8			−0.553081			−0.276541	+	0.961002i	$0.589188\pi$
$912$	4243.81	−	7350.49i	0.154086	−	0.266885i
$913$	1054.31	+	1826.11i	0.0382174	+	0.0661945i
$914$	−7684.87	−	13310.6i	−0.278110	−	0.481701i
$915$	8164.82	−	14141.9i	0.294995	−	0.510947i
$916$	40419.6			1.45797
$917$		0			0
$918$	−3001.08			−0.107898
$919$	−12409.1	+	21493.1i	−0.445415	+	0.771482i	−0.998081	−	0.0619209i	$-0.980277\pi$
$919$	−12409.1	+	21493.1i	−0.445415	+	0.771482i	0.552666	+	0.833403i	$0.313611\pi$
$920$	1262.22	+	2186.23i	0.0452328	+	0.0783455i
$921$	5570.06	+	9647.62i	0.199283	+	0.345168i
$922$	−43565.0	+	75456.8i	−1.55611	+	2.69527i
$923$	−46550.1			−1.66004
$924$		0			0
$925$	−3528.44			−0.125421
$926$	−24878.1	+	43090.2i	−0.882880	+	1.52919i
$927$	25266.8	+	43763.4i	0.895223	+	1.55057i
$928$	−10846.9	−	18787.4i	−0.383694	−	0.664577i
$929$	−19953.2	+	34560.0i	−0.704675	+	1.22053i	0.262133	+	0.965032i	$0.415574\pi$
$929$	−19953.2	+	34560.0i	−0.704675	+	1.22053i	−0.966809	+	0.255502i	$0.917759\pi$
$930$	−395.148			−0.0139327
$931$		0			0
$932$	−47270.3			−1.66136
$933$	20415.8	−	35361.3i	0.716382	−	1.24081i
$934$	17207.3	+	29804.0i	0.602827	+	1.04413i
$935$	−356.597	−	617.644i	−0.0124727	−	0.0216033i
$936$	47999.8	−	83138.1i	1.67620	−	2.90326i
$937$	16923.0			0.590020			0.295010	−	0.955494i	$-0.404677\pi$
$937$	16923.0			0.590020			0.295010	+	0.955494i	$0.404677\pi$
$938$		0			0
$939$	−64856.8			−2.25402
$940$	4318.97	−	7480.68i	0.149861	−	0.259567i
$941$	26507.1	+	45911.6i	0.918285	+	1.59052i	0.802020	+	0.597298i	$0.203759\pi$
$941$	26507.1	+	45911.6i	0.918285	+	1.59052i	0.116265	+	0.993218i	$0.462908\pi$
$942$	41339.1	+	71601.4i	1.42983	+	2.47654i
$943$	−965.550	+	1672.38i	−0.0333432	+	0.0577521i
$944$	6798.71			0.234406
$945$		0			0
$946$	−41587.4			−1.42931
$947$	12899.5	−	22342.5i	0.442636	−	0.766668i	−0.555248	−	0.831685i	$-0.687377\pi$
$947$	12899.5	−	22342.5i	0.442636	−	0.766668i	0.997884	+	0.0650170i	$0.0207101\pi$
$948$	−29581.6	−	51236.8i	−1.01347	−	1.75537i
$949$	−2955.50	−	5119.08i	−0.101095	−	0.175102i
$950$	7215.35	−	12497.4i	0.246418	−	0.426808i
$951$	68560.6			2.33778
$952$		0			0
$953$	−17942.7			−0.609885			−0.304943	−	0.952371i	$-0.598637\pi$
$953$	−17942.7			−0.609885			−0.304943	+	0.952371i	$0.598637\pi$
$954$	38921.6	−	67414.2i	1.32089	−	2.28786i
$955$	−1040.42	−	1802.06i	−0.0352536	−	0.0610610i
$956$	−15278.3	−	26462.8i	−0.516877	−	0.895258i
$957$	−16930.9	+	29325.2i	−0.571889	+	0.990541i
$958$	−26322.9			−0.887739
$959$		0			0
$960$	34094.3			1.14624
$961$	14893.4	−	25796.2i	0.499930	−	0.865905i
$962$	−29022.1	−	50267.7i	−0.972671	−	1.68472i
$963$	−1234.29	−	2137.86i	−0.0413027	−	0.0715384i
$964$	14830.2	−	25686.6i	0.495486	−	0.858206i
$965$	−25905.2			−0.864165
$966$		0			0
$967$	19668.3			0.654073			0.327036	−	0.945012i	$-0.393950\pi$
$967$	19668.3			0.654073			0.327036	+	0.945012i	$0.393950\pi$
$968$	−5284.64	+	9153.27i	−0.175470	+	0.303923i
$969$	−2479.33	−	4294.33i	−0.0821958	−	0.142367i
$970$	−48.4993	−	84.0033i	−0.00160538	−	0.00278060i
$971$	−3166.48	+	5484.51i	−0.104652	+	0.181263i	−0.913596	−	0.406623i	$-0.866706\pi$
$971$	−3166.48	+	5484.51i	−0.104652	+	0.181263i	0.808944	+	0.587886i	$0.200040\pi$
$972$	51886.7			1.71221
$973$		0			0
$974$	9342.76			0.307353
$975$	9322.70	−	16147.4i	0.306221	−	0.530390i
$976$	−1578.75	−	2734.48i	−0.0517773	−	0.0896809i
$977$	5667.04	+	9815.59i	0.185573	+	0.321421i	0.943769	−	0.330605i	$-0.107253\pi$
$977$	5667.04	+	9815.59i	0.185573	+	0.321421i	−0.758197	+	0.652026i	$0.773919\pi$
$978$	11517.8	−	19949.3i	0.376582	−	0.652259i
$979$	279.414			0.00912166
$980$		0			0
$981$	−58887.4			−1.91655
$982$	17656.6	−	30582.2i	0.573774	−	0.993805i
$983$	18827.1	+	32609.6i	0.610877	+	1.05807i	0.991093	+	0.133173i	$0.0425165\pi$
$983$	18827.1	+	32609.6i	0.610877	+	1.05807i	−0.380216	+	0.924898i	$0.624150\pi$
$984$	−9952.57	−	17238.4i	−0.322435	−	0.558475i
$985$	−3630.86	+	6288.83i	−0.117451	+	0.203430i
$986$	2937.40			0.0948741
$987$		0			0
$988$	148591.			4.78473
$989$	3026.47	−	5242.01i	0.0973066	−	0.168540i
$990$	−15086.4	−	26130.3i	−0.484319	−	0.838865i
$991$	26720.8	+	46281.7i	0.856522	+	1.48354i	0.875226	+	0.483715i	$0.160713\pi$
$991$	26720.8	+	46281.7i	0.856522	+	1.48354i	−0.0187038	+	0.999825i	$0.505954\pi$
$992$	164.836	−	285.504i	0.00527575	−	0.00913786i
$993$	17115.1			0.546959
$994$		0			0
$995$	−6386.16			−0.203472
$996$	3930.87	−	6808.46i	0.125055	−	0.216601i
$997$	−18959.7	−	32839.1i	−0.602266	−	1.04315i	−0.992477	−	0.122429i	$-0.960931\pi$
$997$	−18959.7	−	32839.1i	−0.602266	−	1.04315i	0.390212	−	0.920725i	$-0.372402\pi$
$998$	14531.7	+	25169.6i	0.460914	+	0.798327i
$999$	−9667.55	+	16744.7i	−0.306174	+	0.530309i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	245.4.e.m.226.3		6
7.2	even	3		35.4.a.c.1.1	✓	3
7.3	odd	6		245.4.e.n.116.3		6
7.4	even	3	inner	245.4.e.m.116.3		6
7.5	odd	6		245.4.a.l.1.1		3
7.6	odd	2		245.4.e.n.226.3		6
21.2	odd	6		315.4.a.p.1.3		3
21.5	even	6		2205.4.a.bm.1.3		3
28.23	odd	6		560.4.a.u.1.3		3
35.2	odd	12		175.4.b.e.99.1		6
35.9	even	6		175.4.a.f.1.3		3
35.19	odd	6		1225.4.a.y.1.3		3
35.23	odd	12		175.4.b.e.99.6		6
56.37	even	6		2240.4.a.bt.1.3		3
56.51	odd	6		2240.4.a.bv.1.1		3
105.44	odd	6		1575.4.a.ba.1.1		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.a.c.1.1	✓	3	7.2	even	3
175.4.a.f.1.3		3	35.9	even	6
175.4.b.e.99.1		6	35.2	odd	12
175.4.b.e.99.6		6	35.23	odd	12
245.4.a.l.1.1		3	7.5	odd	6
245.4.e.m.116.3		6	7.4	even	3	inner
245.4.e.m.226.3		6	1.1	even	1	trivial
245.4.e.n.116.3		6	7.3	odd	6
245.4.e.n.226.3		6	7.6	odd	2
315.4.a.p.1.3		3	21.2	odd	6
560.4.a.u.1.3		3	28.23	odd	6
1225.4.a.y.1.3		3	35.19	odd	6
1575.4.a.ba.1.1		3	105.44	odd	6
2205.4.a.bm.1.3		3	21.5	even	6
2240.4.a.bt.1.3		3	56.37	even	6
2240.4.a.bv.1.1		3	56.51	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+(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

Introduction

L-functions

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