LMFDB - Embedded newform 35.5.g.a.8.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(8,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([3, 0]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.8");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.g (of order $4$, degree $2$, 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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			8.10
Character	$\chi$	$=$	35.8
Dual form			35.5.g.a.22.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.68989 - 3.68989i) q^{2} +(-5.41571 - 5.41571i) q^{3} -11.2306i q^{4} +(-14.8082 - 20.1424i) q^{5} -39.9667 q^{6} +(13.0958 - 13.0958i) q^{7} +(17.5987 + 17.5987i) q^{8} -22.3403i q^{9} +O(q^{10})$	\(q+(3.68989 - 3.68989i) q^{2} +(-5.41571 - 5.41571i) q^{3} -11.2306i q^{4} +(-14.8082 - 20.1424i) q^{5} -39.9667 q^{6} +(13.0958 - 13.0958i) q^{7} +(17.5987 + 17.5987i) q^{8} -22.3403i q^{9} +(-128.964 - 19.6826i) q^{10} +58.8300 q^{11} +(-60.8214 + 60.8214i) q^{12} +(90.6864 + 90.6864i) q^{13} -96.6441i q^{14} +(-28.8885 + 189.282i) q^{15} +309.563 q^{16} +(18.7384 - 18.7384i) q^{17} +(-82.4331 - 82.4331i) q^{18} -466.090i q^{19} +(-226.211 + 166.305i) q^{20} -141.846 q^{21} +(217.076 - 217.076i) q^{22} +(617.449 + 617.449i) q^{23} -190.619i q^{24} +(-186.434 + 596.546i) q^{25} +669.245 q^{26} +(-559.660 + 559.660i) q^{27} +(-147.073 - 147.073i) q^{28} +33.4645i q^{29} +(591.835 + 805.026i) q^{30} -1029.34 q^{31} +(860.676 - 860.676i) q^{32} +(-318.606 - 318.606i) q^{33} -138.285i q^{34} +(-457.706 - 69.8558i) q^{35} -250.894 q^{36} +(-495.185 + 495.185i) q^{37} +(-1719.82 - 1719.82i) q^{38} -982.261i q^{39} +(93.8751 - 615.085i) q^{40} +1437.24 q^{41} +(-523.396 + 523.396i) q^{42} +(-2157.18 - 2157.18i) q^{43} -660.695i q^{44} +(-449.987 + 330.819i) q^{45} +4556.64 q^{46} +(-722.273 + 722.273i) q^{47} +(-1676.50 - 1676.50i) q^{48} -343.000i q^{49} +(1513.27 + 2889.11i) q^{50} -202.964 q^{51} +(1018.46 - 1018.46i) q^{52} +(2101.64 + 2101.64i) q^{53} +4130.17i q^{54} +(-871.167 - 1184.98i) q^{55} +460.938 q^{56} +(-2524.21 + 2524.21i) q^{57} +(123.480 + 123.480i) q^{58} +3852.92i q^{59} +(2125.75 + 324.434i) q^{60} +5498.61 q^{61} +(-3798.15 + 3798.15i) q^{62} +(-292.564 - 292.564i) q^{63} -1398.58i q^{64} +(483.740 - 3169.55i) q^{65} -2351.24 q^{66} +(1180.08 - 1180.08i) q^{67} +(-210.443 - 210.443i) q^{68} -6687.84i q^{69} +(-1946.65 + 1431.13i) q^{70} -2609.74 q^{71} +(393.159 - 393.159i) q^{72} +(6998.11 + 6998.11i) q^{73} +3654.36i q^{74} +(4240.39 - 2221.05i) q^{75} -5234.45 q^{76} +(770.426 - 770.426i) q^{77} +(-3624.44 - 3624.44i) q^{78} -10261.0i q^{79} +(-4584.08 - 6235.36i) q^{80} +4252.35 q^{81} +(5303.26 - 5303.26i) q^{82} +(-1422.61 - 1422.61i) q^{83} +1593.01i q^{84} +(-654.920 - 99.9547i) q^{85} -15919.5 q^{86} +(181.234 - 181.234i) q^{87} +(1035.33 + 1035.33i) q^{88} +5359.08i q^{89} +(-439.716 + 2881.09i) q^{90} +2375.22 q^{91} +(6934.30 - 6934.30i) q^{92} +(5574.60 + 5574.60i) q^{93} +5330.22i q^{94} +(-9388.18 + 6901.96i) q^{95} -9322.33 q^{96} +(-3093.79 + 3093.79i) q^{97} +(-1265.63 - 1265.63i) q^{98} -1314.28i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) $ 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$e\left(\frac{3}{4}\right)$	$1$

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 $

$2$	3.68989	−	3.68989i	0.922472	−	0.922472i	−0.0747314	−	0.997204i	$-0.523810\pi$
$2$	3.68989	−	3.68989i	0.922472	−	0.922472i	0.997204	+	0.0747314i	$0.0238099\pi$
$3$	−5.41571	−	5.41571i	−0.601745	−	0.601745i	0.339030	−	0.940775i	$-0.389901\pi$
$3$	−5.41571	−	5.41571i	−0.601745	−	0.601745i	−0.940775	+	0.339030i	$0.889901\pi$
$4$		−	11.2306i		−	0.701910i
$5$	−14.8082	−	20.1424i	−0.592328	−	0.805697i
$5$	−14.8082	−	20.1424i	−0.592328	−	0.805697i
$6$	−39.9667			−1.11019
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$7$	13.0958	−	13.0958i	0.267261	−	0.267261i
$8$	17.5987	+	17.5987i	0.274980	+	0.274980i
$9$		−	22.3403i		−	0.275806i
$10$	−128.964	−	19.6826i	−1.28964	−	0.196826i
$11$	58.8300			0.486199			0.243099	−	0.970001i	$-0.421836\pi$
$11$	58.8300			0.486199			0.243099	+	0.970001i	$0.421836\pi$
$12$	−60.8214	+	60.8214i	−0.422371	+	0.422371i
$13$	90.6864	+	90.6864i	0.536606	+	0.536606i	0.922530	−	0.385925i	$-0.126118\pi$
$13$	90.6864	+	90.6864i	0.536606	+	0.536606i	−0.385925	+	0.922530i	$0.626118\pi$
$14$		−	96.6441i		−	0.493082i
$15$	−28.8885	+	189.282i	−0.128393	+	0.841255i
$16$	309.563			1.20923
$17$	18.7384	−	18.7384i	0.0648388	−	0.0648388i	−0.673944	−	0.738783i	$-0.735401\pi$
$17$	18.7384	−	18.7384i	0.0648388	−	0.0648388i	0.738783	+	0.673944i	$0.235401\pi$
$18$	−82.4331	−	82.4331i	−0.254423	−	0.254423i
$19$		−	466.090i		−	1.29111i	−0.763715	−	0.645554i	$-0.776627\pi$
$19$		−	466.090i		−	1.29111i	0.763715	−	0.645554i	$-0.223373\pi$
$20$	−226.211	+	166.305i	−0.565527	+	0.415761i
$21$	−141.846			−0.321646
$22$	217.076	−	217.076i	0.448505	−	0.448505i
$23$	617.449	+	617.449i	1.16720	+	1.16720i	0.982863	+	0.184337i	$0.0590138\pi$
$23$	617.449	+	617.449i	1.16720	+	1.16720i	0.184337	+	0.982863i	$0.440986\pi$
$24$		−	190.619i		−	0.330935i
$25$	−186.434	+	596.546i	−0.298294	+	0.954474i
$26$	669.245			0.990008
$27$	−559.660	+	559.660i	−0.767710	+	0.767710i
$28$	−147.073	−	147.073i	−0.187593	−	0.187593i
$29$			33.4645i			0.0397913i	0.999802	+	0.0198957i	$0.00633341\pi$
$29$			33.4645i			0.0397913i	−0.999802	+	0.0198957i	$0.993667\pi$
$30$	591.835	+	805.026i	0.657595	+	0.894473i
$31$	−1029.34			−1.07111			−0.535556	−	0.844500i	$-0.679898\pi$
$31$	−1029.34			−1.07111			−0.535556	+	0.844500i	$0.679898\pi$
$32$	860.676	−	860.676i	0.840504	−	0.840504i
$33$	−318.606	−	318.606i	−0.292568	−	0.292568i
$34$		−	138.285i		−	0.119624i
$35$	−457.706	−	69.8558i	−0.373638	−	0.0570251i
$36$	−250.894			−0.193591
$37$	−495.185	+	495.185i	−0.361713	+	0.361713i	−0.864443	−	0.502730i	$-0.832329\pi$
$37$	−495.185	+	495.185i	−0.361713	+	0.361713i	0.502730	+	0.864443i	$0.332329\pi$
$38$	−1719.82	−	1719.82i	−1.19101	−	1.19101i
$39$		−	982.261i		−	0.645800i
$40$	93.8751	−	615.085i	0.0586719	−	0.384428i
$41$	1437.24			0.854992			0.427496	−	0.904017i	$-0.359396\pi$
$41$	1437.24			0.854992			0.427496	+	0.904017i	$0.359396\pi$
$42$	−523.396	+	523.396i	−0.296710	+	0.296710i
$43$	−2157.18	−	2157.18i	−1.16667	−	1.16667i	−0.982985	−	0.183687i	$-0.941197\pi$
$43$	−2157.18	−	2157.18i	−1.16667	−	1.16667i	−0.183687	−	0.982985i	$-0.558803\pi$
$44$		−	660.695i		−	0.341268i
$45$	−449.987	+	330.819i	−0.222216	+	0.163368i
$46$	4556.64			2.15342
$47$	−722.273	+	722.273i	−0.326968	+	0.326968i	−0.851433	−	0.524464i	$-0.824266\pi$
$47$	−722.273	+	722.273i	−0.326968	+	0.326968i	0.524464	+	0.851433i	$0.324266\pi$
$48$	−1676.50	−	1676.50i	−0.727650	−	0.727650i
$49$		−	343.000i		−	0.142857i
$50$	1513.27	+	2889.11i	0.605307	+	1.15564i
$51$	−202.964			−0.0780329
$52$	1018.46	−	1018.46i	0.376649	−	0.376649i
$53$	2101.64	+	2101.64i	0.748180	+	0.748180i	0.974137	−	0.225957i	$-0.0725510\pi$
$53$	2101.64	+	2101.64i	0.748180	+	0.748180i	−0.225957	+	0.974137i	$0.572551\pi$
$54$			4130.17i			1.41638i
$55$	−871.167	−	1184.98i	−0.287989	−	0.391729i
$56$	460.938			0.146983
$57$	−2524.21	+	2524.21i	−0.776918	+	0.776918i
$58$	123.480	+	123.480i	0.0367064	+	0.0367064i
$59$			3852.92i			1.10684i	0.832902	+	0.553421i	$0.186678\pi$
$59$			3852.92i			1.10684i	−0.832902	+	0.553421i	$0.813322\pi$
$60$	2125.75	+	324.434i	0.590485	+	0.0901206i
$61$	5498.61			1.47772			0.738862	−	0.673857i	$-0.235363\pi$
$61$	5498.61			1.47772			0.738862	+	0.673857i	$0.235363\pi$
$62$	−3798.15	+	3798.15i	−0.988071	+	0.988071i
$63$	−292.564	−	292.564i	−0.0737122	−	0.0737122i
$64$		−	1398.58i		−	0.341451i
$65$	483.740	−	3169.55i	0.114495	−	0.750188i
$66$	−2351.24			−0.539771
$67$	1180.08	−	1180.08i	0.262883	−	0.262883i	−0.563341	−	0.826224i	$-0.690484\pi$
$67$	1180.08	−	1180.08i	0.262883	−	0.262883i	0.826224	+	0.563341i	$0.190484\pi$
$68$	−210.443	−	210.443i	−0.0455111	−	0.0455111i
$69$		−	6687.84i		−	1.40471i
$70$	−1946.65	+	1431.13i	−0.397275	+	0.292067i
$71$	−2609.74			−0.517702			−0.258851	−	0.965917i	$-0.583344\pi$
$71$	−2609.74			−0.517702			−0.258851	+	0.965917i	$0.583344\pi$
$72$	393.159	−	393.159i	0.0758409	−	0.0758409i
$73$	6998.11	+	6998.11i	1.31321	+	1.31321i	0.919034	+	0.394178i	$0.128971\pi$
$73$	6998.11	+	6998.11i	1.31321	+	1.31321i	0.394178	+	0.919034i	$0.371029\pi$
$74$			3654.36i			0.667341i
$75$	4240.39	−	2221.05i	0.753847	−	0.394853i
$76$	−5234.45			−0.906242
$77$	770.426	−	770.426i	0.129942	−	0.129942i
$78$	−3624.44	−	3624.44i	−0.595732	−	0.595732i
$79$		−	10261.0i		−	1.64413i	−0.569391	−	0.822067i	$-0.692821\pi$
$79$		−	10261.0i		−	1.64413i	0.569391	−	0.822067i	$-0.307179\pi$
$80$	−4584.08	−	6235.36i	−0.716262	−	0.974274i
$81$	4252.35			0.648125
$82$	5303.26	−	5303.26i	0.788706	−	0.788706i
$83$	−1422.61	−	1422.61i	−0.206504	−	0.206504i	0.596276	−	0.802780i	$-0.296647\pi$
$83$	−1422.61	−	1422.61i	−0.206504	−	0.206504i	−0.802780	+	0.596276i	$0.796647\pi$
$84$			1593.01i			0.225767i
$85$	−654.920	−	99.9547i	−0.0906463	−	0.0138346i
$86$	−15919.5			−2.15244
$87$	181.234	−	181.234i	0.0239442	−	0.0239442i
$88$	1035.33	+	1035.33i	0.133695	+	0.133695i
$89$			5359.08i			0.676566i	0.941044	+	0.338283i	$0.109846\pi$
$89$			5359.08i			0.676566i	−0.941044	+	0.338283i	$0.890154\pi$
$90$	−439.716	+	2881.09i	−0.0542859	+	0.355690i
$91$	2375.22			0.286828
$92$	6934.30	−	6934.30i	0.819270	−	0.819270i
$93$	5574.60	+	5574.60i	0.644537	+	0.644537i
$94$			5330.22i			0.603239i
$95$	−9388.18	+	6901.96i	−1.04024	+	0.764760i
$96$	−9322.33			−1.01154
$97$	−3093.79	+	3093.79i	−0.328812	+	0.328812i	−0.852135	−	0.523323i	$-0.824692\pi$
$97$	−3093.79	+	3093.79i	−0.328812	+	0.328812i	0.523323	+	0.852135i	$0.324692\pi$
$98$	−1265.63	−	1265.63i	−0.131782	−	0.131782i
$99$		−	1314.28i		−	0.134096i
$100$	6699.55	+	2093.76i	0.669955	+	0.209376i
$101$	−15070.6			−1.47736			−0.738681	−	0.674056i	$-0.764551\pi$
$101$	−15070.6			−1.47736			−0.738681	+	0.674056i	$0.764551\pi$
$102$	−748.913	+	748.913i	−0.0719832	+	0.0719832i
$103$	3480.59	+	3480.59i	0.328079	+	0.328079i	0.851856	−	0.523777i	$-0.175477\pi$
$103$	3480.59	+	3480.59i	0.328079	+	0.328079i	−0.523777	+	0.851856i	$0.675477\pi$
$104$			3191.92i			0.295111i
$105$	2100.49	+	2857.12i	0.190520	+	0.259149i
$106$	15509.6			1.38035
$107$	9084.98	−	9084.98i	0.793518	−	0.793518i	−0.188547	−	0.982064i	$-0.560378\pi$
$107$	9084.98	−	9084.98i	0.793518	−	0.793518i	0.982064	+	0.188547i	$0.0603776\pi$
$108$	6285.30	+	6285.30i	0.538863	+	0.538863i
$109$		−	14035.8i		−	1.18136i	−0.806905	−	0.590681i	$-0.798859\pi$
$109$		−	14035.8i		−	1.18136i	0.806905	−	0.590681i	$-0.201141\pi$
$110$	−7586.95	−	1157.93i	−0.627021	−	0.0956968i
$111$	5363.56			0.435318
$112$	4053.98	−	4053.98i	0.323181	−	0.323181i
$113$	2840.13	+	2840.13i	0.222424	+	0.222424i	0.809518	−	0.587095i	$-0.199728\pi$
$113$	2840.13	+	2840.13i	0.222424	+	0.222424i	−0.587095	+	0.809518i	$0.699728\pi$
$114$			18628.1i			1.43337i
$115$	3293.60	−	21580.2i	0.249044	−	1.63177i
$116$	375.825			0.0279300
$117$	2025.96	−	2025.96i	0.147999	−	0.147999i
$118$	14216.8	+	14216.8i	1.02103	+	1.02103i
$119$		−	490.789i		−	0.0346578i
$120$	−3839.52	+	2822.72i	−0.266633	+	0.196022i
$121$	−11180.0			−0.763611
$122$	20289.3	−	20289.3i	1.36316	−	1.36316i
$123$	−7783.68	−	7783.68i	−0.514487	−	0.514487i
$124$			11560.1i			0.751825i
$125$	14776.6	−	5078.55i	0.945705	−	0.325027i
$126$	−2159.05			−0.135995
$127$	−22225.8	+	22225.8i	−1.37800	+	1.37800i	−0.530008	+	0.847993i	$0.677811\pi$
$127$	−22225.8	+	22225.8i	−1.37800	+	1.37800i	−0.847993	+	0.530008i	$0.822189\pi$
$128$	8610.20	+	8610.20i	0.525525	+	0.525525i
$129$			23365.3i			1.40408i
$130$	−9910.32	−	13480.2i	−0.586410	−	0.797646i
$131$	−21851.6			−1.27333			−0.636664	−	0.771141i	$-0.719686\pi$
$131$	−21851.6			−1.27333			−0.636664	+	0.771141i	$0.719686\pi$
$132$	−3578.13	+	3578.13i	−0.205356	+	0.205356i
$133$	−6103.82	−	6103.82i	−0.345063	−	0.345063i
$134$		−	8708.74i		−	0.485004i
$135$	19560.5	+	2985.35i	1.07328	+	0.163805i
$136$	659.544			0.0356587
$137$	−22705.8	+	22705.8i	−1.20975	+	1.20975i	−0.238645	+	0.971107i	$0.576703\pi$
$137$	−22705.8	+	22705.8i	−1.20975	+	1.20975i	−0.971107	+	0.238645i	$0.923297\pi$
$138$	−24677.4	−	24677.4i	−1.29581	−	1.29581i
$139$		−	18608.8i		−	0.963138i	−0.876408	−	0.481569i	$-0.840067\pi$
$139$		−	18608.8i		−	0.963138i	0.876408	−	0.481569i	$-0.159933\pi$
$140$	−784.520	+	5140.30i	−0.0400265	+	0.262260i
$141$	7823.24			0.393503
$142$	−9629.63	+	9629.63i	−0.477566	+	0.477566i
$143$	5335.08	+	5335.08i	0.260897	+	0.260897i
$144$		−	6915.73i		−	0.333513i
$145$	674.056	−	495.550i	0.0320598	−	0.0235695i
$146$	51644.5			2.42280
$147$	−1857.59	+	1857.59i	−0.0859636	+	0.0859636i
$148$	5561.21	+	5561.21i	0.253890	+	0.253890i
$149$			14411.1i			0.649117i	0.945866	+	0.324559i	$0.105216\pi$
$149$			14411.1i			0.649117i	−0.945866	+	0.324559i	$0.894784\pi$
$150$	7451.15	−	23842.0i	0.331162	−	1.05964i
$151$	−2652.53			−0.116334			−0.0581671	−	0.998307i	$-0.518526\pi$
$151$	−2652.53			−0.116334			−0.0581671	+	0.998307i	$0.518526\pi$
$152$	8202.57	−	8202.57i	0.355028	−	0.355028i
$153$	−418.621	−	418.621i	−0.0178829	−	0.0178829i
$154$		−	5685.58i		−	0.239736i
$155$	15242.7	+	20733.4i	0.634450	+	0.862992i
$156$	−11031.3			−0.453293
$157$	−18983.9	+	18983.9i	−0.770170	+	0.770170i	−0.978136	−	0.207966i	$-0.933316\pi$
$157$	−18983.9	+	18983.9i	−0.770170	+	0.770170i	0.207966	+	0.978136i	$0.433316\pi$
$158$	−37862.1	−	37862.1i	−1.51667	−	1.51667i
$159$		−	22763.7i		−	0.900427i
$160$	−30081.2	−	4591.03i	−1.17505	−	0.179337i
$161$	16172.0			0.623895
$162$	15690.7	−	15690.7i	0.597878	−	0.597878i
$163$	−26111.6	−	26111.6i	−0.982785	−	0.982785i	0.0170698	−	0.999854i	$-0.494566\pi$
$163$	−26111.6	−	26111.6i	−0.982785	−	0.982785i	−0.999854	+	0.0170698i	$0.994566\pi$
$164$		−	16141.0i		−	0.600128i
$165$	−1699.51	+	11135.5i	−0.0624247	+	0.409017i
$166$	−10498.5			−0.380989
$167$	−47.7040	+	47.7040i	−0.00171049	+	0.00171049i	−0.707962	−	0.706251i	$-0.750385\pi$
$167$	−47.7040	+	47.7040i	−0.00171049	+	0.00171049i	0.706251	+	0.707962i	$0.250385\pi$
$168$	−2496.30	−	2496.30i	−0.0884461	−	0.0884461i
$169$		−	12113.0i		−	0.424109i
$170$	−2785.40	+	2047.76i	−0.0963807	+	0.0708567i
$171$	−10412.6			−0.356095
$172$	−24226.3	+	24226.3i	−0.818899	+	0.818899i
$173$	20794.9	+	20794.9i	0.694806	+	0.694806i	0.963286	−	0.268479i	$-0.0865210\pi$
$173$	20794.9	+	20794.9i	0.694806	+	0.694806i	−0.268479	+	0.963286i	$0.586521\pi$
$174$		−	1337.47i		−	0.0441758i
$175$	5370.75	+	10253.8i	0.175371	+	0.334816i
$176$	18211.6			0.587927
$177$	20866.3	−	20866.3i	0.666037	−	0.666037i
$178$	19774.4	+	19774.4i	0.624113	+	0.624113i
$179$			18069.2i			0.563939i	0.959423	+	0.281970i	$0.0909877\pi$
$179$			18069.2i			0.563939i	−0.959423	+	0.281970i	$0.909012\pi$
$180$	3715.29	+	5053.61i	0.114669	+	0.155976i
$181$	35446.6			1.08198			0.540988	−	0.841030i	$-0.318050\pi$
$181$	35446.6			1.08198			0.540988	+	0.841030i	$0.318050\pi$
$182$	8764.30	−	8764.30i	0.264591	−	0.264591i
$183$	−29778.9	−	29778.9i	−0.889213	−	0.889213i
$184$			21732.6i			0.641912i
$185$	17307.0	+	2641.42i	0.505684	+	0.0771782i
$186$	41139.3			1.18913
$187$	1102.38	−	1102.38i	0.0315246	−	0.0315246i
$188$	8111.54	+	8111.54i	0.229503	+	0.229503i
$189$			14658.4i			0.410358i
$190$	−9173.88	+	60108.8i	−0.254124	+	1.66506i
$191$	−18088.9			−0.495845			−0.247922	−	0.968780i	$-0.579748\pi$
$191$	−18088.9			−0.495845			−0.247922	+	0.968780i	$0.579748\pi$
$192$	−7574.31	+	7574.31i	−0.205466	+	0.205466i
$193$	28809.2	+	28809.2i	0.773423	+	0.773423i	0.978703	−	0.205280i	$-0.0658106\pi$
$193$	28809.2	+	28809.2i	0.773423	+	0.773423i	−0.205280	+	0.978703i	$0.565811\pi$
$194$			22831.5i			0.606640i
$195$	−19785.1	+	14545.5i	−0.520319	+	0.382525i
$196$	−3852.08			−0.100273
$197$	51897.3	−	51897.3i	1.33725	−	1.33725i	0.438534	−	0.898715i	$-0.355498\pi$
$197$	51897.3	−	51897.3i	1.33725	−	1.33725i	0.898715	−	0.438534i	$-0.144502\pi$
$198$	−4849.54	−	4849.54i	−0.123700	−	0.123700i
$199$			21817.7i			0.550939i	0.961310	+	0.275469i	$0.0888333\pi$
$199$			21817.7i			0.550939i	−0.961310	+	0.275469i	$0.911167\pi$
$200$	−13779.4	+	7217.44i	−0.344486	+	0.180436i
$201$	−12781.9			−0.316377
$202$	−55608.7	+	55608.7i	−1.36282	+	1.36282i
$203$	438.245	+	438.245i	0.0106347	+	0.0106347i
$204$			2279.40i			0.0547721i
$205$	−21283.0	−	28949.5i	−0.506436	−	0.688864i
$206$	25686.0			0.605288
$207$	13794.0	−	13794.0i	0.321920	−	0.321920i
$208$	28073.2	+	28073.2i	0.648881	+	0.648881i
$209$		−	27420.1i		−	0.627735i
$210$	18293.0	+	2791.90i	0.414808	+	0.0633085i
$211$	−43403.1			−0.974891			−0.487445	−	0.873154i	$-0.662071\pi$
$211$	−43403.1			−0.974891			−0.487445	+	0.873154i	$0.662071\pi$
$212$	23602.6	−	23602.6i	0.525155	−	0.525155i
$213$	14133.6	+	14133.6i	0.311525	+	0.311525i
$214$		−	67045.2i		−	1.46400i
$215$	−11506.8	+	75394.6i	−0.248931	+	1.63104i
$216$	−19698.6			−0.422209
$217$	−13480.0	+	13480.0i	−0.286267	+	0.286267i
$218$	−51790.4	−	51790.4i	−1.08977	−	1.08977i
$219$		−	75799.4i		−	1.58044i
$220$	−13308.0	+	9783.70i	−0.274958	+	0.202143i
$221$	3398.64			0.0695858
$222$	19790.9	−	19790.9i	0.401569	−	0.401569i
$223$	−15100.3	−	15100.3i	−0.303652	−	0.303652i	0.538789	−	0.842441i	$-0.318882\pi$
$223$	−15100.3	−	15100.3i	−0.303652	−	0.303652i	−0.842441	+	0.538789i	$0.818882\pi$
$224$		−	22542.5i		−	0.449268i
$225$	13327.0	+	4164.98i	0.263249	+	0.0822713i
$226$	20959.5			0.410359
$227$	31349.3	−	31349.3i	0.608381	−	0.608381i	−0.334142	−	0.942523i	$-0.608447\pi$
$227$	31349.3	−	31349.3i	0.608381	−	0.608381i	0.942523	+	0.334142i	$0.108447\pi$
$228$	28348.3	+	28348.3i	0.545327	+	0.545327i
$229$		−	54019.7i		−	1.03010i	−0.857159	−	0.515052i	$-0.827773\pi$
$229$		−	54019.7i		−	1.03010i	0.857159	−	0.515052i	$-0.172227\pi$
$230$	−67475.6	−	91781.7i	−1.27553	−	1.73500i
$231$	−8344.81			−0.156384
$232$	−588.932	+	588.932i	−0.0109418	+	0.0109418i
$233$	−43078.3	−	43078.3i	−0.793500	−	0.793500i	0.188562	−	0.982061i	$-0.439617\pi$
$233$	−43078.3	−	43078.3i	−0.793500	−	0.793500i	−0.982061	+	0.188562i	$0.939617\pi$
$234$		−	14951.1i		−	0.273050i
$235$	25243.9	+	3852.76i	0.457110	+	0.0697647i
$236$	43270.4			0.776904
$237$	−55570.7	+	55570.7i	−0.989349	+	0.989349i
$238$	−1810.96	−	1810.96i	−0.0319709	−	0.0319709i
$239$			13420.6i			0.234951i	0.993076	+	0.117475i	$0.0374801\pi$
$239$			13420.6i			0.234951i	−0.993076	+	0.117475i	$0.962520\pi$
$240$	−8942.83	+	58594.9i	−0.155257	+	1.01727i
$241$	−56201.9			−0.967648			−0.483824	−	0.875165i	$-0.660752\pi$
$241$	−56201.9			−0.967648			−0.483824	+	0.875165i	$0.660752\pi$
$242$	−41253.1	+	41253.1i	−0.704410	+	0.704410i
$243$	22303.0	+	22303.0i	0.377704	+	0.377704i
$244$		−	61752.5i		−	1.03723i
$245$	−6908.85	+	5079.22i	−0.115100	+	0.0846183i
$246$	−57441.8			−0.949200
$247$	42268.0	−	42268.0i	0.692816	−	0.692816i
$248$	−18115.0	−	18115.0i	−0.294534	−	0.294534i
$249$			15408.8i			0.248526i
$250$	35784.9	−	73263.4i	0.572558	−	1.17221i
$251$	51757.5			0.821534			0.410767	−	0.911740i	$-0.365261\pi$
$251$	51757.5			0.821534			0.410767	+	0.911740i	$0.365261\pi$
$252$	−3285.65	+	3285.65i	−0.0517393	+	0.0517393i
$253$	36324.5	+	36324.5i	0.567491	+	0.567491i
$254$			164021.i			2.54233i
$255$	3005.53	+	4088.18i	0.0462211	+	0.0628709i
$256$	85918.7			1.31102
$257$	−35425.6	+	35425.6i	−0.536353	+	0.536353i	−0.922456	−	0.386103i	$-0.873821\pi$
$257$	−35425.6	+	35425.6i	−0.536353	+	0.536353i	0.386103	+	0.922456i	$0.373821\pi$
$258$	86215.2	+	86215.2i	1.29522	+	1.29522i
$259$			12969.7i			0.193344i
$260$	−35595.8	−	5432.67i	−0.526565	−	0.0803650i
$261$	747.606			0.0109747
$262$	−80630.0	+	80630.0i	−1.17461	+	1.17461i
$263$	33455.5	+	33455.5i	0.483678	+	0.483678i	0.906304	−	0.422626i	$-0.138892\pi$
$263$	33455.5	+	33455.5i	0.483678	+	0.483678i	−0.422626	+	0.906304i	$0.638892\pi$
$264$		−	11214.1i		−	0.160900i
$265$	11210.6	−	73453.5i	0.159638	−	1.04597i
$266$	−45044.8			−0.636622
$267$	29023.2	−	29023.2i	0.407120	−	0.407120i
$268$	−13253.0	−	13253.0i	−0.184520	−	0.184520i
$269$		−	37095.3i		−	0.512642i	−0.966592	−	0.256321i	$-0.917490\pi$
$269$		−	37095.3i		−	0.512642i	0.966592	−	0.256321i	$-0.0825105\pi$
$270$	83191.6	−	61160.4i	1.14117	−	0.838963i
$271$	−33530.1			−0.456559			−0.228279	−	0.973596i	$-0.573310\pi$
$271$	−33530.1			−0.456559			−0.228279	+	0.973596i	$0.573310\pi$
$272$	5800.73	−	5800.73i	0.0784052	−	0.0784052i
$273$	−12863.5	−	12863.5i	−0.172597	−	0.172597i
$274$			167564.i			2.23193i
$275$	−10967.9	+	35094.8i	−0.145030	+	0.464064i
$276$	−75108.2			−0.985983
$277$	44691.5	−	44691.5i	0.582459	−	0.582459i	−0.353120	−	0.935578i	$-0.614879\pi$
$277$	44691.5	−	44691.5i	0.582459	−	0.582459i	0.935578	+	0.353120i	$0.114879\pi$
$278$	−68664.3	−	68664.3i	−0.888468	−	0.888468i
$279$			22995.7i			0.295419i
$280$	−6825.66	−	9284.40i	−0.0870620	−	0.118424i
$281$	−10609.2			−0.134359			−0.0671797	−	0.997741i	$-0.521400\pi$
$281$	−10609.2			−0.134359			−0.0671797	+	0.997741i	$0.521400\pi$
$282$	28866.9	−	28866.9i	0.362996	−	0.362996i
$283$	−21964.5	−	21964.5i	−0.274251	−	0.274251i	0.556558	−	0.830809i	$-0.312122\pi$
$283$	−21964.5	−	21964.5i	−0.274251	−	0.274251i	−0.830809	+	0.556558i	$0.812122\pi$
$284$			29308.8i			0.363380i
$285$	88222.6	+	13464.6i	1.08615	+	0.165770i
$286$	39371.7			0.481340
$287$	18821.8	−	18821.8i	0.228506	−	0.228506i
$288$	−19227.7	−	19227.7i	−0.231816	−	0.231816i
$289$			82818.7i			0.991592i
$290$	658.670	−	4315.72i	0.00783199	−	0.0513165i
$291$	33510.1			0.395722
$292$	78592.7	−	78592.7i	0.921757	−	0.921757i
$293$	−18838.8	−	18838.8i	−0.219441	−	0.219441i	0.588822	−	0.808263i	$-0.299592\pi$
$293$	−18838.8	−	18838.8i	−0.219441	−	0.219441i	−0.808263	+	0.588822i	$0.799592\pi$
$294$			13708.6i			0.158598i
$295$	77607.1	−	57054.8i	0.891779	−	0.655614i
$296$	−17429.2			−0.198927
$297$	−32924.8	+	32924.8i	−0.373260	+	0.373260i
$298$	53175.2	+	53175.2i	0.598793	+	0.598793i
$299$			111988.i			1.25265i
$300$	−24943.6	−	47622.0i	−0.277151	−	0.529133i
$301$	−56499.9			−0.623612
$302$	−9787.56	+	9787.56i	−0.107315	+	0.107315i
$303$	81617.7	+	81617.7i	0.888995	+	0.888995i
$304$		−	144284.i		−	1.56125i
$305$	−81424.6	−	110755.i	−0.875298	−	1.19060i
$306$	−3089.33			−0.0329930
$307$	−53554.6	+	53554.6i	−0.568225	+	0.568225i	−0.931631	−	0.363406i	$-0.881614\pi$
$307$	−53554.6	+	53554.6i	−0.568225	+	0.568225i	0.363406	+	0.931631i	$0.381614\pi$
$308$	−8652.32	−	8652.32i	−0.0912077	−	0.0912077i
$309$		−	37699.7i		−	0.394840i
$310$	132748.	+	20260.1i	1.38135	+	0.210823i
$311$	141225.			1.46012			0.730062	−	0.683381i	$-0.239491\pi$
$311$	141225.			1.46012			0.730062	+	0.683381i	$0.239491\pi$
$312$	17286.5	−	17286.5i	0.177582	−	0.177582i
$313$	−60441.2	−	60441.2i	−0.616942	−	0.616942i	0.327804	−	0.944746i	$-0.393691\pi$
$313$	−60441.2	−	60441.2i	−0.616942	−	0.616942i	−0.944746	+	0.327804i	$0.893691\pi$
$314$			140097.i			1.42092i
$315$	−1560.60	+	10225.3i	−0.0157279	+	0.103051i
$316$	−115237.			−1.15403
$317$	42023.3	−	42023.3i	0.418188	−	0.418188i	−0.466391	−	0.884579i	$-0.654446\pi$
$317$	42023.3	−	42023.3i	0.418188	−	0.418188i	0.884579	+	0.466391i	$0.154446\pi$
$318$	−83995.5	−	83995.5i	−0.830619	−	0.830619i
$319$			1968.72i			0.0193465i
$320$	−28170.8	+	20710.5i	−0.275106	+	0.202251i
$321$	−98403.2			−0.954991
$322$	59672.8	−	59672.8i	0.575526	−	0.575526i
$323$	−8733.79	−	8733.79i	−0.0837139	−	0.0837139i
$324$		−	47756.3i		−	0.454926i
$325$	−71005.6	+	37191.6i	−0.672243	+	0.352110i
$326$	−192698.			−1.81318
$327$	−76013.6	+	76013.6i	−0.710879	+	0.710879i
$328$	25293.6	+	25293.6i	0.235105	+	0.235105i
$329$			18917.5i			0.174772i
$330$	34817.7	+	47359.7i	0.319722	+	0.434892i
$331$	138028.			1.25983			0.629913	−	0.776666i	$-0.283091\pi$
$331$	138028.			1.25983			0.629913	+	0.776666i	$0.283091\pi$
$332$	−15976.7	+	15976.7i	−0.144947	+	0.144947i
$333$	11062.6	+	11062.6i	0.0997626	+	0.0997626i
$334$			352.045i			0.00315577i
$335$	−41244.6	−	6294.80i	−0.367517	−	0.0560909i
$336$	−43910.3			−0.388945
$337$	27775.7	−	27775.7i	0.244571	−	0.244571i	−0.574167	−	0.818738i	$-0.694674\pi$
$337$	27775.7	−	27775.7i	0.244571	−	0.244571i	0.818738	+	0.574167i	$0.194674\pi$
$338$	−44695.5	−	44695.5i	−0.391228	−	0.391228i
$339$		−	30762.6i		−	0.267685i
$340$	−1122.55	+	7355.12i	−0.00971062	+	0.0636256i
$341$	−60556.1			−0.520773
$342$	−38421.2	+	38421.2i	−0.328488	+	0.328488i
$343$	−4491.86	−	4491.86i	−0.0381802	−	0.0381802i
$344$		−	75926.9i		−	0.641622i
$345$	−134709.	+	99035.0i	−1.13177	+	0.832052i
$346$	153461.			1.28188
$347$	−12498.3	+	12498.3i	−0.103798	+	0.103798i	−0.757099	−	0.653300i	$-0.773384\pi$
$347$	−12498.3	+	12498.3i	−0.103798	+	0.103798i	0.653300	+	0.757099i	$0.273384\pi$
$348$	−2035.36	−	2035.36i	−0.0168067	−	0.0168067i
$349$		−	45819.8i		−	0.376185i	−0.982151	−	0.188093i	$-0.939769\pi$
$349$		−	45819.8i		−	0.376185i	0.982151	−	0.188093i	$-0.0602306\pi$
$350$	57652.7	+	18017.7i	0.470634	+	0.147084i
$351$	−101507.			−0.823915
$352$	50633.6	−	50633.6i	0.408652	−	0.408652i
$353$	50727.5	+	50727.5i	0.407094	+	0.407094i	0.880724	−	0.473630i	$-0.157057\pi$
$353$	50727.5	+	50727.5i	0.407094	+	0.407094i	−0.473630	+	0.880724i	$0.657057\pi$
$354$		−	153988.i		−	1.22880i
$355$	38645.5	+	52566.4i	0.306650	+	0.417111i
$356$	60185.5			0.474888
$357$	−2657.97	+	2657.97i	−0.0208552	+	0.0208552i
$358$	66673.3	+	66673.3i	0.520218	+	0.520218i
$359$		−	39847.8i		−	0.309183i	−0.987979	−	0.154591i	$-0.950594\pi$
$359$		−	39847.8i		−	0.309183i	0.987979	−	0.154591i	$-0.0494061\pi$
$360$	−13741.2	−	2097.19i	−0.106028	−	0.0161821i
$361$	−86918.8			−0.666960
$362$	130794.	−	130794.i	0.998093	−	0.998093i
$363$	60547.7	+	60547.7i	0.459499	+	0.459499i
$364$		−	26675.1i		−	0.201327i
$365$	37329.4	−	244588.i	0.280198	−	1.83590i
$366$	−219761.			−1.64055
$367$	−72997.2	+	72997.2i	−0.541969	+	0.541969i	−0.924106	−	0.382137i	$-0.875188\pi$
$367$	−72997.2	+	72997.2i	−0.541969	+	0.541969i	0.382137	+	0.924106i	$0.375188\pi$
$368$	191140.	+	191140.i	1.41142	+	1.41142i
$369$		−	32108.4i		−	0.235812i
$370$	73607.6	−	54114.5i	0.537674	−	0.395285i
$371$	55045.2			0.399919
$372$	62605.9	−	62605.9i	0.452407	−	0.452407i
$373$	−126446.	−	126446.i	−0.908840	−	0.908840i	0.0873385	−	0.996179i	$-0.472164\pi$
$373$	−126446.	−	126446.i	−0.908840	−	0.908840i	−0.996179	+	0.0873385i	$0.972164\pi$
$374$		−	8135.34i		−	0.0581611i
$375$	−107530.	−	52522.0i	−0.764657	−	0.373490i
$376$	−25422.1			−0.179819
$377$	−3034.78	+	3034.78i	−0.0213523	+	0.0213523i
$378$	54087.9	+	54087.9i	0.378544	+	0.378544i
$379$			150298.i			1.04635i	0.852226	+	0.523173i	$0.175252\pi$
$379$			150298.i			1.04635i	−0.852226	+	0.523173i	$0.824748\pi$
$380$	77512.9	+	105435.i	0.536793	+	0.730156i
$381$	240736.			1.65841
$382$	−66746.1	+	66746.1i	−0.457403	+	0.457403i
$383$	−48516.0	−	48516.0i	−0.330740	−	0.330740i	0.522127	−	0.852868i	$-0.325139\pi$
$383$	−48516.0	−	48516.0i	−0.330740	−	0.330740i	−0.852868	+	0.522127i	$0.825139\pi$
$384$		−	93260.6i		−	0.632464i
$385$	−26926.9	−	4109.62i	−0.181662	−	0.0277255i
$386$	212606.			1.42692
$387$	−48191.9	+	48191.9i	−0.321775	+	0.321775i
$388$	34745.0	+	34745.0i	0.230797	+	0.230797i
$389$			209327.i			1.38333i	0.722218	+	0.691665i	$0.243123\pi$
$389$			209327.i			1.38333i	−0.722218	+	0.691665i	$0.756877\pi$
$390$	−19333.5	+	126676.i	−0.127110	+	0.832849i
$391$	23140.0			0.151360
$392$	6036.35	−	6036.35i	0.0392828	−	0.0392828i
$393$	118342.	+	118342.i	0.766219	+	0.766219i
$394$		−	382990.i		−	2.46715i
$395$	−206682.	+	151948.i	−1.32467	+	0.973867i
$396$	−14760.1			−0.0941236
$397$	26149.0	−	26149.0i	0.165911	−	0.165911i	−0.619269	−	0.785179i	$-0.712571\pi$
$397$	26149.0	−	26149.0i	0.165911	−	0.165911i	0.785179	+	0.619269i	$0.212571\pi$
$398$	80505.0	+	80505.0i	0.508226	+	0.508226i
$399$			66113.0i			0.415280i
$400$	−57713.1	+	184669.i	−0.360707	+	1.15418i
$401$	−30989.9			−0.192722			−0.0963609	−	0.995346i	$-0.530720\pi$
$401$	−30989.9			−0.192722			−0.0963609	+	0.995346i	$0.530720\pi$
$402$	−47163.9	+	47163.9i	−0.291849	+	0.291849i
$403$	−93347.0	−	93347.0i	−0.574765	−	0.574765i
$404$			169251.i			1.03698i
$405$	−62969.7	−	85652.6i	−0.383903	−	0.522193i
$406$	3234.15			0.0196204
$407$	−29131.8	+	29131.8i	−0.175865	+	0.175865i
$408$	−3571.89	−	3571.89i	−0.0214575	−	0.0214575i
$409$			70714.6i			0.422730i	0.977407	+	0.211365i	$0.0677908\pi$
$409$			70714.6i			0.422730i	−0.977407	+	0.211365i	$0.932209\pi$
$410$	−185352.	−	28288.7i	−1.10263	−	0.168285i
$411$	245936.			1.45592
$412$	39089.0	−	39089.0i	0.230282	−	0.230282i
$413$	50457.0	+	50457.0i	0.295816	+	0.295816i
$414$		−	101796.i		−	0.593925i
$415$	−7588.49	+	49721.0i	−0.0440615	+	0.288698i
$416$	156103.			0.902038
$417$	−100780.	+	100780.i	−0.579563	+	0.579563i
$418$	−101177.	−	101177.i	−0.579068	−	0.579068i
$419$		−	94930.1i		−	0.540724i	−0.962759	−	0.270362i	$-0.912857\pi$
$419$		−	94930.1i		−	0.540724i	0.962759	−	0.270362i	$-0.0871434\pi$
$420$	32087.1	−	23589.6i	0.181900	−	0.133728i
$421$	−111250.			−0.627676			−0.313838	−	0.949477i	$-0.601615\pi$
$421$	−111250.			−0.627676			−0.313838	+	0.949477i	$0.601615\pi$
$422$	−160153.	+	160153.i	−0.899309	+	0.899309i
$423$	16135.8	+	16135.8i	0.0901798	+	0.0901798i
$424$			73972.1i			0.411468i
$425$	7684.86	+	14671.8i	0.0425459	+	0.0812281i
$426$	104303.			0.574746
$427$	72008.7	−	72008.7i	0.394938	−	0.394938i
$428$	−102030.	−	102030.i	−0.556978	−	0.556978i
$429$		−	57786.5i		−	0.313987i
$430$	235739.	+	320657.i	1.27495	+	1.73422i
$431$	247126.			1.33035			0.665173	−	0.746689i	$-0.268358\pi$
$431$	247126.			1.33035			0.665173	+	0.746689i	$0.268358\pi$
$432$	−173250.	+	173250.i	−0.928339	+	0.928339i
$433$	−2688.79	−	2688.79i	−0.0143410	−	0.0143410i	0.699900	−	0.714241i	$-0.253228\pi$
$433$	−2688.79	−	2688.79i	−0.0143410	−	0.0143410i	−0.714241	+	0.699900i	$0.753228\pi$
$434$			99479.5i			0.528146i
$435$	−6334.24	−	966.740i	−0.0334747	−	0.00510895i
$436$	−157630.			−0.829210
$437$	287787.	−	287787.i	1.50698	−	1.50698i
$438$	−279691.	−	279691.i	−1.45791	−	1.45791i
$439$		−	324182.i		−	1.68213i	−0.540934	−	0.841065i	$-0.681929\pi$
$439$		−	324182.i		−	1.68213i	0.540934	−	0.841065i	$-0.318071\pi$
$440$	5522.68	−	36185.5i	0.0285262	−	0.186909i
$441$	−7662.71			−0.0394008
$442$	12540.6	−	12540.6i	0.0641910	−	0.0641910i
$443$	−180535.	−	180535.i	−0.919928	−	0.919928i	0.0770961	−	0.997024i	$-0.475435\pi$
$443$	−180535.	−	180535.i	−0.919928	−	0.919928i	−0.997024	+	0.0770961i	$0.975435\pi$
$444$		−	60235.8i		−	0.305554i
$445$	107945.	−	79358.3i	0.545107	−	0.400749i
$446$	−111437.			−0.560222
$447$	78046.0	−	78046.0i	0.390603	−	0.390603i
$448$	−18315.5	−	18315.5i	−0.0912565	−	0.0912565i
$449$			98163.0i			0.486917i	0.969911	+	0.243459i	$0.0782820\pi$
$449$			98163.0i			0.486917i	−0.969911	+	0.243459i	$0.921718\pi$
$450$	64543.5	−	33806.8i	0.318733	−	0.166947i
$451$	84553.0			0.415696
$452$	31896.2	−	31896.2i	0.156121	−	0.156121i
$453$	14365.3	+	14365.3i	0.0700035	+	0.0700035i
$454$		−	231351.i		−	1.12243i
$455$	−35172.8	−	47842.7i	−0.169896	−	0.231096i
$456$	−88845.4			−0.427273
$457$	−8778.56	+	8778.56i	−0.0420331	+	0.0420331i	−0.727811	−	0.685778i	$-0.759462\pi$
$457$	−8778.56	+	8778.56i	−0.0420331	+	0.0420331i	0.685778	+	0.727811i	$0.259462\pi$
$458$	−199327.	−	199327.i	−0.950243	−	0.950243i
$459$			20974.3i			0.0995548i
$460$	−242358.	−	36989.0i	−1.14536	−	0.174806i
$461$	190575.			0.896737			0.448368	−	0.893849i	$-0.352005\pi$
$461$	190575.			0.896737			0.448368	+	0.893849i	$0.352005\pi$
$462$	−30791.4	+	30791.4i	−0.144260	+	0.144260i
$463$	−96817.3	−	96817.3i	−0.451638	−	0.451638i	0.444260	−	0.895898i	$-0.353467\pi$
$463$	−96817.3	−	96817.3i	−0.451638	−	0.451638i	−0.895898	+	0.444260i	$0.853467\pi$
$464$			10359.4i			0.0481170i
$465$	29736.1	−	194836.i	0.137524	−	0.901078i
$466$	−317908.			−1.46396
$467$	−133875.	+	133875.i	−0.613853	+	0.613853i	−0.943948	−	0.330094i	$-0.892919\pi$
$467$	−133875.	+	133875.i	−0.613853	+	0.613853i	0.330094	+	0.943948i	$0.392919\pi$
$468$	−22752.6	−	22752.6i	−0.103882	−	0.103882i
$469$		−	30908.2i		−	0.140517i
$470$	107363.	−	78931.0i	0.486027	−	0.357315i
$471$	205623.			0.926892
$472$	−67806.3	+	67806.3i	−0.304359	+	0.304359i
$473$	−126907.	−	126907.i	−0.567234	−	0.567234i
$474$			410100.i			1.82529i
$475$	278044.	+	86895.0i	1.23233	+	0.385130i
$476$	−5511.84			−0.0243267
$477$	46951.1	−	46951.1i	0.206352	−	0.206352i
$478$	49520.6	+	49520.6i	0.216736	+	0.216736i
$479$		−	19912.2i		−	0.0867856i	−0.999058	−	0.0433928i	$-0.986183\pi$
$479$		−	19912.2i		−	0.0867856i	0.999058	−	0.0433928i	$-0.0138167\pi$
$480$	138047.	+	187774.i	0.599163	+	0.814993i
$481$	−89813.1			−0.388195
$482$	−207379.	+	207379.i	−0.892628	+	0.892628i
$483$	−87582.6	−	87582.6i	−0.375426	−	0.375426i
$484$			125558.i			0.535986i
$485$	108130.	+	16502.9i	0.459688	+	0.0701581i
$486$	164591.			0.696842
$487$	42819.4	−	42819.4i	0.180544	−	0.180544i	−0.611049	−	0.791593i	$-0.709252\pi$
$487$	42819.4	−	42819.4i	0.180544	−	0.180544i	0.791593	+	0.611049i	$0.209252\pi$
$488$	96768.4	+	96768.4i	0.406344	+	0.406344i
$489$			282825.i			1.18277i
$490$	−6751.15	+	44234.6i	−0.0281181	+	0.184234i
$491$	−210345.			−0.872509			−0.436254	−	0.899823i	$-0.643695\pi$
$491$	−210345.			−0.872509			−0.436254	+	0.899823i	$0.643695\pi$
$492$	−87415.1	+	87415.1i	−0.361124	+	0.361124i
$493$	627.073	+	627.073i	0.00258003	+	0.00258003i
$494$		−	311928.i		−	1.27821i
$495$	−26472.8	+	19462.1i	−0.108041	+	0.0794291i
$496$	−318646.			−1.29522
$497$	−34176.6	+	34176.6i	−0.138362	+	0.138362i
$498$	56856.9	+	56856.9i	0.229258	+	0.229258i
$499$			397649.i			1.59698i	0.602011	+	0.798488i	$0.294366\pi$
$499$			397649.i			1.59698i	−0.602011	+	0.798488i	$0.705634\pi$
$500$	−57035.0	−	165950.i	−0.228140	−	0.663800i
$501$	516.701			0.00205856
$502$	190979.	−	190979.i	0.757842	−	0.757842i
$503$	147414.	+	147414.i	0.582644	+	0.582644i	0.935629	−	0.352985i	$-0.114833\pi$
$503$	147414.	+	147414.i	0.582644	+	0.582644i	−0.352985	+	0.935629i	$0.614833\pi$
$504$		−	10297.5i		−	0.0405387i
$505$	223168.	+	303558.i	0.875083	+	1.19031i
$506$	268067.			1.04699
$507$	−65600.3	+	65600.3i	−0.255205	+	0.255205i
$508$	249608.	+	249608.i	0.967233	+	0.967233i
$509$		−	343629.i		−	1.32634i	−0.748470	−	0.663168i	$-0.769211\pi$
$509$		−	343629.i		−	1.32634i	0.748470	−	0.663168i	$-0.230789\pi$
$510$	26175.0	+	3994.86i	0.100634	+	0.0153589i
$511$	183292.			0.701941
$512$	179267.	−	179267.i	0.683850	−	0.683850i
$513$	260852.	+	260852.i	0.991196	+	0.991196i
$514$			261433.i			0.989542i
$515$	18566.2	−	121649.i	0.0700017	−	0.458663i
$516$	262405.			0.985537
$517$	−42491.4	+	42491.4i	−0.158972	+	0.158972i
$518$	47856.8	+	47856.8i	0.178354	+	0.178354i
$519$		−	225238.i		−	0.836193i
$520$	64293.0	−	47266.6i	0.237770	−	0.174803i
$521$	−539599.			−1.98790			−0.993952	−	0.109811i	$-0.964975\pi$
$521$	−539599.			−1.98790			−0.993952	+	0.109811i	$0.964975\pi$
$522$	2758.58	−	2758.58i	0.0101238	−	0.0101238i
$523$	60008.9	+	60008.9i	0.219388	+	0.219388i	0.808240	−	0.588853i	$-0.200420\pi$
$523$	60008.9	+	60008.9i	0.219388	+	0.219388i	−0.588853	+	0.808240i	$0.700420\pi$
$524$			245406.i			0.893763i
$525$	26444.9	−	84617.7i	0.0959453	−	0.307003i
$526$	246894.			0.892359
$527$	−19288.2	+	19288.2i	−0.0694497	+	0.0694497i
$528$	−98628.8	−	98628.8i	−0.353782	−	0.353782i
$529$			482645.i			1.72471i
$530$	−229670.	−	312401.i	−0.817621	−	1.11214i
$531$	86075.2			0.305273
$532$	−68549.4	+	68549.4i	−0.242203	+	0.242203i
$533$	130338.	+	130338.i	0.458794	+	0.458794i
$534$		−	214185.i		−	0.751114i
$535$	−317526.	−	48461.2i	−1.10936	−	0.169312i
$536$	41535.8			0.144575
$537$	97857.4	−	97857.4i	0.339348	−	0.339348i
$538$	−136878.	−	136878.i	−0.472898	−	0.472898i
$539$		−	20178.7i		−	0.0694570i
$540$	33527.1	−	219675.i	0.114976	−	0.753345i
$541$	−21605.5			−0.0738193			−0.0369096	−	0.999319i	$-0.511751\pi$
$541$	−21605.5			−0.0738193			−0.0369096	+	0.999319i	$0.511751\pi$
$542$	−123723.	+	123723.i	−0.421163	+	0.421163i
$543$	−191968.	−	191968.i	−0.651074	−	0.651074i
$544$		−	32255.4i		−	0.108995i
$545$	−282714.	+	207844.i	−0.951819	+	0.699754i
$546$	−94929.8			−0.318432
$547$	−225012.	+	225012.i	−0.752023	+	0.752023i	−0.974857	−	0.222833i	$-0.928469\pi$
$547$	−225012.	+	225012.i	−0.752023	+	0.752023i	0.222833	+	0.974857i	$0.428469\pi$
$548$	254999.	+	254999.i	0.849137	+	0.849137i
$549$		−	122840.i		−	0.407565i
$550$	89025.7	+	169966.i	0.294300	+	0.561873i
$551$	15597.5			0.0513749
$552$	117697.	−	117697.i	0.386268	−	0.386268i
$553$	−134376.	−	134376.i	−0.439413	−	0.439413i
$554$		−	329813.i		−	1.07460i
$555$	−79424.7	−	108035.i	−0.257851	−	0.350735i
$556$	−208987.			−0.676036
$557$	360189.	−	360189.i	1.16097	−	1.16097i	0.176705	−	0.984264i	$-0.443456\pi$
$557$	360189.	−	360189.i	1.16097	−	1.16097i	0.984264	−	0.176705i	$-0.0565438\pi$
$558$	84851.6	+	84851.6i	0.272516	+	0.272516i
$559$		−	391253.i		−	1.25209i
$560$	−141689.	−	21624.8i	−0.451815	−	0.0689566i
$561$	−11940.4			−0.0379395
$562$	−39146.6	+	39146.6i	−0.123943	+	0.123943i
$563$	−115815.	−	115815.i	−0.365383	−	0.365383i	0.500407	−	0.865790i	$-0.333184\pi$
$563$	−115815.	−	115815.i	−0.365383	−	0.365383i	−0.865790	+	0.500407i	$0.833184\pi$
$564$		−	87859.4i		−	0.276204i
$565$	15149.8	−	99264.2i	0.0474582	−	0.310954i
$566$	−162093.			−0.505978
$567$	55687.9	−	55687.9i	0.173219	−	0.173219i
$568$	−45927.9	−	45927.9i	−0.142357	−	0.142357i
$569$			190399.i			0.588085i	0.955792	+	0.294043i	$0.0950008\pi$
$569$			190399.i			0.588085i	−0.955792	+	0.294043i	$0.904999\pi$
$570$	375215.	−	275848.i	1.15486	−	0.849026i
$571$	−148108.			−0.454262			−0.227131	−	0.973864i	$-0.572935\pi$
$571$	−148108.			−0.454262			−0.227131	+	0.973864i	$0.572935\pi$
$572$	59916.0	−	59916.0i	0.183126	−	0.183126i
$573$	97964.2	+	97964.2i	0.298372	+	0.298372i
$574$		−	138901.i		−	0.421581i
$575$	−483450.	+	253223.i	−1.46223	+	0.765893i
$576$	−31244.7			−0.0941740
$577$	259813.	−	259813.i	0.780384	−	0.780384i	−0.199511	−	0.979896i	$-0.563935\pi$
$577$	259813.	−	259813.i	0.780384	−	0.780384i	0.979896	+	0.199511i	$0.0639355\pi$
$578$	305592.	+	305592.i	0.914716	+	0.914716i
$579$		−	312045.i		−	0.930807i
$580$	−5565.30	−	7570.03i	−0.0165437	−	0.0225031i
$581$	−37260.4			−0.110381
$582$	123649.	−	123649.i	0.365043	−	0.365043i
$583$	123639.	+	123639.i	0.363764	+	0.363764i
$584$			246315.i			0.722213i
$585$	−70808.5	−	10806.9i	−0.206906	−	0.0315783i
$586$	−139026.			−0.404857
$587$	−3256.15	+	3256.15i	−0.00944991	+	0.00944991i	−0.711816	−	0.702366i	$-0.752127\pi$
$587$	−3256.15	+	3256.15i	−0.00944991	+	0.00944991i	0.702366	+	0.711816i	$0.252127\pi$
$588$	20861.8	+	20861.8i	0.0603387	+	0.0603387i
$589$			479765.i			1.38292i
$590$	75835.6	−	496887.i	0.217856	−	1.42743i
$591$	−562121.			−1.60937
$592$	−153291.	+	153291.i	−0.437395	+	0.437395i
$593$	270954.	+	270954.i	0.770524	+	0.770524i	0.978198	−	0.207674i	$-0.0665893\pi$
$593$	270954.	+	270954.i	0.770524	+	0.770524i	−0.207674	+	0.978198i	$0.566589\pi$
$594$			242978.i			0.688643i
$595$	−9885.69	+	7267.71i	−0.0279237	+	0.0205288i
$596$	161844.			0.455622
$597$	118158.	−	118158.i	0.331525	−	0.331525i
$598$	413225.	+	413225.i	1.15554	+	1.15554i
$599$		−	22355.2i		−	0.0623053i	−0.999515	−	0.0311526i	$-0.990082\pi$
$599$		−	22355.2i		−	0.0623053i	0.999515	−	0.0311526i	$-0.00991780\pi$
$600$	113713.	+	35537.8i	0.315869	+	0.0987161i
$601$	−599464.			−1.65964			−0.829820	−	0.558031i	$-0.811557\pi$
$601$	−599464.			−1.65964			−0.829820	+	0.558031i	$0.811557\pi$
$602$	−208478.	+	208478.i	−0.575265	+	0.575265i
$603$	−26363.3	−	26363.3i	−0.0725046	−	0.0725046i
$604$			29789.5i			0.0816561i
$605$	165556.	+	225193.i	0.452308	+	0.615239i
$606$	602321.			1.64015
$607$	221901.	−	221901.i	0.602258	−	0.602258i	−0.338653	−	0.940911i	$-0.609971\pi$
$607$	221901.	−	221901.i	0.602258	−	0.602258i	0.940911	+	0.338653i	$0.109971\pi$
$608$	−401152.	−	401152.i	−1.08518	−	1.08518i
$609$		−	4746.81i		−	0.0127987i
$610$	−709123.	−	108227.i	−1.90573	−	0.290855i
$611$	−131001.			−0.350906
$612$	−4701.35	+	4701.35i	−0.0125522	+	0.0125522i
$613$	−56020.3	−	56020.3i	−0.149082	−	0.149082i	0.628626	−	0.777708i	$-0.283618\pi$
$613$	−56020.3	−	56020.3i	−0.149082	−	0.149082i	−0.777708	+	0.628626i	$0.783618\pi$
$614$			395221.i			1.04834i
$615$	−41519.8	+	272044.i	−0.109775	+	0.719266i
$616$	27117.0			0.0714628
$617$	−376138.	+	376138.i	−0.988045	+	0.988045i	−0.999929	−	0.0118843i	$-0.996217\pi$
$617$	−376138.	+	376138.i	−0.988045	+	0.988045i	0.0118843	+	0.999929i	$0.496217\pi$
$618$	−139108.	−	139108.i	−0.364229	−	0.364229i
$619$		−	133682.i		−	0.348891i	−0.984667	−	0.174446i	$-0.944187\pi$
$619$		−	133682.i		−	0.348891i	0.984667	−	0.174446i	$-0.0558134\pi$
$620$	232848.	−	171184.i	0.605743	−	0.445327i
$621$	−691123.			−1.79214
$622$	521103.	−	521103.i	1.34692	−	1.34692i
$623$	70181.4	+	70181.4i	0.180820	+	0.180820i
$624$		−	304072.i		−	0.780922i
$625$	−321110.	−	222433.i	−0.822041	−	0.569428i
$626$	−446042.			−1.13822
$627$	−148499.	+	148499.i	−0.377736	+	0.377736i
$628$	213200.	+	213200.i	0.540590	+	0.540590i
$629$			18558.0i			0.0469061i
$630$	31971.7	+	43488.6i	0.0805536	+	0.109571i
$631$	74938.8			0.188212			0.0941061	−	0.995562i	$-0.470001\pi$
$631$	74938.8			0.188212			0.0941061	+	0.995562i	$0.470001\pi$
$632$	180581.	−	180581.i	0.452103	−	0.452103i
$633$	235058.	+	235058.i	0.586636	+	0.586636i
$634$		−	310123.i		−	0.771534i
$635$	776805.	+	118557.i	1.92648	+	0.294022i
$636$	−255649.			−0.632019
$637$	31105.4	−	31105.4i	0.0766580	−	0.0766580i
$638$	7264.36	+	7264.36i	0.0178466	+	0.0178466i
$639$			58302.2i			0.142785i
$640$	45928.6	−	300932.i	0.112130	−	0.734697i
$641$	772221.			1.87943			0.939714	−	0.341961i	$-0.111091\pi$
$641$	772221.			1.87943			0.939714	+	0.341961i	$0.111091\pi$
$642$	−363097.	+	363097.i	−0.880953	+	0.880953i
$643$	−397464.	−	397464.i	−0.961336	−	0.961336i	0.0379437	−	0.999280i	$-0.487919\pi$
$643$	−397464.	−	397464.i	−0.961336	−	0.961336i	−0.999280	+	0.0379437i	$0.987919\pi$
$644$		−	181620.i		−	0.437918i
$645$	470633.	−	345998.i	1.13126	−	0.831675i
$646$	−64453.5			−0.154448
$647$	289594.	−	289594.i	0.691800	−	0.691800i	−0.270828	−	0.962628i	$-0.587297\pi$
$647$	289594.	−	289594.i	0.691800	−	0.691800i	0.962628	+	0.270828i	$0.0872974\pi$
$648$	74835.8	+	74835.8i	0.178221	+	0.178221i
$649$			226667.i			0.538145i
$650$	−124770.	+	399236.i	−0.295314	+	0.944937i
$651$	146008.			0.344519
$652$	−293248.	+	293248.i	−0.689827	+	0.689827i
$653$	98311.6	+	98311.6i	0.230557	+	0.230557i	0.812925	−	0.582368i	$-0.197874\pi$
$653$	98311.6	+	98311.6i	0.230557	+	0.230557i	−0.582368	+	0.812925i	$0.697874\pi$
$654$			560963.i			1.31153i
$655$	323583.	+	440144.i	0.754229	+	1.02592i
$656$	444917.			1.03388
$657$	156340.	−	156340.i	0.362191	−	0.362191i
$658$	69803.5	+	69803.5i	0.161222	+	0.161222i
$659$		−	462521.i		−	1.06503i	−0.846422	−	0.532513i	$-0.821248\pi$
$659$		−	462521.i		−	1.06503i	0.846422	−	0.532513i	$-0.178752\pi$
$660$	125058.	+	19086.5i	0.287093	+	0.0438165i
$661$	751.874			0.00172085			0.000860423	−	1.00000i	$-0.499726\pi$
$661$	751.874			0.00172085			0.000860423		1.00000i	$0.499726\pi$
$662$	509307.	−	509307.i	1.16215	−	1.16215i
$663$	−18406.0	−	18406.0i	−0.0418729	−	0.0418729i
$664$		−	50072.0i		−	0.113569i
$665$	−32559.1	+	213332.i	−0.0736256	+	0.482407i
$666$	81639.3			0.184056
$667$	−20662.6	+	20662.6i	−0.0464445	+	0.0464445i
$668$	535.743	+	535.743i	0.00120061	+	0.00120061i
$669$			163558.i			0.365442i
$670$	−175415.	+	128961.i	−0.390766	+	0.287282i
$671$	323484.			0.718468
$672$	−122083.	+	122083.i	−0.270345	+	0.270345i
$673$	47103.9	+	47103.9i	0.103999	+	0.103999i	0.757191	−	0.653193i	$-0.226571\pi$
$673$	47103.9	+	47103.9i	0.103999	+	0.103999i	−0.653193	+	0.757191i	$0.726571\pi$
$674$		−	204978.i		−	0.451220i
$675$	−229524.	−	438203.i	−0.503755	−	0.961763i
$676$	−136035.			−0.297686
$677$	−261543.	+	261543.i	−0.570645	+	0.570645i	−0.932309	−	0.361663i	$-0.882209\pi$
$677$	−261543.	+	261543.i	−0.570645	+	0.570645i	0.361663	+	0.932309i	$0.382209\pi$
$678$	−113511.	−	113511.i	−0.246932	−	0.246932i
$679$			81031.4i			0.175757i
$680$	−9766.66	−	13284.8i	−0.0211217	−	0.0287301i
$681$	−339557.			−0.732180
$682$	−223445.	+	223445.i	−0.480399	+	0.480399i
$683$	−210280.	−	210280.i	−0.450772	−	0.450772i	0.444838	−	0.895611i	$-0.353261\pi$
$683$	−210280.	−	210280.i	−0.450772	−	0.450772i	−0.895611	+	0.444838i	$0.853261\pi$
$684$			116939.i			0.249947i
$685$	793583.	+	121118.i	1.69126	+	0.258123i
$686$	−33148.9			−0.0704403
$687$	−292555.	+	292555.i	−0.619860	+	0.619860i
$688$	−667783.	−	667783.i	−1.41078	−	1.41078i
$689$			381180.i			0.802955i
$690$	−131634.	+	862490.i	−0.276485	+	1.81157i
$691$	405248.			0.848721			0.424361	−	0.905493i	$-0.360499\pi$
$691$	405248.			0.848721			0.424361	+	0.905493i	$0.360499\pi$
$692$	233538.	−	233538.i	0.487692	−	0.487692i
$693$	−17211.5	−	17211.5i	−0.0358388	−	0.0358388i
$694$			92234.5i			0.191502i
$695$	−374826.	+	275563.i	−0.775997	+	0.570494i
$696$	6378.96			0.0131684
$697$	26931.6	−	26931.6i	0.0554367	−	0.0554367i
$698$	−169070.	−	169070.i	−0.347021	−	0.347021i
$699$			466599.i			0.954969i
$700$	115155.	−	60316.5i	0.235011	−	0.123095i
$701$	776018.			1.57920			0.789598	−	0.613625i	$-0.210289\pi$
$701$	776018.			1.57920			0.789598	+	0.613625i	$0.210289\pi$
$702$	−374550.	+	374550.i	−0.760039	+	0.760039i
$703$	230801.	+	230801.i	0.467011	+	0.467011i
$704$		−	82278.6i		−	0.166013i
$705$	−115848.	−	157579.i	−0.233083	−	0.317044i
$706$	374358.			0.751065
$707$	−197361.	+	197361.i	−0.394841	+	0.394841i
$708$	−234340.	−	234340.i	−0.467498	−	0.467498i
$709$			411451.i			0.818513i	0.912419	+	0.409257i	$0.134212\pi$
$709$			411451.i			0.818513i	−0.912419	+	0.409257i	$0.865788\pi$
$710$	336562.	+	51366.5i	0.667649	+	0.101897i
$711$	−229234.			−0.453461
$712$	−94312.7	+	94312.7i	−0.186042	+	0.186042i
$713$	−635564.	−	635564.i	−1.25020	−	1.25020i
$714$			19615.2i			0.0384766i
$715$	28458.5	−	186464.i	0.0556672	−	0.364741i
$716$	202927.			0.395835
$717$	72682.2	−	72682.2i	0.141380	−	0.141380i
$718$	−147034.	−	147034.i	−0.285212	−	0.285212i
$719$		−	471072.i		−	0.911233i	−0.890176	−	0.455617i	$-0.849419\pi$
$719$		−	471072.i		−	0.911233i	0.890176	−	0.455617i	$-0.150581\pi$
$720$	−139300.	+	102410.i	−0.268710	+	0.197549i
$721$	91162.2			0.175366
$722$	−320721.	+	320721.i	−0.615252	+	0.615252i
$723$	304373.	+	304373.i	0.582277	+	0.582277i
$724$		−	398086.i		−	0.759450i
$725$	−19963.1	−	6238.92i	−0.0379798	−	0.0118695i
$726$	446829.			0.847750
$727$	−179969.	+	179969.i	−0.340510	+	0.340510i	−0.856559	−	0.516049i	$-0.827402\pi$
$727$	−179969.	+	179969.i	−0.340510	+	0.340510i	0.516049	+	0.856559i	$0.327402\pi$
$728$	41800.8	+	41800.8i	0.0788718	+	0.0788718i
$729$		−	586014.i		−	1.10269i
$730$	−764762.	−	1.04024e6i	−1.43510	−	1.95205i
$731$	−80844.2			−0.151291
$732$	−334433.	+	334433.i	−0.624148	+	0.624148i
$733$	−96617.9	−	96617.9i	−0.179825	−	0.179825i	0.611455	−	0.791279i	$-0.290585\pi$
$733$	−96617.9	−	96617.9i	−0.179825	−	0.179825i	−0.791279	+	0.611455i	$0.790585\pi$
$734$			538703.i			0.999902i
$735$	64923.8	+	9908.76i	0.120179	+	0.0183419i
$736$	1.06285e6			1.96207
$737$	69424.2	−	69424.2i	0.127813	−	0.127813i
$738$	−118476.	−	118476.i	−0.217530	−	0.217530i
$739$		−	571596.i		−	1.04665i	−0.852134	−	0.523324i	$-0.824692\pi$
$739$		−	571596.i		−	1.04665i	0.852134	−	0.523324i	$-0.175308\pi$
$740$	29664.7	−	194368.i	0.0541722	−	0.354945i
$741$	−457822.			−0.833797
$742$	203111.	−	203111.i	0.368914	−	0.368914i
$743$	−647230.	−	647230.i	−1.17241	−	1.17241i	−0.981632	−	0.190782i	$-0.938898\pi$
$743$	−647230.	−	647230.i	−1.17241	−	1.17241i	−0.190782	−	0.981632i	$-0.561102\pi$
$744$			196211.i			0.354469i
$745$	290274.	−	213402.i	0.522992	−	0.384491i
$746$	−933144.			−1.67676
$747$	−31781.4	+	31781.4i	−0.0569550	+	0.0569550i
$748$	−12380.4	−	12380.4i	−0.0221274	−	0.0221274i
$749$		−	237950.i		−	0.424153i
$750$	−590573.	+	202973.i	−1.04991	+	0.360841i
$751$	716592.			1.27055			0.635275	−	0.772286i	$-0.280887\pi$
$751$	716592.			1.27055			0.635275	+	0.772286i	$0.280887\pi$
$752$	−223589.	+	223589.i	−0.395381	+	0.395381i
$753$	−280303.	−	280303.i	−0.494354	−	0.494354i
$754$			22396.0i			0.0393937i
$755$	39279.3	+	53428.5i	0.0689080	+	0.0937300i
$756$	164622.			0.288035
$757$	38892.4	−	38892.4i	0.0678693	−	0.0678693i	−0.672357	−	0.740227i	$-0.734718\pi$
$757$	38892.4	−	38892.4i	0.0678693	−	0.0678693i	0.740227	+	0.672357i	$0.234718\pi$
$758$	554584.	+	554584.i	0.965226	+	0.965226i
$759$		−	393446.i		−	0.682970i
$760$	−286685.	−	43754.2i	−0.496338	−	0.0757518i
$761$	−673905.			−1.16367			−0.581835	−	0.813307i	$-0.697665\pi$
$761$	−673905.			−1.16367			−0.581835	+	0.813307i	$0.697665\pi$
$762$	888291.	−	888291.i	1.52984	−	1.52984i
$763$	−183810.	−	183810.i	−0.315732	−	0.315732i
$764$			203149.i			0.348039i
$765$	−2233.01	+	14631.1i	−0.00381565	+	0.0250008i
$766$	−358037.			−0.610198
$767$	−349407.	+	349407.i	−0.593938	+	0.593938i
$768$	−465310.	−	465310.i	−0.788897	−	0.788897i
$769$		−	182164.i		−	0.308043i	−0.988068	−	0.154021i	$-0.950778\pi$
$769$		−	182164.i		−	0.308043i	0.988068	−	0.154021i	$-0.0492225\pi$
$770$	−114521.	+	84193.2i	−0.193154	+	0.142002i
$771$	383709.			0.645496
$772$	323544.	−	323544.i	0.542873	−	0.542873i
$773$	618979.	+	618979.i	1.03590	+	1.03590i	0.999331	+	0.0365671i	$0.0116423\pi$
$773$	618979.	+	618979.i	1.03590	+	1.03590i	0.0365671	+	0.999331i	$0.488358\pi$
$774$			355645.i			0.593657i
$775$	191904.	−	614048.i	0.319507	−	1.02235i
$776$	−108893.			−0.180833
$777$	70240.1	−	70240.1i	0.116344	−	0.116344i
$778$	772393.	+	772393.i	1.27608	+	1.27608i
$779$		−	669884.i		−	1.10389i
$780$	163354.	+	222198.i	0.268499	+	0.365217i
$781$	−153531.			−0.251706
$782$	85384.2	−	85384.2i	0.139625	−	0.139625i
$783$	−18728.8	−	18728.8i	−0.0305482	−	0.0305482i
$784$		−	106180.i		−	0.172747i
$785$	663500.	+	101264.i	1.07672	+	0.164330i
$786$	873336.			1.41363
$787$	41089.9	−	41089.9i	0.0663415	−	0.0663415i	−0.673158	−	0.739499i	$-0.735062\pi$
$787$	41089.9	−	41089.9i	0.0663415	−	0.0663415i	0.739499	+	0.673158i	$0.235062\pi$
$788$	−582836.	−	582836.i	−0.938629	−	0.938629i
$789$		−	362370.i		−	0.582101i
$790$	−201964.	+	1.32330e6i	−0.323609	+	2.12034i
$791$	74387.5			0.118890
$792$	23129.6	−	23129.6i	0.0368738	−	0.0368738i
$793$	498649.	+	498649.i	0.792955	+	0.792955i
$794$		−	192974.i		−	0.306096i
$795$	−458516.	+	337090.i	−0.725471	+	0.533348i
$796$	245025.			0.386710
$797$	−418332.	+	418332.i	−0.658574	+	0.658574i	−0.955043	−	0.296469i	$-0.904191\pi$
$797$	−418332.	+	418332.i	−0.658574	+	0.658574i	0.296469	+	0.955043i	$0.404191\pi$
$798$	243950.	+	243950.i	0.383084	+	0.383084i
$799$			27068.5i			0.0424005i
$800$	352974.	+	673892.i	0.551521	+	1.05296i
$801$	119723.			0.186601
$802$	−114349.	+	114349.i	−0.177781	+	0.177781i
$803$	411699.	+	411699.i	0.638482	+	0.638482i
$804$			143548.i			0.222068i
$805$	−239478.	−	325743.i	−0.369550	−	0.502670i
$806$	−688880.			−1.06041
$807$	−200897.	+	200897.i	−0.308480	+	0.308480i
$808$	−265222.	−	265222.i	−0.406244	−	0.406244i
$809$		−	717373.i		−	1.09609i	−0.836447	−	0.548047i	$-0.815371\pi$
$809$		−	717373.i		−	1.09609i	0.836447	−	0.548047i	$-0.184629\pi$
$810$	−548400.	−	83697.5i	−0.835848	−	0.127568i
$811$	1.04158e6			1.58362			0.791812	−	0.610765i	$-0.209138\pi$
$811$	1.04158e6			1.58362			0.791812	+	0.610765i	$0.209138\pi$
$812$	4921.74	−	4921.74i	0.00746459	−	0.00746459i
$813$	181589.	+	181589.i	0.274732	+	0.274732i
$814$			214986.i			0.324460i
$815$	−139285.	+	912617.i	−0.209695	+	1.37396i
$816$	−62830.1			−0.0943599
$817$	−1.00544e6	+	1.00544e6i	−1.50630	+	1.50630i
$818$	260929.	+	260929.i	0.389956	+	0.389956i
$819$		−	53063.1i		−	0.0791088i
$820$	−325119.	+	239020.i	−0.483521	+	0.355473i
$821$	−892265.			−1.32375			−0.661877	−	0.749612i	$-0.730240\pi$
$821$	−892265.			−1.32375			−0.661877	+	0.749612i	$0.730240\pi$
$822$	907477.	−	907477.i	1.34305	−	1.34305i
$823$	126260.	+	126260.i	0.186409	+	0.186409i	0.794142	−	0.607733i	$-0.207921\pi$
$823$	126260.	+	126260.i	0.186409	+	0.186409i	−0.607733	+	0.794142i	$0.707921\pi$
$824$			122508.i			0.180430i
$825$	249462.	−	130664.i	0.366519	−	0.191977i
$826$	372362.			0.545764
$827$	−298491.	+	298491.i	−0.436435	+	0.436435i	−0.890810	−	0.454375i	$-0.849863\pi$
$827$	−298491.	+	298491.i	−0.436435	+	0.436435i	0.454375	+	0.890810i	$0.349863\pi$
$828$	−154914.	−	154914.i	−0.225959	−	0.225959i
$829$		−	624542.i		−	0.908767i	−0.890806	−	0.454384i	$-0.849860\pi$
$829$		−	624542.i		−	0.908767i	0.890806	−	0.454384i	$-0.150140\pi$
$830$	155464.	+	211466.i	0.225670	+	0.306961i
$831$	−484072.			−0.700983
$832$	126832.	−	126832.i	0.183224	−	0.183224i
$833$	−6427.28	−	6427.28i	−0.00926269	−	0.00926269i
$834$			743732.i			1.06926i
$835$	1667.28	+	254.463i	0.00239131	+	0.000364966i
$836$	−307943.			−0.440614
$837$	576080.	−	576080.i	0.822303	−	0.822303i
$838$	−350282.	−	350282.i	−0.498803	−	0.498803i
$839$			778116.i			1.10540i	0.833380	+	0.552701i	$0.186403\pi$
$839$			778116.i			1.10540i	−0.833380	+	0.552701i	$0.813597\pi$
$840$	−13315.8	+	87247.4i	−0.0188716	+	0.123650i
$841$	706161.			0.998417
$842$	−410500.	+	410500.i	−0.579013	+	0.579013i
$843$	57456.0	+	57456.0i	0.0808501	+	0.0808501i
$844$			487441.i			0.684286i
$845$	−243984.	+	179371.i	−0.341703	+	0.251212i
$846$	119078.			0.166377
$847$	−146411.	+	146411.i	−0.204084	+	0.204084i
$848$	650590.	+	650590.i	0.904723	+	0.904723i
$849$			237906.i			0.330058i
$850$	82493.7	+	25781.1i	0.114178	+	0.0356832i
$851$	−611503.			−0.844383
$852$	158728.	−	158728.i	0.218662	−	0.218662i
$853$	756967.	+	756967.i	1.04035	+	1.04035i	0.999151	+	0.0411974i	$0.0131173\pi$
$853$	756967.	+	756967.i	1.04035	+	1.04035i	0.0411974	+	0.999151i	$0.486883\pi$
$854$		−	531408.i		−	0.728640i
$855$	154192.	+	209734.i	0.210925	+	0.286905i
$856$	319768.			0.436402
$857$	393557.	−	393557.i	0.535853	−	0.535853i	−0.386455	−	0.922308i	$-0.626301\pi$
$857$	393557.	−	393557.i	0.535853	−	0.535853i	0.922308	+	0.386455i	$0.126301\pi$
$858$	−213226.	−	213226.i	−0.289644	−	0.289644i
$859$			45899.9i			0.0622051i	0.999516	+	0.0311025i	$0.00990184\pi$
$859$			45899.9i			0.0622051i	−0.999516	+	0.0311025i	$0.990098\pi$
$860$	846724.	+	129228.i	1.14484	+	0.174727i
$861$	−203867.			−0.275005
$862$	911869.	−	911869.i	1.22721	−	1.22721i
$863$	101268.	+	101268.i	0.135972	+	0.135972i	0.771817	−	0.635845i	$-0.219348\pi$
$863$	101268.	+	101268.i	0.135972	+	0.135972i	−0.635845	+	0.771817i	$0.719348\pi$
$864$			963372.i			1.29053i
$865$	110924.	−	726793.i	0.148250	−	0.971357i
$866$	−19842.6			−0.0264584
$867$	448522.	−	448522.i	0.596686	−	0.596686i
$868$	151388.	+	151388.i	0.200934	+	0.200934i
$869$		−	603657.i		−	0.799375i
$870$	−26939.8	+	19805.5i	−0.0355923	+	0.0261666i
$871$	214034.			0.282129
$872$	247011.	−	247011.i	0.324850	−	0.324850i
$873$	69116.2	+	69116.2i	0.0906883	+	0.0906883i
$874$		−	2.12380e6i		−	2.78030i
$875$	127004.	−	260020.i	0.165883	−	0.339617i
$876$	−851270.			−1.10933
$877$	−44909.1	+	44909.1i	−0.0583895	+	0.0583895i	−0.735699	−	0.677309i	$-0.763146\pi$
$877$	−44909.1	+	44909.1i	−0.0583895	+	0.0583895i	0.677309	+	0.735699i	$0.263146\pi$
$878$	−1.19620e6	−	1.19620e6i	−1.55172	−	1.55172i
$879$			204051.i			0.264095i
$880$	−269682.	−	366826.i	−0.348246	−	0.473691i
$881$	−954666.			−1.22998			−0.614992	−	0.788533i	$-0.710841\pi$
$881$	−954666.			−1.22998			−0.614992	+	0.788533i	$0.710841\pi$
$882$	−28274.6	+	28274.6i	−0.0363462	+	0.0363462i
$883$	−708672.	−	708672.i	−0.908916	−	0.908916i	0.0872691	−	0.996185i	$-0.472186\pi$
$883$	−708672.	−	708672.i	−0.908916	−	0.908916i	−0.996185	+	0.0872691i	$0.972186\pi$
$884$		−	38168.6i		−	0.0488430i
$885$	−729289.	−	111305.i	−0.931136	−	0.142111i
$886$	−1.33231e6			−1.69722
$887$	20953.6	−	20953.6i	0.0266325	−	0.0266325i	−0.693665	−	0.720298i	$-0.744005\pi$
$887$	20953.6	−	20953.6i	0.0266325	−	0.0266325i	0.720298	+	0.693665i	$0.244005\pi$
$888$	94391.6	+	94391.6i	0.119704	+	0.119704i
$889$			582129.i			0.736572i
$890$	105481.	−	691128.i	0.133166	−	0.872526i
$891$	250166.			0.315118
$892$	−169585.	+	169585.i	−0.213137	+	0.213137i
$893$	336644.	+	336644.i	0.422152	+	0.422152i
$894$		−	575963.i		−	0.720641i
$895$	363957.	−	267572.i	0.454364	−	0.334037i
$896$	225515.			0.280905
$897$	606496.	−	606496.i	0.753777	−	0.753777i
$898$	362211.	+	362211.i	0.449168	+	0.449168i
$899$		−	34446.3i		−	0.0426210i
$900$	46775.1	−	149670.i	0.0577471	−	0.184777i
$901$	78762.8			0.0970222
$902$	311991.	−	311991.i	0.383468	−	0.383468i
$903$	305987.	+	305987.i	0.375256	+	0.375256i
$904$			99965.1i			0.122324i
$905$	−524901.	−	713981.i	−0.640885	−	0.871745i
$906$	106013.			0.129153
$907$	−388490.	+	388490.i	−0.472242	+	0.472242i	−0.902640	−	0.430397i	$-0.858374\pi$
$907$	−388490.	+	388490.i	−0.472242	+	0.472242i	0.430397	+	0.902640i	$0.358374\pi$
$908$	−352070.	−	352070.i	−0.427029	−	0.427029i
$909$			336680.i			0.407465i
$910$	−306318.	−	46750.6i	−0.369904	−	0.0564553i
$911$	−511824.			−0.616714			−0.308357	−	0.951271i	$-0.599779\pi$
$911$	−511824.			−0.616714			−0.308357	+	0.951271i	$0.599779\pi$
$912$	−781402.	+	781402.i	−0.939474	+	0.939474i
$913$	−83692.0	−	83692.0i	−0.100402	−	0.100402i
$914$			64783.9i			0.0775487i
$915$	−158847.	+	1.04079e6i	−0.189730	+	1.24314i
$916$	−606672.			−0.723041
$917$	−286164.	+	286164.i	−0.340311	+	0.340311i
$918$	77392.9	+	77392.9i	0.0918366	+	0.0918366i
$919$		−	96227.2i		−	0.113938i	−0.998376	−	0.0569688i	$-0.981856\pi$
$919$		−	96227.2i		−	0.113938i	0.998376	−	0.0569688i	$-0.0181436\pi$
$920$	437747.	−	321821.i	0.517187	−	0.380223i
$921$	580072.			0.683853
$922$	703202.	−	703202.i	0.827215	−	0.827215i
$923$	−236667.	−	236667.i	−0.277802	−	0.277802i
$924$			93716.9i			0.109768i
$925$	−203082.	−	387720.i	−0.237349	−	0.453143i
$926$	−714490.			−0.833248
$927$	77757.3	−	77757.3i	0.0904861	−	0.0904861i
$928$	28802.1	+	28802.1i	0.0334448	+	0.0334448i
$929$			600335.i			0.695604i	0.937568	+	0.347802i	$0.113072\pi$
$929$			600335.i			0.695604i	−0.937568	+	0.347802i	$0.886928\pi$
$930$	−609199.	−	828645.i	−0.704358	−	0.958082i
$931$	−159869.			−0.184444
$932$	−483794.	+	483794.i	−0.556966	+	0.556966i
$933$	−764831.	−	764831.i	−0.878622	−	0.878622i
$934$			987965.i			1.13253i
$935$	−38529.0	−	5880.34i	−0.0440721	−	0.00672635i
$936$	71308.4			0.0813933
$937$	−641234.	+	641234.i	−0.730360	+	0.730360i	−0.970691	−	0.240331i	$-0.922744\pi$
$937$	−641234.	+	641234.i	−0.730360	+	0.730360i	0.240331	+	0.970691i	$0.422744\pi$
$938$	−114048.	−	114048.i	−0.129623	−	0.129623i
$939$			654663.i			0.742483i
$940$	43268.6	−	283503.i	0.0489686	−	0.320850i
$941$	1.07984e6			1.21950			0.609749	−	0.792595i	$-0.291270\pi$
$941$	1.07984e6			1.21950			0.609749	+	0.792595i	$0.291270\pi$
$942$	758725.	−	758725.i	0.855032	−	0.855032i
$943$	887423.	+	887423.i	0.997947	+	0.997947i
$944$			1.19272e6i			1.33843i
$945$	295256.	−	217065.i	0.330624	−	0.243067i
$946$	−936544.			−1.04652
$947$	24749.7	−	24749.7i	0.0275975	−	0.0275975i	−0.693173	−	0.720771i	$-0.743788\pi$
$947$	24749.7	−	24749.7i	0.0275975	−	0.0275975i	0.720771	+	0.693173i	$0.243788\pi$
$948$	624091.	+	624091.i	0.694434	+	0.694434i
$949$			1.26927e6i			1.40935i
$950$	1.34659e6	−	705319.i	1.49206	−	0.781517i
$951$	−455172.			−0.503286
$952$	8637.25	−	8637.25i	0.00953019	−	0.00953019i
$953$	289360.	+	289360.i	0.318605	+	0.318605i	0.848231	−	0.529626i	$-0.177668\pi$
$953$	289360.	+	289360.i	0.318605	+	0.318605i	−0.529626	+	0.848231i	$0.677668\pi$
$954$		−	346489.i		−	0.380709i
$955$	267864.	+	364354.i	0.293703	+	0.399501i
$956$	150721.			0.164914
$957$	10662.0	−	10662.0i	0.0116417	−	0.0116417i
$958$	−73473.7	−	73473.7i	−0.0800573	−	0.0800573i
$959$			594702.i			0.646640i
$960$	264727.	+	40402.9i	0.287247	+	0.0438400i
$961$	136018.			0.147282
$962$	−331401.	+	331401.i	−0.358099	+	0.358099i
$963$	−202961.	−	202961.i	−0.218857	−	0.218857i
$964$			631180.i			0.679202i
$965$	153674.	−	1.00690e6i	0.165024	−	1.08126i
$966$	−646341.			−0.692639
$967$	−254563.	+	254563.i	−0.272234	+	0.272234i	−0.829999	−	0.557765i	$-0.811659\pi$
$967$	−254563.	+	254563.i	−0.272234	+	0.272234i	0.557765	+	0.829999i	$0.311659\pi$
$968$	−196754.	−	196754.i	−0.209977	−	0.209977i
$969$			94599.3i			0.100749i
$970$	459882.	−	338094.i	0.488768	−	0.359330i
$971$	861405.			0.913627			0.456813	−	0.889563i	$-0.348991\pi$
$971$	861405.			0.913627			0.456813	+	0.889563i	$0.348991\pi$
$972$	250475.	−	250475.i	0.265114	−	0.265114i
$973$	−243697.	−	243697.i	−0.257409	−	0.257409i
$974$		−	315998.i		−	0.333093i
$975$	585964.	+	183127.i	0.616399	+	0.192638i
$976$	1.70217e6			1.78691
$977$	37416.1	−	37416.1i	0.0391984	−	0.0391984i	−0.687236	−	0.726434i	$-0.741176\pi$
$977$	37416.1	−	37416.1i	0.0391984	−	0.0391984i	0.726434	+	0.687236i	$0.241176\pi$
$978$	1.04359e6	+	1.04359e6i	1.09107	+	1.09107i
$979$			315275.i			0.328945i
$980$	57042.5	+	77590.3i	0.0593945	+	0.0807895i
$981$	−313563.			−0.325826
$982$	−776151.	+	776151.i	−0.804865	+	0.804865i
$983$	−194549.	−	194549.i	−0.201336	−	0.201336i	0.599236	−	0.800572i	$-0.295471\pi$
$983$	−194549.	−	194549.i	−0.201336	−	0.201336i	−0.800572	+	0.599236i	$0.795471\pi$
$984$		−	273965.i		−	0.282947i
$985$	−1.81384e6	−	276831.i	−1.86951	−	0.285327i
$986$	4627.66			0.00476000
$987$	102452.	−	102452.i	0.105168	−	0.105168i
$988$	−474694.	−	474694.i	−0.486295	−	0.486295i
$989$		−	2.66389e6i		−	2.72348i
$990$	−25868.5	+	169495.i	−0.0263937	+	0.172936i
$991$	814684.			0.829548			0.414774	−	0.909924i	$-0.363861\pi$
$991$	814684.			0.829548			0.414774	+	0.909924i	$0.363861\pi$
$992$	−885927.	+	885927.i	−0.900274	+	0.900274i
$993$	−747517.	−	747517.i	−0.758094	−	0.758094i
$994$			252216.i			0.255270i
$995$	439462.	−	323081.i	0.443890	−	0.326337i
$996$	173050.			0.174443
$997$	−1.24250e6	+	1.24250e6i	−1.24999	+	1.24999i	−0.294266	+	0.955724i	$0.595075\pi$
$997$	−1.24250e6	+	1.24250e6i	−1.24999	+	1.24999i	−0.955724	+	0.294266i	$0.904925\pi$
$998$	1.46728e6	+	1.46728e6i	1.47317	+	1.47317i
$999$		−	554271.i		−	0.555382i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.g.a.8.10	✓	24
5.2	odd	4	inner	35.5.g.a.22.10	yes	24
5.3	odd	4		175.5.g.c.57.3		24
5.4	even	2		175.5.g.c.43.3		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.g.a.8.10	✓	24	1.1	even	1	trivial
35.5.g.a.22.10	yes	24	5.2	odd	4	inner
175.5.g.c.43.3		24	5.4	even	2
175.5.g.c.57.3		24	5.3	odd	4

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.g (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.68989 - 3.68989i) q^{2} +(-5.41571 - 5.41571i) q^{3} -11.2306i q^{4} +(-14.8082 - 20.1424i) q^{5} -39.9667 q^{6} +(13.0958 - 13.0958i) q^{7} +(17.5987 + 17.5987i) q^{8} -22.3403i q^{9} +O(q^{10})\)	\(q+(3.68989 - 3.68989i) q^{2} +(-5.41571 - 5.41571i) q^{3} -11.2306i q^{4} +(-14.8082 - 20.1424i) q^{5} -39.9667 q^{6} +(13.0958 - 13.0958i) q^{7} +(17.5987 + 17.5987i) q^{8} -22.3403i q^{9} +(-128.964 - 19.6826i) q^{10} +58.8300 q^{11} +(-60.8214 + 60.8214i) q^{12} +(90.6864 + 90.6864i) q^{13} -96.6441i q^{14} +(-28.8885 + 189.282i) q^{15} +309.563 q^{16} +(18.7384 - 18.7384i) q^{17} +(-82.4331 - 82.4331i) q^{18} -466.090i q^{19} +(-226.211 + 166.305i) q^{20} -141.846 q^{21} +(217.076 - 217.076i) q^{22} +(617.449 + 617.449i) q^{23} -190.619i q^{24} +(-186.434 + 596.546i) q^{25} +669.245 q^{26} +(-559.660 + 559.660i) q^{27} +(-147.073 - 147.073i) q^{28} +33.4645i q^{29} +(591.835 + 805.026i) q^{30} -1029.34 q^{31} +(860.676 - 860.676i) q^{32} +(-318.606 - 318.606i) q^{33} -138.285i q^{34} +(-457.706 - 69.8558i) q^{35} -250.894 q^{36} +(-495.185 + 495.185i) q^{37} +(-1719.82 - 1719.82i) q^{38} -982.261i q^{39} +(93.8751 - 615.085i) q^{40} +1437.24 q^{41} +(-523.396 + 523.396i) q^{42} +(-2157.18 - 2157.18i) q^{43} -660.695i q^{44} +(-449.987 + 330.819i) q^{45} +4556.64 q^{46} +(-722.273 + 722.273i) q^{47} +(-1676.50 - 1676.50i) q^{48} -343.000i q^{49} +(1513.27 + 2889.11i) q^{50} -202.964 q^{51} +(1018.46 - 1018.46i) q^{52} +(2101.64 + 2101.64i) q^{53} +4130.17i q^{54} +(-871.167 - 1184.98i) q^{55} +460.938 q^{56} +(-2524.21 + 2524.21i) q^{57} +(123.480 + 123.480i) q^{58} +3852.92i q^{59} +(2125.75 + 324.434i) q^{60} +5498.61 q^{61} +(-3798.15 + 3798.15i) q^{62} +(-292.564 - 292.564i) q^{63} -1398.58i q^{64} +(483.740 - 3169.55i) q^{65} -2351.24 q^{66} +(1180.08 - 1180.08i) q^{67} +(-210.443 - 210.443i) q^{68} -6687.84i q^{69} +(-1946.65 + 1431.13i) q^{70} -2609.74 q^{71} +(393.159 - 393.159i) q^{72} +(6998.11 + 6998.11i) q^{73} +3654.36i q^{74} +(4240.39 - 2221.05i) q^{75} -5234.45 q^{76} +(770.426 - 770.426i) q^{77} +(-3624.44 - 3624.44i) q^{78} -10261.0i q^{79} +(-4584.08 - 6235.36i) q^{80} +4252.35 q^{81} +(5303.26 - 5303.26i) q^{82} +(-1422.61 - 1422.61i) q^{83} +1593.01i q^{84} +(-654.920 - 99.9547i) q^{85} -15919.5 q^{86} +(181.234 - 181.234i) q^{87} +(1035.33 + 1035.33i) q^{88} +5359.08i q^{89} +(-439.716 + 2881.09i) q^{90} +2375.22 q^{91} +(6934.30 - 6934.30i) q^{92} +(5574.60 + 5574.60i) q^{93} +5330.22i q^{94} +(-9388.18 + 6901.96i) q^{95} -9322.33 q^{96} +(-3093.79 + 3093.79i) q^{97} +(-1265.63 - 1265.63i) q^{98} -1314.28i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6}+O(q^{10}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6	\( 24 q + 20 q^{3} - 48 q^{5} + 72 q^{6} - 112 q^{10} + 156 q^{11} - 80 q^{12} - 560 q^{13} + 896 q^{15} - 1480 q^{16} + 1320 q^{17} + 340 q^{18} + 180 q^{20} + 196 q^{21} - 2020 q^{22} + 1920 q^{23} - 676 q^{25} + 2208 q^{26} - 340 q^{27} - 5356 q^{30} - 2112 q^{31} - 1200 q^{32} - 6140 q^{33} + 3904 q^{36} + 3980 q^{37} + 9120 q^{38} + 14716 q^{40} + 6384 q^{41} + 4900 q^{42} - 12220 q^{43} - 10528 q^{45} - 8080 q^{46} - 11820 q^{47} - 4040 q^{48} + 10728 q^{50} - 5900 q^{51} + 3600 q^{52} + 24240 q^{53} + 4636 q^{55} - 10584 q^{56} + 6460 q^{57} + 6100 q^{58} - 30088 q^{60} + 440 q^{61} - 16680 q^{62} + 7840 q^{63} - 14652 q^{65} + 4832 q^{66} - 5940 q^{67} - 47040 q^{68} - 6272 q^{70} + 8928 q^{71} + 46720 q^{72} - 2500 q^{73} + 60708 q^{75} + 47816 q^{76} + 5880 q^{77} - 17940 q^{78} + 16140 q^{80} - 11360 q^{81} - 32120 q^{82} + 15120 q^{83} + 18816 q^{85} - 41208 q^{86} - 25460 q^{87} + 52920 q^{88} - 55680 q^{90} - 11172 q^{91} + 19800 q^{92} + 1460 q^{93} - 35508 q^{95} + 20568 q^{96} - 33840 q^{97}+O(q^{100}) \) 24 * q + 20 * q^3 - 48 * q^5 + 72 * q^6 - 112 * q^10 + 156 * q^11 - 80 * q^12 - 560 * q^13 + 896 * q^15 - 1480 * q^16 + 1320 * q^17 + 340 * q^18 + 180 * q^20 + 196 * q^21 - 2020 * q^22 + 1920 * q^23 - 676 * q^25 + 2208 * q^26 - 340 * q^27 - 5356 * q^30 - 2112 * q^31 - 1200 * q^32 - 6140 * q^33 + 3904 * q^36 + 3980 * q^37 + 9120 * q^38 + 14716 * q^40 + 6384 * q^41 + 4900 * q^42 - 12220 * q^43 - 10528 * q^45 - 8080 * q^46 - 11820 * q^47 - 4040 * q^48 + 10728 * q^50 - 5900 * q^51 + 3600 * q^52 + 24240 * q^53 + 4636 * q^55 - 10584 * q^56 + 6460 * q^57 + 6100 * q^58 - 30088 * q^60 + 440 * q^61 - 16680 * q^62 + 7840 * q^63 - 14652 * q^65 + 4832 * q^66 - 5940 * q^67 - 47040 * q^68 - 6272 * q^70 + 8928 * q^71 + 46720 * q^72 - 2500 * q^73 + 60708 * q^75 + 47816 * q^76 + 5880 * q^77 - 17940 * q^78 + 16140 * q^80 - 11360 * q^81 - 32120 * q^82 + 15120 * q^83 + 18816 * q^85 - 41208 * q^86 - 25460 * q^87 + 52920 * q^88 - 55680 * q^90 - 11172 * q^91 + 19800 * q^92 + 1460 * q^93 - 35508 * q^95 + 20568 * q^96 - 33840 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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