LMFDB - Embedded newform 45.5.i.a.11.12

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [45,5,Mod(11,45)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("45.11"); S:= CuspForms(chi, 5); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(45, base_ring=CyclotomicField(6)) chi = DirichletCharacter(H, H._module([1, 0])) N = Newforms(chi, 5, names="a")

Level:	$ N $	$=$	$ 45 = 3^{2} \cdot 5 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	45.i (of order $6$, degree $2$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$4.65164833877$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.12
Character	$\chi$	$=$	45.11
Dual form			45.5.i.a.41.12

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(3.10572 + 1.79309i) q^{2} +(-5.44105 - 7.16903i) q^{3} +(-1.56968 - 2.71877i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-4.04367 - 32.0212i) q^{6} +(45.9054 - 79.5105i) q^{7} -68.6371i q^{8} +(-21.7900 + 78.0141i) q^{9} -40.0946 q^{10} +(-110.654 - 63.8862i) q^{11} +(-10.9502 + 26.0461i) q^{12} +(37.9859 + 65.7935i) q^{13} +(285.138 - 164.625i) q^{14} +(92.7588 + 38.9974i) q^{15} +(97.9573 - 169.667i) q^{16} +325.310i q^{17} +(-207.559 + 203.218i) q^{18} +384.787 q^{19} +(30.3968 + 17.5496i) q^{20} +(-819.787 + 103.523i) q^{21} +(-229.107 - 396.825i) q^{22} +(125.517 - 72.4675i) q^{23} +(-492.061 + 373.458i) q^{24} +(62.5000 - 108.253i) q^{25} +272.448i q^{26} +(677.845 - 268.266i) q^{27} -288.228 q^{28} +(738.933 + 426.623i) q^{29} +(218.157 + 287.440i) q^{30} +(-734.888 - 1272.86i) q^{31} +(-342.608 + 197.805i) q^{32} +(144.073 + 1140.89i) q^{33} +(-583.309 + 1010.32i) q^{34} +1026.48i q^{35} +(246.306 - 63.2155i) q^{36} +398.987 q^{37} +(1195.04 + 689.956i) q^{38} +(264.992 - 630.308i) q^{39} +(383.693 + 664.576i) q^{40} +(2028.69 - 1171.26i) q^{41} +(-2731.65 - 1148.43i) q^{42} +(364.144 - 630.717i) q^{43} +401.124i q^{44} +(-225.132 - 877.178i) q^{45} +519.762 q^{46} +(-103.864 - 59.9661i) q^{47} +(-1749.34 + 220.908i) q^{48} +(-3014.11 - 5220.60i) q^{49} +(388.215 - 224.136i) q^{50} +(2332.16 - 1770.03i) q^{51} +(119.252 - 206.550i) q^{52} +2470.04i q^{53} +(2586.22 + 382.278i) q^{54} +1428.54 q^{55} +(-5457.37 - 3150.81i) q^{56} +(-2093.64 - 2758.55i) q^{57} +(1529.94 + 2649.94i) q^{58} +(894.636 - 516.518i) q^{59} +(-39.5769 - 313.404i) q^{60} +(-246.737 + 427.360i) q^{61} -5270.87i q^{62} +(5202.66 + 5313.80i) q^{63} -4553.36 q^{64} +(-735.594 - 424.695i) q^{65} +(-1598.27 + 3801.62i) q^{66} +(3995.55 + 6920.50i) q^{67} +(884.444 - 510.634i) q^{68} +(-1202.47 - 505.539i) q^{69} +(-1840.56 + 3187.94i) q^{70} +1325.88i q^{71} +(5354.66 + 1495.60i) q^{72} +7301.22 q^{73} +(1239.14 + 715.418i) q^{74} +(-1116.14 + 140.947i) q^{75} +(-603.993 - 1046.15i) q^{76} +(-10159.2 + 5865.45i) q^{77} +(1953.19 - 1482.40i) q^{78} +(-3408.95 + 5904.47i) q^{79} +2190.39i q^{80} +(-5611.40 - 3399.85i) q^{81} +8400.71 q^{82} +(-6000.80 - 3464.56i) q^{83} +(1568.26 + 2066.31i) q^{84} +(-1818.54 - 3149.80i) q^{85} +(2261.86 - 1305.88i) q^{86} +(-962.097 - 7618.71i) q^{87} +(-4384.96 + 7594.98i) q^{88} -1203.02i q^{89} +(873.660 - 3127.95i) q^{90} +6975.03 q^{91} +(-394.045 - 227.502i) q^{92} +(-5126.63 + 12194.2i) q^{93} +(-215.049 - 372.475i) q^{94} +(-3725.68 + 2151.02i) q^{95} +(3282.22 + 1379.90i) q^{96} +(-476.539 + 825.390i) q^{97} -21618.3i q^{98} +(7395.17 - 7240.51i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) $ 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/45\mathbb{Z}\right)^\times$.

$n$	$11$	$37$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$1$

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 $

$2$	3.10572	+	1.79309i	0.776429	+	0.448272i	0.835163	−	0.550002i	$-0.185373\pi$
$2$	3.10572	+	1.79309i	0.776429	+	0.448272i	−0.0587341	+	0.998274i	$0.518706\pi$
$3$	−5.44105	−	7.16903i	−0.604561	−	0.796559i
$3$	−5.44105	−	7.16903i	−0.604561	−	0.796559i
$4$	−1.56968	−	2.71877i	−0.0981052	−	0.169923i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$5$	−9.68246	+	5.59017i	−0.387298	+	0.223607i
$6$	−4.04367	−	32.0212i	−0.112324	−	0.889479i
$7$	45.9054	−	79.5105i	0.936845	−	1.62266i	0.165535	−	0.986204i	$-0.447065\pi$
$7$	45.9054	−	79.5105i	0.936845	−	1.62266i	0.771310	−	0.636459i	$-0.219602\pi$
$8$		−	68.6371i		−	1.07245i
$9$	−21.7900	+	78.0141i	−0.269012	+	0.963137i
$10$	−40.0946			−0.400946
$11$	−110.654	−	63.8862i	−0.914497	−	0.527985i	−0.0326219	−	0.999468i	$-0.510386\pi$
$11$	−110.654	−	63.8862i	−0.914497	−	0.527985i	−0.881875	+	0.471483i	$0.843719\pi$
$12$	−10.9502	+	26.0461i	−0.0760432	+	0.180875i
$13$	37.9859	+	65.7935i	0.224769	+	0.389311i	0.956250	−	0.292551i	$-0.0945041\pi$
$13$	37.9859	+	65.7935i	0.224769	+	0.389311i	−0.731481	+	0.681861i	$0.761171\pi$
$14$	285.138	−	164.625i	1.45479	−	0.839922i
$15$	92.7588	+	38.9974i	0.412261	+	0.173322i
$16$	97.9573	−	169.667i	0.382646	−	0.662762i
$17$			325.310i			1.12564i	0.826579	+	0.562820i	$0.190284\pi$
$17$			325.310i			1.12564i	−0.826579	+	0.562820i	$0.809716\pi$
$18$	−207.559	+	203.218i	−0.640615	+	0.627217i
$19$	384.787			1.06589			0.532946	−	0.846149i	$-0.321085\pi$
$19$	384.787			1.06589			0.532946	+	0.846149i	$0.321085\pi$
$20$	30.3968	+	17.5496i	0.0759919	+	0.0438740i
$21$	−819.787	+	103.523i	−1.85893	+	0.234747i
$22$	−229.107	−	396.825i	−0.473362	−	0.819886i
$23$	125.517	−	72.4675i	0.237273	−	0.136990i	−0.376650	−	0.926356i	$-0.622924\pi$
$23$	125.517	−	72.4675i	0.237273	−	0.136990i	0.613923	+	0.789366i	$0.289591\pi$
$24$	−492.061	+	373.458i	−0.854273	+	0.648364i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$			272.448i			0.403029i
$27$	677.845	−	268.266i	0.929829	−	0.367991i
$28$	−288.228			−0.367637
$29$	738.933	+	426.623i	0.878636	+	0.507281i	0.870208	−	0.492684i	$-0.163984\pi$
$29$	738.933	+	426.623i	0.878636	+	0.507281i	0.00842764	+	0.999964i	$0.497317\pi$
$30$	218.157	+	287.440i	0.242397	+	0.319377i
$31$	−734.888	−	1272.86i	−0.764712	−	1.32452i	−0.940399	−	0.340074i	$-0.889548\pi$
$31$	−734.888	−	1272.86i	−0.764712	−	1.32452i	0.175686	−	0.984446i	$-0.443785\pi$
$32$	−342.608	+	197.805i	−0.334578	+	0.193169i
$33$	144.073	+	1140.89i	0.132298	+	1.04765i
$34$	−583.309	+	1010.32i	−0.504593	+	0.873980i
$35$			1026.48i			0.837940i
$36$	246.306	−	63.2155i	0.190051	−	0.0487774i
$37$	398.987			0.291444			0.145722	−	0.989326i	$-0.453449\pi$
$37$	398.987			0.291444			0.145722	+	0.989326i	$0.453449\pi$
$38$	1195.04	+	689.956i	0.827589	+	0.477809i
$39$	264.992	−	630.308i	0.174222	−	0.414403i
$40$	383.693	+	664.576i	0.239808	+	0.415360i
$41$	2028.69	−	1171.26i	1.20683	−	0.696766i	0.244768	−	0.969582i	$-0.421288\pi$
$41$	2028.69	−	1171.26i	1.20683	−	0.696766i	0.962066	+	0.272816i	$0.0879549\pi$
$42$	−2731.65	−	1148.43i	−1.54856	−	0.651040i
$43$	364.144	−	630.717i	0.196941	−	0.341112i	−0.750594	−	0.660764i	$-0.770232\pi$
$43$	364.144	−	630.717i	0.196941	−	0.341112i	0.947535	+	0.319651i	$0.103566\pi$
$44$			401.124i			0.207192i
$45$	−225.132	−	877.178i	−0.111176	−	0.433174i
$46$	519.762			0.245634
$47$	−103.864	−	59.9661i	−0.0470187	−	0.0271462i	0.476306	−	0.879279i	$-0.341975\pi$
$47$	−103.864	−	59.9661i	−0.0470187	−	0.0271462i	−0.523325	+	0.852133i	$0.675309\pi$
$48$	−1749.34	+	220.908i	−0.759261	+	0.0958802i
$49$	−3014.11	−	5220.60i	−1.25536	−	2.17434i
$50$	388.215	−	224.136i	0.155286	−	0.0896543i
$51$	2332.16	−	1770.03i	0.896639	−	0.680519i
$52$	119.252	−	206.550i	0.0441019	−	0.0763868i
$53$			2470.04i			0.879331i	0.898162	+	0.439665i	$0.144903\pi$
$53$			2470.04i			0.879331i	−0.898162	+	0.439665i	$0.855097\pi$
$54$	2586.22	+	382.278i	0.886907	+	0.131097i
$55$	1428.54			0.472244
$56$	−5457.37	−	3150.81i	−1.74023	−	1.00472i
$57$	−2093.64	−	2758.55i	−0.644396	−	0.849045i
$58$	1529.94	+	2649.94i	0.454799	+	0.787735i
$59$	894.636	−	516.518i	0.257005	−	0.148382i	−0.365962	−	0.930630i	$-0.619260\pi$
$59$	894.636	−	516.518i	0.257005	−	0.148382i	0.622968	+	0.782248i	$0.285927\pi$
$60$	−39.5769	−	313.404i	−0.0109936	−	0.0870565i
$61$	−246.737	+	427.360i	−0.0663092	+	0.114851i	−0.897274	−	0.441474i	$-0.854456\pi$
$61$	−246.737	+	427.360i	−0.0663092	+	0.114851i	0.830965	+	0.556325i	$0.187789\pi$
$62$		−	5270.87i		−	1.37119i
$63$	5202.66	+	5313.80i	1.31082	+	1.33883i
$64$	−4553.36			−1.11166
$65$	−735.594	−	424.695i	−0.174105	−	0.100520i
$66$	−1598.27	+	3801.62i	−0.366912	+	0.872732i
$67$	3995.55	+	6920.50i	0.890076	+	1.54166i	0.839783	+	0.542923i	$0.182682\pi$
$67$	3995.55	+	6920.50i	0.890076	+	1.54166i	0.0502934	+	0.998734i	$0.483984\pi$
$68$	884.444	−	510.634i	0.191272	−	0.110431i
$69$	−1202.47	−	505.539i	−0.252566	−	0.106183i
$70$	−1840.56	+	3187.94i	−0.375625	+	0.650601i
$71$			1325.88i			0.263019i	0.991315	+	0.131509i	$0.0419824\pi$
$71$			1325.88i			0.263019i	−0.991315	+	0.131509i	$0.958018\pi$
$72$	5354.66	+	1495.60i	1.03292	+	0.288503i
$73$	7301.22			1.37009			0.685046	−	0.728500i	$-0.259782\pi$
$73$	7301.22			1.37009			0.685046	+	0.728500i	$0.259782\pi$
$74$	1239.14	+	715.418i	0.226286	+	0.130646i
$75$	−1116.14	+	140.947i	−0.198424	+	0.0250572i
$76$	−603.993	−	1046.15i	−0.104569	−	0.181120i
$77$	−10159.2	+	5865.45i	−1.71348	+	0.989281i
$78$	1953.19	−	1482.40i	0.321037	−	0.243656i
$79$	−3408.95	+	5904.47i	−0.546218	+	0.946078i	0.452311	+	0.891860i	$0.350600\pi$
$79$	−3408.95	+	5904.47i	−0.546218	+	0.946078i	−0.998529	+	0.0542173i	$0.982734\pi$
$80$			2190.39i			0.342249i
$81$	−5611.40	−	3399.85i	−0.855265	−	0.518190i
$82$	8400.71			1.24936
$83$	−6000.80	−	3464.56i	−0.871070	−	0.502912i	−0.00336631	−	0.999994i	$-0.501072\pi$
$83$	−6000.80	−	3464.56i	−0.871070	−	0.502912i	−0.867704	+	0.497082i	$0.834405\pi$
$84$	1568.26	+	2066.31i	0.222259	+	0.292845i
$85$	−1818.54	−	3149.80i	−0.251701	−	0.435959i
$86$	2261.86	−	1305.88i	0.305822	−	0.176566i
$87$	−962.097	−	7618.71i	−0.127110	−	1.00657i
$88$	−4384.96	+	7594.98i	−0.566240	+	0.980756i
$89$		−	1203.02i		−	0.151877i	−0.997112	−	0.0759386i	$-0.975805\pi$
$89$		−	1203.02i		−	0.151877i	0.997112	−	0.0759386i	$-0.0241953\pi$
$90$	873.660	−	3127.95i	0.107859	−	0.386166i
$91$	6975.03			0.842293
$92$	−394.045	−	227.502i	−0.0465554	−	0.0268788i
$93$	−5126.63	+	12194.2i	−0.592743	+	1.40989i
$94$	−215.049	−	372.475i	−0.0243378	−	0.0421543i
$95$	−3725.68	+	2151.02i	−0.412818	+	0.238341i
$96$	3282.22	+	1379.90i	0.356143	+	0.149729i
$97$	−476.539	+	825.390i	−0.0506472	+	0.0877235i	−0.890238	−	0.455497i	$-0.849462\pi$
$97$	−476.539	+	825.390i	−0.0506472	+	0.0877235i	0.839590	+	0.543220i	$0.182795\pi$
$98$		−	21618.3i		−	2.25096i
$99$	7395.17	−	7240.51i	0.754533	−	0.738752i
$100$	−392.421			−0.0392421
$101$	−1566.23	−	904.263i	−0.153537	−	0.0886445i	0.421263	−	0.906938i	$-0.361587\pi$
$101$	−1566.23	−	904.263i	−0.153537	−	0.0886445i	−0.574800	+	0.818294i	$0.694920\pi$
$102$	10416.8	−	1315.45i	1.00123	−	0.126437i
$103$	−5100.06	−	8833.56i	−0.480729	−	0.832648i	0.519026	−	0.854758i	$-0.326295\pi$
$103$	−5100.06	−	8833.56i	−0.480729	−	0.832648i	−0.999756	+	0.0221106i	$0.992961\pi$
$104$	4515.87	−	2607.24i	0.417518	−	0.241054i
$105$	7358.84	−	5585.11i	0.667468	−	0.506586i
$106$	−4429.00	+	7671.25i	−0.394179	+	0.682738i
$107$			13926.6i			1.21641i	0.793782	+	0.608203i	$0.208109\pi$
$107$			13926.6i			1.21641i	−0.793782	+	0.608203i	$0.791891\pi$
$108$	−1793.36	−	1421.81i	−0.153751	−	0.121898i
$109$	−9756.98			−0.821226			−0.410613	−	0.911810i	$-0.634685\pi$
$109$	−9756.98			−0.821226			−0.410613	+	0.911810i	$0.634685\pi$
$110$	4436.64	+	2561.49i	0.366664	+	0.211694i
$111$	−2170.91	−	2860.35i	−0.176196	−	0.232152i
$112$	−8993.54	−	15577.3i	−0.716959	−	1.24181i
$113$	684.192	−	395.018i	0.0535822	−	0.0309357i	−0.472970	−	0.881079i	$-0.656818\pi$
$113$	684.192	−	395.018i	0.0535822	−	0.0309357i	0.526552	+	0.850143i	$0.323485\pi$
$114$	−1555.95	−	12321.4i	−0.119725	−	0.948088i
$115$	−810.211	+	1403.33i	−0.0612636	+	0.106112i
$116$		−	2678.65i		−	0.199067i
$117$	−5960.53	+	1529.80i	−0.435425	+	0.111754i
$118$	3704.65			0.266062
$119$	25865.6	+	14933.5i	1.82654	+	1.05455i
$120$	2676.67	−	6366.69i	0.185880	−	0.442132i
$121$	842.397	+	1459.07i	0.0575368	+	0.0996567i
$122$	−1532.59	+	884.840i	−0.102969	+	0.0594491i
$123$	−19435.0	−	8170.82i	−1.28462	−	0.540077i
$124$	−2307.08	+	3995.99i	−0.150044	+	0.259885i
$125$			1397.54i			0.0894427i
$126$	6629.90	+	25832.0i	0.417605	+	1.62711i
$127$	−2170.25			−0.134556			−0.0672778	−	0.997734i	$-0.521431\pi$
$127$	−2170.25			−0.134556			−0.0672778	+	0.997734i	$0.521431\pi$
$128$	−8659.71	−	4999.69i	−0.528547	−	0.305157i
$129$	−6502.95	+	821.199i	−0.390779	+	0.0493479i
$130$	−1523.03	−	2637.97i	−0.0901201	−	0.156093i
$131$	−3471.49	+	2004.26i	−0.202289	+	0.116792i	−0.597723	−	0.801703i	$-0.703928\pi$
$131$	−3471.49	+	2004.26i	−0.202289	+	0.116792i	0.395434	+	0.918495i	$0.370594\pi$
$132$	2875.67	−	2182.54i	0.165041	−	0.125260i
$133$	17663.8	−	30594.6i	0.998575	−	1.72958i
$134$			28657.5i			1.59598i
$135$	−5063.56	+	6386.74i	−0.277836	+	0.350439i
$136$	22328.3			1.20720
$137$	1042.08	+	601.645i	0.0555213	+	0.0320553i	0.527504	−	0.849553i	$-0.323128\pi$
$137$	1042.08	+	601.645i	0.0555213	+	0.0320553i	−0.471982	+	0.881608i	$0.656461\pi$
$138$	−2828.05	−	3726.19i	−0.148501	−	0.195662i
$139$	−1782.41	−	3087.23i	−0.0922526	−	0.159786i	0.816206	−	0.577761i	$-0.196073\pi$
$139$	−1782.41	−	3087.23i	−0.0922526	−	0.159786i	−0.908459	+	0.417975i	$0.862740\pi$
$140$	2790.75	−	1611.24i	0.142385	−	0.0822062i
$141$	135.232	+	1070.88i	0.00680208	+	0.0538647i
$142$	−2377.41	+	4117.80i	−0.117904	+	0.204216i
$143$		−	9707.10i		−	0.474698i
$144$	11101.9	+	11339.1i	0.535394	+	0.546831i
$145$	−9539.58			−0.453726
$146$	22675.5	+	13091.7i	1.06378	+	0.614173i
$147$	−21026.7	+	50013.8i	−0.973051	+	2.31449i
$148$	−626.283	−	1084.75i	−0.0285922	−	0.0495231i
$149$	1464.47	−	845.512i	0.0659642	−	0.0380844i	−0.466655	−	0.884439i	$-0.654541\pi$
$149$	1464.47	−	845.512i	0.0659642	−	0.0380844i	0.532619	+	0.846355i	$0.321208\pi$
$150$	−3719.13	−	1563.59i	−0.165295	−	0.0694928i
$151$	−2847.25	+	4931.59i	−0.124874	+	0.216288i	−0.921684	−	0.387942i	$-0.873186\pi$
$151$	−2847.25	+	4931.59i	−0.124874	+	0.216288i	0.796810	+	0.604230i	$0.206519\pi$
$152$		−	26410.6i		−	1.14312i
$153$	−25378.8	−	7088.49i	−1.08415	−	0.302811i
$154$	−42069.0			−1.77387
$155$	14231.1	+	8216.30i	0.592343	+	0.341990i
$156$	−2129.62	+	268.930i	−0.0875088	+	0.0110507i
$157$	18530.1	+	32095.1i	0.751760	+	1.30209i	0.946969	+	0.321324i	$0.104128\pi$
$157$	18530.1	+	32095.1i	0.751760	+	1.30209i	−0.195209	+	0.980762i	$0.562539\pi$
$158$	−21174.4	+	12225.1i	−0.848199	+	0.489708i
$159$	17707.8	−	13439.6i	0.700439	−	0.531609i
$160$	2211.53	−	3830.47i	0.0863877	−	0.149628i
$161$		−	13306.6i		−	0.513352i
$162$	−11331.2	−	20620.7i	−0.431763	−	0.785729i
$163$	30580.9			1.15100			0.575500	−	0.817802i	$-0.304808\pi$
$163$	30580.9			1.15100			0.575500	+	0.817802i	$0.304808\pi$
$164$	−6368.79	−	3677.02i	−0.236793	−	0.136713i
$165$	−7772.75	−	10241.2i	−0.285501	−	0.376170i
$166$	−12424.5	−	21519.9i	−0.450883	−	0.780952i
$167$	37254.7	−	21509.0i	1.33582	−	0.771236i	0.349636	−	0.936886i	$-0.386305\pi$
$167$	37254.7	−	21509.0i	1.33582	−	0.771236i	0.986185	+	0.165649i	$0.0529720\pi$
$168$	7105.54	+	56267.8i	0.251755	+	1.99361i
$169$	11394.6	−	19736.1i	0.398958	−	0.691016i
$170$		−	13043.2i		−	0.451321i
$171$	−8384.49	+	30018.8i	−0.286737	+	1.02660i
$172$	−2286.36			−0.0772838
$173$	−24646.4	−	14229.6i	−0.823495	−	0.475445i	0.0281254	−	0.999604i	$-0.491046\pi$
$173$	−24646.4	−	14229.6i	−0.823495	−	0.475445i	−0.851620	+	0.524160i	$0.824380\pi$
$174$	10673.0	−	25386.7i	0.352524	−	0.838508i
$175$	−5738.18	−	9938.81i	−0.187369	−	0.324533i
$176$	−21678.8	+	12516.2i	−0.699857	+	0.404062i
$177$	−8570.69	−	3603.27i	−0.273571	−	0.115014i
$178$	2157.12	−	3736.24i	0.0680822	−	0.117922i
$179$			55789.5i			1.74119i	0.492000	+	0.870595i	$0.336266\pi$
$179$			55789.5i			1.74119i	−0.492000	+	0.870595i	$0.663734\pi$
$180$	−2031.46	+	1988.97i	−0.0626994	+	0.0613880i
$181$	37548.8			1.14614			0.573072	−	0.819505i	$-0.305752\pi$
$181$	37548.8			1.14614			0.573072	+	0.819505i	$0.305752\pi$
$182$	21662.5	+	12506.8i	0.653981	+	0.377576i
$183$	4406.27	−	556.427i	0.131574	−	0.0166152i
$184$	−4973.96	−	8615.15i	−0.146915	−	0.254464i
$185$	−3863.18	+	2230.41i	−0.112876	+	0.0651689i
$186$	−37787.0	+	28679.1i	−1.09224	+	0.828971i
$187$	20782.8	−	35996.9i	0.594322	−	1.02940i
$188$			376.511i			0.0106527i
$189$	9786.83	−	66210.7i	0.273980	−	1.85355i
$190$	−15427.9			−0.427365
$191$	−26615.9	−	15366.7i	−0.729583	−	0.421225i	0.0886869	−	0.996060i	$-0.471733\pi$
$191$	−26615.9	−	15366.7i	−0.729583	−	0.421225i	−0.818269	+	0.574835i	$0.805066\pi$
$192$	24775.0	+	32643.2i	0.672066	+	0.885502i
$193$	15866.5	+	27481.6i	0.425959	+	0.737782i	0.996509	−	0.0834802i	$-0.0266035\pi$
$193$	15866.5	+	27481.6i	0.425959	+	0.737782i	−0.570551	+	0.821262i	$0.693270\pi$
$194$	−2959.99	+	1708.95i	−0.0786479	+	0.0454074i
$195$	957.749	+	7584.28i	0.0251874	+	0.199455i
$196$	−9462.40	+	16389.4i	−0.246314	+	0.426628i
$197$		−	1131.08i		−	0.0291448i	−0.999894	−	0.0145724i	$-0.995361\pi$
$197$		−	1131.08i		−	0.0291448i	0.999894	−	0.0145724i	$-0.00463870\pi$
$198$	35950.2	−	9226.78i	0.917003	−	0.235353i
$199$	−1899.26			−0.0479599			−0.0239800	−	0.999712i	$-0.507634\pi$
$199$	−1899.26			−0.0479599			−0.0239800	+	0.999712i	$0.507634\pi$
$200$	−7430.18	−	4289.82i	−0.185755	−	0.107245i
$201$	27873.3	−	66299.0i	0.689915	−	1.64102i
$202$	−3242.84	−	5616.77i	−0.0794737	−	0.137652i
$203$	67842.0	−	39168.6i	1.64629	−	0.950487i
$204$	−8473.05	−	3562.22i	−0.203601	−	0.0855973i
$205$	−13095.1	+	22681.4i	−0.311603	+	0.539713i
$206$		−	36579.4i		−	0.861989i
$207$	2918.47	+	11371.2i	0.0681105	+	0.265378i
$208$	14884.0			0.344027
$209$	−42578.3	−	24582.6i	−0.974755	−	0.562775i
$210$	32869.0	−	4150.73i	0.745330	−	0.0941209i
$211$	−2550.45	−	4417.51i	−0.0572865	−	0.0992231i	0.835960	−	0.548790i	$-0.184912\pi$
$211$	−2550.45	−	4417.51i	−0.0572865	−	0.0992231i	−0.893246	+	0.449567i	$0.851578\pi$
$212$	6715.47	−	3877.18i	0.149419	−	0.0862669i
$213$	9505.26	−	7214.17i	0.209510	−	0.159011i
$214$	−24971.6	+	43252.2i	−0.545280	+	0.944453i
$215$			8142.52i			0.176150i
$216$	−18413.0	−	46525.3i	−0.394654	−	0.997199i
$217$	−134941.			−2.86567
$218$	−30302.4	−	17495.1i	−0.637624	−	0.368132i
$219$	−39726.3	−	52342.7i	−0.828304	−	1.09136i
$220$	−2242.35	−	3883.87i	−0.0463296	−	0.0802452i
$221$	−21403.3	+	12357.2i	−0.438224	+	0.253009i
$222$	−1613.37	−	12776.1i	−0.0327362	−	0.259233i
$223$	−18089.0	+	31331.0i	−0.363751	+	0.630034i	−0.988575	−	0.150731i	$-0.951837\pi$
$223$	−18089.0	+	31331.0i	−0.363751	+	0.630034i	0.624824	+	0.780765i	$0.285171\pi$
$224$			36321.3i			0.723877i
$225$	7083.40	+	7234.71i	0.139919	+	0.142908i
$226$	2833.21			0.0554704
$227$	−36018.1	−	20795.1i	−0.698987	−	0.403560i	0.107983	−	0.994153i	$-0.465561\pi$
$227$	−36018.1	−	20795.1i	−0.698987	−	0.403560i	−0.806970	+	0.590592i	$0.798894\pi$
$228$	−4213.50	+	10022.2i	−0.0810538	+	0.192794i
$229$	44049.7	+	76296.3i	0.839985	+	1.45490i	0.889906	+	0.456144i	$0.150770\pi$
$229$	44049.7	+	76296.3i	0.839985	+	1.45490i	−0.0499204	+	0.998753i	$0.515897\pi$
$230$	−5032.57	+	2905.56i	−0.0951337	+	0.0549255i
$231$	97326.5	+	40917.8i	1.82393	+	0.766810i
$232$	29282.2	−	50718.2i	0.544035	−	0.942297i
$233$			52794.4i			0.972470i	0.873828	+	0.486235i	$0.161630\pi$
$233$			52794.4i			0.972470i	−0.873828	+	0.486235i	$0.838370\pi$
$234$	−21254.8	−	5936.63i	−0.388173	−	0.108420i
$235$	1340.88			0.0242803
$236$	−2808.59	−	1621.54i	−0.0504271	−	0.0291141i
$237$	60877.6	−	7687.67i	1.08383	−	0.136867i
$238$	53554.1	+	92758.4i	0.945450	+	1.63757i
$239$	34187.2	−	19738.0i	0.598505	−	0.345547i	−0.169948	−	0.985453i	$-0.554360\pi$
$239$	34187.2	−	19738.0i	0.598505	−	0.345547i	0.768453	+	0.639906i	$0.221027\pi$
$240$	15703.0	−	11918.0i	0.272621	−	0.206910i
$241$	12994.1	−	22506.5i	0.223725	−	0.387502i	−0.732211	−	0.681077i	$-0.761512\pi$
$241$	12994.1	−	22506.5i	0.223725	−	0.387502i	0.955936	+	0.293575i	$0.0948451\pi$
$242$			6041.96i			0.103168i
$243$	6158.29	+	58727.0i	0.104291	+	0.994547i
$244$	1549.19			0.0260211
$245$	58368.0	+	33698.8i	0.972395	+	0.561413i
$246$	−45708.7	−	60224.9i	−0.755315	−	0.995190i
$247$	14616.5	+	25316.5i	0.239579	+	0.414963i
$248$	−87365.7	+	50440.6i	−1.42049	+	0.820119i
$249$	7813.10	+	61870.8i	0.126016	+	0.997900i
$250$	−2505.91	+	4340.37i	−0.0400946	+	0.0694459i
$251$			39630.5i			0.629045i	0.949250	+	0.314522i	$0.101844\pi$
$251$			39630.5i			0.629045i	−0.949250	+	0.314522i	$0.898156\pi$
$252$	6280.47	−	22485.8i	0.0988988	−	0.354085i
$253$	−18518.7			−0.289314
$254$	−6740.17	−	3891.44i	−0.104473	−	0.0603175i
$255$	−12686.3	+	30175.4i	−0.195098	+	0.464058i
$256$	18497.1	+	32038.0i	0.282244	+	0.488860i
$257$	−102809.	+	59356.5i	−1.55655	+	0.898674i	−0.558967	+	0.829190i	$0.688802\pi$
$257$	−102809.	+	59356.5i	−1.55655	+	0.898674i	−0.997583	+	0.0694842i	$0.977865\pi$
$258$	−21668.8	−	9109.95i	−0.325534	−	0.136860i
$259$	18315.7	−	31723.7i	0.273038	−	0.472916i
$260$			2666.55i			0.0394459i
$261$	−49383.9	+	48351.1i	−0.724944	+	0.709782i
$262$	−14375.3			−0.209418
$263$	16425.0	+	9482.97i	0.237462	+	0.137099i	0.614010	−	0.789299i	$-0.289556\pi$
$263$	16425.0	+	9482.97i	0.237462	+	0.137099i	−0.376548	+	0.926397i	$0.622889\pi$
$264$	78307.4	−	9888.73i	1.12356	−	0.141884i
$265$	−13807.9	−	23916.1i	−0.196624	−	0.340563i
$266$	109717.	−	63345.4i	1.55065	−	0.895266i
$267$	−8624.48	+	6545.69i	−0.120979	+	0.0918190i
$268$	12543.5	−	21726.0i	0.174642	−	0.302489i
$269$		−	83103.2i		−	1.14845i	−0.818697	−	0.574226i	$-0.805303\pi$
$269$		−	83103.2i		−	1.14845i	0.818697	−	0.574226i	$-0.194697\pi$
$270$	−27178.0	+	10756.0i	−0.372812	+	0.147545i
$271$	−79680.2			−1.08495			−0.542477	−	0.840070i	$-0.682514\pi$
$271$	−79680.2			−1.08495			−0.542477	+	0.840070i	$0.682514\pi$
$272$	55194.4	+	31866.5i	0.746031	+	0.430721i
$273$	−37951.5	−	50004.2i	−0.509218	−	0.670936i
$274$	2157.60	+	3737.08i	0.0287389	+	0.0497773i
$275$	−13831.8	+	7985.78i	−0.182899	+	0.105597i
$276$	513.050	+	4062.77i	0.00673506	+	0.0533340i
$277$	−12370.9	+	21427.0i	−0.161229	+	0.279256i	−0.935310	−	0.353830i	$-0.884879\pi$
$277$	−12370.9	+	21427.0i	−0.161229	+	0.279256i	0.774081	+	0.633087i	$0.218212\pi$
$278$		−	12784.1i		−	0.165417i
$279$	115315.	−	29596.0i	1.48141	−	0.380211i
$280$	70454.3			0.898652
$281$	−119335.	−	68898.2i	−1.51132	−	0.872559i	−0.999913	−	0.0132195i	$-0.995792\pi$
$281$	−119335.	−	68898.2i	−1.51132	−	0.872559i	−0.511405	−	0.859340i	$-0.670875\pi$
$282$	−1500.20	+	3568.35i	−0.0188647	+	0.0448713i
$283$	−14095.8	−	24414.6i	−0.176001	−	0.304843i	0.764506	−	0.644616i	$-0.222983\pi$
$283$	−14095.8	−	24414.6i	−0.176001	−	0.304843i	−0.940507	+	0.339774i	$0.889650\pi$
$284$	3604.76	−	2081.21i	0.0446930	−	0.0258035i
$285$	35692.4	+	15005.7i	0.439426	+	0.184742i
$286$	17405.7	−	30147.5i	0.212794	−	0.368569i
$287$		−	215069.i		−	2.61105i
$288$	−7966.15	−	31038.4i	−0.0960425	−	0.374209i
$289$	−22305.7			−0.267067
$290$	−29627.2	−	17105.3i	−0.352286	−	0.203392i
$291$	8510.12	−	1074.67i	0.100496	−	0.0126907i
$292$	−11460.6	−	19850.3i	−0.134413	−	0.232810i
$293$	62177.8	−	35898.3i	0.724269	−	0.418157i	−0.0920530	−	0.995754i	$-0.529343\pi$
$293$	62177.8	−	35898.3i	0.724269	−	0.418157i	0.816322	+	0.577597i	$0.196010\pi$
$294$	−154982.	+	117626.i	−1.79302	+	1.36085i
$295$	−5774.85	+	10002.3i	−0.0663585	+	0.114936i
$296$		−	27385.3i		−	0.312561i
$297$	−92144.9	−	13620.3i	−1.04462	−	0.154409i
$298$	6064.31			0.0682887
$299$	9535.78	+	5505.48i	0.106663	+	0.0615819i
$300$	2135.18	+	2813.28i	0.0237242	+	0.0312586i
$301$	−33432.4	−	57906.6i	−0.369007	−	0.639139i
$302$	−17685.5	+	10210.7i	−0.193912	+	0.111955i
$303$	2039.24	+	16148.5i	0.0222118	+	0.175892i
$304$	37692.7	−	65285.6i	0.407859	−	0.706432i
$305$		−	5517.20i		−	0.0593088i
$306$	−66109.0	−	67521.2i	−0.706021	−	0.721103i
$307$	125772.			1.33447			0.667234	−	0.744848i	$-0.267478\pi$
$307$	125772.			1.33447			0.667234	+	0.744848i	$0.267478\pi$
$308$	31893.6	+	18413.8i	0.336203	+	0.194107i
$309$	−35578.4	+	84626.3i	−0.372623	+	0.886316i
$310$	29465.1	+	51035.0i	0.306609	+	0.531062i
$311$	−23886.5	+	13790.9i	−0.246963	+	0.142584i	−0.618373	−	0.785885i	$-0.712208\pi$
$311$	−23886.5	+	13790.9i	−0.246963	+	0.142584i	0.371410	+	0.928469i	$0.378875\pi$
$312$	−43262.5	−	18188.3i	−0.444429	−	0.186846i
$313$	69632.1	−	120606.i	0.710756	−	1.23107i	−0.253818	−	0.967252i	$-0.581686\pi$
$313$	69632.1	−	120606.i	0.710756	−	1.23107i	0.964574	−	0.263813i	$-0.0849803\pi$
$314$			132904.i			1.34797i
$315$	−80079.6	−	22366.9i	−0.807051	−	0.225416i
$316$	21403.9			0.214347
$317$	148979.	+	86012.8i	1.48254	+	0.855942i	0.999803	−	0.0198259i	$-0.00631118\pi$
$317$	148979.	+	86012.8i	1.48254	+	0.855942i	0.482732	+	0.875768i	$0.339645\pi$
$318$	79093.8	−	9988.03i	0.782146	−	0.0987701i
$319$	−54510.7	−	94415.3i	−0.535674	−	0.927814i
$320$	44087.7	−	25454.0i	0.430544	−	0.248575i
$321$	99840.4	−	75775.5i	0.968939	−	0.735391i
$322$	23859.9	−	41326.5i	0.230121	−	0.398582i
$323$			125175.i			1.19981i
$324$	−435.291	+	20592.8i	−0.00414657	+	0.196167i
$325$	9496.47			0.0899074
$326$	94975.6	+	54834.2i	0.893669	+	0.515960i
$327$	53088.2	+	69948.1i	0.496481	+	0.654154i
$328$	−80392.1	−	139243.i	−0.747250	−	1.29427i
$329$	−9535.86	+	5505.53i	−0.0880984	+	0.0508637i
$330$	−5776.54	−	45743.6i	−0.0530445	−	0.420051i
$331$	−64539.9	+	111786.i	−0.589077	+	1.02031i	0.405277	+	0.914194i	$0.367175\pi$
$331$	−64539.9	+	111786.i	−0.589077	+	1.02031i	−0.994354	+	0.106117i	$0.966158\pi$
$332$			21753.1i			0.197353i
$333$	−8693.91	+	31126.6i	−0.0784019	+	0.280701i
$334$	154270.			1.38289
$335$	−77373.5	−	44671.6i	−0.689450	−	0.398054i
$336$	−62739.6	+	149232.i	−0.555729	+	1.32185i
$337$	79353.4	+	137444.i	0.698724	+	1.21023i	0.968909	+	0.247417i	$0.0795818\pi$
$337$	79353.4	+	137444.i	0.698724	+	1.21023i	−0.270185	+	0.962808i	$0.587085\pi$
$338$	70777.1	−	40863.2i	0.619526	−	0.357683i
$339$	−6554.62	−	2755.68i	−0.0570359	−	0.0239789i
$340$	−5709.06	+	9888.38i	−0.0493863	+	0.0855396i
$341$			187797.i			1.61503i
$342$	−79866.1	+	78195.7i	−0.682826	+	0.668545i
$343$	−333018.			−2.83061
$344$	−43290.5	−	24993.8i	−0.365827	−	0.211211i
$345$	14468.9	−	1827.14i	0.121562	−	0.0153509i
$346$	−51029.8	−	88386.1i	−0.426257	−	0.738298i
$347$	−83339.5	+	48116.1i	−0.692137	+	0.399605i	−0.804412	−	0.594072i	$-0.797519\pi$
$347$	−83339.5	+	48116.1i	−0.692137	+	0.399605i	0.112275	+	0.993677i	$0.464186\pi$
$348$	−19203.3	+	14574.7i	−0.158569	+	0.120348i
$349$	30769.5	−	53294.4i	0.252621	−	0.437553i	−0.711625	−	0.702559i	$-0.752041\pi$
$349$	30769.5	−	53294.4i	0.252621	−	0.437553i	0.964247	+	0.265006i	$0.0853740\pi$
$350$		−	41156.2i		−	0.335969i
$351$	43398.7	+	34407.5i	0.352259	+	0.279279i
$352$	50548.0			0.407961
$353$	72608.5	+	41920.6i	0.582691	+	0.336417i	0.762202	−	0.647339i	$-0.224118\pi$
$353$	72608.5	+	41920.6i	0.582691	+	0.336417i	−0.179511	+	0.983756i	$0.557452\pi$
$354$	−20157.2	−	26558.7i	−0.160851	−	0.211934i
$355$	−7411.89	−	12837.8i	−0.0588128	−	0.101867i
$356$	−3270.73	+	1888.36i	−0.0258074	+	0.0148999i
$357$	−33677.2	−	266685.i	−0.264241	−	2.09248i
$358$	−100035.	+	173266.i	−0.780526	+	1.35191i
$359$		−	237704.i		−	1.84437i	−0.386748	−	0.922186i	$-0.626402\pi$
$359$		−	237704.i		−	1.84437i	0.386748	−	0.922186i	$-0.373598\pi$
$360$	−60206.9	+	15452.4i	−0.464559	+	0.119231i
$361$	17739.8			0.136124
$362$	116616.	+	67328.3i	0.889899	+	0.513784i
$363$	5876.62	−	13978.1i	0.0445979	−	0.106080i
$364$	−10948.6	−	18963.5i	−0.0826333	−	0.143125i
$365$	−70693.8	+	40815.1i	−0.530634	+	0.306362i
$366$	14682.3	+	6172.71i	0.109606	+	0.0460801i
$367$	−44243.4	+	76631.8i	−0.328486	+	0.568954i	−0.982212	−	0.187778i	$-0.939872\pi$
$367$	−44243.4	+	76631.8i	−0.328486	+	0.568954i	0.653726	+	0.756731i	$0.273205\pi$
$368$		−	28394.9i		−	0.209674i
$369$	47170.1	+	183788.i	0.346428	+	1.34978i
$370$	−15997.2			−0.116853
$371$	196394.	+	113388.i	1.42686	+	0.823797i
$372$	41200.3	−	5202.81i	0.297724	−	0.0375969i
$373$	26894.2	+	46582.2i	0.193304	+	0.334813i	0.946343	−	0.323163i	$-0.104746\pi$
$373$	26894.2	+	46582.2i	0.193304	+	0.334813i	−0.753039	+	0.657976i	$0.771413\pi$
$374$	129091.	−	74530.8i	0.922897	−	0.532835i
$375$	10019.0	−	7604.10i	0.0712464	−	0.0540736i
$376$	−4115.89	+	7128.94i	−0.0291131	+	0.0504254i
$377$			64822.6i			0.456083i
$378$	149117.	−	188083.i	1.04362	−	1.31633i
$379$	−203995.			−1.42018			−0.710088	−	0.704113i	$-0.751345\pi$
$379$	−203995.			−1.42018			−0.710088	+	0.704113i	$0.751345\pi$
$380$	11696.3	+	6752.85i	0.0809991	+	0.0467649i
$381$	11808.4	+	15558.6i	0.0813471	+	0.107181i
$382$	−55107.6	−	95449.2i	−0.377646	−	0.654102i
$383$	44187.6	−	25511.7i	0.301233	−	0.173917i	−0.341764	−	0.939786i	$-0.611024\pi$
$383$	44187.6	−	25511.7i	0.301233	−	0.173917i	0.642997	+	0.765869i	$0.277691\pi$
$384$	11275.0	+	89285.2i	0.0764636	+	0.605504i
$385$	65577.7	−	113584.i	0.442420	−	0.766294i
$386$			113800.i			0.763781i
$387$	41270.1	+	42151.7i	0.275558	+	0.281445i
$388$	2992.06			0.0198750
$389$	−139063.	−	80288.1i	−0.918994	−	0.530581i	−0.0356800	−	0.999363i	$-0.511360\pi$
$389$	−139063.	−	80288.1i	−0.918994	−	0.530581i	−0.883314	+	0.468782i	$0.844693\pi$
$390$	−10624.8	+	25271.9i	−0.0698538	+	0.166154i
$391$	23574.4	+	40832.1i	0.154201	+	0.267084i
$392$	−358326.	+	206880.i	−2.33188	+	1.34631i
$393$	33257.2	+	13981.9i	0.215328	+	0.0905276i
$394$	2028.12	−	3512.81i	0.0130648	−	0.0226288i
$395$		−	76226.4i		−	0.488552i
$396$	−31293.3	−	8740.48i	−0.199555	−	0.0557372i
$397$	−6908.62			−0.0438339			−0.0219170	−	0.999760i	$-0.506977\pi$
$397$	−6908.62			−0.0438339			−0.0219170	+	0.999760i	$0.506977\pi$
$398$	−5898.57	−	3405.54i	−0.0372375	−	0.0214991i
$399$	−315443.	+	39834.4i	−1.98141	+	0.250215i
$400$	−12244.7	−	21208.4i	−0.0765291	−	0.132552i
$401$	64664.3	−	37333.9i	0.402138	−	0.232175i	−0.285268	−	0.958448i	$-0.592083\pi$
$401$	64664.3	−	37333.9i	0.402138	−	0.232175i	0.687406	+	0.726273i	$0.258749\pi$
$402$	205446.	−	155927.i	1.27129	−	0.964869i
$403$	55830.8	−	96701.7i	0.343766	−	0.595421i
$404$			5677.62i			0.0347859i
$405$	73337.8	+	1550.22i	0.447114	+	0.00945110i
$406$	280931.			1.70431
$407$	−44149.6	−	25489.8i	−0.266525	−	0.153878i
$408$	−121490.	−	160072.i	−0.729825	−	0.961604i
$409$	131692.	+	228096.i	0.787247	+	1.36355i	0.927647	+	0.373457i	$0.121828\pi$
$409$	131692.	+	228096.i	0.787247	+	1.36355i	−0.140400	+	0.990095i	$0.544839\pi$
$410$	−81339.5	+	46961.4i	−0.483876	+	0.279366i
$411$	−1356.80	−	10744.3i	−0.00803214	−	0.0636054i
$412$	−16010.9	+	27731.8i	−0.0943241	+	0.163374i
$413$		−	94843.9i		−	0.556044i
$414$	−11325.6	+	40548.8i	−0.0660785	+	0.236579i
$415$	77470.0			0.449819
$416$	−26028.5	−	15027.6i	−0.150405	−	0.0868366i
$417$	−12434.2	+	29575.9i	−0.0715067	+	0.170085i
$418$	−88157.3	−	152693.i	−0.504552	−	0.873910i
$419$	203579.	−	117537.i	1.15959	−	0.669491i	0.208387	−	0.978047i	$-0.433179\pi$
$419$	203579.	−	117537.i	1.15959	−	0.669491i	0.951206	+	0.308555i	$0.0998454\pi$
$420$	−26735.7	−	11240.1i	−0.151563	−	0.0637196i
$421$	−86903.7	+	150522.i	−0.490314	+	0.849249i	−0.999938	−	0.0111485i	$-0.996451\pi$
$421$	−86903.7	+	150522.i	−0.490314	+	0.849249i	0.509624	+	0.860397i	$0.329785\pi$
$422$		−	18292.7i		−	0.102720i
$423$	6941.40	−	6796.22i	0.0387941	−	0.0379828i
$424$	169536.			0.943042
$425$	35215.9	+	20331.9i	0.194967	+	0.112564i
$426$	42456.3	−	5361.42i	0.233950	−	0.0295434i
$427$	22653.1	+	39236.3i	0.124243	+	0.215195i
$428$	37863.3	−	21860.4i	0.206695	−	0.119336i
$429$	−69590.5	+	52816.8i	−0.378125	+	0.286984i
$430$	−14600.2	+	25288.4i	−0.0789629	+	0.136768i
$431$		−	197181.i		−	1.06148i	−0.847536	−	0.530738i	$-0.821915\pi$
$431$		−	197181.i		−	1.06148i	0.847536	−	0.530738i	$-0.178085\pi$
$432$	20884.1	−	141287.i	0.111904	−	0.757065i
$433$	221520.			1.18151			0.590754	−	0.806851i	$-0.298830\pi$
$433$	221520.			1.18151			0.590754	+	0.806851i	$0.298830\pi$
$434$	−419090.	−	241962.i	−2.22499	−	1.28460i
$435$	51905.3	+	68389.6i	0.274305	+	0.361419i
$436$	15315.4	+	26527.0i	0.0805665	+	0.139545i
$437$	48297.4	−	27884.5i	0.252907	−	0.146016i
$438$	−29523.7	−	233794.i	−0.153894	−	1.21867i
$439$	−35622.0	+	61699.0i	−0.184837	+	0.320147i	−0.943522	−	0.331311i	$-0.892509\pi$
$439$	−35622.0	+	61699.0i	−0.184837	+	0.320147i	0.758685	+	0.651458i	$0.225842\pi$
$440$		−	98050.7i		−	0.506460i
$441$	472957.	−	121387.i	2.43190	−	0.624157i
$442$	−88630.1			−0.453666
$443$	−131949.	−	76180.5i	−0.672353	−	0.388183i	0.124615	−	0.992205i	$-0.460230\pi$
$443$	−131949.	−	76180.5i	−0.672353	−	0.388183i	−0.796967	+	0.604022i	$0.793564\pi$
$444$	−4369.00	+	10392.0i	−0.0221623	+	0.0527151i
$445$	6725.08	+	11648.2i	0.0339608	+	0.0588218i
$446$	−112358.	+	64870.1i	−0.564853	+	0.326118i
$447$	−14029.8	−	5898.36i	−0.0702159	−	0.0295200i
$448$	−209024.	+	362040.i	−1.04145	+	1.80385i
$449$			31495.4i			0.156227i	0.996944	+	0.0781133i	$0.0248896\pi$
$449$			31495.4i			0.156227i	−0.996944	+	0.0781133i	$0.975110\pi$
$450$	9026.57	+	35170.1i	0.0445757	+	0.173680i
$451$	−299310.			−1.47153
$452$	−2147.93	−	1240.11i	−0.0105134	−	0.00606991i
$453$	50846.7	−	6420.97i	0.247780	−	0.0312899i
$454$	−74574.7	−	129167.i	−0.361809	−	0.626672i
$455$	−67535.4	+	38991.6i	−0.326219	+	0.188342i
$456$	−189339.	+	143702.i	−0.910562	+	0.691086i
$457$	−16974.1	+	29399.9i	−0.0812743	+	0.140771i	−0.903798	−	0.427960i	$-0.859232\pi$
$457$	−16974.1	+	29399.9i	−0.0812743	+	0.140771i	0.822523	+	0.568732i	$0.192566\pi$
$458$			315939.i			1.50617i
$459$	87269.6	+	220510.i	0.414226	+	1.04665i
$460$	5087.10			0.0240411
$461$	−164121.	−	94755.2i	−0.772257	−	0.445863i	0.0614223	−	0.998112i	$-0.480436\pi$
$461$	−164121.	−	94755.2i	−0.772257	−	0.445863i	−0.833679	+	0.552249i	$0.813770\pi$
$462$	228900.	+	301594.i	1.07241	+	1.41299i
$463$	−172137.	−	298150.i	−0.802994	−	1.39083i	−0.917637	−	0.397419i	$-0.869906\pi$
$463$	−172137.	−	298150.i	−0.802994	−	1.39083i	0.114643	−	0.993407i	$-0.463428\pi$
$464$	144768.	−	83581.7i	0.672412	−	0.388218i
$465$	−18529.0	−	146728.i	−0.0856930	−	0.678590i
$466$	−94664.9	+	163964.i	−0.435931	+	0.755054i
$467$		−	305284.i		−	1.39982i	−0.714233	−	0.699908i	$-0.753224\pi$
$467$		−	305284.i		−	1.39982i	0.714233	−	0.699908i	$-0.246776\pi$
$468$	13515.3	+	13804.0i	0.0617070	+	0.0630251i
$469$	733670.			3.33545
$470$	4164.40	+	2404.32i	0.0188520	+	0.0108842i
$471$	129267.	−	307474.i	0.582703	−	1.38601i
$472$	−35452.3	−	61405.2i	−0.159133	−	0.275626i
$473$	−80588.2	+	46527.6i	−0.360205	+	0.207964i
$474$	202853.	+	85283.0i	0.902870	+	0.379582i
$475$	24049.2	−	41654.4i	0.106589	−	0.184618i
$476$		−	93763.4i		−	0.413828i
$477$	−192698.	−	53822.1i	−0.846916	−	0.236550i
$478$	141568.			0.619596
$479$	−5122.93	−	2957.73i	−0.0223279	−	0.0128910i	0.488795	−	0.872399i	$-0.337437\pi$
$479$	−5122.93	−	2957.73i	−0.0223279	−	0.0128910i	−0.511122	+	0.859508i	$0.670770\pi$
$480$	−39493.8	+	4987.31i	−0.171414	+	0.0216463i
$481$	15155.9	+	26250.7i	0.0655075	+	0.113462i
$482$	80712.3	−	46599.2i	0.347412	−	0.200579i
$483$	−95395.4	+	72401.9i	−0.408915	+	0.310353i
$484$	2644.59	−	4580.57i	0.0112893	−	0.0195537i
$485$		−	10655.7i		−	0.0453002i
$486$	−86176.7	+	193432.i	−0.364852	+	0.818946i
$487$	267415.			1.12753			0.563765	−	0.825936i	$-0.309353\pi$
$487$	267415.			1.12753			0.563765	+	0.825936i	$0.309353\pi$
$488$	29332.8	+	16935.3i	0.123172	+	0.0711136i
$489$	−166392.	−	219235.i	−0.695849	−	0.916839i
$490$	120850.	+	209318.i	0.503331	+	0.871795i
$491$	−197692.	+	114137.i	−0.820022	+	0.473440i	−0.850424	−	0.526098i	$-0.823654\pi$
$491$	−197692.	+	114137.i	−0.820022	+	0.473440i	0.0304024	+	0.999538i	$0.490321\pi$
$492$	8292.23	+	65664.9i	0.0342563	+	0.271271i
$493$	−138785.	+	240382.i	−0.571016	+	0.989029i
$494$			104834.i			0.429586i
$495$	−31127.8	+	111446.i	−0.127039	+	0.454836i
$496$	−287951.			−1.17045
$497$	105421.	+	60865.0i	0.426791	+	0.246408i
$498$	−86674.4	+	206163.i	−0.349488	+	0.831288i
$499$	74994.0	+	129893.i	0.301180	+	0.521658i	0.976403	−	0.215955i	$-0.0692863\pi$
$499$	74994.0	+	129893.i	0.301180	+	0.521658i	−0.675224	+	0.737613i	$0.735953\pi$
$500$	3799.60	−	2193.70i	0.0151984	−	0.00877479i
$501$	−356903.	−	150048.i	−1.42192	−	0.597800i
$502$	−71060.8	+	123081.i	−0.281983	+	0.488409i
$503$			231439.i			0.914746i	0.889275	+	0.457373i	$0.151210\pi$
$503$			231439.i			0.914746i	−0.889275	+	0.457373i	$0.848790\pi$
$504$	364724.	−	357095.i	1.43583	−	1.40580i
$505$	20219.9			0.0792861
$506$	−57513.8	−	33205.6i	−0.224632	−	0.129691i
$507$	−203488.	+	25696.6i	−0.791629	+	0.0999677i
$508$	3406.60	+	5900.40i	0.0132006	+	0.0228641i
$509$	−232224.	+	134075.i	−0.896339	+	0.517502i	−0.876011	−	0.482292i	$-0.839805\pi$
$509$	−232224.	+	134075.i	−0.896339	+	0.517502i	−0.0203286	+	0.999793i	$0.506471\pi$
$510$	−93507.0	+	70968.6i	−0.359504	+	0.272851i
$511$	335165.	−	580524.i	1.28356	−	2.22320i
$512$			292658.i			1.11640i
$513$	260826.	−	103225.i	0.991097	−	0.392239i
$514$	−425726.			−1.61140
$515$	98762.2	+	57020.4i	0.372371	+	0.214989i
$516$	12440.2	+	16391.0i	0.0467228	+	0.0615611i
$517$	7662.01	+	13271.0i	0.0286656	+	0.0496503i
$518$	113767.	−	65683.1i	0.423989	−	0.244790i
$519$	32089.8	+	254114.i	0.119133	+	0.943397i
$520$	−29149.8	+	50489.0i	−0.107803	+	0.186720i
$521$			163281.i			0.601535i	0.953698	+	0.300767i	$0.0972428\pi$
$521$			163281.i			0.601535i	−0.953698	+	0.300767i	$0.902757\pi$
$522$	−240070.	+	61615.1i	−0.881043	+	0.226124i
$523$	−305108.			−1.11545			−0.557726	−	0.830025i	$-0.688326\pi$
$523$	−305108.			−1.11545			−0.557726	+	0.830025i	$0.688326\pi$
$524$	10898.3	+	6292.12i	0.0396913	+	0.0229158i
$525$	−40029.9	+	95214.7i	−0.145233	+	0.345450i
$526$	34007.6	+	58902.8i	0.122915	+	0.212895i
$527$	414076.	−	239067.i	1.49093	−	0.860791i
$528$	207684.	+	87314.2i	0.744966	+	0.313197i
$529$	−129417.	+	224158.i	−0.462468	+	0.801018i
$530$		−	99035.4i		−	0.352564i
$531$	20801.6	+	81049.1i	0.0737748	+	0.287448i
$532$	−110906.			−0.391861
$533$	154123.	+	88983.0i	0.542517	+	0.313222i
$534$	−38522.2	+	4864.61i	−0.135092	+	0.0170595i
$535$	−77852.2	−	134844.i	−0.271997	−	0.471112i
$536$	475003.	−	274243.i	1.65336	−	0.954566i
$537$	399956.	−	303553.i	1.38696	−	1.05266i
$538$	149011.	−	258095.i	0.514819	−	0.891692i
$539$			770241.i			2.65124i
$540$	25312.3	+	3741.49i	0.0868048	+	0.0128309i
$541$	−203513.			−0.695339			−0.347670	−	0.937617i	$-0.613027\pi$
$541$	−203513.			−0.695339			−0.347670	+	0.937617i	$0.613027\pi$
$542$	−247464.	−	142873.i	−0.842390	−	0.486354i
$543$	−204305.	−	269189.i	−0.692914	−	0.912971i
$544$	−64347.9	−	111454.i	−0.217439	−	0.376615i
$545$	94471.6	−	54543.2i	0.318059	−	0.183632i
$546$	−28204.7	−	223349.i	−0.0946099	−	0.749202i
$547$	−72123.8	+	124922.i	−0.241048	+	0.417508i	−0.961013	−	0.276503i	$-0.910825\pi$
$547$	−72123.8	+	124922.i	−0.241048	+	0.417508i	0.719965	+	0.694011i	$0.244158\pi$
$548$		−	3777.57i		−	0.0125791i
$549$	−27963.8	−	28561.1i	−0.0927792	−	0.0947611i
$550$	−57276.7			−0.189345
$551$	284332.	+	164159.i	0.936531	+	0.540706i
$552$	−34698.7	+	82533.9i	−0.113877	+	0.270866i
$553$	312978.	+	542094.i	1.02344	+	1.77266i
$554$	−76841.1	+	44364.2i	−0.250365	+	0.144548i
$555$	37009.6	+	15559.5i	0.120151	+	0.0505137i
$556$	−5595.64	+	9691.93i	−0.0181009	+	0.0313517i
$557$		−	405708.i		−	1.30769i	−0.756631	−	0.653843i	$-0.773156\pi$
$557$		−	405708.i		−	1.30769i	0.756631	−	0.653843i	$-0.226844\pi$
$558$	411202.	+	114852.i	1.32065	+	0.368868i
$559$	55329.4			0.177065
$560$	174159.	+	100551.i	0.555354	+	0.320634i
$561$	−371143.	+	46868.3i	−1.17928	+	0.148920i
$562$	−247081.	−	427956.i	−0.782287	−	1.35496i
$563$	68266.7	−	39413.8i	0.215373	−	0.124346i	−0.388433	−	0.921477i	$-0.626983\pi$
$563$	68266.7	−	39413.8i	0.215373	−	0.124346i	0.603806	+	0.797131i	$0.293650\pi$
$564$	2699.22	−	2048.61i	0.00848554	−	0.00644024i
$565$	−4416.44	+	7649.50i	−0.0138349	+	0.0239627i
$566$		−	101100.i		−	0.315585i
$567$	−527917.	+	290094.i	−1.64210	+	0.902344i
$568$	91004.4			0.282076
$569$	−255386.	−	147447.i	−0.788811	−	0.455420i	0.0507331	−	0.998712i	$-0.483844\pi$
$569$	−255386.	−	147447.i	−0.788811	−	0.455420i	−0.839544	+	0.543292i	$0.817178\pi$
$570$	83943.9	+	110603.i	0.258368	+	0.340421i
$571$	−191708.	−	332047.i	−0.587986	−	1.01842i	−0.994496	−	0.104775i	$-0.966588\pi$
$571$	−191708.	−	332047.i	−0.587986	−	1.01842i	0.406510	−	0.913646i	$-0.366746\pi$
$572$	−26391.4	+	15237.1i	−0.0806622	+	0.0465703i
$573$	34654.1	+	274421.i	0.105547	+	0.835811i
$574$	385638.	−	667944.i	1.17046	−	2.02729i
$575$		−	18116.9i		−	0.0547958i
$576$	99217.4	−	355226.i	0.299049	−	1.07068i
$577$	−47734.1			−0.143376			−0.0716882	−	0.997427i	$-0.522839\pi$
$577$	−47734.1			−0.143376			−0.0716882	+	0.997427i	$0.522839\pi$
$578$	−69275.2	−	39996.0i	−0.207359	−	0.119719i
$579$	110686.	−	263277.i	0.330169	−	0.785336i
$580$	14974.1	+	25935.9i	0.0445128	+	0.0770985i
$581$	−550938.	+	318084.i	−1.63212	+	0.942302i
$582$	28357.0	+	11921.8i	0.0837171	+	0.0351961i
$583$	157802.	−	273320.i	0.464274	−	0.804146i
$584$		−	501134.i		−	1.46936i
$585$	49160.8	−	48132.6i	0.143650	−	0.140646i
$586$	257475.			0.749791
$587$	483351.	+	279063.i	1.40277	+	0.809889i	0.994676	−	0.103051i	$-0.0328605\pi$
$587$	483351.	+	279063.i	1.40277	+	0.809889i	0.408093	+	0.912940i	$0.366194\pi$
$588$	168981.	−	21339.1i	0.488746	−	0.0617193i
$589$	−282775.	−	489781.i	−0.815100	−	1.41179i
$590$	−35870.1	+	20709.6i	−0.103045	+	0.0594933i
$591$	−8108.74	+	6154.26i	−0.0232155	+	0.0176198i
$592$	39083.7	−	67694.9i	0.111520	−	0.193158i
$593$			368274.i			1.04728i	0.851940	+	0.523639i	$0.175426\pi$
$593$			368274.i			1.04728i	−0.851940	+	0.523639i	$0.824574\pi$
$594$	−261754.	−	207524.i	−0.741857	−	0.588161i
$595$	−333923.			−0.943219
$596$	−4597.51	−	2654.37i	−0.0129429	−	0.00747256i
$597$	10334.0	+	13615.9i	0.0289947	+	0.0382029i
$598$	19743.6	+	34197.0i	0.0552108	+	0.0956280i
$599$	344776.	−	199057.i	0.960912	−	0.554783i	0.0644583	−	0.997920i	$-0.479468\pi$
$599$	344776.	−	199057.i	0.960912	−	0.554783i	0.896454	+	0.443138i	$0.146135\pi$
$600$	9674.16	+	76608.3i	0.0268727	+	0.212801i
$601$	198355.	−	343560.i	0.549153	−	0.951161i	−0.449180	−	0.893441i	$-0.648284\pi$
$601$	198355.	−	343560.i	0.549153	−	0.951161i	0.998333	−	0.0577194i	$-0.0183829\pi$
$602$		−	239789.i		−	0.661661i
$603$	−626959.	+	160912.i	−1.72427	+	0.442541i
$604$	17877.1			0.0490031
$605$	−16312.9	−	9418.28i	−0.0445678	−	0.0257312i
$606$	−22622.3	+	53809.2i	−0.0616016	+	0.146525i
$607$	−304115.	−	526743.i	−0.825393	−	1.42962i	−0.901618	−	0.432532i	$-0.857620\pi$
$607$	−304115.	−	526743.i	−0.825393	−	1.42962i	0.0762252	−	0.997091i	$-0.475713\pi$
$608$	−131831.	+	76112.7i	−0.356624	+	0.205897i
$609$	−649933.	−	273243.i	−1.75240	−	0.736741i
$610$	9892.81	−	17134.9i	0.0265864	−	0.0460491i
$611$		−	9111.46i		−	0.0244065i
$612$	20564.6	+	80125.7i	0.0549058	+	0.213929i
$613$	263736.			0.701856			0.350928	−	0.936402i	$-0.385866\pi$
$613$	263736.			0.701856			0.350928	+	0.936402i	$0.385866\pi$
$614$	390613.	+	225521.i	1.03612	+	0.598204i
$615$	233855.	−	29531.4i	0.618296	−	0.0780790i
$616$	402587.	+	697301.i	1.06096	+	1.83763i
$617$	−431797.	+	249298.i	−1.13425	+	0.654860i	−0.945000	−	0.327069i	$-0.893939\pi$
$617$	−431797.	+	249298.i	−1.13425	+	0.654860i	−0.189250	+	0.981929i	$0.560606\pi$
$618$	−262239.	+	199030.i	−0.686625	+	0.521125i
$619$	−332773.	+	576379.i	−0.868493	+	1.50427i	−0.00495586	+	0.999988i	$0.501578\pi$
$619$	−332773.	+	576379.i	−0.868493	+	1.50427i	−0.863537	+	0.504286i	$0.831756\pi$
$620$		−	51587.9i		−	0.134204i
$621$	65640.9	−	82793.8i	0.170212	−	0.214691i
$622$	−98913.1			−0.255666
$623$	−95652.7	−	55225.1i	−0.246446	−	0.142285i
$624$	−80984.4	−	106704.i	−0.207985	−	0.274038i
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	432515.	−	249713.i	1.10370	−	0.637223i
$627$	55437.3	+	439000.i	0.141015	+	1.11668i
$628$	58172.8	−	100758.i	0.147503	−	0.255483i
$629$			129795.i			0.328061i
$630$	−208599.	−	213055.i	−0.525570	−	0.536797i
$631$	171926.			0.431800			0.215900	−	0.976415i	$-0.430731\pi$
$631$	171926.			0.431800			0.215900	+	0.976415i	$0.430731\pi$
$632$	405266.	+	233980.i	1.01462	+	0.585794i
$633$	−17792.1	+	42320.2i	−0.0444038	+	0.105618i
$634$	308457.	+	534263.i	0.767389	+	1.32916i
$635$	21013.3	−	12132.1i	0.0521132	−	0.0300876i
$636$	−64334.8	−	27047.5i	−0.159049	−	0.0668671i
$637$	228987.	−	396618.i	0.564330	−	0.977448i
$638$		−	390969.i		−	0.960509i
$639$	−103437.	−	28890.8i	−0.253323	−	0.0707552i
$640$	111796.			0.272940
$641$	12301.1	+	7102.04i	0.0299383	+	0.0172849i	0.514894	−	0.857254i	$-0.327831\pi$
$641$	12301.1	+	7102.04i	0.0299383	+	0.0172849i	−0.484956	+	0.874538i	$0.661164\pi$
$642$	445948.	−	56314.7i	1.08197	−	0.136632i
$643$	349385.	+	605153.i	0.845050	+	1.46367i	0.885577	+	0.464492i	$0.153763\pi$
$643$	349385.	+	605153.i	0.845050	+	1.46367i	−0.0405270	+	0.999178i	$0.512904\pi$
$644$	−36177.6	+	20887.1i	−0.0872304	+	0.0503625i
$645$	58373.9	−	44303.8i	0.140314	−	0.106493i
$646$	−224450.	+	388758.i	−0.537841	+	0.931568i
$647$		−	141077.i		−	0.337014i	−0.985700	−	0.168507i	$-0.946105\pi$
$647$		−	141077.i		−	0.337014i	0.985700	−	0.168507i	$-0.0538947\pi$
$648$	−233356.	+	385150.i	−0.555735	+	0.917233i
$649$	−131994.			−0.313374
$650$	29493.3	+	17028.0i	0.0698067	+	0.0403029i
$651$	734223.	+	967399.i	1.73247	+	2.28267i
$652$	−48002.3	−	83142.4i	−0.112919	−	0.195581i
$653$	30383.9	−	17542.2i	0.0712553	−	0.0411393i	−0.463949	−	0.885862i	$-0.653568\pi$
$653$	30383.9	−	17542.2i	0.0712553	−	0.0411393i	0.535204	+	0.844723i	$0.320235\pi$
$654$	39454.0	+	312431.i	0.0922435	+	0.730463i
$655$	22408.4	−	38812.4i	0.0522309	−	0.0904666i
$656$		−	458935.i		−	1.06646i
$657$	−159093.	+	569598.i	−0.368571	+	1.31959i
$658$	−39487.6			−0.0912029
$659$	−438572.	−	253209.i	−1.00988	−	0.583054i	−0.0987232	−	0.995115i	$-0.531476\pi$
$659$	−438572.	−	253209.i	−1.00988	−	0.583054i	−0.911156	+	0.412061i	$0.864809\pi$
$660$	−15642.8	+	37207.8i	−0.0359110	+	0.0854174i
$661$	−32757.8	−	56738.2i	−0.0749743	−	0.129859i	0.826101	−	0.563522i	$-0.190554\pi$
$661$	−32757.8	−	56738.2i	−0.0749743	−	0.129859i	−0.901075	+	0.433663i	$0.857221\pi$
$662$	−400885.	+	231451.i	−0.914753	+	0.528133i
$663$	205045.	+	86204.7i	0.466469	+	0.196112i
$664$	−237798.	+	411877.i	−0.539351	+	0.934183i
$665$			394974.i			0.893153i
$666$	−82813.5	+	81081.5i	−0.186704	+	0.182799i
$667$	123665.			0.277969
$668$	−116956.	−	67524.6i	−0.262102	−	0.151325i
$669$	323036.	−	40793.2i	0.721769	−	0.0911456i
$670$	−160200.	−	277475.i	−0.356873	−	0.618122i
$671$	54604.9	−	31526.1i	0.121279	−	0.0700206i
$672$	260388.	−	197626.i	0.576611	−	0.437628i
$673$	117805.	−	204044.i	0.260096	−	0.450500i	−0.706171	−	0.708041i	$-0.749579\pi$
$673$	117805.	−	204044.i	0.260096	−	0.450500i	0.966267	+	0.257541i	$0.0829124\pi$
$674$			569150.i			1.25287i
$675$	13324.7	−	90145.5i	0.0292449	−	0.197850i
$676$	−71543.9			−0.156559
$677$	−56045.9	−	32358.1i	−0.122283	−	0.0706002i	0.437611	−	0.899165i	$-0.355825\pi$
$677$	−56045.9	−	32358.1i	−0.122283	−	0.0706002i	−0.559894	+	0.828564i	$0.689158\pi$
$678$	−15415.6	−	20311.3i	−0.0335353	−	0.0441855i
$679$	43751.4	+	75779.7i	0.0948971	+	0.164367i
$680$	−216193.	+	124819.i	−0.467546	+	0.269938i
$681$	46895.9	+	371362.i	0.101121	+	0.800761i
$682$	−336736.	+	583244.i	−0.723971	+	1.25395i
$683$		−	687123.i		−	1.47297i	−0.676455	−	0.736484i	$-0.736485\pi$
$683$		−	687123.i		−	1.47297i	0.676455	−	0.736484i	$-0.263515\pi$
$684$	94775.2	−	24324.5i	0.202573	−	0.0519914i
$685$	−13453.2			−0.0286711
$686$	−1.03426e6	−	597131.i	−2.19777	−	1.26888i
$687$	307294.	−	730925.i	0.651089	−	1.54867i
$688$	−71341.2	−	123567.i	−0.150717	−	0.261050i
$689$	−162513.	+	93826.7i	−0.342333	+	0.197646i
$690$	48212.5	+	20269.4i	0.101266	+	0.0425738i
$691$	312656.	−	541537.i	0.654804	−	1.13415i	−0.327139	−	0.944976i	$-0.606084\pi$
$691$	312656.	−	541537.i	0.654804	−	1.13415i	0.981943	−	0.189178i	$-0.0605822\pi$
$692$			89343.8i			0.186574i
$693$	−236218.	−	920372.i	−0.491865	−	1.91645i
$694$	−345105.			−0.716527
$695$	34516.3	+	19928.0i	0.0714585	+	0.0412566i
$696$	−522926.	+	66035.5i	−1.07950	+	0.136320i
$697$	381024.	+	659953.i	0.784308	+	1.35846i
$698$	191123.	−	110345.i	0.392285	−	0.226486i
$699$	378485.	−	287257.i	0.774629	−	0.587917i
$700$	−18014.2	+	31201.6i	−0.0367637	+	0.0636767i
$701$			771775.i			1.57056i	0.619141	+	0.785280i	$0.287481\pi$
$701$			771775.i			1.57056i	−0.619141	+	0.785280i	$0.712519\pi$
$702$	73088.4	+	184678.i	0.148311	+	0.374749i
$703$	153525.			0.310648
$704$	503848.	+	290897.i	1.01661	+	0.586940i
$705$	−7295.81	−	9612.82i	−0.0146790	−	0.0193407i
$706$	150334.	+	260387.i	0.301612	+	0.522408i
$707$	−143797.	+	83021.1i	−0.287680	+	0.166092i
$708$	3656.81	+	28957.7i	0.00729517	+	0.0577694i
$709$	87151.7	−	150951.i	0.173374	−	0.300292i	−0.766224	−	0.642574i	$-0.777866\pi$
$709$	87151.7	−	150951.i	0.173374	−	0.300292i	0.939597	+	0.342282i	$0.111200\pi$
$710$		−	53160.6i		−	0.105456i
$711$	−386351.	−	394604.i	−0.764263	−	0.780589i
$712$	−82571.7			−0.162881
$713$	−184483.	−	106511.i	−0.362891	−	0.209515i
$714$	373597.	−	888634.i	0.732837	−	1.74312i
$715$	54264.3	+	93988.6i	0.106146	+	0.183850i
$716$	151679.	−	87571.8i	0.295869	−	0.170820i
$717$	−327517.	−	137694.i	−0.637082	−	0.267840i
$718$	426225.	−	738242.i	0.826779	−	1.43202i
$719$			21195.4i			0.0410000i	0.999790	+	0.0205000i	$0.00652580\pi$
$719$			21195.4i			0.0410000i	−0.999790	+	0.0205000i	$0.993474\pi$
$720$	−170881.	−	47728.5i	−0.329632	−	0.0920689i
$721$	−936481.			−1.80148
$722$	55094.9	+	31809.1i	0.105691	+	0.0610206i
$723$	−232052.	+	29303.7i	−0.443923	+	0.0560590i
$724$	−58939.7	−	102087.i	−0.112443	−	0.194756i
$725$	92366.6	−	53327.9i	0.175727	−	0.101456i
$726$	43315.0	−	32874.6i	0.0821798	−	0.0623717i
$727$	−20741.3	+	35925.0i	−0.0392434	+	0.0679716i	−0.884980	−	0.465629i	$-0.845828\pi$
$727$	−20741.3	+	35925.0i	−0.0392434	+	0.0679716i	0.845737	+	0.533601i	$0.179161\pi$
$728$		−	478746.i		−	0.903321i
$729$	387508.	−	363685.i	0.729165	−	0.684338i
$730$	−292740.			−0.549333
$731$	205179.	+	118460.i	0.383970	+	0.221685i
$732$	−8429.24	−	11106.2i	−0.0157314	−	0.0207273i
$733$	−154333.	−	267313.i	−0.287244	−	0.497522i	0.685907	−	0.727690i	$-0.259406\pi$
$733$	−154333.	−	267313.i	−0.287244	−	0.497522i	−0.973151	+	0.230168i	$0.926072\pi$
$734$	−274815.	+	158664.i	−0.510091	+	0.294501i
$735$	−75995.7	−	601799.i	−0.140674	−	1.11398i
$736$	−28668.9	+	49655.9i	−0.0529242	+	0.0916675i
$737$		−	1.02104e6i		−	1.87979i
$738$	−183051.	+	655374.i	−0.336093	+	1.20331i
$739$	−146054.			−0.267439			−0.133719	−	0.991019i	$-0.542692\pi$
$739$	−146054.			−0.267439			−0.133719	+	0.991019i	$0.542692\pi$
$740$	12127.9	+	7002.06i	0.0221474	+	0.0127868i
$741$	101966.	−	242534.i	0.185702	−	0.441709i
$742$	406630.	+	704303.i	0.738569	+	1.27924i
$743$	−893060.	+	515608.i	−1.61772	+	0.933990i	−0.630210	+	0.776425i	$0.717031\pi$
$743$	−893060.	+	515608.i	−1.61772	+	0.933990i	−0.987509	+	0.157565i	$0.949636\pi$
$744$	836971.	+	351877.i	1.51204	+	0.635690i
$745$	−9453.12	+	16373.3i	−0.0170319	+	0.0295001i
$746$			192895.i			0.346611i
$747$	401042.	−	392654.i	0.718702	−	0.703670i
$748$	−130490.			−0.233224
$749$	1.10731e6	+	639307.i	1.97382	+	1.13958i
$750$	44751.1	−	5651.20i	0.0795574	−	0.0100466i
$751$	415030.	+	718853.i	0.735867	+	1.27456i	0.954342	+	0.298717i	$0.0965585\pi$
$751$	415030.	+	718853.i	0.735867	+	1.27456i	−0.218475	+	0.975843i	$0.570108\pi$
$752$	−20348.5	+	11748.2i	−0.0359830	+	0.0207748i
$753$	284112.	−	215631.i	0.501071	−	0.380296i
$754$	−116233.	+	201321.i	−0.204449	+	0.354116i
$755$		−	63666.5i		−	0.111691i
$756$	−195374.	+	77321.6i	−0.341840	+	0.135287i
$757$	389997.			0.680564			0.340282	−	0.940323i	$-0.389477\pi$
$757$	389997.			0.680564			0.340282	+	0.940323i	$0.389477\pi$
$758$	−633552.	−	365781.i	−1.10267	−	0.636624i
$759$	100761.	+	132761.i	0.174908	+	0.230456i
$760$	147640.	+	255720.i	0.255609	+	0.442728i
$761$	−310542.	+	179292.i	−0.536230	+	0.309593i	−0.743550	−	0.668681i	$-0.766859\pi$
$761$	−310542.	+	179292.i	−0.536230	+	0.309593i	0.207320	+	0.978273i	$0.433526\pi$
$762$	8775.77	+	69494.0i	0.0151139	+	0.119684i
$763$	−447898.	+	775782.i	−0.769361	+	1.33257i
$764$			96483.4i			0.165297i
$765$	285355.	−	73237.6i	0.487598	−	0.125144i
$766$	182979.			0.311848
$767$	67967.1	+	39240.8i	0.115533	+	0.0667033i
$768$	129037.	−	306927.i	0.218773	−	0.520370i
$769$	−332825.	−	576470.i	−0.562812	−	0.974818i	−0.997250	−	0.0741166i	$-0.976386\pi$
$769$	−332825.	−	576470.i	−0.562812	−	0.974818i	0.434438	−	0.900702i	$-0.356947\pi$
$770$	407331.	−	235173.i	0.687015	−	0.396648i
$771$	984915.	+	414076.i	1.65688	+	0.696580i
$772$	49810.9	−	86274.9i	0.0835775	−	0.144760i
$773$		−	783765.i		−	1.31168i	−0.754901	−	0.655838i	$-0.772315\pi$
$773$		−	783765.i		−	1.31168i	0.754901	−	0.655838i	$-0.227685\pi$
$774$	52591.6	+	204912.i	0.0877879	+	0.342047i
$775$	−183722.			−0.305885
$776$	56652.3	+	32708.2i	0.0940794	+	0.0543168i
$777$	−327084.	+	41304.5i	−0.541773	+	0.0684156i
$778$	−287927.	−	498704.i	−0.475689	−	0.823918i
$779$	780612.	−	450687.i	1.28635	−	0.742677i
$780$	19116.5	−	14508.8i	0.0314210	−	0.0238475i
$781$	84705.4	−	146714.i	0.138870	−	0.240530i
$782$			169084.i			0.276496i
$783$	615331.	+	90954.2i	1.00366	+	0.148354i
$784$	−1.18102e6			−1.92143
$785$	−358834.	−	207173.i	−0.582311	−	0.336197i
$786$	78216.6	+	103057.i	0.126606	+	0.166814i
$787$	318399.	+	551484.i	0.514070	+	0.890396i	0.999867	+	0.0163240i	$0.00519631\pi$
$787$	318399.	+	551484.i	0.514070	+	0.890396i	−0.485796	+	0.874072i	$0.661470\pi$
$788$	−3075.14	+	1775.44i	−0.00495237	+	0.00285925i
$789$	−21385.5	−	169349.i	−0.0343530	−	0.272037i
$790$	136680.	−	236738.i	0.219004	−	0.379326i
$791$		−	72533.9i		−	0.115928i
$792$	−496967.	−	507583.i	−0.792277	−	0.809202i
$793$	−37490.0			−0.0596169
$794$	−21456.2	−	12387.7i	−0.0340339	−	0.0196495i
$795$	−96325.2	+	229118.i	−0.152407	+	0.362514i
$796$	2981.24	+	5163.66i	0.00470512	+	0.00814950i
$797$	93299.4	−	53866.4i	0.146880	−	0.0848011i	−0.424759	−	0.905306i	$-0.639641\pi$
$797$	93299.4	−	53866.4i	0.146880	−	0.0848011i	0.571639	+	0.820505i	$0.306308\pi$
$798$	−1.05110e6	−	441902.i	−1.65059	−	0.693937i
$799$	19507.6	−	33788.1i	0.0305569	−	0.0529261i
$800$			49451.2i			0.0772675i
$801$	93852.5	+	26213.7i	0.146279	+	0.0408568i
$802$	267772.			0.416309
$803$	−807910.	−	466447.i	−1.25295	−	0.723388i
$804$	−224004.	+	28287.4i	−0.346532	+	0.0437604i
$805$	74386.2	+	128841.i	0.114789	+	0.198820i
$806$	346789.	−	200219.i	0.533821	−	0.308202i
$807$	−595769.	+	452169.i	−0.914810	+	0.694310i
$808$	−62066.0	+	107501.i	−0.0950672	+	0.164661i
$809$			389546.i			0.595198i	0.954691	+	0.297599i	$0.0961859\pi$
$809$			389546.i			0.595198i	−0.954691	+	0.297599i	$0.903814\pi$
$810$	224987.	+	136316.i	0.342915	+	0.207766i
$811$	713149.			1.08427			0.542137	−	0.840290i	$-0.317616\pi$
$811$	713149.			1.08427			0.542137	+	0.840290i	$0.317616\pi$
$812$	−212981.	−	122965.i	−0.323019	−	0.186495i
$813$	433544.	+	571229.i	0.655921	+	0.864230i
$814$	−91410.7	−	158328.i	−0.137958	−	0.238951i
$815$	−296098.	+	170952.i	−0.445780	+	0.257371i
$816$	−71863.6	−	569077.i	−0.107927	−	0.854655i
$817$	140118.	−	242691.i	0.209918	−	0.363589i
$818$			944537.i			1.41160i
$819$	−151986.	+	544151.i	−0.226587	+	0.811244i
$820$	82220.8			0.122280
$821$	−374686.	−	216325.i	−0.555880	−	0.320938i	0.195610	−	0.980682i	$-0.437331\pi$
$821$	−374686.	−	216325.i	−0.555880	−	0.320938i	−0.751490	+	0.659744i	$0.770665\pi$
$822$	15051.6	−	35801.5i	0.0222761	−	0.0529856i
$823$	−371613.	−	643653.i	−0.548645	−	0.950281i	−0.998368	−	0.0571131i	$-0.981810\pi$
$823$	−371613.	−	643653.i	−0.548645	−	0.950281i	0.449723	−	0.893168i	$-0.351523\pi$
$824$	−606310.	+	350053.i	−0.892977	+	0.515560i
$825$	132510.	+	55709.4i	0.194688	+	0.0818503i
$826$	170063.	−	294558.i	0.249259	−	0.431729i
$827$			1.26895e6i			1.85539i	0.373344	+	0.927693i	$0.378211\pi$
$827$			1.26895e6i			1.85539i	−0.373344	+	0.927693i	$0.621789\pi$
$828$	26334.6	−	25783.8i	0.0384119	−	0.0376085i
$829$	−664310.			−0.966633			−0.483316	−	0.875446i	$-0.660568\pi$
$829$	−664310.			−0.966633			−0.483316	+	0.875446i	$0.660568\pi$
$830$	240600.	+	138910.i	0.349252	+	0.201641i
$831$	220922.	−	27898.2i	0.319917	−	0.0403993i
$832$	−172963.	−	299581.i	−0.249866	−	0.432781i
$833$	1.69831e6	−	980521.i	2.44753	−	1.41308i
$834$	−91649.4	+	69558.8i	−0.131764	+	0.100005i
$835$	−240478.	+	416520.i	−0.344907	+	0.597397i
$836$			154347.i			0.220844i
$837$	−839607.	−	665660.i	−1.19846	−	0.950170i
$838$	843013.			1.20046
$839$	15297.9	+	8832.27i	0.0217325	+	0.0125472i	0.510827	−	0.859684i	$-0.329339\pi$
$839$	15297.9	+	8832.27i	0.0217325	+	0.0125472i	−0.489094	+	0.872231i	$0.662673\pi$
$840$	−383345.	−	505089.i	−0.543290	−	0.715829i
$841$	10374.1	+	17968.5i	0.0146676	+	0.0254050i
$842$	−539797.	+	311652.i	−0.761388	+	0.439588i
$843$	155375.	+	1.23040e6i	0.218639	+	1.73137i
$844$	−8006.80	+	13868.2i	−0.0112402	+	0.0194686i
$845$			254792.i			0.356839i
$846$	33744.2	−	8660.61i	0.0471475	−	0.0121006i
$847$	154682.			0.215612
$848$	419084.	+	241958.i	0.582787	+	0.336472i
$849$	−98333.0	+	233894.i	−0.136422	+	0.324491i
$850$	72913.6	+	126290.i	0.100919	+	0.174796i
$851$	50079.8	−	28913.6i	0.0691518	−	0.0399248i
$852$	−34533.9	−	14518.7i	−0.0475737	−	0.0200008i
$853$	5371.24	−	9303.25i	0.00738203	−	0.0127861i	−0.862311	−	0.506379i	$-0.830984\pi$
$853$	5371.24	−	9303.25i	0.00738203	−	0.0127861i	0.869693	+	0.493593i	$0.164317\pi$
$854$			162476.i			0.222778i
$855$	−86627.7	−	337526.i	−0.118502	−	0.461717i
$856$	955883.			1.30454
$857$	−557483.	−	321863.i	−0.759049	−	0.438237i	0.0699049	−	0.997554i	$-0.477730\pi$
$857$	−557483.	−	321863.i	−0.759049	−	0.438237i	−0.828954	+	0.559316i	$0.811064\pi$
$858$	−310833.	+	39252.3i	−0.422234	+	0.0533201i
$859$	−161341.	−	279451.i	−0.218655	−	0.378721i	0.735742	−	0.677262i	$-0.236833\pi$
$859$	−161341.	−	279451.i	−0.218655	−	0.378721i	−0.954397	+	0.298541i	$0.903500\pi$
$860$	22137.6	−	12781.2i	0.0299319	−	0.0172812i
$861$	−1.54184e6	+	1.17020e6i	−2.07985	+	1.57854i
$862$	353563.	−	612388.i	0.475830	−	0.824162i
$863$		−	170499.i		−	0.228928i	−0.993427	−	0.114464i	$-0.963485\pi$
$863$		−	170499.i		−	0.228928i	0.993427	−	0.114464i	$-0.0365151\pi$
$864$	−179171.	+	225991.i	−0.240016	+	0.302736i
$865$	318183.			0.425251
$866$	687978.	+	397204.i	0.917358	+	0.529637i
$867$	121366.	+	159910.i	0.161458	+	0.212734i
$868$	211815.	+	366875.i	0.281137	+	0.486943i
$869$	754428.	−	435569.i	0.999030	−	0.576790i
$870$	38574.9	+	305469.i	0.0509644	+	0.403580i
$871$	−303549.	+	525763.i	−0.400122	+	0.693032i
$872$			669691.i			0.880727i
$873$	−54008.3	−	55162.0i	−0.0708650	−	0.0723788i
$874$	199998.			0.261819
$875$	111119.	+	64154.8i	0.145135	+	0.0837940i
$876$	−79950.0	+	190168.i	−0.104186	+	0.247816i
$877$	−168728.	−	292245.i	−0.219375	−	0.379969i	0.735242	−	0.677805i	$-0.237069\pi$
$877$	−168728.	−	292245.i	−0.219375	−	0.379969i	−0.954617	+	0.297836i	$0.903735\pi$
$878$	−221263.	+	127746.i	−0.287026	+	0.165714i
$879$	−595669.	−	250429.i	−0.770951	−	0.324121i
$880$	139936.	−	242376.i	0.180702	−	0.312985i
$881$		−	665851.i		−	0.857878i	−0.903334	−	0.428939i	$-0.858888\pi$
$881$		−	665851.i		−	0.857878i	0.903334	−	0.428939i	$-0.141112\pi$
$882$	1.68653e6	+	471061.i	2.16799	+	0.605536i
$883$	726392.			0.931644			0.465822	−	0.884879i	$-0.345759\pi$
$883$	726392.			0.931644			0.465822	+	0.884879i	$0.345759\pi$
$884$	67192.7	+	38793.7i	0.0859840	+	0.0496429i
$885$	103128.	−	13023.1i	0.131671	−	0.0166276i
$886$	−273196.	−	473190.i	−0.348023	−	0.602793i
$887$	809454.	−	467339.i	1.02883	−	0.593997i	0.112183	−	0.993688i	$-0.464216\pi$
$887$	809454.	−	467339.i	1.02883	−	0.593997i	0.916650	+	0.399690i	$0.130882\pi$
$888$	−196326.	+	149005.i	−0.248973	+	0.188962i
$889$	−99626.1	+	172557.i	−0.126058	+	0.218338i
$890$			48234.6i			0.0608946i
$891$	403721.	+	734698.i	0.508541	+	0.925451i
$892$	113576.			0.142743
$893$	−39965.6	−	23074.1i	−0.0501168	−	0.0289349i
$894$	−32996.2	−	43475.2i	−0.0412847	−	0.0543959i
$895$	−311873.	−	540179.i	−0.389342	−	0.674360i
$896$	−795055.	+	459025.i	−0.990333	+	0.571769i
$897$	−12415.7	−	98317.9i	−0.0154307	−	0.122193i
$898$	−56474.1	+	97815.9i	−0.0700320	+	0.121299i
$899$		−	1.25408e6i		−	1.55170i
$900$	8550.83	−	30614.3i	0.0105566	−	0.0377955i
$901$	−803529.			−0.989811
$902$	−929573.	−	536689.i	−1.14254	−	0.659645i
$903$	−233227.	+	554751.i	−0.286024	+	0.680334i
$904$	−27112.9	−	46960.9i	−0.0331771	−	0.0574645i
$905$	−363565.	+	209904.i	−0.443899	+	0.256285i
$906$	169429.	+	71230.9i	0.206410	+	0.0867784i
$907$	−695259.	+	1.20422e6i	−0.845146	+	1.46384i	0.0403479	+	0.999186i	$0.487153\pi$
$907$	−695259.	+	1.20422e6i	−0.845146	+	1.46384i	−0.885494	+	0.464651i	$0.846180\pi$
$908$			130567.i			0.158365i
$909$	104673.	−	102484.i	0.126680	−	0.124031i
$910$	−279661.			−0.337714
$911$	1.08512e6	+	626493.i	1.30749	+	0.754882i	0.981677	−	0.190551i	$-0.0610274\pi$
$911$	1.08512e6	+	626493.i	1.30749	+	0.754882i	0.325817	+	0.945433i	$0.394361\pi$
$912$	−673122.	+	85002.4i	−0.809290	+	0.102198i
$913$	442676.	+	766737.i	0.531061	+	0.919824i
$914$	−105433.	+	60871.9i	−0.126207	+	0.0728659i
$915$	−39553.0	+	30019.4i	−0.0472429	+	0.0358558i
$916$	138288.	−	239522.i	0.164814	−	0.285466i
$917$			368026.i			0.437663i
$918$	−124359.	+	841323.i	−0.147568	+	0.998338i
$919$	948830.			1.12346			0.561730	−	0.827321i	$-0.310136\pi$
$919$	948830.			1.12346			0.561730	+	0.827321i	$0.310136\pi$
$920$	96320.3	+	55610.5i	0.113800	+	0.0657024i
$921$	−684333.	−	901665.i	−0.806767	−	1.06298i
$922$	−339808.	−	588565.i	−0.399735	−	0.692362i
$923$	−87234.2	+	50364.7i	−0.102396	+	0.0591184i
$924$	−41525.7	−	328836.i	−0.0486378	−	0.385155i
$925$	24936.7	−	43191.6i	0.0291444	−	0.0504796i
$926$		−	1.23463e6i		−	1.43984i
$927$	800272.	−	205394.i	0.931276	−	0.239016i
$928$	−337553.			−0.391963
$929$	−841718.	−	485966.i	−0.975293	−	0.563086i	−0.0744474	−	0.997225i	$-0.523719\pi$
$929$	−841718.	−	485966.i	−0.975293	−	0.563086i	−0.900846	+	0.434139i	$0.857053\pi$
$930$	205551.	−	488920.i	0.237658	−	0.565291i
$931$	−1.15979e6	−	2.00882e6i	−1.33807	−	2.31761i
$932$	143536.	−	82870.5i	0.165245	−	0.0954043i
$933$	228835.	+	96206.3i	0.262881	+	0.110520i
$934$	547401.	−	948127.i	0.627498	−	1.08686i
$935$			464718.i			0.531577i
$936$	105001.	+	409113.i	0.119851	+	0.466973i
$937$	43168.5			0.0491686			0.0245843	−	0.999698i	$-0.492174\pi$
$937$	43168.5			0.0491686			0.0245843	+	0.999698i	$0.492174\pi$
$938$	2.27857e6	+	1.31553e6i	2.58974	+	1.49519i
$939$	−1.24350e6	+	157030.i	−1.41031	+	0.178095i
$940$	−2104.76	−	3645.55i	−0.00238203	−	0.00412579i
$941$	904276.	−	522084.i	1.02123	−	0.589605i	0.106767	−	0.994284i	$-0.465950\pi$
$941$	904276.	−	522084.i	1.02123	−	0.589605i	0.914459	+	0.404679i	$0.132617\pi$
$942$	952796.	−	723140.i	1.07374	−	0.814930i
$943$	169757.	−	294028.i	0.190899	−	0.330648i
$944$		−	202387.i		−	0.227111i
$945$	275368.	+	695792.i	0.308355	+	0.779141i
$946$	−333712.			−0.372898
$947$	−338094.	−	195199.i	−0.376997	−	0.217659i	0.299514	−	0.954092i	$-0.403175\pi$
$947$	−338094.	−	195199.i	−0.376997	−	0.217659i	−0.676511	+	0.736433i	$0.736509\pi$
$948$	−116459.	−	153445.i	−0.129586	−	0.170740i
$949$	277343.	+	480373.i	0.307954	+	0.533391i
$950$	149380.	−	86244.5i	0.165518	−	0.0955618i
$951$	−193971.	−	1.53603e6i	−0.214475	−	1.69840i
$952$	1.02499e6	−	1.77534e6i	1.13096	−	1.95888i
$953$			975874.i			1.07450i	0.843422	+	0.537252i	$0.180538\pi$
$953$			975874.i			1.07450i	−0.843422	+	0.537252i	$0.819462\pi$
$954$	−501958.	−	512680.i	−0.551531	−	0.563313i
$955$	343610.			0.376755
$956$	−107326.	−	61964.8i	−0.117433	−	0.0677999i
$957$	−380270.	+	904507.i	−0.415211	+	0.987616i
$958$	−10606.9	−	18371.7i	−0.0115574	−	0.0200179i
$959$	95674.2	−	55237.5i	0.104030	−	0.0600616i
$960$	−422364.	−	177569.i	−0.458294	−	0.192675i
$961$	−618361.	+	1.07103e6i	−0.669569	+	1.15973i
$962$			108703.i			0.117461i
$963$	−1.08647e6	−	303461.i	−1.17157	−	0.327227i
$964$	−81586.7			−0.0877941
$965$	−307254.	−	177393.i	−0.329946	−	0.190495i
$966$	−426094.	+	53807.5i	−0.456616	+	0.0576619i
$967$	−327389.	−	567055.i	−0.350116	−	0.606418i	0.636154	−	0.771562i	$-0.280524\pi$
$967$	−327389.	−	567055.i	−0.350116	−	0.606418i	−0.986269	+	0.165144i	$0.947191\pi$
$968$	100147.	−	57819.6i	0.106877	−	0.0617056i
$969$	897383.	−	681084.i	0.955720	−	0.725359i
$970$	19106.7	−	33093.7i	0.0203068	−	0.0351724i
$971$		−	377972.i		−	0.400886i	−0.979705	−	0.200443i	$-0.935762\pi$
$971$		−	377972.i		−	0.400886i	0.979705	−	0.200443i	$-0.0642382\pi$
$972$	149999.	−	108926.i	0.158765	−	0.115292i
$973$	−327289.			−0.345705
$974$	830515.	+	479498.i	0.875447	+	0.505439i
$975$	−51670.8	−	68080.5i	−0.0543545	−	0.0716165i
$976$	48339.3	+	83726.1i	0.0507459	+	0.0878944i
$977$	108631.	−	62718.0i	0.113806	−	0.0657057i	−0.442017	−	0.897007i	$-0.645737\pi$
$977$	108631.	−	62718.0i	0.113806	−	0.0657057i	0.555822	+	0.831301i	$0.312403\pi$
$978$	−123659.	−	979238.i	−0.129285	−	1.02379i
$979$	−76856.3	+	133119.i	−0.0801889	+	0.138891i
$980$		−	211586.i		−	0.220310i
$981$	212604.	−	761182.i	0.220919	−	0.790953i
$982$	−818632.			−0.848918
$983$	−627873.	−	362503.i	−0.649778	−	0.375149i	0.138593	−	0.990349i	$-0.455742\pi$
$983$	−627873.	−	362503.i	−0.649778	−	0.375149i	−0.788371	+	0.615200i	$0.789075\pi$
$984$	−560821.	+	1.33396e6i	−0.579208	+	1.37770i
$985$	6322.93	+	10951.6i	0.00651697	+	0.0112877i
$986$	−862053.	+	497706.i	−0.886707	+	0.511940i
$987$	91354.4	+	38407.0i	0.0937768	+	0.0394254i
$988$	45886.4	−	79477.6i	0.0470078	−	0.0814200i
$989$		−	105555.i		−	0.107916i
$990$	−296507.	+	290305.i	−0.302527	+	0.296200i
$991$	1.49593e6			1.52322			0.761610	−	0.648036i	$-0.224409\pi$
$991$	1.49593e6			1.52322			0.761610	+	0.648036i	$0.224409\pi$
$992$	503557.	+	290729.i	0.511712	+	0.295437i
$993$	1.15256e6	−	145547.i	1.16887	−	0.147606i
$994$	218272.	+	378059.i	0.220915	+	0.382637i
$995$	18389.5	−	10617.2i	0.0185748	−	0.0107242i
$996$	155948.	−	118360.i	0.157203	−	0.119312i
$997$	−499732.	+	865561.i	−0.502744	+	0.870778i	0.497251	+	0.867607i	$0.334343\pi$
$997$	−499732.	+	865561.i	−0.502744	+	0.870778i	−0.999995	+	0.00317110i	$0.998991\pi$
$998$			537883.i			0.540041i
$999$	270452.	−	107035.i	0.270993	−	0.107249i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	45.5.i.a.11.12	✓	32
3.2	odd	2		135.5.i.a.116.5		32
9.2	odd	6		405.5.c.b.161.22		32
9.4	even	3		135.5.i.a.71.5		32
9.5	odd	6	inner	45.5.i.a.41.12	yes	32
9.7	even	3		405.5.c.b.161.11		32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
45.5.i.a.11.12	✓	32	1.1	even	1	trivial
45.5.i.a.41.12	yes	32	9.5	odd	6	inner
135.5.i.a.71.5		32	9.4	even	3
135.5.i.a.116.5		32	3.2	odd	2
405.5.c.b.161.11		32	9.7	even	3
405.5.c.b.161.22		32	9.2	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 45 = 3^{2} \cdot 5 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	45.i (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.10572 + 1.79309i) q^{2} +(-5.44105 - 7.16903i) q^{3} +(-1.56968 - 2.71877i) q^{4} +(-9.68246 + 5.59017i) q^{5} +(-4.04367 - 32.0212i) q^{6} +(45.9054 - 79.5105i) q^{7} -68.6371i q^{8} +(-21.7900 + 78.0141i) q^{9} -40.0946 q^{10} +(-110.654 - 63.8862i) q^{11} +(-10.9502 + 26.0461i) q^{12} +(37.9859 + 65.7935i) q^{13} +(285.138 - 164.625i) q^{14} +(92.7588 + 38.9974i) q^{15} +(97.9573 - 169.667i) q^{16} +325.310i q^{17} +(-207.559 + 203.218i) q^{18} +384.787 q^{19} +(30.3968 + 17.5496i) q^{20} +(-819.787 + 103.523i) q^{21} +(-229.107 - 396.825i) q^{22} +(125.517 - 72.4675i) q^{23} +(-492.061 + 373.458i) q^{24} +(62.5000 - 108.253i) q^{25} +272.448i q^{26} +(677.845 - 268.266i) q^{27} -288.228 q^{28} +(738.933 + 426.623i) q^{29} +(218.157 + 287.440i) q^{30} +(-734.888 - 1272.86i) q^{31} +(-342.608 + 197.805i) q^{32} +(144.073 + 1140.89i) q^{33} +(-583.309 + 1010.32i) q^{34} +1026.48i q^{35} +(246.306 - 63.2155i) q^{36} +398.987 q^{37} +(1195.04 + 689.956i) q^{38} +(264.992 - 630.308i) q^{39} +(383.693 + 664.576i) q^{40} +(2028.69 - 1171.26i) q^{41} +(-2731.65 - 1148.43i) q^{42} +(364.144 - 630.717i) q^{43} +401.124i q^{44} +(-225.132 - 877.178i) q^{45} +519.762 q^{46} +(-103.864 - 59.9661i) q^{47} +(-1749.34 + 220.908i) q^{48} +(-3014.11 - 5220.60i) q^{49} +(388.215 - 224.136i) q^{50} +(2332.16 - 1770.03i) q^{51} +(119.252 - 206.550i) q^{52} +2470.04i q^{53} +(2586.22 + 382.278i) q^{54} +1428.54 q^{55} +(-5457.37 - 3150.81i) q^{56} +(-2093.64 - 2758.55i) q^{57} +(1529.94 + 2649.94i) q^{58} +(894.636 - 516.518i) q^{59} +(-39.5769 - 313.404i) q^{60} +(-246.737 + 427.360i) q^{61} -5270.87i q^{62} +(5202.66 + 5313.80i) q^{63} -4553.36 q^{64} +(-735.594 - 424.695i) q^{65} +(-1598.27 + 3801.62i) q^{66} +(3995.55 + 6920.50i) q^{67} +(884.444 - 510.634i) q^{68} +(-1202.47 - 505.539i) q^{69} +(-1840.56 + 3187.94i) q^{70} +1325.88i q^{71} +(5354.66 + 1495.60i) q^{72} +7301.22 q^{73} +(1239.14 + 715.418i) q^{74} +(-1116.14 + 140.947i) q^{75} +(-603.993 - 1046.15i) q^{76} +(-10159.2 + 5865.45i) q^{77} +(1953.19 - 1482.40i) q^{78} +(-3408.95 + 5904.47i) q^{79} +2190.39i q^{80} +(-5611.40 - 3399.85i) q^{81} +8400.71 q^{82} +(-6000.80 - 3464.56i) q^{83} +(1568.26 + 2066.31i) q^{84} +(-1818.54 - 3149.80i) q^{85} +(2261.86 - 1305.88i) q^{86} +(-962.097 - 7618.71i) q^{87} +(-4384.96 + 7594.98i) q^{88} -1203.02i q^{89} +(873.660 - 3127.95i) q^{90} +6975.03 q^{91} +(-394.045 - 227.502i) q^{92} +(-5126.63 + 12194.2i) q^{93} +(-215.049 - 372.475i) q^{94} +(-3725.68 + 2151.02i) q^{95} +(3282.22 + 1379.90i) q^{96} +(-476.539 + 825.390i) q^{97} -21618.3i q^{98} +(7395.17 - 7240.51i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 8 q^{3} + 128 q^{4} + 98 q^{6} - 26 q^{7} - 220 q^{9} - 738 q^{11} - 214 q^{12} + 10 q^{13} + 1998 q^{14} - 50 q^{15} - 1024 q^{16} - 2504 q^{18} + 508 q^{19} - 1620 q^{21} + 672 q^{22} + 1998 q^{23}+ \cdots + 53512 q^{99}+O(q^{100}) \) 32 * q - 8 * q^3 + 128 * q^4 + 98 * q^6 - 26 * q^7 - 220 * q^9 - 738 * q^11 - 214 * q^12 + 10 * q^13 + 1998 * q^14 - 50 * q^15 - 1024 * q^16 - 2504 * q^18 + 508 * q^19 - 1620 * q^21 + 672 * q^22 + 1998 * q^23 + 4164 * q^24 + 2000 * q^25 + 2158 * q^27 - 1664 * q^28 - 270 * q^29 + 2000 * q^30 - 1472 * q^31 - 6048 * q^32 - 1354 * q^33 - 594 * q^34 + 4498 * q^36 + 2068 * q^37 - 7164 * q^38 - 4616 * q^39 + 1650 * q^40 - 13428 * q^41 - 10230 * q^42 + 568 * q^43 - 100 * q^45 + 5724 * q^46 + 12528 * q^47 + 25844 * q^48 - 1674 * q^49 + 1454 * q^51 + 1534 * q^52 + 8456 * q^54 + 21294 * q^56 - 12512 * q^57 - 8190 * q^58 - 4374 * q^59 - 5050 * q^60 - 4478 * q^61 + 5604 * q^63 - 37216 * q^64 - 8550 * q^65 - 19472 * q^66 + 12838 * q^67 + 65736 * q^68 + 8706 * q^69 + 2400 * q^70 - 36372 * q^72 + 29236 * q^73 - 20628 * q^74 + 1000 * q^75 + 6190 * q^76 - 31806 * q^77 - 42430 * q^78 - 3512 * q^79 - 3088 * q^81 + 34692 * q^82 - 43074 * q^83 - 19350 * q^84 - 4350 * q^85 - 10746 * q^86 + 69622 * q^87 - 16128 * q^88 - 26750 * q^90 - 48904 * q^91 + 27036 * q^92 + 27030 * q^93 + 5118 * q^94 + 6300 * q^95 + 53566 * q^96 + 23266 * q^97 + 53512 * q^99

Introduction

L-functions

Modular forms

Varieties

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