LMFDB - Embedded newform 35.5.h.a.31.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(26,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 5]))

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

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

chi := DirichletCharacter("35.26");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.h (of order $6$, 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:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 116 x^{18} - 264 x^{17} + 7945 x^{16} - 15716 x^{15} + 322816 x^{14} + \cdots + 48948907536 $ x^20 - 4x^19 + 116x^18 - 264x^17 + 7945x^16 - 15716x^15 + 322816x^14 - 515828x^13 + 9277999x^12 - 13862388x^11 + 173089454x^10 - 201957712x^9 + 2193435454x^8 - 2149103892x^7 + 14039289876x^6 + 1095579456x^5 + 36238744284x^4 + 13441411080x^3 + 74916126504x^2 + 43989502032*x + 48948907536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{4}\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.3
Root			$2.46009 - 4.26100i$ of defining polynomial
Character	$\chi$	$=$	35.31
Dual form			35.5.h.a.26.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.96009 - 3.39498i) q^{2} +(4.26025 + 2.45966i) q^{3} +(0.316095 - 0.547493i) q^{4} +(9.68246 - 5.59017i) q^{5} -19.2846i q^{6} +(34.8977 - 34.3969i) q^{7} -65.2012 q^{8} +(-28.4002 - 49.1905i) q^{9} +(-37.9570 - 21.9145i) q^{10} +(-2.02863 + 3.51370i) q^{11} +(2.69329 - 1.55497i) q^{12} -128.333i q^{13} +(-185.179 - 51.0557i) q^{14} +54.9997 q^{15} +(122.743 + 212.597i) q^{16} +(467.292 + 269.791i) q^{17} +(-111.334 + 192.836i) q^{18} +(-177.267 + 102.345i) q^{19} -7.06810i q^{20} +(233.278 - 60.7033i) q^{21} +15.9052 q^{22} +(488.257 + 845.686i) q^{23} +(-277.774 - 160.373i) q^{24} +(62.5000 - 108.253i) q^{25} +(-435.688 + 251.544i) q^{26} -677.884i q^{27} +(-7.80108 - 29.9789i) q^{28} -929.025 q^{29} +(-107.804 - 186.722i) q^{30} +(-61.7166 - 35.6321i) q^{31} +(-40.4362 + 70.0375i) q^{32} +(-17.2850 + 9.97949i) q^{33} -2115.26i q^{34} +(145.611 - 528.131i) q^{35} -35.9086 q^{36} +(436.485 + 756.015i) q^{37} +(694.919 + 401.212i) q^{38} +(315.656 - 546.732i) q^{39} +(-631.308 + 364.486i) q^{40} +1281.29i q^{41} +(-663.332 - 672.989i) q^{42} +2282.54 q^{43} +(1.28248 + 2.22132i) q^{44} +(-549.967 - 317.523i) q^{45} +(1914.05 - 3315.24i) q^{46} +(-2281.98 + 1317.50i) q^{47} +1207.62i q^{48} +(34.7001 - 2400.75i) q^{49} -490.022 q^{50} +(1327.19 + 2298.76i) q^{51} +(-70.2614 - 40.5655i) q^{52} +(124.624 - 215.855i) q^{53} +(-2301.40 + 1328.71i) q^{54} +45.3616i q^{55} +(-2275.37 + 2242.72i) q^{56} -1006.94 q^{57} +(1820.97 + 3154.02i) q^{58} +(942.634 + 544.230i) q^{59} +(17.3851 - 30.1119i) q^{60} +(-504.622 + 291.343i) q^{61} +279.368i q^{62} +(-2683.10 - 739.757i) q^{63} +4244.80 q^{64} +(-717.404 - 1242.58i) q^{65} +(67.7603 + 39.1214i) q^{66} +(795.394 - 1377.66i) q^{67} +(295.418 - 170.559i) q^{68} +4803.78i q^{69} +(-2078.40 + 540.839i) q^{70} +4704.68 q^{71} +(1851.72 + 3207.28i) q^{72} +(-2729.46 - 1575.86i) q^{73} +(1711.10 - 2963.71i) q^{74} +(532.532 - 307.457i) q^{75} +129.403i q^{76} +(50.0658 + 192.399i) q^{77} -2474.85 q^{78} +(-2538.96 - 4397.61i) q^{79} +(2376.90 + 1372.30i) q^{80} +(-633.050 + 1096.47i) q^{81} +(4349.93 - 2511.44i) q^{82} -10229.1i q^{83} +(40.5034 - 146.906i) q^{84} +6032.72 q^{85} +(-4473.98 - 7749.15i) q^{86} +(-3957.88 - 2285.09i) q^{87} +(132.269 - 229.097i) q^{88} +(-9007.94 + 5200.73i) q^{89} +2489.50i q^{90} +(-4414.27 - 4478.53i) q^{91} +617.342 q^{92} +(-175.286 - 303.604i) q^{93} +(8945.79 + 5164.85i) q^{94} +(-1144.25 + 1981.91i) q^{95} +(-344.537 + 198.918i) q^{96} -2863.80i q^{97} +(-8218.50 + 4587.88i) q^{98} +230.454 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} - 18 q^{3} - 58 q^{4} - 54 q^{7} - 372 q^{8} + 266 q^{9} + 90 q^{11} + 1266 q^{12} - 690 q^{14} + 100 q^{15} - 126 q^{16} - 864 q^{17} - 848 q^{18} - 1662 q^{19} + 1680 q^{21} + 2584 q^{22}+ \cdots - 36716 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 - 18 * q^3 - 58 * q^4 - 54 * q^7 - 372 * q^8 + 266 * q^9 + 90 * q^11 + 1266 * q^12 - 690 * q^14 + 100 * q^15 - 126 * q^16 - 864 * q^17 - 848 * q^18 - 1662 * q^19 + 1680 * q^21 + 2584 * q^22 - 1242 * q^23 + 1908 * q^24 + 1250 * q^25 - 1350 * q^26 - 134 * q^28 + 840 * q^29 + 800 * q^30 - 3636 * q^31 - 1758 * q^32 + 384 * q^33 + 150 * q^35 - 4164 * q^36 + 1068 * q^37 + 9180 * q^38 + 2976 * q^39 - 4146 * q^42 - 7692 * q^43 - 3618 * q^44 - 1800 * q^45 + 2038 * q^46 - 11412 * q^47 + 416 * q^49 + 1500 * q^50 + 6324 * q^51 - 7476 * q^52 + 1668 * q^53 + 33180 * q^54 + 13500 * q^56 + 15264 * q^57 + 1174 * q^58 + 216 * q^59 - 8250 * q^60 - 5856 * q^61 - 23632 * q^63 - 25788 * q^64 - 4650 * q^65 - 16248 * q^66 + 34 * q^67 - 6444 * q^68 + 900 * q^70 + 10488 * q^71 - 12052 * q^72 + 22776 * q^73 + 2538 * q^74 - 2250 * q^75 + 40488 * q^77 + 23784 * q^78 + 20788 * q^79 + 14400 * q^80 + 4154 * q^81 - 34146 * q^82 - 20316 * q^84 + 12000 * q^85 + 1980 * q^86 - 27474 * q^87 - 36148 * q^88 - 13176 * q^89 + 17976 * q^91 + 61404 * q^92 - 22908 * q^93 - 50610 * q^94 - 6900 * q^95 - 17460 * q^96 - 39606 * q^98 - 36716 * q^99

Character values

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

$n$	$22$	$31$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−1.96009	−	3.39498i	−0.490022	−	0.848744i	0.509912	−	0.860227i	$-0.329678\pi$
$2$	−1.96009	−	3.39498i	−0.490022	−	0.848744i	−0.999934	+	0.0114830i	$0.996345\pi$
$3$	4.26025	+	2.45966i	0.473362	+	0.273295i	0.717646	−	0.696408i	$-0.245220\pi$
$3$	4.26025	+	2.45966i	0.473362	+	0.273295i	−0.244284	+	0.969704i	$0.578553\pi$
$4$	0.316095	−	0.547493i	0.0197559	−	0.0342183i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$6$		−	19.2846i		−	0.535684i
$7$	34.8977	−	34.3969i	0.712198	−	0.701979i
$7$	34.8977	−	34.3969i	0.712198	−	0.701979i
$8$	−65.2012			−1.01877
$9$	−28.4002	−	49.1905i	−0.350619	−	0.607290i
$10$	−37.9570	−	21.9145i	−0.379570	−	0.219145i
$11$	−2.02863	+	3.51370i	−0.0167656	+	0.0290388i	−0.874286	−	0.485410i	$-0.838670\pi$
$11$	−2.02863	+	3.51370i	−0.0167656	+	0.0290388i	0.857521	+	0.514449i	$0.172004\pi$
$12$	2.69329	−	1.55497i	0.0187034	−	0.0107984i
$13$		−	128.333i		−	0.759368i	−0.925116	−	0.379684i	$-0.876033\pi$
$13$		−	128.333i		−	0.759368i	0.925116	−	0.379684i	$-0.123967\pi$
$14$	−185.179	−	51.0557i	−0.944793	−	0.260489i
$15$	54.9997			0.244443
$16$	122.743	+	212.597i	0.479463	+	0.830455i
$17$	467.292	+	269.791i	1.61693	+	0.933534i	0.987709	+	0.156307i	$0.0499589\pi$
$17$	467.292	+	269.791i	1.61693	+	0.933534i	0.629220	+	0.777227i	$0.283374\pi$
$18$	−111.334	+	192.836i	−0.343623	+	0.595172i
$19$	−177.267	+	102.345i	−0.491045	+	0.283505i	−0.725008	−	0.688741i	$-0.758164\pi$
$19$	−177.267	+	102.345i	−0.491045	+	0.283505i	0.233963	+	0.972246i	$0.424831\pi$
$20$		−	7.06810i		−	0.0176703i
$21$	233.278	−	60.7033i	0.528975	−	0.137649i
$22$	15.9052			0.0328620
$23$	488.257	+	845.686i	0.922981	+	1.59865i	0.794777	+	0.606902i	$0.207588\pi$
$23$	488.257	+	845.686i	0.922981	+	1.59865i	0.128204	+	0.991748i	$0.459079\pi$
$24$	−277.774	−	160.373i	−0.482246	−	0.278425i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$	−435.688	+	251.544i	−0.644509	+	0.372107i
$27$		−	677.884i		−	0.929881i
$28$	−7.80108	−	29.9789i	−0.00995036	−	0.0382384i
$29$	−929.025			−1.10467			−0.552334	−	0.833623i	$-0.686263\pi$
$29$	−929.025			−1.10467			−0.552334	+	0.833623i	$0.686263\pi$
$30$	−107.804	−	186.722i	−0.119783	−	0.207469i
$31$	−61.7166	−	35.6321i	−0.0642212	−	0.0370781i	0.467546	−	0.883969i	$-0.345138\pi$
$31$	−61.7166	−	35.6321i	−0.0642212	−	0.0370781i	−0.531767	+	0.846891i	$0.678472\pi$
$32$	−40.4362	+	70.0375i	−0.0394884	+	0.0683960i
$33$	−17.2850	+	9.97949i	−0.0158724	+	0.00916391i
$34$		−	2115.26i		−	1.82981i
$35$	145.611	−	528.131i	0.118866	−	0.431127i
$36$	−35.9086			−0.0277072
$37$	436.485	+	756.015i	0.318835	+	0.552239i	0.980245	−	0.197786i	$-0.0633751\pi$
$37$	436.485	+	756.015i	0.318835	+	0.552239i	−0.661410	+	0.750024i	$0.730042\pi$
$38$	694.919	+	401.212i	0.481246	+	0.277847i
$39$	315.656	−	546.732i	0.207532	−	0.359455i
$40$	−631.308	+	364.486i	−0.394567	+	0.227804i
$41$			1281.29i			0.762217i	0.924530	+	0.381108i	$0.124457\pi$
$41$			1281.29i			0.762217i	−0.924530	+	0.381108i	$0.875543\pi$
$42$	−663.332	−	672.989i	−0.376038	−	0.381513i
$43$	2282.54			1.23447			0.617235	−	0.786779i	$-0.288253\pi$
$43$	2282.54			1.23447			0.617235	+	0.786779i	$0.288253\pi$
$44$	1.28248	+	2.22132i	0.000662439	+	0.00114738i
$45$	−549.967	−	317.523i	−0.271588	−	0.156802i
$46$	1914.05	−	3315.24i	0.904563	−	1.56675i
$47$	−2281.98	+	1317.50i	−1.03304	+	0.596426i	−0.917854	−	0.396918i	$-0.870080\pi$
$47$	−2281.98	+	1317.50i	−1.03304	+	0.596426i	−0.115185	+	0.993344i	$0.536746\pi$
$48$			1207.62i			0.524141i
$49$	34.7001	−	2400.75i	0.0144523	−	0.999896i
$50$	−490.022			−0.196009
$51$	1327.19	+	2298.76i	0.510261	+	0.883799i
$52$	−70.2614	−	40.5655i	−0.0259843	−	0.0150020i
$53$	124.624	−	215.855i	0.0443660	−	0.0768442i	−0.842990	−	0.537930i	$-0.819207\pi$
$53$	124.624	−	215.855i	0.0443660	−	0.0768442i	0.887356	+	0.461086i	$0.152540\pi$
$54$	−2301.40	+	1328.71i	−0.789231	+	0.455663i
$55$			45.3616i			0.0149956i
$56$	−2275.37	+	2242.72i	−0.725565	+	0.715154i
$57$	−1006.94			−0.309922
$58$	1820.97	+	3154.02i	0.541312	+	0.937579i
$59$	942.634	+	544.230i	0.270794	+	0.156343i	0.629248	−	0.777204i	$-0.283363\pi$
$59$	942.634	+	544.230i	0.270794	+	0.156343i	−0.358454	+	0.933547i	$0.616696\pi$
$60$	17.3851	−	30.1119i	0.00482920	−	0.00836442i
$61$	−504.622	+	291.343i	−0.135615	+	0.0782971i	−0.566272	−	0.824218i	$-0.691615\pi$
$61$	−504.622	+	291.343i	−0.135615	+	0.0782971i	0.430658	+	0.902515i	$0.358282\pi$
$62$			279.368i			0.0726765i
$63$	−2683.10	−	739.757i	−0.676015	−	0.186384i
$64$	4244.80			1.03633
$65$	−717.404	−	1242.58i	−0.169800	−	0.294102i
$66$	67.7603	+	39.1214i	0.0155556	+	0.00898104i
$67$	795.394	−	1377.66i	0.177187	−	0.306897i	−0.763729	−	0.645537i	$-0.776633\pi$
$67$	795.394	−	1377.66i	0.177187	−	0.306897i	0.940916	+	0.338640i	$0.109967\pi$
$68$	295.418	−	170.559i	0.0638879	−	0.0368857i
$69$			4803.78i			1.00899i
$70$	−2078.40	+	540.839i	−0.424164	+	0.110375i
$71$	4704.68			0.933283			0.466642	−	0.884446i	$-0.345464\pi$
$71$	4704.68			0.933283			0.466642	+	0.884446i	$0.345464\pi$
$72$	1851.72	+	3207.28i	0.357200	+	0.618688i
$73$	−2729.46	−	1575.86i	−0.512191	−	0.295713i	0.221543	−	0.975151i	$-0.428891\pi$
$73$	−2729.46	−	1575.86i	−0.512191	−	0.295713i	−0.733734	+	0.679437i	$0.762224\pi$
$74$	1711.10	−	2963.71i	0.312473	−	0.541219i
$75$	532.532	−	307.457i	0.0946723	−	0.0546591i
$76$			129.403i			0.0224036i
$77$	50.0658	+	192.399i	0.00844422	+	0.0324505i
$78$	−2474.85			−0.406781
$79$	−2538.96	−	4397.61i	−0.406820	−	0.704633i	0.587711	−	0.809071i	$-0.300029\pi$
$79$	−2538.96	−	4397.61i	−0.406820	−	0.704633i	−0.994531	+	0.104438i	$0.966696\pi$
$80$	2376.90	+	1372.30i	0.371391	+	0.214423i
$81$	−633.050	+	1096.47i	−0.0964868	+	0.167120i
$82$	4349.93	−	2511.44i	0.646927	−	0.373503i
$83$		−	10229.1i		−	1.48484i	−0.669935	−	0.742419i	$-0.733678\pi$
$83$		−	10229.1i		−	1.48484i	0.669935	−	0.742419i	$-0.266322\pi$
$84$	40.5034	−	146.906i	0.00574028	−	0.0208200i
$85$	6032.72			0.834978
$86$	−4473.98	−	7749.15i	−0.604918	−	1.04775i
$87$	−3957.88	−	2285.09i	−0.522907	−	0.301901i
$88$	132.269	−	229.097i	0.0170802	−	0.0295838i
$89$	−9007.94	+	5200.73i	−1.13722	+	0.656576i	−0.945741	−	0.324921i	$-0.894662\pi$
$89$	−9007.94	+	5200.73i	−1.13722	+	0.656576i	−0.191481	+	0.981496i	$0.561329\pi$
$90$			2489.50i			0.307345i
$91$	−4414.27	−	4478.53i	−0.533060	−	0.540820i
$92$	617.342			0.0729374
$93$	−175.286	−	303.604i	−0.0202666	−	0.0351027i
$94$	8945.79	+	5164.85i	1.01243	+	0.584524i
$95$	−1144.25	+	1981.91i	−0.126787	+	0.219602i
$96$	−344.537	+	198.918i	−0.0373846	+	0.0215840i
$97$		−	2863.80i		−	0.304368i	−0.988352	−	0.152184i	$-0.951369\pi$
$97$		−	2863.80i		−	0.304368i	0.988352	−	0.152184i	$-0.0486307\pi$
$98$	−8218.50	+	4587.88i	−0.855737	+	0.477705i
$99$	230.454			0.0235133
$100$	−39.5119	−	68.4366i	−0.00395119	−	0.00684366i
$101$	−6980.81	−	4030.37i	−0.684326	−	0.395096i	0.117157	−	0.993113i	$-0.462622\pi$
$101$	−6980.81	−	4030.37i	−0.684326	−	0.395096i	−0.801483	+	0.598018i	$0.795955\pi$
$102$	5202.82	−	9011.55i	0.500079	−	0.866162i
$103$	8640.35	−	4988.51i	0.814435	−	0.470214i	−0.0340584	−	0.999420i	$-0.510843\pi$
$103$	8640.35	−	4988.51i	0.814435	−	0.470214i	0.848494	+	0.529205i	$0.177510\pi$
$104$			8367.47i			0.773620i
$105$	1919.36	−	1891.82i	0.174092	−	0.171594i
$106$	−977.098			−0.0869614
$107$	3243.95	+	5618.69i	0.283339	+	0.490758i	0.972205	−	0.234131i	$-0.0752244\pi$
$107$	3243.95	+	5618.69i	0.283339	+	0.490758i	−0.688866	+	0.724889i	$0.741891\pi$
$108$	−371.136	−	214.276i	−0.0318190	−	0.0183707i
$109$	−9510.71	+	16473.0i	−0.800497	+	1.38650i	0.118792	+	0.992919i	$0.462098\pi$
$109$	−9510.71	+	16473.0i	−0.800497	+	1.38650i	−0.919289	+	0.393583i	$0.871235\pi$
$110$	154.002	−	88.9129i	0.0127274	−	0.00734817i
$111$			4294.42i			0.348545i
$112$	11596.1	+	3197.16i	0.924435	+	0.254876i
$113$	−11617.6			−0.909826			−0.454913	−	0.890536i	$-0.650330\pi$
$113$	−11617.6			−0.909826			−0.454913	+	0.890536i	$0.650330\pi$
$114$	1973.69	+	3418.53i	0.151869	+	0.263045i
$115$	9455.05	+	5458.88i	0.714938	+	0.412770i
$116$	−293.660	+	508.634i	−0.0218237	+	0.0377998i
$117$	−6312.77	+	3644.68i	−0.461156	+	0.266249i
$118$		−	4266.96i		−	0.306446i
$119$	25587.4	−	6658.33i	1.80689	−	0.470188i
$120$	−3586.04			−0.249031
$121$	7312.27	+	12665.2i	0.499438	+	0.865052i
$122$	1978.21	+	1142.12i	0.132908	+	0.0767347i
$123$	−3151.53	+	5458.60i	−0.208310	+	0.360804i
$124$	−39.0166	+	22.5263i	−0.00253750	+	0.00146503i
$125$		−	1397.54i		−	0.0894427i
$126$	2747.67	+	10559.1i	0.173070	+	0.665096i
$127$	−17194.7			−1.06607			−0.533037	−	0.846092i	$-0.678949\pi$
$127$	−17194.7			−1.06607			−0.533037	+	0.846092i	$0.678949\pi$
$128$	−7673.21	−	13290.4i	−0.468335	−	0.811181i
$129$	9724.19	+	5614.26i	0.584351	+	0.337375i
$130$	−2812.35	+	4871.14i	−0.166411	+	0.288233i
$131$	26000.5	−	15011.4i	1.51509	−	0.874739i	0.515248	−	0.857041i	$-0.327700\pi$
$131$	26000.5	−	15011.4i	1.51509	−	0.874739i	0.999843	−	0.0176975i	$-0.00563359\pi$
$132$			12.6179i			0.000724166i
$133$	−2665.85	+	9669.06i	−0.150707	+	0.546615i
$134$	−6236.17			−0.347303
$135$	−3789.48	−	6563.58i	−0.207928	−	0.360142i
$136$	−30468.0	−	17590.7i	−1.64728	−	0.951055i
$137$	−14293.7	+	24757.4i	−0.761558	+	1.31906i	0.180489	+	0.983577i	$0.442232\pi$
$137$	−14293.7	+	24757.4i	−0.761558	+	1.31906i	−0.942047	+	0.335481i	$0.891101\pi$
$138$	16308.7	−	9415.84i	0.856371	−	0.494426i
$139$		−	7816.35i		−	0.404552i	−0.979329	−	0.202276i	$-0.935166\pi$
$139$		−	7816.35i		−	0.404552i	0.979329	−	0.202276i	$-0.0648338\pi$
$140$	−243.121	−	246.660i	−0.0124041	−	0.0125847i
$141$	−12962.4			−0.652002
$142$	−9221.60	−	15972.3i	−0.457330	−	0.792118i
$143$	450.924	+	260.341i	0.0220511	+	0.0127312i
$144$	6971.82	−	12075.5i	0.336218	−	0.582347i
$145$	−8995.25	+	5193.41i	−0.427836	+	0.247011i
$146$			12355.3i			0.579625i
$147$	6052.86	−	10142.5i	0.280108	−	0.469362i
$148$	551.883			0.0251955
$149$	−10335.4	−	17901.4i	−0.465538	−	0.806335i	0.533688	−	0.845682i	$-0.320806\pi$
$149$	−10335.4	−	17901.4i	−0.465538	−	0.806335i	−0.999226	+	0.0393465i	$0.987472\pi$
$150$	−2087.62	−	1205.29i	−0.0927831	−	0.0535684i
$151$	14407.3	−	24954.2i	0.631871	−	1.09443i	−0.355297	−	0.934753i	$-0.615620\pi$
$151$	14407.3	−	24954.2i	0.631871	−	1.09443i	0.987169	−	0.159680i	$-0.0510463\pi$
$152$	11558.0	−	6673.03i	0.500261	−	0.288826i
$153$		−	30648.5i		−	1.30926i
$154$	555.056	−	547.091i	0.0234043	−	0.0230684i
$155$	−796.758			−0.0331637
$156$	−199.554	−	345.638i	−0.00819997	−	0.0142028i
$157$	−20437.2	−	11799.4i	−0.829128	−	0.478697i	0.0244259	−	0.999702i	$-0.492224\pi$
$157$	−20437.2	−	11799.4i	−0.829128	−	0.478697i	−0.853554	+	0.521004i	$0.825558\pi$
$158$	−9953.19	+	17239.4i	−0.398702	+	0.690572i
$159$	1061.86	−	613.066i	0.0420023	−	0.0242501i
$160$			904.180i			0.0353195i
$161$	46128.1	+	12717.9i	1.77956	+	0.490643i
$162$	4963.34			0.189123
$163$	22184.3	+	38424.3i	0.834969	+	1.44621i	0.894055	+	0.447956i	$0.147848\pi$
$163$	22184.3	+	38424.3i	0.834969	+	1.44621i	−0.0590860	+	0.998253i	$0.518819\pi$
$164$	701.495	+	405.008i	0.0260817	+	0.0150583i
$165$	−111.574	+	193.252i	−0.00409822	+	0.00709833i
$166$	−34727.4	+	20049.9i	−1.26025	+	0.727604i
$167$			8815.11i			0.316078i	0.987433	+	0.158039i	$0.0505172\pi$
$167$			8815.11i			0.316078i	−0.987433	+	0.158039i	$0.949483\pi$
$168$	−15210.0	+	3957.93i	−0.538903	+	0.140233i
$169$	12091.6			0.423361
$170$	−11824.7	−	20480.9i	−0.409158	−	0.708683i
$171$	10068.8	+	5813.24i	0.344339	+	0.198804i
$172$	721.498	−	1249.67i	0.0243881	−	0.0422415i
$173$	34952.5	−	20179.8i	1.16785	−	0.674257i	0.214675	−	0.976685i	$-0.431131\pi$
$173$	34952.5	−	20179.8i	1.16785	−	0.674257i	0.953172	+	0.302429i	$0.0977974\pi$
$174$			17915.9i			0.591752i
$175$	−1542.47	−	5927.60i	−0.0503664	−	0.193554i
$176$	−995.999			−0.0321539
$177$	2677.24	+	4637.12i	0.0854557	+	0.148014i
$178$	35312.7	+	20387.8i	1.11453	+	0.643474i
$179$	−9948.24	+	17230.9i	−0.310485	+	0.537775i	−0.978467	−	0.206402i	$-0.933825\pi$
$179$	−9948.24	+	17230.9i	−0.310485	+	0.537775i	0.667983	+	0.744177i	$0.267158\pi$
$180$	−347.683	+	200.735i	−0.0107310	+	0.00619553i
$181$			15639.2i			0.477373i	0.971097	+	0.238687i	$0.0767169\pi$
$181$			15639.2i			0.477373i	−0.971097	+	0.238687i	$0.923283\pi$
$182$	−6552.14	+	23764.7i	−0.197807	+	0.717445i
$183$	−2866.42			−0.0855929
$184$	−31834.9	−	55139.7i	−0.940304	−	1.62865i
$185$	8452.50	+	4880.05i	0.246969	+	0.142587i
$186$	−687.151	+	1190.18i	−0.0198622	+	0.0344023i
$187$	−1895.93	+	1094.62i	−0.0542174	+	0.0313025i
$188$			1665.83i			0.0471318i
$189$	−23317.1	−	23656.6i	−0.652757	−	0.662260i
$190$	8971.37			0.248514
$191$	4338.44	+	7514.40i	0.118923	+	0.205981i	0.919341	−	0.393461i	$-0.128722\pi$
$191$	4338.44	+	7514.40i	0.118923	+	0.205981i	−0.800418	+	0.599442i	$0.795389\pi$
$192$	18083.9	+	10440.8i	0.490558	+	0.283224i
$193$	−33151.1	+	57419.4i	−0.889986	+	1.54150i	−0.0500963	+	0.998744i	$0.515953\pi$
$193$	−33151.1	+	57419.4i	−0.889986	+	1.54150i	−0.839890	+	0.542757i	$0.817381\pi$
$194$	−9722.53	+	5613.30i	−0.258331	+	0.149147i
$195$		−	7058.28i		−	0.185622i
$196$	−1303.42	−	777.863i	−0.0339292	−	0.0202484i
$197$	9835.73			0.253440			0.126720	−	0.991939i	$-0.459555\pi$
$197$	9835.73			0.253440			0.126720	+	0.991939i	$0.459555\pi$
$198$	−451.711	−	782.386i	−0.0115221	−	0.0199568i
$199$	−35893.5	−	20723.1i	−0.906380	−	0.523299i	−0.0271152	−	0.999632i	$-0.508632\pi$
$199$	−35893.5	−	20723.1i	−0.906380	−	0.523299i	−0.879265	+	0.476334i	$0.841965\pi$
$200$	−4075.07	+	7058.23i	−0.101877	+	0.176456i
$201$	6777.16	−	3912.80i	0.167747	−	0.0968490i
$202$			31599.6i			0.774424i
$203$	−32420.8	+	31955.6i	−0.786742	+	0.775453i
$204$	1678.07			0.0403228
$205$	7162.61	+	12406.0i	0.170437	+	0.295205i
$206$	−33871.7	−	19555.8i	−0.798183	−	0.460831i
$207$	27733.1	−	48035.2i	0.647230	−	1.12103i
$208$	27283.2	−	15751.9i	0.630621	−	0.364089i
$209$		−	830.484i		−	0.0190125i
$210$	−10184.8	−	2808.05i	−0.230948	−	0.0636746i
$211$	−24775.9			−0.556500			−0.278250	−	0.960509i	$-0.589754\pi$
$211$	−24775.9			−0.556500			−0.278250	+	0.960509i	$0.589754\pi$
$212$	−78.7861	−	136.462i	−0.00175298	−	0.00303626i
$213$	20043.1	+	11571.9i	0.441781	+	0.255062i
$214$	12716.9	−	22026.3i	0.277685	−	0.480965i
$215$	22100.6	−	12759.8i	0.478108	−	0.276036i
$216$			44198.8i			0.947334i
$217$	−3379.40	+	879.384i	−0.0717663	+	0.0186749i
$218$	74567.4			1.56905
$219$	−7752.14	−	13427.1i	−0.161634	−	0.279959i
$220$	24.8352	+	14.3386i	0.000513123	+	0.000296252i
$221$	34623.2	−	59969.1i	0.708896	−	1.22784i
$222$	14579.4	−	8417.45i	0.295825	−	0.170795i
$223$			1080.30i			0.0217238i	0.999941	+	0.0108619i	$0.00345752\pi$
$223$			1080.30i			0.0217238i	−0.999941	+	0.0108619i	$0.996542\pi$
$224$	997.946	+	3835.03i	0.0198889	+	0.0764315i
$225$	−7100.04			−0.140248
$226$	22771.5	+	39441.4i	0.445835	+	0.772209i
$227$	−4356.35	−	2515.14i	−0.0845417	−	0.0488102i	0.457133	−	0.889398i	$-0.348876\pi$
$227$	−4356.35	−	2515.14i	−0.0845417	−	0.0488102i	−0.541675	+	0.840588i	$0.682210\pi$
$228$	−318.288	+	551.291i	−0.00612281	+	0.0106050i
$229$	−57327.0	+	33097.8i	−1.09317	+	0.631143i	−0.934419	−	0.356176i	$-0.884080\pi$
$229$	−57327.0	+	33097.8i	−1.09317	+	0.631143i	−0.158752	+	0.987318i	$0.550747\pi$
$230$		−	42799.6i		−	0.809065i
$231$	−259.942	+	942.812i	−0.00487139	+	0.0176686i
$232$	60573.5			1.12540
$233$	−25613.5	−	44363.9i	−0.471800	−	0.817181i	0.527680	−	0.849443i	$-0.323062\pi$
$233$	−25613.5	−	44363.9i	−0.471800	−	0.817181i	−0.999479	+	0.0322624i	$0.989729\pi$
$234$	24747.2	+	14287.8i	0.451954	+	0.260936i
$235$	−14730.1	+	25513.4i	−0.266730	+	0.461989i
$236$	595.924	−	344.057i	0.0106996	−	0.00617741i
$237$		−	24979.9i		−	0.444728i
$238$	−72758.5	−	73817.8i	−1.28449	−	1.30319i
$239$	−55351.4			−0.969020			−0.484510	−	0.874786i	$-0.661002\pi$
$239$	−55351.4			−0.969020			−0.484510	+	0.874786i	$0.661002\pi$
$240$	6750.80	+	11692.7i	0.117201	+	0.202999i
$241$	−16502.1	−	9527.51i	−0.284123	−	0.164038i	0.351166	−	0.936313i	$-0.385785\pi$
$241$	−16502.1	−	9527.51i	−0.284123	−	0.164038i	−0.635288	+	0.772275i	$0.719119\pi$
$242$	28665.4	−	49649.9i	0.489472	−	0.847790i
$243$	−52946.1	+	30568.5i	−0.896647	+	0.517680i
$244$			368.369i			0.00618733i
$245$	−13084.6	−	23439.1i	−0.217986	−	0.390490i
$246$	24709.1			0.408307
$247$	13134.3	+	22749.2i	0.215284	+	0.372883i
$248$	4023.99	+	2323.25i	0.0654266	+	0.0377740i
$249$	25160.0	−	43578.4i	0.405800	−	0.702866i
$250$	−4744.62	+	2739.31i	−0.0759140	+	0.0438289i
$251$		−	54163.9i		−	0.859730i	−0.902893	−	0.429865i	$-0.858561\pi$
$251$		−	54163.9i		−	0.859730i	0.902893	−	0.429865i	$-0.141439\pi$
$252$	−1253.13	+	1235.15i	−0.0197330	+	0.0194499i
$253$	−3961.98			−0.0618972
$254$	33703.2	+	58375.6i	0.522400	+	0.904824i
$255$	25700.9	+	14838.4i	0.395247	+	0.228196i
$256$	3878.03	−	6716.95i	0.0591741	−	0.102493i
$257$	−73195.9	+	42259.7i	−1.10821	+	0.639823i	−0.938364	−	0.345648i	$-0.887659\pi$
$257$	−73195.9	+	42259.7i	−1.10821	+	0.639823i	−0.169842	+	0.985471i	$0.554326\pi$
$258$		−	44017.8i		−	0.661286i
$259$	41236.9	+	11369.4i	0.614733	+	0.169488i
$260$	−907.071			−0.0134182
$261$	26384.5	+	45699.2i	0.387317	+	0.670854i
$262$	−101927.	−	58847.3i	−1.48486	−	0.857283i
$263$	−15717.1	+	27222.8i	−0.227227	+	0.393569i	−0.956985	−	0.290136i	$-0.906299\pi$
$263$	−15717.1	+	27222.8i	−0.227227	+	0.393569i	0.729758	+	0.683705i	$0.239633\pi$
$264$	1127.00	−	650.675i	0.0161702	−	0.00933590i
$265$		−	2786.68i		−	0.0396822i
$266$	38051.5	−	9901.73i	0.537785	−	0.139942i
$267$	−51168.1			−0.717756
$268$	−502.840	−	870.945i	−0.00700101	−	0.0121261i
$269$	19642.1	+	11340.4i	0.271447	+	0.156720i	0.629545	−	0.776964i	$-0.283241\pi$
$269$	19642.1	+	11340.4i	0.271447	+	0.156720i	−0.358098	+	0.933684i	$0.616575\pi$
$270$	−14855.5	+	25730.4i	−0.203779	+	0.352955i
$271$	−70700.5	+	40818.9i	−0.962684	+	0.555806i	−0.896998	−	0.442034i	$-0.854257\pi$
$271$	−70700.5	+	40818.9i	−0.962684	+	0.555806i	−0.0656861	+	0.997840i	$0.520924\pi$
$272$			132460.i			1.79038i
$273$	−7790.24	−	29937.3i	−0.104526	−	0.401686i
$274$	112068.			1.49272
$275$	253.579	+	439.212i	0.00335311	+	0.00580776i
$276$	2630.04	+	1518.45i	0.0345258	+	0.0199335i
$277$	30024.4	−	52003.7i	0.391304	−	0.677758i	−0.601318	−	0.799010i	$-0.705357\pi$
$277$	30024.4	−	52003.7i	0.391304	−	0.677758i	0.992622	+	0.121252i	$0.0386908\pi$
$278$	−26536.3	+	15320.7i	−0.343361	+	0.198240i
$279$			4047.83i			0.0520012i
$280$	−9494.00	+	34434.8i	−0.121097	+	0.439219i
$281$	−67317.8			−0.852545			−0.426273	−	0.904595i	$-0.640174\pi$
$281$	−67317.8			−0.852545			−0.426273	+	0.904595i	$0.640174\pi$
$282$	25407.6	+	44007.2i	0.319495	+	0.553382i
$283$	120718.	+	69696.4i	1.50729	+	0.870236i	0.999964	+	0.00848447i	$0.00270072\pi$
$283$	120718.	+	69696.4i	1.50729	+	0.870236i	0.507330	+	0.861752i	$0.330633\pi$
$284$	1487.13	−	2575.78i	0.0184379	−	0.0319354i
$285$	−9749.63	+	5628.95i	−0.120032	+	0.0693007i
$286$		−	2041.17i		−	0.0249543i
$287$	44072.3	+	44713.9i	0.535060	+	0.542849i
$288$	4593.57			0.0553816
$289$	103814.	+	179812.i	1.24297	+	2.15289i
$290$	35263.0	+	20359.1i	0.419298	+	0.242082i
$291$	7043.97	−	12200.5i	0.0831824	−	0.144076i
$292$	−1725.54	+	996.241i	−0.0202376	+	0.0116842i
$293$		−	149331.i		−	1.73946i	−0.493529	−	0.869729i	$-0.664293\pi$
$293$		−	149331.i		−	1.73946i	0.493529	−	0.869729i	$-0.335707\pi$
$294$	−46297.5	−	669.178i	−0.535628	−	0.00774189i
$295$	12169.4			0.139837
$296$	−28459.4	−	49293.0i	−0.324819	−	0.562603i
$297$	2381.88	+	1375.18i	0.0270027	+	0.0155900i
$298$	−40516.6	+	70176.9i	−0.456248	+	0.790245i
$299$	108529.	−	62659.5i	1.21396	−	0.700882i
$300$		−	388.743i		−	0.00431937i
$301$	79655.3	−	78512.3i	0.879188	−	0.866572i
$302$	−112958.			−1.23852
$303$	−19826.7	−	34340.8i	−0.215956	−	0.374047i
$304$	−43516.5	−	25124.3i	−0.470876	−	0.271860i
$305$	−3257.32	+	5641.84i	−0.0350155	+	0.0606487i
$306$	−104051.	+	60073.7i	−1.11123	+	0.641567i
$307$		−	73073.3i		−	0.775322i	−0.921802	−	0.387661i	$-0.873283\pi$
$307$		−	73073.3i		−	0.775322i	0.921802	−	0.387661i	$-0.126717\pi$
$308$	121.162	+	33.4056i	0.00127722	+	0.000352143i
$309$	49080.1			0.514030
$310$	1561.72	+	2704.97i	0.0162510	+	0.0281475i
$311$	−6908.17	−	3988.43i	−0.0714237	−	0.0412365i	0.463863	−	0.885907i	$-0.346463\pi$
$311$	−6908.17	−	3988.43i	−0.0714237	−	0.0412365i	−0.535287	+	0.844671i	$0.679796\pi$
$312$	−20581.1	+	35647.6i	−0.211427	+	0.366202i
$313$	43470.5	−	25097.7i	0.443717	−	0.256180i	−0.261456	−	0.965215i	$-0.584203\pi$
$313$	43470.5	−	25097.7i	0.443717	−	0.256180i	0.705173	+	0.709035i	$0.250869\pi$
$314$			92511.6i			0.938290i
$315$	−30114.4	+	7836.33i	−0.303496	+	0.0789754i
$316$	−3210.21			−0.0321484
$317$	−26563.7	−	46009.6i	−0.264344	−	0.457857i	0.703047	−	0.711143i	$-0.251822\pi$
$317$	−26563.7	−	46009.6i	−0.264344	−	0.457857i	−0.967392	+	0.253286i	$0.918489\pi$
$318$	−4162.69	−	2403.33i	−0.0411642	−	0.0237662i
$319$	1884.65	−	3264.31i	0.0185204	−	0.0320782i
$320$	41100.1	−	23729.1i	0.401368	−	0.231730i
$321$			31916.1i			0.309742i
$322$	−47238.0	−	181532.i	−0.455596	−	1.75082i
$323$	−110447.			−1.05865
$324$	400.208	+	693.180i	0.00381237	+	0.00660322i
$325$	−13892.5	−	8020.82i	−0.131526	−	0.0759368i
$326$	86966.4	−	150630.i	0.818308	−	1.41735i
$327$	−81036.1	+	46786.2i	−0.757849	+	0.437545i
$328$		−	83541.4i		−	0.776522i
$329$	−34317.9	+	124471.i	−0.317051	+	1.14994i
$330$	874.781			0.00803289
$331$	17868.7	+	30949.5i	0.163094	+	0.282487i	0.935977	−	0.352062i	$-0.114519\pi$
$331$	17868.7	+	30949.5i	0.163094	+	0.282487i	−0.772883	+	0.634549i	$0.781186\pi$
$332$	−5600.33	−	3233.35i	−0.0508086	−	0.0293344i
$333$	24792.5	−	42941.9i	0.223579	−	0.387251i
$334$	29927.1	−	17278.4i	0.268269	−	0.154885i
$335$		−	17785.5i		−	0.158481i
$336$	41538.5	+	42143.2i	0.367936	+	0.373292i
$337$	181205.			1.59555			0.797773	−	0.602958i	$-0.206011\pi$
$337$	181205.			1.59555			0.797773	+	0.602958i	$0.206011\pi$
$338$	−23700.6	−	41050.7i	−0.207456	−	0.359325i
$339$	−49493.8	−	28575.3i	−0.430677	−	0.248651i
$340$	1906.91	−	3302.87i	0.0164958	−	0.0285715i
$341$	250.401	−	144.569i	0.00215341	−	0.00124327i
$342$		−	45577.9i		−	0.389675i
$343$	−81367.5	−	84974.2i	−0.691612	−	0.722269i
$344$	−148824.			−1.25764
$345$	26854.0	+	46512.4i	0.225616	+	0.390779i
$346$	−137020.	−	79108.6i	−1.14454	−	0.660802i
$347$	−37151.3	+	64348.0i	−0.308543	+	0.534412i	−0.978044	−	0.208399i	$-0.933175\pi$
$347$	−37151.3	+	64348.0i	−0.308543	+	0.534412i	0.669501	+	0.742811i	$0.266508\pi$
$348$	−2502.13	+	1444.61i	−0.0206610	+	0.0119287i
$349$		−	136513.i		−	1.12078i	−0.828228	−	0.560392i	$-0.810651\pi$
$349$		−	136513.i		−	1.12078i	0.828228	−	0.560392i	$-0.189349\pi$
$350$	−17100.7	+	16855.3i	−0.139597	+	0.137594i
$351$	−86994.9			−0.706122
$352$	−164.060	−	284.161i	−0.00132409	−	0.00229339i
$353$	180773.	+	104369.i	1.45072	+	0.837574i	0.998522	−	0.0543440i	$-0.0173068\pi$
$353$	180773.	+	104369.i	1.45072	+	0.837574i	0.452198	+	0.891918i	$0.350640\pi$
$354$	10495.3	−	18178.3i	0.0837504	−	0.145060i
$355$	45552.9	−	26300.0i	0.361459	−	0.208688i
$356$			6575.71i			0.0518851i
$357$	125386.	+	34570.2i	0.983815	+	0.271247i
$358$	77997.8			0.608578
$359$	332.773	+	576.380i	0.00258202	+	0.00447219i	0.867314	−	0.497762i	$-0.165845\pi$
$359$	332.773	+	576.380i	0.00258202	+	0.00447219i	−0.864732	+	0.502234i	$0.832511\pi$
$360$	35858.5	+	20702.9i	0.276686	+	0.159745i
$361$	−44211.4	+	76576.4i	−0.339250	+	0.587598i
$362$	53094.8	−	30654.3i	0.405168	−	0.233924i
$363$			71942.8i			0.545976i
$364$	−3847.29	+	1001.14i	−0.0290370	+	0.00755598i
$365$	−35237.2			−0.264494
$366$	5618.45	+	9731.43i	0.0419425	+	0.0726465i
$367$	150440.	+	86856.4i	1.11694	+	0.644866i	0.940618	−	0.339466i	$-0.110246\pi$
$367$	150440.	+	86856.4i	1.11694	+	0.644866i	0.176323	+	0.984332i	$0.443580\pi$
$368$	−119860.	+	207603.i	−0.885071	+	1.53299i
$369$	63027.1	−	36388.7i	0.462887	−	0.267248i
$370$		−	38261.4i		−	0.279484i
$371$	−3075.67	−	11819.5i	−0.0223456	−	0.0858723i
$372$	−221.628			−0.00160154
$373$	−97956.5	−	169666.i	−0.704070	−	1.21948i	−0.967026	−	0.254677i	$-0.918031\pi$
$373$	−97956.5	−	169666.i	−0.704070	−	1.21948i	0.262957	−	0.964808i	$-0.415302\pi$
$374$	7432.39	+	4291.09i	0.0531355	+	0.0306778i
$375$	3437.48	−	5953.89i	0.0244443	−	0.0423388i
$376$	148788.	−	85902.8i	1.05243	−	0.607620i
$377$			119225.i			0.838848i
$378$	−34609.9	+	125530.i	−0.242223	+	0.878546i
$379$	−26433.0			−0.184021			−0.0920106	−	0.995758i	$-0.529329\pi$
$379$	−26433.0			−0.184021			−0.0920106	+	0.995758i	$0.529329\pi$
$380$	723.386	+	1252.94i	0.00500960	+	0.00867688i
$381$	−73253.8	−	42293.1i	−0.504639	−	0.291353i
$382$	17007.5	−	29457.8i	0.116550	−	0.201871i
$383$	−67922.7	+	39215.2i	−0.463039	+	0.267336i	−0.713321	−	0.700837i	$-0.752810\pi$
$383$	−67922.7	+	39215.2i	−0.463039	+	0.267336i	0.250282	+	0.968173i	$0.419477\pi$
$384$		−	75493.9i		−	0.511976i
$385$	1560.30	+	1583.02i	0.0105266	+	0.0106798i
$386$	259917.			1.74445
$387$	−64824.4	−	112279.i	−0.432829	−	0.749682i
$388$	−1567.91	−	905.233i	−0.0104150	−	0.00601308i
$389$	−78230.0	+	135498.i	−0.516980	+	0.895436i	0.482825	+	0.875717i	$0.339611\pi$
$389$	−78230.0	+	135498.i	−0.516980	+	0.895436i	−0.999806	+	0.0197193i	$0.993723\pi$
$390$	−23962.7	+	13834.9i	−0.157546	+	0.0909590i
$391$			526910.i			3.44654i
$392$	−2262.49	+	156532.i	−0.0147236	+	1.01866i
$393$	147692.			0.956248
$394$	−19278.9	−	33392.1i	−0.124191	−	0.215105i
$395$	−49166.8	−	28386.5i	−0.315121	−	0.181935i
$396$	72.8454	−	126.172i	0.000464528	−	0.000804585i
$397$	103379.	−	59685.8i	0.655920	−	0.378696i	−0.134801	−	0.990873i	$-0.543039\pi$
$397$	103379.	−	59685.8i	0.655920	−	0.378696i	0.790721	+	0.612177i	$0.209706\pi$
$398$			162477.i			1.02571i
$399$	−35139.8	+	34635.6i	−0.220726	+	0.217559i
$400$	30685.7			0.191785
$401$	−102316.	−	177216.i	−0.636287	−	1.10208i	−0.986241	−	0.165315i	$-0.947136\pi$
$401$	−102316.	−	177216.i	−0.636287	−	1.10208i	0.349953	−	0.936767i	$-0.386197\pi$
$402$	−26567.7	−	15338.9i	−0.164400	−	0.0949164i
$403$	−4572.78	+	7920.28i	−0.0281559	+	0.0487675i
$404$	−4413.20	+	2547.96i	−0.0270390	+	0.0156110i
$405$			14155.4i			0.0863004i
$406$	172036.	+	47432.1i	1.04368	+	0.287753i
$407$	−3541.87			−0.0213818
$408$	−86534.3	−	149882.i	−0.519838	−	0.900386i
$409$	−259774.	−	149981.i	−1.55292	−	0.896580i	−0.997902	−	0.0647435i	$-0.979377\pi$
$409$	−259774.	−	149981.i	−1.55292	−	0.896580i	−0.555021	−	0.831837i	$-0.687290\pi$
$410$	28078.7	−	48633.7i	0.167036	−	0.289314i
$411$	−121790.	+	70315.2i	−0.720985	+	0.416261i
$412$		−	6307.37i		−	0.0371581i
$413$	51615.6	−	13431.4i	0.302608	−	0.0787444i
$414$	−217438.			−1.26863
$415$	−57182.1	−	99042.4i	−0.332020	−	0.575076i
$416$	8988.13	+	5189.30i	0.0519377	+	0.0299862i
$417$	19225.6	−	33299.6i	0.110562	−	0.191499i
$418$	−2819.47	+	1627.82i	−0.0161367	+	0.00931654i
$419$		−	92912.0i		−	0.529229i	−0.964354	−	0.264615i	$-0.914755\pi$
$419$		−	92912.0i		−	0.529229i	0.964354	−	0.264615i	$-0.0852447\pi$
$420$	−429.057	−	1648.83i	−0.00243230	−	0.00934712i
$421$	13799.5			0.0778575			0.0389288	−	0.999242i	$-0.487605\pi$
$421$	13799.5			0.0778575			0.0389288	+	0.999242i	$0.487605\pi$
$422$	48563.1	+	84113.7i	0.272698	+	0.472326i
$423$	129617.	+	74834.6i	0.724407	+	0.418236i
$424$	−8125.64	+	14074.0i	−0.0451987	+	0.0782864i
$425$	58411.5	−	33723.9i	0.323386	−	0.186707i
$426$		−	90728.0i		−	0.499945i
$427$	−7588.81	+	27524.7i	−0.0416215	+	0.150962i
$428$	4101.59			0.0223905
$429$	1280.70	+	2218.24i	0.00695877	+	0.0120529i
$430$	−86638.2	−	50020.6i	−0.468568	−	0.270528i
$431$	91180.4	−	157929.i	0.490848	−	0.850173i	−0.509097	−	0.860709i	$-0.670020\pi$
$431$	91180.4	−	157929.i	0.490848	−	0.850173i	0.999944	+	0.0105360i	$0.00335376\pi$
$432$	144116.	−	83205.2i	0.772225	−	0.445844i
$433$			76313.7i			0.407030i	0.979072	+	0.203515i	$0.0652366\pi$
$433$			76313.7i			0.407030i	−0.979072	+	0.203515i	$0.934763\pi$
$434$	9609.42	+	9749.32i	0.0510173	+	0.0517601i
$435$	−51096.1			−0.270028
$436$	6012.58	+	10414.1i	0.0316292	+	0.0547833i
$437$	−173104.	−	99941.5i	−0.906450	−	0.523339i
$438$	−30389.8	+	52636.6i	−0.158409	+	0.274372i
$439$	214124.	−	123625.i	1.11106	−	0.641469i	0.171955	−	0.985105i	$-0.444992\pi$
$439$	214124.	−	123625.i	1.11106	−	0.641469i	0.939103	+	0.343635i	$0.111658\pi$
$440$		−	2957.63i		−	0.0152770i
$441$	−119080.	+	66474.7i	−0.612294	+	0.341806i
$442$	−271458.			−1.38950
$443$	43759.6	+	75793.8i	0.222980	+	0.386213i	0.955711	−	0.294305i	$-0.0950882\pi$
$443$	43759.6	+	75793.8i	0.222980	+	0.386213i	−0.732732	+	0.680518i	$0.761755\pi$
$444$	2351.16	+	1357.44i	0.0119266	+	0.00688583i
$445$	−58146.0	+	100712.i	−0.293630	+	0.508581i
$446$	3667.60	−	2117.49i	0.0184379	−	0.0106451i
$447$		−	101686.i		−	0.508917i
$448$	148134.	−	146008.i	0.738071	−	0.727480i
$449$	110205.			0.546649			0.273325	−	0.961922i	$-0.411877\pi$
$449$	110205.			0.546649			0.273325	+	0.961922i	$0.411877\pi$
$450$	13916.7	+	24104.5i	0.0687245	+	0.119034i
$451$	−4502.05	−	2599.26i	−0.0221339	−	0.0127790i
$452$	−3672.26	+	6360.54i	−0.0179745	+	0.0311327i
$453$	122758.	−	70874.1i	0.598207	−	0.345375i
$454$			19719.6i			0.0956724i
$455$	−67776.7	−	18686.7i	−0.327384	−	0.0902630i
$456$	65653.5			0.315739
$457$	29732.2	+	51497.6i	0.142362	+	0.246578i	0.928386	−	0.371618i	$-0.121197\pi$
$457$	29732.2	+	51497.6i	0.142362	+	0.246578i	−0.786024	+	0.618196i	$0.787864\pi$
$458$	224732.	+	129749.i	1.07136	+	0.618548i
$459$	182887.	−	316770.i	0.868076	−	1.50355i
$460$	5977.39	−	3451.05i	0.0282485	−	0.0163093i
$461$		−	151883.i		−	0.714672i	−0.933976	−	0.357336i	$-0.883685\pi$
$461$		−	151883.i		−	0.714672i	0.933976	−	0.357336i	$-0.116315\pi$
$462$	3710.34	−	965.499i	0.0173832	−	0.00452343i
$463$	37079.6			0.172971			0.0864853	−	0.996253i	$-0.472436\pi$
$463$	37079.6			0.172971			0.0864853	+	0.996253i	$0.472436\pi$
$464$	−114031.	−	197507.i	−0.529648	−	0.917376i
$465$	−3394.39	−	1959.75i	−0.0156984	−	0.00906349i
$466$	−100410.	+	173915.i	−0.462385	+	0.800874i
$467$	−128746.	+	74331.5i	−0.590337	+	0.340831i	−0.765231	−	0.643756i	$-0.777375\pi$
$467$	−128746.	+	74331.5i	−0.590337	+	0.340831i	0.174894	+	0.984587i	$0.444042\pi$
$468$			4608.26i			0.0210400i
$469$	−19630.0	−	75436.4i	−0.0892429	−	0.342954i
$470$	115490.			0.522814
$471$	−58045.1	−	100537.i	−0.261652	−	0.453194i
$472$	−61460.9	−	35484.4i	−0.275876	−	0.159277i
$473$	−4630.43	+	8020.14i	−0.0206966	+	0.0358476i
$474$	−84806.3	+	48962.9i	−0.377460	+	0.217927i
$475$			25586.3i			0.113402i
$476$	4442.67	−	16113.6i	0.0196079	−	0.0711178i
$477$	−14157.4			−0.0622223
$478$	108494.	+	187917.i	0.474841	+	0.822449i
$479$	−27463.6	−	15856.1i	−0.119698	−	0.0691076i	0.438956	−	0.898509i	$-0.355349\pi$
$479$	−27463.6	−	15856.1i	−0.119698	−	0.0691076i	−0.558654	+	0.829401i	$0.688682\pi$
$480$	−2223.97	+	3852.04i	−0.00965267	+	0.0167189i
$481$	97021.7	−	56015.5i	0.419352	−	0.242113i
$482$			74699.1i			0.321530i
$483$	165235.	+	167641.i	0.708286	+	0.718598i
$484$	9245.49			0.0394675
$485$	−16009.1	−	27728.6i	−0.0680588	−	0.117881i
$486$	207558.	+	119834.i	0.878755	+	0.507349i
$487$	−146158.	+	253153.i	−0.616262	+	1.06740i	0.373900	+	0.927469i	$0.378020\pi$
$487$	−146158.	+	253153.i	−0.616262	+	1.06740i	−0.990162	+	0.139928i	$0.955313\pi$
$488$	32901.9	−	18995.9i	0.138160	−	0.0797666i
$489$			218263.i			0.912773i
$490$	−53928.3	+	90364.8i	−0.224608	+	0.376363i
$491$	−294859.			−1.22307			−0.611535	−	0.791217i	$-0.709448\pi$
$491$	−294859.			−1.22307			−0.611535	+	0.791217i	$0.709448\pi$
$492$	1992.36	+	3450.88i	0.00823073	+	0.0142560i
$493$	−434126.	−	250643.i	−1.78617	−	1.03124i
$494$	51488.8	−	89181.1i	0.210988	−	0.365443i
$495$	2231.36	−	1288.28i	0.00910667	−	0.00525774i
$496$		−	17494.3i		−	0.0711105i
$497$	164183.	−	161827.i	0.664683	−	0.655145i
$498$	−197263.			−0.795404
$499$	12847.3	+	22252.1i	0.0515952	+	0.0893656i	0.890670	−	0.454651i	$-0.150236\pi$
$499$	12847.3	+	22252.1i	0.0515952	+	0.0893656i	−0.839074	+	0.544017i	$0.816903\pi$
$500$	−765.144	−	441.756i	−0.00306058	−	0.00176703i
$501$	−21682.2	+	37554.6i	−0.0863828	+	0.149619i
$502$	−183885.	+	106166.i	−0.729691	+	0.421287i
$503$		−	166628.i		−	0.658584i	−0.944228	−	0.329292i	$-0.893190\pi$
$503$		−	166628.i		−	0.658584i	0.944228	−	0.329292i	$-0.106810\pi$
$504$	174942.	+	48233.1i	0.688703	+	0.189882i
$505$	−90121.9			−0.353385
$506$	7765.83	+	13450.8i	0.0303310	+	0.0525348i
$507$	51513.3	+	29741.2i	0.200403	+	0.115703i
$508$	−5435.16	+	9413.98i	−0.0210613	+	0.0364792i
$509$	−77277.1	+	44616.0i	−0.298274	+	0.172209i	−0.641667	−	0.766983i	$-0.721757\pi$
$509$	−77277.1	+	44616.0i	−0.298274	+	0.172209i	0.343393	+	0.939192i	$0.388424\pi$
$510$		−	116339.i		−	0.447284i
$511$	−149457.	+	38891.4i	−0.572366	+	0.148940i
$512$	−275948.			−1.05266
$513$	69378.2	+	120167.i	0.263626	+	0.456613i
$514$	286941.	+	165665.i	1.08609	+	0.627055i
$515$	55773.2	−	96602.0i	0.210286	−	0.364227i
$516$	6147.53	−	3549.28i	0.0230888	−	0.0133303i
$517$		−	10690.9i		−	0.0399976i
$518$	−42229.2	−	162283.i	−0.157381	−	0.604804i
$519$	198542.			0.737085
$520$	46775.6	+	81017.7i	0.172987	+	0.299622i
$521$	222367.	+	128384.i	0.819210	+	0.472971i	0.850144	−	0.526550i	$-0.176515\pi$
$521$	222367.	+	128384.i	0.819210	+	0.472971i	−0.0309338	+	0.999521i	$0.509848\pi$
$522$	103432.	−	179149.i	0.379589	−	0.657467i
$523$	−138960.	+	80228.7i	−0.508027	+	0.293310i	−0.732022	−	0.681281i	$-0.761423\pi$
$523$	−138960.	+	80228.7i	−0.508027	+	0.293310i	0.223995	+	0.974590i	$0.428090\pi$
$524$		−	18980.1i		−	0.0691251i
$525$	8008.55	−	29047.0i	0.0290559	−	0.105386i
$526$	123228.			0.445386
$527$	−19226.5	−	33301.2i	−0.0692274	−	0.119905i
$528$	−4243.21	−	2449.82i	−0.0152204	−	0.00878752i
$529$	−336869.	+	583474.i	−1.20379	+	2.08502i
$530$	−9460.71	+	5462.14i	−0.0336800	+	0.0194452i
$531$		−	61824.9i		−	0.219267i
$532$	4451.08	+	4515.88i	0.0157269	+	0.0159558i
$533$	164431.			0.578802
$534$	100294.	+	173715.i	0.351717	+	0.609191i
$535$	62818.9	+	36268.5i	0.219474	+	0.126713i
$536$	−51860.6	+	89825.2i	−0.180513	+	0.312657i
$537$	−84764.1	+	48938.6i	−0.293943	+	0.169708i
$538$		−	88912.8i		−	0.307185i
$539$	8365.11	+	4992.17i	0.0287935	+	0.0171835i
$540$	−4791.35			−0.0164312
$541$	73178.3	+	126749.i	0.250028	+	0.433060i	0.963533	−	0.267589i	$-0.0862270\pi$
$541$	73178.3	+	126749.i	0.250028	+	0.433060i	−0.713506	+	0.700650i	$0.752894\pi$
$542$	277159.	+	160018.i	0.943474	+	0.544715i
$543$	−38467.2	+	66627.1i	−0.130464	+	0.225970i
$544$	−37791.0	+	21818.7i	−0.127700	+	0.0737276i
$545$			212666.i			0.715987i
$546$	−86366.8	+	85127.4i	−0.289709	+	0.285551i
$547$	572616.			1.91377			0.956884	−	0.290471i	$-0.0938120\pi$
$547$	572616.			1.91377			0.956884	+	0.290471i	$0.0938120\pi$
$548$	9036.33	+	15651.4i	0.0300906	+	0.0521185i
$549$	28662.7	+	16548.4i	0.0950981	+	0.0549049i
$550$	994.076	−	1721.79i	0.00328620	−	0.00569187i
$551$	164686.	−	95081.3i	0.542441	−	0.313178i
$552$		−	313212.i		−	1.02792i
$553$	−239868.	−	66134.0i	−0.784373	−	0.216259i
$554$	−235402.			−0.766991
$555$	24006.5	+	41580.5i	0.0779370	+	0.134991i
$556$	−4279.39	−	2470.71i	−0.0138431	−	0.00799231i
$557$	129224.	−	223823.i	0.416518	−	0.721431i	−0.579068	−	0.815279i	$-0.696583\pi$
$557$	129224.	−	223823.i	0.416518	−	0.721431i	0.995587	+	0.0938481i	$0.0299168\pi$
$558$	13742.3	−	7934.11i	0.0441357	−	0.0254818i
$559$		−	292925.i		−	0.937417i
$560$	130151.	−	33867.9i	0.415024	−	0.107997i
$561$	−10769.5			−0.0342193
$562$	131949.	+	228542.i	0.417766	+	0.723592i
$563$	−335516.	−	193710.i	−1.05851	−	0.611132i	−0.133492	−	0.991050i	$-0.542619\pi$
$563$	−335516.	−	193710.i	−1.05851	−	0.611132i	−0.925020	+	0.379918i	$0.875952\pi$
$564$	−4097.36	+	7096.84i	−0.0128809	+	0.0223104i
$565$	−112487.	+	64944.2i	−0.352374	+	0.203443i
$566$		−	546445.i		−	1.70574i
$567$	15623.4	+	60039.4i	0.0485969	+	0.186754i
$568$	−306751.			−0.950800
$569$	229897.	+	398193.i	0.710083	+	1.22990i	0.964826	+	0.262891i	$0.0846758\pi$
$569$	229897.	+	398193.i	0.710083	+	1.22990i	−0.254743	+	0.967009i	$0.581991\pi$
$570$	38220.3	+	22066.5i	0.117637	+	0.0679178i
$571$	93363.4	−	161710.i	0.286355	−	0.495981i	−0.686582	−	0.727052i	$-0.740890\pi$
$571$	93363.4	−	161710.i	0.286355	−	0.495981i	0.972937	+	0.231071i	$0.0742231\pi$
$572$	285.069	−	164.585i	0.000871282	−	0.000503035i
$573$			42684.4i			0.130005i
$574$	65417.0	−	237268.i	0.198549	−	0.720137i
$575$	122064.			0.369192
$576$	−120553.	−	208804.i	−0.363356	−	0.629352i
$577$	−88901.0	−	51327.0i	−0.267027	−	0.154168i	0.360509	−	0.932756i	$-0.382603\pi$
$577$	−88901.0	−	51327.0i	−0.267027	−	0.154168i	−0.627536	+	0.778588i	$0.715936\pi$
$578$	406971.	−	704894.i	1.21817	−	2.10993i
$579$	−282464.	+	163081.i	−0.842571	+	0.486458i
$580$			6566.44i			0.0195197i
$581$	−351848.	−	356971.i	−1.04232	−	1.05750i
$582$	−55227.3			−0.163045
$583$	505.633	+	875.783i	0.00148764	+	0.00257667i
$584$	177964.	+	102748.i	0.521804	+	0.301263i
$585$	−40748.8	+	70578.9i	−0.119070	+	0.206235i
$586$	−506974.	+	292702.i	−1.47635	+	0.852374i
$587$		−	17024.6i		−	0.0494084i	−0.999695	−	0.0247042i	$-0.992136\pi$
$587$		−	17024.6i		−	0.0494084i	0.999695	−	0.0247042i	$-0.00786439\pi$
$588$	−3639.64	−	6519.87i	−0.0105270	−	0.0188575i
$589$	14587.1			0.0420473
$590$	−23853.0	−	41314.7i	−0.0685235	−	0.118686i
$591$	41902.7	+	24192.6i	0.119969	+	0.0692639i
$592$	−107151.	+	185590.i	−0.305740	+	0.529556i
$593$	−200795.	+	115929.i	−0.571009	+	0.329672i	−0.757552	−	0.652775i	$-0.773605\pi$
$593$	−200795.	+	115929.i	−0.571009	+	0.329672i	0.186543	+	0.982447i	$0.440271\pi$
$594$		−	10781.9i		−	0.0305578i
$595$	210528.	−	207507.i	0.594670	−	0.586137i
$596$	−13067.9			−0.0367885
$597$	−101944.	−	176572.i	−0.286030	−	0.495419i
$598$	−425455.	−	245637.i	−1.18974	−	0.686896i
$599$	253163.	−	438491.i	0.705580	−	1.22210i	−0.260902	−	0.965365i	$-0.584020\pi$
$599$	253163.	−	438491.i	0.705580	−	1.22210i	0.966482	−	0.256735i	$-0.0826468\pi$
$600$	−34721.7	+	20046.6i	−0.0964492	+	0.0556850i
$601$			52748.9i			0.146038i	0.997331	+	0.0730188i	$0.0232633\pi$
$601$			52748.9i			0.146038i	−0.997331	+	0.0730188i	$0.976737\pi$
$602$	−422679.	−	116537.i	−1.16632	−	0.321565i
$603$	−90357.2			−0.248501
$604$	−9108.15	−	15775.8i	−0.0249664	−	0.0432431i
$605$	141601.	+	81753.7i	0.386863	+	0.223355i
$606$	−77724.2	+	134622.i	−0.211646	+	0.366582i
$607$	365518.	−	211032.i	0.992046	−	0.572758i	0.0861609	−	0.996281i	$-0.472540\pi$
$607$	365518.	−	211032.i	0.992046	−	0.572758i	0.905885	+	0.423523i	$0.139207\pi$
$608$		−	16553.8i		−	0.0447807i
$609$	−216721.	+	56394.9i	−0.584341	+	0.152057i
$610$	25538.5			0.0686336
$611$	169079.	+	292854.i	0.452906	+	0.784457i
$612$	−16779.8	−	9687.83i	−0.0448006	−	0.0258657i
$613$	159572.	−	276387.i	0.424654	−	0.735522i	−0.571734	−	0.820439i	$-0.693729\pi$
$613$	159572.	−	276387.i	0.424654	−	0.735522i	0.996388	+	0.0849166i	$0.0270624\pi$
$614$	−248082.	+	143230.i	−0.658050	+	0.379925i
$615$			70470.3i			0.186318i
$616$	−3264.35	−	12544.6i	−0.00860270	−	0.0330595i
$617$	223191.			0.586281			0.293141	−	0.956069i	$-0.405300\pi$
$617$	223191.			0.586281			0.293141	+	0.956069i	$0.405300\pi$
$618$	−96201.4	−	166626.i	−0.251886	−	0.436280i
$619$	132645.	+	76582.5i	0.346186	+	0.199870i	0.663004	−	0.748616i	$-0.269281\pi$
$619$	132645.	+	76582.5i	0.346186	+	0.199870i	−0.316818	+	0.948486i	$0.602615\pi$
$620$	−251.851	+	436.219i	−0.000655180	+	0.00113481i
$621$	573276.	−	330981.i	1.48655	−	0.858263i
$622$			31270.7i			0.0808272i
$623$	−135467.	+	491339.i	−0.349026	+	1.26592i
$624$	154978.			0.398016
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	−170412.	−	98387.6i	−0.434863	−	0.251068i
$627$	2042.71	−	3538.07i	0.00519602	−	0.00899978i
$628$	−12920.2	+	7459.47i	−0.0327604	+	0.0189142i
$629$			471040.i			1.19057i
$630$	85631.1	+	86877.8i	0.215750	+	0.218891i
$631$	236090.			0.592950			0.296475	−	0.955041i	$-0.404189\pi$
$631$	236090.			0.592950			0.296475	+	0.955041i	$0.404189\pi$
$632$	165543.	+	286730.i	0.414455	+	0.717858i
$633$	−105552.	−	60940.4i	−0.263426	−	0.152089i
$634$	−104134.	+	180366.i	−0.259069	+	0.448721i
$635$	−166487.	+	96121.4i	−0.412889	+	0.238381i
$636$		−	775.148i		−	0.00191633i
$637$	−308096.	−	4453.17i	−0.759288	−	0.0109746i
$638$	−14776.3			−0.0363016
$639$	−133614.	−	231426.i	−0.327227	−	0.566774i
$640$	−148591.	−	85789.1i	−0.362771	−	0.209446i
$641$	−109547.	+	189741.i	−0.266615	+	0.461791i	−0.967985	−	0.251006i	$-0.919239\pi$
$641$	−109547.	+	189741.i	−0.266615	+	0.461791i	0.701370	+	0.712797i	$0.252572\pi$
$642$	108354.	−	62558.4i	0.262891	−	0.151780i
$643$			446197.i			1.07921i	0.841919	+	0.539604i	$0.181426\pi$
$643$			446197.i			1.07921i	−0.841919	+	0.539604i	$0.818574\pi$
$644$	21543.8	−	21234.7i	0.0519459	−	0.0512005i
$645$	125539.			0.301758
$646$	216487.	+	374966.i	0.518760	+	0.898519i
$647$	433740.	+	250420.i	1.03615	+	0.598219i	0.918739	−	0.394865i	$-0.129209\pi$
$647$	433740.	+	250420.i	1.03615	+	0.598219i	0.117406	+	0.993084i	$0.462542\pi$
$648$	41275.6	−	71491.4i	0.0982977	−	0.170257i
$649$	−3824.52	+	2208.09i	−0.00908003	+	0.00524236i
$650$			62886.1i			0.148843i
$651$	−16560.1	−	4565.78i	−0.0390752	−	0.0107734i
$652$	28049.4			0.0659824
$653$	366141.	+	634176.i	0.858662	+	1.48725i	0.873205	+	0.487353i	$0.162037\pi$
$653$	366141.	+	634176.i	0.858662	+	1.48725i	−0.0145426	+	0.999894i	$0.504629\pi$
$654$	317676.	+	183410.i	0.742727	+	0.428813i
$655$	167832.	−	290694.i	0.391195	−	0.677570i
$656$	−272397.	+	157268.i	−0.632987	+	0.365455i
$657$			179018.i			0.414731i
$658$	489843.	−	127466.i	1.13137	−	0.294404i
$659$	676087.			1.55680			0.778398	−	0.627772i	$-0.216033\pi$
$659$	676087.			1.55680			0.778398	+	0.627772i	$0.216033\pi$
$660$	70.5361	+	122.172i	0.000161929	+	0.000280468i
$661$	−515452.	−	297596.i	−1.17974	−	0.681121i	−0.223783	−	0.974639i	$-0.571841\pi$
$661$	−515452.	−	297596.i	−1.17974	−	0.681121i	−0.955954	+	0.293518i	$0.905174\pi$
$662$	70048.6	−	121328.i	0.159839	−	0.276850i
$663$	295007.	−	170322.i	0.671128	−	0.387476i
$664$			666946.i			1.51271i
$665$	28239.7	+	108523.i	0.0638582	+	0.245402i
$666$	−194382.			−0.438236
$667$	−453603.	−	785663.i	−1.01959	−	1.76598i
$668$	4826.21	+	2786.41i	0.0108157	+	0.00624442i
$669$	−2657.17	+	4602.36i	−0.00593701	+	0.0102832i
$670$	−60381.5	+	34861.3i	−0.134510	+	0.0776593i
$671$		−	2364.12i		−	0.00525078i
$672$	−5181.36	+	18792.8i	−0.0114737	+	0.0416153i
$673$	197982.			0.437114			0.218557	−	0.975824i	$-0.429865\pi$
$673$	197982.			0.437114			0.218557	+	0.975824i	$0.429865\pi$
$674$	−355177.	−	615185.i	−0.781853	−	1.35421i
$675$	−73383.1	−	42367.7i	−0.161060	−	0.0929881i
$676$	3822.10	−	6620.07i	0.00836389	−	0.0144867i
$677$	−694105.	+	400742.i	−1.51443	+	0.874354i	−0.514569	+	0.857449i	$0.672048\pi$
$677$	−694105.	+	400742.i	−1.51443	+	0.874354i	−0.999857	+	0.0169049i	$0.994619\pi$
$678$			224040.i			0.487379i
$679$	−98506.0	−	99940.0i	−0.213660	−	0.216770i
$680$	−393340.			−0.850650
$681$	−12372.8	−	21430.3i	−0.0266792	−	0.0462098i
$682$	−981.616	−	566.736i	−0.00211044	−	0.00121846i
$683$	300591.	−	520639.i	0.644369	−	1.11608i	−0.340078	−	0.940397i	$-0.610453\pi$
$683$	300591.	−	520639.i	0.644369	−	1.11608i	0.984447	−	0.175683i	$-0.0562133\pi$
$684$	6365.41	−	3675.07i	0.0136055	−	0.00785514i
$685$			319617.i			0.681159i
$686$	−128998.	+	442798.i	−0.274116	+	0.940930i
$687$	−325637.			−0.689954
$688$	280165.	+	485259.i	0.591884	+	1.02517i
$689$	−27701.4	−	15993.4i	−0.0583530	−	0.0336901i
$690$	105272.	−	182337.i	0.221114	−	0.382981i
$691$	275054.	−	158803.i	0.576053	−	0.332584i	−0.183510	−	0.983018i	$-0.558746\pi$
$691$	275054.	−	158803.i	0.576053	−	0.332584i	0.759563	+	0.650434i	$0.225413\pi$
$692$		−	25515.0i		−	0.0532823i
$693$	8042.32	−	7926.91i	0.0167461	−	0.0165058i
$694$	291280.			0.604772
$695$	−43694.7	−	75681.5i	−0.0904606	−	0.156682i
$696$	258059.	+	148990.i	0.532721	+	0.307567i
$697$	−345680.	+	598735.i	−0.711555	+	1.23245i
$698$	−463457.	+	267577.i	−0.951258	+	0.549209i
$699$		−	252002.i		−	0.515763i
$700$	−3732.88	−	1029.19i	−0.00761813	−	0.00210039i
$701$	149455.			0.304141			0.152070	−	0.988370i	$-0.451406\pi$
$701$	149455.			0.304141			0.152070	+	0.988370i	$0.451406\pi$
$702$	170518.	+	295346.i	0.346016	+	0.599317i
$703$	−154749.	−	89344.4i	−0.313125	−	0.180783i
$704$	−8611.14	+	14914.9i	−0.0173746	+	0.0300937i
$705$	−125508.	+	72462.3i	−0.252519	+	0.145792i
$706$		−	818292.i		−	1.64172i
$707$	−382247.	+	99467.8i	−0.764725	+	0.198996i
$708$	3385.05			0.00675303
$709$	−483101.	−	836755.i	−0.961049	−	1.66459i	−0.719876	−	0.694103i	$-0.755801\pi$
$709$	−483101.	−	836755.i	−0.961049	−	1.66459i	−0.241173	−	0.970482i	$-0.577532\pi$
$710$	−178575.	−	103101.i	−0.354246	−	0.204524i
$711$	−144214.	+	249786.i	−0.285278	+	0.494116i
$712$	587328.	−	339094.i	1.15857	−	0.668898i
$713$		−	69590.5i		−	0.136890i
$714$	−128403.	−	493444.i	−0.251872	−	0.967924i
$715$	5821.40			0.0113872
$716$	6289.18	+	10893.2i	0.0122678	+	0.0212485i
$717$	−235811.	−	136145.i	−0.458697	−	0.264829i
$718$	1304.53	−	2259.51i	0.00253050	−	0.00438295i
$719$	−345459.	+	199451.i	−0.668249	+	0.385814i	−0.795413	−	0.606068i	$-0.792746\pi$
$719$	−345459.	+	199451.i	−0.668249	+	0.385814i	0.127164	+	0.991882i	$0.459413\pi$
$720$		−	155895.i		−	0.300723i
$721$	129939.	−	471289.i	0.249959	−	0.906602i
$722$	346633.			0.664961
$723$	−46868.8	−	81179.2i	−0.0896618	−	0.155299i
$724$	8562.36	+	4943.48i	0.0163349	+	0.00943096i
$725$	−58064.1	+	100570.i	−0.110467	+	0.191334i
$726$	244244.	−	141014.i	0.463394	−	0.267541i
$727$		−	205022.i		−	0.387911i	−0.981010	−	0.193956i	$-0.937868\pi$
$727$		−	205022.i		−	0.387911i	0.981010	−	0.193956i	$-0.0621318\pi$
$728$	287815.	+	292006.i	0.543064	+	0.550970i
$729$	−198198.			−0.372944
$730$	69068.1	+	119629.i	0.129608	+	0.224488i
$731$	1.06661e6	+	615809.i	1.99605	+	1.15242i
$732$	−906.062	+	1569.35i	−0.00169097	+	0.00292884i
$733$	639014.	−	368935.i	1.18933	−	0.686660i	0.231176	−	0.972912i	$-0.425743\pi$
$733$	639014.	−	368935.i	1.18933	−	0.686660i	0.958154	+	0.286252i	$0.0924093\pi$
$734$		−	680986.i		−	1.26400i
$735$	1908.49	−	132040.i	0.00353277	−	0.244417i
$736$	−78972.9			−0.145788
$737$	3227.13	+	5589.55i	0.00594129	+	0.0102906i
$738$	−247078.	−	142650.i	−0.453650	−	0.261915i
$739$	125759.	−	217820.i	0.230276	−	0.398850i	−0.727613	−	0.685988i	$-0.759370\pi$
$739$	125759.	−	217820.i	0.230276	−	0.398850i	0.957889	+	0.287138i	$0.0927037\pi$
$740$	5343.59	−	3085.12i	0.00975819	−	0.00563390i
$741$			129223.i			0.235345i
$742$	−34098.5	+	33609.2i	−0.0619337	+	0.0610450i
$743$	−744120.			−1.34792			−0.673962	−	0.738766i	$-0.735409\pi$
$743$	−744120.			−1.34792			−0.673962	+	0.738766i	$0.735409\pi$
$744$	11428.8	+	19795.3i	0.0206469	+	0.0357616i
$745$	−200144.	−	115553.i	−0.360604	−	0.208195i
$746$	−384007.	+	665120.i	−0.690020	+	1.19515i
$747$	−503172.	+	290507.i	−0.901728	+	0.520613i
$748$			1384.01i			0.00247364i
$749$	306472.	+	84497.4i	0.546296	+	0.150619i
$750$	−26951.1			−0.0479130
$751$	−36239.0	−	62767.9i	−0.0642535	−	0.111290i	0.832109	−	0.554612i	$-0.187133\pi$
$751$	−36239.0	−	62767.9i	−0.0642535	−	0.111290i	−0.896363	+	0.443322i	$0.853800\pi$
$752$	−560194.	−	323428.i	−0.990609	−	0.571929i
$753$	133225.	−	230752.i	0.234960	−	0.406963i
$754$	404765.	−	233691.i	0.711967	−	0.411055i
$755$		−	322157.i		−	0.565163i
$756$	−20322.2	+	5288.23i	−0.0355572	+	0.00925266i
$757$	372201.			0.649511			0.324755	−	0.945798i	$-0.394718\pi$
$757$	372201.			0.649511			0.324755	+	0.945798i	$0.394718\pi$
$758$	51811.0	+	89739.3i	0.0901745	+	0.156187i
$759$	−16879.0	−	9745.11i	−0.0292998	−	0.0169162i
$760$	74606.8	−	129223.i	0.129167	−	0.223723i
$761$	302279.	−	174521.i	0.521961	−	0.301354i	−0.215776	−	0.976443i	$-0.569228\pi$
$761$	302279.	−	174521.i	0.521961	−	0.301354i	0.737737	+	0.675089i	$0.235895\pi$
$762$			331593.i			0.571079i
$763$	234720.	+	902010.i	0.403182	+	1.54940i
$764$	5485.44			0.00939777
$765$	−171330.	−	296752.i	−0.292759	−	0.507074i
$766$	266269.	+	153731.i	0.453799	+	0.262001i
$767$	69842.7	−	120971.i	0.118722	−	0.205632i
$768$	33042.8	−	19077.3i	0.0560215	−	0.0323440i
$769$			57476.6i			0.0971938i	0.998818	+	0.0485969i	$0.0154750\pi$
$769$			57476.6i			0.0971938i	−0.998818	+	0.0485969i	$0.984525\pi$
$770$	2315.97	−	8400.04i	0.00390618	−	0.0141677i
$771$	−415778.			−0.699443
$772$	20957.8	+	36300.0i	0.0351650	+	0.0609076i
$773$	−683472.	−	394603.i	−1.14383	−	0.660391i	−0.196454	−	0.980513i	$-0.562943\pi$
$773$	−683472.	−	394603.i	−1.14383	−	0.660391i	−0.947376	+	0.320122i	$0.896276\pi$
$774$	−254123.	+	440154.i	−0.424192	+	0.734722i
$775$	−7714.57	+	4454.01i	−0.0128442	+	0.00741563i
$776$			186723.i			0.310081i
$777$	147715.	+	149865.i	0.244671	+	0.248233i
$778$	613351.			1.01333
$779$	−131134.	−	227130.i	−0.216092	−	0.374282i
$780$	−3864.35	−	2231.09i	−0.00635167	−	0.00366714i
$781$	−9544.07	+	16530.8i	−0.0156470	+	0.0271014i
$782$	1.78885e6	−	1.03279e6i	2.92523	−	1.68888i
$783$			629771.i			1.02721i
$784$	514650.	−	287297.i	0.837298	−	0.467411i
$785$	−263843.			−0.428160
$786$	−289489.	−	501409.i	−0.468583	−	0.811610i
$787$	319390.	+	184400.i	0.515670	+	0.297722i	0.735161	−	0.677892i	$-0.237106\pi$
$787$	319390.	+	184400.i	0.515670	+	0.297722i	−0.219491	+	0.975614i	$0.570440\pi$
$788$	3109.03	−	5384.99i	0.00500694	−	0.00867227i
$789$	−133918.	+	77317.3i	−0.215121	+	0.124200i
$790$			222560.i			0.356610i
$791$	−405427.	+	399609.i	−0.647977	+	0.638679i
$792$	−15025.9			−0.0239546
$793$	37389.0	+	64759.7i	0.0594563	+	0.102981i
$794$	−405264.	−	233979.i	−0.642831	−	0.371139i
$795$	6854.28	−	11872.0i	0.0108450	−	0.0187840i
$796$	−22691.5	+	13101.0i	−0.0358128	+	0.0206765i
$797$		−	407584.i		−	0.641653i	−0.947138	−	0.320827i	$-0.896039\pi$
$797$		−	407584.i		−	0.641653i	0.947138	−	0.320827i	$-0.103961\pi$
$798$	186464.	+	51410.0i	0.292812	+	0.0807312i
$799$	−1.42180e6			−2.22713
$800$	5054.52	+	8754.69i	0.00789769	+	0.0136792i
$801$	511654.	+	295403.i	0.797464	+	0.460416i
$802$	−401096.	+	694718.i	−0.623590	+	1.08009i
$803$	11074.2	−	6393.67i	0.0171743	−	0.00991560i
$804$		−	4947.26i		−	0.00765337i
$805$	517728.	−	134723.i	0.798933	−	0.207897i
$806$	35852.2			0.0551882
$807$	55787.0	+	96626.0i	0.0856616	+	0.148370i
$808$	455157.	+	262785.i	0.697170	+	0.402511i
$809$	−345828.	+	598992.i	−0.528401	+	0.915217i	0.471051	+	0.882106i	$0.343875\pi$
$809$	−345828.	+	598992.i	−0.528401	+	0.915217i	−0.999452	+	0.0331107i	$0.989459\pi$
$810$	48057.3	−	27745.9i	0.0732469	−	0.0422891i
$811$		−	588050.i		−	0.894071i	−0.894516	−	0.447036i	$-0.852480\pi$
$811$		−	588050.i		−	0.894071i	0.894516	−	0.447036i	$-0.147520\pi$
$812$	7247.40	+	27851.2i	0.0109918	+	0.0422408i
$813$	−401603.			−0.607597
$814$	6942.39	+	12024.6i	0.0104776	+	0.0181477i
$815$	429597.	+	248028.i	0.646764	+	0.373410i
$816$	−325806.	+	564312.i	−0.489303	+	0.847498i
$817$	−404619.	+	233607.i	−0.606180	+	0.349978i
$818$			1.17590e6i			1.75738i
$819$	−94935.4	+	344331.i	−0.141534	+	0.513344i
$820$	9056.26			0.0134686
$821$	92501.1	+	160217.i	0.137234	+	0.237696i	0.926449	−	0.376421i	$-0.122846\pi$
$821$	92501.1	+	160217.i	0.137234	+	0.237696i	−0.789215	+	0.614117i	$0.789512\pi$
$822$	477437.	+	275648.i	0.706598	+	0.407954i
$823$	−201632.	+	349236.i	−0.297687	+	0.515608i	−0.975606	−	0.219528i	$-0.929548\pi$
$823$	−201632.	+	349236.i	−0.297687	+	0.515608i	0.677920	+	0.735136i	$0.262882\pi$
$824$	−563361.	+	325256.i	−0.829721	+	0.479040i
$825$			2494.87i			0.00366556i
$826$	−146770.	−	148907.i	−0.215119	−	0.218251i
$827$	−619021.			−0.905096			−0.452548	−	0.891740i	$-0.649485\pi$
$827$	−619021.			−0.905096			−0.452548	+	0.891740i	$0.649485\pi$
$828$	−17532.6	−	30367.4i	−0.0255733	−	0.0442942i
$829$	−63086.7	−	36423.1i	−0.0917971	−	0.0529991i	0.453399	−	0.891308i	$-0.350211\pi$
$829$	−63086.7	−	36423.1i	−0.0917971	−	0.0529991i	−0.545196	+	0.838309i	$0.683545\pi$
$830$	−224164.	+	388264.i	−0.325395	+	0.563600i
$831$	255823.	−	147699.i	0.370457	−	0.213883i
$832$		−	544748.i		−	0.786954i
$833$	663917.	−	1.11249e6i	0.956805	−	1.60327i
$834$	−150735.			−0.216712
$835$	49277.9	+	85351.9i	0.0706772	+	0.122417i
$836$	−454.684	−	262.512i	−0.000650574	−	0.000375609i
$837$	−24154.4	+	41836.7i	−0.0344783	+	0.0597181i
$838$	−315434.	+	182116.i	−0.449180	+	0.259334i
$839$		−	758487.i		−	1.07752i	−0.842460	−	0.538758i	$-0.818894\pi$
$839$		−	758487.i		−	1.07752i	0.842460	−	0.538758i	$-0.181106\pi$
$840$	−125145.	+	123349.i	−0.177359	+	0.174814i
$841$	155807.			0.220289
$842$	−27048.3	−	46849.1i	−0.0381519	−	0.0660811i
$843$	−286791.	−	165579.i	−0.403562	−	0.232997i
$844$	−7831.55	+	13564.6i	−0.0109942	+	0.0190425i
$845$	117077.	−	67594.2i	0.163967	−	0.0946664i
$846$		−	586730.i		−	0.819781i
$847$	690826.	+	190467.i	0.962946	+	0.265494i
$848$	61186.8			0.0850875
$849$	342859.	+	593849.i	0.475663	+	0.823873i
$850$	−228984.	−	132204.i	−0.316933	−	0.182981i
$851$	−426234.	+	738259.i	−0.588557	+	1.01941i
$852$	12671.1	−	7315.65i	0.0174556	−	0.0100780i
$853$		−	374578.i		−	0.514806i	−0.966304	−	0.257403i	$-0.917133\pi$
$853$		−	374578.i		−	0.514806i	0.966304	−	0.257403i	$-0.0828668\pi$
$854$	108320.	−	28187.0i	0.148523	−	0.0386485i
$855$	129988.			0.177816
$856$	−211510.	−	366345.i	−0.288657	−	0.499969i
$857$	481633.	+	278071.i	0.655774	+	0.378612i	0.790665	−	0.612249i	$-0.209735\pi$
$857$	481633.	+	278071.i	0.655774	+	0.378612i	−0.134891	+	0.990860i	$0.543068\pi$
$858$	5020.57	−	8695.89i	0.00681991	−	0.0118124i
$859$	882189.	−	509332.i	1.19557	−	0.690263i	0.236006	−	0.971752i	$-0.424161\pi$
$859$	882189.	−	509332.i	1.19557	−	0.690263i	0.959565	+	0.281489i	$0.0908281\pi$
$860$		−	16133.2i		−	0.0218134i
$861$	77778.3	+	298896.i	0.104918	+	0.403193i
$862$	−714887.			−0.962106
$863$	−56151.2	−	97256.7i	−0.0753941	−	0.130586i	0.825863	−	0.563870i	$-0.190688\pi$
$863$	−56151.2	−	97256.7i	−0.0753941	−	0.130586i	−0.901258	+	0.433284i	$0.857355\pi$
$864$	47477.3	+	27411.0i	0.0636002	+	0.0367196i
$865$	225617.	−	390781.i	0.301537	−	0.522277i
$866$	259083.	−	149582.i	0.345465	−	0.199454i
$867$			1.02139e6i			1.35879i
$868$	−586.756	+	2128.17i	−0.000778786	+	0.00282466i
$869$	20602.5			0.0272823
$870$	100153.	+	173470.i	0.132320	+	0.229185i
$871$	−176800.	−	102075.i	−0.233048	−	0.134550i
$872$	620109.	−	1.07406e6i	0.815521	−	1.41252i
$873$	−140872.	+	81332.3i	−0.184840	+	0.106717i
$874$			783578.i			1.02579i
$875$	−48071.2	−	48771.0i	−0.0627869	−	0.0637009i
$876$	−9801.65			−0.0127729
$877$	−270009.	−	467669.i	−0.351058	−	0.608051i	0.635377	−	0.772202i	$-0.280845\pi$
$877$	−270009.	−	467669.i	−0.351058	−	0.608051i	−0.986435	+	0.164151i	$0.947511\pi$
$878$	−839405.	−	484631.i	−1.08889	−	0.628669i
$879$	367303.	−	636187.i	0.475386	−	0.823393i
$880$	−9643.72	+	5567.81i	−0.0124532	+	0.00718983i
$881$		−	54276.2i		−	0.0699291i	−0.999389	−	0.0349645i	$-0.988868\pi$
$881$		−	54276.2i		−	0.0699291i	0.999389	−	0.0349645i	$-0.0111318\pi$
$882$	459087.	+	273976.i	0.590143	+	0.352188i
$883$	602170.			0.772320			0.386160	−	0.922432i	$-0.373801\pi$
$883$	602170.			0.772320			0.386160	+	0.922432i	$0.373801\pi$
$884$	−21888.4	−	37911.9i	−0.0280098	−	0.0485144i
$885$	51844.6	+	29932.5i	0.0661937	+	0.0382169i
$886$	171545.	−	297125.i	0.218530	−	0.378506i
$887$	−581380.	+	335660.i	−0.738946	+	0.426631i	−0.821686	−	0.569941i	$-0.806966\pi$
$887$	−581380.	+	335660.i	−0.738946	+	0.426631i	0.0827400	+	0.996571i	$0.473633\pi$
$888$		−	280001.i		−	0.355086i
$889$	−600056.	+	591446.i	−0.759256	+	0.748361i
$890$	455885.			0.575540
$891$	−2568.45	−	4448.69i	−0.00323531	−	0.00560372i
$892$	591.457	+	341.478i	0.000743351	+	0.000429174i
$893$	269681.	−	467100.i	0.338179	−	0.585743i
$894$	−345222.	+	199314.i	−0.431941	+	0.249381i
$895$			222449.i			0.277706i
$896$	−724926.	−	199869.i	−0.902979	−	0.248960i
$897$	616484.			0.766191
$898$	−216012.	−	374143.i	−0.267870	−	0.463965i
$899$	57336.3	+	33103.1i	0.0709431	+	0.0409590i
$900$	−2244.29	+	3887.22i	−0.00277072	+	0.00479904i
$901$	116472.	−	67245.0i	0.143473	−	0.0828344i
$902$			20379.1i			0.0250480i
$903$	532465.	−	138557.i	0.653004	−	0.169924i
$904$	757479.			0.926902
$905$	87425.9	+	151426.i	0.106744	+	0.184886i
$906$	−481232.	−	277839.i	−0.586270	−	0.338483i
$907$	−59090.8	+	102348.i	−0.0718298	+	0.124413i	−0.899703	−	0.436502i	$-0.856217\pi$
$907$	−59090.8	+	102348.i	−0.0718298	+	0.124413i	0.827873	+	0.560915i	$0.189551\pi$
$908$	−2754.04	+	1590.05i	−0.00334040	+	0.00192858i
$909$			457853.i			0.554113i
$910$	69407.6	+	266728.i	0.0838155	+	0.322096i
$911$	−186604.			−0.224846			−0.112423	−	0.993660i	$-0.535861\pi$
$911$	−186604.			−0.224846			−0.112423	+	0.993660i	$0.535861\pi$
$912$	−123594.	−	214071.i	−0.148596	−	0.257377i
$913$	35941.8	+	20751.0i	0.0431179	+	0.0248942i
$914$	116555.	−	201880.i	0.139521	−	0.241658i
$915$	−27754.0	+	16023.8i	−0.0331500	+	0.0191392i
$916$			41848.1i			0.0498753i
$917$	391011.	−	1.41820e6i	0.464998	−	1.68655i
$918$	−1.43390e6			−1.70151
$919$	209914.	+	363582.i	0.248548	+	0.430498i	0.963123	−	0.269061i	$-0.0867132\pi$
$919$	209914.	+	363582.i	0.248548	+	0.430498i	−0.714575	+	0.699559i	$0.753380\pi$
$920$	−616481.	−	355925.i	−0.728356	−	0.420517i
$921$	179735.	−	311311.i	0.211892	−	0.367008i
$922$	−515638.	+	297704.i	−0.606573	+	0.350205i
$923$		−	603766.i		−	0.708705i
$924$	434.016	+	440.335i	0.000508349	+	0.000515750i
$925$	109121.			0.127534
$926$	−72679.3	−	125884.i	−0.0847595	−	0.146808i
$927$	−490774.	−	283349.i	−0.571113	−	0.329732i
$928$	37566.2	−	65066.6i	0.0436216	−	0.0755548i
$929$	1.37158e6	−	791883.i	1.58924	−	0.917550i	0.595812	−	0.803124i	$-0.296830\pi$
$929$	1.37158e6	−	791883.i	1.58924	−	0.917550i	0.993432	−	0.114426i	$-0.0365029\pi$
$930$			15365.2i			0.0177653i
$931$	239554.	+	429125.i	0.276378	+	0.495091i
$932$	−32385.2			−0.0372834
$933$	−19620.4	−	33983.5i	−0.0225395	−	0.0390395i
$934$	504707.	+	291393.i	0.578556	+	0.334030i
$935$	−12238.2	+	21197.1i	−0.0139989	+	0.0242468i
$936$	411600.	−	237637.i	0.469812	−	0.271246i
$937$		−	861051.i		−	0.980730i	−0.871517	−	0.490365i	$-0.836863\pi$
$937$		−	861051.i		−	0.980730i	0.871517	−	0.490365i	$-0.163137\pi$
$938$	−217628.	+	214505.i	−0.247349	+	0.243799i
$939$	246927.			0.280052
$940$	9312.25	+	16129.3i	0.0105390	+	0.0182541i
$941$	94534.0	+	54579.2i	0.106760	+	0.0616379i	0.552429	−	0.833560i	$-0.313701\pi$
$941$	94534.0	+	54579.2i	0.106760	+	0.0616379i	−0.445669	+	0.895198i	$0.647034\pi$
$942$	−227547.	+	394123.i	−0.256430	+	0.444150i
$943$	−1.08357e6	+	625597.i	−1.21852	+	0.703511i
$944$			267201.i			0.299843i
$945$	−358011.	−	98707.2i	−0.400897	−	0.110531i
$946$	36304.2			0.0405672
$947$	−379764.	−	657771.i	−0.423461	−	0.733457i	0.572814	−	0.819685i	$-0.305852\pi$
$947$	−379764.	−	657771.i	−0.423461	−	0.733457i	−0.996275	+	0.0862287i	$0.972518\pi$
$948$	−13676.3	−	7896.03i	−0.0152178	−	0.00878602i
$949$	−202235.	+	350281.i	−0.224555	+	0.388941i
$950$	86864.9	−	50151.5i	0.0962492	−	0.0555695i
$951$		−	261350.i		−	0.288976i
$952$	−1.66833e6	+	434131.i	−1.84081	+	0.479013i
$953$	455733.			0.501793			0.250897	−	0.968014i	$-0.419275\pi$
$953$	455733.			0.501793			0.250897	+	0.968014i	$0.419275\pi$
$954$	27749.7	+	48064.0i	0.0304903	+	0.0528108i
$955$	84013.6	+	48505.3i	0.0921176	+	0.0531841i
$956$	−17496.3	+	30304.5i	−0.0191439	+	0.0331582i
$957$	16058.2	−	9271.20i	0.0175337	−	0.0101231i
$958$			124318.i			0.135457i
$959$	352762.	+	1.35564e6i	0.383570	+	1.47403i
$960$	233462.			0.253323
$961$	−459221.	−	795394.i	−0.497250	−	0.861263i
$962$	−380343.	−	219591.i	−0.410984	−	0.237282i
$963$	184258.	−	319143.i	0.198688	−	0.344139i
$964$	−10432.5	+	6023.19i	−0.0112262	+	0.00648146i
$965$			741281.i			0.796028i
$966$	245261.	−	889562.i	0.262829	−	0.953283i
$967$	−70127.4			−0.0749954			−0.0374977	−	0.999297i	$-0.511939\pi$
$967$	−70127.4			−0.0749954			−0.0374977	+	0.999297i	$0.511939\pi$
$968$	−476769.	−	825787.i	−0.508811	−	0.881287i
$969$	−470534.	−	271663.i	−0.501122	−	0.289323i
$970$	−62758.7	+	108701.i	−0.0667007	+	0.115529i
$971$	−1.57539e6	+	909551.i	−1.67089	+	0.964691i	−0.703756	+	0.710442i	$0.748495\pi$
$971$	−1.57539e6	+	909551.i	−1.67089	+	0.964691i	−0.967139	+	0.254249i	$0.918172\pi$
$972$			38650.2i			0.0409090i
$973$	−268859.	−	272773.i	−0.283987	−	0.288121i
$974$	1.14593e6			1.20793
$975$	−39457.0	−	68341.5i	−0.0415063	−	0.0718911i
$976$	−123877.	−	71520.5i	−0.130044	−	0.0750812i
$977$	−509253.	+	882052.i	−0.533512	+	0.924070i	0.465722	+	0.884931i	$0.345795\pi$
$977$	−509253.	+	882052.i	−0.533512	+	0.924070i	−0.999234	+	0.0391389i	$0.987539\pi$
$978$	740998.	−	427816.i	0.774711	−	0.447279i
$979$		−	42201.5i		−	0.0440314i
$980$	−16968.7	−	245.264i	−0.0176684	−	0.000255377i
$981$	1.08042e6			1.12268
$982$	577950.	+	1.00104e6i	0.599332	+	1.03807i
$983$	162454.	+	93793.0i	0.168122	+	0.0970652i	0.581700	−	0.813403i	$-0.302388\pi$
$983$	162454.	+	93793.0i	0.168122	+	0.0970652i	−0.413578	+	0.910469i	$0.635721\pi$
$984$	205483.	−	355907.i	0.212220	−	0.367576i
$985$	95234.1	−	54983.4i	0.0981567	−	0.0566708i
$986$			1.96513e6i			2.02133i
$987$	−452360.	+	445869.i	−0.464354	+	0.457691i
$988$	16606.7			0.0170126
$989$	1.11446e6	+	1.93031e6i	1.13939	+	1.97349i
$990$	−8747.34	−	5050.28i	−0.00892494	−	0.00515282i
$991$	918331.	−	1.59060e6i	0.935087	−	1.61962i	0.160609	−	0.987018i	$-0.448654\pi$
$991$	918331.	−	1.59060e6i	0.935087	−	1.61962i	0.774479	−	0.632600i	$-0.218012\pi$
$992$	4991.16	−	2881.65i	0.00507199	−	0.00292832i
$993$			175804.i			0.178291i
$994$	−871210.	−	240201.i	−0.881760	−	0.243110i
$995$	−463384.			−0.468053
$996$	−15905.9	−	27549.8i	−0.0160339	−	0.0277715i
$997$	1.46893e6	+	848087.i	1.47778	+	0.853198i	0.999685	−	0.0251082i	$-0.00799302\pi$
$997$	1.46893e6	+	848087.i	1.47778	+	0.853198i	0.478098	+	0.878306i	$0.341326\pi$
$998$	50363.6	−	87232.3i	0.0505656	−	0.0875823i
$999$	512490.	−	295886.i	0.513516	−	0.296479i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.h.a.31.3	yes	20
5.2	odd	4		175.5.j.b.24.15		40
5.3	odd	4		175.5.j.b.24.6		40
5.4	even	2		175.5.i.b.101.8		20
7.3	odd	6		245.5.d.a.146.16		20
7.4	even	3		245.5.d.a.146.15		20
7.5	odd	6	inner	35.5.h.a.26.3	✓	20
35.12	even	12		175.5.j.b.124.6		40
35.19	odd	6		175.5.i.b.26.8		20
35.33	even	12		175.5.j.b.124.15		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.h.a.26.3	✓	20	7.5	odd	6	inner
35.5.h.a.31.3	yes	20	1.1	even	1	trivial
175.5.i.b.26.8		20	35.19	odd	6
175.5.i.b.101.8		20	5.4	even	2
175.5.j.b.24.6		40	5.3	odd	4
175.5.j.b.24.15		40	5.2	odd	4
175.5.j.b.124.6		40	35.12	even	12
175.5.j.b.124.15		40	35.33	even	12
245.5.d.a.146.15		20	7.4	even	3
245.5.d.a.146.16		20	7.3	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.96009 - 3.39498i) q^{2} +(4.26025 + 2.45966i) q^{3} +(0.316095 - 0.547493i) q^{4} +(9.68246 - 5.59017i) q^{5} -19.2846i q^{6} +(34.8977 - 34.3969i) q^{7} -65.2012 q^{8} +(-28.4002 - 49.1905i) q^{9} +(-37.9570 - 21.9145i) q^{10} +(-2.02863 + 3.51370i) q^{11} +(2.69329 - 1.55497i) q^{12} -128.333i q^{13} +(-185.179 - 51.0557i) q^{14} +54.9997 q^{15} +(122.743 + 212.597i) q^{16} +(467.292 + 269.791i) q^{17} +(-111.334 + 192.836i) q^{18} +(-177.267 + 102.345i) q^{19} -7.06810i q^{20} +(233.278 - 60.7033i) q^{21} +15.9052 q^{22} +(488.257 + 845.686i) q^{23} +(-277.774 - 160.373i) q^{24} +(62.5000 - 108.253i) q^{25} +(-435.688 + 251.544i) q^{26} -677.884i q^{27} +(-7.80108 - 29.9789i) q^{28} -929.025 q^{29} +(-107.804 - 186.722i) q^{30} +(-61.7166 - 35.6321i) q^{31} +(-40.4362 + 70.0375i) q^{32} +(-17.2850 + 9.97949i) q^{33} -2115.26i q^{34} +(145.611 - 528.131i) q^{35} -35.9086 q^{36} +(436.485 + 756.015i) q^{37} +(694.919 + 401.212i) q^{38} +(315.656 - 546.732i) q^{39} +(-631.308 + 364.486i) q^{40} +1281.29i q^{41} +(-663.332 - 672.989i) q^{42} +2282.54 q^{43} +(1.28248 + 2.22132i) q^{44} +(-549.967 - 317.523i) q^{45} +(1914.05 - 3315.24i) q^{46} +(-2281.98 + 1317.50i) q^{47} +1207.62i q^{48} +(34.7001 - 2400.75i) q^{49} -490.022 q^{50} +(1327.19 + 2298.76i) q^{51} +(-70.2614 - 40.5655i) q^{52} +(124.624 - 215.855i) q^{53} +(-2301.40 + 1328.71i) q^{54} +45.3616i q^{55} +(-2275.37 + 2242.72i) q^{56} -1006.94 q^{57} +(1820.97 + 3154.02i) q^{58} +(942.634 + 544.230i) q^{59} +(17.3851 - 30.1119i) q^{60} +(-504.622 + 291.343i) q^{61} +279.368i q^{62} +(-2683.10 - 739.757i) q^{63} +4244.80 q^{64} +(-717.404 - 1242.58i) q^{65} +(67.7603 + 39.1214i) q^{66} +(795.394 - 1377.66i) q^{67} +(295.418 - 170.559i) q^{68} +4803.78i q^{69} +(-2078.40 + 540.839i) q^{70} +4704.68 q^{71} +(1851.72 + 3207.28i) q^{72} +(-2729.46 - 1575.86i) q^{73} +(1711.10 - 2963.71i) q^{74} +(532.532 - 307.457i) q^{75} +129.403i q^{76} +(50.0658 + 192.399i) q^{77} -2474.85 q^{78} +(-2538.96 - 4397.61i) q^{79} +(2376.90 + 1372.30i) q^{80} +(-633.050 + 1096.47i) q^{81} +(4349.93 - 2511.44i) q^{82} -10229.1i q^{83} +(40.5034 - 146.906i) q^{84} +6032.72 q^{85} +(-4473.98 - 7749.15i) q^{86} +(-3957.88 - 2285.09i) q^{87} +(132.269 - 229.097i) q^{88} +(-9007.94 + 5200.73i) q^{89} +2489.50i q^{90} +(-4414.27 - 4478.53i) q^{91} +617.342 q^{92} +(-175.286 - 303.604i) q^{93} +(8945.79 + 5164.85i) q^{94} +(-1144.25 + 1981.91i) q^{95} +(-344.537 + 198.918i) q^{96} -2863.80i q^{97} +(-8218.50 + 4587.88i) q^{98} +230.454 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 18 q^{3} - 58 q^{4} - 54 q^{7} - 372 q^{8} + 266 q^{9} + 90 q^{11} + 1266 q^{12} - 690 q^{14} + 100 q^{15} - 126 q^{16} - 864 q^{17} - 848 q^{18} - 1662 q^{19} + 1680 q^{21} + 2584 q^{22}+ \cdots - 36716 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 - 18 * q^3 - 58 * q^4 - 54 * q^7 - 372 * q^8 + 266 * q^9 + 90 * q^11 + 1266 * q^12 - 690 * q^14 + 100 * q^15 - 126 * q^16 - 864 * q^17 - 848 * q^18 - 1662 * q^19 + 1680 * q^21 + 2584 * q^22 - 1242 * q^23 + 1908 * q^24 + 1250 * q^25 - 1350 * q^26 - 134 * q^28 + 840 * q^29 + 800 * q^30 - 3636 * q^31 - 1758 * q^32 + 384 * q^33 + 150 * q^35 - 4164 * q^36 + 1068 * q^37 + 9180 * q^38 + 2976 * q^39 - 4146 * q^42 - 7692 * q^43 - 3618 * q^44 - 1800 * q^45 + 2038 * q^46 - 11412 * q^47 + 416 * q^49 + 1500 * q^50 + 6324 * q^51 - 7476 * q^52 + 1668 * q^53 + 33180 * q^54 + 13500 * q^56 + 15264 * q^57 + 1174 * q^58 + 216 * q^59 - 8250 * q^60 - 5856 * q^61 - 23632 * q^63 - 25788 * q^64 - 4650 * q^65 - 16248 * q^66 + 34 * q^67 - 6444 * q^68 + 900 * q^70 + 10488 * q^71 - 12052 * q^72 + 22776 * q^73 + 2538 * q^74 - 2250 * q^75 + 40488 * q^77 + 23784 * q^78 + 20788 * q^79 + 14400 * q^80 + 4154 * q^81 - 34146 * q^82 - 20316 * q^84 + 12000 * q^85 + 1980 * q^86 - 27474 * q^87 - 36148 * q^88 - 13176 * q^89 + 17976 * q^91 + 61404 * q^92 - 22908 * q^93 - 50610 * q^94 - 6900 * q^95 - 17460 * q^96 - 39606 * q^98 - 36716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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