LMFDB - Embedded newform 16.6.e.a.5.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [16,6,Mod(5,16)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(16, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 6, names="a")

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

chi := DirichletCharacter("16.5");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 16 = 2^{4} $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	16.e (of order $4$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.56614111701$
Analytic rank:	$0$
Dimension:	$18$
Relative dimension:	$9$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{18} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{18} - 5 x^{16} - 30 x^{15} - 42 x^{14} - 344 x^{13} + 2904 x^{12} + 5344 x^{11} + 16576 x^{10} + \cdots + 68719476736 $ x^18 - 5x^16 - 30x^15 - 42x^14 - 344x^13 + 2904x^12 + 5344x^11 + 16576x^10 - 297472x^9 + 265216x^8 + 1368064x^7 + 11894784x^6 - 22544384x^5 - 44040192x^4 - 503316480x^3 - 1342177280*x^2 + 68719476736
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{36} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			5.5
Root			$2.81847 + 2.83835i$ of defining polynomial
Character	$\chi$	$=$	16.5
Dual form			16.6.e.a.13.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0198738 + 5.65682i) q^{2} +(-8.39316 + 8.39316i) q^{3} +(-31.9992 - 0.224845i) q^{4} +(-8.40645 - 8.40645i) q^{5} +(-47.3118 - 47.6454i) q^{6} +149.265i q^{7} +(1.90786 - 181.009i) q^{8} +102.110i q^{9} +O(q^{10})$	\(q+(-0.0198738 + 5.65682i) q^{2} +(-8.39316 + 8.39316i) q^{3} +(-31.9992 - 0.224845i) q^{4} +(-8.40645 - 8.40645i) q^{5} +(-47.3118 - 47.6454i) q^{6} +149.265i q^{7} +(1.90786 - 181.009i) q^{8} +102.110i q^{9} +(47.7208 - 47.3867i) q^{10} +(349.799 + 349.799i) q^{11} +(270.462 - 266.687i) q^{12} +(450.009 - 450.009i) q^{13} +(-844.364 - 2.96646i) q^{14} +141.113 q^{15} +(1023.90 + 14.3897i) q^{16} -1297.54 q^{17} +(-577.616 - 2.02931i) q^{18} +(116.652 - 116.652i) q^{19} +(267.110 + 270.890i) q^{20} +(-1252.80 - 1252.80i) q^{21} +(-1985.70 + 1971.80i) q^{22} +3529.57i q^{23} +(1503.23 + 1535.25i) q^{24} -2983.66i q^{25} +(2536.68 + 2554.56i) q^{26} +(-2896.56 - 2896.56i) q^{27} +(33.5615 - 4776.35i) q^{28} +(3456.03 - 3456.03i) q^{29} +(-2.80446 + 798.253i) q^{30} +5057.13 q^{31} +(-101.749 + 5791.73i) q^{32} -5871.84 q^{33} +(25.7871 - 7339.95i) q^{34} +(1254.79 - 1254.79i) q^{35} +(22.9589 - 3267.43i) q^{36} +(7891.56 + 7891.56i) q^{37} +(657.562 + 662.198i) q^{38} +7554.00i q^{39} +(-1537.68 + 1505.61i) q^{40} +18454.0i q^{41} +(7111.78 - 7061.98i) q^{42} +(-11241.6 - 11241.6i) q^{43} +(-11114.6 - 11271.9i) q^{44} +(858.380 - 858.380i) q^{45} +(-19966.2 - 70.1461i) q^{46} -2447.40 q^{47} +(-8714.52 + 8472.97i) q^{48} -5472.97 q^{49} +(16878.0 + 59.2968i) q^{50} +(10890.5 - 10890.5i) q^{51} +(-14501.1 + 14298.8i) q^{52} +(7566.16 + 7566.16i) q^{53} +(16442.9 - 16327.8i) q^{54} -5881.14i q^{55} +(27018.3 + 284.776i) q^{56} +1958.16i q^{57} +(19481.5 + 19618.8i) q^{58} +(-4637.07 - 4637.07i) q^{59} +(-4515.52 - 31.7287i) q^{60} +(24740.9 - 24740.9i) q^{61} +(-100.505 + 28607.3i) q^{62} -15241.4 q^{63} +(-32760.7 - 690.679i) q^{64} -7565.96 q^{65} +(116.696 - 33215.9i) q^{66} +(-8651.11 + 8651.11i) q^{67} +(41520.3 + 291.746i) q^{68} +(-29624.3 - 29624.3i) q^{69} +(7073.17 + 7123.04i) q^{70} -15763.6i q^{71} +(18482.8 + 194.811i) q^{72} -25383.0i q^{73} +(-44798.0 + 44484.3i) q^{74} +(25042.4 + 25042.4i) q^{75} +(-3759.00 + 3706.55i) q^{76} +(-52212.7 + 52212.7i) q^{77} +(-42731.6 - 150.127i) q^{78} +37413.3 q^{79} +(-8486.39 - 8728.32i) q^{80} +23810.0 q^{81} +(-104391. - 366.751i) q^{82} +(-24351.5 + 24351.5i) q^{83} +(39807.0 + 40370.4i) q^{84} +(10907.7 + 10907.7i) q^{85} +(63815.4 - 63368.6i) q^{86} +58014.1i q^{87} +(63984.3 - 62649.5i) q^{88} -78890.8i q^{89} +(4838.64 + 4872.76i) q^{90} +(67170.5 + 67170.5i) q^{91} +(793.608 - 112944. i) q^{92} +(-42445.3 + 42445.3i) q^{93} +(48.6392 - 13844.5i) q^{94} -1961.26 q^{95} +(-47756.9 - 49464.9i) q^{96} +155532. q^{97} +(108.769 - 30959.6i) q^{98} +(-35717.9 + 35717.9i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) $ 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/16\mathbb{Z}\right)^\times$.

$n$	$5$	$15$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.0198738	+	5.65682i	−0.00351323	+	0.999994i
$2$	−0.0198738	+	5.65682i	−0.00351323	+	0.999994i
$3$	−8.39316	+	8.39316i	−0.538422	+	0.538422i	−0.923065	−	0.384644i	$-0.874324\pi$
$3$	−8.39316	+	8.39316i	−0.538422	+	0.538422i	0.384644	+	0.923065i	$0.374324\pi$
$4$	−31.9992	−	0.224845i	−0.999975	−	0.00702642i
$5$	−8.40645	−	8.40645i	−0.150379	−	0.150379i	0.627908	−	0.778287i	$-0.283911\pi$
$5$	−8.40645	−	8.40645i	−0.150379	−	0.150379i	−0.778287	+	0.627908i	$0.783911\pi$
$6$	−47.3118	−	47.6454i	−0.536527	−	0.540310i
$7$			149.265i			1.15136i	0.817674	+	0.575681i	$0.195263\pi$
$7$			149.265i			1.15136i	−0.817674	+	0.575681i	$0.804737\pi$
$8$	1.90786	−	181.009i	0.0105395	−	0.999944i
$9$			102.110i			0.420204i
$10$	47.7208	−	47.3867i	0.150907	−	0.149850i
$11$	349.799	+	349.799i	0.871640	+	0.871640i	0.992651	−	0.121011i	$-0.0386138\pi$
$11$	349.799	+	349.799i	0.871640	+	0.871640i	−0.121011	+	0.992651i	$0.538614\pi$
$12$	270.462	−	266.687i	0.542191	−	0.534625i
$13$	450.009	−	450.009i	0.738521	−	0.738521i	−0.233771	−	0.972292i	$-0.575106\pi$
$13$	450.009	−	450.009i	0.738521	−	0.738521i	0.972292	+	0.233771i	$0.0751065\pi$
$14$	−844.364	−	2.96646i	−1.15136	−	0.00404500i
$15$	141.113			0.161935
$16$	1023.90	+	14.3897i	0.999901	+	0.0140525i
$17$	−1297.54			−1.08893			−0.544463	−	0.838785i	$-0.683267\pi$
$17$	−1297.54			−1.08893			−0.544463	+	0.838785i	$0.683267\pi$
$18$	−577.616	−	2.02931i	−0.420202	−	0.00147627i
$19$	116.652	−	116.652i	0.0741325	−	0.0741325i	−0.669068	−	0.743201i	$-0.733307\pi$
$19$	116.652	−	116.652i	0.0741325	−	0.0741325i	0.743201	+	0.669068i	$0.233307\pi$
$20$	267.110	+	270.890i	0.149319	+	0.151432i
$21$	−1252.80	−	1252.80i	−0.619919	−	0.619919i
$22$	−1985.70	+	1971.80i	−0.874697	+	0.868572i
$23$			3529.57i			1.39124i	0.718409	+	0.695621i	$0.244871\pi$
$23$			3529.57i			1.39124i	−0.718409	+	0.695621i	$0.755129\pi$
$24$	1503.23	+	1535.25i	0.532717	+	0.544066i
$25$		−	2983.66i		−	0.954772i
$26$	2536.68	+	2554.56i	0.735922	+	0.741111i
$27$	−2896.56	−	2896.56i	−0.764669	−	0.764669i
$28$	33.5615	−	4776.35i	0.00808995	−	1.15133i
$29$	3456.03	−	3456.03i	0.763103	−	0.763103i	−0.213779	−	0.976882i	$-0.568577\pi$
$29$	3456.03	−	3456.03i	0.763103	−	0.763103i	0.976882	+	0.213779i	$0.0685774\pi$
$30$	−2.80446	+	798.253i	−0.000568914	+	0.161934i
$31$	5057.13			0.945148			0.472574	−	0.881291i	$-0.343325\pi$
$31$	5057.13			0.945148			0.472574	+	0.881291i	$0.343325\pi$
$32$	−101.749	+	5791.73i	−0.0175653	+	0.999846i
$33$	−5871.84			−0.938619
$34$	25.7871	−	7339.95i	0.00382565	−	1.08892i
$35$	1254.79	−	1254.79i	0.173141	−	0.173141i
$36$	22.9589	−	3267.43i	0.00295253	−	0.420194i
$37$	7891.56	+	7891.56i	0.947674	+	0.947674i	0.998697	−	0.0510239i	$-0.0162485\pi$
$37$	7891.56	+	7891.56i	0.947674	+	0.947674i	−0.0510239	+	0.998697i	$0.516248\pi$
$38$	657.562	+	662.198i	0.0738716	+	0.0743925i
$39$			7554.00i			0.795271i
$40$	−1537.68	+	1505.61i	−0.151956	+	0.148786i
$41$			18454.0i			1.71447i	0.514924	+	0.857236i	$0.327820\pi$
$41$			18454.0i			1.71447i	−0.514924	+	0.857236i	$0.672180\pi$
$42$	7111.78	−	7061.98i	0.622093	−	0.617737i
$43$	−11241.6	−	11241.6i	−0.927169	−	0.927169i	0.0703531	−	0.997522i	$-0.477587\pi$
$43$	−11241.6	−	11241.6i	−0.927169	−	0.927169i	−0.997522	+	0.0703531i	$0.977587\pi$
$44$	−11114.6	−	11271.9i	−0.865494	−	0.877743i
$45$	858.380	−	858.380i	0.0631900	−	0.0631900i
$46$	−19966.2	−	70.1461i	−1.39123	−	0.00488775i
$47$	−2447.40			−0.161607			−0.0808035	−	0.996730i	$-0.525749\pi$
$47$	−2447.40			−0.161607			−0.0808035	+	0.996730i	$0.525749\pi$
$48$	−8714.52	+	8472.97i	−0.545935	+	0.530802i
$49$	−5472.97			−0.325636
$50$	16878.0	+	59.2968i	0.954766	+	0.00335433i
$51$	10890.5	−	10890.5i	0.586302	−	0.586302i
$52$	−14501.1	+	14298.8i	−0.743692	+	0.733314i
$53$	7566.16	+	7566.16i	0.369987	+	0.369987i	0.867472	−	0.497486i	$-0.165743\pi$
$53$	7566.16	+	7566.16i	0.369987	+	0.369987i	−0.497486	+	0.867472i	$0.665743\pi$
$54$	16442.9	−	16327.8i	0.767350	−	0.761978i
$55$		−	5881.14i		−	0.262153i
$56$	27018.3	+	284.776i	1.15130	+	0.0121348i
$57$			1958.16i			0.0798291i
$58$	19481.5	+	19618.8i	0.760417	+	0.765779i
$59$	−4637.07	−	4637.07i	−0.173426	−	0.173426i	0.615057	−	0.788483i	$-0.289133\pi$
$59$	−4637.07	−	4637.07i	−0.173426	−	0.173426i	−0.788483	+	0.615057i	$0.789133\pi$
$60$	−4515.52	−	31.7287i	−0.161931	−	0.00113782i
$61$	24740.9	−	24740.9i	0.851316	−	0.851316i	−0.138979	−	0.990295i	$-0.544382\pi$
$61$	24740.9	−	24740.9i	0.851316	−	0.851316i	0.990295	+	0.138979i	$0.0443822\pi$
$62$	−100.505	+	28607.3i	−0.00332052	+	0.945142i
$63$	−15241.4			−0.483808
$64$	−32760.7	−	690.679i	−0.999778	−	0.0210779i
$65$	−7565.96			−0.222116
$66$	116.696	−	33215.9i	0.00329759	−	0.938613i
$67$	−8651.11	+	8651.11i	−0.235442	+	0.235442i	−0.814960	−	0.579517i	$-0.803241\pi$
$67$	−8651.11	+	8651.11i	−0.235442	+	0.235442i	0.579517	+	0.814960i	$0.303241\pi$
$68$	41520.3	+	291.746i	1.08890	+	0.00765125i
$69$	−29624.3	−	29624.3i	−0.749075	−	0.749075i
$70$	7073.17	+	7123.04i	0.172532	+	0.173748i
$71$		−	15763.6i		−	0.371117i	−0.982633	−	0.185558i	$-0.940591\pi$
$71$		−	15763.6i		−	0.371117i	0.982633	−	0.185558i	$-0.0594093\pi$
$72$	18482.8	+	194.811i	0.420181	+	0.00442875i
$73$		−	25383.0i		−	0.557488i	−0.960365	−	0.278744i	$-0.910082\pi$
$73$		−	25383.0i		−	0.557488i	0.960365	−	0.278744i	$-0.0899181\pi$
$74$	−44798.0	+	44484.3i	−0.950997	+	0.944338i
$75$	25042.4	+	25042.4i	0.514070	+	0.514070i
$76$	−3759.00	+	3706.55i	−0.0746516	+	0.0736098i
$77$	−52212.7	+	52212.7i	−1.00357	+	1.00357i
$78$	−42731.6	−	150.127i	−0.795267	−	0.00279397i
$79$	37413.3			0.674464			0.337232	−	0.941422i	$-0.390509\pi$
$79$	37413.3			0.674464			0.337232	+	0.941422i	$0.390509\pi$
$80$	−8486.39	−	8728.32i	−0.148251	−	0.152478i
$81$	23810.0			0.403224
$82$	−104391.	−	366.751i	−1.71446	−	0.00602333i
$83$	−24351.5	+	24351.5i	−0.387998	+	0.387998i	−0.873973	−	0.485975i	$-0.838465\pi$
$83$	−24351.5	+	24351.5i	−0.387998	+	0.387998i	0.485975	+	0.873973i	$0.338465\pi$
$84$	39807.0	+	40370.4i	0.615547	+	0.624259i
$85$	10907.7	+	10907.7i	0.163752	+	0.163752i
$86$	63815.4	−	63368.6i	0.930421	−	0.923906i
$87$			58014.1i			0.821742i
$88$	63984.3	−	62649.5i	0.880778	−	0.862405i
$89$		−	78890.8i		−	1.05573i	−0.849330	−	0.527863i	$-0.822994\pi$
$89$		−	78890.8i		−	1.05573i	0.849330	−	0.527863i	$-0.177006\pi$
$90$	4838.64	+	4872.76i	0.0629676	+	0.0634116i
$91$	67170.5	+	67170.5i	0.850306	+	0.850306i
$92$	793.608	−	112944.i	0.00977544	−	1.39121i
$93$	−42445.3	+	42445.3i	−0.508888	+	0.508888i
$94$	48.6392	−	13844.5i	0.000567763	−	0.161606i
$95$	−1961.26			−0.0222960
$96$	−47756.9	−	49464.9i	−0.528881	−	0.547796i
$97$	155532.			1.67838			0.839191	−	0.543836i	$-0.183029\pi$
$97$	155532.			1.67838			0.839191	+	0.543836i	$0.183029\pi$
$98$	108.769	−	30959.6i	0.00114403	−	0.325634i
$99$	−35717.9	+	35717.9i	−0.366267	+	0.366267i
$100$	−670.863	+	95474.9i	−0.00670863	+	0.954749i
$101$	−63677.8	−	63677.8i	−0.621133	−	0.621133i	0.324688	−	0.945821i	$-0.394741\pi$
$101$	−63677.8	−	63677.8i	−0.621133	−	0.621133i	−0.945821	+	0.324688i	$0.894741\pi$
$102$	61389.0	+	61821.9i	0.584238	+	0.588358i
$103$		−	130330.i		−	1.21046i	−0.796051	−	0.605230i	$-0.793081\pi$
$103$		−	130330.i		−	1.21046i	0.796051	−	0.605230i	$-0.206919\pi$
$104$	−80597.3	−	82314.4i	−0.730696	−	0.746264i
$105$			21063.3i			0.186446i
$106$	−42950.8	+	42650.0i	−0.371284	+	0.368684i
$107$	64258.3	+	64258.3i	0.542588	+	0.542588i	0.924287	−	0.381699i	$-0.124661\pi$
$107$	64258.3	+	64258.3i	0.542588	+	0.542588i	−0.381699	+	0.924287i	$0.624661\pi$
$108$	92036.4	+	93339.0i	0.759277	+	0.770023i
$109$	23170.2	−	23170.2i	0.186794	−	0.186794i	−0.607514	−	0.794309i	$-0.707833\pi$
$109$	23170.2	−	23170.2i	0.186794	−	0.186794i	0.794309	+	0.607514i	$0.207833\pi$
$110$	33268.5	+	116.881i	0.262151	+	0.000921004i
$111$	−132470.			−1.02050
$112$	−2147.88	+	152832.i	−0.0161795	+	1.15125i
$113$	−160562.			−1.18289			−0.591447	−	0.806344i	$-0.701443\pi$
$113$	−160562.			−1.18289			−0.591447	+	0.806344i	$0.701443\pi$
$114$	−11077.0	−	38.9161i	−0.0798286	−	0.000280458i
$115$	29671.2	−	29671.2i	0.209214	−	0.209214i
$116$	−111367.	+	109813.i	−0.768446	+	0.757722i
$117$	45950.3	+	45950.3i	0.310330	+	0.310330i
$118$	26323.2	−	26138.9i	0.174034	−	0.172815i
$119$		−	193677.i		−	1.25375i
$120$	269.224	−	25542.8i	0.00170671	−	0.161926i
$121$			83667.8i			0.519511i
$122$	139463.	+	140446.i	0.848320	+	0.854301i
$123$	−154887.	−	154887.i	−0.923108	−	0.923108i
$124$	−161824.	−	1137.07i	−0.945125	−	0.00664100i
$125$	−51352.2	+	51352.2i	−0.293957	+	0.293957i
$126$	302.904	−	86217.7i	0.00169973	−	0.483805i
$127$	−86951.3			−0.478373			−0.239186	−	0.970974i	$-0.576881\pi$
$127$	−86951.3			−0.478373			−0.239186	+	0.970974i	$0.576881\pi$
$128$	4558.13	−	185308.i	0.0245902	−	0.999698i
$129$	188706.			0.998416
$130$	150.365	−	42799.3i	0.000780346	−	0.222115i
$131$	87812.2	−	87812.2i	0.447071	−	0.447071i	−0.447309	−	0.894380i	$-0.647617\pi$
$131$	87812.2	−	87812.2i	0.447071	−	0.447071i	0.894380	+	0.447309i	$0.147617\pi$
$132$	187894.	+	1320.26i	0.938596	+	0.00659513i
$133$	17412.1	+	17412.1i	0.0853534	+	0.0853534i
$134$	−48765.8	−	49109.7i	−0.234614	−	0.236268i
$135$			48699.6i			0.229981i
$136$	−2475.52	+	234867.i	−0.0114768	+	1.08887i
$137$			162912.i			0.741567i	0.928719	+	0.370784i	$0.120911\pi$
$137$			162912.i			0.741567i	−0.928719	+	0.370784i	$0.879089\pi$
$138$	168168.	−	166990.i	0.751702	−	0.746438i
$139$	−40693.6	−	40693.6i	−0.178644	−	0.178644i	0.612120	−	0.790765i	$-0.290317\pi$
$139$	−40693.6	−	40693.6i	−0.178644	−	0.178644i	−0.790765	+	0.612120i	$0.790317\pi$
$140$	−40434.3	+	39870.1i	−0.174353	+	0.171920i
$141$	20541.4	−	20541.4i	0.0870127	−	0.0870127i
$142$	89172.0	+	313.284i	0.371114	+	0.00130382i
$143$	314826.			1.28745
$144$	−1469.33	+	104550.i	−0.00590492	+	0.420163i
$145$	−58106.0			−0.229509
$146$	143587.	+	504.457i	0.557485	+	0.00195858i
$147$	45935.5	−	45935.5i	0.175330	−	0.175330i
$148$	−250749.	−	254298.i	−0.940991	−	0.954309i
$149$	168858.	+	168858.i	0.623097	+	0.623097i	0.946322	−	0.323225i	$-0.104767\pi$
$149$	168858.	+	168858.i	0.623097	+	0.623097i	−0.323225	+	0.946322i	$0.604767\pi$
$150$	−142158.	+	141162.i	−0.515873	+	0.512261i
$151$			393082.i			1.40295i	0.712695	+	0.701474i	$0.247474\pi$
$151$			393082.i			1.40295i	−0.712695	+	0.701474i	$0.752526\pi$
$152$	−20892.6	−	21337.7i	−0.0733471	−	0.0749097i
$153$		−	132491.i		−	0.457572i
$154$	−294320.	−	296395.i	−1.00004	−	1.00709i
$155$	−42512.5	−	42512.5i	−0.142131	−	0.142131i
$156$	1698.48	−	241722.i	0.00558791	−	0.795252i
$157$	238093.	−	238093.i	0.770898	−	0.770898i	−0.207366	−	0.978263i	$-0.566489\pi$
$157$	238093.	−	238093.i	0.770898	−	0.770898i	0.978263	+	0.207366i	$0.0664890\pi$
$158$	−743.546	+	211640.i	−0.00236955	+	0.674460i
$159$	−127008.			−0.398418
$160$	49543.2	−	47832.5i	0.152997	−	0.147715i
$161$	−526841.			−1.60182
$162$	−473.195	+	134689.i	−0.00141662	+	0.403221i
$163$	−372164.	+	372164.i	−1.09715	+	1.09715i	−0.102404	+	0.994743i	$0.532653\pi$
$163$	−372164.	+	372164.i	−1.09715	+	1.09715i	−0.994743	+	0.102404i	$0.967347\pi$
$164$	4149.29	−	590513.i	0.0120466	−	1.71443i
$165$	49361.3	+	49361.3i	0.141149	+	0.141149i
$166$	−137268.	−	138236.i	−0.386633	−	0.389359i
$167$			291185.i			0.807937i	0.914773	+	0.403969i	$0.132369\pi$
$167$			291185.i			0.807937i	−0.914773	+	0.403969i	$0.867631\pi$
$168$	−229159.	+	224379.i	−0.626418	+	0.613350i
$169$		−	33723.4i		−	0.0908269i
$170$	−61919.7	+	61486.2i	−0.164326	+	0.163176i
$171$	11911.3	+	11911.3i	0.0311508	+	0.0311508i
$172$	357196.	+	362252.i	0.920631	+	0.933661i
$173$	−72379.5	+	72379.5i	−0.183865	+	0.183865i	−0.793038	−	0.609172i	$-0.791502\pi$
$173$	−72379.5	+	72379.5i	−0.183865	+	0.183865i	0.609172	+	0.793038i	$0.291502\pi$
$174$	−328175.	−	1152.96i	−0.821737	−	0.00288697i
$175$	445356.			1.09929
$176$	353125.	+	363192.i	0.859305	+	0.883802i
$177$	77839.3			0.186752
$178$	446271.	+	1567.86i	1.05572	+	0.00370901i
$179$	528658.	−	528658.i	1.23322	−	1.23322i	0.270506	−	0.962718i	$-0.412809\pi$
$179$	528658.	−	528658.i	1.23322	−	1.23322i	0.962718	−	0.270506i	$-0.0871909\pi$
$180$	−27660.5	+	27274.5i	−0.0636324	+	0.0627444i
$181$	−403074.	−	403074.i	−0.914511	−	0.914511i	0.0821122	−	0.996623i	$-0.473833\pi$
$181$	−403074.	−	403074.i	−0.914511	−	0.914511i	−0.996623	+	0.0821122i	$0.973833\pi$
$182$	−381306.	+	378636.i	−0.853288	+	0.847313i
$183$			415309.i			0.916734i
$184$	638885.	+	6733.92i	1.39116	+	0.0146630i
$185$		−	132680.i		−	0.285021i
$186$	−239262.	−	240949.i	−0.507097	−	0.510673i
$187$	−453879.	−	453879.i	−0.949152	−	0.949152i
$188$	78314.9	+	550.286i	0.161603	+	0.00113552i
$189$	432355.	−	432355.i	0.880411	−	0.880411i
$190$	38.9778	−	11094.5i	7.83309e−5	−	0.0222958i
$191$	−24750.9			−0.0490916			−0.0245458	−	0.999699i	$-0.507814\pi$
$191$	−24750.9			−0.0490916			−0.0245458	+	0.999699i	$0.507814\pi$
$192$	280763.	−	269169.i	0.549651	−	0.526953i
$193$	−398037.			−0.769184			−0.384592	−	0.923087i	$-0.625658\pi$
$193$	−398037.			−0.769184			−0.384592	+	0.923087i	$0.625658\pi$
$194$	−3091.02	+	879818.i	−0.00589654	+	1.67837i
$195$	63502.3	−	63502.3i	0.119592	−	0.119592i
$196$	175131.	+	1230.57i	0.325628	+	0.00228806i
$197$	−7422.30	−	7422.30i	−0.0136261	−	0.0136261i	0.700261	−	0.713887i	$-0.253067\pi$
$197$	−7422.30	−	7422.30i	−0.0136261	−	0.0136261i	−0.713887	+	0.700261i	$0.753067\pi$
$198$	−201340.	−	202759.i	−0.364978	−	0.367551i
$199$		−	603057.i		−	1.07951i	−0.841823	−	0.539754i	$-0.818517\pi$
$199$		−	603057.i		−	1.07951i	0.841823	−	0.539754i	$-0.181483\pi$
$200$	−540071.	−	5692.40i	−0.954719	−	0.0100628i
$201$		−	145220.i		−	0.253535i
$202$	361479.	−	358948.i	0.623312	−	0.618947i
$203$	515864.	+	515864.i	0.878608	+	0.878608i
$204$	−350935.	+	346038.i	−0.590407	+	0.582168i
$205$	155132.	−	155132.i	0.257821	−	0.257821i
$206$	737252.	+	2590.15i	1.21045	+	0.00425262i
$207$	−360404.			−0.584606
$208$	467239.	−	454288.i	0.748826	−	0.728070i
$209$	81609.6			0.129234
$210$	−119151.	−	418.608i	−0.186445	−	0.000655027i
$211$	−507660.	+	507660.i	−0.784995	+	0.784995i	−0.980669	−	0.195674i	$-0.937310\pi$
$211$	−507660.	+	507660.i	−0.784995	+	0.784995i	0.195674	+	0.980669i	$0.437310\pi$
$212$	−240410.	−	243812.i	−0.367378	−	0.372577i
$213$	132307.	+	132307.i	0.199817	+	0.199817i
$214$	−364775.	+	362221.i	−0.544491	+	0.540678i
$215$			189005.i			0.278854i
$216$	−529831.	+	518778.i	−0.772685	+	0.756567i
$217$			754851.i			1.08821i
$218$	130609.	+	131530.i	0.186137	+	0.187449i
$219$	213043.	+	213043.i	0.300164	+	0.300164i
$220$	−1322.35	+	188192.i	−0.00184200	+	0.262146i
$221$	−583905.	+	583905.i	−0.804196	+	0.804196i
$222$	2632.69	−	749361.i	0.00358524	−	1.02049i
$223$	−750167.			−1.01017			−0.505087	−	0.863069i	$-0.668540\pi$
$223$	−750167.			−1.01017			−0.505087	+	0.863069i	$0.668540\pi$
$224$	−864500.	−	15187.5i	−1.15119	−	0.0202240i
$225$	304661.			0.401199
$226$	3190.97	−	908268.i	0.00415578	−	1.18289i
$227$	102424.	−	102424.i	0.131929	−	0.131929i	−0.638059	−	0.769988i	$-0.720262\pi$
$227$	102424.	−	102424.i	0.131929	−	0.131929i	0.769988	+	0.638059i	$0.220262\pi$
$228$	440.283	−	62659.6i	0.000560912	−	0.0798271i
$229$	369144.	+	369144.i	0.465165	+	0.465165i	0.900344	−	0.435179i	$-0.143315\pi$
$229$	369144.	+	369144.i	0.465165	+	0.465165i	−0.435179	+	0.900344i	$0.643315\pi$
$230$	167255.	+	168434.i	0.208477	+	0.209948i
$231$		−	876459.i		−	1.08069i
$232$	−618980.	−	632168.i	−0.755017	−	0.771103i
$233$			28040.5i			0.0338374i	0.999857	+	0.0169187i	$0.00538564\pi$
$233$			28040.5i			0.0338374i	−0.999857	+	0.0169187i	$0.994614\pi$
$234$	−260846.	+	259019.i	−0.311418	+	0.309238i
$235$	20573.9	+	20573.9i	0.0243023	+	0.0243023i
$236$	147340.	+	149425.i	0.172203	+	0.174640i
$237$	−314016.	+	314016.i	−0.363146	+	0.363146i
$238$	1.09560e6	+	3849.11i	1.25374	+	0.00440471i
$239$	744107.			0.842637			0.421319	−	0.906913i	$-0.361567\pi$
$239$	744107.			0.842637			0.421319	+	0.906913i	$0.361567\pi$
$240$	144486.	+	2030.59i	0.161919	+	0.00227559i
$241$	1.53433e6			1.70167			0.850837	−	0.525430i	$-0.176095\pi$
$241$	1.53433e6			1.70167			0.850837	+	0.525430i	$0.176095\pi$
$242$	−473294.	−	1662.80i	−0.519508	−	0.00182516i
$243$	504023.	−	504023.i	0.547564	−	0.547564i
$244$	−797252.	+	786126.i	−0.857277	+	0.845313i
$245$	46008.2	+	46008.2i	0.0489689	+	0.0489689i
$246$	879247.	−	873091.i	0.926346	−	0.919860i
$247$		−	104989.i		−	0.109497i
$248$	9648.28	−	915387.i	0.00996140	−	0.945096i
$249$		−	408772.i		−	0.417813i
$250$	−289469.	−	291511.i	−0.292922	−	0.294988i
$251$	−529339.	−	529339.i	−0.530334	−	0.530334i	0.390338	−	0.920672i	$-0.372358\pi$
$251$	−529339.	−	529339.i	−0.530334	−	0.530334i	−0.920672	+	0.390338i	$0.872358\pi$
$252$	487712.	+	3426.95i	0.483796	+	0.00339943i
$253$	−1.23464e6	+	1.23464e6i	−1.21266	+	1.21266i
$254$	1728.05	−	491868.i	0.00168063	−	0.478370i
$255$	−183100.			−0.176335
$256$	1.04816e6	+	29467.3i	0.999605	+	0.0281022i
$257$	759923.			0.717690			0.358845	−	0.933397i	$-0.383171\pi$
$257$	759923.			0.717690			0.358845	+	0.933397i	$0.383171\pi$
$258$	−3750.31	+	1.06748e6i	−0.00350766	+	0.998409i
$259$	−1.17793e6	+	1.17793e6i	−1.09112	+	1.09112i
$260$	242105.	+	1701.17i	0.222111	+	0.00156068i
$261$	352894.	+	352894.i	0.320659	+	0.320659i
$262$	494992.	+	498483.i	0.445497	+	0.448639i
$263$		−	1.67826e6i		−	1.49613i	−0.663625	−	0.748065i	$-0.730983\pi$
$263$		−	1.67826e6i		−	1.49613i	0.663625	−	0.748065i	$-0.269017\pi$
$264$	−11202.6	+	1.06286e6i	−0.00989259	+	0.938567i
$265$		−	127209.i		−	0.111277i
$266$	−98842.9	+	98150.8i	−0.0856527	+	0.0850530i
$267$	662143.	+	662143.i	0.568426	+	0.568426i
$268$	278774.	−	274883.i	0.237091	−	0.233782i
$269$	229027.	−	229027.i	0.192977	−	0.192977i	−0.604004	−	0.796981i	$-0.706429\pi$
$269$	229027.	−	229027.i	0.192977	−	0.192977i	0.796981	+	0.604004i	$0.206429\pi$
$270$	−275485.	−	967.848i	−0.229979	−	0.000807974i
$271$	673023.			0.556681			0.278341	−	0.960482i	$-0.410216\pi$
$271$	673023.			0.556681			0.278341	+	0.960482i	$0.410216\pi$
$272$	−1.32855e6	−	18671.3i	−1.08882	−	0.0153021i
$273$	−1.12755e6			−0.915646
$274$	−921562.	−	3237.68i	−0.741563	−	0.00260530i
$275$	1.04368e6	−	1.04368e6i	0.832217	−	0.832217i
$276$	941293.	+	954614.i	0.743793	+	0.754319i
$277$	−1.52410e6	−	1.52410e6i	−1.19347	−	1.19347i	−0.976085	−	0.217388i	$-0.930246\pi$
$277$	−1.52410e6	−	1.52410e6i	−1.19347	−	1.19347i	−0.217388	−	0.976085i	$-0.569754\pi$
$278$	231005.	−	229387.i	0.179271	−	0.178015i
$279$			516382.i			0.397155i
$280$	−224734.	−	229522.i	−0.171307	−	0.174956i
$281$		−	763179.i		−	0.576581i	−0.957543	−	0.288291i	$-0.906913\pi$
$281$		−	763179.i		−	0.576581i	0.957543	−	0.288291i	$-0.0930869\pi$
$282$	115791.	+	116607.i	0.0867065	+	0.0873179i
$283$	−134303.	−	134303.i	−0.0996828	−	0.0996828i	0.655507	−	0.755189i	$-0.272455\pi$
$283$	−134303.	−	134303.i	−0.0996828	−	0.0996828i	−0.755189	+	0.655507i	$0.772455\pi$
$284$	−3544.38	+	504424.i	−0.00260762	+	0.371107i
$285$	16461.2	−	16461.2i	0.0120046	−	0.0120046i
$286$	−6256.79	+	1.78091e6i	−0.00452310	+	1.28744i
$287$	−2.75453e6			−1.97398
$288$	−591391.	−	10389.6i	−0.420140	−	0.00738101i
$289$	263755.			0.185762
$290$	1154.79	−	328695.i	0.000806320	−	0.229508i
$291$	−1.30541e6	+	1.30541e6i	−0.903677	+	0.903677i
$292$	−5707.25	+	812235.i	−0.00391714	+	0.557474i
$293$	−539523.	−	539523.i	−0.367148	−	0.367148i	0.499288	−	0.866436i	$-0.333595\pi$
$293$	−539523.	−	539523.i	−0.367148	−	0.367148i	−0.866436	+	0.499288i	$0.833595\pi$
$294$	258936.	+	260762.i	0.174712	+	0.175944i
$295$			77962.6i			0.0521592i
$296$	1.44350e6	−	1.41339e6i	0.957609	−	0.937633i
$297$		−	2.02643e6i		−	1.33303i
$298$	−958554.	+	951842.i	−0.625282	+	0.620904i
$299$	1.58834e6	+	1.58834e6i	1.02746	+	1.02746i
$300$	−795705.	−	806967.i	−0.510445	−	0.517669i
$301$	1.67798e6	−	1.67798e6i	1.06751	−	1.06751i
$302$	−2.22360e6	−	7812.05i	−1.40294	−	0.00492888i
$303$	1.06892e6			0.668863
$304$	121119.	−	117761.i	0.0751669	−	0.0730834i
$305$	−415966.			−0.256040
$306$	749480.	+	2633.11i	0.457569	+	0.00160756i
$307$	636215.	−	636215.i	0.385264	−	0.385264i	−0.487731	−	0.872994i	$-0.662175\pi$
$307$	636215.	−	636215.i	0.385264	−	0.385264i	0.872994	+	0.487731i	$0.162175\pi$
$308$	1.68250e6	−	1.65902e6i	1.01060	−	0.996497i
$309$	1.09388e6	+	1.09388e6i	0.651738	+	0.651738i
$310$	241331.	−	239641.i	0.142629	−	0.141630i
$311$			2.18876e6i			1.28321i	0.767035	+	0.641605i	$0.221731\pi$
$311$			2.18876e6i			1.28321i	−0.767035	+	0.641605i	$0.778269\pi$
$312$	1.36734e6	+	14411.9i	0.795227	+	0.00838178i
$313$			3.03627e6i			1.75178i	0.482510	+	0.875891i	$0.339725\pi$
$313$			3.03627e6i			1.75178i	−0.482510	+	0.875891i	$0.660275\pi$
$314$	1.34212e6	+	1.35158e6i	0.768185	+	0.773601i
$315$	128126.	+	128126.i	0.0727546	+	0.0727546i
$316$	−1.19720e6	−	8412.21i	−0.674447	−	0.00473906i
$317$	−155122.	+	155122.i	−0.0867012	+	0.0867012i	−0.749127	−	0.662426i	$-0.769527\pi$
$317$	−155122.	+	155122.i	−0.0867012	+	0.0867012i	0.662426	+	0.749127i	$0.269527\pi$
$318$	2524.14	−	718462.i	0.00139973	−	0.398415i
$319$	2.41783e6			1.33030
$320$	269595.	+	281208.i	0.147176	+	0.153515i
$321$	−1.07866e6			−0.584282
$322$	10470.3	−	2.98024e6i	0.00562758	−	1.60181i
$323$	−151361.	+	151361.i	−0.0807249	+	0.0807249i
$324$	−761900.	−	5353.56i	−0.403214	−	0.00283322i
$325$	−1.34268e6	−	1.34268e6i	−0.705119	−	0.705119i
$326$	−2.09787e6	−	2.11266e6i	−1.09329	−	1.10099i
$327$			388943.i			0.201148i
$328$	3.34034e6	+	35207.5i	1.71438	+	0.0180697i
$329$		−	365311.i		−	0.186068i
$330$	−280209.	+	278247.i	−0.141644	+	0.140652i
$331$	−130039.	−	130039.i	−0.0652385	−	0.0652385i	0.673735	−	0.738973i	$-0.264689\pi$
$331$	−130039.	−	130039.i	−0.0652385	−	0.0652385i	−0.738973	+	0.673735i	$0.764689\pi$
$332$	784703.	−	773752.i	0.390715	−	0.385263i
$333$	−805805.	+	805805.i	−0.398217	+	0.398217i
$334$	−1.64718e6	−	5786.96i	−0.807932	−	0.00283847i
$335$	145450.			0.0708113
$336$	−1.26472e6	−	1.30077e6i	−0.611146	−	0.628569i
$337$	582351.			0.279325			0.139663	−	0.990199i	$-0.455398\pi$
$337$	582351.			0.279325			0.139663	+	0.990199i	$0.455398\pi$
$338$	190767.	+	670.213i	0.0908264	+	0.000319096i
$339$	1.34762e6	−	1.34762e6i	0.636895	−	0.636895i
$340$	−346586.	−	351491.i	−0.162597	−	0.164898i
$341$	1.76898e6	+	1.76898e6i	0.823829	+	0.823829i
$342$	−67616.9	+	67143.4i	−0.0312601	+	0.0310412i
$343$			1.69177e6i			0.776437i
$344$	−2.05629e6	+	2.01340e6i	−0.936889	+	0.917346i
$345$			498070.i			0.225290i
$346$	−407999.	−	410876.i	−0.183218	−	0.184510i
$347$	−2.91361e6	−	2.91361e6i	−1.29899	−	1.29899i	−0.929056	−	0.369938i	$-0.879379\pi$
$347$	−2.91361e6	−	2.91361e6i	−1.29899	−	1.29899i	−0.369938	−	0.929056i	$-0.620621\pi$
$348$	13044.2	−	1.85641e6i	0.00577390	−	0.821721i
$349$	2.14024e6	−	2.14024e6i	0.940588	−	0.940588i	−0.0577439	−	0.998331i	$-0.518391\pi$
$349$	2.14024e6	−	2.14024e6i	0.940588	−	0.940588i	0.998331	+	0.0577439i	$0.0183907\pi$
$350$	−8850.92	+	2.51930e6i	−0.00386206	+	1.09928i
$351$	−2.60696e6			−1.12945
$352$	−2.06153e6	+	1.99035e6i	−0.886816	+	0.856195i
$353$	−2.37354e6			−1.01382			−0.506910	−	0.861999i	$-0.669212\pi$
$353$	−2.37354e6			−1.01382			−0.506910	+	0.861999i	$0.669212\pi$
$354$	−1546.97	+	440323.i	−0.000656104	+	0.186751i
$355$	−132516.	+	132516.i	−0.0558082	+	0.0558082i
$356$	−17738.2	+	2.52444e6i	−0.00741797	+	1.05570i
$357$	1.62556e6	+	1.62556e6i	0.675046	+	0.675046i
$358$	2.98001e6	+	3.00103e6i	1.22888	+	1.23755i
$359$			396946.i			0.162553i	0.996692	+	0.0812767i	$0.0258997\pi$
$359$			396946.i			0.162553i	−0.996692	+	0.0812767i	$0.974100\pi$
$360$	−153737.	−	157012.i	−0.0625205	−	0.0638525i
$361$			2.44888e6i			0.989009i
$362$	2.28813e6	−	2.27211e6i	0.917718	−	0.911292i
$363$	−702238.	−	702238.i	−0.279716	−	0.279716i
$364$	−2.13430e6	−	2.16451e6i	−0.844310	−	0.856259i
$365$	−213381.	+	213381.i	−0.0838346	+	0.0838346i
$366$	−2.34933e6	−	8253.77i	−0.916728	−	0.00322070i
$367$	3.66169e6			1.41911			0.709555	−	0.704650i	$-0.248896\pi$
$367$	3.66169e6			1.41911			0.709555	+	0.704650i	$0.248896\pi$
$368$	−50789.7	+	3.61393e6i	−0.0195504	+	1.39110i
$369$	−1.88433e6			−0.720428
$370$	750547.	+	2636.86i	0.285019	+	0.00100134i
$371$	−1.12936e6	+	1.12936e6i	−0.425989	+	0.425989i
$372$	1.36776e6	−	1.34867e6i	0.512451	−	0.505300i
$373$	−1.11361e6	−	1.11361e6i	−0.414440	−	0.414440i	0.468842	−	0.883282i	$-0.344671\pi$
$373$	−1.11361e6	−	1.11361e6i	−0.414440	−	0.414440i	−0.883282	+	0.468842i	$0.844671\pi$
$374$	2.57653e6	−	2.55849e6i	0.952481	−	0.945811i
$375$		−	862014.i		−	0.316546i
$376$	−4669.29	+	443002.i	−0.00170326	+	0.161598i
$377$		−	3.11049e6i		−	1.12713i
$378$	2.43716e6	+	2.45434e6i	0.877313	+	0.883499i
$379$	−2.47036e6	−	2.47036e6i	−0.883410	−	0.883410i	0.110469	−	0.993880i	$-0.464765\pi$
$379$	−2.47036e6	−	2.47036e6i	−0.883410	−	0.883410i	−0.993880	+	0.110469i	$0.964765\pi$
$380$	62758.8	+	440.980i	0.0222954	+	0.000156661i
$381$	729796.	−	729796.i	0.257566	−	0.257566i
$382$	491.895	−	140011.i	0.000172470	−	0.0490913i
$383$	−1.19954e6			−0.417848			−0.208924	−	0.977932i	$-0.566996\pi$
$383$	−1.19954e6			−0.417848			−0.208924	+	0.977932i	$0.566996\pi$
$384$	1.51706e6	+	1.59358e6i	0.525019	+	0.551499i
$385$	877847.			0.301833
$386$	7910.52	−	2.25162e6i	0.00270232	−	0.769179i
$387$	1.14788e6	−	1.14788e6i	0.389600	−	0.389600i
$388$	−4.97691e6	−	34970.7i	−1.67834	−	0.0117930i
$389$	1.44929e6	+	1.44929e6i	0.485602	+	0.485602i	0.906915	−	0.421313i	$-0.138431\pi$
$389$	1.44929e6	+	1.44929e6i	0.485602	+	0.485602i	−0.421313	+	0.906915i	$0.638431\pi$
$390$	357959.	+	360483.i	0.119171	+	0.120012i
$391$		−	4.57977e6i		−	1.51496i
$392$	−10441.6	+	990658.i	−0.00343205	+	0.325618i
$393$			1.47404e6i			0.481425i
$394$	42134.1	−	41839.1i	0.0136739	−	0.0135782i
$395$	−314513.	−	314513.i	−0.101425	−	0.101425i
$396$	1.15097e6	−	1.13491e6i	0.368831	−	0.363684i
$397$	−815195.	+	815195.i	−0.259588	+	0.259588i	−0.824887	−	0.565298i	$-0.808761\pi$
$397$	−815195.	+	815195.i	−0.259588	+	0.259588i	0.565298	+	0.824887i	$0.308761\pi$
$398$	3.41139e6	+	11985.1i	1.07950	+	0.00379256i
$399$	−292284.			−0.0919122
$400$	42934.2	−	3.05497e6i	0.0134169	−	0.954678i
$401$	2.87334e6			0.892331			0.446165	−	0.894951i	$-0.352789\pi$
$401$	2.87334e6			0.892331			0.446165	+	0.894951i	$0.352789\pi$
$402$	821485.	+	2886.08i	0.253533	+	0.000890725i
$403$	2.27575e6	−	2.27575e6i	0.698012	−	0.698012i
$404$	2.02332e6	+	2.05196e6i	0.616754	+	0.625482i
$405$	−200157.	−	200157.i	−0.0606365	−	0.0606365i
$406$	−2.92840e6	+	2.90790e6i	−0.881689	+	0.875516i
$407$			5.52092e6i			1.65206i
$408$	−1.95050e6	−	1.99205e6i	−0.580090	−	0.592449i
$409$		−	732036.i		−	0.216384i	−0.994130	−	0.108192i	$-0.965494\pi$
$409$		−	732036.i		−	0.216384i	0.994130	−	0.108192i	$-0.0345060\pi$
$410$	874473.	+	880639.i	0.256913	+	0.258725i
$411$	−1.36734e6	−	1.36734e6i	−0.399276	−	0.399276i
$412$	−29304.0	+	4.17045e6i	−0.00850519	+	1.21043i
$413$	692151.	−	692151.i	0.199676	−	0.199676i
$414$	7162.60	−	2.03874e6i	0.00205385	−	0.584602i
$415$	409419.			0.116694
$416$	2.56054e6	+	2.65212e6i	0.725435	+	0.751380i
$417$	683095.			0.192372
$418$	−1621.90	+	461651.i	−0.000454028	+	0.129233i
$419$	−1.00885e6	+	1.00885e6i	−0.280731	+	0.280731i	−0.833400	−	0.552670i	$-0.813609\pi$
$419$	−1.00885e6	+	1.00885e6i	−0.280731	+	0.280731i	0.552670	+	0.833400i	$0.313609\pi$
$420$	4735.98	−	674008.i	0.00131005	−	0.186441i
$421$	−370156.	−	370156.i	−0.101784	−	0.101784i	0.654381	−	0.756165i	$-0.272929\pi$
$421$	−370156.	−	370156.i	−0.101784	−	0.101784i	−0.756165	+	0.654381i	$0.772929\pi$
$422$	−2.86165e6	−	2.88183e6i	−0.782232	−	0.787748i
$423$		−	249903.i		−	0.0679080i
$424$	1.38398e6	−	1.35511e6i	0.373866	−	0.366067i
$425$			3.87142e6i			1.03968i
$426$	−751064.	+	745806.i	−0.200518	+	0.199114i
$427$	3.69294e6	+	3.69294e6i	0.980173	+	0.980173i
$428$	−2.04177e6	−	2.07066e6i	−0.538762	−	0.546387i
$429$	−2.64238e6	+	2.64238e6i	−0.693190	+	0.693190i
$430$	−1.06917e6	−	3756.25i	−0.278852	−	0.000979678i
$431$	−2.53222e6			−0.656612			−0.328306	−	0.944571i	$-0.606478\pi$
$431$	−2.53222e6			−0.656612			−0.328306	+	0.944571i	$0.606478\pi$
$432$	−2.92411e6	−	3.00747e6i	−0.753848	−	0.775339i
$433$	−3.65369e6			−0.936509			−0.468255	−	0.883594i	$-0.655117\pi$
$433$	−3.65369e6			−0.936509			−0.468255	+	0.883594i	$0.655117\pi$
$434$	−4.27006e6	−	15001.8i	−1.08820	−	0.00382313i
$435$	487693.	−	487693.i	0.123573	−	0.123573i
$436$	−746638.	+	736219.i	−0.188102	+	0.185477i
$437$	411732.	+	411732.i	0.103136	+	0.103136i
$438$	−1.20938e6	+	1.20091e6i	−0.301216	+	0.299107i
$439$		−	4.24474e6i		−	1.05121i	−0.850728	−	0.525605i	$-0.823839\pi$
$439$		−	4.24474e6i		−	1.05121i	0.850728	−	0.525605i	$-0.176161\pi$
$440$	−1.06454e6	−	11220.4i	−0.262138	−	0.00276297i
$441$		−	558843.i		−	0.136834i
$442$	−3.29144e6	−	3.31465e6i	−0.801365	−	0.807016i
$443$	5.64377e6	+	5.64377e6i	1.36634	+	1.36634i	0.865590	+	0.500753i	$0.166943\pi$
$443$	5.64377e6	+	5.64377e6i	1.36634	+	1.36634i	0.500753	+	0.865590i	$0.333057\pi$
$444$	4.23895e6	+	29785.3i	1.02047	+	0.00717043i
$445$	−663191.	+	663191.i	−0.158759	+	0.158759i
$446$	14908.7	−	4.24356e6i	0.00354897	−	1.01017i
$447$	−2.83450e6			−0.670977
$448$	103094.	−	4.89002e6i	0.0242683	−	1.15111i
$449$	1.85004e6			0.433077			0.216538	−	0.976274i	$-0.430523\pi$
$449$	1.85004e6			0.433077			0.216538	+	0.976274i	$0.430523\pi$
$450$	−6054.78	+	1.72341e6i	−0.00140951	+	0.401197i
$451$	−6.45518e6	+	6.45518e6i	−1.49440	+	1.49440i
$452$	5.13784e6	+	36101.5i	1.18286	+	0.00831150i
$453$	−3.29920e6	−	3.29920e6i	−0.755377	−	0.755377i
$454$	577361.	+	581432.i	0.131464	+	0.132391i
$455$		−	1.12933e6i		−	0.255737i
$456$	354445.	+	3735.89i	0.0798246	+	0.000841360i
$457$		−	307765.i		−	0.0689333i	−0.999406	−	0.0344667i	$-0.989027\pi$
$457$		−	307765.i		−	0.0689333i	0.999406	−	0.0344667i	$-0.0109733\pi$
$458$	−2.09552e6	+	2.08084e6i	−0.466796	+	0.463528i
$459$	3.75841e6	+	3.75841e6i	0.832668	+	0.832668i
$460$	−956126.	+	942783.i	−0.210679	+	0.207739i
$461$	3.27987e6	−	3.27987e6i	0.718794	−	0.718794i	−0.249564	−	0.968358i	$-0.580287\pi$
$461$	3.27987e6	−	3.27987e6i	0.718794	−	0.718794i	0.968358	+	0.249564i	$0.0802874\pi$
$462$	4.95797e6	+	17418.6i	1.08068	+	0.00379672i
$463$	7.69300e6			1.66780			0.833899	−	0.551917i	$-0.186104\pi$
$463$	7.69300e6			1.66780			0.833899	+	0.551917i	$0.186104\pi$
$464$	3.58836e6	−	3.48890e6i	0.773751	−	0.752304i
$465$	713629.			0.153052
$466$	−158620.	−	557.273i	−0.0338372	−	0.000118878i
$467$	321990.	−	321990.i	0.0683205	−	0.0683205i	−0.672121	−	0.740441i	$-0.734617\pi$
$467$	321990.	−	321990.i	0.0683205	−	0.0683205i	0.740441	+	0.672121i	$0.234617\pi$
$468$	−1.46004e6	−	1.48070e6i	−0.308142	−	0.312503i
$469$	−1.29131e6	−	1.29131e6i	−0.271080	−	0.271080i
$470$	−116792.	+	115974.i	−0.0243876	+	0.0242168i
$471$			3.99670e6i			0.830136i
$472$	−848199.	+	830506.i	−0.175244	+	0.171588i
$473$		−	7.86464e6i		−	1.61631i
$474$	−1.77009e6	−	1.78257e6i	−0.361868	−	0.364419i
$475$	−348051.	−	348051.i	−0.0707797	−	0.0707797i
$476$	−43547.4	+	6.19751e6i	−0.00880937	+	1.25372i
$477$	−772578.	+	772578.i	−0.155470	+	0.155470i
$478$	−14788.3	+	4.20928e6i	−0.00296038	+	0.842632i
$479$	−6.37093e6			−1.26872			−0.634358	−	0.773040i	$-0.718735\pi$
$479$	−6.37093e6			−1.26872			−0.634358	+	0.773040i	$0.718735\pi$
$480$	−14358.1	+	817290.i	−0.00284443	+	0.161910i
$481$	7.10255e6			1.39975
$482$	−30493.0	+	8.67943e6i	−0.00597837	+	1.70166i
$483$	4.42186e6	−	4.42186e6i	0.862457	−	0.862457i
$484$	18812.3	−	2.67730e6i	0.00365030	−	0.519499i
$485$	−1.30747e6	−	1.30747e6i	−0.252394	−	0.252394i
$486$	2.84115e6	+	2.86119e6i	0.545637	+	0.549485i
$487$			612655.i			0.117056i	0.998286	+	0.0585280i	$0.0186407\pi$
$487$			612655.i			0.117056i	−0.998286	+	0.0585280i	$0.981359\pi$
$488$	−4.43113e6	−	4.52553e6i	−0.842296	−	0.860241i
$489$		−	6.24726e6i		−	1.18146i
$490$	−261175.	+	259346.i	−0.0491406	+	0.0487966i
$491$	−2.67875e6	−	2.67875e6i	−0.501452	−	0.501452i	0.410437	−	0.911889i	$-0.365376\pi$
$491$	−2.67875e6	−	2.67875e6i	−0.501452	−	0.501452i	−0.911889	+	0.410437i	$0.865376\pi$
$492$	4.92144e6	+	4.99109e6i	0.916599	+	0.929572i
$493$	−4.48434e6	+	4.48434e6i	−0.830963	+	0.830963i
$494$	593904.	+	2086.53i	0.109496	+	0.000384688i
$495$	600521.			0.110158
$496$	5.17799e6	+	72770.8i	0.945055	+	0.0132817i
$497$	2.35295e6			0.427290
$498$	2.31235e6	+	8123.86i	0.417811	+	0.00146787i
$499$	−2.96619e6	+	2.96619e6i	−0.533271	+	0.533271i	−0.921544	−	0.388273i	$-0.873072\pi$
$499$	−2.96619e6	+	2.96619e6i	−0.533271	+	0.533271i	0.388273	+	0.921544i	$0.373072\pi$
$500$	1.65478e6	−	1.63168e6i	0.296015	−	0.291884i
$501$	−2.44396e6	−	2.44396e6i	−0.435011	−	0.435011i
$502$	3.00489e6	−	2.98385e6i	0.532194	−	0.528467i
$503$		−	8.60760e6i		−	1.51692i	−0.651721	−	0.758459i	$-0.725953\pi$
$503$		−	8.60760e6i		−	1.51692i	0.651721	−	0.758459i	$-0.274047\pi$
$504$	−29078.4	+	2.75883e6i	−0.00509910	+	0.483781i
$505$			1.07061e6i			0.186811i
$506$	−6.95961e6	−	7.00868e6i	−1.20839	−	1.21691i
$507$	283046.	+	283046.i	0.0489032	+	0.0489032i
$508$	2.78237e6	+	19550.6i	0.478361	+	0.00336125i
$509$	−3.82736e6	+	3.82736e6i	−0.654794	+	0.654794i	−0.954143	−	0.299350i	$-0.903230\pi$
$509$	−3.82736e6	+	3.82736e6i	−0.654794	+	0.654794i	0.299350	+	0.954143i	$0.403230\pi$
$510$	3638.91	−	1.03577e6i	0.000619506	−	0.176334i
$511$	3.78878e6			0.641871
$512$	−187522.	+	5.92868e6i	−0.0316139	+	0.999500i
$513$	−675780.			−0.113374
$514$	−15102.6	+	4.29875e6i	−0.00252141	+	0.717686i
$515$	−1.09561e6	+	1.09561e6i	−0.182028	+	0.182028i
$516$	−6.03844e6	−	42429.7i	−0.998391	−	0.00701528i
$517$	−856098.	−	856098.i	−0.140863	−	0.140863i
$518$	−6.63994e6	−	6.68676e6i	−1.08728	−	1.09494i
$519$		−	1.21498e6i		−	0.197994i
$520$	−14434.8	+	1.36951e6i	−0.00234100	+	0.222104i
$521$		−	1.05103e6i		−	0.169637i	−0.996396	−	0.0848184i	$-0.972969\pi$
$521$		−	1.05103e6i		−	0.169637i	0.996396	−	0.0848184i	$-0.0270310\pi$
$522$	−2.00327e6	+	1.98925e6i	−0.321784	+	0.319531i
$523$	−1.89188e6	−	1.89188e6i	−0.302440	−	0.302440i	0.539528	−	0.841968i	$-0.318603\pi$
$523$	−1.89188e6	−	1.89188e6i	−0.302440	−	0.302440i	−0.841968	+	0.539528i	$0.818603\pi$
$524$	−2.82966e6	+	2.79018e6i	−0.450201	+	0.443919i
$525$	−3.73794e6	+	3.73794e6i	−0.591881	+	0.591881i
$526$	9.49360e6	+	33353.4i	1.49612	+	0.00525625i
$527$	−6.56183e6			−1.02920
$528$	−6.01217e6	−	84494.3i	−0.938527	−	0.0131899i
$529$	−6.02154e6			−0.935553
$530$	719599.	+	2528.13i	0.111276	+	0.000390940i
$531$	473490.	−	473490.i	0.0728742	−	0.0728742i
$532$	−553257.	−	561087.i	−0.0847516	−	0.0859510i
$533$	8.30446e6	+	8.30446e6i	1.26617	+	1.26617i
$534$	−3.75878e6	+	3.73246e6i	−0.570419	+	0.566425i
$535$		−	1.08037e6i		−	0.163188i
$536$	1.54943e6	+	1.58244e6i	0.232948	+	0.237911i
$537$			8.87422e6i			1.32799i
$538$	1.29101e6	+	1.30012e6i	0.192298	+	0.193654i
$539$	−1.91444e6	−	1.91444e6i	−0.283837	−	0.283837i
$540$	10949.9	−	1.55835e6i	0.00161594	−	0.229975i
$541$	4.19581e6	−	4.19581e6i	0.616343	−	0.616343i	−0.328248	−	0.944591i	$-0.606458\pi$
$541$	4.19581e6	−	4.19581e6i	0.616343	−	0.616343i	0.944591	+	0.328248i	$0.106458\pi$
$542$	−13375.5	+	3.80717e6i	−0.00195575	+	0.556678i
$543$	6.76614e6			0.984785
$544$	132023.	−	7.51500e6i	0.0191273	−	1.08876i
$545$	−389558.			−0.0561800
$546$	22408.7	−	6.37832e6i	0.00321687	−	0.915640i
$547$	848209.	−	848209.i	0.121209	−	0.121209i	−0.643900	−	0.765109i	$-0.722685\pi$
$547$	848209.	−	848209.i	0.121209	−	0.121209i	0.765109	+	0.643900i	$0.222685\pi$
$548$	36629.9	−	5.21304e6i	0.00521056	−	0.741549i
$549$	2.52628e6	+	2.52628e6i	0.357727	+	0.357727i
$550$	5.88318e6	+	5.92467e6i	0.829288	+	0.835136i
$551$		−	806307.i		−	0.113141i
$552$	−5.41879e6	+	5.30575e6i	−0.756928	+	0.741138i
$553$			5.58449e6i			0.776553i
$554$	8.65182e6	−	8.59124e6i	1.19766	−	1.18927i
$555$	1.11361e6	+	1.11361e6i	0.153461	+	0.153461i
$556$	1.29301e6	+	1.31131e6i	0.177384	+	0.179895i
$557$	6.98719e6	−	6.98719e6i	0.954255	−	0.954255i	−0.0447436	−	0.998999i	$-0.514247\pi$
$557$	6.98719e6	−	6.98719e6i	0.954255	−	0.954255i	0.998999	+	0.0447436i	$0.0142471\pi$
$558$	−2.92108e6	−	10262.5i	−0.397153	−	0.00139530i
$559$	−1.01177e7			−1.36947
$560$	1.30283e6	−	1.26672e6i	0.175557	−	0.170691i
$561$	7.61895e6			1.02209
$562$	4.31716e6	+	15167.3i	0.576577	+	0.00202566i
$563$	2.67792e6	−	2.67792e6i	0.356063	−	0.356063i	−0.506296	−	0.862360i	$-0.668986\pi$
$563$	2.67792e6	−	2.67792e6i	0.356063	−	0.356063i	0.862360	+	0.506296i	$0.168986\pi$
$564$	−661928.	+	652691.i	−0.0876220	+	0.0863992i
$565$	1.34975e6	+	1.34975e6i	0.177883	+	0.177883i
$566$	762398.	−	757060.i	0.100032	−	0.0993320i
$567$			3.55399e6i			0.464257i
$568$	−2.85336e6	−	30074.7i	−0.371096	−	0.00391139i
$569$			5.25084e6i			0.679904i	0.940443	+	0.339952i	$0.110411\pi$
$569$			5.25084e6i			0.679904i	−0.940443	+	0.339952i	$0.889589\pi$
$570$	92790.8	+	93445.1i	0.0119624	+	0.0120467i
$571$	−1.56084e6	−	1.56084e6i	−0.200341	−	0.200341i	0.599805	−	0.800146i	$-0.295245\pi$
$571$	−1.56084e6	−	1.56084e6i	−0.200341	−	0.200341i	−0.800146	+	0.599805i	$0.795245\pi$
$572$	−1.00742e7	−	70787.1i	−1.28742	−	0.00904615i
$573$	207738.	−	207738.i	0.0264320	−	0.0264320i
$574$	54743.0	−	1.55819e7i	0.00693504	−	1.97397i
$575$	1.05311e7			1.32832
$576$	70525.0	−	3.34519e6i	0.00885701	−	0.420111i
$577$	−3.35047e6			−0.418954			−0.209477	−	0.977814i	$-0.567176\pi$
$577$	−3.35047e6			−0.418954			−0.209477	+	0.977814i	$0.567176\pi$
$578$	−5241.83	+	1.49202e6i	−0.000652624	+	0.185761i
$579$	3.34079e6	−	3.34079e6i	0.414145	−	0.414145i
$580$	1.85934e6	+	13064.9i	0.229504	+	0.00161263i
$581$	−3.63482e6	−	3.63482e6i	−0.446727	−	0.446727i
$582$	−7.35851e6	−	7.41039e6i	−0.900497	−	0.906847i
$583$			5.29327e6i			0.644990i
$584$	−4.59456e6	−	48427.1i	−0.557457	−	0.00587565i
$585$		−	772558.i		−	0.0933343i
$586$	3.06271e6	−	3.04126e6i	0.368436	−	0.365856i
$587$	−2.60193e6	−	2.60193e6i	−0.311674	−	0.311674i	0.533884	−	0.845558i	$-0.320732\pi$
$587$	−2.60193e6	−	2.60193e6i	−0.311674	−	0.311674i	−0.845558	+	0.533884i	$0.820732\pi$
$588$	−1.48023e6	+	1.45957e6i	−0.176557	+	0.174093i
$589$	589925.	−	589925.i	0.0700662	−	0.0700662i
$590$	−441020.	−	1549.42i	−0.0521589	−	0.000183247i
$591$	124593.			0.0146732
$592$	7.96661e6	+	8.19372e6i	0.934263	+	0.960897i
$593$	−4.71406e6			−0.550502			−0.275251	−	0.961372i	$-0.588761\pi$
$593$	−4.71406e6			−0.550502			−0.275251	+	0.961372i	$0.588761\pi$
$594$	1.14631e7	+	40272.9i	1.33302	+	0.00468325i
$595$	−1.62814e6	+	1.62814e6i	−0.188538	+	0.188538i
$596$	−5.36535e6	−	5.44128e6i	−0.618703	−	0.627460i
$597$	5.06156e6	+	5.06156e6i	0.581230	+	0.581230i
$598$	−9.01652e6	+	8.95339e6i	−1.03106	+	1.02385i
$599$			7.11555e6i			0.810292i	0.914252	+	0.405146i	$0.132779\pi$
$599$			7.11555e6i			0.810292i	−0.914252	+	0.405146i	$0.867221\pi$
$600$	4.58068e6	−	4.48512e6i	0.519459	−	0.508623i
$601$			7.11657e6i			0.803682i	0.915709	+	0.401841i	$0.131630\pi$
$601$			7.11657e6i			0.803682i	−0.915709	+	0.401841i	$0.868370\pi$
$602$	9.45869e6	+	9.52539e6i	1.06375	+	1.07125i
$603$	−883362.	−	883362.i	−0.0989339	−	0.0989339i
$604$	88382.8	−	1.25783e7i	0.00985769	−	1.40291i
$605$	703350.	−	703350.i	0.0781237	−	0.0781237i
$606$	−21243.5	+	6.04667e6i	−0.00234987	+	0.668859i
$607$	−1.18314e7			−1.30336			−0.651679	−	0.758495i	$-0.725935\pi$
$607$	−1.18314e7			−1.30336			−0.651679	+	0.758495i	$0.725935\pi$
$608$	663748.	+	687486.i	0.0728189	+	0.0754232i
$609$	−8.65946e6			−0.946123
$610$	8266.84	−	2.35305e6i	0.000899529	−	0.256039i
$611$	−1.10135e6	+	1.10135e6i	−0.119350	+	0.119350i
$612$	−29790.1	+	4.23962e6i	−0.00321509	+	0.457561i
$613$	2.99721e6	+	2.99721e6i	0.322156	+	0.322156i	0.849594	−	0.527438i	$-0.176847\pi$
$613$	2.99721e6	+	2.99721e6i	0.322156	+	0.322156i	−0.527438	+	0.849594i	$0.676847\pi$
$614$	3.58631e6	+	3.61160e6i	0.383908	+	0.386615i
$615$			2.60410e6i			0.277633i
$616$	9.35137e6	+	9.55059e6i	0.992941	+	1.01409i
$617$		−	6.83487e6i		−	0.722799i	−0.932411	−	0.361399i	$-0.882299\pi$
$617$		−	6.83487e6i		−	0.722799i	0.932411	−	0.361399i	$-0.117701\pi$
$618$	−6.20961e6	+	6.16613e6i	−0.654023	+	0.649444i
$619$	−5.84289e6	−	5.84289e6i	−0.612917	−	0.612917i	0.330788	−	0.943705i	$-0.392685\pi$
$619$	−5.84289e6	−	5.84289e6i	−0.612917	−	0.612917i	−0.943705	+	0.330788i	$0.892685\pi$
$620$	1.35081e6	+	1.36993e6i	0.141128	+	0.143126i
$621$	1.02236e7	−	1.02236e7i	1.06384	−	1.06384i
$622$	−1.23814e7	−	43499.1i	−1.28320	−	0.00450821i
$623$	1.17756e7			1.21552
$624$	−108700.	+	7.73453e6i	−0.0111755	+	0.795193i
$625$	−8.46057e6			−0.866362
$626$	−1.71756e7	−	60342.4i	−1.75177	−	0.00615441i
$627$	−684963.	+	684963.i	−0.0695822	+	0.0695822i
$628$	−7.67231e6	+	7.56524e6i	−0.776295	+	0.765462i
$629$	−1.02396e7	−	1.02396e7i	−1.03195	−	1.03195i
$630$	−727331.	+	722239.i	−0.0730098	+	0.0724985i
$631$			85274.3i			0.00852599i	0.999991	+	0.00426300i	$0.00135696\pi$
$631$			85274.3i			0.00852599i	−0.999991	+	0.00426300i	$0.998643\pi$
$632$	71379.3	−	6.77216e6i	0.00710852	−	0.674426i
$633$		−	8.52174e6i		−	0.845316i
$634$	−874414.	−	880579.i	−0.0863960	−	0.0870052i
$635$	730952.	+	730952.i	0.0719373	+	0.0719373i
$636$	4.06416e6	+	28557.2i	0.398408	+	0.00279945i
$637$	−2.46289e6	+	2.46289e6i	−0.240489	+	0.240489i
$638$	−48051.6	+	1.36773e7i	−0.00467365	+	1.33029i
$639$	1.60962e6			0.155945
$640$	−1.59610e6	+	1.51946e6i	−0.154032	+	0.146636i
$641$	−4.28879e6			−0.412277			−0.206139	−	0.978523i	$-0.566090\pi$
$641$	−4.28879e6			−0.412277			−0.206139	+	0.978523i	$0.566090\pi$
$642$	21437.1	−	6.10179e6i	0.00205272	−	0.584278i
$643$	1.04018e7	−	1.04018e7i	0.992154	−	0.992154i	−0.00781557	−	0.999969i	$-0.502488\pi$
$643$	1.04018e7	−	1.04018e7i	0.992154	−	0.992154i	0.999969	+	0.00781557i	$0.00248780\pi$
$644$	1.68585e7	+	118458.i	1.60178	+	0.0112551i
$645$	−1.58635e6	−	1.58635e6i	−0.150141	−	0.150141i
$646$	−853213.	−	859229.i	−0.0804408	−	0.0810080i
$647$			2.98777e6i			0.280599i	0.990109	+	0.140300i	$0.0448066\pi$
$647$			2.98777e6i			0.280599i	−0.990109	+	0.140300i	$0.955193\pi$
$648$	45426.0	−	4.30982e6i	0.00424978	−	0.403201i
$649$		−	3.24408e6i		−	0.302329i
$650$	7.62196e6	−	7.56859e6i	0.707592	−	0.702638i
$651$	−6.33559e6	−	6.33559e6i	−0.585915	−	0.585915i
$652$	1.19926e7	−	1.18253e7i	1.10483	−	1.08941i
$653$	−2.51085e6	+	2.51085e6i	−0.230429	+	0.230429i	−0.812872	−	0.582443i	$-0.802097\pi$
$653$	−2.51085e6	+	2.51085e6i	−0.230429	+	0.230429i	0.582443	+	0.812872i	$0.302097\pi$
$654$	−2.20018e6	−	7729.78i	−0.201147	−	0.000706680i
$655$	−1.47638e6			−0.134460
$656$	−265548.	+	1.88950e7i	−0.0240926	+	1.71430i
$657$	2.59185e6			0.234259
$658$	2.06650e6	+	7260.12i	0.186067	+	0.000653701i
$659$	−3.81406e6	+	3.81406e6i	−0.342117	+	0.342117i	−0.857163	−	0.515046i	$-0.827775\pi$
$659$	−3.81406e6	+	3.81406e6i	−0.342117	+	0.342117i	0.515046	+	0.857163i	$0.327775\pi$
$660$	−1.56843e6	−	1.59062e6i	−0.140154	−	0.142137i
$661$	−8.10382e6	−	8.10382e6i	−0.721416	−	0.721416i	0.247477	−	0.968894i	$-0.420398\pi$
$661$	−8.10382e6	−	8.10382e6i	−0.721416	−	0.721416i	−0.968894	+	0.247477i	$0.920398\pi$
$662$	738192.	−	733023.i	0.0654673	−	0.0650089i
$663$		−	9.80162e6i		−	0.865992i
$664$	4.36138e6	+	4.45430e6i	0.383887	+	0.392066i
$665$		−	292747.i		−	0.0256707i
$666$	−4.54228e6	−	4.57431e6i	−0.396815	−	0.399613i
$667$	1.21983e7	+	1.21983e7i	1.06166	+	1.06166i
$668$	65471.5	−	9.31768e6i	0.00567690	−	0.807917i
$669$	6.29628e6	−	6.29628e6i	0.543899	−	0.543899i
$670$	−2890.65	+	822786.i	−0.000248776	+	0.0708108i
$671$	1.73087e7			1.48408
$672$	7.38336e6	−	7.12842e6i	0.630712	−	0.608934i
$673$	1.41013e6			0.120011			0.0600055	−	0.998198i	$-0.480888\pi$
$673$	1.41013e6			0.120011			0.0600055	+	0.998198i	$0.480888\pi$
$674$	−11573.5	+	3.29425e6i	−0.000981333	+	0.279323i
$675$	−8.64236e6	+	8.64236e6i	−0.730084	+	0.730084i
$676$	−7582.55	+	1.07912e6i	−0.000638188	+	0.0908247i
$677$	1.60314e7	+	1.60314e7i	1.34431	+	1.34431i	0.891720	+	0.452587i	$0.149499\pi$
$677$	1.60314e7	+	1.60314e7i	1.34431	+	1.34431i	0.452587	+	0.891720i	$0.350501\pi$
$678$	7.59646e6	+	7.65002e6i	0.634654	+	0.639129i
$679$			2.32155e7i			1.93243i
$680$	1.99521e6	−	1.95359e6i	0.165469	−	0.162017i
$681$			1.71933e6i			0.142066i
$682$	−1.00420e7	+	9.97164e6i	−0.826718	+	0.820929i
$683$	273502.	+	273502.i	0.0224341	+	0.0224341i	0.718235	−	0.695801i	$-0.244950\pi$
$683$	273502.	+	273502.i	0.0224341	+	0.0224341i	−0.695801	+	0.718235i	$0.744950\pi$
$684$	−378474.	−	383831.i	−0.0309312	−	0.0313689i
$685$	1.36951e6	−	1.36951e6i	0.111516	−	0.111516i
$686$	−9.57005e6	−	33622.0i	−0.776433	−	0.00272780i
$687$	−6.19657e6			−0.500910
$688$	−1.13485e7	−	1.16721e7i	−0.914048	−	0.940107i
$689$	6.80968e6			0.546486
$690$	−2.81749e6	−	9898.56i	−0.225289	−	0.000791497i
$691$	−6.17051e6	+	6.17051e6i	−0.491616	+	0.491616i	−0.908815	−	0.417199i	$-0.863012\pi$
$691$	−6.17051e6	+	6.17051e6i	−0.491616	+	0.491616i	0.417199	+	0.908815i	$0.363012\pi$
$692$	2.33236e6	−	2.29981e6i	0.185153	−	0.182569i
$693$	−5.33142e6	−	5.33142e6i	−0.421706	−	0.421706i
$694$	1.65397e7	−	1.64238e7i	1.30355	−	1.29442i
$695$			684177.i			0.0537287i
$696$	1.05011e7	+	110683.i	0.821696	+	0.00866076i
$697$		−	2.39448e7i		−	1.86693i
$698$	1.20644e7	+	1.21495e7i	0.937277	+	0.943886i
$699$	−235349.	−	235349.i	−0.0182188	−	0.0182188i
$700$	−1.42510e7	−	100136.i	−1.09926	−	0.00772406i
$701$	−1.21416e7	+	1.21416e7i	−0.933211	+	0.933211i	−0.997905	−	0.0646937i	$-0.979393\pi$
$701$	−1.21416e7	+	1.21416e7i	−0.933211	+	0.933211i	0.0646937	+	0.997905i	$0.479393\pi$
$702$	51810.2	−	1.47471e7i	0.00396801	−	1.12944i
$703$	1.84114e6			0.140507
$704$	−1.12181e7	−	1.17013e7i	−0.853074	−	0.889818i
$705$	−345361.			−0.0261698
$706$	47171.4	−	1.34267e7i	0.00356178	−	1.01381i
$707$	9.50486e6	−	9.50486e6i	0.715150	−	0.715150i
$708$	−2.49080e6	−	17501.8i	−0.186748	−	0.00131220i
$709$	4.03475e6	+	4.03475e6i	0.301440	+	0.301440i	0.841577	−	0.540137i	$-0.181628\pi$
$709$	4.03475e6	+	4.03475e6i	0.301440	+	0.301440i	−0.540137	+	0.841577i	$0.681628\pi$
$710$	−746986.	−	752254.i	−0.0556118	−	0.0560039i
$711$			3.82026e6i			0.283413i
$712$	−1.42800e7	−	150512.i	−1.05567	−	0.0111268i
$713$			1.78495e7i			1.31493i
$714$	−9.22782e6	+	9.16321e6i	−0.677413	+	0.672670i
$715$	−2.64657e6	−	2.64657e6i	−0.193605	−	0.193605i
$716$	−1.70355e7	+	1.67978e7i	−1.24186	+	1.22453i
$717$	−6.24541e6	+	6.24541e6i	−0.453694	+	0.453694i
$718$	−2.24545e6	−	7888.85i	−0.162552	−	0.000571087i
$719$	−1.49286e7			−1.07695			−0.538477	−	0.842640i	$-0.681000\pi$
$719$	−1.49286e7			−1.07695			−0.538477	+	0.842640i	$0.681000\pi$
$720$	891246.	−	866542.i	0.0640717	−	0.0622958i
$721$	1.94536e7			1.39368
$722$	−1.38529e7	−	48668.7i	−0.989003	−	0.00347462i
$723$	−1.28779e7	+	1.28779e7i	−0.916218	+	0.916218i
$724$	1.28074e7	+	1.29887e7i	0.908063	+	0.920914i
$725$	−1.03116e7	−	1.03116e7i	−0.728589	−	0.728589i
$726$	3.98639e6	−	3.95848e6i	0.280697	−	0.278732i
$727$		−	2.17243e7i		−	1.52444i	−0.647317	−	0.762221i	$-0.724109\pi$
$727$		−	2.17243e7i		−	1.52444i	0.647317	−	0.762221i	$-0.275891\pi$
$728$	1.22866e7	−	1.20303e7i	0.859220	−	0.841297i
$729$			1.42465e7i			0.992865i
$730$	−1.20282e6	−	1.21130e6i	−0.0835395	−	0.0841286i
$731$	1.45865e7	+	1.45865e7i	1.00962	+	1.00962i
$732$	93380.2	−	1.32895e7i	0.00644135	−	0.916711i
$733$	565657.	−	565657.i	0.0388860	−	0.0388860i	−0.687396	−	0.726282i	$-0.741246\pi$
$733$	565657.	−	565657.i	0.0388860	−	0.0388860i	0.726282	+	0.687396i	$0.241246\pi$
$734$	−72771.8	+	2.07135e7i	−0.00498566	+	1.41910i
$735$	−772309.			−0.0527318
$736$	−2.04423e7	−	359130.i	−1.39103	−	0.0244376i
$737$	−6.05230e6			−0.410442
$738$	37448.8	−	1.06593e7i	0.00253103	−	0.720424i
$739$	1.17006e7	−	1.17006e7i	0.788126	−	0.788126i	−0.193061	−	0.981187i	$-0.561842\pi$
$739$	1.17006e7	−	1.17006e7i	0.788126	−	0.788126i	0.981187	+	0.193061i	$0.0618416\pi$
$740$	−29832.5	+	4.24566e6i	−0.00200267	+	0.285014i
$741$	881190.	+	881190.i	0.0589555	+	0.0589555i
$742$	−6.36615e6	−	6.41104e6i	−0.424490	−	0.427483i
$743$		−	1.37400e7i		−	0.913090i	−0.889700	−	0.456545i	$-0.849087\pi$
$743$		−	1.37400e7i		−	0.913090i	0.889700	−	0.456545i	$-0.150913\pi$
$744$	7.60202e6	+	7.76397e6i	0.503496	+	0.514223i
$745$		−	2.83899e6i		−	0.187402i
$746$	6.32163e6	−	6.27737e6i	0.415894	−	0.412982i
$747$	−2.48652e6	−	2.48652e6i	−0.163039	−	0.163039i
$748$	1.44217e7	+	1.46258e7i	0.942459	+	0.955798i
$749$	−9.59150e6	+	9.59150e6i	−0.624715	+	0.624715i
$750$	4.87626e6	+	17131.5i	0.316544	+	0.00111210i
$751$	−7.70950e6			−0.498800			−0.249400	−	0.968401i	$-0.580233\pi$
$751$	−7.70950e6			−0.498800			−0.249400	+	0.968401i	$0.580233\pi$
$752$	−2.50589e6	−	35217.5i	−0.161591	−	0.00227098i
$753$	8.88565e6			0.571086
$754$	1.75955e7	+	61817.4i	1.12713	+	0.00395988i
$755$	3.30443e6	−	3.30443e6i	0.210974	−	0.210974i
$756$	−1.39322e7	+	1.37378e7i	−0.886575	+	0.874203i
$757$	1.65778e7	+	1.65778e7i	1.05145	+	1.05145i	0.998603	+	0.0528433i	$0.0168284\pi$
$757$	1.65778e7	+	1.65778e7i	1.05145	+	1.05145i	0.0528433	+	0.998603i	$0.483172\pi$
$758$	1.40235e7	−	1.39253e7i	0.886508	−	0.880301i
$759$		−	2.07251e7i		−	1.30585i
$760$	−3741.80	+	355006.i	−0.000234989	+	0.0222947i
$761$			2.97835e7i			1.86429i	0.362080	+	0.932147i	$0.382067\pi$
$761$			2.97835e7i			1.86429i	−0.362080	+	0.932147i	$0.617933\pi$
$762$	4.11382e6	+	4.14283e6i	0.256660	+	0.258470i
$763$	3.45850e6	+	3.45850e6i	0.215068	+	0.215068i
$764$	792009.	+	5565.12i	0.0490904	+	0.000344938i
$765$	−1.11378e6	+	1.11378e6i	−0.0688093	+	0.0688093i
$766$	23839.5	−	6.78558e6i	0.00146799	−	0.417845i
$767$	−4.17345e6			−0.256157
$768$	−9.04472e6	+	8.55007e6i	−0.553340	+	0.523078i
$769$	8.05448e6			0.491158			0.245579	−	0.969377i	$-0.421022\pi$
$769$	8.05448e6			0.491158			0.245579	+	0.969377i	$0.421022\pi$
$770$	−17446.2	+	4.96582e6i	−0.00106041	+	0.301831i
$771$	−6.37816e6	+	6.37816e6i	−0.386420	+	0.386420i
$772$	1.27369e7	+	89496.8i	0.769165	+	0.00540461i
$773$	−1.82770e7	−	1.82770e7i	−1.10016	−	1.10016i	−0.994391	−	0.105769i	$-0.966270\pi$
$773$	−1.82770e7	−	1.82770e7i	−1.10016	−	1.10016i	−0.105769	−	0.994391i	$-0.533730\pi$
$774$	6.47054e6	+	6.51617e6i	0.388229	+	0.390967i
$775$		−	1.50888e7i		−	0.902401i
$776$	296733.	−	2.81528e7i	0.0176893	−	1.67829i
$777$		−	1.97732e7i		−	1.17496i
$778$	−8.22716e6	+	8.16956e6i	−0.487305	+	0.483893i
$779$	2.15270e6	+	2.15270e6i	0.127098	+	0.127098i
$780$	−2.04630e6	+	2.01775e6i	−0.120430	+	0.118749i
$781$	5.51410e6	−	5.51410e6i	0.323480	−	0.323480i
$782$	2.59069e7	+	91017.5i	1.51495	+	0.00532241i
$783$	−2.00212e7			−1.16704
$784$	−5.60376e6	−	78754.6i	−0.325604	−	0.00457600i
$785$	−4.00303e6			−0.231854
$786$	−8.33840e6	−	29294.9i	−0.481422	−	0.00169136i
$787$	957052.	−	957052.i	0.0550806	−	0.0550806i	−0.679030	−	0.734111i	$-0.737599\pi$
$787$	957052.	−	957052.i	0.0550806	−	0.0550806i	0.734111	+	0.679030i	$0.237599\pi$
$788$	235839.	+	239177.i	0.0135301	+	0.0137215i
$789$	1.40859e7	+	1.40859e7i	0.805549	+	0.805549i
$790$	1.78540e6	−	1.77289e6i	0.101781	−	0.101068i
$791$		−	2.39662e7i		−	1.36194i
$792$	6.39712e6	+	6.53341e6i	0.362386	+	0.370107i
$793$		−	2.22673e7i		−	1.25743i
$794$	−4.59521e6	−	4.62761e6i	−0.258675	−	0.260499i
$795$	1.06769e6	+	1.06769e6i	0.0599137	+	0.0599137i
$796$	−135595.	+	1.92974e7i	−0.00758507	+	1.07948i
$797$	3.45071e6	−	3.45071e6i	0.192426	−	0.192426i	−0.604318	−	0.796743i	$-0.706554\pi$
$797$	3.45071e6	−	3.45071e6i	0.192426	−	0.192426i	0.796743	+	0.604318i	$0.206554\pi$
$798$	5808.81	−	1.65340e6i	0.000322909	−	0.0919117i
$799$	3.17560e6			0.175978
$800$	1.72806e7	+	303585.i	0.954625	+	0.0167708i
$801$	8.05551e6			0.443621
$802$	−57104.2	+	1.62540e7i	−0.00313496	+	0.892325i
$803$	8.87894e6	−	8.87894e6i	0.485929	−	0.485929i
$804$	−32652.1	+	4.64693e6i	−0.00178144	+	0.253528i
$805$	4.42886e6	+	4.42886e6i	0.240881	+	0.240881i
$806$	1.28283e7	+	1.29188e7i	0.695555	+	0.700460i
$807$			3.84452e6i			0.207806i
$808$	−1.16478e7	+	1.14048e7i	−0.627645	+	0.614552i
$809$		−	1.13220e7i		−	0.608209i	−0.952639	−	0.304104i	$-0.901643\pi$
$809$		−	1.13220e7i		−	0.608209i	0.952639	−	0.304104i	$-0.0983572\pi$
$810$	1.13623e6	−	1.12828e6i	0.0608491	−	0.0604231i
$811$	−6.80820e6	−	6.80820e6i	−0.363480	−	0.363480i	0.501613	−	0.865092i	$-0.332740\pi$
$811$	−6.80820e6	−	6.80820e6i	−0.363480	−	0.363480i	−0.865092	+	0.501613i	$0.832740\pi$
$812$	−1.63912e7	−	1.66232e7i	−0.872413	−	0.884760i
$813$	−5.64879e6	+	5.64879e6i	−0.299729	+	0.299729i
$814$	−3.12309e7	−	109722.i	−1.65205	−	0.00580407i
$815$	6.25715e6			0.329976
$816$	1.13075e7	−	1.09940e7i	0.594483	−	0.578005i
$817$	−2.62272e6			−0.137467
$818$	4.14100e6	+	14548.4i	0.216382	+	0.000760205i
$819$	−6.85876e6	+	6.85876e6i	−0.357302	+	0.357302i
$820$	−4.99900e6	+	4.92923e6i	−0.259626	+	0.256003i
$821$	−2.63059e7	−	2.63059e7i	−1.36206	−	1.36206i	−0.871292	−	0.490765i	$-0.836718\pi$
$821$	−2.63059e7	−	2.63059e7i	−1.36206	−	1.36206i	−0.490765	−	0.871292i	$-0.663282\pi$
$822$	7.76199e6	−	7.70764e6i	0.400676	−	0.397871i
$823$			3.31660e7i			1.70684i	0.521222	+	0.853421i	$0.325476\pi$
$823$			3.31660e7i			1.70684i	−0.521222	+	0.853421i	$0.674524\pi$
$824$	−2.35909e7	−	248650.i	−1.21039	−	0.0127577i
$825$			1.75196e7i			0.896168i
$826$	3.90162e6	+	3.92913e6i	0.198973	+	0.200376i
$827$	−1.19767e7	−	1.19767e7i	−0.608937	−	0.608937i	0.333731	−	0.942668i	$-0.391692\pi$
$827$	−1.19767e7	−	1.19767e7i	−0.608937	−	0.608937i	−0.942668	+	0.333731i	$0.891692\pi$
$828$	1.15326e7	+	81035.1i	0.584591	+	0.00410768i
$829$	−2.20232e7	+	2.20232e7i	−1.11300	+	1.11300i	−0.120254	+	0.992743i	$0.538371\pi$
$829$	−2.20232e7	+	2.20232e7i	−1.11300	+	1.11300i	−0.992743	+	0.120254i	$0.961629\pi$
$830$	−8136.72	+	2.31601e6i	−0.000409972	+	0.116693i
$831$	2.55840e7			1.28518
$832$	−1.50534e7	+	1.44318e7i	−0.753924	+	0.722791i
$833$	7.10140e6			0.354594
$834$	−13575.7	+	3.86415e6i	−0.000675846	+	0.192370i
$835$	2.44783e6	−	2.44783e6i	0.121497	−	0.121497i
$836$	−2.61144e6	−	18349.5i	−0.129230	−	0.000908050i
$837$	−1.46483e7	−	1.46483e7i	−0.722725	−	0.722725i
$838$	−5.68681e6	−	5.72691e6i	−0.279743	−	0.281715i
$839$			3.30790e7i			1.62236i	0.584797	+	0.811179i	$0.301174\pi$
$839$			3.30790e7i			1.62236i	−0.584797	+	0.811179i	$0.698826\pi$
$840$	3.81265e6	+	40185.7i	0.186435	+	0.00196505i
$841$		−	3.37718e6i		−	0.164651i
$842$	2.10126e6	−	2.08655e6i	0.102141	−	0.101426i
$843$	6.40548e6	+	6.40548e6i	0.310444	+	0.310444i
$844$	1.63589e7	−	1.61306e7i	0.790491	−	0.779460i
$845$	−283494.	+	283494.i	−0.0136585	+	0.0136585i
$846$	1.41366e6	+	4966.53i	0.0679076	+	0.000238576i
$847$	−1.24887e7			−0.598146
$848$	7.63811e6	+	7.85586e6i	0.364751	+	0.375149i
$849$	2.25446e6			0.107343
$850$	−2.19000e7	−	76940.0i	−1.03967	−	0.00365263i
$851$	−2.78539e7	+	2.78539e7i	−1.31844	+	1.31844i
$852$	−4.20396e6	−	4.26346e6i	−0.198408	−	0.201216i
$853$	2.43697e7	+	2.43697e7i	1.14677	+	1.14677i	0.987183	+	0.159591i	$0.0510175\pi$
$853$	2.43697e7	+	2.43697e7i	1.14677	+	1.14677i	0.159591	+	0.987183i	$0.448983\pi$
$854$	−2.09637e7	+	2.08169e7i	−0.983611	+	0.976724i
$855$		−	200264.i		−	0.00936886i
$856$	1.17539e7	−	1.15088e7i	0.548276	−	0.536839i
$857$		−	1.60983e7i		−	0.748736i	−0.927280	−	0.374368i	$-0.877860\pi$
$857$		−	1.60983e7i		−	0.748736i	0.927280	−	0.374368i	$-0.122140\pi$
$858$	−1.48950e7	−	1.50000e7i	−0.690751	−	0.695621i
$859$	1.46034e7	+	1.46034e7i	0.675258	+	0.675258i	0.958923	−	0.283665i	$-0.0915504\pi$
$859$	1.46034e7	+	1.46034e7i	0.675258	+	0.675258i	−0.283665	+	0.958923i	$0.591550\pi$
$860$	42496.8	−	6.04800e6i	0.00195934	−	0.278847i
$861$	2.31192e7	−	2.31192e7i	1.06283	−	1.06283i
$862$	50325.0	−	1.43243e7i	0.00230683	−	0.656608i
$863$	1.73946e7			0.795038			0.397519	−	0.917594i	$-0.369871\pi$
$863$	1.73946e7			0.795038			0.397519	+	0.917594i	$0.369871\pi$
$864$	1.70708e7	−	1.64814e7i	0.777982	−	0.751119i
$865$	1.21691e6			0.0552991
$866$	72612.8	−	2.06683e7i	0.00329017	−	0.936504i
$867$	−2.21374e6	+	2.21374e6i	−0.100018	+	0.100018i
$868$	169725.	−	2.41546e7i	0.00764620	−	1.08818i
$869$	1.30872e7	+	1.30872e7i	0.587889	+	0.587889i
$870$	2.74910e6	+	2.76848e6i	0.123138	+	0.124006i
$871$			7.78615e6i			0.347758i
$872$	−4.14982e6	−	4.23823e6i	−0.184815	−	0.188753i
$873$			1.58813e7i			0.705264i
$874$	−2.33728e6	+	2.32091e6i	−0.103498	+	0.102773i
$875$	−7.66507e6	−	7.66507e6i	−0.338451	−	0.338451i
$876$	−6.76932e6	−	6.86512e6i	−0.298047	−	0.302265i
$877$	1.01924e7	−	1.01924e7i	0.447484	−	0.447484i	−0.447033	−	0.894517i	$-0.647519\pi$
$877$	1.01924e7	−	1.01924e7i	0.447484	−	0.447484i	0.894517	+	0.447033i	$0.147519\pi$
$878$	2.40117e7	+	84359.2i	1.05120	+	0.00369315i
$879$	9.05661e6			0.395361
$880$	84628.1	−	6.02169e6i	0.00368390	−	0.262127i
$881$	−3.40921e7			−1.47984			−0.739920	−	0.672695i	$-0.765136\pi$
$881$	−3.40921e7			−1.47984			−0.739920	+	0.672695i	$0.765136\pi$
$882$	3.16127e6	+	11106.3i	0.136833	+	0.000480728i
$883$	1.70559e7	−	1.70559e7i	0.736159	−	0.736159i	−0.235673	−	0.971832i	$-0.575729\pi$
$883$	1.70559e7	−	1.70559e7i	0.736159	−	0.736159i	0.971832	+	0.235673i	$0.0757294\pi$
$884$	1.88158e7	−	1.85532e7i	0.809826	−	0.798525i
$885$	−654353.	−	654353.i	−0.0280837	−	0.0280837i
$886$	−3.20379e7	+	3.18136e7i	−1.37113	+	1.36153i
$887$		−	8.10941e6i		−	0.346083i	−0.984915	−	0.173042i	$-0.944641\pi$
$887$		−	8.10941e6i		−	0.346083i	0.984915	−	0.173042i	$-0.0553595\pi$
$888$	−252734.	+	2.39784e7i	−0.0107555	+	1.02044i
$889$		−	1.29788e7i		−	0.550781i
$890$	−3.73837e6	−	3.76473e6i	−0.158200	−	0.159316i
$891$	8.32871e6	+	8.32871e6i	0.351466	+	0.351466i
$892$	2.40048e7	+	168672.i	1.01015	+	0.00709790i
$893$	−285494.	+	285494.i	−0.0119803	+	0.0119803i
$894$	56332.4	−	1.60343e7i	0.00235730	−	0.670973i
$895$	−8.88827e6			−0.370902
$896$	2.76599e7	+	680368.i	1.15101	+	0.0283122i
$897$	−2.66624e7			−1.10641
$898$	−36767.3	+	1.04653e7i	−0.00152150	+	0.433074i
$899$	1.74776e7	−	1.74776e7i	0.721245	−	0.721245i
$900$	−9.74891e6	−	68501.6i	−0.401190	−	0.00281899i
$901$	−9.81740e6	−	9.81740e6i	−0.402888	−	0.402888i
$902$	−3.63875e7	−	3.66441e7i	−1.48914	−	1.49964i
$903$			2.81672e7i			1.14954i
$904$	−306328.	+	2.90631e7i	−0.0124671	+	1.18283i
$905$			6.77685e6i			0.275047i
$906$	1.87286e7	−	1.85974e7i	0.758026	−	0.752719i
$907$	2.06810e6	+	2.06810e6i	0.0834742	+	0.0834742i	0.747611	−	0.664137i	$-0.231201\pi$
$907$	2.06810e6	+	2.06810e6i	0.0834742	+	0.0834742i	−0.664137	+	0.747611i	$0.731201\pi$
$908$	−3.30053e6	+	3.25447e6i	−0.132852	+	0.130998i
$909$	6.50212e6	−	6.50212e6i	0.261003	−	0.261003i
$910$	6.38842e6	+	22444.1i	0.255735	+	0.000898461i
$911$	3.11975e7			1.24544			0.622722	−	0.782443i	$-0.286027\pi$
$911$	3.11975e7			1.24544			0.622722	+	0.782443i	$0.286027\pi$
$912$	−28177.4	+	2.00496e6i	−0.00112180	+	0.0798212i
$913$	−1.70362e7			−0.676390
$914$	1.74097e6	+	6116.48i	0.0689329	+	0.000242179i
$915$	3.49127e6	−	3.49127e6i	0.137858	−	0.137858i
$916$	−1.17293e7	−	1.18953e7i	−0.461885	−	0.468422i
$917$	1.31073e7	+	1.31073e7i	0.514741	+	0.514741i
$918$	−2.13353e7	+	2.11859e7i	−0.835589	+	0.829738i
$919$			147120.i			0.00574623i	0.999996	+	0.00287312i	$0.000914543\pi$
$919$			147120.i			0.00574623i	−0.999996	+	0.00287312i	$0.999085\pi$
$920$	−5.31415e6	−	5.42737e6i	−0.206997	−	0.211407i
$921$			1.06797e7i			0.414869i
$922$	1.84885e7	+	1.86188e7i	0.716264	+	0.721315i
$923$	−7.09378e6	−	7.09378e6i	−0.274077	−	0.274077i
$924$	−197068.	+	2.80460e7i	−0.00759339	+	1.08066i
$925$	2.35458e7	−	2.35458e7i	0.904812	−	0.904812i
$926$	−152889.	+	4.35179e7i	−0.00585936	+	1.66779i
$927$	1.33079e7			0.508640
$928$	1.96647e7	+	2.03680e7i	0.749581	+	0.776389i
$929$	2.63584e7			1.00203			0.501014	−	0.865439i	$-0.332961\pi$
$929$	2.63584e7			1.00203			0.501014	+	0.865439i	$0.332961\pi$
$930$	−14182.5	+	4.03687e6i	−0.000537708	+	0.153051i
$931$	−638433.	+	638433.i	−0.0241402	+	0.0241402i
$932$	6304.78	−	897275.i	0.000237755	−	0.0338365i
$933$	−1.83706e7	−	1.83706e7i	−0.690908	−	0.690908i
$934$	1.81504e6	+	1.82784e6i	0.0680800	+	0.0685601i
$935$			7.63102e6i			0.285465i
$936$	8.40509e6	−	8.22976e6i	0.313583	−	0.307042i
$937$			6.40597e6i			0.238362i	0.992873	+	0.119181i	$0.0380268\pi$
$937$			6.40597e6i			0.238362i	−0.992873	+	0.119181i	$0.961973\pi$
$938$	7.33035e6	−	7.27902e6i	0.272030	−	0.270126i
$939$	−2.54839e7	−	2.54839e7i	−0.943197	−	0.943197i
$940$	−653724.	−	662976.i	−0.0241310	−	0.0244725i
$941$	5.71655e6	−	5.71655e6i	0.210455	−	0.210455i	−0.594006	−	0.804461i	$-0.702454\pi$
$941$	5.71655e6	−	5.71655e6i	0.210455	−	0.210455i	0.804461	+	0.594006i	$0.202454\pi$
$942$	−2.26086e7	−	79429.7i	−0.830131	−	0.00291646i
$943$	−6.51346e7			−2.38524
$944$	−4.68116e6	−	4.81462e6i	−0.170972	−	0.175846i
$945$	−7.26913e6			−0.264791
$946$	4.44888e7	+	156300.i	1.61630	+	0.00567849i
$947$	−6.91363e6	+	6.91363e6i	−0.250514	+	0.250514i	−0.821181	−	0.570668i	$-0.806685\pi$
$947$	−6.91363e6	+	6.91363e6i	−0.250514	+	0.250514i	0.570668	+	0.821181i	$0.306685\pi$
$948$	1.01189e7	−	9.97766e6i	0.365689	−	0.360585i
$949$	−1.14226e7	−	1.14226e7i	−0.411717	−	0.411717i
$950$	1.97578e6	−	1.96194e6i	0.0710279	−	0.0705306i
$951$		−	2.60393e6i		−	0.0933636i
$952$	−3.50574e7	−	369508.i	−1.25368	−	0.0132139i
$953$			3.28676e6i			0.117229i	0.998281	+	0.0586145i	$0.0186683\pi$
$953$			3.28676e6i			0.117229i	−0.998281	+	0.0586145i	$0.981332\pi$
$954$	−4.35498e6	−	4.38569e6i	−0.154923	−	0.156015i
$955$	208067.	+	208067.i	0.00738236	+	0.00738236i
$956$	−2.38108e7	−	167309.i	−0.842617	−	0.00592072i
$957$	−2.02933e7	+	2.02933e7i	−0.716263	+	0.716263i
$958$	126615.	−	3.60392e7i	0.00445729	−	1.26871i
$959$	−2.43170e7			−0.853813
$960$	−4.62298e6	−	97464.1i	−0.161899	−	0.00341324i
$961$	−3.05459e6			−0.106695
$962$	−141155.	+	4.01778e7i	−0.00491766	+	1.39975i
$963$	−6.56139e6	+	6.56139e6i	−0.227998	+	0.227998i
$964$	−4.90974e7	−	344987.i	−1.70163	−	0.0119567i
$965$	3.34608e6	+	3.34608e6i	0.115669	+	0.115669i
$966$	2.49258e7	+	2.51015e7i	0.859421	+	0.865481i
$967$			1.51880e7i			0.522316i	0.965296	+	0.261158i	$0.0841044\pi$
$967$			1.51880e7i			0.522316i	−0.965296	+	0.261158i	$0.915896\pi$
$968$	1.51447e7	+	159626.i	0.519483	+	0.00547540i
$969$		−	2.54079e6i		−	0.0869280i
$970$	7.42213e6	−	7.37016e6i	0.253279	−	0.251506i
$971$	−3.90513e7	−	3.90513e7i	−1.32919	−	1.32919i	−0.906077	−	0.423112i	$-0.860938\pi$
$971$	−3.90513e7	−	3.90513e7i	−1.32919	−	1.32919i	−0.423112	−	0.906077i	$-0.639062\pi$
$972$	−1.62417e7	+	1.60150e7i	−0.551398	+	0.543703i
$973$	6.07411e6	−	6.07411e6i	0.205684	−	0.205684i
$974$	−3.46568e6	−	12175.8i	−0.117055	−	0.000411245i
$975$	2.25386e7			0.759303
$976$	2.56882e7	−	2.49762e7i	0.863195	−	0.839269i
$977$	−3.10298e7			−1.04002			−0.520011	−	0.854159i	$-0.674072\pi$
$977$	−3.10298e7			−1.04002			−0.520011	+	0.854159i	$0.674072\pi$
$978$	3.53396e7	+	124157.i	1.18145	+	0.00415072i
$979$	2.75959e7	−	2.75959e7i	0.920212	−	0.920212i
$980$	−1.46188e6	−	1.48257e6i	−0.0486236	−	0.0493118i
$981$	2.36590e6	+	2.36590e6i	0.0784918	+	0.0784918i
$982$	1.52065e7	−	1.51000e7i	0.503210	−	0.499687i
$983$		−	4.38623e6i		−	0.144780i	−0.997376	−	0.0723899i	$-0.976937\pi$
$983$		−	4.38623e6i		−	0.144780i	0.997376	−	0.0723899i	$-0.0230626\pi$
$984$	−2.83315e7	+	2.77405e7i	−0.932786	+	0.913328i
$985$			124790.i			0.00409818i
$986$	−2.52780e7	−	2.54562e7i	−0.828038	−	0.833877i
$987$	3.06611e6	+	3.06611e6i	0.100183	+	0.100183i
$988$	−23606.3	+	3.35957e6i	−0.000769370	+	0.109494i
$989$	3.96782e7	−	3.96782e7i	1.28992	−	1.28992i
$990$	−11934.7	+	3.39704e6i	−0.000387010	+	0.110157i
$991$	3.62368e7			1.17210			0.586051	−	0.810274i	$-0.300682\pi$
$991$	3.62368e7			1.17210			0.586051	+	0.810274i	$0.300682\pi$
$992$	−514558.	+	2.92895e7i	−0.0166018	+	0.945002i
$993$	2.18288e6			0.0702516
$994$	−46762.2	+	1.33102e7i	−0.00150117	+	0.427287i
$995$	−5.06957e6	+	5.06957e6i	−0.162335	+	0.162335i
$996$	−91910.4	+	1.30804e7i	−0.00293573	+	0.417803i
$997$	4.38036e7	+	4.38036e7i	1.39563	+	1.39563i	0.812058	+	0.583576i	$0.198347\pi$
$997$	4.38036e7	+	4.38036e7i	1.39563	+	1.39563i	0.583576	+	0.812058i	$0.301653\pi$
$998$	−1.67203e7	−	1.68382e7i	−0.531394	−	0.535141i
$999$		−	4.57168e7i		−	1.44931i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	16.6.e.a.5.5	✓	18
3.2	odd	2		144.6.k.a.37.5		18
4.3	odd	2		64.6.e.a.49.7		18
8.3	odd	2		128.6.e.a.97.3		18
8.5	even	2		128.6.e.b.97.7		18
12.11	even	2		576.6.k.a.433.5		18
16.3	odd	4		64.6.e.a.17.7		18
16.5	even	4		128.6.e.b.33.7		18
16.11	odd	4		128.6.e.a.33.3		18
16.13	even	4	inner	16.6.e.a.13.5	yes	18
32.3	odd	8		1024.6.a.l.1.13		18
32.13	even	8		1024.6.a.k.1.13		18
32.19	odd	8		1024.6.a.l.1.6		18
32.29	even	8		1024.6.a.k.1.6		18
48.29	odd	4		144.6.k.a.109.5		18
48.35	even	4		576.6.k.a.145.5		18

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
16.6.e.a.5.5	✓	18	1.1	even	1	trivial
16.6.e.a.13.5	yes	18	16.13	even	4	inner
64.6.e.a.17.7		18	16.3	odd	4
64.6.e.a.49.7		18	4.3	odd	2
128.6.e.a.33.3		18	16.11	odd	4
128.6.e.a.97.3		18	8.3	odd	2
128.6.e.b.33.7		18	16.5	even	4
128.6.e.b.97.7		18	8.5	even	2
144.6.k.a.37.5		18	3.2	odd	2
144.6.k.a.109.5		18	48.29	odd	4
576.6.k.a.145.5		18	48.35	even	4
576.6.k.a.433.5		18	12.11	even	2
1024.6.a.k.1.6		18	32.29	even	8
1024.6.a.k.1.13		18	32.13	even	8
1024.6.a.l.1.6		18	32.19	odd	8
1024.6.a.l.1.13		18	32.3	odd	8

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:	\( N \)	\(=\)	\( 16 = 2^{4} \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	16.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.0198738 + 5.65682i) q^{2} +(-8.39316 + 8.39316i) q^{3} +(-31.9992 - 0.224845i) q^{4} +(-8.40645 - 8.40645i) q^{5} +(-47.3118 - 47.6454i) q^{6} +149.265i q^{7} +(1.90786 - 181.009i) q^{8} +102.110i q^{9} +O(q^{10})\)	\(q+(-0.0198738 + 5.65682i) q^{2} +(-8.39316 + 8.39316i) q^{3} +(-31.9992 - 0.224845i) q^{4} +(-8.40645 - 8.40645i) q^{5} +(-47.3118 - 47.6454i) q^{6} +149.265i q^{7} +(1.90786 - 181.009i) q^{8} +102.110i q^{9} +(47.7208 - 47.3867i) q^{10} +(349.799 + 349.799i) q^{11} +(270.462 - 266.687i) q^{12} +(450.009 - 450.009i) q^{13} +(-844.364 - 2.96646i) q^{14} +141.113 q^{15} +(1023.90 + 14.3897i) q^{16} -1297.54 q^{17} +(-577.616 - 2.02931i) q^{18} +(116.652 - 116.652i) q^{19} +(267.110 + 270.890i) q^{20} +(-1252.80 - 1252.80i) q^{21} +(-1985.70 + 1971.80i) q^{22} +3529.57i q^{23} +(1503.23 + 1535.25i) q^{24} -2983.66i q^{25} +(2536.68 + 2554.56i) q^{26} +(-2896.56 - 2896.56i) q^{27} +(33.5615 - 4776.35i) q^{28} +(3456.03 - 3456.03i) q^{29} +(-2.80446 + 798.253i) q^{30} +5057.13 q^{31} +(-101.749 + 5791.73i) q^{32} -5871.84 q^{33} +(25.7871 - 7339.95i) q^{34} +(1254.79 - 1254.79i) q^{35} +(22.9589 - 3267.43i) q^{36} +(7891.56 + 7891.56i) q^{37} +(657.562 + 662.198i) q^{38} +7554.00i q^{39} +(-1537.68 + 1505.61i) q^{40} +18454.0i q^{41} +(7111.78 - 7061.98i) q^{42} +(-11241.6 - 11241.6i) q^{43} +(-11114.6 - 11271.9i) q^{44} +(858.380 - 858.380i) q^{45} +(-19966.2 - 70.1461i) q^{46} -2447.40 q^{47} +(-8714.52 + 8472.97i) q^{48} -5472.97 q^{49} +(16878.0 + 59.2968i) q^{50} +(10890.5 - 10890.5i) q^{51} +(-14501.1 + 14298.8i) q^{52} +(7566.16 + 7566.16i) q^{53} +(16442.9 - 16327.8i) q^{54} -5881.14i q^{55} +(27018.3 + 284.776i) q^{56} +1958.16i q^{57} +(19481.5 + 19618.8i) q^{58} +(-4637.07 - 4637.07i) q^{59} +(-4515.52 - 31.7287i) q^{60} +(24740.9 - 24740.9i) q^{61} +(-100.505 + 28607.3i) q^{62} -15241.4 q^{63} +(-32760.7 - 690.679i) q^{64} -7565.96 q^{65} +(116.696 - 33215.9i) q^{66} +(-8651.11 + 8651.11i) q^{67} +(41520.3 + 291.746i) q^{68} +(-29624.3 - 29624.3i) q^{69} +(7073.17 + 7123.04i) q^{70} -15763.6i q^{71} +(18482.8 + 194.811i) q^{72} -25383.0i q^{73} +(-44798.0 + 44484.3i) q^{74} +(25042.4 + 25042.4i) q^{75} +(-3759.00 + 3706.55i) q^{76} +(-52212.7 + 52212.7i) q^{77} +(-42731.6 - 150.127i) q^{78} +37413.3 q^{79} +(-8486.39 - 8728.32i) q^{80} +23810.0 q^{81} +(-104391. - 366.751i) q^{82} +(-24351.5 + 24351.5i) q^{83} +(39807.0 + 40370.4i) q^{84} +(10907.7 + 10907.7i) q^{85} +(63815.4 - 63368.6i) q^{86} +58014.1i q^{87} +(63984.3 - 62649.5i) q^{88} -78890.8i q^{89} +(4838.64 + 4872.76i) q^{90} +(67170.5 + 67170.5i) q^{91} +(793.608 - 112944. i) q^{92} +(-42445.3 + 42445.3i) q^{93} +(48.6392 - 13844.5i) q^{94} -1961.26 q^{95} +(-47756.9 - 49464.9i) q^{96} +155532. q^{97} +(108.769 - 30959.6i) q^{98} +(-35717.9 + 35717.9i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8}+O(q^{10}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8	\( 18 q - 2 q^{2} - 2 q^{3} - 24 q^{4} - 2 q^{5} + 112 q^{6} + 244 q^{8} - 436 q^{10} - 606 q^{11} + 4 q^{12} - 2 q^{13} - 100 q^{14} + 1796 q^{15} - 872 q^{16} - 4 q^{17} - 3138 q^{18} - 2362 q^{19} + 2972 q^{20} + 484 q^{21} + 4420 q^{22} + 8368 q^{24} + 7368 q^{26} + 4216 q^{27} - 7336 q^{28} + 4070 q^{29} - 30444 q^{30} - 11536 q^{31} - 23992 q^{32} - 4 q^{33} - 1740 q^{34} + 8636 q^{35} + 6892 q^{36} - 10650 q^{37} + 53248 q^{38} + 75272 q^{40} + 33400 q^{42} - 15382 q^{43} - 40124 q^{44} + 5762 q^{45} - 92532 q^{46} + 44176 q^{47} - 147992 q^{48} - 14410 q^{49} - 85050 q^{50} - 2748 q^{51} + 91572 q^{52} + 24726 q^{53} + 208672 q^{54} + 191128 q^{56} + 106776 q^{58} - 29734 q^{59} - 154368 q^{60} - 48082 q^{61} - 273872 q^{62} - 12156 q^{63} - 283776 q^{64} + 27684 q^{65} - 153356 q^{66} - 75210 q^{67} + 133712 q^{68} + 22804 q^{69} + 412160 q^{70} + 470244 q^{72} + 147148 q^{74} + 154726 q^{75} - 87468 q^{76} + 41060 q^{77} - 631780 q^{78} - 52864 q^{79} - 554456 q^{80} - 13126 q^{81} - 93216 q^{82} + 227838 q^{83} + 190888 q^{84} - 138652 q^{85} + 470468 q^{86} + 590328 q^{88} + 280152 q^{90} - 231164 q^{91} - 221896 q^{92} + 180688 q^{93} - 460912 q^{94} - 250380 q^{95} - 597328 q^{96} - 4 q^{97} - 444646 q^{98} - 296770 q^{99}+O(q^{100}) \) 18 * q - 2 * q^2 - 2 * q^3 - 24 * q^4 - 2 * q^5 + 112 * q^6 + 244 * q^8 - 436 * q^10 - 606 * q^11 + 4 * q^12 - 2 * q^13 - 100 * q^14 + 1796 * q^15 - 872 * q^16 - 4 * q^17 - 3138 * q^18 - 2362 * q^19 + 2972 * q^20 + 484 * q^21 + 4420 * q^22 + 8368 * q^24 + 7368 * q^26 + 4216 * q^27 - 7336 * q^28 + 4070 * q^29 - 30444 * q^30 - 11536 * q^31 - 23992 * q^32 - 4 * q^33 - 1740 * q^34 + 8636 * q^35 + 6892 * q^36 - 10650 * q^37 + 53248 * q^38 + 75272 * q^40 + 33400 * q^42 - 15382 * q^43 - 40124 * q^44 + 5762 * q^45 - 92532 * q^46 + 44176 * q^47 - 147992 * q^48 - 14410 * q^49 - 85050 * q^50 - 2748 * q^51 + 91572 * q^52 + 24726 * q^53 + 208672 * q^54 + 191128 * q^56 + 106776 * q^58 - 29734 * q^59 - 154368 * q^60 - 48082 * q^61 - 273872 * q^62 - 12156 * q^63 - 283776 * q^64 + 27684 * q^65 - 153356 * q^66 - 75210 * q^67 + 133712 * q^68 + 22804 * q^69 + 412160 * q^70 + 470244 * q^72 + 147148 * q^74 + 154726 * q^75 - 87468 * q^76 + 41060 * q^77 - 631780 * q^78 - 52864 * q^79 - 554456 * q^80 - 13126 * q^81 - 93216 * q^82 + 227838 * q^83 + 190888 * q^84 - 138652 * q^85 + 470468 * q^86 + 590328 * q^88 + 280152 * q^90 - 231164 * q^91 - 221896 * q^92 + 180688 * q^93 - 460912 * q^94 - 250380 * q^95 - 597328 * q^96 - 4 * q^97 - 444646 * q^98 - 296770 * q^99

Introduction

L-functions

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