LMFDB - Embedded newform 74.6.c.b.47.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,6,Mod(47,74)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(74, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([4]))

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

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

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 6);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 6 $
Character orbit:	$[\chi]$	$=$	74.c (of order $3$, 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:	$11.8684026662$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 1317 x^{14} - 2712 x^{13} + 1206654 x^{12} - 2683704 x^{11} + 572597881 x^{10} + \cdots + 683643854869056 $ x^16 + 1317x^14 - 2712x^13 + 1206654x^12 - 2683704x^11 + 572597881x^10 - 1472178324x^9 + 197936317446x^8 - 538366712748x^7 + 33466187997381x^6 - 131063526625884x^5 + 4041550479749833x^4 - 11057529820868736x^3 + 29709621477714456x^2 - 4628457422701056x + 683643854869056
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{10}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			47.7
Root			$-10.0937 - 17.4828i$ of defining polynomial
Character	$\chi$	$=$	74.47
Dual form			74.6.c.b.63.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(9.59367 + 16.6167i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-34.0877 - 59.0415i) q^{5} +76.7494 q^{6} +(-46.0584 - 79.7755i) q^{7} -64.0000 q^{8} +(-62.5771 + 108.387i) q^{9} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(9.59367 + 16.6167i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-34.0877 - 59.0415i) q^{5} +76.7494 q^{6} +(-46.0584 - 79.7755i) q^{7} -64.0000 q^{8} +(-62.5771 + 108.387i) q^{9} -272.701 q^{10} -135.129 q^{11} +(153.499 - 265.868i) q^{12} +(-248.902 - 431.111i) q^{13} -368.467 q^{14} +(654.051 - 1132.85i) q^{15} +(-128.000 + 221.703i) q^{16} +(805.084 - 1394.45i) q^{17} +(250.308 + 433.547i) q^{18} +(-282.003 - 488.443i) q^{19} +(-545.402 + 944.665i) q^{20} +(883.739 - 1530.68i) q^{21} +(-270.258 + 468.101i) q^{22} +641.557 q^{23} +(-613.995 - 1063.47i) q^{24} +(-761.436 + 1318.85i) q^{25} -1991.22 q^{26} +2261.15 q^{27} +(-736.935 + 1276.41i) q^{28} -6836.51 q^{29} +(-2616.21 - 4531.40i) q^{30} -2219.67 q^{31} +(512.000 + 886.810i) q^{32} +(-1296.38 - 2245.40i) q^{33} +(-3220.34 - 5577.78i) q^{34} +(-3140.05 + 5438.72i) q^{35} +2002.47 q^{36} +(-5541.16 + 6216.07i) q^{37} -2256.02 q^{38} +(4775.77 - 8271.88i) q^{39} +(2181.61 + 3778.66i) q^{40} +(4967.35 + 8603.70i) q^{41} +(-3534.96 - 6122.72i) q^{42} +16940.5 q^{43} +(1081.03 + 1872.40i) q^{44} +8532.42 q^{45} +(1283.11 - 2222.42i) q^{46} +16159.1 q^{47} -4911.96 q^{48} +(4160.74 - 7206.62i) q^{49} +(3045.74 + 5275.38i) q^{50} +30894.8 q^{51} +(-3982.43 + 6897.78i) q^{52} +(-11709.9 + 20282.2i) q^{53} +(4522.30 - 7832.85i) q^{54} +(4606.23 + 7978.23i) q^{55} +(2947.74 + 5105.64i) q^{56} +(5410.88 - 9371.92i) q^{57} +(-13673.0 + 23682.4i) q^{58} +(3880.08 - 6720.50i) q^{59} -20929.6 q^{60} +(-19218.7 - 33287.7i) q^{61} +(-4439.34 + 7689.17i) q^{62} +11528.8 q^{63} +4096.00 q^{64} +(-16969.0 + 29391.1i) q^{65} -10371.1 q^{66} +(13402.3 + 23213.5i) q^{67} -25762.7 q^{68} +(6154.88 + 10660.6i) q^{69} +(12560.2 + 21754.9i) q^{70} +(249.453 + 432.066i) q^{71} +(4004.93 - 6936.75i) q^{72} +20636.4 q^{73} +(10450.8 + 31627.3i) q^{74} -29219.9 q^{75} +(-4512.04 + 7815.09i) q^{76} +(6223.83 + 10780.0i) q^{77} +(-19103.1 - 33087.5i) q^{78} +(-20198.9 - 34985.6i) q^{79} +17452.9 q^{80} +(36898.9 + 63910.9i) q^{81} +39738.8 q^{82} +(8271.77 - 14327.1i) q^{83} -28279.6 q^{84} -109774. q^{85} +(33881.0 - 58683.5i) q^{86} +(-65587.3 - 113600. i) q^{87} +8648.26 q^{88} +(7116.04 - 12325.3i) q^{89} +(17064.8 - 29557.2i) q^{90} +(-22928.1 + 39712.6i) q^{91} +(-5132.45 - 8889.67i) q^{92} +(-21294.8 - 36883.7i) q^{93} +(32318.1 - 55976.6i) q^{94} +(-19225.6 + 33299.7i) q^{95} +(-9823.92 + 17015.5i) q^{96} +105497. q^{97} +(-16643.0 - 28826.5i) q^{98} +(8455.98 - 14646.2i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9}+O(q^{10}) $ 16 * q + 32 * q^2 - 8 * q^3 - 128 * q^4 + 70 * q^5 - 64 * q^6 - 32 * q^7 - 1024 * q^8 - 698 * q^9	\( 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9} + 560 q^{10} - 240 q^{11} - 128 q^{12} + 1614 q^{13} - 256 q^{14} + 728 q^{15} - 2048 q^{16} + 216 q^{17} + 2792 q^{18} - 950 q^{19} + 1120 q^{20} + 1718 q^{21} - 480 q^{22} + 1716 q^{23} + 512 q^{24} - 11760 q^{25} + 12912 q^{26} - 92 q^{27} - 512 q^{28} + 1112 q^{29} - 2912 q^{30} - 16816 q^{31} + 8192 q^{32} + 4744 q^{33} - 864 q^{34} - 5004 q^{35} + 22336 q^{36} + 3556 q^{37} - 7600 q^{38} + 17710 q^{39} - 4480 q^{40} - 8080 q^{41} - 6872 q^{42} - 19012 q^{43} + 1920 q^{44} - 58672 q^{45} + 3432 q^{46} + 29392 q^{47} + 4096 q^{48} + 474 q^{49} + 47040 q^{50} - 17856 q^{51} + 25824 q^{52} - 29250 q^{53} - 184 q^{54} + 15772 q^{55} + 2048 q^{56} + 16182 q^{57} + 2224 q^{58} + 61478 q^{59} - 23296 q^{60} - 132002 q^{61} - 33632 q^{62} - 103324 q^{63} + 65536 q^{64} - 37426 q^{65} + 37952 q^{66} - 45658 q^{67} - 6912 q^{68} - 23816 q^{69} + 20016 q^{70} + 13236 q^{71} + 44672 q^{72} + 270632 q^{73} - 81304 q^{74} + 419904 q^{75} - 15200 q^{76} - 184084 q^{77} - 70840 q^{78} + 123974 q^{79} - 35840 q^{80} + 96448 q^{81} - 64640 q^{82} - 16936 q^{83} - 54976 q^{84} - 251316 q^{85} - 38024 q^{86} + 168290 q^{87} + 15360 q^{88} + 52892 q^{89} - 117344 q^{90} - 432546 q^{91} - 13728 q^{92} + 220328 q^{93} + 58784 q^{94} + 47026 q^{95} + 8192 q^{96} - 546140 q^{97} - 1896 q^{98} - 9800 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 - 8 * q^3 - 128 * q^4 + 70 * q^5 - 64 * q^6 - 32 * q^7 - 1024 * q^8 - 698 * q^9 + 560 * q^10 - 240 * q^11 - 128 * q^12 + 1614 * q^13 - 256 * q^14 + 728 * q^15 - 2048 * q^16 + 216 * q^17 + 2792 * q^18 - 950 * q^19 + 1120 * q^20 + 1718 * q^21 - 480 * q^22 + 1716 * q^23 + 512 * q^24 - 11760 * q^25 + 12912 * q^26 - 92 * q^27 - 512 * q^28 + 1112 * q^29 - 2912 * q^30 - 16816 * q^31 + 8192 * q^32 + 4744 * q^33 - 864 * q^34 - 5004 * q^35 + 22336 * q^36 + 3556 * q^37 - 7600 * q^38 + 17710 * q^39 - 4480 * q^40 - 8080 * q^41 - 6872 * q^42 - 19012 * q^43 + 1920 * q^44 - 58672 * q^45 + 3432 * q^46 + 29392 * q^47 + 4096 * q^48 + 474 * q^49 + 47040 * q^50 - 17856 * q^51 + 25824 * q^52 - 29250 * q^53 - 184 * q^54 + 15772 * q^55 + 2048 * q^56 + 16182 * q^57 + 2224 * q^58 + 61478 * q^59 - 23296 * q^60 - 132002 * q^61 - 33632 * q^62 - 103324 * q^63 + 65536 * q^64 - 37426 * q^65 + 37952 * q^66 - 45658 * q^67 - 6912 * q^68 - 23816 * q^69 + 20016 * q^70 + 13236 * q^71 + 44672 * q^72 + 270632 * q^73 - 81304 * q^74 + 419904 * q^75 - 15200 * q^76 - 184084 * q^77 - 70840 * q^78 + 123974 * q^79 - 35840 * q^80 + 96448 * q^81 - 64640 * q^82 - 16936 * q^83 - 54976 * q^84 - 251316 * q^85 - 38024 * q^86 + 168290 * q^87 + 15360 * q^88 + 52892 * q^89 - 117344 * q^90 - 432546 * q^91 - 13728 * q^92 + 220328 * q^93 + 58784 * q^94 + 47026 * q^95 + 8192 * q^96 - 546140 * q^97 - 1896 * q^98 - 9800 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/74\mathbb{Z}\right)^\times$.

$n$	$39$
$\chi(n)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$2$	2.00000	−	3.46410i	0.353553	−	0.612372i
$3$	9.59367	+	16.6167i	0.615434	+	1.06596i	0.990308	+	0.138888i	$0.0443527\pi$
$3$	9.59367	+	16.6167i	0.615434	+	1.06596i	−0.374874	+	0.927076i	$0.622314\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	−34.0877	−	59.0415i	−0.609778	−	1.05617i	−0.991277	−	0.131798i	$-0.957925\pi$
$5$	−34.0877	−	59.0415i	−0.609778	−	1.05617i	0.381498	−	0.924370i	$-0.375408\pi$
$6$	76.7494			0.870356
$7$	−46.0584	−	79.7755i	−0.355275	−	0.615354i	0.631890	−	0.775058i	$-0.282279\pi$
$7$	−46.0584	−	79.7755i	−0.355275	−	0.615354i	−0.987165	+	0.159704i	$0.948946\pi$
$8$	−64.0000			−0.353553
$9$	−62.5771	+	108.387i	−0.257519	+	0.446036i
$10$	−272.701			−0.862357
$11$	−135.129			−0.336718			−0.168359	−	0.985726i	$-0.553847\pi$
$11$	−135.129			−0.336718			−0.168359	+	0.985726i	$0.553847\pi$
$12$	153.499	−	265.868i	0.307717	−	0.532982i
$13$	−248.902	−	431.111i	−0.408479	−	0.707507i	0.586240	−	0.810137i	$-0.300608\pi$
$13$	−248.902	−	431.111i	−0.408479	−	0.707507i	−0.994720	+	0.102630i	$0.967274\pi$
$14$	−368.467			−0.502434
$15$	654.051	−	1132.85i	0.750557	−	1.30000i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	805.084	−	1394.45i	0.675645	−	1.17025i	−0.300634	−	0.953739i	$-0.597198\pi$
$17$	805.084	−	1394.45i	0.675645	−	1.17025i	0.976280	−	0.216513i	$-0.0694683\pi$
$18$	250.308	+	433.547i	0.182093	+	0.315395i
$19$	−282.003	−	488.443i	−0.179213	−	0.310406i	0.762398	−	0.647108i	$-0.224022\pi$
$19$	−282.003	−	488.443i	−0.179213	−	0.310406i	−0.941611	+	0.336702i	$0.890688\pi$
$20$	−545.402	+	944.665i	−0.304889	+	0.528084i
$21$	883.739	−	1530.68i	0.437296	−	0.757419i
$22$	−270.258	+	468.101i	−0.119048	+	0.206197i
$23$	641.557			0.252881			0.126440	−	0.991974i	$-0.459645\pi$
$23$	641.557			0.252881			0.126440	+	0.991974i	$0.459645\pi$
$24$	−613.995	−	1063.47i	−0.217589	−	0.376875i
$25$	−761.436	+	1318.85i	−0.243659	+	0.422031i
$26$	−1991.22			−0.577677
$27$	2261.15			0.596925
$28$	−736.935	+	1276.41i	−0.177637	+	0.307677i
$29$	−6836.51			−1.50952			−0.754761	−	0.655999i	$-0.772247\pi$
$29$	−6836.51			−1.50952			−0.754761	+	0.655999i	$0.772247\pi$
$30$	−2616.21	−	4531.40i	−0.530724	−	0.919241i
$31$	−2219.67			−0.414844			−0.207422	−	0.978252i	$-0.566507\pi$
$31$	−2219.67			−0.414844			−0.207422	+	0.978252i	$0.566507\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	−1296.38	−	2245.40i	−0.207228	−	0.358930i
$34$	−3220.34	−	5577.78i	−0.477753	−	0.827493i
$35$	−3140.05	+	5438.72i	−0.433277	+	0.750459i
$36$	2002.47			0.257519
$37$	−5541.16	+	6216.07i	−0.665421	+	0.746468i
$37$	−5541.16	+	6216.07i	−0.665421	+	0.746468i
$38$	−2256.02			−0.253445
$39$	4775.77	−	8271.88i	0.502785	−	0.870848i
$40$	2181.61	+	3778.66i	0.215589	+	0.373412i
$41$	4967.35	+	8603.70i	0.461493	+	0.799329i	0.999036	−	0.0439072i	$-0.0139806\pi$
$41$	4967.35	+	8603.70i	0.461493	+	0.799329i	−0.537543	+	0.843237i	$0.680647\pi$
$42$	−3534.96	−	6122.72i	−0.309215	−	0.535576i
$43$	16940.5			1.39719			0.698593	−	0.715519i	$-0.253810\pi$
$43$	16940.5			1.39719			0.698593	+	0.715519i	$0.253810\pi$
$44$	1081.03	+	1872.40i	0.0841796	+	0.145803i
$45$	8532.42			0.628118
$46$	1283.11	−	2222.42i	0.0894068	−	0.154857i
$47$	16159.1			1.06702			0.533509	−	0.845795i	$-0.320873\pi$
$47$	16159.1			1.06702			0.533509	+	0.845795i	$0.320873\pi$
$48$	−4911.96			−0.307717
$49$	4160.74	−	7206.62i	0.247560	−	0.428787i
$50$	3045.74	+	5275.38i	0.172293	+	0.298421i
$51$	30894.8			1.66326
$52$	−3982.43	+	6897.78i	−0.204240	+	0.353754i
$53$	−11709.9	+	20282.2i	−0.572617	+	0.991802i	0.423679	+	0.905812i	$0.360738\pi$
$53$	−11709.9	+	20282.2i	−0.572617	+	0.991802i	−0.996296	+	0.0859893i	$0.972595\pi$
$54$	4522.30	−	7832.85i	0.211045	−	0.365540i
$55$	4606.23	+	7978.23i	0.205324	+	0.355631i
$56$	2947.74	+	5105.64i	0.125609	+	0.217560i
$57$	5410.88	−	9371.92i	0.220587	−	0.382069i
$58$	−13673.0	+	23682.4i	−0.533697	+	0.924390i
$59$	3880.08	−	6720.50i	0.145114	−	0.251346i	−0.784301	−	0.620380i	$-0.786978\pi$
$59$	3880.08	−	6720.50i	0.145114	−	0.251346i	0.929416	+	0.369035i	$0.120312\pi$
$60$	−20929.6			−0.750557
$61$	−19218.7	−	33287.7i	−0.661300	−	1.14541i	−0.980274	−	0.197642i	$-0.936672\pi$
$61$	−19218.7	−	33287.7i	−0.661300	−	1.14541i	0.318974	−	0.947763i	$-0.396662\pi$
$62$	−4439.34	+	7689.17i	−0.146669	+	0.254039i
$63$	11528.8			0.365960
$64$	4096.00			0.125000
$65$	−16969.0	+	29391.1i	−0.498164	+	0.862845i
$66$	−10371.1			−0.293065
$67$	13402.3	+	23213.5i	0.364748	+	0.631762i	0.988736	−	0.149672i	$-0.0478219\pi$
$67$	13402.3	+	23213.5i	0.364748	+	0.631762i	−0.623988	+	0.781434i	$0.714489\pi$
$68$	−25762.7			−0.675645
$69$	6154.88	+	10660.6i	0.155631	+	0.269561i
$70$	12560.2	+	21754.9i	0.306373	+	0.530654i
$71$	249.453	+	432.066i	0.00587278	+	0.0101720i	0.868947	−	0.494905i	$-0.164797\pi$
$71$	249.453	+	432.066i	0.00587278	+	0.0101720i	−0.863074	+	0.505077i	$0.831464\pi$
$72$	4004.93	−	6936.75i	0.0910467	−	0.157697i
$73$	20636.4			0.453238			0.226619	−	0.973983i	$-0.427233\pi$
$73$	20636.4			0.453238			0.226619	+	0.973983i	$0.427233\pi$
$74$	10450.8	+	31627.3i	0.221855	+	0.671402i
$75$	−29219.9			−0.599826
$76$	−4512.04	+	7815.09i	−0.0896064	+	0.155203i
$77$	6223.83	+	10780.0i	0.119627	+	0.207201i
$78$	−19103.1	−	33087.5i	−0.355522	−	0.615783i
$79$	−20198.9	−	34985.6i	−0.364134	−	0.630698i	0.624503	−	0.781022i	$-0.285302\pi$
$79$	−20198.9	−	34985.6i	−0.364134	−	0.630698i	−0.988637	+	0.150324i	$0.951968\pi$
$80$	17452.9			0.304889
$81$	36898.9	+	63910.9i	0.624887	+	1.08234i
$82$	39738.8			0.652650
$83$	8271.77	−	14327.1i	0.131796	−	0.228278i	−0.792573	−	0.609777i	$-0.791259\pi$
$83$	8271.77	−	14327.1i	0.131796	−	0.228278i	0.924369	+	0.381499i	$0.124592\pi$
$84$	−28279.6			−0.437296
$85$	−109774.			−1.64798
$86$	33881.0	−	58683.5i	0.493980	−	0.855599i
$87$	−65587.3	−	113600.i	−0.929012	−	1.60910i
$88$	8648.26			0.119048
$89$	7116.04	−	12325.3i	0.0952277	−	0.164939i	−0.814476	−	0.580197i	$-0.802975\pi$
$89$	7116.04	−	12325.3i	0.0952277	−	0.164939i	0.909704	+	0.415258i	$0.136309\pi$
$90$	17064.8	−	29557.2i	0.222073	−	0.384642i
$91$	−22928.1	+	39712.6i	−0.290245	+	0.502719i
$92$	−5132.45	−	8889.67i	−0.0632201	−	0.109500i
$93$	−21294.8	−	36883.7i	−0.255309	−	0.442208i
$94$	32318.1	−	55976.6i	0.377248	−	0.653412i
$95$	−19225.6	+	33299.7i	−0.218560	+	0.378558i
$96$	−9823.92	+	17015.5i	−0.108794	+	0.188438i
$97$	105497.			1.13844			0.569220	−	0.822185i	$-0.307245\pi$
$97$	105497.			1.13844			0.569220	+	0.822185i	$0.307245\pi$
$98$	−16643.0	−	28826.5i	−0.175051	−	0.303198i
$99$	8455.98	−	14646.2i	0.0867113	−	0.150188i
$100$	24365.9			0.243659
$101$	111937.			1.09187			0.545936	−	0.837827i	$-0.316174\pi$
$101$	111937.			1.09187			0.545936	+	0.837827i	$0.316174\pi$
$102$	61789.7	−	107023.i	0.588052	−	1.01854i
$103$	−104161.			−0.967417			−0.483709	−	0.875229i	$-0.660711\pi$
$103$	−104161.			−0.967417			−0.483709	+	0.875229i	$0.660711\pi$
$104$	15929.7	+	27591.1i	0.144419	+	0.250142i
$105$	−120498.			−1.06662
$106$	46839.7	+	81128.7i	0.404901	+	0.701310i
$107$	−19987.4	−	34619.2i	−0.168771	−	0.292320i	0.769217	−	0.638988i	$-0.220646\pi$
$107$	−19987.4	−	34619.2i	−0.168771	−	0.292320i	−0.937988	+	0.346668i	$0.887313\pi$
$108$	−18089.2	−	31331.4i	−0.149231	−	0.258476i
$109$	92078.9	−	159485.i	0.742324	−	1.28574i	−0.209110	−	0.977892i	$-0.567057\pi$
$109$	92078.9	−	159485.i	0.742324	−	1.28574i	0.951434	−	0.307851i	$-0.0996100\pi$
$110$	36849.8			0.290371
$111$	−156451.	−	32441.0i	−1.20523	−	0.249912i
$112$	23581.9			0.177637
$113$	−20231.4	+	35041.8i	−0.149049	+	0.258161i	−0.930876	−	0.365335i	$-0.880955\pi$
$113$	−20231.4	+	35041.8i	−0.149049	+	0.258161i	0.781827	+	0.623495i	$0.214288\pi$
$114$	−21643.5	−	37487.7i	−0.155979	−	0.270163i
$115$	−21869.2	−	37878.5i	−0.154201	−	0.267084i
$116$	54692.1	+	94729.5i	0.377381	+	0.653643i
$117$	62302.3			0.420765
$118$	−15520.3	−	26882.0i	−0.102611	−	0.177728i
$119$	−148324.			−0.960158
$120$	−41859.3	+	72502.4i	−0.265362	+	0.459621i
$121$	−142791.			−0.886621
$122$	−153749.			−0.935220
$123$	−95310.3	+	165082.i	−0.568037	+	0.983870i
$124$	17757.4	+	30756.7i	0.103711	+	0.179633i
$125$	−109226.			−0.625244
$126$	23057.6	−	39937.0i	0.129386	−	0.224104i
$127$	137936.	−	238912.i	0.758870	−	1.31440i	−0.184557	−	0.982822i	$-0.559085\pi$
$127$	137936.	−	238912.i	0.758870	−	1.31440i	0.943427	−	0.331580i	$-0.107582\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	162521.	+	281495.i	0.859877	+	1.48935i
$130$	67875.9	+	117565.i	0.352255	+	0.610124i
$131$	−28664.3	+	49647.9i	−0.145936	+	0.252769i	−0.929722	−	0.368263i	$-0.879953\pi$
$131$	−28664.3	+	49647.9i	−0.145936	+	0.252769i	0.783786	+	0.621031i	$0.213286\pi$
$132$	−20742.1	+	35926.4i	−0.103614	+	0.179465i
$133$	−25977.2	+	44993.8i	−0.127340	+	0.220559i
$134$	107218.			0.515831
$135$	−77077.2	−	133502.i	−0.363992	−	0.630453i
$136$	−51525.4	+	89244.6i	−0.238877	+	0.413747i
$137$	−8353.45			−0.0380246			−0.0190123	−	0.999819i	$-0.506052\pi$
$137$	−8353.45			−0.0380246			−0.0190123	+	0.999819i	$0.506052\pi$
$138$	49239.1			0.220096
$139$	101709.	−	176165.i	0.446500	−	0.773361i	−0.551655	−	0.834072i	$-0.686004\pi$
$139$	101709.	−	176165.i	0.446500	−	0.773361i	0.998155	+	0.0607115i	$0.0193370\pi$
$140$	100482.			0.433277
$141$	155025.	+	268511.i	0.656679	+	1.13740i
$142$	1995.63			0.00830536
$143$	33633.9	+	58255.6i	0.137543	+	0.238231i
$144$	−16019.7	−	27747.0i	−0.0643797	−	0.111509i
$145$	233041.	+	403638.i	0.920474	+	1.59431i
$146$	41272.8	−	71486.6i	0.160244	−	0.277551i
$147$	159667.			0.609428
$148$	130462.	+	27052.0i	0.489586	+	0.101519i
$149$	68586.1			0.253087			0.126544	−	0.991961i	$-0.459612\pi$
$149$	68586.1			0.253087			0.126544	+	0.991961i	$0.459612\pi$
$150$	−58439.7	+	101221.i	−0.212070	+	0.367317i
$151$	203821.	+	353028.i	0.727456	+	1.25999i	0.957955	+	0.286918i	$0.0926308\pi$
$151$	203821.	+	353028.i	0.727456	+	1.25999i	−0.230499	+	0.973073i	$0.574036\pi$
$152$	18048.2	+	31260.3i	0.0633613	+	0.109745i
$153$	100760.	+	174521.i	0.347983	+	0.602724i
$154$	49790.6			0.169179
$155$	75663.4	+	131053.i	0.252963	+	0.438144i
$156$	−152825.			−0.502785
$157$	240578.	−	416693.i	0.778945	−	1.34917i	−0.153606	−	0.988132i	$-0.549089\pi$
$157$	240578.	−	416693.i	0.778945	−	1.34917i	0.932551	−	0.361040i	$-0.117578\pi$
$158$	−161592.			−0.514963
$159$	−449364.			−1.40963
$160$	34905.8	−	60458.5i	0.107795	−	0.186706i
$161$	−29549.1	−	51180.5i	−0.0898420	−	0.155611i
$162$	295192.			0.883724
$163$	168248.	−	291414.i	0.495999	−	0.859096i	−0.503990	−	0.863709i	$-0.668135\pi$
$163$	168248.	−	291414.i	0.495999	−	0.859096i	0.999989	+	0.00461345i	$0.00146851\pi$
$164$	79477.6	−	137659.i	0.230747	−	0.399665i
$165$	−88381.3	+	153081.i	−0.252726	+	0.437735i
$166$	−33087.1	−	57308.5i	−0.0931941	−	0.161417i
$167$	−272417.	−	471840.i	−0.755862	−	1.30919i	−0.944944	−	0.327231i	$-0.893885\pi$
$167$	−272417.	−	471840.i	−0.755862	−	1.30919i	0.189082	−	0.981961i	$-0.439449\pi$
$168$	−56559.3	+	97963.6i	−0.154608	+	0.267788i
$169$	61742.0	−	106940.i	0.166289	−	0.288021i
$170$	−219547.	+	380267.i	−0.582648	+	1.00918i
$171$	70587.6			0.184603
$172$	−135524.	−	234734.i	−0.349297	−	0.605000i
$173$	−354935.	+	614766.i	−0.901641	+	1.56169i	−0.0762777	+	0.997087i	$0.524304\pi$
$173$	−354935.	+	614766.i	−0.901641	+	1.56169i	−0.825363	+	0.564602i	$0.809030\pi$
$174$	−524698.			−1.31382
$175$	140282.			0.346264
$176$	17296.5	−	29958.4i	0.0420898	−	0.0729017i
$177$	148897.			0.357234
$178$	−28464.2	−	49301.4i	−0.0673362	−	0.116630i
$179$	−659371.			−1.53814			−0.769072	−	0.639162i	$-0.779281\pi$
$179$	−659371.			−1.53814			−0.769072	+	0.639162i	$0.779281\pi$
$180$	−68259.4	−	118229.i	−0.157029	−	0.271983i
$181$	−243011.	−	420908.i	−0.551353	−	0.954972i	−0.998177	−	0.0603502i	$-0.980778\pi$
$181$	−243011.	−	420908.i	−0.551353	−	0.954972i	0.446824	−	0.894622i	$-0.352555\pi$
$182$	91712.3	+	158850.i	0.205234	+	0.355476i
$183$	368755.	−	638703.i	0.813974	−	1.40984i
$184$	−41059.6			−0.0894068
$185$	555891.	+	115267.i	1.19415	+	0.247615i
$186$	−170358.			−0.361061
$187$	−108790.	+	188430.i	−0.227502	+	0.394045i
$188$	−129272.	−	223907.i	−0.266754	−	0.462032i
$189$	−104145.	−	180384.i	−0.212072	−	0.367320i
$190$	76902.5	+	133199.i	0.154545	+	0.267681i
$191$	215498.			0.427425			0.213713	−	0.976897i	$-0.431444\pi$
$191$	215498.			0.427425			0.213713	+	0.976897i	$0.431444\pi$
$192$	39295.7	+	68062.1i	0.0769293	+	0.133245i
$193$	768952.			1.48596			0.742978	−	0.669316i	$-0.233413\pi$
$193$	768952.			1.48596			0.742978	+	0.669316i	$0.233413\pi$
$194$	210994.	−	365452.i	0.402500	−	0.697150i
$195$	−651179.			−1.22635
$196$	−133144.			−0.247560
$197$	81865.7	−	141796.i	0.150292	−	0.260314i	−0.781043	−	0.624478i	$-0.785312\pi$
$197$	81865.7	−	141796.i	0.150292	−	0.260314i	0.931335	+	0.364164i	$0.118645\pi$
$198$	−33823.9	−	58584.7i	−0.0613142	−	0.106199i
$199$	320656.			0.573993			0.286996	−	0.957932i	$-0.407343\pi$
$199$	320656.			0.573993			0.286996	+	0.957932i	$0.407343\pi$
$200$	48731.9	−	84406.1i	0.0861466	−	0.149210i
$201$	−257155.	+	445405.i	−0.448957	+	0.777616i
$202$	223875.	−	387762.i	0.386035	−	0.668632i
$203$	314879.	+	545387.i	0.536295	+	0.928890i
$204$	−247159.	−	428092.i	−0.415815	−	0.720213i
$205$	338651.	−	586560.i	0.562817	−	0.974828i
$206$	−208323.	+	360826.i	−0.342034	+	0.592420i
$207$	−40146.7	+	69536.2i	−0.0651215	+	0.112794i
$208$	127438.			0.204240
$209$	38106.7	+	66002.8i	0.0603443	+	0.104519i
$210$	−240997.	+	417419.i	−0.377105	+	0.653166i
$211$	−229146.			−0.354328			−0.177164	−	0.984181i	$-0.556692\pi$
$211$	−229146.			−0.354328			−0.177164	+	0.984181i	$0.556692\pi$
$212$	374717.			0.572617
$213$	−4786.35	+	8290.20i	−0.00722862	+	0.0125203i
$214$	−159899.			−0.238678
$215$	−577461.	−	1.00019e6i	−0.851974	−	1.47566i
$216$	−144714.			−0.211045
$217$	102235.	+	177075.i	0.147383	+	0.255275i
$218$	−368315.	−	637941.i	−0.524903	−	0.909158i
$219$	197979.	+	342909.i	0.278938	+	0.483136i
$220$	73699.7	−	127652.i	0.102662	−	0.177815i
$221$	−801548.			−1.10395
$222$	−425281.	+	477079.i	−0.579153	+	0.649693i
$223$	653709.			0.880284			0.440142	−	0.897928i	$-0.354928\pi$
$223$	653709.			0.880284			0.440142	+	0.897928i	$0.354928\pi$
$224$	47163.8	−	81690.2i	0.0628043	−	0.108780i
$225$	−95296.9	−	165059.i	−0.125494	−	0.217362i
$226$	80925.6	+	140167.i	0.105394	+	0.182547i
$227$	−591449.	−	1.02442e6i	−0.761820	−	1.31951i	−0.941911	−	0.335862i	$-0.890973\pi$
$227$	−591449.	−	1.02442e6i	−0.761820	−	1.31951i	0.180091	−	0.983650i	$-0.442361\pi$
$228$	−173148.			−0.220587
$229$	661469.	+	1.14570e6i	0.833529	+	1.44372i	0.895222	+	0.445620i	$0.147017\pi$
$229$	661469.	+	1.14570e6i	0.833529	+	1.44372i	−0.0616927	+	0.998095i	$0.519650\pi$
$230$	−174953.			−0.218073
$231$	−119419.	+	206839.i	−0.147246	+	0.255037i
$232$	437537.			0.533697
$233$	−621676.			−0.750195			−0.375098	−	0.926985i	$-0.622391\pi$
$233$	−621676.			−0.750195			−0.375098	+	0.926985i	$0.622391\pi$
$234$	124605.	−	215821.i	0.148763	−	0.257665i
$235$	−550824.	−	954056.i	−0.650644	−	1.12695i
$236$	−124163.			−0.145114
$237$	387564.	−	671281.i	0.448201	−	0.776307i
$238$	−296647.	+	513808.i	−0.339467	+	0.587975i
$239$	291684.	−	505212.i	0.330307	−	0.572109i	−0.652265	−	0.757991i	$-0.726181\pi$
$239$	291684.	−	505212.i	0.330307	−	0.572109i	0.982572	+	0.185882i	$0.0595143\pi$
$240$	167437.	+	290010.i	0.187639	+	0.325001i
$241$	774228.	+	1.34100e6i	0.858670	+	1.48726i	0.873198	+	0.487366i	$0.162042\pi$
$241$	774228.	+	1.34100e6i	0.858670	+	1.48726i	−0.0145279	+	0.999894i	$0.504625\pi$
$242$	−285582.	+	494643.i	−0.313468	+	0.542942i
$243$	−433263.	+	750434.i	−0.470691	+	0.815261i
$244$	−307499.	+	532603.i	−0.330650	+	0.572703i
$245$	−567320.			−0.603827
$246$	381241.	+	660329.i	0.401663	+	0.695701i
$247$	−140382.	+	243149.i	−0.146410	+	0.253589i
$248$	142059.			0.146669
$249$	317427.			0.324448
$250$	−218451.	+	378369.i	−0.221057	+	0.382882i
$251$	1.49609e6			1.49890			0.749451	−	0.662060i	$-0.230318\pi$
$251$	1.49609e6			1.49890			0.749451	+	0.662060i	$0.230318\pi$
$252$	−92230.5	−	159748.i	−0.0914899	−	0.158465i
$253$	−86692.9			−0.0851495
$254$	−551743.	−	955647.i	−0.536602	−	0.929422i
$255$	−1.05313e6	−	1.82408e6i	−1.01422	−	1.75668i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−296162.	+	512968.i	−0.279703	+	0.484459i	−0.971311	−	0.237814i	$-0.923569\pi$
$257$	−296162.	+	512968.i	−0.279703	+	0.484459i	0.691608	+	0.722273i	$0.256903\pi$
$258$	1.30017e6			1.21605
$259$	751107.	+	155747.i	0.695749	+	0.144268i
$260$	543007.			0.498164
$261$	427809.	−	740987.i	0.388731	−	0.673301i
$262$	114657.	+	198592.i	0.103192	+	0.178734i
$263$	−16889.5	−	29253.5i	−0.0150566	−	0.0260788i	0.858399	−	0.512983i	$-0.171460\pi$
$263$	−16889.5	−	29253.5i	−0.0150566	−	0.0260788i	−0.873456	+	0.486904i	$0.838126\pi$
$264$	82968.5	+	143706.i	0.0732662	+	0.126901i
$265$	1.59665e6			1.39668
$266$	103909.	+	179975.i	0.0900426	+	0.155958i
$267$	273076.			0.234426
$268$	214437.	−	371416.i	0.182374	−	0.315881i
$269$	−1.05684e6			−0.890491			−0.445246	−	0.895408i	$-0.646884\pi$
$269$	−1.05684e6			−0.890491			−0.445246	+	0.895408i	$0.646884\pi$
$270$	−616618.			−0.514762
$271$	−1.03758e6	+	1.79714e6i	−0.858218	+	1.48648i	0.0154098	+	0.999881i	$0.495095\pi$
$271$	−1.03758e6	+	1.79714e6i	−0.858218	+	1.48648i	−0.873627	+	0.486595i	$0.838239\pi$
$272$	206101.	+	356978.i	0.168911	+	0.292563i
$273$	−879858.			−0.714506
$274$	−16706.9	+	28937.2i	−0.0134437	+	0.0232852i
$275$	102892.	−	178214.i	0.0820446	−	0.142105i
$276$	98478.1	−	170569.i	0.0778157	−	0.134781i
$277$	606916.	+	1.05121e6i	0.475257	+	0.823170i	0.999598	−	0.0283384i	$-0.00902159\pi$
$277$	606916.	+	1.05121e6i	0.475257	+	0.823170i	−0.524341	+	0.851508i	$0.675688\pi$
$278$	−406835.	−	704659.i	−0.315723	−	0.546849i
$279$	138901.	−	240583.i	0.106830	−	0.185035i
$280$	200963.	−	348078.i	0.153187	−	0.265327i
$281$	−166013.	+	287542.i	−0.125423	+	0.217238i	−0.921898	−	0.387433i	$-0.873362\pi$
$281$	−166013.	+	287542.i	−0.125423	+	0.217238i	0.796476	+	0.604671i	$0.206695\pi$
$282$	1.24020e6			0.928685
$283$	526144.	+	911308.i	0.390516	+	0.676393i	0.992518	−	0.122102i	$-0.0389634\pi$
$283$	526144.	+	911308.i	0.390516	+	0.676393i	−0.602002	+	0.798495i	$0.705630\pi$
$284$	3991.26	−	6913.06i	0.00293639	−	0.00508598i
$285$	−737777.			−0.538038
$286$	269071.			0.194515
$287$	457577.	−	792546.i	0.327913	−	0.567963i
$288$	−128158.			−0.0910467
$289$	−586392.	−	1.01566e6i	−0.412993	−	0.715326i
$290$	1.86433e6			1.30175
$291$	1.01210e6	+	1.75301e6i	0.700636	+	1.21354i
$292$	−165091.	−	285946.i	−0.113310	−	0.196258i
$293$	653270.	+	1.13150e6i	0.444553	+	0.769989i	0.998021	−	0.0628818i	$-0.0200291\pi$
$293$	653270.	+	1.13150e6i	0.444553	+	0.769989i	−0.553468	+	0.832871i	$0.686696\pi$
$294$	319334.	−	553103.i	0.215465	−	0.373197i
$295$	−529051.			−0.353951
$296$	354634.	−	397828.i	0.235262	−	0.263916i
$297$	−305547.			−0.200996
$298$	137172.	−	237589.i	0.0894799	−	0.154984i
$299$	−159685.	−	276582.i	−0.103296	−	0.178915i
$300$	233759.	+	404882.i	0.149956	+	0.259732i
$301$	−780252.	−	1.35144e6i	−0.496385	−	0.859764i
$302$	1.63057e6			1.02878
$303$	1.07389e6	+	1.86003e6i	0.671975	+	1.16390i
$304$	144385.			0.0896064
$305$	−1.31024e6	+	2.26940e6i	−0.806493	+	1.39689i
$306$	806077.			0.492122
$307$	−1.33989e6			−0.811377			−0.405688	−	0.914011i	$-0.632968\pi$
$307$	−1.33989e6			−0.811377			−0.405688	+	0.914011i	$0.632968\pi$
$308$	99581.3	−	172480.i	0.0598137	−	0.103600i
$309$	−999291.	−	1.73082e6i	−0.595382	−	1.03123i
$310$	605307.			0.357743
$311$	−1.51024e6	+	2.61581e6i	−0.885411	+	1.53358i	−0.0401682	+	0.999193i	$0.512789\pi$
$311$	−1.51024e6	+	2.61581e6i	−0.885411	+	1.53358i	−0.845242	+	0.534383i	$0.820544\pi$
$312$	−305649.	+	529400.i	−0.177761	+	0.307891i
$313$	−233083.	+	403711.i	−0.134477	+	0.232921i	−0.925398	−	0.378998i	$-0.876269\pi$
$313$	−233083.	+	403711.i	−0.134477	+	0.232921i	0.790920	+	0.611919i	$0.209602\pi$
$314$	−962312.	−	1.66677e6i	−0.550797	−	0.954008i
$315$	−392990.	−	680679.i	−0.223154	−	0.386514i
$316$	−323183.	+	559770.i	−0.182067	+	0.315349i
$317$	−1.34279e6	+	2.32578e6i	−0.750515	+	1.29993i	0.197059	+	0.980392i	$0.436861\pi$
$317$	−1.34279e6	+	2.32578e6i	−0.750515	+	1.29993i	−0.947573	+	0.319538i	$0.896472\pi$
$318$	−898729.	+	1.55664e6i	−0.498380	+	0.863220i
$319$	923811.			0.508284
$320$	−139623.	−	241834.i	−0.0762223	−	0.132021i
$321$	383506.	−	664251.i	0.207735	−	0.359807i
$322$	−236393.			−0.127056
$323$	−908143.			−0.484337
$324$	590383.	−	1.02257e6i	0.312443	−	0.541168i
$325$	758092.			0.398120
$326$	−672992.	−	1.16566e6i	−0.350724	−	0.607473i
$327$	3.53350e6			1.82741
$328$	−317910.	−	550637.i	−0.163162	−	0.282606i
$329$	−744261.	−	1.28910e6i	−0.379084	−	0.656593i
$330$	353525.	+	612324.i	0.178705	+	0.309525i
$331$	1.78627e6	−	3.09390e6i	0.896141	−	1.55216i	0.0637538	−	0.997966i	$-0.479693\pi$
$331$	1.78627e6	−	3.09390e6i	0.896141	−	1.55216i	0.832387	−	0.554195i	$-0.186974\pi$
$332$	−264697.			−0.131796
$333$	−326989.	−	989571.i	−0.161593	−	0.489031i
$334$	−2.17933e6			−1.06895
$335$	913707.	−	1.58259e6i	0.444831	−	0.770469i
$336$	226237.	+	391854.i	0.109324	+	0.189355i
$337$	−1.22083e6	−	2.11454e6i	−0.585571	−	1.01424i	−0.994804	−	0.101809i	$-0.967537\pi$
$337$	−1.22083e6	−	2.11454e6i	−0.585571	−	1.01424i	0.409233	−	0.912430i	$-0.365796\pi$
$338$	−246968.	−	427761.i	−0.117584	−	0.203662i
$339$	−776373.			−0.366920
$340$	878189.	+	1.52107e6i	0.411994	+	0.713595i
$341$	299942.			0.139685
$342$	141175.	−	244523.i	0.0652669	−	0.113046i
$343$	−2.31476e6			−1.06236
$344$	−1.08419e6			−0.493980
$345$	419611.	−	726788.i	0.189801	−	0.328745i
$346$	1.41974e6	+	2.45906e6i	0.637557	+	1.10428i
$347$	−3.51007e6			−1.56492			−0.782461	−	0.622700i	$-0.786036\pi$
$347$	−3.51007e6			−1.56492			−0.782461	+	0.622700i	$0.786036\pi$
$348$	−1.04940e6	+	1.81761e6i	−0.464506	+	0.804548i
$349$	−221108.	+	382970.i	−0.0971719	+	0.168307i	−0.910513	−	0.413481i	$-0.864313\pi$
$349$	−221108.	+	382970.i	−0.0971719	+	0.168307i	0.813341	+	0.581787i	$0.197646\pi$
$350$	280564.	−	485952.i	0.122423	−	0.212043i
$351$	−562805.	−	974806.i	−0.243832	−	0.422329i
$352$	−69186.1	−	119834.i	−0.0297620	−	0.0515493i
$353$	−1.29526e6	+	2.24345e6i	−0.553247	+	0.958252i	0.444791	+	0.895635i	$0.353278\pi$
$353$	−1.29526e6	+	2.24345e6i	−0.553247	+	0.958252i	−0.998038	+	0.0626173i	$0.980055\pi$
$354$	297794.	−	515794.i	0.126301	−	0.218760i
$355$	17006.6	−	29456.2i	0.00716219	−	0.0124053i
$356$	−227713.			−0.0952277
$357$	−1.42297e6	−	2.46465e6i	−0.590914	−	1.02349i
$358$	−1.31874e6	+	2.28413e6i	−0.543816	+	0.941917i
$359$	4.23612e6			1.73473			0.867366	−	0.497671i	$-0.165811\pi$
$359$	4.23612e6			1.73473			0.867366	+	0.497671i	$0.165811\pi$
$360$	−546075.			−0.222073
$361$	1.07900e6	−	1.86888e6i	0.435766	−	0.754768i
$362$	−1.94409e6			−0.779732
$363$	−1.36989e6	−	2.37272e6i	−0.545657	−	0.945105i
$364$	733699.			0.290245
$365$	−703446.	−	1.21840e6i	−0.276375	−	0.478696i
$366$	−1.47502e6	−	2.55481e6i	−0.575566	−	0.996910i
$367$	796993.	+	1.38043e6i	0.308880	+	0.534995i	0.978118	−	0.208053i	$-0.0667126\pi$
$367$	796993.	+	1.38043e6i	0.308880	+	0.534995i	−0.669238	+	0.743048i	$0.733379\pi$
$368$	−82119.2	+	142235.i	−0.0316101	+	0.0547502i
$369$	−1.24337e6			−0.475373
$370$	1.51108e6	−	1.69513e6i	0.573830	−	0.643722i
$371$	2.15736e6			0.813745
$372$	−340717.	+	590139.i	−0.127655	+	0.221104i
$373$	−2.58028e6	−	4.46918e6i	−0.960274	−	1.66324i	−0.721809	−	0.692092i	$-0.756689\pi$
$373$	−2.58028e6	−	4.46918e6i	−0.960274	−	1.66324i	−0.238464	−	0.971151i	$-0.576644\pi$
$374$	435161.	+	753721.i	0.160868	+	0.278632i
$375$	−1.04787e6	−	1.81497e6i	−0.384796	−	0.666487i
$376$	−1.03418e6			−0.377248
$377$	1.70162e6	+	2.94730e6i	0.616609	+	1.06800i
$378$	−833160.			−0.299915
$379$	331840.	−	574765.i	0.118667	−	0.205538i	−0.800572	−	0.599236i	$-0.795471\pi$
$379$	331840.	−	574765.i	0.118667	−	0.205538i	0.919240	+	0.393698i	$0.128804\pi$
$380$	615220.			0.218560
$381$	5.29324e6			1.86814
$382$	430996.	−	746508.i	0.151118	−	0.261744i
$383$	979388.	+	1.69635e6i	0.341160	+	0.590906i	0.984648	−	0.174550i	$-0.0558470\pi$
$383$	979388.	+	1.69635e6i	0.341160	+	0.590906i	−0.643489	+	0.765456i	$0.722514\pi$
$384$	314365.			0.108794
$385$	424312.	−	734929.i	0.145893	−	0.252693i
$386$	1.53790e6	−	2.66373e6i	0.525365	−	0.909958i
$387$	−1.06009e6	+	1.83612e6i	−0.359802	+	0.623195i
$388$	−843975.	−	1.46181e6i	−0.284610	−	0.492959i
$389$	2.20368e6	+	3.81689e6i	0.738372	+	1.27890i	0.953228	+	0.302252i	$0.0977385\pi$
$389$	2.20368e6	+	3.81689e6i	0.738372	+	1.27890i	−0.214856	+	0.976646i	$0.568928\pi$
$390$	−1.30236e6	+	2.25575e6i	−0.433580	+	0.750982i
$391$	516507.	−	894616.i	0.170858	−	0.295934i
$392$	−266287.	+	461223.i	−0.0875257	+	0.151599i
$393$	−1.09998e6			−0.359256
$394$	−327463.	−	567182.i	−0.106273	−	0.184070i
$395$	−1.37707e6	+	2.38515e6i	−0.444082	+	0.769172i
$396$	−270591.			−0.0867113
$397$	2.69296e6			0.857538			0.428769	−	0.903414i	$-0.358947\pi$
$397$	2.69296e6			0.857538			0.428769	+	0.903414i	$0.358947\pi$
$398$	641311.	−	1.11078e6i	0.202937	−	0.351497i
$399$	−996867.			−0.313476
$400$	−194928.	−	337624.i	−0.0609149	−	0.105508i
$401$	6.13209e6			1.90435			0.952177	−	0.305548i	$-0.0988396\pi$
$401$	6.13209e6			1.90435			0.952177	+	0.305548i	$0.0988396\pi$
$402$	1.02862e6	+	1.78162e6i	0.317460	+	0.549857i
$403$	552481.	+	956925.i	0.169455	+	0.293505i
$404$	−895499.	−	1.55105e6i	−0.272968	−	0.472794i
$405$	2.51560e6	−	4.35714e6i	0.762085	−	1.31997i
$406$	2.51903e6			0.758436
$407$	748771.	−	839971.i	0.224059	−	0.251350i
$408$	−1.97727e6			−0.588052
$409$	930962.	−	1.61247e6i	0.275184	−	0.476633i	−0.694997	−	0.719012i	$-0.744594\pi$
$409$	930962.	−	1.61247e6i	0.275184	−	0.476633i	0.970182	+	0.242379i	$0.0779278\pi$
$410$	−1.35460e6	−	2.34624e6i	−0.397972	−	0.689307i
$411$	−80140.2	−	138807.i	−0.0234016	−	0.0405328i
$412$	833291.	+	1.44330e6i	0.241854	+	0.418904i
$413$	−714842.			−0.206222
$414$	160587.	+	278145.i	0.0460479	+	0.0797572i
$415$	−1.12786e6			−0.321466
$416$	254876.	−	441458.i	0.0722096	−	0.125071i
$417$	3.90304e6			1.09917
$418$	304854.			0.0853397
$419$	−2.48930e6	+	4.31160e6i	−0.692696	+	1.19978i	0.278255	+	0.960507i	$0.410244\pi$
$419$	−2.48930e6	+	4.31160e6i	−0.692696	+	1.19978i	−0.970951	+	0.239277i	$0.923089\pi$
$420$	963987.	+	1.66967e6i	0.266654	+	0.461858i
$421$	−2.06569e6			−0.568015			−0.284007	−	0.958822i	$-0.591664\pi$
$421$	−2.06569e6			−0.568015			−0.284007	+	0.958822i	$0.591664\pi$
$422$	−458291.	+	793784.i	−0.125274	+	0.216981i
$423$	−1.01119e6	+	1.75143e6i	−0.274777	+	0.475928i
$424$	749435.	−	1.29806e6i	0.202451	−	0.350655i
$425$	1.22604e6	+	2.12356e6i	0.329255	+	0.570286i
$426$	19145.4	+	33160.8i	0.00511141	+	0.00885322i
$427$	−1.77036e6	+	3.06636e6i	−0.469886	+	0.813867i
$428$	−319799.	+	553908.i	−0.0843855	+	0.146160i
$429$	−645345.	+	1.11777e6i	−0.169297	+	0.293231i
$430$	−4.61969e6			−1.20487
$431$	503984.	+	872925.i	0.130684	+	0.226352i	0.923941	−	0.382536i	$-0.124949\pi$
$431$	503984.	+	872925.i	0.130684	+	0.226352i	−0.793256	+	0.608888i	$0.791616\pi$
$432$	−289427.	+	501302.i	−0.0746156	+	0.129238i
$433$	−1.99100e6			−0.510330			−0.255165	−	0.966897i	$-0.582130\pi$
$433$	−1.99100e6			−0.510330			−0.255165	+	0.966897i	$0.582130\pi$
$434$	817877.			0.208432
$435$	−4.47143e6	+	7.74475e6i	−1.13298	+	1.96238i
$436$	−2.94652e6			−0.742324
$437$	−180921.	−	313364.i	−0.0453194	−	0.0784956i
$438$	1.58383e6			0.394479
$439$	2.68792e6	+	4.65562e6i	0.665665	+	1.15296i	0.979105	+	0.203357i	$0.0651852\pi$
$439$	2.68792e6	+	4.65562e6i	0.665665	+	1.15296i	−0.313440	+	0.949608i	$0.601482\pi$
$440$	−294799.	−	510606.i	−0.0725929	−	0.125735i
$441$	520734.	+	901938.i	0.127503	+	0.220841i
$442$	−1.60310e6	+	2.77664e6i	−0.390305	+	0.676028i
$443$	−2.33081e6			−0.564283			−0.282141	−	0.959373i	$-0.591045\pi$
$443$	−2.33081e6			−0.564283			−0.282141	+	0.959373i	$0.591045\pi$
$444$	802090.	+	2.42737e6i	0.193093	+	0.584358i
$445$	−970276.			−0.232271
$446$	1.30742e6	−	2.26452e6i	0.311227	−	0.539061i
$447$	657993.	+	1.13968e6i	0.155759	+	0.269782i
$448$	−188655.	−	326761.i	−0.0444093	−	0.0769192i
$449$	−1.25489e6	−	2.17353e6i	−0.293758	−	0.508803i	0.680937	−	0.732342i	$-0.261573\pi$
$449$	−1.25489e6	−	2.17353e6i	−0.293758	−	0.508803i	−0.974695	+	0.223538i	$0.928239\pi$
$450$	−762375.			−0.177475
$451$	−671233.	−	1.16261e6i	−0.155393	−	0.269149i
$452$	647404.			0.149049
$453$	−3.91078e6	+	6.77368e6i	−0.895403	+	1.55088i
$454$	−4.73159e6			−1.07738
$455$	3.12626e6			0.707940
$456$	−346296.	+	599803.i	−0.0779895	+	0.135082i
$457$	−1.01807e6	−	1.76334e6i	−0.228027	−	0.394954i	0.729197	−	0.684304i	$-0.239894\pi$
$457$	−1.01807e6	−	1.76334e6i	−0.228027	−	0.394954i	−0.957223	+	0.289351i	$0.906561\pi$
$458$	5.29175e6			1.17879
$459$	1.82041e6	−	3.15305e6i	0.403310	−	0.698553i
$460$	−349907.	+	606056.i	−0.0771005	+	0.133542i
$461$	2.03248e6	−	3.52035e6i	0.445424	−	0.771497i	−0.552658	−	0.833408i	$-0.686386\pi$
$461$	2.03248e6	−	3.52035e6i	0.445424	−	0.771497i	0.998082	+	0.0619116i	$0.0197197\pi$
$462$	477675.	+	827358.i	0.104118	+	0.180338i
$463$	−1.06025e6	−	1.83641e6i	−0.229856	−	0.398122i	0.727909	−	0.685673i	$-0.240492\pi$
$463$	−1.06025e6	−	1.83641e6i	−0.229856	−	0.398122i	−0.957765	+	0.287551i	$0.907159\pi$
$464$	875074.	−	1.51567e6i	0.188690	−	0.326821i
$465$	−1.45178e6	+	2.51456e6i	−0.311364	+	0.539298i
$466$	−1.24335e6	+	2.15355e6i	−0.265234	+	0.459399i
$467$	4.17404e6			0.885655			0.442828	−	0.896607i	$-0.353975\pi$
$467$	4.17404e6			0.885655			0.442828	+	0.896607i	$0.353975\pi$
$468$	−498418.	−	863286.i	−0.105191	−	0.182196i
$469$	1.23458e6	−	2.13835e6i	0.259171	−	0.448898i
$470$	−4.40660e6			−0.920150
$471$	9.23210e6			1.91756
$472$	−248325.	+	430112.i	−0.0513057	+	0.0888641i
$473$	−2.28915e6			−0.470459
$474$	−1.55026e6	−	2.68512e6i	−0.316926	−	0.548932i
$475$	858908.			0.174668
$476$	1.18659e6	+	2.05523e6i	0.240040	+	0.415761i
$477$	−1.46555e6	−	2.53840e6i	−0.294919	−	0.510815i
$478$	−1.16674e6	−	2.02085e6i	−0.233563	−	0.404542i
$479$	2.63539e6	−	4.56462e6i	0.524814	−	0.909005i	−0.474768	−	0.880111i	$-0.657468\pi$
$479$	2.63539e6	−	4.56462e6i	0.524814	−	0.909005i	0.999582	−	0.0288939i	$-0.00919848\pi$
$480$	1.33950e6			0.265362
$481$	4.05902e6	+	841663.i	0.799943	+	0.165873i
$482$	6.19382e6			1.21434
$483$	566969.	−	982018.i	0.110584	−	0.191537i
$484$	1.14233e6	+	1.97857e6i	0.221655	+	0.383918i
$485$	−3.59614e6	−	6.22870e6i	−0.694197	−	1.20238i
$486$	1.73305e6	+	3.00174e6i	0.332829	+	0.576477i
$487$	−4.47199e6			−0.854434			−0.427217	−	0.904149i	$-0.640506\pi$
$487$	−4.47199e6			−0.854434			−0.427217	+	0.904149i	$0.640506\pi$
$488$	1.22999e6	+	2.13041e6i	0.233805	+	0.404962i
$489$	6.45647e6			1.22102
$490$	−1.13464e6	+	1.96525e6i	−0.213485	+	0.369767i
$491$	6.88226e6			1.28833			0.644165	−	0.764886i	$-0.277205\pi$
$491$	6.88226e6			1.28833			0.644165	+	0.764886i	$0.277205\pi$
$492$	3.04993e6			0.568037
$493$	−5.50397e6	+	9.53315e6i	−1.01990	+	1.76652i
$494$	561528.	+	972596.i	0.103527	+	0.179314i
$495$	−1.15298e6			−0.211499
$496$	284118.	−	492107.i	0.0518555	−	0.0898163i
$497$	22978.9	−	39800.6i	0.00417290	−	0.00722767i
$498$	634853.	−	1.09960e6i	0.114710	−	0.198683i
$499$	2.40255e6	+	4.16134e6i	0.431938	+	0.748138i	0.997040	−	0.0768829i	$-0.0244968\pi$
$499$	2.40255e6	+	4.16134e6i	0.431938	+	0.748138i	−0.565103	+	0.825021i	$0.691163\pi$
$500$	873805.	+	1.51347e6i	0.156311	+	0.270738i
$501$	5.22696e6	−	9.05335e6i	0.930367	−	1.61144i
$502$	2.99218e6	−	5.18260e6i	0.529942	−	0.917886i
$503$	4.64810e6	−	8.05075e6i	0.819136	−	1.41878i	−0.0871842	−	0.996192i	$-0.527787\pi$
$503$	4.64810e6	−	8.05075e6i	0.819136	−	1.41878i	0.906320	−	0.422592i	$-0.138880\pi$
$504$	−737844.			−0.129386
$505$	−3.81568e6	−	6.60895e6i	−0.665800	−	1.15320i
$506$	−173386.	+	300313.i	−0.0301049	+	0.0521432i
$507$	2.36933e6			0.409360
$508$	−4.41394e6			−0.758870
$509$	−4.73897e6	+	8.20813e6i	−0.810754	+	1.40427i	0.101582	+	0.994827i	$0.467610\pi$
$509$	−4.73897e6	+	8.20813e6i	−0.810754	+	1.40427i	−0.912337	+	0.409441i	$0.865724\pi$
$510$	−8.42506e6			−1.43433
$511$	−950480.	−	1.64628e6i	−0.161024	−	0.278902i
$512$	−262144.			−0.0441942
$513$	−637650.	−	1.10444e6i	−0.106977	−	0.185289i
$514$	1.18465e6	+	2.05187e6i	0.197780	+	0.342564i
$515$	3.55062e6	+	6.14985e6i	0.589910	+	1.02175i
$516$	2.60034e6	−	4.50392e6i	0.429938	−	0.744675i
$517$	−2.18356e6			−0.359284
$518$	2.04174e6	−	2.29042e6i	0.334330	−	0.375051i
$519$	−1.36205e7			−2.21960
$520$	1.08601e6	−	1.88103e6i	0.176128	−	0.305062i
$521$	−5.60533e6	−	9.70871e6i	−0.904704	−	1.56699i	−0.821314	−	0.570477i	$-0.806758\pi$
$521$	−5.60533e6	−	9.70871e6i	−0.904704	−	1.56699i	−0.0833909	−	0.996517i	$-0.526575\pi$
$522$	−1.71124e6	−	2.96395e6i	−0.274874	−	0.476096i
$523$	−1.69754e6	−	2.94023e6i	−0.271372	−	0.470031i	0.697841	−	0.716253i	$-0.254144\pi$
$523$	−1.69754e6	−	2.94023e6i	−0.271372	−	0.470031i	−0.969214	+	0.246222i	$0.920811\pi$
$524$	917256.			0.145936
$525$	1.34582e6	+	2.33103e6i	0.213103	+	0.369105i
$526$	−135116.			−0.0212933
$527$	−1.78702e6	+	3.09521e6i	−0.280287	+	0.485472i
$528$	663748.			0.103614
$529$	−6.02475e6			−0.936051
$530$	3.19331e6	−	5.53097e6i	0.493800	−	0.855287i
$531$	485608.	+	841098.i	0.0747394	+	0.129452i
$532$	831270.			0.127340
$533$	2.47277e6	−	4.28296e6i	0.377021	−	0.653019i
$534$	546152.	−	945962.i	0.0828820	−	0.143556i
$535$	−1.36265e6	+	2.36018e6i	−0.205826	+	0.356501i
$536$	−857748.	−	1.48566e6i	−0.128958	−	0.223361i
$537$	−6.32579e6	−	1.09566e7i	−0.946627	−	1.63961i
$538$	−2.11369e6	+	3.66101e6i	−0.314836	+	0.545312i
$539$	−562237.	+	973823.i	−0.0833580	+	0.144380i
$540$	−1.23324e6	+	2.13603e6i	−0.181996	+	0.315226i
$541$	−7.33573e6			−1.07758			−0.538791	−	0.842439i	$-0.681119\pi$
$541$	−7.33573e6			−1.07758			−0.538791	+	0.842439i	$0.681119\pi$
$542$	4.15031e6	+	7.18855e6i	0.606852	+	1.05110i
$543$	4.66274e6	−	8.07611e6i	0.678644	−	1.17545i
$544$	1.64881e6			0.238877
$545$	−1.25550e7			−1.81061
$546$	−1.75972e6	+	3.04792e6i	−0.252616	+	0.437544i
$547$	−7.06038e6			−1.00893			−0.504464	−	0.863433i	$-0.668310\pi$
$547$	−7.06038e6			−1.00893			−0.504464	+	0.863433i	$0.668310\pi$
$548$	66827.6	+	115749.i	0.00950614	+	0.0164651i
$549$	4.81059e6			0.681189
$550$	−411568.	−	712857.i	−0.0580143	−	0.100484i
$551$	1.92791e6	+	3.33925e6i	0.270526	+	0.468565i
$552$	−393913.	−	682277.i	−0.0550240	−	0.0953044i
$553$	−1.86066e6	+	3.22276e6i	−0.258735	+	0.448142i
$554$	4.85533e6			0.672116
$555$	3.41767e6	+	1.03429e7i	0.470975	+	1.42532i
$556$	−3.25468e6			−0.446500
$557$	−1.58864e6	+	2.75161e6i	−0.216965	+	0.375794i	−0.953878	−	0.300193i	$-0.902949\pi$
$557$	−1.58864e6	+	2.75161e6i	−0.216965	+	0.375794i	0.736914	+	0.675987i	$0.236282\pi$
$558$	−555602.	−	962331.i	−0.0755403	−	0.130840i
$559$	−4.21652e6	−	7.30323e6i	−0.570722	−	0.988520i
$560$	−803852.	−	1.39231e6i	−0.108319	−	0.187615i
$561$	−4.17479e6			−0.560051
$562$	664051.	+	1.15017e6i	0.0886871	+	0.153611i
$563$	−1.11141e7			−1.47776			−0.738878	−	0.673839i	$-0.764644\pi$
$563$	−1.11141e7			−1.47776			−0.738878	+	0.673839i	$0.764644\pi$
$564$	2.48040e6	−	4.29617e6i	0.328340	−	0.568701i
$565$	2.75856e6			0.363548
$566$	4.20915e6			0.552272
$567$	3.39902e6	−	5.88727e6i	0.444013	−	0.769053i
$568$	−15965.0	−	27652.2i	−0.00207634	−	0.00359633i
$569$	1.20516e6			0.156050			0.0780250	−	0.996951i	$-0.475139\pi$
$569$	1.20516e6			0.156050			0.0780250	+	0.996951i	$0.475139\pi$
$570$	−1.47555e6	+	2.55573e6i	−0.190225	+	0.329480i
$571$	3.22132e6	−	5.57949e6i	0.413469	−	0.716150i	−0.581797	−	0.813334i	$-0.697650\pi$
$571$	3.22132e6	−	5.57949e6i	0.413469	−	0.716150i	0.995266	+	0.0971841i	$0.0309836\pi$
$572$	538142.	−	932090.i	0.0687713	−	0.119115i
$573$	2.06742e6	+	3.58088e6i	0.263052	+	0.455620i
$574$	−1.83031e6	−	3.17019e6i	−0.231870	−	0.401610i
$575$	−488504.	+	846114.i	−0.0616167	+	0.106723i
$576$	−256316.	+	443952.i	−0.0321899	+	0.0557545i
$577$	−2.30308e6	+	3.98904e6i	−0.287984	+	0.498803i	−0.973328	−	0.229416i	$-0.926318\pi$
$577$	−2.30308e6	+	3.98904e6i	−0.287984	+	0.498803i	0.685344	+	0.728219i	$0.259652\pi$
$578$	−4.69113e6			−0.584061
$579$	7.37707e6	+	1.27775e7i	0.914508	+	1.58397i
$580$	3.72865e6	−	6.45821e6i	0.460237	−	0.797154i
$581$	−1.52394e6			−0.187296
$582$	8.09682e6			0.990848
$583$	1.58235e6	−	2.74071e6i	0.192811	−	0.333958i
$584$	−1.32073e6			−0.160244
$585$	−2.12374e6	−	3.67842e6i	−0.256573	−	0.444398i
$586$	5.22616e6			0.628693
$587$	5.85251e6	+	1.01368e7i	0.701046	+	1.21425i	0.968099	+	0.250566i	$0.0806168\pi$
$587$	5.85251e6	+	1.01368e7i	0.701046	+	1.21425i	−0.267053	+	0.963682i	$0.586050\pi$
$588$	−1.27734e6	−	2.21241e6i	−0.152357	−	0.263890i
$589$	625953.	+	1.08418e6i	0.0743453	+	0.128770i
$590$	−1.05810e6	+	1.83269e6i	−0.125140	+	0.216750i
$591$	3.14157e6			0.369980
$592$	−668850.	−	2.02415e6i	−0.0784376	−	0.237376i
$593$	−7.53183e6			−0.879557			−0.439778	−	0.898106i	$-0.644943\pi$
$593$	−7.53183e6			−0.879557			−0.439778	+	0.898106i	$0.644943\pi$
$594$	−611094.	+	1.05845e6i	−0.0710627	+	0.123084i
$595$	5.05600e6	+	8.75726e6i	0.585484	+	1.01409i
$596$	−548689.	−	950357.i	−0.0632719	−	0.109590i
$597$	3.07627e6	+	5.32825e6i	0.353255	+	0.611855i
$598$	−1.27748e6			−0.146083
$599$	−1.93378e6	−	3.34940e6i	−0.220211	−	0.381417i	0.734661	−	0.678435i	$-0.237341\pi$
$599$	−1.93378e6	−	3.34940e6i	−0.220211	−	0.381417i	−0.954872	+	0.297018i	$0.904008\pi$
$600$	1.87007e6			0.212070
$601$	−960212.	+	1.66314e6i	−0.108438	+	0.187820i	−0.915138	−	0.403142i	$-0.867918\pi$
$601$	−960212.	+	1.66314e6i	−0.108438	+	0.187820i	0.806700	+	0.590962i	$0.201252\pi$
$602$	−6.24202e6			−0.701994
$603$	−3.35471e6			−0.375718
$604$	3.26114e6	−	5.64846e6i	0.363728	−	0.629995i
$605$	4.86741e6	+	8.43061e6i	0.540642	+	0.936420i
$606$	8.59112e6			0.950317
$607$	6.93198e6	−	1.20065e7i	0.763635	−	1.32265i	−0.177331	−	0.984151i	$-0.556746\pi$
$607$	6.93198e6	−	1.20065e7i	0.763635	−	1.32265i	0.940965	−	0.338503i	$-0.109920\pi$
$608$	288771.	−	500166.i	0.0316807	−	0.0548725i
$609$	−6.04169e6	+	1.04645e7i	−0.660109	+	1.14334i
$610$	5.24095e6	+	9.07760e6i	0.570277	+	0.987748i
$611$	−4.02202e6	−	6.96635e6i	−0.435855	−	0.754922i
$612$	1.61215e6	−	2.79233e6i	0.173991	−	0.301362i
$613$	−1.59666e6	+	2.76550e6i	−0.171618	+	0.297251i	−0.938986	−	0.343956i	$-0.888233\pi$
$613$	−1.59666e6	+	2.76550e6i	−0.171618	+	0.297251i	0.767368	+	0.641207i	$0.221566\pi$
$614$	−2.67978e6	+	4.64151e6i	−0.286865	+	0.496865i
$615$	1.29956e7			1.38551
$616$	−398325.	−	689919.i	−0.0422947	−	0.0732566i
$617$	5.59435e6	−	9.68970e6i	0.591612	−	1.02470i	−0.402403	−	0.915462i	$-0.631825\pi$
$617$	5.59435e6	−	9.68970e6i	0.591612	−	1.02470i	0.994015	−	0.109240i	$-0.0348416\pi$
$618$	−7.99432e6			−0.841997
$619$	−164725.			−0.0172795			−0.00863976	−	0.999963i	$-0.502750\pi$
$619$	−164725.			−0.0172795			−0.00863976	+	0.999963i	$0.502750\pi$
$620$	1.21061e6	−	2.09685e6i	0.126481	−	0.219072i
$621$	1.45065e6			0.150951
$622$	6.04096e6	+	1.04632e7i	0.626080	+	1.08440i
$623$	−1.31101e6			−0.135328
$624$	1.22260e6	+	2.11760e6i	0.125696	+	0.217712i
$625$	6.10273e6	+	1.05702e7i	0.624920	+	1.08239i
$626$	932330.	+	1.61484e6i	0.0950898	+	0.164700i
$627$	−731167.	+	1.26642e6i	−0.0742759	+	0.128650i
$628$	−7.69849e6			−0.778945
$629$	4.20687e6	+	1.27313e7i	0.423968	+	1.28306i
$630$	−3.14392e6			−0.315588
$631$	8.10644e6	−	1.40408e7i	0.810507	−	1.40384i	−0.102003	−	0.994784i	$-0.532525\pi$
$631$	8.10644e6	−	1.40408e7i	0.810507	−	1.40384i	0.912510	−	0.409055i	$-0.134142\pi$
$632$	1.29273e6	+	2.23908e6i	0.128741	+	0.222986i
$633$	−2.19835e6	−	3.80765e6i	−0.218066	−	0.377701i
$634$	5.37115e6	+	9.30311e6i	0.530694	+	0.919189i
$635$	−1.88076e7			−1.85097
$636$	3.59492e6	+	6.22658e6i	0.352408	+	0.610389i
$637$	−4.14247e6			−0.404493
$638$	1.84762e6	−	3.20018e6i	0.179706	−	0.311259i
$639$	−62440.3			−0.00604941
$640$	−1.11698e6			−0.107795
$641$	2.10140e6	−	3.63973e6i	0.202005	−	0.349884i	−0.747169	−	0.664634i	$-0.768587\pi$
$641$	2.10140e6	−	3.63973e6i	0.202005	−	0.349884i	0.949175	+	0.314750i	$0.101921\pi$
$642$	−1.53402e6	−	2.65701e6i	−0.146891	−	0.254422i
$643$	731043.			0.0697293			0.0348647	−	0.999392i	$-0.488900\pi$
$643$	731043.			0.0697293			0.0348647	+	0.999392i	$0.488900\pi$
$644$	−472785.	+	818888.i	−0.0449210	+	0.0778055i
$645$	1.10799e7	−	1.91910e7i	1.04867	−	1.81635i
$646$	−1.81629e6	+	3.14590e6i	−0.171239	+	0.296595i
$647$	2.27715e6	+	3.94414e6i	0.213860	+	0.370417i	0.952919	−	0.303224i	$-0.0980629\pi$
$647$	2.27715e6	+	3.94414e6i	0.213860	+	0.370417i	−0.739059	+	0.673641i	$0.764730\pi$
$648$	−2.36153e6	−	4.09029e6i	−0.220931	−	0.382664i
$649$	−524311.	+	908134.i	−0.0488627	+	0.0846327i
$650$	1.51618e6	−	2.62611e6i	0.140757	−	0.243797i
$651$	−1.96161e6	+	3.39761e6i	−0.181410	+	0.314211i
$652$	−5.38394e6			−0.495999
$653$	715227.	+	1.23881e6i	0.0656388	+	0.113690i	0.896977	−	0.442077i	$-0.145758\pi$
$653$	715227.	+	1.23881e6i	0.0656388	+	0.113690i	−0.831338	+	0.555767i	$0.812425\pi$
$654$	7.06700e6	−	1.22404e7i	0.646086	−	1.11905i
$655$	3.90839e6			0.355955
$656$	−2.54328e6			−0.230747
$657$	−1.29137e6	+	2.23671e6i	−0.116717	+	0.202161i
$658$	−5.95409e6			−0.536106
$659$	7.11647e6	+	1.23261e7i	0.638338	+	1.10563i	0.985797	+	0.167939i	$0.0537113\pi$
$659$	7.11647e6	+	1.23261e7i	0.638338	+	1.10563i	−0.347459	+	0.937695i	$0.612955\pi$
$660$	2.82820e6			0.252726
$661$	7.29284e6	+	1.26316e7i	0.649221	+	1.12448i	0.983309	+	0.181942i	$0.0582385\pi$
$661$	7.29284e6	+	1.26316e7i	0.649221	+	1.12448i	−0.334088	+	0.942542i	$0.608428\pi$
$662$	−7.14506e6	−	1.23756e7i	−0.633667	−	1.09754i
$663$	−7.68979e6	−	1.33191e7i	−0.679408	−	1.17677i
$664$	−529393.	+	916936.i	−0.0465970	+	0.0807085i
$665$	3.54201e6			0.310596
$666$	−4.08195e6	−	846418.i	−0.356601	−	0.0739434i
$667$	−4.38601e6			−0.381729
$668$	−4.35867e6	+	7.54944e6i	−0.377931	+	0.654596i
$669$	6.27147e6	+	1.08625e7i	0.541757	+	0.938350i
$670$	−3.65483e6	−	6.33034e6i	−0.314543	−	0.544804i
$671$	2.59700e6	+	4.49813e6i	0.222672	+	0.385679i
$672$	1.80990e6			0.154608
$673$	−4.65013e6	−	8.05426e6i	−0.395756	−	0.685469i	0.597442	−	0.801912i	$-0.296184\pi$
$673$	−4.65013e6	−	8.05426e6i	−0.395756	−	0.685469i	−0.993197	+	0.116443i	$0.962851\pi$
$674$	−9.76662e6			−0.828123
$675$	−1.72172e6	+	2.98211e6i	−0.145446	+	0.251921i
$676$	−1.97574e6			−0.166289
$677$	1.13249e7			0.949649			0.474824	−	0.880081i	$-0.342512\pi$
$677$	1.13249e7			0.949649			0.474824	+	0.880081i	$0.342512\pi$
$678$	−1.55275e6	+	2.68944e6i	−0.129726	+	0.224692i
$679$	−4.85902e6	−	8.41607e6i	−0.404459	−	0.700544i
$680$	7.02552e6			0.582648
$681$	1.13483e7	−	1.96559e7i	0.937701	−	1.62415i
$682$	599884.	−	1.03903e6i	0.0493863	−	0.0855395i
$683$	−2.54228e6	+	4.40335e6i	−0.208531	+	0.361187i	−0.951252	−	0.308415i	$-0.900202\pi$
$683$	−2.54228e6	+	4.40335e6i	−0.208531	+	0.361187i	0.742721	+	0.669601i	$0.233535\pi$
$684$	−564701.	−	978091.i	−0.0461507	−	0.0799353i
$685$	284749.	+	493200.i	0.0231866	+	0.0401603i
$686$	−4.62951e6	+	8.01855e6i	−0.375600	+	0.650558i
$687$	−1.26918e7	+	2.19829e7i	−1.02597	+	1.77702i
$688$	−2.16838e6	+	3.75575e6i	−0.174648	+	0.302500i
$689$	1.16585e7			0.935609
$690$	−1.67844e6	−	2.90715e6i	−0.134210	−	0.232458i
$691$	−5.59151e6	+	9.68478e6i	−0.445486	+	0.771604i	−0.998086	−	0.0618424i	$-0.980302\pi$
$691$	−5.59151e6	+	9.68478e6i	−0.445486	+	0.771604i	0.552600	+	0.833447i	$0.313636\pi$
$692$	1.13579e7			0.901641
$693$	−1.55788e6			−0.123225
$694$	−7.02015e6	+	1.21593e7i	−0.553283	+	0.958315i
$695$	−1.38681e7			−1.08906
$696$	4.19758e6	+	7.27043e6i	0.328455	+	0.568901i
$697$	1.59965e7			1.24722
$698$	884431.	+	1.53188e6i	0.0687109	+	0.119011i
$699$	−5.96415e6	−	1.03302e7i	−0.461696	−	0.799681i
$700$	−1.12226e6	−	1.94381e6i	−0.0865660	−	0.149937i
$701$	−5.41923e6	+	9.38638e6i	−0.416526	+	0.721445i	−0.995587	−	0.0938396i	$-0.970086\pi$
$701$	−5.41923e6	+	9.38638e6i	−0.416526	+	0.721445i	0.579061	+	0.815284i	$0.303419\pi$
$702$	−4.50244e6			−0.344830
$703$	4.59882e6	+	953592.i	0.350960	+	0.0727737i
$704$	−553488.			−0.0420898
$705$	1.05689e7	−	1.83058e7i	0.800858	−	1.38713i
$706$	5.18103e6	+	8.97380e6i	0.391205	+	0.677586i
$707$	−5.15566e6	−	8.92986e6i	−0.387914	−	0.671887i
$708$	−1.19117e6	−	2.06318e6i	−0.0893084	−	0.154687i
$709$	1.54016e6			0.115067			0.0575336	−	0.998344i	$-0.481676\pi$
$709$	1.54016e6			0.115067			0.0575336	+	0.998344i	$0.481676\pi$
$710$	−68026.3	−	117825.i	−0.00506443	−	0.00877185i
$711$	5.05597e6			0.375085
$712$	−455427.	+	788822.i	−0.0336681	+	0.0583148i
$713$	−1.42404e6			−0.104906
$714$	−1.13837e7			−0.835679
$715$	2.29300e6	−	3.97159e6i	0.167741	−	0.290536i
$716$	5.27496e6	+	9.13651e6i	0.384536	+	0.666036i
$717$	1.11933e7			0.813130
$718$	8.47224e6	−	1.46744e7i	0.613320	−	1.06230i
$719$	9.00098e6	−	1.55902e7i	0.649333	−	1.12468i	−0.333949	−	0.942591i	$-0.608381\pi$
$719$	9.00098e6	−	1.55902e7i	0.649333	−	1.12468i	0.983282	−	0.182087i	$-0.0582854\pi$
$720$	−1.09215e6	+	1.89166e6i	−0.0785147	+	0.135991i
$721$	4.79751e6	+	8.30953e6i	0.343699	+	0.595304i
$722$	−4.31599e6	−	7.47552e6i	−0.308133	−	0.533702i
$723$	−1.48554e7	+	2.57303e7i	−1.05691	+	1.83062i
$724$	−3.88818e6	+	6.73453e6i	−0.275677	+	0.477486i
$725$	5.20557e6	−	9.01631e6i	0.367810	−	0.637065i
$726$	−1.09591e7			−0.771675
$727$	−4.97923e6	−	8.62428e6i	−0.349403	−	0.605183i	0.636741	−	0.771078i	$-0.280282\pi$
$727$	−4.97923e6	−	8.62428e6i	−0.349403	−	0.605183i	−0.986143	+	0.165895i	$0.946949\pi$
$728$	1.46740e6	−	2.54161e6i	0.102617	−	0.177738i
$729$	1.30655e6			0.0910555
$730$	−5.62757e6			−0.390853
$731$	1.36385e7	−	2.36226e7i	0.944003	−	1.63506i
$732$	−1.18002e7			−0.813974
$733$	4.66245e6	+	8.07559e6i	0.320519	+	0.555155i	0.980595	−	0.196043i	$-0.0628093\pi$
$733$	4.66245e6	+	8.07559e6i	0.320519	+	0.555155i	−0.660076	+	0.751199i	$0.729476\pi$
$734$	6.37594e6			0.436822
$735$	−5.44268e6	−	9.42699e6i	−0.371616	−	0.643658i
$736$	328477.	+	568939.i	0.0223517	+	0.0387143i
$737$	−1.81104e6	−	3.13682e6i	−0.122817	−	0.212726i
$738$	−2.48674e6	+	4.30716e6i	−0.168070	+	0.291105i
$739$	−1.32637e7			−0.893415			−0.446707	−	0.894680i	$-0.647403\pi$
$739$	−1.32637e7			−0.893415			−0.446707	+	0.894680i	$0.647403\pi$
$740$	−2.84994e6	−	8.62480e6i	−0.191318	−	0.578988i
$741$	−5.38712e6			−0.360422
$742$	4.31472e6	−	7.47332e6i	0.287702	−	0.498315i
$743$	−5.82037e6	−	1.00812e7i	−0.386793	−	0.669945i	0.605223	−	0.796056i	$-0.293084\pi$
$743$	−5.82037e6	−	1.00812e7i	−0.386793	−	0.669945i	−0.992016	+	0.126111i	$0.959751\pi$
$744$	1.36287e6	+	2.36056e6i	0.0902654	+	0.156344i
$745$	−2.33794e6	−	4.04943e6i	−0.154327	−	0.267303i
$746$	−2.06423e7			−1.35803
$747$	1.03525e6	+	1.79310e6i	0.0678801	+	0.117572i
$748$	3.48129e6			0.227502
$749$	−1.84118e6	+	3.18902e6i	−0.119920	+	0.207708i
$750$	−8.38299e6			−0.544184
$751$	819478.			0.0530197			0.0265099	−	0.999649i	$-0.491561\pi$
$751$	819478.			0.0530197			0.0265099	+	0.999649i	$0.491561\pi$
$752$	−2.06836e6	+	3.58250e6i	−0.133377	+	0.231016i
$753$	1.43530e7	+	2.48601e7i	0.922475	+	1.59777i
$754$	1.36130e7			0.872017
$755$	1.38956e7	−	2.40678e7i	0.887174	−	1.53663i
$756$	−1.66632e6	+	2.88615e6i	−0.106036	+	0.183660i
$757$	−6.46812e6	+	1.12031e7i	−0.410241	+	0.710558i	−0.994916	−	0.100710i	$-0.967889\pi$
$757$	−6.46812e6	+	1.12031e7i	−0.410241	+	0.710558i	0.584675	+	0.811267i	$0.301222\pi$
$758$	−1.32736e6	−	2.29906e6i	−0.0839105	−	0.145337i
$759$	−831703.	−	1.44055e6i	−0.0524039	−	0.0907663i
$760$	1.23044e6	−	2.13118e6i	0.0772727	−	0.133840i
$761$	−7.96802e6	+	1.38010e7i	−0.498757	+	0.863873i	−0.999999	−	0.00143466i	$-0.999543\pi$
$761$	−7.96802e6	+	1.38010e7i	−0.498757	+	0.863873i	0.501242	+	0.865307i	$0.332877\pi$
$762$	1.05865e7	−	1.83363e7i	0.660487	−	1.14400i
$763$	−1.69640e7			−1.05492
$764$	−1.72399e6	−	2.98603e6i	−0.106856	−	0.185081i
$765$	6.86932e6	−	1.18980e7i	0.424385	−	0.735056i
$766$	7.83510e6			0.482473
$767$	−3.86304e6			−0.237105
$768$	628731.	−	1.08899e6i	0.0384646	−	0.0666227i
$769$	9.28632e6			0.566276			0.283138	−	0.959079i	$-0.408625\pi$
$769$	9.28632e6			0.566276			0.283138	+	0.959079i	$0.408625\pi$
$770$	−1.69725e6	−	2.93972e6i	−0.103162	−	0.178681i
$771$	−1.13651e7			−0.688554
$772$	−6.15161e6	−	1.06549e7i	−0.371489	−	0.643438i
$773$	2.63852e6	+	4.57005e6i	0.158822	+	0.275088i	0.934444	−	0.356109i	$-0.115897\pi$
$773$	2.63852e6	+	4.57005e6i	0.158822	+	0.275088i	−0.775622	+	0.631198i	$0.782564\pi$
$774$	4.24034e6	+	7.34449e6i	0.254418	+	0.440666i
$775$	1.69014e6	−	2.92740e6i	0.101081	−	0.175077i
$776$	−6.75180e6			−0.402500
$777$	4.61788e6	+	1.39751e7i	0.274404	+	0.830430i
$778$	1.76295e7			1.04422
$779$	2.80161e6	−	4.85253e6i	0.165411	−	0.286500i
$780$	5.20943e6	+	9.02300e6i	0.306587	+	0.531025i
$781$	−33708.4	−	58384.7i	−0.00197747	−	0.00342508i
$782$	−2.06603e6	−	3.57846e6i	−0.120815	−	0.209257i
$783$	−1.54584e7			−0.901072
$784$	1.06515e6	+	1.84489e6i	0.0618900	+	0.107197i
$785$	−3.28029e7			−1.89993
$786$	−2.19996e6	+	3.81045e6i	−0.127016	+	0.219999i
$787$	6.29449e6			0.362263			0.181131	−	0.983459i	$-0.442024\pi$
$787$	6.29449e6			0.362263			0.181131	+	0.983459i	$0.442024\pi$
$788$	−2.61970e6			−0.150292
$789$	324065.	−	561297.i	0.0185327	−	0.0320996i
$790$	5.50828e6	+	9.54062e6i	0.314013	+	0.543887i
$791$	3.72730e6			0.211814
$792$	−541183.	+	937356.i	−0.0306571	+	0.0530996i
$793$	−9.56713e6	+	1.65708e7i	−0.540255	+	0.935749i
$794$	5.38591e6	−	9.32868e6i	0.303185	−	0.525132i
$795$	1.53178e7	+	2.65312e7i	0.859564	+	1.48881i
$796$	−2.56525e6	−	4.44314e6i	−0.143498	−	0.248546i
$797$	3.23882e6	−	5.60979e6i	0.180609	−	0.312825i	−0.761479	−	0.648190i	$-0.775526\pi$
$797$	3.23882e6	−	5.60979e6i	0.180609	−	0.312825i	0.942088	+	0.335365i	$0.108860\pi$
$798$	−1.99373e6	+	3.45325e6i	−0.110831	+	0.191964i
$799$	1.30094e7	−	2.25329e7i	0.720925	−	1.24868i
$800$	−1.55942e6			−0.0861466
$801$	890602.	+	1.54257e6i	0.0490459	+	0.0849499i
$802$	1.22642e7	−	2.12422e7i	0.673291	−	1.16617i
$803$	−2.78858e6			−0.152614
$804$	8.22895e6			0.448957
$805$	−2.01452e6	+	3.48925e6i	−0.109567	+	0.189776i
$806$	4.41985e6			0.239646
$807$	−1.01390e7	−	1.75613e7i	−0.548039	−	0.949231i
$808$	−7.16399e6			−0.386035
$809$	−2.36395e6	−	4.09449e6i	−0.126989	−	0.219952i	0.795519	−	0.605928i	$-0.207198\pi$
$809$	−2.36395e6	−	4.09449e6i	−0.126989	−	0.219952i	−0.922509	+	0.385976i	$0.873865\pi$
$810$	−1.00624e7	−	1.74286e7i	−0.538876	−	0.933360i
$811$	−2.86277e6	−	4.95846e6i	−0.152839	−	0.264725i	0.779431	−	0.626488i	$-0.215508\pi$
$811$	−2.86277e6	−	4.95846e6i	−0.152839	−	0.264725i	−0.932270	+	0.361763i	$0.882175\pi$
$812$	5.03807e6	−	8.72619e6i	0.268147	−	0.464445i
$813$	−3.98167e7			−2.11271
$814$	−1.41220e6	−	4.27376e6i	−0.0747027	−	0.226073i
$815$	−2.29407e7			−1.20980
$816$	−3.95454e6	+	6.84946e6i	−0.207908	+	0.360107i
$817$	−4.77726e6	−	8.27446e6i	−0.250394	−	0.433695i
$818$	−3.72385e6	−	6.44989e6i	−0.194585	−	0.337031i
$819$	−2.86955e6	−	4.97020e6i	−0.149487	−	0.258919i
$820$	−1.08368e7			−0.562817
$821$	3.96089e6	+	6.86046e6i	0.205085	+	0.355218i	0.950160	−	0.311763i	$-0.100919\pi$
$821$	3.96089e6	+	6.86046e6i	0.205085	+	0.355218i	−0.745074	+	0.666981i	$0.767586\pi$
$822$	−641122.			−0.0330949
$823$	1.80499e7	−	3.12634e7i	0.928916	−	1.60893i	0.143776	−	0.989610i	$-0.454075\pi$
$823$	1.80499e7	−	3.12634e7i	0.928916	−	1.60893i	0.785139	−	0.619319i	$-0.212591\pi$
$824$	6.66633e6			0.342034
$825$	3.94845e6			0.201972
$826$	−1.42968e6	+	2.47628e6i	−0.0729104	+	0.126285i
$827$	1.54843e7	+	2.68196e7i	0.787278	+	1.36361i	0.927629	+	0.373503i	$0.121844\pi$
$827$	1.54843e7	+	2.68196e7i	0.787278	+	1.36361i	−0.140351	+	0.990102i	$0.544823\pi$
$828$	1.28470e6			0.0651215
$829$	1.65175e6	−	2.86091e6i	0.0834751	−	0.144583i	−0.821265	−	0.570546i	$-0.806731\pi$
$829$	1.65175e6	−	2.86091e6i	0.0834751	−	0.144583i	0.904740	+	0.425963i	$0.140065\pi$
$830$	−2.25572e6	+	3.90703e6i	−0.113655	+	0.196857i
$831$	−1.16451e7	+	2.01699e7i	−0.584980	+	1.01321i
$832$	−1.01950e6	−	1.76583e6i	−0.0510599	−	0.0884384i
$833$	−6.69949e6	−	1.16039e7i	−0.334526	−	0.579415i
$834$	7.80608e6	−	1.35205e7i	0.388614	−	0.673099i
$835$	−1.85721e7	+	3.21678e7i	−0.921817	+	1.59663i
$836$	609708.	−	1.05604e6i	0.0301721	−	0.0522597i
$837$	−5.01901e6			−0.247630
$838$	9.95721e6	+	1.72464e7i	0.489810	+	0.848376i
$839$	1.15257e7	−	1.99631e7i	0.565279	−	0.979092i	−0.431745	−	0.901996i	$-0.642102\pi$
$839$	1.15257e7	−	1.99631e7i	0.565279	−	0.979092i	0.997024	−	0.0770961i	$-0.0245648\pi$
$840$	7.71189e6			0.377105
$841$	2.62268e7			1.27866
$842$	−4.13138e6	+	7.15576e6i	−0.200824	+	0.347837i
$843$	−6.37069e6			−0.308757
$844$	1.83316e6	+	3.17513e6i	0.0885820	+	0.153428i
$845$	−8.41856e6			−0.405598
$846$	4.04475e6	+	7.00571e6i	0.194297	+	0.336532i
$847$	6.57674e6	+	1.13912e7i	0.314994	+	0.545585i
$848$	−2.99774e6	−	5.19224e6i	−0.143154	−	0.247950i
$849$	−1.00953e7	+	1.74856e7i	−0.480673	+	0.832551i
$850$	9.80832e6			0.465637
$851$	−3.55497e6	+	3.98796e6i	−0.168272	+	0.188767i
$852$	153163.			0.00722862
$853$	1.56119e7	−	2.70407e7i	0.734656	−	1.27246i	−0.220218	−	0.975451i	$-0.570677\pi$
$853$	1.56119e7	−	2.70407e7i	0.734656	−	1.27246i	0.954874	−	0.297011i	$-0.0959897\pi$
$854$	7.08145e6	+	1.22654e7i	0.332260	+	0.575491i
$855$	−2.40617e6	−	4.16760e6i	−0.112567	−	0.194971i
$856$	1.27920e6	+	2.21563e6i	0.0596695	+	0.103351i
$857$	1.87882e7			0.873844			0.436922	−	0.899500i	$-0.356069\pi$
$857$	1.87882e7			0.873844			0.436922	+	0.899500i	$0.356069\pi$
$858$	2.58138e6	+	4.47108e6i	0.119711	+	0.207345i
$859$	249444.			0.0115343			0.00576714	−	0.999983i	$-0.498164\pi$
$859$	249444.			0.0115343			0.00576714	+	0.999983i	$0.498164\pi$
$860$	−9.23938e6	+	1.60031e7i	−0.425987	+	0.737832i
$861$	1.75594e7			0.807237
$862$	4.03187e6			0.184815
$863$	−2.20181e6	+	3.81365e6i	−0.100636	+	0.174307i	−0.911947	−	0.410308i	$-0.865421\pi$
$863$	−2.20181e6	+	3.81365e6i	−0.100636	+	0.174307i	0.811311	+	0.584615i	$0.198754\pi$
$864$	1.15771e6	+	2.00521e6i	0.0527612	+	0.0913851i
$865$	4.83956e7			2.19921
$866$	−3.98200e6	+	6.89703e6i	−0.180429	+	0.312512i
$867$	1.12513e7	−	1.94878e7i	0.508341	−	0.880472i
$868$	1.63575e6	−	2.83321e6i	0.0736917	−	0.127638i
$869$	2.72946e6	+	4.72757e6i	0.122611	+	0.212368i
$870$	1.78857e7	+	3.09790e7i	0.801140	+	1.38762i
$871$	6.67173e6	−	1.15558e7i	0.297984	−	0.516123i
$872$	−5.89305e6	+	1.02071e7i	−0.262451	+	0.454579i
$873$	−6.60169e6	+	1.14345e7i	−0.293170	+	0.507785i
$874$	−1.44737e6			−0.0640914
$875$	5.03076e6	+	8.71353e6i	0.222133	+	0.384746i
$876$	3.16766e6	−	5.48655e6i	0.139469	−	0.241568i
$877$	−5.33171e6			−0.234082			−0.117041	−	0.993127i	$-0.537341\pi$
$877$	−5.33171e6			−0.234082			−0.117041	+	0.993127i	$0.537341\pi$
$878$	2.15034e7			0.941392
$879$	−1.25345e7	+	2.17104e7i	−0.547187	+	0.947755i
$880$	−2.35839e6			−0.102662
$881$	−3.98810e6	−	6.90760e6i	−0.173112	−	0.299838i	0.766394	−	0.642370i	$-0.222049\pi$
$881$	−3.98810e6	−	6.90760e6i	−0.173112	−	0.299838i	−0.939506	+	0.342532i	$0.888716\pi$
$882$	4.16587e6			0.180316
$883$	−6.19420e6	−	1.07287e7i	−0.267352	−	0.463068i	0.700825	−	0.713333i	$-0.252815\pi$
$883$	−6.19420e6	−	1.07287e7i	−0.267352	−	0.463068i	−0.968177	+	0.250266i	$0.919482\pi$
$884$	6.41239e6	+	1.11066e7i	0.275987	+	0.478024i
$885$	−5.07554e6	−	8.79110e6i	−0.217833	−	0.377299i
$886$	−4.66161e6	+	8.07415e6i	−0.199504	+	0.345551i
$887$	2.10380e7			0.897833			0.448916	−	0.893574i	$-0.351810\pi$
$887$	2.10380e7			0.897833			0.448916	+	0.893574i	$0.351810\pi$
$888$	1.00128e7	+	2.07623e6i	0.426114	+	0.0883572i
$889$	−2.54124e7			−1.07843
$890$	−1.94055e6	+	3.36114e6i	−0.0821203	+	0.142237i
$891$	−4.98612e6	−	8.63621e6i	−0.210411	−	0.364442i
$892$	−5.22968e6	−	9.05806e6i	−0.220071	−	0.381174i
$893$	−4.55690e6	−	7.89278e6i	−0.191223	−	0.331208i
$894$	5.26394e6			0.220276
$895$	2.24764e7	+	3.89303e7i	0.937927	+	1.62454i
$896$	−1.50924e6			−0.0628043
$897$	3.06393e6	−	5.30688e6i	0.127144	−	0.220221i
$898$	−1.00391e7			−0.415436
$899$	1.51748e7			0.626216
$900$	−1.52475e6	+	2.64094e6i	−0.0627469	+	0.108681i
$901$	1.88549e7	+	3.26577e7i	0.773772	+	1.34021i
$902$	−5.36987e6			−0.219759
$903$	1.49710e7	−	2.59305e7i	0.610985	−	1.05826i
$904$	1.29481e6	−	2.24267e6i	0.0526968	−	0.0912736i
$905$	−1.65674e7	+	2.86955e7i	−0.672407	+	1.16464i
$906$	1.56431e7	+	2.70947e7i	0.633145	+	1.09664i
$907$	5.35983e6	+	9.28349e6i	0.216338	+	0.374708i	0.953686	−	0.300805i	$-0.0972554\pi$
$907$	5.35983e6	+	9.28349e6i	0.216338	+	0.374708i	−0.737348	+	0.675513i	$0.763922\pi$
$908$	−9.46318e6	+	1.63907e7i	−0.380910	+	0.659756i
$909$	−7.00471e6	+	1.21325e7i	−0.281178	+	0.487014i
$910$	6.25252e6	−	1.08297e7i	0.250295	−	0.433523i
$911$	2.58224e6			0.103086			0.0515431	−	0.998671i	$-0.483586\pi$
$911$	2.58224e6			0.103086			0.0515431	+	0.998671i	$0.483586\pi$
$912$	1.38519e6	+	2.39921e6i	0.0551469	+	0.0955172i
$913$	−1.11776e6	+	1.93601e6i	−0.0443783	+	0.0768654i
$914$	−8.14453e6			−0.322478
$915$	−5.02800e7			−1.98537
$916$	1.05835e7	−	1.83312e7i	0.416765	−	0.721858i
$917$	5.28092e6			0.207389
$918$	−7.28166e6	−	1.26122e7i	−0.285183	−	0.493951i
$919$	2.05587e7			0.802982			0.401491	−	0.915863i	$-0.368492\pi$
$919$	2.05587e7			0.802982			0.401491	+	0.915863i	$0.368492\pi$
$920$	1.39963e6	+	2.42422e6i	0.0545183	+	0.0944285i
$921$	−1.28544e7	−	2.22646e7i	−0.499349	−	0.864898i
$922$	−8.12991e6	−	1.40814e7i	−0.314962	−	0.545531i
$923$	124179.	−	215084.i	0.00479782	−	0.00831007i
$924$	3.82140e6			0.147246
$925$	−3.97880e6	−	1.20411e7i	−0.152896	−	0.462712i
$926$	−8.48199e6			−0.325065
$927$	6.51812e6	−	1.12897e7i	0.249128	−	0.431503i
$928$	−3.50029e6	−	6.06269e6i	−0.133424	−	0.231098i
$929$	6.91111e6	+	1.19704e7i	0.262729	+	0.455061i	0.966966	−	0.254905i	$-0.0820440\pi$
$929$	6.91111e6	+	1.19704e7i	0.262729	+	0.455061i	−0.704237	+	0.709965i	$0.748711\pi$
$930$	5.80712e6	+	1.00582e7i	0.220168	+	0.381341i
$931$	−4.69336e6			−0.177464
$932$	4.97341e6	+	8.61419e6i	0.187549	+	0.324844i
$933$	−5.79549e7			−2.17965
$934$	8.34808e6	−	1.44593e7i	0.313126	−	0.542351i
$935$	1.48336e7			0.554904
$936$	−3.98735e6			−0.148763
$937$	−1.97170e7	+	3.41509e7i	−0.733656	+	1.27073i	0.221655	+	0.975125i	$0.428854\pi$
$937$	−1.97170e7	+	3.41509e7i	−0.733656	+	1.27073i	−0.955311	+	0.295604i	$0.904479\pi$
$938$	−4.93832e6	−	8.55341e6i	−0.183262	−	0.317419i
$939$	−8.94447e6			−0.331048
$940$	−8.81319e6	+	1.52649e7i	−0.325322	+	0.563474i
$941$	6.07344e6	−	1.05195e7i	0.223594	−	0.387277i	−0.732302	−	0.680980i	$-0.761554\pi$
$941$	6.07344e6	−	1.05195e7i	0.223594	−	0.387277i	0.955897	+	0.293703i	$0.0948876\pi$
$942$	1.84642e7	−	3.19809e7i	0.677959	−	1.17426i
$943$	3.18684e6	+	5.51976e6i	0.116703	+	0.202135i
$944$	993301.	+	1.72045e6i	0.0362786	+	0.0628364i
$945$	−7.10011e6	+	1.22978e7i	−0.258634	+	0.447967i
$946$	−4.57830e6	+	7.92985e6i	−0.166332	+	0.288096i
$947$	−2.41426e7	+	4.18163e7i	−0.874801	+	1.51520i	−0.0178275	+	0.999841i	$0.505675\pi$
$947$	−2.41426e7	+	4.18163e7i	−0.874801	+	1.51520i	−0.856974	+	0.515360i	$0.827658\pi$
$948$	−1.24021e7			−0.448201
$949$	−5.13644e6	−	8.89658e6i	−0.185139	−	0.320669i
$950$	1.71782e6	−	2.97534e6i	0.0617543	−	0.106962i
$951$	−5.15291e7			−1.84757
$952$	9.49271e6			0.339467
$953$	−1.49163e6	+	2.58357e6i	−0.0532020	+	0.0921486i	−0.891400	−	0.453218i	$-0.850276\pi$
$953$	−1.49163e6	+	2.58357e6i	−0.0532020	+	0.0921486i	0.838198	+	0.545366i	$0.183609\pi$
$954$	−1.17244e7			−0.417079
$955$	−7.34583e6	−	1.27233e7i	−0.260635	−	0.451433i
$956$	−9.33390e6			−0.330307
$957$	8.86274e6	+	1.53507e7i	0.312815	+	0.541812i
$958$	−1.05415e7	−	1.82585e7i	−0.371100	−	0.642763i
$959$	384747.	+	666401.i	0.0135092	+	0.0233985i
$960$	2.67899e6	−	4.64016e6i	0.0938196	−	0.162500i
$961$	−2.37022e7			−0.827905
$962$	1.10337e7	−	1.23775e7i	0.384398	−	0.431218i
$963$	5.00302e6			0.173847
$964$	1.23876e7	−	2.14560e7i	0.429335	−	0.743630i
$965$	−2.62118e7	−	4.54001e7i	−0.906104	−	1.56942i
$966$	−2.26787e6	−	3.92807e6i	−0.0781945	−	0.135437i
$967$	1.10037e7	+	1.90589e7i	0.378418	+	0.655438i	0.990832	−	0.135098i	$-0.0431350\pi$
$967$	1.10037e7	+	1.90589e7i	0.378418	+	0.655438i	−0.612415	+	0.790537i	$0.709802\pi$
$968$	9.13863e6			0.313468
$969$	−8.71243e6	−	1.50904e7i	−0.298078	−	0.516286i
$970$	−2.87691e7			−0.981742
$971$	1.86613e7	−	3.23223e7i	0.635176	−	1.10016i	−0.351302	−	0.936262i	$-0.614261\pi$
$971$	1.86613e7	−	3.23223e7i	0.635176	−	1.10016i	0.986478	−	0.163895i	$-0.0524057\pi$
$972$	1.38644e7			0.470691
$973$	−1.87382e7			−0.634520
$974$	−8.94399e6	+	1.54914e7i	−0.302088	+	0.523232i
$975$	7.27289e6	+	1.25970e7i	0.245016	+	0.424381i
$976$	9.83996e6			0.330650
$977$	−2.85968e7	+	4.95311e7i	−0.958476	+	1.66013i	−0.232271	+	0.972651i	$0.574616\pi$
$977$	−2.85968e7	+	4.95311e7i	−0.958476	+	1.66013i	−0.726205	+	0.687478i	$0.758718\pi$
$978$	1.29129e7	−	2.23659e7i	0.431696	−	0.747719i
$979$	−961583.	+	1.66551e6i	−0.0320649	+	0.0555381i
$980$	4.53856e6	+	7.86101e6i	0.150957	+	0.261465i
$981$	1.15241e7	+	1.99602e7i	0.382325	+	0.662206i
$982$	1.37645e7	−	2.38408e7i	0.455494	−	0.788938i
$983$	1.87558e7	−	3.24860e7i	0.619087	−	1.07229i	−0.370566	−	0.928806i	$-0.620836\pi$
$983$	1.87558e7	−	3.24860e7i	0.619087	−	1.07229i	0.989653	−	0.143483i	$-0.0458304\pi$
$984$	6.09986e6	−	1.05653e7i	0.200832	−	0.347850i
$985$	−1.11624e7			−0.366580
$986$	2.20159e7	+	3.81326e7i	0.721180	+	1.24912i
$987$	1.42804e7	−	2.47344e7i	0.466603	−	0.808180i
$988$	4.49223e6			0.146410
$989$	1.08683e7			0.353321
$990$	−2.30596e6	+	3.99403e6i	−0.0747761	+	0.129516i
$991$	2.75186e7			0.890108			0.445054	−	0.895504i	$-0.353184\pi$
$991$	2.75186e7			0.890108			0.445054	+	0.895504i	$0.353184\pi$
$992$	−1.13647e6	−	1.96843e6i	−0.0366673	−	0.0635097i
$993$	6.85474e7			2.20606
$994$	−91915.5	−	159202.i	−0.00295068	−	0.00511073i
$995$	−1.09304e7	−	1.89320e7i	−0.350008	−	0.606232i
$996$	−2.53941e6	−	4.39839e6i	−0.0811120	−	0.140490i
$997$	1.19718e7	−	2.07357e7i	0.381435	−	0.660664i	−0.609833	−	0.792530i	$-0.708763\pi$
$997$	1.19718e7	−	2.07357e7i	0.381435	−	0.660664i	0.991268	+	0.131866i	$0.0420968\pi$
$998$	1.92204e7			0.610852
$999$	−1.25294e7	+	1.40555e7i	−0.397206	+	0.445586i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.c.b.47.7	✓	16
37.26	even	3	inner	74.6.c.b.63.7	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.c.b.47.7	✓	16	1.1	even	1	trivial
74.6.c.b.63.7	yes	16	37.26	even	3	inner

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:	\( N \)	\(=\)	\( 74 = 2 \cdot 37 \)
Weight:	\( k \)	\(=\)	\( 6 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(9.59367 + 16.6167i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-34.0877 - 59.0415i) q^{5} +76.7494 q^{6} +(-46.0584 - 79.7755i) q^{7} -64.0000 q^{8} +(-62.5771 + 108.387i) q^{9} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(9.59367 + 16.6167i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(-34.0877 - 59.0415i) q^{5} +76.7494 q^{6} +(-46.0584 - 79.7755i) q^{7} -64.0000 q^{8} +(-62.5771 + 108.387i) q^{9} -272.701 q^{10} -135.129 q^{11} +(153.499 - 265.868i) q^{12} +(-248.902 - 431.111i) q^{13} -368.467 q^{14} +(654.051 - 1132.85i) q^{15} +(-128.000 + 221.703i) q^{16} +(805.084 - 1394.45i) q^{17} +(250.308 + 433.547i) q^{18} +(-282.003 - 488.443i) q^{19} +(-545.402 + 944.665i) q^{20} +(883.739 - 1530.68i) q^{21} +(-270.258 + 468.101i) q^{22} +641.557 q^{23} +(-613.995 - 1063.47i) q^{24} +(-761.436 + 1318.85i) q^{25} -1991.22 q^{26} +2261.15 q^{27} +(-736.935 + 1276.41i) q^{28} -6836.51 q^{29} +(-2616.21 - 4531.40i) q^{30} -2219.67 q^{31} +(512.000 + 886.810i) q^{32} +(-1296.38 - 2245.40i) q^{33} +(-3220.34 - 5577.78i) q^{34} +(-3140.05 + 5438.72i) q^{35} +2002.47 q^{36} +(-5541.16 + 6216.07i) q^{37} -2256.02 q^{38} +(4775.77 - 8271.88i) q^{39} +(2181.61 + 3778.66i) q^{40} +(4967.35 + 8603.70i) q^{41} +(-3534.96 - 6122.72i) q^{42} +16940.5 q^{43} +(1081.03 + 1872.40i) q^{44} +8532.42 q^{45} +(1283.11 - 2222.42i) q^{46} +16159.1 q^{47} -4911.96 q^{48} +(4160.74 - 7206.62i) q^{49} +(3045.74 + 5275.38i) q^{50} +30894.8 q^{51} +(-3982.43 + 6897.78i) q^{52} +(-11709.9 + 20282.2i) q^{53} +(4522.30 - 7832.85i) q^{54} +(4606.23 + 7978.23i) q^{55} +(2947.74 + 5105.64i) q^{56} +(5410.88 - 9371.92i) q^{57} +(-13673.0 + 23682.4i) q^{58} +(3880.08 - 6720.50i) q^{59} -20929.6 q^{60} +(-19218.7 - 33287.7i) q^{61} +(-4439.34 + 7689.17i) q^{62} +11528.8 q^{63} +4096.00 q^{64} +(-16969.0 + 29391.1i) q^{65} -10371.1 q^{66} +(13402.3 + 23213.5i) q^{67} -25762.7 q^{68} +(6154.88 + 10660.6i) q^{69} +(12560.2 + 21754.9i) q^{70} +(249.453 + 432.066i) q^{71} +(4004.93 - 6936.75i) q^{72} +20636.4 q^{73} +(10450.8 + 31627.3i) q^{74} -29219.9 q^{75} +(-4512.04 + 7815.09i) q^{76} +(6223.83 + 10780.0i) q^{77} +(-19103.1 - 33087.5i) q^{78} +(-20198.9 - 34985.6i) q^{79} +17452.9 q^{80} +(36898.9 + 63910.9i) q^{81} +39738.8 q^{82} +(8271.77 - 14327.1i) q^{83} -28279.6 q^{84} -109774. q^{85} +(33881.0 - 58683.5i) q^{86} +(-65587.3 - 113600. i) q^{87} +8648.26 q^{88} +(7116.04 - 12325.3i) q^{89} +(17064.8 - 29557.2i) q^{90} +(-22928.1 + 39712.6i) q^{91} +(-5132.45 - 8889.67i) q^{92} +(-21294.8 - 36883.7i) q^{93} +(32318.1 - 55976.6i) q^{94} +(-19225.6 + 33299.7i) q^{95} +(-9823.92 + 17015.5i) q^{96} +105497. q^{97} +(-16643.0 - 28826.5i) q^{98} +(8455.98 - 14646.2i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9}+O(q^{10}) \) 16 * q + 32 * q^2 - 8 * q^3 - 128 * q^4 + 70 * q^5 - 64 * q^6 - 32 * q^7 - 1024 * q^8 - 698 * q^9	\( 16 q + 32 q^{2} - 8 q^{3} - 128 q^{4} + 70 q^{5} - 64 q^{6} - 32 q^{7} - 1024 q^{8} - 698 q^{9} + 560 q^{10} - 240 q^{11} - 128 q^{12} + 1614 q^{13} - 256 q^{14} + 728 q^{15} - 2048 q^{16} + 216 q^{17} + 2792 q^{18} - 950 q^{19} + 1120 q^{20} + 1718 q^{21} - 480 q^{22} + 1716 q^{23} + 512 q^{24} - 11760 q^{25} + 12912 q^{26} - 92 q^{27} - 512 q^{28} + 1112 q^{29} - 2912 q^{30} - 16816 q^{31} + 8192 q^{32} + 4744 q^{33} - 864 q^{34} - 5004 q^{35} + 22336 q^{36} + 3556 q^{37} - 7600 q^{38} + 17710 q^{39} - 4480 q^{40} - 8080 q^{41} - 6872 q^{42} - 19012 q^{43} + 1920 q^{44} - 58672 q^{45} + 3432 q^{46} + 29392 q^{47} + 4096 q^{48} + 474 q^{49} + 47040 q^{50} - 17856 q^{51} + 25824 q^{52} - 29250 q^{53} - 184 q^{54} + 15772 q^{55} + 2048 q^{56} + 16182 q^{57} + 2224 q^{58} + 61478 q^{59} - 23296 q^{60} - 132002 q^{61} - 33632 q^{62} - 103324 q^{63} + 65536 q^{64} - 37426 q^{65} + 37952 q^{66} - 45658 q^{67} - 6912 q^{68} - 23816 q^{69} + 20016 q^{70} + 13236 q^{71} + 44672 q^{72} + 270632 q^{73} - 81304 q^{74} + 419904 q^{75} - 15200 q^{76} - 184084 q^{77} - 70840 q^{78} + 123974 q^{79} - 35840 q^{80} + 96448 q^{81} - 64640 q^{82} - 16936 q^{83} - 54976 q^{84} - 251316 q^{85} - 38024 q^{86} + 168290 q^{87} + 15360 q^{88} + 52892 q^{89} - 117344 q^{90} - 432546 q^{91} - 13728 q^{92} + 220328 q^{93} + 58784 q^{94} + 47026 q^{95} + 8192 q^{96} - 546140 q^{97} - 1896 q^{98} - 9800 q^{99}+O(q^{100}) \) 16 * q + 32 * q^2 - 8 * q^3 - 128 * q^4 + 70 * q^5 - 64 * q^6 - 32 * q^7 - 1024 * q^8 - 698 * q^9 + 560 * q^10 - 240 * q^11 - 128 * q^12 + 1614 * q^13 - 256 * q^14 + 728 * q^15 - 2048 * q^16 + 216 * q^17 + 2792 * q^18 - 950 * q^19 + 1120 * q^20 + 1718 * q^21 - 480 * q^22 + 1716 * q^23 + 512 * q^24 - 11760 * q^25 + 12912 * q^26 - 92 * q^27 - 512 * q^28 + 1112 * q^29 - 2912 * q^30 - 16816 * q^31 + 8192 * q^32 + 4744 * q^33 - 864 * q^34 - 5004 * q^35 + 22336 * q^36 + 3556 * q^37 - 7600 * q^38 + 17710 * q^39 - 4480 * q^40 - 8080 * q^41 - 6872 * q^42 - 19012 * q^43 + 1920 * q^44 - 58672 * q^45 + 3432 * q^46 + 29392 * q^47 + 4096 * q^48 + 474 * q^49 + 47040 * q^50 - 17856 * q^51 + 25824 * q^52 - 29250 * q^53 - 184 * q^54 + 15772 * q^55 + 2048 * q^56 + 16182 * q^57 + 2224 * q^58 + 61478 * q^59 - 23296 * q^60 - 132002 * q^61 - 33632 * q^62 - 103324 * q^63 + 65536 * q^64 - 37426 * q^65 + 37952 * q^66 - 45658 * q^67 - 6912 * q^68 - 23816 * q^69 + 20016 * q^70 + 13236 * q^71 + 44672 * q^72 + 270632 * q^73 - 81304 * q^74 + 419904 * q^75 - 15200 * q^76 - 184084 * q^77 - 70840 * q^78 + 123974 * q^79 - 35840 * q^80 + 96448 * q^81 - 64640 * q^82 - 16936 * q^83 - 54976 * q^84 - 251316 * q^85 - 38024 * q^86 + 168290 * q^87 + 15360 * q^88 + 52892 * q^89 - 117344 * q^90 - 432546 * q^91 - 13728 * q^92 + 220328 * q^93 + 58784 * q^94 + 47026 * q^95 + 8192 * q^96 - 546140 * q^97 - 1896 * q^98 - 9800 * q^99

Introduction

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