LMFDB - Embedded newform 74.6.c.b.47.5

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			47.5
Root			$0.0781534 + 0.135366i$ of defining polynomial
Character	$\chi$	$=$	74.47
Dual form			74.6.c.b.63.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.00000 - 3.46410i) q^{2} +(-0.578153 - 1.00139i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(40.4037 + 69.9813i) q^{5} -4.62523 q^{6} +(-85.9598 - 148.887i) q^{7} -64.0000 q^{8} +(120.831 - 209.286i) q^{9} +O(q^{10})$	\(q+(2.00000 - 3.46410i) q^{2} +(-0.578153 - 1.00139i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(40.4037 + 69.9813i) q^{5} -4.62523 q^{6} +(-85.9598 - 148.887i) q^{7} -64.0000 q^{8} +(120.831 - 209.286i) q^{9} +323.230 q^{10} +646.275 q^{11} +(-9.25045 + 16.0223i) q^{12} +(176.561 + 305.813i) q^{13} -687.678 q^{14} +(46.7191 - 80.9199i) q^{15} +(-128.000 + 221.703i) q^{16} +(890.829 - 1542.96i) q^{17} +(-483.326 - 837.145i) q^{18} +(-1131.30 - 1959.47i) q^{19} +(646.460 - 1119.70i) q^{20} +(-99.3959 + 172.159i) q^{21} +(1292.55 - 2238.76i) q^{22} -1204.39 q^{23} +(37.0018 + 64.0890i) q^{24} +(-1702.42 + 2948.68i) q^{25} +1412.49 q^{26} -560.419 q^{27} +(-1375.36 + 2382.19i) q^{28} +7130.04 q^{29} +(-186.876 - 323.679i) q^{30} -2669.15 q^{31} +(512.000 + 886.810i) q^{32} +(-373.646 - 647.174i) q^{33} +(-3563.32 - 6171.84i) q^{34} +(6946.19 - 12031.2i) q^{35} -3866.61 q^{36} +(912.234 + 8277.18i) q^{37} -9050.38 q^{38} +(204.159 - 353.613i) q^{39} +(-2585.84 - 4478.80i) q^{40} +(6201.74 + 10741.7i) q^{41} +(397.583 + 688.635i) q^{42} -17897.4 q^{43} +(-5170.20 - 8955.05i) q^{44} +19528.2 q^{45} +(-2408.78 + 4172.13i) q^{46} +17504.1 q^{47} +296.015 q^{48} +(-6374.67 + 11041.2i) q^{49} +(6809.69 + 11794.7i) q^{50} -2060.14 q^{51} +(2824.98 - 4893.00i) q^{52} +(-6660.30 + 11536.0i) q^{53} +(-1120.84 + 1941.35i) q^{54} +(26111.9 + 45227.2i) q^{55} +(5501.43 + 9528.75i) q^{56} +(-1308.13 + 2265.74i) q^{57} +(14260.1 - 24699.2i) q^{58} +(-3848.38 + 6665.59i) q^{59} -1495.01 q^{60} +(-7262.53 - 12579.1i) q^{61} +(-5338.29 + 9246.20i) q^{62} -41546.6 q^{63} +4096.00 q^{64} +(-14267.5 + 24711.9i) q^{65} -2989.17 q^{66} +(-11231.9 - 19454.2i) q^{67} -28506.5 q^{68} +(696.322 + 1206.07i) q^{69} +(-27784.8 - 48124.6i) q^{70} +(14111.3 + 24441.5i) q^{71} +(-7733.21 + 13394.3i) q^{72} +8460.37 q^{73} +(30497.5 + 13394.3i) q^{74} +3937.05 q^{75} +(-18100.8 + 31351.4i) q^{76} +(-55553.7 - 96221.8i) q^{77} +(-816.635 - 1414.45i) q^{78} +(44395.4 + 76895.1i) q^{79} -20686.7 q^{80} +(-29038.0 - 50295.4i) q^{81} +49613.9 q^{82} +(19980.5 - 34607.2i) q^{83} +3180.67 q^{84} +143971. q^{85} +(-35794.8 + 61998.4i) q^{86} +(-4122.26 - 7139.96i) q^{87} -41361.6 q^{88} +(-65715.7 + 113823. i) q^{89} +(39056.3 - 67647.6i) q^{90} +(30354.3 - 52575.2i) q^{91} +(9635.12 + 16688.5i) q^{92} +(1543.18 + 2672.86i) q^{93} +(35008.2 - 60636.0i) q^{94} +(91417.3 - 158339. i) q^{95} +(592.029 - 1025.42i) q^{96} -137338. q^{97} +(25498.7 + 44165.0i) q^{98} +(78090.4 - 135257. i) 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
$3$	−0.578153	−	1.00139i	−0.0370886	−	0.0642393i	0.846885	−	0.531776i	$-0.178475\pi$
$3$	−0.578153	−	1.00139i	−0.0370886	−	0.0642393i	−0.883974	+	0.467536i	$0.845142\pi$
$4$	−8.00000	−	13.8564i	−0.250000	−	0.433013i
$5$	40.4037	+	69.9813i	0.722764	+	1.25186i	0.959888	+	0.280385i	$0.0904620\pi$
$5$	40.4037	+	69.9813i	0.722764	+	1.25186i	−0.237124	+	0.971479i	$0.576205\pi$
$6$	−4.62523			−0.0524511
$7$	−85.9598	−	148.887i	−0.663056	−	1.14845i	−0.979808	−	0.199938i	$-0.935926\pi$
$7$	−85.9598	−	148.887i	−0.663056	−	1.14845i	0.316753	−	0.948508i	$-0.397408\pi$
$8$	−64.0000			−0.353553
$9$	120.831	−	209.286i	0.497249	−	0.861260i
$10$	323.230			1.02214
$11$	646.275			1.61041			0.805204	−	0.592998i	$-0.202056\pi$
$11$	646.275			1.61041			0.805204	+	0.592998i	$0.202056\pi$
$12$	−9.25045	+	16.0223i	−0.0185443	+	0.0321196i
$13$	176.561	+	305.813i	0.289759	+	0.501877i	0.973752	−	0.227611i	$-0.0730916\pi$
$13$	176.561	+	305.813i	0.289759	+	0.501877i	−0.683993	+	0.729488i	$0.739758\pi$
$14$	−687.678			−0.937703
$15$	46.7191	−	80.9199i	0.0536125	−	0.0928596i
$16$	−128.000	+	221.703i	−0.125000	+	0.216506i
$17$	890.829	−	1542.96i	0.747605	−	1.29489i	−0.201363	−	0.979517i	$-0.564537\pi$
$17$	890.829	−	1542.96i	0.747605	−	1.29489i	0.948968	−	0.315373i	$-0.102130\pi$
$18$	−483.326	−	837.145i	−0.351608	−	0.609003i
$19$	−1131.30	−	1959.47i	−0.718941	−	1.24524i	−0.961420	−	0.275085i	$-0.911294\pi$
$19$	−1131.30	−	1959.47i	−0.718941	−	1.24524i	0.242479	−	0.970157i	$-0.422039\pi$
$20$	646.460	−	1119.70i	0.361382	−	0.625932i
$21$	−99.3959	+	172.159i	−0.0491836	+	0.0851885i
$22$	1292.55	−	2238.76i	0.569365	−	0.986169i
$23$	−1204.39			−0.474731			−0.237366	−	0.971420i	$-0.576284\pi$
$23$	−1204.39			−0.474731			−0.237366	+	0.971420i	$0.576284\pi$
$24$	37.0018	+	64.0890i	0.0131128	+	0.0227120i
$25$	−1702.42	+	2948.68i	−0.544776	+	0.943579i
$26$	1412.49			0.409781
$27$	−560.419			−0.147946
$28$	−1375.36	+	2382.19i	−0.331528	+	0.574223i
$29$	7130.04			1.57433			0.787167	−	0.616740i	$-0.211547\pi$
$29$	7130.04			1.57433			0.787167	+	0.616740i	$0.211547\pi$
$30$	−186.876	−	323.679i	−0.0379098	−	0.0656617i
$31$	−2669.15			−0.498848			−0.249424	−	0.968394i	$-0.580241\pi$
$31$	−2669.15			−0.498848			−0.249424	+	0.968394i	$0.580241\pi$
$32$	512.000	+	886.810i	0.0883883	+	0.153093i
$33$	−373.646	−	647.174i	−0.0597277	−	0.103451i
$34$	−3563.32	−	6171.84i	−0.528636	−	0.915625i
$35$	6946.19	−	12031.2i	0.958466	−	1.66011i
$36$	−3866.61			−0.497249
$37$	912.234	+	8277.18i	0.109547	+	0.993982i
$37$	912.234	+	8277.18i	0.109547	+	0.993982i
$38$	−9050.38			−1.01674
$39$	204.159	−	353.613i	0.0214935	−	0.0372278i
$40$	−2585.84	−	4478.80i	−0.255536	−	0.442601i
$41$	6201.74	+	10741.7i	0.576175	+	0.997964i	0.995913	+	0.0903184i	$0.0287885\pi$
$41$	6201.74	+	10741.7i	0.576175	+	0.997964i	−0.419738	+	0.907645i	$0.637878\pi$
$42$	397.583	+	688.635i	0.0347780	+	0.0602373i
$43$	−17897.4			−1.47611			−0.738055	−	0.674740i	$-0.764256\pi$
$43$	−17897.4			−1.47611			−0.738055	+	0.674740i	$0.764256\pi$
$44$	−5170.20	−	8955.05i	−0.402602	−	0.697327i
$45$	19528.2			1.43757
$46$	−2408.78	+	4172.13i	−0.167843	+	0.290712i
$47$	17504.1			1.15583			0.577917	−	0.816096i	$-0.303866\pi$
$47$	17504.1			1.15583			0.577917	+	0.816096i	$0.303866\pi$
$48$	296.015			0.0185443
$49$	−6374.67	+	11041.2i	−0.379286	+	0.656943i
$50$	6809.69	+	11794.7i	0.385214	+	0.667211i
$51$	−2060.14			−0.110910
$52$	2824.98	−	4893.00i	0.144879	−	0.250938i
$53$	−6660.30	+	11536.0i	−0.325690	+	0.564112i	−0.981652	−	0.190683i	$-0.938930\pi$
$53$	−6660.30	+	11536.0i	−0.325690	+	0.564112i	0.655962	+	0.754794i	$0.272263\pi$
$54$	−1120.84	+	1941.35i	−0.0523068	+	0.0905981i
$55$	26111.9	+	45227.2i	1.16394	+	2.01601i
$56$	5501.43	+	9528.75i	0.234426	+	0.406037i
$57$	−1308.13	+	2265.74i	−0.0533289	+	0.0923684i
$58$	14260.1	−	24699.2i	0.556611	−	0.964079i
$59$	−3848.38	+	6665.59i	−0.143929	+	0.249292i	−0.928973	−	0.370148i	$-0.879307\pi$
$59$	−3848.38	+	6665.59i	−0.143929	+	0.249292i	0.785044	+	0.619440i	$0.212640\pi$
$60$	−1495.01			−0.0536125
$61$	−7262.53	−	12579.1i	−0.249898	−	0.432837i	0.713599	−	0.700554i	$-0.247064\pi$
$61$	−7262.53	−	12579.1i	−0.249898	−	0.432837i	−0.963497	+	0.267718i	$0.913731\pi$
$62$	−5338.29	+	9246.20i	−0.176369	+	0.305481i
$63$	−41546.6			−1.31882
$64$	4096.00			0.125000
$65$	−14267.5	+	24711.9i	−0.418854	+	0.725477i
$66$	−2989.17			−0.0844677
$67$	−11231.9	−	19454.2i	−0.305680	−	0.529453i	0.671733	−	0.740794i	$-0.265550\pi$
$67$	−11231.9	−	19454.2i	−0.305680	−	0.529453i	−0.977412	+	0.211341i	$0.932217\pi$
$68$	−28506.5			−0.747605
$69$	696.322	+	1206.07i	0.0176071	+	0.0304964i
$70$	−27784.8	−	48124.6i	−0.677738	−	1.17388i
$71$	14111.3	+	24441.5i	0.332217	+	0.575416i	0.982946	−	0.183893i	$-0.0588701\pi$
$71$	14111.3	+	24441.5i	0.332217	+	0.575416i	−0.650729	+	0.759310i	$0.725537\pi$
$72$	−7733.21	+	13394.3i	−0.175804	+	0.304502i
$73$	8460.37			0.185816			0.0929078	−	0.995675i	$-0.470384\pi$
$73$	8460.37			0.185816			0.0929078	+	0.995675i	$0.470384\pi$
$74$	30497.5	+	13394.3i	0.647418	+	0.284342i
$75$	3937.05			0.0808198
$76$	−18100.8	+	31351.4i	−0.359470	+	0.622621i
$77$	−55553.7	−	96221.8i	−1.06779	−	1.84947i
$78$	−816.635	−	1414.45i	−0.0151982	−	0.0263240i
$79$	44395.4	+	76895.1i	0.800332	+	1.38622i	0.919397	+	0.393330i	$0.128677\pi$
$79$	44395.4	+	76895.1i	0.800332	+	1.38622i	−0.119065	+	0.992886i	$0.537990\pi$
$80$	−20686.7			−0.361382
$81$	−29038.0	−	50295.4i	−0.491762	−	0.851756i
$82$	49613.9			0.814834
$83$	19980.5	−	34607.2i	0.318354	−	0.551406i	−0.661790	−	0.749689i	$-0.730203\pi$
$83$	19980.5	−	34607.2i	0.318354	−	0.551406i	0.980145	+	0.198283i	$0.0635364\pi$
$84$	3180.67			0.0491836
$85$	143971.			2.16137
$86$	−35794.8	+	61998.4i	−0.521884	+	0.903929i
$87$	−4122.26	−	7139.96i	−0.0583898	−	0.101134i
$88$	−41361.6			−0.569365
$89$	−65715.7	+	113823.i	−0.879416	+	1.52319i	−0.0274331	+	0.999624i	$0.508733\pi$
$89$	−65715.7	+	113823.i	−0.879416	+	1.52319i	−0.851983	+	0.523570i	$0.824600\pi$
$90$	39056.3	−	67647.6i	0.508259	−	0.880331i
$91$	30354.3	−	52575.2i	0.384252	−	0.665545i
$92$	9635.12	+	16688.5i	0.118683	+	0.205565i
$93$	1543.18	+	2672.86i	0.0185016	+	0.0320456i
$94$	35008.2	−	60636.0i	0.408649	−	0.707800i
$95$	91417.3	−	158339.i	1.03925	−	1.80003i
$96$	592.029	−	1025.42i	0.00655639	−	0.0113560i
$97$	−137338.			−1.48205			−0.741023	−	0.671479i	$-0.765659\pi$
$97$	−137338.			−1.48205			−0.741023	+	0.671479i	$0.765659\pi$
$98$	25498.7	+	44165.0i	0.268196	+	0.464529i
$99$	78090.4	−	135257.i	0.800774	−	1.38698i
$100$	54477.6			0.544776
$101$	−110662.			−1.07943			−0.539715	−	0.841848i	$-0.681468\pi$
$101$	−110662.			−1.07943			−0.539715	+	0.841848i	$0.681468\pi$
$102$	−4120.29	+	7136.55i	−0.0392127	+	0.0679184i
$103$	−68548.4			−0.636655			−0.318327	−	0.947981i	$-0.603121\pi$
$103$	−68548.4			−0.636655			−0.318327	+	0.947981i	$0.603121\pi$
$104$	−11299.9	−	19572.0i	−0.102445	−	0.177440i
$105$	−16063.9			−0.142192
$106$	26641.2	+	46143.9i	0.230298	+	0.398887i
$107$	−13064.3	−	22628.1i	−0.110313	−	0.191068i	0.805583	−	0.592483i	$-0.201852\pi$
$107$	−13064.3	−	22628.1i	−0.110313	−	0.191068i	−0.915897	+	0.401414i	$0.868519\pi$
$108$	4483.35	+	7765.39i	0.0369865	+	0.0640625i
$109$	102264.	−	177126.i	0.824433	−	1.42796i	−0.0779187	−	0.996960i	$-0.524827\pi$
$109$	102264.	−	177126.i	0.824433	−	1.42796i	0.902352	−	0.431000i	$-0.141839\pi$
$110$	208896.			1.64607
$111$	7761.29	−	5698.99i	0.0597897	−	0.0439026i
$112$	44011.4			0.331528
$113$	−95006.0	+	164555.i	−0.699930	+	1.21231i	0.268560	+	0.963263i	$0.413452\pi$
$113$	−95006.0	+	164555.i	−0.699930	+	1.21231i	−0.968490	+	0.249052i	$0.919881\pi$
$114$	5232.51	+	9062.97i	0.0377093	+	0.0653143i
$115$	−48661.9	−	84284.8i	−0.343118	−	0.594299i
$116$	−57040.3	−	98796.7i	−0.393584	−	0.681707i
$117$	85336.5			0.576329
$118$	15393.5	+	26662.3i	0.101773	+	0.176276i
$119$	−306302.			−1.98282
$120$	−2990.02	+	5178.87i	−0.0189549	+	0.0328308i
$121$	256621.			1.59341
$122$	−58100.3			−0.353410
$123$	7171.12	−	12420.7i	0.0427390	−	0.0740261i
$124$	21353.2	+	36984.8i	0.124712	+	0.216008i
$125$	−22613.7			−0.129449
$126$	−83093.2	+	143922.i	−0.466272	+	0.807606i
$127$	−22053.8	+	38198.3i	−0.121332	+	0.210152i	−0.920293	−	0.391230i	$-0.872050\pi$
$127$	−22053.8	+	38198.3i	−0.121332	+	0.210152i	0.798961	+	0.601382i	$0.205383\pi$
$128$	8192.00	−	14189.0i	0.0441942	−	0.0765466i
$129$	10347.4	+	17922.3i	0.0547468	+	0.0948243i
$130$	57069.8	+	98847.8i	0.296175	+	0.512990i
$131$	8743.52	−	15144.2i	0.0445152	−	0.0771025i	−0.842909	−	0.538056i	$-0.819159\pi$
$131$	8743.52	−	15144.2i	0.0445152	−	0.0771025i	0.887425	+	0.460953i	$0.152492\pi$
$132$	−5978.34	+	10354.8i	−0.0298639	+	0.0517257i
$133$	−194492.	+	336870.i	−0.953396	+	1.65133i
$134$	−89855.3			−0.432297
$135$	−22643.0	−	39218.9i	−0.106930	−	0.185208i
$136$	−57013.1	+	98749.5i	−0.264318	+	0.457813i
$137$	93337.3			0.424868			0.212434	−	0.977175i	$-0.431861\pi$
$137$	93337.3			0.424868			0.212434	+	0.977175i	$0.431861\pi$
$138$	5570.58			0.0249002
$139$	37483.1	−	64922.6i	0.164550	−	0.285009i	−0.771945	−	0.635689i	$-0.780716\pi$
$139$	37483.1	−	64922.6i	0.164550	−	0.285009i	0.936495	+	0.350680i	$0.114049\pi$
$140$	−222278.			−0.958466
$141$	−10120.1	−	17528.5i	−0.0428682	−	0.0742499i
$142$	112891.			0.469825
$143$	114107.	+	197639.i	0.466630	+	0.808226i
$144$	30932.9	+	53577.3i	0.124312	+	0.215315i
$145$	288080.	+	498970.i	1.13787	+	1.97085i
$146$	16920.7	−	29307.6i	0.0656958	−	0.113788i
$147$	14742.1			0.0562687
$148$	107394.	−	78857.8i	0.403020	−	0.295931i
$149$	−267249.			−0.986166			−0.493083	−	0.869982i	$-0.664130\pi$
$149$	−267249.			−0.986166			−0.493083	+	0.869982i	$0.664130\pi$
$150$	7874.10	−	13638.3i	0.0285741	−	0.0494918i
$151$	−221144.	−	383032.i	−0.789282	−	1.36708i	−0.926407	−	0.376523i	$-0.877120\pi$
$151$	−221144.	−	383032.i	−0.789282	−	1.36708i	0.137125	−	0.990554i	$-0.456214\pi$
$152$	72403.1	+	125406.i	0.254184	+	0.440259i
$153$	−215280.	−	372877.i	−0.743491	−	1.28776i
$154$	−444430.			−1.51008
$155$	−107844.	−	186790.i	−0.360549	−	0.624490i
$156$	−6533.08			−0.0214935
$157$	−190368.	+	329726.i	−0.616373	+	1.06759i	0.373769	+	0.927522i	$0.378065\pi$
$157$	−190368.	+	329726.i	−0.616373	+	1.06759i	−0.990142	+	0.140068i	$0.955268\pi$
$158$	355163.			1.13184
$159$	15402.7			0.0483175
$160$	−41373.4	+	71660.9i	−0.127768	+	0.221300i
$161$	103529.	+	179318.i	0.314773	+	0.545203i
$162$	−232304.			−0.695456
$163$	−100143.	+	173454.i	−0.295225	+	0.511345i	−0.975037	−	0.222041i	$-0.928728\pi$
$163$	−100143.	+	173454.i	−0.295225	+	0.511345i	0.679812	+	0.733386i	$0.262061\pi$
$164$	99227.9	−	171868.i	0.288087	−	0.498982i
$165$	30193.4	−	52296.5i	0.0863381	−	0.149542i
$166$	−79922.0	−	138429.i	−0.225111	−	0.389903i
$167$	295943.	+	512588.i	0.821139	+	1.42225i	0.904835	+	0.425763i	$0.139994\pi$
$167$	295943.	+	512588.i	0.821139	+	1.42225i	−0.0836956	+	0.996491i	$0.526672\pi$
$168$	6361.34	−	11018.2i	0.0173890	−	0.0301187i
$169$	123299.	−	213560.i	0.332080	−	0.575179i
$170$	287943.	−	498731.i	0.764159	−	1.32356i
$171$	−546786.			−1.42997
$172$	143179.	+	247994.i	0.369028	+	0.639175i
$173$	−32890.1	+	56967.2i	−0.0835506	+	0.144714i	−0.904773	−	0.425895i	$-0.859959\pi$
$173$	−32890.1	+	56967.2i	−0.0835506	+	0.144714i	0.821222	+	0.570609i	$0.193293\pi$
$174$	−32978.1			−0.0825756
$175$	585360.			1.44487
$176$	−82723.2	+	143281.i	−0.201301	+	0.348664i
$177$	8899.81			0.0213524
$178$	262863.	+	455292.i	0.621841	+	1.07706i
$179$	747782.			1.74439			0.872193	−	0.489163i	$-0.162698\pi$
$179$	747782.			1.74439			0.872193	+	0.489163i	$0.162698\pi$
$180$	−156225.	−	270590.i	−0.359394	−	0.622488i
$181$	223818.	+	387665.i	0.507808	+	0.879549i	0.999959	+	0.00903904i	$0.00287726\pi$
$181$	223818.	+	387665.i	0.507808	+	0.879549i	−0.492152	+	0.870510i	$0.663789\pi$
$182$	−121417.	−	210301.i	−0.271708	−	0.470611i
$183$	−8397.72	+	14545.3i	−0.0185367	+	0.0321066i
$184$	77081.0			0.167843
$185$	−542391.	+	398269.i	−1.16515	+	0.855553i
$186$	12345.4			0.0261651
$187$	575721.	−	997178.i	1.20395	−	2.08530i
$188$	−140033.	−	242544.i	−0.288958	−	0.500491i
$189$	48173.5	+	83438.9i	0.0980965	+	0.169908i
$190$	−365669.	−	633358.i	−0.734860	−	1.27281i
$191$	622992.			1.23566			0.617830	−	0.786312i	$-0.288012\pi$
$191$	622992.			1.23566			0.617830	+	0.786312i	$0.288012\pi$
$192$	−2368.12	−	4101.70i	−0.00463607	−	0.00802991i
$193$	523859.			1.01233			0.506164	−	0.862437i	$-0.331063\pi$
$193$	523859.			1.01233			0.506164	+	0.862437i	$0.331063\pi$
$194$	−274676.	+	475753.i	−0.523983	+	0.907564i
$195$	32995.1			0.0621388
$196$	203989.			0.379286
$197$	45111.8	−	78135.9i	0.0828180	−	0.143445i	−0.821641	−	0.570005i	$-0.806941\pi$
$197$	45111.8	−	78135.9i	0.0828180	−	0.143445i	0.904459	+	0.426560i	$0.140275\pi$
$198$	−312362.	−	541026.i	−0.566232	−	0.980743i
$199$	−168650.			−0.301893			−0.150946	−	0.988542i	$-0.548232\pi$
$199$	−168650.			−0.301893			−0.150946	+	0.988542i	$0.548232\pi$
$200$	108955.	−	188716.i	0.192607	−	0.333606i
$201$	−12987.5	+	22495.1i	−0.0226744	+	0.0392733i
$202$	−221324.	+	383344.i	−0.381636	+	0.661013i
$203$	−612897.	−	1.06157e6i	−1.04387	−	1.80804i
$204$	16481.1	+	28546.2i	0.0277276	+	0.0480256i
$205$	−501147.	+	868012.i	−0.832876	+	1.44258i
$206$	−137097.	+	237459.i	−0.225092	+	0.389870i
$207$	−145528.	+	252062.i	−0.236059	+	0.408867i
$208$	−90399.3			−0.144879
$209$	−731130.	−	1.26635e6i	−1.15779	−	2.00535i
$210$	−32127.7	+	55646.8i	−0.0502726	+	0.0870747i
$211$	315198.			0.487391			0.243695	−	0.969852i	$-0.421640\pi$
$211$	315198.			0.487391			0.243695	+	0.969852i	$0.421640\pi$
$212$	213130.			0.325690
$213$	16317.0	−	28261.9i	0.0246429	−	0.0426827i
$214$	−104515.			−0.156007
$215$	−723122.	−	1.25248e6i	−1.06688	−	1.84789i
$216$	35866.8			0.0523068
$217$	229439.	+	397401.i	0.330764	+	0.572900i
$218$	−409055.	−	708504.i	−0.582962	−	1.00972i
$219$	−4891.39	−	8472.14i	−0.00689164	−	0.0119367i
$220$	417791.	−	723635.i	0.581972	−	1.00801i
$221$	629143.			0.866500
$222$	−4219.29	−	38283.9i	−0.00574589	−	0.0521355i
$223$	108302.			0.145839			0.0729196	−	0.997338i	$-0.476768\pi$
$223$	108302.			0.145839			0.0729196	+	0.997338i	$0.476768\pi$
$224$	88022.8	−	152460.i	0.117213	−	0.203019i
$225$	411413.	+	712588.i	0.541778	+	0.938387i
$226$	380024.	+	658221.i	0.494925	+	0.857236i
$227$	−28009.3	−	48513.5i	−0.0360776	−	0.0624882i	0.847423	−	0.530919i	$-0.178153\pi$
$227$	−28009.3	−	48513.5i	−0.0360776	−	0.0624882i	−0.883500	+	0.468430i	$0.844820\pi$
$228$	41860.1			0.0533289
$229$	162338.	+	281177.i	0.204565	+	0.354316i	0.949994	−	0.312268i	$-0.101089\pi$
$229$	162338.	+	281177.i	0.204565	+	0.354316i	−0.745429	+	0.666585i	$0.767755\pi$
$230$	−389295.			−0.485243
$231$	−64237.1	+	111262.i	−0.0792056	+	0.137188i
$232$	−456323.			−0.556611
$233$	803296.			0.969361			0.484681	−	0.874691i	$-0.338936\pi$
$233$	803296.			0.969361			0.484681	+	0.874691i	$0.338936\pi$
$234$	170673.	−	295614.i	0.203763	−	0.352928i
$235$	707231.	+	1.22496e6i	0.835395	+	1.44695i
$236$	123148.			0.143929
$237$	51334.7	−	88914.3i	0.0593663	−	0.102826i
$238$	−612604.	+	1.06106e6i	−0.701031	+	1.21422i
$239$	−577166.	+	999680.i	−0.653591	+	1.13205i	0.328655	+	0.944450i	$0.393405\pi$
$239$	−577166.	+	999680.i	−0.653591	+	1.13205i	−0.982245	+	0.187602i	$0.939929\pi$
$240$	11960.1	+	20715.5i	0.0134031	+	0.0232149i
$241$	−37865.0	−	65584.2i	−0.0419948	−	0.0727372i	0.844264	−	0.535927i	$-0.180038\pi$
$241$	−37865.0	−	65584.2i	−0.0419948	−	0.0727372i	−0.886259	+	0.463190i	$0.846705\pi$
$242$	513242.	−	888961.i	0.563357	−	0.975763i
$243$	−101668.	+	176094.i	−0.110451	+	0.191306i
$244$	−116201.	+	201265.i	−0.124949	+	0.216418i
$245$	−1.03024e6			−1.09654
$246$	−28684.5	−	49682.9i	−0.0302210	−	0.0523443i
$247$	399486.	−	691931.i	0.416639	−	0.721639i
$248$	170825.			0.176369
$249$	−46207.2			−0.0472292
$250$	−45227.5	+	78336.3i	−0.0457670	+	0.0792708i
$251$	−592206.			−0.593319			−0.296660	−	0.954983i	$-0.595873\pi$
$251$	−592206.			−0.593319			−0.296660	+	0.954983i	$0.595873\pi$
$252$	332373.	+	575686.i	0.329704	+	0.571064i
$253$	−778368.			−0.764511
$254$	88215.1	+	152793.i	0.0857944	+	0.148600i
$255$	−83237.5	−	144172.i	−0.0801620	−	0.138845i
$256$	−32768.0	−	56755.8i	−0.0312500	−	0.0541266i
$257$	−231855.	+	401585.i	−0.218970	+	0.379267i	−0.954493	−	0.298232i	$-0.903603\pi$
$257$	−231855.	+	401585.i	−0.218970	+	0.379267i	0.735523	+	0.677499i	$0.236936\pi$
$258$	82779.6			0.0774237
$259$	1.15395e6	−	847325.i	1.06890	−	0.784875i
$260$	456558.			0.418854
$261$	861533.	−	1.49222e6i	0.782836	−	1.35591i
$262$	−34974.1	−	60576.9i	−0.0314770	−	0.0545197i
$263$	−462933.	−	801823.i	−0.412694	−	0.714808i	0.582489	−	0.812839i	$-0.302079\pi$
$263$	−462933.	−	801823.i	−0.412694	−	0.714808i	−0.995183	+	0.0980309i	$0.968746\pi$
$264$	23913.4	+	41419.2i	0.0211169	+	0.0365756i
$265$	−1.07640e6			−0.941588
$266$	777969.	+	1.34748e6i	0.674153	+	1.16767i
$267$	151975.			0.130465
$268$	−179711.	+	311268.i	−0.152840	+	0.264727i
$269$	−63285.0			−0.0533237			−0.0266618	−	0.999645i	$-0.508488\pi$
$269$	−63285.0			−0.0533237			−0.0266618	+	0.999645i	$0.508488\pi$
$270$	−181144.			−0.151222
$271$	−59466.1	+	102998.i	−0.0491865	+	0.0851936i	−0.889570	−	0.456798i	$-0.848996\pi$
$271$	−59466.1	+	102998.i	−0.0491865	+	0.0851936i	0.840384	+	0.541992i	$0.182330\pi$
$272$	228052.	+	394998.i	0.186901	+	0.323722i
$273$	−70197.8			−0.0570055
$274$	186675.	−	323330.i	0.150213	−	0.260177i
$275$	−1.10023e6	+	1.90566e6i	−0.877311	+	1.51955i
$276$	11141.2	−	19297.0i	0.00880354	−	0.0152482i
$277$	206212.	+	357170.i	0.161478	+	0.279689i	0.935399	−	0.353594i	$-0.115040\pi$
$277$	206212.	+	357170.i	0.161478	+	0.279689i	−0.773921	+	0.633283i	$0.781707\pi$
$278$	−149932.	−	259690.i	−0.116355	−	0.201532i
$279$	−322517.	+	558616.i	−0.248052	+	0.429638i
$280$	−444556.	+	769994.i	−0.338869	+	0.586938i
$281$	−857708.	+	1.48559e6i	−0.647998	+	1.12237i	0.335602	+	0.942004i	$0.391060\pi$
$281$	−857708.	+	1.48559e6i	−0.647998	+	1.12237i	−0.983600	+	0.180362i	$0.942273\pi$
$282$	−80960.4			−0.0606248
$283$	1.20304e6	+	2.08372e6i	0.892921	+	1.54658i	0.836357	+	0.548186i	$0.184681\pi$
$283$	1.20304e6	+	2.08372e6i	0.892921	+	1.54658i	0.0565642	+	0.998399i	$0.481985\pi$
$284$	225781.	−	391064.i	0.166108	−	0.287708i
$285$	−211413.			−0.154177
$286$	912856.			0.659914
$287$	1.06620e6	−	1.84671e6i	0.764072	−	1.32341i
$288$	247463.			0.175804
$289$	−877224.	−	1.51940e6i	−0.617826	−	1.07011i
$290$	2.30464e6			1.60919
$291$	79402.5	+	137529.i	0.0549670	+	0.0952056i
$292$	−67683.0	−	117230.i	−0.0464539	−	0.0804605i
$293$	329763.	+	571166.i	0.224405	+	0.388681i	0.956141	−	0.292908i	$-0.0946228\pi$
$293$	329763.	+	571166.i	0.224405	+	0.388681i	−0.731736	+	0.681588i	$0.761289\pi$
$294$	29484.3	−	51068.3i	0.0198940	−	0.0344574i
$295$	−621955.			−0.416106
$296$	−58383.0	−	529740.i	−0.0387309	−	0.351426i
$297$	−362185.			−0.238254
$298$	−534498.	+	925777.i	−0.348662	+	0.603901i
$299$	−212648.	−	368318.i	−0.137557	−	0.238256i
$300$	−31496.4	−	54553.3i	−0.0202049	−	0.0349960i
$301$	1.53846e6	+	2.66469e6i	0.978744	+	1.69523i
$302$	−1.76915e6			−1.11621
$303$	63979.5	+	110816.i	0.0400345	+	0.0693418i
$304$	579225.			0.359470
$305$	586867.	−	1.01648e6i	0.361235	−	0.625678i
$306$	−1.72224e6			−1.05146
$307$	−2.68684e6			−1.62703			−0.813514	−	0.581545i	$-0.802448\pi$
$307$	−2.68684e6			−1.62703			−0.813514	+	0.581545i	$0.802448\pi$
$308$	−888859.	+	1.53955e6i	−0.533895	+	0.924734i
$309$	39631.5	+	68643.7i	0.0236126	+	0.0408982i
$310$	−862748.			−0.509894
$311$	481189.	−	833444.i	0.282108	−	0.488625i	−0.689796	−	0.724004i	$-0.742300\pi$
$311$	481189.	−	833444.i	0.282108	−	0.488625i	0.971904	+	0.235379i	$0.0756331\pi$
$312$	−13066.2	+	22631.2i	−0.00759909	+	0.0131620i
$313$	310564.	−	537913.i	0.179180	−	0.310349i	−0.762420	−	0.647083i	$-0.775989\pi$
$313$	310564.	−	537913.i	0.179180	−	0.310349i	0.941600	+	0.336733i	$0.109322\pi$
$314$	761470.	+	1.31891e6i	0.435842	+	0.754900i
$315$	−1.67864e6	−	2.90749e6i	−0.953192	−	1.65098i
$316$	710327.	−	1.23032e6i	0.400166	−	0.693108i
$317$	117139.	−	202890.i	0.0654714	−	0.113400i	−0.831432	−	0.555627i	$-0.812478\pi$
$317$	117139.	−	202890.i	0.0654714	−	0.113400i	0.896903	+	0.442227i	$0.145812\pi$
$318$	30805.4	−	53356.5i	0.0170828	−	0.0295883i
$319$	4.60797e6			2.53532
$320$	165494.	+	286643.i	0.0903455	+	0.156483i
$321$	−15106.4	+	26165.0i	−0.00818273	+	0.0141729i
$322$	828233.			0.445157
$323$	−4.03117e6			−2.14993
$324$	−464609.	+	804726.i	−0.245881	+	0.425878i
$325$	−1.20233e6			−0.631414
$326$	400574.	+	693814.i	0.208756	+	0.361576i
$327$	−236496.			−0.122308
$328$	−396911.	−	687471.i	−0.203708	−	0.352833i
$329$	−1.50465e6	−	2.60613e6i	−0.766382	−	1.32741i
$330$	−120774.	−	209186.i	−0.0610502	−	0.105742i
$331$	37012.9	−	64108.2i	0.0185688	−	0.0321620i	−0.856592	−	0.515995i	$-0.827422\pi$
$331$	37012.9	−	64108.2i	0.0185688	−	0.0321620i	0.875160	+	0.483833i	$0.160756\pi$
$332$	−639376.			−0.318354
$333$	1.84253e6	+	809226.i	0.910549	+	0.399907i
$334$	2.36754e6			1.16127
$335$	907623.	−	1.57205e6i	0.441869	−	0.765339i
$336$	−25445.3	−	44072.6i	−0.0122959	−	0.0212971i
$337$	−42100.9	−	72920.9i	−0.0201937	−	0.0349766i	0.855752	−	0.517386i	$-0.173095\pi$
$337$	−42100.9	−	72920.9i	−0.0201937	−	0.0349766i	−0.875946	+	0.482410i	$0.839762\pi$
$338$	−493196.	−	854240.i	−0.234816	−	0.406713i
$339$	219712.			0.103838
$340$	−1.15177e6	−	1.99492e6i	−0.540342	−	0.935899i
$341$	−1.72500e6			−0.803349
$342$	−1.09357e6	+	1.89412e6i	−0.505571	+	0.875674i
$343$	−697592.			−0.320159
$344$	1.14543e6			0.521884
$345$	−56268.0	+	97459.1i	−0.0254515	+	0.0440834i
$346$	131560.	+	227869.i	0.0590792	+	0.102328i
$347$	1.60416e6			0.715195			0.357598	−	0.933876i	$-0.383596\pi$
$347$	1.60416e6			0.715195			0.357598	+	0.933876i	$0.383596\pi$
$348$	−65956.1	+	114239.i	−0.0291949	+	0.0505670i
$349$	1.25971e6	−	2.18188e6i	0.553613	−	0.958887i	−0.444397	−	0.895830i	$-0.646582\pi$
$349$	1.25971e6	−	2.18188e6i	0.553613	−	0.958887i	0.998010	−	0.0630564i	$-0.0200848\pi$
$350$	1.17072e6	−	2.02775e6i	0.510838	−	0.884797i
$351$	−98948.2	−	171383.i	−0.0428687	−	0.0742507i
$352$	330893.	+	573123.i	0.142341	+	0.246542i
$353$	−200443.	+	347178.i	−0.0856159	+	0.148291i	−0.905654	−	0.424019i	$-0.860619\pi$
$353$	−200443.	+	347178.i	−0.0856159	+	0.148291i	0.820038	+	0.572310i	$0.193952\pi$
$354$	17799.6	−	30829.8i	0.00754923	−	0.0130756i
$355$	−1.14030e6	+	1.97506e6i	−0.480229	+	0.831780i
$356$	2.10290e6			0.879416
$357$	177089.	+	306728.i	0.0735398	+	0.127375i
$358$	1.49556e6	−	2.59039e6i	0.616733	−	1.06821i
$359$	1.27839e6			0.523513			0.261756	−	0.965134i	$-0.415698\pi$
$359$	1.27839e6			0.523513			0.261756	+	0.965134i	$0.415698\pi$
$360$	−1.24980e6			−0.508259
$361$	−1.32162e6	+	2.28911e6i	−0.533751	+	0.924484i
$362$	1.79055e6			0.718148
$363$	−148366.	−	256978.i	−0.0590974	−	0.102360i
$364$	−971337.			−0.384252
$365$	341831.	+	592068.i	0.134301	+	0.232616i
$366$	33590.9	+	58181.1i	0.0131075	+	0.0227028i
$367$	−135636.	−	234929.i	−0.0525666	−	0.0910480i	0.838545	−	0.544833i	$-0.183407\pi$
$367$	−135636.	−	234929.i	−0.0525666	−	0.0910480i	−0.891111	+	0.453785i	$0.850074\pi$
$368$	154162.	−	267016.i	0.0593414	−	0.102782i
$369$	2.99746e6			1.14601
$370$	294861.	+	2.67543e6i	0.111973	+	1.01599i
$371$	2.29007e6			0.863803
$372$	24690.8	−	42765.8i	0.00925078	−	0.0160228i
$373$	−1.04342e6	−	1.80725e6i	−0.388317	−	0.672585i	0.603906	−	0.797055i	$-0.293610\pi$
$373$	−1.04342e6	−	1.80725e6i	−0.388317	−	0.672585i	−0.992223	+	0.124471i	$0.960277\pi$
$374$	−2.30288e6	−	3.98871e6i	−0.851320	−	1.47453i
$375$	13074.2	+	22645.2i	0.00480106	+	0.00831569i
$376$	−1.12026e6			−0.408649
$377$	1.25889e6	+	2.18046e6i	0.456177	+	0.790122i
$378$	385388.			0.138729
$379$	1.32483e6	−	2.29467e6i	0.473763	−	0.820581i	−0.525786	−	0.850617i	$-0.676229\pi$
$379$	1.32483e6	−	2.29467e6i	0.473763	−	0.820581i	0.999549	+	0.0300357i	$0.00956208\pi$
$380$	−2.92535e6			−1.03925
$381$	51001.9			0.0180001
$382$	1.24598e6	−	2.15811e6i	0.436872	−	0.756684i
$383$	−704251.	−	1.21980e6i	−0.245319	−	0.424904i	0.716902	−	0.697173i	$-0.245559\pi$
$383$	−704251.	−	1.21980e6i	−0.245319	−	0.424904i	−0.962221	+	0.272269i	$0.912226\pi$
$384$	−18944.9			−0.00655639
$385$	4.48915e6	−	7.77544e6i	1.54352	−	2.67346i
$386$	1.04772e6	−	1.81470e6i	0.357912	−	0.619922i
$387$	−2.16257e6	+	3.74568e6i	−0.733994	+	1.27132i
$388$	1.09871e6	+	1.90301e6i	0.370512	+	0.641745i
$389$	−1.78520e6	−	3.09205e6i	−0.598153	−	1.03603i	−0.993094	−	0.117325i	$-0.962568\pi$
$389$	−1.78520e6	−	3.09205e6i	−0.598153	−	1.03603i	0.394940	−	0.918707i	$-0.370765\pi$
$390$	65990.2	−	114298.i	0.0219694	−	0.0380521i
$391$	−1.07291e6	+	1.85833e6i	−0.354911	+	0.614724i
$392$	407979.	−	706640.i	0.134098	−	0.232265i
$393$	−20220.4			−0.00660401
$394$	−180447.	−	312544.i	−0.0585612	−	0.101431i
$395$	−3.58748e6	+	6.21370e6i	−1.15690	+	2.00381i
$396$	−2.49889e6			−0.800774
$397$	−813002.			−0.258890			−0.129445	−	0.991587i	$-0.541320\pi$
$397$	−813002.			−0.258890			−0.129445	+	0.991587i	$0.541320\pi$
$398$	−337299.	+	584219.i	−0.106735	+	0.184871i
$399$	449785.			0.141440
$400$	−435820.	−	754863.i	−0.136194	−	0.235895i
$401$	3.40545e6			1.05758			0.528790	−	0.848753i	$-0.322646\pi$
$401$	3.40545e6			1.05758			0.528790	+	0.848753i	$0.322646\pi$
$402$	51950.2	+	89980.3i	0.0160333	+	0.0277704i
$403$	−471267.	−	816259.i	−0.144546	−	0.250360i
$404$	885295.	+	1.53338e6i	0.269857	+	0.467407i
$405$	2.34649e6	−	4.06424e6i	0.710855	−	1.23124i
$406$	−4.90317e6			−1.47626
$407$	589555.	+	5.34934e6i	0.176416	+	1.60072i
$408$	131849.			0.0392127
$409$	−987071.	+	1.70966e6i	−0.291770	+	0.505360i	−0.974228	−	0.225564i	$-0.927577\pi$
$409$	−987071.	+	1.70966e6i	−0.291770	+	0.505360i	0.682459	+	0.730924i	$0.260911\pi$
$410$	2.00459e6	+	3.47205e6i	0.588933	+	1.02006i
$411$	−53963.2	−	93467.1i	−0.0157577	−	0.0272932i
$412$	548387.	+	949834.i	0.159164	+	0.275680i
$413$	1.32322e6			0.381731
$414$	582113.	+	1.00825e6i	0.166919	+	0.289113i
$415$	3.22915e6			0.920381
$416$	−180799.	+	313152.i	−0.0512226	+	0.0887201i
$417$	−86683.9			−0.0244117
$418$	−5.84904e6			−1.63736
$419$	−1.93595e6	+	3.35316e6i	−0.538714	+	0.933080i	0.460260	+	0.887784i	$0.347756\pi$
$419$	−1.93595e6	+	3.35316e6i	−0.538714	+	0.933080i	−0.998974	+	0.0452957i	$0.985577\pi$
$420$	128511.	+	222587.i	0.0355481	+	0.0615711i
$421$	1.22230e6			0.336102			0.168051	−	0.985778i	$-0.446253\pi$
$421$	1.22230e6			0.336102			0.168051	+	0.985778i	$0.446253\pi$
$422$	630396.	−	1.09188e6i	0.172319	−	0.298465i
$423$	2.11505e6	−	3.66337e6i	0.574737	−	0.995473i
$424$	426259.	−	738303.i	0.115149	−	0.199444i
$425$	3.03314e6	+	5.25355e6i	0.814554	+	1.41085i
$426$	−65268.0	−	113048.i	−0.0174251	−	0.0301812i
$427$	−1.24857e6	+	2.16259e6i	−0.331393	+	0.573990i
$428$	−209030.	+	362050.i	−0.0551567	+	0.0955342i
$429$	131943.	−	228532.i	0.0346132	−	0.0599519i
$430$	−5.78498e6			−1.50880
$431$	1.98291e6	+	3.43450e6i	0.514174	+	0.890575i	0.999865	+	0.0164447i	$0.00523475\pi$
$431$	1.98291e6	+	3.43450e6i	0.514174	+	0.890575i	−0.485691	+	0.874131i	$0.661432\pi$
$432$	71733.6	−	124246.i	0.0184933	−	0.0320313i
$433$	−1.91179e6			−0.490027			−0.245013	−	0.969520i	$-0.578792\pi$
$433$	−1.91179e6			−0.490027			−0.245013	+	0.969520i	$0.578792\pi$
$434$	1.83551e6			0.467771
$435$	333109.	−	576962.i	0.0844041	−	0.146192i
$436$	−3.27244e6			−0.824433
$437$	1.36252e6	+	2.35996e6i	0.341303	+	0.591155i
$438$	−39131.1			−0.00974624
$439$	100272.	+	173676.i	0.0248324	+	0.0430110i	0.878175	−	0.478340i	$-0.158761\pi$
$439$	100272.	+	173676.i	0.0248324	+	0.0430110i	−0.853342	+	0.521351i	$0.825428\pi$
$440$	−1.67116e6	−	2.89454e6i	−0.411517	−	0.712768i
$441$	1.54052e6	+	2.66826e6i	0.377200	+	0.653329i
$442$	1.25829e6	−	2.17941e6i	0.306354	−	0.530621i
$443$	−7.13297e6			−1.72688			−0.863438	−	0.504454i	$-0.831694\pi$
$443$	−7.13297e6			−1.72688			−0.863438	+	0.504454i	$0.831694\pi$
$444$	−141058.	−	61951.7i	−0.0339578	−	0.0149140i
$445$	−1.06206e7			−2.54244
$446$	216604.	−	375169.i	0.0515619	−	0.0893079i
$447$	154511.	+	267621.i	0.0365755	+	0.0633506i
$448$	−352091.	−	609840.i	−0.0828820	−	0.143556i
$449$	781564.	+	1.35371e6i	0.182957	+	0.316891i	0.942886	−	0.333115i	$-0.108100\pi$
$449$	781564.	+	1.35371e6i	0.182957	+	0.316891i	−0.759929	+	0.650006i	$0.774766\pi$
$450$	3.29130e6			0.766190
$451$	4.00803e6	+	6.94212e6i	0.927876	+	1.60713i
$452$	3.04019e6			0.699930
$453$	−255710.	+	442903.i	−0.0585467	+	0.101406i
$454$	−224074.			−0.0510214
$455$	4.90571e6			1.11090
$456$	83720.2	−	145008.i	0.0188546	−	0.0326572i
$457$	−1.22319e6	−	2.11862e6i	−0.273969	−	0.474529i	0.695905	−	0.718134i	$-0.255003\pi$
$457$	−1.22319e6	−	2.11862e6i	−0.273969	−	0.474529i	−0.969875	+	0.243605i	$0.921670\pi$
$458$	1.29870e6			0.289298
$459$	−499238.	+	864705.i	−0.110605	+	0.191574i
$460$	−778590.	+	1.34856e6i	−0.171559	+	0.297149i
$461$	1.03062e6	−	1.78508e6i	0.225863	−	0.391205i	−0.730715	−	0.682682i	$-0.760813\pi$
$461$	1.03062e6	−	1.78508e6i	0.225863	−	0.391205i	0.956578	+	0.291477i	$0.0941466\pi$
$462$	256948.	+	445048.i	0.0560068	+	0.0970067i
$463$	−3.63356e6	−	6.29350e6i	−0.787734	−	1.36439i	−0.927352	−	0.374189i	$-0.877921\pi$
$463$	−3.63356e6	−	6.29350e6i	−0.787734	−	1.36439i	0.139619	−	0.990205i	$-0.455412\pi$
$464$	−912645.	+	1.58075e6i	−0.196792	+	0.340853i
$465$	−124700.	+	215987.i	−0.0267445	+	0.0463229i
$466$	1.60659e6	−	2.78270e6i	0.342721	−	0.593610i
$467$	−5.98917e6			−1.27079			−0.635396	−	0.772186i	$-0.719163\pi$
$467$	−5.98917e6			−1.27079			−0.635396	+	0.772186i	$0.719163\pi$
$468$	−682692.	−	1.18246e6i	−0.144082	−	0.249558i
$469$	−1.93099e6	+	3.34457e6i	−0.405366	+	0.702114i
$470$	5.65785e6			1.18143
$471$	440247.			0.0914416
$472$	246296.	−	426598.i	0.0508865	−	0.0881380i
$473$	−1.15667e7			−2.37714
$474$	−205339.	−	355657.i	−0.0419783	−	0.0727086i
$475$	7.70379e6			1.56664
$476$	2.45042e6	+	4.24424e6i	0.495704	+	0.858584i
$477$	1.60955e6	+	2.78782e6i	0.323898	+	0.561008i
$478$	2.30866e6	+	3.99872e6i	0.462158	+	0.800482i
$479$	−4.77027e6	+	8.26234e6i	−0.949957	+	1.64537i	−0.204448	+	0.978877i	$0.565540\pi$
$479$	−4.77027e6	+	8.26234e6i	−0.949957	+	1.64537i	−0.745508	+	0.666496i	$0.767793\pi$
$480$	95680.7			0.0189549
$481$	−2.37020e6	+	1.74040e6i	−0.467114	+	0.342994i
$482$	−302920.			−0.0593896
$483$	119711.	−	207346.i	0.0233490	−	0.0404416i
$484$	−2.05297e6	−	3.55584e6i	−0.398353	−	0.689968i
$485$	−5.54897e6	−	9.61110e6i	−1.07117	−	1.85532i
$486$	406671.	+	704375.i	0.0781003	+	0.135274i
$487$	−2.44745e6			−0.467618			−0.233809	−	0.972283i	$-0.575119\pi$
$487$	−2.44745e6			−0.467618			−0.233809	+	0.972283i	$0.575119\pi$
$488$	464802.	+	805061.i	0.0883524	+	0.153031i
$489$	231593.			0.0437979
$490$	−2.06048e6	+	3.56886e6i	−0.387685	+	0.671490i
$491$	8.94639e6			1.67473			0.837364	−	0.546646i	$-0.184095\pi$
$491$	8.94639e6			1.67473			0.837364	+	0.546646i	$0.184095\pi$
$492$	−229476.			−0.0427390
$493$	6.35165e6	−	1.10014e7i	1.17698	−	2.03859i
$494$	−1.59795e6	−	2.76772e6i	−0.294608	−	0.510276i
$495$	1.26206e7			2.31508
$496$	341651.	−	591757.i	0.0623560	−	0.108004i
$497$	2.42601e6	−	4.20197e6i	0.440557	−	0.763066i
$498$	−92414.3	+	160066.i	−0.0166981	+	0.0289219i
$499$	425263.	+	736577.i	0.0764550	+	0.132424i	0.901718	−	0.432325i	$-0.142307\pi$
$499$	425263.	+	736577.i	0.0764550	+	0.132424i	−0.825263	+	0.564748i	$0.808973\pi$
$500$	180910.	+	313345.i	0.0323622	+	0.0560529i
$501$	342201.	−	592709.i	0.0609097	−	0.105499i
$502$	−1.18441e6	+	2.05146e6i	−0.209770	+	0.363332i
$503$	679867.	−	1.17756e6i	0.119813	−	0.207522i	−0.799880	−	0.600159i	$-0.795104\pi$
$503$	679867.	−	1.17756e6i	0.119813	−	0.207522i	0.919693	+	0.392637i	$0.128437\pi$
$504$	2.65898e6			0.466272
$505$	−4.47115e6	−	7.74426e6i	−0.780173	−	1.35130i
$506$	−1.55674e6	+	2.69634e6i	−0.270295	+	0.468165i
$507$	−285143.			−0.0492654
$508$	705721.			0.121332
$509$	1.48874e6	−	2.57857e6i	0.254697	−	0.441148i	−0.710116	−	0.704084i	$-0.751358\pi$
$509$	1.48874e6	−	2.57857e6i	0.254697	−	0.441148i	0.964813	+	0.262937i	$0.0846910\pi$
$510$	−665900.			−0.113366
$511$	−727252.	−	1.25964e6i	−0.123206	−	0.213399i
$512$	−262144.			−0.0441942
$513$	634001.	+	1.09812e6i	0.106364	+	0.184229i
$514$	927421.	+	1.60634e6i	0.154835	+	0.268182i
$515$	−2.76961e6	−	4.79711e6i	−0.460151	−	0.797005i
$516$	165559.	−	286757.i	0.0273734	−	0.0474121i
$517$	1.13125e7			1.86136
$518$	−627324.	−	5.69204e6i	−0.102723	−	0.932059i
$519$	76062.0			0.0123951
$520$	913117.	−	1.58156e6i	0.148087	−	0.256495i
$521$	3.41479e6	+	5.91458e6i	0.551149	+	0.954618i	0.998192	+	0.0601057i	$0.0191438\pi$
$521$	3.41479e6	+	5.91458e6i	0.551149	+	0.954618i	−0.447043	+	0.894513i	$0.647523\pi$
$522$	−3.44613e6	−	5.96888e6i	−0.553549	−	0.958774i
$523$	−2.06235e6	−	3.57209e6i	−0.329691	−	0.571042i	0.652759	−	0.757565i	$-0.273611\pi$
$523$	−2.06235e6	−	3.57209e6i	−0.329691	−	0.571042i	−0.982451	+	0.186523i	$0.940278\pi$
$524$	−279793.			−0.0445152
$525$	−338428.	−	586174.i	−0.0535880	−	0.0928172i
$526$	−3.70346e6			−0.583638
$527$	−2.37775e6	+	4.11839e6i	−0.372941	+	0.645953i
$528$	191307.			0.0298639
$529$	−4.98579e6			−0.774630
$530$	−2.15281e6	+	3.72878e6i	−0.332902	+	0.576602i
$531$	930010.	+	1.61083e6i	0.143137	+	0.247920i
$532$	6.22375e6			0.953396
$533$	−2.18997e6	+	3.79314e6i	−0.333903	+	0.578337i
$534$	303950.	−	526457.i	0.0461264	−	0.0798932i
$535$	1.05570e6	−	1.82852e6i	0.159461	−	0.276195i
$536$	718843.	+	1.24507e6i	0.108074	+	0.187190i
$537$	−432333.	−	748822.i	−0.0646967	−	0.112058i
$538$	−126570.	+	219226.i	−0.0188528	+	0.0326540i
$539$	−4.11979e6	+	7.13569e6i	−0.610806	+	1.05795i
$540$	−362288.	+	627502.i	−0.0534650	+	0.0926042i
$541$	1.04365e7			1.53307			0.766533	−	0.642205i	$-0.221980\pi$
$541$	1.04365e7			1.53307			0.766533	+	0.642205i	$0.221980\pi$
$542$	237864.	+	411993.i	0.0347801	+	0.0602410i
$543$	258803.	−	448259.i	0.0376677	−	0.0652424i
$544$	1.82442e6			0.264318
$545$	1.65273e7			2.38348
$546$	−140396.	+	243172.i	−0.0201545	+	0.0349086i
$547$	−9.43501e6			−1.34826			−0.674130	−	0.738612i	$-0.735481\pi$
$547$	−9.43501e6			−1.34826			−0.674130	+	0.738612i	$0.735481\pi$
$548$	−746698.	−	1.29332e6i	−0.106217	−	0.183973i
$549$	−3.51017e6			−0.497047
$550$	4.40094e6	+	7.62265e6i	0.620352	+	1.07448i
$551$	−8.06620e6	−	1.39711e7i	−1.13185	−	1.96043i
$552$	−44564.6	−	77188.2i	−0.00622505	−	0.0107821i
$553$	7.63244e6	−	1.32198e7i	1.06133	−	1.83828i
$554$	1.64970e6			0.228365
$555$	712408.	+	312885.i	0.0981739	+	0.0431173i
$556$	−1.19946e6			−0.164550
$557$	4.75436e6	−	8.23479e6i	0.649313	−	1.12464i	−0.333975	−	0.942582i	$-0.608390\pi$
$557$	4.75436e6	−	8.23479e6i	0.649313	−	1.12464i	0.983287	−	0.182060i	$-0.0582766\pi$
$558$	1.29007e6	+	2.23446e6i	0.175399	+	0.303800i
$559$	−3.15998e6	−	5.47325e6i	−0.427716	−	0.740826i
$560$	1.77823e6	+	3.07998e6i	0.239616	+	0.415028i
$561$	−1.33142e6			−0.178611
$562$	3.43083e6	+	5.94238e6i	0.458204	+	0.793633i
$563$	−8.61074e6			−1.14490			−0.572452	−	0.819938i	$-0.694008\pi$
$563$	−8.61074e6			−1.14490			−0.572452	+	0.819938i	$0.694008\pi$
$564$	−161921.	+	280455.i	−0.0214341	+	0.0371249i
$565$	−1.53544e7			−2.02354
$566$	9.62430e6			1.26278
$567$	−4.99221e6	+	8.64676e6i	−0.652131	+	1.12952i
$568$	−903124.	−	1.56426e6i	−0.117456	−	0.203440i
$569$	−1.52294e7			−1.97198			−0.985992	−	0.166793i	$-0.946659\pi$
$569$	−1.52294e7			−1.97198			−0.985992	+	0.166793i	$0.946659\pi$
$570$	−422826.	+	732356.i	−0.0545098	+	0.0944137i
$571$	3.67655e6	−	6.36798e6i	0.471901	−	0.817356i	−0.527582	−	0.849504i	$-0.676901\pi$
$571$	3.67655e6	−	6.36798e6i	0.471901	−	0.817356i	0.999483	+	0.0321478i	$0.0102347\pi$
$572$	1.82571e6	−	3.16223e6i	0.233315	−	0.404113i
$573$	−360185.	−	623859.i	−0.0458288	−	0.0793779i
$574$	−4.26480e6	−	7.38686e6i	−0.540280	−	0.935793i
$575$	2.05038e6	−	3.55137e6i	0.258622	−	0.447946i
$576$	494926.	−	857237.i	0.0621561	−	0.107658i
$577$	2.65338e6	−	4.59578e6i	0.331787	−	0.574672i	−0.651075	−	0.759013i	$-0.725682\pi$
$577$	2.65338e6	−	4.59578e6i	0.331787	−	0.574672i	0.982862	+	0.184341i	$0.0590151\pi$
$578$	−7.01780e6			−0.873738
$579$	−302871.	−	524588.i	−0.0375458	−	0.0650312i
$580$	4.60928e6	−	7.98351e6i	0.568936	−	0.985426i
$581$	−6.87008e6			−0.844347
$582$	635220.			0.0777350
$583$	−4.30439e6	+	7.45542e6i	−0.524494	+	0.908450i
$584$	−541464.			−0.0656958
$585$	3.44791e6	+	5.97196e6i	0.416550	+	0.721485i
$586$	2.63810e6			0.317357
$587$	1.12598e6	+	1.95026e6i	0.134876	+	0.233613i	0.925550	−	0.378625i	$-0.123603\pi$
$587$	1.12598e6	+	1.95026e6i	0.134876	+	0.233613i	−0.790674	+	0.612238i	$0.790270\pi$
$588$	−117937.	−	204273.i	−0.0140672	−	0.0243651i
$589$	3.01960e6	+	5.23010e6i	0.358642	+	0.621186i
$590$	−1.24391e6	+	2.15452e6i	−0.147116	+	0.254812i
$591$	−104326.			−0.0122864
$592$	−1.95184e6	−	857235.i	−0.228897	−	0.100530i
$593$	−2.90482e6			−0.339220			−0.169610	−	0.985511i	$-0.554251\pi$
$593$	−2.90482e6			−0.339220			−0.169610	+	0.985511i	$0.554251\pi$
$594$	−724370.	+	1.25465e6i	−0.0842353	+	0.145900i
$595$	−1.23757e7	−	2.14354e7i	−1.43311	−	2.48221i
$596$	2.13799e6	+	3.70311e6i	0.246542	+	0.427023i
$597$	97505.3	+	168884.i	0.0111968	+	0.0193934i
$598$	−1.70119e6			−0.194536
$599$	2.85327e6	+	4.94201e6i	0.324919	+	0.562777i	0.981496	−	0.191482i	$-0.0613295\pi$
$599$	2.85327e6	+	4.94201e6i	0.324919	+	0.562777i	−0.656577	+	0.754259i	$0.727996\pi$
$600$	−251971.			−0.0285741
$601$	−7.43246e6	+	1.28734e7i	−0.839357	+	1.45381i	0.0510769	+	0.998695i	$0.483735\pi$
$601$	−7.43246e6	+	1.28734e7i	−0.839357	+	1.45381i	−0.890433	+	0.455113i	$0.849599\pi$
$602$	1.23077e7			1.38415
$603$	−5.42868e6			−0.607996
$604$	−3.53830e6	+	6.12851e6i	−0.394641	+	0.683538i
$605$	1.03684e7	+	1.79587e7i	1.15166	+	1.99474i
$606$	511836.			0.0566173
$607$	−1.99749e6	+	3.45975e6i	−0.220045	+	0.381130i	−0.954822	−	0.297180i	$-0.903954\pi$
$607$	−1.99749e6	+	3.45975e6i	−0.220045	+	0.381130i	0.734776	+	0.678310i	$0.237287\pi$
$608$	1.15845e6	−	2.00649e6i	0.127092	−	0.220130i
$609$	−708697.	+	1.22750e6i	−0.0774314	+	0.134115i
$610$	−2.34747e6	−	4.06593e6i	−0.255432	−	0.442421i
$611$	3.09054e6	+	5.35298e6i	0.334913	+	0.580086i
$612$	−3.44449e6	+	5.96603e6i	−0.371746	+	0.643882i
$613$	−5.97713e6	+	1.03527e7i	−0.642453	+	1.11276i	0.342430	+	0.939543i	$0.388750\pi$
$613$	−5.97713e6	+	1.03527e7i	−0.642453	+	1.11276i	−0.984883	+	0.173219i	$0.944583\pi$
$614$	−5.37367e6	+	9.30747e6i	−0.575241	+	0.996347i
$615$	1.15896e6			0.123561
$616$	3.55544e6	+	6.15820e6i	0.377521	+	0.653886i
$617$	7.75753e6	−	1.34364e7i	0.820372	−	1.42093i	−0.0850342	−	0.996378i	$-0.527100\pi$
$617$	7.75753e6	−	1.34364e7i	0.820372	−	1.42093i	0.905406	−	0.424547i	$-0.139567\pi$
$618$	317052.			0.0333933
$619$	1.13670e7			1.19240			0.596199	−	0.802837i	$-0.296677\pi$
$619$	1.13670e7			1.19240			0.596199	+	0.802837i	$0.296677\pi$
$620$	−1.72550e6	+	2.98865e6i	−0.180275	+	0.312245i
$621$	674963.			0.0702346
$622$	−1.92476e6	−	3.33378e6i	−0.199480	−	0.345510i
$623$	2.25956e7			2.33241
$624$	52264.6	+	90525.0i	0.00537337	+	0.00930694i
$625$	4.40639e6	+	7.63210e6i	0.451215	+	0.781527i
$626$	−1.24226e6	−	2.15165e6i	−0.126700	−	0.219450i
$627$	−845411.	+	1.46429e6i	−0.0858813	+	0.148751i
$628$	6.09176e6			0.616373
$629$	1.35840e7	+	5.96601e6i	1.36899	+	0.601254i
$630$	−1.34291e7			−1.34802
$631$	1.69526e6	−	2.93628e6i	0.169498	−	0.293579i	−0.768746	−	0.639555i	$-0.779119\pi$
$631$	1.69526e6	−	2.93628e6i	0.169498	−	0.293579i	0.938243	+	0.345976i	$0.112452\pi$
$632$	−2.84131e6	−	4.92129e6i	−0.282960	−	0.490102i
$633$	−182233.	−	315636.i	−0.0180766	−	0.0313096i
$634$	−468554.	−	811560.i	−0.0462953	−	0.0801858i
$635$	−3.56422e6			−0.350776
$636$	−123222.	−	213426.i	−0.0120794	−	0.0209221i
$637$	−4.50207e6			−0.439606
$638$	9.21594e6	−	1.59625e7i	0.896371	−	1.55256i
$639$	6.82036e6			0.660778
$640$	1.32395e6			0.127768
$641$	1.57548e6	−	2.72881e6i	0.151449	−	0.262318i	−0.780311	−	0.625392i	$-0.784939\pi$
$641$	1.57548e6	−	2.72881e6i	0.151449	−	0.262318i	0.931761	+	0.363073i	$0.118273\pi$
$642$	60425.6	+	104660.i	0.00578606	+	0.0100218i
$643$	−1.07323e7			−1.02368			−0.511841	−	0.859080i	$-0.671036\pi$
$643$	−1.07323e7			−1.02368			−0.511841	+	0.859080i	$0.671036\pi$
$644$	1.65647e6	−	2.86908e6i	0.157387	−	0.272602i
$645$	−836151.	+	1.44826e6i	−0.0791380	+	0.137071i
$646$	−8.06234e6	+	1.39644e7i	−0.760116	+	1.31656i
$647$	3.85774e6	+	6.68181e6i	0.362304	+	0.627528i	0.988340	−	0.152266i	$-0.0486570\pi$
$647$	3.85774e6	+	6.68181e6i	0.362304	+	0.627528i	−0.626036	+	0.779794i	$0.715324\pi$
$648$	1.85843e6	+	3.21890e6i	0.173864	+	0.301141i
$649$	−2.48711e6	+	4.30780e6i	−0.231784	+	0.401462i
$650$	−2.40465e6	+	4.16498e6i	−0.223239	+	0.386660i
$651$	265302.	−	459517.i	0.0245351	−	0.0424961i
$652$	3.20459e6			0.295225
$653$	−4.10964e6	−	7.11810e6i	−0.377156	−	0.653253i	0.613491	−	0.789701i	$-0.289765\pi$
$653$	−4.10964e6	−	7.11810e6i	−0.377156	−	0.653253i	−0.990647	+	0.136448i	$0.956431\pi$
$654$	−472993.	+	819248.i	−0.0432425	+	0.0748981i
$655$	1.41308e6			0.128696
$656$	−3.17529e6			−0.288087
$657$	1.02228e6	−	1.77064e6i	0.0923966	−	0.160036i
$658$	−1.20372e7			−1.08383
$659$	−4.84529e6	−	8.39229e6i	−0.434617	−	0.752778i	0.562648	−	0.826697i	$-0.309783\pi$
$659$	−4.84529e6	−	8.39229e6i	−0.434617	−	0.752778i	−0.997264	+	0.0739187i	$0.976449\pi$
$660$	−966189.			−0.0863381
$661$	7.77971e6	+	1.34749e7i	0.692564	+	1.19956i	0.970995	+	0.239100i	$0.0768523\pi$
$661$	7.77971e6	+	1.34749e7i	0.692564	+	1.19956i	−0.278431	+	0.960456i	$0.589814\pi$
$662$	−148051.	−	256433.i	−0.0131301	−	0.0227420i
$663$	−363741.	−	630018.i	−0.0321372	−	0.0556633i
$664$	−1.27875e6	+	2.21486e6i	−0.112555	+	0.194952i
$665$	−3.14329e7			−2.75632
$666$	6.48830e6	−	4.76425e6i	0.566820	−	0.416207i
$667$	−8.58735e6			−0.747385
$668$	4.73509e6	−	8.20141e6i	0.410570	−	0.711127i
$669$	−62615.1	−	108453.i	−0.00540896	−	0.00936860i
$670$	−3.63049e6	−	6.28819e6i	−0.312448	−	0.541176i
$671$	−4.69360e6	−	8.12955e6i	−0.402438	−	0.697044i
$672$	−203563.			−0.0173890
$673$	4.31854e6	+	7.47994e6i	0.367536	+	0.636591i	0.989180	−	0.146709i	$-0.0468682\pi$
$673$	4.31854e6	+	7.47994e6i	0.367536	+	0.636591i	−0.621644	+	0.783300i	$0.713535\pi$
$674$	−336807.			−0.0285582
$675$	954071.	−	1.65250e6i	0.0805974	−	0.139599i
$676$	−3.94556e6			−0.332080
$677$	1.23212e7			1.03319			0.516597	−	0.856228i	$-0.327198\pi$
$677$	1.23212e7			1.03319			0.516597	+	0.856228i	$0.327198\pi$
$678$	439424.	−	761105.i	0.0367121	−	0.0635873i
$679$	1.18056e7	+	2.04478e7i	0.982680	+	1.70205i
$680$	−9.21416e6			−0.764159
$681$	−32387.3	+	56096.5i	−0.00267613	+	0.00463520i
$682$	−3.45001e6	+	5.97559e6i	−0.284027	+	0.491949i
$683$	4.17008e6	−	7.22279e6i	0.342052	−	0.592452i	−0.642761	−	0.766067i	$-0.722211\pi$
$683$	4.17008e6	−	7.22279e6i	0.342052	−	0.592452i	0.984814	+	0.173614i	$0.0555446\pi$
$684$	4.37428e6	+	7.57648e6i	0.357492	+	0.619195i
$685$	3.77117e6	+	6.53186e6i	0.307079	+	0.531876i
$686$	−1.39518e6	+	2.41653e6i	−0.113193	+	0.196057i
$687$	187712.	−	325127.i	0.0151740	−	0.0262822i
$688$	2.29087e6	−	3.96790e6i	0.184514	−	0.319587i
$689$	−4.70380e6			−0.377486
$690$	225072.	+	389836.i	0.0179970	+	0.0311716i
$691$	6.43958e6	−	1.11537e7i	0.513053	−	0.888635i	−0.486832	−	0.873496i	$-0.661848\pi$
$691$	6.43958e6	−	1.11537e7i	0.513053	−	0.888635i	0.999885	−	0.0151389i	$-0.00481905\pi$
$692$	1.05248e6			0.0835506
$693$	−2.68505e7			−2.12383
$694$	3.20833e6	−	5.55698e6i	0.252860	−	0.437966i
$695$	6.05783e6			0.475724
$696$	263824.	+	456957.i	0.0206439	+	0.0357563i
$697$	2.20988e7			1.72300
$698$	−5.03884e6	−	8.72752e6i	−0.391464	−	0.678035i
$699$	−464428.	−	804413.i	−0.0359522	−	0.0622710i
$700$	−4.68288e6	−	8.11098e6i	−0.361217	−	0.625646i
$701$	9.63151e6	−	1.66823e7i	0.740286	−	1.28221i	−0.212079	−	0.977252i	$-0.568023\pi$
$701$	9.63151e6	−	1.66823e7i	0.740286	−	1.28221i	0.952365	−	0.304960i	$-0.0986432\pi$
$702$	−791585.			−0.0606254
$703$	1.51868e7	−	1.11515e7i	1.15899	−	0.851027i
$704$	2.64714e6			0.201301
$705$	817776.	−	1.41643e6i	0.0619672	−	0.107330i
$706$	801773.	+	1.38871e6i	0.0605396	+	0.104858i
$707$	9.51247e6	+	1.64761e7i	0.715722	+	1.23967i
$708$	−71198.5	−	123319.i	−0.00533811	−	0.00924588i
$709$	−1.74809e7			−1.30602			−0.653008	−	0.757351i	$-0.726493\pi$
$709$	−1.74809e7			−1.30602			−0.653008	+	0.757351i	$0.726493\pi$
$710$	4.56120e6	+	7.90023e6i	0.339573	+	0.588158i
$711$	2.14575e7			1.59186
$712$	4.20581e6	−	7.28467e6i	0.310921	−	0.538530i
$713$	3.21469e6			0.236819
$714$	1.41672e6			0.104001
$715$	−9.22070e6	+	1.59707e7i	−0.674526	+	1.16831i
$716$	−5.98226e6	−	1.03616e7i	−0.436096	−	0.755341i
$717$	1.33476e6			0.0969629
$718$	2.55678e6	−	4.42847e6i	0.185090	−	0.320585i
$719$	−1.24013e6	+	2.14796e6i	−0.0894631	+	0.154955i	−0.907284	−	0.420518i	$-0.861848\pi$
$719$	−1.24013e6	+	2.14796e6i	−0.0894631	+	0.154955i	0.817821	+	0.575472i	$0.195182\pi$
$720$	−2.49961e6	+	4.32944e6i	−0.179697	+	0.311244i
$721$	5.89240e6	+	1.02059e7i	0.422138	+	0.731164i
$722$	5.28648e6	+	9.15646e6i	0.377419	+	0.653709i
$723$	−43783.6	+	75835.4i	−0.00311505	+	0.00539543i
$724$	3.58109e6	−	6.20264e6i	0.253904	−	0.439774i
$725$	−1.21383e7	+	2.10242e7i	−0.857659	+	1.48551i
$726$	−1.18693e6			−0.0835764
$727$	4.38234e6	+	7.59044e6i	0.307518	+	0.532636i	0.977819	−	0.209453i	$-0.0671683\pi$
$727$	4.38234e6	+	7.59044e6i	0.307518	+	0.532636i	−0.670301	+	0.742089i	$0.733835\pi$
$728$	−1.94267e6	+	3.36481e6i	−0.135854	+	0.235306i
$729$	−1.38774e7			−0.967138
$730$	2.73465e6			0.189930
$731$	−1.59435e7	+	2.76150e7i	−1.10355	+	1.91140i
$732$	268727.			0.0185367
$733$	−5.13017e6	−	8.88572e6i	−0.352673	−	0.610847i	0.634044	−	0.773297i	$-0.281394\pi$
$733$	−5.13017e6	−	8.88572e6i	−0.352673	−	0.610847i	−0.986717	+	0.162450i	$0.948060\pi$
$734$	−1.08509e6			−0.0743404
$735$	595638.	+	1.03167e6i	0.0406690	+	0.0704408i
$736$	−616648.	−	1.06807e6i	−0.0419607	−	0.0726780i
$737$	−7.25891e6	−	1.25728e7i	−0.492269	−	0.852635i
$738$	5.99493e6	−	1.03835e7i	0.405175	−	0.701784i
$739$	1.00671e6			0.0678098			0.0339049	−	0.999425i	$-0.489206\pi$
$739$	1.00671e6			0.0678098			0.0339049	+	0.999425i	$0.489206\pi$
$740$	9.85770e6	+	4.32944e6i	0.661753	+	0.290638i
$741$	−923857.			−0.0618101
$742$	4.58015e6	−	7.93305e6i	0.305400	−	0.528969i
$743$	−2.39829e6	−	4.15395e6i	−0.159378	−	0.276051i	0.775266	−	0.631634i	$-0.217616\pi$
$743$	−2.39829e6	−	4.15395e6i	−0.159378	−	0.276051i	−0.934645	+	0.355583i	$0.884282\pi$
$744$	−98763.3	−	171063.i	−0.00654129	−	0.0113298i
$745$	−1.07979e7	−	1.87024e7i	−0.712766	−	1.23455i
$746$	−8.34735e6			−0.549163
$747$	−4.82855e6	−	8.36329e6i	−0.316603	−	0.548372i
$748$	−1.84231e7			−1.20395
$749$	−2.24602e6	+	3.89022e6i	−0.146288	+	0.253378i
$750$	104594.			0.00678973
$751$	2.28611e6			0.147910			0.0739551	−	0.997262i	$-0.476438\pi$
$751$	2.28611e6			0.147910			0.0739551	+	0.997262i	$0.476438\pi$
$752$	−2.24053e6	+	3.88070e6i	−0.144479	+	0.250245i
$753$	342386.	+	593030.i	0.0220054	+	0.0381144i
$754$	1.00711e7			0.645132
$755$	1.78701e7	−	3.09519e7i	1.14093	−	1.97615i
$756$	770776.	−	1.33502e6i	0.0490483	−	0.0849541i
$757$	1.77608e6	−	3.07626e6i	0.112648	−	0.195111i	−0.804189	−	0.594373i	$-0.797400\pi$
$757$	1.77608e6	−	3.07626e6i	0.112648	−	0.195111i	0.916837	+	0.399262i	$0.130734\pi$
$758$	−5.29931e6	−	9.17867e6i	−0.335001	−	0.580239i
$759$	450016.	+	779450.i	0.0283546	+	0.0491116i
$760$	−5.85071e6	+	1.01337e7i	−0.367430	+	0.636407i
$761$	9.71882e6	−	1.68335e7i	0.608348	−	1.05369i	−0.383165	−	0.923680i	$-0.625166\pi$
$761$	9.71882e6	−	1.68335e7i	0.608348	−	1.05369i	0.991513	−	0.130009i	$-0.0415008\pi$
$762$	102004.	−	176676.i	0.00636398	−	0.0110227i
$763$	−3.51623e7			−2.18658
$764$	−4.98394e6	−	8.63243e6i	−0.308915	−	0.535057i
$765$	1.73963e7	−	3.01312e7i	1.07474	−	1.86150i
$766$	−5.63401e6			−0.346933
$767$	−2.71789e6			−0.166818
$768$	−37889.9	+	65627.2i	−0.00231803	+	0.00401495i
$769$	2.92450e7			1.78335			0.891674	−	0.452678i	$-0.149531\pi$
$769$	2.92450e7			1.78335			0.891674	+	0.452678i	$0.149531\pi$
$770$	−1.79566e7	−	3.11018e7i	−1.09143	−	1.89042i
$771$	536192.			0.0324851
$772$	−4.19087e6	−	7.25881e6i	−0.253082	−	0.438351i
$773$	−5.86383e6	−	1.01565e7i	−0.352966	−	0.611355i	0.633802	−	0.773496i	$-0.281494\pi$
$773$	−5.86383e6	−	1.01565e7i	−0.352966	−	0.611355i	−0.986768	+	0.162141i	$0.948160\pi$
$774$	8.65028e6	+	1.49827e7i	0.519012	+	0.898956i
$775$	4.54402e6	−	7.87047e6i	0.271760	−	0.470703i
$776$	8.78964e6			0.523983
$777$	−1.51566e6	−	665669.i	−0.0900637	−	0.0395554i
$778$	−1.42816e7			−0.845917
$779$	1.40320e7	−	2.43042e7i	0.828470	−	1.43495i
$780$	−263961.	−	457193.i	−0.0155347	−	0.0269069i
$781$	9.11979e6	+	1.57959e7i	0.535005	+	0.926655i
$782$	4.29162e6	+	7.43331e6i	0.250960	+	0.434676i
$783$	−3.99581e6			−0.232917
$784$	−1.63191e6	−	2.82656e6i	−0.0948216	−	0.164236i
$785$	−3.07662e7			−1.78197
$786$	−40440.8	+	70045.4i	−0.00233487	+	0.00404412i
$787$	−6.28779e6			−0.361877			−0.180939	−	0.983494i	$-0.557914\pi$
$787$	−6.28779e6			−0.361877			−0.180939	+	0.983494i	$0.557914\pi$
$788$	−1.44358e6			−0.0828180
$789$	−535292.	+	927154.i	−0.0306125	+	0.0530224i
$790$	1.43499e7	+	2.48548e7i	0.818054	+	1.41691i
$791$	3.26668e7			1.85637
$792$	−4.99779e6	+	8.65642e6i	−0.283116	+	0.490372i
$793$	2.56456e6	−	4.44195e6i	0.144820	−	0.250836i
$794$	−1.62600e6	+	2.81632e6i	−0.0915315	+	0.158537i
$795$	622327.	+	1.07790e6i	0.0349221	+	0.0604869i
$796$	1.34920e6	+	2.33688e6i	0.0754732	+	0.130723i
$797$	−1.63958e7	+	2.83984e7i	−0.914296	+	1.58361i	−0.106368	+	0.994327i	$0.533922\pi$
$797$	−1.63958e7	+	2.83984e7i	−0.914296	+	1.58361i	−0.807928	+	0.589281i	$0.799411\pi$
$798$	899571.	−	1.55810e6i	0.0500067	−	0.0866141i
$799$	1.55932e7	−	2.70082e7i	0.864107	−	1.49668i
$800$	−3.48656e6			−0.192607
$801$	1.58811e7	+	2.75068e7i	0.874577	+	1.51481i
$802$	6.81089e6	−	1.17968e7i	0.373911	−	0.647632i
$803$	5.46773e6			0.299239
$804$	415601.			0.0226744
$805$	−8.36593e6	+	1.44902e7i	−0.455014	+	0.788107i
$806$	−3.77014e6			−0.204418
$807$	36588.4	+	63373.0i	0.00197770	+	0.00342547i
$808$	7.08236e6			0.381636
$809$	5.68955e6	+	9.85459e6i	0.305637	+	0.529380i	0.977403	−	0.211384i	$-0.0677971\pi$
$809$	5.68955e6	+	9.85459e6i	0.305637	+	0.529380i	−0.671766	+	0.740764i	$0.734464\pi$
$810$	−9.38596e6	−	1.62570e7i	−0.502651	−	0.870617i
$811$	2.04693e6	+	3.54538e6i	0.109282	+	0.189283i	0.915480	−	0.402364i	$-0.131811\pi$
$811$	2.04693e6	+	3.54538e6i	0.109282	+	0.189283i	−0.806197	+	0.591647i	$0.798478\pi$
$812$	−9.80635e6	+	1.69851e7i	−0.521936	+	0.904020i
$813$	137522.			0.00729703
$814$	1.97098e7	+	8.65640e6i	1.04261	+	0.457906i
$815$	−1.61847e7			−0.853513
$816$	263698.	−	456739.i	0.0138638	−	0.0240128i
$817$	2.02473e7	+	3.50693e7i	1.06124	+	1.83811i
$818$	3.94828e6	+	6.83863e6i	0.206312	+	0.357343i
$819$	−7.33551e6	−	1.27055e7i	−0.382138	−	0.661883i
$820$	1.60367e7			0.832876
$821$	−9.93209e6	−	1.72029e7i	−0.514260	−	0.890724i	−0.999863	−	0.0165448i	$-0.994733\pi$
$821$	−9.93209e6	−	1.72029e7i	−0.514260	−	0.890724i	0.485603	−	0.874179i	$-0.338600\pi$
$822$	−431706.			−0.0222848
$823$	8.68045e6	−	1.50350e7i	0.446728	−	0.773755i	−0.551443	−	0.834212i	$-0.685923\pi$
$823$	8.68045e6	−	1.50350e7i	0.446728	−	0.773755i	0.998171	+	0.0604575i	$0.0192560\pi$
$824$	4.38710e6			0.225092
$825$	2.54442e6			0.130153
$826$	2.64645e6	−	4.58378e6i	0.134962	−	0.233762i
$827$	−2.30400e6	−	3.99064e6i	−0.117144	−	0.202899i	0.801491	−	0.598007i	$-0.204040\pi$
$827$	−2.30400e6	−	3.99064e6i	−0.117144	−	0.202899i	−0.918635	+	0.395108i	$0.870707\pi$
$828$	4.65690e6			0.236059
$829$	8.58810	−	14.8750i	4.34021e−7	−	7.51747e-7i	−0.866025	−	0.500000i	$-0.833333\pi$
$829$	8.58810	−	14.8750i	4.34021e−7	−	7.51747e-7i	0.866026	+	0.500000i	$0.166667\pi$
$830$	6.45829e6	−	1.11861e7i	0.325404	−	0.563616i
$831$	238444.	−	412998.i	0.0119780	−	0.0207465i
$832$	723194.	+	1.25261e6i	0.0362198	+	0.0627346i
$833$	1.13575e7	+	1.96717e7i	0.567113	+	0.982268i
$834$	−173368.	+	300282.i	−0.00863084	+	0.0149491i
$835$	−2.39144e7	+	4.14209e7i	−1.18698	+	2.05591i
$836$	−1.16981e7	+	2.02617e7i	−0.578894	+	1.00267i
$837$	1.49584e6			0.0738026
$838$	7.74379e6	+	1.34126e7i	0.380928	+	0.659787i
$839$	−58416.1	+	101180.i	−0.00286502	+	0.00496236i	−0.867454	−	0.497517i	$-0.834245\pi$
$839$	−58416.1	+	101180.i	−0.00286502	+	0.00496236i	0.864589	+	0.502479i	$0.167579\pi$
$840$	1.02809e6			0.0502726
$841$	3.03263e7			1.47853
$842$	2.44459e6	−	4.23415e6i	0.118830	−	0.205819i
$843$	1.98355e6			0.0961333
$844$	−2.52158e6	−	4.36751e6i	−0.121848	−	0.211046i
$845$	1.99269e7			0.960061
$846$	−8.46019e6	−	1.46535e7i	−0.406400	−	0.703906i
$847$	−2.20591e7	−	3.82074e7i	−1.05652	−	1.82995i
$848$	−1.70504e6	−	2.95321e6i	−0.0814225	−	0.141028i
$849$	1.39108e6	−	2.40942e6i	0.0662343	−	0.114721i
$850$	2.42651e7			1.15195
$851$	−1.09869e6	−	9.96896e6i	−0.0520056	−	0.471874i
$852$	−522144.			−0.0246429
$853$	1.72333e6	−	2.98490e6i	0.0810954	−	0.140461i	−0.822625	−	0.568584i	$-0.807491\pi$
$853$	1.72333e6	−	2.98490e6i	0.0810954	−	0.140461i	0.903721	+	0.428123i	$0.140825\pi$
$854$	4.99429e6	+	8.65036e6i	0.234330	+	0.405872i
$855$	−2.20922e7	−	3.82648e7i	−1.03353	−	1.79013i
$856$	836118.	+	1.44820e6i	0.0390017	+	0.0675529i
$857$	−3.98074e7			−1.85145			−0.925725	−	0.378198i	$-0.876544\pi$
$857$	−3.98074e7			−1.85145			−0.925725	+	0.378198i	$0.876544\pi$
$858$	−527771.	−	914126.i	−0.0244753	−	0.0423924i
$859$	−3.26940e7			−1.51177			−0.755884	−	0.654706i	$-0.772793\pi$
$859$	−3.26940e7			−1.51177			−0.755884	+	0.654706i	$0.772793\pi$
$860$	−1.15700e7	+	2.00397e7i	−0.533440	+	0.923945i
$861$	−2.46571e6			−0.113353
$862$	1.58633e7			0.727152
$863$	5.48612e6	−	9.50225e6i	0.250749	−	0.434309i	−0.712983	−	0.701181i	$-0.752657\pi$
$863$	5.48612e6	−	9.50225e6i	0.250749	−	0.434309i	0.963732	+	0.266871i	$0.0859899\pi$
$864$	−286935.	−	496985.i	−0.0130767	−	0.0226495i
$865$	−5.31552e6			−0.241549
$866$	−3.82358e6	+	6.62263e6i	−0.173251	+	0.300079i
$867$	−1.01434e6	+	1.75689e6i	−0.0458285	+	0.0793774i
$868$	3.67103e6	−	6.35841e6i	0.165382	−	0.286450i
$869$	2.86917e7	+	4.96954e7i	1.28886	+	2.23237i
$870$	−1.33244e6	−	2.30785e6i	−0.0596827	−	0.103373i
$871$	3.96624e6	−	6.86972e6i	0.177147	−	0.306827i
$872$	−6.54488e6	+	1.13361e7i	−0.291481	+	0.504860i
$873$	−1.65948e7	+	2.87430e7i	−0.736946	+	1.27643i
$874$	1.09002e7			0.482676
$875$	1.94387e6	+	3.36689e6i	0.0858317	+	0.148665i
$876$	−78262.3	+	135554.i	−0.00344582	+	0.00596833i
$877$	−2.27367e7			−0.998227			−0.499113	−	0.866537i	$-0.666341\pi$
$877$	−2.27367e7			−0.998227			−0.499113	+	0.866537i	$0.666341\pi$
$878$	802176.			0.0351183
$879$	381307.	−	660443.i	0.0166457	−	0.0288312i
$880$	−1.33693e7			−0.581972
$881$	−5.91581e6	−	1.02465e7i	−0.256788	−	0.444769i	0.708592	−	0.705619i	$-0.249331\pi$
$881$	−5.91581e6	−	1.02465e7i	−0.256788	−	0.444769i	−0.965380	+	0.260849i	$0.915997\pi$
$882$	1.23242e7			0.533441
$883$	7.08676e6	+	1.22746e7i	0.305876	+	0.529793i	0.977456	−	0.211139i	$-0.0677173\pi$
$883$	7.08676e6	+	1.22746e7i	0.305876	+	0.529793i	−0.671580	+	0.740932i	$0.734384\pi$
$884$	−5.03314e6	−	8.71766e6i	−0.216625	−	0.375206i
$885$	359586.	+	622820.i	0.0154328	+	0.0267304i
$886$	−1.42659e7	+	2.47093e7i	−0.610543	+	1.05749i
$887$	−2.46798e7			−1.05325			−0.526626	−	0.850097i	$-0.676543\pi$
$887$	−2.46798e7			−1.05325			−0.526626	+	0.850097i	$0.676543\pi$
$888$	−496722.	+	364735.i	−0.0211388	+	0.0155219i
$889$	7.58295e6			0.321799
$890$	−2.12413e7	+	3.67910e7i	−0.898889	+	1.55692i
$891$	−1.87666e7	−	3.25047e7i	−0.791937	−	1.37168i
$892$	−866415.	−	1.50068e6i	−0.0364598	−	0.0631502i
$893$	−1.98024e7	−	3.42987e7i	−0.830975	−	1.43929i
$894$	1.23609e6			0.0517256
$895$	3.02132e7	+	5.23308e7i	1.26078	+	2.18373i
$896$	−2.81673e6			−0.117213
$897$	−245887.	+	425888.i	−0.0102036	+	0.0176732i
$898$	6.25251e6			0.258740
$899$	−1.90311e7			−0.785354
$900$	6.58260e6	−	1.14014e7i	0.270889	−	0.469194i
$901$	1.18664e7	+	2.05532e7i	0.486975	+	0.843465i
$902$	3.20643e7			1.31221
$903$	1.77893e6	−	3.08119e6i	0.0726004	−	0.125748i
$904$	6.08038e6	−	1.05315e7i	0.247463	−	0.428618i
$905$	−1.80862e7	+	3.13262e7i	−0.734050	+	1.27141i
$906$	1.02284e6	+	1.77161e6i	0.0413987	+	0.0717047i
$907$	6.17443e6	+	1.06944e7i	0.249218	+	0.431658i	0.963309	−	0.268395i	$-0.0864932\pi$
$907$	6.17443e6	+	1.06944e7i	0.249218	+	0.431658i	−0.714091	+	0.700053i	$0.753160\pi$
$908$	−448149.	+	776216.i	−0.0180388	+	0.0312441i
$909$	−1.33714e7	+	2.31600e7i	−0.536745	+	0.929670i
$910$	9.81142e6	−	1.69939e7i	0.392761	−	0.680282i
$911$	−1.14971e7			−0.458977			−0.229488	−	0.973311i	$-0.573705\pi$
$911$	−1.14971e7			−0.458977			−0.229488	+	0.973311i	$0.573705\pi$
$912$	−334881.	−	580030.i	−0.0133322	−	0.0230921i
$913$	1.29129e7	−	2.23658e7i	0.512681	−	0.887989i
$914$	−9.78549e6			−0.387451
$915$	−1.35720e6			−0.0535908
$916$	2.59740e6	−	4.49883e6i	0.102282	−	0.177158i
$917$	−3.00636e6			−0.118064
$918$	1.99695e6	+	3.45882e6i	0.0782097	+	0.135463i
$919$	−3.35738e7			−1.31133			−0.655665	−	0.755052i	$-0.727612\pi$
$919$	−3.35738e7			−1.31133			−0.655665	+	0.755052i	$0.727612\pi$
$920$	3.11436e6	+	5.39423e6i	0.121311	+	0.210116i
$921$	1.55340e6	+	2.69057e6i	0.0603441	+	0.104519i
$922$	−4.12246e6	−	7.14031e6i	−0.159709	−	0.276624i
$923$	−4.98302e6	+	8.63084e6i	−0.192525	+	0.333464i
$924$	2.05559e6			0.0792056
$925$	−2.59598e7	−	1.14014e7i	−0.997579	−	0.438130i
$926$	−2.90685e7			−1.11402
$927$	−8.28280e6	+	1.43462e7i	−0.316576	+	0.548326i
$928$	3.65058e6	+	6.32299e6i	0.139153	+	0.241020i
$929$	−2.24384e7	−	3.88644e7i	−0.853005	−	1.47745i	−0.878483	−	0.477773i	$-0.841444\pi$
$929$	−2.24384e7	−	3.88644e7i	−0.853005	−	1.47745i	0.0254782	−	0.999675i	$-0.491889\pi$
$930$	498801.	+	863948.i	0.0189112	+	0.0327552i
$931$	2.88466e7			1.09074
$932$	−6.42636e6	−	1.11308e7i	−0.242340	−	0.419746i
$933$	−1.11281e6			−0.0418519
$934$	−1.19783e7	+	2.07471e7i	−0.449293	+	0.778198i
$935$	9.30451e7			3.48068
$936$	−5.46154e6			−0.203763
$937$	1.04005e7	−	1.80141e7i	0.386994	−	0.670293i	−0.605050	−	0.796187i	$-0.706847\pi$
$937$	1.04005e7	−	1.80141e7i	0.386994	−	0.670293i	0.992044	+	0.125895i	$0.0401802\pi$
$938$	7.72394e6	+	1.33783e7i	0.286637	+	0.496470i
$939$	−718214.			−0.0265822
$940$	1.13157e7	−	1.95994e7i	0.417697	−	0.723473i
$941$	1.12683e7	−	1.95173e7i	0.414844	−	0.718530i	−0.580568	−	0.814211i	$-0.697170\pi$
$941$	1.12683e7	−	1.95173e7i	0.414844	−	0.718530i	0.995412	+	0.0956813i	$0.0305030\pi$
$942$	880493.	−	1.52506e6i	0.0323295	−	0.0559963i
$943$	−7.46932e6	−	1.29372e7i	−0.273528	−	0.473764i
$944$	−985185.	−	1.70639e6i	−0.0359822	−	0.0623230i
$945$	−3.89278e6	+	6.74249e6i	−0.141801	+	0.245607i
$946$	−2.31333e7	+	4.00681e7i	−0.840446	+	1.45570i
$947$	1.16609e7	−	2.01972e7i	0.422529	−	0.731841i	−0.573658	−	0.819095i	$-0.694476\pi$
$947$	1.16609e7	−	2.01972e7i	0.422529	−	0.731841i	0.996186	+	0.0872544i	$0.0278093\pi$
$948$	−1.64271e6			−0.0593663
$949$	1.49377e6	+	2.58729e6i	0.0538417	+	0.0932566i
$950$	1.54076e7	−	2.66867e7i	0.553893	−	0.959370i
$951$	−270896.			−0.00971296
$952$	1.96033e7			0.701031
$953$	1.08727e7	−	1.88320e7i	0.387797	−	0.671683i	−0.604356	−	0.796714i	$-0.706570\pi$
$953$	1.08727e7	−	1.88320e7i	0.387797	−	0.671683i	0.992153	+	0.125031i	$0.0399030\pi$
$954$	1.28764e7			0.458061
$955$	2.51712e7	+	4.35978e7i	0.893091	+	1.54688i
$956$	1.84693e7			0.653591
$957$	−2.66411e6	−	4.61438e6i	−0.0940314	−	0.162867i
$958$	1.90811e7	+	3.30494e7i	0.671721	+	1.16345i
$959$	−8.02325e6	−	1.38967e7i	−0.281711	−	0.487938i
$960$	191361.	−	331448.i	0.00670157	−	0.0116075i
$961$	−2.15048e7			−0.751151
$962$	1.28852e6	+	1.16914e7i	0.0448904	+	0.407314i
$963$	−6.31434e6			−0.219413
$964$	−605840.	+	1.04935e6i	−0.0209974	+	0.0363686i
$965$	2.11659e7	+	3.66604e7i	0.731674	+	1.26730i
$966$	−478846.	−	829385.i	−0.0165102	−	0.0285965i
$967$	−4.04106e6	−	6.99933e6i	−0.138973	−	0.240708i	0.788135	−	0.615502i	$-0.211047\pi$
$967$	−4.04106e6	−	6.99933e6i	−0.138973	−	0.240708i	−0.927108	+	0.374794i	$0.877713\pi$
$968$	−1.64237e7			−0.563357
$969$	2.33064e6	+	4.03678e6i	0.0797379	+	0.138110i
$970$	−4.43918e7			−1.51486
$971$	−6.82405e6	+	1.18196e7i	−0.232271	+	0.402304i	−0.958476	−	0.285173i	$-0.907949\pi$
$971$	−6.82405e6	+	1.18196e7i	−0.232271	+	0.402304i	0.726205	+	0.687478i	$0.241282\pi$
$972$	3.25337e6			0.110451
$973$	−1.28881e7			−0.436424
$974$	−4.89490e6	+	8.47821e6i	−0.165328	+	0.286356i
$975$	695129.	+	1.20400e6i	0.0234182	+	0.0405616i
$976$	3.71842e6			0.124949
$977$	6.06644e6	−	1.05074e7i	0.203328	−	0.352175i	−0.746271	−	0.665643i	$-0.768158\pi$
$977$	6.06644e6	−	1.05074e7i	0.203328	−	0.352175i	0.949599	+	0.313468i	$0.101491\pi$
$978$	463186.	−	802262.i	0.0154849	−	0.0268206i
$979$	−4.24705e7	+	7.35610e7i	−1.41622	+	2.45296i
$980$	8.24193e6	+	1.42754e7i	0.274135	+	0.474815i
$981$	−2.47134e7	−	4.28048e7i	−0.819897	−	1.42010i
$982$	1.78928e7	−	3.09912e7i	0.592106	−	1.02556i
$983$	2.06117e7	−	3.57004e7i	0.680345	−	1.17839i	−0.294531	−	0.955642i	$-0.595163\pi$
$983$	2.06117e7	−	3.57004e7i	0.680345	−	1.17839i	0.974876	−	0.222750i	$-0.0715034\pi$
$984$	−458951.	+	794927.i	−0.0151105	+	0.0261722i
$985$	7.29074e6			0.239431
$986$	−2.54066e7	−	4.40055e7i	−0.832251	−	1.44150i
$987$	−1.73984e6	+	3.01348e6i	−0.0568480	+	0.0984637i
$988$	−1.27836e7			−0.416639
$989$	2.15555e7			0.700755
$990$	2.52412e7	−	4.37190e7i	0.818505	−	1.41769i
$991$	1.11763e7			0.361504			0.180752	−	0.983529i	$-0.442147\pi$
$991$	1.11763e7			0.361504			0.180752	+	0.983529i	$0.442147\pi$
$992$	−1.36660e6	−	2.36703e6i	−0.0440924	−	0.0763702i
$993$	−85596.5			−0.00275475
$994$	−9.70404e6	−	1.68079e7i	−0.311521	−	0.539569i
$995$	−6.81407e6	−	1.18023e7i	−0.218197	−	0.377929i
$996$	369657.	+	640265.i	0.0118073	+	0.0204509i
$997$	2.47017e7	−	4.27845e7i	0.787024	−	1.36317i	−0.140758	−	0.990044i	$-0.544954\pi$
$997$	2.47017e7	−	4.27845e7i	0.787024	−	1.36317i	0.927782	−	0.373122i	$-0.121713\pi$
$998$	3.40210e6			0.108124
$999$	−511234.	−	4.63869e6i	−0.0162071	−	0.147056i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.6.c.b.47.5	✓	16
37.26	even	3	inner	74.6.c.b.63.5	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.6.c.b.47.5	✓	16	1.1	even	1	trivial
74.6.c.b.63.5	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)

\(f(q)\)	\(=\)	\(q+(2.00000 - 3.46410i) q^{2} +(-0.578153 - 1.00139i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(40.4037 + 69.9813i) q^{5} -4.62523 q^{6} +(-85.9598 - 148.887i) q^{7} -64.0000 q^{8} +(120.831 - 209.286i) q^{9} +O(q^{10})\)	\(q+(2.00000 - 3.46410i) q^{2} +(-0.578153 - 1.00139i) q^{3} +(-8.00000 - 13.8564i) q^{4} +(40.4037 + 69.9813i) q^{5} -4.62523 q^{6} +(-85.9598 - 148.887i) q^{7} -64.0000 q^{8} +(120.831 - 209.286i) q^{9} +323.230 q^{10} +646.275 q^{11} +(-9.25045 + 16.0223i) q^{12} +(176.561 + 305.813i) q^{13} -687.678 q^{14} +(46.7191 - 80.9199i) q^{15} +(-128.000 + 221.703i) q^{16} +(890.829 - 1542.96i) q^{17} +(-483.326 - 837.145i) q^{18} +(-1131.30 - 1959.47i) q^{19} +(646.460 - 1119.70i) q^{20} +(-99.3959 + 172.159i) q^{21} +(1292.55 - 2238.76i) q^{22} -1204.39 q^{23} +(37.0018 + 64.0890i) q^{24} +(-1702.42 + 2948.68i) q^{25} +1412.49 q^{26} -560.419 q^{27} +(-1375.36 + 2382.19i) q^{28} +7130.04 q^{29} +(-186.876 - 323.679i) q^{30} -2669.15 q^{31} +(512.000 + 886.810i) q^{32} +(-373.646 - 647.174i) q^{33} +(-3563.32 - 6171.84i) q^{34} +(6946.19 - 12031.2i) q^{35} -3866.61 q^{36} +(912.234 + 8277.18i) q^{37} -9050.38 q^{38} +(204.159 - 353.613i) q^{39} +(-2585.84 - 4478.80i) q^{40} +(6201.74 + 10741.7i) q^{41} +(397.583 + 688.635i) q^{42} -17897.4 q^{43} +(-5170.20 - 8955.05i) q^{44} +19528.2 q^{45} +(-2408.78 + 4172.13i) q^{46} +17504.1 q^{47} +296.015 q^{48} +(-6374.67 + 11041.2i) q^{49} +(6809.69 + 11794.7i) q^{50} -2060.14 q^{51} +(2824.98 - 4893.00i) q^{52} +(-6660.30 + 11536.0i) q^{53} +(-1120.84 + 1941.35i) q^{54} +(26111.9 + 45227.2i) q^{55} +(5501.43 + 9528.75i) q^{56} +(-1308.13 + 2265.74i) q^{57} +(14260.1 - 24699.2i) q^{58} +(-3848.38 + 6665.59i) q^{59} -1495.01 q^{60} +(-7262.53 - 12579.1i) q^{61} +(-5338.29 + 9246.20i) q^{62} -41546.6 q^{63} +4096.00 q^{64} +(-14267.5 + 24711.9i) q^{65} -2989.17 q^{66} +(-11231.9 - 19454.2i) q^{67} -28506.5 q^{68} +(696.322 + 1206.07i) q^{69} +(-27784.8 - 48124.6i) q^{70} +(14111.3 + 24441.5i) q^{71} +(-7733.21 + 13394.3i) q^{72} +8460.37 q^{73} +(30497.5 + 13394.3i) q^{74} +3937.05 q^{75} +(-18100.8 + 31351.4i) q^{76} +(-55553.7 - 96221.8i) q^{77} +(-816.635 - 1414.45i) q^{78} +(44395.4 + 76895.1i) q^{79} -20686.7 q^{80} +(-29038.0 - 50295.4i) q^{81} +49613.9 q^{82} +(19980.5 - 34607.2i) q^{83} +3180.67 q^{84} +143971. q^{85} +(-35794.8 + 61998.4i) q^{86} +(-4122.26 - 7139.96i) q^{87} -41361.6 q^{88} +(-65715.7 + 113823. i) q^{89} +(39056.3 - 67647.6i) q^{90} +(30354.3 - 52575.2i) q^{91} +(9635.12 + 16688.5i) q^{92} +(1543.18 + 2672.86i) q^{93} +(35008.2 - 60636.0i) q^{94} +(91417.3 - 158339. i) q^{95} +(592.029 - 1025.42i) q^{96} -137338. q^{97} +(25498.7 + 44165.0i) q^{98} +(78090.4 - 135257. i) 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

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