LMFDB - Embedded newform 74.4.c.a.63.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [74,4,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, 4, names="a")

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

chi := DirichletCharacter("74.47");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 74 = 2 \cdot 37 $
Weight:	$ k $	$=$	$ 4 $
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:	$4.36614134042$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{8} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 48x^{6} + 157x^{5} + 1944x^{4} + 3005x^{3} + 12895x^{2} - 11550x + 44100 $ x^8 - x^7 + 48x^6 + 157x^5 + 1944x^4 + 3005x^3 + 12895x^2 - 11550x + 44100
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			63.2
Root			$0.810477 - 1.40379i$ of defining polynomial
Character	$\chi$	$=$	74.63
Dual form			74.4.c.a.47.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 1.73205i) q^{2} +(-1.31048 + 2.26981i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(0.0116171 - 0.0201213i) q^{5} -5.24191 q^{6} +(-10.2956 + 17.8325i) q^{7} -8.00000 q^{8} +(10.0653 + 17.4336i) q^{9} +O(q^{10})$	\(q+(1.00000 + 1.73205i) q^{2} +(-1.31048 + 2.26981i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(0.0116171 - 0.0201213i) q^{5} -5.24191 q^{6} +(-10.2956 + 17.8325i) q^{7} -8.00000 q^{8} +(10.0653 + 17.4336i) q^{9} +0.0464682 q^{10} -53.0010 q^{11} +(-5.24191 - 9.07925i) q^{12} +(16.8156 - 29.1254i) q^{13} -41.1824 q^{14} +(0.0304478 + 0.0527371i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(37.2657 + 64.5460i) q^{17} +(-20.1306 + 34.8672i) q^{18} +(9.14813 - 15.8450i) q^{19} +(0.0464682 + 0.0804854i) q^{20} +(-26.9843 - 46.7381i) q^{21} +(-53.0010 - 91.8005i) q^{22} +193.513 q^{23} +(10.4838 - 18.1585i) q^{24} +(62.4997 + 108.253i) q^{25} +67.2622 q^{26} -123.527 q^{27} +(-41.1824 - 71.3299i) q^{28} +13.3072 q^{29} +(-0.0608956 + 0.105474i) q^{30} +53.1699 q^{31} +(16.0000 - 27.7128i) q^{32} +(69.4566 - 120.302i) q^{33} +(-74.5313 + 129.092i) q^{34} +(0.239209 + 0.414322i) q^{35} -80.5224 q^{36} +(201.416 + 100.422i) q^{37} +36.5925 q^{38} +(44.0728 + 76.3363i) q^{39} +(-0.0929365 + 0.160971i) q^{40} +(182.337 - 315.817i) q^{41} +(53.9685 - 93.4763i) q^{42} +81.2969 q^{43} +(106.002 - 183.601i) q^{44} +0.467717 q^{45} +(193.513 + 335.174i) q^{46} -533.131 q^{47} +41.9353 q^{48} +(-40.4984 - 70.1452i) q^{49} +(-124.999 + 216.505i) q^{50} -195.343 q^{51} +(67.2622 + 116.502i) q^{52} +(-204.317 - 353.887i) q^{53} +(-123.527 - 213.955i) q^{54} +(-0.615716 + 1.06645i) q^{55} +(82.3647 - 142.660i) q^{56} +(23.9768 + 41.5291i) q^{57} +(13.3072 + 23.0487i) q^{58} +(99.7992 + 172.857i) q^{59} -0.243582 q^{60} +(-107.409 + 186.037i) q^{61} +(53.1699 + 92.0930i) q^{62} -414.513 q^{63} +64.0000 q^{64} +(-0.390695 - 0.676703i) q^{65} +277.827 q^{66} +(-148.074 + 256.471i) q^{67} -298.125 q^{68} +(-253.594 + 439.238i) q^{69} +(-0.478418 + 0.828644i) q^{70} +(-326.724 + 565.902i) q^{71} +(-80.5224 - 139.469i) q^{72} -127.670 q^{73} +(27.4798 + 449.285i) q^{74} -327.618 q^{75} +(36.5925 + 63.3801i) q^{76} +(545.677 - 945.140i) q^{77} +(-88.1456 + 152.673i) q^{78} +(-132.929 + 230.239i) q^{79} -0.371746 q^{80} +(-109.884 + 190.324i) q^{81} +729.349 q^{82} +(-383.833 - 664.819i) q^{83} +215.874 q^{84} +1.73167 q^{85} +(81.2969 + 140.810i) q^{86} +(-17.4388 + 30.2048i) q^{87} +424.008 q^{88} +(-97.3860 - 168.678i) q^{89} +(0.467717 + 0.810109i) q^{90} +(346.252 + 599.726i) q^{91} +(-387.025 + 670.348i) q^{92} +(-69.6780 + 120.686i) q^{93} +(-533.131 - 923.410i) q^{94} +(-0.212549 - 0.368145i) q^{95} +(41.9353 + 72.6340i) q^{96} +1031.14 q^{97} +(80.9968 - 140.290i) q^{98} +(-533.471 - 923.999i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9}+O(q^{10}) $ 8 * q + 8 * q^2 - 5 * q^3 - 16 * q^4 - 10 * q^5 - 20 * q^6 + 3 * q^7 - 64 * q^8 + 7 * q^9	\( 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9} - 40 q^{10} + 64 q^{11} - 20 q^{12} - 61 q^{13} + 12 q^{14} - 43 q^{15} - 64 q^{16} + 12 q^{17} - 14 q^{18} - 71 q^{19} - 40 q^{20} + 67 q^{21} + 64 q^{22} - 52 q^{23} + 40 q^{24} + 48 q^{25} - 244 q^{26} + 658 q^{27} + 12 q^{28} + 322 q^{29} + 86 q^{30} - 112 q^{31} + 128 q^{32} + 280 q^{33} - 24 q^{34} - 359 q^{35} - 56 q^{36} + 557 q^{37} - 284 q^{38} - 389 q^{39} + 80 q^{40} + 92 q^{41} - 134 q^{42} + 532 q^{43} - 128 q^{44} + 330 q^{45} - 52 q^{46} + 280 q^{47} + 160 q^{48} + 87 q^{49} - 96 q^{50} - 1306 q^{51} - 244 q^{52} + 159 q^{53} + 658 q^{54} - 872 q^{55} - 24 q^{56} - 469 q^{57} + 322 q^{58} + 263 q^{59} + 344 q^{60} - 206 q^{61} - 112 q^{62} - 2328 q^{63} + 512 q^{64} - 731 q^{65} + 1120 q^{66} + 245 q^{67} - 96 q^{68} - 360 q^{69} + 718 q^{70} - 957 q^{71} - 56 q^{72} - 272 q^{73} - 178 q^{74} - 3232 q^{75} - 284 q^{76} + 744 q^{77} + 778 q^{78} + 173 q^{79} + 320 q^{80} - 528 q^{81} + 368 q^{82} + 1217 q^{83} - 536 q^{84} + 2988 q^{85} + 532 q^{86} - 2336 q^{87} - 512 q^{88} - 2136 q^{89} + 330 q^{90} + 1575 q^{91} + 104 q^{92} + 2608 q^{93} + 280 q^{94} + 891 q^{95} + 160 q^{96} + 5262 q^{97} - 174 q^{98} - 176 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 5 * q^3 - 16 * q^4 - 10 * q^5 - 20 * q^6 + 3 * q^7 - 64 * q^8 + 7 * q^9 - 40 * q^10 + 64 * q^11 - 20 * q^12 - 61 * q^13 + 12 * q^14 - 43 * q^15 - 64 * q^16 + 12 * q^17 - 14 * q^18 - 71 * q^19 - 40 * q^20 + 67 * q^21 + 64 * q^22 - 52 * q^23 + 40 * q^24 + 48 * q^25 - 244 * q^26 + 658 * q^27 + 12 * q^28 + 322 * q^29 + 86 * q^30 - 112 * q^31 + 128 * q^32 + 280 * q^33 - 24 * q^34 - 359 * q^35 - 56 * q^36 + 557 * q^37 - 284 * q^38 - 389 * q^39 + 80 * q^40 + 92 * q^41 - 134 * q^42 + 532 * q^43 - 128 * q^44 + 330 * q^45 - 52 * q^46 + 280 * q^47 + 160 * q^48 + 87 * q^49 - 96 * q^50 - 1306 * q^51 - 244 * q^52 + 159 * q^53 + 658 * q^54 - 872 * q^55 - 24 * q^56 - 469 * q^57 + 322 * q^58 + 263 * q^59 + 344 * q^60 - 206 * q^61 - 112 * q^62 - 2328 * q^63 + 512 * q^64 - 731 * q^65 + 1120 * q^66 + 245 * q^67 - 96 * q^68 - 360 * q^69 + 718 * q^70 - 957 * q^71 - 56 * q^72 - 272 * q^73 - 178 * q^74 - 3232 * q^75 - 284 * q^76 + 744 * q^77 + 778 * q^78 + 173 * q^79 + 320 * q^80 - 528 * q^81 + 368 * q^82 + 1217 * q^83 - 536 * q^84 + 2988 * q^85 + 532 * q^86 - 2336 * q^87 - 512 * q^88 - 2136 * q^89 + 330 * q^90 + 1575 * q^91 + 104 * q^92 + 2608 * q^93 + 280 * q^94 + 891 * q^95 + 160 * q^96 + 5262 * q^97 - 174 * q^98 - 176 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$39$
$\chi(n)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$2$	1.00000	+	1.73205i	0.353553	+	0.612372i
$3$	−1.31048	+	2.26981i	−0.252201	+	0.436826i	−0.964132	−	0.265425i	$-0.914488\pi$
$3$	−1.31048	+	2.26981i	−0.252201	+	0.436826i	0.711930	+	0.702250i	$0.247821\pi$
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	0.0116171	−	0.0201213i	0.00103906	−	0.00179971i	−0.865505	−	0.500900i	$-0.833003\pi$
$5$	0.0116171	−	0.0201213i	0.00103906	−	0.00179971i	0.866544	+	0.499100i	$0.166336\pi$
$6$	−5.24191			−0.356667
$7$	−10.2956	+	17.8325i	−0.555910	+	0.962864i	0.441922	+	0.897053i	$0.354297\pi$
$7$	−10.2956	+	17.8325i	−0.555910	+	0.962864i	−0.997832	+	0.0658105i	$0.979037\pi$
$8$	−8.00000			−0.353553
$9$	10.0653	+	17.4336i	0.372789	+	0.645689i
$10$	0.0464682			0.00146946
$11$	−53.0010			−1.45276			−0.726382	−	0.687291i	$-0.758800\pi$
$11$	−53.0010			−1.45276			−0.726382	+	0.687291i	$0.758800\pi$
$12$	−5.24191	−	9.07925i	−0.126101	−	0.218413i
$13$	16.8156	−	29.1254i	0.358754	−	0.621379i	−0.628999	−	0.777406i	$-0.716535\pi$
$13$	16.8156	−	29.1254i	0.358754	−	0.621379i	0.987753	+	0.156026i	$0.0498685\pi$
$14$	−41.1824			−0.786175
$15$	0.0304478	+	0.0527371i	0.000524106	+	0.000907778i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	37.2657	+	64.5460i	0.531662	+	0.920865i	0.999317	+	0.0369542i	$0.0117656\pi$
$17$	37.2657	+	64.5460i	0.531662	+	0.920865i	−0.467655	+	0.883911i	$0.654901\pi$
$18$	−20.1306	+	34.8672i	−0.263602	+	0.456571i
$19$	9.14813	−	15.8450i	0.110459	−	0.191321i	−0.805496	−	0.592601i	$-0.798101\pi$
$19$	9.14813	−	15.8450i	0.110459	−	0.191321i	0.915956	+	0.401280i	$0.131435\pi$
$20$	0.0464682	+	0.0804854i	0.000519531	+	0.000899854i
$21$	−26.9843	−	46.7381i	−0.280402	−	0.485671i
$22$	−53.0010	−	91.8005i	−0.513630	−	0.889633i
$23$	193.513			1.75436			0.877178	−	0.480165i	$-0.159423\pi$
$23$	193.513			1.75436			0.877178	+	0.480165i	$0.159423\pi$
$24$	10.4838	−	18.1585i	0.0891667	−	0.154441i
$25$	62.4997	+	108.253i	0.499998	+	0.866022i
$26$	67.2622			0.507354
$27$	−123.527			−0.880474
$28$	−41.1824	−	71.3299i	−0.277955	−	0.481432i
$29$	13.3072			0.0852098			0.0426049	−	0.999092i	$-0.486434\pi$
$29$	13.3072			0.0852098			0.0426049	+	0.999092i	$0.486434\pi$
$30$	−0.0608956	+	0.105474i	−0.000370599	+	0.000641896i
$31$	53.1699			0.308052			0.154026	−	0.988067i	$-0.450776\pi$
$31$	53.1699			0.308052			0.154026	+	0.988067i	$0.450776\pi$
$32$	16.0000	−	27.7128i	0.0883883	−	0.153093i
$33$	69.4566	−	120.302i	0.366389	−	0.634605i
$34$	−74.5313	+	129.092i	−0.375942	+	0.651150i
$35$	0.239209	+	0.414322i	0.00115525	+	0.00200095i
$36$	−80.5224			−0.372789
$37$	201.416	+	100.422i	0.894935	+	0.446197i
$37$	201.416	+	100.422i	0.894935	+	0.446197i
$38$	36.5925			0.156213
$39$	44.0728	+	76.3363i	0.180956	+	0.313426i
$40$	−0.0929365	+	0.160971i	−0.000367364	+	0.000636293i
$41$	182.337	−	315.817i	0.694544	−	1.20299i	−0.275790	−	0.961218i	$-0.588940\pi$
$41$	182.337	−	315.817i	0.694544	−	1.20299i	0.970334	−	0.241767i	$-0.0777271\pi$
$42$	53.9685	−	93.4763i	0.198274	−	0.343421i
$43$	81.2969			0.288318			0.144159	−	0.989555i	$-0.453952\pi$
$43$	81.2969			0.288318			0.144159	+	0.989555i	$0.453952\pi$
$44$	106.002	−	183.601i	0.363191	−	0.629066i
$45$	0.467717			0.00154940
$46$	193.513	+	335.174i	0.620259	+	1.07432i
$47$	−533.131			−1.65458			−0.827289	−	0.561777i	$-0.810118\pi$
$47$	−533.131			−1.65458			−0.827289	+	0.561777i	$0.810118\pi$
$48$	41.9353			0.126101
$49$	−40.4984	−	70.1452i	−0.118071	−	0.204505i
$50$	−124.999	+	216.505i	−0.353552	+	0.612370i
$51$	−195.343			−0.536343
$52$	67.2622	+	116.502i	0.179377	+	0.310690i
$53$	−204.317	−	353.887i	−0.529529	−	0.917172i	−0.999407	−	0.0344402i	$-0.989035\pi$
$53$	−204.317	−	353.887i	−0.529529	−	0.917172i	0.469877	−	0.882732i	$-0.344298\pi$
$54$	−123.527	−	213.955i	−0.311295	−	0.539178i
$55$	−0.615716	+	1.06645i	−0.00150951	+	0.00261455i
$56$	82.3647	−	142.660i	0.196544	−	0.340424i
$57$	23.9768	+	41.5291i	0.0557160	+	0.0965029i
$58$	13.3072	+	23.0487i	0.0301262	+	0.0521801i
$59$	99.7992	+	172.857i	0.220216	+	0.381426i	0.954874	−	0.297013i	$-0.0959904\pi$
$59$	99.7992	+	172.857i	0.220216	+	0.381426i	−0.734657	+	0.678438i	$0.762657\pi$
$60$	−0.243582			−0.000524106
$61$	−107.409	+	186.037i	−0.225447	+	0.390486i	−0.956453	−	0.291885i	$-0.905718\pi$
$61$	−107.409	+	186.037i	−0.225447	+	0.390486i	0.731006	+	0.682371i	$0.239051\pi$
$62$	53.1699	+	92.0930i	0.108913	+	0.188642i
$63$	−414.513			−0.828948
$64$	64.0000			0.125000
$65$	−0.390695	−	0.676703i	−0.000745534	−	0.00129130i
$66$	277.827			0.518153
$67$	−148.074	+	256.471i	−0.270001	+	0.467655i	−0.968862	−	0.247602i	$-0.920357\pi$
$67$	−148.074	+	256.471i	−0.270001	+	0.467655i	0.698861	+	0.715258i	$0.253691\pi$
$68$	−298.125			−0.531662
$69$	−253.594	+	439.238i	−0.442451	+	0.766348i
$70$	−0.478418	+	0.828644i	−0.000816884	+	0.00141489i
$71$	−326.724	+	565.902i	−0.546126	+	0.945919i	0.452409	+	0.891811i	$0.350565\pi$
$71$	−326.724	+	565.902i	−0.546126	+	0.945919i	−0.998535	+	0.0541081i	$0.982768\pi$
$72$	−80.5224	−	139.469i	−0.131801	−	0.228286i
$73$	−127.670			−0.204694			−0.102347	−	0.994749i	$-0.532635\pi$
$73$	−127.670			−0.204694			−0.102347	+	0.994749i	$0.532635\pi$
$74$	27.4798	+	449.285i	0.0431684	+	0.705788i
$75$	−327.618			−0.504401
$76$	36.5925	+	63.3801i	0.0552296	+	0.0956605i
$77$	545.677	−	945.140i	0.807606	−	1.39881i
$78$	−88.1456	+	152.673i	−0.127955	+	0.221625i
$79$	−132.929	+	230.239i	−0.189312	+	0.327898i	−0.945021	−	0.327010i	$-0.893959\pi$
$79$	−132.929	+	230.239i	−0.189312	+	0.327898i	0.755709	+	0.654907i	$0.227292\pi$
$80$	−0.371746			−0.000519531
$81$	−109.884	+	190.324i	−0.150732	+	0.261075i
$82$	729.349			0.982233
$83$	−383.833	−	664.819i	−0.507605	−	0.879197i	−0.999961	−	0.00880344i	$-0.997198\pi$
$83$	−383.833	−	664.819i	−0.507605	−	0.879197i	0.492357	−	0.870394i	$-0.336136\pi$
$84$	215.874			0.280402
$85$	1.73167			0.00220972
$86$	81.2969	+	140.810i	0.101936	+	0.176558i
$87$	−17.4388	+	30.2048i	−0.0214900	+	0.0372218i
$88$	424.008			0.513630
$89$	−97.3860	−	168.678i	−0.115988	−	0.200896i	0.802186	−	0.597074i	$-0.203670\pi$
$89$	−97.3860	−	168.678i	−0.115988	−	0.200896i	−0.918174	+	0.396177i	$0.870337\pi$
$90$	0.467717	+	0.810109i	0.000547796	+	0.000948811i
$91$	346.252	+	599.726i	0.398869	+	0.690862i
$92$	−387.025	+	670.348i	−0.438589	+	0.759659i
$93$	−69.6780	+	120.686i	−0.0776911	+	0.134565i
$94$	−533.131	−	923.410i	−0.584981	−	1.01322i
$95$	−0.212549	−	0.368145i	−0.000229548	−	0.000397589i
$96$	41.9353	+	72.6340i	0.0445833	+	0.0772206i
$97$	1031.14			1.07934			0.539670	−	0.841877i	$-0.318549\pi$
$97$	1031.14			1.07934			0.539670	+	0.841877i	$0.318549\pi$
$98$	80.9968	−	140.290i	0.0834889	−	0.144607i
$99$	−533.471	−	923.999i	−0.541574	−	0.938034i
$100$	−499.998			−0.499998
$101$	1626.16			1.60207			0.801036	−	0.598616i	$-0.204282\pi$
$101$	1626.16			1.60207			0.801036	+	0.598616i	$0.204282\pi$
$102$	−195.343	−	338.344i	−0.189626	−	0.328442i
$103$	1845.09			1.76507			0.882534	−	0.470248i	$-0.155836\pi$
$103$	1845.09			1.76507			0.882534	+	0.470248i	$0.155836\pi$
$104$	−134.524	+	233.003i	−0.126839	+	0.219691i
$105$	−1.25391			−0.00116542
$106$	408.633	−	707.774i	0.374434	−	0.648539i
$107$	308.080	−	533.610i	0.278348	−	0.482112i	−0.692627	−	0.721296i	$-0.743547\pi$
$107$	308.080	−	533.610i	0.278348	−	0.482112i	0.970974	+	0.239184i	$0.0768800\pi$
$108$	247.054	−	427.911i	0.220119	−	0.381257i
$109$	−202.926	−	351.479i	−0.178319	−	0.308858i	0.762986	−	0.646415i	$-0.223733\pi$
$109$	−202.926	−	351.479i	−0.178319	−	0.308858i	−0.941305	+	0.337557i	$0.890399\pi$
$110$	−2.46286			−0.00213477
$111$	−491.890	+	325.576i	−0.420614	+	0.278399i
$112$	329.459			0.277955
$113$	−1169.50	−	2025.64i	−0.973607	−	1.68634i	−0.684457	−	0.729053i	$-0.739961\pi$
$113$	−1169.50	−	2025.64i	−0.973607	−	1.68634i	−0.289150	−	0.957284i	$-0.593373\pi$
$114$	−47.9537	+	83.0582i	−0.0393971	+	0.0682378i
$115$	2.24805	−	3.89374i	0.00182288	−	0.00315733i
$116$	−26.6144	+	46.0975i	−0.0213024	+	0.0368969i
$117$	677.014			0.534957
$118$	−199.598	+	345.715i	−0.155716	+	0.269709i
$119$	−1534.69			−1.18222
$120$	−0.243582	−	0.421897i	−0.000185299	−	0.000320948i
$121$	1478.11			1.11052
$122$	−429.635			−0.318830
$123$	477.898	+	827.743i	0.350330	+	0.606789i
$124$	−106.340	+	184.186i	−0.0770129	+	0.133390i
$125$	5.80852			0.00415624
$126$	−414.513	−	717.957i	−0.293077	−	0.507625i
$127$	583.018	+	1009.82i	0.407358	+	0.705565i	0.994593	−	0.103852i	$-0.0331168\pi$
$127$	583.018	+	1009.82i	0.407358	+	0.705565i	−0.587235	+	0.809417i	$0.699784\pi$
$128$	64.0000	+	110.851i	0.0441942	+	0.0765466i
$129$	−106.538	+	184.529i	−0.0727141	+	0.125945i
$130$	0.781389	−	1.35341i	0.000527172	−	0.000913089i
$131$	556.904	+	964.586i	0.371427	+	0.643330i	0.989785	−	0.142566i	$-0.0455353\pi$
$131$	556.904	+	964.586i	0.371427	+	0.643330i	−0.618358	+	0.785896i	$0.712202\pi$
$132$	277.827	+	481.210i	0.183195	+	0.317302i
$133$	188.371	+	326.268i	0.122811	+	0.212714i
$134$	−592.294			−0.381839
$135$	−1.43502	+	2.48553i	−0.000914867	+	0.00158460i
$136$	−298.125	−	516.368i	−0.187971	−	0.325575i
$137$	−1188.33			−0.741062			−0.370531	−	0.928820i	$-0.620824\pi$
$137$	−1188.33			−0.741062			−0.370531	+	0.928820i	$0.620824\pi$
$138$	−1014.38			−0.625720
$139$	441.052	+	763.925i	0.269134	+	0.466153i	0.968638	−	0.248475i	$-0.0799293\pi$
$139$	441.052	+	763.925i	0.269134	+	0.466153i	−0.699505	+	0.714628i	$0.746596\pi$
$140$	−1.91367			−0.00115525
$141$	698.656	−	1210.11i	0.417287	−	0.722762i
$142$	−1306.90			−0.772339
$143$	−891.242	+	1543.68i	−0.521184	+	0.902718i
$144$	161.045	−	278.938i	0.0931972	−	0.161422i
$145$	0.154590	−	0.267758i	8.85382e−5	−	0.000153353i
$146$	−127.670	−	221.131i	−0.0723702	−	0.125349i
$147$	212.289			0.119111
$148$	−750.704	+	496.881i	−0.416943	+	0.275969i
$149$	−94.8654			−0.0521589			−0.0260795	−	0.999660i	$-0.508302\pi$
$149$	−94.8654			−0.0521589			−0.0260795	+	0.999660i	$0.508302\pi$
$150$	−327.618	−	567.451i	−0.178333	−	0.308881i
$151$	−720.887	+	1248.61i	−0.388510	+	0.672918i	−0.992249	−	0.124263i	$-0.960343\pi$
$151$	−720.887	+	1248.61i	−0.388510	+	0.672918i	0.603740	+	0.797182i	$0.293677\pi$
$152$	−73.1851	+	126.760i	−0.0390532	+	0.0676422i
$153$	−750.180	+	1299.35i	−0.396395	+	0.686576i
$154$	2182.71			1.14213
$155$	0.617678	−	1.06985i	0.000320085	−	0.000554403i
$156$	−352.582			−0.180956
$157$	1076.13	+	1863.91i	0.547034	+	0.947491i	0.998476	+	0.0551901i	$0.0175765\pi$
$157$	1076.13	+	1863.91i	0.547034	+	0.947491i	−0.451442	+	0.892301i	$0.649090\pi$
$158$	−531.714			−0.267727
$159$	1071.01			0.534192
$160$	−0.371746	−	0.643883i	−0.000183682	−	0.000318146i
$161$	−1992.33	+	3450.81i	−0.975264	+	1.68921i
$162$	−439.534			−0.213167
$163$	−1772.32	−	3069.75i	−0.851650	−	1.47510i	−0.879718	−	0.475495i	$-0.842269\pi$
$163$	−1772.32	−	3069.75i	−0.851650	−	1.47510i	0.0280681	−	0.999606i	$-0.491064\pi$
$164$	729.349	+	1263.27i	0.347272	+	0.601493i
$165$	−1.61376	−	2.79512i	−0.000761402	−	0.00131879i
$166$	767.667	−	1329.64i	0.358931	−	0.621686i
$167$	1609.39	−	2787.54i	0.745738	−	1.29166i	−0.204111	−	0.978948i	$-0.565430\pi$
$167$	1609.39	−	2787.54i	0.745738	−	1.29166i	0.949849	−	0.312709i	$-0.101236\pi$
$168$	215.874	+	373.905i	0.0991372	+	0.171711i
$169$	532.974	+	923.138i	0.242592	+	0.420181i
$170$	1.73167	+	2.99934i	0.000781253	+	0.00135317i
$171$	368.315			0.164712
$172$	−162.594	+	281.621i	−0.0720794	+	0.124845i
$173$	−226.822	−	392.866i	−0.0996816	−	0.172654i	0.811871	−	0.583837i	$-0.198449\pi$
$173$	−226.822	−	392.866i	−0.0996816	−	0.172654i	−0.911553	+	0.411183i	$0.865116\pi$
$174$	−69.7551			−0.0303915
$175$	−2573.89			−1.11181
$176$	424.008	+	734.404i	0.181596	+	0.314533i
$177$	−523.138			−0.222155
$178$	194.772	−	337.355i	0.0820156	−	0.142055i
$179$	−2719.55			−1.13558			−0.567790	−	0.823173i	$-0.692202\pi$
$179$	−2719.55			−1.13558			−0.567790	+	0.823173i	$0.692202\pi$
$180$	−0.935434	+	1.62022i	−0.000387351	+	0.000670911i
$181$	633.057	−	1096.49i	0.259971	−	0.450283i	−0.706263	−	0.707950i	$-0.749620\pi$
$181$	633.057	−	1096.49i	0.259971	−	0.450283i	0.966234	+	0.257667i	$0.0829536\pi$
$182$	−692.504	+	1199.45i	−0.282043	+	0.488513i
$183$	−281.513	−	487.595i	−0.113716	−	0.196962i
$184$	−1548.10			−0.620259
$185$	4.36049	−	2.88615i	0.00173292	−	0.00114699i
$186$	−278.712			−0.109872
$187$	−1975.12	−	3421.00i	−0.772379	−	1.33780i
$188$	1066.26	−	1846.82i	0.413644	−	0.716453i
$189$	1271.78	−	2202.80i	0.489464	−	0.847777i
$190$	0.425098	−	0.736291i	0.000162315	−	0.000281138i
$191$	1566.43			0.593419			0.296710	−	0.954968i	$-0.404111\pi$
$191$	1566.43			0.593419			0.296710	+	0.954968i	$0.404111\pi$
$192$	−83.8705	+	145.268i	−0.0315252	+	0.0546032i
$193$	3168.51			1.18173			0.590866	−	0.806769i	$-0.298786\pi$
$193$	3168.51			1.18173			0.590866	+	0.806769i	$0.298786\pi$
$194$	1031.14	+	1785.98i	0.381604	+	0.660958i
$195$	2.04799			0.000752099
$196$	323.987			0.118071
$197$	−1689.41	−	2926.15i	−0.610993	−	1.05827i	−0.991073	−	0.133318i	$-0.957437\pi$
$197$	−1689.41	−	2926.15i	−0.610993	−	1.05827i	0.380080	−	0.924954i	$-0.375896\pi$
$198$	1066.94	−	1848.00i	0.382951	−	0.663291i
$199$	−1463.09			−0.521183			−0.260592	−	0.965449i	$-0.583918\pi$
$199$	−1463.09			−0.521183			−0.260592	+	0.965449i	$0.583918\pi$
$200$	−499.998	−	866.022i	−0.176776	−	0.306185i
$201$	−388.094	−	672.199i	−0.136189	−	0.235887i
$202$	1626.16	+	2816.60i	0.566418	+	0.981065i
$203$	−137.005	+	237.300i	−0.0473689	+	0.0820454i
$204$	390.686	−	676.689i	0.134086	−	0.232244i
$205$	−4.23645	−	7.33774i	−0.00144335	−	0.00249995i
$206$	1845.09	+	3195.79i	0.624046	+	1.08088i
$207$	1947.76	+	3373.63i	0.654004	+	1.13277i
$208$	−538.098			−0.179377
$209$	−484.860	+	839.803i	−0.160471	+	0.277944i
$210$	−1.25391	−	2.17184i	−0.000412039	−	0.000713672i
$211$	3631.67			1.18490			0.592451	−	0.805606i	$-0.298160\pi$
$211$	3631.67			1.18490			0.592451	+	0.805606i	$0.298160\pi$
$212$	1634.53			0.529529
$213$	−856.328	−	1483.20i	−0.275468	−	0.477124i
$214$	1232.32			0.393643
$215$	0.944431	−	1.63580i	0.000299580	−	0.000518887i
$216$	988.217			0.311295
$217$	−547.416	+	948.152i	−0.171249	+	0.296612i
$218$	405.853	−	702.957i	0.126091	−	0.218396i
$219$	167.309	−	289.787i	0.0516241	−	0.0894156i
$220$	−2.46286	−	4.26581i	−0.000754756	−	0.00130728i
$221$	2506.57			0.762942
$222$	−1055.80	−	526.404i	−0.319193	−	0.159144i
$223$	873.014			0.262159			0.131079	−	0.991372i	$-0.458156\pi$
$223$	873.014			0.262159			0.131079	+	0.991372i	$0.458156\pi$
$224$	329.459	+	570.640i	0.0982719	+	0.170212i
$225$	−1258.16	+	2179.19i	−0.372787	+	0.645686i
$226$	2339.01	−	4051.28i	0.688444	−	1.19242i
$227$	3320.25	−	5750.84i	0.970805	−	1.68148i	0.277669	−	0.960677i	$-0.410438\pi$
$227$	3320.25	−	5750.84i	0.970805	−	1.68148i	0.693136	−	0.720807i	$-0.256228\pi$
$228$	−191.815			−0.0557160
$229$	−3000.53	+	5197.07i	−0.865853	+	1.49970i	0.000343767		1.00000i	$0.499891\pi$
$229$	−3000.53	+	5197.07i	−0.865853	+	1.49970i	−0.866197	+	0.499702i	$0.833443\pi$
$230$	8.99220			0.00257795
$231$	1430.19	+	2477.17i	0.407359	+	0.705566i
$232$	−106.458			−0.0301262
$233$	−4325.81			−1.21628			−0.608140	−	0.793830i	$-0.708084\pi$
$233$	−4325.81			−1.21628			−0.608140	+	0.793830i	$0.708084\pi$
$234$	677.014	+	1172.62i	0.189136	+	0.327593i
$235$	−6.19341	+	10.7273i	−0.00171921	+	0.00297775i
$236$	−798.394			−0.220216
$237$	−348.400	−	603.446i	−0.0954894	−	0.165393i
$238$	−1534.69	−	2658.16i	−0.417979	−	0.723961i
$239$	1569.48	+	2718.42i	0.424775	+	0.735732i	0.996399	−	0.0847836i	$-0.0270199\pi$
$239$	1569.48	+	2718.42i	0.424775	+	0.735732i	−0.571624	+	0.820515i	$0.693687\pi$
$240$	0.487165	−	0.843794i	0.000131026	−	0.000226944i
$241$	1491.60	−	2583.53i	0.398682	−	0.690538i	−0.594881	−	0.803813i	$-0.702801\pi$
$241$	1491.60	−	2583.53i	0.398682	−	0.690538i	0.993564	+	0.113276i	$0.0361343\pi$
$242$	1478.11	+	2560.16i	0.392630	+	0.680055i
$243$	−1955.62	−	3387.23i	−0.516267	−	0.894200i
$244$	−429.635	−	744.149i	−0.112723	−	0.195243i
$245$	−1.88189			−0.000490732
$246$	−955.795	+	1655.49i	−0.247721	+	0.429065i
$247$	−307.662	−	532.886i	−0.0792553	−	0.137274i
$248$	−425.359			−0.108913
$249$	2012.02			0.512075
$250$	5.80852	+	10.0606i	0.00146945	+	0.00254517i
$251$	5975.96			1.50279			0.751393	−	0.659855i	$-0.229382\pi$
$251$	5975.96			1.50279			0.751393	+	0.659855i	$0.229382\pi$
$252$	829.026	−	1435.91i	0.207237	−	0.358945i
$253$	−10256.4			−2.54867
$254$	−1166.04	+	2019.63i	−0.288046	+	0.498909i
$255$	−2.26931	+	3.93057i	−0.000557294	+	0.000965261i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1153.13	−	1997.27i	−0.279883	−	0.484772i	0.691472	−	0.722403i	$-0.256962\pi$
$257$	−1153.13	−	1997.27i	−0.279883	−	0.484772i	−0.971356	+	0.237631i	$0.923629\pi$
$258$	−426.151			−0.102833
$259$	−3864.47	+	2557.84i	−0.927130	+	0.613655i
$260$	3.12556			0.000745534
$261$	133.941	+	231.992i	0.0317652	+	0.0550190i
$262$	−1113.81	+	1929.17i	−0.262639	+	0.454903i
$263$	1945.06	−	3368.94i	0.456036	−	0.789878i	−0.542711	−	0.839920i	$-0.682602\pi$
$263$	1945.06	−	3368.94i	0.456036	−	0.789878i	0.998747	+	0.0500415i	$0.0159354\pi$
$264$	−555.653	+	962.419i	−0.129538	+	0.224367i
$265$	−9.49424			−0.00220086
$266$	−376.742	+	652.536i	−0.0868403	+	0.150412i
$267$	510.489			0.117009
$268$	−592.294	−	1025.88i	−0.135000	−	0.233828i
$269$	2599.02			0.589088			0.294544	−	0.955638i	$-0.404832\pi$
$269$	2599.02			0.589088			0.294544	+	0.955638i	$0.404832\pi$
$270$	−5.74009			−0.00129382
$271$	973.359	+	1685.91i	0.218182	+	0.377903i	0.954252	−	0.299003i	$-0.0966540\pi$
$271$	973.359	+	1685.91i	0.218182	+	0.377903i	−0.736070	+	0.676905i	$0.763321\pi$
$272$	596.250	−	1032.74i	0.132915	−	0.230216i
$273$	−1815.02			−0.402381
$274$	−1188.33	−	2058.24i	−0.262005	−	0.453806i
$275$	−3312.55	−	5737.50i	−0.726379	−	1.25813i
$276$	−1014.38	−	1756.95i	−0.221226	−	0.383174i
$277$	−3716.14	+	6436.55i	−0.806070	+	1.39615i	0.109496	+	0.993987i	$0.465076\pi$
$277$	−3716.14	+	6436.55i	−0.806070	+	1.39615i	−0.915566	+	0.402167i	$0.868257\pi$
$278$	−882.105	+	1527.85i	−0.190306	+	0.329620i
$279$	535.171	+	926.944i	0.114838	+	0.198906i
$280$	−1.91367	−	3.31458i	−0.000408442	−	0.000707443i
$281$	−1167.06	−	2021.40i	−0.247761	−	0.429134i	0.715144	−	0.698978i	$-0.246361\pi$
$281$	−1167.06	−	2021.40i	−0.247761	−	0.429134i	−0.962904	+	0.269844i	$0.913028\pi$
$282$	2794.62			0.590133
$283$	246.743	−	427.372i	0.0518282	−	0.0897690i	−0.838947	−	0.544213i	$-0.816829\pi$
$283$	246.743	−	427.372i	0.0518282	−	0.0897690i	0.890776	+	0.454443i	$0.150162\pi$
$284$	−1306.90	−	2263.61i	−0.273063	−	0.472959i
$285$	1.11416			0.000231569
$286$	−3564.97			−0.737066
$287$	3754.54	+	6503.05i	0.772207	+	1.33750i
$288$	644.179			0.131801
$289$	−320.958	+	555.916i	−0.0653284	+	0.113152i
$290$	0.618362			0.000125212
$291$	−1351.28	+	2340.48i	−0.272211	+	0.471483i
$292$	255.340	−	442.262i	0.0511735	−	0.0886351i
$293$	−2557.90	+	4430.42i	−0.510015	+	0.883372i	0.489918	+	0.871769i	$0.337027\pi$
$293$	−2557.90	+	4430.42i	−0.510015	+	0.883372i	−0.999933	+	0.0116032i	$0.996307\pi$
$294$	212.289	+	367.695i	0.0421120	+	0.0729402i
$295$	4.63750			0.000915273
$296$	−1611.33	−	803.377i	−0.316407	−	0.157755i
$297$	6547.07			1.27912
$298$	−94.8654	−	164.312i	−0.0184410	−	0.0319407i
$299$	3254.02	−	5636.13i	0.629381	−	1.09012i
$300$	655.236	−	1134.90i	0.126100	−	0.218412i
$301$	−836.999	+	1449.73i	−0.160279	+	0.277611i
$302$	−2883.55			−0.549436
$303$	−2131.05	+	3691.09i	−0.404045	+	0.699827i
$304$	−292.740			−0.0552296
$305$	2.49555	+	4.32241i	0.000468507	+	0.000811477i
$306$	−3000.72			−0.560587
$307$	5929.75			1.10237			0.551187	−	0.834382i	$-0.314175\pi$
$307$	5929.75			1.10237			0.551187	+	0.834382i	$0.314175\pi$
$308$	2182.71	+	3780.56i	0.403803	+	0.699407i
$309$	−2417.95	+	4188.01i	−0.445153	+	0.771027i
$310$	2.47071			0.000452668
$311$	791.323	+	1370.61i	0.144282	+	0.249904i	0.929105	−	0.369816i	$-0.120579\pi$
$311$	791.323	+	1370.61i	0.144282	+	0.249904i	−0.784823	+	0.619720i	$0.787246\pi$
$312$	−352.582	−	610.691i	−0.0639777	−	0.110813i
$313$	−4196.68	−	7268.86i	−0.757860	−	1.31265i	−0.943940	−	0.330118i	$-0.892912\pi$
$313$	−4196.68	−	7268.86i	−0.757860	−	1.31265i	0.186079	−	0.982535i	$-0.440422\pi$
$314$	−2152.26	+	3727.82i	−0.386811	+	0.669977i
$315$	−4.81542	+	8.34055i	−0.000861328	+	0.00149186i
$316$	−531.714	−	920.956i	−0.0946559	−	0.163949i
$317$	3951.84	+	6844.79i	0.700181	+	1.21275i	0.968403	+	0.249392i	$0.0802307\pi$
$317$	3951.84	+	6844.79i	0.700181	+	1.21275i	−0.268222	+	0.963357i	$0.586436\pi$
$318$	1071.01	+	1855.04i	0.188866	+	0.327125i
$319$	−705.295			−0.123790
$320$	0.743492	−	1.28777i	0.000129883	−	0.000224963i
$321$	807.463	+	1398.57i	0.140399	+	0.243179i
$322$	−7969.31			−1.37923
$323$	1363.64			0.234908
$324$	−439.534	−	761.296i	−0.0753660	−	0.130538i
$325$	4203.87			0.717504
$326$	3544.64	−	6139.50i	0.602208	−	1.04305i
$327$	1063.72			0.179890
$328$	−1458.70	+	2526.54i	−0.245558	+	0.425320i
$329$	5488.90	−	9507.05i	0.919795	−	1.59313i
$330$	3.22753	−	5.59024i	0.000538393	−	0.000932523i
$331$	−4945.32	−	8565.55i	−0.821207	−	1.42237i	−0.904784	−	0.425871i	$-0.859968\pi$
$331$	−4945.32	−	8565.55i	−0.821207	−	1.42237i	0.0835769	−	0.996501i	$-0.473366\pi$
$332$	3070.67			0.507605
$333$	276.592	+	4522.19i	0.0455170	+	0.744187i
$334$	6437.56			1.05463
$335$	3.44036	+	5.95888i	0.000561095	+	0.000971846i
$336$	−431.748	+	747.810i	−0.0701006	+	0.121418i
$337$	−1383.48	+	2396.27i	−0.223630	+	0.387338i	−0.955907	−	0.293668i	$-0.905124\pi$
$337$	−1383.48	+	2396.27i	−0.223630	+	0.387338i	0.732278	+	0.681006i	$0.238457\pi$
$338$	−1065.95	+	1846.28i	−0.171538	+	0.297113i
$339$	6130.43			0.982181
$340$	−3.46334	+	5.99868i	−0.000552429	+	0.000956836i
$341$	−2818.06			−0.447527
$342$	368.315	+	637.940i	0.0582344	+	0.100865i
$343$	−5394.96			−0.849272
$344$	−650.375			−0.101936
$345$	5.89203	+	10.2053i	0.000919468	+	0.00159257i
$346$	453.643	−	785.733i	0.0704855	−	0.122085i
$347$	−5968.31			−0.923331			−0.461665	−	0.887054i	$-0.652748\pi$
$347$	−5968.31			−0.923331			−0.461665	+	0.887054i	$0.652748\pi$
$348$	−69.7551	−	120.819i	−0.0107450	−	0.0186109i
$349$	−2652.04	−	4593.47i	−0.406763	−	0.704535i	0.587762	−	0.809034i	$-0.300009\pi$
$349$	−2652.04	−	4593.47i	−0.406763	−	0.704535i	−0.994525	+	0.104499i	$0.966676\pi$
$350$	−2573.89	−	4458.10i	−0.393086	−	0.680845i
$351$	−2077.18	+	3597.78i	−0.315873	+	0.547109i
$352$	−848.016	+	1468.81i	−0.128407	+	0.222408i
$353$	3798.20	+	6578.68i	0.572685	+	0.991920i	0.996289	+	0.0860726i	$0.0274317\pi$
$353$	3798.20	+	6578.68i	0.572685	+	0.991920i	−0.423603	+	0.905848i	$0.639235\pi$
$354$	−523.138	−	906.102i	−0.0785438	−	0.136042i
$355$	7.59114	+	13.1482i	0.00113492	+	0.00196574i
$356$	779.088			0.115988
$357$	2011.17	−	3483.45i	0.298158	−	0.516426i
$358$	−2719.55	−	4710.40i	−0.401488	−	0.695398i
$359$	7218.20			1.06117			0.530587	−	0.847630i	$-0.321971\pi$
$359$	7218.20			1.06117			0.530587	+	0.847630i	$0.321971\pi$
$360$	−3.74173			−0.000547796
$361$	3262.12	+	5650.16i	0.475598	+	0.823759i
$362$	2532.23			0.367655
$363$	−1937.03	+	3355.03i	−0.280076	+	0.485106i
$364$	−2770.02			−0.398869
$365$	−1.48315	+	2.56889i	−0.000212690	+	0.000368389i
$366$	563.026	−	975.190i	0.0804094	−	0.139273i
$367$	6397.09	−	11080.1i	0.909878	−	1.57596i	0.0956469	−	0.995415i	$-0.469508\pi$
$367$	6397.09	−	11080.1i	0.909878	−	1.57596i	0.814232	−	0.580540i	$-0.197159\pi$
$368$	−1548.10	−	2681.39i	−0.219295	−	0.379829i
$369$	7341.12			1.03567
$370$	9.35945	+	4.66644i	0.00131507	+	0.000655667i
$371$	8414.25			1.17748
$372$	−278.712	−	482.743i	−0.0388455	−	0.0672824i
$373$	6424.75	−	11128.0i	0.891852	−	1.54473i	0.0541994	−	0.998530i	$-0.482739\pi$
$373$	6424.75	−	11128.0i	0.891852	−	1.54473i	0.837653	−	0.546203i	$-0.183927\pi$
$374$	3950.24	−	6842.01i	0.546155	−	0.945968i
$375$	−7.61193	+	13.1843i	−0.00104821	+	0.00181555i
$376$	4265.05			0.584981
$377$	223.768	−	387.577i	0.0305693	−	0.0529476i
$378$	5087.14			0.692207
$379$	−4799.77	−	8313.44i	−0.650521	−	1.12674i	−0.982997	−	0.183624i	$-0.941217\pi$
$379$	−4799.77	−	8313.44i	−0.650521	−	1.12674i	0.332476	−	0.943112i	$-0.392116\pi$
$380$	1.70039			0.000229548
$381$	−3056.13			−0.410945
$382$	1566.43	+	2713.14i	0.209805	+	0.363393i
$383$	−2669.65	+	4623.98i	−0.356170	+	0.616904i	−0.987317	−	0.158759i	$-0.949251\pi$
$383$	−2669.65	+	4623.98i	−0.356170	+	0.616904i	0.631148	+	0.775663i	$0.282584\pi$
$384$	−335.482			−0.0445833
$385$	−12.6783	−	21.9595i	−0.00167830	−	0.00290691i
$386$	3168.51	+	5488.02i	0.417806	+	0.723661i
$387$	818.277	+	1417.30i	0.107482	+	0.186164i
$388$	−2062.27	+	3571.96i	−0.269835	+	0.467368i
$389$	881.555	−	1526.90i	0.114901	−	0.199015i	−0.802839	−	0.596196i	$-0.796678\pi$
$389$	881.555	−	1526.90i	0.114901	−	0.199015i	0.917740	+	0.397181i	$0.130011\pi$
$390$	2.04799	+	3.54722i	0.000265907	+	0.000460565i
$391$	7211.38	+	12490.5i	0.932724	+	1.61553i
$392$	323.987	+	561.162i	0.0417444	+	0.0723035i
$393$	−2919.24			−0.374698
$394$	3378.82	−	5852.30i	0.432037	−	0.748311i
$395$	3.08848	+	5.34940i	0.000393413	+	0.000681412i
$396$	4267.77			0.541574
$397$	−12197.5			−1.54200			−0.771002	−	0.636832i	$-0.780244\pi$
$397$	−12197.5			−1.54200			−0.771002	+	0.636832i	$0.780244\pi$
$398$	−1463.09	−	2534.14i	−0.184266	−	0.319158i
$399$	−987.423			−0.123892
$400$	999.996	−	1732.04i	0.124999	−	0.216505i
$401$	−9992.66			−1.24441			−0.622206	−	0.782853i	$-0.713764\pi$
$401$	−9992.66			−1.24441			−0.622206	+	0.782853i	$0.713764\pi$
$402$	776.188	−	1344.40i	0.0963004	−	0.166797i
$403$	894.082	−	1548.60i	0.110515	−	0.191417i
$404$	−3252.33	+	5633.20i	−0.400518	+	0.693718i
$405$	2.55305	+	4.42201i	0.000313239	+	0.000542547i
$406$	−548.021			−0.0669898
$407$	−10675.3	−	5322.48i	−1.30013	−	0.648219i
$408$	1562.75			0.189626
$409$	−3359.98	−	5819.65i	−0.406211	−	0.703577i	0.588251	−	0.808678i	$-0.299817\pi$
$409$	−3359.98	−	5819.65i	−0.406211	−	0.703577i	−0.994462	+	0.105101i	$0.966483\pi$
$410$	8.47289	−	14.6755i	0.00102060	−	0.00176773i
$411$	1557.27	−	2697.28i	0.186897	−	0.323715i
$412$	−3690.18	+	6391.58i	−0.441267	+	0.764297i
$413$	−4109.97			−0.489681
$414$	−3895.53	+	6747.25i	−0.462451	+	0.800989i
$415$	−17.8361			−0.00210973
$416$	−538.098	−	932.013i	−0.0634193	−	0.109845i
$417$	−2311.96			−0.271504
$418$	−1939.44			−0.226941
$419$	807.082	+	1397.91i	0.0941015	+	0.162989i	0.909233	−	0.416287i	$-0.136669\pi$
$419$	807.082	+	1397.91i	0.0941015	+	0.162989i	−0.815132	+	0.579276i	$0.803336\pi$
$420$	2.50782	−	4.34368i	0.000291355	−	0.000504642i
$421$	11172.7			1.29341			0.646703	−	0.762742i	$-0.276147\pi$
$421$	11172.7			1.29341			0.646703	+	0.762742i	$0.276147\pi$
$422$	3631.67	+	6290.24i	0.418926	+	0.725602i
$423$	−5366.12	−	9294.39i	−0.616808	−	1.06834i
$424$	1634.53	+	2831.10i	0.187217	+	0.324269i
$425$	−4658.19	+	8068.22i	−0.531659	+	0.920861i
$426$	1712.66	−	2966.41i	0.194785	−	0.337378i
$427$	−2211.67	−	3830.73i	−0.250656	−	0.434149i
$428$	1232.32	+	2134.44i	0.139174	+	0.241056i
$429$	−2335.90	−	4045.90i	−0.262887	−	0.455334i
$430$	3.77772			0.000423670
$431$	−3907.35	+	6767.72i	−0.436683	+	0.756357i	−0.997431	−	0.0716295i	$-0.977180\pi$
$431$	−3907.35	+	6767.72i	−0.436683	+	0.756357i	0.560749	+	0.827986i	$0.310513\pi$
$432$	988.217	+	1711.64i	0.110059	+	0.190628i
$433$	10590.2			1.17536			0.587682	−	0.809092i	$-0.300041\pi$
$433$	10590.2			1.17536			0.587682	+	0.809092i	$0.300041\pi$
$434$	−2189.66			−0.242183
$435$	0.405174	+	0.701783i	4.46589e−5	+	7.73515e-5i
$436$	1623.41			0.178319
$437$	1770.28	−	3066.22i	0.193785	−	0.335645i
$438$	669.235			0.0730075
$439$	−8076.92	+	13989.6i	−0.878110	+	1.52093i	−0.0246983	+	0.999695i	$0.507863\pi$
$439$	−8076.92	+	13989.6i	−0.878110	+	1.52093i	−0.853412	+	0.521237i	$0.825471\pi$
$440$	4.92573	−	8.53161i	0.000533693	−	0.000924384i
$441$	815.257	−	1412.07i	0.0880312	−	0.152474i
$442$	2506.57	+	4341.51i	0.269741	+	0.467205i
$443$	−9027.16			−0.968157			−0.484078	−	0.875025i	$-0.660845\pi$
$443$	−9027.16			−0.968157			−0.484078	+	0.875025i	$0.660845\pi$
$444$	−144.046	−	2355.11i	−0.0153967	−	0.251731i
$445$	−4.52536			−0.000482073
$446$	873.014	+	1512.10i	0.0926870	+	0.160539i
$447$	124.319	−	215.327i	0.0131546	−	0.0227844i
$448$	−658.918	+	1141.28i	−0.0694887	+	0.120358i
$449$	4118.87	−	7134.09i	0.432921	−	0.749841i	−0.564203	−	0.825636i	$-0.690816\pi$
$449$	4118.87	−	7134.09i	0.432921	−	0.749841i	0.997123	+	0.0757956i	$0.0241497\pi$
$450$	−5032.63			−0.527201
$451$	−9664.06	+	16738.6i	−1.00901	+	1.74765i
$452$	9356.03			0.973607
$453$	−1889.41	−	3272.56i	−0.195965	−	0.339422i
$454$	13281.0			1.37293
$455$	16.0897			0.00165780
$456$	−191.815	−	332.233i	−0.0196986	−	0.0341189i
$457$	−8678.15	+	15031.0i	−0.888286	+	1.53856i	−0.0463856	+	0.998924i	$0.514770\pi$
$457$	−8678.15	+	15031.0i	−0.888286	+	1.53856i	−0.841900	+	0.539633i	$0.818563\pi$
$458$	−12002.1			−1.22450
$459$	−4603.32	−	7973.18i	−0.468115	−	0.810798i
$460$	8.99220	+	15.5749i	0.000911442	+	0.00157866i
$461$	6965.90	+	12065.3i	0.703762	+	1.21895i	0.967136	+	0.254258i	$0.0818314\pi$
$461$	6965.90	+	12065.3i	0.703762	+	1.21895i	−0.263374	+	0.964694i	$0.584835\pi$
$462$	−2860.39	+	4954.34i	−0.288046	+	0.498911i
$463$	−4757.69	+	8240.55i	−0.477556	+	0.827151i	−0.999669	−	0.0257250i	$-0.991811\pi$
$463$	−4757.69	+	8240.55i	−0.477556	+	0.827151i	0.522113	+	0.852876i	$0.325144\pi$
$464$	−106.458	−	184.390i	−0.0106512	−	0.0184485i
$465$	1.61891	+	2.80403i	0.000161452	+	0.000279642i
$466$	−4325.81	−	7492.52i	−0.430020	−	0.744816i
$467$	5347.94			0.529921			0.264961	−	0.964259i	$-0.414641\pi$
$467$	5347.94			0.529921			0.264961	+	0.964259i	$0.414641\pi$
$468$	−1354.03	+	2345.25i	−0.133739	+	0.231643i
$469$	−3049.01	−	5281.04i	−0.300192	−	0.519948i
$470$	−24.7737			−0.00243133
$471$	−5640.96			−0.551851
$472$	−798.394	−	1382.86i	−0.0778582	−	0.134854i
$473$	−4308.82			−0.418858
$474$	696.799	−	1206.89i	0.0675212	−	0.116950i
$475$	2287.02			0.220918
$476$	3069.38	−	5316.31i	0.295556	−	0.511918i
$477$	4113.02	−	7123.96i	0.394805	−	0.683823i
$478$	−3138.96	+	5436.84i	−0.300361	+	0.520241i
$479$	3779.28	+	6545.90i	0.360500	+	0.624405i	0.988043	−	0.154177i	$-0.0492727\pi$
$479$	3779.28	+	6545.90i	0.360500	+	0.624405i	−0.627543	+	0.778582i	$0.715939\pi$
$480$	1.94866			0.000185299
$481$	6311.76	−	4177.67i	0.598319	−	0.396019i
$482$	5966.40			0.563822
$483$	−5221.80	−	9044.42i	−0.491926	−	0.852040i
$484$	−2956.22	+	5120.32i	−0.277631	+	0.480871i
$485$	11.9788	−	20.7478i	0.00112150	−	0.00194250i
$486$	3911.23	−	6774.45i	0.365056	−	0.632295i
$487$	367.133			0.0341609			0.0170805	−	0.999854i	$-0.494563\pi$
$487$	367.133			0.0341609			0.0170805	+	0.999854i	$0.494563\pi$
$488$	859.269	−	1488.30i	0.0797075	−	0.138058i
$489$	9290.35			0.859150
$490$	−1.88189	−	3.25953i	−0.000173500	−	0.000300511i
$491$	−7768.16			−0.713996			−0.356998	−	0.934105i	$-0.616200\pi$
$491$	−7768.16			−0.713996			−0.356998	+	0.934105i	$0.616200\pi$
$492$	−3823.18			−0.350330
$493$	495.901	+	858.926i	0.0453028	+	0.0784667i
$494$	615.324	−	1065.77i	0.0560420	−	0.0970675i
$495$	−24.7895			−0.00225092
$496$	−425.359	−	736.744i	−0.0385065	−	0.0666951i
$497$	−6727.63	−	11652.6i	−0.607194	−	1.05169i
$498$	2012.02	+	3484.92i	0.181046	+	0.313580i
$499$	3852.99	−	6673.58i	0.345659	−	0.598698i	−0.639815	−	0.768529i	$-0.720989\pi$
$499$	3852.99	−	6673.58i	0.345659	−	0.598698i	0.985473	+	0.169831i	$0.0543222\pi$
$500$	−11.6170	+	20.1213i	−0.00103906	+	0.00179970i
$501$	4218.14	+	7306.03i	0.376153	+	0.651515i
$502$	5975.96	+	10350.7i	0.531315	+	0.920265i
$503$	2455.98	+	4253.88i	0.217707	+	0.377080i	0.954107	−	0.299467i	$-0.0968089\pi$
$503$	2455.98	+	4253.88i	0.217707	+	0.377080i	−0.736400	+	0.676547i	$0.763476\pi$
$504$	3316.10			0.293077
$505$	18.8912	−	32.7206i	0.00166465	−	0.00288326i
$506$	−10256.4	−	17764.6i	−0.901090	−	1.56073i
$507$	−2793.80			−0.244728
$508$	−4664.14			−0.407358
$509$	−3404.80	−	5897.28i	−0.296493	−	0.513541i	0.678838	−	0.734288i	$-0.262484\pi$
$509$	−3404.80	−	5897.28i	−0.296493	−	0.513541i	−0.975331	+	0.220747i	$0.929150\pi$
$510$	−9.07726			−0.000788133
$511$	1314.44	−	2276.68i	0.113791	−	0.197092i
$512$	−512.000			−0.0441942
$513$	−1130.04	+	1957.29i	−0.0972565	+	0.168453i
$514$	2306.25	−	3994.54i	0.197907	−	0.342786i
$515$	21.4345	−	37.1257i	0.00183401	−	0.00317661i
$516$	−426.151	−	738.115i	−0.0363571	−	0.0629723i
$517$	28256.5			2.40371
$518$	−8294.79	−	4135.62i	−0.703575	−	0.350789i
$519$	1188.98			0.100559
$520$	3.12556	+	5.41362i	0.000263586	+	0.000456545i
$521$	−9139.05	+	15829.3i	−0.768501	+	1.33108i	0.169875	+	0.985466i	$0.445664\pi$
$521$	−9139.05	+	15829.3i	−0.768501	+	1.33108i	−0.938376	+	0.345617i	$0.887670\pi$
$522$	−267.882	+	463.985i	−0.0224614	+	0.0389043i
$523$	10310.1	−	17857.6i	0.862005	−	1.49304i	−0.00798592	−	0.999968i	$-0.502542\pi$
$523$	10310.1	−	17857.6i	0.862005	−	1.49304i	0.869991	−	0.493068i	$-0.164125\pi$
$524$	−4455.23			−0.371427
$525$	3373.02	−	5842.24i	0.280401	−	0.485669i
$526$	7780.24			0.644933
$527$	1981.41	+	3431.91i	0.163779	+	0.283674i
$528$	−2222.61			−0.183195
$529$	25280.2			2.07777
$530$	−9.49424	−	16.4445i	−0.000778120	−	0.00134774i
$531$	−2009.02	+	3479.72i	−0.164188	+	0.284382i
$532$	−1506.97			−0.122811
$533$	−6132.21	−	10621.3i	−0.498340	−	0.863150i
$534$	510.489	+	884.192i	0.0413689	+	0.0716531i
$535$	−7.15796	−	12.3980i	−0.000578441	−	0.00100189i
$536$	1184.59	−	2051.77i	0.0954598	−	0.165341i
$537$	3563.91	−	6172.88i	0.286395	−	0.496051i
$538$	2599.02	+	4501.63i	0.208274	+	0.360742i
$539$	2146.46	+	3717.77i	0.171529	+	0.297098i
$540$	−5.74009	−	9.94213i	−0.000457434	−	0.000792298i
$541$	5574.20			0.442982			0.221491	−	0.975162i	$-0.428908\pi$
$541$	5574.20			0.442982			0.221491	+	0.975162i	$0.428908\pi$
$542$	−1946.72	+	3371.81i	−0.154278	+	0.267217i
$543$	1659.21	+	2873.84i	0.131130	+	0.227124i
$544$	2385.00			0.187971
$545$	−9.42963			−0.000741140
$546$	−1815.02	−	3143.71i	−0.142263	−	0.246407i
$547$	−17048.3			−1.33260			−0.666300	−	0.745684i	$-0.732123\pi$
$547$	−17048.3			−1.33260			−0.666300	+	0.745684i	$0.732123\pi$
$548$	2376.65	−	4116.48i	0.185266	−	0.320889i
$549$	−4324.40			−0.336176
$550$	6625.10	−	11475.0i	0.513628	−	0.889629i
$551$	121.736	−	210.853i	0.00941220	−	0.0163024i
$552$	2028.75	−	3513.90i	0.156430	−	0.270945i
$553$	−2737.16	−	4740.89i	−0.210480	−	0.364563i
$554$	−14864.6			−1.13996
$555$	0.836698	+	13.6797i	6.39926e−5	+	0.00104626i
$556$	−3528.42			−0.269134
$557$	−2393.69	−	4146.00i	−0.182090	−	0.315389i	0.760502	−	0.649335i	$-0.224953\pi$
$557$	−2393.69	−	4146.00i	−0.182090	−	0.315389i	−0.942592	+	0.333947i	$0.891620\pi$
$558$	−1070.34	+	1853.89i	−0.0812029	+	0.140648i
$559$	1367.05	−	2367.80i	0.103435	−	0.179155i
$560$	3.82734	−	6.62916i	0.000288812	−	0.000500237i
$561$	10353.4			0.779181
$562$	2334.11	−	4042.80i	0.175193	−	0.303444i
$563$	12569.1			0.940893			0.470446	−	0.882429i	$-0.344093\pi$
$563$	12569.1			0.940893			0.470446	+	0.882429i	$0.344093\pi$
$564$	2794.62	+	4840.43i	0.208643	+	0.361381i
$565$	−54.3448			−0.00404655
$566$	986.974			0.0732961
$567$	−2262.63	−	3918.99i	−0.167587	−	0.290269i
$568$	2613.79	−	4527.22i	0.193085	−	0.334433i
$569$	−18342.4			−1.35141			−0.675707	−	0.737170i	$-0.736162\pi$
$569$	−18342.4			−1.35141			−0.675707	+	0.737170i	$0.736162\pi$
$570$	1.11416	+	1.92978i	8.18721e−5	+	0.000141807i
$571$	3173.35	+	5496.41i	0.232575	+	0.402833i	0.958565	−	0.284873i	$-0.0919514\pi$
$571$	3173.35	+	5496.41i	0.232575	+	0.402833i	−0.725990	+	0.687705i	$0.758618\pi$
$572$	−3564.97	−	6174.70i	−0.260592	−	0.451359i
$573$	−2052.77	+	3555.51i	−0.149661	+	0.259221i
$574$	−7509.08	+	13006.1i	−0.546033	+	0.945757i
$575$	12094.5	+	20948.3i	0.877174	+	1.51931i
$576$	644.179	+	1115.75i	0.0465986	+	0.0807112i
$577$	971.080	+	1681.96i	0.0700634	+	0.121353i	0.898929	−	0.438095i	$-0.144346\pi$
$577$	971.080	+	1681.96i	0.0700634	+	0.121353i	−0.828865	+	0.559448i	$0.811013\pi$
$578$	−1283.83			−0.0923883
$579$	−4152.26	+	7191.93i	−0.298035	+	0.516211i
$580$	0.618362	+	1.07103i	4.42691e−5	+	7.66763e-5i
$581$	15807.2			1.12873
$582$	−5405.12			−0.384964
$583$	10829.0	+	18756.4i	0.769282	+	1.33243i
$584$	1021.36			0.0723702
$585$	7.86492	−	13.6224i	0.000555854	−	0.000962767i
$586$	−10231.6			−0.721270
$587$	2032.11	−	3519.72i	0.142886	−	0.247486i	−0.785696	−	0.618613i	$-0.787695\pi$
$587$	2032.11	−	3519.72i	0.142886	−	0.247486i	0.928582	+	0.371126i	$0.121028\pi$
$588$	−424.578	+	735.390i	−0.0297777	+	0.0515765i
$589$	486.406	−	842.479i	0.0340272	−	0.0589368i
$590$	4.63750	+	8.03238i	0.000323598	+	0.000560488i
$591$	8855.75			0.616373
$592$	−219.838	−	3594.28i	−0.0152623	−	0.249534i
$593$	18472.1			1.27918			0.639592	−	0.768714i	$-0.279103\pi$
$593$	18472.1			1.27918			0.639592	+	0.768714i	$0.279103\pi$
$594$	6547.07	+	11339.9i	0.452238	+	0.783299i
$595$	−17.8286	+	30.8800i	−0.00122840	+	0.00212766i
$596$	189.731	−	328.624i	0.0130397	−	0.0225855i
$597$	1917.34	−	3320.93i	0.131443	−	0.227666i
$598$	13016.1			0.890080
$599$	2783.36	−	4820.92i	0.189858	−	0.328844i	−0.755345	−	0.655328i	$-0.772531\pi$
$599$	2783.36	−	4820.92i	0.189858	−	0.328844i	0.945203	+	0.326484i	$0.105864\pi$
$600$	2620.94			0.178333
$601$	−8309.75	−	14392.9i	−0.563996	−	0.976870i	−0.997142	−	0.0755465i	$-0.975930\pi$
$601$	−8309.75	−	14392.9i	−0.563996	−	0.976870i	0.433146	−	0.901324i	$-0.357403\pi$
$602$	−3348.00			−0.226668
$603$	−5961.62			−0.402613
$604$	−2883.55	−	4994.45i	−0.194255	−	0.336459i
$605$	17.1713	−	29.7415i	0.00115390	−	0.00199862i
$606$	−8524.20			−0.571406
$607$	−6216.96	−	10768.1i	−0.415714	−	0.720038i	0.579789	−	0.814767i	$-0.303135\pi$
$607$	−6216.96	−	10768.1i	−0.415714	−	0.720038i	−0.995503	+	0.0947286i	$0.969802\pi$
$608$	−292.740	−	507.041i	−0.0195266	−	0.0338211i
$609$	−359.085	−	621.953i	−0.0238930	−	0.0413839i
$610$	−4.99109	+	8.64482i	−0.000331284	+	0.000573801i
$611$	−8964.89	+	15527.6i	−0.593585	+	1.02812i
$612$	−3000.72	−	5197.40i	−0.198198	−	0.343288i
$613$	6536.56	+	11321.6i	0.430684	+	0.745966i	0.996932	−	0.0782686i	$-0.0249392\pi$
$613$	6536.56	+	11321.6i	0.430684	+	0.745966i	−0.566249	+	0.824234i	$0.691606\pi$
$614$	5929.75	+	10270.6i	0.389748	+	0.675063i
$615$	22.2071			0.00145606
$616$	−4365.41	+	7561.12i	−0.285532	+	0.494556i
$617$	−9127.84	−	15809.9i	−0.595580	−	1.03157i	−0.993465	−	0.114139i	$-0.963589\pi$
$617$	−9127.84	−	15809.9i	−0.595580	−	1.03157i	0.397885	−	0.917435i	$-0.369744\pi$
$618$	−9671.79			−0.629541
$619$	12821.4			0.832530			0.416265	−	0.909243i	$-0.363339\pi$
$619$	12821.4			0.832530			0.416265	+	0.909243i	$0.363339\pi$
$620$	2.47071	+	4.27940i	0.000160042	+	0.000277201i
$621$	−23904.1			−1.54467
$622$	−1582.65	+	2741.22i	−0.102023	+	0.176709i
$623$	4010.59			0.257915
$624$	705.165	−	1221.38i	0.0452391	−	0.0783564i
$625$	−7812.40	+	13531.5i	−0.499994	+	0.866014i
$626$	8393.36	−	14537.7i	0.535888	−	0.928186i
$627$	−1270.80	−	2201.09i	−0.0809422	−	0.140196i
$628$	−8609.02			−0.547034
$629$	1024.05	+	16742.9i	0.0649151	+	1.06134i
$630$	−19.2617			−0.00121810
$631$	−8255.82	−	14299.5i	−0.520854	−	0.902146i	−0.999706	−	0.0242501i	$-0.992280\pi$
$631$	−8255.82	−	14299.5i	−0.520854	−	0.902146i	0.478852	−	0.877896i	$-0.341053\pi$
$632$	1063.43	−	1841.91i	0.0669318	−	0.115929i
$633$	−4759.22	+	8243.21i	−0.298834	+	0.517596i
$634$	−7903.68	+	13689.6i	−0.495103	+	0.857543i
$635$	27.0918			0.00169308
$636$	−2142.02	+	3710.09i	−0.133548	+	0.231312i
$637$	−2724.01			−0.169434
$638$	−705.295	−	1221.61i	−0.0437663	−	0.0758054i
$639$	−13154.3			−0.814359
$640$	2.97397			0.000183682
$641$	−5389.26	−	9334.47i	−0.332080	−	0.575179i	0.650840	−	0.759215i	$-0.274417\pi$
$641$	−5389.26	−	9334.47i	−0.332080	−	0.575179i	−0.982919	+	0.184036i	$0.941084\pi$
$642$	−1614.93	+	2797.13i	−0.0992773	+	0.171953i
$643$	343.719			0.0210808			0.0105404	−	0.999944i	$-0.496645\pi$
$643$	343.719			0.0210808			0.0105404	+	0.999944i	$0.496645\pi$
$644$	−7969.31	−	13803.3i	−0.487632	−	0.844603i
$645$	2.47531	+	4.28736i	0.000151109	+	0.000261728i
$646$	1363.64	+	2361.90i	0.0830524	+	0.143851i
$647$	−8721.70	+	15106.4i	−0.529962	+	0.917921i	0.469427	+	0.882971i	$0.344460\pi$
$647$	−8721.70	+	15106.4i	−0.529962	+	0.917921i	−0.999389	+	0.0349495i	$0.988873\pi$
$648$	879.068	−	1522.59i	0.0532918	−	0.0923041i
$649$	−5289.46	−	9161.62i	−0.319922	−	0.554122i
$650$	4203.87	+	7281.32i	0.253676	+	0.439380i
$651$	−1434.75	−	2485.06i	−0.0863784	−	0.149612i
$652$	14178.6			0.851650
$653$	6610.85	−	11450.3i	0.396175	−	0.686196i	−0.597075	−	0.802185i	$-0.703671\pi$
$653$	6610.85	−	11450.3i	0.396175	−	0.686196i	0.993250	+	0.115989i	$0.0370039\pi$
$654$	1063.72	+	1842.42i	0.0636006	+	0.110159i
$655$	25.8784			0.00154374
$656$	−5834.79			−0.347272
$657$	−1285.04	−	2225.75i	−0.0763076	−	0.132169i
$658$	21955.6			1.30079
$659$	−1619.13	+	2804.42i	−0.0957092	+	0.165773i	−0.909904	−	0.414818i	$-0.863845\pi$
$659$	−1619.13	+	2804.42i	−0.0957092	+	0.165773i	0.814195	+	0.580591i	$0.197179\pi$
$660$	12.9101			0.000761402
$661$	−4260.94	+	7380.16i	−0.250728	+	0.434274i	−0.963726	−	0.266892i	$-0.914003\pi$
$661$	−4260.94	+	7380.16i	−0.250728	+	0.434274i	0.712998	+	0.701166i	$0.247337\pi$
$662$	9890.65	−	17131.1i	0.580681	−	1.00577i
$663$	−3284.80	+	5689.45i	−0.192415	+	0.333273i
$664$	3070.67	+	5318.55i	0.179465	+	0.310843i
$665$	8.75326			0.000510432
$666$	−7556.06	+	5001.26i	−0.439627	+	0.290983i
$667$	2575.11			0.149488
$668$	6437.56	+	11150.2i	0.372869	+	0.645828i
$669$	−1144.07	+	1981.58i	−0.0661168	+	0.114518i
$670$	−6.88072	+	11.9178i	−0.000396754	+	0.000687199i
$671$	5692.77	−	9860.16i	0.327521	−	0.567284i
$672$	−1726.99			−0.0991372
$673$	3008.39	−	5210.68i	0.172310	−	0.298450i	−0.766917	−	0.641746i	$-0.778210\pi$
$673$	3008.39	−	5210.68i	0.172310	−	0.298450i	0.939227	+	0.343296i	$0.111544\pi$
$674$	−5533.94			−0.316260
$675$	−7720.41	−	13372.1i	−0.440235	−	0.762510i
$676$	−4263.79			−0.242592
$677$	−18121.4			−1.02874			−0.514372	−	0.857567i	$-0.671975\pi$
$677$	−18121.4			−1.02874			−0.514372	+	0.857567i	$0.671975\pi$
$678$	6130.43	+	10618.2i	0.347253	+	0.601460i
$679$	−10616.1	+	18387.7i	−0.600015	+	1.03926i
$680$	−13.8534			−0.000781253
$681$	8702.22	+	15072.7i	0.489677	+	0.848145i
$682$	−2818.06	−	4881.02i	−0.158225	−	0.274053i
$683$	9108.52	+	15776.4i	0.510290	+	0.883848i	0.999929	+	0.0119227i	$0.00379520\pi$
$683$	9108.52	+	15776.4i	0.510290	+	0.883848i	−0.489639	+	0.871925i	$0.662871\pi$
$684$	−736.630	+	1275.88i	−0.0411780	+	0.0713223i
$685$	−13.8049	+	23.9107i	−0.000770009	+	0.00133370i
$686$	−5394.96	−	9344.34i	−0.300263	−	0.520071i
$687$	−7864.25	−	13621.3i	−0.436739	−	0.756454i
$688$	−650.375	−	1126.48i	−0.0360397	−	0.0624226i
$689$	−13742.8			−0.759882
$690$	−11.7841	+	20.4106i	−0.000650162	+	0.00112611i
$691$	−10383.2	−	17984.3i	−0.571631	−	0.990095i	−0.996399	−	0.0847920i	$-0.972977\pi$
$691$	−10383.2	−	17984.3i	−0.571631	−	0.990095i	0.424767	−	0.905303i	$-0.360356\pi$
$692$	1814.57			0.0996816
$693$	21969.6			1.20427
$694$	−5968.31	−	10337.4i	−0.326447	−	0.565422i
$695$	20.4949			0.00111859
$696$	139.510	−	241.639i	0.00759787	−	0.0131599i
$697$	27179.7			1.47705
$698$	5304.08	−	9186.93i	0.287625	−	0.498181i
$699$	5668.87	−	9818.77i	0.306747	−	0.531302i
$700$	5147.77	−	8916.20i	0.277954	−	0.481430i
$701$	−4604.29	−	7974.87i	−0.248077	−	0.429681i	0.714915	−	0.699211i	$-0.246465\pi$
$701$	−4604.29	−	7974.87i	−0.248077	−	0.429681i	−0.962992	+	0.269530i	$0.913132\pi$
$702$	−8308.71			−0.446712
$703$	3433.77	−	2272.77i	0.184221	−	0.121933i
$704$	−3392.07			−0.181596
$705$	−16.2327	−	28.1158i	−0.000867173	−	0.00150199i
$706$	−7596.41	+	13157.4i	−0.404950	+	0.701394i
$707$	−16742.3	+	28998.5i	−0.890608	+	1.54258i
$708$	1046.28	−	1812.20i	0.0555388	−	0.0961961i
$709$	−16368.4			−0.867035			−0.433518	−	0.901145i	$-0.642728\pi$
$709$	−16368.4			−0.867035			−0.433518	+	0.901145i	$0.642728\pi$
$710$	−15.1823	+	26.2965i	−0.000802508	+	0.00138999i
$711$	−5351.86			−0.282293
$712$	779.088	+	1349.42i	0.0410078	+	0.0710276i
$713$	10289.1			0.540432
$714$	8044.69			0.421660
$715$	20.7072	+	35.8660i	0.00108309	+	0.00187596i
$716$	5439.11	−	9420.81i	0.283895	−	0.491721i
$717$	−8227.07			−0.428515
$718$	7218.20	+	12502.3i	0.375182	+	0.649834i
$719$	−13435.6	−	23271.2i	−0.696891	−	1.20705i	−0.969539	−	0.244937i	$-0.921233\pi$
$719$	−13435.6	−	23271.2i	−0.696891	−	1.20705i	0.272648	−	0.962114i	$-0.412101\pi$
$720$	−3.74173	−	6.48087i	−0.000193675	−	0.000335455i
$721$	−18996.3	+	32902.5i	−0.981218	+	1.69952i
$722$	−6524.25	+	11300.3i	−0.336298	+	0.582486i
$723$	3909.42	+	6771.31i	0.201096	+	0.348309i
$724$	2532.23	+	4385.95i	0.129986	+	0.225142i
$725$	831.696	+	1440.54i	0.0426047	+	0.0737935i
$726$	−7748.11			−0.396087
$727$	8351.46	−	14465.2i	0.426050	−	0.737941i	−0.570468	−	0.821320i	$-0.693238\pi$
$727$	8351.46	−	14465.2i	0.426050	−	0.737941i	0.996518	+	0.0833794i	$0.0265713\pi$
$728$	−2770.02	−	4797.81i	−0.141022	−	0.244256i
$729$	4317.45			0.219349
$730$	−5.93261			−0.000300789
$731$	3029.58	+	5247.39i	0.153287	+	0.265502i
$732$	2252.11			0.113716
$733$	−2209.14	+	3826.34i	−0.111318	+	0.192809i	−0.916302	−	0.400488i	$-0.868841\pi$
$733$	−2209.14	+	3826.34i	−0.111318	+	0.192809i	0.804984	+	0.593297i	$0.202174\pi$
$734$	25588.4			1.28676
$735$	2.46617	−	4.27154i	0.000123763	−	0.000214365i
$736$	3096.20	−	5362.78i	0.155065	−	0.268580i
$737$	7848.05	−	13593.2i	0.392248	−	0.679393i
$738$	7341.12	+	12715.2i	0.366166	+	0.634217i
$739$	16835.9			0.838052			0.419026	−	0.907974i	$-0.362372\pi$
$739$	16835.9			0.838052			0.419026	+	0.907974i	$0.362372\pi$
$740$	1.27694	+	20.8775i	6.34340e−5	+	0.00103712i
$741$	1612.74			0.0799532
$742$	8414.25	+	14573.9i	0.416303	+	0.721058i
$743$	13662.1	−	23663.5i	0.674584	−	1.16841i	−0.302007	−	0.953306i	$-0.597657\pi$
$743$	13662.1	−	23663.5i	0.674584	−	1.16841i	0.976590	−	0.215107i	$-0.0690101\pi$
$744$	557.424	−	965.486i	0.0274679	−	0.0475759i
$745$	−1.10206	+	1.90882i	−5.41963e−5	+	9.38708e-5i
$746$	25699.0			1.26127
$747$	7726.79	−	13383.2i	0.378459	−	0.655510i
$748$	15800.9			0.772379
$749$	6343.73	+	10987.7i	0.309472	+	0.536022i
$750$	−30.4477			−0.00148239
$751$	−22288.6			−1.08298			−0.541492	−	0.840706i	$-0.682140\pi$
$751$	−22288.6			−1.08298			−0.541492	+	0.840706i	$0.682140\pi$
$752$	4265.05	+	7387.28i	0.206822	+	0.358226i
$753$	−7831.36	+	13564.3i	−0.379005	+	0.656456i
$754$	895.071			0.0432315
$755$	16.7492	+	29.0104i	0.000807371	+	0.00139841i
$756$	5087.14	+	8811.18i	0.244732	+	0.423888i
$757$	10454.4	+	18107.5i	0.501943	+	0.869390i	0.999997	+	0.00224476i	$0.000714529\pi$
$757$	10454.4	+	18107.5i	0.501943	+	0.869390i	−0.498055	+	0.867146i	$0.665952\pi$
$758$	9599.53	−	16626.9i	0.459988	−	0.796722i
$759$	13440.7	−	23280.0i	0.642777	−	1.11332i
$760$	1.70039	+	2.94516i	8.11574e−5	+	0.000140569i
$761$	−18049.6	−	31262.9i	−0.859789	−	1.48920i	−0.872130	−	0.489274i	$-0.837262\pi$
$761$	−18049.6	−	31262.9i	−0.859789	−	1.48920i	0.0123418	−	0.999924i	$-0.496071\pi$
$762$	−3056.13	−	5293.36i	−0.145291	−	0.251651i
$763$	8356.99			0.396518
$764$	−3132.86	+	5426.28i	−0.148355	+	0.256958i
$765$	17.4298	+	30.1893i	0.000823758	+	0.00142679i
$766$	−10678.6			−0.503700
$767$	6712.72			0.316013
$768$	−335.482	−	581.072i	−0.0157626	−	0.0273016i
$769$	14359.7			0.673373			0.336686	−	0.941617i	$-0.390694\pi$
$769$	14359.7			0.673373			0.336686	+	0.941617i	$0.390694\pi$
$770$	25.3566	−	43.9190i	0.00118674	−	0.00205549i
$771$	6044.58			0.282348
$772$	−6337.02	+	10976.0i	−0.295433	+	0.511705i
$773$	−15641.3	+	27091.5i	−0.727786	+	1.26056i	0.230031	+	0.973183i	$0.426117\pi$
$773$	−15641.3	+	27091.5i	−0.727786	+	1.26056i	−0.957817	+	0.287379i	$0.907216\pi$
$774$	−1636.55	+	2834.60i	−0.0760009	+	0.131638i
$775$	3323.11	+	5755.79i	0.154025	+	0.266779i
$776$	−8249.08			−0.381604
$777$	−741.522	−	12123.6i	−0.0342367	−	0.559759i
$778$	3526.22			0.162495
$779$	−3336.09	−	5778.28i	−0.153438	−	0.265762i
$780$	−4.09597	+	7.09443i	−0.000188025	+	0.000325668i
$781$	17316.7	−	29993.4i	0.793393	−	1.37420i
$782$	−14422.8	+	24980.9i	−0.659535	+	1.14235i
$783$	−1643.80			−0.0750250
$784$	−647.974	+	1122.32i	−0.0295178	+	0.0511263i
$785$	50.0058			0.00227361
$786$	−2919.24	−	5056.27i	−0.132476	−	0.229455i
$787$	−2064.18			−0.0934943			−0.0467471	−	0.998907i	$-0.514885\pi$
$787$	−2064.18			−0.0934943			−0.0467471	+	0.998907i	$0.514885\pi$
$788$	13515.3			0.610993
$789$	5097.91	+	8829.85i	0.230026	+	0.398417i
$790$	−6.17696	+	10.6988i	−0.000278185	+	0.000481831i
$791$	48162.9			2.16495
$792$	4267.77	+	7391.99i	0.191475	+	0.331645i
$793$	3612.27	+	6256.64i	0.161760	+	0.280176i
$794$	−12197.5	−	21126.7i	−0.545181	−	0.944281i
$795$	12.4420	−	21.5502i	0.000555059	−	0.000961390i
$796$	2926.17	−	5068.28i	0.130296	−	0.225679i
$797$	−18480.4	−	32009.1i	−0.821344	−	1.42261i	−0.904682	−	0.426087i	$-0.859892\pi$
$797$	−18480.4	−	32009.1i	−0.821344	−	1.42261i	0.0833384	−	0.996521i	$-0.473442\pi$
$798$	−987.423	−	1710.27i	−0.0438025	−	0.0758681i
$799$	−19867.5	−	34411.5i	−0.879675	−	1.52364i
$800$	3999.98			0.176776
$801$	1960.44	−	3395.58i	0.0864778	−	0.149784i
$802$	−9992.66	−	17307.8i	−0.439966	−	0.762044i
$803$	6766.65			0.297372
$804$	3104.75			0.136189
$805$	46.2900	+	80.1766i	0.00202672	+	0.00351038i
$806$	3576.33			0.156291
$807$	−3405.95	+	5899.28i	−0.148569	+	0.257329i
$808$	−13009.3			−0.566418
$809$	−18494.7	+	32033.7i	−0.803756	+	1.39215i	0.113371	+	0.993553i	$0.463835\pi$
$809$	−18494.7	+	32033.7i	−0.803756	+	1.39215i	−0.917128	+	0.398594i	$0.869498\pi$
$810$	−5.10610	+	8.84402i	−0.000221494	+	0.000383638i
$811$	−5043.80	+	8736.11i	−0.218387	+	0.378257i	−0.954315	−	0.298803i	$-0.903413\pi$
$811$	−5043.80	+	8736.11i	−0.218387	+	0.378257i	0.735928	+	0.677060i	$0.236746\pi$
$812$	−548.021	−	949.201i	−0.0236845	−	0.0410227i
$813$	−5102.26			−0.220103
$814$	−1456.46	−	23812.6i	−0.0627135	−	1.02534i
$815$	−82.3567			−0.00353967
$816$	1562.75	+	2706.75i	0.0670429	+	0.116122i
$817$	743.714	−	1288.15i	0.0318473	−	0.0551612i
$818$	6719.95	−	11639.3i	0.287234	−	0.497504i
$819$	−6970.26	+	12072.8i	−0.297388	+	0.515091i
$820$	33.8916			0.00144335
$821$	2862.27	−	4957.59i	0.121673	−	0.210744i	−0.798754	−	0.601657i	$-0.794507\pi$
$821$	2862.27	−	4957.59i	0.121673	−	0.210744i	0.920428	+	0.390913i	$0.127841\pi$
$822$	6229.10			0.264312
$823$	−7415.53	−	12844.1i	−0.314082	−	0.544005i	0.665160	−	0.746701i	$-0.268363\pi$
$823$	−7415.53	−	12844.1i	−0.314082	−	0.544005i	−0.979242	+	0.202695i	$0.935030\pi$
$824$	−14760.7			−0.624046
$825$	17364.1			0.732776
$826$	−4109.97	−	7118.67i	−0.173128	−	0.299867i
$827$	218.570	−	378.574i	0.00919035	−	0.0159182i	−0.861394	−	0.507938i	$-0.830408\pi$
$827$	218.570	−	378.574i	0.00919035	−	0.0159182i	0.870584	+	0.492020i	$0.163741\pi$
$828$	−15582.1			−0.654004
$829$	951.723	+	1648.43i	0.0398730	+	0.0690620i	0.885273	−	0.465071i	$-0.153971\pi$
$829$	951.723	+	1648.43i	0.0398730	+	0.0690620i	−0.845400	+	0.534133i	$0.820638\pi$
$830$	−17.8361	−	30.8930i	−0.000745902	−	0.00129194i
$831$	−9739.84	−	16869.9i	−0.406584	−	0.704224i
$832$	1076.20	−	1864.03i	0.0448442	−	0.0776724i
$833$	3018.40	−	5228.02i	0.125548	−	0.217455i
$834$	−2311.96	−	4004.43i	−0.0959910	−	0.166261i
$835$	−37.3928	−	64.7662i	−0.00154974	−	0.00268422i
$836$	−1939.44	−	3359.21i	−0.0802356	−	0.138972i
$837$	−6567.93			−0.271232
$838$	−1614.16	+	2795.81i	−0.0665398	+	0.115250i
$839$	15688.0	+	27172.3i	0.645541	+	1.11811i	0.984176	+	0.177192i	$0.0567012\pi$
$839$	15688.0	+	27172.3i	0.645541	+	1.11811i	−0.338636	+	0.940918i	$0.609965\pi$
$840$	10.0313			0.000412039
$841$	−24211.9			−0.992739
$842$	11172.7	+	19351.7i	0.457288	+	0.792046i
$843$	6117.60			0.249942
$844$	−7263.34	+	12580.5i	−0.296226	+	0.513078i
$845$	24.7664			0.00100827
$846$	10732.2	−	18588.8i	0.436149	−	0.755432i
$847$	−15218.0	+	26358.4i	−0.617352	+	1.06928i
$848$	−3269.07	+	5662.19i	−0.132382	+	0.229293i
$849$	646.703	+	1120.12i	0.0261423	+	0.0452798i
$850$	−18632.7			−0.751880
$851$	38976.6	+	19433.0i	1.57003	+	0.782789i
$852$	6850.63			0.275468
$853$	−5806.62	−	10057.4i	−0.233077	−	0.403701i	0.725635	−	0.688080i	$-0.241546\pi$
$853$	−5806.62	−	10057.4i	−0.233077	−	0.403701i	−0.958712	+	0.284378i	$0.908213\pi$
$854$	4423.34	−	7661.45i	0.177241	−	0.306990i
$855$	4.27874	−	7.41099i	0.000171146	−	0.000296433i
$856$	−2464.64	+	4268.88i	−0.0984107	+	0.170452i
$857$	−6170.78			−0.245963			−0.122981	−	0.992409i	$-0.539246\pi$
$857$	−6170.78			−0.245963			−0.122981	+	0.992409i	$0.539246\pi$
$858$	4671.81	−	8091.81i	0.185889	−	0.321969i
$859$	−19283.2			−0.765931			−0.382965	−	0.923763i	$-0.625097\pi$
$859$	−19283.2			−0.765931			−0.382965	+	0.923763i	$0.625097\pi$
$860$	3.77772	+	6.54321i	0.000149790	+	0.000259444i
$861$	−19681.0			−0.779007
$862$	−15629.4			−0.617563
$863$	6393.35	+	11073.6i	0.252181	+	0.436790i	0.964126	−	0.265445i	$-0.0855188\pi$
$863$	6393.35	+	11073.6i	0.252181	+	0.436790i	−0.711945	+	0.702235i	$0.752185\pi$
$864$	−1976.43	+	3423.28i	−0.0778237	+	0.134795i
$865$	−10.5400			−0.000414301
$866$	10590.2	+	18342.8i	0.415554	+	0.719761i
$867$	−841.217	−	1457.03i	−0.0329518	−	0.0570742i
$868$	−2189.66	−	3792.61i	−0.0856244	−	0.148306i
$869$	7045.35	−	12202.9i	0.275025	−	0.476358i
$870$	−0.810349	+	1.40357i	−3.15786e−5	+	5.46958e-5i
$871$	4979.88	+	8625.40i	0.193728	+	0.335546i
$872$	1623.41	+	2811.83i	0.0630454	+	0.109198i
$873$	10378.7	+	17976.4i	0.402366	+	0.696918i
$874$	7081.12			0.274053
$875$	−59.8021	+	103.580i	−0.00231049	+	0.00400189i
$876$	669.235	+	1159.15i	0.0258121	+	0.0447078i
$877$	4308.12			0.165878			0.0829390	−	0.996555i	$-0.473569\pi$
$877$	4308.12			0.165878			0.0829390	+	0.996555i	$0.473569\pi$
$878$	−32307.7			−1.24184
$879$	−6704.15	−	11611.9i	−0.257253	−	0.445575i
$880$	19.7029			0.000754756
$881$	−21526.7	+	37285.3i	−0.823215	+	1.42585i	0.0800605	+	0.996790i	$0.474489\pi$
$881$	−21526.7	+	37285.3i	−0.823215	+	1.42585i	−0.903276	+	0.429061i	$0.858845\pi$
$882$	3261.03			0.124495
$883$	8204.28	−	14210.2i	0.312680	−	0.541577i	−0.666262	−	0.745718i	$-0.732107\pi$
$883$	8204.28	−	14210.2i	0.312680	−	0.541577i	0.978942	+	0.204141i	$0.0654401\pi$
$884$	−5013.14	+	8683.02i	−0.190736	+	0.330364i
$885$	−6.07733	+	10.5262i	−0.000230833	+	0.000399815i
$886$	−9027.16	−	15635.5i	−0.342295	−	0.592872i
$887$	36932.0			1.39803			0.699017	−	0.715105i	$-0.253621\pi$
$887$	36932.0			1.39803			0.699017	+	0.715105i	$0.253621\pi$
$888$	3935.12	−	2604.61i	0.148710	−	0.0984289i
$889$	−24010.0			−0.905817
$890$	−4.52536	−	7.83815i	−0.000170439	−	0.000295208i
$891$	5823.94	−	10087.4i	0.218978	−	0.379281i
$892$	−1746.03	+	3024.21i	−0.0655396	+	0.113518i
$893$	−4877.15	+	8447.47i	−0.182763	+	0.316555i
$894$	497.276			0.0186034
$895$	−31.5932	+	54.7211i	−0.00117994	+	0.00204371i
$896$	−2635.67			−0.0982719
$897$	8528.65	+	14772.1i	0.317462	+	0.549860i
$898$	16475.5			0.612242
$899$	707.542			0.0262490
$900$	−5032.63	−	8716.77i	−0.186394	−	0.322843i
$901$	15228.0	−	26375.7i	0.563061	−	0.975250i
$902$	−38656.3			−1.42695
$903$	−2193.74	−	3799.66i	−0.0808449	−	0.140028i
$904$	9356.03	+	16205.1i	0.344222	+	0.596210i
$905$	−14.7085	−	25.4759i	−0.000540252	−	0.000935744i
$906$	3778.82	−	6545.12i	0.138568	−	0.240008i
$907$	−11721.3	+	20301.9i	−0.429106	+	0.743233i	−0.996794	−	0.0800106i	$-0.974505\pi$
$907$	−11721.3	+	20301.9i	−0.429106	+	0.743233i	0.567688	+	0.823244i	$0.307838\pi$
$908$	13281.0	+	23003.4i	0.485403	+	0.840742i
$909$	16367.8	+	28349.9i	0.597235	+	1.03444i
$910$	16.0897	+	27.8682i	0.000586120	+	0.00101519i
$911$	11451.5			0.416472			0.208236	−	0.978079i	$-0.433228\pi$
$911$	11451.5			0.416472			0.208236	+	0.978079i	$0.433228\pi$
$912$	383.629	−	664.466i	0.0139290	−	0.0241257i
$913$	20343.6	+	35236.1i	0.737430	+	1.27727i
$914$	−34712.6			−1.25623
$915$	−13.0814			−0.000472632
$916$	−12002.1	−	20788.3i	−0.432927	−	0.749851i
$917$	−22934.6			−0.825919
$918$	9206.64	−	15946.4i	0.331007	−	0.573321i
$919$	−30982.2			−1.11209			−0.556043	−	0.831153i	$-0.687681\pi$
$919$	−30982.2			−1.11209			−0.556043	+	0.831153i	$0.687681\pi$
$920$	−17.9844	+	31.1499i	−0.000644487	+	0.00111628i
$921$	−7770.80	+	13459.4i	−0.278020	+	0.481545i
$922$	−13931.8	+	24130.6i	−0.497635	+	0.861929i
$923$	10988.1	+	19031.9i	0.391850	+	0.678703i
$924$	−11441.6			−0.407359
$925$	1717.48	+	28080.2i	0.0610490	+	0.998130i
$926$	−19030.7			−0.675366
$927$	18571.4	+	32166.6i	0.657998	+	1.13969i
$928$	212.915	−	368.780i	0.00753155	−	0.0130450i
$929$	−14055.5	+	24344.9i	−0.496391	+	0.859775i	−0.999991	−	0.00416220i	$-0.998675\pi$
$929$	−14055.5	+	24344.9i	−0.496391	+	0.859775i	0.503600	+	0.863937i	$0.332008\pi$
$930$	−3.23781	+	5.60806i	−0.000114164	+	0.000197737i
$931$	−1481.94			−0.0521682
$932$	8651.61	−	14985.0i	0.304070	−	0.526664i
$933$	−4148.04			−0.145553
$934$	5347.94	+	9262.90i	0.187355	+	0.324509i
$935$	−91.7803			−0.00321020
$936$	−5416.11			−0.189136
$937$	−17719.6	−	30691.3i	−0.617795	−	1.07005i	−0.989887	−	0.141857i	$-0.954693\pi$
$937$	−17719.6	−	30691.3i	−0.617795	−	1.07005i	0.372092	−	0.928196i	$-0.378641\pi$
$938$	6098.02	−	10562.1i	0.212268	−	0.367659i
$939$	21998.6			0.764534
$940$	−24.7737	−	42.9092i	−0.000859604	−	0.00148888i
$941$	−8866.86	−	15357.9i	−0.307175	−	0.532042i	0.670568	−	0.741848i	$-0.266050\pi$
$941$	−8866.86	−	15357.9i	−0.307175	−	0.532042i	−0.977743	+	0.209805i	$0.932717\pi$
$942$	−5640.96	−	9770.43i	−0.195109	−	0.337938i
$943$	35284.6	−	61114.7i	1.21848	−	2.11046i
$944$	1596.79	−	2765.72i	0.0550540	−	0.0953564i
$945$	−29.5488	−	51.1800i	−0.00101717	−	0.00176179i
$946$	−4308.82	−	7463.09i	−0.148089	−	0.256497i
$947$	−4516.97	−	7823.62i	−0.154997	−	0.268462i	0.778061	−	0.628189i	$-0.216203\pi$
$947$	−4516.97	−	7823.62i	−0.154997	−	0.268462i	−0.933058	+	0.359726i	$0.882870\pi$
$948$	2787.20			0.0954894
$949$	−2146.84	+	3718.44i	−0.0734347	+	0.127193i
$950$	2287.02	+	3961.24i	0.0781061	+	0.135284i
$951$	−20715.2			−0.706347
$952$	12277.5			0.417979
$953$	4371.23	+	7571.19i	0.148581	+	0.257350i	0.930703	−	0.365775i	$-0.119196\pi$
$953$	4371.23	+	7571.19i	0.148581	+	0.257350i	−0.782122	+	0.623125i	$0.785863\pi$
$954$	16452.1			0.558339
$955$	18.1973	−	31.5187i	0.000616599	−	0.00106798i
$956$	−12555.8			−0.424775
$957$	924.273	−	1600.89i	0.0312199	−	0.0540745i
$958$	−7558.55	+	13091.8i	−0.254912	+	0.441521i
$959$	12234.5	−	21190.8i	0.411964	−	0.713542i
$960$	1.94866	+	3.37518i	6.55132e−5	+	0.000113472i
$961$	−26964.0			−0.905104
$962$	13547.7	+	6754.61i	0.454049	+	0.226380i
$963$	12403.7			0.415059
$964$	5966.40	+	10334.1i	0.199341	+	0.345269i
$965$	36.8088	−	63.7547i	0.00122789	−	0.00212677i
$966$	10443.6	−	18088.8i	0.347844	−	0.602484i
$967$	17779.8	−	30795.5i	0.591272	−	1.02411i	−0.402790	−	0.915292i	$-0.631959\pi$
$967$	17779.8	−	30795.5i	0.591272	−	1.02411i	0.994061	−	0.108820i	$-0.0347072\pi$
$968$	−11824.9			−0.392630
$969$	−1787.03	+	3095.22i	−0.0592441	+	0.102614i
$970$	47.9150			0.00158604
$971$	4762.43	+	8248.78i	0.157398	+	0.272622i	0.933930	−	0.357457i	$-0.116356\pi$
$971$	4762.43	+	8248.78i	0.157398	+	0.272622i	−0.776531	+	0.630079i	$0.783023\pi$
$972$	15644.9			0.516267
$973$	−18163.6			−0.598456
$974$	367.133	+	635.893i	0.0120777	+	0.0209192i
$975$	−5509.08	+	9542.00i	−0.180956	+	0.313424i
$976$	3437.08			0.112723
$977$	−20404.9	−	35342.4i	−0.668180	−	1.15732i	−0.978413	−	0.206661i	$-0.933740\pi$
$977$	−20404.9	−	35342.4i	−0.668180	−	1.15732i	0.310233	−	0.950661i	$-0.399593\pi$
$978$	9290.35	+	16091.4i	0.303755	+	0.526120i
$979$	5161.56	+	8940.08i	0.168503	+	0.291855i
$980$	3.76378	−	6.51905i	0.000122683	−	0.000212493i
$981$	4085.03	−	7075.48i	0.132951	−	0.230278i
$982$	−7768.16	−	13454.8i	−0.252436	−	0.437231i
$983$	−22848.6	−	39574.9i	−0.741360	−	1.28407i	−0.951876	−	0.306483i	$-0.900848\pi$
$983$	−22848.6	−	39574.9i	−0.741360	−	1.28407i	0.210516	−	0.977590i	$-0.432486\pi$
$984$	−3823.18	−	6621.94i	−0.123860	−	0.214532i
$985$	−78.5040			−0.00253944
$986$	−991.802	+	1717.85i	−0.0320339	+	0.0554843i
$987$	14386.1	+	24917.5i	0.463947	+	0.803581i
$988$	2461.29			0.0792553
$989$	15732.0			0.505812
$990$	−24.7895	−	42.9366i	−0.000795819	−	0.00137840i
$991$	−1575.66			−0.0505070			−0.0252535	−	0.999681i	$-0.508039\pi$
$991$	−1575.66			−0.0505070			−0.0252535	+	0.999681i	$0.508039\pi$
$992$	850.719	−	1473.49i	0.0272282	−	0.0471606i
$993$	25922.9			0.828438
$994$	13455.3	−	23305.2i	0.429351	−	0.743658i
$995$	−16.9968	+	29.4393i	−0.000541541	+	0.000937977i
$996$	−4024.04	+	6969.84i	−0.128019	+	0.221735i
$997$	16897.3	+	29267.0i	0.536753	+	0.929683i	0.999076	+	0.0429719i	$0.0136826\pi$
$997$	16897.3	+	29267.0i	0.536753	+	0.929683i	−0.462323	+	0.886711i	$0.652984\pi$
$998$	15412.0			0.488835
$999$	−24880.3	−	12404.9i	−0.787967	−	0.392865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	74.4.c.a.63.2	yes	8
3.2	odd	2		666.4.f.a.433.2		8
37.10	even	3	inner	74.4.c.a.47.2	✓	8
111.47	odd	6		666.4.f.a.343.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
74.4.c.a.47.2	✓	8	37.10	even	3	inner
74.4.c.a.63.2	yes	8	1.1	even	1	trivial
666.4.f.a.343.2		8	111.47	odd	6
666.4.f.a.433.2		8	3.2	odd	2

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	74.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.31048 + 2.26981i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(0.0116171 - 0.0201213i) q^{5} -5.24191 q^{6} +(-10.2956 + 17.8325i) q^{7} -8.00000 q^{8} +(10.0653 + 17.4336i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 1.73205i) q^{2} +(-1.31048 + 2.26981i) q^{3} +(-2.00000 + 3.46410i) q^{4} +(0.0116171 - 0.0201213i) q^{5} -5.24191 q^{6} +(-10.2956 + 17.8325i) q^{7} -8.00000 q^{8} +(10.0653 + 17.4336i) q^{9} +0.0464682 q^{10} -53.0010 q^{11} +(-5.24191 - 9.07925i) q^{12} +(16.8156 - 29.1254i) q^{13} -41.1824 q^{14} +(0.0304478 + 0.0527371i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(37.2657 + 64.5460i) q^{17} +(-20.1306 + 34.8672i) q^{18} +(9.14813 - 15.8450i) q^{19} +(0.0464682 + 0.0804854i) q^{20} +(-26.9843 - 46.7381i) q^{21} +(-53.0010 - 91.8005i) q^{22} +193.513 q^{23} +(10.4838 - 18.1585i) q^{24} +(62.4997 + 108.253i) q^{25} +67.2622 q^{26} -123.527 q^{27} +(-41.1824 - 71.3299i) q^{28} +13.3072 q^{29} +(-0.0608956 + 0.105474i) q^{30} +53.1699 q^{31} +(16.0000 - 27.7128i) q^{32} +(69.4566 - 120.302i) q^{33} +(-74.5313 + 129.092i) q^{34} +(0.239209 + 0.414322i) q^{35} -80.5224 q^{36} +(201.416 + 100.422i) q^{37} +36.5925 q^{38} +(44.0728 + 76.3363i) q^{39} +(-0.0929365 + 0.160971i) q^{40} +(182.337 - 315.817i) q^{41} +(53.9685 - 93.4763i) q^{42} +81.2969 q^{43} +(106.002 - 183.601i) q^{44} +0.467717 q^{45} +(193.513 + 335.174i) q^{46} -533.131 q^{47} +41.9353 q^{48} +(-40.4984 - 70.1452i) q^{49} +(-124.999 + 216.505i) q^{50} -195.343 q^{51} +(67.2622 + 116.502i) q^{52} +(-204.317 - 353.887i) q^{53} +(-123.527 - 213.955i) q^{54} +(-0.615716 + 1.06645i) q^{55} +(82.3647 - 142.660i) q^{56} +(23.9768 + 41.5291i) q^{57} +(13.3072 + 23.0487i) q^{58} +(99.7992 + 172.857i) q^{59} -0.243582 q^{60} +(-107.409 + 186.037i) q^{61} +(53.1699 + 92.0930i) q^{62} -414.513 q^{63} +64.0000 q^{64} +(-0.390695 - 0.676703i) q^{65} +277.827 q^{66} +(-148.074 + 256.471i) q^{67} -298.125 q^{68} +(-253.594 + 439.238i) q^{69} +(-0.478418 + 0.828644i) q^{70} +(-326.724 + 565.902i) q^{71} +(-80.5224 - 139.469i) q^{72} -127.670 q^{73} +(27.4798 + 449.285i) q^{74} -327.618 q^{75} +(36.5925 + 63.3801i) q^{76} +(545.677 - 945.140i) q^{77} +(-88.1456 + 152.673i) q^{78} +(-132.929 + 230.239i) q^{79} -0.371746 q^{80} +(-109.884 + 190.324i) q^{81} +729.349 q^{82} +(-383.833 - 664.819i) q^{83} +215.874 q^{84} +1.73167 q^{85} +(81.2969 + 140.810i) q^{86} +(-17.4388 + 30.2048i) q^{87} +424.008 q^{88} +(-97.3860 - 168.678i) q^{89} +(0.467717 + 0.810109i) q^{90} +(346.252 + 599.726i) q^{91} +(-387.025 + 670.348i) q^{92} +(-69.6780 + 120.686i) q^{93} +(-533.131 - 923.410i) q^{94} +(-0.212549 - 0.368145i) q^{95} +(41.9353 + 72.6340i) q^{96} +1031.14 q^{97} +(80.9968 - 140.290i) q^{98} +(-533.471 - 923.999i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9}+O(q^{10}) \) 8 * q + 8 * q^2 - 5 * q^3 - 16 * q^4 - 10 * q^5 - 20 * q^6 + 3 * q^7 - 64 * q^8 + 7 * q^9	\( 8 q + 8 q^{2} - 5 q^{3} - 16 q^{4} - 10 q^{5} - 20 q^{6} + 3 q^{7} - 64 q^{8} + 7 q^{9} - 40 q^{10} + 64 q^{11} - 20 q^{12} - 61 q^{13} + 12 q^{14} - 43 q^{15} - 64 q^{16} + 12 q^{17} - 14 q^{18} - 71 q^{19} - 40 q^{20} + 67 q^{21} + 64 q^{22} - 52 q^{23} + 40 q^{24} + 48 q^{25} - 244 q^{26} + 658 q^{27} + 12 q^{28} + 322 q^{29} + 86 q^{30} - 112 q^{31} + 128 q^{32} + 280 q^{33} - 24 q^{34} - 359 q^{35} - 56 q^{36} + 557 q^{37} - 284 q^{38} - 389 q^{39} + 80 q^{40} + 92 q^{41} - 134 q^{42} + 532 q^{43} - 128 q^{44} + 330 q^{45} - 52 q^{46} + 280 q^{47} + 160 q^{48} + 87 q^{49} - 96 q^{50} - 1306 q^{51} - 244 q^{52} + 159 q^{53} + 658 q^{54} - 872 q^{55} - 24 q^{56} - 469 q^{57} + 322 q^{58} + 263 q^{59} + 344 q^{60} - 206 q^{61} - 112 q^{62} - 2328 q^{63} + 512 q^{64} - 731 q^{65} + 1120 q^{66} + 245 q^{67} - 96 q^{68} - 360 q^{69} + 718 q^{70} - 957 q^{71} - 56 q^{72} - 272 q^{73} - 178 q^{74} - 3232 q^{75} - 284 q^{76} + 744 q^{77} + 778 q^{78} + 173 q^{79} + 320 q^{80} - 528 q^{81} + 368 q^{82} + 1217 q^{83} - 536 q^{84} + 2988 q^{85} + 532 q^{86} - 2336 q^{87} - 512 q^{88} - 2136 q^{89} + 330 q^{90} + 1575 q^{91} + 104 q^{92} + 2608 q^{93} + 280 q^{94} + 891 q^{95} + 160 q^{96} + 5262 q^{97} - 174 q^{98} - 176 q^{99}+O(q^{100}) \) 8 * q + 8 * q^2 - 5 * q^3 - 16 * q^4 - 10 * q^5 - 20 * q^6 + 3 * q^7 - 64 * q^8 + 7 * q^9 - 40 * q^10 + 64 * q^11 - 20 * q^12 - 61 * q^13 + 12 * q^14 - 43 * q^15 - 64 * q^16 + 12 * q^17 - 14 * q^18 - 71 * q^19 - 40 * q^20 + 67 * q^21 + 64 * q^22 - 52 * q^23 + 40 * q^24 + 48 * q^25 - 244 * q^26 + 658 * q^27 + 12 * q^28 + 322 * q^29 + 86 * q^30 - 112 * q^31 + 128 * q^32 + 280 * q^33 - 24 * q^34 - 359 * q^35 - 56 * q^36 + 557 * q^37 - 284 * q^38 - 389 * q^39 + 80 * q^40 + 92 * q^41 - 134 * q^42 + 532 * q^43 - 128 * q^44 + 330 * q^45 - 52 * q^46 + 280 * q^47 + 160 * q^48 + 87 * q^49 - 96 * q^50 - 1306 * q^51 - 244 * q^52 + 159 * q^53 + 658 * q^54 - 872 * q^55 - 24 * q^56 - 469 * q^57 + 322 * q^58 + 263 * q^59 + 344 * q^60 - 206 * q^61 - 112 * q^62 - 2328 * q^63 + 512 * q^64 - 731 * q^65 + 1120 * q^66 + 245 * q^67 - 96 * q^68 - 360 * q^69 + 718 * q^70 - 957 * q^71 - 56 * q^72 - 272 * q^73 - 178 * q^74 - 3232 * q^75 - 284 * q^76 + 744 * q^77 + 778 * q^78 + 173 * q^79 + 320 * q^80 - 528 * q^81 + 368 * q^82 + 1217 * q^83 - 536 * q^84 + 2988 * q^85 + 532 * q^86 - 2336 * q^87 - 512 * q^88 - 2136 * q^89 + 330 * q^90 + 1575 * q^91 + 104 * q^92 + 2608 * q^93 + 280 * q^94 + 891 * q^95 + 160 * q^96 + 5262 * q^97 - 174 * q^98 - 176 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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