LMFDB - Embedded newform 19.4.c.b.11.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [19,4,Mod(7,19)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(19, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([2]))

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("19.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	19.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:	$1.12103629011$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 19x^{2} + 18x + 324 $ x^4 - x^3 + 19x^2 + 18x + 324
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.2
Root			$-1.88600 + 3.26665i$ of defining polynomial
Character	$\chi$	$=$	19.11
Dual form			19.4.c.b.7.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.88600 - 3.26665i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-3.11400 - 5.39360i) q^{4} +(-2.61400 + 4.52758i) q^{5} +(1.88600 + 3.26665i) q^{6} -7.08801 q^{7} +6.68399 q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})$	\(q+(1.88600 - 3.26665i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-3.11400 - 5.39360i) q^{4} +(-2.61400 + 4.52758i) q^{5} +(1.88600 + 3.26665i) q^{6} -7.08801 q^{7} +6.68399 q^{8} +(13.0000 + 22.5167i) q^{9} +(9.86001 + 17.0780i) q^{10} -29.3160 q^{11} +6.22800 q^{12} +(-35.9300 - 62.2326i) q^{13} +(-13.3680 + 23.1540i) q^{14} +(-2.61400 - 4.52758i) q^{15} +(37.5180 - 64.9831i) q^{16} +(-26.1060 + 45.2170i) q^{17} +98.0720 q^{18} +(54.8340 - 62.0663i) q^{19} +32.5600 q^{20} +(3.54400 - 6.13839i) q^{21} +(-55.2900 + 95.7651i) q^{22} +(-36.5620 - 63.3273i) q^{23} +(-3.34200 + 5.78851i) q^{24} +(48.8340 + 84.5830i) q^{25} -271.056 q^{26} -53.0000 q^{27} +(22.0720 + 38.2299i) q^{28} +(108.826 + 188.492i) q^{29} -19.7200 q^{30} -14.6320 q^{31} +(-114.782 - 198.808i) q^{32} +(14.6580 - 25.3884i) q^{33} +(98.4720 + 170.558i) q^{34} +(18.5280 - 32.0915i) q^{35} +(80.9640 - 140.234i) q^{36} +377.792 q^{37} +(-99.3320 - 296.181i) q^{38} +71.8600 q^{39} +(-17.4720 + 30.2623i) q^{40} +(-35.2720 + 61.0929i) q^{41} +(-13.3680 - 23.1540i) q^{42} +(32.8940 - 56.9740i) q^{43} +(91.2900 + 158.119i) q^{44} -135.928 q^{45} -275.824 q^{46} +(-186.054 - 322.255i) q^{47} +(37.5180 + 64.9831i) q^{48} -292.760 q^{49} +368.404 q^{50} +(-26.1060 - 45.2170i) q^{51} +(-223.772 + 387.584i) q^{52} +(146.214 + 253.250i) q^{53} +(-99.9580 + 173.132i) q^{54} +(76.6320 - 132.731i) q^{55} -47.3762 q^{56} +(26.3340 + 78.5208i) q^{57} +820.984 q^{58} +(-268.872 + 465.700i) q^{59} +(-16.2800 + 28.1978i) q^{60} +(-147.702 - 255.827i) q^{61} +(-27.5960 + 47.7977i) q^{62} +(-92.1441 - 159.598i) q^{63} -265.628 q^{64} +375.684 q^{65} +(-55.2900 - 95.7651i) q^{66} +(-485.032 - 840.100i) q^{67} +325.176 q^{68} +73.1240 q^{69} +(-69.8878 - 121.049i) q^{70} +(-397.158 + 687.898i) q^{71} +(86.8919 + 150.501i) q^{72} +(-129.468 + 224.245i) q^{73} +(712.516 - 1234.11i) q^{74} -97.6680 q^{75} +(-505.514 - 102.478i) q^{76} +207.792 q^{77} +(135.528 - 234.741i) q^{78} +(148.966 - 258.017i) q^{79} +(196.144 + 339.732i) q^{80} +(-324.500 + 562.050i) q^{81} +(133.046 + 230.443i) q^{82} +1417.29 q^{83} -44.1441 q^{84} +(-136.482 - 236.394i) q^{85} +(-124.076 - 214.906i) q^{86} -217.652 q^{87} -195.948 q^{88} +(18.4941 + 32.0327i) q^{89} +(-256.360 + 444.029i) q^{90} +(254.672 + 441.105i) q^{91} +(-227.708 + 394.402i) q^{92} +(7.31601 - 12.6717i) q^{93} -1403.59 q^{94} +(137.674 + 410.507i) q^{95} +229.564 q^{96} +(-504.264 + 873.411i) q^{97} +(-552.146 + 956.345i) q^{98} +(-381.108 - 660.099i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - q^{2} - 2 q^{3} - 21 q^{4} - 19 q^{5} - q^{6} + 40 q^{7} + 78 q^{8} + 52 q^{9}+O(q^{10}) $ 4 * q - q^2 - 2 * q^3 - 21 * q^4 - 19 * q^5 - q^6 + 40 * q^7 + 78 * q^8 + 52 * q^9	\( 4 q - q^{2} - 2 q^{3} - 21 q^{4} - 19 q^{5} - q^{6} + 40 q^{7} + 78 q^{8} + 52 q^{9} - 46 q^{10} - 66 q^{11} + 42 q^{12} - 101 q^{13} - 156 q^{14} - 19 q^{15} + 39 q^{16} + 75 q^{17} - 52 q^{18} + 57 q^{19} + 472 q^{20} - 20 q^{21} - 93 q^{22} - q^{23} - 39 q^{24} + 33 q^{25} - 264 q^{26} - 212 q^{27} - 356 q^{28} + 85 q^{29} + 92 q^{30} + 44 q^{31} - 143 q^{32} + 33 q^{33} + 804 q^{34} - 336 q^{35} + 546 q^{36} + 896 q^{37} - 722 q^{38} + 202 q^{39} - 480 q^{40} - 124 q^{41} - 156 q^{42} + 311 q^{43} + 237 q^{44} - 988 q^{45} - 1240 q^{46} - 411 q^{47} + 39 q^{48} + 196 q^{49} + 1354 q^{50} + 75 q^{51} - 878 q^{52} - 261 q^{53} + 53 q^{54} + 204 q^{55} + 1656 q^{56} - 57 q^{57} + 2908 q^{58} - 204 q^{59} - 236 q^{60} - 531 q^{61} - 230 q^{62} + 520 q^{63} - 1934 q^{64} + 1554 q^{65} - 93 q^{66} - 556 q^{67} - 3108 q^{68} + 2 q^{69} - 1920 q^{70} - 1563 q^{71} + 1014 q^{72} + 234 q^{73} + 1090 q^{74} - 66 q^{75} + 1387 q^{76} + 216 q^{77} + 132 q^{78} + 331 q^{79} - 104 q^{80} - 1298 q^{81} + 11 q^{82} + 2918 q^{83} + 712 q^{84} + 1479 q^{85} + 922 q^{86} - 170 q^{87} - 630 q^{88} - 601 q^{89} + 1196 q^{90} - 280 q^{91} + 610 q^{92} - 22 q^{93} - 2436 q^{94} - 1235 q^{95} + 286 q^{96} + 324 q^{97} - 2969 q^{98} - 858 q^{99}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 - 21 * q^4 - 19 * q^5 - q^6 + 40 * q^7 + 78 * q^8 + 52 * q^9 - 46 * q^10 - 66 * q^11 + 42 * q^12 - 101 * q^13 - 156 * q^14 - 19 * q^15 + 39 * q^16 + 75 * q^17 - 52 * q^18 + 57 * q^19 + 472 * q^20 - 20 * q^21 - 93 * q^22 - q^23 - 39 * q^24 + 33 * q^25 - 264 * q^26 - 212 * q^27 - 356 * q^28 + 85 * q^29 + 92 * q^30 + 44 * q^31 - 143 * q^32 + 33 * q^33 + 804 * q^34 - 336 * q^35 + 546 * q^36 + 896 * q^37 - 722 * q^38 + 202 * q^39 - 480 * q^40 - 124 * q^41 - 156 * q^42 + 311 * q^43 + 237 * q^44 - 988 * q^45 - 1240 * q^46 - 411 * q^47 + 39 * q^48 + 196 * q^49 + 1354 * q^50 + 75 * q^51 - 878 * q^52 - 261 * q^53 + 53 * q^54 + 204 * q^55 + 1656 * q^56 - 57 * q^57 + 2908 * q^58 - 204 * q^59 - 236 * q^60 - 531 * q^61 - 230 * q^62 + 520 * q^63 - 1934 * q^64 + 1554 * q^65 - 93 * q^66 - 556 * q^67 - 3108 * q^68 + 2 * q^69 - 1920 * q^70 - 1563 * q^71 + 1014 * q^72 + 234 * q^73 + 1090 * q^74 - 66 * q^75 + 1387 * q^76 + 216 * q^77 + 132 * q^78 + 331 * q^79 - 104 * q^80 - 1298 * q^81 + 11 * q^82 + 2918 * q^83 + 712 * q^84 + 1479 * q^85 + 922 * q^86 - 170 * q^87 - 630 * q^88 - 601 * q^89 + 1196 * q^90 - 280 * q^91 + 610 * q^92 - 22 * q^93 - 2436 * q^94 - 1235 * q^95 + 286 * q^96 + 324 * q^97 - 2969 * q^98 - 858 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/19\mathbb{Z}\right)^\times$.

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

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 $

$2$	1.88600	−	3.26665i	0.666802	−	1.15493i	−0.311991	−	0.950085i	$-0.600996\pi$
$2$	1.88600	−	3.26665i	0.666802	−	1.15493i	0.978793	−	0.204850i	$-0.0656707\pi$
$3$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i	−0.910119	−	0.414346i	$-0.864010\pi$
$3$	−0.500000	+	0.866025i	−0.0962250	+	0.166667i	0.813894	+	0.581013i	$0.197344\pi$
$4$	−3.11400	−	5.39360i	−0.389250	−	0.674201i
$5$	−2.61400	+	4.52758i	−0.233803	+	0.404959i	−0.958924	−	0.283662i	$-0.908450\pi$
$5$	−2.61400	+	4.52758i	−0.233803	+	0.404959i	0.725121	+	0.688621i	$0.241784\pi$
$6$	1.88600	+	3.26665i	0.128326	+	0.222267i
$7$	−7.08801			−0.382716			−0.191358	−	0.981520i	$-0.561289\pi$
$7$	−7.08801			−0.382716			−0.191358	+	0.981520i	$0.561289\pi$
$8$	6.68399			0.295394
$9$	13.0000	+	22.5167i	0.481481	+	0.833950i
$10$	9.86001	+	17.0780i	0.311801	+	0.540055i
$11$	−29.3160			−0.803555			−0.401778	−	0.915737i	$-0.631608\pi$
$11$	−29.3160			−0.803555			−0.401778	+	0.915737i	$0.631608\pi$
$12$	6.22800			0.149822
$13$	−35.9300	−	62.2326i	−0.766553	−	1.32771i	−0.939422	−	0.342764i	$-0.888637\pi$
$13$	−35.9300	−	62.2326i	−0.766553	−	1.32771i	0.172868	−	0.984945i	$-0.444696\pi$
$14$	−13.3680	+	23.1540i	−0.255196	+	0.442013i
$15$	−2.61400	−	4.52758i	−0.0449954	−	0.0779344i
$16$	37.5180	−	64.9831i	0.586219	−	1.01536i
$17$	−26.1060	+	45.2170i	−0.372449	+	0.645101i	−0.989942	−	0.141476i	$-0.954815\pi$
$17$	−26.1060	+	45.2170i	−0.372449	+	0.645101i	0.617492	+	0.786577i	$0.288149\pi$
$18$	98.0720			1.28421
$19$	54.8340	−	62.0663i	0.662094	−	0.749421i
$19$	54.8340	−	62.0663i	0.662094	−	0.749421i
$20$	32.5600			0.364031
$21$	3.54400	−	6.13839i	0.0368269	−	0.0637861i
$22$	−55.2900	+	95.7651i	−0.535812	+	0.928054i
$23$	−36.5620	−	63.3273i	−0.331466	−	0.574115i	0.651334	−	0.758791i	$-0.274210\pi$
$23$	−36.5620	−	63.3273i	−0.331466	−	0.574115i	−0.982799	+	0.184676i	$0.940876\pi$
$24$	−3.34200	+	5.78851i	−0.0284243	+	0.0492323i
$25$	48.8340	+	84.5830i	0.390672	+	0.676664i
$26$	−271.056			−2.04456
$27$	−53.0000			−0.377772
$28$	22.0720	+	38.2299i	0.148972	+	0.258028i
$29$	108.826	+	188.492i	0.696844	+	1.20697i	0.969555	+	0.244874i	$0.0787465\pi$
$29$	108.826	+	188.492i	0.696844	+	1.20697i	−0.272711	+	0.962096i	$0.587920\pi$
$30$	−19.7200			−0.120012
$31$	−14.6320			−0.0847738			−0.0423869	−	0.999101i	$-0.513496\pi$
$31$	−14.6320			−0.0847738			−0.0423869	+	0.999101i	$0.513496\pi$
$32$	−114.782	−	198.808i	−0.634087	−	1.09827i
$33$	14.6580	−	25.3884i	0.0773221	−	0.133926i
$34$	98.4720	+	170.558i	0.496700	+	0.860310i
$35$	18.5280	−	32.0915i	0.0894803	−	0.154984i
$36$	80.9640	−	140.234i	0.374833	−	0.649230i
$37$	377.792			1.67861			0.839306	−	0.543660i	$-0.182962\pi$
$37$	377.792			1.67861			0.839306	+	0.543660i	$0.182962\pi$
$38$	−99.3320	−	296.181i	−0.424047	−	1.26439i
$39$	71.8600			0.295046
$40$	−17.4720	+	30.2623i	−0.0690640	+	0.119622i
$41$	−35.2720	+	61.0929i	−0.134355	+	0.232710i	−0.925351	−	0.379112i	$-0.876230\pi$
$41$	−35.2720	+	61.0929i	−0.134355	+	0.232710i	0.790996	+	0.611822i	$0.209563\pi$
$42$	−13.3680	−	23.1540i	−0.0491125	−	0.0850654i
$43$	32.8940	−	56.9740i	0.116658	−	0.202057i	−0.801783	−	0.597615i	$-0.796115\pi$
$43$	32.8940	−	56.9740i	0.116658	−	0.202057i	0.918441	+	0.395557i	$0.129449\pi$
$44$	91.2900	+	158.119i	0.312784	+	0.541757i
$45$	−135.928			−0.450288
$46$	−275.824			−0.884088
$47$	−186.054	−	322.255i	−0.577421	−	1.00012i	−0.995774	−	0.0918375i	$-0.970726\pi$
$47$	−186.054	−	322.255i	−0.577421	−	1.00012i	0.418353	−	0.908284i	$-0.362607\pi$
$48$	37.5180	+	64.9831i	0.112818	+	0.195406i
$49$	−292.760			−0.853528
$50$	368.404			1.04200
$51$	−26.1060	−	45.2170i	−0.0716779	−	0.124150i
$52$	−223.772	+	387.584i	−0.596761	+	1.03362i
$53$	146.214	+	253.250i	0.378944	+	0.656351i	0.990909	−	0.134534i	$-0.0429538\pi$
$53$	146.214	+	253.250i	0.378944	+	0.656351i	−0.611965	+	0.790885i	$0.709621\pi$
$54$	−99.9580	+	173.132i	−0.251899	+	0.436303i
$55$	76.6320	−	132.731i	0.187874	−	0.325407i
$56$	−47.3762			−0.113052
$57$	26.3340	+	78.5208i	0.0611934	+	0.182462i
$58$	820.984			1.85863
$59$	−268.872	+	465.700i	−0.593291	+	1.02761i	0.400495	+	0.916299i	$0.368838\pi$
$59$	−268.872	+	465.700i	−0.593291	+	1.02761i	−0.993786	+	0.111311i	$0.964495\pi$
$60$	−16.2800	+	28.1978i	−0.0350289	+	0.0606719i
$61$	−147.702	−	255.827i	−0.310021	−	0.536973i	0.668345	−	0.743851i	$-0.267003\pi$
$61$	−147.702	−	255.827i	−0.310021	−	0.536973i	−0.978367	+	0.206878i	$0.933670\pi$
$62$	−27.5960	+	47.7977i	−0.0565273	+	0.0979082i
$63$	−92.1441	−	159.598i	−0.184271	−	0.319167i
$64$	−265.628			−0.518805
$65$	375.684			0.716890
$66$	−55.2900	−	95.7651i	−0.103117	−	0.178604i
$67$	−485.032	−	840.100i	−0.884420	−	1.53186i	−0.846378	−	0.532583i	$-0.821221\pi$
$67$	−485.032	−	840.100i	−0.884420	−	1.53186i	−0.0380420	−	0.999276i	$-0.512112\pi$
$68$	325.176			0.579904
$69$	73.1240			0.127581
$70$	−69.8878	−	121.049i	−0.119331	−	0.206688i
$71$	−397.158	+	687.898i	−0.663859	+	1.14984i	0.315734	+	0.948848i	$0.397749\pi$
$71$	−397.158	+	687.898i	−0.663859	+	1.14984i	−0.979593	+	0.200990i	$0.935584\pi$
$72$	86.8919	+	150.501i	0.142227	+	0.246344i
$73$	−129.468	+	224.245i	−0.207577	+	0.359533i	−0.950951	−	0.309343i	$-0.899891\pi$
$73$	−129.468	+	224.245i	−0.207577	+	0.359533i	0.743374	+	0.668876i	$0.233224\pi$
$74$	712.516	−	1234.11i	1.11930	−	1.93869i
$75$	−97.6680			−0.150370
$76$	−505.514	−	102.478i	−0.762980	−	0.154672i
$77$	207.792			0.307534
$78$	135.528	−	234.741i	0.196738	−	0.340759i
$79$	148.966	−	258.017i	0.212152	−	0.367458i	−0.740236	−	0.672347i	$-0.765286\pi$
$79$	148.966	−	258.017i	0.212152	−	0.367458i	0.952388	+	0.304890i	$0.0986196\pi$
$80$	196.144	+	339.732i	0.274120	+	0.474789i
$81$	−324.500	+	562.050i	−0.445130	+	0.770988i
$82$	133.046	+	230.443i	0.179177	+	0.310343i
$83$	1417.29			1.87431			0.937157	−	0.348908i	$-0.113448\pi$
$83$	1417.29			1.87431			0.937157	+	0.348908i	$0.113448\pi$
$84$	−44.1441			−0.0573395
$85$	−136.482	−	236.394i	−0.174160	−	0.301653i
$86$	−124.076	−	214.906i	−0.155575	−	0.269464i
$87$	−217.652			−0.268216
$88$	−195.948			−0.237365
$89$	18.4941	+	32.0327i	0.0220266	+	0.0381512i	0.876829	−	0.480803i	$-0.159655\pi$
$89$	18.4941	+	32.0327i	0.0220266	+	0.0381512i	−0.854802	+	0.518954i	$0.826321\pi$
$90$	−256.360	+	444.029i	−0.300253	+	0.520053i
$91$	254.672	+	441.105i	0.293372	+	0.508136i
$92$	−227.708	+	394.402i	−0.258046	+	0.446949i
$93$	7.31601	−	12.6717i	0.00815736	−	0.0141290i
$94$	−1403.59			−1.54010
$95$	137.674	+	410.507i	0.148685	+	0.443338i
$96$	229.564			0.244060
$97$	−504.264	+	873.411i	−0.527838	+	0.914242i	0.471635	+	0.881794i	$0.343664\pi$
$97$	−504.264	+	873.411i	−0.527838	+	0.914242i	−0.999473	+	0.0324485i	$0.989670\pi$
$98$	−552.146	+	956.345i	−0.569134	+	0.985770i
$99$	−381.108	−	660.099i	−0.386897	−	0.670125i
$100$	304.138	−	526.783i	0.304138	−	0.526783i
$101$	−469.286	−	812.827i	−0.462334	−	0.800786i	0.536743	−	0.843746i	$-0.319654\pi$
$101$	−469.286	−	812.827i	−0.462334	−	0.800786i	−0.999077	+	0.0429601i	$0.986321\pi$
$102$	−196.944			−0.191180
$103$	305.384			0.292140			0.146070	−	0.989274i	$-0.453338\pi$
$103$	305.384			0.292140			0.146070	+	0.989274i	$0.453338\pi$
$104$	−240.156	−	415.962i	−0.226435	−	0.392197i
$105$	18.5280	+	32.0915i	0.0172205	+	0.0298268i
$106$	1103.04			1.01072
$107$	325.328			0.293931			0.146966	−	0.989142i	$-0.453049\pi$
$107$	325.328			0.293931			0.146966	+	0.989142i	$0.453049\pi$
$108$	165.042	+	285.861i	0.147048	+	0.254694i
$109$	676.274	−	1171.34i	0.594269	−	1.02930i	−0.399381	−	0.916785i	$-0.630775\pi$
$109$	676.274	−	1171.34i	0.594269	−	1.02930i	0.993650	−	0.112519i	$-0.0358919\pi$
$110$	−289.056	−	500.660i	−0.250549	−	0.433964i
$111$	−188.896	+	327.178i	−0.161524	+	0.279769i
$112$	−265.928	+	460.601i	−0.224356	+	0.388595i
$113$	950.484			0.791275			0.395637	−	0.918407i	$-0.370524\pi$
$113$	950.484			0.791275			0.395637	+	0.918407i	$0.370524\pi$
$114$	306.166	+	62.0663i	0.251536	+	0.0509916i
$115$	382.292			0.309991
$116$	677.768	−	1173.93i	0.542493	−	0.939626i
$117$	934.180	−	1618.05i	0.738162	−	1.27853i
$118$	1014.19	+	1756.62i	0.791215	+	1.37042i
$119$	185.040	−	320.498i	0.142543	−	0.246891i
$120$	−17.4720	−	30.2623i	−0.0132914	−	0.0230213i
$121$	−471.572			−0.354299
$122$	−1114.26			−0.826892
$123$	−35.2720	−	61.0929i	−0.0258567	−	0.0447851i
$124$	45.5641	+	78.9193i	0.0329982	+	0.0571545i
$125$	−1164.11			−0.832968
$126$	−695.135			−0.491489
$127$	268.974	+	465.876i	0.187934	+	0.325510i	0.944561	−	0.328336i	$-0.106488\pi$
$127$	268.974	+	465.876i	0.187934	+	0.325510i	−0.756628	+	0.653846i	$0.773154\pi$
$128$	417.282	−	722.753i	0.288147	−	0.499086i
$129$	32.8940	+	56.9740i	0.0224508	+	0.0388859i
$130$	708.540	−	1227.23i	0.478024	−	0.827962i
$131$	−1307.11	+	2263.98i	−0.871775	+	1.50996i	−0.0116170	+	0.999933i	$0.503698\pi$
$131$	−1307.11	+	2263.98i	−0.871775	+	1.50996i	−0.860158	+	0.510027i	$0.829635\pi$
$132$	−182.580			−0.120391
$133$	−388.664	+	439.927i	−0.253394	+	0.286816i
$134$	−3659.08			−2.35893
$135$	138.542	−	239.962i	0.0883244	−	0.152982i
$136$	−174.492	+	302.230i	−0.110019	+	0.190559i
$137$	−553.032	−	957.880i	−0.344881	−	0.597352i	0.640451	−	0.767999i	$-0.278747\pi$
$137$	−553.032	−	957.880i	−0.344881	−	0.597352i	−0.985332	+	0.170647i	$0.945414\pi$
$138$	137.912	−	238.871i	0.0850714	−	0.147348i
$139$	698.652	+	1210.10i	0.426323	+	0.738413i	0.996543	−	0.0830788i	$-0.0264753\pi$
$139$	698.652	+	1210.10i	0.426323	+	0.738413i	−0.570220	+	0.821492i	$0.693142\pi$
$140$	−230.785			−0.139321
$141$	372.108			0.222249
$142$	1498.08	+	2594.75i	0.885325	+	1.53343i
$143$	1053.32	+	1824.41i	0.615968	+	1.06689i
$144$	1950.94			1.12901
$145$	−1137.88			−0.651698
$146$	488.354	+	845.854i	0.276825	+	0.479475i
$147$	146.380	−	253.538i	0.0821308	−	0.142255i
$148$	−1176.44	−	2037.66i	−0.653399	−	1.13172i
$149$	540.222	−	935.692i	0.297025	−	0.514463i	−0.678429	−	0.734666i	$-0.737339\pi$
$149$	540.222	−	935.692i	0.297025	−	0.514463i	0.975454	+	0.220204i	$0.0706722\pi$
$150$	−184.202	+	319.047i	−0.100267	+	0.173667i
$151$	1518.36			0.818294			0.409147	−	0.912468i	$-0.365826\pi$
$151$	1518.36			0.818294			0.409147	+	0.912468i	$0.365826\pi$
$152$	366.510	−	414.851i	0.195578	−	0.221374i
$153$	−1357.51			−0.717310
$154$	391.896	−	678.784i	0.205064	−	0.355182i
$155$	38.2481	−	66.2476i	0.0198204	−	0.0343299i
$156$	−223.772	−	387.584i	−0.114847	−	0.198920i
$157$	378.522	−	655.620i	0.192416	−	0.333275i	−0.753634	−	0.657294i	$-0.771701\pi$
$157$	378.522	−	655.620i	0.192416	−	0.333275i	0.946051	+	0.324019i	$0.105034\pi$
$158$	−561.900	−	973.240i	−0.282926	−	0.490043i
$159$	−292.428			−0.145856
$160$	1200.16			0.593006
$161$	259.152	+	448.864i	0.126857	+	0.219723i
$162$	1224.01	+	2120.06i	0.593628	+	1.02819i
$163$	−3933.24			−1.89003			−0.945017	−	0.327021i	$-0.893955\pi$
$163$	−3933.24			−1.89003			−0.945017	+	0.327021i	$0.893955\pi$
$164$	439.348			0.209191
$165$	76.6320	+	132.731i	0.0361563	+	0.0626246i
$166$	2673.01	−	4629.80i	1.24980	−	2.16471i
$167$	−1247.53	−	2160.78i	−0.578063	−	1.00123i	−0.995701	−	0.0926207i	$-0.970476\pi$
$167$	−1247.53	−	2160.78i	−0.578063	−	1.00123i	0.417639	−	0.908613i	$-0.362858\pi$
$168$	23.6881	−	41.0290i	0.0108784	−	0.0188420i
$169$	−1483.43	+	2569.38i	−0.675207	+	1.16949i
$170$	−1029.62			−0.464520
$171$	2110.37	+	427.817i	0.943766	+	0.191321i
$172$	−409.727			−0.181636
$173$	867.406	−	1502.39i	0.381200	−	0.660258i	−0.610034	−	0.792375i	$-0.708844\pi$
$173$	867.406	−	1502.39i	0.381200	−	0.660258i	0.991234	+	0.132117i	$0.0421775\pi$
$174$	−410.492	+	710.993i	−0.178847	+	0.309772i
$175$	−346.136	−	599.525i	−0.149517	−	0.258970i
$176$	−1099.88	+	1905.05i	−0.471059	+	0.815899i
$177$	−268.872	−	465.700i	−0.114179	−	0.197764i
$178$	139.519			0.0587495
$179$	1531.54			0.639512			0.319756	−	0.947500i	$-0.396399\pi$
$179$	1531.54			0.639512			0.319756	+	0.947500i	$0.396399\pi$
$180$	423.280	+	733.142i	0.175274	+	0.303584i
$181$	−1346.53	−	2332.26i	−0.552966	−	0.957765i	−0.998059	−	0.0622804i	$-0.980163\pi$
$181$	−1346.53	−	2332.26i	−0.552966	−	0.957765i	0.445093	−	0.895484i	$-0.353171\pi$
$182$	1921.25			0.782485
$183$	295.404			0.119327
$184$	−244.380	−	423.279i	−0.0979128	−	0.169590i
$185$	−987.548	+	1710.48i	−0.392465	+	0.679769i
$186$	−27.5960	−	47.7977i	−0.0108787	−	0.0188424i
$187$	765.324	−	1325.58i	0.299284	−	0.518375i
$188$	−1158.74	+	2007.00i	−0.449522	+	0.778595i
$189$	375.664			0.144580
$190$	1600.64	+	324.483i	0.611170	+	0.123897i
$191$	−2569.49			−0.973412			−0.486706	−	0.873566i	$-0.661802\pi$
$191$	−2569.49			−0.973412			−0.486706	+	0.873566i	$0.661802\pi$
$192$	132.814	−	230.041i	0.0499220	−	0.0864674i
$193$	345.390	−	598.232i	0.128817	−	0.223118i	−0.794401	−	0.607393i	$-0.792215\pi$
$193$	345.390	−	598.232i	0.128817	−	0.223118i	0.923219	+	0.384275i	$0.125549\pi$
$194$	1902.09	+	3294.51i	0.703927	+	1.21924i
$195$	−187.842	+	325.352i	−0.0689828	+	0.119482i
$196$	911.655	+	1579.03i	0.332236	+	0.575449i
$197$	1726.93			0.624561			0.312281	−	0.949990i	$-0.398907\pi$
$197$	1726.93			0.624561			0.312281	+	0.949990i	$0.398907\pi$
$198$	−2875.08			−1.03193
$199$	1811.84	+	3138.20i	0.645416	+	1.11789i	0.984205	+	0.177031i	$0.0566494\pi$
$199$	1811.84	+	3138.20i	0.645416	+	1.11789i	−0.338789	+	0.940862i	$0.610017\pi$
$200$	326.406	+	565.352i	0.115402	+	0.199882i
$201$	970.064			0.340413
$202$	−3540.30			−1.23314
$203$	−771.360	−	1336.03i	−0.266694	−	0.461927i
$204$	−162.588	+	281.611i	−0.0558012	+	0.0966506i
$205$	−184.402	−	319.394i	−0.0628253	−	0.108817i
$206$	575.955	−	997.584i	0.194800	−	0.337403i
$207$	950.612	−	1646.51i	0.319189	−	0.552852i
$208$	−5392.09			−1.79747
$209$	−1607.51	+	1819.54i	−0.532029	+	0.602201i
$210$	139.776			0.0459306
$211$	−668.986	+	1158.72i	−0.218270	+	0.378054i	−0.954279	−	0.298917i	$-0.903375\pi$
$211$	−668.986	+	1158.72i	−0.218270	+	0.378054i	0.736009	+	0.676971i	$0.236708\pi$
$212$	910.621	−	1577.24i	0.295008	−	0.510969i
$213$	−397.158	−	687.898i	−0.127760	−	0.221286i
$214$	613.569	−	1062.73i	0.195994	−	0.339471i
$215$	171.970	+	297.860i	0.0545499	+	0.0944832i
$216$	−354.252			−0.111592
$217$	103.712			0.0324443
$218$	−2550.91	−	4418.30i	−0.792520	−	1.37268i
$219$	−129.468	−	224.245i	−0.0399481	−	0.0691922i
$220$	−954.528			−0.292519
$221$	3751.96			1.14201
$222$	712.516	+	1234.11i	0.215410	+	0.373101i
$223$	607.098	−	1051.53i	0.182306	−	0.315764i	−0.760359	−	0.649503i	$-0.774977\pi$
$223$	607.098	−	1051.53i	0.182306	−	0.315764i	0.942666	+	0.333739i	$0.108310\pi$
$224$	813.576	+	1409.15i	0.242676	+	0.420326i
$225$	−1269.68	+	2199.16i	−0.376203	+	0.651602i
$226$	1792.61	−	3104.90i	0.527624	−	0.913871i
$227$	1616.12			0.472537			0.236268	−	0.971688i	$-0.424076\pi$
$227$	1616.12			0.472537			0.236268	+	0.971688i	$0.424076\pi$
$228$	341.506	−	386.549i	0.0991965	−	0.112280i
$229$	4536.14			1.30898			0.654490	−	0.756071i	$-0.272883\pi$
$229$	4536.14			1.30898			0.654490	+	0.756071i	$0.272883\pi$
$230$	721.004	−	1248.81i	0.206702	−	0.358019i
$231$	−103.896	+	179.953i	−0.0295925	+	0.0512556i
$232$	727.393	+	1259.88i	0.205843	+	0.356531i
$233$	−12.1721	+	21.0828i	−0.00342242	+	0.00592780i	−0.867732	−	0.497033i	$-0.834423\pi$
$233$	−12.1721	+	21.0828i	−0.00342242	+	0.00592780i	0.864309	+	0.502961i	$0.167756\pi$
$234$	−3523.73	−	6103.28i	−0.984416	−	1.70506i
$235$	1945.38			0.540011
$236$	3349.07			0.923754
$237$	148.966	+	258.017i	0.0408286	+	0.0707172i
$238$	−697.970	−	1208.92i	−0.190095	−	0.329255i
$239$	3202.37			0.866712			0.433356	−	0.901223i	$-0.357329\pi$
$239$	3202.37			0.866712			0.433356	+	0.901223i	$0.357329\pi$
$240$	−392.288			−0.105509
$241$	3085.70	+	5344.58i	0.824760	+	1.42853i	0.902102	+	0.431522i	$0.142023\pi$
$241$	3085.70	+	5344.58i	0.824760	+	1.42853i	−0.0773424	+	0.997005i	$0.524643\pi$
$242$	−889.385	+	1540.46i	−0.236247	+	0.409192i
$243$	−1040.00	−	1801.33i	−0.274552	−	0.475537i
$244$	−919.888	+	1593.29i	−0.241352	+	0.418033i
$245$	765.275	−	1325.49i	0.199558	−	0.345644i
$246$	−266.092			−0.0689651
$247$	−5832.74	−	1182.42i	−1.50254	−	0.304597i
$248$	−97.8003			−0.0250416
$249$	−708.646	+	1227.41i	−0.180356	+	0.312386i
$250$	−2195.51	+	3802.73i	−0.555425	+	0.962024i
$251$	−1914.41	−	3315.85i	−0.481420	−	0.833844i	0.518353	−	0.855167i	$-0.326545\pi$
$251$	−1914.41	−	3315.85i	−0.481420	−	0.833844i	−0.999773	+	0.0213232i	$0.993212\pi$
$252$	−573.873	+	993.978i	−0.143455	+	0.248471i
$253$	1071.85	+	1856.50i	0.266351	+	0.461333i
$254$	2029.14			0.501258
$255$	272.964			0.0670341
$256$	−2636.50	−	4566.55i	−0.643677	−	1.11488i
$257$	−2127.04	−	3684.15i	−0.516270	−	0.894206i	−0.999822	−	0.0188899i	$-0.993987\pi$
$257$	−2127.04	−	3684.15i	−0.516270	−	0.894206i	0.483552	−	0.875316i	$-0.339347\pi$
$258$	248.152			0.0598810
$259$	−2677.79			−0.642432
$260$	−1169.88	−	2026.29i	−0.279049	−	0.483328i
$261$	−2829.48	+	4900.80i	−0.671035	+	1.16227i
$262$	4930.41	+	8539.73i	1.16260	+	2.01369i
$263$	−3321.43	+	5752.88i	−0.778737	+	1.34881i	0.153933	+	0.988081i	$0.450806\pi$
$263$	−3321.43	+	5752.88i	−0.778737	+	1.34881i	−0.932670	+	0.360731i	$0.882527\pi$
$264$	97.9740	−	169.696i	0.0228405	−	0.0395608i
$265$	−1528.81			−0.354394
$266$	704.066	+	2099.33i	0.162290	+	0.483903i
$267$	−36.9881			−0.00847804
$268$	−3020.78	+	5232.14i	−0.688520	+	1.19255i
$269$	1960.17	−	3395.11i	0.444289	−	0.769531i	−0.553714	−	0.832707i	$-0.686790\pi$
$269$	1960.17	−	3395.11i	0.444289	−	0.769531i	0.998002	+	0.0631764i	$0.0201231\pi$
$270$	−522.580	−	905.136i	−0.117790	−	0.204018i
$271$	3243.19	−	5617.37i	0.726973	−	1.25915i	−0.231183	−	0.972910i	$-0.574260\pi$
$271$	3243.19	−	5617.37i	0.726973	−	1.25915i	0.958157	−	0.286245i	$-0.0924070\pi$
$272$	1958.89	+	3392.90i	0.436674	+	0.756341i
$273$	−509.344			−0.112919
$274$	−4172.08			−0.919870
$275$	−1431.62	−	2479.64i	−0.313927	−	0.543737i
$276$	−227.708	−	394.402i	−0.0496609	−	0.0860153i
$277$	−2395.03			−0.519507			−0.259754	−	0.965675i	$-0.583641\pi$
$277$	−2395.03			−0.519507			−0.259754	+	0.965675i	$0.583641\pi$
$278$	5270.64			1.13709
$279$	−190.216	−	329.464i	−0.0408170	−	0.0706971i
$280$	123.841	−	214.500i	0.0264319	−	0.0457814i
$281$	206.619	+	357.875i	0.0438644	+	0.0759753i	0.887124	−	0.461531i	$-0.152700\pi$
$281$	206.619	+	357.875i	0.0438644	+	0.0759753i	−0.843260	+	0.537506i	$0.819366\pi$
$282$	701.796	−	1215.55i	0.148196	−	0.256684i
$283$	2333.03	−	4040.92i	0.490050	−	0.848791i	−0.509884	−	0.860243i	$-0.670312\pi$
$283$	2333.03	−	4040.92i	0.490050	−	0.848791i	0.999934	+	0.0114514i	$0.00364518\pi$
$284$	4947.00			1.03363
$285$	−424.346	−	86.0240i	−0.0881969	−	0.0178794i
$286$	7946.28			1.64291
$287$	250.008	−	433.027i	0.0514199	−	0.0890619i
$288$	2984.33	−	5169.02i	0.610602	−	1.05759i
$289$	1093.45	+	1893.91i	0.222563	+	0.385490i
$290$	−2146.05	+	3717.07i	−0.434553	+	0.752669i
$291$	−504.264	−	873.411i	−0.101582	−	0.175946i
$292$	1612.65			0.323197
$293$	−2978.87			−0.593951			−0.296975	−	0.954885i	$-0.595978\pi$
$293$	−2978.87			−0.593951			−0.296975	+	0.954885i	$0.595978\pi$
$294$	−552.146	−	956.345i	−0.109530	−	0.189711i
$295$	−1405.66	−	2434.68i	−0.277427	−	0.480517i
$296$	2525.16			0.495851
$297$	1553.75			0.303561
$298$	−2037.72	−	3529.43i	−0.396114	−	0.686089i
$299$	−2627.35	+	4550.70i	−0.508172	+	0.880179i
$300$	304.138	+	526.783i	0.0585314	+	0.101379i
$301$	−233.153	+	403.832i	−0.0446469	+	0.0773306i
$302$	2863.63	−	4959.95i	0.545640	−	0.945076i
$303$	938.572			0.177952
$304$	−1976.00	−	5891.89i	−0.372801	−	1.11159i
$305$	1544.37			0.289936
$306$	−2560.27	+	4434.52i	−0.478304	+	0.828446i
$307$	−966.524	+	1674.07i	−0.179682	+	0.311219i	−0.941772	−	0.336253i	$-0.890840\pi$
$307$	−966.524	+	1674.07i	−0.179682	+	0.311219i	0.762090	+	0.647472i	$0.224174\pi$
$308$	−647.064	−	1120.75i	−0.119708	−	0.207339i
$309$	−152.692	+	264.471i	−0.0281112	+	0.0486900i
$310$	−144.272	−	249.886i	−0.0264325	−	0.0457825i
$311$	−8777.42			−1.60039			−0.800196	−	0.599739i	$-0.795271\pi$
$311$	−8777.42			−1.60039			−0.800196	+	0.599739i	$0.795271\pi$
$312$	480.312			0.0871548
$313$	3050.29	+	5283.26i	0.550839	+	0.954081i	0.998214	+	0.0597346i	$0.0190254\pi$
$313$	3050.29	+	5283.26i	0.550839	+	0.954081i	−0.447375	+	0.894346i	$0.647641\pi$
$314$	−1427.79	−	2473.00i	−0.256607	−	0.444457i
$315$	963.458			0.172332
$316$	−1855.52			−0.330320
$317$	−2683.32	−	4647.64i	−0.475426	−	0.823462i	0.524178	−	0.851609i	$-0.324373\pi$
$317$	−2683.32	−	4647.64i	−0.475426	−	0.823462i	−0.999604	+	0.0281470i	$0.991039\pi$
$318$	−551.520	+	955.260i	−0.0972569	+	0.168454i
$319$	−3190.34	−	5525.84i	−0.559953	−	0.969867i
$320$	694.351	−	1202.65i	0.121298	−	0.210095i
$321$	−162.664	+	281.742i	−0.0282835	+	0.0489885i
$322$	1955.04			0.338355
$323$	1374.95	+	4099.73i	0.236856	+	0.706239i
$324$	4041.97			0.693068
$325$	3509.21	−	6078.14i	0.598942	−	1.03740i
$326$	−7418.10	+	12848.5i	−1.26028	+	2.18287i
$327$	676.274	+	1171.34i	0.114367	+	0.198090i
$328$	−235.758	+	408.345i	−0.0396877	+	0.0687410i
$329$	1318.75	+	2284.15i	0.220988	+	0.382763i
$330$	578.112			0.0964364
$331$	5549.57			0.921547			0.460773	−	0.887518i	$-0.347572\pi$
$331$	5549.57			0.921547			0.460773	+	0.887518i	$0.347572\pi$
$332$	−4413.45	−	7644.31i	−0.729576	−	1.26366i
$333$	4911.30	+	8506.62i	0.808220	+	1.39988i
$334$	−9411.34			−1.54181
$335$	5071.49			0.827120
$336$	−265.928	−	460.601i	−0.0431773	−	0.0747852i
$337$	−1568.43	+	2716.60i	−0.253524	+	0.439117i	−0.964494	−	0.264106i	$-0.914923\pi$
$337$	−1568.43	+	2716.60i	−0.253524	+	0.439117i	0.710969	+	0.703223i	$0.248256\pi$
$338$	5595.50	+	9691.69i	0.900459	+	1.55964i
$339$	−475.242	+	823.144i	−0.0761404	+	0.131879i
$340$	−850.011	+	1472.26i	−0.135583	+	0.234837i
$341$	428.952			0.0681204
$342$	5377.68	−	6086.97i	0.850269	−	0.962415i
$343$	4506.27			0.709376
$344$	219.863	−	380.814i	0.0344600	−	0.0596864i
$345$	−191.146	+	331.075i	−0.0298289	+	0.0516651i
$346$	−3271.86	−	5667.02i	−0.508370	−	0.880523i
$347$	−2736.22	+	4739.26i	−0.423308	+	0.733190i	−0.996261	−	0.0863979i	$-0.972464\pi$
$347$	−2736.22	+	4739.26i	−0.423308	+	0.733190i	0.572953	+	0.819588i	$0.305798\pi$
$348$	677.768	+	1173.93i	0.104403	+	0.180831i
$349$	−5103.53			−0.782767			−0.391384	−	0.920228i	$-0.628003\pi$
$349$	−5103.53			−0.782767			−0.391384	+	0.920228i	$0.628003\pi$
$350$	−2611.25			−0.398792
$351$	1904.29	+	3298.33i	0.289583	+	0.501572i
$352$	3364.95	+	5828.27i	0.509524	+	0.882522i
$353$	−2533.34			−0.381972			−0.190986	−	0.981593i	$-0.561168\pi$
$353$	−2533.34			−0.381972			−0.190986	+	0.981593i	$0.561168\pi$
$354$	−2028.37			−0.304539
$355$	−2076.34	−	3596.33i	−0.310425	−	0.537671i
$356$	115.181	−	199.499i	0.0171477	−	0.0297007i
$357$	185.040	+	320.498i	0.0274323	+	0.0475142i
$358$	2888.48	−	5003.00i	0.426428	−	0.738595i
$359$	1280.16	−	2217.31i	0.188202	−	0.325975i	−0.756449	−	0.654053i	$-0.773068\pi$
$359$	1280.16	−	2217.31i	0.188202	−	0.325975i	0.944651	+	0.328078i	$0.106401\pi$
$360$	−908.542			−0.133012
$361$	−845.461	−	6806.69i	−0.123263	−	0.992374i
$362$	−10158.2			−1.47487
$363$	235.786	−	408.393i	0.0340924	−	0.0590498i
$364$	1586.10	−	2747.20i	0.228390	−	0.395584i
$365$	−676.859	−	1172.35i	−0.0970641	−	0.168120i
$366$	557.132	−	964.981i	0.0795677	−	0.137815i
$367$	3397.53	+	5884.69i	0.483241	+	0.836998i	0.999815	−	0.0192446i	$-0.00612612\pi$
$367$	3397.53	+	5884.69i	0.483241	+	0.836998i	−0.516574	+	0.856243i	$0.672793\pi$
$368$	−5486.94			−0.777246
$369$	−1834.14			−0.258758
$370$	3725.03	+	6451.95i	0.523393	+	0.906543i
$371$	−1036.37	−	1795.04i	−0.145028	−	0.251196i
$372$	−91.1281			−0.0127010
$373$	−613.529			−0.0851672			−0.0425836	−	0.999093i	$-0.513559\pi$
$373$	−613.529			−0.0851672			−0.0425836	+	0.999093i	$0.513559\pi$
$374$	−2886.80	−	5000.09i	−0.399126	−	0.691306i
$375$	582.054	−	1008.15i	0.0801524	−	0.138828i
$376$	−1243.58	−	2153.95i	−0.170566	−	0.295430i
$377$	7820.24	−	13545.1i	1.06834	−	1.85041i
$378$	708.503	−	1227.16i	0.0964060	−	0.166980i
$379$	6250.72			0.847172			0.423586	−	0.905856i	$-0.360771\pi$
$379$	6250.72			0.847172			0.423586	+	0.905856i	$0.360771\pi$
$380$	1785.39	−	2020.88i	0.241023	−	0.272813i
$381$	−537.948			−0.0723357
$382$	−4846.06	+	8393.62i	−0.649073	+	1.12423i
$383$	−254.379	+	440.598i	−0.0339378	+	0.0587820i	−0.882495	−	0.470321i	$-0.844138\pi$
$383$	−254.379	+	440.598i	−0.0339378	+	0.0587820i	0.848558	+	0.529103i	$0.177471\pi$
$384$	417.282	+	722.753i	0.0554540	+	0.0960491i
$385$	−543.168	+	940.795i	−0.0719024	+	0.124539i
$386$	−1302.81	−	2256.53i	−0.171791	−	0.297551i
$387$	1710.49			0.224674
$388$	6281.11			0.821843
$389$	1002.71	+	1736.75i	0.130693	+	0.226367i	0.923944	−	0.382528i	$-0.124946\pi$
$389$	1002.71	+	1736.75i	0.130693	+	0.226367i	−0.793251	+	0.608895i	$0.791613\pi$
$390$	708.540	+	1227.23i	0.0919957	+	0.159341i
$391$	3817.95			0.493817
$392$	−1956.81			−0.252127
$393$	−1307.11	−	2263.98i	−0.167773	−	0.290592i
$394$	3256.99	−	5641.27i	0.416459	−	0.721328i
$395$	778.794	+	1348.91i	0.0992035	+	0.171826i
$396$	−2373.54	+	4111.09i	−0.301199	+	0.521692i
$397$	−3294.61	+	5706.43i	−0.416503	+	0.721404i	−0.995585	−	0.0938649i	$-0.970078\pi$
$397$	−3294.61	+	5706.43i	−0.416503	+	0.721404i	0.579082	+	0.815269i	$0.303411\pi$
$398$	13668.5			1.72146
$399$	−186.656	−	556.556i	−0.0234197	−	0.0698312i
$400$	7328.62			0.916078
$401$	5441.83	−	9425.52i	0.677685	−	1.17379i	−0.297991	−	0.954569i	$-0.596316\pi$
$401$	5441.83	−	9425.52i	0.677685	−	1.17379i	0.975676	−	0.219217i	$-0.0703502\pi$
$402$	1829.54	−	3168.86i	0.226988	−	0.393155i
$403$	525.728	+	910.588i	0.0649836	+	0.112555i
$404$	−2922.71	+	5062.29i	−0.359927	+	0.623411i
$405$	−1696.49	−	2938.40i	−0.208146	−	0.360519i
$406$	−5819.14			−0.711328
$407$	−11075.4			−1.34886
$408$	−174.492	−	302.230i	−0.0211732	−	0.0366731i
$409$	2785.51	+	4824.65i	0.336760	+	0.583285i	0.983821	−	0.179153i	$-0.0573357\pi$
$409$	2785.51	+	4824.65i	0.336760	+	0.583285i	−0.647062	+	0.762438i	$0.724002\pi$
$410$	−1391.13			−0.167568
$411$	1106.06			0.132745
$412$	−950.967	−	1647.12i	−0.113715	−	0.196961i
$413$	1905.77	−	3300.89i	0.227062	−	0.393283i
$414$	−3585.71	−	6210.64i	−0.425672	−	0.737285i
$415$	−3704.80	+	6416.90i	−0.438221	+	0.759020i
$416$	−8248.24	+	14286.4i	−0.972123	+	1.68377i
$417$	−1397.30			−0.164092
$418$	2912.02	+	8682.83i	0.340745	+	1.01601i
$419$	−9667.52			−1.12718			−0.563591	−	0.826054i	$-0.690581\pi$
$419$	−9667.52			−1.12718			−0.563591	+	0.826054i	$0.690581\pi$
$420$	115.393	−	199.866i	0.0134062	−	0.0232201i
$421$	−3043.76	+	5271.95i	−0.352361	+	0.610307i	−0.986663	−	0.162778i	$-0.947954\pi$
$421$	−3043.76	+	5271.95i	−0.352361	+	0.610307i	0.634302	+	0.773086i	$0.281288\pi$
$422$	2523.42	+	4370.68i	0.291085	+	0.504174i
$423$	4837.40	−	8378.63i	0.556035	−	0.963080i
$424$	977.294	+	1692.72i	0.111938	+	0.193882i
$425$	−5099.45			−0.582022
$426$	−2996.16			−0.340762
$427$	1046.91	+	1813.31i	0.118650	+	0.205508i
$428$	−1013.07	−	1754.69i	−0.114413	−	0.198169i
$429$	−2106.65			−0.237086
$430$	1297.34			0.145496
$431$	4797.73	+	8309.91i	0.536191	+	0.928710i	0.999105	+	0.0423069i	$0.0134707\pi$
$431$	4797.73	+	8309.91i	0.536191	+	0.928710i	−0.462914	+	0.886403i	$0.653196\pi$
$432$	−1988.45	+	3444.10i	−0.221457	+	0.383575i
$433$	−149.587	−	259.092i	−0.0166021	−	0.0287556i	0.857605	−	0.514309i	$-0.171952\pi$
$433$	−149.587	−	259.092i	−0.0166021	−	0.0287556i	−0.874207	+	0.485553i	$0.838618\pi$
$434$	195.601	−	338.790i	0.0216339	−	0.0374711i
$435$	568.942	−	985.437i	0.0627096	−	0.108616i
$436$	−8423.67			−0.925277
$437$	−5935.33	−	1203.22i	−0.649715	−	0.131711i
$438$	−976.708			−0.106550
$439$	−3069.29	+	5316.17i	−0.333689	+	0.577966i	−0.983232	−	0.182359i	$-0.941627\pi$
$439$	−3069.29	+	5316.17i	−0.333689	+	0.577966i	0.649543	+	0.760325i	$0.274960\pi$
$440$	512.208	−	887.170i	0.0554967	−	0.0961231i
$441$	−3805.88	−	6591.98i	−0.410958	−	0.711800i
$442$	7076.20	−	12256.3i	0.761494	−	1.31895i
$443$	3467.18	+	6005.34i	0.371853	+	0.644068i	0.989851	−	0.142112i	$-0.0453892\pi$
$443$	3467.18	+	6005.34i	0.371853	+	0.644068i	−0.617998	+	0.786180i	$0.712056\pi$
$444$	2352.89			0.251494
$445$	−193.374			−0.0205996
$446$	−2289.98	−	3966.35i	−0.243124	−	0.421104i
$447$	540.222	+	935.692i	0.0571625	+	0.0990084i
$448$	1882.77			0.198555
$449$	6679.68			0.702079			0.351039	−	0.936361i	$-0.385828\pi$
$449$	6679.68			0.702079			0.351039	+	0.936361i	$0.385828\pi$
$450$	4789.25	+	8295.23i	0.501706	+	0.868980i
$451$	1034.03	−	1791.00i	0.107962	−	0.186995i
$452$	−2959.81	−	5126.54i	−0.308004	−	0.533478i
$453$	−759.180	+	1314.94i	−0.0787404	+	0.136382i
$454$	3048.01	−	5279.31i	0.315089	−	0.545749i
$455$	−2662.85			−0.274366
$456$	176.016	+	524.833i	0.0180762	+	0.0538981i
$457$	−7224.17			−0.739458			−0.369729	−	0.929140i	$-0.620549\pi$
$457$	−7224.17			−0.739458			−0.369729	+	0.929140i	$0.620549\pi$
$458$	8555.16	−	14818.0i	0.872831	−	1.51179i
$459$	1383.62	−	2396.50i	0.140701	−	0.243701i
$460$	−1190.46	−	2061.93i	−0.120664	−	0.208996i
$461$	−287.898	+	498.654i	−0.0290862	+	0.0503788i	−0.880202	−	0.474599i	$-0.842593\pi$
$461$	−287.898	+	498.654i	−0.0290862	+	0.0503788i	0.851116	+	0.524978i	$0.175926\pi$
$462$	391.896	+	678.784i	0.0394646	+	0.0683547i
$463$	9326.41			0.936145			0.468073	−	0.883690i	$-0.344949\pi$
$463$	9326.41			0.936145			0.468073	+	0.883690i	$0.344949\pi$
$464$	16331.7			1.63401
$465$	38.2481	+	66.2476i	0.00381443	+	0.00660679i
$466$	45.9133	+	79.5242i	0.00456415	+	0.00790534i
$467$	8972.71			0.889095			0.444547	−	0.895755i	$-0.353364\pi$
$467$	8972.71			0.889095			0.444547	+	0.895755i	$0.353364\pi$
$468$	−11636.1			−1.14932
$469$	3437.91	+	5954.64i	0.338482	+	0.586268i
$470$	3668.99	−	6354.88i	0.360081	−	0.623678i
$471$	378.522	+	655.620i	0.0370306	+	0.0641388i
$472$	−1797.14	+	3112.74i	−0.175254	+	0.303549i
$473$	−964.320	+	1670.25i	−0.0937410	+	0.162364i
$474$	1123.80			0.108898
$475$	7927.52	+	1607.08i	0.765768	+	0.155237i
$476$	−2304.85			−0.221939
$477$	−3801.57	+	6584.51i	−0.364909	+	0.632042i
$478$	6039.67	−	10461.0i	0.577925	−	1.00100i
$479$	5086.69	+	8810.41i	0.485213	+	0.840413i	0.999856	−	0.0169915i	$-0.00540883\pi$
$479$	5086.69	+	8810.41i	0.485213	+	0.840413i	−0.514643	+	0.857405i	$0.672076\pi$
$480$	−600.080	+	1039.37i	−0.0570621	+	0.0988344i
$481$	−13574.1	−	23511.0i	−1.28675	−	2.22871i
$482$	23278.5			2.19981
$483$	−518.304			−0.0488274
$484$	1468.47	+	2543.47i	0.137911	+	0.238869i
$485$	−2636.29	−	4566.19i	−0.246820	−	0.427505i
$486$	−7845.76			−0.732286
$487$	−18171.7			−1.69084			−0.845421	−	0.534101i	$-0.820650\pi$
$487$	−18171.7			−1.69084			−0.845421	+	0.534101i	$0.820650\pi$
$488$	−987.239	−	1709.95i	−0.0915783	−	0.158618i
$489$	1966.62	−	3406.29i	0.181869	−	0.315006i
$490$	−2886.62	−	4999.77i	−0.266131	−	0.460952i
$491$	−2834.58	+	4909.64i	−0.260535	+	0.451260i	−0.966384	−	0.257102i	$-0.917232\pi$
$491$	−2834.58	+	4909.64i	−0.260535	+	0.451260i	0.705849	+	0.708362i	$0.250566\pi$
$492$	−219.674	+	380.486i	−0.0201294	+	0.0348652i
$493$	−11364.1			−1.03816
$494$	−14863.1	+	16823.5i	−1.35369	+	1.53223i
$495$	3984.86			0.361831
$496$	−548.964	+	950.833i	−0.0496960	+	0.0860760i
$497$	2815.06	−	4875.83i	0.254070	−	0.440062i
$498$	2673.01	+	4629.80i	0.240523	+	0.416599i
$499$	−4916.33	+	8515.33i	−0.441052	+	0.763925i	−0.997768	−	0.0667782i	$-0.978728\pi$
$499$	−4916.33	+	8515.33i	−0.441052	+	0.763925i	0.556716	+	0.830703i	$0.312061\pi$
$500$	3625.03	+	6278.74i	0.324233	+	0.561587i
$501$	2495.05			0.222496
$502$	−14442.3			−1.28405
$503$	−6731.56	−	11659.4i	−0.596711	−	1.03353i	−0.993303	−	0.115539i	$-0.963141\pi$
$503$	−6731.56	−	11659.4i	−0.596711	−	1.03353i	0.396592	−	0.917995i	$-0.370193\pi$
$504$	−615.891	−	1066.75i	−0.0544324	−	0.0942797i
$505$	4906.85			0.432380
$506$	8086.06			0.710413
$507$	−1483.43	−	2569.38i	−0.129944	−	0.225069i
$508$	1675.17	−	2901.48i	0.146306	−	0.253410i
$509$	3455.44	+	5984.99i	0.300903	+	0.521179i	0.976341	−	0.216238i	$-0.0693787\pi$
$509$	3455.44	+	5984.99i	0.300903	+	0.521179i	−0.675438	+	0.737417i	$0.736045\pi$
$510$	514.811	−	891.679i	0.0446985	−	0.0774200i
$511$	917.671	−	1589.45i	0.0794430	−	0.137599i
$512$	−13213.3			−1.14052
$513$	−2906.20	+	3289.52i	−0.250121	+	0.283110i
$514$	−16046.4			−1.37700
$515$	−798.275	+	1382.65i	−0.0683033	+	0.118305i
$516$	204.864	−	354.834i	0.0174779	−	0.0302727i
$517$	5454.36	+	9447.23i	0.463989	+	0.803653i
$518$	−5050.32	+	8747.41i	−0.428375	+	0.741968i
$519$	867.406	+	1502.39i	0.0733620	+	0.127067i
$520$	2511.07			0.211765
$521$	20868.5			1.75483			0.877413	−	0.479736i	$-0.159268\pi$
$521$	20868.5			1.75483			0.877413	+	0.479736i	$0.159268\pi$
$522$	10672.8	+	18485.8i	0.894895	+	1.55000i
$523$	−5601.31	−	9701.75i	−0.468314	−	0.811143i	0.531030	−	0.847353i	$-0.321805\pi$
$523$	−5601.31	−	9701.75i	−0.468314	−	0.811143i	−0.999344	+	0.0362093i	$0.988472\pi$
$524$	16281.3			1.35735
$525$	692.272			0.0575490
$526$	12528.4	+	21699.9i	1.03853	+	1.79878i
$527$	381.984	−	661.615i	0.0315739	−	0.0546877i
$528$	−1099.88	−	1905.05i	−0.0906554	−	0.157020i
$529$	3409.94	−	5906.19i	0.280261	−	0.485427i
$530$	−2883.34	+	4994.10i	−0.236310	+	0.409302i
$531$	−13981.3			−1.14263
$532$	3583.09	+	726.368i	0.292005	+	0.0591956i
$533$	5069.29			0.411961
$534$	−69.7597	+	120.827i	−0.00565318	+	0.00979159i
$535$	−850.407	+	1472.95i	−0.0687220	+	0.119030i
$536$	−3241.95	−	5615.23i	−0.261252	−	0.452502i
$537$	−765.770	+	1326.35i	−0.0615371	+	0.106585i
$538$	−7393.77	−	12806.4i	−0.592505	−	1.02625i
$539$	8582.56			0.685857
$540$	−1725.68			−0.137521
$541$	−4935.74	−	8548.96i	−0.392244	−	0.679387i	0.600501	−	0.799624i	$-0.294968\pi$
$541$	−4935.74	−	8548.96i	−0.392244	−	0.679387i	−0.992745	+	0.120237i	$0.961635\pi$
$542$	−12233.3	−	21188.7i	−0.969495	−	1.67921i
$543$	2693.06			0.212837
$544$	11986.0			0.944662
$545$	3535.56	+	6123.77i	0.277884	+	0.481309i
$546$	−960.624	+	1663.85i	−0.0752947	+	0.130414i
$547$	−2836.57	−	4913.08i	−0.221724	−	0.384037i	0.733608	−	0.679573i	$-0.237835\pi$
$547$	−2836.57	−	4913.08i	−0.221724	−	0.384037i	−0.955331	+	0.295536i	$0.904502\pi$
$548$	−3444.28	+	5965.67i	−0.268490	+	0.465038i
$549$	3840.25	−	6651.51i	0.298539	−	0.517085i
$550$	−10800.1			−0.837308
$551$	17666.4	+	3581.35i	1.36590	+	0.276898i
$552$	488.761			0.0376867
$553$	−1055.87	+	1828.82i	−0.0811940	+	0.140632i
$554$	−4517.03	+	7823.73i	−0.346409	+	0.599997i
$555$	−987.548	−	1710.48i	−0.0755299	−	0.130822i
$556$	4351.21	−	7536.51i	0.331892	−	0.574855i
$557$	1872.36	+	3243.02i	0.142431	+	0.246698i	0.928412	−	0.371553i	$-0.121175\pi$
$557$	1872.36	+	3243.02i	0.142431	+	0.246698i	−0.785980	+	0.618252i	$0.787841\pi$
$558$	−1434.99			−0.108867
$559$	−4727.52			−0.357698
$560$	−1390.27	−	2408.02i	−0.104910	−	0.181710i
$561$	765.324	+	1325.58i	0.0575972	+	0.0997612i
$562$	1558.74			0.116995
$563$	−6154.63			−0.460722			−0.230361	−	0.973105i	$-0.573991\pi$
$563$	−6154.63			−0.460722			−0.230361	+	0.973105i	$0.573991\pi$
$564$	−1158.74	−	2007.00i	−0.0865105	−	0.149841i
$565$	−2484.57	+	4303.39i	−0.185003	+	0.320434i
$566$	−8800.19	−	15242.4i	−0.653533	−	1.13195i
$567$	2300.06	−	3983.82i	0.170359	−	0.295070i
$568$	−2654.60	+	4597.91i	−0.196100	+	0.339655i
$569$	−14284.3			−1.05243			−0.526213	−	0.850353i	$-0.676388\pi$
$569$	−14284.3			−1.05243			−0.526213	+	0.850353i	$0.676388\pi$
$570$	−1081.33	+	1223.95i	−0.0794594	+	0.0899396i
$571$	6698.43			0.490929			0.245464	−	0.969406i	$-0.421060\pi$
$571$	6698.43			0.490929			0.245464	+	0.969406i	$0.421060\pi$
$572$	6560.10	−	11362.4i	0.479531	−	0.830572i
$573$	1284.74	−	2225.24i	0.0936666	−	0.162235i
$574$	−943.031	−	1633.38i	−0.0685738	−	0.118773i
$575$	3570.94	−	6185.05i	0.258989	−	0.448582i
$576$	−3453.16	−	5981.05i	−0.249795	−	0.432657i
$577$	18843.0			1.35952			0.679761	−	0.733434i	$-0.262084\pi$
$577$	18843.0			1.35952			0.679761	+	0.733434i	$0.262084\pi$
$578$	8249.00			0.593622
$579$	345.390	+	598.232i	0.0247909	+	0.0429390i
$580$	3543.37	+	6137.30i	0.253673	+	0.439375i
$581$	−10045.8			−0.717331
$582$	−3804.17			−0.270942
$583$	−4286.41	−	7424.29i	−0.304503	−	0.527414i
$584$	−865.364	+	1498.85i	−0.0613168	+	0.106204i
$585$	4883.89	+	8459.15i	0.345169	+	0.597851i
$586$	−5618.16	+	9730.93i	−0.396048	+	0.685974i
$587$	−632.666	+	1095.81i	−0.0444854	+	0.0770510i	−0.887411	−	0.460980i	$-0.847498\pi$
$587$	−632.666	+	1095.81i	−0.0444854	+	0.0770510i	0.842925	+	0.538031i	$0.180831\pi$
$588$	−1823.31			−0.127878
$589$	−802.332	+	908.155i	−0.0561282	+	0.0635312i
$590$	−10604.3			−0.739955
$591$	−863.464	+	1495.56i	−0.0600984	+	0.104094i
$592$	14174.0	−	24550.1i	0.984034	−	1.70440i
$593$	9330.90	+	16161.6i	0.646162	+	1.11919i	0.984032	+	0.177993i	$0.0569603\pi$
$593$	9330.90	+	16161.6i	0.646162	+	1.11919i	−0.337870	+	0.941193i	$0.609706\pi$
$594$	2930.37	−	5075.55i	0.202415	−	0.350593i
$595$	967.387	+	1675.56i	0.0666538	+	0.115448i
$596$	−6729.01			−0.462468
$597$	−3623.68			−0.248421
$598$	9910.36	+	17165.2i	0.677700	+	1.17381i
$599$	2997.25	+	5191.38i	0.204448	+	0.354114i	0.949957	−	0.312382i	$-0.101127\pi$
$599$	2997.25	+	5191.38i	0.204448	+	0.354114i	−0.745509	+	0.666496i	$0.767794\pi$
$600$	−652.813			−0.0444183
$601$	4896.52			0.332335			0.166167	−	0.986098i	$-0.446861\pi$
$601$	4896.52			0.332335			0.166167	+	0.986098i	$0.446861\pi$
$602$	879.453	+	1523.26i	0.0595412	+	0.103128i
$603$	12610.8	−	21842.6i	0.851663	−	1.47512i
$604$	−4728.17	−	8189.43i	−0.318521	−	0.551694i
$605$	1232.69	−	2135.08i	0.0828362	−	0.143477i
$606$	1770.15	−	3065.99i	0.118659	−	0.205523i
$607$	22590.6			1.51059			0.755293	−	0.655387i	$-0.227494\pi$
$607$	22590.6			1.51059			0.755293	+	0.655387i	$0.227494\pi$
$608$	−18633.3	−	3777.36i	−1.24289	−	0.251961i
$609$	1542.72			0.102650
$610$	2912.69	−	5044.92i	0.193330	−	0.334857i
$611$	−13369.8	+	23157.3i	−0.885247	+	1.53329i
$612$	4227.29	+	7321.89i	0.279213	+	0.483611i
$613$	−11986.2	+	20760.8i	−0.789754	+	1.36789i	0.136363	+	0.990659i	$0.456459\pi$
$613$	−11986.2	+	20760.8i	−0.789754	+	1.36789i	−0.926117	+	0.377235i	$0.876875\pi$
$614$	3645.73	+	6314.59i	0.239625	+	0.415042i
$615$	368.804			0.0241815
$616$	1388.88			0.0908435
$617$	−6792.09	−	11764.2i	−0.443176	−	0.767603i	0.554748	−	0.832019i	$-0.312815\pi$
$617$	−6792.09	−	11764.2i	−0.443176	−	0.767603i	−0.997923	+	0.0644161i	$0.979482\pi$
$618$	575.955	+	997.584i	0.0374892	+	0.0649332i
$619$	4821.53			0.313076			0.156538	−	0.987672i	$-0.449967\pi$
$619$	4821.53			0.313076			0.156538	+	0.987672i	$0.449967\pi$
$620$	−476.418			−0.0308603
$621$	1937.79	+	3356.35i	0.125219	+	0.216885i
$622$	−16554.2	+	28672.8i	−1.06714	+	1.84835i
$623$	−131.086	−	227.048i	−0.00842994	−	0.0146011i
$624$	2696.04	−	4669.69i	0.172962	−	0.299579i
$625$	−3061.27	+	5302.28i	−0.195922	+	0.339346i
$626$	23011.4			1.46920
$627$	−772.008	−	2301.92i	−0.0491723	−	0.146618i
$628$	−4714.87			−0.299592
$629$	−9862.65	+	17082.6i	−0.625198	+	1.08287i
$630$	1817.08	−	3147.28i	0.114912	−	0.199033i
$631$	−8603.46	−	14901.6i	−0.542786	−	0.940134i	−0.998743	−	0.0501315i	$-0.984036\pi$
$631$	−8603.46	−	14901.6i	−0.542786	−	0.940134i	0.455956	−	0.890002i	$-0.349297\pi$
$632$	995.688	−	1724.58i	0.0626683	−	0.108545i
$633$	−668.986	−	1158.72i	−0.0420060	−	0.0727565i
$634$	−20242.9			−1.26806
$635$	−2812.39			−0.175758
$636$	910.621	+	1577.24i	0.0567743	+	0.0983360i
$637$	10518.9	+	18219.2i	0.654275	+	1.13324i
$638$	−24068.0			−1.49351
$639$	−20652.2			−1.27854
$640$	2181.55	+	3778.55i	0.134739	+	0.233376i
$641$	13214.3	−	22887.8i	0.814247	−	1.41032i	−0.0956196	−	0.995418i	$-0.530483\pi$
$641$	13214.3	−	22887.8i	0.814247	−	1.41032i	0.909867	−	0.414900i	$-0.136183\pi$
$642$	613.569	+	1062.73i	0.0377190	+	0.0653313i
$643$	−2984.35	+	5169.05i	−0.183035	+	0.317026i	−0.942913	−	0.333040i	$-0.891925\pi$
$643$	−2984.35	+	5169.05i	−0.183035	+	0.317026i	0.759878	+	0.650066i	$0.225259\pi$
$644$	1614.00	−	2795.53i	0.0987584	−	0.171055i
$645$	−343.939			−0.0209963
$646$	15985.6	+	3240.61i	0.973596	+	0.197369i
$647$	−28557.3			−1.73525			−0.867624	−	0.497221i	$-0.834354\pi$
$647$	−28557.3			−1.73525			−0.867624	+	0.497221i	$0.834354\pi$
$648$	−2168.96	+	3756.74i	−0.131489	+	0.227745i
$649$	7882.26	−	13652.5i	0.476742	−	0.825741i
$650$	−13236.8	−	22926.7i	−0.798751	−	1.38348i
$651$	−51.8559	+	89.8171i	−0.00312196	+	0.00540739i
$652$	12248.1	+	21214.4i	0.735695	+	1.27426i
$653$	−10621.5			−0.636529			−0.318264	−	0.948002i	$-0.603100\pi$
$653$	−10621.5			−0.636529			−0.318264	+	0.948002i	$0.603100\pi$
$654$	5101.82			0.305041
$655$	−6833.56	−	11836.1i	−0.407648	−	0.706067i
$656$	2646.67	+	4584.17i	0.157523	+	0.272838i
$657$	−6732.34			−0.399777
$658$	9948.67			0.589422
$659$	−14653.8	−	25381.2i	−0.866209	−	1.50032i	−0.865841	−	0.500319i	$-0.833216\pi$
$659$	−14653.8	−	25381.2i	−0.866209	−	1.50032i	−0.000368192	−	1.00000i	$-0.500117\pi$
$660$	477.264	−	826.646i	0.0281477	−	0.0487532i
$661$	12656.7	+	21922.0i	0.744761	+	1.28996i	0.950307	+	0.311316i	$0.100770\pi$
$661$	12656.7	+	21922.0i	0.744761	+	1.28996i	−0.205546	+	0.978647i	$0.565897\pi$
$662$	10466.5	−	18128.5i	0.614489	−	1.06433i
$663$	−1875.98	+	3249.29i	−0.109890	+	0.190335i
$664$	9473.17			0.553660
$665$	−975.836	−	2909.67i	−0.0569042	−	0.169673i
$666$	37050.8			2.15569
$667$	7957.80	−	13783.3i	0.461960	−	0.800138i
$668$	−7769.59	+	13457.3i	−0.450022	+	0.779460i
$669$	607.098	+	1051.53i	0.0350849	+	0.0607688i
$670$	9564.84	−	16566.8i	0.551526	−	0.955270i
$671$	4330.03	+	7499.84i	0.249119	+	0.431487i
$672$	−1627.15			−0.0934059
$673$	−19742.0			−1.13076			−0.565379	−	0.824831i	$-0.691270\pi$
$673$	−19742.0			−1.13076			−0.565379	+	0.824831i	$0.691270\pi$
$674$	5916.11	+	10247.0i	0.338101	+	0.585608i
$675$	−2588.20	−	4482.90i	−0.147585	−	0.255625i
$676$	18477.6			1.05130
$677$	16806.5			0.954101			0.477050	−	0.878876i	$-0.341706\pi$
$677$	16806.5			0.954101			0.477050	+	0.878876i	$0.341706\pi$
$678$	1792.61	+	3104.90i	0.101541	+	0.175875i
$679$	3574.23	−	6190.75i	0.202012	−	0.349895i
$680$	−912.246	−	1580.06i	−0.0514457	−	0.0891065i
$681$	−808.062	+	1399.60i	−0.0454699	+	0.0787561i
$682$	809.004	−	1401.24i	0.0454228	−	0.0786746i
$683$	19613.8			1.09883			0.549416	−	0.835549i	$-0.314850\pi$
$683$	19613.8			1.09883			0.549416	+	0.835549i	$0.314850\pi$
$684$	−4264.21	−	12714.7i	−0.238372	−	0.710759i
$685$	5782.50			0.322537
$686$	8498.83	−	14720.4i	0.473013	−	0.819283i
$687$	−2268.07	+	3928.41i	−0.125957	+	0.218163i
$688$	−2468.23	−	4275.11i	−0.136774	−	0.236900i
$689$	10506.9	−	18198.6i	0.580962	−	1.00626i
$690$	721.004	+	1248.81i	0.0397799	+	0.0689008i
$691$	−26813.1			−1.47615			−0.738073	−	0.674721i	$-0.764264\pi$
$691$	−26813.1			−1.47615			−0.738073	+	0.674721i	$0.764264\pi$
$692$	−10804.4			−0.593529
$693$	2701.30	+	4678.78i	0.148072	+	0.256468i
$694$	10321.0	+	17876.5i	0.564525	+	0.977786i
$695$	−7305.11			−0.398703
$696$	−1454.79			−0.0792292
$697$	−1841.62	−	3189.78i	−0.100081	−	0.173345i
$698$	−9625.26	+	16671.4i	−0.521951	+	0.904045i
$699$	−12.1721	−	21.0828i	−0.000658645	−	0.00114081i
$700$	−2155.73	+	3733.84i	−0.116399	+	0.201608i
$701$	−11880.8	+	20578.2i	−0.640133	+	1.10874i	0.345269	+	0.938504i	$0.387788\pi$
$701$	−11880.8	+	20578.2i	−0.640133	+	1.10874i	−0.985403	+	0.170240i	$0.945546\pi$
$702$	14366.0			0.772377
$703$	20715.9	−	23448.2i	1.11140	−	1.25799i
$704$	7787.15			0.416888
$705$	−972.690	+	1684.75i	−0.0519626	+	0.0900019i
$706$	−4777.88	+	8275.53i	−0.254700	+	0.441153i
$707$	3326.30	+	5761.33i	0.176943	+	0.306474i
$708$	−1674.53	+	2900.38i	−0.0888882	+	0.153959i
$709$	−16797.5	−	29094.2i	−0.889766	−	1.54112i	−0.840152	−	0.542351i	$-0.817534\pi$
$709$	−16797.5	−	29094.2i	−0.889766	−	1.54112i	−0.0496141	−	0.998768i	$-0.515799\pi$
$710$	−15663.9			−0.827967
$711$	7746.23			0.408589
$712$	123.614	+	214.106i	0.00650652	+	0.0112696i
$713$	534.976	+	926.605i	0.0280996	+	0.0486699i
$714$	1395.94			0.0731677
$715$	−11013.6			−0.576061
$716$	−4769.21	−	8260.52i	−0.248930	−	0.431159i
$717$	−1601.18	+	2773.33i	−0.0833994	+	0.144452i
$718$	−4828.77	−	8363.68i	−0.250986	−	0.434721i
$719$	4240.88	−	7345.42i	0.219970	−	0.380998i	−0.734829	−	0.678253i	$-0.762738\pi$
$719$	4240.88	−	7345.42i	0.219970	−	0.380998i	0.954798	+	0.297254i	$0.0960709\pi$
$720$	−5099.75	+	8833.02i	−0.263967	+	0.457204i
$721$	−2164.57			−0.111807
$722$	−23829.6	−	10075.6i	−1.22832	−	0.519356i
$723$	−6171.39			−0.317450
$724$	−8386.19	+	14525.3i	−0.430484	+	0.745620i
$725$	−10628.8	+	18409.7i	−0.544475	+	0.943059i
$726$	−889.385	−	1540.46i	−0.0454658	−	0.0787491i
$727$	−13353.8	+	23129.4i	−0.681243	+	1.17995i	0.293359	+	0.956002i	$0.405227\pi$
$727$	−13353.8	+	23129.4i	−0.681243	+	1.17995i	−0.974602	+	0.223945i	$0.928106\pi$
$728$	1702.23	+	2948.34i	0.0866604	+	0.150100i
$729$	−15443.0			−0.784586
$730$	−5106.23			−0.258890
$731$	1717.46	+	2974.73i	0.0868982	+	0.150512i
$732$	−919.888	−	1593.29i	−0.0464481	−	0.0804505i
$733$	10084.7			0.508165			0.254083	−	0.967182i	$-0.418226\pi$
$733$	10084.7			0.508165			0.254083	+	0.967182i	$0.418226\pi$
$734$	25631.0			1.28890
$735$	765.275	+	1325.49i	0.0384049	+	0.0665192i
$736$	−8393.33	+	14537.7i	−0.420356	+	0.728078i
$737$	14219.2	+	24628.4i	0.710680	+	1.23093i
$738$	−3459.20	+	5991.51i	−0.172540	+	0.298849i
$739$	12282.3	−	21273.5i	0.611380	−	1.05894i	−0.379628	−	0.925139i	$-0.623948\pi$
$739$	12282.3	−	21273.5i	0.611380	−	1.05894i	0.991008	−	0.133802i	$-0.0427188\pi$
$740$	12300.9			0.611067
$741$	3940.37	−	4460.09i	0.195348	−	0.221114i
$742$	−7818.35			−0.386820
$743$	−15497.5	+	26842.5i	−0.765207	+	1.32538i	0.174929	+	0.984581i	$0.444030\pi$
$743$	−15497.5	+	26842.5i	−0.765207	+	1.32538i	−0.940137	+	0.340797i	$0.889303\pi$
$744$	48.9001	−	84.6975i	0.00240963	−	0.00417360i
$745$	2824.28	+	4891.80i	0.138891	+	0.240566i
$746$	−1157.12	+	2004.19i	−0.0567896	+	0.0983625i
$747$	18424.8	+	31912.7i	0.902447	+	1.56308i
$748$	−9532.88			−0.465985
$749$	−2305.93			−0.112492
$750$	−2195.51	−	3802.73i	−0.106892	−	0.185142i
$751$	4873.06	+	8440.39i	0.236778	+	0.410112i	0.959788	−	0.280726i	$-0.0905751\pi$
$751$	4873.06	+	8440.39i	0.236778	+	0.410112i	−0.723010	+	0.690838i	$0.757242\pi$
$752$	−27921.5			−1.35398
$753$	3828.82			0.185299
$754$	−29498.0	−	51092.0i	−1.42474	−	2.46772i
$755$	−3968.99	+	6874.50i	−0.191320	+	0.331376i
$756$	−1169.82	−	2026.19i	−0.0562776	−	0.0974757i
$757$	17424.7	−	30180.5i	0.836609	−	1.44905i	−0.0561053	−	0.998425i	$-0.517868\pi$
$757$	17424.7	−	30180.5i	0.836609	−	1.44905i	0.892714	−	0.450624i	$-0.148798\pi$
$758$	11788.9	−	20418.9i	0.564896	−	0.978428i
$759$	−2143.70			−0.102519
$760$	920.214	+	2743.82i	0.0439206	+	0.130959i
$761$	30366.0			1.44647			0.723237	−	0.690600i	$-0.242654\pi$
$761$	30366.0			1.44647			0.723237	+	0.690600i	$0.242654\pi$
$762$	−1014.57	+	1757.29i	−0.0482336	+	0.0835430i
$763$	−4793.44	+	8302.48i	−0.227437	+	0.393932i
$764$	8001.38	+	13858.8i	0.378900	+	0.656275i
$765$	3548.54	−	6146.25i	0.167709	−	0.290481i
$766$	959.519	+	1661.94i	0.0452596	+	0.0783919i
$767$	38642.3			1.81916
$768$	5273.00			0.247751
$769$	−2274.82	−	3940.11i	−0.106674	−	0.184765i	0.807747	−	0.589529i	$-0.200687\pi$
$769$	−2274.82	−	3940.11i	−0.106674	−	0.184765i	−0.914421	+	0.404765i	$0.867353\pi$
$770$	2048.83	+	3548.68i	0.0958893	+	0.166085i
$771$	4254.09			0.198712
$772$	−4302.17			−0.200568
$773$	−3396.46	−	5882.85i	−0.158037	−	0.273728i	0.776124	−	0.630580i	$-0.217183\pi$
$773$	−3396.46	−	5882.85i	−0.158037	−	0.273728i	−0.934161	+	0.356853i	$0.883850\pi$
$774$	3225.98	−	5587.56i	0.149813	−	0.259484i
$775$	−714.540	−	1237.62i	−0.0331187	−	0.0573634i
$776$	−3370.50	+	5837.88i	−0.155920	+	0.270061i
$777$	1338.90	−	2319.04i	0.0618181	−	0.107072i
$778$	7564.48			0.348586
$779$	1857.71	+	5539.17i	0.0854419	+	0.254764i
$780$	2339.76			0.107406
$781$	11643.1	−	20166.4i	0.533447	−	0.923958i
$782$	7200.67	−	12471.9i	0.329278	−	0.570326i
$783$	−5767.78	−	9990.09i	−0.263249	−	0.455960i
$784$	−10983.8	+	19024.5i	−0.500354	+	0.866639i
$785$	1978.91	+	3427.58i	0.0899751	+	0.155841i
$786$	−9860.83			−0.447486
$787$	788.944			0.0357342			0.0178671	−	0.999840i	$-0.494312\pi$
$787$	788.944			0.0357342			0.0178671	+	0.999840i	$0.494312\pi$
$788$	−5377.65	−	9314.37i	−0.243110	−	0.421080i
$789$	−3321.43	−	5752.88i	−0.149868	−	0.259579i
$790$	5875.23			0.264596
$791$	−6737.04			−0.302834
$792$	−2547.32	−	4412.09i	−0.114287	−	0.197951i
$793$	−10613.9	+	18383.8i	−0.475296	+	0.823236i
$794$	12427.3	+	21524.7i	0.555450	+	0.962068i
$795$	764.407	−	1323.99i	0.0341015	−	0.0590656i
$796$	11284.1	−	19544.7i	0.502456	−	0.870280i
$797$	−28442.4			−1.26409			−0.632046	−	0.774931i	$-0.717785\pi$
$797$	−28442.4			−1.26409			−0.632046	+	0.774931i	$0.717785\pi$
$798$	−2170.11	−	439.927i	−0.0962669	−	0.0195153i
$799$	19428.5			0.860240
$800$	11210.5	−	19417.2i	0.495440	−	0.858128i
$801$	−480.846	+	832.850i	−0.0212108	+	0.0367382i
$802$	−20526.6	−	35553.1i	−0.903764	−	1.56537i
$803$	3795.49	−	6573.98i	0.166799	−	0.288905i
$804$	−3020.78	−	5232.14i	−0.132506	−	0.229507i
$805$	−2709.69			−0.118639
$806$	3966.10			0.173325
$807$	1960.17	+	3395.11i	0.0855034	+	0.148096i
$808$	−3136.71	−	5432.93i	−0.136570	−	0.236547i
$809$	−2883.47			−0.125312			−0.0626561	−	0.998035i	$-0.519957\pi$
$809$	−2883.47			−0.125312			−0.0626561	+	0.998035i	$0.519957\pi$
$810$	−12798.3			−0.555168
$811$	9282.37	+	16077.5i	0.401909	+	0.696126i	0.993956	−	0.109777i	$-0.0350136\pi$
$811$	9282.37	+	16077.5i	0.401909	+	0.696126i	−0.592048	+	0.805903i	$0.701680\pi$
$812$	−4804.03	+	8320.82i	−0.207621	+	0.359610i
$813$	3243.19	+	5617.37i	0.139906	+	0.242324i
$814$	−20888.1	+	36179.3i	−0.899421	+	1.55784i
$815$	10281.5	−	17808.1i	0.441896	−	0.765386i
$816$	−3917.78			−0.168076
$817$	−1732.46	−	5165.72i	−0.0741875	−	0.221207i
$818$	21013.9			0.898208
$819$	−6621.48	+	11468.7i	−0.282507	+	0.489316i
$820$	−1148.46	+	1989.18i	−0.0489095	+	0.0847137i
$821$	−5207.33	−	9019.35i	−0.221360	−	0.383408i	0.733861	−	0.679300i	$-0.237716\pi$
$821$	−5207.33	−	9019.35i	−0.221360	−	0.383408i	−0.955221	+	0.295892i	$0.904383\pi$
$822$	2086.04	−	3613.12i	0.0885145	−	0.153312i
$823$	−15108.8	−	26169.3i	−0.639928	−	1.10839i	−0.985448	−	0.169977i	$-0.945631\pi$
$823$	−15108.8	−	26169.3i	−0.639928	−	1.10839i	0.345520	−	0.938411i	$-0.387703\pi$
$824$	2041.19			0.0862963
$825$	2863.24			0.120830
$826$	−7188.56	−	12450.9i	−0.302811	−	0.524484i
$827$	−9683.41	−	16772.2i	−0.407165	−	0.705230i	0.587406	−	0.809292i	$-0.300149\pi$
$827$	−9683.41	−	16772.2i	−0.407165	−	0.705230i	−0.994571	+	0.104063i	$0.966816\pi$
$828$	−11840.8			−0.496977
$829$	−2567.99			−0.107588			−0.0537938	−	0.998552i	$-0.517131\pi$
$829$	−2567.99			−0.107588			−0.0537938	+	0.998552i	$0.517131\pi$
$830$	13974.5	+	24204.6i	0.584413	+	1.01223i
$831$	1197.52	−	2074.16i	0.0499896	−	0.0865846i
$832$	9544.01	+	16530.7i	0.397691	+	0.688821i
$833$	7642.80	−	13237.7i	0.317896	−	0.550612i
$834$	−2635.32	+	4564.50i	−0.109417	+	0.189515i
$835$	13044.1			0.540612
$836$	14819.7	+	3004.26i	0.613097	+	0.124288i
$837$	775.497			0.0320252
$838$	−18233.0	+	31580.4i	−0.751607	+	1.30182i
$839$	−4483.99	+	7766.49i	−0.184511	+	0.319582i	−0.943412	−	0.331624i	$-0.892403\pi$
$839$	−4483.99	+	7766.49i	−0.184511	+	0.319582i	0.758901	+	0.651206i	$0.225737\pi$
$840$	123.841	+	214.500i	0.00508682	+	0.00881064i
$841$	−11491.7	+	19904.2i	−0.471184	+	0.816115i
$842$	11481.1	+	19885.8i	0.469910	+	0.813908i
$843$	−413.239			−0.0168834
$844$	8332.88			0.339846
$845$	−7755.37	−	13432.7i	−0.315731	−	0.546863i
$846$	−18246.7	−	31604.2i	−0.741530	−	1.28437i
$847$	3342.50			0.135596
$848$	21942.6			0.888577
$849$	2333.03	+	4040.92i	0.0943102	+	0.163350i
$850$	−9617.56	+	16658.1i	−0.388094	+	0.672198i
$851$	−13812.8	−	23924.5i	−0.556402	−	0.963716i
$852$	−2473.50	+	4284.23i	−0.0994609	+	0.172271i
$853$	3262.76	−	5651.27i	0.130967	−	0.226841i	−0.793083	−	0.609114i	$-0.791525\pi$
$853$	3262.76	−	5651.27i	0.130967	−	0.226841i	0.924050	+	0.382273i	$0.124858\pi$
$854$	7897.92			0.316465
$855$	−7453.48	+	8436.55i	−0.298133	+	0.337455i
$856$	2174.49			0.0868254
$857$	4114.01	−	7125.67i	0.163981	−	0.284024i	−0.772312	−	0.635244i	$-0.780900\pi$
$857$	4114.01	−	7125.67i	0.163981	−	0.284024i	0.936293	+	0.351220i	$0.114233\pi$
$858$	−3973.14	+	6881.68i	−0.158090	+	0.273819i
$859$	20919.1	+	36232.9i	0.830907	+	1.43917i	0.897320	+	0.441381i	$0.145511\pi$
$859$	20919.1	+	36232.9i	0.830907	+	1.43917i	−0.0664128	+	0.997792i	$0.521155\pi$
$860$	1071.03	−	1855.07i	0.0424671	−	0.0735552i
$861$	250.008	+	433.027i	0.00989577	+	0.0171400i
$862$	36194.1			1.43013
$863$	19858.2			0.783291			0.391645	−	0.920116i	$-0.371906\pi$
$863$	19858.2			0.783291			0.391645	+	0.920116i	$0.371906\pi$
$864$	6083.45	+	10536.8i	0.239541	+	0.414897i
$865$	4534.80	+	7854.50i	0.178252	+	0.308741i
$866$	−1128.49			−0.0442812
$867$	−2186.90			−0.0856645
$868$	−322.958	−	559.380i	−0.0126289	−	0.0218740i
$869$	−4367.09	+	7564.02i	−0.170476	+	0.295272i
$870$	−2146.05	−	3717.07i	−0.0836298	−	0.144851i
$871$	−34854.4	+	60369.6i	−1.35591	+	2.34850i
$872$	4520.21	−	7829.24i	0.175543	−	0.304050i
$873$	−26221.7			−1.01658
$874$	−15124.5	+	17119.4i	−0.585349	+	0.662554i
$875$	8251.21			0.318791
$876$	−806.327	+	1396.60i	−0.0310996	+	0.0538661i
$877$	21820.1	−	37793.5i	0.840151	−	1.45518i	−0.0496149	−	0.998768i	$-0.515799\pi$
$877$	21820.1	−	37793.5i	0.840151	−	1.45518i	0.889766	−	0.456416i	$-0.150867\pi$
$878$	11577.4	+	20052.6i	0.445009	+	0.770778i
$879$	1489.44	−	2579.78i	0.0571529	−	0.0989918i
$880$	−5750.16	−	9959.57i	−0.220270	−	0.381519i
$881$	−22269.3			−0.851614			−0.425807	−	0.904814i	$-0.640010\pi$
$881$	−22269.3			−0.851614			−0.425807	+	0.904814i	$0.640010\pi$
$882$	−28711.6			−1.09611
$883$	−6723.37	−	11645.2i	−0.256239	−	0.443820i	0.708992	−	0.705216i	$-0.249150\pi$
$883$	−6723.37	−	11645.2i	−0.256239	−	0.443820i	−0.965231	+	0.261397i	$0.915817\pi$
$884$	−11683.6	−	20236.6i	−0.444527	−	0.769943i
$885$	2811.33			0.106782
$886$	26156.4			0.991809
$887$	−6730.60	−	11657.7i	−0.254782	−	0.441295i	0.710054	−	0.704147i	$-0.248670\pi$
$887$	−6730.60	−	11657.7i	−0.254782	−	0.441295i	−0.964836	+	0.262852i	$0.915337\pi$
$888$	−1262.58	+	2186.85i	−0.0477133	+	0.0826419i
$889$	−1906.49	−	3302.13i	−0.0719253	−	0.124578i
$890$	−364.703	+	631.685i	−0.0137358	+	0.0237912i
$891$	9513.04	−	16477.1i	0.357687	−	0.619532i
$892$	−7562.01			−0.283851
$893$	−30203.3	−	6122.85i	−1.13182	−	0.229444i
$894$	4075.44			0.152464
$895$	−4003.44	+	6934.17i	−0.149520	+	0.258976i
$896$	−2957.70	+	5122.88i	−0.110279	+	0.191008i
$897$	−2627.35	−	4550.70i	−0.0977977	−	0.169391i
$898$	12597.9	−	21820.2i	0.468148	−	0.810855i
$899$	−1592.34	−	2758.02i	−0.0590741	−	0.102319i
$900$	15815.2			0.585748
$901$	−15268.3			−0.564550
$902$	−3900.38	−	6755.65i	−0.143978	−	0.249378i
$903$	−233.153	−	403.832i	−0.00859229	−	0.0148823i
$904$	6353.03			0.233737
$905$	14079.3			0.517141
$906$	2863.63	+	4959.95i	0.105008	+	0.181880i
$907$	−7665.23	+	13276.6i	−0.280617	+	0.486043i	−0.971537	−	0.236888i	$-0.923873\pi$
$907$	−7665.23	+	13276.6i	−0.280617	+	0.486043i	0.690920	+	0.722932i	$0.257206\pi$
$908$	−5032.61	−	8716.73i	−0.183935	−	0.318585i
$909$	12201.4	−	21133.5i	0.445210	−	0.771127i
$910$	−5022.14	+	8698.60i	−0.182948	+	0.316875i
$911$	−25605.0			−0.931211			−0.465605	−	0.884992i	$-0.654163\pi$
$911$	−25605.0			−0.931211			−0.465605	+	0.884992i	$0.654163\pi$
$912$	6090.53	+	1234.68i	0.221138	+	0.0448293i
$913$	−41549.3			−1.50611
$914$	−13624.8	+	23598.8i	−0.493072	+	0.854026i
$915$	−772.186	+	1337.47i	−0.0278991	+	0.0483227i
$916$	−14125.5	−	24466.1i	−0.509520	−	0.882515i
$917$	9264.79	−	16047.1i	0.333643	−	0.577886i
$918$	−5219.01	−	9039.60i	−0.187640	−	0.325001i
$919$	22796.3			0.818260			0.409130	−	0.912476i	$-0.365832\pi$
$919$	22796.3			0.818260			0.409130	+	0.912476i	$0.365832\pi$
$920$	2555.24			0.0915693
$921$	−966.524	−	1674.07i	−0.0345798	−	0.0598941i
$922$	1085.95	+	1880.92i	0.0387895	+	0.0671854i
$923$	57079.6			2.03553
$924$	1294.13			0.0460754
$925$	18449.1	+	31954.8i	0.655787	+	1.13586i
$926$	17589.6	−	30466.1i	0.624223	−	1.08119i
$927$	3970.00	+	6876.24i	0.140660	+	0.243630i
$928$	24982.5	−	43271.0i	0.883720	−	1.53065i
$929$	−9507.88	+	16468.1i	−0.335784	+	0.581595i	−0.983635	−	0.180172i	$-0.942335\pi$
$929$	−9507.88	+	16468.1i	−0.335784	+	0.581595i	0.647851	+	0.761767i	$0.275668\pi$
$930$	288.544			0.0101739
$931$	−16053.2	+	18170.6i	−0.565116	+	0.639652i
$932$	151.616			0.00532870
$933$	4388.71	−	7601.47i	0.153998	−	0.266732i
$934$	16922.5	−	29310.7i	0.592850	−	1.02685i
$935$	4001.11	+	6930.13i	0.139947	+	0.242395i
$936$	6244.05	−	10815.0i	0.218048	−	0.377671i
$937$	5943.40	+	10294.3i	0.207217	+	0.358911i	0.950837	−	0.309692i	$-0.100226\pi$
$937$	5943.40	+	10294.3i	0.207217	+	0.358911i	−0.743620	+	0.668603i	$0.766893\pi$
$938$	25935.6			0.902802
$939$	−6100.58			−0.212018
$940$	−6057.91	−	10492.6i	−0.210199	−	0.364076i
$941$	−6692.57	−	11591.9i	−0.231851	−	0.401578i	0.726502	−	0.687164i	$-0.241145\pi$
$941$	−6692.57	−	11591.9i	−0.231851	−	0.401578i	−0.958353	+	0.285587i	$0.907811\pi$
$942$	2855.57			0.0987682
$943$	5158.46			0.178136
$944$	20175.1	+	34944.3i	0.695597	+	1.20481i
$945$	−981.986	+	1700.85i	−0.0338032	+	0.0585489i
$946$	3637.42	+	6300.19i	0.125013	+	0.216529i
$947$	−19363.6	+	33538.7i	−0.664447	+	1.15086i	0.314988	+	0.949096i	$0.398000\pi$
$947$	−19363.6	+	33538.7i	−0.664447	+	1.15086i	−0.979435	+	0.201761i	$0.935334\pi$
$948$	927.760	−	1606.93i	0.0317851	−	0.0550534i
$949$	18607.2			0.636474
$950$	20201.1	−	22865.5i	0.689905	−	0.780899i
$951$	5366.63			0.182992
$952$	1236.80	−	2142.21i	0.0421061	−	0.0729300i
$953$	8966.56	−	15530.5i	0.304780	−	0.527894i	−0.672432	−	0.740159i	$-0.734750\pi$
$953$	8966.56	−	15530.5i	0.304780	−	0.527894i	0.977212	+	0.212264i	$0.0680838\pi$
$954$	14339.5	+	24836.8i	0.486645	+	0.842893i
$955$	6716.64	−	11633.6i	0.227587	−	0.394192i
$956$	−9972.18	−	17272.3i	−0.337367	−	0.584337i
$957$	6380.69			0.215526
$958$	38374.0			1.29416
$959$	3919.90	+	6789.46i	0.131992	+	0.228616i
$960$	694.351	+	1202.65i	0.0233438	+	0.0404327i
$961$	−29576.9			−0.992813
$962$	−102403.			−3.43202
$963$	4229.26	+	7325.30i	0.141522	+	0.245124i
$964$	19217.7	−	33286.1i	0.642076	−	1.11211i
$965$	1805.70	+	3127.56i	0.0602357	+	0.104331i
$966$	−977.521	+	1693.12i	−0.0325582	+	0.0563925i
$967$	2228.90	−	3860.56i	0.0741225	−	0.128384i	−0.826582	−	0.562817i	$-0.809718\pi$
$967$	2228.90	−	3860.56i	0.0741225	−	0.128384i	0.900704	+	0.434433i	$0.143051\pi$
$968$	−3151.98			−0.104658
$969$	−4237.95	−	859.122i	−0.140498	−	0.0284819i
$970$	−19888.2			−0.658321
$971$	11366.9	−	19688.0i	0.375676	−	0.650689i	−0.614752	−	0.788720i	$-0.710744\pi$
$971$	11366.9	−	19688.0i	0.375676	−	0.650689i	0.990428	+	0.138031i	$0.0440774\pi$
$972$	−6477.12	+	11218.7i	−0.213738	+	0.370206i
$973$	−4952.05	−	8577.21i	−0.163161	−	0.282603i
$974$	−34271.9	+	59360.7i	−1.12746	+	1.95281i
$975$	3509.21	+	6078.14i	0.115266	+	0.199647i
$976$	−22165.9			−0.726962
$977$	−40581.2			−1.32887			−0.664435	−	0.747346i	$-0.731328\pi$
$977$	−40581.2			−1.32887			−0.664435	+	0.747346i	$0.731328\pi$
$978$	−7418.10	−	12848.5i	−0.242541	−	0.420093i
$979$	−542.172	−	939.070i	−0.0176996	−	0.0306566i
$980$	−9532.26			−0.310711
$981$	35166.3			1.14452
$982$	10692.0	+	18519.2i	0.347451	+	0.601803i
$983$	6635.59	−	11493.2i	0.215303	−	0.372915i	−0.738064	−	0.674731i	$-0.764260\pi$
$983$	6635.59	−	11493.2i	0.215303	−	0.372915i	0.953366	+	0.301816i	$0.0975929\pi$
$984$	−235.758	−	408.345i	−0.00763789	−	0.0132292i
$985$	−4514.19	+	7818.81i	−0.146024	+	0.252922i
$986$	−21432.6	+	37122.4i	−0.692245	+	1.19900i
$987$	−2637.50			−0.0850585
$988$	11785.6	+	35141.5i	0.379505	+	1.13158i
$989$	−4810.68			−0.154672
$990$	7515.46	−	13017.2i	0.241270	−	0.417891i
$991$	−20603.2	+	35685.8i	−0.660426	+	1.14389i	0.320078	+	0.947391i	$0.396291\pi$
$991$	−20603.2	+	35685.8i	−0.660426	+	1.14389i	−0.980504	+	0.196500i	$0.937042\pi$
$992$	1679.49	+	2908.97i	0.0537540	+	0.0931046i
$993$	−2774.79	+	4806.07i	−0.0886759	+	0.153591i
$994$	−10618.4	−	18391.6i	−0.338828	−	0.586868i
$995$	−18944.6			−0.603601
$996$	8826.89			0.280814
$997$	19382.2	+	33571.0i	0.615689	+	1.06640i	0.990263	+	0.139208i	$0.0444555\pi$
$997$	19382.2	+	33571.0i	0.615689	+	1.06640i	−0.374574	+	0.927197i	$0.622211\pi$
$998$	18544.4	+	32119.8i	0.588189	+	1.01877i
$999$	−20023.0			−0.634133

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	19.4.c.b.11.2	yes	4
3.2	odd	2		171.4.f.d.163.1		4
4.3	odd	2		304.4.i.d.49.2		4
19.7	even	3	inner	19.4.c.b.7.2	✓	4
19.8	odd	6		361.4.a.e.1.2		2
19.11	even	3		361.4.a.f.1.1		2
57.26	odd	6		171.4.f.d.64.1		4
76.7	odd	6		304.4.i.d.273.2		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.c.b.7.2	✓	4	19.7	even	3	inner
19.4.c.b.11.2	yes	4	1.1	even	1	trivial
171.4.f.d.64.1		4	57.26	odd	6
171.4.f.d.163.1		4	3.2	odd	2
304.4.i.d.49.2		4	4.3	odd	2
304.4.i.d.273.2		4	76.7	odd	6
361.4.a.e.1.2		2	19.8	odd	6
361.4.a.f.1.1		2	19.11	even	3

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:	\( N \)	\(=\)	\( 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	19.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.88600 - 3.26665i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-3.11400 - 5.39360i) q^{4} +(-2.61400 + 4.52758i) q^{5} +(1.88600 + 3.26665i) q^{6} -7.08801 q^{7} +6.68399 q^{8} +(13.0000 + 22.5167i) q^{9} +O(q^{10})\)	\(q+(1.88600 - 3.26665i) q^{2} +(-0.500000 + 0.866025i) q^{3} +(-3.11400 - 5.39360i) q^{4} +(-2.61400 + 4.52758i) q^{5} +(1.88600 + 3.26665i) q^{6} -7.08801 q^{7} +6.68399 q^{8} +(13.0000 + 22.5167i) q^{9} +(9.86001 + 17.0780i) q^{10} -29.3160 q^{11} +6.22800 q^{12} +(-35.9300 - 62.2326i) q^{13} +(-13.3680 + 23.1540i) q^{14} +(-2.61400 - 4.52758i) q^{15} +(37.5180 - 64.9831i) q^{16} +(-26.1060 + 45.2170i) q^{17} +98.0720 q^{18} +(54.8340 - 62.0663i) q^{19} +32.5600 q^{20} +(3.54400 - 6.13839i) q^{21} +(-55.2900 + 95.7651i) q^{22} +(-36.5620 - 63.3273i) q^{23} +(-3.34200 + 5.78851i) q^{24} +(48.8340 + 84.5830i) q^{25} -271.056 q^{26} -53.0000 q^{27} +(22.0720 + 38.2299i) q^{28} +(108.826 + 188.492i) q^{29} -19.7200 q^{30} -14.6320 q^{31} +(-114.782 - 198.808i) q^{32} +(14.6580 - 25.3884i) q^{33} +(98.4720 + 170.558i) q^{34} +(18.5280 - 32.0915i) q^{35} +(80.9640 - 140.234i) q^{36} +377.792 q^{37} +(-99.3320 - 296.181i) q^{38} +71.8600 q^{39} +(-17.4720 + 30.2623i) q^{40} +(-35.2720 + 61.0929i) q^{41} +(-13.3680 - 23.1540i) q^{42} +(32.8940 - 56.9740i) q^{43} +(91.2900 + 158.119i) q^{44} -135.928 q^{45} -275.824 q^{46} +(-186.054 - 322.255i) q^{47} +(37.5180 + 64.9831i) q^{48} -292.760 q^{49} +368.404 q^{50} +(-26.1060 - 45.2170i) q^{51} +(-223.772 + 387.584i) q^{52} +(146.214 + 253.250i) q^{53} +(-99.9580 + 173.132i) q^{54} +(76.6320 - 132.731i) q^{55} -47.3762 q^{56} +(26.3340 + 78.5208i) q^{57} +820.984 q^{58} +(-268.872 + 465.700i) q^{59} +(-16.2800 + 28.1978i) q^{60} +(-147.702 - 255.827i) q^{61} +(-27.5960 + 47.7977i) q^{62} +(-92.1441 - 159.598i) q^{63} -265.628 q^{64} +375.684 q^{65} +(-55.2900 - 95.7651i) q^{66} +(-485.032 - 840.100i) q^{67} +325.176 q^{68} +73.1240 q^{69} +(-69.8878 - 121.049i) q^{70} +(-397.158 + 687.898i) q^{71} +(86.8919 + 150.501i) q^{72} +(-129.468 + 224.245i) q^{73} +(712.516 - 1234.11i) q^{74} -97.6680 q^{75} +(-505.514 - 102.478i) q^{76} +207.792 q^{77} +(135.528 - 234.741i) q^{78} +(148.966 - 258.017i) q^{79} +(196.144 + 339.732i) q^{80} +(-324.500 + 562.050i) q^{81} +(133.046 + 230.443i) q^{82} +1417.29 q^{83} -44.1441 q^{84} +(-136.482 - 236.394i) q^{85} +(-124.076 - 214.906i) q^{86} -217.652 q^{87} -195.948 q^{88} +(18.4941 + 32.0327i) q^{89} +(-256.360 + 444.029i) q^{90} +(254.672 + 441.105i) q^{91} +(-227.708 + 394.402i) q^{92} +(7.31601 - 12.6717i) q^{93} -1403.59 q^{94} +(137.674 + 410.507i) q^{95} +229.564 q^{96} +(-504.264 + 873.411i) q^{97} +(-552.146 + 956.345i) q^{98} +(-381.108 - 660.099i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - q^{2} - 2 q^{3} - 21 q^{4} - 19 q^{5} - q^{6} + 40 q^{7} + 78 q^{8} + 52 q^{9}+O(q^{10}) \) 4 * q - q^2 - 2 * q^3 - 21 * q^4 - 19 * q^5 - q^6 + 40 * q^7 + 78 * q^8 + 52 * q^9	\( 4 q - q^{2} - 2 q^{3} - 21 q^{4} - 19 q^{5} - q^{6} + 40 q^{7} + 78 q^{8} + 52 q^{9} - 46 q^{10} - 66 q^{11} + 42 q^{12} - 101 q^{13} - 156 q^{14} - 19 q^{15} + 39 q^{16} + 75 q^{17} - 52 q^{18} + 57 q^{19} + 472 q^{20} - 20 q^{21} - 93 q^{22} - q^{23} - 39 q^{24} + 33 q^{25} - 264 q^{26} - 212 q^{27} - 356 q^{28} + 85 q^{29} + 92 q^{30} + 44 q^{31} - 143 q^{32} + 33 q^{33} + 804 q^{34} - 336 q^{35} + 546 q^{36} + 896 q^{37} - 722 q^{38} + 202 q^{39} - 480 q^{40} - 124 q^{41} - 156 q^{42} + 311 q^{43} + 237 q^{44} - 988 q^{45} - 1240 q^{46} - 411 q^{47} + 39 q^{48} + 196 q^{49} + 1354 q^{50} + 75 q^{51} - 878 q^{52} - 261 q^{53} + 53 q^{54} + 204 q^{55} + 1656 q^{56} - 57 q^{57} + 2908 q^{58} - 204 q^{59} - 236 q^{60} - 531 q^{61} - 230 q^{62} + 520 q^{63} - 1934 q^{64} + 1554 q^{65} - 93 q^{66} - 556 q^{67} - 3108 q^{68} + 2 q^{69} - 1920 q^{70} - 1563 q^{71} + 1014 q^{72} + 234 q^{73} + 1090 q^{74} - 66 q^{75} + 1387 q^{76} + 216 q^{77} + 132 q^{78} + 331 q^{79} - 104 q^{80} - 1298 q^{81} + 11 q^{82} + 2918 q^{83} + 712 q^{84} + 1479 q^{85} + 922 q^{86} - 170 q^{87} - 630 q^{88} - 601 q^{89} + 1196 q^{90} - 280 q^{91} + 610 q^{92} - 22 q^{93} - 2436 q^{94} - 1235 q^{95} + 286 q^{96} + 324 q^{97} - 2969 q^{98} - 858 q^{99}+O(q^{100}) \) 4 * q - q^2 - 2 * q^3 - 21 * q^4 - 19 * q^5 - q^6 + 40 * q^7 + 78 * q^8 + 52 * q^9 - 46 * q^10 - 66 * q^11 + 42 * q^12 - 101 * q^13 - 156 * q^14 - 19 * q^15 + 39 * q^16 + 75 * q^17 - 52 * q^18 + 57 * q^19 + 472 * q^20 - 20 * q^21 - 93 * q^22 - q^23 - 39 * q^24 + 33 * q^25 - 264 * q^26 - 212 * q^27 - 356 * q^28 + 85 * q^29 + 92 * q^30 + 44 * q^31 - 143 * q^32 + 33 * q^33 + 804 * q^34 - 336 * q^35 + 546 * q^36 + 896 * q^37 - 722 * q^38 + 202 * q^39 - 480 * q^40 - 124 * q^41 - 156 * q^42 + 311 * q^43 + 237 * q^44 - 988 * q^45 - 1240 * q^46 - 411 * q^47 + 39 * q^48 + 196 * q^49 + 1354 * q^50 + 75 * q^51 - 878 * q^52 - 261 * q^53 + 53 * q^54 + 204 * q^55 + 1656 * q^56 - 57 * q^57 + 2908 * q^58 - 204 * q^59 - 236 * q^60 - 531 * q^61 - 230 * q^62 + 520 * q^63 - 1934 * q^64 + 1554 * q^65 - 93 * q^66 - 556 * q^67 - 3108 * q^68 + 2 * q^69 - 1920 * q^70 - 1563 * q^71 + 1014 * q^72 + 234 * q^73 + 1090 * q^74 - 66 * q^75 + 1387 * q^76 + 216 * q^77 + 132 * q^78 + 331 * q^79 - 104 * q^80 - 1298 * q^81 + 11 * q^82 + 2918 * q^83 + 712 * q^84 + 1479 * q^85 + 922 * q^86 - 170 * q^87 - 630 * q^88 - 601 * q^89 + 1196 * q^90 - 280 * q^91 + 610 * q^92 - 22 * q^93 - 2436 * q^94 - 1235 * q^95 + 286 * q^96 + 324 * q^97 - 2969 * q^98 - 858 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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