LMFDB - Embedded newform 37.4.e.a.27.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [37,4,Mod(11,37)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(37, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("37.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 37 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	37.e (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.18307067021$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 82 x^{14} + 2679 x^{12} + 44392 x^{10} + 392767 x^{8} + 1779258 x^{6} + 3438825 x^{4} + \cdots + 82944 $ x^16 + 82x^14 + 2679x^12 + 44392x^10 + 392767x^8 + 1779258x^6 + 3438825x^4 + 1208748*x^2 + 82944
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{12}\cdot 3^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			27.5
Root			$-0.301955i$ of defining polynomial
Character	$\chi$	$=$	37.27
Dual form			37.4.e.a.11.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.261501 - 0.150978i) q^{2} +(0.675960 + 1.17080i) q^{3} +(-3.95441 - 6.84924i) q^{4} +(17.4040 - 10.0482i) q^{5} -0.408219i q^{6} +(10.5914 + 18.3449i) q^{7} +4.80375i q^{8} +(12.5862 - 21.7999i) q^{9} +O(q^{10})$	\(q+(-0.261501 - 0.150978i) q^{2} +(0.675960 + 1.17080i) q^{3} +(-3.95441 - 6.84924i) q^{4} +(17.4040 - 10.0482i) q^{5} -0.408219i q^{6} +(10.5914 + 18.3449i) q^{7} +4.80375i q^{8} +(12.5862 - 21.7999i) q^{9} -6.06822 q^{10} -53.3435 q^{11} +(5.34605 - 9.25963i) q^{12} +(-9.28008 + 5.35786i) q^{13} -6.39629i q^{14} +(23.5288 + 13.5844i) q^{15} +(-30.9100 + 53.5377i) q^{16} +(58.6576 + 33.8660i) q^{17} +(-6.58258 + 3.80046i) q^{18} +(-59.0317 + 34.0820i) q^{19} +(-137.645 - 79.4695i) q^{20} +(-14.3188 + 24.8009i) q^{21} +(13.9494 + 8.05367i) q^{22} +137.471i q^{23} +(-5.62422 + 3.24715i) q^{24} +(139.433 - 241.505i) q^{25} +3.23567 q^{26} +70.5328 q^{27} +(83.7659 - 145.087i) q^{28} +202.800i q^{29} +(-4.10188 - 7.10466i) q^{30} -214.828i q^{31} +(49.4474 - 28.5485i) q^{32} +(-36.0581 - 62.4544i) q^{33} +(-10.2260 - 17.7120i) q^{34} +(368.667 + 212.850i) q^{35} -199.083 q^{36} +(-165.387 + 152.643i) q^{37} +20.5825 q^{38} +(-12.5459 - 7.24339i) q^{39} +(48.2691 + 83.6046i) q^{40} +(-89.4937 - 155.008i) q^{41} +(7.48876 - 4.32364i) q^{42} -173.529i q^{43} +(210.942 + 365.362i) q^{44} -505.873i q^{45} +(20.7550 - 35.9488i) q^{46} -84.7846 q^{47} -83.5758 q^{48} +(-52.8576 + 91.5521i) q^{49} +(-72.9238 + 42.1026i) q^{50} +91.5682i q^{51} +(73.3945 + 42.3743i) q^{52} +(-193.547 + 335.233i) q^{53} +(-18.4444 - 10.6489i) q^{54} +(-928.390 + 536.006i) q^{55} +(-88.1245 + 50.8787i) q^{56} +(-79.8061 - 46.0761i) q^{57} +(30.6183 - 53.0325i) q^{58} +(109.309 + 63.1098i) q^{59} -214.873i q^{60} +(380.801 - 219.855i) q^{61} +(-32.4342 + 56.1776i) q^{62} +533.223 q^{63} +477.320 q^{64} +(-107.674 + 186.496i) q^{65} +21.7758i q^{66} +(-171.325 - 296.744i) q^{67} -535.680i q^{68} +(-160.951 + 92.9249i) q^{69} +(-64.2713 - 111.321i) q^{70} +(0.101892 + 0.176482i) q^{71} +(104.721 + 60.4608i) q^{72} -1.97518 q^{73} +(66.2947 - 14.9466i) q^{74} +377.005 q^{75} +(466.871 + 269.548i) q^{76} +(-564.985 - 978.582i) q^{77} +(2.18718 + 3.78831i) q^{78} +(-28.7722 + 16.6116i) q^{79} +1242.36i q^{80} +(-292.149 - 506.017i) q^{81} +54.0462i q^{82} +(225.261 - 390.163i) q^{83} +226.490 q^{84} +1361.17 q^{85} +(-26.1990 + 45.3780i) q^{86} +(-237.438 + 137.085i) q^{87} -256.249i q^{88} +(-150.387 - 86.8260i) q^{89} +(-76.3756 + 132.286i) q^{90} +(-196.579 - 113.495i) q^{91} +(941.572 - 543.617i) q^{92} +(251.520 - 145.215i) q^{93} +(22.1713 + 12.8006i) q^{94} +(-684.925 + 1186.33i) q^{95} +(66.8489 + 38.5952i) q^{96} -829.748i q^{97} +(27.6446 - 15.9606i) q^{98} +(-671.389 + 1162.88i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 6 q^{2} - 3 q^{3} + 18 q^{4} + 18 q^{5} + 23 q^{7} - 53 q^{9}+O(q^{10}) $ 16 * q - 6 * q^2 - 3 * q^3 + 18 * q^4 + 18 * q^5 + 23 * q^7 - 53 * q^9	\( 16 q - 6 q^{2} - 3 q^{3} + 18 q^{4} + 18 q^{5} + 23 q^{7} - 53 q^{9} - 4 q^{10} + 36 q^{11} + 14 q^{12} - 9 q^{13} - 93 q^{15} + 90 q^{16} - 210 q^{17} - 144 q^{18} - 135 q^{19} - 18 q^{20} + 71 q^{21} + 18 q^{22} - 126 q^{24} - 72 q^{25} - 276 q^{26} + 1170 q^{27} + 256 q^{28} - 236 q^{30} - 552 q^{32} + 336 q^{33} + 274 q^{34} - 27 q^{35} + 180 q^{36} - 33 q^{37} + 1344 q^{38} - 909 q^{39} - 756 q^{40} + 642 q^{41} + 846 q^{42} - 6 q^{44} + 74 q^{46} - 468 q^{47} - 284 q^{48} + 187 q^{49} - 1932 q^{50} + 180 q^{52} - 249 q^{53} - 342 q^{54} + 162 q^{55} - 996 q^{56} - 141 q^{57} - 1496 q^{58} - 1455 q^{59} + 1188 q^{61} - 510 q^{62} - 3472 q^{63} + 3476 q^{64} + 579 q^{65} - 1033 q^{67} + 810 q^{69} + 2934 q^{70} + 2319 q^{71} + 5196 q^{72} - 1672 q^{73} - 1110 q^{74} + 4364 q^{75} - 3450 q^{76} - 2472 q^{77} + 2622 q^{78} + 1569 q^{79} - 1508 q^{81} + 975 q^{83} + 3064 q^{84} + 3128 q^{85} - 36 q^{86} - 5892 q^{87} + 522 q^{89} - 2908 q^{90} - 1773 q^{91} - 3462 q^{92} + 222 q^{93} - 1614 q^{94} - 4311 q^{95} + 378 q^{96} + 5748 q^{98} - 3606 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 3 * q^3 + 18 * q^4 + 18 * q^5 + 23 * q^7 - 53 * q^9 - 4 * q^10 + 36 * q^11 + 14 * q^12 - 9 * q^13 - 93 * q^15 + 90 * q^16 - 210 * q^17 - 144 * q^18 - 135 * q^19 - 18 * q^20 + 71 * q^21 + 18 * q^22 - 126 * q^24 - 72 * q^25 - 276 * q^26 + 1170 * q^27 + 256 * q^28 - 236 * q^30 - 552 * q^32 + 336 * q^33 + 274 * q^34 - 27 * q^35 + 180 * q^36 - 33 * q^37 + 1344 * q^38 - 909 * q^39 - 756 * q^40 + 642 * q^41 + 846 * q^42 - 6 * q^44 + 74 * q^46 - 468 * q^47 - 284 * q^48 + 187 * q^49 - 1932 * q^50 + 180 * q^52 - 249 * q^53 - 342 * q^54 + 162 * q^55 - 996 * q^56 - 141 * q^57 - 1496 * q^58 - 1455 * q^59 + 1188 * q^61 - 510 * q^62 - 3472 * q^63 + 3476 * q^64 + 579 * q^65 - 1033 * q^67 + 810 * q^69 + 2934 * q^70 + 2319 * q^71 + 5196 * q^72 - 1672 * q^73 - 1110 * q^74 + 4364 * q^75 - 3450 * q^76 - 2472 * q^77 + 2622 * q^78 + 1569 * q^79 - 1508 * q^81 + 975 * q^83 + 3064 * q^84 + 3128 * q^85 - 36 * q^86 - 5892 * q^87 + 522 * q^89 - 2908 * q^90 - 1773 * q^91 - 3462 * q^92 + 222 * q^93 - 1614 * q^94 - 4311 * q^95 + 378 * q^96 + 5748 * q^98 - 3606 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/37\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{6}\right)$

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 $

$2$	−0.261501	−	0.150978i	−0.0924546	−	0.0533787i	0.453060	−	0.891480i	$-0.350332\pi$
$2$	−0.261501	−	0.150978i	−0.0924546	−	0.0533787i	−0.545514	+	0.838101i	$0.683666\pi$
$3$	0.675960	+	1.17080i	0.130089	+	0.225320i	0.923711	−	0.383091i	$-0.125140\pi$
$3$	0.675960	+	1.17080i	0.130089	+	0.225320i	−0.793622	+	0.608411i	$0.791807\pi$
$4$	−3.95441	−	6.84924i	−0.494301	−	0.856155i
$5$	17.4040	−	10.0482i	1.55666	−	0.898739i	0.559089	−	0.829107i	$-0.311151\pi$
$5$	17.4040	−	10.0482i	1.55666	−	0.898739i	0.997573	−	0.0696319i	$-0.0221825\pi$
$6$		−	0.408219i		−	0.0277758i
$7$	10.5914	+	18.3449i	0.571885	+	0.990533i	0.996372	+	0.0850995i	$0.0271208\pi$
$7$	10.5914	+	18.3449i	0.571885	+	0.990533i	−0.424488	+	0.905434i	$0.639546\pi$
$8$			4.80375i			0.212298i
$9$	12.5862	−	21.7999i	0.466154	−	0.807402i
$10$	−6.06822			−0.191894
$11$	−53.3435			−1.46215			−0.731075	−	0.682297i	$-0.760981\pi$
$11$	−53.3435			−1.46215			−0.731075	+	0.682297i	$0.760981\pi$
$12$	5.34605	−	9.25963i	0.128606	−	0.222752i
$13$	−9.28008	+	5.35786i	−0.197987	+	0.114308i	−0.595716	−	0.803195i	$-0.703132\pi$
$13$	−9.28008	+	5.35786i	−0.197987	+	0.114308i	0.397729	+	0.917503i	$0.369798\pi$
$14$		−	6.39629i		−	0.122106i
$15$	23.5288	+	13.5844i	0.405008	+	0.233831i
$16$	−30.9100	+	53.5377i	−0.482969	+	0.836527i
$17$	58.6576	+	33.8660i	0.836856	+	0.483159i	0.856194	−	0.516654i	$-0.172823\pi$
$17$	58.6576	+	33.8660i	0.836856	+	0.483159i	−0.0193384	+	0.999813i	$0.506156\pi$
$18$	−6.58258	+	3.80046i	−0.0861961	+	0.0497653i
$19$	−59.0317	+	34.0820i	−0.712779	+	0.411523i	−0.812089	−	0.583533i	$-0.801670\pi$
$19$	−59.0317	+	34.0820i	−0.712779	+	0.411523i	0.0993103	+	0.995057i	$0.468336\pi$
$20$	−137.645	−	79.4695i	−1.53892	−	0.888496i
$21$	−14.3188	+	24.8009i	−0.148791	+	0.257714i
$22$	13.9494	+	8.05367i	0.135183	+	0.0780477i
$23$			137.471i			1.24629i	0.782106	+	0.623145i	$0.214145\pi$
$23$			137.471i			1.24629i	−0.782106	+	0.623145i	$0.785855\pi$
$24$	−5.62422	+	3.24715i	−0.0478350	+	0.0276175i
$25$	139.433	−	241.505i	1.11546	−	1.93204i
$26$	3.23567			0.0244064
$27$	70.5328			0.502742
$28$	83.7659	−	145.087i	0.565367	−	0.979244i
$29$			202.800i			1.29859i	0.760537	+	0.649294i	$0.224936\pi$
$29$			202.800i			1.29859i	−0.760537	+	0.649294i	$0.775064\pi$
$30$	−4.10188	−	7.10466i	−0.0249632	−	0.0432376i
$31$		−	214.828i		−	1.24465i	−0.782759	−	0.622325i	$-0.786188\pi$
$31$		−	214.828i		−	1.24465i	0.782759	−	0.622325i	$-0.213812\pi$
$32$	49.4474	−	28.5485i	0.273161	−	0.157709i
$33$	−36.0581	−	62.4544i	−0.190209	−	0.329452i
$34$	−10.2260	−	17.7120i	−0.0515808	−	0.0893405i
$35$	368.667	+	212.850i	1.78046	+	1.02795i
$36$	−199.083			−0.921682
$37$	−165.387	+	152.643i	−0.734852	+	0.678228i
$37$	−165.387	+	152.643i	−0.734852	+	0.678228i
$38$	20.5825			0.0878662
$39$	−12.5459	−	7.24339i	−0.0515117	−	0.0297403i
$40$	48.2691	+	83.6046i	0.190800	+	0.330476i
$41$	−89.4937	−	155.008i	−0.340892	−	0.590442i	0.643707	−	0.765272i	$-0.277396\pi$
$41$	−89.4937	−	155.008i	−0.340892	−	0.590442i	−0.984599	+	0.174830i	$0.944062\pi$
$42$	7.48876	−	4.32364i	0.0275129	−	0.0158846i
$43$		−	173.529i		−	0.615417i	−0.951481	−	0.307708i	$-0.900438\pi$
$43$		−	173.529i		−	0.615417i	0.951481	−	0.307708i	$-0.0995621\pi$
$44$	210.942	+	365.362i	0.722743	+	1.25183i
$45$		−	505.873i		−	1.67580i
$46$	20.7550	−	35.9488i	0.0665253	−	0.115225i
$47$	−84.7846			−0.263130			−0.131565	−	0.991308i	$-0.542000\pi$
$47$	−84.7846			−0.263130			−0.131565	+	0.991308i	$0.542000\pi$
$48$	−83.5758			−0.251315
$49$	−52.8576	+	91.5521i	−0.154104	+	0.266916i
$50$	−72.9238	+	42.1026i	−0.206260	+	0.119084i
$51$			91.5682i			0.251414i
$52$	73.3945	+	42.3743i	0.195731	+	0.113005i
$53$	−193.547	+	335.233i	−0.501617	+	0.868827i	0.498381	+	0.866958i	$0.333928\pi$
$53$	−193.547	+	335.233i	−0.501617	+	0.868827i	−0.999998	+	0.00186865i	$0.999405\pi$
$54$	−18.4444	−	10.6489i	−0.0464808	−	0.0268357i
$55$	−928.390	+	536.006i	−2.27608	+	1.31409i
$56$	−88.1245	+	50.8787i	−0.210288	+	0.121410i
$57$	−79.8061	−	46.0761i	−0.185449	−	0.107069i
$58$	30.6183	−	53.0325i	0.0693169	−	0.120060i
$59$	109.309	+	63.1098i	0.241201	+	0.139258i	0.615729	−	0.787958i	$-0.288862\pi$
$59$	109.309	+	63.1098i	0.241201	+	0.139258i	−0.374528	+	0.927216i	$0.622195\pi$
$60$		−	214.873i		−	0.462333i
$61$	380.801	−	219.855i	0.799287	−	0.461469i	−0.0439347	−	0.999034i	$-0.513989\pi$
$61$	380.801	−	219.855i	0.799287	−	0.461469i	0.843222	+	0.537566i	$0.180656\pi$
$62$	−32.4342	+	56.1776i	−0.0664378	+	0.115074i
$63$	533.223			1.06634
$64$	477.320			0.932265
$65$	−107.674	+	186.496i	−0.205466	+	0.355877i
$66$			21.7758i			0.0406124i
$67$	−171.325	−	296.744i	−0.312399	−	0.541090i	0.666482	−	0.745521i	$-0.267799\pi$
$67$	−171.325	−	296.744i	−0.312399	−	0.541090i	−0.978881	+	0.204430i	$0.934466\pi$
$68$		−	535.680i		−	0.955305i
$69$	−160.951	+	92.9249i	−0.280814	+	0.162128i
$70$	−64.2713	−	111.321i	−0.109741	−	0.190077i
$71$	0.101892	+	0.176482i	0.000170315	+	0.000294994i	0.866111	−	0.499852i	$-0.166612\pi$
$71$	0.101892	+	0.176482i	0.000170315	+	0.000294994i	−0.865940	+	0.500147i	$0.833279\pi$
$72$	104.721	+	60.4608i	0.171410	+	0.0989635i
$73$	−1.97518			−0.00316681			−0.00158341	−	0.999999i	$-0.500504\pi$
$73$	−1.97518			−0.00316681			−0.00158341	+	0.999999i	$0.500504\pi$
$74$	66.2947	−	14.9466i	0.104143	−	0.0234799i
$75$	377.005			0.580437
$76$	466.871	+	269.548i	0.704655	+	0.406833i
$77$	−564.985	−	978.582i	−0.836181	−	1.44831i
$78$	2.18718	+	3.78831i	0.00317499	+	0.00549925i
$79$	−28.7722	+	16.6116i	−0.0409762	+	0.0236576i	−0.520348	−	0.853954i	$-0.674198\pi$
$79$	−28.7722	+	16.6116i	−0.0409762	+	0.0236576i	0.479372	+	0.877612i	$0.340864\pi$
$80$			1242.36i			1.73625i
$81$	−292.149	−	506.017i	−0.400753	−	0.694124i
$82$			54.0462i			0.0727855i
$83$	225.261	−	390.163i	0.297899	−	0.515976i	−0.677756	−	0.735287i	$-0.737048\pi$
$83$	225.261	−	390.163i	0.297899	−	0.515976i	0.975655	+	0.219311i	$0.0703809\pi$
$84$	226.490			0.294191
$85$	1361.17			1.73694
$86$	−26.1990	+	45.3780i	−0.0328501	+	0.0568981i
$87$	−237.438	+	137.085i	−0.292598	+	0.168932i
$88$		−	256.249i		−	0.310412i
$89$	−150.387	−	86.8260i	−0.179112	−	0.103411i	0.407763	−	0.913088i	$-0.366309\pi$
$89$	−150.387	−	86.8260i	−0.179112	−	0.103411i	−0.586876	+	0.809677i	$0.699642\pi$
$90$	−76.3756	+	132.286i	−0.0894521	+	0.154936i
$91$	−196.579	−	113.495i	−0.226451	−	0.130742i
$92$	941.572	−	543.617i	1.06702	−	0.616043i
$93$	251.520	−	145.215i	0.280445	−	0.161915i
$94$	22.1713	+	12.8006i	0.0243276	+	0.0140455i
$95$	−684.925	+	1186.33i	−0.739704	+	1.28120i
$96$	66.8489	+	38.5952i	0.0710702	+	0.0410324i
$97$		−	829.748i		−	0.868538i	−0.900783	−	0.434269i	$-0.857007\pi$
$97$		−	829.748i		−	0.868538i	0.900783	−	0.434269i	$-0.142993\pi$
$98$	27.6446	−	15.9606i	0.0284952	−	0.0164517i
$99$	−671.389	+	1162.88i	−0.681587	+	1.18054i
$100$	−2205.50			−2.20550
$101$	−461.980			−0.455136			−0.227568	−	0.973762i	$-0.573077\pi$
$101$	−461.980			−0.455136			−0.227568	+	0.973762i	$0.573077\pi$
$102$	13.8247	−	23.9452i	0.0134201	−	0.0232444i
$103$		−	925.123i		−	0.885000i	−0.896768	−	0.442500i	$-0.854092\pi$
$103$		−	925.123i		−	0.885000i	0.896768	−	0.442500i	$-0.145908\pi$
$104$	−25.7378	−	44.5792i	−0.0242673	−	0.0420322i
$105$			575.513i			0.534898i
$106$	101.225	−	58.4425i	0.0927536	−	0.0535513i
$107$	916.214	+	1586.93i	0.827792	+	1.43378i	0.899766	+	0.436372i	$0.143737\pi$
$107$	916.214	+	1586.93i	0.827792	+	1.43378i	−0.0719740	+	0.997407i	$0.522930\pi$
$108$	−278.916	−	483.096i	−0.248506	−	0.430425i
$109$	4.10484	+	2.36993i	0.00360709	+	0.00208255i	0.501802	−	0.864982i	$-0.332670\pi$
$109$	4.10484	+	2.36993i	0.00360709	+	0.00208255i	−0.498195	+	0.867065i	$0.666004\pi$
$110$	323.700			0.280578
$111$	−290.510	−	90.4541i	−0.248414	−	0.0773471i
$112$	−1309.53			−1.10481
$113$	−1678.83	−	969.273i	−1.39762	−	0.806916i	−0.403477	−	0.914990i	$-0.632199\pi$
$113$	−1678.83	−	969.273i	−1.39762	−	0.806916i	−0.994143	+	0.108073i	$0.965532\pi$
$114$	13.9129	+	24.0979i	0.0114304	+	0.0197980i
$115$	1381.34	+	2392.55i	1.12009	+	1.94005i
$116$	1389.03	−	801.956i	1.11179	−	0.641894i
$117$			269.739i			0.213140i
$118$	−19.0563	−	33.0065i	−0.0148668	−	0.0257500i
$119$			1434.76i			1.10524i
$120$	−65.2560	+	113.027i	−0.0496419	+	0.0859823i
$121$	1514.53			1.13789
$122$	−132.773			−0.0985303
$123$	120.988	−	209.558i	0.0886923	−	0.153620i
$124$	−1471.41	+	849.517i	−1.06561	+	0.615233i
$125$		−	3092.16i		−	2.21257i
$126$	−139.438	−	80.5047i	−0.0985884	−	0.0569201i
$127$	511.977	−	886.770i	0.357721	−	0.619592i	−0.629858	−	0.776710i	$-0.716887\pi$
$127$	511.977	−	886.770i	0.357721	−	0.619592i	0.987580	+	0.157118i	$0.0502204\pi$
$128$	−520.399	−	300.452i	−0.359353	−	0.207473i
$129$	203.167	−	117.299i	0.138666	−	0.0800587i
$130$	56.3136	−	32.5127i	0.0379925	−	0.0219350i
$131$	514.845	+	297.246i	0.343376	+	0.198248i	0.661764	−	0.749712i	$-0.269808\pi$
$131$	514.845	+	297.246i	0.343376	+	0.198248i	−0.318388	+	0.947960i	$0.603141\pi$
$132$	−285.177	+	493.941i	−0.188041	+	0.325697i
$133$	−1250.46	−	721.955i	−0.815254	−	0.470687i
$134$			103.465i			0.0667017i
$135$	1227.55	−	708.728i	0.782600	−	0.451834i
$136$	−162.684	+	281.777i	−0.102574	+	0.177663i
$137$	724.622			0.451888			0.225944	−	0.974140i	$-0.427453\pi$
$137$	724.622			0.451888			0.225944	+	0.974140i	$0.427453\pi$
$138$	56.1183			0.0346167
$139$	−540.156	+	935.577i	−0.329607	+	0.570897i	−0.982434	−	0.186611i	$-0.940250\pi$
$139$	−540.156	+	935.577i	−0.329607	+	0.570897i	0.652827	+	0.757507i	$0.273583\pi$
$140$		−	3366.79i		−	2.03247i
$141$	−57.3110	−	99.2656i	−0.0342302	−	0.0592885i
$142$		−	0.0615337i		−	3.63648e-5i
$143$	495.032	−	285.807i	0.289487	−	0.167135i
$144$	778.077	+	1347.67i	0.450276	+	0.779901i
$145$	2037.78	+	3529.54i	1.16709	+	2.02146i
$146$	0.516511	+	0.298208i	0.000292786	+	0.000169040i
$147$	−142.919			−0.0801886
$148$	1699.50	+	529.163i	0.943907	+	0.293898i
$149$	2700.25			1.48465			0.742326	−	0.670039i	$-0.233723\pi$
$149$	2700.25			1.48465			0.742326	+	0.670039i	$0.233723\pi$
$150$	−98.5871	−	56.9193i	−0.0536640	−	0.0309829i
$151$	−808.778	−	1400.84i	−0.435877	−	0.754961i	0.561490	−	0.827484i	$-0.310228\pi$
$151$	−808.778	−	1400.84i	−0.435877	−	0.754961i	−0.997367	+	0.0725225i	$0.976895\pi$
$152$	−163.721	−	283.574i	−0.0873655	−	0.151321i
$153$	1476.55	−	852.485i	0.780207	−	0.450453i
$154$			341.200i			0.178537i
$155$	−2158.63	−	3738.86i	−1.11862	−	1.93750i
$156$			114.573i			0.0588027i
$157$	−565.697	+	979.815i	−0.287564	+	0.498075i	−0.973228	−	0.229843i	$-0.926179\pi$
$157$	−565.697	+	979.815i	−0.287564	+	0.498075i	0.685664	+	0.727918i	$0.259512\pi$
$158$	10.0319			0.00505125
$159$	−523.320			−0.261019
$160$	573.722	−	993.716i	0.283479	−	0.491001i
$161$	−2521.89	+	1456.02i	−1.23449	+	0.712734i
$162$			176.432i			0.0855666i
$163$	−1486.93	−	858.478i	−0.714510	−	0.412523i	0.0982186	−	0.995165i	$-0.468686\pi$
$163$	−1486.93	−	858.478i	−0.714510	−	0.412523i	−0.812729	+	0.582642i	$0.802019\pi$
$164$	−707.790	+	1225.93i	−0.337007	+	0.583713i
$165$	−1255.11	−	724.638i	−0.592183	−	0.341897i
$166$	−117.812	+	68.0187i	−0.0550842	+	0.0318029i
$167$	198.982	−	114.882i	0.0922016	−	0.0532326i	−0.453190	−	0.891414i	$-0.649714\pi$
$167$	198.982	−	114.882i	0.0922016	−	0.0532326i	0.545392	+	0.838181i	$0.316381\pi$
$168$	−119.137	−	68.7840i	−0.0547122	−	0.0315881i
$169$	−1041.09	+	1803.22i	−0.473867	+	0.820762i
$170$	−355.947	−	205.506i	−0.160588	−	0.0927153i
$171$			1715.84i			0.767332i
$172$	−1188.54	+	686.205i	−0.526892	+	0.304201i
$173$	−1102.34	+	1909.30i	−0.484445	+	0.839084i	−0.999840	−	0.0178690i	$-0.994312\pi$
$173$	−1102.34	+	1909.30i	−0.484445	+	0.839084i	0.515395	+	0.856953i	$0.327645\pi$
$174$	82.7870			0.0360694
$175$	5907.19			2.55167
$176$	1648.85	−	2855.89i	0.706174	−	1.22313i
$177$			170.639i			0.0724632i
$178$	26.2176	+	45.4102i	0.0110398	+	0.0191215i
$179$		−	766.164i		−	0.319920i	−0.987123	−	0.159960i	$-0.948863\pi$
$179$		−	766.164i		−	0.319920i	0.987123	−	0.159960i	$-0.0511366\pi$
$180$	−3464.85	+	2000.43i	−1.43475	+	0.828352i
$181$	323.569	+	560.437i	0.132877	+	0.230149i	0.924784	−	0.380492i	$-0.124245\pi$
$181$	323.569	+	560.437i	0.132877	+	0.230149i	−0.791908	+	0.610641i	$0.790912\pi$
$182$	34.2704	+	59.3581i	0.0139576	+	0.0241753i
$183$	514.812	+	297.227i	0.207956	+	0.120064i
$184$	−660.377			−0.264585
$185$	−1344.61	+	4318.46i	−0.534366	+	1.71621i
$186$	−87.6968			−0.0345712
$187$	−3129.00	−	1806.53i	−1.22361	−	0.706451i
$188$	335.273	+	580.710i	0.130066	+	0.225280i
$189$	747.045	+	1293.92i	0.287511	+	0.497983i
$190$	358.217	−	206.817i	0.136778	−	0.0789688i
$191$		−	2745.66i		−	1.04015i	−0.854120	−	0.520075i	$-0.825904\pi$
$191$		−	2745.66i		−	1.04015i	0.854120	−	0.520075i	$-0.174096\pi$
$192$	322.649	+	558.845i	0.121277	+	0.210058i
$193$		−	4053.47i		−	1.51179i	−0.654693	−	0.755895i	$-0.727202\pi$
$193$		−	4053.47i		−	1.51179i	0.654693	−	0.755895i	$-0.272798\pi$
$194$	−125.273	+	216.980i	−0.0463614	+	0.0803003i
$195$	−291.133			−0.106915
$196$	836.083			0.304695
$197$	−381.471	+	660.727i	−0.137963	+	0.238959i	−0.926725	−	0.375739i	$-0.877389\pi$
$197$	−381.471	+	660.727i	−0.137963	+	0.238959i	0.788762	+	0.614698i	$0.210722\pi$
$198$	351.138	−	202.730i	0.126032	−	0.0727645i
$199$			169.461i			0.0603658i	0.999544	+	0.0301829i	$0.00960897\pi$
$199$			169.461i			0.0603658i	−0.999544	+	0.0301829i	$0.990391\pi$
$200$	1160.13	+	669.802i	0.410168	+	0.236811i
$201$	231.618	−	401.174i	0.0812790	−	0.140779i
$202$	120.808	+	69.7486i	0.0420794	+	0.0242945i
$203$	−3720.36	+	2147.95i	−1.28629	+	0.742643i
$204$	627.172	−	362.098i	0.215249	−	0.124274i
$205$	−3115.10	−	1798.50i	−1.06131	−	0.612746i
$206$	−139.673	+	241.920i	−0.0472401	+	0.0818223i
$207$	2996.85	+	1730.23i	1.00626	+	0.580963i
$208$		−	662.446i		−	0.220829i
$209$	3148.95	−	1818.05i	1.04219	−	0.601709i
$210$	86.8896	−	150.497i	0.0285522	−	0.0494538i
$211$	−5698.02			−1.85909			−0.929546	−	0.368707i	$-0.879800\pi$
$211$	−5698.02			−1.85909			−0.929546	+	0.368707i	$0.879800\pi$
$212$	3061.46			0.991801
$213$	−0.137750	+	0.238590i	−4.43121e−5	+	7.67508e-5i
$214$		−	553.312i		−	0.176746i
$215$	−1743.66	−	3020.10i	−0.553099	−	0.957996i
$216$			338.822i			0.106731i
$217$	3941.00	−	2275.34i	1.23287	−	0.711796i
$218$	−0.715613	−	1.23948i	−0.000222328	−	0.000385083i
$219$	−1.33514	−	2.31253i	−0.000411966	−	0.000713546i
$220$	7342.47	+	4239.18i	2.25013	+	1.29912i
$221$	−725.796			−0.220915
$222$	62.3120	+	67.5143i	0.0188383	+	0.0204111i
$223$	5108.92			1.53416			0.767082	−	0.641550i	$-0.221708\pi$
$223$	5108.92			1.53416			0.767082	+	0.641550i	$0.221708\pi$
$224$	1047.44	+	604.739i	0.312433	+	0.180383i
$225$	−3509.85	−	6079.24i	−1.03996	−	1.80126i
$226$	292.677	+	506.932i	0.0861442	+	0.149206i
$227$	195.439	−	112.837i	0.0571443	−	0.0329923i	−0.471156	−	0.882050i	$-0.656163\pi$
$227$	195.439	−	112.837i	0.0571443	−	0.0329923i	0.528300	+	0.849058i	$0.322830\pi$
$228$			728.815i			0.211697i
$229$	2810.31	+	4867.59i	0.810962	+	1.40463i	0.912192	+	0.409764i	$0.134389\pi$
$229$	2810.31	+	4867.59i	0.810962	+	1.40463i	−0.101230	+	0.994863i	$0.532278\pi$
$230$		−	834.204i		−	0.239156i
$231$	763.814	−	1322.96i	0.217555	−	0.376817i
$232$	−974.203			−0.275688
$233$	−671.973			−0.188937			−0.0944687	−	0.995528i	$-0.530115\pi$
$233$	−671.973			−0.188937			−0.0944687	+	0.995528i	$0.530115\pi$
$234$	40.7246	−	70.5371i	0.0113771	−	0.0197058i
$235$	−1475.59	+	851.934i	−0.409604	+	0.236485i
$236$		−	998.248i		−	0.275341i
$237$	−38.8977	−	22.4576i	−0.0106611	−	0.00615518i
$238$	216.616	−	375.191i	0.0589965	−	0.102185i
$239$	1604.89	+	926.583i	0.434358	+	0.250777i	0.701202	−	0.712963i	$-0.252647\pi$
$239$	1604.89	+	926.583i	0.434358	+	0.250777i	−0.266843	+	0.963740i	$0.585981\pi$
$240$	−1454.55	+	839.787i	−0.391213	+	0.225867i
$241$	−6322.93	+	3650.54i	−1.69002	+	0.975735i	−0.735534	+	0.677488i	$0.763069\pi$
$241$	−6322.93	+	3650.54i	−1.69002	+	0.975735i	−0.954489	+	0.298247i	$0.903598\pi$
$242$	−396.050	−	228.660i	−0.105203	−	0.0607388i
$243$	1347.15	−	2333.34i	0.355638	−	0.615983i
$244$	−3011.68	−	1738.80i	−0.790178	−	0.456209i
$245$			2124.50i			0.553997i
$246$	−63.2772	+	36.5331i	−0.0164000	+	0.00946856i
$247$	365.213	−	632.567i	0.0940806	−	0.162952i
$248$	1031.98			0.264237
$249$	609.069			0.155013
$250$	−466.847	+	808.603i	−0.118104	+	0.204562i
$251$		−	1017.55i		−	0.255885i	−0.991782	−	0.127942i	$-0.959163\pi$
$251$		−	1017.55i		−	0.255885i	0.991782	−	0.127942i	$-0.0408373\pi$
$252$	−2108.58	−	3652.17i	−0.527096	−	0.912957i
$253$		−	7333.18i		−	1.82226i
$254$	−267.765	+	154.594i	−0.0661459	+	0.0381894i
$255$	920.096	+	1593.65i	0.225956	+	0.391366i
$256$	−1818.56	−	3149.83i	−0.443983	−	0.769002i
$257$	3962.31	+	2287.64i	0.961721	+	0.555250i	0.896702	−	0.442634i	$-0.145956\pi$
$257$	3962.31	+	2287.64i	0.961721	+	0.555250i	0.0650185	+	0.997884i	$0.479289\pi$
$258$	−70.8379			−0.0170937
$259$	−4551.93	−	1417.30i	−1.09206	−	0.340027i
$260$	1703.15			0.406248
$261$	4421.02	+	2552.48i	1.04848	+	0.605342i
$262$	−89.7550	−	155.460i	−0.0211644	−	0.0366579i
$263$	1213.56	+	2101.95i	0.284531	+	0.492821i	0.972495	−	0.232923i	$-0.0748290\pi$
$263$	1213.56	+	2101.95i	0.284531	+	0.492821i	−0.687965	+	0.725744i	$0.741496\pi$
$264$	300.015	−	173.214i	0.0699420	−	0.0403810i
$265$			7779.20i			1.80329i
$266$	217.998	+	377.584i	0.0502493	+	0.0870344i
$267$		−	234.764i		−	0.0538101i
$268$	−1354.98	+	2346.90i	−0.308838	+	0.534923i
$269$	−794.850			−0.180159			−0.0900797	−	0.995935i	$-0.528712\pi$
$269$	−794.850			−0.180159			−0.0900797	+	0.995935i	$0.528712\pi$
$270$	−428.009			−0.0964732
$271$	3598.39	−	6232.59i	0.806592	−	1.39706i	−0.108619	−	0.994083i	$-0.534643\pi$
$271$	3598.39	−	6232.59i	0.806592	−	1.39706i	0.915211	−	0.402975i	$-0.132024\pi$
$272$	−3626.21	+	2093.60i	−0.808351	+	0.466702i
$273$		−	306.872i		−	0.0680321i
$274$	−189.489	−	109.402i	−0.0417791	−	0.0241212i
$275$	−7437.84	+	12882.7i	−1.63098	+	2.82494i
$276$	1272.93	+	734.926i	0.277614	+	0.160280i
$277$	−2420.71	+	1397.60i	−0.525077	+	0.303154i	−0.739010	−	0.673695i	$-0.764706\pi$
$277$	−2420.71	+	1397.60i	−0.525077	+	0.303154i	0.213932	+	0.976849i	$0.431373\pi$
$278$	282.503	−	163.103i	0.0609474	−	0.0351880i
$279$	−4683.21	−	2703.85i	−1.00493	−	0.580199i
$280$	−1022.48	+	1770.99i	−0.218232	+	0.377988i
$281$	1132.16	+	653.655i	0.240353	+	0.138768i	0.615339	−	0.788263i	$-0.289019\pi$
$281$	1132.16	+	653.655i	0.240353	+	0.138768i	−0.374986	+	0.927031i	$0.622352\pi$
$282$			34.6107i			0.00730865i
$283$	−1619.63	+	935.094i	−0.340201	+	0.196415i	−0.660361	−	0.750948i	$-0.729597\pi$
$283$	−1619.63	+	935.094i	−0.340201	+	0.196415i	0.320160	+	0.947364i	$0.396263\pi$
$284$	0.805847	−	1.39577i	0.000168374	−	0.000291632i
$285$	−1851.93			−0.384908
$286$	−172.602			−0.0356858
$287$	1895.74	−	3283.51i	0.389902	−	0.675330i
$288$		−	1437.26i		−	0.294068i
$289$	−162.693	−	281.792i	−0.0331148	−	0.0573565i
$290$		−	1230.64i		−	0.249191i
$291$	971.467	−	560.877i	0.195699	−	0.112987i
$292$	7.81067	+	13.5285i	0.00156536	+	0.00271128i
$293$	1054.85	+	1827.06i	0.210325	+	0.364293i	0.951816	−	0.306669i	$-0.0992145\pi$
$293$	1054.85	+	1827.06i	0.210325	+	0.364293i	−0.741491	+	0.670962i	$0.765881\pi$
$294$	37.3733	+	21.5775i	0.00741380	+	0.00428036i
$295$	2536.56			0.500625
$296$	−733.262	−	794.480i	−0.143986	−	0.156007i
$297$	−3762.46			−0.735085
$298$	−706.118	−	407.677i	−0.137263	−	0.0792487i
$299$	−736.550	−	1275.74i	−0.142461	−	0.246749i
$300$	−1490.83	−	2582.20i	−0.286911	−	0.496944i
$301$	3183.38	−	1837.92i	0.609591	−	0.351947i
$302$			488.430i			0.0930661i
$303$	−312.280	−	540.885i	−0.0592079	−	0.102551i
$304$		−	4213.90i		−	0.795012i
$305$	4418.30	−	7652.73i	0.829480	−	1.43670i
$306$	−514.825			−0.0961783
$307$	5696.77			1.05906			0.529531	−	0.848291i	$-0.322368\pi$
$307$	5696.77			1.05906			0.529531	+	0.848291i	$0.322368\pi$
$308$	−4468.36	+	7739.43i	−0.826651	+	1.43180i
$309$	1083.13	−	625.346i	0.199408	−	0.115128i
$310$			1303.62i			0.238841i
$311$	5344.83	+	3085.84i	0.974526	+	0.562643i	0.900613	−	0.434622i	$-0.143118\pi$
$311$	5344.83	+	3085.84i	0.974526	+	0.562643i	0.0739127	+	0.997265i	$0.476451\pi$
$312$	34.7955	−	60.2675i	0.00631380	−	0.0109358i
$313$	2051.78	+	1184.60i	0.370522	+	0.213921i	0.673687	−	0.739017i	$-0.264710\pi$
$313$	2051.78	+	1184.60i	0.370522	+	0.213921i	−0.303164	+	0.952938i	$0.598043\pi$
$314$	295.860	−	170.815i	0.0531731	−	0.0306995i
$315$	9280.21	−	5357.93i	1.65994	−	0.958366i
$316$	227.554	+	131.378i	0.0405092	+	0.0233880i
$317$	−3211.74	+	5562.90i	−0.569052	+	0.985627i	0.427608	+	0.903964i	$0.359356\pi$
$317$	−3211.74	+	5562.90i	−0.569052	+	0.985627i	−0.996660	+	0.0816627i	$0.973977\pi$
$318$	136.849	+	79.0097i	0.0241324	+	0.0139328i
$319$		−	10818.1i		−	1.89873i
$320$	8307.28	−	4796.21i	1.45122	−	0.837863i
$321$	−1238.65	+	2145.40i	−0.215373	+	0.373036i
$322$	879.304			0.152179
$323$	−4616.87			−0.795324
$324$	−2310.55	+	4002.00i	−0.396185	+	0.686213i
$325$			2988.25i			0.510025i
$326$	259.222	+	448.986i	0.0440398	+	0.0762792i
$327$			6.40792i			0.00108367i
$328$	744.619	−	429.906i	0.125350	−	0.0723707i
$329$	−897.992	−	1555.37i	−0.150480	−	0.260639i
$330$	218.808	+	378.987i	0.0365000	+	0.0632198i
$331$	4038.79	+	2331.80i	0.670670	+	0.387212i	0.796331	−	0.604862i	$-0.206772\pi$
$331$	4038.79	+	2331.80i	0.670670	+	0.387212i	−0.125660	+	0.992073i	$0.540105\pi$
$332$	−3563.10			−0.589007
$333$	1246.02	+	5526.62i	0.205049	+	0.909479i
$334$	−69.3786			−0.0113659
$335$	−5963.49	−	3443.02i	−0.972598	−	0.561530i
$336$	−885.189	−	1533.19i	−0.143723	−	0.248936i
$337$	−35.0492	−	60.7070i	−0.00566544	−	0.00981283i	0.863179	−	0.504898i	$-0.168470\pi$
$337$	−35.0492	−	60.7070i	−0.00566544	−	0.00981283i	−0.868844	+	0.495086i	$0.835137\pi$
$338$	544.490	−	314.362i	0.0876224	−	0.0505888i
$339$		−	2620.76i		−	0.419882i
$340$	−5382.62	−	9322.98i	−0.858570	−	1.48709i
$341$			11459.6i			1.81987i
$342$	259.054	−	448.695i	0.0409592	−	0.0709434i
$343$	5026.38			0.791251
$344$	833.591			0.130652
$345$	−1867.46	+	3234.53i	−0.291422	+	0.504757i
$346$	576.524	−	332.856i	0.0895783	−	0.0517181i
$347$		−	4404.10i		−	0.681338i	−0.940183	−	0.340669i	$-0.889346\pi$
$347$		−	4404.10i		−	0.681338i	0.940183	−	0.340669i	$-0.110654\pi$
$348$	1877.86	+	1084.18i	0.289263	+	0.167006i
$349$	6166.17	−	10680.1i	0.945752	−	1.63809i	0.191513	−	0.981490i	$-0.438661\pi$
$349$	6166.17	−	10680.1i	0.945752	−	1.63809i	0.754239	−	0.656600i	$-0.228006\pi$
$350$	−1544.74	−	891.854i	−0.235913	−	0.136205i
$351$	−654.550	+	377.905i	−0.0995365	+	0.0574674i
$352$	−2637.70	+	1522.87i	−0.399402	+	0.230595i
$353$	5584.40	+	3224.16i	0.842005	+	0.486132i	0.857945	−	0.513741i	$-0.171741\pi$
$353$	5584.40	+	3224.16i	0.842005	+	0.486132i	−0.0159402	+	0.999873i	$0.505074\pi$
$354$	25.7626	−	44.6222i	0.00386799	−	0.00669956i
$355$	3.54666	+	2.04767i	0.000530246	+	0.000306138i
$356$			1373.38i			0.204464i
$357$	−1679.81	+	969.840i	−0.249034	+	0.143780i
$358$	−115.674	+	200.353i	−0.0170769	+	0.0295781i
$359$	2162.44			0.317909			0.158954	−	0.987286i	$-0.449188\pi$
$359$	2162.44			0.317909			0.158954	+	0.987286i	$0.449188\pi$
$360$	2430.09			0.355770
$361$	−1106.34	+	1916.24i	−0.161298	+	0.279376i
$362$		−	195.407i		−	0.0283711i
$363$	1023.76	+	1773.20i	0.148026	+	0.256388i
$364$			1795.22i			0.258503i
$365$	−34.3760	+	19.8470i	−0.00492966	+	0.00284614i
$366$	−89.7492	−	155.450i	−0.0128177	−	0.0222009i
$367$	−471.389	−	816.471i	−0.0670472	−	0.116129i	0.830553	−	0.556939i	$-0.188024\pi$
$367$	−471.389	−	816.471i	−0.0670472	−	0.116129i	−0.897600	+	0.440810i	$0.854691\pi$
$368$	−7359.89	−	4249.23i	−1.04256	−	0.601920i
$369$	−4505.53			−0.635633
$370$	1003.61	−	926.274i	0.141014	−	0.130148i
$371$	−8199.77			−1.14747
$372$	−1989.22	−	1148.48i	−0.277248	−	0.160069i
$373$	5203.43	+	9012.61i	0.722315	+	1.25109i	0.960070	+	0.279761i	$0.0902552\pi$
$373$	5203.43	+	9012.61i	0.722315	+	1.25109i	−0.237755	+	0.971325i	$0.576411\pi$
$374$	545.491	+	944.818i	0.0754189	+	0.130629i
$375$	3620.29	−	2090.18i	0.498536	−	0.287830i
$376$		−	407.284i		−	0.0558619i
$377$	−1086.57	−	1882.00i	−0.148439	−	0.257104i
$378$		−	451.148i		−	0.0613877i
$379$	−6506.80	+	11270.1i	−0.881878	+	1.52746i	−0.0326278	+	0.999468i	$0.510388\pi$
$379$	−6506.80	+	11270.1i	−0.881878	+	1.52746i	−0.849250	+	0.527990i	$0.822946\pi$
$380$	10833.9			1.46255
$381$	1384.30			0.186142
$382$	−414.533	+	717.992i	−0.0555218	+	0.0961667i
$383$	−8690.32	+	5017.36i	−1.15941	+	0.669386i	−0.951163	−	0.308690i	$-0.900110\pi$
$383$	−8690.32	+	5017.36i	−1.15941	+	0.669386i	−0.208248	+	0.978076i	$0.566776\pi$
$384$		−	812.375i		−	0.107959i
$385$	−19666.0	−	11354.2i	−2.60330	−	1.50302i
$386$	−611.984	+	1059.99i	−0.0806973	+	0.139772i
$387$	−3782.91	−	2184.06i	−0.496889	−	0.286879i
$388$	−5683.15	+	3281.17i	−0.743603	+	0.429319i
$389$	3009.16	−	1737.34i	0.392212	−	0.226444i	−0.290906	−	0.956752i	$-0.593957\pi$
$389$	3009.16	−	1737.34i	0.392212	−	0.226444i	0.683118	+	0.730308i	$0.260623\pi$
$390$	76.1315	+	43.9545i	0.00988479	+	0.00570698i
$391$	−4655.59	+	8063.71i	−0.602156	+	1.04297i
$392$	−439.794	−	253.915i	−0.0566656	−	0.0327159i
$393$			803.706i			0.103159i
$394$	199.510	−	115.187i	0.0255106	−	0.0147286i
$395$	−333.834	+	578.218i	−0.0425241	+	0.0736539i
$396$	10619.8			1.34764
$397$	−2275.64			−0.287686			−0.143843	−	0.989601i	$-0.545946\pi$
$397$	−2275.64			−0.287686			−0.143843	+	0.989601i	$0.545946\pi$
$398$	25.5849	−	44.3143i	0.00322224	−	0.00558109i
$399$		−	1952.05i		−	0.244924i
$400$	8619.76	+	14929.9i	1.07747	+	1.86623i
$401$			2679.45i			0.333680i	0.985984	+	0.166840i	$0.0533563\pi$
$401$			2679.45i			0.333680i	−0.985984	+	0.166840i	$0.946644\pi$
$402$	−121.137	+	69.9383i	−0.0150292	+	0.00867713i
$403$	1151.02	+	1993.62i	0.142273	+	0.246425i
$404$	1826.86	+	3164.21i	0.224974	+	0.389667i
$405$	−10169.1	−	5871.15i	−1.24767	−	0.720345i
$406$	1297.17			0.158565
$407$	8822.33	−	8142.53i	1.07446	−	0.991672i
$408$	−439.871			−0.0533746
$409$	7012.23	+	4048.51i	0.847757	+	0.489453i	0.859893	−	0.510474i	$-0.170530\pi$
$409$	7012.23	+	4048.51i	0.847757	+	0.489453i	−0.0121365	+	0.999926i	$0.503863\pi$
$410$	543.068	+	940.621i	0.0654151	+	0.113302i
$411$	489.815	+	848.385i	0.0587854	+	0.101819i
$412$	−6336.39	+	3658.32i	−0.757698	+	0.437457i
$413$			2673.70i			0.318557i
$414$	−522.452	−	904.914i	−0.0620221	−	0.107425i
$415$		−	9053.88i		−	1.07093i
$416$	−305.917	+	529.864i	−0.0360549	+	0.0624489i
$417$	−1460.50			−0.171513
$418$	−1097.94			−0.128474
$419$	7440.77	−	12887.8i	0.867554	−	1.50265i	0.00306615	−	0.999995i	$-0.499024\pi$
$419$	7440.77	−	12887.8i	0.867554	−	1.50265i	0.864488	−	0.502653i	$-0.167643\pi$
$420$	3941.83	−	2275.82i	0.457956	−	0.264401i
$421$		−	13949.6i		−	1.61488i	−0.589951	−	0.807439i	$-0.700853\pi$
$421$		−	13949.6i		−	1.61488i	0.589951	−	0.807439i	$-0.299147\pi$
$422$	1490.04	+	860.274i	0.171881	+	0.0992358i
$423$	−1067.11	+	1848.29i	−0.122659	+	0.212452i
$424$	−1610.38	−	929.752i	−0.184450	−	0.106492i
$425$	16357.6	−	9444.07i	1.86697	−	1.07789i
$426$	0.0720435	−	0.0415944i	8.19371e−6	−	4.73064e-6i
$427$	8066.46	+	4657.17i	0.914200	+	0.527814i
$428$	7246.18	−	12550.7i	0.818358	−	1.41744i
$429$	669.243	+	386.388i	0.0753179	+	0.0434848i
$430$			1053.01i			0.118095i
$431$	−9584.05	+	5533.35i	−1.07111	+	0.618404i	−0.928484	−	0.371372i	$-0.878887\pi$
$431$	−9584.05	+	5533.35i	−1.07111	+	0.618404i	−0.142624	+	0.989777i	$0.545554\pi$
$432$	−2180.17	+	3776.17i	−0.242809	+	0.420558i
$433$	−8988.57			−0.997606			−0.498803	−	0.866715i	$-0.666227\pi$
$433$	−8988.57			−0.997606			−0.498803	+	0.866715i	$0.666227\pi$
$434$	−1374.10			−0.151979
$435$	−2754.92	+	4771.65i	−0.303651	+	0.525939i
$436$		−	37.4867i		−	0.00411764i
$437$	−4685.28	−	8115.14i	−0.512877	−	0.888329i
$438$			0.806307i			8.79608e-5i
$439$	−12214.9	+	7052.29i	−1.32799	+	0.766715i	−0.984988	−	0.172621i	$-0.944776\pi$
$439$	−12214.9	+	7052.29i	−1.32799	+	0.766715i	−0.343000	+	0.939335i	$0.611443\pi$
$440$	−2574.84	−	4459.76i	−0.278979	−	0.483206i
$441$	1330.55	+	2304.58i	0.143672	+	0.248848i
$442$	189.796	+	109.579i	0.0204246	+	0.0117922i
$443$	8808.26			0.944679			0.472340	−	0.881417i	$-0.343410\pi$
$443$	8808.26			0.944679			0.472340	+	0.881417i	$0.343410\pi$
$444$	529.253	+	2347.46i	0.0565704	+	0.250914i
$445$	−3489.78			−0.371756
$446$	−1335.99	−	771.332i	−0.141840	−	0.0818916i
$447$	1825.26	+	3161.45i	0.193136	+	0.334522i
$448$	5055.51	+	8756.40i	0.533148	+	0.923440i
$449$	8483.73	−	4898.08i	0.891697	−	0.514822i	0.0171998	−	0.999852i	$-0.494525\pi$
$449$	8483.73	−	4898.08i	0.891697	−	0.514822i	0.874497	+	0.485031i	$0.161192\pi$
$450$			2119.64i			0.222046i
$451$	4773.91	+	8268.65i	0.498436	+	0.863316i
$452$			15331.6i			1.59544i
$453$	1093.40	−	1893.83i	0.113405	−	0.196424i
$454$	−68.1434			−0.00704433
$455$	−4561.68			−0.470011
$456$	221.338	−	383.369i	0.0227305	−	0.0393704i
$457$	14332.2	−	8274.71i	1.46703	−	0.846990i	0.467711	−	0.883882i	$-0.345079\pi$
$457$	14332.2	−	8274.71i	1.46703	−	0.846990i	0.999319	+	0.0368915i	$0.0117456\pi$
$458$		−	1697.17i		−	0.173152i
$459$	4137.28	+	2388.66i	0.420723	+	0.242904i
$460$	10924.8	−	18922.2i	1.10732	−	1.91794i
$461$	−12485.8	−	7208.69i	−1.26144	−	0.728291i	−0.288085	−	0.957605i	$-0.593019\pi$
$461$	−12485.8	−	7208.69i	−1.26144	−	0.728291i	−0.973353	+	0.229314i	$0.926352\pi$
$462$	−399.476	+	230.638i	−0.0402280	+	0.0232256i
$463$	6427.31	−	3710.81i	0.645145	−	0.372475i	−0.141449	−	0.989946i	$-0.545176\pi$
$463$	6427.31	−	3710.81i	0.645145	−	0.372475i	0.786594	+	0.617471i	$0.211843\pi$
$464$	−10857.5	−	6268.56i	−1.08630	−	0.627178i
$465$	2918.30	−	5054.64i	0.291038	−	0.504093i
$466$	175.722	+	101.453i	0.0174681	+	0.0100852i
$467$			12741.4i			1.26253i	0.775566	+	0.631267i	$0.217465\pi$
$467$			12741.4i			1.26253i	−0.775566	+	0.631267i	$0.782535\pi$
$468$	1847.51	−	1066.66i	0.182481	−	0.105356i
$469$	3629.16	−	6285.90i	0.357312	−	0.618882i
$470$	514.492			0.0504931
$471$	−1529.55			−0.149635
$472$	−303.164	+	525.095i	−0.0295641	+	0.0512065i
$473$			9256.64i			0.899832i
$474$	6.78119	+	11.7454i	0.000657110	+	0.00113815i
$475$			19008.6i			1.83616i
$476$	9827.01	−	5673.63i	0.946261	−	0.546324i
$477$	4872.03	+	8438.60i	0.467662	+	0.810014i
$478$	−279.787	−	484.605i	−0.0267723	−	0.0463709i
$479$	−10103.9	−	5833.50i	−0.963800	−	0.556450i	−0.0664594	−	0.997789i	$-0.521170\pi$
$479$	−10103.9	−	5833.50i	−0.963800	−	0.556450i	−0.897340	+	0.441339i	$0.854504\pi$
$480$	1551.25			0.147510
$481$	716.966	−	2302.67i	0.0679643	−	0.218280i
$482$	2204.60			0.208334
$483$	−3409.40	−	1968.42i	−0.321187	−	0.185437i
$484$	−5989.06	−	10373.4i	−0.562458	−	0.974207i
$485$	−8337.48	−	14440.9i	−0.780589	−	1.35202i
$486$	−704.565	+	406.781i	−0.0657607	+	0.0379670i
$487$		−	12121.3i		−	1.12786i	−0.825822	−	0.563931i	$-0.809289\pi$
$487$		−	12121.3i		−	1.12786i	0.825822	−	0.563931i	$-0.190711\pi$
$488$	1056.13	+	1829.27i	0.0979688	+	0.169687i
$489$		−	2321.19i		−	0.214658i
$490$	320.752	−	555.558i	0.0295716	−	0.0512195i
$491$	−17439.7			−1.60294			−0.801470	−	0.598035i	$-0.795948\pi$
$491$	−17439.7			−1.60294			−0.801470	+	0.598035i	$0.795948\pi$
$492$	−1913.75			−0.175363
$493$	−6868.03	+	11895.8i	−0.627425	+	1.08673i
$494$	−191.007	+	110.278i	−0.0173964	+	0.0100438i
$495$			26985.0i			2.45028i
$496$	11501.4	+	6640.33i	1.04118	+	0.601128i
$497$	−2.15837	+	3.73841i	−0.000194801	+	0.000337405i
$498$	−159.272	−	91.9559i	−0.0143316	−	0.00827438i
$499$	9042.50	−	5220.69i	0.811218	−	0.468357i	−0.0361604	−	0.999346i	$-0.511513\pi$
$499$	9042.50	−	5220.69i	0.811218	−	0.468357i	0.847379	+	0.530989i	$0.178179\pi$
$500$	−21178.9	+	12227.7i	−1.89430	+	1.09368i
$501$	269.007	+	155.312i	0.0239888	+	0.0138499i
$502$	−153.627	+	266.090i	−0.0136588	+	0.0236577i
$503$	7085.92	+	4091.06i	0.628122	+	0.362646i	0.780024	−	0.625749i	$-0.215207\pi$
$503$	7085.92	+	4091.06i	0.628122	+	0.362646i	−0.151902	+	0.988396i	$0.548540\pi$
$504$			2561.47i			0.226383i
$505$	−8040.30	+	4642.07i	−0.708492	+	0.409048i
$506$	−1107.15	+	1917.63i	−0.0972700	+	0.168477i
$507$	−2814.93			−0.246579
$508$	−8098.27			−0.707289
$509$	7216.22	−	12498.9i	0.628396	−	1.08841i	−0.359478	−	0.933154i	$-0.617045\pi$
$509$	7216.22	−	12498.9i	0.628396	−	1.08841i	0.987874	−	0.155260i	$-0.0496214\pi$
$510$		−	555.656i		−	0.0482448i
$511$	−20.9200	−	36.2345i	−0.00181105	−	0.00313683i
$512$			5905.48i			0.509742i
$513$	−4163.67	+	2403.90i	−0.358344	+	0.206890i
$514$	−690.766	−	1196.44i	−0.0592770	−	0.102671i
$515$	−9295.83	−	16100.8i	−0.795385	−	1.37765i
$516$	−1606.81	−	927.695i	−0.137085	−	0.0791463i
$517$	4522.71			0.384736
$518$	976.352	+	1057.87i	0.0828155	+	0.0897296i
$519$	−2980.54			−0.252083
$520$	−895.883	−	517.238i	−0.0755520	−	0.0436200i
$521$	3811.69	+	6602.04i	0.320524	+	0.555164i	0.980596	−	0.196038i	$-0.0628076\pi$
$521$	3811.69	+	6602.04i	0.320524	+	0.555164i	−0.660072	+	0.751202i	$0.729474\pi$
$522$	−770.734	−	1334.95i	−0.0646247	−	0.111933i
$523$	−19327.8	+	11158.9i	−1.61596	+	0.932975i	−0.628011	+	0.778205i	$0.716131\pi$
$523$	−19327.8	+	11158.9i	−1.61596	+	0.932975i	−0.987950	+	0.154771i	$0.950536\pi$
$524$		−	4701.73i		−	0.391977i
$525$	3993.03	+	6916.13i	0.331943	+	0.574942i
$526$		−	732.884i		−	0.0607514i
$527$	7275.34	−	12601.3i	0.601364	−	1.04159i
$528$	4458.22			0.367461
$529$	−6731.26			−0.553239
$530$	1174.49	−	2034.27i	0.0962574	−	0.166723i
$531$	2751.57	−	1588.62i	0.224874	−	0.129831i
$532$			11419.6i			0.930646i
$533$	1661.02	+	958.989i	0.134984	+	0.0779333i
$534$	−35.4441	+	61.3909i	−0.00287231	+	0.00497499i
$535$	31891.6	+	18412.6i	2.57719	+	1.48794i
$536$	1425.49	−	823.004i	0.114872	−	0.0663216i
$537$	897.022	−	517.896i	0.0720845	−	0.0416180i
$538$	207.854	+	120.005i	0.0166566	+	0.00961666i
$539$	2819.61	−	4883.70i	0.225323	−	0.390271i
$540$	−9708.50	−	5605.21i	−0.773681	−	0.446685i
$541$		−	5473.20i		−	0.434956i	−0.976065	−	0.217478i	$-0.930217\pi$
$541$		−	5473.20i		−	0.434956i	0.976065	−	0.217478i	$-0.0697830\pi$
$542$	−1881.96	+	1086.55i	−0.149146	+	0.0861096i
$543$	−437.439	+	757.667i	−0.0345715	+	0.0598795i
$544$	3867.28			0.304795
$545$	95.2543			0.00748669
$546$	−46.3308	+	80.2474i	−0.00363146	+	0.00628987i
$547$			941.477i			0.0735917i	0.999323	+	0.0367959i	$0.0117151\pi$
$547$			941.477i			0.0735917i	−0.999323	+	0.0367959i	$0.988285\pi$
$548$	−2865.45	−	4963.11i	−0.223369	−	0.386886i
$549$		−	11068.5i		−	0.860462i
$550$	3890.01	−	2245.90i	0.301583	−	0.174119i
$551$	−6911.83	−	11971.6i	−0.534399	−	0.925606i
$552$	−446.388	−	773.167i	−0.0344195	−	0.0596163i
$553$	−609.478	−	351.882i	−0.0468674	−	0.0270589i
$554$	844.024			0.0647277
$555$	−5964.94	+	1344.84i	−0.456212	+	0.102856i
$556$	8543.99			0.651702
$557$	20472.1	+	11819.6i	1.55732	+	0.899121i	0.997512	+	0.0705015i	$0.0224600\pi$
$557$	20472.1	+	11819.6i	1.55732	+	0.899121i	0.559812	+	0.828620i	$0.310873\pi$
$558$	816.443	+	1414.12i	0.0619405	+	0.107284i
$559$	929.744	+	1610.36i	0.0703470	+	0.121845i
$560$	−22791.0	+	13158.4i	−1.71982	+	0.992937i
$561$		−	4884.56i		−	0.367605i
$562$	−197.375	−	341.863i	−0.0148145	−	0.0256595i
$563$		−	13925.5i		−	1.04243i	−0.853425	−	0.521215i	$-0.825479\pi$
$563$		−	13925.5i		−	1.04243i	0.853425	−	0.521215i	$-0.174521\pi$
$564$	−453.263	+	785.074i	−0.0338401	+	0.0586127i
$565$	−38957.8			−2.90083
$566$	564.713			0.0419376
$567$	6188.56	−	10718.9i	0.458369	−	0.793918i
$568$	−0.847778	+	0.489465i	−6.26267e−5	+	3.61575e-5i
$569$			13622.3i			1.00365i	0.864969	+	0.501825i	$0.167338\pi$
$569$			13622.3i			1.00365i	−0.864969	+	0.501825i	$0.832662\pi$
$570$	484.281	+	279.600i	0.0355865	+	0.0205459i
$571$	−7316.58	+	12672.7i	−0.536234	+	0.928784i	0.462869	+	0.886427i	$0.346820\pi$
$571$	−7316.58	+	12672.7i	−0.536234	+	0.928784i	−0.999103	+	0.0423572i	$0.986513\pi$
$572$	−3915.12	−	2260.39i	−0.286188	−	0.165230i
$573$	3214.61	−	1855.95i	0.234367	−	0.135312i
$574$	−991.474	+	572.428i	−0.0720964	+	0.0416249i
$575$	33199.9	+	19168.0i	2.40788	+	1.39019i
$576$	6007.62	−	10405.5i	0.434579	−	0.752713i
$577$	−14175.9	−	8184.47i	−1.02279	−	0.590510i	−0.107881	−	0.994164i	$-0.534407\pi$
$577$	−14175.9	−	8184.47i	−1.02279	−	0.590510i	−0.914912	+	0.403654i	$0.867740\pi$
$578$			98.2520i			0.00707049i
$579$	4745.79	−	2739.99i	0.340636	−	0.196666i
$580$	16116.4	−	27914.5i	1.15379	−	1.99842i
$581$	9543.36			0.681455
$582$	−338.719			−0.0241243
$583$	10324.5	−	17882.5i	0.733440	−	1.27036i
$584$		−	9.48828i		−	0.000672308i
$585$	2710.40	+	4694.55i	0.191557	+	0.331787i
$586$		−	637.037i		−	0.0449075i
$587$	2978.78	−	1719.80i	0.209451	−	0.120926i	−0.391605	−	0.920133i	$-0.628080\pi$
$587$	2978.78	−	1719.80i	0.209451	−	0.120926i	0.601056	+	0.799207i	$0.294747\pi$
$588$	565.159	+	978.883i	0.0396373	+	0.0686539i
$589$	7321.74	+	12681.6i	0.512202	+	0.887161i
$590$	−663.313	−	382.964i	−0.0462850	−	0.0267227i
$591$	−1031.44			−0.0717896
$592$	−3060.06	−	13572.7i	−0.212445	−	0.942287i
$593$	26151.7			1.81100			0.905498	−	0.424352i	$-0.139498\pi$
$593$	26151.7			1.81100			0.905498	+	0.424352i	$0.139498\pi$
$594$	983.888	+	568.048i	0.0679620	+	0.0392379i
$595$	14416.8	+	24970.6i	0.993327	+	1.72049i
$596$	−10677.9	−	18494.7i	−0.733866	−	1.27109i
$597$	−198.405	+	114.549i	−0.0136016	+	0.00785290i
$598$			444.810i			0.0304175i
$599$	6327.16	+	10959.0i	0.431587	+	0.747531i	0.997010	−	0.0772699i	$-0.0246203\pi$
$599$	6327.16	+	10959.0i	0.431587	+	0.747531i	−0.565423	+	0.824801i	$0.691287\pi$
$600$			1811.04i			0.123226i
$601$	−7081.97	+	12266.3i	−0.480665	+	0.832536i	−0.999754	−	0.0221844i	$-0.992938\pi$
$601$	−7081.97	+	12266.3i	−0.480665	+	0.832536i	0.519089	+	0.854720i	$0.326271\pi$
$602$	−1109.94			−0.0751459
$603$	−8625.30			−0.582503
$604$	−6396.48	+	11079.0i	−0.430909	+	0.746357i
$605$	26358.8	−	15218.3i	1.77130	−	1.02266i
$606$			188.589i			0.0126418i
$607$	−5557.36	−	3208.54i	−0.371608	−	0.214548i	0.302553	−	0.953133i	$-0.402161\pi$
$607$	−5557.36	−	3208.54i	−0.371608	−	0.214548i	−0.674161	+	0.738585i	$0.735495\pi$
$608$	−1945.98	+	3370.53i	−0.129802	+	0.224824i
$609$	−5029.62	−	2903.86i	−0.334665	−	0.193219i
$610$	−2310.78	+	1334.13i	−0.153378	+	0.0885531i
$611$	786.808	−	454.264i	0.0520963	−	0.0300778i
$612$	−11677.7	−	6742.15i	−0.771315	−	0.445319i
$613$	8737.25	−	15133.4i	0.575684	−	0.997114i	−0.420283	−	0.907393i	$-0.638069\pi$
$613$	8737.25	−	15133.4i	0.575684	−	0.997114i	0.995967	−	0.0897208i	$-0.0285975\pi$
$614$	−1489.71	−	860.086i	−0.0979151	−	0.0565313i
$615$		−	4862.87i		−	0.318845i
$616$	4700.87	−	2714.05i	0.307473	−	0.177520i
$617$	1038.55	−	1798.81i	0.0677638	−	0.117370i	−0.830153	−	0.557536i	$-0.811747\pi$
$617$	1038.55	−	1798.81i	0.0677638	−	0.117370i	0.897917	+	0.440165i	$0.145080\pi$
$618$	−377.653			−0.0245816
$619$	−19199.3			−1.24666			−0.623332	−	0.781957i	$-0.714221\pi$
$619$	−19199.3			−1.24666			−0.623332	+	0.781957i	$0.714221\pi$
$620$	−17072.2	+	29570.0i	−1.10587	+	1.91542i
$621$			9696.21i			0.626563i
$622$	−931.785	−	1613.90i	−0.0600662	−	0.104038i
$623$		−	3678.45i		−	0.236556i
$624$	775.590	−	447.787i	0.0497571	−	0.0287273i
$625$	−13641.5	−	23627.8i	−0.873058	−	1.51218i
$626$	−357.695	−	619.546i	−0.0228377	−	0.0395560i
$627$	4257.14	+	2457.86i	0.271154	+	0.156551i
$628$	8947.99			0.568573
$629$	−14870.6	+	3352.69i	−0.942657	+	0.212529i
$630$	−3235.71			−0.204625
$631$	436.113	+	251.790i	0.0275141	+	0.0158853i	0.513694	−	0.857973i	$-0.328277\pi$
$631$	436.113	+	251.790i	0.0275141	+	0.0158853i	−0.486180	+	0.873859i	$0.661610\pi$
$632$	−79.7982	−	138.214i	−0.00502247	−	0.00869917i
$633$	−3851.64	−	6671.23i	−0.241847	−	0.418890i
$634$	1679.75	−	969.803i	0.105223	−	0.0607505i
$635$		−	20577.8i		−	1.28599i
$636$	2069.42	+	3584.35i	0.129022	+	0.223473i
$637$		−	1132.81i		−	0.0704611i
$638$	−1633.29	+	2828.94i	−0.101352	+	0.175546i
$639$	5.12972			0.000317572
$640$	−12076.0			−0.745855
$641$	−7992.24	+	13843.0i	−0.492472	+	0.852987i	−0.999962	−	0.00867084i	$-0.997240\pi$
$641$	−7992.24	+	13843.0i	−0.492472	+	0.852987i	0.507490	+	0.861657i	$0.330573\pi$
$642$	647.816	−	374.017i	0.0398244	−	0.0229926i
$643$			7934.66i			0.486645i	0.969945	+	0.243322i	$0.0782373\pi$
$643$			7934.66i			0.486645i	−0.969945	+	0.243322i	$0.921763\pi$
$644$	19945.2	+	11515.4i	1.22042	+	0.704611i
$645$	2357.28	−	4082.94i	0.143904	−	0.249249i
$646$	1207.32	+	697.045i	0.0735313	+	0.0424533i
$647$	−17331.1	+	10006.1i	−1.05310	+	0.608007i	−0.923516	−	0.383561i	$-0.874698\pi$
$647$	−17331.1	+	10006.1i	−1.05310	+	0.608007i	−0.129584	+	0.991568i	$0.541364\pi$
$648$	2430.78	−	1403.41i	0.147361	−	0.0850790i
$649$	−5830.94	−	3366.49i	−0.352672	−	0.203616i
$650$	451.159	−	781.430i	0.0272245	−	0.0471542i
$651$	5327.91	+	3076.07i	0.320764	+	0.185193i
$652$			13579.1i			0.815642i
$653$	−17185.2	+	9921.90i	−1.02988	+	0.594600i	−0.916950	−	0.399003i	$-0.869356\pi$
$653$	−17185.2	+	9921.90i	−1.02988	+	0.594600i	−0.112928	+	0.993603i	$0.536023\pi$
$654$	0.967452	−	1.67568i	5.78446e−5	−	0.000100190i
$655$	11947.2			0.712694
$656$	11065.0			0.658562
$657$	−24.8599	+	43.0586i	−0.00147622	+	0.00255689i
$658$			542.307i			0.0321297i
$659$	11953.2	+	20703.5i	0.706571	+	1.22382i	0.966122	+	0.258088i	$0.0830923\pi$
$659$	11953.2	+	20703.5i	0.706571	+	1.22382i	−0.259550	+	0.965730i	$0.583574\pi$
$660$			11462.1i			0.676000i
$661$	6893.91	−	3980.20i	0.405661	−	0.234208i	−0.283263	−	0.959042i	$-0.591417\pi$
$661$	6893.91	−	3980.20i	0.405661	−	0.234208i	0.688924	+	0.724834i	$0.258083\pi$
$662$	−704.098	−	1219.53i	−0.0413377	−	0.0715990i
$663$	−490.609	−	849.760i	−0.0287386	−	0.0497767i
$664$	1874.25	+	1082.10i	0.109541	+	0.0632433i
$665$	−29017.4			−1.69210
$666$	508.561	−	1633.34i	0.0295891	−	0.0950308i
$667$	−27879.1			−1.61842
$668$	−1573.71	−	908.583i	−0.0911508	−	0.0526259i
$669$	3453.42	+	5981.51i	0.199577	+	0.345678i
$670$	1039.64	+	1800.71i	0.0599474	+	0.103832i
$671$	−20313.2	+	11727.8i	−1.16868	+	0.674737i
$672$			1635.12i			0.0938632i
$673$	1337.43	+	2316.50i	0.0766037	+	0.132681i	0.901783	−	0.432190i	$-0.142259\pi$
$673$	1337.43	+	2316.50i	0.0766037	+	0.132681i	−0.825179	+	0.564872i	$0.808926\pi$
$674$			21.1666i			0.00120965i
$675$	9834.61	−	17034.0i	0.560791	−	0.971319i
$676$	16467.5			0.936933
$677$	175.250			0.00994891			0.00497446	−	0.999988i	$-0.498417\pi$
$677$	175.250			0.00994891			0.00497446	+	0.999988i	$0.498417\pi$
$678$	−395.676	+	685.331i	−0.0224128	+	0.0388200i
$679$	15221.7	−	8788.24i	0.860315	−	0.496703i
$680$			6538.72i			0.368748i
$681$	264.218	+	152.546i	0.0148676	+	0.00858383i
$682$	1730.15	−	2996.71i	0.0971421	−	0.168255i
$683$	−8860.08	−	5115.37i	−0.496371	−	0.286580i	0.230843	−	0.972991i	$-0.425852\pi$
$683$	−8860.08	−	5115.37i	−0.496371	−	0.286580i	−0.727214	+	0.686411i	$0.759185\pi$
$684$	11752.2	−	6785.15i	0.656956	−	0.379293i
$685$	12611.3	−	7281.15i	0.703436	−	0.406129i
$686$	−1314.40	−	758.871i	−0.0731547	−	0.0422359i
$687$	−3799.31	+	6580.60i	−0.210994	+	0.365452i
$688$	9290.35	+	5363.79i	0.514813	+	0.297227i
$689$		−	4147.99i		−	0.229355i
$690$	976.684	−	563.889i	0.0538866	−	0.0311114i
$691$	−5260.88	+	9112.11i	−0.289629	+	0.501651i	−0.973721	−	0.227744i	$-0.926865\pi$
$691$	−5260.88	+	9112.11i	−0.289629	+	0.501651i	0.684092	+	0.729395i	$0.260198\pi$
$692$	17436.4			0.957848
$693$	−28443.9			−1.55916
$694$	−664.920	+	1151.68i	−0.0363689	+	0.0629928i
$695$			21710.4i			1.18492i
$696$	−658.522	−	1140.59i	−0.0358638	−	0.0621179i
$697$		−	12123.2i		−	0.658820i
$698$	−3224.92	+	1861.91i	−0.174878	+	0.100966i
$699$	−454.227	−	786.744i	−0.0245786	−	0.0425714i
$700$	−23359.5	−	40459.8i	−1.26129	−	2.18462i
$701$	−16958.5	−	9790.97i	−0.913712	−	0.527532i	−0.0320881	−	0.999485i	$-0.510216\pi$
$701$	−16958.5	−	9790.97i	−0.913712	−	0.527532i	−0.881623	+	0.471953i	$0.843549\pi$
$702$	228.221			0.0122701
$703$	4560.70	−	14647.5i	0.244680	−	0.785835i
$704$	−25461.9			−1.36311
$705$	−1994.88	−	1151.75i	−0.106570	−	0.0615281i
$706$	−973.551	−	1686.24i	−0.0518981	−	0.0898902i
$707$	−4893.03	−	8474.98i	−0.260285	−	0.450827i
$708$	1168.75	−	674.776i	0.0620398	−	0.0358187i
$709$			10152.2i			0.537762i	0.963173	+	0.268881i	$0.0866538\pi$
$709$			10152.2i			0.537762i	−0.963173	+	0.268881i	$0.913346\pi$
$710$	−0.618304	−	1.07093i	−3.26824e−5	−	5.66077e-5i
$711$			836.306i			0.0441124i
$712$	417.091	−	722.422i	0.0219538	−	0.0380252i
$713$	29532.6			1.55120
$714$	585.696			0.0306991
$715$	5743.69	−	9948.37i	0.300422	−	0.520347i
$716$	−5247.64	+	3029.73i	−0.273902	+	0.158137i
$717$			2505.33i			0.130493i
$718$	−565.480	−	326.480i	−0.0293921	−	0.0169695i
$719$	4854.87	−	8408.89i	0.251817	−	0.436159i	−0.712209	−	0.701967i	$-0.752305\pi$
$719$	4854.87	−	8408.89i	0.251817	−	0.436159i	0.964026	+	0.265808i	$0.0856387\pi$
$720$	27083.3	+	15636.6i	1.40186	+	0.809362i
$721$	16971.3	−	9798.39i	0.876622	−	0.506118i
$722$	578.618	−	334.065i	0.0298254	−	0.0172197i
$723$	−8548.09	−	4935.24i	−0.439705	−	0.253864i
$724$	2559.05	−	4432.40i	0.131362	−	0.227526i
$725$	48977.3	+	28277.1i	2.50893	+	1.44853i
$726$		−	618.259i		−	0.0316057i
$727$	−14848.7	+	8572.88i	−0.757506	+	0.437346i	−0.828400	−	0.560138i	$-0.810748\pi$
$727$	−14848.7	+	8572.88i	−0.757506	+	0.437346i	0.0708937	+	0.997484i	$0.477415\pi$
$728$	545.202	−	944.317i	0.0277562	−	0.0480752i
$729$	−12133.5			−0.616448
$730$	11.9858			0.000607692
$731$	5876.73	−	10178.8i	0.297344	−	0.515015i
$732$		−	4701.43i		−	0.237390i
$733$	−4413.65	−	7644.66i	−0.222403	−	0.385214i	0.733134	−	0.680084i	$-0.238057\pi$
$733$	−4413.65	−	7644.66i	−0.222403	−	0.385214i	−0.955537	+	0.294870i	$0.904724\pi$
$734$			284.677i			0.0143156i
$735$	−2487.36	+	1436.08i	−0.124827	+	0.0720686i
$736$	3924.58	+	6797.58i	0.196552	+	0.340438i
$737$	9139.08	+	15829.4i	0.456774	+	0.791156i
$738$	1178.20	+	680.234i	0.0587671	+	0.0339292i
$739$	−4075.92			−0.202889			−0.101445	−	0.994841i	$-0.532346\pi$
$739$	−4075.92			−0.202889			−0.101445	+	0.994841i	$0.532346\pi$
$740$	34895.3	−	7867.40i	1.73348	−	0.390826i
$741$	987.476			0.0489553
$742$	2144.25	+	1237.98i	0.106089	+	0.0612504i
$743$	−209.349	−	362.604i	−0.0103368	−	0.0179039i	0.860811	−	0.508925i	$-0.169957\pi$
$743$	−209.349	−	362.604i	−0.0103368	−	0.0179039i	−0.871148	+	0.491021i	$0.836624\pi$
$744$	697.576	+	1208.24i	0.0343742	+	0.0595378i
$745$	46995.2	−	27132.7i	2.31110	−	1.33431i
$746$		−	3142.41i		−	0.154225i
$747$	−5670.34	−	9821.31i	−0.277733	−	0.481048i
$748$			28575.0i			1.39680i
$749$	−19408.1	+	33615.8i	−0.946803	+	1.63991i
$750$	−1262.28			−0.0614559
$751$	15116.1			0.734480			0.367240	−	0.930126i	$-0.380303\pi$
$751$	15116.1			0.734480			0.367240	+	0.930126i	$0.380303\pi$
$752$	2620.70	−	4539.18i	0.127084	−	0.220115i
$753$	1191.34	−	687.822i	0.0576560	−	0.0332877i
$754$			656.194i			0.0316939i
$755$	−28152.0	−	16253.5i	−1.35703	−	0.783480i
$756$	5908.24	−	10233.4i	0.284234	−	0.492307i
$757$	−10581.5	−	6109.21i	−0.508044	−	0.293320i	0.223985	−	0.974593i	$-0.428093\pi$
$757$	−10581.5	−	6109.21i	−0.508044	−	0.293320i	−0.732029	+	0.681273i	$0.761427\pi$
$758$	3403.07	−	1964.76i	0.163067	−	0.0941470i
$759$	8585.66	−	4956.94i	0.410593	−	0.237056i
$760$	−5698.82	−	3290.21i	−0.271997	−	0.157038i
$761$	−4909.17	+	8502.93i	−0.233847	+	0.405034i	−0.958937	−	0.283620i	$-0.908465\pi$
$761$	−4909.17	+	8502.93i	−0.233847	+	0.405034i	0.725090	+	0.688654i	$0.241798\pi$
$762$	−361.997	−	208.999i	−0.0172097	−	0.00993600i
$763$			100.404i			0.00476392i
$764$	−18805.7	+	10857.5i	−0.890530	+	0.514148i
$765$	17131.9	−	29673.3i	0.809679	−	1.40241i
$766$	3030.03			0.142924
$767$	−1352.53			−0.0636729
$768$	2458.54	−	4258.32i	0.115514	−	0.200077i
$769$			27772.4i			1.30234i	0.758933	+	0.651168i	$0.225721\pi$
$769$			27772.4i			1.30234i	−0.758933	+	0.651168i	$0.774279\pi$
$770$	3428.45	+	5938.25i	0.160458	+	0.277922i
$771$			6185.42i			0.288927i
$772$	−27763.2	+	16029.1i	−1.29433	+	0.747280i
$773$	−20114.3	−	34838.9i	−0.935912	−	1.62105i	−0.773000	−	0.634406i	$-0.781245\pi$
$773$	−20114.3	−	34838.9i	−0.935912	−	1.62105i	−0.162912	−	0.986641i	$-0.552089\pi$
$774$	659.490	+	1142.27i	0.0306264	+	0.0530465i
$775$	−51882.0	−	29954.1i	−2.40472	−	1.38836i
$776$	3985.91			0.184389
$777$	−1417.55	−	6287.42i	−0.0654494	−	0.290296i
$778$	−1049.20			−0.0483490
$779$	10565.9	+	6100.24i	0.485961	+	0.280570i
$780$	1151.26	+	1994.04i	0.0528483	+	0.0915359i
$781$	−5.43528	−	9.41418i	−0.000249026	−	0.000431326i
$782$	2434.88	−	1405.78i	0.111344	−	0.0642846i
$783$			14304.1i			0.652855i
$784$	−3267.66	−	5659.75i	−0.148855	−	0.257824i
$785$			22737.0i			1.03378i
$786$	121.342	−	210.170i	0.00550650	−	0.00953755i
$787$	29024.1			1.31461			0.657304	−	0.753626i	$-0.271697\pi$
$787$	29024.1			1.31461			0.657304	+	0.753626i	$0.271697\pi$
$788$	6033.98			0.272781
$789$	−1640.64	+	2841.67i	−0.0740283	+	0.128221i
$790$	174.596	−	100.803i	0.00786310	−	0.00453976i
$791$		−	41064.0i		−	1.84585i
$792$	−5586.19	−	3225.19i	−0.250627	−	0.144700i
$793$	−2355.91	+	4080.55i	−0.105499	+	0.182730i
$794$	595.083	+	343.571i	0.0265979	+	0.0153563i
$795$	−9107.87	+	5258.43i	−0.406318	+	0.234588i
$796$	1160.68	−	670.120i	0.0516825	−	0.0298389i
$797$	25099.0	+	14490.9i	1.11550	+	0.644032i	0.940247	−	0.340492i	$-0.110594\pi$
$797$	25099.0	+	14490.9i	1.11550	+	0.644032i	0.175249	+	0.984524i	$0.443927\pi$
$798$	−294.716	+	510.463i	−0.0130737	+	0.0226444i
$799$	−4973.26	−	2871.31i	−0.220202	−	0.127134i
$800$		−	15922.4i		−	0.703677i
$801$	−3785.59	+	2185.61i	−0.166988	+	0.0964104i
$802$	404.538	−	700.680i	0.0178114	−	0.0308502i
$803$	105.363			0.00463036
$804$	−3663.65			−0.160705
$805$	−29260.7	+	50681.1i	−1.28112	+	2.21897i
$806$		−	695.110i		−	0.0303774i
$807$	−537.287	−	930.608i	−0.0234367	−	0.0405935i
$808$		−	2219.24i		−	0.0966243i
$809$	5727.96	−	3307.04i	0.248930	−	0.143720i	−0.370344	−	0.928895i	$-0.620760\pi$
$809$	5727.96	−	3307.04i	0.248930	−	0.143720i	0.619274	+	0.785175i	$0.287427\pi$
$810$	1772.82	+	3070.62i	0.0769021	+	0.133198i
$811$	10792.1	+	18692.5i	0.467278	+	0.809349i	0.999301	−	0.0373808i	$-0.0119015\pi$
$811$	10792.1	+	18692.5i	0.467278	+	0.809349i	−0.532023	+	0.846730i	$0.678568\pi$
$812$	29423.6	+	16987.7i	1.27163	+	0.734179i
$813$	9729.47			0.419714
$814$	−3536.39	+	797.305i	−0.152273	+	0.0343311i
$815$	−34504.7			−1.48300
$816$	−4902.35	−	2830.37i	−0.210315	−	0.121425i
$817$	5914.21	+	10243.7i	0.253258	+	0.438656i
$818$	−1222.47	−	2117.38i	−0.0522527	−	0.0905043i
$819$	−4948.35	+	2856.93i	−0.211122	+	0.121892i
$820$			28448.1i			1.21153i
$821$	−5086.95	−	8810.86i	−0.216243	−	0.374545i	0.737413	−	0.675442i	$-0.236047\pi$
$821$	−5086.95	−	8810.86i	−0.216243	−	0.374545i	−0.953656	+	0.300897i	$0.902714\pi$
$822$		−	295.805i		−	0.0125515i
$823$	17505.4	−	30320.3i	0.741435	−	1.28420i	−0.210407	−	0.977614i	$-0.567479\pi$
$823$	17505.4	−	30320.3i	0.741435	−	1.28420i	0.951842	−	0.306589i	$-0.0991879\pi$
$824$	4444.06			0.187884
$825$	−20110.7			−0.848686
$826$	403.668	−	699.174i	0.0170041	−	0.0294520i
$827$	5476.32	−	3161.75i	0.230266	−	0.132944i	−0.380429	−	0.924810i	$-0.624224\pi$
$827$	5476.32	−	3161.75i	0.230266	−	0.132944i	0.610695	+	0.791866i	$0.290890\pi$
$828$		−	27368.2i		−	1.14868i
$829$	2578.94	+	1488.95i	0.108046	+	0.0623804i	0.553049	−	0.833149i	$-0.313464\pi$
$829$	2578.94	+	1488.95i	0.108046	+	0.0623804i	−0.445003	+	0.895529i	$0.646797\pi$
$830$	−1366.93	+	2367.60i	−0.0571650	+	0.0990127i
$831$	−3272.61	−	1889.44i	−0.136613	−	0.0788736i
$832$	−4429.57	+	2557.41i	−0.184576	+	0.106565i
$833$	−6201.00	+	3580.15i	−0.257925	+	0.148913i
$834$	381.921	+	220.502i	0.0158571	+	0.00915511i
$835$	2308.72	−	3998.82i	0.0956845	−	0.165730i
$836$	−24904.5	−	14378.6i	−1.03031	−	0.594851i
$837$		−	15152.4i		−	0.625739i
$838$	−3891.54	+	2246.78i	−0.160419	+	0.0926178i
$839$	−18760.4	+	32493.9i	−0.771966	+	1.33708i	0.164518	+	0.986374i	$0.447393\pi$
$839$	−18760.4	+	32493.9i	−0.771966	+	1.33708i	−0.936484	+	0.350711i	$0.885940\pi$
$840$	−2764.62			−0.113558
$841$	−16739.0			−0.686332
$842$	−2106.08	+	3647.84i	−0.0862000	+	0.149303i
$843$			1767.38i			0.0722085i
$844$	22532.3	+	39027.1i	0.918951	+	1.59167i
$845$			41844.2i			1.70353i
$846$	558.102	−	322.220i	0.0226808	−	0.0130948i
$847$	16041.0	+	27783.9i	0.650739	+	1.12711i
$848$	−11965.1	−	20724.1i	−0.484532	−	0.839233i
$849$	−2189.61	−	1264.17i	−0.0885126	−	0.0511028i
$850$	−5703.38			−0.230146
$851$	−20984.0	−	22736.0i	−0.845269	−	0.915838i
$852$	2.17888			8.76141e−5
$853$	−21269.6	−	12280.0i	−0.853760	−	0.492918i	0.00815794	−	0.999967i	$-0.497403\pi$
$853$	−21269.6	−	12280.0i	−0.853760	−	0.492918i	−0.861918	+	0.507048i	$0.830737\pi$
$854$	−1406.26	−	2435.71i	−0.0563480	−	0.0975975i
$855$	17241.2	+	29862.6i	0.689632	+	1.19448i
$856$	−7623.22	+	4401.27i	−0.304388	+	0.175739i
$857$		−	28732.4i		−	1.14525i	−0.819818	−	0.572625i	$-0.805925\pi$
$857$		−	28732.4i		−	1.14525i	0.819818	−	0.572625i	$-0.194075\pi$
$858$	−116.672	−	202.082i	−0.00464232	−	0.00804074i
$859$		−	13905.2i		−	0.552315i	−0.961112	−	0.276157i	$-0.910939\pi$
$859$		−	13905.2i		−	0.552315i	0.961112	−	0.276157i	$-0.0890611\pi$
$860$	−13790.3	+	23885.4i	−0.546796	+	0.947078i
$861$	5125.77			0.202887
$862$	3341.65			0.132038
$863$	10762.1	−	18640.4i	0.424501	−	0.735258i	−0.571873	−	0.820343i	$-0.693783\pi$
$863$	10762.1	−	18640.4i	0.424501	−	0.735258i	0.996374	+	0.0850849i	$0.0271161\pi$
$864$	3487.66	−	2013.60i	0.137330	−	0.0792872i
$865$			44306.0i			1.74156i
$866$	2350.52	+	1357.07i	0.0922332	+	0.0532509i
$867$	219.948	−	380.961i	0.00861571	−	0.0149228i
$868$	−31168.6	−	17995.2i	−1.21882	−	0.703684i
$869$	1534.81	−	886.122i	0.0599135	−	0.0345911i
$870$	1440.83	−	831.861i	0.0561478	−	0.0324169i
$871$	3179.82	+	1835.87i	0.123702	+	0.0714192i
$872$	−11.3846	+	19.7186i	−0.000442122	+	0.000765777i
$873$	−18088.4	−	10443.3i	−0.701259	−	0.404872i
$874$			2829.49i			0.109507i
$875$	56725.4	−	32750.4i	2.19162	−	1.26533i
$876$	−10.5594	+	18.2894i	−0.000407271	+	0.000705414i
$877$	19989.1			0.769651			0.384825	−	0.922989i	$-0.374262\pi$
$877$	19989.1			0.769651			0.384825	+	0.922989i	$0.374262\pi$
$878$	4258.96			0.163705
$879$	−1426.08	+	2470.04i	−0.0547217	+	0.0947808i
$880$		−	66271.9i		−	2.53867i
$881$	−6903.50	−	11957.2i	−0.264001	−	0.457263i	0.703301	−	0.710893i	$-0.251709\pi$
$881$	−6903.50	−	11957.2i	−0.264001	−	0.457263i	−0.967301	+	0.253630i	$0.918375\pi$
$882$		−	803.532i		−	0.0306761i
$883$	30957.2	−	17873.2i	1.17983	−	0.681178i	0.223858	−	0.974622i	$-0.428135\pi$
$883$	30957.2	−	17873.2i	1.17983	−	0.681178i	0.955976	+	0.293444i	$0.0948014\pi$
$884$	2870.10	+	4971.15i	0.109199	+	0.189138i
$885$	1714.61	+	2969.80i	0.0651256	+	0.112801i
$886$	−2303.37	−	1329.85i	−0.0873399	−	0.0504257i
$887$	25605.7			0.969284			0.484642	−	0.874713i	$-0.338950\pi$
$887$	25605.7			0.969284			0.484642	+	0.874713i	$0.338950\pi$
$888$	434.519	−	1395.54i	0.0164206	−	0.0527378i
$889$	21690.3			0.818301
$890$	912.582	+	526.879i	0.0343706	+	0.0198439i
$891$	15584.2	+	26992.7i	0.585961	+	1.01491i
$892$	−20202.8	−	34992.2i	−0.758339	−	1.31348i
$893$	5004.98	−	2889.63i	0.187553	−	0.108284i
$894$		−	1102.29i		−	0.0412374i
$895$	−7698.57	−	13334.3i	−0.287525	−	0.498008i
$896$		−	12728.9i		−	0.474601i
$897$	995.756	−	1724.70i	0.0370650	−	0.0641985i
$898$	−2958.00			−0.109922
$899$	43567.1			1.61629
$900$	−27758.8	+	48079.7i	−1.02810	+	1.78073i
$901$	−22706.0	+	13109.3i	−0.839563	+	0.484722i
$902$		−	2883.01i		−	0.106423i
$903$	4303.67	+	2484.73i	0.158602	+	0.0915687i
$904$	4656.15	−	8064.69i	0.171307	−	0.296712i
$905$	11262.8	+	6502.57i	0.413688	+	0.238843i
$906$	−571.852	+	330.159i	−0.0209697	+	0.0121068i
$907$	20552.0	−	11865.7i	0.752391	−	0.434393i	−0.0741664	−	0.997246i	$-0.523630\pi$
$907$	20552.0	−	11865.7i	0.752391	−	0.434393i	0.826557	+	0.562853i	$0.190296\pi$
$908$	−1545.69	−	892.406i	−0.0564930	−	0.0326162i
$909$	−5814.55	+	10071.1i	−0.212163	+	0.367478i
$910$	1192.88	+	688.712i	0.0434547	+	0.0250886i
$911$			6100.05i			0.221848i	0.993829	+	0.110924i	$0.0353810\pi$
$911$			6100.05i			0.221848i	−0.993829	+	0.110924i	$0.964619\pi$
$912$	4933.62	−	2848.43i	0.179132	−	0.103422i
$913$	−12016.2	+	20812.7i	−0.435573	+	0.754434i
$914$	−4997.18			−0.180845
$915$	11946.4			0.431623
$916$	22226.2	−	38496.9i	0.801719	−	1.38862i
$917$			12593.1i			0.453500i
$918$	−721.269	−	1249.27i	−0.0259318	−	0.0449153i
$919$		−	40234.3i		−	1.44418i	−0.691797	−	0.722092i	$-0.743181\pi$
$919$		−	40234.3i		−	1.44418i	0.691797	−	0.722092i	$-0.256819\pi$
$920$	−11493.2	+	6635.60i	−0.411869	+	0.237793i
$921$	3850.79	+	6669.77i	0.137772	+	0.238628i
$922$	2176.70	+	3770.16i	0.0777504	+	0.134668i
$923$	−1.89113	−	1.09185i	−6.74404e−5	−	3.89367e-5i
$924$	−12081.7			−0.430152
$925$	13803.7	+	61225.4i	0.490663	+	2.17630i
$926$	−2241.00			−0.0795288
$927$	−20167.5	−	11643.7i	−0.714551	−	0.412546i
$928$	5789.64	+	10027.9i	0.204800	+	0.354723i
$929$	18537.6	+	32108.1i	0.654682	+	1.13394i	0.981974	+	0.189019i	$0.0605307\pi$
$929$	18537.6	+	32108.1i	0.654682	+	1.13394i	−0.327292	+	0.944923i	$0.606136\pi$
$930$	−1526.28	+	881.196i	−0.0538157	+	0.0310705i
$931$		−	7205.96i		−	0.253669i
$932$	2657.26	+	4602.51i	0.0933920	+	0.161760i
$933$			8343.61i			0.292774i
$934$	1923.67	−	3331.90i	0.0673924	−	0.116727i
$935$	−72609.5			−2.53966
$936$	−1295.76			−0.0452492
$937$	10548.6	−	18270.7i	0.367778	−	0.637010i	−0.621440	−	0.783462i	$-0.713452\pi$
$937$	10548.6	−	18270.7i	0.367778	−	0.637010i	0.989218	+	0.146452i	$0.0467853\pi$
$938$	−1898.06	+	1095.85i	−0.0660702	+	0.0381457i
$939$			3202.96i			0.111315i
$940$	11670.2	+	6737.79i	0.404936	+	0.233790i
$941$	7768.39	−	13455.2i	0.269120	−	0.466130i	−0.699515	−	0.714618i	$-0.746600\pi$
$941$	7768.39	−	13455.2i	0.269120	−	0.466130i	0.968635	+	0.248488i	$0.0799337\pi$
$942$	399.980	+	230.928i	0.0138344	+	0.00798732i
$943$	21309.1	−	12302.8i	0.735863	−	0.424850i
$944$	−6757.51	+	3901.45i	−0.232985	+	0.134514i
$945$	26003.1	+	15012.9i	0.895114	+	0.516794i
$946$	1397.55	−	2420.62i	0.0480319	−	0.0831936i
$947$	−20448.2	−	11805.8i	−0.701664	−	0.405106i	0.106303	−	0.994334i	$-0.466099\pi$
$947$	−20448.2	−	11805.8i	−0.701664	−	0.405106i	−0.807967	+	0.589228i	$0.799432\pi$
$948$			355.226i			0.0121701i
$949$	18.3298	−	10.5827i	0.000626988	−	0.000361992i
$950$	2869.88	−	4970.77i	0.0980116	−	0.169761i
$951$	−8684.04			−0.296109
$952$	−6892.23			−0.234641
$953$	15698.3	−	27190.3i	0.533597	−	0.924217i	−0.465633	−	0.884978i	$-0.654173\pi$
$953$	15698.3	−	27190.3i	0.533597	−	0.924217i	0.999230	−	0.0392389i	$-0.0124933\pi$
$954$		−	2942.27i		−	0.0998527i
$955$	−27588.9	−	47785.4i	−0.934824	−	1.61916i
$956$		−	14656.4i		−	0.495837i
$957$	12665.8	−	7312.58i	0.427822	−	0.247003i
$958$	1761.46	+	3050.93i	0.0594051	+	0.102893i
$959$	7674.79	+	13293.1i	0.258427	+	0.447610i
$960$	11230.8	+	6484.09i	0.377575	+	0.217993i
$961$	−16359.9			−0.549155
$962$	−535.138	+	493.903i	−0.0179351	+	0.0165531i
$963$	46126.5			1.54351
$964$	50006.9	+	28871.5i	1.67076	+	0.964614i
$965$	−40730.1	−	70546.7i	−1.35870	−	2.35334i
$966$	594.374	+	1029.49i	0.0197968	+	0.0342890i
$967$	−42202.7	+	24365.7i	−1.40346	+	0.810288i	−0.994746	−	0.102374i	$-0.967356\pi$
$967$	−42202.7	+	24365.7i	−1.40346	+	0.810288i	−0.408715	+	0.912662i	$0.634023\pi$
$968$			7275.41i			0.241571i
$969$	−3120.82	−	5405.42i	−0.103463	−	0.179202i
$970$			5035.10i			0.166667i
$971$	11422.2	−	19783.8i	0.377502	−	0.653853i	−0.613196	−	0.789931i	$-0.710116\pi$
$971$	11422.2	−	19783.8i	0.377502	−	0.653853i	0.990698	+	0.136078i	$0.0434497\pi$
$972$	−21308.8			−0.703169
$973$	−22884.1			−0.753989
$974$	−1830.05	+	3169.73i	−0.0602037	+	0.104276i
$975$	−3498.63	+	2019.94i	−0.114919	+	0.0663485i
$976$			27182.9i			0.891501i
$977$	127.352	+	73.5270i	0.00417028	+	0.00240771i	0.502084	−	0.864819i	$-0.332567\pi$
$977$	127.352	+	73.5270i	0.00417028	+	0.00240771i	−0.497913	+	0.867227i	$0.665900\pi$
$978$	−350.447	+	606.993i	−0.0114582	+	0.0198461i
$979$	8022.17	+	4631.60i	0.261889	+	0.151202i
$980$	14551.2	−	8401.14i	0.474307	−	0.273841i
$981$	103.328	−	59.6567i	0.00336292	−	0.00194158i
$982$	4560.50	+	2633.01i	0.148199	+	0.0855628i
$983$	−16971.8	+	29396.1i	−0.550679	+	0.953804i	0.447547	+	0.894261i	$0.352298\pi$
$983$	−16971.8	+	29396.1i	−0.550679	+	0.953804i	−0.998226	+	0.0595436i	$0.981035\pi$
$984$	1006.67	+	581.198i	0.0326131	+	0.0188292i
$985$			15332.4i			0.495971i
$986$	3591.99	−	2073.84i	0.116017	−	0.0669822i
$987$	1214.01	−	2102.73i	0.0391514	−	0.0678123i
$988$	−5776.80			−0.186017
$989$	23855.2			0.766988
$990$	4074.14	−	7056.61i	0.130793	−	0.226539i
$991$			23093.7i			0.740259i	0.928980	+	0.370130i	$0.120687\pi$
$991$			23093.7i			0.740259i	−0.928980	+	0.370130i	$0.879313\pi$
$992$	−6133.00	−	10622.7i	−0.196293	−	0.339990i
$993$			6304.80i			0.201487i
$994$	1.12883	−	0.651732i	3.60205e−5	−	2.07964e-5i
$995$	1702.78	+	2949.31i	0.0542531	+	0.0939691i
$996$	−2408.51	−	4171.66i	−0.0766231	−	0.132715i
$997$	16810.8	+	9705.71i	0.534005	+	0.308308i	0.742646	−	0.669684i	$-0.233571\pi$
$997$	16810.8	+	9705.71i	0.534005	+	0.308308i	−0.208641	+	0.977992i	$0.566904\pi$
$998$	−3152.83			−0.100001
$999$	−11665.2	+	10766.4i	−0.369441	+	0.340974i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	37.4.e.a.27.5	yes	16
3.2	odd	2		333.4.s.c.64.4		16
37.11	even	6	inner	37.4.e.a.11.5	✓	16
37.14	odd	12		1369.4.a.g.1.8		16
37.23	odd	12		1369.4.a.g.1.9		16
111.11	odd	6		333.4.s.c.307.4		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
37.4.e.a.11.5	✓	16	37.11	even	6	inner
37.4.e.a.27.5	yes	16	1.1	even	1	trivial
333.4.s.c.64.4		16	3.2	odd	2
333.4.s.c.307.4		16	111.11	odd	6
1369.4.a.g.1.8		16	37.14	odd	12
1369.4.a.g.1.9		16	37.23	odd	12

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:	\( N \)	\(=\)	\( 37 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	37.e (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.261501 - 0.150978i) q^{2} +(0.675960 + 1.17080i) q^{3} +(-3.95441 - 6.84924i) q^{4} +(17.4040 - 10.0482i) q^{5} -0.408219i q^{6} +(10.5914 + 18.3449i) q^{7} +4.80375i q^{8} +(12.5862 - 21.7999i) q^{9} +O(q^{10})\)	\(q+(-0.261501 - 0.150978i) q^{2} +(0.675960 + 1.17080i) q^{3} +(-3.95441 - 6.84924i) q^{4} +(17.4040 - 10.0482i) q^{5} -0.408219i q^{6} +(10.5914 + 18.3449i) q^{7} +4.80375i q^{8} +(12.5862 - 21.7999i) q^{9} -6.06822 q^{10} -53.3435 q^{11} +(5.34605 - 9.25963i) q^{12} +(-9.28008 + 5.35786i) q^{13} -6.39629i q^{14} +(23.5288 + 13.5844i) q^{15} +(-30.9100 + 53.5377i) q^{16} +(58.6576 + 33.8660i) q^{17} +(-6.58258 + 3.80046i) q^{18} +(-59.0317 + 34.0820i) q^{19} +(-137.645 - 79.4695i) q^{20} +(-14.3188 + 24.8009i) q^{21} +(13.9494 + 8.05367i) q^{22} +137.471i q^{23} +(-5.62422 + 3.24715i) q^{24} +(139.433 - 241.505i) q^{25} +3.23567 q^{26} +70.5328 q^{27} +(83.7659 - 145.087i) q^{28} +202.800i q^{29} +(-4.10188 - 7.10466i) q^{30} -214.828i q^{31} +(49.4474 - 28.5485i) q^{32} +(-36.0581 - 62.4544i) q^{33} +(-10.2260 - 17.7120i) q^{34} +(368.667 + 212.850i) q^{35} -199.083 q^{36} +(-165.387 + 152.643i) q^{37} +20.5825 q^{38} +(-12.5459 - 7.24339i) q^{39} +(48.2691 + 83.6046i) q^{40} +(-89.4937 - 155.008i) q^{41} +(7.48876 - 4.32364i) q^{42} -173.529i q^{43} +(210.942 + 365.362i) q^{44} -505.873i q^{45} +(20.7550 - 35.9488i) q^{46} -84.7846 q^{47} -83.5758 q^{48} +(-52.8576 + 91.5521i) q^{49} +(-72.9238 + 42.1026i) q^{50} +91.5682i q^{51} +(73.3945 + 42.3743i) q^{52} +(-193.547 + 335.233i) q^{53} +(-18.4444 - 10.6489i) q^{54} +(-928.390 + 536.006i) q^{55} +(-88.1245 + 50.8787i) q^{56} +(-79.8061 - 46.0761i) q^{57} +(30.6183 - 53.0325i) q^{58} +(109.309 + 63.1098i) q^{59} -214.873i q^{60} +(380.801 - 219.855i) q^{61} +(-32.4342 + 56.1776i) q^{62} +533.223 q^{63} +477.320 q^{64} +(-107.674 + 186.496i) q^{65} +21.7758i q^{66} +(-171.325 - 296.744i) q^{67} -535.680i q^{68} +(-160.951 + 92.9249i) q^{69} +(-64.2713 - 111.321i) q^{70} +(0.101892 + 0.176482i) q^{71} +(104.721 + 60.4608i) q^{72} -1.97518 q^{73} +(66.2947 - 14.9466i) q^{74} +377.005 q^{75} +(466.871 + 269.548i) q^{76} +(-564.985 - 978.582i) q^{77} +(2.18718 + 3.78831i) q^{78} +(-28.7722 + 16.6116i) q^{79} +1242.36i q^{80} +(-292.149 - 506.017i) q^{81} +54.0462i q^{82} +(225.261 - 390.163i) q^{83} +226.490 q^{84} +1361.17 q^{85} +(-26.1990 + 45.3780i) q^{86} +(-237.438 + 137.085i) q^{87} -256.249i q^{88} +(-150.387 - 86.8260i) q^{89} +(-76.3756 + 132.286i) q^{90} +(-196.579 - 113.495i) q^{91} +(941.572 - 543.617i) q^{92} +(251.520 - 145.215i) q^{93} +(22.1713 + 12.8006i) q^{94} +(-684.925 + 1186.33i) q^{95} +(66.8489 + 38.5952i) q^{96} -829.748i q^{97} +(27.6446 - 15.9606i) q^{98} +(-671.389 + 1162.88i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 6 q^{2} - 3 q^{3} + 18 q^{4} + 18 q^{5} + 23 q^{7} - 53 q^{9}+O(q^{10}) \) 16 * q - 6 * q^2 - 3 * q^3 + 18 * q^4 + 18 * q^5 + 23 * q^7 - 53 * q^9	\( 16 q - 6 q^{2} - 3 q^{3} + 18 q^{4} + 18 q^{5} + 23 q^{7} - 53 q^{9} - 4 q^{10} + 36 q^{11} + 14 q^{12} - 9 q^{13} - 93 q^{15} + 90 q^{16} - 210 q^{17} - 144 q^{18} - 135 q^{19} - 18 q^{20} + 71 q^{21} + 18 q^{22} - 126 q^{24} - 72 q^{25} - 276 q^{26} + 1170 q^{27} + 256 q^{28} - 236 q^{30} - 552 q^{32} + 336 q^{33} + 274 q^{34} - 27 q^{35} + 180 q^{36} - 33 q^{37} + 1344 q^{38} - 909 q^{39} - 756 q^{40} + 642 q^{41} + 846 q^{42} - 6 q^{44} + 74 q^{46} - 468 q^{47} - 284 q^{48} + 187 q^{49} - 1932 q^{50} + 180 q^{52} - 249 q^{53} - 342 q^{54} + 162 q^{55} - 996 q^{56} - 141 q^{57} - 1496 q^{58} - 1455 q^{59} + 1188 q^{61} - 510 q^{62} - 3472 q^{63} + 3476 q^{64} + 579 q^{65} - 1033 q^{67} + 810 q^{69} + 2934 q^{70} + 2319 q^{71} + 5196 q^{72} - 1672 q^{73} - 1110 q^{74} + 4364 q^{75} - 3450 q^{76} - 2472 q^{77} + 2622 q^{78} + 1569 q^{79} - 1508 q^{81} + 975 q^{83} + 3064 q^{84} + 3128 q^{85} - 36 q^{86} - 5892 q^{87} + 522 q^{89} - 2908 q^{90} - 1773 q^{91} - 3462 q^{92} + 222 q^{93} - 1614 q^{94} - 4311 q^{95} + 378 q^{96} + 5748 q^{98} - 3606 q^{99}+O(q^{100}) \) 16 * q - 6 * q^2 - 3 * q^3 + 18 * q^4 + 18 * q^5 + 23 * q^7 - 53 * q^9 - 4 * q^10 + 36 * q^11 + 14 * q^12 - 9 * q^13 - 93 * q^15 + 90 * q^16 - 210 * q^17 - 144 * q^18 - 135 * q^19 - 18 * q^20 + 71 * q^21 + 18 * q^22 - 126 * q^24 - 72 * q^25 - 276 * q^26 + 1170 * q^27 + 256 * q^28 - 236 * q^30 - 552 * q^32 + 336 * q^33 + 274 * q^34 - 27 * q^35 + 180 * q^36 - 33 * q^37 + 1344 * q^38 - 909 * q^39 - 756 * q^40 + 642 * q^41 + 846 * q^42 - 6 * q^44 + 74 * q^46 - 468 * q^47 - 284 * q^48 + 187 * q^49 - 1932 * q^50 + 180 * q^52 - 249 * q^53 - 342 * q^54 + 162 * q^55 - 996 * q^56 - 141 * q^57 - 1496 * q^58 - 1455 * q^59 + 1188 * q^61 - 510 * q^62 - 3472 * q^63 + 3476 * q^64 + 579 * q^65 - 1033 * q^67 + 810 * q^69 + 2934 * q^70 + 2319 * q^71 + 5196 * q^72 - 1672 * q^73 - 1110 * q^74 + 4364 * q^75 - 3450 * q^76 - 2472 * q^77 + 2622 * q^78 + 1569 * q^79 - 1508 * q^81 + 975 * q^83 + 3064 * q^84 + 3128 * q^85 - 36 * q^86 - 5892 * q^87 + 522 * q^89 - 2908 * q^90 - 1773 * q^91 - 3462 * q^92 + 222 * q^93 - 1614 * q^94 - 4311 * q^95 + 378 * q^96 + 5748 * q^98 - 3606 * q^99

Introduction

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