LMFDB - Embedded newform 65.4.e.a.61.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [65,4,Mod(16,65)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(65, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("65.16");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 65 = 5 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	65.e (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:	$3.83512415037$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} - 2 x^{13} + 45 x^{12} - 52 x^{11} + 1311 x^{10} - 1336 x^{9} + 20343 x^{8} - 11166 x^{7} + \cdots + 1157776 $ x^14 - 2x^13 + 45x^12 - 52x^11 + 1311x^10 - 1336x^9 + 20343x^8 - 11166x^7 + 216447x^6 - 107836x^5 + 1201133x^4 + 4392x^3 + 3890980x^2 - 1936800*x + 1157776
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			61.7
Root			$-2.26209 + 3.91806i$ of defining polynomial
Character	$\chi$	$=$	65.61
Dual form			65.4.e.a.16.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(2.26209 - 3.91806i) q^{2} +(0.652503 - 1.13017i) q^{3} +(-6.23413 - 10.7978i) q^{4} -5.00000 q^{5} +(-2.95204 - 5.11309i) q^{6} +(-11.9953 - 20.7765i) q^{7} -20.2152 q^{8} +(12.6485 + 21.9078i) q^{9} +(-11.3105 + 19.5903i) q^{10} +(29.3205 - 50.7846i) q^{11} -16.2711 q^{12} +(17.8486 + 43.3408i) q^{13} -108.538 q^{14} +(-3.26251 + 5.65084i) q^{15} +(4.14434 - 7.17821i) q^{16} +(60.0480 + 104.006i) q^{17} +114.448 q^{18} +(-27.3664 - 47.3999i) q^{19} +(31.1706 + 53.9891i) q^{20} -31.3079 q^{21} +(-132.651 - 229.759i) q^{22} +(-36.1994 + 62.6992i) q^{23} +(-13.1905 + 22.8466i) q^{24} +25.0000 q^{25} +(210.187 + 28.1089i) q^{26} +68.2478 q^{27} +(-149.561 + 259.047i) q^{28} +(85.9073 - 148.796i) q^{29} +(14.7602 + 25.5654i) q^{30} +33.9594 q^{31} +(-99.6106 - 172.531i) q^{32} +(-38.2634 - 66.2741i) q^{33} +543.337 q^{34} +(59.9766 + 103.882i) q^{35} +(157.704 - 273.152i) q^{36} +(-15.0648 + 26.0931i) q^{37} -247.621 q^{38} +(60.6287 + 8.10803i) q^{39} +101.076 q^{40} +(-168.452 + 291.767i) q^{41} +(-70.8214 + 122.666i) q^{42} +(187.918 + 325.483i) q^{43} -731.150 q^{44} +(-63.2424 - 109.539i) q^{45} +(163.773 + 283.663i) q^{46} -521.206 q^{47} +(-5.40839 - 9.36761i) q^{48} +(-116.275 + 201.395i) q^{49} +(56.5523 - 97.9515i) q^{50} +156.726 q^{51} +(356.716 - 462.919i) q^{52} -178.510 q^{53} +(154.383 - 267.399i) q^{54} +(-146.602 + 253.923i) q^{55} +(242.488 + 420.001i) q^{56} -71.4265 q^{57} +(-388.661 - 673.180i) q^{58} +(-94.7555 - 164.121i) q^{59} +81.3557 q^{60} +(67.5234 + 116.954i) q^{61} +(76.8193 - 133.055i) q^{62} +(303.445 - 525.582i) q^{63} -835.004 q^{64} +(-89.2432 - 216.704i) q^{65} -346.221 q^{66} +(-174.172 + 301.676i) q^{67} +(748.694 - 1296.78i) q^{68} +(47.2404 + 81.8228i) q^{69} +542.690 q^{70} +(128.762 + 223.022i) q^{71} +(-255.692 - 442.871i) q^{72} +754.283 q^{73} +(68.1562 + 118.050i) q^{74} +(16.3126 - 28.2542i) q^{75} +(-341.211 + 590.995i) q^{76} -1406.83 q^{77} +(168.915 - 219.206i) q^{78} +22.0508 q^{79} +(-20.7217 + 35.8911i) q^{80} +(-296.977 + 514.379i) q^{81} +(762.106 + 1320.01i) q^{82} -519.665 q^{83} +(195.177 + 338.057i) q^{84} +(-300.240 - 520.031i) q^{85} +1700.35 q^{86} +(-112.110 - 194.179i) q^{87} +(-592.720 + 1026.62i) q^{88} +(451.105 - 781.338i) q^{89} -572.241 q^{90} +(686.370 - 890.719i) q^{91} +902.687 q^{92} +(22.1586 - 38.3798i) q^{93} +(-1179.02 + 2042.11i) q^{94} +(136.832 + 237.000i) q^{95} -259.985 q^{96} +(712.566 + 1234.20i) q^{97} +(526.051 + 911.147i) q^{98} +1483.44 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18}+ \cdots + 11378 q^{99}+O(q^{100}) $ 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/65\mathbb{Z}\right)^\times$.

$n$	$27$	$41$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	2.26209	−	3.91806i	0.799771	−	1.38524i	−0.119995	−	0.992775i	$-0.538288\pi$
$2$	2.26209	−	3.91806i	0.799771	−	1.38524i	0.919765	−	0.392469i	$-0.128379\pi$
$3$	0.652503	−	1.13017i	0.125574	−	0.217501i	−0.796383	−	0.604793i	$-0.793256\pi$
$3$	0.652503	−	1.13017i	0.125574	−	0.217501i	0.921957	+	0.387292i	$0.126589\pi$
$4$	−6.23413	−	10.7978i	−0.779266	−	1.34973i
$5$	−5.00000			−0.447214
$5$	−5.00000			−0.447214
$6$	−2.95204	−	5.11309i	−0.200861	−	0.347902i
$7$	−11.9953	−	20.7765i	−0.647686	−	1.12183i	−0.983674	−	0.179959i	$-0.942403\pi$
$7$	−11.9953	−	20.7765i	−0.647686	−	1.12183i	0.335988	−	0.941866i	$-0.390930\pi$
$8$	−20.2152			−0.893394
$9$	12.6485	+	21.9078i	0.468462	+	0.811400i
$10$	−11.3105	+	19.5903i	−0.357668	+	0.619500i
$11$	29.3205	−	50.7846i	0.803678	−	1.39201i	−0.113502	−	0.993538i	$-0.536207\pi$
$11$	29.3205	−	50.7846i	0.803678	−	1.39201i	0.917180	−	0.398473i	$-0.130460\pi$
$12$	−16.2711			−0.391423
$13$	17.8486	+	43.3408i	0.380794	+	0.924660i
$13$	17.8486	+	43.3408i	0.380794	+	0.924660i
$14$	−108.538			−2.07200
$15$	−3.26251	+	5.65084i	−0.0561585	+	0.0972693i
$16$	4.14434	−	7.17821i	0.0647554	−	0.112160i
$17$	60.0480	+	104.006i	0.856693	+	1.48384i	0.875065	+	0.484005i	$0.160818\pi$
$17$	60.0480	+	104.006i	0.856693	+	1.48384i	−0.0183718	+	0.999831i	$0.505848\pi$
$18$	114.448			1.49865
$19$	−27.3664	−	47.3999i	−0.330436	−	0.572331i	0.652162	−	0.758080i	$-0.273862\pi$
$19$	−27.3664	−	47.3999i	−0.330436	−	0.572331i	−0.982597	+	0.185749i	$0.940529\pi$
$20$	31.1706	+	53.9891i	0.348498	+	0.603617i
$21$	−31.3079			−0.325331
$22$	−132.651	−	229.759i	−1.28552	−	2.22658i
$23$	−36.1994	+	62.6992i	−0.328178	+	0.568421i	−0.982150	−	0.188097i	$-0.939768\pi$
$23$	−36.1994	+	62.6992i	−0.328178	+	0.568421i	0.653972	+	0.756519i	$0.273101\pi$
$24$	−13.1905	+	22.8466i	−0.112187	+	0.194314i
$25$	25.0000			0.200000
$26$	210.187	+	28.1089i	1.58543	+	0.212023i
$27$	68.2478			0.486455
$28$	−149.561	+	259.047i	−1.00944	+	1.74840i
$29$	85.9073	−	148.796i	0.550089	−	0.952783i	−0.448178	−	0.893944i	$-0.647927\pi$
$29$	85.9073	−	148.796i	0.550089	−	0.952783i	0.998268	−	0.0588385i	$-0.0187397\pi$
$30$	14.7602	+	25.5654i	0.0898278	+	0.155586i
$31$	33.9594			0.196751			0.0983756	−	0.995149i	$-0.468635\pi$
$31$	33.9594			0.196751			0.0983756	+	0.995149i	$0.468635\pi$
$32$	−99.6106	−	172.531i	−0.550276	−	0.953106i
$33$	−38.2634	−	66.2741i	−0.201842	−	0.349601i
$34$	543.337			2.74063
$35$	59.9766	+	103.882i	0.289654	+	0.501696i
$36$	157.704	−	273.152i	0.730113	−	1.26459i
$37$	−15.0648	+	26.0931i	−0.0669364	+	0.115937i	−0.897551	−	0.440910i	$-0.854656\pi$
$37$	−15.0648	+	26.0931i	−0.0669364	+	0.115937i	0.830615	+	0.556847i	$0.187989\pi$
$38$	−247.621			−1.05709
$39$	60.6287	+	8.10803i	0.248932	+	0.0332903i
$40$	101.076			0.399538
$41$	−168.452	+	291.767i	−0.641651	+	1.11137i	0.343413	+	0.939185i	$0.388417\pi$
$41$	−168.452	+	291.767i	−0.641651	+	1.11137i	−0.985064	+	0.172188i	$0.944916\pi$
$42$	−70.8214	+	122.666i	−0.260190	+	0.450662i
$43$	187.918	+	325.483i	0.666447	+	1.15432i	0.978891	+	0.204384i	$0.0655191\pi$
$43$	187.918	+	325.483i	0.666447	+	1.15432i	−0.312444	+	0.949936i	$0.601148\pi$
$44$	−731.150			−2.50512
$45$	−63.2424	−	109.539i	−0.209503	−	0.362869i
$46$	163.773	+	283.663i	0.524934	+	0.909213i
$47$	−521.206			−1.61757			−0.808783	−	0.588107i	$-0.799874\pi$
$47$	−521.206			−1.61757			−0.808783	+	0.588107i	$0.799874\pi$
$48$	−5.40839	−	9.36761i	−0.0162632	−	0.0281687i
$49$	−116.275	+	201.395i	−0.338995	+	0.587156i
$50$	56.5523	−	97.9515i	0.159954	−	0.277049i
$51$	156.726			0.430314
$52$	356.716	−	462.919i	0.951299	−	1.23452i
$53$	−178.510			−0.462645			−0.231323	−	0.972877i	$-0.574305\pi$
$53$	−178.510			−0.462645			−0.231323	+	0.972877i	$0.574305\pi$
$54$	154.383	−	267.399i	0.389053	−	0.673859i
$55$	−146.602	+	253.923i	−0.359416	+	0.622526i
$56$	242.488	+	420.001i	0.578639	+	1.00223i
$57$	−71.4265			−0.165977
$58$	−388.661	−	673.180i	−0.879891	−	1.52402i
$59$	−94.7555	−	164.121i	−0.209087	−	0.362149i	0.742340	−	0.670023i	$-0.233716\pi$
$59$	−94.7555	−	164.121i	−0.209087	−	0.362149i	−0.951427	+	0.307874i	$0.900382\pi$
$60$	81.3557			0.175050
$61$	67.5234	+	116.954i	0.141729	+	0.245482i	0.928148	−	0.372212i	$-0.121400\pi$
$61$	67.5234	+	116.954i	0.141729	+	0.245482i	−0.786419	+	0.617694i	$0.788067\pi$
$62$	76.8193	−	133.055i	0.157356	−	0.272548i
$63$	303.445	−	525.582i	0.606833	−	1.05107i
$64$	−835.004			−1.63087
$65$	−89.2432	−	216.704i	−0.170296	−	0.413520i
$66$	−346.221			−0.645711
$67$	−174.172	+	301.676i	−0.317590	+	0.550083i	−0.979985	−	0.199073i	$-0.936207\pi$
$67$	−174.172	+	301.676i	−0.317590	+	0.550083i	0.662394	+	0.749155i	$0.269540\pi$
$68$	748.694	−	1296.78i	1.33518	−	2.31261i
$69$	47.2404	+	81.8228i	0.0824214	+	0.142758i
$70$	542.690			0.926627
$71$	128.762	+	223.022i	0.215228	+	0.372786i	0.953343	−	0.301889i	$-0.0976171\pi$
$71$	128.762	+	223.022i	0.215228	+	0.372786i	−0.738115	+	0.674675i	$0.764284\pi$
$72$	−255.692	−	442.871i	−0.418522	−	0.724901i
$73$	754.283			1.20935			0.604673	−	0.796474i	$-0.293304\pi$
$73$	754.283			1.20935			0.604673	+	0.796474i	$0.293304\pi$
$74$	68.1562	+	118.050i	0.107067	+	0.185446i
$75$	16.3126	−	28.2542i	0.0251148	−	0.0435002i
$76$	−341.211	+	590.995i	−0.514994	+	0.891996i
$77$	−1406.83			−2.08212
$78$	168.915	−	219.206i	0.245204	−	0.318207i
$79$	22.0508			0.0314040			0.0157020	−	0.999877i	$-0.495002\pi$
$79$	22.0508			0.0314040			0.0157020	+	0.999877i	$0.495002\pi$
$80$	−20.7217	+	35.8911i	−0.0289595	+	0.0501593i
$81$	−296.977	+	514.379i	−0.407376	+	0.705596i
$82$	762.106	+	1320.01i	1.02635	+	1.77769i
$83$	−519.665			−0.687237			−0.343619	−	0.939109i	$-0.611653\pi$
$83$	−519.665			−0.687237			−0.343619	+	0.939109i	$0.611653\pi$
$84$	195.177	+	338.057i	0.253519	+	0.439108i
$85$	−300.240	−	520.031i	−0.383125	−	0.663592i
$86$	1700.35			2.13202
$87$	−112.110	−	194.179i	−0.138154	−	0.239290i
$88$	−592.720	+	1026.62i	−0.718001	+	1.24361i
$89$	451.105	−	781.338i	0.537271	−	0.930580i	−0.461779	−	0.886995i	$-0.652789\pi$
$89$	451.105	−	781.338i	0.537271	−	0.930580i	0.999050	−	0.0435850i	$-0.0138779\pi$
$90$	−572.241			−0.670216
$91$	686.370	−	890.719i	0.790672	−	1.02607i
$92$	902.687			1.02295
$93$	22.1586	−	38.3798i	0.0247069	−	0.0427936i
$94$	−1179.02	+	2042.11i	−1.29368	+	2.24072i
$95$	136.832	+	237.000i	0.147775	+	0.255954i
$96$	−259.985			−0.276402
$97$	712.566	+	1234.20i	0.745878	+	1.29190i	0.949784	+	0.312907i	$0.101303\pi$
$97$	712.566	+	1234.20i	0.745878	+	1.29190i	−0.203906	+	0.978990i	$0.565364\pi$
$98$	526.051	+	911.147i	0.542236	+	0.939181i
$99$	1483.44			1.50597
$100$	−155.853	−	269.946i	−0.155853	−	0.269946i
$101$	−351.627	+	609.036i	−0.346418	+	0.600014i	−0.985610	−	0.169033i	$-0.945935\pi$
$101$	−351.627	+	609.036i	−0.346418	+	0.600014i	0.639192	+	0.769047i	$0.279269\pi$
$102$	354.529	−	614.062i	0.344153	−	0.596090i
$103$	−66.3873			−0.0635081			−0.0317541	−	0.999496i	$-0.510109\pi$
$103$	−66.3873			−0.0635081			−0.0317541	+	0.999496i	$0.510109\pi$
$104$	−360.814	−	876.143i	−0.340199	−	0.826086i
$105$	156.540			0.145492
$106$	−403.805	+	699.412i	−0.370010	+	0.640876i
$107$	295.321	−	511.511i	0.266820	−	0.462146i	−0.701219	−	0.712946i	$-0.747360\pi$
$107$	295.321	−	511.511i	0.266820	−	0.462146i	0.968039	+	0.250800i	$0.0806937\pi$
$108$	−425.465	−	736.928i	−0.379078	−	0.656583i
$109$	822.089			0.722402			0.361201	−	0.932488i	$-0.382367\pi$
$109$	822.089			0.722402			0.361201	+	0.932488i	$0.382367\pi$
$110$	663.257	+	1148.79i	0.574900	+	0.995757i
$111$	19.6597	+	34.0516i	0.0168110	+	0.0291174i
$112$	−198.851			−0.167765
$113$	−350.024	−	606.260i	−0.291394	−	0.504709i	0.682746	−	0.730656i	$-0.260786\pi$
$113$	−350.024	−	606.260i	−0.291394	−	0.504709i	−0.974140	+	0.225947i	$0.927452\pi$
$114$	−161.573	+	279.853i	−0.132743	+	0.229918i
$115$	180.997	−	313.496i	0.146766	−	0.254206i
$116$	−2142.23			−1.71466
$117$	−723.744	+	939.220i	−0.571882	+	0.742145i
$118$	−857.382			−0.668885
$119$	1440.59	−	2495.18i	1.10974	−	1.92212i
$120$	65.9524	−	114.233i	0.0501717	−	0.0868999i
$121$	−1053.88	−	1825.38i	−0.791797	−	1.37143i
$122$	610.977			0.453404
$123$	219.830	+	380.757i	0.161150	+	0.279119i
$124$	−211.707	−	366.688i	−0.153322	−	0.265561i
$125$	−125.000			−0.0894427
$126$	−1372.84	−	2377.83i	−0.970654	−	1.68122i
$127$	934.052	−	1617.83i	0.652628	−	1.13038i	−0.329855	−	0.944032i	$-0.607000\pi$
$127$	934.052	−	1617.83i	0.652628	−	1.13038i	0.982483	−	0.186353i	$-0.0596668\pi$
$128$	−1091.97	+	1891.35i	−0.754044	+	1.30604i
$129$	490.468			0.334754
$130$	−1050.94	−	140.544i	−0.709024	−	0.0948196i
$131$	1319.18			0.879824			0.439912	−	0.898041i	$-0.355010\pi$
$131$	1319.18			0.879824			0.439912	+	0.898041i	$0.355010\pi$
$132$	−477.078	+	826.323i	−0.314578	+	0.544865i
$133$	−656.537	+	1137.15i	−0.428037	+	0.741382i
$134$	787.988	+	1364.84i	0.507999	+	0.879880i
$135$	−341.239			−0.217549
$136$	−1213.88	−	2102.51i	−0.765365	−	1.32565i
$137$	−1021.20	−	1768.78i	−0.636841	−	1.10304i	−0.986122	−	0.166023i	$-0.946907\pi$
$137$	−1021.20	−	1768.78i	−0.636841	−	1.10304i	0.349280	−	0.937018i	$-0.386426\pi$
$138$	427.449			0.263673
$139$	−446.779	−	773.844i	−0.272628	−	0.472206i	0.696906	−	0.717163i	$-0.254560\pi$
$139$	−446.779	−	773.844i	−0.272628	−	0.472206i	−0.969534	+	0.244957i	$0.921226\pi$
$140$	747.803	−	1295.23i	0.451435	−	0.781908i
$141$	−340.088	+	589.050i	−0.203125	+	0.351822i
$142$	1165.08			0.688533
$143$	2724.38	+	364.338i	1.59317	+	0.213059i
$144$	209.679			0.121342
$145$	−429.537	+	743.979i	−0.246007	+	0.426097i
$146$	1706.26	−	2955.33i	0.967199	−	1.67524i
$147$	151.740	+	262.821i	0.0851380	+	0.147463i
$148$	375.665			0.208645
$149$	−1296.53	−	2245.65i	−0.712856	−	1.23470i	−0.963781	−	0.266696i	$-0.914068\pi$
$149$	−1296.53	−	2245.65i	−0.712856	−	1.23470i	0.250925	−	0.968006i	$-0.419265\pi$
$150$	−73.8011	−	127.827i	−0.0401722	−	0.0695803i
$151$	−2707.82			−1.45933			−0.729667	−	0.683802i	$-0.760325\pi$
$151$	−2707.82			−1.45933			−0.729667	+	0.683802i	$0.760325\pi$
$152$	553.217	+	958.200i	0.295209	+	0.511317i
$153$	−1519.03	+	2631.04i	−0.802657	+	1.39024i
$154$	−3182.39	+	5512.06i	−1.66522	+	2.88425i
$155$	−169.797			−0.0879898
$156$	−290.418	−	705.204i	−0.149051	−	0.361933i
$157$	−287.720			−0.146258			−0.0731291	−	0.997322i	$-0.523299\pi$
$157$	−287.720			−0.146258			−0.0731291	+	0.997322i	$0.523299\pi$
$158$	49.8810	−	86.3965i	0.0251160	−	0.0435021i
$159$	−116.478	+	201.746i	−0.0580963	+	0.100626i
$160$	498.053	+	862.653i	0.246091	+	0.426242i
$161$	1736.89			0.850226
$162$	1343.58	+	2327.15i	0.651615	+	1.12863i
$163$	845.925	+	1465.18i	0.406490	+	0.704062i	0.994494	−	0.104797i	$-0.0334192\pi$
$163$	845.925	+	1465.18i	0.406490	+	0.704062i	−0.588003	+	0.808858i	$0.700086\pi$
$164$	4200.59			2.00007
$165$	191.317	+	331.371i	0.0902667	+	0.156346i
$166$	−1175.53	+	2036.08i	−0.549632	+	0.951991i
$167$	−1764.25	+	3055.77i	−0.817496	+	1.41595i	0.0900251	+	0.995939i	$0.471305\pi$
$167$	−1764.25	+	3055.77i	−0.817496	+	1.41595i	−0.907521	+	0.420006i	$0.862028\pi$
$168$	632.896			0.290649
$169$	−1559.85	+	1547.15i	−0.709992	+	0.704210i
$170$	−2716.68			−1.22565
$171$	692.286	−	1199.07i	0.309593	−	0.536231i
$172$	2343.01	−	4058.21i	1.03868	−	1.79904i
$173$	−296.017	−	512.717i	−0.130091	−	0.225325i	0.793620	−	0.608413i	$-0.208194\pi$
$173$	−296.017	−	512.717i	−0.130091	−	0.225325i	−0.923712	+	0.383089i	$0.874860\pi$
$174$	−1014.41			−0.441966
$175$	−299.883	−	519.412i	−0.129537	−	0.224365i
$176$	−243.028	−	420.937i	−0.104085	−	0.180280i
$177$	−247.313			−0.105024
$178$	−2040.88	−	3534.92i	−0.859386	−	1.48850i
$179$	−1385.83	+	2400.32i	−0.578668	+	1.00228i	0.416964	+	0.908923i	$0.363094\pi$
$179$	−1385.83	+	2400.32i	−0.578668	+	1.00228i	−0.995632	+	0.0933600i	$0.970239\pi$
$180$	−788.522	+	1365.76i	−0.326517	+	0.565543i
$181$	1899.01			0.779845			0.389923	−	0.920848i	$-0.372502\pi$
$181$	1899.01			0.779845			0.389923	+	0.920848i	$0.372502\pi$
$182$	−1937.26	−	4704.13i	−0.789006	−	1.91590i
$183$	176.237			0.0711902
$184$	731.778	−	1267.48i	0.293193	−	0.507824i
$185$	75.3242	−	130.465i	0.0299349	−	0.0518487i
$186$	−100.250	−	173.637i	−0.0395197	−	0.0684501i
$187$	7042.55			2.75402
$188$	3249.26	+	5627.89i	1.26051	+	2.18328i
$189$	−818.654	−	1417.95i	−0.315070	−	0.545718i
$190$	1238.11			0.472745
$191$	−156.763	−	271.521i	−0.0593871	−	0.102862i	0.834803	−	0.550548i	$-0.185581\pi$
$191$	−156.763	−	271.521i	−0.0593871	−	0.102862i	−0.894190	+	0.447687i	$0.852248\pi$
$192$	−544.842	+	943.695i	−0.204795	+	0.354715i
$193$	1232.01	−	2133.90i	0.459492	−	0.795863i	−0.539442	−	0.842023i	$-0.681365\pi$
$193$	1232.01	−	2133.90i	0.459492	−	0.795863i	0.998934	+	0.0461596i	$0.0146983\pi$
$194$	6447.56			2.38612
$195$	−303.143	−	40.5401i	−0.111326	−	0.0148879i
$196$	2899.50			1.05667
$197$	−1957.86	+	3391.11i	−0.708080	+	1.22643i	0.257488	+	0.966281i	$0.417105\pi$
$197$	−1957.86	+	3391.11i	−0.708080	+	1.22643i	−0.965568	+	0.260149i	$0.916228\pi$
$198$	3355.68	−	5812.20i	1.20443	−	2.08614i
$199$	−1264.32	−	2189.87i	−0.450379	−	0.780080i	0.548030	−	0.836459i	$-0.315378\pi$
$199$	−1264.32	−	2189.87i	−0.450379	−	0.780080i	−0.998409	+	0.0563789i	$0.982045\pi$
$200$	−505.380			−0.178679
$201$	227.296	+	393.688i	0.0797623	+	0.138152i
$202$	1590.83	+	2755.39i	0.554110	+	0.959746i
$203$	−4121.94			−1.42514
$204$	−977.050	−	1692.30i	−0.335329	−	0.580807i
$205$	842.258	−	1458.83i	0.286955	−	0.497021i
$206$	−150.174	+	260.109i	−0.0507919	+	0.0879742i
$207$	−1831.47			−0.614956
$208$	385.081	+	51.4978i	0.128368	+	0.0171670i
$209$	−3209.58			−1.06226
$210$	354.107	−	613.331i	0.116360	−	0.201542i
$211$	−1350.64	+	2339.38i	−0.440674	+	0.763269i	−0.997740	−	0.0671992i	$-0.978594\pi$
$211$	−1350.64	+	2339.38i	−0.440674	+	0.763269i	0.557066	+	0.830468i	$0.311927\pi$
$212$	1112.85	+	1927.52i	0.360524	+	0.624445i
$213$	336.069			0.108108
$214$	−1336.09	−	2314.17i	−0.426790	−	0.739222i
$215$	−939.590	−	1627.42i	−0.298044	−	0.516228i
$216$	−1379.64			−0.434597
$217$	−407.354	−	705.557i	−0.127433	−	0.220721i
$218$	1859.64	−	3220.99i	0.577756	−	1.00070i
$219$	492.172	−	852.467i	0.151863	−	0.263034i
$220$	3655.75			1.12032
$221$	−3435.94	+	4458.90i	−1.04582	+	1.35719i
$222$	177.888			0.0537796
$223$	−1348.76	+	2336.13i	−0.405022	+	0.701518i	−0.994324	−	0.106395i	$-0.966069\pi$
$223$	−1348.76	+	2336.13i	−0.405022	+	0.701518i	0.589302	+	0.807913i	$0.299403\pi$
$224$	−2389.72	+	4139.12i	−0.712812	+	1.23463i
$225$	316.212	+	547.695i	0.0936924	+	0.162280i
$226$	−3167.15			−0.932193
$227$	−346.491	−	600.141i	−0.101310	−	0.175475i	0.810914	−	0.585165i	$-0.198970\pi$
$227$	−346.491	−	600.141i	−0.101310	−	0.175475i	−0.912225	+	0.409690i	$0.865637\pi$
$228$	445.282	+	771.251i	0.129340	+	0.224023i
$229$	4862.62			1.40319			0.701596	−	0.712575i	$-0.252471\pi$
$229$	4862.62			1.40319			0.701596	+	0.712575i	$0.252471\pi$
$230$	−818.864	−	1418.31i	−0.234758	−	0.406612i
$231$	−917.963	+	1589.96i	−0.261461	+	0.452864i
$232$	−1736.63	+	3007.94i	−0.491447	+	0.851211i
$233$	−5035.20			−1.41574			−0.707868	−	0.706344i	$-0.750343\pi$
$233$	−5035.20			−1.41574			−0.707868	+	0.706344i	$0.750343\pi$
$234$	2042.74	+	4960.28i	0.570677	+	1.38574i
$235$	2606.03			0.723398
$236$	−1181.44	+	2046.31i	−0.325868	+	0.564420i
$237$	14.3882	−	24.9211i	0.00394353	−	0.00683039i
$238$	−6517.50	−	11288.6i	−1.77507	−	3.07451i
$239$	6434.46			1.74147			0.870734	−	0.491754i	$-0.163644\pi$
$239$	6434.46			1.74147			0.870734	+	0.491754i	$0.163644\pi$
$240$	27.0420	+	46.8380i	0.00727313	+	0.0125974i
$241$	1833.46	+	3175.64i	0.490056	+	0.848802i	0.999935	−	0.0114445i	$-0.00364298\pi$
$241$	1833.46	+	3175.64i	0.490056	+	0.848802i	−0.509878	+	0.860246i	$0.670310\pi$
$242$	−9535.91			−2.53302
$243$	1308.90	+	2267.08i	0.345540	+	0.598492i
$244$	841.899	−	1458.21i	0.220890	−	0.382592i
$245$	581.376	−	1006.97i	0.151603	−	0.262584i
$246$	1989.10			0.515531
$247$	1565.90	−	2032.11i	0.403384	−	0.523481i
$248$	−686.496			−0.175776
$249$	−339.083	+	587.309i	−0.0862992	+	0.149475i
$250$	−282.762	+	489.757i	−0.0715337	+	0.123900i
$251$	592.081	+	1025.51i	0.148892	+	0.257888i	0.930818	−	0.365483i	$-0.119096\pi$
$251$	592.081	+	1025.51i	0.148892	+	0.257888i	−0.781926	+	0.623371i	$0.785763\pi$
$252$	−7566.86			−1.89154
$253$	2122.77	+	3676.74i	0.527499	+	0.913655i
$254$	−4225.83	−	7319.34i	−1.04391	−	1.80810i
$255$	−783.630			−0.192442
$256$	1600.27	+	2771.74i	0.390690	+	0.676695i
$257$	171.224	−	296.568i	0.0415590	−	0.0719822i	−0.844498	−	0.535559i	$-0.820101\pi$
$257$	171.224	−	296.568i	0.0415590	−	0.0719822i	0.886057	+	0.463577i	$0.153434\pi$
$258$	1109.48	−	1921.68i	0.267727	−	0.463716i
$259$	722.830			0.173415
$260$	−1783.58	+	2314.59i	−0.425434	+	0.552096i
$261$	4346.39			1.03078
$262$	2984.10	−	5168.61i	0.703657	−	1.21877i
$263$	2084.57	−	3610.58i	0.488746	−	0.846533i	−0.511170	−	0.859479i	$-0.670788\pi$
$263$	2084.57	−	3610.58i	0.488746	−	0.846533i	0.999916	+	0.0129469i	$0.00412123\pi$
$264$	773.502	+	1339.75i	0.180325	+	0.312332i
$265$	892.549			0.206901
$266$	2970.29	+	5144.70i	0.684663	+	1.18587i
$267$	−588.695	−	1019.65i	−0.134935	−	0.233714i
$268$	4343.25			0.989949
$269$	−3523.03	−	6102.06i	−0.798523	−	1.38308i	−0.920578	−	0.390559i	$-0.872282\pi$
$269$	−3523.03	−	6102.06i	−0.798523	−	1.38308i	0.122055	−	0.992523i	$-0.461052\pi$
$270$	−771.914	+	1336.99i	−0.173990	+	0.301359i
$271$	427.890	−	741.127i	0.0959131	−	0.166126i	−0.814076	−	0.580758i	$-0.802756\pi$
$271$	427.890	−	741.127i	0.0959131	−	0.166126i	0.909989	+	0.414632i	$0.136090\pi$
$272$	995.439			0.221902
$273$	−558.804	−	1356.91i	−0.123884	−	0.300820i
$274$	−9240.22			−2.03731
$275$	733.012	−	1269.61i	0.160736	−	0.278402i
$276$	589.005	−	1020.19i	0.128456	−	0.222493i
$277$	−1386.44	−	2401.39i	−0.300734	−	0.520887i	0.675568	−	0.737297i	$-0.263898\pi$
$277$	−1386.44	−	2401.39i	−0.300734	−	0.520887i	−0.976302	+	0.216411i	$0.930565\pi$
$278$	−4042.62			−0.872160
$279$	429.535	+	743.976i	0.0921705	+	0.159644i
$280$	−1212.44	−	2100.01i	−0.258775	−	0.448212i
$281$	−3642.98			−0.773387			−0.386693	−	0.922208i	$-0.626383\pi$
$281$	−3642.98			−0.773387			−0.386693	+	0.922208i	$0.626383\pi$
$282$	1538.62	+	2664.97i	0.324906	+	0.562754i
$283$	−2277.44	+	3944.64i	−0.478374	+	0.828568i	−0.999693	−	0.0247941i	$-0.992107\pi$
$283$	−2277.44	+	3944.64i	−0.478374	+	0.828568i	0.521319	+	0.853362i	$0.325440\pi$
$284$	1605.43	−	2780.69i	0.335440	−	0.580999i
$285$	357.133			0.0742270
$286$	7590.29	−	9850.10i	1.56931	−	2.03653i
$287$	8082.52			1.66236
$288$	2519.85	−	4364.50i	0.515567	−	0.892988i
$289$	−4755.03	+	8235.96i	−0.967847	+	1.67636i
$290$	1943.30	+	3365.90i	0.393499	+	0.681560i
$291$	1859.80			0.374652
$292$	−4702.30	−	8144.62i	−0.942401	−	1.63229i
$293$	1194.27	+	2068.53i	0.238123	+	0.412440i	0.960176	−	0.279397i	$-0.0901347\pi$
$293$	1194.27	+	2068.53i	0.238123	+	0.412440i	−0.722053	+	0.691838i	$0.756801\pi$
$294$	1373.00			0.272364
$295$	473.777	+	820.606i	0.0935064	+	0.161958i
$296$	304.539	−	527.477i	0.0598006	−	0.103578i
$297$	2001.06	−	3465.94i	0.390954	−	0.677151i
$298$	−11731.4			−2.28048
$299$	−3363.54	−	449.815i	−0.650565	−	0.0870017i
$300$	−406.778			−0.0782845
$301$	4508.27	−	7808.56i	0.863297	−	1.49527i
$302$	−6125.35	+	10609.4i	−1.16713	+	2.02153i
$303$	458.875	+	794.796i	0.0870023	+	0.150692i
$304$	−453.663			−0.0855899
$305$	−337.617	−	584.770i	−0.0633833	−	0.109783i
$306$	6872.39	+	11903.3i	1.28388	+	2.22375i
$307$	2433.64			0.452427			0.226214	−	0.974078i	$-0.427365\pi$
$307$	2433.64			0.452427			0.226214	+	0.974078i	$0.427365\pi$
$308$	8770.38	+	15190.7i	1.62253	+	2.81030i
$309$	−43.3179	+	75.0288i	−0.00797498	+	0.0138131i
$310$	−384.097	+	665.275i	−0.0703717	+	0.121887i
$311$	−8792.93			−1.60322			−0.801610	−	0.597848i	$-0.796023\pi$
$311$	−8792.93			−1.60322			−0.801610	+	0.597848i	$0.796023\pi$
$312$	−1225.62	−	163.905i	−0.222395	−	0.0297414i
$313$	4131.37			0.746066			0.373033	−	0.927818i	$-0.378318\pi$
$313$	4131.37			0.746066			0.373033	+	0.927818i	$0.378318\pi$
$314$	−650.848	+	1127.30i	−0.116973	+	0.202603i
$315$	−1517.23	+	2627.91i	−0.271384	+	0.470051i
$316$	−137.468	−	238.101i	−0.0244720	−	0.0423868i
$317$	−1517.03			−0.268785			−0.134392	−	0.990928i	$-0.542908\pi$
$317$	−1517.03			−0.268785			−0.134392	+	0.990928i	$0.542908\pi$
$318$	526.968	+	912.736i	0.0929274	+	0.160955i
$319$	−5037.69	−	8725.53i	−0.884190	−	1.53146i
$320$	4175.02			0.729346
$321$	−385.396	−	667.525i	−0.0670115	−	0.116067i
$322$	3929.01	−	6805.25i	0.679986	−	1.17777i
$323$	3286.59	−	5692.55i	0.566164	−	0.980625i
$324$	7405.57			1.26982
$325$	446.216	+	1083.52i	0.0761588	+	0.184932i
$326$	7654.24			1.30040
$327$	536.415	−	929.099i	0.0907151	−	0.157123i
$328$	3405.28	−	5898.12i	0.573248	−	0.992894i
$329$	6252.03	+	10828.8i	1.04768	+	1.81463i
$330$	1731.11			0.288771
$331$	−948.440	−	1642.75i	−0.157495	−	0.272790i	0.776469	−	0.630155i	$-0.217009\pi$
$331$	−948.440	−	1642.75i	−0.157495	−	0.272790i	−0.933965	+	0.357365i	$0.883675\pi$
$332$	3239.66	+	5611.26i	0.535540	+	0.927583i
$333$	−762.190			−0.125429
$334$	7981.80	+	13824.9i	1.30762	+	2.26486i
$335$	870.862	−	1508.38i	0.142031	−	0.246004i
$336$	−129.751	+	224.735i	−0.0210669	+	0.0364890i
$337$	831.978			0.134483			0.0672414	−	0.997737i	$-0.478580\pi$
$337$	831.978			0.134483			0.0672414	+	0.997737i	$0.478580\pi$
$338$	2533.30	+	9611.39i	0.407672	+	1.54672i
$339$	−913.567			−0.146366
$340$	−3743.47	+	6483.88i	−0.597112	+	1.03423i
$341$	995.706	−	1724.61i	0.158125	−	0.273880i
$342$	−3132.03	−	5424.84i	−0.495207	−	0.857724i
$343$	−2649.75			−0.417123
$344$	−3798.80	−	6579.72i	−0.595400	−	1.03126i
$345$	−236.202	−	409.114i	−0.0368600	−	0.0638434i
$346$	−2678.48			−0.416173
$347$	−113.311	−	196.261i	−0.0175299	−	0.0303627i	0.857127	−	0.515105i	$-0.172247\pi$
$347$	−113.311	−	196.261i	−0.0175299	−	0.0303627i	−0.874657	+	0.484742i	$0.838914\pi$
$348$	−1397.81	+	2421.08i	−0.215317	+	0.372941i
$349$	1437.37	−	2489.60i	0.220461	−	0.381849i	−0.734487	−	0.678623i	$-0.762577\pi$
$349$	1437.37	−	2489.60i	0.220461	−	0.381849i	0.954948	+	0.296773i	$0.0959105\pi$
$350$	−2713.45			−0.414400
$351$	1218.13	+	2957.92i	0.185239	+	0.449806i
$352$	−11682.5			−1.76898
$353$	−4734.09	+	8199.69i	−0.713797	+	1.23633i	0.249625	+	0.968343i	$0.419693\pi$
$353$	−4734.09	+	8199.69i	−0.713797	+	1.23633i	−0.963422	+	0.267990i	$0.913641\pi$
$354$	−559.444	+	968.986i	−0.0839947	+	0.145483i
$355$	−643.809	−	1115.11i	−0.0962530	−	0.166715i
$356$	−11249.0			−1.67471
$357$	−1879.98	−	3256.22i	−0.278709	−	0.482738i
$358$	6269.74	+	10859.5i	0.925604	+	1.60319i
$359$	−8449.69			−1.24222			−0.621111	−	0.783723i	$-0.713318\pi$
$359$	−8449.69			−1.24222			−0.621111	+	0.783723i	$0.713318\pi$
$360$	1278.46	+	2214.35i	0.187169	+	0.324185i
$361$	1931.66	−	3345.74i	0.281625	−	0.487788i
$362$	4295.73	−	7440.42i	0.623697	−	1.08028i
$363$	−2750.64			−0.397717
$364$	−13896.7	−	1858.45i	−2.00106	−	0.267607i
$365$	−3771.42			−0.540836
$366$	398.664	−	690.506i	0.0569358	−	0.0986157i
$367$	−428.469	+	742.130i	−0.0609425	+	0.105556i	−0.894887	−	0.446293i	$-0.852744\pi$
$367$	−428.469	+	742.130i	−0.0609425	+	0.105556i	0.833944	+	0.551848i	$0.186077\pi$
$368$	300.046	+	519.694i	0.0425026	+	0.0736167i
$369$	−8522.62			−1.20236
$370$	−340.781	−	590.250i	−0.0478820	−	0.0829341i
$371$	2141.28	+	3708.81i	0.299649	+	0.519007i
$372$	−552.558			−0.0770129
$373$	135.981	+	235.526i	0.0188762	+	0.0326945i	0.875309	−	0.483564i	$-0.160658\pi$
$373$	135.981	+	235.526i	0.0188762	+	0.0326945i	−0.856433	+	0.516258i	$0.827325\pi$
$374$	15930.9	−	27593.1i	2.20259	−	3.81499i
$375$	−81.5628	+	141.271i	−0.0112317	+	0.0194539i
$376$	10536.3			1.44512
$377$	7982.26	+	1067.49i	1.09047	+	0.145831i
$378$	−7407.49			−1.00794
$379$	133.479	−	231.193i	0.0180907	−	0.0313340i	−0.856838	−	0.515585i	$-0.827575\pi$
$379$	133.479	−	231.193i	0.0180907	−	0.0313340i	0.874929	+	0.484251i	$0.160908\pi$
$380$	1706.05	−	2954.97i	0.230312	−	0.398913i
$381$	−1218.94	−	2111.27i	−0.163906	−	0.283894i
$382$	−1418.45			−0.189984
$383$	−2263.57	−	3920.61i	−0.301992	−	0.523065i	0.674595	−	0.738188i	$-0.264318\pi$
$383$	−2263.57	−	3920.61i	−0.301992	−	0.523065i	−0.976587	+	0.215123i	$0.930985\pi$
$384$	1425.03	+	2468.22i	0.189377	+	0.328010i
$385$	7034.17			0.931155
$386$	−5573.83	−	9654.16i	−0.734976	−	1.27302i
$387$	−4753.75	+	8233.74i	−0.624411	+	1.08151i
$388$	8884.45	−	15388.3i	1.16247	−	2.01346i
$389$	7560.47			0.985427			0.492713	−	0.870192i	$-0.336005\pi$
$389$	7560.47			0.985427			0.492713	+	0.870192i	$0.336005\pi$
$390$	−844.577	+	1096.03i	−0.109659	+	0.142307i
$391$	−8694.81			−1.12459
$392$	2350.53	−	4071.23i	0.302856	−	0.524562i
$393$	860.766	−	1490.89i	0.110483	−	0.191363i
$394$	8857.72	+	15342.0i	1.13260	+	1.96173i
$395$	−110.254			−0.0140443
$396$	−9247.94	−	16017.9i	−1.17355	−	2.03265i
$397$	−1046.36	−	1812.35i	−0.132280	−	0.229116i	0.792275	−	0.610164i	$-0.208897\pi$
$397$	−1046.36	−	1812.35i	−0.132280	−	0.229116i	−0.924555	+	0.381048i	$0.875563\pi$
$398$	−11440.1			−1.44080
$399$	856.784	+	1483.99i	0.107501	+	0.186197i
$400$	103.609	−	179.455i	0.0129511	−	0.0224319i
$401$	7859.30	−	13612.7i	0.978740	−	1.69523i	0.311742	−	0.950167i	$-0.399087\pi$
$401$	7859.30	−	13612.7i	0.978740	−	1.69523i	0.666997	−	0.745060i	$-0.267579\pi$
$402$	2056.66			0.255166
$403$	606.129	+	1471.83i	0.0749217	+	0.181928i
$404$	8768.36			1.07981
$405$	1484.89	−	2571.90i	0.182184	−	0.315552i
$406$	−9324.22	+	16150.0i	−1.13979	+	1.97417i
$407$	883.417	+	1530.12i	0.107591	+	0.186352i
$408$	−3168.25			−0.384440
$409$	−4039.08	−	6995.89i	−0.488312	−	0.845781i	0.511598	−	0.859225i	$-0.329054\pi$
$409$	−4039.08	−	6995.89i	−0.488312	−	0.845781i	−0.999910	+	0.0134440i	$0.995721\pi$
$410$	−3810.53	−	6600.03i	−0.458997	−	0.795006i
$411$	−2665.35			−0.319883
$412$	413.867	+	716.838i	0.0494897	+	0.0857187i
$413$	−2273.24	+	3937.37i	−0.270845	+	0.469117i
$414$	−4142.95	+	7175.81i	−0.491824	+	0.851864i
$415$	2598.33			0.307342
$416$	5699.70	−	7396.64i	0.671757	−	0.871755i
$417$	−1166.10			−0.136940
$418$	−7260.37	+	12575.3i	−0.849561	+	1.47148i
$419$	2285.24	−	3958.15i	0.266447	−	0.461500i	−0.701495	−	0.712675i	$-0.747484\pi$
$419$	2285.24	−	3958.15i	0.266447	−	0.461500i	0.967942	+	0.251175i	$0.0808170\pi$
$420$	−975.887	−	1690.29i	−0.113377	−	0.196375i
$421$	4464.14			0.516791			0.258395	−	0.966039i	$-0.416806\pi$
$421$	4464.14			0.516791			0.258395	+	0.966039i	$0.416806\pi$
$422$	6110.56	+	10583.8i	0.704875	+	1.22088i
$423$	−6592.46	−	11418.5i	−0.757769	−	1.31249i
$424$	3608.61			0.413325
$425$	1501.20	+	2600.16i	0.171339	+	0.296767i
$426$	760.220	−	1316.74i	0.0864619	−	0.149756i
$427$	1619.93	−	2805.80i	0.183592	−	0.317991i
$428$	−7364.28			−0.831696
$429$	2189.42	−	2841.27i	0.246402	−	0.319762i
$430$	−8501.76			−0.953468
$431$	−7798.80	+	13507.9i	−0.871589	+	1.50964i	−0.0112369	+	0.999937i	$0.503577\pi$
$431$	−7798.80	+	13507.9i	−0.871589	+	1.50964i	−0.860352	+	0.509700i	$0.829756\pi$
$432$	282.842	−	489.897i	0.0315006	−	0.0545606i
$433$	−6754.48	−	11699.1i	−0.749653	−	1.29844i	−0.947989	−	0.318303i	$-0.896887\pi$
$433$	−6754.48	−	11699.1i	−0.749653	−	1.29844i	0.198336	−	0.980134i	$-0.436446\pi$
$434$	−3685.89			−0.407669
$435$	560.548	+	970.897i	0.0617844	+	0.107014i
$436$	−5125.01	−	8876.77i	−0.562944	−	0.975047i
$437$	3962.59			0.433767
$438$	−2226.68	−	3856.72i	−0.242910	−	0.420733i
$439$	−788.131	+	1365.08i	−0.0856844	+	0.148410i	−0.905683	−	0.423956i	$-0.860641\pi$
$439$	−788.131	+	1365.08i	−0.0856844	+	0.148410i	0.819998	+	0.572366i	$0.193974\pi$
$440$	2963.60	−	5133.10i	0.321100	−	0.556162i
$441$	−5882.82			−0.635225
$442$	9697.83	+	23548.7i	1.04362	+	2.53415i
$443$	4117.26			0.441573			0.220787	−	0.975322i	$-0.429138\pi$
$443$	4117.26			0.441573			0.220787	+	0.975322i	$0.429138\pi$
$444$	245.122	−	424.564i	0.0262004	−	0.0453804i
$445$	−2255.53	+	3906.69i	−0.240275	+	0.416168i
$446$	6102.05	+	10569.1i	0.647849	+	1.12211i
$447$	−3383.94			−0.358065
$448$	10016.1	+	17348.5i	1.05629	+	1.82955i
$449$	−925.027	−	1602.19i	−0.0972266	−	0.168401i	0.813309	−	0.581832i	$-0.197664\pi$
$449$	−925.027	−	1602.19i	−0.0972266	−	0.168401i	−0.910536	+	0.413430i	$0.864330\pi$
$450$	2861.20			0.299730
$451$	9878.16	+	17109.5i	1.03136	+	1.78637i
$452$	−4364.19	+	7559.00i	−0.454147	+	0.786605i
$453$	−1766.86	+	3060.29i	−0.183255	+	0.317407i
$454$	−3135.18			−0.324100
$455$	−3431.85	+	4453.60i	−0.353599	+	0.458874i
$456$	1443.90			0.148283
$457$	−1686.09	+	2920.39i	−0.172586	+	0.298928i	−0.939323	−	0.343033i	$-0.888546\pi$
$457$	−1686.09	+	2920.39i	−0.172586	+	0.298928i	0.766737	+	0.641961i	$0.221879\pi$
$458$	10999.7	−	19052.0i	1.12223	−	1.94376i
$459$	4098.15	+	7098.20i	0.416743	+	0.721820i
$460$	−4513.43			−0.457478
$461$	−2597.03	−	4498.19i	−0.262377	−	0.454450i	0.704496	−	0.709708i	$-0.251173\pi$
$461$	−2597.03	−	4498.19i	−0.262377	−	0.454450i	−0.966873	+	0.255258i	$0.917840\pi$
$462$	4153.03	+	7193.27i	0.418218	+	0.724375i
$463$	2058.57			0.206631			0.103315	−	0.994649i	$-0.467055\pi$
$463$	2058.57			0.206631			0.103315	+	0.994649i	$0.467055\pi$
$464$	−712.059	−	1233.32i	−0.0712425	−	0.123396i
$465$	−110.793	+	191.899i	−0.0110493	+	0.0191379i
$466$	−11390.1	+	19728.2i	−1.13226	+	1.96114i
$467$	1702.66			0.168714			0.0843572	−	0.996436i	$-0.473116\pi$
$467$	1702.66			0.168714			0.0843572	+	0.996436i	$0.473116\pi$
$468$	14653.4	+	1959.64i	1.44734	+	0.193557i
$469$	8357.02			0.822796
$470$	5895.08	−	10210.6i	0.578552	−	1.00208i
$471$	−187.738	+	325.171i	−0.0183662	+	0.0318113i
$472$	1915.50	+	3317.75i	0.186797	+	0.323542i
$473$	22039.4			2.14244
$474$	−65.0950	−	112.748i	−0.00630783	−	0.0109255i
$475$	−684.159	−	1185.00i	−0.0660871	−	0.114466i
$476$	−35923.3			−3.45912
$477$	−2257.88	−	3910.76i	−0.216732	−	0.375390i
$478$	14555.4	−	25210.6i	1.39277	−	2.41236i
$479$	−6462.23	+	11192.9i	−0.616423	+	1.06768i	0.373710	+	0.927546i	$0.378085\pi$
$479$	−6462.23	+	11192.9i	−0.616423	+	1.06768i	−0.990133	+	0.140130i	$0.955248\pi$
$480$	1299.92			0.123611
$481$	−1399.78	−	187.196i	−0.132691	−	0.0177452i
$482$	16589.8			1.56773
$483$	1133.33	−	1962.98i	0.106766	−	0.184925i
$484$	−13140.1	+	22759.3i	−1.23404	+	2.13742i
$485$	−3562.83	−	6171.00i	−0.333567	−	0.577754i
$486$	11843.4			1.10541
$487$	−9121.29	−	15798.5i	−0.848717	−	1.47002i	−0.882354	−	0.470587i	$-0.844042\pi$
$487$	−9121.29	−	15798.5i	−0.848717	−	1.47002i	0.0336365	−	0.999434i	$-0.489291\pi$
$488$	−1365.00	−	2364.25i	−0.126620	−	0.219313i
$489$	2207.87			0.204179
$490$	−2630.25	−	4555.73i	−0.242495	−	0.420014i
$491$	232.918	−	403.425i	0.0214082	−	0.0370801i	−0.855123	−	0.518425i	$-0.826518\pi$
$491$	232.918	−	403.425i	0.0214082	−	0.0370801i	0.876531	+	0.481345i	$0.159852\pi$
$492$	2740.90	−	4747.37i	0.251157	−	0.435017i
$493$	20634.3			1.88503
$494$	−4419.70	−	10732.1i	−0.402534	−	0.977449i
$495$	−7417.19			−0.673491
$496$	140.739	−	243.768i	0.0127407	−	0.0220675i
$497$	3089.08	−	5350.44i	0.278801	−	0.482897i
$498$	1534.07	+	2657.09i	0.138039	+	0.239091i
$499$	15702.6			1.40871			0.704355	−	0.709848i	$-0.251236\pi$
$499$	15702.6			1.40871			0.704355	+	0.709848i	$0.251236\pi$
$500$	779.266	+	1349.73i	0.0696997	+	0.120723i
$501$	2302.36	+	3987.80i	0.205313	+	0.355612i
$502$	5357.37			0.476317
$503$	665.427	+	1152.55i	0.0589860	+	0.102167i	0.894010	−	0.448046i	$-0.147880\pi$
$503$	665.427	+	1152.55i	0.0589860	+	0.102167i	−0.835025	+	0.550213i	$0.814547\pi$
$504$	−6134.20	+	10624.8i	−0.542141	+	0.939016i
$505$	1758.14	−	3045.18i	0.154923	−	0.268334i
$506$	19207.6			1.68751
$507$	730.731	+	2772.41i	0.0640097	+	0.242854i
$508$	−23292.0			−2.03428
$509$	−2410.80	+	4175.63i	−0.209935	+	0.363618i	−0.951694	−	0.307049i	$-0.900659\pi$
$509$	−2410.80	+	4175.63i	−0.209935	+	0.363618i	0.741759	+	0.670667i	$0.233992\pi$
$510$	−1772.64	+	3070.31i	−0.153910	+	0.266580i
$511$	−9047.87	−	15671.4i	−0.783276	−	1.35667i
$512$	−2991.74			−0.258237
$513$	−1867.69	−	3234.94i	−0.160742	−	0.278414i
$514$	−774.649	−	1341.73i	−0.0664753	−	0.115139i
$515$	331.937			0.0284017
$516$	−3057.64	−	5295.99i	−0.260862	−	0.451827i
$517$	−15282.0	+	26469.2i	−1.30000	+	2.25167i
$518$	1635.11	−	2832.09i	0.138692	−	0.240222i
$519$	−772.609			−0.0653444
$520$	1804.07	+	4380.72i	0.152142	+	0.369437i
$521$	20701.6			1.74080			0.870398	−	0.492349i	$-0.163862\pi$
$521$	20701.6			1.74080			0.870398	+	0.492349i	$0.163862\pi$
$522$	9831.94	−	17029.4i	0.824391	−	1.42789i
$523$	8558.21	−	14823.3i	0.715534	−	1.23934i	−0.247219	−	0.968960i	$-0.579517\pi$
$523$	8558.21	−	14823.3i	0.715534	−	1.23934i	0.962753	−	0.270382i	$-0.0871500\pi$
$524$	−8223.91	−	14244.2i	−0.685617	−	1.18752i
$525$	−782.698			−0.0650661
$526$	−9430.98	−	16334.9i	−0.781769	−	1.35406i
$527$	2039.20	+	3531.99i	0.168555	+	0.291947i
$528$	−634.307			−0.0522815
$529$	3462.71	+	5997.58i	0.284598	+	0.492939i
$530$	2019.03	−	3497.06i	0.165473	−	0.286608i
$531$	2397.03	−	4151.77i	0.195898	−	0.339306i
$532$	16371.7			1.33422
$533$	−15652.0	−	2093.19i	−1.27198	−	0.170105i
$534$	−5326.73			−0.431667
$535$	−1476.61	+	2557.56i	−0.119326	+	0.206678i
$536$	3520.93	−	6098.43i	0.283733	−	0.491441i
$537$	1808.51	+	3132.44i	0.145332	+	0.251722i
$538$	−31877.6			−2.55454
$539$	6818.49	+	11810.0i	0.544886	+	0.943769i
$540$	2127.33	+	3684.64i	0.169529	+	0.293633i
$541$	845.992			0.0672311			0.0336156	−	0.999435i	$-0.489298\pi$
$541$	845.992			0.0672311			0.0336156	+	0.999435i	$0.489298\pi$
$542$	−1935.85	−	3353.00i	−0.153417	−	0.265726i
$543$	1239.11	−	2146.20i	0.0979284	−	0.169617i
$544$	11962.8	−	20720.2i	0.942836	−	1.63304i
$545$	−4110.45			−0.323068
$546$	−6580.52	−	880.030i	−0.515788	−	0.0689776i
$547$	−8021.60			−0.627018			−0.313509	−	0.949585i	$-0.601505\pi$
$547$	−8021.60			−0.627018			−0.313509	+	0.949585i	$0.601505\pi$
$548$	−12732.6	+	22053.5i	−0.992538	+	1.71913i
$549$	−1708.14	+	2958.58i	−0.132790	+	0.229998i
$550$	−3316.28	−	5743.97i	−0.257103	−	0.445316i
$551$	−9403.89			−0.727076
$552$	−954.975	−	1654.06i	−0.0736348	−	0.127539i
$553$	−264.507	−	458.139i	−0.0203399	−	0.0352298i
$554$	−12545.1			−0.962073
$555$	−98.2985	−	170.258i	−0.00751809	−	0.0130217i
$556$	−5570.56	+	9648.49i	−0.424900	+	0.735948i
$557$	−8938.04	+	15481.1i	−0.679923	+	1.17766i	0.295081	+	0.955472i	$0.404653\pi$
$557$	−8938.04	+	15481.1i	−0.679923	+	1.17766i	−0.975004	+	0.222189i	$0.928680\pi$
$558$	3886.59			0.294861
$559$	−10752.6	+	13954.0i	−0.813574	+	1.05580i
$560$	994.254			0.0750266
$561$	4595.28	−	7959.26i	0.345834	−	0.599002i
$562$	−8240.75	+	14273.4i	−0.618532	+	1.07133i
$563$	5676.27	+	9831.58i	0.424913	+	0.735971i	0.996412	−	0.0846314i	$-0.0269713\pi$
$563$	5676.27	+	9831.58i	0.424913	+	0.735971i	−0.571499	+	0.820603i	$0.693638\pi$
$564$	8480.61			0.633152
$565$	1750.12	+	3031.30i	0.130315	+	0.225713i
$566$	10303.6	+	17846.3i	0.765179	+	1.32533i
$567$	14249.3			1.05541
$568$	−2602.94	−	4508.43i	−0.192284	−	0.333045i
$569$	6158.56	−	10666.9i	0.453744	−	0.785907i	−0.544871	−	0.838520i	$-0.683422\pi$
$569$	6158.56	−	10666.9i	0.453744	−	0.785907i	0.998615	+	0.0526127i	$0.0167549\pi$
$570$	807.867	−	1399.27i	0.0593646	−	0.102823i
$571$	−12308.0			−0.902053			−0.451026	−	0.892511i	$-0.648942\pi$
$571$	−12308.0			−0.902053			−0.451026	+	0.892511i	$0.648942\pi$
$572$	−13050.0	−	31688.7i	−0.953933	−	2.31638i
$573$	−409.152			−0.0298300
$574$	18283.4	−	31667.8i	1.32950	−	2.30277i
$575$	−904.985	+	1567.48i	−0.0656356	+	0.113684i
$576$	−10561.5	−	18293.1i	−0.764000	−	1.32329i
$577$	1025.50			0.0739895			0.0369948	−	0.999315i	$-0.488222\pi$
$577$	1025.50			0.0739895			0.0369948	+	0.999315i	$0.488222\pi$
$578$	21512.6	+	37261.0i	1.54811	+	2.68141i
$579$	−1607.78	−	2784.75i	−0.115401	−	0.199880i
$580$	10711.1			0.766821
$581$	6233.55	+	10796.8i	0.445114	+	0.770960i
$582$	4207.05	−	7286.83i	0.299636	−	0.518984i
$583$	−5233.99	+	9065.54i	−0.371818	+	0.644007i
$584$	−15248.0			−1.08042
$585$	3618.72	−	4696.10i	0.255753	−	0.331897i
$586$	10806.2			0.761774
$587$	−4590.13	+	7950.34i	−0.322751	+	0.559022i	−0.981055	−	0.193731i	$-0.937941\pi$
$587$	−4590.13	+	7950.34i	−0.322751	+	0.559022i	0.658303	+	0.752753i	$0.271274\pi$
$588$	1891.93	−	3276.92i	0.132690	−	0.229826i
$589$	−929.346	−	1609.67i	−0.0650136	−	0.112607i
$590$	4286.91			0.299135
$591$	2555.02	+	4425.42i	0.177833	+	0.308016i
$592$	124.868	+	216.277i	0.00866898	+	0.0150151i
$593$	−12396.9			−0.858485			−0.429243	−	0.903189i	$-0.641219\pi$
$593$	−12396.9			−0.858485			−0.429243	+	0.903189i	$0.641219\pi$
$594$	−9053.16	−	15680.5i	−0.625346	−	1.08313i
$595$	−7202.95	+	12475.9i	−0.496289	+	0.859599i
$596$	−16165.4	+	27999.3i	−1.11101	+	1.92432i
$597$	−3299.90			−0.226224
$598$	−9371.05	+	12161.0i	−0.640821	+	0.831609i
$599$	8858.65			0.604265			0.302132	−	0.953266i	$-0.402302\pi$
$599$	8858.65			0.604265			0.302132	+	0.953266i	$0.402302\pi$
$600$	−329.762	+	571.164i	−0.0224375	+	0.0388628i
$601$	5638.06	−	9765.40i	0.382664	−	0.662794i	−0.608778	−	0.793341i	$-0.708340\pi$
$601$	5638.06	−	9765.40i	0.382664	−	0.662794i	0.991442	+	0.130547i	$0.0416733\pi$
$602$	−20396.3	−	35327.4i	−1.38088	−	2.39175i
$603$	−8812.07			−0.595116
$604$	16880.9	+	29238.6i	1.13721	+	1.96971i
$605$	5269.41	+	9126.88i	0.354102	+	0.613323i
$606$	4152.07			0.278328
$607$	−6670.55	−	11553.7i	−0.446045	−	0.772573i	0.552079	−	0.833792i	$-0.313835\pi$
$607$	−6670.55	−	11553.7i	−0.446045	−	0.772573i	−0.998124	+	0.0612187i	$0.980501\pi$
$608$	−5451.96	+	9443.07i	−0.363662	+	0.629880i
$609$	−2689.58	+	4658.49i	−0.178961	+	0.309969i
$610$	−3054.88			−0.202768
$611$	−9302.81	−	22589.5i	−0.615960	−	1.49570i
$612$	37879.4			2.50193
$613$	7335.82	−	12706.0i	0.483346	−	0.837179i	−0.516471	−	0.856304i	$-0.672755\pi$
$613$	7335.82	−	12706.0i	0.483346	−	0.837179i	0.999817	+	0.0191252i	$0.00608812\pi$
$614$	5505.12	−	9535.14i	0.361838	−	0.626722i
$615$	−1099.15	−	1903.78i	−0.0720683	−	0.124826i
$616$	28439.4			1.86016
$617$	−10365.7	−	17954.0i	−0.676351	−	1.17147i	−0.976072	−	0.217447i	$-0.930227\pi$
$617$	−10365.7	−	17954.0i	−0.676351	−	1.17147i	0.299721	−	0.954027i	$-0.403106\pi$
$618$	195.978	+	339.444i	0.0127563	+	0.0220946i
$619$	13271.2			0.861737			0.430869	−	0.902415i	$-0.358207\pi$
$619$	13271.2			0.861737			0.430869	+	0.902415i	$0.358207\pi$
$620$	1058.54	+	1833.44i	0.0685675	+	0.118762i
$621$	−2470.53	+	4279.08i	−0.159644	+	0.276512i
$622$	−19890.4	+	34451.2i	−1.28221	+	2.22085i
$623$	−21644.6			−1.39193
$624$	309.467	−	401.603i	0.0198535	−	0.0257644i
$625$	625.000			0.0400000
$626$	9345.54	−	16186.9i	0.596682	−	1.03348i
$627$	−2094.26	+	3627.36i	−0.133392	+	0.231041i
$628$	1793.68	+	3106.75i	0.113974	+	0.197409i
$629$	−3618.46			−0.229376
$630$	6864.21	+	11889.2i	0.434090	+	0.751866i
$631$	−11617.1	−	20121.3i	−0.732912	−	1.26944i	−0.955633	−	0.294559i	$-0.904827\pi$
$631$	−11617.1	−	20121.3i	−0.732912	−	1.26944i	0.222721	−	0.974882i	$-0.428506\pi$
$632$	−445.762			−0.0280561
$633$	1762.60	+	3052.91i	0.110674	+	0.191694i
$634$	−3431.66	+	5943.80i	−0.214966	+	0.372332i
$635$	−4670.26	+	8089.13i	−0.291864	+	0.505523i
$636$	2904.56			0.181090
$637$	−10804.0	−	1444.84i	−0.672007	−	0.0898693i
$638$	−45582.9			−2.82860
$639$	−3257.28	+	5641.78i	−0.201653	+	0.349273i
$640$	5459.86	−	9456.75i	0.337219	−	0.584080i
$641$	14917.9	+	25838.6i	0.919223	+	1.59214i	0.800597	+	0.599203i	$0.204516\pi$
$641$	14917.9	+	25838.6i	0.919223	+	1.59214i	0.118626	+	0.992939i	$0.462151\pi$
$642$	−3487.20			−0.214375
$643$	12803.5	+	22176.4i	0.785260	+	1.36011i	0.928844	+	0.370472i	$0.120804\pi$
$643$	12803.5	+	22176.4i	0.785260	+	1.36011i	−0.143584	+	0.989638i	$0.545863\pi$
$644$	−10828.0	−	18754.7i	−0.662552	−	1.14757i
$645$	−2452.34			−0.149707
$646$	−14869.2	−	25754.1i	−0.905603	−	1.56855i
$647$	14450.5	−	25028.9i	0.878062	−	1.52085i	0.0245977	−	0.999697i	$-0.492170\pi$
$647$	14450.5	−	25028.9i	0.878062	−	1.52085i	0.853465	−	0.521151i	$-0.174497\pi$
$648$	6003.45	−	10398.3i	0.363947	−	0.630375i
$649$	−11113.1			−0.672153
$650$	5254.68	+	702.722i	0.317085	+	0.0424046i
$651$	−1063.20			−0.0640092
$652$	10547.2	−	18268.3i	0.633528	−	1.09730i
$653$	7795.30	−	13501.9i	0.467157	−	0.809140i	−0.532139	−	0.846657i	$-0.678611\pi$
$653$	7795.30	−	13501.9i	0.467157	−	0.809140i	0.999296	+	0.0375170i	$0.0119448\pi$
$654$	−2426.84	−	4203.41i	−0.145103	−	0.251325i
$655$	−6595.88			−0.393469
$656$	1396.24	+	2418.36i	0.0831008	+	0.143935i
$657$	9540.54	+	16524.7i	0.566532	+	0.981263i
$658$	56570.6			3.35160
$659$	6078.56	+	10528.4i	0.359312	+	0.622347i	0.987846	−	0.155435i	$-0.0496779\pi$
$659$	6078.56	+	10528.4i	0.359312	+	0.622347i	−0.628534	+	0.777782i	$0.716345\pi$
$660$	2385.39	−	4131.61i	0.140683	−	0.243671i
$661$	−903.057	+	1564.14i	−0.0531389	+	0.0920393i	−0.891371	−	0.453274i	$-0.850256\pi$
$661$	−903.057	+	1564.14i	−0.0531389	+	0.0920393i	0.838232	+	0.545313i	$0.183589\pi$
$662$	−8581.84			−0.503841
$663$	2797.35	+	6792.63i	0.163861	+	0.397894i
$664$	10505.1			0.613974
$665$	3282.68	−	5685.77i	0.191424	−	0.331556i
$666$	−1724.14	+	2986.30i	−0.100314	+	0.173749i
$667$	6219.59	+	10772.6i	0.361055	+	0.625365i
$668$	43994.3			2.54819
$669$	1760.14	+	3048.66i	0.101721	+	0.176185i
$670$	−3939.94	−	6824.18i	−0.227184	−	0.393494i
$671$	7919.28			0.455619
$672$	3118.60	+	5401.57i	0.179022	+	0.310075i
$673$	−111.959	+	193.919i	−0.00641263	+	0.0111070i	−0.869214	−	0.494436i	$-0.835375\pi$
$673$	−111.959	+	193.919i	−0.00641263	+	0.0111070i	0.862801	+	0.505543i	$0.168708\pi$
$674$	1882.01	−	3259.74i	0.107555	−	0.186291i
$675$	1706.20			0.0972911
$676$	26430.2	+	7197.88i	1.50376	+	0.409529i
$677$	−25647.4			−1.45600			−0.727998	−	0.685579i	$-0.759549\pi$
$677$	−25647.4			−1.45600			−0.727998	+	0.685579i	$0.759549\pi$
$678$	−2066.57	+	3579.41i	−0.117059	+	0.202753i
$679$	17094.9	−	29609.3i	0.966189	−	1.67349i
$680$	6069.42	+	10512.5i	0.342282	+	0.592849i
$681$	−904.346			−0.0508878
$682$	−4504.76	−	7802.47i	−0.252927	−	0.438082i
$683$	4814.00	+	8338.10i	0.269697	+	0.467128i	0.968783	−	0.247909i	$-0.0797433\pi$
$683$	4814.00	+	8338.10i	0.269697	+	0.467128i	−0.699087	+	0.715037i	$0.746410\pi$
$684$	−17263.2			−0.965022
$685$	5106.02	+	8843.88i	0.284804	+	0.493295i
$686$	−5993.99	+	10381.9i	−0.333603	+	0.577817i
$687$	3172.87	−	5495.58i	0.176205	−	0.305195i
$688$	3115.19			0.172624
$689$	−3186.16	−	7736.76i	−0.176173	−	0.427789i
$690$	−2137.24			−0.117918
$691$	7026.84	−	12170.8i	0.386850	−	0.670044i	−0.605174	−	0.796093i	$-0.706896\pi$
$691$	7026.84	−	12170.8i	0.386850	−	0.670044i	0.992024	+	0.126049i	$0.0402297\pi$
$692$	−3690.82	+	6392.69i	−0.202751	+	0.351176i
$693$	−17794.3	−	30820.7i	−0.975397	−	1.68944i
$694$	−1025.28			−0.0560796
$695$	2233.90	+	3869.22i	0.121923	+	0.211177i
$696$	2266.32	+	3925.38i	0.123426	+	0.213780i
$697$	−40460.7			−2.19879
$698$	−6502.94	−	11263.4i	−0.352636	−	0.610784i
$699$	−3285.48	+	5690.61i	−0.177780	+	0.307924i
$700$	−3739.02	+	6476.17i	−0.201888	+	0.349680i
$701$	18572.1			1.00065			0.500326	−	0.865837i	$-0.333213\pi$
$701$	18572.1			1.00065			0.500326	+	0.865837i	$0.333213\pi$
$702$	14344.8	+	1918.37i	0.771239	+	0.103140i
$703$	1649.08			0.0884726
$704$	−24482.7	+	42405.3i	−1.31069	+	2.27019i
$705$	1700.44	−	2945.25i	0.0908401	−	0.157340i
$706$	21417.9	+	37096.9i	1.14175	+	1.97756i
$707$	16871.5			0.897481
$708$	1541.78	+	2670.44i	0.0818412	+	0.141753i
$709$	13072.4	+	22642.1i	0.692448	+	1.19935i	0.971034	+	0.238943i	$0.0768009\pi$
$709$	13072.4	+	22642.1i	0.692448	+	1.19935i	−0.278586	+	0.960411i	$0.589866\pi$
$710$	−5825.42			−0.307921
$711$	278.909	+	483.085i	0.0147116	+	0.0254812i
$712$	−9119.19	+	15794.9i	−0.479995	+	0.831375i
$713$	−1229.31	+	2129.23i	−0.0645695	+	0.111838i
$714$	−17010.7			−0.891612
$715$	−13621.9	−	1821.69i	−0.712489	−	0.0952829i
$716$	34557.7			1.80375
$717$	4198.50	−	7272.02i	0.218683	−	0.378771i
$718$	−19114.0	+	33106.4i	−0.993492	+	1.72078i
$719$	−14024.9	−	24291.9i	−0.727456	−	1.25999i	−0.957955	−	0.286919i	$-0.907369\pi$
$719$	−14024.9	−	24291.9i	−0.727456	−	1.25999i	0.230498	−	0.973073i	$-0.425964\pi$
$720$	−1048.39			−0.0542657
$721$	796.337	+	1379.30i	0.0411333	+	0.0712450i
$722$	−8739.20	−	15136.7i	−0.450470	−	0.780237i
$723$	4785.35			0.246154
$724$	−11838.6	−	20505.1i	−0.607707	−	1.05258i
$725$	2147.68	−	3719.90i	0.110018	−	0.190557i
$726$	−6222.21	+	10777.2i	−0.318082	+	0.550935i
$727$	19837.1			1.01199			0.505996	−	0.862536i	$-0.331125\pi$
$727$	19837.1			1.01199			0.505996	+	0.862536i	$0.331125\pi$
$728$	−13875.1	+	18006.1i	−0.706382	+	0.916689i
$729$	−12620.5			−0.641189
$730$	−8531.29	+	14776.6i	−0.432544	+	0.749189i
$731$	−22568.2	+	39089.3i	−1.14188	+	1.97780i
$732$	−1098.68	−	1902.97i	−0.0554761	−	0.0960874i
$733$	18080.4			0.911070			0.455535	−	0.890218i	$-0.349448\pi$
$733$	18080.4			0.911070			0.455535	+	0.890218i	$0.349448\pi$
$734$	1938.47	+	3357.53i	0.0974800	+	0.168840i
$735$	−758.699	−	1314.11i	−0.0380749	−	0.0659476i
$736$	14423.4			0.722354
$737$	10213.6	+	17690.5i	0.510481	+	0.884179i
$738$	−19279.0	+	33392.1i	−0.961610	+	1.66556i
$739$	−11987.2	+	20762.4i	−0.596693	+	1.03350i	0.396613	+	0.917986i	$0.370186\pi$
$739$	−11987.2	+	20762.4i	−0.596693	+	1.03350i	−0.993306	+	0.115516i	$0.963148\pi$
$740$	−1878.32			−0.0933088
$741$	−1274.87	−	3095.68i	−0.0632030	−	0.153472i
$742$	19375.1			0.958601
$743$	5130.54	−	8886.35i	0.253326	−	0.438773i	−0.711114	−	0.703077i	$-0.751809\pi$
$743$	5130.54	−	8886.35i	0.253326	−	0.438773i	0.964439	+	0.264304i	$0.0851422\pi$
$744$	−447.941	+	775.856i	−0.0220730	+	0.0382315i
$745$	6482.63	+	11228.2i	0.318799	+	0.552176i
$746$	1230.40			0.0603865
$747$	−6572.98	−	11384.7i	−0.321945	−	0.557625i
$748$	−43904.1	−	76044.2i	−2.14612	−	3.71718i
$749$	−14169.9			−0.691263
$750$	369.005	+	639.136i	0.0179656	+	0.0311173i
$751$	5330.48	−	9232.66i	0.259004	−	0.448608i	−0.706972	−	0.707242i	$-0.749939\pi$
$751$	5330.48	−	9232.66i	0.259004	−	0.448608i	0.965975	+	0.258634i	$0.0832725\pi$
$752$	−2160.05	+	3741.32i	−0.104746	+	0.181426i
$753$	1545.34			0.0747878
$754$	22239.1	−	28860.2i	1.07414	−	1.39394i
$755$	13539.1			0.652634
$756$	−10207.2	+	17679.4i	−0.491047	+	0.850519i
$757$	11009.5	−	19069.1i	0.528598	−	0.915559i	−0.470846	−	0.882216i	$-0.656051\pi$
$757$	11009.5	−	19069.1i	0.528598	−	0.915559i	0.999444	−	0.0333434i	$-0.0106155\pi$
$758$	−603.885	−	1045.96i	−0.0289368	−	0.0501200i
$759$	5540.45			0.264961
$760$	−2766.08	−	4791.00i	−0.132022	−	0.228668i
$761$	−9441.19	−	16352.6i	−0.449728	−	0.778952i	0.548640	−	0.836059i	$-0.315146\pi$
$761$	−9441.19	−	16352.6i	−0.449728	−	0.778952i	−0.998368	+	0.0571069i	$0.981812\pi$
$762$	−11029.4			−0.524350
$763$	−9861.22	−	17080.1i	−0.467890	−	0.810409i
$764$	−1954.56	+	3385.39i	−0.0925567	+	0.160313i
$765$	7595.16	−	13155.2i	0.358959	−	0.621735i
$766$	−20481.6			−0.966096
$767$	5421.89	−	7036.12i	0.255245	−	0.331238i
$768$	4176.71			0.196242
$769$	−6314.10	+	10936.3i	−0.296089	+	0.512841i	−0.975238	−	0.221160i	$-0.929016\pi$
$769$	−6314.10	+	10936.3i	−0.296089	+	0.512841i	0.679149	+	0.734001i	$0.262349\pi$
$770$	15911.9	−	27560.3i	0.744710	−	1.28988i
$771$	−223.448	−	387.023i	−0.0104375	−	0.0180782i
$772$	−30722.0			−1.43226
$773$	−17631.7	−	30539.0i	−0.820399	−	1.42097i	−0.905385	−	0.424591i	$-0.860418\pi$
$773$	−17631.7	−	30539.0i	−0.820399	−	1.42097i	0.0849860	−	0.996382i	$-0.472915\pi$
$774$	21506.9	+	37251.0i	0.998770	+	1.72992i
$775$	848.985			0.0393503
$776$	−14404.7	−	24949.6i	−0.666363	−	1.15417i
$777$	471.649	−	816.920i	0.0217765	−	0.0377179i
$778$	17102.5	−	29622.4i	0.788115	−	1.36506i
$779$	18439.6			0.848098
$780$	1452.09	+	3526.02i	0.0666578	+	0.161861i
$781$	15101.4			0.691897
$782$	−19668.5	+	34066.8i	−0.899416	+	1.55783i
$783$	5862.99	−	10155.0i	0.267594	−	0.463486i
$784$	963.769	+	1669.30i	0.0439035	+	0.0760431i
$785$	1438.60			0.0654086
$786$	−3894.26	−	6745.06i	−0.176722	−	0.306092i
$787$	600.047	+	1039.31i	0.0271783	+	0.0470743i	0.879295	−	0.476278i	$-0.158014\pi$
$787$	600.047	+	1039.31i	0.0271783	+	0.0470743i	−0.852116	+	0.523352i	$0.824681\pi$
$788$	48822.2			2.20713
$789$	−2720.38	−	4711.83i	−0.122748	−	0.212605i
$790$	−249.405	+	431.982i	−0.0112322	+	0.0194547i
$791$	−8397.31	+	14544.6i	−0.377464	+	0.653786i
$792$	−29988.0			−1.34543
$793$	−3863.68	+	5013.99i	−0.173018	+	0.224530i
$794$	−9467.86			−0.423176
$795$	582.390	−	1008.73i	0.0259815	−	0.0450012i
$796$	−15763.9	+	27303.9i	−0.701930	+	1.21578i
$797$	12676.0	+	21955.6i	0.563373	+	0.975791i	0.997199	+	0.0747944i	$0.0238300\pi$
$797$	12676.0	+	21955.6i	0.563373	+	0.975791i	−0.433826	+	0.900997i	$0.642837\pi$
$798$	7752.50			0.343904
$799$	−31297.4	−	54208.6i	−1.38576	−	2.40020i
$800$	−2490.27	−	4313.27i	−0.110055	−	0.190621i
$801$	22823.2			1.00676
$802$	−35556.9	−	61586.4i	−1.56553	−	2.71158i
$803$	22116.0	−	38306.0i	0.971924	−	1.68342i
$804$	2833.98	−	4908.60i	0.124312	−	0.215315i
$805$	−8684.47			−0.380233
$806$	7137.83	+	954.560i	0.311935	+	0.0417158i
$807$	−9195.13			−0.401095
$808$	7108.22	−	12311.8i	0.309488	−	0.536049i
$809$	9153.53	−	15854.4i	0.397801	−	0.689012i	−0.595653	−	0.803242i	$-0.703107\pi$
$809$	9153.53	−	15854.4i	0.397801	−	0.689012i	0.993454	+	0.114230i	$0.0364401\pi$
$810$	−6717.90	−	11635.7i	−0.291411	−	0.504739i
$811$	−32841.1			−1.42196			−0.710979	−	0.703213i	$-0.751748\pi$
$811$	−32841.1			−1.42196			−0.710979	+	0.703213i	$0.751748\pi$
$812$	25696.7	+	44508.0i	1.11056	+	1.92355i
$813$	−558.399	−	967.175i	−0.0240884	−	0.0417224i
$814$	7993.49			0.344191
$815$	−4229.62	−	7325.92i	−0.181788	−	0.314866i
$816$	649.526	−	1125.01i	0.0278652	−	0.0482639i
$817$	10285.3	−	17814.6i	0.440436	−	0.762857i
$818$	−36547.1			−1.56215
$819$	28195.2	+	3770.62i	1.20296	+	0.160874i
$820$	−21003.0			−0.894458
$821$	18072.9	−	31303.2i	0.768269	−	1.33068i	−0.170233	−	0.985404i	$-0.554452\pi$
$821$	18072.9	−	31303.2i	0.768269	−	1.33068i	0.938501	−	0.345276i	$-0.112215\pi$
$822$	−6029.27	+	10443.0i	−0.255833	+	0.443116i
$823$	22734.6	+	39377.5i	0.962914	+	1.66782i	0.715119	+	0.699003i	$0.246373\pi$
$823$	22734.6	+	39377.5i	0.962914	+	1.66782i	0.247795	+	0.968812i	$0.420294\pi$
$824$	1342.03			0.0567378
$825$	−956.585	−	1656.85i	−0.0403685	−	0.0699203i
$826$	10284.6	+	17813.4i	0.433228	+	0.750372i
$827$	39893.8			1.67744			0.838721	−	0.544562i	$-0.183304\pi$
$827$	39893.8			1.67744			0.838721	+	0.544562i	$0.183304\pi$
$828$	11417.6	+	19775.9i	0.479214	+	0.830024i
$829$	−22437.3	+	38862.5i	−0.940023	+	1.62817i	−0.174601	+	0.984639i	$0.555863\pi$
$829$	−22437.3	+	38862.5i	−0.940023	+	1.62817i	−0.765422	+	0.643528i	$0.777470\pi$
$830$	5877.66	−	10180.4i	0.245803	−	0.425743i
$831$	−3618.63			−0.151058
$832$	−14903.7	−	36189.8i	−0.621025	−	1.50800i
$833$	−27928.4			−1.16166
$834$	−2637.82	+	4568.84i	−0.109521	+	0.189696i
$835$	8821.26	−	15278.9i	0.365595	−	0.633230i
$836$	20008.9	+	34656.5i	0.827779	+	1.43376i
$837$	2317.65			0.0957107
$838$	−10338.8	−	17907.4i	−0.426193	−	0.738187i
$839$	7603.80	+	13170.2i	0.312887	+	0.541937i	0.978986	−	0.203927i	$-0.0653705\pi$
$839$	7603.80	+	13170.2i	0.312887	+	0.541937i	−0.666099	+	0.745863i	$0.732037\pi$
$840$	−3164.48			−0.129982
$841$	−2565.64	−	4443.82i	−0.105197	−	0.182206i
$842$	10098.3	−	17490.8i	0.413314	−	0.715881i
$843$	−2377.05	+	4117.17i	−0.0971174	+	0.168212i
$844$	33680.3			1.37361
$845$	7799.26	−	7735.75i	0.317518	−	0.314932i
$846$	−59651.0			−2.42417
$847$	−25283.3	+	43791.9i	−1.02567	+	1.77652i
$848$	−739.806	+	1281.38i	−0.0299588	+	0.0518901i
$849$	2972.07	+	5147.78i	0.120143	+	0.208094i
$850$	13583.4			0.548126
$851$	−1090.68	−	1889.11i	−0.0439341	−	0.0760961i
$852$	−2095.10	−	3628.82i	−0.0842452	−	0.145917i
$853$	28655.7			1.15024			0.575119	−	0.818070i	$-0.304956\pi$
$853$	28655.7			1.15024			0.575119	+	0.818070i	$0.304956\pi$
$854$	−7328.86	−	12694.0i	−0.293663	−	0.508640i
$855$	−3461.43	+	5995.37i	−0.138454	+	0.239810i
$856$	−5969.98	+	10340.3i	−0.238376	+	0.412879i
$857$	1554.72			0.0619700			0.0309850	−	0.999520i	$-0.490136\pi$
$857$	1554.72			0.0619700			0.0309850	+	0.999520i	$0.490136\pi$
$858$	−6179.58	−	15005.5i	−0.245883	−	0.597063i
$859$	26263.8			1.04320			0.521600	−	0.853190i	$-0.325335\pi$
$859$	26263.8			1.04320			0.521600	+	0.853190i	$0.325335\pi$
$860$	−11715.0	+	20291.1i	−0.464511	+	0.804557i
$861$	5273.86	−	9134.60i	0.208749	−	0.361564i
$862$	35283.2	+	61112.3i	1.39414	+	2.41473i
$863$	−39092.9			−1.54199			−0.770995	−	0.636842i	$-0.780241\pi$
$863$	−39092.9			−1.54199			−0.770995	+	0.636842i	$0.780241\pi$
$864$	−6798.21	−	11774.8i	−0.267685	−	0.463644i
$865$	1480.09	+	2563.59i	0.0581786	+	0.100768i
$866$	−61117.1			−2.39820
$867$	6205.34	+	10748.0i	0.243073	+	0.421015i
$868$	−5078.99	+	8797.07i	−0.198608	+	0.344000i
$869$	646.541	−	1119.84i	0.0252387	−	0.0437147i
$870$	5072.04			0.197653
$871$	−16183.6	−	2164.28i	−0.629576	−	0.0841948i
$872$	−16618.7			−0.645390
$873$	−18025.8	+	31221.5i	−0.698831	+	1.21041i
$874$	8963.74	−	15525.6i	0.346914	−	0.600873i
$875$	1499.41	+	2597.06i	0.0579308	+	0.100339i
$876$	−12273.0			−0.473365
$877$	5096.77	+	8827.86i	0.196244	+	0.339904i	0.947307	−	0.320326i	$-0.103792\pi$
$877$	5096.77	+	8827.86i	0.196244	+	0.339904i	−0.751064	+	0.660230i	$0.770459\pi$
$878$	3565.65	+	6175.89i	0.137056	+	0.237388i
$879$	3117.05			0.119608
$880$	1215.14	+	2104.69i	0.0465482	+	0.0806239i
$881$	−19092.1	+	33068.4i	−0.730111	+	1.26459i	0.226724	+	0.973959i	$0.427198\pi$
$881$	−19092.1	+	33068.4i	−0.730111	+	1.26459i	−0.956835	+	0.290631i	$0.906135\pi$
$882$	−13307.5	+	23049.2i	−0.508034	+	0.879941i
$883$	16130.4			0.614756			0.307378	−	0.951587i	$-0.400548\pi$
$883$	16130.4			0.614756			0.307378	+	0.951587i	$0.400548\pi$
$884$	69566.5	+	9303.31i	2.64680	+	0.353964i
$885$	1236.56			0.0469679
$886$	9313.63	−	16131.7i	0.353157	−	0.611686i
$887$	11702.5	−	20269.4i	0.442990	−	0.767282i	−0.554919	−	0.831904i	$-0.687251\pi$
$887$	11702.5	−	20269.4i	0.442990	−	0.767282i	0.997910	+	0.0646222i	$0.0205842\pi$
$888$	−397.425	−	688.360i	−0.0150188	−	0.0260134i
$889$	−44817.0			−1.69079
$890$	10204.4	+	17674.6i	0.384329	+	0.665678i
$891$	17415.0	+	30163.7i	0.654798	+	1.13414i
$892$	33633.4			1.26248
$893$	14263.5	+	24705.1i	0.534502	+	0.925784i
$894$	−7654.80	+	13258.5i	−0.286370	+	0.496007i
$895$	6929.14	−	12001.6i	0.258788	−	0.448235i
$896$	52394.2			1.95353
$897$	−2703.09	+	3507.86i	−0.100617	+	0.130573i
$898$	−8369.99			−0.311036
$899$	2917.36	−	5053.02i	0.108231	−	0.187461i
$900$	3942.61	−	6828.80i	0.146023	−	0.252919i
$901$	−10719.2	−	18566.1i	−0.396345	−	0.686490i
$902$	89381.3			3.29941
$903$	−5883.32	−	10190.2i	−0.216816	−	0.375536i
$904$	7075.81	+	12255.7i	0.260330	+	0.450904i
$905$	−9495.03			−0.348757
$906$	7993.61	+	13845.3i	0.293124	+	0.507705i
$907$	20488.4	−	35486.9i	0.750062	−	1.29914i	−0.197731	−	0.980256i	$-0.563357\pi$
$907$	20488.4	−	35486.9i	0.750062	−	1.29914i	0.947792	−	0.318888i	$-0.103309\pi$
$908$	−4320.14	+	7482.71i	−0.157895	+	0.273483i
$909$	−17790.2			−0.649135
$910$	9686.29	+	23520.6i	0.352854	+	0.856815i
$911$	25793.8			0.938077			0.469039	−	0.883178i	$-0.344601\pi$
$911$	25793.8			0.938077			0.469039	+	0.883178i	$0.344601\pi$
$912$	−296.016	+	512.715i	−0.0107479	+	0.0186159i
$913$	−15236.8	+	26391.0i	−0.552317	+	0.956642i
$914$	7628.17	+	13212.4i	0.276059	+	0.478148i
$915$	−881.184			−0.0318372
$916$	−30314.2	−	52505.7i	−1.09346	−	1.89393i
$917$	−15823.9	−	27407.9i	−0.569850	−	0.987009i
$918$	37081.5			1.33320
$919$	1717.07	+	2974.06i	0.0616333	+	0.106752i	0.895196	−	0.445673i	$-0.147036\pi$
$919$	1717.07	+	2974.06i	0.0616333	+	0.106752i	−0.833562	+	0.552425i	$0.813702\pi$
$920$	−3658.89	+	6337.39i	−0.131120	+	0.227106i
$921$	1587.96	−	2750.42i	0.0568132	−	0.0984033i
$922$	−23498.9			−0.839365
$923$	−7367.72	+	9561.28i	−0.262743	+	0.340968i
$924$	22890.8			0.814991
$925$	−376.621	+	652.327i	−0.0133873	+	0.0231874i
$926$	4656.68	−	8065.61i	0.165257	−	0.286234i
$927$	−839.699	−	1454.40i	−0.0297512	−	0.0515305i
$928$	−34229.1			−1.21080
$929$	4023.78	+	6969.39i	0.142105	+	0.246134i	0.928289	−	0.371859i	$-0.121279\pi$
$929$	4023.78	+	6969.39i	0.142105	+	0.246134i	−0.786184	+	0.617993i	$0.787946\pi$
$930$	501.248	+	868.187i	0.0176737	+	0.0306118i
$931$	12728.1			0.448064
$932$	31390.0	+	54369.2i	1.10324	+	1.91086i
$933$	−5737.41	+	9937.48i	−0.201323	+	0.348702i
$934$	3851.57	−	6671.12i	0.134933	−	0.233711i
$935$	−35212.7			−1.23164
$936$	14630.6	−	18986.5i	0.510916	−	0.663028i
$937$	−15695.8			−0.547234			−0.273617	−	0.961839i	$-0.588220\pi$
$937$	−15695.8			−0.547234			−0.273617	+	0.961839i	$0.588220\pi$
$938$	18904.3	−	32743.3i	0.658048	−	1.13977i
$939$	2695.73	−	4669.14i	0.0936866	−	0.162270i
$940$	−16246.3	−	28139.4i	−0.563719	−	0.976390i
$941$	−26525.2			−0.918913			−0.459457	−	0.888200i	$-0.651956\pi$
$941$	−26525.2			−0.918913			−0.459457	+	0.888200i	$0.651956\pi$
$942$	849.361	+	1471.14i	0.0293776	+	0.0508834i
$943$	−12195.7	−	21123.6i	−0.421152	−	0.729457i
$944$	−1570.80			−0.0541579
$945$	4093.27	+	7089.75i	0.140904	+	0.244053i
$946$	49855.1	−	86351.6i	1.71346	−	2.96779i
$947$	18797.8	−	32558.7i	0.645032	−	1.11723i	−0.339263	−	0.940692i	$-0.610178\pi$
$947$	18797.8	−	32558.7i	0.645032	−	1.11723i	0.984294	−	0.176536i	$-0.0564891\pi$
$948$	−358.792			−0.0122922
$949$	13462.9	+	32691.3i	0.460512	+	1.11823i
$950$	−6190.53			−0.211418
$951$	−989.864	+	1714.50i	−0.0337524	+	0.0584609i
$952$	−29121.8	+	50440.5i	−0.991433	+	1.71721i
$953$	16832.3	+	29154.5i	0.572144	+	0.990982i	0.996346	+	0.0854141i	$0.0272213\pi$
$953$	16832.3	+	29154.5i	0.572144	+	0.990982i	−0.424202	+	0.905568i	$0.639445\pi$
$954$	−20430.1			−0.693343
$955$	783.813	+	1357.60i	0.0265587	+	0.0460011i
$956$	−40113.3	−	69478.2i	−1.35707	−	2.35051i
$957$	−13148.4			−0.444126
$958$	29236.3	+	50638.8i	0.985994	+	1.70779i
$959$	−24499.3	+	42434.1i	−0.824947	+	1.42885i
$960$	2724.21	−	4718.47i	0.0915870	−	0.158633i
$961$	−28637.8			−0.961289
$962$	−3899.88	+	5060.97i	−0.130704	+	0.169618i
$963$	14941.5			0.499981
$964$	22860.0	−	39594.7i	0.763768	−	1.32288i
$965$	−6160.04	+	10669.5i	−0.205491	+	0.355921i
$966$	−5127.38	−	8880.89i	−0.170777	−	0.295795i
$967$	−13710.0			−0.455929			−0.227965	−	0.973669i	$-0.573207\pi$
$967$	−13710.0			−0.455929			−0.227965	+	0.973669i	$0.573207\pi$
$968$	21304.4	+	36900.4i	0.707387	+	1.22523i
$969$	−4289.02	−	7428.80i	−0.142191	−	0.246282i
$970$	−32237.8			−1.06711
$971$	6877.35	+	11911.9i	0.227296	+	0.393688i	0.957006	−	0.290069i	$-0.0936781\pi$
$971$	6877.35	+	11911.9i	0.227296	+	0.393688i	−0.729710	+	0.683757i	$0.760345\pi$
$972$	16319.7	−	28266.6i	0.538534	−	0.932769i
$973$	−10718.5	+	18565.0i	−0.353155	+	0.611683i
$974$	−82532.8			−2.71512
$975$	1515.72	+	202.701i	0.0497864	+	0.00665807i
$976$	1119.36			0.0367109
$977$	−11013.5	+	19076.0i	−0.360648	+	0.624661i	−0.988068	−	0.154020i	$-0.950778\pi$
$977$	−11013.5	+	19076.0i	−0.360648	+	0.624661i	0.627419	+	0.778682i	$0.284111\pi$
$978$	4994.41	−	8650.57i	0.163296	−	0.282837i
$979$	−26453.3	−	45818.4i	−0.863585	−	1.49577i
$980$	−14497.5			−0.472557
$981$	10398.2	+	18010.2i	0.338418	+	0.586158i
$982$	−1053.76	−	1825.17i	−0.0342433	−	0.0593111i
$983$	33898.3			1.09989			0.549944	−	0.835202i	$-0.314649\pi$
$983$	33898.3			1.09989			0.549944	+	0.835202i	$0.314649\pi$
$984$	−4443.91	−	7697.08i	−0.143970	−	0.249364i
$985$	9789.30	−	16955.6i	0.316663	−	0.548477i
$986$	46676.6	−	80846.3i	1.50759	−	2.61123i
$987$	16317.9			0.526244
$988$	−31704.3	−	4239.90i	−1.02090	−	0.136528i
$989$	−27210.1			−0.874854
$990$	−16778.4	+	29061.0i	−0.538638	+	0.932949i
$991$	−19201.7	+	33258.4i	−0.615502	+	1.06608i	0.374794	+	0.927108i	$0.377713\pi$
$991$	−19201.7	+	33258.4i	−0.615502	+	1.06608i	−0.990296	+	0.138973i	$0.955620\pi$
$992$	−3382.72	−	5859.04i	−0.108268	−	0.187525i
$993$	−2475.44			−0.0791094
$994$	−13975.5	−	24206.4i	−0.445953	−	0.772414i
$995$	6321.61	+	10949.4i	0.201416	+	0.348862i
$996$	8455.55			0.269000
$997$	180.778	+	313.117i	0.00574252	+	0.00994634i	0.868882	−	0.495019i	$-0.164839\pi$
$997$	180.778	+	313.117i	0.00574252	+	0.00994634i	−0.863140	+	0.504965i	$0.831505\pi$
$998$	35520.8	−	61523.9i	1.12665	−	1.95141i
$999$	−1028.14	+	1780.80i	−0.0325616	+	0.0563983i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	65.4.e.a.61.7	yes	14
13.3	even	3	inner	65.4.e.a.16.7	✓	14
13.4	even	6		845.4.a.h.1.7		7
13.9	even	3		845.4.a.k.1.1		7

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.4.e.a.16.7	✓	14	13.3	even	3	inner
65.4.e.a.61.7	yes	14	1.1	even	1	trivial
845.4.a.h.1.7		7	13.4	even	6
845.4.a.k.1.1		7	13.9	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:	\( N \)	\(=\)	\( 65 = 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	65.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.26209 - 3.91806i) q^{2} +(0.652503 - 1.13017i) q^{3} +(-6.23413 - 10.7978i) q^{4} -5.00000 q^{5} +(-2.95204 - 5.11309i) q^{6} +(-11.9953 - 20.7765i) q^{7} -20.2152 q^{8} +(12.6485 + 21.9078i) q^{9} +(-11.3105 + 19.5903i) q^{10} +(29.3205 - 50.7846i) q^{11} -16.2711 q^{12} +(17.8486 + 43.3408i) q^{13} -108.538 q^{14} +(-3.26251 + 5.65084i) q^{15} +(4.14434 - 7.17821i) q^{16} +(60.0480 + 104.006i) q^{17} +114.448 q^{18} +(-27.3664 - 47.3999i) q^{19} +(31.1706 + 53.9891i) q^{20} -31.3079 q^{21} +(-132.651 - 229.759i) q^{22} +(-36.1994 + 62.6992i) q^{23} +(-13.1905 + 22.8466i) q^{24} +25.0000 q^{25} +(210.187 + 28.1089i) q^{26} +68.2478 q^{27} +(-149.561 + 259.047i) q^{28} +(85.9073 - 148.796i) q^{29} +(14.7602 + 25.5654i) q^{30} +33.9594 q^{31} +(-99.6106 - 172.531i) q^{32} +(-38.2634 - 66.2741i) q^{33} +543.337 q^{34} +(59.9766 + 103.882i) q^{35} +(157.704 - 273.152i) q^{36} +(-15.0648 + 26.0931i) q^{37} -247.621 q^{38} +(60.6287 + 8.10803i) q^{39} +101.076 q^{40} +(-168.452 + 291.767i) q^{41} +(-70.8214 + 122.666i) q^{42} +(187.918 + 325.483i) q^{43} -731.150 q^{44} +(-63.2424 - 109.539i) q^{45} +(163.773 + 283.663i) q^{46} -521.206 q^{47} +(-5.40839 - 9.36761i) q^{48} +(-116.275 + 201.395i) q^{49} +(56.5523 - 97.9515i) q^{50} +156.726 q^{51} +(356.716 - 462.919i) q^{52} -178.510 q^{53} +(154.383 - 267.399i) q^{54} +(-146.602 + 253.923i) q^{55} +(242.488 + 420.001i) q^{56} -71.4265 q^{57} +(-388.661 - 673.180i) q^{58} +(-94.7555 - 164.121i) q^{59} +81.3557 q^{60} +(67.5234 + 116.954i) q^{61} +(76.8193 - 133.055i) q^{62} +(303.445 - 525.582i) q^{63} -835.004 q^{64} +(-89.2432 - 216.704i) q^{65} -346.221 q^{66} +(-174.172 + 301.676i) q^{67} +(748.694 - 1296.78i) q^{68} +(47.2404 + 81.8228i) q^{69} +542.690 q^{70} +(128.762 + 223.022i) q^{71} +(-255.692 - 442.871i) q^{72} +754.283 q^{73} +(68.1562 + 118.050i) q^{74} +(16.3126 - 28.2542i) q^{75} +(-341.211 + 590.995i) q^{76} -1406.83 q^{77} +(168.915 - 219.206i) q^{78} +22.0508 q^{79} +(-20.7217 + 35.8911i) q^{80} +(-296.977 + 514.379i) q^{81} +(762.106 + 1320.01i) q^{82} -519.665 q^{83} +(195.177 + 338.057i) q^{84} +(-300.240 - 520.031i) q^{85} +1700.35 q^{86} +(-112.110 - 194.179i) q^{87} +(-592.720 + 1026.62i) q^{88} +(451.105 - 781.338i) q^{89} -572.241 q^{90} +(686.370 - 890.719i) q^{91} +902.687 q^{92} +(22.1586 - 38.3798i) q^{93} +(-1179.02 + 2042.11i) q^{94} +(136.832 + 237.000i) q^{95} -259.985 q^{96} +(712.566 + 1234.20i) q^{97} +(526.051 + 911.147i) q^{98} +1483.44 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q - 2 q^{2} + 4 q^{3} - 30 q^{4} - 70 q^{5} - 23 q^{6} - 7 q^{7} + 42 q^{8} - 87 q^{9} + 10 q^{10} - 87 q^{11} - 158 q^{12} + 123 q^{13} + 132 q^{14} - 20 q^{15} + 134 q^{16} + 114 q^{17} + 414 q^{18}+ \cdots + 11378 q^{99}+O(q^{100}) \) 14 * q - 2 * q^2 + 4 * q^3 - 30 * q^4 - 70 * q^5 - 23 * q^6 - 7 * q^7 + 42 * q^8 - 87 * q^9 + 10 * q^10 - 87 * q^11 - 158 * q^12 + 123 * q^13 + 132 * q^14 - 20 * q^15 + 134 * q^16 + 114 * q^17 + 414 * q^18 - 245 * q^19 + 150 * q^20 - 76 * q^21 - 338 * q^22 + 74 * q^23 - 334 * q^24 + 350 * q^25 + 243 * q^26 - 884 * q^27 - 230 * q^28 + 88 * q^29 + 115 * q^30 + 1000 * q^31 - 80 * q^32 + 194 * q^33 + 854 * q^34 + 35 * q^35 - 425 * q^36 - 633 * q^37 - 596 * q^38 + 970 * q^39 - 210 * q^40 - 162 * q^41 + 1439 * q^42 + 280 * q^43 + 440 * q^44 + 435 * q^45 + 11 * q^46 + 950 * q^47 - 2281 * q^48 - 1694 * q^49 - 50 * q^50 - 860 * q^51 - 956 * q^52 - 1206 * q^53 - 51 * q^54 + 435 * q^55 + 1277 * q^56 + 916 * q^57 + 1213 * q^58 - 1410 * q^59 + 790 * q^60 - 412 * q^61 + 56 * q^62 - 1241 * q^63 - 2358 * q^64 - 615 * q^65 + 4346 * q^66 - 1398 * q^67 + 493 * q^68 - 1080 * q^69 - 660 * q^70 + 584 * q^71 - 1545 * q^72 + 5076 * q^73 - 3840 * q^74 + 100 * q^75 - 3292 * q^76 - 5506 * q^77 + 1179 * q^78 + 928 * q^79 - 670 * q^80 + 473 * q^81 + 1583 * q^82 + 932 * q^83 + 3081 * q^84 - 570 * q^85 + 9858 * q^86 + 282 * q^87 - 3389 * q^88 - 443 * q^89 - 2070 * q^90 + 487 * q^91 + 6182 * q^92 + 2116 * q^93 - 2017 * q^94 + 1225 * q^95 + 954 * q^96 + 1870 * q^97 - 1364 * q^98 + 11378 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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