LMFDB - Embedded newform 201.4.e.a.163.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [201,4,Mod(37,201)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(201, 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("201.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 201 = 3 \cdot 67 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	201.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:	$11.8593839112$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.1
Character	$\chi$	$=$	201.163
Dual form			201.4.e.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.81607 + 4.87758i) q^{2} +3.00000 q^{3} +(-11.8605 - 20.5430i) q^{4} -14.5837 q^{5} +(-8.44821 + 14.6327i) q^{6} +(-2.46134 - 4.26316i) q^{7} +88.5430 q^{8} +9.00000 q^{9} +O(q^{10})$	\(q+(-2.81607 + 4.87758i) q^{2} +3.00000 q^{3} +(-11.8605 - 20.5430i) q^{4} -14.5837 q^{5} +(-8.44821 + 14.6327i) q^{6} +(-2.46134 - 4.26316i) q^{7} +88.5430 q^{8} +9.00000 q^{9} +(41.0687 - 71.1331i) q^{10} +(12.2658 + 21.2451i) q^{11} +(-35.5815 - 61.6290i) q^{12} +(33.4503 - 57.9377i) q^{13} +27.7252 q^{14} -43.7511 q^{15} +(-154.459 + 267.531i) q^{16} +(-21.9779 + 38.0668i) q^{17} +(-25.3446 + 43.8982i) q^{18} +(-1.64957 + 2.85714i) q^{19} +(172.970 + 299.593i) q^{20} +(-7.38401 - 12.7895i) q^{21} -138.166 q^{22} +(33.7700 - 58.4913i) q^{23} +265.629 q^{24} +87.6840 q^{25} +(188.397 + 326.313i) q^{26} +27.0000 q^{27} +(-58.3854 + 101.126i) q^{28} +(136.066 + 235.673i) q^{29} +(123.206 - 213.399i) q^{30} +(66.9620 + 115.982i) q^{31} +(-515.764 - 893.329i) q^{32} +(36.7975 + 63.7352i) q^{33} +(-123.783 - 214.398i) q^{34} +(35.8954 + 62.1726i) q^{35} +(-106.745 - 184.887i) q^{36} +(-188.286 + 326.121i) q^{37} +(-9.29063 - 16.0918i) q^{38} +(100.351 - 173.813i) q^{39} -1291.28 q^{40} +(-123.013 - 213.065i) q^{41} +83.1756 q^{42} +277.991 q^{43} +(290.958 - 503.954i) q^{44} -131.253 q^{45} +(190.197 + 329.432i) q^{46} +(132.951 + 230.278i) q^{47} +(-463.377 + 802.593i) q^{48} +(159.384 - 276.061i) q^{49} +(-246.924 + 427.685i) q^{50} +(-65.9337 + 114.200i) q^{51} -1586.95 q^{52} +455.834 q^{53} +(-76.0339 + 131.695i) q^{54} +(-178.881 - 309.831i) q^{55} +(-217.934 - 377.473i) q^{56} +(-4.94872 + 8.57143i) q^{57} -1532.68 q^{58} +580.366 q^{59} +(518.910 + 898.778i) q^{60} +(-6.53198 + 11.3137i) q^{61} -754.279 q^{62} +(-22.1520 - 38.3684i) q^{63} +3338.36 q^{64} +(-487.829 + 844.945i) q^{65} -414.498 q^{66} +(489.889 + 246.519i) q^{67} +1042.68 q^{68} +(101.310 - 175.474i) q^{69} -404.336 q^{70} +(55.2452 + 95.6874i) q^{71} +796.887 q^{72} +(441.261 - 764.287i) q^{73} +(-1060.45 - 1836.76i) q^{74} +263.052 q^{75} +78.2591 q^{76} +(60.3807 - 104.582i) q^{77} +(565.191 + 978.940i) q^{78} +(525.813 + 910.735i) q^{79} +(2252.58 - 3901.59i) q^{80} +81.0000 q^{81} +1385.66 q^{82} +(-172.842 + 299.371i) q^{83} +(-175.156 + 303.379i) q^{84} +(320.519 - 555.155i) q^{85} +(-782.841 + 1355.92i) q^{86} +(408.197 + 707.018i) q^{87} +(1086.05 + 1881.10i) q^{88} -651.397 q^{89} +(369.618 - 640.198i) q^{90} -329.330 q^{91} -1602.12 q^{92} +(200.886 + 347.945i) q^{93} -1497.60 q^{94} +(24.0569 - 41.6677i) q^{95} +(-1547.29 - 2679.99i) q^{96} +(515.614 - 893.070i) q^{97} +(897.671 + 1554.81i) q^{98} +(110.393 + 191.206i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) $ 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/201\mathbb{Z}\right)^\times$.

$n$	$68$	$136$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.81607	+	4.87758i	−0.995631	+	1.72448i	−0.416953	+	0.908928i	$0.636902\pi$
$2$	−2.81607	+	4.87758i	−0.995631	+	1.72448i	−0.578678	+	0.815556i	$0.696431\pi$
$3$	3.00000			0.577350
$3$	3.00000			0.577350
$4$	−11.8605	−	20.5430i	−1.48256	−	2.56787i
$5$	−14.5837			−1.30440			−0.652202	−	0.758045i	$-0.726155\pi$
$5$	−14.5837			−1.30440			−0.652202	+	0.758045i	$0.726155\pi$
$6$	−8.44821	+	14.6327i	−0.574828	+	0.995631i
$7$	−2.46134	−	4.26316i	−0.132900	−	0.230189i	0.791893	−	0.610659i	$-0.209095\pi$
$7$	−2.46134	−	4.26316i	−0.132900	−	0.230189i	−0.924793	+	0.380470i	$0.875762\pi$
$8$	88.5430			3.91308
$9$	9.00000			0.333333
$10$	41.0687	−	71.1331i	1.29871	−	2.24943i
$11$	12.2658	+	21.2451i	0.336208	+	0.582330i	0.983716	−	0.179729i	$-0.0575221\pi$
$11$	12.2658	+	21.2451i	0.336208	+	0.582330i	−0.647508	+	0.762059i	$0.724189\pi$
$12$	−35.5815	−	61.6290i	−0.855958	−	1.48256i
$13$	33.4503	−	57.9377i	0.713650	−	1.23608i	−0.249827	−	0.968290i	$-0.580374\pi$
$13$	33.4503	−	57.9377i	0.713650	−	1.23608i	0.963478	−	0.267788i	$-0.0862928\pi$
$14$	27.7252			0.529276
$15$	−43.7511			−0.753098
$16$	−154.459	+	267.531i	−2.41342	+	4.18017i
$17$	−21.9779	+	38.0668i	−0.313554	+	0.543092i	−0.979129	−	0.203239i	$-0.934853\pi$
$17$	−21.9779	+	38.0668i	−0.313554	+	0.543092i	0.665575	+	0.746331i	$0.268186\pi$
$18$	−25.3446	+	43.8982i	−0.331877	+	0.574828i
$19$	−1.64957	+	2.85714i	−0.0199178	+	0.0344986i	−0.875812	−	0.482652i	$-0.839674\pi$
$19$	−1.64957	+	2.85714i	−0.0199178	+	0.0344986i	0.855895	+	0.517150i	$0.173007\pi$
$20$	172.970	+	299.593i	1.93386	+	3.34955i
$21$	−7.38401	−	12.7895i	−0.0767297	−	0.132900i
$22$	−138.166			−1.33896
$23$	33.7700	−	58.4913i	0.306154	−	0.530273i	−0.671364	−	0.741128i	$-0.734291\pi$
$23$	33.7700	−	58.4913i	0.306154	−	0.530273i	0.977517	+	0.210854i	$0.0676246\pi$
$24$	265.629			2.25922
$25$	87.6840			0.701472
$26$	188.397	+	326.313i	1.42107	+	2.46136i
$27$	27.0000			0.192450
$28$	−58.3854	+	101.126i	−0.394064	+	0.682540i
$29$	136.066	+	235.673i	0.871268	+	1.50908i	0.860686	+	0.509137i	$0.170035\pi$
$29$	136.066	+	235.673i	0.871268	+	1.50908i	0.0105825	+	0.999944i	$0.496631\pi$
$30$	123.206	−	213.399i	0.749808	−	1.29871i
$31$	66.9620	+	115.982i	0.387959	+	0.671965i	0.992175	−	0.124856i	$-0.0398468\pi$
$31$	66.9620	+	115.982i	0.387959	+	0.671965i	−0.604216	+	0.796821i	$0.706513\pi$
$32$	−515.764	−	893.329i	−2.84922	−	4.93499i
$33$	36.7975	+	63.7352i	0.194110	+	0.336208i
$34$	−123.783	−	214.398i	−0.624369	−	1.08144i
$35$	35.8954	+	62.1726i	0.173355	+	0.300260i
$36$	−106.745	−	184.887i	−0.494188	−	0.855958i
$37$	−188.286	+	326.121i	−0.836596	+	1.44903i	0.0561285	+	0.998424i	$0.482124\pi$
$37$	−188.286	+	326.121i	−0.836596	+	1.44903i	−0.892724	+	0.450603i	$0.851209\pi$
$38$	−9.29063	−	16.0918i	−0.0396615	−	0.0686958i
$39$	100.351	−	173.813i	0.412026	−	0.713650i
$40$	−1291.28			−5.10424
$41$	−123.013	−	213.065i	−0.468572	−	0.811591i	0.530783	−	0.847508i	$-0.321898\pi$
$41$	−123.013	−	213.065i	−0.468572	−	0.811591i	−0.999355	+	0.0359174i	$0.988565\pi$
$42$	83.1756			0.305578
$43$	277.991			0.985887			0.492944	−	0.870061i	$-0.335921\pi$
$43$	277.991			0.985887			0.492944	+	0.870061i	$0.335921\pi$
$44$	290.958	−	503.954i	0.996900	−	1.72668i
$45$	−131.253			−0.434802
$46$	190.197	+	329.432i	0.609632	+	1.05591i
$47$	132.951	+	230.278i	0.412615	+	0.714670i	0.995175	−	0.0981177i	$-0.0312822\pi$
$47$	132.951	+	230.278i	0.412615	+	0.714670i	−0.582560	+	0.812788i	$0.697949\pi$
$48$	−463.377	+	802.593i	−1.39339	+	2.41342i
$49$	159.384	−	276.061i	0.464675	−	0.804841i
$50$	−246.924	+	427.685i	−0.698407	+	1.20968i
$51$	−65.9337	+	114.200i	−0.181031	+	0.313554i
$52$	−1586.95			−4.23213
$53$	455.834			1.18139			0.590694	−	0.806895i	$-0.298854\pi$
$53$	455.834			1.18139			0.590694	+	0.806895i	$0.298854\pi$
$54$	−76.0339	+	131.695i	−0.191609	+	0.331877i
$55$	−178.881	−	309.831i	−0.438552	−	0.759594i
$56$	−217.934	−	377.473i	−0.520048	−	0.900749i
$57$	−4.94872	+	8.57143i	−0.0114995	+	0.0199178i
$58$	−1532.68			−3.46985
$59$	580.366			1.28063			0.640316	−	0.768112i	$-0.278804\pi$
$59$	580.366			1.28063			0.640316	+	0.768112i	$0.278804\pi$
$60$	518.910	+	898.778i	1.11652	+	1.93386i
$61$	−6.53198	+	11.3137i	−0.0137104	+	0.0237471i	−0.872799	−	0.488079i	$-0.837698\pi$
$61$	−6.53198	+	11.3137i	−0.0137104	+	0.0237471i	0.859089	+	0.511827i	$0.171031\pi$
$62$	−754.279			−1.54506
$63$	−22.1520	−	38.3684i	−0.0442999	−	0.0767297i
$64$	3338.36			6.52024
$65$	−487.829	+	844.945i	−0.930889	+	1.61235i
$66$	−414.498			−0.773047
$67$	489.889	+	246.519i	0.893276	+	0.449508i
$67$	489.889	+	246.519i	0.893276	+	0.449508i
$68$	1042.68			1.85946
$69$	101.310	−	175.474i	0.176758	−	0.306154i
$70$	−404.336			−0.690391
$71$	55.2452	+	95.6874i	0.0923436	+	0.159944i	0.908497	−	0.417892i	$-0.137231\pi$
$71$	55.2452	+	95.6874i	0.0923436	+	0.159944i	−0.816153	+	0.577835i	$0.803898\pi$
$72$	796.887			1.30436
$73$	441.261	−	764.287i	0.707476	−	1.22538i	−0.258314	−	0.966061i	$-0.583167\pi$
$73$	441.261	−	764.287i	0.707476	−	1.22538i	0.965790	−	0.259324i	$-0.0834996\pi$
$74$	−1060.45	−	1836.76i	−1.66588	−	2.88539i
$75$	263.052			0.404995
$76$	78.2591			0.118117
$77$	60.3807	−	104.582i	0.0893639	−	0.154783i
$78$	565.191	+	978.940i	0.820453	+	1.42107i
$79$	525.813	+	910.735i	0.748843	+	1.29703i	0.948378	+	0.317143i	$0.102724\pi$
$79$	525.813	+	910.735i	0.748843	+	1.29703i	−0.199535	+	0.979891i	$0.563943\pi$
$80$	2252.58	−	3901.59i	3.14808	−	5.45264i
$81$	81.0000			0.111111
$82$	1385.66			1.86610
$83$	−172.842	+	299.371i	−0.228577	+	0.395907i	−0.957387	−	0.288809i	$-0.906741\pi$
$83$	−172.842	+	299.371i	−0.228577	+	0.395907i	0.728810	+	0.684716i	$0.240074\pi$
$84$	−175.156	+	303.379i	−0.227513	+	0.394064i
$85$	320.519	−	555.155i	0.409002	−	0.708411i
$86$	−782.841	+	1355.92i	−0.981580	+	1.70015i
$87$	408.197	+	707.018i	0.503027	+	0.871268i
$88$	1086.05	+	1881.10i	1.31561	+	2.27870i
$89$	−651.397			−0.775819			−0.387910	−	0.921697i	$-0.626803\pi$
$89$	−651.397			−0.775819			−0.387910	+	0.921697i	$0.626803\pi$
$90$	369.618	−	640.198i	0.432902	−	0.749808i
$91$	−329.330			−0.379376
$92$	−1602.12			−1.81557
$93$	200.886	+	347.945i	0.223988	+	0.387959i
$94$	−1497.60			−1.64325
$95$	24.0569	−	41.6677i	0.0259809	−	0.0450002i
$96$	−1547.29	−	2679.99i	−1.64500	−	2.84922i
$97$	515.614	−	893.070i	0.539718	−	0.934820i	−0.459201	−	0.888333i	$-0.651864\pi$
$97$	515.614	−	893.070i	0.539718	−	0.934820i	0.998919	−	0.0464869i	$-0.0148026\pi$
$98$	897.671	+	1554.81i	0.925291	+	1.60265i
$99$	110.393	+	191.206i	0.112069	+	0.194110i
$100$	−1039.98	−	1801.29i	−1.03998	−	1.80129i
$101$	145.024	+	251.189i	0.142876	+	0.247468i	0.928578	−	0.371136i	$-0.121032\pi$
$101$	145.024	+	251.189i	0.142876	+	0.247468i	−0.785703	+	0.618604i	$0.787698\pi$
$102$	−371.348	−	643.193i	−0.360479	−	0.624369i
$103$	−76.6911	−	132.833i	−0.0733650	−	0.127072i	0.827009	−	0.562189i	$-0.190040\pi$
$103$	−76.6911	−	132.833i	−0.0733650	−	0.127072i	−0.900374	+	0.435117i	$0.856707\pi$
$104$	2961.79	−	5129.97i	2.79257	−	4.83688i
$105$	107.686	+	186.518i	0.100087	+	0.173355i
$106$	−1283.66	+	2223.36i	−1.17623	+	2.03729i
$107$	−668.568			−0.604046			−0.302023	−	0.953301i	$-0.597662\pi$
$107$	−668.568			−0.604046			−0.302023	+	0.953301i	$0.597662\pi$
$108$	−320.234	−	554.661i	−0.285319	−	0.494188i
$109$	−644.689			−0.566514			−0.283257	−	0.959044i	$-0.591415\pi$
$109$	−644.689			−0.566514			−0.283257	+	0.959044i	$0.591415\pi$
$110$	2014.97			1.74654
$111$	−564.858	+	978.363i	−0.483009	+	0.836596i
$112$	1520.70			1.28297
$113$	773.291	+	1339.38i	0.643762	+	1.11503i	0.984586	+	0.174901i	$0.0559607\pi$
$113$	773.291	+	1339.38i	0.643762	+	1.11503i	−0.340824	+	0.940127i	$0.610706\pi$
$114$	−27.8719	−	48.2755i	−0.0228986	−	0.0396615i
$115$	−492.491	+	853.020i	−0.399348	+	0.691691i
$116$	3227.62	−	5590.40i	2.58342	−	4.47462i
$117$	301.053	−	521.439i	0.237883	−	0.412026i
$118$	−1634.35	+	2830.78i	−1.27504	+	2.20843i
$119$	216.380			0.166685
$120$	−3873.85			−2.94694
$121$	364.598	−	631.503i	0.273928	−	0.474457i
$122$	−36.7890	−	63.7204i	−0.0273010	−	0.0472867i
$123$	−369.040	−	639.196i	−0.270530	−	0.468572i
$124$	1588.41	−	2751.20i	1.15035	−	1.99246i
$125$	544.205			0.389402
$126$	249.527			0.176425
$127$	1155.87	+	2002.02i	0.807610	+	1.39882i	0.914515	+	0.404553i	$0.132573\pi$
$127$	1155.87	+	2002.02i	0.807610	+	1.39882i	−0.106905	+	0.994269i	$0.534094\pi$
$128$	−5274.95	+	9136.49i	−3.64254	+	6.30906i
$129$	833.972			0.569202
$130$	−2747.52	−	4758.85i	−1.85364	−	3.21061i
$131$	−1004.06			−0.669661			−0.334830	−	0.942278i	$-0.608679\pi$
$131$	−1004.06			−0.669661			−0.334830	+	0.942278i	$0.608679\pi$
$132$	872.874	−	1511.86i	0.575560	−	0.996900i
$133$	16.2406			0.0105883
$134$	−2581.98	+	1695.26i	−1.66454	+	1.09290i
$135$	−393.760			−0.251033
$136$	−1945.99	+	3370.55i	−1.22696	+	2.12516i
$137$	−905.303			−0.564564			−0.282282	−	0.959331i	$-0.591091\pi$
$137$	−905.303			−0.564564			−0.282282	+	0.959331i	$0.591091\pi$
$138$	570.592	+	988.295i	0.351971	+	0.609632i
$139$	720.979			0.439947			0.219973	−	0.975506i	$-0.429403\pi$
$139$	720.979			0.439947			0.219973	+	0.975506i	$0.429403\pi$
$140$	851.475	−	1474.80i	0.514020	−	0.890308i
$141$	398.853	+	690.834i	0.238223	+	0.412615i
$142$	−622.297			−0.367761
$143$	1641.19			0.959740
$144$	−1390.13	+	2407.78i	−0.804475	+	1.39339i
$145$	−1984.34	−	3436.98i	−1.13649	−	1.96845i
$146$	2485.25	+	4304.57i	1.40877	+	2.44006i
$147$	478.151	−	828.182i	0.268280	−	0.464675i
$148$	8932.67			4.96123
$149$	−821.331			−0.451584			−0.225792	−	0.974176i	$-0.572497\pi$
$149$	−821.331			−0.451584			−0.225792	+	0.974176i	$0.572497\pi$
$150$	−740.773	+	1283.06i	−0.403226	+	0.698407i
$151$	1189.91	−	2060.98i	0.641279	−	1.11073i	−0.343869	−	0.939018i	$-0.611737\pi$
$151$	1189.91	−	2060.98i	0.641279	−	1.11073i	0.985148	−	0.171710i	$-0.0549292\pi$
$152$	−146.058	+	252.980i	−0.0779399	+	0.134996i
$153$	−197.801	+	342.601i	−0.104518	+	0.181031i
$154$	340.073	+	589.023i	0.177947	+	0.308213i
$155$	−976.554	−	1691.44i	−0.506056	−	0.876515i
$156$	−4760.86			−2.44342
$157$	−714.640	+	1237.79i	−0.363277	+	0.629214i	−0.988498	−	0.151234i	$-0.951675\pi$
$157$	−714.640	+	1237.79i	−0.363277	+	0.629214i	0.625221	+	0.780448i	$0.285009\pi$
$158$	−5922.91			−2.98229
$159$	1367.50			0.682075
$160$	7521.74	+	13028.0i	3.71654	+	6.43723i
$161$	−332.477			−0.162751
$162$	−228.102	+	395.084i	−0.110626	+	0.191609i
$163$	−1184.87	−	2052.25i	−0.569361	−	0.986163i	−0.996629	−	0.0820378i	$-0.973857\pi$
$163$	−1184.87	−	2052.25i	−0.569361	−	0.986163i	0.427268	−	0.904125i	$-0.359476\pi$
$164$	−2918.00	+	5054.13i	−1.38938	+	2.40647i
$165$	−536.644	−	929.494i	−0.253198	−	0.438552i
$166$	−973.472	−	1686.10i	−0.455157	−	0.788355i
$167$	530.706	+	919.210i	0.245912	+	0.425932i	0.962388	−	0.271680i	$-0.0875793\pi$
$167$	530.706	+	919.210i	0.245912	+	0.425932i	−0.716476	+	0.697612i	$0.754246\pi$
$168$	−653.802	−	1132.42i	−0.300250	−	0.520048i
$169$	−1139.35	−	1973.41i	−0.518594	−	0.898231i
$170$	1805.21	+	3126.71i	0.814429	+	1.41063i
$171$	−14.8462	+	25.7143i	−0.00663926	+	0.0114995i
$172$	−3297.11	−	5710.76i	−1.46164	−	2.53164i
$173$	447.947	−	775.867i	0.196860	−	0.340972i	−0.750649	−	0.660702i	$-0.770259\pi$
$173$	447.947	−	775.867i	0.196860	−	0.340972i	0.947509	+	0.319730i	$0.103592\pi$
$174$	−4598.05			−2.00332
$175$	−215.820	−	373.811i	−0.0932254	−	0.161471i
$176$	−7578.28			−3.24565
$177$	1741.10			0.739373
$178$	1834.38	−	3177.24i	0.772430	−	1.33789i
$179$	−2584.28			−1.07909			−0.539547	−	0.841955i	$-0.681405\pi$
$179$	−2584.28			−1.07909			−0.539547	+	0.841955i	$0.681405\pi$
$180$	1556.73	+	2696.33i	0.644621	+	1.11652i
$181$	−1670.93	−	2894.13i	−0.686182	−	1.18850i	−0.973064	−	0.230537i	$-0.925952\pi$
$181$	−1670.93	−	2894.13i	−0.686182	−	1.18850i	0.286881	−	0.957966i	$-0.407382\pi$
$182$	927.417	−	1606.33i	0.377718	−	0.654227i
$183$	−19.5959	+	33.9411i	−0.00791570	+	0.0137104i
$184$	2990.09	−	5179.00i	1.19800	−	2.07500i
$185$	2745.91	−	4756.05i	1.09126	−	1.89012i
$186$	−2262.84			−0.892039
$187$	−1078.31			−0.421678
$188$	3153.73	−	5462.43i	1.22346	−	2.11909i
$189$	−66.4561	−	115.105i	−0.0255766	−	0.0442999i
$190$	135.492	+	234.678i	0.0517347	+	0.0896071i
$191$	366.502	−	634.801i	0.138844	−	0.240485i	−0.788215	−	0.615399i	$-0.788995\pi$
$191$	366.502	−	634.801i	0.138844	−	0.240485i	0.927059	+	0.374915i	$0.122328\pi$
$192$	10015.1			3.76446
$193$	−3753.75			−1.40001			−0.700003	−	0.714140i	$-0.746818\pi$
$193$	−3753.75			−1.40001			−0.700003	+	0.714140i	$0.746818\pi$
$194$	2904.01	+	5029.89i	1.07472	+	1.86147i
$195$	−1463.49	+	2534.84i	−0.537449	+	0.930889i
$196$	−7561.48			−2.75564
$197$	540.287	+	935.804i	0.195400	+	0.338443i	0.947032	−	0.321140i	$-0.104066\pi$
$197$	540.287	+	935.804i	0.195400	+	0.338443i	−0.751631	+	0.659583i	$0.770733\pi$
$198$	−1243.49			−0.446319
$199$	619.937	−	1073.76i	0.220835	−	0.382497i	−0.734227	−	0.678904i	$-0.762455\pi$
$199$	619.937	−	1073.76i	0.220835	−	0.382497i	0.955062	+	0.296407i	$0.0957885\pi$
$200$	7763.80			2.74492
$201$	1469.67	+	739.556i	0.515733	+	0.259524i
$202$	−1633.59			−0.569006
$203$	669.807	−	1160.14i	0.231583	−	0.401113i
$204$	3128.03			1.07356
$205$	1793.99	+	3107.28i	0.611208	+	1.05864i
$206$	863.870			0.292178
$207$	303.930	−	526.422i	0.102051	−	0.176758i
$208$	10333.4	+	17898.0i	3.44468	+	5.96637i
$209$	−80.9336			−0.0267861
$210$	−1213.01			−0.398597
$211$	2657.62	−	4603.13i	0.867099	−	1.50186i	0.00215047	−	0.999998i	$-0.499315\pi$
$211$	2657.62	−	4603.13i	0.867099	−	1.50186i	0.864948	−	0.501861i	$-0.167351\pi$
$212$	−5406.42	−	9364.19i	−1.75148	−	3.03366i
$213$	165.735	+	287.062i	0.0533146	+	0.0923436i
$214$	1882.73	−	3260.99i	0.601407	−	1.04167i
$215$	−4054.13			−1.28600
$216$	2390.66			0.753073
$217$	329.632	−	570.940i	0.103119	−	0.178608i
$218$	1815.49	−	3144.52i	0.564039	−	0.976944i
$219$	1323.78	−	2292.86i	0.408461	−	0.707476i
$220$	−4243.24	+	7349.51i	−1.30036	+	2.25229i
$221$	1470.34	+	2546.70i	0.447536	+	0.775155i
$222$	−3181.36	−	5510.28i	−0.961797	−	1.66588i
$223$	610.424			0.183305			0.0916524	−	0.995791i	$-0.470785\pi$
$223$	610.424			0.183305			0.0916524	+	0.995791i	$0.470785\pi$
$224$	−2538.94	+	4397.57i	−0.757321	+	1.31172i
$225$	789.156			0.233824
$226$	−8710.57			−2.56380
$227$	50.9449	+	88.2392i	0.0148957	+	0.0258002i	0.873377	−	0.487044i	$-0.161925\pi$
$227$	50.9449	+	88.2392i	0.0148957	+	0.0258002i	−0.858481	+	0.512845i	$0.828592\pi$
$228$	234.777			0.0681952
$229$	−1900.04	+	3290.97i	−0.548290	+	0.949666i	0.450102	+	0.892977i	$0.351388\pi$
$229$	−1900.04	+	3290.97i	−0.548290	+	0.949666i	−0.998392	+	0.0566888i	$0.981946\pi$
$230$	−2773.78	−	4804.33i	−0.795207	−	1.37734i
$231$	181.142	−	313.747i	0.0515943	−	0.0893639i
$232$	12047.7	+	20867.2i	3.40934	+	5.90516i
$233$	2758.92	+	4778.59i	0.775720	+	1.34359i	0.934389	+	0.356254i	$0.115946\pi$
$233$	2758.92	+	4778.59i	0.775720	+	1.34359i	−0.158669	+	0.987332i	$0.550720\pi$
$234$	1695.57	+	2936.82i	0.473688	+	0.820453i
$235$	−1938.92	−	3358.30i	−0.538217	−	0.932219i
$236$	−6883.44	−	11922.5i	−1.89862	−	3.28850i
$237$	1577.44	+	2732.20i	0.432345	+	0.748843i
$238$	−609.341	+	1055.41i	−0.165957	+	0.287446i
$239$	1224.84	+	2121.49i	0.331500	+	0.574175i	0.982806	−	0.184640i	$-0.0591120\pi$
$239$	1224.84	+	2121.49i	0.331500	+	0.574175i	−0.651306	+	0.758815i	$0.725779\pi$
$240$	6757.75	−	11704.8i	1.81755	−	3.14808i
$241$	1213.99			0.324480			0.162240	−	0.986751i	$-0.448128\pi$
$241$	1213.99			0.324480			0.162240	+	0.986751i	$0.448128\pi$
$242$	2053.47	+	3556.71i	0.545463	+	0.944769i
$243$	243.000			0.0641500
$244$	309.890			0.0813061
$245$	−2324.40	+	4025.98i	−0.606125	+	1.04984i
$246$	4156.97			1.07739
$247$	110.358	+	191.145i	0.0284287	+	0.0492399i
$248$	5929.02	+	10269.4i	1.51812	+	2.62946i
$249$	−518.527	+	898.114i	−0.131969	+	0.228577i
$250$	−1532.52	+	2654.40i	−0.387700	+	0.671517i
$251$	2541.72	−	4402.39i	0.639171	−	1.10708i	−0.346444	−	0.938071i	$-0.612611\pi$
$251$	2541.72	−	4402.39i	0.639171	−	1.10708i	0.985615	−	0.169006i	$-0.0540556\pi$
$252$	−525.469	+	910.138i	−0.131355	+	0.227513i
$253$	1656.87			0.411725
$254$	−13020.0			−3.21633
$255$	961.556	−	1665.46i	0.236137	−	0.409002i
$256$	−16355.8	−	28329.1i	−3.99312	−	6.91629i
$257$	985.023	+	1706.11i	0.239082	+	0.414102i	0.960451	−	0.278449i	$-0.0898203\pi$
$257$	985.023	+	1706.11i	0.239082	+	0.414102i	−0.721369	+	0.692551i	$0.756487\pi$
$258$	−2348.52	+	4067.76i	−0.566716	+	0.981580i
$259$	1853.74			0.444733
$260$	23143.6			5.52041
$261$	1224.59	+	2121.06i	0.290423	+	0.503027i
$262$	2827.52	−	4897.40i	0.666735	−	1.15482i
$263$	575.430			0.134915			0.0674573	−	0.997722i	$-0.478511\pi$
$263$	575.430			0.134915			0.0674573	+	0.997722i	$0.478511\pi$
$264$	3258.16	+	5643.30i	0.759568	+	1.31561i
$265$	−6647.74			−1.54101
$266$	−45.7347	+	79.2149i	−0.0105420	+	0.0182593i
$267$	−1954.19			−0.447919
$268$	−746.100	−	12987.6i	−0.170057	−	2.96025i
$269$	3796.33			0.860470			0.430235	−	0.902717i	$-0.358431\pi$
$269$	3796.33			0.860470			0.430235	+	0.902717i	$0.358431\pi$
$270$	1108.85	−	1920.59i	0.249936	−	0.432902i
$271$	−6746.99			−1.51236			−0.756182	−	0.654361i	$-0.772938\pi$
$271$	−6746.99			−1.51236			−0.756182	+	0.654361i	$0.772938\pi$
$272$	−6789.37	−	11759.5i	−1.51348	−	2.62142i
$273$	−987.991			−0.219033
$274$	2549.40	−	4415.69i	0.562098	−	0.973582i
$275$	1075.52	+	1862.85i	0.235841	+	0.408488i
$276$	−4806.35			−1.04822
$277$	1794.48			0.389242			0.194621	−	0.980878i	$-0.437652\pi$
$277$	1794.48			0.389242			0.194621	+	0.980878i	$0.437652\pi$
$278$	−2030.33	+	3516.63i	−0.438025	+	0.758681i
$279$	602.658	+	1043.84i	0.129320	+	0.223988i
$280$	3178.28	+	5504.95i	0.678353	+	1.17494i
$281$	−1012.15	+	1753.09i	−0.214874	+	0.372173i	−0.953234	−	0.302234i	$-0.902268\pi$
$281$	−1012.15	+	1753.09i	−0.214874	+	0.372173i	0.738359	+	0.674408i	$0.235601\pi$
$282$	−4492.79			−0.948731
$283$	7571.22			1.59033			0.795163	−	0.606395i	$-0.207385\pi$
$283$	7571.22			1.59033			0.795163	+	0.606395i	$0.207385\pi$
$284$	1310.47	−	2269.80i	0.273810	−	0.474253i
$285$	72.1706	−	125.003i	0.0150001	−	0.0259809i
$286$	−4621.70	+	8005.01i	−0.955548	+	1.65506i
$287$	−605.555	+	1048.85i	−0.124546	+	0.215720i
$288$	−4641.87	−	8039.96i	−0.949740	−	1.64500i
$289$	1490.44	+	2581.53i	0.303368	+	0.525448i
$290$	22352.2			4.52609
$291$	1546.84	−	2679.21i	0.311607	−	0.539718i
$292$	−20934.3			−4.19551
$293$	−8780.15			−1.75065			−0.875327	−	0.483531i	$-0.839354\pi$
$293$	−8780.15			−1.75065			−0.875327	+	0.483531i	$0.839354\pi$
$294$	2693.01	+	4664.44i	0.534217	+	0.925291i
$295$	−8463.88			−1.67046
$296$	−16671.4	+	28875.7i	−3.27367	+	5.67016i
$297$	331.178	+	573.617i	0.0647033	+	0.112069i
$298$	2312.93	−	4006.10i	0.449611	−	0.778750i
$299$	−2259.24	−	3913.11i	−0.436973	−	0.756860i
$300$	−3119.93	−	5403.88i	−0.600431	−	1.03998i
$301$	−684.228	−	1185.12i	−0.131024	−	0.226940i
$302$	6701.71	+	11607.7i	1.27695	+	2.21175i
$303$	435.072	+	753.567i	0.0824893	+	0.142876i
$304$	−509.583	−	882.624i	−0.0961401	−	0.166520i
$305$	95.2603	−	164.996i	0.0178839	−	0.0309758i
$306$	−1114.04	−	1929.58i	−0.208123	−	0.360479i
$307$	−1302.50	+	2255.99i	−0.242141	+	0.419401i	−0.961324	−	0.275420i	$-0.911183\pi$
$307$	−1302.50	+	2255.99i	−0.242141	+	0.419401i	0.719183	+	0.694821i	$0.244516\pi$
$308$	−2864.58			−0.529951
$309$	−230.073	−	398.499i	−0.0423573	−	0.0733650i
$310$	11000.2			2.01538
$311$	−4795.81			−0.874423			−0.437212	−	0.899359i	$-0.644034\pi$
$311$	−4795.81			−0.874423			−0.437212	+	0.899359i	$0.644034\pi$
$312$	8885.38	−	15389.9i	1.61229	−	2.79257i
$313$	6619.68			1.19542			0.597710	−	0.801712i	$-0.296077\pi$
$313$	6619.68			1.19542			0.597710	+	0.801712i	$0.296077\pi$
$314$	−4024.95	−	6971.42i	−0.723380	−	1.25293i
$315$	323.058	+	559.554i	0.0577850	+	0.100087i
$316$	12472.8	−	21603.6i	2.22041	−	3.84587i
$317$	4165.40	−	7214.68i	0.738019	−	1.27829i	−0.215367	−	0.976533i	$-0.569095\pi$
$317$	4165.40	−	7214.68i	0.738019	−	1.27829i	0.953386	−	0.301754i	$-0.0975720\pi$
$318$	−3850.98	+	6670.09i	−0.679095	+	1.17623i
$319$	−3337.92	+	5781.45i	−0.585855	+	1.01473i
$320$	−48685.6			−8.50503
$321$	−2005.70			−0.348746
$322$	936.280	−	1621.68i	0.162040	−	0.280661i
$323$	−72.5082	−	125.588i	−0.0124906	−	0.0216344i
$324$	−960.701	−	1663.98i	−0.164729	−	0.285319i
$325$	2933.06	−	5080.21i	0.500606	−	0.867075i
$326$	13346.7			2.26750
$327$	−1934.07			−0.327077
$328$	−10892.0	−	18865.4i	−1.83356	−	3.17582i
$329$	654.475	−	1133.58i	0.109673	−	0.189959i
$330$	6044.90			1.00837
$331$	3123.54	+	5410.13i	0.518686	+	0.898391i	0.999764	+	0.0217132i	$0.00691208\pi$
$331$	3123.54	+	5410.13i	0.518686	+	0.898391i	−0.481078	+	0.876678i	$0.659755\pi$
$332$	8199.98			1.35552
$333$	−1694.58	+	2935.09i	−0.278865	+	0.483009i
$334$	−5978.02			−0.979350
$335$	−7144.39	−	3595.15i	−1.16519	−	0.586341i
$336$	4562.11			0.740725
$337$	−1390.18	+	2407.86i	−0.224712	+	0.389212i	−0.956233	−	0.292606i	$-0.905477\pi$
$337$	−1390.18	+	2407.86i	−0.224712	+	0.389212i	0.731521	+	0.681819i	$0.238811\pi$
$338$	12834.0			2.06531
$339$	2319.87	+	4018.14i	0.371676	+	0.643762i
$340$	−15206.1			−2.42548
$341$	−1642.69	+	2845.23i	−0.260870	+	0.451840i
$342$	−83.6156	−	144.827i	−0.0132205	−	0.0228986i
$343$	−3257.66			−0.512820
$344$	24614.1			3.85786
$345$	−1477.47	+	2559.06i	−0.230564	+	0.399348i
$346$	2522.90	+	4369.79i	0.392000	+	0.678964i
$347$	−3425.55	−	5933.23i	−0.529952	−	0.917904i	−0.999389	−	0.0349380i	$-0.988877\pi$
$347$	−3425.55	−	5933.23i	−0.529952	−	0.917904i	0.469438	−	0.882966i	$-0.344457\pi$
$348$	9682.85	−	16771.2i	1.49154	−	2.58342i
$349$	2286.21			0.350654			0.175327	−	0.984510i	$-0.443902\pi$
$349$	2286.21			0.350654			0.175327	+	0.984510i	$0.443902\pi$
$350$	2431.06			0.371273
$351$	903.159	−	1564.32i	0.137342	−	0.237883i
$352$	12652.6	−	21914.9i	1.91586	−	3.31837i
$353$	−3490.25	+	6045.29i	−0.526253	+	0.911496i	0.473279	+	0.880912i	$0.343070\pi$
$353$	−3490.25	+	6045.29i	−0.526253	+	0.911496i	−0.999532	+	0.0305841i	$0.990263\pi$
$354$	−4903.06	+	8492.34i	−0.736143	+	1.27504i
$355$	−805.678	−	1395.48i	−0.120453	−	0.208631i
$356$	7725.89	+	13381.6i	1.15020	+	1.99221i
$357$	649.140			0.0962357
$358$	7277.51	−	12605.0i	1.07438	−	1.86088i
$359$	−6853.34			−1.00754			−0.503768	−	0.863839i	$-0.668053\pi$
$359$	−6853.34			−1.00754			−0.503768	+	0.863839i	$0.668053\pi$
$360$	−11621.5			−1.70141
$361$	3424.06	+	5930.64i	0.499207	+	0.864651i
$362$	18821.8			2.73274
$363$	1093.80	−	1894.51i	0.158152	−	0.273928i
$364$	3906.02	+	6765.43i	0.562449	+	0.974189i
$365$	−6435.22	+	11146.1i	−0.922835	+	1.59840i
$366$	−110.367	−	191.161i	−0.0157622	−	0.0273010i
$367$	−242.806	−	420.552i	−0.0345350	−	0.0598164i	0.848241	−	0.529610i	$-0.177662\pi$
$367$	−242.806	−	420.552i	−0.0345350	−	0.0598164i	−0.882776	+	0.469794i	$0.844328\pi$
$368$	10432.2	+	18069.0i	1.47776	+	2.55955i
$369$	−1107.12	−	1917.59i	−0.156191	−	0.270530i
$370$	15465.3	+	26786.7i	2.17298	+	3.76372i
$371$	−1121.96	−	1943.29i	−0.157006	−	0.271943i
$372$	4765.22	−	8253.61i	0.664154	−	1.15035i
$373$	2600.81	+	4504.73i	0.361032	+	0.625325i	0.988131	−	0.153614i	$-0.0490913\pi$
$373$	2600.81	+	4504.73i	0.361032	+	0.625325i	−0.627099	+	0.778939i	$0.715758\pi$
$374$	3036.59	−	5259.54i	0.419836	−	0.727177i
$375$	1632.62			0.224821
$376$	11771.9	+	20389.5i	1.61460	+	2.79656i
$377$	18205.8			2.48712
$378$	748.580			0.101859
$379$	−1680.09	+	2909.99i	−0.227705	+	0.394397i	−0.957128	−	0.289667i	$-0.906456\pi$
$379$	−1680.09	+	2909.99i	−0.227705	+	0.394397i	0.729423	+	0.684063i	$0.239789\pi$
$380$	−1141.31			−0.154073
$381$	3467.60	+	6006.05i	0.466274	+	0.807610i
$382$	2064.19	+	3575.29i	0.276475	+	0.478868i
$383$	−5409.58	+	9369.66i	−0.721714	+	1.25005i	0.238598	+	0.971118i	$0.423312\pi$
$383$	−5409.58	+	9369.66i	−0.721714	+	1.25005i	−0.960312	+	0.278927i	$0.910021\pi$
$384$	−15824.9	+	27409.5i	−2.10302	+	3.64254i
$385$	−880.574	+	1525.20i	−0.116567	+	0.201900i
$386$	10570.8	−	18309.2i	1.39389	−	2.41429i
$387$	2501.91			0.328629
$388$	−24461.8			−3.20067
$389$	−1523.89	+	2639.45i	−0.198622	+	0.344024i	−0.948082	−	0.318026i	$-0.896980\pi$
$389$	−1523.89	+	2639.45i	−0.198622	+	0.344024i	0.749460	+	0.662050i	$0.230313\pi$
$390$	−8242.57	−	14276.6i	−1.07020	−	1.85364i
$391$	1484.39	+	2571.03i	0.191991	+	0.332539i
$392$	14112.3	−	24443.2i	1.81831	−	3.14941i
$393$	−3012.19			−0.386629
$394$	−6085.94			−0.778186
$395$	−7668.29	−	13281.9i	−0.976794	−	1.69186i
$396$	2618.62	−	4535.59i	0.332300	−	0.575560i
$397$	5590.77			0.706783			0.353391	−	0.935476i	$-0.385028\pi$
$397$	5590.77			0.706783			0.353391	+	0.935476i	$0.385028\pi$
$398$	3491.57	+	6047.58i	0.439740	+	0.761653i
$399$	48.7218			0.00611314
$400$	−13543.6	+	23458.2i	−1.69295	+	2.93227i
$401$	2093.78			0.260744			0.130372	−	0.991465i	$-0.458383\pi$
$401$	2093.78			0.260744			0.130372	+	0.991465i	$0.458383\pi$
$402$	−7745.93	+	5085.78i	−0.961025	+	0.630984i
$403$	8959.61			1.10747
$404$	3440.12	−	5958.46i	0.423644	−	0.733773i
$405$	−1181.28			−0.144934
$406$	3772.45	+	6534.07i	0.461142	+	0.798721i
$407$	−9237.95			−1.12508
$408$	−5837.96	+	10111.6i	−0.708388	+	1.22696i
$409$	4102.76	+	7106.20i	0.496011	+	0.859117i	0.999989	−	0.00459956i	$-0.00146409\pi$
$409$	4102.76	+	7106.20i	0.496011	+	0.859117i	−0.503978	+	0.863716i	$0.668131\pi$
$410$	−20208.0			−2.43415
$411$	−2715.91			−0.325951
$412$	−1819.19	+	3150.93i	−0.217537	+	0.376784i
$413$	−1428.48	−	2474.19i	−0.170195	−	0.294787i
$414$	1711.78	+	2964.88i	0.203211	+	0.351971i
$415$	2520.68	−	4365.94i	0.298157	−	0.516423i
$416$	−69009.9			−8.13339
$417$	2162.94			0.254003
$418$	227.915	−	394.760i	0.0266691	−	0.0461922i
$419$	3336.62	−	5779.19i	0.389032	−	0.673823i	−0.603288	−	0.797524i	$-0.706143\pi$
$419$	3336.62	−	5779.19i	0.389032	−	0.673823i	0.992320	+	0.123701i	$0.0394763\pi$
$420$	2554.42	−	4424.39i	0.296769	−	0.514020i
$421$	−648.411	+	1123.08i	−0.0750632	+	0.130013i	−0.901114	−	0.433583i	$-0.857249\pi$
$421$	−648.411	+	1123.08i	−0.0750632	+	0.130013i	0.826051	+	0.563596i	$0.190583\pi$
$422$	14968.1	+	25925.5i	1.72662	+	2.99060i
$423$	1196.56	+	2072.50i	0.137538	+	0.238223i
$424$	40360.9			4.62287
$425$	−1927.11	+	3337.85i	−0.219949	+	0.380964i
$426$	−1866.89			−0.212327
$427$	64.3096			0.00728843
$428$	7929.55	+	13734.4i	0.895536	+	1.55111i
$429$	4923.56			0.554106
$430$	11416.7	−	19774.3i	1.28038	−	2.21768i
$431$	−1469.53	−	2545.30i	−0.164234	−	0.284461i	0.772149	−	0.635441i	$-0.219182\pi$
$431$	−1469.53	−	2545.30i	−0.164234	−	0.284461i	−0.936383	+	0.350980i	$0.885849\pi$
$432$	−4170.40	+	7223.34i	−0.464464	+	0.804475i
$433$	−8208.19	−	14217.0i	−0.910994	−	1.57789i	−0.812663	−	0.582734i	$-0.801983\pi$
$433$	−8208.19	−	14217.0i	−0.910994	−	1.57789i	−0.0983306	−	0.995154i	$-0.531350\pi$
$434$	1856.54	+	3215.61i	0.205338	+	0.355655i
$435$	−5953.02	−	10310.9i	−0.656151	−	1.13649i
$436$	7646.34	+	13243.8i	0.839892	+	1.45474i
$437$	111.412	+	192.971i	0.0121958	+	0.0211237i
$438$	7455.74	+	12913.7i	0.813354	+	1.40877i
$439$	2800.72	−	4850.99i	0.304490	−	0.527392i	−0.672658	−	0.739954i	$-0.734847\pi$
$439$	2800.72	−	4850.99i	0.304490	−	0.527392i	0.977148	+	0.212562i	$0.0681807\pi$
$440$	−15838.7	−	27433.4i	−1.71609	−	2.97235i
$441$	1434.45	−	2484.55i	0.154892	−	0.268280i
$442$	−16562.3			−1.78232
$443$	−3250.34	−	5629.75i	−0.348596	−	0.603786i	0.637404	−	0.770530i	$-0.280008\pi$
$443$	−3250.34	−	5629.75i	−0.348596	−	0.603786i	−0.986000	+	0.166743i	$0.946675\pi$
$444$	26798.0			2.86436
$445$	9499.77			1.01198
$446$	−1719.00	+	2977.39i	−0.182504	+	0.316106i
$447$	−2463.99			−0.260722
$448$	−8216.84	−	14232.0i	−0.866538	−	1.50089i
$449$	−5079.81	−	8798.49i	−0.533922	−	0.924781i	−0.999215	−	0.0396237i	$-0.987384\pi$
$449$	−5079.81	−	8798.49i	−0.533922	−	0.924781i	0.465292	−	0.885157i	$-0.345949\pi$
$450$	−2222.32	+	3849.17i	−0.232802	+	0.403226i
$451$	3017.72	−	5226.85i	0.315076	−	0.545727i
$452$	18343.2	−	31771.4i	1.90884	−	3.30620i
$453$	3569.72	−	6182.93i	0.370243	−	0.641279i
$454$	−573.858			−0.0593227
$455$	4802.85			0.494860
$456$	−438.174	+	758.940i	−0.0449986	+	0.0779399i
$457$	−33.4178	−	57.8814i	−0.00342061	−	0.00592468i	0.864310	−	0.502959i	$-0.167755\pi$
$457$	−33.4178	−	57.8814i	−0.00342061	−	0.00592468i	−0.867731	+	0.497035i	$0.834422\pi$
$458$	−10701.3	−	18535.2i	−1.09179	−	1.89103i
$459$	−593.403	+	1027.80i	−0.0603435	+	0.104518i
$460$	23364.8			2.36824
$461$	−6286.24			−0.635096			−0.317548	−	0.948242i	$-0.602860\pi$
$461$	−6286.24			−0.635096			−0.317548	+	0.948242i	$0.602860\pi$
$462$	1020.22	+	1767.07i	0.102738	+	0.177947i
$463$	−1173.69	+	2032.89i	−0.117810	+	0.204053i	−0.918899	−	0.394492i	$-0.870921\pi$
$463$	−1173.69	+	2032.89i	−0.117810	+	0.204053i	0.801090	+	0.598544i	$0.204254\pi$
$464$	−84066.4			−8.41096
$465$	−2929.66	−	5074.32i	−0.292172	−	0.506056i
$466$	−31077.2			−3.08932
$467$	−2876.76	+	4982.70i	−0.285055	+	0.493730i	−0.972623	−	0.232391i	$-0.925345\pi$
$467$	−2876.76	+	4982.70i	−0.285055	+	0.493730i	0.687568	+	0.726120i	$0.258679\pi$
$468$	−14282.6			−1.41071
$469$	−154.833	−	2695.24i	−0.0152442	−	0.265362i
$470$	21840.5			2.14346
$471$	−2143.92	+	3713.38i	−0.209738	+	0.363277i
$472$	51387.3			5.01122
$473$	3409.79	+	5905.92i	0.331463	+	0.574111i
$474$	−17768.7			−1.72182
$475$	−144.641	+	250.526i	−0.0139718	+	0.0241998i
$476$	−2566.38	−	4445.09i	−0.247121	−	0.428026i
$477$	4102.50			0.393796
$478$	−13797.0			−1.32021
$479$	−1288.14	+	2231.13i	−0.122874	+	0.212824i	−0.920900	−	0.389799i	$-0.872545\pi$
$479$	−1288.14	+	2231.13i	−0.122874	+	0.212824i	0.798026	+	0.602623i	$0.205878\pi$
$480$	22565.2	+	39084.1i	2.14574	+	3.71654i
$481$	12596.5	+	21817.7i	1.19407	+	2.06820i
$482$	−3418.67	+	5921.31i	−0.323063	+	0.559561i
$483$	−997.432			−0.0939642
$484$	−17297.3			−1.62446
$485$	−7519.56	+	13024.3i	−0.704011	+	1.21938i
$486$	−684.305	+	1185.25i	−0.0638698	+	0.110626i
$487$	−8999.68	+	15587.9i	−0.837401	+	1.45042i	0.0546594	+	0.998505i	$0.482593\pi$
$487$	−8999.68	+	15587.9i	−0.837401	+	1.45042i	−0.892060	+	0.451916i	$0.850741\pi$
$488$	−578.361	+	1001.75i	−0.0536499	+	0.0929244i
$489$	−3554.60	−	6156.75i	−0.328721	−	0.569361i
$490$	−13091.4	−	22674.9i	−1.20695	−	2.09050i
$491$	−2568.52			−0.236081			−0.118041	−	0.993009i	$-0.537661\pi$
$491$	−2568.52			−0.236081			−0.118041	+	0.993009i	$0.537661\pi$
$492$	−8754.00	+	15162.4i	−0.802156	+	1.38938i
$493$	−11961.8			−1.09276
$494$	−1243.10			−0.113218
$495$	−1609.93	−	2788.48i	−0.146184	−	0.253198i
$496$	−41371.6			−3.74524
$497$	271.954	−	471.038i	0.0245449	−	0.0425130i
$498$	−2920.41	−	5058.31i	−0.262785	−	0.455157i
$499$	9881.97	−	17116.1i	0.886529	−	1.53551i	0.0425772	−	0.999093i	$-0.486443\pi$
$499$	9881.97	−	17116.1i	0.886529	−	1.53551i	0.843951	−	0.536420i	$-0.180224\pi$
$500$	−6454.55	−	11179.6i	−0.577312	−	0.999934i
$501$	1592.12	+	2757.63i	0.141977	+	0.245912i
$502$	14315.3	+	24794.9i	1.27276	+	2.20448i
$503$	−5877.75	−	10180.6i	−0.521026	−	0.902443i	−0.999701	−	0.0244512i	$-0.992216\pi$
$503$	−5877.75	−	10180.6i	−0.521026	−	0.902443i	0.478675	−	0.877992i	$-0.341117\pi$
$504$	−1961.41	−	3397.26i	−0.173349	−	0.300250i
$505$	−2114.99	−	3663.26i	−0.186368	−	0.322798i
$506$	−4665.86	+	8081.51i	−0.409927	+	0.710014i
$507$	−3418.05	−	5920.24i	−0.299410	−	0.518594i
$508$	27418.3	−	47489.9i	2.39467	−	4.14768i
$509$	13310.3			1.15907			0.579536	−	0.814947i	$-0.303234\pi$
$509$	13310.3			1.15907			0.579536	+	0.814947i	$0.303234\pi$
$510$	5415.62	+	9380.13i	0.470211	+	0.814429i
$511$	−4344.37			−0.376093
$512$	99837.5			8.61765
$513$	−44.5385	+	77.1429i	−0.00383318	+	0.00663926i
$514$	−11095.6			−0.952149
$515$	1118.44	+	1937.19i	0.0956977	+	0.165753i
$516$	−9891.32	−	17132.3i	−0.843878	−	1.46164i
$517$	−3261.51	+	5649.11i	−0.277449	+	0.480556i
$518$	−5220.27	+	9041.77i	−0.442791	+	0.766936i
$519$	1343.84	−	2327.60i	0.113657	−	0.196860i
$520$	−43193.9	+	74814.0i	−3.64265	+	6.30925i
$521$	5398.22			0.453935			0.226968	−	0.973902i	$-0.427119\pi$
$521$	5398.22			0.453935			0.226968	+	0.973902i	$0.427119\pi$
$522$	−13794.1			−1.15662
$523$	−4399.51	+	7620.18i	−0.367834	+	0.637107i	−0.989227	−	0.146392i	$-0.953234\pi$
$523$	−4399.51	+	7620.18i	−0.367834	+	0.637107i	0.621393	+	0.783499i	$0.286567\pi$
$524$	11908.7	+	20626.5i	0.992814	+	1.71960i
$525$	−647.459	−	1121.43i	−0.0538237	−	0.0932254i
$526$	−1620.45	+	2806.70i	−0.134325	+	0.232658i
$527$	−5886.74			−0.486585
$528$	−22734.9			−1.87388
$529$	3802.67	+	6586.43i	0.312540	+	0.541335i
$530$	18720.5	−	32424.9i	1.53428	−	2.65744i
$531$	5223.30			0.426877
$532$	−192.622	−	333.631i	−0.0156978	−	0.0271894i
$533$	−16459.4			−1.33759
$534$	5503.14	−	9531.71i	0.445963	−	0.772430i
$535$	9750.18			0.787920
$536$	43376.2	+	21827.5i	3.49546	+	1.75896i
$537$	−7752.83			−0.623016
$538$	−10690.7	+	18516.9i	−0.856711	+	1.48387i
$539$	7819.90			0.624911
$540$	4670.19	+	8089.00i	0.372172	+	0.644621i
$541$	11537.1			0.916858			0.458429	−	0.888731i	$-0.348412\pi$
$541$	11537.1			0.916858			0.458429	+	0.888731i	$0.348412\pi$
$542$	19000.0	−	32909.0i	1.50576	−	2.60805i
$543$	−5012.78	−	8682.39i	−0.396168	−	0.686182i
$544$	45341.6			3.57354
$545$	9401.94			0.738963
$546$	2782.25	−	4819.00i	0.218076	−	0.377718i
$547$	−1240.09	−	2147.90i	−0.0969332	−	0.167893i	0.813481	−	0.581592i	$-0.197570\pi$
$547$	−1240.09	−	2147.90i	−0.0969332	−	0.167893i	−0.910414	+	0.413699i	$0.864237\pi$
$548$	10737.4	+	18597.6i	0.837002	+	1.44973i
$549$	−58.7878	+	101.823i	−0.00457013	+	0.00791570i
$550$	−12114.9			−0.939241
$551$	−897.801			−0.0694149
$552$	8970.28	−	15537.0i	0.691668	−	1.19800i
$553$	2588.41	−	4483.25i	0.199042	−	0.344751i
$554$	−5053.39	+	8752.73i	−0.387542	+	0.671242i
$555$	8237.72	−	14268.1i	0.630039	−	1.09126i
$556$	−8551.17	−	14811.1i	−0.652249	−	1.12973i
$557$	10067.1	+	17436.7i	0.765809	+	1.32642i	0.939818	+	0.341676i	$0.110995\pi$
$557$	10067.1	+	17436.7i	0.765809	+	1.32642i	−0.174009	+	0.984744i	$0.555672\pi$
$558$	−6788.51			−0.515019
$559$	9298.88	−	16106.1i	0.703579	−	1.21863i
$560$	−22177.5			−1.67352
$561$	−3234.93			−0.243456
$562$	−5700.56	−	9873.66i	−0.427871	−	0.741095i
$563$	18133.1			1.35741			0.678703	−	0.734413i	$-0.262542\pi$
$563$	18133.1			1.35741			0.678703	+	0.734413i	$0.262542\pi$
$564$	9461.20	−	16387.3i	0.706362	−	1.22346i
$565$	−11277.4	−	19533.1i	−0.839726	−	1.45445i
$566$	−21321.1	+	36929.2i	−1.58338	+	2.74249i
$567$	−199.368	−	345.316i	−0.0147666	−	0.0255766i
$568$	4891.57	+	8472.45i	0.361348	+	0.625873i
$569$	−7607.88	−	13177.2i	−0.560525	−	0.970858i	−0.997451	−	0.0713604i	$-0.977266\pi$
$569$	−7607.88	−	13177.2i	−0.560525	−	0.970858i	0.436925	−	0.899498i	$-0.356067\pi$
$570$	406.475	+	704.035i	0.0298690	+	0.0517347i
$571$	1201.61	+	2081.26i	0.0880665	+	0.152536i	0.906694	−	0.421789i	$-0.138598\pi$
$571$	1201.61	+	2081.26i	0.0880665	+	0.152536i	−0.818627	+	0.574325i	$0.805265\pi$
$572$	−19465.3	−	33714.9i	−1.42288	−	2.46449i
$573$	1099.51	−	1904.40i	0.0801615	−	0.138844i
$574$	−3410.57	−	5907.28i	−0.248004	−	0.429556i
$575$	2961.09	−	5128.75i	0.214758	−	0.371972i
$576$	30045.3			2.17341
$577$	7083.32	+	12268.7i	0.511061	+	0.885184i	0.999918	+	0.0128199i	$0.00408082\pi$
$577$	7083.32	+	12268.7i	0.511061	+	0.885184i	−0.488857	+	0.872364i	$0.662586\pi$
$578$	−16788.8			−1.20817
$579$	−11261.3			−0.808294
$580$	−47070.6	+	81528.6i	−3.36983	+	5.83671i
$581$	1701.69			0.121511
$582$	8712.03	+	15089.7i	0.620490	+	1.07472i
$583$	5591.18	+	9684.22i	0.397192	+	0.687957i
$584$	39070.6	−	67672.3i	2.76841	−	4.79503i
$585$	−4390.46	+	7604.51i	−0.310296	+	0.537449i
$586$	24725.5	−	42825.9i	1.74301	−	3.01898i
$587$	−10128.1	+	17542.4i	−0.712150	+	1.23348i	0.251899	+	0.967754i	$0.418945\pi$
$587$	−10128.1	+	17542.4i	−0.712150	+	1.23348i	−0.964049	+	0.265726i	$0.914388\pi$
$588$	−22684.4			−1.59097
$589$	−441.835			−0.0309092
$590$	23834.9	−	41283.2i	1.66316	−	2.88068i
$591$	1620.86	+	2807.41i	0.112814	+	0.195400i
$592$	−58165.0	−	100745.i	−4.03812	−	6.99423i
$593$	−3611.77	+	6255.76i	−0.250114	+	0.433210i	−0.963557	−	0.267503i	$-0.913801\pi$
$593$	−3611.77	+	6255.76i	−0.250114	+	0.433210i	0.713443	+	0.700713i	$0.247135\pi$
$594$	−3730.48			−0.257682
$595$	−3155.62			−0.217425
$596$	9741.40	+	16872.6i	0.669502	+	1.15961i
$597$	1859.81	−	3221.29i	0.127499	−	0.220835i
$598$	25448.7			1.74026
$599$	−6250.18	−	10825.6i	−0.426336	−	0.738436i	0.570208	−	0.821501i	$-0.306863\pi$
$599$	−6250.18	−	10825.6i	−0.426336	−	0.738436i	−0.996544	+	0.0830641i	$0.973529\pi$
$600$	23291.4			1.58478
$601$	176.748	−	306.137i	0.0119962	−	0.0207780i	−0.859965	−	0.510353i	$-0.829515\pi$
$601$	176.748	−	306.137i	0.0119962	−	0.0207780i	0.871961	+	0.489575i	$0.162848\pi$
$602$	7707.34			0.521807
$603$	4409.00	+	2218.67i	0.297759	+	0.149836i
$604$	−56451.5			−3.80295
$605$	−5317.19	+	9209.64i	−0.357313	+	0.618885i
$606$	−4900.78			−0.328516
$607$	577.817	+	1000.81i	0.0386373	+	0.0669218i	0.884697	−	0.466166i	$-0.154365\pi$
$607$	577.817	+	1000.81i	0.0386373	+	0.0669218i	−0.846060	+	0.533088i	$0.821032\pi$
$608$	3403.16			0.227001
$609$	2009.42	−	3480.42i	0.133704	−	0.231583i
$610$	536.520	+	929.279i	0.0356115	+	0.0616810i
$611$	17789.0			1.17785
$612$	9384.08			0.619819
$613$	−783.193	+	1356.53i	−0.0516034	+	0.0893797i	−0.890673	−	0.454644i	$-0.849766\pi$
$613$	−783.193	+	1356.53i	−0.0516034	+	0.0893797i	0.839070	+	0.544024i	$0.183100\pi$
$614$	−7335.84	−	12706.1i	−0.482167	−	0.835138i
$615$	5381.96	+	9321.84i	0.352881	+	0.611208i
$616$	5346.29	−	9260.04i	0.349688	−	0.605678i
$617$	−17670.4			−1.15297			−0.576485	−	0.817108i	$-0.695576\pi$
$617$	−17670.4			−1.15297			−0.576485	+	0.817108i	$0.695576\pi$
$618$	2591.61			0.168689
$619$	3371.19	−	5839.07i	0.218901	−	0.379147i	−0.735571	−	0.677447i	$-0.763086\pi$
$619$	3371.19	−	5839.07i	0.218901	−	0.379147i	0.954472	+	0.298300i	$0.0964196\pi$
$620$	−23164.8	+	40122.7i	−1.50052	+	2.59898i
$621$	911.790	−	1579.27i	0.0589193	−	0.102051i
$622$	13505.3	−	23391.9i	0.870603	−	1.50793i
$623$	1603.31	+	2777.01i	0.103106	+	0.178585i
$624$	31000.3	+	53694.0i	1.98879	+	3.44468i
$625$	−18897.0			−1.20941
$626$	−18641.5	+	32288.0i	−1.19020	+	2.06148i
$627$	−242.801			−0.0154650
$628$	33904.0			2.15432
$629$	−8276.26	−	14334.9i	−0.524636	−	0.908697i
$630$	−3639.02			−0.230130
$631$	−11349.7	+	19658.2i	−0.716044	+	1.24022i	0.246512	+	0.969140i	$0.420716\pi$
$631$	−11349.7	+	19658.2i	−0.716044	+	1.24022i	−0.962556	+	0.271085i	$0.912618\pi$
$632$	46557.0	+	80639.2i	2.93028	+	5.07540i
$633$	7972.85	−	13809.4i	0.500620	−	0.867099i
$634$	23460.1	+	40634.1i	1.46959	+	2.54541i
$635$	−16856.8	−	29196.8i	−1.05345	−	1.82463i
$636$	−16219.3	−	28092.6i	−1.01122	−	1.75148i
$637$	−10662.9	−	18468.6i	−0.663232	−	1.14875i
$638$	−18799.6	−	32561.9i	−1.16659	−	2.02059i
$639$	497.206	+	861.187i	0.0307812	+	0.0533146i
$640$	76928.3	−	133244.i	4.75134	−	8.22956i
$641$	3198.01	+	5539.12i	0.197058	+	0.341314i	0.947573	−	0.319539i	$-0.103528\pi$
$641$	3198.01	+	5539.12i	0.197058	+	0.341314i	−0.750515	+	0.660853i	$0.770195\pi$
$642$	5648.20	−	9782.97i	0.347222	−	0.601407i
$643$	−15862.6			−0.972880			−0.486440	−	0.873714i	$-0.661705\pi$
$643$	−15862.6			−0.972880			−0.486440	+	0.873714i	$0.661705\pi$
$644$	3943.35	+	6830.08i	0.241288	+	0.417924i
$645$	−12162.4			−0.742470
$646$	816.753			0.0497442
$647$	−5587.39	+	9677.64i	−0.339510	+	0.588049i	−0.984341	−	0.176277i	$-0.943595\pi$
$647$	−5587.39	+	9677.64i	−0.339510	+	0.588049i	0.644831	+	0.764326i	$0.276928\pi$
$648$	7171.98			0.434787
$649$	7118.68	+	12329.9i	0.430559	+	0.745749i
$650$	16519.4	+	28612.4i	0.996837	+	1.72657i
$651$	988.897	−	1712.82i	0.0595360	−	0.103119i
$652$	−28106.2	+	48681.4i	−1.68823	+	2.92410i
$653$	−5663.17	+	9808.90i	−0.339383	+	0.587828i	−0.984317	−	0.176410i	$-0.943552\pi$
$653$	−5663.17	+	9808.90i	−0.339383	+	0.587828i	0.644934	+	0.764238i	$0.276885\pi$
$654$	5446.47	−	9433.56i	0.325648	−	0.564039i
$655$	14643.0			0.873509
$656$	76002.1			4.52345
$657$	3971.35	−	6878.59i	0.235825	−	0.408461i
$658$	3686.09	+	6384.50i	0.218387	+	0.378258i
$659$	−10513.1	−	18209.3i	−0.621447	−	1.07638i	−0.989216	−	0.146461i	$-0.953212\pi$
$659$	−10513.1	−	18209.3i	−0.621447	−	1.07638i	0.367769	−	0.929917i	$-0.380122\pi$
$660$	−12729.7	+	22048.5i	−0.750764	+	1.30036i
$661$	−1689.46			−0.0994136			−0.0497068	−	0.998764i	$-0.515829\pi$
$661$	−1689.46			−0.0994136			−0.0497068	+	0.998764i	$0.515829\pi$
$662$	−35184.4			−2.06568
$663$	4411.01	+	7640.09i	0.258385	+	0.447536i
$664$	−15304.0	+	26507.2i	−0.894441	+	1.54922i
$665$	−236.848			−0.0138114
$666$	−9544.09	−	16530.8i	−0.555294	−	0.961797i
$667$	18379.8			1.06697
$668$	12588.9	−	21804.6i	0.729159	−	1.26294i
$669$	1831.27			0.105831
$670$	37654.7	−	24723.1i	2.17124	−	1.42558i
$671$	−320.481			−0.0184382
$672$	−7616.81	+	13192.7i	−0.437239	+	0.757321i
$673$	14985.8			0.858334			0.429167	−	0.903225i	$-0.358807\pi$
$673$	14985.8			0.858334			0.429167	+	0.903225i	$0.358807\pi$
$674$	−7829.69	−	13561.4i	−0.447460	−	0.775024i
$675$	2367.47			0.134998
$676$	−27026.6	+	46811.4i	−1.53770	+	2.66337i
$677$	−10147.6	−	17576.1i	−0.576075	−	0.997792i	−0.995924	−	0.0901978i	$-0.971250\pi$
$677$	−10147.6	−	17576.1i	−0.576075	−	0.997792i	0.419848	−	0.907594i	$-0.362083\pi$
$678$	−26131.7			−1.48021
$679$	−5076.40			−0.286914
$680$	28379.7	−	49155.0i	1.60046	−	2.77207i
$681$	152.835	+	264.718i	0.00860006	+	0.0148957i
$682$	−9251.87	−	16024.7i	−0.519461	−	0.899733i
$683$	16478.2	−	28541.1i	0.923164	−	1.59897i	0.128677	−	0.991687i	$-0.458927\pi$
$683$	16478.2	−	28541.1i	0.923164	−	1.59897i	0.794487	−	0.607281i	$-0.207740\pi$
$684$	704.332			0.0393725
$685$	13202.7			0.736420
$686$	9173.81	−	15889.5i	0.510580	−	0.884350i
$687$	−5700.13	+	9872.91i	−0.316555	+	0.548290i
$688$	−42938.2	+	74371.1i	−2.37936	+	4.12118i
$689$	15247.8	−	26410.0i	0.843098	−	1.46029i
$690$	−8321.34	−	14413.0i	−0.459113	−	0.795207i
$691$	−6916.86	−	11980.3i	−0.380795	−	0.659557i	0.610381	−	0.792108i	$-0.291016\pi$
$691$	−6916.86	−	11980.3i	−0.380795	−	0.659557i	−0.991176	+	0.132551i	$0.957683\pi$
$692$	−21251.5			−1.16743
$693$	543.427	−	941.242i	0.0297880	−	0.0515943i
$694$	38586.4			2.11055
$695$	−10514.5			−0.573869
$696$	36143.0	+	62601.5i	1.96839	+	3.40934i
$697$	10814.3			0.587691
$698$	−6438.13	+	11151.2i	−0.349122	+	0.604697i
$699$	8276.75	+	14335.8i	0.447862	+	0.775720i
$700$	−5119.46	+	8867.17i	−0.276425	+	0.478782i
$701$	−1159.41	−	2008.16i	−0.0624686	−	0.108199i	0.833100	−	0.553123i	$-0.186564\pi$
$701$	−1159.41	−	2008.16i	−0.0624686	−	0.108199i	−0.895568	+	0.444924i	$0.853231\pi$
$702$	5086.72	+	8810.46i	0.273484	+	0.473688i
$703$	−621.183	−	1075.92i	−0.0333263	−	0.0577228i
$704$	40947.8	+	70923.7i	2.19216	+	3.79693i
$705$	−5816.75	−	10074.9i	−0.310740	−	0.538217i
$706$	−19657.6	−	34047.9i	−1.04791	−	1.81503i
$707$	713.906	−	1236.52i	0.0379763	−	0.0657768i
$708$	−20650.3	−	35767.4i	−1.09617	−	1.89862i
$709$	853.793	−	1478.81i	0.0452255	−	0.0783328i	−0.842527	−	0.538655i	$-0.818933\pi$
$709$	853.793	−	1478.81i	0.0452255	−	0.0783328i	0.887752	+	0.460322i	$0.152266\pi$
$710$	9075.39			0.479709
$711$	4732.32	+	8196.61i	0.249614	+	0.432345i
$712$	−57676.6			−3.03584
$713$	9045.23			0.475100
$714$	−1828.02	+	3166.23i	−0.0958152	+	0.165957i
$715$	−23934.5			−1.25189
$716$	30650.8	+	53088.8i	1.59983	+	2.77098i
$717$	3674.53	+	6364.47i	0.191392	+	0.331500i
$718$	19299.5	−	33427.7i	1.00313	−	1.73748i
$719$	4294.60	−	7438.47i	0.222756	−	0.385825i	−0.732888	−	0.680350i	$-0.761828\pi$
$719$	4294.60	−	7438.47i	0.222756	−	0.385825i	0.955644	+	0.294525i	$0.0951613\pi$
$720$	20273.3	−	35114.3i	1.04936	−	1.81755i
$721$	−377.525	+	653.893i	−0.0195004	+	0.0337756i
$722$	−38569.6			−1.98810
$723$	3641.96			0.187339
$724$	−39636.1	+	68651.7i	−2.03462	+	3.52406i
$725$	11930.8	+	20664.7i	0.611170	+	1.05858i
$726$	6160.41	+	10670.1i	0.314923	+	0.545463i
$727$	1911.58	−	3310.95i	0.0975192	−	0.168908i	−0.813138	−	0.582071i	$-0.802243\pi$
$727$	1911.58	−	3310.95i	0.0975192	−	0.168908i	0.910657	+	0.413163i	$0.135576\pi$
$728$	−29159.9			−1.48453
$729$	729.000			0.0370370
$730$	−36244.1	−	62776.6i	−1.83761	−	3.18283i
$731$	−6109.64	+	10582.2i	−0.309129	+	0.535427i
$732$	929.671			0.0469421
$733$	16621.7	+	28789.6i	0.837566	+	1.45071i	0.891924	+	0.452185i	$0.149355\pi$
$733$	16621.7	+	28789.6i	0.837566	+	1.45071i	−0.0543586	+	0.998521i	$0.517311\pi$
$734$	2735.03			0.137537
$735$	−6973.20	+	12077.9i	−0.349946	+	0.606125i
$736$	−69669.4			−3.48919
$737$	771.598	+	13431.5i	0.0385647	+	0.671310i
$738$	12470.9			0.622033
$739$	−6848.55	+	11862.0i	−0.340904	+	0.590463i	−0.984601	−	0.174818i	$-0.944066\pi$
$739$	−6848.55	+	11862.0i	−0.340904	+	0.590463i	0.643697	+	0.765280i	$0.277400\pi$
$740$	−130271.			−6.47145
$741$	331.073	+	573.435i	0.0164133	+	0.0284287i
$742$	12638.1			0.625281
$743$	11647.2	−	20173.5i	0.575093	−	0.996091i	−0.420938	−	0.907089i	$-0.638299\pi$
$743$	11647.2	−	20173.5i	0.575093	−	0.996091i	0.996031	−	0.0890016i	$-0.0283676\pi$
$744$	17787.1	+	30808.1i	0.876485	+	1.51812i
$745$	11978.0			0.589048
$746$	−29296.2			−1.43782
$747$	−1555.58	+	2694.34i	−0.0761923	+	0.131969i
$748$	12789.3	+	22151.7i	0.625164	+	1.08282i
$749$	1645.57	+	2850.21i	0.0802775	+	0.139045i
$750$	−4597.56	+	7963.21i	−0.223839	+	0.387700i
$751$	−11067.6			−0.537765			−0.268882	−	0.963173i	$-0.586654\pi$
$751$	−11067.6			−0.537765			−0.268882	+	0.963173i	$0.586654\pi$
$752$	−82142.0			−3.98326
$753$	7625.16	−	13207.2i	0.369025	−	0.639171i
$754$	−51268.8	+	88800.1i	−2.47626	+	4.28900i
$755$	−17353.2	+	30056.6i	−0.836487	+	1.44884i
$756$	−1576.41	+	2730.42i	−0.0758377	+	0.131355i
$757$	16138.4	+	27952.6i	0.774850	+	1.34208i	0.934878	+	0.354968i	$0.115508\pi$
$757$	16138.4	+	27952.6i	0.774850	+	1.34208i	−0.160028	+	0.987112i	$0.551158\pi$
$758$	−9462.48	−	16389.5i	−0.453420	−	0.785347i
$759$	4970.61			0.237710
$760$	2130.06	−	3689.38i	0.101665	−	0.176089i
$761$	21745.4			1.03584			0.517918	−	0.855430i	$-0.326707\pi$
$761$	21745.4			1.03584			0.517918	+	0.855430i	$0.326707\pi$
$762$	−39060.0			−1.85695
$763$	1586.80	+	2748.41i	0.0752895	+	0.130405i
$764$	−17387.6			−0.823379
$765$	2884.67	−	4996.39i	0.136334	−	0.236137i
$766$	−30467.5	−	52771.3i	−1.43712	−	2.48917i
$767$	19413.4	−	33625.1i	0.913923	−	1.58296i
$768$	−49067.5	−	84987.4i	−2.30543	−	3.99312i
$769$	−12967.4	−	22460.2i	−0.608084	−	1.05323i	−0.991556	−	0.129680i	$-0.958605\pi$
$769$	−12967.4	−	22460.2i	−0.608084	−	1.05323i	0.383472	−	0.923552i	$-0.374728\pi$
$770$	−4959.52	−	8590.13i	−0.232115	−	0.402035i
$771$	2955.07	+	5118.33i	0.138034	+	0.239082i
$772$	44521.4	+	77113.4i	2.07560	+	3.59504i
$773$	6811.49	+	11797.8i	0.316937	+	0.548951i	0.979847	−	0.199748i	$-0.0640123\pi$
$773$	6811.49	+	11797.8i	0.316937	+	0.548951i	−0.662910	+	0.748699i	$0.730679\pi$
$774$	−7045.57	+	12203.3i	−0.327193	+	0.566716i
$775$	5871.50	+	10169.7i	0.272143	+	0.471365i
$776$	45654.0	−	79075.0i	2.11196	−	3.65803i
$777$	5561.23			0.256767
$778$	−8582.74	−	14865.7i	−0.395509	−	0.685042i
$779$	811.678			0.0373317
$780$	69430.8			3.18721
$781$	−1355.26	+	2347.37i	−0.0620933	+	0.107549i
$782$	−16720.5			−0.764611
$783$	3673.78	+	6363.17i	0.167676	+	0.290423i
$784$	49236.5	+	85280.2i	2.24292	+	3.88485i
$785$	10422.1	−	18051.6i	0.473860	−	0.820750i
$786$	8482.55	−	14692.2i	0.384940	−	0.666735i
$787$	4001.49	−	6930.78i	0.181242	−	0.313921i	−0.761062	−	0.648680i	$-0.775322\pi$
$787$	4001.49	−	6930.78i	0.181242	−	0.313921i	0.942304	+	0.334759i	$0.108655\pi$
$788$	12816.2	−	22198.2i	0.579386	−	1.00353i
$789$	1726.29			0.0778930
$790$	86377.8			3.89011
$791$	3806.66	−	6593.33i	0.171112	−	0.296374i
$792$	9774.48	+	16929.9i	0.438537	+	0.759568i
$793$	436.994	+	756.895i	0.0195689	+	0.0338943i
$794$	−15744.0	+	27269.4i	−0.703695	+	1.21884i
$795$	−19943.2			−0.889702
$796$	−29411.1			−1.30961
$797$	7865.41	+	13623.3i	0.349570	+	0.605473i	0.986173	−	0.165719i	$-0.0529944\pi$
$797$	7865.41	+	13623.3i	0.349570	+	0.605473i	−0.636603	+	0.771192i	$0.719661\pi$
$798$	−137.204	+	237.645i	−0.00608643	+	0.0105420i
$799$	−11687.9			−0.517509
$800$	−45224.2	−	78330.7i	−1.99865	−	3.46176i
$801$	−5862.57			−0.258606
$802$	−5896.23	+	10212.6i	−0.259605	+	0.449649i
$803$	21649.8			0.951437
$804$	−2238.30	−	38962.9i	−0.0981825	−	1.70910i
$805$	4848.75			0.212293
$806$	−25230.9	+	43701.2i	−1.10263	+	1.90981i
$807$	11389.0			0.496793
$808$	12840.9	+	22241.0i	0.559084	+	0.968362i
$809$	−15927.6			−0.692194			−0.346097	−	0.938199i	$-0.612493\pi$
$809$	−15927.6			−0.692194			−0.346097	+	0.938199i	$0.612493\pi$
$810$	3326.56	−	5761.78i	0.144301	−	0.249936i
$811$	12400.6	+	21478.4i	0.536921	+	0.929975i	0.999068	+	0.0431713i	$0.0137461\pi$
$811$	12400.6	+	21478.4i	0.536921	+	0.929975i	−0.462146	+	0.886804i	$0.652921\pi$
$812$	−31777.0			−1.37334
$813$	−20241.0			−0.873164
$814$	26014.7	−	45058.8i	1.12017	−	1.94019i
$815$	17279.7	+	29929.4i	0.742678	+	1.28636i
$816$	−20368.1	−	35278.6i	−0.873807	−	1.51348i
$817$	−458.566	+	794.259i	−0.0196367	+	0.0340117i
$818$	−46214.7			−1.97538
$819$	−2963.97			−0.126459
$820$	42555.2	−	73707.8i	1.81231	−	3.13901i
$821$	8229.63	−	14254.1i	0.349837	−	0.605935i	−0.636383	−	0.771373i	$-0.719570\pi$
$821$	8229.63	−	14254.1i	0.349837	−	0.605935i	0.986220	+	0.165438i	$0.0529037\pi$
$822$	7648.19	−	13247.1i	0.324527	−	0.562098i
$823$	2357.99	−	4084.16i	0.0998717	−	0.172983i	−0.811760	−	0.583992i	$-0.801490\pi$
$823$	2357.99	−	4084.16i	0.0998717	−	0.172983i	0.911631	+	0.411009i	$0.134823\pi$
$824$	−6790.45	−	11761.4i	−0.287083	−	0.497243i
$825$	3226.55	+	5588.55i	0.136163	+	0.235841i
$826$	16090.8			0.677808
$827$	15636.6	−	27083.4i	0.657484	−	1.13880i	−0.323781	−	0.946132i	$-0.604954\pi$
$827$	15636.6	−	27083.4i	0.657484	−	1.13880i	0.981265	−	0.192663i	$-0.0617125\pi$
$828$	−14419.1			−0.605189
$829$	5816.19			0.243672			0.121836	−	0.992550i	$-0.461122\pi$
$829$	5816.19			0.243672			0.121836	+	0.992550i	$0.461122\pi$
$830$	14196.8	+	24589.6i	0.593709	+	1.02833i
$831$	5383.45			0.224729
$832$	111669.	−	193417.i	4.65317	−	8.05953i
$833$	7005.83	+	12134.5i	0.291402	+	0.504723i
$834$	−6090.98	+	10549.9i	−0.252894	+	0.438025i
$835$	−7739.65	−	13405.5i	−0.320768	−	0.555587i
$836$	959.913	+	1662.62i	0.0397121	+	0.0687833i
$837$	1807.98	+	3131.51i	0.0746628	+	0.129320i
$838$	18792.3	+	32549.2i	0.774664	+	1.34176i
$839$	−11028.2	−	19101.4i	−0.453796	−	0.785998i	0.544822	−	0.838552i	$-0.316597\pi$
$839$	−11028.2	−	19101.4i	−0.453796	−	0.785998i	−0.998618	+	0.0525535i	$0.983264\pi$
$840$	9534.85	+	16514.8i	0.391647	+	0.678353i
$841$	−24833.3	+	43012.5i	−1.01822	+	1.76360i
$842$	−3651.94	−	6325.35i	−0.149471	−	0.258891i
$843$	−3036.44	+	5259.28i	−0.124058	+	0.214874i
$844$	−126083.			−5.14211
$845$	16615.9	+	28779.7i	0.676456	+	1.17166i
$846$	−13478.4			−0.547750
$847$	−3589.60			−0.145620
$848$	−70407.7	+	121950.i	−2.85119	+	4.93841i
$849$	22713.7			0.918176
$850$	−10853.7	−	18799.2i	−0.437977	−	0.758598i
$851$	12716.8	+	22026.2i	0.512254	+	0.887249i
$852$	3931.41	−	6809.41i	0.158084	−	0.273810i
$853$	13217.6	−	22893.6i	0.530554	−	0.918947i	−0.468810	−	0.883299i	$-0.655317\pi$
$853$	13217.6	−	22893.6i	0.530554	−	0.918947i	0.999364	−	0.0356479i	$-0.0113495\pi$
$854$	−181.100	+	313.675i	−0.00725659	+	0.0125688i
$855$	216.512	−	375.009i	0.00866028	−	0.0150001i
$856$	−59197.0			−2.36368
$857$	39149.5			1.56047			0.780233	−	0.625489i	$-0.215100\pi$
$857$	39149.5			1.56047			0.780233	+	0.625489i	$0.215100\pi$
$858$	−13865.1	+	24015.0i	−0.551686	+	0.955548i
$859$	392.091	+	679.122i	0.0155739	+	0.0269748i	0.873707	−	0.486452i	$-0.161709\pi$
$859$	392.091	+	679.122i	0.0155739	+	0.0269748i	−0.858133	+	0.513427i	$0.828376\pi$
$860$	48084.0	+	83283.9i	1.90657	+	3.30228i
$861$	−1816.66	+	3146.55i	−0.0719068	+	0.124546i
$862$	16553.2			0.654066
$863$	7640.92			0.301390			0.150695	−	0.988580i	$-0.451849\pi$
$863$	7640.92			0.301390			0.150695	+	0.988580i	$0.451849\pi$
$864$	−13925.6	−	24119.9i	−0.548333	−	0.949740i
$865$	−6532.72	+	11315.0i	−0.256785	+	0.444765i
$866$	92459.3			3.62806
$867$	4471.33	+	7744.58i	0.175149	+	0.303368i
$868$	−15638.4			−0.611524
$869$	−12899.1	+	22341.9i	−0.503534	+	0.872147i
$870$	67056.5			2.61314
$871$	30669.7	−	20136.9i	1.19311	−	0.783368i
$872$	−57082.7			−2.21682
$873$	4640.53	−	8037.63i	0.179906	−	0.311607i
$874$	−1254.98			−0.0485701
$875$	−1339.47	−	2320.03i	−0.0517514	−	0.0896360i
$876$	−62803.0			−2.42228
$877$	10235.3	−	17728.0i	0.394095	−	0.682592i	−0.598891	−	0.800831i	$-0.704392\pi$
$877$	10235.3	−	17728.0i	0.394095	−	0.682592i	0.992985	+	0.118239i	$0.0377249\pi$
$878$	15774.1	+	27321.5i	0.606319	+	1.05018i
$879$	−26340.4			−1.01074
$880$	110519.			4.23364
$881$	−1672.68	+	2897.17i	−0.0639660	+	0.110792i	−0.896235	−	0.443580i	$-0.853708\pi$
$881$	−1672.68	+	2897.17i	−0.0639660	+	0.110792i	0.832269	+	0.554372i	$0.187042\pi$
$882$	8079.04	+	13993.3i	0.308430	+	0.534217i
$883$	−16237.9	−	28124.8i	−0.618854	−	1.07189i	−0.989695	−	0.143190i	$-0.954264\pi$
$883$	−16237.9	−	28124.8i	−0.618854	−	1.07189i	0.370841	−	0.928696i	$-0.379069\pi$
$884$	34877.9	−	60410.2i	1.32700	−	2.29843i
$885$	−25391.6			−0.964441
$886$	36612.7			1.38829
$887$	−14943.4	+	25882.8i	−0.565672	+	0.979772i	0.431315	+	0.902201i	$0.358050\pi$
$887$	−14943.4	+	25882.8i	−0.565672	+	0.979772i	−0.996987	+	0.0775707i	$0.975284\pi$
$888$	−50014.2	+	86627.2i	−1.89005	+	3.27367i
$889$	5689.95	−	9855.28i	0.214662	−	0.371806i
$890$	−26752.0	+	46335.8i	−1.00756	+	1.74515i
$891$	993.533	+	1720.85i	0.0373565	+	0.0647033i
$892$	−7239.93	−	12539.9i	−0.271761	−	0.470704i
$893$	−877.250			−0.0328735
$894$	6938.78	−	12018.3i	0.259583	−	0.449611i
$895$	37688.3			1.40758
$896$	51933.8			1.93637
$897$	−6777.71	−	11739.3i	−0.252287	−	0.436973i
$898$	57220.4			2.12636
$899$	−18222.5	+	31562.3i	−0.676033	+	1.17092i
$900$	−9359.79	−	16211.6i	−0.346659	−	0.600431i
$901$	−10018.3	+	17352.1i	−0.370429	+	0.641602i
$902$	16996.2	+	29438.4i	0.627398	+	1.08669i
$903$	−2052.69	−	3555.36i	−0.0756468	−	0.131024i
$904$	68469.5	+	118593.i	2.51909	+	4.36320i
$905$	24368.3	+	42207.1i	0.895060	+	1.55029i
$906$	20105.1	+	34823.1i	0.737250	+	1.27695i
$907$	−2602.43	−	4507.54i	−0.0952725	−	0.165017i	0.814450	−	0.580234i	$-0.197039\pi$
$907$	−2602.43	−	4507.54i	−0.0952725	−	0.165017i	−0.909722	+	0.415217i	$0.863706\pi$
$908$	1208.46	−	2093.12i	0.0441678	−	0.0765008i
$909$	1305.22	+	2260.70i	0.0476252	+	0.0824893i
$910$	−13525.2	+	23426.3i	−0.492698	+	0.853377i
$911$	4591.49			0.166984			0.0834922	−	0.996508i	$-0.473393\pi$
$911$	4591.49			0.166984			0.0834922	+	0.996508i	$0.473393\pi$
$912$	−1528.75	−	2647.87i	−0.0555065	−	0.0961401i
$913$	−8480.22			−0.307398
$914$	376.428			0.0136227
$915$	285.781	−	494.987i	0.0103253	−	0.0178839i
$916$	90141.9			3.25150
$917$	2471.34	+	4280.49i	0.0889977	+	0.154149i
$918$	−3342.13	−	5788.74i	−0.120160	−	0.208123i
$919$	−5493.79	+	9515.52i	−0.197196	+	0.341554i	−0.947618	−	0.319405i	$-0.896517\pi$
$919$	−5493.79	+	9515.52i	−0.197196	+	0.341554i	0.750422	+	0.660959i	$0.229850\pi$
$920$	−43606.6	+	75528.9i	−1.56268	+	2.70664i
$921$	−3907.49	+	6767.97i	−0.139800	+	0.242141i
$922$	17702.5	−	30661.6i	0.632322	−	1.09521i
$923$	7391.88			0.263604
$924$	−8593.75			−0.305967
$925$	−16509.7	+	28595.6i	−0.586848	+	1.01645i
$926$	−6610.38	−	11449.5i	−0.234590	−	0.406322i
$927$	−690.220	−	1195.50i	−0.0244550	−	0.0423573i
$928$	140356.	−	243103.i	4.96487	−	8.59940i
$929$	−7890.88			−0.278678			−0.139339	−	0.990245i	$-0.544498\pi$
$929$	−7890.88			−0.278678			−0.139339	+	0.990245i	$0.544498\pi$
$930$	33000.5			1.16358
$931$	525.830	+	910.764i	0.0185106	+	0.0320613i
$932$	65444.3	−	113353.i	2.30011	−	3.98390i
$933$	−14387.4			−0.504848
$934$	−16202.3	−	28063.3i	−0.567619	−	0.983145i
$935$	15725.7			0.550039
$936$	26656.1	−	46169.8i	0.930858	−	1.61229i
$937$	−44680.9			−1.55780			−0.778902	−	0.627145i	$-0.784223\pi$
$937$	−44680.9			−1.55780			−0.778902	+	0.627145i	$0.784223\pi$
$938$	13582.3	+	6834.78i	0.472790	+	0.237914i
$939$	19859.0			0.690176
$940$	−45993.1	+	79662.3i	−1.59588	+	2.76415i
$941$	−29301.7			−1.01510			−0.507549	−	0.861623i	$-0.669448\pi$
$941$	−29301.7			−1.01510			−0.507549	+	0.861623i	$0.669448\pi$
$942$	−12074.9	−	20914.3i	−0.417644	−	0.723380i
$943$	−16616.6			−0.573820
$944$	−89642.9	+	155266.i	−3.09071	+	5.35326i
$945$	969.175	+	1678.66i	0.0333622	+	0.0577850i
$946$	−38408.8			−1.32006
$947$	−51192.3			−1.75663			−0.878314	−	0.478083i	$-0.841332\pi$
$947$	−51192.3			−1.75663			−0.878314	+	0.478083i	$0.841332\pi$
$948$	37418.4	−	64810.7i	1.28196	−	2.22041i
$949$	−29520.7	−	51131.3i	−1.00978	−	1.74899i
$950$	−814.639	−	1411.00i	−0.0278215	−	0.0481882i
$951$	12496.2	−	21644.1i	0.426096	−	0.738019i
$952$	19158.9			0.652252
$953$	28475.8			0.967912			0.483956	−	0.875092i	$-0.339199\pi$
$953$	28475.8			0.967912			0.483956	+	0.875092i	$0.339199\pi$
$954$	−11552.9	+	20010.3i	−0.392076	+	0.679095i
$955$	−5344.95	+	9257.73i	−0.181109	+	0.313689i
$956$	29054.5	−	50323.9i	0.982939	−	1.70250i
$957$	−10013.8	+	17344.3i	−0.338244	+	0.585855i
$958$	−7255.01	−	12566.0i	−0.244675	−	0.423789i
$959$	2228.26	+	3859.45i	0.0750304	+	0.129956i
$960$	−146057.			−4.91038
$961$	5927.67	−	10267.0i	0.198975	−	0.344635i
$962$	−141890.			−4.75543
$963$	−6017.11			−0.201349
$964$	−14398.5	−	24938.9i	−0.481063	−	0.833225i
$965$	54743.6			1.82617
$966$	2808.84	−	4865.05i	0.0935537	−	0.162040i
$967$	−11012.0	−	19073.3i	−0.366206	−	0.634288i	0.622763	−	0.782411i	$-0.286010\pi$
$967$	−11012.0	−	19073.3i	−0.366206	−	0.634288i	−0.988969	+	0.148123i	$0.952677\pi$
$968$	32282.6	−	55915.1i	1.07190	−	1.85659i
$969$	−217.525	−	376.764i	−0.00721146	−	0.0124906i
$970$	−42351.2	−	73354.4i	−1.40187	−	2.42811i
$971$	−20877.0	−	36160.0i	−0.689983	−	1.19509i	−0.971843	−	0.235630i	$-0.924285\pi$
$971$	−20877.0	−	36160.0i	−0.689983	−	1.19509i	0.281860	−	0.959456i	$-0.409049\pi$
$972$	−2882.10	−	4991.95i	−0.0951065	−	0.164729i
$973$	−1774.57	−	3073.65i	−0.0584688	−	0.101271i
$974$	−50687.5	−	87793.2i	−1.66749	−	2.88817i
$975$	8799.18	−	15240.6i	0.289025	−	0.500606i
$976$	−2017.85	−	3495.01i	−0.0661780	−	0.114624i
$977$	1789.32	−	3099.19i	0.0585930	−	0.101486i	−0.835241	−	0.549884i	$-0.814672\pi$
$977$	1789.32	−	3099.19i	0.0585930	−	0.101486i	0.893834	+	0.448398i	$0.148005\pi$
$978$	40040.0			1.30914
$979$	−7989.93	−	13839.0i	−0.260837	−	0.451783i
$980$	110274.			3.59447
$981$	−5802.20			−0.188838
$982$	7233.14	−	12528.2i	0.235050	−	0.407118i
$983$	−6265.54			−0.203296			−0.101648	−	0.994820i	$-0.532411\pi$
$983$	−6265.54			−0.203296			−0.101648	+	0.994820i	$0.532411\pi$
$984$	−32675.9	−	56596.3i	−1.05861	−	1.83356i
$985$	−7879.38	−	13647.5i	−0.254881	−	0.441467i
$986$	33685.1	−	58344.4i	1.08799	−	1.88445i
$987$	1963.42	−	3400.75i	0.0633196	−	0.109673i
$988$	2617.79	−	4534.15i	0.0842946	−	0.146003i
$989$	9387.74	−	16260.0i	0.301833	−	0.522790i
$990$	18134.7			0.582181
$991$	−17460.1			−0.559675			−0.279837	−	0.960047i	$-0.590281\pi$
$991$	−17460.1			−0.559675			−0.279837	+	0.960047i	$0.590281\pi$
$992$	69073.2	−	119638.i	2.21076	−	3.82915i
$993$	9370.61	+	16230.4i	0.299464	+	0.518686i
$994$	1531.68	+	2652.95i	0.0488753	+	0.0846545i
$995$	−9040.96	+	15659.4i	−0.288058	+	0.498931i
$996$	24599.9			0.782610
$997$	−22880.6			−0.726815			−0.363407	−	0.931630i	$-0.618387\pi$
$997$	−22880.6			−0.726815			−0.363407	+	0.931630i	$0.618387\pi$
$998$	55656.7	+	96400.2i	1.76531	+	3.05761i
$999$	−5083.73	+	8805.27i	−0.161003	+	0.278865i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	201.4.e.a.163.1	yes	32
67.37	even	3	inner	201.4.e.a.37.1	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
201.4.e.a.37.1	✓	32	67.37	even	3	inner
201.4.e.a.163.1	yes	32	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 201 = 3 \cdot 67 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	201.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.81607 + 4.87758i) q^{2} +3.00000 q^{3} +(-11.8605 - 20.5430i) q^{4} -14.5837 q^{5} +(-8.44821 + 14.6327i) q^{6} +(-2.46134 - 4.26316i) q^{7} +88.5430 q^{8} +9.00000 q^{9} +O(q^{10})\)	\(q+(-2.81607 + 4.87758i) q^{2} +3.00000 q^{3} +(-11.8605 - 20.5430i) q^{4} -14.5837 q^{5} +(-8.44821 + 14.6327i) q^{6} +(-2.46134 - 4.26316i) q^{7} +88.5430 q^{8} +9.00000 q^{9} +(41.0687 - 71.1331i) q^{10} +(12.2658 + 21.2451i) q^{11} +(-35.5815 - 61.6290i) q^{12} +(33.4503 - 57.9377i) q^{13} +27.7252 q^{14} -43.7511 q^{15} +(-154.459 + 267.531i) q^{16} +(-21.9779 + 38.0668i) q^{17} +(-25.3446 + 43.8982i) q^{18} +(-1.64957 + 2.85714i) q^{19} +(172.970 + 299.593i) q^{20} +(-7.38401 - 12.7895i) q^{21} -138.166 q^{22} +(33.7700 - 58.4913i) q^{23} +265.629 q^{24} +87.6840 q^{25} +(188.397 + 326.313i) q^{26} +27.0000 q^{27} +(-58.3854 + 101.126i) q^{28} +(136.066 + 235.673i) q^{29} +(123.206 - 213.399i) q^{30} +(66.9620 + 115.982i) q^{31} +(-515.764 - 893.329i) q^{32} +(36.7975 + 63.7352i) q^{33} +(-123.783 - 214.398i) q^{34} +(35.8954 + 62.1726i) q^{35} +(-106.745 - 184.887i) q^{36} +(-188.286 + 326.121i) q^{37} +(-9.29063 - 16.0918i) q^{38} +(100.351 - 173.813i) q^{39} -1291.28 q^{40} +(-123.013 - 213.065i) q^{41} +83.1756 q^{42} +277.991 q^{43} +(290.958 - 503.954i) q^{44} -131.253 q^{45} +(190.197 + 329.432i) q^{46} +(132.951 + 230.278i) q^{47} +(-463.377 + 802.593i) q^{48} +(159.384 - 276.061i) q^{49} +(-246.924 + 427.685i) q^{50} +(-65.9337 + 114.200i) q^{51} -1586.95 q^{52} +455.834 q^{53} +(-76.0339 + 131.695i) q^{54} +(-178.881 - 309.831i) q^{55} +(-217.934 - 377.473i) q^{56} +(-4.94872 + 8.57143i) q^{57} -1532.68 q^{58} +580.366 q^{59} +(518.910 + 898.778i) q^{60} +(-6.53198 + 11.3137i) q^{61} -754.279 q^{62} +(-22.1520 - 38.3684i) q^{63} +3338.36 q^{64} +(-487.829 + 844.945i) q^{65} -414.498 q^{66} +(489.889 + 246.519i) q^{67} +1042.68 q^{68} +(101.310 - 175.474i) q^{69} -404.336 q^{70} +(55.2452 + 95.6874i) q^{71} +796.887 q^{72} +(441.261 - 764.287i) q^{73} +(-1060.45 - 1836.76i) q^{74} +263.052 q^{75} +78.2591 q^{76} +(60.3807 - 104.582i) q^{77} +(565.191 + 978.940i) q^{78} +(525.813 + 910.735i) q^{79} +(2252.58 - 3901.59i) q^{80} +81.0000 q^{81} +1385.66 q^{82} +(-172.842 + 299.371i) q^{83} +(-175.156 + 303.379i) q^{84} +(320.519 - 555.155i) q^{85} +(-782.841 + 1355.92i) q^{86} +(408.197 + 707.018i) q^{87} +(1086.05 + 1881.10i) q^{88} -651.397 q^{89} +(369.618 - 640.198i) q^{90} -329.330 q^{91} -1602.12 q^{92} +(200.886 + 347.945i) q^{93} -1497.60 q^{94} +(24.0569 - 41.6677i) q^{95} +(-1547.29 - 2679.99i) q^{96} +(515.614 - 893.070i) q^{97} +(897.671 + 1554.81i) q^{98} +(110.393 + 191.206i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9}+O(q^{10}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9	\( 32 q + 2 q^{2} + 96 q^{3} - 66 q^{4} + 4 q^{5} + 6 q^{6} - 14 q^{7} + 108 q^{8} + 288 q^{9} - 2 q^{10} + 16 q^{11} - 198 q^{12} + 88 q^{13} + 214 q^{14} + 12 q^{15} - 298 q^{16} + 52 q^{17} + 18 q^{18} - 2 q^{19} + 164 q^{20} - 42 q^{21} - 506 q^{22} + 160 q^{23} + 324 q^{24} + 572 q^{25} + 353 q^{26} + 864 q^{27} - 433 q^{28} + 48 q^{29} - 6 q^{30} + 292 q^{31} - 525 q^{32} + 48 q^{33} + 138 q^{34} - 328 q^{35} - 594 q^{36} - 616 q^{37} - 194 q^{38} + 264 q^{39} - 1794 q^{40} + 124 q^{41} + 642 q^{42} - 292 q^{43} - 179 q^{44} + 36 q^{45} + 1324 q^{46} + 402 q^{47} - 894 q^{48} + 172 q^{49} + 171 q^{50} + 156 q^{51} - 3344 q^{52} + 852 q^{53} + 54 q^{54} + 1238 q^{55} - 47 q^{56} - 6 q^{57} - 3320 q^{58} + 1200 q^{59} + 492 q^{60} - 454 q^{61} - 5810 q^{62} - 126 q^{63} + 2340 q^{64} - 24 q^{65} - 1518 q^{66} + 110 q^{67} + 906 q^{68} + 480 q^{69} - 10 q^{70} + 406 q^{71} + 972 q^{72} + 1274 q^{73} - 1945 q^{74} + 1716 q^{75} - 2698 q^{76} + 1436 q^{77} + 1059 q^{78} + 1236 q^{79} + 6697 q^{80} + 2592 q^{81} + 2950 q^{82} + 2190 q^{83} - 1299 q^{84} + 2032 q^{85} + 273 q^{86} + 144 q^{87} + 1938 q^{88} - 2160 q^{89} - 18 q^{90} - 3020 q^{91} - 3020 q^{92} + 876 q^{93} - 2886 q^{94} - 102 q^{95} - 1575 q^{96} + 1860 q^{97} + 2612 q^{98} + 144 q^{99}+O(q^{100}) \) 32 * q + 2 * q^2 + 96 * q^3 - 66 * q^4 + 4 * q^5 + 6 * q^6 - 14 * q^7 + 108 * q^8 + 288 * q^9 - 2 * q^10 + 16 * q^11 - 198 * q^12 + 88 * q^13 + 214 * q^14 + 12 * q^15 - 298 * q^16 + 52 * q^17 + 18 * q^18 - 2 * q^19 + 164 * q^20 - 42 * q^21 - 506 * q^22 + 160 * q^23 + 324 * q^24 + 572 * q^25 + 353 * q^26 + 864 * q^27 - 433 * q^28 + 48 * q^29 - 6 * q^30 + 292 * q^31 - 525 * q^32 + 48 * q^33 + 138 * q^34 - 328 * q^35 - 594 * q^36 - 616 * q^37 - 194 * q^38 + 264 * q^39 - 1794 * q^40 + 124 * q^41 + 642 * q^42 - 292 * q^43 - 179 * q^44 + 36 * q^45 + 1324 * q^46 + 402 * q^47 - 894 * q^48 + 172 * q^49 + 171 * q^50 + 156 * q^51 - 3344 * q^52 + 852 * q^53 + 54 * q^54 + 1238 * q^55 - 47 * q^56 - 6 * q^57 - 3320 * q^58 + 1200 * q^59 + 492 * q^60 - 454 * q^61 - 5810 * q^62 - 126 * q^63 + 2340 * q^64 - 24 * q^65 - 1518 * q^66 + 110 * q^67 + 906 * q^68 + 480 * q^69 - 10 * q^70 + 406 * q^71 + 972 * q^72 + 1274 * q^73 - 1945 * q^74 + 1716 * q^75 - 2698 * q^76 + 1436 * q^77 + 1059 * q^78 + 1236 * q^79 + 6697 * q^80 + 2592 * q^81 + 2950 * q^82 + 2190 * q^83 - 1299 * q^84 + 2032 * q^85 + 273 * q^86 + 144 * q^87 + 1938 * q^88 - 2160 * q^89 - 18 * q^90 - 3020 * q^91 - 3020 * q^92 + 876 * q^93 - 2886 * q^94 - 102 * q^95 - 1575 * q^96 + 1860 * q^97 + 2612 * q^98 + 144 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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