LMFDB - Embedded newform 42.4.f.a.5.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [42,4,Mod(5,42)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(42, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("42.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 42 = 2 \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	42.f (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.47808022024$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 2 x^{15} - x^{14} - 2 x^{13} + 9 x^{12} - 24 x^{11} + 714 x^{10} - 1940 x^{9} - 2834 x^{8} + \cdots + 43046721 $ x^16 - 2x^15 - x^14 - 2x^13 + 9x^12 - 24x^11 + 714x^10 - 1940x^9 - 2834x^8 - 17460x^7 + 57834x^6 - 17496x^5 + 59049x^4 - 118098x^3 - 531441x^2 - 9565938x + 43046721
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{8} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			5.3
Root			$-1.62928 - 2.51902i$ of defining polynomial
Character	$\chi$	$=$	42.5
Dual form			42.4.f.a.17.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.73205 - 1.00000i) q^{2} +(2.82199 - 4.36307i) q^{3} +(2.00000 + 3.46410i) q^{4} +(2.24534 - 3.88904i) q^{5} +(-9.25090 + 4.73506i) q^{6} +(-9.71288 - 15.7690i) q^{7} -8.00000i q^{8} +(-11.0727 - 24.6251i) q^{9} +O(q^{10})$	\(q+(-1.73205 - 1.00000i) q^{2} +(2.82199 - 4.36307i) q^{3} +(2.00000 + 3.46410i) q^{4} +(2.24534 - 3.88904i) q^{5} +(-9.25090 + 4.73506i) q^{6} +(-9.71288 - 15.7690i) q^{7} -8.00000i q^{8} +(-11.0727 - 24.6251i) q^{9} +(-7.77808 + 4.49068i) q^{10} +(20.2835 - 11.7107i) q^{11} +(20.7581 + 1.04953i) q^{12} +5.91384i q^{13} +(1.05425 + 37.0255i) q^{14} +(-10.6318 - 20.7714i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(58.0418 + 100.531i) q^{17} +(-5.44659 + 53.7246i) q^{18} +(8.02533 + 4.63343i) q^{19} +17.9627 q^{20} +(-96.2107 - 2.12191i) q^{21} -46.8428 q^{22} +(107.721 + 62.1928i) q^{23} +(-34.9045 - 22.5759i) q^{24} +(52.4169 + 90.7888i) q^{25} +(5.91384 - 10.2431i) q^{26} +(-138.688 - 21.1808i) q^{27} +(35.1995 - 65.1843i) q^{28} -207.807i q^{29} +(-2.35656 + 46.6089i) q^{30} +(122.764 - 70.8780i) q^{31} +(27.7128 - 16.0000i) q^{32} +(6.14540 - 121.546i) q^{33} -232.167i q^{34} +(-83.1348 + 2.36716i) q^{35} +(63.1584 - 87.6072i) q^{36} +(-149.838 + 259.526i) q^{37} +(-9.26685 - 16.0507i) q^{38} +(25.8025 + 16.6888i) q^{39} +(-31.1123 - 17.9627i) q^{40} -508.379 q^{41} +(164.520 + 99.8859i) q^{42} +391.127 q^{43} +(81.1341 + 46.8428i) q^{44} +(-120.630 - 12.2294i) q^{45} +(-124.386 - 215.442i) q^{46} +(-40.2575 + 69.7281i) q^{47} +(37.8805 + 74.0072i) q^{48} +(-154.320 + 306.324i) q^{49} -209.668i q^{50} +(602.419 + 30.4585i) q^{51} +(-20.4862 + 11.8277i) q^{52} +(258.697 - 149.359i) q^{53} +(219.034 + 175.374i) q^{54} -105.178i q^{55} +(-126.152 + 77.7031i) q^{56} +(42.8634 - 21.9396i) q^{57} +(-207.807 + 359.932i) q^{58} +(102.276 + 177.147i) q^{59} +(50.6906 - 78.3725i) q^{60} +(-543.757 - 313.939i) q^{61} -283.512 q^{62} +(-280.764 + 413.786i) q^{63} -64.0000 q^{64} +(22.9992 + 13.2786i) q^{65} +(-132.190 + 204.378i) q^{66} +(51.3894 + 89.0091i) q^{67} +(-232.167 + 402.126i) q^{68} +(575.340 - 294.487i) q^{69} +(146.361 + 79.0348i) q^{70} -46.9785i q^{71} +(-197.001 + 88.5817i) q^{72} +(-228.182 + 131.741i) q^{73} +(519.053 - 299.675i) q^{74} +(544.038 + 27.5067i) q^{75} +37.0674i q^{76} +(-381.677 - 206.105i) q^{77} +(-28.0024 - 54.7084i) q^{78} +(533.634 - 924.281i) q^{79} +(35.9254 + 62.2246i) q^{80} +(-483.790 + 545.333i) q^{81} +(880.538 + 508.379i) q^{82} -270.436 q^{83} +(-185.071 - 337.527i) q^{84} +521.294 q^{85} +(-677.452 - 391.127i) q^{86} +(-906.676 - 586.430i) q^{87} +(-93.6856 - 162.268i) q^{88} +(443.765 - 768.624i) q^{89} +(196.708 + 141.812i) q^{90} +(93.2551 - 57.4405i) q^{91} +497.543i q^{92} +(37.1945 - 735.646i) q^{93} +(139.456 - 80.5151i) q^{94} +(36.0392 - 20.8072i) q^{95} +(8.39628 - 166.065i) q^{96} +219.564i q^{97} +(573.614 - 376.249i) q^{98} +(-512.971 - 369.815i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9	$ 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36} - 962 q^{37} + 594 q^{39} - 144 q^{40} - 180 q^{42} + 1732 q^{43} - 2394 q^{45} + 168 q^{46} + 820 q^{49} + 1638 q^{51} + 744 q^{52} + 180 q^{54} - 2664 q^{57} - 780 q^{58} - 4620 q^{61} - 2016 q^{63} - 1024 q^{64} - 2016 q^{66} - 706 q^{67} - 60 q^{70} + 192 q^{72} + 3294 q^{73} + 6174 q^{75} + 2832 q^{78} - 2656 q^{79} + 126 q^{81} + 432 q^{82} - 432 q^{84} + 5232 q^{85} + 1026 q^{87} + 48 q^{88} + 4098 q^{91} + 2016 q^{93} + 3888 q^{94} - 192 q^{96} - 4284 q^{99}+O(q^{100}) $ 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/42\mathbb{Z}\right)^\times$.

$n$	$29$	$31$
$\chi(n)$	$-1$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$2$	−1.73205	−	1.00000i	−0.612372	−	0.353553i
$3$	2.82199	−	4.36307i	0.543093	−	0.839673i
$3$	2.82199	−	4.36307i	0.543093	−	0.839673i
$4$	2.00000	+	3.46410i	0.250000	+	0.433013i
$5$	2.24534	−	3.88904i	0.200829	−	0.347846i	−0.747967	−	0.663736i	$-0.768970\pi$
$5$	2.24534	−	3.88904i	0.200829	−	0.347846i	0.948796	+	0.315890i	$0.102303\pi$
$6$	−9.25090	+	4.73506i	−0.629444	+	0.322180i
$7$	−9.71288	−	15.7690i	−0.524446	−	0.851443i
$7$	−9.71288	−	15.7690i	−0.524446	−	0.851443i
$8$		−	8.00000i		−	0.353553i
$9$	−11.0727	−	24.6251i	−0.410101	−	0.912040i
$10$	−7.77808	+	4.49068i	−0.245964	+	0.142008i
$11$	20.2835	−	11.7107i	0.555974	−	0.320992i	−0.195554	−	0.980693i	$-0.562650\pi$
$11$	20.2835	−	11.7107i	0.555974	−	0.320992i	0.751528	+	0.659701i	$0.229317\pi$
$12$	20.7581	+	1.04953i	0.499362	+	0.0252479i
$13$			5.91384i			0.126170i	0.998008	+	0.0630848i	$0.0200939\pi$
$13$			5.91384i			0.126170i	−0.998008	+	0.0630848i	$0.979906\pi$
$14$	1.05425	+	37.0255i	0.0201258	+	0.706820i
$15$	−10.6318	−	20.7714i	−0.183008	−	0.357544i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	58.0418	+	100.531i	0.828071	+	1.43426i	0.899549	+	0.436819i	$0.143895\pi$
$17$	58.0418	+	100.531i	0.828071	+	1.43426i	−0.0714778	+	0.997442i	$0.522772\pi$
$18$	−5.44659	+	53.7246i	−0.0713207	+	0.703501i
$19$	8.02533	+	4.63343i	0.0969019	+	0.0559464i	0.547668	−	0.836696i	$-0.315516\pi$
$19$	8.02533	+	4.63343i	0.0969019	+	0.0559464i	−0.450766	+	0.892642i	$0.648849\pi$
$20$	17.9627			0.200829
$21$	−96.2107	−	2.12191i	−0.999757	−	0.0220494i
$22$	−46.8428			−0.453951
$23$	107.721	+	62.1928i	0.976583	+	0.563830i	0.901237	−	0.433327i	$-0.142661\pi$
$23$	107.721	+	62.1928i	0.976583	+	0.563830i	0.0753461	+	0.997157i	$0.475994\pi$
$24$	−34.9045	−	22.5759i	−0.296869	−	0.192012i
$25$	52.4169	+	90.7888i	0.419335	+	0.726310i
$26$	5.91384	−	10.2431i	0.0446077	−	0.0772628i
$27$	−138.688	−	21.1808i	−0.988538	−	0.150972i
$28$	35.1995	−	65.1843i	0.237574	−	0.439953i
$29$		−	207.807i		−	1.33065i	−0.746555	−	0.665324i	$-0.768293\pi$
$29$		−	207.807i		−	1.33065i	0.746555	−	0.665324i	$-0.231707\pi$
$30$	−2.35656	+	46.6089i	−0.0143416	+	0.283653i
$31$	122.764	−	70.8780i	0.711262	−	0.410647i	−0.100266	−	0.994961i	$-0.531970\pi$
$31$	122.764	−	70.8780i	0.711262	−	0.410647i	0.811528	+	0.584314i	$0.198636\pi$
$32$	27.7128	−	16.0000i	0.153093	−	0.0883883i
$33$	6.14540	−	121.546i	0.0324175	−	0.641165i
$34$		−	232.167i		−	1.17107i
$35$	−83.1348	+	2.36716i	−0.401496	+	0.0114321i
$36$	63.1584	−	87.6072i	0.292400	−	0.405589i
$37$	−149.838	+	259.526i	−0.665761	+	1.15313i	0.313317	+	0.949648i	$0.398560\pi$
$37$	−149.838	+	259.526i	−0.665761	+	1.15313i	−0.979078	+	0.203483i	$0.934774\pi$
$38$	−9.26685	−	16.0507i	−0.0395601	−	0.0685200i
$39$	25.8025	+	16.6888i	0.105941	+	0.0685218i
$40$	−31.1123	−	17.9627i	−0.122982	−	0.0710038i
$41$	−508.379			−1.93647			−0.968237	−	0.250032i	$-0.919559\pi$
$41$	−508.379			−1.93647			−0.968237	+	0.250032i	$0.919559\pi$
$42$	164.520	+	99.8859i	0.604428	+	0.366970i
$43$	391.127			1.38712			0.693562	−	0.720397i	$-0.256041\pi$
$43$	391.127			1.38712			0.693562	+	0.720397i	$0.256041\pi$
$44$	81.1341	+	46.8428i	0.277987	+	0.160496i
$45$	−120.630	−	12.2294i	−0.399610	−	0.0405123i
$46$	−124.386	−	215.442i	−0.398688	−	0.690548i
$47$	−40.2575	+	69.7281i	−0.124940	+	0.216402i	−0.921709	−	0.387881i	$-0.873207\pi$
$47$	−40.2575	+	69.7281i	−0.124940	+	0.216402i	0.796770	+	0.604283i	$0.206540\pi$
$48$	37.8805	+	74.0072i	0.113908	+	0.222542i
$49$	−154.320	+	306.324i	−0.449912	+	0.893073i
$50$		−	209.668i		−	0.593030i
$51$	602.419	+	30.4585i	1.65403	+	0.0836282i
$52$	−20.4862	+	11.8277i	−0.0546330	+	0.0315424i
$53$	258.697	−	149.359i	0.670467	−	0.387094i	−0.125786	−	0.992057i	$-0.540145\pi$
$53$	258.697	−	149.359i	0.670467	−	0.387094i	0.796254	+	0.604963i	$0.206812\pi$
$54$	219.034	+	175.374i	0.551977	+	0.441952i
$55$		−	105.178i		−	0.257858i
$56$	−126.152	+	77.7031i	−0.301031	+	0.185420i
$57$	42.8634	−	21.9396i	0.0996034	−	0.0509818i
$58$	−207.807	+	359.932i	−0.470455	+	0.814852i
$59$	102.276	+	177.147i	0.225682	+	0.390892i	0.956524	−	0.291655i	$-0.0942058\pi$
$59$	102.276	+	177.147i	0.225682	+	0.390892i	−0.730842	+	0.682547i	$0.760872\pi$
$60$	50.6906	−	78.3725i	0.109069	−	0.168631i
$61$	−543.757	−	313.939i	−1.14133	−	0.658946i	−0.194569	−	0.980889i	$-0.562331\pi$
$61$	−543.757	−	313.939i	−1.14133	−	0.658946i	−0.946759	+	0.321943i	$0.895664\pi$
$62$	−283.512			−0.580743
$63$	−280.764	+	413.786i	−0.561475	+	0.827494i
$64$	−64.0000			−0.125000
$65$	22.9992	+	13.2786i	0.0438876	+	0.0253385i
$66$	−132.190	+	204.378i	−0.246538	+	0.381170i
$67$	51.3894	+	89.0091i	0.0937048	+	0.162301i	0.909067	−	0.416649i	$-0.136796\pi$
$67$	51.3894	+	89.0091i	0.0937048	+	0.162301i	−0.815363	+	0.578951i	$0.803462\pi$
$68$	−232.167	+	402.126i	−0.414036	+	0.717131i
$69$	575.340	−	294.487i	1.00381	−	0.513798i
$70$	146.361	+	79.0348i	0.249907	+	0.134949i
$71$		−	46.9785i		−	0.0785256i	−0.999229	−	0.0392628i	$-0.987499\pi$
$71$		−	46.9785i		−	0.0785256i	0.999229	−	0.0392628i	$-0.0125010\pi$
$72$	−197.001	+	88.5817i	−0.322455	+	0.144992i
$73$	−228.182	+	131.741i	−0.365845	+	0.211221i	−0.671642	−	0.740876i	$-0.734411\pi$
$73$	−228.182	+	131.741i	−0.365845	+	0.211221i	0.305797	+	0.952097i	$0.401077\pi$
$74$	519.053	−	299.675i	0.815387	−	0.470764i
$75$	544.038	+	27.5067i	0.837601	+	0.0423493i
$76$			37.0674i			0.0559464i
$77$	−381.677	−	206.105i	−0.564885	−	0.305038i
$78$	−28.0024	−	54.7084i	−0.0406493	−	0.0794167i
$79$	533.634	−	924.281i	0.759981	−	1.31633i	−0.182878	−	0.983136i	$-0.558541\pi$
$79$	533.634	−	924.281i	0.759981	−	1.31633i	0.942860	−	0.333190i	$-0.108125\pi$
$80$	35.9254	+	62.2246i	0.0502073	+	0.0869616i
$81$	−483.790	+	545.333i	−0.663635	+	0.748056i
$82$	880.538	+	508.379i	1.18584	+	0.684647i
$83$	−270.436			−0.357642			−0.178821	−	0.983882i	$-0.557228\pi$
$83$	−270.436			−0.357642			−0.178821	+	0.983882i	$0.557228\pi$
$84$	−185.071	−	337.527i	−0.240392	−	0.438420i
$85$	521.294			0.665203
$86$	−677.452	−	391.127i	−0.849436	−	0.490422i
$87$	−906.676	−	586.430i	−1.11731	−	0.722665i
$88$	−93.6856	−	162.268i	−0.113488	−	0.196567i
$89$	443.765	−	768.624i	0.528528	−	0.915438i	−0.470918	−	0.882177i	$-0.656077\pi$
$89$	443.765	−	768.624i	0.528528	−	0.915438i	0.999447	−	0.0332610i	$-0.0105893\pi$
$90$	196.708	+	141.812i	0.230387	+	0.166092i
$91$	93.2551	−	57.4405i	0.107426	−	0.0661692i
$92$			497.543i			0.563830i
$93$	37.1945	−	735.646i	0.0414719	−	0.820246i
$94$	139.456	−	80.5151i	0.153019	−	0.0883457i
$95$	36.0392	−	20.8072i	0.0389215	−	0.0224713i
$96$	8.39628	−	166.065i	0.00892648	−	0.176551i
$97$			219.564i			0.229828i	0.993375	+	0.114914i	$0.0366593\pi$
$97$			219.564i			0.229828i	−0.993375	+	0.114914i	$0.963341\pi$
$98$	573.614	−	376.249i	0.591263	−	0.387825i
$99$	−512.971	−	369.815i	−0.520763	−	0.375432i
$100$	−209.668	+	363.155i	−0.209668	+	0.363155i
$101$	492.533	+	853.093i	0.485237	+	0.840455i	0.999856	−	0.0169642i	$-0.00540012\pi$
$101$	492.533	+	853.093i	0.485237	+	0.840455i	−0.514619	+	0.857419i	$0.672067\pi$
$102$	−1012.96	−	655.175i	−0.983315	−	0.636000i
$103$	−1112.87	−	642.516i	−1.06461	−	0.614650i	−0.137903	−	0.990446i	$-0.544036\pi$
$103$	−1112.87	−	642.516i	−1.06461	−	0.614650i	−0.926703	+	0.375796i	$0.877369\pi$
$104$	47.3107			0.0446077
$105$	−224.278	+	369.403i	−0.208450	+	0.343334i
$106$	−597.435			−0.547434
$107$	158.409	+	91.4575i	0.143121	+	0.0826311i	0.569851	−	0.821748i	$-0.307001\pi$
$107$	158.409	+	91.4575i	0.143121	+	0.0826311i	−0.426729	+	0.904379i	$0.640334\pi$
$108$	−204.004	−	522.791i	−0.181762	−	0.465793i
$109$	291.471	+	504.843i	0.256127	+	0.443625i	0.965201	−	0.261509i	$-0.0842201\pi$
$109$	291.471	+	504.843i	0.256127	+	0.443625i	−0.709074	+	0.705134i	$0.750887\pi$
$110$	−105.178	+	182.174i	−0.0911666	+	0.157905i
$111$	709.490	+	1386.13i	0.606683	+	1.18528i
$112$	296.204	−	8.43404i	0.249899	−	0.00711555i
$113$			2283.94i			1.90137i	0.310152	+	0.950687i	$0.399620\pi$
$113$			2283.94i			1.90137i	−0.310152	+	0.950687i	$0.600380\pi$
$114$	−96.1811	−	4.86294i	−0.0790192	−	0.00399523i
$115$	483.741	−	279.288i	0.392253	−	0.226467i
$116$	719.865	−	415.614i	0.576188	−	0.332662i
$117$	145.629	−	65.4823i	0.115072	−	0.0517422i
$118$		−	409.104i		−	0.319162i
$119$	1021.52	−	1891.71i	0.786914	−	1.45725i
$120$	−166.171	+	85.0545i	−0.126411	+	0.0647032i
$121$	−391.219	+	677.611i	−0.293928	+	0.509099i
$122$	627.877	+	1087.51i	0.465945	+	0.807041i
$123$	−1434.64	+	2218.09i	−1.05169	+	1.62601i
$124$	491.057	+	283.512i	0.355631	+	0.205324i
$125$	1032.11			0.738517
$126$	900.083	−	435.934i	0.636395	−	0.308223i
$127$	−1554.48			−1.08613			−0.543064	−	0.839692i	$-0.682736\pi$
$127$	−1554.48			−1.08613			−0.543064	+	0.839692i	$0.682736\pi$
$128$	110.851	+	64.0000i	0.0765466	+	0.0441942i
$129$	1103.76	−	1706.51i	0.753337	−	1.16473i
$130$	−26.5572	−	45.9983i	−0.0179170	−	0.0310332i
$131$	−1047.46	+	1814.26i	−0.698605	+	1.21002i	0.270345	+	0.962763i	$0.412862\pi$
$131$	−1047.46	+	1814.26i	−0.698605	+	1.21002i	−0.968950	+	0.247256i	$0.920471\pi$
$132$	433.338	−	221.804i	0.285737	−	0.146254i
$133$	−4.88481	−	171.555i	−0.00318471	−	0.111847i
$134$		−	205.558i		−	0.132519i
$135$	−393.775	+	491.805i	−0.251042	+	0.313540i
$136$	804.251	−	464.335i	0.507088	−	0.292767i
$137$	529.002	−	305.420i	0.329896	−	0.190465i	−0.325899	−	0.945405i	$-0.605667\pi$
$137$	529.002	−	305.420i	0.329896	−	0.190465i	0.655795	+	0.754939i	$0.272334\pi$
$138$	−1291.00	−	65.2735i	−0.796359	−	0.0402641i
$139$			1806.61i			1.10241i	0.834370	+	0.551204i	$0.185831\pi$
$139$			1806.61i			1.10241i	−0.834370	+	0.551204i	$0.814169\pi$
$140$	−174.470	−	283.253i	−0.105324	−	0.170995i
$141$	190.622	+	372.419i	0.113853	+	0.222435i
$142$	−46.9785	+	81.3691i	−0.0277630	+	0.0480869i
$143$	69.2553	+	119.954i	0.0404994	+	0.0701470i
$144$	429.797	+	43.5727i	0.248725	+	0.0252157i
$145$	−808.170	−	466.597i	−0.462861	−	0.267233i
$146$	526.964			0.298711
$147$	901.023	+	1537.75i	0.505545	+	0.862800i
$148$	−1198.70			−0.665761
$149$	−2341.75	−	1352.01i	−1.28754	−	0.743363i	−0.309328	−	0.950956i	$-0.600104\pi$
$149$	−2341.75	−	1352.01i	−1.28754	−	0.743363i	−0.978215	+	0.207592i	$0.933437\pi$
$150$	−914.794	−	591.681i	−0.497951	−	0.322070i
$151$	−770.352	−	1334.29i	−0.415168	−	0.719092i	0.580278	−	0.814418i	$-0.302944\pi$
$151$	−770.352	−	1334.29i	−0.415168	−	0.719092i	−0.995446	+	0.0953266i	$0.969610\pi$
$152$	37.0674	−	64.2026i	0.0197800	−	0.0342600i
$153$	1832.91	−	2542.44i	0.968512	−	1.34343i
$154$	454.979	+	738.662i	0.238073	+	0.386514i
$155$		−	636.580i		−	0.329880i
$156$	−6.20678	+	122.760i	−0.00318552	+	0.0630043i
$157$	477.498	−	275.684i	0.242729	−	0.140140i	−0.373701	−	0.927549i	$-0.621911\pi$
$157$	477.498	−	275.684i	0.242729	−	0.140140i	0.616430	+	0.787409i	$0.288578\pi$
$158$	−1848.56	+	1067.27i	−0.930783	+	0.537388i
$159$	78.3786	−	1550.20i	0.0390933	−	0.773201i
$160$		−	143.702i		−	0.0710038i
$161$	−65.5670	−	2302.72i	−0.0320957	−	1.12720i
$162$	1383.28	−	460.755i	0.670870	−	0.223459i
$163$	1155.82	−	2001.94i	0.555403	−	0.961986i	−0.442469	−	0.896784i	$-0.645897\pi$
$163$	1155.82	−	2001.94i	0.555403	−	0.961986i	0.997872	−	0.0652023i	$-0.0207693\pi$
$164$	−1016.76	−	1761.08i	−0.484119	−	0.838518i
$165$	−458.899	−	296.811i	−0.216516	−	0.140041i
$166$	468.410	+	270.436i	0.219010	+	0.126445i
$167$	−2580.87			−1.19589			−0.597944	−	0.801538i	$-0.704016\pi$
$167$	−2580.87			−1.19589			−0.597944	+	0.801538i	$0.704016\pi$
$168$	−16.9753	+	769.686i	−0.00779565	+	0.353467i
$169$	2162.03			0.984081
$170$	−902.908	−	521.294i	−0.407352	−	0.235185i
$171$	25.2364	−	248.929i	0.0112858	−	0.111322i
$172$	782.254	+	1354.90i	0.346781	+	0.600642i
$173$	−501.050	+	867.845i	−0.220197	+	0.381393i	−0.954868	−	0.297031i	$-0.904004\pi$
$173$	−501.050	+	867.845i	−0.220197	+	0.381393i	0.734670	+	0.678424i	$0.237337\pi$
$174$	983.979	+	1922.40i	0.428708	+	0.837569i
$175$	922.524	−	1708.38i	0.398493	−	0.737951i
$176$			374.743i			0.160496i
$177$	1061.53	+	53.6712i	0.450787	+	0.0227919i
$178$	−1537.25	+	887.530i	−0.647312	+	0.373726i
$179$	2598.36	−	1500.17i	1.08498	−	0.626411i	0.152742	−	0.988266i	$-0.451190\pi$
$179$	2598.36	−	1500.17i	1.08498	−	0.626411i	0.932234	+	0.361855i	$0.117856\pi$
$180$	−198.896	−	442.333i	−0.0823601	−	0.183164i
$181$			967.850i			0.397457i	0.980055	+	0.198729i	$0.0636812\pi$
$181$			967.850i			0.397457i	−0.980055	+	0.198729i	$0.936319\pi$
$182$	−218.963	+	6.23469i	−0.0891792	+	0.00253927i
$183$	−2904.21	+	1486.52i	−1.17315	+	0.600473i
$184$	497.543	−	861.769i	0.199344	−	0.345274i
$185$	672.872	+	1165.45i	0.267408	+	0.463165i
$186$	−800.068	+	1236.98i	−0.315397	+	0.487634i
$187$	2354.59	+	1359.42i	0.920773	+	0.531608i
$188$	−322.060			−0.124940
$189$	1013.06	+	2392.69i	0.389891	+	0.920861i
$190$	−83.2289			−0.0317792
$191$	356.214	+	205.660i	0.134946	+	0.0779113i	0.565953	−	0.824437i	$-0.308508\pi$
$191$	356.214	+	205.660i	0.134946	+	0.0779113i	−0.431007	+	0.902349i	$0.641842\pi$
$192$	−180.608	+	279.236i	−0.0678866	+	0.104959i
$193$	−408.212	−	707.043i	−0.152247	−	0.263700i	0.779806	−	0.626021i	$-0.215318\pi$
$193$	−408.212	−	707.043i	−0.152247	−	0.263700i	−0.932053	+	0.362321i	$0.881984\pi$
$194$	219.564	−	380.296i	0.0812566	−	0.140741i
$195$	122.839	−	62.8749i	0.0451111	−	0.0230901i
$196$	−1369.78	+	78.0686i	−0.499190	+	0.0284507i
$197$			633.331i			0.229051i	0.993420	+	0.114525i	$0.0365347\pi$
$197$			633.331i			0.229051i	−0.993420	+	0.114525i	$0.963465\pi$
$198$	518.677	+	1153.51i	0.186166	+	0.414022i
$199$	−2964.48	+	1711.54i	−1.05601	+	0.609688i	−0.924326	−	0.381603i	$-0.875372\pi$
$199$	−2964.48	+	1711.54i	−1.05601	+	0.609688i	−0.131685	+	0.991292i	$0.542039\pi$
$200$	726.310	−	419.335i	0.256789	−	0.148257i
$201$	533.373	+	26.9675i	0.187170	+	0.00946339i
$202$		−	1970.13i		−	0.686228i
$203$	−3276.90	+	2018.41i	−1.13297	+	0.697854i
$204$	1099.33	+	2147.76i	0.377295	+	0.737123i
$205$	−1141.48	+	1977.11i	−0.388901	+	0.673596i
$206$	1285.03	+	2225.74i	0.434623	+	0.752790i
$207$	338.739	−	3341.29i	0.113739	−	1.12191i
$208$	−81.9446	−	47.3107i	−0.0273165	−	0.0157712i
$209$	217.043			0.0718333
$210$	757.863	−	415.547i	0.249036	−	0.136550i
$211$	1023.65			0.333986			0.166993	−	0.985958i	$-0.446594\pi$
$211$	1023.65			0.333986			0.166993	+	0.985958i	$0.446594\pi$
$212$	1034.79	+	597.435i	0.335234	+	0.193547i
$213$	−204.970	−	132.573i	−0.0659358	−	0.0426467i
$214$	−182.915	−	316.818i	−0.0584290	−	0.101202i
$215$	878.212	−	1521.11i	0.278575	−	0.482506i
$216$	−169.447	+	1109.50i	−0.0533768	+	0.349501i
$217$	−2310.07	−	1247.43i	−0.722661	−	0.390237i
$218$		−	1165.88i		−	0.362219i
$219$	−69.1334	+	1367.35i	−0.0213315	+	0.421903i
$220$	364.347	−	210.356i	0.111656	−	0.0644645i
$221$	−594.527	+	343.250i	−0.180960	+	0.104477i
$222$	157.260	−	3110.34i	0.0475432	−	0.940327i
$223$			1521.32i			0.456840i	0.973563	+	0.228420i	$0.0733559\pi$
$223$			1521.32i			0.456840i	−0.973563	+	0.228420i	$0.926644\pi$
$224$	−521.475	−	281.596i	−0.155547	−	0.0839952i
$225$	1655.28	−	2296.05i	0.490454	−	0.680311i
$226$	2283.94	−	3955.90i	0.672237	−	1.16435i
$227$	729.575	+	1263.66i	0.213320	+	0.369481i	0.952752	−	0.303751i	$-0.0982390\pi$
$227$	729.575	+	1263.66i	0.213320	+	0.369481i	−0.739432	+	0.673232i	$0.764906\pi$
$228$	161.728	+	104.604i	0.0469766	+	0.0303841i
$229$	4152.17	+	2397.26i	1.19818	+	0.691770i	0.960149	−	0.279488i	$-0.0901646\pi$
$229$	4152.17	+	2397.26i	1.19818	+	0.691770i	0.238031	+	0.971257i	$0.423498\pi$
$230$	−1117.15			−0.320273
$231$	−1976.34	+	1083.66i	−0.562917	+	0.308655i
$232$	−1662.46			−0.470455
$233$	1445.76	+	834.708i	0.406501	+	0.234693i	0.689285	−	0.724490i	$-0.257925\pi$
$233$	1445.76	+	834.708i	0.406501	+	0.234693i	−0.282784	+	0.959183i	$0.591258\pi$
$234$	−317.719	−	32.2103i	−0.0887604	−	0.00899851i
$235$	180.784	+	313.126i	0.0501831	+	0.0869196i
$236$	−409.104	+	708.590i	−0.112841	+	0.195446i
$237$	−2526.79	−	4936.60i	−0.692543	−	1.35302i
$238$	−3661.04	+	2255.01i	−0.997100	+	0.614163i
$239$		−	3529.25i		−	0.955181i	−0.878583	−	0.477590i	$-0.841510\pi$
$239$		−	3529.25i		−	0.955181i	0.878583	−	0.477590i	$-0.158490\pi$
$240$	372.872	+	18.8525i	0.100286	+	0.00507051i
$241$	−4269.15	+	2464.80i	−1.14108	+	0.658803i	−0.946698	−	0.322123i	$-0.895603\pi$
$241$	−4269.15	+	2464.80i	−1.14108	+	0.658803i	−0.194382	+	0.980926i	$0.562270\pi$
$242$	1355.22	−	782.438i	0.359987	−	0.207839i
$243$	1014.07	+	3649.73i	0.267707	+	0.963500i
$244$		−	2511.51i		−	0.658946i
$245$	844.806	+	1287.96i	0.220297	+	0.335855i
$246$	4702.97	−	2407.21i	1.21890	−	0.623894i
$247$	−27.4014	+	47.4605i	−0.00705873	+	0.0122261i
$248$	−567.024	−	982.114i	−0.145186	−	0.251469i
$249$	−763.170	+	1179.93i	−0.194233	+	0.300302i
$250$	−1787.67	−	1032.11i	−0.452248	−	0.261105i
$251$	−1294.99			−0.325652			−0.162826	−	0.986655i	$-0.552061\pi$
$251$	−1294.99			−0.325652			−0.162826	+	0.986655i	$0.552061\pi$
$252$	−1994.92	−	145.023i	−0.498684	−	0.0362524i
$253$	2913.29			0.723940
$254$	2692.45	+	1554.48i	0.665114	+	0.384004i
$255$	1471.09	−	2274.44i	0.361267	−	0.558553i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−728.040	+	1261.00i	−0.176708	+	0.306067i	−0.940751	−	0.339098i	$-0.889878\pi$
$257$	−728.040	+	1261.00i	−0.176708	+	0.306067i	0.764043	+	0.645165i	$0.223211\pi$
$258$	−3618.28	+	1852.01i	−0.873117	+	0.446904i
$259$	5547.82	−	157.967i	1.33098	−	0.0378980i
$260$			106.229i			0.0253385i
$261$	−5117.27	+	2300.99i	−1.21360	+	0.545700i
$262$	3628.52	−	2094.93i	0.855613	−	0.493988i
$263$	1850.30	−	1068.27i	0.433820	−	0.250466i	−0.267153	−	0.963654i	$-0.586083\pi$
$263$	1850.30	−	1068.27i	0.433820	−	0.250466i	0.700973	+	0.713188i	$0.252749\pi$
$264$	−972.368	−	49.1632i	−0.226686	−	0.0114613i
$265$		−	1341.44i		−	0.310959i
$266$	−163.094	+	302.027i	−0.0375938	+	0.0696182i
$267$	−2101.26	−	4105.23i	−0.481628	−	0.940958i
$268$	−205.558	+	356.036i	−0.0468524	+	0.0811507i
$269$	−1443.73	−	2500.61i	−0.327233	−	0.566784i	0.654729	−	0.755864i	$-0.272783\pi$
$269$	−1443.73	−	2500.61i	−0.327233	−	0.566784i	−0.981962	+	0.189080i	$0.939449\pi$
$270$	1173.84	−	458.057i	0.264584	−	0.103246i
$271$	−5072.92	−	2928.85i	−1.13711	−	0.656513i	−0.191400	−	0.981512i	$-0.561303\pi$
$271$	−5072.92	−	2928.85i	−1.13711	−	0.656513i	−0.945714	+	0.324999i	$0.894636\pi$
$272$	−1857.34			−0.414036
$273$	12.5486	−	568.975i	0.00278197	−	0.126139i
$274$	−1221.68			−0.269359
$275$	2126.40	+	1227.68i	0.466279	+	0.269206i
$276$	2170.81	+	1404.06i	0.473433	+	0.306212i
$277$	1401.52	+	2427.50i	0.304003	+	0.526549i	0.977039	−	0.213061i	$-0.0683433\pi$
$277$	1401.52	+	2427.50i	0.304003	+	0.526549i	−0.673036	+	0.739610i	$0.735010\pi$
$278$	1806.61	−	3129.14i	0.389760	−	0.675085i
$279$	−3104.71	−	2238.27i	−0.666215	−	0.480293i
$280$	18.9373	+	665.078i	0.00404185	+	0.141950i
$281$		−	4665.53i		−	0.990469i	−0.868759	−	0.495235i	$-0.835082\pi$
$281$		−	4665.53i		−	0.990469i	0.868759	−	0.495235i	$-0.164918\pi$
$282$	42.2517	−	835.670i	0.00892217	−	0.176466i
$283$	4654.53	−	2687.29i	0.977679	−	0.564463i	0.0761103	−	0.997099i	$-0.475750\pi$
$283$	4654.53	−	2687.29i	0.977679	−	0.564463i	0.901569	+	0.432636i	$0.142417\pi$
$284$	162.738	−	93.9569i	0.0340026	−	0.0196314i
$285$	10.9190	−	215.959i	0.00226941	−	0.0448853i
$286$		−	277.021i		−	0.0572748i
$287$	4937.83	+	8016.61i	1.01558	+	1.64880i
$288$	−700.857	−	505.267i	−0.143397	−	0.103379i
$289$	−4281.21	+	7415.27i	−0.871404	+	1.50932i
$290$	933.194	+	1616.34i	0.188962	+	0.327292i
$291$	957.973	+	619.608i	0.192981	+	0.124818i
$292$	−912.729	−	526.964i	−0.182923	−	0.105610i
$293$	1302.13			0.259630			0.129815	−	0.991538i	$-0.458562\pi$
$293$	1302.13			0.259630			0.129815	+	0.991538i	$0.458562\pi$
$294$	−22.8658	−	3564.49i	−0.00453593	−	0.707092i
$295$	918.578			0.181294
$296$	2076.21	+	1198.70i	0.407694	+	0.235382i
$297$	−3061.13	+	1194.51i	−0.598063	+	0.233376i
$298$	2704.02	+	4683.51i	0.525637	+	0.910430i
$299$	−367.799	+	637.046i	−0.0711383	+	0.123215i
$300$	992.789	+	1939.61i	0.191062	+	0.373279i
$301$	−3798.97	−	6167.66i	−0.727472	−	1.18106i
$302$			3081.41i			0.587136i
$303$	5112.03	+	258.465i	0.969235	+	0.0490048i
$304$	−128.405	+	74.1348i	−0.0242255	+	0.0139866i
$305$	−2441.84	+	1409.80i	−0.458424	+	0.264671i
$306$	−5717.14	+	2570.72i	−1.06806	+	0.480256i
$307$		−	644.894i		−	0.119889i	−0.998202	−	0.0599447i	$-0.980908\pi$
$307$		−	644.894i		−	0.119889i	0.998202	−	0.0599447i	$-0.0190924\pi$
$308$	−49.3842	−	1734.38i	−0.00913613	−	0.320862i
$309$	−5943.85	+	3042.35i	−1.09428	+	0.560108i
$310$	−636.580	+	1102.59i	−0.116630	+	0.202009i
$311$	668.420	+	1157.74i	0.121873	+	0.211091i	0.920506	−	0.390727i	$-0.127776\pi$
$311$	668.420	+	1157.74i	0.121873	+	0.211091i	−0.798633	+	0.601818i	$0.794443\pi$
$312$	133.511	−	206.420i	0.0242261	−	0.0374559i
$313$	−1459.67	−	842.739i	−0.263595	−	0.152187i	0.362378	−	0.932031i	$-0.381965\pi$
$313$	−1459.67	−	842.739i	−0.263595	−	0.152187i	−0.625973	+	0.779844i	$0.715298\pi$
$314$	−1102.73			−0.198188
$315$	978.819	+	2020.99i	0.175080	+	0.361492i
$316$	4269.07			0.759981
$317$	2609.95	+	1506.85i	0.462427	+	0.266982i	0.713064	−	0.701099i	$-0.247307\pi$
$317$	2609.95	+	1506.85i	0.462427	+	0.266982i	−0.250637	+	0.968081i	$0.580640\pi$
$318$	−1685.96	+	2606.65i	−0.297308	+	0.459666i
$319$	−2433.57	−	4215.06i	−0.427127	−	0.739806i
$320$	−143.702	+	248.899i	−0.0251036	+	0.0434808i
$321$	846.064	−	433.057i	0.147111	−	0.0752987i
$322$	−2189.16	+	4054.00i	−0.378872	+	0.701616i
$323$			1075.73i			0.185310i
$324$	−2856.67	−	585.232i	−0.489827	−	0.100348i
$325$	−536.910	+	309.985i	−0.0916382	+	0.0529074i
$326$	−4003.87	+	2311.64i	−0.680227	+	0.392729i
$327$	3025.19	+	152.955i	0.511601	+	0.0258667i
$328$			4067.03i			0.684647i
$329$	1490.56	−	42.4417i	0.249778	−	0.00711211i
$330$	498.024	+	972.991i	0.0830768	+	0.162307i
$331$	394.460	−	683.225i	0.0655030	−	0.113454i	−0.831414	−	0.555653i	$-0.812468\pi$
$331$	394.460	−	683.225i	0.0655030	−	0.113454i	0.896917	+	0.442199i	$0.145801\pi$
$332$	−540.873	−	936.819i	−0.0894104	−	0.154863i
$333$	8049.97	+	816.104i	1.32473	+	0.134301i
$334$	4470.19	+	2580.87i	0.732329	+	0.422811i
$335$	461.547			0.0752746
$336$	799.088	−	1316.16i	0.129743	−	0.213698i
$337$	1906.16			0.308116			0.154058	−	0.988062i	$-0.450766\pi$
$337$	1906.16			0.308116			0.154058	+	0.988062i	$0.450766\pi$
$338$	−3744.74	−	2162.03i	−0.602624	−	0.347925i
$339$	9964.99	+	6445.27i	1.59653	+	1.03262i
$340$	1042.59	+	1805.82i	0.166301	+	0.288042i
$341$	1660.06	−	2875.31i	0.263629	−	0.456618i
$342$	−292.640	+	405.921i	−0.0462694	+	0.0641805i
$343$	6329.30	−	541.828i	0.996356	−	0.0852944i
$344$		−	3129.02i		−	0.490422i
$345$	146.561	−	2898.74i	0.0228713	−	0.452356i
$346$	1735.69	−	1002.10i	0.269686	−	0.155703i
$347$	−4538.98	+	2620.58i	−0.702205	+	0.405418i	−0.808168	−	0.588952i	$-0.799541\pi$
$347$	−4538.98	+	2620.58i	−0.702205	+	0.405418i	0.105963	+	0.994370i	$0.466207\pi$
$348$	218.101	−	4313.68i	0.0335961	−	0.664475i
$349$		−	4502.54i		−	0.690588i	−0.938495	−	0.345294i	$-0.887779\pi$
$349$		−	4502.54i		−	0.690588i	0.938495	−	0.345294i	$-0.112221\pi$
$350$	−3306.24	+	2036.48i	−0.504931	+	0.311012i
$351$	125.260	−	820.179i	0.0190481	−	0.124723i
$352$	374.743	−	649.073i	0.0567439	−	0.0982833i
$353$	−4799.70	−	8313.33i	−0.723689	−	1.25347i	−0.959511	−	0.281671i	$-0.909111\pi$
$353$	−4799.70	−	8313.33i	−0.723689	−	1.25347i	0.235822	−	0.971796i	$-0.424222\pi$
$354$	−1784.95	−	1154.49i	−0.267992	−	0.173335i
$355$	−182.701	−	105.483i	−0.0273148	−	0.0157702i
$356$	3550.12			0.528528
$357$	−5370.93	−	9795.36i	−0.796245	−	1.45217i
$358$	−6000.66			−0.885879
$359$	−8803.94	−	5082.96i	−1.29430	−	0.747265i	−0.314888	−	0.949129i	$-0.601967\pi$
$359$	−8803.94	−	5082.96i	−1.29430	−	0.747265i	−0.979414	+	0.201863i	$0.935300\pi$
$360$	−97.8354	+	965.040i	−0.0143233	+	0.141283i
$361$	−3386.56	−	5865.70i	−0.493740	−	0.855183i
$362$	967.850	−	1676.37i	0.140522	−	0.243392i
$363$	1852.44	+	3619.13i	0.267846	+	0.523292i
$364$	385.490	+	208.164i	0.0555087	+	0.0299746i
$365$			1183.21i			0.169677i
$366$	6516.77	+	329.489i	0.930702	+	0.0470565i
$367$	332.544	−	191.995i	0.0472988	−	0.0273080i	−0.476164	−	0.879356i	$-0.657973\pi$
$367$	332.544	−	191.995i	0.0472988	−	0.0273080i	0.523463	+	0.852048i	$0.324640\pi$
$368$	−1723.54	+	995.085i	−0.244146	+	0.140958i
$369$	5629.14	+	12518.9i	0.794149	+	1.76614i
$370$		−	2691.49i		−	0.378173i
$371$	−4867.92	−	2628.68i	−0.681213	−	0.367855i
$372$	2622.74	−	1342.45i	0.365545	−	0.187104i
$373$	1481.79	−	2566.54i	0.205695	−	0.356275i	−0.744659	−	0.667445i	$-0.767388\pi$
$373$	1481.79	−	2566.54i	0.205695	−	0.356275i	0.950354	+	0.311171i	$0.100721\pi$
$374$	−2718.84	−	4709.17i	−0.375904	−	0.651085i
$375$	2912.61	−	4503.16i	0.401083	−	0.620113i
$376$	557.825	+	322.060i	0.0765096	+	0.0441728i
$377$	1228.94			0.167887
$378$	638.019	−	5157.33i	0.0868152	−	0.701757i
$379$	−13195.4			−1.78839			−0.894195	−	0.447677i	$-0.852251\pi$
$379$	−13195.4			−1.78839			−0.894195	+	0.447677i	$0.852251\pi$
$380$	144.157	+	83.2289i	0.0194607	+	0.0112357i
$381$	−4386.74	+	6782.32i	−0.589868	+	0.911991i
$382$	−411.321	−	712.428i	−0.0550916	−	0.0954214i
$383$	4475.95	−	7752.57i	0.597155	−	1.03430i	−0.396084	−	0.918214i	$-0.629631\pi$
$383$	4475.95	−	7752.57i	0.597155	−	1.03430i	0.993239	−	0.116088i	$-0.0370356\pi$
$384$	592.058	−	303.044i	0.0786805	−	0.0402725i
$385$	−1658.55	+	1021.58i	−0.219552	+	0.135233i
$386$			1632.85i			0.215310i
$387$	−4330.84	−	9631.54i	−0.568860	−	1.26511i
$388$	−760.593	+	439.128i	−0.0995186	+	0.0574571i
$389$	−7594.74	+	4384.82i	−0.989893	+	0.571515i	−0.905242	−	0.424896i	$-0.860311\pi$
$389$	−7594.74	+	4384.82i	−0.989893	+	0.571515i	−0.0846507	+	0.996411i	$0.526977\pi$
$390$	−275.638	−	13.9363i	−0.0357884	−	0.00180947i
$391$			14439.1i			1.86757i
$392$	2450.59	+	1234.56i	0.315749	+	0.159068i
$393$	4959.80	+	9689.97i	0.636613	+	1.24375i
$394$	633.331	−	1096.96i	0.0809816	−	0.140264i
$395$	−2396.38	−	4150.65i	−0.305253	−	0.528713i
$396$	255.133	−	2516.61i	0.0323761	−	0.319355i
$397$	−1187.30	−	685.490i	−0.150098	−	0.0866594i	0.423070	−	0.906097i	$-0.360953\pi$
$397$	−1187.30	−	685.490i	−0.150098	−	0.0866594i	−0.573168	+	0.819438i	$0.694286\pi$
$398$	6846.17			0.862229
$399$	−762.291	−	462.814i	−0.0956448	−	0.0580694i
$400$	−1677.34			−0.209668
$401$	−2392.14	−	1381.10i	−0.297899	−	0.171992i	0.343599	−	0.939116i	$-0.388354\pi$
$401$	−2392.14	−	1381.10i	−0.297899	−	0.171992i	−0.641499	+	0.767124i	$0.721687\pi$
$402$	−896.862	−	580.082i	−0.111272	−	0.0719699i
$403$	419.161	+	726.008i	0.0518112	+	0.0897396i
$404$	−1970.13	+	3412.37i	−0.242618	+	0.420227i
$405$	1034.55	+	3105.94i	0.126931	+	0.381075i
$406$	7694.16	−	219.081i	0.940529	−	0.0267804i
$407$			7018.82i			0.854815i
$408$	243.668	−	4819.35i	0.0295670	−	0.584788i
$409$	2310.01	−	1333.69i	0.279273	−	0.161239i	−0.353821	−	0.935313i	$-0.615118\pi$
$409$	2310.01	−	1333.69i	0.279273	−	0.161239i	0.633094	+	0.774075i	$0.281784\pi$
$410$	3954.21	−	2282.97i	0.476304	−	0.274994i
$411$	160.274	−	3169.96i	0.0192354	−	0.380445i
$412$		−	5140.13i		−	0.614650i
$413$	1800.03	−	3333.40i	0.214465	−	0.397157i
$414$	−3928.00	+	5448.54i	−0.466306	+	0.646814i
$415$	−607.221	+	1051.74i	−0.0718249	+	0.124404i
$416$	94.6215	+	163.889i	0.0111519	+	0.0193157i
$417$	7882.37	+	5098.24i	0.925662	+	0.598710i
$418$	−375.929	−	217.043i	−0.0439887	−	0.0253969i
$419$	14480.6			1.68836			0.844179	−	0.536061i	$-0.180088\pi$
$419$	14480.6			1.68836			0.844179	+	0.536061i	$0.180088\pi$
$420$	−1728.20	−	38.1152i	−0.200780	−	0.00442817i
$421$	14248.8			1.64951			0.824753	−	0.565494i	$-0.191314\pi$
$421$	14248.8			1.64951			0.824753	+	0.565494i	$0.191314\pi$
$422$	−1773.02	−	1023.65i	−0.204524	−	0.118082i
$423$	2162.82	+	219.266i	0.248605	+	0.0252035i
$424$	−1194.87	−	2069.58i	−0.136859	−	0.237046i
$425$	−6084.75	+	10539.1i	−0.694479	+	1.20287i
$426$	222.446	+	434.593i	0.0252994	+	0.0494275i
$427$	330.971	+	11623.7i	0.0375101	+	1.31736i
$428$			731.660i			0.0826311i
$429$	718.804	+	36.3429i	0.0808955	+	0.00409010i
$430$	−3042.22	+	1756.42i	−0.341183	+	0.196982i
$431$	−4826.49	+	2786.57i	−0.539405	+	0.311426i	−0.744838	−	0.667246i	$-0.767473\pi$
$431$	−4826.49	+	2786.57i	−0.539405	+	0.311426i	0.205433	+	0.978671i	$0.434140\pi$
$432$	1402.99	−	1752.27i	0.156254	−	0.195153i
$433$		−	2939.93i		−	0.326291i	−0.986602	−	0.163146i	$-0.947836\pi$
$433$		−	2939.93i		−	0.326291i	0.986602	−	0.163146i	$-0.0521640\pi$
$434$	2753.72	+	4470.69i	0.304568	+	0.494469i
$435$	−4316.44	+	2209.37i	−0.475765	+	0.243520i
$436$	−1165.88	+	2019.37i	−0.128064	+	0.221813i
$437$	576.332	+	998.236i	0.0630885	+	0.109273i
$438$	1487.09	−	2299.18i	0.162228	−	0.250820i
$439$	−8290.73	−	4786.66i	−0.901355	−	0.520398i	−0.0237157	−	0.999719i	$-0.507550\pi$
$439$	−8290.73	−	4786.66i	−0.901355	−	0.520398i	−0.877640	+	0.479321i	$0.840883\pi$
$440$	−841.424			−0.0911666
$441$	9252.00	+	408.300i	0.999028	+	0.0440881i
$442$	1373.00			0.147753
$443$	6197.42	+	3578.08i	0.664669	+	0.383747i	0.794054	−	0.607848i	$-0.207967\pi$
$443$	6197.42	+	3578.08i	0.664669	+	0.383747i	−0.129385	+	0.991594i	$0.541300\pi$
$444$	−3382.73	+	5230.01i	−0.361570	+	0.559021i
$445$	−1992.81	−	3451.64i	−0.212288	−	0.367693i
$446$	1521.32	−	2635.01i	0.161517	−	0.279756i
$447$	−12507.3	+	6401.86i	−1.32344	+	0.677400i
$448$	621.625	+	1009.21i	0.0655558	+	0.106430i
$449$			14839.2i			1.55970i	0.625964	+	0.779852i	$0.284706\pi$
$449$			14839.2i			1.55970i	−0.625964	+	0.779852i	$0.715294\pi$
$450$	−5163.08	+	2321.59i	−0.540867	+	0.243202i
$451$	−10311.7	+	5953.48i	−1.07663	+	0.621593i
$452$	−7911.81	+	4567.88i	−0.823319	+	0.475343i
$453$	−7995.52	−	404.256i	−0.829276	−	0.0419284i
$454$		−	2918.30i		−	0.301680i
$455$	−13.9990	−	491.646i	−0.00144238	−	0.0506565i
$456$	−175.516	−	342.907i	−0.0180248	−	0.0352151i
$457$	3787.42	−	6560.00i	0.387676	−	0.671474i	−0.604461	−	0.796635i	$-0.706611\pi$
$457$	3787.42	−	6560.00i	0.387676	−	0.671474i	0.992136	+	0.125161i	$0.0399447\pi$
$458$	−4794.52	−	8304.35i	−0.489155	−	0.847242i
$459$	−5920.37	−	15171.9i	−0.602046	−	1.54284i
$460$	1934.96	+	1117.15i	0.196126	+	0.113234i
$461$	14850.5			1.50034			0.750170	−	0.661245i	$-0.229971\pi$
$461$	14850.5			1.50034			0.750170	+	0.661245i	$0.229971\pi$
$462$	4506.78	+	99.3961i	0.453841	+	0.0100094i
$463$	3361.43			0.337406			0.168703	−	0.985667i	$-0.446042\pi$
$463$	3361.43			0.337406			0.168703	+	0.985667i	$0.446042\pi$
$464$	2879.46	+	1662.46i	0.288094	+	0.166331i
$465$	−2777.44	−	1796.42i	−0.276991	−	0.179155i
$466$	−1669.42	−	2891.51i	−0.165953	−	0.287439i
$467$	−115.422	+	199.917i	−0.0114371	+	0.0198096i	−0.871687	−	0.490063i	$-0.836974\pi$
$467$	−115.422	+	199.917i	−0.0114371	+	0.0198096i	0.860250	+	0.509872i	$0.170307\pi$
$468$	518.095	+	373.509i	0.0511730	+	0.0368920i
$469$	904.441	−	1674.89i	0.0890473	−	0.164903i
$470$		−	723.134i		−	0.0709696i
$471$	144.670	−	2861.33i	0.0141529	−	0.279922i
$472$	1417.18	−	818.209i	0.138201	−	0.0797905i
$473$	7933.44	−	4580.37i	0.771205	−	0.445255i
$474$	−560.068	+	11077.2i	−0.0542716	+	1.07340i
$475$			971.480i			0.0938411i
$476$	8596.11	−	244.763i	0.827736	−	0.0235687i
$477$	−6542.45	−	4716.63i	−0.628005	−	0.452745i
$478$	−3529.25	+	6112.84i	−0.337707	+	0.584926i
$479$	−2200.43	−	3811.26i	−0.209896	−	0.363551i	0.741786	−	0.670637i	$-0.233979\pi$
$479$	−2200.43	−	3811.26i	−0.209896	−	0.363551i	−0.951682	+	0.307087i	$0.900646\pi$
$480$	−626.980	−	405.525i	−0.0596200	−	0.0385617i
$481$	−1534.80	−	886.116i	−0.145490	−	0.0839988i
$482$	9859.18			0.931688
$483$	−10232.0	−	6212.19i	−0.963913	−	0.585226i
$484$	−3129.75			−0.293928
$485$	853.894	+	492.996i	0.0799450	+	0.0461563i
$486$	1893.31	−	7335.60i	0.176712	−	0.684670i
$487$	5972.31	+	10344.3i	0.555711	+	0.962520i	0.997848	+	0.0655721i	$0.0208872\pi$
$487$	5972.31	+	10344.3i	0.555711	+	0.962520i	−0.442137	+	0.896948i	$0.645779\pi$
$488$	−2511.51	+	4350.06i	−0.232973	+	0.403520i
$489$	−5472.87	−	10692.4i	−0.506118	−	0.988804i
$490$	−175.290	−	3075.61i	−0.0161608	−	0.283555i
$491$		−	19916.7i		−	1.83060i	−0.402768	−	0.915302i	$-0.631952\pi$
$491$		−	19916.7i		−	1.83060i	0.402768	−	0.915302i	$-0.368048\pi$
$492$	−10553.0	−	533.562i	−0.967002	−	0.0488919i
$493$	20891.1	−	12061.5i	1.90850	−	1.10187i
$494$	94.9211	−	54.8027i	0.00864514	−	0.00499128i
$495$	−2590.02	+	1164.61i	−0.235177	+	0.105748i
$496$			2268.09i			0.205324i
$497$	−740.801	+	456.296i	−0.0668601	+	0.0411825i
$498$	2501.78	−	1280.53i	0.225115	−	0.115225i
$499$	−665.569	+	1152.80i	−0.0597093	+	0.103420i	−0.894335	−	0.447398i	$-0.852351\pi$
$499$	−665.569	+	1152.80i	−0.0597093	+	0.103420i	0.834626	+	0.550818i	$0.185684\pi$
$500$	2064.22	+	3575.33i	0.184629	+	0.319787i
$501$	−7283.19	+	11260.5i	−0.649479	+	1.00416i
$502$	2242.98	+	1294.99i	0.199421	+	0.115136i
$503$	−10393.2			−0.921288			−0.460644	−	0.887585i	$-0.652382\pi$
$503$	−10393.2			−0.921288			−0.460644	+	0.887585i	$0.652382\pi$
$504$	3310.29	+	2246.11i	0.292563	+	0.198511i
$505$	4423.62			0.389799
$506$	−5045.96	−	2913.29i	−0.443321	−	0.255951i
$507$	6101.22	−	9433.07i	0.534447	−	0.826306i
$508$	−3108.97	−	5384.89i	−0.271532	−	0.470307i
$509$	5132.02	−	8888.91i	0.446901	−	0.774055i	−0.551281	−	0.834319i	$-0.685861\pi$
$509$	5132.02	−	8888.91i	0.446901	−	0.774055i	0.998182	+	0.0602640i	$0.0191943\pi$
$510$	−4822.44	+	2468.36i	−0.418708	+	0.214315i
$511$	4293.73	+	2318.61i	0.371709	+	0.200723i
$512$			512.000i			0.0441942i
$513$	−1014.88	−	812.584i	−0.0873449	−	0.0699346i
$514$	2522.00	−	1456.08i	0.216422	−	0.124951i
$515$	−4997.54	+	2885.33i	−0.427608	+	0.246879i
$516$	8119.05	+	410.501i	0.692677	+	0.0350219i
$517$			1885.78i			0.160418i
$518$	−9767.06	−	5274.21i	−0.828456	−	0.447366i
$519$	2372.50	+	4635.17i	0.200658	+	0.392026i
$520$	106.229	−	183.993i	0.00895852	−	0.0155166i
$521$	1549.97	+	2684.63i	0.130337	+	0.225750i	0.923806	−	0.382860i	$-0.125061\pi$
$521$	1549.97	+	2684.63i	0.130337	+	0.225750i	−0.793470	+	0.608610i	$0.791727\pi$
$522$	11164.4	+	1131.84i	0.936112	+	0.0949028i
$523$	−8265.94	−	4772.34i	−0.691098	−	0.399005i	0.112925	−	0.993603i	$-0.463978\pi$
$523$	−8265.94	−	4772.34i	−0.691098	−	0.399005i	−0.804023	+	0.594598i	$0.797311\pi$
$524$	−8379.70			−0.698605
$525$	−4850.42	−	8846.07i	−0.403219	−	0.735380i
$526$	−4273.10			−0.354213
$527$	14250.9	+	8227.77i	1.17795	+	0.680090i
$528$	1635.03	+	1057.52i	0.134764	+	0.0871642i
$529$	1652.39	+	2862.03i	0.135809	+	0.235229i
$530$	−1341.44	+	2323.45i	−0.109941	+	0.190423i
$531$	3229.80	−	4480.06i	0.263957	−	0.366136i
$532$	584.514	−	360.031i	0.0476352	−	0.0293409i
$533$		−	3006.47i		−	0.244324i
$534$	−465.747	+	9211.72i	−0.0377432	+	0.746498i
$535$	711.364	−	410.706i	0.0574859	−	0.0331895i
$536$	712.073	−	411.115i	0.0573822	−	0.0331296i
$537$	787.238	−	15570.3i	0.0632622	−	1.25122i
$538$			5774.91i			0.462777i
$539$	457.119	+	8020.53i	0.0365297	+	0.640944i
$540$	−2491.21	−	380.465i	−0.198527	−	0.0303196i
$541$	3403.83	−	5895.60i	0.270503	−	0.468524i	−0.698488	−	0.715622i	$-0.746143\pi$
$541$	3403.83	−	5895.60i	0.270503	−	0.468524i	0.968991	+	0.247098i	$0.0794768\pi$
$542$	5857.70	+	10145.8i	0.464225	+	0.804061i
$543$	4222.79	+	2731.27i	0.333734	+	0.215856i
$544$	3217.01	+	1857.34i	0.253544	+	0.146384i
$545$	2617.80			0.205751
$546$	−590.710	+	972.945i	−0.0463004	+	0.0762604i
$547$	−14906.9			−1.16521			−0.582606	−	0.812754i	$-0.697967\pi$
$547$	−14906.9			−1.16521			−0.582606	+	0.812754i	$0.697967\pi$
$548$	2116.01	+	1221.68i	0.164948	+	0.0952327i
$549$	−1709.89	+	16866.2i	−0.132926	+	1.31117i
$550$	−2455.36	−	4252.80i	−0.190358	−	0.329709i
$551$	962.859	−	1667.72i	0.0744449	−	0.128942i
$552$	−2355.89	−	4602.72i	−0.181655	−	0.354900i
$553$	−19758.1	+	562.586i	−1.51935	+	0.0432615i
$554$		−	5606.06i		−	0.429925i
$555$	6983.77	+	353.102i	0.534135	+	0.0270060i
$556$	−6258.29	+	3613.22i	−0.477357	+	0.275602i
$557$	−10661.9	+	6155.67i	−0.811061	+	0.468266i	−0.847324	−	0.531076i	$-0.821788\pi$
$557$	−10661.9	+	6155.67i	−0.811061	+	0.468266i	0.0362634	+	0.999342i	$0.488454\pi$
$558$	3139.25	+	6981.50i	0.238163	+	0.529661i
$559$			2313.06i			0.175013i
$560$	632.278	−	1170.89i	0.0477118	−	0.0883554i
$561$	12575.9	−	6436.95i	0.946442	−	0.484435i
$562$	−4665.53	+	8080.93i	−0.350184	+	0.606536i
$563$	−417.925	−	723.867i	−0.0312850	−	0.0541872i	0.849959	−	0.526849i	$-0.176627\pi$
$563$	−417.925	−	723.867i	−0.0312850	−	0.0541872i	−0.881244	+	0.472662i	$0.843293\pi$
$564$	−908.852	+	1405.17i	−0.0678538	+	0.104908i
$565$	8882.34	+	5128.22i	0.661386	+	0.381851i
$566$	−10749.2			−0.798271
$567$	13298.3	+	2332.11i	0.984969	+	0.172732i
$568$	−375.828			−0.0277630
$569$	−5291.04	−	3054.78i	−0.389828	−	0.225067i	0.292258	−	0.956340i	$-0.405593\pi$
$569$	−5291.04	−	3054.78i	−0.389828	−	0.225067i	−0.682086	+	0.731272i	$0.738927\pi$
$570$	−234.871	+	363.133i	−0.0172591	+	0.0266842i
$571$	6319.69	+	10946.0i	0.463171	+	0.802236i	0.999117	−	0.0420166i	$-0.0133782\pi$
$571$	6319.69	+	10946.0i	0.463171	+	0.802236i	−0.535946	+	0.844252i	$0.680045\pi$
$572$	−277.021	+	479.815i	−0.0202497	+	0.0350735i
$573$	1902.54	−	973.814i	0.138708	−	0.0709977i
$574$	−535.961	−	18823.0i	−0.0389731	−	1.36874i
$575$			13039.8i			0.945736i
$576$	708.654	+	1576.01i	0.0512626	+	0.114005i
$577$	−15334.7	+	8853.51i	−1.10640	+	0.638781i	−0.937895	−	0.346920i	$-0.887228\pi$
$577$	−15334.7	+	8853.51i	−1.10640	+	0.638781i	−0.168506	+	0.985701i	$0.553894\pi$
$578$	14830.5	−	8562.42i	1.06725	−	0.616176i
$579$	−4236.85	−	214.216i	−0.304106	−	0.0153757i
$580$		−	3732.78i		−	0.267233i
$581$	2626.72	+	4264.50i	0.187564	+	0.304512i
$582$	−1039.65	−	2031.17i	−0.0740462	−	0.144664i
$583$	3498.19	−	6059.05i	0.248508	−	0.430429i
$584$	1053.93	+	1825.46i	0.0746779	+	0.129346i
$585$	72.3229	−	713.386i	0.00511143	−	0.0504186i
$586$	−2255.36	−	1302.13i	−0.158990	−	0.0917929i
$587$	−11725.2			−0.824446			−0.412223	−	0.911083i	$-0.635248\pi$
$587$	−11725.2			−0.824446			−0.412223	+	0.911083i	$0.635248\pi$
$588$	−3524.88	+	6196.74i	−0.247217	+	0.434607i
$589$	1313.63			0.0918968
$590$	−1591.02	−	918.578i	−0.111019	−	0.0640970i
$591$	2763.27	+	1787.26i	0.192328	+	0.124396i
$592$	−2397.40	−	4152.42i	−0.166440	−	0.288283i
$593$	7523.76	−	13031.5i	0.521018	−	0.902430i	−0.478683	−	0.877988i	$-0.658886\pi$
$593$	7523.76	−	13031.5i	0.521018	−	0.902430i	0.999701	−	0.0244425i	$-0.00778108\pi$
$594$	6496.54	+	992.170i	0.448748	+	0.0685340i
$595$	−5063.27	−	8220.26i	−0.348864	−	0.566383i
$596$		−	10816.1i		−	0.743363i
$597$	−898.161	+	17764.2i	−0.0615734	+	1.21782i
$598$	1274.09	−	735.597i	0.0871262	−	0.0503023i
$599$	5292.70	−	3055.74i	0.361025	−	0.208438i	−0.308505	−	0.951223i	$-0.599829\pi$
$599$	5292.70	−	3055.74i	0.361025	−	0.208438i	0.669530	+	0.742785i	$0.266495\pi$
$600$	220.054	−	4352.30i	0.0149727	−	0.296137i
$601$		−	7494.08i		−	0.508636i	−0.967121	−	0.254318i	$-0.918149\pi$
$601$		−	7494.08i		−	0.508636i	0.967121	−	0.254318i	$-0.0818509\pi$
$602$	412.347	+	14481.7i	0.0279170	+	0.980447i
$603$	1622.84	−	2251.04i	0.109597	−	0.152022i
$604$	3081.41	−	5337.15i	0.207584	−	0.359546i
$605$	1756.84	+	3042.93i	0.118059	+	0.204484i
$606$	−8595.82	−	5559.70i	−0.576207	−	0.372686i
$607$	17917.1	+	10344.5i	1.19808	+	0.691711i	0.960127	−	0.279565i	$-0.0901904\pi$
$607$	17917.1	+	10344.5i	1.19808	+	0.691711i	0.237953	+	0.971277i	$0.423524\pi$
$608$	296.539			0.0197800
$609$	−440.947	+	19993.3i	−0.0293400	+	1.33032i
$610$	5639.19			0.374302
$611$	−412.361	−	238.077i	−0.0273033	−	0.0157636i
$612$	12473.1	+	1264.52i	0.823848	+	0.0835215i
$613$	11645.5	+	20170.6i	0.767305	+	1.32901i	0.939019	+	0.343865i	$0.111736\pi$
$613$	11645.5	+	20170.6i	0.767305	+	1.32901i	−0.171714	+	0.985147i	$0.554931\pi$
$614$	−644.894	+	1116.99i	−0.0423873	+	0.0734169i
$615$	5404.99	+	10559.7i	0.354391	+	0.692374i
$616$	−1648.84	+	3053.42i	−0.107847	+	0.199717i
$617$		−	11640.9i		−	0.759554i	−0.925078	−	0.379777i	$-0.876001\pi$
$617$		−	11640.9i		−	0.759554i	0.925078	−	0.379777i	$-0.123999\pi$
$618$	13337.4	+	674.343i	0.868138	+	0.0438933i
$619$	−13978.4	+	8070.44i	−0.907657	+	0.524036i	−0.879676	−	0.475573i	$-0.842241\pi$
$619$	−13978.4	+	8070.44i	−0.907657	+	0.524036i	−0.0279803	+	0.999608i	$0.508908\pi$
$620$	2205.18	−	1273.16i	0.142842	−	0.0824699i
$621$	−13622.3	−	10907.0i	−0.880266	−	0.704805i
$622$		−	2673.68i		−	0.172355i
$623$	−16430.6	+	467.841i	−1.05663	+	0.0300861i
$624$	−437.667	+	224.019i	−0.0280781	+	0.0143717i
$625$	−4234.68	+	7334.68i	−0.271019	+	0.469420i
$626$	1685.48	+	2919.33i	0.107612	+	0.186390i
$627$	612.493	−	946.972i	0.0390121	−	0.0603165i
$628$	1909.99	+	1102.73i	0.121365	+	0.0700699i
$629$	−34787.4			−2.20519
$630$	325.626	−	4479.28i	0.0205925	−	0.283268i
$631$	9424.67			0.594596			0.297298	−	0.954785i	$-0.403914\pi$
$631$	9424.67			0.594596			0.297298	+	0.954785i	$0.403914\pi$
$632$	−7394.25	−	4269.07i	−0.465392	−	0.268694i
$633$	2888.74	−	4466.26i	0.181385	−	0.280439i
$634$	−3013.71	−	5219.90i	−0.188785	−	0.326985i
$635$	−3490.34	+	6045.45i	−0.218126	+	0.377805i
$636$	5526.81	−	2828.89i	0.344579	−	0.176372i
$637$	−1811.55	−	912.623i	−0.112679	−	0.0567652i
$638$			9734.27i			0.604049i
$639$	−1156.85	+	520.179i	−0.0716185	+	0.0322034i
$640$	497.797	−	287.403i	0.0307456	−	0.0177510i
$641$	1459.54	−	842.666i	0.0899351	−	0.0519241i	−0.454358	−	0.890819i	$-0.650131\pi$
$641$	1459.54	−	842.666i	0.0899351	−	0.0519241i	0.544293	+	0.838895i	$0.316798\pi$
$642$	−1898.48	−	95.9879i	−0.116709	−	0.00590084i
$643$		−	10186.5i		−	0.624752i	−0.949958	−	0.312376i	$-0.898875\pi$
$643$		−	10186.5i		−	0.624752i	0.949958	−	0.312376i	$-0.101125\pi$
$644$	7845.72	−	4832.57i	0.480070	−	0.295699i
$645$	−4158.39	−	8124.26i	−0.253855	−	0.495957i
$646$	1075.73	−	1863.22i	0.0655171	−	0.113479i
$647$	−163.793	−	283.698i	−0.00995266	−	0.0172385i	0.861006	−	0.508594i	$-0.169835\pi$
$647$	−163.793	−	283.698i	−0.00995266	−	0.0172385i	−0.870959	+	0.491356i	$0.836501\pi$
$648$	4362.66	+	3870.32i	0.264478	+	0.234630i
$649$	4149.04	+	2395.45i	0.250946	+	0.144884i
$650$	1239.94			0.0748223
$651$	−11961.6	+	6558.72i	−0.720143	+	0.394864i
$652$	9246.55			0.555403
$653$	−1769.92	−	1021.87i	−0.106068	−	0.0612384i	0.446028	−	0.895019i	$-0.352838\pi$
$653$	−1769.92	−	1021.87i	−0.106068	−	0.0612384i	−0.552096	+	0.833781i	$0.686172\pi$
$654$	−5086.83	−	3290.12i	−0.304145	−	0.196718i
$655$	4703.82	+	8147.25i	0.280600	+	0.486014i
$656$	4067.03	−	7044.31i	0.242059	−	0.419259i
$657$	5770.73	+	4160.28i	0.342675	+	0.247044i
$658$	−2624.16	−	1417.04i	−0.155472	−	0.0839546i
$659$		−	27567.4i		−	1.62955i	−0.579778	−	0.814774i	$-0.696861\pi$
$659$		−	27567.4i		−	1.62955i	0.579778	−	0.814774i	$-0.303139\pi$
$660$	110.388	−	2183.29i	0.00651037	−	0.128765i
$661$	18417.0	−	10633.0i	1.08372	−	0.625684i	0.151820	−	0.988408i	$-0.451487\pi$
$661$	18417.0	−	10633.0i	1.08372	−	0.625684i	0.931897	+	0.362724i	$0.118153\pi$
$662$	−1366.45	+	788.920i	−0.0802244	+	0.0463176i
$663$	−180.127	+	3562.61i	−0.0105513	+	0.208688i
$664$			2163.49i			0.126445i
$665$	−678.152	−	366.202i	−0.0395453	−	0.0213544i
$666$	−13126.9	−	9463.50i	−0.763747	−	0.550606i
$667$	12924.1	−	22385.2i	0.750260	−	1.29949i
$668$	−5161.73	−	8940.38i	−0.298972	−	0.517835i
$669$	6637.64	+	4293.16i	0.383596	+	0.248107i
$670$	−799.422	−	461.547i	−0.0460961	−	0.0266136i
$671$	−14705.8			−0.846065
$672$	−2700.22	+	1480.57i	−0.155005	+	0.0849912i
$673$	−9377.40			−0.537106			−0.268553	−	0.963265i	$-0.586545\pi$
$673$	−9377.40			−0.537106			−0.268553	+	0.963265i	$0.586545\pi$
$674$	−3301.56	−	1906.16i	−0.188682	−	0.108935i
$675$	−5346.62	−	13701.5i	−0.304876	−	0.781293i
$676$	4324.05	+	7489.48i	0.246020	+	0.426120i
$677$	−5342.31	+	9253.15i	−0.303282	+	0.525299i	−0.976877	−	0.213801i	$-0.931416\pi$
$677$	−5342.31	+	9253.15i	−0.303282	+	0.525299i	0.673596	+	0.739100i	$0.264749\pi$
$678$	−10814.6	−	21128.5i	−0.612585	−	1.19681i
$679$	3462.30	−	2132.60i	0.195686	−	0.120533i
$680$		−	4170.35i		−	0.235185i
$681$	7572.30	+	382.857i	0.426096	+	0.0215435i
$682$	−5750.62	+	3320.12i	−0.322878	+	0.186414i
$683$	24985.9	−	14425.6i	1.39979	−	0.808172i	0.405424	−	0.914129i	$-0.367124\pi$
$683$	24985.9	−	14425.6i	1.39979	−	0.808172i	0.994371	+	0.105957i	$0.0337906\pi$
$684$	912.788	−	410.437i	0.0510253	−	0.0229436i
$685$		−	2743.08i		−	0.153004i
$686$	−11504.5	−	5390.83i	−0.640297	−	0.300033i
$687$	22176.8	−	11351.2i	1.23158	−	0.630384i
$688$	−3129.02	+	5419.61i	−0.173390	+	0.300321i
$689$	883.284	+	1529.89i	0.0488395	+	0.0845926i
$690$	−3152.59	+	4874.21i	−0.173938	+	0.268924i
$691$	−1139.99	−	658.171i	−0.0627599	−	0.0362344i	0.468292	−	0.883574i	$-0.344870\pi$
$691$	−1139.99	−	658.171i	−0.0627599	−	0.0362344i	−0.531052	+	0.847339i	$0.678203\pi$
$692$	−4008.40			−0.220197
$693$	−849.162	+	11681.0i	−0.0465469	+	0.640294i
$694$	10482.3			0.573348
$695$	7025.98	+	4056.45i	0.383469	+	0.221396i
$696$	−4691.44	+	7253.41i	−0.255501	+	0.395028i
$697$	−29507.3	−	51108.1i	−1.60354	−	2.77741i
$698$	−4502.54	+	7798.62i	−0.244160	+	0.422897i
$699$	7721.80	−	3952.39i	0.417833	−	0.213867i
$700$	7763.05	−	221.043i	0.419165	−	0.0119352i
$701$			12811.2i			0.690259i	0.938555	+	0.345129i	$0.112165\pi$
$701$			12811.2i			0.690259i	−0.938555	+	0.345129i	$0.887835\pi$
$702$	−1037.14	+	1295.33i	−0.0557609	+	0.0696427i
$703$	−2404.99	+	1388.52i	−0.129027	+	0.0744938i
$704$	−1298.15	+	749.485i	−0.0694968	+	0.0401240i
$705$	1876.36	+	94.8693i	0.100238	+	0.00506807i
$706$			19198.8i			1.02345i
$707$	8668.46	−	16052.7i	0.461119	−	0.853925i
$708$	1937.13	+	3784.58i	0.102828	+	0.200895i
$709$	−16482.9	+	28549.2i	−0.873101	+	1.51226i	−0.0143290	+	0.999897i	$0.504561\pi$
$709$	−16482.9	+	28549.2i	−0.873101	+	1.51226i	−0.858772	+	0.512358i	$0.828772\pi$
$710$	210.965	+	365.402i	0.0111512	+	0.0193145i
$711$	−28669.3	−	2906.48i	−1.51221	−	0.153308i
$712$	−6148.99	−	3550.12i	−0.323656	−	0.186863i
$713$	17632.4			0.926141
$714$	−492.638	+	22337.0i	−0.0258214	+	1.17079i
$715$	622.006			0.0325339
$716$	10393.4	+	6000.66i	0.542488	+	0.313206i
$717$	−15398.4	−	9959.52i	−0.802039	−	0.518752i
$718$	10165.9	+	17607.9i	0.528396	+	0.915210i
$719$	−4307.48	+	7460.77i	−0.223424	+	0.386982i	−0.955845	−	0.293870i	$-0.905057\pi$
$719$	−4307.48	+	7460.77i	−0.223424	+	0.386982i	0.732421	+	0.680851i	$0.238390\pi$
$720$	1134.50	−	1573.66i	0.0587224	−	0.0814541i
$721$	677.375	+	23789.5i	0.0349886	+	1.22880i
$722$			13546.3i			0.698254i
$723$	−1293.44	+	25582.2i	−0.0665335	+	1.31592i
$724$	−3352.73	+	1935.70i	−0.172104	+	0.0993643i
$725$	18866.5	−	10892.6i	0.966463	−	0.557988i
$726$	410.598	−	8120.96i	0.0209900	−	0.415147i
$727$		−	26635.3i		−	1.35880i	−0.733768	−	0.679400i	$-0.762240\pi$
$727$		−	26635.3i		−	1.35880i	0.733768	−	0.679400i	$-0.237760\pi$
$728$	−459.524	−	746.041i	−0.0233943	−	0.0379809i
$729$	18785.7	+	5875.05i	0.954415	+	0.298484i
$730$	1183.21	−	2049.38i	0.0599900	−	0.103906i
$731$	22701.7	+	39320.5i	1.14864	+	1.98950i
$732$	−10957.9	−	7087.46i	−0.553299	−	0.357869i
$733$	−5328.35	−	3076.33i	−0.268496	−	0.155016i	0.359708	−	0.933065i	$-0.382876\pi$
$733$	−5328.35	−	3076.33i	−0.268496	−	0.155016i	−0.628204	+	0.778049i	$0.716210\pi$
$734$	−767.978			−0.0386193
$735$	8003.48	−	51.3415i	0.401650	−	0.00257655i
$736$	3980.34			0.199344
$737$	2084.72	+	1203.61i	0.104195	+	0.0601569i
$738$	2768.93	−	27312.5i	0.138111	−	1.36231i
$739$	−7364.30	−	12755.3i	−0.366577	−	0.634929i	0.622451	−	0.782659i	$-0.286137\pi$
$739$	−7364.30	−	12755.3i	−0.366577	−	0.634929i	−0.989028	+	0.147729i	$0.952804\pi$
$740$	−2691.49	+	4661.80i	−0.133704	+	0.231582i
$741$	129.747	+	253.487i	0.00643236	+	0.0125669i
$742$	5802.82	+	9420.93i	0.287100	+	0.466109i
$743$			27255.1i			1.34575i	0.739755	+	0.672876i	$0.234941\pi$
$743$			27255.1i			1.34575i	−0.739755	+	0.672876i	$0.765059\pi$
$744$	−5885.17	−	297.556i	−0.290001	−	0.0146625i
$745$	−10516.1	+	6071.45i	−0.517152	+	0.298578i
$746$	−5133.08	+	2963.59i	−0.251924	+	0.145449i
$747$	2994.47	+	6659.52i	0.146669	+	0.326184i
$748$			10875.4i			0.531608i
$749$	−96.4195	−	3386.26i	−0.00470373	−	0.165195i
$750$	−9547.94	+	4887.10i	−0.464855	+	0.237936i
$751$	3075.69	−	5327.25i	0.149445	−	0.258847i	−0.781577	−	0.623809i	$-0.785585\pi$
$751$	3075.69	−	5327.25i	0.149445	−	0.258847i	0.931023	+	0.364961i	$0.118918\pi$
$752$	−644.121	−	1115.65i	−0.0312349	−	0.0541005i
$753$	−3654.44	+	5650.11i	−0.176859	+	0.273441i
$754$	−2128.58	−	1228.94i	−0.102810	−	0.0593571i
$755$	−6918.80			−0.333511
$756$	−6262.41	+	8294.73i	−0.301272	+	0.399043i
$757$	−21107.3			−1.01342			−0.506710	−	0.862117i	$-0.669139\pi$
$757$	−21107.3			−1.01342			−0.506710	+	0.862117i	$0.669139\pi$
$758$	22855.0	+	13195.4i	1.09516	+	0.632292i
$759$	8221.27	−	12710.9i	0.393166	−	0.607873i
$760$	−166.458	−	288.313i	−0.00794481	−	0.0137608i
$761$	−7530.97	+	13044.0i	−0.358735	+	0.621348i	−0.987750	−	0.156046i	$-0.950125\pi$
$761$	−7530.97	+	13044.0i	−0.358735	+	0.621348i	0.629015	+	0.777393i	$0.283459\pi$
$762$	14380.4	−	7360.58i	0.683657	−	0.349929i
$763$	5129.82	−	9499.67i	0.243397	−	0.450736i
$764$			1645.28i			0.0779113i
$765$	−5772.14	−	12836.9i	−0.272800	−	0.606692i
$766$	−15505.1	+	8951.90i	−0.731362	+	0.422252i
$767$	−1047.62	+	604.845i	−0.0493187	+	0.0284742i
$768$	−1328.52	−	67.1702i	−0.0624203	−	0.00315599i
$769$			26099.2i			1.22387i	0.790906	+	0.611937i	$0.209610\pi$
$769$			26099.2i			1.22387i	−0.790906	+	0.611937i	$0.790390\pi$
$770$	3894.27	−	110.884i	0.182259	−	0.00518960i
$771$	3447.31	+	6735.03i	0.161027	+	0.314599i
$772$	1632.85	−	2828.17i	0.0761236	−	0.131850i
$773$	8.84542	+	15.3207i	0.000411575	+	0.000712869i	0.866231	−	0.499644i	$-0.166536\pi$
$773$	8.84542	+	15.3207i	0.000411575	+	0.000712869i	−0.865820	+	0.500356i	$0.833202\pi$
$774$	−2130.31	+	21013.1i	−0.0989306	+	0.975842i
$775$	12869.8	+	7430.41i	0.596514	+	0.344398i
$776$	1756.51			0.0812566
$777$	14966.7	−	24651.3i	0.691025	−	1.13817i
$778$	17539.3			0.808244
$779$	−4079.91	−	2355.54i	−0.187648	−	0.108339i
$780$	463.483	+	299.776i	0.0212761	+	0.0137612i
$781$	−550.151	−	952.889i	−0.0252061	−	0.0436582i
$782$	14439.1	−	25009.3i	0.660285	−	1.14365i
$783$	−4401.53	+	28820.4i	−0.200891	+	1.31540i
$784$	−3009.99	−	4588.91i	−0.137117	−	0.209043i
$785$		−	2476.01i		−	0.112577i
$786$	1099.35	−	21743.3i	0.0498886	−	0.986716i
$787$	2066.21	−	1192.93i	0.0935865	−	0.0540322i	−0.452476	−	0.891776i	$-0.649459\pi$
$787$	2066.21	−	1192.93i	0.0935865	−	0.0540322i	0.546063	+	0.837744i	$0.316126\pi$
$788$	−2193.92	+	1266.66i	−0.0991819	+	0.0572627i
$789$	560.596	−	11087.7i	0.0252950	−	0.500293i
$790$			9585.51i			0.431693i
$791$	36015.4	−	22183.7i	1.61891	−	0.997169i
$792$	−2958.52	+	4103.77i	−0.132735	+	0.184117i
$793$	1856.58	−	3215.70i	0.0831390	−	0.144001i
$794$	1370.98	+	2374.61i	0.0612774	+	0.106136i
$795$	−5852.81	−	3785.54i	−0.261104	−	0.168880i
$796$	−11857.9	−	6846.17i	−0.528005	−	0.304844i
$797$	13183.5			0.585927			0.292964	−	0.956124i	$-0.405359\pi$
$797$	13183.5			0.585927			0.292964	+	0.956124i	$0.405359\pi$
$798$	857.512	+	1563.91i	0.0380396	+	0.0693756i
$799$	−9346.49			−0.413836
$800$	2905.24	+	1677.34i	0.128395	+	0.0741287i
$801$	−23841.1	−	2417.01i	−1.05167	−	0.106618i
$802$	2762.20	+	4784.28i	0.121617	+	0.210647i
$803$	−3085.56	+	5344.35i	−0.135600	+	0.234867i
$804$	973.329	+	1901.59i	0.0426948	+	0.0834130i
$805$	−9102.59	−	4915.39i	−0.398539	−	0.215211i
$806$		−	1676.64i		−	0.0732721i
$807$	−14984.5	−	757.621i	−0.653630	−	0.0330477i
$808$	6824.74	−	3940.27i	0.297146	−	0.171557i
$809$	26645.9	−	15384.0i	1.15800	−	0.668570i	0.207174	−	0.978304i	$-0.433574\pi$
$809$	26645.9	−	15384.0i	1.15800	−	0.668570i	0.950823	+	0.309734i	$0.100240\pi$
$810$	1314.04	−	6414.19i	0.0570009	−	0.278237i
$811$		−	42776.4i		−	1.85214i	−0.377357	−	0.926068i	$-0.623167\pi$
$811$		−	42776.4i		−	1.85214i	0.377357	−	0.926068i	$-0.376833\pi$
$812$	−13545.8	−	7314.70i	−0.585422	−	0.316128i
$813$	−27094.5	+	13868.3i	−1.16881	+	0.598256i
$814$	7018.82	−	12156.9i	0.302223	−	0.523465i
$815$	−5190.41	−	8990.05i	−0.223082	−	0.386390i
$816$	−5241.40	+	8103.69i	−0.224860	+	0.347654i
$817$	3138.92	+	1812.26i	0.134415	+	0.0776045i
$818$	−5334.75			−0.228026
$819$	−2447.06	−	1660.39i	−0.104405	−	0.0708411i
$820$	−9131.86			−0.388901
$821$	−36141.5	−	20866.3i	−1.53635	−	0.887014i	−0.999048	−	0.0436263i	$-0.986109\pi$
$821$	−36141.5	−	20866.3i	−1.53635	−	0.887014i	−0.537305	−	0.843388i	$-0.680558\pi$
$822$	−3447.57	+	5330.27i	−0.146287	+	0.226173i
$823$	7822.35	+	13548.7i	0.331312	+	0.573850i	0.982769	−	0.184836i	$-0.0591753\pi$
$823$	7822.35	+	13548.7i	0.331312	+	0.573850i	−0.651457	+	0.758685i	$0.725842\pi$
$824$	−5140.13	+	8902.96i	−0.217312	+	0.376395i
$825$	11357.1	−	5813.13i	0.479278	−	0.245318i
$826$	−6451.15	+	3973.58i	−0.271748	+	0.167383i
$827$			24395.1i			1.02576i	0.858461	+	0.512879i	$0.171421\pi$
$827$			24395.1i			1.02576i	−0.858461	+	0.512879i	$0.828579\pi$
$828$	12252.0	−	5509.15i	0.514236	−	0.231227i
$829$	32786.9	−	18929.5i	1.37362	−	0.793062i	0.382242	−	0.924062i	$-0.375152\pi$
$829$	32786.9	−	18929.5i	1.37362	−	0.793062i	0.991382	+	0.131000i	$0.0418188\pi$
$830$	2103.48	−	1214.44i	0.0879671	−	0.0507878i
$831$	14546.4	+	735.470i	0.607231	+	0.0307018i
$832$		−	378.486i		−	0.0157712i
$833$	−39752.2	+	2265.62i	−1.65346	+	0.0942367i
$834$	−8554.42	−	16712.8i	−0.355174	−	0.693905i
$835$	−5794.92	+	10037.1i	−0.240169	+	0.415986i
$836$	434.085	+	751.858i	0.0179583	+	0.0311047i
$837$	−18527.2	+	7229.68i	−0.765105	+	0.298559i
$838$	−25081.1	−	14480.6i	−1.03390	−	0.596925i
$839$	40533.9			1.66792			0.833960	−	0.551826i	$-0.186069\pi$
$839$	40533.9			1.66792			0.833960	+	0.551826i	$0.186069\pi$
$840$	2955.22	+	1794.22i	0.121387	+	0.0736983i
$841$	−18794.8			−0.770625
$842$	−24679.6	−	14248.8i	−1.01011	−	0.583188i
$843$	−20356.0	−	13166.1i	−0.831670	−	0.537917i
$844$	2047.30	+	3546.03i	0.0834965	+	0.144620i
$845$	4854.48	−	8408.21i	0.197632	−	0.342309i
$846$	−3526.85	−	2542.60i	−0.143328	−	0.103329i
$847$	14485.1	−	412.444i	0.587619	−	0.0167317i
$848$			4779.48i			0.193547i
$849$	1410.20	−	27891.6i	0.0570060	−	1.12749i
$850$	21078.2	−	12169.5i	0.850560	−	0.491071i
$851$	−32281.4	+	18637.6i	−1.30034	+	0.750752i
$852$	49.3055	−	975.183i	0.00198261	−	0.0392127i
$853$			38466.5i			1.54404i	0.635598	+	0.772021i	$0.280754\pi$
$853$			38466.5i			1.54404i	−0.635598	+	0.772021i	$0.719246\pi$
$854$	11050.5	−	20463.9i	0.442786	−	0.819976i
$855$	−911.431	−	657.075i	−0.0364565	−	0.0262824i
$856$	731.660	−	1267.27i	0.0292145	−	0.0506010i
$857$	13054.1	+	22610.3i	0.520326	+	0.901230i	0.999721	+	0.0236312i	$0.00752274\pi$
$857$	13054.1	+	22610.3i	0.520326	+	0.901230i	−0.479395	+	0.877599i	$0.659144\pi$
$858$	−1208.66	−	781.751i	−0.0480921	−	0.0311055i
$859$	21033.3	+	12143.6i	0.835445	+	0.482345i	0.855713	−	0.517450i	$-0.173119\pi$
$859$	21033.3	+	12143.6i	0.835445	+	0.482345i	−0.0202681	+	0.999795i	$0.506452\pi$
$860$	7025.70			0.278575
$861$	48911.5	+	1078.73i	1.93600	+	0.0426982i
$862$	11146.3			0.440423
$863$	−32475.9	−	18750.0i	−1.28099	−	0.739579i	−0.303960	−	0.952685i	$-0.598309\pi$
$863$	−32475.9	−	18750.0i	−1.28099	−	0.739579i	−0.977029	+	0.213106i	$0.931642\pi$
$864$	−4182.33	+	1632.03i	−0.164683	+	0.0642624i
$865$	2250.06	+	3897.21i	0.0884441	+	0.153190i
$866$	−2939.93	+	5092.11i	−0.115361	+	0.199812i
$867$	20271.8	+	39605.1i	0.794079	+	1.55139i
$868$	−298.894	−	10497.2i	−0.0116879	−	0.410481i
$869$		−	24996.9i		−	0.975791i
$870$	9685.67	+	489.710i	0.377442	+	0.0190836i
$871$	−526.386	+	303.909i	−0.0204775	+	0.0118227i
$872$	4038.74	−	2331.77i	0.156845	−	0.0905546i
$873$	5406.79	−	2431.17i	0.209613	−	0.0942528i
$874$		−	2305.33i		−	0.0892206i
$875$	−10024.8	−	16275.3i	−0.387313	−	0.628806i
$876$	−4874.89	+	2495.21i	−0.188022	+	0.0962389i
$877$	7420.70	−	12853.0i	0.285723	−	0.494887i	−0.687061	−	0.726600i	$-0.741100\pi$
$877$	7420.70	−	12853.0i	0.285723	−	0.494887i	0.972784	+	0.231713i	$0.0744329\pi$
$878$	9573.31	+	16581.5i	0.367977	+	0.637355i
$879$	3674.61	−	5681.30i	0.141003	−	0.218004i
$880$	1457.39	+	841.424i	0.0558279	+	0.0322323i
$881$	−30469.3			−1.16520			−0.582598	−	0.812760i	$-0.697964\pi$
$881$	−30469.3			−1.16520			−0.582598	+	0.812760i	$0.697964\pi$
$882$	−15616.6	−	9959.19i	−0.596189	−	0.380208i
$883$	−6758.53			−0.257580			−0.128790	−	0.991672i	$-0.541109\pi$
$883$	−6758.53			−0.257580			−0.128790	+	0.991672i	$0.541109\pi$
$884$	−2378.11	−	1373.00i	−0.0904801	−	0.0522387i
$885$	2592.22	−	4007.82i	0.0984593	−	0.152227i
$886$	−7156.17	−	12394.8i	−0.271350	−	0.469992i
$887$	−17666.5	+	30599.4i	−0.668754	+	1.15832i	0.309499	+	0.950900i	$0.399839\pi$
$887$	−17666.5	+	30599.4i	−0.668754	+	1.15832i	−0.978253	+	0.207416i	$0.933495\pi$
$888$	11089.1	−	5675.92i	0.419059	−	0.214495i
$889$	15098.5	+	24512.6i	0.569616	+	0.924776i
$890$			7971.22i			0.300220i
$891$	−3426.74	+	16726.8i	−0.128844	+	0.628922i
$892$	−5270.02	+	3042.65i	−0.197818	+	0.114210i
$893$	−646.160	+	373.061i	−0.0242138	+	0.0139798i
$894$	28065.2	+	1418.98i	1.04993	+	0.0530849i
$895$		−	13473.5i		−	0.503207i
$896$	−67.4723	−	2369.63i	−0.00251573	−	0.0883525i
$897$	1741.55	+	3402.47i	0.0648257	+	0.126650i
$898$	14839.2	−	25702.3i	0.551439	−	0.955120i
$899$	−14728.9	−	25511.3i	−0.546427	−	0.946439i
$900$	11264.3	+	1141.97i	0.417197	+	0.0422953i
$901$	30030.5	+	17338.1i	1.11039	+	0.641084i
$902$	23813.9			0.879065
$903$	−37630.6	−	829.935i	−1.38679	−	0.0305853i
$904$	18271.5			0.672237
$905$	3764.01	+	2173.15i	0.138254	+	0.0798210i
$906$	13444.4	+	8695.71i	0.493002	+	0.318869i
$907$	10481.2	+	18153.9i	0.383706	+	0.664598i	0.991589	−	0.129429i	$-0.0413144\pi$
$907$	10481.2	+	18153.9i	0.383706	+	0.664598i	−0.607883	+	0.794027i	$0.707981\pi$
$908$	−2918.30	+	5054.65i	−0.106660	+	0.184740i
$909$	15553.8	−	21574.7i	0.567533	−	0.787226i
$910$	−467.399	+	865.555i	−0.0170265	+	0.0315306i
$911$		−	5419.65i		−	0.197103i	−0.995132	−	0.0985516i	$-0.968579\pi$
$911$		−	5419.65i		−	0.197103i	0.995132	−	0.0985516i	$-0.0314209\pi$
$912$	−38.9035	+	769.449i	−0.00141253	+	0.0279375i
$913$	−5485.41	+	3167.00i	−0.198840	+	0.114800i
$914$	−13120.0	+	7574.83i	−0.474804	+	0.274128i
$915$	−739.815	+	14632.3i	−0.0267296	+	0.528667i
$916$			19178.1i			0.691770i
$917$	38782.8	−	1104.29i	1.39664	−	0.0397677i
$918$	−4917.50	+	32198.8i	−0.176799	+	1.15765i
$919$	−12706.3	+	22007.9i	−0.456084	+	0.789961i	−0.998750	−	0.0499878i	$-0.984082\pi$
$919$	−12706.3	+	22007.9i	−0.456084	+	0.789961i	0.542666	+	0.839949i	$0.317415\pi$
$920$	−2234.30	−	3869.93i	−0.0800682	−	0.138682i
$921$	−2813.71	−	1819.89i	−0.100668	−	0.0651110i
$922$	−25721.8	−	14850.5i	−0.918767	−	0.530450i
$923$	277.823			0.00990754
$924$	−7706.58	−	4678.94i	−0.274381	−	0.166586i
$925$	−31416.1			−1.11671
$926$	−5822.17	−	3361.43i	−0.206618	−	0.119291i
$927$	−3499.52	+	34518.9i	−0.123991	+	1.22303i
$928$	−3324.91	−	5758.92i	−0.117614	−	0.203713i
$929$	276.744	−	479.335i	0.00977360	−	0.0169284i	−0.861097	−	0.508440i	$-0.830222\pi$
$929$	276.744	−	479.335i	0.00977360	−	0.0169284i	0.870871	+	0.491512i	$0.163556\pi$
$930$	3014.25	+	5888.94i	0.106281	+	0.207641i
$931$	−2657.80	+	1743.32i	−0.0935615	+	0.0613696i
$932$			6677.66i			0.234693i
$933$	6937.57	+	350.765i	0.243436	+	0.0123082i
$934$	399.835	−	230.845i	0.0140075	−	0.00808723i
$935$	10573.7	−	6104.72i	0.369836	−	0.213525i
$936$	−523.858	−	1165.03i	−0.0182936	−	0.0406840i
$937$			18956.6i			0.660923i	0.943819	+	0.330462i	$0.107204\pi$
$937$			18956.6i			0.660923i	−0.943819	+	0.330462i	$0.892796\pi$
$938$	−3241.43	+	1996.56i	−0.112832	+	0.0694989i
$939$	−7796.09	+	3990.42i	−0.270943	+	0.138682i
$940$	−723.134	+	1252.51i	−0.0250915	+	0.0434598i
$941$	16542.7	+	28652.8i	0.573089	+	0.992619i	0.996246	+	0.0865632i	$0.0275884\pi$
$941$	16542.7	+	28652.8i	0.573089	+	0.992619i	−0.423157	+	0.906056i	$0.639078\pi$
$942$	−3111.91	+	4811.30i	−0.107634	+	0.166413i
$943$	−54763.2	−	31617.5i	−1.89113	−	1.09184i
$944$	−3272.83			−0.112841
$945$	11579.9	+	1432.57i	0.398620	+	0.0493137i
$946$	−18321.5			−0.629686
$947$	−11619.3	−	6708.40i	−0.398708	−	0.230194i	0.287219	−	0.957865i	$-0.407269\pi$
$947$	−11619.3	−	6708.40i	−0.398708	−	0.230194i	−0.685926	+	0.727671i	$0.740603\pi$
$948$	12047.3	−	18626.2i	0.412740	−	0.638135i
$949$	−779.096	−	1349.43i	−0.0266497	−	0.0461586i
$950$	971.480	−	1682.65i	0.0331779	−	0.0574657i
$951$	13939.8	−	7135.05i	0.475319	−	0.243291i
$952$	−15133.7	−	8172.17i	−0.515215	−	0.278216i
$953$			36353.5i			1.23568i	0.786303	+	0.617841i	$0.211993\pi$
$953$			36353.5i			1.23568i	−0.786303	+	0.617841i	$0.788007\pi$
$954$	6615.23	+	14711.9i	0.224503	+	0.499282i
$955$	1599.64	−	923.554i	0.0542023	−	0.0312937i
$956$	12225.7	−	7058.50i	0.413605	−	0.238795i
$957$	−25258.1	−	1277.06i	−0.853165	−	0.0431362i
$958$			8801.72i			0.296838i
$959$	−9954.29	−	5375.31i	−0.335183	−	0.180999i
$960$	680.436	+	1329.37i	0.0228760	+	0.0446929i
$961$	−4848.13	+	8397.21i	−0.162738	+	0.281871i
$962$	1772.23	+	3069.60i	0.0593961	+	0.102877i
$963$	498.131	−	4913.52i	0.0166688	−	0.164419i
$964$	−17076.6	−	9859.18i	−0.570540	−	0.329401i
$965$	−3666.29			−0.122303
$966$	11510.1	+	20991.8i	0.383365	+	0.699171i
$967$	3453.28			0.114840			0.0574198	−	0.998350i	$-0.481713\pi$
$967$	3453.28			0.114840			0.0574198	+	0.998350i	$0.481713\pi$
$968$	5420.89	+	3129.75i	0.179994	+	0.103919i
$969$	4693.48	+	3035.70i	0.155600	+	0.100641i
$970$	−985.992	−	1707.79i	−0.0326374	−	0.0565296i
$971$	25320.0	−	43855.6i	0.836826	−	1.44943i	−0.0557091	−	0.998447i	$-0.517742\pi$
$971$	25320.0	−	43855.6i	0.836826	−	1.44943i	0.892535	−	0.450978i	$-0.148925\pi$
$972$	−10614.9	+	10812.3i	−0.350281	+	0.356796i
$973$	28488.4	−	17547.4i	0.938638	−	0.578154i
$974$		−	23889.2i		−	0.785894i
$975$	−162.670	+	3217.35i	−0.00534320	+	0.105680i
$976$	8700.12	−	5023.02i	0.285332	−	0.164737i
$977$	−26914.6	+	15539.1i	−0.881344	+	0.508844i	−0.871101	−	0.491103i	$-0.836594\pi$
$977$	−26914.6	+	15539.1i	−0.881344	+	0.508844i	−0.0102426	+	0.999948i	$0.503260\pi$
$978$	−1213.07	+	23992.6i	−0.0396623	+	0.784456i
$979$		−	20787.2i		−	0.678613i
$980$	−2772.00	+	5502.41i	−0.0903554	+	0.179355i
$981$	9204.42	−	12767.5i	0.299566	−	0.415529i
$982$	−19916.7	+	34496.7i	−0.647216	+	1.12101i
$983$	−20154.8	−	34909.1i	−0.653956	−	1.13268i	−0.982155	−	0.188076i	$-0.939775\pi$
$983$	−20154.8	−	34909.1i	−0.653956	−	1.13268i	0.328199	−	0.944609i	$-0.393558\pi$
$984$	17744.7	+	11477.1i	0.574880	+	0.371827i
$985$	2463.05	+	1422.04i	0.0796744	+	0.0460001i
$986$	−48246.0			−1.55828
$987$	4021.16	−	6623.17i	0.129681	−	0.213594i
$988$	−219.211			−0.00705873
$989$	42132.6	+	24325.3i	1.35464	+	0.782102i
$990$	5650.65	+	572.861i	0.181403	+	0.0183906i
$991$	−2007.28	−	3476.71i	−0.0643425	−	0.111444i	0.832060	−	0.554686i	$-0.187162\pi$
$991$	−2007.28	−	3476.71i	−0.0643425	−	0.111444i	−0.896402	+	0.443242i	$0.853828\pi$
$992$	2268.09	−	3928.46i	0.0725928	−	0.125734i
$993$	−1867.79	−	3649.11i	−0.0596904	−	0.116617i
$994$	1739.40	−	49.5273i	0.0555035	−	0.00158039i
$995$			15372.0i			0.489773i
$996$	−5613.74	−	283.832i	−0.178593	−	0.00902970i
$997$	36113.8	−	20850.3i	1.14718	−	0.662323i	0.198980	−	0.980004i	$-0.436237\pi$
$997$	36113.8	−	20850.3i	1.14718	−	0.662323i	0.948198	+	0.317680i	$0.102904\pi$
$998$	2305.60	−	1331.14i	0.0731287	−	0.0422209i
$999$	26277.7	−	32819.5i	0.832221	−	1.03940i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	42.4.f.a.5.3	✓	16
3.2	odd	2	inner	42.4.f.a.5.8	yes	16
4.3	odd	2		336.4.bc.e.257.3		16
7.2	even	3		294.4.d.a.293.14		16
7.3	odd	6	inner	42.4.f.a.17.8	yes	16
7.4	even	3		294.4.f.a.227.5		16
7.5	odd	6		294.4.d.a.293.11		16
7.6	odd	2		294.4.f.a.215.2		16
12.11	even	2		336.4.bc.e.257.1		16
21.2	odd	6		294.4.d.a.293.3		16
21.5	even	6		294.4.d.a.293.6		16
21.11	odd	6		294.4.f.a.227.2		16
21.17	even	6	inner	42.4.f.a.17.3	yes	16
21.20	even	2		294.4.f.a.215.5		16
28.3	even	6		336.4.bc.e.17.1		16
84.59	odd	6		336.4.bc.e.17.3		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.f.a.5.3	✓	16	1.1	even	1	trivial
42.4.f.a.5.8	yes	16	3.2	odd	2	inner
42.4.f.a.17.3	yes	16	21.17	even	6	inner
42.4.f.a.17.8	yes	16	7.3	odd	6	inner
294.4.d.a.293.3		16	21.2	odd	6
294.4.d.a.293.6		16	21.5	even	6
294.4.d.a.293.11		16	7.5	odd	6
294.4.d.a.293.14		16	7.2	even	3
294.4.f.a.215.2		16	7.6	odd	2
294.4.f.a.215.5		16	21.20	even	2
294.4.f.a.227.2		16	21.11	odd	6
294.4.f.a.227.5		16	7.4	even	3
336.4.bc.e.17.1		16	28.3	even	6
336.4.bc.e.17.3		16	84.59	odd	6
336.4.bc.e.257.1		16	12.11	even	2
336.4.bc.e.257.3		16	4.3	odd	2

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 42 = 2 \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	42.f (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.73205 - 1.00000i) q^{2} +(2.82199 - 4.36307i) q^{3} +(2.00000 + 3.46410i) q^{4} +(2.24534 - 3.88904i) q^{5} +(-9.25090 + 4.73506i) q^{6} +(-9.71288 - 15.7690i) q^{7} -8.00000i q^{8} +(-11.0727 - 24.6251i) q^{9} +O(q^{10})\)	\(q+(-1.73205 - 1.00000i) q^{2} +(2.82199 - 4.36307i) q^{3} +(2.00000 + 3.46410i) q^{4} +(2.24534 - 3.88904i) q^{5} +(-9.25090 + 4.73506i) q^{6} +(-9.71288 - 15.7690i) q^{7} -8.00000i q^{8} +(-11.0727 - 24.6251i) q^{9} +(-7.77808 + 4.49068i) q^{10} +(20.2835 - 11.7107i) q^{11} +(20.7581 + 1.04953i) q^{12} +5.91384i q^{13} +(1.05425 + 37.0255i) q^{14} +(-10.6318 - 20.7714i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(58.0418 + 100.531i) q^{17} +(-5.44659 + 53.7246i) q^{18} +(8.02533 + 4.63343i) q^{19} +17.9627 q^{20} +(-96.2107 - 2.12191i) q^{21} -46.8428 q^{22} +(107.721 + 62.1928i) q^{23} +(-34.9045 - 22.5759i) q^{24} +(52.4169 + 90.7888i) q^{25} +(5.91384 - 10.2431i) q^{26} +(-138.688 - 21.1808i) q^{27} +(35.1995 - 65.1843i) q^{28} -207.807i q^{29} +(-2.35656 + 46.6089i) q^{30} +(122.764 - 70.8780i) q^{31} +(27.7128 - 16.0000i) q^{32} +(6.14540 - 121.546i) q^{33} -232.167i q^{34} +(-83.1348 + 2.36716i) q^{35} +(63.1584 - 87.6072i) q^{36} +(-149.838 + 259.526i) q^{37} +(-9.26685 - 16.0507i) q^{38} +(25.8025 + 16.6888i) q^{39} +(-31.1123 - 17.9627i) q^{40} -508.379 q^{41} +(164.520 + 99.8859i) q^{42} +391.127 q^{43} +(81.1341 + 46.8428i) q^{44} +(-120.630 - 12.2294i) q^{45} +(-124.386 - 215.442i) q^{46} +(-40.2575 + 69.7281i) q^{47} +(37.8805 + 74.0072i) q^{48} +(-154.320 + 306.324i) q^{49} -209.668i q^{50} +(602.419 + 30.4585i) q^{51} +(-20.4862 + 11.8277i) q^{52} +(258.697 - 149.359i) q^{53} +(219.034 + 175.374i) q^{54} -105.178i q^{55} +(-126.152 + 77.7031i) q^{56} +(42.8634 - 21.9396i) q^{57} +(-207.807 + 359.932i) q^{58} +(102.276 + 177.147i) q^{59} +(50.6906 - 78.3725i) q^{60} +(-543.757 - 313.939i) q^{61} -283.512 q^{62} +(-280.764 + 413.786i) q^{63} -64.0000 q^{64} +(22.9992 + 13.2786i) q^{65} +(-132.190 + 204.378i) q^{66} +(51.3894 + 89.0091i) q^{67} +(-232.167 + 402.126i) q^{68} +(575.340 - 294.487i) q^{69} +(146.361 + 79.0348i) q^{70} -46.9785i q^{71} +(-197.001 + 88.5817i) q^{72} +(-228.182 + 131.741i) q^{73} +(519.053 - 299.675i) q^{74} +(544.038 + 27.5067i) q^{75} +37.0674i q^{76} +(-381.677 - 206.105i) q^{77} +(-28.0024 - 54.7084i) q^{78} +(533.634 - 924.281i) q^{79} +(35.9254 + 62.2246i) q^{80} +(-483.790 + 545.333i) q^{81} +(880.538 + 508.379i) q^{82} -270.436 q^{83} +(-185.071 - 337.527i) q^{84} +521.294 q^{85} +(-677.452 - 391.127i) q^{86} +(-906.676 - 586.430i) q^{87} +(-93.6856 - 162.268i) q^{88} +(443.765 - 768.624i) q^{89} +(196.708 + 141.812i) q^{90} +(93.2551 - 57.4405i) q^{91} +497.543i q^{92} +(37.1945 - 735.646i) q^{93} +(139.456 - 80.5151i) q^{94} +(36.0392 - 20.8072i) q^{95} +(8.39628 - 166.065i) q^{96} +219.564i q^{97} +(573.614 - 376.249i) q^{98} +(-512.971 - 369.815i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9	\( 16 q + 32 q^{4} + 80 q^{7} + 18 q^{9} - 36 q^{10} - 128 q^{16} - 48 q^{18} - 342 q^{19} - 450 q^{21} + 24 q^{22} - 48 q^{24} - 194 q^{25} + 88 q^{28} + 360 q^{30} + 804 q^{31} + 1332 q^{33} + 144 q^{36} - 962 q^{37} + 594 q^{39} - 144 q^{40} - 180 q^{42} + 1732 q^{43} - 2394 q^{45} + 168 q^{46} + 820 q^{49} + 1638 q^{51} + 744 q^{52} + 180 q^{54} - 2664 q^{57} - 780 q^{58} - 4620 q^{61} - 2016 q^{63} - 1024 q^{64} - 2016 q^{66} - 706 q^{67} - 60 q^{70} + 192 q^{72} + 3294 q^{73} + 6174 q^{75} + 2832 q^{78} - 2656 q^{79} + 126 q^{81} + 432 q^{82} - 432 q^{84} + 5232 q^{85} + 1026 q^{87} + 48 q^{88} + 4098 q^{91} + 2016 q^{93} + 3888 q^{94} - 192 q^{96} - 4284 q^{99}+O(q^{100}) \) 16 * q + 32 * q^4 + 80 * q^7 + 18 * q^9 - 36 * q^10 - 128 * q^16 - 48 * q^18 - 342 * q^19 - 450 * q^21 + 24 * q^22 - 48 * q^24 - 194 * q^25 + 88 * q^28 + 360 * q^30 + 804 * q^31 + 1332 * q^33 + 144 * q^36 - 962 * q^37 + 594 * q^39 - 144 * q^40 - 180 * q^42 + 1732 * q^43 - 2394 * q^45 + 168 * q^46 + 820 * q^49 + 1638 * q^51 + 744 * q^52 + 180 * q^54 - 2664 * q^57 - 780 * q^58 - 4620 * q^61 - 2016 * q^63 - 1024 * q^64 - 2016 * q^66 - 706 * q^67 - 60 * q^70 + 192 * q^72 + 3294 * q^73 + 6174 * q^75 + 2832 * q^78 - 2656 * q^79 + 126 * q^81 + 432 * q^82 - 432 * q^84 + 5232 * q^85 + 1026 * q^87 + 48 * q^88 + 4098 * q^91 + 2016 * q^93 + 3888 * q^94 - 192 * q^96 - 4284 * q^99

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