LMFDB - Embedded newform 114.4.e.e.49.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [114,4,Mod(7,114)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(114, 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("114.7");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 114 = 2 \cdot 3 \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	114.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:	$6.72621774065$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.6967728.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 8x^{4} + 5x^{3} + 50x^{2} - 7x + 1 $ x^6 - x^5 + 8x^4 + 5x^3 + 50x^2 - 7x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{19}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			49.3
Root			$1.56632 + 2.71294i$ of defining polynomial
Character	$\chi$	$=$	114.49
Dual form			114.4.e.e.7.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.49420 - 11.2483i) q^{5} +(-3.00000 - 5.19615i) q^{6} -25.6033 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.49420 - 11.2483i) q^{5} +(-3.00000 - 5.19615i) q^{6} -25.6033 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-12.9884 - 22.4966i) q^{10} +26.7726 q^{11} -12.0000 q^{12} +(4.29582 + 7.44059i) q^{13} +(-25.6033 + 44.3461i) q^{14} +(-19.4826 - 33.7448i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-4.08468 + 7.07488i) q^{17} -18.0000 q^{18} +(11.5302 - 82.0125i) q^{19} -51.9536 q^{20} +(-38.4049 + 66.5192i) q^{21} +(26.7726 - 46.3715i) q^{22} +(-78.4501 - 135.880i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-21.8492 - 37.8439i) q^{25} +17.1833 q^{26} -27.0000 q^{27} +(51.2065 + 88.6923i) q^{28} +(103.679 + 179.577i) q^{29} -77.9304 q^{30} +94.5197 q^{31} +(16.0000 + 27.7128i) q^{32} +(40.1589 - 69.5573i) q^{33} +(8.16936 + 14.1498i) q^{34} +(-166.273 + 287.993i) q^{35} +(-18.0000 + 31.1769i) q^{36} +197.387 q^{37} +(-130.520 - 101.983i) q^{38} +25.7749 q^{39} +(-51.9536 + 89.9862i) q^{40} +(188.369 - 326.265i) q^{41} +(76.8098 + 133.038i) q^{42} +(254.122 - 440.152i) q^{43} +(-53.5452 - 92.7431i) q^{44} -116.896 q^{45} -313.800 q^{46} +(183.244 + 317.387i) q^{47} +(24.0000 + 41.5692i) q^{48} +312.527 q^{49} -87.3968 q^{50} +(12.2540 + 21.2246i) q^{51} +(17.1833 - 29.7623i) q^{52} +(101.665 + 176.088i) q^{53} +(-27.0000 + 46.7654i) q^{54} +(173.867 - 301.146i) q^{55} +204.826 q^{56} +(-195.780 - 152.975i) q^{57} +414.715 q^{58} +(-296.102 + 512.864i) q^{59} +(-77.9304 + 134.979i) q^{60} +(254.530 + 440.859i) q^{61} +(94.5197 - 163.713i) q^{62} +(115.215 + 199.558i) q^{63} +64.0000 q^{64} +111.592 q^{65} +(-80.3178 - 139.115i) q^{66} +(125.360 + 217.129i) q^{67} +32.6774 q^{68} -470.701 q^{69} +(332.545 + 575.985i) q^{70} +(57.7180 - 99.9706i) q^{71} +(36.0000 + 62.3538i) q^{72} +(416.335 - 721.114i) q^{73} +(197.387 - 341.885i) q^{74} -131.095 q^{75} +(-307.160 + 124.083i) q^{76} -685.466 q^{77} +(25.7749 - 44.6435i) q^{78} +(-184.715 + 319.935i) q^{79} +(103.907 + 179.972i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-376.738 - 652.529i) q^{82} -1288.29 q^{83} +307.239 q^{84} +(53.0535 + 91.8913i) q^{85} +(-508.244 - 880.304i) q^{86} +622.072 q^{87} -214.181 q^{88} +(-30.5372 - 52.8919i) q^{89} +(-116.896 + 202.469i) q^{90} +(-109.987 - 190.503i) q^{91} +(-313.800 + 543.518i) q^{92} +(141.780 - 245.569i) q^{93} +732.975 q^{94} +(-847.621 - 662.300i) q^{95} +96.0000 q^{96} +(-123.755 + 214.350i) q^{97} +(312.527 - 541.312i) q^{98} +(-120.477 - 208.672i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) $ 6 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 - 34 * q^7 - 48 * q^8 - 27 * q^9	\( 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9} + 4 q^{10} - 104 q^{11} - 72 q^{12} - 75 q^{13} - 34 q^{14} + 6 q^{15} - 48 q^{16} + 48 q^{17} - 108 q^{18} + 104 q^{19} + 16 q^{20} - 51 q^{21} - 104 q^{22} + 238 q^{23} - 72 q^{24} - 229 q^{25} - 300 q^{26} - 162 q^{27} + 68 q^{28} + 8 q^{29} + 24 q^{30} + 214 q^{31} + 96 q^{32} - 156 q^{33} - 96 q^{34} + 294 q^{35} - 108 q^{36} + 610 q^{37} - 430 q^{38} - 450 q^{39} + 16 q^{40} - 16 q^{41} + 102 q^{42} + 331 q^{43} + 208 q^{44} + 36 q^{45} + 952 q^{46} + 766 q^{47} + 144 q^{48} + 2284 q^{49} - 916 q^{50} - 144 q^{51} - 300 q^{52} + 118 q^{53} - 162 q^{54} + 1400 q^{55} + 272 q^{56} - 645 q^{57} + 32 q^{58} - 936 q^{59} + 24 q^{60} + 399 q^{61} + 214 q^{62} + 153 q^{63} + 384 q^{64} + 740 q^{65} + 312 q^{66} - 61 q^{67} - 384 q^{68} + 1428 q^{69} - 588 q^{70} - 974 q^{71} + 216 q^{72} - 91 q^{73} + 610 q^{74} - 1374 q^{75} - 1276 q^{76} - 72 q^{77} - 450 q^{78} + 321 q^{79} - 32 q^{80} - 243 q^{81} + 32 q^{82} - 4296 q^{83} + 408 q^{84} + 1680 q^{85} - 662 q^{86} + 48 q^{87} + 832 q^{88} - 1116 q^{89} + 36 q^{90} - 1367 q^{91} + 952 q^{92} + 321 q^{93} + 3064 q^{94} - 4198 q^{95} + 576 q^{96} - 1382 q^{97} + 2284 q^{98} + 468 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 - 34 * q^7 - 48 * q^8 - 27 * q^9 + 4 * q^10 - 104 * q^11 - 72 * q^12 - 75 * q^13 - 34 * q^14 + 6 * q^15 - 48 * q^16 + 48 * q^17 - 108 * q^18 + 104 * q^19 + 16 * q^20 - 51 * q^21 - 104 * q^22 + 238 * q^23 - 72 * q^24 - 229 * q^25 - 300 * q^26 - 162 * q^27 + 68 * q^28 + 8 * q^29 + 24 * q^30 + 214 * q^31 + 96 * q^32 - 156 * q^33 - 96 * q^34 + 294 * q^35 - 108 * q^36 + 610 * q^37 - 430 * q^38 - 450 * q^39 + 16 * q^40 - 16 * q^41 + 102 * q^42 + 331 * q^43 + 208 * q^44 + 36 * q^45 + 952 * q^46 + 766 * q^47 + 144 * q^48 + 2284 * q^49 - 916 * q^50 - 144 * q^51 - 300 * q^52 + 118 * q^53 - 162 * q^54 + 1400 * q^55 + 272 * q^56 - 645 * q^57 + 32 * q^58 - 936 * q^59 + 24 * q^60 + 399 * q^61 + 214 * q^62 + 153 * q^63 + 384 * q^64 + 740 * q^65 + 312 * q^66 - 61 * q^67 - 384 * q^68 + 1428 * q^69 - 588 * q^70 - 974 * q^71 + 216 * q^72 - 91 * q^73 + 610 * q^74 - 1374 * q^75 - 1276 * q^76 - 72 * q^77 - 450 * q^78 + 321 * q^79 - 32 * q^80 - 243 * q^81 + 32 * q^82 - 4296 * q^83 + 408 * q^84 + 1680 * q^85 - 662 * q^86 + 48 * q^87 + 832 * q^88 - 1116 * q^89 + 36 * q^90 - 1367 * q^91 + 952 * q^92 + 321 * q^93 + 3064 * q^94 - 4198 * q^95 + 576 * q^96 - 1382 * q^97 + 2284 * q^98 + 468 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

$n$	$77$	$97$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$3$	1.50000	−	2.59808i	0.288675	−	0.500000i
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	6.49420	−	11.2483i	0.580859	−	1.00608i	−0.414519	−	0.910041i	$-0.636050\pi$
$5$	6.49420	−	11.2483i	0.580859	−	1.00608i	0.995378	−	0.0960362i	$-0.0306165\pi$
$6$	−3.00000	−	5.19615i	−0.204124	−	0.353553i
$7$	−25.6033			−1.38245			−0.691223	−	0.722642i	$-0.742928\pi$
$7$	−25.6033			−1.38245			−0.691223	+	0.722642i	$0.742928\pi$
$8$	−8.00000			−0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−12.9884	−	22.4966i	−0.410729	−	0.711404i
$11$	26.7726			0.733841			0.366920	−	0.930252i	$-0.380412\pi$
$11$	26.7726			0.733841			0.366920	+	0.930252i	$0.380412\pi$
$12$	−12.0000			−0.288675
$13$	4.29582	+	7.44059i	0.0916498	+	0.158742i	0.908205	−	0.418525i	$-0.137453\pi$
$13$	4.29582	+	7.44059i	0.0916498	+	0.158742i	−0.816556	+	0.577267i	$0.804119\pi$
$14$	−25.6033	+	44.3461i	−0.488768	+	0.846572i
$15$	−19.4826	−	33.7448i	−0.335359	−	0.580859i
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−4.08468	+	7.07488i	−0.0582753	+	0.100936i	−0.893691	−	0.448682i	$-0.851893\pi$
$17$	−4.08468	+	7.07488i	−0.0582753	+	0.100936i	0.835416	+	0.549618i	$0.185227\pi$
$18$	−18.0000			−0.235702
$19$	11.5302	−	82.0125i	0.139221	−	0.990261i
$19$	11.5302	−	82.0125i	0.139221	−	0.990261i
$20$	−51.9536			−0.580859
$21$	−38.4049	+	66.5192i	−0.399078	+	0.691223i
$22$	26.7726	−	46.3715i	0.259452	−	0.449384i
$23$	−78.4501	−	135.880i	−0.711217	−	1.23186i	−0.964401	−	0.264445i	$-0.914811\pi$
$23$	−78.4501	−	135.880i	−0.711217	−	1.23186i	0.253184	−	0.967418i	$-0.418522\pi$
$24$	−12.0000	+	20.7846i	−0.102062	+	0.176777i
$25$	−21.8492	−	37.8439i	−0.174794	−	0.302752i
$26$	17.1833			0.129612
$27$	−27.0000			−0.192450
$28$	51.2065	+	88.6923i	0.345611	+	0.598617i
$29$	103.679	+	179.577i	0.663884	+	1.14988i	0.979587	+	0.201023i	$0.0644266\pi$
$29$	103.679	+	179.577i	0.663884	+	1.14988i	−0.315702	+	0.948858i	$0.602240\pi$
$30$	−77.9304			−0.474269
$31$	94.5197			0.547621			0.273810	−	0.961784i	$-0.411716\pi$
$31$	94.5197			0.547621			0.273810	+	0.961784i	$0.411716\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$	40.1589	−	69.5573i	0.211842	−	0.366920i
$34$	8.16936	+	14.1498i	0.0412069	+	0.0713724i
$35$	−166.273	+	287.993i	−0.803006	+	1.39085i
$36$	−18.0000	+	31.1769i	−0.0833333	+	0.144338i
$37$	197.387			0.877035			0.438517	−	0.898723i	$-0.355504\pi$
$37$	197.387			0.877035			0.438517	+	0.898723i	$0.355504\pi$
$38$	−130.520	−	101.983i	−0.557187	−	0.435366i
$39$	25.7749			0.105828
$40$	−51.9536	+	89.9862i	−0.205365	+	0.355702i
$41$	188.369	−	326.265i	0.717519	−	1.24278i	−0.244461	−	0.969659i	$-0.578611\pi$
$41$	188.369	−	326.265i	0.717519	−	1.24278i	0.961980	−	0.273120i	$-0.0880557\pi$
$42$	76.8098	+	133.038i	0.282191	+	0.488768i
$43$	254.122	−	440.152i	0.901238	−	1.56099i	0.0753479	−	0.997157i	$-0.475993\pi$
$43$	254.122	−	440.152i	0.901238	−	1.56099i	0.825890	−	0.563832i	$-0.190673\pi$
$44$	−53.5452	−	92.7431i	−0.183460	−	0.317762i
$45$	−116.896			−0.387239
$46$	−313.800			−1.00581
$47$	183.244	+	317.387i	0.568699	+	0.985015i	0.996695	+	0.0812344i	$0.0258862\pi$
$47$	183.244	+	317.387i	0.568699	+	0.985015i	−0.427996	+	0.903780i	$0.640780\pi$
$48$	24.0000	+	41.5692i	0.0721688	+	0.125000i
$49$	312.527			0.911156
$50$	−87.3968			−0.247196
$51$	12.2540	+	21.2246i	0.0336453	+	0.0582753i
$52$	17.1833	−	29.7623i	0.0458249	−	0.0793711i
$53$	101.665	+	176.088i	0.263485	+	0.456370i	0.967166	−	0.254147i	$-0.0817946\pi$
$53$	101.665	+	176.088i	0.263485	+	0.456370i	−0.703680	+	0.710517i	$0.748461\pi$
$54$	−27.0000	+	46.7654i	−0.0680414	+	0.117851i
$55$	173.867	−	301.146i	0.426258	−	0.738300i
$56$	204.826			0.488768
$57$	−195.780	−	152.975i	−0.454941	−	0.355474i
$58$	414.715			0.938874
$59$	−296.102	+	512.864i	−0.653376	+	1.13168i	0.328922	+	0.944357i	$0.393315\pi$
$59$	−296.102	+	512.864i	−0.653376	+	1.13168i	−0.982298	+	0.187324i	$0.940019\pi$
$60$	−77.9304	+	134.979i	−0.167679	+	0.290429i
$61$	254.530	+	440.859i	0.534250	+	0.925348i	0.999199	+	0.0400106i	$0.0127392\pi$
$61$	254.530	+	440.859i	0.534250	+	0.925348i	−0.464949	+	0.885337i	$0.653927\pi$
$62$	94.5197	−	163.713i	0.193613	−	0.335348i
$63$	115.215	+	199.558i	0.230408	+	0.399078i
$64$	64.0000			0.125000
$65$	111.592			0.212942
$66$	−80.3178	−	139.115i	−0.149795	−	0.259452i
$67$	125.360	+	217.129i	0.228584	+	0.395919i	0.957389	−	0.288803i	$-0.0932572\pi$
$67$	125.360	+	217.129i	0.228584	+	0.395919i	−0.728805	+	0.684721i	$0.759924\pi$
$68$	32.6774			0.0582753
$69$	−470.701			−0.821242
$70$	332.545	+	575.985i	0.567811	+	0.983477i
$71$	57.7180	−	99.9706i	0.0964771	−	0.167103i	−0.813747	−	0.581219i	$-0.802576\pi$
$71$	57.7180	−	99.9706i	0.0964771	−	0.167103i	0.910224	+	0.414116i	$0.135909\pi$
$72$	36.0000	+	62.3538i	0.0589256	+	0.102062i
$73$	416.335	−	721.114i	0.667512	−	1.15616i	−0.311086	−	0.950382i	$-0.600693\pi$
$73$	416.335	−	721.114i	0.667512	−	1.15616i	0.978598	−	0.205782i	$-0.0659739\pi$
$74$	197.387	−	341.885i	0.310079	−	0.537072i
$75$	−131.095			−0.201834
$76$	−307.160	+	124.083i	−0.463601	+	0.187281i
$77$	−685.466			−1.01449
$78$	25.7749	−	44.6435i	0.0374159	−	0.0648062i
$79$	−184.715	+	319.935i	−0.263064	+	0.455640i	−0.967054	−	0.254569i	$-0.918066\pi$
$79$	−184.715	+	319.935i	−0.263064	+	0.455640i	0.703991	+	0.710209i	$0.251400\pi$
$80$	103.907	+	179.972i	0.145215	+	0.251519i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−376.738	−	652.529i	−0.507363	−	0.878778i
$83$	−1288.29			−1.70371			−0.851854	−	0.523780i	$-0.824521\pi$
$83$	−1288.29			−1.70371			−0.851854	+	0.523780i	$0.824521\pi$
$84$	307.239			0.399078
$85$	53.0535	+	91.8913i	0.0676995	+	0.117259i
$86$	−508.244	−	880.304i	−0.637271	−	1.10379i
$87$	622.072			0.766588
$88$	−214.181			−0.259452
$89$	−30.5372	−	52.8919i	−0.0363700	−	0.0629947i	0.847267	−	0.531167i	$-0.178246\pi$
$89$	−30.5372	−	52.8919i	−0.0363700	−	0.0629947i	−0.883637	+	0.468172i	$0.844913\pi$
$90$	−116.896	+	202.469i	−0.136910	+	0.237135i
$91$	−109.987	−	190.503i	−0.126701	−	0.219452i
$92$	−313.800	+	543.518i	−0.355608	+	0.615932i
$93$	141.780	−	245.569i	0.158084	−	0.273810i
$94$	732.975			0.804261
$95$	−847.621	−	662.300i	−0.915411	−	0.715269i
$96$	96.0000			0.102062
$97$	−123.755	+	214.350i	−0.129541	+	0.224371i	−0.923499	−	0.383602i	$-0.874684\pi$
$97$	−123.755	+	214.350i	−0.129541	+	0.224371i	0.793958	+	0.607973i	$0.208017\pi$
$98$	312.527	−	541.312i	0.322142	−	0.557967i
$99$	−120.477	−	208.672i	−0.122307	−	0.211842i
$100$	−87.3968	+	151.376i	−0.0873968	+	0.151376i
$101$	423.006	+	732.668i	0.416739	+	0.721813i	0.995609	−	0.0936064i	$-0.0298395\pi$
$101$	423.006	+	732.668i	0.416739	+	0.721813i	−0.578870	+	0.815420i	$0.696506\pi$
$102$	49.0162			0.0475816
$103$	−1422.55			−1.36085			−0.680427	−	0.732816i	$-0.738206\pi$
$103$	−1422.55			−1.36085			−0.680427	+	0.732816i	$0.738206\pi$
$104$	−34.3666	−	59.5247i	−0.0324031	−	0.0561238i
$105$	498.818	+	863.978i	0.463616	+	0.803006i
$106$	406.659			0.372624
$107$	286.239			0.258615			0.129307	−	0.991605i	$-0.458725\pi$
$107$	286.239			0.258615			0.129307	+	0.991605i	$0.458725\pi$
$108$	54.0000	+	93.5307i	0.0481125	+	0.0833333i
$109$	16.1427	−	27.9600i	0.0141852	−	0.0245695i	−0.858846	−	0.512234i	$-0.828818\pi$
$109$	16.1427	−	27.9600i	0.0141852	−	0.0245695i	0.873031	+	0.487665i	$0.162151\pi$
$110$	−347.733	−	602.292i	−0.301410	−	0.522057i
$111$	296.081	−	512.827i	0.253178	−	0.438517i
$112$	204.826	−	354.769i	0.172806	−	0.299308i
$113$	−297.098			−0.247333			−0.123666	−	0.992324i	$-0.539465\pi$
$113$	−297.098			−0.247333			−0.123666	+	0.992324i	$0.539465\pi$
$114$	−460.740	+	186.125i	−0.378529	+	0.152914i
$115$	−2037.88			−1.65247
$116$	414.715	−	718.307i	0.331942	−	0.574941i
$117$	38.6624	−	66.9653i	0.0305499	−	0.0529140i
$118$	592.204	+	1025.73i	0.462007	+	0.800219i
$119$	104.581	−	181.140i	0.0805625	−	0.139538i
$120$	155.861	+	269.959i	0.118567	+	0.205365i
$121$	−614.227			−0.461478
$122$	1018.12			0.755543
$123$	−565.107	−	978.794i	−0.414260	−	0.717519i
$124$	−189.039	−	327.426i	−0.136905	−	0.237127i
$125$	1055.98			0.755596
$126$	460.859			0.325846
$127$	−1333.60	−	2309.86i	−0.931792	−	1.61391i	−0.780258	−	0.625458i	$-0.784912\pi$
$127$	−1333.60	−	2309.86i	−0.931792	−	1.61391i	−0.151534	−	0.988452i	$-0.548421\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$	−762.365	−	1320.46i	−0.520330	−	0.901238i
$130$	111.592	−	193.283i	0.0752865	−	0.130400i
$131$	−411.138	+	712.112i	−0.274208	+	0.474943i	−0.969935	−	0.243364i	$-0.921749\pi$
$131$	−411.138	+	712.112i	−0.274208	+	0.474943i	0.695727	+	0.718307i	$0.255082\pi$
$132$	−321.271			−0.211842
$133$	−295.210	+	2099.79i	−0.192466	+	1.36898i
$134$	501.438			0.323266
$135$	−175.343	+	303.704i	−0.111786	+	0.193620i
$136$	32.6774	−	56.5990i	0.0206034	−	0.0356862i
$137$	1222.61	+	2117.62i	0.762443	+	1.32059i	0.941588	+	0.336768i	$0.109334\pi$
$137$	1222.61	+	2117.62i	0.762443	+	1.32059i	−0.179144	+	0.983823i	$0.557333\pi$
$138$	−470.701	+	815.277i	−0.290353	+	0.502906i
$139$	−752.171	−	1302.80i	−0.458980	−	0.794977i	0.539927	−	0.841712i	$-0.318452\pi$
$139$	−752.171	−	1302.80i	−0.458980	−	0.794977i	−0.998907	+	0.0467345i	$0.985119\pi$
$140$	1330.18			0.803006
$141$	1099.46			0.656677
$142$	−115.436	−	199.941i	−0.0682196	−	0.118160i
$143$	115.010	+	199.204i	0.0672564	+	0.116491i
$144$	144.000			0.0833333
$145$	2693.24			1.54249
$146$	−832.671	−	1442.23i	−0.472002	−	0.817532i
$147$	468.790	−	811.968i	0.263028	−	0.455578i
$148$	−394.775	−	683.770i	−0.219259	−	0.379767i
$149$	360.374	−	624.186i	0.198141	−	0.343190i	−0.749785	−	0.661682i	$-0.769843\pi$
$149$	360.374	−	624.186i	0.198141	−	0.343190i	0.947926	+	0.318492i	$0.103176\pi$
$150$	−131.095	+	227.064i	−0.0713592	+	0.123598i
$151$	1801.25			0.970752			0.485376	−	0.874306i	$-0.338683\pi$
$151$	1801.25			0.970752			0.485376	+	0.874306i	$0.338683\pi$
$152$	−92.2414	+	656.100i	−0.0492222	+	0.350110i
$153$	73.5243			0.0388502
$154$	−685.466	+	1187.26i	−0.358678	+	0.621249i
$155$	613.830	−	1063.18i	0.318090	−	0.550948i
$156$	−51.5499	−	89.2870i	−0.0264570	−	0.0458249i
$157$	−1914.55	+	3316.11i	−0.973236	+	1.68569i	−0.287599	+	0.957751i	$0.592857\pi$
$157$	−1914.55	+	3316.11i	−0.973236	+	1.68569i	−0.685637	+	0.727943i	$0.740476\pi$
$158$	369.429	+	639.870i	0.186014	+	0.322186i
$159$	609.988			0.304247
$160$	415.629			0.205365
$161$	2008.58	+	3478.96i	0.983218	+	1.70298i
$162$	81.0000	+	140.296i	0.0392837	+	0.0680414i
$163$	−956.496			−0.459623			−0.229812	−	0.973235i	$-0.573811\pi$
$163$	−956.496			−0.459623			−0.229812	+	0.973235i	$0.573811\pi$
$164$	−1506.95			−0.717519
$165$	−521.600	−	903.438i	−0.246100	−	0.426258i
$166$	−1288.29	+	2231.38i	−0.602351	+	1.04330i
$167$	1389.88	+	2407.35i	0.644027	+	1.11549i	0.984525	+	0.175242i	$0.0560708\pi$
$167$	1389.88	+	2407.35i	0.644027	+	1.11549i	−0.340499	+	0.940245i	$0.610596\pi$
$168$	307.239	−	532.154i	0.141095	−	0.244384i
$169$	1061.59	−	1838.73i	0.483201	−	0.836928i
$170$	212.214			0.0957415
$171$	−691.110	+	279.188i	−0.309067	+	0.124854i
$172$	−2032.97			−0.901238
$173$	154.776	−	268.080i	0.0680196	−	0.117813i	−0.830010	−	0.557749i	$-0.811665\pi$
$173$	154.776	−	268.080i	0.0680196	−	0.117813i	0.898029	+	0.439935i	$0.144999\pi$
$174$	622.072	−	1077.46i	0.271030	−	0.469437i
$175$	559.411	+	968.928i	0.241643	+	0.418538i
$176$	−214.181	+	370.972i	−0.0917301	+	0.158881i
$177$	888.306	+	1538.59i	0.377227	+	0.653376i
$178$	−122.149			−0.0514350
$179$	4650.29			1.94178			0.970890	−	0.239524i	$-0.0769913\pi$
$179$	4650.29			1.94178			0.970890	+	0.239524i	$0.0769913\pi$
$180$	233.791	+	404.938i	0.0968098	+	0.167679i
$181$	134.864	+	233.591i	0.0553833	+	0.0959266i	0.892388	−	0.451269i	$-0.149029\pi$
$181$	134.864	+	233.591i	0.0553833	+	0.0959266i	−0.837005	+	0.547196i	$0.815695\pi$
$182$	−439.948			−0.179182
$183$	1527.18			0.616899
$184$	627.601	+	1087.04i	0.251453	+	0.435529i
$185$	1281.87	−	2220.27i	0.509433	−	0.882364i
$186$	−283.559	−	491.139i	−0.111783	−	0.193613i
$187$	−109.358	+	189.413i	−0.0427648	+	0.0740708i
$188$	732.975	−	1269.55i	0.284349	−	0.492507i
$189$	691.288			0.266052
$190$	−1994.76	+	805.822i	−0.761658	+	0.307687i
$191$	−1949.96			−0.738715			−0.369357	−	0.929287i	$-0.620422\pi$
$191$	−1949.96			−0.738715			−0.369357	+	0.929287i	$0.620422\pi$
$192$	96.0000	−	166.277i	0.0360844	−	0.0625000i
$193$	−1465.65	+	2538.58i	−0.546631	+	0.946793i	0.451871	+	0.892083i	$0.350757\pi$
$193$	−1465.65	+	2538.58i	−0.546631	+	0.946793i	−0.998502	+	0.0547095i	$0.982577\pi$
$194$	247.510	+	428.701i	0.0915990	+	0.158654i
$195$	167.388	−	289.924i	0.0614712	−	0.106471i
$196$	−625.053	−	1082.62i	−0.227789	−	0.394542i
$197$	−1236.48			−0.447186			−0.223593	−	0.974683i	$-0.571779\pi$
$197$	−1236.48			−0.447186			−0.223593	+	0.974683i	$0.571779\pi$
$198$	−481.907			−0.172968
$199$	2254.50	+	3904.91i	0.803103	+	1.39102i	0.917564	+	0.397588i	$0.130153\pi$
$199$	2254.50	+	3904.91i	0.803103	+	1.39102i	−0.114461	+	0.993428i	$0.536514\pi$
$200$	174.794	+	302.752i	0.0617989	+	0.107039i
$201$	752.157			0.263946
$202$	1692.02			0.589358
$203$	−2654.51	−	4597.75i	−0.917784	−	1.58965i
$204$	49.0162	−	84.8985i	0.0168226	−	0.0291377i
$205$	−2446.61	−	4237.65i	−0.833554	−	1.44376i
$206$	−1422.55	+	2463.93i	−0.481135	+	0.833350i
$207$	−706.051	+	1222.92i	−0.237072	+	0.410621i
$208$	−137.466			−0.0458249
$209$	308.693	−	2195.69i	0.102166	−	0.726694i
$210$	1995.27			0.655651
$211$	0.952349	−	1.64952i	0.000310722	−	0.000538187i	−0.865870	−	0.500269i	$-0.833234\pi$
$211$	0.952349	−	1.64952i	0.000310722	−	0.000538187i	0.866181	+	0.499731i	$0.166568\pi$
$212$	406.659	−	704.354i	0.131743	−	0.228185i
$213$	−173.154	−	299.912i	−0.0557011	−	0.0964771i
$214$	286.239	−	495.781i	0.0914342	−	0.158369i
$215$	−3300.63	−	5716.87i	−1.04698	−	1.81343i
$216$	216.000			0.0680414
$217$	−2420.01			−0.757056
$218$	−32.2854	−	55.9200i	−0.0100305	−	0.0173733i
$219$	−1249.01	−	2163.34i	−0.385388	−	0.667512i
$220$	−1390.93			−0.426258
$221$	−70.1883			−0.0213637
$222$	−592.162	−	1025.65i	−0.179024	−	0.310079i
$223$	2330.11	−	4035.88i	0.699713	−	1.21194i	−0.268853	−	0.963181i	$-0.586645\pi$
$223$	2330.11	−	4035.88i	0.699713	−	1.21194i	0.968566	−	0.248757i	$-0.0800220\pi$
$224$	−409.652	−	709.538i	−0.122192	−	0.211643i
$225$	−196.643	+	340.595i	−0.0582646	+	0.100917i
$226$	−297.098	+	514.588i	−0.0874453	+	0.151460i
$227$	−4045.15			−1.18276			−0.591380	−	0.806393i	$-0.701416\pi$
$227$	−4045.15			−1.18276			−0.591380	+	0.806393i	$0.701416\pi$
$228$	−138.362	+	984.150i	−0.0401897	+	0.285864i
$229$	5062.73			1.46094			0.730468	−	0.682947i	$-0.239302\pi$
$229$	5062.73			1.46094			0.730468	+	0.682947i	$0.239302\pi$
$230$	−2037.88	+	3529.72i	−0.584235	+	1.01192i
$231$	−1028.20	+	1780.89i	−0.292859	+	0.507247i
$232$	−829.429	−	1436.61i	−0.234719	−	0.406544i
$233$	−216.545	+	375.066i	−0.0608854	+	0.105457i	−0.894861	−	0.446344i	$-0.852726\pi$
$233$	−216.545	+	375.066i	−0.0608854	+	0.105457i	0.833976	+	0.551801i	$0.186059\pi$
$234$	−77.3248	−	133.931i	−0.0216021	−	0.0374159i
$235$	4760.08			1.32133
$236$	2368.82			0.653376
$237$	554.144	+	959.806i	0.151880	+	0.263064i
$238$	−209.162	−	362.280i	−0.0569663	−	0.0986685i
$239$	−4165.22			−1.12730			−0.563652	−	0.826012i	$-0.690604\pi$
$239$	−4165.22			−1.12730			−0.563652	+	0.826012i	$0.690604\pi$
$240$	623.443			0.167679
$241$	−2084.71	−	3610.82i	−0.557212	−	0.965119i	−0.997728	−	0.0673743i	$-0.978538\pi$
$241$	−2084.71	−	3610.82i	−0.557212	−	0.965119i	0.440516	−	0.897745i	$-0.354795\pi$
$242$	−614.227	+	1063.87i	−0.163157	+	0.282596i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	1018.12	−	1763.44i	0.267125	−	0.462674i
$245$	2029.61	−	3515.39i	0.529253	−	0.916693i
$246$	−2260.43			−0.585852
$247$	659.753	−	266.520i	0.169956	−	0.0686570i
$248$	−756.158			−0.193613
$249$	−1932.43	+	3347.06i	−0.491818	+	0.851854i
$250$	1055.98	−	1829.01i	0.267143	−	0.462706i
$251$	3566.12	+	6176.71i	0.896780	+	1.55327i	0.831587	+	0.555395i	$0.187433\pi$
$251$	3566.12	+	6176.71i	0.896780	+	1.55327i	0.0651931	+	0.997873i	$0.479234\pi$
$252$	460.859	−	798.230i	0.115204	−	0.199539i
$253$	−2100.31	−	3637.85i	−0.521920	−	0.903991i
$254$	−5334.38			−1.31775
$255$	318.321			0.0781726
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	538.758	+	933.157i	0.130766	+	0.226493i	0.923972	−	0.382460i	$-0.124923\pi$
$257$	538.758	+	933.157i	0.130766	+	0.226493i	−0.793206	+	0.608953i	$0.791590\pi$
$258$	−3049.46			−0.735857
$259$	−5053.76			−1.21245
$260$	−223.183	−	386.565i	−0.0532356	−	0.0922067i
$261$	933.108	−	1616.19i	0.221295	−	0.383294i
$262$	822.276	+	1424.22i	0.193895	+	0.335835i
$263$	−1244.58	+	2155.68i	−0.291803	+	0.505417i	−0.974236	−	0.225530i	$-0.927588\pi$
$263$	−1244.58	+	2155.68i	−0.291803	+	0.505417i	0.682433	+	0.730948i	$0.260922\pi$
$264$	−321.271	+	556.458i	−0.0748973	+	0.129726i
$265$	2640.92			0.612191
$266$	3341.73	+	2611.11i	0.770280	+	0.601869i
$267$	−183.223			−0.0419965
$268$	501.438	−	868.517i	0.114292	−	0.197959i
$269$	3090.64	−	5353.14i	0.700519	−	1.21333i	−0.267765	−	0.963484i	$-0.586285\pi$
$269$	3090.64	−	5353.14i	0.700519	−	1.21333i	0.968284	−	0.249850i	$-0.0803814\pi$
$270$	350.687	+	607.407i	0.0790449	+	0.136910i
$271$	−3016.36	+	5224.48i	−0.676128	+	1.17109i	0.300010	+	0.953936i	$0.403010\pi$
$271$	−3016.36	+	5224.48i	−0.676128	+	1.17109i	−0.976138	+	0.217152i	$0.930323\pi$
$272$	−65.3549	−	113.198i	−0.0145688	−	0.0252340i
$273$	−659.923			−0.146302
$274$	4890.45			1.07826
$275$	−584.961	−	1013.18i	−0.128271	−	0.222171i
$276$	941.401	+	1630.55i	0.205311	+	0.355608i
$277$	912.717			0.197978			0.0989889	−	0.995089i	$-0.468439\pi$
$277$	912.717			0.197978			0.0989889	+	0.995089i	$0.468439\pi$
$278$	−3008.68			−0.649096
$279$	−425.339	−	736.708i	−0.0912701	−	0.158084i
$280$	1330.18	−	2303.94i	0.283905	−	0.491739i
$281$	167.443	+	290.020i	0.0355474	+	0.0615699i	0.883252	−	0.468899i	$-0.155349\pi$
$281$	167.443	+	290.020i	0.0355474	+	0.0615699i	−0.847704	+	0.530469i	$0.822016\pi$
$282$	1099.46	−	1904.32i	0.232170	−	0.402131i
$283$	1388.47	−	2404.90i	0.291646	−	0.505146i	−0.682553	−	0.730836i	$-0.739130\pi$
$283$	1388.47	−	2404.90i	0.291646	−	0.505146i	0.974199	+	0.225690i	$0.0724637\pi$
$284$	−461.744			−0.0964771
$285$	−2992.14	+	1208.73i	−0.621891	+	0.251225i
$286$	460.042			0.0951149
$287$	−4822.86	+	8353.43i	−0.991931	+	1.71808i
$288$	144.000	−	249.415i	0.0294628	−	0.0510310i
$289$	2423.13	+	4196.99i	0.493208	+	0.854261i
$290$	2693.24	−	4664.83i	0.545353	−	0.944580i
$291$	371.266	+	643.051i	0.0747903	+	0.129541i
$292$	−3330.68			−0.667512
$293$	−3067.85			−0.611692			−0.305846	−	0.952081i	$-0.598939\pi$
$293$	−3067.85			−0.611692			−0.305846	+	0.952081i	$0.598939\pi$
$294$	−937.580	−	1623.94i	−0.185989	−	0.322142i
$295$	3845.89	+	6661.28i	0.759039	+	1.31469i
$296$	−1579.10			−0.310079
$297$	−722.861			−0.141228
$298$	−720.747	−	1248.37i	−0.140107	−	0.242672i
$299$	674.016	−	1167.43i	0.130366	−	0.225800i
$300$	262.191	+	454.127i	0.0504586	+	0.0873968i
$301$	−6506.35	+	11269.3i	−1.24591	+	2.15798i
$302$	1801.25	−	3119.85i	0.343213	−	0.594462i
$303$	2538.04			0.481209
$304$	1044.16	+	815.867i	0.196995	+	0.153925i
$305$	6611.88			1.24129
$306$	73.5243	−	127.348i	0.0137356	−	0.0237908i
$307$	3743.90	−	6484.63i	0.696013	−	1.20553i	−0.273825	−	0.961779i	$-0.588289\pi$
$307$	3743.90	−	6484.63i	0.696013	−	1.20553i	0.969838	−	0.243750i	$-0.0783776\pi$
$308$	1370.93	+	2374.52i	0.253624	+	0.439289i
$309$	−2133.82	+	3695.89i	−0.392845	+	0.680427i
$310$	−1227.66	−	2126.37i	−0.224924	−	0.389579i
$311$	−6681.88			−1.21831			−0.609156	−	0.793051i	$-0.708492\pi$
$311$	−6681.88			−1.21831			−0.609156	+	0.793051i	$0.708492\pi$
$312$	−206.200			−0.0374159
$313$	−4081.01	−	7068.52i	−0.736972	−	1.27647i	−0.953853	−	0.300275i	$-0.902921\pi$
$313$	−4081.01	−	7068.52i	−0.736972	−	1.27647i	0.216880	−	0.976198i	$-0.430412\pi$
$314$	3829.11	+	6632.21i	0.688182	+	1.19197i
$315$	2992.91			0.535337
$316$	1477.72			0.263064
$317$	1419.77	+	2459.11i	0.251553	+	0.435702i	0.963954	−	0.266071i	$-0.0857255\pi$
$317$	1419.77	+	2459.11i	0.251553	+	0.435702i	−0.712401	+	0.701773i	$0.752392\pi$
$318$	609.988	−	1056.53i	0.107567	−	0.186312i
$319$	2775.75	+	4807.74i	0.487185	+	0.843830i
$320$	415.629	−	719.890i	0.0726073	−	0.125760i
$321$	429.359	−	743.672i	0.0746557	−	0.129307i
$322$	8034.31			1.39048
$323$	533.131	+	416.570i	0.0918397	+	0.0717602i
$324$	324.000			0.0555556
$325$	187.721	−	325.142i	0.0320396	−	0.0554942i
$326$	−956.496	+	1656.70i	−0.162501	+	0.281461i
$327$	−48.4281	−	83.8799i	−0.00818985	−	0.0141852i
$328$	−1506.95	+	2610.12i	−0.253681	+	0.439389i
$329$	−4691.63	−	8126.15i	−0.786195	−	1.36173i
$330$	−2086.40			−0.348038
$331$	11056.2			1.83597			0.917984	−	0.396617i	$-0.129816\pi$
$331$	11056.2			1.83597			0.917984	+	0.396617i	$0.129816\pi$
$332$	2576.57	+	4462.75i	0.425927	+	0.737727i
$333$	−888.243	−	1538.48i	−0.146172	−	0.253178i
$334$	5559.54			0.910791
$335$	3256.44			0.531099
$336$	−614.478	−	1064.31i	−0.0997694	−	0.172806i
$337$	2525.16	−	4373.71i	0.408174	−	0.706977i	−0.586512	−	0.809941i	$-0.699499\pi$
$337$	2525.16	−	4373.71i	0.408174	−	0.706977i	0.994685	+	0.102964i	$0.0328325\pi$
$338$	−2123.18	−	3677.46i	−0.341674	−	0.591797i
$339$	−445.646	+	771.882i	−0.0713988	+	0.123666i
$340$	212.214	−	367.565i	0.0338497	−	0.0586295i
$341$	2530.54			0.401866
$342$	−207.543	+	1476.23i	−0.0328148	+	0.233407i
$343$	780.217			0.122822
$344$	−2032.97	+	3521.22i	−0.318636	+	0.551893i
$345$	−3056.82	+	5294.57i	−0.477026	+	0.826233i
$346$	−309.552	−	536.160i	−0.0480972	−	0.0833067i
$347$	3007.43	−	5209.01i	0.465265	−	0.805863i	−0.533948	−	0.845517i	$-0.679292\pi$
$347$	3007.43	−	5209.01i	0.465265	−	0.805863i	0.999213	+	0.0396541i	$0.0126256\pi$
$348$	−1244.14	−	2154.92i	−0.191647	−	0.331942i
$349$	−2514.51			−0.385669			−0.192834	−	0.981231i	$-0.561768\pi$
$349$	−2514.51			−0.385669			−0.192834	+	0.981231i	$0.561768\pi$
$350$	2237.64			0.341735
$351$	−115.987	−	200.896i	−0.0176380	−	0.0305499i
$352$	428.362	+	741.945i	0.0648630	+	0.112346i
$353$	4578.03			0.690266			0.345133	−	0.938554i	$-0.387834\pi$
$353$	4578.03			0.690266			0.345133	+	0.938554i	$0.387834\pi$
$354$	3553.23			0.533480
$355$	−749.665	−	1298.46i	−0.112079	−	0.194127i
$356$	−122.149	+	211.568i	−0.0181850	+	0.0314974i
$357$	−313.743	−	543.419i	−0.0465128	−	0.0805625i
$358$	4650.29	−	8054.53i	0.686523	−	1.18909i
$359$	−3986.22	+	6904.33i	−0.586029	+	1.01503i	0.408717	+	0.912661i	$0.365976\pi$
$359$	−3986.22	+	6904.33i	−0.586029	+	1.01503i	−0.994746	+	0.102371i	$0.967357\pi$
$360$	935.164			0.136910
$361$	−6593.11	−	1891.24i	−0.961235	−	0.275731i
$362$	539.456			0.0783238
$363$	−921.341	+	1595.81i	−0.133217	+	0.230739i
$364$	−439.948	+	762.013i	−0.0633504	+	0.109726i
$365$	−5407.53	−	9366.11i	−0.775460	−	1.34314i
$366$	1527.18	−	2645.15i	0.218107	−	0.377772i
$367$	−2732.75	−	4733.26i	−0.388688	−	0.673227i	0.603585	−	0.797298i	$-0.293738\pi$
$367$	−2732.75	−	4733.26i	−0.388688	−	0.673227i	−0.992273	+	0.124071i	$0.960405\pi$
$368$	2510.40			0.355608
$369$	−3390.64			−0.478346
$370$	−2563.75	−	4440.54i	−0.360224	−	0.623926i
$371$	−2602.95	−	4508.44i	−0.364254	−	0.630907i
$372$	−1134.24			−0.158084
$373$	9245.54			1.28342			0.641710	−	0.766947i	$-0.278225\pi$
$373$	9245.54			1.28342			0.641710	+	0.766947i	$0.278225\pi$
$374$	218.715	+	378.826i	0.0302393	+	0.0523760i
$375$	1583.97	−	2743.51i	0.218122	−	0.377798i
$376$	−1465.95	−	2539.10i	−0.201065	−	0.348255i
$377$	−890.771	+	1542.86i	−0.121690	+	0.210773i
$378$	691.288	−	1197.35i	0.0940635	−	0.162923i
$379$	6098.42			0.826530			0.413265	−	0.910611i	$-0.364388\pi$
$379$	6098.42			0.826530			0.413265	+	0.910611i	$0.364388\pi$
$380$	−599.034	+	4260.84i	−0.0808679	+	0.575202i
$381$	−8001.58			−1.07594
$382$	−1949.96	+	3377.44i	−0.261175	+	0.452368i
$383$	−2264.90	+	3922.93i	−0.302170	+	0.523374i	−0.976627	−	0.214940i	$-0.931044\pi$
$383$	−2264.90	+	3922.93i	−0.302170	+	0.523374i	0.674457	+	0.738314i	$0.264378\pi$
$384$	−192.000	−	332.554i	−0.0255155	−	0.0441942i
$385$	−4451.55	+	7710.32i	−0.589278	+	1.02066i
$386$	2931.30	+	5077.16i	0.386526	+	0.669484i
$387$	−4574.19			−0.600825
$388$	990.042			0.129541
$389$	2779.46	+	4814.17i	0.362273	+	0.627475i	0.988335	−	0.152298i	$-0.0486674\pi$
$389$	2779.46	+	4814.17i	0.362273	+	0.627475i	−0.626061	+	0.779774i	$0.715334\pi$
$390$	−334.775	−	579.848i	−0.0434667	−	0.0752865i
$391$	1281.77			0.165786
$392$	−2500.21			−0.322142
$393$	1233.41	+	2136.34i	0.158314	+	0.274208i
$394$	−1236.48	+	2141.65i	−0.158104	+	0.273844i
$395$	2399.15	+	4155.45i	0.305606	+	0.529324i
$396$	−481.907	+	834.688i	−0.0611534	+	0.105921i
$397$	−4695.83	+	8133.41i	−0.593645	+	1.02822i	0.400092	+	0.916475i	$0.368978\pi$
$397$	−4695.83	+	8133.41i	−0.593645	+	1.02822i	−0.993737	+	0.111748i	$0.964355\pi$
$398$	9018.01			1.13576
$399$	5012.59	+	3916.66i	0.628931	+	0.491424i
$400$	699.175			0.0873968
$401$	−4766.06	+	8255.07i	−0.593531	+	1.02803i	0.400222	+	0.916418i	$0.368933\pi$
$401$	−4766.06	+	8255.07i	−0.593531	+	1.02803i	−0.993752	+	0.111607i	$0.964400\pi$
$402$	752.157	−	1302.77i	0.0933189	−	0.161633i
$403$	406.040	+	703.282i	0.0501893	+	0.0869304i
$404$	1692.02	−	2930.67i	0.208370	−	0.360907i
$405$	526.030	+	911.111i	0.0645399	+	0.111786i
$406$	−10618.0			−1.29794
$407$	5284.58			0.643604
$408$	−98.0323	−	169.797i	−0.0118954	−	0.0206034i
$409$	−3289.74	−	5698.00i	−0.397720	−	0.688871i	0.595725	−	0.803189i	$-0.296865\pi$
$409$	−3289.74	−	5698.00i	−0.397720	−	0.688871i	−0.993444	+	0.114318i	$0.963532\pi$
$410$	−9786.44			−1.17882
$411$	7335.67			0.880394
$412$	2845.10	+	4927.86i	0.340214	+	0.589267i
$413$	7581.18	−	13131.0i	0.903258	−	1.56449i
$414$	1412.10	+	2445.83i	0.167635	+	0.290353i
$415$	−8366.38	+	14491.0i	−0.989613	+	1.71406i
$416$	−137.466	+	238.099i	−0.0162015	+	0.0280619i
$417$	−4513.02			−0.529985
$418$	−3494.35	−	2730.36i	−0.408886	−	0.319489i
$419$	4136.42			0.482285			0.241143	−	0.970490i	$-0.422478\pi$
$419$	4136.42			0.482285			0.241143	+	0.970490i	$0.422478\pi$
$420$	1995.27	−	3455.91i	0.231808	−	0.401503i
$421$	−3896.23	+	6748.47i	−0.451047	+	0.781235i	−0.998451	−	0.0556325i	$-0.982282\pi$
$421$	−3896.23	+	6748.47i	−0.451047	+	0.781235i	0.547405	+	0.836868i	$0.315616\pi$
$422$	−1.90470	−	3.29903i	−0.000219714	−	0.000380555i
$423$	1649.19	−	2856.49i	0.189566	−	0.328338i
$424$	−813.317	−	1408.71i	−0.0931561	−	0.161351i
$425$	356.988			0.0407446
$426$	−692.617			−0.0787732
$427$	−6516.80	−	11287.4i	−0.738571	−	1.27924i
$428$	−572.479	−	991.562i	−0.0646537	−	0.111984i
$429$	690.063			0.0776610
$430$	−13202.5			−1.48066
$431$	3675.30	+	6365.80i	0.410749	+	0.711438i	0.994972	−	0.100155i	$-0.0319340\pi$
$431$	3675.30	+	6365.80i	0.410749	+	0.711438i	−0.584223	+	0.811593i	$0.698601\pi$
$432$	216.000	−	374.123i	0.0240563	−	0.0416667i
$433$	−5346.31	−	9260.08i	−0.593365	−	1.02774i	−0.993775	−	0.111403i	$-0.964466\pi$
$433$	−5346.31	−	9260.08i	−0.593365	−	1.02774i	0.400410	−	0.916336i	$-0.368868\pi$
$434$	−2420.01	+	4191.58i	−0.267660	+	0.463600i
$435$	4039.86	−	6997.24i	0.445279	−	0.771246i
$436$	−129.142			−0.0141852
$437$	−12048.4	+	4867.18i	−1.31888	+	0.532789i
$438$	−4996.02			−0.545021
$439$	4809.83	−	8330.87i	0.522917	−	0.905719i	−0.476727	−	0.879051i	$-0.658177\pi$
$439$	4809.83	−	8330.87i	0.522917	−	0.905719i	0.999644	−	0.0266676i	$-0.00848958\pi$
$440$	−1390.93	+	2409.17i	−0.150705	+	0.261029i
$441$	−1406.37	−	2435.90i	−0.151859	−	0.263028i
$442$	−70.1883	+	121.570i	−0.00755321	+	0.0130825i
$443$	−6302.23	−	10915.8i	−0.675909	−	1.17071i	−0.976202	−	0.216862i	$-0.930418\pi$
$443$	−6302.23	−	10915.8i	−0.675909	−	1.17071i	0.300293	−	0.953847i	$-0.402916\pi$
$444$	−2368.65			−0.253178
$445$	−793.258			−0.0845034
$446$	−4660.23	−	8071.75i	−0.494772	−	0.856970i
$447$	−1081.12	−	1872.56i	−0.114397	−	0.198141i
$448$	−1638.61			−0.172806
$449$	14957.9			1.57218			0.786088	−	0.618114i	$-0.212103\pi$
$449$	14957.9			1.57218			0.786088	+	0.618114i	$0.212103\pi$
$450$	393.286	+	681.191i	0.0411993	+	0.0713592i
$451$	5043.13	−	8734.96i	0.526545	−	0.912002i
$452$	594.195	+	1029.18i	0.0618332	+	0.107098i
$453$	2701.87	−	4679.78i	0.280232	−	0.485376i
$454$	−4045.15	+	7006.41i	−0.418168	+	0.724289i
$455$	−2857.11			−0.294381
$456$	1566.24	+	1223.80i	0.160846	+	0.125679i
$457$	−2003.50			−0.205076			−0.102538	−	0.994729i	$-0.532696\pi$
$457$	−2003.50			−0.205076			−0.102538	+	0.994729i	$0.532696\pi$
$458$	5062.73	−	8768.90i	0.516519	−	0.894637i
$459$	110.286	−	191.022i	0.0112151	−	0.0194251i
$460$	4075.76	+	7059.43i	0.413116	+	0.715538i
$461$	567.329	−	982.642i	0.0573170	−	0.0992759i	−0.835943	−	0.548816i	$-0.815079\pi$
$461$	567.329	−	982.642i	0.0573170	−	0.0992759i	0.893260	+	0.449540i	$0.148412\pi$
$462$	2056.40	+	3561.79i	0.207083	+	0.358678i
$463$	−2934.33			−0.294536			−0.147268	−	0.989097i	$-0.547048\pi$
$463$	−2934.33			−0.294536			−0.147268	+	0.989097i	$0.547048\pi$
$464$	−3317.72			−0.331942
$465$	−1841.49	−	3189.55i	−0.183649	−	0.318090i
$466$	433.089	+	750.132i	0.0430525	+	0.0745691i
$467$	−930.578			−0.0922098			−0.0461049	−	0.998937i	$-0.514681\pi$
$467$	−930.578			−0.0922098			−0.0461049	+	0.998937i	$0.514681\pi$
$468$	−309.299			−0.0305499
$469$	−3209.61	−	5559.21i	−0.316005	−	0.547336i
$470$	4760.08	−	8244.70i	0.467162	−	0.809149i
$471$	5743.66	+	9948.32i	0.561898	+	0.973236i
$472$	2368.82	−	4102.91i	0.231003	−	0.400110i
$473$	6803.51	−	11784.0i	0.661365	−	1.14552i
$474$	2216.58			0.214791
$475$	−3355.60	+	1355.56i	−0.324138	+	0.130942i
$476$	−836.649			−0.0805625
$477$	914.982	−	1584.80i	0.0878284	−	0.152123i
$478$	−4165.22	+	7214.38i	−0.398562	+	0.690330i
$479$	−7799.60	−	13509.3i	−0.743994	−	1.28863i	−0.950663	−	0.310224i	$-0.899596\pi$
$479$	−7799.60	−	13509.3i	−0.743994	−	1.28863i	0.206670	−	0.978411i	$-0.433737\pi$
$480$	623.443	−	1079.83i	0.0592836	−	0.102682i
$481$	847.942	+	1468.68i	0.0803801	+	0.139222i
$482$	−8338.84			−0.788016
$483$	12051.5			1.13532
$484$	1228.45	+	2127.74i	0.115369	+	0.199826i
$485$	1607.38	+	2784.07i	0.150490	+	0.260656i
$486$	486.000			0.0453609
$487$	13580.1			1.26360			0.631799	−	0.775132i	$-0.282317\pi$
$487$	13580.1			1.26360			0.631799	+	0.775132i	$0.282317\pi$
$488$	−2036.24	−	3526.87i	−0.188886	−	0.327160i
$489$	−1434.74	+	2485.05i	−0.132682	+	0.229812i
$490$	−4059.22	−	7030.77i	−0.374238	−	0.648200i
$491$	−398.489	+	690.202i	−0.0366264	+	0.0634387i	−0.883758	−	0.467945i	$-0.844994\pi$
$491$	−398.489	+	690.202i	−0.0366264	+	0.0634387i	0.847131	+	0.531384i	$0.178328\pi$
$492$	−2260.43	+	3915.17i	−0.207130	+	0.358760i
$493$	−1693.98			−0.154752
$494$	198.126	−	1409.25i	0.0180448	−	0.128350i
$495$	−3129.60			−0.284172
$496$	−756.158	+	1309.70i	−0.0684526	+	0.118563i
$497$	−1477.77	+	2559.57i	−0.133374	+	0.231011i
$498$	3864.86	+	6694.13i	0.347768	+	0.602351i
$499$	−4450.66	+	7708.78i	−0.399277	+	0.691567i	−0.993637	−	0.112632i	$-0.964072\pi$
$499$	−4450.66	+	7708.78i	−0.399277	+	0.691567i	0.594360	+	0.804199i	$0.297405\pi$
$500$	−2111.95	−	3658.01i	−0.188899	−	0.327183i
$501$	8339.30			0.743658
$502$	14264.5			1.26824
$503$	10112.6	+	17515.5i	0.896416	+	1.55264i	0.832042	+	0.554712i	$0.187172\pi$
$503$	10112.6	+	17515.5i	0.896416	+	1.55264i	0.0643734	+	0.997926i	$0.479495\pi$
$504$	−921.717	−	1596.46i	−0.0814614	−	0.141095i
$505$	10988.3			0.968266
$506$	−8401.26			−0.738106
$507$	−3184.78	−	5516.19i	−0.278976	−	0.483201i
$508$	−5334.38	+	9239.43i	−0.465896	+	0.806955i
$509$	−10533.2	−	18244.0i	−0.917240	−	1.58871i	−0.803588	−	0.595185i	$-0.797079\pi$
$509$	−10533.2	−	18244.0i	−0.917240	−	1.58871i	−0.113651	−	0.993521i	$-0.536255\pi$
$510$	318.321	−	551.348i	0.0276382	−	0.0478708i
$511$	−10659.5	+	18462.9i	−0.922799	+	1.59833i
$512$	−512.000			−0.0441942
$513$	−311.315	+	2214.34i	−0.0267931	+	0.190576i
$514$	2155.03			0.184931
$515$	−9238.32	+	16001.2i	−0.790464	+	1.36912i
$516$	−3049.46	+	5281.82i	−0.260165	+	0.450619i
$517$	4905.91	+	8497.29i	0.417334	+	0.722844i
$518$	−5053.76	+	8753.37i	−0.428667	+	0.742473i
$519$	−464.328	−	804.239i	−0.0392712	−	0.0680196i
$520$	−892.734			−0.0752865
$521$	−1660.93			−0.139668			−0.0698338	−	0.997559i	$-0.522247\pi$
$521$	−1660.93			−0.139668			−0.0698338	+	0.997559i	$0.522247\pi$
$522$	−1866.22	−	3232.38i	−0.156479	−	0.271030i
$523$	−11157.9	−	19326.0i	−0.932889	−	1.61581i	−0.778356	−	0.627823i	$-0.783946\pi$
$523$	−11157.9	−	19326.0i	−0.932889	−	1.61581i	−0.154532	−	0.987988i	$-0.549387\pi$
$524$	3289.10			0.274208
$525$	3356.47			0.279025
$526$	2489.16	+	4311.36i	0.206336	+	0.357384i
$527$	−386.083	+	668.715i	−0.0319128	+	0.0552745i
$528$	642.543	+	1112.92i	0.0529604	+	0.0917301i
$529$	−6225.34	+	10782.6i	−0.511658	+	0.886217i
$530$	2640.92	−	4574.21i	0.216442	−	0.374889i
$531$	5329.84			0.435584
$532$	7864.30	−	3176.94i	0.640903	−	0.258905i
$533$	3236.80			0.263042
$534$	−183.223	+	317.352i	−0.0148480	+	0.0257175i
$535$	1858.89	−	3219.70i	0.150219	−	0.260186i
$536$	−1002.88	−	1737.03i	−0.0808166	−	0.139978i
$537$	6975.43	−	12081.8i	0.560544	−	0.970890i
$538$	−6181.28	−	10706.3i	−0.495342	−	0.857957i
$539$	8367.16			0.668644
$540$	1402.75			0.111786
$541$	5689.92	+	9855.22i	0.452178	+	0.783196i	0.998521	−	0.0543657i	$-0.0173137\pi$
$541$	5689.92	+	9855.22i	0.452178	+	0.783196i	−0.546343	+	0.837562i	$0.683980\pi$
$542$	6032.71	+	10449.0i	0.478095	+	0.828084i
$543$	809.185			0.0639511
$544$	−261.420			−0.0206034
$545$	−209.668	−	363.155i	−0.0164792	−	0.0285429i
$546$	−659.923	+	1143.02i	−0.0517254	+	0.0895911i
$547$	8265.48	+	14316.2i	0.646081	+	1.11905i	0.984051	+	0.177888i	$0.0569266\pi$
$547$	8265.48	+	14316.2i	0.646081	+	1.11905i	−0.337969	+	0.941157i	$0.609740\pi$
$548$	4890.45	−	8470.50i	0.381222	−	0.660295i
$549$	2290.77	−	3967.73i	0.178083	−	0.308449i
$550$	−2339.84			−0.181402
$551$	15923.0	−	6432.40i	1.23111	−	0.497331i
$552$	3765.61			0.290353
$553$	4729.30	−	8191.38i	0.363671	−	0.629897i
$554$	912.717	−	1580.87i	0.0699957	−	0.121236i
$555$	−3845.62	−	6660.81i	−0.294121	−	0.509433i
$556$	−3008.68	+	5211.19i	−0.229490	+	0.397489i
$557$	3662.66	+	6343.91i	0.278621	+	0.482586i	0.971042	−	0.238908i	$-0.0767894\pi$
$557$	3662.66	+	6343.91i	0.278621	+	0.482586i	−0.692421	+	0.721493i	$0.743456\pi$
$558$	−1701.35			−0.129075
$559$	4366.65			0.330393
$560$	−2660.36	−	4607.88i	−0.200751	−	0.347712i
$561$	328.073	+	568.239i	0.0246903	+	0.0427648i
$562$	669.773			0.0502716
$563$	10864.0			0.813258			0.406629	−	0.913593i	$-0.366704\pi$
$563$	10864.0			0.813258			0.406629	+	0.913593i	$0.366704\pi$
$564$	−2198.92	−	3808.65i	−0.164169	−	0.284349i
$565$	−1929.41	+	3341.84i	−0.143665	+	0.248836i
$566$	−2776.94	−	4809.80i	−0.206225	−	0.357192i
$567$	1036.93	−	1796.02i	0.0768025	−	0.133026i
$568$	−461.744	+	799.765i	−0.0341098	+	0.0590799i
$569$	−19930.0			−1.46838			−0.734192	−	0.678941i	$-0.762439\pi$
$569$	−19930.0			−1.46838			−0.734192	+	0.678941i	$0.762439\pi$
$570$	−898.551	+	6391.27i	−0.0660284	+	0.469650i
$571$	1218.32			0.0892906			0.0446453	−	0.999003i	$-0.485784\pi$
$571$	1218.32			0.0892906			0.0446453	+	0.999003i	$0.485784\pi$
$572$	460.042	−	796.816i	0.0336282	−	0.0582457i
$573$	−2924.95	+	5066.16i	−0.213249	+	0.369357i
$574$	9645.72	+	16706.9i	0.701401	+	1.21486i
$575$	−3428.15	+	5937.72i	−0.248632	+	0.430644i
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−9186.43			−0.662801			−0.331400	−	0.943490i	$-0.607521\pi$
$577$	−9186.43			−0.662801			−0.331400	+	0.943490i	$0.607521\pi$
$578$	9692.52			0.697501
$579$	4396.95	+	7615.74i	0.315598	+	0.546631i
$580$	−5386.48	−	9329.65i	−0.385623	−	0.667919i
$581$	32984.3			2.35528
$582$	1485.06			0.105769
$583$	2721.83	+	4714.35i	0.193356	+	0.334903i
$584$	−3330.68	+	5768.91i	−0.236001	+	0.408766i
$585$	−502.163	−	869.772i	−0.0354904	−	0.0614712i
$586$	−3067.85	+	5313.67i	−0.216266	+	0.374583i
$587$	−272.446	+	471.890i	−0.0191568	+	0.0331805i	−0.875445	−	0.483318i	$-0.839432\pi$
$587$	−272.446	+	471.890i	−0.0191568	+	0.0331805i	0.856288	+	0.516499i	$0.172765\pi$
$588$	−3750.32			−0.263028
$589$	1089.83	−	7751.80i	0.0762404	−	0.542287i
$590$	15383.6			1.07344
$591$	−1854.72	+	3212.47i	−0.129091	+	0.223593i
$592$	−1579.10	+	2735.08i	−0.109629	+	0.189884i
$593$	−6061.77	−	10499.3i	−0.419776	−	0.727073i	0.576141	−	0.817350i	$-0.304558\pi$
$593$	−6061.77	−	10499.3i	−0.419776	−	0.727073i	−0.995917	+	0.0902776i	$0.971225\pi$
$594$	−722.861	+	1252.03i	−0.0499315	+	0.0864840i
$595$	−1358.34	−	2352.72i	−0.0935908	−	0.162104i
$596$	−2882.99			−0.198141
$597$	13527.0			0.927344
$598$	−1348.03	−	2334.86i	−0.0921825	−	0.159665i
$599$	12652.6	+	21915.0i	0.863058	+	1.49486i	0.868962	+	0.494879i	$0.164787\pi$
$599$	12652.6	+	21915.0i	0.863058	+	1.49486i	−0.00590371	+	0.999983i	$0.501879\pi$
$600$	1048.76			0.0713592
$601$	−15329.1			−1.04041			−0.520206	−	0.854041i	$-0.674145\pi$
$601$	−15329.1			−1.04041			−0.520206	+	0.854041i	$0.674145\pi$
$602$	13012.7	+	22538.6i	0.880993	+	1.52592i
$603$	1128.24	−	1954.16i	0.0761946	−	0.131973i
$604$	−3602.50	−	6239.71i	−0.242688	−	0.420348i
$605$	−3988.91	+	6909.00i	−0.268053	+	0.464282i
$606$	2538.04	−	4396.01i	0.170133	−	0.294679i
$607$	−1137.90			−0.0760891			−0.0380446	−	0.999276i	$-0.512113\pi$
$607$	−1137.90			−0.0760891			−0.0380446	+	0.999276i	$0.512113\pi$
$608$	2457.28	−	992.667i	0.163908	−	0.0662137i
$609$	−15927.1			−1.05977
$610$	6611.88	−	11452.1i	0.438864	−	0.760135i
$611$	−1574.37	+	2726.88i	−0.104242	+	0.180553i
$612$	−147.049	−	254.696i	−0.00971256	−	0.0168226i
$613$	6426.89	−	11131.7i	0.423458	−	0.733451i	−0.572817	−	0.819683i	$-0.694149\pi$
$613$	6426.89	−	11131.7i	0.423458	−	0.733451i	0.996275	+	0.0862324i	$0.0274827\pi$
$614$	−7487.81	−	12969.3i	−0.492155	−	0.852438i
$615$	−14679.7			−0.962506
$616$	5483.73			0.358678
$617$	9015.61	+	15615.5i	0.588257	+	1.01889i	0.994461	+	0.105109i	$0.0335192\pi$
$617$	9015.61	+	15615.5i	0.588257	+	1.01889i	−0.406203	+	0.913783i	$0.633148\pi$
$618$	4267.65	+	7391.79i	0.277783	+	0.481135i
$619$	−28147.3			−1.82768			−0.913841	−	0.406071i	$-0.866898\pi$
$619$	−28147.3			−1.82768			−0.913841	+	0.406071i	$0.866898\pi$
$620$	−4910.64			−0.318090
$621$	2118.15	+	3668.75i	0.136874	+	0.237072i
$622$	−6681.88	+	11573.4i	−0.430738	+	0.746060i
$623$	781.851	+	1354.21i	0.0502796	+	0.0870868i
$624$	−206.200	+	357.148i	−0.0132285	+	0.0229125i
$625$	9588.88	−	16608.4i	0.613688	−	1.06294i
$626$	−16324.0			−1.04224
$627$	−5241.53	−	4095.54i	−0.333854	−	0.260862i
$628$	15316.4			0.973236
$629$	−806.264	+	1396.49i	−0.0511095	+	0.0885242i
$630$	2992.91	−	5183.87i	0.189270	−	0.327826i
$631$	−512.279	−	887.293i	−0.0323193	−	0.0559787i	0.849413	−	0.527728i	$-0.176956\pi$
$631$	−512.279	−	887.293i	−0.0323193	−	0.0559787i	−0.881733	+	0.471749i	$0.843623\pi$
$632$	1477.72	−	2559.48i	0.0930070	−	0.161093i
$633$	−2.85705	−	4.94855i	−0.000179396	−	0.000310722i
$634$	5679.08			0.355749
$635$	−34642.5			−2.16496
$636$	−1219.98	−	2113.06i	−0.0760616	−	0.131743i
$637$	1342.56	+	2325.38i	0.0835073	+	0.144639i
$638$	11103.0			0.688984
$639$	−1038.92			−0.0643180
$640$	−831.257	−	1439.78i	−0.0513411	−	0.0889255i
$641$	−8738.48	+	15135.5i	−0.538454	+	0.932630i	0.460533	+	0.887642i	$0.347658\pi$
$641$	−8738.48	+	15135.5i	−0.538454	+	0.932630i	−0.998988	+	0.0449875i	$0.985675\pi$
$642$	−858.718	−	1487.34i	−0.0527896	−	0.0914342i
$643$	6716.23	−	11632.9i	0.411917	−	0.713460i	−0.583183	−	0.812341i	$-0.698193\pi$
$643$	6716.23	−	11632.9i	0.411917	−	0.713460i	0.995099	+	0.0988805i	$0.0315262\pi$
$644$	8034.31	−	13915.8i	0.491609	−	0.851492i
$645$	−19803.8			−1.20895
$646$	1254.65	−	506.841i	0.0764142	−	0.0308690i
$647$	−2658.09			−0.161515			−0.0807575	−	0.996734i	$-0.525734\pi$
$647$	−2658.09			−0.161515			−0.0807575	+	0.996734i	$0.525734\pi$
$648$	324.000	−	561.184i	0.0196419	−	0.0340207i
$649$	−7927.43	+	13730.7i	−0.479474	+	0.830474i
$650$	−375.442	−	650.284i	−0.0226554	−	0.0392404i
$651$	−3630.02	+	6287.37i	−0.218543	+	0.378528i
$652$	1912.99	+	3313.40i	0.114906	+	0.199023i
$653$	−9989.77			−0.598668			−0.299334	−	0.954148i	$-0.596764\pi$
$653$	−9989.77			−0.598668			−0.299334	+	0.954148i	$0.596764\pi$
$654$	−193.712			−0.0115822
$655$	5340.02	+	9249.19i	0.318553	+	0.551749i
$656$	3013.90	+	5220.23i	0.179380	+	0.310695i
$657$	−7494.03			−0.445008
$658$	−18766.5			−1.11185
$659$	−10032.3	−	17376.5i	−0.593025	−	1.02715i	−0.993822	−	0.110983i	$-0.964600\pi$
$659$	−10032.3	−	17376.5i	−0.593025	−	1.02715i	0.400797	−	0.916167i	$-0.368733\pi$
$660$	−2086.40	+	3613.75i	−0.123050	+	0.213129i
$661$	−11859.5	−	20541.3i	−0.697855	−	1.20872i	−0.969209	−	0.246241i	$-0.920805\pi$
$661$	−11859.5	−	20541.3i	−0.697855	−	1.20872i	0.271354	−	0.962480i	$-0.412529\pi$
$662$	11056.2	−	19150.0i	0.649113	−	1.12430i
$663$	−105.282	+	182.355i	−0.00616717	+	0.0106818i
$664$	10306.3			0.602351
$665$	21701.8	+	16957.0i	1.26551	+	0.988821i
$666$	−3552.97			−0.206719
$667$	16267.2	−	28175.6i	0.944331	−	1.63563i
$668$	5559.54	−	9629.40i	0.322013	−	0.557743i
$669$	−6990.34	−	12107.6i	−0.403979	−	0.699713i
$670$	3256.44	−	5640.32i	0.187772	−	0.325231i
$671$	6814.44	+	11803.0i	0.392054	+	0.679058i
$672$	−2457.91			−0.141095
$673$	−10144.0			−0.581014			−0.290507	−	0.956873i	$-0.593824\pi$
$673$	−10144.0			−0.581014			−0.290507	+	0.956873i	$0.593824\pi$
$674$	−5050.33	−	8747.43i	−0.288622	−	0.499908i
$675$	589.929	+	1021.79i	0.0336391	+	0.0582646i
$676$	−8492.73			−0.483201
$677$	−16883.4			−0.958469			−0.479234	−	0.877687i	$-0.659086\pi$
$677$	−16883.4			−0.958469			−0.479234	+	0.877687i	$0.659086\pi$
$678$	891.293	+	1543.76i	0.0504866	+	0.0874453i
$679$	3168.54	−	5488.07i	0.179083	−	0.310181i
$680$	−424.428	−	735.130i	−0.0239354	−	0.0414573i
$681$	−6067.73	+	10509.6i	−0.341433	+	0.591380i
$682$	2530.54	−	4383.02i	0.142081	−	0.246092i
$683$	−16610.2			−0.930560			−0.465280	−	0.885164i	$-0.654046\pi$
$683$	−16610.2			−0.930560			−0.465280	+	0.885164i	$0.654046\pi$
$684$	2349.35	+	1835.70i	0.131330	+	0.102617i
$685$	31759.5			1.77149
$686$	780.217	−	1351.38i	0.0434240	−	0.0752125i
$687$	7594.09	−	13153.3i	0.421736	−	0.730468i
$688$	4065.95	+	7042.43i	0.225309	+	0.390247i
$689$	−873.467	+	1512.89i	−0.0482967	+	0.0836524i
$690$	6113.65	+	10589.1i	0.337308	+	0.584235i
$691$	24812.1			1.36598			0.682992	−	0.730426i	$-0.260678\pi$
$691$	24812.1			1.36598			0.682992	+	0.730426i	$0.260678\pi$
$692$	−1238.21			−0.0680196
$693$	3084.60	+	5342.68i	0.169082	+	0.292859i
$694$	−6014.85	−	10418.0i	−0.328992	−	0.569831i
$695$	−19539.0			−1.06641
$696$	−4976.58			−0.271030
$697$	1538.85	+	2665.37i	0.0836273	+	0.144847i
$698$	−2514.51	+	4355.25i	−0.136355	+	0.236173i
$699$	649.634	+	1125.20i	0.0351522	+	0.0608854i
$700$	2237.64	−	3875.71i	0.120821	−	0.209269i
$701$	−6533.58	+	11316.5i	−0.352025	+	0.609726i	−0.986604	−	0.163132i	$-0.947840\pi$
$701$	−6533.58	+	11316.5i	−0.352025	+	0.609726i	0.634579	+	0.772858i	$0.281174\pi$
$702$	−463.949			−0.0249439
$703$	2275.91	−	16188.2i	0.122102	−	0.868494i
$704$	1713.45			0.0917301
$705$	7140.12	−	12367.1i	0.381436	−	0.660667i
$706$	4578.03	−	7929.37i	0.244046	−	0.422700i
$707$	−10830.3	−	18758.7i	−0.576119	−	0.997868i
$708$	3553.23	−	6154.37i	0.188614	−	0.326688i
$709$	−5222.61	−	9045.83i	−0.276642	−	0.479158i	0.693906	−	0.720066i	$-0.255888\pi$
$709$	−5222.61	−	9045.83i	−0.276642	−	0.479158i	−0.970548	+	0.240907i	$0.922555\pi$
$710$	−2998.66			−0.158504
$711$	3324.86			0.175376
$712$	244.297	+	423.135i	0.0128587	+	0.0222720i
$713$	−7415.08	−	12843.3i	−0.389477	−	0.674594i
$714$	−1254.97			−0.0657790
$715$	2987.60			0.156266
$716$	−9300.57	−	16109.1i	−0.485445	−	0.840816i
$717$	−6247.83	+	10821.6i	−0.325425	+	0.563652i
$718$	7972.44	+	13808.7i	0.414385	+	0.717736i
$719$	−324.001	+	561.185i	−0.0168055	+	0.0291080i	−0.874306	−	0.485375i	$-0.838683\pi$
$719$	−324.001	+	561.185i	−0.0168055	+	0.0291080i	0.857500	+	0.514483i	$0.172016\pi$
$720$	935.164	−	1619.75i	0.0484049	−	0.0838397i
$721$	36421.9			1.88131
$722$	−9868.83	+	9528.36i	−0.508698	+	0.491148i
$723$	−12508.3			−0.643413
$724$	539.456	−	934.366i	0.0276916	−	0.0479633i
$725$	4530.59	−	7847.22i	0.232086	−	0.401984i
$726$	1842.68	+	3191.62i	0.0941988	+	0.163157i
$727$	−8436.61	+	14612.6i	−0.430394	+	0.745465i	−0.996907	−	0.0785881i	$-0.974959\pi$
$727$	−8436.61	+	14612.6i	−0.430394	+	0.745465i	0.566513	+	0.824053i	$0.308292\pi$
$728$	879.897	+	1524.03i	0.0447955	+	0.0775881i
$729$	729.000			0.0370370
$730$	−21630.1			−1.09667
$731$	2076.01	+	3595.76i	0.105040	+	0.181934i
$732$	−3054.36	−	5290.31i	−0.154225	−	0.267125i
$733$	−23662.1			−1.19233			−0.596166	−	0.802861i	$-0.703310\pi$
$733$	−23662.1			−1.19233			−0.596166	+	0.802861i	$0.703310\pi$
$734$	−10931.0			−0.549688
$735$	−6088.83	−	10546.2i	−0.305564	−	0.529253i
$736$	2510.40	−	4348.15i	0.125727	−	0.217765i
$737$	3356.20	+	5813.12i	0.167744	+	0.290541i
$738$	−3390.64	+	5872.76i	−0.169121	+	0.292926i
$739$	−8638.65	+	14962.6i	−0.430011	+	0.744800i	−0.996874	−	0.0790119i	$-0.974823\pi$
$739$	−8638.65	+	14962.6i	−0.430011	+	0.744800i	0.566863	+	0.823812i	$0.308157\pi$
$740$	−10255.0			−0.509433
$741$	297.190	−	2113.87i	0.0147335	−	0.104797i
$742$	−10411.8			−0.515133
$743$	−12899.3	+	22342.2i	−0.636915	+	1.10317i	0.349190	+	0.937052i	$0.386457\pi$
$743$	−12899.3	+	22342.2i	−0.636915	+	1.10317i	−0.986106	+	0.166118i	$0.946877\pi$
$744$	−1134.24	+	1964.55i	−0.0558913	+	0.0968066i
$745$	−4680.68	−	8107.17i	−0.230184	−	0.398690i
$746$	9245.54	−	16013.7i	0.453758	−	0.785932i
$747$	5797.28	+	10041.2i	0.283951	+	0.491818i
$748$	874.861			0.0427648
$749$	−7328.66			−0.357521
$750$	−3167.93	−	5487.02i	−0.154235	−	0.267143i
$751$	−7578.27	−	13125.9i	−0.368222	−	0.637780i	0.621065	−	0.783759i	$-0.286700\pi$
$751$	−7578.27	−	13125.9i	−0.368222	−	0.637780i	−0.989288	+	0.145979i	$0.953367\pi$
$752$	−5863.80			−0.284349
$753$	21396.7			1.03551
$754$	1781.54	+	3085.72i	0.0860476	+	0.149039i
$755$	11697.7	−	20261.0i	0.563870	−	0.976651i
$756$	−1382.58	−	2394.69i	−0.0665130	−	0.115204i
$757$	−3727.46	+	6456.14i	−0.178965	+	0.309977i	−0.941526	−	0.336939i	$-0.890608\pi$
$757$	−3727.46	+	6456.14i	−0.178965	+	0.309977i	0.762561	+	0.646916i	$0.223942\pi$
$758$	6098.42	−	10562.8i	0.292222	−	0.506144i
$759$	−12601.9			−0.602661
$760$	6780.97	+	5298.40i	0.323647	+	0.252886i
$761$	23295.2			1.10966			0.554830	−	0.831964i	$-0.312783\pi$
$761$	23295.2			1.10966			0.554830	+	0.831964i	$0.312783\pi$
$762$	−8001.58	+	13859.1i	−0.380402	+	0.658876i
$763$	−413.306	+	715.867i	−0.0196103	+	0.0339661i
$764$	3899.93	+	6754.88i	0.184679	+	0.319873i
$765$	477.481	−	827.021i	0.0225665	−	0.0390863i
$766$	4529.81	+	7845.86i	0.213667	+	0.370082i
$767$	−5088.01			−0.239527
$768$	−768.000			−0.0360844
$769$	18986.9	+	32886.3i	0.890358	+	1.54215i	0.839446	+	0.543443i	$0.182880\pi$
$769$	18986.9	+	32886.3i	0.890358	+	1.54215i	0.0509122	+	0.998703i	$0.483787\pi$
$770$	8903.10	+	15420.6i	0.416683	+	0.721716i
$771$	3232.55			0.150995
$772$	11725.2			0.546631
$773$	−4169.69	−	7222.11i	−0.194014	−	0.336043i	0.752563	−	0.658521i	$-0.228818\pi$
$773$	−4169.69	−	7222.11i	−0.194014	−	0.336043i	−0.946577	+	0.322478i	$0.895484\pi$
$774$	−4574.19	+	7922.73i	−0.212424	+	0.367929i
$775$	−2065.18	−	3577.00i	−0.0957206	−	0.165793i
$776$	990.042	−	1714.80i	0.0457995	−	0.0793271i
$777$	−7580.64	+	13130.1i	−0.350005	+	0.606226i
$778$	11117.8			0.512332
$779$	−24585.9	−	19210.5i	−1.13078	−	0.883553i
$780$	−1339.10			−0.0614712
$781$	1545.26	−	2676.47i	0.0707988	−	0.122627i
$782$	1281.77	−	2220.10i	0.0586140	−	0.101522i
$783$	−2799.32	−	4848.57i	−0.127765	−	0.221295i
$784$	−2500.21	+	4330.50i	−0.113895	+	0.197271i
$785$	24867.0	+	43070.9i	1.13063	+	1.95830i
$786$	4933.66			0.223890
$787$	−42901.7			−1.94318			−0.971588	−	0.236680i	$-0.923941\pi$
$787$	−42901.7			−1.94318			−0.971588	+	0.236680i	$0.923941\pi$
$788$	2472.96	+	4283.29i	0.111796	+	0.193637i
$789$	3733.74	+	6467.03i	0.168472	+	0.291803i
$790$	9596.59			0.432192
$791$	7606.67			0.341924
$792$	963.814	+	1669.38i	0.0432420	+	0.0748973i
$793$	−2186.83	+	3787.71i	−0.0979278	+	0.169616i
$794$	9391.66	+	16266.8i	0.419770	+	0.727063i
$795$	3961.38	−	6861.32i	0.176724	−	0.306095i
$796$	9018.01	−	15619.7i	0.401552	−	0.695508i
$797$	5540.21			0.246229			0.123114	−	0.992392i	$-0.460712\pi$
$797$	5540.21			0.246229			0.123114	+	0.992392i	$0.460712\pi$
$798$	11796.4	−	4765.41i	0.523295	−	0.211395i
$799$	−2993.97			−0.132564
$800$	699.175	−	1211.01i	0.0308995	−	0.0535194i
$801$	−274.834	+	476.027i	−0.0121233	+	0.0209982i
$802$	9532.13	+	16510.1i	0.419690	+	0.726924i
$803$	11146.4	−	19306.1i	0.489847	−	0.848440i
$804$	−1504.31	−	2605.55i	−0.0659864	−	0.114292i
$805$	52176.4			2.28444
$806$	1624.16			0.0709784
$807$	−9271.92	−	16059.4i	−0.404445	−	0.700519i
$808$	−3384.05	−	5861.34i	−0.147340	−	0.255200i
$809$	20817.8			0.904715			0.452357	−	0.891837i	$-0.350583\pi$
$809$	20817.8			0.904715			0.452357	+	0.891837i	$0.350583\pi$
$810$	2104.12			0.0912731
$811$	10334.0	+	17899.0i	0.447441	+	0.774991i	0.998219	−	0.0596612i	$-0.0190020\pi$
$811$	10334.0	+	17899.0i	0.447441	+	0.774991i	−0.550777	+	0.834652i	$0.685669\pi$
$812$	−10618.0	+	18391.0i	−0.458892	+	0.794824i
$813$	9049.07	+	15673.5i	0.390363	+	0.676128i
$814$	5284.58	−	9153.15i	0.227548	−	0.394125i
$815$	−6211.68	+	10758.9i	−0.266976	+	0.462416i
$816$	−392.129			−0.0168226
$817$	−33167.9	−	25916.2i	−1.42032	−	1.10978i
$818$	−13159.0			−0.562461
$819$	−989.884	+	1714.53i	−0.0422336	+	0.0731508i
$820$	−9786.44	+	16950.6i	−0.416777	+	0.721879i
$821$	3750.50	+	6496.07i	0.159432	+	0.276144i	0.934664	−	0.355532i	$-0.115700\pi$
$821$	3750.50	+	6496.07i	0.159432	+	0.276144i	−0.775232	+	0.631676i	$0.782367\pi$
$822$	7335.67	−	12705.7i	0.311266	−	0.539129i
$823$	181.148	+	313.757i	0.00767244	+	0.0132891i	0.869836	−	0.493341i	$-0.164224\pi$
$823$	181.148	+	313.757i	0.00767244	+	0.0132891i	−0.862164	+	0.506630i	$0.830891\pi$
$824$	11380.4			0.481135
$825$	−3509.76			−0.148114
$826$	−15162.4	−	26262.0i	−0.638700	−	1.10626i
$827$	4389.51	+	7602.85i	0.184568	+	0.319682i	0.943431	−	0.331569i	$-0.107578\pi$
$827$	4389.51	+	7602.85i	0.184568	+	0.319682i	−0.758863	+	0.651251i	$0.774245\pi$
$828$	5648.41			0.237072
$829$	11789.0			0.493909			0.246954	−	0.969027i	$-0.420570\pi$
$829$	11789.0			0.493909			0.246954	+	0.969027i	$0.420570\pi$
$830$	16732.8	+	28982.0i	0.699762	+	1.21202i
$831$	1369.08	−	2371.31i	0.0571513	−	0.0989889i
$832$	274.933	+	476.198i	0.0114562	+	0.0198428i
$833$	−1276.57	+	2211.09i	−0.0530979	+	0.0919683i
$834$	−4513.02	+	7816.79i	−0.187378	+	0.324548i
$835$	36104.7			1.49635
$836$	−8223.48	+	3322.04i	−0.340209	+	0.137434i
$837$	−2552.03			−0.105390
$838$	4136.42	−	7164.49i	0.170514	−	0.295338i
$839$	5380.60	−	9319.48i	0.221405	−	0.383485i	−0.733830	−	0.679334i	$-0.762269\pi$
$839$	5380.60	−	9319.48i	0.221405	−	0.383485i	0.955235	+	0.295848i	$0.0956023\pi$
$840$	−3990.54	−	6911.82i	−0.163913	−	0.283905i
$841$	−9304.03	+	16115.1i	−0.381485	+	0.660751i
$842$	7792.46	+	13496.9i	0.318938	+	0.552417i
$843$	1004.66			0.0410466
$844$	−7.61879			−0.000310722
$845$	−13788.4	−	23882.2i	−0.561343	−	0.972274i
$846$	−3298.39	−	5712.97i	−0.134044	−	0.232170i
$847$	15726.2			0.637968
$848$	−3253.27			−0.131743
$849$	−4165.41	−	7214.69i	−0.168382	−	0.291646i
$850$	356.988	−	618.322i	0.0144054	−	0.0249509i
$851$	−15485.1	−	26820.9i	−0.623762	−	1.08039i
$852$	−692.617	+	1199.65i	−0.0278505	+	0.0482385i
$853$	−2445.13	+	4235.09i	−0.0981472	+	0.169996i	−0.910918	−	0.412588i	$-0.864625\pi$
$853$	−2445.13	+	4235.09i	−0.0981472	+	0.169996i	0.812771	+	0.582584i	$0.197958\pi$
$854$	−26067.2			−1.04450
$855$	−1347.83	+	9586.90i	−0.0539119	+	0.383468i
$856$	−2289.91			−0.0914342
$857$	15162.2	−	26261.7i	0.604353	−	1.04677i	−0.387801	−	0.921743i	$-0.626765\pi$
$857$	15162.2	−	26261.7i	0.604353	−	1.04677i	0.992153	−	0.125026i	$-0.0399015\pi$
$858$	690.063	−	1195.22i	0.0274573	−	0.0475574i
$859$	7535.78	+	13052.4i	0.299322	+	0.518441i	0.975981	−	0.217856i	$-0.0699062\pi$
$859$	7535.78	+	13052.4i	0.299322	+	0.518441i	−0.676659	+	0.736296i	$0.736573\pi$
$860$	−13202.5	+	22867.5i	−0.523492	+	0.906714i
$861$	14468.6	+	25060.3i	0.572692	+	0.991931i
$862$	14701.2			0.580887
$863$	283.180			0.0111698			0.00558490	−	0.999984i	$-0.498222\pi$
$863$	283.180			0.0111698			0.00558490	+	0.999984i	$0.498222\pi$
$864$	−432.000	−	748.246i	−0.0170103	−	0.0294628i
$865$	−2010.29	−	3481.93i	−0.0790196	−	0.136866i
$866$	−21385.2			−0.839145
$867$	14538.8			0.569508
$868$	4840.02	+	8383.17i	0.189264	+	0.327815i
$869$	−4945.30	+	8565.50i	−0.193047	+	0.334367i
$870$	−8079.72	−	13994.5i	−0.314860	−	0.545353i
$871$	−1077.05	+	1865.50i	−0.0418993	+	0.0725717i
$872$	−129.142	+	223.680i	−0.00501524	+	0.00868665i
$873$	2227.59			0.0863604
$874$	−3618.17	+	25735.6i	−0.140030	+	0.996017i
$875$	−27036.4			−1.04457
$876$	−4996.02	+	8653.37i	−0.192694	+	0.333756i
$877$	1100.91	−	1906.84i	0.0423891	−	0.0734200i	−0.844052	−	0.536261i	$-0.819836\pi$
$877$	1100.91	−	1906.84i	0.0423891	−	0.0734200i	0.886442	+	0.462841i	$0.153170\pi$
$878$	−9619.66	−	16661.7i	−0.369758	−	0.640440i
$879$	−4601.77	+	7970.51i	−0.176580	+	0.305846i
$880$	2781.87	+	4818.33i	0.106564	+	0.184575i
$881$	21218.9			0.811443			0.405722	−	0.913997i	$-0.367020\pi$
$881$	21218.9			0.811443			0.405722	+	0.913997i	$0.367020\pi$
$882$	−5625.48			−0.214762
$883$	4365.12	+	7560.60i	0.166362	+	0.288148i	0.937138	−	0.348958i	$-0.113465\pi$
$883$	4365.12	+	7560.60i	0.166362	+	0.288148i	−0.770776	+	0.637106i	$0.780131\pi$
$884$	140.377	+	243.139i	0.00534092	+	0.00925075i
$885$	23075.3			0.876463
$886$	−25208.9			−0.955880
$887$	5773.98	+	10000.8i	0.218570	+	0.378574i	0.954371	−	0.298624i	$-0.0965276\pi$
$887$	5773.98	+	10000.8i	0.218570	+	0.378574i	−0.735801	+	0.677197i	$0.763194\pi$
$888$	−2368.65	+	4102.62i	−0.0895120	+	0.155039i
$889$	34144.4	+	59139.8i	1.28815	+	2.23114i
$890$	−793.258	+	1373.96i	−0.0298765	+	0.0517476i
$891$	−1084.29	+	1878.05i	−0.0407689	+	0.0706139i
$892$	−18640.9			−0.699713
$893$	28142.6	−	11368.7i	1.05460	−	0.426025i
$894$	−4324.48			−0.161781
$895$	30199.9	−	52307.7i	1.12790	−	1.95358i
$896$	−1638.61	+	2838.15i	−0.0610960	+	0.105821i
$897$	−2022.05	−	3502.29i	−0.0752667	−	0.130366i
$898$	14957.9	−	25907.9i	0.555848	−	0.962758i
$899$	9799.68	+	16973.5i	0.363557	+	0.629699i
$900$	1573.14			0.0582646
$901$	−1661.07			−0.0614188
$902$	−10086.3	−	17469.9i	−0.372323	−	0.644883i
$903$	19519.0	+	33808.0i	0.719328	+	1.24591i
$904$	2376.78			0.0874453
$905$	3503.34			0.128679
$906$	−5403.75	−	9359.56i	−0.198154	−	0.343213i
$907$	3641.48	−	6307.22i	0.133311	−	0.230902i	−0.791640	−	0.610988i	$-0.790772\pi$
$907$	3641.48	−	6307.22i	0.133311	−	0.230902i	0.924951	+	0.380086i	$0.124106\pi$
$908$	8090.31	+	14012.8i	0.295690	+	0.512150i
$909$	3807.05	−	6594.01i	0.138913	−	0.240604i
$910$	−2857.11	+	4948.66i	−0.104079	+	0.180271i
$911$	32720.6			1.18999			0.594995	−	0.803729i	$-0.297154\pi$
$911$	32720.6			1.18999			0.594995	+	0.803729i	$0.297154\pi$
$912$	3685.92	−	1489.00i	0.133830	−	0.0540633i
$913$	−34490.8			−1.25025
$914$	−2003.50	+	3470.16i	−0.0725053	+	0.125583i
$915$	9917.81	−	17178.2i	0.358331	−	0.620647i
$916$	−10125.5	−	17537.8i	−0.365234	−	0.632604i
$917$	10526.5	−	18232.4i	0.379078	−	0.656583i
$918$	−220.573	−	382.043i	−0.00793027	−	0.0137356i
$919$	1970.84			0.0707421			0.0353710	−	0.999374i	$-0.488739\pi$
$919$	1970.84			0.0707421			0.0353710	+	0.999374i	$0.488739\pi$
$920$	16303.1			0.584235
$921$	−11231.7	−	19453.9i	−0.401843	−	0.696013i
$922$	−1134.66	−	1965.28i	−0.0405292	−	0.0701987i
$923$	991.786			0.0353684
$924$	8225.59			0.292859
$925$	−4312.76	−	7469.92i	−0.153300	−	0.265524i
$926$	−2934.33	+	5082.42i	−0.104134	+	0.180366i
$927$	6401.47	+	11087.7i	0.226809	+	0.392845i
$928$	−3317.72	+	5746.45i	−0.117359	+	0.203272i
$929$	−5378.74	+	9316.25i	−0.189958	+	0.329017i	−0.945236	−	0.326388i	$-0.894168\pi$
$929$	−5378.74	+	9316.25i	−0.189958	+	0.329017i	0.755278	+	0.655404i	$0.227502\pi$
$930$	−7365.95			−0.259720
$931$	3603.49	−	25631.1i	0.126852	−	0.902283i
$932$	1732.36			0.0608854
$933$	−10022.8	+	17360.0i	−0.351696	+	0.609156i
$934$	−930.578	+	1611.81i	−0.0326011	+	0.0564668i
$935$	1420.38	+	2460.17i	0.0496806	+	0.0860494i
$936$	−309.299	+	535.722i	−0.0108010	+	0.0187079i
$937$	−16289.2	−	28213.7i	−0.567923	−	0.983671i	−0.996771	−	0.0802948i	$-0.974414\pi$
$937$	−16289.2	−	28213.7i	−0.567923	−	0.983671i	0.428848	−	0.903377i	$-0.358920\pi$
$938$	−12838.5			−0.446898
$939$	−24486.1			−0.850982
$940$	−9520.16	−	16489.4i	−0.330334	−	0.572154i
$941$	−22922.7	−	39703.3i	−0.794112	−	1.37544i	−0.923402	−	0.383835i	$-0.874603\pi$
$941$	−22922.7	−	39703.3i	−0.794112	−	1.37544i	0.129290	−	0.991607i	$-0.458730\pi$
$942$	22974.7			0.794644
$943$	−59110.3			−2.04125
$944$	−4737.63	−	8205.82i	−0.163344	−	0.282920i
$945$	4489.36	−	7775.80i	0.154539	−	0.267669i
$946$	−13607.0	−	23568.0i	−0.467655	−	0.810003i
$947$	14122.0	−	24460.0i	0.484586	−	0.839328i	−0.515257	−	0.857036i	$-0.672304\pi$
$947$	14122.0	−	24460.0i	0.484586	−	0.839328i	0.999843	+	0.0177080i	$0.00563693\pi$
$948$	2216.58	−	3839.22i	0.0759399	−	0.131532i
$949$	7154.01			0.244709
$950$	−1007.70	+	7167.64i	−0.0344149	+	0.244788i
$951$	8518.62			0.290468
$952$	−836.649	+	1449.12i	−0.0284831	+	0.0493342i
$953$	22346.7	−	38705.7i	0.759582	−	1.31563i	−0.183483	−	0.983023i	$-0.558737\pi$
$953$	22346.7	−	38705.7i	0.759582	−	1.31563i	0.943064	−	0.332611i	$-0.107930\pi$
$954$	−1829.96	−	3169.59i	−0.0621041	−	0.107567i
$955$	−12663.5	+	21933.7i	−0.429089	+	0.743204i
$956$	8330.45	+	14428.8i	0.281826	+	0.488137i
$957$	16654.5			0.562553
$958$	−31198.4			−1.05217
$959$	−31302.8	−	54218.1i	−1.05404	−	1.82564i
$960$	−1246.89	−	2159.67i	−0.0419199	−	0.0726073i
$961$	−20857.0			−0.700112
$962$	3391.77			0.113675
$963$	−1288.08	−	2231.01i	−0.0431025	−	0.0746557i
$964$	−8338.84	+	14443.3i	−0.278606	+	0.482560i
$965$	19036.4	+	32972.1i	0.635031	+	1.09991i
$966$	12051.5	−	20873.8i	0.401397	−	0.695240i
$967$	−22790.5	+	39474.3i	−0.757905	+	1.31273i	0.186013	+	0.982547i	$0.440443\pi$
$967$	−22790.5	+	39474.3i	−0.757905	+	1.31273i	−0.943917	+	0.330182i	$0.892890\pi$
$968$	4913.82			0.163157
$969$	1881.98	−	760.261i	0.0623919	−	0.0252045i
$970$	6429.53			0.212824
$971$	2367.98	−	4101.46i	0.0782616	−	0.135553i	−0.824238	−	0.566243i	$-0.808396\pi$
$971$	2367.98	−	4101.46i	0.0782616	−	0.135553i	0.902500	+	0.430690i	$0.141730\pi$
$972$	486.000	−	841.777i	0.0160375	−	0.0277778i
$973$	19258.0	+	33355.9i	0.634516	+	1.09901i
$974$	13580.1	−	23521.4i	0.446749	−	0.773792i
$975$	−563.162	−	975.426i	−0.0184981	−	0.0320396i
$976$	−8144.96			−0.267125
$977$	−57565.1			−1.88503			−0.942514	−	0.334167i	$-0.891545\pi$
$977$	−57565.1			−1.88503			−0.942514	+	0.334167i	$0.891545\pi$
$978$	2869.49	+	4970.10i	0.0938202	+	0.162501i
$979$	−817.560	−	1416.06i	−0.0266898	−	0.0462281i
$980$	−16236.9			−0.529253
$981$	−290.569			−0.00945682
$982$	796.977	+	1380.40i	0.0258987	+	0.0448579i
$983$	−17314.2	+	29989.0i	−0.561786	+	0.973043i	0.435554	+	0.900162i	$0.356552\pi$
$983$	−17314.2	+	29989.0i	−0.561786	+	0.973043i	−0.997341	+	0.0728802i	$0.976781\pi$
$984$	4520.85	+	7830.35i	0.146463	+	0.253681i
$985$	−8029.95	+	13908.3i	−0.259752	+	0.449903i
$986$	−1693.98	+	2934.05i	−0.0547132	+	0.0947661i
$987$	−28149.8			−0.907820
$988$	−2242.76	−	1752.41i	−0.0722183	−	0.0564288i
$989$	−79743.5			−2.56390
$990$	−3129.60	+	5420.63i	−0.100470	+	0.174019i
$991$	−15787.8	+	27345.2i	−0.506069	+	0.876537i	0.493906	+	0.869515i	$0.335569\pi$
$991$	−15787.8	+	27345.2i	−0.506069	+	0.876537i	−0.999975	+	0.00702215i	$0.997765\pi$
$992$	1512.32	+	2619.41i	0.0484033	+	0.0838369i
$993$	16584.3	−	28724.9i	0.529998	−	0.917984i
$994$	2955.54	+	5119.14i	0.0943099	+	0.163350i
$995$	58564.8			1.86596
$996$	15459.4			0.491818
$997$	−19361.7	−	33535.4i	−0.615035	−	1.06527i	−0.990378	−	0.138386i	$-0.955808\pi$
$997$	−19361.7	−	33535.4i	−0.615035	−	1.06527i	0.375343	−	0.926886i	$-0.377525\pi$
$998$	8901.33	+	15417.6i	0.282331	+	0.489012i
$999$	−5329.46			−0.168785

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	114.4.e.e.49.3	yes	6
3.2	odd	2		342.4.g.g.163.1		6
19.7	even	3	inner	114.4.e.e.7.3	✓	6
19.8	odd	6		2166.4.a.w.1.1		3
19.11	even	3		2166.4.a.s.1.1		3
57.26	odd	6		342.4.g.g.235.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.e.7.3	✓	6	19.7	even	3	inner
114.4.e.e.49.3	yes	6	1.1	even	1	trivial
342.4.g.g.163.1		6	3.2	odd	2
342.4.g.g.235.1		6	57.26	odd	6
2166.4.a.s.1.1		3	19.11	even	3
2166.4.a.w.1.1		3	19.8	odd	6

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:	\( N \)	\(=\)	\( 114 = 2 \cdot 3 \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	114.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.49420 - 11.2483i) q^{5} +(-3.00000 - 5.19615i) q^{6} -25.6033 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(1.50000 - 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(6.49420 - 11.2483i) q^{5} +(-3.00000 - 5.19615i) q^{6} -25.6033 q^{7} -8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-12.9884 - 22.4966i) q^{10} +26.7726 q^{11} -12.0000 q^{12} +(4.29582 + 7.44059i) q^{13} +(-25.6033 + 44.3461i) q^{14} +(-19.4826 - 33.7448i) q^{15} +(-8.00000 + 13.8564i) q^{16} +(-4.08468 + 7.07488i) q^{17} -18.0000 q^{18} +(11.5302 - 82.0125i) q^{19} -51.9536 q^{20} +(-38.4049 + 66.5192i) q^{21} +(26.7726 - 46.3715i) q^{22} +(-78.4501 - 135.880i) q^{23} +(-12.0000 + 20.7846i) q^{24} +(-21.8492 - 37.8439i) q^{25} +17.1833 q^{26} -27.0000 q^{27} +(51.2065 + 88.6923i) q^{28} +(103.679 + 179.577i) q^{29} -77.9304 q^{30} +94.5197 q^{31} +(16.0000 + 27.7128i) q^{32} +(40.1589 - 69.5573i) q^{33} +(8.16936 + 14.1498i) q^{34} +(-166.273 + 287.993i) q^{35} +(-18.0000 + 31.1769i) q^{36} +197.387 q^{37} +(-130.520 - 101.983i) q^{38} +25.7749 q^{39} +(-51.9536 + 89.9862i) q^{40} +(188.369 - 326.265i) q^{41} +(76.8098 + 133.038i) q^{42} +(254.122 - 440.152i) q^{43} +(-53.5452 - 92.7431i) q^{44} -116.896 q^{45} -313.800 q^{46} +(183.244 + 317.387i) q^{47} +(24.0000 + 41.5692i) q^{48} +312.527 q^{49} -87.3968 q^{50} +(12.2540 + 21.2246i) q^{51} +(17.1833 - 29.7623i) q^{52} +(101.665 + 176.088i) q^{53} +(-27.0000 + 46.7654i) q^{54} +(173.867 - 301.146i) q^{55} +204.826 q^{56} +(-195.780 - 152.975i) q^{57} +414.715 q^{58} +(-296.102 + 512.864i) q^{59} +(-77.9304 + 134.979i) q^{60} +(254.530 + 440.859i) q^{61} +(94.5197 - 163.713i) q^{62} +(115.215 + 199.558i) q^{63} +64.0000 q^{64} +111.592 q^{65} +(-80.3178 - 139.115i) q^{66} +(125.360 + 217.129i) q^{67} +32.6774 q^{68} -470.701 q^{69} +(332.545 + 575.985i) q^{70} +(57.7180 - 99.9706i) q^{71} +(36.0000 + 62.3538i) q^{72} +(416.335 - 721.114i) q^{73} +(197.387 - 341.885i) q^{74} -131.095 q^{75} +(-307.160 + 124.083i) q^{76} -685.466 q^{77} +(25.7749 - 44.6435i) q^{78} +(-184.715 + 319.935i) q^{79} +(103.907 + 179.972i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-376.738 - 652.529i) q^{82} -1288.29 q^{83} +307.239 q^{84} +(53.0535 + 91.8913i) q^{85} +(-508.244 - 880.304i) q^{86} +622.072 q^{87} -214.181 q^{88} +(-30.5372 - 52.8919i) q^{89} +(-116.896 + 202.469i) q^{90} +(-109.987 - 190.503i) q^{91} +(-313.800 + 543.518i) q^{92} +(141.780 - 245.569i) q^{93} +732.975 q^{94} +(-847.621 - 662.300i) q^{95} +96.0000 q^{96} +(-123.755 + 214.350i) q^{97} +(312.527 - 541.312i) q^{98} +(-120.477 - 208.672i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9}+O(q^{10}) \) 6 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 - 34 * q^7 - 48 * q^8 - 27 * q^9	\( 6 q + 6 q^{2} + 9 q^{3} - 12 q^{4} - 2 q^{5} - 18 q^{6} - 34 q^{7} - 48 q^{8} - 27 q^{9} + 4 q^{10} - 104 q^{11} - 72 q^{12} - 75 q^{13} - 34 q^{14} + 6 q^{15} - 48 q^{16} + 48 q^{17} - 108 q^{18} + 104 q^{19} + 16 q^{20} - 51 q^{21} - 104 q^{22} + 238 q^{23} - 72 q^{24} - 229 q^{25} - 300 q^{26} - 162 q^{27} + 68 q^{28} + 8 q^{29} + 24 q^{30} + 214 q^{31} + 96 q^{32} - 156 q^{33} - 96 q^{34} + 294 q^{35} - 108 q^{36} + 610 q^{37} - 430 q^{38} - 450 q^{39} + 16 q^{40} - 16 q^{41} + 102 q^{42} + 331 q^{43} + 208 q^{44} + 36 q^{45} + 952 q^{46} + 766 q^{47} + 144 q^{48} + 2284 q^{49} - 916 q^{50} - 144 q^{51} - 300 q^{52} + 118 q^{53} - 162 q^{54} + 1400 q^{55} + 272 q^{56} - 645 q^{57} + 32 q^{58} - 936 q^{59} + 24 q^{60} + 399 q^{61} + 214 q^{62} + 153 q^{63} + 384 q^{64} + 740 q^{65} + 312 q^{66} - 61 q^{67} - 384 q^{68} + 1428 q^{69} - 588 q^{70} - 974 q^{71} + 216 q^{72} - 91 q^{73} + 610 q^{74} - 1374 q^{75} - 1276 q^{76} - 72 q^{77} - 450 q^{78} + 321 q^{79} - 32 q^{80} - 243 q^{81} + 32 q^{82} - 4296 q^{83} + 408 q^{84} + 1680 q^{85} - 662 q^{86} + 48 q^{87} + 832 q^{88} - 1116 q^{89} + 36 q^{90} - 1367 q^{91} + 952 q^{92} + 321 q^{93} + 3064 q^{94} - 4198 q^{95} + 576 q^{96} - 1382 q^{97} + 2284 q^{98} + 468 q^{99}+O(q^{100}) \) 6 * q + 6 * q^2 + 9 * q^3 - 12 * q^4 - 2 * q^5 - 18 * q^6 - 34 * q^7 - 48 * q^8 - 27 * q^9 + 4 * q^10 - 104 * q^11 - 72 * q^12 - 75 * q^13 - 34 * q^14 + 6 * q^15 - 48 * q^16 + 48 * q^17 - 108 * q^18 + 104 * q^19 + 16 * q^20 - 51 * q^21 - 104 * q^22 + 238 * q^23 - 72 * q^24 - 229 * q^25 - 300 * q^26 - 162 * q^27 + 68 * q^28 + 8 * q^29 + 24 * q^30 + 214 * q^31 + 96 * q^32 - 156 * q^33 - 96 * q^34 + 294 * q^35 - 108 * q^36 + 610 * q^37 - 430 * q^38 - 450 * q^39 + 16 * q^40 - 16 * q^41 + 102 * q^42 + 331 * q^43 + 208 * q^44 + 36 * q^45 + 952 * q^46 + 766 * q^47 + 144 * q^48 + 2284 * q^49 - 916 * q^50 - 144 * q^51 - 300 * q^52 + 118 * q^53 - 162 * q^54 + 1400 * q^55 + 272 * q^56 - 645 * q^57 + 32 * q^58 - 936 * q^59 + 24 * q^60 + 399 * q^61 + 214 * q^62 + 153 * q^63 + 384 * q^64 + 740 * q^65 + 312 * q^66 - 61 * q^67 - 384 * q^68 + 1428 * q^69 - 588 * q^70 - 974 * q^71 + 216 * q^72 - 91 * q^73 + 610 * q^74 - 1374 * q^75 - 1276 * q^76 - 72 * q^77 - 450 * q^78 + 321 * q^79 - 32 * q^80 - 243 * q^81 + 32 * q^82 - 4296 * q^83 + 408 * q^84 + 1680 * q^85 - 662 * q^86 + 48 * q^87 + 832 * q^88 - 1116 * q^89 + 36 * q^90 - 1367 * q^91 + 952 * q^92 + 321 * q^93 + 3064 * q^94 - 4198 * q^95 + 576 * q^96 - 1382 * q^97 + 2284 * q^98 + 468 * q^99

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