LMFDB - Embedded newform 114.4.e.e.7.3

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			7.3
Root			$1.56632 - 2.71294i$ of defining polynomial
Character	$\chi$	$=$	114.7
Dual form			114.4.e.e.49.3

$q$-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 $\left(\mathbb{Z}/114\mathbb{Z}\right)^\times$.

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

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	0.995378	+	0.0960362i	$0.0306165\pi$
$5$	6.49420	+	11.2483i	0.580859	+	1.00608i	−0.414519	+	0.910041i	$0.636050\pi$
$6$	−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	−0.816556	−	0.577267i	$-0.804119\pi$
$13$	4.29582	−	7.44059i	0.0916498	−	0.158742i	0.908205	+	0.418525i	$0.137453\pi$
$14$	−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	0.835416	−	0.549618i	$-0.185227\pi$
$17$	−4.08468	−	7.07488i	−0.0582753	−	0.100936i	−0.893691	+	0.448682i	$0.851893\pi$
$18$	−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	0.253184	+	0.967418i	$0.418522\pi$
$23$	−78.4501	+	135.880i	−0.711217	+	1.23186i	−0.964401	+	0.264445i	$0.914811\pi$
$24$	−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	−0.315702	−	0.948858i	$-0.602240\pi$
$29$	103.679	−	179.577i	0.663884	−	1.14988i	0.979587	−	0.201023i	$-0.0644266\pi$
$30$	−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	0.961980	+	0.273120i	$0.0880557\pi$
$41$	188.369	+	326.265i	0.717519	+	1.24278i	−0.244461	+	0.969659i	$0.578611\pi$
$42$	76.8098	−	133.038i	0.282191	−	0.488768i
$43$	254.122	+	440.152i	0.901238	+	1.56099i	0.825890	+	0.563832i	$0.190673\pi$
$43$	254.122	+	440.152i	0.901238	+	1.56099i	0.0753479	+	0.997157i	$0.475993\pi$
$44$	−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	−0.427996	−	0.903780i	$-0.640780\pi$
$47$	183.244	−	317.387i	0.568699	−	0.985015i	0.996695	−	0.0812344i	$-0.0258862\pi$
$48$	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	−0.703680	−	0.710517i	$-0.748461\pi$
$53$	101.665	−	176.088i	0.263485	−	0.456370i	0.967166	+	0.254147i	$0.0817946\pi$
$54$	−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	−0.982298	−	0.187324i	$-0.940019\pi$
$59$	−296.102	−	512.864i	−0.653376	−	1.13168i	0.328922	−	0.944357i	$-0.393315\pi$
$60$	−77.9304	−	134.979i	−0.167679	−	0.290429i
$61$	254.530	−	440.859i	0.534250	−	0.925348i	−0.464949	−	0.885337i	$-0.653927\pi$
$61$	254.530	−	440.859i	0.534250	−	0.925348i	0.999199	−	0.0400106i	$-0.0127392\pi$
$62$	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	−0.728805	−	0.684721i	$-0.759924\pi$
$67$	125.360	−	217.129i	0.228584	−	0.395919i	0.957389	+	0.288803i	$0.0932572\pi$
$68$	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	0.910224	−	0.414116i	$-0.135909\pi$
$71$	57.7180	+	99.9706i	0.0964771	+	0.167103i	−0.813747	+	0.581219i	$0.802576\pi$
$72$	36.0000	−	62.3538i	0.0589256	−	0.102062i
$73$	416.335	+	721.114i	0.667512	+	1.15616i	0.978598	+	0.205782i	$0.0659739\pi$
$73$	416.335	+	721.114i	0.667512	+	1.15616i	−0.311086	+	0.950382i	$0.600693\pi$
$74$	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	0.703991	−	0.710209i	$-0.251400\pi$
$79$	−184.715	−	319.935i	−0.263064	−	0.455640i	−0.967054	+	0.254569i	$0.918066\pi$
$80$	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	−0.883637	−	0.468172i	$-0.844913\pi$
$89$	−30.5372	+	52.8919i	−0.0363700	+	0.0629947i	0.847267	+	0.531167i	$0.178246\pi$
$90$	−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	0.793958	−	0.607973i	$-0.208017\pi$
$97$	−123.755	−	214.350i	−0.129541	−	0.224371i	−0.923499	+	0.383602i	$0.874684\pi$
$98$	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	−0.578870	−	0.815420i	$-0.696506\pi$
$101$	423.006	−	732.668i	0.416739	−	0.721813i	0.995609	+	0.0936064i	$0.0298395\pi$
$102$	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	0.873031	−	0.487665i	$-0.162151\pi$
$109$	16.1427	+	27.9600i	0.0141852	+	0.0245695i	−0.858846	+	0.512234i	$0.828818\pi$
$110$	−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	−0.151534	+	0.988452i	$0.548421\pi$
$127$	−1333.60	+	2309.86i	−0.931792	+	1.61391i	−0.780258	+	0.625458i	$0.784912\pi$
$128$	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	0.695727	−	0.718307i	$-0.255082\pi$
$131$	−411.138	−	712.112i	−0.274208	−	0.474943i	−0.969935	+	0.243364i	$0.921749\pi$
$132$	−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	−0.179144	−	0.983823i	$-0.557333\pi$
$137$	1222.61	−	2117.62i	0.762443	−	1.32059i	0.941588	−	0.336768i	$-0.109334\pi$
$138$	−470.701	−	815.277i	−0.290353	−	0.502906i
$139$	−752.171	+	1302.80i	−0.458980	+	0.794977i	−0.998907	−	0.0467345i	$-0.985119\pi$
$139$	−752.171	+	1302.80i	−0.458980	+	0.794977i	0.539927	+	0.841712i	$0.318452\pi$
$140$	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	0.947926	−	0.318492i	$-0.103176\pi$
$149$	360.374	+	624.186i	0.198141	+	0.343190i	−0.749785	+	0.661682i	$0.769843\pi$
$150$	−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	−0.685637	−	0.727943i	$-0.740476\pi$
$157$	−1914.55	−	3316.11i	−0.973236	−	1.68569i	−0.287599	−	0.957751i	$-0.592857\pi$
$158$	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	−0.340499	−	0.940245i	$-0.610596\pi$
$167$	1389.88	−	2407.35i	0.644027	−	1.11549i	0.984525	−	0.175242i	$-0.0560708\pi$
$168$	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	0.898029	−	0.439935i	$-0.144999\pi$
$173$	154.776	+	268.080i	0.0680196	+	0.117813i	−0.830010	+	0.557749i	$0.811665\pi$
$174$	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	−0.837005	−	0.547196i	$-0.815695\pi$
$181$	134.864	−	233.591i	0.0553833	−	0.0959266i	0.892388	+	0.451269i	$0.149029\pi$
$182$	−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	−0.998502	−	0.0547095i	$-0.982577\pi$
$193$	−1465.65	−	2538.58i	−0.546631	−	0.946793i	0.451871	−	0.892083i	$-0.350757\pi$
$194$	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	−0.114461	−	0.993428i	$-0.536514\pi$
$199$	2254.50	−	3904.91i	0.803103	−	1.39102i	0.917564	−	0.397588i	$-0.130153\pi$
$200$	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	0.866181	−	0.499731i	$-0.166568\pi$
$211$	0.952349	+	1.64952i	0.000310722	+	0.000538187i	−0.865870	+	0.500269i	$0.833234\pi$
$212$	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	0.968566	+	0.248757i	$0.0800220\pi$
$223$	2330.11	+	4035.88i	0.699713	+	1.21194i	−0.268853	+	0.963181i	$0.586645\pi$
$224$	−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	0.833976	−	0.551801i	$-0.186059\pi$
$233$	−216.545	−	375.066i	−0.0608854	−	0.105457i	−0.894861	+	0.446344i	$0.852726\pi$
$234$	−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	0.440516	+	0.897745i	$0.354795\pi$
$241$	−2084.71	+	3610.82i	−0.557212	+	0.965119i	−0.997728	+	0.0673743i	$0.978538\pi$
$242$	−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	0.0651931	−	0.997873i	$-0.479234\pi$
$251$	3566.12	−	6176.71i	0.896780	−	1.55327i	0.831587	−	0.555395i	$-0.187433\pi$
$252$	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	−0.793206	−	0.608953i	$-0.791590\pi$
$257$	538.758	−	933.157i	0.130766	−	0.226493i	0.923972	+	0.382460i	$0.124923\pi$
$258$	−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	0.682433	−	0.730948i	$-0.260922\pi$
$263$	−1244.58	−	2155.68i	−0.291803	−	0.505417i	−0.974236	+	0.225530i	$0.927588\pi$
$264$	−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	0.968284	+	0.249850i	$0.0803814\pi$
$269$	3090.64	+	5353.14i	0.700519	+	1.21333i	−0.267765	+	0.963484i	$0.586285\pi$
$270$	350.687	−	607.407i	0.0790449	−	0.136910i
$271$	−3016.36	−	5224.48i	−0.676128	−	1.17109i	−0.976138	−	0.217152i	$-0.930323\pi$
$271$	−3016.36	−	5224.48i	−0.676128	−	1.17109i	0.300010	−	0.953936i	$-0.403010\pi$
$272$	−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	−0.847704	−	0.530469i	$-0.822016\pi$
$281$	167.443	−	290.020i	0.0355474	−	0.0615699i	0.883252	+	0.468899i	$0.155349\pi$
$282$	1099.46	+	1904.32i	0.232170	+	0.402131i
$283$	1388.47	+	2404.90i	0.291646	+	0.505146i	0.974199	−	0.225690i	$-0.0724637\pi$
$283$	1388.47	+	2404.90i	0.291646	+	0.505146i	−0.682553	+	0.730836i	$0.739130\pi$
$284$	−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	0.969838	+	0.243750i	$0.0783776\pi$
$307$	3743.90	+	6484.63i	0.696013	+	1.20553i	−0.273825	+	0.961779i	$0.588289\pi$
$308$	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	0.216880	+	0.976198i	$0.430412\pi$
$313$	−4081.01	+	7068.52i	−0.736972	+	1.27647i	−0.953853	+	0.300275i	$0.902921\pi$
$314$	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	−0.712401	−	0.701773i	$-0.752392\pi$
$317$	1419.77	−	2459.11i	0.251553	−	0.435702i	0.963954	+	0.266071i	$0.0857255\pi$
$318$	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	0.994685	−	0.102964i	$-0.0328325\pi$
$337$	2525.16	+	4373.71i	0.408174	+	0.706977i	−0.586512	+	0.809941i	$0.699499\pi$
$338$	−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	0.999213	−	0.0396541i	$-0.0126256\pi$
$347$	3007.43	+	5209.01i	0.465265	+	0.805863i	−0.533948	+	0.845517i	$0.679292\pi$
$348$	−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	−0.994746	−	0.102371i	$-0.967357\pi$
$359$	−3986.22	−	6904.33i	−0.586029	−	1.01503i	0.408717	−	0.912661i	$-0.365976\pi$
$360$	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	−0.992273	−	0.124071i	$-0.960405\pi$
$367$	−2732.75	+	4733.26i	−0.388688	+	0.673227i	0.603585	+	0.797298i	$0.293738\pi$
$368$	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	0.674457	−	0.738314i	$-0.264378\pi$
$383$	−2264.90	−	3922.93i	−0.302170	−	0.523374i	−0.976627	+	0.214940i	$0.931044\pi$
$384$	−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	−0.626061	−	0.779774i	$-0.715334\pi$
$389$	2779.46	−	4814.17i	0.362273	−	0.627475i	0.988335	+	0.152298i	$0.0486674\pi$
$390$	−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	−0.993737	−	0.111748i	$-0.964355\pi$
$397$	−4695.83	−	8133.41i	−0.593645	−	1.02822i	0.400092	−	0.916475i	$-0.368978\pi$
$398$	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	−0.993752	−	0.111607i	$-0.964400\pi$
$401$	−4766.06	−	8255.07i	−0.593531	−	1.02803i	0.400222	−	0.916418i	$-0.368933\pi$
$402$	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	−0.993444	−	0.114318i	$-0.963532\pi$
$409$	−3289.74	+	5698.00i	−0.397720	+	0.688871i	0.595725	+	0.803189i	$0.296865\pi$
$410$	−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	0.547405	−	0.836868i	$-0.315616\pi$
$421$	−3896.23	−	6748.47i	−0.451047	−	0.781235i	−0.998451	+	0.0556325i	$0.982282\pi$
$422$	−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	−0.584223	−	0.811593i	$-0.698601\pi$
$431$	3675.30	−	6365.80i	0.410749	−	0.711438i	0.994972	+	0.100155i	$0.0319340\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	−5346.31	+	9260.08i	−0.593365	+	1.02774i	0.400410	+	0.916336i	$0.368868\pi$
$433$	−5346.31	+	9260.08i	−0.593365	+	1.02774i	−0.993775	+	0.111403i	$0.964466\pi$
$434$	−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	0.999644	+	0.0266676i	$0.00848958\pi$
$439$	4809.83	+	8330.87i	0.522917	+	0.905719i	−0.476727	+	0.879051i	$0.658177\pi$
$440$	−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	0.300293	+	0.953847i	$0.402916\pi$
$443$	−6302.23	+	10915.8i	−0.675909	+	1.17071i	−0.976202	+	0.216862i	$0.930418\pi$
$444$	−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	0.893260	−	0.449540i	$-0.148412\pi$
$461$	567.329	+	982.642i	0.0573170	+	0.0992759i	−0.835943	+	0.548816i	$0.815079\pi$
$462$	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	0.206670	+	0.978411i	$0.433737\pi$
$479$	−7799.60	+	13509.3i	−0.743994	+	1.28863i	−0.950663	+	0.310224i	$0.899596\pi$
$480$	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	0.847131	−	0.531384i	$-0.178328\pi$
$491$	−398.489	−	690.202i	−0.0366264	−	0.0634387i	−0.883758	+	0.467945i	$0.844994\pi$
$492$	−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	0.594360	−	0.804199i	$-0.297405\pi$
$499$	−4450.66	−	7708.78i	−0.399277	−	0.691567i	−0.993637	+	0.112632i	$0.964072\pi$
$500$	−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	0.0643734	−	0.997926i	$-0.479495\pi$
$503$	10112.6	−	17515.5i	0.896416	−	1.55264i	0.832042	−	0.554712i	$-0.187172\pi$
$504$	−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	−0.113651	+	0.993521i	$0.536255\pi$
$509$	−10533.2	+	18244.0i	−0.917240	+	1.58871i	−0.803588	+	0.595185i	$0.797079\pi$
$510$	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	−0.154532	+	0.987988i	$0.549387\pi$
$523$	−11157.9	+	19326.0i	−0.932889	+	1.61581i	−0.778356	+	0.627823i	$0.783946\pi$
$524$	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	−0.546343	−	0.837562i	$-0.683980\pi$
$541$	5689.92	−	9855.22i	0.452178	−	0.783196i	0.998521	+	0.0543657i	$0.0173137\pi$
$542$	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	−0.337969	−	0.941157i	$-0.609740\pi$
$547$	8265.48	−	14316.2i	0.646081	−	1.11905i	0.984051	−	0.177888i	$-0.0569266\pi$
$548$	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	−0.692421	−	0.721493i	$-0.743456\pi$
$557$	3662.66	−	6343.91i	0.278621	−	0.482586i	0.971042	+	0.238908i	$0.0767894\pi$
$558$	−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	0.856288	−	0.516499i	$-0.172765\pi$
$587$	−272.446	−	471.890i	−0.0191568	−	0.0331805i	−0.875445	+	0.483318i	$0.839432\pi$
$588$	−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	−0.995917	−	0.0902776i	$-0.971225\pi$
$593$	−6061.77	+	10499.3i	−0.419776	+	0.727073i	0.576141	+	0.817350i	$0.304558\pi$
$594$	−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	−0.00590371	−	0.999983i	$-0.501879\pi$
$599$	12652.6	−	21915.0i	0.863058	−	1.49486i	0.868962	−	0.494879i	$-0.164787\pi$
$600$	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	0.996275	−	0.0862324i	$-0.0274827\pi$
$613$	6426.89	+	11131.7i	0.423458	+	0.733451i	−0.572817	+	0.819683i	$0.694149\pi$
$614$	−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	−0.406203	−	0.913783i	$-0.633148\pi$
$617$	9015.61	−	15615.5i	0.588257	−	1.01889i	0.994461	−	0.105109i	$-0.0335192\pi$
$618$	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	−0.881733	−	0.471749i	$-0.843623\pi$
$631$	−512.279	+	887.293i	−0.0323193	+	0.0559787i	0.849413	+	0.527728i	$0.176956\pi$
$632$	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	−0.998988	−	0.0449875i	$-0.985675\pi$
$641$	−8738.48	−	15135.5i	−0.538454	−	0.932630i	0.460533	−	0.887642i	$-0.347658\pi$
$642$	−858.718	+	1487.34i	−0.0527896	+	0.0914342i
$643$	6716.23	+	11632.9i	0.411917	+	0.713460i	0.995099	−	0.0988805i	$-0.0315262\pi$
$643$	6716.23	+	11632.9i	0.411917	+	0.713460i	−0.583183	+	0.812341i	$0.698193\pi$
$644$	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	0.400797	+	0.916167i	$0.368733\pi$
$659$	−10032.3	+	17376.5i	−0.593025	+	1.02715i	−0.993822	+	0.110983i	$0.964600\pi$
$660$	−2086.40	−	3613.75i	−0.123050	−	0.213129i
$661$	−11859.5	+	20541.3i	−0.697855	+	1.20872i	0.271354	+	0.962480i	$0.412529\pi$
$661$	−11859.5	+	20541.3i	−0.697855	+	1.20872i	−0.969209	+	0.246241i	$0.920805\pi$
$662$	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	0.634579	−	0.772858i	$-0.281174\pi$
$701$	−6533.58	−	11316.5i	−0.352025	−	0.609726i	−0.986604	+	0.163132i	$0.947840\pi$
$702$	−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	−0.970548	−	0.240907i	$-0.922555\pi$
$709$	−5222.61	+	9045.83i	−0.276642	+	0.479158i	0.693906	+	0.720066i	$0.255888\pi$
$710$	−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	0.857500	−	0.514483i	$-0.172016\pi$
$719$	−324.001	−	561.185i	−0.0168055	−	0.0291080i	−0.874306	+	0.485375i	$0.838683\pi$
$720$	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	0.566513	−	0.824053i	$-0.308292\pi$
$727$	−8436.61	−	14612.6i	−0.430394	−	0.745465i	−0.996907	+	0.0785881i	$0.974959\pi$
$728$	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	0.566863	−	0.823812i	$-0.308157\pi$
$739$	−8638.65	−	14962.6i	−0.430011	−	0.744800i	−0.996874	+	0.0790119i	$0.974823\pi$
$740$	−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	−0.986106	−	0.166118i	$-0.946877\pi$
$743$	−12899.3	−	22342.2i	−0.636915	−	1.10317i	0.349190	−	0.937052i	$-0.386457\pi$
$744$	−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	−0.989288	−	0.145979i	$-0.953367\pi$
$751$	−7578.27	+	13125.9i	−0.368222	+	0.637780i	0.621065	+	0.783759i	$0.286700\pi$
$752$	−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	0.762561	−	0.646916i	$-0.223942\pi$
$757$	−3727.46	−	6456.14i	−0.178965	−	0.309977i	−0.941526	+	0.336939i	$0.890608\pi$
$758$	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	0.0509122	−	0.998703i	$-0.483787\pi$
$769$	18986.9	−	32886.3i	0.890358	−	1.54215i	0.839446	−	0.543443i	$-0.182880\pi$
$770$	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	−0.946577	−	0.322478i	$-0.895484\pi$
$773$	−4169.69	+	7222.11i	−0.194014	+	0.336043i	0.752563	+	0.658521i	$0.228818\pi$
$774$	−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	−0.550777	−	0.834652i	$-0.685669\pi$
$811$	10334.0	−	17899.0i	0.447441	−	0.774991i	0.998219	+	0.0596612i	$0.0190020\pi$
$812$	−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	−0.775232	−	0.631676i	$-0.782367\pi$
$821$	3750.50	−	6496.07i	0.159432	−	0.276144i	0.934664	+	0.355532i	$0.115700\pi$
$822$	7335.67	+	12705.7i	0.311266	+	0.539129i
$823$	181.148	−	313.757i	0.00767244	−	0.0132891i	−0.862164	−	0.506630i	$-0.830891\pi$
$823$	181.148	−	313.757i	0.00767244	−	0.0132891i	0.869836	+	0.493341i	$0.164224\pi$
$824$	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	−0.758863	−	0.651251i	$-0.774245\pi$
$827$	4389.51	−	7602.85i	0.184568	−	0.319682i	0.943431	+	0.331569i	$0.107578\pi$
$828$	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	0.955235	−	0.295848i	$-0.0956023\pi$
$839$	5380.60	+	9319.48i	0.221405	+	0.383485i	−0.733830	+	0.679334i	$0.762269\pi$
$840$	−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	0.812771	−	0.582584i	$-0.197958\pi$
$853$	−2445.13	−	4235.09i	−0.0981472	−	0.169996i	−0.910918	+	0.412588i	$0.864625\pi$
$854$	−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	0.992153	+	0.125026i	$0.0399015\pi$
$857$	15162.2	+	26261.7i	0.604353	+	1.04677i	−0.387801	+	0.921743i	$0.626765\pi$
$858$	690.063	+	1195.22i	0.0274573	+	0.0475574i
$859$	7535.78	−	13052.4i	0.299322	−	0.518441i	−0.676659	−	0.736296i	$-0.736573\pi$
$859$	7535.78	−	13052.4i	0.299322	−	0.518441i	0.975981	+	0.217856i	$0.0699062\pi$
$860$	−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	0.886442	−	0.462841i	$-0.153170\pi$
$877$	1100.91	+	1906.84i	0.0423891	+	0.0734200i	−0.844052	+	0.536261i	$0.819836\pi$
$878$	−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	−0.770776	−	0.637106i	$-0.780131\pi$
$883$	4365.12	−	7560.60i	0.166362	−	0.288148i	0.937138	+	0.348958i	$0.113465\pi$
$884$	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	−0.735801	−	0.677197i	$-0.763194\pi$
$887$	5773.98	−	10000.8i	0.218570	−	0.378574i	0.954371	+	0.298624i	$0.0965276\pi$
$888$	−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	0.924951	−	0.380086i	$-0.124106\pi$
$907$	3641.48	+	6307.22i	0.133311	+	0.230902i	−0.791640	+	0.610988i	$0.790772\pi$
$908$	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	0.755278	−	0.655404i	$-0.227502\pi$
$929$	−5378.74	−	9316.25i	−0.189958	−	0.329017i	−0.945236	+	0.326388i	$0.894168\pi$
$930$	−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	0.428848	+	0.903377i	$0.358920\pi$
$937$	−16289.2	+	28213.7i	−0.567923	+	0.983671i	−0.996771	+	0.0802948i	$0.974414\pi$
$938$	−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	0.129290	+	0.991607i	$0.458730\pi$
$941$	−22922.7	+	39703.3i	−0.794112	+	1.37544i	−0.923402	+	0.383835i	$0.874603\pi$
$942$	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	0.999843	−	0.0177080i	$-0.00563693\pi$
$947$	14122.0	+	24460.0i	0.484586	+	0.839328i	−0.515257	+	0.857036i	$0.672304\pi$
$948$	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	0.943064	+	0.332611i	$0.107930\pi$
$953$	22346.7	+	38705.7i	0.759582	+	1.31563i	−0.183483	+	0.983023i	$0.558737\pi$
$954$	−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	−0.943917	−	0.330182i	$-0.892890\pi$
$967$	−22790.5	−	39474.3i	−0.757905	−	1.31273i	0.186013	−	0.982547i	$-0.440443\pi$
$968$	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	0.902500	−	0.430690i	$-0.141730\pi$
$971$	2367.98	+	4101.46i	0.0782616	+	0.135553i	−0.824238	+	0.566243i	$0.808396\pi$
$972$	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	−0.997341	−	0.0728802i	$-0.976781\pi$
$983$	−17314.2	−	29989.0i	−0.561786	−	0.973043i	0.435554	−	0.900162i	$-0.356552\pi$
$984$	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	−0.999975	−	0.00702215i	$-0.997765\pi$
$991$	−15787.8	−	27345.2i	−0.506069	−	0.876537i	0.493906	−	0.869515i	$-0.335569\pi$
$992$	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	0.375343	+	0.926886i	$0.377525\pi$
$997$	−19361.7	+	33535.4i	−0.615035	+	1.06527i	−0.990378	+	0.138386i	$0.955808\pi$
$998$	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.7.3	✓	6
3.2	odd	2		342.4.g.g.235.1		6
19.7	even	3		2166.4.a.s.1.1		3
19.11	even	3	inner	114.4.e.e.49.3	yes	6
19.12	odd	6		2166.4.a.w.1.1		3
57.11	odd	6		342.4.g.g.163.1		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.e.7.3	✓	6	1.1	even	1	trivial
114.4.e.e.49.3	yes	6	19.11	even	3	inner
342.4.g.g.163.1		6	57.11	odd	6
342.4.g.g.235.1		6	3.2	odd	2
2166.4.a.s.1.1		3	19.7	even	3
2166.4.a.w.1.1		3	19.12	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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