LMFDB - Embedded newform 210.4.i.i.121.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [210,4,Mod(121,210)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(210, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 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("210.121");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 210 = 2 \cdot 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	210.i (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:	$12.3904011012$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{295})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 295x^{2} + 87025 $ x^4 + 295*x^2 + 87025
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			121.1
Root			$-8.58778 + 14.8745i$ of defining polynomial
Character	$\chi$	$=$	210.121
Dual form			210.4.i.i.151.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} -6.00000 q^{6} +(-2.58778 + 18.3386i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} -6.00000 q^{6} +(-2.58778 + 18.3386i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.00000 + 8.66025i) q^{10} +(-3.91222 - 6.77616i) q^{11} +(6.00000 - 10.3923i) q^{12} -32.8244 q^{13} +(-29.1756 - 22.8207i) q^{14} +15.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(34.4389 + 59.6499i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(-22.8511 + 39.5793i) q^{19} -20.0000 q^{20} +(-51.5267 + 20.7846i) q^{21} +15.6489 q^{22} +(-108.790 + 188.430i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(32.8244 - 56.8536i) q^{26} -27.0000 q^{27} +(68.7023 - 27.7128i) q^{28} -126.527 q^{29} +(-15.0000 + 25.9808i) q^{30} +(-84.5534 - 146.451i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(11.7367 - 20.3285i) q^{33} -137.756 q^{34} +(72.9389 + 57.0519i) q^{35} +36.0000 q^{36} +(121.290 - 210.081i) q^{37} +(-45.7023 - 79.1586i) q^{38} +(-49.2367 - 85.2804i) q^{39} +(20.0000 - 34.6410i) q^{40} -286.985 q^{41} +(15.5267 - 110.031i) q^{42} -54.2289 q^{43} +(-15.6489 + 27.1046i) q^{44} +(22.5000 + 38.9711i) q^{45} +(-217.580 - 376.860i) q^{46} +(-113.351 + 196.330i) q^{47} -48.0000 q^{48} +(-329.607 - 94.9125i) q^{49} +50.0000 q^{50} +(-103.317 + 178.950i) q^{51} +(65.6489 + 113.707i) q^{52} +(26.8778 + 46.5538i) q^{53} +(27.0000 - 46.7654i) q^{54} -39.1222 q^{55} +(-20.7023 + 146.709i) q^{56} -137.107 q^{57} +(126.527 - 219.151i) q^{58} +(435.301 + 753.964i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(232.351 - 402.444i) q^{61} +338.214 q^{62} +(-131.290 - 102.693i) q^{63} +64.0000 q^{64} +(-82.0611 + 142.134i) q^{65} +(23.4733 + 40.6570i) q^{66} +(105.359 + 182.487i) q^{67} +(137.756 - 238.600i) q^{68} -652.740 q^{69} +(-171.756 + 69.2820i) q^{70} +236.389 q^{71} +(-36.0000 + 62.3538i) q^{72} +(176.183 + 305.158i) q^{73} +(242.580 + 420.161i) q^{74} +(37.5000 - 64.9519i) q^{75} +182.809 q^{76} +(134.389 - 54.2093i) q^{77} +196.947 q^{78} +(-391.362 + 677.860i) q^{79} +(40.0000 + 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(286.985 - 497.072i) q^{82} +956.709 q^{83} +(175.053 + 136.924i) q^{84} +344.389 q^{85} +(54.2289 - 93.9273i) q^{86} +(-189.790 - 328.726i) q^{87} +(-31.2977 - 54.2093i) q^{88} +(-93.0190 + 161.114i) q^{89} -90.0000 q^{90} +(84.9425 - 601.953i) q^{91} +870.320 q^{92} +(253.660 - 439.352i) q^{93} +(-226.702 - 392.660i) q^{94} +(114.256 + 197.897i) q^{95} +(48.0000 - 83.1384i) q^{96} +10.1068 q^{97} +(494.000 - 475.983i) q^{98} +70.4199 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 24 q^{6} + 24 q^{7} + 32 q^{8} - 18 q^{9}+O(q^{10}) $ 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 24 * q^6 + 24 * q^7 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 24 q^{6} + 24 q^{7} + 32 q^{8} - 18 q^{9} + 20 q^{10} - 50 q^{11} + 24 q^{12} - 200 q^{13} - 48 q^{14} + 60 q^{15} - 32 q^{16} - 34 q^{17} - 36 q^{18} + 46 q^{19} - 80 q^{20} + 200 q^{22} - 126 q^{23} + 48 q^{24} - 50 q^{25} + 200 q^{26} - 108 q^{27} - 300 q^{29} - 60 q^{30} + 74 q^{31} - 64 q^{32} + 150 q^{33} + 136 q^{34} + 120 q^{35} + 144 q^{36} + 176 q^{37} + 92 q^{38} - 300 q^{39} + 80 q^{40} + 20 q^{41} - 144 q^{42} + 264 q^{43} - 200 q^{44} + 90 q^{45} - 252 q^{46} - 316 q^{47} - 192 q^{48} - 494 q^{49} + 200 q^{50} + 102 q^{51} + 400 q^{52} - 236 q^{53} + 108 q^{54} - 500 q^{55} + 192 q^{56} + 276 q^{57} + 300 q^{58} + 58 q^{59} - 120 q^{60} + 792 q^{61} - 296 q^{62} - 216 q^{63} + 256 q^{64} - 500 q^{65} + 300 q^{66} + 868 q^{67} - 136 q^{68} - 756 q^{69} - 772 q^{71} - 144 q^{72} + 1220 q^{73} + 352 q^{74} + 150 q^{75} - 368 q^{76} - 1180 q^{77} + 1200 q^{78} - 54 q^{79} + 160 q^{80} - 162 q^{81} - 20 q^{82} - 364 q^{83} + 288 q^{84} - 340 q^{85} - 264 q^{86} - 450 q^{87} - 400 q^{88} + 418 q^{89} - 360 q^{90} - 1790 q^{91} + 1008 q^{92} - 222 q^{93} - 632 q^{94} - 230 q^{95} + 192 q^{96} - 784 q^{97} + 1976 q^{98} + 900 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 24 * q^6 + 24 * q^7 + 32 * q^8 - 18 * q^9 + 20 * q^10 - 50 * q^11 + 24 * q^12 - 200 * q^13 - 48 * q^14 + 60 * q^15 - 32 * q^16 - 34 * q^17 - 36 * q^18 + 46 * q^19 - 80 * q^20 + 200 * q^22 - 126 * q^23 + 48 * q^24 - 50 * q^25 + 200 * q^26 - 108 * q^27 - 300 * q^29 - 60 * q^30 + 74 * q^31 - 64 * q^32 + 150 * q^33 + 136 * q^34 + 120 * q^35 + 144 * q^36 + 176 * q^37 + 92 * q^38 - 300 * q^39 + 80 * q^40 + 20 * q^41 - 144 * q^42 + 264 * q^43 - 200 * q^44 + 90 * q^45 - 252 * q^46 - 316 * q^47 - 192 * q^48 - 494 * q^49 + 200 * q^50 + 102 * q^51 + 400 * q^52 - 236 * q^53 + 108 * q^54 - 500 * q^55 + 192 * q^56 + 276 * q^57 + 300 * q^58 + 58 * q^59 - 120 * q^60 + 792 * q^61 - 296 * q^62 - 216 * q^63 + 256 * q^64 - 500 * q^65 + 300 * q^66 + 868 * q^67 - 136 * q^68 - 756 * q^69 - 772 * q^71 - 144 * q^72 + 1220 * q^73 + 352 * q^74 + 150 * q^75 - 368 * q^76 - 1180 * q^77 + 1200 * q^78 - 54 * q^79 + 160 * q^80 - 162 * q^81 - 20 * q^82 - 364 * q^83 + 288 * q^84 - 340 * q^85 - 264 * q^86 - 450 * q^87 - 400 * q^88 + 418 * q^89 - 360 * q^90 - 1790 * q^91 + 1008 * q^92 - 222 * q^93 - 632 * q^94 - 230 * q^95 + 192 * q^96 - 784 * q^97 + 1976 * q^98 + 900 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/210\mathbb{Z}\right)^\times$.

$n$	$31$	$71$	$127$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

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
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$5$	2.50000	−	4.33013i	0.223607	−	0.387298i
$6$	−6.00000			−0.408248
$7$	−2.58778	+	18.3386i	−0.139727	+	0.990190i
$7$	−2.58778	+	18.3386i	−0.139727	+	0.990190i
$8$	8.00000			0.353553
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$	5.00000	+	8.66025i	0.158114	+	0.273861i
$11$	−3.91222	−	6.77616i	−0.107234	−	0.185735i	0.807415	−	0.589985i	$-0.200866\pi$
$11$	−3.91222	−	6.77616i	−0.107234	−	0.185735i	−0.914649	+	0.404249i	$0.867533\pi$
$12$	6.00000	−	10.3923i	0.144338	−	0.250000i
$13$	−32.8244			−0.700297			−0.350148	−	0.936694i	$-0.613869\pi$
$13$	−32.8244			−0.700297			−0.350148	+	0.936694i	$0.613869\pi$
$14$	−29.1756	−	22.8207i	−0.556964	−	0.435650i
$15$	15.0000			0.258199
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	34.4389	+	59.6499i	0.491333	+	0.851014i	0.999950	−	0.00997894i	$-0.00317645\pi$
$17$	34.4389	+	59.6499i	0.491333	+	0.851014i	−0.508617	+	0.860993i	$0.669843\pi$
$18$	−9.00000	−	15.5885i	−0.117851	−	0.204124i
$19$	−22.8511	+	39.5793i	−0.275916	+	0.477901i	−0.970366	−	0.241640i	$-0.922315\pi$
$19$	−22.8511	+	39.5793i	−0.275916	+	0.477901i	0.694450	+	0.719541i	$0.255648\pi$
$20$	−20.0000			−0.223607
$21$	−51.5267	+	20.7846i	−0.535431	+	0.215980i
$22$	15.6489			0.151652
$23$	−108.790	+	188.430i	−0.986274	+	1.70828i	−0.350139	+	0.936698i	$0.613866\pi$
$23$	−108.790	+	188.430i	−0.986274	+	1.70828i	−0.636135	+	0.771578i	$0.719468\pi$
$24$	12.0000	+	20.7846i	0.102062	+	0.176777i
$25$	−12.5000	−	21.6506i	−0.100000	−	0.173205i
$26$	32.8244	−	56.8536i	0.247592	−	0.428843i
$27$	−27.0000			−0.192450
$28$	68.7023	−	27.7128i	0.463697	−	0.187044i
$29$	−126.527			−0.810187			−0.405093	−	0.914275i	$-0.632761\pi$
$29$	−126.527			−0.810187			−0.405093	+	0.914275i	$0.632761\pi$
$30$	−15.0000	+	25.9808i	−0.0912871	+	0.158114i
$31$	−84.5534	−	146.451i	−0.489879	−	0.848495i	0.510054	−	0.860143i	$-0.329626\pi$
$31$	−84.5534	−	146.451i	−0.489879	−	0.848495i	−0.999932	+	0.0116480i	$0.996292\pi$
$32$	−16.0000	−	27.7128i	−0.0883883	−	0.153093i
$33$	11.7367	−	20.3285i	0.0619118	−	0.107234i
$34$	−137.756			−0.694850
$35$	72.9389	+	57.0519i	0.352255	+	0.275529i
$36$	36.0000			0.166667
$37$	121.290	−	210.081i	0.538918	−	0.933433i	−0.460045	−	0.887896i	$-0.652167\pi$
$37$	121.290	−	210.081i	0.538918	−	0.933433i	0.998963	−	0.0455374i	$-0.0145000\pi$
$38$	−45.7023	−	79.1586i	−0.195102	−	0.337927i
$39$	−49.2367	−	85.2804i	−0.202158	−	0.350148i
$40$	20.0000	−	34.6410i	0.0790569	−	0.136931i
$41$	−286.985			−1.09316			−0.546579	−	0.837408i	$-0.684070\pi$
$41$	−286.985			−1.09316			−0.546579	+	0.837408i	$0.684070\pi$
$42$	15.5267	−	110.031i	0.0570433	−	0.404243i
$43$	−54.2289			−0.192322			−0.0961609	−	0.995366i	$-0.530656\pi$
$43$	−54.2289			−0.192322			−0.0961609	+	0.995366i	$0.530656\pi$
$44$	−15.6489	+	27.1046i	−0.0536172	+	0.0928677i
$45$	22.5000	+	38.9711i	0.0745356	+	0.129099i
$46$	−217.580	−	376.860i	−0.697401	−	1.20793i
$47$	−113.351	+	196.330i	−0.351786	+	0.609312i	−0.986563	−	0.163384i	$-0.947759\pi$
$47$	−113.351	+	196.330i	−0.351786	+	0.609312i	0.634776	+	0.772696i	$0.281092\pi$
$48$	−48.0000			−0.144338
$49$	−329.607	−	94.9125i	−0.960953	−	0.276713i
$50$	50.0000			0.141421
$51$	−103.317	+	178.950i	−0.283671	+	0.491333i
$52$	65.6489	+	113.707i	0.175074	+	0.303237i
$53$	26.8778	+	46.5538i	0.0696595	+	0.120654i	0.898751	−	0.438459i	$-0.144475\pi$
$53$	26.8778	+	46.5538i	0.0696595	+	0.120654i	−0.829092	+	0.559112i	$0.811142\pi$
$54$	27.0000	−	46.7654i	0.0680414	−	0.117851i
$55$	−39.1222			−0.0959133
$56$	−20.7023	+	146.709i	−0.0494010	+	0.350085i
$57$	−137.107			−0.318601
$58$	126.527	−	219.151i	0.286444	−	0.496136i
$59$	435.301	+	753.964i	0.960532	+	1.66369i	0.721167	+	0.692761i	$0.243606\pi$
$59$	435.301	+	753.964i	0.960532	+	1.66369i	0.239365	+	0.970930i	$0.423061\pi$
$60$	−30.0000	−	51.9615i	−0.0645497	−	0.111803i
$61$	232.351	−	402.444i	0.487697	−	0.844716i	−0.512203	−	0.858864i	$-0.671170\pi$
$61$	232.351	−	402.444i	0.487697	−	0.844716i	0.999900	+	0.0141486i	$0.00450378\pi$
$62$	338.214			0.692793
$63$	−131.290	−	102.693i	−0.262555	−	0.205367i
$64$	64.0000			0.125000
$65$	−82.0611	+	142.134i	−0.156591	+	0.271224i
$66$	23.4733	+	40.6570i	0.0437782	+	0.0758262i
$67$	105.359	+	182.487i	0.192114	+	0.332751i	0.945951	−	0.324311i	$-0.105132\pi$
$67$	105.359	+	182.487i	0.192114	+	0.332751i	−0.753837	+	0.657062i	$0.771799\pi$
$68$	137.756	−	238.600i	0.245667	−	0.425507i
$69$	−652.740			−1.13885
$70$	−171.756	+	69.2820i	−0.293268	+	0.118297i
$71$	236.389			0.395130			0.197565	−	0.980290i	$-0.436697\pi$
$71$	236.389			0.395130			0.197565	+	0.980290i	$0.436697\pi$
$72$	−36.0000	+	62.3538i	−0.0589256	+	0.102062i
$73$	176.183	+	305.158i	0.282475	+	0.489261i	0.971994	−	0.235007i	$-0.0755112\pi$
$73$	176.183	+	305.158i	0.282475	+	0.489261i	−0.689519	+	0.724268i	$0.742178\pi$
$74$	242.580	+	420.161i	0.381072	+	0.660037i
$75$	37.5000	−	64.9519i	0.0577350	−	0.100000i
$76$	182.809			0.275916
$77$	134.389	−	54.2093i	0.198897	−	0.0802301i
$78$	196.947			0.285895
$79$	−391.362	+	677.860i	−0.557363	+	0.965382i	0.440352	+	0.897825i	$0.354854\pi$
$79$	−391.362	+	677.860i	−0.557363	+	0.965382i	−0.997715	+	0.0675566i	$0.978480\pi$
$80$	40.0000	+	69.2820i	0.0559017	+	0.0968246i
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$	286.985	−	497.072i	0.386490	−	0.669420i
$83$	956.709			1.26521			0.632605	−	0.774474i	$-0.281986\pi$
$83$	956.709			1.26521			0.632605	+	0.774474i	$0.281986\pi$
$84$	175.053	+	136.924i	0.227380	+	0.177853i
$85$	344.389			0.439462
$86$	54.2289	−	93.9273i	0.0679960	−	0.117773i
$87$	−189.790	−	328.726i	−0.233881	−	0.405093i
$88$	−31.2977	−	54.2093i	−0.0379131	−	0.0656674i
$89$	−93.0190	+	161.114i	−0.110786	+	0.191888i	−0.916088	−	0.400978i	$-0.868670\pi$
$89$	−93.0190	+	161.114i	−0.110786	+	0.191888i	0.805301	+	0.592866i	$0.202004\pi$
$90$	−90.0000			−0.105409
$91$	84.9425	−	601.953i	0.0978505	−	0.693427i
$92$	870.320			0.986274
$93$	253.660	−	439.352i	0.282832	−	0.489879i
$94$	−226.702	−	392.660i	−0.248751	−	0.430849i
$95$	114.256	+	197.897i	0.123393	+	0.213724i
$96$	48.0000	−	83.1384i	0.0510310	−	0.0883883i
$97$	10.1068			0.0105792			0.00528962	−	0.999986i	$-0.498316\pi$
$97$	10.1068			0.0105792			0.00528962	+	0.999986i	$0.498316\pi$
$98$	494.000	−	475.983i	0.509199	−	0.490628i
$99$	70.4199			0.0714896
$100$	−50.0000	+	86.6025i	−0.0500000	+	0.0866025i
$101$	725.210	+	1256.10i	0.714466	+	1.23749i	0.963165	+	0.268911i	$0.0866637\pi$
$101$	725.210	+	1256.10i	0.714466	+	1.23749i	−0.248699	+	0.968581i	$0.580003\pi$
$102$	−206.633	−	357.900i	−0.200586	−	0.347425i
$103$	322.695	−	558.923i	0.308699	−	0.534683i	−0.669379	−	0.742921i	$-0.733440\pi$
$103$	322.695	−	558.923i	0.308699	−	0.534683i	0.978078	+	0.208238i	$0.0667730\pi$
$104$	−262.595			−0.247592
$105$	−38.8167	+	275.079i	−0.0360774	+	0.255666i
$106$	−107.511			−0.0985134
$107$	262.477	−	454.623i	0.237146	−	0.410749i	−0.722748	−	0.691111i	$-0.757121\pi$
$107$	262.477	−	454.623i	0.237146	−	0.410749i	0.959894	+	0.280363i	$0.0904548\pi$
$108$	54.0000	+	93.5307i	0.0481125	+	0.0833333i
$109$	528.256	+	914.966i	0.464199	+	0.804017i	0.999165	−	0.0408571i	$-0.0130088\pi$
$109$	528.256	+	914.966i	0.464199	+	0.804017i	−0.534966	+	0.844874i	$0.679676\pi$
$110$	39.1222	−	67.7616i	0.0339105	−	0.0587347i
$111$	727.740			0.622289
$112$	−233.405	−	182.566i	−0.196917	−	0.154026i
$113$	252.809			0.210463			0.105231	−	0.994448i	$-0.466442\pi$
$113$	252.809			0.210463			0.105231	+	0.994448i	$0.466442\pi$
$114$	137.107	−	237.476i	0.112642	−	0.195102i
$115$	543.950	+	942.149i	0.441075	+	0.763964i
$116$	253.053	+	438.301i	0.202547	+	0.350821i
$117$	147.710	−	255.841i	0.116716	−	0.202158i
$118$	−1741.21			−1.35840
$119$	−1183.02	+	477.200i	−0.911318	+	0.367603i
$120$	120.000			0.0912871
$121$	634.889	−	1099.66i	0.477002	−	0.826191i
$122$	464.702	+	804.888i	0.344854	+	0.597304i
$123$	−430.477	−	745.608i	−0.315567	−	0.546579i
$124$	−338.214	+	585.803i	−0.244939	+	0.424247i
$125$	−125.000			−0.0894427
$126$	309.160	−	124.708i	0.218589	−	0.0881733i
$127$	2419.14			1.69027			0.845135	−	0.534552i	$-0.179520\pi$
$127$	2419.14			1.69027			0.845135	+	0.534552i	$0.179520\pi$
$128$	−64.0000	+	110.851i	−0.0441942	+	0.0765466i
$129$	−81.3434	−	140.891i	−0.0555185	−	0.0961609i
$130$	−164.122	−	284.268i	−0.110727	−	0.191784i
$131$	825.282	−	1429.43i	0.550422	−	0.953358i	−0.447822	−	0.894123i	$-0.647800\pi$
$131$	825.282	−	1429.43i	0.550422	−	0.953358i	0.998244	−	0.0592359i	$-0.0188664\pi$
$132$	−93.8932			−0.0619118
$133$	−666.695	−	521.480i	−0.434660	−	0.339985i
$134$	−421.435			−0.271690
$135$	−67.5000	+	116.913i	−0.0430331	+	0.0745356i
$136$	275.511	+	477.200i	0.173712	+	0.300879i
$137$	885.950	+	1534.51i	0.552495	+	0.956950i	0.998094	+	0.0617168i	$0.0196575\pi$
$137$	885.950	+	1534.51i	0.552495	+	0.956950i	−0.445599	+	0.895233i	$0.647009\pi$
$138$	652.740	−	1130.58i	0.402644	−	0.697401i
$139$	−2360.54			−1.44042			−0.720211	−	0.693755i	$-0.755955\pi$
$139$	−2360.54			−1.44042			−0.720211	+	0.693755i	$0.755955\pi$
$140$	51.7556	−	366.772i	0.0312439	−	0.221413i
$141$	−680.107			−0.406208
$142$	−236.389	+	409.438i	−0.139700	+	0.241967i
$143$	128.416	+	222.424i	0.0750959	+	0.130070i
$144$	−72.0000	−	124.708i	−0.0416667	−	0.0721688i
$145$	−316.317	+	547.877i	−0.181163	+	0.313784i
$146$	−704.733			−0.399480
$147$	−247.820	−	998.712i	−0.139047	−	0.560356i
$148$	−970.320			−0.538918
$149$	−587.587	+	1017.73i	−0.323067	+	0.559569i	−0.981119	−	0.193404i	$-0.938047\pi$
$149$	−587.587	+	1017.73i	−0.323067	+	0.559569i	0.658052	+	0.752972i	$0.271381\pi$
$150$	75.0000	+	129.904i	0.0408248	+	0.0707107i
$151$	1089.95	+	1887.84i	0.587408	+	1.01742i	0.994571	+	0.104065i	$0.0331849\pi$
$151$	1089.95	+	1887.84i	0.587408	+	1.01742i	−0.407163	+	0.913356i	$0.633482\pi$
$152$	−182.809	+	316.635i	−0.0975511	+	0.168963i
$153$	−619.900			−0.327555
$154$	−40.4959	+	286.978i	−0.0211899	+	0.150165i
$155$	−845.534			−0.438161
$156$	−196.947	+	341.122i	−0.101079	+	0.175074i
$157$	−1352.34	−	2342.31i	−0.687440	−	1.19068i	−0.972663	−	0.232220i	$-0.925401\pi$
$157$	−1352.34	−	2342.31i	−0.687440	−	1.19068i	0.285223	−	0.958461i	$-0.407932\pi$
$158$	−782.725	−	1355.72i	−0.394115	−	0.682628i
$159$	−80.6335	+	139.661i	−0.0402179	+	0.0696595i
$160$	−160.000			−0.0790569
$161$	−3174.01	−	2482.67i	−1.55371	−	1.21529i
$162$	162.000			0.0785674
$163$	1300.43	−	2252.41i	0.624891	−	1.08234i	−0.363670	−	0.931528i	$-0.618477\pi$
$163$	1300.43	−	2252.41i	0.624891	−	1.08234i	0.988562	−	0.150816i	$-0.0481901\pi$
$164$	573.969	+	994.144i	0.273289	+	0.473351i
$165$	−58.6833	−	101.642i	−0.0276878	−	0.0479567i
$166$	−956.709	+	1657.07i	−0.447320	+	0.774780i
$167$	−3581.70			−1.65964			−0.829821	−	0.558029i	$-0.811558\pi$
$167$	−3581.70			−1.65964			−0.829821	+	0.558029i	$0.811558\pi$
$168$	−412.214	+	166.277i	−0.189303	+	0.0763604i
$169$	−1119.56			−0.509584
$170$	−344.389	+	596.499i	−0.155373	+	0.269114i
$171$	−205.660	−	356.214i	−0.0919721	−	0.159300i
$172$	108.458	+	187.855i	0.0480804	+	0.0832778i
$173$	1273.34	−	2205.48i	0.559595	−	0.969247i	−0.437935	−	0.899007i	$-0.644290\pi$
$173$	1273.34	−	2205.48i	0.559595	−	0.969247i	0.997530	−	0.0702403i	$-0.0223766\pi$
$174$	759.160			0.330757
$175$	429.389	−	173.205i	0.185479	−	0.0748176i
$176$	125.191			0.0536172
$177$	−1305.90	+	2261.89i	−0.554564	+	0.960532i
$178$	−186.038	−	322.227i	−0.0783378	−	0.135685i
$179$	1967.11	+	3407.13i	0.821388	+	1.42269i	0.904649	+	0.426158i	$0.140133\pi$
$179$	1967.11	+	3407.13i	0.821388	+	1.42269i	−0.0832607	+	0.996528i	$0.526533\pi$
$180$	90.0000	−	155.885i	0.0372678	−	0.0645497i
$181$	−2931.18			−1.20372			−0.601859	−	0.798602i	$-0.705573\pi$
$181$	−2931.18			−1.20372			−0.601859	+	0.798602i	$0.705573\pi$
$182$	957.671	+	749.078i	0.390040	+	0.305084i
$183$	1394.11			0.563144
$184$	−870.320	+	1507.44i	−0.348700	+	0.603967i
$185$	−606.450	−	1050.40i	−0.241011	−	0.417444i
$186$	507.320	+	878.705i	0.199992	+	0.346396i
$187$	269.465	−	466.727i	0.105376	−	0.182516i
$188$	906.809			0.351786
$189$	69.8701	−	495.142i	0.0268905	−	0.190562i
$190$	−457.023			−0.174505
$191$	1722.16	−	2982.87i	0.652414	−	1.13001i	−0.330121	−	0.943939i	$-0.607090\pi$
$191$	1722.16	−	2982.87i	0.652414	−	1.13001i	0.982535	−	0.186076i	$-0.0595771\pi$
$192$	96.0000	+	166.277i	0.0360844	+	0.0625000i
$193$	912.443	+	1580.40i	0.340306	+	0.589428i	0.984489	−	0.175444i	$-0.0561360\pi$
$193$	912.443	+	1580.40i	0.340306	+	0.589428i	−0.644183	+	0.764871i	$0.722803\pi$
$194$	−10.1068	+	17.5054i	−0.00374033	+	0.00647844i
$195$	−492.367			−0.180816
$196$	330.427	+	1331.62i	0.120418	+	0.485283i
$197$	−1760.47			−0.636690			−0.318345	−	0.947975i	$-0.603127\pi$
$197$	−1760.47			−0.636690			−0.318345	+	0.947975i	$0.603127\pi$
$198$	−70.4199	+	121.971i	−0.0252754	+	0.0437782i
$199$	−841.733	−	1457.92i	−0.299844	−	0.519344i	0.676256	−	0.736666i	$-0.263601\pi$
$199$	−841.733	−	1457.92i	−0.299844	−	0.519344i	−0.976100	+	0.217322i	$0.930268\pi$
$200$	−100.000	−	173.205i	−0.0353553	−	0.0612372i
$201$	−316.077	+	547.461i	−0.110917	+	0.192114i
$202$	−2900.84			−1.01041
$203$	327.423	−	2320.32i	0.113205	−	0.802239i
$204$	826.534			0.283671
$205$	−717.461	+	1242.68i	−0.244437	+	0.423378i
$206$	645.389	+	1117.85i	0.218283	+	0.378078i
$207$	−979.110	−	1695.87i	−0.328758	−	0.569425i
$208$	262.595	−	454.829i	0.0875371	−	0.151619i
$209$	357.594			0.118351
$210$	−437.633	−	342.311i	−0.143808	−	0.112484i
$211$	5897.72			1.92425			0.962124	−	0.272614i	$-0.0878882\pi$
$211$	5897.72			1.92425			0.962124	+	0.272614i	$0.0878882\pi$
$212$	107.511	−	186.215i	0.0348297	−	0.0603269i
$213$	354.584	+	614.157i	0.114064	+	0.197565i
$214$	524.954	+	909.247i	0.167687	+	0.290443i
$215$	−135.572	+	234.818i	−0.0430045	+	0.0744859i
$216$	−216.000			−0.0680414
$217$	2904.50	−	1171.61i	0.908620	−	0.366515i
$218$	−2113.02			−0.656477
$219$	−528.550	+	915.475i	−0.163087	+	0.282475i
$220$	78.2444	+	135.523i	0.0239783	+	0.0415317i
$221$	−1130.44	−	1957.98i	−0.344079	−	0.595962i
$222$	−727.740	+	1260.48i	−0.220012	+	0.381072i
$223$	−78.3677			−0.0235331			−0.0117666	−	0.999931i	$-0.503745\pi$
$223$	−78.3677			−0.0235331			−0.0117666	+	0.999931i	$0.503745\pi$
$224$	549.618	−	221.703i	0.163942	−	0.0661300i
$225$	225.000			0.0666667
$226$	−252.809	+	437.878i	−0.0744098	+	0.128881i
$227$	−387.714	−	671.541i	−0.113363	−	0.196351i	0.803761	−	0.594952i	$-0.202829\pi$
$227$	−387.714	−	671.541i	−0.113363	−	0.196351i	−0.917124	+	0.398601i	$0.869496\pi$
$228$	274.214	+	474.952i	0.0796502	+	0.137958i
$229$	−583.110	+	1009.98i	−0.168266	+	0.291446i	−0.937810	−	0.347148i	$-0.887150\pi$
$229$	−583.110	+	1009.98i	−0.168266	+	0.291446i	0.769544	+	0.638594i	$0.220484\pi$
$230$	−2175.80			−0.623774
$231$	342.423	+	267.839i	0.0975317	+	0.0762880i
$232$	−1012.21			−0.286444
$233$	−704.153	+	1219.63i	−0.197985	+	0.342921i	−0.947875	−	0.318642i	$-0.896773\pi$
$233$	−704.153	+	1219.63i	−0.197985	+	0.342921i	0.749890	+	0.661563i	$0.230107\pi$
$234$	295.420	+	511.682i	0.0825308	+	0.142948i
$235$	566.756	+	981.650i	0.157324	+	0.272493i
$236$	1741.21	−	3015.86i	0.480266	−	0.831845i
$237$	−2348.17			−0.643588
$238$	356.482	−	2526.24i	0.0970894	−	0.688033i
$239$	4474.37			1.21097			0.605487	−	0.795855i	$-0.292978\pi$
$239$	4474.37			1.21097			0.605487	+	0.795855i	$0.292978\pi$
$240$	−120.000	+	207.846i	−0.0322749	+	0.0559017i
$241$	−1485.23	−	2572.49i	−0.396979	−	0.687588i	0.596372	−	0.802708i	$-0.296608\pi$
$241$	−1485.23	−	2572.49i	−0.396979	−	0.687588i	−0.993352	+	0.115120i	$0.963275\pi$
$242$	1269.78	+	2199.32i	0.337291	+	0.584205i
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$	−1858.81			−0.487697
$245$	−1235.00	+	1189.96i	−0.322046	+	0.310301i
$246$	1721.91			0.446280
$247$	750.075	−	1299.17i	0.193223	−	0.334673i
$248$	−676.427	−	1171.61i	−0.173198	−	0.299988i
$249$	1435.06	+	2485.60i	0.365235	+	0.632605i
$250$	125.000	−	216.506i	0.0316228	−	0.0547723i
$251$	−4254.34			−1.06985			−0.534924	−	0.844900i	$-0.679660\pi$
$251$	−4254.34			−1.06985			−0.534924	+	0.844900i	$0.679660\pi$
$252$	−93.1602	+	660.189i	−0.0232878	+	0.165032i
$253$	1702.44			0.423050
$254$	−2419.14	+	4190.08i	−0.597601	+	1.03508i
$255$	516.584	+	894.749i	0.126862	+	0.219731i
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	−1326.58	+	2297.70i	−0.321982	+	0.557690i	−0.980897	−	0.194528i	$-0.937683\pi$
$257$	−1326.58	+	2297.70i	−0.321982	+	0.557690i	0.658915	+	0.752218i	$0.271016\pi$
$258$	325.374			0.0785150
$259$	3538.71	+	2767.93i	0.848975	+	0.664057i
$260$	656.489			0.156591
$261$	569.370	−	986.178i	0.135031	−	0.233881i
$262$	1650.56	+	2858.86i	0.389207	+	0.674126i
$263$	3298.82	+	5713.72i	0.773436	+	1.33963i	0.935669	+	0.352878i	$0.114797\pi$
$263$	3298.82	+	5713.72i	0.773436	+	1.33963i	−0.162233	+	0.986752i	$0.551870\pi$
$264$	93.8932	−	162.628i	0.0218891	−	0.0379131i
$265$	268.778			0.0623053
$266$	1569.92	−	633.269i	0.361873	−	0.145971i
$267$	−558.114			−0.127925
$268$	421.435	−	729.947i	0.0960569	−	0.166376i
$269$	−2331.85	−	4038.88i	−0.528532	−	0.915445i	−0.999447	−	0.0332659i	$-0.989409\pi$
$269$	−2331.85	−	4038.88i	−0.528532	−	0.915445i	0.470914	−	0.882179i	$-0.343924\pi$
$270$	−135.000	−	233.827i	−0.0304290	−	0.0527046i
$271$	−451.337	+	781.738i	−0.101169	+	0.175230i	−0.912166	−	0.409820i	$-0.865592\pi$
$271$	−451.337	+	781.738i	−0.101169	+	0.175230i	0.810998	+	0.585049i	$0.198925\pi$
$272$	−1102.05			−0.245667
$273$	1691.33	−	682.243i	0.374961	−	0.151250i
$274$	−3543.80			−0.781346
$275$	−97.8054	+	169.404i	−0.0214469	+	0.0371471i
$276$	1305.48	+	2261.16i	0.284713	+	0.493137i
$277$	−322.588	−	558.738i	−0.0699726	−	0.121196i	0.828916	−	0.559373i	$-0.188958\pi$
$277$	−322.588	−	558.738i	−0.0699726	−	0.121196i	−0.898889	+	0.438176i	$0.855625\pi$
$278$	2360.54	−	4088.58i	0.509266	−	0.882074i
$279$	1521.96			0.326586
$280$	583.511	+	456.415i	0.124541	+	0.0974143i
$281$	−4459.75			−0.946785			−0.473392	−	0.880852i	$-0.656971\pi$
$281$	−4459.75			−0.946785			−0.473392	+	0.880852i	$0.656971\pi$
$282$	680.107	−	1177.98i	0.143616	−	0.248751i
$283$	2755.61	+	4772.86i	0.578813	+	1.00253i	0.995616	+	0.0935364i	$0.0298172\pi$
$283$	2755.61	+	4772.86i	0.578813	+	1.00253i	−0.416803	+	0.908997i	$0.636850\pi$
$284$	−472.778	−	818.876i	−0.0987825	−	0.171096i
$285$	−342.767	+	593.690i	−0.0712413	+	0.123393i
$286$	−513.665			−0.106202
$287$	742.654	−	5262.89i	0.152744	−	1.08243i
$288$	288.000			0.0589256
$289$	84.4229	−	146.225i	0.0171836	−	0.0297628i
$290$	−632.633	−	1095.75i	−0.128102	−	0.221879i
$291$	15.1602	+	26.2582i	0.00305397	+	0.00528962i
$292$	704.733	−	1220.63i	0.141238	−	0.244631i
$293$	2837.19			0.565701			0.282851	−	0.959164i	$-0.408720\pi$
$293$	2837.19			0.565701			0.282851	+	0.959164i	$0.408720\pi$
$294$	1977.64	+	569.475i	0.392307	+	0.112968i
$295$	4353.01			0.859126
$296$	970.320	−	1680.64i	0.190536	−	0.330018i
$297$	105.630	+	182.956i	0.0206373	+	0.0357448i
$298$	−1175.17	−	2035.46i	−0.228443	−	0.395675i
$299$	3570.97	−	6185.10i	0.690684	−	1.19630i
$300$	−300.000			−0.0577350
$301$	140.333	−	994.482i	0.0268726	−	0.190435i
$302$	−4359.79			−0.830720
$303$	−2175.63	+	3768.30i	−0.412497	+	0.714466i
$304$	−365.618	−	633.269i	−0.0689791	−	0.119475i
$305$	−1161.76	−	2012.22i	−0.218105	−	0.377768i
$306$	619.900	−	1073.70i	0.115808	−	0.200586i
$307$	7929.20			1.47408			0.737041	−	0.675848i	$-0.236222\pi$
$307$	7929.20			1.47408			0.737041	+	0.675848i	$0.236222\pi$
$308$	−456.565	−	357.119i	−0.0844649	−	0.0660673i
$309$	1936.17			0.356455
$310$	845.534	−	1464.51i	0.154913	−	0.268318i
$311$	−4140.93	−	7172.29i	−0.755017	−	1.30773i	−0.945366	−	0.326012i	$-0.894295\pi$
$311$	−4140.93	−	7172.29i	−0.755017	−	1.30773i	0.190349	−	0.981717i	$-0.439038\pi$
$312$	−393.893	−	682.243i	−0.0714738	−	0.123796i
$313$	−342.703	+	593.579i	−0.0618872	+	0.107192i	−0.895309	−	0.445446i	$-0.853045\pi$
$313$	−342.703	+	593.579i	−0.0618872	+	0.107192i	0.833422	+	0.552638i	$0.186379\pi$
$314$	5409.34			0.972188
$315$	−772.900	+	311.769i	−0.138248	+	0.0557657i
$316$	3130.90			0.557363
$317$	−2896.87	+	5017.53i	−0.513264	+	0.888999i	0.486618	+	0.873615i	$0.338230\pi$
$317$	−2896.87	+	5017.53i	−0.513264	+	0.888999i	−0.999882	+	0.0153840i	$0.995103\pi$
$318$	−161.267	−	279.323i	−0.0284384	−	0.0492567i
$319$	495.000	+	857.365i	0.0868799	+	0.150480i
$320$	160.000	−	277.128i	0.0279508	−	0.0484123i
$321$	1574.86			0.273832
$322$	7474.12	−	3014.88i	1.29353	−	0.521778i
$323$	−3147.87			−0.542267
$324$	−162.000	+	280.592i	−0.0277778	+	0.0481125i
$325$	410.305	+	710.670i	0.0700297	+	0.121295i
$326$	2600.85	+	4504.81i	0.441865	+	0.765333i
$327$	−1584.77	+	2744.90i	−0.268006	+	0.464199i
$328$	−2295.88			−0.386490
$329$	−3307.08	−	2586.76i	−0.554181	−	0.433473i
$330$	234.733			0.0391565
$331$	780.150	−	1351.26i	0.129550	−	0.224387i	−0.793953	−	0.607980i	$-0.791980\pi$
$331$	780.150	−	1351.26i	0.129550	−	0.224387i	0.923502	+	0.383593i	$0.125314\pi$
$332$	−1913.42	−	3314.14i	−0.316303	−	0.547852i
$333$	1091.61	+	1890.72i	0.179639	+	0.311144i
$334$	3581.70	−	6203.69i	0.586772	−	1.01632i
$335$	1053.59			0.171832
$336$	124.214	−	880.252i	0.0201679	−	0.142922i
$337$	1543.88			0.249556			0.124778	−	0.992185i	$-0.460178\pi$
$337$	1543.88			0.249556			0.124778	+	0.992185i	$0.460178\pi$
$338$	1119.56	−	1939.13i	0.180165	−	0.312055i
$339$	379.214	+	656.817i	0.0607553	+	0.105231i
$340$	−688.778	−	1193.00i	−0.109865	−	0.190292i
$341$	−661.583	+	1145.89i	−0.105064	+	0.181976i
$342$	822.641			0.130068
$343$	2593.51	−	5798.91i	0.408269	−	0.912862i
$344$	−433.832			−0.0679960
$345$	−1631.85	+	2826.45i	−0.254655	+	0.441075i
$346$	2546.67	+	4410.96i	0.395693	+	0.685361i
$347$	239.604	+	415.006i	0.0370680	+	0.0642037i	0.883964	−	0.467555i	$-0.154865\pi$
$347$	239.604	+	415.006i	0.0370680	+	0.0642037i	−0.846896	+	0.531758i	$0.821532\pi$
$348$	−759.160	+	1314.90i	−0.116940	+	0.202547i
$349$	−9446.15			−1.44883			−0.724414	−	0.689366i	$-0.757889\pi$
$349$	−9446.15			−1.44883			−0.724414	+	0.689366i	$0.757889\pi$
$350$	−129.389	+	916.929i	−0.0197604	+	0.140034i
$351$	886.260			0.134772
$352$	−125.191	+	216.837i	−0.0189565	+	0.0328337i
$353$	3447.72	+	5971.62i	0.519840	+	0.900390i	0.999734	+	0.0230630i	$0.00734183\pi$
$353$	3447.72	+	5971.62i	0.519840	+	0.900390i	−0.479894	+	0.877327i	$0.659325\pi$
$354$	−2611.81	−	4523.78i	−0.392136	−	0.679199i
$355$	590.973	−	1023.59i	0.0883537	−	0.153033i
$356$	744.152			0.110786
$357$	−3014.32	−	2357.76i	−0.446877	−	0.349541i
$358$	−7868.43			−1.16162
$359$	1414.83	−	2450.55i	0.207999	−	0.360265i	−0.743085	−	0.669197i	$-0.766638\pi$
$359$	1414.83	−	2450.55i	0.207999	−	0.360265i	0.951084	+	0.308932i	$0.0999715\pi$
$360$	180.000	+	311.769i	0.0263523	+	0.0456435i
$361$	2385.15	+	4131.20i	0.347740	+	0.602304i
$362$	2931.18	−	5076.96i	0.425579	−	0.737124i
$363$	3809.33			0.550794
$364$	−2255.11	+	909.657i	−0.324725	+	0.130986i
$365$	1761.83			0.252654
$366$	−1394.11	+	2414.66i	−0.199101	+	0.344854i
$367$	117.848	+	204.118i	0.0167618	+	0.0290323i	0.874285	−	0.485414i	$-0.161331\pi$
$367$	117.848	+	204.118i	0.0167618	+	0.0290323i	−0.857523	+	0.514446i	$0.827998\pi$
$368$	−1740.64	−	3014.88i	−0.246568	−	0.427069i
$369$	1291.43	−	2236.82i	0.182193	−	0.315567i
$370$	2425.80			0.340842
$371$	−923.283	+	372.430i	−0.129203	+	0.0521175i
$372$	−2029.28			−0.282832
$373$	−5935.43	+	10280.5i	−0.823928	+	1.42708i	0.0788083	+	0.996890i	$0.474889\pi$
$373$	−5935.43	+	10280.5i	−0.823928	+	1.42708i	−0.902736	+	0.430195i	$0.858445\pi$
$374$	538.930	+	933.454i	0.0745118	+	0.129058i
$375$	−187.500	−	324.760i	−0.0258199	−	0.0447214i
$376$	−906.809	+	1570.64i	−0.124375	+	0.215424i
$377$	4153.17			0.567371
$378$	787.740	+	616.160i	0.107188	+	0.0838409i
$379$	2277.70			0.308701			0.154351	−	0.988016i	$-0.450671\pi$
$379$	2277.70			0.308701			0.154351	+	0.988016i	$0.450671\pi$
$380$	457.023	−	791.586i	0.0616967	−	0.106862i
$381$	3628.72	+	6285.12i	0.487939	+	0.845135i
$382$	3444.32	+	5965.74i	0.461327	+	0.799041i
$383$	−2029.07	+	3514.46i	−0.270707	+	0.468879i	−0.969043	−	0.246891i	$-0.920591\pi$
$383$	−2029.07	+	3514.46i	−0.270707	+	0.468879i	0.698336	+	0.715770i	$0.253924\pi$
$384$	−384.000			−0.0510310
$385$	101.240	−	717.445i	0.0134017	−	0.0949724i
$386$	−3649.77			−0.481266
$387$	244.030	−	422.673i	0.0320536	−	0.0555185i
$388$	−20.2135	−	35.0109i	−0.00264481	−	0.00458095i
$389$	1701.16	+	2946.49i	0.221728	+	0.384044i	0.955333	−	0.295532i	$-0.0954970\pi$
$389$	1701.16	+	2946.49i	0.221728	+	0.384044i	−0.733605	+	0.679576i	$0.762164\pi$
$390$	492.367	−	852.804i	0.0639281	−	0.110727i
$391$	−14986.4			−1.93836
$392$	−2636.85	−	759.300i	−0.339748	−	0.0978327i
$393$	4951.69			0.635572
$394$	1760.47	−	3049.21i	0.225104	−	0.389891i
$395$	1956.81	+	3389.30i	0.249261	+	0.431732i
$396$	−140.840	−	243.942i	−0.0178724	−	0.0309559i
$397$	−2600.77	+	4504.67i	−0.328788	+	0.569478i	−0.982272	−	0.187463i	$-0.939974\pi$
$397$	−2600.77	+	4504.67i	−0.328788	+	0.569478i	0.653483	+	0.756941i	$0.273307\pi$
$398$	3366.93			0.424043
$399$	354.802	−	2514.34i	0.0445171	−	0.315475i
$400$	400.000			0.0500000
$401$	426.130	−	738.080i	0.0530672	−	0.0919151i	−0.838272	−	0.545253i	$-0.816434\pi$
$401$	426.130	−	738.080i	0.0530672	−	0.0919151i	0.891339	+	0.453338i	$0.149767\pi$
$402$	−632.153	−	1094.92i	−0.0784302	−	0.135845i
$403$	2775.42	+	4807.16i	0.343060	+	0.594198i
$404$	2900.84	−	5024.40i	0.357233	−	0.618746i
$405$	−405.000			−0.0496904
$406$	3691.49	+	2887.43i	0.451245	+	0.352958i
$407$	−1898.05			−0.231162
$408$	−826.534	+	1431.60i	−0.100293	+	0.173712i
$409$	−7347.38	−	12726.0i	−0.888276	−	1.53854i	−0.841912	−	0.539614i	$-0.818570\pi$
$409$	−7347.38	−	12726.0i	−0.888276	−	1.53854i	−0.0463634	−	0.998925i	$-0.514763\pi$
$410$	−1434.92	−	2485.36i	−0.172843	−	0.299374i
$411$	−2657.85	+	4603.53i	−0.318983	+	0.552495i
$412$	−2581.56			−0.308699
$413$	−14953.1	+	6031.71i	−1.78158	+	0.718647i
$414$	3916.44			0.464934
$415$	2391.77	−	4142.67i	0.282910	−	0.490014i
$416$	525.191	+	909.657i	0.0618981	+	0.107211i
$417$	−3540.81	−	6132.87i	−0.415814	−	0.720211i
$418$	−357.594	+	619.372i	−0.0418433	+	0.0724748i
$419$	283.053			0.0330025			0.0165013	−	0.999864i	$-0.494747\pi$
$419$	283.053			0.0330025			0.0165013	+	0.999864i	$0.494747\pi$
$420$	1030.53	−	415.692i	0.119726	−	0.0482945i
$421$	−10854.3			−1.25655			−0.628274	−	0.777992i	$-0.716238\pi$
$421$	−10854.3			−1.25655			−0.628274	+	0.777992i	$0.716238\pi$
$422$	−5897.72	+	10215.2i	−0.680324	+	1.17836i
$423$	−1020.16	−	1766.97i	−0.117262	−	0.203104i
$424$	215.023	+	372.430i	0.0246283	+	0.0426575i
$425$	860.973	−	1491.25i	0.0982666	−	0.170203i
$426$	−1418.33			−0.161311
$427$	6778.98	+	5302.43i	0.768285	+	0.600942i
$428$	−2099.82			−0.237146
$429$	−385.249	+	667.271i	−0.0433566	+	0.0750959i
$430$	−271.145	−	469.636i	−0.0304087	−	0.0526695i
$431$	3652.17	+	6325.74i	0.408164	+	0.706961i	0.994684	−	0.102974i	$-0.0328358\pi$
$431$	3652.17	+	6325.74i	0.408164	+	0.706961i	−0.586520	+	0.809935i	$0.699502\pi$
$432$	216.000	−	374.123i	0.0240563	−	0.0416667i
$433$	2406.12			0.267046			0.133523	−	0.991046i	$-0.457371\pi$
$433$	2406.12			0.267046			0.133523	+	0.991046i	$0.457371\pi$
$434$	−875.223	+	6202.35i	−0.0968019	+	0.685997i
$435$	−1897.90			−0.209189
$436$	2113.02	−	3659.86i	0.232100	−	0.402008i
$437$	−4971.95	−	8611.67i	−0.544258	−	0.942682i
$438$	−1057.10	−	1830.95i	−0.115320	−	0.199740i
$439$	−6550.07	+	11345.1i	−0.712114	+	1.23342i	0.251949	+	0.967741i	$0.418929\pi$
$439$	−6550.07	+	11345.1i	−0.712114	+	1.23342i	−0.964062	+	0.265676i	$0.914405\pi$
$440$	−312.977			−0.0339105
$441$	2223.00	−	2141.92i	0.240039	−	0.231284i
$442$	4521.75			0.486601
$443$	−4860.10	+	8417.94i	−0.521242	+	0.902818i	0.478453	+	0.878113i	$0.341198\pi$
$443$	−4860.10	+	8417.94i	−0.521242	+	0.902818i	−0.999695	+	0.0247043i	$0.992136\pi$
$444$	−1455.48	−	2520.97i	−0.155572	−	0.269459i
$445$	465.095	+	805.568i	0.0495452	+	0.0858148i
$446$	78.3677	−	135.737i	0.00832021	−	0.0144110i
$447$	−3525.52			−0.373046
$448$	−165.618	+	1173.67i	−0.0174659	+	0.123774i
$449$	11339.0			1.19181			0.595905	−	0.803055i	$-0.296794\pi$
$449$	11339.0			1.19181			0.595905	+	0.803055i	$0.296794\pi$
$450$	−225.000	+	389.711i	−0.0235702	+	0.0408248i
$451$	1122.75	+	1944.65i	0.117224	+	0.203038i
$452$	−505.618	−	875.756i	−0.0526156	−	0.0911330i
$453$	−3269.84	+	5663.53i	−0.339140	+	0.587408i
$454$	1550.86			0.160320
$455$	−2394.18	−	1872.70i	−0.246683	−	0.192952i
$456$	−1096.85			−0.112642
$457$	2893.24	−	5011.23i	0.296148	−	0.512944i	−0.679103	−	0.734043i	$-0.737631\pi$
$457$	2893.24	−	5011.23i	0.296148	−	0.512944i	0.975251	+	0.221099i	$0.0709643\pi$
$458$	−1166.22	−	2019.95i	−0.118982	−	0.206083i
$459$	−929.851	−	1610.55i	−0.0945571	−	0.163778i
$460$	2175.80	−	3768.60i	0.220537	−	0.381982i
$461$	9403.13			0.949995			0.474997	−	0.879987i	$-0.342449\pi$
$461$	9403.13			0.949995			0.474997	+	0.879987i	$0.342449\pi$
$462$	−806.335	+	325.256i	−0.0811993	+	0.0327538i
$463$	−13355.7			−1.34059			−0.670295	−	0.742094i	$-0.733833\pi$
$463$	−13355.7			−1.34059			−0.670295	+	0.742094i	$0.733833\pi$
$464$	1012.21	−	1753.21i	0.101273	−	0.175411i
$465$	−1268.30	−	2196.76i	−0.126486	−	0.219080i
$466$	−1408.31	−	2439.26i	−0.139997	−	0.242482i
$467$	−2867.44	+	4966.56i	−0.284132	+	0.492130i	−0.972398	−	0.233327i	$-0.925039\pi$
$467$	−2867.44	+	4966.56i	−0.284132	+	0.492130i	0.688267	+	0.725458i	$0.258372\pi$
$468$	−1181.68			−0.116716
$469$	−3619.19	+	1459.89i	−0.356330	+	0.143735i
$470$	−2267.02			−0.222489
$471$	4057.01	−	7026.94i	0.396894	−	0.687440i
$472$	3482.41	+	6031.71i	0.339599	+	0.588203i
$473$	212.155	+	367.464i	0.0206235	+	0.0357210i
$474$	2348.17	−	4067.16i	0.227543	−	0.394115i
$475$	1142.56			0.110366
$476$	4019.10	+	3143.69i	0.387006	+	0.302711i
$477$	−483.801			−0.0464397
$478$	−4474.37	+	7749.83i	−0.428144	+	0.741567i
$479$	−7321.19	−	12680.7i	−0.698358	−	1.20959i	−0.969035	−	0.246922i	$-0.920581\pi$
$479$	−7321.19	−	12680.7i	−0.698358	−	1.20959i	0.270677	−	0.962670i	$-0.412752\pi$
$480$	−240.000	−	415.692i	−0.0228218	−	0.0395285i
$481$	−3981.28	+	6895.77i	−0.377403	+	0.653680i
$482$	5940.92			0.561413
$483$	1689.15	−	11970.3i	0.159128	−	1.12768i
$484$	−5079.11			−0.477002
$485$	25.2669	−	43.7636i	0.00236559	−	0.00409732i
$486$	243.000	+	420.888i	0.0226805	+	0.0392837i
$487$	−2836.53	−	4913.01i	−0.263933	−	0.457145i	0.703351	−	0.710843i	$-0.251686\pi$
$487$	−2836.53	−	4913.01i	−0.263933	−	0.457145i	−0.967283	+	0.253698i	$0.918353\pi$
$488$	1858.81	−	3219.55i	0.172427	−	0.298652i
$489$	7802.56			0.721563
$490$	−826.068	−	3329.04i	−0.0761590	−	0.306920i
$491$	−7355.77			−0.676092			−0.338046	−	0.941130i	$-0.609766\pi$
$491$	−7355.77			−0.676092			−0.338046	+	0.941130i	$0.609766\pi$
$492$	−1721.91	+	2982.43i	−0.157784	+	0.273289i
$493$	−4357.44	−	7547.31i	−0.398072	−	0.689480i
$494$	1500.15	+	2598.34i	0.136630	+	0.236649i
$495$	176.050	−	304.927i	0.0159856	−	0.0276878i
$496$	2705.71			0.244939
$497$	−611.723	+	4335.04i	−0.0552104	+	0.391254i
$498$	−5740.26			−0.516520
$499$	−10223.6	+	17707.8i	−0.917177	+	1.58860i	−0.113495	+	0.993539i	$0.536204\pi$
$499$	−10223.6	+	17707.8i	−0.917177	+	1.58860i	−0.803682	+	0.595058i	$0.797129\pi$
$500$	250.000	+	433.013i	0.0223607	+	0.0387298i
$501$	−5372.55	−	9305.53i	−0.479098	−	0.829821i
$502$	4254.34	−	7368.74i	0.378248	−	0.655145i
$503$	11116.9			0.985448			0.492724	−	0.870186i	$-0.336001\pi$
$503$	11116.9			0.985448			0.492724	+	0.870186i	$0.336001\pi$
$504$	−1050.32	−	821.547i	−0.0928274	−	0.0726083i
$505$	7252.10			0.639038
$506$	−1702.44	+	2948.71i	−0.149571	+	0.259064i
$507$	−1679.33	−	2908.69i	−0.147104	−	0.254792i
$508$	−4838.29	−	8380.16i	−0.422568	−	0.731909i
$509$	7854.88	−	13605.1i	0.684011	−	1.18474i	−0.289736	−	0.957107i	$-0.593567\pi$
$509$	7854.88	−	13605.1i	0.684011	−	1.18474i	0.973747	−	0.227635i	$-0.0730992\pi$
$510$	−2066.33			−0.179409
$511$	−6052.09	+	2441.27i	−0.523931	+	0.211341i
$512$	512.000			0.0441942
$513$	616.980	−	1068.64i	0.0531001	−	0.0919721i
$514$	−2653.15	−	4595.39i	−0.227676	−	0.394346i
$515$	−1613.47	−	2794.62i	−0.138055	−	0.239118i
$516$	−325.374	+	563.564i	−0.0277593	+	0.0480804i
$517$	1773.82			0.150894
$518$	−8332.90	+	3361.29i	−0.706808	+	0.285109i
$519$	7640.01			0.646165
$520$	−656.489	+	1137.07i	−0.0553633	+	0.0958921i
$521$	8097.17	+	14024.7i	0.680889	+	1.17933i	0.974710	+	0.223474i	$0.0717398\pi$
$521$	8097.17	+	14024.7i	0.680889	+	1.17933i	−0.293821	+	0.955861i	$0.594927\pi$
$522$	1138.74	+	1972.36i	0.0954814	+	0.165379i
$523$	−8365.97	+	14490.3i	−0.699461	+	1.21150i	0.269192	+	0.963086i	$0.413243\pi$
$523$	−8365.97	+	14490.3i	−0.699461	+	1.21150i	−0.968653	+	0.248416i	$0.920090\pi$
$524$	−6602.26			−0.550422
$525$	1094.08	+	855.778i	0.0909519	+	0.0711414i
$526$	−13195.3			−1.09380
$527$	5823.85	−	10087.2i	0.481387	−	0.833787i
$528$	187.786	+	325.256i	0.0154779	+	0.0268086i
$529$	−17587.0	−	30461.7i	−1.44547	−	2.50363i
$530$	−268.778	+	465.538i	−0.0220283	+	0.0381541i
$531$	−7835.42			−0.640355
$532$	−473.070	+	3352.46i	−0.0385530	+	0.273210i
$533$	9420.11			0.765535
$534$	558.114	−	966.682i	0.0452284	−	0.0783378i
$535$	−1312.38	−	2273.12i	−0.106055	−	0.183692i
$536$	842.871	+	1459.89i	0.0679225	+	0.117645i
$537$	−5901.32	+	10221.4i	−0.474229	+	0.821388i
$538$	9327.39			0.747458
$539$	646.351	+	2604.79i	0.0516518	+	0.208156i
$540$	540.000			0.0430331
$541$	12492.9	−	21638.3i	0.992811	−	1.71960i	0.392745	−	0.919647i	$-0.371525\pi$
$541$	12492.9	−	21638.3i	0.992811	−	1.71960i	0.600065	−	0.799951i	$-0.295141\pi$
$542$	−902.674	−	1563.48i	−0.0715372	−	0.123906i
$543$	−4396.77	−	7615.44i	−0.347484	−	0.601859i
$544$	1102.05	−	1908.80i	0.0868562	−	0.150439i
$545$	5282.56			0.415192
$546$	−509.655	+	3611.72i	−0.0399473	+	0.283090i
$547$	21010.7			1.64233			0.821164	−	0.570692i	$-0.193325\pi$
$547$	21010.7			1.64233			0.821164	+	0.570692i	$0.193325\pi$
$548$	3543.80	−	6138.04i	0.276248	−	0.478475i
$549$	2091.16	+	3622.00i	0.162566	+	0.281572i
$550$	−195.611	−	338.808i	−0.0151652	−	0.0262669i
$551$	2891.28	−	5007.84i	0.223544	−	0.387189i
$552$	−5221.92			−0.402644
$553$	−11418.2	−	8931.18i	−0.878033	−	0.686786i
$554$	1290.35			0.0989563
$555$	1819.35	−	3151.21i	0.139148	−	0.241011i
$556$	4721.08	+	8177.16i	0.360105	+	0.623721i
$557$	10437.2	+	18077.8i	0.793964	+	1.37519i	0.923495	+	0.383611i	$0.125320\pi$
$557$	10437.2	+	18077.8i	0.793964	+	1.37519i	−0.129530	+	0.991575i	$0.541347\pi$
$558$	−1521.96	+	2636.11i	−0.115465	+	0.199992i
$559$	1780.03			0.134682
$560$	−1374.05	+	554.256i	−0.103686	+	0.0418243i
$561$	1616.79			0.121677
$562$	4459.75	−	7724.52i	0.334739	−	0.579785i
$563$	10267.8	+	17784.4i	0.768628	+	1.33130i	0.938307	+	0.345804i	$0.112394\pi$
$563$	10267.8	+	17784.4i	0.768628	+	1.33130i	−0.169678	+	0.985499i	$0.554273\pi$
$564$	1360.21	+	2355.96i	0.101552	+	0.175893i
$565$	632.023	−	1094.70i	0.0470609	−	0.0815118i
$566$	−11022.4			−0.818565
$567$	1391.22	−	561.184i	0.103044	−	0.0415653i
$568$	1891.11			0.139700
$569$	9924.76	−	17190.2i	0.731226	−	1.26652i	−0.225133	−	0.974328i	$-0.572282\pi$
$569$	9924.76	−	17190.2i	0.731226	−	1.26652i	0.956359	−	0.292193i	$-0.0943849\pi$
$570$	−685.534	−	1187.38i	−0.0503752	−	0.0872524i
$571$	−690.132	−	1195.34i	−0.0505799	−	0.0876070i	0.839627	−	0.543164i	$-0.182774\pi$
$571$	−690.132	−	1195.34i	−0.0505799	−	0.0876070i	−0.890207	+	0.455557i	$0.849440\pi$
$572$	513.665	−	889.695i	0.0375480	−	0.0650350i
$573$	10333.0			0.753343
$574$	8372.94	+	6549.20i	0.608850	+	0.476234i
$575$	5439.50			0.394509
$576$	−288.000	+	498.831i	−0.0208333	+	0.0360844i
$577$	5872.85	+	10172.1i	0.423726	+	0.733916i	0.996301	−	0.0859373i	$-0.0273885\pi$
$577$	5872.85	+	10172.1i	0.423726	+	0.733916i	−0.572574	+	0.819853i	$0.694055\pi$
$578$	168.846	+	292.450i	0.0121506	+	0.0210455i
$579$	−2737.33	+	4741.19i	−0.196476	+	0.340306i
$580$	2530.53			0.181163
$581$	−2475.76	+	17544.7i	−0.176784	+	1.25280i
$582$	−60.6406			−0.00431896
$583$	210.304	−	364.257i	0.0149398	−	0.0258765i
$584$	1409.47	+	2441.27i	0.0998701	+	0.172980i
$585$	−738.550	−	1279.21i	−0.0521971	−	0.0904079i
$586$	−2837.19	+	4914.16i	−0.200006	+	0.346420i
$587$	10286.3			0.723272			0.361636	−	0.932319i	$-0.382218\pi$
$587$	10286.3			0.723272			0.361636	+	0.932319i	$0.382218\pi$
$588$	−2964.00	+	2855.90i	−0.207880	+	0.200298i
$589$	7728.56			0.540662
$590$	−4353.01	+	7539.64i	−0.303747	+	0.526105i
$591$	−2640.70	−	4573.82i	−0.183797	−	0.318345i
$592$	1940.64	+	3361.29i	0.134729	+	0.233358i
$593$	−7919.78	+	13717.5i	−0.548443	+	0.949931i	0.449939	+	0.893059i	$0.351446\pi$
$593$	−7919.78	+	13717.5i	−0.548443	+	0.949931i	−0.998382	+	0.0568712i	$0.981888\pi$
$594$	−422.520			−0.0291855
$595$	−891.204	+	6315.61i	−0.0614047	+	0.435151i
$596$	4700.70			0.323067
$597$	2525.20	−	4373.77i	0.173115	−	0.299844i
$598$	7141.94	+	12370.2i	0.488388	+	0.845912i
$599$	5260.42	+	9111.31i	0.358823	+	0.621500i	0.987764	−	0.155953i	$-0.0498449\pi$
$599$	5260.42	+	9111.31i	0.358823	+	0.621500i	−0.628942	+	0.777453i	$0.716512\pi$
$600$	300.000	−	519.615i	0.0204124	−	0.0353553i
$601$	7734.31			0.524941			0.262470	−	0.964940i	$-0.415463\pi$
$601$	7734.31			0.524941			0.262470	+	0.964940i	$0.415463\pi$
$602$	1582.16	+	1237.55i	0.107116	+	0.0837850i
$603$	−1896.46			−0.128076
$604$	4359.79	−	7551.37i	0.293704	−	0.508710i
$605$	−3174.45	−	5498.30i	−0.213322	−	0.369484i
$606$	−4351.26	−	7536.60i	−0.291680	−	0.505204i
$607$	945.663	−	1637.94i	0.0632344	−	0.109525i	−0.832675	−	0.553762i	$-0.813192\pi$
$607$	945.663	−	1637.94i	0.0632344	−	0.109525i	0.895909	+	0.444237i	$0.146525\pi$
$608$	1462.47			0.0975511
$609$	6519.50	−	2629.81i	0.433799	−	0.174984i
$610$	4647.02			0.308447
$611$	3720.69	−	6444.42i	0.246355	−	0.426699i
$612$	1239.80	+	2147.40i	0.0818888	+	0.141836i
$613$	−6791.21	−	11762.7i	−0.447462	−	0.775027i	0.550758	−	0.834665i	$-0.314339\pi$
$613$	−6791.21	−	11762.7i	−0.447462	−	0.775027i	−0.998220	+	0.0596380i	$0.981005\pi$
$614$	−7929.20	+	13733.8i	−0.521167	+	0.902688i
$615$	−4304.77			−0.282252
$616$	1075.11	−	433.674i	0.0703207	−	0.0283656i
$617$	−22334.6			−1.45731			−0.728653	−	0.684883i	$-0.759853\pi$
$617$	−22334.6			−1.45731			−0.728653	+	0.684883i	$0.759853\pi$
$618$	−1936.17	+	3353.54i	−0.126026	+	0.218283i
$619$	−3503.23	−	6067.77i	−0.227474	−	0.393997i	0.729585	−	0.683891i	$-0.239713\pi$
$619$	−3503.23	−	6067.77i	−0.227474	−	0.393997i	−0.957059	+	0.289894i	$0.906380\pi$
$620$	1691.07	+	2929.02i	0.109540	+	0.189729i
$621$	2937.33	−	5087.61i	0.189808	−	0.328758i
$622$	16563.7			1.06776
$623$	−2713.88	−	2122.76i	−0.174525	−	0.136512i
$624$	1575.57			0.101079
$625$	−312.500	+	541.266i	−0.0200000	+	0.0346410i
$626$	−685.406	−	1187.16i	−0.0437609	−	0.0757961i
$627$	536.392	+	929.057i	0.0341649	+	0.0591754i
$628$	−5409.34	+	9369.26i	−0.343720	+	0.595341i
$629$	16708.4			1.05915
$630$	232.900	−	1650.47i	0.0147285	−	0.104375i
$631$	11554.9			0.728993			0.364497	−	0.931205i	$-0.381241\pi$
$631$	11554.9			0.728993			0.364497	+	0.931205i	$0.381241\pi$
$632$	−3130.90	+	5422.88i	−0.197058	+	0.341314i
$633$	8846.59	+	15322.7i	0.555482	+	0.962124i
$634$	−5793.75	−	10035.1i	−0.362932	−	0.628617i
$635$	6047.86	−	10475.2i	0.377956	−	0.654639i
$636$	645.068			0.0402179
$637$	10819.2	+	3115.45i	0.672952	+	0.193781i
$638$	−1980.00			−0.122867
$639$	−1063.75	+	1842.47i	−0.0658550	+	0.114064i
$640$	320.000	+	554.256i	0.0197642	+	0.0342327i
$641$	12940.8	+	22414.0i	0.797393	+	1.38113i	0.921308	+	0.388833i	$0.127122\pi$
$641$	12940.8	+	22414.0i	0.797393	+	1.38113i	−0.123915	+	0.992293i	$0.539545\pi$
$642$	−1574.86	+	2727.74i	−0.0968144	+	0.167687i
$643$	−10120.7			−0.620716			−0.310358	−	0.950620i	$-0.600449\pi$
$643$	−10120.7			−0.620716			−0.310358	+	0.950620i	$0.600449\pi$
$644$	−2252.20	+	15960.4i	−0.137809	+	0.976598i
$645$	−813.434			−0.0496573
$646$	3147.87	−	5452.27i	0.191720	−	0.332069i
$647$	−8130.91	−	14083.2i	−0.494064	−	0.855743i	0.505913	−	0.862585i	$-0.331156\pi$
$647$	−8130.91	−	14083.2i	−0.494064	−	0.855743i	−0.999977	+	0.00684126i	$0.997822\pi$
$648$	−324.000	−	561.184i	−0.0196419	−	0.0340207i
$649$	3405.99	−	5899.34i	0.206004	−	0.356810i
$650$	−1641.22			−0.0990369
$651$	7400.68	+	5788.71i	0.445554	+	0.348506i
$652$	−10403.4			−0.624891
$653$	7340.21	−	12713.6i	0.439885	−	0.761903i	−0.557795	−	0.829979i	$-0.688353\pi$
$653$	7340.21	−	12713.6i	0.439885	−	0.761903i	0.997680	+	0.0680756i	$0.0216859\pi$
$654$	−3169.53	−	5489.79i	−0.189509	−	0.328238i
$655$	−4126.41	−	7147.15i	−0.246156	−	0.426355i
$656$	2295.88	−	3976.58i	0.136645	−	0.236676i
$657$	−3171.30			−0.188317
$658$	7787.48	−	3141.28i	0.461379	−	0.186109i
$659$	5940.61			0.351158			0.175579	−	0.984465i	$-0.443820\pi$
$659$	5940.61			0.351158			0.175579	+	0.984465i	$0.443820\pi$
$660$	−234.733	+	406.570i	−0.0138439	+	0.0239783i
$661$	−13491.7	−	23368.3i	−0.793897	−	1.37507i	−0.923537	−	0.383509i	$-0.874715\pi$
$661$	−13491.7	−	23368.3i	−0.793897	−	1.37507i	0.129640	−	0.991561i	$-0.458618\pi$
$662$	1560.30	+	2702.52i	0.0916054	+	0.158665i
$663$	3391.31	−	5873.93i	0.198654	−	0.344079i
$664$	7653.68			0.447320
$665$	−3924.81	+	1583.17i	−0.228869	+	0.0923200i
$666$	−4366.44			−0.254048
$667$	13764.8	−	23841.4i	0.799066	−	1.38402i
$668$	7163.40	+	12407.4i	0.414911	+	0.718646i
$669$	−117.551	−	203.605i	−0.00679343	−	0.0117666i
$670$	−1053.59	+	1824.87i	−0.0607517	+	0.105225i
$671$	−3636.03			−0.209192
$672$	1400.43	+	1095.40i	0.0803908	+	0.0628807i
$673$	16002.0			0.916543			0.458272	−	0.888812i	$-0.348469\pi$
$673$	16002.0			0.916543			0.458272	+	0.888812i	$0.348469\pi$
$674$	−1543.88	+	2674.07i	−0.0882314	+	0.152821i
$675$	337.500	+	584.567i	0.0192450	+	0.0333333i
$676$	2239.11	+	3878.26i	0.127396	+	0.220656i
$677$	−8877.67	+	15376.6i	−0.503983	+	0.872925i	0.496006	+	0.868319i	$0.334799\pi$
$677$	−8877.67	+	15376.6i	−0.503983	+	0.872925i	−0.999989	+	0.00460562i	$0.998534\pi$
$678$	−1516.85			−0.0859210
$679$	−26.1541	+	185.344i	−0.00147821	+	0.0104755i
$680$	2755.11			0.155373
$681$	1163.14	−	2014.62i	0.0654504	−	0.113363i
$682$	−1323.17	−	2291.79i	−0.0742912	−	0.128676i
$683$	−5310.74	−	9198.46i	−0.297525	−	0.515329i	0.678044	−	0.735021i	$-0.262828\pi$
$683$	−5310.74	−	9198.46i	−0.297525	−	0.515329i	−0.975569	+	0.219693i	$0.929495\pi$
$684$	−822.641	+	1424.86i	−0.0459860	+	0.0796502i
$685$	8859.50			0.494167
$686$	7450.49	+	10291.0i	0.414666	+	0.572758i
$687$	−3498.66			−0.194297
$688$	433.832	−	751.418i	0.0240402	−	0.0416389i
$689$	−882.249	−	1528.10i	−0.0487823	−	0.0844935i
$690$	−3263.70	−	5652.90i	−0.180068	−	0.311887i
$691$	−9992.87	+	17308.2i	−0.550140	+	0.952871i	0.448124	+	0.893972i	$0.352092\pi$
$691$	−9992.87	+	17308.2i	−0.550140	+	0.952871i	−0.998264	+	0.0588992i	$0.981241\pi$
$692$	−10186.7			−0.559595
$693$	−182.231	+	1291.40i	−0.00998903	+	0.0707883i
$694$	−958.415			−0.0524221
$695$	−5901.36	+	10221.4i	−0.322088	+	0.557873i
$696$	−1518.32	−	2629.81i	−0.0826893	−	0.143222i
$697$	−9883.44	−	17118.6i	−0.537105	−	0.930292i
$698$	9446.15	−	16361.2i	0.512238	−	0.887222i
$699$	−4224.92			−0.228614
$700$	−1458.78	−	1141.04i	−0.0787666	−	0.0616102i
$701$	2403.01			0.129473			0.0647363	−	0.997902i	$-0.479379\pi$
$701$	2403.01			0.129473			0.0647363	+	0.997902i	$0.479379\pi$
$702$	−886.260	+	1535.05i	−0.0476492	+	0.0825308i
$703$	5543.23	+	9601.15i	0.297392	+	0.515099i
$704$	−250.382	−	433.674i	−0.0134043	−	0.0232169i
$705$	−1700.27	+	2944.95i	−0.0908309	+	0.157324i
$706$	−13790.9			−0.735165
$707$	−24911.8	+	10048.8i	−1.32518	+	0.534546i
$708$	10447.2			0.554564
$709$	122.017	−	211.339i	0.00646323	−	0.0111946i	−0.862776	−	0.505587i	$-0.831276\pi$
$709$	122.017	−	211.339i	0.00646323	−	0.0111946i	0.869239	+	0.494392i	$0.164609\pi$
$710$	1181.95	+	2047.19i	0.0624755	+	0.108211i
$711$	−3522.26	−	6100.74i	−0.185788	−	0.321794i
$712$	−744.152	+	1288.91i	−0.0391689	+	0.0678426i
$713$	36794.3			1.93262
$714$	7098.09	−	2863.20i	0.372044	−	0.150073i
$715$	1284.16			0.0671678
$716$	7868.43	−	13628.5i	0.410694	−	0.711343i
$717$	6711.55	+	11624.7i	0.349578	+	0.605487i
$718$	2829.65	+	4901.10i	0.147078	+	0.254746i
$719$	5581.70	−	9667.78i	0.289516	−	0.501457i	−0.684178	−	0.729315i	$-0.739839\pi$
$719$	5581.70	−	9667.78i	0.289516	−	0.501457i	0.973694	+	0.227858i	$0.0731722\pi$
$720$	−720.000			−0.0372678
$721$	9414.80	+	7364.13i	0.486304	+	0.380381i
$722$	−9540.61			−0.491779
$723$	4455.69	−	7717.48i	0.229196	−	0.396979i
$724$	5862.37	+	10153.9i	0.300930	+	0.521226i
$725$	1581.58	+	2739.38i	0.0810187	+	0.140328i
$726$	−3809.33	+	6597.96i	−0.194735	+	0.337291i
$727$	−28908.7			−1.47478			−0.737389	−	0.675469i	$-0.763941\pi$
$727$	−28908.7			−1.47478			−0.737389	+	0.675469i	$0.763941\pi$
$728$	679.540	−	4815.63i	0.0345954	−	0.245163i
$729$	729.000			0.0370370
$730$	−1761.83	+	3051.58i	−0.0893265	+	0.154718i
$731$	−1867.59	−	3234.75i	−0.0944941	−	0.163669i
$732$	−2788.21	−	4829.33i	−0.140786	−	0.243848i
$733$	5200.37	−	9007.31i	0.262047	−	0.453878i	−0.704739	−	0.709467i	$-0.748936\pi$
$733$	5200.37	−	9007.31i	0.262047	−	0.453878i	0.966786	+	0.255589i	$0.0822692\pi$
$734$	−471.390			−0.0237048
$735$	−4944.10	−	1423.69i	−0.248117	−	0.0714469i
$736$	6962.56			0.348700
$737$	824.373	−	1427.86i	0.0412024	−	0.0713647i
$738$	2582.86	+	4473.65i	0.128830	+	0.223140i
$739$	9966.69	+	17262.8i	0.496117	+	0.859300i	0.999990	−	0.00447759i	$-0.00142527\pi$
$739$	9966.69	+	17262.8i	0.496117	+	0.859300i	−0.503873	+	0.863778i	$0.668092\pi$
$740$	−2425.80	+	4201.61i	−0.120506	+	0.208722i
$741$	4500.45			0.223115
$742$	278.216	−	1971.60i	0.0137650	−	0.0975470i
$743$	−37573.6			−1.85524			−0.927619	−	0.373527i	$-0.878148\pi$
$743$	−37573.6			−1.85524			−0.927619	+	0.373527i	$0.878148\pi$
$744$	2029.28	−	3514.82i	0.0999960	−	0.173198i
$745$	2937.94	+	5088.65i	0.144480	+	0.250247i
$746$	−11870.9	−	20560.9i	−0.582605	−	1.00910i
$747$	−4305.19	+	7456.81i	−0.210868	+	0.365235i
$748$	−2155.72			−0.105376
$749$	7657.91	+	5989.92i	0.373583	+	0.292212i
$750$	750.000			0.0365148
$751$	2444.45	−	4233.91i	0.118774	−	0.205723i	−0.800508	−	0.599322i	$-0.795437\pi$
$751$	2444.45	−	4233.91i	0.118774	−	0.205723i	0.919282	+	0.393599i	$0.128770\pi$
$752$	−1813.62	−	3141.28i	−0.0879466	−	0.152328i
$753$	−6381.51	−	11053.1i	−0.308838	−	0.534924i
$754$	−4153.17	+	7193.50i	−0.200596	+	0.347443i
$755$	10899.5			0.525394
$756$	−1854.96	+	748.246i	−0.0892385	+	0.0359966i
$757$	−15222.3			−0.730863			−0.365431	−	0.930838i	$-0.619078\pi$
$757$	−15222.3			−0.730863			−0.365431	+	0.930838i	$0.619078\pi$
$758$	−2277.70	+	3945.10i	−0.109142	+	0.189040i
$759$	2553.66	+	4423.07i	0.122124	+	0.211525i
$760$	914.045	+	1583.17i	0.0436262	+	0.0755628i
$761$	−2461.50	+	4263.44i	−0.117253	+	0.203087i	−0.918678	−	0.395007i	$-0.870742\pi$
$761$	−2461.50	+	4263.44i	−0.117253	+	0.203087i	0.801425	+	0.598095i	$0.204075\pi$
$762$	−14514.9			−0.690050
$763$	−18146.2	+	7319.72i	−0.860990	+	0.347303i
$764$	−13777.3			−0.652414
$765$	−1549.75	+	2684.25i	−0.0732436	+	0.126862i
$766$	−4058.15	−	7028.92i	−0.191419	−	0.331547i
$767$	−14288.5	−	24748.4i	−0.672658	−	1.16508i
$768$	384.000	−	665.108i	0.0180422	−	0.0312500i
$769$	−17900.3			−0.839402			−0.419701	−	0.907663i	$-0.637865\pi$
$769$	−17900.3			−0.839402			−0.419701	+	0.907663i	$0.637865\pi$
$770$	1141.41	+	892.797i	0.0534203	+	0.0417847i
$771$	−7959.45			−0.371793
$772$	3649.77	−	6321.59i	0.170153	−	0.294714i
$773$	−5179.63	−	8971.39i	−0.241007	−	0.417437i	0.719994	−	0.693980i	$-0.244144\pi$
$773$	−5179.63	−	8971.39i	−0.241007	−	0.417437i	−0.961001	+	0.276543i	$0.910811\pi$
$774$	488.061	+	845.346i	0.0226653	+	0.0392575i
$775$	−2113.83	+	3661.27i	−0.0979757	+	0.169699i
$776$	80.8541			0.00374033
$777$	−1883.23	+	13345.7i	−0.0869506	+	0.616184i
$778$	−6804.63			−0.313570
$779$	6557.92	−	11358.7i	0.301620	−	0.522421i
$780$	984.733	+	1705.61i	0.0452040	+	0.0782956i
$781$	−924.806	−	1601.81i	−0.0423715	−	0.0733896i
$782$	14986.4	−	25957.3i	0.685312	−	1.18700i
$783$	3416.22			0.155921
$784$	3952.00	−	3807.87i	0.180029	−	0.173463i
$785$	−13523.4			−0.614865
$786$	−4951.69	+	8576.59i	−0.224709	+	0.389207i
$787$	392.771	+	680.299i	0.0177901	+	0.0308133i	0.874783	−	0.484514i	$-0.161004\pi$
$787$	392.771	+	680.299i	0.0177901	+	0.0308133i	−0.856993	+	0.515328i	$0.827670\pi$
$788$	3520.93	+	6098.43i	0.159173	+	0.275695i
$789$	−9896.45	+	17141.2i	−0.446544	+	0.773436i
$790$	−7827.25			−0.352508
$791$	−654.215	+	4636.16i	−0.0294073	+	0.208398i
$792$	563.359			0.0252754
$793$	−7626.79	+	13210.0i	−0.341533	+	0.591552i
$794$	−5201.54	−	9009.34i	−0.232488	−	0.402682i
$795$	403.167	+	698.306i	0.0179860	+	0.0311527i
$796$	−3366.93	+	5831.70i	−0.149922	+	0.259672i
$797$	2669.30			0.118634			0.0593170	−	0.998239i	$-0.481108\pi$
$797$	2669.30			0.118634			0.0593170	+	0.998239i	$0.481108\pi$
$798$	4000.17	+	3128.88i	0.177449	+	0.138798i
$799$	−15614.8			−0.691377
$800$	−400.000	+	692.820i	−0.0176777	+	0.0306186i
$801$	−837.171	−	1450.02i	−0.0369288	−	0.0639626i
$802$	852.261	+	1476.16i	0.0375242	+	0.0649938i
$803$	1378.53	−	2387.69i	0.0605821	−	0.104931i
$804$	2528.61			0.110917
$805$	−18685.3	+	7537.19i	−0.818100	+	0.330002i
$806$	−11101.7			−0.485161
$807$	6995.54	−	12116.6i	0.305148	−	0.528532i
$808$	5801.68	+	10048.8i	0.252602	+	0.437519i
$809$	−4031.11	−	6982.08i	−0.175187	−	0.303433i	0.765039	−	0.643984i	$-0.222720\pi$
$809$	−4031.11	−	6982.08i	−0.175187	−	0.303433i	−0.940226	+	0.340551i	$0.889386\pi$
$810$	405.000	−	701.481i	0.0175682	−	0.0304290i
$811$	2794.93			0.121015			0.0605075	−	0.998168i	$-0.480728\pi$
$811$	2794.93			0.121015			0.0605075	+	0.998168i	$0.480728\pi$
$812$	−8692.67	+	3506.41i	−0.375681	+	0.151541i
$813$	−2708.02			−0.116820
$814$	1898.05	−	3287.52i	0.0817281	−	0.141557i
$815$	−6502.14	−	11262.0i	−0.279460	−	0.484039i
$816$	−1653.07	−	2863.20i	−0.0709178	−	0.122833i
$817$	1239.19	−	2146.34i	0.0530647	−	0.0919108i
$818$	29389.5			1.25621
$819$	4309.52	+	3370.85i	0.183867	+	0.143818i
$820$	5739.69			0.244437
$821$	13501.7	−	23385.6i	0.573948	−	0.994107i	−0.422207	−	0.906499i	$-0.638745\pi$
$821$	13501.7	−	23385.6i	0.573948	−	0.994107i	0.996155	−	0.0876074i	$-0.0279221\pi$
$822$	−5315.70	−	9207.06i	−0.225555	−	0.390673i
$823$	−17321.0	−	30000.8i	−0.733623	−	1.27067i	−0.955325	−	0.295558i	$-0.904494\pi$
$823$	−17321.0	−	30000.8i	−0.733623	−	1.27067i	0.221702	−	0.975115i	$-0.428839\pi$
$824$	2581.56	−	4471.39i	0.109142	−	0.189039i
$825$	−586.833			−0.0247647
$826$	4505.86	−	31931.2i	0.189805	−	1.34507i
$827$	−28417.3			−1.19488			−0.597441	−	0.801913i	$-0.703816\pi$
$827$	−28417.3			−1.19488			−0.597441	+	0.801913i	$0.703816\pi$
$828$	−3916.44	+	6783.48i	−0.164379	+	0.284713i
$829$	12726.2	+	22042.3i	0.533169	+	0.923477i	0.999250	+	0.0387341i	$0.0123325\pi$
$829$	12726.2	+	22042.3i	0.533169	+	0.923477i	−0.466080	+	0.884743i	$0.654334\pi$
$830$	4783.55	+	8285.35i	0.200047	+	0.346492i
$831$	967.763	−	1676.22i	0.0403987	−	0.0699726i
$832$	−2100.76			−0.0875371
$833$	−5689.77	−	22929.7i	−0.236661	−	0.953742i
$834$	14163.3			0.588050
$835$	−8954.25	+	15509.2i	−0.371107	+	0.642777i
$836$	−715.189	−	1238.74i	−0.0295877	−	0.0512474i
$837$	2282.94	+	3954.17i	0.0942772	+	0.163293i
$838$	−283.053	+	490.263i	−0.0116682	+	0.0202098i
$839$	−41344.7			−1.70128			−0.850642	−	0.525745i	$-0.823787\pi$
$839$	−41344.7			−1.70128			−0.850642	+	0.525745i	$0.823787\pi$
$840$	−310.534	+	2200.63i	−0.0127553	+	0.0903916i
$841$	−8380.00			−0.343597
$842$	10854.3	−	18800.2i	0.444257	−	0.769475i
$843$	−6689.63	−	11586.8i	−0.273313	−	0.473392i
$844$	−11795.4	−	20430.3i	−0.481062	−	0.833223i
$845$	−2798.89	+	4847.82i	−0.113946	+	0.197361i
$846$	4080.64			0.165834
$847$	18523.2	+	14488.6i	0.751436	+	0.587763i
$848$	−860.090			−0.0348297
$849$	−8266.83	+	14318.6i	−0.334178	+	0.578813i
$850$	1721.95	+	2982.50i	0.0694850	+	0.120352i
$851$	26390.3	+	45709.3i	1.06304	+	1.84124i
$852$	1418.33	−	2456.63i	0.0570321	−	0.0987825i
$853$	30225.5			1.21325			0.606625	−	0.794988i	$-0.292523\pi$
$853$	30225.5			1.21325			0.606625	+	0.794988i	$0.292523\pi$
$854$	−15963.0	+	6439.10i	−0.639630	+	0.258011i
$855$	−2056.60			−0.0822623
$856$	2099.82	−	3636.99i	0.0838437	−	0.145222i
$857$	−14201.0	−	24596.9i	−0.566042	−	0.980413i	−0.996952	−	0.0780182i	$-0.975141\pi$
$857$	−14201.0	−	24596.9i	−0.566042	−	0.980413i	0.430910	−	0.902395i	$-0.358193\pi$
$858$	−770.498	−	1334.54i	−0.0306578	−	0.0531008i
$859$	−22954.7	+	39758.8i	−0.911764	+	1.57922i	−0.100194	+	0.994968i	$0.531946\pi$
$859$	−22954.7	+	39758.8i	−0.911764	+	1.57922i	−0.811571	+	0.584254i	$0.801387\pi$
$860$	1084.58			0.0430045
$861$	14787.4	−	5964.86i	0.585310	−	0.236100i
$862$	−14608.7			−0.577231
$863$	−10270.6	+	17789.2i	−0.405116	+	0.701682i	−0.994335	−	0.106291i	$-0.966102\pi$
$863$	−10270.6	+	17789.2i	−0.405116	+	0.701682i	0.589219	+	0.807974i	$0.299436\pi$
$864$	432.000	+	748.246i	0.0170103	+	0.0294628i
$865$	−6366.68	−	11027.4i	−0.250258	−	0.433460i
$866$	−2406.12	+	4167.53i	−0.0944151	+	0.163532i
$867$	506.538			0.0198419
$868$	−9867.57	−	7718.29i	−0.385861	−	0.301815i
$869$	6124.38			0.239074
$870$	1897.90	−	3287.26i	0.0739596	−	0.128102i
$871$	−3458.34	−	5990.03i	−0.134537	−	0.233025i
$872$	4226.05	+	7319.72i	0.164119	+	0.284263i
$873$	−45.4805	+	78.7745i	−0.00176321	+	0.00305397i
$874$	19887.8			0.769697
$875$	323.473	−	2292.32i	0.0124976	−	0.0885653i
$876$	4228.40			0.163087
$877$	−22502.9	+	38976.2i	−0.866442	+	1.50072i	−0.000833382		1.00000i	$0.500265\pi$
$877$	−22502.9	+	38976.2i	−0.866442	+	1.50072i	−0.865608	+	0.500722i	$0.833068\pi$
$878$	−13100.1	−	22690.1i	−0.503540	−	0.872158i
$879$	4255.79	+	7371.24i	0.163304	+	0.282851i
$880$	312.977	−	542.093i	0.0119892	−	0.0207658i
$881$	−13039.0			−0.498633			−0.249316	−	0.968422i	$-0.580206\pi$
$881$	−13039.0			−0.498633			−0.249316	+	0.968422i	$0.580206\pi$
$882$	1486.92	+	5992.27i	0.0567656	+	0.228765i
$883$	50384.1			1.92023			0.960113	−	0.279611i	$-0.0902055\pi$
$883$	50384.1			1.92023			0.960113	+	0.279611i	$0.0902055\pi$
$884$	−4521.75	+	7831.90i	−0.172040	+	0.297981i
$885$	6529.52	+	11309.5i	0.248008	+	0.429563i
$886$	−9720.19	−	16835.9i	−0.368574	−	0.638388i
$887$	11947.1	−	20692.9i	0.452247	−	0.783315i	−0.546278	−	0.837604i	$-0.683956\pi$
$887$	11947.1	−	20692.9i	0.452247	−	0.783315i	0.998525	+	0.0542887i	$0.0172891\pi$
$888$	5821.92			0.220012
$889$	−6260.22	+	44363.7i	−0.236177	+	1.67369i
$890$	−1860.38			−0.0700675
$891$	−316.890	+	548.869i	−0.0119149	+	0.0206373i
$892$	156.735	+	271.474i	0.00588328	+	0.0101901i
$893$	−5180.40	−	8972.72i	−0.194127	−	0.336238i
$894$	3525.52	−	6106.39i	0.131892	−	0.228443i
$895$	19671.1			0.734672
$896$	−1867.24	−	1460.53i	−0.0696205	−	0.0544563i
$897$	21425.8			0.797534
$898$	−11339.0	+	19639.8i	−0.421368	+	0.729831i
$899$	10698.3	+	18529.9i	0.396893	+	0.687439i
$900$	−450.000	−	779.423i	−0.0166667	−	0.0288675i
$901$	−1851.29	+	3206.52i	−0.0684520	+	0.118562i
$902$	−4490.99			−0.165780
$903$	2794.24	−	1127.13i	0.102975	−	0.0415376i
$904$	2022.47			0.0744098
$905$	−7327.96	+	12692.4i	−0.269160	+	0.466198i
$906$	−6539.68	−	11327.1i	−0.239808	−	0.415360i
$907$	24047.2	+	41650.9i	0.880345	+	1.52480i	0.850958	+	0.525233i	$0.176022\pi$
$907$	24047.2	+	41650.9i	0.880345	+	1.52480i	0.0293865	+	0.999568i	$0.490645\pi$
$908$	−1550.86	+	2686.16i	−0.0566817	+	0.0981756i
$909$	−13053.8			−0.476311
$910$	5637.78	−	2274.14i	0.205374	−	0.0828430i
$911$	−32936.0			−1.19782			−0.598912	−	0.800815i	$-0.704400\pi$
$911$	−32936.0			−1.19782			−0.598912	+	0.800815i	$0.704400\pi$
$912$	1096.85	−	1899.81i	0.0398251	−	0.0689791i
$913$	−3742.86	−	6482.82i	−0.135674	−	0.234994i
$914$	5786.47	+	10022.5i	0.209409	+	0.362706i
$915$	3485.27	−	6036.66i	0.125923	−	0.218105i
$916$	4664.88			0.168266
$917$	24078.1	+	18833.6i	0.867097	+	0.678232i
$918$	3719.40			0.133724
$919$	−20987.8	+	36351.9i	−0.753344	+	1.30483i	0.192850	+	0.981228i	$0.438227\pi$
$919$	−20987.8	+	36351.9i	−0.753344	+	1.30483i	−0.946194	+	0.323601i	$0.895106\pi$
$920$	4351.60	+	7537.19i	0.155944	+	0.270102i
$921$	11893.8	+	20600.7i	0.425531	+	0.737041i
$922$	−9403.13	+	16286.7i	−0.335874	+	0.581751i
$923$	−7759.34			−0.276708
$924$	242.975	−	1721.87i	0.00865076	−	0.0613044i
$925$	−6064.50			−0.215567
$926$	13355.7	−	23132.8i	0.473970	−	0.820941i
$927$	2904.25	+	5030.31i	0.102900	+	0.178228i
$928$	2024.43	+	3506.41i	0.0716111	+	0.124034i
$929$	6011.06	−	10411.5i	0.212289	−	0.367696i	−0.740141	−	0.672451i	$-0.765241\pi$
$929$	6011.06	−	10411.5i	0.212289	−	0.367696i	0.952431	+	0.304756i	$0.0985748\pi$
$930$	5073.20			0.178878
$931$	11288.5	−	10876.8i	0.397384	−	0.382891i
$932$	5633.22			0.197985
$933$	12422.8	−	21516.9i	0.435909	−	0.755017i
$934$	−5734.89	−	9933.12i	−0.200911	−	0.347989i
$935$	−1347.33	−	2333.64i	−0.0471254	−	0.0816236i
$936$	1181.68	−	2046.73i	0.0412654	−	0.0714738i
$937$	46293.9			1.61404			0.807021	−	0.590523i	$-0.201078\pi$
$937$	46293.9			1.61404			0.807021	+	0.590523i	$0.201078\pi$
$938$	1090.58	−	7728.52i	0.0379625	−	0.269025i
$939$	−2056.22			−0.0714612
$940$	2267.02	−	3926.60i	0.0786618	−	0.136246i
$941$	4085.53	+	7076.35i	0.141535	+	0.245146i	0.928075	−	0.372394i	$-0.121463\pi$
$941$	4085.53	+	7076.35i	0.141535	+	0.245146i	−0.786540	+	0.617540i	$0.788130\pi$
$942$	8114.01	+	14053.9i	0.280646	+	0.486094i
$943$	31221.1	−	54076.5i	1.07815	−	1.86741i
$944$	−13929.6			−0.480266
$945$	−1969.35	−	1540.40i	−0.0677915	−	0.0530256i
$946$	−848.622			−0.0291660
$947$	11124.3	−	19267.8i	0.381721	−	0.661161i	−0.609587	−	0.792719i	$-0.708665\pi$
$947$	11124.3	−	19267.8i	0.381721	−	0.661161i	0.991308	+	0.131558i	$0.0419981\pi$
$948$	4696.35	+	8134.31i	0.160897	+	0.278682i
$949$	−5783.12	−	10016.7i	−0.197817	−	0.342628i
$950$	−1142.56	+	1978.97i	−0.0390204	+	0.0675854i
$951$	−17381.2			−0.592666
$952$	−9464.12	+	3817.60i	−0.322200	+	0.129967i
$953$	−29181.9			−0.991915			−0.495958	−	0.868347i	$-0.665183\pi$
$953$	−29181.9			−0.991915			−0.495958	+	0.868347i	$0.665183\pi$
$954$	483.801	−	837.968i	0.0164189	−	0.0284384i
$955$	−8610.80	−	14914.3i	−0.291769	−	0.505358i
$956$	−8948.73	−	15499.7i	−0.302743	−	0.524367i
$957$	−1485.00	+	2572.10i	−0.0501601	+	0.0868799i
$958$	29284.8			0.987628
$959$	−30433.4	+	12276.1i	−1.02476	+	0.413363i
$960$	960.000			0.0322749
$961$	596.950	−	1033.95i	0.0200379	−	0.0347067i
$962$	−7962.55	−	13791.5i	−0.266864	−	0.462222i
$963$	2362.29	+	4091.61i	0.0790486	+	0.136916i
$964$	−5940.92	+	10290.0i	−0.198490	+	0.343794i
$965$	9124.43			0.304379
$966$	19044.1	+	14896.0i	0.634299	+	0.496140i
$967$	25172.0			0.837100			0.418550	−	0.908194i	$-0.362538\pi$
$967$	25172.0			0.837100			0.418550	+	0.908194i	$0.362538\pi$
$968$	5079.11	−	8797.28i	0.168646	−	0.292103i
$969$	−4721.81	−	8178.41i	−0.156539	−	0.271134i
$970$	50.5338	+	87.5272i	0.00167273	+	0.00289725i
$971$	2133.20	−	3694.82i	0.0705023	−	0.122114i	−0.828619	−	0.559813i	$-0.810873\pi$
$971$	2133.20	−	3694.82i	0.0705023	−	0.122114i	0.899122	+	0.437699i	$0.144206\pi$
$972$	−972.000			−0.0320750
$973$	6108.57	−	43289.0i	0.201266	−	1.42629i
$974$	11346.1			0.373257
$975$	−1230.92	+	2132.01i	−0.0404317	+	0.0700297i
$976$	3717.62	+	6439.10i	0.121924	+	0.211179i
$977$	11198.0	+	19395.4i	0.366688	+	0.635122i	0.989046	−	0.147611i	$-0.0471583\pi$
$977$	11198.0	+	19395.4i	0.366688	+	0.635122i	−0.622357	+	0.782733i	$0.713825\pi$
$978$	−7802.56	+	13514.4i	−0.255111	+	0.441865i
$979$	1455.64			0.0475205
$980$	6592.14	+	1898.25i	0.214876	+	0.0618749i
$981$	−9508.60			−0.309466
$982$	7355.77	−	12740.6i	0.239035	−	0.414020i
$983$	−8843.45	−	15317.3i	−0.286940	−	0.496995i	0.686138	−	0.727472i	$-0.259305\pi$
$983$	−8843.45	−	15317.3i	−0.286940	−	0.496995i	−0.973078	+	0.230477i	$0.925971\pi$
$984$	−3443.82	−	5964.86i	−0.111570	−	0.193245i
$985$	−4401.16	+	7623.04i	−0.142368	+	0.246589i
$986$	17429.8			0.562958
$987$	1759.97	−	12472.2i	0.0567583	−	0.402223i
$988$	−6000.60			−0.193223
$989$	5899.57	−	10218.4i	0.189682	−	0.328539i
$990$	352.100	+	609.854i	0.0113035	+	0.0195782i
$991$	20981.6	+	36341.2i	0.672555	+	1.16490i	0.977177	+	0.212426i	$0.0681363\pi$
$991$	20981.6	+	36341.2i	0.672555	+	1.16490i	−0.304623	+	0.952473i	$0.598530\pi$
$992$	−2705.71	+	4686.42i	−0.0865991	+	0.149994i
$993$	4680.90			0.149591
$994$	−6896.79	−	5394.58i	−0.220073	−	0.172138i
$995$	−8417.33			−0.268188
$996$	5740.26	−	9942.42i	0.182617	−	0.316303i
$997$	11603.2	+	20097.3i	0.368582	+	0.638403i	0.989344	−	0.145596i	$-0.0465100\pi$
$997$	11603.2	+	20097.3i	0.368582	+	0.638403i	−0.620762	+	0.783999i	$0.713177\pi$
$998$	−20447.2	−	35415.6i	−0.648542	−	1.12331i
$999$	−3274.83	+	5672.17i	−0.103715	+	0.179639i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	210.4.i.i.121.1	✓	4
3.2	odd	2		630.4.k.m.541.1		4
7.2	even	3		1470.4.a.bn.1.1		2
7.4	even	3	inner	210.4.i.i.151.1	yes	4
7.5	odd	6		1470.4.a.bs.1.1		2
21.11	odd	6		630.4.k.m.361.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
210.4.i.i.121.1	✓	4	1.1	even	1	trivial
210.4.i.i.151.1	yes	4	7.4	even	3	inner
630.4.k.m.361.1		4	21.11	odd	6
630.4.k.m.541.1		4	3.2	odd	2
1470.4.a.bn.1.1		2	7.2	even	3
1470.4.a.bs.1.1		2	7.5	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:	\( N \)	\(=\)	\( 210 = 2 \cdot 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	210.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} -6.00000 q^{6} +(-2.58778 + 18.3386i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.00000 + 1.73205i) q^{2} +(1.50000 + 2.59808i) q^{3} +(-2.00000 - 3.46410i) q^{4} +(2.50000 - 4.33013i) q^{5} -6.00000 q^{6} +(-2.58778 + 18.3386i) q^{7} +8.00000 q^{8} +(-4.50000 + 7.79423i) q^{9} +(5.00000 + 8.66025i) q^{10} +(-3.91222 - 6.77616i) q^{11} +(6.00000 - 10.3923i) q^{12} -32.8244 q^{13} +(-29.1756 - 22.8207i) q^{14} +15.0000 q^{15} +(-8.00000 + 13.8564i) q^{16} +(34.4389 + 59.6499i) q^{17} +(-9.00000 - 15.5885i) q^{18} +(-22.8511 + 39.5793i) q^{19} -20.0000 q^{20} +(-51.5267 + 20.7846i) q^{21} +15.6489 q^{22} +(-108.790 + 188.430i) q^{23} +(12.0000 + 20.7846i) q^{24} +(-12.5000 - 21.6506i) q^{25} +(32.8244 - 56.8536i) q^{26} -27.0000 q^{27} +(68.7023 - 27.7128i) q^{28} -126.527 q^{29} +(-15.0000 + 25.9808i) q^{30} +(-84.5534 - 146.451i) q^{31} +(-16.0000 - 27.7128i) q^{32} +(11.7367 - 20.3285i) q^{33} -137.756 q^{34} +(72.9389 + 57.0519i) q^{35} +36.0000 q^{36} +(121.290 - 210.081i) q^{37} +(-45.7023 - 79.1586i) q^{38} +(-49.2367 - 85.2804i) q^{39} +(20.0000 - 34.6410i) q^{40} -286.985 q^{41} +(15.5267 - 110.031i) q^{42} -54.2289 q^{43} +(-15.6489 + 27.1046i) q^{44} +(22.5000 + 38.9711i) q^{45} +(-217.580 - 376.860i) q^{46} +(-113.351 + 196.330i) q^{47} -48.0000 q^{48} +(-329.607 - 94.9125i) q^{49} +50.0000 q^{50} +(-103.317 + 178.950i) q^{51} +(65.6489 + 113.707i) q^{52} +(26.8778 + 46.5538i) q^{53} +(27.0000 - 46.7654i) q^{54} -39.1222 q^{55} +(-20.7023 + 146.709i) q^{56} -137.107 q^{57} +(126.527 - 219.151i) q^{58} +(435.301 + 753.964i) q^{59} +(-30.0000 - 51.9615i) q^{60} +(232.351 - 402.444i) q^{61} +338.214 q^{62} +(-131.290 - 102.693i) q^{63} +64.0000 q^{64} +(-82.0611 + 142.134i) q^{65} +(23.4733 + 40.6570i) q^{66} +(105.359 + 182.487i) q^{67} +(137.756 - 238.600i) q^{68} -652.740 q^{69} +(-171.756 + 69.2820i) q^{70} +236.389 q^{71} +(-36.0000 + 62.3538i) q^{72} +(176.183 + 305.158i) q^{73} +(242.580 + 420.161i) q^{74} +(37.5000 - 64.9519i) q^{75} +182.809 q^{76} +(134.389 - 54.2093i) q^{77} +196.947 q^{78} +(-391.362 + 677.860i) q^{79} +(40.0000 + 69.2820i) q^{80} +(-40.5000 - 70.1481i) q^{81} +(286.985 - 497.072i) q^{82} +956.709 q^{83} +(175.053 + 136.924i) q^{84} +344.389 q^{85} +(54.2289 - 93.9273i) q^{86} +(-189.790 - 328.726i) q^{87} +(-31.2977 - 54.2093i) q^{88} +(-93.0190 + 161.114i) q^{89} -90.0000 q^{90} +(84.9425 - 601.953i) q^{91} +870.320 q^{92} +(253.660 - 439.352i) q^{93} +(-226.702 - 392.660i) q^{94} +(114.256 + 197.897i) q^{95} +(48.0000 - 83.1384i) q^{96} +10.1068 q^{97} +(494.000 - 475.983i) q^{98} +70.4199 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 24 q^{6} + 24 q^{7} + 32 q^{8} - 18 q^{9}+O(q^{10}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 24 * q^6 + 24 * q^7 + 32 * q^8 - 18 * q^9	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 10 q^{5} - 24 q^{6} + 24 q^{7} + 32 q^{8} - 18 q^{9} + 20 q^{10} - 50 q^{11} + 24 q^{12} - 200 q^{13} - 48 q^{14} + 60 q^{15} - 32 q^{16} - 34 q^{17} - 36 q^{18} + 46 q^{19} - 80 q^{20} + 200 q^{22} - 126 q^{23} + 48 q^{24} - 50 q^{25} + 200 q^{26} - 108 q^{27} - 300 q^{29} - 60 q^{30} + 74 q^{31} - 64 q^{32} + 150 q^{33} + 136 q^{34} + 120 q^{35} + 144 q^{36} + 176 q^{37} + 92 q^{38} - 300 q^{39} + 80 q^{40} + 20 q^{41} - 144 q^{42} + 264 q^{43} - 200 q^{44} + 90 q^{45} - 252 q^{46} - 316 q^{47} - 192 q^{48} - 494 q^{49} + 200 q^{50} + 102 q^{51} + 400 q^{52} - 236 q^{53} + 108 q^{54} - 500 q^{55} + 192 q^{56} + 276 q^{57} + 300 q^{58} + 58 q^{59} - 120 q^{60} + 792 q^{61} - 296 q^{62} - 216 q^{63} + 256 q^{64} - 500 q^{65} + 300 q^{66} + 868 q^{67} - 136 q^{68} - 756 q^{69} - 772 q^{71} - 144 q^{72} + 1220 q^{73} + 352 q^{74} + 150 q^{75} - 368 q^{76} - 1180 q^{77} + 1200 q^{78} - 54 q^{79} + 160 q^{80} - 162 q^{81} - 20 q^{82} - 364 q^{83} + 288 q^{84} - 340 q^{85} - 264 q^{86} - 450 q^{87} - 400 q^{88} + 418 q^{89} - 360 q^{90} - 1790 q^{91} + 1008 q^{92} - 222 q^{93} - 632 q^{94} - 230 q^{95} + 192 q^{96} - 784 q^{97} + 1976 q^{98} + 900 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 10 * q^5 - 24 * q^6 + 24 * q^7 + 32 * q^8 - 18 * q^9 + 20 * q^10 - 50 * q^11 + 24 * q^12 - 200 * q^13 - 48 * q^14 + 60 * q^15 - 32 * q^16 - 34 * q^17 - 36 * q^18 + 46 * q^19 - 80 * q^20 + 200 * q^22 - 126 * q^23 + 48 * q^24 - 50 * q^25 + 200 * q^26 - 108 * q^27 - 300 * q^29 - 60 * q^30 + 74 * q^31 - 64 * q^32 + 150 * q^33 + 136 * q^34 + 120 * q^35 + 144 * q^36 + 176 * q^37 + 92 * q^38 - 300 * q^39 + 80 * q^40 + 20 * q^41 - 144 * q^42 + 264 * q^43 - 200 * q^44 + 90 * q^45 - 252 * q^46 - 316 * q^47 - 192 * q^48 - 494 * q^49 + 200 * q^50 + 102 * q^51 + 400 * q^52 - 236 * q^53 + 108 * q^54 - 500 * q^55 + 192 * q^56 + 276 * q^57 + 300 * q^58 + 58 * q^59 - 120 * q^60 + 792 * q^61 - 296 * q^62 - 216 * q^63 + 256 * q^64 - 500 * q^65 + 300 * q^66 + 868 * q^67 - 136 * q^68 - 756 * q^69 - 772 * q^71 - 144 * q^72 + 1220 * q^73 + 352 * q^74 + 150 * q^75 - 368 * q^76 - 1180 * q^77 + 1200 * q^78 - 54 * q^79 + 160 * q^80 - 162 * q^81 - 20 * q^82 - 364 * q^83 + 288 * q^84 - 340 * q^85 - 264 * q^86 - 450 * q^87 - 400 * q^88 + 418 * q^89 - 360 * q^90 - 1790 * q^91 + 1008 * q^92 - 222 * q^93 - 632 * q^94 - 230 * q^95 + 192 * q^96 - 784 * q^97 + 1976 * q^98 + 900 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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