LMFDB - Embedded newform 35.4.e.a.11.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,4,Mod(11,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("35.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	35.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:	$2.06506685020$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			11.1
Root			$0.500000 + 0.866025i$ of defining polynomial
Character	$\chi$	$=$	35.11
Dual form			35.4.e.a.16.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.50000 - 2.59808i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.50000 - 4.33013i) q^{5} -6.00000 q^{6} +(-14.0000 - 12.1244i) q^{7} -21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(-7.50000 + 12.9904i) q^{10} +(22.5000 - 38.9711i) q^{11} +(1.00000 + 1.73205i) q^{12} +59.0000 q^{13} +(-10.5000 + 54.5596i) q^{14} -10.0000 q^{15} +(35.5000 + 61.4878i) q^{16} +(27.0000 - 46.7654i) q^{17} +(34.5000 - 59.7558i) q^{18} +(60.5000 + 104.789i) q^{19} +5.00000 q^{20} +(-35.0000 + 12.1244i) q^{21} -135.000 q^{22} +(-34.5000 - 59.7558i) q^{23} +(-21.0000 + 36.3731i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-88.5000 - 153.286i) q^{26} +100.000 q^{27} +(17.5000 - 6.06218i) q^{28} -162.000 q^{29} +(15.0000 + 25.9808i) q^{30} +(44.0000 - 76.2102i) q^{31} +(22.5000 - 38.9711i) q^{32} +(-45.0000 - 77.9423i) q^{33} -162.000 q^{34} +(-17.5000 + 90.9327i) q^{35} -23.0000 q^{36} +(129.500 + 224.301i) q^{37} +(181.500 - 314.367i) q^{38} +(59.0000 - 102.191i) q^{39} +(52.5000 + 90.9327i) q^{40} +195.000 q^{41} +(84.0000 + 72.7461i) q^{42} -286.000 q^{43} +(22.5000 + 38.9711i) q^{44} +(57.5000 - 99.5929i) q^{45} +(-103.500 + 179.267i) q^{46} +(-22.5000 - 38.9711i) q^{47} +142.000 q^{48} +(49.0000 + 339.482i) q^{49} +75.0000 q^{50} +(-54.0000 - 93.5307i) q^{51} +(-29.5000 + 51.0955i) q^{52} +(-298.500 + 517.017i) q^{53} +(-150.000 - 259.808i) q^{54} -225.000 q^{55} +(294.000 + 254.611i) q^{56} +242.000 q^{57} +(243.000 + 420.888i) q^{58} +(180.000 - 311.769i) q^{59} +(5.00000 - 8.66025i) q^{60} +(-196.000 - 339.482i) q^{61} -264.000 q^{62} +(80.5000 - 418.290i) q^{63} +433.000 q^{64} +(-147.500 - 255.477i) q^{65} +(-135.000 + 233.827i) q^{66} +(140.000 - 242.487i) q^{67} +(27.0000 + 46.7654i) q^{68} -138.000 q^{69} +(262.500 - 90.9327i) q^{70} +48.0000 q^{71} +(-241.500 - 418.290i) q^{72} +(-334.000 + 578.505i) q^{73} +(388.500 - 672.902i) q^{74} +(25.0000 + 43.3013i) q^{75} -121.000 q^{76} +(-787.500 + 272.798i) q^{77} -354.000 q^{78} +(-391.000 - 677.232i) q^{79} +(177.500 - 307.439i) q^{80} +(-210.500 + 364.597i) q^{81} +(-292.500 - 506.625i) q^{82} +768.000 q^{83} +(7.00000 - 36.3731i) q^{84} -270.000 q^{85} +(429.000 + 743.050i) q^{86} +(-162.000 + 280.592i) q^{87} +(-472.500 + 818.394i) q^{88} +(597.000 + 1034.03i) q^{89} -345.000 q^{90} +(-826.000 - 715.337i) q^{91} +69.0000 q^{92} +(-88.0000 - 152.420i) q^{93} +(-67.5000 + 116.913i) q^{94} +(302.500 - 523.945i) q^{95} +(-45.0000 - 77.9423i) q^{96} +902.000 q^{97} +(808.500 - 636.529i) q^{98} +1035.00 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 3 q^{2} + 2 q^{3} - q^{4} - 5 q^{5} - 12 q^{6} - 28 q^{7} - 42 q^{8} + 23 q^{9} - 15 q^{10} + 45 q^{11} + 2 q^{12} + 118 q^{13} - 21 q^{14} - 20 q^{15} + 71 q^{16} + 54 q^{17} + 69 q^{18} + 121 q^{19}+ \cdots + 2070 q^{99}+O(q^{100}) $ 2 * q - 3 * q^2 + 2 * q^3 - q^4 - 5 * q^5 - 12 * q^6 - 28 * q^7 - 42 * q^8 + 23 * q^9 - 15 * q^10 + 45 * q^11 + 2 * q^12 + 118 * q^13 - 21 * q^14 - 20 * q^15 + 71 * q^16 + 54 * q^17 + 69 * q^18 + 121 * q^19 + 10 * q^20 - 70 * q^21 - 270 * q^22 - 69 * q^23 - 42 * q^24 - 25 * q^25 - 177 * q^26 + 200 * q^27 + 35 * q^28 - 324 * q^29 + 30 * q^30 + 88 * q^31 + 45 * q^32 - 90 * q^33 - 324 * q^34 - 35 * q^35 - 46 * q^36 + 259 * q^37 + 363 * q^38 + 118 * q^39 + 105 * q^40 + 390 * q^41 + 168 * q^42 - 572 * q^43 + 45 * q^44 + 115 * q^45 - 207 * q^46 - 45 * q^47 + 284 * q^48 + 98 * q^49 + 150 * q^50 - 108 * q^51 - 59 * q^52 - 597 * q^53 - 300 * q^54 - 450 * q^55 + 588 * q^56 + 484 * q^57 + 486 * q^58 + 360 * q^59 + 10 * q^60 - 392 * q^61 - 528 * q^62 + 161 * q^63 + 866 * q^64 - 295 * q^65 - 270 * q^66 + 280 * q^67 + 54 * q^68 - 276 * q^69 + 525 * q^70 + 96 * q^71 - 483 * q^72 - 668 * q^73 + 777 * q^74 + 50 * q^75 - 242 * q^76 - 1575 * q^77 - 708 * q^78 - 782 * q^79 + 355 * q^80 - 421 * q^81 - 585 * q^82 + 1536 * q^83 + 14 * q^84 - 540 * q^85 + 858 * q^86 - 324 * q^87 - 945 * q^88 + 1194 * q^89 - 690 * q^90 - 1652 * q^91 + 138 * q^92 - 176 * q^93 - 135 * q^94 + 605 * q^95 - 90 * q^96 + 1804 * q^97 + 1617 * q^98 + 2070 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

$n$	$22$	$31$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.50000	−	2.59808i	−0.530330	−	0.918559i	−0.999374	−	0.0353837i	$-0.988735\pi$
$2$	−1.50000	−	2.59808i	−0.530330	−	0.918559i	0.469044	−	0.883175i	$-0.344599\pi$
$3$	1.00000	−	1.73205i	0.192450	−	0.333333i	−0.753612	−	0.657320i	$-0.771690\pi$
$3$	1.00000	−	1.73205i	0.192450	−	0.333333i	0.946062	+	0.323987i	$0.105023\pi$
$4$	−0.500000	+	0.866025i	−0.0625000	+	0.108253i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	−6.00000			−0.408248
$7$	−14.0000	−	12.1244i	−0.755929	−	0.654654i
$7$	−14.0000	−	12.1244i	−0.755929	−	0.654654i
$8$	−21.0000			−0.928078
$9$	11.5000	+	19.9186i	0.425926	+	0.737725i
$10$	−7.50000	+	12.9904i	−0.237171	+	0.410792i
$11$	22.5000	−	38.9711i	0.616728	−	1.06820i	−0.373351	−	0.927690i	$-0.621791\pi$
$11$	22.5000	−	38.9711i	0.616728	−	1.06820i	0.990079	−	0.140514i	$-0.0448754\pi$
$12$	1.00000	+	1.73205i	0.0240563	+	0.0416667i
$13$	59.0000			1.25874			0.629371	−	0.777105i	$-0.283312\pi$
$13$	59.0000			1.25874			0.629371	+	0.777105i	$0.283312\pi$
$14$	−10.5000	+	54.5596i	−0.200446	+	1.04155i
$15$	−10.0000			−0.172133
$16$	35.5000	+	61.4878i	0.554688	+	0.960747i
$17$	27.0000	−	46.7654i	0.385204	−	0.667192i	−0.606594	−	0.795012i	$-0.707465\pi$
$17$	27.0000	−	46.7654i	0.385204	−	0.667192i	0.991797	+	0.127820i	$0.0407979\pi$
$18$	34.5000	−	59.7558i	0.451763	−	0.782476i
$19$	60.5000	+	104.789i	0.730508	+	1.26528i	0.956666	+	0.291186i	$0.0940500\pi$
$19$	60.5000	+	104.789i	0.730508	+	1.26528i	−0.226158	+	0.974091i	$0.572617\pi$
$20$	5.00000			0.0559017
$21$	−35.0000	+	12.1244i	−0.363696	+	0.125988i
$22$	−135.000			−1.30828
$23$	−34.5000	−	59.7558i	−0.312772	−	0.541736i	0.666190	−	0.745782i	$-0.267924\pi$
$23$	−34.5000	−	59.7558i	−0.312772	−	0.541736i	−0.978961	+	0.204046i	$0.934591\pi$
$24$	−21.0000	+	36.3731i	−0.178609	+	0.309359i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	−88.5000	−	153.286i	−0.667549	−	1.15623i
$27$	100.000			0.712778
$28$	17.5000	−	6.06218i	0.118114	−	0.0409159i
$29$	−162.000			−1.03733			−0.518666	−	0.854977i	$-0.673571\pi$
$29$	−162.000			−1.03733			−0.518666	+	0.854977i	$0.673571\pi$
$30$	15.0000	+	25.9808i	0.0912871	+	0.158114i
$31$	44.0000	−	76.2102i	0.254924	−	0.441541i	−0.709951	−	0.704251i	$-0.751283\pi$
$31$	44.0000	−	76.2102i	0.254924	−	0.441541i	0.964875	+	0.262710i	$0.0846163\pi$
$32$	22.5000	−	38.9711i	0.124296	−	0.215287i
$33$	−45.0000	−	77.9423i	−0.237379	−	0.411152i
$34$	−162.000			−0.817140
$35$	−17.5000	+	90.9327i	−0.0845154	+	0.439155i
$36$	−23.0000			−0.106481
$37$	129.500	+	224.301i	0.575396	+	0.996616i	0.995998	+	0.0893706i	$0.0284856\pi$
$37$	129.500	+	224.301i	0.575396	+	0.996616i	−0.420602	+	0.907245i	$0.638181\pi$
$38$	181.500	−	314.367i	0.774821	−	1.34203i
$39$	59.0000	−	102.191i	0.242245	−	0.419581i
$40$	52.5000	+	90.9327i	0.207524	+	0.359443i
$41$	195.000			0.742778			0.371389	−	0.928477i	$-0.378882\pi$
$41$	195.000			0.742778			0.371389	+	0.928477i	$0.378882\pi$
$42$	84.0000	+	72.7461i	0.308607	+	0.267261i
$43$	−286.000			−1.01429			−0.507146	−	0.861860i	$-0.669300\pi$
$43$	−286.000			−1.01429			−0.507146	+	0.861860i	$0.669300\pi$
$44$	22.5000	+	38.9711i	0.0770910	+	0.133525i
$45$	57.5000	−	99.5929i	0.190480	−	0.329921i
$46$	−103.500	+	179.267i	−0.331744	+	0.574598i
$47$	−22.5000	−	38.9711i	−0.0698290	−	0.120947i	0.828997	−	0.559253i	$-0.188912\pi$
$47$	−22.5000	−	38.9711i	−0.0698290	−	0.120947i	−0.898826	+	0.438306i	$0.855579\pi$
$48$	142.000			0.426999
$49$	49.0000	+	339.482i	0.142857	+	0.989743i
$50$	75.0000			0.212132
$51$	−54.0000	−	93.5307i	−0.148265	−	0.256802i
$52$	−29.5000	+	51.0955i	−0.0786714	+	0.136263i
$53$	−298.500	+	517.017i	−0.773625	+	1.33996i	0.161939	+	0.986801i	$0.448225\pi$
$53$	−298.500	+	517.017i	−0.773625	+	1.33996i	−0.935564	+	0.353157i	$0.885108\pi$
$54$	−150.000	−	259.808i	−0.378008	−	0.654729i
$55$	−225.000			−0.551618
$56$	294.000	+	254.611i	0.701561	+	0.607569i
$57$	242.000			0.562345
$58$	243.000	+	420.888i	0.550129	+	0.952851i
$59$	180.000	−	311.769i	0.397187	−	0.687947i	−0.596191	−	0.802843i	$-0.703320\pi$
$59$	180.000	−	311.769i	0.397187	−	0.687947i	0.993378	+	0.114895i	$0.0366533\pi$
$60$	5.00000	−	8.66025i	0.0107583	−	0.0186339i
$61$	−196.000	−	339.482i	−0.411397	−	0.712561i	0.583646	−	0.812009i	$-0.301626\pi$
$61$	−196.000	−	339.482i	−0.411397	−	0.712561i	−0.995043	+	0.0994477i	$0.968292\pi$
$62$	−264.000			−0.540775
$63$	80.5000	−	418.290i	0.160985	−	0.836502i
$64$	433.000			0.845703
$65$	−147.500	−	255.477i	−0.281463	−	0.487509i
$66$	−135.000	+	233.827i	−0.251778	+	0.436092i
$67$	140.000	−	242.487i	0.255279	−	0.442157i	−0.709692	−	0.704512i	$-0.751166\pi$
$67$	140.000	−	242.487i	0.255279	−	0.442157i	0.964971	+	0.262355i	$0.0844992\pi$
$68$	27.0000	+	46.7654i	0.0481505	+	0.0833990i
$69$	−138.000			−0.240772
$70$	262.500	−	90.9327i	0.448211	−	0.155265i
$71$	48.0000			0.0802331			0.0401166	−	0.999195i	$-0.487227\pi$
$71$	48.0000			0.0802331			0.0401166	+	0.999195i	$0.487227\pi$
$72$	−241.500	−	418.290i	−0.395292	−	0.684666i
$73$	−334.000	+	578.505i	−0.535503	+	0.927519i	0.463635	+	0.886026i	$0.346545\pi$
$73$	−334.000	+	578.505i	−0.535503	+	0.927519i	−0.999139	+	0.0414929i	$0.986789\pi$
$74$	388.500	−	672.902i	0.610300	−	1.05707i
$75$	25.0000	+	43.3013i	0.0384900	+	0.0666667i
$76$	−121.000			−0.182627
$77$	−787.500	+	272.798i	−1.16551	+	0.403743i
$78$	−354.000			−0.513880
$79$	−391.000	−	677.232i	−0.556847	−	0.964488i	−0.997757	−	0.0669365i	$-0.978678\pi$
$79$	−391.000	−	677.232i	−0.556847	−	0.964488i	0.440910	−	0.897551i	$-0.354656\pi$
$80$	177.500	−	307.439i	0.248064	−	0.429659i
$81$	−210.500	+	364.597i	−0.288752	+	0.500133i
$82$	−292.500	−	506.625i	−0.393917	−	0.682285i
$83$	768.000			1.01565			0.507825	−	0.861460i	$-0.330450\pi$
$83$	768.000			1.01565			0.507825	+	0.861460i	$0.330450\pi$
$84$	7.00000	−	36.3731i	0.00909241	−	0.0472456i
$85$	−270.000			−0.344537
$86$	429.000	+	743.050i	0.537910	+	0.931687i
$87$	−162.000	+	280.592i	−0.199635	+	0.345778i
$88$	−472.500	+	818.394i	−0.572371	+	0.991376i
$89$	597.000	+	1034.03i	0.711032	+	1.23154i	0.964470	+	0.264192i	$0.0851054\pi$
$89$	597.000	+	1034.03i	0.711032	+	1.23154i	−0.253438	+	0.967352i	$0.581561\pi$
$90$	−345.000			−0.404069
$91$	−826.000	−	715.337i	−0.951520	−	0.824041i
$92$	69.0000			0.0781929
$93$	−88.0000	−	152.420i	−0.0981202	−	0.169949i
$94$	−67.5000	+	116.913i	−0.0740648	+	0.128284i
$95$	302.500	−	523.945i	0.326693	−	0.565849i
$96$	−45.0000	−	77.9423i	−0.0478416	−	0.0828641i
$97$	902.000			0.944167			0.472084	−	0.881554i	$-0.343502\pi$
$97$	902.000			0.944167			0.472084	+	0.881554i	$0.343502\pi$
$98$	808.500	−	636.529i	0.833376	−	0.656113i
$99$	1035.00			1.05072
$100$	−12.5000	−	21.6506i	−0.0125000	−	0.0216506i
$101$	−342.000	+	592.361i	−0.336933	+	0.583586i	−0.983854	−	0.178971i	$-0.942723\pi$
$101$	−342.000	+	592.361i	−0.336933	+	0.583586i	0.646921	+	0.762557i	$0.276056\pi$
$102$	−162.000	+	280.592i	−0.157259	+	0.272380i
$103$	758.000	+	1312.89i	0.725126	+	1.25595i	0.958922	+	0.283669i	$0.0915518\pi$
$103$	758.000	+	1312.89i	0.725126	+	1.25595i	−0.233796	+	0.972286i	$0.575115\pi$
$104$	−1239.00			−1.16821
$105$	140.000	+	121.244i	0.130120	+	0.112687i
$106$	1791.00			1.64111
$107$	366.000	+	633.931i	0.330678	+	0.572751i	0.982645	−	0.185496i	$-0.0593892\pi$
$107$	366.000	+	633.931i	0.330678	+	0.572751i	−0.651967	+	0.758247i	$0.726056\pi$
$108$	−50.0000	+	86.6025i	−0.0445486	+	0.0771605i
$109$	800.000	−	1385.64i	0.702992	−	1.21762i	−0.264420	−	0.964408i	$-0.585180\pi$
$109$	800.000	−	1385.64i	0.702992	−	1.21762i	0.967411	−	0.253210i	$-0.0814863\pi$
$110$	337.500	+	584.567i	0.292540	+	0.506694i
$111$	518.000			0.442940
$112$	248.500	−	1291.24i	0.209652	−	1.08938i
$113$	−1392.00			−1.15883			−0.579417	−	0.815031i	$-0.696720\pi$
$113$	−1392.00			−1.15883			−0.579417	+	0.815031i	$0.696720\pi$
$114$	−363.000	−	628.734i	−0.298229	−	0.516547i
$115$	−172.500	+	298.779i	−0.139876	+	0.242272i
$116$	81.0000	−	140.296i	0.0648333	−	0.112295i
$117$	678.500	+	1175.20i	0.536131	+	0.928606i
$118$	−1080.00			−0.842560
$119$	−945.000	+	327.358i	−0.727966	+	0.252175i
$120$	210.000			0.159752
$121$	−347.000	−	601.022i	−0.260706	−	0.451556i
$122$	−588.000	+	1018.45i	−0.436353	+	0.755785i
$123$	195.000	−	337.750i	0.142948	−	0.247593i
$124$	44.0000	+	76.2102i	0.0318655	+	0.0551926i
$125$	125.000			0.0894427
$126$	−1207.50	+	418.290i	−0.853751	+	0.295748i
$127$	803.000			0.561061			0.280530	−	0.959845i	$-0.409490\pi$
$127$	803.000			0.561061			0.280530	+	0.959845i	$0.409490\pi$
$128$	−829.500	−	1436.74i	−0.572798	−	0.992115i
$129$	−286.000	+	495.367i	−0.195201	+	0.338098i
$130$	−442.500	+	766.432i	−0.298537	+	0.517081i
$131$	−1009.50	−	1748.51i	−0.673286	−	1.16617i	−0.976967	−	0.213391i	$-0.931549\pi$
$131$	−1009.50	−	1748.51i	−0.673286	−	1.16617i	0.303681	−	0.952774i	$-0.401784\pi$
$132$	90.0000			0.0593447
$133$	423.500	−	2200.57i	0.276106	−	1.43469i
$134$	−840.000			−0.541529
$135$	−250.000	−	433.013i	−0.159382	−	0.276058i
$136$	−567.000	+	982.073i	−0.357499	+	0.619206i
$137$	−30.0000	+	51.9615i	−0.0187086	+	0.0324042i	−0.875228	−	0.483710i	$-0.839289\pi$
$137$	−30.0000	+	51.9615i	−0.0187086	+	0.0324042i	0.856520	+	0.516115i	$0.172622\pi$
$138$	207.000	+	358.535i	0.127688	+	0.221163i
$139$	−1708.00			−1.04224			−0.521118	−	0.853485i	$-0.674485\pi$
$139$	−1708.00			−1.04224			−0.521118	+	0.853485i	$0.674485\pi$
$140$	−70.0000	−	60.6218i	−0.0422577	−	0.0365963i
$141$	−90.0000			−0.0537544
$142$	−72.0000	−	124.708i	−0.0425500	−	0.0736988i
$143$	1327.50	−	2299.30i	0.776302	−	1.34459i
$144$	−816.500	+	1414.22i	−0.472512	+	0.818414i
$145$	405.000	+	701.481i	0.231955	+	0.401757i
$146$	2004.00			1.13597
$147$	637.000	+	254.611i	0.357407	+	0.142857i
$148$	−259.000			−0.143849
$149$	543.000	+	940.504i	0.298552	+	0.517108i	0.975805	−	0.218643i	$-0.0701629\pi$
$149$	543.000	+	940.504i	0.298552	+	0.517108i	−0.677253	+	0.735751i	$0.736830\pi$
$150$	75.0000	−	129.904i	0.0408248	−	0.0707107i
$151$	1433.00	−	2482.03i	0.772291	−	1.33765i	−0.164014	−	0.986458i	$-0.552444\pi$
$151$	1433.00	−	2482.03i	0.772291	−	1.33765i	0.936305	−	0.351189i	$-0.114222\pi$
$152$	−1270.50	−	2200.57i	−0.677968	−	1.17428i
$153$	1242.00			0.656273
$154$	1890.00	+	1636.79i	0.988965	+	0.856468i
$155$	−440.000			−0.228011
$156$	59.0000	+	102.191i	0.0302806	+	0.0524476i
$157$	114.500	−	198.320i	0.0582044	−	0.100813i	−0.835455	−	0.549559i	$-0.814796\pi$
$157$	114.500	−	198.320i	0.0582044	−	0.100813i	0.893659	+	0.448746i	$0.148129\pi$
$158$	−1173.00	+	2031.70i	−0.590626	+	1.02299i
$159$	597.000	+	1034.03i	0.297768	+	0.515750i
$160$	−225.000			−0.111174
$161$	−241.500	+	1254.87i	−0.118217	+	0.614271i
$162$	1263.00			0.612535
$163$	614.000	+	1063.48i	0.295044	+	0.511031i	0.974995	−	0.222226i	$-0.0713323\pi$
$163$	614.000	+	1063.48i	0.295044	+	0.511031i	−0.679951	+	0.733258i	$0.737999\pi$
$164$	−97.5000	+	168.875i	−0.0464236	+	0.0804080i
$165$	−225.000	+	389.711i	−0.106159	+	0.183873i
$166$	−1152.00	−	1995.32i	−0.538630	−	0.932934i
$167$	−1929.00			−0.893835			−0.446918	−	0.894575i	$-0.647478\pi$
$167$	−1929.00			−0.893835			−0.446918	+	0.894575i	$0.647478\pi$
$168$	735.000	−	254.611i	0.337539	−	0.116927i
$169$	1284.00			0.584433
$170$	405.000	+	701.481i	0.182718	+	0.316477i
$171$	−1391.50	+	2410.15i	−0.622285	+	1.07783i
$172$	143.000	−	247.683i	0.0633933	−	0.109800i
$173$	349.500	+	605.352i	0.153595	+	0.266035i	0.932547	−	0.361049i	$-0.117581\pi$
$173$	349.500	+	605.352i	0.153595	+	0.266035i	−0.778951	+	0.627084i	$0.784248\pi$
$174$	972.000			0.423489
$175$	437.500	−	151.554i	0.188982	−	0.0654654i
$176$	3195.00			1.36836
$177$	−360.000	−	623.538i	−0.152877	−	0.264791i
$178$	1791.00	−	3102.10i	0.754164	−	1.30625i
$179$	−1558.50	+	2699.40i	−0.650770	+	1.12717i	0.332167	+	0.943221i	$0.392220\pi$
$179$	−1558.50	+	2699.40i	−0.650770	+	1.12717i	−0.982936	+	0.183945i	$0.941113\pi$
$180$	57.5000	+	99.5929i	0.0238100	+	0.0412401i
$181$	−1798.00			−0.738366			−0.369183	−	0.929357i	$-0.620362\pi$
$181$	−1798.00			−0.738366			−0.369183	+	0.929357i	$0.620362\pi$
$182$	−619.500	+	3219.02i	−0.252310	+	1.31104i
$183$	−784.000			−0.316694
$184$	724.500	+	1254.87i	0.290276	+	0.502773i
$185$	647.500	−	1121.50i	0.257325	−	0.445700i
$186$	−264.000	+	457.261i	−0.104072	+	0.180258i
$187$	−1215.00	−	2104.44i	−0.475132	−	0.822952i
$188$	45.0000			0.0174572
$189$	−1400.00	−	1212.44i	−0.538810	−	0.466623i
$190$	−1815.00			−0.693021
$191$	1194.00	+	2068.07i	0.452329	+	0.783457i	0.998530	−	0.0541974i	$-0.0172600\pi$
$191$	1194.00	+	2068.07i	0.452329	+	0.783457i	−0.546201	+	0.837654i	$0.683927\pi$
$192$	433.000	−	749.978i	0.162756	−	0.281901i
$193$	−136.000	+	235.559i	−0.0507228	+	0.0878544i	−0.890272	−	0.455429i	$-0.849486\pi$
$193$	−136.000	+	235.559i	−0.0507228	+	0.0878544i	0.839549	+	0.543284i	$0.182819\pi$
$194$	−1353.00	−	2343.46i	−0.500720	−	0.867273i
$195$	−590.000			−0.216671
$196$	−318.500	−	127.306i	−0.116071	−	0.0463942i
$197$	−2109.00			−0.762741			−0.381371	−	0.924422i	$-0.624548\pi$
$197$	−2109.00			−0.762741			−0.381371	+	0.924422i	$0.624548\pi$
$198$	−1552.50	−	2689.01i	−0.557229	−	0.965149i
$199$	−712.000	+	1233.22i	−0.253630	+	0.439300i	−0.964522	−	0.264001i	$-0.914958\pi$
$199$	−712.000	+	1233.22i	−0.253630	+	0.439300i	0.710893	+	0.703301i	$0.248291\pi$
$200$	262.500	−	454.663i	0.0928078	−	0.160748i
$201$	−280.000	−	484.974i	−0.0982571	−	0.170186i
$202$	2052.00			0.714744
$203$	2268.00	+	1964.15i	0.784150	+	0.679094i
$204$	108.000			0.0370662
$205$	−487.500	−	844.375i	−0.166090	−	0.287677i
$206$	2274.00	−	3938.68i	0.769112	−	1.33214i
$207$	793.500	−	1374.38i	0.266435	−	0.461479i
$208$	2094.50	+	3627.78i	0.698209	+	1.20933i
$209$	5445.00			1.80210
$210$	105.000	−	545.596i	0.0345033	−	0.179284i
$211$	−3625.00			−1.18273			−0.591363	−	0.806405i	$-0.701410\pi$
$211$	−3625.00			−1.18273			−0.591363	+	0.806405i	$0.701410\pi$
$212$	−298.500	−	517.017i	−0.0967031	−	0.167495i
$213$	48.0000	−	83.1384i	0.0154409	−	0.0267444i
$214$	1098.00	−	1901.79i	0.350737	−	0.607494i
$215$	715.000	+	1238.42i	0.226803	+	0.392834i
$216$	−2100.00			−0.661513
$217$	−1540.00	+	533.472i	−0.481760	+	0.166887i
$218$	−4800.00			−1.49127
$219$	668.000	+	1157.01i	0.206115	+	0.357002i
$220$	112.500	−	194.856i	0.0344761	−	0.0597144i
$221$	1593.00	−	2759.16i	0.484872	−	0.839823i
$222$	−777.000	−	1345.80i	−0.234905	−	0.406867i
$223$	−4960.00			−1.48944			−0.744722	−	0.667374i	$-0.767418\pi$
$223$	−4960.00			−1.48944			−0.744722	+	0.667374i	$0.767418\pi$
$224$	−787.500	+	272.798i	−0.234898	+	0.0813709i
$225$	−575.000			−0.170370
$226$	2088.00	+	3616.52i	0.614565	+	1.06446i
$227$	750.000	−	1299.04i	0.219292	−	0.379825i	−0.735300	−	0.677742i	$-0.762959\pi$
$227$	750.000	−	1299.04i	0.219292	−	0.379825i	0.954592	+	0.297917i	$0.0962920\pi$
$228$	−121.000	+	209.578i	−0.0351466	+	0.0608757i
$229$	−3046.00	−	5275.83i	−0.878975	−	1.52243i	−0.852467	−	0.522781i	$-0.824894\pi$
$229$	−3046.00	−	5275.83i	−0.878975	−	1.52243i	−0.0265085	−	0.999649i	$-0.508439\pi$
$230$	1035.00			0.296721
$231$	−315.000	+	1636.79i	−0.0897207	+	0.466202i
$232$	3402.00			0.962725
$233$	−69.0000	−	119.512i	−0.0194006	−	0.0336028i	0.856162	−	0.516707i	$-0.172842\pi$
$233$	−69.0000	−	119.512i	−0.0194006	−	0.0336028i	−0.875563	+	0.483104i	$0.839509\pi$
$234$	2035.50	−	3525.59i	0.568653	−	0.984936i
$235$	−112.500	+	194.856i	−0.0312285	+	0.0540893i
$236$	180.000	+	311.769i	0.0496483	+	0.0859934i
$237$	−1564.00			−0.428661
$238$	2268.00	+	1964.15i	0.617700	+	0.534944i
$239$	−5502.00			−1.48910			−0.744550	−	0.667567i	$-0.767336\pi$
$239$	−5502.00			−1.48910			−0.744550	+	0.667567i	$0.767336\pi$
$240$	−355.000	−	614.878i	−0.0954798	−	0.165376i
$241$	−1775.50	+	3075.26i	−0.474564	+	0.821970i	−0.999576	−	0.0291256i	$-0.990728\pi$
$241$	−1775.50	+	3075.26i	−0.474564	+	0.821970i	0.525011	+	0.851095i	$0.324061\pi$
$242$	−1041.00	+	1803.06i	−0.276521	+	0.478948i
$243$	1771.00	+	3067.46i	0.467530	+	0.809785i
$244$	392.000			0.102849
$245$	1347.50	−	1060.88i	0.351382	−	0.276642i
$246$	−1170.00			−0.303238
$247$	3569.50	+	6182.56i	0.919522	+	1.59266i
$248$	−924.000	+	1600.41i	−0.236589	+	0.409784i
$249$	768.000	−	1330.22i	0.195462	−	0.338550i
$250$	−187.500	−	324.760i	−0.0474342	−	0.0821584i
$251$	7065.00			1.77665			0.888324	−	0.459216i	$-0.151870\pi$
$251$	7065.00			1.77665			0.888324	+	0.459216i	$0.151870\pi$
$252$	322.000	+	278.860i	0.0804924	+	0.0697085i
$253$	−3105.00			−0.771580
$254$	−1204.50	−	2086.26i	−0.297547	−	0.515367i
$255$	−270.000	+	467.654i	−0.0663061	+	0.114846i
$256$	−756.500	+	1310.30i	−0.184692	+	0.319897i
$257$	2040.00	+	3533.38i	0.495143	+	0.857613i	0.999984	−	0.00559954i	$-0.00178240\pi$
$257$	2040.00	+	3533.38i	0.495143	+	0.857613i	−0.504842	+	0.863212i	$0.668449\pi$
$258$	1716.00			0.414083
$259$	906.500	−	4710.31i	0.217479	−	1.13006i
$260$	295.000			0.0703659
$261$	−1863.00	−	3226.81i	−0.441827	−	0.765267i
$262$	−3028.50	+	5245.52i	−0.714127	+	1.23690i
$263$	1644.00	−	2847.49i	0.385450	−	0.667619i	−0.606381	−	0.795174i	$-0.707380\pi$
$263$	1644.00	−	2847.49i	0.385450	−	0.667619i	0.991832	+	0.127555i	$0.0407128\pi$
$264$	945.000	+	1636.79i	0.220306	+	0.381581i
$265$	2985.00			0.691951
$266$	−6352.50	+	2200.57i	−1.46427	+	0.507239i
$267$	2388.00			0.547353
$268$	140.000	+	242.487i	0.0319099	+	0.0552696i
$269$	1632.00	−	2826.71i	0.369906	−	0.640697i	−0.619644	−	0.784883i	$-0.712723\pi$
$269$	1632.00	−	2826.71i	0.369906	−	0.640697i	0.989551	+	0.144186i	$0.0460564\pi$
$270$	−750.000	+	1299.04i	−0.169050	+	0.292803i
$271$	1376.00	+	2383.30i	0.308436	+	0.534226i	0.978020	−	0.208510i	$-0.0668612\pi$
$271$	1376.00	+	2383.30i	0.308436	+	0.534226i	−0.669585	+	0.742736i	$0.733528\pi$
$272$	3834.00			0.854671
$273$	−2065.00	+	715.337i	−0.457800	+	0.158587i
$274$	180.000			0.0396869
$275$	562.500	+	974.279i	0.123346	+	0.213641i
$276$	69.0000	−	119.512i	0.0150482	−	0.0260643i
$277$	2345.00	−	4061.66i	0.508655	−	0.881016i	−0.491295	−	0.870993i	$-0.663476\pi$
$277$	2345.00	−	4061.66i	0.508655	−	0.881016i	0.999950	−	0.0100228i	$-0.00319040\pi$
$278$	2562.00	+	4437.51i	0.552729	+	0.957354i
$279$	2024.00			0.434314
$280$	367.500	−	1909.59i	0.0784369	−	0.407570i
$281$	7821.00			1.66036			0.830181	−	0.557494i	$-0.188237\pi$
$281$	7821.00			1.66036			0.830181	+	0.557494i	$0.188237\pi$
$282$	135.000	+	233.827i	0.0285076	+	0.0493765i
$283$	329.000	−	569.845i	0.0691061	−	0.119695i	−0.829402	−	0.558652i	$-0.811319\pi$
$283$	329.000	−	569.845i	0.0691061	−	0.119695i	0.898508	+	0.438957i	$0.144652\pi$
$284$	−24.0000	+	41.5692i	−0.00501457	+	0.00868549i
$285$	−605.000	−	1047.89i	−0.125744	−	0.217795i
$286$	−7965.00			−1.64678
$287$	−2730.00	−	2364.25i	−0.561487	−	0.486262i
$288$	1035.00			0.211764
$289$	998.500	+	1729.45i	0.203236	+	0.352016i
$290$	1215.00	−	2104.44i	0.246025	−	0.426128i
$291$	902.000	−	1562.31i	0.181705	−	0.314722i
$292$	−334.000	−	578.505i	−0.0669379	−	0.115940i
$293$	−5997.00			−1.19573			−0.597864	−	0.801597i	$-0.703984\pi$
$293$	−5997.00			−1.19573			−0.597864	+	0.801597i	$0.703984\pi$
$294$	−294.000	−	2036.89i	−0.0583212	−	0.404061i
$295$	−1800.00			−0.355254
$296$	−2719.50	−	4710.31i	−0.534013	−	0.924937i
$297$	2250.00	−	3897.11i	0.439590	−	0.761392i
$298$	1629.00	−	2821.51i	0.316663	−	0.548476i
$299$	−2035.50	−	3525.59i	−0.393699	−	0.681907i
$300$	−50.0000			−0.00962250
$301$	4004.00	+	3467.57i	0.766733	+	0.664011i
$302$	−8598.00			−1.63828
$303$	684.000	+	1184.72i	0.129686	+	0.224622i
$304$	−4295.50	+	7440.02i	−0.810407	+	1.40367i
$305$	−980.000	+	1697.41i	−0.183982	+	0.318667i
$306$	−1863.00	−	3226.81i	−0.348041	−	0.602825i
$307$	−6226.00			−1.15745			−0.578724	−	0.815523i	$-0.696449\pi$
$307$	−6226.00			−1.15745			−0.578724	+	0.815523i	$0.696449\pi$
$308$	157.500	−	818.394i	0.0291376	−	0.151404i
$309$	3032.00			0.558202
$310$	660.000	+	1143.15i	0.120921	+	0.209441i
$311$	−2340.00	+	4053.00i	−0.426653	+	0.738985i	−0.996573	−	0.0827149i	$-0.973641\pi$
$311$	−2340.00	+	4053.00i	−0.426653	+	0.738985i	0.569920	+	0.821700i	$0.306974\pi$
$312$	−1239.00	+	2146.01i	−0.224822	+	0.389404i
$313$	−514.000	−	890.274i	−0.0928211	−	0.160771i	0.815876	−	0.578227i	$-0.196255\pi$
$313$	−514.000	−	890.274i	−0.0928211	−	0.160771i	−0.908697	+	0.417456i	$0.862922\pi$
$314$	−687.000			−0.123470
$315$	−2012.50	+	697.150i	−0.359973	+	0.124698i
$316$	782.000			0.139212
$317$	−4311.00	−	7466.87i	−0.763817	−	1.32297i	−0.940870	−	0.338768i	$-0.889990\pi$
$317$	−4311.00	−	7466.87i	−0.763817	−	1.32297i	0.177053	−	0.984201i	$-0.443344\pi$
$318$	1791.00	−	3102.10i	0.315831	−	0.547036i
$319$	−3645.00	+	6313.33i	−0.639752	+	1.10808i
$320$	−1082.50	−	1874.94i	−0.189105	−	0.327539i
$321$	1464.00			0.254556
$322$	3622.50	−	1254.87i	0.626938	−	0.217178i
$323$	6534.00			1.12558
$324$	−210.500	−	364.597i	−0.0360940	−	0.0625166i
$325$	−737.500	+	1277.39i	−0.125874	+	0.218021i
$326$	1842.00	−	3190.44i	0.312942	−	0.542031i
$327$	−1600.00	−	2771.28i	−0.270582	−	0.468661i
$328$	−4095.00			−0.689355
$329$	−157.500	+	818.394i	−0.0263929	+	0.137141i
$330$	1350.00			0.225197
$331$	999.500	+	1731.18i	0.165974	+	0.287476i	0.937001	−	0.349327i	$-0.113590\pi$
$331$	999.500	+	1731.18i	0.165974	+	0.287476i	−0.771027	+	0.636803i	$0.780256\pi$
$332$	−384.000	+	665.108i	−0.0634781	+	0.109947i
$333$	−2978.50	+	5158.91i	−0.490153	+	0.848969i
$334$	2893.50	+	5011.69i	0.474028	+	0.821040i
$335$	−1400.00			−0.228329
$336$	−1988.00	−	1721.66i	−0.322781	−	0.279536i
$337$	5114.00			0.826639			0.413319	−	0.910586i	$-0.364369\pi$
$337$	5114.00			0.826639			0.413319	+	0.910586i	$0.364369\pi$
$338$	−1926.00	−	3335.93i	−0.309943	−	0.536836i
$339$	−1392.00	+	2411.01i	−0.223018	+	0.386278i
$340$	135.000	−	233.827i	0.0215335	−	0.0372972i
$341$	−1980.00	−	3429.46i	−0.314437	−	0.544621i
$342$	8349.00			1.32006
$343$	3430.00	−	5346.84i	0.539949	−	0.841698i
$344$	6006.00			0.941342
$345$	345.000	+	597.558i	0.0538382	+	0.0932505i
$346$	1048.50	−	1816.06i	0.162912	−	0.282173i
$347$	−2160.00	+	3741.23i	−0.334164	+	0.578789i	−0.983324	−	0.181863i	$-0.941787\pi$
$347$	−2160.00	+	3741.23i	−0.334164	+	0.578789i	0.649160	+	0.760652i	$0.275121\pi$
$348$	−162.000	−	280.592i	−0.0249543	−	0.0432222i
$349$	7922.00			1.21506			0.607529	−	0.794298i	$-0.292161\pi$
$349$	7922.00			1.21506			0.607529	+	0.794298i	$0.292161\pi$
$350$	−1050.00	−	909.327i	−0.160357	−	0.138873i
$351$	5900.00			0.897204
$352$	−1012.50	−	1753.70i	−0.153314	−	0.265547i
$353$	−414.000	+	717.069i	−0.0624221	+	0.108118i	−0.895548	−	0.444966i	$-0.853216\pi$
$353$	−414.000	+	717.069i	−0.0624221	+	0.108118i	0.833125	+	0.553084i	$0.186549\pi$
$354$	−1080.00	+	1870.61i	−0.162151	+	0.280853i
$355$	−120.000	−	207.846i	−0.0179407	−	0.0310742i
$356$	−1194.00			−0.177758
$357$	−378.000	+	1964.15i	−0.0560389	+	0.291187i
$358$	9351.00			1.38049
$359$	675.000	+	1169.13i	0.0992344	+	0.171879i	0.911368	−	0.411593i	$-0.135027\pi$
$359$	675.000	+	1169.13i	0.0992344	+	0.171879i	−0.812134	+	0.583472i	$0.801694\pi$
$360$	−1207.50	+	2091.45i	−0.176780	+	0.306192i
$361$	−3891.00	+	6739.41i	−0.567284	+	0.982564i
$362$	2697.00	+	4671.34i	0.391578	+	0.678233i
$363$	−1388.00			−0.200692
$364$	1032.50	−	357.668i	0.148675	−	0.0515025i
$365$	3340.00			0.478969
$366$	1176.00	+	2036.89i	0.167952	+	0.290902i
$367$	−1400.50	+	2425.74i	−0.199198	+	0.345020i	−0.948268	−	0.317470i	$-0.897167\pi$
$367$	−1400.50	+	2425.74i	−0.199198	+	0.345020i	0.749071	+	0.662490i	$0.230500\pi$
$368$	2449.50	−	4242.66i	0.346981	−	0.600989i
$369$	2242.50	+	3884.12i	0.316368	+	0.547966i
$370$	−3885.00			−0.545869
$371$	10447.5	−	3619.12i	1.46201	−	0.506456i
$372$	176.000			0.0245300
$373$	−3301.00	−	5717.50i	−0.458229	−	0.793675i	0.540639	−	0.841255i	$-0.318183\pi$
$373$	−3301.00	−	5717.50i	−0.458229	−	0.793675i	−0.998867	+	0.0475795i	$0.984849\pi$
$374$	−3645.00	+	6313.33i	−0.503953	+	0.872872i
$375$	125.000	−	216.506i	0.0172133	−	0.0298142i
$376$	472.500	+	818.394i	0.0648067	+	0.112249i
$377$	−9558.00			−1.30573
$378$	−1050.00	+	5455.96i	−0.142873	+	0.742392i
$379$	−8305.00			−1.12559			−0.562796	−	0.826596i	$-0.690274\pi$
$379$	−8305.00			−1.12559			−0.562796	+	0.826596i	$0.690274\pi$
$380$	302.500	+	523.945i	0.0408366	+	0.0707311i
$381$	803.000	−	1390.84i	0.107976	−	0.187020i
$382$	3582.00	−	6204.21i	0.479767	−	0.830981i
$383$	−472.500	−	818.394i	−0.0630382	−	0.109185i	0.832784	−	0.553598i	$-0.186746\pi$
$383$	−472.500	−	818.394i	−0.0630382	−	0.109185i	−0.895822	+	0.444413i	$0.853412\pi$
$384$	−3318.00			−0.440940
$385$	3150.00	+	2727.98i	0.416984	+	0.361119i
$386$	816.000			0.107599
$387$	−3289.00	−	5696.72i	−0.432014	−	0.748270i
$388$	−451.000	+	781.155i	−0.0590105	+	0.102209i
$389$	−6018.00	+	10423.5i	−0.784382	+	1.35859i	0.144985	+	0.989434i	$0.453687\pi$
$389$	−6018.00	+	10423.5i	−0.784382	+	1.35859i	−0.929367	+	0.369156i	$0.879647\pi$
$390$	885.000	+	1532.86i	0.114907	+	0.199025i
$391$	−3726.00			−0.481923
$392$	−1029.00	−	7129.12i	−0.132583	−	0.918559i
$393$	−4038.00			−0.518296
$394$	3163.50	+	5479.34i	0.404505	+	0.700623i
$395$	−1955.00	+	3386.16i	−0.249030	+	0.431332i
$396$	−517.500	+	896.336i	−0.0656701	+	0.113744i
$397$	1349.00	+	2336.54i	0.170540	+	0.295384i	0.938609	−	0.344983i	$-0.112115\pi$
$397$	1349.00	+	2336.54i	0.170540	+	0.295384i	−0.768069	+	0.640367i	$0.778782\pi$
$398$	4272.00			0.538030
$399$	−3388.00	−	2934.09i	−0.425093	−	0.368141i
$400$	−1775.00			−0.221875
$401$	−3526.50	−	6108.08i	−0.439165	−	0.760655i	0.558461	−	0.829531i	$-0.311392\pi$
$401$	−3526.50	−	6108.08i	−0.439165	−	0.760655i	−0.997625	+	0.0688756i	$0.978059\pi$
$402$	−840.000	+	1454.92i	−0.104217	+	0.180510i
$403$	2596.00	−	4496.40i	0.320883	−	0.555786i
$404$	−342.000	−	592.361i	−0.0421167	−	0.0729482i
$405$	2105.00			0.258267
$406$	1701.00	−	8838.66i	0.207929	−	1.08043i
$407$	11655.0			1.41945
$408$	1134.00	+	1964.15i	0.137601	+	0.238333i
$409$	5435.00	−	9413.70i	0.657074	−	1.13809i	−0.324295	−	0.945956i	$-0.605127\pi$
$409$	5435.00	−	9413.70i	0.657074	−	1.13809i	0.981369	−	0.192130i	$-0.0615396\pi$
$410$	−1462.50	+	2533.12i	−0.176165	+	0.305127i
$411$	60.0000	+	103.923i	0.00720093	+	0.0124724i
$412$	−1516.00			−0.181281
$413$	−6300.00	+	2182.38i	−0.750612	+	0.260020i
$414$	−4761.00			−0.565194
$415$	−1920.00	−	3325.54i	−0.227106	−	0.393360i
$416$	1327.50	−	2299.30i	0.156457	−	0.270991i
$417$	−1708.00	+	2958.34i	−0.200578	+	0.347412i
$418$	−8167.50	−	14146.5i	−0.955707	−	1.65533i
$419$	−9729.00			−1.13435			−0.567175	−	0.823597i	$-0.691964\pi$
$419$	−9729.00			−1.13435			−0.567175	+	0.823597i	$0.691964\pi$
$420$	−175.000	+	60.6218i	−0.0203313	+	0.00704295i
$421$	−12550.0			−1.45285			−0.726425	−	0.687246i	$-0.758819\pi$
$421$	−12550.0			−1.45285			−0.726425	+	0.687246i	$0.758819\pi$
$422$	5437.50	+	9418.03i	0.627235	+	1.08640i
$423$	517.500	−	896.336i	0.0594840	−	0.103029i
$424$	6268.50	−	10857.4i	0.717984	−	1.24358i
$425$	675.000	+	1169.13i	0.0770407	+	0.133438i
$426$	−288.000			−0.0327550
$427$	−1372.00	+	7129.12i	−0.155494	+	0.807968i
$428$	−732.000			−0.0826695
$429$	−2655.00	−	4598.59i	−0.298799	−	0.517534i
$430$	2145.00	−	3715.25i	0.240561	−	0.416663i
$431$	−1494.00	+	2587.68i	−0.166969	+	0.289198i	−0.937353	−	0.348382i	$-0.886731\pi$
$431$	−1494.00	+	2587.68i	−0.166969	+	0.289198i	0.770384	+	0.637580i	$0.220065\pi$
$432$	3550.00	+	6148.78i	0.395369	+	0.684799i
$433$	16616.0			1.84414			0.922072	−	0.387019i	$-0.126495\pi$
$433$	16616.0			1.84414			0.922072	+	0.387019i	$0.126495\pi$
$434$	3696.00	+	3200.83i	0.408787	+	0.354020i
$435$	1620.00			0.178559
$436$	800.000	+	1385.64i	0.0878740	+	0.152202i
$437$	4174.50	−	7230.45i	0.456964	−	0.791485i
$438$	2004.00	−	3471.03i	0.218618	−	0.378658i
$439$	−3673.00	−	6361.82i	−0.399323	−	0.691647i	0.594320	−	0.804229i	$-0.297421\pi$
$439$	−3673.00	−	6361.82i	−0.399323	−	0.691647i	−0.993642	+	0.112581i	$0.964088\pi$
$440$	4725.00			0.511944
$441$	−6198.50	+	4880.05i	−0.669312	+	0.526947i
$442$	−9558.00			−1.02857
$443$	−6.00000	−	10.3923i	−0.000643496	−	0.00111457i	0.865703	−	0.500557i	$-0.166871\pi$
$443$	−6.00000	−	10.3923i	−0.000643496	−	0.00111457i	−0.866347	+	0.499443i	$0.833538\pi$
$444$	−259.000	+	448.601i	−0.0276838	+	0.0479497i
$445$	2985.00	−	5170.17i	0.317983	−	0.550763i
$446$	7440.00	+	12886.5i	0.789897	+	1.36814i
$447$	2172.00			0.229826
$448$	−6062.00	−	5249.85i	−0.639291	−	0.553643i
$449$	9669.00			1.01628			0.508138	−	0.861275i	$-0.330334\pi$
$449$	9669.00			1.01628			0.508138	+	0.861275i	$0.330334\pi$
$450$	862.500	+	1493.89i	0.0903525	+	0.156495i
$451$	4387.50	−	7599.37i	0.458092	−	0.793438i
$452$	696.000	−	1205.51i	0.0724272	−	0.125448i
$453$	−2866.00	−	4964.06i	−0.297255	−	0.514860i
$454$	−4500.00			−0.465188
$455$	−1032.50	+	5365.03i	−0.106383	+	0.552783i
$456$	−5082.00			−0.521900
$457$	4817.00	+	8343.29i	0.493063	+	0.854010i	0.999968	−	0.00799181i	$-0.00254390\pi$
$457$	4817.00	+	8343.29i	0.493063	+	0.854010i	−0.506905	+	0.862002i	$0.669211\pi$
$458$	−9138.00	+	15827.5i	−0.932294	+	1.61478i
$459$	2700.00	−	4676.54i	0.274565	−	0.475560i
$460$	−172.500	−	298.779i	−0.0174845	−	0.0302840i
$461$	−342.000			−0.0345521			−0.0172761	−	0.999851i	$-0.505499\pi$
$461$	−342.000			−0.0345521			−0.0172761	+	0.999851i	$0.505499\pi$
$462$	4725.00	−	1636.79i	0.475816	−	0.164827i
$463$	2411.00			0.242006			0.121003	−	0.992652i	$-0.461389\pi$
$463$	2411.00			0.242006			0.121003	+	0.992652i	$0.461389\pi$
$464$	−5751.00	−	9961.02i	−0.575395	−	0.996614i
$465$	−440.000	+	762.102i	−0.0438807	+	0.0760035i
$466$	−207.000	+	358.535i	−0.0205774	+	0.0356412i
$467$	603.000	+	1044.43i	0.0597506	+	0.103491i	0.894353	−	0.447361i	$-0.147636\pi$
$467$	603.000	+	1044.43i	0.0597506	+	0.103491i	−0.834603	+	0.550852i	$0.814303\pi$
$468$	−1357.00			−0.134033
$469$	−4900.00	+	1697.41i	−0.482433	+	0.167120i
$470$	675.000			0.0662456
$471$	−229.000	−	396.640i	−0.0224029	−	0.0388030i
$472$	−3780.00	+	6547.15i	−0.368620	+	0.638468i
$473$	−6435.00	+	11145.7i	−0.625543	+	1.08347i
$474$	2346.00	+	4063.39i	0.227332	+	0.393751i
$475$	−3025.00			−0.292203
$476$	189.000	−	982.073i	0.0181992	−	0.0945656i
$477$	−13731.0			−1.31803
$478$	8253.00	+	14294.6i	0.789714	+	1.36783i
$479$	216.000	−	374.123i	0.0206039	−	0.0356871i	−0.855540	−	0.517737i	$-0.826774\pi$
$479$	216.000	−	374.123i	0.0206039	−	0.0356871i	0.876144	+	0.482050i	$0.160108\pi$
$480$	−225.000	+	389.711i	−0.0213954	+	0.0370579i
$481$	7640.50	+	13233.7i	0.724276	+	1.25448i
$482$	10653.0			1.00670
$483$	1932.00	+	1673.16i	0.182006	+	0.157622i
$484$	694.000			0.0651766
$485$	−2255.00	−	3905.77i	−0.211122	−	0.365674i
$486$	5313.00	−	9202.39i	0.495890	−	0.858907i
$487$	5948.00	−	10302.2i	0.553449	−	0.958602i	−0.444574	−	0.895742i	$-0.646645\pi$
$487$	5948.00	−	10302.2i	0.553449	−	0.958602i	0.998022	−	0.0628592i	$-0.0200219\pi$
$488$	4116.00	+	7129.12i	0.381809	+	0.661312i
$489$	2456.00			0.227125
$490$	−4777.50	−	1909.59i	−0.440460	−	0.176054i
$491$	−12276.0			−1.12833			−0.564163	−	0.825663i	$-0.690801\pi$
$491$	−12276.0			−1.12833			−0.564163	+	0.825663i	$0.690801\pi$
$492$	195.000	+	337.750i	0.0178685	+	0.0309491i
$493$	−4374.00	+	7575.99i	−0.399584	+	0.692100i
$494$	10708.5	−	18547.7i	0.975300	−	1.68927i
$495$	−2587.50	−	4481.68i	−0.234948	−	0.406943i
$496$	6248.00			0.565612
$497$	−672.000	−	581.969i	−0.0606505	−	0.0525249i
$498$	−4608.00			−0.414637
$499$	5438.00	+	9418.89i	0.487852	+	0.844985i	0.999902	−	0.0139706i	$-0.00444712\pi$
$499$	5438.00	+	9418.89i	0.487852	+	0.844985i	−0.512050	+	0.858956i	$0.671114\pi$
$500$	−62.5000	+	108.253i	−0.00559017	+	0.00968246i
$501$	−1929.00	+	3341.13i	−0.172019	+	0.297945i
$502$	−10597.5	−	18355.4i	−0.942210	−	1.63196i
$503$	12000.0			1.06372			0.531862	−	0.846831i	$-0.321492\pi$
$503$	12000.0			1.06372			0.531862	+	0.846831i	$0.321492\pi$
$504$	−1690.50	+	8784.10i	−0.149406	+	0.776339i
$505$	3420.00			0.301362
$506$	4657.50	+	8067.03i	0.409192	+	0.708741i
$507$	1284.00	−	2223.95i	0.112474	−	0.194811i
$508$	−401.500	+	695.418i	−0.0350663	+	0.0607366i
$509$	5841.00	+	10116.9i	0.508640	+	0.880990i	0.999950	+	0.0100055i	$0.00318492\pi$
$509$	5841.00	+	10116.9i	0.508640	+	0.880990i	−0.491310	+	0.870985i	$0.663482\pi$
$510$	1620.00			0.140656
$511$	11690.0	−	4049.53i	1.01201	−	0.350569i
$512$	−8733.00			−0.753804
$513$	6050.00	+	10478.9i	0.520690	+	0.901862i
$514$	6120.00	−	10600.2i	0.525178	−	0.909635i
$515$	3790.00	−	6564.47i	0.324286	−	0.561680i
$516$	−286.000	−	495.367i	−0.0244001	−	0.0422622i
$517$	−2025.00			−0.172262
$518$	−13597.5	+	4710.31i	−1.15336	+	0.399535i
$519$	1398.00			0.118238
$520$	3097.50	+	5365.03i	0.261220	+	0.452446i
$521$	−4804.50	+	8321.64i	−0.404010	+	0.699765i	−0.994206	−	0.107495i	$-0.965717\pi$
$521$	−4804.50	+	8321.64i	−0.404010	+	0.699765i	0.590196	+	0.807260i	$0.299050\pi$
$522$	−5589.00	+	9680.43i	−0.468628	+	0.811688i
$523$	−10594.0	−	18349.3i	−0.885742	−	1.53415i	−0.844860	−	0.534987i	$-0.820317\pi$
$523$	−10594.0	−	18349.3i	−0.885742	−	1.53415i	−0.0408820	−	0.999164i	$-0.513017\pi$
$524$	2019.00			0.168321
$525$	175.000	−	909.327i	0.0145479	−	0.0755929i
$526$	−9864.00			−0.817663
$527$	−2376.00	−	4115.35i	−0.196395	−	0.340166i
$528$	3195.00	−	5533.90i	0.263342	−	0.456122i
$529$	3703.00	−	6413.78i	0.304348	−	0.527146i
$530$	−4477.50	−	7755.26i	−0.366963	−	0.635598i
$531$	8280.00			0.676688
$532$	1694.00	+	1467.05i	0.138053	+	0.119557i
$533$	11505.0			0.934966
$534$	−3582.00	−	6204.21i	−0.290278	−	0.502776i
$535$	1830.00	−	3169.65i	0.147884	−	0.256142i
$536$	−2940.00	+	5092.23i	−0.236919	+	0.410356i
$537$	3117.00	+	5398.80i	0.250481	+	0.433846i
$538$	−9792.00			−0.784690
$539$	14332.5	+	5728.76i	1.14535	+	0.457802i
$540$	500.000			0.0398455
$541$	−4036.00	−	6990.56i	−0.320742	−	0.555541i	0.659900	−	0.751354i	$-0.270599\pi$
$541$	−4036.00	−	6990.56i	−0.320742	−	0.555541i	−0.980641	+	0.195813i	$0.937265\pi$
$542$	4128.00	−	7149.91i	0.327145	−	0.566632i
$543$	−1798.00	+	3114.23i	−0.142099	+	0.246122i
$544$	−1215.00	−	2104.44i	−0.0957586	−	0.165859i
$545$	−8000.00			−0.628775
$546$	4956.00	+	4292.02i	0.388456	+	0.336413i
$547$	344.000			0.0268892			0.0134446	−	0.999910i	$-0.495720\pi$
$547$	344.000			0.0268892			0.0134446	+	0.999910i	$0.495720\pi$
$548$	−30.0000	−	51.9615i	−0.00233857	−	0.00405052i
$549$	4508.00	−	7808.09i	0.350449	−	0.606996i
$550$	1687.50	−	2922.84i	0.130828	−	0.226600i
$551$	−9801.00	−	16975.8i	−0.757780	−	1.31251i
$552$	2898.00			0.223455
$553$	−2737.00	+	14221.9i	−0.210468	+	1.09363i
$554$	−14070.0			−1.07902
$555$	−1295.00	−	2243.01i	−0.0990445	−	0.171550i
$556$	854.000	−	1479.17i	0.0651397	−	0.112825i
$557$	−9181.50	+	15902.8i	−0.698443	+	1.20974i	0.270563	+	0.962702i	$0.412790\pi$
$557$	−9181.50	+	15902.8i	−0.698443	+	1.20974i	−0.969006	+	0.247036i	$0.920543\pi$
$558$	−3036.00	−	5258.51i	−0.230330	−	0.398943i
$559$	−16874.0			−1.27673
$560$	−6212.50	+	2152.07i	−0.468797	+	0.162396i
$561$	−4860.00			−0.365756
$562$	−11731.5	−	20319.6i	−0.880540	−	1.52514i
$563$	3147.00	−	5450.76i	0.235578	−	0.408033i	−0.723863	−	0.689944i	$-0.757635\pi$
$563$	3147.00	−	5450.76i	0.235578	−	0.408033i	0.959440	+	0.281912i	$0.0909685\pi$
$564$	45.0000	−	77.9423i	0.00335965	−	0.00581908i
$565$	3480.00	+	6027.54i	0.259123	+	0.448815i
$566$	−1974.00			−0.146596
$567$	7367.50	−	2552.18i	0.545689	−	0.189032i
$568$	−1008.00			−0.0744626
$569$	−5866.50	−	10161.1i	−0.432226	−	0.748637i	0.564839	−	0.825201i	$-0.308938\pi$
$569$	−5866.50	−	10161.1i	−0.432226	−	0.748637i	−0.997065	+	0.0765642i	$0.975605\pi$
$570$	−1815.00	+	3143.67i	−0.133372	+	0.231007i
$571$	−526.000	+	911.059i	−0.0385506	+	0.0667717i	−0.884657	−	0.466242i	$-0.845607\pi$
$571$	−526.000	+	911.059i	−0.0385506	+	0.0667717i	0.846106	+	0.533014i	$0.178941\pi$
$572$	1327.50	+	2299.30i	0.0970377	+	0.168074i
$573$	4776.00			0.348203
$574$	−2047.50	+	10639.1i	−0.148887	+	0.773638i
$575$	1725.00			0.125109
$576$	4979.50	+	8624.75i	0.360207	+	0.623897i
$577$	6578.00	−	11393.4i	0.474603	−	0.822036i	−0.524974	−	0.851118i	$-0.675925\pi$
$577$	6578.00	−	11393.4i	0.474603	−	0.822036i	0.999577	+	0.0290821i	$0.00925844\pi$
$578$	2995.50	−	5188.36i	0.215565	−	0.373369i
$579$	272.000	+	471.118i	0.0195232	+	0.0338152i
$580$	−810.000			−0.0579887
$581$	−10752.0	−	9311.51i	−0.767759	−	0.664899i
$582$	−5412.00			−0.385455
$583$	13432.5	+	23265.8i	0.954232	+	1.65278i
$584$	7014.00	−	12148.6i	0.496989	−	0.860810i
$585$	3392.50	−	5875.98i	0.239765	−	0.415285i
$586$	8995.50	+	15580.7i	0.634131	+	1.09835i
$587$	−13368.0			−0.939960			−0.469980	−	0.882677i	$-0.655739\pi$
$587$	−13368.0			−0.939960			−0.469980	+	0.882677i	$0.655739\pi$
$588$	−539.000	+	424.352i	−0.0378027	+	0.0297619i
$589$	10648.0			0.744895
$590$	2700.00	+	4676.54i	0.188402	+	0.326322i
$591$	−2109.00	+	3652.90i	−0.146790	+	0.254247i
$592$	−9194.50	+	15925.3i	−0.638330	+	1.10562i
$593$	−13332.0	−	23091.7i	−0.923237	−	1.59909i	−0.794372	−	0.607431i	$-0.792200\pi$
$593$	−13332.0	−	23091.7i	−0.923237	−	1.59909i	−0.128865	−	0.991662i	$-0.541133\pi$
$594$	−13500.0			−0.932511
$595$	3780.00	+	3273.58i	0.260445	+	0.225552i
$596$	−1086.00			−0.0746381
$597$	1424.00	+	2466.44i	0.0976222	+	0.169087i
$598$	−6106.50	+	10576.8i	−0.417581	+	0.723271i
$599$	−3807.00	+	6593.92i	−0.259682	+	0.449783i	−0.966157	−	0.257955i	$-0.916951\pi$
$599$	−3807.00	+	6593.92i	−0.259682	+	0.449783i	0.706474	+	0.707739i	$0.250285\pi$
$600$	−525.000	−	909.327i	−0.0357217	−	0.0618718i
$601$	6410.00			0.435057			0.217529	−	0.976054i	$-0.430200\pi$
$601$	6410.00			0.435057			0.217529	+	0.976054i	$0.430200\pi$
$602$	3003.00	−	15604.0i	0.203311	−	1.05643i
$603$	6440.00			0.434921
$604$	1433.00	+	2482.03i	0.0965363	+	0.167206i
$605$	−1735.00	+	3005.11i	−0.116591	+	0.201942i
$606$	2052.00	−	3554.17i	0.137552	−	0.238248i
$607$	10734.5	+	18592.7i	0.717792	+	1.24325i	0.961873	+	0.273498i	$0.0881806\pi$
$607$	10734.5	+	18592.7i	0.717792	+	1.24325i	−0.244080	+	0.969755i	$0.578486\pi$
$608$	5445.00			0.363197
$609$	5670.00	−	1964.15i	0.377274	−	0.130692i
$610$	5880.00			0.390286
$611$	−1327.50	−	2299.30i	−0.0878967	−	0.152242i
$612$	−621.000	+	1075.60i	−0.0410171	+	0.0710436i
$613$	−1868.50	+	3236.34i	−0.123113	+	0.213237i	−0.920994	−	0.389578i	$-0.872621\pi$
$613$	−1868.50	+	3236.34i	−0.123113	+	0.213237i	0.797881	+	0.602815i	$0.205954\pi$
$614$	9339.00	+	16175.6i	0.613830	+	1.06318i
$615$	−1950.00			−0.127856
$616$	16537.5	−	5728.76i	1.08168	−	0.374705i
$617$	18078.0			1.17957			0.589784	−	0.807561i	$-0.299213\pi$
$617$	18078.0			1.17957			0.589784	+	0.807561i	$0.299213\pi$
$618$	−4548.00	−	7877.37i	−0.296031	−	0.512741i
$619$	−6143.50	+	10640.9i	−0.398915	+	0.690940i	−0.993592	−	0.113024i	$-0.963946\pi$
$619$	−6143.50	+	10640.9i	−0.398915	+	0.690940i	0.594678	+	0.803964i	$0.297280\pi$
$620$	220.000	−	381.051i	0.0142507	−	0.0246829i
$621$	−3450.00	−	5975.58i	−0.222937	−	0.386138i
$622$	14040.0			0.905069
$623$	4179.00	−	21714.7i	0.268745	−	1.39644i
$624$	8378.00			0.537481
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	−1542.00	+	2670.82i	−0.0984516	+	0.170523i
$627$	5445.00	−	9431.02i	0.346814	−	0.600699i
$628$	114.500	+	198.320i	0.00727555	+	0.0126016i
$629$	13986.0			0.886579
$630$	4830.00	+	4182.90i	0.305447	+	0.264525i
$631$	−9580.00			−0.604396			−0.302198	−	0.953245i	$-0.597720\pi$
$631$	−9580.00			−0.604396			−0.302198	+	0.953245i	$0.597720\pi$
$632$	8211.00	+	14221.9i	0.516798	+	0.895120i
$633$	−3625.00	+	6278.68i	−0.227616	+	0.394242i
$634$	−12933.0	+	22400.6i	−0.810150	+	1.40322i
$635$	−2007.50	−	3477.09i	−0.125457	−	0.217298i
$636$	−1194.00			−0.0744421
$637$	2891.00	+	20029.4i	0.179820	+	1.24583i
$638$	21870.0			1.35712
$639$	552.000	+	956.092i	0.0341734	+	0.0591900i
$640$	−4147.50	+	7183.68i	−0.256163	+	0.443687i
$641$	−5389.50	+	9334.89i	−0.332094	+	0.575204i	−0.982922	−	0.184021i	$-0.941089\pi$
$641$	−5389.50	+	9334.89i	−0.332094	+	0.575204i	0.650828	+	0.759225i	$0.274422\pi$
$642$	−2196.00	−	3803.58i	−0.134999	−	0.233825i
$643$	8882.00			0.544746			0.272373	−	0.962192i	$-0.412191\pi$
$643$	8882.00			0.544746			0.272373	+	0.962192i	$0.412191\pi$
$644$	−966.000	−	836.581i	−0.0591083	−	0.0511893i
$645$	2860.00			0.174593
$646$	−9801.00	−	16975.8i	−0.596928	−	1.03391i
$647$	5509.50	−	9542.73i	0.334777	−	0.579851i	−0.648665	−	0.761074i	$-0.724672\pi$
$647$	5509.50	−	9542.73i	0.334777	−	0.579851i	0.983442	+	0.181223i	$0.0580056\pi$
$648$	4420.50	−	7656.53i	0.267984	−	0.464162i
$649$	−8100.00	−	14029.6i	−0.489912	−	0.848552i
$650$	4425.00			0.267020
$651$	−616.000	+	3200.83i	−0.0370859	+	0.192704i
$652$	−1228.00			−0.0737610
$653$	−11161.5	−	19332.3i	−0.668887	−	1.15855i	−0.978216	−	0.207591i	$-0.933438\pi$
$653$	−11161.5	−	19332.3i	−0.668887	−	1.15855i	0.309329	−	0.950955i	$-0.399896\pi$
$654$	−4800.00	+	8313.84i	−0.286995	+	0.497090i
$655$	−5047.50	+	8742.53i	−0.301103	+	0.521525i
$656$	6922.50	+	11990.1i	0.412009	+	0.713621i
$657$	−15364.0			−0.912339
$658$	2362.50	−	818.394i	0.139969	−	0.0484868i
$659$	−11856.0			−0.700826			−0.350413	−	0.936595i	$-0.613959\pi$
$659$	−11856.0			−0.700826			−0.350413	+	0.936595i	$0.613959\pi$
$660$	−225.000	−	389.711i	−0.0132699	−	0.0229841i
$661$	16622.0	−	28790.1i	0.978095	−	1.69411i	0.308777	−	0.951134i	$-0.400080\pi$
$661$	16622.0	−	28790.1i	0.978095	−	1.69411i	0.669318	−	0.742976i	$-0.266586\pi$
$662$	2998.50	−	5193.55i	0.176042	−	0.304914i
$663$	−3186.00	−	5518.31i	−0.186627	−	0.323248i
$664$	−16128.0			−0.942602
$665$	−10587.5	+	3667.62i	−0.617392	+	0.213871i
$666$	17871.0			1.03977
$667$	5589.00	+	9680.43i	0.324448	+	0.561961i
$668$	964.500	−	1670.56i	0.0558647	−	0.0967605i
$669$	−4960.00	+	8590.97i	−0.286644	+	0.496482i
$670$	2100.00	+	3637.31i	0.121090	+	0.209733i
$671$	−17640.0			−1.01488
$672$	−315.000	+	1636.79i	−0.0180824	+	0.0939590i
$673$	−12322.0			−0.705763			−0.352881	−	0.935668i	$-0.614798\pi$
$673$	−12322.0			−0.705763			−0.352881	+	0.935668i	$0.614798\pi$
$674$	−7671.00	−	13286.6i	−0.438392	−	0.759316i
$675$	−1250.00	+	2165.06i	−0.0712778	+	0.123457i
$676$	−642.000	+	1111.98i	−0.0365271	+	0.0632668i
$677$	6298.50	+	10909.3i	0.357564	+	0.619320i	0.987553	−	0.157285i	$-0.0502740\pi$
$677$	6298.50	+	10909.3i	0.357564	+	0.619320i	−0.629989	+	0.776604i	$0.716941\pi$
$678$	8352.00			0.473092
$679$	−12628.0	−	10936.2i	−0.713723	−	0.618103i
$680$	5670.00			0.319757
$681$	−1500.00	−	2598.08i	−0.0844055	−	0.146195i
$682$	−5940.00	+	10288.4i	−0.333511	+	0.577658i
$683$	4170.00	−	7222.65i	0.233617	−	0.404637i	−0.725253	−	0.688483i	$-0.758277\pi$
$683$	4170.00	−	7222.65i	0.233617	−	0.404637i	0.958870	+	0.283846i	$0.0916104\pi$
$684$	−1391.50	−	2410.15i	−0.0777856	−	0.134729i
$685$	300.000			0.0167334
$686$	−19036.5	−	891.140i	−1.05950	−	0.0495975i
$687$	−12184.0			−0.676636
$688$	−10153.0	−	17585.5i	−0.562616	−	0.974479i
$689$	−17611.5	+	30504.0i	−0.973795	+	1.68666i
$690$	1035.00	−	1792.67i	0.0571040	−	0.0989071i
$691$	10100.0	+	17493.7i	0.556038	+	0.963086i	0.997822	+	0.0659643i	$0.0210124\pi$
$691$	10100.0	+	17493.7i	0.556038	+	0.963086i	−0.441784	+	0.897121i	$0.645654\pi$
$692$	−699.000			−0.0383988
$693$	−14490.0	−	12548.7i	−0.794271	−	0.687859i
$694$	12960.0			0.708869
$695$	4270.00	+	7395.86i	0.233051	+	0.403656i
$696$	3402.00	−	5892.44i	0.185277	−	0.320908i
$697$	5265.00	−	9119.25i	0.286121	−	0.495576i
$698$	−11883.0	−	20582.0i	−0.644381	−	1.11610i
$699$	−276.000			−0.0149346
$700$	−87.5000	+	454.663i	−0.00472456	+	0.0245495i
$701$	474.000			0.0255388			0.0127694	−	0.999918i	$-0.495935\pi$
$701$	474.000			0.0255388			0.0127694	+	0.999918i	$0.495935\pi$
$702$	−8850.00	−	15328.6i	−0.475814	−	0.824135i
$703$	−15669.5	+	27140.4i	−0.840663	+	1.45607i
$704$	9742.50	−	16874.5i	0.521569	−	0.903383i
$705$	225.000	+	389.711i	0.0120198	+	0.0208190i
$706$	2484.00			0.132417
$707$	11970.0	−	4146.53i	0.636744	−	0.220575i
$708$	720.000			0.0382193
$709$	12563.0	+	21759.8i	0.665463	+	1.15262i	0.979160	+	0.203093i	$0.0650993\pi$
$709$	12563.0	+	21759.8i	0.665463	+	1.15262i	−0.313696	+	0.949523i	$0.601567\pi$
$710$	−360.000	+	623.538i	−0.0190290	+	0.0329591i
$711$	8993.00	−	15576.3i	0.474351	−	0.821601i
$712$	−12537.0	−	21714.7i	−0.659893	−	1.14297i
$713$	−6072.00			−0.318932
$714$	5670.00	−	1964.15i	0.297191	−	0.102950i
$715$	−13275.0			−0.694345
$716$	−1558.50	−	2699.40i	−0.0813462	−	0.140896i
$717$	−5502.00	+	9529.74i	−0.286577	+	0.496367i
$718$	2025.00	−	3507.40i	0.105254	−	0.182305i
$719$	3648.00	+	6318.52i	0.189218	+	0.327734i	0.944990	−	0.327100i	$-0.106072\pi$
$719$	3648.00	+	6318.52i	0.189218	+	0.327734i	−0.755772	+	0.654835i	$0.772738\pi$
$720$	8165.00			0.422627
$721$	5306.00	−	27570.8i	0.274072	−	1.42412i
$722$	23346.0			1.20339
$723$	3551.00	+	6150.51i	0.182660	+	0.316376i
$724$	899.000	−	1557.11i	0.0461479	−	0.0799305i
$725$	2025.00	−	3507.40i	0.103733	−	0.179671i
$726$	2082.00	+	3606.13i	0.106433	+	0.184347i
$727$	−15421.0			−0.786703			−0.393352	−	0.919388i	$-0.628684\pi$
$727$	−15421.0			−0.786703			−0.393352	+	0.919388i	$0.628684\pi$
$728$	17346.0	+	15022.1i	0.883085	+	0.764774i
$729$	−4283.00			−0.217599
$730$	−5010.00	−	8677.57i	−0.254012	−	0.439961i
$731$	−7722.00	+	13374.9i	−0.390709	+	0.676728i
$732$	392.000	−	678.964i	0.0197934	−	0.0342831i
$733$	14583.5	+	25259.4i	0.734862	+	1.27282i	0.954784	+	0.297301i	$0.0960864\pi$
$733$	14583.5	+	25259.4i	0.734862	+	1.27282i	−0.219922	+	0.975517i	$0.570580\pi$
$734$	8403.00			0.422562
$735$	−490.000	−	3394.82i	−0.0245904	−	0.170367i
$736$	−3105.00			−0.155505
$737$	−6300.00	−	10911.9i	−0.314876	−	0.545381i
$738$	6727.50	−	11652.4i	0.335559	−	0.581206i
$739$	6690.50	−	11588.3i	0.333037	−	0.576836i	−0.650069	−	0.759875i	$-0.725260\pi$
$739$	6690.50	−	11588.3i	0.333037	−	0.576836i	0.983106	+	0.183039i	$0.0585934\pi$
$740$	647.500	+	1121.50i	0.0321656	+	0.0557125i
$741$	14278.0			0.707848
$742$	−25074.0	−	21714.7i	−1.24056	−	1.07436i
$743$	5487.00			0.270927			0.135463	−	0.990782i	$-0.456748\pi$
$743$	5487.00			0.270927			0.135463	+	0.990782i	$0.456748\pi$
$744$	1848.00	+	3200.83i	0.0910631	+	0.157726i
$745$	2715.00	−	4702.52i	0.133517	−	0.231258i
$746$	−9903.00	+	17152.5i	−0.486025	+	0.841820i
$747$	8832.00	+	15297.5i	0.432592	+	0.749271i
$748$	2430.00			0.118783
$749$	2562.00	−	13312.5i	0.124985	−	0.649439i
$750$	−750.000			−0.0365148
$751$	−3319.00	−	5748.68i	−0.161268	−	0.279324i	0.774056	−	0.633117i	$-0.218225\pi$
$751$	−3319.00	−	5748.68i	−0.161268	−	0.279324i	−0.935324	+	0.353793i	$0.884892\pi$
$752$	1597.50	−	2766.95i	0.0774665	−	0.134176i
$753$	7065.00	−	12236.9i	0.341916	−	0.592216i
$754$	14337.0	+	24832.4i	0.692470	+	1.19939i
$755$	−14330.0			−0.690758
$756$	1750.00	−	606.218i	0.0841890	−	0.0291639i
$757$	14846.0			0.712797			0.356398	−	0.934334i	$-0.384005\pi$
$757$	14846.0			0.712797			0.356398	+	0.934334i	$0.384005\pi$
$758$	12457.5	+	21577.0i	0.596935	+	1.03392i
$759$	−3105.00	+	5378.02i	−0.148491	+	0.257193i
$760$	−6352.50	+	11002.9i	−0.303197	+	0.525152i
$761$	1825.50	+	3161.86i	0.0869571	+	0.150614i	0.906223	−	0.422799i	$-0.138952\pi$
$761$	1825.50	+	3161.86i	0.0869571	+	0.150614i	−0.819266	+	0.573413i	$0.805619\pi$
$762$	−4818.00			−0.229052
$763$	−28000.0	+	9699.48i	−1.32853	+	0.460216i
$764$	−2388.00			−0.113082
$765$	−3105.00	−	5378.02i	−0.146747	−	0.254173i
$766$	−1417.50	+	2455.18i	−0.0668621	+	0.115809i
$767$	10620.0	−	18394.4i	0.499956	−	0.865949i
$768$	1513.00	+	2620.59i	0.0710881	+	0.123128i
$769$	29855.0			1.40000			0.699999	−	0.714144i	$-0.253184\pi$
$769$	29855.0			1.40000			0.699999	+	0.714144i	$0.253184\pi$
$770$	2362.50	−	12275.9i	0.110570	−	0.574536i
$771$	8160.00			0.381161
$772$	−136.000	−	235.559i	−0.00634035	−	0.0109818i
$773$	3259.50	−	5645.62i	0.151664	−	0.262689i	−0.780175	−	0.625561i	$-0.784870\pi$
$773$	3259.50	−	5645.62i	0.151664	−	0.262689i	0.931839	+	0.362871i	$0.118204\pi$
$774$	−9867.00	+	17090.1i	−0.458220	+	0.793660i
$775$	1100.00	+	1905.26i	0.0509847	+	0.0883081i
$776$	−18942.0			−0.876261
$777$	−7252.00	−	6280.42i	−0.334831	−	0.289973i
$778$	36108.0			1.66393
$779$	11797.5	+	20433.9i	0.542605	+	0.939819i
$780$	295.000	−	510.955i	0.0135419	−	0.0234553i
$781$	1080.00	−	1870.61i	0.0494820	−	0.0857053i
$782$	5589.00	+	9680.43i	0.255578	+	0.442675i
$783$	−16200.0			−0.739388
$784$	−19134.5	+	15064.5i	−0.871652	+	0.686248i
$785$	−1145.00			−0.0520596
$786$	6057.00	+	10491.0i	0.274868	+	0.476085i
$787$	−17557.0	+	30409.6i	−0.795222	+	1.37736i	0.127477	+	0.991842i	$0.459312\pi$
$787$	−17557.0	+	30409.6i	−0.795222	+	1.37736i	−0.922698	+	0.385523i	$0.874021\pi$
$788$	1054.50	−	1826.45i	0.0476713	−	0.0825692i
$789$	−3288.00	−	5694.98i	−0.148360	−	0.256967i
$790$	11730.0			0.528272
$791$	19488.0	+	16877.1i	0.875997	+	0.758636i
$792$	−21735.0			−0.975151
$793$	−11564.0	−	20029.4i	−0.517843	−	0.896931i
$794$	4047.00	−	7009.61i	0.180885	−	0.313302i
$795$	2985.00	−	5170.17i	0.133166	−	0.230650i
$796$	−712.000	−	1233.22i	−0.0317037	−	0.0549125i
$797$	20910.0			0.929323			0.464661	−	0.885488i	$-0.346176\pi$
$797$	20910.0			0.929323			0.464661	+	0.885488i	$0.346176\pi$
$798$	−2541.00	+	13203.4i	−0.112720	+	0.585709i
$799$	−2430.00			−0.107594
$800$	562.500	+	974.279i	0.0248592	+	0.0430574i
$801$	−13731.0	+	23782.8i	−0.605694	+	1.04909i
$802$	−10579.5	+	18324.2i	−0.465804	+	0.806797i
$803$	15030.0	+	26032.7i	0.660520	+	1.14405i
$804$	560.000			0.0245643
$805$	6037.50	−	2091.45i	0.264340	−	0.0915702i
$806$	−15576.0			−0.680696
$807$	−3264.00	−	5653.41i	−0.142377	−	0.246604i
$808$	7182.00	−	12439.6i	0.312700	−	0.541613i
$809$	−2215.50	+	3837.36i	−0.0962829	+	0.166767i	−0.910143	−	0.414294i	$-0.864029\pi$
$809$	−2215.50	+	3837.36i	−0.0962829	+	0.166767i	0.813860	+	0.581060i	$0.197362\pi$
$810$	−3157.50	−	5468.95i	−0.136967	−	0.237234i
$811$	−9577.00			−0.414666			−0.207333	−	0.978270i	$-0.566478\pi$
$811$	−9577.00			−0.414666			−0.207333	+	0.978270i	$0.566478\pi$
$812$	−2835.00	+	982.073i	−0.122523	+	0.0424433i
$813$	5504.00			0.237434
$814$	−17482.5	−	30280.6i	−0.752778	−	1.30385i
$815$	3070.00	−	5317.40i	0.131948	−	0.228540i
$816$	3834.00	−	6640.68i	0.164481	−	0.284890i
$817$	−17303.0	−	29969.7i	−0.740949	−	1.28336i
$818$	−32610.0			−1.39387
$819$	4749.50	−	24679.1i	0.202639	−	1.05294i
$820$	975.000			0.0415225
$821$	5469.00	+	9472.59i	0.232484	+	0.402674i	0.958539	−	0.284963i	$-0.0919813\pi$
$821$	5469.00	+	9472.59i	0.232484	+	0.402674i	−0.726054	+	0.687637i	$0.758648\pi$
$822$	180.000	−	311.769i	0.00763774	−	0.0132290i
$823$	−5770.00	+	9993.93i	−0.244386	+	0.423289i	−0.961959	−	0.273195i	$-0.911920\pi$
$823$	−5770.00	+	9993.93i	−0.244386	+	0.423289i	0.717573	+	0.696483i	$0.245253\pi$
$824$	−15918.0	−	27570.8i	−0.672973	−	1.16562i
$825$	2250.00			0.0949514
$826$	15120.0	+	13094.3i	0.636915	+	0.551585i
$827$	−18762.0			−0.788898			−0.394449	−	0.918918i	$-0.629065\pi$
$827$	−18762.0			−0.788898			−0.394449	+	0.918918i	$0.629065\pi$
$828$	793.500	+	1374.38i	0.0333044	+	0.0576849i
$829$	19805.0	−	34303.3i	0.829742	−	1.43716i	−0.0684987	−	0.997651i	$-0.521821\pi$
$829$	19805.0	−	34303.3i	0.829742	−	1.43716i	0.898241	−	0.439504i	$-0.144846\pi$
$830$	−5760.00	+	9976.61i	−0.240883	+	0.417221i
$831$	−4690.00	−	8123.32i	−0.195781	−	0.339103i
$832$	25547.0			1.06452
$833$	17199.0	+	6874.51i	0.715378	+	0.285940i
$834$	10248.0			0.425491
$835$	4822.50	+	8352.82i	0.199868	+	0.346181i
$836$	−2722.50	+	4715.51i	−0.112631	+	0.195083i
$837$	4400.00	−	7621.02i	0.181704	−	0.314721i
$838$	14593.5	+	25276.7i	0.601580	+	1.04197i
$839$	39162.0			1.61147			0.805734	−	0.592277i	$-0.201771\pi$
$839$	39162.0			1.61147			0.805734	+	0.592277i	$0.201771\pi$
$840$	−2940.00	−	2546.11i	−0.120761	−	0.104583i
$841$	1855.00			0.0760589
$842$	18825.0	+	32605.9i	0.770490	+	1.33453i
$843$	7821.00	−	13546.4i	0.319537	−	0.553454i
$844$	1812.50	−	3139.34i	0.0739204	−	0.128034i
$845$	−3210.00	−	5559.88i	−0.130683	−	0.226350i
$846$	−3105.00			−0.126185
$847$	−2429.00	+	12621.5i	−0.0985377	+	0.512017i
$848$	−42387.0			−1.71648
$849$	−658.000	−	1139.69i	−0.0265989	−	0.0460707i
$850$	2025.00	−	3507.40i	0.0817140	−	0.141533i
$851$	8935.50	−	15476.7i	0.359935	−	0.623426i
$852$	48.0000	+	83.1384i	0.00193011	+	0.00334305i
$853$	−11527.0			−0.462693			−0.231346	−	0.972871i	$-0.574313\pi$
$853$	−11527.0			−0.462693			−0.231346	+	0.972871i	$0.574313\pi$
$854$	20580.0	−	7129.12i	0.824629	−	0.285660i
$855$	13915.0			0.556588
$856$	−7686.00	−	13312.5i	−0.306895	−	0.531558i
$857$	20913.0	−	36222.4i	0.833576	−	1.44380i	−0.0616089	−	0.998100i	$-0.519623\pi$
$857$	20913.0	−	36222.4i	0.833576	−	1.44380i	0.895185	−	0.445695i	$-0.147044\pi$
$858$	−7965.00	+	13795.8i	−0.316924	+	0.548928i
$859$	−17596.0	−	30477.2i	−0.698915	−	1.21056i	−0.968843	−	0.247675i	$-0.920333\pi$
$859$	−17596.0	−	30477.2i	−0.698915	−	1.21056i	0.269928	−	0.962880i	$-0.413000\pi$
$860$	−1430.00			−0.0567007
$861$	−6825.00	+	2364.25i	−0.270146	+	0.0935812i
$862$	8964.00			0.354194
$863$	4531.50	+	7848.79i	0.178742	+	0.309590i	0.941450	−	0.337153i	$-0.109464\pi$
$863$	4531.50	+	7848.79i	0.178742	+	0.309590i	−0.762708	+	0.646743i	$0.776131\pi$
$864$	2250.00	−	3897.11i	0.0885955	−	0.153452i
$865$	1747.50	−	3026.76i	0.0686899	−	0.118974i
$866$	−24924.0	−	43169.6i	−0.978005	−	1.69395i
$867$	3994.00			0.156451
$868$	308.000	−	1600.41i	0.0120440	−	0.0625825i
$869$	−35190.0			−1.37369
$870$	−2430.00	−	4208.88i	−0.0946951	−	0.164017i
$871$	8260.00	−	14306.7i	0.321331	−	0.556562i
$872$	−16800.0	+	29098.5i	−0.652431	+	1.13004i
$873$	10373.0	+	17966.6i	0.402145	+	0.696536i
$874$	−25047.0			−0.969368
$875$	−1750.00	−	1515.54i	−0.0676123	−	0.0585540i
$876$	−1336.00			−0.0515288
$877$	−14219.5	−	24628.9i	−0.547501	−	0.948300i	−0.998445	−	0.0557473i	$-0.982246\pi$
$877$	−14219.5	−	24628.9i	−0.547501	−	0.948300i	0.450944	−	0.892552i	$-0.351087\pi$
$878$	−11019.0	+	19085.5i	−0.423546	+	0.733603i
$879$	−5997.00	+	10387.1i	−0.230118	+	0.398576i
$880$	−7987.50	−	13834.8i	−0.305976	−	0.529965i
$881$	−9303.00			−0.355762			−0.177881	−	0.984052i	$-0.556924\pi$
$881$	−9303.00			−0.355762			−0.177881	+	0.984052i	$0.556924\pi$
$882$	21976.5	+	8784.10i	0.838988	+	0.335347i
$883$	−14728.0			−0.561310			−0.280655	−	0.959809i	$-0.590552\pi$
$883$	−14728.0			−0.561310			−0.280655	+	0.959809i	$0.590552\pi$
$884$	1593.00	+	2759.16i	0.0606090	+	0.104978i
$885$	−1800.00	+	3117.69i	−0.0683687	+	0.118418i
$886$	−18.0000	+	31.1769i	−0.000682530	+	0.00118218i
$887$	8508.00	+	14736.3i	0.322064	+	0.557831i	0.980914	−	0.194443i	$-0.0622901\pi$
$887$	8508.00	+	14736.3i	0.322064	+	0.557831i	−0.658850	+	0.752274i	$0.728957\pi$
$888$	−10878.0			−0.411083
$889$	−11242.0	−	9735.86i	−0.424122	−	0.367301i
$890$	−17910.0			−0.674544
$891$	9472.50	+	16406.9i	0.356162	+	0.616891i
$892$	2480.00	−	4295.49i	0.0930903	−	0.161237i
$893$	2722.50	−	4715.51i	0.102021	−	0.176706i
$894$	−3258.00	−	5643.02i	−0.121883	−	0.211108i
$895$	15585.0			0.582066
$896$	−5806.50	+	30171.5i	−0.216497	+	1.12495i
$897$	−8142.00			−0.303070
$898$	−14503.5	−	25120.8i	−0.538962	−	0.933510i
$899$	−7128.00	+	12346.1i	−0.264441	+	0.458025i
$900$	287.500	−	497.965i	0.0106481	−	0.0184431i
$901$	16119.0	+	27918.9i	0.596006	+	1.03231i
$902$	−26325.0			−0.971759
$903$	10010.0	−	3467.57i	0.368895	−	0.127789i
$904$	29232.0			1.07549
$905$	4495.00	+	7785.57i	0.165104	+	0.285968i
$906$	−8598.00	+	14892.2i	−0.315286	+	0.546092i
$907$	12461.0	−	21583.1i	0.456186	−	0.790137i	−0.542570	−	0.840011i	$-0.682548\pi$
$907$	12461.0	−	21583.1i	0.456186	−	0.790137i	0.998756	+	0.0498735i	$0.0158818\pi$
$908$	750.000	+	1299.04i	0.0274115	+	0.0474781i
$909$	−15732.0			−0.574035
$910$	15487.5	−	5365.03i	0.564182	−	0.195438i
$911$	30714.0			1.11701			0.558507	−	0.829500i	$-0.311374\pi$
$911$	30714.0			1.11701			0.558507	+	0.829500i	$0.311374\pi$
$912$	8591.00	+	14880.0i	0.311926	+	0.540272i
$913$	17280.0	−	29929.8i	0.626380	−	1.08492i
$914$	14451.0	−	25029.9i	0.522972	−	0.905814i
$915$	1960.00	+	3394.82i	0.0708149	+	0.122655i
$916$	6092.00			0.219744
$917$	−7066.50	+	36718.6i	−0.254478	+	1.32231i
$918$	−16200.0			−0.582440
$919$	−8713.00	−	15091.4i	−0.312748	−	0.541695i	0.666208	−	0.745766i	$-0.267916\pi$
$919$	−8713.00	−	15091.4i	−0.312748	−	0.541695i	−0.978956	+	0.204070i	$0.934583\pi$
$920$	3622.50	−	6274.35i	0.129816	−	0.224847i
$921$	−6226.00	+	10783.7i	−0.222751	+	0.385816i
$922$	513.000	+	888.542i	0.0183240	+	0.0317382i
$923$	2832.00			0.100993
$924$	−1260.00	−	1091.19i	−0.0448603	−	0.0388502i
$925$	−6475.00			−0.230159
$926$	−3616.50	−	6263.96i	−0.128343	−	0.222296i
$927$	−17434.0	+	30196.6i	−0.617700	+	1.06989i
$928$	−3645.00	+	6313.33i	−0.128936	+	0.223324i
$929$	−13324.5	−	23078.7i	−0.470573	−	0.815057i	0.528860	−	0.848709i	$-0.322620\pi$
$929$	−13324.5	−	23078.7i	−0.470573	−	0.815057i	−0.999434	+	0.0336519i	$0.989286\pi$
$930$	2640.00			0.0930850
$931$	−32609.5	+	25673.3i	−1.14794	+	0.903769i
$932$	138.000			0.00485015
$933$	4680.00	+	8106.00i	0.164219	+	0.284436i
$934$	1809.00	−	3133.28i	0.0633750	−	0.109769i
$935$	−6075.00	+	10522.2i	−0.212485	+	0.368035i
$936$	−14248.5	−	24679.1i	−0.497571	−	0.861819i
$937$	27686.0			0.965274			0.482637	−	0.875820i	$-0.339679\pi$
$937$	27686.0			0.965274			0.482637	+	0.875820i	$0.339679\pi$
$938$	11760.0	+	10184.5i	0.409358	+	0.354514i
$939$	−2056.00			−0.0714537
$940$	−112.500	−	194.856i	−0.00390356	−	0.00676116i
$941$	8904.00	−	15422.2i	0.308461	−	0.534271i	−0.669565	−	0.742754i	$-0.733519\pi$
$941$	8904.00	−	15422.2i	0.308461	−	0.534271i	0.978026	+	0.208483i	$0.0668526\pi$
$942$	−687.000	+	1189.92i	−0.0237619	+	0.0411567i
$943$	−6727.50	−	11652.4i	−0.232320	−	0.402390i
$944$	25560.0			0.881258
$945$	−1750.00	+	9093.27i	−0.0602407	+	0.313020i
$946$	38610.0			1.32698
$947$	3453.00	+	5980.77i	0.118487	+	0.205226i	0.919168	−	0.393865i	$-0.128862\pi$
$947$	3453.00	+	5980.77i	0.118487	+	0.205226i	−0.800681	+	0.599091i	$0.795529\pi$
$948$	782.000	−	1354.46i	0.0267913	−	0.0464039i
$949$	−19706.0	+	34131.8i	−0.674061	+	1.16751i
$950$	4537.50	+	7859.18i	0.154964	+	0.268406i
$951$	−17244.0			−0.587986
$952$	19845.0	−	6874.51i	0.675609	−	0.234038i
$953$	−20940.0			−0.711766			−0.355883	−	0.934530i	$-0.615820\pi$
$953$	−20940.0			−0.711766			−0.355883	+	0.934530i	$0.615820\pi$
$954$	20596.5	+	35674.2i	0.698990	+	1.21069i
$955$	5970.00	−	10340.3i	0.202288	−	0.350372i
$956$	2751.00	−	4764.87i	0.0930687	−	0.161200i
$957$	7290.00	+	12626.7i	0.246241	+	0.426501i
$958$	−1296.00			−0.0437076
$959$	1050.00	−	363.731i	0.0353559	−	0.0122476i
$960$	−4330.00			−0.145573
$961$	11023.5	+	19093.3i	0.370028	+	0.640907i
$962$	22921.5	−	39701.2i	0.768211	−	1.33058i
$963$	−8418.00	+	14580.4i	−0.281689	+	0.487899i
$964$	−1775.50	−	3075.26i	−0.0593205	−	0.102746i
$965$	1360.00			0.0453678
$966$	1449.00	−	7529.22i	0.0482617	−	0.250775i
$967$	9176.00			0.305150			0.152575	−	0.988292i	$-0.451243\pi$
$967$	9176.00			0.305150			0.152575	+	0.988292i	$0.451243\pi$
$968$	7287.00	+	12621.5i	0.241956	+	0.419079i
$969$	6534.00	−	11317.2i	0.216617	−	0.375192i
$970$	−6765.00	+	11717.3i	−0.223929	+	0.387856i
$971$	−14881.5	−	25775.5i	−0.491833	−	0.851880i	0.508123	−	0.861285i	$-0.330340\pi$
$971$	−14881.5	−	25775.5i	−0.491833	−	0.851880i	−0.999956	+	0.00940465i	$0.997006\pi$
$972$	−3542.00			−0.116882
$973$	23912.0	+	20708.4i	0.787856	+	0.682303i
$974$	−35688.0			−1.17404
$975$	1475.00	+	2554.77i	0.0484490	+	0.0839162i
$976$	13916.0	−	24103.2i	0.456394	−	0.790497i
$977$	19245.0	−	33333.3i	0.630197	−	1.09153i	−0.357315	−	0.933984i	$-0.616308\pi$
$977$	19245.0	−	33333.3i	0.630197	−	1.09153i	0.987511	−	0.157548i	$-0.0503591\pi$
$978$	−3684.00	−	6380.88i	−0.120451	−	0.208628i
$979$	53730.0			1.75405
$980$	245.000	+	1697.41i	0.00798596	+	0.0553283i
$981$	36800.0			1.19769
$982$	18414.0	+	31894.0i	0.598385	+	1.03643i
$983$	6304.50	−	10919.7i	0.204560	−	0.354308i	−0.745433	−	0.666581i	$-0.767757\pi$
$983$	6304.50	−	10919.7i	0.204560	−	0.354308i	0.949992	+	0.312273i	$0.101090\pi$
$984$	−4095.00	+	7092.75i	−0.132666	+	0.229785i
$985$	5272.50	+	9132.24i	0.170554	+	0.295408i
$986$	26244.0			0.847646
$987$	1260.00	+	1091.19i	0.0406345	+	0.0351905i
$988$	−7139.00			−0.229880
$989$	9867.00	+	17090.1i	0.317242	+	0.549479i
$990$	−7762.50	+	13445.0i	−0.249200	+	0.431628i
$991$	−9910.00	+	17164.6i	−0.317660	+	0.550204i	−0.979999	−	0.199000i	$-0.936231\pi$
$991$	−9910.00	+	17164.6i	−0.317660	+	0.550204i	0.662339	+	0.749204i	$0.269564\pi$
$992$	−1980.00	−	3429.46i	−0.0633720	−	0.109764i
$993$	3998.00			0.127767
$994$	−504.000	+	2618.86i	−0.0160824	+	0.0835666i
$995$	7120.00			0.226853
$996$	768.000	+	1330.22i	0.0244327	+	0.0423188i
$997$	−23017.0	+	39866.6i	−0.731149	+	1.26639i	0.225243	+	0.974303i	$0.427682\pi$
$997$	−23017.0	+	39866.6i	−0.731149	+	1.26639i	−0.956392	+	0.292085i	$0.905651\pi$
$998$	16314.0	−	28256.7i	0.517446	−	0.896242i
$999$	12950.0	+	22430.1i	0.410130	+	0.710366i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.4.e.a.11.1	✓	2
3.2	odd	2		315.4.j.b.46.1		2
4.3	odd	2		560.4.q.b.81.1		2
5.2	odd	4		175.4.k.b.74.2		4
5.3	odd	4		175.4.k.b.74.1		4
5.4	even	2		175.4.e.b.151.1		2
7.2	even	3	inner	35.4.e.a.16.1	yes	2
7.3	odd	6		245.4.a.f.1.1		1
7.4	even	3		245.4.a.e.1.1		1
7.5	odd	6		245.4.e.a.226.1		2
7.6	odd	2		245.4.e.a.116.1		2
21.2	odd	6		315.4.j.b.226.1		2
21.11	odd	6		2205.4.a.e.1.1		1
21.17	even	6		2205.4.a.g.1.1		1
28.23	odd	6		560.4.q.b.401.1		2
35.2	odd	12		175.4.k.b.149.1		4
35.4	even	6		1225.4.a.b.1.1		1
35.9	even	6		175.4.e.b.51.1		2
35.23	odd	12		175.4.k.b.149.2		4
35.24	odd	6		1225.4.a.a.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.4.e.a.11.1	✓	2	1.1	even	1	trivial
35.4.e.a.16.1	yes	2	7.2	even	3	inner
175.4.e.b.51.1		2	35.9	even	6
175.4.e.b.151.1		2	5.4	even	2
175.4.k.b.74.1		4	5.3	odd	4
175.4.k.b.74.2		4	5.2	odd	4
175.4.k.b.149.1		4	35.2	odd	12
175.4.k.b.149.2		4	35.23	odd	12
245.4.a.e.1.1		1	7.4	even	3
245.4.a.f.1.1		1	7.3	odd	6
245.4.e.a.116.1		2	7.6	odd	2
245.4.e.a.226.1		2	7.5	odd	6
315.4.j.b.46.1		2	3.2	odd	2
315.4.j.b.226.1		2	21.2	odd	6
560.4.q.b.81.1		2	4.3	odd	2
560.4.q.b.401.1		2	28.23	odd	6
1225.4.a.a.1.1		1	35.24	odd	6
1225.4.a.b.1.1		1	35.4	even	6
2205.4.a.e.1.1		1	21.11	odd	6
2205.4.a.g.1.1		1	21.17	even	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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	35.e (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{2} +(1.00000 - 1.73205i) q^{3} +(-0.500000 + 0.866025i) q^{4} +(-2.50000 - 4.33013i) q^{5} -6.00000 q^{6} +(-14.0000 - 12.1244i) q^{7} -21.0000 q^{8} +(11.5000 + 19.9186i) q^{9} +(-7.50000 + 12.9904i) q^{10} +(22.5000 - 38.9711i) q^{11} +(1.00000 + 1.73205i) q^{12} +59.0000 q^{13} +(-10.5000 + 54.5596i) q^{14} -10.0000 q^{15} +(35.5000 + 61.4878i) q^{16} +(27.0000 - 46.7654i) q^{17} +(34.5000 - 59.7558i) q^{18} +(60.5000 + 104.789i) q^{19} +5.00000 q^{20} +(-35.0000 + 12.1244i) q^{21} -135.000 q^{22} +(-34.5000 - 59.7558i) q^{23} +(-21.0000 + 36.3731i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(-88.5000 - 153.286i) q^{26} +100.000 q^{27} +(17.5000 - 6.06218i) q^{28} -162.000 q^{29} +(15.0000 + 25.9808i) q^{30} +(44.0000 - 76.2102i) q^{31} +(22.5000 - 38.9711i) q^{32} +(-45.0000 - 77.9423i) q^{33} -162.000 q^{34} +(-17.5000 + 90.9327i) q^{35} -23.0000 q^{36} +(129.500 + 224.301i) q^{37} +(181.500 - 314.367i) q^{38} +(59.0000 - 102.191i) q^{39} +(52.5000 + 90.9327i) q^{40} +195.000 q^{41} +(84.0000 + 72.7461i) q^{42} -286.000 q^{43} +(22.5000 + 38.9711i) q^{44} +(57.5000 - 99.5929i) q^{45} +(-103.500 + 179.267i) q^{46} +(-22.5000 - 38.9711i) q^{47} +142.000 q^{48} +(49.0000 + 339.482i) q^{49} +75.0000 q^{50} +(-54.0000 - 93.5307i) q^{51} +(-29.5000 + 51.0955i) q^{52} +(-298.500 + 517.017i) q^{53} +(-150.000 - 259.808i) q^{54} -225.000 q^{55} +(294.000 + 254.611i) q^{56} +242.000 q^{57} +(243.000 + 420.888i) q^{58} +(180.000 - 311.769i) q^{59} +(5.00000 - 8.66025i) q^{60} +(-196.000 - 339.482i) q^{61} -264.000 q^{62} +(80.5000 - 418.290i) q^{63} +433.000 q^{64} +(-147.500 - 255.477i) q^{65} +(-135.000 + 233.827i) q^{66} +(140.000 - 242.487i) q^{67} +(27.0000 + 46.7654i) q^{68} -138.000 q^{69} +(262.500 - 90.9327i) q^{70} +48.0000 q^{71} +(-241.500 - 418.290i) q^{72} +(-334.000 + 578.505i) q^{73} +(388.500 - 672.902i) q^{74} +(25.0000 + 43.3013i) q^{75} -121.000 q^{76} +(-787.500 + 272.798i) q^{77} -354.000 q^{78} +(-391.000 - 677.232i) q^{79} +(177.500 - 307.439i) q^{80} +(-210.500 + 364.597i) q^{81} +(-292.500 - 506.625i) q^{82} +768.000 q^{83} +(7.00000 - 36.3731i) q^{84} -270.000 q^{85} +(429.000 + 743.050i) q^{86} +(-162.000 + 280.592i) q^{87} +(-472.500 + 818.394i) q^{88} +(597.000 + 1034.03i) q^{89} -345.000 q^{90} +(-826.000 - 715.337i) q^{91} +69.0000 q^{92} +(-88.0000 - 152.420i) q^{93} +(-67.5000 + 116.913i) q^{94} +(302.500 - 523.945i) q^{95} +(-45.0000 - 77.9423i) q^{96} +902.000 q^{97} +(808.500 - 636.529i) q^{98} +1035.00 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 3 q^{2} + 2 q^{3} - q^{4} - 5 q^{5} - 12 q^{6} - 28 q^{7} - 42 q^{8} + 23 q^{9} - 15 q^{10} + 45 q^{11} + 2 q^{12} + 118 q^{13} - 21 q^{14} - 20 q^{15} + 71 q^{16} + 54 q^{17} + 69 q^{18} + 121 q^{19}+ \cdots + 2070 q^{99}+O(q^{100}) \) 2 * q - 3 * q^2 + 2 * q^3 - q^4 - 5 * q^5 - 12 * q^6 - 28 * q^7 - 42 * q^8 + 23 * q^9 - 15 * q^10 + 45 * q^11 + 2 * q^12 + 118 * q^13 - 21 * q^14 - 20 * q^15 + 71 * q^16 + 54 * q^17 + 69 * q^18 + 121 * q^19 + 10 * q^20 - 70 * q^21 - 270 * q^22 - 69 * q^23 - 42 * q^24 - 25 * q^25 - 177 * q^26 + 200 * q^27 + 35 * q^28 - 324 * q^29 + 30 * q^30 + 88 * q^31 + 45 * q^32 - 90 * q^33 - 324 * q^34 - 35 * q^35 - 46 * q^36 + 259 * q^37 + 363 * q^38 + 118 * q^39 + 105 * q^40 + 390 * q^41 + 168 * q^42 - 572 * q^43 + 45 * q^44 + 115 * q^45 - 207 * q^46 - 45 * q^47 + 284 * q^48 + 98 * q^49 + 150 * q^50 - 108 * q^51 - 59 * q^52 - 597 * q^53 - 300 * q^54 - 450 * q^55 + 588 * q^56 + 484 * q^57 + 486 * q^58 + 360 * q^59 + 10 * q^60 - 392 * q^61 - 528 * q^62 + 161 * q^63 + 866 * q^64 - 295 * q^65 - 270 * q^66 + 280 * q^67 + 54 * q^68 - 276 * q^69 + 525 * q^70 + 96 * q^71 - 483 * q^72 - 668 * q^73 + 777 * q^74 + 50 * q^75 - 242 * q^76 - 1575 * q^77 - 708 * q^78 - 782 * q^79 + 355 * q^80 - 421 * q^81 - 585 * q^82 + 1536 * q^83 + 14 * q^84 - 540 * q^85 + 858 * q^86 - 324 * q^87 - 945 * q^88 + 1194 * q^89 - 690 * q^90 - 1652 * q^91 + 138 * q^92 - 176 * q^93 - 135 * q^94 + 605 * q^95 - 90 * q^96 + 1804 * q^97 + 1617 * q^98 + 2070 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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