LMFDB - Embedded newform 546.4.i.a.235.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,4,Mod(79,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("546.79");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	546.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:	$32.2150428631$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{-5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - 5x^{2} + 25 $ x^4 - 5*x^2 + 25
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.1
Root			$1.93649 + 1.11803i$ of defining polynomial
Character	$\chi$	$=$	546.235
Dual form			546.4.i.a.79.1

$q$-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} +(-0.436492 - 0.756026i) q^{5} -6.00000 q^{6} +(-10.8095 + 15.0385i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-0.872983 + 1.51205i) q^{10} +(0.682458 - 1.18205i) q^{11} +(6.00000 + 10.3923i) q^{12} +13.0000 q^{13} +(36.8569 + 3.68410i) q^{14} -2.61895 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-12.5716 + 21.7746i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(-6.26210 - 10.8463i) q^{19} +3.49193 q^{20} +(22.8569 + 50.6415i) q^{21} -2.72983 q^{22} +(39.5474 + 68.4981i) q^{23} +(12.0000 - 20.7846i) q^{24} +(62.1190 - 107.593i) q^{25} +(-13.0000 - 22.5167i) q^{26} -27.0000 q^{27} +(-30.4758 - 67.5220i) q^{28} +3.98387 q^{29} +(2.61895 + 4.53615i) q^{30} +(97.5706 - 168.997i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-2.04738 - 3.54616i) q^{33} +50.2863 q^{34} +(16.0877 + 1.60808i) q^{35} +36.0000 q^{36} +(-90.7853 - 157.245i) q^{37} +(-12.5242 + 21.6926i) q^{38} +(19.5000 - 33.7750i) q^{39} +(-3.49193 - 6.04821i) q^{40} +408.554 q^{41} +(64.8569 - 90.2308i) q^{42} +295.044 q^{43} +(2.72983 + 4.72821i) q^{44} +(-3.92843 + 6.80423i) q^{45} +(79.0948 - 136.996i) q^{46} +(-178.389 - 308.979i) q^{47} -48.0000 q^{48} +(-109.310 - 325.116i) q^{49} -248.476 q^{50} +(37.7147 + 65.3238i) q^{51} +(-26.0000 + 45.0333i) q^{52} +(181.292 - 314.008i) q^{53} +(27.0000 + 46.7654i) q^{54} -1.19155 q^{55} +(-86.4758 + 120.308i) q^{56} -37.5726 q^{57} +(-3.98387 - 6.90026i) q^{58} +(-155.809 + 269.870i) q^{59} +(5.23790 - 9.07231i) q^{60} +(121.380 + 210.236i) q^{61} -390.282 q^{62} +(165.856 + 16.5785i) q^{63} +64.0000 q^{64} +(-5.67439 - 9.82833i) q^{65} +(-4.09475 + 7.09232i) q^{66} +(128.690 - 222.897i) q^{67} +(-50.2863 - 87.0984i) q^{68} +237.284 q^{69} +(-13.3024 - 29.4728i) q^{70} +75.4435 q^{71} +(-36.0000 - 62.3538i) q^{72} +(127.737 - 221.247i) q^{73} +(-181.571 + 314.489i) q^{74} +(-186.357 - 322.780i) q^{75} +50.0968 q^{76} +(10.3992 + 23.0405i) q^{77} -78.0000 q^{78} +(-27.8548 - 48.2459i) q^{79} +(-6.98387 + 12.0964i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-408.554 - 707.637i) q^{82} +33.5201 q^{83} +(-221.141 - 22.1046i) q^{84} +21.9496 q^{85} +(-295.044 - 511.032i) q^{86} +(5.97580 - 10.3504i) q^{87} +(5.45967 - 9.45642i) q^{88} +(-551.114 - 954.557i) q^{89} +15.7137 q^{90} +(-140.523 + 195.500i) q^{91} -316.379 q^{92} +(-292.712 - 506.991i) q^{93} +(-356.778 + 617.958i) q^{94} +(-5.46671 + 9.46862i) q^{95} +(48.0000 + 83.1384i) q^{96} +1335.57 q^{97} +(-453.806 + 514.447i) q^{98} -12.2843 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 6 q^{5} - 24 q^{6} - 20 q^{7} + 32 q^{8} - 18 q^{9} + 12 q^{10} - 36 q^{11} + 24 q^{12} + 52 q^{13} + 8 q^{14} + 36 q^{15} - 32 q^{16} - 120 q^{17} - 36 q^{18} - 118 q^{19}+ \cdots + 648 q^{99}+O(q^{100}) $ 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 6 * q^5 - 24 * q^6 - 20 * q^7 + 32 * q^8 - 18 * q^9 + 12 * q^10 - 36 * q^11 + 24 * q^12 + 52 * q^13 + 8 * q^14 + 36 * q^15 - 32 * q^16 - 120 * q^17 - 36 * q^18 - 118 * q^19 - 48 * q^20 - 48 * q^21 + 144 * q^22 + 42 * q^23 + 48 * q^24 + 202 * q^25 - 52 * q^26 - 108 * q^27 + 64 * q^28 - 108 * q^29 - 36 * q^30 - 28 * q^31 - 64 * q^32 + 108 * q^33 + 480 * q^34 + 258 * q^35 + 144 * q^36 - 154 * q^37 - 236 * q^38 + 78 * q^39 + 48 * q^40 + 1092 * q^41 + 120 * q^42 - 400 * q^43 - 144 * q^44 + 54 * q^45 + 84 * q^46 - 822 * q^47 - 192 * q^48 - 902 * q^49 - 808 * q^50 + 360 * q^51 - 104 * q^52 + 90 * q^53 + 108 * q^54 - 516 * q^55 - 160 * q^56 - 708 * q^57 + 108 * q^58 - 600 * q^59 - 72 * q^60 + 44 * q^61 + 112 * q^62 + 36 * q^63 + 256 * q^64 + 78 * q^65 + 216 * q^66 + 50 * q^67 - 480 * q^68 + 252 * q^69 - 456 * q^70 - 132 * q^71 - 144 * q^72 - 70 * q^73 - 308 * q^74 - 606 * q^75 + 944 * q^76 + 1188 * q^77 - 312 * q^78 + 1004 * q^79 + 96 * q^80 - 162 * q^81 - 1092 * q^82 - 1632 * q^83 - 48 * q^84 - 1260 * q^85 + 400 * q^86 - 162 * q^87 - 288 * q^88 + 282 * q^89 - 216 * q^90 - 260 * q^91 - 336 * q^92 + 84 * q^93 - 1644 * q^94 + 714 * q^95 + 192 * q^96 + 2972 * q^97 - 328 * q^98 + 648 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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
$5$	−0.436492	−	0.756026i	−0.0390410	−	0.0676210i	0.845845	−	0.533429i	$-0.179097\pi$
$5$	−0.436492	−	0.756026i	−0.0390410	−	0.0676210i	−0.884886	+	0.465808i	$0.845764\pi$
$6$	−6.00000			−0.408248
$7$	−10.8095	+	15.0385i	−0.583657	+	0.812000i
$7$	−10.8095	+	15.0385i	−0.583657	+	0.812000i
$8$	8.00000			0.353553
$9$	−4.50000	−	7.79423i	−0.166667	−	0.288675i
$10$	−0.872983	+	1.51205i	−0.0276062	+	0.0478153i
$11$	0.682458	−	1.18205i	0.0187063	−	0.0324002i	−0.856521	−	0.516113i	$-0.827379\pi$
$11$	0.682458	−	1.18205i	0.0187063	−	0.0324002i	0.875227	+	0.483712i	$0.160712\pi$
$12$	6.00000	+	10.3923i	0.144338	+	0.250000i
$13$	13.0000			0.277350
$13$	13.0000			0.277350
$14$	36.8569	+	3.68410i	0.703601	+	0.0703298i
$15$	−2.61895			−0.0450807
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−12.5716	+	21.7746i	−0.179356	+	0.310654i	−0.941660	−	0.336565i	$-0.890735\pi$
$17$	−12.5716	+	21.7746i	−0.179356	+	0.310654i	0.762304	+	0.647219i	$0.224068\pi$
$18$	−9.00000	+	15.5885i	−0.117851	+	0.204124i
$19$	−6.26210	−	10.8463i	−0.0756118	−	0.130963i	0.825740	−	0.564050i	$-0.190758\pi$
$19$	−6.26210	−	10.8463i	−0.0756118	−	0.130963i	−0.901352	+	0.433087i	$0.857424\pi$
$20$	3.49193			0.0390410
$21$	22.8569	+	50.6415i	0.237513	+	0.526233i
$22$	−2.72983			−0.0264547
$23$	39.5474	+	68.4981i	0.358530	+	0.620993i	0.987716	−	0.156263i	$-0.0499446\pi$
$23$	39.5474	+	68.4981i	0.358530	+	0.620993i	−0.629185	+	0.777255i	$0.716611\pi$
$24$	12.0000	−	20.7846i	0.102062	−	0.176777i
$25$	62.1190	−	107.593i	0.496952	−	0.860745i
$26$	−13.0000	−	22.5167i	−0.0980581	−	0.169842i
$27$	−27.0000			−0.192450
$28$	−30.4758	−	67.5220i	−0.205692	−	0.455731i
$29$	3.98387			0.0255098			0.0127549	−	0.999919i	$-0.495940\pi$
$29$	3.98387			0.0255098			0.0127549	+	0.999919i	$0.495940\pi$
$30$	2.61895	+	4.53615i	0.0159384	+	0.0276062i
$31$	97.5706	−	168.997i	0.565296	−	0.979122i	−0.431726	−	0.902005i	$-0.642095\pi$
$31$	97.5706	−	168.997i	0.565296	−	0.979122i	0.997022	−	0.0771171i	$-0.0245715\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$	−2.04738	−	3.54616i	−0.0108001	−	0.0187063i
$34$	50.2863			0.253648
$35$	16.0877	+	1.60808i	0.0776948	+	0.00776614i
$36$	36.0000			0.166667
$37$	−90.7853	−	157.245i	−0.403379	−	0.698672i	0.590753	−	0.806853i	$-0.298831\pi$
$37$	−90.7853	−	157.245i	−0.403379	−	0.698672i	−0.994131	+	0.108180i	$0.965498\pi$
$38$	−12.5242	+	21.6926i	−0.0534656	+	0.0926052i
$39$	19.5000	−	33.7750i	0.0800641	−	0.138675i
$40$	−3.49193	−	6.04821i	−0.0138031	−	0.0239076i
$41$	408.554			1.55623			0.778116	−	0.628121i	$-0.216176\pi$
$41$	408.554			1.55623			0.778116	+	0.628121i	$0.216176\pi$
$42$	64.8569	−	90.2308i	0.238277	−	0.331498i
$43$	295.044			1.04637			0.523184	−	0.852220i	$-0.324744\pi$
$43$	295.044			1.04637			0.523184	+	0.852220i	$0.324744\pi$
$44$	2.72983	+	4.72821i	0.00935313	+	0.0162001i
$45$	−3.92843	+	6.80423i	−0.0130137	+	0.0225403i
$46$	79.0948	−	136.996i	0.253519	−	0.439108i
$47$	−178.389	−	308.979i	−0.553632	−	0.958920i	−0.998009	−	0.0630792i	$-0.979908\pi$
$47$	−178.389	−	308.979i	−0.553632	−	0.958920i	0.444376	−	0.895840i	$-0.353425\pi$
$48$	−48.0000			−0.144338
$49$	−109.310	−	325.116i	−0.318690	−	0.947859i
$50$	−248.476			−0.702796
$51$	37.7147	+	65.3238i	0.103551	+	0.179356i
$52$	−26.0000	+	45.0333i	−0.0693375	+	0.120096i
$53$	181.292	−	314.008i	0.469857	−	0.813816i	−0.529549	−	0.848279i	$-0.677639\pi$
$53$	181.292	−	314.008i	0.469857	−	0.813816i	0.999406	+	0.0344633i	$0.0109722\pi$
$54$	27.0000	+	46.7654i	0.0680414	+	0.117851i
$55$	−1.19155			−0.00292125
$56$	−86.4758	+	120.308i	−0.206354	+	0.287086i
$57$	−37.5726			−0.0873090
$58$	−3.98387	−	6.90026i	−0.00901909	−	0.0156215i
$59$	−155.809	+	269.870i	−0.343808	+	0.595493i	−0.985136	−	0.171774i	$-0.945050\pi$
$59$	−155.809	+	269.870i	−0.343808	+	0.595493i	0.641329	+	0.767266i	$0.278384\pi$
$60$	5.23790	−	9.07231i	0.0112702	−	0.0195205i
$61$	121.380	+	210.236i	0.254772	+	0.441279i	0.964834	−	0.262861i	$-0.0846661\pi$
$61$	121.380	+	210.236i	0.254772	+	0.441279i	−0.710061	+	0.704140i	$0.751333\pi$
$62$	−390.282			−0.799450
$63$	165.856	+	16.5785i	0.331680	+	0.0331538i
$64$	64.0000			0.125000
$65$	−5.67439	−	9.82833i	−0.0108280	−	0.0187547i
$66$	−4.09475	+	7.09232i	−0.00763680	+	0.0132273i
$67$	128.690	−	222.897i	0.234656	−	0.406435i	−0.724517	−	0.689257i	$-0.757937\pi$
$67$	128.690	−	222.897i	0.234656	−	0.406435i	0.959173	+	0.282822i	$0.0912704\pi$
$68$	−50.2863	−	87.0984i	−0.0896781	−	0.155327i
$69$	237.284			0.413995
$70$	−13.3024	−	29.4728i	−0.0227135	−	0.0503239i
$71$	75.4435			0.126106			0.0630528	−	0.998010i	$-0.479916\pi$
$71$	75.4435			0.126106			0.0630528	+	0.998010i	$0.479916\pi$
$72$	−36.0000	−	62.3538i	−0.0589256	−	0.102062i
$73$	127.737	−	221.247i	0.204801	−	0.354726i	−0.745268	−	0.666765i	$-0.767679\pi$
$73$	127.737	−	221.247i	0.204801	−	0.354726i	0.950069	+	0.312039i	$0.101012\pi$
$74$	−181.571	+	314.489i	−0.285232	+	0.494036i
$75$	−186.357	−	322.780i	−0.286915	−	0.496952i
$76$	50.0968			0.0756118
$77$	10.3992	+	23.0405i	0.0153909	+	0.0341001i
$78$	−78.0000			−0.113228
$79$	−27.8548	−	48.2459i	−0.0396697	−	0.0687100i	0.845509	−	0.533961i	$-0.179297\pi$
$79$	−27.8548	−	48.2459i	−0.0396697	−	0.0687100i	−0.885179	+	0.465251i	$0.845964\pi$
$80$	−6.98387	+	12.0964i	−0.00976025	+	0.0169052i
$81$	−40.5000	+	70.1481i	−0.0555556	+	0.0962250i
$82$	−408.554	−	707.637i	−0.550211	−	0.952993i
$83$	33.5201			0.0443290			0.0221645	−	0.999754i	$-0.492944\pi$
$83$	33.5201			0.0443290			0.0221645	+	0.999754i	$0.492944\pi$
$84$	−221.141	−	22.1046i	−0.287244	−	0.0287120i
$85$	21.9496			0.0280090
$86$	−295.044	−	511.032i	−0.369947	−	0.640767i
$87$	5.97580	−	10.3504i	0.00736406	−	0.0127549i
$88$	5.45967	−	9.45642i	0.00661366	−	0.0114552i
$89$	−551.114	−	954.557i	−0.656381	−	1.13689i	−0.981546	−	0.191228i	$-0.938753\pi$
$89$	−551.114	−	954.557i	−0.656381	−	1.13689i	0.325164	−	0.945658i	$-0.394580\pi$
$90$	15.7137			0.0184041
$91$	−140.523	+	195.500i	−0.161877	+	0.225208i
$92$	−316.379			−0.358530
$93$	−292.712	−	506.991i	−0.326374	−	0.565296i
$94$	−356.778	+	617.958i	−0.391477	+	0.678059i
$95$	−5.46671	+	9.46862i	−0.00590392	+	0.0102259i
$96$	48.0000	+	83.1384i	0.0510310	+	0.0883883i
$97$	1335.57			1.39800			0.699001	−	0.715121i	$-0.253628\pi$
$97$	1335.57			1.39800			0.699001	+	0.715121i	$0.253628\pi$
$98$	−453.806	+	514.447i	−0.467769	+	0.530275i
$99$	−12.2843			−0.0124708
$100$	248.476	+	430.373i	0.248476	+	0.430373i
$101$	121.968	−	211.254i	0.120161	−	0.208125i	−0.799670	−	0.600440i	$-0.794992\pi$
$101$	121.968	−	211.254i	0.120161	−	0.208125i	0.919831	+	0.392315i	$0.128326\pi$
$102$	75.4294	−	130.648i	0.0732218	−	0.126824i
$103$	−594.571	−	1029.83i	−0.568784	−	0.985163i	−0.996687	−	0.0813382i	$-0.974081\pi$
$103$	−594.571	−	1029.83i	−0.568784	−	0.985163i	0.427902	−	0.903825i	$-0.359253\pi$
$104$	104.000			0.0980581
$105$	28.3095	−	39.3850i	0.0263116	−	0.0366055i
$106$	−725.169			−0.664478
$107$	−154.379	−	267.392i	−0.139480	−	0.241587i	0.787820	−	0.615906i	$-0.211210\pi$
$107$	−154.379	−	267.392i	−0.139480	−	0.241587i	−0.927300	+	0.374319i	$0.877876\pi$
$108$	54.0000	−	93.5307i	0.0481125	−	0.0833333i
$109$	468.282	−	811.089i	0.411498	−	0.712736i	−0.583556	−	0.812073i	$-0.698339\pi$
$109$	468.282	−	811.089i	0.411498	−	0.712736i	0.995054	+	0.0993374i	$0.0316723\pi$
$110$	1.19155	+	2.06382i	0.00103282	+	0.00178889i
$111$	−544.712			−0.465781
$112$	294.855	+	29.4728i	0.248760	+	0.0248653i
$113$	−2162.88			−1.80059			−0.900294	−	0.435283i	$-0.856648\pi$
$113$	−2162.88			−1.80059			−0.900294	+	0.435283i	$0.856648\pi$
$114$	37.5726	+	65.0777i	0.0308684	+	0.0534656i
$115$	34.5242	−	59.7977i	0.0279948	−	0.0484884i
$116$	−7.96773	+	13.8005i	−0.00637746	+	0.0110461i
$117$	−58.5000	−	101.325i	−0.0462250	−	0.0800641i
$118$	623.238			0.486218
$119$	−191.564	−	424.429i	−0.147569	−	0.326953i
$120$	−20.9516			−0.0159384
$121$	664.569	+	1151.07i	0.499300	+	0.864813i
$122$	242.760	−	420.473i	0.180151	−	0.312031i
$123$	612.832	−	1061.46i	0.449245	−	0.778116i
$124$	390.282	+	675.989i	0.282648	+	0.489561i
$125$	−217.581			−0.155688
$126$	−137.141	−	303.849i	−0.0969643	−	0.214834i
$127$	318.990			0.222880			0.111440	−	0.993771i	$-0.464454\pi$
$127$	318.990			0.222880			0.111440	+	0.993771i	$0.464454\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$	442.566	−	766.548i	0.302060	−	0.523184i
$130$	−11.3488	+	19.6567i	−0.00765657	+	0.0132616i
$131$	334.469	+	579.317i	0.223074	+	0.386375i	0.955740	−	0.294213i	$-0.0950576\pi$
$131$	334.469	+	579.317i	0.223074	+	0.386375i	−0.732666	+	0.680588i	$0.761724\pi$
$132$	16.3790			0.0108001
$133$	230.801	+	23.0702i	0.150474	+	0.0150409i
$134$	−514.758			−0.331853
$135$	11.7853	+	20.4127i	0.00751344	+	0.0130137i
$136$	−100.573	+	174.197i	−0.0634120	+	0.109833i
$137$	124.642	−	215.886i	0.0777292	−	0.134631i	−0.824541	−	0.565803i	$-0.808566\pi$
$137$	124.642	−	215.886i	0.0777292	−	0.134631i	0.902270	+	0.431172i	$0.141900\pi$
$138$	−237.284	−	410.988i	−0.146369	−	0.253519i
$139$	−289.575			−0.176701			−0.0883504	−	0.996089i	$-0.528160\pi$
$139$	−289.575			−0.176701			−0.0883504	+	0.996089i	$0.528160\pi$
$140$	−37.7460	+	52.5133i	−0.0227865	+	0.0317013i
$141$	−1070.33			−0.639280
$142$	−75.4435	−	130.672i	−0.0445851	−	0.0772236i
$143$	8.87196	−	15.3667i	0.00518819	−	0.00898620i
$144$	−72.0000	+	124.708i	−0.0416667	+	0.0721688i
$145$	−1.73892	−	3.01191i	−0.000995930	−	0.00172500i
$146$	−510.948			−0.289632
$147$	−1008.64	−	203.677i	−0.565927	−	0.114279i
$148$	726.282			0.403379
$149$	−1184.70	−	2051.97i	−0.651373	−	1.12821i	−0.982790	−	0.184727i	$-0.940860\pi$
$149$	−1184.70	−	2051.97i	−0.651373	−	1.12821i	0.331417	−	0.943485i	$-0.392473\pi$
$150$	−372.714	+	645.559i	−0.202880	+	0.351398i
$151$	524.475	−	908.417i	0.282657	−	0.489576i	−0.689382	−	0.724398i	$-0.742118\pi$
$151$	524.475	−	908.417i	0.282657	−	0.489576i	0.972038	+	0.234823i	$0.0754510\pi$
$152$	−50.0968	−	86.7702i	−0.0267328	−	0.0463026i
$153$	226.288			0.119571
$154$	29.5081	−	41.0525i	0.0154404	−	0.0214812i
$155$	−170.355			−0.0882790
$156$	78.0000	+	135.100i	0.0400320	+	0.0693375i
$157$	1040.14	−	1801.58i	0.528741	−	0.915807i	−0.470697	−	0.882295i	$-0.655998\pi$
$157$	1040.14	−	1801.58i	0.528741	−	0.915807i	0.999438	−	0.0335118i	$-0.0106691\pi$
$158$	−55.7096	+	96.4919i	−0.0280507	+	0.0485853i
$159$	−543.877	−	942.023i	−0.271272	−	0.469857i
$160$	27.9355			0.0138031
$161$	−1457.59	−	145.697i	−0.713505	−	0.0713198i
$162$	162.000			0.0785674
$163$	−401.028	−	694.601i	−0.192705	−	0.333775i	0.753441	−	0.657516i	$-0.228393\pi$
$163$	−401.028	−	694.601i	−0.192705	−	0.333775i	−0.946146	+	0.323741i	$0.895059\pi$
$164$	−817.109	+	1415.27i	−0.389058	+	0.673868i
$165$	−1.78732	+	3.09574i	−0.000843291	+	0.00146062i
$166$	−33.5201	−	58.0585i	−0.0156727	−	0.0271459i
$167$	1091.02			0.505545			0.252772	−	0.967526i	$-0.418658\pi$
$167$	1091.02			0.505545			0.252772	+	0.967526i	$0.418658\pi$
$168$	182.855	+	405.132i	0.0839735	+	0.186051i
$169$	169.000			0.0769231
$170$	−21.9496	−	38.0177i	−0.00990267	−	0.0171519i
$171$	−56.3589	+	97.6165i	−0.0252039	+	0.0436545i
$172$	−590.089	+	1022.06i	−0.261592	+	0.453091i
$173$	782.097	+	1354.63i	0.343709	+	0.595322i	0.985118	−	0.171877i	$-0.0549832\pi$
$173$	782.097	+	1354.63i	0.343709	+	0.595322i	−0.641409	+	0.767199i	$0.721650\pi$
$174$	−23.9032			−0.0104144
$175$	946.562	+	2097.20i	0.408877	+	0.905905i
$176$	−21.8387			−0.00935313
$177$	467.428	+	809.610i	0.198498	+	0.343808i
$178$	−1102.23	+	1909.11i	−0.464132	+	0.803900i
$179$	−850.843	+	1473.70i	−0.355279	+	0.615362i	−0.987166	−	0.159699i	$-0.948948\pi$
$179$	−850.843	+	1473.70i	−0.355279	+	0.615362i	0.631887	+	0.775061i	$0.282281\pi$
$180$	−15.7137	−	27.2169i	−0.00650683	−	0.0112702i
$181$	3480.65			1.42936			0.714682	−	0.699450i	$-0.246572\pi$
$181$	3480.65			1.42936			0.714682	+	0.699450i	$0.246572\pi$
$182$	479.139	+	47.8933i	0.195144	+	0.0195060i
$183$	728.280			0.294186
$184$	316.379	+	547.985i	0.126760	+	0.219554i
$185$	−79.2540	+	137.272i	−0.0314966	+	0.0545537i
$186$	−585.423	+	1013.98i	−0.230781	+	0.399725i
$187$	17.1592	+	29.7205i	0.00671017	+	0.0116224i
$188$	1427.11			0.553632
$189$	291.856	−	406.038i	0.112325	−	0.156270i
$190$	21.8668			0.00834941
$191$	1039.73	+	1800.87i	0.393887	+	0.682233i	0.992958	−	0.118463i	$-0.0377967\pi$
$191$	1039.73	+	1800.87i	0.393887	+	0.682233i	−0.599071	+	0.800696i	$0.704463\pi$
$192$	96.0000	−	166.277i	0.0360844	−	0.0625000i
$193$	−777.356	+	1346.42i	−0.289924	+	0.502163i	−0.973791	−	0.227443i	$-0.926963\pi$
$193$	−777.356	+	1346.42i	−0.289924	+	0.502163i	0.683867	+	0.729606i	$0.260297\pi$
$194$	−1335.57	−	2313.27i	−0.494268	−	0.856098i
$195$	−34.0464			−0.0125031
$196$	1344.85	+	271.569i	0.490107	+	0.0989682i
$197$	221.430			0.0800823			0.0400412	−	0.999198i	$-0.487251\pi$
$197$	221.430			0.0800823			0.0400412	+	0.999198i	$0.487251\pi$
$198$	12.2843	+	21.2769i	0.00440911	+	0.00763680i
$199$	483.642	−	837.693i	0.172284	−	0.298404i	−0.766934	−	0.641726i	$-0.778219\pi$
$199$	483.642	−	837.693i	0.172284	−	0.298404i	0.939218	+	0.343322i	$0.111552\pi$
$200$	496.952	−	860.745i	0.175699	−	0.304319i
$201$	−386.069	−	668.690i	−0.135478	−	0.234656i
$202$	−487.871			−0.169933
$203$	−43.0635	+	59.9112i	−0.0148890	+	0.0207140i
$204$	−301.718			−0.103551
$205$	−178.331	−	308.878i	−0.0607568	−	0.105234i
$206$	−1189.14	+	2059.65i	−0.402191	+	0.696616i
$207$	355.926	−	616.483i	0.119510	−	0.206998i
$208$	−104.000	−	180.133i	−0.0346688	−	0.0600481i
$209$	−17.0945			−0.00565766
$210$	−96.5262	−	9.64848i	−0.0317188	−	0.00317051i
$211$	5226.42			1.70522			0.852611	−	0.522547i	$-0.175018\pi$
$211$	5226.42			1.70522			0.852611	+	0.522547i	$0.175018\pi$
$212$	725.169	+	1256.03i	0.234928	+	0.406908i
$213$	113.165	−	196.008i	0.0364036	−	0.0630528i
$214$	−308.758	+	534.785i	−0.0986274	+	0.170828i
$215$	−128.784	−	223.061i	−0.0408513	−	0.0707565i
$216$	−216.000			−0.0680414
$217$	1486.77	+	3294.08i	0.465108	+	1.03049i
$218$	−1873.13			−0.581946
$219$	−383.211	−	663.740i	−0.118242	−	0.204801i
$220$	2.38310	−	4.12765i	0.000730311	−	0.00126494i
$221$	−163.430	+	283.070i	−0.0497444	+	0.0861599i
$222$	544.712	+	943.468i	0.164679	+	0.285232i
$223$	6341.86			1.90441			0.952203	−	0.305465i	$-0.0988120\pi$
$223$	6341.86			1.90441			0.952203	+	0.305465i	$0.0988120\pi$
$224$	−243.806	−	540.176i	−0.0727232	−	0.161125i
$225$	−1118.14			−0.331301
$226$	2162.88	+	3746.21i	0.636604	+	1.10263i
$227$	−1841.18	+	3189.02i	−0.538342	+	0.932436i	0.460652	+	0.887581i	$0.347616\pi$
$227$	−1841.18	+	3189.02i	−0.538342	+	0.932436i	−0.998994	+	0.0448546i	$0.985718\pi$
$228$	75.1452	−	130.155i	0.0218272	−	0.0378059i
$229$	−1722.96	−	2984.25i	−0.497189	−	0.861156i	0.502806	−	0.864399i	$-0.332301\pi$
$229$	−1722.96	−	2984.25i	−0.497189	−	0.861156i	−0.999995	+	0.00324297i	$0.998968\pi$
$230$	−138.097			−0.0395906
$231$	75.4598	+	7.54274i	0.0214930	+	0.00214838i
$232$	31.8709			0.00901909
$233$	2086.67	+	3614.22i	0.586705	+	1.01620i	0.994661	+	0.103201i	$0.0329084\pi$
$233$	2086.67	+	3614.22i	0.586705	+	1.01620i	−0.407956	+	0.913002i	$0.633758\pi$
$234$	−117.000	+	202.650i	−0.0326860	+	0.0566139i
$235$	−155.731	+	269.734i	−0.0432287	+	0.0748744i
$236$	−623.238	−	1079.48i	−0.171904	−	0.297746i
$237$	−167.129			−0.0458067
$238$	−543.569	+	756.228i	−0.148043	+	0.205962i
$239$	6266.60			1.69604			0.848018	−	0.529967i	$-0.177796\pi$
$239$	6266.60			1.69604			0.848018	+	0.529967i	$0.177796\pi$
$240$	20.9516	+	36.2892i	0.00563508	+	0.00976025i
$241$	−2150.05	+	3723.99i	−0.574675	+	0.995366i	0.421402	+	0.906874i	$0.361538\pi$
$241$	−2150.05	+	3723.99i	−0.574675	+	0.995366i	−0.996077	+	0.0884922i	$0.971795\pi$
$242$	1329.14	−	2302.13i	0.353059	−	0.611515i
$243$	121.500	+	210.444i	0.0320750	+	0.0555556i
$244$	−971.040			−0.254772
$245$	−198.083	+	224.552i	−0.0516532	+	0.0585555i
$246$	−2451.33			−0.635329
$247$	−81.4073	−	141.002i	−0.0209709	−	0.0363227i
$248$	780.564	−	1351.98i	0.199862	−	0.346172i
$249$	50.2802	−	87.0878i	0.0127967	−	0.0221645i
$250$	217.581	+	376.861i	0.0550440	+	0.0953390i
$251$	1885.18			0.474070			0.237035	−	0.971501i	$-0.423824\pi$
$251$	1885.18			0.474070			0.237035	+	0.971501i	$0.423824\pi$
$252$	−389.141	+	541.385i	−0.0972761	+	0.135333i
$253$	107.958			0.0268271
$254$	−318.990	−	552.506i	−0.0788000	−	0.136486i
$255$	32.9243	−	57.0266i	0.00808550	−	0.0140045i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−1378.94	−	2388.40i	−0.334693	−	0.579705i	0.648733	−	0.761016i	$-0.275299\pi$
$257$	−1378.94	−	2388.40i	−0.334693	−	0.579705i	−0.983426	+	0.181311i	$0.941966\pi$
$258$	−1770.27			−0.427178
$259$	3346.06	+	334.462i	0.802757	+	0.0802412i
$260$	45.3951			0.0108280
$261$	−17.9274	−	31.0512i	−0.00425164	−	0.00736406i
$262$	668.938	−	1158.63i	0.157737	−	0.273209i
$263$	−1143.14	+	1979.98i	−0.268019	+	0.464223i	−0.968350	−	0.249595i	$-0.919702\pi$
$263$	−1143.14	+	1979.98i	−0.268019	+	0.464223i	0.700331	+	0.713818i	$0.253036\pi$
$264$	−16.3790	−	28.3693i	−0.00381840	−	0.00661366i
$265$	−316.530			−0.0733747
$266$	−190.843	−	422.830i	−0.0439899	−	0.0974637i
$267$	−3306.68			−0.757924
$268$	514.758	+	891.587i	0.117328	+	0.203218i
$269$	−2322.86	+	4023.31i	−0.526495	+	0.911916i	0.473028	+	0.881047i	$0.343161\pi$
$269$	−2322.86	+	4023.31i	−0.526495	+	0.911916i	−0.999523	+	0.0308691i	$0.990173\pi$
$270$	23.5706	−	40.8254i	0.00531281	−	0.00920205i
$271$	1633.94	+	2830.06i	0.366253	+	0.634369i	0.988976	−	0.148073i	$-0.0473071\pi$
$271$	1633.94	+	2830.06i	0.366253	+	0.634369i	−0.622723	+	0.782442i	$0.713974\pi$
$272$	402.290			0.0896781
$273$	297.139	+	658.340i	0.0658743	+	0.145951i
$274$	−498.569			−0.109926
$275$	−84.7872	−	146.856i	−0.0185922	−	0.0322027i
$276$	−474.569	+	821.977i	−0.103499	+	0.179265i
$277$	467.487	−	809.711i	0.101403	−	0.175635i	−0.810860	−	0.585240i	$-0.801000\pi$
$277$	467.487	−	809.711i	0.101403	−	0.175635i	0.912263	+	0.409605i	$0.134334\pi$
$278$	289.575	+	501.558i	0.0624731	+	0.108207i
$279$	−1756.27			−0.376864
$280$	128.702	+	12.8646i	0.0274693	+	0.00274575i
$281$	−1100.98			−0.233732			−0.116866	−	0.993148i	$-0.537285\pi$
$281$	−1100.98			−0.233732			−0.116866	+	0.993148i	$0.537285\pi$
$282$	1070.33	+	1853.87i	0.226020	+	0.391477i
$283$	−963.446	+	1668.74i	−0.202371	+	0.350517i	−0.949292	−	0.314396i	$-0.898198\pi$
$283$	−963.446	+	1668.74i	−0.202371	+	0.350517i	0.746921	+	0.664913i	$0.231531\pi$
$284$	−150.887	+	261.344i	−0.0315264	+	0.0546053i
$285$	16.4001	+	28.4059i	0.00340863	+	0.00590392i
$286$	−35.4878			−0.00733720
$287$	−4416.26	+	6144.03i	−0.908305	+	1.26366i
$288$	288.000			0.0589256
$289$	2140.41	+	3707.30i	0.435663	+	0.754590i
$290$	−3.47785	+	6.02381i	−0.000704229	+	0.00121976i
$291$	2003.35	−	3469.90i	0.403569	−	0.699001i
$292$	510.948	+	884.987i	0.102400	+	0.177363i
$293$	−805.860			−0.160679			−0.0803394	−	0.996768i	$-0.525600\pi$
$293$	−805.860			−0.160679			−0.0803394	+	0.996768i	$0.525600\pi$
$294$	655.863	+	1950.69i	0.130104	+	0.386962i
$295$	272.038			0.0536904
$296$	−726.282	−	1257.96i	−0.142616	−	0.247018i
$297$	−18.4264	+	31.9154i	−0.00360002	+	0.00623542i
$298$	−2369.41	+	4103.93i	−0.460590	+	0.797766i
$299$	514.116	+	890.475i	0.0994384	+	0.172232i
$300$	1490.85			0.286915
$301$	−3189.27	+	4437.01i	−0.610720	+	0.849651i
$302$	−2097.90			−0.399737
$303$	−365.903	−	633.763i	−0.0693749	−	0.120161i
$304$	−100.194	+	173.540i	−0.0189030	+	0.0327409i
$305$	105.963	−	183.533i	0.0198931	−	0.0344559i
$306$	−226.288	−	391.943i	−0.0422747	−	0.0732218i
$307$	2026.64			0.376763			0.188382	−	0.982096i	$-0.439676\pi$
$307$	2026.64			0.376763			0.188382	+	0.982096i	$0.439676\pi$
$308$	−100.613	−	10.0570i	−0.0186135	−	0.00186055i
$309$	−3567.42			−0.656775
$310$	170.355	+	295.063i	0.0312113	+	0.0540596i
$311$	−791.273	+	1370.53i	−0.144273	+	0.249889i	−0.929102	−	0.369825i	$-0.879418\pi$
$311$	−791.273	+	1370.53i	−0.144273	+	0.249889i	0.784828	+	0.619713i	$0.212751\pi$
$312$	156.000	−	270.200i	0.0283069	−	0.0490290i
$313$	1361.59	+	2358.35i	0.245884	+	0.425884i	0.962380	−	0.271708i	$-0.0875884\pi$
$313$	1361.59	+	2358.35i	0.245884	+	0.425884i	−0.716496	+	0.697592i	$0.754255\pi$
$314$	−4160.57			−0.747753
$315$	−59.8609	−	132.628i	−0.0107072	−	0.0237229i
$316$	222.838			0.0396697
$317$	−4506.22	−	7804.99i	−0.798405	−	1.38288i	−0.920655	−	0.390378i	$-0.872344\pi$
$317$	−4506.22	−	7804.99i	−0.798405	−	1.38288i	0.122250	−	0.992499i	$-0.460989\pi$
$318$	−1087.75	+	1884.05i	−0.191818	+	0.332239i
$319$	2.71882	−	4.70914i	0.000477194	−	0.000826524i
$320$	−27.9355	−	48.3856i	−0.00488013	−	0.00845262i
$321$	−926.274			−0.161058
$322$	1205.24	+	2670.32i	0.208588	+	0.462146i
$323$	314.898			0.0542458
$324$	−162.000	−	280.592i	−0.0277778	−	0.0481125i
$325$	807.546	−	1398.71i	0.137830	−	0.238728i
$326$	−802.057	+	1389.20i	−0.136263	+	0.236015i
$327$	−1404.85	−	2433.27i	−0.237579	−	0.411498i
$328$	3268.44			0.550211
$329$	6574.86	+	657.204i	1.10177	+	0.110130i
$330$	7.14930			0.00119259
$331$	−803.960	−	1392.50i	−0.133503	−	0.231235i	0.791521	−	0.611142i	$-0.209289\pi$
$331$	−803.960	−	1392.50i	−0.133503	−	0.231235i	−0.925025	+	0.379907i	$0.875956\pi$
$332$	−67.0402	+	116.117i	−0.0110823	+	0.0191950i
$333$	−817.067	+	1415.20i	−0.134460	+	0.232891i
$334$	−1091.02	−	1889.71i	−0.178737	−	0.309582i
$335$	−224.688			−0.0366448
$336$	518.855	−	721.846i	0.0842436	−	0.117202i
$337$	3867.33			0.625124			0.312562	−	0.949897i	$-0.398813\pi$
$337$	3867.33			0.625124			0.312562	+	0.949897i	$0.398813\pi$
$338$	−169.000	−	292.717i	−0.0271964	−	0.0471056i
$339$	−3244.32	+	5619.32i	−0.519785	+	0.900294i
$340$	−43.8991	+	76.0355i	−0.00700224	+	0.0121282i
$341$	−133.176	−	230.667i	−0.0211492	−	0.0366314i
$342$	225.436			0.0356437
$343$	6070.83	+	1870.47i	0.955667	+	0.294448i
$344$	2360.35			0.369947
$345$	−103.573	−	179.393i	−0.0161628	−	0.0279948i
$346$	1564.19	−	2709.26i	0.243039	−	0.420956i
$347$	2626.99	−	4550.08i	0.406409	−	0.703922i	−0.588075	−	0.808806i	$-0.700114\pi$
$347$	2626.99	−	4550.08i	0.406409	−	0.703922i	0.994484	+	0.104885i	$0.0334474\pi$
$348$	23.9032	+	41.4016i	0.00368203	+	0.00637746i
$349$	−4793.05			−0.735146			−0.367573	−	0.929995i	$-0.619811\pi$
$349$	−4793.05			−0.735146			−0.367573	+	0.929995i	$0.619811\pi$
$350$	2685.89	−	3736.69i	0.410191	−	0.570670i
$351$	−351.000			−0.0533761
$352$	21.8387	+	37.8257i	0.00330683	+	0.00572760i
$353$	−1479.43	+	2562.44i	−0.223065	+	0.386360i	−0.955737	−	0.294222i	$-0.904940\pi$
$353$	−1479.43	+	2562.44i	−0.223065	+	0.386360i	0.732672	+	0.680582i	$0.238273\pi$
$354$	934.857	−	1619.22i	0.140359	−	0.243109i
$355$	−32.9305	−	57.0373i	−0.00492329	−	0.00852739i
$356$	4408.91			0.656381
$357$	−1390.05	−	138.945i	−0.206076	−	0.0205987i
$358$	3403.37			0.502441
$359$	−2522.64	−	4369.34i	−0.370863	−	0.642354i	0.618835	−	0.785521i	$-0.287605\pi$
$359$	−2522.64	−	4369.34i	−0.370863	−	0.642354i	−0.989699	+	0.143167i	$0.954271\pi$
$360$	−31.4274	+	54.4339i	−0.00460103	+	0.00796921i
$361$	3351.07	−	5804.23i	0.488566	−	0.846221i
$362$	−3480.65	−	6028.66i	−0.505356	−	0.875303i
$363$	3987.41			0.576542
$364$	−396.185	−	877.786i	−0.0570488	−	0.126397i
$365$	−223.024			−0.0319825
$366$	−728.280	−	1261.42i	−0.104010	−	0.180151i
$367$	−4621.83	+	8005.25i	−0.657378	+	1.13861i	0.323914	+	0.946087i	$0.395001\pi$
$367$	−4621.83	+	8005.25i	−0.657378	+	1.13861i	−0.981292	+	0.192526i	$0.938332\pi$
$368$	632.758	−	1095.97i	0.0896326	−	0.155248i
$369$	−1838.49	−	3184.37i	−0.259372	−	0.449245i
$370$	317.016			0.0445429
$371$	2762.51	+	6120.61i	0.386584	+	0.856513i
$372$	2341.69			0.326374
$373$	−3959.27	−	6857.66i	−0.549607	−	0.951947i	−0.998301	−	0.0582619i	$-0.981444\pi$
$373$	−3959.27	−	6857.66i	−0.549607	−	0.951947i	0.448694	−	0.893685i	$-0.351889\pi$
$374$	34.3183	−	59.4410i	0.00474481	−	0.00821824i
$375$	−326.371	+	565.291i	−0.0449432	+	0.0778440i
$376$	−1427.11	−	2471.83i	−0.195739	−	0.339029i
$377$	51.7903			0.00707516
$378$	−995.135	−	99.4707i	−0.135408	−	0.0135350i
$379$	−5799.37			−0.785999			−0.393000	−	0.919539i	$-0.628563\pi$
$379$	−5799.37			−0.785999			−0.393000	+	0.919539i	$0.628563\pi$
$380$	−21.8668	−	37.8745i	−0.00295196	−	0.00511295i
$381$	478.485	−	828.760i	0.0643399	−	0.111440i
$382$	2079.47	−	3601.74i	0.278520	−	0.482412i
$383$	−178.000	−	308.305i	−0.0237477	−	0.0411322i	0.853907	−	0.520425i	$-0.174226\pi$
$383$	−178.000	−	308.305i	−0.0237477	−	0.0411322i	−0.877655	+	0.479293i	$0.840893\pi$
$384$	−384.000			−0.0510310
$385$	12.8800	−	17.9191i	0.00170500	−	0.00237205i
$386$	3109.42			0.410014
$387$	−1327.70	−	2299.64i	−0.174395	−	0.302060i
$388$	−2671.13	+	4626.54i	−0.349501	+	0.605353i
$389$	4534.60	−	7854.16i	0.591037	−	1.02371i	−0.403056	−	0.915175i	$-0.632052\pi$
$389$	4534.60	−	7854.16i	0.591037	−	1.02371i	0.994093	−	0.108531i	$-0.0346146\pi$
$390$	34.0464	+	58.9700i	0.00442052	+	0.00765657i
$391$	−1988.69			−0.257219
$392$	−874.484	−	2600.93i	−0.112674	−	0.335119i
$393$	2006.81			0.257583
$394$	−221.430	−	383.528i	−0.0283134	−	0.0490402i
$395$	−24.3168	+	42.1179i	−0.00309749	+	0.00536502i
$396$	24.5685	−	42.5539i	0.00311771	−	0.00540003i
$397$	−2508.60	−	4345.03i	−0.317136	−	0.549297i	0.662753	−	0.748838i	$-0.269388\pi$
$397$	−2508.60	−	4345.03i	−0.317136	−	0.549297i	−0.979889	+	0.199542i	$0.936055\pi$
$398$	−1934.57			−0.243646
$399$	406.140	−	565.034i	0.0509585	−	0.0708949i
$400$	−1987.81			−0.248476
$401$	−2457.14	−	4255.89i	−0.305995	−	0.529998i	0.671488	−	0.741016i	$-0.265656\pi$
$401$	−2457.14	−	4255.89i	−0.305995	−	0.529998i	−0.977482	+	0.211018i	$0.932322\pi$
$402$	−772.137	+	1337.38i	−0.0957977	+	0.165927i
$403$	1268.42	−	2196.96i	0.156785	−	0.271560i
$404$	487.871	+	845.017i	0.0600804	+	0.104062i
$405$	70.7117			0.00867578
$406$	146.833	+	14.6770i	0.0179487	+	0.00179410i
$407$	−247.829			−0.0301828
$408$	301.718	+	522.591i	0.0366109	+	0.0634120i
$409$	2025.90	−	3508.95i	0.244924	−	0.424222i	−0.717186	−	0.696882i	$-0.754570\pi$
$409$	2025.90	−	3508.95i	0.244924	−	0.424222i	0.962110	+	0.272660i	$0.0879035\pi$
$410$	−356.661	+	617.755i	−0.0429616	+	0.0744116i
$411$	−373.926	−	647.659i	−0.0448770	−	0.0777292i
$412$	4756.56			0.568784
$413$	−2374.21	−	5260.29i	−0.282875	−	0.626736i
$414$	−1423.71			−0.169013
$415$	−14.6312	−	25.3421i	−0.00173065	−	0.00299757i
$416$	−208.000	+	360.267i	−0.0245145	+	0.0424604i
$417$	−434.362	+	752.337i	−0.0510091	+	0.0883504i
$418$	17.0945	+	29.6085i	0.00200028	+	0.00346459i
$419$	7107.75			0.828727			0.414363	−	0.910112i	$-0.364004\pi$
$419$	7107.75			0.828727			0.414363	+	0.910112i	$0.364004\pi$
$420$	79.8146	+	176.837i	0.00927275	+	0.0205447i
$421$	7169.00			0.829919			0.414960	−	0.909840i	$-0.363796\pi$
$421$	7169.00			0.829919			0.414960	+	0.909840i	$0.363796\pi$
$422$	−5226.42	−	9052.43i	−0.602887	−	1.04423i
$423$	−1605.50	+	2780.81i	−0.184544	+	0.319640i
$424$	1450.34	−	2512.06i	0.166119	−	0.287727i
$425$	1561.87	+	2705.23i	0.178263	+	0.308760i
$426$	−452.661			−0.0514824
$427$	−4473.69	−	447.176i	−0.507018	−	0.0506800i
$428$	1235.03			0.139480
$429$	−26.6159	−	46.1000i	−0.00299540	−	0.00518819i
$430$	−257.569	+	446.122i	−0.0288862	+	0.0500324i
$431$	1504.02	−	2605.05i	0.168089	−	0.291138i	−0.769659	−	0.638455i	$-0.779574\pi$
$431$	1504.02	−	2605.05i	0.168089	−	0.291138i	0.937748	+	0.347317i	$0.112907\pi$
$432$	216.000	+	374.123i	0.0240563	+	0.0416667i
$433$	2841.60			0.315377			0.157689	−	0.987489i	$-0.449596\pi$
$433$	2841.60			0.315377			0.157689	+	0.987489i	$0.449596\pi$
$434$	4218.75	−	5869.24i	0.466604	−	0.649154i
$435$	−10.4335			−0.00115000
$436$	1873.13	+	3244.35i	0.205749	+	0.356368i
$437$	495.299	−	857.883i	0.0542183	−	0.0939088i
$438$	−766.421	+	1327.48i	−0.0836096	+	0.144816i
$439$	−6770.73	−	11727.2i	−0.736103	−	1.27497i	−0.954238	−	0.299049i	$-0.903331\pi$
$439$	−6770.73	−	11727.2i	−0.736103	−	1.27497i	0.218135	−	0.975919i	$-0.430003\pi$
$440$	−9.53240			−0.00103282
$441$	−2042.13	+	2315.01i	−0.220508	+	0.249974i
$442$	653.722			0.0703493
$443$	2172.91	+	3763.58i	0.233043	+	0.403642i	0.958702	−	0.284412i	$-0.0917985\pi$
$443$	2172.91	+	3763.58i	0.233043	+	0.403642i	−0.725659	+	0.688054i	$0.758465\pi$
$444$	1089.42	−	1886.94i	0.116445	−	0.201689i
$445$	−481.113	+	833.312i	−0.0512516	+	0.0887703i
$446$	−6341.86	−	10984.4i	−0.673309	−	1.16621i
$447$	−7108.22			−0.752141
$448$	−691.806	+	962.461i	−0.0729571	+	0.101500i
$449$	−4142.72			−0.435428			−0.217714	−	0.976013i	$-0.569860\pi$
$449$	−4142.72			−0.435428			−0.217714	+	0.976013i	$0.569860\pi$
$450$	1118.14	+	1936.68i	0.117133	+	0.202880i
$451$	278.821	−	482.933i	0.0291113	−	0.0504222i
$452$	4325.75	−	7492.43i	0.450147	−	0.779677i
$453$	−1573.42	−	2725.25i	−0.163192	−	0.282657i
$454$	7364.73			0.761331
$455$	209.140	+	20.9050i	0.0215487	+	0.00215394i
$456$	−300.581			−0.0308684
$457$	−8113.06	−	14052.2i	−0.830444	−	1.43837i	−0.897686	−	0.440635i	$-0.854753\pi$
$457$	−8113.06	−	14052.2i	−0.830444	−	1.43837i	0.0672418	−	0.997737i	$-0.478580\pi$
$458$	−3445.92	+	5968.50i	−0.351566	+	0.608930i
$459$	339.433	−	587.914i	0.0345171	−	0.0597854i
$460$	138.097	+	239.191i	0.0139974	+	0.0242442i
$461$	−777.223			−0.0785225			−0.0392612	−	0.999229i	$-0.512500\pi$
$461$	−777.223			−0.0785225			−0.0392612	+	0.999229i	$0.512500\pi$
$462$	−62.3954	−	138.243i	−0.00628333	−	0.0139213i
$463$	−14826.0			−1.48817			−0.744084	−	0.668086i	$-0.767114\pi$
$463$	−14826.0			−1.48817			−0.744084	+	0.668086i	$0.767114\pi$
$464$	−31.8709	−	55.2021i	−0.00318873	−	0.00552304i
$465$	−255.532	+	442.595i	−0.0254839	+	0.0441395i
$466$	4173.34	−	7228.43i	0.414863	−	0.718563i
$467$	7822.95	+	13549.7i	0.775167	+	1.34263i	0.934701	+	0.355435i	$0.115667\pi$
$467$	7822.95	+	13549.7i	0.775167	+	1.34263i	−0.159534	+	0.987192i	$0.550999\pi$
$468$	468.000			0.0462250
$469$	1960.96	+	4344.69i	0.193067	+	0.427759i
$470$	622.923			0.0611347
$471$	−3120.43	−	5404.74i	−0.305269	−	0.528741i
$472$	−1246.48	+	2158.96i	−0.121554	+	0.210538i
$473$	201.355	−	348.758i	0.0195736	−	0.0339025i
$474$	167.129	+	289.476i	0.0161951	+	0.0280507i
$475$	−1555.98			−0.150302
$476$	1853.39	+	185.260i	0.178467	+	0.0178390i
$477$	−3263.26			−0.313238
$478$	−6266.60	−	10854.1i	−0.599639	−	1.03861i
$479$	−5009.31	+	8676.38i	−0.477831	+	0.827628i	−0.999677	−	0.0254119i	$-0.991910\pi$
$479$	−5009.31	+	8676.38i	−0.477831	+	0.827628i	0.521846	+	0.853040i	$0.325244\pi$
$480$	41.9032	−	72.5785i	0.00398461	−	0.00690154i
$481$	−1180.21	−	2044.18i	−0.111877	−	0.193777i
$482$	8600.19			0.812713
$483$	−2564.92	+	3568.39i	−0.241631	+	0.336164i
$484$	−5316.55			−0.499300
$485$	−582.964	−	1009.72i	−0.0545794	−	0.0945343i
$486$	243.000	−	420.888i	0.0226805	−	0.0392837i
$487$	−6467.57	+	11202.2i	−0.601794	+	1.04234i	0.390756	+	0.920494i	$0.372214\pi$
$487$	−6467.57	+	11202.2i	−0.601794	+	1.04234i	−0.992549	+	0.121843i	$0.961120\pi$
$488$	971.040	+	1681.89i	0.0900757	+	0.156016i
$489$	−2406.17			−0.222517
$490$	587.018	+	118.537i	0.0541199	+	0.0109285i
$491$	−786.588			−0.0722978			−0.0361489	−	0.999346i	$-0.511509\pi$
$491$	−786.588			−0.0722978			−0.0361489	+	0.999346i	$0.511509\pi$
$492$	2451.33	+	4245.82i	0.224623	+	0.389058i
$493$	−50.0835	+	86.7471i	−0.00457535	+	0.00792473i
$494$	−162.815	+	282.003i	−0.0148287	+	0.0256841i
$495$	5.36197	+	9.28721i	0.000486874	+	0.000843291i
$496$	−3122.26			−0.282648
$497$	−815.505	+	1134.55i	−0.0736024	+	0.102398i
$498$	−201.121			−0.0180972
$499$	−5038.45	−	8726.86i	−0.452008	−	0.782901i	0.546502	−	0.837458i	$-0.315959\pi$
$499$	−5038.45	−	8726.86i	−0.452008	−	0.782901i	−0.998511	+	0.0545562i	$0.982626\pi$
$500$	435.161	−	753.721i	0.0389220	−	0.0674149i
$501$	1636.54	−	2834.56i	0.145938	−	0.252772i
$502$	−1885.18	−	3265.23i	−0.167609	−	0.290307i
$503$	1332.89			0.118152			0.0590762	−	0.998253i	$-0.481185\pi$
$503$	1332.89			0.118152			0.0590762	+	0.998253i	$0.481185\pi$
$504$	1326.85	+	132.628i	0.117267	+	0.0117216i
$505$	−212.952			−0.0187648
$506$	−107.958	−	186.988i	−0.00948480	−	0.0164282i
$507$	253.500	−	439.075i	0.0222058	−	0.0384615i
$508$	−637.980	+	1105.01i	−0.0557200	+	0.0965099i
$509$	−6520.69	−	11294.2i	−0.567828	−	0.983507i	−0.996780	−	0.0801802i	$-0.974450\pi$
$509$	−6520.69	−	11294.2i	−0.567828	−	0.983507i	0.428952	−	0.903327i	$-0.358883\pi$
$510$	−131.697			−0.0114346
$511$	1946.44	+	4312.53i	0.168504	+	0.373337i
$512$	512.000			0.0441942
$513$	169.077	+	292.849i	0.0145515	+	0.0252039i
$514$	−2757.88	+	4776.79i	−0.236663	+	0.409913i
$515$	−519.050	+	899.021i	−0.0444118	+	0.0769235i
$516$	1770.27	+	3066.19i	0.151030	+	0.261592i
$517$	−486.973			−0.0414256
$518$	−2766.75	−	6130.01i	−0.234680	−	0.519956i
$519$	4692.58			0.396881
$520$	−45.3951	−	78.6267i	−0.00382829	−	0.00663078i
$521$	−11141.6	+	19297.8i	−0.936893	+	1.62275i	−0.165669	+	0.986181i	$0.552978\pi$
$521$	−11141.6	+	19297.8i	−0.936893	+	1.62275i	−0.771224	+	0.636564i	$0.780355\pi$
$522$	−35.8548	+	62.1023i	−0.00300636	+	0.00520718i
$523$	7512.02	+	13011.2i	0.628065	+	1.08784i	0.987940	+	0.154839i	$0.0494859\pi$
$523$	7512.02	+	13011.2i	0.628065	+	1.08784i	−0.359875	+	0.933000i	$0.617181\pi$
$524$	−2675.75			−0.223074
$525$	6868.53	+	686.557i	0.570985	+	0.0570739i
$526$	4572.56			0.379036
$527$	2453.23	+	4249.12i	0.202779	+	0.351223i
$528$	−32.7580	+	56.7385i	−0.00270002	+	0.00467657i
$529$	2955.51	−	5119.09i	0.242912	−	0.420736i
$530$	316.530	+	548.247i	0.0259419	+	0.0449327i
$531$	2804.57			0.229205
$532$	−541.520	+	753.379i	−0.0441313	+	0.0613968i
$533$	5311.21			0.431621
$534$	3306.68	+	5727.34i	0.267967	+	0.464132i
$535$	−134.770	+	233.429i	−0.0108909	+	0.0188636i
$536$	1029.52	−	1783.17i	0.0829633	−	0.143697i
$537$	2552.53	+	4421.11i	0.205121	+	0.355279i
$538$	9291.43			0.744577
$539$	−458.904	−	92.6672i	−0.0366723	−	0.00740530i
$540$	−94.2822			−0.00751344
$541$	−12531.2	−	21704.6i	−0.995855	−	1.72487i	−0.576698	−	0.816957i	$-0.695659\pi$
$541$	−12531.2	−	21704.6i	−0.995855	−	1.72487i	−0.419157	−	0.907914i	$-0.637674\pi$
$542$	3267.87	−	5660.12i	0.258980	−	0.448566i
$543$	5220.98	−	9043.00i	0.412622	−	0.714682i
$544$	−402.290	−	696.787i	−0.0317060	−	0.0549164i
$545$	−817.605			−0.0642612
$546$	843.139	−	1173.00i	0.0660861	−	0.0919409i
$547$	−3347.07			−0.261628			−0.130814	−	0.991407i	$-0.541759\pi$
$547$	−3347.07			−0.261628			−0.130814	+	0.991407i	$0.541759\pi$
$548$	498.569	+	863.546i	0.0388646	+	0.0673154i
$549$	1092.42	−	1892.13i	0.0849242	−	0.147093i
$550$	−169.574	+	293.711i	−0.0131467	+	0.0227707i
$551$	−24.9474	−	43.2101i	−0.00192885	−	0.00334086i
$552$	1898.27			0.146369
$553$	1026.64	+	102.620i	0.0789461	+	0.00789122i
$554$	−1869.95			−0.143405
$555$	237.762	+	411.816i	0.0181846	+	0.0314966i
$556$	579.149	−	1003.12i	0.0441752	−	0.0765137i
$557$	5383.23	−	9324.03i	0.409506	−	0.709285i	−0.585329	−	0.810796i	$-0.699034\pi$
$557$	5383.23	−	9324.03i	0.409506	−	0.709285i	0.994834	+	0.101511i	$0.0323678\pi$
$558$	1756.27	+	3041.95i	0.133242	+	0.230781i
$559$	3835.58			0.290210
$560$	−106.419	−	235.782i	−0.00803043	−	0.0177922i
$561$	102.955			0.00774824
$562$	1100.98	+	1906.95i	0.0826368	+	0.143131i
$563$	−7726.52	+	13382.7i	−0.578391	+	1.00180i	0.417274	+	0.908781i	$0.362986\pi$
$563$	−7726.52	+	13382.7i	−0.578391	+	1.00180i	−0.995664	+	0.0930210i	$0.970348\pi$
$564$	2140.67	−	3707.75i	0.159820	−	0.276816i
$565$	944.078	+	1635.19i	0.0702967	+	0.121757i
$566$	3853.79			0.286196
$567$	−617.135	−	1367.32i	−0.0457094	−	0.101274i
$568$	603.548			0.0445851
$569$	−8331.22	−	14430.1i	−0.613819	−	1.06317i	−0.990590	−	0.136859i	$-0.956299\pi$
$569$	−8331.22	−	14430.1i	−0.613819	−	1.06317i	0.376772	−	0.926306i	$-0.377034\pi$
$570$	32.8003	−	56.8117i	0.00241027	−	0.00417470i
$571$	−3124.73	+	5412.18i	−0.229012	+	0.396660i	−0.957515	−	0.288382i	$-0.906883\pi$
$571$	−3124.73	+	5412.18i	−0.229012	+	0.396660i	0.728504	+	0.685042i	$0.240216\pi$
$572$	35.4878	+	61.4667i	0.00259409	+	0.00449310i
$573$	6238.40			0.454822
$574$	15058.0	+	1505.16i	1.09497	+	0.109449i
$575$	9826.57			0.712689
$576$	−288.000	−	498.831i	−0.0208333	−	0.0360844i
$577$	−5493.29	+	9514.65i	−0.396341	+	0.686482i	−0.993271	−	0.115811i	$-0.963053\pi$
$577$	−5493.29	+	9514.65i	−0.396341	+	0.686482i	0.596931	+	0.802293i	$0.296387\pi$
$578$	4280.82	−	7414.60i	0.308060	−	0.533576i
$579$	2332.07	+	4039.26i	0.167388	+	0.289924i
$580$	13.9114			0.000995930
$581$	−362.335	+	504.091i	−0.0258729	+	0.0359952i
$582$	−8013.40			−0.570732
$583$	−247.449	−	428.594i	−0.0175785	−	0.0304469i
$584$	1021.90	−	1769.97i	0.0724081	−	0.125414i
$585$	−51.0695	+	88.4550i	−0.00360934	+	0.00625156i
$586$	805.860	+	1395.79i	0.0568085	+	0.0983952i
$587$	−21875.9			−1.53819			−0.769094	−	0.639135i	$-0.779292\pi$
$587$	−21875.9			−1.53819			−0.769094	+	0.639135i	$0.779292\pi$
$588$	2722.84	−	3086.68i	0.190966	−	0.216484i
$589$	−2443.99			−0.170972
$590$	−272.038	−	471.184i	−0.0189824	−	0.0328785i
$591$	332.145	−	575.291i	0.0231178	−	0.0400412i
$592$	−1452.56	+	2515.92i	−0.100845	+	0.174668i
$593$	5097.91	+	8829.83i	0.353029	+	0.611463i	0.986779	−	0.162075i	$-0.0518185\pi$
$593$	5097.91	+	8829.83i	0.353029	+	0.611463i	−0.633750	+	0.773538i	$0.718485\pi$
$594$	73.7055			0.00509120
$595$	−237.263	+	330.087i	−0.0163476	+	0.0227433i
$596$	9477.62			0.651373
$597$	−1450.93	−	2513.08i	−0.0994681	−	0.172284i
$598$	1028.23	−	1780.95i	0.0703136	−	0.121787i
$599$	−5909.48	+	10235.5i	−0.403096	+	0.698183i	−0.994098	−	0.108487i	$-0.965399\pi$
$599$	−5909.48	+	10235.5i	−0.403096	+	0.698183i	0.591002	+	0.806670i	$0.298733\pi$
$600$	−1490.85	−	2582.24i	−0.101440	−	0.175699i
$601$	2791.00			0.189429			0.0947147	−	0.995504i	$-0.469806\pi$
$601$	2791.00			0.189429			0.0947147	+	0.995504i	$0.469806\pi$
$602$	10874.4	+	1086.97i	0.736225	+	0.0735909i
$603$	−2316.41			−0.156437
$604$	2097.90	+	3633.67i	0.141328	+	0.244788i
$605$	580.157	−	1004.86i	0.0389864	−	0.0675264i
$606$	−731.806	+	1267.53i	−0.0490555	+	0.0849665i
$607$	−3193.88	−	5531.96i	−0.213568	−	0.369910i	0.739261	−	0.673419i	$-0.235175\pi$
$607$	−3193.88	−	5531.96i	−0.213568	−	0.369910i	−0.952829	+	0.303509i	$0.901842\pi$
$608$	400.774			0.0267328
$609$	91.0586	+	201.749i	0.00605892	+	0.0134241i
$610$	−423.851			−0.0281332
$611$	−2319.06	−	4016.73i	−0.153550	−	0.265956i
$612$	−452.577	+	783.886i	−0.0298927	+	0.0517757i
$613$	1260.97	−	2184.06i	0.0830830	−	0.143904i	−0.821490	−	0.570223i	$-0.806857\pi$
$613$	1260.97	−	2184.06i	0.0830830	−	0.143904i	0.904573	+	0.426319i	$0.140190\pi$
$614$	−2026.64	−	3510.24i	−0.133206	−	0.230719i
$615$	−1069.98			−0.0701559
$616$	83.1939	+	184.324i	0.00544152	+	0.0120562i
$617$	−9890.40			−0.645336			−0.322668	−	0.946512i	$-0.604580\pi$
$617$	−9890.40			−0.645336			−0.322668	+	0.946512i	$0.604580\pi$
$618$	3567.42	+	6178.96i	0.232205	+	0.402191i
$619$	1190.17	−	2061.43i	0.0772810	−	0.133855i	−0.824795	−	0.565432i	$-0.808709\pi$
$619$	1190.17	−	2061.43i	0.0772810	−	0.133855i	0.902076	+	0.431577i	$0.142043\pi$
$620$	340.710	−	590.127i	0.0220697	−	0.0382259i
$621$	−1067.78	−	1849.45i	−0.0689992	−	0.119510i
$622$	3165.09			0.204033
$623$	20312.3	+	2030.36i	1.30625	+	0.130569i
$624$	−624.000			−0.0400320
$625$	−7669.90	−	13284.7i	−0.490873	−	0.850218i
$626$	2723.18	−	4716.69i	0.173866	−	0.301145i
$627$	−25.6417	+	44.4128i	−0.00163323	+	0.00282883i
$628$	4160.57	+	7206.32i	0.264371	+	0.457903i
$629$	4565.26			0.289394
$630$	−169.857	+	236.310i	−0.0107417	+	0.0149441i
$631$	3648.51			0.230182			0.115091	−	0.993355i	$-0.463284\pi$
$631$	3648.51			0.230182			0.115091	+	0.993355i	$0.463284\pi$
$632$	−222.838	−	385.967i	−0.0140254	−	0.0242927i
$633$	7839.63	−	13578.6i	0.492255	−	0.852611i
$634$	−9012.43	+	15610.0i	−0.564557	+	0.977842i
$635$	−139.236	−	241.164i	−0.00870146	−	0.0150714i
$636$	4351.02			0.271272
$637$	−1421.04	−	4226.50i	−0.0883886	−	0.262889i
$638$	−10.8753			−0.000674854
$639$	−339.496	−	588.024i	−0.0210176	−	0.0364036i
$640$	−55.8709	+	96.7713i	−0.00345077	+	0.00597691i
$641$	14446.6	−	25022.3i	0.890182	−	1.54184i	0.0505256	−	0.998723i	$-0.483910\pi$
$641$	14446.6	−	25022.3i	0.890182	−	1.54184i	0.839657	−	0.543118i	$-0.182756\pi$
$642$	926.274	+	1604.35i	0.0569426	+	0.0986274i
$643$	−9462.65			−0.580358			−0.290179	−	0.956972i	$-0.593715\pi$
$643$	−9462.65			−0.580358			−0.290179	+	0.956972i	$0.593715\pi$
$644$	3419.89	−	4757.85i	0.209259	−	0.291127i
$645$	−772.706			−0.0471710
$646$	−314.898	−	545.419i	−0.0191788	−	0.0332186i
$647$	−16068.4	+	27831.2i	−0.976371	+	1.69112i	−0.301038	+	0.953612i	$0.597333\pi$
$647$	−16068.4	+	27831.2i	−0.976371	+	1.69112i	−0.675334	+	0.737512i	$0.736000\pi$
$648$	−324.000	+	561.184i	−0.0196419	+	0.0340207i
$649$	212.667	+	368.350i	0.0128627	+	0.0222789i
$650$	−3230.19			−0.194920
$651$	10788.4	+	1078.38i	0.649511	+	0.0649232i
$652$	3208.23			0.192705
$653$	3063.10	+	5305.44i	0.183565	+	0.317945i	0.943092	−	0.332531i	$-0.107903\pi$
$653$	3063.10	+	5305.44i	0.183565	+	0.317945i	−0.759527	+	0.650476i	$0.774569\pi$
$654$	−2809.69	+	4866.53i	−0.167993	+	0.290973i
$655$	291.986	−	505.734i	0.0174181	−	0.0301689i
$656$	−3268.44	−	5661.10i	−0.194529	−	0.336934i
$657$	−2299.26			−0.136534
$658$	−5436.55	−	12045.2i	−0.322095	−	0.713633i
$659$	14682.3			0.867893			0.433947	−	0.900939i	$-0.357121\pi$
$659$	14682.3			0.867893			0.433947	+	0.900939i	$0.357121\pi$
$660$	−7.14930	−	12.3829i	−0.000421645	−	0.000730311i
$661$	8347.47	−	14458.2i	0.491194	−	0.850772i	−0.508755	−	0.860911i	$-0.669894\pi$
$661$	8347.47	−	14458.2i	0.491194	−	0.850772i	0.999949	+	0.0101391i	$0.00322744\pi$
$662$	−1607.92	+	2785.00i	−0.0944012	+	0.163508i
$663$	490.291	+	849.210i	0.0287200	+	0.0497444i
$664$	268.161			0.0156727
$665$	−83.3012	−	184.562i	−0.00485756	−	0.0107624i
$666$	3268.27			0.190154
$667$	157.551	+	272.887i	0.00914605	+	0.0158414i
$668$	−2182.05	+	3779.42i	−0.126386	+	0.218907i
$669$	9512.80	−	16476.6i	0.549755	−	0.952203i
$670$	224.688	+	389.170i	0.0129559	+	0.0224402i
$671$	331.347			0.0190634
$672$	−1769.13	−	176.837i	−0.101556	−	0.0101512i
$673$	−8889.23			−0.509145			−0.254572	−	0.967054i	$-0.581935\pi$
$673$	−8889.23			−0.509145			−0.254572	+	0.967054i	$0.581935\pi$
$674$	−3867.33	−	6698.41i	−0.221015	−	0.382809i
$675$	−1677.21	+	2905.02i	−0.0956384	+	0.165651i
$676$	−338.000	+	585.433i	−0.0192308	+	0.0333087i
$677$	12309.9	+	21321.4i	0.698831	+	1.21041i	0.968872	+	0.247562i	$0.0796295\pi$
$677$	12309.9	+	21321.4i	0.698831	+	1.21041i	−0.270041	+	0.962849i	$0.587037\pi$
$678$	12977.3			0.735087
$679$	−14436.8	+	20084.9i	−0.815954	+	1.13518i
$680$	175.596			0.00990267
$681$	5523.55	+	9567.07i	0.310812	+	0.538342i
$682$	−266.351	+	461.334i	−0.0149547	+	0.0259023i
$683$	−13653.8	+	23649.1i	−0.764933	+	1.32490i	0.175349	+	0.984506i	$0.443895\pi$
$683$	−13653.8	+	23649.1i	−0.764933	+	1.32490i	−0.940282	+	0.340396i	$0.889439\pi$
$684$	−225.436	−	390.466i	−0.0126020	−	0.0218272i
$685$	−217.621			−0.0121385
$686$	−2831.08	−	12385.5i	−0.157567	−	0.689328i
$687$	−10337.7			−0.574104
$688$	−2360.35	−	4088.25i	−0.130796	−	0.226545i
$689$	2356.80	−	4082.10i	0.130315	−	0.225712i
$690$	−207.145	+	358.786i	−0.0114288	+	0.0197953i
$691$	11719.9	+	20299.5i	0.645220	+	1.11755i	0.984251	+	0.176779i	$0.0565677\pi$
$691$	11719.9	+	20299.5i	0.645220	+	1.11755i	−0.339030	+	0.940775i	$0.610099\pi$
$692$	−6256.77			−0.343709
$693$	132.786	−	184.736i	0.00727869	−	0.0101263i
$694$	−10507.9			−0.574750
$695$	126.397	+	218.926i	0.00689857	+	0.0119487i
$696$	47.8064	−	82.8031i	0.00260359	−	0.00450955i
$697$	−5136.17	+	8896.11i	−0.279120	+	0.483449i
$698$	4793.05	+	8301.80i	0.259913	+	0.450183i
$699$	12520.0			0.677468
$700$	−9158.04	−	915.410i	−0.494487	−	0.0494275i
$701$	−6820.69			−0.367495			−0.183748	−	0.982973i	$-0.558823\pi$
$701$	−6820.69			−0.367495			−0.183748	+	0.982973i	$0.558823\pi$
$702$	351.000	+	607.950i	0.0188713	+	0.0326860i
$703$	−1137.01	+	1969.36i	−0.0610004	+	0.105656i
$704$	43.6773	−	75.6514i	0.00233828	−	0.00405003i
$705$	467.192	+	809.201i	0.0249581	+	0.0432287i
$706$	5917.71			0.315462
$707$	1858.53	+	4117.75i	0.0988646	+	0.219044i
$708$	−3739.43			−0.198498
$709$	5883.86	+	10191.1i	0.311668	+	0.539826i	0.978724	−	0.205183i	$-0.0657788\pi$
$709$	5883.86	+	10191.1i	0.311668	+	0.539826i	−0.667055	+	0.745008i	$0.732446\pi$
$710$	−65.8609	+	114.075i	−0.00348129	+	0.00602977i
$711$	−250.693	+	434.213i	−0.0132232	+	0.0229033i
$712$	−4408.91	−	7636.46i	−0.232066	−	0.401950i
$713$	15434.6			0.810704
$714$	1149.39	+	2546.58i	0.0602447	+	0.133478i
$715$	−15.4901			−0.000810208
$716$	−3403.37	−	5894.81i	−0.177640	−	0.307681i
$717$	9399.90	−	16281.1i	0.489604	−	0.848018i
$718$	−5045.28	+	8738.68i	−0.262240	+	0.454213i
$719$	13052.7	+	22608.0i	0.677031	+	1.17265i	0.975871	+	0.218349i	$0.0700671\pi$
$719$	13052.7	+	22608.0i	0.677031	+	1.17265i	−0.298840	+	0.954303i	$0.596600\pi$
$720$	125.710			0.00650683
$721$	21914.0	+	2190.46i	1.13193	+	0.113144i
$722$	−13404.3			−0.690936
$723$	6450.14	+	11172.0i	0.331789	+	0.574675i
$724$	−6961.30	+	12057.3i	−0.357341	+	0.618932i
$725$	247.474	−	428.637i	0.0126772	−	0.0219575i
$726$	−3987.41	−	6906.40i	−0.203838	−	0.353059i
$727$	3185.30			0.162498			0.0812492	−	0.996694i	$-0.474109\pi$
$727$	3185.30			0.162498			0.0812492	+	0.996694i	$0.474109\pi$
$728$	−1124.19	+	1564.00i	−0.0572323	+	0.0796232i
$729$	729.000			0.0370370
$730$	223.024	+	386.289i	0.0113075	+	0.0195852i
$731$	−3709.17	+	6424.47i	−0.187673	+	0.325058i
$732$	−1456.56	+	2522.84i	−0.0735465	+	0.127386i
$733$	−15213.1	−	26349.9i	−0.766590	−	1.32777i	−0.939402	−	0.342818i	$-0.888619\pi$
$733$	−15213.1	−	26349.9i	−0.766590	−	1.32777i	0.172812	−	0.984955i	$-0.444715\pi$
$734$	18487.3			0.929673
$735$	286.279	+	851.462i	0.0143667	+	0.0427301i
$736$	−2531.03			−0.126760
$737$	−175.650	−	304.236i	−0.00877906	−	0.0152058i
$738$	−3676.99	+	6368.73i	−0.183404	+	0.317664i
$739$	3431.25	−	5943.09i	0.170799	−	0.295833i	−0.767900	−	0.640569i	$-0.778698\pi$
$739$	3431.25	−	5943.09i	0.170799	−	0.295833i	0.938699	+	0.344737i	$0.112032\pi$
$740$	−317.016	−	549.088i	−0.0157483	−	0.0272769i
$741$	−488.444			−0.0242152
$742$	7838.70	−	10905.4i	0.387827	−	0.539556i
$743$	−10344.6			−0.510777			−0.255388	−	0.966839i	$-0.582203\pi$
$743$	−10344.6			−0.510777			−0.255388	+	0.966839i	$0.582203\pi$
$744$	−2341.69	−	4055.93i	−0.115391	−	0.199862i
$745$	−1034.23	+	1791.33i	−0.0508605	+	0.0880930i
$746$	−7918.55	+	13715.3i	−0.388631	+	0.673128i
$747$	−150.840	−	261.263i	−0.00738817	−	0.0127967i
$748$	−137.273			−0.00671017
$749$	5689.92	+	568.748i	0.277577	+	0.0277458i
$750$	1305.48			0.0635593
$751$	−14803.6	−	25640.6i	−0.719297	−	1.24586i	−0.961279	−	0.275578i	$-0.911131\pi$
$751$	−14803.6	−	25640.6i	−0.719297	−	1.24586i	0.241982	−	0.970281i	$-0.422203\pi$
$752$	−2854.23	+	4943.66i	−0.138408	+	0.239730i
$753$	2827.77	−	4897.84i	0.136852	−	0.237035i
$754$	−51.7903	−	89.7034i	−0.00250145	−	0.00433263i
$755$	−915.715			−0.0441408
$756$	822.847	+	1823.10i	0.0395855	+	0.0877055i
$757$	−2000.42			−0.0960456			−0.0480228	−	0.998846i	$-0.515292\pi$
$757$	−2000.42			−0.0960456			−0.0480228	+	0.998846i	$0.515292\pi$
$758$	5799.37	+	10044.8i	0.277893	+	0.481324i
$759$	161.937	−	280.482i	0.00774430	−	0.0134135i
$760$	−43.7337	+	75.7489i	−0.00208735	+	0.00361540i
$761$	8928.15	+	15464.0i	0.425290	+	0.736623i	0.996447	−	0.0842171i	$-0.0268389\pi$
$761$	8928.15	+	15464.0i	0.425290	+	0.736623i	−0.571158	+	0.820840i	$0.693506\pi$
$762$	−1913.94			−0.0909904
$763$	7135.64	+	15809.7i	0.338568	+	0.750130i
$764$	−8317.87			−0.393887
$765$	−98.7730	−	171.080i	−0.00466816	−	0.00808550i
$766$	−355.999	+	616.609i	−0.0167921	+	0.0290849i
$767$	−2025.52	+	3508.31i	−0.0953552	+	0.165160i
$768$	384.000	+	665.108i	0.0180422	+	0.0312500i
$769$	9259.72			0.434218			0.217109	−	0.976147i	$-0.430337\pi$
$769$	9259.72			0.434218			0.217109	+	0.976147i	$0.430337\pi$
$770$	−43.9168	−	4.38979i	−0.00205539	−	0.000205451i
$771$	−8273.65			−0.386470
$772$	−3109.42	−	5385.68i	−0.144962	−	0.251081i
$773$	−12200.8	+	21132.4i	−0.567699	+	0.983283i	0.429094	+	0.903260i	$0.358833\pi$
$773$	−12200.8	+	21132.4i	−0.567699	+	0.983283i	−0.996793	+	0.0800234i	$0.974500\pi$
$774$	−2655.40	+	4599.29i	−0.123316	+	0.213589i
$775$	−12122.0	−	20995.9i	−0.561850	−	0.973153i
$776$	10684.5			0.494268
$777$	5888.05	−	8191.62i	0.271857	−	0.378215i
$778$	−18138.4			−0.835852
$779$	−2558.41	−	4431.29i	−0.117669	−	0.203809i
$780$	68.0927	−	117.940i	0.00312578	−	0.00541401i
$781$	51.4871	−	89.1782i	0.00235897	−	0.00408585i
$782$	1988.69	+	3444.51i	0.0909405	+	0.157514i
$783$	−107.564			−0.00490937
$784$	−3630.45	+	4115.58i	−0.165381	+	0.187481i
$785$	−1816.05			−0.0825704
$786$	−2006.81	−	3475.90i	−0.0910695	−	0.157737i
$787$	−10707.4	+	18545.7i	−0.484976	+	0.840004i	−0.999851	−	0.0172619i	$-0.994505\pi$
$787$	−10707.4	+	18545.7i	−0.484976	+	0.840004i	0.514875	+	0.857265i	$0.327838\pi$
$788$	−442.859	+	767.055i	−0.0200206	+	0.0346767i
$789$	3429.42	+	5939.93i	0.154741	+	0.268019i
$790$	97.2671			0.00438052
$791$	23379.6	−	32526.3i	1.05092	−	1.46208i
$792$	−98.2740			−0.00440911
$793$	1577.94	+	2733.07i	0.0706612	+	0.122389i
$794$	−5017.21	+	8690.06i	−0.224249	+	0.388411i
$795$	−474.796	+	822.370i	−0.0211815	+	0.0366874i
$796$	1934.57	+	3350.77i	0.0861419	+	0.149202i
$797$	−31332.4			−1.39254			−0.696268	−	0.717781i	$-0.745158\pi$
$797$	−31332.4			−1.39254			−0.696268	+	0.717781i	$0.745158\pi$
$798$	−1384.81	−	138.421i	−0.0614307	−	0.00614042i
$799$	8970.53			0.397190
$800$	1987.81	+	3442.98i	0.0878495	+	0.152160i
$801$	−4960.02	+	8591.01i	−0.218794	+	0.378962i
$802$	−4914.28	+	8511.79i	−0.216371	+	0.374765i
$803$	−174.350	−	301.983i	−0.00766212	−	0.0132712i
$804$	3088.55			0.135478
$805$	526.076	+	1165.57i	0.0230332	+	0.0510323i
$806$	−5073.67			−0.221727
$807$	6968.58	+	12069.9i	0.303972	+	0.526495i
$808$	975.742	−	1690.03i	0.0424833	−	0.0735832i
$809$	−10441.4	+	18085.0i	−0.453769	+	0.785950i	−0.998616	−	0.0525845i	$-0.983254\pi$
$809$	−10441.4	+	18085.0i	−0.453769	+	0.785950i	0.544848	+	0.838535i	$0.316587\pi$
$810$	−70.7117	−	122.476i	−0.00306735	−	0.00531281i
$811$	18964.9			0.821143			0.410572	−	0.911828i	$-0.365329\pi$
$811$	18964.9			0.821143			0.410572	+	0.911828i	$0.365329\pi$
$812$	−121.412	−	268.999i	−0.00524718	−	0.0116256i
$813$	9803.62			0.422913
$814$	247.829	+	429.252i	0.0106712	+	0.0184831i
$815$	−350.091	+	606.375i	−0.0150468	+	0.0260618i
$816$	603.436	−	1045.18i	0.0258878	−	0.0448390i
$817$	−1847.60	−	3200.13i	−0.0791178	−	0.137036i
$818$	−8103.58			−0.346375
$819$	2156.13	+	215.520i	0.0919916	+	0.00919521i
$820$	1426.64			0.0607568
$821$	−3998.74	−	6926.01i	−0.169984	−	0.294421i	0.768430	−	0.639934i	$-0.221038\pi$
$821$	−3998.74	−	6926.01i	−0.169984	−	0.294421i	−0.938414	+	0.345513i	$0.887705\pi$
$822$	−747.853	+	1295.32i	−0.0317328	+	0.0549628i
$823$	−11648.7	+	20176.1i	−0.493374	+	0.854549i	−0.999971	−	0.00763436i	$-0.997570\pi$
$823$	−11648.7	+	20176.1i	−0.493374	+	0.854549i	0.506597	+	0.862183i	$0.330903\pi$
$824$	−4756.56	−	8238.61i	−0.201096	−	0.348308i
$825$	−508.723			−0.0214684
$826$	−6736.87	+	9372.54i	−0.283784	+	0.394809i
$827$	28133.7			1.18296			0.591479	−	0.806321i	$-0.298544\pi$
$827$	28133.7			1.18296			0.591479	+	0.806321i	$0.298544\pi$
$828$	1423.71	+	2465.93i	0.0597551	+	0.103499i
$829$	19171.8	−	33206.6i	0.803216	−	1.39121i	−0.114273	−	0.993449i	$-0.536454\pi$
$829$	19171.8	−	33206.6i	0.803216	−	1.39121i	0.917489	−	0.397761i	$-0.130213\pi$
$830$	−29.2625	+	50.6841i	−0.00122375	+	0.00211960i
$831$	−1402.46	−	2429.13i	−0.0585449	−	0.101403i
$832$	832.000			0.0346688
$833$	8453.47	+	1707.02i	0.351615	+	0.0710022i
$834$	1737.45			0.0721378
$835$	−476.223	−	824.842i	−0.0197370	−	0.0341854i
$836$	34.1890	−	59.2171i	0.00141441	−	0.00244984i
$837$	−2634.40	+	4562.92i	−0.108791	+	0.188432i
$838$	−7107.75	−	12311.0i	−0.292999	−	0.507489i
$839$	18531.3			0.762542			0.381271	−	0.924463i	$-0.375486\pi$
$839$	18531.3			0.762542			0.381271	+	0.924463i	$0.375486\pi$
$840$	226.476	−	315.080i	0.00930257	−	0.0129420i
$841$	−24373.1			−0.999349
$842$	−7169.00	−	12417.1i	−0.293421	−	0.508220i
$843$	−1651.46	+	2860.42i	−0.0674727	+	0.116866i
$844$	−10452.8	+	18104.9i	−0.426305	+	0.738382i
$845$	−73.7671	−	127.768i	−0.00300315	−	0.00520162i
$846$	6422.01			0.260985
$847$	−24493.9	−	2448.34i	−0.993649	−	0.0993222i
$848$	−5801.35			−0.234928
$849$	2890.34	+	5006.21i	0.116839	+	0.202371i
$850$	3123.73	−	5410.46i	0.126051	−	0.218326i
$851$	7180.64	−	12437.2i	0.289247	−	0.500990i
$852$	452.661	+	784.032i	0.0182018	+	0.0315264i
$853$	−33920.2			−1.36156			−0.680778	−	0.732490i	$-0.738358\pi$
$853$	−33920.2			−1.36156			−0.680778	+	0.732490i	$0.738358\pi$
$854$	3699.15	+	8195.83i	0.148223	+	0.328402i
$855$	98.4008			0.00393595
$856$	−1235.03	−	2139.14i	−0.0493137	−	0.0854138i
$857$	−16772.5	+	29050.8i	−0.668539	+	1.15794i	0.309774	+	0.950810i	$0.399747\pi$
$857$	−16772.5	+	29050.8i	−0.668539	+	1.15794i	−0.978313	+	0.207133i	$0.933587\pi$
$858$	−53.2318	+	92.2001i	−0.00211807	+	0.00366860i
$859$	9472.35	+	16406.6i	0.376243	+	0.651672i	0.990512	−	0.137425i	$-0.0438825\pi$
$859$	9472.35	+	16406.6i	0.376243	+	0.651672i	−0.614269	+	0.789096i	$0.710549\pi$
$860$	1030.28			0.0408513
$861$	9338.27	+	20689.8i	0.369625	+	0.818940i
$862$	−6016.10			−0.237714
$863$	14868.1	+	25752.3i	0.586460	+	1.01578i	0.994692	+	0.102901i	$0.0328124\pi$
$863$	14868.1	+	25752.3i	0.586460	+	1.01578i	−0.408231	+	0.912879i	$0.633854\pi$
$864$	432.000	−	748.246i	0.0170103	−	0.0294628i
$865$	682.757	−	1182.57i	0.0268375	−	0.0464839i
$866$	−2841.60	−	4921.79i	−0.111503	−	0.193128i
$867$	12842.5			0.503060
$868$	−14384.6	−	1437.84i	−0.562493	−	0.0562252i
$869$	−76.0390			−0.00296829
$870$	10.4335	+	18.0714i	0.000406587	+	0.000704229i
$871$	1672.96	−	2897.66i	0.0650818	−	0.112725i
$872$	3746.26	−	6488.71i	0.145487	−	0.251990i
$873$	−6010.05	−	10409.7i	−0.233000	−	0.403569i
$874$	−1981.20			−0.0766762
$875$	2351.93	−	3272.08i	0.0908683	−	0.126419i
$876$	3065.69			0.118242
$877$	−12832.0	−	22225.6i	−0.494076	−	0.855765i	0.505900	−	0.862592i	$-0.331160\pi$
$877$	−12832.0	−	22225.6i	−0.494076	−	0.855765i	−0.999977	+	0.00682663i	$0.997827\pi$
$878$	−13541.5	+	23454.5i	−0.520503	+	0.901538i
$879$	−1208.79	+	2093.69i	−0.0463840	+	0.0803394i
$880$	9.53240	+	16.5106i	0.000365156	+	0.000632468i
$881$	−30032.8			−1.14850			−0.574252	−	0.818679i	$-0.694707\pi$
$881$	−30032.8			−1.14850			−0.574252	+	0.818679i	$0.694707\pi$
$882$	6051.85	+	1222.06i	0.231039	+	0.0466541i
$883$	6717.80			0.256027			0.128013	−	0.991772i	$-0.459140\pi$
$883$	6717.80			0.256027			0.128013	+	0.991772i	$0.459140\pi$
$884$	−653.722	−	1132.28i	−0.0248722	−	0.0430800i
$885$	408.057	−	706.776i	0.0154991	−	0.0268452i
$886$	4345.81	−	7527.17i	0.164786	−	0.285418i
$887$	12705.3	+	22006.2i	0.480949	+	0.833028i	0.999761	−	0.0218601i	$-0.00695883\pi$
$887$	12705.3	+	22006.2i	0.480949	+	0.833028i	−0.518812	+	0.854888i	$0.673625\pi$
$888$	−4357.69			−0.164679
$889$	−3448.11	+	4797.11i	−0.130085	+	0.180979i
$890$	1924.45			0.0724807
$891$	55.2791	+	95.7463i	0.00207847	+	0.00360002i
$892$	−12683.7	+	21968.9i	−0.476102	+	0.824632i
$893$	−2234.18	+	3869.71i	−0.0837223	+	0.145011i
$894$	7108.22	+	12311.8i	0.265922	+	0.460590i
$895$	1485.54			0.0554818
$896$	2358.84	+	235.782i	0.0879501	+	0.00879123i
$897$	3084.70			0.114822
$898$	4142.72	+	7175.41i	0.153947	+	0.266644i
$899$	388.708	−	673.262i	0.0144206	−	0.0249773i
$900$	2236.28	−	3873.35i	0.0828253	−	0.143458i
$901$	4558.26	+	7895.14i	0.168543	+	0.291926i
$902$	−1115.29			−0.0411696
$903$	6743.78	+	14941.5i	0.248526	+	0.550633i
$904$	−17303.0			−0.636604
$905$	−1519.28	−	2631.46i	−0.0558038	−	0.0966550i
$906$	−3146.85	+	5450.50i	−0.115394	+	0.199868i
$907$	14325.1	−	24811.7i	0.524428	−	0.908336i	−0.475168	−	0.879895i	$-0.657613\pi$
$907$	14325.1	−	24811.7i	0.524428	−	0.908336i	0.999595	−	0.0284404i	$-0.00905408\pi$
$908$	−7364.73	−	12756.1i	−0.269171	−	0.466218i
$909$	−2195.42			−0.0801072
$910$	−172.932	−	383.146i	−0.00629959	−	0.0139573i
$911$	10504.4			0.382025			0.191012	−	0.981588i	$-0.438823\pi$
$911$	10504.4			0.382025			0.191012	+	0.981588i	$0.438823\pi$
$912$	300.581	+	520.621i	0.0109136	+	0.0189030i
$913$	22.8761	−	39.6225i	0.000829231	−	0.00143627i
$914$	−16226.1	+	28104.5i	−0.587213	+	1.01708i
$915$	−317.888	−	550.599i	−0.0114853	−	0.0198931i
$916$	13783.7			0.497189
$917$	−12327.5	−	1232.22i	−0.443935	−	0.0443745i
$918$	−1357.73			−0.0488146
$919$	−22015.2	−	38131.5i	−0.790224	−	1.36871i	−0.925828	−	0.377945i	$-0.876631\pi$
$919$	−22015.2	−	38131.5i	−0.790224	−	1.36871i	0.135604	−	0.990763i	$-0.456703\pi$
$920$	276.194	−	478.381i	0.00989764	−	0.0171432i
$921$	3039.96	−	5265.36i	0.108762	−	0.188382i
$922$	777.223	+	1346.19i	0.0277619	+	0.0480850i
$923$	980.766			0.0349754
$924$	−177.048	+	246.315i	−0.00630353	+	0.00876966i
$925$	−22557.9			−0.801839
$926$	14826.0	+	25679.4i	0.526147	+	0.911313i
$927$	−5351.13	+	9268.44i	−0.189595	+	0.328388i
$928$	−63.7419	+	110.404i	−0.00225477	+	0.00390538i
$929$	3134.27	+	5428.71i	0.110691	+	0.191722i	0.916049	−	0.401066i	$-0.131360\pi$
$929$	3134.27	+	5428.71i	0.110691	+	0.191722i	−0.805358	+	0.592789i	$0.798027\pi$
$930$	1022.13			0.0360397
$931$	−2841.78	+	3221.52i	−0.100038	+	0.113406i
$932$	−16693.3			−0.586705
$933$	2373.82	+	4111.58i	0.0832962	+	0.144273i
$934$	15645.9	−	27099.5i	0.548125	−	0.949381i
$935$	14.9797	−	25.9455i	0.000523943	−	0.000907497i
$936$	−468.000	−	810.600i	−0.0163430	−	0.0283069i
$937$	20424.6			0.712106			0.356053	−	0.934466i	$-0.384122\pi$
$937$	20424.6			0.712106			0.356053	+	0.934466i	$0.384122\pi$
$938$	5564.26	−	7741.17i	0.193688	−	0.269465i
$939$	8169.55			0.283923
$940$	−622.923	−	1078.93i	−0.0216144	−	0.0374372i
$941$	12682.6	−	21966.9i	0.439363	−	0.760999i	−0.558278	−	0.829654i	$-0.688538\pi$
$941$	12682.6	−	21966.9i	0.439363	−	0.760999i	0.997640	+	0.0686554i	$0.0218709\pi$
$942$	−6240.85	+	10809.5i	−0.215858	+	0.373877i
$943$	16157.3	+	27985.2i	0.557956	+	0.966408i
$944$	4985.90			0.171904
$945$	−434.368	−	43.4181i	−0.0149524	−	0.00149460i
$946$	−805.422			−0.0276813
$947$	−13926.3	−	24121.0i	−0.477870	−	0.827694i	0.521809	−	0.853063i	$-0.325258\pi$
$947$	−13926.3	−	24121.0i	−0.477870	−	0.827694i	−0.999678	+	0.0253682i	$0.991924\pi$
$948$	334.258	−	578.951i	0.0114517	−	0.0198349i
$949$	1660.58	−	2876.21i	0.0568016	−	0.0983832i
$950$	1555.98	+	2695.04i	0.0531396	+	0.0920406i
$951$	−27037.3			−0.921918
$952$	−1532.52	−	3395.43i	−0.0521734	−	0.115595i
$953$	23126.7			0.786095			0.393047	−	0.919518i	$-0.371421\pi$
$953$	23126.7			0.786095			0.393047	+	0.919518i	$0.371421\pi$
$954$	3263.26	+	5652.14i	0.110746	+	0.191818i
$955$	907.670	−	1572.13i	0.0307555	−	0.0532701i
$956$	−12533.2	+	21708.1i	−0.424009	+	0.734405i
$957$	−8.15647	−	14.1274i	−0.000275508	−	0.000477194i
$958$	20037.2			0.675755
$959$	1899.28	+	4208.05i	0.0639532	+	0.141694i
$960$	−167.613			−0.00563508
$961$	−4144.52	−	7178.53i	−0.139120	−	0.240963i
$962$	−2360.42	+	4088.36i	−0.0791090	+	0.137021i
$963$	−1389.41	+	2406.53i	−0.0464934	+	0.0805289i
$964$	−8600.19	−	14896.0i	−0.287337	−	0.497683i
$965$	1357.24			0.0452757
$966$	8745.55	+	874.179i	0.291287	+	0.0291162i
$967$	−47434.1			−1.57743			−0.788717	−	0.614756i	$-0.789254\pi$
$967$	−47434.1			−1.57743			−0.788717	+	0.614756i	$0.789254\pi$
$968$	5316.55	+	9208.53i	0.176529	+	0.305758i
$969$	472.347	−	818.129i	0.0156594	−	0.0271229i
$970$	−1165.93	+	2019.45i	−0.0385935	+	0.0668459i
$971$	3395.07	+	5880.43i	0.112207	+	0.194348i	0.916660	−	0.399668i	$-0.130875\pi$
$971$	3395.07	+	5880.43i	0.112207	+	0.194348i	−0.804453	+	0.594016i	$0.797541\pi$
$972$	−972.000			−0.0320750
$973$	3130.15	−	4354.76i	0.103133	−	0.143481i
$974$	25870.3			0.851065
$975$	−2422.64	−	4196.13i	−0.0795759	−	0.137830i
$976$	1942.08	−	3363.78i	0.0636931	−	0.110320i
$977$	18648.8	−	32300.7i	0.610675	−	1.05772i	−0.380452	−	0.924801i	$-0.624232\pi$
$977$	18648.8	−	32300.7i	0.610675	−	1.05772i	0.991127	−	0.132919i	$-0.0424350\pi$
$978$	2406.17	+	4167.61i	0.0786716	+	0.136263i
$979$	−1504.45			−0.0491138
$980$	−381.705	−	1135.28i	−0.0124420	−	0.0370054i
$981$	−8429.08			−0.274332
$982$	786.588	+	1362.41i	0.0255611	+	0.0442732i
$983$	6288.55	−	10892.1i	0.204042	−	0.353411i	−0.745785	−	0.666187i	$-0.767925\pi$
$983$	6288.55	−	10892.1i	0.204042	−	0.353411i	0.949827	+	0.312775i	$0.101259\pi$
$984$	4902.65	−	8491.64i	0.158832	−	0.275105i
$985$	−96.6522	−	167.407i	−0.00312649	−	0.00541525i
$986$	200.334			0.00647052
$987$	11569.8	−	16096.2i	0.373120	−	0.519095i
$988$	651.258			0.0209709
$989$	11668.2	+	20210.0i	0.375155	+	0.649787i
$990$	10.7239	−	18.5744i	0.000344272	−	0.000596297i
$991$	1362.15	−	2359.31i	0.0436631	−	0.0756267i	−0.843368	−	0.537337i	$-0.819431\pi$
$991$	1362.15	−	2359.31i	0.0436631	−	0.0756267i	0.887031	+	0.461710i	$0.152764\pi$
$992$	3122.26	+	5407.91i	0.0999312	+	0.173086i
$993$	−4823.76			−0.154156
$994$	2780.61	+	277.942i	0.0887280	+	0.00886899i
$995$	−844.423			−0.0269045
$996$	201.121	+	348.351i	0.00639834	+	0.0110823i
$997$	5988.30	−	10372.0i	0.190222	−	0.329474i	−0.755102	−	0.655608i	$-0.772413\pi$
$997$	5988.30	−	10372.0i	0.190222	−	0.329474i	0.945324	+	0.326134i	$0.105746\pi$
$998$	−10076.9	+	17453.7i	−0.319618	+	0.553595i
$999$	2451.20	+	4245.61i	0.0776302	+	0.134460i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.4.i.a.235.1	yes	4
7.2	even	3	inner	546.4.i.a.79.1	✓	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.4.i.a.79.1	✓	4	7.2	even	3	inner
546.4.i.a.235.1	yes	4	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	546.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} +(-0.436492 - 0.756026i) q^{5} -6.00000 q^{6} +(-10.8095 + 15.0385i) q^{7} +8.00000 q^{8} +(-4.50000 - 7.79423i) q^{9} +(-0.872983 + 1.51205i) q^{10} +(0.682458 - 1.18205i) q^{11} +(6.00000 + 10.3923i) q^{12} +13.0000 q^{13} +(36.8569 + 3.68410i) q^{14} -2.61895 q^{15} +(-8.00000 - 13.8564i) q^{16} +(-12.5716 + 21.7746i) q^{17} +(-9.00000 + 15.5885i) q^{18} +(-6.26210 - 10.8463i) q^{19} +3.49193 q^{20} +(22.8569 + 50.6415i) q^{21} -2.72983 q^{22} +(39.5474 + 68.4981i) q^{23} +(12.0000 - 20.7846i) q^{24} +(62.1190 - 107.593i) q^{25} +(-13.0000 - 22.5167i) q^{26} -27.0000 q^{27} +(-30.4758 - 67.5220i) q^{28} +3.98387 q^{29} +(2.61895 + 4.53615i) q^{30} +(97.5706 - 168.997i) q^{31} +(-16.0000 + 27.7128i) q^{32} +(-2.04738 - 3.54616i) q^{33} +50.2863 q^{34} +(16.0877 + 1.60808i) q^{35} +36.0000 q^{36} +(-90.7853 - 157.245i) q^{37} +(-12.5242 + 21.6926i) q^{38} +(19.5000 - 33.7750i) q^{39} +(-3.49193 - 6.04821i) q^{40} +408.554 q^{41} +(64.8569 - 90.2308i) q^{42} +295.044 q^{43} +(2.72983 + 4.72821i) q^{44} +(-3.92843 + 6.80423i) q^{45} +(79.0948 - 136.996i) q^{46} +(-178.389 - 308.979i) q^{47} -48.0000 q^{48} +(-109.310 - 325.116i) q^{49} -248.476 q^{50} +(37.7147 + 65.3238i) q^{51} +(-26.0000 + 45.0333i) q^{52} +(181.292 - 314.008i) q^{53} +(27.0000 + 46.7654i) q^{54} -1.19155 q^{55} +(-86.4758 + 120.308i) q^{56} -37.5726 q^{57} +(-3.98387 - 6.90026i) q^{58} +(-155.809 + 269.870i) q^{59} +(5.23790 - 9.07231i) q^{60} +(121.380 + 210.236i) q^{61} -390.282 q^{62} +(165.856 + 16.5785i) q^{63} +64.0000 q^{64} +(-5.67439 - 9.82833i) q^{65} +(-4.09475 + 7.09232i) q^{66} +(128.690 - 222.897i) q^{67} +(-50.2863 - 87.0984i) q^{68} +237.284 q^{69} +(-13.3024 - 29.4728i) q^{70} +75.4435 q^{71} +(-36.0000 - 62.3538i) q^{72} +(127.737 - 221.247i) q^{73} +(-181.571 + 314.489i) q^{74} +(-186.357 - 322.780i) q^{75} +50.0968 q^{76} +(10.3992 + 23.0405i) q^{77} -78.0000 q^{78} +(-27.8548 - 48.2459i) q^{79} +(-6.98387 + 12.0964i) q^{80} +(-40.5000 + 70.1481i) q^{81} +(-408.554 - 707.637i) q^{82} +33.5201 q^{83} +(-221.141 - 22.1046i) q^{84} +21.9496 q^{85} +(-295.044 - 511.032i) q^{86} +(5.97580 - 10.3504i) q^{87} +(5.45967 - 9.45642i) q^{88} +(-551.114 - 954.557i) q^{89} +15.7137 q^{90} +(-140.523 + 195.500i) q^{91} -316.379 q^{92} +(-292.712 - 506.991i) q^{93} +(-356.778 + 617.958i) q^{94} +(-5.46671 + 9.46862i) q^{95} +(48.0000 + 83.1384i) q^{96} +1335.57 q^{97} +(-453.806 + 514.447i) q^{98} -12.2843 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 4 q^{2} + 6 q^{3} - 8 q^{4} + 6 q^{5} - 24 q^{6} - 20 q^{7} + 32 q^{8} - 18 q^{9} + 12 q^{10} - 36 q^{11} + 24 q^{12} + 52 q^{13} + 8 q^{14} + 36 q^{15} - 32 q^{16} - 120 q^{17} - 36 q^{18} - 118 q^{19}+ \cdots + 648 q^{99}+O(q^{100}) \) 4 * q - 4 * q^2 + 6 * q^3 - 8 * q^4 + 6 * q^5 - 24 * q^6 - 20 * q^7 + 32 * q^8 - 18 * q^9 + 12 * q^10 - 36 * q^11 + 24 * q^12 + 52 * q^13 + 8 * q^14 + 36 * q^15 - 32 * q^16 - 120 * q^17 - 36 * q^18 - 118 * q^19 - 48 * q^20 - 48 * q^21 + 144 * q^22 + 42 * q^23 + 48 * q^24 + 202 * q^25 - 52 * q^26 - 108 * q^27 + 64 * q^28 - 108 * q^29 - 36 * q^30 - 28 * q^31 - 64 * q^32 + 108 * q^33 + 480 * q^34 + 258 * q^35 + 144 * q^36 - 154 * q^37 - 236 * q^38 + 78 * q^39 + 48 * q^40 + 1092 * q^41 + 120 * q^42 - 400 * q^43 - 144 * q^44 + 54 * q^45 + 84 * q^46 - 822 * q^47 - 192 * q^48 - 902 * q^49 - 808 * q^50 + 360 * q^51 - 104 * q^52 + 90 * q^53 + 108 * q^54 - 516 * q^55 - 160 * q^56 - 708 * q^57 + 108 * q^58 - 600 * q^59 - 72 * q^60 + 44 * q^61 + 112 * q^62 + 36 * q^63 + 256 * q^64 + 78 * q^65 + 216 * q^66 + 50 * q^67 - 480 * q^68 + 252 * q^69 - 456 * q^70 - 132 * q^71 - 144 * q^72 - 70 * q^73 - 308 * q^74 - 606 * q^75 + 944 * q^76 + 1188 * q^77 - 312 * q^78 + 1004 * q^79 + 96 * q^80 - 162 * q^81 - 1092 * q^82 - 1632 * q^83 - 48 * q^84 - 1260 * q^85 + 400 * q^86 - 162 * q^87 - 288 * q^88 + 282 * q^89 - 216 * q^90 - 260 * q^91 - 336 * q^92 + 84 * q^93 - 1644 * q^94 + 714 * q^95 + 192 * q^96 + 2972 * q^97 - 328 * q^98 + 648 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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