LMFDB - Embedded newform 43.4.c.a.6.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [43,4,Mod(6,43)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(43, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("43.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 43 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	43.c (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:	$2.53708213025$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{3})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - x^{19} + 60 x^{18} - 25 x^{17} + 2336 x^{16} - 645 x^{15} + 52478 x^{14} - 2415 x^{13} + \cdots + 589824 $ x^20 - x^19 + 60x^18 - 25x^17 + 2336x^16 - 645x^15 + 52478x^14 - 2415x^13 + 850704x^12 - 4147x^11 + 8670544x^10 + 873865x^9 + 62344097x^8 + 3655316x^7 + 215661012x^6 + 43840208x^5 + 507687824x^4 - 3907840x^3 + 17517568x^2 + 245760x + 589824
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{6}\cdot 3 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			6.3
Root			$1.77920 - 3.08166i$ of defining polynomial
Character	$\chi$	$=$	43.6
Dual form			43.4.c.a.36.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-3.55840 q^{2} +(0.194544 - 0.336960i) q^{3} +4.66219 q^{4} +(0.863899 - 1.49632i) q^{5} +(-0.692264 + 1.19904i) q^{6} +(10.5931 + 18.3477i) q^{7} +11.8773 q^{8} +(13.4243 + 23.2516i) q^{9} +O(q^{10})$	\(q-3.55840 q^{2} +(0.194544 - 0.336960i) q^{3} +4.66219 q^{4} +(0.863899 - 1.49632i) q^{5} +(-0.692264 + 1.19904i) q^{6} +(10.5931 + 18.3477i) q^{7} +11.8773 q^{8} +(13.4243 + 23.2516i) q^{9} +(-3.07410 + 5.32449i) q^{10} +23.7473 q^{11} +(0.907001 - 1.57097i) q^{12} +(15.0918 + 26.1397i) q^{13} +(-37.6943 - 65.2885i) q^{14} +(-0.336133 - 0.582199i) q^{15} -79.5615 q^{16} +(-25.8318 - 44.7420i) q^{17} +(-47.7690 - 82.7384i) q^{18} +(-14.6223 + 25.3265i) q^{19} +(4.02766 - 6.97612i) q^{20} +8.24326 q^{21} -84.5025 q^{22} +(46.7486 - 80.9709i) q^{23} +(2.31065 - 4.00216i) q^{24} +(61.0074 + 105.668i) q^{25} +(-53.7025 - 93.0155i) q^{26} +20.9518 q^{27} +(49.3869 + 85.5406i) q^{28} +(29.8117 + 51.6354i) q^{29} +(1.19609 + 2.07169i) q^{30} +(-56.7895 + 98.3623i) q^{31} +188.093 q^{32} +(4.61990 - 8.00190i) q^{33} +(91.9198 + 159.210i) q^{34} +36.6053 q^{35} +(62.5867 + 108.403i) q^{36} +(-34.3468 + 59.4904i) q^{37} +(52.0318 - 90.1218i) q^{38} +11.7440 q^{39} +(10.2607 - 17.7721i) q^{40} +53.9480 q^{41} -29.3328 q^{42} +(28.8941 - 280.486i) q^{43} +110.715 q^{44} +46.3890 q^{45} +(-166.350 + 288.127i) q^{46} -455.571 q^{47} +(-15.4782 + 26.8090i) q^{48} +(-52.9259 + 91.6704i) q^{49} +(-217.088 - 376.008i) q^{50} -20.1017 q^{51} +(70.3607 + 121.868i) q^{52} +(331.355 - 573.924i) q^{53} -74.5550 q^{54} +(20.5153 - 35.5336i) q^{55} +(125.816 + 217.921i) q^{56} +(5.68934 + 9.85423i) q^{57} +(-106.082 - 183.739i) q^{58} -457.110 q^{59} +(-1.56711 - 2.71432i) q^{60} +(303.441 + 525.575i) q^{61} +(202.080 - 350.012i) q^{62} +(-284.409 + 492.611i) q^{63} -32.8190 q^{64} +52.1511 q^{65} +(-16.4394 + 28.4739i) q^{66} +(214.223 - 371.045i) q^{67} +(-120.433 - 208.596i) q^{68} +(-18.1893 - 31.5048i) q^{69} -130.256 q^{70} +(69.9564 + 121.168i) q^{71} +(159.444 + 276.165i) q^{72} +(-240.962 - 417.359i) q^{73} +(122.219 - 211.690i) q^{74} +47.4744 q^{75} +(-68.1718 + 118.077i) q^{76} +(251.557 + 435.710i) q^{77} -41.7900 q^{78} +(-552.271 - 956.561i) q^{79} +(-68.7331 + 119.049i) q^{80} +(-358.380 + 620.733i) q^{81} -191.968 q^{82} +(628.529 - 1088.64i) q^{83} +38.4317 q^{84} -89.2643 q^{85} +(-102.817 + 998.079i) q^{86} +23.1987 q^{87} +282.053 q^{88} +(-312.270 + 540.868i) q^{89} -165.070 q^{90} +(-319.736 + 553.799i) q^{91} +(217.951 - 377.502i) q^{92} +(22.0961 + 38.2716i) q^{93} +1621.10 q^{94} +(25.2643 + 43.7591i) q^{95} +(36.5924 - 63.3799i) q^{96} +1121.21 q^{97} +(188.331 - 326.200i) q^{98} +(318.792 + 552.163i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

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

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 $

$2$	−3.55840			−1.25808			−0.629042	−	0.777372i	$-0.716553\pi$
$2$	−3.55840			−1.25808			−0.629042	+	0.777372i	$0.716553\pi$
$3$	0.194544	−	0.336960i	0.0374400	−	0.0648480i	−0.846698	−	0.532073i	$-0.821413\pi$
$3$	0.194544	−	0.336960i	0.0374400	−	0.0648480i	0.884138	+	0.467225i	$0.154746\pi$
$4$	4.66219			0.582774
$5$	0.863899	−	1.49632i	0.0772695	−	0.133835i	−0.824801	−	0.565422i	$-0.808713\pi$
$5$	0.863899	−	1.49632i	0.0772695	−	0.133835i	0.902071	+	0.431588i	$0.142046\pi$
$6$	−0.692264	+	1.19904i	−0.0471026	+	0.0815841i
$7$	10.5931	+	18.3477i	0.571972	+	0.990684i	0.996363	+	0.0852052i	$0.0271546\pi$
$7$	10.5931	+	18.3477i	0.571972	+	0.990684i	−0.424392	+	0.905479i	$0.639512\pi$
$8$	11.8773			0.524905
$9$	13.4243	+	23.2516i	0.497196	+	0.861170i
$10$	−3.07410	+	5.32449i	−0.0972115	+	0.168375i
$11$	23.7473			0.650917			0.325459	−	0.945556i	$-0.394481\pi$
$11$	23.7473			0.650917			0.325459	+	0.945556i	$0.394481\pi$
$12$	0.907001	−	1.57097i	0.0218190	−	0.0377917i
$13$	15.0918	+	26.1397i	0.321977	+	0.557681i	0.980896	−	0.194533i	$-0.0623192\pi$
$13$	15.0918	+	26.1397i	0.321977	+	0.557681i	−0.658919	+	0.752214i	$0.728986\pi$
$14$	−37.6943	−	65.2885i	−0.719588	−	1.24636i
$15$	−0.336133	−	0.582199i	−0.00578594	−	0.0100215i
$16$	−79.5615			−1.24315
$17$	−25.8318	−	44.7420i	−0.368537	−	0.638325i	0.620800	−	0.783969i	$-0.286808\pi$
$17$	−25.8318	−	44.7420i	−0.368537	−	0.638325i	−0.989337	+	0.145644i	$0.953475\pi$
$18$	−47.7690	−	82.7384i	−0.625515	−	1.08342i
$19$	−14.6223	+	25.3265i	−0.176557	+	0.305805i	−0.940699	−	0.339243i	$-0.889829\pi$
$19$	−14.6223	+	25.3265i	−0.176557	+	0.305805i	0.764142	+	0.645048i	$0.223163\pi$
$20$	4.02766	−	6.97612i	0.0450306	−	0.0779953i
$21$	8.24326			0.0856584
$22$	−84.5025			−0.818908
$23$	46.7486	−	80.9709i	0.423815	−	0.734070i	−0.572494	−	0.819909i	$-0.694024\pi$
$23$	46.7486	−	80.9709i	0.423815	−	0.734070i	0.996309	+	0.0858394i	$0.0273572\pi$
$24$	2.31065	−	4.00216i	0.0196525	−	0.0340390i
$25$	61.0074	+	105.668i	0.488059	+	0.845343i
$26$	−53.7025	−	93.0155i	−0.405074	−	0.701609i
$27$	20.9518			0.149340
$28$	49.3869	+	85.5406i	0.333330	+	0.577345i
$29$	29.8117	+	51.6354i	0.190893	+	0.330636i	0.945546	−	0.325487i	$-0.105528\pi$
$29$	29.8117	+	51.6354i	0.190893	+	0.330636i	−0.754654	+	0.656123i	$0.772195\pi$
$30$	1.19609	+	2.07169i	0.00727919	+	0.0126079i
$31$	−56.7895	+	98.3623i	−0.329022	+	0.569884i	−0.982318	−	0.187219i	$-0.940053\pi$
$31$	−56.7895	+	98.3623i	−0.329022	+	0.569884i	0.653296	+	0.757103i	$0.273386\pi$
$32$	188.093			1.03908
$33$	4.61990	−	8.00190i	0.0243703	−	0.0422107i
$34$	91.9198	+	159.210i	0.463651	+	0.803066i
$35$	36.6053			0.176784
$36$	62.5867	+	108.403i	0.289753	+	0.501867i
$37$	−34.3468	+	59.4904i	−0.152610	+	0.264329i	−0.932186	−	0.361979i	$-0.882101\pi$
$37$	−34.3468	+	59.4904i	−0.152610	+	0.264329i	0.779576	+	0.626308i	$0.215435\pi$
$38$	52.0318	−	90.1218i	0.222123	−	0.384728i
$39$	11.7440			0.0482193
$40$	10.2607	−	17.7721i	0.0405592	−	0.0702505i
$41$	53.9480			0.205494			0.102747	−	0.994708i	$-0.467237\pi$
$41$	53.9480			0.205494			0.102747	+	0.994708i	$0.467237\pi$
$42$	−29.3328			−0.107765
$43$	28.8941	−	280.486i	0.102472	−	0.994736i
$43$	28.8941	−	280.486i	0.102472	−	0.994736i
$44$	110.715			0.379338
$45$	46.3890			0.153672
$46$	−166.350	+	288.127i	−0.533195	+	0.923521i
$47$	−455.571			−1.41387			−0.706935	−	0.707279i	$-0.749923\pi$
$47$	−455.571			−1.41387			−0.706935	+	0.707279i	$0.749923\pi$
$48$	−15.4782	+	26.8090i	−0.0465435	+	0.0806156i
$49$	−52.9259	+	91.6704i	−0.154303	+	0.267261i
$50$	−217.088	−	376.008i	−0.614019	−	1.06351i
$51$	−20.1017			−0.0551921
$52$	70.3607	+	121.868i	0.187640	+	0.325002i
$53$	331.355	−	573.924i	0.858776	−	1.48744i	−0.0143217	−	0.999897i	$-0.504559\pi$
$53$	331.355	−	573.924i	0.858776	−	1.48744i	0.873097	−	0.487546i	$-0.162108\pi$
$54$	−74.5550			−0.187882
$55$	20.5153	−	35.5336i	0.0502961	−	0.0871153i
$56$	125.816	+	217.921i	0.300231	+	0.520015i
$57$	5.68934	+	9.85423i	0.0132206	+	0.0228987i
$58$	−106.082	−	183.739i	−0.240159	−	0.415968i
$59$	−457.110			−1.00866			−0.504328	−	0.863512i	$-0.668260\pi$
$59$	−457.110			−1.00866			−0.504328	+	0.863512i	$0.668260\pi$
$60$	−1.56711	−	2.71432i	−0.00337189	−	0.00584029i
$61$	303.441	+	525.575i	0.636911	+	1.10316i	0.986107	+	0.166113i	$0.0531216\pi$
$61$	303.441	+	525.575i	0.636911	+	1.10316i	−0.349195	+	0.937050i	$0.613545\pi$
$62$	202.080	−	350.012i	0.413938	−	0.716961i
$63$	−284.409	+	492.611i	−0.568765	+	0.985129i
$64$	−32.8190			−0.0640996
$65$	52.1511			0.0995160
$66$	−16.4394	+	28.4739i	−0.0306599	+	0.0531045i
$67$	214.223	−	371.045i	0.390620	−	0.676573i	−0.601912	−	0.798563i	$-0.705594\pi$
$67$	214.223	−	371.045i	0.390620	−	0.676573i	0.992531	+	0.121989i	$0.0389274\pi$
$68$	−120.433	−	208.596i	−0.214774	−	0.371999i
$69$	−18.1893	−	31.5048i	−0.0317353	−	0.0549671i
$70$	−130.256			−0.222409
$71$	69.9564	+	121.168i	0.116934	+	0.202535i	0.918551	−	0.395302i	$-0.129360\pi$
$71$	69.9564	+	121.168i	0.116934	+	0.202535i	−0.801617	+	0.597837i	$0.796027\pi$
$72$	159.444	+	276.165i	0.260981	+	0.452033i
$73$	−240.962	−	417.359i	−0.386336	−	0.669153i	0.605618	−	0.795756i	$-0.292926\pi$
$73$	−240.962	−	417.359i	−0.386336	−	0.669153i	−0.991954	+	0.126603i	$0.959593\pi$
$74$	122.219	−	211.690i	0.191996	−	0.332547i
$75$	47.4744			0.0730917
$76$	−68.1718	+	118.077i	−0.102893	+	0.178215i
$77$	251.557	+	435.710i	0.372306	+	0.644853i
$78$	−41.7900			−0.0606639
$79$	−552.271	−	956.561i	−0.786523	−	1.36230i	−0.928085	−	0.372368i	$-0.878546\pi$
$79$	−552.271	−	956.561i	−0.786523	−	1.36230i	0.141563	−	0.989929i	$-0.454787\pi$
$80$	−68.7331	+	119.049i	−0.0960575	+	0.166376i
$81$	−358.380	+	620.733i	−0.491605	+	0.851485i
$82$	−191.968			−0.258529
$83$	628.529	−	1088.64i	0.831205	−	1.43969i	−0.0658778	−	0.997828i	$-0.520985\pi$
$83$	628.529	−	1088.64i	0.831205	−	1.43969i	0.897083	−	0.441862i	$-0.145682\pi$
$84$	38.4317			0.0499195
$85$	−89.2643			−0.113907
$86$	−102.817	+	998.079i	−0.128919	+	1.25146i
$87$	23.1987			0.0285881
$88$	282.053			0.341670
$89$	−312.270	+	540.868i	−0.371916	+	0.644178i	−0.989860	−	0.142044i	$-0.954633\pi$
$89$	−312.270	+	540.868i	−0.371916	+	0.644178i	0.617944	+	0.786222i	$0.287966\pi$
$90$	−165.070			−0.193333
$91$	−319.736	+	553.799i	−0.368324	+	0.637955i
$92$	217.951	−	377.502i	0.246988	−	0.427797i
$93$	22.0961	+	38.2716i	0.0246372	+	0.0426729i
$94$	1621.10			1.77877
$95$	25.2643	+	43.7591i	0.0272849	+	0.0472588i
$96$	36.5924	−	63.3799i	0.0389031	−	0.0673822i
$97$	1121.21			1.17362			0.586812	−	0.809723i	$-0.300383\pi$
$97$	1121.21			1.17362			0.586812	+	0.809723i	$0.300383\pi$
$98$	188.331	−	326.200i	0.194126	−	0.336236i
$99$	318.792	+	552.163i	0.323634	+	0.560550i
$100$	284.428	+	492.644i	0.284428	+	0.492644i
$101$	469.250	+	812.764i	0.462298	+	0.800724i	0.999075	−	0.0430005i	$-0.0136917\pi$
$101$	469.250	+	812.764i	0.462298	+	0.800724i	−0.536777	+	0.843724i	$0.680358\pi$
$102$	71.5298			0.0694363
$103$	−546.509	−	946.581i	−0.522807	−	0.905528i	−0.999648	−	0.0265383i	$-0.991552\pi$
$103$	−546.509	−	946.581i	−0.522807	−	0.905528i	0.476841	−	0.878990i	$-0.341782\pi$
$104$	179.249	+	310.468i	0.169008	+	0.292730i
$105$	7.12135	−	12.3345i	0.00661878	−	0.0114641i
$106$	−1179.09	+	2042.25i	−1.08041	+	1.87133i
$107$	−686.795			−0.620513			−0.310257	−	0.950653i	$-0.600415\pi$
$107$	−686.795			−0.620513			−0.310257	+	0.950653i	$0.600415\pi$
$108$	97.6814			0.0870315
$109$	757.376	−	1311.81i	0.665537	−	1.15274i	−0.313603	−	0.949554i	$-0.601536\pi$
$109$	757.376	−	1311.81i	0.665537	−	1.15274i	0.979140	−	0.203189i	$-0.0651306\pi$
$110$	−73.0016	+	126.442i	−0.0632766	+	0.109598i
$111$	13.3639	+	23.1470i	0.0114274	+	0.0197929i
$112$	−842.800	−	1459.77i	−0.711046	−	1.23157i
$113$	−825.248			−0.687016			−0.343508	−	0.939150i	$-0.611615\pi$
$113$	−825.248			−0.687016			−0.343508	+	0.939150i	$0.611615\pi$
$114$	−20.2449	−	35.0653i	−0.0166326	−	0.0288085i
$115$	−80.7721	−	139.901i	−0.0654960	−	0.113442i
$116$	138.988	+	240.734i	0.111247	+	0.192686i
$117$	−405.193	+	701.815i	−0.320172	+	0.554554i
$118$	1626.58			1.26897
$119$	547.276	−	947.909i	0.421586	−	0.730208i
$120$	−3.99233	−	6.91492i	−0.00303707	−	0.00526036i
$121$	−767.064			−0.576307
$122$	−1079.76	−	1870.20i	−0.801287	−	1.38787i
$123$	10.4953	−	18.1783i	0.00769370	−	0.0133259i
$124$	−264.763	+	458.584i	−0.191746	+	0.332113i
$125$	426.792			0.305387
$126$	1012.04	−	1752.90i	0.715553	−	1.23937i
$127$	−1637.13			−1.14387			−0.571936	−	0.820298i	$-0.693808\pi$
$127$	−1637.13			−1.14387			−0.571936	+	0.820298i	$0.693808\pi$
$128$	−1387.96			−0.958436
$129$	−88.8912	−	64.3029i	−0.0606700	−	0.0438880i
$130$	−185.574			−0.125199
$131$	−2493.85			−1.66327			−0.831636	−	0.555321i	$-0.812596\pi$
$131$	−2493.85			−1.66327			−0.831636	+	0.555321i	$0.812596\pi$
$132$	21.5388	−	37.3064i	0.0142024	−	0.0245993i
$133$	−619.578			−0.403942
$134$	−762.291	+	1320.33i	−0.491432	+	0.851186i
$135$	18.1003	−	31.3506i	0.0115394	−	0.0199869i
$136$	−306.811	−	531.412i	−0.193447	−	0.335060i
$137$	2800.85			1.74666			0.873331	−	0.487128i	$-0.161955\pi$
$137$	2800.85			1.74666			0.873331	+	0.487128i	$0.161955\pi$
$138$	64.7248	+	112.107i	0.0399256	+	0.0691532i
$139$	664.380	−	1150.74i	0.405410	−	0.702191i	−0.588959	−	0.808163i	$-0.700462\pi$
$139$	664.380	−	1150.74i	0.405410	−	0.702191i	0.994369	+	0.105972i	$0.0337954\pi$
$140$	170.661			0.103025
$141$	−88.6286	+	153.509i	−0.0529353	+	0.0916866i
$142$	−248.933	−	431.164i	−0.147112	−	0.254806i
$143$	358.389	+	620.748i	0.209581	+	0.363004i
$144$	−1068.06	−	1849.93i	−0.618089	−	1.07056i
$145$	103.017			0.0590008
$146$	857.439	+	1485.13i	0.486042	+	0.841850i
$147$	20.5928	+	35.6678i	0.0115542	+	0.0200125i
$148$	−160.131	+	277.355i	−0.0889372	+	0.154044i
$149$	−873.974	+	1513.77i	−0.480529	+	0.832300i	−0.999750	−	0.0223396i	$-0.992888\pi$
$149$	−873.974	+	1513.77i	−0.480529	+	0.832300i	0.519222	+	0.854639i	$0.326222\pi$
$150$	−168.933			−0.0919554
$151$	2145.54			1.15630			0.578151	−	0.815929i	$-0.303774\pi$
$151$	2145.54			1.15630			0.578151	+	0.815929i	$0.303774\pi$
$152$	−173.672	+	300.809i	−0.0926756	+	0.160519i
$153$	693.548	−	1201.26i	0.366471	−	0.634746i
$154$	−895.140	−	1550.43i	−0.468392	−	0.811279i
$155$	98.1208	+	169.950i	0.0508468	+	0.0880692i
$156$	54.7530			0.0281009
$157$	1678.23	+	2906.78i	0.853103	+	1.47762i	0.878394	+	0.477938i	$0.158616\pi$
$157$	1678.23	+	2906.78i	0.853103	+	1.47762i	−0.0252906	+	0.999680i	$0.508051\pi$
$158$	1965.20	+	3403.82i	0.989511	+	1.71388i
$159$	−128.926	−	223.307i	−0.0643051	−	0.111380i
$160$	162.494	−	281.447i	0.0802891	−	0.139065i
$161$	1980.84			0.969641
$162$	1275.26	−	2208.81i	0.618480	−	1.07124i
$163$	1709.11	+	2960.27i	0.821277	+	1.42249i	0.904732	+	0.425982i	$0.140071\pi$
$163$	1709.11	+	2960.27i	0.821277	+	1.42249i	−0.0834545	+	0.996512i	$0.526595\pi$
$164$	251.516			0.119757
$165$	−7.98225	−	13.8257i	−0.00376617	−	0.00652319i
$166$	−2236.56	+	3873.83i	−1.04573	+	1.81125i
$167$	−153.016	+	265.031i	−0.0709024	+	0.122807i	−0.899297	−	0.437338i	$-0.855921\pi$
$167$	−153.016	+	265.031i	−0.0709024	+	0.122807i	0.828395	+	0.560145i	$0.189255\pi$
$168$	97.9073			0.0449626
$169$	642.977	−	1113.67i	0.292661	−	0.506905i
$170$	317.638			0.143304
$171$	−785.175			−0.351134
$172$	134.710	−	1307.68i	0.0597183	−	0.579706i
$173$	961.005			0.422334			0.211167	−	0.977450i	$-0.432274\pi$
$173$	961.005			0.422334			0.211167	+	0.977450i	$0.432274\pi$
$174$	−82.5503			−0.0359662
$175$	−1292.51	+	2238.69i	−0.558312	+	0.967024i
$176$	−1889.37			−0.809187
$177$	−88.9280	+	154.028i	−0.0377641	+	0.0654093i
$178$	1111.18	−	1924.62i	0.467902	−	0.810430i
$179$	−931.715	−	1613.78i	−0.389048	−	0.673851i	0.603273	−	0.797534i	$-0.293863\pi$
$179$	−931.715	−	1613.78i	−0.389048	−	0.673851i	−0.992322	+	0.123683i	$0.960529\pi$
$180$	216.274			0.0895563
$181$	667.231	+	1155.68i	0.274005	+	0.474590i	0.969884	−	0.243569i	$-0.0783182\pi$
$181$	667.231	+	1155.68i	0.274005	+	0.474590i	−0.695879	+	0.718159i	$0.744985\pi$
$182$	1137.75	−	1970.64i	0.463382	−	0.802601i
$183$	236.130			0.0953838
$184$	555.245	−	961.712i	0.222463	−	0.385317i
$185$	59.3443	+	102.787i	0.0235842	+	0.0408491i
$186$	−78.6267	−	136.185i	−0.0309956	−	0.0536860i
$187$	−613.437	−	1062.50i	−0.239887	−	0.415497i
$188$	−2123.96			−0.823966
$189$	221.944	+	384.418i	0.0854183	+	0.147949i
$190$	−89.9005	−	155.712i	−0.0343267	−	0.0594555i
$191$	691.818	−	1198.26i	0.262085	−	0.453944i	−0.704711	−	0.709495i	$-0.748923\pi$
$191$	691.818	−	1198.26i	0.262085	−	0.453944i	0.966796	+	0.255550i	$0.0822566\pi$
$192$	−6.38473	+	11.0587i	−0.00239989	+	0.00415673i
$193$	−3458.85			−1.29002			−0.645009	−	0.764175i	$-0.723146\pi$
$193$	−3458.85			−1.29002			−0.645009	+	0.764175i	$0.723146\pi$
$194$	−3989.71			−1.47652
$195$	10.1457	−	17.5728i	0.00372588	−	0.00645341i
$196$	−246.751	+	427.385i	−0.0899237	+	0.155752i
$197$	−1537.12	−	2662.37i	−0.555915	−	0.962873i	−0.997832	−	0.0658170i	$-0.979035\pi$
$197$	−1537.12	−	2662.37i	−0.555915	−	0.962873i	0.441917	−	0.897056i	$-0.354299\pi$
$198$	−1134.39	−	1964.82i	−0.407158	−	0.705219i
$199$	1601.35			0.570434			0.285217	−	0.958463i	$-0.407934\pi$
$199$	1601.35			0.570434			0.285217	+	0.958463i	$0.407934\pi$
$200$	724.600	+	1255.04i	0.256185	+	0.443725i
$201$	−83.3516	−	144.369i	−0.0292496	−	0.0506618i
$202$	−1669.78	−	2892.14i	−0.581609	−	1.00738i
$203$	−631.594	+	1093.95i	−0.218371	+	0.378229i
$204$	−93.7178			−0.0321645
$205$	46.6057	−	80.7234i	0.0158784	−	0.0275023i
$206$	1944.69	+	3368.31i	0.657734	+	1.13923i
$207$	2510.27			0.842878
$208$	−1200.72	−	2079.71i	−0.400265	−	0.693280i
$209$	−347.240	+	601.437i	−0.114924	+	0.199054i
$210$	−25.3406	+	43.8912i	−0.00832698	+	0.0144228i
$211$	−1648.37			−0.537811			−0.268906	−	0.963167i	$-0.586662\pi$
$211$	−1648.37			−0.537811			−0.268906	+	0.963167i	$0.586662\pi$
$212$	1544.84	−	2675.74i	0.500472	−	0.866843i
$213$	54.4384			0.0175120
$214$	2443.89			0.780658
$215$	−394.734	−	285.546i	−0.125212	−	0.0905771i
$216$	248.850			0.0783894
$217$	−2406.30			−0.752766
$218$	−2695.05	+	4667.96i	−0.837300	+	1.45025i
$219$	−187.511			−0.0578576
$220$	95.6463	−	165.664i	0.0293112	−	0.0507685i
$221$	779.695	−	1350.47i	0.237321	−	0.411052i
$222$	−47.5541	−	82.3661i	−0.0143767	−	0.0249011i
$223$	3002.40			0.901596			0.450798	−	0.892626i	$-0.351140\pi$
$223$	3002.40			0.901596			0.450798	+	0.892626i	$0.351140\pi$
$224$	1992.48	+	3451.09i	0.594324	+	1.02940i
$225$	−1637.96	+	2837.03i	−0.485322	+	0.840603i
$226$	2936.56			0.864324
$227$	1939.96	−	3360.11i	0.567223	−	0.982459i	−0.429616	−	0.903012i	$-0.641351\pi$
$227$	1939.96	−	3360.11i	0.567223	−	0.982459i	0.996839	−	0.0794472i	$-0.0253155\pi$
$228$	26.5248	+	45.9423i	0.00770460	+	0.0133448i
$229$	1257.69	+	2178.38i	0.362927	+	0.628608i	0.988441	−	0.151605i	$-0.0484441\pi$
$229$	1257.69	+	2178.38i	0.362927	+	0.628608i	−0.625514	+	0.780213i	$0.715111\pi$
$230$	287.419	+	497.825i	0.0823994	+	0.142720i
$231$	195.756			0.0557566
$232$	354.081	+	613.286i	0.100201	+	0.173553i
$233$	−2649.83	−	4589.64i	−0.745048	−	1.29046i	−0.950172	−	0.311725i	$-0.899093\pi$
$233$	−2649.83	−	4589.64i	−0.745048	−	1.29046i	0.205125	−	0.978736i	$-0.434240\pi$
$234$	1441.84	−	2497.34i	0.402803	−	0.697675i
$235$	−393.568	+	681.679i	−0.109249	+	0.189225i
$236$	−2131.14			−0.587818
$237$	−429.763			−0.117790
$238$	−1947.42	+	3373.04i	−0.530390	+	0.918662i
$239$	−922.917	+	1598.54i	−0.249785	+	0.432640i	−0.963466	−	0.267831i	$-0.913693\pi$
$239$	−922.917	+	1598.54i	−0.249785	+	0.432640i	0.713681	+	0.700471i	$0.247027\pi$
$240$	26.7432	+	46.3206i	0.00719278	+	0.0124583i
$241$	−3529.31	−	6112.95i	−0.943332	−	1.63390i	−0.759058	−	0.651023i	$-0.774340\pi$
$241$	−3529.31	−	6112.95i	−0.943332	−	1.63390i	−0.184274	−	0.982875i	$-0.558993\pi$
$242$	2729.52			0.725042
$243$	422.291	+	731.430i	0.111481	+	0.193092i
$244$	1414.70	+	2450.33i	0.371175	+	0.642894i
$245$	91.4453	+	158.388i	0.0238458	+	0.0413022i
$246$	−37.3463	+	64.6857i	−0.00967932	+	0.0167651i
$247$	−882.703			−0.227389
$248$	−674.503	+	1168.27i	−0.172706	+	0.299135i
$249$	−244.553	−	423.578i	−0.0622406	−	0.107804i
$250$	−1518.69			−0.384203
$251$	−14.1036	−	24.4282i	−0.00354667	−	0.00614301i	0.864247	−	0.503068i	$-0.167796\pi$
$251$	−14.1036	−	24.4282i	−0.00354667	−	0.00614301i	−0.867793	+	0.496925i	$0.834462\pi$
$252$	−1325.97	+	2296.65i	−0.331461	+	0.574107i
$253$	1110.15	−	1922.84i	0.275869	−	0.477819i
$254$	5825.56			1.43909
$255$	−17.3658	+	30.0785i	−0.00426467	+	0.00738662i
$256$	5201.48			1.26989
$257$	−8065.79			−1.95771			−0.978853	−	0.204566i	$-0.934422\pi$
$257$	−8065.79			−1.95771			−0.978853	+	0.204566i	$0.934422\pi$
$258$	316.310	+	228.815i	0.0763279	+	0.0552148i
$259$	−1455.35			−0.349155
$260$	243.138			0.0579953
$261$	−800.402	+	1386.34i	−0.189822	+	0.328782i
$262$	8874.11			2.09254
$263$	−203.361	+	352.232i	−0.0476798	+	0.0825838i	−0.888880	−	0.458139i	$-0.848516\pi$
$263$	−203.361	+	352.232i	−0.0476798	+	0.0825838i	0.841201	+	0.540723i	$0.181849\pi$
$264$	54.8717	−	95.0406i	0.0127921	−	0.0221566i
$265$	−572.515	−	991.625i	−0.132714	−	0.229868i
$266$	2204.71			0.508192
$267$	121.500	+	210.445i	0.0278491	+	0.0482360i
$268$	998.749	−	1729.88i	0.227643	−	0.394289i
$269$	3936.94			0.892339			0.446170	−	0.894948i	$-0.352788\pi$
$269$	3936.94			0.892339			0.446170	+	0.894948i	$0.352788\pi$
$270$	−64.4080	+	111.558i	−0.0145176	+	0.0251452i
$271$	−1813.04	−	3140.28i	−0.406400	−	0.703906i	0.588083	−	0.808800i	$-0.299883\pi$
$271$	−1813.04	−	3140.28i	−0.406400	−	0.703906i	−0.994483	+	0.104895i	$0.966549\pi$
$272$	2055.22	+	3559.74i	0.458147	+	0.793533i
$273$	124.405	+	215.476i	0.0275801	+	0.0477701i
$274$	−9966.53			−2.19745
$275$	1448.76	+	2509.33i	0.317686	+	0.550248i
$276$	−84.8020	−	146.881i	−0.0184945	−	0.0320334i
$277$	−289.082	+	500.705i	−0.0627049	+	0.108608i	−0.895674	−	0.444712i	$-0.853306\pi$
$277$	−289.082	+	500.705i	−0.0627049	+	0.108608i	0.832969	+	0.553320i	$0.186639\pi$
$278$	−2364.13	+	4094.79i	−0.510040	+	0.883415i
$279$	−3049.44			−0.654355
$280$	434.771			0.0927948
$281$	1476.53	−	2557.43i	0.313461	−	0.542931i	−0.665648	−	0.746266i	$-0.731845\pi$
$281$	1476.53	−	2557.43i	0.313461	−	0.542931i	0.979109	+	0.203335i	$0.0651781\pi$
$282$	315.376	−	546.247i	0.0665970	−	0.115349i
$283$	1752.83	+	3035.99i	0.368180	+	0.637707i	0.989281	−	0.146024i	$-0.0466476\pi$
$283$	1752.83	+	3035.99i	0.368180	+	0.637707i	−0.621101	+	0.783731i	$0.713314\pi$
$284$	326.150	+	564.908i	0.0681459	+	0.118032i
$285$	19.6601			0.00408618
$286$	−1275.29	−	2208.87i	−0.263670	−	0.456689i
$287$	571.475	+	989.823i	0.117537	+	0.203580i
$288$	2525.02	+	4373.47i	0.516626	+	0.894823i
$289$	1121.94	−	1943.25i	0.228361	−	0.395532i
$290$	−366.576			−0.0742279
$291$	218.124	−	377.803i	0.0439405	−	0.0761072i
$292$	−1123.41	−	1945.81i	−0.225146	−	0.389965i
$293$	1731.50			0.345240			0.172620	−	0.984988i	$-0.444777\pi$
$293$	1731.50			0.345240			0.172620	+	0.984988i	$0.444777\pi$
$294$	−73.2774	−	126.920i	−0.0145361	−	0.0251773i
$295$	−394.897	+	683.982i	−0.0779383	+	0.134993i
$296$	−407.945	+	706.582i	−0.0801059	+	0.138748i
$297$	497.550			0.0972081
$298$	3109.95	−	5386.59i	0.604545	−	1.04710i
$299$	2822.07			0.545835
$300$	221.335			0.0425959
$301$	5452.35	−	2441.06i	1.04408	−	0.467443i
$302$	−7634.69			−1.45473
$303$	365.159			0.0692337
$304$	1163.37	−	2015.01i	0.219486	−	0.380161i
$305$	1048.57			0.196855
$306$	−2467.92	+	4274.56i	−0.461051	+	0.798564i
$307$	−814.438	+	1410.65i	−0.151409	+	0.262247i	−0.931746	−	0.363112i	$-0.881714\pi$
$307$	−814.438	+	1410.65i	−0.151409	+	0.262247i	0.780337	+	0.625359i	$0.215048\pi$
$308$	1172.81	+	2031.36i	0.216970	+	0.375804i
$309$	−425.280			−0.0782955
$310$	−349.153	−	604.750i	−0.0639695	−	0.110798i
$311$	−1209.05	+	2094.14i	−0.220447	+	0.381825i	−0.954944	−	0.296787i	$-0.904085\pi$
$311$	−1209.05	+	2094.14i	−0.220447	+	0.381825i	0.734497	+	0.678612i	$0.237418\pi$
$312$	139.487			0.0253106
$313$	−2998.58	+	5193.70i	−0.541501	+	0.937908i	0.457317	+	0.889304i	$0.348811\pi$
$313$	−2998.58	+	5193.70i	−0.541501	+	0.937908i	−0.998818	+	0.0486039i	$0.984523\pi$
$314$	−5971.80	−	10343.5i	−1.07327	−	1.85897i
$315$	491.401	+	851.132i	0.0878963	+	0.152241i
$316$	−2574.79	−	4459.67i	−0.458365	−	0.793911i
$317$	4943.75			0.875927			0.437963	−	0.898993i	$-0.355700\pi$
$317$	4943.75			0.875927			0.437963	+	0.898993i	$0.355700\pi$
$318$	458.771	+	794.614i	0.0809012	+	0.140125i
$319$	707.948	+	1226.20i	0.124255	+	0.215217i
$320$	−28.3523	+	49.1076i	−0.00495294	+	0.00857875i
$321$	−133.612	+	231.422i	−0.0232320	+	0.0402390i
$322$	−7048.62			−1.21989
$323$	1510.88			0.260271
$324$	−1670.84	+	2893.97i	−0.286495	+	0.496223i
$325$	−1841.42	+	3189.43i	−0.314288	+	0.544362i
$326$	−6081.71	−	10533.8i	−1.03324	−	1.78962i
$327$	−294.686	−	510.411i	−0.0498354	−	0.0863174i
$328$	640.754			0.107865
$329$	−4825.89	−	8358.69i	−0.808693	−	1.40070i
$330$	28.4040	+	49.1972i	0.00473815	+	0.00820672i
$331$	1116.16	+	1933.24i	0.185346	+	0.321029i	0.943693	−	0.330822i	$-0.107326\pi$
$331$	1116.16	+	1933.24i	0.185346	+	0.321029i	−0.758347	+	0.651851i	$0.773993\pi$
$332$	2930.32	−	5075.47i	0.484405	−	0.839013i
$333$	−1844.33			−0.303509
$334$	544.490	−	943.084i	0.0892011	−	0.154501i
$335$	−370.134	−	641.092i	−0.0603660	−	0.104557i
$336$	−655.846			−0.106486
$337$	1012.09	+	1753.00i	0.163597	+	0.283359i	0.936156	−	0.351584i	$-0.114357\pi$
$337$	1012.09	+	1753.00i	0.163597	+	0.283359i	−0.772559	+	0.634943i	$0.781024\pi$
$338$	−2287.97	+	3962.88i	−0.368193	+	0.637728i
$339$	−160.547	+	278.076i	−0.0257219	+	0.0445516i
$340$	−416.167			−0.0663819
$341$	−1348.60	+	2335.84i	−0.214166	+	0.370947i
$342$	2793.96			0.441755
$343$	5024.25			0.790916
$344$	343.183	−	3331.40i	0.0537883	−	0.522142i
$345$	−62.8549			−0.00980868
$346$	−3419.64			−0.531332
$347$	1411.63	−	2445.01i	0.218387	−	0.378257i	−0.735928	−	0.677060i	$-0.763254\pi$
$347$	1411.63	−	2445.01i	0.218387	−	0.378257i	0.954315	+	0.298803i	$0.0965872\pi$
$348$	108.157			0.0166604
$349$	−3649.78	+	6321.60i	−0.559794	+	0.969592i	0.437719	+	0.899112i	$0.355786\pi$
$349$	−3649.78	+	6321.60i	−0.559794	+	0.969592i	−0.997513	+	0.0704802i	$0.977547\pi$
$350$	4599.26	−	7966.15i	0.702402	−	1.21660i
$351$	316.200	+	547.675i	0.0480841	+	0.0832841i
$352$	4466.72			0.676355
$353$	−6356.99	−	11010.6i	−0.958494	−	1.66016i	−0.726162	−	0.687523i	$-0.758698\pi$
$353$	−6356.99	−	11010.6i	−0.958494	−	1.66016i	−0.232331	−	0.972637i	$-0.574635\pi$
$354$	316.441	−	548.092i	0.0475103	−	0.0822903i
$355$	241.741			0.0361417
$356$	−1455.86	+	2521.63i	−0.216743	+	0.375410i
$357$	−212.938	−	368.820i	−0.0315683	−	0.0546779i
$358$	3315.41	+	5742.46i	0.489455	+	0.847761i
$359$	2905.50	+	5032.47i	0.427149	+	0.739843i	0.996618	−	0.0821690i	$-0.0261847\pi$
$359$	2905.50	+	5032.47i	0.427149	+	0.739843i	−0.569470	+	0.822012i	$0.692851\pi$
$360$	550.974			0.0806635
$361$	3001.88	+	5199.41i	0.437655	+	0.758041i
$362$	−2374.27	−	4112.36i	−0.344721	−	0.597074i
$363$	−149.228	+	258.470i	−0.0215769	+	0.0373723i
$364$	−1490.67	+	2581.92i	−0.214649	+	0.371783i
$365$	−832.668			−0.119408
$366$	−840.244			−0.120001
$367$	−5964.64	+	10331.1i	−0.848370	+	1.46942i	0.0342921	+	0.999412i	$0.489082\pi$
$367$	−5964.64	+	10331.1i	−0.848370	+	1.46942i	−0.882662	+	0.470008i	$0.844251\pi$
$368$	−3719.39	+	6442.17i	−0.526865	+	0.912558i
$369$	724.215	+	1254.38i	0.102171	+	0.176965i
$370$	−211.171	−	365.758i	−0.0296709	−	0.0513915i
$371$	14040.3			1.96478
$372$	103.016	+	178.429i	0.0143579	+	0.0248686i
$373$	186.985	+	323.868i	0.0259563	+	0.0449577i	0.878712	−	0.477353i	$-0.158404\pi$
$373$	186.985	+	323.868i	0.0259563	+	0.0449577i	−0.852755	+	0.522310i	$0.825070\pi$
$374$	2182.85	+	3780.81i	0.301798	+	0.522730i
$375$	83.0297	−	143.812i	0.0114337	−	0.0198037i
$376$	−5410.93			−0.742148
$377$	−899.822	+	1558.54i	−0.122926	+	0.212914i
$378$	−789.765	−	1367.91i	−0.107463	−	0.186132i
$379$	14078.0			1.90802			0.954009	−	0.299779i	$-0.0969129\pi$
$379$	14078.0			1.90802			0.954009	+	0.299779i	$0.0969129\pi$
$380$	117.787	+	204.013i	0.0159009	+	0.0275412i
$381$	−318.494	+	551.647i	−0.0428266	+	0.0741778i
$382$	−2461.76	+	4263.90i	−0.329725	+	0.571100i
$383$	12802.1			1.70798			0.853992	−	0.520285i	$-0.174174\pi$
$383$	12802.1			1.70798			0.853992	+	0.520285i	$0.174174\pi$
$384$	−270.020	+	467.688i	−0.0358838	+	0.0621527i
$385$	869.280			0.115072
$386$	12308.0			1.62295
$387$	6909.62	−	3093.49i	0.907585	−	0.406333i
$388$	5227.29			0.683958
$389$	9445.56			1.23113			0.615564	−	0.788087i	$-0.288928\pi$
$389$	9445.56			1.23113			0.615564	+	0.788087i	$0.288928\pi$
$390$	−36.1023	+	62.5311i	−0.00468747	+	0.00811893i
$391$	−4830.40			−0.624767
$392$	−628.614	+	1088.79i	−0.0809944	+	0.140286i
$393$	−485.163	+	840.328i	−0.0622729	+	0.107860i
$394$	5469.68	+	9473.77i	0.699387	+	1.21137i
$395$	−1908.42			−0.243097
$396$	1486.27	+	2574.29i	0.188605	+	0.326674i
$397$	−5529.88	+	9578.04i	−0.699085	+	1.21085i	0.269699	+	0.962945i	$0.413076\pi$
$397$	−5529.88	+	9578.04i	−0.699085	+	1.21085i	−0.968784	+	0.247907i	$0.920257\pi$
$398$	−5698.23			−0.717654
$399$	−120.535	+	208.773i	−0.0151236	+	0.0261948i
$400$	−4853.84	−	8407.09i	−0.606730	−	1.05089i
$401$	−6136.30	−	10628.4i	−0.764170	−	1.32358i	−0.940684	−	0.339284i	$-0.889815\pi$
$401$	−6136.30	−	10628.4i	−0.764170	−	1.32358i	0.176514	−	0.984298i	$-0.443518\pi$
$402$	296.598	+	513.723i	0.0367984	+	0.0637368i
$403$	−3428.22			−0.423751
$404$	2187.73	+	3789.26i	0.269415	+	0.466641i
$405$	619.209	+	1072.50i	0.0759722	+	0.131588i
$406$	2247.46	−	3892.72i	0.274728	−	0.475843i
$407$	−815.645	+	1412.74i	−0.0993366	+	0.172056i
$408$	−238.753			−0.0289706
$409$	−7464.92			−0.902486			−0.451243	−	0.892401i	$-0.649019\pi$
$409$	−7464.92			−0.902486			−0.451243	+	0.892401i	$0.649019\pi$
$410$	−165.841	+	287.246i	−0.0199764	+	0.0346001i
$411$	544.888	−	943.774i	0.0653950	−	0.113267i
$412$	−2547.93	−	4413.14i	−0.304678	−	0.527718i
$413$	−4842.20	−	8386.93i	−0.576922	−	0.999259i
$414$	−8932.53			−1.06041
$415$	−1085.97	−	1880.96i	−0.128454	−	0.222488i
$416$	2838.66	+	4916.71i	0.334560	+	0.579474i
$417$	−258.502	−	447.739i	−0.0303571	−	0.0525800i
$418$	1235.62	−	2140.15i	0.144584	−	0.250426i
$419$	−16392.7			−1.91131			−0.955653	−	0.294494i	$-0.904849\pi$
$419$	−16392.7			−1.91131			−0.955653	+	0.294494i	$0.904849\pi$
$420$	33.2011	−	57.5059i	0.00385725	−	0.00668096i
$421$	638.000	+	1105.05i	0.0738580	+	0.127926i	0.900589	−	0.434671i	$-0.143136\pi$
$421$	638.000	+	1105.05i	0.0738580	+	0.127926i	−0.826731	+	0.562597i	$0.809802\pi$
$422$	5865.54			0.676611
$423$	−6115.73	−	10592.7i	−0.702971	−	1.21758i
$424$	3935.59	−	6816.64i	0.450776	−	0.780767i
$425$	3151.86	−	5459.18i	0.359736	−	0.623081i
$426$	−193.713			−0.0220316
$427$	−6428.73	+	11134.9i	−0.728590	+	1.26196i
$428$	−3201.97			−0.361619
$429$	278.890			0.0313868
$430$	1404.62	+	1016.09i	0.157527	+	0.113954i
$431$	−2155.82			−0.240933			−0.120467	−	0.992717i	$-0.538439\pi$
$431$	−2155.82			−0.240933			−0.120467	+	0.992717i	$0.538439\pi$
$432$	−1666.96			−0.185652
$433$	1762.94	−	3053.49i	0.195661	−	0.338895i	−0.751456	−	0.659783i	$-0.770648\pi$
$433$	1762.94	−	3053.49i	0.195661	−	0.338895i	0.947117	+	0.320888i	$0.103981\pi$
$434$	8562.57			0.947042
$435$	20.0414	−	34.7127i	0.00220899	−	0.00382608i
$436$	3531.03	−	6115.93i	0.387857	−	0.671788i
$437$	1367.14	+	2367.96i	0.149655	+	0.259210i
$438$	667.238			0.0727897
$439$	−7625.80	−	13208.3i	−0.829065	−	1.43598i	−0.898773	−	0.438415i	$-0.855540\pi$
$439$	−7625.80	−	13208.3i	−0.829065	−	1.43598i	0.0697079	−	0.997567i	$-0.477793\pi$
$440$	243.665	−	422.041i	0.0264007	−	0.0457273i
$441$	−2841.97			−0.306876
$442$	−2774.46	+	4805.51i	−0.298570	+	0.517138i
$443$	−3198.76	−	5540.41i	−0.343064	−	0.594205i	0.641936	−	0.766758i	$-0.278132\pi$
$443$	−3198.76	−	5540.41i	−0.343064	−	0.594205i	−0.985000	+	0.172553i	$0.944798\pi$
$444$	62.3051	+	107.916i	0.00665962	+	0.0115348i
$445$	539.540	+	934.510i	0.0574756	+	0.0995506i
$446$	−10683.7			−1.13428
$447$	340.053	+	588.988i	0.0359820	+	0.0623226i
$448$	−347.653	−	602.153i	−0.0366631	−	0.0635024i
$449$	−890.569	+	1542.51i	−0.0936048	+	0.162128i	−0.909025	−	0.416741i	$-0.863172\pi$
$449$	−890.569	+	1542.51i	−0.0936048	+	0.162128i	0.815421	+	0.578869i	$0.196506\pi$
$450$	5828.52	−	10095.3i	0.610576	−	1.05755i
$451$	1281.12			0.133760
$452$	−3847.46			−0.400375
$453$	417.402	−	722.962i	0.0432920	−	0.0749839i
$454$	−6903.14	+	11956.6i	−0.713614	+	1.23602i
$455$	552.439	+	956.853i	0.0569203	+	0.0985889i
$456$	67.5738	+	117.041i	0.00693955	+	0.0120196i
$457$	4608.14			0.471684			0.235842	−	0.971791i	$-0.424215\pi$
$457$	4608.14			0.471684			0.235842	+	0.971791i	$0.424215\pi$
$458$	−4475.35	−	7751.53i	−0.456593	−	0.790841i
$459$	−541.224	−	937.427i	−0.0550374	−	0.0953276i
$460$	−376.575	−	652.247i	−0.0381693	−	0.0661112i
$461$	−1153.29	+	1997.56i	−0.116517	+	0.201813i	−0.918385	−	0.395688i	$-0.870506\pi$
$461$	−1153.29	+	1997.56i	−0.116517	+	0.201813i	0.801868	+	0.597501i	$0.203840\pi$
$462$	−696.576			−0.0701464
$463$	3886.13	−	6730.98i	0.390073	−	0.675627i	−0.602386	−	0.798205i	$-0.705783\pi$
$463$	3886.13	−	6730.98i	0.390073	−	0.675627i	0.992459	+	0.122579i	$0.0391163\pi$
$464$	−2371.86	−	4108.19i	−0.237308	−	0.411030i
$465$	76.3552			0.00761481
$466$	9429.15	+	16331.8i	0.937332	+	1.62351i
$467$	−6172.57	+	10691.2i	−0.611633	+	1.05938i	0.379332	+	0.925260i	$0.376154\pi$
$467$	−6172.57	+	10691.2i	−0.611633	+	1.05938i	−0.990965	+	0.134119i	$0.957180\pi$
$468$	−1889.09	+	3271.99i	−0.186588	+	0.323179i
$469$	9077.12			0.893694
$470$	1400.47	−	2425.68i	0.137444	−	0.238061i
$471$	1305.96			0.127761
$472$	−5429.22			−0.529449
$473$	686.159	−	6660.78i	0.0667011	−	0.647491i
$474$	1529.27			0.148189
$475$	−3568.26			−0.344680
$476$	2551.50	−	4419.33i	0.245689	−	0.425546i
$477$	17792.8			1.70792
$478$	3284.11	−	5688.24i	0.314250	−	0.544297i
$479$	−7195.31	+	12462.6i	−0.686351	+	1.18880i	0.286659	+	0.958033i	$0.407455\pi$
$479$	−7195.31	+	12462.6i	−0.686351	+	1.18880i	−0.973010	+	0.230763i	$0.925878\pi$
$480$	−63.2243	−	109.508i	−0.00601205	−	0.0104132i
$481$	−2073.41			−0.196548
$482$	12558.7	+	21752.3i	1.18679	+	2.05558i
$483$	385.361	−	667.464i	0.0363034	−	0.0628793i
$484$	−3576.20			−0.335856
$485$	968.612	−	1677.69i	0.0906854	−	0.157072i
$486$	−1502.68	−	2602.72i	−0.140253	−	0.242925i
$487$	−303.362	−	525.439i	−0.0282272	−	0.0488910i	0.851567	−	0.524246i	$-0.175653\pi$
$487$	−303.362	−	525.439i	−0.0282272	−	0.0488910i	−0.879794	+	0.475355i	$0.842320\pi$
$488$	3604.04	+	6242.38i	0.334318	+	0.579056i
$489$	1329.99			0.122994
$490$	−325.399	−	563.607i	−0.0300000	−	0.0519616i
$491$	−3519.32	−	6095.63i	−0.323471	−	0.560269i	0.657730	−	0.753253i	$-0.271517\pi$
$491$	−3519.32	−	6095.63i	−0.323471	−	0.560269i	−0.981202	+	0.192984i	$0.938183\pi$
$492$	48.9309	−	84.7508i	0.00448369	−	0.00776598i
$493$	1540.18	−	2667.67i	0.140702	−	0.243703i
$494$	3141.01			0.286074
$495$	1101.61			0.100028
$496$	4518.26	−	7825.85i	0.409024	−	0.708450i
$497$	−1482.11	+	2567.08i	−0.133766	+	0.231689i
$498$	870.217	+	1507.26i	0.0783039	+	0.135626i
$499$	−1570.98	−	2721.01i	−0.140935	−	0.244107i	0.786914	−	0.617063i	$-0.211678\pi$
$499$	−1570.98	−	2721.01i	−0.140935	−	0.244107i	−0.927849	+	0.372956i	$0.878344\pi$
$500$	1989.78			0.177972
$501$	59.5365	+	103.120i	0.00530917	+	0.00919575i
$502$	50.1864	+	86.9254i	0.00446201	+	0.00772842i
$503$	6353.47	+	11004.5i	0.563195	+	0.975483i	0.997215	+	0.0745796i	$0.0237615\pi$
$503$	6353.47	+	11004.5i	0.563195	+	0.975483i	−0.434020	+	0.900903i	$0.642905\pi$
$504$	−3378.00	+	5850.86i	−0.298548	+	0.517100i
$505$	1621.54			0.142886
$506$	−3950.37	+	6842.24i	−0.347066	+	0.601136i
$507$	−250.175	−	433.315i	−0.0219145	−	0.0379570i
$508$	−7632.61			−0.666619
$509$	4538.91	+	7861.62i	0.395253	+	0.684598i	0.993133	−	0.116987i	$-0.0373237\pi$
$509$	4538.91	+	7861.62i	0.395253	+	0.684598i	−0.597881	+	0.801585i	$0.703990\pi$
$510$	61.7945	−	107.031i	0.00536531	−	0.00929298i
$511$	5105.06	−	8842.22i	0.441946	−	0.765473i
$512$	−7405.22			−0.639194
$513$	−306.363	+	530.637i	−0.0263670	+	0.0456690i
$514$	28701.3			2.46296
$515$	−1888.51			−0.161588
$516$	−414.428	−	299.792i	−0.0353569	−	0.0255768i
$517$	−10818.6			−0.920312
$518$	5178.71			0.439266
$519$	186.958	−	323.820i	0.0158122	−	0.0273875i
$520$	619.411			0.0522365
$521$	−4299.38	+	7446.75i	−0.361534	+	0.626196i	−0.988214	−	0.153082i	$-0.951080\pi$
$521$	−4299.38	+	7446.75i	−0.361534	+	0.626196i	0.626679	+	0.779277i	$0.284414\pi$
$522$	2848.15	−	4933.14i	0.238812	−	0.413635i
$523$	−3947.47	−	6837.23i	−0.330040	−	0.571646i	0.652479	−	0.757807i	$-0.273729\pi$
$523$	−3947.47	−	6837.23i	−0.330040	−	0.571646i	−0.982519	+	0.186160i	$0.940396\pi$
$524$	−11626.8			−0.969312
$525$	502.900	+	871.048i	0.0418064	+	0.0724107i
$526$	723.640	−	1253.38i	0.0599852	−	0.103897i
$527$	5867.90			0.485028
$528$	−367.566	+	636.643i	−0.0302960	+	0.0524741i
$529$	1712.64	+	2966.38i	0.140761	+	0.243805i
$530$	2037.23	+	3528.59i	0.166966	+	0.289193i
$531$	−6136.39	−	10628.5i	−0.501500	−	0.868624i
$532$	−2888.59			−0.235407
$533$	814.171	+	1410.19i	0.0661645	+	0.114600i
$534$	−432.347	−	748.847i	−0.0350365	−	0.0606850i
$535$	−593.321	+	1027.66i	−0.0479468	+	0.0830462i
$536$	2544.38	−	4407.00i	0.205038	−	0.355137i
$537$	−725.038			−0.0582639
$538$	−14009.2			−1.12264
$539$	−1256.85	+	2176.93i	−0.100438	+	0.173965i
$540$	84.3869	−	146.162i	0.00672488	−	0.0116478i
$541$	6770.44	+	11726.8i	0.538048	+	0.931927i	0.999009	+	0.0445065i	$0.0141715\pi$
$541$	6770.44	+	11726.8i	0.538048	+	0.931927i	−0.460961	+	0.887421i	$0.652495\pi$
$542$	6451.52	+	11174.4i	0.511285	+	0.885572i
$543$	519.223			0.0410349
$544$	−4858.79	−	8415.67i	−0.382939	−	0.663270i
$545$	−1308.59	−	2266.55i	−0.102851	−	0.178144i
$546$	−442.684	−	766.751i	−0.0346980	−	0.0600987i
$547$	2197.81	−	3806.72i	0.171795	−	0.297557i	−0.767253	−	0.641345i	$-0.778377\pi$
$547$	2197.81	−	3806.72i	0.171795	−	0.297557i	0.939047	+	0.343788i	$0.111710\pi$
$548$	13058.1			1.01791
$549$	−8146.96	+	14110.9i	−0.633340	+	1.09698i
$550$	−5155.27	−	8929.19i	−0.399675	−	0.692258i
$551$	−1743.66			−0.134814
$552$	−216.039	−	374.190i	−0.0166580	−	0.0288525i
$553$	11700.5	−	20265.8i	0.899737	−	1.55839i
$554$	1028.67	−	1781.71i	0.0788880	−	0.136638i
$555$	46.1803			0.00353197
$556$	3097.47	−	5364.97i	0.236262	−	0.409218i
$557$	−11923.4			−0.907024			−0.453512	−	0.891250i	$-0.649829\pi$
$557$	−11923.4			−0.907024			−0.453512	+	0.891250i	$0.649829\pi$
$558$	10851.1			0.823233
$559$	7767.87	−	3477.74i	0.587739	−	0.263135i
$560$	−2912.38			−0.219769
$561$	−477.361			−0.0359255
$562$	−5254.09	+	9100.35i	−0.394360	+	0.683052i
$563$	−12331.1			−0.923080			−0.461540	−	0.887119i	$-0.652703\pi$
$563$	−12331.1			−0.923080			−0.461540	+	0.887119i	$0.652703\pi$
$564$	−413.203	+	715.689i	−0.0308493	+	0.0534325i
$565$	−712.931	+	1234.83i	−0.0530854	+	0.0919466i
$566$	−6237.27	−	10803.3i	−0.463201	−	0.802288i
$567$	−15185.4			−1.12474
$568$	830.890	+	1439.14i	0.0613792	+	0.106312i
$569$	−6686.03	+	11580.5i	−0.492606	+	0.853219i	−0.999964	−	0.00851635i	$-0.997289\pi$
$569$	−6686.03	+	11580.5i	−0.492606	+	0.853219i	0.507357	+	0.861736i	$0.330622\pi$
$570$	−69.9584			−0.00514076
$571$	1644.61	−	2848.54i	0.120533	−	0.208770i	−0.799445	−	0.600740i	$-0.794873\pi$
$571$	1644.61	−	2848.54i	0.120533	−	0.208770i	0.919978	+	0.391970i	$0.128206\pi$
$572$	1670.88	+	2894.05i	0.122138	+	0.211549i
$573$	−269.178	−	466.230i	−0.0196249	−	0.0339913i
$574$	−2033.53	−	3522.18i	−0.147871	−	0.256120i
$575$	11408.0			0.827387
$576$	−440.572	−	763.093i	−0.0318701	−	0.0552006i
$577$	−2373.02	−	4110.19i	−0.171213	−	0.296550i	0.767631	−	0.640892i	$-0.221435\pi$
$577$	−2373.02	−	4110.19i	−0.171213	−	0.296550i	−0.938844	+	0.344342i	$0.888102\pi$
$578$	−3992.29	+	6914.85i	−0.287297	+	0.497612i
$579$	−672.898	+	1165.49i	−0.0482983	+	0.0836550i
$580$	480.286			0.0343841
$581$	26632.2			1.90170
$582$	−776.174	+	1344.37i	−0.0552808	+	0.0957492i
$583$	7868.80	−	13629.2i	0.558992	−	0.968203i
$584$	−2861.97	−	4957.08i	−0.202790	−	0.351242i
$585$	700.092	+	1212.59i	0.0494790	+	0.0857002i
$586$	−6161.37			−0.434341
$587$	10336.1	+	17902.6i	0.726773	+	1.25881i	0.958240	+	0.285965i	$0.0923142\pi$
$587$	10336.1	+	17902.6i	0.726773	+	1.25881i	−0.231467	+	0.972843i	$0.574352\pi$
$588$	96.0077	+	166.290i	0.00673348	+	0.0116627i
$589$	−1660.78	−	2876.56i	−0.116182	−	0.201234i
$590$	1405.20	−	2433.88i	0.0980529	−	0.169833i
$591$	−1196.15			−0.0832538
$592$	2732.68	−	4733.14i	0.189717	−	0.328600i
$593$	327.619	+	567.453i	0.0226875	+	0.0392960i	0.877146	−	0.480223i	$-0.159444\pi$
$593$	327.619	+	567.453i	0.0226875	+	0.0392960i	−0.854459	+	0.519519i	$0.826111\pi$
$594$	−1770.48			−0.122296
$595$	−945.582	−	1637.80i	−0.0651514	−	0.112846i
$596$	−4074.63	+	7057.47i	−0.280039	+	0.485043i
$597$	311.532	−	539.590i	0.0213571	−	0.0369915i
$598$	−10042.1			−0.686706
$599$	−8910.60	+	15433.6i	−0.607809	+	1.05276i	0.383792	+	0.923420i	$0.374618\pi$
$599$	−8910.60	+	15433.6i	−0.607809	+	1.05276i	−0.991601	+	0.129336i	$0.958715\pi$
$600$	563.866			0.0383662
$601$	−20715.1			−1.40597			−0.702984	−	0.711205i	$-0.748150\pi$
$601$	−20715.1			−1.40597			−0.702984	+	0.711205i	$0.748150\pi$
$602$	−19401.6	+	8686.26i	−1.31354	+	0.588082i
$603$	11503.2			0.776859
$604$	10002.9			0.673863
$605$	−662.666	+	1147.77i	−0.0445309	+	0.0771298i
$606$	−1299.38			−0.0871018
$607$	12715.3	−	22023.5i	0.850244	−	1.47267i	−0.0307439	−	0.999527i	$-0.509788\pi$
$607$	12715.3	−	22023.5i	0.850244	−	1.47267i	0.880988	−	0.473139i	$-0.156879\pi$
$608$	−2750.35	+	4763.75i	−0.183456	+	0.317756i
$609$	245.746	+	425.644i	0.0163516	+	0.0283218i
$610$	−3731.22			−0.247660
$611$	−6875.37	−	11908.5i	−0.455234	−	0.788488i
$612$	3233.45	−	5600.50i	0.213570	−	0.369913i
$613$	16857.5			1.11071			0.555357	−	0.831612i	$-0.312582\pi$
$613$	16857.5			1.11071			0.555357	+	0.831612i	$0.312582\pi$
$614$	2898.09	−	5019.65i	0.190485	−	0.329929i
$615$	−18.1337	−	31.4085i	−0.00118898	−	0.00205937i
$616$	2987.81	+	5175.03i	0.195426	+	0.338487i
$617$	4823.36	+	8354.31i	0.314718	+	0.545108i	0.979378	−	0.202038i	$-0.0647566\pi$
$617$	4823.36	+	8354.31i	0.314718	+	0.545108i	−0.664659	+	0.747147i	$0.731423\pi$
$618$	1513.31			0.0985023
$619$	−4120.97	−	7137.73i	−0.267586	−	0.463473i	0.700652	−	0.713503i	$-0.252893\pi$
$619$	−4120.97	−	7137.73i	−0.267586	−	0.463473i	−0.968238	+	0.250030i	$0.919559\pi$
$620$	457.458	+	792.340i	0.0296322	+	0.0513244i
$621$	979.469	−	1696.49i	0.0632926	−	0.109626i
$622$	4302.29	−	7451.78i	0.277341	−	0.480368i
$623$	−13231.6			−0.850902
$624$	−934.374			−0.0599437
$625$	−7257.21	+	12569.9i	−0.464462	+	0.804471i
$626$	10670.1	−	18481.2i	0.681254	−	1.17997i
$627$	135.107	+	234.012i	0.00860549	+	0.0149052i
$628$	7824.22	+	13551.9i	0.497166	+	0.861117i
$629$	3548.96			0.224970
$630$	−1748.60	−	3028.67i	−0.110581	−	0.191532i
$631$	−10717.0	−	18562.4i	−0.676130	−	1.17109i	−0.976137	−	0.217154i	$-0.930323\pi$
$631$	−10717.0	−	18562.4i	−0.676130	−	1.17109i	0.300008	−	0.953937i	$-0.403011\pi$
$632$	−6559.46	−	11361.3i	−0.412850	−	0.715077i
$633$	−320.679	+	555.433i	−0.0201356	+	0.0348760i
$634$	−17591.8			−1.10199
$635$	−1414.32	+	2449.67i	−0.0883865	+	0.153090i
$636$	−601.078	−	1041.10i	−0.0374753	−	0.0649092i
$637$	−3194.98			−0.198728
$638$	−2519.16	−	4363.31i	−0.156324	−	0.270761i
$639$	−1878.23	+	3253.19i	−0.116278	+	0.201400i
$640$	−1199.06	+	2076.83i	−0.0740579	+	0.128272i
$641$	−4316.55			−0.265980			−0.132990	−	0.991117i	$-0.542458\pi$
$641$	−4316.55			−0.265980			−0.132990	+	0.991117i	$0.542458\pi$
$642$	475.443	−	823.492i	0.0292278	−	0.0506241i
$643$	−19770.6			−1.21256			−0.606280	−	0.795251i	$-0.707339\pi$
$643$	−19770.6			−1.21256			−0.606280	+	0.795251i	$0.707339\pi$
$644$	9235.06			0.565082
$645$	−173.011	+	77.4582i	−0.0105617	+	0.00472855i
$646$	−5376.30			−0.327442
$647$	−5551.13			−0.337307			−0.168653	−	0.985675i	$-0.553942\pi$
$647$	−5551.13			−0.337307			−0.168653	+	0.985675i	$0.553942\pi$
$648$	−4256.57	+	7372.60i	−0.258046	+	0.446949i
$649$	−10855.2			−0.656552
$650$	6552.49	−	11349.3i	0.395400	−	0.684853i
$651$	−468.131	+	810.826i	−0.0281835	+	0.0488153i
$652$	7968.22	+	13801.4i	0.478619	+	0.828992i
$653$	4038.70			0.242031			0.121016	−	0.992651i	$-0.461385\pi$
$653$	4038.70			0.242031			0.121016	+	0.992651i	$0.461385\pi$
$654$	1048.61	+	1816.24i	0.0626970	+	0.108594i
$655$	−2154.44	+	3731.59i	−0.128520	+	0.222604i
$656$	−4292.19			−0.255460
$657$	6469.50	−	11205.5i	0.384169	−	0.665401i
$658$	17172.4	+	29743.5i	1.01740	+	1.76219i
$659$	−4865.19	−	8426.76i	−0.287589	−	0.498118i	0.685645	−	0.727936i	$-0.259520\pi$
$659$	−4865.19	−	8426.76i	−0.287589	−	0.498118i	−0.973234	+	0.229818i	$0.926187\pi$
$660$	−37.2148	−	64.4579i	−0.00219482	−	0.00380155i
$661$	15692.3			0.923389			0.461695	−	0.887039i	$-0.347242\pi$
$661$	15692.3			0.923389			0.461695	+	0.887039i	$0.347242\pi$
$662$	−3971.74	−	6879.25i	−0.233181	−	0.403882i
$663$	−303.370	−	525.452i	−0.0177706	−	0.0307796i
$664$	7465.20	−	12930.1i	0.436304	−	0.755701i
$665$	−535.253	+	927.086i	−0.0312124	+	0.0540614i
$666$	6562.85			0.381840
$667$	5574.62			0.323613
$668$	−713.387	+	1235.62i	−0.0413200	+	0.0715684i
$669$	584.099	−	1011.69i	0.0337557	−	0.0584666i
$670$	1317.09	+	2281.26i	0.0759454	+	0.131541i
$671$	7205.91	+	12481.0i	0.414577	+	0.718068i
$672$	1550.50			0.0890059
$673$	10801.9	+	18709.4i	0.618696	+	1.07161i	0.989724	+	0.142992i	$0.0456722\pi$
$673$	10801.9	+	18709.4i	0.618696	+	1.07161i	−0.371028	+	0.928622i	$0.620994\pi$
$674$	−3601.43	−	6237.86i	−0.205819	−	0.356489i
$675$	1278.22	+	2213.94i	0.0728868	+	0.126244i
$676$	2997.68	−	5192.14i	0.170555	−	0.295411i
$677$	24227.5			1.37539			0.687694	−	0.726000i	$-0.258623\pi$
$677$	24227.5			1.37539			0.687694	+	0.726000i	$0.258623\pi$
$678$	571.290	−	989.503i	0.0323603	−	0.0560496i
$679$	11877.0	+	20571.6i	0.671280	+	1.16269i
$680$	−1060.21			−0.0597903
$681$	−754.814	−	1307.38i	−0.0424736	−	0.0735665i
$682$	4798.85	−	8311.86i	0.269439	−	0.466682i
$683$	−5194.02	+	8996.31i	−0.290986	+	0.504003i	−0.974043	−	0.226362i	$-0.927317\pi$
$683$	−5194.02	+	8996.31i	−0.290986	+	0.504003i	0.683057	+	0.730365i	$0.260650\pi$
$684$	−3660.64			−0.204631
$685$	2419.65	−	4190.96i	0.134964	−	0.233764i
$686$	−17878.3			−0.995038
$687$	978.701			0.0543519
$688$	−2298.86	+	22315.9i	−0.127388	+	1.23660i
$689$	20002.9			1.10602
$690$	223.663			0.0123401
$691$	3581.17	−	6202.76i	0.197155	−	0.341482i	−0.750450	−	0.660927i	$-0.770163\pi$
$691$	3581.17	−	6202.76i	0.197155	−	0.341482i	0.947605	+	0.319445i	$0.103496\pi$
$692$	4480.39			0.246125
$693$	−6753.96	+	11698.2i	−0.370219	+	0.641238i
$694$	−5023.14	+	8700.33i	−0.274749	+	0.475879i
$695$	−1147.92	−	1988.25i	−0.0626517	−	0.108516i
$696$	275.537			0.0150060
$697$	−1393.57	−	2413.74i	−0.0757323	−	0.131172i
$698$	12987.4	−	22494.8i	0.704268	−	1.21983i
$699$	−2062.03			−0.111578
$700$	−6025.92	+	10437.2i	−0.325369	+	0.563556i
$701$	13529.1	+	23433.0i	0.728938	+	1.26256i	0.957333	+	0.288988i	$0.0933189\pi$
$701$	13529.1	+	23433.0i	0.728938	+	1.26256i	−0.228395	+	0.973569i	$0.573348\pi$
$702$	−1125.17	−	1948.84i	−0.0604938	−	0.104778i
$703$	−1004.46	−	1739.77i	−0.0538887	−	0.0933380i
$704$	−779.363			−0.0417235
$705$	153.132	+	265.233i	0.00818056	+	0.0141692i
$706$	22620.7	+	39180.2i	1.20587	+	2.08862i
$707$	−9941.58	+	17219.3i	−0.528843	+	0.915982i
$708$	−414.599	+	718.107i	−0.0220079	+	0.0381188i
$709$	17177.5			0.909895			0.454948	−	0.890518i	$-0.349658\pi$
$709$	17177.5			0.909895			0.454948	+	0.890518i	$0.349658\pi$
$710$	−860.211			−0.0454692
$711$	14827.7	−	25682.3i	0.782113	−	1.35466i
$712$	−3708.91	+	6424.02i	−0.195221	+	0.338133i
$713$	5309.66	+	9196.60i	0.278890	+	0.483051i
$714$	757.719	+	1312.41i	0.0397156	+	0.0687894i
$715$	1238.45			0.0647767
$716$	−4343.83	−	7523.74i	−0.226727	−	0.392703i
$717$	359.096	+	621.972i	0.0187039	+	0.0323961i
$718$	−10338.9	−	17907.5i	−0.537389	−	0.930785i
$719$	−7371.25	+	12767.4i	−0.382339	+	0.662230i	−0.991396	−	0.130896i	$-0.958215\pi$
$719$	−7371.25	+	12767.4i	−0.382339	+	0.662230i	0.609058	+	0.793126i	$0.291548\pi$
$720$	−3690.78			−0.191038
$721$	11578.4	−	20054.4i	0.598061	−	1.03587i
$722$	−10681.9	−	18501.6i	−0.550607	−	0.953679i
$723$	−2746.42			−0.141273
$724$	3110.76	+	5387.99i	0.159683	+	0.276579i
$725$	−3637.46	+	6300.27i	−0.186334	+	0.322740i
$726$	531.011	−	919.738i	0.0271456	−	0.0470175i
$727$	−31249.1			−1.59418			−0.797088	−	0.603864i	$-0.793627\pi$
$727$	−31249.1			−1.59418			−0.797088	+	0.603864i	$0.793627\pi$
$728$	−3797.59	+	6577.61i	−0.193335	+	0.334866i
$729$	−19023.9			−0.966515
$730$	2962.96			0.150225
$731$	−13295.9	+	5952.67i	−0.672730	+	0.301186i
$732$	1100.88			0.0555872
$733$	−18663.2			−0.940439			−0.470220	−	0.882549i	$-0.655825\pi$
$733$	−18663.2			−0.940439			−0.470220	+	0.882549i	$0.655825\pi$
$734$	21224.6	−	36762.0i	1.06732	−	1.84865i
$735$	71.1605			0.00357115
$736$	8793.10	−	15230.1i	0.440378	−	0.762757i
$737$	5087.23	−	8811.34i	0.254261	−	0.440393i
$738$	−2577.04	−	4463.57i	−0.128540	−	0.222637i
$739$	15750.2			0.784008			0.392004	−	0.919963i	$-0.371782\pi$
$739$	15750.2			0.784008			0.392004	+	0.919963i	$0.371782\pi$
$740$	276.674	+	479.214i	0.0137443	+	0.0238058i
$741$	−171.725	+	297.436i	−0.00851344	+	0.0147457i
$742$	−49960.8			−2.47186
$743$	8241.57	−	14274.8i	0.406937	−	0.704835i	−0.587608	−	0.809146i	$-0.699930\pi$
$743$	8241.57	−	14274.8i	0.406937	−	0.704835i	0.994545	+	0.104311i	$0.0332636\pi$
$744$	262.441	+	454.561i	0.0129322	+	0.0223992i
$745$	1510.05	+	2615.49i	0.0742604	+	0.128623i
$746$	−665.367	−	1152.45i	−0.0326552	−	0.0565605i
$747$	33750.3			1.65309
$748$	−2859.96	−	4953.59i	−0.139800	−	0.242141i
$749$	−7275.26	−	12601.1i	−0.354916	−	0.614733i
$750$	−295.453	+	511.739i	−0.0143845	+	0.0249148i
$751$	−11125.8	+	19270.4i	−0.540594	+	0.936336i	0.458276	+	0.888810i	$0.348467\pi$
$751$	−11125.8	+	19270.4i	−0.540594	+	0.936336i	−0.998870	+	0.0475261i	$0.984866\pi$
$752$	36245.9			1.75765
$753$	−10.9751			−0.000531149
$754$	3201.92	−	5545.90i	0.154651	−	0.267864i
$755$	1853.53	−	3210.41i	0.0893469	−	0.154753i
$756$	1034.75	+	1792.23i	0.0497795	+	0.0862207i
$757$	−7281.24	−	12611.5i	−0.349592	−	0.605511i	0.636585	−	0.771207i	$-0.280347\pi$
$757$	−7281.24	−	12611.5i	−0.349592	−	0.605511i	−0.986177	+	0.165695i	$0.947013\pi$
$758$	−50095.1			−2.40044
$759$	−431.947	−	748.155i	−0.0206570	−	0.0357791i
$760$	300.071	+	519.738i	0.0143220	+	0.0248064i
$761$	−565.433	−	979.359i	−0.0269342	−	0.0466514i	0.852244	−	0.523144i	$-0.175241\pi$
$761$	−565.433	−	979.359i	−0.0269342	−	0.0466514i	−0.879178	+	0.476493i	$0.841908\pi$
$762$	1133.33	−	1962.98i	0.0538794	−	0.0933219i
$763$	32091.7			1.52267
$764$	3225.39	−	5586.54i	0.152736	−	0.264547i
$765$	−1198.31	−	2075.54i	−0.0566340	−	0.0980930i
$766$	−45555.1			−2.14879
$767$	−6898.60	−	11948.7i	−0.324764	−	0.562508i
$768$	1011.92	−	1752.69i	0.0475448	−	0.0823499i
$769$	783.163	−	1356.48i	0.0367251	−	0.0636097i	−0.847079	−	0.531468i	$-0.821641\pi$
$769$	783.163	−	1356.48i	0.0367251	−	0.0636097i	0.883804	+	0.467858i	$0.154974\pi$
$770$	−3093.24			−0.144770
$771$	−1569.15	+	2717.85i	−0.0732965	+	0.126953i
$772$	−16125.8			−0.751789
$773$	−29874.3			−1.39004			−0.695022	−	0.718989i	$-0.744605\pi$
$773$	−29874.3			−1.39004			−0.695022	+	0.718989i	$0.744605\pi$
$774$	−24587.2	+	11007.9i	−1.14182	+	0.511201i
$775$	−13858.3			−0.642329
$776$	13316.9			0.616042
$777$	−283.130	+	490.395i	−0.0130723	+	0.0226420i
$778$	−33611.0			−1.54886
$779$	−788.842	+	1366.32i	−0.0362814	+	0.0628412i
$780$	47.3010	−	81.9278i	0.00217134	−	0.00376088i
$781$	1661.28	+	2877.42i	0.0761142	+	0.131834i
$782$	17188.5			0.786009
$783$	624.610	+	1081.86i	0.0285080	+	0.0493772i
$784$	4210.86	−	7293.43i	0.191821	−	0.332245i
$785$	5799.28			0.263675
$786$	1726.40	−	2990.22i	0.0783445	−	0.135697i
$787$	−1857.40	−	3217.11i	−0.0841285	−	0.145715i	0.820891	−	0.571085i	$-0.193477\pi$
$787$	−1857.40	−	3217.11i	−0.0841285	−	0.145715i	−0.905020	+	0.425370i	$0.860144\pi$
$788$	−7166.35	−	12412.5i	−0.323973	−	0.561137i
$789$	79.1254	+	137.049i	0.00357026	+	0.00618388i
$790$	6790.93			0.305836
$791$	−8741.91	−	15141.4i	−0.392954	−	0.680616i
$792$	3786.37	+	6558.18i	0.169877	+	0.294236i
$793$	−9158.91	+	15863.7i	−0.410142	+	0.710386i
$794$	19677.5	−	34082.5i	0.879508	−	1.52335i
$795$	−445.517			−0.0198753
$796$	7465.78			0.332434
$797$	17253.6	−	29884.1i	0.766818	−	1.32817i	−0.172462	−	0.985016i	$-0.555172\pi$
$797$	17253.6	−	29884.1i	0.766818	−	1.32817i	0.939280	−	0.343151i	$-0.111494\pi$
$798$	428.912	−	742.897i	0.0190267	−	0.0329552i
$799$	11768.2	+	20383.2i	0.521064	+	0.902509i
$800$	11475.1	+	19875.4i	0.507132	+	0.878378i
$801$	−16768.0			−0.739662
$802$	21835.4	+	37820.0i	0.961390	+	1.66518i
$803$	−5722.21	−	9911.16i	−0.251473	−	0.435563i
$804$	−388.601	−	673.077i	−0.0170459	−	0.0295244i
$805$	1711.25	−	2963.97i	0.0749237	−	0.129772i
$806$	12199.0			0.533114
$807$	765.907	−	1326.59i	0.0334092	−	0.0578664i
$808$	5573.40	+	9653.41i	0.242663	+	0.420304i
$809$	−3865.29			−0.167981			−0.0839904	−	0.996467i	$-0.526767\pi$
$809$	−3865.29			−0.167981			−0.0839904	+	0.996467i	$0.526767\pi$
$810$	−2203.39	−	3816.38i	−0.0955793	−	0.165548i
$811$	15852.7	−	27457.6i	0.686390	−	1.18886i	−0.286608	−	0.958048i	$-0.592528\pi$
$811$	15852.7	−	27457.6i	0.686390	−	1.18886i	0.972998	−	0.230815i	$-0.0741391\pi$
$812$	−2944.61	+	5100.22i	−0.127261	+	0.220422i
$813$	−1410.86			−0.0608625
$814$	2902.39	−	5027.08i	0.124974	−	0.216461i
$815$	5906.01			0.253839
$816$	1599.32			0.0686120
$817$	6681.22	+	4833.12i	0.286103	+	0.206964i
$818$	26563.2			1.13540
$819$	−17168.9			−0.732517
$820$	217.284	−	376.348i	0.00925354	−	0.0160276i
$821$	−26341.2			−1.11975			−0.559874	−	0.828578i	$-0.689150\pi$
$821$	−26341.2			−1.11975			−0.559874	+	0.828578i	$0.689150\pi$
$822$	−1938.93	+	3358.32i	−0.0822723	+	0.142500i
$823$	−11427.7	+	19793.3i	−0.484014	+	0.838336i	−0.999831	−	0.0183621i	$-0.994155\pi$
$823$	−11427.7	+	19793.3i	−0.484014	+	0.838336i	0.515818	+	0.856698i	$0.327488\pi$
$824$	−6491.02	−	11242.8i	−0.274424	−	0.475316i
$825$	1127.39			0.0475766
$826$	17230.5	+	29844.0i	0.725817	+	1.25715i
$827$	−1053.12	+	1824.05i	−0.0442811	+	0.0766970i	−0.887316	−	0.461161i	$-0.847433\pi$
$827$	−1053.12	+	1824.05i	−0.0442811	+	0.0766970i	0.843035	+	0.537858i	$0.180766\pi$
$828$	11703.4			0.491207
$829$	−23647.3	+	40958.3i	−0.990718	+	1.71597i	−0.377637	+	0.925954i	$0.623263\pi$
$829$	−23647.3	+	40958.3i	−0.990718	+	1.71597i	−0.613081	+	0.790020i	$0.710070\pi$
$830$	3864.32	+	6693.20i	0.161605	+	0.279909i
$831$	112.478	+	194.818i	0.00469534	+	0.00813258i
$832$	−495.296	−	857.878i	−0.0206386	−	0.0357471i
$833$	5468.69			0.227466
$834$	919.854	+	1593.23i	0.0381918	+	0.0661501i
$835$	264.380	+	457.920i	0.0109572	+	0.0189784i
$836$	−1618.90	+	2804.01i	−0.0669746	+	0.116003i
$837$	−1189.84	+	2060.87i	−0.0491362	+	0.0851065i
$838$	58331.9			2.40458
$839$	18592.7			0.765068			0.382534	−	0.923941i	$-0.375052\pi$
$839$	18592.7			0.765068			0.382534	+	0.923941i	$0.375052\pi$
$840$	84.5820	−	146.500i	0.00347424	−	0.00601755i
$841$	10417.0	−	18042.8i	0.427120	−	0.739793i
$842$	−2270.26	−	3932.20i	−0.0929195	−	0.160941i
$843$	−574.501	−	995.065i	−0.0234720	−	0.0406546i
$844$	−7684.99			−0.313422
$845$	−1110.93	−	1924.20i	−0.0452276	−	0.0783365i
$846$	21762.2	+	37693.2i	0.884396	+	1.53182i
$847$	−8125.56	−	14073.9i	−0.329631	−	0.570938i
$848$	−26363.1	+	45662.2i	−1.06759	+	1.84911i
$849$	1364.01			0.0551386
$850$	−11215.6	+	19425.9i	−0.452578	+	0.783887i
$851$	3211.33	+	5562.18i	0.129357	+	0.224053i
$852$	253.802			0.0102055
$853$	8686.87	+	15046.1i	0.348690	+	0.603950i	0.986017	−	0.166644i	$-0.0532931\pi$
$853$	8686.87	+	15046.1i	0.348690	+	0.603950i	−0.637327	+	0.770594i	$0.719960\pi$
$854$	22876.0	−	39622.3i	0.916627	−	1.58765i
$855$	−678.312	+	1174.87i	−0.0271319	+	0.0469938i
$856$	−8157.23			−0.325711
$857$	8806.43	−	15253.2i	0.351017	−	0.607980i	−0.635411	−	0.772175i	$-0.719169\pi$
$857$	8806.43	−	15253.2i	0.351017	−	0.607980i	0.986428	+	0.164194i	$0.0525024\pi$
$858$	−992.400			−0.0394872
$859$	29606.2			1.17596			0.587980	−	0.808876i	$-0.299923\pi$
$859$	29606.2			1.17596			0.587980	+	0.808876i	$0.299923\pi$
$860$	−1840.32	−	1331.27i	−0.0729704	−	0.0527860i
$861$	444.708			0.0176023
$862$	7671.26			0.303114
$863$	−10411.0	+	18032.4i	−0.410654	+	0.711273i	−0.994961	−	0.100259i	$-0.968033\pi$
$863$	−10411.0	+	18032.4i	−0.410654	+	0.711273i	0.584308	+	0.811532i	$0.301366\pi$
$864$	3940.90			0.155176
$865$	830.212	−	1437.97i	0.0326336	−	0.0565230i
$866$	−6273.23	+	10865.5i	−0.246158	+	0.426358i
$867$	−436.531	−	756.095i	−0.0170996	−	0.0296174i
$868$	−11218.6			−0.438692
$869$	−13115.0	−	22715.8i	−0.511961	−	0.886743i
$870$	−71.3151	+	123.521i	−0.00277909	+	0.00481353i
$871$	12932.0			0.503083
$872$	8995.55	−	15580.7i	0.349344	−	0.605081i
$873$	15051.5	+	26069.9i	0.583522	+	1.01069i
$874$	−4864.83	−	8426.13i	−0.188278	−	0.326108i
$875$	4521.03	+	7830.65i	0.174673	+	0.302542i
$876$	−874.212			−0.0337179
$877$	−20154.8	−	34909.1i	−0.776029	−	1.34412i	−0.934214	−	0.356712i	$-0.883898\pi$
$877$	−20154.8	−	34909.1i	−0.776029	−	1.34412i	0.158185	−	0.987409i	$-0.449436\pi$
$878$	27135.6	+	47000.3i	1.04303	+	1.80659i
$879$	336.853	−	583.446i	0.0129258	−	0.0223881i
$880$	−1632.23	+	2827.10i	−0.0625255	+	0.108297i
$881$	−9468.84			−0.362104			−0.181052	−	0.983474i	$-0.557950\pi$
$881$	−9468.84			−0.362104			−0.181052	+	0.983474i	$0.557950\pi$
$882$	10112.9			0.386075
$883$	11002.8	−	19057.3i	0.419334	−	0.726308i	−0.576538	−	0.817070i	$-0.695597\pi$
$883$	11002.8	−	19057.3i	0.419334	−	0.726308i	0.995873	+	0.0907619i	$0.0289302\pi$
$884$	3635.09	−	6296.15i	0.138305	−	0.239550i
$885$	153.650	+	266.129i	0.00583602	+	0.0101083i
$886$	11382.4	+	19715.0i	0.431604	+	0.747559i
$887$	−5478.27			−0.207376			−0.103688	−	0.994610i	$-0.533064\pi$
$887$	−5478.27			−0.207376			−0.103688	+	0.994610i	$0.533064\pi$
$888$	158.727	+	274.923i	0.00599833	+	0.0103894i
$889$	−17342.2	−	30037.6i	−0.654263	−	1.13322i
$890$	−1919.90	−	3325.36i	−0.0723091	−	0.125243i
$891$	−8510.58	+	14740.7i	−0.319994	+	0.554247i
$892$	13997.8			0.525426
$893$	6661.48	−	11538.0i	0.249628	−	0.432369i
$894$	−1210.04	−	2095.85i	−0.0452683	−	0.0784070i
$895$	−3219.63			−0.120246
$896$	−14702.8	−	25466.0i	−0.548198	−	0.949507i
$897$	549.017	−	950.926i	0.0204361	−	0.0353963i
$898$	3169.00	−	5488.87i	0.117763	−	0.203971i
$899$	−6771.96			−0.251232
$900$	−7636.49	+	13226.8i	−0.282833	+	0.489881i
$901$	−34238.0			−1.26596
$902$	−4558.74			−0.168281
$903$	238.182	−	2312.12i	0.00877763	−	0.0852075i
$904$	−9801.68			−0.360619
$905$	2305.68			0.0846889
$906$	−1485.28	+	2572.58i	−0.0544649	+	0.0943360i
$907$	−45128.8			−1.65213			−0.826063	−	0.563578i	$-0.809424\pi$
$907$	−45128.8			−1.65213			−0.826063	+	0.563578i	$0.809424\pi$
$908$	9044.46	−	15665.5i	0.330563	−	0.572551i
$909$	−12598.7	+	21821.6i	−0.459706	+	0.796234i
$910$	−1965.80	−	3404.86i	−0.0716105	−	0.124033i
$911$	255.420			0.00928916			0.00464458	−	0.999989i	$-0.498522\pi$
$911$	255.420			0.00928916			0.00464458	+	0.999989i	$0.498522\pi$
$912$	−452.653	−	784.018i	−0.0164351	−	0.0284665i
$913$	14925.9	−	25852.4i	0.541046	−	0.937119i
$914$	−16397.6			−0.593418
$915$	203.993	−	353.325i	0.00737026	−	0.0127657i
$916$	5863.58	+	10156.0i	0.211504	+	0.366336i
$917$	−26417.5	−	45756.5i	−0.951345	−	1.64778i
$918$	1925.89	+	3335.74i	0.0692416	+	0.119930i
$919$	−10556.9			−0.378934			−0.189467	−	0.981887i	$-0.560676\pi$
$919$	−10556.9			−0.378934			−0.189467	+	0.981887i	$0.560676\pi$
$920$	−959.351	−	1661.64i	−0.0343792	−	0.0595465i
$921$	316.888	+	548.866i	0.0113375	+	0.0196371i
$922$	4103.88	−	7108.13i	0.146588	−	0.253898i
$923$	−2111.53	+	3657.28i	−0.0753000	+	0.130423i
$924$	912.649			0.0324935
$925$	−8381.63			−0.297931
$926$	−13828.4	+	23951.5i	−0.490745	+	0.849995i
$927$	14673.0	−	25414.4i	0.519875	−	0.900450i
$928$	5607.38	+	9712.27i	0.198353	+	0.343557i
$929$	8506.61	+	14733.9i	0.300423	+	0.520348i	0.976232	−	0.216729i	$-0.0695389\pi$
$929$	8506.61	+	14733.9i	0.300423	+	0.520348i	−0.675809	+	0.737077i	$0.736206\pi$
$930$	−271.702			−0.00958007
$931$	−1547.79	−	2680.86i	−0.0544864	−	0.0943733i
$932$	−12354.0	−	21397.8i	−0.434194	−	0.752047i
$933$	470.427	+	814.804i	0.0165071	+	0.0285911i
$934$	21964.5	−	38043.6i	0.769485	−	1.33279i
$935$	−2119.79			−0.0741439
$936$	−4812.58	+	8335.63i	−0.168060	+	0.291088i
$937$	3447.46	+	5971.17i	0.120196	+	0.208185i	0.919845	−	0.392282i	$-0.128314\pi$
$937$	3447.46	+	5971.17i	0.120196	+	0.208185i	−0.799649	+	0.600468i	$0.794981\pi$
$938$	−32300.0			−1.12434
$939$	1166.71	+	2020.80i	0.0405476	+	0.0702305i
$940$	−1834.89	+	3178.12i	−0.0636675	+	0.110275i
$941$	−17387.9	+	30116.7i	−0.602370	+	1.04333i	0.390092	+	0.920776i	$0.372443\pi$
$941$	−17387.9	+	30116.7i	−0.602370	+	1.04333i	−0.992461	+	0.122559i	$0.960890\pi$
$942$	−4647.11			−0.160734
$943$	2521.99	−	4368.22i	0.0870916	−	0.150847i
$944$	36368.4			1.25391
$945$	766.949			0.0264009
$946$	−2441.63	+	23701.7i	−0.0839155	+	0.814598i
$947$	39895.0			1.36897			0.684485	−	0.729027i	$-0.260027\pi$
$947$	39895.0			1.36897			0.684485	+	0.729027i	$0.260027\pi$
$948$	−2003.64			−0.0686447
$949$	7273.09	−	12597.4i	0.248782	−	0.430904i
$950$	12697.3			0.433637
$951$	961.777	−	1665.85i	0.0327947	−	0.0568021i
$952$	6500.13	−	11258.6i	0.221293	−	0.383290i
$953$	−8682.96	−	15039.3i	−0.295140	−	0.511198i	0.679877	−	0.733326i	$-0.262033\pi$
$953$	−8682.96	−	15039.3i	−0.295140	−	0.511198i	−0.975017	+	0.222128i	$0.928700\pi$
$954$	−63314.0			−2.14871
$955$	−1195.32	−	2070.36i	−0.0405023	−	0.0701521i
$956$	−4302.81	+	7452.69i	−0.145568	+	0.252131i
$957$	550.908			0.0186085
$958$	25603.8	−	44347.1i	0.863487	−	1.49560i
$959$	29669.6	+	51389.2i	0.999041	+	1.73039i
$960$	11.0315	+	19.1072i	0.000370876	+	0.000642376i
$961$	8445.40	+	14627.9i	0.283488	+	0.491016i
$962$	7378.03			0.247274
$963$	−9219.74	−	15969.1i	−0.308517	−	0.534367i
$964$	−16454.3	−	28499.7i	−0.549749	−	0.952193i
$965$	−2988.10	+	5175.54i	−0.0996790	+	0.172649i
$966$	−1371.27	+	2375.10i	−0.0456727	+	0.0791074i
$967$	7707.52			0.256315			0.128158	−	0.991754i	$-0.459094\pi$
$967$	7707.52			0.256315			0.128158	+	0.991754i	$0.459094\pi$
$968$	−9110.61			−0.302506
$969$	293.932	−	509.105i	0.00974454	−	0.0168780i
$970$	−3446.71	+	5969.87i	−0.114090	+	0.197609i
$971$	11807.2	+	20450.6i	0.390226	+	0.675891i	0.992479	−	0.122414i	$-0.0390635\pi$
$971$	11807.2	+	20450.6i	0.390226	+	0.675891i	−0.602253	+	0.798305i	$0.705730\pi$
$972$	1968.80	+	3410.06i	0.0649685	+	0.112529i
$973$	28151.3			0.927532
$974$	1079.48	+	1869.72i	0.0355122	+	0.0615089i
$975$	716.473	+	1240.97i	0.0235338	+	0.0407618i
$976$	−24142.2	−	41815.5i	−0.791775	−	1.37140i
$977$	1184.51	−	2051.63i	0.0387880	−	0.0671828i	−0.845980	−	0.533215i	$-0.820984\pi$
$977$	1184.51	−	2051.63i	0.0387880	−	0.0671828i	0.884768	+	0.466032i	$0.154317\pi$
$978$	−4732.64			−0.154737
$979$	−7415.58	+	12844.2i	−0.242087	+	0.419307i
$980$	426.335	+	738.434i	0.0138967	+	0.0240698i
$981$	40669.0			1.32361
$982$	12523.1	+	21690.7i	0.406954	+	0.704865i
$983$	−18382.4	+	31839.2i	−0.596446	+	1.03307i	0.396895	+	0.917864i	$0.370088\pi$
$983$	−18382.4	+	31839.2i	−0.596446	+	1.03307i	−0.993341	+	0.115211i	$0.963246\pi$
$984$	124.655	−	215.909i	0.00403847	−	0.00699483i
$985$	−5311.67			−0.171821
$986$	−5480.57	+	9492.63i	−0.177015	+	0.306599i
$987$	−3755.39			−0.121110
$988$	−4115.33			−0.132516
$989$	−21360.4	−	15451.9i	−0.686776	−	0.496806i
$990$	−3919.98			−0.125844
$991$	21854.8			0.700546			0.350273	−	0.936648i	$-0.386089\pi$
$991$	21854.8			0.700546			0.350273	+	0.936648i	$0.386089\pi$
$992$	−10681.7	+	18501.3i	−0.341880	+	0.592154i
$993$	868.568			0.0277575
$994$	5273.92	−	9134.69i	0.168288	−	0.291484i
$995$	1383.40	−	2396.12i	0.0440772	−	0.0763439i
$996$	−1140.15	−	1974.80i	−0.0362722	−	0.0628253i
$997$	−32490.3			−1.03207			−0.516037	−	0.856566i	$-0.672593\pi$
$997$	−32490.3			−1.03207			−0.516037	+	0.856566i	$0.672593\pi$
$998$	5590.16	+	9682.44i	0.177308	+	0.307107i
$999$	−719.628	+	1246.43i	−0.0227908	+	0.0394749i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.c.a.6.3	✓	20
43.6	even	3		1849.4.a.d.1.3		10
43.36	even	3	inner	43.4.c.a.36.3	yes	20
43.37	odd	6		1849.4.a.f.1.8		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.3	✓	20	1.1	even	1	trivial
43.4.c.a.36.3	yes	20	43.36	even	3	inner
1849.4.a.d.1.3		10	43.6	even	3
1849.4.a.f.1.8		10	43.37	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 43 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	43.c (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q-3.55840 q^{2} +(0.194544 - 0.336960i) q^{3} +4.66219 q^{4} +(0.863899 - 1.49632i) q^{5} +(-0.692264 + 1.19904i) q^{6} +(10.5931 + 18.3477i) q^{7} +11.8773 q^{8} +(13.4243 + 23.2516i) q^{9} +O(q^{10})\)	\(q-3.55840 q^{2} +(0.194544 - 0.336960i) q^{3} +4.66219 q^{4} +(0.863899 - 1.49632i) q^{5} +(-0.692264 + 1.19904i) q^{6} +(10.5931 + 18.3477i) q^{7} +11.8773 q^{8} +(13.4243 + 23.2516i) q^{9} +(-3.07410 + 5.32449i) q^{10} +23.7473 q^{11} +(0.907001 - 1.57097i) q^{12} +(15.0918 + 26.1397i) q^{13} +(-37.6943 - 65.2885i) q^{14} +(-0.336133 - 0.582199i) q^{15} -79.5615 q^{16} +(-25.8318 - 44.7420i) q^{17} +(-47.7690 - 82.7384i) q^{18} +(-14.6223 + 25.3265i) q^{19} +(4.02766 - 6.97612i) q^{20} +8.24326 q^{21} -84.5025 q^{22} +(46.7486 - 80.9709i) q^{23} +(2.31065 - 4.00216i) q^{24} +(61.0074 + 105.668i) q^{25} +(-53.7025 - 93.0155i) q^{26} +20.9518 q^{27} +(49.3869 + 85.5406i) q^{28} +(29.8117 + 51.6354i) q^{29} +(1.19609 + 2.07169i) q^{30} +(-56.7895 + 98.3623i) q^{31} +188.093 q^{32} +(4.61990 - 8.00190i) q^{33} +(91.9198 + 159.210i) q^{34} +36.6053 q^{35} +(62.5867 + 108.403i) q^{36} +(-34.3468 + 59.4904i) q^{37} +(52.0318 - 90.1218i) q^{38} +11.7440 q^{39} +(10.2607 - 17.7721i) q^{40} +53.9480 q^{41} -29.3328 q^{42} +(28.8941 - 280.486i) q^{43} +110.715 q^{44} +46.3890 q^{45} +(-166.350 + 288.127i) q^{46} -455.571 q^{47} +(-15.4782 + 26.8090i) q^{48} +(-52.9259 + 91.6704i) q^{49} +(-217.088 - 376.008i) q^{50} -20.1017 q^{51} +(70.3607 + 121.868i) q^{52} +(331.355 - 573.924i) q^{53} -74.5550 q^{54} +(20.5153 - 35.5336i) q^{55} +(125.816 + 217.921i) q^{56} +(5.68934 + 9.85423i) q^{57} +(-106.082 - 183.739i) q^{58} -457.110 q^{59} +(-1.56711 - 2.71432i) q^{60} +(303.441 + 525.575i) q^{61} +(202.080 - 350.012i) q^{62} +(-284.409 + 492.611i) q^{63} -32.8190 q^{64} +52.1511 q^{65} +(-16.4394 + 28.4739i) q^{66} +(214.223 - 371.045i) q^{67} +(-120.433 - 208.596i) q^{68} +(-18.1893 - 31.5048i) q^{69} -130.256 q^{70} +(69.9564 + 121.168i) q^{71} +(159.444 + 276.165i) q^{72} +(-240.962 - 417.359i) q^{73} +(122.219 - 211.690i) q^{74} +47.4744 q^{75} +(-68.1718 + 118.077i) q^{76} +(251.557 + 435.710i) q^{77} -41.7900 q^{78} +(-552.271 - 956.561i) q^{79} +(-68.7331 + 119.049i) q^{80} +(-358.380 + 620.733i) q^{81} -191.968 q^{82} +(628.529 - 1088.64i) q^{83} +38.4317 q^{84} -89.2643 q^{85} +(-102.817 + 998.079i) q^{86} +23.1987 q^{87} +282.053 q^{88} +(-312.270 + 540.868i) q^{89} -165.070 q^{90} +(-319.736 + 553.799i) q^{91} +(217.951 - 377.502i) q^{92} +(22.0961 + 38.2716i) q^{93} +1621.10 q^{94} +(25.2643 + 43.7591i) q^{95} +(36.5924 - 63.3799i) q^{96} +1121.21 q^{97} +(188.331 - 326.200i) q^{98} +(318.792 + 552.163i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9	\( 20 q - 2 q^{2} - 5 q^{3} + 78 q^{4} - 19 q^{5} + 15 q^{6} - 51 q^{7} - 72 q^{8} - 117 q^{9} + 27 q^{10} + 54 q^{11} - 72 q^{12} - 15 q^{13} + 96 q^{14} + 65 q^{15} + 134 q^{16} - 82 q^{17} + 247 q^{18} + 78 q^{19} - 495 q^{20} - 18 q^{21} + 380 q^{22} - 61 q^{23} + 202 q^{24} - 151 q^{25} - 21 q^{26} - 194 q^{27} - 794 q^{28} - 53 q^{29} + 627 q^{30} + 253 q^{31} - 798 q^{32} - 424 q^{33} - 231 q^{34} + 710 q^{35} - 1092 q^{36} - 129 q^{37} - 854 q^{38} + 1382 q^{39} + 1345 q^{40} + 782 q^{41} + 62 q^{42} + 1025 q^{43} + 754 q^{44} + 1888 q^{45} - 40 q^{46} - 668 q^{47} - 2401 q^{48} - 115 q^{49} + 424 q^{50} + 1590 q^{51} - 564 q^{52} + 773 q^{53} + 364 q^{54} - 1242 q^{55} - 923 q^{56} - 765 q^{57} + 1328 q^{58} - 2966 q^{59} - 1075 q^{60} + 437 q^{61} + 1509 q^{62} - 2222 q^{63} - 1476 q^{64} - 2126 q^{65} + 1483 q^{66} - 642 q^{67} - 1052 q^{68} - 3503 q^{69} - 170 q^{70} - 1545 q^{71} + 3834 q^{72} + 1292 q^{73} - 2232 q^{74} + 164 q^{75} - 252 q^{76} + 1448 q^{77} + 5644 q^{78} - 1405 q^{79} - 3157 q^{80} + 974 q^{81} + 6608 q^{82} + 543 q^{83} + 7304 q^{84} + 1946 q^{85} + 2776 q^{86} + 2818 q^{87} - 5372 q^{88} - 2196 q^{89} - 1484 q^{90} - 3513 q^{91} + 2629 q^{92} - 983 q^{93} + 9878 q^{94} - 149 q^{95} + 3540 q^{96} - 850 q^{97} - 213 q^{98} - 3181 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 - 5 * q^3 + 78 * q^4 - 19 * q^5 + 15 * q^6 - 51 * q^7 - 72 * q^8 - 117 * q^9 + 27 * q^10 + 54 * q^11 - 72 * q^12 - 15 * q^13 + 96 * q^14 + 65 * q^15 + 134 * q^16 - 82 * q^17 + 247 * q^18 + 78 * q^19 - 495 * q^20 - 18 * q^21 + 380 * q^22 - 61 * q^23 + 202 * q^24 - 151 * q^25 - 21 * q^26 - 194 * q^27 - 794 * q^28 - 53 * q^29 + 627 * q^30 + 253 * q^31 - 798 * q^32 - 424 * q^33 - 231 * q^34 + 710 * q^35 - 1092 * q^36 - 129 * q^37 - 854 * q^38 + 1382 * q^39 + 1345 * q^40 + 782 * q^41 + 62 * q^42 + 1025 * q^43 + 754 * q^44 + 1888 * q^45 - 40 * q^46 - 668 * q^47 - 2401 * q^48 - 115 * q^49 + 424 * q^50 + 1590 * q^51 - 564 * q^52 + 773 * q^53 + 364 * q^54 - 1242 * q^55 - 923 * q^56 - 765 * q^57 + 1328 * q^58 - 2966 * q^59 - 1075 * q^60 + 437 * q^61 + 1509 * q^62 - 2222 * q^63 - 1476 * q^64 - 2126 * q^65 + 1483 * q^66 - 642 * q^67 - 1052 * q^68 - 3503 * q^69 - 170 * q^70 - 1545 * q^71 + 3834 * q^72 + 1292 * q^73 - 2232 * q^74 + 164 * q^75 - 252 * q^76 + 1448 * q^77 + 5644 * q^78 - 1405 * q^79 - 3157 * q^80 + 974 * q^81 + 6608 * q^82 + 543 * q^83 + 7304 * q^84 + 1946 * q^85 + 2776 * q^86 + 2818 * q^87 - 5372 * q^88 - 2196 * q^89 - 1484 * q^90 - 3513 * q^91 + 2629 * q^92 - 983 * q^93 + 9878 * q^94 - 149 * q^95 + 3540 * q^96 - 850 * q^97 - 213 * q^98 - 3181 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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