LMFDB - Embedded newform 43.4.c.a.36.10

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			36.10
Root			$-2.46280 - 4.26569i$ of defining polynomial
Character	$\chi$	$=$	43.36
Dual form			43.4.c.a.6.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+4.92559 q^{2} +(-2.49565 - 4.32260i) q^{3} +16.2615 q^{4} +(-1.06165 - 1.83883i) q^{5} +(-12.2926 - 21.2914i) q^{6} +(-14.5255 + 25.1588i) q^{7} +40.6926 q^{8} +(1.04342 - 1.80726i) q^{9} +O(q^{10})$	\(q+4.92559 q^{2} +(-2.49565 - 4.32260i) q^{3} +16.2615 q^{4} +(-1.06165 - 1.83883i) q^{5} +(-12.2926 - 21.2914i) q^{6} +(-14.5255 + 25.1588i) q^{7} +40.6926 q^{8} +(1.04342 - 1.80726i) q^{9} +(-5.22925 - 9.05732i) q^{10} +23.0490 q^{11} +(-40.5830 - 70.2918i) q^{12} +(-31.8958 + 55.2452i) q^{13} +(-71.5465 + 123.922i) q^{14} +(-5.29901 + 9.17816i) q^{15} +70.3437 q^{16} +(8.60879 - 14.9109i) q^{17} +(5.13947 - 8.90182i) q^{18} +(-71.0762 - 123.108i) q^{19} +(-17.2640 - 29.9021i) q^{20} +145.002 q^{21} +113.530 q^{22} +(19.1844 + 33.2283i) q^{23} +(-101.555 - 175.898i) q^{24} +(60.2458 - 104.349i) q^{25} +(-157.106 + 272.115i) q^{26} -145.181 q^{27} +(-236.205 + 409.120i) q^{28} +(108.987 - 188.770i) q^{29} +(-26.1008 + 45.2079i) q^{30} +(120.155 + 208.115i) q^{31} +20.9431 q^{32} +(-57.5224 - 99.6317i) q^{33} +(42.4034 - 73.4449i) q^{34} +61.6837 q^{35} +(16.9676 - 29.3887i) q^{36} +(-13.6335 - 23.6139i) q^{37} +(-350.092 - 606.378i) q^{38} +318.404 q^{39} +(-43.2013 - 74.8268i) q^{40} +175.750 q^{41} +714.221 q^{42} +(101.732 + 262.978i) q^{43} +374.811 q^{44} -4.43099 q^{45} +(94.4945 + 163.669i) q^{46} +25.7311 q^{47} +(-175.553 - 304.068i) q^{48} +(-250.478 - 433.840i) q^{49} +(296.746 - 513.980i) q^{50} -85.9383 q^{51} +(-518.673 + 898.368i) q^{52} +(97.5022 + 168.879i) q^{53} -715.105 q^{54} +(-24.4699 - 42.3832i) q^{55} +(-591.079 + 1023.78i) q^{56} +(-354.763 + 614.468i) q^{57} +(536.824 - 929.806i) q^{58} -781.699 q^{59} +(-86.1697 + 149.250i) q^{60} +(347.816 - 602.435i) q^{61} +(591.835 + 1025.09i) q^{62} +(30.3124 + 52.5025i) q^{63} -459.592 q^{64} +135.449 q^{65} +(-283.332 - 490.745i) q^{66} +(14.5437 + 25.1904i) q^{67} +(139.992 - 242.473i) q^{68} +(95.7552 - 165.853i) q^{69} +303.829 q^{70} +(-470.586 + 815.079i) q^{71} +(42.4596 - 73.5422i) q^{72} +(118.308 - 204.916i) q^{73} +(-67.1532 - 116.313i) q^{74} -601.411 q^{75} +(-1155.80 - 2001.91i) q^{76} +(-334.797 + 579.886i) q^{77} +1568.33 q^{78} +(-85.9210 + 148.820i) q^{79} +(-74.6802 - 129.350i) q^{80} +(334.150 + 578.765i) q^{81} +865.673 q^{82} +(-159.343 - 275.990i) q^{83} +2357.95 q^{84} -36.5580 q^{85} +(501.090 + 1295.32i) q^{86} -1087.97 q^{87} +937.925 q^{88} +(418.989 + 725.710i) q^{89} -21.8252 q^{90} +(-926.603 - 1604.92i) q^{91} +(311.966 + 540.342i) q^{92} +(599.731 - 1038.76i) q^{93} +126.741 q^{94} +(-150.916 + 261.394i) q^{95} +(-52.2668 - 90.5288i) q^{96} +665.680 q^{97} +(-1233.75 - 2136.92i) q^{98} +(24.0498 - 41.6555i) 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 $\left(\mathbb{Z}/43\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	4.92559			1.74146			0.870730	−	0.491761i	$-0.163647\pi$
$2$	4.92559			1.74146			0.870730	+	0.491761i	$0.163647\pi$
$3$	−2.49565	−	4.32260i	−0.480289	−	0.831885i	0.519455	−	0.854498i	$-0.326135\pi$
$3$	−2.49565	−	4.32260i	−0.480289	−	0.831885i	−0.999744	+	0.0226128i	$0.992801\pi$
$4$	16.2615			2.03268
$5$	−1.06165	−	1.83883i	−0.0949567	−	0.164470i	0.814634	−	0.579976i	$-0.196938\pi$
$5$	−1.06165	−	1.83883i	−0.0949567	−	0.164470i	−0.909591	+	0.415506i	$0.863605\pi$
$6$	−12.2926	−	21.2914i	−0.836404	−	1.44869i
$7$	−14.5255	+	25.1588i	−0.784301	+	1.35845i	0.145115	+	0.989415i	$0.453645\pi$
$7$	−14.5255	+	25.1588i	−0.784301	+	1.35845i	−0.929416	+	0.369034i	$0.879689\pi$
$8$	40.6926			1.79838
$9$	1.04342	−	1.80726i	0.0386452	−	0.0669355i
$10$	−5.22925	−	9.05732i	−0.165363	−	0.286418i
$11$	23.0490			0.631776			0.315888	−	0.948796i	$-0.397698\pi$
$11$	23.0490			0.631776			0.315888	+	0.948796i	$0.397698\pi$
$12$	−40.5830	−	70.2918i	−0.976275	−	1.69096i
$13$	−31.8958	+	55.2452i	−0.680486	+	1.17864i	0.294347	+	0.955699i	$0.404898\pi$
$13$	−31.8958	+	55.2452i	−0.680486	+	1.17864i	−0.974833	+	0.222937i	$0.928435\pi$
$14$	−71.5465	+	123.922i	−1.36583	+	2.36569i
$15$	−5.29901	+	9.17816i	−0.0912133	+	0.157986i
$16$	70.3437			1.09912
$17$	8.60879	−	14.9109i	0.122820	−	0.212730i	−0.798059	−	0.602580i	$-0.794140\pi$
$17$	8.60879	−	14.9109i	0.122820	−	0.212730i	0.920879	+	0.389849i	$0.127473\pi$
$18$	5.13947	−	8.90182i	0.0672992	−	0.116566i
$19$	−71.0762	−	123.108i	−0.858210	−	1.48646i	−0.873635	−	0.486582i	$-0.838243\pi$
$19$	−71.0762	−	123.108i	−0.858210	−	1.48646i	0.0154245	−	0.999881i	$-0.495090\pi$
$20$	−17.2640	−	29.9021i	−0.193017	−	0.334315i
$21$	145.002			1.50676
$22$	113.530			1.10021
$23$	19.1844	+	33.2283i	0.173923	+	0.301243i	0.939788	−	0.341758i	$-0.111022\pi$
$23$	19.1844	+	33.2283i	0.173923	+	0.301243i	−0.765865	+	0.643001i	$0.777689\pi$
$24$	−101.555	−	175.898i	−0.863741	−	1.49604i
$25$	60.2458	−	104.349i	0.481966	−	0.834790i
$26$	−157.106	+	272.115i	−1.18504	+	2.05255i
$27$	−145.181			−1.03482
$28$	−236.205	+	409.120i	−1.59424	+	2.76130i
$29$	108.987	−	188.770i	0.697873	−	1.20875i	−0.271330	−	0.962486i	$-0.587463\pi$
$29$	108.987	−	188.770i	0.697873	−	1.20875i	0.969203	−	0.246264i	$-0.0792032\pi$
$30$	−26.1008	+	45.2079i	−0.158844	+	0.275126i
$31$	120.155	+	208.115i	0.696145	+	1.20576i	0.969793	+	0.243929i	$0.0784363\pi$
$31$	120.155	+	208.115i	0.696145	+	1.20576i	−0.273648	+	0.961830i	$0.588230\pi$
$32$	20.9431			0.115696
$33$	−57.5224	−	99.6317i	−0.303435	−	0.525565i
$34$	42.4034	−	73.4449i	0.213886	−	0.370462i
$35$	61.6837			0.297899
$36$	16.9676	−	29.3887i	0.0785536	−	0.136059i
$37$	−13.6335	−	23.6139i	−0.0605767	−	0.104922i	0.834147	−	0.551543i	$-0.185961\pi$
$37$	−13.6335	−	23.6139i	−0.0605767	−	0.104922i	−0.894723	+	0.446621i	$0.852627\pi$
$38$	−350.092	−	606.378i	−1.49454	−	2.58862i
$39$	318.404			1.30732
$40$	−43.2013	−	74.8268i	−0.170768	−	0.295779i
$41$	175.750			0.669452			0.334726	−	0.942316i	$-0.391356\pi$
$41$	175.750			0.669452			0.334726	+	0.942316i	$0.391356\pi$
$42$	714.221			2.62397
$43$	101.732	+	262.978i	0.360790	+	0.932647i
$43$	101.732	+	262.978i	0.360790	+	0.932647i
$44$	374.811			1.28420
$45$	−4.43099			−0.0146785
$46$	94.4945	+	163.669i	0.302879	+	0.524603i
$47$	25.7311			0.0798566			0.0399283	−	0.999203i	$-0.487287\pi$
$47$	25.7311			0.0798566			0.0399283	+	0.999203i	$0.487287\pi$
$48$	−175.553	−	304.068i	−0.527895	−	0.914341i
$49$	−250.478	−	433.840i	−0.730256	−	1.26484i
$50$	296.746	−	513.980i	0.839325	−	1.45375i
$51$	−85.9383			−0.235956
$52$	−518.673	+	898.368i	−1.38321	+	2.39579i
$53$	97.5022	+	168.879i	0.252697	+	0.437685i	0.964268	−	0.264930i	$-0.0853490\pi$
$53$	97.5022	+	168.879i	0.252697	+	0.437685i	−0.711570	+	0.702615i	$0.752016\pi$
$54$	−715.105			−1.80210
$55$	−24.4699	−	42.3832i	−0.0599914	−	0.103908i
$56$	−591.079	+	1023.78i	−1.41047	+	2.44300i
$57$	−354.763	+	614.468i	−0.824377	+	1.42786i
$58$	536.824	−	929.806i	1.21532	−	2.10499i
$59$	−781.699			−1.72489			−0.862445	−	0.506150i	$-0.831068\pi$
$59$	−781.699			−1.72489			−0.862445	+	0.506150i	$0.831068\pi$
$60$	−86.1697	+	149.250i	−0.185408	+	0.321136i
$61$	347.816	−	602.435i	0.730053	−	1.26449i	−0.226807	−	0.973940i	$-0.572829\pi$
$61$	347.816	−	602.435i	0.730053	−	1.26449i	0.956860	−	0.290549i	$-0.0938380\pi$
$62$	591.835	+	1025.09i	1.21231	+	2.09978i
$63$	30.3124	+	52.5025i	0.0606190	+	0.104995i
$64$	−459.592			−0.897641
$65$	135.449			0.258467
$66$	−283.332	−	490.745i	−0.528420	−	0.915251i
$67$	14.5437	+	25.1904i	0.0265193	+	0.0459327i	0.878980	−	0.476858i	$-0.158224\pi$
$67$	14.5437	+	25.1904i	0.0265193	+	0.0459327i	−0.852461	+	0.522791i	$0.824891\pi$
$68$	139.992	−	242.473i	0.249654	−	0.432414i
$69$	95.7552	−	165.853i	0.167066	−	0.289367i
$70$	303.829			0.518778
$71$	−470.586	+	815.079i	−0.786596	+	1.36242i	0.141445	+	0.989946i	$0.454825\pi$
$71$	−470.586	+	815.079i	−0.786596	+	1.36242i	−0.928041	+	0.372478i	$0.878508\pi$
$72$	42.4596	−	73.5422i	0.0694988	−	0.120375i
$73$	118.308	−	204.916i	0.189684	−	0.328542i	−0.755461	−	0.655194i	$-0.772587\pi$
$73$	118.308	−	204.916i	0.189684	−	0.328542i	0.945145	+	0.326652i	$0.105920\pi$
$74$	−67.1532	−	116.313i	−0.105492	−	0.182717i
$75$	−601.411			−0.925932
$76$	−1155.80	−	2001.91i	−1.74447	−	3.02151i
$77$	−334.797	+	579.886i	−0.495503	+	0.858236i
$78$	1568.33			2.27664
$79$	−85.9210	+	148.820i	−0.122365	+	0.211943i	−0.920700	−	0.390271i	$-0.872381\pi$
$79$	−85.9210	+	148.820i	−0.122365	+	0.211943i	0.798335	+	0.602214i	$0.205715\pi$
$80$	−74.6802	−	129.350i	−0.104369	−	0.180772i
$81$	334.150	+	578.765i	0.458368	+	0.793916i
$82$	865.673			1.16582
$83$	−159.343	−	275.990i	−0.210724	−	0.364986i	0.741217	−	0.671266i	$-0.234249\pi$
$83$	−159.343	−	275.990i	−0.210724	−	0.364986i	−0.951941	+	0.306280i	$0.900916\pi$
$84$	2357.95			3.06277
$85$	−36.5580			−0.0466503
$86$	501.090	+	1295.32i	0.628301	+	1.62417i
$87$	−1087.97			−1.34072
$88$	937.925			1.13617
$89$	418.989	+	725.710i	0.499019	+	0.864327i	0.999999	−	0.00113199i	$-0.000360323\pi$
$89$	418.989	+	725.710i	0.499019	+	0.864327i	−0.500980	+	0.865459i	$0.667027\pi$
$90$	−21.8252			−0.0255620
$91$	−926.603	−	1604.92i	−1.06741	−	1.84881i
$92$	311.966	+	540.342i	0.353530	+	0.612332i
$93$	599.731	−	1038.76i	0.668701	−	1.15822i
$94$	126.741			0.139067
$95$	−150.916	+	261.394i	−0.162986	+	0.282299i
$96$	−52.2668	−	90.5288i	−0.0555673	−	0.0962454i
$97$	665.680			0.696800			0.348400	−	0.937346i	$-0.386725\pi$
$97$	665.680			0.696800			0.348400	+	0.937346i	$0.386725\pi$
$98$	−1233.75	−	2136.92i	−1.27171	−	2.20267i
$99$	24.0498	−	41.6555i	0.0244152	−	0.0422883i
$100$	979.685	−	1696.86i	0.979685	−	1.69686i
$101$	−574.699	+	995.408i	−0.566185	+	0.980662i	0.430753	+	0.902470i	$0.358248\pi$
$101$	−574.699	+	995.408i	−0.566185	+	0.980662i	−0.996938	+	0.0781918i	$0.975085\pi$
$102$	−423.297			−0.410908
$103$	−228.068	+	395.025i	−0.218177	+	0.377893i	−0.954251	−	0.299008i	$-0.903344\pi$
$103$	−228.068	+	395.025i	−0.218177	+	0.377893i	0.736074	+	0.676901i	$0.236678\pi$
$104$	−1297.93	+	2248.07i	−1.22377	+	2.11963i
$105$	−153.941	−	266.634i	−0.143077	−	0.247817i
$106$	480.256	+	831.828i	0.440062	+	0.762211i
$107$	1294.04			1.16916			0.584579	−	0.811337i	$-0.301260\pi$
$107$	1294.04			1.16916			0.584579	+	0.811337i	$0.301260\pi$
$108$	−2360.86			−2.10346
$109$	−285.157	−	493.906i	−0.250578	−	0.434014i	0.713107	−	0.701055i	$-0.247287\pi$
$109$	−285.157	−	493.906i	−0.250578	−	0.434014i	−0.963685	+	0.267041i	$0.913954\pi$
$110$	−120.529	−	208.762i	−0.104473	−	0.180952i
$111$	−68.0491	+	117.864i	−0.0581886	+	0.100786i
$112$	−1021.77	+	1769.76i	−0.862041	+	1.49310i
$113$	1279.23			1.06496			0.532479	−	0.846443i	$-0.321261\pi$
$113$	1279.23			1.06496			0.532479	+	0.846443i	$0.321261\pi$
$114$	−1747.42	+	3026.62i	−1.43562	+	2.48657i
$115$	40.7341	−	70.5536i	0.0330302	−	0.0572101i
$116$	1772.28	−	3069.68i	1.41855	−	2.45701i
$117$	66.5616	+	115.288i	0.0525951	+	0.0910973i
$118$	−3850.33			−3.00383
$119$	250.093	+	433.174i	0.192656	+	0.333689i
$120$	−215.631	+	373.484i	−0.164036	+	0.284119i
$121$	−799.743			−0.600859
$122$	1713.20	−	2967.35i	1.27136	−	2.20206i
$123$	−438.611	−	759.697i	−0.321530	−	0.556907i
$124$	1953.90	+	3384.25i	1.41504	+	2.45093i
$125$	−521.251			−0.372977
$126$	149.306	+	258.606i	0.105566	+	0.182845i
$127$	1045.65			0.730600			0.365300	−	0.930890i	$-0.380966\pi$
$127$	1045.65			0.730600			0.365300	+	0.930890i	$0.380966\pi$
$128$	−2431.31			−1.67890
$129$	882.863	−	1096.05i	0.602572	−	0.748075i
$130$	667.165			0.450110
$131$	2490.19			1.66083			0.830416	−	0.557144i	$-0.188103\pi$
$131$	2490.19			1.66083			0.830416	+	0.557144i	$0.188103\pi$
$132$	−935.398	−	1620.16i	−0.616788	−	1.06831i
$133$	4129.66			2.69238
$134$	71.6362	+	124.078i	0.0461823	+	0.0799900i
$135$	154.132	+	266.964i	0.0982632	+	0.170197i
$136$	350.315	−	606.763i	0.220877	−	0.382570i
$137$	−1551.43			−0.967498			−0.483749	−	0.875207i	$-0.660725\pi$
$137$	−1551.43			−0.967498			−0.483749	+	0.875207i	$0.660725\pi$
$138$	471.651	−	816.924i	0.290939	−	0.503922i
$139$	−299.608	−	518.935i	−0.182823	−	0.316658i	0.760018	−	0.649902i	$-0.225190\pi$
$139$	−299.608	−	518.935i	−0.182823	−	0.316658i	−0.942841	+	0.333244i	$0.891857\pi$
$140$	1003.07			0.605533
$141$	−64.2158	−	111.225i	−0.0383542	−	0.0664315i
$142$	−2317.92	+	4014.75i	−1.36983	+	2.37261i
$143$	−735.168	+	1273.35i	−0.429915	+	0.744634i
$144$	73.3981	−	127.129i	0.0424758	−	0.0735702i
$145$	−462.822			−0.265071
$146$	582.737	−	1009.33i	0.330327	−	0.572142i
$147$	−1250.21	+	2165.43i	−0.701467	+	1.21498i
$148$	−221.701	−	383.997i	−0.123133	−	0.213273i
$149$	−124.255	−	215.216i	−0.0683178	−	0.118330i	0.829843	−	0.557997i	$-0.188430\pi$
$149$	−124.255	−	215.216i	−0.0683178	−	0.118330i	−0.898161	+	0.439667i	$0.855097\pi$
$150$	−2962.30			−1.61247
$151$	−1548.14			−0.834342			−0.417171	−	0.908828i	$-0.636978\pi$
$151$	−1548.14			−0.834342			−0.417171	+	0.908828i	$0.636978\pi$
$152$	−2892.28	−	5009.57i	−1.54339	−	2.67322i
$153$	−17.9652	−	31.1166i	−0.00949281	−	0.0164420i
$154$	−1649.08	+	2856.28i	−0.862898	+	1.49458i
$155$	255.125	−	441.889i	0.132207	−	0.228990i
$156$	5177.72			2.65737
$157$	1213.93	−	2102.59i	0.617083	−	1.06882i	−0.372932	−	0.927859i	$-0.621648\pi$
$157$	1213.93	−	2102.59i	0.617083	−	1.06882i	0.990015	−	0.140961i	$-0.0450192\pi$
$158$	−423.212	+	733.025i	−0.213095	+	0.369091i
$159$	486.664	−	842.926i	0.242735	−	0.420430i
$160$	−22.2342	−	38.5108i	−0.0109861	−	0.0190284i
$161$	−1114.65			−0.545631
$162$	1645.89	+	2850.76i	0.798229	+	1.38257i
$163$	933.879	−	1617.53i	0.448755	−	0.777266i	−0.549551	−	0.835460i	$-0.685201\pi$
$163$	933.879	−	1617.53i	0.448755	−	0.777266i	0.998305	+	0.0581945i	$0.0185344\pi$
$164$	2857.95			1.36078
$165$	−122.137	+	211.548i	−0.0576264	+	0.0998118i
$166$	−784.857	−	1359.41i	−0.366968	−	0.635608i
$167$	−1294.46	−	2242.08i	−0.599813	−	1.03891i	−0.992848	−	0.119383i	$-0.961908\pi$
$167$	−1294.46	−	2242.08i	−0.599813	−	1.03891i	0.393036	−	0.919523i	$-0.371425\pi$
$168$	5900.52			2.70973
$169$	−936.189	−	1621.53i	−0.426122	−	0.738064i
$170$	−180.070			−0.0812397
$171$	−296.650			−0.132663
$172$	1654.31	+	4276.42i	0.733371	+	1.89578i
$173$	−28.1713			−0.0123805			−0.00619024	−	0.999981i	$-0.501970\pi$
$173$	−28.1713			−0.0123805			−0.00619024	+	0.999981i	$0.501970\pi$
$174$	−5358.91			−2.33481
$175$	1750.20	+	3031.43i	0.756013	+	1.30945i
$176$	1621.35			0.694398
$177$	1950.85	+	3378.97i	0.828446	+	1.43491i
$178$	2063.77	+	3574.55i	0.869022	+	1.50519i
$179$	42.3818	−	73.4074i	0.0176970	−	0.0306521i	−0.857041	−	0.515248i	$-0.827700\pi$
$179$	42.3818	−	73.4074i	0.0176970	−	0.0306521i	0.874738	+	0.484596i	$0.161033\pi$
$180$	−72.0544			−0.0298368
$181$	47.7536	−	82.7117i	0.0196105	−	0.0339664i	−0.856054	−	0.516887i	$-0.827091\pi$
$181$	47.7536	−	82.7117i	0.0196105	−	0.0339664i	0.875664	+	0.482921i	$0.160424\pi$
$182$	−4564.07	−	7905.20i	−1.85885	−	3.21963i
$183$	−3472.11			−1.40255
$184$	780.664	+	1352.15i	0.312779	+	0.541749i
$185$	−28.9480	+	50.1394i	−0.0115043	+	0.0199261i
$186$	2954.03	−	5116.53i	1.16452	−	2.01700i
$187$	198.424	−	343.681i	0.0775947	−	0.134398i
$188$	418.425			0.162323
$189$	2108.83	−	3652.59i	0.811611	−	1.40575i
$190$	−743.350	+	1287.52i	−0.283833	+	0.491613i
$191$	419.228	+	726.124i	0.158818	+	0.275081i	0.934443	−	0.356113i	$-0.115898\pi$
$191$	419.228	+	726.124i	0.158818	+	0.275081i	−0.775625	+	0.631195i	$0.782565\pi$
$192$	1146.98	+	1986.63i	0.431127	+	0.746733i
$193$	−433.994			−0.161863			−0.0809315	−	0.996720i	$-0.525790\pi$
$193$	−433.994			−0.161863			−0.0809315	+	0.996720i	$0.525790\pi$
$194$	3278.87			1.21345
$195$	−338.033	−	585.490i	−0.124139	−	0.215015i
$196$	−4073.14	−	7054.88i	−1.48438	−	2.57102i
$197$	−2119.49	+	3671.06i	−0.766534	+	1.32768i	0.172898	+	0.984940i	$0.444687\pi$
$197$	−2119.49	+	3671.06i	−0.766534	+	1.32768i	−0.939432	+	0.342736i	$0.888646\pi$
$198$	118.460	−	205.178i	0.0425180	−	0.0736434i
$199$	−762.010			−0.271445			−0.135722	−	0.990747i	$-0.543335\pi$
$199$	−762.010			−0.271445			−0.135722	+	0.990747i	$0.543335\pi$
$200$	2451.56	−	4246.23i	0.866758	−	1.50127i
$201$	72.5919	−	125.733i	0.0254738	−	0.0441220i
$202$	−2830.73	+	4902.98i	−0.985989	+	1.70778i
$203$	3166.16	+	5483.95i	1.09468	+	1.89605i
$204$	−1397.48			−0.479624
$205$	−186.585	−	323.174i	−0.0635689	−	0.110105i
$206$	−1123.37	+	1945.73i	−0.379946	+	0.658086i
$207$	80.0696			0.0268851
$208$	−2243.67	+	3886.15i	−0.747935	+	1.29546i
$209$	−1638.24	−	2837.51i	−0.542197	−	0.939112i
$210$	−758.252	−	1313.33i	−0.249163	−	0.431564i
$211$	−4221.37			−1.37731			−0.688653	−	0.725092i	$-0.741797\pi$
$211$	−4221.37			−1.37731			−0.688653	+	0.725092i	$0.741797\pi$
$212$	1585.53	+	2746.22i	0.513654	+	0.889675i
$213$	4697.68			1.51117
$214$	6373.93			2.03604
$215$	375.569	−	466.258i	0.119133	−	0.147900i
$216$	−5907.82			−1.86100
$217$	−6981.23			−2.18395
$218$	−1404.57	−	2432.78i	−0.436372	−	0.755819i
$219$	−1181.02			−0.364412
$220$	−397.917	−	689.213i	−0.121944	−	0.211212i
$221$	549.169	+	951.189i	0.167154	+	0.289520i
$222$	−335.182	+	580.552i	−0.101333	+	0.175514i
$223$	−4232.56			−1.27100			−0.635500	−	0.772101i	$-0.719206\pi$
$223$	−4232.56			−1.27100			−0.635500	+	0.772101i	$0.719206\pi$
$224$	−304.209	+	526.905i	−0.0907402	+	0.157167i
$225$	−125.724	−	217.760i	−0.0372514	−	0.0645214i
$226$	6300.99			1.85458
$227$	2168.53	+	3756.00i	0.634054	+	1.09821i	0.986715	+	0.162463i	$0.0519438\pi$
$227$	2168.53	+	3756.00i	0.634054	+	1.09821i	−0.352660	+	0.935751i	$0.614723\pi$
$228$	−5768.97	+	9992.15i	−1.67570	+	2.90240i
$229$	216.659	−	375.265i	0.0625208	−	0.108289i	−0.833071	−	0.553166i	$-0.813419\pi$
$229$	216.659	−	375.265i	0.0625208	−	0.108289i	0.895592	+	0.444877i	$0.146753\pi$
$230$	200.640	−	347.518i	0.0575209	−	0.0996291i
$231$	3342.15			0.951938
$232$	4434.95	−	7681.57i	1.25504	−	2.17379i
$233$	−1210.84	+	2097.24i	−0.340450	+	0.589676i	−0.984516	−	0.175293i	$-0.943913\pi$
$233$	−1210.84	+	2097.24i	−0.340450	+	0.589676i	0.644066	+	0.764970i	$0.277246\pi$
$234$	327.855	+	567.862i	0.0915922	+	0.158642i
$235$	−27.3173	−	47.3150i	−0.00758292	−	0.0131340i
$236$	−12711.6			−3.50616
$237$	857.717			0.235083
$238$	1231.86	+	2133.64i	0.335502	+	0.581107i
$239$	−1339.43	−	2319.97i	−0.362514	−	0.627893i	0.625860	−	0.779935i	$-0.284748\pi$
$239$	−1339.43	−	2319.97i	−0.362514	−	0.627893i	−0.988374	+	0.152043i	$0.951415\pi$
$240$	−372.752	+	645.625i	−0.100254	+	0.173646i
$241$	880.058	−	1524.31i	0.235226	−	0.407424i	−0.724112	−	0.689682i	$-0.757750\pi$
$241$	880.058	−	1524.31i	0.235226	−	0.407424i	0.959338	+	0.282258i	$0.0910836\pi$
$242$	−3939.21			−1.04637
$243$	−292.102	+	505.936i	−0.0771127	+	0.133563i
$244$	5656.00	−	9796.47i	1.48397	−	2.57031i
$245$	−531.839	+	921.171i	−0.138685	+	0.240210i
$246$	−2160.42	−	3741.96i	−0.559932	−	0.969831i
$247$	9068.14			2.33600
$248$	4889.43	+	8468.74i	1.25193	+	2.16841i
$249$	−795.328	+	1377.55i	−0.202417	+	0.350597i
$250$	−2567.47			−0.649525
$251$	3032.08	−	5251.72i	0.762483	−	1.32066i	−0.179083	−	0.983834i	$-0.557313\pi$
$251$	3032.08	−	5251.72i	0.762483	−	1.32066i	0.941567	−	0.336826i	$-0.109353\pi$
$252$	492.923	+	853.768i	0.123219	+	0.213422i
$253$	442.181	+	765.880i	0.109880	+	0.190318i
$254$	5150.43			1.27231
$255$	91.2362	+	158.026i	0.0224056	+	0.0388077i
$256$	−8298.90			−2.02610
$257$	1567.63			0.380490			0.190245	−	0.981737i	$-0.439072\pi$
$257$	1567.63			0.380490			0.190245	+	0.981737i	$0.439072\pi$
$258$	4348.62	−	5398.69i	1.04935	−	1.30274i
$259$	792.132			0.190041
$260$	2202.59			0.525381
$261$	−227.438	−	393.934i	−0.0539389	−	0.0934249i
$262$	12265.7			2.89227
$263$	−3207.47	−	5555.50i	−0.752020	−	1.30254i	−0.946842	−	0.321698i	$-0.895746\pi$
$263$	−3207.47	−	5555.50i	−0.752020	−	1.30254i	0.194823	−	0.980838i	$-0.437587\pi$
$264$	−2340.74	−	4054.28i	−0.545691	−	0.945165i
$265$	207.026	−	358.580i	0.0479906	−	0.0831222i
$266$	20341.0			4.68867
$267$	2091.30	−	3622.24i	0.479347	−	0.830253i
$268$	236.501	+	409.632i	0.0539053	+	0.0933667i
$269$	−2303.53			−0.522115			−0.261057	−	0.965323i	$-0.584071\pi$
$269$	−2303.53			−0.522115			−0.261057	+	0.965323i	$0.584071\pi$
$270$	759.189	+	1314.95i	0.171121	+	0.296391i
$271$	423.547	−	733.604i	0.0949396	−	0.164440i	−0.814644	−	0.579962i	$-0.803068\pi$
$271$	423.547	−	733.604i	0.0949396	−	0.164440i	0.909583	+	0.415521i	$0.136401\pi$
$272$	605.574	−	1048.89i	0.134994	−	0.233816i
$273$	−4624.96	+	8010.67i	−1.02533	+	1.77593i
$274$	−7641.69			−1.68486
$275$	1388.61	−	2405.14i	0.304495	−	0.527401i
$276$	1557.12	−	2697.01i	0.339593	−	0.588192i
$277$	−2987.28	−	5174.13i	−0.647973	−	1.12232i	−0.983606	−	0.180330i	$-0.942284\pi$
$277$	−2987.28	−	5174.13i	−0.647973	−	1.12232i	0.335633	−	0.941993i	$-0.391050\pi$
$278$	−1475.74	−	2556.07i	−0.318379	−	0.551448i
$279$	501.490			0.107611
$280$	2510.07			0.535734
$281$	−402.038	−	696.351i	−0.0853509	−	0.147832i	0.820190	−	0.572092i	$-0.193868\pi$
$281$	−402.038	−	696.351i	−0.0853509	−	0.147832i	−0.905541	+	0.424259i	$0.860534\pi$
$282$	−316.301	−	547.850i	−0.0667924	−	0.115688i
$283$	−1814.80	+	3143.33i	−0.381197	+	0.660252i	−0.991234	−	0.132121i	$-0.957821\pi$
$283$	−1814.80	+	3143.33i	−0.381197	+	0.660252i	0.610037	+	0.792373i	$0.291155\pi$
$284$	−7652.42	+	13254.4i	−1.59890	+	2.76938i
$285$	1506.53			0.313121
$286$	−3621.14	+	6271.99i	−0.748680	+	1.29675i
$287$	−2552.85	+	4421.66i	−0.525052	+	0.909416i
$288$	21.8525	−	37.8497i	0.00447108	−	0.00774415i
$289$	2308.28	+	3998.05i	0.469831	+	0.813770i
$290$	−2279.67			−0.461610
$291$	−1661.31	−	2877.47i	−0.334665	−	0.579657i
$292$	1923.86	−	3332.23i	0.385567	−	0.667822i
$293$	1201.21			0.239507			0.119753	−	0.992804i	$-0.461790\pi$
$293$	1201.21			0.239507			0.119753	+	0.992804i	$0.461790\pi$
$294$	−6158.03	+	10666.0i	−1.22158	+	2.11583i
$295$	829.889	+	1437.41i	0.163790	+	0.283693i
$296$	−554.784	−	960.914i	−0.108940	−	0.188689i
$297$	−3346.29			−0.653776
$298$	−612.029	−	1060.06i	−0.118973	−	0.206067i
$299$	−2447.61			−0.473408
$300$	−9779.82			−1.88213
$301$	−8093.93	−	1260.43i	−1.54992	−	0.241362i
$302$	−7625.50			−1.45297
$303$	5737.00			1.08773
$304$	−4999.76	−	8659.84i	−0.943276	−	1.63380i
$305$	−1477.03			−0.277294
$306$	−88.4893	−	153.268i	−0.0165314	−	0.0286332i
$307$	2656.96	+	4602.00i	0.493944	+	0.855537i	0.999976	−	0.00697837i	$-0.00222130\pi$
$307$	2656.96	+	4602.00i	0.493944	+	0.855537i	−0.506031	+	0.862515i	$0.668888\pi$
$308$	−5444.30	+	9429.80i	−1.00720	+	1.74452i
$309$	2276.71			0.419151
$310$	1256.64	−	2176.57i	0.230234	−	0.398776i
$311$	3726.87	+	6455.12i	0.679522	+	1.17697i	0.975125	+	0.221655i	$0.0711459\pi$
$311$	3726.87	+	6455.12i	0.679522	+	1.17697i	−0.295604	+	0.955311i	$0.595521\pi$
$312$	12956.7			2.35105
$313$	−1163.28	−	2014.85i	−0.210071	−	0.363854i	0.741666	−	0.670770i	$-0.234036\pi$
$313$	−1163.28	−	2014.85i	−0.210071	−	0.363854i	−0.951737	+	0.306916i	$0.900703\pi$
$314$	5979.32	−	10356.5i	1.07463	−	1.86131i
$315$	64.3621	−	111.478i	0.0115124	−	0.0199400i
$316$	−1397.20	+	2420.03i	−0.248730	+	0.430813i
$317$	−4109.44			−0.728105			−0.364052	−	0.931379i	$-0.618607\pi$
$317$	−4109.44			−0.728105			−0.364052	+	0.931379i	$0.618607\pi$
$318$	2397.11	−	4151.91i	0.422714	−	0.732162i
$319$	2512.03	−	4350.97i	0.440899	−	0.763660i
$320$	487.925	+	845.111i	0.0852370	+	0.147635i
$321$	−3229.48	−	5593.63i	−0.561533	−	0.972605i
$322$	−5490.30			−0.950194
$323$	−2447.52			−0.421621
$324$	5433.77	+	9411.57i	0.931717	+	1.61378i
$325$	3843.18	+	6656.59i	0.655943	+	1.13613i
$326$	4599.91	−	7967.27i	0.781488	−	1.35358i
$327$	−1423.30	+	2465.23i	−0.240700	+	0.416905i
$328$	7151.73			1.20393
$329$	−373.755	+	647.363i	−0.0626316	+	0.108481i
$330$	−601.597	+	1042.00i	−0.100354	+	0.173818i
$331$	3641.88	−	6307.93i	0.604761	−	1.04748i	−0.387328	−	0.921942i	$-0.626602\pi$
$331$	3641.88	−	6307.93i	0.604761	−	1.04748i	0.992089	−	0.125535i	$-0.0400648\pi$
$332$	−2591.15	−	4488.00i	−0.428336	−	0.741900i
$333$	−56.9020			−0.00936400
$334$	−6376.01	−	11043.6i	−1.04455	−	1.80921i
$335$	30.8805	−	53.4866i	0.00503637	−	0.00872324i
$336$	10200.0			1.65611
$337$	−1742.99	+	3018.95i	−0.281741	+	0.487990i	−0.971814	−	0.235750i	$-0.924245\pi$
$337$	−1742.99	+	3018.95i	−0.281741	+	0.487990i	0.690072	+	0.723740i	$0.257579\pi$
$338$	−4611.29	−	7986.99i	−0.742074	−	1.28531i
$339$	−3192.52	−	5529.62i	−0.511487	−	0.885922i
$340$	−594.488			−0.0948253
$341$	2769.46	+	4796.84i	0.439808	+	0.761770i
$342$	−1461.18			−0.231027
$343$	4588.75			0.722360
$344$	4139.74	+	10701.3i	0.648836	+	1.67725i
$345$	−406.633			−0.0634562
$346$	−138.760			−0.0215601
$347$	−2910.68	−	5041.44i	−0.450298	−	0.779939i	0.548106	−	0.836409i	$-0.315349\pi$
$347$	−2910.68	−	5041.44i	−0.450298	−	0.779939i	−0.998404	+	0.0564698i	$0.982016\pi$
$348$	−17692.0			−2.72526
$349$	665.229	+	1152.21i	0.102031	+	0.176723i	0.912521	−	0.409029i	$-0.134132\pi$
$349$	665.229	+	1152.21i	0.102031	+	0.176723i	−0.810490	+	0.585752i	$0.800799\pi$
$350$	8620.75	+	14931.6i	1.31657	+	2.28036i
$351$	4630.68	−	8020.58i	0.704181	−	1.21968i
$352$	482.719			0.0730937
$353$	−2763.65	+	4786.78i	−0.416698	+	0.721741i	−0.995605	−	0.0936519i	$-0.970146\pi$
$353$	−2763.65	+	4786.78i	−0.416698	+	0.721741i	0.578907	+	0.815393i	$0.303479\pi$
$354$	9609.10	+	16643.4i	1.44271	+	2.49884i
$355$	1998.39			0.298770
$356$	6813.37	+	11801.1i	1.01435	+	1.75690i
$357$	1248.29	−	2162.11i	0.185061	−	0.320534i
$358$	208.755	−	361.575i	0.0308186	−	0.0533794i
$359$	2058.02	−	3564.59i	0.302557	−	0.524044i	−0.674157	−	0.738588i	$-0.735493\pi$
$359$	2058.02	−	3564.59i	0.302557	−	0.524044i	0.976714	+	0.214544i	$0.0688264\pi$
$360$	−180.309			−0.0263975
$361$	−6674.14	+	11560.0i	−0.973049	+	1.68537i
$362$	235.215	−	407.404i	0.0341509	−	0.0591511i
$363$	1995.88	+	3456.97i	0.288586	+	0.499845i
$364$	−15067.9	−	26098.4i	−2.16971	−	3.75805i
$365$	−502.406			−0.0720469
$366$	−17102.2			−2.44248
$367$	456.260	+	790.265i	0.0648953	+	0.112402i	0.896648	−	0.442745i	$-0.145995\pi$
$367$	456.260	+	790.265i	0.0648953	+	0.112402i	−0.831752	+	0.555147i	$0.812662\pi$
$368$	1349.50	+	2337.40i	0.191162	+	0.331102i
$369$	183.381	−	317.626i	0.0258711	−	0.0448101i
$370$	−142.586	+	246.966i	−0.0200343	+	0.0347005i
$371$	−5665.06			−0.792763
$372$	9752.51	−	16891.8i	1.35926	−	2.35430i
$373$	4687.72	−	8119.36i	0.650726	−	1.12709i	−0.332221	−	0.943202i	$-0.607798\pi$
$373$	4687.72	−	8119.36i	0.650726	−	1.12709i	0.982947	−	0.183889i	$-0.0588686\pi$
$374$	977.357	−	1692.83i	0.135128	−	0.234049i
$375$	1300.86	+	2253.16i	0.179137	+	0.310274i
$376$	1047.07			0.143612
$377$	6952.44	+	12042.0i	0.949785	+	1.64508i
$378$	10387.2	−	17991.2i	1.41339	−	2.44806i
$379$	7385.27			1.00094			0.500469	−	0.865754i	$-0.333161\pi$
$379$	7385.27			1.00094			0.500469	+	0.865754i	$0.333161\pi$
$380$	−2454.11	+	4250.65i	−0.331298	+	0.573825i
$381$	−2609.57	−	4519.91i	−0.350899	−	0.607775i
$382$	2064.95	+	3576.59i	0.276576	+	0.479043i
$383$	−5230.52			−0.697826			−0.348913	−	0.937155i	$-0.613449\pi$
$383$	−5230.52			−0.697826			−0.348913	+	0.937155i	$0.613449\pi$
$384$	6067.70	+	10509.6i	0.806357	+	1.39665i
$385$	1421.75			0.188205
$386$	−2137.68			−0.281878
$387$	581.419	+	90.5416i	0.0763700	+	0.0118927i
$388$	10824.9			1.41637
$389$	13237.2			1.72533			0.862664	−	0.505778i	$-0.168795\pi$
$389$	13237.2			1.72533			0.862664	+	0.505778i	$0.168795\pi$
$390$	−1665.01	−	2883.89i	−0.216183	−	0.374439i
$391$	660.618			0.0854447
$392$	−10192.6	−	17654.1i	−1.31328	−	2.27466i
$393$	−6214.65	−	10764.1i	−0.797679	−	1.38162i
$394$	−10439.7	+	18082.1i	−1.33489	+	2.31209i
$395$	364.872			0.0464777
$396$	391.086	−	677.380i	0.0496283	−	0.0859587i
$397$	4371.55	+	7571.74i	0.552649	+	0.957217i	0.998082	+	0.0619013i	$0.0197164\pi$
$397$	4371.55	+	7571.74i	0.552649	+	0.957217i	−0.445433	+	0.895315i	$0.646950\pi$
$398$	−3753.35			−0.472710
$399$	−10306.2	−	17850.8i	−1.29312	−	2.23975i
$400$	4237.91	−	7340.28i	0.529739	−	0.917535i
$401$	−2223.95	+	3852.00i	−0.276955	+	0.479700i	−0.970626	−	0.240592i	$-0.922659\pi$
$401$	−2223.95	+	3852.00i	−0.276955	+	0.479700i	0.693672	+	0.720291i	$0.255992\pi$
$402$	357.558	−	619.309i	0.0443617	−	0.0768366i
$403$	−15329.8			−1.89487
$404$	−9345.46	+	16186.8i	−1.15088	+	1.99338i
$405$	709.500	−	1228.89i	0.0870502	−	0.150775i
$406$	15595.2	+	27011.7i	1.90635	+	3.30189i
$407$	−314.239	−	544.278i	−0.0382709	−	0.0662871i
$408$	−3497.06			−0.424338
$409$	−1000.16			−0.120916			−0.0604582	−	0.998171i	$-0.519256\pi$
$409$	−1000.16			−0.120916			−0.0604582	+	0.998171i	$0.519256\pi$
$410$	−919.040	−	1591.82i	−0.110703	−	0.191743i
$411$	3871.82	+	6706.19i	0.464679	+	0.804847i
$412$	−3708.72	+	6423.69i	−0.443484	+	0.768137i
$413$	11354.5	−	19666.6i	1.35283	−	2.34318i
$414$	394.390			0.0468194
$415$	−338.332	+	586.008i	−0.0400194	+	0.0693156i
$416$	−667.999	+	1157.01i	−0.0787292	+	0.136363i
$417$	−1495.43	+	2590.17i	−0.175616	+	0.304175i
$418$	−8069.28	−	13976.4i	−0.944214	−	1.63543i
$419$	9483.42			1.10572			0.552858	−	0.833275i	$-0.313537\pi$
$419$	9483.42			1.10572			0.552858	+	0.833275i	$0.313537\pi$
$420$	−2503.31	−	4335.86i	−0.290831	−	0.503734i
$421$	−3991.99	+	6914.34i	−0.462133	+	0.800437i	−0.999067	−	0.0431868i	$-0.986249\pi$
$421$	−3991.99	+	6914.34i	−0.462133	+	0.800437i	0.536934	+	0.843624i	$0.319582\pi$
$422$	−20792.8			−2.39852
$423$	26.8483	−	46.5027i	0.00308608	−	0.00534525i
$424$	3967.62	+	6872.13i	0.454445	+	0.787123i
$425$	−1037.29	−	1796.63i	−0.118390	−	0.205058i
$426$	23138.9			2.63165
$427$	10104.4	+	17501.3i	1.14516	+	1.98348i
$428$	21043.0			2.37653
$429$	7338.90			0.825933
$430$	1849.90	−	2296.60i	0.207465	−	0.257562i
$431$	13979.0			1.56229			0.781143	−	0.624353i	$-0.214637\pi$
$431$	13979.0			1.56229			0.781143	+	0.624353i	$0.214637\pi$
$432$	−10212.6			−1.13739
$433$	−3505.75	−	6072.14i	−0.389089	−	0.673922i	0.603238	−	0.797561i	$-0.293877\pi$
$433$	−3505.75	−	6072.14i	−0.389089	−	0.673922i	−0.992327	+	0.123639i	$0.960544\pi$
$434$	−34386.7			−3.80326
$435$	1155.04	+	2000.59i	0.127311	+	0.220508i
$436$	−4637.06	−	8031.63i	−0.509347	−	0.882214i
$437$	2727.11	−	4723.49i	0.298524	−	0.517059i
$438$	−5817.24			−0.634609
$439$	3316.57	−	5744.47i	0.360572	−	0.624530i	−0.627483	−	0.778631i	$-0.715915\pi$
$439$	3316.57	−	5744.47i	0.360572	−	0.624530i	0.988055	+	0.154101i	$0.0492480\pi$
$440$	−995.747	−	1724.68i	−0.107887	−	0.186866i
$441$	−1045.42			−0.112884
$442$	2704.99	+	4685.17i	0.291093	+	0.504188i
$443$	2660.36	−	4607.88i	0.285322	−	0.494192i	−0.687366	−	0.726312i	$-0.741233\pi$
$443$	2660.36	−	4607.88i	0.285322	−	0.494192i	0.972687	+	0.232120i	$0.0745663\pi$
$444$	−1106.58	+	1916.65i	−0.118279	+	0.204865i
$445$	889.637	−	1540.90i	0.0947705	−	0.164147i
$446$	−20847.9			−2.21340
$447$	−620.194	+	1074.21i	−0.0656245	+	0.113665i
$448$	6675.78	−	11562.8i	0.704020	−	1.21940i
$449$	−8241.08	−	14274.0i	−0.866193	−	1.50029i	−0.865858	−	0.500290i	$-0.833227\pi$
$449$	−8241.08	−	14274.0i	−0.866193	−	1.50029i	−0.000334817	−	1.00000i	$-0.500107\pi$
$450$	−619.263	−	1072.60i	−0.0648719	−	0.112361i
$451$	4050.86			0.422944
$452$	20802.2			2.16472
$453$	3863.62	+	6691.98i	0.400725	+	0.694077i
$454$	10681.3	+	18500.5i	1.10418	+	1.91250i
$455$	−1967.45	+	3407.73i	−0.202716	+	0.351114i
$456$	−14436.2	+	25004.3i	−1.48254	+	2.56784i
$457$	−9047.06			−0.926047			−0.463024	−	0.886346i	$-0.653236\pi$
$457$	−9047.06			−0.926047			−0.463024	+	0.886346i	$0.653236\pi$
$458$	1067.18	−	1848.40i	0.108877	−	0.188581i
$459$	−1249.84	+	2164.78i	−0.127097	+	0.220138i
$460$	662.397	−	1147.31i	0.0671400	−	0.116290i
$461$	−2882.84	−	4993.23i	−0.291252	−	0.504464i	0.682854	−	0.730555i	$-0.260739\pi$
$461$	−2882.84	−	4993.23i	−0.291252	−	0.504464i	−0.974106	+	0.226091i	$0.927405\pi$
$462$	16462.1			1.65776
$463$	3675.34	+	6365.87i	0.368915	+	0.638979i	0.989396	−	0.145242i	$-0.0463961\pi$
$463$	3675.34	+	6365.87i	0.368915	+	0.638979i	−0.620481	+	0.784221i	$0.713063\pi$
$464$	7666.52	−	13278.8i	0.767046	−	1.32856i
$465$	−2546.81			−0.253991
$466$	−5964.11	+	10330.1i	−0.592880	+	1.02690i
$467$	−2527.27	−	4377.36i	−0.250424	−	0.433748i	0.713218	−	0.700942i	$-0.247237\pi$
$467$	−2527.27	−	4377.36i	−0.250424	−	0.433748i	−0.963643	+	0.267194i	$0.913903\pi$
$468$	1082.39	+	1874.75i	0.106909	+	0.185172i
$469$	−845.014			−0.0831964
$470$	−134.554	−	233.055i	−0.0132054	−	0.0228723i
$471$	−12118.2			−1.18551
$472$	−31809.4			−3.10201
$473$	2344.82	+	6061.39i	0.227938	+	0.589224i
$474$	4224.76			0.409388
$475$	−17128.2			−1.65451
$476$	4066.89	+	7044.05i	0.391608	+	0.678285i
$477$	406.944			0.0390622
$478$	−6597.51	−	11427.2i	−0.631304	−	1.09345i
$479$	−802.672	−	1390.27i	−0.0765658	−	0.132616i	0.825200	−	0.564840i	$-0.191062\pi$
$479$	−802.672	−	1390.27i	−0.0765658	−	0.132616i	−0.901766	+	0.432224i	$0.857729\pi$
$480$	−110.978	+	192.219i	−0.0105530	+	0.0182783i
$481$	1739.41			0.164886
$482$	4334.81	−	7508.11i	0.409637	−	0.709512i
$483$	2781.78	+	4818.18i	0.262060	+	0.453902i
$484$	−13005.0			−1.22136
$485$	−706.718	−	1224.07i	−0.0661658	−	0.114603i
$486$	−1438.78	+	2492.04i	−0.134289	+	0.232595i
$487$	−39.9234	+	69.1493i	−0.00371479	+	0.00643420i	−0.867877	−	0.496779i	$-0.834516\pi$
$487$	−39.9234	+	69.1493i	−0.00371479	+	0.00643420i	0.864162	+	0.503214i	$0.167849\pi$
$488$	14153.5	−	24514.7i	1.31291	−	2.27403i
$489$	−9322.55			−0.862127
$490$	−2619.62	+	4537.32i	−0.241515	+	0.418316i
$491$	−8444.82	+	14626.9i	−0.776191	+	1.34440i	0.157932	+	0.987450i	$0.449517\pi$
$491$	−8444.82	+	14626.9i	−0.776191	+	1.34440i	−0.934123	+	0.356952i	$0.883816\pi$
$492$	−7132.46	−	12353.8i	−0.653569	−	1.13202i
$493$	−1876.49	−	3250.17i	−0.171425	−	0.296917i
$494$	44666.0			4.06805
$495$	−102.130			−0.00927353
$496$	8452.15	+	14639.6i	0.765147	+	1.32527i
$497$	−13671.0	−	23678.8i	−1.23386	−	2.13710i
$498$	−3917.46	+	6785.25i	−0.352502	+	0.610551i
$499$	−9295.32	+	16100.0i	−0.833899	+	1.44436i	0.0610238	+	0.998136i	$0.480563\pi$
$499$	−9295.32	+	16100.0i	−0.833899	+	1.44436i	−0.894923	+	0.446220i	$0.852770\pi$
$500$	−8476.32			−0.758145
$501$	−6461.07	+	11190.9i	−0.576167	+	0.997950i
$502$	14934.8	−	25867.8i	1.32783	−	2.29988i
$503$	−1633.64	+	2829.55i	−0.144812	+	0.250822i	−0.929303	−	0.369319i	$-0.879591\pi$
$503$	−1633.64	+	2829.55i	−0.144812	+	0.250822i	0.784491	+	0.620140i	$0.212924\pi$
$504$	1233.49	+	2136.47i	0.109016	+	0.188821i
$505$	2440.51			0.215052
$506$	2178.01	+	3772.42i	0.191352	+	0.331431i
$507$	−4672.81	+	8093.54i	−0.409323	+	0.708968i
$508$	17003.8			1.48508
$509$	−5558.38	+	9627.39i	−0.484029	+	0.838363i	−0.999832	−	0.0183447i	$-0.994160\pi$
$509$	−5558.38	+	9627.39i	−0.484029	+	0.838363i	0.515803	+	0.856707i	$0.327494\pi$
$510$	449.393	+	778.371i	0.0390185	+	0.0675820i
$511$	3436.96	+	5952.98i	0.297538	+	0.515351i
$512$	−21426.5			−1.84947
$513$	10318.9	+	17872.9i	0.888094	+	1.53822i
$514$	7721.49			0.662608
$515$	968.511			0.0828693
$516$	14356.6	−	17823.4i	1.22484	−	1.52060i
$517$	593.076			0.0504515
$518$	3901.72			0.330949
$519$	70.3058	+	121.773i	0.00594621	+	0.0102991i
$520$	5511.76			0.464821
$521$	10518.9	+	18219.3i	0.884534	+	1.53206i	0.846247	+	0.532790i	$0.178857\pi$
$521$	10518.9	+	18219.3i	0.884534	+	1.53206i	0.0382865	+	0.999267i	$0.487810\pi$
$522$	−1120.27	−	1940.36i	−0.0939325	−	0.162696i
$523$	3152.37	−	5460.07i	0.263563	−	0.456505i	−0.703623	−	0.710573i	$-0.748436\pi$
$523$	3152.37	−	5460.07i	0.263563	−	0.456505i	0.967186	+	0.254069i	$0.0817689\pi$
$524$	40494.2			3.37595
$525$	8735.77	−	15130.8i	0.726210	−	1.25783i
$526$	−15798.7	−	27364.2i	−1.30961	−	2.26832i
$527$	4137.56			0.342002
$528$	−4046.33	−	7008.46i	−0.333512	−	0.577659i
$529$	5347.42	−	9262.00i	0.439502	−	0.761239i
$530$	1019.73	−	1766.22i	0.0835738	−	0.144754i
$531$	−815.642	+	1412.73i	−0.0666588	+	0.115456i
$532$	67154.3			5.47276
$533$	−5605.69	+	9709.34i	−0.455553	+	0.789040i
$534$	10300.9	−	17841.7i	0.834764	−	1.44585i
$535$	−1373.82	−	2379.52i	−0.111019	−	0.192291i
$536$	591.820	+	1025.06i	0.0476917	+	0.0826044i
$537$	−423.081			−0.0339987
$538$	−11346.3			−0.909242
$539$	−5773.27	−	9999.59i	−0.461358	−	0.799096i
$540$	2506.41	+	4341.22i	0.199738	+	0.345956i
$541$	8737.39	−	15133.6i	0.694362	−	1.20267i	−0.276033	−	0.961148i	$-0.589020\pi$
$541$	8737.39	−	15133.6i	0.694362	−	1.20267i	0.970395	−	0.241522i	$-0.0776466\pi$
$542$	2086.22	−	3613.44i	0.165334	−	0.286366i
$543$	−476.706			−0.0376748
$544$	180.295	−	312.280i	0.0142097	−	0.0246120i
$545$	−605.472	+	1048.71i	−0.0475882	+	0.0824252i
$546$	−22780.7	+	39457.3i	−1.78557	+	3.09270i
$547$	5118.23	+	8865.04i	0.400073	+	0.692947i	0.993734	−	0.111768i	$-0.0356515\pi$
$547$	5118.23	+	8865.04i	0.400073	+	0.692947i	−0.593661	+	0.804715i	$0.702318\pi$
$548$	−25228.5			−1.96662
$549$	−725.837	−	1257.19i	−0.0564262	−	0.0977330i
$550$	6839.71	−	11846.7i	0.530266	−	0.918448i
$551$	−30985.4			−2.39569
$552$	3896.53	−	6748.99i	0.300448	−	0.520392i
$553$	−2496.08	−	4323.34i	−0.191943	−	0.332454i
$554$	−14714.2	−	25485.7i	−1.12842	−	1.95448i
$555$	288.977			0.0221016
$556$	−4872.06	−	8438.65i	−0.371621	−	0.643667i
$557$	−3645.32			−0.277302			−0.138651	−	0.990341i	$-0.544277\pi$
$557$	−3645.32			−0.277302			−0.138651	+	0.990341i	$0.544277\pi$
$558$	2470.13			0.187400
$559$	−17773.1	−	2767.72i	−1.34476	−	0.209413i
$560$	4339.06			0.327426
$561$	−1980.79			−0.149072
$562$	−1980.28	−	3429.94i	−0.148635	−	0.257444i
$563$	16269.7			1.21791			0.608956	−	0.793204i	$-0.291588\pi$
$563$	16269.7			1.21791			0.608956	+	0.793204i	$0.291588\pi$
$564$	−1044.24	−	1808.68i	−0.0779621	−	0.135034i
$565$	−1358.10	−	2352.29i	−0.101125	−	0.175153i
$566$	−8938.97	+	15482.8i	−0.663839	+	1.14980i
$567$	−19414.7			−1.43799
$568$	−19149.4	+	33167.7i	−1.41460	+	2.45015i
$569$	10592.2	+	18346.2i	0.780398	+	1.35169i	0.931710	+	0.363203i	$0.118317\pi$
$569$	10592.2	+	18346.2i	0.780398	+	1.35169i	−0.151312	+	0.988486i	$0.548350\pi$
$570$	7420.58			0.545287
$571$	−7403.77	−	12823.7i	−0.542623	−	0.939851i	−0.998752	−	0.0499377i	$-0.984098\pi$
$571$	−7403.77	−	12823.7i	−0.542623	−	0.939851i	0.456129	−	0.889914i	$-0.349236\pi$
$572$	−11954.9	+	20706.5i	−0.873881	+	1.51361i
$573$	2092.50	−	3624.31i	0.152557	−	0.264237i
$574$	−12574.3	+	21779.3i	−0.914357	+	1.58371i
$575$	4623.12			0.335300
$576$	−479.548	+	830.602i	−0.0346895	+	0.0600840i
$577$	−8914.45	+	15440.3i	−0.643177	+	1.11402i	0.341542	+	0.939866i	$0.389051\pi$
$577$	−8914.45	+	15440.3i	−0.643177	+	1.11402i	−0.984719	+	0.174149i	$0.944283\pi$
$578$	11369.6	+	19692.8i	0.818191	+	1.41715i
$579$	1083.10	+	1875.98i	0.0777410	+	0.134651i
$580$	−7526.16			−0.538805
$581$	9258.10			0.661086
$582$	−8182.93	−	14173.2i	−0.582806	−	1.00945i
$583$	2247.33	+	3892.49i	0.159648	+	0.276519i
$584$	4814.27	−	8338.56i	0.341123	−	0.590842i
$585$	141.330	−	244.791i	0.00998851	−	0.0173006i
$586$	5916.68			0.417092
$587$	6221.52	−	10776.0i	0.437461	−	0.757705i	−0.560032	−	0.828471i	$-0.689211\pi$
$587$	6221.52	−	10776.0i	0.437461	−	0.757705i	0.997493	+	0.0707664i	$0.0225445\pi$
$588$	−20330.3	+	35213.1i	−1.42586	+	2.46966i
$589$	17080.3	−	29584.0i	1.19488	−	2.06959i
$590$	4087.70	+	7080.10i	0.285234	+	0.494039i
$591$	21158.0			1.47263
$592$	−959.032	−	1661.09i	−0.0665810	−	0.115322i
$593$	3.90253	−	6.75939i	0.000270249	−	0.000468086i	−0.865890	−	0.500234i	$-0.833247\pi$
$593$	3.90253	−	6.75939i	0.000270249	−	0.000468086i	0.866160	+	0.499766i	$0.166581\pi$
$594$	−16482.5			−1.13852
$595$	531.022	−	919.757i	0.0365879	−	0.0633721i
$596$	−2020.57	−	3499.72i	−0.138868	−	0.240527i
$597$	1901.71	+	3293.87i	0.130372	+	0.225811i
$598$	−12055.9			−0.824421
$599$	−5948.88	−	10303.8i	−0.405784	−	0.702839i	0.588628	−	0.808404i	$-0.299668\pi$
$599$	−5948.88	−	10303.8i	−0.405784	−	0.702839i	−0.994412	+	0.105565i	$0.966335\pi$
$600$	−24473.0			−1.66518
$601$	24907.2			1.69049			0.845245	−	0.534378i	$-0.179454\pi$
$601$	24907.2			1.69049			0.845245	+	0.534378i	$0.179454\pi$
$602$	−39867.4	−	6208.35i	−2.69913	−	0.420322i
$603$	60.7007			0.00409938
$604$	−25175.0			−1.69595
$605$	849.046	+	1470.59i	0.0570556	+	0.0988231i
$606$	28258.1			1.89424
$607$	2848.77	+	4934.21i	0.190491	+	0.329940i	0.945413	−	0.325875i	$-0.105659\pi$
$607$	2848.77	+	4934.21i	0.190491	+	0.329940i	−0.754922	+	0.655814i	$0.772325\pi$
$608$	−1488.56	−	2578.26i	−0.0992911	−	0.171977i
$609$	15803.3	−	27372.1i	1.05153	−	1.82130i
$610$	−7275.26			−0.482896
$611$	−820.714	+	1421.52i	−0.0543413	+	0.0941219i
$612$	−292.141	−	506.002i	−0.0192959	−	0.0334215i
$613$	−14073.4			−0.927277			−0.463638	−	0.886024i	$-0.653456\pi$
$613$	−14073.4			−0.927277			−0.463638	+	0.886024i	$0.653456\pi$
$614$	13087.1	+	22667.6i	0.860185	+	1.48988i
$615$	−931.301	+	1613.06i	−0.0610629	+	0.105764i
$616$	−13623.8	+	23597.1i	−0.891101	+	1.54343i
$617$	−9794.80	+	16965.1i	−0.639099	+	1.10695i	0.346532	+	0.938038i	$0.387359\pi$
$617$	−9794.80	+	16965.1i	−0.639099	+	1.10695i	−0.985631	+	0.168913i	$0.945974\pi$
$618$	11214.2			0.729935
$619$	11224.9	−	19442.1i	0.728865	−	1.26243i	−0.228498	−	0.973544i	$-0.573381\pi$
$619$	11224.9	−	19442.1i	0.728865	−	1.26243i	0.957363	−	0.288887i	$-0.0932852\pi$
$620$	4148.71	−	7185.77i	0.268736	−	0.465464i
$621$	−2785.22	−	4824.14i	−0.179979	−	0.311733i
$622$	18357.0	+	31795.3i	1.18336	+	2.04964i
$623$	−24344.0			−1.56553
$624$	22397.7			1.43690
$625$	−6977.34	−	12085.1i	−0.446550	−	0.773447i
$626$	−5729.82	−	9924.34i	−0.365830	−	0.633637i
$627$	−8176.94	+	14162.9i	−0.520822	+	0.902090i
$628$	19740.3	−	34191.1i	1.25434	−	2.17257i
$629$	−469.473			−0.0297601
$630$	317.022	−	549.097i	0.0200483	−	0.0347247i
$631$	5878.40	−	10181.7i	0.370864	−	0.642356i	−0.618834	−	0.785522i	$-0.712395\pi$
$631$	5878.40	−	10181.7i	0.370864	−	0.642356i	0.989699	+	0.143165i	$0.0457281\pi$
$632$	−3496.35	+	6055.86i	−0.220059	+	0.381154i
$633$	10535.1	+	18247.3i	0.661504	+	1.14576i
$634$	−20241.4			−1.26797
$635$	−1110.11	−	1922.77i	−0.0693753	−	0.120162i
$636$	7913.87	−	13707.2i	0.493404	−	0.854602i
$637$	31956.8			1.98771
$638$	12373.3	−	21431.1i	0.767809	−	1.32988i
$639$	982.040	+	1700.94i	0.0607964	+	0.105302i
$640$	2581.19	+	4470.76i	0.159423	+	0.276129i
$641$	2855.08			0.175926			0.0879632	−	0.996124i	$-0.471964\pi$
$641$	2855.08			0.175926			0.0879632	+	0.996124i	$0.471964\pi$
$642$	−15907.1	−	27552.0i	−0.977888	−	1.69375i
$643$	−24848.3			−1.52398			−0.761992	−	0.647587i	$-0.775778\pi$
$643$	−24848.3			−1.52398			−0.761992	+	0.647587i	$0.775778\pi$
$644$	−18125.8			−1.10910
$645$	−2952.74	−	459.815i	−0.180254	−	0.0280701i
$646$	−12055.5			−0.734237
$647$	19091.2			1.16005			0.580026	−	0.814598i	$-0.303042\pi$
$647$	19091.2			1.16005			0.580026	+	0.814598i	$0.303042\pi$
$648$	13597.5	+	23551.5i	0.824319	+	1.42776i
$649$	−18017.4			−1.08975
$650$	18929.9	+	32787.6i	1.14230	+	1.97852i
$651$	17422.7	+	30177.1i	1.04893	+	1.81679i
$652$	15186.2	−	26303.3i	0.912176	−	1.57994i
$653$	20520.4			1.22975			0.614875	−	0.788624i	$-0.289206\pi$
$653$	20520.4			1.22975			0.614875	+	0.788624i	$0.289206\pi$
$654$	−7010.62	+	12142.7i	−0.419169	+	0.726023i
$655$	−2643.71	−	4579.03i	−0.157707	−	0.273157i
$656$	12362.9			0.735808
$657$	−246.890	−	427.627i	−0.0146607	−	0.0253932i
$658$	−1840.97	+	3188.65i	−0.109070	+	0.188916i
$659$	16098.4	−	27883.2i	0.951598	−	1.64822i	0.209629	−	0.977781i	$-0.432774\pi$
$659$	16098.4	−	27883.2i	0.951598	−	1.64822i	0.741969	−	0.670435i	$-0.233892\pi$
$660$	−1986.13	+	3440.07i	−0.117136	+	0.202886i
$661$	19587.1			1.15257			0.576286	−	0.817248i	$-0.304501\pi$
$661$	19587.1			1.15257			0.576286	+	0.817248i	$0.304501\pi$
$662$	17938.4	−	31070.3i	1.05317	−	1.82414i
$663$	2741.07	−	4747.68i	0.160565	−	0.278106i
$664$	−6484.08	−	11230.7i	−0.378962	−	0.656382i
$665$	−4384.24	−	7593.73i	−0.255660	−	0.442815i
$666$	−280.276			−0.0163070
$667$	8363.37			0.485503
$668$	−21049.9	−	36459.5i	−1.21923	−	2.11177i
$669$	10563.0	+	18295.7i	0.610447	+	1.05733i
$670$	152.105	−	263.453i	0.00877063	−	0.0151912i
$671$	8016.81	−	13885.5i	0.461230	−	0.798874i
$672$	3036.80			0.174326
$673$	−2342.45	+	4057.24i	−0.134167	+	0.232385i	−0.925279	−	0.379287i	$-0.876169\pi$
$673$	−2342.45	+	4057.24i	−0.134167	+	0.232385i	0.791112	+	0.611672i	$0.209503\pi$
$674$	−8585.27	+	14870.1i	−0.490641	+	0.849816i
$675$	−8746.57	+	15149.5i	−0.498749	+	0.863859i
$676$	−15223.8	−	26368.4i	−0.866171	−	1.50025i
$677$	10407.0			0.590804			0.295402	−	0.955373i	$-0.404546\pi$
$677$	10407.0			0.590804			0.295402	+	0.955373i	$0.404546\pi$
$678$	−15725.1	−	27236.6i	−0.890735	−	1.54280i
$679$	−9669.31	+	16747.7i	−0.546501	+	0.946567i
$680$	−1487.64			−0.0838949
$681$	10823.8	−	18747.4i	0.609058	−	1.05492i
$682$	13641.2	+	23627.3i	0.765908	+	1.32659i
$683$	−1576.28	−	2730.19i	−0.0883082	−	0.152954i	0.818488	−	0.574524i	$-0.194813\pi$
$683$	−1576.28	−	2730.19i	−0.0883082	−	0.152954i	−0.906796	+	0.421569i	$0.861479\pi$
$684$	−4823.96			−0.269662
$685$	1647.07	+	2852.81i	0.0918704	+	0.159124i
$686$	22602.3			1.25796
$687$	−2162.83			−0.120112
$688$	7156.19	+	18498.9i	0.396551	+	1.02509i
$689$	−12439.7			−0.687828
$690$	−2002.91			−0.110507
$691$	4766.78	+	8256.31i	0.262427	+	0.454537i	0.966886	−	0.255208i	$-0.0821438\pi$
$691$	4766.78	+	8256.31i	0.262427	+	0.454537i	−0.704459	+	0.709744i	$0.748810\pi$
$692$	−458.107			−0.0251656
$693$	698.670	+	1210.13i	0.0382977	+	0.0663335i
$694$	−14336.8	−	24832.1i	−0.784176	−	1.35823i
$695$	−636.156	+	1101.85i	−0.0347205	+	0.0601377i
$696$	−44272.4			−2.41112
$697$	1512.99	−	2620.58i	0.0822221	−	0.142413i
$698$	3276.65	+	5675.32i	0.177683	+	0.307757i
$699$	12087.4			0.654057
$700$	28460.8	+	49295.5i	1.53674	+	2.66171i
$701$	−10621.1	+	18396.3i	−0.572260	+	0.991183i	0.424074	+	0.905628i	$0.360600\pi$
$701$	−10621.1	+	18396.3i	−0.572260	+	0.991183i	−0.996333	+	0.0855551i	$0.972734\pi$
$702$	22808.9	−	39506.1i	1.22630	−	2.12402i
$703$	−1938.04	+	3356.78i	−0.103975	+	0.180090i
$704$	−10593.1			−0.567108
$705$	−136.349	+	236.164i	−0.00728398	+	0.0126162i
$706$	−13612.6	+	23577.7i	−0.725662	+	1.25688i
$707$	−16695.5	−	28917.5i	−0.888119	−	1.53827i
$708$	31723.7	+	54947.1i	1.68397	+	2.91672i
$709$	−13947.6			−0.738808			−0.369404	−	0.929269i	$-0.620438\pi$
$709$	−13947.6			−0.738808			−0.369404	+	0.929269i	$0.620438\pi$
$710$	9843.25			0.520296
$711$	179.304	+	310.563i	0.00945769	+	0.0163812i
$712$	17049.8	+	29531.1i	0.897425	+	1.55439i
$713$	−4610.20	+	7985.11i	−0.242151	+	0.419417i
$714$	6148.58	−	10649.7i	0.322276	−	0.558198i
$715$	3121.96			0.163293
$716$	689.190	−	1193.71i	0.0359724	−	0.0623060i
$717$	−6685.53	+	11579.7i	−0.348223	+	0.603140i
$718$	10137.0	−	17557.7i	0.526891	−	0.912602i
$719$	10392.6	+	18000.6i	0.539054	+	0.933668i	0.998955	+	0.0456983i	$0.0145513\pi$
$719$	10392.6	+	18000.6i	0.539054	+	0.933668i	−0.459902	+	0.887970i	$0.652115\pi$
$720$	−311.692			−0.0161334
$721$	−6625.58	−	11475.8i	−0.342232	−	0.592764i
$722$	−32874.1	+	56939.7i	−1.69453	+	2.93501i
$723$	−8785.28			−0.451906
$724$	776.544	−	1345.01i	0.0398619	−	0.0690429i
$725$	−13132.0	−	22745.2i	−0.672702	−	1.16515i
$726$	9830.90	+	17027.6i	0.502561	+	0.870460i
$727$	−31418.7			−1.60283			−0.801414	−	0.598110i	$-0.795919\pi$
$727$	−31418.7			−1.60283			−0.801414	+	0.598110i	$0.795919\pi$
$728$	−37705.9	−	65308.6i	−1.91961	−	3.32486i
$729$	20960.1			1.06488
$730$	−2474.65			−0.125467
$731$	4797.02	+	747.017i	0.242715	+	0.0377967i
$732$	−56461.6			−2.85093
$733$	−3390.31			−0.170838			−0.0854188	−	0.996345i	$-0.527223\pi$
$733$	−3390.31			−0.170838			−0.0854188	+	0.996345i	$0.527223\pi$
$734$	2247.35	+	3892.53i	0.113013	+	0.195743i
$735$	5309.14			0.266436
$736$	401.781	+	695.906i	0.0201221	+	0.0348525i
$737$	335.217	+	580.613i	0.0167543	+	0.0290192i
$738$	903.262	−	1564.50i	0.0450536	−	0.0780350i
$739$	−30523.6			−1.51939			−0.759694	−	0.650280i	$-0.774651\pi$
$739$	−30523.6			−1.51939			−0.759694	+	0.650280i	$0.774651\pi$
$740$	−470.737	+	815.340i	−0.0233846	+	0.0405034i
$741$	−22630.9	−	39197.9i	−1.12195	−	1.94328i
$742$	−27903.8			−1.38057
$743$	662.159	+	1146.89i	0.0326948	+	0.0566291i	0.881910	−	0.471418i	$-0.156258\pi$
$743$	662.159	+	1146.89i	0.0326948	+	0.0566291i	−0.849215	+	0.528047i	$0.822924\pi$
$744$	24404.6	−	42270.1i	1.20258	−	2.08293i
$745$	−263.830	+	456.967i	−0.0129745	+	0.0224724i
$746$	23089.8	−	39992.7i	1.13321	−	1.96278i
$747$	−665.046			−0.0325740
$748$	3226.67	−	5588.76i	0.157726	−	0.273189i
$749$	−18796.6	+	32556.6i	−0.916972	+	1.58824i
$750$	6407.52	+	11098.2i	0.311960	+	0.540330i
$751$	20034.1	+	34700.0i	0.973440	+	1.68605i	0.684989	+	0.728553i	$0.259807\pi$
$751$	20034.1	+	34700.0i	0.973440	+	1.68605i	0.288451	+	0.957495i	$0.406860\pi$
$752$	1810.02			0.0877720
$753$	−30268.1			−1.46485
$754$	34244.9	+	59313.9i	1.65401	+	2.86483i
$755$	1643.58	+	2846.76i	0.0792264	+	0.137224i
$756$	34292.6	−	59396.5i	1.64975	−	2.85745i
$757$	8225.29	−	14246.6i	0.394919	−	0.684019i	−0.598172	−	0.801368i	$-0.704106\pi$
$757$	8225.29	−	14246.6i	0.394919	−	0.684019i	0.993091	+	0.117349i	$0.0374395\pi$
$758$	36376.8			1.74310
$759$	2207.06	−	3822.75i	0.105548	−	0.182815i
$760$	−6141.16	+	10636.8i	−0.293110	+	0.507681i
$761$	2020.75	−	3500.04i	0.0962577	−	0.166723i	−0.813875	−	0.581040i	$-0.802646\pi$
$761$	2020.75	−	3500.04i	0.0962577	−	0.166723i	0.910133	+	0.414317i	$0.135979\pi$
$762$	−12853.7	−	22263.3i	−0.611076	−	1.05842i
$763$	16568.1			0.786115
$764$	6817.26	+	11807.8i	0.322827	+	0.559153i
$765$	−38.1455	+	66.0699i	−0.00180281	+	0.00312256i
$766$	−25763.4			−1.21524
$767$	24933.0	−	43185.1i	1.17376	−	2.03302i
$768$	20711.2	+	35872.8i	0.973113	+	1.68548i
$769$	111.741	+	193.540i	0.00523988	+	0.00907574i	0.868633	−	0.495455i	$-0.164999\pi$
$769$	111.741	+	193.540i	0.00523988	+	0.00907574i	−0.863394	+	0.504531i	$0.831665\pi$
$770$	7002.96			0.327752
$771$	−3912.25	−	6776.22i	−0.182745	−	0.316524i
$772$	−7057.38			−0.329016
$773$	32479.7			1.51127			0.755637	−	0.654991i	$-0.227327\pi$
$773$	32479.7			1.51127			0.755637	+	0.654991i	$0.227327\pi$
$774$	2863.84	+	445.971i	0.132995	+	0.0207107i
$775$	28955.4			1.34207
$776$	27088.3			1.25311
$777$	−1976.89	−	3424.07i	−0.0912747	−	0.158092i
$778$	65201.0			3.00459
$779$	−12491.6	−	21636.1i	−0.574530	−	0.995116i
$780$	−5496.91	−	9520.93i	−0.252335	−	0.437057i
$781$	−10846.5	+	18786.8i	−0.496953	+	0.860747i
$782$	3253.93			0.148799
$783$	−15822.8	+	27405.9i	−0.722173	+	1.25084i
$784$	−17619.5	−	30517.9i	−0.802639	−	1.39021i
$785$	−5155.06			−0.234385
$786$	−30610.9	−	53019.6i	−1.38913	−	2.40604i
$787$	−6023.76	+	10433.5i	−0.272839	+	0.472570i	−0.969588	−	0.244745i	$-0.921296\pi$
$787$	−6023.76	+	10433.5i	−0.272839	+	0.472570i	0.696749	+	0.717315i	$0.254629\pi$
$788$	−34466.0	+	59696.8i	−1.55812	+	2.69875i
$789$	−16009.5	+	27729.2i	−0.722373	+	1.25119i
$790$	1797.21			0.0809390
$791$	−18581.5	+	32184.0i	−0.835247	+	1.44669i
$792$	978.652	−	1695.07i	0.0439077	−	0.0760503i
$793$	22187.8	+	38430.3i	0.993581	+	1.72093i
$794$	21532.5	+	37295.3i	0.962417	+	1.66695i
$795$	−2066.66			−0.0921974
$796$	−12391.4			−0.551761
$797$	883.058	+	1529.50i	0.0392466	+	0.0679771i	0.884981	−	0.465626i	$-0.154171\pi$
$797$	883.058	+	1529.50i	0.0392466	+	0.0679771i	−0.845735	+	0.533603i	$0.820838\pi$
$798$	−50764.1	−	87926.0i	−2.25192	−	3.90044i
$799$	221.513	−	383.672i	0.00980799	−	0.0169879i
$800$	1261.74	−	2185.39i	0.0557614	−	0.0965816i
$801$	1748.73			0.0771389
$802$	−10954.3	+	18973.4i	−0.482306	+	0.835378i
$803$	2726.88	−	4723.10i	0.119838	−	0.207565i
$804$	1180.45	−	2044.60i	0.0517802	−	0.0896860i
$805$	1183.36	+	2049.65i	0.0518113	+	0.0897398i
$806$	−75508.3			−3.29984
$807$	5748.82	+	9957.25i	0.250766	+	0.434339i
$808$	−23386.0	+	40505.8i	−1.01822	+	1.76360i
$809$	−3710.99			−0.161275			−0.0806374	−	0.996744i	$-0.525696\pi$
$809$	−3710.99			−0.161275			−0.0806374	+	0.996744i	$0.525696\pi$
$810$	3494.71	−	6053.01i	0.151594	−	0.262569i
$811$	−21222.5	−	36758.4i	−0.918894	−	1.59157i	−0.801099	−	0.598532i	$-0.795751\pi$
$811$	−21222.5	−	36758.4i	−0.918894	−	1.59157i	−0.117795	−	0.993038i	$-0.537583\pi$
$812$	51486.4	+	89177.1i	2.22515	+	3.85407i
$813$	−4228.10			−0.182394
$814$	−1547.81	−	2680.89i	−0.0666473	−	0.115436i
$815$	−3965.80			−0.170449
$816$	−6045.21			−0.259344
$817$	25143.9	−	31215.5i	1.07671	−	1.33671i
$818$	−4926.39			−0.210571
$819$	−3867.35			−0.165001
$820$	−3034.14	−	5255.29i	−0.129216	−	0.223808i
$821$	−6953.99			−0.295610			−0.147805	−	0.989016i	$-0.547221\pi$
$821$	−6953.99			−0.295610			−0.147805	+	0.989016i	$0.547221\pi$
$822$	19071.0	+	33032.0i	0.809219	+	1.40161i
$823$	320.049	+	554.341i	0.0135555	+	0.0234789i	0.872724	−	0.488215i	$-0.162352\pi$
$823$	320.049	+	554.341i	0.0135555	+	0.0234789i	−0.859168	+	0.511693i	$0.829018\pi$
$824$	−9280.69	+	16074.6i	−0.392364	+	0.679595i
$825$	−13861.9			−0.584982
$826$	55927.8	−	96869.8i	2.35591	−	4.08055i
$827$	−1879.92	−	3256.11i	−0.0790461	−	0.136912i	0.823793	−	0.566891i	$-0.191854\pi$
$827$	−1879.92	−	3256.11i	−0.0790461	−	0.136912i	−0.902839	+	0.429980i	$0.858521\pi$
$828$	1302.05			0.0546490
$829$	−5476.78	−	9486.05i	−0.229453	−	0.397424i	0.728193	−	0.685372i	$-0.240360\pi$
$829$	−5476.78	−	9486.05i	−0.229453	−	0.397424i	−0.957646	+	0.287948i	$0.907027\pi$
$830$	−1666.48	+	2886.44i	−0.0696922	+	0.120710i
$831$	−14910.5	+	25825.7i	−0.622429	+	1.07808i
$832$	14659.1	−	25390.3i	0.610832	−	1.05799i
$833$	−8625.25			−0.358760
$834$	−7365.90	+	12758.1i	−0.305828	+	0.529709i
$835$	−2748.53	+	4760.60i	−0.113912	+	0.197302i
$836$	−26640.1	−	46142.0i	−1.10211	−	1.90892i
$837$	−17444.3	−	30214.4i	−0.720386	−	1.24774i
$838$	46711.5			1.92556
$839$	−16737.8			−0.688741			−0.344371	−	0.938834i	$-0.611908\pi$
$839$	−16737.8			−0.688741			−0.344371	+	0.938834i	$0.611908\pi$
$840$	−6264.27	−	10850.0i	−0.257307	−	0.445669i
$841$	−11561.7	−	20025.4i	−0.474052	−	0.821083i
$842$	−19662.9	+	34057.2i	−0.804786	+	1.39393i
$843$	−2006.70	+	3475.70i	−0.0819862	+	0.142004i
$844$	−68645.7			−2.79963
$845$	−1987.81	+	3442.98i	−0.0809262	+	0.140168i
$846$	132.244	−	229.053i	0.00537428	−	0.00930853i
$847$	11616.6	−	20120.6i	0.471254	−	0.816236i
$848$	6858.66	+	11879.6i	0.277745	+	0.481068i
$849$	18116.5			0.732339
$850$	−5109.26	−	8849.49i	−0.206172	−	0.357100i
$851$	523.101	−	906.038i	0.0210713	−	0.0364966i
$852$	76391.2			3.07174
$853$	−18970.6	+	32858.0i	−0.761477	+	1.31892i	0.180612	+	0.983554i	$0.442192\pi$
$853$	−18970.6	+	32858.0i	−0.761477	+	1.31892i	−0.942089	+	0.335363i	$0.891141\pi$
$854$	49770.0	+	86204.2i	1.99426	+	3.45415i
$855$	314.938	+	545.488i	0.0125972	+	0.0218191i
$856$	52658.1			2.10259
$857$	−4788.74	−	8294.35i	−0.190876	−	0.330606i	0.754665	−	0.656110i	$-0.227799\pi$
$857$	−4788.74	−	8294.35i	−0.190876	−	0.330606i	−0.945541	+	0.325504i	$0.894466\pi$
$858$	36148.4			1.43833
$859$	8238.62			0.327239			0.163619	−	0.986524i	$-0.447683\pi$
$859$	8238.62			0.327239			0.163619	+	0.986524i	$0.447683\pi$
$860$	6107.30	−	7582.04i	0.242160	−	0.300634i
$861$	25484.1			1.00871
$862$	68854.9			2.72066
$863$	18252.8	+	31614.7i	0.719967	+	1.24702i	0.961012	+	0.276506i	$0.0891765\pi$
$863$	18252.8	+	31614.7i	0.719967	+	1.24702i	−0.241045	+	0.970514i	$0.577490\pi$
$864$	−3040.55			−0.119724
$865$	29.9080	+	51.8022i	0.00117561	+	0.00203622i
$866$	−17267.9	−	29908.9i	−0.677583	−	1.17361i
$867$	11521.3	−	19955.5i	0.451309	−	0.781690i
$868$	−113525.			−4.43928
$869$	−1980.40	+	3430.14i	−0.0773076	+	0.133901i
$870$	5689.27	+	9854.11i	0.221706	+	0.384006i
$871$	−1855.53			−0.0721840
$872$	−11603.8	−	20098.3i	−0.450635	−	0.780522i
$873$	694.585	−	1203.06i	0.0269280	−	0.0466407i
$874$	13432.6	−	23266.0i	0.519868	−	0.900438i
$875$	7571.42	−	13114.1i	0.292526	−	0.506670i
$876$	−19205.2			−0.740734
$877$	11886.5	−	20588.1i	0.457673	−	0.792713i	−0.541164	−	0.840917i	$-0.682016\pi$
$877$	11886.5	−	20588.1i	0.457673	−	0.792713i	0.998838	+	0.0482036i	$0.0153496\pi$
$878$	16336.1	−	28294.9i	0.627923	−	1.08759i
$879$	−2997.81	−	5192.36i	−0.115033	−	0.199242i
$880$	−1721.31	−	2981.39i	−0.0659377	−	0.114208i
$881$	15658.7			0.598812			0.299406	−	0.954126i	$-0.403211\pi$
$881$	15658.7			0.598812			0.299406	+	0.954126i	$0.403211\pi$
$882$	−5149.29			−0.196582
$883$	−19847.7	−	34377.2i	−0.756430	−	1.31018i	−0.944660	−	0.328050i	$-0.893608\pi$
$883$	−19847.7	−	34377.2i	−0.756430	−	1.31018i	0.188230	−	0.982125i	$-0.439725\pi$
$884$	8930.30	+	15467.7i	0.339772	+	0.588503i
$885$	4142.23	−	7174.56i	0.157333	−	0.272509i
$886$	13103.8	−	22696.5i	0.496876	−	0.860615i
$887$	20917.3			0.791810			0.395905	−	0.918291i	$-0.370431\pi$
$887$	20917.3			0.791810			0.395905	+	0.918291i	$0.370431\pi$
$888$	−2769.10	+	4796.22i	−0.104645	+	0.181251i
$889$	−15188.5	+	26307.3i	−0.573010	+	0.992482i
$890$	4381.99	−	7589.83i	0.165039	−	0.285856i
$891$	7701.83	+	13340.0i	0.289586	+	0.501578i
$892$	−68827.6			−2.58354
$893$	−1828.87	−	3167.69i	−0.0685338	−	0.118704i
$894$	−3054.82	+	5291.11i	−0.114283	+	0.197943i
$895$	−179.978			−0.00672180
$896$	35315.9	−	61168.9i	1.31676	−	2.28070i
$897$	6108.38	+	10580.0i	0.227372	+	0.393821i
$898$	−40592.2	−	70307.8i	−1.50844	−	2.61270i
$899$	52381.2			1.94328
$900$	−2044.45	−	3541.09i	−0.0757204	−	0.131152i
$901$	3357.51			0.124145
$902$	19952.9			0.736540
$903$	14751.3	+	38132.4i	0.543625	+	1.40528i
$904$	52055.4			1.91520
$905$	−202.790			−0.00744859
$906$	19030.6	+	32962.0i	0.697847	+	1.20871i
$907$	16836.4			0.616365			0.308182	−	0.951327i	$-0.400279\pi$
$907$	16836.4			0.616365			0.308182	+	0.951327i	$0.400279\pi$
$908$	35263.5	+	61078.1i	1.28883	+	2.23232i
$909$	1199.31	+	2077.26i	0.0437607	+	0.0757958i
$910$	−9690.88	+	16785.1i	−0.353021	+	0.611451i
$911$	−11490.2			−0.417880			−0.208940	−	0.977928i	$-0.567001\pi$
$911$	−11490.2			−0.417880			−0.208940	+	0.977928i	$0.567001\pi$
$912$	−24955.3	+	43223.9i	−0.906090	+	1.56939i
$913$	−3672.69	−	6361.29i	−0.133131	−	0.230589i
$914$	−44562.1			−1.61267
$915$	3686.16	+	6384.62i	0.133181	+	0.230676i
$916$	3523.20	−	6102.36i	0.127085	−	0.220118i
$917$	−36171.2	+	62650.3i	−1.30259	+	2.25616i
$918$	−6156.19	+	10662.8i	−0.221334	+	0.383361i
$919$	−19214.3			−0.689687			−0.344843	−	0.938660i	$-0.612068\pi$
$919$	−19214.3			−0.689687			−0.344843	+	0.938660i	$0.612068\pi$
$920$	1657.58	−	2871.01i	0.0594009	−	0.102885i
$921$	13261.7	−	22970.0i	0.474472	−	0.821810i
$922$	−14199.7	−	24594.6i	−0.507204	−	0.878504i
$923$	−30019.5	−	51995.3i	−1.07053	−	1.85422i
$924$	54348.3			1.93499
$925$	−3285.45			−0.116784
$926$	18103.2	+	31355.7i	0.642450	+	1.11276i
$927$	475.942	+	824.356i	0.0168630	+	0.0292075i
$928$	2282.52	−	3953.44i	0.0807408	−	0.139847i
$929$	5595.82	−	9692.24i	0.197624	−	0.342295i	−0.750133	−	0.661286i	$-0.770011\pi$
$929$	5595.82	−	9692.24i	0.197624	−	0.342295i	0.947758	+	0.318991i	$0.103344\pi$
$930$	−12544.6			−0.442315
$931$	−35606.0	+	61671.4i	−1.25343	+	2.17100i
$932$	−19690.1	+	34104.2i	−0.692027	+	1.19863i
$933$	18601.9	−	32219.5i	0.652733	−	1.13057i
$934$	−12448.3	−	21561.1i	−0.436104	−	0.755355i
$935$	−842.627			−0.0294726
$936$	2708.57	+	4691.38i	0.0945858	+	0.163827i
$937$	11281.9	−	19540.8i	0.393344	−	0.681291i	−0.599545	−	0.800341i	$-0.704652\pi$
$937$	11281.9	−	19540.8i	0.393344	−	0.681291i	0.992888	+	0.119050i	$0.0379850\pi$
$938$	−4162.19			−0.144883
$939$	−5806.27	+	10056.7i	−0.201790	+	0.349510i
$940$	−444.220	−	769.412i	−0.0154137	−	0.0266973i
$941$	−5365.36	−	9293.07i	−0.185872	−	0.321940i	0.757998	−	0.652257i	$-0.226178\pi$
$941$	−5365.36	−	9293.07i	−0.185872	−	0.321940i	−0.943870	+	0.330317i	$0.892844\pi$
$942$	−59689.3			−2.06452
$943$	3371.66	+	5839.88i	0.116433	+	0.201668i
$944$	−54987.6			−1.89586
$945$	−8955.33			−0.308272
$946$	11549.6	+	29856.0i	0.396946	+	1.02611i
$947$	3278.75			0.112508			0.0562540	−	0.998416i	$-0.482084\pi$
$947$	3278.75			0.112508			0.0562540	+	0.998416i	$0.482084\pi$
$948$	13947.7			0.477850
$949$	7547.07	+	13071.9i	0.258154	+	0.447136i
$950$	−84366.4			−2.88127
$951$	10255.7	+	17763.5i	0.349700	+	0.605699i
$952$	10177.0	+	17627.0i	0.346468	+	0.600099i
$953$	−8313.23	+	14398.9i	−0.282573	+	0.489430i	−0.972018	−	0.234908i	$-0.924521\pi$
$953$	−8313.23	+	14398.9i	−0.282573	+	0.489430i	0.689445	+	0.724338i	$0.257855\pi$
$954$	2004.44			0.0680253
$955$	890.145	−	1541.78i	0.0301617	−	0.0522416i
$956$	−21781.2	−	37726.1i	−0.736876	−	1.27631i
$957$	−25076.7			−0.847036
$958$	−3953.64	−	6847.90i	−0.133336	−	0.230945i
$959$	22535.2	−	39032.0i	0.758810	−	1.31430i
$960$	2435.38	−	4218.21i	0.0818767	−	0.141815i
$961$	−13979.0	+	24212.3i	−0.469236	+	0.812740i
$962$	8567.63			0.287143
$963$	1350.23	−	2338.67i	0.0451824	−	0.0782582i
$964$	14311.0	−	24787.4i	0.478141	−	0.828164i
$965$	460.749	+	798.041i	0.0153700	+	0.0266216i
$966$	13701.9	+	23732.4i	0.456368	+	0.790452i
$967$	26130.0			0.868959			0.434480	−	0.900682i	$-0.356932\pi$
$967$	26130.0			0.868959			0.434480	+	0.900682i	$0.356932\pi$
$968$	−32543.7			−1.08057
$969$	6108.16	+	10579.7i	0.202500	+	0.350740i
$970$	−3481.01	−	6029.28i	−0.115225	−	0.199576i
$971$	13781.4	−	23870.1i	0.455476	−	0.788907i	−0.543240	−	0.839578i	$-0.682803\pi$
$971$	13781.4	−	23870.1i	0.455476	−	0.788907i	0.998715	+	0.0506706i	$0.0161359\pi$
$972$	−4750.02	+	8227.27i	−0.156746	+	0.271492i
$973$	17407.7			0.573553
$974$	−196.646	+	340.601i	−0.00646915	+	0.0112049i
$975$	19182.5	−	33225.1i	0.630084	−	1.09134i
$976$	24466.6	−	42377.5i	0.802416	−	1.38983i
$977$	9878.20	+	17109.5i	0.323471	+	0.560269i	0.981202	−	0.192985i	$-0.0618167\pi$
$977$	9878.20	+	17109.5i	0.323471	+	0.560269i	−0.657730	+	0.753253i	$0.728483\pi$
$978$	−45919.1			−1.50136
$979$	9657.28	+	16726.9i	0.315269	+	0.546061i
$980$	−8648.48	+	14979.6i	−0.281904	+	0.488271i
$981$	−1190.15			−0.0387346
$982$	−41595.8	+	72046.0i	−1.35171	+	2.34122i
$983$	−4313.80	−	7471.72i	−0.139968	−	0.242432i	0.787516	−	0.616294i	$-0.211367\pi$
$983$	−4313.80	−	7471.72i	−0.139968	−	0.242432i	−0.927484	+	0.373862i	$0.878033\pi$
$984$	−17848.2	−	30914.1i	−0.578233	−	1.00153i
$985$	9000.60			0.291150
$986$	−9242.81	−	16009.0i	−0.298530	−	0.517070i
$987$	3731.06			0.120325
$988$	147461.			4.74835
$989$	−6786.67	+	8425.46i	−0.218204	+	0.270894i
$990$	−503.050			−0.0161495
$991$	16965.9			0.543833			0.271917	−	0.962321i	$-0.412342\pi$
$991$	16965.9			0.543833			0.271917	+	0.962321i	$0.412342\pi$
$992$	2516.43	+	4358.58i	0.0805409	+	0.139501i
$993$	−36355.5			−1.16184
$994$	−67337.6	−	116632.i	−2.14871	−	3.72168i
$995$	808.987	+	1401.21i	0.0257755	+	0.0446444i
$996$	−12933.2	+	22401.0i	−0.411450	+	0.712653i
$997$	−45169.5			−1.43484			−0.717419	−	0.696642i	$-0.754677\pi$
$997$	−45169.5			−1.43484			−0.717419	+	0.696642i	$0.754677\pi$
$998$	−45785.0	+	79301.9i	−1.45220	+	2.51529i
$999$	1979.33	+	3428.31i	0.0626860	+	0.108575i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	43.4.c.a.36.10	yes	20
43.6	even	3	inner	43.4.c.a.6.10	✓	20
43.7	odd	6		1849.4.a.f.1.1		10
43.36	even	3		1849.4.a.d.1.10		10

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
43.4.c.a.6.10	✓	20	43.6	even	3	inner
43.4.c.a.36.10	yes	20	1.1	even	1	trivial
1849.4.a.d.1.10		10	43.36	even	3
1849.4.a.f.1.1		10	43.7	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)

\(f(q)\)	\(=\)	\(q+4.92559 q^{2} +(-2.49565 - 4.32260i) q^{3} +16.2615 q^{4} +(-1.06165 - 1.83883i) q^{5} +(-12.2926 - 21.2914i) q^{6} +(-14.5255 + 25.1588i) q^{7} +40.6926 q^{8} +(1.04342 - 1.80726i) q^{9} +O(q^{10})\)	\(q+4.92559 q^{2} +(-2.49565 - 4.32260i) q^{3} +16.2615 q^{4} +(-1.06165 - 1.83883i) q^{5} +(-12.2926 - 21.2914i) q^{6} +(-14.5255 + 25.1588i) q^{7} +40.6926 q^{8} +(1.04342 - 1.80726i) q^{9} +(-5.22925 - 9.05732i) q^{10} +23.0490 q^{11} +(-40.5830 - 70.2918i) q^{12} +(-31.8958 + 55.2452i) q^{13} +(-71.5465 + 123.922i) q^{14} +(-5.29901 + 9.17816i) q^{15} +70.3437 q^{16} +(8.60879 - 14.9109i) q^{17} +(5.13947 - 8.90182i) q^{18} +(-71.0762 - 123.108i) q^{19} +(-17.2640 - 29.9021i) q^{20} +145.002 q^{21} +113.530 q^{22} +(19.1844 + 33.2283i) q^{23} +(-101.555 - 175.898i) q^{24} +(60.2458 - 104.349i) q^{25} +(-157.106 + 272.115i) q^{26} -145.181 q^{27} +(-236.205 + 409.120i) q^{28} +(108.987 - 188.770i) q^{29} +(-26.1008 + 45.2079i) q^{30} +(120.155 + 208.115i) q^{31} +20.9431 q^{32} +(-57.5224 - 99.6317i) q^{33} +(42.4034 - 73.4449i) q^{34} +61.6837 q^{35} +(16.9676 - 29.3887i) q^{36} +(-13.6335 - 23.6139i) q^{37} +(-350.092 - 606.378i) q^{38} +318.404 q^{39} +(-43.2013 - 74.8268i) q^{40} +175.750 q^{41} +714.221 q^{42} +(101.732 + 262.978i) q^{43} +374.811 q^{44} -4.43099 q^{45} +(94.4945 + 163.669i) q^{46} +25.7311 q^{47} +(-175.553 - 304.068i) q^{48} +(-250.478 - 433.840i) q^{49} +(296.746 - 513.980i) q^{50} -85.9383 q^{51} +(-518.673 + 898.368i) q^{52} +(97.5022 + 168.879i) q^{53} -715.105 q^{54} +(-24.4699 - 42.3832i) q^{55} +(-591.079 + 1023.78i) q^{56} +(-354.763 + 614.468i) q^{57} +(536.824 - 929.806i) q^{58} -781.699 q^{59} +(-86.1697 + 149.250i) q^{60} +(347.816 - 602.435i) q^{61} +(591.835 + 1025.09i) q^{62} +(30.3124 + 52.5025i) q^{63} -459.592 q^{64} +135.449 q^{65} +(-283.332 - 490.745i) q^{66} +(14.5437 + 25.1904i) q^{67} +(139.992 - 242.473i) q^{68} +(95.7552 - 165.853i) q^{69} +303.829 q^{70} +(-470.586 + 815.079i) q^{71} +(42.4596 - 73.5422i) q^{72} +(118.308 - 204.916i) q^{73} +(-67.1532 - 116.313i) q^{74} -601.411 q^{75} +(-1155.80 - 2001.91i) q^{76} +(-334.797 + 579.886i) q^{77} +1568.33 q^{78} +(-85.9210 + 148.820i) q^{79} +(-74.6802 - 129.350i) q^{80} +(334.150 + 578.765i) q^{81} +865.673 q^{82} +(-159.343 - 275.990i) q^{83} +2357.95 q^{84} -36.5580 q^{85} +(501.090 + 1295.32i) q^{86} -1087.97 q^{87} +937.925 q^{88} +(418.989 + 725.710i) q^{89} -21.8252 q^{90} +(-926.603 - 1604.92i) q^{91} +(311.966 + 540.342i) q^{92} +(599.731 - 1038.76i) q^{93} +126.741 q^{94} +(-150.916 + 261.394i) q^{95} +(-52.2668 - 90.5288i) q^{96} +665.680 q^{97} +(-1233.75 - 2136.92i) q^{98} +(24.0498 - 41.6555i) 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

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Database

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