LMFDB - Embedded newform 128.4.k.a.5.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,4,Mod(5,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 1]))

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

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

chi := DirichletCharacter("128.5");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	128.k (of order $32$, degree $16$, 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:	$7.55224448073$
Analytic rank:	$0$
Dimension:	$752$
Relative dimension:	$47$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			5.9
Character	$\chi$	$=$	128.5
Dual form			128.4.k.a.77.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-2.42367 - 1.45802i) q^{2} +(-4.84264 - 1.46900i) q^{3} +(3.74833 + 7.06753i) q^{4} +(-16.3353 - 1.60888i) q^{5} +(9.59512 + 10.6211i) q^{6} +(-11.5654 - 17.3089i) q^{7} +(1.21991 - 22.5945i) q^{8} +(-1.15646 - 0.772719i) q^{9} +O(q^{10})$	\(q+(-2.42367 - 1.45802i) q^{2} +(-4.84264 - 1.46900i) q^{3} +(3.74833 + 7.06753i) q^{4} +(-16.3353 - 1.60888i) q^{5} +(9.59512 + 10.6211i) q^{6} +(-11.5654 - 17.3089i) q^{7} +(1.21991 - 22.5945i) q^{8} +(-1.15646 - 0.772719i) q^{9} +(37.2455 + 27.7166i) q^{10} +(-19.5121 + 36.5045i) q^{11} +(-7.76964 - 39.7318i) q^{12} +(3.26062 + 33.1056i) q^{13} +(2.79399 + 58.8136i) q^{14} +(76.7424 + 31.7878i) q^{15} +(-35.9000 + 52.9829i) q^{16} +(46.5328 - 19.2745i) q^{17} +(1.67622 + 3.55895i) q^{18} +(80.5519 - 98.1527i) q^{19} +(-49.8592 - 121.481i) q^{20} +(30.5805 + 100.810i) q^{21} +(100.515 - 60.0258i) q^{22} +(-17.9173 - 90.0761i) q^{23} +(-39.0989 + 107.625i) q^{24} +(141.655 + 28.1768i) q^{25} +(40.3661 - 84.9911i) q^{26} +(91.1454 + 111.061i) q^{27} +(78.9799 - 146.618i) q^{28} +(-76.1648 + 40.7110i) q^{29} +(-139.651 - 188.935i) q^{30} +(155.388 + 155.388i) q^{31} +(164.260 - 76.0700i) q^{32} +(148.115 - 148.115i) q^{33} +(-140.883 - 21.1309i) q^{34} +(161.076 + 301.353i) q^{35} +(1.12643 - 11.0697i) q^{36} +(-211.911 + 173.910i) q^{37} +(-338.340 + 120.443i) q^{38} +(32.8421 - 165.109i) q^{39} +(-56.2795 + 367.125i) q^{40} +(-470.768 + 93.6416i) q^{41} +(72.8669 - 288.918i) q^{42} +(480.874 - 145.872i) q^{43} +(-331.135 - 1.07103i) q^{44} +(17.6478 + 14.4832i) q^{45} +(-87.9076 + 244.438i) q^{46} +(-111.707 - 269.684i) q^{47} +(251.683 - 203.840i) q^{48} +(-34.5778 + 83.4781i) q^{49} +(-302.241 - 274.827i) q^{50} +(-253.656 + 24.9829i) q^{51} +(-221.753 + 147.135i) q^{52} +(-27.3748 - 14.6321i) q^{53} +(-58.9766 - 402.067i) q^{54} +(377.467 - 564.919i) q^{55} +(-405.194 + 240.200i) q^{56} +(-534.270 + 356.988i) q^{57} +(243.956 + 12.3803i) q^{58} +(-68.2668 + 693.124i) q^{59} +(62.9954 + 661.531i) q^{60} +(-94.1740 + 310.450i) q^{61} +(-150.049 - 603.168i) q^{62} +28.9538i q^{63} +(-509.024 - 55.1265i) q^{64} -546.035i q^{65} +(-574.937 + 143.027i) q^{66} +(-85.5872 + 282.143i) q^{67} +(310.644 + 256.625i) q^{68} +(-45.5549 + 462.527i) q^{69} +(48.9837 - 965.232i) q^{70} +(136.766 - 91.3844i) q^{71} +(-18.8700 + 25.1869i) q^{72} +(254.844 - 381.401i) q^{73} +(767.166 - 112.531i) q^{74} +(-644.590 - 344.541i) q^{75} +(995.633 + 201.394i) q^{76} +(857.517 - 84.4581i) q^{77} +(-320.331 + 352.284i) q^{78} +(122.328 - 295.325i) q^{79} +(671.679 - 807.732i) q^{80} +(-263.865 - 637.026i) q^{81} +(1277.52 + 459.435i) q^{82} +(-103.048 - 84.5690i) q^{83} +(-597.854 + 593.999i) q^{84} +(-791.137 + 239.989i) q^{85} +(-1378.16 - 347.582i) q^{86} +(428.643 - 85.2625i) q^{87} +(800.999 + 485.398i) q^{88} +(-161.679 + 812.817i) q^{89} +(-21.6556 - 60.8333i) q^{90} +(535.311 - 439.318i) q^{91} +(569.456 - 464.266i) q^{92} +(-524.223 - 980.753i) q^{93} +(-122.466 + 816.496i) q^{94} +(-1473.75 + 1473.75i) q^{95} +(-907.199 + 127.082i) q^{96} +(516.852 + 516.852i) q^{97} +(205.518 - 151.908i) q^{98} +(50.7726 - 27.1385i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) $ 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{32}\right)$	$1$

Coefficient data

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

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

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

$2$	−2.42367	−	1.45802i	−0.856896	−	0.515489i
$2$	−2.42367	−	1.45802i	−0.856896	−	0.515489i
$3$	−4.84264	−	1.46900i	−0.931967	−	0.282709i	−0.212440	−	0.977174i	$-0.568141\pi$
$3$	−4.84264	−	1.46900i	−0.931967	−	0.282709i	−0.719527	+	0.694465i	$0.755641\pi$
$4$	3.74833	+	7.06753i	0.468542	+	0.883441i
$5$	−16.3353	−	1.60888i	−1.46107	−	0.143903i	−0.663975	−	0.747755i	$-0.731132\pi$
$5$	−16.3353	−	1.60888i	−1.46107	−	0.143903i	−0.797096	+	0.603852i	$0.793632\pi$
$6$	9.59512	+	10.6211i	0.652865	+	0.722671i
$7$	−11.5654	−	17.3089i	−0.624474	−	0.934591i	−0.999970	−	0.00776726i	$-0.997528\pi$
$7$	−11.5654	−	17.3089i	−0.624474	−	0.934591i	0.375496	−	0.926824i	$-0.377472\pi$
$8$	1.21991	−	22.5945i	0.0539128	−	0.998546i
$9$	−1.15646	−	0.772719i	−0.0428317	−	0.0286192i
$10$	37.2455	+	27.7166i	1.17781	+	0.876476i
$11$	−19.5121	+	36.5045i	−0.534828	+	1.00059i	0.458870	+	0.888503i	$0.348254\pi$
$11$	−19.5121	+	36.5045i	−0.534828	+	1.00059i	−0.993698	+	0.112090i	$0.964246\pi$
$12$	−7.76964	−	39.7318i	−0.186909	−	0.955799i
$13$	3.26062	+	33.1056i	0.0695641	+	0.706296i	0.965201	+	0.261510i	$0.0842204\pi$
$13$	3.26062	+	33.1056i	0.0695641	+	0.706296i	−0.895637	+	0.444786i	$0.853280\pi$
$14$	2.79399	+	58.8136i	0.0533376	+	1.12276i
$15$	76.7424	+	31.7878i	1.32099	+	0.547171i
$16$	−35.9000	+	52.9829i	−0.560937	+	0.827858i
$17$	46.5328	−	19.2745i	0.663874	−	0.274986i	−0.0251935	−	0.999683i	$-0.508020\pi$
$17$	46.5328	−	19.2745i	0.663874	−	0.274986i	0.689068	+	0.724697i	$0.258020\pi$
$18$	1.67622	+	3.55895i	0.0219494	+	0.0466030i
$19$	80.5519	−	98.1527i	0.972625	−	1.18515i	−0.0100767	−	0.999949i	$-0.503208\pi$
$19$	80.5519	−	98.1527i	0.972625	−	1.18515i	0.982701	−	0.185197i	$-0.0592924\pi$
$20$	−49.8592	−	121.481i	−0.557443	−	1.35820i
$21$	30.5805	+	100.810i	0.317772	+	1.04755i
$22$	100.515	−	60.0258i	0.974087	−	0.581706i
$23$	−17.9173	−	90.0761i	−0.162435	−	0.816616i	−0.972971	−	0.230927i	$-0.925824\pi$
$23$	−17.9173	−	90.0761i	−0.162435	−	0.816616i	0.810536	−	0.585689i	$-0.199176\pi$
$24$	−39.0989	+	107.625i	−0.332543	+	0.915370i
$25$	141.655	+	28.1768i	1.13324	+	0.225415i
$26$	40.3661	−	84.9911i	0.304479	−	0.641082i
$27$	91.1454	+	111.061i	0.649664	+	0.791618i
$28$	78.9799	−	146.618i	0.533064	−	0.989581i
$29$	−76.1648	+	40.7110i	−0.487705	+	0.260684i	−0.696871	−	0.717196i	$-0.745425\pi$
$29$	−76.1648	+	40.7110i	−0.487705	+	0.260684i	0.209166	+	0.977880i	$0.432925\pi$
$30$	−139.651	−	188.935i	−0.849888	−	1.14982i
$31$	155.388	+	155.388i	0.900274	+	0.900274i	0.995460	−	0.0951856i	$-0.0303445\pi$
$31$	155.388	+	155.388i	0.900274	+	0.900274i	−0.0951856	+	0.995460i	$0.530344\pi$
$32$	164.260	−	76.0700i	0.907417	−	0.420232i
$33$	148.115	−	148.115i	0.781319	−	0.781319i
$34$	−140.883	−	21.1309i	−0.710624	−	0.106586i
$35$	161.076	+	301.353i	0.777911	+	1.45537i
$36$	1.12643	−	11.0697i	0.00521496	−	0.0512486i
$37$	−211.911	+	173.910i	−0.941564	+	0.772722i	−0.973952	−	0.226754i	$-0.927189\pi$
$37$	−211.911	+	173.910i	−0.941564	+	0.772722i	0.0323879	+	0.999475i	$0.489689\pi$
$38$	−338.340	+	120.443i	−1.44437	+	0.514170i
$39$	32.8421	−	165.109i	0.134845	−	0.677911i
$40$	−56.2795	+	367.125i	−0.222464	+	1.45119i
$41$	−470.768	+	93.6416i	−1.79321	+	0.356692i	−0.975681	−	0.219195i	$-0.929657\pi$
$41$	−470.768	+	93.6416i	−1.79321	+	0.356692i	−0.817530	+	0.575887i	$0.804657\pi$
$42$	72.8669	−	288.918i	0.267705	−	1.06145i
$43$	480.874	−	145.872i	1.70541	−	0.517330i	0.720957	−	0.692980i	$-0.243703\pi$
$43$	480.874	−	145.872i	1.70541	−	0.517330i	0.984453	+	0.175649i	$0.0562025\pi$
$44$	−331.135	−	1.07103i	−1.13455	−	0.00366962i
$45$	17.6478	+	14.4832i	0.0584618	+	0.0479783i
$46$	−87.9076	+	244.438i	−0.281767	+	0.783489i
$47$	−111.707	−	269.684i	−0.346683	−	0.836967i	−0.997007	−	0.0773101i	$-0.975367\pi$
$47$	−111.707	−	269.684i	−0.346683	−	0.836967i	0.650324	−	0.759657i	$-0.274633\pi$
$48$	251.683	−	203.840i	0.756818	−	0.612955i
$49$	−34.5778	+	83.4781i	−0.100810	+	0.243376i
$50$	−302.241	−	274.827i	−0.854867	−	0.777328i
$51$	−253.656	+	24.9829i	−0.696450	+	0.0685943i
$52$	−221.753	+	147.135i	−0.591378	+	0.392385i
$53$	−27.3748	−	14.6321i	−0.0709476	−	0.0379223i	0.435541	−	0.900169i	$-0.356557\pi$
$53$	−27.3748	−	14.6321i	−0.0709476	−	0.0379223i	−0.506489	+	0.862246i	$0.669057\pi$
$54$	−58.9766	−	402.067i	−0.148624	−	1.01323i
$55$	377.467	−	564.919i	0.925410	−	1.38497i
$56$	−405.194	+	240.200i	−0.966899	+	0.573179i
$57$	−534.270	+	356.988i	−1.24151	+	0.829548i
$58$	243.956	+	12.3803i	0.552293	+	0.0280278i
$59$	−68.2668	+	693.124i	−0.150637	+	1.52944i	0.561544	+	0.827447i	$0.310207\pi$
$59$	−68.2668	+	693.124i	−0.150637	+	1.52944i	−0.712181	+	0.701995i	$0.752293\pi$
$60$	62.9954	+	661.531i	0.135544	+	1.42339i
$61$	−94.1740	+	310.450i	−0.197668	+	0.651624i	0.800933	+	0.598753i	$0.204337\pi$
$61$	−94.1740	+	310.450i	−0.197668	+	0.651624i	−0.998601	+	0.0528706i	$0.983163\pi$
$62$	−150.049	−	603.168i	−0.307360	−	1.23552i
$63$			28.9538i			0.0579021i
$64$	−509.024	−	55.1265i	−0.994187	−	0.107669i
$65$		−	546.035i		−	1.04196i
$66$	−574.937	+	143.027i	−1.07227	+	0.266748i
$67$	−85.5872	+	282.143i	−0.156062	+	0.514467i	−0.999750	−	0.0223670i	$-0.992880\pi$
$67$	−85.5872	+	282.143i	−0.156062	+	0.514467i	0.843688	+	0.536834i	$0.180380\pi$
$68$	310.644	+	256.625i	0.553987	+	0.457652i
$69$	−45.5549	+	462.527i	−0.0794807	+	0.806981i
$70$	48.9837	−	965.232i	0.0836381	−	1.64810i
$71$	136.766	−	91.3844i	0.228608	−	0.152751i	−0.435991	−	0.899951i	$-0.643602\pi$
$71$	136.766	−	91.3844i	0.228608	−	0.152751i	0.664600	+	0.747200i	$0.268602\pi$
$72$	−18.8700	+	25.1869i	−0.0308868	+	0.0412264i
$73$	254.844	−	381.401i	0.408592	−	0.611501i	−0.568917	−	0.822395i	$-0.692637\pi$
$73$	254.844	−	381.401i	0.408592	−	0.611501i	0.977509	+	0.210894i	$0.0676374\pi$
$74$	767.166	−	112.531i	1.20515	−	0.176776i
$75$	−644.590	−	344.541i	−0.992412	−	0.530455i
$76$	995.633	+	201.394i	1.50272	+	0.303966i
$77$	857.517	−	84.4581i	1.26913	−	0.124999i
$78$	−320.331	+	352.284i	−0.465004	+	0.511388i
$79$	122.328	−	295.325i	0.174214	−	0.420590i	−0.812520	−	0.582933i	$-0.801905\pi$
$79$	122.328	−	295.325i	0.174214	−	0.420590i	0.986734	+	0.162343i	$0.0519050\pi$
$80$	671.679	−	807.732i	0.938701	−	1.12884i
$81$	−263.865	−	637.026i	−0.361955	−	0.873836i
$82$	1277.52	+	459.435i	1.72047	+	0.618733i
$83$	−103.048	−	84.5690i	−0.136277	−	0.111839i	0.563786	−	0.825921i	$-0.309344\pi$
$83$	−103.048	−	84.5690i	−0.136277	−	0.111839i	−0.700062	+	0.714082i	$0.746844\pi$
$84$	−597.854	+	593.999i	−0.776562	+	0.771555i
$85$	−791.137	+	239.989i	−1.00954	+	0.306240i
$86$	−1378.16	−	347.582i	−1.72804	−	0.435822i
$87$	428.643	−	85.2625i	0.528223	−	0.105070i
$88$	800.999	+	485.398i	0.970304	+	0.587995i
$89$	−161.679	+	812.817i	−0.192561	+	0.968072i	0.756743	+	0.653713i	$0.226790\pi$
$89$	−161.679	+	812.817i	−0.192561	+	0.968072i	−0.949304	+	0.314359i	$0.898210\pi$
$90$	−21.6556	−	60.8333i	−0.0253633	−	0.0712488i
$91$	535.311	−	439.318i	0.616657	−	0.506078i
$92$	569.456	−	464.266i	0.645325	−	0.526121i
$93$	−524.223	−	980.753i	−0.584510	−	1.09354i
$94$	−122.466	+	816.496i	−0.134376	+	0.895905i
$95$	−1473.75	+	1473.75i	−1.59162	+	1.59162i
$96$	−907.199	+	127.082i	−0.964486	+	0.135107i
$97$	516.852	+	516.852i	0.541015	+	0.541015i	0.923826	−	0.382812i	$-0.125044\pi$
$97$	516.852	+	516.852i	0.541015	+	0.541015i	−0.382812	+	0.923826i	$0.625044\pi$
$98$	205.518	−	151.908i	0.211841	−	0.156582i
$99$	50.7726	−	27.1385i	0.0515438	−	0.0275507i
$100$	331.828	+	1106.76i	0.331828	+	1.10676i
$101$	−452.955	−	551.928i	−0.446245	−	0.543751i	0.500500	−	0.865737i	$-0.333150\pi$
$101$	−452.955	−	551.928i	−0.446245	−	0.543751i	−0.946745	+	0.321986i	$0.895650\pi$
$102$	651.204	+	309.286i	0.632145	+	0.300234i
$103$	105.712	+	21.0275i	0.101128	+	0.0201155i	0.245395	−	0.969423i	$-0.421082\pi$
$103$	105.712	+	21.0275i	0.101128	+	0.0201155i	−0.144267	+	0.989539i	$0.546082\pi$
$104$	751.983	−	33.2863i	0.709019	−	0.0313845i
$105$	−337.348	−	1695.96i	−0.313541	−	1.57628i
$106$	45.0135	+	75.3766i	0.0412462	+	0.0690681i
$107$	−362.549	−	1195.16i	−0.327560	−	1.07982i	−0.953863	−	0.300241i	$-0.902933\pi$
$107$	−362.549	−	1195.16i	−0.327560	−	1.07982i	0.626304	−	0.779579i	$-0.284567\pi$
$108$	−443.283	+	1060.47i	−0.394953	+	0.944846i
$109$	100.507	−	122.469i	0.0883198	−	0.107618i	−0.726975	−	0.686663i	$-0.759075\pi$
$109$	100.507	−	122.469i	0.0883198	−	0.107618i	0.815295	+	0.579045i	$0.196575\pi$
$110$	−1738.52	+	818.820i	−1.50692	+	0.709740i
$111$	1281.68	−	530.890i	1.09596	−	0.453962i
$112$	1332.27	+	8.61834i	1.12400	+	0.00727104i
$113$	2037.18	+	843.827i	1.69594	+	0.702483i	0.999880	−	0.0154965i	$-0.00493288\pi$
$113$	2037.18	+	843.827i	1.69594	+	0.702483i	0.696064	+	0.717980i	$0.254933\pi$
$114$	1815.39	−	86.2417i	1.49146	−	0.0708533i
$115$	147.761	+	1500.24i	0.119816	+	1.21651i
$116$	−573.217	−	385.699i	−0.458809	−	0.308718i
$117$	21.8106	−	40.8047i	0.0172341	−	0.0322427i
$118$	1176.05	−	1580.37i	0.917491	−	1.23292i
$119$	−871.792	−	582.513i	−0.671572	−	0.448730i
$120$	811.848	−	1695.18i	0.617593	−	1.28957i
$121$	−212.395	−	317.871i	−0.159575	−	0.238821i
$122$	680.890	−	615.120i	0.505286	−	0.456478i
$123$	2417.32	+	238.085i	1.77205	+	0.174532i
$124$	−515.763	+	1680.65i	−0.373523	+	1.21716i
$125$	−305.192	−	92.5790i	−0.218378	−	0.0662441i
$126$	42.2153	−	70.1743i	0.0298479	−	0.0496161i
$127$	663.291			0.463445			0.231723	−	0.972782i	$-0.425564\pi$
$127$	663.291			0.463445			0.231723	+	0.972782i	$0.425564\pi$
$128$	1153.33	+	875.777i	0.796413	+	0.604754i
$129$	−2542.99			−1.73564
$130$	−796.133	+	1323.41i	−0.537119	+	0.892851i
$131$	1721.46	+	522.198i	1.14813	+	0.348280i	0.806313	−	0.591489i	$-0.201460\pi$
$131$	1721.46	+	522.198i	1.14813	+	0.348280i	0.341812	+	0.939768i	$0.388960\pi$
$132$	1601.99	+	491.623i	1.05633	+	0.324169i
$133$	−2630.53	−	259.085i	−1.71501	−	0.168913i
$134$	618.806	−	559.033i	0.398931	−	0.360396i
$135$	−1310.20	−	1960.85i	−0.835290	−	1.25010i
$136$	−378.733	−	1074.90i	−0.238794	−	0.677734i
$137$	2112.05	+	1411.23i	1.31711	+	0.880067i	0.997716	−	0.0675545i	$-0.0215196\pi$
$137$	2112.05	+	1411.23i	1.31711	+	0.880067i	0.319397	+	0.947621i	$0.396520\pi$
$138$	784.785	−	1054.59i	0.484097	−	0.650527i
$139$	247.279	−	462.626i	0.150892	−	0.282298i	−0.795107	−	0.606469i	$-0.792585\pi$
$139$	247.279	−	462.626i	0.150892	−	0.282298i	0.945999	+	0.324171i	$0.105085\pi$
$140$	−1526.05	+	2267.98i	−0.921249	+	1.36914i
$141$	144.790	+	1470.08i	0.0864790	+	0.878036i
$142$	−464.717	+	22.0768i	−0.274635	+	0.0130468i
$143$	−1272.13	−	526.932i	−0.743920	−	0.308142i
$144$	82.4576	−	33.5318i	0.0477185	−	0.0194050i
$145$	1309.67	−	542.484i	0.750085	−	0.310696i
$146$	−1173.75	+	552.821i	−0.665343	+	0.313368i
$147$	290.077	−	353.460i	0.162756	−	0.198319i
$148$	−2023.43	−	845.810i	−1.12382	−	0.469764i
$149$	293.951	+	969.028i	0.161620	+	0.532791i	0.999923	−	0.0124142i	$-0.00395167\pi$
$149$	293.951	+	969.028i	0.161620	+	0.532791i	−0.838303	+	0.545205i	$0.816452\pi$
$150$	1059.92	+	1774.88i	0.576950	+	0.966122i
$151$	−40.1455	−	201.825i	−0.0216357	−	0.108770i	0.968458	−	0.249175i	$-0.0801595\pi$
$151$	−40.1455	−	201.825i	−0.0216357	−	0.108770i	−0.990094	+	0.140405i	$0.955160\pi$
$152$	−2119.45	−	1939.77i	−1.13099	−	1.03510i
$153$	−68.7069	−	13.6667i	−0.0363047	−	0.00722146i
$154$	−2201.48	−	1045.58i	−1.15195	−	0.547113i
$155$	−2288.30	−	2788.31i	−1.18581	−	1.44492i
$156$	1290.01	−	386.769i	0.662075	−	0.198502i
$157$	−3133.76	+	1675.03i	−1.59300	+	0.851477i	−0.594111	+	0.804383i	$0.702496\pi$
$157$	−3133.76	+	1675.03i	−1.59300	+	0.851477i	−0.998890	+	0.0470944i	$0.985004\pi$
$158$	−727.072	+	537.413i	−0.366093	+	0.270597i
$159$	111.072	+	111.072i	0.0553998	+	0.0553998i
$160$	−2805.62	+	978.350i	−1.38627	+	0.483408i
$161$	−1351.90	+	1351.90i	−0.661766	+	0.661766i
$162$	−289.278	+	1928.66i	−0.140295	+	0.935370i
$163$	1514.49	+	2833.41i	0.727755	+	1.36153i	0.924539	+	0.381087i	$0.124450\pi$
$163$	1514.49	+	2833.41i	0.727755	+	1.36153i	−0.196784	+	0.980447i	$0.563050\pi$
$164$	−2426.41	−	2976.17i	−1.15531	−	1.41707i
$165$	−2657.80	+	2181.20i	−1.25400	+	1.02913i
$166$	126.450	+	355.213i	0.0591229	+	0.166084i
$167$	−308.204	+	1549.45i	−0.142812	+	0.717963i	0.841322	+	0.540534i	$0.181778\pi$
$167$	−308.204	+	1549.45i	−0.142812	+	0.717963i	−0.984134	+	0.177429i	$0.943222\pi$
$168$	2315.06	−	567.971i	1.06316	−	0.260833i
$169$	1069.43	−	212.724i	0.486770	−	0.0968246i
$170$	2267.36	+	571.843i	1.02293	+	0.257990i
$171$	−168.999	+	51.2653i	−0.0755771	+	0.0229261i
$172$	2833.43	+	2851.82i	1.25609	+	1.26424i
$173$	−681.497	−	559.290i	−0.299499	−	0.245792i	0.472626	−	0.881263i	$-0.343306\pi$
$173$	−681.497	−	559.290i	−0.299499	−	0.245792i	−0.772125	+	0.635471i	$0.780806\pi$
$174$	−1163.20	−	418.324i	−0.506795	−	0.182259i
$175$	−1150.58	−	2777.76i	−0.497006	−	1.19988i
$176$	−1233.63	−	2344.32i	−0.528344	−	1.00403i
$177$	1348.79	−	3256.27i	0.572776	−	1.38280i
$178$	1576.96	−	1734.27i	0.664036	−	0.730274i
$179$	1269.01	−	124.987i	0.529891	−	0.0521897i	0.170466	−	0.985364i	$-0.445473\pi$
$179$	1269.01	−	124.987i	0.529891	−	0.0521897i	0.359425	+	0.933174i	$0.382973\pi$
$180$	−36.2104	+	179.014i	−0.0149943	+	0.0741274i
$181$	−2494.69	−	1333.44i	−1.02447	−	0.547591i	−0.128502	−	0.991709i	$-0.541017\pi$
$181$	−2494.69	−	1333.44i	−1.02447	−	0.547591i	−0.895968	+	0.444118i	$0.853517\pi$
$182$	−1937.95	+	284.266i	−0.789289	+	0.115776i
$183$	912.102	−	1365.06i	0.368440	−	0.551410i
$184$	−2057.08	+	294.947i	−0.824186	+	0.118173i
$185$	3741.42	−	2499.94i	1.48689	−	0.993508i
$186$	−159.417	+	3141.35i	−0.0628444	+	1.23836i
$187$	−204.344	+	2074.74i	−0.0799099	+	0.811338i
$188$	1487.29	−	1800.36i	0.576976	−	0.698428i
$189$	868.206	−	2862.09i	0.334141	−	1.10152i
$190$	5720.66	−	1423.12i	2.18432	−	0.543390i
$191$		−	1044.29i		−	0.395615i	−0.980241	−	0.197808i	$-0.936618\pi$
$191$		−	1044.29i		−	0.395615i	0.980241	−	0.197808i	$-0.0633821\pi$
$192$	2384.04	+	1014.71i	0.896110	+	0.381409i
$193$			1072.56i			0.400024i	0.979793	+	0.200012i	$0.0640981\pi$
$193$			1072.56i			0.400024i	−0.979793	+	0.200012i	$0.935902\pi$
$194$	−499.096	−	2006.26i	−0.184706	−	0.742480i
$195$	−802.126	+	2644.25i	−0.294571	+	0.971072i
$196$	−719.593	+	68.5244i	−0.262242	+	0.0249725i
$197$	155.654	−	1580.38i	0.0562938	−	0.571560i	−0.925122	−	0.379669i	$-0.876038\pi$
$197$	155.654	−	1580.38i	0.0562938	−	0.571560i	0.981416	−	0.191891i	$-0.0614621\pi$
$198$	−162.624	−	8.25288i	−0.0583698	−	0.00296215i
$199$	−1688.65	+	1128.32i	−0.601534	+	0.401932i	−0.818716	−	0.574199i	$-0.805314\pi$
$199$	−1688.65	+	1128.32i	−0.601534	+	0.401932i	0.217182	+	0.976131i	$0.430314\pi$
$200$	809.447	−	3166.24i	0.286183	−	1.11944i
$201$	828.936	−	1240.59i	0.290889	−	0.435346i
$202$	293.090	+	1998.11i	0.102088	+	0.695973i
$203$	1585.54	+	847.488i	0.548192	+	0.293015i
$204$	−1127.36	−	1699.08i	−0.386915	−	0.583133i
$205$	7840.79	−	772.250i	2.67134	−	0.263104i
$206$	−225.553	−	205.095i	−0.0762865	−	0.0693671i
$207$	−48.8830	+	118.014i	−0.0164135	+	0.0396258i
$208$	−1871.09	−	1015.73i	−0.623734	−	0.338599i
$209$	2011.28	+	4855.67i	0.665662	+	1.60705i
$210$	−1655.14	+	4602.32i	−0.543882	+	1.51233i
$211$	−930.034	−	763.260i	−0.303442	−	0.249028i	0.470333	−	0.882489i	$-0.344134\pi$
$211$	−930.034	−	763.260i	−0.303442	−	0.249028i	−0.773775	+	0.633461i	$0.781634\pi$
$212$	0.803165	−	248.319i	0.000260196	−	0.0804462i
$213$	−796.555	+	241.632i	−0.256240	+	0.0777294i
$214$	−863.878	+	3425.28i	−0.275951	+	1.09415i
$215$	−8089.90	+	1609.18i	−2.56617	+	0.510443i
$216$	2620.56	−	1923.90i	0.825492	−	0.606041i
$217$	892.463	−	4486.72i	0.279191	−	1.40359i
$218$	−422.158	+	150.281i	−0.131157	+	0.0466895i
$219$	−1794.40	+	1472.62i	−0.553671	+	0.454386i
$220$	5407.45	+	550.253i	1.65714	+	0.168627i
$221$	789.821	+	1477.65i	0.240403	+	0.449763i
$222$	−3880.42	−	582.021i	−1.17314	−	0.175958i
$223$	−2097.65	+	2097.65i	−0.629905	+	0.629905i	−0.948044	−	0.318139i	$-0.896942\pi$
$223$	−2097.65	+	2097.65i	−0.629905	+	0.629905i	0.318139	+	0.948044i	$0.396942\pi$
$224$	−3216.42	−	1963.37i	−0.959403	−	0.585640i
$225$	−142.044	−	142.044i	−0.0420872	−	0.0420872i
$226$	−3707.13	−	5015.41i	−1.09113	−	1.47620i
$227$	−4837.56	+	2585.73i	−1.41445	+	0.756039i	−0.988856	−	0.148875i	$-0.952435\pi$
$227$	−4837.56	+	2585.73i	−1.41445	+	0.756039i	−0.425594	+	0.904914i	$0.639935\pi$
$228$	−4525.65	−	2437.86i	−1.31455	−	0.708120i
$229$	3847.44	+	4688.12i	1.11024	+	1.35284i	0.929293	+	0.369344i	$0.120418\pi$
$229$	3847.44	+	4688.12i	1.11024	+	1.35284i	0.180951	+	0.983492i	$0.442082\pi$
$230$	1829.27	−	3851.53i	0.524428	−	1.10419i
$231$	−4276.72	−	850.692i	−1.21813	−	0.242301i
$232$	826.930	+	1770.57i	0.234011	+	0.501050i
$233$	−673.696	−	3386.90i	−0.189422	−	0.952288i	−0.952165	−	0.305586i	$-0.901148\pi$
$233$	−673.696	−	3386.90i	−0.189422	−	0.952288i	0.762743	−	0.646702i	$-0.223852\pi$
$234$	−112.356	+	67.0968i	−0.0313886	+	0.0187447i
$235$	1390.87	+	4585.09i	0.386087	+	1.27276i
$236$	−5154.56	+	2115.58i	−1.42175	+	0.583529i
$237$	−1026.22	+	1250.45i	−0.281267	+	0.342724i
$238$	1263.62	+	2682.91i	0.344152	+	0.730703i
$239$	4899.83	−	2029.57i	1.32612	−	0.549298i	0.396576	−	0.918002i	$-0.370198\pi$
$239$	4899.83	−	2029.57i	1.32612	−	0.549298i	0.929547	+	0.368704i	$0.120198\pi$
$240$	−4439.26	+	2924.86i	−1.19397	+	0.786662i
$241$	6094.68	+	2524.50i	1.62902	+	0.674761i	0.995121	−	0.0986583i	$-0.0314551\pi$
$241$	6094.68	+	2524.50i	1.62902	+	0.674761i	0.633895	+	0.773419i	$0.281455\pi$
$242$	51.3107	+	1080.09i	0.0136296	+	0.286904i
$243$	−38.2138	−	387.991i	−0.0100881	−	0.102427i
$244$	−2547.11	+	498.093i	−0.668287	+	0.130685i
$245$	699.144	−	1308.01i	0.182313	−	0.341083i
$246$	−5511.65	−	4101.55i	−1.42850	−	1.06303i
$247$	3512.06	+	2346.68i	0.904724	+	0.604517i
$248$	3700.47	−	3321.35i	0.947501	−	0.850428i
$249$	374.791	+	560.915i	0.0953872	+	0.142757i
$250$	604.702	+	669.358i	0.152979	+	0.169336i
$251$	−353.740	−	34.8403i	−0.0889556	−	0.00876136i	0.0534414	−	0.998571i	$-0.482981\pi$
$251$	−353.740	−	34.8403i	−0.0889556	−	0.00876136i	−0.142397	+	0.989810i	$0.545481\pi$
$252$	−204.632	+	108.528i	−0.0511531	+	0.0271295i
$253$	3637.79	+	1103.51i	0.903975	+	0.274218i
$254$	−1607.60	−	967.093i	−0.397124	−	0.238901i
$255$	4183.74			1.02743
$256$	−1518.38	−	3804.17i	−0.370699	−	0.928753i
$257$	3704.51			0.899148			0.449574	−	0.893243i	$-0.351576\pi$
$257$	3704.51			0.899148			0.449574	+	0.893243i	$0.351576\pi$
$258$	6163.36	+	3707.73i	1.48726	+	0.894703i
$259$	5461.03	+	1656.59i	1.31016	+	0.397433i
$260$	3859.12	−	2046.72i	0.920510	−	0.488202i
$261$	119.539	+	11.7736i	0.0283498	+	0.00279221i
$262$	−3410.86	−	3775.56i	−0.804289	−	0.890286i
$263$	−210.473	−	314.994i	−0.0493471	−	0.0738532i	0.805976	−	0.591949i	$-0.201641\pi$
$263$	−210.473	−	314.994i	−0.0493471	−	0.0738532i	−0.855323	+	0.518095i	$0.826641\pi$
$264$	−3165.90	−	3527.27i	−0.738060	−	0.822306i
$265$	423.634	+	283.063i	0.0982023	+	0.0656167i
$266$	5997.78	+	4463.31i	1.38251	+	1.02881i
$267$	1976.98	−	3698.67i	0.453144	−	0.847772i
$268$	−2314.87	+	452.677i	−0.527623	+	0.103178i
$269$	765.075	+	7767.94i	0.173411	+	1.76067i	0.550823	+	0.834622i	$0.314314\pi$
$269$	765.075	+	7767.94i	0.173411	+	1.76067i	−0.377413	+	0.926045i	$0.623186\pi$
$270$	316.520	+	6662.76i	0.0713437	+	1.50179i
$271$	590.820	+	244.726i	0.132435	+	0.0548562i	0.447917	−	0.894075i	$-0.352166\pi$
$271$	590.820	+	244.726i	0.132435	+	0.0548562i	−0.315482	+	0.948932i	$0.602166\pi$
$272$	−649.306	+	3157.40i	−0.144743	+	0.703844i
$273$	−3237.68	+	1341.09i	−0.717777	+	0.297313i
$274$	−3061.30	−	6499.76i	−0.674964	−	1.43308i
$275$	−3792.55	+	4621.24i	−0.831635	+	1.01335i
$276$	−3439.68	+	1411.74i	−0.750160	+	0.307888i
$277$	−1157.93	−	3817.17i	−0.251166	−	0.827984i	−0.988338	−	0.152278i	$-0.951339\pi$
$277$	−1157.93	−	3817.17i	−0.251166	−	0.827984i	0.737171	−	0.675706i	$-0.236161\pi$
$278$	−1273.84	+	760.714i	−0.274820	+	0.164117i
$279$	−59.6280	−	299.770i	−0.0127951	−	0.0643254i
$280$	7005.41	−	3271.82i	1.49519	−	0.698316i
$281$	−5424.83	−	1079.07i	−1.15167	−	0.229081i	−0.417906	−	0.908490i	$-0.637236\pi$
$281$	−5424.83	−	1079.07i	−1.15167	−	0.229081i	−0.733759	+	0.679410i	$0.762236\pi$
$282$	1792.49	−	3774.09i	0.378515	−	0.796965i
$283$	−3755.50	−	4576.09i	−0.788839	−	0.961203i	0.211029	−	0.977480i	$-0.432319\pi$
$283$	−3755.50	−	4576.09i	−0.788839	−	0.961203i	−0.999868	+	0.0162769i	$0.994819\pi$
$284$	1158.51	+	624.062i	0.242059	+	0.130392i
$285$	9301.80	−	4971.92i	1.93330	−	1.03337i
$286$	2314.93	+	3131.90i	0.478618	+	0.647528i
$287$	7065.46	+	7065.46i	1.45317	+	1.45317i
$288$	−248.740	−	38.9552i	−0.0508929	−	0.00797034i
$289$	−1680.22	+	1680.22i	−0.341995	+	0.341995i
$290$	−3965.17	−	594.732i	−0.802905	−	0.120427i
$291$	−1743.68	−	3262.19i	−0.351258	−	0.657157i
$292$	3650.80	+	371.499i	0.731668	+	0.0744532i
$293$	5025.83	−	4124.60i	1.00209	−	0.822394i	0.0179593	−	0.999839i	$-0.494283\pi$
$293$	5025.83	−	4124.60i	1.00209	−	0.822394i	0.984131	+	0.177445i	$0.0567831\pi$
$294$	−1218.40	+	433.730i	−0.241696	+	0.0860397i
$295$	2230.31	−	11212.5i	0.440182	−	2.21295i
$296$	3670.91	+	5000.17i	0.720836	+	0.981855i
$297$	−5832.66	+	1160.19i	−1.13955	+	0.226670i
$298$	700.425	−	2777.19i	0.136156	−	0.539860i
$299$	2923.61	−	886.866i	0.565473	−	0.171534i
$300$	18.9120	−	5847.12i	0.00363962	−	1.12528i
$301$	−8086.38	−	6636.32i	−1.54848	−	1.27080i
$302$	−196.966	+	547.690i	−0.0375302	+	0.104358i
$303$	1382.72	+	3338.18i	0.262162	+	0.632915i
$304$	2308.61	+	7791.56i	0.435552	+	1.46999i
$305$	2037.84	−	4919.77i	0.382578	−	0.923624i
$306$	146.596	+	133.300i	0.0273868	+	0.0249027i
$307$	−7976.10	+	785.577i	−1.48280	+	0.146043i	−0.806786	−	0.590844i	$-0.798795\pi$
$307$	−7976.10	+	785.577i	−1.48280	+	0.146043i	−0.676016	+	0.736887i	$0.736295\pi$
$308$	3811.17	+	5743.95i	0.705070	+	1.06264i
$309$	−481.037	−	257.120i	−0.0885607	−	0.0473367i
$310$	1480.67	+	10094.3i	0.271279	+	1.84942i
$311$	−4568.95	+	6837.92i	−0.833060	+	1.24676i	0.133686	+	0.991024i	$0.457319\pi$
$311$	−4568.95	+	6837.92i	−0.833060	+	1.24676i	−0.966746	+	0.255738i	$0.917681\pi$
$312$	−3690.48	−	943.469i	−0.669655	−	0.171197i
$313$	−3682.12	+	2460.31i	−0.664939	+	0.444298i	−0.841692	−	0.539957i	$-0.818440\pi$
$313$	−3682.12	+	2460.31i	−0.664939	+	0.444298i	0.176754	+	0.984255i	$0.443440\pi$
$314$	10037.4	+	509.380i	1.80396	+	0.0915477i
$315$	46.5832	−	472.968i	0.00833228	−	0.0845991i
$316$	2545.74	−	242.422i	0.453193	−	0.0431561i
$317$	−536.028	+	1767.05i	−0.0949727	+	0.313083i	−0.991536	−	0.129833i	$-0.958556\pi$
$317$	−536.028	+	1767.05i	−0.0949727	+	0.313083i	0.896563	+	0.442916i	$0.146056\pi$
$318$	−107.256	−	431.147i	−0.0189139	−	0.0760299i
$319$		−	3574.72i		−	0.627416i
$320$	8226.35	+	1719.47i	1.43708	+	0.300378i
$321$			6320.33i			1.09896i
$322$	5247.64	−	1305.45i	0.908198	−	0.225931i
$323$	1856.46	−	6119.92i	0.319802	−	1.05425i
$324$	3513.15	−	4252.66i	0.602392	−	0.729194i
$325$	−470.930	+	4781.44i	−0.0803770	+	0.816081i
$326$	460.560	−	9075.42i	0.0782456	−	1.54184i
$327$	−666.627	+	445.426i	−0.112736	+	0.0753276i
$328$	1541.49	+	10751.0i	0.259496	+	1.80983i
$329$	−3375.99	+	5052.53i	−0.565728	+	0.846671i
$330$	9621.87	−	1411.37i	1.60505	−	0.235434i
$331$	1295.39	+	692.401i	0.215109	+	0.114978i	0.575433	−	0.817849i	$-0.304834\pi$
$331$	1295.39	+	692.401i	0.215109	+	0.114978i	−0.360324	+	0.932827i	$0.617334\pi$
$332$	211.437	−	1045.29i	0.0349522	−	0.172794i
$333$	379.449	−	37.3725i	0.0624435	−	0.00615015i
$334$	3006.12	−	3305.98i	0.492477	−	0.541602i
$335$	1852.03	−	4471.19i	0.302051	−	0.729215i
$336$	−6439.06	−	1998.84i	−1.04548	−	0.324541i
$337$	−1279.69	−	3089.44i	−0.206851	−	0.499384i	0.786073	−	0.618134i	$-0.212111\pi$
$337$	−1279.69	−	3089.44i	−0.206851	−	0.499384i	−0.992924	+	0.118750i	$0.962111\pi$
$338$	−2902.11	−	1043.69i	−0.467024	−	0.167956i
$339$	−8625.75	−	7078.97i	−1.38197	−	1.13415i
$340$	−4661.57	−	4691.83i	−0.743557	−	0.748382i
$341$	−8704.30	+	2640.42i	−1.38230	+	0.419316i
$342$	484.344	+	122.155i	0.0765799	+	0.0193139i
$343$	−5158.28	+	1026.05i	−0.812015	+	0.161520i
$344$	−2709.27	−	11043.1i	−0.424635	−	1.73082i
$345$	1488.30	−	7482.21i	0.232254	−	1.16762i
$346$	836.265	+	2349.17i	0.129936	+	0.365007i
$347$	7523.37	−	6174.27i	1.16391	−	0.955193i	0.164393	−	0.986395i	$-0.447433\pi$
$347$	7523.37	−	6174.27i	1.16391	−	0.955193i	0.999513	+	0.0312016i	$0.00993338\pi$
$348$	2209.29	+	2709.86i	0.340318	+	0.417424i
$349$	−5417.30	−	10135.0i	−0.830892	−	1.55449i	−0.832191	−	0.554490i	$-0.812913\pi$
$349$	−5417.30	−	10135.0i	−0.830892	−	1.55449i	0.00129891	−	0.999999i	$-0.499587\pi$
$350$	−1261.40	+	8409.94i	−0.192642	+	1.28437i
$351$	−3379.55	+	3379.55i	−0.513924	+	0.513924i
$352$	−428.153	+	7480.52i	−0.0648314	+	1.13271i
$353$	5471.75	+	5471.75i	0.825020	+	0.825020i	0.986823	−	0.161803i	$-0.0517310\pi$
$353$	5471.75	+	5471.75i	0.825020	+	0.825020i	−0.161803	+	0.986823i	$0.551731\pi$
$354$	−8016.74	+	5925.55i	−1.20363	+	0.889659i
$355$	−2381.14	+	1272.75i	−0.355994	+	0.190283i
$356$	−6350.64	+	1904.04i	−0.945458	+	0.283465i
$357$	3366.06	+	4101.56i	0.499023	+	0.608061i
$358$	−3257.90	−	1547.33i	−0.480965	−	0.228432i
$359$	5614.07	+	1116.71i	0.825346	+	0.164171i	0.589653	−	0.807656i	$-0.299264\pi$
$359$	5614.07	+	1116.71i	0.825346	+	0.164171i	0.235692	+	0.971828i	$0.424264\pi$
$360$	348.769	−	381.075i	0.0510604	−	0.0557901i
$361$	−1807.23	−	9085.57i	−0.263483	−	1.32462i
$362$	4102.12	+	6869.14i	0.595587	+	0.997332i
$363$	561.599	+	1851.34i	0.0812020	+	0.267687i
$364$	5111.42	+	2136.61i	0.736020	+	0.307662i
$365$	−4776.57	+	5820.27i	−0.684979	+	0.834649i
$366$	−4200.92	+	1978.58i	−0.599961	+	0.282574i
$367$	−287.936	+	119.267i	−0.0409541	+	0.0169637i	−0.403066	−	0.915171i	$-0.632056\pi$
$367$	−287.936	+	119.267i	−0.0409541	+	0.0169637i	0.362112	+	0.932134i	$0.382056\pi$
$368$	5415.73	+	2284.42i	0.767158	+	0.323597i
$369$	616.781	+	255.479i	0.0870145	+	0.0360426i
$370$	−12712.9	+	603.938i	−1.78625	+	0.0848575i
$371$	63.3353	+	643.054i	0.00886309	+	0.0899884i
$372$	4966.54	−	7381.15i	0.692212	−	1.02875i
$373$	−820.753	+	1535.52i	−0.113933	+	0.213153i	−0.932424	−	0.361365i	$-0.882311\pi$
$373$	−820.753	+	1535.52i	−0.113933	+	0.213153i	0.818491	+	0.574519i	$0.194811\pi$
$374$	3520.29	−	4730.55i	0.486711	−	0.654040i
$375$	1341.94	+	896.654i	0.184793	+	0.123475i
$376$	−6229.65	+	2194.97i	−0.854441	+	0.301056i
$377$	−1596.11	−	2388.74i	−0.218047	−	0.326330i
$378$	−6277.24	+	5670.89i	−0.854143	+	0.771638i
$379$	1211.03	+	119.276i	0.164132	+	0.0161656i	0.179750	−	0.983712i	$-0.442471\pi$
$379$	1211.03	+	119.276i	0.164132	+	0.0161656i	−0.0156171	+	0.999878i	$0.504971\pi$
$380$	−15939.9	−	4891.68i	−2.15184	−	0.660362i
$381$	−3212.08	−	974.373i	−0.431915	−	0.131020i
$382$	−1522.61	+	2531.02i	−0.203935	+	0.339001i
$383$	−3468.04			−0.462686			−0.231343	−	0.972872i	$-0.574312\pi$
$383$	−3468.04			−0.462686			−0.231343	+	0.972872i	$0.574312\pi$
$384$	−4298.64	−	5935.31i	−0.571261	−	0.788763i
$385$	−14143.7			−1.87228
$386$	1563.82	−	2599.53i	0.206208	−	0.342779i
$387$	−668.827	−	202.887i	−0.0878512	−	0.0266494i
$388$	−1715.53	+	5590.21i	−0.224467	+	0.731443i
$389$	9534.36	+	939.053i	1.24270	+	0.122396i	0.697916	−	0.716179i	$-0.254111\pi$
$389$	9534.36	+	939.053i	1.24270	+	0.122396i	0.544786	+	0.838575i	$0.316611\pi$
$390$	5799.47	−	5239.28i	0.752994	−	0.680259i
$391$	−2569.91	−	3846.15i	−0.332394	−	0.497463i
$392$	1843.96	+	883.103i	0.237587	+	0.113784i
$393$	−7569.29	−	5057.64i	−0.971553	−	0.649171i
$394$	−2681.48	+	3603.37i	−0.342871	+	0.460749i
$395$	−2473.40	+	4627.40i	−0.315064	+	0.589442i
$396$	382.115	+	257.112i	0.0484899	+	0.0326272i
$397$	−1033.63	−	10494.7i	−0.130672	−	1.32673i	−0.807184	−	0.590299i	$-0.799010\pi$
$397$	−1033.63	−	10494.7i	−0.130672	−	1.32673i	0.676513	−	0.736431i	$-0.263490\pi$
$398$	5737.84	−	272.581i	0.722643	−	0.0343298i
$399$	12358.1	+	5118.90i	1.55058	+	0.642270i
$400$	−6578.29	+	6493.72i	−0.822286	+	0.811715i
$401$	−9762.39	+	4043.71i	−1.21574	+	0.503575i	−0.896052	−	0.443949i	$-0.853577\pi$
$401$	−9762.39	+	4043.71i	−1.21574	+	0.503575i	−0.319685	+	0.947524i	$0.603577\pi$
$402$	−3817.88	+	1798.17i	−0.473678	+	0.223096i
$403$	−4637.55	+	5650.88i	−0.573233	+	0.698487i
$404$	2202.94	−	5270.08i	0.271288	−	0.649001i
$405$	3285.40	+	10830.5i	0.403094	+	1.32882i
$406$	−2607.16	−	4365.78i	−0.318698	−	0.533670i
$407$	−2213.70	−	11129.0i	−0.269605	−	1.35540i
$408$	255.040	+	5761.71i	0.0309470	+	0.699135i
$409$	5063.21	+	1007.14i	0.612127	+	0.121760i	0.491411	−	0.870928i	$-0.336481\pi$
$409$	5063.21	+	1007.14i	0.612127	+	0.121760i	0.120715	+	0.992687i	$0.461481\pi$
$410$	−20129.4	−	9560.37i	−2.42469	−	1.15159i
$411$	−8154.80	−	9936.66i	−0.978703	−	1.19255i
$412$	247.633	+	825.943i	0.0296116	+	0.0987652i
$413$	12786.7	−	6834.65i	1.52347	−	0.814313i
$414$	290.543	−	214.754i	0.0344914	−	0.0254942i
$415$	1547.25	+	1547.25i	0.183016	+	0.183016i
$416$	3053.94	+	5189.90i	0.359932	+	0.611672i
$417$	−1877.08	+	1877.08i	−0.220434	+	0.220434i
$418$	2205.00	−	14701.0i	0.258014	−	1.72022i
$419$	7218.27	+	13504.4i	0.841612	+	1.57455i	0.818281	+	0.574818i	$0.194927\pi$
$419$	7218.27	+	13504.4i	0.841612	+	1.57455i	0.0233307	+	0.999728i	$0.492573\pi$
$420$	10721.8	−	8741.26i	1.24564	−	1.01555i
$421$	−9839.35	+	8074.95i	−1.13905	+	0.934795i	−0.998471	−	0.0552739i	$-0.982397\pi$
$421$	−9839.35	+	8074.95i	−1.13905	+	0.934795i	−0.140580	+	0.990069i	$0.544897\pi$
$422$	1141.24	+	3205.90i	0.131647	+	0.369812i
$423$	−79.2060	+	398.195i	−0.00910432	+	0.0457705i
$424$	−364.001	+	600.671i	−0.0416921	+	0.0687999i
$425$	7134.68	−	1419.18i	0.814312	−	0.161977i
$426$	2282.89	+	575.759i	0.259639	+	0.0654827i
$427$	6462.70	−	1960.44i	0.732441	−	0.222183i
$428$	7087.90	−	7042.19i	0.800482	−	0.795321i
$429$	5386.39	+	4420.50i	0.606194	+	0.497491i
$430$	21953.5	+	7895.15i	2.46207	+	0.885437i
$431$	1797.40	+	4339.30i	0.200876	+	0.484957i	0.991930	−	0.126789i	$-0.0404672\pi$
$431$	1797.40	+	4339.30i	0.200876	+	0.484957i	−0.791054	+	0.611747i	$0.790467\pi$
$432$	−9156.45	+	842.063i	−1.01977	+	0.0937819i
$433$	877.429	−	2118.30i	0.0973823	−	0.235102i	−0.867680	−	0.497124i	$-0.834389\pi$
$433$	877.429	−	2118.30i	0.0973823	−	0.235102i	0.965062	+	0.262022i	$0.0843894\pi$
$434$	−8704.77	+	9573.08i	−0.962771	+	1.05881i
$435$	−7139.18	+	703.148i	−0.786891	+	0.0775020i
$436$	1242.29	+	251.286i	0.136456	+	0.0276018i
$437$	−10284.5	−	5497.17i	−1.12580	−	0.601752i
$438$	6496.14	−	952.877i	0.708670	−	0.103950i
$439$	435.086	−	651.152i	0.0473019	−	0.0707923i	−0.807065	−	0.590463i	$-0.798945\pi$
$439$	435.086	−	651.152i	0.0473019	−	0.0707923i	0.854367	+	0.519670i	$0.173945\pi$
$440$	−12303.6	−	9217.82i	−1.33307	−	0.998733i
$441$	104.493	−	69.8198i	0.0112831	−	0.00753912i
$442$	240.186	−	4732.91i	0.0258473	−	0.509325i
$443$	562.212	−	5708.23i	0.0602968	−	0.612204i	−0.916791	−	0.399367i	$-0.869230\pi$
$443$	562.212	−	5708.23i	0.0602968	−	0.612204i	0.977088	−	0.212837i	$-0.0682702\pi$
$444$	8556.25	+	7068.37i	0.914553	+	0.755518i
$445$	3948.80	−	13017.5i	0.420654	−	1.38671i
$446$	8142.42	−	2025.58i	0.864473	−	0.215054i
$447$		−	5124.47i		−	0.542235i
$448$	4932.90	+	9448.19i	0.520217	+	0.996395i
$449$			7324.15i			0.769818i	0.922955	+	0.384909i	$0.125767\pi$
$449$			7324.15i			0.769818i	−0.922955	+	0.384909i	$0.874233\pi$
$450$	137.164	+	551.372i	0.0143689	+	0.0577599i
$451$	5767.32	−	19012.3i	0.602156	−	1.98504i
$452$	1672.25	+	17560.8i	0.174018	+	1.82741i
$453$	−102.071	+	1036.34i	−0.0105865	+	0.107487i
$454$	15494.7	+	786.326i	1.60177	+	0.0812866i
$455$	−9451.26	+	6315.13i	−0.973806	+	0.650677i
$456$	7414.21	+	12507.1i	0.761408	+	1.28442i
$457$	−4890.43	+	7319.05i	−0.500580	+	0.749170i	−0.992602	−	0.121412i	$-0.961258\pi$
$457$	−4890.43	+	7319.05i	−0.500580	+	0.749170i	0.492023	+	0.870582i	$0.336258\pi$
$458$	−2489.53	−	16972.1i	−0.253991	−	1.73156i
$459$	6381.90	+	3411.19i	0.648979	+	0.346887i
$460$	−10049.2	+	6667.73i	−1.01858	+	0.675835i
$461$	−6794.74	+	669.223i	−0.686469	+	0.0676113i	−0.435238	−	0.900316i	$-0.643336\pi$
$461$	−6794.74	+	669.223i	−0.686469	+	0.0676113i	−0.251232	+	0.967927i	$0.580836\pi$
$462$	9125.02	+	8297.35i	0.918905	+	0.835558i
$463$	1842.26	−	4447.62i	0.184918	−	0.446432i	−0.804050	−	0.594562i	$-0.797325\pi$
$463$	1842.26	−	4447.62i	0.184918	−	0.446432i	0.988968	+	0.148130i	$0.0473254\pi$
$464$	577.330	−	5496.96i	0.0577627	−	0.549978i
$465$	6985.41	+	16864.3i	0.696647	+	1.68185i
$466$	−3305.36	+	9190.98i	−0.328579	+	0.913657i
$467$	12282.4	+	10079.9i	1.21705	+	0.998806i	0.999742	+	0.0227022i	$0.00722697\pi$
$467$	12282.4	+	10079.9i	1.21705	+	0.998806i	0.217306	+	0.976104i	$0.430273\pi$
$468$	370.142	+	1.19719i	0.0365594	+	0.000118248i
$469$	5873.43	−	1781.69i	0.578273	−	0.175417i
$470$	3314.15	−	13140.6i	0.325256	−	1.28964i
$471$	17636.3	−	3508.08i	1.72535	−	0.343193i
$472$	15577.5	+	2388.00i	1.51910	+	0.232874i
$473$	−4057.88	+	20400.3i	−0.394464	+	1.98310i
$474$	4310.41	−	1534.43i	0.417687	−	0.148689i
$475$	14176.2	−	11634.1i	1.36936	−	1.12381i
$476$	849.159	−	8344.87i	0.0817671	−	0.803543i
$477$	20.3512	+	38.0745i	0.00195350	+	0.00365474i
$478$	−14834.7	−	2225.05i	−1.41951	−	0.212911i
$479$	−7800.93	+	7800.93i	−0.744120	+	0.744120i	−0.973368	−	0.229248i	$-0.926373\pi$
$479$	−7800.93	+	7800.93i	−0.744120	+	0.744120i	0.229248	+	0.973368i	$0.426373\pi$
$480$	15023.8	−	616.342i	1.42862	−	0.0586084i
$481$	−6448.38	−	6448.38i	−0.611270	−	0.611270i
$482$	−11090.7	−	15004.7i	−1.04807	−	1.41794i
$483$	8532.68	−	4560.81i	0.803831	−	0.429657i
$484$	1450.44	−	2692.59i	0.136217	−	0.252873i
$485$	−7611.37	−	9274.48i	−0.712607	−	0.868314i
$486$	−473.083	+	996.078i	−0.0441553	+	0.0929692i
$487$	3505.25	+	697.237i	0.326156	+	0.0648764i	0.355452	−	0.934694i	$-0.384327\pi$
$487$	3505.25	+	697.237i	0.326156	+	0.0648764i	−0.0292968	+	0.999571i	$0.509327\pi$
$488$	6899.59	+	2506.54i	0.640020	+	0.232511i
$489$	−3171.85	−	15946.0i	−0.293326	−	1.47465i
$490$	−3601.60	+	2150.80i	−0.332048	+	0.198293i
$491$	−148.266	−	488.766i	−0.0136276	−	0.0449241i	0.949863	−	0.312667i	$-0.101222\pi$
$491$	−148.266	−	488.766i	−0.0136276	−	0.0449241i	−0.963490	+	0.267743i	$0.913722\pi$
$492$	7378.25	+	17976.9i	0.676092	+	1.64728i
$493$	−2759.48	+	3362.44i	−0.252091	+	0.307173i
$494$	−5090.54	−	10808.2i	−0.463632	−	0.984384i
$495$	−873.046	+	361.628i	−0.0792738	+	0.0328363i
$496$	−13811.3	+	2654.48i	−1.25030	+	0.240302i
$497$	−3163.52	−	1310.37i	−0.285520	−	0.118266i
$498$	−90.5426	−	1905.92i	−0.00814721	−	0.171499i
$499$	253.872	+	2577.61i	0.0227753	+	0.231242i	0.999833	+	0.0182674i	$0.00581502\pi$
$499$	253.872	+	2577.61i	0.0227753	+	0.231242i	−0.977058	+	0.212974i	$0.931685\pi$
$500$	−489.657	−	2503.97i	−0.0437963	−	0.223962i
$501$	3768.66	−	7050.67i	0.336071	−	0.628744i
$502$	806.550	+	600.203i	0.0717093	+	0.0533632i
$503$	3744.59	+	2502.05i	0.331934	+	0.221791i	0.710357	−	0.703842i	$-0.248533\pi$
$503$	3744.59	+	2502.05i	0.331934	+	0.221791i	−0.378423	+	0.925633i	$0.623533\pi$
$504$	654.196	+	35.3209i	0.0578179	+	0.00312167i
$505$	6511.16	+	9744.64i	0.573748	+	0.858675i
$506$	−7207.84	−	7978.52i	−0.633256	−	0.700966i
$507$	−5491.38	−	540.854i	−0.481027	−	0.0473770i
$508$	2486.23	+	4687.83i	0.217143	+	0.409426i
$509$	8093.58	+	2455.16i	0.704797	+	0.213798i	0.622283	−	0.782792i	$-0.286205\pi$
$509$	8093.58	+	2455.16i	0.704797	+	0.213798i	0.0825136	+	0.996590i	$0.473705\pi$
$510$	−10140.0	−	6099.98i	−0.880404	−	0.529631i
$511$	−9548.99			−0.826659
$512$	−1866.52	+	11433.9i	−0.161112	+	0.986936i
$513$	18242.9			1.57006
$514$	−8978.51	−	5401.27i	−0.770477	−	0.463501i
$515$	−1693.01	−	513.568i	−0.144860	−	0.0439428i
$516$	−9531.96	−	17972.6i	−0.813220	−	1.53334i
$517$	12024.3	+	1184.29i	1.02288	+	0.100745i
$518$	−10820.4	−	11977.3i	−0.917800	−	1.01593i
$519$	2478.65	+	3709.56i	0.209635	+	0.313741i
$520$	−12337.4	−	666.113i	−1.04044	−	0.0561750i
$521$	−938.551	−	627.120i	−0.0789226	−	0.0527344i	0.515483	−	0.856900i	$-0.327613\pi$
$521$	−938.551	−	627.120i	−0.0789226	−	0.0527344i	−0.594405	+	0.804165i	$0.702613\pi$
$522$	−272.558	−	202.826i	−0.0228535	−	0.0170067i
$523$	2074.34	−	3880.82i	0.173431	−	0.324467i	−0.780155	−	0.625586i	$-0.784860\pi$
$523$	2074.34	−	3880.82i	0.173431	−	0.324467i	0.953587	+	0.301119i	$0.0973600\pi$
$524$	2761.94	+	14123.8i	0.230260	+	1.17748i
$525$	1491.35	+	15141.9i	0.123977	+	1.25875i
$526$	50.8463	+	1070.32i	0.00421484	+	0.0887224i
$527$	10225.7	+	4235.61i	0.845231	+	0.350106i
$528$	2530.24	+	13164.9i	0.208551	+	1.08509i
$529$	3448.16	−	1428.28i	0.283403	−	0.117389i
$530$	−614.035	−	1303.72i	−0.0503245	−	0.106849i
$531$	614.538	−	748.816i	0.0502235	−	0.0611975i
$532$	−8029.02	−	19562.5i	−0.654327	−	1.59425i
$533$	−4635.06	−	15279.7i	−0.376673	−	1.24172i
$534$	−10184.3	+	6081.87i	−0.825314	+	0.492862i
$535$	3999.45	+	20106.6i	0.323199	+	1.62483i
$536$	6270.48	+	2277.99i	0.505305	+	0.183571i
$537$	−6328.99	−	1258.91i	−0.508596	−	0.101166i
$538$	9471.55	−	19942.4i	0.759010	−	1.59810i
$539$	−2372.64	−	2891.07i	−0.189605	−	0.231034i
$540$	8947.32	−	16609.8i	0.713021	−	1.32365i
$541$	−8928.40	+	4772.33i	−0.709542	+	0.379258i	−0.786344	−	0.617788i	$-0.788029\pi$
$541$	−8928.40	+	4772.33i	−0.709542	+	0.379258i	0.0768028	+	0.997046i	$0.475529\pi$
$542$	−1075.14	−	1454.56i	−0.0852049	−	0.115275i
$543$	10122.1	+	10122.1i	0.799964	+	0.799964i
$544$	6177.27	−	6705.79i	0.486853	−	0.528508i
$545$	−1838.85	+	1838.85i	−0.144528	+	0.144528i
$546$	9802.39	+	1470.25i	0.768322	+	0.115240i
$547$	−747.987	−	1399.39i	−0.0584673	−	0.109385i	0.850990	−	0.525182i	$-0.176003\pi$
$547$	−747.987	−	1399.39i	−0.0584673	−	0.109385i	−0.909457	+	0.415797i	$0.863503\pi$
$548$	−2057.22	+	20216.7i	−0.160365	+	1.57594i
$549$	348.799	−	286.252i	0.0271154	−	0.0222531i
$550$	15929.8	−	5670.72i	1.23500	−	0.439637i
$551$	−2139.33	+	10755.1i	−0.165406	+	0.831550i
$552$	10395.0	+	1593.53i	0.801522	+	0.122872i
$553$	−6526.51	+	1298.20i	−0.501872	+	0.0998286i
$554$	−2759.10	+	10939.8i	−0.211594	+	0.838970i
$555$	−21790.8	+	6610.15i	−1.66661	+	0.505559i
$556$	4196.51	+	13.5733i	0.320093	+	0.00103531i
$557$	13677.6	+	11224.9i	1.04047	+	0.853889i	0.989460	−	0.144809i	$-0.0462569\pi$
$557$	13677.6	+	11224.9i	1.04047	+	0.853889i	0.0510070	+	0.998698i	$0.483757\pi$
$558$	−292.554	+	813.483i	−0.0221950	+	0.0617159i
$559$	6397.12	+	15444.0i	0.484024	+	1.16854i
$560$	−21749.2	−	2284.26i	−1.64120	−	0.172370i
$561$	4037.36	−	9747.06i	0.303846	−	0.733549i
$562$	11574.7	+	10524.8i	0.868769	+	0.789969i
$563$	−10952.8	+	1078.75i	−0.819901	+	0.0807532i	−0.499265	−	0.866449i	$-0.666397\pi$
$563$	−10952.8	+	1078.75i	−0.819901	+	0.0807532i	−0.320636	+	0.947202i	$0.603897\pi$
$564$	−9847.12	+	6533.66i	−0.735174	+	0.487796i
$565$	−31920.3	−	17061.7i	−2.37681	−	1.27043i
$566$	2430.04	+	16566.5i	0.180463	+	1.23029i
$567$	−7974.50	+	11934.7i	−0.590648	+	0.883967i
$568$	−1897.94	−	3201.65i	−0.140204	−	0.236511i
$569$	5442.50	−	3636.56i	0.400987	−	0.267931i	−0.338683	−	0.940900i	$-0.609982\pi$
$569$	5442.50	−	3636.56i	0.400987	−	0.267931i	0.739670	+	0.672970i	$0.234982\pi$
$570$	−29793.7	−	1511.97i	−2.18933	−	0.111104i
$571$	1141.69	−	11591.8i	0.0836747	−	0.849563i	−0.858137	−	0.513421i	$-0.828378\pi$
$571$	1141.69	−	11591.8i	0.0836747	−	0.849563i	0.941811	−	0.336142i	$-0.109122\pi$
$572$	−1044.25	−	10965.9i	−0.0763324	−	0.801587i
$573$	−1534.07	+	5057.14i	−0.111844	+	0.368700i
$574$	−6822.72	−	27425.9i	−0.496124	−	1.99432i
$575$		−	13264.5i		−	0.962034i
$576$	546.066	+	457.083i	0.0395013	+	0.0330645i
$577$			6315.71i			0.455678i	0.973699	+	0.227839i	$0.0731661\pi$
$577$			6315.71i			0.455678i	−0.973699	+	0.227839i	$0.926834\pi$
$578$	6522.10	−	1622.50i	0.469349	−	0.116759i
$579$	1575.59	−	5194.03i	0.113090	−	0.372809i
$580$	8743.11	+	7222.74i	0.625928	+	0.517083i
$581$	−272.005	+	2761.72i	−0.0194229	+	0.197204i
$582$	−530.256	+	10448.8i	−0.0377660	+	0.744185i
$583$	1068.28	−	713.801i	0.0758895	−	0.0507077i
$584$	−8306.68	−	6223.35i	−0.588583	−	0.440966i
$585$	−421.932	+	631.466i	−0.0298201	+	0.0446289i
$586$	−18194.7	+	2668.87i	−1.28262	+	0.188140i
$587$	−14614.5	−	7811.59i	−1.02760	−	0.549266i	−0.130668	−	0.991426i	$-0.541712\pi$
$587$	−14614.5	−	7811.59i	−1.02760	−	0.549266i	−0.896936	+	0.442160i	$0.854212\pi$
$588$	3585.39	+	725.242i	0.251461	+	0.0508648i
$589$	27768.5	−	2734.96i	1.94259	−	0.191328i
$590$	−21753.7	+	23923.6i	−1.51794	+	1.66936i
$591$	−3075.35	+	7424.56i	−0.214049	+	0.516761i
$592$	−1606.70	−	17471.0i	−0.111546	−	1.21293i
$593$	−803.732	−	1940.38i	−0.0556582	−	0.134371i	0.893604	−	0.448856i	$-0.148168\pi$
$593$	−803.732	−	1940.38i	−0.0556582	−	0.134371i	−0.949263	+	0.314485i	$0.898168\pi$
$594$	15828.0	+	5692.25i	1.09332	+	0.393191i
$595$	13303.8	+	10918.1i	0.916640	+	0.752267i
$596$	−5746.81	+	5709.75i	−0.394964	+	0.392417i
$597$	9835.03	−	2983.42i	0.674239	−	0.204528i
$598$	−8378.92	−	2113.22i	−0.572976	−	0.144508i
$599$	26446.0	−	5260.44i	1.80393	−	0.358824i	0.825339	−	0.564637i	$-0.190984\pi$
$599$	26446.0	−	5260.44i	1.80393	−	0.358824i	0.978591	+	0.205813i	$0.0659840\pi$
$600$	−8571.07	+	14143.9i	−0.583187	+	0.962370i
$601$	−5013.70	+	25205.6i	−0.340288	+	1.71074i	0.309730	+	0.950825i	$0.399761\pi$
$601$	−5013.70	+	25205.6i	−0.340288	+	1.71074i	−0.650018	+	0.759919i	$0.725239\pi$
$602$	9922.79	+	27874.4i	0.671799	+	1.88717i
$603$	316.995	−	260.151i	0.0214080	−	0.0175691i
$604$	1275.93	−	1040.24i	0.0859548	−	0.0700772i
$605$	2958.11	+	5534.23i	0.198784	+	0.371898i
$606$	1515.89	−	10106.7i	0.101615	−	0.677484i
$607$	393.552	−	393.552i	0.0263160	−	0.0263160i	−0.693826	−	0.720142i	$-0.744076\pi$
$607$	393.552	−	393.552i	0.0263160	−	0.0263160i	0.720142	+	0.693826i	$0.244076\pi$
$608$	5764.97	−	22250.2i	0.384540	−	1.48415i
$609$	−6433.24	−	6433.24i	−0.428059	−	0.428059i
$610$	−12112.2	+	8952.68i	−0.803948	+	0.594235i
$611$	8563.83	−	4577.46i	0.567030	−	0.303084i
$612$	−160.947	−	536.815i	−0.0106305	−	0.0354567i
$613$	−12414.9	−	15127.6i	−0.817996	−	0.996731i	−0.999910	−	0.0134165i	$-0.995729\pi$
$613$	−12414.9	−	15127.6i	−0.817996	−	0.996731i	0.181914	−	0.983314i	$-0.441771\pi$
$614$	20476.8	+	9725.36i	1.34589	+	0.639224i
$615$	−39104.6	−	7778.38i	−2.56398	−	0.510007i
$616$	−862.196	−	19478.2i	−0.0563943	−	1.27403i
$617$	1162.33	+	5843.44i	0.0758408	+	0.381277i	1.00000		0.000730729i	$-0.000232598\pi$
$617$	1162.33	+	5843.44i	0.0758408	+	0.381277i	−0.924159	+	0.382008i	$0.875233\pi$
$618$	790.988	+	1324.54i	0.0514858	+	0.0862147i
$619$	−3113.70	−	10264.5i	−0.202181	−	0.666503i	−0.998129	−	0.0611377i	$-0.980527\pi$
$619$	−3113.70	−	10264.5i	−0.202181	−	0.666503i	0.795948	−	0.605365i	$-0.206973\pi$
$620$	11129.1	−	26624.1i	0.720896	−	1.72460i
$621$	8370.86	−	10199.9i	0.540920	−	0.659113i
$622$	21043.5	−	9911.21i	1.35654	−	0.638912i
$623$	15938.8	−	6602.08i	1.02500	−	0.424569i
$624$	7568.90	+	7667.47i	0.485575	+	0.491898i
$625$	−11843.0	−	4905.53i	−0.757952	−	0.313954i
$626$	12511.4	−	594.367i	0.798814	−	0.0379484i
$627$	−2606.95	−	26468.9i	−0.166047	−	1.68591i
$628$	−23584.7	−	15869.4i	−1.49862	−	1.00837i
$629$	−6508.75	+	12177.0i	−0.412593	+	0.771907i
$630$	−802.500	+	1078.40i	−0.0507498	+	0.0681974i
$631$	25652.4	+	17140.4i	1.61839	+	1.08137i	0.936927	+	0.349524i	$0.113657\pi$
$631$	25652.4	+	17140.4i	1.61839	+	1.08137i	0.681465	+	0.731851i	$0.261343\pi$
$632$	−6523.49	−	3124.20i	−0.410586	−	0.196636i
$633$	3382.60	+	5062.41i	0.212395	+	0.317872i
$634$	3875.55	−	3501.20i	0.242773	−	0.219322i
$635$	−10835.0	−	1067.16i	−0.677126	−	0.0666911i
$636$	−368.669	+	1201.34i	−0.0229854	+	0.0748996i
$637$	−2876.34	−	872.528i	−0.178909	−	0.0542713i
$638$	−5212.02	+	8663.92i	−0.323426	+	0.537630i
$639$	−228.779			−0.0141633
$640$	−17430.9	−	16161.6i	−1.07659	−	0.998194i
$641$	−22323.4			−1.37554			−0.687769	−	0.725929i	$-0.741410\pi$
$641$	−22323.4			−1.37554			−0.687769	+	0.725929i	$0.741410\pi$
$642$	9215.19	−	15318.4i	0.566502	−	0.941695i
$643$	−3773.31	−	1144.62i	−0.231423	−	0.0702013i	0.172443	−	0.985019i	$-0.444834\pi$
$643$	−3773.31	−	1144.62i	−0.231423	−	0.0702013i	−0.403866	+	0.914818i	$0.632334\pi$
$644$	−14621.9	−	4487.21i	−0.894696	−	0.274566i
$645$	41540.4	+	4091.37i	2.53589	+	0.249764i
$646$	−13422.4	+	12125.9i	−0.817490	+	0.738525i
$647$	−13518.5	−	20231.9i	−0.821435	−	1.22937i	−0.970635	−	0.240558i	$-0.922670\pi$
$647$	−13518.5	−	20231.9i	−0.821435	−	1.22937i	0.149199	−	0.988807i	$-0.452330\pi$
$648$	−14715.2	+	5184.79i	−0.892079	+	0.314317i
$649$	−23970.1	−	16016.3i	−1.44978	−	0.968715i
$650$	8112.82	−	10902.0i	0.489556	−	0.657863i
$651$	−10912.9	+	20416.5i	−0.657003	+	1.22917i
$652$	−14348.4	+	21324.3i	−0.861852	+	1.28086i
$653$	1536.25	+	15597.9i	0.0920648	+	0.934749i	0.924641	+	0.380839i	$0.124365\pi$
$653$	1536.25	+	15597.9i	0.0920648	+	0.934749i	−0.832577	+	0.553910i	$0.813135\pi$
$654$	2265.12	−	107.607i	0.135433	−	0.00643388i
$655$	−27280.3	−	11299.9i	−1.62737	−	0.674080i
$656$	11939.2	−	28304.4i	0.710588	−	1.68461i
$657$	−589.431	+	244.150i	−0.0350014	+	0.0144980i
$658$	15549.0	−	7323.37i	0.921220	−	0.433883i
$659$	−8837.53	+	10768.6i	−0.522399	+	0.636545i	−0.965648	−	0.259853i	$-0.916326\pi$
$659$	−8837.53	+	10768.6i	−0.522399	+	0.636545i	0.443249	+	0.896399i	$0.353826\pi$
$660$	−25378.0	−	10608.2i	−1.49672	−	0.625643i
$661$	8129.94	+	26800.8i	0.478393	+	1.57705i	0.781379	+	0.624056i	$0.214516\pi$
$661$	8129.94	+	26800.8i	0.478393	+	1.57705i	−0.302986	+	0.952995i	$0.597984\pi$
$662$	−2130.06	−	3566.86i	−0.125056	−	0.209411i
$663$	−1654.15	−	8315.98i	−0.0968958	−	0.487128i
$664$	−2036.50	+	2225.14i	−0.119024	+	0.130049i
$665$	42553.6	+	8464.43i	2.48144	+	0.493589i
$666$	−974.148	−	462.667i	−0.0566779	−	0.0269189i
$667$	5031.75	+	6131.20i	0.292099	+	0.355924i
$668$	−12106.0	+	3629.60i	−0.701192	+	0.210230i
$669$	13239.6	−	7076.71i	0.765131	−	0.408971i
$670$	−11007.8	+	8136.37i	−0.634728	+	0.469158i
$671$	−9495.30	−	9495.30i	−0.546292	−	0.546292i
$672$	12691.8	+	14232.8i	0.728566	+	0.817029i
$673$	−1685.44	+	1685.44i	−0.0965361	+	0.0965361i	−0.753725	−	0.657189i	$-0.771745\pi$
$673$	−1685.44	+	1685.44i	−0.0965361	+	0.0965361i	0.657189	+	0.753725i	$0.271745\pi$
$674$	−1402.94	+	9353.58i	−0.0801766	+	0.534550i
$675$	9781.81	+	18300.5i	0.557781	+	1.04353i
$676$	5512.03	+	6760.90i	0.313611	+	0.384667i
$677$	11550.1	−	9478.94i	0.655697	−	0.538117i	−0.246662	−	0.969102i	$-0.579334\pi$
$677$	11550.1	−	9478.94i	0.655697	−	0.538117i	0.902359	+	0.430985i	$0.141834\pi$
$678$	10584.6	+	29733.6i	0.599559	+	1.68424i
$679$	2968.52	−	14923.7i	0.167778	−	0.843477i
$680$	4457.31	+	18168.1i	0.251368	+	1.02458i
$681$	27225.0	−	5415.39i	1.53196	−	0.304726i
$682$	24946.1	+	6291.57i	1.40064	+	0.353250i
$683$	−19807.5	+	6008.53i	−1.10968	+	0.336618i	−0.791351	−	0.611362i	$-0.790622\pi$
$683$	−19807.5	+	6008.53i	−1.10968	+	0.336618i	−0.318330	+	0.947980i	$0.603122\pi$
$684$	−995.785	−	1002.25i	−0.0556649	−	0.0560261i
$685$	−32230.4	−	26450.8i	−1.79775	−	1.47538i
$686$	13998.0	+	5034.10i	0.779074	+	0.280179i
$687$	−11744.9	−	28354.8i	−0.652252	−	1.57467i
$688$	−9534.67	+	30714.9i	−0.528351	+	1.70203i
$689$	395.147	−	953.970i	0.0218489	−	0.0527480i
$690$	−14516.4	+	15964.4i	−0.800913	+	0.880804i
$691$	25491.9	−	2510.73i	1.40341	−	0.138224i	0.632201	−	0.774805i	$-0.282152\pi$
$691$	25491.9	−	2510.73i	1.40341	−	0.138224i	0.771210	+	0.636581i	$0.219652\pi$
$692$	1398.32	−	6912.91i	0.0768154	−	0.379753i
$693$	−1056.94	−	564.948i	−0.0579364	−	0.0309677i
$694$	−27236.4	+	3995.13i	−1.48974	+	0.218520i
$695$	−4783.68	+	7159.29i	−0.261087	+	0.390744i
$696$	−1403.56	−	9789.00i	−0.0764393	−	0.533119i
$697$	−20101.3	+	13431.2i	−1.09238	+	0.729906i
$698$	−1647.41	+	32462.5i	−0.0893344	+	1.76035i
$699$	−1712.88	+	17391.2i	−0.0926856	+	0.941052i
$700$	15319.1	−	18543.8i	0.827154	−	1.00127i
$701$	7367.31	−	24286.8i	0.396946	−	1.30856i	−0.499849	−	0.866112i	$-0.666611\pi$
$701$	7367.31	−	24286.8i	0.396946	−	1.30856i	0.896796	−	0.442445i	$-0.145889\pi$
$702$	13118.4	−	3263.45i	0.705301	−	0.175457i
$703$			34808.4i			1.86746i
$704$	11944.5	−	17506.0i	0.639452	−	0.937192i
$705$		−	24247.1i		−	1.29532i
$706$	−5283.77	−	21239.7i	−0.281667	−	1.13224i
$707$	−4314.63	+	14223.4i	−0.229517	+	0.756615i
$708$	28069.5	−	2672.96i	1.48999	−	0.141887i
$709$	−62.5059	+	634.633i	−0.00331094	+	0.0336166i	−0.996698	−	0.0811949i	$-0.974126\pi$
$709$	−62.5059	+	634.633i	−0.00331094	+	0.0336166i	0.993387	+	0.114811i	$0.0366264\pi$
$710$	7626.80	+	387.045i	0.403139	+	0.0204585i
$711$	−369.669	+	247.005i	−0.0194988	+	0.0130287i
$712$	18168.0	+	4644.63i	0.956282	+	0.244473i
$713$	11212.6	−	16780.9i	0.588942	−	0.881414i
$714$	−2178.05	−	14848.6i	−0.114162	−	0.778286i
$715$	19932.8	+	10654.3i	1.04258	+	0.557269i
$716$	5640.04	+	8500.30i	0.294383	+	0.443675i
$717$	−26709.5	+	2630.66i	−1.39119	+	0.137021i
$718$	−11978.4	−	10892.0i	−0.622607	−	0.566135i
$719$	2945.21	−	7110.36i	0.152764	−	0.368806i	−0.828907	−	0.559386i	$-0.811037\pi$
$719$	2945.21	−	7110.36i	0.152764	−	0.368806i	0.981672	+	0.190580i	$0.0610369\pi$
$720$	−1400.92	+	415.087i	−0.0725126	+	0.0214852i
$721$	−858.645	−	2072.95i	−0.0443517	−	0.107075i
$722$	−8866.84	+	24655.4i	−0.457050	+	1.27088i
$723$	−25805.9	−	21178.3i	−1.32743	−	1.08939i
$724$	73.1932	−	22629.5i	0.00375719	−	1.16163i
$725$	−11936.2	+	3620.81i	−0.611447	+	0.185480i
$726$	1338.17	−	5305.87i	0.0684081	−	0.271239i
$727$	34689.4	−	6900.15i	1.76968	−	0.352012i	0.800686	−	0.599085i	$-0.204469\pi$
$727$	34689.4	−	6900.15i	1.76968	−	0.352012i	0.968997	+	0.247073i	$0.0794687\pi$
$728$	−9273.15	−	12631.0i	−0.472096	−	0.643045i
$729$	−4016.87	+	20194.2i	−0.204078	+	1.02597i
$730$	20062.9	−	7142.05i	1.01721	−	0.362108i
$731$	19564.8	−	16056.4i	0.989919	−	0.812406i
$732$	13066.4	+	1329.62i	0.659768	+	0.0671368i
$733$	15805.8	+	29570.5i	0.796452	+	1.49006i	0.870155	+	0.492778i	$0.164018\pi$
$733$	15805.8	+	29570.5i	0.796452	+	1.49006i	−0.0737029	+	0.997280i	$0.523482\pi$
$734$	871.756	+	130.754i	0.0438380	+	0.00657523i
$735$	−5307.16	+	5307.16i	−0.266337	+	0.266337i
$736$	−9795.18	−	13432.9i	−0.490564	−	0.672751i
$737$	−8629.52	−	8629.52i	−0.431306	−	0.431306i
$738$	−1122.38	−	1518.48i	−0.0559828	−	0.0757398i
$739$	−4751.30	+	2539.62i	−0.236508	+	0.126416i	−0.585394	−	0.810749i	$-0.699060\pi$
$739$	−4751.30	+	2539.62i	−0.236508	+	0.126416i	0.348886	+	0.937165i	$0.386560\pi$
$740$	31692.5	+	17072.0i	1.57438	+	0.848080i
$741$	−13560.4	−	16523.4i	−0.672270	−	0.819164i
$742$	784.084	−	1650.89i	0.0387933	−	0.0816796i
$743$	−14475.9	−	2879.43i	−0.714762	−	0.142175i	−0.175703	−	0.984443i	$-0.556220\pi$
$743$	−14475.9	−	2879.43i	−0.714762	−	0.142175i	−0.539059	+	0.842268i	$0.681220\pi$
$744$	−22799.1	+	10648.1i	−1.12346	+	0.524704i
$745$	−3242.72	−	16302.3i	−0.159469	−	0.801704i
$746$	4228.06	−	2524.92i	0.207507	−	0.123919i
$747$	53.8219	+	177.427i	0.00263620	+	0.00869039i
$748$	−15429.3	+	6332.62i	−0.754211	+	0.309550i
$749$	−16493.9	+	20097.9i	−0.804638	+	0.980454i
$750$	−1945.07	−	4129.77i	−0.0946985	−	0.201064i
$751$	18850.5	−	7808.11i	0.915929	−	0.379390i	0.125606	−	0.992080i	$-0.459913\pi$
$751$	18850.5	−	7808.11i	0.915929	−	0.379390i	0.790323	+	0.612690i	$0.209913\pi$
$752$	18298.9	+	3763.10i	0.887358	+	0.182481i
$753$	1661.86	+	688.363i	0.0804268	+	0.0333139i
$754$	385.590	+	8116.68i	0.0186238	+	0.392032i
$755$	331.074	+	3361.46i	0.0159590	+	0.162034i
$756$	23482.2	−	4592.00i	1.12968	−	0.220912i
$757$	−6214.16	+	11625.9i	−0.298359	+	0.558190i	−0.985774	−	0.168074i	$-0.946245\pi$
$757$	−6214.16	+	11625.9i	−0.298359	+	0.558190i	0.687416	+	0.726264i	$0.258745\pi$
$758$	−2761.22	−	2054.79i	−0.132311	−	0.0984608i
$759$	−15995.4	−	10687.8i	−0.764951	−	0.511124i
$760$	31500.9	+	35096.6i	1.50350	+	1.67511i
$761$	−1016.01	−	1520.57i	−0.0483975	−	0.0724319i	0.806482	−	0.591259i	$-0.201369\pi$
$761$	−1016.01	−	1520.57i	−0.0483975	−	0.0724319i	−0.854879	+	0.518827i	$0.826369\pi$
$762$	6364.35	+	7044.84i	0.302567	+	0.334918i
$763$	−3282.20	−	323.269i	−0.155732	−	0.0153383i
$764$	7380.58	−	3914.36i	0.349503	−	0.185362i
$765$	1100.36	+	333.790i	0.0520046	+	0.0157754i
$766$	8405.38	+	5056.49i	0.396474	+	0.238510i
$767$	−23168.9			−1.09072
$768$	1764.66	+	20652.8i	0.0829122	+	0.970367i
$769$	−9076.36			−0.425620			−0.212810	−	0.977094i	$-0.568262\pi$
$769$	−9076.36			−0.425620			−0.212810	+	0.977094i	$0.568262\pi$
$770$	34279.5	+	20621.8i	1.60435	+	0.965140i
$771$	−17939.6	−	5441.93i	−0.837976	−	0.254197i
$772$	−7580.35	+	4020.32i	−0.353398	+	0.187428i
$773$	−12062.7	−	1188.07i	−0.561275	−	0.0552807i	−0.186598	−	0.982436i	$-0.559746\pi$
$773$	−12062.7	−	1188.07i	−0.561275	−	0.0552807i	−0.374676	+	0.927156i	$0.622246\pi$
$774$	1325.20	+	1466.90i	0.0615419	+	0.0681221i
$775$	17633.1	+	26389.7i	0.817288	+	1.22316i
$776$	12308.5	−	11047.5i	0.569395	−	0.511060i
$777$	−24012.3	−	16044.5i	−1.10867	−	0.740789i
$778$	−21739.0	−	16177.3i	−1.00177	−	0.745480i
$779$	−28730.1	+	53750.2i	−1.32139	+	2.47214i
$780$	−21695.0	+	4242.50i	−0.995904	+	0.194751i
$781$	667.347	+	6775.69i	0.0305756	+	0.310440i
$782$	620.844	+	13068.8i	0.0283905	+	0.597620i
$783$	−11463.5	−	4748.32i	−0.523207	−	0.216719i
$784$	−3181.57	−	4828.89i	−0.144933	−	0.219975i
$785$	53885.8	−	22320.2i	2.45002	−	1.01483i
$786$	10971.3	+	23294.2i	0.497879	+	1.05710i
$787$	−9098.03	+	11086.0i	−0.412083	+	0.502125i	−0.937145	−	0.348939i	$-0.886542\pi$
$787$	−9098.03	+	11086.0i	−0.412083	+	0.502125i	0.525062	+	0.851064i	$0.324042\pi$
$788$	11752.8	−	4823.70i	0.531316	−	0.218068i
$789$	556.517	+	1834.59i	0.0251109	+	0.0827796i
$790$	12741.5	−	7609.01i	0.573828	−	0.342679i
$791$	−8955.13	−	45020.5i	−0.402538	−	2.02370i
$792$	−551.243	−	1180.29i	−0.0247318	−	0.0529542i
$793$	−10584.7	−	2105.43i	−0.473990	−	0.0942825i
$794$	−12796.3	+	26942.6i	−0.571943	+	1.20423i
$795$	−1635.69	−	1993.09i	−0.0729709	−	0.0889153i
$796$	−14304.1	−	7705.26i	−0.636927	−	0.343098i
$797$	7767.63	−	4151.88i	0.345224	−	0.184526i	−0.289668	−	0.957127i	$-0.593545\pi$
$797$	7767.63	−	4151.88i	0.345224	−	0.184526i	0.634892	+	0.772601i	$0.281045\pi$
$798$	−22488.5	−	30424.9i	−0.997599	−	1.34966i
$799$	−10396.1	−	10396.1i	−0.460308	−	0.460308i
$800$	25411.6	−	6147.34i	1.12304	−	0.271676i
$801$	815.054	−	815.054i	0.0359532	−	0.0359532i
$802$	29556.6	+	4433.17i	1.30135	+	0.195188i
$803$	8950.32	+	16744.9i	0.393337	+	0.735882i
$804$	11875.0	+	1208.38i	0.520896	+	0.0530055i
$805$	24258.6	−	19908.5i	1.06212	−	0.871657i
$806$	19479.0	−	6934.18i	0.851264	−	0.303035i
$807$	7706.11	−	38741.2i	0.336144	−	1.68991i
$808$	−13023.1	+	9561.00i	−0.567019	+	0.416281i
$809$	31508.2	−	6267.36i	1.36931	−	0.272372i	0.544962	−	0.838461i	$-0.316544\pi$
$809$	31508.2	−	6267.36i	1.36931	−	0.272372i	0.824344	+	0.566089i	$0.191544\pi$
$810$	7828.44	−	31039.8i	0.339584	−	1.34645i
$811$	9086.40	−	2756.33i	0.393424	−	0.119344i	−0.0873735	−	0.996176i	$-0.527847\pi$
$811$	9086.40	−	2756.33i	0.393424	−	0.119344i	0.480797	+	0.876832i	$0.340347\pi$
$812$	−46.5190	+	14382.5i	−0.00201047	+	0.621585i
$813$	−2501.63	−	2053.03i	−0.107916	−	0.0885647i
$814$	−10861.1	+	30200.7i	−0.467669	+	1.30041i
$815$	−20181.0	−	48721.2i	−0.867373	−	2.09402i
$816$	7782.58	−	14336.3i	0.333878	−	0.615039i
$817$	24417.6	−	58949.3i	1.04561	−	2.52433i
$818$	−10803.1	−	9823.25i	−0.461763	−	0.419880i
$819$	−958.532	+	94.4072i	−0.0408960	+	0.00402791i
$820$	34847.8	+	52520.3i	1.48407	+	2.23669i
$821$	23320.1	+	12464.8i	0.991322	+	0.529873i	0.885563	−	0.464519i	$-0.153773\pi$
$821$	23320.1	+	12464.8i	0.991322	+	0.529873i	0.105759	+	0.994392i	$0.466273\pi$
$822$	5276.66	+	35973.1i	0.223898	+	1.52640i
$823$	−19052.2	+	28513.6i	−0.806946	+	1.20768i	0.168120	+	0.985767i	$0.446230\pi$
$823$	−19052.2	+	28513.6i	−0.806946	+	1.20768i	−0.975066	+	0.221914i	$0.928770\pi$
$824$	604.065	−	2362.87i	0.0255383	−	0.0998960i
$825$	25154.6	−	16807.8i	1.06154	−	0.709298i
$826$	−40955.9	−	2078.43i	−1.72523	−	0.0875520i
$827$	−222.475	+	2258.83i	−0.00935455	+	0.0949784i	−0.998728	−	0.0504163i	$-0.983945\pi$
$827$	−222.475	+	2258.83i	−0.00935455	+	0.0949784i	0.989374	+	0.145395i	$0.0464452\pi$
$828$	−1017.30	+	96.8738i	−0.0426975	+	0.00406594i
$829$	−8363.09	+	27569.4i	−0.350377	+	1.15504i	0.587837	+	0.808980i	$0.299980\pi$
$829$	−8363.09	+	27569.4i	−0.350377	+	1.15504i	−0.938213	+	0.346057i	$0.887520\pi$
$830$	−1494.09	−	6005.95i	−0.0624828	−	0.251168i
$831$			20186.2i			0.842661i
$832$	165.263	−	17031.3i	0.00688639	−	0.709680i
$833$			4550.94i			0.189293i
$834$	7286.25	−	1812.59i	0.302521	−	0.0752578i
$835$	7527.48	−	24814.8i	0.311975	−	1.02844i
$836$	−26778.6	+	32415.5i	−1.10784	+	1.34104i
$837$	−3094.64	+	31420.4i	−0.127797	+	1.29755i
$838$	2195.09	−	43254.7i	0.0904871	−	1.78306i
$839$	−6475.35	+	4326.69i	−0.266453	+	0.178038i	−0.681619	−	0.731708i	$-0.738724\pi$
$839$	−6475.35	+	4326.69i	−0.266453	+	0.178038i	0.415166	+	0.909746i	$0.363724\pi$
$840$	−38731.0	+	5553.30i	−1.59089	+	0.228103i
$841$	−9406.10	+	14077.2i	−0.385670	+	0.577196i
$842$	35620.8	−	5224.99i	1.45793	−	0.213854i
$843$	24685.3	+	13194.6i	1.00855	+	0.539082i
$844$	1908.28	−	9434.00i	0.0778267	−	0.384753i
$845$	−17811.7	+	1754.30i	−0.725139	+	0.0714200i
$846$	772.547	−	849.609i	0.0313957	−	0.0345274i
$847$	−3045.56	+	7352.63i	−0.123550	+	0.298275i
$848$	1758.01	−	925.104i	0.0711914	−	0.0374625i
$849$	11464.3	+	27677.2i	0.463431	+	1.11882i
$850$	−19361.3	−	6962.92i	−0.781278	−	0.280972i
$851$	19462.0	+	15972.1i	0.783960	+	0.643379i
$852$	−4693.50	−	4723.96i	−0.188728	−	0.189953i
$853$	43933.9	−	13327.2i	1.76350	−	0.534953i	0.768961	−	0.639295i	$-0.220774\pi$
$853$	43933.9	−	13327.2i	1.76350	−	0.534953i	0.994541	+	0.104343i	$0.0332738\pi$
$854$	−18521.8	−	4671.32i	−0.742159	−	0.187177i
$855$	2843.13	−	565.533i	0.113723	−	0.0226208i
$856$	−27446.4	+	6733.62i	−1.09591	+	0.268867i
$857$	−1396.14	+	7018.88i	−0.0556491	+	0.279767i	−0.998583	−	0.0532124i	$-0.983054\pi$
$857$	−1396.14	+	7018.88i	−0.0556491	+	0.279767i	0.942934	+	0.332979i	$0.108054\pi$
$858$	−6609.63	−	18567.3i	−0.262994	−	0.738785i
$859$	−27699.0	+	22732.0i	−1.10021	+	0.902917i	−0.995794	−	0.0916170i	$-0.970796\pi$
$859$	−27699.0	+	22732.0i	−1.10021	+	0.902917i	−0.104413	+	0.994534i	$0.533296\pi$
$860$	−41696.6	−	51143.9i	−1.65330	−	2.02790i
$861$	−23836.3	−	44594.7i	−0.943485	−	1.76514i
$862$	1970.51	−	13137.7i	0.0778605	−	0.519107i
$863$	−8261.86	+	8261.86i	−0.325883	+	0.325883i	−0.851019	−	0.525136i	$-0.824015\pi$
$863$	−8261.86	+	8261.86i	−0.325883	+	0.325883i	0.525136	+	0.851019i	$0.324015\pi$
$864$	23419.9	+	11309.4i	0.922179	+	0.445318i
$865$	10232.6	+	10232.6i	0.402219	+	0.402219i
$866$	−5215.13	+	3854.75i	−0.204639	+	0.151258i
$867$	10604.9	−	5668.46i	0.415413	−	0.222043i
$868$	35055.3	−	10510.2i	1.37080	−	0.410990i
$869$	8393.82	+	10227.9i	0.327665	+	0.399261i
$870$	18328.2	+	8704.90i	0.714236	+	0.339223i
$871$	−9619.60	−	1913.46i	−0.374222	−	0.0744374i
$872$	−2644.51	−	2420.31i	−0.102700	−	0.0939933i
$873$	−198.335	−	997.098i	−0.00768915	−	0.0386560i
$874$	16911.2	+	28318.3i	0.654495	+	1.09598i
$875$	1927.24	+	6353.25i	0.0744600	+	0.245462i
$876$	−17133.8	−	7162.06i	−0.660842	−	0.276237i
$877$	−769.763	+	937.959i	−0.0296386	+	0.0361147i	−0.787619	−	0.616163i	$-0.788686\pi$
$877$	−769.763	+	937.959i	−0.0296386	+	0.0361147i	0.757980	+	0.652278i	$0.226186\pi$
$878$	−2003.90	+	943.811i	−0.0770254	+	0.0362780i
$879$	−30397.3	+	12591.0i	−1.16641	+	0.483144i
$880$	16380.0	+	40279.9i	0.627466	+	1.54299i
$881$	7522.07	+	3115.74i	0.287656	+	0.119151i	0.521846	−	0.853040i	$-0.325244\pi$
$881$	7522.07	+	3115.74i	0.287656	+	0.119151i	−0.234190	+	0.972191i	$0.575244\pi$
$882$	−355.055	+	16.8672i	−0.0135548	+	0.000643931i
$883$	−4665.61	−	47370.8i	−0.177815	−	1.80538i	−0.507883	−	0.861426i	$-0.669572\pi$
$883$	−4665.61	−	47370.8i	−0.177815	−	1.80538i	0.330068	−	0.943957i	$-0.392928\pi$
$884$	−7482.83	+	11120.8i	−0.284700	+	0.423115i
$885$	−27271.8	+	51022.0i	−1.03586	+	1.93795i
$886$	−9685.35	+	13015.1i	−0.367253	+	0.493513i
$887$	26853.5	+	17942.9i	1.01652	+	0.679217i	0.947947	−	0.318429i	$-0.103155\pi$
$887$	26853.5	+	17942.9i	1.01652	+	0.679217i	0.0685731	+	0.997646i	$0.478155\pi$
$888$	−10431.7	−	29606.6i	−0.394216	−	1.11884i
$889$	−7671.23	−	11480.8i	−0.289409	−	0.433132i
$890$	−28550.4	+	25792.6i	−1.07529	+	0.971425i
$891$	28402.9	+	2797.44i	1.06794	+	0.105183i
$892$	−22687.9	−	6962.50i	−0.851621	−	0.261347i
$893$	−35468.4	−	10759.2i	−1.32912	−	0.403185i
$894$	−7471.60	+	12420.0i	−0.279516	+	0.464639i
$895$	−20930.8			−0.781719
$896$	1819.98	−	30091.5i	0.0678585	−	1.12197i
$897$	−15460.8			−0.575497
$898$	10678.8	−	17751.3i	0.396833	−	0.659654i
$899$	−18161.1	−	5509.10i	−0.673755	−	0.204381i
$900$	471.473	−	1536.33i	0.0174620	−	0.0569012i
$901$	−1555.85	−	153.238i	−0.0575283	−	0.00566605i
$902$	−41698.5	+	37670.6i	−1.53925	+	1.39057i
$903$	29410.7	+	44016.2i	1.08386	+	1.62211i
$904$	21551.0	−	44999.7i	0.792895	−	1.65560i
$905$	38606.2	+	25795.8i	1.41802	+	0.947493i
$906$	1758.39	−	2362.92i	0.0644798	−	0.0866477i
$907$	13209.7	−	24713.5i	0.483594	−	0.904741i	−0.515267	−	0.857030i	$-0.672307\pi$
$907$	13209.7	−	24713.5i	0.483594	−	0.904741i	0.998861	−	0.0477111i	$-0.0151927\pi$
$908$	−36407.5	−	24497.4i	−1.33064	−	0.895347i
$909$	97.3377	+	988.287i	0.00355169	+	0.0360609i
$910$	32114.3	−	1525.62i	1.16987	−	0.0555756i
$911$	−6378.07	−	2641.88i	−0.231959	−	0.0960807i	0.263676	−	0.964611i	$-0.415065\pi$
$911$	−6378.07	−	2641.88i	−0.231959	−	0.0960807i	−0.495636	+	0.868530i	$0.665065\pi$
$912$	266.021	−	41123.1i	0.00965881	−	1.49311i
$913$	5097.82	−	2111.59i	0.184790	−	0.0765426i
$914$	22524.1	−	10608.6i	0.815134	−	0.383918i
$915$	−17095.7	+	20831.1i	−0.617667	+	0.752629i
$916$	−18711.9	+	44764.5i	−0.674956	+	1.61470i
$917$	−10870.7	−	35835.9i	−0.391475	−	1.29052i
$918$	−10494.0	−	17572.6i	−0.377291	−	0.631788i
$919$	7142.26	+	35906.6i	0.256367	+	1.28884i	0.867548	+	0.497354i	$0.165695\pi$
$919$	7142.26	+	35906.6i	0.256367	+	1.28884i	−0.611181	+	0.791491i	$0.709305\pi$
$920$	34077.5	−	1508.43i	1.22120	−	0.0540560i
$921$	39779.4	+	7912.62i	1.42321	+	0.283094i
$922$	17443.9	+	8284.91i	0.623086	+	0.295932i
$923$	3471.28	+	4229.77i	0.123791	+	0.150839i
$924$	−10018.3	−	33414.5i	−0.356685	−	1.18967i
$925$	−34918.3	+	18664.2i	−1.24120	+	0.663434i
$926$	−10949.8	+	8093.48i	−0.388587	+	0.287223i
$927$	−106.003	−	106.003i	−0.00375577	−	0.00375577i
$928$	−9413.95	+	12481.0i	−0.333004	+	0.441498i
$929$	36687.8	−	36687.8i	1.29568	−	1.29568i	0.364461	−	0.931219i	$-0.381253\pi$
$929$	36687.8	−	36687.8i	1.29568	−	1.29568i	0.931219	−	0.364461i	$-0.118747\pi$
$930$	7658.19	−	51058.3i	0.270024	−	1.80029i
$931$	5408.30	+	10118.2i	0.190387	+	0.356188i
$932$	21411.8	−	17456.6i	0.752539	−	0.613530i
$933$	32170.7	−	26401.8i	1.12885	−	0.926427i
$934$	−15071.7	−	42338.4i	−0.528010	−	1.48325i
$935$	6676.04	−	33562.7i	0.233508	−	1.17392i
$936$	−895.356	−	542.577i	−0.0312667	−	0.0189473i
$937$	−4023.47	+	800.318i	−0.140279	+	0.0279032i	−0.264730	−	0.964323i	$-0.585283\pi$
$937$	−4023.47	+	800.318i	−0.140279	+	0.0279032i	0.124452	+	0.992226i	$0.460283\pi$
$938$	−16833.0	−	4245.39i	−0.585945	−	0.147779i
$939$	21445.4	−	6505.39i	0.745308	−	0.226087i
$940$	−27191.8	+	27016.5i	−0.943509	+	0.937425i
$941$	−18393.7	−	15095.3i	−0.637214	−	0.522948i	0.259395	−	0.965771i	$-0.416477\pi$
$941$	−18393.7	−	15095.3i	−0.637214	−	0.522948i	−0.896609	+	0.442823i	$0.853977\pi$
$942$	−47859.4	−	17211.7i	−1.65535	−	0.595317i
$943$	16869.7	+	40727.2i	0.582560	+	1.40643i
$944$	−34273.0	−	28500.1i	−1.18166	−	0.982627i
$945$	−18787.1	+	45356.2i	−0.646715	+	1.56131i
$946$	39579.1	−	43527.2i	1.36028	−	1.49597i
$947$	7163.70	−	705.563i	0.245817	−	0.0242109i	0.0256419	−	0.999671i	$-0.491837\pi$
$947$	7163.70	−	705.563i	0.245817	−	0.0242109i	0.220175	+	0.975460i	$0.429337\pi$
$948$	−12684.2	−	2565.73i	−0.434562	−	0.0879018i
$949$	13457.5	+	7193.16i	0.460324	+	0.246048i
$950$	−51321.1	+	7527.96i	−1.75271	+	0.257094i
$951$	5191.59	−	7769.76i	0.177023	−	0.264933i
$952$	−14225.1	+	18987.1i	−0.484284	+	0.646403i
$953$	9123.36	−	6096.03i	0.310110	−	0.207209i	−0.390770	−	0.920488i	$-0.627791\pi$
$953$	9123.36	−	6096.03i	0.310110	−	0.207209i	0.700879	+	0.713280i	$0.252791\pi$
$954$	6.18885	−	121.952i	0.000210033	−	0.00413874i
$955$	−1680.15	+	17058.8i	−0.0569302	+	0.578022i
$956$	32710.3	+	27022.1i	1.10662	+	0.914183i
$957$	−5251.25	+	17311.1i	−0.177376	+	0.584731i
$958$	30280.8	−	7532.92i	1.02122	−	0.254048i
$959$		−	52878.6i		−	1.78054i
$960$	−37311.4	−	20411.3i	−1.25440	−	0.686219i
$961$			18499.8i			0.620986i
$962$	6226.84	+	25030.6i	0.208692	+	0.838897i
$963$	−504.253	+	1662.30i	−0.0168737	+	0.0556250i
$964$	5002.92	+	52537.0i	0.167151	+	1.75529i
$965$	1725.63	−	17520.6i	0.0575646	−	0.584463i
$966$	−27330.2	−	1386.95i	−0.910283	−	0.0461951i
$967$	25807.8	−	17244.3i	0.858247	−	0.573462i	−0.0467376	−	0.998907i	$-0.514882\pi$
$967$	25807.8	−	17244.3i	0.858247	−	0.573462i	0.904984	+	0.425445i	$0.139882\pi$
$968$	−7441.25	+	4411.18i	−0.247077	+	0.146468i
$969$	−17980.3	+	26909.5i	−0.596090	+	0.892112i
$970$	4925.02	+	33575.8i	0.163024	+	1.11140i
$971$	15591.5	+	8333.81i	0.515297	+	0.275432i	0.708480	−	0.705731i	$-0.249381\pi$
$971$	15591.5	+	8333.81i	0.515297	+	0.275432i	−0.193183	+	0.981163i	$0.561881\pi$
$972$	2598.90	−	1724.40i	0.0857611	−	0.0569034i
$973$	−10867.4	+	1070.35i	−0.358061	+	0.0352660i
$974$	−7478.96	−	6800.60i	−0.246038	−	0.223722i
$975$	9304.47	−	22463.0i	0.305622	−	0.737837i
$976$	−13067.7	−	16134.8i	−0.428573	−	0.529161i
$977$	−7091.14	−	17119.5i	−0.232207	−	0.560596i	0.764230	−	0.644944i	$-0.223119\pi$
$977$	−7091.14	−	17119.5i	−0.232207	−	0.560596i	−0.996436	+	0.0843478i	$0.973119\pi$
$978$	−15562.1	+	43272.4i	−0.508815	+	1.41483i
$979$	−26516.8	−	21761.8i	−0.865659	−	0.710428i
$980$	11865.0	+	38.3763i	0.386748	+	0.00125090i
$981$	−210.866	+	63.9655i	−0.00686283	+	0.00208182i
$982$	−353.286	+	1400.78i	−0.0114805	+	0.0455201i
$983$	−9231.40	+	1836.24i	−0.299528	+	0.0595798i	−0.342566	−	0.939494i	$-0.611296\pi$
$983$	−9231.40	+	1836.24i	−0.299528	+	0.0595798i	0.0430385	+	0.999073i	$0.486296\pi$
$984$	8328.33	−	54327.7i	0.269815	−	1.76007i
$985$	−5085.30	+	25565.5i	−0.164498	+	0.826990i
$986$	11590.6	−	4126.04i	0.374360	−	0.133266i
$987$	23770.9	−	19508.3i	0.766601	−	0.629133i
$988$	−3420.88	+	33617.7i	−0.110155	+	1.08251i
$989$	−21755.5	−	40701.7i	−0.699479	−	1.30863i
$990$	2643.24	+	396.457i	0.0848561	+	0.0127275i
$991$	−10743.7	+	10743.7i	−0.344385	+	0.344385i	−0.858013	−	0.513628i	$-0.828301\pi$
$991$	−10743.7	+	10743.7i	−0.344385	+	0.344385i	0.513628	+	0.858013i	$0.328301\pi$
$992$	37344.4	+	13703.7i	1.19525	+	0.438600i
$993$	−5255.98	−	5255.98i	−0.167969	−	0.167969i
$994$	5756.77	+	7788.40i	0.183696	+	0.248524i
$995$	29399.9	−	15714.6i	0.936723	−	0.500689i
$996$	−2559.44	+	4751.34i	−0.0814246	+	0.151157i
$997$	17684.8	+	21549.0i	0.561770	+	0.684519i	0.973997	−	0.226563i	$-0.0727488\pi$
$997$	17684.8	+	21549.0i	0.561770	+	0.684519i	−0.412227	+	0.911081i	$0.635249\pi$
$998$	3142.91	−	6617.42i	0.0996865	−	0.209890i
$999$	−38629.3	−	7683.85i	−1.22340	−	0.243350i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.4.k.a.5.9	✓	752
128.77	even	32	inner	128.4.k.a.77.9	yes	752

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
128.4.k.a.5.9	✓	752	1.1	even	1	trivial
128.4.k.a.77.9	yes	752	128.77	even	32	inner

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:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	128.k (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.42367 - 1.45802i) q^{2} +(-4.84264 - 1.46900i) q^{3} +(3.74833 + 7.06753i) q^{4} +(-16.3353 - 1.60888i) q^{5} +(9.59512 + 10.6211i) q^{6} +(-11.5654 - 17.3089i) q^{7} +(1.21991 - 22.5945i) q^{8} +(-1.15646 - 0.772719i) q^{9} +O(q^{10})\)	\(q+(-2.42367 - 1.45802i) q^{2} +(-4.84264 - 1.46900i) q^{3} +(3.74833 + 7.06753i) q^{4} +(-16.3353 - 1.60888i) q^{5} +(9.59512 + 10.6211i) q^{6} +(-11.5654 - 17.3089i) q^{7} +(1.21991 - 22.5945i) q^{8} +(-1.15646 - 0.772719i) q^{9} +(37.2455 + 27.7166i) q^{10} +(-19.5121 + 36.5045i) q^{11} +(-7.76964 - 39.7318i) q^{12} +(3.26062 + 33.1056i) q^{13} +(2.79399 + 58.8136i) q^{14} +(76.7424 + 31.7878i) q^{15} +(-35.9000 + 52.9829i) q^{16} +(46.5328 - 19.2745i) q^{17} +(1.67622 + 3.55895i) q^{18} +(80.5519 - 98.1527i) q^{19} +(-49.8592 - 121.481i) q^{20} +(30.5805 + 100.810i) q^{21} +(100.515 - 60.0258i) q^{22} +(-17.9173 - 90.0761i) q^{23} +(-39.0989 + 107.625i) q^{24} +(141.655 + 28.1768i) q^{25} +(40.3661 - 84.9911i) q^{26} +(91.1454 + 111.061i) q^{27} +(78.9799 - 146.618i) q^{28} +(-76.1648 + 40.7110i) q^{29} +(-139.651 - 188.935i) q^{30} +(155.388 + 155.388i) q^{31} +(164.260 - 76.0700i) q^{32} +(148.115 - 148.115i) q^{33} +(-140.883 - 21.1309i) q^{34} +(161.076 + 301.353i) q^{35} +(1.12643 - 11.0697i) q^{36} +(-211.911 + 173.910i) q^{37} +(-338.340 + 120.443i) q^{38} +(32.8421 - 165.109i) q^{39} +(-56.2795 + 367.125i) q^{40} +(-470.768 + 93.6416i) q^{41} +(72.8669 - 288.918i) q^{42} +(480.874 - 145.872i) q^{43} +(-331.135 - 1.07103i) q^{44} +(17.6478 + 14.4832i) q^{45} +(-87.9076 + 244.438i) q^{46} +(-111.707 - 269.684i) q^{47} +(251.683 - 203.840i) q^{48} +(-34.5778 + 83.4781i) q^{49} +(-302.241 - 274.827i) q^{50} +(-253.656 + 24.9829i) q^{51} +(-221.753 + 147.135i) q^{52} +(-27.3748 - 14.6321i) q^{53} +(-58.9766 - 402.067i) q^{54} +(377.467 - 564.919i) q^{55} +(-405.194 + 240.200i) q^{56} +(-534.270 + 356.988i) q^{57} +(243.956 + 12.3803i) q^{58} +(-68.2668 + 693.124i) q^{59} +(62.9954 + 661.531i) q^{60} +(-94.1740 + 310.450i) q^{61} +(-150.049 - 603.168i) q^{62} +28.9538i q^{63} +(-509.024 - 55.1265i) q^{64} -546.035i q^{65} +(-574.937 + 143.027i) q^{66} +(-85.5872 + 282.143i) q^{67} +(310.644 + 256.625i) q^{68} +(-45.5549 + 462.527i) q^{69} +(48.9837 - 965.232i) q^{70} +(136.766 - 91.3844i) q^{71} +(-18.8700 + 25.1869i) q^{72} +(254.844 - 381.401i) q^{73} +(767.166 - 112.531i) q^{74} +(-644.590 - 344.541i) q^{75} +(995.633 + 201.394i) q^{76} +(857.517 - 84.4581i) q^{77} +(-320.331 + 352.284i) q^{78} +(122.328 - 295.325i) q^{79} +(671.679 - 807.732i) q^{80} +(-263.865 - 637.026i) q^{81} +(1277.52 + 459.435i) q^{82} +(-103.048 - 84.5690i) q^{83} +(-597.854 + 593.999i) q^{84} +(-791.137 + 239.989i) q^{85} +(-1378.16 - 347.582i) q^{86} +(428.643 - 85.2625i) q^{87} +(800.999 + 485.398i) q^{88} +(-161.679 + 812.817i) q^{89} +(-21.6556 - 60.8333i) q^{90} +(535.311 - 439.318i) q^{91} +(569.456 - 464.266i) q^{92} +(-524.223 - 980.753i) q^{93} +(-122.466 + 816.496i) q^{94} +(-1473.75 + 1473.75i) q^{95} +(-907.199 + 127.082i) q^{96} +(516.852 + 516.852i) q^{97} +(205.518 - 151.908i) q^{98} +(50.7726 - 27.1385i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9}+O(q^{10}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9	\( 752 q - 16 q^{2} - 16 q^{3} - 16 q^{4} - 16 q^{5} - 16 q^{6} - 16 q^{7} - 16 q^{8} - 16 q^{9} - 16 q^{10} - 16 q^{11} - 16 q^{12} - 16 q^{13} - 16 q^{14} - 16 q^{15} - 16 q^{16} - 16 q^{17} - 16 q^{18} - 16 q^{19} - 16 q^{20} - 16 q^{21} - 16 q^{22} - 16 q^{23} - 16 q^{24} - 16 q^{25} - 16 q^{26} - 16 q^{27} - 16 q^{28} - 16 q^{29} - 16 q^{30} - 16 q^{31} - 16 q^{32} - 16 q^{33} - 16 q^{34} - 16 q^{35} - 16 q^{36} - 16 q^{37} - 16 q^{38} - 16 q^{39} - 16 q^{40} - 16 q^{41} - 16 q^{42} - 16 q^{43} - 16 q^{44} - 16 q^{45} - 16 q^{46} - 16 q^{47} - 16 q^{48} - 16 q^{49} + 5696 q^{50} - 16 q^{51} + 6608 q^{52} - 16 q^{53} + 3440 q^{54} - 16 q^{55} - 800 q^{56} - 16 q^{57} - 4768 q^{58} - 16 q^{59} - 9808 q^{60} - 16 q^{61} - 5872 q^{62} - 12112 q^{64} - 10960 q^{66} - 16 q^{67} - 4144 q^{68} - 16 q^{69} - 4048 q^{70} - 16 q^{71} + 1280 q^{72} - 16 q^{73} + 5248 q^{74} - 16 q^{75} + 11888 q^{76} - 16 q^{77} + 14096 q^{78} - 16 q^{79} + 10016 q^{80} - 16 q^{81} - 16 q^{82} - 16 q^{83} - 16 q^{84} - 16 q^{85} - 16 q^{86} - 16 q^{87} - 16 q^{88} - 16 q^{89} - 16 q^{90} - 16 q^{91} - 16 q^{92} - 16 q^{93} - 16 q^{94} - 16 q^{95} - 16 q^{96} - 16 q^{97} - 16 q^{98} - 16 q^{99}+O(q^{100}) \) 752 * q - 16 * q^2 - 16 * q^3 - 16 * q^4 - 16 * q^5 - 16 * q^6 - 16 * q^7 - 16 * q^8 - 16 * q^9 - 16 * q^10 - 16 * q^11 - 16 * q^12 - 16 * q^13 - 16 * q^14 - 16 * q^15 - 16 * q^16 - 16 * q^17 - 16 * q^18 - 16 * q^19 - 16 * q^20 - 16 * q^21 - 16 * q^22 - 16 * q^23 - 16 * q^24 - 16 * q^25 - 16 * q^26 - 16 * q^27 - 16 * q^28 - 16 * q^29 - 16 * q^30 - 16 * q^31 - 16 * q^32 - 16 * q^33 - 16 * q^34 - 16 * q^35 - 16 * q^36 - 16 * q^37 - 16 * q^38 - 16 * q^39 - 16 * q^40 - 16 * q^41 - 16 * q^42 - 16 * q^43 - 16 * q^44 - 16 * q^45 - 16 * q^46 - 16 * q^47 - 16 * q^48 - 16 * q^49 + 5696 * q^50 - 16 * q^51 + 6608 * q^52 - 16 * q^53 + 3440 * q^54 - 16 * q^55 - 800 * q^56 - 16 * q^57 - 4768 * q^58 - 16 * q^59 - 9808 * q^60 - 16 * q^61 - 5872 * q^62 - 12112 * q^64 - 10960 * q^66 - 16 * q^67 - 4144 * q^68 - 16 * q^69 - 4048 * q^70 - 16 * q^71 + 1280 * q^72 - 16 * q^73 + 5248 * q^74 - 16 * q^75 + 11888 * q^76 - 16 * q^77 + 14096 * q^78 - 16 * q^79 + 10016 * q^80 - 16 * q^81 - 16 * q^82 - 16 * q^83 - 16 * q^84 - 16 * q^85 - 16 * q^86 - 16 * q^87 - 16 * q^88 - 16 * q^89 - 16 * q^90 - 16 * q^91 - 16 * q^92 - 16 * q^93 - 16 * q^94 - 16 * q^95 - 16 * q^96 - 16 * q^97 - 16 * q^98 - 16 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more