LMFDB - Embedded newform 105.4.s.a.101.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [105,4,Mod(26,105)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(105, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 0, 5]))

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

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

chi := DirichletCharacter("105.26");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 105 = 3 \cdot 5 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	105.s (of order $6$, 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:	$6.19520055060$
Analytic rank:	$0$
Dimension:	$32$
Relative dimension:	$16$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			101.12
Character	$\chi$	$=$	105.101
Dual form			105.4.s.a.26.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.43022 - 1.40309i) q^{2} +(-2.49879 + 4.55588i) q^{3} +(-0.0626967 + 0.108594i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(0.319698 + 14.5778i) q^{6} +(-12.1846 + 13.9476i) q^{7} +22.8013i q^{8} +(-14.5121 - 22.7684i) q^{9} +O(q^{10})$	\(q+(2.43022 - 1.40309i) q^{2} +(-2.49879 + 4.55588i) q^{3} +(-0.0626967 + 0.108594i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(0.319698 + 14.5778i) q^{6} +(-12.1846 + 13.9476i) q^{7} +22.8013i q^{8} +(-14.5121 - 22.7684i) q^{9} +(-12.1511 - 7.01543i) q^{10} +(-24.0891 - 13.9078i) q^{11} +(-0.338075 - 0.556992i) q^{12} +85.9357i q^{13} +(-10.0417 + 50.9917i) q^{14} +(25.9745 - 0.569634i) q^{15} +(31.4906 + 54.5433i) q^{16} +(18.2622 - 31.6311i) q^{17} +(-67.2136 - 34.9703i) q^{18} +(-55.3090 + 31.9327i) q^{19} +0.626967 q^{20} +(-33.0966 - 90.3638i) q^{21} -78.0556 q^{22} +(100.947 - 58.2816i) q^{23} +(-103.880 - 56.9755i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(120.575 + 208.843i) q^{26} +(139.993 - 9.22216i) q^{27} +(-0.750683 - 2.19764i) q^{28} -80.6309i q^{29} +(62.3245 - 37.8288i) q^{30} +(268.943 + 155.274i) q^{31} +(-4.91394 - 2.83706i) q^{32} +(123.556 - 74.9942i) q^{33} -102.494i q^{34} +(90.8563 + 17.8921i) q^{35} +(3.38237 - 0.148425i) q^{36} +(-41.0061 - 71.0246i) q^{37} +(-89.6086 + 155.207i) q^{38} +(-391.513 - 214.735i) q^{39} +(98.7323 - 57.0031i) q^{40} -85.8751 q^{41} +(-207.220 - 173.166i) q^{42} -94.2097 q^{43} +(3.02061 - 1.74395i) q^{44} +(-62.3096 + 119.760i) q^{45} +(163.548 - 283.274i) q^{46} +(199.272 + 345.149i) q^{47} +(-327.181 + 7.17524i) q^{48} +(-46.0690 - 339.892i) q^{49} +70.1543i q^{50} +(98.4741 + 162.240i) q^{51} +(-9.33209 - 5.38789i) q^{52} +(-121.612 - 70.2126i) q^{53} +(327.273 - 218.834i) q^{54} +139.078i q^{55} +(-318.022 - 277.825i) q^{56} +(-7.27597 - 331.774i) q^{57} +(-113.132 - 195.951i) q^{58} +(-443.739 + 768.579i) q^{59} +(-1.56666 + 2.85639i) q^{60} +(98.2925 - 56.7492i) q^{61} +871.453 q^{62} +(494.388 + 75.0157i) q^{63} -519.772 q^{64} +(372.113 - 214.839i) q^{65} +(195.044 - 355.612i) q^{66} +(130.409 - 225.874i) q^{67} +(2.28996 + 3.96633i) q^{68} +(13.2797 + 605.534i) q^{69} +(245.905 - 83.9975i) q^{70} +390.768i q^{71} +(519.147 - 330.895i) q^{72} +(-183.140 - 105.736i) q^{73} +(-199.307 - 115.070i) q^{74} +(-67.4029 - 111.049i) q^{75} -8.00829i q^{76} +(487.497 - 166.522i) q^{77} +(-1252.75 + 27.4735i) q^{78} +(529.006 + 916.266i) q^{79} +(157.453 - 272.716i) q^{80} +(-307.797 + 660.834i) q^{81} +(-208.695 + 120.490i) q^{82} +1000.70 q^{83} +(11.8880 + 2.07142i) q^{84} -182.622 q^{85} +(-228.950 + 132.184i) q^{86} +(367.345 + 201.480i) q^{87} +(317.116 - 549.261i) q^{88} +(-490.935 - 850.325i) q^{89} +(16.6080 + 378.469i) q^{90} +(-1198.59 - 1047.10i) q^{91} +14.6162i q^{92} +(-1379.44 + 837.274i) q^{93} +(968.549 + 559.192i) q^{94} +(276.545 + 159.663i) q^{95} +(25.2042 - 15.2981i) q^{96} +1695.07i q^{97} +(-588.856 - 761.373i) q^{98} +(32.9248 + 750.301i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) $ 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/105\mathbb{Z}\right)^\times$.

$n$	$22$	$31$	$71$
$\chi(n)$	$1$	$e\left(\frac{1}{6}\right)$	$-1$

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 $

$2$	2.43022	−	1.40309i	0.859211	−	0.496066i	−0.00453667	−	0.999990i	$-0.501444\pi$
$2$	2.43022	−	1.40309i	0.859211	−	0.496066i	0.863748	+	0.503924i	$0.168111\pi$
$3$	−2.49879	+	4.55588i	−0.480892	+	0.876780i
$3$	−2.49879	+	4.55588i	−0.480892	+	0.876780i
$4$	−0.0626967	+	0.108594i	−0.00783708	+	0.0135742i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$5$	−2.50000	−	4.33013i	−0.223607	−	0.387298i
$6$	0.319698	+	14.5778i	0.0217527	+	0.991893i
$7$	−12.1846	+	13.9476i	−0.657909	+	0.753098i
$7$	−12.1846	+	13.9476i	−0.657909	+	0.753098i
$8$			22.8013i			1.00768i
$9$	−14.5121	−	22.7684i	−0.537486	−	0.843273i
$10$	−12.1511	−	7.01543i	−0.384251	−	0.221847i
$11$	−24.0891	−	13.9078i	−0.660284	−	0.381215i	0.132101	−	0.991236i	$-0.457828\pi$
$11$	−24.0891	−	13.9078i	−0.660284	−	0.381215i	−0.792385	+	0.610021i	$0.791161\pi$
$12$	−0.338075	−	0.556992i	−0.00813282	−	0.0133991i
$13$			85.9357i			1.83341i	0.399568	+	0.916703i	$0.369160\pi$
$13$			85.9357i			1.83341i	−0.399568	+	0.916703i	$0.630840\pi$
$14$	−10.0417	+	50.9917i	−0.191697	+	0.973436i
$15$	25.9745	−	0.569634i	0.447106	−	0.00980526i
$16$	31.4906	+	54.5433i	0.492040	+	0.852238i
$17$	18.2622	−	31.6311i	0.260544	−	0.451275i	−0.705843	−	0.708368i	$-0.749432\pi$
$17$	18.2622	−	31.6311i	0.260544	−	0.451275i	0.966386	+	0.257094i	$0.0827649\pi$
$18$	−67.2136	−	34.9703i	−0.880133	−	0.457921i
$19$	−55.3090	+	31.9327i	−0.667829	+	0.385571i	−0.795254	−	0.606277i	$-0.792662\pi$
$19$	−55.3090	+	31.9327i	−0.667829	+	0.385571i	0.127424	+	0.991848i	$0.459329\pi$
$20$	0.626967			0.00700970
$21$	−33.0966	−	90.3638i	−0.343918	−	0.939000i
$22$	−78.0556			−0.756432
$23$	100.947	−	58.2816i	0.915166	−	0.528372i	0.0330766	−	0.999453i	$-0.489469\pi$
$23$	100.947	−	58.2816i	0.915166	−	0.528372i	0.882090	+	0.471081i	$0.156136\pi$
$24$	−103.880	−	56.9755i	−0.883516	−	0.484587i
$25$	−12.5000	+	21.6506i	−0.100000	+	0.173205i
$26$	120.575	+	208.843i	0.909491	+	1.57528i
$27$	139.993	−	9.22216i	0.997837	−	0.0657335i
$28$	−0.750683	−	2.19764i	−0.00506663	−	0.0148327i
$29$		−	80.6309i		−	0.516303i	−0.966104	−	0.258151i	$-0.916887\pi$
$29$		−	80.6309i		−	0.516303i	0.966104	−	0.258151i	$-0.0831133\pi$
$30$	62.3245	−	37.8288i	0.379295	−	0.230219i
$31$	268.943	+	155.274i	1.55818	+	0.899615i	0.997431	+	0.0716286i	$0.0228196\pi$
$31$	268.943	+	155.274i	1.55818	+	0.899615i	0.560748	+	0.827987i	$0.310514\pi$
$32$	−4.91394	−	2.83706i	−0.0271459	−	0.0156727i
$33$	123.556	−	74.9942i	0.651767	−	0.395601i
$34$		−	102.494i		−	0.516987i
$35$	90.8563	+	17.8921i	0.438786	+	0.0864092i
$36$	3.38237	−	0.148425i	0.0156591	−	0.000687154i
$37$	−41.0061	−	71.0246i	−0.182199	−	0.315578i	0.760430	−	0.649420i	$-0.224988\pi$
$37$	−41.0061	−	71.0246i	−0.182199	−	0.315578i	−0.942629	+	0.333842i	$0.891655\pi$
$38$	−89.6086	+	155.207i	−0.382538	+	0.662575i
$39$	−391.513	−	214.735i	−1.60749	−	0.881671i
$40$	98.7323	−	57.0031i	0.390274	−	0.225325i
$41$	−85.8751			−0.327108			−0.163554	−	0.986534i	$-0.552296\pi$
$41$	−85.8751			−0.327108			−0.163554	+	0.986534i	$0.552296\pi$
$42$	−207.220	−	173.166i	−0.761304	−	0.636194i
$43$	−94.2097			−0.334113			−0.167056	−	0.985947i	$-0.553426\pi$
$43$	−94.2097			−0.334113			−0.167056	+	0.985947i	$0.553426\pi$
$44$	3.02061	−	1.74395i	0.0103494	−	0.00597523i
$45$	−62.3096	+	119.760i	−0.206413	+	0.396729i
$46$	163.548	−	283.274i	0.524214	−	0.907966i
$47$	199.272	+	345.149i	0.618443	+	1.07117i	0.989770	+	0.142672i	$0.0455696\pi$
$47$	199.272	+	345.149i	0.618443	+	1.07117i	−0.371327	+	0.928502i	$0.621097\pi$
$48$	−327.181	+	7.17524i	−0.983844	+	0.0215762i
$49$	−46.0690	−	339.892i	−0.134312	−	0.990939i
$50$			70.1543i			0.198426i
$51$	98.4741	+	162.240i	0.270375	+	0.445454i
$52$	−9.33209	−	5.38789i	−0.0248871	−	0.0143686i
$53$	−121.612	−	70.2126i	−0.315182	−	0.181971i	0.334061	−	0.942552i	$-0.391581\pi$
$53$	−121.612	−	70.2126i	−0.315182	−	0.181971i	−0.649243	+	0.760581i	$0.724914\pi$
$54$	327.273	−	218.834i	0.824745	−	0.551472i
$55$			139.078i			0.340969i
$56$	−318.022	−	277.825i	−0.758884	−	0.662963i
$57$	−7.27597	−	331.774i	−0.0169075	−	0.770958i
$58$	−113.132	−	195.951i	−0.256120	−	0.443613i
$59$	−443.739	+	768.579i	−0.979151	+	1.69594i	−0.313657	+	0.949536i	$0.601554\pi$
$59$	−443.739	+	768.579i	−0.979151	+	1.69594i	−0.665494	+	0.746403i	$0.731779\pi$
$60$	−1.56666	+	2.85639i	−0.00337091	+	0.00614596i
$61$	98.2925	−	56.7492i	0.206313	−	0.119115i	−0.393284	−	0.919417i	$-0.628661\pi$
$61$	98.2925	−	56.7492i	0.206313	−	0.119115i	0.599597	+	0.800302i	$0.295328\pi$
$62$	871.453			1.78507
$63$	494.388	+	75.0157i	0.988683	+	0.150017i
$64$	−519.772			−1.01518
$65$	372.113	−	214.839i	0.710075	−	0.409962i
$66$	195.044	−	355.612i	0.363762	−	0.663224i
$67$	130.409	−	225.874i	0.237790	−	0.411865i	−0.722290	−	0.691591i	$-0.756910\pi$
$67$	130.409	−	225.874i	0.237790	−	0.411865i	0.960080	+	0.279726i	$0.0902436\pi$
$68$	2.28996	+	3.96633i	0.00408380	+	0.00707336i
$69$	13.2797	+	605.534i	0.0231693	+	1.05649i
$70$	245.905	−	83.9975i	0.419875	−	0.143423i
$71$			390.768i			0.653178i	0.945166	+	0.326589i	$0.105899\pi$
$71$			390.768i			0.653178i	−0.945166	+	0.326589i	$0.894101\pi$
$72$	519.147	−	330.895i	0.849752	−	0.541615i
$73$	−183.140	−	105.736i	−0.293629	−	0.169527i	0.345948	−	0.938254i	$-0.387557\pi$
$73$	−183.140	−	105.736i	−0.293629	−	0.169527i	−0.639577	+	0.768727i	$0.720891\pi$
$74$	−199.307	−	115.070i	−0.313095	−	0.180765i
$75$	−67.4029	−	111.049i	−0.103774	−	0.170971i
$76$		−	8.00829i		−	0.0120870i
$77$	487.497	−	166.522i	0.721499	−	0.246454i
$78$	−1252.75	+	27.4735i	−1.81854	+	0.0398816i
$79$	529.006	+	916.266i	0.753390	+	1.30491i	0.946171	+	0.323669i	$0.104916\pi$
$79$	529.006	+	916.266i	0.753390	+	1.30491i	−0.192780	+	0.981242i	$0.561750\pi$
$80$	157.453	−	272.716i	0.220047	−	0.381133i
$81$	−307.797	+	660.834i	−0.422218	+	0.906494i
$82$	−208.695	+	120.490i	−0.281055	+	0.162267i
$83$	1000.70			1.32338			0.661691	−	0.749777i	$-0.269839\pi$
$83$	1000.70			1.32338			0.661691	+	0.749777i	$0.269839\pi$
$84$	11.8880	+	2.07142i	0.0154415	+	0.00269060i
$85$	−182.622			−0.233037
$86$	−228.950	+	132.184i	−0.287073	+	0.165742i
$87$	367.345	+	201.480i	0.452684	+	0.248286i
$88$	317.116	−	549.261i	0.384144	−	0.665357i
$89$	−490.935	−	850.325i	−0.584708	−	1.01274i	−0.994912	−	0.100750i	$-0.967876\pi$
$89$	−490.935	−	850.325i	−0.584708	−	1.01274i	0.410204	−	0.911994i	$-0.365458\pi$
$90$	16.6080	+	378.469i	0.0194515	+	0.443268i
$91$	−1198.59	−	1047.10i	−1.38073	−	1.20621i
$92$			14.6162i			0.0165636i
$93$	−1379.44	+	837.274i	−1.53808	+	0.933562i
$94$	968.549	+	559.192i	1.06275	+	0.613577i
$95$	276.545	+	159.663i	0.298662	+	0.172433i
$96$	25.2042	−	15.2981i	0.0267958	−	0.0162641i
$97$			1695.07i			1.77431i	0.461471	+	0.887155i	$0.347322\pi$
$97$			1695.07i			1.77431i	−0.461471	+	0.887155i	$0.652678\pi$
$98$	−588.856	−	761.373i	−0.606974	−	0.784799i
$99$	32.9248	+	750.301i	0.0334249	+	0.761698i
$100$	−1.56742	−	2.71485i	−0.00156742	−	0.00271485i
$101$	−425.895	+	737.672i	−0.419586	+	0.726744i	−0.995898	−	0.0904858i	$-0.971158\pi$
$101$	−425.895	+	737.672i	−0.419586	+	0.726744i	0.576312	+	0.817230i	$0.304491\pi$
$102$	466.950	+	256.111i	0.453284	+	0.248615i
$103$	464.853	−	268.383i	0.444692	−	0.256743i	−0.260894	−	0.965368i	$-0.584017\pi$
$103$	464.853	−	268.383i	0.444692	−	0.256743i	0.705586	+	0.708624i	$0.250684\pi$
$104$	−1959.44			−1.84749
$105$	−308.545	+	369.222i	−0.286771	+	0.343166i
$106$	−394.058			−0.361078
$107$	−302.571	+	174.690i	−0.273371	+	0.157831i	−0.630418	−	0.776255i	$-0.717117\pi$
$107$	−302.571	+	174.690i	−0.273371	+	0.157831i	0.357048	+	0.934086i	$0.383783\pi$
$108$	−7.77561	+	15.7805i	−0.00692785	+	0.0140600i
$109$	−451.455	+	781.943i	−0.396711	+	0.687124i	−0.993318	−	0.115410i	$-0.963182\pi$
$109$	−451.455	+	781.943i	−0.396711	+	0.687124i	0.596607	+	0.802534i	$0.296515\pi$
$110$	195.139	+	337.990i	0.169143	+	0.292965i
$111$	426.045	−	9.34339i	0.364310	−	0.00798950i
$112$	−1144.45	−	225.373i	−0.965536	−	0.190141i
$113$		−	593.728i		−	0.494277i	−0.968980	−	0.247138i	$-0.920510\pi$
$113$		−	593.728i		−	0.494277i	0.968980	−	0.247138i	$-0.0794902\pi$
$114$	−483.190	−	796.075i	−0.396973	−	0.654028i
$115$	−504.733	−	291.408i	−0.409275	−	0.236295i
$116$	8.75602	+	5.05529i	0.00700841	+	0.00404631i
$117$	1956.62	−	1247.11i	1.54606	−	0.985430i
$118$			2490.42i			1.94289i
$119$	218.658	+	640.127i	0.168440	+	0.493112i
$120$	12.9884	+	592.252i	0.00988059	+	0.450541i
$121$	−278.644	−	482.626i	−0.209350	−	0.362604i
$122$	159.248	−	275.826i	0.118177	−	0.204689i
$123$	214.584	−	391.237i	0.157304	−	0.286802i
$124$	−33.7236	+	19.4704i	−0.0244232	+	0.0141007i
$125$	125.000			0.0894427
$126$	1306.72	−	511.365i	0.923907	−	0.361556i
$127$	1046.00			0.730846			0.365423	−	0.930842i	$-0.380924\pi$
$127$	1046.00			0.730846			0.365423	+	0.930842i	$0.380924\pi$
$128$	−1223.85	+	706.588i	−0.845107	+	0.487923i
$129$	235.410	−	429.208i	0.160672	−	0.292943i
$130$	602.876	−	1044.21i	0.406737	−	0.704489i
$131$	−825.312	−	1429.48i	−0.550442	−	0.953393i	−0.998243	−	0.0592598i	$-0.981126\pi$
$131$	−825.312	−	1429.48i	−0.550442	−	0.953393i	0.447801	−	0.894133i	$-0.352207\pi$
$132$	0.397365	+	18.1193i	0.000262017	+	0.0119476i
$133$	228.537	−	1160.51i	0.148998	−	0.756612i
$134$		−	731.898i		−	0.471838i
$135$	−389.915	−	583.131i	−0.248582	−	0.371762i
$136$	721.229	+	416.402i	0.454742	+	0.262545i
$137$	1238.14	+	714.842i	0.772129	+	0.445789i	0.833634	−	0.552318i	$-0.186256\pi$
$137$	1238.14	+	714.842i	0.772129	+	0.445789i	−0.0615043	+	0.998107i	$0.519590\pi$
$138$	881.889	+	1452.95i	0.543996	+	0.896254i
$139$		−	2068.52i		−	1.26223i	−0.775691	−	0.631113i	$-0.782599\pi$
$139$		−	2068.52i		−	1.26223i	0.775691	−	0.631113i	$-0.217401\pi$
$140$	−7.63937	+	8.74466i	−0.00461174	+	0.00527899i
$141$	−2070.40	+	45.4049i	−1.23659	+	0.0271190i
$142$	548.281	+	949.651i	0.324019	+	0.561218i
$143$	1195.18	−	2070.11i	0.698923	−	1.21057i
$144$	784.866	−	1508.53i	0.454205	−	0.872990i
$145$	−349.142	+	201.577i	−0.199963	+	0.115449i
$146$	−593.426			−0.336386
$147$	1663.62	+	639.433i	0.933425	+	0.358773i
$148$	10.2838			0.00571163
$149$	1879.74	−	1085.27i	1.03352	−	0.596702i	0.115527	−	0.993304i	$-0.463144\pi$
$149$	1879.74	−	1085.27i	1.03352	−	0.596702i	0.917990	+	0.396602i	$0.129811\pi$
$150$	−319.615	−	175.301i	−0.173976	−	0.0954217i
$151$	124.075	−	214.904i	0.0668679	−	0.115819i	−0.830653	−	0.556790i	$-0.812033\pi$
$151$	124.075	−	214.904i	0.0668679	−	0.115819i	0.897521	+	0.440972i	$0.145366\pi$
$152$	−728.105	−	1261.12i	−0.388534	−	0.672960i
$153$	−985.212	+	43.2332i	−0.520586	+	0.0228444i
$154$	951.079	−	1088.68i	0.497663	−	0.569667i
$155$		−	1552.74i		−	0.804640i
$156$	47.8655	−	29.0527i	0.0245661	−	0.0149108i
$157$	936.894	+	540.916i	0.476256	+	0.274967i	0.718855	−	0.695160i	$-0.244666\pi$
$157$	936.894	+	540.916i	0.476256	+	0.274967i	−0.242599	+	0.970127i	$0.578000\pi$
$158$	2571.20	+	1484.48i	1.29464	+	0.747463i
$159$	623.763	−	378.603i	0.311117	−	0.188837i
$160$			28.3706i			0.0140181i
$161$	−417.113	+	2118.10i	−0.204181	+	1.03683i
$162$	179.194	+	2037.84i	0.0869063	+	0.988318i
$163$	1562.95	+	2707.12i	0.751043	+	1.30085i	0.947317	+	0.320296i	$0.103782\pi$
$163$	1562.95	+	2707.12i	0.751043	+	1.30085i	−0.196274	+	0.980549i	$0.562884\pi$
$164$	5.38408	−	9.32550i	0.00256357	−	0.00444024i
$165$	−633.624	−	347.527i	−0.298955	−	0.163969i
$166$	2431.91	−	1404.06i	1.13706	−	0.656485i
$167$	−2280.34			−1.05664			−0.528318	−	0.849047i	$-0.677177\pi$
$167$	−2280.34			−1.05664			−0.528318	+	0.849047i	$0.677177\pi$
$168$	2060.41	−	754.644i	0.946214	−	0.346560i
$169$	−5187.95			−2.36138
$170$	−443.812	+	256.235i	−0.200228	+	0.115602i
$171$	1529.71	+	795.885i	0.684091	+	0.355923i
$172$	5.90663	−	10.2306i	0.00261847	−	0.00453532i
$173$	−1382.85	−	2395.16i	−0.607721	−	1.05260i	−0.991615	−	0.129227i	$-0.958750\pi$
$173$	−1382.85	−	2395.16i	−0.607721	−	1.05260i	0.383894	−	0.923377i	$-0.374583\pi$
$174$	1175.42	−	25.7776i	0.512117	−	0.0112310i
$175$	−149.666	−	438.150i	−0.0646495	−	0.189263i
$176$		−	1751.86i		−	0.750293i
$177$	−2392.74	−	3942.14i	−1.01610	−	1.67406i
$178$	−2386.16	−	1377.65i	−1.00478	−	0.580108i
$179$	−40.5047	−	23.3854i	−0.0169132	−	0.00976485i	0.491520	−	0.870867i	$-0.336442\pi$
$179$	−40.5047	−	23.3854i	−0.0169132	−	0.00976485i	−0.508433	+	0.861102i	$0.669775\pi$
$180$	−9.09861	−	14.2750i	−0.00376761	−	0.00591109i
$181$		−	2972.20i		−	1.22056i	−0.792185	−	0.610281i	$-0.791057\pi$
$181$		−	2972.20i		−	1.22056i	0.792185	−	0.610281i	$-0.208943\pi$
$182$	−4382.01	−	862.940i	−1.78470	−	0.351458i
$183$	12.9305	+	589.614i	0.00522323	+	0.238172i
$184$	1328.89	+	2301.71i	0.532431	+	0.922197i
$185$	−205.030	+	355.123i	−0.0814818	+	0.141131i
$186$	−2177.58	+	3970.23i	−0.858428	+	1.56512i
$187$	−879.840	+	507.976i	−0.344066	+	0.198646i
$188$	−49.9748			−0.0193872
$189$	−1577.13	+	2064.93i	−0.606982	+	0.794715i
$190$	896.086			0.342152
$191$	−1299.10	+	750.038i	−0.492146	+	0.284140i	−0.725464	−	0.688260i	$-0.758375\pi$
$191$	−1299.10	+	750.038i	−0.492146	+	0.284140i	0.233318	+	0.972400i	$0.425042\pi$
$192$	1298.80	−	2368.02i	0.488191	−	0.890088i
$193$	1372.79	−	2377.75i	0.512000	−	0.886809i	−0.487904	−	0.872898i	$-0.662238\pi$
$193$	1372.79	−	2377.75i	0.512000	−	0.886809i	0.999903	−	0.0139118i	$-0.00442842\pi$
$194$	2378.33	+	4119.38i	0.880175	+	1.52451i
$195$	48.9519	+	2232.14i	0.0179770	+	0.819727i
$196$	39.7986	+	16.3073i	0.0145038	+	0.00594289i
$197$		−	965.562i		−	0.349205i	−0.984639	−	0.174603i	$-0.944136\pi$
$197$		−	965.562i		−	0.349205i	0.984639	−	0.174603i	$-0.0558641\pi$
$198$	1132.75	+	1777.20i	0.406571	+	0.637878i
$199$	1443.98	+	833.685i	0.514379	+	0.296977i	0.734632	−	0.678466i	$-0.237355\pi$
$199$	1443.98	+	833.685i	0.514379	+	0.296977i	−0.220253	+	0.975443i	$0.570688\pi$
$200$	−493.662	−	285.016i	−0.174536	−	0.100768i
$201$	703.193	+	1158.54i	0.246763	+	0.406552i
$202$			2390.27i			0.832569i
$203$	1124.60	+	982.458i	0.388826	+	0.339680i
$204$	−23.7923	+	0.521776i	−0.00816565	+	0.000179077i
$205$	214.688	+	371.850i	0.0731436	+	0.126688i
$206$	753.129	−	1304.46i	0.254723	−	0.441194i
$207$	−2791.93	−	1452.60i	−0.937450	−	0.487743i
$208$	−4687.22	+	2706.17i	−1.56250	+	0.902110i
$209$	1776.46			0.587943
$210$	−231.781	+	1330.21i	−0.0761640	+	0.437109i
$211$	3997.61			1.30430			0.652148	−	0.758091i	$-0.273868\pi$
$211$	3997.61			1.30430			0.652148	+	0.758091i	$0.273868\pi$
$212$	15.2493	−	8.80420i	0.00494022	−	0.00285224i
$213$	−1780.29	−	976.447i	−0.572693	−	0.314108i
$214$	−490.209	+	849.067i	−0.156589	+	0.271220i
$215$	235.524	+	407.940i	0.0747099	+	0.129401i
$216$	210.277	+	3192.01i	0.0662385	+	1.00550i
$217$	−5442.67	+	1859.14i	−1.70264	+	0.581596i
$218$			2533.72i			0.787180i
$219$	939.348	−	570.152i	0.289841	−	0.175924i
$220$	−15.1030	−	8.71975i	−0.00462840	−	0.00267221i
$221$	2718.24	+	1569.38i	0.827370	+	0.477682i
$222$	1022.27	−	620.485i	0.309056	−	0.187587i
$223$		−	2415.43i		−	0.725332i	−0.931919	−	0.362666i	$-0.881867\pi$
$223$		−	2415.43i		−	0.725332i	0.931919	−	0.362666i	$-0.118133\pi$
$224$	99.4447	−	33.9689i	0.0296626	−	0.0101323i
$225$	674.351	−	29.5919i	0.199808	−	0.00876798i
$226$	−833.052	−	1442.89i	−0.245194	−	0.424688i
$227$	−2731.73	+	4731.50i	−0.798728	+	1.38344i	0.121716	+	0.992565i	$0.461160\pi$
$227$	−2731.73	+	4731.50i	−0.798728	+	1.38344i	−0.920445	+	0.390873i	$0.872173\pi$
$228$	36.4848	+	20.0110i	0.0105977	+	0.00581255i
$229$	−1834.84	+	1059.35i	−0.529475	+	0.305692i	−0.740803	−	0.671723i	$-0.765555\pi$
$229$	−1834.84	+	1059.35i	−0.529475	+	0.305692i	0.211328	+	0.977415i	$0.432221\pi$
$230$	−1635.48			−0.468872
$231$	−459.498	+	2637.08i	−0.130878	+	0.751114i
$232$	1838.49			0.520269
$233$	5622.64	−	3246.23i	1.58091	−	0.912738i	0.586181	−	0.810180i	$-0.300631\pi$
$233$	5622.64	−	3246.23i	1.58091	−	0.912738i	0.994727	−	0.102557i	$-0.0327025\pi$
$234$	3005.20	−	5776.05i	0.839556	−	1.61364i
$235$	996.360	−	1725.75i	0.276576	−	0.479044i
$236$	−55.6419	−	96.3747i	−0.0153474	−	0.0265824i
$237$	−5496.27	+	120.536i	−1.50642	+	0.0330365i
$238$	1429.54	+	1248.85i	0.389342	+	0.340130i
$239$		−	5184.62i		−	1.40320i	−0.712571	−	0.701600i	$-0.752469\pi$
$239$		−	5184.62i		−	1.40320i	0.712571	−	0.701600i	$-0.247531\pi$
$240$	849.022	+	1398.80i	0.228351	+	0.376216i
$241$	2579.58	+	1489.32i	0.689483	+	0.398073i	0.803418	−	0.595415i	$-0.203012\pi$
$241$	2579.58	+	1489.32i	0.689483	+	0.398073i	−0.113936	+	0.993488i	$0.536346\pi$
$242$	−1354.33	−	781.925i	−0.359751	−	0.207703i
$243$	−2241.56	−	3053.57i	−0.591755	−	0.806118i
$244$			14.2320i			0.00373405i
$245$	−1356.60	+	1049.22i	−0.353756	+	0.273600i
$246$	−27.4541	−	1251.87i	−0.00711549	−	0.324456i
$247$	−2744.16	−	4753.02i	−0.706909	−	1.22440i
$248$	−3540.45	+	6132.24i	−0.906527	+	1.57015i
$249$	−2500.53	+	4559.05i	−0.636404	+	1.16031i
$250$	303.777	−	175.386i	0.0768502	−	0.0443695i
$251$	3306.05			0.831377			0.415689	−	0.909507i	$-0.363541\pi$
$251$	3306.05			0.831377			0.415689	+	0.909507i	$0.363541\pi$
$252$	−39.1427	+	48.9843i	−0.00978477	+	0.0122449i
$253$	−3242.28			−0.805693
$254$	2542.00	−	1467.63i	0.627951	−	0.362548i
$255$	456.334	−	832.006i	0.112066	−	0.204322i
$256$	96.2783	−	166.759i	0.0235054	−	0.0407126i
$257$	1647.41	+	2853.40i	0.399855	+	0.692569i	0.993708	−	0.112005i	$-0.0357273\pi$
$257$	1647.41	+	2853.40i	0.399855	+	0.692569i	−0.593853	+	0.804574i	$0.702394\pi$
$258$	−30.1187	−	1373.37i	−0.00726786	−	0.331404i
$259$	1490.27	+	293.475i	0.357531	+	0.0704078i
$260$			53.8789i			0.0128516i
$261$	−1835.83	+	1170.12i	−0.435384	+	0.277505i
$262$	−4011.38	−	2315.97i	−0.945892	−	0.546111i
$263$	541.149	+	312.433i	0.126877	+	0.0732526i	0.562095	−	0.827072i	$-0.309995\pi$
$263$	541.149	+	312.433i	0.126877	+	0.0732526i	−0.435218	+	0.900325i	$0.643329\pi$
$264$	1709.96	+	2817.23i	0.398640	+	0.656775i
$265$			702.126i			0.162760i
$266$	−1072.91	−	3140.96i	−0.247309	−	0.724002i
$267$	5100.72	−	111.861i	1.16914	−	0.0256397i
$268$	16.3524	+	28.3231i	0.00372716	+	0.00645564i
$269$	−462.054	+	800.301i	−0.104728	+	0.181395i	−0.913627	−	0.406553i	$-0.866731\pi$
$269$	−462.054	+	800.301i	−0.104728	+	0.181395i	0.808899	+	0.587948i	$0.200064\pi$
$270$	−1765.76	−	870.050i	−0.398003	−	0.196109i
$271$	1455.03	−	840.059i	0.326149	−	0.188302i	−0.327981	−	0.944684i	$-0.606368\pi$
$271$	1455.03	−	840.059i	0.326149	−	0.188302i	0.654130	+	0.756382i	$0.273035\pi$
$272$	2300.35			0.512792
$273$	7765.48	−	2844.18i	1.72157	−	0.630541i
$274$	4011.94			0.884563
$275$	602.227	−	347.696i	0.132057	−	0.0762431i
$276$	−66.5899	−	36.5229i	−0.0145226	−	0.00796529i
$277$	−2112.42	+	3658.82i	−0.458206	+	0.793635i	−0.998866	−	0.0476055i	$-0.984841\pi$
$277$	−2112.42	+	3658.82i	−0.458206	+	0.793635i	0.540661	+	0.841241i	$0.318174\pi$
$278$	−2902.31	−	5026.95i	−0.626147	−	1.08452i
$279$	−367.589	−	8376.75i	−0.0788781	−	1.79750i
$280$	−407.963	+	2071.64i	−0.0870731	+	0.442157i
$281$			3709.92i			0.787598i	0.919197	+	0.393799i	$0.128839\pi$
$281$			3709.92i			0.787598i	−0.919197	+	0.393799i	$0.871161\pi$
$282$	−4967.81	+	3015.29i	−1.04904	+	0.636731i
$283$	2822.28	+	1629.44i	0.592817	+	0.342263i	0.766210	−	0.642590i	$-0.222140\pi$
$283$	2822.28	+	1629.44i	0.592817	+	0.342263i	−0.173394	+	0.984853i	$0.555473\pi$
$284$	−42.4350	−	24.4999i	−0.00886639	−	0.00511901i
$285$	−1418.43	+	860.942i	−0.294810	+	0.178940i
$286$		−	6707.76i		−	1.38685i
$287$	1046.36	−	1197.75i	0.215207	−	0.246344i
$288$	6.71634	+	153.054i	0.00137418	+	0.0313153i
$289$	1789.48	+	3099.47i	0.364234	+	0.630872i
$290$	−565.661	+	979.753i	−0.114540	+	0.198390i
$291$	−7722.53	−	4235.62i	−1.55568	−	0.853252i
$292$	22.9645	−	13.2586i	0.00460239	−	0.00265719i
$293$	3214.82			0.640995			0.320498	−	0.947249i	$-0.396150\pi$
$293$	3214.82			0.640995			0.320498	+	0.947249i	$0.396150\pi$
$294$	4940.15	−	780.248i	0.979984	−	0.154779i
$295$	4437.39			0.875779
$296$	1619.45	−	934.991i	0.318002	−	0.183599i
$297$	−3500.55	−	1724.84i	−0.683915	−	0.336988i
$298$	3045.45	−	5274.87i	0.592007	−	1.02539i
$299$	5008.47	+	8674.92i	0.968720	+	1.67787i
$300$	16.2852	−	0.357142i	0.00313408	−	6.87319e-5i
$301$	1147.91	−	1314.00i	0.219816	−	0.251619i
$302$		−	696.350i		−	0.132684i
$303$	−2296.53	−	3783.62i	−0.435419	−	0.717370i
$304$	−3483.42	−	2011.16i	−0.657198	−	0.379433i
$305$	−491.463	−	283.746i	−0.0922658	−	0.0532697i
$306$	−2333.62	+	1487.40i	−0.435961	+	0.277873i
$307$			2608.00i			0.484841i	0.970171	+	0.242421i	$0.0779414\pi$
$307$			2608.00i			0.484841i	−0.970171	+	0.242421i	$0.922059\pi$
$308$	−12.4812	+	63.3795i	−0.00230903	+	0.0117253i
$309$	61.1520	+	2788.45i	0.0112583	+	0.513363i
$310$	−2178.63	−	3773.50i	−0.399155	−	0.691356i
$311$	−1745.39	+	3023.10i	−0.318237	+	0.551203i	−0.980120	−	0.198404i	$-0.936424\pi$
$311$	−1745.39	+	3023.10i	−0.318237	+	0.551203i	0.661883	+	0.749607i	$0.269757\pi$
$312$	4896.23	−	8926.99i	0.888444	−	1.61984i
$313$	106.942	−	61.7431i	0.0193122	−	0.0111499i	−0.490313	−	0.871547i	$-0.663117\pi$
$313$	106.942	−	61.7431i	0.0193122	−	0.0111499i	0.509625	+	0.860397i	$0.329784\pi$
$314$	3035.81			0.545607
$315$	−911.143	−	2328.30i	−0.162975	−	0.416460i
$316$	−132.668			−0.0236175
$317$	−1236.29	+	713.773i	−0.219044	+	0.126465i	−0.605508	−	0.795840i	$-0.707030\pi$
$317$	−1236.29	+	713.773i	−0.219044	+	0.126465i	0.386463	+	0.922305i	$0.373697\pi$
$318$	984.666	−	1795.28i	0.173639	−	0.316586i
$319$	−1121.40	+	1942.32i	−0.196823	+	0.340907i
$320$	1299.43	+	2250.68i	0.227001	+	0.393177i
$321$	−39.8037	−	1814.99i	−0.00692094	−	0.315585i
$322$	1958.20	+	5732.69i	0.338902	+	0.992143i
$323$			2332.65i			0.401833i
$324$	−52.4647	−	74.8570i	−0.00899600	−	0.0128356i
$325$	−1860.56	−	1074.20i	−0.317555	−	0.183341i
$326$	7596.64	+	4385.92i	1.29061	+	0.745134i
$327$	−2434.35	−	4010.68i	−0.411681	−	0.678261i
$328$		−	1958.06i		−	0.329621i
$329$	−7242.05	−	1426.16i	−1.21358	−	0.238987i
$330$	−2027.46	+	44.4631i	−0.338205	+	0.00741701i
$331$	628.044	+	1087.80i	0.104291	+	0.180638i	0.913448	−	0.406954i	$-0.133409\pi$
$331$	628.044	+	1087.80i	0.104291	+	0.180638i	−0.809157	+	0.587592i	$0.800076\pi$
$332$	−62.7403	+	108.669i	−0.0103715	+	0.0179639i
$333$	−1022.03	+	1964.36i	−0.168189	+	0.323262i
$334$	−5541.73	+	3199.52i	−0.907874	+	0.524161i
$335$	−1304.09			−0.212686
$336$	3886.50	−	4650.80i	0.631030	−	0.755125i
$337$	9967.19			1.61112			0.805560	−	0.592514i	$-0.201865\pi$
$337$	9967.19			1.61112			0.805560	+	0.592514i	$0.201865\pi$
$338$	−12607.9	+	7279.15i	−2.02893	+	1.17140i
$339$	2704.96	+	1483.60i	0.433372	+	0.237694i
$340$	11.4498	−	19.8317i	0.00182633	−	0.00316330i
$341$	−4319.06	−	7480.82i	−0.685894	−	1.18800i
$342$	4834.21	−	212.135i	0.764340	−	0.0335408i
$343$	5302.00	+	3498.91i	0.834639	+	0.550797i
$344$		−	2148.10i		−	0.336680i
$345$	2588.84	−	1571.34i	0.403996	−	0.245212i
$346$	−6721.23	−	3880.50i	−1.04432	−	0.602940i
$347$	−1070.64	−	618.133i	−0.165634	−	0.0956286i	0.414892	−	0.909871i	$-0.363819\pi$
$347$	−1070.64	−	618.133i	−0.165634	−	0.0956286i	−0.580525	+	0.814242i	$0.697153\pi$
$348$	−44.9107	+	27.2593i	−0.00691801	+	0.00419900i
$349$		−	5146.90i		−	0.789419i	−0.918806	−	0.394709i	$-0.870845\pi$
$349$		−	5146.90i		−	0.789419i	0.918806	−	0.394709i	$-0.129155\pi$
$350$	−978.482	−	854.805i	−0.149434	−	0.130546i
$351$	792.513	+	12030.4i	0.120516	+	1.82944i
$352$	78.9148	+	136.685i	0.0119494	+	0.0206969i
$353$	−2739.65	+	4745.21i	−0.413078	+	0.715473i	−0.995225	−	0.0976115i	$-0.968880\pi$
$353$	−2739.65	+	4745.21i	−0.413078	+	0.715473i	0.582146	+	0.813084i	$0.302213\pi$
$354$	−11346.0	−	6223.03i	−1.70349	−	0.934322i
$355$	1692.08	−	976.920i	0.252975	−	0.146055i
$356$	123.120			0.0183296
$357$	−3462.72	−	603.362i	−0.513352	−	0.0894490i
$358$	−131.247			−0.0193760
$359$	6276.82	−	3623.92i	0.922779	−	0.532767i	0.0382584	−	0.999268i	$-0.487819\pi$
$359$	6276.82	−	3623.92i	0.922779	−	0.532767i	0.884521	+	0.466501i	$0.154486\pi$
$360$	−2730.68	−	1420.74i	−0.399777	−	0.207999i
$361$	−1390.11	+	2407.74i	−0.202669	+	0.351034i
$362$	−4170.25	−	7223.08i	−0.605479	−	1.04872i
$363$	2895.06	−	63.4901i	0.418599	−	0.00918008i
$364$	188.856	−	64.5105i	0.0271944	−	0.00928920i
$365$			1057.36i			0.151629i
$366$	858.703	+	1414.75i	0.122637	+	0.202049i
$367$	6955.56	+	4015.79i	0.989311	+	0.571179i	0.905068	−	0.425266i	$-0.139820\pi$
$367$	6955.56	+	4015.79i	0.989311	+	0.571179i	0.0842427	+	0.996445i	$0.473153\pi$
$368$	6357.73	+	3670.64i	0.900597	+	0.519960i
$369$	1246.23	+	1955.24i	0.175816	+	0.275841i
$370$			1150.70i			0.161681i
$371$	2461.09	−	840.673i	0.344403	−	0.117643i
$372$	−4.43639	−	202.293i	−0.000618323	−	0.0281947i
$373$	2282.32	+	3953.10i	0.316821	+	0.548750i	0.979823	−	0.199868i	$-0.0640512\pi$
$373$	2282.32	+	3953.10i	0.316821	+	0.548750i	−0.663002	+	0.748618i	$0.730718\pi$
$374$	−1425.47	+	2468.98i	−0.197083	+	0.341359i
$375$	−312.349	+	569.485i	−0.0430123	+	0.0784216i
$376$	−7869.84	+	4543.65i	−1.07940	+	0.623194i
$377$	6929.08			0.946593
$378$	−935.509	+	7231.07i	−0.127295	+	0.983932i
$379$	−1417.61			−0.192131			−0.0960654	−	0.995375i	$-0.530626\pi$
$379$	−1417.61			−0.192131			−0.0960654	+	0.995375i	$0.530626\pi$
$380$	−34.6769	+	20.0207i	−0.00468128	+	0.00270274i
$381$	−2613.73	+	4765.45i	−0.351458	+	0.640791i
$382$	−2104.74	+	3645.51i	−0.281905	+	0.488273i
$383$	−3347.60	−	5798.21i	−0.446617	−	0.773563i	0.551546	−	0.834144i	$-0.314038\pi$
$383$	−3347.60	−	5798.21i	−0.446617	−	0.773563i	−0.998163	+	0.0605810i	$0.980705\pi$
$384$	−160.999	−	7341.31i	−0.0213956	−	0.975611i
$385$	−1939.80	−	1694.62i	−0.256783	−	0.224327i
$386$		−	7704.60i		−	1.01594i
$387$	1367.18	+	2145.00i	0.179581	+	0.281748i
$388$	−184.074	−	106.275i	−0.0240849	−	0.0139054i
$389$	−4110.14	−	2372.99i	−0.535714	−	0.309294i	0.207626	−	0.978208i	$-0.433426\pi$
$389$	−4110.14	−	2372.99i	−0.535714	−	0.309294i	−0.743340	+	0.668914i	$0.766760\pi$
$390$	3250.85	+	5355.90i	0.422085	+	0.695401i
$391$		−	4257.41i		−	0.550655i
$392$	7749.97	−	1050.43i	0.998552	−	0.135344i
$393$	8574.84	−	188.050i	1.10062	−	0.0241371i
$394$	−1354.77	−	2346.53i	−0.173229	−	0.300041i
$395$	2645.03	−	4581.33i	0.336926	−	0.583574i
$396$	−83.5423	−	43.4659i	−0.0106014	−	0.00551577i
$397$	−6938.85	+	4006.14i	−0.877206	+	0.506455i	−0.869736	−	0.493517i	$-0.835711\pi$
$397$	−6938.85	+	4006.14i	−0.877206	+	0.506455i	−0.00746972	+	0.999972i	$0.502378\pi$
$398$	4678.93			0.589280
$399$	4716.10	+	3941.07i	0.591730	+	0.494487i
$400$	−1574.53			−0.196816
$401$	2244.94	−	1296.12i	0.279569	−	0.161409i	−0.353659	−	0.935374i	$-0.615063\pi$
$401$	2244.94	−	1296.12i	0.279569	−	0.161409i	0.633228	+	0.773965i	$0.281729\pi$
$402$	3334.44	+	1828.86i	0.413698	+	0.226903i
$403$	−13343.6	+	23111.8i	−1.64936	+	2.85678i
$404$	−53.4045	−	92.4992i	−0.00657666	−	0.0113911i
$405$	3630.99	−	319.286i	0.445495	−	0.0391739i
$406$	4111.51	+	809.670i	0.502588	+	0.0989735i
$407$			2281.22i			0.277828i
$408$	−3699.28	+	2245.33i	−0.448876	+	0.272452i
$409$	−261.391	−	150.914i	−0.0316014	−	0.0182451i	0.484116	−	0.875004i	$-0.339141\pi$
$409$	−261.391	−	150.914i	−0.0316014	−	0.0182451i	−0.515717	+	0.856759i	$0.672475\pi$
$410$	1043.48	+	602.451i	0.125692	+	0.0725681i
$411$	−6350.60	+	3854.60i	−0.762170	+	0.462611i
$412$			67.3069i			0.00804848i
$413$	−5313.00	−	15553.9i	−0.633016	−	1.85317i
$414$	−8823.11	+	387.176i	−1.04742	+	0.0459630i
$415$	−2501.74	−	4333.14i	−0.295917	−	0.512543i
$416$	243.805	−	422.283i	0.0287345	−	0.0497696i
$417$	9423.92	+	5168.79i	1.10669	+	0.606994i
$418$	4317.18	−	2492.52i	0.505167	−	0.291659i
$419$	−10783.5			−1.25730			−0.628649	−	0.777689i	$-0.716392\pi$
$419$	−10783.5			−1.25730			−0.628649	+	0.777689i	$0.716392\pi$
$420$	−20.7505	−	56.6551i	−0.00241076	−	0.00658211i
$421$	−5534.80			−0.640735			−0.320368	−	0.947293i	$-0.603806\pi$
$421$	−5534.80			−0.640735			−0.320368	+	0.947293i	$0.603806\pi$
$422$	9715.05	−	5608.99i	1.12067	−	0.647017i
$423$	4966.63	−	9545.95i	0.570888	−	1.09726i
$424$	1600.94	−	2772.90i	0.183369	−	0.317604i
$425$	456.556	+	790.778i	0.0521087	+	0.0902549i
$426$	−5696.54	+	124.928i	−0.647883	+	0.0142084i
$427$	−406.146	+	2062.41i	−0.0460299	+	0.233740i
$428$		−	43.8098i		−	0.00494773i
$429$	6444.69	+	10617.9i	0.725297	+	1.19495i
$430$	1144.75	+	660.922i	0.128383	+	0.0741220i
$431$	6212.61	+	3586.85i	0.694318	+	0.400865i	0.805228	−	0.592966i	$-0.202043\pi$
$431$	6212.61	+	3586.85i	0.694318	+	0.400865i	−0.110910	+	0.993830i	$0.535376\pi$
$432$	4911.46	+	7345.25i	0.546997	+	0.818052i
$433$		−	10709.7i		−	1.18862i	−0.804235	−	0.594312i	$-0.797425\pi$
$433$		−	10709.7i		−	1.18862i	0.804235	−	0.594312i	$-0.202575\pi$
$434$	−10618.3	+	12154.6i	−1.17442	+	1.34434i
$435$	−45.9301	−	2094.35i	−0.00506248	−	0.230842i
$436$	−56.6094	−	98.0504i	−0.00621812	−	0.0107701i
$437$	−3722.17	+	6446.99i	−0.407450	+	0.705724i
$438$	1482.85	−	2703.58i	0.161765	−	0.294936i
$439$	10964.7	−	6330.49i	1.19207	−	0.688241i	0.233293	−	0.972407i	$-0.425050\pi$
$439$	10964.7	−	6330.49i	1.19207	−	0.688241i	0.958775	+	0.284166i	$0.0917166\pi$
$440$	−3171.16			−0.343589
$441$	−7070.23	+	5981.47i	−0.763441	+	0.645877i
$442$	8807.89			0.947848
$443$	−11816.8	+	6822.43i	−1.26734	+	0.731701i	−0.974485	−	0.224454i	$-0.927940\pi$
$443$	−11816.8	+	6822.43i	−1.26734	+	0.731701i	−0.292859	+	0.956156i	$0.594607\pi$
$444$	−25.6970	+	46.8517i	−0.00274668	+	0.00500785i
$445$	−2454.68	+	4251.62i	−0.261489	+	0.452913i
$446$	−3389.05	−	5870.01i	−0.359812	−	0.623213i
$447$	247.282	+	11275.7i	0.0261656	+	1.19312i
$448$	6333.23	−	7249.55i	0.667895	−	0.764529i
$449$		−	14986.9i		−	1.57523i	−0.616170	−	0.787613i	$-0.711317\pi$
$449$		−	14986.9i		−	1.57523i	0.616170	−	0.787613i	$-0.288683\pi$
$450$	1597.30	−	1018.09i	0.167328	−	0.106651i
$451$	2068.65	+	1194.34i	0.215984	+	0.124699i
$452$	64.4752	+	37.2248i	0.00670943	+	0.00387369i
$453$	669.039	+	1102.27i	0.0693912	+	0.114325i
$454$			15331.4i			1.58489i
$455$	−1537.57	+	7807.81i	−0.158423	+	0.804474i
$456$	7564.87	−	165.901i	0.776881	−	0.0170374i
$457$	−3558.68	−	6163.82i	−0.364263	−	0.630922i	0.624395	−	0.781109i	$-0.285346\pi$
$457$	−3558.68	−	6163.82i	−0.364263	−	0.630922i	−0.988658	+	0.150187i	$0.952012\pi$
$458$	−2972.71	+	5148.88i	−0.303287	+	0.525309i
$459$	2264.87	−	4596.54i	0.230316	−	0.467425i
$460$	63.2902	−	36.5406i	0.00641504	−	0.00370373i
$461$	−13314.0			−1.34511			−0.672554	−	0.740048i	$-0.734803\pi$
$461$	−13314.0			−1.34511			−0.672554	+	0.740048i	$0.734803\pi$
$462$	2583.37	+	7053.40i	0.260150	+	0.710289i
$463$	−4293.87			−0.431000			−0.215500	−	0.976504i	$-0.569138\pi$
$463$	−4293.87			−0.431000			−0.215500	+	0.976504i	$0.569138\pi$
$464$	4397.87	−	2539.11i	0.440013	−	0.254042i
$465$	7074.11	+	3879.97i	0.705492	+	0.386945i
$466$	9109.49	−	15778.1i	0.905556	−	1.56847i
$467$	2815.93	+	4877.34i	0.279027	+	0.483290i	0.971143	−	0.238497i	$-0.0766546\pi$
$467$	2815.93	+	4877.34i	0.279027	+	0.483290i	−0.692116	+	0.721786i	$0.743321\pi$
$468$	12.7550	+	290.666i	0.00125983	+	0.0287095i
$469$	1561.41	+	4571.08i	0.153730	+	0.450049i
$470$		−	5591.92i		−	0.548800i
$471$	−4805.45	+	2916.74i	−0.470113	+	0.285343i
$472$	−17524.6	−	10117.8i	−1.70897	−	0.986674i
$473$	2269.42	+	1310.25i	0.220609	+	0.127369i
$474$	−13188.0	+	8004.67i	−1.27794	+	0.775668i
$475$		−	1596.63i		−	0.154229i
$476$	−83.2230	−	16.3889i	−0.00801370	−	0.00157812i
$477$	166.218	+	3787.84i	0.0159552	+	0.363591i
$478$	−7274.47	−	12599.7i	−0.696080	−	1.20565i
$479$	−1528.74	+	2647.85i	−0.145824	+	0.252575i	−0.929680	−	0.368368i	$-0.879917\pi$
$479$	−1528.74	+	2647.85i	−0.145824	+	0.252575i	0.783856	+	0.620943i	$0.213250\pi$
$480$	−129.253	−	70.8922i	−0.0122908	−	0.00674119i
$481$	6103.56	−	3523.89i	0.578582	−	0.334045i
$482$	8358.58			0.789882
$483$	−8607.53	−	7193.00i	−0.810883	−	0.677625i
$484$	69.8803			0.00656277
$485$	7339.86	−	4237.67i	0.687187	−	0.396748i
$486$	−9731.91	−	4275.73i	−0.908330	−	0.399077i
$487$	6763.76	−	11715.2i	0.629354	−	1.09007i	−0.358328	−	0.933596i	$-0.616653\pi$
$487$	6763.76	−	11715.2i	0.629354	−	1.09007i	0.987682	−	0.156477i	$-0.0500137\pi$
$488$	1293.95	+	2241.19i	0.120030	+	0.207898i
$489$	−16238.8	+	356.125i	−1.50173	+	0.0329336i
$490$	−1824.70	+	4453.25i	−0.168228	+	0.410566i
$491$			1703.15i			0.156542i	0.996932	+	0.0782709i	$0.0249399\pi$
$491$			1703.15i			0.156542i	−0.996932	+	0.0782709i	$0.975060\pi$
$492$	29.0322	+	47.8317i	0.00266031	+	0.00438297i
$493$	−2550.44	−	1472.50i	−0.232994	−	0.134519i
$494$	−13337.8	−	7700.58i	−1.21477	−	0.701347i
$495$	3166.59	−	2018.32i	0.287530	−	0.183266i
$496$			19558.7i			1.77059i
$497$	−5450.26	−	4761.37i	−0.491907	−	0.429732i
$498$	319.921	+	14587.9i	0.0287871	+	1.31265i
$499$	−5574.26	−	9654.90i	−0.500077	−	0.866158i	−1.00000		8.83931e-5i	$-0.999972\pi$
$499$	−5574.26	−	9654.90i	−0.500077	−	0.866158i	0.499923	−	0.866070i	$-0.333361\pi$
$500$	−7.83708	+	13.5742i	−0.000700970	+	0.00121412i
$501$	5698.09	−	10389.0i	0.508128	−	0.926437i
$502$	8034.41	−	4638.67i	0.714329	−	0.412418i
$503$	−10859.4			−0.962616			−0.481308	−	0.876551i	$-0.659838\pi$
$503$	−10859.4			−0.962616			−0.481308	+	0.876551i	$0.659838\pi$
$504$	−1710.45	+	11272.7i	−0.151170	+	0.996279i
$505$	4258.95			0.375289
$506$	−7879.45	+	4549.20i	−0.692261	+	0.399677i
$507$	12963.6	−	23635.7i	1.13557	−	2.07041i
$508$	−65.5807	+	113.589i	−0.00572770	+	0.00992067i
$509$	2304.73	+	3991.90i	0.200698	+	0.347619i	0.948753	−	0.316017i	$-0.102346\pi$
$509$	2304.73	+	3991.90i	0.200698	+	0.347619i	−0.748056	+	0.663636i	$0.769012\pi$
$510$	−58.3840	−	2662.23i	−0.00506919	−	0.231148i
$511$	3706.25	−	1266.00i	0.320851	−	0.109598i
$512$		−	11845.8i		−	1.02249i
$513$	−7448.37	+	4980.41i	−0.641040	+	0.428636i
$514$	8007.13	+	4622.92i	0.687119	+	0.396709i
$515$	−2324.26	−	1341.91i	−0.198872	−	0.114819i
$516$	31.8499	+	52.4740i	0.00271728	+	0.00447682i
$517$		−	11085.8i		−	0.943040i
$518$	4033.44	−	1377.76i	0.342122	−	0.116864i
$519$	14367.5	−	315.086i	1.21515	−	0.0266488i
$520$	4898.61	+	8484.64i	0.413112	+	0.715531i
$521$	8384.02	−	14521.5i	0.705011	−	1.22111i	−0.261677	−	0.965155i	$-0.584276\pi$
$521$	8384.02	−	14521.5i	0.705011	−	1.22111i	0.966688	−	0.255959i	$-0.0823911\pi$
$522$	−2819.69	+	5419.49i	−0.236426	+	0.454415i
$523$	12237.3	−	7065.19i	1.02313	−	0.590706i	0.108123	−	0.994138i	$-0.465516\pi$
$523$	12237.3	−	7065.19i	1.02313	−	0.590706i	0.915010	+	0.403432i	$0.132183\pi$
$524$	206.977			0.0172554
$525$	2370.14	+	412.985i	0.197031	+	0.0343317i
$526$	1753.48			0.145352
$527$	9822.99	−	5671.31i	0.811947	−	0.468778i
$528$	7981.28	+	4377.53i	0.657842	+	0.360810i
$529$	709.982	−	1229.72i	0.0583531	−	0.101070i
$530$	985.144	+	1706.32i	0.0807395	+	0.139845i
$531$	23938.9	−	1050.49i	1.95642	−	0.0858518i
$532$	111.696	+	97.5781i	0.00910271	+	0.00795216i
$533$		−	7379.74i		−	0.599722i
$534$	12238.9	−	7428.60i	0.991815	−	0.601998i
$535$	1512.86	+	873.448i	0.122255	+	0.0705840i
$536$	5150.22	+	2973.48i	0.415029	+	0.239617i
$537$	207.754	−	126.100i	0.0166951	−	0.0101333i
$538$			2593.21i			0.207809i
$539$	−3617.40	+	8828.41i	−0.289077	+	0.705503i
$540$	87.7708	−	5.78198i	0.00699454	−	0.000460772i
$541$	1131.29	+	1959.45i	0.0899038	+	0.155718i	0.907470	−	0.420116i	$-0.138011\pi$
$541$	1131.29	+	1959.45i	0.0899038	+	0.155718i	−0.817567	+	0.575834i	$0.804677\pi$
$542$	2357.35	−	4083.05i	0.186821	−	0.323583i
$543$	13541.0	+	7426.89i	1.07016	+	0.586958i
$544$	−179.479	+	103.622i	−0.0141454	+	0.00816685i
$545$	4514.55			0.354829
$546$	14881.2	−	17807.6i	1.16640	−	1.39578i
$547$	−19607.6			−1.53265			−0.766325	−	0.642453i	$-0.777917\pi$
$547$	−19607.6			−1.53265			−0.766325	+	0.642453i	$0.777917\pi$
$548$	−155.255	+	89.6365i	−0.0121025	+	0.00698737i
$549$	−2718.52	−	1414.41i	−0.211336	−	0.109955i
$550$	975.694	−	1689.95i	0.0756432	−	0.131018i
$551$	2574.76	+	4459.61i	0.199072	+	0.344802i
$552$	−13806.9	+	302.793i	−1.06461	+	0.0233473i
$553$	−19225.4	−	3786.02i	−1.47839	−	0.291136i
$554$			11855.6i			0.909201i
$555$	−1105.57	−	1821.47i	−0.0845566	−	0.139310i
$556$	224.628	+	129.689i	0.0171337	+	0.00989217i
$557$	11749.7	+	6783.69i	0.893807	+	0.516040i	0.875186	−	0.483787i	$-0.160739\pi$
$557$	11749.7	+	6783.69i	0.893807	+	0.516040i	0.0186213	+	0.999827i	$0.494072\pi$
$558$	−12646.6	−	19841.6i	−0.959452	−	1.50530i
$559$		−	8095.98i		−	0.612564i
$560$	1885.22	+	5519.03i	0.142259	+	0.416467i
$561$	−115.744	−	5277.77i	−0.00871073	−	0.397197i
$562$	5205.33	+	9015.90i	0.390701	+	0.676713i
$563$	5510.60	−	9544.64i	0.412512	−	0.714491i	−0.582652	−	0.812722i	$-0.697985\pi$
$563$	5510.60	−	9544.64i	0.412512	−	0.714491i	0.995164	+	0.0982305i	$0.0313182\pi$
$564$	124.876	−	227.679i	0.00932313	−	0.0169983i
$565$	−2570.92	+	1484.32i	−0.191433	+	0.110524i
$566$	9145.00			0.679140
$567$	−5466.63	−	12345.0i	−0.404898	−	0.914362i
$568$	−8910.01			−0.658196
$569$	13470.2	−	7777.05i	0.992447	−	0.572989i	0.0864419	−	0.996257i	$-0.472450\pi$
$569$	13470.2	−	7777.05i	0.992447	−	0.572989i	0.906005	+	0.423268i	$0.139117\pi$
$570$	−2239.13	+	4082.46i	−0.164538	+	0.299992i
$571$	−10646.0	+	18439.3i	−0.780244	+	1.35142i	0.151555	+	0.988449i	$0.451572\pi$
$571$	−10646.0	+	18439.3i	−0.780244	+	1.35142i	−0.931799	+	0.362974i	$0.881762\pi$
$572$	149.868	+	259.578i	0.0109550	+	0.0189747i
$573$	−170.899	−	7792.75i	−0.0124597	−	0.568144i
$574$	862.331	−	4378.92i	0.0627055	−	0.318419i
$575$			2914.08i			0.211349i
$576$	7542.99	+	11834.4i	0.545644	+	0.856073i
$577$	9634.85	+	5562.68i	0.695154	+	0.401348i	0.805540	−	0.592541i	$-0.201875\pi$
$577$	9634.85	+	5562.68i	0.695154	+	0.401348i	−0.110386	+	0.993889i	$0.535209\pi$
$578$	8697.66	+	5021.60i	0.625908	+	0.361368i
$579$	7402.43	+	12195.8i	0.531320	+	0.875370i
$580$		−	50.5529i		−	0.00361913i
$581$	−12193.1	+	13957.3i	−0.870664	+	0.996635i
$582$	−24710.4	+	541.910i	−1.75993	+	0.0385961i
$583$	1953.01	+	3382.71i	0.138740	+	0.240305i
$584$	2410.91	−	4175.82i	0.170829	−	0.295885i
$585$	−10291.7	−	5354.62i	−0.727365	−	0.378438i
$586$	7812.71	−	4510.67i	0.550751	−	0.317976i
$587$	−8446.93			−0.593939			−0.296969	−	0.954887i	$-0.595976\pi$
$587$	−8446.93			−0.593939			−0.296969	+	0.954887i	$0.595976\pi$
$588$	−173.742	+	140.569i	−0.0121854	+	0.00985879i
$589$	−19833.3			−1.38746
$590$	10783.8	−	6226.04i	0.752480	−	0.434444i
$591$	4398.99	+	2412.74i	0.306176	+	0.167930i
$592$	2582.61	−	4473.21i	0.179298	−	0.310554i
$593$	−4553.02	−	7886.07i	−0.315296	−	0.546108i	0.664205	−	0.747551i	$-0.268770\pi$
$593$	−4553.02	−	7886.07i	−0.315296	−	0.546108i	−0.979500	+	0.201443i	$0.935437\pi$
$594$	−10927.2	+	719.840i	−0.754796	+	0.0497229i
$595$	2225.19	−	2547.14i	0.153317	−	0.175500i
$596$			272.171i			0.0187056i
$597$	−7406.38	+	4495.42i	−0.507744	+	0.308183i
$598$	24343.3	+	14054.6i	1.66467	+	0.961098i
$599$	−19603.3	−	11318.0i	−1.33718	−	0.772020i	−0.350790	−	0.936454i	$-0.614087\pi$
$599$	−19603.3	−	11318.0i	−1.33718	−	0.772020i	−0.986388	+	0.164434i	$0.947420\pi$
$600$	2532.05	−	1536.87i	0.172284	−	0.104571i
$601$			17057.3i			1.15770i	0.815433	+	0.578852i	$0.196499\pi$
$601$			17057.3i			1.15770i	−0.815433	+	0.578852i	$0.803501\pi$
$602$	946.024	−	4803.91i	0.0640483	−	0.325237i
$603$	−7035.29	+	308.723i	−0.475123	+	0.0208494i
$604$	15.5581	+	26.9475i	0.00104810	+	0.00181536i
$605$	−1393.22	+	2413.13i	−0.0936240	+	0.162162i
$606$	−10889.8	−	5972.78i	−0.729980	−	0.400376i
$607$	−9937.67	+	5737.52i	−0.664510	+	0.383655i	−0.793993	−	0.607927i	$-0.792001\pi$
$607$	−9937.67	+	5737.52i	−0.664510	+	0.383655i	0.129483	+	0.991582i	$0.458668\pi$
$608$	362.380			0.0241718
$609$	−7286.11	+	2668.61i	−0.484808	+	0.177566i
$610$	−1592.48			−0.105701
$611$	−29660.7	+	17124.6i	−1.96390	+	1.13386i
$612$	57.0747	−	109.699i	0.00376978	−	0.00724559i
$613$	445.189	−	771.089i	0.0293328	−	0.0508059i	−0.850986	−	0.525188i	$-0.823995\pi$
$613$	445.189	−	771.089i	0.0293328	−	0.0508059i	0.880319	+	0.474382i	$0.157328\pi$
$614$	3659.24	+	6338.00i	0.240513	+	0.416581i
$615$	−2230.56	+	48.9174i	−0.146252	+	0.00320738i
$616$	3796.91	+	11115.5i	0.248347	+	0.727042i
$617$			19376.2i			1.26427i	0.774858	+	0.632135i	$0.217821\pi$
$617$			19376.2i			1.26427i	−0.774858	+	0.632135i	$0.782179\pi$
$618$	4061.04	+	6690.73i	0.264335	+	0.435503i
$619$	−3199.16	−	1847.04i	−0.207731	−	0.119933i	0.392526	−	0.919741i	$-0.371601\pi$
$619$	−3199.16	−	1847.04i	−0.207731	−	0.119933i	−0.600256	+	0.799808i	$0.704935\pi$
$620$	168.618	+	97.3518i	0.0109224	+	0.00630603i
$621$	13594.3	−	9089.94i	0.878455	−	0.587386i
$622$			9795.71i			0.631466i
$623$	17841.8	+	3513.55i	1.14738	+	0.225951i
$624$	−616.609	−	28116.5i	−0.0395579	−	1.80379i
$625$	−312.500	−	541.266i	−0.0200000	−	0.0346410i
$626$	173.262	−	300.098i	0.0110622	−	0.0191603i
$627$	−4438.99	+	8093.33i	−0.282737	+	0.515497i
$628$	−117.480	+	67.8273i	−0.00746492	+	0.00430988i
$629$	−2995.45			−0.189883
$630$	−5481.08	−	4379.87i	−0.346622	−	0.276981i
$631$	−23709.8			−1.49584			−0.747919	−	0.663790i	$-0.768947\pi$
$631$	−23709.8			−1.49584			−0.747919	+	0.663790i	$0.768947\pi$
$632$	−20892.0	+	12062.0i	−1.31494	+	0.759179i
$633$	−9989.17	+	18212.6i	−0.627226	+	1.14358i
$634$	−2002.97	+	3469.25i	−0.125470	+	0.217321i
$635$	−2615.00	−	4529.31i	−0.163422	−	0.283055i
$636$	2.00607	+	91.4739i	0.000125072	+	0.00570311i
$637$	29208.9	−	3958.98i	1.81679	−	0.246249i
$638$			6293.69i			0.390548i
$639$	8897.15	−	5670.87i	0.550807	−	0.351074i
$640$	6119.23	+	3532.94i	0.377944	+	0.218206i
$641$	13606.1	+	7855.47i	0.838389	+	0.484044i	0.856716	−	0.515788i	$-0.172501\pi$
$641$	13606.1	+	7855.47i	0.838389	+	0.484044i	−0.0183271	+	0.999832i	$0.505834\pi$
$642$	−2643.32	−	4354.97i	−0.162498	−	0.267721i
$643$			18532.3i			1.13661i	0.822817	+	0.568306i	$0.192401\pi$
$643$			18532.3i			1.13661i	−0.822817	+	0.568306i	$0.807599\pi$
$644$	−203.861	−	178.094i	−0.0124740	−	0.0108973i
$645$	−2447.05	+	53.6650i	−0.149384	+	0.00327606i
$646$	3272.91	+	5668.84i	0.199336	+	0.345259i
$647$	−9934.33	+	17206.8i	−0.603646	+	1.04555i	0.388618	+	0.921399i	$0.372953\pi$
$647$	−9934.33	+	17206.8i	−0.603646	+	1.04555i	−0.992264	+	0.124146i	$0.960381\pi$
$648$	−15067.9	−	7018.16i	−0.913459	−	0.425462i
$649$	21378.5	−	12342.9i	1.29304	−	0.746535i
$650$	−6028.76			−0.363796
$651$	5130.07	−	29441.7i	0.308853	−	1.77252i
$652$	−391.968			−0.0235440
$653$	−6427.24	+	3710.77i	−0.385172	+	0.222379i	−0.680066	−	0.733151i	$-0.738049\pi$
$653$	−6427.24	+	3710.77i	−0.385172	+	0.222379i	0.294894	+	0.955530i	$0.404716\pi$
$654$	−11543.3	−	6331.23i	−0.690183	−	0.378549i
$655$	−4126.56	+	7147.41i	−0.246165	+	0.426370i
$656$	−2704.25	−	4683.91i	−0.160950	−	0.278774i
$657$	250.314	+	5704.25i	0.0148641	+	0.338727i
$658$	−19600.8	+	6695.34i	−1.16127	+	0.396674i
$659$			17588.3i			1.03967i	0.854267	+	0.519835i	$0.174007\pi$
$659$			17588.3i			1.03967i	−0.854267	+	0.519835i	$0.825993\pi$
$660$	77.4655	−	47.0189i	0.00456869	−	0.00277304i
$661$	−4632.70	−	2674.69i	−0.272604	−	0.157388i	0.357467	−	0.933926i	$-0.383641\pi$
$661$	−4632.70	−	2674.69i	−0.272604	−	0.157388i	−0.630070	+	0.776538i	$0.716974\pi$
$662$	3052.57	+	1762.40i	0.179217	+	0.103471i
$663$	−13942.2	+	8462.45i	−0.816698	+	0.495708i
$664$			22817.1i			1.33355i
$665$	−5596.52	+	1911.69i	−0.326351	+	0.111477i
$666$	272.412	+	6207.82i	0.0158495	+	0.361183i
$667$	−4699.29	−	8139.42i	−0.272800	−	0.472503i
$668$	142.970	−	247.631i	0.00828095	−	0.0143430i
$669$	11004.4	+	6035.64i	0.635956	+	0.348806i
$670$	−3169.21	+	1829.74i	−0.182742	+	0.105506i
$671$	−3157.03			−0.181633
$672$	−93.7332	+	537.940i	−0.00538071	+	0.0308802i
$673$	27375.7			1.56798			0.783992	−	0.620770i	$-0.213180\pi$
$673$	27375.7			1.56798			0.783992	+	0.620770i	$0.213180\pi$
$674$	24222.4	−	13984.8i	1.38429	−	0.799222i
$675$	−1550.24	+	3146.21i	−0.0883983	+	0.179404i
$676$	325.267	−	563.380i	0.0185063	−	0.0320539i
$677$	971.809	+	1683.22i	0.0551693	+	0.0955561i	0.892291	−	0.451460i	$-0.149097\pi$
$677$	971.809	+	1683.22i	0.0551693	+	0.0955561i	−0.837122	+	0.547017i	$0.815763\pi$
$678$	8655.25	−	189.814i	0.490270	−	0.0107519i
$679$	−23642.1	−	20653.8i	−1.33623	−	1.16733i
$680$		−	4164.02i		−	0.234828i
$681$	−14730.1	−	24268.4i	−0.828869	−	1.36559i
$682$	−20992.5	−	12120.0i	−1.17866	−	0.680498i
$683$	19324.1	+	11156.8i	1.08260	+	0.625039i	0.931597	−	0.363494i	$-0.118416\pi$
$683$	19324.1	+	11156.8i	1.08260	+	0.625039i	0.151003	+	0.988533i	$0.451750\pi$
$684$	−182.336	+	116.217i	−0.0101927	+	0.00649660i
$685$		−	7148.42i		−	0.398726i
$686$	17794.3	+	1063.95i	0.990363	+	0.0592155i
$687$	−241.376	−	11006.4i	−0.0134047	−	0.611238i
$688$	−2966.72	−	5138.50i	−0.164397	−	0.284744i
$689$	6033.77	−	10450.8i	0.333626	−	0.577858i
$690$	4086.72	−	7451.06i	0.225477	−	0.411097i
$691$	−16757.3	+	9674.84i	−0.922545	+	0.532631i	−0.884446	−	0.466643i	$-0.845463\pi$
$691$	−16757.3	+	9674.84i	−0.922545	+	0.532631i	−0.0380987	+	0.999274i	$0.512130\pi$
$692$	346.799			0.0190510
$693$	−10866.0	−	8682.93i	−0.595623	−	0.475955i
$694$	−3469.18			−0.189752
$695$	−8956.94	+	5171.29i	−0.488858	+	0.282242i
$696$	−4593.99	+	8375.92i	−0.250193	+	0.456162i
$697$	−1568.27	+	2716.32i	−0.0852259	+	0.147616i
$698$	−7221.54	−	12508.1i	−0.391604	−	0.678278i
$699$	739.666	+	33727.7i	0.0400239	+	1.82504i
$700$	56.9639	+	11.2178i	0.00307576	+	0.000605703i
$701$		−	28722.6i		−	1.54756i	−0.633457	−	0.773778i	$-0.718365\pi$
$701$		−	28722.6i		−	1.54756i	0.633457	−	0.773778i	$-0.281635\pi$
$702$	18805.6	+	28124.5i	1.01107	+	1.51209i
$703$	4536.01	+	2618.87i	0.243356	+	0.140501i
$704$	12520.8	+	7228.90i	0.670307	+	0.387002i
$705$	5372.60	+	8851.58i	0.287013	+	0.472865i
$706$			15375.8i			0.819656i
$707$	−5099.35	−	14928.5i	−0.271260	−	0.794120i
$708$	578.109	−	12.6782i	0.0306874	−	0.000672989i
$709$	6371.21	+	11035.3i	0.337483	+	0.584538i	0.983959	−	0.178397i	$-0.0570910\pi$
$709$	6371.21	+	11035.3i	0.337483	+	0.584538i	−0.646475	+	0.762935i	$0.723758\pi$
$710$	2741.41	−	4748.26i	0.144906	−	0.250984i
$711$	13184.9	−	25341.6i	0.695459	−	1.33668i
$712$	19388.5	−	11193.9i	1.02052	−	0.589200i
$713$	36198.5			1.90132
$714$	−9261.74	+	3392.20i	−0.485451	+	0.177801i
$715$	−11951.8			−0.625136
$716$	5.07902	−	2.93238i	0.000265101	−	0.000153056i
$717$	23620.5	+	12955.3i	1.23030	+	0.674788i
$718$	10169.3	−	17613.8i	0.528575	−	0.915518i
$719$	14977.1	+	25941.1i	0.776844	+	1.34553i	0.933752	+	0.357920i	$0.116514\pi$
$719$	14977.1	+	25941.1i	0.776844	+	1.34553i	−0.156908	+	0.987613i	$0.550153\pi$
$720$	−8494.28	+	372.747i	−0.439671	+	0.0192937i
$721$	−1920.78	+	9753.72i	−0.0992143	+	0.503810i
$722$			7801.77i			0.402149i
$723$	−13231.0	+	8030.76i	−0.680589	+	0.413094i
$724$	322.762	+	186.347i	0.0165682	+	0.00956564i
$725$	1745.71	+	1007.89i	0.0894263	+	0.0516303i
$726$	6946.55	−	4216.32i	0.355111	−	0.215540i
$727$		−	22314.5i		−	1.13837i	−0.822208	−	0.569187i	$-0.807258\pi$
$727$		−	22314.5i		−	1.13837i	0.822208	−	0.569187i	$-0.192742\pi$
$728$	23875.1	−	27329.5i	1.21548	−	1.39134i
$729$	19512.9	−	2582.07i	0.991358	−	0.131183i
$730$	1483.57	+	2569.61i	0.0752181	+	0.130282i
$731$	−1720.48	+	2979.96i	−0.0870509	+	0.150777i
$732$	−64.8391	−	35.5626i	−0.00327394	−	0.00179567i
$733$	20477.0	−	11822.4i	1.03183	−	0.595729i	0.114324	−	0.993443i	$-0.463530\pi$
$733$	20477.0	−	11822.4i	1.03183	−	0.595729i	0.917509	+	0.397714i	$0.130196\pi$
$734$	22538.0			1.13337
$735$	−1390.24	−	8802.29i	−0.0697682	−	0.441738i
$736$	−661.394			−0.0331241
$737$	−6282.84	+	3627.40i	−0.314018	+	0.181299i
$738$	5771.97	+	3003.08i	0.287899	+	0.149790i
$739$	11238.4	−	19465.6i	0.559422	−	0.968947i	−0.438123	−	0.898915i	$-0.644356\pi$
$739$	11238.4	−	19465.6i	0.559422	−	0.968947i	0.997545	−	0.0700321i	$-0.0223102\pi$
$740$	−25.7095	−	44.5301i	−0.00127716	−	0.00221211i
$741$	28511.3	−	625.266i	1.41348	−	0.0309983i
$742$	4801.45	−	5496.14i	0.237556	−	0.271927i
$743$			9463.03i			0.467247i	0.972327	+	0.233624i	$0.0750584\pi$
$743$			9463.03i			0.467247i	−0.972327	+	0.233624i	$0.924942\pi$
$744$	−19090.9	−	31453.0i	−0.940735	−	1.54990i
$745$	−9398.69	−	5426.34i	−0.462203	−	0.266853i
$746$	11093.1	+	6404.59i	0.544433	+	0.314328i
$747$	−14522.2	−	22784.2i	−0.711299	−	1.11597i
$748$		−	127.394i		−	0.00622724i
$749$	1250.23	−	6348.66i	0.0609911	−	0.309713i
$750$	39.9623	+	1822.22i	0.00194562	+	0.0887176i
$751$	−5562.36	−	9634.29i	−0.270271	−	0.468123i	0.698660	−	0.715454i	$-0.253780\pi$
$751$	−5562.36	−	9634.29i	−0.270271	−	0.468123i	−0.968931	+	0.247331i	$0.920447\pi$
$752$	−12550.4	+	21737.9i	−0.608597	+	1.05412i
$753$	−8261.11	+	15062.0i	−0.399803	+	0.728935i
$754$	16839.2	−	9722.09i	0.813324	−	0.469573i
$755$	−1240.75			−0.0598085
$756$	−125.357	−	300.731i	−0.00603068	−	0.0144676i
$757$	−8997.42			−0.431990			−0.215995	−	0.976394i	$-0.569300\pi$
$757$	−8997.42			−0.431990			−0.215995	+	0.976394i	$0.569300\pi$
$758$	−3445.09	+	1989.02i	−0.165081	+	0.0953095i
$759$	8101.77	−	14771.4i	0.387452	−	0.706416i
$760$	−3640.53	+	6305.58i	−0.173758	+	0.300957i
$761$	−3552.99	−	6153.96i	−0.169245	−	0.293142i	0.768909	−	0.639358i	$-0.220800\pi$
$761$	−3552.99	−	6153.96i	−0.169245	−	0.293142i	−0.938155	+	0.346216i	$0.887466\pi$
$762$	334.404	+	15248.4i	0.0158979	+	0.724921i
$763$	−5405.38	−	15824.4i	−0.256472	−	0.750827i
$764$		−	188.099i		−	0.00890733i
$765$	2650.24	+	4158.01i	0.125254	+	0.196514i
$766$	−16270.8	−	9393.94i	−0.767477	−	0.443103i
$767$	−66048.4	−	38133.1i	−3.10935	−	1.79518i
$768$	519.155	+	855.328i	0.0243924	+	0.0401875i
$769$		−	6684.54i		−	0.313460i	−0.987641	−	0.156730i	$-0.949905\pi$
$769$		−	6684.54i		−	0.313460i	0.987641	−	0.156730i	$-0.0500953\pi$
$770$	−7091.84	−	1396.58i	−0.331912	−	0.0653627i
$771$	−17116.3	+	375.368i	−0.799517	+	0.0175338i
$772$	172.139	+	298.154i	0.00802517	+	0.0139000i
$773$	−6796.83	+	11772.5i	−0.316255	+	0.547770i	−0.979703	−	0.200452i	$-0.935759\pi$
$773$	−6796.83	+	11772.5i	−0.316255	+	0.547770i	0.663449	+	0.748222i	$0.269092\pi$
$774$	6332.17	+	3294.54i	0.294064	+	0.152997i
$775$	−6723.57	+	3881.86i	−0.311636	+	0.179923i
$776$	−38649.7			−1.78794
$777$	−5060.89	+	6056.14i	−0.233666	+	0.279618i
$778$	−13318.1			−0.613722
$779$	4749.67	−	2742.22i	0.218452	−	0.126124i
$780$	−245.466	−	134.632i	−0.0112681	−	0.00618025i
$781$	5434.74	−	9413.24i	0.249002	−	0.431283i
$782$	−5973.51	−	10346.4i	−0.273161	−	0.473129i
$783$	−743.591	−	11287.7i	−0.0339384	−	0.515186i
$784$	17088.1	−	13216.2i	0.778429	−	0.602048i
$785$		−	5409.16i		−	0.245938i
$786$	20574.9	−	12488.2i	0.933691	−	0.566719i
$787$	29235.8	+	16879.3i	1.32420	+	0.764525i	0.984395	−	0.175972i	$-0.0563067\pi$
$787$	29235.8	+	16879.3i	1.32420	+	0.764525i	0.339802	+	0.940497i	$0.389640\pi$
$788$	104.854	+	60.5375i	0.00474019	+	0.00273675i
$789$	−2775.62	+	1684.71i	−0.125241	+	0.0760168i
$790$		−	14844.8i		−	0.668551i
$791$	8281.06	+	7234.37i	0.372239	+	0.325189i
$792$	−17107.8	+	750.726i	−0.767550	+	0.0336817i
$793$	4876.79	+	8446.84i	0.218386	+	0.378255i
$794$	−11241.9	+	19471.6i	−0.502470	+	0.870304i
$795$	−3198.80	−	1754.46i	−0.142704	−	0.0782697i
$796$	−181.066	+	104.539i	−0.00806246	+	0.00465486i
$797$	6735.51			0.299353			0.149676	−	0.988735i	$-0.452177\pi$
$797$	6735.51			0.299353			0.149676	+	0.988735i	$0.452177\pi$
$798$	16990.8	+	2960.56i	0.753719	+	0.131332i
$799$	14556.6			0.644525
$800$	122.849	−	70.9266i	0.00542919	−	0.00313454i
$801$	−12236.0	+	23517.8i	−0.539747	+	1.03740i
$802$	3637.13	−	6299.69i	0.160139	−	0.277369i
$803$	2941.11	+	5094.16i	0.129252	+	0.223872i
$804$	−169.898	+	3.72595i	−0.00745253	+	0.000163438i
$805$	10214.4	−	3489.10i	0.447219	−	0.152763i
$806$			74888.9i			3.27277i
$807$	−2491.50	−	4104.85i	−0.108680	−	0.179055i
$808$	−16819.9	−	9710.95i	−0.732328	−	0.422809i
$809$	−34977.4	−	20194.2i	−1.52007	−	0.877615i	−0.999720	−	0.0236636i	$-0.992467\pi$
$809$	−34977.4	−	20194.2i	−1.52007	−	0.877615i	−0.520353	−	0.853951i	$-0.674200\pi$
$810$	8376.11	−	5870.53i	0.363341	−	0.254653i
$811$			684.087i			0.0296197i	0.999890	+	0.0148098i	$0.00471429\pi$
$811$			684.087i			0.0296197i	−0.999890	+	0.0148098i	$0.995286\pi$
$812$	−177.198	+	60.5282i	−0.00765816	+	0.00261592i
$813$	191.410	+	8728.05i	0.00825714	+	0.376514i
$814$	3200.75	+	5543.87i	0.137821	+	0.238713i
$815$	7814.77	−	13535.6i	0.335877	−	0.581756i
$816$	−5748.09	+	10480.1i	−0.246597	+	0.449605i
$817$	5210.64	−	3008.37i	0.223130	−	0.128824i
$818$	−846.983			−0.0362030
$819$	−6446.53	+	42485.6i	−0.275043	+	1.81266i
$820$	−53.8408			−0.00229293
$821$	22370.6	−	12915.7i	0.950963	−	0.549039i	0.0575828	−	0.998341i	$-0.481661\pi$
$821$	22370.6	−	12915.7i	0.950963	−	0.549039i	0.893380	+	0.449302i	$0.148327\pi$
$822$	−10025.0	+	18277.9i	−0.425379	+	0.775567i
$823$	7811.01	−	13529.1i	0.330832	−	0.573017i	−0.651843	−	0.758354i	$-0.726004\pi$
$823$	7811.01	−	13529.1i	0.330832	−	0.573017i	0.982675	+	0.185336i	$0.0593374\pi$
$824$	6119.47	+	10599.2i	0.258716	+	0.448109i
$825$	79.2237	+	3612.49i	0.00334329	+	0.152449i
$826$	−34735.3	−	30344.8i	−1.46319	−	1.27825i
$827$		−	9428.48i		−	0.396445i	−0.980157	−	0.198223i	$-0.936483\pi$
$827$		−	9428.48i		−	0.396445i	0.980157	−	0.198223i	$-0.0635169\pi$
$828$	332.788	−	212.113i	0.0139676	−	0.00890268i
$829$	7480.78	+	4319.03i	0.313411	+	0.180948i	0.648452	−	0.761255i	$-0.275417\pi$
$829$	7480.78	+	4319.03i	0.313411	+	0.180948i	−0.335041	+	0.942204i	$0.608750\pi$
$830$	−12159.5	−	7020.32i	−0.508511	−	0.293589i
$831$	−11390.6	−	18766.5i	−0.475496	−	0.783398i
$832$		−	44667.0i		−	1.86124i
$833$	−11592.5	−	4749.97i	−0.482180	−	0.197571i
$834$	30154.4	−	661.301i	1.25199	−	0.0274568i
$835$	5700.86	+	9874.17i	0.236271	+	0.409233i
$836$	−111.378	+	192.912i	−0.00460776	+	0.00798087i
$837$	39082.0	+	19257.0i	1.61394	+	0.795245i
$838$	−26206.2	+	15130.2i	−1.08029	+	0.623703i
$839$	46267.6			1.90386			0.951928	−	0.306323i	$-0.0990988\pi$
$839$	46267.6			1.90386			0.951928	+	0.306323i	$0.0990988\pi$
$840$	−8418.73	−	7035.22i	−0.345802	−	0.288974i
$841$	17887.7			0.733431
$842$	−13450.8	+	7765.80i	−0.550527	+	0.317847i
$843$	−16901.9	−	9270.29i	−0.690550	−	0.378750i
$844$	−250.637	+	434.116i	−0.0102219	+	0.0177048i
$845$	12969.9	+	22464.5i	0.528021	+	0.914559i
$846$	−1323.81	−	30167.3i	−0.0537983	−	1.22597i
$847$	10126.6	+	1994.22i	0.410809	+	0.0808998i
$848$		−	8844.14i		−	0.358147i
$849$	−14475.8	+	8786.34i	−0.585170	+	0.355178i
$850$	2219.06	+	1281.17i	0.0895448	+	0.0516987i
$851$	−8278.85	−	4779.80i	−0.333485	−	0.192537i
$852$	217.655	−	132.109i	0.00875202	−	0.00531218i
$853$			31971.2i			1.28332i	0.766989	+	0.641660i	$0.221754\pi$
$853$			31971.2i			1.28332i	−0.766989	+	0.641660i	$0.778246\pi$
$854$	1906.72	+	5581.96i	0.0764011	+	0.223666i
$855$	−377.980	−	8613.53i	−0.0151189	−	0.344534i
$856$	−3983.14	−	6899.01i	−0.159043	−	0.275471i
$857$	5393.33	−	9341.53i	0.214974	−	0.372346i	−0.738291	−	0.674483i	$-0.764367\pi$
$857$	5393.33	−	9341.53i	0.214974	−	0.372346i	0.953265	+	0.302137i	$0.0977000\pi$
$858$	30559.8	+	16761.3i	1.21596	+	0.666924i
$859$	−34980.3	+	20195.9i	−1.38942	+	0.802183i	−0.993250	−	0.115994i	$-0.962995\pi$
$859$	−34980.3	+	20195.9i	−1.38942	+	0.802183i	−0.396171	+	0.918177i	$0.629661\pi$
$860$	−59.0663			−0.00234203
$861$	2842.17	+	7760.00i	0.112498	+	0.307154i
$862$	20130.7			0.795421
$863$	5078.88	−	2932.30i	0.200333	−	0.115662i	−0.396478	−	0.918044i	$-0.629768\pi$
$863$	5078.88	−	2932.30i	0.200333	−	0.115662i	0.596811	+	0.802382i	$0.296434\pi$
$864$	−714.080	−	351.851i	−0.0281175	−	0.0138544i
$865$	−6914.23	+	11975.8i	−0.271781	+	0.470739i
$866$	−15026.6	−	26026.8i	−0.589635	−	1.02128i
$867$	−18592.4	+	407.740i	−0.728293	+	0.0159718i
$868$	139.346	−	707.602i	0.00544900	−	0.0276700i
$869$		−	29429.3i		−	1.14882i
$870$	−3050.17	−	5025.28i	−0.118863	−	0.195831i
$871$	19410.7	+	11206.8i	0.755115	+	0.435966i
$872$	−17829.3	−	10293.7i	−0.692403	−	0.399759i
$873$	38593.9	−	24599.0i	1.49623	−	0.953667i
$874$			20890.1i			0.808488i
$875$	−1523.08	+	1743.45i	−0.0588452	+	0.0673591i
$876$	3.02101	+	137.754i	0.000116519	+	0.00531310i
$877$	18366.7	+	31812.0i	0.707182	+	1.22487i	0.965898	+	0.258921i	$0.0833671\pi$
$877$	18366.7	+	31812.0i	0.707182	+	1.22487i	−0.258717	+	0.965953i	$0.583300\pi$
$878$	17764.4	−	30768.9i	0.682826	−	1.18269i
$879$	−8033.15	+	14646.3i	−0.308250	+	0.562012i
$880$	−7585.78	+	4379.65i	−0.290587	+	0.167771i
$881$	−10406.1			−0.397944			−0.198972	−	0.980005i	$-0.563760\pi$
$881$	−10406.1			−0.397944			−0.198972	+	0.980005i	$0.563760\pi$
$882$	−8789.67	+	24456.4i	−0.335560	+	0.933662i
$883$	2473.58			0.0942723			0.0471362	−	0.998888i	$-0.484991\pi$
$883$	2473.58			0.0942723			0.0471362	+	0.998888i	$0.484991\pi$
$884$	−340.850	+	196.790i	−0.0129683	+	0.00748727i
$885$	−11088.1	+	20216.2i	−0.421155	+	0.767866i
$886$	−19144.9	+	33160.0i	−0.725944	+	1.25737i
$887$	18708.6	+	32404.2i	0.708199	+	1.22664i	0.965525	+	0.260311i	$0.0838252\pi$
$887$	18708.6	+	32404.2i	0.708199	+	1.22664i	−0.257326	+	0.966325i	$0.582841\pi$
$888$	213.041	+	9714.37i	0.00805089	+	0.367109i
$889$	−12745.1	+	14589.1i	−0.480830	+	0.550398i
$890$			13776.5i			0.518864i
$891$	16605.3	−	11638.1i	0.624354	−	0.437588i
$892$	262.300	+	151.439i	0.00984582	+	0.00568449i
$893$	−22043.1	−	12726.6i	−0.826029	−	0.476908i
$894$	16421.8	+	27055.5i	0.614346	+	1.01216i
$895$			233.854i			0.00873395i
$896$	5056.95	−	25679.2i	0.188550	−	0.957457i
$897$	−52037.0	+	1141.20i	−1.93697	+	0.0424788i
$898$	−21028.0	−	36421.5i	−0.781416	−	1.35345i
$899$	12519.9	−	21685.1i	0.464474	−	0.804492i
$900$	−39.0661	+	75.0857i	−0.00144689	+	0.00278095i
$901$	−4441.81	+	2564.48i	−0.164238	+	0.0948226i
$902$	6703.03			0.247435
$903$	3118.02	+	8513.14i	0.114907	+	0.313732i
$904$	13537.8			0.498074
$905$	−12870.0	+	7430.49i	−0.472721	+	0.272926i
$906$	3172.49	+	1740.03i	0.116334	+	0.0638065i
$907$	−22097.6	+	38274.2i	−0.808975	+	1.40119i	0.104600	+	0.994514i	$0.466644\pi$
$907$	−22097.6	+	38274.2i	−0.808975	+	1.40119i	−0.913575	+	0.406671i	$0.866689\pi$
$908$	−342.541	−	593.298i	−0.0125194	−	0.0216842i
$909$	22976.2	−	1008.25i	0.838365	−	0.0367892i
$910$	7218.39	+	21132.0i	0.262953	+	0.769802i
$911$		−	32577.6i		−	1.18479i	−0.805647	−	0.592396i	$-0.798182\pi$
$911$		−	32577.6i		−	1.18479i	0.805647	−	0.592396i	$-0.201818\pi$
$912$	17866.9	−	10844.6i	0.648720	−	0.393751i
$913$	−24105.8	−	13917.5i	−0.873808	−	0.504493i
$914$	−17296.7	−	9986.27i	−0.625957	−	0.361397i
$915$	2520.78	−	1530.02i	0.0910757	−	0.0552798i
$916$		−	265.670i		−	0.00958295i
$917$	29993.9	+	5906.64i	1.08014	+	0.212709i
$918$	−945.215	−	14348.4i	−0.0339834	−	0.515869i
$919$	−5380.69	−	9319.64i	−0.193137	−	0.334523i	0.753151	−	0.657847i	$-0.228533\pi$
$919$	−5380.69	−	9319.64i	−0.193137	−	0.334523i	−0.946288	+	0.323325i	$0.895199\pi$
$920$	6644.47	−	11508.6i	0.238110	−	0.412419i
$921$	−11881.7	−	6516.83i	−0.425099	−	0.233156i
$922$	−32355.9	+	18680.7i	−1.15573	+	0.667263i
$923$	−33581.0			−1.19754
$924$	−257.562	−	215.235i	−0.00917009	−	0.00766310i
$925$	2050.30			0.0728796
$926$	−10435.0	+	6024.67i	−0.370320	+	0.213804i
$927$	−12856.6	−	6689.14i	−0.455520	−	0.237001i
$928$	−228.755	+	396.215i	−0.00809187	+	0.0140155i
$929$	7101.10	+	12299.5i	0.250785	+	0.434373i	0.963742	−	0.266835i	$-0.0859779\pi$
$929$	7101.10	+	12299.5i	0.250785	+	0.434373i	−0.712957	+	0.701208i	$0.752645\pi$
$930$	22635.6	−	496.409i	0.798117	−	0.0175031i
$931$	13401.7	+	17328.0i	0.471775	+	0.609991i
$932$			814.112i			0.0286128i
$933$	−9411.52	−	15505.9i	−0.330246	−	0.544093i
$934$	13686.7	+	7901.99i	0.479487	+	0.276832i
$935$	4399.20	+	2539.88i	0.153871	+	0.0888374i
$936$	28435.7	+	44613.3i	0.993001	+	1.55794i
$937$		−	50384.1i		−	1.75665i	−0.478069	−	0.878323i	$-0.658663\pi$
$937$		−	50384.1i		−	1.75665i	0.478069	−	0.878323i	$-0.341337\pi$
$938$	10208.2	+	8917.91i	0.355340	+	0.310427i
$939$	14.0684	+	641.499i	0.000488929	+	0.0222945i
$940$	124.937	+	216.397i	0.00433510	+	0.00750861i
$941$	20595.8	−	35673.0i	0.713501	−	1.23582i	−0.250034	−	0.968237i	$-0.580442\pi$
$941$	20595.8	−	35673.0i	0.713501	−	1.23582i	0.963535	−	0.267583i	$-0.0862248\pi$
$942$	−7585.84	+	13830.8i	−0.262378	+	0.478377i
$943$	−8668.80	+	5004.93i	−0.299358	+	0.172835i
$944$	−55894.4			−1.92713
$945$	12884.2	+	1666.88i	0.443517	+	0.0573794i
$946$	7353.59			0.252733
$947$	10607.9	−	6124.48i	0.364003	−	0.210157i	−0.306832	−	0.951764i	$-0.599269\pi$
$947$	10607.9	−	6124.48i	0.364003	−	0.210157i	0.670835	+	0.741606i	$0.265936\pi$
$948$	331.509	−	604.418i	0.0113575	−	0.0207074i
$949$	9086.49	−	15738.3i	0.310811	−	0.538341i
$950$	−2240.22	−	3880.17i	−0.0765076	−	0.132515i
$951$	−162.636	−	7415.96i	−0.00554555	−	0.252870i
$952$	−14595.7	+	4985.68i	−0.496901	+	0.169734i
$953$			28622.1i			0.972885i	0.873713	+	0.486443i	$0.161706\pi$
$953$			28622.1i			0.972885i	−0.873713	+	0.486443i	$0.838294\pi$
$954$	5718.61	+	8972.05i	0.194074	+	0.304487i
$955$	6495.52	+	3750.19i	0.220094	+	0.127071i
$956$	563.017	+	325.058i	0.0190474	+	0.0109970i
$957$	−6046.85	−	9962.42i	−0.204250	−	0.336509i
$958$			8579.80i			0.289354i
$959$	−25056.6	+	8558.99i	−0.843713	+	0.288200i
$960$	−13500.8	+	296.080i	−0.453893	+	0.00995409i
$961$	33324.7	+	57720.0i	1.11862	+	1.93750i
$962$	9888.64	−	17127.6i	0.331416	−	0.574030i
$963$	8368.35	+	4353.94i	0.280027	+	0.145694i
$964$	−323.462	+	186.751i	−0.0108071	+	0.00623946i
$965$	−13727.9			−0.457946
$966$	−31010.6	−	5403.43i	−1.03287	−	0.179972i
$967$	31204.2			1.03770			0.518852	−	0.854864i	$-0.326360\pi$
$967$	31204.2			1.03770			0.518852	+	0.854864i	$0.326360\pi$
$968$	11004.5	−	6353.44i	0.365390	−	0.210958i
$969$	−10627.3	−	5828.79i	−0.352319	−	0.193238i
$970$	11891.6	−	20596.9i	0.393626	−	0.681781i
$971$	2791.00	+	4834.16i	0.0922425	+	0.159769i	0.908454	−	0.417984i	$-0.137263\pi$
$971$	2791.00	+	4834.16i	0.0922425	+	0.159769i	−0.816212	+	0.577753i	$0.803930\pi$
$972$	472.138	−	51.9712i	0.0155801	−	0.00171500i
$973$	28850.8	+	25204.1i	0.950579	+	0.830429i
$974$		−	37960.6i		−	1.24880i
$975$	9543.07	−	5792.32i	0.313459	−	0.190259i
$976$	6190.58	+	3574.13i	0.203028	+	0.117218i
$977$	23500.1	+	13567.8i	0.769533	+	0.444290i	0.832708	−	0.553712i	$-0.186789\pi$
$977$	23500.1	+	13567.8i	0.769533	+	0.444290i	−0.0631748	+	0.998002i	$0.520123\pi$
$978$	−38964.1	+	23649.9i	−1.27396	+	0.773252i
$979$			27311.4i			0.891599i
$980$	−28.8838	−	213.101i	−0.000941488	−	0.00694619i
$981$	24355.1	−	1068.75i	0.792660	−	0.0347836i
$982$	2389.66	+	4139.02i	0.0776550	+	0.134502i
$983$	−17755.0	+	30752.6i	−0.576091	+	0.997819i	0.419831	+	0.907602i	$0.362089\pi$
$983$	−17755.0	+	30752.6i	−0.576091	+	0.997819i	−0.995922	+	0.0902170i	$0.971244\pi$
$984$	8920.69	+	4892.78i	0.289005	+	0.158512i
$985$	−4181.01	+	2413.91i	−0.135247	+	0.0780847i
$986$	−8264.18			−0.266922
$987$	24593.8	−	29430.3i	0.793139	−	0.949114i
$988$	688.198			0.0221604
$989$	−9510.15	+	5490.69i	−0.305769	+	0.176536i
$990$	4863.61	−	9347.95i	0.156137	−	0.300098i
$991$	13584.1	−	23528.4i	0.435432	−	0.754191i	−0.561899	−	0.827206i	$-0.689929\pi$
$991$	13584.1	−	23528.4i	0.435432	−	0.754191i	0.997331	+	0.0730155i	$0.0232623\pi$
$992$	−881.046	−	1526.02i	−0.0281988	−	0.0488418i
$993$	−6525.26	+	143.102i	−0.208532	+	0.00457322i
$994$	−19925.9	−	3923.97i	−0.635827	−	0.125212i
$995$		−	8336.85i		−	0.265624i
$996$	−338.310	−	557.379i	−0.0107628	−	0.0177322i
$997$	−24712.5	−	14267.8i	−0.785008	−	0.453225i	0.0531939	−	0.998584i	$-0.483060\pi$
$997$	−24712.5	−	14267.8i	−0.785008	−	0.453225i	−0.838202	+	0.545359i	$0.816393\pi$
$998$	−27093.3	−	15642.3i	−0.859343	−	0.496142i
$999$	−6395.55	−	9564.77i	−0.202549	−	0.302919i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	105.4.s.a.101.12	yes	32
3.2	odd	2		105.4.s.b.101.5	yes	32
7.5	odd	6		105.4.s.b.26.5	yes	32
21.5	even	6	inner	105.4.s.a.26.12	✓	32

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
105.4.s.a.26.12	✓	32	21.5	even	6	inner
105.4.s.a.101.12	yes	32	1.1	even	1	trivial
105.4.s.b.26.5	yes	32	7.5	odd	6
105.4.s.b.101.5	yes	32	3.2	odd	2

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:	\( N \)	\(=\)	\( 105 = 3 \cdot 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	105.s (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.43022 - 1.40309i) q^{2} +(-2.49879 + 4.55588i) q^{3} +(-0.0626967 + 0.108594i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(0.319698 + 14.5778i) q^{6} +(-12.1846 + 13.9476i) q^{7} +22.8013i q^{8} +(-14.5121 - 22.7684i) q^{9} +O(q^{10})\)	\(q+(2.43022 - 1.40309i) q^{2} +(-2.49879 + 4.55588i) q^{3} +(-0.0626967 + 0.108594i) q^{4} +(-2.50000 - 4.33013i) q^{5} +(0.319698 + 14.5778i) q^{6} +(-12.1846 + 13.9476i) q^{7} +22.8013i q^{8} +(-14.5121 - 22.7684i) q^{9} +(-12.1511 - 7.01543i) q^{10} +(-24.0891 - 13.9078i) q^{11} +(-0.338075 - 0.556992i) q^{12} +85.9357i q^{13} +(-10.0417 + 50.9917i) q^{14} +(25.9745 - 0.569634i) q^{15} +(31.4906 + 54.5433i) q^{16} +(18.2622 - 31.6311i) q^{17} +(-67.2136 - 34.9703i) q^{18} +(-55.3090 + 31.9327i) q^{19} +0.626967 q^{20} +(-33.0966 - 90.3638i) q^{21} -78.0556 q^{22} +(100.947 - 58.2816i) q^{23} +(-103.880 - 56.9755i) q^{24} +(-12.5000 + 21.6506i) q^{25} +(120.575 + 208.843i) q^{26} +(139.993 - 9.22216i) q^{27} +(-0.750683 - 2.19764i) q^{28} -80.6309i q^{29} +(62.3245 - 37.8288i) q^{30} +(268.943 + 155.274i) q^{31} +(-4.91394 - 2.83706i) q^{32} +(123.556 - 74.9942i) q^{33} -102.494i q^{34} +(90.8563 + 17.8921i) q^{35} +(3.38237 - 0.148425i) q^{36} +(-41.0061 - 71.0246i) q^{37} +(-89.6086 + 155.207i) q^{38} +(-391.513 - 214.735i) q^{39} +(98.7323 - 57.0031i) q^{40} -85.8751 q^{41} +(-207.220 - 173.166i) q^{42} -94.2097 q^{43} +(3.02061 - 1.74395i) q^{44} +(-62.3096 + 119.760i) q^{45} +(163.548 - 283.274i) q^{46} +(199.272 + 345.149i) q^{47} +(-327.181 + 7.17524i) q^{48} +(-46.0690 - 339.892i) q^{49} +70.1543i q^{50} +(98.4741 + 162.240i) q^{51} +(-9.33209 - 5.38789i) q^{52} +(-121.612 - 70.2126i) q^{53} +(327.273 - 218.834i) q^{54} +139.078i q^{55} +(-318.022 - 277.825i) q^{56} +(-7.27597 - 331.774i) q^{57} +(-113.132 - 195.951i) q^{58} +(-443.739 + 768.579i) q^{59} +(-1.56666 + 2.85639i) q^{60} +(98.2925 - 56.7492i) q^{61} +871.453 q^{62} +(494.388 + 75.0157i) q^{63} -519.772 q^{64} +(372.113 - 214.839i) q^{65} +(195.044 - 355.612i) q^{66} +(130.409 - 225.874i) q^{67} +(2.28996 + 3.96633i) q^{68} +(13.2797 + 605.534i) q^{69} +(245.905 - 83.9975i) q^{70} +390.768i q^{71} +(519.147 - 330.895i) q^{72} +(-183.140 - 105.736i) q^{73} +(-199.307 - 115.070i) q^{74} +(-67.4029 - 111.049i) q^{75} -8.00829i q^{76} +(487.497 - 166.522i) q^{77} +(-1252.75 + 27.4735i) q^{78} +(529.006 + 916.266i) q^{79} +(157.453 - 272.716i) q^{80} +(-307.797 + 660.834i) q^{81} +(-208.695 + 120.490i) q^{82} +1000.70 q^{83} +(11.8880 + 2.07142i) q^{84} -182.622 q^{85} +(-228.950 + 132.184i) q^{86} +(367.345 + 201.480i) q^{87} +(317.116 - 549.261i) q^{88} +(-490.935 - 850.325i) q^{89} +(16.6080 + 378.469i) q^{90} +(-1198.59 - 1047.10i) q^{91} +14.6162i q^{92} +(-1379.44 + 837.274i) q^{93} +(968.549 + 559.192i) q^{94} +(276.545 + 159.663i) q^{95} +(25.2042 - 15.2981i) q^{96} +1695.07i q^{97} +(-588.856 - 761.373i) q^{98} +(32.9248 + 750.301i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9}+O(q^{10}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9	\( 32 q - 2 q^{3} + 64 q^{4} - 80 q^{5} - 28 q^{6} + 46 q^{7} + 100 q^{9} + 36 q^{11} + 246 q^{12} + 18 q^{14} + 20 q^{15} - 376 q^{16} - 72 q^{17} - 442 q^{18} - 198 q^{19} - 640 q^{20} - 218 q^{21} + 204 q^{22} + 72 q^{23} - 50 q^{24} - 400 q^{25} - 312 q^{26} + 508 q^{27} + 350 q^{28} + 40 q^{30} + 510 q^{31} + 810 q^{32} + 290 q^{33} - 70 q^{35} - 612 q^{36} - 658 q^{37} - 192 q^{38} - 648 q^{39} - 1404 q^{41} + 1892 q^{42} + 332 q^{43} + 2034 q^{44} - 490 q^{45} - 468 q^{46} + 408 q^{47} + 2810 q^{48} + 980 q^{49} - 888 q^{51} + 3378 q^{52} + 1152 q^{53} + 2714 q^{54} - 3354 q^{56} - 816 q^{57} - 1080 q^{58} - 48 q^{59} - 420 q^{60} - 1662 q^{61} - 2076 q^{62} + 874 q^{63} - 1952 q^{64} + 870 q^{65} - 1892 q^{66} - 1298 q^{67} + 1182 q^{68} + 2450 q^{69} - 450 q^{70} - 2708 q^{72} + 378 q^{73} + 2898 q^{74} - 50 q^{75} - 3528 q^{77} - 1896 q^{78} - 326 q^{79} - 1880 q^{80} - 3308 q^{81} - 2916 q^{82} - 1536 q^{83} + 1380 q^{84} + 720 q^{85} + 5202 q^{86} - 1090 q^{87} + 1668 q^{88} - 1590 q^{89} + 910 q^{90} + 2082 q^{91} - 4950 q^{93} - 1152 q^{94} + 990 q^{95} + 7416 q^{96} - 7830 q^{98} + 3128 q^{99}+O(q^{100}) \) 32 * q - 2 * q^3 + 64 * q^4 - 80 * q^5 - 28 * q^6 + 46 * q^7 + 100 * q^9 + 36 * q^11 + 246 * q^12 + 18 * q^14 + 20 * q^15 - 376 * q^16 - 72 * q^17 - 442 * q^18 - 198 * q^19 - 640 * q^20 - 218 * q^21 + 204 * q^22 + 72 * q^23 - 50 * q^24 - 400 * q^25 - 312 * q^26 + 508 * q^27 + 350 * q^28 + 40 * q^30 + 510 * q^31 + 810 * q^32 + 290 * q^33 - 70 * q^35 - 612 * q^36 - 658 * q^37 - 192 * q^38 - 648 * q^39 - 1404 * q^41 + 1892 * q^42 + 332 * q^43 + 2034 * q^44 - 490 * q^45 - 468 * q^46 + 408 * q^47 + 2810 * q^48 + 980 * q^49 - 888 * q^51 + 3378 * q^52 + 1152 * q^53 + 2714 * q^54 - 3354 * q^56 - 816 * q^57 - 1080 * q^58 - 48 * q^59 - 420 * q^60 - 1662 * q^61 - 2076 * q^62 + 874 * q^63 - 1952 * q^64 + 870 * q^65 - 1892 * q^66 - 1298 * q^67 + 1182 * q^68 + 2450 * q^69 - 450 * q^70 - 2708 * q^72 + 378 * q^73 + 2898 * q^74 - 50 * q^75 - 3528 * q^77 - 1896 * q^78 - 326 * q^79 - 1880 * q^80 - 3308 * q^81 - 2916 * q^82 - 1536 * q^83 + 1380 * q^84 + 720 * q^85 + 5202 * q^86 - 1090 * q^87 + 1668 * q^88 - 1590 * q^89 + 910 * q^90 + 2082 * q^91 - 4950 * q^93 - 1152 * q^94 + 990 * q^95 + 7416 * q^96 - 7830 * q^98 + 3128 * q^99

Introduction

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