LMFDB - Embedded newform 35.5.h.a.31.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [35,5,Mod(26,35)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(35, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("35.26");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 35 = 5 \cdot 7 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	35.h (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:	$3.61794870793$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$10$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 4 x^{19} + 116 x^{18} - 264 x^{17} + 7945 x^{16} - 15716 x^{15} + 322816 x^{14} + \cdots + 48948907536 $ x^20 - 4x^19 + 116x^18 - 264x^17 + 7945x^16 - 15716x^15 + 322816x^14 - 515828x^13 + 9277999x^12 - 13862388x^11 + 173089454x^10 - 201957712x^9 + 2193435454x^8 - 2149103892x^7 + 14039289876x^6 + 1095579456x^5 + 36238744284x^4 + 13441411080x^3 + 74916126504x^2 + 43989502032*x + 48948907536
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{4}\cdot 7^{3} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			31.7
Root			$-0.681265 + 1.17999i$ of defining polynomial
Character	$\chi$	$=$	35.31
Dual form			35.5.h.a.26.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.18127 + 2.04601i) q^{2} +(-7.64511 - 4.41391i) q^{3} +(5.20922 - 9.02264i) q^{4} +(9.68246 - 5.59017i) q^{5} -20.8560i q^{6} +(1.69012 - 48.9708i) q^{7} +62.4144 q^{8} +(-1.53484 - 2.65843i) q^{9} +(22.8751 + 13.2069i) q^{10} +(56.4068 - 97.6995i) q^{11} +(-79.6502 + 45.9861i) q^{12} +313.449i q^{13} +(102.191 - 54.3896i) q^{14} -98.6980 q^{15} +(-9.61965 - 16.6617i) q^{16} +(-352.502 - 203.517i) q^{17} +(3.62611 - 6.28061i) q^{18} +(106.640 - 61.5688i) q^{19} -116.482i q^{20} +(-229.074 + 366.928i) q^{21} +266.526 q^{22} +(288.451 + 499.612i) q^{23} +(-477.165 - 275.491i) q^{24} +(62.5000 - 108.253i) q^{25} +(-641.320 + 370.266i) q^{26} +742.152i q^{27} +(-433.042 - 270.349i) q^{28} +741.613 q^{29} +(-116.588 - 201.937i) q^{30} +(1263.78 + 729.642i) q^{31} +(522.042 - 904.203i) q^{32} +(-862.473 + 497.949i) q^{33} -961.629i q^{34} +(-257.391 - 483.606i) q^{35} -31.9814 q^{36} +(269.606 + 466.972i) q^{37} +(251.941 + 145.458i) q^{38} +(1383.53 - 2396.35i) q^{39} +(604.325 - 348.907i) q^{40} -1444.11i q^{41} +(-1021.33 - 35.2491i) q^{42} +1017.68 q^{43} +(-587.672 - 1017.88i) q^{44} +(-29.7221 - 17.1601i) q^{45} +(-681.475 + 1180.35i) q^{46} +(-826.140 + 476.972i) q^{47} +169.841i q^{48} +(-2395.29 - 165.533i) q^{49} +295.316 q^{50} +(1796.61 + 3111.82i) q^{51} +(2828.14 + 1632.82i) q^{52} +(-1578.68 + 2734.35i) q^{53} +(-1518.45 + 876.678i) q^{54} -1261.29i q^{55} +(105.488 - 3056.49i) q^{56} -1087.04 q^{57} +(876.041 + 1517.35i) q^{58} +(-790.264 - 456.259i) q^{59} +(-514.140 + 890.516i) q^{60} +(-1476.15 + 852.257i) q^{61} +3447.60i q^{62} +(-132.779 + 70.6695i) q^{63} +2158.85 q^{64} +(1752.23 + 3034.95i) q^{65} +(-2037.62 - 1176.42i) q^{66} +(2680.16 - 4642.17i) q^{67} +(-3672.52 + 2120.33i) q^{68} -5092.79i q^{69} +(685.417 - 1097.89i) q^{70} -4952.36 q^{71} +(-95.7963 - 165.924i) q^{72} +(1207.07 + 696.902i) q^{73} +(-636.953 + 1103.24i) q^{74} +(-955.639 + 551.738i) q^{75} -1282.90i q^{76} +(-4689.09 - 2927.41i) q^{77} +6537.28 q^{78} +(5068.88 + 8779.55i) q^{79} +(-186.284 - 107.551i) q^{80} +(3151.47 - 5458.50i) q^{81} +(2954.66 - 1705.88i) q^{82} -6357.92i q^{83} +(2117.36 + 3978.26i) q^{84} -4550.77 q^{85} +(1202.15 + 2082.19i) q^{86} +(-5669.71 - 3273.41i) q^{87} +(3520.60 - 6097.85i) q^{88} +(-156.641 + 90.4366i) q^{89} -81.0824i q^{90} +(15349.8 + 529.765i) q^{91} +6010.43 q^{92} +(-6441.14 - 11156.4i) q^{93} +(-1951.78 - 1126.86i) q^{94} +(688.361 - 1192.28i) q^{95} +(-7982.14 + 4608.49i) q^{96} +5069.26i q^{97} +(-2490.79 - 5096.32i) q^{98} -346.303 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q + 6 q^{2} - 18 q^{3} - 58 q^{4} - 54 q^{7} - 372 q^{8} + 266 q^{9} + 90 q^{11} + 1266 q^{12} - 690 q^{14} + 100 q^{15} - 126 q^{16} - 864 q^{17} - 848 q^{18} - 1662 q^{19} + 1680 q^{21} + 2584 q^{22}+ \cdots - 36716 q^{99}+O(q^{100}) $ 20 * q + 6 * q^2 - 18 * q^3 - 58 * q^4 - 54 * q^7 - 372 * q^8 + 266 * q^9 + 90 * q^11 + 1266 * q^12 - 690 * q^14 + 100 * q^15 - 126 * q^16 - 864 * q^17 - 848 * q^18 - 1662 * q^19 + 1680 * q^21 + 2584 * q^22 - 1242 * q^23 + 1908 * q^24 + 1250 * q^25 - 1350 * q^26 - 134 * q^28 + 840 * q^29 + 800 * q^30 - 3636 * q^31 - 1758 * q^32 + 384 * q^33 + 150 * q^35 - 4164 * q^36 + 1068 * q^37 + 9180 * q^38 + 2976 * q^39 - 4146 * q^42 - 7692 * q^43 - 3618 * q^44 - 1800 * q^45 + 2038 * q^46 - 11412 * q^47 + 416 * q^49 + 1500 * q^50 + 6324 * q^51 - 7476 * q^52 + 1668 * q^53 + 33180 * q^54 + 13500 * q^56 + 15264 * q^57 + 1174 * q^58 + 216 * q^59 - 8250 * q^60 - 5856 * q^61 - 23632 * q^63 - 25788 * q^64 - 4650 * q^65 - 16248 * q^66 + 34 * q^67 - 6444 * q^68 + 900 * q^70 + 10488 * q^71 - 12052 * q^72 + 22776 * q^73 + 2538 * q^74 - 2250 * q^75 + 40488 * q^77 + 23784 * q^78 + 20788 * q^79 + 14400 * q^80 + 4154 * q^81 - 34146 * q^82 - 20316 * q^84 + 12000 * q^85 + 1980 * q^86 - 27474 * q^87 - 36148 * q^88 - 13176 * q^89 + 17976 * q^91 + 61404 * q^92 - 22908 * q^93 - 50610 * q^94 - 6900 * q^95 - 17460 * q^96 - 39606 * q^98 - 36716 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/35\mathbb{Z}\right)^\times$.

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

Coefficient data

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

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

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

$2$	1.18127	+	2.04601i	0.295316	+	0.511503i	0.975058	−	0.221948i	$-0.0712416\pi$
$2$	1.18127	+	2.04601i	0.295316	+	0.511503i	−0.679742	+	0.733451i	$0.737908\pi$
$3$	−7.64511	−	4.41391i	−0.849457	−	0.490434i	0.0110107	−	0.999939i	$-0.496495\pi$
$3$	−7.64511	−	4.41391i	−0.849457	−	0.490434i	−0.860468	+	0.509505i	$0.829828\pi$
$4$	5.20922	−	9.02264i	0.325577	−	0.563915i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$5$	9.68246	−	5.59017i	0.387298	−	0.223607i
$6$		−	20.8560i		−	0.579333i
$7$	1.69012	−	48.9708i	0.0344922	−	0.999405i
$7$	1.69012	−	48.9708i	0.0344922	−	0.999405i
$8$	62.4144			0.975225
$9$	−1.53484	−	2.65843i	−0.0189487	−	0.0328201i
$10$	22.8751	+	13.2069i	0.228751	+	0.132069i
$11$	56.4068	−	97.6995i	0.466172	−	0.807434i	−0.533081	−	0.846064i	$-0.678966\pi$
$11$	56.4068	−	97.6995i	0.466172	−	0.807434i	0.999254	+	0.0386302i	$0.0122994\pi$
$12$	−79.6502	+	45.9861i	−0.553126	+	0.319348i
$13$			313.449i			1.85473i	0.374163	+	0.927363i	$0.377930\pi$
$13$			313.449i			1.85473i	−0.374163	+	0.927363i	$0.622070\pi$
$14$	102.191	−	54.3896i	0.521385	−	0.277498i
$15$	−98.6980			−0.438658
$16$	−9.61965	−	16.6617i	−0.0375767	−	0.0650848i
$17$	−352.502	−	203.517i	−1.21973	−	0.704211i	−0.254869	−	0.966976i	$-0.582032\pi$
$17$	−352.502	−	203.517i	−1.21973	−	0.704211i	−0.964860	+	0.262765i	$0.915366\pi$
$18$	3.62611	−	6.28061i	0.0111917	−	0.0193846i
$19$	106.640	−	61.5688i	0.295403	−	0.170551i	−0.344973	−	0.938613i	$-0.612112\pi$
$19$	106.640	−	61.5688i	0.295403	−	0.170551i	0.640376	+	0.768062i	$0.278779\pi$
$20$		−	116.482i		−	0.291205i
$21$	−229.074	+	366.928i	−0.519442	+	0.832035i
$22$	266.526			0.550673
$23$	288.451	+	499.612i	0.545276	+	0.944446i	0.998589	+	0.0530948i	$0.0169086\pi$
$23$	288.451	+	499.612i	0.545276	+	0.944446i	−0.453313	+	0.891351i	$0.649758\pi$
$24$	−477.165	−	275.491i	−0.828411	−	0.478284i
$25$	62.5000	−	108.253i	0.100000	−	0.173205i
$26$	−641.320	+	370.266i	−0.948698	+	0.547731i
$27$			742.152i			1.01804i
$28$	−433.042	−	270.349i	−0.552350	−	0.344834i
$29$	741.613			0.881822			0.440911	−	0.897551i	$-0.354655\pi$
$29$	741.613			0.881822			0.440911	+	0.897551i	$0.354655\pi$
$30$	−116.588	−	201.937i	−0.129543	−	0.224375i
$31$	1263.78	+	729.642i	1.31506	+	0.759252i	0.982930	−	0.183980i	$-0.0588981\pi$
$31$	1263.78	+	729.642i	1.31506	+	0.759252i	0.332134	+	0.943232i	$0.392231\pi$
$32$	522.042	−	904.203i	0.509806	−	0.883011i
$33$	−862.473	+	497.949i	−0.791986	+	0.457253i
$34$		−	961.629i		−	0.831859i
$35$	−257.391	−	483.606i	−0.210115	−	0.394781i
$36$	−31.9814			−0.0246770
$37$	269.606	+	466.972i	0.196937	+	0.341104i	0.947534	−	0.319656i	$-0.103567\pi$
$37$	269.606	+	466.972i	0.196937	+	0.341104i	−0.750597	+	0.660760i	$0.770234\pi$
$38$	251.941	+	145.458i	0.174474	+	0.100733i
$39$	1383.53	−	2396.35i	0.909621	−	1.57551i
$40$	604.325	−	348.907i	0.377703	−	0.218067i
$41$		−	1444.11i		−	0.859077i	−0.903049	−	0.429538i	$-0.858676\pi$
$41$		−	1444.11i		−	0.859077i	0.903049	−	0.429538i	$-0.141324\pi$
$42$	−1021.33	−	35.2491i	−0.578988	−	0.0199825i
$43$	1017.68			0.550396			0.275198	−	0.961388i	$-0.411257\pi$
$43$	1017.68			0.550396			0.275198	+	0.961388i	$0.411257\pi$
$44$	−587.672	−	1017.88i	−0.303549	−	0.525763i
$45$	−29.7221	−	17.1601i	−0.0146776	−	0.00847411i
$46$	−681.475	+	1180.35i	−0.322058	+	0.557821i
$47$	−826.140	+	476.972i	−0.373988	+	0.215922i	−0.675199	−	0.737635i	$-0.735942\pi$
$47$	−826.140	+	476.972i	−0.373988	+	0.215922i	0.301211	+	0.953557i	$0.402609\pi$
$48$			169.841i			0.0737157i
$49$	−2395.29	−	165.533i	−0.997621	−	0.0689434i
$50$	295.316			0.118127
$51$	1796.61	+	3111.82i	0.690738	+	1.19639i
$52$	2828.14	+	1632.82i	1.04591	+	0.603855i
$53$	−1578.68	+	2734.35i	−0.562007	+	0.973425i	0.435314	+	0.900279i	$0.356637\pi$
$53$	−1578.68	+	2734.35i	−0.562007	+	0.973425i	−0.997321	+	0.0731463i	$0.976696\pi$
$54$	−1518.45	+	876.678i	−0.520731	+	0.300644i
$55$		−	1261.29i		−	0.416957i
$56$	105.488	−	3056.49i	0.0336377	−	0.974645i
$57$	−1087.04			−0.334576
$58$	876.041	+	1517.35i	0.260417	+	0.451055i
$59$	−790.264	−	456.259i	−0.227022	−	0.131071i	0.382175	−	0.924090i	$-0.375175\pi$
$59$	−790.264	−	456.259i	−0.227022	−	0.131071i	−0.609198	+	0.793018i	$0.708508\pi$
$60$	−514.140	+	890.516i	−0.142817	+	0.247366i
$61$	−1476.15	+	852.257i	−0.396709	+	0.229040i	−0.685063	−	0.728484i	$-0.740225\pi$
$61$	−1476.15	+	852.257i	−0.396709	+	0.229040i	0.288354	+	0.957524i	$0.406892\pi$
$62$			3447.60i			0.896878i
$63$	−132.779	+	70.6695i	−0.0334541	+	0.0178054i
$64$	2158.85			0.527063
$65$	1752.23	+	3034.95i	0.414729	+	0.718332i
$66$	−2037.62	−	1176.42i	−0.467773	−	0.270069i
$67$	2680.16	−	4642.17i	0.597051	−	1.03412i	−0.396203	−	0.918163i	$-0.629672\pi$
$67$	2680.16	−	4642.17i	0.597051	−	1.03412i	0.993254	−	0.115959i	$-0.0369943\pi$
$68$	−3672.52	+	2120.33i	−0.794230	+	0.458549i
$69$		−	5092.79i		−	1.06969i
$70$	685.417	−	1097.89i	0.139881	−	0.224060i
$71$	−4952.36			−0.982416			−0.491208	−	0.871042i	$-0.663445\pi$
$71$	−4952.36			−0.982416			−0.491208	+	0.871042i	$0.663445\pi$
$72$	−95.7963	−	165.924i	−0.0184792	−	0.0320070i
$73$	1207.07	+	696.902i	0.226510	+	0.130775i	0.608961	−	0.793200i	$-0.291587\pi$
$73$	1207.07	+	696.902i	0.226510	+	0.130775i	−0.382451	+	0.923976i	$0.624920\pi$
$74$	−636.953	+	1103.24i	−0.116317	+	0.201467i
$75$	−955.639	+	551.738i	−0.169891	+	0.0980868i
$76$		−	1282.90i		−	0.222109i
$77$	−4689.09	−	2927.41i	−0.790874	−	0.493745i
$78$	6537.28			1.07450
$79$	5068.88	+	8779.55i	0.812190	+	1.40675i	0.911328	+	0.411680i	$0.135058\pi$
$79$	5068.88	+	8779.55i	0.812190	+	1.40675i	−0.0991386	+	0.995074i	$0.531609\pi$
$80$	−186.284	−	107.551i	−0.0291068	−	0.0168048i
$81$	3151.47	−	5458.50i	0.480333	−	0.831962i
$82$	2954.66	−	1705.88i	0.439420	−	0.253699i
$83$		−	6357.92i		−	0.922909i	−0.887164	−	0.461455i	$-0.847328\pi$
$83$		−	6357.92i		−	0.922909i	0.887164	−	0.461455i	$-0.152672\pi$
$84$	2117.36	+	3978.26i	0.300079	+	0.563812i
$85$	−4550.77			−0.629865
$86$	1202.15	+	2082.19i	0.162541	+	0.281529i
$87$	−5669.71	−	3273.41i	−0.749070	−	0.432476i
$88$	3520.60	−	6097.85i	0.454623	−	0.787429i
$89$	−156.641	+	90.4366i	−0.0197754	+	0.0114173i	−0.509855	−	0.860260i	$-0.670301\pi$
$89$	−156.641	+	90.4366i	−0.0197754	+	0.0114173i	0.490080	+	0.871678i	$0.336968\pi$
$90$		−	81.0824i		−	0.0100102i
$91$	15349.8	+	529.765i	1.85362	+	0.0639736i
$92$	6010.43			0.710117
$93$	−6441.14	−	11156.4i	−0.744727	−	1.28990i
$94$	−1951.78	−	1126.86i	−0.220890	−	0.127531i
$95$	688.361	−	1192.28i	0.0762726	−	0.132108i
$96$	−7982.14	+	4608.49i	−0.866117	+	0.500053i
$97$			5069.26i			0.538768i	0.963033	+	0.269384i	$0.0868200\pi$
$97$			5069.26i			0.538768i	−0.963033	+	0.269384i	$0.913180\pi$
$98$	−2490.79	−	5096.32i	−0.259349	−	0.530646i
$99$	−346.303			−0.0353334
$100$	−651.153	−	1127.83i	−0.0651153	−	0.112783i
$101$	3450.13	+	1991.93i	0.338215	+	0.195269i	0.659482	−	0.751720i	$-0.270775\pi$
$101$	3450.13	+	1991.93i	0.338215	+	0.195269i	−0.321267	+	0.946989i	$0.604109\pi$
$102$	−4244.54	+	7351.76i	−0.407972	+	0.706629i
$103$	4255.91	−	2457.15i	0.401161	−	0.231610i	−0.285824	−	0.958282i	$-0.592267\pi$
$103$	4255.91	−	2457.15i	0.401161	−	0.231610i	0.686985	+	0.726672i	$0.258934\pi$
$104$			19563.7i			1.80877i
$105$	−166.811	+	4833.32i	−0.0151303	+	0.438397i
$106$	−7459.35			−0.663880
$107$	−4274.95	−	7404.44i	−0.373391	−	0.646732i	0.616694	−	0.787203i	$-0.288472\pi$
$107$	−4274.95	−	7404.44i	−0.373391	−	0.646732i	−0.990085	+	0.140471i	$0.955138\pi$
$108$	6696.17	+	3866.03i	0.574089	+	0.331450i
$109$	−4551.17	+	7882.86i	−0.383063	+	0.663484i	−0.991498	−	0.130119i	$-0.958464\pi$
$109$	−4551.17	+	7882.86i	−0.383063	+	0.663484i	0.608436	+	0.793603i	$0.291797\pi$
$110$	2580.62	−	1489.92i	0.213275	−	0.123134i
$111$		−	4760.07i		−	0.386338i
$112$	−832.197	+	442.922i	−0.0663422	+	0.0353095i
$113$	−10497.8			−0.822135			−0.411068	−	0.911605i	$-0.634844\pi$
$113$	−10497.8			−0.822135			−0.411068	+	0.911605i	$0.634844\pi$
$114$	−1284.08	−	2224.09i	−0.0988057	−	0.171136i
$115$	5585.83	+	3224.98i	0.422369	+	0.243855i
$116$	3863.23	−	6691.31i	0.287101	−	0.497273i
$117$	833.280	−	481.095i	0.0608722	−	0.0351446i
$118$		−	2155.85i		−	0.154830i
$119$	−10562.2	+	16918.3i	−0.745863	+	1.19471i
$120$	−6160.17			−0.427790
$121$	957.041	+	1657.64i	0.0653672	+	0.113219i
$122$	−3487.46	−	2013.48i	−0.234309	−	0.135278i
$123$	−6374.16	+	11040.4i	−0.421321	+	0.729749i
$124$	13166.6	−	7601.73i	0.856308	−	0.494390i
$125$		−	1397.54i		−	0.0894427i
$126$	−301.438	−	188.189i	−0.0189870	−	0.0118537i
$127$	3934.73			0.243954			0.121977	−	0.992533i	$-0.461077\pi$
$127$	3934.73			0.243954			0.121977	+	0.992533i	$0.461077\pi$
$128$	−5802.49	−	10050.2i	−0.354156	−	0.613416i
$129$	−7780.30	−	4491.96i	−0.467538	−	0.269933i
$130$	−4139.70	+	7170.17i	−0.244953	+	0.424270i
$131$	6358.23	−	3670.93i	0.370505	−	0.213911i	−0.303174	−	0.952935i	$-0.598046\pi$
$131$	6358.23	−	3670.93i	0.370505	−	0.213911i	0.673679	+	0.739024i	$0.264713\pi$
$132$			10375.7i			0.595484i
$133$	−2834.84	−	5326.33i	−0.160260	−	0.301110i
$134$	12663.9			0.705275
$135$	4148.75	+	7185.85i	0.227641	+	0.394285i
$136$	−22001.2	−	12702.4i	−1.18951	−	0.686764i
$137$	4805.69	−	8323.71i	0.256044	−	0.443482i	−0.709134	−	0.705073i	$-0.750914\pi$
$137$	4805.69	−	8323.71i	0.256044	−	0.443482i	0.965179	+	0.261592i	$0.0842474\pi$
$138$	10419.9	−	6015.93i	0.547149	−	0.315896i
$139$		−	6348.86i		−	0.328599i	−0.986410	−	0.164300i	$-0.947464\pi$
$139$		−	6348.86i		−	0.328599i	0.986410	−	0.164300i	$-0.0525364\pi$
$140$	−5704.21	−	196.868i	−0.291031	−	0.0100443i
$141$	8421.25			0.423583
$142$	−5850.05	−	10132.6i	−0.290124	−	0.502509i
$143$	30623.8	+	17680.6i	1.49757	+	0.864621i
$144$	−29.5293	+	51.1462i	−0.00142406	+	0.00246654i
$145$	7180.63	−	4145.74i	0.341528	−	0.197181i
$146$			3292.90i			0.154480i
$147$	17581.6	+	11838.1i	0.813623	+	0.547832i
$148$	5617.76			0.256472
$149$	−5996.35	−	10386.0i	−0.270094	−	0.467816i	0.698792	−	0.715325i	$-0.253721\pi$
$149$	−5996.35	−	10386.0i	−0.270094	−	0.467816i	−0.968886	+	0.247509i	$0.920388\pi$
$150$	−2257.73	−	1303.50i	−0.100343	−	0.0579333i
$151$	−19255.3	+	33351.1i	−0.844493	+	1.46271i	0.0415675	+	0.999136i	$0.486765\pi$
$151$	−19255.3	+	33351.1i	−0.844493	+	1.46271i	−0.886061	+	0.463569i	$0.846568\pi$
$152$	6655.89	−	3842.78i	0.288084	−	0.166325i
$153$			1249.47i			0.0533754i
$154$	450.460	−	13052.0i	0.0189939	−	0.550345i
$155$	16315.3			0.679096
$156$	−14414.3	−	24966.3i	−0.592302	−	1.02590i
$157$	−3758.93	−	2170.22i	−0.152498	−	0.0880450i	0.421809	−	0.906685i	$-0.361395\pi$
$157$	−3758.93	−	2170.22i	−0.152498	−	0.0880450i	−0.574307	+	0.818640i	$0.694729\pi$
$158$	−11975.4	+	20742.0i	−0.479706	+	0.830875i
$159$	24138.3	−	13936.3i	0.954802	−	0.551255i
$160$		−	11673.2i		−	0.455985i
$161$	24953.9	−	13281.3i	0.962692	−	0.512376i
$162$	14890.9			0.567401
$163$	−13383.3	−	23180.5i	−0.503718	−	0.872464i	−0.999991	−	0.00429800i	$-0.998632\pi$
$163$	−13383.3	−	23180.5i	−0.503718	−	0.872464i	0.496273	−	0.868166i	$-0.334701\pi$
$164$	−13029.7	−	7522.69i	−0.484447	−	0.279695i
$165$	−5567.24	+	9642.74i	−0.204490	+	0.354187i
$166$	13008.4	−	7510.39i	0.472071	−	0.272550i
$167$		−	2791.76i		−	0.100103i	−0.998747	−	0.0500513i	$-0.984062\pi$
$167$		−	2791.76i		−	0.100103i	0.998747	−	0.0500513i	$-0.0159385\pi$
$168$	−14297.5	+	22901.6i	−0.506573	+	0.811421i
$169$	−69689.1			−2.44001
$170$	−5375.67	−	9310.94i	−0.186009	−	0.322178i
$171$	−327.352	−	188.997i	−0.0111950	−	0.00646343i
$172$	5301.34	−	9182.19i	0.179196	−	0.310377i
$173$	−6153.06	+	3552.47i	−0.205589	+	0.118697i	−0.599260	−	0.800555i	$-0.704538\pi$
$173$	−6153.06	+	3552.47i	−0.205589	+	0.118697i	0.393671	+	0.919251i	$0.371205\pi$
$174$		−	15467.1i		−	0.510869i
$175$	−5195.62	−	3243.64i	−0.169653	−	0.105915i
$176$	−2170.45			−0.0700689
$177$	4027.77	+	6976.31i	0.128564	+	0.222679i
$178$	−370.068	−	213.659i	−0.0116800	−	0.00674344i
$179$	22495.5	−	38963.4i	0.702085	−	1.21605i	−0.265648	−	0.964070i	$-0.585586\pi$
$179$	22495.5	−	38963.4i	0.702085	−	1.21605i	0.967733	−	0.251977i	$-0.0810807\pi$
$180$	−309.658	+	178.781i	−0.00955736	+	0.00551794i
$181$			61782.2i			1.88584i	0.333013	+	0.942922i	$0.391935\pi$
$181$			61782.2i			1.88584i	−0.333013	+	0.942922i	$0.608065\pi$
$182$	17048.3	+	32031.8i	0.514682	+	0.967025i
$183$	15047.1			0.449316
$184$	18003.5	+	31183.0i	0.531767	+	0.921047i
$185$	5220.90	+	3014.29i	0.152547	+	0.0880728i
$186$	15217.4	−	26357.3i	0.439860	−	0.761860i
$187$	−39767.0	+	22959.5i	−1.13721	+	0.656567i
$188$			9938.63i			0.281197i
$189$	36343.8	+	1254.32i	1.01743	+	0.0351145i
$190$	3252.55			0.0900982
$191$	19870.9	+	34417.3i	0.544690	+	0.943432i	0.998626	+	0.0523972i	$0.0166862\pi$
$191$	19870.9	+	34417.3i	0.544690	+	0.943432i	−0.453936	+	0.891034i	$0.649980\pi$
$192$	−16504.7	−	9528.97i	−0.447717	−	0.258490i
$193$	−36668.3	+	63511.3i	−0.984409	+	1.70505i	−0.339877	+	0.940470i	$0.610385\pi$
$193$	−36668.3	+	63511.3i	−0.984409	+	1.70505i	−0.644533	+	0.764577i	$0.722948\pi$
$194$	−10371.8	+	5988.15i	−0.275581	+	0.159107i
$195$		−	30936.7i		−	0.813590i
$196$	−13971.1	+	20749.5i	−0.363680	+	0.540127i
$197$	−70971.8			−1.82875			−0.914373	−	0.404872i	$-0.867316\pi$
$197$	−70971.8			−1.82875			−0.914373	+	0.404872i	$0.867316\pi$
$198$	−409.075	−	708.539i	−0.0104345	−	0.0180731i
$199$	−2968.18	−	1713.68i	−0.0749521	−	0.0432736i	0.462056	−	0.886851i	$-0.347112\pi$
$199$	−2968.18	−	1713.68i	−0.0749521	−	0.0432736i	−0.537008	+	0.843577i	$0.680445\pi$
$200$	3900.90	−	6756.56i	0.0975225	−	0.168914i
$201$	−40980.3	+	23660.0i	−1.01434	+	0.585628i
$202$			9412.01i			0.230664i
$203$	1253.41	−	36317.4i	0.0304160	−	0.881298i
$204$	37435.8			0.899552
$205$	−8072.81	−	13982.5i	−0.192095	−	0.332719i
$206$	10054.7	+	5805.10i	0.236938	+	0.136796i
$207$	885.454	−	1533.65i	0.0206645	−	0.0357920i
$208$	5222.59	−	3015.27i	0.120715	−	0.0696946i
$209$		−	13891.6i		−	0.318024i
$210$	−10086.1	+	5368.14i	−0.228709	+	0.121726i
$211$	−8102.71			−0.181998			−0.0909988	−	0.995851i	$-0.529006\pi$
$211$	−8102.71			−0.181998			−0.0909988	+	0.995851i	$0.529006\pi$
$212$	16447.4	+	28487.7i	0.365953	+	0.633849i
$213$	37861.4	+	21859.3i	0.834520	+	0.481811i
$214$	10099.7	−	17493.2i	0.220537	−	0.381981i
$215$	9853.67	−	5689.02i	0.213168	−	0.123072i
$216$			46320.9i			0.992819i
$217$	37867.1	−	60655.0i	0.804160	−	1.28809i
$218$	−21504.6			−0.452499
$219$	−6152.12	−	10655.8i	−0.128273	−	0.222176i
$220$	−11380.2	−	6570.37i	−0.235128	−	0.135751i
$221$	63792.1	−	110491.i	1.30612	−	2.26226i
$222$	9739.16	−	5622.90i	0.197613	−	0.114092i
$223$		−	74216.1i		−	1.49241i	−0.665716	−	0.746205i	$-0.731874\pi$
$223$		−	74216.1i		−	1.49241i	0.665716	−	0.746205i	$-0.268126\pi$
$224$	−43397.3	−	27093.0i	−0.864901	−	0.539960i
$225$	−383.711			−0.00757947
$226$	−12400.7	−	21478.7i	−0.242790	−	0.420524i
$227$	−20693.0	−	11947.1i	−0.401580	−	0.231852i	0.285585	−	0.958353i	$-0.407812\pi$
$227$	−20693.0	−	11947.1i	−0.401580	−	0.231852i	−0.687166	+	0.726501i	$0.741145\pi$
$228$	−5662.62	+	9807.94i	−0.108930	+	0.188672i
$229$	33123.8	−	19124.1i	0.631640	−	0.364678i	−0.149747	−	0.988724i	$-0.547846\pi$
$229$	33123.8	−	19124.1i	0.631640	−	0.364678i	0.781387	+	0.624047i	$0.214513\pi$
$230$			15238.2i			0.288057i
$231$	22927.3	+	43077.6i	0.429664	+	0.807287i
$232$	46287.3			0.859975
$233$	43530.0	+	75396.1i	0.801820	+	1.38879i	0.918417	+	0.395613i	$0.129468\pi$
$233$	43530.0	+	75396.1i	0.801820	+	1.38879i	−0.116598	+	0.993179i	$0.537199\pi$
$234$	1968.65	+	1136.60i	0.0359531	+	0.0207576i
$235$	−5332.71	+	9236.53i	−0.0965634	+	0.167253i
$236$	−8233.33	+	4753.51i	−0.147826	+	0.0853475i
$237$		−	89494.2i		−	1.59330i
$238$	−47091.8	−	1625.27i	−0.831364	−	0.0286927i
$239$	−7221.47			−0.126424			−0.0632121	−	0.998000i	$-0.520134\pi$
$239$	−7221.47			−0.126424			−0.0632121	+	0.998000i	$0.520134\pi$
$240$	949.440	+	1644.48i	0.0164833	+	0.0285500i
$241$	−70163.0	−	40508.6i	−1.20802	−	0.697451i	−0.245694	−	0.969347i	$-0.579016\pi$
$241$	−70163.0	−	40508.6i	−1.20802	−	0.697451i	−0.962326	+	0.271897i	$0.912349\pi$
$242$	−2261.04	+	3916.23i	−0.0386080	+	0.0668710i
$243$	3873.87	−	2236.58i	0.0656043	−	0.0378767i
$244$			17758.4i			0.298280i
$245$	−24117.6	+	11787.3i	−0.401793	+	0.196373i
$246$	−30118.3			−0.497691
$247$	19298.7	+	33426.3i	0.316325	+	0.547891i
$248$	78877.8	+	45540.1i	1.28248	+	0.740442i
$249$	−28063.3	+	48607.0i	−0.452626	+	0.783971i
$250$	2859.39	−	1650.87i	0.0457502	−	0.0264139i
$251$		−	9872.20i		−	0.156699i	−0.996926	−	0.0783496i	$-0.975035\pi$
$251$		−	9872.20i		−	0.156699i	0.996926	−	0.0783496i	$-0.0249650\pi$
$252$	−54.0523	+	1566.15i	−0.000851164	+	0.0246623i
$253$	65082.4			1.01677
$254$	4647.96	+	8050.50i	0.0720435	+	0.124783i
$255$	34791.2	+	20086.7i	0.535043	+	0.308907i
$256$	30979.4	−	53657.9i	0.472708	−	0.818754i
$257$	−51696.2	+	29846.8i	−0.782694	+	0.451889i	−0.837384	−	0.546615i	$-0.815916\pi$
$257$	−51696.2	+	29846.8i	−0.782694	+	0.451889i	0.0546901	+	0.998503i	$0.482583\pi$
$258$		−	21224.8i		−	0.318863i
$259$	23323.7	−	12413.6i	0.347694	−	0.185054i
$260$	36511.1			0.540105
$261$	−1138.26	−	1971.52i	−0.0167094	−	0.0289415i
$262$	15021.5	+	8672.68i	0.218832	+	0.126343i
$263$	−28159.4	+	48773.6i	−0.407110	+	0.705136i	−0.994565	−	0.104121i	$-0.966797\pi$
$263$	−28159.4	+	48773.6i	−0.407110	+	0.705136i	0.587454	+	0.809257i	$0.300130\pi$
$264$	−53830.7	+	31079.2i	−0.772365	+	0.445925i
$265$			35300.3i			0.502674i
$266$	7549.02	−	12091.9i	0.106691	−	0.170896i
$267$	1596.71			0.0223978
$268$	−27923.1	−	48364.3i	−0.388771	−	0.673372i
$269$	34003.8	+	19632.1i	0.469919	+	0.271308i	0.716206	−	0.697889i	$-0.245877\pi$
$269$	34003.8	+	19632.1i	0.469919	+	0.271308i	−0.246287	+	0.969197i	$0.579211\pi$
$270$	−9801.56	+	16976.8i	−0.134452	+	0.232878i
$271$	−71447.6	+	41250.3i	−0.972857	+	0.561679i	−0.900106	−	0.435671i	$-0.856511\pi$
$271$	−71447.6	+	41250.3i	−0.972857	+	0.561679i	−0.0727506	+	0.997350i	$0.523178\pi$
$272$			7831.04i			0.105848i
$273$	−115013.	−	71802.9i	−1.54320	−	0.963422i
$274$	22707.2			0.302456
$275$	−7050.85	−	12212.4i	−0.0932344	−	0.161487i
$276$	−45950.4	−	26529.5i	−0.603213	−	0.348265i
$277$	−8905.27	+	15424.4i	−0.116061	+	0.201024i	−0.918204	−	0.396109i	$-0.870360\pi$
$277$	−8905.27	+	15424.4i	−0.116061	+	0.201024i	0.802142	+	0.597133i	$0.203694\pi$
$278$	12989.8	−	7499.69i	0.168079	−	0.0970407i
$279$		−	4479.54i		−	0.0575473i
$280$	−16064.9	−	30184.0i	−0.204909	−	0.385000i
$281$	141355.			1.79019			0.895095	−	0.445876i	$-0.147108\pi$
$281$	141355.			1.79019			0.895095	+	0.445876i	$0.147108\pi$
$282$	9947.73	+	17230.0i	0.125091	+	0.216664i
$283$	−26201.4	−	15127.4i	−0.327154	−	0.188882i	0.327423	−	0.944878i	$-0.393820\pi$
$283$	−26201.4	−	15127.4i	−0.327154	−	0.188882i	−0.654577	+	0.755996i	$0.727153\pi$
$284$	−25798.0	+	44683.4i	−0.319852	+	0.553999i
$285$	−10525.2	+	6076.72i	−0.129581	+	0.0748134i
$286$			83542.1i			1.02135i
$287$	−70719.2	−	2440.71i	−0.858566	−	0.0296315i
$288$	−3205.01			−0.0386406
$289$	41077.7	+	71148.7i	0.491825	+	0.851866i
$290$	16964.5	+	9794.44i	0.201718	+	0.116462i
$291$	22375.3	−	38755.1i	0.264230	−	0.457660i
$292$	12575.8	−	7260.64i	0.147492	−	0.0851548i
$293$		−	126488.i		−	1.47337i	−0.676233	−	0.736687i	$-0.736389\pi$
$293$		−	126488.i		−	1.47337i	0.676233	−	0.736687i	$-0.263611\pi$
$294$	−3452.35	+	49956.1i	−0.0399412	+	0.577954i
$295$	−10202.3			−0.117234
$296$	16827.3	+	29145.8i	0.192058	+	0.332653i
$297$	72507.8	+	41862.4i	0.822000	+	0.474582i
$298$	14166.6	−	24537.2i	0.159526	−	0.276307i
$299$	−156603.	+	90414.6i	−1.75169	+	1.01134i
$300$			11496.5i			0.127739i
$301$	1720.00	−	49836.8i	0.0189844	−	0.550069i
$302$	−90982.4			−0.997570
$303$	−17584.4	−	30457.1i	−0.191533	−	0.331744i
$304$	−2051.68	−	1184.54i	−0.0222005	−	0.0128175i
$305$	−9528.53	+	16503.9i	−0.102430	+	0.177414i
$306$	−2556.42	+	1475.95i	−0.0273017	+	0.0157626i
$307$			100711.i			1.06856i	0.845306	+	0.534282i	$0.179418\pi$
$307$			100711.i			1.06856i	−0.845306	+	0.534282i	$0.820582\pi$
$308$	−50839.5	+	27058.4i	−0.535920	+	0.285234i
$309$	−43382.6			−0.454358
$310$	19272.7	+	33381.3i	0.200548	+	0.347360i
$311$	−137912.	−	79623.3i	−1.42587	−	0.823226i	−0.429078	−	0.903267i	$-0.641162\pi$
$311$	−137912.	−	79623.3i	−1.42587	−	0.823226i	−0.996792	+	0.0800410i	$0.974495\pi$
$312$	86352.4	−	149567.i	0.887085	−	1.53648i
$313$	149376.	−	86242.1i	1.52472	−	0.880300i	0.525153	−	0.851008i	$-0.324008\pi$
$313$	149376.	−	86242.1i	1.52472	−	0.880300i	0.999571	−	0.0292920i	$-0.00932528\pi$
$314$		−	10254.4i		−	0.104004i
$315$	−890.577	+	1426.51i	−0.00897533	+	0.0143766i
$316$	105620.			1.05772
$317$	36813.7	+	63763.3i	0.366346	+	0.634530i	0.988991	−	0.147974i	$-0.0472753\pi$
$317$	36813.7	+	63763.3i	0.366346	+	0.634530i	−0.622645	+	0.782504i	$0.713942\pi$
$318$	57027.6	+	32924.9i	0.563937	+	0.325589i
$319$	41832.0	−	72455.2i	0.411081	−	0.712013i
$320$	20903.0	−	12068.3i	0.204131	−	0.117855i
$321$			75477.0i			0.732495i
$322$	56650.9	+	35367.3i	0.546380	+	0.341107i
$323$	−50121.2			−0.480415
$324$	−32833.4	−	56869.1i	−0.312770	−	0.541734i
$325$	33931.8	+	19590.5i	0.321248	+	0.185473i
$326$	31618.4	−	54764.7i	0.297512	−	0.515306i
$327$	69588.4	−	40176.9i	0.650791	−	0.375734i
$328$		−	90133.2i		−	0.837793i
$329$	21961.5	+	41262.9i	0.202894	+	0.381214i
$330$	−26305.5			−0.241557
$331$	25791.2	+	44671.7i	0.235405	+	0.407734i	0.959390	−	0.282082i	$-0.0910249\pi$
$331$	25791.2	+	44671.7i	0.235405	+	0.407734i	−0.723985	+	0.689816i	$0.757692\pi$
$332$	−57365.2	−	33119.8i	−0.520442	−	0.300478i
$333$	827.607	−	1433.46i	0.00746338	−	0.0129270i
$334$	5711.97	−	3297.81i	0.0512028	−	0.0295619i
$335$		−	59930.2i		−	0.534018i
$336$	8317.25	+	287.051i	0.0736718	+	0.00254262i
$337$	26290.2			0.231491			0.115746	−	0.993279i	$-0.463074\pi$
$337$	26290.2			0.231491			0.115746	+	0.993279i	$0.463074\pi$
$338$	−82321.3	−	142585.i	−0.720574	−	1.24807i
$339$	80257.2	+	46336.5i	0.698368	+	0.403203i
$340$	−23706.0	+	41060.0i	−0.205069	+	0.355190i
$341$	142571.	−	82313.5i	1.22609	−	0.707885i
$342$		−	893.022i		−	0.00763502i
$343$	−12154.6	+	117019.i	−0.103312	+	0.994649i
$344$	63518.0			0.536760
$345$	−28469.5	−	49310.7i	−0.239190	−	0.414288i
$346$	−14536.8	−	8392.82i	−0.121427	−	0.0701061i
$347$	28005.7	−	48507.3i	0.232588	−	0.402854i	−0.725981	−	0.687715i	$-0.758614\pi$
$347$	28005.7	−	48507.3i	0.232588	−	0.402854i	0.958569	+	0.284860i	$0.0919473\pi$
$348$	−59069.6	+	34103.9i	−0.487759	+	0.281608i
$349$			97457.4i			0.800136i	0.916485	+	0.400068i	$0.131014\pi$
$349$			97457.4i			0.800136i	−0.916485	+	0.400068i	$0.868986\pi$
$350$	499.120	−	14461.9i	0.00407445	−	0.118056i
$351$	−232626.			−1.88819
$352$	−58893.4	−	102006.i	−0.475315	−	0.823270i
$353$	13445.1	+	7762.53i	0.107898	+	0.0622951i	0.552978	−	0.833196i	$-0.313491\pi$
$353$	13445.1	+	7762.53i	0.107898	+	0.0622951i	−0.445080	+	0.895491i	$0.646825\pi$
$354$	−9515.73	+	16481.7i	−0.0759339	+	0.131521i
$355$	−47951.0	+	27684.5i	−0.380488	+	0.219675i
$356$			1884.42i			0.0148688i
$357$	155425.	−	82722.1i	1.21951	−	0.649061i
$358$	106293.			0.829349
$359$	271.507	+	470.263i	0.00210665	+	0.00364882i	0.867077	−	0.498174i	$-0.165996\pi$
$359$	271.507	+	470.263i	0.00210665	+	0.00364882i	−0.864970	+	0.501823i	$0.832663\pi$
$360$	−1855.09	−	1071.04i	−0.0143139	−	0.00826416i
$361$	−57579.1	+	99729.8i	−0.441825	+	0.765263i
$362$	−126407.	+	72981.1i	−0.964615	+	0.556921i
$363$		−	16897.2i		−	0.128233i
$364$	84740.7	−	135736.i	0.639572	−	1.02446i
$365$	15583.2			0.116969
$366$	17774.7	+	30786.6i	0.132690	+	0.229826i
$367$	−153603.	−	88682.9i	−1.14043	−	0.658427i	−0.193893	−	0.981023i	$-0.562111\pi$
$367$	−153603.	−	88682.9i	−1.14043	−	0.658427i	−0.946537	+	0.322595i	$0.895445\pi$
$368$	5549.59	−	9612.18i	0.0409794	−	0.0709784i
$369$	−3839.06	+	2216.48i	−0.0281950	+	0.0162784i
$370$			14242.7i			0.104037i
$371$	131235.	+	81930.6i	0.953461	+	0.595248i
$372$	−134213.			−0.969862
$373$	95843.8	+	166006.i	0.688884	+	1.19318i	0.972199	+	0.234156i	$0.0752325\pi$
$373$	95843.8	+	166006.i	0.688884	+	1.19318i	−0.283315	+	0.959027i	$0.591434\pi$
$374$	−93950.7	−	54242.5i	−0.671671	−	0.387790i
$375$	−6168.62	+	10684.4i	−0.0438658	+	0.0759777i
$376$	−51563.1	+	29769.9i	−0.364723	+	0.210573i
$377$			232457.i			1.63554i
$378$	40365.3	+	75841.5i	0.282504	+	0.530791i
$379$	150128.			1.04516			0.522582	−	0.852589i	$-0.324969\pi$
$379$	150128.			1.04516			0.522582	+	0.852589i	$0.324969\pi$
$380$	−7171.65	−	12421.7i	−0.0496652	−	0.0860226i
$381$	−30081.4	−	17367.5i	−0.207228	−	0.119643i
$382$	−46945.5	+	81312.0i	−0.321712	+	0.557221i
$383$	1659.42	−	958.064i	0.0113125	−	0.00653126i	−0.494333	−	0.869273i	$-0.664588\pi$
$383$	1659.42	−	958.064i	0.0113125	−	0.00653126i	0.505646	+	0.862741i	$0.331254\pi$
$384$			102447.i			0.694761i
$385$	−61766.7	−	2131.74i	−0.416709	−	0.0143818i
$386$	−173260.			−1.16285
$387$	−1561.98	−	2705.43i	−0.0104293	−	0.0180640i
$388$	45738.2	+	26406.9i	0.303819	+	0.175410i
$389$	18629.1	−	32266.5i	0.123110	−	0.213232i	−0.797883	−	0.602813i	$-0.794047\pi$
$389$	18629.1	−	32266.5i	0.123110	−	0.213232i	0.920992	+	0.389580i	$0.127380\pi$
$390$	63296.9	−	36544.5i	0.416153	−	0.240266i
$391$		−	234819.i		−	1.53596i
$392$	−149500.	−	10331.6i	−0.972904	−	0.0672353i
$393$	−64812.6			−0.419637
$394$	−83836.6	−	145209.i	−0.540059	−	0.935409i
$395$	98158.4	+	56671.8i	0.629119	+	0.363222i
$396$	−1803.97	+	3124.56i	−0.0115037	+	0.0199250i
$397$	220648.	−	127391.i	1.39997	−	0.808274i	0.405582	−	0.914059i	$-0.367069\pi$
$397$	220648.	−	127391.i	1.39997	−	0.808274i	0.994389	+	0.105785i	$0.0337354\pi$
$398$		−	8097.23i		−	0.0511176i
$399$	−1837.22	+	53233.1i	−0.0115403	+	0.334377i
$400$	−2404.91			−0.0150307
$401$	−10345.4	−	17918.8i	−0.0643368	−	0.111435i	0.832063	−	0.554681i	$-0.187160\pi$
$401$	−10345.4	−	17918.8i	−0.0643368	−	0.111435i	−0.896400	+	0.443247i	$0.853827\pi$
$402$	−96817.1	−	55897.4i	−0.599101	−	0.345891i
$403$	−228705.	+	396129.i	−1.40820	+	2.43908i
$404$	35945.0	−	20752.9i	0.220230	−	0.127150i
$405$		−	70468.9i		−	0.429623i
$406$	75786.4	−	40336.0i	0.459769	−	0.244704i
$407$	60830.5			0.367226
$408$	112134.	+	194222.i	0.673625	+	1.16675i
$409$	−76648.2	−	44252.9i	−0.458200	−	0.264542i	0.253087	−	0.967444i	$-0.418554\pi$
$409$	−76648.2	−	44252.9i	−0.458200	−	0.264542i	−0.711287	+	0.702901i	$0.751887\pi$
$410$	19072.3	−	33034.1i	0.113458	−	0.196515i
$411$	−73480.1	+	42423.8i	−0.434997	+	0.251146i
$412$		−	51199.4i		−	0.301627i
$413$	−23679.0	+	37928.8i	−0.138824	+	0.222366i
$414$	4183.83			0.0244103
$415$	−35541.9	−	61560.3i	−0.206369	−	0.357441i
$416$	283421.	+	163633.i	1.63774	+	0.945551i
$417$	−28023.3	+	48537.8i	−0.161156	+	0.279131i
$418$	28422.4	−	16409.7i	0.162670	−	0.0939177i
$419$		−	208106.i		−	1.18538i	−0.805432	−	0.592688i	$-0.798067\pi$
$419$		−	208106.i		−	1.18538i	0.805432	−	0.592688i	$-0.201933\pi$
$420$	42740.4	+	26682.9i	0.242292	+	0.151264i
$421$	−20020.3			−0.112956			−0.0564778	−	0.998404i	$-0.517987\pi$
$421$	−20020.3			−0.112956			−0.0564778	+	0.998404i	$0.517987\pi$
$422$	−9571.45	−	16578.2i	−0.0537468	−	0.0930923i
$423$	2535.99	+	1464.16i	0.0141732	+	0.00818289i
$424$	−98532.2	+	170663.i	−0.548083	+	0.949308i
$425$	−44062.7	+	25439.6i	−0.243946	+	0.140842i
$426$			103286.i			0.569146i
$427$	39240.9	+	73728.9i	0.215220	+	0.404373i
$428$	−89076.8			−0.486270
$429$	−156081.	−	270341.i	−0.848080	−	1.46892i
$430$	23279.6	+	13440.5i	0.125904	+	0.0726905i
$431$	12223.5	−	21171.8i	0.0658025	−	0.113973i	−0.831247	−	0.555903i	$-0.812373\pi$
$431$	12223.5	−	21171.8i	0.0658025	−	0.113973i	0.897050	+	0.441930i	$0.145706\pi$
$432$	12365.5	−	7139.24i	0.0662590	−	0.0382546i
$433$			62356.0i			0.332585i	0.986076	+	0.166292i	$0.0531795\pi$
$433$			62356.0i			0.332585i	−0.986076	+	0.166292i	$0.946820\pi$
$434$	168832.	+	5826.85i	0.896345	+	0.0309353i
$435$	−73195.7			−0.386818
$436$	47416.1	+	82127.1i	0.249433	+	0.432030i
$437$	61521.1	+	35519.2i	0.322152	+	0.185995i
$438$	14534.6	−	25174.6i	0.0757625	−	0.131224i
$439$	163500.	−	94396.7i	0.848376	−	0.489810i	−0.0117263	−	0.999931i	$-0.503733\pi$
$439$	163500.	−	94396.7i	0.848376	−	0.489810i	0.860103	+	0.510121i	$0.170399\pi$
$440$		−	78723.0i		−	0.406627i
$441$	3236.33	+	6621.76i	0.0166409	+	0.0340484i
$442$	301421.			1.54287
$443$	−144661.	−	250560.i	−0.737129	−	1.27674i	−0.953783	−	0.300496i	$-0.902848\pi$
$443$	−144661.	−	250560.i	−0.737129	−	1.27674i	0.216654	−	0.976248i	$-0.430486\pi$
$444$	−42948.4	−	24796.3i	−0.217862	−	0.125783i
$445$	−1011.11	+	1751.30i	−0.00510598	+	0.00884381i
$446$	151847.	−	87668.9i	0.763372	−	0.440733i
$447$			105869.i			0.529852i
$448$	3648.71	−	105721.i	0.0181796	−	0.526750i
$449$	−236914.			−1.17516			−0.587581	−	0.809165i	$-0.699920\pi$
$449$	−236914.			−1.17516			−0.587581	+	0.809165i	$0.699920\pi$
$450$	−453.264	−	785.077i	−0.00223834	−	0.00387692i
$451$	−141089.	−	81457.6i	−0.693648	−	0.400478i
$452$	−54685.6	+	94718.3i	−0.267668	+	0.463614i
$453$	294418.	−	169982.i	1.43472	−	0.828337i
$454$		−	56450.9i		−	0.273879i
$455$	151586.	−	80678.8i	0.732210	−	0.389706i
$456$	−67846.7			−0.326287
$457$	−61797.0	−	107036.i	−0.295893	−	0.512502i	0.679299	−	0.733862i	$-0.262284\pi$
$457$	−61797.0	−	107036.i	−0.295893	−	0.512502i	−0.975192	+	0.221359i	$0.928951\pi$
$458$	78256.1	+	45181.2i	0.373067	+	0.215390i
$459$	151040.	−	261610.i	0.716915	−	1.24173i
$460$	58195.7	−	33599.3i	0.275027	−	0.158787i
$461$		−	74323.1i		−	0.349721i	−0.984593	−	0.174861i	$-0.944053\pi$
$461$		−	74323.1i		−	0.349721i	0.984593	−	0.174861i	$-0.0559475\pi$
$462$	−61054.1	+	97795.6i	−0.286043	+	0.458179i
$463$	24703.3			0.115237			0.0576186	−	0.998339i	$-0.481649\pi$
$463$	24703.3			0.115237			0.0576186	+	0.998339i	$0.481649\pi$
$464$	−7134.05	−	12356.5i	−0.0331360	−	0.0573933i
$465$	−124732.	−	72014.1i	−0.576863	−	0.333052i
$466$	−102841.	+	178126.i	−0.473581	+	0.820266i
$467$	−57164.2	+	33003.7i	−0.262114	+	0.151332i	−0.625298	−	0.780386i	$-0.715023\pi$
$467$	−57164.2	+	33003.7i	−0.262114	+	0.151332i	0.363185	+	0.931717i	$0.381689\pi$
$468$		−	10024.5i		−	0.0457690i
$469$	−222801.	−	139096.i	−1.01291	−	0.632365i
$470$	−25197.4			−0.114067
$471$	19158.3	+	33183.2i	0.0863605	+	0.149581i
$472$	−49323.9	−	28477.1i	−0.221398	−	0.127824i
$473$	57404.2	−	99427.1i	0.256579	−	0.444408i
$474$	183106.	−	105716.i	0.814979	−	0.470528i
$475$		−	15392.2i		−	0.0682203i
$476$	97627.4	+	183430.i	0.430881	+	0.809574i
$477$	9692.09			0.0425972
$478$	−8530.48	−	14775.2i	−0.0373351	−	0.0646663i
$479$	299681.	+	173021.i	1.30613	+	0.754096i	0.981449	−	0.191726i	$-0.0614084\pi$
$479$	299681.	+	173021.i	1.30613	+	0.754096i	0.324685	+	0.945822i	$0.394742\pi$
$480$	−51524.5	+	89243.0i	−0.223631	+	0.387339i
$481$	−146372.	+	84507.7i	−0.632655	+	0.365264i
$482$		−	191406.i		−	0.823874i
$483$	−249398.	−	8607.41i	−1.06905	−	0.0368959i
$484$	19941.8			0.0851281
$485$	28338.1	+	49082.9i	0.120472	+	0.208664i
$486$	9152.14	+	5283.99i	0.0387481	+	0.0223712i
$487$	104034.	−	180193.i	0.438651	−	0.759766i	−0.558935	−	0.829212i	$-0.688790\pi$
$487$	104034.	−	180193.i	0.438651	−	0.759766i	0.997586	+	0.0694459i	$0.0221231\pi$
$488$	−92133.2	+	53193.1i	−0.386880	+	0.223365i
$489$			236290.i			0.988161i
$490$	−52606.3	−	35421.0i	−0.219101	−	0.147526i
$491$	31227.4			0.129531			0.0647653	−	0.997901i	$-0.479370\pi$
$491$	31227.4			0.129531			0.0647653	+	0.997901i	$0.479370\pi$
$492$	66408.9	+	115024.i	0.274344	+	0.475178i
$493$	−261420.	−	150931.i	−1.07558	−	0.620989i
$494$	−45593.7	+	78970.6i	−0.186832	+	0.323602i
$495$	−3353.06	+	1935.89i	−0.0136846	+	0.00790078i
$496$		−	28075.6i		−	0.114121i
$497$	−8370.08	+	242521.i	−0.0338857	+	0.981832i
$498$	−132601.			−0.534672
$499$	46479.8	+	80505.4i	0.186665	+	0.323314i	0.944136	−	0.329555i	$-0.106899\pi$
$499$	46479.8	+	80505.4i	0.186665	+	0.323314i	−0.757471	+	0.652869i	$0.773565\pi$
$500$	−12609.5	−	7280.11i	−0.0504381	−	0.0291205i
$501$	−12322.6	+	21343.3i	−0.0490937	+	0.0850328i
$502$	20198.6	−	11661.7i	0.0801521	−	0.0462758i
$503$			401841.i			1.58825i	0.607757	+	0.794123i	$0.292069\pi$
$503$			401841.i			1.58825i	−0.607757	+	0.794123i	$0.707931\pi$
$504$	−8287.35	+	4410.79i	−0.0326253	+	0.0173642i
$505$	44541.0			0.174654
$506$	76879.6	+	133159.i	0.300269	+	0.520081i
$507$	532781.	+	307601.i	2.07268	+	1.19666i
$508$	20496.9	−	35501.7i	0.0794256	−	0.137569i
$509$	−241739.	+	139568.i	−0.933064	+	0.538704i	−0.887779	−	0.460270i	$-0.847753\pi$
$509$	−241739.	+	139568.i	−0.933064	+	0.538704i	−0.0452844	+	0.998974i	$0.514419\pi$
$510$			94910.9i			0.364901i
$511$	36168.0	−	57933.4i	0.138510	−	0.221864i
$512$	−39300.4			−0.149919
$513$	45693.4	+	79143.3i	0.173628	+	0.300732i
$514$	−122134.	−	70514.0i	−0.462285	−	0.266900i
$515$	27471.8	−	47582.5i	0.103579	−	0.179404i
$516$	−81058.6	+	46799.2i	−0.304439	+	0.175768i
$517$			107618.i			0.402628i
$518$	52949.8	+	33056.7i	0.197335	+	0.123197i
$519$	62721.1			0.232851
$520$	109364.	+	189425.i	0.404454	+	0.700535i
$521$	−213004.	−	122978.i	−0.784715	−	0.453056i	0.0533834	−	0.998574i	$-0.482999\pi$
$521$	−213004.	−	122978.i	−0.784715	−	0.453056i	−0.838099	+	0.545518i	$0.816333\pi$
$522$	2689.17	−	4657.78i	0.00986910	−	0.0170938i
$523$	−242584.	+	140056.i	−0.886869	+	0.512034i	−0.872917	−	0.487869i	$-0.837774\pi$
$523$	−242584.	+	140056.i	−0.886869	+	0.512034i	−0.0139516	+	0.999903i	$0.504441\pi$
$524$		−	76490.8i		−	0.278578i
$525$	25404.0	+	47731.0i	0.0921685	+	0.173174i
$526$	−133055.			−0.480905
$527$	−296989.	−	514399.i	−1.06935	−	1.85216i
$528$	16593.4	+	9580.19i	0.0595205	+	0.0343642i
$529$	−26487.6	+	45877.8i	−0.0946522	+	0.163942i
$530$	−72224.9	+	41699.0i	−0.257119	+	0.148448i
$531$			2801.15i			0.00993451i
$532$	−62824.9	−	2168.26i	−0.221977	−	0.00766104i
$533$	452654.			1.59335
$534$	1886.14	+	3266.90i	0.00661443	+	0.0114565i
$535$	−82784.1	−	47795.4i	−0.289228	−	0.166986i
$536$	167281.	−	289739.i	0.582259	−	1.00850i
$537$	−343961.	+	198586.i	−1.19278	+	0.688653i
$538$			92762.8i			0.320486i
$539$	−151283.	+	224681.i	−0.520730	+	0.773373i
$540$	86447.2			0.296458
$541$	−96042.2	−	166350.i	−0.328146	−	0.568366i	0.653998	−	0.756496i	$-0.273091\pi$
$541$	−96042.2	−	166350.i	−0.328146	−	0.568366i	−0.982144	+	0.188130i	$0.939757\pi$
$542$	−168797.	−	97455.0i	−0.574601	−	0.331746i
$543$	272701.	−	472331.i	0.924883	−	1.60194i
$544$	−368041.	+	212489.i	−1.24365	+	0.718022i
$545$			101767.i			0.342622i
$546$	11048.8	−	320136.i	0.0370620	−	1.07386i
$547$	103731.			0.346685			0.173342	−	0.984862i	$-0.444543\pi$
$547$	103731.			0.346685			0.173342	+	0.984862i	$0.444543\pi$
$548$	−50067.9	−	86720.1i	−0.166724	−	0.288774i
$549$	4531.33	+	2616.16i	0.0150342	+	0.00868001i
$550$	16657.9	−	28852.3i	0.0550673	−	0.0953793i
$551$	79085.8	−	45660.2i	0.260493	−	0.150396i
$552$		−	317863.i		−	1.04319i
$553$	438509.	−	233389.i	1.43393	−	0.763184i
$554$	−42078.0			−0.137099
$555$	−26609.6	−	46089.2i	−0.0863878	−	0.149628i
$556$	−57283.5	−	33072.6i	−0.185302	−	0.106984i
$557$	−26740.9	+	46316.6i	−0.0861918	+	0.149289i	−0.905898	−	0.423495i	$-0.860803\pi$
$557$	−26740.9	+	46316.6i	−0.0861918	+	0.149289i	0.819707	+	0.572784i	$0.194136\pi$
$558$	9165.19	−	5291.53i	0.0294356	−	0.0169947i
$559$			318991.i			1.02083i
$560$	−5581.70	+	8940.69i	−0.0177988	+	0.0285099i
$561$	405364.			1.28801
$562$	166978.	+	289214.i	0.528672	+	0.915687i
$563$	−2115.51	−	1221.39i	−0.00667417	−	0.00385334i	0.496659	−	0.867946i	$-0.334560\pi$
$563$	−2115.51	−	1221.39i	−0.00667417	−	0.00385334i	−0.503333	+	0.864092i	$0.667893\pi$
$564$	43868.2	−	75981.9i	0.137909	−	0.238865i
$565$	−101645.	+	58684.7i	−0.318412	+	0.183835i
$566$		−	71477.9i		−	0.223120i
$567$	−261981.	−	163555.i	−0.814899	−	0.508744i
$568$	−309099.			−0.958077
$569$	312029.	+	540450.i	0.963763	+	1.66929i	0.712903	+	0.701263i	$0.247380\pi$
$569$	312029.	+	540450.i	0.963763	+	1.66929i	0.250860	+	0.968023i	$0.419286\pi$
$570$	−24866.1	−	14356.4i	−0.0765345	−	0.0441872i
$571$	−38637.1	+	66921.3i	−0.118504	+	0.205254i	−0.919175	−	0.393850i	$-0.871143\pi$
$571$	−38637.1	+	66921.3i	−0.118504	+	0.205254i	0.800671	+	0.599104i	$0.204476\pi$
$572$	319052.	−	184205.i	0.975146	−	0.563001i
$573$		−	350832.i		−	1.06854i
$574$	−78544.4	−	147575.i	−0.238392	−	0.447910i
$575$	72112.8			0.218110
$576$	−3313.50	−	5739.15i	−0.00998715	−	0.0172983i
$577$	−477830.	−	275875.i	−1.43523	−	0.828631i	−0.437718	−	0.899112i	$-0.644213\pi$
$577$	−477830.	−	275875.i	−1.43523	−	0.828631i	−0.997513	+	0.0704812i	$0.977547\pi$
$578$	−97047.3	+	168091.i	−0.290488	+	0.503140i
$579$	560666.	−	323701.i	1.67243	−	0.965576i
$580$		−	86384.4i		−	0.256791i
$581$	−311353.	−	10745.6i	−0.922360	−	0.0318332i
$582$	105724.			0.312126
$583$	178096.	+	308472.i	0.523984	+	0.907567i
$584$	75338.5	+	43496.7i	0.220898	+	0.127535i
$585$	5378.80	−	9316.36i	0.0157171	−	0.0272229i
$586$	258795.	−	149416.i	0.753635	−	0.435112i
$587$			45284.3i			0.131423i	0.997839	+	0.0657115i	$0.0209317\pi$
$587$			45284.3i			0.131423i	−0.997839	+	0.0657115i	$0.979068\pi$
$588$	198397.	−	96965.1i	0.573827	−	0.280453i
$589$	179693.			0.517964
$590$	−12051.6	−	20874.0i	−0.0346210	−	0.0599654i
$591$	542588.	+	313263.i	1.55344	+	0.896880i
$592$	5187.03	−	8984.21i	0.0148005	−	0.0256352i
$593$	−30166.0	+	17416.4i	−0.0857844	+	0.0495277i	−0.542279	−	0.840199i	$-0.682438\pi$
$593$	−30166.0	+	17416.4i	−0.0857844	+	0.0495277i	0.456494	+	0.889726i	$0.349105\pi$
$594$			197802.i			0.560607i
$595$	−7691.35	+	222855.i	−0.0217254	+	0.629490i
$596$	−124945.			−0.351745
$597$	15128.0	+	26202.5i	0.0424457	+	0.0735181i
$598$	−369979.	−	213607.i	−1.03460	−	0.597329i
$599$	53294.7	−	92309.1i	0.148535	−	0.257271i	−0.782151	−	0.623089i	$-0.785877\pi$
$599$	53294.7	−	92309.1i	0.148535	−	0.257271i	0.930686	+	0.365818i	$0.119211\pi$
$600$	−59645.6	+	34436.4i	−0.165682	+	0.0956567i
$601$		−	112464.i		−	0.311362i	−0.987807	−	0.155681i	$-0.950243\pi$
$601$		−	112464.i		−	0.311362i	0.987807	−	0.155681i	$-0.0497573\pi$
$602$	103998.	−	55351.3i	0.286968	−	0.152734i
$603$	−16454.5			−0.0452533
$604$	200610.	+	347467.i	0.549894	+	0.952445i
$605$	18533.0	+	10700.0i	0.0506332	+	0.0292331i
$606$	41543.8	−	71955.9i	0.113125	−	0.195939i
$607$	−288800.	+	166739.i	−0.783826	+	0.452542i	−0.837784	−	0.546001i	$-0.816149\pi$
$607$	−288800.	+	166739.i	−0.783826	+	0.452542i	0.0539585	+	0.998543i	$0.482816\pi$
$608$		−	128566.i		−	0.347792i
$609$	−169884.	+	272118.i	−0.458056	+	0.733707i
$610$	−45022.9			−0.120997
$611$	−149506.	−	258953.i	−0.400477	−	0.693646i
$612$	11273.5	+	6508.75i	0.0300992	+	0.0173778i
$613$	162337.	−	281175.i	0.432012	−	0.748266i	−0.565035	−	0.825067i	$-0.691137\pi$
$613$	162337.	−	281175.i	0.432012	−	0.748266i	0.997046	+	0.0768010i	$0.0244706\pi$
$614$	−206056.	+	118967.i	−0.546574	+	0.315564i
$615$			142531.i			0.376841i
$616$	−292667.	−	182713.i	−0.771280	−	0.481512i
$617$	54190.8			0.142349			0.0711747	−	0.997464i	$-0.477325\pi$
$617$	54190.8			0.142349			0.0711747	+	0.997464i	$0.477325\pi$
$618$	−51246.3	−	88761.2i	−0.134179	−	0.232405i
$619$	−27588.2	−	15928.1i	−0.0720016	−	0.0415702i	0.463567	−	0.886062i	$-0.346569\pi$
$619$	−27588.2	−	15928.1i	−0.0720016	−	0.0415702i	−0.535569	+	0.844492i	$0.679903\pi$
$620$	84990.0	−	147207.i	0.221098	−	0.382953i
$621$	−370788.	+	214074.i	−0.961484	+	0.555113i
$622$		−	376225.i		−	0.972449i
$623$	4164.01	+	7823.68i	0.0107284	+	0.0201574i
$624$	−53236.4			−0.136722
$625$	−7812.50	−	13531.6i	−0.0200000	−	0.0346410i
$626$	352905.	+	203750.i	0.900552	+	0.519934i
$627$	−61316.3	+	106203.i	−0.155970	+	0.270148i
$628$	−39162.3	+	22610.3i	−0.0992998	+	0.0573308i
$629$		−	219478.i		−	0.554740i
$630$	−3970.67	−	137.039i	−0.0100042	−	0.000345273i
$631$	83642.3			0.210071			0.105036	−	0.994468i	$-0.466504\pi$
$631$	83642.3			0.210071			0.105036	+	0.994468i	$0.466504\pi$
$632$	316371.	+	547970.i	0.792068	+	1.37190i
$633$	61946.1	+	35764.6i	0.154599	+	0.0892578i
$634$	−86973.6	+	150643.i	−0.216376	+	0.374774i
$635$	38097.9	−	21995.8i	0.0944829	−	0.0545497i
$636$		−	290389.i		−	0.717903i
$637$	51886.1	−	750799.i	0.127871	−	1.85031i
$638$	197659.			0.485596
$639$	7601.10	+	13165.5i	0.0186155	+	0.0322430i
$640$	−112365.	−	64873.9i	−0.274328	−	0.158383i
$641$	−142082.	+	246094.i	−0.345799	+	0.598942i	−0.985499	−	0.169683i	$-0.945726\pi$
$641$	−142082.	+	246094.i	−0.345799	+	0.598942i	0.639699	+	0.768625i	$0.279059\pi$
$642$	−154427.	+	89158.4i	−0.374673	+	0.216318i
$643$			121681.i			0.294307i	0.989114	+	0.147153i	$0.0470111\pi$
$643$			121681.i			0.294307i	−0.989114	+	0.147153i	$0.952989\pi$
$644$	10158.3	−	294336.i	0.0244935	−	0.709694i
$645$	−100443.			−0.241436
$646$	−59206.4	−	102549.i	−0.141874	−	0.245733i
$647$	499313.	+	288279.i	1.19279	+	0.688659i	0.958939	−	0.283613i	$-0.0915331\pi$
$647$	499313.	+	288279.i	1.19279	+	0.688659i	0.233853	+	0.972272i	$0.424866\pi$
$648$	196697.	−	340689.i	0.468433	−	0.811350i
$649$	−89152.6	+	51472.3i	−0.211663	+	0.122204i
$650$			92566.5i			0.219092i
$651$	−557224.	+	296572.i	−1.31482	+	0.699792i
$652$	−278866.			−0.655995
$653$	−218047.	−	377668.i	−0.511355	−	0.885694i	−0.999913	−	0.0131622i	$-0.995810\pi$
$653$	−218047.	−	377668.i	−0.511355	−	0.885694i	0.488558	−	0.872531i	$-0.337523\pi$
$654$	164405.	+	94919.1i	0.384378	+	0.221921i
$655$	41042.2	−	71087.2i	0.0956640	−	0.165695i
$656$	−24061.3	+	13891.8i	−0.0559129	+	0.0322813i
$657$		−	4278.54i		−	0.00991208i
$658$	−58482.1	+	93675.9i	−0.135074	+	0.216359i
$659$	−378597.			−0.871779			−0.435890	−	0.900000i	$-0.643566\pi$
$659$	−378597.			−0.871779			−0.435890	+	0.900000i	$0.643566\pi$
$660$	58002.0	+	100462.i	0.133154	+	0.230630i
$661$	651728.	+	376275.i	1.49164	+	0.861197i	0.999954	−	0.00957646i	$-0.00304833\pi$
$661$	651728.	+	376275.i	1.49164	+	0.861197i	0.491684	+	0.870774i	$0.336382\pi$
$662$	−60932.6	+	105538.i	−0.139038	+	0.240821i
$663$	−975395.	+	563145.i	−2.21898	+	1.28113i
$664$		−	396826.i		−	0.900044i
$665$	−57223.3	−	35724.7i	−0.129399	−	0.0807840i
$666$	3910.49			0.00881623
$667$	213919.	+	370519.i	0.480837	+	0.832834i
$668$	−25189.1	−	14542.9i	−0.0564494	−	0.0325911i
$669$	−327583.	+	567390.i	−0.731929	+	1.26774i
$670$	122618.	−	70793.5i	0.273152	−	0.157704i
$671$			192293.i			0.427088i
$672$	212191.	+	398681.i	0.469881	+	0.882850i
$673$	−97686.9			−0.215678			−0.107839	−	0.994168i	$-0.534393\pi$
$673$	−97686.9			−0.215678			−0.107839	+	0.994168i	$0.534393\pi$
$674$	31055.8	+	53790.1i	0.0683632	+	0.118408i
$675$	80340.3	+	46384.5i	0.176330	+	0.101804i
$676$	−363026.	+	628779.i	−0.794409	+	1.37596i
$677$	358909.	−	207216.i	0.783082	−	0.452112i	−0.0544397	−	0.998517i	$-0.517337\pi$
$677$	358909.	−	207216.i	0.783082	−	0.452112i	0.837521	+	0.546405i	$0.184004\pi$
$678$			218943.i			0.476290i
$679$	248246.	+	8567.66i	0.538447	+	0.0185833i
$680$	−284034.			−0.614260
$681$	105467.	+	182674.i	0.227417	+	0.393897i
$682$	336829.	+	194468.i	0.724170	+	0.418100i
$683$	320551.	−	555211.i	0.687157	−	1.19019i	−0.285597	−	0.958350i	$-0.592192\pi$
$683$	320551.	−	555211.i	0.687157	−	1.19019i	0.972754	−	0.231840i	$-0.0744747\pi$
$684$	−3410.51	+	1969.06i	−0.00728965	+	0.00420868i
$685$		−	107459.i		−	0.229013i
$686$	−253781.	+	113363.i	−0.539276	+	0.240891i
$687$	−337647.			−0.715401
$688$	−9789.75	−	16956.3i	−0.0206821	−	0.0358224i
$689$	−857079.	−	494835.i	−1.80544	−	1.04237i
$690$	67260.2	−	116498.i	0.141273	−	0.244692i
$691$	510907.	−	294973.i	1.07001	−	0.617768i	0.141823	−	0.989892i	$-0.454704\pi$
$691$	510907.	−	294973.i	1.07001	−	0.617768i	0.928183	+	0.372124i	$0.121370\pi$
$692$			74022.5i			0.154579i
$693$	−585.292	+	16958.7i	−0.00121873	+	0.0353124i
$694$	132329.			0.274748
$695$	−35491.2	−	61472.6i	−0.0734770	−	0.127266i
$696$	−353872.	−	204308.i	−0.730512	−	0.421761i
$697$	−293900.	+	509050.i	−0.604971	+	1.04784i
$698$	−199399.	+	115123.i	−0.409272	+	0.236293i
$699$		−	768549.i		−	1.57296i
$700$	−56331.3	+	29981.4i	−0.114962	+	0.0611864i
$701$	726881.			1.47920			0.739601	−	0.673046i	$-0.235014\pi$
$701$	726881.			1.47920			0.739601	+	0.673046i	$0.235014\pi$
$702$	−274794.	−	475956.i	−0.557612	−	0.965813i
$703$	57501.8	+	33198.7i	0.116351	+	0.0671754i
$704$	121774.	−	210919.i	0.245702	−	0.425569i
$705$	81538.4	−	47076.2i	0.164053	−	0.0947160i
$706$			36678.4i			0.0735870i
$707$	103378.	−	165589.i	0.206818	−	0.331279i
$708$	83926.3			0.167429
$709$	27376.8	+	47418.0i	0.0544616	+	0.0943302i	0.891971	−	0.452093i	$-0.149322\pi$
$709$	27376.8	+	47418.0i	0.0544616	+	0.0943302i	−0.837509	+	0.546423i	$0.815989\pi$
$710$	−113286.	−	65405.6i	−0.224729	−	0.129747i
$711$	15559.9	−	26950.5i	0.0307798	−	0.0533123i
$712$	−9776.63	+	5644.54i	−0.0192854	+	0.0111344i
$713$			841864.i			1.65601i
$714$	352848.	+	220284.i	0.692136	+	0.432103i
$715$	395351.			0.773341
$716$	−234368.	−	405938.i	−0.457165	−	0.791833i
$717$	55209.0	+	31874.9i	0.107392	+	0.0620027i
$718$	−641.443	+	1111.01i	−0.00124425	+	0.00215511i
$719$	729749.	−	421321.i	1.41161	−	0.814996i	0.416073	−	0.909331i	$-0.363406\pi$
$719$	729749.	−	421321.i	1.41161	−	0.814996i	0.995540	+	0.0943355i	$0.0300726\pi$
$720$			660.295i			0.00127372i
$721$	−113136.	−	212568.i	−0.217635	−	0.408911i
$722$	−272065.			−0.521912
$723$	357603.	+	619386.i	0.684107	+	1.18491i
$724$	557438.	+	321837.i	1.06346	+	0.613987i
$725$	46350.8	−	80281.9i	0.0881822	−	0.152736i
$726$	34571.8	−	19960.0i	0.0655916	−	0.0378693i
$727$		−	163904.i		−	0.310113i	−0.987906	−	0.155057i	$-0.950444\pi$
$727$		−	163904.i		−	0.310113i	0.987906	−	0.155057i	$-0.0495560\pi$
$728$	958051.	+	33065.0i	1.80770	+	0.0623886i
$729$	−550026.			−1.03497
$730$	18407.9	+	31883.4i	0.0345429	+	0.0598300i
$731$	−358735.	−	207116.i	−0.671334	−	0.387595i
$732$	78383.9	−	135765.i	0.146287	−	0.253376i
$733$	494785.	−	285664.i	0.920892	−	0.531677i	0.0369727	−	0.999316i	$-0.488229\pi$
$733$	494785.	−	285664.i	0.920892	−	0.531677i	0.883920	+	0.467639i	$0.154895\pi$
$734$		−	419032.i		−	0.777777i
$735$	236410.	+	16337.8i	0.437614	+	0.0302425i
$736$	602334.			1.11194
$737$	−302359.	−	523701.i	−0.556657	−	0.964158i
$738$	−9069.89	−	5236.50i	−0.0166529	−	0.00961454i
$739$	443959.	−	768959.i	0.812931	−	1.40804i	−0.0978725	−	0.995199i	$-0.531204\pi$
$739$	443959.	−	768959.i	0.812931	−	1.40804i	0.910804	−	0.412839i	$-0.135463\pi$
$740$	54393.7	−	31404.2i	0.0993311	−	0.0573489i
$741$		−	340730.i		−	0.620546i
$742$	−12607.2	+	365291.i	−0.0228987	+	0.663485i
$743$	−1.05528e6			−1.91157			−0.955783	−	0.294074i	$-0.904989\pi$
$743$	−1.05528e6			−1.91157			−0.955783	+	0.294074i	$0.904989\pi$
$744$	−402020.	−	696319.i	−0.726276	−	1.25795i
$745$	−116119.	−	67041.2i	−0.209214	−	0.120790i
$746$	−226434.	+	392195.i	−0.406877	+	0.704732i
$747$	−16902.1	+	9758.41i	−0.0302899	+	0.0174879i
$748$			478404.i			0.855051i
$749$	−369827.	+	196834.i	−0.659227	+	0.350862i
$750$	−29147.1			−0.0518171
$751$	−323750.	−	560751.i	−0.574023	−	0.994237i	−0.996147	−	0.0876993i	$-0.972049\pi$
$751$	−323750.	−	560751.i	−0.574023	−	0.994237i	0.422124	−	0.906538i	$-0.361285\pi$
$752$	15894.4	+	9176.61i	0.0281065	+	0.0162273i
$753$	−43575.0	+	75474.1i	−0.0768506	+	0.133109i
$754$	−475611.	+	274594.i	−0.836583	+	0.483001i
$755$			430561.i			0.755338i
$756$	200640.	−	321383.i	0.351055	−	0.562314i
$757$	131510.			0.229491			0.114745	−	0.993395i	$-0.463395\pi$
$757$	131510.			0.229491			0.114745	+	0.993395i	$0.463395\pi$
$758$	177342.	+	307165.i	0.308654	+	0.534605i
$759$	−497563.	−	287268.i	−0.863702	−	0.498659i
$760$	42963.6	−	74415.1i	0.0743830	−	0.128835i
$761$	21820.4	−	12598.0i	0.0376784	−	0.0217536i	−0.481042	−	0.876697i	$-0.659742\pi$
$761$	21820.4	−	12598.0i	0.0376784	−	0.0217536i	0.518721	+	0.854944i	$0.326408\pi$
$762$		−	82062.6i		−	0.141330i
$763$	378338.	+	236198.i	0.649877	+	0.405720i
$764$	414047.			0.709354
$765$	6984.73	+	12097.9i	0.0119351	+	0.0206722i
$766$	3920.42	+	2263.46i	0.00668152	+	0.00385758i
$767$	143014.	−	247707.i	0.243101	−	0.421064i
$768$	−473682.	+	273480.i	−0.803090	+	0.463664i
$769$		−	319994.i		−	0.541115i	−0.962704	−	0.270557i	$-0.912792\pi$
$769$		−	319994.i		−	0.541115i	0.962704	−	0.270557i	$-0.0872080\pi$
$770$	−68601.3	−	128893.i	−0.115705	−	0.217395i
$771$	526964.			0.886487
$772$	382026.	+	661689.i	0.641001	+	1.11025i
$773$	−716378.	−	413601.i	−1.19890	−	0.692186i	−0.238591	−	0.971120i	$-0.576686\pi$
$773$	−716378.	−	413601.i	−1.19890	−	0.692186i	−0.960310	+	0.278934i	$0.910019\pi$
$774$	3690.23	−	6391.67i	0.00615987	−	0.0106692i
$775$	157972.	−	91205.2i	0.263013	−	0.151850i
$776$			316395.i			0.525420i
$777$	−233105.	−	8045.08i	−0.386108	−	0.0133257i
$778$	88023.6			0.145425
$779$	−88912.1	−	154000.i	−0.146516	−	0.253774i
$780$	−279131.	−	161156.i	−0.458796	−	0.264886i
$781$	−279347.	+	483843.i	−0.457975	+	0.793236i
$782$	480442.	−	277383.i	0.785646	−	0.453593i
$783$			550389.i			0.897731i
$784$	20283.7	+	41502.0i	0.0330002	+	0.0675206i
$785$	−48527.6			−0.0787498
$786$	−76560.8	−	132607.i	−0.123926	−	0.214646i
$787$	127433.	+	73573.4i	0.205746	+	0.118788i	0.599333	−	0.800500i	$-0.295433\pi$
$787$	127433.	+	73573.4i	0.205746	+	0.118788i	−0.393587	+	0.919287i	$0.628766\pi$
$788$	−369708.	+	640354.i	−0.595397	+	1.03126i
$789$	430564.	−	248586.i	0.691646	−	0.399322i
$790$			267778.i			0.429062i
$791$	−17742.6	+	514088.i	−0.0283573	+	0.821646i
$792$	−21614.3			−0.0344580
$793$	−267139.	−	462698.i	−0.424806	−	0.735786i
$794$	521288.	+	300966.i	0.826869	+	0.477393i
$795$	155812.	−	269875.i	0.246529	−	0.427000i
$796$	−30923.8	+	17853.9i	−0.0488053	+	0.0281777i
$797$		−	85804.0i		−	0.135080i	−0.997717	−	0.0675400i	$-0.978485\pi$
$797$		−	85804.0i		−	0.135080i	0.997717	−	0.0675400i	$-0.0215150\pi$
$798$	−111086.	+	59123.4i	−0.174443	+	0.0928440i
$799$	388288.			0.608219
$800$	−65255.2	−	113025.i	−0.101961	−	0.176602i
$801$	480.838	+	277.612i	0.000749434	+	0.000432686i
$802$	24441.4	−	42333.7i	0.0379994	−	0.0658169i
$803$	136174.	−	78620.1i	0.211185	−	0.121928i
$804$			493000.i			0.762667i
$805$	167371.	−	268092.i	0.258278	−	0.413707i
$806$	−1.08065e6			−1.66346
$807$	−173308.	−	300179.i	−0.266117	−	0.460928i
$808$	215338.	+	124325.i	0.329836	+	0.190431i
$809$	−189747.	+	328652.i	−0.289920	+	0.502156i	−0.973790	−	0.227447i	$-0.926962\pi$
$809$	−189747.	+	328652.i	−0.289920	+	0.502156i	0.683870	+	0.729604i	$0.260295\pi$
$810$	144180.	−	83242.5i	0.219753	−	0.126875i
$811$			686920.i			1.04439i	0.852825	+	0.522197i	$0.174888\pi$
$811$			686920.i			1.04439i	−0.852825	+	0.522197i	$0.825112\pi$
$812$	−321150.	−	200495.i	−0.487074	−	0.304082i
$813$	728299.			1.10187
$814$	71857.0	+	124460.i	0.108448	+	0.187837i
$815$	−259166.	−	149630.i	−0.390178	−	0.225269i
$816$	34565.5	−	59869.2i	0.0519113	−	0.0899131i
$817$	108526.	−	62657.5i	0.162589	−	0.0938705i
$818$		−	209097.i		−	0.312494i
$819$	−22151.3	−	41619.5i	−0.0330241	−	0.0620482i
$820$	−168212.			−0.250167
$821$	407240.	+	705361.i	0.604177	+	1.04647i	0.992181	+	0.124808i	$0.0398314\pi$
$821$	407240.	+	705361.i	0.604177	+	1.04647i	−0.388004	+	0.921658i	$0.626835\pi$
$822$	−173599.	−	100227.i	−0.256923	−	0.148335i
$823$	91290.1	−	158119.i	0.134780	−	0.233445i	−0.790734	−	0.612160i	$-0.790301\pi$
$823$	91290.1	−	158119.i	0.134780	−	0.233445i	0.925513	+	0.378715i	$0.123634\pi$
$824$	265630.	−	153362.i	0.391222	−	0.225872i
$825$			124487.i			0.182901i
$826$	−105574.	−	3643.65i	−0.154738	−	0.00534043i
$827$	−1.07962e6			−1.57855			−0.789275	−	0.614040i	$-0.789543\pi$
$827$	−1.07962e6			−1.57855			−0.789275	+	0.614040i	$0.789543\pi$
$828$	−9225.06	−	15978.3i	−0.0134558	−	0.0233061i
$829$	−1.00399e6	−	579653.i	−1.46090	−	0.843450i	−0.461845	−	0.886961i	$-0.652812\pi$
$829$	−1.00399e6	−	579653.i	−1.46090	−	0.843450i	−0.999053	+	0.0435111i	$0.986146\pi$
$830$	83968.7	−	145438.i	0.121888	−	0.211116i
$831$	136164.	−	78614.1i	0.197178	−	0.113841i
$832$			676689.i			0.977558i
$833$	810654.	+	545832.i	1.16828	+	0.786627i
$834$	−132412.			−0.190368
$835$	−15606.4	−	27031.1i	−0.0223836	−	0.0387696i
$836$	−125339.	−	72364.5i	−0.179339	−	0.103541i
$837$	−541505.	+	937914.i	−0.772950	+	1.33879i
$838$	425787.	−	245828.i	0.606324	−	0.350061i
$839$			652032.i			0.926286i	0.886284	+	0.463143i	$0.153278\pi$
$839$			652032.i			0.926286i	−0.886284	+	0.463143i	$0.846722\pi$
$840$	−10411.4	+	301669.i	−0.0147554	+	0.427535i
$841$	−157292.			−0.222389
$842$	−23649.3	−	40961.9i	−0.0333576	−	0.0577771i
$843$	−1.08068e6	−	623929.i	−1.52069	−	0.877970i
$844$	−42208.9	+	73107.9i	−0.0592541	+	0.102631i
$845$	−674761.	+	389574.i	−0.945011	+	0.545602i
$846$			6918.22i			0.00966616i
$847$	82793.7	−	44065.5i	0.115407	−	0.0614231i
$848$	60745.3			0.0844736
$849$	133542.	+	231301.i	0.185269	+	0.320895i
$850$	−104099.	−	60101.8i	−0.144082	−	0.0831859i
$851$	−155536.	+	269397.i	−0.214770	+	0.371992i
$852$	394457.	−	227740.i	0.543400	−	0.313732i
$853$			440903.i			0.605962i	0.952997	+	0.302981i	$0.0979819\pi$
$853$			440903.i			0.605962i	−0.952997	+	0.302981i	$0.902018\pi$
$854$	−104496.	+	167381.i	−0.143280	+	0.229504i
$855$	−4226.10			−0.00578106
$856$	−266819.	−	462144.i	−0.364140	−	0.630710i
$857$	992254.	+	572878.i	1.35102	+	0.780011i	0.988392	−	0.151924i	$-0.0485469\pi$
$857$	992254.	+	572878.i	1.35102	+	0.780011i	0.362626	+	0.931935i	$0.381880\pi$
$858$	368747.	−	638689.i	0.500904	−	0.867590i
$859$	66164.8	−	38200.3i	0.0896687	−	0.0517703i	−0.454495	−	0.890749i	$-0.650180\pi$
$859$	66164.8	−	38200.3i	0.0896687	−	0.0517703i	0.544164	+	0.838979i	$0.316847\pi$
$860$		−	118542.i		−	0.160278i
$861$	529883.	+	330808.i	0.714782	+	0.446241i
$862$	57756.9			0.0777301
$863$	−279307.	−	483775.i	−0.375026	−	0.649563i	0.615305	−	0.788289i	$-0.289033\pi$
$863$	−279307.	−	483775.i	−0.375026	−	0.649563i	−0.990331	+	0.138725i	$0.955699\pi$
$864$	671056.	+	387434.i	0.898941	+	0.519004i
$865$	−39717.8	+	68793.3i	−0.0530827	+	0.0919420i
$866$	−127581.	+	73658.9i	−0.170118	+	0.0982177i
$867$		−	725253.i		−	0.964831i
$868$	−350010.	−	657627.i	−0.464559	−	0.872851i
$869$	1.14368e6			1.51448
$870$	−86463.5	−	149759.i	−0.114234	−	0.197859i
$871$	1.45508e6	+	840093.i	1.91801	+	1.10737i
$872$	−284058.	+	492004.i	−0.373572	+	0.647046i
$873$	13476.3	−	7780.53i	0.0176824	−	0.0102089i
$874$			167830.i			0.219709i
$875$	−68438.8	−	2362.01i	−0.0893895	−	0.00308508i
$876$	−128191.			−0.167051
$877$	−766947.	−	1.32839e6i	−0.997163	−	1.72714i	−0.563764	−	0.825936i	$-0.690647\pi$
$877$	−766947.	−	1.32839e6i	−0.997163	−	1.72714i	−0.433399	−	0.901202i	$-0.642686\pi$
$878$	386274.	+	223015.i	0.501079	+	0.289298i
$879$	−558305.	+	967013.i	−0.722593	+	1.25157i
$880$	−21015.3	+	12133.2i	−0.0271376	+	0.0156679i
$881$		−	1.04666e6i		−	1.34851i	−0.738498	−	0.674256i	$-0.764464\pi$
$881$		−	1.04666e6i		−	1.34851i	0.738498	−	0.674256i	$-0.235536\pi$
$882$	−9725.23	+	14443.6i	−0.0125015	+	0.0185669i
$883$	−554282.			−0.710901			−0.355450	−	0.934695i	$-0.615673\pi$
$883$	−554282.			−0.710901			−0.355450	+	0.934695i	$0.615673\pi$
$884$	−664615.	−	1.15115e6i	−0.850482	−	1.47308i
$885$	77997.5	+	45031.9i	0.0995850	+	0.0574954i
$886$	341766.	−	591955.i	0.435372	−	0.754087i
$887$	−142874.	+	82488.6i	−0.181596	+	0.104845i	−0.588043	−	0.808830i	$-0.700101\pi$
$887$	−142874.	+	82488.6i	−0.181596	+	0.104845i	0.406446	+	0.913675i	$0.366768\pi$
$888$		−	297097.i		−	0.376766i
$889$	6650.16	−	192687.i	0.00841450	−	0.243809i
$890$	−4777.56			−0.00603151
$891$	−355528.	−	615793.i	−0.447836	−	0.775674i
$892$	−669625.	−	386608.i	−0.841593	−	0.485894i
$893$	−58733.3	+	101729.i	−0.0736514	+	0.127568i
$894$	−216610.	+	125060.i	−0.271021	+	0.156474i
$895$		−	503015.i		−	0.627964i
$896$	−501974.	+	267167.i	−0.625267	+	0.332787i
$897$	1.59633e6			1.98398
$898$	−279858.	−	484729.i	−0.347045	−	0.601099i
$899$	937232.	+	541111.i	1.15965	+	0.669526i
$900$	−1998.84	+	3462.09i	−0.00246770	+	0.00427418i
$901$	1.11297e6	−	642575.i	1.37099	−	0.791543i
$902$		−	384892.i		−	0.473070i
$903$	−233125.	+	373416.i	−0.285899	+	0.457949i
$904$	−655217.			−0.801767
$905$	345373.	+	598203.i	0.421688	+	0.730384i
$906$	695571.	+	401588.i	0.847393	+	0.489243i
$907$	97474.0	−	168830.i	0.118488	−	0.205227i	−0.800681	−	0.599091i	$-0.795529\pi$
$907$	97474.0	−	168830.i	0.118488	−	0.205227i	0.919169	+	0.393864i	$0.128862\pi$
$908$	−215589.	+	124471.i	−0.261490	+	0.150971i
$909$		−	12229.2i		−	0.0148003i
$910$	344133.	+	214843.i	0.415569	+	0.259441i
$911$	−1.42407e6			−1.71591			−0.857955	−	0.513726i	$-0.828265\pi$
$911$	−1.42407e6			−1.71591			−0.857955	+	0.513726i	$0.828265\pi$
$912$	10456.9	+	18111.9i	0.0125723	+	0.0217758i
$913$	−621166.	−	358630.i	−0.745188	−	0.430234i
$914$	145997.	−	252875.i	0.174764	−	0.302701i
$915$	145693.	−	84116.1i	0.174019	−	0.100470i
$916$		−	398486.i		−	0.474922i
$917$	−169022.	−	317572.i	−0.201004	−	0.377663i
$918$	713675.			0.846867
$919$	616265.	+	1.06740e6i	0.729687	+	1.26385i	0.957016	+	0.290037i	$0.0936675\pi$
$919$	616265.	+	1.06740e6i	0.729687	+	1.26385i	−0.227329	+	0.973818i	$0.572999\pi$
$920$	348636.	+	201285.i	0.411905	+	0.237813i
$921$	444529.	−	769948.i	0.524060	−	0.907699i
$922$	152066.	−	87795.3i	0.178883	−	0.103278i
$923$		−	1.55231e6i		−	1.82211i
$924$	508107.	+	17536.2i	0.595130	+	0.0205396i
$925$	67401.6			0.0787747
$926$	29181.1	+	50543.2i	0.0340314	+	0.0589442i
$927$	−13064.3	−	7542.69i	−0.0152029	−	0.00877741i
$928$	387153.	−	670568.i	0.449559	−	0.778659i
$929$	−310706.	+	179386.i	−0.360013	+	0.207854i	−0.669087	−	0.743184i	$-0.733315\pi$
$929$	−310706.	+	179386.i	−0.360013	+	0.207854i	0.309073	+	0.951038i	$0.399981\pi$
$930$		−	340271.i		−	0.393423i
$931$	−265626.	+	129823.i	−0.306458	+	0.149779i
$932$	907030.			1.04421
$933$	702900.	+	1.21746e6i	0.807477	+	1.39859i
$934$	−135052.	−	77972.4i	−0.154813	−	0.0893813i
$935$	−256695.	+	444608.i	−0.293625	+	0.508574i
$936$	52008.7	−	30027.2i	0.0593641	−	0.0342739i
$937$			941678.i			1.07256i	0.844039	+	0.536282i	$0.180172\pi$
$937$			941678.i			1.07256i	−0.844039	+	0.536282i	$0.819828\pi$
$938$	21403.5	−	620163.i	0.0243265	−	0.704856i
$939$	−1.52266e6			−1.72692
$940$	55558.6	+	96230.3i	0.0628776	+	0.108907i
$941$	−700931.	−	404683.i	−0.791583	−	0.457020i	0.0489369	−	0.998802i	$-0.484417\pi$
$941$	−700931.	−	404683.i	−0.791583	−	0.457020i	−0.840519	+	0.541781i	$0.817750\pi$
$942$	−45262.1	+	78396.2i	−0.0510074	+	0.0883473i
$943$	721494.	−	416555.i	0.811352	−	0.468434i
$944$			17556.2i			0.0197009i
$945$	358909.	−	191023.i	0.401903	−	0.213906i
$946$	271239.			0.303088
$947$	567520.	+	982974.i	0.632822	+	1.09608i	0.986972	+	0.160891i	$0.0514368\pi$
$947$	567520.	+	982974.i	0.632822	+	1.09608i	−0.354150	+	0.935188i	$0.615230\pi$
$948$	−807474.	−	466195.i	−0.898487	−	0.518742i
$949$	−218443.	+	378354.i	−0.242552	+	0.420113i
$950$	31492.6	−	18182.3i	0.0348949	−	0.0201466i
$951$		−	649970.i		−	0.718674i
$952$	−659231.	+	1.05595e6i	−0.727384	+	1.16511i
$953$	175576.			0.193322			0.0966608	−	0.995317i	$-0.469184\pi$
$953$	175576.			0.193322			0.0966608	+	0.995317i	$0.469184\pi$
$954$	11448.9	+	19830.1i	0.0125796	+	0.0217886i
$955$	384797.	+	222163.i	0.421915	+	0.243593i
$956$	−37618.3	+	65156.8i	−0.0411607	+	0.0712925i
$957$	−639621.	+	369285.i	−0.698391	+	0.403216i
$958$			817533.i			0.890788i
$959$	−399497.	−	249407.i	−0.434386	−	0.271189i
$960$	−213074.			−0.231200
$961$	602993.	+	1.04441e6i	0.652928	+	1.13091i
$962$	−345808.	−	199652.i	−0.373667	−	0.215737i
$963$	−13122.8	+	22729.3i	−0.0141505	+	0.0245095i
$964$	−730990.	+	422037.i	−0.786606	+	0.454147i
$965$			819927.i			0.880482i
$966$	−276994.	−	520439.i	−0.296836	−	0.557719i
$967$	−406655.			−0.434884			−0.217442	−	0.976073i	$-0.569771\pi$
$967$	−406655.			−0.434884			−0.217442	+	0.976073i	$0.569771\pi$
$968$	59733.1	+	103461.i	0.0637477	+	0.110414i
$969$	383182.	+	221230.i	0.408092	+	0.235612i
$970$	−66949.5	+	115960.i	−0.0711548	+	0.123244i
$971$	−593480.	+	342646.i	−0.629459	+	0.363418i	−0.780543	−	0.625103i	$-0.785057\pi$
$971$	−593480.	+	342646.i	−0.629459	+	0.363418i	0.151084	+	0.988521i	$0.451724\pi$
$972$		−	46603.4i		−	0.0493270i
$973$	−310909.	−	10730.3i	−0.328404	−	0.0113341i
$974$	491569.			0.518163
$975$	−172942.	−	299544.i	−0.181924	−	0.315102i
$976$	28400.1	+	16396.8i	0.0298140	+	0.0172131i
$977$	666825.	−	1.15497e6i	0.698590	−	1.20999i	−0.270365	−	0.962758i	$-0.587144\pi$
$977$	666825.	−	1.15497e6i	0.698590	−	1.20999i	0.968955	−	0.247236i	$-0.0795223\pi$
$978$	−483452.	+	279121.i	−0.505447	+	0.291820i
$979$			20405.0i			0.0212897i
$980$	−19281.6	+	279007.i	−0.0200766	+	0.290512i
$981$	27941.3			0.0290341
$982$	36887.8	+	63891.5i	0.0382525	+	0.0662553i
$983$	885533.	+	511263.i	0.916427	+	0.529099i	0.882493	−	0.470325i	$-0.155863\pi$
$983$	885533.	+	511263.i	0.916427	+	0.529099i	0.0339336	+	0.999424i	$0.489197\pi$
$984$	−397839.	+	689078.i	−0.410882	+	0.711669i
$985$	−687182.	+	396745.i	−0.708271	+	0.408920i
$986$		−	713157.i		−	0.733552i
$987$	14232.9	−	412396.i	0.0146103	−	0.423331i
$988$	402124.			0.411952
$989$	293552.	+	508446.i	0.300118	+	0.519820i
$990$	−7921.71	−	4573.60i	−0.00808255	−	0.00466646i
$991$	−683213.	+	1.18336e6i	−0.695679	+	1.20495i	0.274272	+	0.961652i	$0.411563\pi$
$991$	−683213.	+	1.18336e6i	−0.695679	+	1.20495i	−0.969951	+	0.243300i	$0.921770\pi$
$992$	1.31949e6	−	761807.i	1.34086	−	0.774144i
$993$		−	455361.i		−	0.461803i
$994$	−506089.	+	269357.i	−0.512217	+	0.272618i
$995$	−38319.0			−0.0387051
$996$	292376.	+	506410.i	0.294729	+	0.510485i
$997$	−330246.	−	190668.i	−0.332237	−	0.191817i	0.324597	−	0.945852i	$-0.394771\pi$
$997$	−330246.	−	190668.i	−0.332237	−	0.191817i	−0.656834	+	0.754035i	$0.728105\pi$
$998$	−109810.	+	190196.i	−0.110251	+	0.190960i
$999$	−346564.	+	200089.i	−0.347258	+	0.200490i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	35.5.h.a.31.7	yes	20
5.2	odd	4		175.5.j.b.24.7		40
5.3	odd	4		175.5.j.b.24.14		40
5.4	even	2		175.5.i.b.101.4		20
7.3	odd	6		245.5.d.a.146.7		20
7.4	even	3		245.5.d.a.146.8		20
7.5	odd	6	inner	35.5.h.a.26.7	✓	20
35.12	even	12		175.5.j.b.124.14		40
35.19	odd	6		175.5.i.b.26.4		20
35.33	even	12		175.5.j.b.124.7		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
35.5.h.a.26.7	✓	20	7.5	odd	6	inner
35.5.h.a.31.7	yes	20	1.1	even	1	trivial
175.5.i.b.26.4		20	35.19	odd	6
175.5.i.b.101.4		20	5.4	even	2
175.5.j.b.24.7		40	5.2	odd	4
175.5.j.b.24.14		40	5.3	odd	4
175.5.j.b.124.7		40	35.33	even	12
175.5.j.b.124.14		40	35.12	even	12
245.5.d.a.146.7		20	7.3	odd	6
245.5.d.a.146.8		20	7.4	even	3

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:	\( N \)	\(=\)	\( 35 = 5 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	35.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.18127 + 2.04601i) q^{2} +(-7.64511 - 4.41391i) q^{3} +(5.20922 - 9.02264i) q^{4} +(9.68246 - 5.59017i) q^{5} -20.8560i q^{6} +(1.69012 - 48.9708i) q^{7} +62.4144 q^{8} +(-1.53484 - 2.65843i) q^{9} +(22.8751 + 13.2069i) q^{10} +(56.4068 - 97.6995i) q^{11} +(-79.6502 + 45.9861i) q^{12} +313.449i q^{13} +(102.191 - 54.3896i) q^{14} -98.6980 q^{15} +(-9.61965 - 16.6617i) q^{16} +(-352.502 - 203.517i) q^{17} +(3.62611 - 6.28061i) q^{18} +(106.640 - 61.5688i) q^{19} -116.482i q^{20} +(-229.074 + 366.928i) q^{21} +266.526 q^{22} +(288.451 + 499.612i) q^{23} +(-477.165 - 275.491i) q^{24} +(62.5000 - 108.253i) q^{25} +(-641.320 + 370.266i) q^{26} +742.152i q^{27} +(-433.042 - 270.349i) q^{28} +741.613 q^{29} +(-116.588 - 201.937i) q^{30} +(1263.78 + 729.642i) q^{31} +(522.042 - 904.203i) q^{32} +(-862.473 + 497.949i) q^{33} -961.629i q^{34} +(-257.391 - 483.606i) q^{35} -31.9814 q^{36} +(269.606 + 466.972i) q^{37} +(251.941 + 145.458i) q^{38} +(1383.53 - 2396.35i) q^{39} +(604.325 - 348.907i) q^{40} -1444.11i q^{41} +(-1021.33 - 35.2491i) q^{42} +1017.68 q^{43} +(-587.672 - 1017.88i) q^{44} +(-29.7221 - 17.1601i) q^{45} +(-681.475 + 1180.35i) q^{46} +(-826.140 + 476.972i) q^{47} +169.841i q^{48} +(-2395.29 - 165.533i) q^{49} +295.316 q^{50} +(1796.61 + 3111.82i) q^{51} +(2828.14 + 1632.82i) q^{52} +(-1578.68 + 2734.35i) q^{53} +(-1518.45 + 876.678i) q^{54} -1261.29i q^{55} +(105.488 - 3056.49i) q^{56} -1087.04 q^{57} +(876.041 + 1517.35i) q^{58} +(-790.264 - 456.259i) q^{59} +(-514.140 + 890.516i) q^{60} +(-1476.15 + 852.257i) q^{61} +3447.60i q^{62} +(-132.779 + 70.6695i) q^{63} +2158.85 q^{64} +(1752.23 + 3034.95i) q^{65} +(-2037.62 - 1176.42i) q^{66} +(2680.16 - 4642.17i) q^{67} +(-3672.52 + 2120.33i) q^{68} -5092.79i q^{69} +(685.417 - 1097.89i) q^{70} -4952.36 q^{71} +(-95.7963 - 165.924i) q^{72} +(1207.07 + 696.902i) q^{73} +(-636.953 + 1103.24i) q^{74} +(-955.639 + 551.738i) q^{75} -1282.90i q^{76} +(-4689.09 - 2927.41i) q^{77} +6537.28 q^{78} +(5068.88 + 8779.55i) q^{79} +(-186.284 - 107.551i) q^{80} +(3151.47 - 5458.50i) q^{81} +(2954.66 - 1705.88i) q^{82} -6357.92i q^{83} +(2117.36 + 3978.26i) q^{84} -4550.77 q^{85} +(1202.15 + 2082.19i) q^{86} +(-5669.71 - 3273.41i) q^{87} +(3520.60 - 6097.85i) q^{88} +(-156.641 + 90.4366i) q^{89} -81.0824i q^{90} +(15349.8 + 529.765i) q^{91} +6010.43 q^{92} +(-6441.14 - 11156.4i) q^{93} +(-1951.78 - 1126.86i) q^{94} +(688.361 - 1192.28i) q^{95} +(-7982.14 + 4608.49i) q^{96} +5069.26i q^{97} +(-2490.79 - 5096.32i) q^{98} -346.303 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q + 6 q^{2} - 18 q^{3} - 58 q^{4} - 54 q^{7} - 372 q^{8} + 266 q^{9} + 90 q^{11} + 1266 q^{12} - 690 q^{14} + 100 q^{15} - 126 q^{16} - 864 q^{17} - 848 q^{18} - 1662 q^{19} + 1680 q^{21} + 2584 q^{22}+ \cdots - 36716 q^{99}+O(q^{100}) \) 20 * q + 6 * q^2 - 18 * q^3 - 58 * q^4 - 54 * q^7 - 372 * q^8 + 266 * q^9 + 90 * q^11 + 1266 * q^12 - 690 * q^14 + 100 * q^15 - 126 * q^16 - 864 * q^17 - 848 * q^18 - 1662 * q^19 + 1680 * q^21 + 2584 * q^22 - 1242 * q^23 + 1908 * q^24 + 1250 * q^25 - 1350 * q^26 - 134 * q^28 + 840 * q^29 + 800 * q^30 - 3636 * q^31 - 1758 * q^32 + 384 * q^33 + 150 * q^35 - 4164 * q^36 + 1068 * q^37 + 9180 * q^38 + 2976 * q^39 - 4146 * q^42 - 7692 * q^43 - 3618 * q^44 - 1800 * q^45 + 2038 * q^46 - 11412 * q^47 + 416 * q^49 + 1500 * q^50 + 6324 * q^51 - 7476 * q^52 + 1668 * q^53 + 33180 * q^54 + 13500 * q^56 + 15264 * q^57 + 1174 * q^58 + 216 * q^59 - 8250 * q^60 - 5856 * q^61 - 23632 * q^63 - 25788 * q^64 - 4650 * q^65 - 16248 * q^66 + 34 * q^67 - 6444 * q^68 + 900 * q^70 + 10488 * q^71 - 12052 * q^72 + 22776 * q^73 + 2538 * q^74 - 2250 * q^75 + 40488 * q^77 + 23784 * q^78 + 20788 * q^79 + 14400 * q^80 + 4154 * q^81 - 34146 * q^82 - 20316 * q^84 + 12000 * q^85 + 1980 * q^86 - 27474 * q^87 - 36148 * q^88 - 13176 * q^89 + 17976 * q^91 + 61404 * q^92 - 22908 * q^93 - 50610 * q^94 - 6900 * q^95 - 17460 * q^96 - 39606 * q^98 - 36716 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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