LMFDB - Embedded newform 31.4.g.a.7.1

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [31,4,Mod(7,31)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(31, base_ring=CyclotomicField(30)) chi = DirichletCharacter(H, H._module([28])) N = Newforms(chi, 4, names="a")

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("31.7"); S:= CuspForms(chi, 4); N := Newforms(S);

Level:	$ N $	$=$	$ 31 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	31.g (of order $15$, degree $8$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

gp:f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.82905921018$
Analytic rank:	$0$
Dimension:	$56$
Relative dimension:	$7$ over $\Q(\zeta_{15})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{15}]$

Embedding invariants

Embedding label			7.1
Character	$\chi$	$=$	31.7
Dual form			31.4.g.a.9.1

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.65450 - 5.09202i) q^{2} +(-3.03615 + 0.645354i) q^{3} +(-16.7192 + 12.1472i) q^{4} +(4.36814 - 7.56584i) q^{5} +(8.30946 + 14.3924i) q^{6} +(-10.2190 - 4.54979i) q^{7} +(54.8634 + 39.8606i) q^{8} +(-15.8640 + 7.06311i) q^{9} +(-45.7525 - 9.72500i) q^{10} +(-7.30901 - 69.5406i) q^{11} +(42.9227 - 47.6705i) q^{12} +(-8.72426 - 9.68927i) q^{13} +(-6.26031 + 59.5629i) q^{14} +(-8.37969 + 25.7900i) q^{15} +(61.1103 - 188.078i) q^{16} +(-4.06483 + 38.6743i) q^{17} +(62.2124 + 69.0939i) q^{18} +(90.0339 - 99.9927i) q^{19} +(18.8720 + 179.555i) q^{20} +(33.9626 + 7.21898i) q^{21} +(-342.010 + 152.273i) q^{22} +(48.9682 + 35.5775i) q^{23} +(-192.298 - 85.6165i) q^{24} +(24.3387 + 42.1558i) q^{25} +(-34.9037 + 60.4550i) q^{26} +(111.409 - 80.9433i) q^{27} +(226.120 - 48.0634i) q^{28} +(-7.02700 - 21.6269i) q^{29} +145.188 q^{30} +(-146.847 - 90.7027i) q^{31} -516.287 q^{32} +(67.0696 + 206.419i) q^{33} +(203.655 - 43.2883i) q^{34} +(-79.0610 + 57.4412i) q^{35} +(179.436 - 310.793i) q^{36} +(5.99876 + 10.3902i) q^{37} +(-658.126 - 293.017i) q^{38} +(32.7412 + 23.7879i) q^{39} +(541.230 - 240.971i) q^{40} +(101.987 + 21.6779i) q^{41} +(-19.4319 - 184.882i) q^{42} +(-264.451 + 293.702i) q^{43} +(966.925 + 1073.88i) q^{44} +(-15.8578 + 150.877i) q^{45} +(100.143 - 308.210i) q^{46} +(78.1197 - 240.428i) q^{47} +(-64.1632 + 610.472i) q^{48} +(-145.785 - 161.910i) q^{49} +(174.390 - 193.680i) q^{50} +(-12.6171 - 120.044i) q^{51} +(263.560 + 56.0214i) q^{52} +(297.631 - 132.514i) q^{53} +(-596.491 - 433.376i) q^{54} +(-558.060 - 248.465i) q^{55} +(-379.291 - 656.952i) q^{56} +(-208.826 + 361.697i) q^{57} +(-98.4983 + 71.5632i) q^{58} +(-212.048 + 45.0722i) q^{59} +(-173.175 - 532.978i) q^{60} -28.6679 q^{61} +(-218.902 + 897.815i) q^{62} +194.250 q^{63} +(365.312 + 1124.32i) q^{64} +(-111.416 + 23.6823i) q^{65} +(940.123 - 683.040i) q^{66} +(85.9501 - 148.870i) q^{67} +(-401.823 - 695.978i) q^{68} +(-171.635 - 76.4167i) q^{69} +(423.298 + 307.544i) q^{70} +(777.917 - 346.351i) q^{71} +(-1151.89 - 244.842i) q^{72} +(76.5344 + 728.177i) q^{73} +(42.9820 - 47.7363i) q^{74} +(-101.101 - 112.284i) q^{75} +(-290.661 + 2765.46i) q^{76} +(-241.704 + 743.889i) q^{77} +(66.9581 - 206.076i) q^{78} +(-4.95029 + 47.0988i) q^{79} +(-1156.03 - 1283.90i) q^{80} +(27.7134 - 30.7789i) q^{81} +(-58.3521 - 555.184i) q^{82} +(8.31790 + 1.76802i) q^{83} +(-655.517 + 291.855i) q^{84} +(274.848 + 199.689i) q^{85} +(1933.07 + 860.659i) q^{86} +(35.2920 + 61.1275i) q^{87} +(2370.93 - 4106.58i) q^{88} +(-11.8413 + 8.60322i) q^{89} +(794.507 - 168.878i) q^{90} +(45.0690 + 138.708i) q^{91} -1250.87 q^{92} +(504.385 + 180.619i) q^{93} -1353.51 q^{94} +(-363.249 - 1117.96i) q^{95} +(1567.52 - 333.187i) q^{96} +(573.772 - 416.870i) q^{97} +(-583.250 + 1010.22i) q^{98} +(607.123 + 1051.57i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) $ 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/31\mathbb{Z}\right)^\times$.

$n$	$3$
$\chi(n)$	$e\left(\frac{14}{15}\right)$

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 $

$2$	−1.65450	−	5.09202i	−0.584953	−	1.80030i	−0.599457	−	0.800407i	$-0.704617\pi$
$2$	−1.65450	−	5.09202i	−0.584953	−	1.80030i	0.0145039	−	0.999895i	$-0.495383\pi$
$3$	−3.03615	+	0.645354i	−0.584308	+	0.124198i	−0.490575	−	0.871399i	$-0.663213\pi$
$3$	−3.03615	+	0.645354i	−0.584308	+	0.124198i	−0.0937326	+	0.995597i	$0.529880\pi$
$4$	−16.7192	+	12.1472i	−2.08990	+	1.51840i
$5$	4.36814	−	7.56584i	0.390699	−	0.676710i	−0.601843	−	0.798614i	$-0.705567\pi$
$5$	4.36814	−	7.56584i	0.390699	−	0.676710i	0.992542	+	0.121904i	$0.0389002\pi$
$6$	8.30946	+	14.3924i	0.565387	+	0.979279i
$7$	−10.2190	−	4.54979i	−0.551773	−	0.245665i	0.111859	−	0.993724i	$-0.464319\pi$
$7$	−10.2190	−	4.54979i	−0.551773	−	0.245665i	−0.663633	+	0.748059i	$0.730986\pi$
$8$	54.8634	+	39.8606i	2.42464	+	1.76161i
$9$	−15.8640	+	7.06311i	−0.587555	+	0.261597i
$10$	−45.7525	−	9.72500i	−1.44682	−	0.307532i
$11$	−7.30901	−	69.5406i	−0.200341	−	1.90612i	−0.384341	−	0.923191i	$-0.625571\pi$
$11$	−7.30901	−	69.5406i	−0.200341	−	1.90612i	0.184000	−	0.982926i	$-0.441095\pi$
$12$	42.9227	−	47.6705i	1.03256	−	1.14677i
$13$	−8.72426	−	9.68927i	−0.186129	−	0.206717i	0.642858	−	0.765986i	$-0.277749\pi$
$13$	−8.72426	−	9.68927i	−0.186129	−	0.206717i	−0.828986	+	0.559269i	$0.811082\pi$
$14$	−6.26031	+	59.5629i	−0.119510	+	1.13706i
$15$	−8.37969	+	25.7900i	−0.144242	+	0.443931i
$16$	61.1103	−	188.078i	0.954849	−	2.93872i
$17$	−4.06483	+	38.6743i	−0.0579921	+	0.551758i	0.926496	+	0.376305i	$0.122806\pi$
$17$	−4.06483	+	38.6743i	−0.0579921	+	0.551758i	−0.984488	+	0.175453i	$0.943861\pi$
$18$	62.2124	+	69.0939i	0.814645	+	0.904755i
$19$	90.0339	−	99.9927i	1.08712	−	1.20736i	0.110161	−	0.993914i	$-0.464863\pi$
$19$	90.0339	−	99.9927i	1.08712	−	1.20736i	0.976954	−	0.213450i	$-0.0684700\pi$
$20$	18.8720	+	179.555i	0.210996	+	2.00749i
$21$	33.9626	+	7.21898i	0.352917	+	0.0750147i
$22$	−342.010	+	152.273i	−3.31440	+	1.47566i
$23$	48.9682	+	35.5775i	0.443938	+	0.322540i	0.787198	−	0.616701i	$-0.211531\pi$
$23$	48.9682	+	35.5775i	0.443938	+	0.322540i	−0.343260	+	0.939240i	$0.611531\pi$
$24$	−192.298	−	85.6165i	−1.63553	−	0.728183i
$25$	24.3387	+	42.1558i	0.194709	+	0.337246i
$26$	−34.9037	+	60.4550i	−0.263276	+	0.456008i
$27$	111.409	−	80.9433i	0.794099	−	0.576946i
$28$	226.120	−	48.0634i	1.52617	−	0.324397i
$29$	−7.02700	−	21.6269i	−0.0449959	−	0.138483i	0.926035	−	0.377438i	$-0.123195\pi$
$29$	−7.02700	−	21.6269i	−0.0449959	−	0.138483i	−0.971031	+	0.238955i	$0.923195\pi$
$30$	145.188			0.883584
$31$	−146.847	−	90.7027i	−0.850790	−	0.525506i
$31$	−146.847	−	90.7027i	−0.850790	−	0.525506i
$32$	−516.287			−2.85211
$33$	67.0696	+	206.419i	0.353797	+	1.08888i
$34$	203.655	−	43.2883i	1.02725	−	0.218349i
$35$	−79.0610	+	57.4412i	−0.381821	+	0.277409i
$36$	179.436	−	310.793i	0.830723	−	1.43885i
$37$	5.99876	+	10.3902i	0.0266538	+	0.0461657i	0.879045	−	0.476739i	$-0.158181\pi$
$37$	5.99876	+	10.3902i	0.0266538	+	0.0461657i	−0.852391	+	0.522905i	$0.824848\pi$
$38$	−658.126	−	293.017i	−2.80953	−	1.25088i
$39$	32.7412	+	23.7879i	0.134430	+	0.0976694i
$40$	541.230	−	240.971i	2.13940	−	0.952522i
$41$	101.987	+	21.6779i	0.388478	+	0.0825736i	0.398010	−	0.917381i	$-0.369701\pi$
$41$	101.987	+	21.6779i	0.388478	+	0.0825736i	−0.00953189	+	0.999955i	$0.503034\pi$
$42$	−19.4319	−	184.882i	−0.0713906	−	0.679236i
$43$	−264.451	+	293.702i	−0.937869	+	1.04161i	0.0611856	+	0.998126i	$0.480512\pi$
$43$	−264.451	+	293.702i	−0.937869	+	1.04161i	−0.999054	+	0.0434822i	$0.986155\pi$
$44$	966.925	+	1073.88i	3.31294	+	3.67939i
$45$	−15.8578	+	150.877i	−0.0525321	+	0.499810i
$46$	100.143	−	308.210i	0.320986	−	0.987893i
$47$	78.1197	−	240.428i	0.242445	−	0.746170i	−0.753601	−	0.657332i	$-0.771685\pi$
$47$	78.1197	−	240.428i	0.242445	−	0.746170i	0.996046	−	0.0888376i	$-0.0283152\pi$
$48$	−64.1632	+	610.472i	−0.192941	+	1.83571i
$49$	−145.785	−	161.910i	−0.425028	−	0.472042i
$50$	174.390	−	193.680i	0.493249	−	0.547809i
$51$	−12.6171	−	120.044i	−0.0346422	−	0.329599i
$52$	263.560	+	56.0214i	0.702869	+	0.149399i
$53$	297.631	−	132.514i	0.771373	−	0.343437i	0.0169759	−	0.999856i	$-0.494596\pi$
$53$	297.631	−	132.514i	0.771373	−	0.343437i	0.754397	+	0.656419i	$0.227929\pi$
$54$	−596.491	−	433.376i	−1.50319	−	1.09213i
$55$	−558.060	−	248.465i	−1.36816	−	0.609145i
$56$	−379.291	−	656.952i	−0.905088	−	1.56766i
$57$	−208.826	+	361.697i	−0.485257	+	0.840490i
$58$	−98.4983	+	71.5632i	−0.222991	+	0.162012i
$59$	−212.048	+	45.0722i	−0.467904	+	0.0994560i	−0.435829	−	0.900030i	$-0.643545\pi$
$59$	−212.048	+	45.0722i	−0.467904	+	0.0994560i	−0.0320746	+	0.999485i	$0.510211\pi$
$60$	−173.175	−	532.978i	−0.372614	−	1.14679i
$61$	−28.6679			−0.0601728			−0.0300864	−	0.999547i	$-0.509578\pi$
$61$	−28.6679			−0.0601728			−0.0300864	+	0.999547i	$0.509578\pi$
$62$	−218.902	+	897.815i	−0.448397	+	1.83907i
$63$	194.250			0.388463
$64$	365.312	+	1124.32i	0.713501	+	2.19593i
$65$	−111.416	+	23.6823i	−0.212608	+	0.0451911i
$66$	940.123	−	683.040i	1.75335	−	1.27388i
$67$	85.9501	−	148.870i	0.156723	−	0.271453i	−0.776962	−	0.629548i	$-0.783240\pi$
$67$	85.9501	−	148.870i	0.156723	−	0.271453i	0.933685	+	0.358095i	$0.116574\pi$
$68$	−401.823	−	695.978i	−0.716592	−	1.24117i
$69$	−171.635	−	76.4167i	−0.299455	−	0.133326i
$70$	423.298	+	307.544i	0.722768	+	0.525122i
$71$	777.917	−	346.351i	1.30031	−	0.578934i	0.364420	−	0.931235i	$-0.381267\pi$
$71$	777.917	−	346.351i	1.30031	−	0.578934i	0.935887	+	0.352301i	$0.114601\pi$
$72$	−1151.89	−	244.842i	−1.88544	−	0.400763i
$73$	76.5344	+	728.177i	0.122708	+	1.16749i	0.866535	+	0.499116i	$0.166342\pi$
$73$	76.5344	+	728.177i	0.122708	+	1.16749i	−0.743827	+	0.668372i	$0.766991\pi$
$74$	42.9820	−	47.7363i	0.0675210	−	0.0749897i
$75$	−101.101	−	112.284i	−0.155656	−	0.172873i
$76$	−290.661	+	2765.46i	−0.438699	+	4.17394i
$77$	−241.704	+	743.889i	−0.357724	+	1.10096i
$78$	66.9581	−	206.076i	0.0971988	−	0.299147i
$79$	−4.95029	+	47.0988i	−0.00705001	+	0.0670764i	−0.997481	−	0.0709308i	$-0.977403\pi$
$79$	−4.95029	+	47.0988i	−0.00705001	+	0.0670764i	0.990431	+	0.138007i	$0.0440697\pi$
$80$	−1156.03	−	1283.90i	−1.61560	−	1.79431i
$81$	27.7134	−	30.7789i	0.0380157	−	0.0422207i
$82$	−58.3521	−	555.184i	−0.0785843	−	0.747680i
$83$	8.31790	+	1.76802i	0.0110001	+	0.00233814i	0.213408	−	0.976963i	$-0.431543\pi$
$83$	8.31790	+	1.76802i	0.0110001	+	0.00233814i	−0.202408	+	0.979301i	$0.564877\pi$
$84$	−655.517	+	291.855i	−0.851462	+	0.379095i
$85$	274.848	+	199.689i	0.350723	+	0.254815i
$86$	1933.07	+	860.659i	2.42382	+	1.07915i
$87$	35.2920	+	61.1275i	0.0434908	+	0.0753283i
$88$	2370.93	−	4106.58i	2.87207	−	4.97458i
$89$	−11.8413	+	8.60322i	−0.0141031	+	0.0102465i	−0.594814	−	0.803863i	$-0.702774\pi$
$89$	−11.8413	+	8.60322i	−0.0141031	+	0.0102465i	0.580711	+	0.814110i	$0.302774\pi$
$90$	794.507	−	168.878i	0.930537	−	0.197792i
$91$	45.0690	+	138.708i	0.0519177	+	0.159786i
$92$	−1250.87			−1.41753
$93$	504.385	+	180.619i	0.562390	+	0.201390i
$94$	−1353.51			−1.48515
$95$	−363.249	−	1117.96i	−0.392300	−	1.20738i
$96$	1567.52	−	333.187i	1.66651	−	0.354227i
$97$	573.772	−	416.870i	0.600595	−	0.436358i	−0.245495	−	0.969398i	$-0.578950\pi$
$97$	573.772	−	416.870i	0.600595	−	0.436358i	0.846090	+	0.533040i	$0.178950\pi$
$98$	−583.250	+	1010.22i	−0.601196	+	1.04130i
$99$	607.123	+	1051.57i	0.616345	+	1.06754i
$100$	−918.997	−	409.164i	−0.918997	−	0.409164i
$101$	527.032	+	382.911i	0.519224	+	0.377238i	0.816311	−	0.577612i	$-0.196015\pi$
$101$	527.032	+	382.911i	0.519224	+	0.377238i	−0.297088	+	0.954850i	$0.596015\pi$
$102$	−590.392	+	262.860i	−0.573113	+	0.255166i
$103$	−958.141	−	203.659i	−0.916586	−	0.194826i	−0.274614	−	0.961554i	$-0.588550\pi$
$103$	−958.141	−	203.659i	−0.916586	−	0.194826i	−0.641972	+	0.766728i	$0.721883\pi$
$104$	−92.4224	−	879.341i	−0.0871420	−	0.829100i
$105$	202.971	−	225.422i	0.188647	−	0.209514i
$106$	−1167.19	−	1296.30i	−1.06951	−	1.18781i
$107$	90.6103	−	862.100i	0.0818657	−	0.778900i	−0.874164	−	0.485631i	$-0.838590\pi$
$107$	90.6103	−	862.100i	0.0818657	−	0.778900i	0.956030	−	0.293269i	$-0.0947433\pi$
$108$	−879.432	+	2706.61i	−0.783550	+	2.41152i
$109$	171.773	−	528.663i	0.150944	−	0.464557i	−0.846784	−	0.531937i	$-0.821464\pi$
$109$	171.773	−	528.663i	0.150944	−	0.464557i	0.997727	+	0.0673806i	$0.0214642\pi$
$110$	−341.877	+	3252.74i	−0.296333	+	2.81942i
$111$	−24.9185	−	27.6748i	−0.0213077	−	0.0236646i
$112$	−1480.20	+	1643.93i	−1.24880	+	1.38694i
$113$	−125.529	−	1194.33i	−0.104503	−	0.994278i	−0.913603	−	0.406607i	$-0.866712\pi$
$113$	−125.529	−	1194.33i	−0.104503	−	0.994278i	0.809100	−	0.587671i	$-0.199955\pi$
$114$	2187.27	+	464.919i	1.79699	+	0.381961i
$115$	483.074	−	215.078i	0.391712	−	0.174401i
$116$	380.192	+	276.225i	0.304309	+	0.221094i
$117$	206.838	+	92.0902i	0.163437	+	0.0727670i
$118$	580.342	+	1005.18i	0.452753	+	0.784190i
$119$	217.498	−	376.718i	0.167546	−	0.290199i
$120$	−1487.75	+	1080.91i	−1.13177	+	0.822276i
$121$	−3480.56	+	739.817i	−2.61500	+	0.555835i
$122$	47.4309	+	145.977i	0.0351983	+	0.108329i
$123$	−323.636			−0.237246
$124$	3556.94	−	267.303i	2.57599	−	0.193585i
$125$	1517.29			1.08569
$126$	−321.386	−	989.123i	−0.227233	−	0.699350i
$127$	264.374	−	56.1945i	0.184720	−	0.0392634i	−0.114623	−	0.993409i	$-0.536566\pi$
$127$	264.374	−	56.1945i	0.184720	−	0.0392634i	0.299343	+	0.954146i	$0.403233\pi$
$128$	1779.16	−	1292.63i	1.22857	−	0.892606i
$129$	613.370	−	1062.39i	0.418638	−	0.725102i
$130$	304.929	+	528.152i	0.205723	+	0.356323i
$131$	−218.263	−	97.1771i	−0.145571	−	0.0648122i	0.332658	−	0.943047i	$-0.392054\pi$
$131$	−218.263	−	97.1771i	−0.145571	−	0.0648122i	−0.478229	+	0.878235i	$0.658721\pi$
$132$	−3628.76	−	2636.45i	−2.39275	−	1.73844i
$133$	−1375.00	+	612.190i	−0.896449	+	0.399125i
$134$	−900.253	−	191.355i	−0.580373	−	0.123362i
$135$	−125.755	−	1196.47i	−0.0801721	−	0.762786i
$136$	−1764.59	+	1959.78i	−1.11259	+	1.23566i
$137$	651.534	+	723.602i	0.406309	+	0.451252i	0.911220	−	0.411919i	$-0.135141\pi$
$137$	651.534	+	723.602i	0.406309	+	0.451252i	−0.504911	+	0.863171i	$0.668475\pi$
$138$	−105.146	+	1000.40i	−0.0648597	+	0.617099i
$139$	725.274	−	2232.16i	0.442568	−	1.36208i	−0.442562	−	0.896738i	$-0.645930\pi$
$139$	725.274	−	2232.16i	0.442568	−	1.36208i	0.885129	−	0.465345i	$-0.154070\pi$
$140$	624.086	−	1920.74i	0.376749	−	1.15951i
$141$	−82.0223	+	780.390i	−0.0489895	+	0.466104i
$142$	−3050.69	−	3388.13i	−1.80287	−	2.00230i
$143$	−610.032	+	677.510i	−0.356738	+	0.396197i
$144$	358.963	+	3415.30i	0.207733	+	1.97645i
$145$	−194.320	−	41.3041i	−0.111293	−	0.0236560i
$146$	3581.27	−	1594.48i	2.03005	−	0.903837i
$147$	547.114	+	397.501i	0.306974	+	0.223030i
$148$	−226.506	−	100.847i	−0.125802	−	0.0560105i
$149$	−642.276	−	1112.45i	−0.353136	−	0.611650i	0.633661	−	0.773611i	$-0.281551\pi$
$149$	−642.276	−	1112.45i	−0.353136	−	0.611650i	−0.986797	+	0.161961i	$0.948218\pi$
$150$	−404.482	+	700.584i	−0.220172	+	0.381350i
$151$	−904.362	+	657.057i	−0.487390	+	0.354110i	−0.804180	−	0.594386i	$-0.797395\pi$
$151$	−904.362	+	657.057i	−0.487390	+	0.354110i	0.316790	+	0.948496i	$0.397395\pi$
$152$	8925.34	−	1897.14i	4.76277	−	1.01236i
$153$	−208.676	−	642.239i	−0.110264	−	0.339359i
$154$	4187.80			2.19131
$155$	−1327.69	+	714.818i	−0.688017	+	0.370423i
$156$	−836.362			−0.429247
$157$	567.671	+	1747.11i	0.288567	+	0.888119i	0.985307	+	0.170794i	$0.0546334\pi$
$157$	567.671	+	1747.11i	0.288567	+	0.888119i	−0.696739	+	0.717324i	$0.745367\pi$
$158$	248.019	−	52.7180i	0.124882	−	0.0265444i
$159$	−818.134	+	594.409i	−0.408065	+	0.296476i
$160$	−2255.21	+	3906.14i	−1.11431	+	1.93005i
$161$	−338.535	−	586.360i	−0.165716	−	0.287029i
$162$	−202.579	−	90.1938i	−0.0982474	−	0.0437426i
$163$	1789.14	+	1299.88i	0.859730	+	0.624631i	0.927812	−	0.373049i	$-0.121688\pi$
$163$	1789.14	+	1299.88i	0.859730	+	0.624631i	−0.0680813	+	0.997680i	$0.521688\pi$
$164$	−1968.46	+	876.414i	−0.937260	+	0.417295i
$165$	1854.70	+	394.229i	0.875082	+	0.186004i
$166$	−4.75913	−	45.2801i	−0.00222518	−	0.0211712i
$167$	−1962.02	+	2179.05i	−0.909137	+	1.00970i	0.0907672	+	0.995872i	$0.471068\pi$
$167$	−1962.02	+	2179.05i	−0.909137	+	1.00970i	−0.999904	+	0.0138270i	$0.995599\pi$
$168$	1575.55	+	1749.83i	0.723550	+	0.803584i
$169$	211.880	−	2015.90i	0.0964405	−	0.917570i
$170$	562.083	−	1729.91i	0.253587	−	0.780461i
$171$	−722.038	+	2222.20i	−0.322898	+	0.993779i
$172$	853.740	−	8122.80i	0.378471	−	3.60092i
$173$	2556.03	+	2838.76i	1.12330	+	1.24756i	0.965589	+	0.260071i	$0.0837461\pi$
$173$	2556.03	+	2838.76i	1.12330	+	1.24756i	0.157715	+	0.987485i	$0.449587\pi$
$174$	252.872	−	280.843i	0.110174	−	0.122360i
$175$	−56.9166	−	541.525i	−0.0245857	−	0.233917i
$176$	−13525.7	−	2874.98i	−5.79285	−	1.23131i
$177$	614.722	−	273.692i	0.261047	−	0.116226i
$178$	63.3992	+	46.0622i	0.0266965	+	0.0193961i
$179$	234.202	+	104.273i	0.0977938	+	0.0435406i	0.455050	−	0.890466i	$-0.349621\pi$
$179$	234.202	+	104.273i	0.0977938	+	0.0435406i	−0.357257	+	0.934006i	$0.616288\pi$
$180$	−1567.61	−	2715.17i	−0.649124	−	1.12432i
$181$	−1248.22	+	2161.99i	−0.512595	+	0.887841i	0.487298	+	0.873236i	$0.337983\pi$
$181$	−1248.22	+	2161.99i	−0.512595	+	0.887841i	−0.999893	+	0.0146054i	$0.995351\pi$
$182$	631.738	−	458.984i	0.257294	−	0.186935i
$183$	87.0399	−	18.5009i	0.0351594	−	0.00747337i
$184$	1268.42	+	3903.80i	0.508203	+	1.56409i
$185$	104.814			0.0416544
$186$	85.2122	−	2867.17i	0.0335917	−	1.13028i
$187$	2719.14			1.06333
$188$	1614.43	+	4968.69i	0.626298	+	1.92755i
$189$	−1506.76	+	320.272i	−0.579898	+	0.123261i
$190$	−5091.71	+	3699.34i	−1.94416	+	1.41252i
$191$	969.282	−	1678.85i	0.367198	−	0.636005i	−0.621928	−	0.783074i	$-0.713651\pi$
$191$	969.282	−	1678.85i	0.367198	−	0.636005i	0.989126	+	0.147069i	$0.0469839\pi$
$192$	−1834.72	−	3177.84i	−0.689635	−	1.19448i
$193$	1074.44	+	478.369i	0.400723	+	0.178413i	0.597195	−	0.802096i	$-0.296282\pi$
$193$	1074.44	+	478.369i	0.400723	+	0.178413i	−0.196472	+	0.980509i	$0.562948\pi$
$194$	−3072.02	−	2231.95i	−1.13690	−	0.826004i
$195$	322.993	−	143.806i	0.118616	−	0.0528111i
$196$	4404.16	+	936.133i	1.60501	+	0.341156i
$197$	−449.289	−	4274.70i	−0.162490	−	1.54599i	−0.706988	−	0.707225i	$-0.749947\pi$
$197$	−449.289	−	4274.70i	−0.162490	−	1.54599i	0.544499	−	0.838762i	$-0.316720\pi$
$198$	4350.12	−	4831.30i	1.56136	−	1.73407i
$199$	2386.78	+	2650.79i	0.850224	+	0.944269i	0.999005	−	0.0446012i	$-0.0142017\pi$
$199$	2386.78	+	2650.79i	0.850224	+	0.944269i	−0.148781	+	0.988870i	$0.547535\pi$
$200$	−345.053	+	3282.96i	−0.121995	+	1.16070i
$201$	−164.884	+	507.460i	−0.0578607	+	0.178077i
$202$	1077.82	−	3317.18i	0.375421	−	1.15543i
$203$	−26.5888	+	252.976i	−0.00919296	+	0.0874652i
$204$	1669.15	+	1853.78i	0.572862	+	0.636227i
$205$	609.503	−	676.922i	0.207656	−	0.230626i
$206$	548.205	+	5215.83i	0.185414	+	1.76410i
$207$	−1028.12	−	218.533i	−0.345213	−	0.0733774i
$208$	−2355.48	+	1048.73i	−0.785209	+	0.349598i
$209$	−7611.62	−	5530.16i	−2.51917	−	1.83028i
$210$	−1483.67	−	660.573i	−0.487538	−	0.217066i
$211$	1080.01	+	1870.63i	0.352375	+	0.610331i	0.986665	−	0.162764i	$-0.0520410\pi$
$211$	1080.01	+	1870.63i	0.352375	+	0.610331i	−0.634290	+	0.773095i	$0.718708\pi$
$212$	−3366.48	+	5830.91i	−1.09062	+	1.88900i
$213$	−2138.36	+	1553.61i	−0.687876	+	0.499771i
$214$	−4539.74	+	964.952i	−1.45014	+	0.308237i
$215$	1066.95	+	3283.73i	0.338443	+	1.04162i
$216$	9338.72			2.94176
$217$	1087.95	+	1595.01i	0.340345	+	0.498970i
$218$	−2976.16			−0.924637
$219$	−702.302	−	2161.46i	−0.216699	−	0.666932i
$220$	12348.5	−	2624.75i	3.78424	−	0.804366i
$221$	410.188	−	298.019i	0.124852	−	0.0907101i
$222$	−99.6930	+	172.673i	−0.0301394	+	0.0522030i
$223$	2957.90	+	5123.23i	0.888232	+	1.53846i	0.841964	+	0.539533i	$0.181399\pi$
$223$	2957.90	+	5123.23i	0.888232	+	1.53846i	0.0462672	+	0.998929i	$0.485267\pi$
$224$	5275.92	+	2348.99i	1.57372	+	0.700664i
$225$	−683.859	−	496.853i	−0.202625	−	0.147216i
$226$	−5873.88	+	2615.22i	−1.72887	+	0.769743i
$227$	−2747.93	−	584.090i	−0.803464	−	0.170782i	−0.212165	−	0.977234i	$-0.568051\pi$
$227$	−2747.93	−	584.090i	−0.803464	−	0.170782i	−0.591299	+	0.806452i	$0.701385\pi$
$228$	−902.207	−	8583.92i	−0.262062	−	2.49335i
$229$	2520.30	−	2799.08i	0.727276	−	0.807722i	−0.260189	−	0.965558i	$-0.583785\pi$
$229$	2520.30	−	2799.08i	0.727276	−	0.807722i	0.987465	+	0.157836i	$0.0504516\pi$
$230$	−1894.43	−	2103.97i	−0.543108	−	0.603182i
$231$	253.779	−	2414.54i	0.0722832	−	0.687729i
$232$	476.535	−	1466.62i	0.134854	−	0.415037i
$233$	1549.61	−	4769.21i	0.435701	−	1.34095i	−0.456665	−	0.889639i	$-0.650956\pi$
$233$	1549.61	−	4769.21i	0.435701	−	1.34095i	0.892366	−	0.451312i	$-0.149044\pi$
$234$	126.712	−	1205.59i	0.0353993	−	0.336802i
$235$	−1477.80	−	1641.26i	−0.410217	−	0.455593i
$236$	2997.77	−	3329.36i	0.826857	−	0.918318i
$237$	−15.3656	−	146.194i	−0.00421140	−	0.0400688i
$238$	−2278.10	−	484.226i	−0.620452	−	0.131881i
$239$	5062.21	−	2253.84i	1.37007	−	0.609996i	0.415943	−	0.909391i	$-0.363452\pi$
$239$	5062.21	−	2253.84i	1.37007	−	0.609996i	0.954129	+	0.299395i	$0.0967849\pi$
$240$	4338.46	+	3152.08i	1.16686	+	0.847774i
$241$	−4671.75	−	2080.00i	−1.24869	−	0.555951i	−0.327419	−	0.944879i	$-0.606179\pi$
$241$	−4671.75	−	2080.00i	−1.24869	−	0.555951i	−0.921268	+	0.388928i	$0.872846\pi$
$242$	9525.75	+	16499.1i	2.53032	+	4.38265i
$243$	−1923.35	+	3331.34i	−0.507749	+	0.879447i
$244$	479.303	−	348.234i	0.125755	−	0.0913664i
$245$	−1861.80	+	395.737i	−0.485493	+	0.103195i
$246$	535.456	+	1647.96i	0.138778	+	0.427115i
$247$	−1754.34			−0.451926
$248$	−4441.06	−	10829.7i	−1.13713	−	2.77292i
$249$	−26.3954			−0.00671783
$250$	−2510.36	−	7726.10i	−0.635077	−	1.95457i
$251$	−6247.65	+	1327.98i	−1.57111	+	0.333949i	−0.909436	−	0.415844i	$-0.863486\pi$
$251$	−6247.65	+	1327.98i	−1.57111	+	0.333949i	−0.661672	+	0.749793i	$0.730153\pi$
$252$	−3247.69	+	2359.59i	−0.811847	+	0.589842i
$253$	2116.17	−	3665.31i	0.525860	−	0.910815i
$254$	−723.550	−	1253.23i	−0.178739	−	0.309584i
$255$	−963.349	−	428.911i	−0.236577	−	0.105331i
$256$	−1874.52	−	1361.92i	−0.457646	−	0.332499i
$257$	−16.0218	+	7.13336i	−0.00388876	+	0.00173139i	−0.408680	−	0.912678i	$-0.634011\pi$
$257$	−16.0218	+	7.13336i	−0.00388876	+	0.00173139i	0.404791	+	0.914409i	$0.367344\pi$
$258$	−6424.53	−	1365.58i	−1.55028	−	0.329523i
$259$	−14.0283	−	133.470i	−0.00336554	−	0.0320209i
$260$	1575.12	−	1749.34i	0.375710	−	0.417268i
$261$	264.229	+	293.456i	0.0626643	+	0.0695957i
$262$	−133.712	+	1272.18i	−0.0315295	+	0.299983i
$263$	369.940	−	1138.56i	0.0867357	−	0.266945i	−0.898276	−	0.439431i	$-0.855180\pi$
$263$	369.940	−	1138.56i	0.0867357	−	0.266945i	0.985012	+	0.172486i	$0.0551800\pi$
$264$	−4548.32	+	13998.3i	−1.06034	+	3.26339i
$265$	297.515	−	2830.67i	0.0689669	−	0.656176i
$266$	5392.22	+	5988.67i	1.24293	+	1.38041i
$267$	30.3999	−	33.7625i	0.00696795	−	0.00773870i
$268$	371.337	+	3533.04i	0.0846381	+	0.805278i
$269$	5577.81	+	1185.60i	1.26426	+	0.268726i	0.790791	−	0.612086i	$-0.209670\pi$
$269$	5577.81	+	1185.60i	1.26426	+	0.268726i	0.473465	+	0.880812i	$0.343003\pi$
$270$	−5884.42	+	2619.91i	−1.32635	+	0.590528i
$271$	1733.87	+	1259.73i	0.388653	+	0.282373i	0.764903	−	0.644145i	$-0.222787\pi$
$271$	1733.87	+	1259.73i	0.388653	+	0.282373i	−0.376250	+	0.926518i	$0.622787\pi$
$272$	7025.39	+	3127.90i	1.56609	+	0.697268i
$273$	−226.352	−	392.053i	−0.0501811	−	0.0869163i
$274$	2606.64	−	4514.82i	0.574717	−	0.995440i
$275$	2753.65	−	2000.64i	0.603823	−	0.438703i
$276$	3797.84	−	807.257i	0.828273	−	0.176055i
$277$	1546.66	+	4760.13i	0.335487	+	1.03252i	0.966482	+	0.256736i	$0.0826469\pi$
$277$	1546.66	+	4760.13i	0.335487	+	1.03252i	−0.630995	+	0.775787i	$0.717353\pi$
$278$	−12566.2			−2.71104
$279$	2970.22	+	401.713i	0.637357	+	0.0862004i
$280$	−6627.19			−1.41447
$281$	29.5355	+	90.9008i	0.00627024	+	0.0192978i	0.954143	−	0.299352i	$-0.0967705\pi$
$281$	29.5355	+	90.9008i	0.00627024	+	0.0192978i	−0.947872	+	0.318650i	$0.896771\pi$
$282$	4109.47	−	873.494i	0.867784	−	0.184453i
$283$	−885.742	+	643.529i	−0.186049	+	0.135173i	−0.676911	−	0.736065i	$-0.736682\pi$
$283$	−885.742	+	643.529i	−0.186049	+	0.135173i	0.490862	+	0.871237i	$0.336682\pi$
$284$	−8798.95	+	15240.2i	−1.83846	+	3.18430i
$285$	1824.36	+	3159.89i	0.379178	+	0.656756i
$286$	4459.19	+	1985.36i	0.921949	+	0.410478i
$287$	−943.569	−	685.543i	−0.194067	−	0.140998i
$288$	8190.37	−	3646.59i	1.67577	−	0.746101i
$289$	3326.46	+	707.062i	0.677074	+	0.143916i
$290$	111.182	+	1057.82i	0.0225131	+	0.214198i
$291$	−1473.03	+	1635.97i	−0.296737	+	0.329560i
$292$	−10124.9	−	11244.8i	−2.02916	−	2.25361i
$293$	42.7167	−	406.422i	0.00851719	−	0.0810357i	−0.989438	−	0.144960i	$-0.953695\pi$
$293$	42.7167	−	406.422i	0.00851719	−	0.0810357i	0.997955	+	0.0639238i	$0.0203615\pi$
$294$	1118.89	−	3443.58i	0.221955	−	0.683108i
$295$	−585.247	+	1801.20i	−0.115506	+	0.355492i
$296$	−85.0455	+	809.154i	−0.0166999	+	0.158889i
$297$	−6443.14	−	7155.83i	−1.25882	−	1.39806i
$298$	−4602.00	+	5111.04i	−0.894586	+	0.993539i
$299$	−82.4914	−	784.853i	−0.0159552	−	0.151803i
$300$	3054.27	+	649.205i	0.587795	+	0.124940i
$301$	4038.70	−	1798.15i	0.773378	−	0.344330i
$302$	4842.02	+	3517.93i	0.922605	+	0.670312i
$303$	−1847.26	−	822.453i	−0.350239	−	0.155936i
$304$	−13304.5	−	23044.0i	−2.51008	−	4.34758i
$305$	−125.225	+	216.897i	−0.0235094	+	0.0407195i
$306$	−2925.04	+	2125.17i	−0.546449	+	0.397018i
$307$	−463.295	+	98.4763i	−0.0861291	+	0.0183073i	−0.250775	−	0.968045i	$-0.580685\pi$
$307$	−463.295	+	98.4763i	−0.0861291	+	0.0183073i	0.164646	+	0.986353i	$0.447352\pi$
$308$	−4995.07	−	15373.3i	−0.924093	−	2.84407i
$309$	3040.49			0.559765
$310$	5836.53	+	5577.97i	1.06933	+	1.02196i
$311$	4755.79			0.867125			0.433563	−	0.901123i	$-0.357256\pi$
$311$	4755.79			0.867125			0.433563	+	0.901123i	$0.357256\pi$
$312$	848.094	+	2610.17i	0.153891	+	0.473627i
$313$	763.824	−	162.356i	0.137936	−	0.0293192i	−0.138426	−	0.990373i	$-0.544204\pi$
$313$	763.824	−	162.356i	0.137936	−	0.0293192i	0.276362	+	0.961054i	$0.410871\pi$
$314$	7957.12	−	5781.18i	1.43008	−	1.03902i
$315$	848.510	−	1469.66i	0.151772	−	0.262876i
$316$	−489.354	−	847.586i	−0.0871149	−	0.150888i
$317$	2280.51	+	1015.35i	0.404057	+	0.179898i	0.598695	−	0.800977i	$-0.295686\pi$
$317$	2280.51	+	1015.35i	0.404057	+	0.179898i	−0.194637	+	0.980875i	$0.562353\pi$
$318$	4380.35	+	3182.51i	0.772445	+	0.561214i
$319$	−1452.59	+	646.733i	−0.254950	+	0.113511i
$320$	10102.1	+	2147.28i	1.76477	+	0.375114i
$321$	281.253	+	2675.94i	0.0489034	+	0.465285i
$322$	−2425.65	+	2693.96i	−0.419802	+	0.466238i
$323$	3501.17	+	3888.45i	0.603129	+	0.669842i
$324$	−89.4688	+	851.239i	−0.0153410	+	0.145960i
$325$	196.122	−	603.602i	0.0334735	−	0.103021i
$326$	3658.91	−	11261.0i	0.621621	−	1.91315i
$327$	−180.354	+	1715.95i	−0.0305003	+	0.290191i
$328$	4731.23	+	5254.57i	0.796459	+	0.884558i
$329$	−1892.20	+	2101.50i	−0.317083	+	0.352156i
$330$	−1061.18	−	10096.4i	−0.177018	−	1.68421i
$331$	1800.26	+	382.656i	0.298946	+	0.0635429i	0.354943	−	0.934888i	$-0.384500\pi$
$331$	1800.26	+	382.656i	0.298946	+	0.0635429i	−0.0559970	+	0.998431i	$0.517834\pi$
$332$	−160.545	+	71.4793i	−0.0265393	+	0.0118161i
$333$	−168.551	−	122.460i	−0.0277374	−	0.0201524i
$334$	14341.9	+	6385.43i	2.34957	+	1.04609i
$335$	−750.884	−	1300.57i	−0.122463	−	0.212113i
$336$	3433.20	−	5946.48i	0.557430	−	0.965496i
$337$	−5260.71	+	3822.13i	−0.850354	+	0.617818i	−0.925244	−	0.379374i	$-0.876140\pi$
$337$	−5260.71	+	3822.13i	−0.850354	+	0.617818i	0.0748897	+	0.997192i	$0.476140\pi$
$338$	−10615.6	+	2256.41i	−1.70832	+	0.363114i
$339$	1151.89	+	3545.16i	0.184549	+	0.567985i
$340$	−7020.89			−1.11989
$341$	−5234.22	+	10874.8i	−0.831228	+	1.72699i
$342$	12510.1			1.97798
$343$	1938.76	+	5966.88i	0.305199	+	0.939304i
$344$	−26215.8	+	5572.34i	−4.10890	+	0.873374i
$345$	−1327.88	+	964.763i	−0.207220	+	0.150554i
$346$	10226.1	−	17712.1i	1.58890	−	2.75205i
$347$	−1377.28	−	2385.52i	−0.213073	−	0.369052i	0.739602	−	0.673044i	$-0.235014\pi$
$347$	−1377.28	−	2385.52i	−0.213073	−	0.369052i	−0.952675	+	0.303992i	$0.901680\pi$
$348$	−1332.58	−	593.304i	−0.205270	−	0.0913920i
$349$	−6662.56	−	4840.63i	−1.02189	−	0.742444i	−0.0552180	−	0.998474i	$-0.517585\pi$
$349$	−6662.56	−	4840.63i	−1.02189	−	0.742444i	−0.966669	+	0.256030i	$0.917585\pi$
$350$	−2663.29	+	1185.77i	−0.406740	+	0.181092i
$351$	−1756.24	−	373.301i	−0.267069	−	0.0567673i
$352$	3773.55	+	35902.9i	0.571394	+	5.43645i
$353$	−6025.85	+	6692.38i	−0.908565	+	1.00906i	0.0913471	+	0.995819i	$0.470883\pi$
$353$	−6025.85	+	6692.38i	−0.908565	+	1.00906i	−0.999912	+	0.0132448i	$0.995784\pi$
$354$	−2410.70	−	2677.36i	−0.361942	−	0.401977i
$355$	777.615	−	7398.51i	0.116258	−	1.10612i
$356$	93.4721	−	287.678i	0.0139158	−	0.0428283i
$357$	−417.241	+	1284.13i	−0.0618564	+	0.190374i
$358$	143.476	−	1365.08i	0.0211814	−	0.201528i
$359$	−6940.58	−	7708.30i	−1.02036	−	1.13323i	−0.991028	−	0.133657i	$-0.957328\pi$
$359$	−6940.58	−	7708.30i	−1.02036	−	1.13323i	−0.0293345	−	0.999570i	$-0.509339\pi$
$360$	−6884.07	+	7645.53i	−1.00784	+	1.11932i
$361$	−1175.49	−	11184.0i	−0.171379	−	1.63056i
$362$	13074.1	+	2778.98i	1.89823	+	0.403480i
$363$	10090.1	−	4492.39i	1.45893	−	0.649557i
$364$	−2438.43	−	1771.62i	−0.351122	−	0.255105i
$365$	5843.58	+	2601.73i	0.837992	+	0.373098i
$366$	−238.214	−	412.600i	−0.0340210	−	0.0589260i
$367$	−3104.72	+	5377.54i	−0.441595	+	0.764865i	−0.997808	−	0.0661750i	$-0.978920\pi$
$367$	−3104.72	+	5377.54i	−0.441595	+	0.764865i	0.556213	+	0.831040i	$0.312254\pi$
$368$	9683.81	−	7035.70i	1.37175	−	0.996634i
$369$	−1771.03	+	376.443i	−0.249854	+	0.0531080i
$370$	−173.414	−	533.714i	−0.0243659	−	0.0749905i
$371$	−3644.40			−0.509994
$372$	−10626.9	+	3107.06i	−1.48113	+	0.433047i
$373$	8275.30			1.14874			0.574369	−	0.818597i	$-0.305248\pi$
$373$	8275.30			1.14874			0.574369	+	0.818597i	$0.305248\pi$
$374$	−4498.82	−	13845.9i	−0.622001	−	1.91432i
$375$	−4606.74	+	979.192i	−0.634375	+	0.134841i
$376$	13869.5	−	10076.8i	1.90230	−	1.38210i
$377$	−148.243	+	256.765i	−0.0202518	+	0.0350771i
$378$	4123.77	+	7142.57i	0.561121	+	0.971890i
$379$	−10761.5	−	4791.34i	−1.45853	−	0.649379i	−0.484292	−	0.874906i	$-0.660923\pi$
$379$	−10761.5	−	4791.34i	−1.45853	−	0.649379i	−0.974237	+	0.225527i	$0.927590\pi$
$380$	19653.4	+	14279.0i	2.65315	+	1.92763i
$381$	−766.415	+	341.230i	−0.103057	+	0.0458838i
$382$	−10152.4	−	2157.96i	−1.35979	−	0.289033i
$383$	−901.890	−	8580.91i	−0.120325	−	1.14482i	−0.873442	−	0.486928i	$-0.838117\pi$
$383$	−901.890	−	8580.91i	−0.120325	−	1.14482i	0.753117	−	0.657887i	$-0.228549\pi$
$384$	−4567.58	+	5072.81i	−0.607001	+	0.674143i
$385$	4572.35	+	5078.11i	0.605269	+	0.672220i
$386$	658.216	−	6262.51i	0.0867936	−	0.825786i
$387$	2120.79	−	6527.13i	0.278569	−	0.857346i
$388$	−4529.20	+	13939.5i	−0.592617	+	1.82389i
$389$	−1469.49	+	13981.3i	−0.191533	+	1.82231i	0.302814	+	0.953050i	$0.402074\pi$
$389$	−1469.49	+	13981.3i	−0.191533	+	1.82231i	−0.494347	+	0.869265i	$0.664593\pi$
$390$	−1266.65	−	1406.76i	−0.164460	−	0.182652i
$391$	−1574.98	+	1749.19i	−0.203709	+	0.226241i
$392$	−1544.40	−	14694.0i	−0.198990	−	1.89326i
$393$	725.394	+	154.187i	0.0931076	+	0.0197906i
$394$	−21023.5	+	9360.26i	−2.68819	+	1.19686i
$395$	334.719	+	243.188i	0.0426368	+	0.0309774i
$396$	−22924.2	−	10206.5i	−2.90905	−	1.29519i
$397$	−3315.60	−	5742.79i	−0.419157	−	0.726001i	0.576698	−	0.816957i	$-0.304341\pi$
$397$	−3315.60	−	5742.79i	−0.419157	−	0.726001i	−0.995855	+	0.0909567i	$0.971008\pi$
$398$	9548.95	−	16539.3i	1.20263	−	2.08301i
$399$	3779.63	−	2746.06i	0.474231	−	0.344549i
$400$	9415.93	−	2001.42i	1.17699	−	0.250177i
$401$	−73.5396	−	226.332i	−0.00915808	−	0.0281857i	0.946373	−	0.323076i	$-0.104717\pi$
$401$	−73.5396	−	226.332i	−0.00915808	−	0.0281857i	−0.955531	+	0.294890i	$0.904717\pi$
$402$	2856.80			0.354438
$403$	402.287	+	2214.15i	0.0497254	+	0.273685i
$404$	−13462.8			−1.65792
$405$	−111.812	−	344.122i	−0.0137185	−	0.0422212i
$406$	1332.15	−	283.157i	0.162841	−	0.0346130i
$407$	678.693	−	493.100i	0.0826574	−	0.0600541i
$408$	4092.81	−	7088.96i	0.496628	−	0.860186i
$409$	2554.10	+	4423.83i	0.308783	+	0.534828i	0.978096	−	0.208152i	$-0.0667450\pi$
$409$	2554.10	+	4423.83i	0.308783	+	0.534828i	−0.669314	+	0.742980i	$0.733412\pi$
$410$	−4455.32	−	1983.64i	−0.536665	−	0.238939i
$411$	−2445.14	−	1776.49i	−0.293454	−	0.213207i
$412$	18493.2	−	8233.71i	2.21140	−	0.984577i
$413$	2371.99	+	504.181i	0.282610	+	0.0600705i
$414$	588.244	+	5596.76i	0.0698324	+	0.664410i
$415$	49.7104	−	55.2089i	0.00587997	−	0.00653036i
$416$	4504.22	+	5002.44i	0.530859	+	0.589579i
$417$	−761.505	+	7245.24i	−0.0894271	+	0.850842i
$418$	−15566.3	+	47908.2i	−1.82147	+	5.60590i
$419$	2106.03	−	6481.71i	0.245552	−	0.755733i	−0.749993	−	0.661446i	$-0.769943\pi$
$419$	2106.03	−	6481.71i	0.245552	−	0.755733i	0.995545	−	0.0942866i	$-0.0300570\pi$
$420$	−655.263	+	6234.41i	−0.0761275	+	0.724305i
$421$	4501.78	+	4999.74i	0.521149	+	0.578794i	0.945055	−	0.326912i	$-0.106008\pi$
$421$	4501.78	+	4999.74i	0.521149	+	0.578794i	−0.423906	+	0.905706i	$0.639341\pi$
$422$	7738.43	−	8594.40i	0.892656	−	0.991395i
$423$	458.876	+	4365.91i	0.0527454	+	0.501839i
$424$	21611.1	+	4593.59i	2.47530	+	0.526142i
$425$	−1729.28	+	769.924i	−0.197370	+	0.0878748i
$426$	11448.9	+	8318.11i	1.30212	+	0.946042i
$427$	292.956	+	130.433i	0.0332018	+	0.0147824i
$428$	8957.16	+	15514.3i	1.01159	+	1.75213i
$429$	1414.92	−	2450.71i	0.159237	−	0.275807i
$430$	14955.5	−	10865.8i	1.67726	−	1.21860i
$431$	−1882.54	+	400.146i	−0.210391	+	0.0447200i	−0.311901	−	0.950114i	$-0.600966\pi$
$431$	−1882.54	+	400.146i	−0.210391	+	0.0447200i	0.101510	+	0.994834i	$0.467633\pi$
$432$	−8415.45	−	25900.1i	−0.937242	−	2.88453i
$433$	−6491.92			−0.720512			−0.360256	−	0.932854i	$-0.617311\pi$
$433$	−6491.92			−0.720512			−0.360256	+	0.932854i	$0.617311\pi$
$434$	6321.83	−	8178.80i	0.699211	−	0.904597i
$435$	616.642			0.0679672
$436$	3549.87	+	10925.4i	0.389926	+	1.20007i
$437$	7966.28	−	1693.29i	0.872034	−	0.185357i
$438$	−9844.26	+	7152.27i	−1.07392	+	0.780248i
$439$	−1045.22	+	1810.37i	−0.113634	+	0.196820i	−0.917233	−	0.398351i	$-0.869583\pi$
$439$	−1045.22	+	1810.37i	−0.113634	+	0.196820i	0.803599	+	0.595171i	$0.202916\pi$
$440$	−20713.2	−	35876.2i	−2.24423	−	3.88712i
$441$	3456.32	+	1538.85i	0.373212	+	0.166165i
$442$	−2196.18	−	1595.61i	−0.236338	−	0.171710i
$443$	2663.71	−	1185.96i	0.285681	−	0.127193i	−0.258894	−	0.965906i	$-0.583358\pi$
$443$	2663.71	−	1185.96i	0.285681	−	0.127193i	0.544574	+	0.838713i	$0.316691\pi$
$444$	752.788	+	160.010i	0.0804633	+	0.0171030i
$445$	13.3661	+	127.170i	0.00142385	+	0.0135470i
$446$	21193.8	−	23538.1i	2.25012	−	2.49901i
$447$	2667.97	+	2963.09i	0.282306	+	0.313533i
$448$	1382.27	−	13151.5i	0.145773	−	1.38694i
$449$	2292.59	−	7055.87i	0.240967	−	0.741619i	−0.755307	−	0.655371i	$-0.772512\pi$
$449$	2292.59	−	7055.87i	0.240967	−	0.741619i	0.996274	−	0.0862481i	$-0.0274878\pi$
$450$	−1398.54	+	4304.27i	−0.146506	+	0.450900i
$451$	762.074	−	7250.65i	0.0795669	−	0.757028i
$452$	16606.5	+	18443.4i	1.72811	+	1.91926i
$453$	2321.74	−	2578.56i	0.240806	−	0.267442i
$454$	1572.24	+	14958.9i	0.162531	+	1.54638i
$455$	1246.31	+	264.912i	0.128413	+	0.0272951i
$456$	−25874.3	+	11520.0i	−2.65719	+	1.18306i
$457$	−9309.50	−	6763.75i	−0.952910	−	0.692330i	−0.00141690	−	0.999999i	$-0.500451\pi$
$457$	−9309.50	−	6763.75i	−0.952910	−	0.692330i	−0.951493	+	0.307669i	$0.900451\pi$
$458$	−18422.8	−	8202.36i	−1.87957	−	0.836837i
$459$	2677.57	+	4637.68i	0.272283	+	0.471609i
$460$	−5464.00	+	9463.92i	−0.553827	+	0.959256i
$461$	−2821.00	+	2049.57i	−0.285004	+	0.207068i	−0.721097	−	0.692834i	$-0.756362\pi$
$461$	−2821.00	+	2049.57i	−0.285004	+	0.207068i	0.436093	+	0.899902i	$0.356362\pi$
$462$	−12714.8	+	2702.61i	−1.28040	+	0.272158i
$463$	−3236.05	−	9959.52i	−0.324820	−	0.999694i	−0.971522	−	0.236951i	$-0.923852\pi$
$463$	−3236.05	−	9959.52i	−0.324820	−	0.999694i	0.646701	−	0.762743i	$-0.276148\pi$
$464$	−4496.97			−0.449928
$465$	3569.76	−	3027.13i	0.356008	−	0.301892i
$466$	−26848.8			−2.66898
$467$	−259.239	−	797.855i	−0.0256877	−	0.0790585i	0.937391	−	0.348279i	$-0.113234\pi$
$467$	−259.239	−	797.855i	−0.0256877	−	0.0790585i	−0.963079	+	0.269221i	$0.913234\pi$
$468$	−4576.80	+	972.829i	−0.452057	+	0.0960877i
$469$	−1555.65	+	1130.25i	−0.153162	+	0.111279i
$470$	−5912.33	+	10240.5i	−0.580246	+	1.00502i
$471$	−2851.04	−	4938.14i	−0.278915	−	0.483095i
$472$	−13430.3	−	5979.55i	−1.30970	−	0.583117i
$473$	22357.1	+	16243.4i	2.17332	+	1.57901i
$474$	−719.000	+	320.119i	−0.0696725	+	0.0310202i
$475$	6406.58	+	1361.76i	0.618850	+	0.131541i
$476$	939.674	+	8940.40i	0.0904830	+	0.860888i
$477$	−3785.66	+	4204.40i	−0.363382	+	0.403577i
$478$	−19852.0	−	22047.9i	−1.89960	−	2.10972i
$479$	−425.370	+	4047.12i	−0.0405755	+	0.386050i	0.955322	+	0.295566i	$0.0955081\pi$
$479$	−425.370	+	4047.12i	−0.0405755	+	0.386050i	−0.995898	+	0.0904841i	$0.971159\pi$
$480$	4326.32	−	13315.1i	0.411393	−	1.26614i
$481$	48.3383	−	148.770i	0.00458220	−	0.0141026i
$482$	−2861.99	+	27230.0i	−0.270456	+	2.57322i
$483$	1406.25	+	1561.80i	0.132478	+	0.147131i
$484$	49205.5	−	54648.2i	4.62110	−	5.13225i
$485$	−647.654	−	6162.02i	−0.0606360	−	0.576913i
$486$	20145.4	+	4282.05i	1.88028	+	0.399666i
$487$	5954.20	−	2650.98i	0.554026	−	0.246668i	−0.110574	−	0.993868i	$-0.535269\pi$
$487$	5954.20	−	2650.98i	0.554026	−	0.246668i	0.664599	+	0.747200i	$0.268602\pi$
$488$	−1572.82	−	1142.72i	−0.145898	−	0.106001i
$489$	−6270.98	−	2792.02i	−0.579925	−	0.258199i
$490$	5095.44	+	8825.56i	0.469772	+	0.813670i
$491$	−4938.63	+	8553.95i	−0.453925	+	0.786221i	−0.998626	−	0.0524096i	$-0.983310\pi$
$491$	−4938.63	+	8553.95i	−0.453925	+	0.786221i	0.544701	+	0.838630i	$0.316643\pi$
$492$	5410.94	−	3931.28i	0.495821	−	0.360235i
$493$	864.967	−	183.854i	0.0790185	−	0.0167959i
$494$	2902.55	+	8933.12i	0.264356	+	0.813603i
$495$	10608.0			0.963220
$496$	−26033.1	+	22075.8i	−2.35669	+	1.99846i
$497$	−9525.35			−0.859699
$498$	43.6711	+	134.406i	0.00392962	+	0.0120941i
$499$	6752.74	−	1435.34i	0.605800	−	0.128767i	0.105208	−	0.994450i	$-0.466449\pi$
$499$	6752.74	−	1435.34i	0.605800	−	0.128767i	0.500592	+	0.865683i	$0.333116\pi$
$500$	−25367.9	+	18430.9i	−2.26898	+	1.64851i
$501$	4550.74	−	7882.12i	0.405813	−	0.702888i
$502$	17098.8	+	29616.0i	1.52023	+	2.63312i
$503$	−7746.43	−	3448.93i	−0.686672	−	0.305726i	0.0335823	−	0.999436i	$-0.489308\pi$
$503$	−7746.43	−	3448.93i	−0.686672	−	0.305726i	−0.720255	+	0.693710i	$0.755975\pi$
$504$	10657.2	+	7742.90i	0.941883	+	0.684318i
$505$	5199.19	−	2314.83i	0.458141	−	0.203977i
$506$	−22165.1	−	4711.33i	−1.94735	−	0.413921i
$507$	657.671	+	6257.32i	0.0576098	+	0.548121i
$508$	−3737.52	+	4150.93i	−0.326428	+	0.362535i
$509$	13760.0	+	15282.0i	1.19823	+	1.33077i	0.930063	+	0.367399i	$0.119752\pi$
$509$	13760.0	+	15282.0i	1.19823	+	1.33077i	0.268168	+	0.963372i	$0.413582\pi$
$510$	−590.163	+	5615.03i	−0.0512409	+	0.487525i
$511$	2530.94	−	7789.44i	0.219104	−	0.674334i
$512$	1603.09	−	4933.80i	0.138373	−	0.425869i
$513$	1936.83	−	18427.7i	0.166692	−	1.58597i
$514$	62.8312	+	69.7812i	0.00539176	+	0.00598816i
$515$	−5726.15	+	6359.53i	−0.489950	+	0.544144i
$516$	2649.99	+	25213.0i	0.226084	+	2.15105i
$517$	−17290.5	−	3675.20i	−1.47086	−	0.312641i
$518$	−656.422	+	292.258i	−0.0556787	+	0.0247897i
$519$	−9592.51	−	6969.37i	−0.811300	−	0.589444i
$520$	−7056.67	−	3141.83i	−0.595107	−	0.264959i
$521$	1103.73	+	1911.71i	0.0928121	+	0.160755i	0.908693	−	0.417464i	$-0.137081\pi$
$521$	1103.73	+	1911.71i	0.0928121	+	0.160755i	−0.815881	+	0.578219i	$0.803748\pi$
$522$	1057.12	−	1830.98i	0.0886376	−	0.153525i
$523$	−16295.6	+	11839.5i	−1.36244	+	0.989872i	−0.364157	+	0.931338i	$0.618643\pi$
$523$	−16295.6	+	11839.5i	−1.36244	+	0.989872i	−0.998285	+	0.0585347i	$0.981357\pi$
$524$	4829.61	−	1026.57i	0.402639	−	0.0855835i
$525$	522.283	+	1607.42i	0.0434177	+	0.133626i
$526$	−6409.63			−0.531318
$527$	4104.77	−	5310.50i	0.339291	−	0.438955i
$528$	42921.6			3.53773
$529$	−2627.68	−	8087.18i	−0.215968	−	0.664681i
$530$	−14906.1	+	3168.38i	−1.22166	+	0.259671i
$531$	3045.58	−	2212.74i	0.248902	−	0.180838i
$532$	15552.5	−	26937.7i	1.26746	−	2.19530i
$533$	−679.714	−	1177.30i	−0.0552377	−	0.0956744i
$534$	−222.216	−	98.9369i	−0.0180079	−	0.00801764i
$535$	−6126.71	−	4451.32i	−0.495104	−	0.359714i
$536$	10649.6	−	4741.49i	0.858192	−	0.382092i
$537$	−778.366	−	165.447i	−0.0625493	−	0.0132953i
$538$	−3191.37	−	30363.9i	−0.255743	−	2.43323i
$539$	−10193.8	+	11321.4i	−0.814616	+	0.904723i
$540$	16636.3	+	18476.5i	1.32577	+	1.47241i
$541$	322.071	−	3064.30i	0.0255951	−	0.243521i	−0.974243	−	0.225502i	$-0.927598\pi$
$541$	322.071	−	3064.30i	0.0255951	−	0.243521i	0.999838	−	0.0180183i	$-0.00573571\pi$
$542$	3545.88	−	10913.1i	0.281012	−	0.864867i
$543$	2394.55	−	7369.67i	0.189245	−	0.582436i
$544$	2098.62	−	19967.0i	0.165400	−	1.57367i
$545$	−3249.45	−	3608.88i	−0.255397	−	0.283647i
$546$	−1621.84	+	1801.24i	−0.127122	+	0.141183i
$547$	954.017	+	9076.86i	0.0745719	+	0.709504i	0.966385	+	0.257100i	$0.0827669\pi$
$547$	954.017	+	9076.86i	0.0745719	+	0.709504i	−0.891813	+	0.452404i	$0.850566\pi$
$548$	−19682.9	−	4183.72i	−1.53432	−	0.326131i
$549$	454.787	−	202.484i	0.0353549	−	0.0157410i
$550$	−14743.2	−	10711.6i	−1.14301	−	0.830442i
$551$	−2795.20	−	1244.50i	−0.216115	−	0.0962206i
$552$	−6370.45	−	11033.9i	−0.491204	−	0.850790i
$553$	264.877	−	458.780i	0.0203683	−	0.0352790i
$554$	21679.8	−	15751.3i	1.66261	−	1.20796i
$555$	−318.231	+	67.6420i	−0.0243390	+	0.00517341i
$556$	14988.5	+	46130.0i	1.14327	+	3.51861i
$557$	15246.7			1.15983			0.579914	−	0.814678i	$-0.303086\pi$
$557$	15246.7			1.15983			0.579914	+	0.814678i	$0.303086\pi$
$558$	−2868.70	−	15789.1i	−0.217637	−	1.19786i
$559$	5152.90			0.389883
$560$	5971.99	+	18379.9i	0.450648	+	1.38695i
$561$	−8255.73	+	1754.81i	−0.621314	+	0.132064i
$562$	414.003	−	300.791i	0.0310741	−	0.0225767i
$563$	3677.17	−	6369.04i	0.275265	−	0.476773i	−0.694937	−	0.719071i	$-0.744568\pi$
$563$	3677.17	−	6369.04i	0.275265	−	0.476773i	0.970202	+	0.242298i	$0.0779011\pi$
$564$	−8108.20	−	14043.8i	−0.605349	−	1.04850i
$565$	−9584.47	−	4267.28i	−0.713667	−	0.317745i
$566$	4742.32	+	3445.50i	0.352181	+	0.255875i
$567$	−423.241	+	188.439i	−0.0313482	+	0.0139571i
$568$	56484.9	+	12006.2i	4.17263	+	0.886921i
$569$	2042.97	+	19437.5i	0.150520	+	1.43210i	0.765439	+	0.643509i	$0.222522\pi$
$569$	2042.97	+	19437.5i	0.150520	+	1.43210i	−0.614919	+	0.788590i	$0.710811\pi$
$570$	13071.8	−	14517.7i	0.960557	−	1.06681i
$571$	−4701.31	−	5221.33i	−0.344560	−	0.382672i	0.545811	−	0.837908i	$-0.316222\pi$
$571$	−4701.31	−	5221.33i	−0.344560	−	0.382672i	−0.890371	+	0.455236i	$0.849555\pi$
$572$	1969.40	−	18737.6i	0.143959	−	1.36968i
$573$	−1859.44	+	5722.76i	−0.135566	+	0.417228i
$574$	−1929.67	+	5938.90i	−0.140318	+	0.431855i
$575$	−307.976	+	2930.20i	−0.0223365	+	0.212518i
$576$	−13736.5	−	15255.9i	−0.993669	−	1.10358i
$577$	−5045.57	+	5603.68i	−0.364038	+	0.404305i	−0.897140	−	0.441746i	$-0.854359\pi$
$577$	−5045.57	+	5603.68i	−0.364038	+	0.404305i	0.533102	+	0.846051i	$0.321026\pi$
$578$	−1903.25	−	18108.3i	−0.136964	−	1.30312i
$579$	−3570.87	−	759.011i	−0.256304	−	0.0544791i
$580$	3750.61	−	1669.88i	0.268510	−	0.119548i
$581$	−76.9564	−	55.9121i	−0.00549516	−	0.00399247i
$582$	10767.5	+	4794.00i	0.766886	+	0.341439i
$583$	−11390.5	−	19728.9i	−0.809169	−	1.40152i
$584$	−24826.6	+	43001.0i	−1.75913	+	3.04690i
$585$	1600.24	−	1162.64i	0.113097	−	0.0821697i
$586$	−2140.19	+	454.911i	−0.150871	+	0.0320686i
$587$	−7181.55	−	22102.5i	−0.504965	−	1.55412i	−0.800830	−	0.598891i	$-0.795608\pi$
$587$	−7181.55	−	22102.5i	−0.504965	−	1.55412i	0.295866	−	0.955230i	$-0.404392\pi$
$588$	−13975.8			−0.980193
$589$	−22290.8	+	6517.31i	−1.55938	+	0.455927i
$590$	10140.1			0.707559
$591$	4122.80	+	12688.7i	0.286953	+	0.883151i
$592$	2320.75	−	493.291i	0.161119	−	0.0342468i
$593$	10769.7	−	7824.67i	0.745801	−	0.541856i	−0.148722	−	0.988879i	$-0.547516\pi$
$593$	10769.7	−	7824.67i	0.745801	−	0.541856i	0.894522	+	0.447023i	$0.147516\pi$
$594$	−25777.5	+	44647.9i	−1.78058	+	3.08405i
$595$	−1900.12	−	3291.11i	−0.130920	−	0.226760i
$596$	24251.5	+	10797.5i	1.66675	+	0.742084i
$597$	−8957.33	−	6507.88i	−0.614069	−	0.446147i
$598$	−3860.01	+	1718.59i	−0.263959	+	0.117522i
$599$	23636.6	+	5024.12i	1.61230	+	0.342704i	0.923901	−	0.382631i	$-0.124982\pi$
$599$	23636.6	+	5024.12i	1.61230	+	0.342704i	0.688396	+	0.725335i	$0.258315\pi$
$600$	−1071.04	−	10190.3i	−0.0728750	−	0.693359i
$601$	−1490.08	+	1654.90i	−0.101134	+	0.112321i	−0.791587	−	0.611057i	$-0.790745\pi$
$601$	−1490.08	+	1654.90i	−0.101134	+	0.112321i	0.690453	+	0.723378i	$0.257411\pi$
$602$	−15838.2	−	17590.1i	−1.07229	−	1.19090i
$603$	−312.028	+	2968.75i	−0.0210726	+	0.200492i
$604$	7138.79	−	21970.9i	0.480916	−	1.48011i
$605$	−9606.26	+	29565.0i	−0.645537	+	1.98676i
$606$	−1131.66	+	10767.0i	−0.0758591	+	0.721751i
$607$	15631.8	+	17360.8i	1.04526	+	1.16088i	0.986692	+	0.162598i	$0.0519872\pi$
$607$	15631.8	+	17360.8i	1.04526	+	1.16088i	0.0585694	+	0.998283i	$0.481346\pi$
$608$	−46483.3	+	51624.9i	−3.10057	+	3.44353i
$609$	−82.5313	−	785.233i	−0.00549152	−	0.0522483i
$610$	1311.63	+	278.795i	0.0870594	+	0.0185050i
$611$	−3011.11	+	1340.63i	−0.199372	+	0.0887662i
$612$	11290.3	+	8202.88i	0.745724	+	0.541800i
$613$	15696.9	+	6988.71i	1.03424	+	0.460475i	0.852421	−	0.522856i	$-0.175134\pi$
$613$	15696.9	+	6988.71i	1.03424	+	0.460475i	0.181823	+	0.983331i	$0.441800\pi$
$614$	1267.96	+	2196.18i	0.0833402	+	0.144349i
$615$	−1413.69	+	2448.58i	−0.0926918	+	0.160547i
$616$	−42912.6	+	31177.8i	−2.80681	+	2.03927i
$617$	16918.9	−	3596.23i	1.10394	−	0.234649i	0.380324	−	0.924853i	$-0.375812\pi$
$617$	16918.9	−	3596.23i	1.10394	−	0.234649i	0.723615	+	0.690204i	$0.242479\pi$
$618$	−5030.49	−	15482.2i	−0.327437	−	1.00775i
$619$	14653.2			0.951472			0.475736	−	0.879588i	$-0.342182\pi$
$619$	14653.2			0.951472			0.475736	+	0.879588i	$0.342182\pi$
$620$	13514.9	−	28078.9i	0.875436	−	1.81883i
$621$	8335.25			0.538619
$622$	−7868.44	−	24216.6i	−0.507228	−	1.56109i
$623$	160.149	−	34.0407i	0.0102989	−	0.00218911i
$624$	6474.80	−	4704.22i	0.415384	−	0.301794i
$625$	3585.43	−	6210.14i	0.229467	−	0.397449i
$626$	−2090.47	−	3620.79i	−0.133469	−	0.231176i
$627$	26678.9	+	11878.2i	1.69929	+	0.756572i
$628$	−30713.5	−	22314.7i	−1.95160	−	1.41792i
$629$	−426.216	+	189.763i	−0.0270180	+	0.0120292i
$630$	−8887.41	−	1889.08i	−0.562036	−	0.119465i
$631$	1471.48	+	14000.2i	0.0928345	+	0.883262i	0.937504	+	0.347974i	$0.113130\pi$
$631$	1471.48	+	14000.2i	0.0928345	+	0.883262i	−0.844670	+	0.535288i	$0.820203\pi$
$632$	−2148.98	+	2386.68i	−0.135256	+	0.150217i
$633$	−4486.30	−	4982.54i	−0.281697	−	0.312856i
$634$	1397.08	−	13292.3i	0.0875158	−	0.832657i
$635$	729.666	−	2245.68i	0.0455999	−	0.140342i
$636$	6458.13	−	19876.1i	0.402644	−	1.23921i
$637$	−296.929	+	2825.09i	−0.0184690	+	0.175721i
$638$	5696.48	+	6326.58i	0.353489	+	0.392589i
$639$	−9894.56	+	10989.0i	−0.612555	+	0.680311i
$640$	−2008.25	−	19107.2i	−0.124036	−	1.18012i
$641$	−13287.4	−	2824.32i	−0.818751	−	0.174031i	−0.220548	−	0.975376i	$-0.570785\pi$
$641$	−13287.4	−	2824.32i	−0.818751	−	0.174031i	−0.598202	+	0.801345i	$0.704118\pi$
$642$	13160.6	−	5859.48i	0.809047	−	0.360211i
$643$	22659.8	+	16463.3i	1.38976	+	1.00972i	0.995892	+	0.0905536i	$0.0288636\pi$
$643$	22659.8	+	16463.3i	1.38976	+	1.00972i	0.393869	+	0.919167i	$0.371136\pi$
$644$	12782.7	+	5691.21i	0.782155	+	0.348238i
$645$	−5358.58	−	9281.33i	−0.327122	−	0.566592i
$646$	14007.4	−	24261.5i	0.853116	−	1.47764i
$647$	−11941.3	+	8675.89i	−0.725599	+	0.527179i	−0.888168	−	0.459519i	$-0.848022\pi$
$647$	−11941.3	+	8675.89i	−0.725599	+	0.527179i	0.162569	+	0.986697i	$0.448022\pi$
$648$	2747.32	−	583.961i	0.166551	−	0.0354014i
$649$	4684.21	+	14416.5i	0.283315	+	0.871954i
$650$	−3398.04			−0.205049
$651$	−4332.52	−	4140.59i	−0.260837	−	0.249282i
$652$	−45702.9			−2.74519
$653$	4502.35	+	13856.8i	0.269817	+	0.830412i	0.990544	+	0.137193i	$0.0438082\pi$
$653$	4502.35	+	13856.8i	0.269817	+	0.830412i	−0.720727	+	0.693219i	$0.756192\pi$
$654$	9036.07	−	1920.68i	0.540273	−	0.114838i
$655$	−1688.63	+	1226.86i	−0.100733	+	0.0731870i
$656$	10309.6	−	17856.7i	0.613599	−	1.06279i
$657$	−6357.33	−	11011.2i	−0.377509	−	0.653864i
$658$	13831.5	+	6158.19i	0.819466	+	0.364850i
$659$	−22846.3	−	16598.8i	−1.35048	−	0.981180i	−0.998988	−	0.0449882i	$-0.985675\pi$
$659$	−22846.3	−	16598.8i	−1.35048	−	0.981180i	−0.351490	−	0.936191i	$-0.614325\pi$
$660$	−35797.9	+	15938.3i	−2.11126	+	0.939994i
$661$	−19775.4	−	4203.38i	−1.16365	−	0.247341i	−0.414694	−	0.909961i	$-0.636111\pi$
$661$	−19775.4	−	4203.38i	−1.16365	−	0.247341i	−0.748956	+	0.662619i	$0.769445\pi$
$662$	−1030.03	−	9800.05i	−0.0604730	−	0.575362i
$663$	−1053.07	+	1169.55i	−0.0616858	+	0.0685090i
$664$	385.874	+	428.556i	0.0225524	+	0.0250470i
$665$	−1374.47	+	13077.2i	−0.0801496	+	0.762573i
$666$	−344.699	+	1060.88i	−0.0200553	+	0.0617238i
$667$	425.330	−	1309.03i	0.0246909	−	0.0759908i
$668$	6334.11	−	60265.0i	0.366877	−	3.49060i
$669$	−12286.9	−	13646.0i	−0.710075	−	0.788618i
$670$	−5380.19	+	5975.31i	−0.310231	+	0.344547i
$671$	209.534	+	1993.58i	0.0120551	+	0.114696i
$672$	−17534.4	−	3727.06i	−1.00656	−	0.213950i
$673$	7959.63	−	3543.86i	0.455901	−	0.202980i	−0.165921	−	0.986139i	$-0.553060\pi$
$673$	7959.63	−	3543.86i	0.455901	−	0.202980i	0.621822	+	0.783159i	$0.286393\pi$
$674$	28166.2	+	20464.0i	1.60968	+	1.16950i
$675$	6123.78	+	2726.48i	0.349191	+	0.155470i
$676$	20945.1	+	36278.0i	1.19169	+	2.06406i
$677$	9575.63	−	16585.5i	0.543606	−	0.941553i	−0.455087	−	0.890447i	$-0.650392\pi$
$677$	9575.63	−	16585.5i	0.543606	−	0.941553i	0.998693	−	0.0511064i	$-0.0162748\pi$
$678$	16146.2	−	11730.9i	0.914591	−	0.664489i
$679$	−7760.04	+	1649.45i	−0.438591	+	0.0932253i
$680$	7119.38	+	21911.2i	0.401494	+	1.23567i
$681$	8720.07			0.490681
$682$	64034.6	+	8660.46i	3.59532	+	0.486256i
$683$	8706.31			0.487757			0.243878	−	0.969806i	$-0.421580\pi$
$683$	8706.31			0.487757			0.243878	+	0.969806i	$0.421580\pi$
$684$	−14921.7	−	45924.2i	−0.834129	−	2.56718i
$685$	8320.65	−	1768.61i	0.464111	−	0.0986498i
$686$	27175.8	−	19744.4i	1.51250	−	1.09890i
$687$	−5845.62	+	10124.9i	−0.324635	+	0.562285i
$688$	39078.3	+	67685.7i	2.16548	+	3.75072i
$689$	−3880.57	−	1727.74i	−0.214569	−	0.0955323i
$690$	7109.57	+	5165.41i	0.392256	+	0.284991i
$691$	−7392.94	+	3291.55i	−0.407006	+	0.181211i	−0.600019	−	0.799985i	$-0.704840\pi$
$691$	−7392.94	+	3291.55i	−0.407006	+	0.181211i	0.193014	+	0.981196i	$0.438174\pi$
$692$	−77217.8	−	16413.2i	−4.24188	−	0.901640i
$693$	−1419.77	−	13508.2i	−0.0778250	−	0.740455i
$694$	−9868.39	+	10960.0i	−0.539768	+	0.599473i
$695$	−13720.1	−	15237.7i	−0.748824	−	0.831654i
$696$	−500.341	+	4760.43i	−0.0272491	+	0.259258i
$697$	−1252.93	+	3856.14i	−0.0680894	+	0.209557i
$698$	−13625.4	+	41934.7i	−0.738867	+	2.27400i
$699$	−1627.02	+	15480.1i	−0.0880396	+	0.837641i
$700$	7529.61	+	8362.48i	0.406561	+	0.451532i
$701$	10253.1	−	11387.2i	0.552431	−	0.613537i	−0.400658	−	0.916228i	$-0.631218\pi$
$701$	10253.1	−	11387.2i	0.552431	−	0.613537i	0.953089	+	0.302691i	$0.0978850\pi$
$702$	1004.84	+	9560.45i	0.0540248	+	0.514011i
$703$	1579.03	+	335.634i	0.0847146	+	0.0180066i
$704$	75515.6	−	33621.7i	4.04276	−	1.79995i
$705$	5546.02	+	4029.42i	0.296277	+	0.215258i
$706$	44047.5	+	19611.2i	2.34809	+	1.04544i
$707$	−3643.57	−	6310.84i	−0.193820	−	0.335705i
$708$	−6953.07	+	12043.1i	−0.369085	+	0.639274i
$709$	18911.1	−	13739.7i	1.00172	−	0.727793i	0.0392650	−	0.999229i	$-0.487498\pi$
$709$	18911.1	−	13739.7i	1.00172	−	0.727793i	0.962457	+	0.271435i	$0.0874984\pi$
$710$	−38959.9	+	8281.19i	−2.05935	+	0.437729i
$711$	−254.133	−	782.140i	−0.0134047	−	0.0412553i
$712$	−992.584			−0.0522453
$713$	−3963.85	−	9665.99i	−0.208201	−	0.507706i
$714$	7229.17			0.378914
$715$	2461.22	+	7574.87i	0.128734	+	0.396201i
$716$	−5182.30	+	1101.53i	−0.270491	+	0.0574947i
$717$	−13915.1	+	10109.9i	−0.724783	+	0.526586i
$718$	−27767.6	+	48095.0i	−1.44329	+	2.49984i
$719$	8610.87	+	14914.5i	0.446636	+	0.773596i	0.998165	−	0.0605597i	$-0.0192886\pi$
$719$	8610.87	+	14914.5i	0.446636	+	0.773596i	−0.551529	+	0.834156i	$0.685955\pi$
$720$	27407.6	+	12202.7i	1.41864	+	0.631620i
$721$	8864.62	+	6440.52i	0.457886	+	0.332674i
$722$	−55004.5	+	24489.6i	−2.83526	+	1.26234i
$723$	15526.5	+	3300.25i	0.798666	+	0.169762i
$724$	−5392.80	−	51309.1i	−0.276826	−	2.63382i
$725$	740.670	−	822.598i	0.0379418	−	0.0421386i
$726$	−39569.3	−	43946.2i	−2.02280	−	2.24655i
$727$	3075.35	−	29260.0i	0.156889	−	1.49270i	−0.578849	−	0.815434i	$-0.696498\pi$
$727$	3075.35	−	29260.0i	0.156889	−	1.49270i	0.735739	−	0.677266i	$-0.236835\pi$
$728$	−3056.35	+	9406.47i	−0.155599	+	0.478883i
$729$	3344.13	−	10292.2i	0.169899	−	0.522896i
$730$	3579.87	−	34060.2i	0.181503	−	1.72688i
$731$	−10283.8	−	11421.3i	−0.520327	−	0.577882i
$732$	−1230.50	+	1366.61i	−0.0621321	+	0.0690047i
$733$	−3672.37	−	34940.3i	−0.185051	−	1.76064i	−0.555246	−	0.831686i	$-0.687376\pi$
$733$	−3672.37	−	34940.3i	−0.185051	−	1.76064i	0.370195	−	0.928954i	$-0.379291\pi$
$734$	32519.3	+	6912.19i	1.63530	+	0.347594i
$735$	5397.30	−	2403.03i	0.270861	−	0.120595i
$736$	−25281.6	−	18368.2i	−1.26616	−	0.919918i
$737$	−10980.7	−	4888.93i	−0.548819	−	0.244350i
$738$	4847.02	+	8395.28i	0.241763	+	0.418746i
$739$	−4697.87	+	8136.95i	−0.233848	+	0.405037i	−0.958937	−	0.283618i	$-0.908465\pi$
$739$	−4697.87	+	8136.95i	−0.233848	+	0.405037i	0.725089	+	0.688655i	$0.241799\pi$
$740$	−1752.40	+	1273.19i	−0.0870534	+	0.0632480i
$741$	5326.43	−	1132.17i	0.264064	−	0.0561285i
$742$	6029.65	+	18557.3i	0.298323	+	0.918142i
$743$	−35878.6			−1.77155			−0.885773	−	0.464119i	$-0.846371\pi$
$743$	−35878.6			−1.77155			−0.885773	+	0.464119i	$0.846371\pi$
$744$	20472.7	+	30014.4i	1.00882	+	1.47901i
$745$	−11222.2			−0.551879
$746$	−13691.5	−	42138.0i	−0.671958	−	2.06807i
$747$	−144.443	+	30.7023i	−0.00707482	+	0.00150380i
$748$	−45461.8	+	33030.0i	−2.22226	+	1.61457i
$749$	−4848.31	+	8397.53i	−0.236520	+	0.409665i
$750$	12607.9	+	21837.5i	0.613834	+	1.06319i
$751$	23204.1	+	10331.1i	1.12747	+	0.501981i	0.883794	−	0.467876i	$-0.154981\pi$
$751$	23204.1	+	10331.1i	1.12747	+	0.501981i	0.243674	+	0.969857i	$0.421647\pi$
$752$	−40445.3	−	29385.2i	−1.96129	−	1.42496i
$753$	18111.8	−	8063.89i	0.876534	−	0.390258i
$754$	1552.72	+	330.041i	0.0749957	+	0.0159408i
$755$	1020.81	+	9712.38i	0.0492068	+	0.468172i
$756$	21301.4	−	23657.6i	1.02477	−	1.13812i
$757$	−3862.52	−	4289.76i	−0.185450	−	0.205963i	0.643250	−	0.765656i	$-0.277586\pi$
$757$	−3862.52	−	4289.76i	−0.185450	−	0.205963i	−0.828700	+	0.559693i	$0.810919\pi$
$758$	−6592.68	+	62725.2i	−0.315906	+	3.00565i
$759$	−4059.59	+	12494.1i	−0.194142	+	0.597507i
$760$	24633.7	−	75814.7i	1.17573	−	3.61854i
$761$	2210.32	−	21029.8i	0.105288	−	1.00175i	−0.806541	−	0.591178i	$-0.798663\pi$
$761$	2210.32	−	21029.8i	0.105288	−	1.00175i	0.911829	−	0.410569i	$-0.134670\pi$
$762$	3005.58	+	3338.04i	0.142888	+	0.158693i
$763$	−4160.65	+	4620.87i	−0.197412	+	0.219248i
$764$	4187.67	+	39843.0i	0.198304	+	1.88674i
$765$	−5770.60	−	1226.58i	−0.272728	−	0.0579701i
$766$	−42202.0	+	18789.5i	−1.99063	+	0.886285i
$767$	2286.68	+	1661.37i	0.107650	+	0.0782120i
$768$	6570.24	+	2925.26i	0.308702	+	0.137443i
$769$	8865.33	+	15355.2i	0.415724	+	0.720055i	0.995504	−	0.0947178i	$-0.0301949\pi$
$769$	8865.33	+	15355.2i	0.415724	+	0.720055i	−0.579780	+	0.814773i	$0.696862\pi$
$770$	18292.9	−	31684.2i	0.856144	−	1.48288i
$771$	44.0410	−	31.9977i	0.00205720	−	0.00149464i
$772$	−23774.5	+	5053.43i	−1.10837	+	0.235592i
$773$	−11374.7	−	35007.8i	−0.529264	−	1.62891i	−0.755727	−	0.654886i	$-0.772717\pi$
$773$	−11374.7	−	35007.8i	−0.529264	−	1.62891i	0.226464	−	0.974020i	$-0.427283\pi$
$774$	−36745.2			−1.70643
$775$	249.589	−	8398.03i	0.0115684	−	0.389247i
$776$	48095.8			2.22492
$777$	128.727	+	396.182i	0.00594346	+	0.0182921i
$778$	73624.4	−	15649.3i	3.39275	−	0.721152i
$779$	11349.9	−	8246.17i	0.522017	−	0.379268i
$780$	−3653.35	+	6327.78i	−0.167706	+	0.290476i
$781$	−29771.3	−	51565.4i	−1.36402	−	2.36255i
$782$	11512.7	+	5125.79i	0.526463	+	0.234396i
$783$	−2533.42	−	1840.64i	−0.115628	−	0.0840090i
$784$	−39360.8	+	17524.5i	−1.79304	+	0.798312i
$785$	15698.0	+	3336.72i	0.713741	+	0.151710i
$786$	−415.038	−	3948.82i	−0.0188345	−	0.179198i
$787$	8692.64	−	9654.16i	0.393722	−	0.437273i	−0.513394	−	0.858153i	$-0.671612\pi$
$787$	8692.64	−	9654.16i	0.393722	−	0.437273i	0.907116	+	0.420880i	$0.138279\pi$
$788$	59437.3	+	66011.8i	2.68701	+	2.98423i
$789$	−388.421	+	3695.58i	−0.0175262	+	0.166750i
$790$	684.524	−	2106.75i	0.0308282	−	0.0948795i
$791$	−4151.18	+	12776.0i	−0.186598	+	0.574289i
$792$	−8607.29	+	81892.9i	−0.386170	+	3.67416i
$793$	250.106	+	277.771i	0.0111999	+	0.0124387i
$794$	−23756.7	+	26384.5i	−1.06183	+	1.17928i
$795$	923.482	+	8786.34i	0.0411981	+	0.391974i
$796$	−72104.7	−	15326.3i	−3.21066	−	0.682447i
$797$	−4488.55	+	1998.43i	−0.199489	+	0.0888181i	−0.504049	−	0.863675i	$-0.668157\pi$
$797$	−4488.55	+	1998.43i	−0.199489	+	0.0888181i	0.304561	+	0.952493i	$0.401490\pi$
$798$	−20236.4	−	14702.6i	−0.897695	−	0.652214i
$799$	8980.82	+	3998.52i	0.397645	+	0.177043i
$800$	−12565.7	−	21764.5i	−0.555332	−	0.961863i
$801$	127.085	−	220.118i	0.00560591	−	0.00970972i
$802$	−1030.81	+	748.930i	−0.0453857	+	0.0329746i
$803$	50078.5	−	10644.5i	2.20079	−	0.467791i
$804$	−3407.49	−	10487.2i	−0.149469	−	0.460018i
$805$	−5915.08			−0.258980
$806$	10608.9	−	5711.77i	0.463628	−	0.249613i
$807$	−17700.2			−0.772090
$808$	13651.7	+	42015.6i	0.594387	+	1.82934i
$809$	−14375.1	+	3055.52i	−0.624724	+	0.132789i	−0.509387	−	0.860537i	$-0.670128\pi$
$809$	−14375.1	+	3055.52i	−0.624724	+	0.132789i	−0.115336	+	0.993326i	$0.536795\pi$
$810$	−1567.28	+	1138.70i	−0.0679861	+	0.0493948i
$811$	−14035.1	+	24309.5i	−0.607694	+	1.05256i	0.383926	+	0.923364i	$0.374572\pi$
$811$	−14035.1	+	24309.5i	−0.607694	+	1.05256i	−0.991620	+	0.129192i	$0.958762\pi$
$812$	−2628.41	−	4552.53i	−0.113595	−	0.196752i
$813$	−6077.25	−	2705.77i	−0.262163	−	0.116722i
$814$	−3633.77	−	2640.09i	−0.156466	−	0.113679i
$815$	17649.9	−	7858.25i	0.758589	−	0.337746i
$816$	−23348.7	−	4962.93i	−1.00168	−	0.212913i
$817$	5558.57	+	52886.3i	0.238029	+	2.26470i
$818$	18300.5	−	20324.8i	0.782227	−	0.868752i
$819$	−1694.68	−	1882.14i	−0.0723041	−	0.0803018i
$820$	−1967.69	+	18721.3i	−0.0837985	+	0.797290i
$821$	−6687.77	+	20582.9i	−0.284293	+	0.874965i	0.702316	+	0.711865i	$0.252149\pi$
$821$	−6687.77	+	20582.9i	−0.284293	+	0.874965i	−0.986610	+	0.163100i	$0.947851\pi$
$822$	−5000.48	+	15389.9i	−0.212180	+	0.653022i
$823$	2107.13	−	20048.0i	0.0892465	−	0.849124i	−0.854721	−	0.519087i	$-0.826272\pi$
$823$	2107.13	−	20048.0i	0.0892465	−	0.849124i	0.943968	−	0.330037i	$-0.107061\pi$
$824$	−44448.9	−	49365.5i	−1.87919	−	2.08705i
$825$	−7069.37	+	7851.33i	−0.298332	+	0.331331i
$826$	−1357.14	−	12912.4i	−0.0571684	−	0.543921i
$827$	−29977.0	−	6371.80i	−1.26046	−	0.267919i	−0.471227	−	0.882012i	$-0.656189\pi$
$827$	−29977.0	−	6371.80i	−1.26046	−	0.267919i	−0.789234	+	0.614093i	$0.789522\pi$
$828$	19843.9	−	8835.06i	0.832877	−	0.370821i
$829$	15727.4	+	11426.6i	0.658907	+	0.478724i	0.866294	−	0.499535i	$-0.166496\pi$
$829$	15727.4	+	11426.6i	0.658907	+	0.478724i	−0.207387	+	0.978259i	$0.566496\pi$
$830$	−363.371	−	161.783i	−0.0151961	−	0.00676575i
$831$	−7767.87	−	13454.3i	−0.324265	−	0.561644i
$832$	7706.72	−	13348.4i	0.321133	−	0.556218i
$833$	6854.35	−	4979.98i	0.285101	−	0.207138i
$834$	38152.8	−	8109.63i	1.58408	−	0.336707i
$835$	7915.94	+	24362.8i	0.328075	+	1.00971i
$836$	194436.			8.04391
$837$	−23701.8	+	1781.18i	−0.978800	+	0.0735564i
$838$	−36489.4			−1.50418
$839$	2926.70	+	9007.46i	0.120430	+	0.370646i	0.993041	−	0.117770i	$-0.0375747\pi$
$839$	2926.70	+	9007.46i	0.120430	+	0.370646i	−0.872611	+	0.488417i	$0.837575\pi$
$840$	20121.2	−	4276.88i	0.826483	−	0.175674i
$841$	19312.8	−	14031.6i	0.791864	−	0.575323i
$842$	18010.6	−	31195.2i	0.737156	−	1.27679i
$843$	−148.337	−	256.928i	−0.00606051	−	0.0104971i
$844$	−40779.9	−	18156.4i	−1.66315	−	0.740483i
$845$	−14326.5	−	10408.8i	−0.583249	−	0.423755i
$846$	21472.1	−	9560.00i	0.872608	−	0.388510i
$847$	38933.8	+	8275.64i	1.57944	+	0.335720i
$848$	−6734.65	−	64075.9i	−0.272723	−	2.59478i
$849$	2273.94	−	2525.47i	0.0919217	−	0.102089i
$850$	6781.55	+	7531.68i	0.273653	+	0.303923i
$851$	−75.9071	+	722.208i	−0.00305765	+	0.0290916i
$852$	16879.6	−	51950.1i	0.678739	−	2.08894i
$853$	−6337.07	+	19503.5i	−0.254370	+	0.782869i	0.739584	+	0.673065i	$0.235022\pi$
$853$	−6337.07	+	19503.5i	−0.254370	+	0.782869i	−0.993953	+	0.109805i	$0.964978\pi$
$854$	179.470	−	1707.54i	0.00719125	−	0.0684202i
$855$	13658.9	+	15169.7i	0.546344	+	0.606776i
$856$	39335.0	−	43685.9i	1.57061	−	1.74434i
$857$	4167.91	+	39655.1i	0.166130	+	1.58062i	0.686790	+	0.726856i	$0.259019\pi$
$857$	4167.91	+	39655.1i	0.166130	+	1.58062i	−0.520661	+	0.853764i	$0.674314\pi$
$858$	−14820.0	−	3150.10i	−0.589683	−	0.125341i
$859$	−23695.7	+	10550.0i	−0.941197	+	0.419048i	−0.819216	−	0.573485i	$-0.805591\pi$
$859$	−23695.7	+	10550.0i	−0.941197	+	0.419048i	−0.121981	+	0.992532i	$0.538925\pi$
$860$	−57726.6	−	41940.8i	−2.28891	−	1.66299i
$861$	3307.24	+	1472.48i	0.130906	+	0.0582832i
$862$	5152.20	+	8923.88i	0.203579	+	0.352609i
$863$	−6150.44	+	10652.9i	−0.242600	+	0.420195i	−0.961454	−	0.274966i	$-0.911333\pi$
$863$	−6150.44	+	10652.9i	−0.242600	+	0.420195i	0.718854	+	0.695161i	$0.244667\pi$
$864$	−57518.9	+	41790.0i	−2.26485	+	1.64551i
$865$	32642.8	−	6938.43i	1.28311	−	0.272733i
$866$	10740.9	+	33057.0i	0.421466	+	1.29714i
$867$	−10556.0			−0.413493
$868$	−37564.5	−	13451.8i	−1.46892	−	0.526017i
$869$	3311.46			0.129268
$870$	−1020.23	−	3139.95i	−0.0397576	−	0.122361i
$871$	−2192.29	+	465.986i	−0.0852847	+	0.0181278i
$872$	30496.8	−	22157.3i	1.18435	−	0.860481i
$873$	−6157.93	+	10665.8i	−0.238733	+	0.413498i
$874$	−21802.4	−	37762.9i	−0.843797	−	1.46150i
$875$	−15505.2	−	6903.37i	−0.599054	−	0.266716i
$876$	37997.6	+	27606.9i	1.46555	+	1.06478i
$877$	34894.1	−	15535.9i	1.34355	−	0.598186i	0.396132	−	0.918193i	$-0.370352\pi$
$877$	34894.1	−	15535.9i	1.34355	−	0.598186i	0.947415	+	0.320008i	$0.103685\pi$
$878$	10947.7	+	2327.01i	0.420807	+	0.0894452i
$879$	132.592	+	1261.53i	0.00508784	+	0.0484076i
$880$	−80834.0	+	89775.3i	−3.09649	+	3.43901i
$881$	22795.8	+	25317.3i	0.871748	+	0.968174i	0.999721	−	0.0236034i	$-0.00751388\pi$
$881$	22795.8	+	25317.3i	0.871748	+	0.968174i	−0.127973	+	0.991778i	$0.540847\pi$
$882$	2117.39	−	20145.7i	0.0808349	−	0.769093i
$883$	8191.71	−	25211.5i	0.312201	−	0.960854i	−0.664691	−	0.747118i	$-0.731437\pi$
$883$	8191.71	−	25211.5i	0.312201	−	0.960854i	0.976891	−	0.213736i	$-0.0685632\pi$
$884$	−3237.91	+	9965.27i	−0.123193	+	0.379150i
$885$	614.484	−	5846.42i	0.0233397	−	0.222062i
$886$	−10446.0	−	11601.5i	−0.396096	−	0.439909i
$887$	−1533.73	+	1703.38i	−0.0580582	+	0.0644802i	−0.771474	−	0.636261i	$-0.780480\pi$
$887$	−1533.73	+	1703.38i	−0.0580582	+	0.0644802i	0.713416	+	0.700741i	$0.247147\pi$
$888$	−263.980	−	2511.60i	−0.00997587	−	0.0949141i
$889$	−2957.31	−	628.596i	−0.111569	−	0.0237148i
$890$	625.436	−	278.462i	0.0235558	−	0.0104877i
$891$	−2342.94	−	1702.25i	−0.0880937	−	0.0640038i
$892$	−111687.	−	49726.1i	−4.19231	−	1.86654i
$893$	−17007.6	−	29458.0i	−0.637333	−	1.10389i
$894$	10673.9	−	18487.8i	0.399318	−	0.691638i
$895$	1811.95	−	1316.46i	0.0676722	−	0.0491668i
$896$	−24062.4	+	5114.61i	−0.897173	+	0.190700i
$897$	756.964	+	2329.70i	0.0281765	+	0.0867183i
$898$	−39721.7			−1.47609
$899$	−929.723	+	3813.21i	−0.0344917	+	0.141466i
$900$	17468.9			0.646998
$901$	3915.06	+	12049.3i	0.144761	+	0.445528i
$902$	−38181.3	+	8115.69i	−1.40942	+	0.299582i
$903$	−11101.7	+	8065.83i	−0.409125	+	0.297247i
$904$	40719.8	−	70528.8i	1.49814	−	2.59486i
$905$	10904.8	+	18887.7i	0.400541	+	0.693757i
$906$	−16971.4	−	7556.15i	−0.622337	−	0.277082i
$907$	7588.52	+	5513.38i	0.277809	+	0.201840i	0.717961	−	0.696083i	$-0.245076\pi$
$907$	7588.52	+	5513.38i	0.277809	+	0.201840i	−0.440152	+	0.897923i	$0.645076\pi$
$908$	53038.2	−	23614.1i	1.93847	−	0.863064i
$909$	−11065.4	−	2352.02i	−0.403757	−	0.0858212i
$910$	−713.084	−	6784.54i	−0.0259764	−	0.247149i
$911$	864.473	−	960.094i	0.0314394	−	0.0349170i	−0.727220	−	0.686404i	$-0.759188\pi$
$911$	864.473	−	960.094i	0.0314394	−	0.0349170i	0.758659	+	0.651487i	$0.225855\pi$
$912$	55265.9	+	61379.0i	2.00662	+	2.22858i
$913$	62.1539	−	591.354i	0.00225300	−	0.0214359i
$914$	−19038.6	+	58594.8i	−0.688994	+	2.12051i
$915$	240.228	−	739.345i	0.00867944	−	0.0267126i
$916$	−8136.43	+	77412.9i	−0.293488	+	2.79235i
$917$	1788.29	+	1986.10i	0.0643999	+	0.0715233i
$918$	19185.1	−	21307.3i	0.689765	−	0.766061i
$919$	1924.23	+	18307.9i	0.0690692	+	0.657150i	0.973210	+	0.229916i	$0.0738452\pi$
$919$	1924.23	+	18307.9i	0.0690692	+	0.657150i	−0.904141	+	0.427234i	$0.859488\pi$
$920$	35076.2	+	7455.68i	1.25699	+	0.267181i
$921$	1343.08	−	597.978i	0.0480521	−	0.0213942i
$922$	15103.8	+	10973.6i	0.539498	+	0.391968i
$923$	−10142.6	−	4515.79i	−0.361700	−	0.161039i
$924$	25087.0	+	43451.9i	0.893183	+	1.54704i
$925$	−292.004	+	505.765i	−0.0103795	+	0.0179778i
$926$	−45360.1	+	32956.0i	−1.60975	+	1.16955i
$927$	16638.4	−	3536.60i	0.589511	−	0.125304i
$928$	3627.94	+	11165.7i	0.128333	+	0.394968i
$929$	−15127.2			−0.534240			−0.267120	−	0.963663i	$-0.586072\pi$
$929$	−15127.2			−0.534240			−0.267120	+	0.963663i	$0.586072\pi$
$930$	−21320.4	−	13168.9i	−0.751744	−	0.464329i
$931$	−29315.4			−1.03198
$932$	32024.3	+	98560.8i	1.12553	+	3.46402i
$933$	−14439.3	+	3069.17i	−0.506668	+	0.107696i
$934$	−3633.79	+	2640.10i	−0.127303	+	0.0924911i
$935$	11877.6	−	20572.6i	0.415443	−	0.719568i
$936$	7677.07	+	13297.1i	0.268091	+	0.464346i
$937$	7600.59	+	3384.00i	0.264995	+	0.117983i	0.534934	−	0.844894i	$-0.320337\pi$
$937$	7600.59	+	3384.00i	0.264995	+	0.117983i	−0.269938	+	0.962878i	$0.587003\pi$
$938$	8329.05	+	6051.41i	0.289929	+	0.210646i
$939$	−2214.31	+	985.874i	−0.0769555	+	0.0342628i
$940$	44644.4	+	9489.46i	1.54908	+	0.329268i
$941$	−1293.23	−	12304.2i	−0.0448013	−	0.426256i	−0.993817	−	0.111028i	$-0.964586\pi$
$941$	−1293.23	−	12304.2i	−0.0448013	−	0.426256i	0.949016	−	0.315228i	$-0.102081\pi$
$942$	−20428.1	+	22687.7i	−0.706564	+	0.784719i
$943$	4222.85	+	4689.95i	0.145827	+	0.161957i
$944$	−4481.23	+	42636.0i	−0.154504	+	1.47000i
$945$	−4158.62	+	12798.9i	−0.143153	+	0.440581i
$946$	45721.9	−	140718.i	1.57140	−	4.83628i
$947$	4058.34	−	38612.5i	0.139259	−	1.32496i	−0.672120	−	0.740442i	$-0.734616\pi$
$947$	4058.34	−	38612.5i	0.139259	−	1.32496i	0.811379	−	0.584520i	$-0.198717\pi$
$948$	2032.75	+	2257.59i	0.0696419	+	0.0773452i
$949$	6387.80	−	7094.37i	0.218500	−	0.242669i
$950$	−3665.56	−	34875.5i	−0.125186	−	1.19106i
$951$	−7579.23	−	1611.02i	−0.258437	−	0.0549324i
$952$	26948.9	−	11998.4i	0.917456	−	0.408478i
$953$	−17333.6	−	12593.6i	−0.589182	−	0.428065i	0.252841	−	0.967508i	$-0.418635\pi$
$953$	−17333.6	−	12593.6i	−0.589182	−	0.428065i	−0.842023	+	0.539442i	$0.818635\pi$
$954$	27672.2	+	12320.5i	0.939122	+	0.418124i
$955$	−8467.92	−	14666.9i	−0.286927	−	0.496973i
$956$	−57258.2	+	99174.1i	−1.93709	+	3.35515i
$957$	3992.90	−	2901.01i	0.134872	−	0.0979899i
$958$	21311.8	−	4529.97i	0.718741	−	0.152773i
$959$	−3365.78	−	10358.8i	−0.113334	−	0.348805i
$960$	−32057.4			−1.07776
$961$	13337.0	+	26638.8i	0.447686	+	0.894191i
$962$	−837.516			−0.0280692
$963$	4651.66	+	14316.3i	0.155657	+	0.479063i
$964$	103374.	−	21972.8i	3.45379	−	0.734125i
$965$	8312.56	−	6039.43i	0.277296	−	0.201467i
$966$	5626.09	−	9744.68i	0.187388	−	0.324565i
$967$	−18868.6	−	32681.3i	−0.627479	−	1.08683i	−0.988056	−	0.154096i	$-0.950753\pi$
$967$	−18868.6	−	32681.3i	−0.627479	−	1.08683i	0.360577	−	0.932730i	$-0.382580\pi$
$968$	−220445.	−	98148.5i	−7.31960	−	3.25890i
$969$	−13139.5	−	9546.42i	−0.435606	−	0.316486i
$970$	−30305.6	+	13492.9i	−1.00315	+	0.446631i
$971$	−37323.1	−	7933.27i	−1.23353	−	0.262194i	−0.455392	−	0.890291i	$-0.650501\pi$
$971$	−37323.1	−	7933.27i	−1.23353	−	0.262194i	−0.778135	+	0.628097i	$0.783834\pi$
$972$	−8309.61	−	79060.6i	−0.274209	−	2.60892i
$973$	−17567.4	+	19510.6i	−0.578814	+	0.642838i
$974$	−23350.1	−	25932.9i	−0.768156	−	0.853124i
$975$	−205.920	+	1959.20i	−0.00676380	+	0.0643533i
$976$	−1751.90	+	5391.80i	−0.0574560	+	0.176831i
$977$	−9433.97	+	29034.8i	−0.308925	+	0.950772i	0.669259	+	0.743029i	$0.266612\pi$
$977$	−9433.97	+	29034.8i	−0.308925	+	0.950772i	−0.978183	+	0.207743i	$0.933388\pi$
$978$	−3841.70	+	36551.3i	−0.125607	+	1.19507i
$979$	684.822	+	760.571i	0.0223565	+	0.0248294i
$980$	26320.6	−	29232.0i	0.857940	−	0.952839i
$981$	1009.00	+	9599.95i	0.0328387	+	0.312439i
$982$	51727.9	+	10995.1i	1.68096	+	0.357299i
$983$	−42528.4	+	18934.8i	−1.37990	+	0.614372i	−0.956543	−	0.291590i	$-0.905816\pi$
$983$	−42528.4	+	18934.8i	−1.37990	+	0.614372i	−0.423359	+	0.905962i	$0.639149\pi$
$984$	−17755.8	−	12900.3i	−0.575238	−	0.417935i
$985$	−34304.2	−	15273.2i	−1.10967	−	0.494056i
$986$	−2367.28	−	4100.24i	−0.0764599	−	0.132432i
$987$	4388.79	−	7601.61i	0.141537	−	0.245149i
$988$	29331.1	−	21310.3i	0.944479	−	0.686204i
$989$	−23398.8	+	4973.58i	−0.752315	+	0.159910i
$990$	−17550.9	−	54016.2i	−0.563439	−	1.73409i
$991$	32791.4			1.05111			0.525556	−	0.850759i	$-0.323857\pi$
$991$	32791.4			1.05111			0.525556	+	0.850759i	$0.323857\pi$
$992$	75815.1	+	46828.6i	2.42654	+	1.49880i
$993$	−5712.80			−0.182568
$994$	15759.7	+	48503.3i	0.502884	+	1.54772i
$995$	30481.3	−	6478.99i	0.971177	−	0.206430i
$996$	441.310	−	320.630i	0.0140396	−	0.0102004i
$997$	−16774.8	+	29054.8i	−0.532861	+	0.922942i	0.466403	+	0.884572i	$0.345550\pi$
$997$	−16774.8	+	29054.8i	−0.532861	+	0.922942i	−0.999264	+	0.0383696i	$0.987784\pi$
$998$	−18481.2	−	32010.3i	−0.586184	−	1.01530i
$999$	1509.33	+	671.997i	0.0478009	+	0.0212823i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	31.4.g.a.7.1	✓	56
31.3	odd	30		961.4.a.l.1.1		28
31.9	even	15	inner	31.4.g.a.9.1	yes	56
31.28	even	15		961.4.a.m.1.1		28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
31.4.g.a.7.1	✓	56	1.1	even	1	trivial
31.4.g.a.9.1	yes	56	31.9	even	15	inner
961.4.a.l.1.1		28	31.3	odd	30
961.4.a.m.1.1		28	31.28	even	15

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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 31 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	31.g (of order \(15\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.65450 - 5.09202i) q^{2} +(-3.03615 + 0.645354i) q^{3} +(-16.7192 + 12.1472i) q^{4} +(4.36814 - 7.56584i) q^{5} +(8.30946 + 14.3924i) q^{6} +(-10.2190 - 4.54979i) q^{7} +(54.8634 + 39.8606i) q^{8} +(-15.8640 + 7.06311i) q^{9} +(-45.7525 - 9.72500i) q^{10} +(-7.30901 - 69.5406i) q^{11} +(42.9227 - 47.6705i) q^{12} +(-8.72426 - 9.68927i) q^{13} +(-6.26031 + 59.5629i) q^{14} +(-8.37969 + 25.7900i) q^{15} +(61.1103 - 188.078i) q^{16} +(-4.06483 + 38.6743i) q^{17} +(62.2124 + 69.0939i) q^{18} +(90.0339 - 99.9927i) q^{19} +(18.8720 + 179.555i) q^{20} +(33.9626 + 7.21898i) q^{21} +(-342.010 + 152.273i) q^{22} +(48.9682 + 35.5775i) q^{23} +(-192.298 - 85.6165i) q^{24} +(24.3387 + 42.1558i) q^{25} +(-34.9037 + 60.4550i) q^{26} +(111.409 - 80.9433i) q^{27} +(226.120 - 48.0634i) q^{28} +(-7.02700 - 21.6269i) q^{29} +145.188 q^{30} +(-146.847 - 90.7027i) q^{31} -516.287 q^{32} +(67.0696 + 206.419i) q^{33} +(203.655 - 43.2883i) q^{34} +(-79.0610 + 57.4412i) q^{35} +(179.436 - 310.793i) q^{36} +(5.99876 + 10.3902i) q^{37} +(-658.126 - 293.017i) q^{38} +(32.7412 + 23.7879i) q^{39} +(541.230 - 240.971i) q^{40} +(101.987 + 21.6779i) q^{41} +(-19.4319 - 184.882i) q^{42} +(-264.451 + 293.702i) q^{43} +(966.925 + 1073.88i) q^{44} +(-15.8578 + 150.877i) q^{45} +(100.143 - 308.210i) q^{46} +(78.1197 - 240.428i) q^{47} +(-64.1632 + 610.472i) q^{48} +(-145.785 - 161.910i) q^{49} +(174.390 - 193.680i) q^{50} +(-12.6171 - 120.044i) q^{51} +(263.560 + 56.0214i) q^{52} +(297.631 - 132.514i) q^{53} +(-596.491 - 433.376i) q^{54} +(-558.060 - 248.465i) q^{55} +(-379.291 - 656.952i) q^{56} +(-208.826 + 361.697i) q^{57} +(-98.4983 + 71.5632i) q^{58} +(-212.048 + 45.0722i) q^{59} +(-173.175 - 532.978i) q^{60} -28.6679 q^{61} +(-218.902 + 897.815i) q^{62} +194.250 q^{63} +(365.312 + 1124.32i) q^{64} +(-111.416 + 23.6823i) q^{65} +(940.123 - 683.040i) q^{66} +(85.9501 - 148.870i) q^{67} +(-401.823 - 695.978i) q^{68} +(-171.635 - 76.4167i) q^{69} +(423.298 + 307.544i) q^{70} +(777.917 - 346.351i) q^{71} +(-1151.89 - 244.842i) q^{72} +(76.5344 + 728.177i) q^{73} +(42.9820 - 47.7363i) q^{74} +(-101.101 - 112.284i) q^{75} +(-290.661 + 2765.46i) q^{76} +(-241.704 + 743.889i) q^{77} +(66.9581 - 206.076i) q^{78} +(-4.95029 + 47.0988i) q^{79} +(-1156.03 - 1283.90i) q^{80} +(27.7134 - 30.7789i) q^{81} +(-58.3521 - 555.184i) q^{82} +(8.31790 + 1.76802i) q^{83} +(-655.517 + 291.855i) q^{84} +(274.848 + 199.689i) q^{85} +(1933.07 + 860.659i) q^{86} +(35.2920 + 61.1275i) q^{87} +(2370.93 - 4106.58i) q^{88} +(-11.8413 + 8.60322i) q^{89} +(794.507 - 168.878i) q^{90} +(45.0690 + 138.708i) q^{91} -1250.87 q^{92} +(504.385 + 180.619i) q^{93} -1353.51 q^{94} +(-363.249 - 1117.96i) q^{95} +(1567.52 - 333.187i) q^{96} +(573.772 - 416.870i) q^{97} +(-583.250 + 1010.22i) q^{98} +(607.123 + 1051.57i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 56 q - 6 q^{2} + q^{3} - 42 q^{4} - 53 q^{6} - 71 q^{7} - 7 q^{8} + 4 q^{9} + 48 q^{10} - 25 q^{11} + 319 q^{12} - 45 q^{13} - 50 q^{14} + 217 q^{15} - 322 q^{16} + 61 q^{17} + 285 q^{18} - 143 q^{19}+ \cdots - 6383 q^{99}+O(q^{100}) \) 56 * q - 6 * q^2 + q^3 - 42 * q^4 - 53 * q^6 - 71 * q^7 - 7 * q^8 + 4 * q^9 + 48 * q^10 - 25 * q^11 + 319 * q^12 - 45 * q^13 - 50 * q^14 + 217 * q^15 - 322 * q^16 + 61 * q^17 + 285 * q^18 - 143 * q^19 + 95 * q^20 - 257 * q^21 - 1147 * q^22 - 244 * q^23 - 226 * q^24 - 96 * q^25 - 1019 * q^26 + 124 * q^27 + 1920 * q^28 - 142 * q^29 + 2430 * q^30 + 112 * q^31 + 618 * q^32 + 134 * q^33 + 2488 * q^34 + 813 * q^35 - 857 * q^36 - 866 * q^37 - 1186 * q^38 - 1090 * q^39 - 663 * q^40 - 333 * q^41 - 3347 * q^42 + 703 * q^43 + 1327 * q^44 - 1201 * q^45 - 818 * q^46 + 1886 * q^47 - 3046 * q^48 + 1346 * q^49 - 4015 * q^50 - 3179 * q^51 - 4447 * q^52 - 1613 * q^53 + 1276 * q^54 + 2486 * q^55 + 4558 * q^56 + 104 * q^57 + 415 * q^58 + 863 * q^59 + 9839 * q^60 + 6180 * q^61 + 427 * q^62 + 3128 * q^63 + 2807 * q^64 + 5398 * q^65 + 7976 * q^66 + 1026 * q^67 - 4992 * q^68 - 4882 * q^69 - 7786 * q^70 + 583 * q^71 - 299 * q^72 - 3709 * q^73 - 5029 * q^74 - 5668 * q^75 - 9928 * q^76 - 9614 * q^77 - 4597 * q^78 + 2323 * q^79 - 2582 * q^80 - 1715 * q^81 - 4314 * q^82 - 2399 * q^83 - 1740 * q^84 + 733 * q^85 + 11232 * q^86 + 4919 * q^87 + 3611 * q^88 - 2244 * q^89 + 10029 * q^90 + 9776 * q^91 + 15424 * q^92 - 2975 * q^93 + 988 * q^94 + 5791 * q^95 + 20204 * q^96 + 10170 * q^97 + 2332 * q^98 - 6383 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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