LMFDB - Embedded newform 85.3.p.a.14.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [85,3,Mod(14,85)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(85, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([8, 9]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("85.14");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 85 = 5 \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	85.p (of order $16$, degree $8$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$2.31608224706$
Analytic rank:	$0$
Dimension:	$128$
Relative dimension:	$16$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			14.6
Character	$\chi$	$=$	85.14
Dual form			85.3.p.a.79.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-0.439826 - 1.06183i) q^{2} +(5.22866 + 1.04004i) q^{3} +(1.89438 - 1.89438i) q^{4} +(-1.35606 - 4.81260i) q^{5} +(-1.19534 - 6.00940i) q^{6} +(-5.63579 + 8.43455i) q^{7} +(-7.09205 - 2.93762i) q^{8} +(17.9423 + 7.43192i) q^{9} +(-4.51375 + 3.55661i) q^{10} +(-5.05533 + 1.00557i) q^{11} +(11.8753 - 7.93484i) q^{12} +(-11.3092 + 11.3092i) q^{13} +(11.4349 + 2.27453i) q^{14} +(-2.08505 - 26.5738i) q^{15} -1.89364i q^{16} +(16.3967 - 4.48859i) q^{17} -22.3204i q^{18} +(8.40501 - 3.48147i) q^{19} +(-11.6858 - 6.54801i) q^{20} +(-38.2399 + 38.2399i) q^{21} +(3.29121 + 4.92564i) q^{22} +(8.96803 - 1.78385i) q^{23} +(-34.0266 - 22.7359i) q^{24} +(-21.3222 + 13.0523i) q^{25} +(16.9825 + 7.03440i) q^{26} +(46.1906 + 30.8636i) q^{27} +(5.30194 + 26.6546i) q^{28} +(14.4912 + 21.6877i) q^{29} +(-27.2999 + 13.9018i) q^{30} +(-15.2246 - 3.02836i) q^{31} +(-30.3789 + 12.5834i) q^{32} -27.4784 q^{33} +(-11.9778 - 15.4364i) q^{34} +(48.2346 + 15.6850i) q^{35} +(48.0684 - 19.9106i) q^{36} +(-14.7427 - 2.93250i) q^{37} +(-7.39348 - 7.39348i) q^{38} +(-70.8939 + 47.3698i) q^{39} +(-4.52036 + 38.1148i) q^{40} +(-42.0816 - 28.1180i) q^{41} +(57.4233 + 23.7855i) q^{42} +(20.4833 - 49.4510i) q^{43} +(-7.67181 + 11.4817i) q^{44} +(11.4361 - 96.4270i) q^{45} +(-5.83852 - 8.73797i) q^{46} +(14.8708 - 14.8708i) q^{47} +(1.96947 - 9.90120i) q^{48} +(-20.6281 - 49.8006i) q^{49} +(23.2375 + 16.8999i) q^{50} +(90.4012 - 6.41600i) q^{51} +42.8479i q^{52} +(-17.4848 - 42.2121i) q^{53} +(12.4561 - 62.6213i) q^{54} +(11.6947 + 22.9657i) q^{55} +(64.7468 - 43.2625i) q^{56} +(47.5678 - 9.46182i) q^{57} +(16.6551 - 24.9261i) q^{58} +(8.64904 - 20.8806i) q^{59} +(-54.2909 - 46.3911i) q^{60} +(-53.4727 + 80.0276i) q^{61} +(3.48056 + 17.4979i) q^{62} +(-163.804 + 109.450i) q^{63} +(21.3668 + 21.3668i) q^{64} +(69.7625 + 39.0906i) q^{65} +(12.0857 + 29.1775i) q^{66} -7.05459 q^{67} +(22.5586 - 39.5648i) q^{68} +48.7460 q^{69} +(-4.55993 - 58.1157i) q^{70} +(8.02497 - 40.3442i) q^{71} +(-105.415 - 105.415i) q^{72} +(52.6636 + 78.8166i) q^{73} +(3.37038 + 16.9440i) q^{74} +(-125.062 + 46.0702i) q^{75} +(9.32708 - 22.5176i) q^{76} +(20.0093 - 48.3066i) q^{77} +(81.4798 + 54.4431i) q^{78} +(30.0861 - 5.98450i) q^{79} +(-9.11333 + 2.56789i) q^{80} +(85.8236 + 85.8236i) q^{81} +(-11.3481 + 57.0506i) q^{82} +(76.5163 - 31.6941i) q^{83} +144.882i q^{84} +(-43.8367 - 72.8240i) q^{85} -61.5178 q^{86} +(53.2136 + 128.469i) q^{87} +(38.8066 + 7.71912i) q^{88} +(-1.82615 + 1.82615i) q^{89} +(-107.419 + 30.2678i) q^{90} +(-31.6518 - 159.124i) q^{91} +(13.6096 - 20.3682i) q^{92} +(-76.4546 - 31.6685i) q^{93} +(-22.3308 - 9.24973i) q^{94} +(-28.1526 - 35.7288i) q^{95} +(-171.928 + 34.1987i) q^{96} +(76.8332 - 51.3383i) q^{97} +(-43.8072 + 43.8072i) q^{98} +(-98.1773 - 19.5287i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 128 q - 16 q^{4} - 8 q^{5} - 16 q^{6} - 16 q^{9} + 16 q^{10} - 96 q^{11} - 16 q^{14} + 16 q^{15} - 16 q^{19} - 120 q^{20} + 224 q^{21} - 160 q^{24} - 240 q^{25} + 288 q^{26} - 176 q^{29} - 200 q^{30} + 48 q^{31}+ \cdots - 1664 q^{99}+O(q^{100}) $ 128 * q - 16 * q^4 - 8 * q^5 - 16 * q^6 - 16 * q^9 + 16 * q^10 - 96 * q^11 - 16 * q^14 + 16 * q^15 - 16 * q^19 - 120 * q^20 + 224 * q^21 - 160 * q^24 - 240 * q^25 + 288 * q^26 - 176 * q^29 - 200 * q^30 + 48 * q^31 + 48 * q^34 + 48 * q^35 - 144 * q^36 + 440 * q^40 - 336 * q^41 - 48 * q^44 + 232 * q^45 - 224 * q^46 - 48 * q^49 - 16 * q^51 + 512 * q^54 - 392 * q^55 - 16 * q^56 + 272 * q^59 - 736 * q^60 - 16 * q^61 + 688 * q^64 - 128 * q^65 - 80 * q^66 + 448 * q^69 + 736 * q^70 + 192 * q^71 + 704 * q^74 + 1048 * q^75 + 496 * q^76 + 304 * q^79 + 1240 * q^80 + 128 * q^81 + 672 * q^85 - 2496 * q^86 - 256 * q^89 + 1104 * q^90 - 1632 * q^91 - 1296 * q^94 + 120 * q^95 - 1728 * q^96 - 1664 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/85\mathbb{Z}\right)^\times$.

$n$	$52$	$71$
$\chi(n)$	$-1$	$e\left(\frac{9}{16}\right)$

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 $

$2$	−0.439826	−	1.06183i	−0.219913	−	0.530917i	0.774965	−	0.632005i	$-0.217768\pi$
$2$	−0.439826	−	1.06183i	−0.219913	−	0.530917i	−0.994877	+	0.101088i	$0.967768\pi$
$3$	5.22866	+	1.04004i	1.74289	+	0.346682i	0.960959	−	0.276689i	$-0.0892373\pi$
$3$	5.22866	+	1.04004i	1.74289	+	0.346682i	0.781926	+	0.623371i	$0.214237\pi$
$4$	1.89438	−	1.89438i	0.473596	−	0.473596i
$5$	−1.35606	−	4.81260i	−0.271212	−	0.962520i
$5$	−1.35606	−	4.81260i	−0.271212	−	0.962520i
$6$	−1.19534	−	6.00940i	−0.199224	−	1.00157i
$7$	−5.63579	+	8.43455i	−0.805113	+	1.20494i	0.170483	+	0.985361i	$0.445467\pi$
$7$	−5.63579	+	8.43455i	−0.805113	+	1.20494i	−0.975595	+	0.219576i	$0.929533\pi$
$8$	−7.09205	−	2.93762i	−0.886506	−	0.367203i
$9$	17.9423	+	7.43192i	1.99358	+	0.825769i
$10$	−4.51375	+	3.55661i	−0.451375	+	0.355661i
$11$	−5.05533	+	1.00557i	−0.459576	+	0.0914153i	−0.419448	−	0.907779i	$-0.637776\pi$
$11$	−5.05533	+	1.00557i	−0.459576	+	0.0914153i	−0.0401274	+	0.999195i	$0.512776\pi$
$12$	11.8753	−	7.93484i	0.989611	−	0.661237i
$13$	−11.3092	+	11.3092i	−0.869937	+	0.869937i	−0.992465	−	0.122528i	$-0.960900\pi$
$13$	−11.3092	+	11.3092i	−0.869937	+	0.869937i	0.122528	+	0.992465i	$0.460900\pi$
$14$	11.4349	+	2.27453i	0.816775	+	0.162467i
$15$	−2.08505	−	26.5738i	−0.139004	−	1.77159i
$16$		−	1.89364i		−	0.118353i
$17$	16.3967	−	4.48859i	0.964513	−	0.264035i
$17$	16.3967	−	4.48859i	0.964513	−	0.264035i
$18$		−	22.3204i		−	1.24002i
$19$	8.40501	−	3.48147i	0.442369	−	0.183235i	−0.150370	−	0.988630i	$-0.548047\pi$
$19$	8.40501	−	3.48147i	0.442369	−	0.183235i	0.592739	+	0.805395i	$0.298047\pi$
$20$	−11.6858	−	6.54801i	−0.584290	−	0.327401i
$21$	−38.2399	+	38.2399i	−1.82095	+	1.82095i
$22$	3.29121	+	4.92564i	0.149600	+	0.223893i
$23$	8.96803	−	1.78385i	0.389914	−	0.0775588i	0.00375992	−	0.999993i	$-0.498803\pi$
$23$	8.96803	−	1.78385i	0.389914	−	0.0775588i	0.386154	+	0.922434i	$0.373803\pi$
$24$	−34.0266	−	22.7359i	−1.41778	−	0.947328i
$25$	−21.3222	+	13.0523i	−0.852888	+	0.522094i
$26$	16.9825	+	7.03440i	0.653175	+	0.270554i
$27$	46.1906	+	30.8636i	1.71076	+	1.14309i
$28$	5.30194	+	26.6546i	0.189355	+	0.951951i
$29$	14.4912	+	21.6877i	0.499698	+	0.747851i	0.992494	−	0.122294i	$-0.0390251\pi$
$29$	14.4912	+	21.6877i	0.499698	+	0.747851i	−0.492796	+	0.870145i	$0.664025\pi$
$30$	−27.2999	+	13.9018i	−0.909996	+	0.463394i
$31$	−15.2246	−	3.02836i	−0.491116	−	0.0976891i	−0.0566814	−	0.998392i	$-0.518052\pi$
$31$	−15.2246	−	3.02836i	−0.491116	−	0.0976891i	−0.434435	+	0.900703i	$0.643052\pi$
$32$	−30.3789	+	12.5834i	−0.949342	+	0.393230i
$33$	−27.4784			−0.832680
$34$	−11.9778	−	15.4364i	−0.352289	−	0.454011i
$35$	48.2346	+	15.6850i	1.37813	+	0.448144i
$36$	48.0684	−	19.9106i	1.33523	−	0.553072i
$37$	−14.7427	−	2.93250i	−0.398450	−	0.0792567i	−0.00820193	−	0.999966i	$-0.502611\pi$
$37$	−14.7427	−	2.93250i	−0.398450	−	0.0792567i	−0.390248	+	0.920710i	$0.627611\pi$
$38$	−7.39348	−	7.39348i	−0.194565	−	0.194565i
$39$	−70.8939	+	47.3698i	−1.81779	+	1.21461i
$40$	−4.52036	+	38.1148i	−0.113009	+	0.952870i
$41$	−42.0816	−	28.1180i	−1.02638	−	0.685805i	−0.0760676	−	0.997103i	$-0.524236\pi$
$41$	−42.0816	−	28.1180i	−1.02638	−	0.685805i	−0.950313	+	0.311297i	$0.899236\pi$
$42$	57.4233	+	23.7855i	1.36722	+	0.566322i
$43$	20.4833	−	49.4510i	0.476355	−	1.15002i	−0.484951	−	0.874542i	$-0.661162\pi$
$43$	20.4833	−	49.4510i	0.476355	−	1.15002i	0.961306	−	0.275482i	$-0.0888376\pi$
$44$	−7.67181	+	11.4817i	−0.174359	+	0.260947i
$45$	11.4361	−	96.4270i	0.254136	−	2.14282i
$46$	−5.83852	−	8.73797i	−0.126924	−	0.189956i
$47$	14.8708	−	14.8708i	0.316399	−	0.316399i	−0.530983	−	0.847382i	$-0.678177\pi$
$47$	14.8708	−	14.8708i	0.316399	−	0.316399i	0.847382	+	0.530983i	$0.178177\pi$
$48$	1.96947	−	9.90120i	0.0410306	−	0.206275i
$49$	−20.6281	−	49.8006i	−0.420981	−	1.01634i
$50$	23.2375	+	16.8999i	0.464749	+	0.337997i
$51$	90.4012	−	6.41600i	1.77257	−	0.125804i
$52$			42.8479i			0.823998i
$53$	−17.4848	−	42.2121i	−0.329903	−	0.796456i	−0.998599	−	0.0529198i	$-0.983147\pi$
$53$	−17.4848	−	42.2121i	−0.329903	−	0.796456i	0.668696	−	0.743536i	$-0.266853\pi$
$54$	12.4561	−	62.6213i	0.230669	−	1.15965i
$55$	11.6947	+	22.9657i	0.212631	+	0.417558i
$56$	64.7468	−	43.2625i	1.15619	−	0.772544i
$57$	47.5678	−	9.46182i	0.834523	−	0.165997i
$58$	16.6551	−	24.9261i	0.287156	−	0.429760i
$59$	8.64904	−	20.8806i	0.146594	−	0.353909i	−0.833478	−	0.552553i	$-0.813654\pi$
$59$	8.64904	−	20.8806i	0.146594	−	0.353909i	0.980072	+	0.198644i	$0.0636537\pi$
$60$	−54.2909	−	46.3911i	−0.904848	−	0.773185i
$61$	−53.4727	+	80.0276i	−0.876602	+	1.31193i	0.0726332	+	0.997359i	$0.476860\pi$
$61$	−53.4727	+	80.0276i	−0.876602	+	1.31193i	−0.949235	+	0.314568i	$0.898140\pi$
$62$	3.48056	+	17.4979i	0.0561380	+	0.282225i
$63$	−163.804	+	109.450i	−2.60006	+	1.73730i
$64$	21.3668	+	21.3668i	0.333857	+	0.333857i
$65$	69.7625	+	39.0906i	1.07327	+	0.601394i
$66$	12.0857	+	29.1775i	0.183117	+	0.442083i
$67$	−7.05459			−0.105292			−0.0526462	−	0.998613i	$-0.516766\pi$
$67$	−7.05459			−0.105292			−0.0526462	+	0.998613i	$0.516766\pi$
$68$	22.5586	−	39.5648i	0.331744	−	0.581836i
$69$	48.7460			0.706464
$70$	−4.55993	−	58.1157i	−0.0651418	−	0.830225i
$71$	8.02497	−	40.3442i	0.113028	−	0.568229i	−0.882219	−	0.470840i	$-0.843951\pi$
$71$	8.02497	−	40.3442i	0.113028	−	0.568229i	0.995246	−	0.0973888i	$-0.0310490\pi$
$72$	−105.415	−	105.415i	−1.46410	−	1.46410i
$73$	52.6636	+	78.8166i	0.721419	+	1.07968i	0.993097	+	0.117292i	$0.0374213\pi$
$73$	52.6636	+	78.8166i	0.721419	+	1.07968i	−0.271678	+	0.962388i	$0.587579\pi$
$74$	3.37038	+	16.9440i	0.0455456	+	0.228973i
$75$	−125.062	+	46.0702i	−1.66749	+	0.614269i
$76$	9.32708	−	22.5176i	0.122725	−	0.296284i
$77$	20.0093	−	48.3066i	0.259861	−	0.627359i
$78$	81.4798	+	54.4431i	1.04461	+	0.697988i
$79$	30.0861	−	5.98450i	0.380837	−	0.0757531i	−0.000959823	−	1.00000i	$-0.500306\pi$
$79$	30.0861	−	5.98450i	0.380837	−	0.0757531i	0.381796	+	0.924246i	$0.375306\pi$
$80$	−9.11333	+	2.56789i	−0.113917	+	0.0320986i
$81$	85.8236	+	85.8236i	1.05955	+	1.05955i
$82$	−11.3481	+	57.0506i	−0.138391	+	0.695740i
$83$	76.5163	−	31.6941i	0.921884	−	0.381857i	0.129290	−	0.991607i	$-0.458730\pi$
$83$	76.5163	−	31.6941i	0.921884	−	0.381857i	0.792594	+	0.609750i	$0.208730\pi$
$84$			144.882i			1.72479i
$85$	−43.8367	−	72.8240i	−0.515726	−	0.856753i
$86$	−61.5178			−0.715323
$87$	53.2136	+	128.469i	0.611651	+	1.47666i
$88$	38.8066	+	7.71912i	0.440985	+	0.0877173i
$89$	−1.82615	+	1.82615i	−0.0205185	+	0.0205185i	−0.717292	−	0.696773i	$-0.754618\pi$
$89$	−1.82615	+	1.82615i	−0.0205185	+	0.0205185i	0.696773	+	0.717292i	$0.254618\pi$
$90$	−107.419	+	30.2678i	−1.19355	+	0.336309i
$91$	−31.6518	−	159.124i	−0.347822	−	1.74862i
$92$	13.6096	−	20.3682i	0.147930	−	0.221393i
$93$	−76.4546	−	31.6685i	−0.822093	−	0.340522i
$94$	−22.3308	−	9.24973i	−0.237562	−	0.0984014i
$95$	−28.1526	−	35.7288i	−0.296343	−	0.376093i
$96$	−171.928	+	34.1987i	−1.79092	+	0.356236i
$97$	76.8332	−	51.3383i	0.792095	−	0.529261i	−0.0924490	−	0.995717i	$-0.529470\pi$
$97$	76.8332	−	51.3383i	0.792095	−	0.529261i	0.884544	+	0.466456i	$0.154470\pi$
$98$	−43.8072	+	43.8072i	−0.447012	+	0.447012i
$99$	−98.1773	−	19.5287i	−0.991690	−	0.197259i
$100$	−15.6663	+	65.1186i	−0.156663	+	0.651186i
$101$		−	59.6901i		−	0.590991i	−0.955344	−	0.295496i	$-0.904515\pi$
$101$		−	59.6901i		−	0.590991i	0.955344	−	0.295496i	$-0.0954848\pi$
$102$	−46.5735	−	93.1690i	−0.456603	−	0.913422i
$103$		−	69.5789i		−	0.675523i	−0.941232	−	0.337761i	$-0.890330\pi$
$103$		−	69.5789i		−	0.675523i	0.941232	−	0.337761i	$-0.109670\pi$
$104$	113.427	−	46.9832i	1.09065	−	0.451761i
$105$	235.889	+	132.178i	2.24656	+	1.25884i
$106$	−37.1320	+	37.1320i	−0.350302	+	0.350302i
$107$	−93.3711	−	139.740i	−0.872627	−	1.30598i	−0.951043	−	0.309058i	$-0.899986\pi$
$107$	−93.3711	−	139.740i	−0.872627	−	1.30598i	0.0784156	−	0.996921i	$-0.475014\pi$
$108$	145.970	−	29.0353i	1.35158	−	0.268845i
$109$	125.132	+	83.6103i	1.14800	+	0.767067i	0.975944	−	0.218021i	$-0.0699602\pi$
$109$	125.132	+	83.6103i	1.14800	+	0.767067i	0.172052	+	0.985088i	$0.444960\pi$
$110$	19.2421	−	22.5187i	0.174928	−	0.204716i
$111$	−74.0344	−	30.6660i	−0.666976	−	0.276271i
$112$	15.9720	+	10.6722i	0.142607	+	0.0952871i
$113$	17.3209	+	87.0780i	0.153282	+	0.770602i	0.978574	+	0.205895i	$0.0660106\pi$
$113$	17.3209	+	87.0780i	0.153282	+	0.770602i	−0.825292	+	0.564707i	$0.808989\pi$
$114$	−30.9684	−	46.3475i	−0.271653	−	0.406557i
$115$	−20.7461	−	40.7405i	−0.180401	−	0.354265i
$116$	68.5368	+	13.6328i	0.590834	+	0.117524i
$117$	−286.961	+	118.863i	−2.45266	+	1.01593i
$118$	−25.9758			−0.220134
$119$	−54.5492	+	163.596i	−0.458396	+	1.37475i
$120$	−63.2765	+	194.588i	−0.527304	+	1.62156i
$121$	−87.2442	+	36.1377i	−0.721027	+	0.298659i
$122$	108.495	+	21.5809i	0.889300	+	0.176893i
$123$	−190.786	−	190.786i	−1.55111	−	1.55111i
$124$	−34.5781	+	23.1044i	−0.278856	+	0.186326i
$125$	91.7299	+	84.9154i	0.733839	+	0.679324i
$126$	188.263	+	125.793i	1.49415	+	0.998359i
$127$	−53.1656	−	22.0219i	−0.418627	−	0.173401i	0.163419	−	0.986557i	$-0.447748\pi$
$127$	−53.1656	−	22.0219i	−0.418627	−	0.173401i	−0.582046	+	0.813156i	$0.697748\pi$
$128$	−37.0431	+	89.4300i	−0.289399	+	0.698672i
$129$	158.531	−	237.259i	1.22893	−	1.83922i
$130$	10.8244	−	91.2692i	0.0832646	−	0.702071i
$131$	23.7912	+	35.6060i	0.181612	+	0.271802i	0.911094	−	0.412198i	$-0.135239\pi$
$131$	23.7912	+	35.6060i	0.181612	+	0.271802i	−0.729482	+	0.684000i	$0.760239\pi$
$132$	−52.0547	+	52.0547i	−0.394354	+	0.394354i
$133$	−18.0042	+	90.5133i	−0.135370	+	0.680551i
$134$	3.10279	+	7.49079i	0.0231551	+	0.0559015i
$135$	85.8967	−	264.149i	0.636272	−	1.95666i
$136$	−129.472	−	16.3341i	−0.952001	−	0.120103i
$137$			183.606i			1.34019i	0.742276	+	0.670094i	$0.233746\pi$
$137$			183.606i			1.34019i	−0.742276	+	0.670094i	$0.766254\pi$
$138$	−21.4398	−	51.7602i	−0.155361	−	0.375074i
$139$	−12.3878	+	62.2775i	−0.0891207	+	0.448040i	0.910298	+	0.413953i	$0.135852\pi$
$139$	−12.3878	+	62.2775i	−0.0891207	+	0.448040i	−0.999419	+	0.0340867i	$0.989148\pi$
$140$	121.088	−	61.6614i	0.864917	−	0.440438i
$141$	93.2204	−	62.2879i	0.661138	−	0.441758i
$142$	−46.3684	+	9.22325i	−0.326538	+	0.0649525i
$143$	45.7995	−	68.5438i	0.320276	−	0.479328i
$144$	14.0734	−	33.9762i	0.0977319	−	0.235946i
$145$	84.7231	−	99.1503i	0.584297	−	0.683795i
$146$	60.5273	−	90.5855i	0.414571	−	0.620449i
$147$	−56.0624	−	281.845i	−0.381377	−	1.91731i
$148$	−33.4835	+	22.3730i	−0.226240	+	0.151169i
$149$	9.09006	+	9.09006i	0.0610071	+	0.0610071i	0.736952	−	0.675945i	$-0.236264\pi$
$149$	9.09006	+	9.09006i	0.0610071	+	0.0610071i	−0.675945	+	0.736952i	$0.736264\pi$
$150$	103.924	+	112.532i	0.692827	+	0.750211i
$151$	−12.2102	−	29.4781i	−0.0808625	−	0.195219i	0.878278	−	0.478151i	$-0.158693\pi$
$151$	−12.2102	−	29.4781i	−0.0808625	−	0.195219i	−0.959140	+	0.282932i	$0.908693\pi$
$152$	−69.8360			−0.459447
$153$	327.553	+	41.3237i	2.14087	+	0.270090i
$154$	−60.0942			−0.390222
$155$	6.07118	+	77.3766i	0.0391689	+	0.499204i
$156$	−44.5637	+	224.037i	−0.285665	+	1.43613i
$157$	−54.3403	−	54.3403i	−0.346116	−	0.346116i	0.512544	−	0.858661i	$-0.328703\pi$
$157$	−54.3403	−	54.3403i	−0.346116	−	0.346116i	−0.858661	+	0.512544i	$0.828703\pi$
$158$	−19.5872	−	29.3143i	−0.123969	−	0.185533i
$159$	−47.5197	−	238.898i	−0.298866	−	1.50250i
$160$	101.754	+	129.138i	0.635965	+	0.807111i
$161$	−35.4959	+	85.6947i	−0.220472	+	0.532266i
$162$	53.3829	−	128.878i	0.329524	−	0.795541i
$163$	233.787	+	156.211i	1.43428	+	0.958352i	0.998293	+	0.0583968i	$0.0185989\pi$
$163$	233.787	+	156.211i	1.43428	+	0.958352i	0.435982	+	0.899955i	$0.356401\pi$
$164$	−132.985	+	26.4524i	−0.810884	+	0.161295i
$165$	37.2624	+	132.243i	0.225833	+	0.801471i
$166$	−67.3077	−	67.3077i	−0.405468	−	0.405468i
$167$	19.6696	−	98.8855i	0.117782	−	0.592129i	−0.876142	−	0.482054i	$-0.839891\pi$
$167$	19.6696	−	98.8855i	0.117782	−	0.592129i	0.993923	−	0.110075i	$-0.0351091\pi$
$168$	383.534	−	158.865i	2.28294	−	0.945625i
$169$		−	86.7954i		−	0.513582i
$170$	−58.0464	+	78.5772i	−0.341450	+	0.462219i
$171$	176.679			1.03321
$172$	−54.8760	−	132.482i	−0.319047	−	0.770247i
$173$	−264.673	−	52.6467i	−1.52990	−	0.304316i	−0.642851	−	0.765991i	$-0.722248\pi$
$173$	−264.673	−	52.6467i	−1.52990	−	0.304316i	−0.887049	+	0.461675i	$0.847248\pi$
$174$	113.008	−	113.008i	0.649471	−	0.649471i
$175$	10.0768	−	253.404i	0.0575815	−	1.44802i
$176$	1.90418	+	9.57298i	0.0108192	+	0.0543919i
$177$	66.9396	−	100.182i	0.378190	−	0.566001i
$178$	2.74225	+	1.13588i	0.0154059	+	0.00638134i
$179$	−138.273	−	57.2744i	−0.772473	−	0.319969i	−0.0385995	−	0.999255i	$-0.512290\pi$
$179$	−138.273	−	57.2744i	−0.772473	−	0.319969i	−0.733874	+	0.679286i	$0.762290\pi$
$180$	−161.005	−	204.334i	−0.894474	−	1.13519i
$181$	310.931	−	61.8480i	1.71785	−	0.341701i	0.764742	−	0.644336i	$-0.222866\pi$
$181$	310.931	−	61.8480i	1.71785	−	0.341701i	0.953107	+	0.302635i	$0.0978662\pi$
$182$	−155.042	+	103.596i	−0.851879	+	0.569207i
$183$	−362.823	+	362.823i	−1.98264	+	1.98264i
$184$	−68.8420	−	13.6935i	−0.374141	−	0.0744213i
$185$	5.87899	+	74.9271i	0.0317783	+	0.405011i
$186$			95.1107i			0.511348i
$187$	−78.3773	+	39.1793i	−0.419130	+	0.209515i
$188$		−	56.3419i		−	0.299691i
$189$	−520.641	+	215.656i	−2.75471	+	1.14104i
$190$	−25.5558	+	45.6078i	−0.134504	+	0.240041i
$191$	−59.6893	+	59.6893i	−0.312509	+	0.312509i	−0.845881	−	0.533372i	$-0.820925\pi$
$191$	−59.6893	+	59.6893i	−0.312509	+	0.312509i	0.533372	+	0.845881i	$0.320925\pi$
$192$	89.4974	+	133.942i	0.466132	+	0.697617i
$193$	−170.196	+	33.8542i	−0.881847	+	0.175410i	−0.615188	−	0.788381i	$-0.710920\pi$
$193$	−170.196	+	33.8542i	−0.881847	+	0.175410i	−0.266659	+	0.963791i	$0.585920\pi$
$194$	−88.3060	−	59.0042i	−0.455185	−	0.304145i
$195$	324.108	+	276.948i	1.66209	+	1.42024i
$196$	−133.419	−	55.2640i	−0.680709	−	0.281959i
$197$	181.508	+	121.280i	0.921362	+	0.615635i	0.923182	−	0.384364i	$-0.125579\pi$
$197$	181.508	+	121.280i	0.921362	+	0.615635i	−0.00181945	+	0.999998i	$0.500579\pi$
$198$	22.4447	+	112.837i	0.113357	+	0.569885i
$199$	201.109	+	300.981i	1.01060	+	1.51247i	0.850919	+	0.525297i	$0.176046\pi$
$199$	201.109	+	300.981i	1.01060	+	1.51247i	0.159679	+	0.987169i	$0.448954\pi$
$200$	189.561	−	29.9313i	0.947805	−	0.149656i
$201$	−36.8860	−	7.33709i	−0.183513	−	0.0365029i
$202$	−63.3810	+	26.2533i	−0.313767	+	0.129967i
$203$	−264.595			−1.30343
$204$	159.100	−	183.409i	0.779903	−	0.899064i
$205$	−78.2556	+	240.651i	−0.381735	+	1.17391i
$206$	−73.8811	+	30.6026i	−0.358646	+	0.148556i
$207$	174.164	+	34.6434i	0.841372	+	0.167359i
$208$	21.4155	+	21.4155i	0.102959	+	0.102959i
$209$	−38.9892	+	26.0518i	−0.186551	+	0.124650i
$210$	36.6007	−	308.610i	0.174289	−	1.46957i
$211$	−8.80401	−	5.88265i	−0.0417252	−	0.0278799i	0.534533	−	0.845148i	$-0.320488\pi$
$211$	−8.80401	−	5.88265i	−0.0417252	−	0.0278799i	−0.576258	+	0.817268i	$0.695488\pi$
$212$	−113.089	−	46.8430i	−0.533439	−	0.220958i
$213$	83.9196	−	202.600i	0.393989	−	0.951173i
$214$	−107.313	+	160.606i	−0.501464	+	0.750494i
$215$	−265.764	−	31.5193i	−1.23611	−	0.146601i
$216$	−236.920	−	354.576i	−1.09685	−	1.64156i
$217$	111.346	−	111.346i	0.513113	−	0.513113i
$218$	33.7441	−	169.643i	0.154789	−	0.778178i
$219$	193.387	+	466.878i	0.883046	+	2.13186i
$220$	65.6601	+	21.3515i	0.298455	+	0.0970523i
$221$	−134.671	+	236.196i	−0.609372	+	1.06876i
$222$			92.0998i			0.414864i
$223$	71.1658	+	171.810i	0.319129	+	0.770446i	0.999301	+	0.0373932i	$0.0119054\pi$
$223$	71.1658	+	171.810i	0.319129	+	0.770446i	−0.680171	+	0.733053i	$0.738095\pi$
$224$	65.0742	−	327.150i	0.290510	−	1.46049i
$225$	−479.572	+	75.7234i	−2.13143	+	0.336548i
$226$	84.8441	−	56.6910i	0.375417	−	0.250845i
$227$	11.2187	−	2.23154i	0.0494215	−	0.00983055i	−0.170318	−	0.985389i	$-0.554479\pi$
$227$	11.2187	−	2.23154i	0.0494215	−	0.00983055i	0.219739	+	0.975559i	$0.429479\pi$
$228$	72.1873	−	108.036i	0.316611	−	0.473842i
$229$	121.568	−	293.492i	0.530866	−	1.28162i	−0.400084	−	0.916478i	$-0.631019\pi$
$229$	121.568	−	293.492i	0.530866	−	1.28162i	0.930950	−	0.365146i	$-0.118981\pi$
$230$	−34.1349	+	39.9477i	−0.148413	+	0.173686i
$231$	154.863	−	231.768i	0.670401	−	1.00333i
$232$	−39.0624	−	196.380i	−0.168372	−	0.846465i
$233$	45.0663	−	30.1123i	0.193418	−	0.129237i	−0.455091	−	0.890445i	$-0.650393\pi$
$233$	45.0663	−	30.1123i	0.193418	−	0.129237i	0.648508	+	0.761208i	$0.275393\pi$
$234$	252.426	+	252.426i	1.07874	+	1.07874i
$235$	−91.7327	−	51.4014i	−0.390352	−	0.218729i
$236$	−23.1713	−	55.9405i	−0.0981836	−	0.237036i
$237$	163.534			0.690017
$238$	197.704	−	14.0315i	0.830687	−	0.0589559i
$239$	−253.401			−1.06026			−0.530129	−	0.847917i	$-0.677856\pi$
$239$	−253.401			−1.06026			−0.530129	+	0.847917i	$0.677856\pi$
$240$	−50.3212	+	3.94834i	−0.209672	+	0.0164514i
$241$	37.5941	−	188.998i	0.155992	−	0.784226i	−0.820996	−	0.570934i	$-0.806581\pi$
$241$	37.5941	−	188.998i	0.155992	−	0.784226i	0.976988	−	0.213292i	$-0.0684187\pi$
$242$	76.7445	+	76.7445i	0.317126	+	0.317126i
$243$	81.7098	+	122.287i	0.336254	+	0.503240i
$244$	50.3051	+	252.901i	0.206168	+	1.03648i
$245$	−211.697	+	166.807i	−0.864071	+	0.680846i
$246$	−118.670	+	286.496i	−0.482400	+	1.16462i
$247$	−55.6812	+	134.426i	−0.225430	+	0.544236i
$248$	99.0775	+	66.2015i	0.399506	+	0.266941i
$249$	433.041	−	86.1372i	1.73912	−	0.345933i
$250$	49.8209	−	134.750i	0.199284	−	0.538999i
$251$	−305.901	−	305.901i	−1.21873	−	1.21873i	−0.968078	−	0.250651i	$-0.919355\pi$
$251$	−305.901	−	305.901i	−1.21873	−	1.21873i	−0.250651	−	0.968078i	$-0.580645\pi$
$252$	−102.967	+	517.648i	−0.408597	+	2.05416i
$253$	−43.5426	+	18.0359i	−0.172105	+	0.0712883i
$254$			66.1388i			0.260389i
$255$	−153.467	−	426.364i	−0.601831	−	1.67202i
$256$	232.121			0.906724
$257$	142.340	+	343.638i	0.553850	+	1.33711i	0.914566	+	0.404437i	$0.132533\pi$
$257$	142.340	+	343.638i	0.553850	+	1.33711i	−0.360715	+	0.932676i	$0.617467\pi$
$258$	−321.656	−	63.9813i	−1.24673	−	0.247989i
$259$	107.821	−	107.821i	0.416296	−	0.416296i
$260$	206.210	−	58.1043i	0.793114	−	0.223478i
$261$	98.8244	+	496.824i	0.378637	+	1.90354i
$262$	27.3437	−	40.9227i	0.104365	−	0.156194i
$263$	27.0841	+	11.2186i	0.102981	+	0.0426562i	0.433579	−	0.901115i	$-0.357250\pi$
$263$	27.0841	+	11.2186i	0.102981	+	0.0426562i	−0.330598	+	0.943772i	$0.607250\pi$
$264$	194.878	+	80.7213i	0.738176	+	0.305762i
$265$	−179.440	+	141.390i	−0.677131	+	0.533546i
$266$	104.029	−	20.6926i	0.391085	−	0.0777917i
$267$	−11.4476	+	7.64903i	−0.0428748	+	0.0286480i
$268$	−13.3641	+	13.3641i	−0.0498661	+	0.0498661i
$269$	−90.9332	−	18.0877i	−0.338042	−	0.0672406i	0.0231508	−	0.999732i	$-0.492630\pi$
$269$	−90.9332	−	18.0877i	−0.338042	−	0.0672406i	−0.361192	+	0.932491i	$0.617630\pi$
$270$	−318.262	+	24.9718i	−1.17875	+	0.0924880i
$271$			180.439i			0.665825i	0.942958	+	0.332913i	$0.108031\pi$
$271$			180.439i			0.665825i	−0.942958	+	0.332913i	$0.891969\pi$
$272$	−8.49978	−	31.0495i	−0.0312492	−	0.114153i
$273$		−	864.925i		−	3.16822i
$274$	194.959	−	80.7545i	0.711528	−	0.294724i
$275$	94.6658	−	87.4248i	0.344239	−	0.317908i
$276$	92.3437	−	92.3437i	0.334579	−	0.334579i
$277$	−28.2097	−	42.2188i	−0.101840	−	0.152414i	0.777050	−	0.629439i	$-0.216715\pi$
$277$	−28.2097	−	42.2188i	−0.101840	−	0.152414i	−0.878890	+	0.477025i	$0.841715\pi$
$278$	71.5768	−	14.2375i	0.257471	−	0.0512141i
$279$	−250.657	−	167.484i	−0.898413	−	0.600300i
$280$	−296.005	−	252.934i	−1.05716	−	0.903336i
$281$	29.0070	+	12.0151i	0.103228	+	0.0427583i	0.433700	−	0.901057i	$-0.357208\pi$
$281$	29.0070	+	12.0151i	0.103228	+	0.0427583i	−0.330472	+	0.943816i	$0.607208\pi$
$282$	−107.140	−	71.5887i	−0.379929	−	0.253861i
$283$	99.0354	+	497.884i	0.349948	+	1.75931i	0.608734	+	0.793374i	$0.291678\pi$
$283$	99.0354	+	497.884i	0.349948	+	1.75931i	−0.258786	+	0.965935i	$0.583322\pi$
$284$	−61.2251	−	91.6299i	−0.215581	−	0.322640i
$285$	−110.041	−	216.094i	−0.386108	−	0.758224i
$286$	−92.9259	−	18.4841i	−0.324916	−	0.0646298i
$287$	474.326	−	196.472i	1.65270	−	0.684572i
$288$	−638.585			−2.21731
$289$	248.705	−	147.196i	0.860571	−	0.509330i
$290$	−142.544	−	46.3529i	−0.491533	−	0.159838i
$291$	455.129	−	188.521i	1.56402	−	0.647837i
$292$	249.074	+	49.5439i	0.852994	+	0.169671i
$293$	−82.6635	−	82.6635i	−0.282128	−	0.282128i	0.551829	−	0.833957i	$-0.313930\pi$
$293$	−82.6635	−	82.6635i	−0.282128	−	0.282128i	−0.833957	+	0.551829i	$0.813930\pi$
$294$	−274.614	+	183.491i	−0.934062	+	0.624120i
$295$	−112.219	−	13.3090i	−0.380402	−	0.0451151i
$296$	95.9411	+	64.1058i	0.324125	+	0.216574i
$297$	−264.544	−	109.578i	−0.890721	−	0.368949i
$298$	5.65409	−	13.6502i	0.0189734	−	0.0458059i
$299$	−81.2472	+	121.595i	−0.271730	+	0.406672i
$300$	−149.640	+	324.189i	−0.498800	+	1.08063i
$301$	301.658	+	451.463i	1.00219	+	1.49988i
$302$	−25.9305	+	25.9305i	−0.0858624	+	0.0858624i
$303$	62.0804	−	312.099i	0.204886	−	1.03003i
$304$	−6.59265	−	15.9161i	−0.0216863	−	0.0523555i
$305$	457.653	+	148.820i	1.50050	+	0.487936i
$306$	−100.187	−	365.982i	−0.327410	−	1.19602i
$307$		−	390.366i		−	1.27155i	−0.771875	−	0.635775i	$-0.780681\pi$
$307$		−	390.366i		−	1.27155i	0.771875	−	0.635775i	$-0.219319\pi$
$308$	−53.6061	−	129.417i	−0.174046	−	0.420184i
$309$	72.3651	−	363.804i	0.234191	−	1.17736i
$310$	79.4907	−	40.4788i	0.256422	−	0.130577i
$311$	−244.904	+	163.640i	−0.787474	+	0.526173i	−0.883067	−	0.469247i	$-0.844525\pi$
$311$	−244.904	+	163.640i	−0.787474	+	0.526173i	0.0955928	+	0.995421i	$0.469525\pi$
$312$	641.938	−	127.689i	2.05749	−	0.409261i
$313$	−80.2632	+	120.122i	−0.256432	+	0.383778i	−0.937240	−	0.348684i	$-0.886629\pi$
$313$	−80.2632	+	120.122i	−0.256432	+	0.383778i	0.680808	+	0.732462i	$0.261629\pi$
$314$	−33.8001	+	81.6006i	−0.107643	+	0.259874i
$315$	748.867	+	639.900i	2.37736	+	2.03143i
$316$	45.6577	−	68.3316i	0.144486	−	0.216239i
$317$	6.34144	+	31.8806i	0.0200045	+	0.100570i	0.989498	−	0.144549i	$-0.0461731\pi$
$317$	6.34144	+	31.8806i	0.0200045	+	0.100570i	−0.969493	+	0.245119i	$0.921173\pi$
$318$	−232.769	+	155.531i	−0.731979	+	0.489093i
$319$	−95.0665	−	95.0665i	−0.298014	−	0.298014i
$320$	73.8553	−	131.805i	0.230798	−	0.411890i
$321$	−342.870	−	827.762i	−1.06813	−	2.57870i
$322$	106.606			0.331073
$323$	122.188	−	94.8113i	0.378290	−	0.293534i
$324$	325.166			1.00360
$325$	93.5254	−	388.748i	0.287771	−	1.19615i
$326$	63.0450	−	316.948i	0.193389	−	0.972234i
$327$	567.312	+	567.312i	1.73490	+	1.73490i
$328$	215.845	+	323.034i	0.658063	+	0.984861i
$329$	41.6198	+	209.237i	0.126504	+	0.635978i
$330$	124.031	−	97.7301i	0.375850	−	0.296152i
$331$	−37.3067	+	90.0664i	−0.112709	+	0.272104i	−0.970162	−	0.242459i	$-0.922046\pi$
$331$	−37.3067	+	90.0664i	−0.112709	+	0.272104i	0.857452	+	0.514563i	$0.172046\pi$
$332$	84.9105	−	204.992i	0.255755	−	0.617446i
$333$	−242.722	−	162.182i	−0.728896	−	0.487033i
$334$	−113.651	+	22.6066i	−0.340273	+	0.0676844i
$335$	9.56644	+	33.9509i	0.0285565	+	0.101346i
$336$	72.4127	+	72.4127i	0.215514	+	0.215514i
$337$	−40.0990	+	201.591i	−0.118988	+	0.598194i	0.874573	+	0.484894i	$0.161142\pi$
$337$	−40.0990	+	201.591i	−0.118988	+	0.598194i	−0.993561	+	0.113300i	$0.963858\pi$
$338$	−92.1623	+	38.1749i	−0.272669	+	0.112943i
$339$			473.316i			1.39621i
$340$	−221.000	−	54.9131i	−0.650001	−	0.161509i
$341$	80.0107			0.234635
$342$	−77.7078	−	187.603i	−0.227216	−	0.548548i
$343$	48.7891	+	9.70476i	0.142242	+	0.0282937i
$344$	−290.537	+	290.537i	−0.844584	+	0.844584i
$345$	−66.1026	−	234.595i	−0.191602	−	0.679986i
$346$	60.5079	+	304.194i	0.174878	+	0.879172i
$347$	−223.148	+	333.965i	−0.643079	+	0.962436i	0.356525	+	0.934286i	$0.383962\pi$
$347$	−223.148	+	333.965i	−0.643079	+	0.962436i	−0.999604	+	0.0281498i	$0.991038\pi$
$348$	344.177	+	142.563i	0.989013	+	0.409663i
$349$	−533.560	−	221.008i	−1.52882	−	0.633260i	−0.549488	−	0.835501i	$-0.685177\pi$
$349$	−533.560	−	221.008i	−1.52882	−	0.633260i	−0.979336	+	0.202242i	$0.935177\pi$
$350$	−273.504	+	100.754i	−0.781441	+	0.287867i
$351$	−871.420	+	173.336i	−2.48268	+	0.493835i
$352$	140.922	−	94.1612i	0.400347	−	0.267503i
$353$	−131.999	+	131.999i	−0.373935	+	0.373935i	−0.868908	−	0.494973i	$-0.835178\pi$
$353$	−131.999	+	131.999i	−0.373935	+	0.373935i	0.494973	+	0.868908i	$0.335178\pi$
$354$	−135.819	−	27.0160i	−0.383668	−	0.0763164i
$355$	−205.043	+	16.0883i	−0.577586	+	0.0453190i
$356$			6.91885i			0.0194350i
$357$	−455.366	+	798.653i	−1.27553	+	2.23712i
$358$			172.013i			0.480484i
$359$	98.9975	−	41.0061i	0.275759	−	0.114223i	−0.240518	−	0.970645i	$-0.577317\pi$
$359$	98.9975	−	41.0061i	0.275759	−	0.114223i	0.516277	+	0.856421i	$0.327317\pi$
$360$	−364.372	+	650.270i	−1.01214	+	1.80631i
$361$	−196.742	+	196.742i	−0.544992	+	0.544992i
$362$	−202.427	−	302.954i	−0.559192	−	0.836890i
$363$	−493.755	+	98.2140i	−1.36021	+	0.270562i
$364$	−361.403	−	241.482i	−0.992865	−	0.663411i
$365$	307.898	−	360.329i	0.843556	−	0.987202i
$366$	544.836	+	225.678i	1.48862	+	0.616608i
$367$	−78.8485	−	52.6849i	−0.214846	−	0.143555i	0.443491	−	0.896279i	$-0.353740\pi$
$367$	−78.8485	−	52.6849i	−0.214846	−	0.143555i	−0.658337	+	0.752723i	$0.728740\pi$
$368$	−3.37797	−	16.9822i	−0.00917928	−	0.0461474i
$369$	−546.067	−	817.248i	−1.47986	−	2.21476i
$370$	76.9743	−	39.1974i	0.208039	−	0.105939i
$371$	454.582	+	90.4219i	1.22529	+	0.243725i
$372$	−204.827	+	84.8420i	−0.550610	+	0.228070i
$373$	595.568			1.59670			0.798349	−	0.602195i	$-0.205707\pi$
$373$	595.568			1.59670			0.798349	+	0.602195i	$0.205707\pi$
$374$	76.0743	+	65.9915i	0.203407	+	0.176448i
$375$	391.308	+	539.397i	1.04349	+	1.43839i
$376$	−149.149	+	61.7795i	−0.396673	+	0.164307i
$377$	−409.154	−	81.3858i	−1.08529	−	0.215878i
$378$	457.982	+	457.982i	1.21159	+	1.21159i
$379$	483.977	−	323.383i	1.27698	−	0.853254i	0.282616	−	0.959233i	$-0.408798\pi$
$379$	483.977	−	323.383i	1.27698	−	0.853254i	0.994368	+	0.105979i	$0.0337977\pi$
$380$	−121.016	−	14.3523i	−0.318463	−	0.0377693i
$381$	−255.081	−	170.440i	−0.669504	−	0.447348i
$382$	89.6330	+	37.1272i	0.234641	+	0.0971916i
$383$	19.8942	−	48.0288i	0.0519430	−	0.125402i	−0.895778	−	0.444502i	$-0.853381\pi$
$383$	19.8942	−	48.0288i	0.0519430	−	0.125402i	0.947721	+	0.319100i	$0.103381\pi$
$384$	−286.697	+	429.072i	−0.746607	+	1.11738i
$385$	−259.614	−	30.7899i	−0.674322	−	0.0799737i
$386$	110.804	+	165.830i	0.287058	+	0.429612i
$387$	735.032	−	735.032i	1.89931	−	1.89931i
$388$	48.2972	−	242.806i	0.124477	−	0.625789i
$389$	68.8145	+	166.133i	0.176901	+	0.427077i	0.987314	−	0.158783i	$-0.0507569\pi$
$389$	68.8145	+	166.133i	0.176901	+	0.427077i	−0.810412	+	0.585860i	$0.800757\pi$
$390$	151.521	−	465.958i	0.388516	−	1.19476i
$391$	139.039	−	69.5032i	0.355599	−	0.177757i
$392$			413.786i			1.05558i
$393$	87.3641	+	210.916i	0.222300	+	0.536681i
$394$	48.9471	−	246.074i	0.124231	−	0.624552i
$395$	−69.5995	−	136.677i	−0.176201	−	0.346018i
$396$	−222.980	+	148.991i	−0.563082	+	0.376239i
$397$	−443.713	+	88.2600i	−1.11767	+	0.222317i	−0.719157	−	0.694847i	$-0.755472\pi$
$397$	−443.713	+	88.2600i	−1.11767	+	0.222317i	−0.398508	+	0.917165i	$0.630472\pi$
$398$	231.138	−	345.923i	0.580750	−	0.869154i
$399$	−188.276	+	454.538i	−0.471869	+	1.13919i
$400$	24.7164	+	40.3766i	0.0617911	+	0.100941i
$401$	−407.152	+	609.346i	−1.01534	+	1.51957i	−0.169925	+	0.985457i	$0.554353\pi$
$401$	−407.152	+	609.346i	−1.01534	+	1.51957i	−0.845416	+	0.534108i	$0.820647\pi$
$402$	8.43266	+	42.3938i	0.0209768	+	0.105457i
$403$	206.426	−	137.930i	0.512224	−	0.342257i
$404$	−113.076	−	113.076i	−0.279891	−	0.279891i
$405$	296.653	−	529.416i	0.732475	−	1.30720i
$406$	116.376	+	280.956i	0.286640	+	0.692010i
$407$	77.4778			0.190363
$408$	−659.978	−	220.062i	−1.61759	−	0.539368i
$409$	−44.6912			−0.109269			−0.0546347	−	0.998506i	$-0.517399\pi$
$409$	−44.6912			−0.109269			−0.0546347	+	0.998506i	$0.517399\pi$
$410$	289.951	−	22.7503i	0.707196	−	0.0554886i
$411$	−190.958	+	960.011i	−0.464618	+	2.33579i
$412$	−131.809	−	131.809i	−0.319925	−	0.319925i
$413$	127.375	+	190.630i	0.308413	+	0.461573i
$414$	−39.8163	−	200.170i	−0.0961747	−	0.483503i
$415$	−256.292	−	325.263i	−0.617570	−	0.783767i
$416$	201.253	−	485.869i	0.483782	−	1.16795i
$417$	−129.543	+	312.744i	−0.310654	+	0.749986i
$418$	44.8111	+	29.9418i	0.107204	+	0.0716312i
$419$	497.303	−	98.9198i	1.18688	−	0.236085i	0.438115	−	0.898919i	$-0.355646\pi$
$419$	497.303	−	98.9198i	1.18688	−	0.236085i	0.748767	+	0.662834i	$0.230646\pi$
$420$	697.260	−	196.469i	1.66014	−	0.467783i
$421$	−166.738	−	166.738i	−0.396053	−	0.396053i	0.480786	−	0.876838i	$-0.340352\pi$
$421$	−166.738	−	166.738i	−0.396053	−	0.396053i	−0.876838	+	0.480786i	$0.840352\pi$
$422$	−2.37416	+	11.9357i	−0.00562598	+	0.0282837i
$423$	377.334	−	156.297i	0.892041	−	0.369496i
$424$			350.735i			0.827204i
$425$	−291.028	+	309.722i	−0.684771	+	0.728758i
$426$	−252.037			−0.591637
$427$	−373.636	−	902.037i	−0.875025	−	2.11250i
$428$	−441.602	−	87.8400i	−1.03178	−	0.205234i
$429$	310.759	−	310.759i	0.724379	−	0.724379i
$430$	83.4218	+	296.060i	0.194004	+	0.688513i
$431$	−66.2226	−	332.924i	−0.153649	−	0.772445i	−0.978363	−	0.206895i	$-0.933664\pi$
$431$	−66.2226	−	332.924i	−0.153649	−	0.772445i	0.824714	−	0.565550i	$-0.191336\pi$
$432$	58.4445	−	87.4683i	0.135288	−	0.202473i
$433$	−107.515	−	44.5341i	−0.248302	−	0.102850i	0.255061	−	0.966925i	$-0.417904\pi$
$433$	−107.515	−	44.5341i	−0.248302	−	0.102850i	−0.503364	+	0.864075i	$0.667904\pi$
$434$	−167.203	−	69.2577i	−0.385260	−	0.159580i
$435$	546.109	−	430.307i	1.25542	−	0.989212i
$436$	395.437	−	78.6574i	0.906966	−	0.180407i
$437$	69.1659	−	46.2152i	0.158274	−	0.105756i
$438$	410.690	−	410.690i	0.937647	−	0.937647i
$439$	−249.098	−	49.5487i	−0.567421	−	0.112867i	−0.0969609	−	0.995288i	$-0.530912\pi$
$439$	−249.098	−	49.5487i	−0.567421	−	0.112867i	−0.470460	+	0.882421i	$0.655912\pi$
$440$	−15.4751	−	197.228i	−0.0351707	−	0.448246i
$441$		−	1046.84i		−	2.37379i
$442$	310.033	+	39.1134i	0.701431	+	0.0884918i
$443$		−	27.1970i		−	0.0613928i	−0.999529	−	0.0306964i	$-0.990227\pi$
$443$		−	27.1970i		−	0.0613928i	0.999529	−	0.0306964i	$-0.00977250\pi$
$444$	−198.343	+	82.1563i	−0.446718	+	0.185037i
$445$	11.2649	+	6.31215i	0.0253143	+	0.0141846i
$446$	151.132	−	151.132i	0.338862	−	0.338862i
$447$	38.0748	+	56.9829i	0.0851784	+	0.127479i
$448$	−300.639	+	59.8008i	−0.671069	+	0.133484i
$449$	571.681	+	381.985i	1.27323	+	0.850746i	0.993990	−	0.109475i	$-0.0349169\pi$
$449$	571.681	+	381.985i	1.27323	+	0.850746i	0.279242	+	0.960221i	$0.409917\pi$
$450$	291.334	+	475.921i	0.647408	+	1.05760i
$451$	241.011	+	99.8300i	0.534392	+	0.221353i
$452$	197.772	+	132.147i	0.437548	+	0.292360i
$453$	−33.1846	−	166.830i	−0.0732551	−	0.368278i
$454$	−7.30378	−	10.9309i	−0.0160876	−	0.0240768i
$455$	−722.879	+	368.109i	−1.58874	+	0.809031i
$456$	−365.148	−	72.6325i	−0.800764	−	0.159282i
$457$	−245.565	+	101.716i	−0.537341	+	0.222574i	−0.634815	−	0.772664i	$-0.718924\pi$
$457$	−245.565	+	101.716i	−0.537341	+	0.222574i	0.0974739	+	0.995238i	$0.468924\pi$
$458$	−365.108			−0.797180
$459$	895.908	+	298.730i	1.95187	+	0.650829i
$460$	−116.479	−	37.8770i	−0.253216	−	0.0823413i
$461$	371.160	−	153.740i	0.805120	−	0.333492i	0.0581151	−	0.998310i	$-0.481491\pi$
$461$	371.160	−	153.740i	0.805120	−	0.333492i	0.747005	+	0.664818i	$0.231491\pi$
$462$	−314.212	−	62.5006i	−0.680112	−	0.135283i
$463$	−104.689	−	104.689i	−0.226111	−	0.226111i	0.584955	−	0.811066i	$-0.301112\pi$
$463$	−104.689	−	104.689i	−0.226111	−	0.226111i	−0.811066	+	0.584955i	$0.801112\pi$
$464$	41.0687	−	27.4412i	0.0885101	−	0.0591405i
$465$	−48.7309	+	410.890i	−0.104798	+	0.883634i
$466$	−51.7956	−	34.6087i	−0.111149	−	0.0742676i
$467$	−247.011	−	102.315i	−0.528932	−	0.219091i	0.102204	−	0.994764i	$-0.467411\pi$
$467$	−247.011	−	102.315i	−0.528932	−	0.219091i	−0.631135	+	0.775673i	$0.717411\pi$
$468$	−318.442	+	768.788i	−0.680432	+	1.64271i
$469$	39.7582	−	59.5023i	0.0847722	−	0.126871i
$470$	−14.2333	+	120.012i	−0.0302836	+	0.255346i
$471$	−227.610	−	340.643i	−0.483249	−	0.723234i
$472$	−122.679	+	122.679i	−0.259913	+	0.259913i
$473$	−53.8234	+	270.589i	−0.113792	+	0.572069i
$474$	−71.9265	−	173.646i	−0.151744	−	0.366341i
$475$	−133.772	+	183.938i	−0.281625	+	0.387237i
$476$	206.576	+	413.250i	0.433984	+	0.868173i
$477$		−	887.327i		−	1.86022i
$478$	111.452	+	269.070i	0.233164	+	0.562908i
$479$	103.750	−	521.586i	0.216597	−	1.08891i	−0.707490	−	0.706723i	$-0.750173\pi$
$479$	103.750	−	521.586i	0.216597	−	1.08891i	0.924087	−	0.382182i	$-0.124827\pi$
$480$	397.729	+	781.046i	0.828603	+	1.62718i
$481$	199.892	−	133.563i	0.415575	−	0.277678i
$482$	−217.220	+	43.2077i	−0.450663	+	0.0896425i
$483$	−274.722	+	411.151i	−0.568783	+	0.851245i
$484$	−96.8153	+	233.733i	−0.200032	+	0.482919i
$485$	−351.261	−	300.150i	−0.724250	−	0.618865i
$486$	93.9106	−	140.547i	0.193232	−	0.289192i
$487$	−42.5052	−	213.688i	−0.0872796	−	0.438784i	−0.999572	−	0.0292454i	$-0.990690\pi$
$487$	−42.5052	−	213.688i	−0.0872796	−	0.438784i	0.912293	−	0.409539i	$-0.134310\pi$
$488$	614.322	−	410.477i	1.25886	−	0.841141i
$489$	1059.92	+	1059.92i	2.16754	+	2.16754i
$490$	270.232	+	151.421i	0.551493	+	0.309023i
$491$	255.964	+	617.953i	0.521312	+	1.25856i	0.937088	+	0.349092i	$0.113510\pi$
$491$	255.964	+	617.953i	0.521312	+	1.25856i	−0.415776	+	0.909467i	$0.636490\pi$
$492$	−722.845			−1.46920
$493$	334.956	+	290.562i	0.679424	+	0.589374i
$494$	167.228			0.338519
$495$	39.1506	+	498.970i	0.0790921	+	1.00802i
$496$	−5.73463	+	28.8299i	−0.0115618	+	0.0581249i
$497$	295.059	+	295.059i	0.593679	+	0.593679i
$498$	−281.926	−	421.932i	−0.566116	−	0.847253i
$499$	46.4490	+	233.515i	0.0930842	+	0.467966i	0.999008	+	0.0445257i	$0.0141777\pi$
$499$	46.4490	+	233.515i	0.0930842	+	0.467966i	−0.905924	+	0.423440i	$0.860822\pi$
$500$	334.634	−	12.9091i	0.669268	−	0.0258182i
$501$	205.691	−	496.581i	0.410560	−	0.991180i
$502$	−190.273	+	459.359i	−0.379029	+	0.915057i
$503$	−644.912	−	430.917i	−1.28213	−	0.856693i	−0.287262	−	0.957852i	$-0.592745\pi$
$503$	−644.912	−	430.917i	−1.28213	−	0.856693i	−0.994870	+	0.101159i	$0.967745\pi$
$504$	1483.23	−	295.032i	2.94291	−	0.585381i
$505$	−287.265	+	80.9434i	−0.568841	+	0.160284i
$506$	38.3023	+	38.3023i	0.0756962	+	0.0756962i
$507$	90.2711	−	453.824i	0.178050	−	0.895116i
$508$	−142.434	+	58.9981i	−0.280382	+	0.116138i
$509$		−	366.934i		−	0.720893i	−0.932780	−	0.360446i	$-0.882624\pi$
$509$		−	366.934i		−	0.720893i	0.932780	−	0.360446i	$-0.117376\pi$
$510$	−385.229	+	350.482i	−0.755351	+	0.687220i
$511$	−961.584			−1.88177
$512$	46.0796	+	111.246i	0.0899992	+	0.217277i
$513$	495.683	+	98.5974i	0.966243	+	0.192198i
$514$	302.282	−	302.282i	0.588097	−	0.588097i
$515$	−334.855	+	94.3531i	−0.650204	+	0.183210i
$516$	−149.140	−	749.779i	−0.289032	−	1.45306i
$517$	−60.2231	+	90.1302i	−0.116486	+	0.174333i
$518$	−161.910	−	67.0653i	−0.312568	−	0.129470i
$519$	−1329.13	−	550.543i	−2.56094	−	1.06078i
$520$	−379.926	−	482.169i	−0.730626	−	0.927248i
$521$	59.0959	−	11.7549i	0.113428	−	0.0225622i	−0.138050	−	0.990425i	$-0.544083\pi$
$521$	59.0959	−	11.7549i	0.113428	−	0.0225622i	0.251478	+	0.967863i	$0.419083\pi$
$522$	484.078	−	323.451i	0.927353	−	0.619637i
$523$	491.096	−	491.096i	0.938998	−	0.938998i	−0.0592454	−	0.998243i	$-0.518869\pi$
$523$	491.096	−	491.096i	0.938998	−	0.938998i	0.998243	+	0.0592454i	$0.0188694\pi$
$524$	112.521	+	22.3818i	0.214735	+	0.0427134i
$525$	316.239	−	1314.48i	0.602360	−	2.50377i
$526$		−	33.6930i		−	0.0640551i
$527$	−263.227	+	18.6819i	−0.499481	+	0.0354494i
$528$			52.0343i			0.0985498i
$529$	−411.489	+	170.444i	−0.777862	+	0.322201i
$530$	229.054	+	128.348i	0.432178	+	0.242166i
$531$	310.366	−	310.366i	0.584494	−	0.584494i
$532$	137.360	+	205.574i	0.258196	+	0.386417i
$533$	793.900	−	157.917i	1.48949	−	0.296279i
$534$	13.1569	+	8.79118i	0.0246384	+	0.0164629i
$535$	−545.895	+	638.853i	−1.02036	+	1.19412i
$536$	50.0315	+	20.7237i	0.0933423	+	0.0386637i
$537$	−663.413	−	443.278i	−1.23541	−	0.825471i
$538$	20.7886	+	104.511i	0.0386405	+	0.194259i
$539$	154.360	+	231.016i	0.286382	+	0.428601i
$540$	−337.679	−	663.122i	−0.625332	−	1.22800i
$541$	294.441	+	58.5679i	0.544253	+	0.108259i	0.459557	−	0.888148i	$-0.348008\pi$
$541$	294.441	+	58.5679i	0.544253	+	0.108259i	0.0846959	+	0.996407i	$0.473008\pi$
$542$	191.596	−	79.3615i	0.353498	−	0.146423i
$543$	1690.07			3.11248
$544$	−441.633	+	342.685i	−0.811826	+	0.629935i
$545$	232.697	−	715.589i	0.426966	−	1.31301i
$546$	−918.406	+	380.416i	−1.68206	+	0.696733i
$547$	228.381	+	45.4278i	0.417515	+	0.0830489i	0.399378	−	0.916787i	$-0.369226\pi$
$547$	228.381	+	45.4278i	0.417515	+	0.0830489i	0.0181377	+	0.999835i	$0.494226\pi$
$548$	347.820	+	347.820i	0.634708	+	0.634708i
$549$	−1554.18	+	1038.47i	−2.83093	+	1.89157i
$550$	−134.467	−	62.0676i	−0.244485	−	0.112850i
$551$	197.304	+	131.834i	0.358083	+	0.239264i
$552$	−345.709	−	143.198i	−0.626285	−	0.259416i
$553$	−119.082	+	287.490i	−0.215339	+	0.519874i
$554$	−32.4219	+	48.5229i	−0.0585234	+	0.0875864i
$555$	−47.1883	+	397.883i	−0.0850240	+	0.716906i
$556$	94.5104	+	141.445i	0.169983	+	0.254397i
$557$	360.583	−	360.583i	0.647366	−	0.647366i	−0.304989	−	0.952356i	$-0.598653\pi$
$557$	360.583	−	360.583i	0.647366	−	0.647366i	0.952356	+	0.304989i	$0.0986529\pi$
$558$	−67.5943	+	339.820i	−0.121137	+	0.608996i
$559$	327.602	+	790.900i	0.586049	+	1.41485i
$560$	29.7018	−	91.3390i	0.0530389	−	0.163105i
$561$	−450.556	+	123.340i	−0.803131	+	0.219857i
$562$		−	36.0851i		−	0.0642084i
$563$	−88.6447	−	214.007i	−0.157451	−	0.380119i	0.825393	−	0.564558i	$-0.190953\pi$
$563$	−88.6447	−	214.007i	−0.157451	−	0.380119i	−0.982844	+	0.184439i	$0.940953\pi$
$564$	58.5981	−	294.593i	0.103897	−	0.522327i
$565$	395.583	−	201.441i	0.700147	−	0.356534i
$566$	485.112	−	324.141i	0.857088	−	0.572688i
$567$	−1207.57	+	240.200i	−2.12975	+	0.423633i
$568$	−175.430	+	262.549i	−0.308855	+	0.462234i
$569$	146.553	−	353.810i	0.257562	−	0.621810i	−0.741214	−	0.671269i	$-0.765750\pi$
$569$	146.553	−	353.810i	0.257562	−	0.621810i	0.998776	+	0.0494588i	$0.0157497\pi$
$570$	−181.057	+	211.888i	−0.317644	+	0.371734i
$571$	80.6707	−	120.732i	0.141280	−	0.211440i	−0.754081	−	0.656781i	$-0.771918\pi$
$571$	80.6707	−	120.732i	0.141280	−	0.211440i	0.895361	+	0.445341i	$0.146918\pi$
$572$	−43.0865	−	216.610i	−0.0753260	−	0.378689i
$573$	−374.174	+	250.015i	−0.653010	+	0.436327i
$574$	−417.241	−	417.241i	−0.726901	−	0.726901i
$575$	−167.935	+	155.089i	−0.292060	+	0.269721i
$576$	224.573	+	542.166i	0.389883	+	0.941260i
$577$	−635.174			−1.10082			−0.550411	−	0.834894i	$-0.685529\pi$
$577$	−635.174			−1.10082			−0.550411	+	0.834894i	$0.685529\pi$
$578$	−265.685	−	199.342i	−0.459662	−	0.344883i
$579$	−925.108			−1.59777
$580$	−27.3307	−	348.327i	−0.0471219	−	0.600564i
$581$	−163.904	+	824.002i	−0.282107	+	1.41825i
$582$	−400.355	−	400.355i	−0.687895	−	0.687895i
$583$	130.839	+	195.814i	0.224423	+	0.335873i
$584$	−141.959	−	713.677i	−0.243081	−	1.22205i
$585$	961.178	+	1219.84i	1.64304	+	2.08520i
$586$	−51.4173	+	124.132i	−0.0877428	+	0.211830i
$587$	−199.142	+	480.771i	−0.339253	+	0.819030i	0.658534	+	0.752551i	$0.271177\pi$
$587$	−199.142	+	480.771i	−0.339253	+	0.819030i	−0.997788	+	0.0664795i	$0.978823\pi$
$588$	−640.126	−	427.718i	−1.08865	−	0.727412i
$589$	−138.506	+	27.5506i	−0.235155	+	0.0467752i
$590$	35.2247	+	125.011i	0.0597029	+	0.211883i
$591$	822.908	+	822.908i	1.39240	+	1.39240i
$592$	−5.55309	+	27.9173i	−0.00938023	+	0.0471576i
$593$	−566.010	+	234.449i	−0.954486	+	0.395361i	−0.804915	−	0.593390i	$-0.797789\pi$
$593$	−566.010	+	234.449i	−0.954486	+	0.395361i	−0.149571	+	0.988751i	$0.547789\pi$
$594$			329.097i			0.554035i
$595$	861.293	+	40.6776i	1.44755	+	0.0683657i
$596$	34.4401			0.0577855
$597$	738.496	+	1782.89i	1.23701	+	2.98641i
$598$	164.848	+	32.7904i	0.275666	+	0.0548334i
$599$	763.522	−	763.522i	1.27466	−	1.27466i	0.331047	−	0.943614i	$-0.392598\pi$
$599$	763.522	−	763.522i	1.27466	−	1.27466i	0.943614	−	0.331047i	$-0.107402\pi$
$600$	1022.28	+	40.6516i	1.70380	+	0.0677527i
$601$	−225.639	−	1134.36i	−0.375440	−	1.88746i	−0.454761	−	0.890613i	$-0.650275\pi$
$601$	−225.639	−	1134.36i	−0.375440	−	1.88746i	0.0793215	−	0.996849i	$-0.474725\pi$
$602$	346.701	−	518.875i	0.575916	−	0.861919i
$603$	−126.575	−	52.4292i	−0.209909	−	0.0869472i
$604$	−78.9737	−	32.7120i	−0.130751	−	0.0541589i
$605$	292.225	+	370.866i	0.483016	+	0.613002i
$606$	−358.702	+	71.3502i	−0.591917	+	0.117740i
$607$	3.38784	−	2.26368i	0.00558129	−	0.00372930i	−0.552776	−	0.833330i	$-0.686432\pi$
$607$	3.38784	−	2.26368i	0.00558129	−	0.00372930i	0.558358	+	0.829600i	$0.311432\pi$
$608$	−211.527	+	211.527i	−0.347906	+	0.347906i
$609$	−1383.48	−	275.191i	−2.27172	−	0.451874i
$610$	−43.2649	−	551.406i	−0.0709260	−	0.903944i
$611$			336.353i			0.550495i
$612$	698.794	−	542.228i	1.14182	−	0.885994i
$613$			1118.48i			1.82460i	0.409520	+	0.912301i	$0.365696\pi$
$613$			1118.48i			1.82460i	−0.409520	+	0.912301i	$0.634304\pi$
$614$	−414.503	+	171.693i	−0.675087	+	0.279630i
$615$	−659.460	+	1176.89i	−1.07229	+	1.91365i
$616$	−283.813	+	283.813i	−0.460736	+	0.460736i
$617$	−35.5241	−	53.1656i	−0.0575756	−	0.0861679i	0.801565	−	0.597908i	$-0.204001\pi$
$617$	−35.5241	−	53.1656i	−0.0575756	−	0.0861679i	−0.859140	+	0.511740i	$0.829001\pi$
$618$	−418.127	+	83.1707i	−0.676581	+	0.134580i
$619$	−226.312	−	151.217i	−0.365609	−	0.244292i	0.359172	−	0.933271i	$-0.383059\pi$
$619$	−226.312	−	151.217i	−0.365609	−	0.244292i	−0.724781	+	0.688979i	$0.758059\pi$
$620$	158.082	+	135.080i	0.254971	+	0.217871i
$621$	469.294	+	194.388i	0.755708	+	0.313024i
$622$	281.474	+	188.075i	0.452530	+	0.302371i
$623$	−5.11096	−	25.6945i	−0.00820379	−	0.0412432i
$624$	89.7014	+	134.248i	0.143752	+	0.215140i
$625$	284.273	−	556.609i	0.454836	−	0.890575i
$626$	162.852	+	32.3932i	0.260147	+	0.0517464i
$627$	−230.956	+	95.6653i	−0.368352	+	0.152576i
$628$	−205.883			−0.327839
$629$	−254.894	+	18.0905i	−0.405237	+	0.0287607i
$630$	350.096	−	1076.62i	0.555709	−	1.70891i
$631$	797.804	−	330.461i	1.26435	−	0.523710i	0.353107	−	0.935583i	$-0.385125\pi$
$631$	797.804	−	330.461i	1.26435	−	0.523710i	0.911242	+	0.411872i	$0.135125\pi$
$632$	−230.952	−	45.9393i	−0.365431	−	0.0726887i
$633$	−39.9149	−	39.9149i	−0.0630567	−	0.0630567i
$634$	31.0627	−	20.7554i	0.0489948	−	0.0327373i
$635$	−33.8869	+	285.728i	−0.0533652	+	0.449965i
$636$	−542.585	−	362.544i	−0.853121	−	0.570037i
$637$	796.492	+	329.918i	1.25038	+	0.517924i
$638$	−59.1321	+	142.757i	−0.0926835	+	0.223758i
$639$	443.821	−	664.225i	0.694556	−	1.03948i
$640$	480.623	+	57.0012i	0.750974	+	0.0890644i
$641$	33.0251	+	49.4255i	0.0515212	+	0.0771069i	0.856336	−	0.516419i	$-0.172735\pi$
$641$	33.0251	+	49.4255i	0.0515212	+	0.0771069i	−0.804815	+	0.593526i	$0.797735\pi$
$642$	−728.142	+	728.142i	−1.13418	+	1.13418i
$643$	223.213	−	1122.17i	0.347144	−	1.74521i	−0.274202	−	0.961672i	$-0.588414\pi$
$643$	223.213	−	1122.17i	0.347144	−	1.74521i	0.621345	−	0.783537i	$-0.286586\pi$
$644$	95.0959	+	229.582i	0.147664	+	0.356493i
$645$	−1356.81	−	441.210i	−2.10358	−	0.684047i
$646$	−154.415	−	88.0425i	−0.239033	−	0.136289i
$647$		−	979.357i		−	1.51369i	−0.653594	−	0.756845i	$-0.726740\pi$
$647$		−	979.357i		−	1.51369i	0.653594	−	0.756845i	$-0.273260\pi$
$648$	−356.548	−	860.783i	−0.550228	−	1.32837i
$649$	−22.7269	+	114.256i	−0.0350183	+	0.176049i
$650$	−453.921	+	71.6730i	−0.698339	+	0.110266i
$651$	697.992	−	466.383i	1.07218	−	0.716411i
$652$	738.807	−	146.958i	1.13314	−	0.225395i
$653$	561.969	−	841.045i	0.860595	−	1.28797i	−0.0956532	−	0.995415i	$-0.530494\pi$
$653$	561.969	−	841.045i	0.860595	−	1.28797i	0.956248	−	0.292557i	$-0.0945060\pi$
$654$	352.872	−	851.909i	0.539560	−	1.30261i
$655$	139.095	−	162.781i	0.212359	−	0.248521i
$656$	−53.2454	+	79.6874i	−0.0811668	+	0.121475i
$657$	359.144	+	1805.54i	0.546643	+	2.74816i
$658$	203.869	−	136.221i	0.309832	−	0.207023i
$659$	−163.152	−	163.152i	−0.247575	−	0.247575i	0.572400	−	0.819975i	$-0.306013\pi$
$659$	−163.152	−	163.152i	−0.247575	−	0.247575i	−0.819975	+	0.572400i	$0.806013\pi$
$660$	321.108	+	179.929i	0.486527	+	0.272620i
$661$	−20.3980	−	49.2452i	−0.0308593	−	0.0745010i	0.907699	−	0.419623i	$-0.137838\pi$
$661$	−20.3980	−	49.2452i	−0.0308593	−	0.0745010i	−0.938558	+	0.345122i	$0.887838\pi$
$662$	112.044			0.169251
$663$	−949.804	+	1094.92i	−1.43259	+	1.65147i
$664$	−635.763			−0.957474
$665$	460.019	−	36.0944i	0.691758	−	0.0542773i
$666$	−65.4546	+	329.062i	−0.0982801	+	0.494088i
$667$	168.646	+	168.646i	0.252842	+	0.252842i
$668$	−150.065	−	224.589i	−0.224649	−	0.336211i
$669$	193.412	+	972.349i	0.289106	+	1.45344i
$670$	31.8426	−	25.0904i	0.0475263	−	0.0374484i
$671$	189.849	−	458.336i	0.282935	−	0.683064i
$672$	680.501	−	1642.87i	1.01265	−	2.44475i
$673$	677.431	+	452.645i	1.00658	+	0.672578i	0.945523	−	0.325556i	$-0.105551\pi$
$673$	677.431	+	452.645i	1.00658	+	0.672578i	0.0610614	+	0.998134i	$0.480551\pi$
$674$	231.693	−	46.0866i	0.343758	−	0.0683777i
$675$	−1387.73	−	55.1839i	−2.05589	−	0.0817539i
$676$	−164.424	−	164.424i	−0.243231	−	0.243231i
$677$	149.918	−	753.687i	0.221444	−	1.11328i	−0.696802	−	0.717264i	$-0.745394\pi$
$677$	149.918	−	753.687i	0.221444	−	1.11328i	0.918246	−	0.396011i	$-0.129606\pi$
$678$	502.582	−	208.176i	0.741272	−	0.307045i
$679$			937.386i			1.38054i
$680$	96.9627	+	645.248i	0.142592	+	0.948894i
$681$	60.9796			0.0895441
$682$	−35.1907	−	84.9580i	−0.0515993	−	0.124572i
$683$	371.496	+	73.8952i	0.543918	+	0.108192i	0.459399	−	0.888230i	$-0.348065\pi$
$683$	371.496	+	73.8952i	0.543918	+	0.108192i	0.0845190	+	0.996422i	$0.473065\pi$
$684$	334.697	−	334.697i	0.489324	−	0.489324i
$685$	883.620	−	248.980i	1.28996	−	0.363475i
$686$	−11.1539	−	56.0743i	−0.0162593	−	0.0817409i
$687$	940.884	−	1408.13i	1.36955	−	2.04968i
$688$	−93.6425	−	38.7880i	−0.136108	−	0.0563779i
$689$	675.124	+	279.646i	0.979861	+	0.405872i
$690$	−220.027	+	173.371i	−0.318880	+	0.251262i
$691$	−1239.34	+	246.520i	−1.79355	+	0.356759i	−0.975774	−	0.218780i	$-0.929792\pi$
$691$	−1239.34	+	246.520i	−1.79355	+	0.356759i	−0.817774	+	0.575539i	$0.804792\pi$
$692$	−601.125	+	401.659i	−0.868677	+	0.580432i
$693$	718.022	−	718.022i	1.03611	−	1.03611i
$694$	452.762	+	90.0599i	0.652394	+	0.129769i
$695$	316.515	−	24.8347i	0.455418	−	0.0357334i
$696$		−	1067.43i		−	1.53366i
$697$	−816.211	−	272.156i	−1.17103	−	0.390468i
$698$			663.756i			0.950940i
$699$	266.954	−	110.576i	0.381909	−	0.158192i
$700$	−460.954	−	499.133i	−0.658506	−	0.713047i
$701$	−53.2635	+	53.2635i	−0.0759822	+	0.0759822i	−0.744077	−	0.668094i	$-0.767110\pi$
$701$	−53.2635	+	53.2635i	−0.0759822	+	0.0759822i	0.668094	+	0.744077i	$0.267110\pi$
$702$	567.327	+	849.064i	0.808158	+	1.20949i
$703$	−134.122	+	26.6784i	−0.190785	+	0.0379494i
$704$	−129.502	−	86.5307i	−0.183952	−	0.122913i
$705$	−426.179	−	364.166i	−0.604509	−	0.516548i
$706$	198.217	+	82.1043i	0.280761	+	0.116295i
$707$	503.460	+	336.401i	0.712107	+	0.475815i
$708$	−62.9743	−	316.593i	−0.0889467	−	0.447165i
$709$	−194.859	−	291.627i	−0.274836	−	0.411321i	0.668216	−	0.743968i	$-0.267058\pi$
$709$	−194.859	−	291.627i	−0.274836	−	0.411321i	−0.943052	+	0.332647i	$0.892058\pi$
$710$	107.266	+	210.645i	0.151079	+	0.296684i
$711$	584.289	+	116.222i	0.821784	+	0.163463i
$712$	18.3157	−	7.58660i	0.0257243	−	0.0106553i
$713$	−141.937			−0.199070
$714$	1048.32	+	132.255i	1.46823	+	0.185230i
$715$	−391.981	−	127.465i	−0.548225	−	0.178273i
$716$	−370.441	+	153.442i	−0.517376	+	0.214304i
$717$	−1324.95	−	263.549i	−1.84791	−	0.367572i
$718$	−87.0833	−	87.0833i	−0.121286	−	0.121286i
$719$	−11.0227	+	7.36514i	−0.0153306	+	0.0102436i	−0.563212	−	0.826312i	$-0.690435\pi$
$719$	−11.0227	+	7.36514i	−0.0153306	+	0.0102436i	0.547881	+	0.836556i	$0.315435\pi$
$720$	−182.598	−	21.6559i	−0.253608	−	0.0300776i
$721$	586.867	+	392.132i	0.813962	+	0.543872i
$722$	295.439	+	122.375i	0.409196	+	0.169494i
$723$	393.134	−	949.109i	0.543753	−	1.31274i
$724$	471.858	−	706.186i	0.651738	−	0.975395i
$725$	−592.060	−	273.284i	−0.816635	−	0.376944i
$726$	321.453	+	481.088i	0.442773	+	0.662656i
$727$	−313.827	+	313.827i	−0.431674	+	0.431674i	−0.889198	−	0.457523i	$-0.848737\pi$
$727$	−313.827	+	313.827i	−0.431674	+	0.431674i	0.457523	+	0.889198i	$0.348737\pi$
$728$	−242.971	+	1221.50i	−0.333751	+	1.67788i
$729$	−117.978	−	284.825i	−0.161836	−	0.390707i
$730$	−518.030	−	168.454i	−0.709631	−	0.230759i
$731$	113.893	−	902.776i	0.155805	−	1.23499i
$732$			1374.65i			1.87794i
$733$	−502.249	−	1212.54i	−0.685197	−	1.65421i	−0.754241	−	0.656598i	$-0.771995\pi$
$733$	−502.249	−	1212.54i	−0.685197	−	1.65421i	0.0690444	−	0.997614i	$-0.478005\pi$
$734$	−21.2629	+	106.896i	−0.0289686	+	0.145635i
$735$	−1280.38	+	652.004i	−1.74201	+	0.887080i
$736$	−249.992	+	167.040i	−0.339663	+	0.226956i
$737$	35.6633	−	7.09387i	0.0483898	−	0.00962533i
$738$	−627.606	+	939.279i	−0.850415	+	1.27274i
$739$	72.9761	−	176.180i	0.0987498	−	0.238403i	−0.866783	−	0.498686i	$-0.833816\pi$
$739$	72.9761	−	176.180i	0.0987498	−	0.238403i	0.965532	+	0.260283i	$0.0838160\pi$
$740$	153.078	+	130.804i	0.206862	+	0.176762i
$741$	−430.948	+	644.959i	−0.581576	+	0.870389i
$742$	−103.924	−	522.460i	−0.140059	−	0.704123i
$743$	162.215	−	108.389i	0.218324	−	0.145880i	−0.441599	−	0.897212i	$-0.645589\pi$
$743$	162.215	−	108.389i	0.218324	−	0.145880i	0.659924	+	0.751333i	$0.270589\pi$
$744$	449.190	+	449.190i	0.603750	+	0.603750i
$745$	31.4201	−	56.0735i	0.0421747	−	0.0752664i
$746$	−261.946	−	632.394i	−0.351134	−	0.847713i
$747$	1608.42			2.15318
$748$	−74.2560	+	222.697i	−0.0992727	+	0.297724i
$749$	1704.86			2.27619
$750$	400.642	−	652.745i	0.534189	−	0.870326i
$751$	78.9869	−	397.094i	0.105176	−	0.528754i	−0.891893	−	0.452246i	$-0.850623\pi$
$751$	78.9869	−	397.094i	0.105176	−	0.528754i	0.997069	−	0.0765079i	$-0.0243770\pi$
$752$	−28.1599	−	28.1599i	−0.0374467	−	0.0374467i
$753$	−1281.30	−	1917.60i	−1.70159	−	2.54661i
$754$	93.5384	+	470.249i	0.124056	+	0.623672i
$755$	−125.308	+	98.7370i	−0.165971	+	0.130777i
$756$	−577.757	+	1394.83i	−0.764229	+	1.84501i
$757$	−447.589	+	1080.58i	−0.591267	+	1.42745i	0.291012	+	0.956719i	$0.406008\pi$
$757$	−447.589	+	1080.58i	−0.591267	+	1.42745i	−0.882279	+	0.470726i	$0.843992\pi$
$758$	−556.245	−	371.671i	−0.733832	−	0.490331i
$759$	−246.427	+	49.0175i	−0.324674	+	0.0645816i
$760$	94.7018	+	336.093i	0.124608	+	0.442227i
$761$	−1014.99	−	1014.99i	−1.33376	−	1.33376i	−0.901981	−	0.431776i	$-0.857887\pi$
$761$	−1014.99	−	1014.99i	−1.33376	−	1.33376i	−0.431776	−	0.901981i	$-0.642113\pi$
$762$	−68.7873	+	345.817i	−0.0902720	+	0.453828i
$763$	−1410.43	+	584.219i	−1.84853	+	0.765687i
$764$			226.149i			0.296007i
$765$	−245.307	−	1632.42i	−0.320663	−	2.13388i
$766$	−59.7485			−0.0780007
$767$	138.329	+	333.956i	0.180351	+	0.435406i
$768$	1213.68	+	241.417i	1.58032	+	0.314345i
$769$	−396.010	+	396.010i	−0.514967	+	0.514967i	−0.916044	−	0.401077i	$-0.868636\pi$
$769$	−396.010	+	396.010i	−0.514967	+	0.514967i	0.401077	+	0.916044i	$0.368636\pi$
$770$	81.4913	+	289.209i	0.105833	+	0.375596i
$771$	386.846	+	1944.81i	0.501746	+	2.52245i
$772$	−258.285	+	386.550i	−0.334565	+	0.500713i
$773$	698.142	+	289.180i	0.903159	+	0.374101i	0.785434	−	0.618946i	$-0.212440\pi$
$773$	698.142	+	289.180i	0.903159	+	0.374101i	0.117725	+	0.993046i	$0.462440\pi$
$774$	−1103.77	−	457.196i	−1.42606	−	0.590692i
$775$	364.149	−	134.145i	0.469870	−	0.173091i
$776$	−695.718	+	138.387i	−0.896544	+	0.178334i
$777$	675.896	−	451.619i	0.869879	−	0.581235i
$778$	146.139	−	146.139i	0.187839	−	0.187839i
$779$	−451.588	−	89.8265i	−0.579702	−	0.115310i
$780$	1138.63	−	89.3402i	1.45978	−	0.114539i
$781$			212.023i			0.271477i
$782$	−134.954	−	117.067i	−0.172575	−	0.149702i
$783$			1449.02i			1.85060i
$784$	−94.3045	+	39.0622i	−0.120286	+	0.0498242i
$785$	−187.829	+	335.207i	−0.239273	+	0.427015i
$786$	185.532	−	185.532i	0.236046	−	0.236046i
$787$	616.957	+	923.341i	0.783935	+	1.17324i	0.981219	+	0.192895i	$0.0617878\pi$
$787$	616.957	+	923.341i	0.783935	+	1.17324i	−0.197284	+	0.980346i	$0.563212\pi$
$788$	573.598	−	114.096i	0.727916	−	0.144791i
$789$	129.946	+	86.8268i	0.164696	+	0.110047i
$790$	−114.516	+	134.017i	−0.144958	+	0.169642i
$791$	−832.081	−	344.659i	−1.05194	−	0.435726i
$792$	638.911	+	426.906i	0.806705	+	0.539023i
$793$	−300.314	−	1509.78i	−0.378706	−	1.90388i
$794$	288.874	+	432.330i	0.363821	+	0.544496i
$795$	−1085.28	+	552.653i	−1.36513	+	0.695161i
$796$	951.151	+	189.196i	1.19491	+	0.237683i
$797$	814.684	−	337.453i	1.02219	−	0.423404i	0.192302	−	0.981336i	$-0.438405\pi$
$797$	814.684	−	337.453i	1.02219	−	0.423404i	0.829887	+	0.557932i	$0.188405\pi$
$798$	565.452			0.708586
$799$	177.083	−	310.581i	0.221631	−	0.388712i
$800$	483.503	−	664.821i	0.604379	−	0.831027i
$801$	−46.3370	+	19.1934i	−0.0578489	+	0.0239618i
$802$	826.099	+	164.321i	1.03005	+	0.204889i
$803$	−345.487	−	345.487i	−0.430246	−	0.430246i
$804$	−83.7756	+	55.9770i	−0.104198	+	0.0696232i
$805$	460.549	+	54.6204i	0.572111	+	0.0678515i
$806$	−237.250	−	158.525i	−0.294355	−	0.196681i
$807$	−456.646	−	189.149i	−0.565857	−	0.234386i
$808$	−175.347	+	423.325i	−0.217014	+	0.523918i
$809$	−747.938	+	1119.37i	−0.924521	+	1.38364i	−0.00104003	+	0.999999i	$0.500331\pi$
$809$	−747.938	+	1119.37i	−0.924521	+	1.38364i	−0.923481	+	0.383644i	$0.874669\pi$
$810$	−692.627	−	82.1446i	−0.855095	−	0.101413i
$811$	−195.074	−	291.948i	−0.240535	−	0.359986i	0.691487	−	0.722389i	$-0.256956\pi$
$811$	−195.074	−	291.948i	−0.240535	−	0.359986i	−0.932021	+	0.362404i	$0.881956\pi$
$812$	−501.246	+	501.246i	−0.617297	+	0.617297i
$813$	−187.664	+	943.452i	−0.230829	+	1.16046i
$814$	−34.0767	−	82.2685i	−0.0418633	−	0.101067i
$815$	434.754	−	1336.95i	0.533440	−	1.64043i
$816$	−12.1496	−	171.187i	−0.0148892	−	0.209788i
$817$		−	486.948i		−	0.596020i
$818$	19.6563	+	47.4546i	0.0240297	+	0.0580129i
$819$	614.695	−	3090.28i	0.750543	−	3.77323i
$820$	307.640	+	604.133i	0.375171	+	0.736747i
$821$	−1237.15	+	826.634i	−1.50688	+	1.00686i	−0.518459	+	0.855102i	$0.673494\pi$
$821$	−1237.15	+	826.634i	−1.50688	+	1.00686i	−0.988417	+	0.151760i	$0.951506\pi$
$822$	1103.36	−	219.472i	1.34229	−	0.266998i
$823$	−779.105	+	1166.01i	−0.946665	+	1.41678i	−0.0379910	+	0.999278i	$0.512096\pi$
$823$	−779.105	+	1166.01i	−0.946665	+	1.41678i	−0.908674	+	0.417506i	$0.862904\pi$
$824$	−204.397	+	493.457i	−0.248054	+	0.598855i
$825$	585.901	−	358.658i	0.710183	−	0.434737i
$826$	146.394	−	219.094i	0.177233	−	0.265247i
$827$	164.450	+	826.748i	0.198852	+	0.999695i	0.943281	+	0.331994i	$0.107722\pi$
$827$	164.450	+	826.748i	0.198852	+	0.999695i	−0.744430	+	0.667701i	$0.767278\pi$
$828$	395.562	−	264.306i	0.477731	−	0.319210i
$829$	686.413	+	686.413i	0.828001	+	0.828001i	0.987240	−	0.159239i	$-0.0509040\pi$
$829$	686.413	+	686.413i	0.828001	+	0.828001i	−0.159239	+	0.987240i	$0.550904\pi$
$830$	−232.652	+	415.198i	−0.280303	+	0.500239i
$831$	−103.589	−	250.087i	−0.124656	−	0.300947i
$832$	−483.283			−0.580869
$833$	−561.768	−	723.976i	−0.674391	−	0.869119i
$834$	389.058			0.466497
$835$	−502.569	+	39.4330i	−0.601879	+	0.0472252i
$836$	−24.5085	+	123.213i	−0.0293164	+	0.147384i
$837$	−609.767	−	609.767i	−0.728515	−	0.728515i
$838$	−323.763	−	484.546i	−0.386352	−	0.578217i
$839$	−165.653	−	832.795i	−0.197441	−	0.992604i	−0.944666	−	0.328033i	$-0.893614\pi$
$839$	−165.653	−	832.795i	−0.197441	−	0.992604i	0.747225	−	0.664571i	$-0.231386\pi$
$840$	−1284.65	−	1630.36i	−1.52934	−	1.94091i
$841$	61.4775	−	148.420i	0.0731004	−	0.176480i
$842$	−103.712	+	250.384i	−0.123174	+	0.297368i
$843$	139.171	+	92.9914i	0.165091	+	0.110310i
$844$	−27.8222	+	5.53417i	−0.0329647	+	0.00655708i
$845$	−417.712	+	117.700i	−0.494333	+	0.139290i
$846$	−331.922	−	331.922i	−0.392343	−	0.392343i
$847$	186.884	−	939.531i	0.220643	−	1.10925i
$848$	−79.9346	+	33.1100i	−0.0942625	+	0.0390448i
$849$			2706.27i			3.18760i
$850$	456.875	+	172.799i	0.537500	+	0.203293i
$851$	−137.444			−0.161508
$852$	−224.826	−	542.778i	−0.263880	−	0.637063i
$853$	777.189	+	154.593i	0.911124	+	0.181234i	0.628330	−	0.777947i	$-0.283739\pi$
$853$	777.189	+	154.593i	0.911124	+	0.181234i	0.282794	+	0.959181i	$0.408739\pi$
$854$	−793.478	+	793.478i	−0.929131	+	0.929131i
$855$	−239.587	−	850.284i	−0.280219	−	0.994484i
$856$	251.690	+	1265.33i	0.294030	+	1.47819i
$857$	−563.967	+	844.036i	−0.658071	+	0.984873i	0.340926	+	0.940090i	$0.389260\pi$
$857$	−563.967	+	844.036i	−0.658071	+	0.984873i	−0.998997	+	0.0447828i	$0.985740\pi$
$858$	−466.654	−	193.294i	−0.543885	−	0.225285i
$859$	1388.46	+	575.120i	1.61637	+	0.669523i	0.993608	−	0.112888i	$-0.0360102\pi$
$859$	1388.46	+	575.120i	1.61637	+	0.669523i	0.622763	+	0.782411i	$0.286010\pi$
$860$	−563.170	+	443.750i	−0.654849	+	0.515989i
$861$	2684.43	−	533.966i	3.11780	−	0.620169i
$862$	−324.383	+	216.746i	−0.376314	+	0.251445i
$863$	−804.719	+	804.719i	−0.932467	+	0.932467i	−0.997860	−	0.0653922i	$-0.979170\pi$
$863$	−804.719	+	804.719i	−0.932467	+	0.932467i	0.0653922	+	0.997860i	$0.479170\pi$
$864$	−1791.59	−	356.369i	−2.07360	−	0.412464i
$865$	105.545	+	1345.16i	0.122017	+	1.55509i
$866$			133.750i			0.154446i
$867$	1453.48	−	510.976i	1.67645	−	0.589360i
$868$		−	421.863i		−	0.486017i
$869$	−146.077	+	60.5072i	−0.168098	+	0.0696286i
$870$	−697.107	−	390.616i	−0.801273	−	0.448984i
$871$	79.7817	−	79.7817i	0.0915978	−	0.0915978i
$872$	−641.824	−	960.558i	−0.736037	−	1.10156i
$873$	1760.10	−	350.106i	2.01616	−	0.401038i
$874$	−79.4938	−	53.1160i	−0.0909540	−	0.0607735i
$875$	−1233.19	+	295.135i	−1.40936	+	0.337297i
$876$	1250.80	+	518.096i	1.42785	+	0.591434i
$877$	1052.31	+	703.134i	1.19990	+	0.801749i	0.984604	−	0.174799i	$-0.0559277\pi$
$877$	1052.31	+	703.134i	1.19990	+	0.801749i	0.215298	+	0.976548i	$0.430928\pi$
$878$	56.9473	+	286.293i	0.0648602	+	0.326074i
$879$	−346.245	−	518.193i	−0.393908	−	0.589525i
$880$	43.4887	−	22.1456i	0.0494190	−	0.0251655i
$881$	−799.621	−	159.055i	−0.907629	−	0.180539i	−0.280864	−	0.959747i	$-0.590621\pi$
$881$	−799.621	−	159.055i	−0.907629	−	0.180539i	−0.626764	+	0.779209i	$0.715621\pi$
$882$	−1111.57	+	460.428i	−1.26028	+	0.522027i
$883$	1066.87			1.20823			0.604117	−	0.796896i	$-0.293526\pi$
$883$	1066.87			1.20823			0.604117	+	0.796896i	$0.293526\pi$
$884$	192.327	+	702.565i	0.217564	+	0.794757i
$885$	−572.911	−	186.300i	−0.647357	−	0.210509i
$886$	−28.8787	+	11.9619i	−0.0325945	+	0.0135011i
$887$	−50.5491	−	10.0548i	−0.0569888	−	0.0113358i	0.166514	−	0.986039i	$-0.446749\pi$
$887$	−50.5491	−	10.0548i	−0.0569888	−	0.0113358i	−0.223502	+	0.974703i	$0.571749\pi$
$888$	434.970	+	434.970i	0.489831	+	0.489831i
$889$	485.375	−	324.317i	0.545979	−	0.364811i
$890$	1.74787	−	14.7377i	0.00196389	−	0.0165592i
$891$	−520.168	−	347.565i	−0.583803	−	0.390084i
$892$	460.289	+	190.658i	0.516019	+	0.213742i
$893$	73.2168	−	176.761i	0.0819897	−	0.197941i
$894$	43.7601	−	65.4916i	0.0489486	−	0.0732568i
$895$	−88.1328	+	743.119i	−0.0984724	+	0.830300i
$896$	−545.535	−	816.451i	−0.608856	−	0.911218i
$897$	−551.278	+	551.278i	−0.614580	+	0.614580i
$898$	154.164	−	775.036i	0.171675	−	0.863069i
$899$	−154.945	−	374.071i	−0.172353	−	0.416097i
$900$	−765.045	+	1051.94i	−0.850050	+	1.16883i
$901$	−476.167	−	613.659i	−0.528488	−	0.681086i
$902$		−	299.821i		−	0.332396i
$903$	1107.72	+	2674.28i	1.22672	+	2.96155i
$904$	132.962	−	668.444i	0.147082	−	0.739429i
$905$	−719.290	−	1412.51i	−0.794795	−	1.56079i
$906$	−162.550	+	108.613i	−0.179415	+	0.119881i
$907$	−1302.90	+	259.163i	−1.43649	+	0.285736i	−0.851095	−	0.525011i	$-0.824061\pi$
$907$	−1302.90	+	259.163i	−1.43649	+	0.285736i	−0.585397	+	0.810747i	$0.699061\pi$
$908$	17.0251	−	25.4799i	0.0187501	−	0.0280616i
$909$	443.612	−	1070.98i	0.488023	−	1.17819i
$910$	708.811	+	605.673i	0.778913	+	0.665575i
$911$	424.980	−	636.028i	0.466498	−	0.698164i	−0.521392	−	0.853317i	$-0.674587\pi$
$911$	424.980	−	636.028i	0.466498	−	0.698164i	0.987890	+	0.155153i	$0.0495871\pi$
$912$	−17.9173	−	90.0763i	−0.0196462	−	0.0987679i
$913$	−354.945	+	237.167i	−0.388768	+	0.259766i
$914$	216.012	+	216.012i	0.236336	+	0.236336i
$915$	2238.13	+	1254.11i	2.44604	+	1.37061i
$916$	−325.689	−	786.284i	−0.355556	−	0.858388i
$917$	−434.403			−0.473722
$918$	−76.8415	−	1082.69i	−0.0837053	−	1.17941i
$919$	451.321			0.491100			0.245550	−	0.969384i	$-0.421031\pi$
$919$	451.321			0.491100			0.245550	+	0.969384i	$0.421031\pi$
$920$	27.4524	+	349.878i	0.0298396	+	0.380302i
$921$	405.998	−	2041.09i	0.440823	−	2.21617i
$922$	−326.492	−	326.492i	−0.354113	−	0.354113i
$923$	365.505	+	547.016i	0.395996	+	0.592651i
$924$	−145.689	−	732.428i	−0.157672	−	0.792671i
$925$	352.622	−	129.899i	0.381213	−	0.140431i
$926$	−65.1174	+	157.207i	−0.0703212	+	0.169770i
$927$	517.105	−	1248.40i	0.557826	−	1.34671i
$928$	−713.133	−	476.500i	−0.768462	−	0.513470i
$929$	−103.986	+	20.6842i	−0.111934	+	0.0222650i	−0.250739	−	0.968055i	$-0.580674\pi$
$929$	−103.986	+	20.6842i	−0.111934	+	0.0222650i	0.138806	+	0.990320i	$0.455674\pi$
$930$	457.729	−	128.976i	0.492182	−	0.138684i
$931$	−346.759	−	346.759i	−0.372458	−	0.372458i
$932$	28.3285	−	142.417i	0.0303954	−	0.152808i
$933$	−1450.71	+	600.906i	−1.55489	+	0.644057i
$934$			307.285i			0.328999i
$935$	294.839	+	324.069i	0.315336	+	0.346598i
$936$	2384.32			2.54735
$937$	−495.956	−	1197.34i	−0.529302	−	1.27785i	−0.931981	−	0.362506i	$-0.881921\pi$
$937$	−495.956	−	1197.34i	−0.529302	−	1.27785i	0.402680	−	0.915341i	$-0.368079\pi$
$938$	−80.6682	−	16.0459i	−0.0860002	−	0.0171065i
$939$	−544.602	+	544.602i	−0.579981	+	0.579981i
$940$	−271.151	+	76.4030i	−0.288459	+	0.0812798i
$941$	109.977	+	552.893i	0.116873	+	0.587559i	0.994189	+	0.107647i	$0.0343316\pi$
$941$	109.977	+	552.893i	0.116873	+	0.587559i	−0.877316	+	0.479913i	$0.840668\pi$
$942$	−261.597	+	391.508i	−0.277704	+	0.415613i
$943$	−427.547	−	177.096i	−0.453391	−	0.187801i
$944$	−39.5404	−	16.3782i	−0.0418860	−	0.0173498i
$945$	1743.89	+	2213.19i	1.84538	+	2.34200i
$946$	310.993	−	61.8603i	0.328745	−	0.0653915i
$947$	367.438	−	245.514i	0.388002	−	0.259255i	−0.346235	−	0.938148i	$-0.612540\pi$
$947$	367.438	−	245.514i	0.388002	−	0.259255i	0.734237	+	0.678893i	$0.237540\pi$
$948$	309.796	−	309.796i	0.326789	−	0.326789i
$949$	−1486.93	−	295.770i	−1.56684	−	0.311665i
$950$	254.147	+	61.1430i	0.267524	+	0.0643611i
$951$			173.288i			0.182217i
$952$	867.448	−	999.985i	0.911185	−	1.05040i
$953$			703.523i			0.738219i	0.929386	+	0.369109i	$0.120337\pi$
$953$			703.523i			0.738219i	−0.929386	+	0.369109i	$0.879663\pi$
$954$	−942.193	+	390.269i	−0.987624	+	0.409087i
$955$	368.203	+	206.318i	0.385553	+	0.216040i
$956$	−480.040	+	480.040i	−0.502134	+	0.502134i
$957$	−398.197	−	595.943i	−0.416088	−	0.622720i
$958$	−599.469	+	119.242i	−0.625750	+	0.124469i
$959$	−1548.63	−	1034.76i	−1.61484	−	1.07900i
$960$	523.247	−	612.349i	0.545049	−	0.637864i
$961$	−665.231	−	275.548i	−0.692227	−	0.286730i
$962$	−229.739	−	153.507i	−0.238814	−	0.159571i
$963$	−636.753	−	3201.17i	−0.661218	−	3.32417i
$964$	−286.818	−	429.254i	−0.297529	−	0.445284i
$965$	393.723	+	773.179i	0.408003	+	0.801221i
$966$	557.404	+	110.875i	0.577023	+	0.114777i
$967$	204.920	−	84.8806i	0.211913	−	0.0877772i	−0.274202	−	0.961672i	$-0.588414\pi$
$967$	204.920	−	84.8806i	0.211913	−	0.0877772i	0.486115	+	0.873895i	$0.338414\pi$
$968$	724.899			0.748863
$969$	737.486	−	368.655i	0.761079	−	0.380449i
$970$	−164.215	+	504.994i	−0.169294	+	0.520613i
$971$	1314.77	−	544.597i	1.35404	−	0.560862i	0.416626	−	0.909078i	$-0.363212\pi$
$971$	1314.77	−	544.597i	1.35404	−	0.560862i	0.937414	+	0.348216i	$0.113212\pi$
$972$	386.449	+	76.8694i	0.397581	+	0.0790838i
$973$	−455.468	−	455.468i	−0.468107	−	0.468107i
$974$	−208.206	+	139.119i	−0.213764	+	0.142832i
$975$	893.328	−	1935.36i	0.916234	−	1.98499i
$976$	151.543	+	101.258i	0.155270	+	0.103748i
$977$	510.829	+	211.592i	0.522854	+	0.216573i	0.628470	−	0.777834i	$-0.283681\pi$
$977$	510.829	+	211.592i	0.522854	+	0.216573i	−0.105616	+	0.994407i	$0.533681\pi$
$978$	659.281	−	1591.65i	0.674111	−	1.62745i
$979$	7.39547	−	11.0681i	0.00755411	−	0.0113055i
$980$	−85.0391	+	717.034i	−0.0867746	+	0.731667i
$981$	1623.76	+	2430.12i	1.65521	+	2.47719i
$982$	543.583	−	543.583i	0.553547	−	0.553547i
$983$	−359.444	+	1807.04i	−0.365660	+	1.83830i	0.159379	+	0.987217i	$0.449051\pi$
$983$	−359.444	+	1807.04i	−0.365660	+	1.83830i	−0.525039	+	0.851078i	$0.675949\pi$
$984$	792.607	+	1913.52i	0.805495	+	1.94464i
$985$	337.536	−	1037.99i	0.342676	−	1.05380i
$986$	161.206	−	483.464i	0.163495	−	0.490328i
$987$			1137.31i			1.15229i
$988$	149.174	+	360.137i	0.150985	+	0.364511i
$989$	95.4814	−	480.017i	0.0965434	−	0.485356i
$990$	512.603	−	261.031i	0.517781	−	0.263668i
$991$	3.14142	−	2.09903i	0.00316995	−	0.00211809i	−0.553984	−	0.832527i	$-0.686893\pi$
$991$	3.14142	−	2.09903i	0.00316995	−	0.00211809i	0.557154	+	0.830409i	$0.311893\pi$
$992$	500.614	−	99.5784i	0.504651	−	0.100381i
$993$	−288.737	+	432.126i	−0.290772	+	0.435172i
$994$	183.529	−	443.077i	0.184636	−	0.445752i
$995$	1175.78	−	1376.00i	1.18169	−	1.38292i
$996$	657.169	−	983.523i	0.659808	−	0.987473i
$997$	−145.756	−	732.766i	−0.146195	−	0.734971i	−0.982435	−	0.186607i	$-0.940251\pi$
$997$	−145.756	−	732.766i	−0.146195	−	0.734971i	0.836240	−	0.548364i	$-0.184749\pi$
$998$	227.524	−	152.027i	0.227980	−	0.152332i
$999$	−590.464	−	590.464i	−0.591055	−	0.591055i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	85.3.p.a.14.6	✓	128
5.2	odd	4		425.3.u.f.201.11		128
5.3	odd	4		425.3.u.f.201.6		128
5.4	even	2	inner	85.3.p.a.14.11	yes	128
17.11	odd	16	inner	85.3.p.a.79.11	yes	128
85.28	even	16		425.3.u.f.351.6		128
85.62	even	16		425.3.u.f.351.11		128
85.79	odd	16	inner	85.3.p.a.79.6	yes	128

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
85.3.p.a.14.6	✓	128	1.1	even	1	trivial
85.3.p.a.14.11	yes	128	5.4	even	2	inner
85.3.p.a.79.6	yes	128	85.79	odd	16	inner
85.3.p.a.79.11	yes	128	17.11	odd	16	inner
425.3.u.f.201.6		128	5.3	odd	4
425.3.u.f.201.11		128	5.2	odd	4
425.3.u.f.351.6		128	85.28	even	16
425.3.u.f.351.11		128	85.62	even	16

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:	\( N \)	\(=\)	\( 85 = 5 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	85.p (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.439826 - 1.06183i) q^{2} +(5.22866 + 1.04004i) q^{3} +(1.89438 - 1.89438i) q^{4} +(-1.35606 - 4.81260i) q^{5} +(-1.19534 - 6.00940i) q^{6} +(-5.63579 + 8.43455i) q^{7} +(-7.09205 - 2.93762i) q^{8} +(17.9423 + 7.43192i) q^{9} +(-4.51375 + 3.55661i) q^{10} +(-5.05533 + 1.00557i) q^{11} +(11.8753 - 7.93484i) q^{12} +(-11.3092 + 11.3092i) q^{13} +(11.4349 + 2.27453i) q^{14} +(-2.08505 - 26.5738i) q^{15} -1.89364i q^{16} +(16.3967 - 4.48859i) q^{17} -22.3204i q^{18} +(8.40501 - 3.48147i) q^{19} +(-11.6858 - 6.54801i) q^{20} +(-38.2399 + 38.2399i) q^{21} +(3.29121 + 4.92564i) q^{22} +(8.96803 - 1.78385i) q^{23} +(-34.0266 - 22.7359i) q^{24} +(-21.3222 + 13.0523i) q^{25} +(16.9825 + 7.03440i) q^{26} +(46.1906 + 30.8636i) q^{27} +(5.30194 + 26.6546i) q^{28} +(14.4912 + 21.6877i) q^{29} +(-27.2999 + 13.9018i) q^{30} +(-15.2246 - 3.02836i) q^{31} +(-30.3789 + 12.5834i) q^{32} -27.4784 q^{33} +(-11.9778 - 15.4364i) q^{34} +(48.2346 + 15.6850i) q^{35} +(48.0684 - 19.9106i) q^{36} +(-14.7427 - 2.93250i) q^{37} +(-7.39348 - 7.39348i) q^{38} +(-70.8939 + 47.3698i) q^{39} +(-4.52036 + 38.1148i) q^{40} +(-42.0816 - 28.1180i) q^{41} +(57.4233 + 23.7855i) q^{42} +(20.4833 - 49.4510i) q^{43} +(-7.67181 + 11.4817i) q^{44} +(11.4361 - 96.4270i) q^{45} +(-5.83852 - 8.73797i) q^{46} +(14.8708 - 14.8708i) q^{47} +(1.96947 - 9.90120i) q^{48} +(-20.6281 - 49.8006i) q^{49} +(23.2375 + 16.8999i) q^{50} +(90.4012 - 6.41600i) q^{51} +42.8479i q^{52} +(-17.4848 - 42.2121i) q^{53} +(12.4561 - 62.6213i) q^{54} +(11.6947 + 22.9657i) q^{55} +(64.7468 - 43.2625i) q^{56} +(47.5678 - 9.46182i) q^{57} +(16.6551 - 24.9261i) q^{58} +(8.64904 - 20.8806i) q^{59} +(-54.2909 - 46.3911i) q^{60} +(-53.4727 + 80.0276i) q^{61} +(3.48056 + 17.4979i) q^{62} +(-163.804 + 109.450i) q^{63} +(21.3668 + 21.3668i) q^{64} +(69.7625 + 39.0906i) q^{65} +(12.0857 + 29.1775i) q^{66} -7.05459 q^{67} +(22.5586 - 39.5648i) q^{68} +48.7460 q^{69} +(-4.55993 - 58.1157i) q^{70} +(8.02497 - 40.3442i) q^{71} +(-105.415 - 105.415i) q^{72} +(52.6636 + 78.8166i) q^{73} +(3.37038 + 16.9440i) q^{74} +(-125.062 + 46.0702i) q^{75} +(9.32708 - 22.5176i) q^{76} +(20.0093 - 48.3066i) q^{77} +(81.4798 + 54.4431i) q^{78} +(30.0861 - 5.98450i) q^{79} +(-9.11333 + 2.56789i) q^{80} +(85.8236 + 85.8236i) q^{81} +(-11.3481 + 57.0506i) q^{82} +(76.5163 - 31.6941i) q^{83} +144.882i q^{84} +(-43.8367 - 72.8240i) q^{85} -61.5178 q^{86} +(53.2136 + 128.469i) q^{87} +(38.8066 + 7.71912i) q^{88} +(-1.82615 + 1.82615i) q^{89} +(-107.419 + 30.2678i) q^{90} +(-31.6518 - 159.124i) q^{91} +(13.6096 - 20.3682i) q^{92} +(-76.4546 - 31.6685i) q^{93} +(-22.3308 - 9.24973i) q^{94} +(-28.1526 - 35.7288i) q^{95} +(-171.928 + 34.1987i) q^{96} +(76.8332 - 51.3383i) q^{97} +(-43.8072 + 43.8072i) q^{98} +(-98.1773 - 19.5287i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 128 q - 16 q^{4} - 8 q^{5} - 16 q^{6} - 16 q^{9} + 16 q^{10} - 96 q^{11} - 16 q^{14} + 16 q^{15} - 16 q^{19} - 120 q^{20} + 224 q^{21} - 160 q^{24} - 240 q^{25} + 288 q^{26} - 176 q^{29} - 200 q^{30} + 48 q^{31}+ \cdots - 1664 q^{99}+O(q^{100}) \) 128 * q - 16 * q^4 - 8 * q^5 - 16 * q^6 - 16 * q^9 + 16 * q^10 - 96 * q^11 - 16 * q^14 + 16 * q^15 - 16 * q^19 - 120 * q^20 + 224 * q^21 - 160 * q^24 - 240 * q^25 + 288 * q^26 - 176 * q^29 - 200 * q^30 + 48 * q^31 + 48 * q^34 + 48 * q^35 - 144 * q^36 + 440 * q^40 - 336 * q^41 - 48 * q^44 + 232 * q^45 - 224 * q^46 - 48 * q^49 - 16 * q^51 + 512 * q^54 - 392 * q^55 - 16 * q^56 + 272 * q^59 - 736 * q^60 - 16 * q^61 + 688 * q^64 - 128 * q^65 - 80 * q^66 + 448 * q^69 + 736 * q^70 + 192 * q^71 + 704 * q^74 + 1048 * q^75 + 496 * q^76 + 304 * q^79 + 1240 * q^80 + 128 * q^81 + 672 * q^85 - 2496 * q^86 - 256 * q^89 + 1104 * q^90 - 1632 * q^91 - 1296 * q^94 + 120 * q^95 - 1728 * q^96 - 1664 * q^99

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