LMFDB - Embedded newform 117.3.w.a.58.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [117,3,Mod(58,117)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(117, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([4, 5]))

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

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

chi := DirichletCharacter("117.58");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 117 = 3^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	117.w (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$3.18801909302$
Analytic rank:	$0$
Dimension:	$104$
Relative dimension:	$26$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			58.3
Character	$\chi$	$=$	117.58
Dual form			117.3.w.a.115.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.46426 + 2.46426i) q^{2} +(-1.28173 - 2.71241i) q^{3} -8.14515i q^{4} +(2.29040 + 8.54788i) q^{5} +(9.84260 + 3.52555i) q^{6} +(1.69578 - 0.454383i) q^{7} +(10.2147 + 10.2147i) q^{8} +(-5.71431 + 6.95317i) q^{9} +(-26.7083 - 15.4201i) q^{10} +(-10.0417 - 10.0417i) q^{11} +(-22.0930 + 10.4399i) q^{12} +(-11.4469 + 6.16186i) q^{13} +(-3.05913 + 5.29856i) q^{14} +(20.2497 - 17.1686i) q^{15} -17.7628 q^{16} +(-7.58364 + 4.37842i) q^{17} +(-3.05287 - 31.2160i) q^{18} +(-12.9554 - 3.47139i) q^{19} +(69.6237 - 18.6556i) q^{20} +(-3.40601 - 4.01725i) q^{21} +49.4907 q^{22} +(-14.5688 + 8.41131i) q^{23} +(14.6139 - 40.7990i) q^{24} +(-46.1697 + 26.6561i) q^{25} +(13.0237 - 43.3925i) q^{26} +(26.1841 + 6.58743i) q^{27} +(-3.70102 - 13.8124i) q^{28} -41.1149 q^{29} +(-7.59251 + 92.2083i) q^{30} +(-1.69440 - 6.32358i) q^{31} +(2.91334 - 2.91334i) q^{32} +(-14.3664 + 40.1079i) q^{33} +(7.89851 - 29.4776i) q^{34} +(7.76803 + 13.4546i) q^{35} +(56.6346 + 46.5439i) q^{36} +(35.5862 - 9.53529i) q^{37} +(40.4799 - 23.3711i) q^{38} +(31.3854 + 23.1508i) q^{39} +(-63.9184 + 110.710i) q^{40} +(52.2324 + 13.9956i) q^{41} +(18.2929 + 1.50625i) q^{42} +(-11.7721 - 6.79663i) q^{43} +(-81.7910 + 81.7910i) q^{44} +(-72.5229 - 32.9197i) q^{45} +(15.1737 - 56.6290i) q^{46} +(-11.5892 + 43.2515i) q^{47} +(22.7672 + 48.1800i) q^{48} +(-39.7660 + 22.9589i) q^{49} +(48.0866 - 179.462i) q^{50} +(21.5963 + 14.9580i) q^{51} +(50.1893 + 93.2367i) q^{52} +38.3056 q^{53} +(-80.7575 + 48.2912i) q^{54} +(62.8357 - 108.835i) q^{55} +(21.9633 + 12.6805i) q^{56} +(7.18956 + 39.5897i) q^{57} +(101.318 - 101.318i) q^{58} +(7.55881 + 7.55881i) q^{59} +(-139.841 - 164.936i) q^{60} +(17.1976 - 29.7871i) q^{61} +(19.7584 + 11.4075i) q^{62} +(-6.53082 + 14.3876i) q^{63} -56.6928i q^{64} +(-78.8888 - 83.7336i) q^{65} +(-63.4339 - 134.239i) q^{66} +(83.3381 + 22.3304i) q^{67} +(35.6629 + 61.7699i) q^{68} +(41.4883 + 28.7355i) q^{69} +(-52.2981 - 14.0132i) q^{70} +(-108.463 - 29.0626i) q^{71} +(-129.395 + 12.6546i) q^{72} +(60.2281 + 60.2281i) q^{73} +(-64.1962 + 111.191i) q^{74} +(131.479 + 91.0650i) q^{75} +(-28.2750 + 105.524i) q^{76} +(-21.5913 - 12.4657i) q^{77} +(-134.391 + 20.2921i) q^{78} +(3.19706 + 5.53747i) q^{79} +(-40.6839 - 151.834i) q^{80} +(-15.6932 - 79.4652i) q^{81} +(-163.203 + 94.2252i) q^{82} +(13.8346 + 3.70698i) q^{83} +(-32.7211 + 27.7425i) q^{84} +(-54.7958 - 54.7958i) q^{85} +(45.7582 - 12.2609i) q^{86} +(52.6983 + 111.520i) q^{87} -205.146i q^{88} +(-30.6602 + 8.21537i) q^{89} +(259.838 - 97.5925i) q^{90} +(-16.6116 + 15.6505i) q^{91} +(68.5113 + 118.665i) q^{92} +(-14.9804 + 12.7010i) q^{93} +(-78.0242 - 135.142i) q^{94} -118.692i q^{95} +(-11.6363 - 4.16804i) q^{96} +(48.7891 + 182.084i) q^{97} +(41.4171 - 154.571i) q^{98} +(127.203 - 12.4402i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 104 q - 2 q^{2} - 2 q^{3} - 2 q^{5} - 32 q^{6} + 18 q^{8} - 2 q^{9} - 12 q^{10} + 22 q^{11} + 54 q^{12} - 2 q^{13} - 4 q^{14} + 70 q^{15} - 324 q^{16} - 12 q^{17} - 86 q^{18} - 36 q^{19} + 134 q^{20} - 32 q^{21}+ \cdots + 940 q^{99}+O(q^{100}) $ 104 * q - 2 * q^2 - 2 * q^3 - 2 * q^5 - 32 * q^6 + 18 * q^8 - 2 * q^9 - 12 * q^10 + 22 * q^11 + 54 * q^12 - 2 * q^13 - 4 * q^14 + 70 * q^15 - 324 * q^16 - 12 * q^17 - 86 * q^18 - 36 * q^19 + 134 * q^20 - 32 * q^21 - 4 * q^22 - 6 * q^23 + 30 * q^24 + 52 * q^26 + 4 * q^27 + 56 * q^28 - 148 * q^29 - 246 * q^30 + 62 * q^31 + 70 * q^32 + 52 * q^33 - 18 * q^34 - 106 * q^35 + 96 * q^36 + 14 * q^37 + 216 * q^38 + 118 * q^39 - 36 * q^40 - 26 * q^41 + 278 * q^42 - 198 * q^43 + 496 * q^44 - 80 * q^45 - 8 * q^47 + 58 * q^48 - 6 * q^49 - 292 * q^50 + 28 * q^52 - 208 * q^53 + 58 * q^54 - 4 * q^55 + 186 * q^56 - 140 * q^57 + 146 * q^58 - 434 * q^59 + 140 * q^60 + 2 * q^61 - 282 * q^62 - 266 * q^63 - 260 * q^65 - 412 * q^66 + 138 * q^67 + 534 * q^68 - 294 * q^69 + 212 * q^70 - 8 * q^71 - 306 * q^72 + 90 * q^73 - 178 * q^74 - 60 * q^75 - 98 * q^76 - 432 * q^77 + 352 * q^78 - 16 * q^79 - 278 * q^80 - 230 * q^81 - 12 * q^82 - 50 * q^83 + 1066 * q^84 + 204 * q^85 + 330 * q^86 - 154 * q^87 + 400 * q^89 - 798 * q^90 + 120 * q^91 + 48 * q^92 - 128 * q^93 + 122 * q^94 + 958 * q^96 - 232 * q^97 + 280 * q^98 + 940 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/117\mathbb{Z}\right)^\times$.

$n$	$28$	$92$
$\chi(n)$	$e\left(\frac{5}{12}\right)$	$e\left(\frac{1}{3}\right)$

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 $

$2$	−2.46426	+	2.46426i	−1.23213	+	1.23213i	−0.268985	+	0.963144i	$0.586688\pi$
$2$	−2.46426	+	2.46426i	−1.23213	+	1.23213i	−0.963144	+	0.268985i	$0.913312\pi$
$3$	−1.28173	−	2.71241i	−0.427245	−	0.904136i
$3$	−1.28173	−	2.71241i	−0.427245	−	0.904136i
$4$		−	8.14515i		−	2.03629i
$5$	2.29040	+	8.54788i	0.458079	+	1.70958i	0.678873	+	0.734255i	$0.262469\pi$
$5$	2.29040	+	8.54788i	0.458079	+	1.70958i	−0.220794	+	0.975321i	$0.570865\pi$
$6$	9.84260	+	3.52555i	1.64043	+	0.587592i
$7$	1.69578	−	0.454383i	0.242255	−	0.0649119i	−0.135649	−	0.990757i	$-0.543312\pi$
$7$	1.69578	−	0.454383i	0.242255	−	0.0649119i	0.377903	+	0.925845i	$0.376645\pi$
$8$	10.2147	+	10.2147i	1.27684	+	1.27684i
$9$	−5.71431	+	6.95317i	−0.634924	+	0.772575i
$10$	−26.7083	−	15.4201i	−2.67083	−	1.54201i
$11$	−10.0417	−	10.0417i	−0.912881	−	0.912881i	0.0836170	−	0.996498i	$-0.473353\pi$
$11$	−10.0417	−	10.0417i	−0.912881	−	0.912881i	−0.996498	+	0.0836170i	$0.973353\pi$
$12$	−22.0930	+	10.4399i	−1.84108	+	0.869993i
$13$	−11.4469	+	6.16186i	−0.880531	+	0.473989i
$13$	−11.4469	+	6.16186i	−0.880531	+	0.473989i
$14$	−3.05913	+	5.29856i	−0.218509	+	0.378469i
$15$	20.2497	−	17.1686i	1.34998	−	1.14457i
$16$	−17.7628			−1.11018
$17$	−7.58364	+	4.37842i	−0.446097	+	0.257554i	−0.706180	−	0.708032i	$-0.749583\pi$
$17$	−7.58364	+	4.37842i	−0.446097	+	0.257554i	0.260084	+	0.965586i	$0.416250\pi$
$18$	−3.05287	−	31.2160i	−0.169604	−	1.73422i
$19$	−12.9554	−	3.47139i	−0.681863	−	0.182705i	−0.0987703	−	0.995110i	$-0.531491\pi$
$19$	−12.9554	−	3.47139i	−0.681863	−	0.182705i	−0.583093	+	0.812406i	$0.698158\pi$
$20$	69.6237	−	18.6556i	3.48119	−	0.932781i
$21$	−3.40601	−	4.01725i	−0.162191	−	0.191298i
$22$	49.4907			2.24958
$23$	−14.5688	+	8.41131i	−0.633427	+	0.365709i	−0.782078	−	0.623181i	$-0.785840\pi$
$23$	−14.5688	+	8.41131i	−0.633427	+	0.365709i	0.148651	+	0.988890i	$0.452507\pi$
$24$	14.6139	−	40.7990i	0.608913	−	1.69996i
$25$	−46.1697	+	26.6561i	−1.84679	+	1.06624i
$26$	13.0237	−	43.3925i	0.500912	−	1.66894i
$27$	26.1841	+	6.58743i	0.969781	+	0.243979i
$28$	−3.70102	−	13.8124i	−0.132179	−	0.493300i
$29$	−41.1149			−1.41775			−0.708877	−	0.705332i	$-0.750798\pi$
$29$	−41.1149			−1.41775			−0.708877	+	0.705332i	$0.750798\pi$
$30$	−7.59251	+	92.2083i	−0.253084	+	3.07361i
$31$	−1.69440	−	6.32358i	−0.0546580	−	0.203986i	0.933197	−	0.359365i	$-0.117007\pi$
$31$	−1.69440	−	6.32358i	−0.0546580	−	0.203986i	−0.987855	+	0.155379i	$0.950340\pi$
$32$	2.91334	−	2.91334i	0.0910420	−	0.0910420i
$33$	−14.3664	+	40.1079i	−0.435345	+	1.21539i
$34$	7.89851	−	29.4776i	0.232309	−	0.866989i
$35$	7.76803	+	13.4546i	0.221944	+	0.384418i
$36$	56.6346	+	46.5439i	1.57318	+	1.29289i
$37$	35.5862	−	9.53529i	0.961789	−	0.257711i	0.256432	−	0.966562i	$-0.417453\pi$
$37$	35.5862	−	9.53529i	0.961789	−	0.257711i	0.705357	+	0.708852i	$0.250787\pi$
$38$	40.4799	−	23.3711i	1.06526	−	0.615028i
$39$	31.3854	+	23.1508i	0.804753	+	0.593610i
$40$	−63.9184	+	110.710i	−1.59796	+	2.76775i
$41$	52.2324	+	13.9956i	1.27396	+	0.341356i	0.831547	−	0.555455i	$-0.187456\pi$
$41$	52.2324	+	13.9956i	1.27396	+	0.341356i	0.442413	+	0.896811i	$0.354123\pi$
$42$	18.2929	+	1.50625i	0.435544	+	0.0358631i
$43$	−11.7721	−	6.79663i	−0.273770	−	0.158061i	0.356830	−	0.934169i	$-0.383858\pi$
$43$	−11.7721	−	6.79663i	−0.273770	−	0.158061i	−0.630600	+	0.776108i	$0.717191\pi$
$44$	−81.7910	+	81.7910i	−1.85889	+	1.85889i
$45$	−72.5229	−	32.9197i	−1.61162	−	0.731550i
$46$	15.1737	−	56.6290i	0.329863	−	1.23106i
$47$	−11.5892	+	43.2515i	−0.246579	+	0.920246i	0.726004	+	0.687690i	$0.241375\pi$
$47$	−11.5892	+	43.2515i	−0.246579	+	0.920246i	−0.972583	+	0.232555i	$0.925291\pi$
$48$	22.7672	+	48.1800i	0.474317	+	1.00375i
$49$	−39.7660	+	22.9589i	−0.811552	+	0.468550i
$50$	48.0866	−	179.462i	0.961732	−	3.58923i
$51$	21.5963	+	14.9580i	0.423456	+	0.293293i
$52$	50.1893	+	93.2367i	0.965178	+	1.79301i
$53$	38.3056			0.722747			0.361373	−	0.932421i	$-0.382308\pi$
$53$	38.3056			0.722747			0.361373	+	0.932421i	$0.382308\pi$
$54$	−80.7575	+	48.2912i	−1.49551	+	0.894282i
$55$	62.8357	−	108.835i	1.14247	−	1.97881i
$56$	21.9633	+	12.6805i	0.392202	+	0.226438i
$57$	7.18956	+	39.5897i	0.126133	+	0.694557i
$58$	101.318	−	101.318i	1.74686	−	1.74686i
$59$	7.55881	+	7.55881i	0.128115	+	0.128115i	0.768257	−	0.640142i	$-0.221124\pi$
$59$	7.55881	+	7.55881i	0.128115	+	0.128115i	−0.640142	+	0.768257i	$0.721124\pi$
$60$	−139.841	−	164.936i	−2.33068	−	2.74894i
$61$	17.1976	−	29.7871i	0.281928	−	0.488314i	−0.689932	−	0.723875i	$-0.742359\pi$
$61$	17.1976	−	29.7871i	0.281928	−	0.488314i	0.971860	+	0.235561i	$0.0756927\pi$
$62$	19.7584	+	11.4075i	0.318683	+	0.183992i
$63$	−6.53082	+	14.3876i	−0.103664	+	0.228374i
$64$		−	56.6928i		−	0.885826i
$65$	−78.8888	−	83.7336i	−1.21367	−	1.28821i
$66$	−63.4339	−	134.239i	−0.961119	−	2.03392i
$67$	83.3381	+	22.3304i	1.24385	+	0.333289i	0.819959	−	0.572423i	$-0.193996\pi$
$67$	83.3381	+	22.3304i	1.24385	+	0.333289i	0.423894	+	0.905712i	$0.360663\pi$
$68$	35.6629	+	61.7699i	0.524454	+	0.908381i
$69$	41.4883	+	28.7355i	0.601279	+	0.416457i
$70$	−52.2981	−	14.0132i	−0.747116	−	0.200189i
$71$	−108.463	−	29.0626i	−1.52765	−	0.409332i	−0.605397	−	0.795924i	$-0.706986\pi$
$71$	−108.463	−	29.0626i	−1.52765	−	0.409332i	−0.922251	+	0.386591i	$0.873652\pi$
$72$	−129.395	+	12.6546i	−1.79715	+	0.175758i
$73$	60.2281	+	60.2281i	0.825042	+	0.825042i	0.986826	−	0.161784i	$-0.0517248\pi$
$73$	60.2281	+	60.2281i	0.825042	+	0.825042i	−0.161784	+	0.986826i	$0.551725\pi$
$74$	−64.1962	+	111.191i	−0.867516	+	1.50258i
$75$	131.479	+	91.0650i	1.75306	+	1.21420i
$76$	−28.2750	+	105.524i	−0.372039	+	1.38847i
$77$	−21.5913	−	12.4657i	−0.280406	−	0.161893i
$78$	−134.391	+	20.2921i	−1.72296	+	0.260155i
$79$	3.19706	+	5.53747i	0.0404691	+	0.0700945i	0.885550	−	0.464543i	$-0.153781\pi$
$79$	3.19706	+	5.53747i	0.0404691	+	0.0700945i	−0.845081	+	0.534638i	$0.820448\pi$
$80$	−40.6839	−	151.834i	−0.508549	−	1.89793i
$81$	−15.6932	−	79.4652i	−0.193744	−	0.981052i
$82$	−163.203	+	94.2252i	−1.99028	+	1.14909i
$83$	13.8346	+	3.70698i	0.166682	+	0.0446624i	0.341195	−	0.939993i	$-0.389168\pi$
$83$	13.8346	+	3.70698i	0.166682	+	0.0446624i	−0.174513	+	0.984655i	$0.555835\pi$
$84$	−32.7211	+	27.7425i	−0.389537	+	0.330268i
$85$	−54.7958	−	54.7958i	−0.644656	−	0.644656i
$86$	45.7582	−	12.2609i	0.532072	−	0.142568i
$87$	52.6983	+	111.520i	0.605728	+	1.28184i
$88$		−	205.146i		−	2.33120i
$89$	−30.6602	+	8.21537i	−0.344496	+	0.0923075i	−0.426919	−	0.904290i	$-0.640401\pi$
$89$	−30.6602	+	8.21537i	−0.344496	+	0.0923075i	0.0824224	+	0.996597i	$0.473734\pi$
$90$	259.838	−	97.5925i	2.88709	−	1.08436i
$91$	−16.6116	+	15.6505i	−0.182545	+	0.171983i
$92$	68.5113	+	118.665i	0.744689	+	1.28984i
$93$	−14.9804	+	12.7010i	−0.161079	+	0.136570i
$94$	−78.0242	−	135.142i	−0.830044	−	1.43768i
$95$		−	118.692i		−	1.24939i
$96$	−11.6363	−	4.16804i	−0.121212	−	0.0434171i
$97$	48.7891	+	182.084i	0.502981	+	1.87715i	0.479722	+	0.877421i	$0.340738\pi$
$97$	48.7891	+	182.084i	0.502981	+	1.87715i	0.0232589	+	0.999729i	$0.492596\pi$
$98$	41.4171	−	154.571i	0.422623	−	1.57725i
$99$	127.203	−	12.4402i	1.28488	−	0.125659i
$100$	217.118	+	376.059i	2.17118	+	3.76059i
$101$		−	90.0839i		−	0.891919i	−0.895053	−	0.445960i	$-0.852862\pi$
$101$		−	90.0839i		−	0.891919i	0.895053	−	0.445960i	$-0.147138\pi$
$102$	−90.0791	+	16.3585i	−0.883129	+	0.160378i
$103$	8.07065	+	4.65959i	0.0783559	+	0.0452388i	0.538666	−	0.842519i	$-0.318928\pi$
$103$	8.07065	+	4.65959i	0.0783559	+	0.0452388i	−0.460310	+	0.887758i	$0.652262\pi$
$104$	−179.868	−	53.9852i	−1.72950	−	0.519088i
$105$	26.5379	−	38.3153i	0.252742	−	0.364908i
$106$	−94.3948	+	94.3948i	−0.890517	+	0.890517i
$107$	−34.8068	+	60.2872i	−0.325298	+	0.563432i	−0.981573	−	0.191090i	$-0.938798\pi$
$107$	−34.8068	+	60.2872i	−0.325298	+	0.563432i	0.656275	+	0.754522i	$0.272131\pi$
$108$	53.6556	−	213.273i	0.496811	−	1.97475i
$109$	8.55814	−	8.55814i	0.0785150	−	0.0785150i	−0.666759	−	0.745274i	$-0.732319\pi$
$109$	8.55814	−	8.55814i	0.0785150	−	0.0785150i	0.745274	+	0.666759i	$0.232319\pi$
$110$	113.353	+	423.040i	1.03048	+	3.84582i
$111$	−71.4756	−	84.3026i	−0.643925	−	0.759482i
$112$	−30.1219	+	8.07113i	−0.268945	+	0.0720637i
$113$	−65.4283			−0.579012			−0.289506	−	0.957176i	$-0.593491\pi$
$113$	−65.4283			−0.579012			−0.289506	+	0.957176i	$0.593491\pi$
$114$	−115.276	−	79.8424i	−1.01120	−	0.700372i
$115$	−105.267	−	105.267i	−0.915367	−	0.915367i
$116$			334.887i			2.88695i
$117$	22.5667	−	114.803i	0.192878	−	0.981223i
$118$	−37.2538			−0.315710
$119$	−10.8707	+	10.8707i	−0.0913506	+	0.0913506i
$120$	382.217	+	31.4721i	3.18514	+	0.262267i
$121$			80.6711i			0.666703i
$122$	31.0238	+	115.783i	0.254294	+	0.949038i
$123$	−28.9862	−	159.614i	−0.235660	−	1.29768i
$124$	−51.5065	+	13.8011i	−0.415375	+	0.111299i
$125$	−177.163	−	177.163i	−1.41730	−	1.41730i
$126$	−19.3610	−	51.5483i	−0.153659	−	0.409114i
$127$	−136.317	−	78.7026i	−1.07336	−	0.619705i	−0.144263	−	0.989539i	$-0.546081\pi$
$127$	−136.317	−	78.7026i	−1.07336	−	0.619705i	−0.929098	+	0.369834i	$0.879415\pi$
$128$	151.359	+	151.359i	1.18249	+	1.18249i
$129$	−3.34652	+	40.6422i	−0.0259420	+	0.315056i
$130$	400.744	+	11.9389i	3.08264	+	0.0918375i
$131$	−23.9115	+	41.4159i	−0.182530	+	0.316152i	−0.942742	−	0.333524i	$-0.891762\pi$
$131$	−23.9115	+	41.4159i	−0.182530	+	0.316152i	0.760211	+	0.649676i	$0.225095\pi$
$132$	326.685	+	117.016i	2.47489	+	0.886487i
$133$	−23.5469			−0.177044
$134$	−260.395	+	150.339i	−1.94324	+	1.12193i
$135$	3.66338	+	238.906i	0.0271361	+	1.76968i
$136$	−122.189	−	32.7405i	−0.898449	−	0.240739i
$137$	184.582	−	49.4587i	1.34732	−	0.361012i	0.488172	−	0.872747i	$-0.337664\pi$
$137$	184.582	−	49.4587i	1.34732	−	0.361012i	0.859143	+	0.511735i	$0.170997\pi$
$138$	−173.050	+	31.4261i	−1.25398	+	0.227725i
$139$	42.9568			0.309042			0.154521	−	0.987990i	$-0.450617\pi$
$139$	42.9568			0.309042			0.154521	+	0.987990i	$0.450617\pi$
$140$	109.590	−	63.2717i	0.782785	−	0.451941i
$141$	132.170	−	24.0023i	0.937377	−	0.170229i
$142$	338.899	−	195.663i	2.38661	−	1.37791i
$143$	176.822	+	53.0707i	1.23652	+	0.371124i
$144$	101.502	−	123.508i	0.704877	−	0.857694i
$145$	−94.1694	−	351.445i	−0.649444	−	2.42376i
$146$	−296.835			−2.03312
$147$	113.243	+	78.4345i	0.770364	+	0.533568i
$148$	−77.6663	−	289.855i	−0.524773	−	1.95848i
$149$	−34.0558	+	34.0558i	−0.228562	+	0.228562i	−0.812092	−	0.583530i	$-0.801671\pi$
$149$	−34.0558	+	34.0558i	−0.228562	+	0.228562i	0.583530	+	0.812092i	$0.301671\pi$
$150$	−548.407	+	99.5916i	−3.65605	+	0.663944i
$151$	−34.3503	+	128.197i	−0.227485	+	0.848987i	0.753908	+	0.656980i	$0.228166\pi$
$151$	−34.3503	+	128.197i	−0.227485	+	0.848987i	−0.981394	+	0.192007i	$0.938500\pi$
$152$	−96.8765	−	167.795i	−0.637345	−	1.10391i
$153$	12.8914	−	77.7501i	0.0842576	−	0.508170i
$154$	83.9254	−	22.4877i	0.544970	−	0.146024i
$155$	50.1724	−	28.9670i	0.323693	−	0.186884i
$156$	188.567	−	255.638i	1.20876	−	1.63871i
$157$	−40.4006	+	69.9759i	−0.257329	+	0.445707i	−0.965525	−	0.260309i	$-0.916176\pi$
$157$	−40.4006	+	69.9759i	−0.257329	+	0.445707i	0.708197	+	0.706015i	$0.249509\pi$
$158$	−21.5241	−	5.76738i	−0.136229	−	0.0365024i
$159$	−49.0976	−	103.900i	−0.308790	−	0.653461i
$160$	31.5756	+	18.2302i	0.197348	+	0.113939i
$161$	−20.8836	+	20.8836i	−0.129712	+	0.129712i
$162$	234.495	+	157.151i	1.44750	+	0.970066i
$163$	−72.3197	+	269.901i	−0.443679	+	1.65583i	0.275722	+	0.961237i	$0.411083\pi$
$163$	−72.3197	+	269.901i	−0.443679	+	1.65583i	−0.719401	+	0.694595i	$0.755584\pi$
$164$	113.996	−	425.440i	0.695100	−	2.59415i
$165$	−375.743	−	30.9390i	−2.27723	−	0.187509i
$166$	−43.2270	+	24.9571i	−0.260404	+	0.150344i
$167$	−11.8841	+	44.3521i	−0.0711623	+	0.265581i	−0.992336	−	0.123571i	$-0.960565\pi$
$167$	−11.8841	+	44.3521i	−0.0711623	+	0.265581i	0.921173	+	0.389152i	$0.127232\pi$
$168$	6.24363	−	75.8266i	0.0371644	−	0.451349i
$169$	93.0630	−	141.068i	0.550668	−	0.834724i
$170$	270.062			1.58860
$171$	98.1684	−	70.2445i	0.574084	−	0.410787i
$172$	−55.3596	+	95.8856i	−0.321858	+	0.557474i
$173$	−35.6702	−	20.5942i	−0.206186	−	0.119041i	0.393352	−	0.919388i	$-0.371315\pi$
$173$	−35.6702	−	20.5942i	−0.206186	−	0.119041i	−0.599538	+	0.800347i	$0.704649\pi$
$174$	−404.677	−	144.953i	−2.32573	−	0.833060i
$175$	−66.1816	+	66.1816i	−0.378181	+	0.378181i
$176$	178.369	+	178.369i	1.01346	+	1.01346i
$177$	10.8142	−	30.1910i	0.0610971	−	0.170570i
$178$	55.3098	−	95.7994i	0.310729	−	0.538199i
$179$	261.123	+	150.760i	1.45879	+	0.842233i	0.998952	−	0.0457701i	$-0.0145742\pi$
$179$	261.123	+	150.760i	1.45879	+	0.842233i	0.459838	+	0.888003i	$0.347907\pi$
$180$	−268.136	+	590.710i	−1.48964	+	3.28172i
$181$			98.1005i			0.541992i	0.962580	+	0.270996i	$0.0873530\pi$
$181$			98.1005i			0.541992i	−0.962580	+	0.270996i	$0.912647\pi$
$182$	2.36851	−	79.5020i	0.0130138	−	0.436824i
$183$	−102.838	−	8.46774i	−0.561954	−	0.0462718i
$184$	−234.735	−	62.8972i	−1.27574	−	0.341832i
$185$	163.013	+	282.347i	0.881152	+	1.52620i
$186$	5.61681	−	68.2142i	0.0301979	−	0.366743i
$187$	120.119	+	32.1859i	0.642349	+	0.172117i
$188$	352.290	+	94.3959i	1.87388	+	0.502106i
$189$	47.3957	−	0.726764i	0.250771	−	0.00384531i
$190$	292.488	+	292.488i	1.53941	+	1.53941i
$191$	45.3323	−	78.5179i	0.237342	−	0.411088i	−0.722609	−	0.691257i	$-0.757057\pi$
$191$	45.3323	−	78.5179i	0.237342	−	0.411088i	0.959951	+	0.280169i	$0.0903905\pi$
$192$	−153.774	+	72.6652i	−0.800907	+	0.378464i
$193$	5.28221	−	19.7135i	0.0273690	−	0.102142i	−0.950890	−	0.309528i	$-0.899829\pi$
$193$	5.28221	−	19.7135i	0.0273690	−	0.102142i	0.978259	+	0.207386i	$0.0664955\pi$
$194$	−568.930	−	328.472i	−2.93263	−	1.69315i
$195$	−126.005	+	321.303i	−0.646181	+	1.64771i
$196$	187.004	+	323.900i	0.954101	+	1.65255i
$197$	−68.1531	−	254.351i	−0.345955	−	1.29112i	−0.891493	−	0.453035i	$-0.850341\pi$
$197$	−68.1531	−	254.351i	−0.345955	−	1.29112i	0.545537	−	0.838086i	$-0.316326\pi$
$198$	−282.805	+	344.117i	−1.42831	+	1.73797i
$199$	43.9695	−	25.3858i	0.220952	−	0.127567i	−0.385439	−	0.922733i	$-0.625950\pi$
$199$	43.9695	−	25.3858i	0.220952	−	0.127567i	0.606391	+	0.795167i	$0.292617\pi$
$200$	−743.895	−	199.326i	−3.71947	−	0.996630i
$201$	−46.2482	−	254.669i	−0.230091	−	1.26701i
$202$	221.990	+	221.990i	1.09896	+	1.09896i
$203$	−69.7218	+	18.6819i	−0.343457	+	0.0920291i
$204$	121.835	−	175.905i	0.597230	−	0.862279i
$205$			478.531i			2.33430i
$206$	−31.3706	+	8.40574i	−0.152285	+	0.0408045i
$207$	24.7655	−	149.364i	0.119640	−	0.721567i
$208$	203.329	−	109.452i	0.977544	−	0.526212i
$209$	95.2355	+	164.953i	0.455672	+	0.789247i
$210$	29.0227	+	159.815i	0.138203	+	0.761024i
$211$	−33.2217	−	57.5417i	−0.157449	−	0.272709i	0.776499	−	0.630118i	$-0.216994\pi$
$211$	−33.2217	−	57.5417i	−0.157449	−	0.272709i	−0.933948	+	0.357409i	$0.883660\pi$
$212$		−	312.004i		−	1.47172i
$213$	60.1912	+	331.446i	0.282588	+	1.55609i
$214$	−62.7903	−	234.336i	−0.293412	−	1.09503i
$215$	31.1340	−	116.194i	0.144809	−	0.540435i
$216$	200.174	+	334.752i	0.926732	+	1.54978i
$217$	−5.74666	−	9.95351i	−0.0264823	−	0.0458687i
$218$			42.1789i			0.193481i
$219$	86.1667	−	240.559i	0.393455	−	1.09845i
$220$	−886.474	−	511.806i	−4.02943	−	2.32639i
$221$	59.8300	−	96.8487i	0.270724	−	0.438229i
$222$	383.878	+	31.6088i	1.72918	+	0.142382i
$223$	−76.8250	+	76.8250i	−0.344507	+	0.344507i	−0.858059	−	0.513552i	$-0.828329\pi$
$223$	−76.8250	+	76.8250i	−0.344507	+	0.344507i	0.513552	+	0.858059i	$0.328329\pi$
$224$	3.61662	−	6.26417i	0.0161456	−	0.0279650i
$225$	78.4838	−	473.347i	0.348817	−	2.10376i
$226$	161.232	−	161.232i	0.713418	−	0.713418i
$227$	−65.8803	−	245.868i	−0.290221	−	1.08312i	−0.944939	−	0.327247i	$-0.893879\pi$
$227$	−65.8803	−	245.868i	−0.290221	−	1.08312i	0.654717	−	0.755874i	$-0.272788\pi$
$228$	322.464	−	58.5600i	1.41432	−	0.256842i
$229$	86.2605	−	23.1134i	0.376683	−	0.100932i	−0.0655096	−	0.997852i	$-0.520867\pi$
$229$	86.2605	−	23.1134i	0.376683	−	0.100932i	0.442193	+	0.896920i	$0.354201\pi$
$230$	518.811			2.25570
$231$	−6.13787	+	74.5422i	−0.0265709	+	0.322693i
$232$	−419.977	−	419.977i	−1.81024	−	1.81024i
$233$			52.3389i			0.224630i	0.993673	+	0.112315i	$0.0358266\pi$
$233$			52.3389i			0.224630i	−0.993673	+	0.112315i	$0.964173\pi$
$234$	227.294	+	338.515i	0.971343	+	1.44664i
$235$	−396.253			−1.68618
$236$	61.5676	−	61.5676i	0.260880	−	0.260880i
$237$	10.9221	−	15.7693i	0.0460848	−	0.0665371i
$238$		−	53.5766i		−	0.225112i
$239$	−67.3526	−	251.363i	−0.281810	−	1.05173i	−0.951139	−	0.308763i	$-0.900085\pi$
$239$	−67.3526	−	251.363i	−0.281810	−	1.05173i	0.669329	−	0.742966i	$-0.266582\pi$
$240$	−359.691	+	304.963i	−1.49871	+	1.27068i
$241$	−108.627	+	29.1066i	−0.450735	+	0.120774i	−0.477043	−	0.878880i	$-0.658292\pi$
$241$	−108.627	+	29.1066i	−0.450735	+	0.120774i	0.0263082	+	0.999654i	$0.491625\pi$
$242$	−198.794	−	198.794i	−0.821465	−	0.821465i
$243$	−195.428	+	144.420i	−0.804229	+	0.594320i
$244$	−242.621	−	140.077i	−0.994347	−	0.574086i
$245$	−287.330	−	287.330i	−1.17278	−	1.17278i
$246$	464.760	+	321.901i	1.88927	+	1.30854i
$247$	169.689	−	40.0927i	0.687001	−	0.162319i
$248$	47.2858	−	81.9014i	0.190668	−	0.330247i
$249$	−7.67748	−	42.2765i	−0.0308333	−	0.169785i
$250$	873.151			3.49260
$251$	239.559	−	138.309i	0.954417	−	0.551033i	0.0599666	−	0.998200i	$-0.480901\pi$
$251$	239.559	−	138.309i	0.954417	−	0.551033i	0.894450	+	0.447168i	$0.147567\pi$
$252$	117.189	+	53.1945i	0.465035	+	0.211089i
$253$	230.759	+	61.8318i	0.912092	+	0.244394i
$254$	529.864	−	141.977i	2.08608	−	0.558963i
$255$	−78.3949	+	218.862i	−0.307431	+	0.858283i
$256$	−519.205			−2.02815
$257$	−328.351	+	189.573i	−1.27763	+	0.737639i	−0.976412	−	0.215916i	$-0.930726\pi$
$257$	−328.351	+	189.573i	−1.27763	+	0.737639i	−0.301217	+	0.953556i	$0.597393\pi$
$258$	−91.9063	−	108.400i	−0.356226	−	0.420154i
$259$	56.0137	−	32.3395i	0.216269	−	0.124863i
$260$	−682.022	+	642.561i	−2.62316	+	2.47139i
$261$	234.943	−	285.879i	0.900166	−	1.09532i
$262$	−43.1354	−	160.984i	−0.164639	−	0.614441i
$263$	−64.1303			−0.243842			−0.121921	−	0.992540i	$-0.538905\pi$
$263$	−64.1303			−0.243842			−0.121921	+	0.992540i	$0.538905\pi$
$264$	−556.440	+	262.943i	−2.10773	+	0.995995i
$265$	87.7350	+	327.431i	0.331075	+	1.23559i
$266$	58.0256	−	58.0256i	0.218141	−	0.218141i
$267$	61.5816	+	72.6330i	0.230643	+	0.272034i
$268$	181.884	−	678.801i	0.678672	−	2.53284i
$269$	−99.5264	−	172.385i	−0.369987	−	0.640836i	0.619576	−	0.784936i	$-0.287304\pi$
$269$	−99.5264	−	172.385i	−0.369987	−	0.640836i	−0.989563	+	0.144101i	$0.953971\pi$
$270$	−597.754	−	579.699i	−2.21390	−	2.14703i
$271$	−33.4259	+	8.95645i	−0.123343	+	0.0330496i	−0.319962	−	0.947430i	$-0.603670\pi$
$271$	−33.4259	+	8.95645i	−0.123343	+	0.0330496i	0.196620	+	0.980480i	$0.437004\pi$
$272$	134.707	−	77.7731i	0.495246	−	0.285931i
$273$	63.7421	+	24.9977i	0.233487	+	0.0915667i
$274$	−332.980	+	576.738i	−1.21525	+	2.10488i
$275$	731.294	+	195.950i	2.65925	+	0.712544i
$276$	234.055	−	337.928i	0.848025	−	1.22438i
$277$	−159.299	−	91.9714i	−0.575087	−	0.332027i	0.184091	−	0.982909i	$-0.441066\pi$
$277$	−159.299	−	91.9714i	−0.575087	−	0.332027i	−0.759179	+	0.650882i	$0.774399\pi$
$278$	−105.857	+	105.857i	−0.380780	+	0.380780i
$279$	53.6513	+	24.3535i	0.192298	+	0.0872885i
$280$	−58.0869	+	216.783i	−0.207453	+	0.774226i
$281$	−117.710	+	439.299i	−0.418896	+	1.56334i	0.358005	+	0.933720i	$0.383457\pi$
$281$	−117.710	+	439.299i	−0.418896	+	1.56334i	−0.776901	+	0.629622i	$0.783210\pi$
$282$	−266.554	+	384.849i	−0.945225	+	1.36471i
$283$	200.960	−	116.025i	0.710107	−	0.409981i	−0.100993	−	0.994887i	$-0.532202\pi$
$283$	200.960	−	116.025i	0.710107	−	0.409981i	0.811101	+	0.584906i	$0.198869\pi$
$284$	−236.719	+	883.447i	−0.833517	+	3.11073i
$285$	−321.941	+	152.132i	−1.12962	+	0.533795i
$286$	−566.514	+	304.955i	−1.98082	+	1.06627i
$287$	94.9340			0.330781
$288$	3.60922	+	36.9047i	0.0125320	+	0.128141i
$289$	−106.159	+	183.873i	−0.367332	+	0.636237i
$290$	1098.11	+	633.994i	3.78658	+	2.18618i
$291$	431.350	−	365.719i	1.48230	−	1.25677i
$292$	490.566	−	490.566i	1.68002	−	1.68002i
$293$	−138.377	−	138.377i	−0.472276	−	0.472276i	0.430374	−	0.902651i	$-0.358382\pi$
$293$	−138.377	−	138.377i	−0.472276	−	0.472276i	−0.902651	+	0.430374i	$0.858382\pi$
$294$	−472.344	+	85.7784i	−1.60661	+	0.291763i
$295$	−47.2991	+	81.9245i	−0.160336	+	0.277710i
$296$	460.903	+	266.103i	1.55710	+	0.898995i
$297$	−196.783	−	329.081i	−0.662571	−	1.10802i
$298$		−	167.844i		−	0.563237i
$299$	114.938	−	186.054i	0.384409	−	0.622256i
$300$	741.738	−	1070.92i	2.47246	−	3.56973i
$301$	−23.0512	−	6.17655i	−0.0765821	−	0.0205201i
$302$	−231.263	−	400.559i	−0.765770	−	1.32635i
$303$	−244.344	+	115.464i	−0.806416	+	0.381068i
$304$	230.124	+	61.6617i	0.756988	+	0.202834i
$305$	294.006	+	78.7787i	0.963955	+	0.258291i
$306$	159.828	+	223.364i	0.522315	+	0.729948i
$307$	−179.861	−	179.861i	−0.585866	−	0.585866i	0.350643	−	0.936509i	$-0.385963\pi$
$307$	−179.861	−	179.861i	−0.585866	−	0.585866i	−0.936509	+	0.350643i	$0.885963\pi$
$308$	−101.535	+	175.864i	−0.329660	+	0.570988i
$309$	2.29429	−	27.8633i	0.00742487	−	0.0901724i
$310$	−52.2554	+	195.020i	−0.168566	+	0.629097i
$311$	379.944	+	219.361i	1.22168	+	0.705340i	0.965277	−	0.261229i	$-0.0841279\pi$
$311$	379.944	+	219.361i	1.22168	+	0.705340i	0.256407	+	0.966569i	$0.417461\pi$
$312$	84.1138	+	557.071i	0.269596	+	1.78548i
$313$	−147.788	−	255.976i	−0.472166	−	0.817815i	0.527327	−	0.849663i	$-0.323194\pi$
$313$	−147.788	−	255.976i	−0.472166	−	0.817815i	−0.999493	+	0.0318471i	$0.989861\pi$
$314$	−72.8812	−	271.996i	−0.232106	−	0.866231i
$315$	−137.941	−	22.8715i	−0.437909	−	0.0726079i
$316$	45.1035	−	26.0405i	0.142733	−	0.0824067i
$317$	11.1996	+	3.00092i	0.0353299	+	0.00946663i	0.276441	−	0.961031i	$-0.410845\pi$
$317$	11.1996	+	3.00092i	0.0353299	+	0.00946663i	−0.241111	+	0.970498i	$0.577512\pi$
$318$	377.026	+	135.048i	1.18562	+	0.424680i
$319$	412.863	+	412.863i	1.29424	+	1.29424i
$320$	484.604	−	129.849i	1.51439	−	0.405779i
$321$	208.137	+	17.1382i	0.648401	+	0.0533899i
$322$		−	102.925i		−	0.319643i
$323$	113.448	−	30.3984i	0.351233	−	0.0941127i
$324$	−647.256	+	127.824i	−1.99770	+	0.394517i
$325$	364.249	−	589.621i	1.12077	−	1.81422i
$326$	−486.891	−	843.320i	−1.49353	−	2.58687i
$327$	−34.1824	−	12.2439i	−0.104533	−	0.0374431i
$328$	390.577	+	676.500i	1.19078	+	2.06250i
$329$			78.6111i			0.238940i
$330$	1002.17	−	849.685i	3.03687	−	2.57480i
$331$	64.1356	+	239.357i	0.193763	+	0.723134i	0.992584	+	0.121564i	$0.0387910\pi$
$331$	64.1356	+	239.357i	0.193763	+	0.723134i	−0.798820	+	0.601569i	$0.794542\pi$
$332$	30.1939	−	112.685i	0.0909454	−	0.339413i
$333$	−137.050	+	301.925i	−0.411562	+	0.906680i
$334$	−80.0095	−	138.581i	−0.239549	−	0.414912i
$335$			763.510i			2.27913i
$336$	60.5004	+	71.3578i	0.180061	+	0.212374i
$337$	223.836	+	129.232i	0.664201	+	0.383477i	0.793876	−	0.608080i	$-0.208060\pi$
$337$	223.836	+	129.232i	0.664201	+	0.383477i	−0.129674	+	0.991557i	$0.541393\pi$
$338$	118.298	+	576.960i	0.349993	+	1.70698i
$339$	83.8617	+	177.468i	0.247380	+	0.523505i
$340$	−446.320	+	446.320i	−1.31270	+	1.31270i
$341$	−46.4848	+	80.5141i	−0.136319	+	0.236112i
$342$	−68.8116	+	415.013i	−0.201204	+	1.21349i
$343$	−117.831	+	117.831i	−0.343530	+	0.343530i
$344$	−50.8231	−	189.674i	−0.147742	−	0.551379i
$345$	−150.603	+	420.452i	−0.436531	+	1.21870i
$346$	138.650	−	37.1511i	0.400722	−	0.107373i
$347$	−530.760			−1.52957			−0.764784	−	0.644287i	$-0.777154\pi$
$347$	−530.760			−1.52957			−0.764784	+	0.644287i	$0.777154\pi$
$348$	908.349	−	429.236i	2.61020	−	1.23344i
$349$	−227.217	−	227.217i	−0.651053	−	0.651053i	0.302194	−	0.953247i	$-0.402281\pi$
$349$	−227.217	−	227.217i	−0.651053	−	0.651053i	−0.953247	+	0.302194i	$0.902281\pi$
$350$		−	326.177i		−	0.931936i
$351$	−340.317	+	85.9370i	−0.969565	+	0.244835i
$352$	−58.5098			−0.166221
$353$	−393.758	+	393.758i	−1.11546	+	1.11546i	−0.123062	+	0.992399i	$0.539271\pi$
$353$	−393.758	+	393.758i	−1.11546	+	1.11546i	−0.992399	+	0.123062i	$0.960729\pi$
$354$	47.7494	+	101.047i	0.134885	+	0.285445i
$355$		−	993.694i		−	2.79914i
$356$	66.9154	+	249.732i	0.187965	+	0.701493i
$357$	43.4192	+	15.5525i	0.121622	+	0.0435643i
$358$	−1014.99	+	271.965i	−2.83516	+	0.759678i
$359$	−372.001	−	372.001i	−1.03622	−	1.03622i	−0.999319	−	0.0368966i	$-0.988253\pi$
$359$	−372.001	−	372.001i	−1.03622	−	1.03622i	−0.0368966	−	0.999319i	$-0.511747\pi$
$360$	−404.535	−	1077.07i	−1.12371	−	2.99185i
$361$	−156.843	−	90.5536i	−0.434469	−	0.250841i
$362$	−241.745	−	241.745i	−0.667804	−	0.667804i
$363$	218.813	−	103.399i	0.602790	−	0.284845i
$364$	127.475	+	135.304i	0.350207	+	0.371714i
$365$	−376.876	+	652.768i	−1.03254	+	1.78841i
$366$	274.285	−	232.552i	0.749413	−	0.635388i
$367$	−321.506			−0.876037			−0.438019	−	0.898966i	$-0.644320\pi$
$367$	−321.506			−0.876037			−0.438019	+	0.898966i	$0.644320\pi$
$368$	258.783	−	149.409i	0.703215	−	0.406002i
$369$	−395.786	+	283.205i	−1.07259	+	0.767494i
$370$	−1097.48	−	294.069i	−2.96617	−	0.794782i
$371$	64.9579	−	17.4054i	0.175089	−	0.0469149i
$372$	103.452	+	122.017i	0.278097	+	0.328003i
$373$	168.148			0.450799			0.225399	−	0.974266i	$-0.427631\pi$
$373$	168.148			0.450799			0.225399	+	0.974266i	$0.427631\pi$
$374$	−375.320	+	216.691i	−1.00353	+	0.579387i
$375$	−253.462	+	707.614i	−0.675899	+	1.88697i
$376$	−560.183	+	323.422i	−1.48985	+	0.860164i
$377$	470.638	−	253.344i	1.24838	−	0.672000i
$378$	−115.004	+	118.586i	−0.304244	+	0.313720i
$379$	144.324	+	538.624i	0.380802	+	1.42117i	0.844679	+	0.535272i	$0.179791\pi$
$379$	144.324	+	538.624i	0.380802	+	1.42117i	−0.463878	+	0.885899i	$0.653542\pi$
$380$	−966.764			−2.54412
$381$	−38.7515	+	470.623i	−0.101710	+	1.23523i
$382$	81.7778	+	305.199i	0.214078	+	0.798950i
$383$	382.205	−	382.205i	0.997925	−	0.997925i	−0.00207258	−	0.999998i	$-0.500660\pi$
$383$	382.205	−	382.205i	0.997925	−	0.997925i	0.999998	+	0.00207258i	$0.000659723\pi$
$384$	216.546	−	604.550i	0.563921	−	1.57435i
$385$	57.1030	−	213.111i	0.148319	−	0.553536i
$386$	35.5624	+	61.5959i	0.0921306	+	0.159575i
$387$	114.528	−	43.0154i	0.295937	−	0.111151i
$388$	1483.10	−	397.395i	3.82242	−	1.02421i
$389$	126.133	−	72.8229i	0.324249	−	0.187205i	−0.329036	−	0.944317i	$-0.606724\pi$
$389$	126.133	−	72.8229i	0.324249	−	0.187205i	0.653285	+	0.757112i	$0.273390\pi$
$390$	−481.264	−	1102.28i	−1.23401	−	2.82637i
$391$	73.6565	−	127.577i	0.188380	−	0.326283i
$392$	−640.718	−	171.680i	−1.63448	−	0.437959i
$393$	142.985	+	11.7735i	0.363829	+	0.0299580i
$394$	794.734	+	458.840i	2.01709	+	1.16457i
$395$	−40.0111	+	40.0111i	−0.101294	+	0.101294i
$396$	−101.328	−	1036.09i	−0.255878	−	2.61638i
$397$	−17.1546	+	64.0220i	−0.0432107	+	0.161264i	−0.984160	−	0.177283i	$-0.943269\pi$
$397$	−17.1546	+	64.0220i	−0.0432107	+	0.161264i	0.940949	+	0.338548i	$0.109936\pi$
$398$	−45.7950	+	170.909i	−0.115063	+	0.429420i
$399$	30.1808	+	63.8687i	0.0756412	+	0.160072i
$400$	820.104	−	473.487i	2.05026	−	1.18372i
$401$	−90.2487	+	336.813i	−0.225059	+	0.839932i	0.757322	+	0.653042i	$0.226507\pi$
$401$	−90.2487	+	336.813i	−0.225059	+	0.839932i	−0.982381	+	0.186890i	$0.940159\pi$
$402$	741.537	+	513.602i	1.84462	+	1.27762i
$403$	58.3606	+	61.9447i	0.144815	+	0.153709i
$404$	−733.746			−1.81620
$405$	643.315	−	316.151i	1.58843	−	0.780619i
$406$	125.776	−	217.850i	0.309792	−	0.536576i
$407$	−453.096	−	261.595i	−1.11326	−	0.642740i
$408$	67.8084	+	373.391i	0.166197	+	0.915175i
$409$	−328.329	+	328.329i	−0.802760	+	0.802760i	−0.983526	−	0.180766i	$-0.942142\pi$
$409$	−328.329	+	328.329i	−0.802760	+	0.802760i	0.180766	+	0.983526i	$0.442142\pi$
$410$	−1179.23	−	1179.23i	−2.87616	−	2.87616i
$411$	−370.738	−	437.270i	−0.902038	−	1.06392i
$412$	37.9531	−	65.7367i	0.0921191	−	0.159555i
$413$	16.2527	+	9.38350i	0.0393528	+	0.0227203i
$414$	307.044	+	429.101i	0.741652	+	1.03648i
$415$			126.747i			0.305415i
$416$	−15.3971	+	51.3004i	−0.0370123	+	0.123318i
$417$	−55.0592	−	116.516i	−0.132036	−	0.279416i
$418$	−641.171	−	171.801i	−1.53390	−	0.411008i
$419$	−337.863	−	585.196i	−0.806356	−	1.39665i	−0.915372	−	0.402610i	$-0.868103\pi$
$419$	−337.863	−	585.196i	−0.806356	−	1.39665i	0.109016	−	0.994040i	$-0.465230\pi$
$420$	−312.084	−	216.155i	−0.743057	−	0.514654i
$421$	506.768	+	135.788i	1.20372	+	0.322537i	0.804297	−	0.594228i	$-0.202542\pi$
$421$	506.768	+	135.788i	1.20372	+	0.322537i	0.399427	+	0.916765i	$0.369209\pi$
$422$	223.665	+	59.9307i	0.530011	+	0.142016i
$423$	−234.511	−	327.735i	−0.554400	−	0.774787i
$424$	391.280	+	391.280i	0.922831	+	0.922831i
$425$	233.423	−	404.301i	0.549231	−	0.951295i
$426$	−965.097	−	668.443i	−2.26549	−	1.56912i
$427$	15.6286	−	58.3268i	0.0366010	−	0.136597i
$428$	491.048	+	283.507i	1.14731	+	0.662399i
$429$	−82.6890	−	547.635i	−0.192748	−	1.27654i
$430$	209.609	+	363.053i	0.487463	+	0.844310i
$431$	160.021	+	597.207i	0.371279	+	1.38563i	0.858707	+	0.512467i	$0.171268\pi$
$431$	160.021	+	597.207i	0.371279	+	1.38563i	−0.487428	+	0.873163i	$0.662065\pi$
$432$	−465.103	−	117.011i	−1.07663	−	0.270860i
$433$	420.399	−	242.717i	0.970897	−	0.560548i	0.0713877	−	0.997449i	$-0.477257\pi$
$433$	420.399	−	242.717i	0.970897	−	0.560548i	0.899510	+	0.436901i	$0.143924\pi$
$434$	38.6893	+	10.3668i	0.0891458	+	0.0238865i
$435$	−832.562	+	705.885i	−1.91394	+	1.62272i
$436$	−69.7073	−	69.7073i	−0.159879	−	0.159879i
$437$	217.944	−	58.3978i	0.498727	−	0.133633i
$438$	380.464	+	805.138i	0.868639	+	1.83821i
$439$		−	124.902i		−	0.284516i	−0.989830	−	0.142258i	$-0.954564\pi$
$439$		−	124.902i		−	0.284516i	0.989830	−	0.142258i	$-0.0454362\pi$
$440$	1753.56	−	469.866i	3.98537	−	1.06788i
$441$	67.5982	−	407.695i	0.153284	−	0.924478i
$442$	91.2236	+	386.097i	0.206388	+	0.873522i
$443$	−307.260	−	532.190i	−0.693589	−	1.20133i	−0.970654	−	0.240481i	$-0.922695\pi$
$443$	−307.260	−	532.190i	−0.693589	−	1.20133i	0.277065	−	0.960851i	$-0.410638\pi$
$444$	−686.657	+	582.180i	−1.54652	+	1.31122i
$445$	−140.448	−	243.263i	−0.315613	−	0.546659i
$446$		−	378.633i		−	0.848953i
$447$	136.024	+	48.7227i	0.304303	+	0.108999i
$448$	−25.7603	−	96.1387i	−0.0575006	−	0.214595i
$449$	−139.464	+	520.486i	−0.310610	+	1.15921i	0.617398	+	0.786651i	$0.288187\pi$
$449$	−139.464	+	520.486i	−0.310610	+	1.15921i	−0.928008	+	0.372560i	$0.878480\pi$
$450$	973.046	+	1359.85i	2.16232	+	3.02190i
$451$	−383.961	−	665.041i	−0.851356	−	1.47459i
$452$			532.923i			1.17903i
$453$	391.750	−	71.1425i	0.864791	−	0.157047i
$454$	768.230	+	443.538i	1.69214	+	0.976955i
$455$	−171.825	−	106.148i	−0.377638	−	0.233293i
$456$	−330.958	+	477.837i	−0.725786	+	1.04789i
$457$	−171.392	+	171.392i	−0.375038	+	0.375038i	−0.869308	−	0.494271i	$-0.835435\pi$
$457$	−171.392	+	171.392i	−0.375038	+	0.375038i	0.494271	+	0.869308i	$0.335435\pi$
$458$	−155.611	+	269.526i	−0.339761	+	0.588484i
$459$	−227.413	+	64.6881i	−0.495454	+	0.140933i
$460$	−857.417	+	857.417i	−1.86395	+	1.86395i
$461$	−61.5292	−	229.630i	−0.133469	−	0.498113i	0.866531	−	0.499124i	$-0.166345\pi$
$461$	−61.5292	−	229.630i	−0.133469	−	0.498113i	−0.999999	+	0.00101129i	$0.999678\pi$
$462$	−168.566	−	198.816i	−0.364861	−	0.430339i
$463$	−431.444	+	115.605i	−0.931844	+	0.249687i	−0.692641	−	0.721283i	$-0.743553\pi$
$463$	−431.444	+	115.605i	−0.931844	+	0.249687i	−0.239203	+	0.970970i	$0.576886\pi$
$464$	730.316			1.57396
$465$	−142.878	−	98.9599i	−0.307265	−	0.212817i
$466$	−128.977	−	128.977i	−0.276774	−	0.276774i
$467$		−	120.666i		−	0.258386i	−0.991619	−	0.129193i	$-0.958761\pi$
$467$		−	120.666i		−	0.258386i	0.991619	−	0.129193i	$-0.0412387\pi$
$468$	−935.088	−	183.809i	−1.99805	−	0.392754i
$469$	151.470			0.322963
$470$	976.470	−	976.470i	2.07760	−	2.07760i
$471$	241.586	+	19.8924i	0.512922	+	0.0422344i
$472$			154.422i			0.327166i
$473$	49.9622	+	186.462i	0.105628	+	0.394211i
$474$	11.9448	+	65.7745i	0.0251999	+	0.138765i
$475$	690.680	−	185.067i	1.45406	−	0.389615i
$476$	88.5437	+	88.5437i	0.186016	+	0.186016i
$477$	−218.890	+	266.345i	−0.458889	+	0.558376i
$478$	785.399	+	453.450i	1.64309	+	0.948640i
$479$	441.886	+	441.886i	0.922518	+	0.922518i	0.997207	−	0.0746891i	$-0.0237964\pi$
$479$	441.886	+	441.886i	0.922518	+	0.922518i	−0.0746891	+	0.997207i	$0.523796\pi$
$480$	8.97616	−	109.012i	0.0187003	−	0.227109i
$481$	−348.596	+	328.427i	−0.724733	+	0.682800i
$482$	195.959	−	339.412i	0.406555	−	0.704173i
$483$	83.4120	+	29.8776i	0.172696	+	0.0618583i
$484$	657.078			1.35760
$485$	−1444.68	+	834.087i	−2.97873	+	1.71977i
$486$	125.696	−	837.472i	0.258635	−	1.72319i
$487$	−108.024	−	28.9450i	−0.221815	−	0.0594353i	0.146200	−	0.989255i	$-0.453296\pi$
$487$	−108.024	−	28.9450i	−0.221815	−	0.0594353i	−0.368015	+	0.929820i	$0.619963\pi$
$488$	479.936	−	128.598i	0.983475	−	0.263521i
$489$	824.775	−	149.781i	1.68666	−	0.306300i
$490$	1416.11			2.89002
$491$	302.974	−	174.922i	0.617054	−	0.356256i	−0.158667	−	0.987332i	$-0.550720\pi$
$491$	302.974	−	174.922i	0.617054	−	0.356256i	0.775721	+	0.631076i	$0.217386\pi$
$492$	−1300.08	+	236.097i	−2.64244	+	0.479871i
$493$	311.801	−	180.018i	0.632455	−	0.365148i
$494$	−319.360	+	516.957i	−0.646477	+	1.04647i
$495$	397.683	+	1058.82i	0.803400	+	2.13904i
$496$	30.0973	+	112.325i	0.0606800	+	0.226461i
$497$	−197.135			−0.396650
$498$	123.100	+	85.2610i	0.247188	+	0.171207i
$499$	−174.617	−	651.681i	−0.349934	−	1.30597i	−0.886740	−	0.462268i	$-0.847036\pi$
$499$	−174.617	−	651.681i	−0.349934	−	1.30597i	0.536806	−	0.843706i	$-0.319631\pi$
$500$	−1443.02	+	1443.02i	−2.88604	+	2.88604i
$501$	135.533	−	24.6130i	0.270525	−	0.0491278i
$502$	−249.505	+	931.164i	−0.497021	+	1.85491i
$503$	213.872	+	370.437i	0.425192	+	0.736455i	0.996438	−	0.0843240i	$-0.0268731\pi$
$503$	213.872	+	370.437i	0.425192	+	0.736455i	−0.571246	+	0.820779i	$0.693540\pi$
$504$	−213.675	+	80.2543i	−0.423959	+	0.159235i
$505$	770.026	−	206.328i	1.52480	−	0.408570i
$506$	−721.020	+	416.281i	−1.42494	+	0.822690i
$507$	−501.917	−	71.6125i	−0.989974	−	0.141248i
$508$	−641.044	+	1110.32i	−1.26190	+	2.18567i
$509$	−207.040	−	55.4763i	−0.406759	−	0.108991i	0.0496375	−	0.998767i	$-0.484193\pi$
$509$	−207.040	−	55.4763i	−0.406759	−	0.108991i	−0.456396	+	0.889777i	$0.650860\pi$
$510$	−346.148	−	732.518i	−0.678721	−	1.43631i
$511$	129.500	+	74.7670i	0.253425	+	0.146315i
$512$	674.020	−	674.020i	1.31644	−	1.31644i
$513$	−316.358	−	176.238i	−0.616681	−	0.343544i
$514$	341.983	−	1276.30i	0.665337	−	2.48307i
$515$	−21.3446	+	79.6593i	−0.0414459	+	0.154678i
$516$	331.037	+	27.2579i	0.641545	+	0.0528253i
$517$	550.694	−	317.943i	1.06517	−	0.614977i
$518$	−58.3393	+	217.725i	−0.112624	+	0.420319i
$519$	−10.1401	+	123.148i	−0.0195378	+	0.237280i
$520$	49.4884	−	1661.14i	0.0951700	−	3.19450i
$521$	692.479			1.32913			0.664567	−	0.747228i	$-0.268616\pi$
$521$	692.479			1.32913			0.664567	+	0.747228i	$0.268616\pi$
$522$	125.518	+	1283.44i	0.240457	+	2.45870i
$523$	−267.793	+	463.831i	−0.512033	+	0.886867i	0.487870	+	0.872916i	$0.337774\pi$
$523$	−267.793	+	463.831i	−0.512033	+	0.886867i	−0.999903	+	0.0139505i	$0.995559\pi$
$524$	337.338	+	194.762i	0.643776	+	0.371684i
$525$	264.339	+	94.6843i	0.503503	+	0.180351i
$526$	158.034	−	158.034i	0.300444	−	0.300444i
$527$	40.5370	+	40.5370i	0.0769203	+	0.0769203i
$528$	255.188	−	712.430i	0.483310	−	1.34930i
$529$	−123.000	+	213.042i	−0.232514	+	0.402726i
$530$	−1023.08	−	590.674i	−1.93033	−	1.11448i
$531$	−95.7512	+	9.36430i	−0.180322	+	0.0176352i
$532$			191.793i			0.360513i
$533$	−684.137	+	161.642i	−1.28356	+	0.303268i
$534$	−330.740	−	27.2334i	−0.619363	−	0.0509989i
$535$	−595.050	−	159.443i	−1.11224	−	0.298024i
$536$	623.177	+	1079.37i	1.16264	+	2.01376i
$537$	74.2309	−	901.507i	0.138233	−	1.67878i
$538$	670.060	+	179.542i	1.24546	+	0.333721i
$539$	629.865	+	168.772i	1.16858	+	0.313120i
$540$	1945.93	−	29.8388i	3.60357	−	0.0552570i
$541$	314.860	+	314.860i	0.581997	+	0.581997i	0.935452	−	0.353455i	$-0.114993\pi$
$541$	314.860	+	314.860i	0.581997	+	0.581997i	−0.353455	+	0.935452i	$0.614993\pi$
$542$	60.2991	−	104.441i	0.111253	−	0.192696i
$543$	266.089	−	125.739i	0.490034	−	0.231563i
$544$	−9.33792	+	34.8496i	−0.0171653	+	0.0640618i
$545$	92.7555	+	53.5524i	0.170194	+	0.0982613i
$546$	−218.678	+	95.4761i	−0.400509	+	0.174865i
$547$	−314.476	−	544.689i	−0.574911	−	0.995776i	−0.996051	−	0.0887799i	$-0.971703\pi$
$547$	−314.476	−	544.689i	−0.574911	−	0.995776i	0.421140	−	0.906996i	$-0.361630\pi$
$548$	−402.848	−	1503.45i	−0.735124	−	2.74352i
$549$	108.843	+	289.791i	0.198256	+	0.527852i
$550$	−2284.97	+	1319.23i	−4.15449	+	2.39859i
$551$	532.659	+	142.726i	0.966714	+	0.259030i
$552$	130.266	+	717.316i	0.235989	+	1.29948i
$553$	7.93765	+	7.93765i	0.0143538	+	0.0143538i
$554$	619.196	−	165.913i	1.11768	−	0.299482i
$555$	556.900	−	804.052i	1.00342	−	1.44874i
$556$		−	349.889i		−	0.629298i
$557$	610.140	−	163.487i	1.09540	−	0.293513i	0.334512	−	0.942391i	$-0.391428\pi$
$557$	610.140	−	163.487i	1.09540	−	0.293513i	0.760892	+	0.648879i	$0.224762\pi$
$558$	−192.224	+	72.1974i	−0.344487	+	0.129386i
$559$	176.634	+	5.26225i	0.315982	+	0.00941368i
$560$	−137.982	−	238.992i	−0.246397	−	0.426772i
$561$	−66.6599	−	367.066i	−0.118823	−	0.654307i
$562$	−792.479	−	1372.61i	−1.41011	−	2.44237i
$563$			390.418i			0.693460i	0.937965	+	0.346730i	$0.112708\pi$
$563$			390.418i			0.693460i	−0.937965	+	0.346730i	$0.887292\pi$
$564$	−195.502	−	1076.55i	−0.346635	−	1.90877i
$565$	−149.857	−	559.274i	−0.265233	−	0.989865i
$566$	−209.304	+	781.133i	−0.369795	+	1.38009i
$567$	−62.7200	−	127.625i	−0.110617	−	0.225088i
$568$	−811.053	−	1404.78i	−1.42791	−	2.47321i
$569$		−	303.853i		−	0.534012i	−0.963695	−	0.267006i	$-0.913966\pi$
$569$		−	303.853i		−	0.534012i	0.963695	−	0.267006i	$-0.0860344\pi$
$570$	418.455	−	1168.24i	0.734131	−	2.04954i
$571$	−294.359	−	169.948i	−0.515515	−	0.297632i	0.219583	−	0.975594i	$-0.429530\pi$
$571$	−294.359	−	169.948i	−0.515515	−	0.297632i	−0.735098	+	0.677961i	$0.762864\pi$
$572$	432.269	−	1440.24i	0.755715	−	2.51790i
$573$	−271.077	−	22.3207i	−0.473083	−	0.0389541i
$574$	−233.942	+	233.942i	−0.407565	+	0.407565i
$575$	448.425	−	776.695i	0.779870	−	1.35077i
$576$	394.195	+	323.961i	0.684366	+	0.562432i
$577$	112.123	−	112.123i	0.194321	−	0.194321i	−0.603239	−	0.797560i	$-0.706124\pi$
$577$	112.123	−	112.123i	0.194321	−	0.194321i	0.797560	+	0.603239i	$0.206124\pi$
$578$	−191.507	−	714.713i	−0.331326	−	1.23653i
$579$	−60.2414	+	10.9399i	−0.104044	+	0.0188945i
$580$	−2862.57	+	767.023i	−4.93547	+	1.32245i
$581$	25.1449			0.0432786
$582$	−161.733	+	1964.18i	−0.277891	+	3.37489i
$583$	−384.653	−	384.653i	−0.659782	−	0.659782i
$584$			1230.43i			2.10689i
$585$	1033.01	−	70.0473i	1.76583	−	0.119739i
$586$	681.993			1.16381
$587$	122.299	−	122.299i	0.208345	−	0.208345i	−0.595218	−	0.803564i	$-0.702934\pi$
$587$	122.299	−	122.299i	0.208345	−	0.208345i	0.803564	+	0.595218i	$0.202934\pi$
$588$	638.860	−	922.385i	1.08650	−	1.56868i
$589$			87.8064i			0.149077i
$590$	−85.3259	−	318.441i	−0.144620	−	0.539730i
$591$	−602.549	+	510.870i	−1.01954	+	0.864416i
$592$	−632.111	+	169.374i	−1.06776	+	0.286104i
$593$	−221.043	−	221.043i	−0.372754	−	0.372754i	0.495725	−	0.868479i	$-0.334902\pi$
$593$	−221.043	−	221.043i	−0.372754	−	0.372754i	−0.868479	+	0.495725i	$0.834902\pi$
$594$	1295.87	+	326.016i	2.18159	+	0.548849i
$595$	−117.820	−	68.0234i	−0.198017	−	0.114325i
$596$	277.389	+	277.389i	0.465418	+	0.465418i
$597$	−125.214	−	86.7253i	−0.209738	−	0.145269i
$598$	175.248	+	741.724i	0.293057	+	1.24034i
$599$	−372.714	+	645.560i	−0.622227	+	1.07773i	0.366843	+	0.930283i	$0.380439\pi$
$599$	−372.714	+	645.560i	−0.622227	+	1.07773i	−0.989070	+	0.147446i	$0.952895\pi$
$600$	412.822	+	2273.23i	0.688037	+	3.78871i
$601$	16.8476			0.0280327			0.0140163	−	0.999902i	$-0.495538\pi$
$601$	16.8476			0.0280327			0.0140163	+	0.999902i	$0.495538\pi$
$602$	72.0248	−	41.5835i	0.119642	−	0.0690756i
$603$	−631.487	+	451.862i	−1.04724	+	0.749356i
$604$	1044.18	+	279.788i	1.72878	+	0.463225i
$605$	−689.567	+	184.769i	−1.13978	+	0.305403i
$606$	317.595	−	886.659i	0.524084	−	1.46313i
$607$	−93.9607			−0.154795			−0.0773976	−	0.997000i	$-0.524661\pi$
$607$	−93.9607			−0.154795			−0.0773976	+	0.997000i	$0.524661\pi$
$608$	−47.8569	+	27.6302i	−0.0787119	+	0.0454444i
$609$	140.038	+	165.169i	0.229947	+	0.271213i
$610$	−918.639	+	530.376i	−1.50597	+	0.869469i
$611$	−133.849	−	566.507i	−0.219066	−	0.927180i
$612$	−633.286	−	105.003i	−1.03478	−	0.171573i
$613$	179.037	+	668.174i	0.292066	+	1.09001i	0.943519	+	0.331318i	$0.107493\pi$
$613$	179.037	+	668.174i	0.292066	+	1.09001i	−0.651453	+	0.758689i	$0.725840\pi$
$614$	886.447			1.44373
$615$	1297.97	−	613.350i	2.11052	−	0.997317i
$616$	−93.2149	−	347.883i	−0.151323	−	0.564745i
$617$	−100.770	+	100.770i	−0.163322	+	0.163322i	−0.784037	−	0.620715i	$-0.786843\pi$
$617$	−100.770	+	100.770i	−0.163322	+	0.163322i	0.620715	+	0.784037i	$0.286843\pi$
$618$	63.0086	+	74.3160i	0.101956	+	0.120252i
$619$	296.163	−	1105.29i	0.478454	−	1.78561i	−0.129431	−	0.991588i	$-0.541315\pi$
$619$	296.163	−	1105.29i	0.478454	−	1.78561i	0.607885	−	0.794025i	$-0.292018\pi$
$620$	−235.941	−	408.661i	−0.380549	−	0.659131i
$621$	−436.880	+	124.271i	−0.703510	+	0.200115i
$622$	−1476.84	+	395.718i	−2.37434	+	0.636203i
$623$	−48.2600	+	27.8630i	−0.0774640	+	0.0447238i
$624$	−557.493	−	411.223i	−0.893418	−	0.659012i
$625$	442.192	−	765.898i	0.707507	−	1.22544i
$626$	994.980	+	266.604i	1.58942	+	0.425885i
$627$	325.352	−	469.743i	0.518903	−	0.749191i
$628$	569.964	+	329.069i	0.907586	+	0.523995i
$629$	−228.124	+	228.124i	−0.362677	+	0.362677i
$630$	396.284	−	283.562i	0.629023	−	0.450098i
$631$	48.5261	−	181.102i	0.0769034	−	0.287007i	−0.916755	−	0.399451i	$-0.869201\pi$
$631$	48.5261	−	181.102i	0.0769034	−	0.287007i	0.993658	+	0.112443i	$0.0358676\pi$
$632$	−23.9066	+	89.2207i	−0.0378269	+	0.141172i
$633$	−113.495	+	163.864i	−0.179297	+	0.258869i
$634$	−34.9937	+	20.2036i	−0.0551952	+	0.0318669i
$635$	360.520	−	1345.48i	0.567749	−	2.11887i
$636$	−846.283	+	399.907i	−1.33063	+	0.628784i
$637$	313.728	−	507.841i	0.492509	−	0.797239i
$638$	−2034.80			−3.18934
$639$	821.869	−	588.089i	1.28618	−	0.920328i
$640$	−947.128	+	1640.47i	−1.47989	+	2.56324i
$641$	1071.30	+	618.515i	1.67129	+	0.964922i	0.966915	+	0.255098i	$0.0821078\pi$
$641$	1071.30	+	618.515i	1.67129	+	0.964922i	0.704379	+	0.709824i	$0.251226\pi$
$642$	−555.136	+	470.670i	−0.864697	+	0.733131i
$643$	−318.501	+	318.501i	−0.495337	+	0.495337i	−0.909983	−	0.414646i	$-0.863905\pi$
$643$	−318.501	+	318.501i	−0.495337	+	0.495337i	0.414646	+	0.909983i	$0.363905\pi$
$644$	170.100	+	170.100i	0.264130	+	0.264130i
$645$	−355.070	+	64.4813i	−0.550496	+	0.0999709i
$646$	−204.657	+	354.476i	−0.316806	+	0.548724i
$647$	579.143	+	334.368i	0.895120	+	0.516798i	0.875614	−	0.483012i	$-0.160457\pi$
$647$	579.143	+	334.368i	0.895120	+	0.516798i	0.0195064	+	0.999810i	$0.493791\pi$
$648$	651.413	−	972.017i	1.00527	−	1.50003i
$649$		−	151.807i		−	0.233908i
$650$	555.375	+	2350.58i	0.854423	+	3.61628i
$651$	−19.6323	+	28.3450i	−0.0301571	+	0.0435408i
$652$	2198.38	+	589.054i	3.37175	+	0.903458i
$653$	514.190	+	890.603i	0.787427	+	1.36386i	0.927538	+	0.373728i	$0.121921\pi$
$653$	514.190	+	890.603i	0.787427	+	1.36386i	−0.140111	+	0.990136i	$0.544746\pi$
$654$	114.406	−	54.0622i	0.174933	−	0.0826639i
$655$	−408.785	−	109.534i	−0.624099	−	0.167227i
$656$	−927.794	−	248.602i	−1.41432	−	0.378966i
$657$	−762.938	+	74.6141i	−1.16125	+	0.113568i
$658$	−193.718	−	193.718i	−0.294405	−	0.294405i
$659$	−227.707	+	394.399i	−0.345533	+	0.598482i	−0.985451	−	0.169962i	$-0.945635\pi$
$659$	−227.707	+	394.399i	−0.345533	+	0.598482i	0.639917	+	0.768444i	$0.278969\pi$
$660$	−252.002	+	3060.48i	−0.381822	+	4.63709i
$661$	142.751	−	532.755i	0.215963	−	0.805984i	−0.769863	−	0.638210i	$-0.779675\pi$
$661$	142.751	−	532.755i	0.215963	−	0.805984i	0.985825	−	0.167774i	$-0.0536580\pi$
$662$	−747.885	−	431.792i	−1.12974	−	0.652253i
$663$	−339.379	−	38.1491i	−0.511884	−	0.0575401i
$664$	103.451	+	179.182i	0.155800	+	0.269853i
$665$	−53.9317	−	201.276i	−0.0811003	−	0.302670i
$666$	−406.293	−	1081.75i	−0.610050	−	1.62425i
$667$	598.995	−	345.830i	0.898043	−	0.518485i
$668$	361.254	+	96.7978i	0.540800	+	0.144907i
$669$	306.850	+	109.911i	0.458669	+	0.164292i
$670$	−1881.49	−	1881.49i	−2.80819	−	2.80819i
$671$	−471.806	+	126.420i	−0.703139	+	0.188406i
$672$	−21.6265	−	1.78075i	−0.0321823	−	0.00264992i
$673$			1041.60i			1.54770i	0.633370	+	0.773849i	$0.281671\pi$
$673$			1041.60i			1.54770i	−0.633370	+	0.773849i	$0.718329\pi$
$674$	−870.050	+	233.129i	−1.29088	+	0.345889i
$675$	−1384.51	+	393.825i	−2.05112	+	0.583445i
$676$	−1149.02	−	758.011i	−1.69974	−	1.12132i
$677$	−356.857	−	618.095i	−0.527115	−	0.912990i	−0.999501	−	0.0315983i	$-0.989940\pi$
$677$	−356.857	−	618.095i	−0.527115	−	0.912990i	0.472385	−	0.881392i	$-0.343393\pi$
$678$	−643.985	−	230.671i	−0.949830	−	0.340223i
$679$	165.471	+	286.605i	0.243699	+	0.422099i
$680$		−	1119.45i		−	1.64624i
$681$	−582.455	+	493.832i	−0.855293	+	0.725157i
$682$	−83.8569	−	312.958i	−0.122957	−	0.458883i
$683$	20.8652	−	77.8698i	0.0305493	−	0.114011i	−0.948968	−	0.315374i	$-0.897870\pi$
$683$	20.8652	−	77.8698i	0.0305493	−	0.114011i	0.979517	+	0.201362i	$0.0645368\pi$
$684$	−572.152	−	799.596i	−0.836479	−	1.16900i
$685$	845.534	+	1464.51i	1.23436	+	2.13797i
$686$		−	580.732i		−	0.846548i
$687$	−173.256	−	204.348i	−0.252192	−	0.297450i
$688$	209.106	+	120.727i	0.303933	+	0.175476i
$689$	−438.480	+	236.034i	−0.636400	+	0.342574i
$690$	−664.979	−	1407.23i	−0.963737	−	2.03946i
$691$	22.9345	−	22.9345i	0.0331903	−	0.0331903i	−0.690317	−	0.723507i	$-0.742529\pi$
$691$	22.9345	−	22.9345i	0.0331903	−	0.0331903i	0.723507	+	0.690317i	$0.242529\pi$
$692$	−167.743	+	290.539i	−0.242403	+	0.419854i
$693$	210.056	−	78.8948i	0.303111	−	0.113845i
$694$	1307.93	−	1307.93i	1.88463	−	1.88463i
$695$	98.3882	+	367.190i	0.141566	+	0.528330i
$696$	−600.849	+	1677.45i	−0.863289	+	2.41012i
$697$	−457.390	+	122.557i	−0.656227	+	0.175836i
$698$	1119.85			1.60436
$699$	141.964	−	67.0845i	0.203096	−	0.0959721i
$700$	539.059	+	539.059i	0.770085	+	0.770085i
$701$		−	1211.96i		−	1.72890i	−0.502723	−	0.864448i	$-0.667668\pi$
$701$		−	1211.96i		−	1.72890i	0.502723	−	0.864448i	$-0.332332\pi$
$702$	626.859	−	1050.40i	0.892961	−	1.49630i
$703$	−494.134			−0.702893
$704$	−569.292	+	569.292i	−0.808653	+	0.808653i
$705$	507.891	+	1074.80i	0.720413	+	1.52454i
$706$		−	1940.64i		−	2.74879i
$707$	−40.9326	−	152.763i	−0.0578962	−	0.216072i
$708$	−245.910	−	88.0832i	−0.347330	−	0.124411i
$709$	942.871	−	252.642i	1.32986	−	0.356335i	0.477198	−	0.878796i	$-0.341653\pi$
$709$	942.871	−	252.642i	1.32986	−	0.356335i	0.852663	+	0.522461i	$0.174986\pi$
$710$	2448.72	+	2448.72i	3.44890	+	3.44890i
$711$	−56.7720	−	9.41313i	−0.0798481	−	0.0132393i
$712$	−397.103	−	229.267i	−0.557728	−	0.322005i
$713$	77.8750	+	77.8750i	0.109222	+	0.109222i
$714$	−145.322	+	68.6709i	−0.203532	+	0.0961778i
$715$	−48.6501	+	1633.00i	−0.0680421	+	2.28392i
$716$	1227.96	−	2126.89i	1.71503	−	2.97051i
$717$	−595.472	+	504.869i	−0.830505	+	0.704141i
$718$	1833.42			2.55350
$719$	−583.567	+	336.922i	−0.811636	+	0.468598i	−0.847524	−	0.530757i	$-0.821908\pi$
$719$	−583.567	+	336.922i	−0.811636	+	0.468598i	0.0358874	+	0.999356i	$0.488574\pi$
$720$	1288.21	+	584.748i	1.78918	+	0.812149i
$721$	15.8033	+	4.23448i	0.0219186	+	0.00587307i
$722$	609.650	−	163.355i	0.844391	−	0.226254i
$723$	218.180	+	257.334i	0.301770	+	0.355926i
$724$	799.043			1.10365
$725$	1898.26	−	1095.96i	2.61829	−	1.51167i
$726$	−284.410	+	794.013i	−0.391749	+	1.09368i
$727$	867.103	−	500.622i	1.19271	−	0.688614i	0.233793	−	0.972286i	$-0.424886\pi$
$727$	867.103	−	500.622i	1.19271	−	0.688614i	0.958921	+	0.283673i	$0.0915529\pi$
$728$	−329.548	−	9.81782i	−0.452675	−	0.0134860i
$729$	642.212	+	344.972i	0.880949	+	0.473212i
$730$	−679.870	−	2537.31i	−0.931329	−	3.47577i
$731$	119.034			0.162837
$732$	−68.9710	+	837.628i	−0.0942227	+	1.14430i
$733$	366.667	+	1368.42i	0.500228	+	1.86688i	0.498522	+	0.866877i	$0.333876\pi$
$733$	366.667	+	1368.42i	0.500228	+	1.86688i	0.00170628	+	0.999999i	$0.499457\pi$
$734$	792.273	−	792.273i	1.07939	−	1.07939i
$735$	−411.076	+	1147.64i	−0.559287	+	1.56141i
$736$	−17.9389	+	66.9490i	−0.0243735	+	0.0909633i
$737$	−612.621	−	1061.09i	−0.831236	−	1.43974i
$738$	277.428	−	1673.21i	0.375919	−	2.26722i
$739$	−699.273	+	187.370i	−0.946243	+	0.253545i	−0.698767	−	0.715349i	$-0.746268\pi$
$739$	−699.273	+	187.370i	−0.946243	+	0.253545i	−0.247475	+	0.968894i	$0.579601\pi$
$740$	2299.76	−	1327.77i	3.10778	−	1.79428i
$741$	−326.244	−	408.878i	−0.440276	−	0.551793i
$742$	−117.182	+	202.965i	−0.157927	+	0.273537i
$743$	−224.468	−	60.1461i	−0.302111	−	0.0809503i	0.104579	−	0.994517i	$-0.466650\pi$
$743$	−224.468	−	60.1461i	−0.302111	−	0.0809503i	−0.406690	+	0.913566i	$0.633317\pi$
$744$	−282.758	−	23.2825i	−0.380051	−	0.0312937i
$745$	−369.106	−	213.103i	−0.495444	−	0.286045i
$746$	−414.360	+	414.360i	−0.555442	+	0.555442i
$747$	−104.831	+	75.0117i	−0.140336	+	0.100417i
$748$	262.159	−	978.390i	0.350480	−	1.30801i
$749$	−31.6313	+	118.050i	−0.0422314	+	0.157610i
$750$	−1119.15	−	2368.34i	−1.49220	−	3.15779i
$751$	−369.691	+	213.441i	−0.492264	+	0.284209i	−0.725513	−	0.688208i	$-0.758398\pi$
$751$	−369.691	+	213.441i	−0.492264	+	0.284209i	0.233249	+	0.972417i	$0.425064\pi$
$752$	205.857	−	768.270i	0.273746	−	1.02164i
$753$	−682.202	−	472.505i	−0.905978	−	0.627497i
$754$	−535.468	+	1784.08i	−0.710169	+	2.36615i
$755$	−1174.49			−1.55561
$756$	−5.91960	−	386.045i	−0.00783016	−	0.510641i
$757$	−328.020	+	568.148i	−0.433316	+	0.750525i	−0.997157	−	0.0753585i	$-0.975990\pi$
$757$	−328.020	+	568.148i	−0.433316	+	0.750525i	0.563841	+	0.825884i	$0.309323\pi$
$758$	−1682.96	−	971.658i	−2.22026	−	1.28187i
$759$	−128.059	−	705.165i	−0.168721	−	0.929071i
$760$	1212.41	−	1212.41i	1.59527	−	1.59527i
$761$	919.455	+	919.455i	1.20822	+	1.20822i	0.971603	+	0.236617i	$0.0760386\pi$
$761$	919.455	+	919.455i	1.20822	+	1.20822i	0.236617	+	0.971603i	$0.423961\pi$
$762$	−1064.24	−	1255.23i	−1.39664	−	1.64728i
$763$	10.6241	−	18.4014i	0.0139241	−	0.0241172i
$764$	−639.540	−	369.238i	−0.837094	−	0.483296i
$765$	694.125	−	67.8842i	0.907352	−	0.0887376i
$766$			1883.71i			2.45915i
$767$	−133.101	−	39.9486i	−0.173535	−	0.0520842i
$768$	665.483	+	1408.30i	0.866515	+	1.83372i
$769$	−1422.26	−	381.093i	−1.84949	−	0.495570i	−0.849980	−	0.526815i	$-0.823386\pi$
$769$	−1422.26	−	381.093i	−1.84949	−	0.495570i	−0.999512	+	0.0312447i	$0.990053\pi$
$770$	384.445	+	665.878i	0.499279	+	0.864777i
$771$	935.059	+	647.638i	1.21279	+	0.839998i
$772$	−160.569	−	43.0244i	−0.207991	−	0.0557311i
$773$	113.735	+	30.4751i	0.147134	+	0.0394244i	0.331634	−	0.943408i	$-0.392400\pi$
$773$	113.735	+	30.4751i	0.147134	+	0.0394244i	−0.184500	+	0.982832i	$0.559067\pi$
$774$	−176.225	+	388.227i	−0.227681	+	0.501585i
$775$	246.792	+	246.792i	0.318441	+	0.318441i
$776$	−1361.56	+	2358.30i	−1.75459	+	3.03904i
$777$	−159.513	−	110.481i	−0.205293	−	0.142190i
$778$	−131.370	+	490.279i	−0.168856	+	0.630179i
$779$	−628.107	−	362.638i	−0.806299	−	0.465517i
$780$	2617.06	+	1026.33i	3.35520	+	1.31581i
$781$	797.315	+	1380.99i	1.02089	+	1.76823i
$782$	132.874	+	495.891i	0.169915	+	0.634132i
$783$	−1076.55	−	270.841i	−1.37491	−	0.345902i
$784$	706.357	−	407.815i	0.900966	−	0.520173i
$785$	−690.679	−	185.067i	−0.879846	−	0.235754i
$786$	−381.365	+	323.339i	−0.485197	+	0.411373i
$787$	−82.6120	−	82.6120i	−0.104971	−	0.104971i	0.652671	−	0.757642i	$-0.273648\pi$
$787$	−82.6120	−	82.6120i	−0.104971	−	0.104971i	−0.757642	+	0.652671i	$0.773648\pi$
$788$	−2071.73	+	555.117i	−2.62909	+	0.704464i
$789$	82.1981	+	173.948i	0.104180	+	0.220466i
$790$		−	197.195i		−	0.249614i
$791$	−110.952	+	29.7295i	−0.140268	+	0.0375848i
$792$	1426.42	+	1172.27i	1.80103	+	1.48014i
$793$	−13.3151	+	446.940i	−0.0167908	+	0.563606i
$794$	−115.493	−	200.040i	−0.145458	−	0.251940i
$795$	775.675	−	657.653i	0.975691	−	0.827237i
$796$	−206.771	−	358.138i	−0.259762	−	0.449922i
$797$			725.326i			0.910071i	0.890473	+	0.455035i	$0.150373\pi$
$797$			725.326i			0.910071i	−0.890473	+	0.455035i	$0.849627\pi$
$798$	−231.762	−	83.0157i	−0.290429	−	0.104030i
$799$	−101.485	−	378.747i	−0.127015	−	0.474026i
$800$	−56.8498	+	212.166i	−0.0710623	+	0.265208i
$801$	118.079	−	260.131i	0.147414	−	0.324757i
$802$	−607.597	−	1052.39i	−0.757603	−	1.31221i
$803$		−	1209.58i		−	1.50633i
$804$	−2074.31	+	376.699i	−2.57999	+	0.468531i
$805$	−226.342	−	130.679i	−0.281170	−	0.162334i
$806$	−296.464	−	8.83218i	−0.367821	−	0.0109580i
$807$	−340.012	+	490.908i	−0.421328	+	0.608312i
$808$	920.181	−	920.181i	1.13884	−	1.13884i
$809$	54.6391	−	94.6376i	0.0675390	−	0.116981i	−0.830278	−	0.557349i	$-0.811819\pi$
$809$	54.6391	−	94.6376i	0.0675390	−	0.116981i	0.897817	+	0.440368i	$0.145152\pi$
$810$	−806.219	+	2364.37i	−0.995332	+	2.91898i
$811$	−585.721	+	585.721i	−0.722221	+	0.722221i	−0.969057	−	0.246837i	$-0.920609\pi$
$811$	−585.721	+	585.721i	−0.722221	+	0.722221i	0.246837	+	0.969057i	$0.420609\pi$
$812$	152.167	+	567.895i	0.187398	+	0.699378i
$813$	67.1367	+	79.1850i	0.0825790	+	0.0973985i
$814$	1761.18	−	471.908i	2.16362	−	0.579739i
$815$	−2472.72			−3.03401
$816$	−383.611	−	265.696i	−0.470111	−	0.325608i
$817$	128.919	+	128.919i	0.157795	+	0.157795i
$818$		−	1618.17i		−	1.97821i
$819$	−13.8964	−	204.935i	−0.0169675	−	0.250226i
$820$	3897.71			4.75330
$821$	88.4764	−	88.4764i	0.107767	−	0.107767i	−0.651167	−	0.758934i	$-0.725720\pi$
$821$	88.4764	−	88.4764i	0.107767	−	0.107767i	0.758934	+	0.651167i	$0.225720\pi$
$822$	1991.14	+	163.952i	2.42231	+	0.199455i
$823$		−	47.7619i		−	0.0580339i	−0.999579	−	0.0290169i	$-0.990762\pi$
$823$		−	47.7619i		−	0.0580339i	0.999579	−	0.0290169i	$-0.00923768\pi$
$824$	34.8430	+	130.036i	0.0422852	+	0.157811i
$825$	−405.829	−	2234.72i	−0.491914	−	2.70875i
$826$	−63.1742	+	16.9275i	−0.0764821	+	0.0204933i
$827$	423.155	+	423.155i	0.511674	+	0.511674i	0.915039	−	0.403365i	$-0.132160\pi$
$827$	423.155	+	423.155i	0.511674	+	0.511674i	−0.403365	+	0.915039i	$0.632160\pi$
$828$	−1216.59	−	201.719i	−1.46932	−	0.243621i
$829$	−839.134	−	484.474i	−1.01222	−	0.584408i	−0.100382	−	0.994949i	$-0.532006\pi$
$829$	−839.134	−	484.474i	−1.01222	−	0.584408i	−0.911842	+	0.410541i	$0.865340\pi$
$830$	−312.338	−	312.338i	−0.376311	−	0.376311i
$831$	−45.2848	+	549.967i	−0.0544943	+	0.661814i
$832$	349.333	+	648.957i	0.419872	+	0.779997i
$833$	201.048	−	348.225i	0.241354	−	0.418037i
$834$	422.807	+	151.446i	0.506963	+	0.181590i
$835$	−406.336			−0.486629
$836$	1343.56	−	775.707i	1.60713	−	0.927879i
$837$	−2.71011	−	176.739i	−0.00323788	−	0.211157i
$838$	2274.66	+	609.493i	2.71439	+	0.727318i
$839$	400.844	−	107.406i	0.477764	−	0.128016i	−0.0118974	−	0.999929i	$-0.503787\pi$
$839$	400.844	−	107.406i	0.477764	−	0.128016i	0.489661	+	0.871913i	$0.337120\pi$
$840$	662.457	−	120.303i	0.788639	−	0.143218i
$841$	849.432			1.01003
$842$	−1583.42	+	914.190i	−1.88055	+	1.08574i
$843$	1342.43	−	243.788i	1.59244	−	0.289191i
$844$	−468.686	+	270.596i	−0.555315	+	0.320611i
$845$	1418.99	+	472.388i	1.67927	+	0.559039i
$846$	1385.52	+	229.727i	1.63773	+	0.271545i
$847$	36.6556	+	136.801i	0.0432770	+	0.161512i
$848$	−680.415			−0.802376
$849$	−572.284	−	396.374i	−0.674068	−	0.466871i
$850$	421.086	+	1571.52i	0.495396	+	1.84884i
$851$	−438.244	+	438.244i	−0.514976	+	0.514976i
$852$	2699.68	−	490.266i	3.16864	−	0.575430i
$853$	−263.235	+	982.405i	−0.308598	+	1.15171i	0.621205	+	0.783648i	$0.286644\pi$
$853$	−263.235	+	982.405i	−0.308598	+	1.15171i	−0.929803	+	0.368057i	$0.880023\pi$
$854$	105.219	+	182.245i	0.123208	+	0.213402i
$855$	825.286	+	678.244i	0.965247	+	0.793267i
$856$	−971.359	+	260.275i	−1.13477	+	0.304059i
$857$	277.234	−	160.061i	0.323493	−	0.186769i	−0.329455	−	0.944171i	$-0.606865\pi$
$857$	277.234	−	160.061i	0.323493	−	0.186769i	0.652948	+	0.757402i	$0.273532\pi$
$858$	1553.28	+	1145.75i	1.81035	+	1.33537i
$859$	826.114	−	1430.87i	0.961716	−	1.66574i	0.243526	−	0.969894i	$-0.421696\pi$
$859$	826.114	−	1430.87i	0.961716	−	1.66574i	0.718190	−	0.695847i	$-0.244971\pi$
$860$	−946.414	−	253.591i	−1.10048	−	0.294873i
$861$	−121.680	−	257.500i	−0.141324	−	0.299071i
$862$	−1866.01	−	1077.34i	−2.16474	−	1.24981i
$863$	279.041	−	279.041i	0.323339	−	0.323339i	−0.526708	−	0.850046i	$-0.676574\pi$
$863$	279.041	−	279.041i	0.323339	−	0.323339i	0.850046	+	0.526708i	$0.176574\pi$
$864$	95.4746	−	57.0918i	0.110503	−	0.0660784i
$865$	94.3377	−	352.073i	0.109061	−	0.407021i
$866$	−437.853	+	1634.09i	−0.505604	+	1.88694i
$867$	634.805	+	52.2704i	0.732186	+	0.0602888i
$868$	−81.0728	+	46.8074i	−0.0934018	+	0.0539256i
$869$	23.5017	−	87.7094i	0.0270445	−	0.100931i
$870$	312.165	−	3791.13i	0.358810	−	4.35762i
$871$	−1091.56	+	257.904i	−1.25323	+	0.296101i
$872$	174.838			0.200502
$873$	−1544.85	−	701.243i	−1.76959	−	0.803257i
$874$	−393.162	+	680.977i	−0.449843	+	0.779150i
$875$	−380.929	−	219.930i	−0.435348	−	0.251348i
$876$	−1959.39	−	701.840i	−2.23675	−	0.801188i
$877$	−492.259	+	492.259i	−0.561299	+	0.561299i	−0.929676	−	0.368377i	$-0.879913\pi$
$877$	−492.259	+	492.259i	−0.561299	+	0.561299i	0.368377	+	0.929676i	$0.379913\pi$
$878$	307.792	+	307.792i	0.350560	+	0.350560i
$879$	−197.972	+	552.697i	−0.225224	+	0.628780i
$880$	−1116.14	+	1933.21i	−1.26834	+	2.19683i
$881$	−108.150	−	62.4404i	−0.122758	−	0.0708745i	0.437363	−	0.899285i	$-0.355912\pi$
$881$	−108.150	−	62.4404i	−0.122758	−	0.0708745i	−0.560122	+	0.828410i	$0.689246\pi$
$882$	838.086	+	1171.24i	0.950211	+	1.32794i
$883$			511.184i			0.578917i	0.957191	+	0.289459i	$0.0934752\pi$
$883$			511.184i			0.578917i	−0.957191	+	0.289459i	$0.906525\pi$
$884$	−788.847	−	487.324i	−0.892361	−	0.551272i
$885$	282.838	+	23.2891i	0.319591	+	0.0263154i
$886$	2068.62	+	554.286i	2.33479	+	0.625605i
$887$	162.087	+	280.743i	0.182736	+	0.316509i	0.942811	−	0.333327i	$-0.108171\pi$
$887$	162.087	+	280.743i	0.182736	+	0.316509i	−0.760075	+	0.649835i	$0.774838\pi$
$888$	131.023	−	1591.23i	0.147549	−	1.79193i
$889$	−266.925	−	71.5223i	−0.300253	−	0.0804525i
$890$	945.563	+	253.363i	1.06243	+	0.284677i
$891$	−640.379	+	955.552i	−0.718719	+	1.07245i
$892$	625.751	+	625.751i	0.701514	+	0.701514i
$893$	300.286	−	520.110i	0.336266	−	0.582430i
$894$	−455.263	+	215.132i	−0.509242	+	0.240640i
$895$	−690.599	+	2577.35i	−0.771619	+	2.87972i
$896$	325.447	+	187.897i	0.363222	+	0.209707i
$897$	−651.976	−	73.2876i	−0.726841	−	0.0817030i
$898$	−938.937	−	1626.29i	−1.04559	−	1.81101i
$899$	69.6649	+	259.993i	0.0774916	+	0.289203i
$900$	−3855.48	−	639.262i	−4.28387	−	0.710291i
$901$	−290.496	+	167.718i	−0.322415	+	0.186146i
$902$	2585.01	+	692.652i	2.86587	+	0.767907i
$903$	12.7922	+	70.4410i	0.0141663	+	0.0780077i
$904$	−668.332	−	668.332i	−0.739305	−	0.739305i
$905$	−838.552	+	224.689i	−0.926576	+	0.248275i
$906$	−790.061	+	1140.69i	−0.872032	+	1.25904i
$907$		−	234.115i		−	0.258120i	−0.991637	−	0.129060i	$-0.958804\pi$
$907$		−	234.115i		−	0.258120i	0.991637	−	0.129060i	$-0.0411960\pi$
$908$	−2002.63	+	536.604i	−2.20554	+	0.590974i
$909$	626.369	+	514.767i	0.689074	+	0.566301i
$910$	684.999	−	161.846i	0.752746	−	0.177852i
$911$	240.121	+	415.901i	0.263579	+	0.456533i	0.967190	−	0.254053i	$-0.0817636\pi$
$911$	240.121	+	415.901i	0.263579	+	0.456533i	−0.703611	+	0.710585i	$0.748430\pi$
$912$	−127.707	−	703.225i	−0.140029	−	0.771080i
$913$	−101.699	−	176.147i	−0.111390	−	0.192932i
$914$		−	844.709i		−	0.924190i
$915$	−163.158	−	898.438i	−0.178315	−	0.981900i
$916$	−188.262	−	702.605i	−0.205527	−	0.767035i
$917$	−21.7300	+	81.0973i	−0.0236968	+	0.0884376i
$918$	400.997	−	719.814i	0.436816	−	0.784111i
$919$	−803.073	−	1390.96i	−0.873855	−	1.51356i	−0.857977	−	0.513687i	$-0.828279\pi$
$919$	−803.073	−	1390.96i	−0.873855	−	1.51356i	−0.0158776	−	0.999874i	$-0.505054\pi$
$920$		−	2150.55i		−	2.33755i
$921$	−257.322	+	718.390i	−0.279394	+	0.780011i
$922$	717.491	+	414.244i	0.778190	+	0.449288i
$923$	1420.64	−	335.658i	1.53916	−	0.363659i
$924$	607.157	+	49.9938i	0.657096	+	0.0541059i
$925$	−1388.83	+	1388.83i	−1.50144	+	1.50144i
$926$	778.309	−	1348.07i	0.840506	−	1.45580i
$927$	−78.5172	+	29.4903i	−0.0847004	+	0.0318126i
$928$	−119.782	+	119.782i	−0.129075	+	0.129075i
$929$	58.9487	+	219.999i	0.0634539	+	0.236813i	0.990368	−	0.138461i	$-0.0442154\pi$
$929$	58.9487	+	219.999i	0.0634539	+	0.236813i	−0.926914	+	0.375274i	$0.877549\pi$
$930$	595.951	−	108.226i	0.640808	−	0.116372i
$931$	594.884	−	159.399i	0.638973	−	0.171212i
$932$	426.308			0.457412
$933$	108.009	−	1311.72i	0.115765	−	1.40592i
$934$	297.353	+	297.353i	0.318365	+	0.318365i
$935$			1100.48i			1.17699i
$936$	1403.19	−	942.168i	1.49914	−	1.00659i
$937$	−48.4170			−0.0516723			−0.0258362	−	0.999666i	$-0.508225\pi$
$937$	−48.4170			−0.0516723			−0.0258362	+	0.999666i	$0.508225\pi$
$938$	−373.261	+	373.261i	−0.397933	+	0.397933i
$939$	−504.887	+	728.955i	−0.537686	+	0.776310i
$940$			3227.54i			3.43355i
$941$	−192.305	−	717.693i	−0.204363	−	0.762692i	−0.989643	−	0.143551i	$-0.954148\pi$
$941$	−192.305	−	717.693i	−0.204363	−	0.762692i	0.785280	−	0.619141i	$-0.212519\pi$
$942$	−644.351	+	546.311i	−0.684024	+	0.579948i
$943$	−878.685	+	235.443i	−0.931797	+	0.249674i
$944$	−134.266	−	134.266i	−0.142231	−	0.142231i
$945$	114.767	+	403.468i	0.121447	+	0.426950i
$946$	−582.610	−	336.370i	−0.615866	−	0.355571i
$947$	1078.80	+	1078.80i	1.13918	+	1.13918i	0.988598	+	0.150582i	$0.0481146\pi$
$947$	1078.80	+	1078.80i	1.13918	+	1.13918i	0.150582	+	0.988598i	$0.451885\pi$
$948$	−128.443	−	88.9620i	−0.135489	−	0.0938418i
$949$	−1060.54	−	318.308i	−1.11754	−	0.335414i
$950$	−1245.96	+	2158.07i	−1.31154	+	2.27165i
$951$	−6.21518	−	34.2242i	−0.00653541	−	0.0359876i
$952$	−222.083			−0.233280
$953$	776.026	−	448.039i	0.814298	−	0.470135i	−0.0341484	−	0.999417i	$-0.510872\pi$
$953$	776.026	−	448.039i	0.814298	−	0.470135i	0.848446	+	0.529282i	$0.177539\pi$
$954$	−116.942	−	1195.75i	−0.122581	−	1.25340i
$955$	774.991	+	207.658i	0.811509	+	0.217443i
$956$	−2047.39	+	548.597i	−2.14162	+	0.573846i
$957$	590.672	−	1649.03i	0.617212	−	1.72313i
$958$	−2177.84			−2.27332
$959$	290.538	−	167.742i	0.302959	−	0.174914i
$960$	−973.337	−	1148.01i	−1.01389	−	1.19584i
$961$	795.134	−	459.071i	0.827402	−	0.477701i
$962$	49.7034	−	1668.36i	0.0516668	−	1.73426i
$963$	−220.290	−	586.518i	−0.228754	−	0.609053i
$964$	237.077	+	884.784i	0.245931	+	0.917826i
$965$	180.607			0.187157
$966$	−279.175	+	131.923i	−0.289001	+	0.136566i
$967$	−428.403	−	1598.82i	−0.443023	−	1.65338i	−0.721105	−	0.692826i	$-0.756365\pi$
$967$	−428.403	−	1598.82i	−0.443023	−	1.65338i	0.278082	−	0.960557i	$-0.410301\pi$
$968$	−824.032	+	824.032i	−0.851273	+	0.851273i
$969$	−227.863	−	268.755i	−0.235153	−	0.277353i
$970$	1504.66	−	5615.48i	1.55120	−	5.78915i
$971$	539.004	+	933.583i	0.555102	+	0.961465i	0.997896	+	0.0648416i	$0.0206542\pi$
$971$	539.004	+	933.583i	0.555102	+	0.961465i	−0.442793	+	0.896624i	$0.646012\pi$
$972$	1176.32	+	1591.79i	1.21021	+	1.63764i
$973$	72.8454	−	19.5189i	0.0748668	−	0.0200605i
$974$	337.527	−	194.872i	0.346537	−	0.200073i
$975$	−2066.16	−	232.254i	−2.11914	−	0.238209i
$976$	−305.478	+	529.104i	−0.312990	+	0.542114i
$977$	1151.61	+	308.572i	1.17872	+	0.315836i	0.794417	−	0.607373i	$-0.207777\pi$
$977$	1151.61	+	308.572i	1.17872	+	0.315836i	0.384299	+	0.923209i	$0.374443\pi$
$978$	−1663.36	+	2401.56i	−1.70078	+	2.45558i
$979$	390.376	+	225.384i	0.398750	+	0.230218i
$980$	−2340.35	+	2340.35i	−2.38811	+	2.38811i
$981$	10.6023	+	108.410i	0.0108077	+	0.110510i
$982$	−315.553	+	1177.66i	−0.321337	+	1.19924i
$983$	314.896	−	1175.21i	0.320342	−	1.19553i	−0.598571	−	0.801070i	$-0.704264\pi$
$983$	314.896	−	1175.21i	0.320342	−	1.19553i	0.918912	−	0.394461i	$-0.129069\pi$
$984$	1334.33	−	1926.50i	1.35602	−	1.95782i
$985$	2018.06	−	1165.13i	2.04880	−	1.18287i
$986$	−324.746	+	1211.97i	−0.329357	+	1.22918i
$987$	213.225	−	100.759i	0.216034	−	0.102086i
$988$	−326.561	−	1382.14i	−0.330527	−	1.39893i
$989$	228.674			0.231218
$990$	−3589.21	−	1629.22i	−3.62546	−	1.64568i
$991$	167.362	−	289.880i	0.168882	−	0.292513i	−0.769145	−	0.639075i	$-0.779318\pi$
$991$	167.362	−	289.880i	0.168882	−	0.292513i	0.938027	+	0.346562i	$0.112651\pi$
$992$	−23.3591	−	13.4864i	−0.0235475	−	0.0135952i
$993$	567.030	−	480.754i	0.571027	−	0.484143i
$994$	485.792	−	485.792i	0.488724	−	0.488724i
$995$	317.702	+	317.702i	0.319299	+	0.319299i
$996$	−344.348	+	62.5342i	−0.345731	+	0.0627853i
$997$	423.182	−	732.973i	0.424455	−	0.735178i	−0.571914	−	0.820314i	$-0.693799\pi$
$997$	423.182	−	732.973i	0.424455	−	0.735178i	0.996369	+	0.0851352i	$0.0271322\pi$
$998$	2036.21	+	1175.61i	2.04029	+	1.17796i
$999$	994.605	−	15.2512i	0.995600	−	0.0152665i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	117.3.w.a.58.3	✓	104
3.2	odd	2		351.3.z.a.253.24		104
9.2	odd	6		351.3.be.a.19.3		104
9.7	even	3		117.3.bb.a.97.24	yes	104
13.11	odd	12		117.3.bb.a.76.24	yes	104
39.11	even	12		351.3.be.a.37.3		104
117.11	even	12		351.3.z.a.154.24		104
117.115	odd	12	inner	117.3.w.a.115.3	yes	104

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
117.3.w.a.58.3	✓	104	1.1	even	1	trivial
117.3.w.a.115.3	yes	104	117.115	odd	12	inner
117.3.bb.a.76.24	yes	104	13.11	odd	12
117.3.bb.a.97.24	yes	104	9.7	even	3
351.3.z.a.154.24		104	117.11	even	12
351.3.z.a.253.24		104	3.2	odd	2
351.3.be.a.19.3		104	9.2	odd	6
351.3.be.a.37.3		104	39.11	even	12

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:	\( N \)	\(=\)	\( 117 = 3^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	117.w (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.46426 + 2.46426i) q^{2} +(-1.28173 - 2.71241i) q^{3} -8.14515i q^{4} +(2.29040 + 8.54788i) q^{5} +(9.84260 + 3.52555i) q^{6} +(1.69578 - 0.454383i) q^{7} +(10.2147 + 10.2147i) q^{8} +(-5.71431 + 6.95317i) q^{9} +(-26.7083 - 15.4201i) q^{10} +(-10.0417 - 10.0417i) q^{11} +(-22.0930 + 10.4399i) q^{12} +(-11.4469 + 6.16186i) q^{13} +(-3.05913 + 5.29856i) q^{14} +(20.2497 - 17.1686i) q^{15} -17.7628 q^{16} +(-7.58364 + 4.37842i) q^{17} +(-3.05287 - 31.2160i) q^{18} +(-12.9554 - 3.47139i) q^{19} +(69.6237 - 18.6556i) q^{20} +(-3.40601 - 4.01725i) q^{21} +49.4907 q^{22} +(-14.5688 + 8.41131i) q^{23} +(14.6139 - 40.7990i) q^{24} +(-46.1697 + 26.6561i) q^{25} +(13.0237 - 43.3925i) q^{26} +(26.1841 + 6.58743i) q^{27} +(-3.70102 - 13.8124i) q^{28} -41.1149 q^{29} +(-7.59251 + 92.2083i) q^{30} +(-1.69440 - 6.32358i) q^{31} +(2.91334 - 2.91334i) q^{32} +(-14.3664 + 40.1079i) q^{33} +(7.89851 - 29.4776i) q^{34} +(7.76803 + 13.4546i) q^{35} +(56.6346 + 46.5439i) q^{36} +(35.5862 - 9.53529i) q^{37} +(40.4799 - 23.3711i) q^{38} +(31.3854 + 23.1508i) q^{39} +(-63.9184 + 110.710i) q^{40} +(52.2324 + 13.9956i) q^{41} +(18.2929 + 1.50625i) q^{42} +(-11.7721 - 6.79663i) q^{43} +(-81.7910 + 81.7910i) q^{44} +(-72.5229 - 32.9197i) q^{45} +(15.1737 - 56.6290i) q^{46} +(-11.5892 + 43.2515i) q^{47} +(22.7672 + 48.1800i) q^{48} +(-39.7660 + 22.9589i) q^{49} +(48.0866 - 179.462i) q^{50} +(21.5963 + 14.9580i) q^{51} +(50.1893 + 93.2367i) q^{52} +38.3056 q^{53} +(-80.7575 + 48.2912i) q^{54} +(62.8357 - 108.835i) q^{55} +(21.9633 + 12.6805i) q^{56} +(7.18956 + 39.5897i) q^{57} +(101.318 - 101.318i) q^{58} +(7.55881 + 7.55881i) q^{59} +(-139.841 - 164.936i) q^{60} +(17.1976 - 29.7871i) q^{61} +(19.7584 + 11.4075i) q^{62} +(-6.53082 + 14.3876i) q^{63} -56.6928i q^{64} +(-78.8888 - 83.7336i) q^{65} +(-63.4339 - 134.239i) q^{66} +(83.3381 + 22.3304i) q^{67} +(35.6629 + 61.7699i) q^{68} +(41.4883 + 28.7355i) q^{69} +(-52.2981 - 14.0132i) q^{70} +(-108.463 - 29.0626i) q^{71} +(-129.395 + 12.6546i) q^{72} +(60.2281 + 60.2281i) q^{73} +(-64.1962 + 111.191i) q^{74} +(131.479 + 91.0650i) q^{75} +(-28.2750 + 105.524i) q^{76} +(-21.5913 - 12.4657i) q^{77} +(-134.391 + 20.2921i) q^{78} +(3.19706 + 5.53747i) q^{79} +(-40.6839 - 151.834i) q^{80} +(-15.6932 - 79.4652i) q^{81} +(-163.203 + 94.2252i) q^{82} +(13.8346 + 3.70698i) q^{83} +(-32.7211 + 27.7425i) q^{84} +(-54.7958 - 54.7958i) q^{85} +(45.7582 - 12.2609i) q^{86} +(52.6983 + 111.520i) q^{87} -205.146i q^{88} +(-30.6602 + 8.21537i) q^{89} +(259.838 - 97.5925i) q^{90} +(-16.6116 + 15.6505i) q^{91} +(68.5113 + 118.665i) q^{92} +(-14.9804 + 12.7010i) q^{93} +(-78.0242 - 135.142i) q^{94} -118.692i q^{95} +(-11.6363 - 4.16804i) q^{96} +(48.7891 + 182.084i) q^{97} +(41.4171 - 154.571i) q^{98} +(127.203 - 12.4402i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 104 q - 2 q^{2} - 2 q^{3} - 2 q^{5} - 32 q^{6} + 18 q^{8} - 2 q^{9} - 12 q^{10} + 22 q^{11} + 54 q^{12} - 2 q^{13} - 4 q^{14} + 70 q^{15} - 324 q^{16} - 12 q^{17} - 86 q^{18} - 36 q^{19} + 134 q^{20} - 32 q^{21}+ \cdots + 940 q^{99}+O(q^{100}) \) 104 * q - 2 * q^2 - 2 * q^3 - 2 * q^5 - 32 * q^6 + 18 * q^8 - 2 * q^9 - 12 * q^10 + 22 * q^11 + 54 * q^12 - 2 * q^13 - 4 * q^14 + 70 * q^15 - 324 * q^16 - 12 * q^17 - 86 * q^18 - 36 * q^19 + 134 * q^20 - 32 * q^21 - 4 * q^22 - 6 * q^23 + 30 * q^24 + 52 * q^26 + 4 * q^27 + 56 * q^28 - 148 * q^29 - 246 * q^30 + 62 * q^31 + 70 * q^32 + 52 * q^33 - 18 * q^34 - 106 * q^35 + 96 * q^36 + 14 * q^37 + 216 * q^38 + 118 * q^39 - 36 * q^40 - 26 * q^41 + 278 * q^42 - 198 * q^43 + 496 * q^44 - 80 * q^45 - 8 * q^47 + 58 * q^48 - 6 * q^49 - 292 * q^50 + 28 * q^52 - 208 * q^53 + 58 * q^54 - 4 * q^55 + 186 * q^56 - 140 * q^57 + 146 * q^58 - 434 * q^59 + 140 * q^60 + 2 * q^61 - 282 * q^62 - 266 * q^63 - 260 * q^65 - 412 * q^66 + 138 * q^67 + 534 * q^68 - 294 * q^69 + 212 * q^70 - 8 * q^71 - 306 * q^72 + 90 * q^73 - 178 * q^74 - 60 * q^75 - 98 * q^76 - 432 * q^77 + 352 * q^78 - 16 * q^79 - 278 * q^80 - 230 * q^81 - 12 * q^82 - 50 * q^83 + 1066 * q^84 + 204 * q^85 + 330 * q^86 - 154 * q^87 + 400 * q^89 - 798 * q^90 + 120 * q^91 + 48 * q^92 - 128 * q^93 + 122 * q^94 + 958 * q^96 - 232 * q^97 + 280 * q^98 + 940 * q^99

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