LMFDB - Embedded newform 896.2.bn.b.29.34

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(29,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(32))

chi = DirichletCharacter(H, H._module([0, 27, 0]))

N = Newforms(chi, 2, names="a")

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

chi := DirichletCharacter("896.29");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.bn (of order $32$, degree $16$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$784$
Relative dimension:	$49$ over $\Q(\zeta_{32})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{32}]$

Embedding invariants

Embedding label			29.34
Character	$\chi$	$=$	896.29
Dual form			896.2.bn.b.309.34

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.688362 + 1.23538i) q^{2} +(-0.129665 + 1.31651i) q^{3} +(-1.05232 + 1.70077i) q^{4} +(-3.05765 + 1.63435i) q^{5} +(-1.71564 + 0.746048i) q^{6} +(0.195090 + 0.980785i) q^{7} +(-2.82547 - 0.129259i) q^{8} +(1.22598 + 0.243862i) q^{9} +O(q^{10})$	\(q+(0.688362 + 1.23538i) q^{2} +(-0.129665 + 1.31651i) q^{3} +(-1.05232 + 1.70077i) q^{4} +(-3.05765 + 1.63435i) q^{5} +(-1.71564 + 0.746048i) q^{6} +(0.195090 + 0.980785i) q^{7} +(-2.82547 - 0.129259i) q^{8} +(1.22598 + 0.243862i) q^{9} +(-4.12380 - 2.65233i) q^{10} +(-0.963388 + 1.17389i) q^{11} +(-2.10263 - 1.60591i) q^{12} +(-1.86830 + 3.49535i) q^{13} +(-1.07735 + 0.916146i) q^{14} +(-1.75516 - 4.23733i) q^{15} +(-1.78526 - 3.57950i) q^{16} +(1.60630 - 3.87794i) q^{17} +(0.542655 + 1.68241i) q^{18} +(0.345129 + 1.13774i) q^{19} +(0.437956 - 6.92021i) q^{20} +(-1.31651 + 0.129665i) q^{21} +(-2.11336 - 0.382085i) q^{22} +(4.01616 - 2.68351i) q^{23} +(0.536534 - 3.70299i) q^{24} +(3.90026 - 5.83716i) q^{25} +(-5.60415 + 0.0980058i) q^{26} +(-1.63205 + 5.38013i) q^{27} +(-1.87339 - 0.700291i) q^{28} +(0.526713 - 0.432262i) q^{29} +(4.02652 - 5.08510i) q^{30} +(-1.11556 + 1.11556i) q^{31} +(3.19313 - 4.66947i) q^{32} +(-1.42052 - 1.42052i) q^{33} +(5.89644 - 0.685046i) q^{34} +(-2.19946 - 2.68005i) q^{35} +(-1.70487 + 1.82849i) q^{36} +(-4.15888 - 1.26158i) q^{37} +(-1.16796 + 1.20954i) q^{38} +(-4.35940 - 2.91286i) q^{39} +(8.85055 - 4.22257i) q^{40} +(3.74232 + 5.60078i) q^{41} +(-1.06642 - 1.53713i) q^{42} +(-0.289942 - 2.94383i) q^{43} +(-0.982736 - 2.87381i) q^{44} +(-4.14717 + 1.25803i) q^{45} +(6.07973 + 3.11425i) q^{46} +(-1.19007 - 0.492941i) q^{47} +(4.94392 - 1.88618i) q^{48} +(-0.923880 + 0.382683i) q^{49} +(9.89589 + 0.800221i) q^{50} +(4.89706 + 2.61753i) q^{51} +(-3.97876 - 6.85577i) q^{52} +(-1.06602 - 0.874857i) q^{53} +(-7.76993 + 1.68729i) q^{54} +(1.02715 - 5.16385i) q^{55} +(-0.424447 - 2.79640i) q^{56} +(-1.54259 + 0.306840i) q^{57} +(0.896576 + 0.353137i) q^{58} +(-0.510343 - 0.954784i) q^{59} +(9.05372 + 1.47388i) q^{60} +(-9.27141 - 0.913154i) q^{61} +(-2.14605 - 0.610229i) q^{62} +1.25000i q^{63} +(7.96658 + 0.730435i) q^{64} -13.7410i q^{65} +(0.777046 - 2.73271i) q^{66} +(4.43942 + 0.437245i) q^{67} +(4.90517 + 6.81277i) q^{68} +(3.01211 + 5.63526i) q^{69} +(1.79685 - 4.56201i) q^{70} +(3.56609 - 0.709340i) q^{71} +(-3.43245 - 0.847495i) q^{72} +(-1.87431 + 9.42282i) q^{73} +(-1.30429 - 6.00622i) q^{74} +(7.17893 + 5.89160i) q^{75} +(-2.29822 - 0.610273i) q^{76} +(-1.33928 - 0.715862i) q^{77} +(0.597634 - 7.39060i) q^{78} +(-11.4219 + 4.73111i) q^{79} +(11.3089 + 8.02711i) q^{80} +(-3.40682 - 1.41115i) q^{81} +(-4.34300 + 8.47854i) q^{82} +(12.2310 - 3.71025i) q^{83} +(1.16485 - 2.37553i) q^{84} +(1.42641 + 14.4826i) q^{85} +(3.43715 - 2.38461i) q^{86} +(0.500780 + 0.749470i) q^{87} +(2.87376 - 3.19227i) q^{88} +(-11.8264 - 7.90214i) q^{89} +(-4.40889 - 4.25734i) q^{90} +(-3.79268 - 1.15050i) q^{91} +(0.337781 + 9.65449i) q^{92} +(-1.32399 - 1.61329i) q^{93} +(-0.210227 - 1.80950i) q^{94} +(-2.91474 - 2.91474i) q^{95} +(5.73335 + 4.80924i) q^{96} +(-5.53704 + 5.53704i) q^{97} +(-1.10872 - 0.877915i) q^{98} +(-1.46736 + 1.20423i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 784 q+O(q^{10}) $ 784 * q	$ 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) $ 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$1$	$1$	$e\left(\frac{27}{32}\right)$

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 $

$2$	0.688362	+	1.23538i	0.486745	+	0.873544i
$2$	0.688362	+	1.23538i	0.486745	+	0.873544i
$3$	−0.129665	+	1.31651i	−0.0748619	+	0.760086i	0.882330	+	0.470631i	$0.155974\pi$
$3$	−0.129665	+	1.31651i	−0.0748619	+	0.760086i	−0.957192	+	0.289454i	$0.906526\pi$
$4$	−1.05232	+	1.70077i	−0.526158	+	0.850387i
$5$	−3.05765	+	1.63435i	−1.36742	+	0.730902i	−0.981470	−	0.191617i	$-0.938627\pi$
$5$	−3.05765	+	1.63435i	−1.36742	+	0.730902i	−0.385951	+	0.922519i	$0.626127\pi$
$6$	−1.71564	+	0.746048i	−0.700407	+	0.304573i
$7$	0.195090	+	0.980785i	0.0737372	+	0.370702i
$7$	0.195090	+	0.980785i	0.0737372	+	0.370702i
$8$	−2.82547	−	0.129259i	−0.998955	−	0.0456999i
$9$	1.22598	+	0.243862i	0.408660	+	0.0812874i
$10$	−4.12380	−	2.65233i	−1.30406	−	0.838739i
$11$	−0.963388	+	1.17389i	−0.290472	+	0.353942i	−0.897716	−	0.440574i	$-0.854775\pi$
$11$	−0.963388	+	1.17389i	−0.290472	+	0.353942i	0.607244	+	0.794515i	$0.292275\pi$
$12$	−2.10263	−	1.60591i	−0.606978	−	0.463586i
$13$	−1.86830	+	3.49535i	−0.518174	+	0.969436i	0.477685	+	0.878531i	$0.341476\pi$
$13$	−1.86830	+	3.49535i	−0.518174	+	0.969436i	−0.995860	+	0.0909047i	$0.971024\pi$
$14$	−1.07735	+	0.916146i	−0.287933	+	0.244850i
$15$	−1.75516	−	4.23733i	−0.453180	−	1.09407i
$16$	−1.78526	−	3.57950i	−0.446316	−	0.894875i
$17$	1.60630	−	3.87794i	0.389584	−	0.940539i	−0.600444	−	0.799667i	$-0.705009\pi$
$17$	1.60630	−	3.87794i	0.389584	−	0.940539i	0.990028	−	0.140872i	$-0.0449906\pi$
$18$	0.542655	+	1.68241i	0.127905	+	0.396548i
$19$	0.345129	+	1.13774i	0.0791780	+	0.261015i	0.987588	−	0.157065i	$-0.0502032\pi$
$19$	0.345129	+	1.13774i	0.0791780	+	0.261015i	−0.908410	+	0.418080i	$0.862703\pi$
$20$	0.437956	−	6.92021i	0.0979299	−	1.54741i
$21$	−1.31651	+	0.129665i	−0.287285	+	0.0282951i
$22$	−2.11336	−	0.382085i	−0.450570	−	0.0814609i
$23$	4.01616	−	2.68351i	0.837428	−	0.559552i	−0.0612691	−	0.998121i	$-0.519515\pi$
$23$	4.01616	−	2.68351i	0.837428	−	0.559552i	0.898697	+	0.438570i	$0.144515\pi$
$24$	0.536534	−	3.70299i	0.109520	−	0.755870i
$25$	3.90026	−	5.83716i	0.780053	−	1.16743i
$26$	−5.60415	+	0.0980058i	−1.09906	+	0.0192205i
$27$	−1.63205	+	5.38013i	−0.314087	+	1.03541i
$28$	−1.87339	−	0.700291i	−0.354038	−	0.132343i
$29$	0.526713	−	0.432262i	0.0978081	−	0.0802691i	−0.584218	−	0.811596i	$-0.698599\pi$
$29$	0.526713	−	0.432262i	0.0978081	−	0.0802691i	0.682027	+	0.731327i	$0.261099\pi$
$30$	4.02652	−	5.08510i	0.735138	−	0.928408i
$31$	−1.11556	+	1.11556i	−0.200360	+	0.200360i	−0.800154	−	0.599794i	$-0.795249\pi$
$31$	−1.11556	+	1.11556i	−0.200360	+	0.200360i	0.599794	+	0.800154i	$0.295249\pi$
$32$	3.19313	−	4.66947i	0.564471	−	0.825453i
$33$	−1.42052	−	1.42052i	−0.247281	−	0.247281i
$34$	5.89644	−	0.685046i	1.01123	−	0.117484i
$35$	−2.19946	−	2.68005i	−0.371777	−	0.453011i
$36$	−1.70487	+	1.82849i	−0.284145	+	0.304749i
$37$	−4.15888	−	1.26158i	−0.683716	−	0.207403i	−0.0707287	−	0.997496i	$-0.522532\pi$
$37$	−4.15888	−	1.26158i	−0.683716	−	0.207403i	−0.612988	+	0.790092i	$0.710032\pi$
$38$	−1.16796	+	1.20954i	−0.189468	+	0.196213i
$39$	−4.35940	−	2.91286i	−0.698062	−	0.466430i
$40$	8.85055	−	4.22257i	1.39939	−	0.667647i
$41$	3.74232	+	5.60078i	0.584452	+	0.874695i	0.999382	−	0.0351590i	$-0.0111938\pi$
$41$	3.74232	+	5.60078i	0.584452	+	0.874695i	−0.414930	+	0.909854i	$0.636194\pi$
$42$	−1.06642	−	1.53713i	−0.164552	−	0.237184i
$43$	−0.289942	−	2.94383i	−0.0442157	−	0.448929i	−0.991648	−	0.128973i	$-0.958832\pi$
$43$	−0.289942	−	2.94383i	−0.0442157	−	0.448929i	0.947432	−	0.319956i	$-0.103668\pi$
$44$	−0.982736	−	2.87381i	−0.148153	−	0.433243i
$45$	−4.14717	+	1.25803i	−0.618223	+	0.187536i
$46$	6.07973	+	3.11425i	0.896407	+	0.459171i
$47$	−1.19007	−	0.492941i	−0.173589	−	0.0719029i	0.294197	−	0.955745i	$-0.404948\pi$
$47$	−1.19007	−	0.492941i	−0.173589	−	0.0719029i	−0.467785	+	0.883842i	$0.654948\pi$
$48$	4.94392	−	1.88618i	0.713594	−	0.272246i
$49$	−0.923880	+	0.382683i	−0.131983	+	0.0546691i
$50$	9.89589	+	0.800221i	1.39949	+	0.113168i
$51$	4.89706	+	2.61753i	0.685725	+	0.366528i
$52$	−3.97876	−	6.85577i	−0.551754	−	0.950725i
$53$	−1.06602	−	0.874857i	−0.146429	−	0.120171i	0.558327	−	0.829621i	$-0.311443\pi$
$53$	−1.06602	−	0.874857i	−0.146429	−	0.120171i	−0.704756	+	0.709450i	$0.748943\pi$
$54$	−7.76993	+	1.68729i	−1.05735	+	0.229611i
$55$	1.02715	−	5.16385i	0.138501	−	0.696294i
$56$	−0.424447	−	2.79640i	−0.0567191	−	0.373684i
$57$	−1.54259	+	0.306840i	−0.204321	+	0.0406420i
$58$	0.896576	+	0.353137i	0.117726	+	0.0463691i
$59$	−0.510343	−	0.954784i	−0.0664410	−	0.124302i	0.846508	−	0.532376i	$-0.178701\pi$
$59$	−0.510343	−	0.954784i	−0.0664410	−	0.124302i	−0.912949	+	0.408074i	$0.866201\pi$
$60$	9.05372	+	1.47388i	1.16883	+	0.190277i
$61$	−9.27141	−	0.913154i	−1.18708	−	0.116917i	−0.514865	−	0.857271i	$-0.672158\pi$
$61$	−9.27141	−	0.913154i	−1.18708	−	0.116917i	−0.672218	+	0.740354i	$0.734658\pi$
$62$	−2.14605	−	0.610229i	−0.272548	−	0.0774991i
$63$			1.25000i			0.157485i
$64$	7.96658	+	0.730435i	0.995823	+	0.0913043i
$65$		−	13.7410i		−	1.70436i
$66$	0.777046	−	2.73271i	0.0956477	−	0.336373i
$67$	4.43942	+	0.437245i	0.542361	+	0.0534179i	0.365489	−	0.930816i	$-0.380902\pi$
$67$	4.43942	+	0.437245i	0.542361	+	0.0534179i	0.176873	+	0.984234i	$0.443402\pi$
$68$	4.90517	+	6.81277i	0.594840	+	0.826169i
$69$	3.01211	+	5.63526i	0.362616	+	0.678406i
$70$	1.79685	−	4.56201i	0.214764	−	0.545264i
$71$	3.56609	−	0.709340i	0.423217	−	0.0841831i	0.0211131	−	0.999777i	$-0.493279\pi$
$71$	3.56609	−	0.709340i	0.423217	−	0.0841831i	0.402104	+	0.915594i	$0.368279\pi$
$72$	−3.43245	−	0.847495i	−0.404518	−	0.0998782i
$73$	−1.87431	+	9.42282i	−0.219372	+	1.10286i	0.701404	+	0.712764i	$0.252557\pi$
$73$	−1.87431	+	9.42282i	−0.219372	+	1.10286i	−0.920776	+	0.390093i	$0.872443\pi$
$74$	−1.30429	−	6.00622i	−0.151620	−	0.698209i
$75$	7.17893	+	5.89160i	0.828952	+	0.680303i
$76$	−2.29822	−	0.610273i	−0.263624	−	0.0700031i
$77$	−1.33928	−	0.715862i	−0.152625	−	0.0815800i
$78$	0.597634	−	7.39060i	0.0676687	−	0.836821i
$79$	−11.4219	+	4.73111i	−1.28507	+	0.532292i	−0.917511	−	0.397710i	$-0.869805\pi$
$79$	−11.4219	+	4.73111i	−1.28507	+	0.532292i	−0.367555	+	0.930002i	$0.619805\pi$
$80$	11.3089	+	8.02711i	1.26437	+	0.897458i
$81$	−3.40682	−	1.41115i	−0.378536	−	0.156795i
$82$	−4.34300	+	8.47854i	−0.479605	+	0.936298i
$83$	12.2310	−	3.71025i	1.34253	−	0.407253i	0.464380	−	0.885636i	$-0.346277\pi$
$83$	12.2310	−	3.71025i	1.34253	−	0.407253i	0.878151	+	0.478383i	$0.158777\pi$
$84$	1.16485	−	2.37553i	0.127096	−	0.259191i
$85$	1.42641	+	14.4826i	0.154716	+	1.57086i
$86$	3.43715	−	2.38461i	0.370638	−	0.257139i
$87$	0.500780	+	0.749470i	0.0536893	+	0.0803516i
$88$	2.87376	−	3.19227i	0.306344	−	0.340297i
$89$	−11.8264	−	7.90214i	−1.25359	−	0.837625i	−0.261757	−	0.965134i	$-0.584302\pi$
$89$	−11.8264	−	7.90214i	−1.25359	−	0.837625i	−0.991837	+	0.127509i	$0.959302\pi$
$90$	−4.40889	−	4.25734i	−0.464738	−	0.448763i
$91$	−3.79268	−	1.15050i	−0.397580	−	0.120605i
$92$	0.337781	+	9.65449i	0.0352161	+	1.00655i
$93$	−1.32399	−	1.61329i	−0.137292	−	0.167290i
$94$	−0.210227	−	1.80950i	−0.0216833	−	0.186636i
$95$	−2.91474	−	2.91474i	−0.299046	−	0.299046i
$96$	5.73335	+	4.80924i	0.585158	+	0.490841i
$97$	−5.53704	+	5.53704i	−0.562201	+	0.562201i	−0.929932	−	0.367731i	$-0.880135\pi$
$97$	−5.53704	+	5.53704i	−0.562201	+	0.562201i	0.367731	+	0.929932i	$0.380135\pi$
$98$	−1.10872	−	0.877915i	−0.111998	−	0.0886828i
$99$	−1.46736	+	1.20423i	−0.147475	+	0.121030i
$100$	5.82338	+	12.7760i	0.582338	+	1.27760i
$101$	−4.79614	+	15.8108i	−0.477234	+	1.57323i	0.306335	+	0.951924i	$0.400897\pi$
$101$	−4.79614	+	15.8108i	−0.477234	+	1.57323i	−0.783569	+	0.621305i	$0.786603\pi$
$102$	0.137308	+	7.85152i	0.0135955	+	0.777417i
$103$	−5.60810	+	8.39311i	−0.552582	+	0.826998i	−0.997651	−	0.0684984i	$-0.978179\pi$
$103$	−5.60810	+	8.39311i	−0.552582	+	0.826998i	0.445069	+	0.895496i	$0.353179\pi$
$104$	5.73064	−	9.63452i	0.561936	−	0.944742i
$105$	3.81350	−	2.54810i	0.372159	−	0.248669i
$106$	0.346973	−	1.91915i	0.0337010	−	0.186404i
$107$	−0.773799	+	0.0762126i	−0.0748060	+	0.00736775i	−0.135351	−	0.990798i	$-0.543216\pi$
$107$	−0.773799	+	0.0762126i	−0.0748060	+	0.00736775i	0.0605449	+	0.998165i	$0.480716\pi$
$108$	−7.43296	−	8.43734i	−0.715237	−	0.811883i
$109$	0.0254045	+	0.0837473i	0.00243331	+	0.00802154i	0.958149	−	0.286271i	$-0.0924159\pi$
$109$	0.0254045	+	0.0837473i	0.00243331	+	0.00802154i	−0.955715	+	0.294293i	$0.904916\pi$
$110$	7.08636	−	2.28568i	0.675658	−	0.217931i
$111$	2.20014	−	5.31162i	0.208828	−	0.504156i
$112$	3.16243	−	2.44929i	0.298822	−	0.231436i
$113$	6.97122	+	16.8300i	0.655797	+	1.58323i	0.804234	+	0.594313i	$0.202576\pi$
$113$	6.97122	+	16.8300i	0.655797	+	1.58323i	−0.148436	+	0.988922i	$0.547424\pi$
$114$	−1.44092	−	1.69446i	−0.134955	−	0.158701i
$115$	−7.89422	+	14.7690i	−0.736140	+	1.37722i
$116$	0.180912	+	1.35070i	0.0167973	+	0.125409i
$117$	−3.14288	+	3.82962i	−0.290560	+	0.354048i
$118$	0.828219	−	1.28770i	0.0762437	−	0.118543i
$119$	4.11680	+	0.818883i	0.377387	+	0.0750669i
$120$	4.41144	+	12.1993i	0.402708	+	1.11364i
$121$	1.69609	+	8.52681i	0.154190	+	0.775165i
$122$	−5.25400	−	12.0823i	−0.475675	−	1.09388i
$123$	−7.85871	+	4.20057i	−0.708596	+	0.378752i
$124$	−0.723394	−	3.07124i	−0.0649627	−	0.275805i
$125$	−0.686552	+	6.97068i	−0.0614071	+	0.623476i
$126$	−1.54422	+	0.860451i	−0.137570	+	0.0766550i
$127$	−11.7477			−1.04244			−0.521220	−	0.853422i	$-0.674523\pi$
$127$	−11.7477			−1.04244			−0.521220	+	0.853422i	$0.674523\pi$
$128$	4.58153	+	10.3445i	0.404954	+	0.914337i
$129$	3.91316			0.344535
$130$	16.9753	−	9.45878i	1.48883	−	0.829590i
$131$	1.94983	−	19.7970i	0.170358	−	1.72967i	−0.407216	−	0.913332i	$-0.633500\pi$
$131$	1.94983	−	19.7970i	0.170358	−	1.72967i	0.577573	−	0.816339i	$-0.304000\pi$
$132$	3.91081	−	0.921147i	0.340393	−	0.0801756i
$133$	−1.04855	+	0.560459i	−0.0909204	+	0.0485980i
$134$	2.51576	+	5.78534i	0.217329	+	0.499777i
$135$	−3.80278	−	19.1179i	−0.327291	−	1.64540i
$136$	−5.03980	+	10.7494i	−0.432160	+	0.921753i
$137$	−6.88888	−	1.37028i	−0.588557	−	0.117071i	−0.108177	−	0.994132i	$-0.534501\pi$
$137$	−6.88888	−	1.37028i	−0.588557	−	0.117071i	−0.480380	+	0.877060i	$0.659501\pi$
$138$	−4.88826	+	7.60020i	−0.416116	+	0.646972i
$139$	5.50510	−	6.70798i	0.466936	−	0.568964i	−0.485291	−	0.874352i	$-0.661286\pi$
$139$	5.50510	−	6.70798i	0.466936	−	0.568964i	0.952228	+	0.305389i	$0.0987865\pi$
$140$	6.87268	−	0.920526i	0.580848	−	0.0777987i
$141$	0.803270	−	1.50281i	0.0676475	−	0.126560i
$142$	3.33106	+	3.91719i	0.279537	+	0.328723i
$143$	−2.30326	−	5.56056i	−0.192608	−	0.464998i
$144$	−1.31579	−	4.82375i	−0.109649	−	0.401979i
$145$	−0.904036	+	2.18254i	−0.0750761	+	0.181250i
$146$	−12.9309	+	4.17082i	−1.07017	+	0.345180i
$147$	−0.384011	−	1.26591i	−0.0316727	−	0.104411i
$148$	6.52213	−	5.74574i	0.536116	−	0.472297i
$149$	8.25326	−	0.812875i	0.676133	−	0.0665933i	0.245878	−	0.969301i	$-0.420924\pi$
$149$	8.25326	−	0.812875i	0.676133	−	0.0665933i	0.430255	+	0.902707i	$0.358424\pi$
$150$	−2.33664	+	12.9242i	−0.190786	+	1.05526i
$151$	10.6113	−	7.09023i	0.863534	−	0.576995i	−0.0430252	−	0.999074i	$-0.513700\pi$
$151$	10.6113	−	7.09023i	0.863534	−	0.576995i	0.906559	+	0.422079i	$0.138700\pi$
$152$	−0.828090	−	3.25926i	−0.0671669	−	0.264361i
$153$	2.91497	−	4.36256i	0.235661	−	0.352692i
$154$	−0.0375521	−	2.14729i	−0.00302603	−	0.173034i
$155$	1.58778	−	5.23420i	0.127533	−	0.420421i
$156$	9.54157	−	4.34911i	0.763937	−	0.348207i
$157$	−12.4553	+	10.2218i	−0.994038	+	0.815786i	−0.982898	−	0.184152i	$-0.941046\pi$
$157$	−12.4553	+	10.2218i	−0.994038	+	0.815786i	−0.0111404	+	0.999938i	$0.503546\pi$
$158$	−13.7071	−	10.8537i	−1.09048	−	0.863471i
$159$	1.28998	−	1.28998i	0.102302	−	0.102302i
$160$	−2.13193	+	19.4963i	−0.168544	+	1.54131i
$161$	3.41547	+	3.41547i	0.269176	+	0.269176i
$162$	−0.601821	−	5.18009i	−0.0472835	−	0.406986i
$163$	−7.20951	−	8.78481i	−0.564692	−	0.688080i	0.409883	−	0.912138i	$-0.365569\pi$
$163$	−7.20951	−	8.78481i	−0.564692	−	0.688080i	−0.974576	+	0.224058i	$0.928069\pi$
$164$	−13.4638	+	0.471055i	−1.05134	+	0.0367832i
$165$	6.66506	+	2.02182i	0.518874	+	0.157399i
$166$	13.0029	+	12.5560i	1.00922	+	0.974532i
$167$	18.5077	+	12.3664i	1.43217	+	0.956944i	0.998436	+	0.0559022i	$0.0178035\pi$
$167$	18.5077	+	12.3664i	1.43217	+	0.956944i	0.433732	+	0.901042i	$0.357196\pi$
$168$	3.73651	−	0.196194i	0.288278	−	0.0151367i
$169$	−1.50450	−	2.25164i	−0.115731	−	0.173203i
$170$	−16.9096	+	11.7314i	−1.29691	+	0.899761i
$171$	0.145669	+	1.47901i	0.0111396	+	0.113102i
$172$	5.31190	+	2.60471i	0.405028	+	0.198607i
$173$	−24.3210	+	7.37769i	−1.84909	+	0.560916i	−0.849655	+	0.527339i	$0.823190\pi$
$173$	−24.3210	+	7.37769i	−1.84909	+	0.560916i	−0.999436	+	0.0335765i	$0.989310\pi$
$174$	−0.581161	+	1.13456i	−0.0440577	+	0.0860107i
$175$	6.48590	+	2.68655i	0.490288	+	0.203084i
$176$	5.92185	+	1.35274i	0.446376	+	0.101967i
$177$	1.32315	−	0.548068i	0.0994543	−	0.0411953i
$178$	1.62129	−	20.0496i	0.121521	−	1.50278i
$179$	1.19042	+	0.636295i	0.0889764	+	0.0475589i	0.515285	−	0.857019i	$-0.327686\pi$
$179$	1.19042	+	0.636295i	0.0889764	+	0.0475589i	−0.426308	+	0.904578i	$0.640186\pi$
$180$	2.22450	−	8.37723i	0.165805	−	0.624402i
$181$	4.55618	+	3.73916i	0.338658	+	0.277929i	0.788315	−	0.615272i	$-0.210954\pi$
$181$	4.55618	+	3.73916i	0.338658	+	0.277929i	−0.449657	+	0.893201i	$0.648454\pi$
$182$	−1.18944	−	5.47734i	−0.0881670	−	0.406008i
$183$	2.40435	−	12.0875i	0.177735	−	0.893532i
$184$	−11.6944	+	7.06307i	−0.862125	+	0.520697i
$185$	14.7783	−	2.93958i	1.08652	−	0.216122i
$186$	1.08164	−	2.74616i	0.0793094	−	0.201358i
$187$	3.00480	+	5.62158i	0.219732	+	0.411091i
$188$	2.09071	−	1.50530i	0.152480	−	0.109785i
$189$	−5.59515	−	0.551074i	−0.406987	−	0.0400847i
$190$	1.59441	−	5.60720i	0.115671	−	0.406789i
$191$		−	19.6909i		−	1.42478i	−0.701782	−	0.712392i	$-0.747612\pi$
$191$		−	19.6909i		−	1.42478i	0.701782	−	0.712392i	$-0.252388\pi$
$192$	−1.99461	+	10.3934i	−0.143948	+	0.750075i
$193$		−	21.1635i		−	1.52338i	−0.647941	−	0.761690i	$-0.724370\pi$
$193$		−	21.1635i		−	1.52338i	0.647941	−	0.761690i	$-0.275630\pi$
$194$	−10.6518	−	3.02885i	−0.764756	−	0.217458i
$195$	18.0901	+	1.78172i	1.29546	+	0.127592i
$196$	0.321355	−	1.97401i	0.0229539	−	0.141001i
$197$	13.1215	+	24.5486i	0.934867	+	1.74901i	0.581556	+	0.813507i	$0.302444\pi$
$197$	13.1215	+	24.5486i	0.934867	+	1.74901i	0.353311	+	0.935506i	$0.385056\pi$
$198$	−2.49776	−	0.983797i	−0.177508	−	0.0699154i
$199$	−15.2290	+	3.02923i	−1.07955	+	0.214736i	−0.702664	−	0.711522i	$-0.748006\pi$
$199$	−15.2290	+	3.02923i	−1.07955	+	0.214736i	−0.376889	+	0.926259i	$0.623006\pi$
$200$	−11.7746	+	15.9886i	−0.832589	+	1.13056i
$201$	−1.15127	+	5.78783i	−0.0812044	+	0.408242i
$202$	−22.8337	+	4.95848i	−1.60658	+	0.348877i
$203$	0.526713	+	0.432262i	0.0369680	+	0.0303389i
$204$	−9.60508	+	5.57432i	−0.672490	+	0.390280i
$205$	−20.5963	−	11.0090i	−1.43851	−	0.768899i
$206$	−14.2291	−	1.15062i	−0.991386	−	0.0801675i
$207$	5.57814	−	2.31054i	0.387708	−	0.160594i
$208$	15.8470	+	0.447473i	1.09879	+	0.0310266i
$209$	−1.66807	−	0.690939i	−0.115383	−	0.0477932i
$210$	5.77293	+	2.95709i	0.398370	+	0.204059i
$211$	−7.37465	+	2.23707i	−0.507692	+	0.154007i	−0.533731	−	0.845654i	$-0.679210\pi$
$211$	−7.37465	+	2.23707i	−0.507692	+	0.154007i	0.0260394	+	0.999661i	$0.491710\pi$
$212$	2.60972	−	0.892427i	0.179236	−	0.0612921i
$213$	0.471455	+	4.78676i	0.0323035	+	0.327983i
$214$	−0.626805	−	0.903472i	−0.0428475	−	0.0617601i
$215$	5.69777	+	8.52732i	0.388585	+	0.581558i
$216$	5.30673	−	14.9905i	0.361077	−	1.01997i
$217$	−1.31176	−	0.876490i	−0.0890480	−	0.0595000i
$218$	−0.0859721	+	0.0890326i	−0.00582276	+	0.00603005i
$219$	−12.1622	−	3.68935i	−0.821843	−	0.249303i
$220$	7.70166	+	7.18096i	0.519246	+	0.484140i
$221$	10.5537	+	12.8597i	0.709920	+	0.865040i
$222$	8.07635	−	0.938307i	0.542049	−	0.0629750i
$223$	10.5000	+	10.5000i	0.703130	+	0.703130i	0.965081	−	0.261951i	$-0.0843660\pi$
$223$	10.5000	+	10.5000i	0.703130	+	0.703130i	−0.261951	+	0.965081i	$0.584366\pi$
$224$	5.20269	+	2.22081i	0.347620	+	0.148384i
$225$	6.20510	−	6.20510i	0.413674	−	0.413674i
$226$	−15.9927	+	20.1972i	−1.06382	+	1.34350i
$227$	15.3230	−	12.5753i	1.01702	−	0.834651i	0.0307106	−	0.999528i	$-0.490223\pi$
$227$	15.3230	−	12.5753i	1.01702	−	0.834651i	0.986314	+	0.164878i	$0.0527230\pi$
$228$	1.10143	−	2.94649i	0.0729437	−	0.195136i
$229$	2.27642	−	7.50435i	0.150430	−	0.495901i	−0.849044	−	0.528322i	$-0.822821\pi$
$229$	2.27642	−	7.50435i	0.150430	−	0.495901i	0.999474	+	0.0324203i	$0.0103215\pi$
$230$	−23.6794	+	0.414108i	−1.56137	+	0.0273055i
$231$	1.11609	−	1.67035i	0.0734336	−	0.109901i
$232$	−1.54409	+	1.15326i	−0.101374	+	0.0757154i
$233$	−18.6396	+	12.4546i	−1.22112	+	0.815928i	−0.987687	−	0.156445i	$-0.949997\pi$
$233$	−18.6396	+	12.4546i	−1.22112	+	0.815928i	−0.233435	+	0.972372i	$0.574997\pi$
$234$	−6.89446	−	1.24649i	−0.450705	−	0.0814854i
$235$	4.44444	−	0.437739i	0.289923	−	0.0285549i
$236$	2.16091	+	0.136757i	0.140664	+	0.00890209i
$237$	−4.74752	−	15.6505i	−0.308385	−	1.01661i
$238$	1.82222	+	5.64949i	0.118117	+	0.366202i
$239$	0.739623	−	1.78561i	0.0478422	−	0.115501i	−0.898152	−	0.439686i	$-0.855090\pi$
$239$	0.739623	−	1.78561i	0.0478422	−	0.115501i	0.945994	+	0.324184i	$0.105090\pi$
$240$	−12.0341	+	13.8473i	−0.776798	+	0.893842i
$241$	4.88684	+	11.7979i	0.314789	+	0.759968i	0.999514	+	0.0311665i	$0.00992222\pi$
$241$	4.88684	+	11.7979i	0.314789	+	0.759968i	−0.684725	+	0.728801i	$0.740078\pi$
$242$	−9.36631	+	7.96484i	−0.602089	+	0.512000i
$243$	−5.65136	+	10.5729i	−0.362535	+	0.678255i
$244$	11.3095	−	14.8077i	0.724018	−	0.947963i
$245$	2.19946	−	2.68005i	0.140518	−	0.171222i
$246$	−10.5989	−	6.81696i	−0.675763	−	0.434634i
$247$	−4.62160	−	0.919293i	−0.294065	−	0.0584932i
$248$	3.29618	−	3.00779i	0.209308	−	0.190995i
$249$	3.29863	+	16.5833i	0.209042	+	1.05093i
$250$	−9.08401	+	3.95020i	−0.574523	+	0.249832i
$251$	6.90165	−	3.68901i	0.435628	−	0.232848i	−0.238979	−	0.971025i	$-0.576813\pi$
$251$	6.90165	−	3.68901i	0.435628	−	0.232848i	0.674608	+	0.738177i	$0.264313\pi$
$252$	−2.12596	−	1.31539i	−0.133923	−	0.0828619i
$253$	−0.718968	+	7.29981i	−0.0452011	+	0.458935i
$254$	−8.08667	−	14.5128i	−0.507403	−	0.910617i
$255$	−19.2514			−1.20557
$256$	−9.62566	+	12.7807i	−0.601604	+	0.798794i
$257$	22.2427			1.38746			0.693731	−	0.720235i	$-0.255966\pi$
$257$	22.2427			1.38746			0.693731	+	0.720235i	$0.255966\pi$
$258$	2.69367	+	4.83424i	0.167701	+	0.300966i
$259$	0.425985	−	4.32510i	0.0264694	−	0.268748i
$260$	23.3703	+	14.4599i	1.44937	+	0.896763i
$261$	0.751151	−	0.401499i	0.0464951	−	0.0248521i
$262$	25.7989	−	11.2187i	1.59386	−	0.693094i
$263$	2.04219	+	10.2668i	0.125927	+	0.633077i	0.991265	+	0.131888i	$0.0421038\pi$
$263$	2.04219	+	10.2668i	0.125927	+	0.633077i	−0.865338	+	0.501189i	$0.832896\pi$
$264$	3.83002	+	4.19725i	0.235721	+	0.258323i
$265$	4.68932	+	0.932763i	0.288063	+	0.0572992i
$266$	−1.41416	−	0.909551i	−0.0867075	−	0.0557681i
$267$	11.9367	−	14.5449i	0.730513	−	0.890133i
$268$	−5.41532	+	7.09033i	−0.330794	+	0.433111i
$269$	−4.39169	+	8.21626i	−0.267766	+	0.500955i	−0.979487	−	0.201508i	$-0.935416\pi$
$269$	−4.39169	+	8.21626i	−0.267766	+	0.500955i	0.711721	+	0.702462i	$0.247916\pi$
$270$	21.0001	−	17.8579i	1.27803	−	1.08680i
$271$	6.05977	+	14.6296i	0.368105	+	0.888683i	0.994061	+	0.108825i	$0.0347088\pi$
$271$	6.05977	+	14.6296i	0.368105	+	0.888683i	−0.625956	+	0.779858i	$0.715291\pi$
$272$	−16.7488	+	1.17341i	−1.01554	+	0.0711485i
$273$	2.00641	−	4.84390i	0.121434	−	0.293166i
$274$	−3.04923	−	9.45362i	−0.184210	−	0.571114i
$275$	3.09472	+	10.2019i	0.186619	+	0.615200i
$276$	−12.7540	−	0.807155i	−0.767701	−	0.0485850i
$277$	7.52933	−	0.741574i	0.452394	−	0.0445569i	0.130745	−	0.991416i	$-0.458263\pi$
$277$	7.52933	−	0.741574i	0.452394	−	0.0445569i	0.321648	+	0.946859i	$0.395763\pi$
$278$	12.0764	+	2.18336i	0.724294	+	0.130949i
$279$	−1.63970	+	1.09561i	−0.0981660	+	0.0655924i
$280$	5.86809	+	7.85671i	0.350686	+	0.469528i
$281$	4.84832	−	7.25602i	0.289226	−	0.432858i	−0.658195	−	0.752848i	$-0.728680\pi$
$281$	4.84832	−	7.25602i	0.289226	−	0.432858i	0.947421	+	0.319990i	$0.103680\pi$
$282$	2.40948	−	0.0421372i	0.143482	−	0.00250924i
$283$	3.01651	−	9.94410i	0.179313	−	0.591115i	−0.820498	−	0.571650i	$-0.806304\pi$
$283$	3.01651	−	9.94410i	0.179313	−	0.591115i	0.999811	−	0.0194655i	$-0.00619646\pi$
$284$	−2.54623	+	6.81156i	−0.151091	+	0.404192i
$285$	4.21521	−	3.45934i	0.249688	−	0.204913i
$286$	5.28392	−	6.67308i	0.312445	−	0.394587i
$287$	−4.76307	+	4.76307i	−0.281155	+	0.281155i
$288$	5.05341	−	4.94599i	0.297775	−	0.291445i
$289$	−0.437433	−	0.437433i	−0.0257314	−	0.0257314i
$290$	−3.31856	+	0.385549i	−0.194873	+	0.0226402i
$291$	−6.57159	−	8.00751i	−0.385233	−	0.469408i
$292$	−14.0537	−	13.1036i	−0.822431	−	0.766828i
$293$	−0.531133	−	0.161117i	−0.0310291	−	0.00941258i	0.274732	−	0.961521i	$-0.411411\pi$
$293$	−0.531133	−	0.161117i	−0.0310291	−	0.00941258i	−0.305761	+	0.952108i	$0.598911\pi$
$294$	1.29954	−	1.34581i	0.0757909	−	0.0784890i
$295$	3.12090	+	2.08532i	0.181706	+	0.121412i
$296$	11.5877	+	4.10214i	0.673524	+	0.238432i
$297$	−4.74340	−	7.09900i	−0.275240	−	0.411926i
$298$	6.68544	+	9.63634i	0.387277	+	0.558218i
$299$	1.87641	+	19.0515i	0.108516	+	1.10178i
$300$	−17.5748	+	6.00992i	−1.01468	+	0.346983i
$301$	2.83070	−	0.858683i	0.163159	−	0.0494937i
$302$	16.0635	+	8.22829i	0.924351	+	0.473485i
$303$	−20.1931	−	8.36425i	−1.16006	−	0.480513i
$304$	3.45639	−	3.26655i	0.198237	−	0.187350i
$305$	29.8411	−	12.3606i	1.70870	−	0.707766i
$306$	7.39596	+	0.598067i	0.422799	+	0.0341892i
$307$	−5.90083	−	3.15406i	−0.336778	−	0.180012i	0.294335	−	0.955702i	$-0.404902\pi$
$307$	−5.90083	−	3.15406i	−0.336778	−	0.180012i	−0.631114	+	0.775690i	$0.717402\pi$
$308$	2.62687	−	1.52451i	0.149680	−	0.0868667i
$309$	−10.3224	−	8.47139i	−0.587222	−	0.481920i
$310$	7.55918	−	1.64152i	0.429332	−	0.0932320i
$311$	2.29847	−	11.5552i	0.130335	−	0.655236i	−0.859282	−	0.511502i	$-0.829089\pi$
$311$	2.29847	−	11.5552i	0.130335	−	0.655236i	0.989616	−	0.143734i	$-0.0459109\pi$
$312$	11.9408	+	8.79369i	0.676017	+	0.497844i
$313$	−31.4061	+	6.24706i	−1.77518	+	0.353105i	−0.970592	−	0.240731i	$-0.922613\pi$
$313$	−31.4061	+	6.24706i	−1.77518	+	0.353105i	−0.804586	+	0.593836i	$0.797613\pi$
$314$	−21.2015	−	8.35067i	−1.19647	−	0.471256i
$315$	−2.04293	−	3.82205i	−0.115106	−	0.215348i
$316$	3.97291	−	24.4047i	0.223494	−	1.37287i
$317$	21.2012	+	2.08814i	1.19078	+	0.117282i	0.673931	−	0.738795i	$-0.264605\pi$
$317$	21.2012	+	2.08814i	1.19078	+	0.117282i	0.516849	+	0.856076i	$0.327105\pi$
$318$	2.48158	+	0.705639i	0.139160	+	0.0395703i
$319$			1.03474i			0.0579343i
$320$	−25.5528	+	10.7867i	−1.42844	+	0.602997i
$321$		−	1.02859i		−	0.0574105i
$322$	−1.86831	+	6.57047i	−0.104117	+	0.366158i
$323$	4.96646	+	0.489154i	0.276341	+	0.0272172i
$324$	5.98510	−	4.30926i	0.332506	−	0.239403i
$325$	13.1160	+	24.5384i	0.727547	+	1.36114i
$326$	5.88981	−	14.9536i	0.326206	−	0.828203i
$327$	−0.113548	+	0.0225861i	−0.00627922	+	0.00124901i
$328$	−9.84987	−	16.3086i	−0.543868	−	0.900490i
$329$	0.251299	−	1.26337i	0.0138546	−	0.0696517i
$330$	2.09026	+	9.62562i	0.115065	+	0.529873i
$331$	26.2411	+	21.5355i	1.44234	+	1.18370i	0.949575	+	0.313540i	$0.101515\pi$
$331$	26.2411	+	21.5355i	1.44234	+	1.18370i	0.492769	+	0.870160i	$0.335985\pi$
$332$	−6.56063	+	24.7066i	−0.360061	+	1.35595i
$333$	−4.79105	−	2.56087i	−0.262548	−	0.140335i
$334$	−2.53724	+	31.3766i	−0.138831	+	1.71685i
$335$	−14.2888	+	5.91861i	−0.780680	+	0.323368i
$336$	2.81445	+	4.48095i	0.153541	+	0.244456i
$337$	−11.2635	−	4.66550i	−0.613563	−	0.254146i	0.0541880	−	0.998531i	$-0.482743\pi$
$337$	−11.2635	−	4.66550i	−0.613563	−	0.254146i	−0.667751	+	0.744385i	$0.732743\pi$
$338$	1.74599	−	3.40857i	0.0949692	−	0.185402i
$339$	−23.0608	+	6.99540i	−1.25249	+	0.379938i
$340$	−26.1327	−	12.8143i	−1.41724	−	0.694952i
$341$	−0.234829	−	2.38426i	−0.0127167	−	0.129115i
$342$	−1.72686	+	1.19805i	−0.0933778	+	0.0647830i
$343$	−0.555570	−	0.831470i	−0.0299980	−	0.0448951i
$344$	0.438706	+	8.35518i	0.0236535	+	0.450481i
$345$	−18.4199	−	12.3078i	−0.991696	−	0.662630i
$346$	−25.8559	−	24.9671i	−1.39002	−	1.34224i
$347$	−19.9473	−	6.05096i	−1.07083	−	0.324833i	−0.294819	−	0.955553i	$-0.595259\pi$
$347$	−19.9473	−	6.05096i	−1.07083	−	0.324833i	−0.776010	+	0.630720i	$0.782759\pi$
$348$	−1.80166	+	0.0630344i	−0.0965790	+	0.00337900i
$349$	3.80036	+	4.63075i	0.203428	+	0.247878i	0.864724	−	0.502247i	$-0.167493\pi$
$349$	3.80036	+	4.63075i	0.203428	+	0.247878i	−0.661296	+	0.750125i	$0.729993\pi$
$350$	1.14575	+	9.86186i	0.0612427	+	0.527138i
$351$	−15.7563	−	15.7563i	−0.841008	−	0.841008i
$352$	2.40523	+	8.24689i	0.128199	+	0.439561i
$353$	−7.14833	+	7.14833i	−0.380467	+	0.380467i	−0.871271	−	0.490803i	$-0.836703\pi$
$353$	−7.14833	+	7.14833i	−0.380467	+	0.380467i	0.490803	+	0.871271i	$0.336703\pi$
$354$	1.58788	+	1.25732i	0.0843949	+	0.0668261i
$355$	−9.74454	+	7.99714i	−0.517187	+	0.424444i
$356$	25.8848	−	11.7985i	1.37189	−	0.625318i
$357$	−1.61187	+	5.31362i	−0.0853091	+	0.281226i
$358$	0.0333782	+	1.90862i	0.00176409	+	0.100874i
$359$	10.2123	−	15.2837i	0.538982	−	0.806644i	−0.457608	−	0.889154i	$-0.651294\pi$
$359$	10.2123	−	15.2837i	0.538982	−	0.806644i	0.996590	+	0.0825103i	$0.0262938\pi$
$360$	11.8803	−	3.01847i	0.626147	−	0.159087i
$361$	14.6226	−	9.77050i	0.769610	−	0.514237i
$362$	−1.48297	+	8.20249i	−0.0779433	+	0.431114i
$363$	−11.4455	+	1.12729i	−0.600735	+	0.0591672i
$364$	5.94782	−	5.23980i	0.311751	−	0.274640i
$365$	−9.66915	−	31.8749i	−0.506106	−	1.66841i
$366$	16.5877	−	5.35028i	0.867051	−	0.279664i
$367$	−5.09220	+	12.2937i	−0.265811	+	0.641724i	−0.999278	−	0.0380014i	$-0.987901\pi$
$367$	−5.09220	+	12.2937i	−0.265811	+	0.641724i	0.733467	+	0.679725i	$0.237901\pi$
$368$	−16.7756	−	9.58508i	−0.874486	−	0.499657i
$369$	3.22219	+	7.77905i	0.167740	+	0.404961i
$370$	13.8043	+	16.2332i	0.717651	+	0.843926i
$371$	0.650077	−	1.21621i	0.0337503	−	0.0631424i
$372$	4.13710	−	0.554123i	0.214499	−	0.0287299i
$373$	11.7661	−	14.3370i	0.609224	−	0.742342i	−0.373457	−	0.927648i	$-0.621828\pi$
$373$	11.7661	−	14.3370i	0.609224	−	0.742342i	0.982681	+	0.185306i	$0.0593275\pi$
$374$	−4.87638	+	7.58174i	−0.252152	+	0.392042i
$375$	−9.08792	−	1.80770i	−0.469298	−	0.0933492i
$376$	3.29878	+	1.54662i	0.170122	+	0.0797607i
$377$	0.526848	+	2.64864i	0.0271340	+	0.136412i
$378$	−3.17070	−	7.29146i	−0.163083	−	0.375032i
$379$	−3.48461	+	1.86256i	−0.178992	+	0.0956733i	−0.558459	−	0.829532i	$-0.688607\pi$
$379$	−3.48461	+	1.86256i	−0.178992	+	0.0956733i	0.379467	+	0.925205i	$0.376107\pi$
$380$	8.02454	−	1.89009i	0.411650	−	0.0969595i
$381$	1.52326	−	15.4659i	0.0780390	−	0.792343i
$382$	24.3257	−	13.5545i	1.24461	−	0.693507i
$383$	31.1197			1.59014			0.795071	−	0.606517i	$-0.207434\pi$
$383$	31.1197			1.59014			0.795071	+	0.606517i	$0.207434\pi$
$384$	−14.2127	+	4.69030i	−0.725290	+	0.239351i
$385$	5.26502			0.268330
$386$	26.1449	−	14.5681i	1.33074	−	0.741499i
$387$	0.362426	−	3.67978i	0.0184232	−	0.187054i
$388$	−3.59054	−	15.2440i	−0.182282	−	0.773895i
$389$	−11.7170	+	6.26287i	−0.594076	+	0.317540i	−0.740892	−	0.671624i	$-0.765597\pi$
$389$	−11.7170	+	6.26287i	−0.594076	+	0.317540i	0.146817	+	0.989164i	$0.453097\pi$
$390$	10.2515	+	23.5746i	0.519102	+	1.19375i
$391$	−3.95537	−	19.8850i	−0.200032	−	1.00563i
$392$	2.65986	−	0.961842i	0.134343	−	0.0485803i
$393$	25.8100	+	5.13394i	1.30194	+	0.258973i
$394$	−21.2944	+	33.1083i	−1.07280	+	1.66797i
$395$	27.1919	−	33.1334i	1.36817	−	1.66712i
$396$	−0.504000	−	3.76288i	−0.0253269	−	0.189092i
$397$	4.65577	−	8.71033i	0.233666	−	0.437159i	−0.737572	−	0.675268i	$-0.764028\pi$
$397$	4.65577	−	8.71033i	0.233666	−	0.437159i	0.971238	+	0.238110i	$0.0765278\pi$
$398$	−14.2253	−	16.7283i	−0.713049	−	0.838514i
$399$	−0.601889	−	1.45309i	−0.0301321	−	0.0727454i
$400$	−27.8571	−	3.54013i	−1.39286	−	0.177007i
$401$	2.10580	−	5.08385i	0.105159	−	0.253875i	−0.862538	−	0.505992i	$-0.831127\pi$
$401$	2.10580	−	5.08385i	0.105159	−	0.253875i	0.967697	+	0.252116i	$0.0811266\pi$
$402$	−7.94265	+	2.56187i	−0.396143	+	0.127774i
$403$	−1.81507	−	5.98347i	−0.0904149	−	0.298058i
$404$	−21.8435	−	24.7951i	−1.08675	−	1.23360i
$405$	12.7232	−	1.25312i	0.632219	−	0.0622681i
$406$	−0.171438	+	0.948242i	−0.00850831	+	0.0470605i
$407$	5.48758	−	3.66668i	0.272009	−	0.181751i
$408$	−13.4982	−	8.02875i	−0.668258	−	0.397482i
$409$	17.2826	−	25.8653i	0.854572	−	1.27896i	−0.104136	−	0.994563i	$-0.533208\pi$
$409$	17.2826	−	25.8653i	0.854572	−	1.27896i	0.958707	−	0.284394i	$-0.0917924\pi$
$410$	−0.577498	−	33.0224i	−0.0285206	−	1.63086i
$411$	2.69723	−	8.89158i	0.133045	−	0.438589i
$412$	−8.37330	−	18.3703i	−0.412523	−	0.905040i
$413$	0.836876	−	0.686806i	0.0411800	−	0.0337955i
$414$	6.69417	+	5.30062i	0.329001	+	0.260511i
$415$	−31.3344	+	31.3344i	−1.53814	+	1.53814i
$416$	10.3557	+	19.8851i	0.507730	+	0.974946i
$417$	8.11729	+	8.11729i	0.397505	+	0.397505i
$418$	−0.294668	−	2.53632i	−0.0144127	−	0.124055i
$419$	21.7573	+	26.5114i	1.06292	+	1.29517i	0.953573	+	0.301162i	$0.0973745\pi$
$419$	21.7573	+	26.5114i	1.06292	+	1.29517i	0.109343	+	0.994004i	$0.465125\pi$
$420$	0.320735	+	9.16730i	0.0156503	+	0.447318i
$421$	21.7755	+	6.60552i	1.06127	+	0.321933i	0.772204	−	0.635375i	$-0.219155\pi$
$421$	21.7755	+	6.60552i	1.06127	+	0.321933i	0.289068	+	0.957308i	$0.406655\pi$
$422$	−7.84006	−	7.57055i	−0.381648	−	0.368529i
$423$	−1.33879	−	0.894548i	−0.0650940	−	0.0434944i
$424$	2.89892	+	2.60967i	0.140784	+	0.126737i
$425$	−16.3712	−	24.5012i	−0.794119	−	1.18848i
$426$	−5.58892	+	3.87745i	−0.270784	+	0.187863i
$427$	−0.913154	−	9.27141i	−0.0441906	−	0.448675i
$428$	0.684661	−	1.39626i	0.0330943	−	0.0674906i
$429$	7.61917	−	2.31125i	0.367857	−	0.111588i
$430$	−6.61233	+	12.9088i	−0.318875	+	0.622517i
$431$	23.4558	+	9.71571i	1.12983	+	0.467989i	0.867722	−	0.497050i	$-0.165584\pi$
$431$	23.4558	+	9.71571i	1.12983	+	0.467989i	0.262104	+	0.965040i	$0.415584\pi$
$432$	22.1718	−	3.76305i	1.06674	−	0.181050i
$433$	−7.90297	+	3.27352i	−0.379792	+	0.157315i	−0.564409	−	0.825496i	$-0.690896\pi$
$433$	−7.90297	+	3.27352i	−0.379792	+	0.157315i	0.184616	+	0.982811i	$0.440896\pi$
$434$	0.179830	−	2.22386i	0.00863213	−	0.106749i
$435$	−2.75610	−	1.47317i	−0.132145	−	0.0706330i
$436$	−0.169169	−	0.0449213i	−0.00810171	−	0.00215134i
$437$	4.43923	+	3.64318i	0.212357	+	0.174277i
$438$	−3.81423	−	17.5645i	−0.182251	−	0.839263i
$439$	6.81108	−	34.2416i	0.325075	−	1.63426i	−0.379898	−	0.925029i	$-0.624041\pi$
$439$	6.81108	−	34.2416i	0.325075	−	1.63426i	0.704973	−	0.709234i	$-0.250959\pi$
$440$	−3.56967	+	14.4576i	−0.170177	+	0.689237i
$441$	−1.22598	+	0.243862i	−0.0583799	+	0.0116125i
$442$	−8.62186	+	21.8900i	−0.410100	+	1.04120i
$443$	16.0146	+	29.9612i	0.760875	+	1.42350i	0.901205	+	0.433393i	$0.142684\pi$
$443$	16.0146	+	29.9612i	0.760875	+	1.42350i	−0.140330	+	0.990105i	$0.544816\pi$
$444$	6.71861	+	9.33144i	0.318851	+	0.442851i
$445$	49.0758	+	4.83354i	2.32641	+	0.229132i
$446$	−5.74365	+	20.1992i	−0.271970	+	0.956460i
$447$			10.9709i			0.518905i
$448$	0.837804	+	7.95601i	0.0395825	+	0.375886i
$449$		−	18.6762i		−	0.881385i	−0.897658	−	0.440692i	$-0.854733\pi$
$449$		−	18.6762i		−	0.881385i	0.897658	−	0.440692i	$-0.145267\pi$
$450$	11.9370	+	3.39429i	0.562716	+	0.160008i
$451$	−10.1800	−	1.00264i	−0.479358	−	0.0472126i
$452$	−35.9600	−	5.85402i	−1.69142	−	0.275350i
$453$	7.95843	+	14.8892i	0.373920	+	0.699554i
$454$	26.0830	+	10.2734i	1.22414	+	0.482153i
$455$	13.4770	−	2.68074i	0.631810	−	0.125675i
$456$	4.39821	−	0.667575i	0.205965	−	0.0312621i
$457$	−5.60774	+	28.1920i	−0.262319	+	1.31877i	0.594894	+	0.803804i	$0.297194\pi$
$457$	−5.60774	+	28.1920i	−0.262319	+	1.31877i	−0.857213	+	0.514962i	$0.827806\pi$
$458$	10.8377	−	2.35347i	0.506413	−	0.109971i
$459$	18.2423	+	14.9711i	0.851477	+	0.698789i
$460$	−16.8116	−	28.9680i	−0.783845	−	1.35064i
$461$	−17.0669	−	9.12246i	−0.794886	−	0.424875i	0.0233717	−	0.999727i	$-0.492560\pi$
$461$	−17.0669	−	9.12246i	−0.794886	−	0.424875i	−0.818258	+	0.574851i	$0.805060\pi$
$462$	2.83179	+	0.228990i	0.131747	+	0.0106536i
$463$	−25.7062	+	10.6479i	−1.19467	+	0.494848i	−0.889273	−	0.457377i	$-0.848789\pi$
$463$	−25.7062	+	10.6479i	−1.19467	+	0.494848i	−0.305396	+	0.952225i	$0.598789\pi$
$464$	−2.48760	−	1.11367i	−0.115484	−	0.0517007i
$465$	6.68498	+	2.76901i	0.310008	+	0.128410i
$466$	−28.2169	−	14.4537i	−1.30712	−	0.669555i
$467$	−7.48539	+	2.27067i	−0.346383	+	0.105074i	−0.458682	−	0.888600i	$-0.651678\pi$
$467$	−7.48539	+	2.27067i	−0.346383	+	0.105074i	0.112300	+	0.993674i	$0.464178\pi$
$468$	−3.20600	−	9.37530i	−0.148198	−	0.433373i
$469$	0.437245	+	4.43942i	0.0201901	+	0.204993i
$470$	3.60015	+	5.18923i	0.166063	+	0.239361i
$471$	−11.8420	−	17.7228i	−0.545652	−	0.816625i
$472$	1.31855	+	2.76368i	0.0606910	+	0.127209i
$473$	3.73506	+	2.49569i	0.171738	+	0.114752i
$474$	16.0662	−	16.6382i	0.737947	−	0.764217i
$475$	7.98725	+	2.42291i	0.366480	+	0.111171i
$476$	−5.72491	+	6.14003i	−0.262401	+	0.281428i
$477$	−1.09357	−	1.33252i	−0.0500711	−	0.0610118i
$478$	2.71503	−	0.315431i	0.124182	−	0.0144275i
$479$	−14.2352	−	14.2352i	−0.650422	−	0.650422i	0.302673	−	0.953094i	$-0.402121\pi$
$479$	−14.2352	−	14.2352i	−0.650422	−	0.650422i	−0.953094	+	0.302673i	$0.902121\pi$
$480$	−25.3905	−	5.33468i	−1.15891	−	0.243493i
$481$	12.1797	−	12.1797i	0.555348	−	0.555348i
$482$	−11.2109	+	14.1583i	−0.510643	+	0.644893i
$483$	−4.93935	+	4.05362i	−0.224748	+	0.184446i
$484$	−16.2870	−	6.08823i	−0.740318	−	0.276738i
$485$	7.88087	−	25.9797i	0.357852	−	1.17968i
$486$	−16.9518	+	0.296454i	−0.768948	+	0.0134474i
$487$	−17.3388	+	25.9494i	−0.785697	+	1.17588i	0.195088	+	0.980786i	$0.437501\pi$
$487$	−17.3388	+	25.9494i	−0.785697	+	1.17588i	−0.980785	+	0.195092i	$0.937499\pi$
$488$	26.0781	+	3.77850i	1.18050	+	0.171045i
$489$	12.5001	−	8.35229i	0.565273	−	0.377704i
$490$	4.82490	+	0.872319i	0.217967	+	0.0394074i
$491$	26.6301	−	2.62284i	1.20180	−	0.118367i	0.522767	−	0.852475i	$-0.324900\pi$
$491$	26.6301	−	2.62284i	1.20180	−	0.118367i	0.679032	+	0.734108i	$0.262400\pi$
$492$	1.12563	−	17.7862i	0.0507471	−	0.801864i
$493$	−0.830231	−	2.73690i	−0.0373917	−	0.123264i
$494$	−2.04566	−	6.34222i	−0.0920385	−	0.285350i
$495$	2.51854	−	6.08029i	0.113200	−	0.273289i
$496$	5.98472	+	2.00158i	0.268722	+	0.0898736i
$497$	1.39142	+	3.35918i	0.0624137	+	0.150680i
$498$	−18.2160	+	15.4904i	−0.816280	+	0.694141i
$499$	0.926771	−	1.73387i	0.0414880	−	0.0776186i	−0.860323	−	0.509749i	$-0.829738\pi$
$499$	0.926771	−	1.73387i	0.0414880	−	0.0776186i	0.901811	+	0.432131i	$0.142238\pi$
$500$	−11.1331	−	8.50302i	−0.497886	−	0.380267i
$501$	−18.6803	+	22.7620i	−0.834574	+	1.01693i
$502$	9.30815	+	5.98677i	0.415443	+	0.267203i
$503$	4.77347	+	0.949502i	0.212838	+	0.0423362i	0.300358	−	0.953827i	$-0.402894\pi$
$503$	4.77347	+	0.949502i	0.212838	+	0.0423362i	−0.0875193	+	0.996163i	$0.527894\pi$
$504$	0.161573	−	3.53183i	0.00719704	−	0.157320i
$505$	−11.1753	−	56.1823i	−0.497296	−	2.50008i
$506$	−9.51293	+	4.13671i	−0.422901	+	0.183899i
$507$	3.15938	−	1.68873i	0.140313	−	0.0749989i
$508$	12.3623	−	19.9802i	0.548488	−	0.886477i
$509$	2.86820	−	29.1214i	0.127131	−	1.29078i	−0.693972	−	0.720002i	$-0.744141\pi$
$509$	2.86820	−	29.1214i	0.127131	−	1.29078i	0.821103	−	0.570780i	$-0.193359\pi$
$510$	−13.2519	−	23.7828i	−0.586806	−	1.05312i
$511$	−9.60742			−0.425007
$512$	−22.4149	−	3.09357i	−0.990610	−	0.136718i
$513$	−6.68445			−0.295125
$514$	15.3110	+	27.4781i	0.675340	+	1.21201i
$515$	3.43033	−	34.8287i	0.151158	−	1.53474i
$516$	−4.11788	+	6.65541i	−0.181280	+	0.292988i
$517$	1.72515	−	0.922114i	0.0758722	−	0.0405545i
$518$	5.63636	−	2.45098i	0.247647	−	0.107690i
$519$	−6.55921	−	32.9754i	−0.287917	−	1.44746i
$520$	−1.77615	+	38.8248i	−0.0778891	+	1.70258i
$521$	−4.90575	−	0.975814i	−0.214925	−	0.0427512i	0.0864534	−	0.996256i	$-0.472447\pi$
$521$	−4.90575	−	0.975814i	−0.214925	−	0.0427512i	−0.301378	+	0.953505i	$0.597447\pi$
$522$	1.01307	+	0.651579i	0.0443407	+	0.0285188i
$523$	0.904651	−	1.10232i	0.0395576	−	0.0482011i	−0.752856	−	0.658185i	$-0.771324\pi$
$523$	0.904651	−	1.10232i	0.0395576	−	0.0482011i	0.792413	+	0.609984i	$0.208824\pi$
$524$	31.6184	+	24.1489i	1.38125	+	1.05495i
$525$	−4.37785	+	8.19038i	−0.191065	+	0.357458i
$526$	−11.2776	+	9.59013i	−0.491726	+	0.418150i
$527$	2.53416	+	6.11800i	0.110390	+	0.266504i
$528$	−2.54875	+	7.62075i	−0.110920	+	0.331651i
$529$	0.126602	−	0.305643i	0.00550442	−	0.0132888i
$530$	2.07563	+	6.43516i	0.0901598	+	0.279525i
$531$	−0.392834	−	1.29500i	−0.0170475	−	0.0561982i
$532$	0.150186	−	2.37312i	0.00651140	−	0.102888i
$533$	−26.5685	+	2.61677i	−1.15081	+	0.113345i
$534$	26.1852	+	4.73416i	1.13314	+	0.204867i
$535$	2.24145	−	1.49769i	0.0969062	−	0.0647507i
$536$	−12.4869	−	1.80926i	−0.539353	−	0.0781480i
$537$	−0.992042	+	1.48470i	−0.0428098	+	0.0640693i
$538$	−13.1733	+	0.230375i	−0.567939	+	0.00993218i
$539$	0.440825	−	1.45321i	0.0189877	−	0.0625940i
$540$	36.5169	+	13.6504i	1.57144	+	0.587418i
$541$	25.0166	−	20.5306i	1.07555	−	0.882680i	0.0820616	−	0.996627i	$-0.473850\pi$
$541$	25.0166	−	20.5306i	1.07555	−	0.882680i	0.993487	+	0.113948i	$0.0363496\pi$
$542$	−13.9017	+	17.5565i	−0.597130	+	0.754118i
$543$	−5.51340	+	5.51340i	−0.236603	+	0.236603i
$544$	−12.9788	−	19.8833i	−0.556462	−	0.852490i
$545$	−0.214550	−	0.214550i	−0.00919031	−	0.00919031i
$546$	7.36519	−	0.855685i	0.315201	−	0.0366199i
$547$	16.1338	+	19.6590i	0.689829	+	0.840560i	0.993691	−	0.112157i	$-0.0357759\pi$
$547$	16.1338	+	19.6590i	0.689829	+	0.840560i	−0.303861	+	0.952716i	$0.598276\pi$
$548$	9.57982	−	10.2745i	0.409230	−	0.438903i
$549$	−11.1439	−	3.38046i	−0.475609	−	0.144274i
$550$	−10.4729	+	10.8458i	−0.446568	+	0.462465i
$551$	0.673585	+	0.450075i	0.0286957	+	0.0191738i
$552$	−7.78223	−	16.3116i	−0.331234	−	0.694269i
$553$	−6.86851	−	10.2795i	−0.292079	−	0.437127i
$554$	6.09903	+	8.79109i	0.259123	+	0.373498i
$555$	1.95376	+	19.8368i	0.0829324	+	0.842027i
$556$	5.61566	+	16.4218i	0.238157	+	0.696441i
$557$	−14.3822	+	4.36279i	−0.609393	+	0.184857i	−0.579873	−	0.814707i	$-0.696898\pi$
$557$	−14.3822	+	4.36279i	−0.609393	+	0.184857i	−0.0295198	+	0.999564i	$0.509398\pi$
$558$	−2.48220	−	1.27147i	−0.105080	−	0.0538255i
$559$	10.8314	+	4.48652i	0.458120	+	0.189759i
$560$	−5.66663	+	12.6576i	−0.239459	+	0.534880i
$561$	−7.79046	+	3.22692i	−0.328914	+	0.136240i
$562$	12.3013	+	0.994734i	0.518900	+	0.0419603i
$563$	−18.1890	−	9.72222i	−0.766574	−	0.409743i	0.0412628	−	0.999148i	$-0.486862\pi$
$563$	−18.1890	−	9.72222i	−0.766574	−	0.409743i	−0.807837	+	0.589406i	$0.799362\pi$
$564$	1.71065	+	2.94761i	0.0720314	+	0.124117i
$565$	−48.8216	−	40.0669i	−2.05394	−	1.68563i
$566$	14.3612	−	3.11861i	0.603645	−	0.131085i
$567$	0.719399	−	3.61666i	0.0302119	−	0.151885i
$568$	−10.1676	+	1.54327i	−0.426622	+	0.0647542i
$569$	−38.0043	+	7.55952i	−1.59322	+	0.316911i	−0.910418	−	0.413690i	$-0.864240\pi$
$569$	−38.0043	+	7.55952i	−1.59322	+	0.316911i	−0.682804	+	0.730602i	$0.739240\pi$
$570$	7.17518	+	2.82610i	0.300535	+	0.118372i
$571$	19.7713	+	36.9895i	0.827403	+	1.54796i	0.836476	+	0.548004i	$0.184612\pi$
$571$	19.7713	+	36.9895i	0.827403	+	1.54796i	−0.00907233	+	0.999959i	$0.502888\pi$
$572$	11.8810	+	1.93414i	0.496770	+	0.0808705i
$573$	25.9232	+	2.55321i	1.08296	+	0.106662i
$574$	−9.16291	−	2.60547i	−0.382452	−	0.108750i
$575$		−	33.9094i		−	1.41412i
$576$	9.58874	+	2.83825i	0.399531	+	0.118260i
$577$			32.6338i			1.35856i	0.733879	+	0.679281i	$0.237708\pi$
$577$			32.6338i			1.35856i	−0.733879	+	0.679281i	$0.762292\pi$
$578$	0.239283	−	0.841508i	0.00995285	−	0.0350021i
$579$	27.8619	+	2.74415i	1.15790	+	0.114043i
$580$	−2.76067	−	3.83428i	−0.114631	−	0.159210i
$581$	6.02511	+	11.2722i	0.249964	+	0.467649i
$582$	5.36866	−	13.6305i	0.222538	−	0.565001i
$583$	2.05397	−	0.408561i	0.0850669	−	0.0169209i
$584$	6.51381	−	26.3816i	0.269543	−	1.09168i
$585$	3.35091	−	16.8462i	0.138543	−	0.696504i
$586$	−0.166571	−	0.767057i	−0.00688098	−	0.0316868i
$587$	14.0398	+	11.5221i	0.579483	+	0.475570i	0.877885	−	0.478871i	$-0.158954\pi$
$587$	14.0398	+	11.5221i	0.579483	+	0.475570i	−0.298402	+	0.954440i	$0.596454\pi$
$588$	2.55713	+	0.679025i	0.105454	+	0.0280025i
$589$	−1.65423	−	0.884202i	−0.0681612	−	0.0364329i
$590$	−0.427847	+	5.29094i	−0.0176142	+	0.217824i
$591$	−34.0197	+	14.0914i	−1.39938	+	0.579644i
$592$	2.90887	+	17.1390i	0.119554	+	0.704408i
$593$	−15.4518	−	6.40037i	−0.634531	−	0.262832i	0.0421456	−	0.999111i	$-0.486581\pi$
$593$	−15.4518	−	6.40037i	−0.634531	−	0.262832i	−0.676677	+	0.736280i	$0.736581\pi$
$594$	5.50477	−	10.7466i	0.225863	−	0.440937i
$595$	−13.9261	+	4.22442i	−0.570913	+	0.173185i
$596$	−7.30252	+	14.8923i	−0.299123	+	0.610014i
$597$	−2.01334	−	20.4418i	−0.0824006	−	0.836628i
$598$	−22.2442	+	15.4324i	−0.909632	+	0.631078i
$599$	−20.6887	−	30.9629i	−0.845318	−	1.26511i	−0.962304	−	0.271975i	$-0.912323\pi$
$599$	−20.6887	−	30.9629i	−0.845318	−	1.26511i	0.116986	−	0.993134i	$-0.462677\pi$
$600$	−19.5223	−	17.5745i	−0.796996	−	0.717475i
$601$	9.26876	+	6.19319i	0.378081	+	0.252625i	0.730061	−	0.683382i	$-0.239492\pi$
$601$	9.26876	+	6.19319i	0.378081	+	0.252625i	−0.351980	+	0.936007i	$0.614492\pi$
$602$	3.00934	+	2.90590i	0.122652	+	0.118435i
$603$	5.33601	+	1.61866i	0.217299	+	0.0659169i
$604$	0.892465	+	25.5086i	0.0363139	+	1.03793i
$605$	−19.1218	−	23.3000i	−0.777412	−	0.947279i
$606$	−3.56714	−	30.7037i	−0.144905	−	1.24725i
$607$	16.1621	+	16.1621i	0.656000	+	0.656000i	0.954431	−	0.298431i	$-0.0964634\pi$
$607$	16.1621	+	16.1621i	0.656000	+	0.656000i	−0.298431	+	0.954431i	$0.596463\pi$
$608$	6.41467	+	2.02137i	0.260149	+	0.0819775i
$609$	−0.637372	+	0.637372i	−0.0258276	+	0.0258276i
$610$	35.8115	+	28.3565i	1.44996	+	1.14812i
$611$	3.94640	−	3.23873i	0.159654	−	0.131025i
$612$	4.35226	+	9.54849i	0.175930	+	0.385975i
$613$	−4.77356	+	15.7363i	−0.192802	+	0.635584i	0.806230	+	0.591602i	$0.201504\pi$
$613$	−4.77356	+	15.7363i	−0.192802	+	0.635584i	−0.999032	+	0.0439818i	$0.985996\pi$
$614$	−0.165453	−	9.46089i	−0.00667714	−	0.381811i
$615$	17.1640	−	25.6877i	0.692118	−	1.03583i
$616$	3.69157	+	2.19576i	0.148738	+	0.0884697i
$617$	−17.4681	+	11.6718i	−0.703241	+	0.469891i	−0.855068	−	0.518517i	$-0.826484\pi$
$617$	−17.4681	+	11.6718i	−0.703241	+	0.469891i	0.151827	+	0.988407i	$0.451484\pi$
$618$	3.35980	−	18.5835i	0.135151	−	0.747537i
$619$	−3.01042	+	0.296500i	−0.120999	+	0.0119174i	−0.158335	−	0.987385i	$-0.550613\pi$
$619$	−3.01042	+	0.296500i	−0.120999	+	0.0119174i	0.0373364	+	0.999303i	$0.488113\pi$
$620$	7.23135	+	8.20848i	0.290418	+	0.329660i
$621$	7.88310	+	25.9871i	0.316338	+	1.04283i
$622$	15.8572	−	5.11469i	0.635817	−	0.205080i
$623$	5.44309	−	13.1408i	0.218073	−	0.526474i
$624$	−2.64390	+	20.8047i	−0.105841	+	0.832854i
$625$	4.13948	+	9.99358i	0.165579	+	0.399743i
$626$	−29.3363	−	34.4982i	−1.17251	−	1.37882i
$627$	1.12592	−	2.10644i	0.0449647	−	0.0841231i
$628$	−4.27805	−	31.9401i	−0.170713	−	1.27455i
$629$	−11.5727	+	14.1014i	−0.461436	+	0.562261i
$630$	3.31540	−	5.15474i	0.132089	−	0.205370i
$631$	13.9733	+	2.77947i	0.556270	+	0.110649i	0.465216	−	0.885197i	$-0.345977\pi$
$631$	13.9733	+	2.77947i	0.556270	+	0.110649i	0.0910536	+	0.995846i	$0.470977\pi$
$632$	32.8838	−	11.8912i	1.30805	−	0.473008i
$633$	−1.98889	−	9.99884i	−0.0790514	−	0.397418i
$634$	12.0145	+	27.6289i	0.477156	+	1.09728i
$635$	35.9203	−	19.1998i	1.42545	−	0.761921i
$636$	0.836498	+	3.55143i	0.0331693	+	0.140823i
$637$	0.388475	−	3.94425i	0.0153919	−	0.156277i
$638$	−1.27829	+	0.712276i	−0.0506082	+	0.0281993i
$639$	4.54493			0.179795
$640$	−30.9153	−	24.1421i	−1.22203	−	0.954302i
$641$	25.8537			1.02116			0.510580	−	0.859830i	$-0.329431\pi$
$641$	25.8537			1.02116			0.510580	+	0.859830i	$0.329431\pi$
$642$	1.27070	−	0.708045i	0.0501506	−	0.0279443i
$643$	1.19828	−	12.1664i	0.0472557	−	0.479795i	−0.942210	−	0.335024i	$-0.891256\pi$
$643$	1.19828	−	12.1664i	0.0472557	−	0.479795i	0.989465	−	0.144771i	$-0.0462445\pi$
$644$	−9.40309	+	2.21479i	−0.370533	+	0.0872749i
$645$	−11.9651	+	6.39546i	−0.471124	+	0.251821i
$646$	2.81443	+	6.47217i	0.110732	+	0.254644i
$647$	−4.13593	−	20.7927i	−0.162600	−	0.817446i	−0.972863	−	0.231380i	$-0.925676\pi$
$647$	−4.13593	−	20.7927i	−0.162600	−	0.817446i	0.810263	−	0.586066i	$-0.199324\pi$
$648$	9.44347	+	4.42753i	0.370975	+	0.173930i
$649$	1.61247	+	0.320740i	0.0632950	+	0.0125902i
$650$	−21.2856	+	33.0945i	−0.834889	+	1.29807i
$651$	1.32399	−	1.61329i	0.0518914	−	0.0632298i
$652$	22.5277	−	3.01735i	0.882251	−	0.118169i
$653$	−2.05480	+	3.84425i	−0.0804104	+	0.150437i	−0.918913	−	0.394460i	$-0.870932\pi$
$653$	−2.05480	+	3.84425i	−0.0804104	+	0.150437i	0.838503	+	0.544898i	$0.183432\pi$
$654$	−0.106064	−	0.124727i	−0.00414745	−	0.00487722i
$655$	26.3932	+	63.7189i	1.03127	+	2.48970i
$656$	13.3670	−	23.3945i	0.521892	−	0.913402i
$657$	−4.59574	+	11.0951i	−0.179297	+	0.432861i
$658$	1.73372	−	0.559204i	0.0675874	−	0.0218000i
$659$	−13.1167	−	43.2400i	−0.510954	−	1.68439i	−0.709836	−	0.704367i	$-0.751231\pi$
$659$	−13.1167	−	43.2400i	−0.510954	−	1.68439i	0.198882	−	0.980023i	$-0.436269\pi$
$660$	−10.4524	+	9.20817i	−0.406860	+	0.358427i
$661$	3.15873	−	0.311108i	0.122860	−	0.0121007i	−0.0364000	−	0.999337i	$-0.511589\pi$
$661$	3.15873	−	0.311108i	0.122860	−	0.0121007i	0.159260	+	0.987237i	$0.449089\pi$
$662$	−8.54113	+	47.2420i	−0.331960	+	1.83611i
$663$	−18.2984	+	12.2266i	−0.710650	+	0.474841i
$664$	−35.0381	+	8.90223i	−1.35974	+	0.345473i
$665$	2.29010	−	3.42737i	0.0888061	−	0.132908i
$666$	−0.134336	−	7.68156i	−0.00520541	−	0.297655i
$667$	0.955384	−	3.14948i	0.0369926	−	0.121948i
$668$	−40.5085	+	18.4640i	−1.56732	+	0.714394i
$669$	−15.1848	+	12.4618i	−0.587076	+	0.481801i
$670$	−17.1476	−	13.5779i	−0.662468	−	0.524560i
$671$	10.0039	−	10.0039i	0.386197	−	0.386197i
$672$	−3.59831	+	6.56142i	−0.138808	+	0.253112i
$673$	−9.97981	−	9.97981i	−0.384694	−	0.384694i	0.488096	−	0.872790i	$-0.337691\pi$
$673$	−9.97981	−	9.97981i	−0.384694	−	0.384694i	−0.872790	+	0.488096i	$0.837691\pi$
$674$	−1.98972	−	17.1263i	−0.0766412	−	0.659679i
$675$	25.0393	+	30.5104i	0.963762	+	1.17435i
$676$	5.41274	−	0.189375i	0.208182	−	0.00728366i
$677$	−31.3151	−	9.49935i	−1.20354	−	0.365090i	−0.376065	−	0.926593i	$-0.622723\pi$
$677$	−31.3151	−	9.49935i	−1.20354	−	0.365090i	−0.827474	+	0.561504i	$0.810223\pi$
$678$	−24.5161	−	23.6734i	−0.941536	−	0.909170i
$679$	−6.51087	−	4.35042i	−0.249864	−	0.166954i
$680$	−2.15828	−	41.1046i	−0.0827665	−	1.57629i
$681$	14.5686	+	21.8034i	0.558269	+	0.835509i
$682$	2.78382	−	1.93134i	0.106598	−	0.0739548i
$683$	3.18362	+	32.3238i	0.121818	+	1.23684i	0.840621	+	0.541624i	$0.182190\pi$
$683$	3.18362	+	32.3238i	0.121818	+	1.23684i	−0.718803	+	0.695213i	$0.755310\pi$
$684$	−2.66875	−	1.30863i	−0.102042	−	0.0500367i
$685$	23.3033	−	7.06897i	0.890373	−	0.270092i
$686$	0.644745	−	1.25869i	0.0246165	−	0.0480570i
$687$	9.58436	+	3.96997i	0.365666	+	0.151464i
$688$	−10.0198	+	6.29336i	−0.382002	+	0.239932i
$689$	5.04957	−	2.09160i	0.192373	−	0.0796836i
$690$	2.52521	−	31.2278i	0.0961330	−	1.18882i
$691$	−15.8678	−	8.48152i	−0.603640	−	0.322652i	0.141112	−	0.989994i	$-0.454932\pi$
$691$	−15.8678	−	8.48152i	−0.603640	−	0.322652i	−0.744752	+	0.667342i	$0.767432\pi$
$692$	13.0456	−	49.1282i	0.495918	−	1.86757i
$693$	−1.46736	−	1.20423i	−0.0557404	−	0.0457450i
$694$	−6.25577	−	28.8078i	−0.237466	−	1.09353i
$695$	−5.86948	+	29.5079i	−0.222642	+	1.11930i
$696$	−1.31806	−	2.18234i	−0.0499611	−	0.0827213i
$697$	27.7308	−	5.51599i	1.05038	−	0.208933i
$698$	−3.10470	+	7.88250i	−0.117515	+	0.298357i
$699$	−13.9797	−	26.1541i	−0.528759	−	0.989239i
$700$	−11.3944	+	8.20396i	−0.430669	+	0.310080i
$701$	−39.4854	−	3.88897i	−1.49134	−	0.146885i	−0.680759	−	0.732507i	$-0.738350\pi$
$701$	−39.4854	−	3.88897i	−1.49134	−	0.146885i	−0.810584	+	0.585623i	$0.800850\pi$
$702$	8.61893	−	30.3110i	0.325301	−	1.14401i
$703$		−	5.16713i		−	0.194882i
$704$	−8.53236	+	8.64821i	−0.321575	+	0.325942i
$705$			5.90789i			0.222504i
$706$	−13.7515	−	3.91025i	−0.517546	−	0.147164i
$707$	−16.4426	−	1.61946i	−0.618389	−	0.0609060i
$708$	−0.460235	+	2.82713i	−0.0172967	+	0.106250i
$709$	2.88063	+	5.38928i	0.108184	+	0.202399i	0.930188	−	0.367084i	$-0.119644\pi$
$709$	2.88063	+	5.38928i	0.108184	+	0.202399i	−0.822004	+	0.569482i	$0.807144\pi$
$710$	−16.5873	−	6.53326i	−0.622509	−	0.245189i
$711$	−15.1568	+	3.01487i	−0.568423	+	0.113066i
$712$	32.3937	+	23.8559i	1.21401	+	0.894039i
$713$	−1.48665	+	7.47389i	−0.0556755	+	0.279899i
$714$	−7.67387	+	1.66643i	−0.287187	+	0.0623644i
$715$	16.1304	+	13.2379i	0.603244	+	0.495070i
$716$	−2.33489	+	1.35506i	−0.0872591	+	0.0506409i
$717$	2.25486	+	1.20525i	0.0842093	+	0.0450108i
$718$	25.9109	+	2.09526i	0.966986	+	0.0781943i
$719$	−8.69985	+	3.60360i	−0.324450	+	0.134391i	−0.538963	−	0.842330i	$-0.681184\pi$
$719$	−8.69985	+	3.60360i	−0.324450	+	0.134391i	0.214513	+	0.976721i	$0.431184\pi$
$720$	11.9069	+	12.5989i	0.443744	+	0.469532i
$721$	−9.32593	−	3.86293i	−0.347316	−	0.143863i
$722$	22.1359	+	11.3388i	0.823813	+	0.421986i
$723$	−16.1656	+	4.90379i	−0.601206	+	0.182374i
$724$	−11.1540	+	3.81425i	−0.414535	+	0.141756i
$725$	−0.468863	−	4.76044i	−0.0174131	−	0.176798i
$726$	−9.27129	−	13.3636i	−0.344090	−	0.495969i
$727$	−17.4377	−	26.0974i	−0.646730	−	0.967900i	−0.999482	−	0.0321828i	$-0.989754\pi$
$727$	−17.4377	−	26.0974i	−0.646730	−	0.967900i	0.352752	−	0.935717i	$-0.385246\pi$
$728$	10.5674	+	3.74093i	0.391653	+	0.138648i
$729$	−22.3847	−	14.9570i	−0.829065	−	0.553963i
$730$	32.7217	−	33.8865i	1.21108	−	1.25420i
$731$	−11.8817	−	3.60428i	−0.439461	−	0.133309i
$732$	18.0279	+	16.8091i	0.666331	+	0.621282i
$733$	−15.2925	−	18.6340i	−0.564841	−	0.688261i	0.409764	−	0.912192i	$-0.365611\pi$
$733$	−15.2925	−	18.6340i	−0.564841	−	0.688261i	−0.974605	+	0.223930i	$0.928111\pi$
$734$	−18.6926	+	2.17170i	−0.689956	+	0.0801588i
$735$	3.24311	+	3.24311i	0.119624	+	0.119624i
$736$	0.293539	−	27.3222i	0.0108200	−	1.00711i
$737$	−4.79016	+	4.79016i	−0.176448	+	0.176448i
$738$	−7.39203	+	9.33542i	−0.272104	+	0.343641i
$739$	−20.7387	+	17.0198i	−0.762884	+	0.626083i	−0.933221	−	0.359303i	$-0.883014\pi$
$739$	−20.7387	+	17.0198i	−0.762884	+	0.626083i	0.170337	+	0.985386i	$0.445514\pi$
$740$	−10.5518	+	28.2278i	−0.387893	+	1.03768i
$741$	1.80951	−	5.96516i	0.0664741	−	0.219136i
$742$	1.94997	−	0.0341012i	0.0715855	−	0.00125189i
$743$	−15.0789	+	22.5671i	−0.553190	+	0.827907i	−0.997694	−	0.0678699i	$-0.978380\pi$
$743$	−15.0789	+	22.5671i	−0.553190	+	0.827907i	0.444505	+	0.895777i	$0.353380\pi$
$744$	3.53237	+	4.72944i	0.129503	+	0.173390i
$745$	−23.9070	+	15.9742i	−0.875886	+	0.585248i
$746$	25.8109	+	4.66650i	0.945005	+	0.170853i
$747$	15.8998	−	1.56599i	0.581743	−	0.0572967i
$748$	−12.7230	−	0.805195i	−0.465200	−	0.0294408i
$749$	−0.225709	−	0.744063i	−0.00824722	−	0.0271875i
$750$	−4.02259	−	12.4714i	−0.146884	−	0.455390i
$751$	6.78100	−	16.3708i	0.247442	−	0.597379i	−0.750543	−	0.660821i	$-0.770208\pi$
$751$	6.78100	−	16.3708i	0.247442	−	0.597379i	0.997985	+	0.0634429i	$0.0202081\pi$
$752$	0.360097	+	5.13987i	0.0131314	+	0.187432i
$753$	3.96170	+	9.56440i	0.144373	+	0.348546i
$754$	−2.90941	+	2.47408i	−0.105955	+	0.0901007i
$755$	−20.8577	+	39.0219i	−0.759088	+	1.42015i
$756$	6.82512	−	8.93618i	0.248227	−	0.325006i
$757$	−19.8867	+	24.2320i	−0.722794	+	0.880727i	−0.996712	−	0.0810261i	$-0.974180\pi$
$757$	−19.8867	+	24.2320i	−0.722794	+	0.880727i	0.273918	+	0.961753i	$0.411680\pi$
$758$	−4.69964	−	3.02269i	−0.170699	−	0.109789i
$759$	−9.51702	−	1.89305i	−0.345446	−	0.0687135i
$760$	7.85876	+	8.61227i	0.285067	+	0.312400i
$761$	7.73278	+	38.8753i	0.280313	+	1.40923i	0.822402	+	0.568907i	$0.192634\pi$
$761$	7.73278	+	38.8753i	0.280313	+	1.40923i	−0.542089	+	0.840321i	$0.682366\pi$
$762$	20.1548	−	8.76435i	0.730132	−	0.317499i
$763$	−0.0771820	+	0.0412546i	−0.00279417	+	0.00149352i
$764$	33.4898	+	20.7211i	1.21162	+	0.749661i
$765$	−1.78301	+	18.1032i	−0.0644650	+	0.654524i
$766$	21.4216	+	38.4446i	0.773994	+	1.38906i
$767$	4.29078			0.154931
$768$	−15.5778	−	14.3295i	−0.562115	−	0.517070i
$769$	30.7470			1.10876			0.554382	−	0.832262i	$-0.312955\pi$
$769$	30.7470			1.10876			0.554382	+	0.832262i	$0.312955\pi$
$770$	3.62424	+	6.50429i	0.130609	+	0.234398i
$771$	−2.88409	+	29.2827i	−0.103868	+	1.05459i
$772$	35.9943	+	22.2707i	1.29546	+	0.801539i
$773$	18.5219	−	9.90016i	0.666186	−	0.356084i	−0.103388	−	0.994641i	$-0.532968\pi$
$773$	18.5219	−	9.90016i	0.666186	−	0.356084i	0.769574	+	0.638557i	$0.220468\pi$
$774$	4.79539	−	2.08528i	0.172367	−	0.0749540i
$775$	2.16072	+	10.8627i	0.0776154	+	0.390199i
$776$	16.3605	−	14.9290i	0.587306	−	0.535921i
$777$	5.63878	+	1.12162i	0.202290	+	0.0402380i
$778$	−15.8025	−	10.1638i	−0.566549	−	0.364390i
$779$	−5.08063	+	6.19077i	−0.182033	+	0.221807i
$780$	−22.0668	+	28.8923i	−0.790119	+	1.03451i
$781$	−2.60284	+	4.86957i	−0.0931370	+	0.174247i
$782$	21.8427	−	18.5744i	0.781094	−	0.664220i
$783$	1.46601	+	3.53926i	0.0523908	+	0.126483i
$784$	3.01918	+	2.62384i	0.107828	+	0.0937085i
$785$	21.3779	−	51.6108i	0.763009	−	1.84207i
$786$	11.4243	+	35.4192i	0.407491	+	1.26336i
$787$	10.2022	+	33.6321i	0.363668	+	1.19885i	0.927771	+	0.373149i	$0.121722\pi$
$787$	10.2022	+	33.6321i	0.363668	+	1.19885i	−0.564103	+	0.825704i	$0.690778\pi$
$788$	−55.5595	−	3.51616i	−1.97922	−	0.125258i
$789$	−13.7811	+	1.35732i	−0.490620	+	0.0483218i
$790$	59.6502	+	10.7845i	2.12226	+	0.383694i
$791$	−15.1466	+	10.1206i	−0.538552	+	0.359849i
$792$	4.30164	−	3.21285i	0.152852	−	0.114164i
$793$	20.5136	−	30.7008i	0.728459	−	1.09022i
$794$	13.9654	−	0.244228i	0.495613	−	0.00866733i
$795$	−1.83603	+	6.05257i	−0.0651172	+	0.214663i
$796$	10.8736	−	29.0887i	0.385406	−	1.03102i
$797$	3.76336	−	3.08851i	0.133305	−	0.109401i	−0.565378	−	0.824832i	$-0.691270\pi$
$797$	3.76336	−	3.08851i	0.133305	−	0.109401i	0.698683	+	0.715431i	$0.253770\pi$
$798$	1.38080	−	1.74381i	0.0488796	−	0.0617302i
$799$	−3.82319	+	3.82319i	−0.135255	+	0.135255i
$800$	−14.8024	−	36.8510i	−0.523343	−	1.30288i
$801$	−12.5719	−	12.5719i	−0.444205	−	0.444205i
$802$	7.73003	−	0.898071i	0.272957	−	0.0317120i
$803$	−9.25567	−	11.2781i	−0.326625	−	0.397994i
$804$	−8.63229	−	8.04867i	−0.304437	−	0.283855i
$805$	−16.0253	−	4.86124i	−0.564819	−	0.171336i
$806$	6.14243	−	6.36109i	0.216358	−	0.224060i
$807$	−10.2473	−	6.84704i	−0.360723	−	0.241027i
$808$	15.5950	−	44.0529i	0.548632	−	1.54978i
$809$	6.61864	+	9.90550i	0.232699	+	0.348259i	0.929381	−	0.369121i	$-0.120341\pi$
$809$	6.61864	+	9.90550i	0.232699	+	0.348259i	−0.696682	+	0.717380i	$0.745341\pi$
$810$	10.3062	+	14.8553i	0.362124	+	0.521962i
$811$	3.28152	+	33.3178i	0.115230	+	1.16995i	0.862723	+	0.505677i	$0.168757\pi$
$811$	3.28152	+	33.3178i	0.115230	+	1.16995i	−0.747493	+	0.664269i	$0.768743\pi$
$812$	−1.28945	+	0.440943i	−0.0452508	+	0.0154741i
$813$	−20.0457	+	6.08078i	−0.703032	+	0.213262i
$814$	8.30718	+	4.25523i	0.291167	+	0.149146i
$815$	36.4016	+	15.0780i	1.27509	+	0.528160i
$816$	0.626918	−	22.2020i	0.0219465	−	0.777226i
$817$	3.24924	−	1.34588i	0.113676	−	0.0470863i
$818$	43.8501	+	3.54590i	1.53318	+	0.123979i
$819$	−4.36918	−	2.33537i	−0.152671	−	0.0816046i
$820$	40.3975	−	23.4448i	1.41074	−	0.818727i
$821$	1.88074	+	1.54348i	0.0656383	+	0.0538679i	0.666640	−	0.745379i	$-0.267732\pi$
$821$	1.88074	+	1.54348i	0.0656383	+	0.0538679i	−0.601002	+	0.799247i	$0.705232\pi$
$822$	12.8411	−	2.78853i	0.447886	−	0.0972610i
$823$	−5.08165	+	25.5472i	−0.177135	+	0.890518i	0.785323	+	0.619087i	$0.212497\pi$
$823$	−5.08165	+	25.5472i	−0.177135	+	0.890518i	−0.962458	+	0.271432i	$0.912503\pi$
$824$	16.9304	−	22.9896i	0.589799	−	0.800881i
$825$	−13.8322	+	2.75139i	−0.481575	+	0.0957912i
$826$	1.42454	+	0.561086i	0.0495660	+	0.0195227i
$827$	12.5717	+	23.5200i	0.437161	+	0.817870i	0.999962	−	0.00872222i	$-0.00277640\pi$
$827$	12.5717	+	23.5200i	0.437161	+	0.817870i	−0.562801	+	0.826592i	$0.690276\pi$
$828$	−1.94025	+	11.9186i	−0.0674285	+	0.414199i
$829$	29.8214	+	2.93715i	1.03574	+	0.102011i	0.601570	−	0.798820i	$-0.294542\pi$
$829$	29.8214	+	2.93715i	1.03574	+	0.102011i	0.434169	+	0.900831i	$0.357042\pi$
$830$	−60.2792	−	17.1404i	−2.09232	−	0.594952i
$831$			10.0086i			0.347193i
$832$	−17.4371	+	26.4813i	−0.604523	+	0.918075i
$833$			4.19745i			0.145433i
$834$	−4.44028	+	15.6155i	−0.153754	+	0.540722i
$835$	−76.8010	−	7.56424i	−2.65781	−	0.261771i
$836$	2.93047	−	2.10993i	0.101352	−	0.0729735i
$837$	−4.18121	−	7.82250i	−0.144524	−	0.270385i
$838$	−17.7747	+	45.1280i	−0.614015	+	1.55892i
$839$	41.8601	−	8.32649i	1.44517	−	0.287463i	0.590671	−	0.806913i	$-0.298863\pi$
$839$	41.8601	−	8.32649i	1.44517	−	0.287463i	0.854501	+	0.519450i	$0.173863\pi$
$840$	−11.1043	+	6.70665i	−0.383134	+	0.231401i
$841$	−5.56704	+	27.9874i	−0.191967	+	0.965083i
$842$	6.82910	+	31.4479i	0.235346	+	1.08377i
$843$	8.92394	+	7.32369i	0.307357	+	0.252241i
$844$	3.95570	−	14.8967i	0.136161	−	0.512766i
$845$	8.28019	+	4.42585i	0.284847	+	0.152254i
$846$	0.183535	−	2.26968i	0.00631007	−	0.0780331i
$847$	−8.03208	+	3.32700i	−0.275986	+	0.114317i
$848$	−1.22843	+	5.37766i	−0.0421845	+	0.184669i
$849$	12.7003	+	5.26065i	0.435875	+	0.180545i
$850$	18.9989	−	37.0903i	0.651658	−	1.27219i
$851$	−20.0882	+	6.09370i	−0.688616	+	0.208889i
$852$	−8.63732	−	4.23534i	−0.295910	−	0.145100i
$853$	2.08483	+	21.1676i	0.0713831	+	0.724764i	0.962553	+	0.271094i	$0.0873855\pi$
$853$	2.08483	+	21.1676i	0.0713831	+	0.724764i	−0.891170	+	0.453670i	$0.850114\pi$
$854$	10.8251	−	7.51018i	0.370428	−	0.256993i
$855$	−2.86261	−	4.28420i	−0.0978993	−	0.146517i
$856$	2.19620	−	0.115316i	0.0750645	−	0.00394142i
$857$	22.4270	+	14.9852i	0.766090	+	0.511885i	0.876149	−	0.482040i	$-0.160104\pi$
$857$	22.4270	+	14.9852i	0.766090	+	0.511885i	−0.110059	+	0.993925i	$0.535104\pi$
$858$	8.10001	+	7.82157i	0.276530	+	0.267024i
$859$	−16.2233	−	4.92129i	−0.553532	−	0.167912i	0.00111244	−	0.999999i	$-0.499646\pi$
$859$	−16.2233	−	4.92129i	−0.553532	−	0.167912i	−0.554645	+	0.832087i	$0.687146\pi$
$860$	−20.4989	+	0.717193i	−0.699007	+	0.0244561i
$861$	−5.65301	−	6.88822i	−0.192654	−	0.234750i
$862$	4.14351	+	35.6647i	0.141128	+	1.21474i
$863$	−38.8700	−	38.8700i	−1.32315	−	1.32315i	−0.911211	−	0.411939i	$-0.864852\pi$
$863$	−38.8700	−	38.8700i	−1.32315	−	1.32315i	−0.411939	−	0.911211i	$-0.635148\pi$
$864$	19.9110	+	24.8002i	0.677387	+	0.843721i
$865$	62.3073	−	62.3073i	2.11851	−	2.11851i
$866$	−9.48413	−	7.50978i	−0.322284	−	0.255193i
$867$	0.632603	−	0.519164i	0.0214843	−	0.0176317i
$868$	2.87110	−	1.30866i	0.0974513	−	0.0444189i
$869$	5.44992	−	17.9660i	0.184876	−	0.609454i
$870$	−0.0772781	−	4.41890i	−0.00261997	−	0.149815i
$871$	−9.82250	+	14.7004i	−0.332823	+	0.498105i
$872$	−0.0609545	−	0.239909i	−0.00206418	−	0.00812436i
$873$	−8.13857	+	5.43802i	−0.275449	+	0.184049i
$874$	−1.44491	+	7.99196i	−0.0488748	+	0.270332i
$875$	−6.97068	+	0.686552i	−0.235652	+	0.0232097i
$876$	19.0732	−	16.8027i	0.644423	−	0.567712i
$877$	10.2670	+	33.8459i	0.346693	+	1.14289i	0.940929	+	0.338604i	$0.109955\pi$
$877$	10.2670	+	33.8459i	0.346693	+	1.14289i	−0.594236	+	0.804291i	$0.702545\pi$
$878$	46.9898	−	15.1564i	1.58583	−	0.511503i
$879$	0.280981	−	0.678349i	0.00947726	−	0.0228801i
$880$	−20.3178	+	5.54214i	−0.684912	+	0.186826i
$881$	−7.05890	−	17.0417i	−0.237820	−	0.574149i	0.759236	−	0.650815i	$-0.225573\pi$
$881$	−7.05890	−	17.0417i	−0.237820	−	0.574149i	−0.997057	+	0.0766656i	$0.975573\pi$
$882$	−1.14518	−	1.34668i	−0.0385602	−	0.0453451i
$883$	−16.1638	+	30.2403i	−0.543954	+	1.01767i	0.448352	+	0.893857i	$0.352011\pi$
$883$	−16.1638	+	30.2403i	−0.543954	+	1.01767i	−0.992306	+	0.123809i	$0.960489\pi$
$884$	−32.9773	+	4.41698i	−1.10915	+	0.148559i
$885$	−3.15000	+	3.83829i	−0.105886	+	0.129023i
$886$	−25.9895	+	40.4082i	−0.873135	+	1.35754i
$887$	−7.51244	−	1.49432i	−0.252243	−	0.0501743i	0.0673490	−	0.997729i	$-0.478546\pi$
$887$	−7.51244	−	1.49432i	−0.252243	−	0.0501743i	−0.319592	+	0.947555i	$0.603546\pi$
$888$	−6.90302	+	14.7234i	−0.231650	+	0.494086i
$889$	−2.29186	−	11.5220i	−0.0768666	−	0.386435i
$890$	27.8106	+	63.9543i	0.932215	+	2.14375i
$891$	4.93863	−	2.63975i	0.165450	−	0.0884350i
$892$	−28.9074	+	6.80879i	−0.967890	+	0.227975i
$893$	0.150112	−	1.52411i	0.00502330	−	0.0510024i
$894$	−13.5532	+	7.55193i	−0.453286	+	0.252574i
$895$	−4.67982			−0.156429
$896$	−9.25196	+	6.51162i	−0.309086	+	0.217538i
$897$	−25.3248			−0.845569
$898$	23.0722	−	12.8560i	0.769928	−	0.429010i
$899$	−0.105366	+	1.06979i	−0.00351414	+	0.0356796i
$900$	4.02375	+	17.0832i	0.134125	+	0.569440i
$901$	−5.10498	+	2.72867i	−0.170072	+	0.0909051i
$902$	−5.76889	−	13.2663i	−0.192083	−	0.441721i
$903$	0.763420	+	3.83797i	0.0254050	+	0.127720i
$904$	−17.5216	−	48.4538i	−0.582759	−	1.61155i
$905$	−20.0423	−	3.98665i	−0.666227	−	0.132521i
$906$	−12.9155	+	20.0808i	−0.429088	+	0.667140i
$907$	10.2638	−	12.5064i	0.340803	−	0.415270i	−0.574201	−	0.818714i	$-0.694687\pi$
$907$	10.2638	−	12.5064i	0.340803	−	0.415270i	0.915004	+	0.403445i	$0.132187\pi$
$908$	5.26305	+	39.2942i	0.174661	+	1.30402i
$909$	−9.73561	+	18.2141i	−0.322910	+	0.604122i
$910$	12.5888	+	14.8038i	0.417313	+	0.490742i
$911$	16.3760	+	39.5351i	0.542560	+	1.30986i	0.922911	+	0.385014i	$0.125803\pi$
$911$	16.3760	+	39.5351i	0.542560	+	1.30986i	−0.380350	+	0.924843i	$0.624197\pi$
$912$	3.85227	+	4.97391i	0.127561	+	0.164703i
$913$	−7.42781	+	17.9323i	−0.245825	+	0.593473i
$914$	−38.6879	+	12.4786i	−1.27968	+	0.412757i
$915$	12.4035	+	40.8888i	0.410046	+	1.35174i
$916$	10.3677	+	11.7686i	0.342558	+	0.388846i
$917$	19.7970	−	1.94983i	0.653754	−	0.0643892i
$918$	−5.93761	+	32.8416i	−0.195970	+	1.08394i
$919$	−21.0353	+	14.0554i	−0.693892	+	0.463644i	−0.851839	−	0.523804i	$-0.824513\pi$
$919$	−21.0353	+	14.0554i	−0.693892	+	0.463644i	0.157947	+	0.987448i	$0.449513\pi$
$920$	24.2139	−	40.7091i	0.798309	−	1.34214i
$921$	4.91747	−	7.35952i	0.162036	−	0.242504i
$922$	−0.478538	−	27.3637i	−0.0157598	−	0.901174i
$923$	−4.18315	+	13.7900i	−0.137690	+	0.453903i
$924$	1.66641	+	3.65596i	0.0548209	+	0.120272i
$925$	−23.5848	+	19.3556i	−0.775464	+	0.636407i
$926$	−30.8493	−	24.4273i	−1.01377	−	0.802731i
$927$	−8.92217	+	8.92217i	−0.293043	+	0.293043i
$928$	−0.336572	−	3.83974i	−0.0110485	−	0.126046i
$929$	−6.30471	−	6.30471i	−0.206851	−	0.206851i	0.596077	−	0.802928i	$-0.296725\pi$
$929$	−6.30471	−	6.30471i	−0.206851	−	0.206851i	−0.802928	+	0.596077i	$0.796725\pi$
$930$	1.18091	+	10.1646i	0.0387237	+	0.333309i
$931$	−0.754251	−	0.919058i	−0.0247196	−	0.0301209i
$932$	−1.56769	−	44.8079i	−0.0513514	−	1.46773i
$933$	14.9145	+	4.52426i	0.488278	+	0.148118i
$934$	−7.95779	−	7.68425i	−0.260387	−	0.251436i
$935$	−18.3752	−	12.2779i	−0.600934	−	0.401531i
$936$	9.37514	−	10.4142i	0.306436	−	0.340400i
$937$	25.9704	+	38.8675i	0.848417	+	1.26975i	0.961124	+	0.276118i	$0.0890480\pi$
$937$	25.9704	+	38.8675i	0.848417	+	1.26975i	−0.112707	+	0.993628i	$0.535952\pi$
$938$	−5.18338	+	3.59609i	−0.169243	+	0.117416i
$939$	−4.15204	−	42.1564i	−0.135497	−	1.37572i
$940$	−3.93245	+	8.01962i	−0.128263	+	0.261571i
$941$	31.1494	−	9.44908i	1.01544	−	0.308031i	0.261664	−	0.965159i	$-0.415729\pi$
$941$	31.1494	−	9.44908i	1.01544	−	0.308031i	0.753779	+	0.657128i	$0.228229\pi$
$942$	13.7428	−	26.8291i	0.447765	−	0.874139i
$943$	30.0595	+	12.4511i	0.978873	+	0.405463i
$944$	−2.50656	+	3.53132i	−0.0815814	+	0.114935i
$945$	18.0086	−	7.45942i	0.585821	−	0.242655i
$946$	−0.512043	+	6.33215i	−0.0166479	+	0.205876i
$947$	35.7017	+	19.0829i	1.16015	+	0.620112i	0.935152	−	0.354248i	$-0.115263\pi$
$947$	35.7017	+	19.0829i	1.16015	+	0.620112i	0.224996	+	0.974360i	$0.427763\pi$
$948$	31.6138	+	8.39479i	1.02677	+	0.272650i
$949$	−29.4342	−	24.1561i	−0.955476	−	0.784139i
$950$	2.50492	+	11.5351i	0.0812702	+	0.374248i
$951$	−5.49810	+	27.6408i	−0.178288	+	0.896315i
$952$	−11.5261	−	2.84586i	−0.373562	−	0.0922350i
$953$	39.7149	−	7.89978i	1.28649	−	0.255899i	0.495973	−	0.868338i	$-0.334811\pi$
$953$	39.7149	−	7.89978i	1.28649	−	0.255899i	0.790518	+	0.612439i	$0.209811\pi$
$954$	0.893391	−	2.26822i	0.0289246	−	0.0734365i
$955$	32.1818	+	60.2078i	1.04138	+	1.94828i
$956$	2.25860	+	3.13695i	0.0730483	+	0.101456i
$957$	−1.36224	−	0.134169i	−0.0440350	−	0.00433707i
$958$	7.78686	−	27.3848i	0.251582	−	0.884762i
$959$		−	7.02384i		−	0.226812i
$960$	−10.8875	−	35.0391i	−0.351394	−	1.13088i
$961$			28.5111i			0.919711i
$962$	23.4306	+	6.66250i	0.755434	+	0.214808i
$963$	−0.967247	−	0.0952655i	−0.0311691	−	0.00306989i
$964$	−25.2080	−	4.10368i	−0.811895	−	0.132171i
$965$	34.5885	+	64.7104i	1.11344	+	2.08310i
$966$	−8.40781	−	3.31160i	−0.270517	−	0.106549i
$967$	45.6638	−	9.08310i	1.46845	−	0.292093i	0.604878	−	0.796318i	$-0.293222\pi$
$967$	45.6638	−	9.08310i	1.46845	−	0.292093i	0.863572	+	0.504226i	$0.168222\pi$
$968$	−3.69008	−	24.3115i	−0.118604	−	0.781401i
$969$	−1.28795	+	6.47495i	−0.0413749	+	0.208005i
$970$	37.5197	−	8.14762i	1.20468	−	0.261604i
$971$	−42.5965	−	34.9580i	−1.36699	−	1.12186i	−0.979828	−	0.199844i	$-0.935957\pi$
$971$	−42.5965	−	34.9580i	−1.36699	−	1.12186i	−0.387159	−	0.922013i	$-0.626543\pi$
$972$	−12.0352	−	20.7378i	−0.386029	−	0.665164i
$973$	7.65308	+	4.09066i	0.245347	+	0.131140i
$974$	−43.9926	−	3.55742i	−1.40962	−	0.113987i
$975$	−34.0056	+	14.0856i	−1.08905	+	0.451100i
$976$	13.2833	+	34.8173i	0.425187	+	1.11447i
$977$	−13.5585	−	5.61610i	−0.433773	−	0.179675i	0.155102	−	0.987898i	$-0.450429\pi$
$977$	−13.5585	−	5.61610i	−0.433773	−	0.179675i	−0.588876	+	0.808224i	$0.700429\pi$
$978$	18.9228	+	9.69293i	0.605085	+	0.309946i
$979$	20.6697	−	6.27007i	0.660605	−	0.200392i
$980$	2.24363	+	6.56104i	0.0716702	+	0.209585i
$981$	0.0107225	+	0.108868i	0.000342344	+	0.00347588i
$982$	21.5713	+	31.0928i	0.688369	+	0.992210i
$983$	20.8668	+	31.2293i	0.665547	+	0.996061i	0.998587	+	0.0531484i	$0.0169256\pi$
$983$	20.8668	+	31.2293i	0.665547	+	0.996061i	−0.333040	+	0.942913i	$0.608074\pi$
$984$	22.7475	−	10.8528i	0.725164	−	0.345974i
$985$	−80.2417	−	53.6158i	−2.55671	−	1.70834i
$986$	2.80961	−	2.90963i	0.0894762	−	0.0926614i
$987$	1.63065	+	0.494651i	0.0519040	+	0.0157449i
$988$	6.42689	−	6.89291i	0.204467	−	0.219293i
$989$	−9.06426	−	11.0448i	−0.288227	−	0.351205i
$990$	9.24512	−	1.07409i	0.293829	−	0.0341370i
$991$	34.2753	+	34.2753i	1.08879	+	1.08879i	0.995653	+	0.0931381i	$0.0296898\pi$
$991$	34.2753	+	34.2753i	1.08879	+	1.08879i	0.0931381	+	0.995653i	$0.470310\pi$
$992$	1.64695	+	8.77120i	0.0522906	+	0.278486i
$993$	−31.7542	+	31.7542i	−1.00769	+	1.00769i
$994$	−3.19206	+	4.03126i	−0.101246	+	0.127864i
$995$	41.6140	−	34.1517i	1.31925	−	1.08268i
$996$	−31.6757	−	11.8407i	−1.00368	−	0.375186i
$997$	10.8636	−	35.8124i	0.344053	−	1.13419i	−0.598777	−	0.800916i	$-0.704346\pi$
$997$	10.8636	−	35.8124i	0.344053	−	1.13419i	0.942830	−	0.333275i	$-0.108154\pi$
$998$	2.77994	−	0.0486158i	0.0879973	−	0.00153891i
$999$	13.5750	−	20.3164i	0.429493	−	0.642782i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.bn.b.29.34	✓	784
128.53	even	32	inner	896.2.bn.b.309.34	yes	784

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.bn.b.29.34	✓	784	1.1	even	1	trivial
896.2.bn.b.309.34	yes	784	128.53	even	32	inner

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.bn (of order \(32\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(0.688362 + 1.23538i) q^{2} +(-0.129665 + 1.31651i) q^{3} +(-1.05232 + 1.70077i) q^{4} +(-3.05765 + 1.63435i) q^{5} +(-1.71564 + 0.746048i) q^{6} +(0.195090 + 0.980785i) q^{7} +(-2.82547 - 0.129259i) q^{8} +(1.22598 + 0.243862i) q^{9} +O(q^{10})\)	\(q+(0.688362 + 1.23538i) q^{2} +(-0.129665 + 1.31651i) q^{3} +(-1.05232 + 1.70077i) q^{4} +(-3.05765 + 1.63435i) q^{5} +(-1.71564 + 0.746048i) q^{6} +(0.195090 + 0.980785i) q^{7} +(-2.82547 - 0.129259i) q^{8} +(1.22598 + 0.243862i) q^{9} +(-4.12380 - 2.65233i) q^{10} +(-0.963388 + 1.17389i) q^{11} +(-2.10263 - 1.60591i) q^{12} +(-1.86830 + 3.49535i) q^{13} +(-1.07735 + 0.916146i) q^{14} +(-1.75516 - 4.23733i) q^{15} +(-1.78526 - 3.57950i) q^{16} +(1.60630 - 3.87794i) q^{17} +(0.542655 + 1.68241i) q^{18} +(0.345129 + 1.13774i) q^{19} +(0.437956 - 6.92021i) q^{20} +(-1.31651 + 0.129665i) q^{21} +(-2.11336 - 0.382085i) q^{22} +(4.01616 - 2.68351i) q^{23} +(0.536534 - 3.70299i) q^{24} +(3.90026 - 5.83716i) q^{25} +(-5.60415 + 0.0980058i) q^{26} +(-1.63205 + 5.38013i) q^{27} +(-1.87339 - 0.700291i) q^{28} +(0.526713 - 0.432262i) q^{29} +(4.02652 - 5.08510i) q^{30} +(-1.11556 + 1.11556i) q^{31} +(3.19313 - 4.66947i) q^{32} +(-1.42052 - 1.42052i) q^{33} +(5.89644 - 0.685046i) q^{34} +(-2.19946 - 2.68005i) q^{35} +(-1.70487 + 1.82849i) q^{36} +(-4.15888 - 1.26158i) q^{37} +(-1.16796 + 1.20954i) q^{38} +(-4.35940 - 2.91286i) q^{39} +(8.85055 - 4.22257i) q^{40} +(3.74232 + 5.60078i) q^{41} +(-1.06642 - 1.53713i) q^{42} +(-0.289942 - 2.94383i) q^{43} +(-0.982736 - 2.87381i) q^{44} +(-4.14717 + 1.25803i) q^{45} +(6.07973 + 3.11425i) q^{46} +(-1.19007 - 0.492941i) q^{47} +(4.94392 - 1.88618i) q^{48} +(-0.923880 + 0.382683i) q^{49} +(9.89589 + 0.800221i) q^{50} +(4.89706 + 2.61753i) q^{51} +(-3.97876 - 6.85577i) q^{52} +(-1.06602 - 0.874857i) q^{53} +(-7.76993 + 1.68729i) q^{54} +(1.02715 - 5.16385i) q^{55} +(-0.424447 - 2.79640i) q^{56} +(-1.54259 + 0.306840i) q^{57} +(0.896576 + 0.353137i) q^{58} +(-0.510343 - 0.954784i) q^{59} +(9.05372 + 1.47388i) q^{60} +(-9.27141 - 0.913154i) q^{61} +(-2.14605 - 0.610229i) q^{62} +1.25000i q^{63} +(7.96658 + 0.730435i) q^{64} -13.7410i q^{65} +(0.777046 - 2.73271i) q^{66} +(4.43942 + 0.437245i) q^{67} +(4.90517 + 6.81277i) q^{68} +(3.01211 + 5.63526i) q^{69} +(1.79685 - 4.56201i) q^{70} +(3.56609 - 0.709340i) q^{71} +(-3.43245 - 0.847495i) q^{72} +(-1.87431 + 9.42282i) q^{73} +(-1.30429 - 6.00622i) q^{74} +(7.17893 + 5.89160i) q^{75} +(-2.29822 - 0.610273i) q^{76} +(-1.33928 - 0.715862i) q^{77} +(0.597634 - 7.39060i) q^{78} +(-11.4219 + 4.73111i) q^{79} +(11.3089 + 8.02711i) q^{80} +(-3.40682 - 1.41115i) q^{81} +(-4.34300 + 8.47854i) q^{82} +(12.2310 - 3.71025i) q^{83} +(1.16485 - 2.37553i) q^{84} +(1.42641 + 14.4826i) q^{85} +(3.43715 - 2.38461i) q^{86} +(0.500780 + 0.749470i) q^{87} +(2.87376 - 3.19227i) q^{88} +(-11.8264 - 7.90214i) q^{89} +(-4.40889 - 4.25734i) q^{90} +(-3.79268 - 1.15050i) q^{91} +(0.337781 + 9.65449i) q^{92} +(-1.32399 - 1.61329i) q^{93} +(-0.210227 - 1.80950i) q^{94} +(-2.91474 - 2.91474i) q^{95} +(5.73335 + 4.80924i) q^{96} +(-5.53704 + 5.53704i) q^{97} +(-1.10872 - 0.877915i) q^{98} +(-1.46736 + 1.20423i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 784 q+O(q^{10}) \) 784 * q	\( 784 q - 112 q^{12} + 160 q^{32} - 112 q^{34} + 160 q^{45} + 128 q^{54} - 64 q^{56} - 144 q^{58} - 96 q^{60} - 96 q^{62} - 96 q^{68} - 96 q^{70} - 144 q^{72} - 144 q^{74} + 256 q^{76} - 256 q^{85} - 160 q^{96}+O(q^{100}) \) 784 * q - 112 * q^12 + 160 * q^32 - 112 * q^34 + 160 * q^45 + 128 * q^54 - 64 * q^56 - 144 * q^58 - 96 * q^60 - 96 * q^62 - 96 * q^68 - 96 * q^70 - 144 * q^72 - 144 * q^74 + 256 * q^76 - 256 * q^85 - 160 * q^96

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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