LMFDB - Embedded newform 357.2.bl.a.10.16

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [357,2,Mod(10,357)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(357, base_ring=CyclotomicField(48))

chi = DirichletCharacter(H, H._module([0, 8, 9]))

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

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

chi := DirichletCharacter("357.10");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 357 = 3 \cdot 7 \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	357.bl (of order $48$, 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:	$2.85065935216$
Analytic rank:	$0$
Dimension:	$384$
Relative dimension:	$24$ over $\Q(\zeta_{48})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{48}]$

Embedding invariants

Embedding label			10.16
Character	$\chi$	$=$	357.10
Dual form			357.2.bl.a.250.16

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.03243 - 0.135922i) q^{2} +(0.442289 + 0.896873i) q^{3} +(-0.884410 + 0.236977i) q^{4} +(-2.20366 + 1.93256i) q^{5} +(0.578538 + 0.865843i) q^{6} +(2.58525 + 0.562582i) q^{7} +(-2.80503 + 1.16188i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-2.01245 + 2.29476i) q^{10} +(-5.38938 + 0.353239i) q^{11} +(-0.603703 - 0.688391i) q^{12} +(1.52303 + 1.52303i) q^{13} +(2.74556 + 0.229435i) q^{14} +(-2.70792 - 1.12166i) q^{15} +(-1.15220 + 0.665221i) q^{16} +(0.240895 - 4.11606i) q^{17} +(-0.520670 + 0.901828i) q^{18} +(0.551372 + 4.18808i) q^{19} +(1.49097 - 2.23139i) q^{20} +(0.638861 + 2.56746i) q^{21} +(-5.51616 + 1.09723i) q^{22} +(5.63769 + 2.78020i) q^{23} +(-2.28269 - 2.00187i) q^{24} +(0.468709 - 3.56020i) q^{25} +(1.77944 + 1.36541i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-2.41974 + 0.115091i) q^{28} +(1.80665 + 9.08263i) q^{29} +(-2.94820 - 0.789967i) q^{30} +(5.24394 - 2.58602i) q^{31} +(3.71832 - 2.85317i) q^{32} +(-2.70047 - 4.67736i) q^{33} +(-0.310757 - 4.28230i) q^{34} +(-6.78424 + 3.75640i) q^{35} +(0.350388 - 0.845912i) q^{36} +(-0.257178 + 3.92377i) q^{37} +(1.13851 + 4.24897i) q^{38} +(-0.692346 + 2.03959i) q^{39} +(3.93593 - 7.98129i) q^{40} +(0.761744 - 3.82955i) q^{41} +(1.00856 + 2.56389i) q^{42} +(-1.20385 - 2.90635i) q^{43} +(4.68272 - 1.58957i) q^{44} +(-0.191698 - 2.92475i) q^{45} +(6.19842 + 2.10408i) q^{46} +(2.29640 - 8.57027i) q^{47} +(-1.10622 - 0.739154i) q^{48} +(6.36700 + 2.90883i) q^{49} -3.73937i q^{50} +(3.79813 - 1.60444i) q^{51} +(-1.70791 - 0.986062i) q^{52} +(-3.09583 - 4.03456i) q^{53} +(-1.03911 - 0.0681070i) q^{54} +(11.1937 - 11.1937i) q^{55} +(-7.90535 + 1.42569i) q^{56} +(-3.51231 + 2.34685i) q^{57} +(3.09977 + 9.13163i) q^{58} +(-3.32705 - 0.438015i) q^{59} +(2.66072 + 0.350290i) q^{60} +(0.610394 + 1.79816i) q^{61} +(5.06251 - 3.38266i) q^{62} +(-2.02012 + 1.70854i) q^{63} +(5.33264 - 5.33264i) q^{64} +(-6.29960 - 0.412898i) q^{65} +(-3.42381 - 4.46200i) q^{66} +(-3.48497 - 2.01205i) q^{67} +(0.762363 + 3.69737i) q^{68} +6.28594i q^{69} +(-6.49368 + 4.80036i) q^{70} +(5.71987 + 3.82190i) q^{71} +(0.785812 - 2.93269i) q^{72} +(-0.614384 - 0.208555i) q^{73} +(0.267810 + 4.08598i) q^{74} +(3.40035 - 1.15426i) q^{75} +(-1.48012 - 3.57332i) q^{76} +(-14.1316 - 2.11876i) q^{77} +(-0.437575 + 2.19984i) q^{78} +(-5.15796 + 10.4593i) q^{79} +(1.25347 - 3.69261i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(0.265928 - 4.05728i) q^{82} +(-4.95239 + 11.9561i) q^{83} +(-1.17344 - 2.11929i) q^{84} +(7.42369 + 9.53596i) q^{85} +(-1.63793 - 2.83697i) q^{86} +(-7.34690 + 5.63748i) q^{87} +(14.7070 - 7.25267i) q^{88} +(3.72533 + 0.998199i) q^{89} +(-0.595454 - 2.99355i) q^{90} +(3.08058 + 4.79425i) q^{91} +(-5.64487 - 1.12284i) q^{92} +(4.63867 + 3.55937i) q^{93} +(1.20598 - 9.16035i) q^{94} +(-9.30876 - 8.16356i) q^{95} +(4.20350 + 2.07294i) q^{96} +(-1.34985 + 0.268502i) q^{97} +(6.96887 + 2.13775i) q^{98} +(3.00061 - 4.49072i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) $ 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/357\mathbb{Z}\right)^\times$.

$n$	$52$	$190$	$239$
$\chi(n)$	$e\left(\frac{1}{6}\right)$	$e\left(\frac{3}{16}\right)$	$1$

Coefficient data

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

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

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

$2$	1.03243	−	0.135922i	0.730040	−	0.0961116i	0.243662	−	0.969860i	$-0.421651\pi$
$2$	1.03243	−	0.135922i	0.730040	−	0.0961116i	0.486378	+	0.873749i	$0.338318\pi$
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$3$	0.442289	+	0.896873i	0.255355	+	0.517810i
$4$	−0.884410	+	0.236977i	−0.442205	+	0.118489i
$5$	−2.20366	+	1.93256i	−0.985508	+	0.864267i	−0.990747	−	0.135719i	$-0.956666\pi$
$5$	−2.20366	+	1.93256i	−0.985508	+	0.864267i	0.00523945	+	0.999986i	$0.498332\pi$
$6$	0.578538	+	0.865843i	0.236187	+	0.353479i
$7$	2.58525	+	0.562582i	0.977131	+	0.212636i
$7$	2.58525	+	0.562582i	0.977131	+	0.212636i
$8$	−2.80503	+	1.16188i	−0.991728	+	0.410787i
$9$	−0.608761	+	0.793353i	−0.202920	+	0.264451i
$10$	−2.01245	+	2.29476i	−0.636394	+	0.725668i
$11$	−5.38938	+	0.353239i	−1.62496	+	0.106506i	−0.850450	−	0.526056i	$-0.823670\pi$
$11$	−5.38938	+	0.353239i	−1.62496	+	0.106506i	−0.774510	+	0.632561i	$0.782004\pi$
$12$	−0.603703	−	0.688391i	−0.174274	−	0.198721i
$13$	1.52303	+	1.52303i	0.422413	+	0.422413i	0.886034	−	0.463621i	$-0.153450\pi$
$13$	1.52303	+	1.52303i	0.422413	+	0.422413i	−0.463621	+	0.886034i	$0.653450\pi$
$14$	2.74556	+	0.229435i	0.733782	+	0.0613191i
$15$	−2.70792	−	1.12166i	−0.699181	−	0.289610i
$16$	−1.15220	+	0.665221i	−0.288049	+	0.166305i
$17$	0.240895	−	4.11606i	0.0584255	−	0.998292i
$17$	0.240895	−	4.11606i	0.0584255	−	0.998292i
$18$	−0.520670	+	0.901828i	−0.122723	+	0.212563i
$19$	0.551372	+	4.18808i	0.126493	+	0.960812i	0.930526	+	0.366227i	$0.119351\pi$
$19$	0.551372	+	4.18808i	0.126493	+	0.960812i	−0.804032	+	0.594586i	$0.797316\pi$
$20$	1.49097	−	2.23139i	0.333391	−	0.498955i
$21$	0.638861	+	2.56746i	0.139411	+	0.560266i
$22$	−5.51616	+	1.09723i	−1.17605	+	0.233931i
$23$	5.63769	+	2.78020i	1.17554	+	0.579712i	0.921840	−	0.387571i	$-0.126686\pi$
$23$	5.63769	+	2.78020i	1.17554	+	0.579712i	0.253699	+	0.967283i	$0.418353\pi$
$24$	−2.28269	−	2.00187i	−0.465953	−	0.408630i
$25$	0.468709	−	3.56020i	0.0937418	−	0.712040i
$26$	1.77944	+	1.36541i	0.348977	+	0.267780i
$27$	−0.980785	−	0.195090i	−0.188752	−	0.0375451i
$28$	−2.41974	+	0.115091i	−0.457288	+	0.0217501i
$29$	1.80665	+	9.08263i	0.335486	+	1.68660i	0.668526	+	0.743689i	$0.266926\pi$
$29$	1.80665	+	9.08263i	0.335486	+	1.68660i	−0.333040	+	0.942913i	$0.608074\pi$
$30$	−2.94820	−	0.789967i	−0.538265	−	0.144228i
$31$	5.24394	−	2.58602i	0.941839	−	0.464463i	0.0945051	−	0.995524i	$-0.469873\pi$
$31$	5.24394	−	2.58602i	0.941839	−	0.464463i	0.847334	+	0.531061i	$0.178206\pi$
$32$	3.71832	−	2.85317i	0.657313	−	0.504374i
$33$	−2.70047	−	4.67736i	−0.470092	−	0.814223i
$34$	−0.310757	−	4.28230i	−0.0532944	−	0.734408i
$35$	−6.78424	+	3.75640i	−1.14675	+	0.634948i
$36$	0.350388	−	0.845912i	0.0583981	−	0.140985i
$37$	−0.257178	+	3.92377i	−0.0422797	+	0.645064i	0.923156	+	0.384424i	$0.125600\pi$
$37$	−0.257178	+	3.92377i	−0.0422797	+	0.645064i	−0.965436	+	0.260640i	$0.916067\pi$
$38$	1.13851	+	4.24897i	0.184690	+	0.689274i
$39$	−0.692346	+	2.03959i	−0.110864	+	0.326595i
$40$	3.93593	−	7.98129i	0.622326	−	1.26195i
$41$	0.761744	−	3.82955i	0.118964	−	0.598075i	−0.874604	−	0.484838i	$-0.838878\pi$
$41$	0.761744	−	3.82955i	0.118964	−	0.598075i	0.993568	−	0.113236i	$-0.0361216\pi$
$42$	1.00856	+	2.56389i	0.155624	+	0.395617i
$43$	−1.20385	−	2.90635i	−0.183585	−	0.443214i	0.805115	−	0.593118i	$-0.202103\pi$
$43$	−1.20385	−	2.90635i	−0.183585	−	0.443214i	−0.988700	+	0.149905i	$0.952103\pi$
$44$	4.68272	−	1.58957i	0.705946	−	0.239636i
$45$	−0.191698	−	2.92475i	−0.0285767	−	0.435996i
$46$	6.19842	+	2.10408i	0.913907	+	0.310230i
$47$	2.29640	−	8.57027i	0.334964	−	1.25010i	−0.568945	−	0.822376i	$-0.692648\pi$
$47$	2.29640	−	8.57027i	0.334964	−	1.25010i	0.903908	−	0.427726i	$-0.140685\pi$
$48$	−1.10622	−	0.739154i	−0.159669	−	0.106688i
$49$	6.36700	+	2.90883i	0.909572	+	0.415547i
$50$		−	3.73937i		−	0.528827i
$51$	3.79813	−	1.60444i	0.531844	−	0.224666i
$52$	−1.70791	−	0.986062i	−0.236844	−	0.136742i
$53$	−3.09583	−	4.03456i	−0.425245	−	0.554190i	0.530767	−	0.847518i	$-0.321904\pi$
$53$	−3.09583	−	4.03456i	−0.425245	−	0.554190i	−0.956012	+	0.293328i	$0.905237\pi$
$54$	−1.03911	−	0.0681070i	−0.141405	−	0.00926818i
$55$	11.1937	−	11.1937i	1.50936	−	1.50936i
$56$	−7.90535	+	1.42569i	−1.05640	+	0.190516i
$57$	−3.51231	+	2.34685i	−0.465217	+	0.310848i
$58$	3.09977	+	9.13163i	0.407020	+	1.19904i
$59$	−3.32705	−	0.438015i	−0.433146	−	0.0570247i	−0.0891988	−	0.996014i	$-0.528431\pi$
$59$	−3.32705	−	0.438015i	−0.433146	−	0.0570247i	−0.343947	+	0.938989i	$0.611764\pi$
$60$	2.66072	+	0.350290i	0.343497	+	0.0452222i
$61$	0.610394	+	1.79816i	0.0781530	+	0.230231i	0.978983	−	0.203940i	$-0.0653747\pi$
$61$	0.610394	+	1.79816i	0.0781530	+	0.230231i	−0.900830	+	0.434171i	$0.857041\pi$
$62$	5.06251	−	3.38266i	0.642939	−	0.429598i
$63$	−2.02012	+	1.70854i	−0.254512	+	0.215255i
$64$	5.33264	−	5.33264i	0.666579	−	0.666579i
$65$	−6.29960	−	0.412898i	−0.781369	−	0.0512137i
$66$	−3.42381	−	4.46200i	−0.421442	−	0.549234i
$67$	−3.48497	−	2.01205i	−0.425757	−	0.245811i	0.271780	−	0.962359i	$-0.412388\pi$
$67$	−3.48497	−	2.01205i	−0.425757	−	0.245811i	−0.697537	+	0.716548i	$0.745721\pi$
$68$	0.762363	+	3.69737i	0.0924501	+	0.448373i
$69$			6.28594i			0.756738i
$70$	−6.49368	+	4.80036i	−0.776144	+	0.573753i
$71$	5.71987	+	3.82190i	0.678824	+	0.453576i	0.846586	−	0.532252i	$-0.178654\pi$
$71$	5.71987	+	3.82190i	0.678824	+	0.453576i	−0.167762	+	0.985828i	$0.553654\pi$
$72$	0.785812	−	2.93269i	0.0926088	−	0.345621i
$73$	−0.614384	−	0.208555i	−0.0719082	−	0.0244096i	0.285254	−	0.958452i	$-0.407922\pi$
$73$	−0.614384	−	0.208555i	−0.0719082	−	0.0244096i	−0.357162	+	0.934043i	$0.616256\pi$
$74$	0.267810	+	4.08598i	0.0311322	+	0.474986i
$75$	3.40035	−	1.15426i	0.392638	−	0.133283i
$76$	−1.48012	−	3.57332i	−0.169781	−	0.409888i
$77$	−14.1316	−	2.11876i	−1.61045	−	0.241455i
$78$	−0.437575	+	2.19984i	−0.0495456	+	0.249083i
$79$	−5.15796	+	10.4593i	−0.580316	+	1.17676i	0.386738	+	0.922190i	$0.373602\pi$
$79$	−5.15796	+	10.4593i	−0.580316	+	1.17676i	−0.967053	+	0.254574i	$0.918065\pi$
$80$	1.25347	−	3.69261i	0.140143	−	0.412847i
$81$	−0.258819	−	0.965926i	−0.0287577	−	0.107325i
$82$	0.265928	−	4.05728i	0.0293669	−	0.448052i
$83$	−4.95239	+	11.9561i	−0.543596	+	1.31236i	0.378574	+	0.925571i	$0.376414\pi$
$83$	−4.95239	+	11.9561i	−0.543596	+	1.31236i	−0.922170	+	0.386785i	$0.873586\pi$
$84$	−1.17344	−	2.11929i	−0.128033	−	0.231234i
$85$	7.42369	+	9.53596i	0.805212	+	1.03432i
$86$	−1.63793	−	2.83697i	−0.176622	−	0.305919i
$87$	−7.34690	+	5.63748i	−0.787671	+	0.604401i
$88$	14.7070	−	7.25267i	1.56777	−	0.773137i
$89$	3.72533	+	0.998199i	0.394884	+	0.105809i	0.450796	−	0.892627i	$-0.351140\pi$
$89$	3.72533	+	0.998199i	0.394884	+	0.105809i	−0.0559122	+	0.998436i	$0.517807\pi$
$90$	−0.595454	−	2.99355i	−0.0627664	−	0.315548i
$91$	3.08058	+	4.79425i	0.322933	+	0.502573i
$92$	−5.64487	−	1.12284i	−0.588519	−	0.117064i
$93$	4.63867	+	3.55937i	0.481007	+	0.369090i
$94$	1.20598	−	9.16035i	0.124388	−	0.944818i
$95$	−9.30876	−	8.16356i	−0.955059	−	0.837564i
$96$	4.20350	+	2.07294i	0.429018	+	0.211568i
$97$	−1.34985	+	0.268502i	−0.137057	+	0.0272623i	−0.263142	−	0.964757i	$-0.584759\pi$
$97$	−1.34985	+	0.268502i	−0.137057	+	0.0272623i	0.126085	+	0.992019i	$0.459759\pi$
$98$	6.96887	+	2.13775i	0.703962	+	0.215945i
$99$	3.00061	−	4.49072i	0.301572	−	0.451335i
$100$	0.429154	+	3.25975i	0.0429154	+	0.325975i
$101$	2.04077	−	3.53472i	0.203064	−	0.351717i	−0.746450	−	0.665441i	$-0.768243\pi$
$101$	2.04077	−	3.53472i	0.203064	−	0.351717i	0.949514	+	0.313724i	$0.101577\pi$
$102$	3.70323	−	2.17272i	0.366675	−	0.215132i
$103$	13.6124	−	7.85911i	1.34127	−	0.774381i	0.354273	−	0.935142i	$-0.384728\pi$
$103$	13.6124	−	7.85911i	1.34127	−	0.774381i	0.986993	+	0.160761i	$0.0513949\pi$
$104$	−6.04174	−	2.50257i	−0.592441	−	0.245397i
$105$	−6.36961	−	4.42318i	−0.621610	−	0.431658i
$106$	−3.74462	−	3.74462i	−0.363710	−	0.363710i
$107$	−4.33079	−	4.93832i	−0.418674	−	0.477406i	0.503604	−	0.863935i	$-0.332007\pi$
$107$	−4.33079	−	4.93832i	−0.418674	−	0.477406i	−0.922277	+	0.386529i	$0.873674\pi$
$108$	0.913649	−	0.0598837i	0.0879159	−	0.00576231i
$109$	3.47766	−	3.96551i	0.333099	−	0.379827i	−0.560909	−	0.827878i	$-0.689548\pi$
$109$	3.47766	−	3.96551i	0.333099	−	0.379827i	0.894008	+	0.448051i	$0.147882\pi$
$110$	10.0353	−	13.0782i	0.956827	−	1.24696i
$111$	−3.63287	+	1.50478i	−0.344817	+	0.142828i
$112$	−3.35295	+	1.07156i	−0.316824	+	0.101252i
$113$	6.55175	+	9.80539i	0.616337	+	0.922414i	0.999999	−	0.00105981i	$-0.000337348\pi$
$113$	6.55175	+	9.80539i	0.616337	+	0.922414i	−0.383662	+	0.923473i	$0.625337\pi$
$114$	−3.30723	+	2.90037i	−0.309751	+	0.271644i
$115$	−17.7965	+	4.76855i	−1.65953	+	0.444669i
$116$	−3.75019	−	7.60464i	−0.348197	−	0.706073i
$117$	−2.13547	+	0.281139i	−0.197424	+	0.0259914i
$118$	−3.49449			−0.321694
$119$	2.93839	−	10.5055i	0.269362	−	0.963039i
$120$	8.89902			0.812365
$121$	18.0148	−	2.37169i	1.63771	−	0.215608i
$122$	0.874601	+	1.77352i	0.0791827	+	0.160567i
$123$	3.77153	−	1.01058i	0.340067	−	0.0911207i
$124$	−4.02496	+	3.52980i	−0.361452	+	0.316985i
$125$	−2.29454	−	3.43402i	−0.205230	−	0.307148i
$126$	−1.85341	+	2.03853i	−0.165115	+	0.181606i
$127$	−7.94172	+	3.28957i	−0.704714	+	0.291902i	−0.706115	−	0.708097i	$-0.749554\pi$
$127$	−7.94172	+	3.28957i	−0.704714	+	0.291902i	0.00140139	+	0.999999i	$0.499554\pi$
$128$	−0.925577	+	1.20624i	−0.0818103	+	0.106617i
$129$	2.07417	−	2.36514i	0.182621	−	0.208239i
$130$	−6.56003	+	0.429967i	−0.575353	+	0.0377106i
$131$	11.7384	+	13.3851i	1.02559	+	1.16946i	0.985398	+	0.170268i	$0.0544635\pi$
$131$	11.7384	+	13.3851i	1.02559	+	1.16946i	0.0401915	+	0.999192i	$0.487203\pi$
$132$	3.49675	+	3.49675i	0.304353	+	0.304353i
$133$	−0.930708	+	11.1374i	−0.0807027	+	0.965737i
$134$	−3.87148	−	1.60362i	−0.334445	−	0.138532i
$135$	2.53834	−	1.46551i	0.218466	−	0.126131i
$136$	4.10666	+	11.8256i	0.352143	+	1.01403i
$137$	−5.29343	+	9.16849i	−0.452248	+	0.783317i	−0.998525	−	0.0542878i	$-0.982711\pi$
$137$	−5.29343	+	9.16849i	−0.452248	+	0.783317i	0.546277	+	0.837604i	$0.316044\pi$
$138$	0.854399	+	6.48981i	0.0727313	+	0.552449i
$139$	4.81306	−	7.20325i	0.408238	−	0.610971i	−0.569199	−	0.822200i	$-0.692746\pi$
$139$	4.81306	−	7.20325i	0.408238	−	0.610971i	0.977437	+	0.211229i	$0.0677465\pi$
$140$	5.10987	−	4.92991i	0.431863	−	0.416654i
$141$	8.70211	−	1.73096i	0.732850	−	0.145773i
$142$	6.42486	+	3.16839i	0.539162	+	0.265885i
$143$	−8.74620	−	7.67021i	−0.731394	−	0.641415i
$144$	0.173658	−	1.31906i	0.0144715	−	0.109922i
$145$	−21.5340	−	16.5236i	−1.78830	−	1.37221i
$146$	−0.662657	−	0.131811i	−0.0548419	−	0.0109087i
$147$	0.207206	+	6.99693i	0.0170901	+	0.577097i
$148$	−0.702393	−	3.53117i	−0.0577364	−	0.290260i
$149$	−15.1341	−	4.05518i	−1.23984	−	0.332213i	−0.421434	−	0.906859i	$-0.638473\pi$
$149$	−15.1341	−	4.05518i	−1.23984	−	0.332213i	−0.818402	+	0.574646i	$0.805140\pi$
$150$	3.35374	−	1.65388i	0.273832	−	0.135039i
$151$	−17.4692	+	13.4046i	−1.42162	+	1.09085i	−0.440433	+	0.897785i	$0.645175\pi$
$151$	−17.4692	+	13.4046i	−1.42162	+	1.09085i	−0.981187	+	0.193062i	$0.938158\pi$
$152$	−6.41267	−	11.1071i	−0.520136	−	0.900902i
$153$	3.11884	+	2.69681i	0.252144	+	0.218025i
$154$	−14.8779	−	0.266676i	−1.19890	−	0.0214893i
$155$	−6.55822	+	15.8329i	−0.526769	+	1.27173i
$156$	0.128983	−	1.96790i	0.0103269	−	0.157558i
$157$	−5.48641	−	20.4755i	−0.437863	−	1.63413i	−0.734121	−	0.679019i	$-0.762405\pi$
$157$	−5.48641	−	20.4755i	−0.437863	−	1.63413i	0.296258	−	0.955108i	$-0.404261\pi$
$158$	−3.90359	+	11.4996i	−0.310553	+	0.914859i
$159$	2.24924	−	4.56101i	0.178376	−	0.361711i
$160$	−2.68001	+	13.4733i	−0.211873	+	1.06516i
$161$	13.0107	+	10.3592i	1.02539	+	0.816417i
$162$	−0.398504	−	0.962074i	−0.0313094	−	0.0755876i
$163$	15.8735	−	5.38833i	1.24331	−	0.422046i	0.379182	−	0.925322i	$-0.376205\pi$
$163$	15.8735	−	5.38833i	1.24331	−	0.422046i	0.864126	+	0.503276i	$0.167872\pi$
$164$	0.233820	+	3.56741i	0.0182583	+	0.278568i
$165$	14.9902	+	5.08849i	1.16699	+	0.396138i
$166$	−3.48790	+	13.0170i	−0.270714	+	1.01032i
$167$	8.99666	+	6.01138i	0.696183	+	0.465174i	0.852632	−	0.522512i	$-0.175005\pi$
$167$	8.99666	+	6.01138i	0.696183	+	0.465174i	−0.156450	+	0.987686i	$0.550005\pi$
$168$	−4.77511	−	6.45953i	−0.368408	−	0.498363i
$169$		−	8.36074i		−	0.643134i
$170$	8.96060	+	8.83618i	0.687247	+	0.677704i
$171$	−3.65828	−	2.11211i	−0.279756	−	0.161517i
$172$	1.75343	+	2.28512i	0.133698	+	0.174239i
$173$	2.29421	+	0.150370i	0.174425	+	0.0114324i	0.152365	−	0.988324i	$-0.451311\pi$
$173$	2.29421	+	0.150370i	0.174425	+	0.0114324i	0.0220598	+	0.999757i	$0.492978\pi$
$174$	−6.81892	+	6.81892i	−0.516941	+	0.516941i
$175$	3.21463	−	8.94030i	0.243003	−	0.675823i
$176$	5.97465	−	3.99213i	0.450356	−	0.300918i
$177$	−1.07867	−	3.17767i	−0.0810782	−	0.238849i
$178$	3.98183	+	0.524218i	0.298451	+	0.0392918i
$179$	5.49255	+	0.723108i	0.410533	+	0.0540477i	0.332964	−	0.942939i	$-0.391951\pi$
$179$	5.49255	+	0.723108i	0.410533	+	0.0540477i	0.0775683	+	0.996987i	$0.475284\pi$
$180$	0.862639	+	2.54125i	0.0642973	+	0.189414i
$181$	10.7614	−	7.19056i	0.799891	−	0.534470i	−0.0871310	−	0.996197i	$-0.527770\pi$
$181$	10.7614	−	7.19056i	0.799891	−	0.534470i	0.887022	+	0.461727i	$0.152770\pi$
$182$	3.83214	+	4.53101i	0.284057	+	0.335861i
$183$	−1.34275	+	1.34275i	−0.0992592	+	0.0992592i
$184$	−19.0441	−	1.24822i	−1.40395	−	0.0920200i
$185$	−7.01619	−	9.14368i	−0.515841	−	0.672257i
$186$	5.27291	+	3.04431i	0.386628	+	0.223220i
$187$	0.155680	+	22.2681i	0.0113845	+	1.62841i
$188$			8.12383i			0.592491i
$189$	−2.42582	−	1.05613i	−0.176452	−	0.0768221i
$190$	−10.7203	−	7.16306i	−0.777730	−	0.519663i
$191$	−5.17495	+	19.3132i	−0.374446	+	1.39745i	0.479706	+	0.877430i	$0.340743\pi$
$191$	−5.17495	+	19.3132i	−0.374446	+	1.39745i	−0.854152	+	0.520023i	$0.825923\pi$
$192$	7.14126	+	2.42413i	0.515376	+	0.174947i
$193$	0.359222	+	5.48067i	0.0258574	+	0.394508i	0.991097	+	0.133141i	$0.0425064\pi$
$193$	0.359222	+	5.48067i	0.0258574	+	0.394508i	−0.965240	+	0.261366i	$0.915827\pi$
$194$	−1.35713	+	0.460685i	−0.0974366	+	0.0330753i
$195$	−2.41593	−	5.83256i	−0.173008	−	0.417678i
$196$	−6.32037	−	1.06376i	−0.451455	−	0.0759831i
$197$	3.73887	−	18.7965i	0.266383	−	1.33920i	−0.583451	−	0.812148i	$-0.698298\pi$
$197$	3.73887	−	18.7965i	0.266383	−	1.33920i	0.849834	−	0.527050i	$-0.176702\pi$
$198$	2.48753	−	5.04422i	0.176781	−	0.358477i
$199$	−7.92241	+	23.3387i	−0.561605	+	1.65443i	0.180055	+	0.983657i	$0.442373\pi$
$199$	−7.92241	+	23.3387i	−0.561605	+	1.65443i	−0.741659	+	0.670777i	$0.765961\pi$
$200$	2.82179	+	10.5310i	0.199530	+	0.744658i
$201$	0.263189	−	4.01548i	0.0185639	−	0.283230i
$202$	1.62651	−	3.92674i	0.114441	−	0.276285i
$203$	−0.439095	+	24.4972i	−0.0308184	+	1.71937i
$204$	−2.97889	+	2.31905i	−0.208564	+	0.162366i
$205$	5.72220	+	9.91114i	0.399656	+	0.692224i
$206$	12.9856	−	9.96422i	0.904751	−	0.694240i
$207$	−5.63769	+	2.78020i	−0.391846	+	0.193237i
$208$	−2.76799	−	0.741680i	−0.191925	−	0.0514262i
$209$	−4.45095	−	22.3764i	−0.307878	−	1.54781i
$210$	−7.17740	−	3.70086i	−0.495287	−	0.255384i
$211$	−2.60783	−	0.518729i	−0.179530	−	0.0357108i	0.104506	−	0.994524i	$-0.466674\pi$
$211$	−2.60783	−	0.518729i	−0.179530	−	0.0357108i	−0.284037	+	0.958813i	$0.591674\pi$
$212$	3.69408	+	2.83457i	0.253711	+	0.194679i
$213$	−0.897920	+	6.82038i	−0.0615245	+	0.467325i
$214$	−5.14248	−	4.50983i	−0.351533	−	0.308286i
$215$	8.26956	+	4.07810i	0.563979	+	0.278124i
$216$	2.97780	−	0.592322i	0.202614	−	0.0403024i
$217$	15.0117	−	3.73536i	1.01906	−	0.253573i
$218$	3.05145	−	4.56681i	0.206670	−	0.309304i
$219$	−0.0846876	−	0.643266i	−0.00572266	−	0.0434679i
$220$	−7.24719	+	12.5525i	−0.488606	+	0.846290i
$221$	6.63579	−	5.90201i	0.446371	−	0.397012i
$222$	−3.54616	+	2.04738i	−0.238003	+	0.137411i
$223$	−16.9064	−	7.00286i	−1.13214	−	0.468946i	−0.263630	−	0.964624i	$-0.584920\pi$
$223$	−16.9064	−	7.00286i	−1.13214	−	0.468946i	−0.868507	+	0.495677i	$0.834920\pi$
$224$	11.2179	−	5.28428i	0.749529	−	0.353071i
$225$	2.53916	+	2.53916i	0.169278	+	0.169278i
$226$	8.09701	+	9.23287i	0.538605	+	0.614162i
$227$	14.3739	−	0.942118i	0.954032	−	0.0625305i	0.419570	−	0.907723i	$-0.362181\pi$
$227$	14.3739	−	0.942118i	0.954032	−	0.0625305i	0.534462	+	0.845193i	$0.320514\pi$
$228$	2.55018	−	2.90792i	0.168889	−	0.192582i
$229$	15.0331	−	19.5915i	0.993413	−	1.29464i	0.0380287	−	0.999277i	$-0.487892\pi$
$229$	15.0331	−	19.5915i	0.993413	−	1.29464i	0.955385	−	0.295365i	$-0.0954412\pi$
$230$	−17.7255	+	7.34214i	−1.16878	+	0.484126i
$231$	−4.34999	−	13.6114i	−0.286209	−	0.895562i
$232$	−15.6206	−	23.3779i	−1.02555	−	1.53484i
$233$	12.8117	−	11.2355i	0.839320	−	0.736064i	−0.127413	−	0.991850i	$-0.540667\pi$
$233$	12.8117	−	11.2355i	0.839320	−	0.736064i	0.966734	+	0.255786i	$0.0823341\pi$
$234$	−2.16651	+	0.580515i	−0.141629	+	0.0379494i
$235$	11.5021	+	23.3239i	0.750313	+	1.52148i
$236$	3.04628	−	0.401050i	0.198296	−	0.0261062i
$237$	−11.6620			−0.757526
$238$	1.60576	−	11.2456i	0.104086	−	0.728946i
$239$	−10.8360			−0.700926			−0.350463	−	0.936577i	$-0.613976\pi$
$239$	−10.8360			−0.700926			−0.350463	+	0.936577i	$0.613976\pi$
$240$	3.86620	−	0.508995i	0.249562	−	0.0328555i
$241$	−6.99260	−	14.1796i	−0.450433	−	0.913387i	−0.997105	−	0.0760404i	$-0.975772\pi$
$241$	−6.99260	−	14.1796i	−0.450433	−	0.913387i	0.546672	−	0.837347i	$-0.315894\pi$
$242$	18.2767	−	4.89722i	1.17487	−	0.314805i
$243$	0.751840	−	0.659346i	0.0482305	−	0.0422971i
$244$	−0.965962	−	1.44566i	−0.0618394	−	0.0925492i
$245$	−19.6522	+	5.89454i	−1.25553	+	0.376589i
$246$	3.75648	−	1.55599i	0.239505	−	0.0992061i
$247$	−5.53883	+	7.21834i	−0.352427	+	0.459292i
$248$	−11.7047	+	13.3467i	−0.743252	+	0.847517i
$249$	−12.9135	+	0.846397i	−0.818361	+	0.0536382i
$250$	−2.83571	−	3.23351i	−0.179346	−	0.204505i
$251$	9.88414	+	9.88414i	0.623882	+	0.623882i	0.946522	−	0.322640i	$-0.104570\pi$
$251$	9.88414	+	9.88414i	0.623882	+	0.623882i	−0.322640	+	0.946522i	$0.604570\pi$
$252$	1.38174	−	1.98977i	0.0870412	−	0.125344i
$253$	−31.3657	−	12.9921i	−1.97195	−	0.816807i
$254$	−7.75216	+	4.47571i	−0.486414	+	0.280831i
$255$	−5.26913	+	10.8757i	−0.329965	+	0.681066i
$256$	−8.33313	+	14.4334i	−0.520820	+	0.902087i
$257$	−0.699645	−	5.31433i	−0.0436426	−	0.331499i	−0.999313	−	0.0370602i	$-0.988201\pi$
$257$	−0.699645	−	5.31433i	−0.0436426	−	0.331499i	0.955670	−	0.294439i	$-0.0951326\pi$
$258$	1.81997	−	2.72377i	0.113306	−	0.169575i
$259$	−2.87231	+	9.99923i	−0.178477	+	0.621322i
$260$	5.66928	−	1.12769i	0.351594	−	0.0699364i
$261$	−8.30555	−	4.09584i	−0.514101	−	0.253526i
$262$	13.9384	+	12.2237i	0.861120	+	0.755182i
$263$	2.24749	−	17.0714i	0.138586	−	1.05267i	−0.770907	−	0.636947i	$-0.780197\pi$
$263$	2.24749	−	17.0714i	0.138586	−	1.05267i	0.909493	−	0.415718i	$-0.136470\pi$
$264$	13.0094	+	9.98250i	0.800676	+	0.614380i
$265$	14.6192	+	2.90794i	0.898051	+	0.178633i
$266$	0.552930	+	11.6251i	0.0339023	+	0.712783i
$267$	0.752414	+	3.78264i	0.0460470	+	0.231494i
$268$	3.55896	+	0.953619i	0.217398	+	0.0582516i
$269$	−0.351623	+	0.173401i	−0.0214388	+	0.0105725i	−0.452977	−	0.891522i	$-0.649638\pi$
$269$	−0.351623	+	0.173401i	−0.0214388	+	0.0105725i	0.431538	+	0.902095i	$0.357971\pi$
$270$	2.42147	−	1.85806i	0.147366	−	0.113078i
$271$	0.905543	+	1.56845i	0.0550078	+	0.0952764i	0.892218	−	0.451605i	$-0.149148\pi$
$271$	0.905543	+	1.56845i	0.0550078	+	0.0952764i	−0.837210	+	0.546881i	$0.815815\pi$
$272$	2.46053	+	4.90276i	0.149192	+	0.297274i
$273$	−2.93732	+	4.88333i	−0.177775	+	0.295553i
$274$	−4.21890	+	10.1853i	−0.254873	+	0.615318i
$275$	−1.26845	+	19.3528i	−0.0764905	+	1.16702i
$276$	−1.48962	−	5.55935i	−0.0896648	−	0.334634i
$277$	−5.53032	+	16.2918i	−0.332285	+	0.978880i	0.644490	+	0.764613i	$0.277070\pi$
$277$	−5.53032	+	16.2918i	−0.332285	+	0.978880i	−0.976775	+	0.214267i	$0.931264\pi$
$278$	3.99007	−	8.09106i	0.239309	−	0.485270i
$279$	−1.14068	+	5.73457i	−0.0682905	+	0.343319i
$280$	14.6655	−	18.4193i	0.876431	−	1.10076i
$281$	−0.765985	−	1.84925i	−0.0456948	−	0.110317i	0.899384	−	0.437159i	$-0.144015\pi$
$281$	−0.765985	−	1.84925i	−0.0456948	−	0.110317i	−0.945079	+	0.326842i	$0.894015\pi$
$282$	8.74906	−	2.96991i	0.520999	−	0.176855i
$283$	0.356912	+	5.44542i	0.0212162	+	0.323696i	0.995254	+	0.0973111i	$0.0310242\pi$
$283$	0.356912	+	5.44542i	0.0212162	+	0.323696i	−0.974038	+	0.226385i	$0.927309\pi$
$284$	−5.96442	−	2.02465i	−0.353923	−	0.120141i
$285$	3.20452	−	11.9594i	0.189819	−	0.708415i
$286$	−10.0724	−	6.73017i	−0.595594	−	0.397963i
$287$	4.12373	−	9.47178i	0.243416	−	0.559101i
$288$			4.68684i			0.276175i
$289$	−16.8839	−	1.98307i	−0.993173	−	0.116651i
$290$	−24.4783	−	14.1325i	−1.43741	−	0.829892i
$291$	−0.837836	−	1.09189i	−0.0491148	−	0.0640077i
$292$	0.592791	+	0.0388535i	0.0346904	+	0.00227373i
$293$	−4.63926	+	4.63926i	−0.271028	+	0.271028i	−0.829514	−	0.558486i	$-0.811383\pi$
$293$	−4.63926	+	4.63926i	−0.271028	+	0.271028i	0.558486	+	0.829514i	$0.311383\pi$
$294$	1.16497	+	7.19569i	0.0679421	+	0.419661i
$295$	8.17820	−	5.46450i	0.476153	−	0.318155i
$296$	−3.83757	−	11.3051i	−0.223054	−	0.657096i
$297$	5.35474	+	0.704965i	0.310714	+	0.0409062i
$298$	−16.1762	−	2.12963i	−0.937060	−	0.123366i
$299$	4.35205	+	12.8207i	0.251685	+	0.741441i
$300$	−2.73377	+	1.82665i	−0.157834	+	0.105462i
$301$	−1.47719	−	8.19088i	−0.0851436	−	0.472115i
$302$	−16.2137	+	16.2137i	−0.932996	+	0.932996i
$303$	4.07280	+	0.266945i	0.233976	+	0.0153356i
$304$	−3.42129	−	4.45871i	−0.196224	−	0.255725i
$305$	−4.82016	−	2.78292i	−0.276002	−	0.159350i
$306$	3.58655	+	2.36036i	0.205030	+	0.134933i
$307$		−	11.4332i		−	0.652530i	−0.945278	−	0.326265i	$-0.894210\pi$
$307$		−	11.4332i		−	0.652530i	0.945278	−	0.326265i	$-0.105790\pi$
$308$	13.0002	−	1.47501i	0.740758	−	0.0840467i
$309$	13.0692	+	8.73257i	0.743482	+	0.496779i
$310$	−4.61887	+	17.2379i	−0.262334	+	0.979044i
$311$	13.8789	+	4.71124i	0.786999	+	0.267150i	0.685871	−	0.727723i	$-0.259422\pi$
$311$	13.8789	+	4.71124i	0.786999	+	0.267150i	0.101128	+	0.994873i	$0.467755\pi$
$312$	−0.427706	−	6.52553i	−0.0242141	−	0.369435i
$313$	−1.73861	+	0.590177i	−0.0982718	+	0.0333588i	−0.370142	−	0.928975i	$-0.620691\pi$
$313$	−1.73861	+	0.590177i	−0.0982718	+	0.0333588i	0.271871	+	0.962334i	$0.412358\pi$
$314$	−8.44743	−	20.3939i	−0.476716	−	1.15089i
$315$	1.14982	−	7.66905i	0.0647853	−	0.432102i
$316$	2.08314	−	10.4726i	0.117186	−	0.589132i
$317$	7.95690	−	16.1350i	0.446904	−	0.906232i	−0.550542	−	0.834808i	$-0.685579\pi$
$317$	7.95690	−	16.1350i	0.446904	−	0.906232i	0.997446	−	0.0714245i	$-0.0227545\pi$
$318$	1.70225	−	5.01465i	0.0954572	−	0.281208i
$319$	−12.9451	−	48.3116i	−0.724784	−	2.70493i
$320$	−1.44569	+	22.0570i	−0.0808165	+	1.23302i
$321$	2.51359	−	6.06833i	0.140295	−	0.338701i
$322$	14.8407	+	8.92669i	0.827042	+	0.497465i
$323$	17.3712	−	1.26059i	0.966561	−	0.0701413i
$324$	0.457805	+	0.792941i	0.0254336	+	0.0440523i
$325$	6.13616	−	4.70844i	0.340373	−	0.261177i
$326$	15.6559	−	7.72064i	0.867101	−	0.427607i
$327$	5.09469	+	1.36512i	0.281737	+	0.0754912i
$328$	2.31276	+	11.6270i	0.127701	+	0.641996i
$329$	10.7582	−	20.8643i	0.593120	−	1.15029i
$330$	16.1680	+	3.21602i	0.890020	+	0.177036i
$331$	−3.86644	−	2.96682i	−0.212519	−	0.163071i	0.497017	−	0.867741i	$-0.334429\pi$
$331$	−3.86644	−	2.96682i	−0.212519	−	0.163071i	−0.709536	+	0.704669i	$0.751095\pi$
$332$	1.54662	−	11.7477i	0.0848817	−	0.644741i
$333$	−2.95638	−	2.59267i	−0.162008	−	0.142078i
$334$	10.1055	+	4.98349i	0.552950	+	0.272685i
$335$	11.5681	−	2.30104i	0.632034	−	0.125719i
$336$	−2.44402	−	2.53324i	−0.133332	−	0.138199i
$337$	0.323941	−	0.484812i	0.0176462	−	0.0264094i	−0.822542	−	0.568705i	$-0.807445\pi$
$337$	0.323941	−	0.484812i	0.0176462	−	0.0264094i	0.840188	+	0.542295i	$0.182445\pi$
$338$	−1.13641	−	8.63190i	−0.0618126	−	0.469514i
$339$	−5.89642	+	10.2129i	−0.320250	+	0.554689i
$340$	−8.82539	−	6.67446i	−0.478624	−	0.361973i
$341$	−27.3481	+	15.7894i	−1.48098	+	0.855046i
$342$	−4.06401	−	1.68337i	−0.219757	−	0.0910262i
$343$	14.8238	+	11.1020i	0.800411	+	0.599451i
$344$	6.75366	+	6.75366i	0.364133	+	0.364133i
$345$	−12.1480	−	13.8521i	−0.654024	−	0.745771i
$346$	2.38905	−	0.156587i	0.128436	−	0.00841815i
$347$	23.5405	−	26.8428i	1.26372	−	1.44100i	0.417048	−	0.908884i	$-0.363065\pi$
$347$	23.5405	−	26.8428i	1.26372	−	1.44100i	0.846673	−	0.532113i	$-0.178602\pi$
$348$	5.16172	−	6.72689i	0.276697	−	0.360599i
$349$	31.2990	−	12.9645i	1.67540	−	0.693972i	0.676306	−	0.736620i	$-0.263580\pi$
$349$	31.2990	−	12.9645i	1.67540	−	0.693972i	0.999090	+	0.0426485i	$0.0135796\pi$
$350$	2.10370	−	9.66720i	0.112448	−	0.516733i
$351$	−1.19664	−	1.79090i	−0.0638719	−	0.0955910i
$352$	−19.0316	+	16.6903i	−1.01439	+	0.889595i
$353$	15.6552	−	4.19481i	0.833245	−	0.223267i	0.183116	−	0.983091i	$-0.441382\pi$
$353$	15.6552	−	4.19481i	0.833245	−	0.223267i	0.650129	+	0.759824i	$0.274715\pi$
$354$	−1.54558	−	3.13412i	−0.0821464	−	0.166576i
$355$	−19.9907	+	2.63183i	−1.06100	+	0.139683i
$356$	−3.53127			−0.187157
$357$	10.7217	−	2.01110i	0.567454	−	0.106439i
$358$	5.76898			0.304900
$359$	31.9136	−	4.20151i	1.68434	−	0.221747i	0.773291	−	0.634051i	$-0.218609\pi$
$359$	31.9136	−	4.20151i	1.68434	−	0.221747i	0.911046	+	0.412304i	$0.135276\pi$
$360$	3.93593	+	7.98129i	0.207442	+	0.420651i
$361$	1.11656	−	0.299182i	0.0587664	−	0.0157464i
$362$	10.1331	−	8.88649i	0.532584	−	0.467063i
$363$	10.0948	+	15.1080i	0.529842	+	0.792964i
$364$	−3.86063	−	3.51005i	−0.202352	−	0.183977i
$365$	1.75694	−	0.727749i	0.0919625	−	0.0380921i
$366$	−1.20379	+	1.56881i	−0.0629232	+	0.0820031i
$367$	−6.40845	+	7.30744i	−0.334518	+	0.381445i	−0.894506	−	0.447056i	$-0.852473\pi$
$367$	−6.40845	+	7.30744i	−0.334518	+	0.381445i	0.559988	+	0.828501i	$0.310806\pi$
$368$	−8.34517	+	0.546972i	−0.435022	+	0.0285129i
$369$	2.57446	+	2.93561i	0.134021	+	0.152822i
$370$	−8.48657	−	8.48657i	−0.441196	−	0.441196i
$371$	−5.73371	−	12.1720i	−0.297679	−	0.631939i
$372$	−4.94598	−	2.04869i	−0.256437	−	0.106220i
$373$	1.41243	−	0.815465i	0.0731327	−	0.0422232i	−0.462988	−	0.886365i	$-0.653223\pi$
$373$	1.41243	−	0.815465i	0.0731327	−	0.0422232i	0.536120	+	0.844141i	$0.319889\pi$
$374$	3.18746	+	22.9692i	0.164820	+	1.18771i
$375$	2.06503	−	3.57673i	0.106638	−	0.184702i
$376$	3.51617	+	26.7080i	0.181333	+	1.37736i
$377$	−11.0816	+	16.5847i	−0.570729	+	0.854156i
$378$	−2.64804	−	0.760659i	−0.136201	−	0.0391241i
$379$	−33.5006	+	6.66368i	−1.72081	+	0.342290i	−0.954051	−	0.299645i	$-0.903132\pi$
$379$	−33.5006	+	6.66368i	−1.72081	+	0.342290i	−0.766759	+	0.641936i	$0.778132\pi$
$380$	10.1673	+	5.01398i	0.521574	+	0.257212i
$381$	−6.46286	−	5.66777i	−0.331102	−	0.290369i
$382$	−2.71770	+	20.6429i	−0.139049	+	1.05618i
$383$	−3.02932	−	2.32448i	−0.154791	−	0.118775i	0.528462	−	0.848957i	$-0.322769\pi$
$383$	−3.02932	−	2.32448i	−0.154791	−	0.118775i	−0.683253	+	0.730181i	$0.739436\pi$
$384$	−1.49121	−	0.296621i	−0.0760981	−	0.0151369i
$385$	35.2359	−	22.6412i	1.79579	−	1.15390i
$386$	1.11582	+	5.60960i	0.0567937	+	0.285521i
$387$	3.03861	+	0.814194i	0.154461	+	0.0413878i
$388$	1.13019	−	0.557350i	0.0573769	−	0.0282952i
$389$	8.53474	−	6.54894i	0.432729	−	0.332044i	−0.369321	−	0.929302i	$-0.620410\pi$
$389$	8.53474	−	6.54894i	0.432729	−	0.332044i	0.802049	+	0.597258i	$0.203743\pi$
$390$	−3.28705	−	5.69335i	−0.166446	−	0.288294i
$391$	12.8016	−	22.5353i	0.647403	−	1.13966i
$392$	−21.2393	−	0.761644i	−1.07275	−	0.0384688i
$393$	−6.81295	+	16.4479i	−0.343668	+	0.829688i
$394$	1.30526	−	19.9144i	0.0657578	−	1.00327i
$395$	−8.84684	−	33.0168i	−0.445133	−	1.66126i
$396$	−1.58957	+	4.68272i	−0.0798788	+	0.235315i
$397$	6.29663	−	12.7683i	0.316019	−	0.640823i	−0.679676	−	0.733512i	$-0.737880\pi$
$397$	6.29663	−	12.7683i	0.316019	−	0.640823i	0.995695	+	0.0926892i	$0.0295463\pi$
$398$	−5.00710	+	25.1724i	−0.250983	+	1.26178i
$399$	−10.4005	+	4.09123i	−0.520676	+	0.204818i
$400$	1.82827	+	4.41384i	0.0914137	+	0.220692i
$401$	−17.9189	+	6.08264i	−0.894827	+	0.303753i	−0.730710	−	0.682688i	$-0.760811\pi$
$401$	−17.9189	+	6.08264i	−0.894827	+	0.303753i	−0.164117	+	0.986441i	$0.552477\pi$
$402$	−0.274069	−	4.18149i	−0.0136693	−	0.208554i
$403$	11.9253	+	4.04809i	0.594041	+	0.201650i
$404$	−0.967231	+	3.60976i	−0.0481215	+	0.179592i
$405$	2.43706	+	1.62839i	0.121098	+	0.0809154i
$406$	2.87638	+	25.3514i	0.142752	+	1.25817i
$407$		−	21.2376i		−	1.05271i
$408$	−8.78970	+	8.91347i	−0.435155	+	0.441282i
$409$	16.9419	+	9.78143i	0.837725	+	0.483661i	0.856490	−	0.516163i	$-0.172640\pi$
$409$	16.9419	+	9.78143i	0.837725	+	0.483661i	−0.0187654	+	0.999824i	$0.505974\pi$
$410$	7.25493	+	9.45481i	0.358295	+	0.466940i
$411$	−10.5642	−	0.692413i	−0.521093	−	0.0341542i
$412$	−10.1765	+	10.1765i	−0.501360	+	0.501360i
$413$	−8.35484	−	3.00412i	−0.411115	−	0.147823i
$414$	−5.44264	+	3.63666i	−0.267491	+	0.178732i
$415$	−12.1925	−	35.9181i	−0.598509	−	1.76315i
$416$	10.0086	+	1.31766i	0.490712	+	0.0646034i
$417$	8.58916	+	1.13078i	0.420613	+	0.0553747i
$418$	−7.63675	−	22.4972i	−0.373526	−	1.10037i
$419$	−12.5095	+	8.35860i	−0.611131	+	0.408344i	−0.822259	−	0.569114i	$-0.807286\pi$
$419$	−12.5095	+	8.35860i	−0.611131	+	0.408344i	0.211128	+	0.977458i	$0.432286\pi$
$420$	6.68154	+	2.40246i	0.326026	+	0.117228i
$421$	19.8167	−	19.8167i	0.965808	−	0.965808i	−0.0336262	−	0.999434i	$-0.510706\pi$
$421$	19.8167	−	19.8167i	0.965808	−	0.965808i	0.999434	+	0.0336262i	$0.0107056\pi$
$422$	−2.76291	−	0.181091i	−0.134496	−	0.00881536i
$423$	5.40129	+	7.03910i	0.262620	+	0.342253i
$424$	13.3716	+	7.72009i	0.649382	+	0.374921i
$425$	−14.5411	−	2.78687i	−0.705346	−	0.135183i
$426$			7.16363i			0.347079i
$427$	0.566405	+	4.99209i	0.0274103	+	0.241584i
$428$	5.00047	+	3.34121i	0.241707	+	0.161503i
$429$	3.01086	−	11.2367i	0.145366	−	0.542512i
$430$	9.09207	+	3.08634i	0.438458	+	0.148837i
$431$	−1.87811	−	28.6544i	−0.0904653	−	1.38023i	−0.765969	−	0.642877i	$-0.777740\pi$
$431$	−1.87811	−	28.6544i	−0.0904653	−	1.38023i	0.675504	−	0.737356i	$-0.263926\pi$
$432$	1.25984	−	0.427657i	0.0606139	−	0.0205756i
$433$	−0.382572	−	0.923612i	−0.0183853	−	0.0443859i	0.914420	−	0.404766i	$-0.132647\pi$
$433$	−0.382572	−	0.923612i	−0.0183853	−	0.0443859i	−0.932806	+	0.360380i	$0.882647\pi$
$434$	14.9909	−	5.89694i	0.719584	−	0.283062i
$435$	5.29533	−	26.6214i	0.253892	−	1.27640i
$436$	−2.13594	+	4.33126i	−0.102293	+	0.207430i
$437$	−8.53525	+	25.1440i	−0.408296	+	1.20280i
$438$	−0.174868	−	0.652618i	−0.00835553	−	0.0311833i
$439$	−1.13189	+	17.2693i	−0.0540221	+	0.824218i	0.881773	+	0.471674i	$0.156350\pi$
$439$	−1.13189	+	17.2693i	−0.0540221	+	0.824218i	−0.935795	+	0.352544i	$0.885317\pi$
$440$	−18.3930	+	44.4045i	−0.876850	+	2.11690i
$441$	−6.18371	+	3.28050i	−0.294463	+	0.156214i
$442$	6.04879	−	6.99537i	0.287711	−	0.332736i
$443$	−8.93393	−	15.4740i	−0.424464	−	0.735193i	0.571907	−	0.820319i	$-0.306204\pi$
$443$	−8.93393	−	15.4740i	−0.424464	−	0.735193i	−0.996370	+	0.0851262i	$0.972871\pi$
$444$	2.85635	−	2.19175i	0.135556	−	0.104016i
$445$	−10.1385	+	4.99973i	−0.480609	+	0.237010i
$446$	−18.4066	−	4.93202i	−0.871576	−	0.233538i
$447$	−3.05668	−	15.3670i	−0.144576	−	0.726832i
$448$	16.7862	−	10.7861i	0.793075	−	0.509597i
$449$	1.74474	+	0.347050i	0.0823392	+	0.0163783i	0.236088	−	0.971732i	$-0.424135\pi$
$449$	1.74474	+	0.347050i	0.0823392	+	0.0163783i	−0.153749	+	0.988110i	$0.549135\pi$
$450$	2.96664	+	2.27638i	0.139849	+	0.107310i
$451$	−2.75259	+	20.9080i	−0.129614	+	0.984518i
$452$	−8.11809	−	7.11937i	−0.381843	−	0.334867i
$453$	−19.7486	−	9.73893i	−0.927870	−	0.457575i
$454$	14.7121	−	2.92641i	0.690471	−	0.137343i
$455$	−16.0537	−	4.61149i	−0.752611	−	0.216190i
$456$	7.12538	−	10.6639i	0.333676	−	0.499382i
$457$	−0.400268	−	3.04034i	−0.0187238	−	0.142221i	0.979530	−	0.201301i	$-0.0645168\pi$
$457$	−0.400268	−	3.04034i	−0.0187238	−	0.142221i	−0.998253	+	0.0590795i	$0.981183\pi$
$458$	12.8577	−	22.2702i	0.600801	−	1.04062i
$459$	−1.03927	+	3.98998i	−0.0485090	+	0.186236i
$460$	14.6093	−	8.43471i	0.681164	−	0.393270i
$461$	−21.8522	−	9.05148i	−1.01776	−	0.421569i	−0.189479	−	0.981885i	$-0.560680\pi$
$461$	−21.8522	−	9.05148i	−1.01776	−	0.421569i	−0.828279	+	0.560315i	$0.810680\pi$
$462$	−6.34116	−	13.4615i	−0.295018	−	0.626288i
$463$	14.2343	+	14.2343i	0.661522	+	0.661522i	0.955739	−	0.294217i	$-0.0950588\pi$
$463$	14.2343	+	14.2343i	0.661522	+	0.661522i	−0.294217	+	0.955739i	$0.595059\pi$
$464$	−8.12357	−	9.26315i	−0.377127	−	0.430031i
$465$	−17.1008	+	1.12084i	−0.793029	+	0.0519779i
$466$	11.7000	−	13.3413i	0.541993	−	0.618025i
$467$	−21.9965	+	28.6664i	−1.01788	+	1.32652i	−0.0736292	+	0.997286i	$0.523458\pi$
$467$	−21.9965	+	28.6664i	−1.01788	+	1.32652i	−0.944247	+	0.329237i	$0.893209\pi$
$468$	1.82200	−	0.754699i	0.0842222	−	0.0348860i
$469$	−7.87757	−	7.16223i	−0.363752	−	0.330721i
$470$	15.0453	+	22.5170i	0.693990	+	1.03863i
$471$	15.9374	−	13.9767i	0.734356	−	0.644013i
$472$	9.84141	−	2.63700i	0.452988	−	0.121378i
$473$	7.51463	+	15.2382i	0.345523	+	0.700652i
$474$	−12.0402	+	1.58512i	−0.553024	+	0.0728070i
$475$	15.1688			0.695994
$476$	−0.109181	+	9.98752i	−0.00500429	+	0.457777i
$477$	5.08546			0.232847
$478$	−11.1875	+	1.47286i	−0.511704	+	0.0673670i
$479$	1.91976	+	3.89288i	0.0877159	+	0.177870i	0.936310	−	0.351174i	$-0.114217\pi$
$479$	1.91976	+	3.89288i	0.0877159	+	0.177870i	−0.848594	+	0.529044i	$0.822551\pi$
$480$	−13.2692	+	3.55546i	−0.605652	+	0.162284i
$481$	−6.36772	+	5.58434i	−0.290343	+	0.254624i
$482$	−9.14670	−	13.6890i	−0.416621	−	0.623517i
$483$	−3.53636	+	16.2507i	−0.160910	+	0.739433i
$484$	−15.3704	+	6.36664i	−0.698656	+	0.289393i
$485$	2.45572	−	3.20036i	0.111509	−	0.145321i
$486$	0.686604	−	0.782922i	0.0311450	−	0.0355140i
$487$	−19.1472	+	1.25497i	−0.867643	+	0.0568683i	−0.492720	−	0.870188i	$-0.663997\pi$
$487$	−19.1472	+	1.25497i	−0.867643	+	0.0568683i	−0.374923	+	0.927056i	$0.622331\pi$
$488$	−3.80143	−	4.33470i	−0.172083	−	0.196223i
$489$	11.8533	+	11.8533i	0.536025	+	0.536025i
$490$	−19.4884	+	8.75689i	−0.880395	+	0.395596i
$491$	33.2668	+	13.7795i	1.50131	+	0.621862i	0.973743	−	0.227652i	$-0.0731048\pi$
$491$	33.2668	+	13.7795i	1.50131	+	0.621862i	0.527566	+	0.849514i	$0.323105\pi$
$492$	−3.09609	+	1.78753i	−0.139583	+	0.0805881i
$493$	37.8199	−	5.24832i	1.70332	−	0.236372i
$494$	−4.73733	+	8.20530i	−0.213143	+	0.369174i
$495$	2.06627	+	15.6949i	0.0928720	+	0.705433i
$496$	−4.32177	+	6.46798i	−0.194053	+	0.290421i
$497$	12.6372	+	13.0984i	0.566854	+	0.587545i
$498$	−13.2173	+	2.62908i	−0.592281	+	0.117812i
$499$	−33.0923	−	16.3193i	−1.48141	−	0.730553i	−0.491323	−	0.870977i	$-0.663487\pi$
$499$	−33.0923	−	16.3193i	−1.48141	−	0.730553i	−0.990091	+	0.140425i	$0.955153\pi$
$500$	2.84309	+	2.49333i	0.127147	+	0.111505i
$501$	−1.41232	+	10.7276i	−0.0630977	+	0.479275i
$502$	11.5482	+	8.86123i	0.515421	+	0.395496i
$503$	22.5347	+	4.48243i	1.00477	+	0.199862i	0.669939	−	0.742416i	$-0.266320\pi$
$503$	22.5347	+	4.48243i	1.00477	+	0.199862i	0.334833	+	0.942277i	$0.391320\pi$
$504$	3.68140	−	7.13964i	0.163982	−	0.318025i
$505$	2.33389	+	11.7332i	0.103857	+	0.522122i
$506$	−34.1489	−	9.15017i	−1.51810	−	0.406775i
$507$	7.49852	−	3.69786i	0.333021	−	0.164228i
$508$	6.24419	−	4.79133i	0.277041	−	0.212581i
$509$	−12.6888	−	21.9776i	−0.562421	−	0.974142i	−0.997284	−	0.0736453i	$-0.976537\pi$
$509$	−12.6888	−	21.9776i	−0.562421	−	0.974142i	0.434864	−	0.900496i	$-0.356797\pi$
$510$	−3.96176	+	11.9447i	−0.175430	+	0.528919i
$511$	−1.47101	−	0.884808i	−0.0650734	−	0.0391416i
$512$	−5.47788	+	13.2248i	−0.242091	+	0.584458i
$513$	0.276277	−	4.21518i	0.0121979	−	0.186105i
$514$	−1.44467	−	5.39159i	−0.0637217	−	0.237813i
$515$	−14.8089	+	43.6255i	−0.652557	+	1.92237i
$516$	−1.27394	+	2.58329i	−0.0560819	+	0.113723i
$517$	−9.34881	+	46.9996i	−0.411160	+	2.06704i
$518$	−1.60635	+	10.7139i	−0.0705788	+	0.470744i
$519$	0.879838	+	2.12412i	0.0386206	+	0.0932384i
$520$	18.1503	−	6.16120i	0.795944	−	0.270187i
$521$	1.28584	+	19.6181i	0.0563336	+	0.859485i	0.928747	+	0.370715i	$0.120887\pi$
$521$	1.28584	+	19.6181i	0.0563336	+	0.859485i	−0.872413	+	0.488770i	$0.837446\pi$
$522$	−9.13163	−	3.09977i	−0.399681	−	0.135673i
$523$	−5.09553	+	19.0168i	−0.222812	+	0.831545i	0.760458	+	0.649388i	$0.224975\pi$
$523$	−5.09553	+	19.0168i	−0.222812	+	0.831545i	−0.983269	+	0.182157i	$0.941692\pi$
$524$	−13.5535	−	9.05618i	−0.592089	−	0.395621i
$525$	9.44011	−	1.07108i	0.412000	−	0.0467457i
$526$		−	17.9305i		−	0.781807i
$527$	−9.38100	−	22.2073i	−0.408643	−	0.967366i
$528$	6.22295	+	3.59282i	0.270819	+	0.156358i
$529$	10.0525	+	13.1007i	0.437065	+	0.569594i
$530$	15.4886	+	1.01518i	0.672781	+	0.0440964i
$531$	2.37288	−	2.37288i	0.102974	−	0.102974i
$532$	−1.81618	−	10.0706i	−0.0787416	−	0.436616i
$533$	6.99268	−	4.67236i	0.302887	−	0.202382i
$534$	1.29096	+	3.80305i	0.0558654	+	0.164574i
$535$	19.0872	+	2.51288i	0.825212	+	0.108641i
$536$	12.1132	+	1.59474i	0.523211	+	0.0688821i
$537$	1.78076	+	5.24594i	0.0768454	+	0.226379i
$538$	−0.339458	+	0.226819i	−0.0146351	+	0.00977884i
$539$	−35.3417	−	13.4277i	−1.52228	−	0.578372i
$540$	−1.89764	+	1.89764i	−0.0816616	+	0.0816616i
$541$	−7.09969	−	0.465338i	−0.305240	−	0.0200065i	−0.0879862	−	0.996122i	$-0.528043\pi$
$541$	−7.09969	−	0.465338i	−0.305240	−	0.0200065i	−0.217253	+	0.976115i	$0.569710\pi$
$542$	1.14810	+	1.49623i	0.0493151	+	0.0642687i
$543$	11.2087	+	6.47133i	0.481011	+	0.277712i
$544$	−10.8481	−	15.9922i	−0.465108	−	0.685658i
$545$			15.4594i			0.662209i
$546$	−2.36883	+	5.44096i	−0.101377	+	0.232851i
$547$	24.4228	+	16.3188i	1.04424	+	0.697742i	0.954496	−	0.298223i	$-0.0963939\pi$
$547$	24.4228	+	16.3188i	1.04424	+	0.697742i	0.0897479	+	0.995965i	$0.471394\pi$
$548$	2.50884	−	9.36312i	0.107172	−	0.399973i
$549$	−1.79816	−	0.610394i	−0.0767437	−	0.0260510i
$550$	1.32089	+	20.1529i	0.0563230	+	0.859323i
$551$	−37.0427	+	12.5743i	−1.57807	+	0.535683i
$552$	−7.30352	−	17.6323i	−0.310858	−	0.750478i
$553$	−19.2188	+	24.1381i	−0.817267	+	1.02646i
$554$	−3.49526	+	17.5719i	−0.148500	+	0.746558i
$555$	5.09753	−	10.3368i	0.216378	−	0.438772i
$556$	−2.54971	+	7.51121i	−0.108132	+	0.318546i
$557$	6.27355	+	23.4132i	0.265819	+	0.992050i	0.961747	+	0.273939i	$0.0883265\pi$
$557$	6.27355	+	23.4132i	0.265819	+	0.992050i	−0.695928	+	0.718111i	$0.745007\pi$
$558$	−0.398215	+	6.07559i	−0.0168578	+	0.257200i
$559$	2.59296	−	6.25996i	0.109670	−	0.264768i
$560$	5.31793	−	8.84113i	0.224724	−	0.373606i
$561$	−19.9028	+	9.98857i	−0.840298	+	0.421718i
$562$	−1.04218	−	1.80511i	−0.0439618	−	0.0761441i
$563$	26.9925	−	20.7121i	1.13760	−	0.872910i	0.144420	−	0.989517i	$-0.453868\pi$
$563$	26.9925	−	20.7121i	1.13760	−	0.872910i	0.993178	+	0.116607i	$0.0372018\pi$
$564$	−7.28604	+	3.59308i	−0.306798	+	0.151296i
$565$	−33.3874	−	8.94612i	−1.40462	−	0.376366i
$566$	1.10864	+	5.57351i	0.0465996	+	0.234272i
$567$	−0.125699	−	2.64276i	−0.00527885	−	0.110986i
$568$	−20.4850	−	4.07472i	−0.859532	−	0.170971i
$569$	−3.65897	−	2.80763i	−0.153392	−	0.117702i	0.529214	−	0.848488i	$-0.322487\pi$
$569$	−3.65897	−	2.80763i	−0.153392	−	0.117702i	−0.682606	+	0.730786i	$0.739154\pi$
$570$	1.68290	−	12.7829i	0.0704887	−	0.535415i
$571$	−0.906172	−	0.794692i	−0.0379221	−	0.0332568i	0.640175	−	0.768229i	$-0.278862\pi$
$571$	−0.906172	−	0.794692i	−0.0379221	−	0.0332568i	−0.678097	+	0.734972i	$0.737195\pi$
$572$	9.55289	+	4.71097i	0.399427	+	0.196975i
$573$	−19.6103	+	3.90073i	−0.819232	+	0.162955i
$574$	2.97005	−	10.3395i	0.123967	−	0.431561i
$575$	12.5405	−	18.7682i	0.522975	−	0.782687i
$576$	0.984361	+	7.47697i	0.0410151	+	0.311540i
$577$	5.09824	−	8.83042i	0.212243	−	0.367615i	−0.740173	−	0.672416i	$-0.765257\pi$
$577$	5.09824	−	8.83042i	0.212243	−	0.367615i	0.952416	+	0.304801i	$0.0985899\pi$
$578$	−17.7011	+	0.247514i	−0.736267	+	0.0102952i
$579$	−4.75659	+	2.74622i	−0.197677	+	0.114129i
$580$	22.9606	+	9.51058i	0.953386	+	0.394905i
$581$	−19.5295	+	28.1234i	−0.810219	+	1.16676i
$582$	−1.01342	−	1.01342i	−0.0420077	−	0.0420077i
$583$	18.1098	+	20.6502i	0.750030	+	0.855246i
$584$	1.96568	−	0.128838i	0.0813405	−	0.00533134i
$585$	4.16253	−	4.74645i	0.172099	−	0.196242i
$586$	−4.15914	+	5.42030i	−0.171812	+	0.223910i
$587$	11.6570	−	4.82847i	0.481134	−	0.199292i	−0.128915	−	0.991656i	$-0.541150\pi$
$587$	11.6570	−	4.82847i	0.481134	−	0.199292i	0.610050	+	0.792363i	$0.291150\pi$
$588$	−1.84137	−	6.13906i	−0.0759367	−	0.253170i
$589$	13.7218	+	20.5362i	0.565398	+	0.846179i
$590$	7.70069	−	6.75332i	0.317032	−	0.278030i
$591$	18.5118	−	4.96021i	0.761473	−	0.204036i
$592$	−2.31386	−	4.69204i	−0.0950989	−	0.192841i
$593$	−4.46429	+	0.587735i	−0.183326	+	0.0241354i	−0.221630	−	0.975131i	$-0.571138\pi$
$593$	−4.46429	+	0.587735i	−0.183326	+	0.0241354i	0.0383039	+	0.999266i	$0.487804\pi$
$594$	5.62423			0.230765
$595$	13.8273	+	28.8292i	0.566864	+	1.18188i
$596$	14.3458			0.587626
$597$	−24.4358	+	3.21703i	−1.00009	+	0.131664i
$598$	6.23581	+	12.6450i	0.255001	+	0.517092i
$599$	−43.6507	+	11.6962i	−1.78352	+	0.477893i	−0.991218	−	0.132237i	$-0.957784\pi$
$599$	−43.6507	+	11.6962i	−1.78352	+	0.477893i	−0.792302	+	0.610129i	$0.791117\pi$
$600$	−8.19697	+	7.18855i	−0.334640	+	0.293471i
$601$	−25.4791	−	38.1321i	−1.03931	−	1.55544i	−0.813751	−	0.581213i	$-0.802578\pi$
$601$	−25.4791	−	38.1321i	−1.03931	−	1.55544i	−0.225562	−	0.974229i	$-0.572422\pi$
$602$	−2.63842	−	8.25575i	−0.107534	−	0.336479i
$603$	3.71778	−	1.53996i	0.151400	−	0.0627119i
$604$	12.2733	−	15.9949i	0.499395	−	0.650824i
$605$	−35.1151	+	40.0411i	−1.42763	+	1.62790i
$606$	4.24117	−	0.277981i	0.172286	−	0.0112922i
$607$	−3.20717	−	3.65707i	−0.130175	−	0.148436i	0.683080	−	0.730343i	$-0.260640\pi$
$607$	−3.20717	−	3.65707i	−0.130175	−	0.148436i	−0.813255	+	0.581907i	$0.802307\pi$
$608$	13.9995	+	13.9995i	0.567754	+	0.567754i
$609$	−22.1651	+	10.4410i	−0.898175	+	0.423092i
$610$	−5.35475	−	2.21801i	−0.216808	−	0.0898046i
$611$	16.5503	−	9.55531i	0.669553	−	0.386566i
$612$	−3.39742	−	1.64600i	−0.137333	−	0.0665355i
$613$	11.5389	−	19.9860i	0.466053	−	0.807228i	−0.533195	−	0.845992i	$-0.679009\pi$
$613$	11.5389	−	19.9860i	0.466053	−	0.807228i	0.999248	+	0.0387643i	$0.0123421\pi$
$614$	−1.55403	−	11.8040i	−0.0627157	−	0.476373i
$615$	−6.35817	+	9.51567i	−0.256386	+	0.383709i
$616$	42.1014	−	10.4761i	1.69631	−	0.422093i
$617$	−12.6510	+	2.51645i	−0.509312	+	0.101308i	−0.443056	−	0.896494i	$-0.646106\pi$
$617$	−12.6510	+	2.51645i	−0.509312	+	0.101308i	−0.0662564	+	0.997803i	$0.521106\pi$
$618$	14.6800	+	7.23939i	0.590517	+	0.291211i
$619$	6.06487	+	5.31875i	0.243768	+	0.213779i	0.772508	−	0.635005i	$-0.219002\pi$
$619$	6.06487	+	5.31875i	0.243768	+	0.213779i	−0.528740	+	0.848784i	$0.677335\pi$
$620$	2.04811	−	15.5570i	0.0822542	−	0.624783i
$621$	−4.98697	−	3.82664i	−0.200120	−	0.153558i
$622$	14.9694	+	2.97759i	0.600217	+	0.119391i
$623$	9.06933	+	4.67640i	0.363355	+	0.187356i
$624$	−0.559057	−	2.81057i	−0.0223802	−	0.112513i
$625$	29.0356	+	7.78007i	1.16143	+	0.311203i
$626$	−1.71477	+	0.845633i	−0.0685362	+	0.0337983i
$627$	18.1002	−	13.8888i	0.722852	−	0.554664i
$628$	9.70447	+	16.8086i	0.387251	+	0.670738i
$629$	16.0885	+	2.00377i	0.641492	+	0.0798957i
$630$	0.144722	−	8.07406i	0.00576584	−	0.321678i
$631$	−10.1762	+	24.5676i	−0.405110	+	0.978022i	0.581295	+	0.813693i	$0.302546\pi$
$631$	−10.1762	+	24.5676i	−0.405110	+	0.978022i	−0.986405	+	0.164330i	$0.947454\pi$
$632$	2.31576	−	35.3316i	0.0921158	−	1.40542i
$633$	−0.688179	−	2.56832i	−0.0273526	−	0.102081i
$634$	6.02186	−	17.7398i	0.239158	−	0.704538i
$635$	11.1436	−	22.5970i	0.442220	−	0.896733i
$636$	−0.908397	+	4.56682i	−0.0360203	+	0.181086i
$637$	5.26691	+	14.1274i	0.208683	+	0.559748i
$638$	−19.9315	−	48.1189i	−0.789096	−	1.90505i
$639$	−6.51415	+	2.21126i	−0.257696	+	0.0874760i
$640$	−0.291463	−	4.44687i	−0.0115211	−	0.175778i
$641$	30.3932	+	10.3171i	1.20046	+	0.407501i	0.848844	−	0.528644i	$-0.177299\pi$
$641$	30.3932	+	10.3171i	1.20046	+	0.407501i	0.351615	+	0.936145i	$0.385633\pi$
$642$	1.77029	−	6.60680i	0.0698676	−	0.260749i
$643$	38.0910	+	25.4516i	1.50216	+	1.00371i	0.989405	+	0.145182i	$0.0463766\pi$
$643$	38.0910	+	25.4516i	1.50216	+	1.00371i	0.512759	+	0.858532i	$0.328623\pi$
$644$	−13.9617	−	6.07851i	−0.550168	−	0.239527i
$645$			9.22044i			0.363055i
$646$	17.7633	−	3.66261i	0.698887	−	0.144104i
$647$	−5.26208	−	3.03806i	−0.206874	−	0.119439i	0.392984	−	0.919545i	$-0.371443\pi$
$647$	−5.26208	−	3.03806i	−0.206874	−	0.119439i	−0.599858	+	0.800107i	$0.704776\pi$
$648$	1.84829	+	2.40873i	0.0726076	+	0.0946240i
$649$	18.0855	+	1.18539i	0.709918	+	0.0465305i
$650$	5.69518	−	5.69518i	0.223383	−	0.223383i
$651$	9.98966	+	11.8115i	0.391526	+	0.462929i
$652$	−12.7618	+	8.52714i	−0.499790	+	0.333949i
$653$	−3.90390	−	11.5005i	−0.152771	−	0.450050i	0.843419	−	0.537256i	$-0.180539\pi$
$653$	−3.90390	−	11.5005i	−0.152771	−	0.450050i	−0.996190	+	0.0872068i	$0.972206\pi$
$654$	5.44547	+	0.716910i	0.212935	+	0.0280334i
$655$	−51.7350	−	6.81104i	−2.02145	−	0.266129i
$656$	1.66982	+	4.91912i	0.0651953	+	0.192059i
$657$	0.539471	−	0.360463i	0.0210468	−	0.0140630i
$658$	8.27121	−	23.0033i	0.322445	−	0.896762i
$659$	−22.9966	+	22.9966i	−0.895821	+	0.895821i	−0.995063	−	0.0992421i	$-0.968358\pi$
$659$	−22.9966	+	22.9966i	−0.895821	+	0.895821i	0.0992421	+	0.995063i	$0.468358\pi$
$660$	−14.4634	−	0.947978i	−0.562985	−	0.0369000i
$661$	−24.7749	−	32.2872i	−0.963630	−	1.25583i	−0.966721	−	0.255832i	$-0.917650\pi$
$661$	−24.7749	−	32.2872i	−0.963630	−	1.25583i	0.00309066	−	0.999995i	$-0.499016\pi$
$662$	−4.39509	−	2.53751i	−0.170820	−	0.0986231i
$663$	8.22828	+	3.34107i	0.319560	+	0.129756i
$664$		−	39.2914i		−	1.52480i
$665$	−19.4728	−	26.3418i	−0.755122	−	1.02149i
$666$	−3.40466	−	2.27492i	−0.131928	−	0.0881514i
$667$	−15.0662	+	56.2279i	−0.583366	+	2.17715i
$668$	−9.38130	−	3.18452i	−0.362973	−	0.123213i
$669$	−1.19684	−	18.2602i	−0.0462723	−	0.705980i
$670$	11.6305	−	3.94803i	0.449327	−	0.152526i
$671$	−3.92483	−	9.47538i	−0.151516	−	0.365793i
$672$	9.70089	+	7.72387i	0.374220	+	0.297955i
$673$	−2.66986	+	13.4223i	−0.102916	+	0.517391i	0.894595	+	0.446877i	$0.147464\pi$
$673$	−2.66986	+	13.4223i	−0.102916	+	0.517391i	−0.997511	+	0.0705140i	$0.977536\pi$
$674$	0.268551	−	0.544567i	0.0103442	−	0.0209759i
$675$	−1.15426	+	3.40035i	−0.0444276	+	0.130879i
$676$	1.98130	+	7.39433i	0.0762040	+	0.284397i
$677$	0.316560	−	4.82977i	0.0121664	−	0.185623i	−0.987450	−	0.157931i	$-0.949518\pi$
$677$	0.316560	−	4.82977i	0.0121664	−	0.185623i	0.999617	−	0.0276919i	$-0.00881572\pi$
$678$	−4.69949	+	11.3456i	−0.180483	+	0.435725i
$679$	−3.64075	−	0.0652578i	−0.139719	−	0.00250437i
$680$	−31.9033	−	18.1232i	−1.22344	−	0.694993i
$681$	7.20239	+	12.4749i	0.275996	+	0.478039i
$682$	−26.0889	+	20.0187i	−0.998997	+	0.766557i
$683$	−13.8376	+	6.82396i	−0.529482	+	0.261112i	−0.687322	−	0.726353i	$-0.741214\pi$
$683$	−13.8376	+	6.82396i	−0.529482	+	0.261112i	0.157840	+	0.987465i	$0.449547\pi$
$684$	3.73595	+	1.00104i	0.142847	+	0.0382759i
$685$	−6.05372	−	30.4341i	−0.231301	−	1.16283i
$686$	16.8136	+	9.44717i	0.641946	+	0.360695i
$687$	24.2200	+	4.81766i	0.924051	+	0.183805i
$688$	3.32043	+	2.54786i	0.126590	+	0.0971361i
$689$	1.42972	−	10.8598i	0.0544681	−	0.413726i
$690$	−14.4247	−	12.6502i	−0.549141	−	0.481584i
$691$	−23.6358	−	11.6559i	−0.899150	−	0.443411i	−0.0668662	−	0.997762i	$-0.521300\pi$
$691$	−23.6358	−	11.6559i	−0.899150	−	0.443411i	−0.832283	+	0.554350i	$0.812967\pi$
$692$	−2.06465	+	0.410685i	−0.0784864	+	0.0156119i
$693$	10.2837	−	9.92154i	0.390646	−	0.376888i
$694$	20.6555	−	30.9131i	0.784070	−	1.17344i
$695$	3.31436	+	25.1750i	0.125721	+	0.954944i
$696$	14.0582	−	24.3495i	0.532875	−	0.922966i
$697$	−15.5791	−	4.05790i	−0.590102	−	0.153704i
$698$	30.5519	−	17.6392i	1.15641	−	0.667652i
$699$	15.7433	+	6.52109i	0.595466	+	0.246650i
$700$	−0.724407	+	8.66869i	−0.0273800	+	0.327646i
$701$	−25.8759	−	25.8759i	−0.977320	−	0.977320i	0.0224280	−	0.999748i	$-0.492860\pi$
$701$	−25.8759	−	25.8759i	−0.977320	−	0.977320i	−0.999748	+	0.0224280i	$0.992860\pi$
$702$	−1.47887	−	1.68633i	−0.0558164	−	0.0636464i
$703$	−16.5749	+	1.08638i	−0.625133	+	0.0409734i
$704$	−26.8559	+	30.6233i	−1.01217	+	1.15416i
$705$	−15.8313	+	20.6318i	−0.596243	+	0.777038i
$706$	15.5928	−	6.45875i	0.586843	−	0.243078i
$707$	7.26446	−	7.99002i	0.273208	−	0.300495i
$708$	1.70703	+	2.55475i	0.0641540	+	0.0960132i
$709$	−18.8699	+	16.5485i	−0.708674	+	0.621490i	−0.935865	−	0.352360i	$-0.885379\pi$
$709$	−18.8699	+	16.5485i	−0.708674	+	0.621490i	0.227191	+	0.973850i	$0.427046\pi$
$710$	−20.2813	+	5.43437i	−0.761145	+	0.203948i
$711$	−5.15796	−	10.4593i	−0.193439	−	0.392255i
$712$	−11.6095	+	1.52841i	−0.435083	+	0.0572797i
$713$	36.7533			1.37642
$714$	10.7961	−	3.53365i	0.404034	−	0.132244i
$715$	34.0968			1.27515
$716$	−5.02903	+	0.662085i	−0.187944	+	0.0247433i
$717$	−4.79266	−	9.71855i	−0.178985	−	0.362946i
$718$	32.3776	−	8.67555i	1.20832	−	0.323769i
$719$	24.3883	−	21.3880i	0.909530	−	0.797636i	−0.0702886	−	0.997527i	$-0.522392\pi$
$719$	24.3883	−	21.3880i	0.909530	−	0.797636i	0.979818	+	0.199891i	$0.0640587\pi$
$720$	2.16648	+	3.24237i	0.0807400	+	0.120836i
$721$	39.6127	−	12.6597i	1.47526	−	0.471470i
$722$	1.11211	−	0.460651i	0.0413884	−	0.0171436i
$723$	9.62454	−	12.5429i	0.357940	−	0.466477i
$724$	−7.81353	+	8.90962i	−0.290387	+	0.331123i
$725$	33.1827	−	2.17491i	1.23238	−	0.0807742i
$726$	12.4758	+	14.2259i	0.463019	+	0.527972i
$727$	−0.0234764	−	0.0234764i	−0.000870692	−	0.000870692i	0.706671	−	0.707542i	$-0.250196\pi$
$727$	−0.0234764	−	0.0234764i	−0.000870692	−	0.000870692i	−0.707542	+	0.706671i	$0.750196\pi$
$728$	−14.2115	−	9.86873i	−0.526712	−	0.365759i
$729$	0.923880	+	0.382683i	0.0342178	+	0.0141735i
$730$	1.71501	−	0.990159i	0.0634752	−	0.0366474i
$731$	−12.2527	+	4.25499i	−0.453182	+	0.157376i
$732$	0.869343	−	1.50575i	0.0321318	−	0.0556540i
$733$	−1.54837	−	11.7610i	−0.0571903	−	0.434403i	−0.995956	−	0.0898462i	$-0.971362\pi$
$733$	−1.54837	−	11.7610i	−0.0571903	−	0.434403i	0.938765	−	0.344557i	$-0.111971\pi$
$734$	−5.62305	+	8.41548i	−0.207550	+	0.310621i
$735$	−13.9786	−	15.0184i	−0.515609	−	0.553964i
$736$	28.8951	−	5.74760i	1.06509	−	0.211859i
$737$	19.4926	+	9.61268i	0.718019	+	0.354088i
$738$	3.05697	+	2.68089i	0.112529	+	0.0986850i
$739$	1.60551	−	12.1950i	0.0590595	−	0.448601i	−0.936209	−	0.351443i	$-0.885691\pi$
$739$	1.60551	−	12.1950i	0.0590595	−	0.448601i	0.995269	−	0.0971588i	$-0.0309755\pi$
$740$	8.37204	+	6.42409i	0.307762	+	0.236154i
$741$	−8.92370	−	1.77503i	−0.327820	−	0.0652075i
$742$	−7.57411	−	11.7874i	−0.278054	−	0.432730i
$743$	5.75416	+	28.9281i	0.211100	+	1.06127i	0.930393	+	0.366564i	$0.119466\pi$
$743$	5.75416	+	28.9281i	0.211100	+	1.06127i	−0.719293	+	0.694707i	$0.755534\pi$
$744$	−17.1472	−	4.59457i	−0.628646	−	0.168445i
$745$	41.1874	−	20.3114i	1.50899	−	0.744151i
$746$	1.34739	−	1.03389i	0.0493316	−	0.0378535i
$747$	−6.47061	−	11.2074i	−0.236747	−	0.410058i
$748$	−5.41472	−	19.6573i	−0.197982	−	0.718741i
$749$	−8.41796	−	15.2032i	−0.307585	−	0.555513i
$750$	1.64584	−	3.97342i	0.0600977	−	0.145089i
$751$	1.96495	−	29.9793i	0.0717019	−	1.09396i	−0.798736	−	0.601681i	$-0.794498\pi$
$751$	1.96495	−	29.9793i	0.0717019	−	1.09396i	0.870438	−	0.492278i	$-0.163836\pi$
$752$	3.05522	+	11.4022i	0.111412	+	0.415797i
$753$	−4.49317	+	13.2365i	−0.163740	+	0.482364i
$754$	−9.18672	+	18.6288i	−0.334561	+	0.678422i
$755$	12.5910	−	63.2993i	0.458234	−	2.30370i
$756$	2.39570	+	0.359188i	0.0871306	+	0.0130635i
$757$	8.05039	+	19.4354i	0.292596	+	0.706390i	1.00000		0.000419944i	$-0.000133672\pi$
$757$	8.05039	+	19.4354i	0.292596	+	0.706390i	−0.707404	+	0.706810i	$0.750134\pi$
$758$	−33.6813	+	11.4333i	−1.22336	+	0.415275i
$759$	−2.22044	−	33.8773i	−0.0805968	−	1.22967i
$760$	35.5964	+	12.0834i	1.29122	+	0.438310i
$761$	−5.42291	+	20.2386i	−0.196580	+	0.733648i	0.795272	+	0.606253i	$0.207328\pi$
$761$	−5.42291	+	20.2386i	−0.196580	+	0.733648i	−0.991852	+	0.127395i	$0.959338\pi$
$762$	−7.44284	−	4.97315i	−0.269626	−	0.180158i
$763$	11.2215	−	8.29535i	0.406247	−	0.300312i
$764$		−	18.3071i		−	0.662329i
$765$	−12.0846	+	0.0844857i	−0.436921	+	0.00305459i
$766$	−3.44352	−	1.98812i	−0.124419	−	0.0718336i
$767$	−4.40010	−	5.73432i	−0.158878	−	0.207054i
$768$	−16.6306	−	1.09003i	−0.600104	−	0.0393329i
$769$	−17.9954	+	17.9954i	−0.648930	+	0.648930i	−0.952734	−	0.303804i	$-0.901743\pi$
$769$	−17.9954	+	17.9954i	−0.648930	+	0.648930i	0.303804	+	0.952734i	$0.401743\pi$
$770$	33.3013	−	28.1648i	1.20009	−	1.01499i
$771$	4.45683	−	2.97796i	0.160509	−	0.107249i
$772$	−1.61649	−	4.76204i	−0.0581789	−	0.171389i
$773$	36.5822	+	4.81614i	1.31577	+	0.173225i	0.755535	−	0.655109i	$-0.227377\pi$
$773$	36.5822	+	4.81614i	1.31577	+	0.173225i	0.560236	+	0.828333i	$0.310710\pi$
$774$	3.24783	+	0.427585i	0.116741	+	0.0153692i
$775$	−6.74887	−	19.8815i	−0.242427	−	0.714166i
$776$	3.47441	−	2.32152i	0.124724	−	0.0833379i
$777$	−10.2384	+	1.84645i	−0.367302	+	0.0662411i
$778$	7.92140	−	7.92140i	0.283996	−	0.283996i
$779$	16.4585	+	1.07874i	0.589685	+	0.0386500i
$780$	3.51885	+	4.58586i	0.125995	+	0.164200i
$781$	−32.1766	−	18.5772i	−1.15137	−	0.664744i
$782$	10.1537	−	25.0062i	0.363095	−	0.894221i
$783$		−	9.26057i		−	0.330946i
$784$	−9.27105	+	0.883924i	−0.331109	+	0.0315687i
$785$	51.6604	+	34.5184i	1.84384	+	1.23201i
$786$	−4.79827	+	17.9074i	−0.171149	+	0.638736i
$787$	0.522435	+	0.177343i	0.0186228	+	0.00632159i	0.330735	−	0.943724i	$-0.392703\pi$
$787$	0.522435	+	0.177343i	0.0186228	+	0.00632159i	−0.312113	+	0.950045i	$0.601037\pi$
$788$	1.14766	+	17.5099i	0.0408837	+	0.623764i
$789$	16.3049	−	5.53476i	0.580469	−	0.197043i
$790$	−13.6215	−	32.8852i	−0.484631	−	1.17000i
$791$	11.4216	+	29.0353i	0.406104	+	1.03237i
$792$	−3.19910	+	16.0830i	−0.113675	+	0.571483i
$793$	−1.80901	+	3.66831i	−0.0642399	+	0.130266i
$794$	4.76535	−	14.0383i	0.169116	−	0.498199i
$795$	3.85786	+	14.3977i	0.136824	+	0.510634i
$796$	1.47593	−	22.5184i	0.0523130	−	0.798143i
$797$	21.3232	−	51.4789i	0.755308	−	1.82347i	0.228361	−	0.973577i	$-0.426663\pi$
$797$	21.3232	−	51.4789i	0.755308	−	1.82347i	0.526947	−	0.849898i	$-0.323337\pi$
$798$	−10.1817	+	5.63757i	−0.360429	+	0.199568i
$799$	−34.7226	−	11.5166i	−1.22840	−	0.407429i
$800$	−8.41503	−	14.5753i	−0.297516	−	0.515314i
$801$	−3.05976	+	2.34784i	−0.108111	+	0.0829568i
$802$	−17.6733	+	8.71549i	−0.624065	+	0.307755i
$803$	3.38482	+	0.906960i	0.119448	+	0.0320059i
$804$	0.718811	+	3.61371i	0.0253505	+	0.127446i
$805$	−48.6910	+	2.31590i	−1.71613	+	0.0816249i
$806$	12.8623	+	2.55846i	0.453054	+	0.0901181i
$807$	−0.311038	−	0.238668i	−0.0109491	−	0.00840151i
$808$	−1.61750	+	12.2861i	−0.0569034	+	0.432224i
$809$	32.8358	+	28.7962i	1.15444	+	1.01242i	0.999701	+	0.0244653i	$0.00778833\pi$
$809$	32.8358	+	28.7962i	1.15444	+	1.01242i	0.154743	+	0.987955i	$0.450545\pi$
$810$	2.73743	+	1.34995i	0.0961836	+	0.0474325i
$811$	−33.5181	+	6.66716i	−1.17698	+	0.234116i	−0.744559	−	0.667557i	$-0.767340\pi$
$811$	−33.5181	+	6.66716i	−1.17698	+	0.234116i	−0.432419	+	0.901673i	$0.642340\pi$
$812$	−5.41694	−	21.7697i	−0.190097	−	0.763965i
$813$	−1.00619	+	1.50586i	−0.0352885	+	0.0528129i
$814$	−2.88666	−	21.9263i	−0.101177	−	0.768518i
$815$	−24.5666	+	42.5505i	−0.860529	+	1.49048i
$816$	−3.30889	+	4.37522i	−0.115834	+	0.153163i
$817$	11.5082	−	6.64429i	0.402623	−	0.232454i
$818$	18.8209	+	7.79588i	0.658058	+	0.272576i
$819$	−5.67887	−	0.474560i	−0.198436	−	0.0165825i
$820$	−7.40949	−	7.40949i	−0.258751	−	0.258751i
$821$	18.4741	+	21.0657i	0.644752	+	0.735199i	0.978222	−	0.207562i	$-0.0665528\pi$
$821$	18.4741	+	21.0657i	0.644752	+	0.735199i	−0.333470	+	0.942761i	$0.608219\pi$
$822$	−11.0009	+	0.721038i	−0.383701	+	0.0251491i
$823$	12.8594	−	14.6634i	0.448252	−	0.511133i	−0.482945	−	0.875651i	$-0.660433\pi$
$823$	12.8594	−	14.6634i	0.448252	−	0.511133i	0.931197	+	0.364518i	$0.118766\pi$
$824$	−29.0518	+	37.8610i	−1.01207	+	1.31895i
$825$	−17.9181	+	7.42190i	−0.623827	+	0.258397i
$826$	−9.03413	−	1.96594i	−0.314338	−	0.0684038i
$827$	14.4232	+	21.5858i	0.501543	+	0.750612i	0.992720	−	0.120448i	$-0.0384331\pi$
$827$	14.4232	+	21.5858i	0.501543	+	0.750612i	−0.491177	+	0.871060i	$0.663433\pi$
$828$	4.32719	−	3.79484i	0.150380	−	0.131880i
$829$	8.94868	−	2.39779i	0.310801	−	0.0832788i	−0.100047	−	0.994983i	$-0.531899\pi$
$829$	8.94868	−	2.39779i	0.310801	−	0.0832788i	0.410848	+	0.911704i	$0.365233\pi$
$830$	−17.4700	−	35.4257i	−0.606394	−	1.22965i
$831$	−17.0577	+	2.24569i	−0.591724	+	0.0779020i
$832$	16.2436			0.563144
$833$	13.5067	−	25.5063i	0.467979	−	0.883740i
$834$	9.02142			0.312386
$835$	−31.4430	+	4.13954i	−1.08813	+	0.143255i
$836$	9.23916	+	18.7352i	0.319543	+	0.647969i
$837$	−5.64768	+	1.51329i	−0.195213	+	0.0523070i
$838$	−11.7791	+	10.3300i	−0.406903	+	0.356844i
$839$	9.88311	+	14.7911i	0.341203	+	0.510646i	0.961899	−	0.273405i	$-0.0881499\pi$
$839$	9.88311	+	14.7911i	0.341203	+	0.510646i	−0.620696	+	0.784051i	$0.713150\pi$
$840$	23.0062	+	5.00643i	0.793788	+	0.172738i
$841$	−52.4376	+	21.7204i	−1.80819	+	0.748979i
$842$	17.7659	−	23.1530i	0.612253	−	0.797904i
$843$	1.31976	−	1.50489i	0.0454548	−	0.0518313i
$844$	2.42932	−	0.159226i	0.0836205	−	0.00548078i
$845$	16.1576	+	18.4243i	0.555840	+	0.633814i
$846$	6.53324	+	6.53324i	0.224617	+	0.224617i
$847$	47.9069	+	4.00339i	1.64610	+	0.137558i
$848$	6.25088	+	2.58920i	0.214656	+	0.0889135i
$849$	−4.72599	+	2.72855i	−0.162196	+	0.0936436i
$850$	−15.3915	−	0.900794i	−0.527924	−	0.0308970i
$851$	−12.3588	+	21.4060i	−0.423653	+	0.733788i
$852$	−0.822144	−	6.24480i	−0.0281662	−	0.213943i
$853$	−30.4919	+	45.6344i	−1.04402	+	1.56249i	−0.237413	+	0.971409i	$0.576299\pi$
$853$	−30.4919	+	45.6344i	−1.04402	+	1.56249i	−0.806611	+	0.591083i	$0.798701\pi$
$854$	1.26331	+	5.07701i	0.0432296	+	0.173732i
$855$	12.1434	−	2.41547i	0.415296	−	0.0826074i
$856$	17.8858	+	8.82028i	0.611322	+	0.301471i
$857$	8.80839	+	7.72475i	0.300889	+	0.263873i	0.796455	−	0.604698i	$-0.206706\pi$
$857$	8.80839	+	7.72475i	0.300889	+	0.263873i	−0.495566	+	0.868570i	$0.665039\pi$
$858$	1.58119	−	12.0103i	0.0539810	−	0.410027i
$859$	−6.85357	−	5.25893i	−0.233841	−	0.179432i	0.485194	−	0.874407i	$-0.338749\pi$
$859$	−6.85357	−	5.25893i	−0.233841	−	0.179432i	−0.719035	+	0.694974i	$0.755416\pi$
$860$	−8.28010	−	1.64701i	−0.282349	−	0.0561627i
$861$	10.3189	−	0.490799i	0.351666	−	0.0167264i
$862$	−5.83379	−	29.3284i	−0.198700	−	0.998931i
$863$	12.4543	+	3.33711i	0.423948	+	0.113596i	0.464484	−	0.885582i	$-0.346240\pi$
$863$	12.4543	+	3.33711i	0.423948	+	0.113596i	−0.0405361	+	0.999178i	$0.512907\pi$
$864$	−4.20350	+	2.07294i	−0.143006	+	0.0705228i
$865$	−5.34626	+	4.10233i	−0.181778	+	0.139483i
$866$	−0.520520	−	0.901566i	−0.0176880	−	0.0306365i
$867$	−5.68901	−	16.0198i	−0.193209	−	0.544062i
$868$	−12.3913	+	6.86103i	−0.420589	+	0.232878i
$869$	24.1036	−	58.1912i	0.817658	−	1.97400i
$870$	1.84863	−	28.2046i	0.0626743	−	0.956224i
$871$	−2.24331	−	8.37214i	−0.0760116	−	0.283679i
$872$	−5.14749	+	15.1640i	−0.174316	+	0.513518i
$873$	0.608720	−	1.23436i	0.0206021	−	0.0417769i
$874$	−5.39443	+	27.1196i	−0.182469	+	0.917335i
$875$	−4.00003	−	10.1686i	−0.135226	−	0.343763i
$876$	0.227338	+	0.548842i	0.00768103	+	0.0185437i
$877$	−1.70535	+	0.578887i	−0.0575855	+	0.0195476i	−0.350084	−	0.936718i	$-0.613847\pi$
$877$	−1.70535	+	0.578887i	−0.0575855	+	0.0195476i	0.292498	+	0.956266i	$0.405513\pi$
$878$	1.17868	+	17.9832i	0.0397786	+	0.606904i
$879$	−6.21271	−	2.10893i	−0.209550	−	0.0711325i
$880$	−5.45107	+	20.3437i	−0.183756	+	0.685785i
$881$	−3.49319	−	2.33408i	−0.117689	−	0.0786370i	0.495333	−	0.868703i	$-0.335046\pi$
$881$	−3.49319	−	2.33408i	−0.117689	−	0.0786370i	−0.613021	+	0.790066i	$0.710046\pi$
$882$	−5.93837	+	4.22740i	−0.199955	+	0.142344i
$883$			0.520402i			0.0175129i	0.999962	+	0.00875647i	$0.00278731\pi$
$883$			0.520402i			0.0175129i	−0.999962	+	0.00875647i	$0.997213\pi$
$884$	−4.47012	+	6.79232i	−0.150346	+	0.228451i
$885$	8.51808	+	4.91792i	0.286332	+	0.165314i
$886$	−11.3269	−	14.7615i	−0.380536	−	0.495924i
$887$	−14.1038	−	0.924410i	−0.473558	−	0.0310387i	−0.173244	−	0.984879i	$-0.555425\pi$
$887$	−14.1038	−	0.924410i	−0.473558	−	0.0310387i	−0.300314	+	0.953840i	$0.597092\pi$
$888$	8.44193	−	8.44193i	0.283293	−	0.283293i
$889$	−22.3820	+	4.03648i	−0.750667	+	0.135379i
$890$	−9.78769	+	6.53993i	−0.328084	+	0.219219i
$891$	1.73608	+	5.11432i	0.0581608	+	0.171336i
$892$	16.6117	+	2.18697i	0.556202	+	0.0732253i
$893$	37.1592	+	4.89210i	1.24348	+	0.163708i
$894$	−5.24452	−	15.4499i	−0.175403	−	0.516721i
$895$	−13.5012	+	9.02120i	−0.451295	+	0.301546i
$896$	−3.07145	+	2.59770i	−0.102610	+	0.0867832i
$897$	−9.57369	+	9.57369i	−0.319656	+	0.319656i
$898$	1.84849	+	0.121157i	0.0616850	+	0.00404305i
$899$	32.9618	+	42.9567i	1.09934	+	1.43269i
$900$	−2.84739	−	1.64394i	−0.0949128	−	0.0547980i
$901$	−17.3523	+	11.7707i	−0.578088	+	0.392140i
$902$			21.9602i			0.731195i
$903$	6.69284	−	4.94758i	0.222724	−	0.164645i
$904$	−29.7706	−	19.8921i	−0.990154	−	0.661600i
$905$	−9.81838	+	36.6427i	−0.326374	+	1.21804i
$906$	−21.7128	−	7.37051i	−0.721360	−	0.244869i
$907$	3.16152	+	48.2354i	0.104976	+	1.60163i	0.647818	+	0.761795i	$0.275682\pi$
$907$	3.16152	+	48.2354i	0.104976	+	1.60163i	−0.542842	+	0.839835i	$0.682652\pi$
$908$	−12.4892	+	4.23951i	−0.414469	+	0.140693i
$909$	1.56194	+	3.77085i	0.0518062	+	0.125071i
$910$	−17.2012	−	2.57899i	−0.570214	−	0.0854925i
$911$	1.08933	−	5.47642i	0.0360911	−	0.181442i	−0.958535	−	0.284975i	$-0.908015\pi$
$911$	1.08933	−	5.47642i	0.0360911	−	0.181442i	0.994626	+	0.103533i	$0.0330147\pi$
$912$	2.48570	−	5.04050i	0.0823097	−	0.166908i
$913$	22.4670	−	66.1856i	0.743548	−	2.19042i
$914$	−0.826499	−	3.08454i	−0.0273382	−	0.102027i
$915$	0.364024	−	5.55393i	0.0120342	−	0.183607i
$916$	−8.65267	+	20.8894i	−0.285892	+	0.690205i
$917$	22.8165	+	41.2076i	0.753466	+	1.36079i
$918$	−0.530649	+	4.26064i	−0.0175140	+	0.140622i
$919$	−6.71831	−	11.6365i	−0.221617	−	0.383851i	0.733682	−	0.679493i	$-0.237800\pi$
$919$	−6.71831	−	11.6365i	−0.221617	−	0.383851i	−0.955299	+	0.295641i	$0.904467\pi$
$920$	44.3791	−	34.0533i	1.46314	−	1.12270i
$921$	10.2542	−	5.05680i	0.337886	−	0.166627i
$922$	−23.7912	−	6.37484i	−0.783522	−	0.209944i
$923$	2.89068	+	14.5324i	0.0951478	+	0.478341i
$924$	7.07276	+	11.0072i	0.232677	+	0.362110i
$925$	13.8489	+	2.75471i	0.455348	+	0.0905743i
$926$	16.6307	+	12.7612i	0.546517	+	0.419357i
$927$	−2.05164	+	15.5837i	−0.0673846	+	0.511837i
$928$	32.6320	+	28.6175i	1.07120	+	0.939414i
$929$	−21.0978	−	10.4043i	−0.692197	−	0.341354i	0.0619319	−	0.998080i	$-0.480274\pi$
$929$	−21.0978	−	10.4043i	−0.692197	−	0.341354i	−0.754129	+	0.656727i	$0.771941\pi$
$930$	−17.5030	+	3.48157i	−0.573947	+	0.114165i
$931$	−8.67182	+	28.2694i	−0.284208	+	0.926492i
$932$	−8.66821	+	12.9729i	−0.283937	+	0.424941i
$933$	1.91308	+	14.5313i	0.0626315	+	0.475734i
$934$	−18.8135	+	32.5859i	−0.615596	+	1.06624i
$935$	−43.3776	−	48.7706i	−1.41860	−	1.59497i
$936$	5.66340	−	3.26976i	0.185114	−	0.106876i
$937$	−28.2350	−	11.6953i	−0.922397	−	0.382069i	−0.129608	−	0.991565i	$-0.541372\pi$
$937$	−28.2350	−	11.6953i	−0.922397	−	0.382069i	−0.792789	+	0.609496i	$0.791372\pi$
$938$	−9.10657	−	6.32378i	−0.297340	−	0.206479i
$939$	−1.29828	−	1.29828i	−0.0423678	−	0.0423678i
$940$	−15.6998	−	17.9022i	−0.512070	−	0.583904i
$941$	−53.7566	+	3.52340i	−1.75242	+	0.114859i	−0.907503	−	0.420045i	$-0.862014\pi$
$941$	−53.7566	+	3.52340i	−1.75242	+	0.114859i	−0.844913	+	0.534904i	$0.820348\pi$
$942$	14.5545	−	16.5963i	0.474212	−	0.540735i
$943$	14.9414	−	19.4720i	0.486558	−	0.634095i
$944$	4.12480	−	1.70855i	0.134251	−	0.0556085i
$945$	7.38672	−	2.36069i	0.240290	−	0.0767932i
$946$	9.82955	+	14.7110i	0.319586	+	0.478295i
$947$	14.2739	−	12.5178i	0.463838	−	0.406775i	−0.395274	−	0.918563i	$-0.629350\pi$
$947$	14.2739	−	12.5178i	0.463838	−	0.406775i	0.859111	+	0.511789i	$0.171017\pi$
$948$	10.3140	−	2.76362i	0.334982	−	0.0897582i
$949$	−0.618090	−	1.25336i	−0.0200641	−	0.0406859i
$950$	15.6608	−	2.06178i	0.508103	−	0.0668931i
$951$	17.9903			0.583375
$952$	3.96388	+	32.8824i	0.128470	+	1.06572i
$953$	2.96495			0.0960442			0.0480221	−	0.998846i	$-0.484708\pi$
$953$	2.96495			0.0960442			0.0480221	+	0.998846i	$0.484708\pi$
$954$	5.25039	−	0.691227i	0.169988	−	0.0223793i
$955$	−25.9200	−	52.5607i	−0.838753	−	1.70082i
$956$	9.58351	−	2.56789i	0.309953	−	0.0830516i
$957$	37.6039	−	32.9777i	1.21556	−	1.06602i
$958$	2.51115	+	3.75820i	0.0811314	+	0.121422i
$959$	−18.8428	+	20.7248i	−0.608467	+	0.669239i
$960$	−20.4217	+	8.45895i	−0.659108	+	0.273011i
$961$	1.93975	−	2.52793i	0.0625726	−	0.0815461i
$962$	−5.81520	+	6.63097i	−0.187490	+	0.213791i
$963$	6.55425	−	0.429589i	0.211208	−	0.0138433i
$964$	9.54456	+	10.8835i	0.307410	+	0.350533i
$965$	−11.3833	−	11.3833i	−0.366443	−	0.366443i
$966$	−1.44222	+	17.2584i	−0.0464025	+	0.555281i
$967$	26.8821	+	11.1350i	0.864472	+	0.358076i	0.770455	−	0.637495i	$-0.220029\pi$
$967$	26.8821	+	11.1350i	0.864472	+	0.358076i	0.0940169	+	0.995571i	$0.470029\pi$
$968$	−47.7764	+	27.5837i	−1.53559	+	0.886574i
$969$	8.81369	+	15.0222i	0.283137	+	0.482584i
$970$	2.10037	−	3.63794i	0.0674387	−	0.116807i
$971$	−2.82902	−	21.4885i	−0.0907875	−	0.689599i	−0.974951	−	0.222421i	$-0.928604\pi$
$971$	−2.82902	−	21.4885i	−0.0907875	−	0.689599i	0.884163	−	0.467178i	$-0.154729\pi$
$972$	−0.508685	+	0.761301i	−0.0163161	+	0.0244187i
$973$	16.4954	−	15.9144i	0.528817	−	0.510193i
$974$	−19.5976	+	3.89821i	−0.627948	+	0.124907i
$975$	6.93682	+	3.42086i	0.222156	+	0.109555i
$976$	−1.89947	−	1.66579i	−0.0608006	−	0.0533207i
$977$	3.34352	−	25.3966i	0.106969	−	0.812508i	−0.850905	−	0.525319i	$-0.823946\pi$
$977$	3.34352	−	25.3966i	0.106969	−	0.812508i	0.957874	−	0.287189i	$-0.0927208\pi$
$978$	13.8489	+	10.6266i	0.442838	+	0.339801i
$979$	−20.4298	−	4.06375i	−0.652941	−	0.129878i
$980$	15.9837	−	9.87032i	0.510582	−	0.315296i
$981$	1.02899	+	5.17306i	0.0328530	+	0.165163i
$982$	36.2186	+	9.70475i	1.15578	+	0.309691i
$983$	−34.7489	+	17.1363i	−1.10832	+	0.546562i	−0.901919	−	0.431906i	$-0.857841\pi$
$983$	−34.7489	+	17.1363i	−1.10832	+	0.546562i	−0.206399	+	0.978468i	$0.566174\pi$
$984$	−9.40507	+	7.21677i	−0.299823	+	0.230062i
$985$	28.0863	+	48.6468i	0.894903	+	1.55002i
$986$	38.3331	−	10.5591i	1.22077	−	0.336270i
$987$	23.4709	+	0.420699i	0.747087	+	0.0133910i
$988$	3.18802	−	7.69655i	0.101424	−	0.244860i
$989$	1.29330	−	19.7320i	0.0411247	−	0.627441i
$990$	4.26657	+	15.9231i	0.135601	+	0.506068i
$991$	−3.80297	+	11.2032i	−0.120805	+	0.355881i	−0.990464	−	0.137773i	$-0.956006\pi$
$991$	−3.80297	+	11.2032i	−0.120805	+	0.355881i	0.869659	+	0.493654i	$0.164339\pi$
$992$	12.1203	−	24.5775i	0.384819	−	0.780337i
$993$	0.950781	−	4.77990i	0.0301721	−	0.151685i
$994$	14.8274	+	11.8056i	0.470296	+	0.374450i
$995$	−27.6451	−	66.7411i	−0.876407	−	2.11583i
$996$	11.2203	−	3.80877i	0.355528	−	0.120685i
$997$	1.78300	+	27.2033i	0.0564681	+	0.861537i	0.928324	+	0.371773i	$0.121250\pi$
$997$	1.78300	+	27.2033i	0.0564681	+	0.861537i	−0.871855	+	0.489763i	$0.837083\pi$
$998$	−36.3837	−	12.3506i	−1.15171	−	0.390952i
$999$	1.01773	−	3.79820i	0.0321994	−	0.120170i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	357.2.bl.a.10.16	✓	384
7.5	odd	6	inner	357.2.bl.a.61.9	yes	384
17.12	odd	16	inner	357.2.bl.a.199.9	yes	384
119.12	even	48	inner	357.2.bl.a.250.16	yes	384

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
357.2.bl.a.10.16	✓	384	1.1	even	1	trivial
357.2.bl.a.61.9	yes	384	7.5	odd	6	inner
357.2.bl.a.199.9	yes	384	17.12	odd	16	inner
357.2.bl.a.250.16	yes	384	119.12	even	48	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:	\( N \)	\(=\)	\( 357 = 3 \cdot 7 \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	357.bl (of order \(48\), degree \(16\), minimal)

\(f(q)\)	\(=\)	\(q+(1.03243 - 0.135922i) q^{2} +(0.442289 + 0.896873i) q^{3} +(-0.884410 + 0.236977i) q^{4} +(-2.20366 + 1.93256i) q^{5} +(0.578538 + 0.865843i) q^{6} +(2.58525 + 0.562582i) q^{7} +(-2.80503 + 1.16188i) q^{8} +(-0.608761 + 0.793353i) q^{9} +(-2.01245 + 2.29476i) q^{10} +(-5.38938 + 0.353239i) q^{11} +(-0.603703 - 0.688391i) q^{12} +(1.52303 + 1.52303i) q^{13} +(2.74556 + 0.229435i) q^{14} +(-2.70792 - 1.12166i) q^{15} +(-1.15220 + 0.665221i) q^{16} +(0.240895 - 4.11606i) q^{17} +(-0.520670 + 0.901828i) q^{18} +(0.551372 + 4.18808i) q^{19} +(1.49097 - 2.23139i) q^{20} +(0.638861 + 2.56746i) q^{21} +(-5.51616 + 1.09723i) q^{22} +(5.63769 + 2.78020i) q^{23} +(-2.28269 - 2.00187i) q^{24} +(0.468709 - 3.56020i) q^{25} +(1.77944 + 1.36541i) q^{26} +(-0.980785 - 0.195090i) q^{27} +(-2.41974 + 0.115091i) q^{28} +(1.80665 + 9.08263i) q^{29} +(-2.94820 - 0.789967i) q^{30} +(5.24394 - 2.58602i) q^{31} +(3.71832 - 2.85317i) q^{32} +(-2.70047 - 4.67736i) q^{33} +(-0.310757 - 4.28230i) q^{34} +(-6.78424 + 3.75640i) q^{35} +(0.350388 - 0.845912i) q^{36} +(-0.257178 + 3.92377i) q^{37} +(1.13851 + 4.24897i) q^{38} +(-0.692346 + 2.03959i) q^{39} +(3.93593 - 7.98129i) q^{40} +(0.761744 - 3.82955i) q^{41} +(1.00856 + 2.56389i) q^{42} +(-1.20385 - 2.90635i) q^{43} +(4.68272 - 1.58957i) q^{44} +(-0.191698 - 2.92475i) q^{45} +(6.19842 + 2.10408i) q^{46} +(2.29640 - 8.57027i) q^{47} +(-1.10622 - 0.739154i) q^{48} +(6.36700 + 2.90883i) q^{49} -3.73937i q^{50} +(3.79813 - 1.60444i) q^{51} +(-1.70791 - 0.986062i) q^{52} +(-3.09583 - 4.03456i) q^{53} +(-1.03911 - 0.0681070i) q^{54} +(11.1937 - 11.1937i) q^{55} +(-7.90535 + 1.42569i) q^{56} +(-3.51231 + 2.34685i) q^{57} +(3.09977 + 9.13163i) q^{58} +(-3.32705 - 0.438015i) q^{59} +(2.66072 + 0.350290i) q^{60} +(0.610394 + 1.79816i) q^{61} +(5.06251 - 3.38266i) q^{62} +(-2.02012 + 1.70854i) q^{63} +(5.33264 - 5.33264i) q^{64} +(-6.29960 - 0.412898i) q^{65} +(-3.42381 - 4.46200i) q^{66} +(-3.48497 - 2.01205i) q^{67} +(0.762363 + 3.69737i) q^{68} +6.28594i q^{69} +(-6.49368 + 4.80036i) q^{70} +(5.71987 + 3.82190i) q^{71} +(0.785812 - 2.93269i) q^{72} +(-0.614384 - 0.208555i) q^{73} +(0.267810 + 4.08598i) q^{74} +(3.40035 - 1.15426i) q^{75} +(-1.48012 - 3.57332i) q^{76} +(-14.1316 - 2.11876i) q^{77} +(-0.437575 + 2.19984i) q^{78} +(-5.15796 + 10.4593i) q^{79} +(1.25347 - 3.69261i) q^{80} +(-0.258819 - 0.965926i) q^{81} +(0.265928 - 4.05728i) q^{82} +(-4.95239 + 11.9561i) q^{83} +(-1.17344 - 2.11929i) q^{84} +(7.42369 + 9.53596i) q^{85} +(-1.63793 - 2.83697i) q^{86} +(-7.34690 + 5.63748i) q^{87} +(14.7070 - 7.25267i) q^{88} +(3.72533 + 0.998199i) q^{89} +(-0.595454 - 2.99355i) q^{90} +(3.08058 + 4.79425i) q^{91} +(-5.64487 - 1.12284i) q^{92} +(4.63867 + 3.55937i) q^{93} +(1.20598 - 9.16035i) q^{94} +(-9.30876 - 8.16356i) q^{95} +(4.20350 + 2.07294i) q^{96} +(-1.34985 + 0.268502i) q^{97} +(6.96887 + 2.13775i) q^{98} +(3.00061 - 4.49072i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 384 q - 16 q^{11} + 32 q^{14} - 64 q^{22} - 16 q^{25} - 48 q^{28} - 64 q^{30} - 64 q^{35} - 32 q^{37} - 48 q^{42} - 64 q^{44} + 32 q^{46} - 64 q^{49} + 80 q^{56} - 32 q^{58} - 288 q^{61} - 528 q^{68} + 176 q^{70}+ \cdots + 32 q^{99}+O(q^{100}) \) 384 * q - 16 * q^11 + 32 * q^14 - 64 * q^22 - 16 * q^25 - 48 * q^28 - 64 * q^30 - 64 * q^35 - 32 * q^37 - 48 * q^42 - 64 * q^44 + 32 * q^46 - 64 * q^49 + 80 * q^56 - 32 * q^58 - 288 * q^61 - 528 * q^68 + 176 * q^70 + 64 * q^71 - 48 * q^73 - 128 * q^74 + 96 * q^77 + 128 * q^78 - 480 * q^80 - 240 * q^82 + 32 * q^85 - 144 * q^87 - 96 * q^88 - 64 * q^91 + 320 * q^92 - 192 * q^94 - 64 * q^95 + 32 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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