LMFDB - Embedded newform 546.2.bw.a.11.18

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [546,2,Mod(11,546)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(546, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 8, 7]))

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

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

chi := DirichletCharacter("546.11");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 546 = 2 \cdot 3 \cdot 7 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	546.bw (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$4.35983195036$
Analytic rank:	$0$
Dimension:	$152$
Relative dimension:	$38$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			11.18
Character	$\chi$	$=$	546.11
Dual form			546.2.bw.a.149.18

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.258819 - 0.965926i) q^{2} +(1.66438 - 0.479415i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.88802 + 0.505894i) q^{5} +(-0.893853 - 1.48359i) q^{6} +(2.05975 - 1.66055i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.54032 - 1.59586i) q^{9} +O(q^{10})$	\(q+(-0.258819 - 0.965926i) q^{2} +(1.66438 - 0.479415i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.88802 + 0.505894i) q^{5} +(-0.893853 - 1.48359i) q^{6} +(2.05975 - 1.66055i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.54032 - 1.59586i) q^{9} -1.95463i q^{10} +(-2.50831 - 2.50831i) q^{11} +(-1.20169 + 1.24738i) q^{12} +(-1.12860 + 3.42436i) q^{13} +(-2.13707 - 1.55978i) q^{14} +(3.38492 - 0.0631461i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.26806 - 2.19634i) q^{17} +(-2.19896 - 2.04072i) q^{18} +(4.32777 + 4.32777i) q^{19} +(-1.88802 + 0.505894i) q^{20} +(2.63212 - 3.75126i) q^{21} +(-1.77364 + 3.07204i) q^{22} +(-3.32215 + 5.75413i) q^{23} +(1.51589 + 0.837897i) q^{24} +(-1.02143 - 0.589721i) q^{25} +(3.59978 + 0.203857i) q^{26} +(3.46298 - 3.87398i) q^{27} +(-0.953521 + 2.46795i) q^{28} +(7.81199 - 4.51025i) q^{29} +(-0.937076 - 3.25324i) q^{30} +(0.803657 - 0.215339i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-5.37731 - 2.97226i) q^{33} +(-1.79330 + 1.79330i) q^{34} +(4.72892 - 2.09314i) q^{35} +(-1.40206 + 2.65221i) q^{36} +(-1.42914 - 5.33363i) q^{37} +(3.06020 - 5.30042i) q^{38} +(-0.236734 + 6.24051i) q^{39} +(0.977313 + 1.69275i) q^{40} +(-6.19829 - 1.66083i) q^{41} +(-4.30468 - 1.57153i) q^{42} +(-4.42594 - 2.55532i) q^{43} +(3.42642 + 0.918106i) q^{44} +(5.60352 - 1.72788i) q^{45} +(6.41789 + 1.71967i) q^{46} +(-2.98417 + 11.1371i) q^{47} +(0.417005 - 1.68110i) q^{48} +(1.48514 - 6.84064i) q^{49} +(-0.305262 + 1.13925i) q^{50} +(-3.16348 - 3.04761i) q^{51} +(-0.734782 - 3.52989i) q^{52} +(4.87278 + 2.81330i) q^{53} +(-4.63827 - 2.34233i) q^{54} +(-3.46681 - 6.00469i) q^{55} +(2.63065 + 0.282277i) q^{56} +(9.27786 + 5.12826i) q^{57} +(-6.37846 - 6.37846i) q^{58} +(-2.62141 + 9.78325i) q^{59} +(-2.89985 + 1.74715i) q^{60} -11.2180 q^{61} +(-0.416003 - 0.720539i) q^{62} +(2.58243 - 7.50540i) q^{63} +1.00000i q^{64} +(-3.86319 + 5.89432i) q^{65} +(-1.47924 + 5.96336i) q^{66} +(-8.42310 - 8.42310i) q^{67} +(2.19634 + 1.26806i) q^{68} +(-2.77070 + 11.1697i) q^{69} +(-3.24575 - 4.02604i) q^{70} +(-1.52491 - 5.69106i) q^{71} +(2.92472 + 0.667838i) q^{72} +(2.77643 + 10.3618i) q^{73} +(-4.78200 + 2.76089i) q^{74} +(-1.98276 - 0.491832i) q^{75} +(-5.91185 - 1.58408i) q^{76} +(-9.33168 - 1.00132i) q^{77} +(6.08914 - 1.38649i) q^{78} +(5.90403 + 10.2261i) q^{79} +(1.38213 - 1.38213i) q^{80} +(3.90648 - 8.10799i) q^{81} +6.41694i q^{82} +(-0.859699 + 0.859699i) q^{83} +(-0.403847 + 4.56475i) q^{84} +(-1.28300 - 4.78824i) q^{85} +(-1.32273 + 4.93650i) q^{86} +(10.8398 - 11.2520i) q^{87} -3.54729i q^{88} +(2.72285 - 0.729586i) q^{89} +(-3.11930 - 4.96538i) q^{90} +(3.36169 + 8.92743i) q^{91} -6.64429i q^{92} +(1.23435 - 0.743691i) q^{93} +11.5299 q^{94} +(5.98154 + 10.3603i) q^{95} +(-1.73175 + 0.0323060i) q^{96} +(6.95381 - 1.86327i) q^{97} +(-6.99193 + 0.335948i) q^{98} +(-10.3748 - 2.36901i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 152 q + 12 q^{7}+O(q^{10}) $ 152 * q + 12 * q^7	$ 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) $ 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/546\mathbb{Z}\right)^\times$.

$n$	$157$	$365$	$379$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$-1$	$e\left(\frac{7}{12}\right)$

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 $

$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$2$	−0.258819	−	0.965926i	−0.183013	−	0.683013i
$3$	1.66438	−	0.479415i	0.960930	−	0.276790i
$3$	1.66438	−	0.479415i	0.960930	−	0.276790i
$4$	−0.866025	+	0.500000i	−0.433013	+	0.250000i
$5$	1.88802	+	0.505894i	0.844349	+	0.226243i	0.654964	−	0.755660i	$-0.272684\pi$
$5$	1.88802	+	0.505894i	0.844349	+	0.226243i	0.189385	+	0.981903i	$0.439350\pi$
$6$	−0.893853	−	1.48359i	−0.364914	−	0.605671i
$7$	2.05975	−	1.66055i	0.778513	−	0.627629i
$7$	2.05975	−	1.66055i	0.778513	−	0.627629i
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.54032	−	1.59586i	0.846774	−	0.531952i
$10$		−	1.95463i		−	0.618107i
$11$	−2.50831	−	2.50831i	−0.756285	−	0.756285i	0.219360	−	0.975644i	$-0.429603\pi$
$11$	−2.50831	−	2.50831i	−0.756285	−	0.756285i	−0.975644	+	0.219360i	$0.929603\pi$
$12$	−1.20169	+	1.24738i	−0.346897	+	0.360086i
$13$	−1.12860	+	3.42436i	−0.313018	+	0.949747i
$13$	−1.12860	+	3.42436i	−0.313018	+	0.949747i
$14$	−2.13707	−	1.55978i	−0.571156	−	0.416870i
$15$	3.38492	−	0.0631461i	0.873983	−	0.0163043i
$16$	0.500000	−	0.866025i	0.125000	−	0.216506i
$17$	−1.26806	−	2.19634i	−0.307549	−	0.532690i	0.670277	−	0.742111i	$-0.266175\pi$
$17$	−1.26806	−	2.19634i	−0.307549	−	0.532690i	−0.977826	+	0.209421i	$0.932842\pi$
$18$	−2.19896	−	2.04072i	−0.518301	−	0.481003i
$19$	4.32777	+	4.32777i	0.992859	+	0.992859i	0.999975	−	0.00711531i	$-0.00226489\pi$
$19$	4.32777	+	4.32777i	0.992859	+	0.992859i	−0.00711531	+	0.999975i	$0.502265\pi$
$20$	−1.88802	+	0.505894i	−0.422175	+	0.113121i
$21$	2.63212	−	3.75126i	0.574375	−	0.818593i
$22$	−1.77364	+	3.07204i	−0.378142	+	0.654962i
$23$	−3.32215	+	5.75413i	−0.692715	+	1.19982i	0.278229	+	0.960515i	$0.410252\pi$
$23$	−3.32215	+	5.75413i	−0.692715	+	1.19982i	−0.970945	+	0.239304i	$0.923081\pi$
$24$	1.51589	+	0.837897i	0.309430	+	0.171035i
$25$	−1.02143	−	0.589721i	−0.204285	−	0.117944i
$26$	3.59978	+	0.203857i	0.705976	+	0.0399796i
$27$	3.46298	−	3.87398i	0.666452	−	0.745548i
$28$	−0.953521	+	2.46795i	−0.180199	+	0.466399i
$29$	7.81199	−	4.51025i	1.45065	−	0.837533i	0.452132	−	0.891951i	$-0.350664\pi$
$29$	7.81199	−	4.51025i	1.45065	−	0.837533i	0.998518	+	0.0544178i	$0.0173303\pi$
$30$	−0.937076	−	3.25324i	−0.171086	−	0.593957i
$31$	0.803657	−	0.215339i	0.144341	−	0.0386761i	−0.185925	−	0.982564i	$-0.559528\pi$
$31$	0.803657	−	0.215339i	0.144341	−	0.0386761i	0.330266	+	0.943888i	$0.392862\pi$
$32$	−0.965926	−	0.258819i	−0.170753	−	0.0457532i
$33$	−5.37731	−	2.97226i	−0.936069	−	0.517404i
$34$	−1.79330	+	1.79330i	−0.307549	+	0.307549i
$35$	4.72892	−	2.09314i	0.799333	−	0.353805i
$36$	−1.40206	+	2.65221i	−0.233676	+	0.442036i
$37$	−1.42914	−	5.33363i	−0.234950	−	0.876844i	−0.978172	−	0.207799i	$-0.933370\pi$
$37$	−1.42914	−	5.33363i	−0.234950	−	0.876844i	0.743222	−	0.669045i	$-0.233297\pi$
$38$	3.06020	−	5.30042i	0.496430	−	0.859841i
$39$	−0.236734	+	6.24051i	−0.0379078	+	0.999281i
$40$	0.977313	+	1.69275i	0.154527	+	0.267648i
$41$	−6.19829	−	1.66083i	−0.968010	−	0.259377i	−0.260023	−	0.965603i	$-0.583730\pi$
$41$	−6.19829	−	1.66083i	−0.968010	−	0.259377i	−0.707987	+	0.706225i	$0.750397\pi$
$42$	−4.30468	−	1.57153i	−0.664227	−	0.242492i
$43$	−4.42594	−	2.55532i	−0.674950	−	0.389682i	0.123000	−	0.992407i	$-0.460749\pi$
$43$	−4.42594	−	2.55532i	−0.674950	−	0.389682i	−0.797950	+	0.602724i	$0.794082\pi$
$44$	3.42642	+	0.918106i	0.516552	+	0.138410i
$45$	5.60352	−	1.72788i	0.835324	−	0.257577i
$46$	6.41789	+	1.71967i	0.946267	+	0.253551i
$47$	−2.98417	+	11.1371i	−0.435286	+	1.62451i	0.305095	+	0.952322i	$0.401312\pi$
$47$	−2.98417	+	11.1371i	−0.435286	+	1.62451i	−0.740381	+	0.672187i	$0.765355\pi$
$48$	0.417005	−	1.68110i	0.0601894	−	0.242646i
$49$	1.48514	−	6.84064i	0.212163	−	0.977234i
$50$	−0.305262	+	1.13925i	−0.0431705	+	0.161115i
$51$	−3.16348	−	3.04761i	−0.442976	−	0.426751i
$52$	−0.734782	−	3.52989i	−0.101896	−	0.489507i
$53$	4.87278	+	2.81330i	0.669328	+	0.386437i	0.795822	−	0.605531i	$-0.207039\pi$
$53$	4.87278	+	2.81330i	0.669328	+	0.386437i	−0.126494	+	0.991967i	$0.540372\pi$
$54$	−4.63827	−	2.34233i	−0.631188	−	0.318750i
$55$	−3.46681	−	6.00469i	−0.467465	−	0.809672i
$56$	2.63065	+	0.282277i	0.351535	+	0.0377209i
$57$	9.27786	+	5.12826i	1.22888	+	0.679255i
$58$	−6.37846	−	6.37846i	−0.837533	−	0.837533i
$59$	−2.62141	+	9.78325i	−0.341279	+	1.27367i	0.555620	+	0.831436i	$0.312481\pi$
$59$	−2.62141	+	9.78325i	−0.341279	+	1.27367i	−0.896899	+	0.442235i	$0.854186\pi$
$60$	−2.89985	+	1.74715i	−0.374370	+	0.225556i
$61$	−11.2180			−1.43632			−0.718160	−	0.695878i	$-0.755015\pi$
$61$	−11.2180			−1.43632			−0.718160	+	0.695878i	$0.755015\pi$
$62$	−0.416003	−	0.720539i	−0.0528325	−	0.0915085i
$63$	2.58243	−	7.50540i	0.325355	−	0.945592i
$64$			1.00000i			0.125000i
$65$	−3.86319	+	5.89432i	−0.479170	+	0.731100i
$66$	−1.47924	+	5.96336i	−0.182081	+	0.734039i
$67$	−8.42310	−	8.42310i	−1.02905	−	1.02905i	−0.999565	−	0.0294801i	$-0.990615\pi$
$67$	−8.42310	−	8.42310i	−1.02905	−	1.02905i	−0.0294801	−	0.999565i	$-0.509385\pi$
$68$	2.19634	+	1.26806i	0.266345	+	0.153774i
$69$	−2.77070	+	11.1697i	−0.333553	+	1.34468i
$70$	−3.24575	−	4.02604i	−0.387942	−	0.481204i
$71$	−1.52491	−	5.69106i	−0.180974	−	0.675404i	−0.995457	−	0.0952161i	$-0.969646\pi$
$71$	−1.52491	−	5.69106i	−0.180974	−	0.675404i	0.814483	−	0.580188i	$-0.197021\pi$
$72$	2.92472	+	0.667838i	0.344682	+	0.0787054i
$73$	2.77643	+	10.3618i	0.324957	+	1.21275i	0.914355	+	0.404913i	$0.132698\pi$
$73$	2.77643	+	10.3618i	0.324957	+	1.21275i	−0.589399	+	0.807842i	$0.700635\pi$
$74$	−4.78200	+	2.76089i	−0.555897	+	0.320947i
$75$	−1.98276	−	0.491832i	−0.228950	−	0.0567919i
$76$	−5.91185	−	1.58408i	−0.678136	−	0.181706i
$77$	−9.33168	−	1.00132i	−1.06344	−	0.114111i
$78$	6.08914	−	1.38649i	0.689459	−	0.156990i
$79$	5.90403	+	10.2261i	0.664255	+	1.15052i	0.979487	+	0.201509i	$0.0645845\pi$
$79$	5.90403	+	10.2261i	0.664255	+	1.15052i	−0.315232	+	0.949015i	$0.602082\pi$
$80$	1.38213	−	1.38213i	0.154527	−	0.154527i
$81$	3.90648	−	8.10799i	0.434053	−	0.900887i
$82$			6.41694i			0.708632i
$83$	−0.859699	+	0.859699i	−0.0943642	+	0.0943642i	−0.752713	−	0.658349i	$-0.771255\pi$
$83$	−0.859699	+	0.859699i	−0.0943642	+	0.0943642i	0.658349	+	0.752713i	$0.271255\pi$
$84$	−0.403847	+	4.56475i	−0.0440634	+	0.498055i
$85$	−1.28300	−	4.78824i	−0.139161	−	0.519357i
$86$	−1.32273	+	4.93650i	−0.142634	+	0.532316i
$87$	10.8398	−	11.2520i	1.16215	−	1.20634i
$88$		−	3.54729i		−	0.378142i
$89$	2.72285	−	0.729586i	0.288622	−	0.0773360i	−0.111603	−	0.993753i	$-0.535599\pi$
$89$	2.72285	−	0.729586i	0.288622	−	0.0773360i	0.400225	+	0.916417i	$0.368932\pi$
$90$	−3.11930	−	4.96538i	−0.328803	−	0.523397i
$91$	3.36169	+	8.92743i	0.352400	+	0.935849i
$92$		−	6.64429i		−	0.692715i
$93$	1.23435	−	0.743691i	0.127996	−	0.0771172i
$94$	11.5299			1.18922
$95$	5.98154	+	10.3603i	0.613693	+	1.06295i
$96$	−1.73175	+	0.0323060i	−0.176746	+	0.00329722i
$97$	6.95381	−	1.86327i	0.706052	−	0.189186i	0.112112	−	0.993696i	$-0.464238\pi$
$97$	6.95381	−	1.86327i	0.706052	−	0.189186i	0.593940	+	0.804509i	$0.297572\pi$
$98$	−6.99193	+	0.335948i	−0.706292	+	0.0339359i
$99$	−10.3748	−	2.36901i	−1.04271	−	0.238095i
$100$	1.17944			0.117944
$101$	5.43555			0.540857			0.270429	−	0.962740i	$-0.412835\pi$
$101$	5.43555			0.540857			0.270429	+	0.962740i	$0.412835\pi$
$102$	−2.12500	+	3.84447i	−0.210406	+	0.380659i
$103$	10.5376	−	6.08387i	1.03830	−	0.599461i	0.118947	−	0.992901i	$-0.462048\pi$
$103$	10.5376	−	6.08387i	1.03830	−	0.599461i	0.919350	+	0.393440i	$0.128715\pi$
$104$	−3.21943	+	1.62335i	−0.315691	+	0.159182i
$105$	6.86724	−	5.75090i	0.670174	−	0.561230i
$106$	1.45627	−	5.43488i	0.141446	−	0.527882i
$107$	6.13823	+	3.54391i	0.593405	+	0.342602i	0.766443	−	0.642313i	$-0.222025\pi$
$107$	6.13823	+	3.54391i	0.593405	+	0.342602i	−0.173038	+	0.984915i	$0.555358\pi$
$108$	−1.06204	+	5.08646i	−0.102195	+	0.489445i
$109$	−7.98018	+	2.13828i	−0.764362	+	0.204810i	−0.619879	−	0.784697i	$-0.712819\pi$
$109$	−7.98018	+	2.13828i	−0.764362	+	0.204810i	−0.144483	+	0.989507i	$0.546152\pi$
$110$	−4.90281	+	4.90281i	−0.467465	+	0.467465i
$111$	−4.93566	−	8.19204i	−0.468472	−	0.777554i
$112$	−0.408204	−	2.61407i	−0.0385716	−	0.247007i
$113$	9.45842	+	5.46082i	0.889774	+	0.513711i	0.873868	−	0.486163i	$-0.161604\pi$
$113$	9.45842	+	5.46082i	0.889774	+	0.513711i	0.0159051	+	0.999874i	$0.494937\pi$
$114$	2.55223	−	10.2890i	0.239039	−	0.963655i
$115$	−9.18327	+	9.18327i	−0.856344	+	0.856344i
$116$	−4.51025	+	7.81199i	−0.418767	+	0.725325i
$117$	2.59778	+	10.5001i	0.240165	+	0.970732i
$118$	10.1284			0.932392
$119$	−6.25901	−	2.41824i	−0.573762	−	0.221679i
$120$	2.43815	+	2.34885i	0.222572	+	0.214420i
$121$			1.58326i			0.143932i
$122$	2.90344	+	10.8358i	0.262865	+	0.981025i
$123$	−11.1125	+	0.207306i	−1.00198	+	0.0186921i
$124$	−0.588318	+	0.588318i	−0.0528325	+	0.0528325i
$125$	−8.54078	−	8.54078i	−0.763911	−	0.763911i
$126$	−7.91804	−	0.551894i	−0.705395	−	0.0491666i
$127$	−11.1018	+	6.40962i	−0.985124	+	0.568762i	−0.903813	−	0.427927i	$-0.859244\pi$
$127$	−11.1018	+	6.40962i	−0.985124	+	0.568762i	−0.0813110	+	0.996689i	$0.525911\pi$
$128$	0.965926	−	0.258819i	0.0853766	−	0.0228766i
$129$	−8.59151	−	2.13116i	−0.756440	−	0.187638i
$130$	6.69334	+	2.20600i	0.587045	+	0.193479i
$131$	−4.78950	+	2.76522i	−0.418461	+	0.241598i	−0.694419	−	0.719571i	$-0.744338\pi$
$131$	−4.78950	+	2.76522i	−0.418461	+	0.241598i	0.275958	+	0.961170i	$0.411005\pi$
$132$	6.14302	−	0.114599i	0.534681	−	0.00997453i
$133$	16.1006	+	1.72765i	1.39610	+	0.149806i
$134$	−5.95603	+	10.3161i	−0.514523	+	0.891180i
$135$	8.49802	−	5.56226i	0.731393	−	0.478723i
$136$	0.656394	−	2.44970i	0.0562853	−	0.210060i
$137$	−3.25759	+	12.1575i	−0.278314	+	1.03868i	0.675273	+	0.737568i	$0.264026\pi$
$137$	−3.25759	+	12.1575i	−0.278314	+	1.03868i	−0.953588	+	0.301116i	$0.902641\pi$
$138$	11.5062	−	0.214650i	0.979477	−	0.0182723i
$139$	−5.11177	+	8.85384i	−0.433574	+	0.750973i	−0.997178	−	0.0750724i	$-0.976081\pi$
$139$	−5.11177	+	8.85384i	−0.433574	+	0.750973i	0.563604	+	0.826045i	$0.309415\pi$
$140$	−3.04879	+	4.17717i	−0.257670	+	0.353036i
$141$	0.372486	+	19.9670i	0.0313690	+	1.68152i
$142$	−5.10246	+	2.94591i	−0.428189	+	0.247215i
$143$	11.4203	−	5.75848i	0.955010	−	0.481548i
$144$	−0.111892	−	2.99791i	−0.00932431	−	0.249826i
$145$	17.0309	−	4.56342i	1.41434	−	0.378972i
$146$	9.29012	−	5.36365i	0.768856	−	0.443899i
$147$	−0.807660	−	12.0974i	−0.0666147	−	0.997779i
$148$	3.90449	+	3.90449i	0.320947	+	0.320947i
$149$	−14.9491	+	14.9491i	−1.22467	+	1.22467i	−0.258723	+	0.965952i	$0.583302\pi$
$149$	−14.9491	+	14.9491i	−1.22467	+	1.22467i	−0.965952	+	0.258723i	$0.916698\pi$
$150$	0.0381030	+	2.04250i	0.00311110	+	0.166769i
$151$	−0.617468	−	2.30442i	−0.0502488	−	0.187531i	0.936240	−	0.351362i	$-0.114281\pi$
$151$	−0.617468	−	2.30442i	−0.0502488	−	0.187531i	−0.986488	+	0.163831i	$0.947615\pi$
$152$			6.12040i			0.496430i
$153$	−6.72631	−	3.55577i	−0.543790	−	0.287467i
$154$	1.44802	+	9.27287i	0.116684	+	0.747229i
$155$	1.62626			0.130624
$156$	−2.91524	−	5.52281i	−0.233406	−	0.442178i
$157$	5.47220	−	9.47812i	0.436729	−	0.756437i	−0.560706	−	0.828015i	$-0.689470\pi$
$157$	5.47220	−	9.47812i	0.436729	−	0.756437i	0.997435	+	0.0715782i	$0.0228036\pi$
$158$	8.34956	−	8.34956i	0.664255	−	0.664255i
$159$	9.45890	+	2.34632i	0.750140	+	0.186075i
$160$	−1.69275	−	0.977313i	−0.133824	−	0.0772633i
$161$	2.71222	+	17.3687i	0.213753	+	1.36884i
$162$	−8.84278	−	1.67487i	−0.694755	−	0.131590i
$163$	−14.4427	+	14.4427i	−1.13124	+	1.13124i	−0.141267	+	0.989972i	$0.545118\pi$
$163$	−14.4427	+	14.4427i	−1.13124	+	1.13124i	−0.989972	+	0.141267i	$0.954882\pi$
$164$	6.19829	−	1.66083i	0.484005	−	0.129689i
$165$	−8.64883	−	8.33205i	−0.673310	−	0.648649i
$166$	1.05291	+	0.607899i	0.0817218	+	0.0471821i
$167$	−0.700037	+	2.61257i	−0.0541705	+	0.202167i	−0.987707	−	0.156314i	$-0.950039\pi$
$167$	−0.700037	+	2.61257i	−0.0541705	+	0.202167i	0.933537	+	0.358481i	$0.116705\pi$
$168$	4.51373	−	0.791357i	0.348242	−	0.0610545i
$169$	−10.4525	−	7.72949i	−0.804039	−	0.594576i
$170$	−4.29302	+	2.47857i	−0.329259	+	0.190098i
$171$	17.9005	+	4.08743i	1.36888	+	0.312574i
$172$	5.11064			0.389682
$173$	8.58139			0.652431			0.326215	−	0.945295i	$-0.394226\pi$
$173$	8.58139			0.652431			0.326215	+	0.945295i	$0.394226\pi$
$174$	−13.6741	−	7.55826i	−1.03663	−	0.572990i
$175$	−3.08314	+	0.481452i	−0.233064	+	0.0363944i
$176$	−3.42642	+	0.918106i	−0.258276	+	0.0692048i
$177$	0.327207	+	17.5398i	0.0245944	+	1.31837i
$178$	−1.40945	−	2.44124i	−0.105643	−	0.182979i
$179$	2.04061			0.152522			0.0762612	−	0.997088i	$-0.475702\pi$
$179$	2.04061			0.152522			0.0762612	+	0.997088i	$0.475702\pi$
$180$	−3.98885	+	4.29815i	−0.297311	+	0.320365i
$181$		−	3.77689i		−	0.280734i	−0.990100	−	0.140367i	$-0.955172\pi$
$181$		−	3.77689i		−	0.280734i	0.990100	−	0.140367i	$-0.0448283\pi$
$182$	7.75317	−	5.55773i	0.574703	−	0.411966i
$183$	−18.6710	+	5.37809i	−1.38020	+	0.397560i
$184$	−6.41789	+	1.71967i	−0.473133	+	0.126776i
$185$		−	10.7930i		−	0.793518i
$186$	−1.03782	−	0.999812i	−0.0760970	−	0.0733098i
$187$	−2.32842	+	8.68978i	−0.170271	+	0.635459i
$188$	−2.98417	−	11.1371i	−0.217643	−	0.812254i
$189$	0.699942	−	13.7299i	0.0509133	−	0.998703i
$190$	8.45917	−	8.45917i	0.613693	−	0.613693i
$191$			9.90152i			0.716449i	0.933635	+	0.358224i	$0.116618\pi$
$191$			9.90152i			0.716449i	−0.933635	+	0.358224i	$0.883382\pi$
$192$	0.479415	+	1.66438i	0.0345988	+	0.120116i
$193$	2.75983	−	2.75983i	0.198657	−	0.198657i	−0.600767	−	0.799424i	$-0.705138\pi$
$193$	2.75983	−	2.75983i	0.198657	−	0.198657i	0.799424	+	0.600767i	$0.205138\pi$
$194$	−3.59956	−	6.23461i	−0.258433	−	0.447619i
$195$	−3.60400	+	11.6625i	−0.258088	+	0.835166i
$196$	2.13415	+	6.66674i	0.152439	+	0.476196i
$197$	4.64694	+	1.24514i	0.331081	+	0.0887129i	0.420530	−	0.907279i	$-0.361844\pi$
$197$	4.64694	+	1.24514i	0.331081	+	0.0887129i	−0.0894493	+	0.995991i	$0.528511\pi$
$198$	0.396912	+	10.6345i	0.0282073	+	0.755758i
$199$	7.60724	−	4.39204i	0.539263	−	0.311344i	−0.205517	−	0.978654i	$-0.565888\pi$
$199$	7.60724	−	4.39204i	0.539263	−	0.311344i	0.744780	+	0.667310i	$0.232554\pi$
$200$	−0.305262	−	1.13925i	−0.0215853	−	0.0805573i
$201$	−18.0574	−	9.98108i	−1.27367	−	0.704011i
$202$	−1.40682	−	5.25034i	−0.0989838	−	0.369412i
$203$	8.60125	−	22.2622i	0.603689	−	1.56250i
$204$	4.26346	+	1.05757i	0.298502	+	0.0740447i
$205$	−10.8623	−	6.27136i	−0.758656	−	0.438010i
$206$	−8.60389	−	8.60389i	−0.599461	−	0.599461i
$207$	0.743442	+	19.9190i	0.0516728	+	1.38447i
$208$	2.40128	+	2.68958i	0.166499	+	0.186489i
$209$		−	21.7108i		−	1.50177i
$210$	−7.33231	−	5.14480i	−0.505978	−	0.355025i
$211$	−8.63034	−	14.9482i	−0.594137	−	1.02908i	−0.993668	−	0.112356i	$-0.964160\pi$
$211$	−8.63034	−	14.9482i	−0.594137	−	1.02908i	0.399531	−	0.916720i	$-0.369173\pi$
$212$	−5.62660			−0.386437
$213$	−5.26641	−	8.74101i	−0.360849	−	0.598924i
$214$	1.83446	−	6.84630i	0.125401	−	0.468004i
$215$	−7.06356	−	7.06356i	−0.481731	−	0.481731i
$216$	5.18802	−	0.290619i	0.353000	−	0.0197741i
$217$	1.29775	−	1.77806i	0.0880971	−	0.120702i
$218$	4.13084	+	7.15483i	0.279776	+	0.484586i
$219$	9.58863	+	15.9149i	0.647940	+	1.07543i
$220$	6.00469	+	3.46681i	0.404836	+	0.233732i
$221$	8.95218	−	1.86349i	0.602189	−	0.125352i
$222$	−6.63546	+	6.88774i	−0.445343	+	0.462275i
$223$	−4.00258	+	14.9378i	−0.268032	+	1.00031i	0.692336	+	0.721576i	$0.256582\pi$
$223$	−4.00258	+	14.9378i	−0.268032	+	1.00031i	−0.960368	+	0.278735i	$0.910085\pi$
$224$	−2.41935	+	1.07087i	−0.161650	+	0.0715502i
$225$	−3.53586	+	0.131970i	−0.235724	+	0.00879798i
$226$	2.82673	−	10.5495i	0.188031	−	0.701742i
$227$	−18.7758	−	5.03096i	−1.24619	−	0.333917i	−0.425329	−	0.905039i	$-0.639842\pi$
$227$	−18.7758	−	5.03096i	−1.24619	−	0.333917i	−0.820865	+	0.571122i	$0.806508\pi$
$228$	−10.5990	+	0.197725i	−0.701935	+	0.0130947i
$229$	5.16146	+	1.38301i	0.341079	+	0.0913917i	0.425292	−	0.905056i	$-0.360171\pi$
$229$	5.16146	+	1.38301i	0.341079	+	0.0913917i	−0.0842139	+	0.996448i	$0.526838\pi$
$230$	11.2472	+	6.49355i	0.741616	+	0.428172i
$231$	−16.0115	+	2.80717i	−1.05348	+	0.184698i
$232$	8.71314	+	2.33468i	0.572046	+	0.153279i
$233$	2.67277	+	4.62938i	0.175099	+	0.303281i	0.940196	−	0.340635i	$-0.110642\pi$
$233$	2.67277	+	4.62938i	0.175099	+	0.303281i	−0.765096	+	0.643916i	$0.777309\pi$
$234$	9.46994	−	5.22688i	0.619069	−	0.341692i
$235$	−11.2684	+	19.5174i	−0.735067	+	1.27317i
$236$	−2.62141	−	9.78325i	−0.170640	−	0.636835i
$237$	14.7291	+	14.1896i	0.956757	+	0.921714i
$238$	−0.715886	+	6.67162i	−0.0464040	+	0.432457i
$239$	−1.77800	+	1.77800i	−0.115009	+	0.115009i	−0.762269	−	0.647260i	$-0.775915\pi$
$239$	−1.77800	+	1.77800i	−0.115009	+	0.115009i	0.647260	+	0.762269i	$0.275915\pi$
$240$	1.63777	−	2.96300i	0.105718	−	0.191261i
$241$	−0.739683	−	0.198197i	−0.0476472	−	0.0127670i	0.234917	−	0.972016i	$-0.424518\pi$
$241$	−0.739683	−	0.198197i	−0.0476472	−	0.0127670i	−0.282564	+	0.959248i	$0.591185\pi$
$242$	1.52931	−	0.409777i	0.0983077	−	0.0263415i
$243$	2.61478	−	15.3676i	0.167738	−	0.985832i
$244$	9.71509	−	5.60901i	0.621945	−	0.359080i
$245$	6.26463	−	12.1640i	0.400232	−	0.777127i
$246$	3.07638	+	10.6802i	0.196143	+	0.680946i
$247$	−19.7042	+	9.93553i	−1.25375	+	0.632182i
$248$	0.720539	+	0.416003i	0.0457543	+	0.0264162i
$249$	−1.01871	+	1.84302i	−0.0645583	+	0.116796i
$250$	−6.03925	+	10.4603i	−0.381955	+	0.661566i
$251$	4.20343	−	7.28055i	0.265318	−	0.459544i	−0.702329	−	0.711853i	$-0.747856\pi$
$251$	4.20343	−	7.28055i	0.265318	−	0.459544i	0.967647	+	0.252308i	$0.0811897\pi$
$252$	1.51625	+	7.79108i	0.0955149	+	0.490792i
$253$	22.7661	−	6.10016i	1.43129	−	0.383514i
$254$	9.06457	+	9.06457i	0.568762	+	0.568762i
$255$	−4.43096	−	7.35435i	−0.277477	−	0.460548i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	3.12455	−	5.41188i	0.194904	−	0.337584i	−0.751965	−	0.659203i	$-0.770894\pi$
$257$	3.12455	−	5.41188i	0.194904	−	0.337584i	0.946869	+	0.321619i	$0.104227\pi$
$258$	0.165104	+	8.85034i	0.0102789	+	0.550998i
$259$	−11.8004	−	8.61279i	−0.733244	−	0.535173i
$260$	0.398463	−	7.03623i	0.0247117	−	0.436368i
$261$	12.6473	−	23.9243i	0.782845	−	1.48088i
$262$	3.91061	+	3.91061i	0.241598	+	0.241598i
$263$		−	29.7002i		−	1.83139i	−0.401874	−	0.915695i	$-0.631641\pi$
$263$		−	29.7002i		−	1.83139i	0.401874	−	0.915695i	$-0.368359\pi$
$264$	−1.70062	−	5.90404i	−0.104666	−	0.363368i
$265$	7.77669	+	7.77669i	0.477718	+	0.477718i
$266$	−2.49837	−	15.9992i	−0.153185	−	0.980971i
$267$	4.18209	−	2.51968i	0.255940	−	0.154202i
$268$	11.5062	+	3.08307i	0.702851	+	0.188328i
$269$	21.4627	−	12.3915i	1.30861	−	0.755524i	0.326743	−	0.945113i	$-0.394049\pi$
$269$	21.4627	−	12.3915i	1.30861	−	0.755524i	0.981863	+	0.189589i	$0.0607157\pi$
$270$	−7.57218	−	6.76884i	−0.460828	−	0.411938i
$271$	−6.91054	−	25.7905i	−0.419786	−	1.56666i	−0.775053	−	0.631896i	$-0.782277\pi$
$271$	−6.91054	−	25.7905i	−0.419786	−	1.56666i	0.355267	−	0.934765i	$-0.384390\pi$
$272$	−2.53611			−0.153774
$273$	9.87507	+	13.2470i	0.597666	+	0.801745i
$274$	12.5863			0.760369
$275$	1.08285	+	4.04126i	0.0652984	+	0.243697i
$276$	−3.18537	−	11.0586i	−0.191737	−	0.665651i
$277$	11.0801	−	6.39709i	0.665738	−	0.384364i	−0.128722	−	0.991681i	$-0.541087\pi$
$277$	11.0801	−	6.39709i	0.665738	−	0.384364i	0.794460	+	0.607317i	$0.207754\pi$
$278$	9.87518	+	2.64605i	0.592274	+	0.158699i
$279$	1.69790	−	1.82955i	0.101650	−	0.109532i
$280$	4.82392	+	1.86378i	0.288285	+	0.111382i
$281$	−6.25598	−	6.25598i	−0.373200	−	0.373200i	0.495441	−	0.868641i	$-0.335006\pi$
$281$	−6.25598	−	6.25598i	−0.373200	−	0.373200i	−0.868641	+	0.495441i	$0.835006\pi$
$282$	19.1902	−	5.52763i	1.14276	−	0.329165i
$283$			13.6939i			0.814018i	0.913424	+	0.407009i	$0.133428\pi$
$283$			13.6939i			0.814018i	−0.913424	+	0.407009i	$0.866572\pi$
$284$	4.16614	+	4.16614i	0.247215	+	0.247215i
$285$	14.9225	+	14.3759i	0.883930	+	0.851554i
$286$	−8.51804	−	9.54072i	−0.503683	−	0.564154i
$287$	−15.5248	+	6.87168i	−0.916401	+	0.405623i
$288$	−2.86680	+	0.883996i	−0.168928	+	0.0520900i
$289$	5.28407	−	9.15228i	0.310828	−	0.538369i
$290$	−8.81586	−	15.2695i	−0.517685	−	0.896657i
$291$	10.6805	−	6.43494i	0.626102	−	0.377223i
$292$	−7.58535	−	7.58535i	−0.443899	−	0.443899i
$293$	4.43762	−	1.18906i	0.259249	−	0.0694655i	−0.126854	−	0.991921i	$-0.540488\pi$
$293$	4.43762	−	1.18906i	0.259249	−	0.0694655i	0.386102	+	0.922456i	$0.373821\pi$
$294$	−11.4762	+	3.91118i	−0.669304	+	0.228105i
$295$	−9.89858	+	17.1448i	−0.576318	+	0.998211i
$296$	2.76089	−	4.78200i	0.160474	−	0.277948i
$297$	−18.4034	+	1.03091i	−1.06787	+	0.0598194i
$298$	18.3088	+	10.5706i	1.06060	+	0.612337i
$299$	−15.9548	−	17.8704i	−0.922691	−	1.03347i
$300$	1.96304	−	0.565442i	0.113336	−	0.0326458i
$301$	−13.3596	+	2.08618i	−0.770033	+	0.120245i
$302$	−2.06609	+	1.19286i	−0.118890	+	0.0686412i
$303$	9.04682	−	2.60588i	0.519726	−	0.149704i
$304$	5.91185	−	1.58408i	0.339068	−	0.0908529i
$305$	−21.1799	−	5.67513i	−1.21276	−	0.324957i
$306$	−1.69371	+	7.41742i	−0.0968230	+	0.424026i
$307$	−5.42627	+	5.42627i	−0.309694	+	0.309694i	−0.844791	−	0.535097i	$-0.820275\pi$
$307$	−5.42627	+	5.42627i	−0.309694	+	0.309694i	0.535097	+	0.844791i	$0.320275\pi$
$308$	8.58213	−	3.79867i	0.489012	−	0.216449i
$309$	14.6218	−	15.1777i	0.831806	−	0.863431i
$310$	−0.420907	−	1.57085i	−0.0239059	−	0.0892181i
$311$	7.38492	−	12.7911i	0.418760	−	0.725314i	−0.577055	−	0.816705i	$-0.695798\pi$
$311$	7.38492	−	12.7911i	0.418760	−	0.725314i	0.995815	+	0.0913914i	$0.0291314\pi$
$312$	−4.58010	+	4.24531i	−0.259297	+	0.240343i
$313$	−9.11510	−	15.7878i	−0.515216	−	0.892380i	−0.999844	−	0.0176598i	$-0.994378\pi$
$313$	−9.11510	−	15.7878i	−0.515216	−	0.892380i	0.484628	−	0.874720i	$-0.338955\pi$
$314$	−10.5715	−	2.83262i	−0.596583	−	0.159854i
$315$	8.67262	−	12.8639i	0.488647	−	0.724801i
$316$	−10.2261	−	5.90403i	−0.575262	−	0.332128i
$317$	−24.3729	−	6.53071i	−1.36892	−	0.366801i	−0.501836	−	0.864963i	$-0.667342\pi$
$317$	−24.3729	−	6.53071i	−1.36892	−	0.366801i	−0.867084	+	0.498162i	$0.834009\pi$
$318$	−0.181773	−	9.74387i	−0.0101933	−	0.546409i
$319$	−30.9080	−	8.28178i	−1.73052	−	0.463691i
$320$	−0.505894	+	1.88802i	−0.0282803	+	0.105544i
$321$	11.9153	+	2.95565i	0.665050	+	0.164968i
$322$	16.0749	−	7.11515i	0.895817	−	0.396512i
$323$	4.01739	−	14.9931i	0.223534	−	0.834239i
$324$	0.670883	+	8.97496i	0.0372713	+	0.498609i
$325$	3.17220	−	2.83217i	0.175962	−	0.157101i
$326$	17.6886	+	10.2125i	0.979681	+	0.565619i
$327$	−12.2569	+	7.38473i	−0.677809	+	0.408377i
$328$	−3.20847	−	5.55723i	−0.177158	−	0.306847i
$329$	12.3470	+	27.8950i	0.680714	+	1.53790i
$330$	−5.80966	+	10.5106i	−0.319811	+	0.578591i
$331$	13.7622	+	13.7622i	0.756440	+	0.756440i	0.975673	−	0.219232i	$-0.0703553\pi$
$331$	13.7622	+	13.7622i	0.756440	+	0.756440i	−0.219232	+	0.975673i	$0.570355\pi$
$332$	0.314672	−	1.17437i	0.0172698	−	0.0644519i
$333$	−12.1422	−	11.2684i	−0.665388	−	0.617507i
$334$	2.70473			0.147996
$335$	−11.6418	−	20.1642i	−0.636060	−	1.10169i
$336$	−1.93263	−	4.15511i	−0.105434	−	0.226680i
$337$		−	4.64457i		−	0.253006i	−0.991966	−	0.126503i	$-0.959625\pi$
$337$		−	4.64457i		−	0.253006i	0.991966	−	0.126503i	$-0.0403753\pi$
$338$	−4.76081	+	12.0969i	−0.258954	+	0.657984i
$339$	18.3604	+	4.55438i	0.997201	+	0.247360i
$340$	3.50523	+	3.50523i	0.190098	+	0.190098i
$341$	−2.55596	−	1.47568i	−0.138413	−	0.0799128i
$342$	−0.684822	−	18.3484i	−0.0370309	−	0.992169i
$343$	−8.30020	−	16.5562i	−0.448169	−	0.893949i
$344$	−1.32273	−	4.93650i	−0.0713168	−	0.266158i
$345$	−10.8819	+	19.6870i	−0.585859	+	1.05991i
$346$	−2.22103	−	8.28899i	−0.119403	−	0.445619i
$347$	−14.0612	+	8.11822i	−0.754843	+	0.435809i	−0.827441	−	0.561552i	$-0.810204\pi$
$347$	−14.0612	+	8.11822i	−0.754843	+	0.435809i	0.0725979	+	0.997361i	$0.476871\pi$
$348$	−3.76159	+	15.1644i	−0.201643	+	0.812897i
$349$	8.30463	+	2.22522i	0.444536	+	0.119113i	0.474142	−	0.880448i	$-0.342758\pi$
$349$	8.30463	+	2.22522i	0.444536	+	0.119113i	−0.0296054	+	0.999562i	$0.509425\pi$
$350$	1.26302	+	2.85348i	0.0675114	+	0.152525i
$351$	9.35758	+	16.2307i	0.499471	+	0.866331i
$352$	1.77364	+	3.07204i	0.0945356	+	0.163740i
$353$	19.5516	−	19.5516i	1.04062	−	1.04062i	0.0414854	−	0.999139i	$-0.486791\pi$
$353$	19.5516	−	19.5516i	1.04062	−	1.04062i	0.999139	−	0.0414854i	$-0.0132090\pi$
$354$	16.8575	−	4.85569i	0.895964	−	0.258077i
$355$		−	11.5163i		−	0.611221i
$356$	−1.99327	+	1.99327i	−0.105643	+	0.105643i
$357$	−11.5767	−	1.02420i	−0.612704	−	0.0542065i
$358$	−0.528149	−	1.97108i	−0.0279135	−	0.104175i
$359$	1.68926	−	6.30441i	0.0891558	−	0.332734i	−0.906913	−	0.421318i	$-0.861568\pi$
$359$	1.68926	−	6.30441i	0.0891558	−	0.332734i	0.996069	+	0.0885842i	$0.0282342\pi$
$360$	5.18408	+	2.74049i	0.273225	+	0.144437i
$361$			18.4593i			0.971539i
$362$	−3.64820	+	0.977531i	−0.191745	+	0.0513779i
$363$	0.759037	+	2.63514i	0.0398391	+	0.138309i
$364$	−7.37502	−	6.05054i	−0.386556	−	0.317135i
$365$			20.9679i			1.09751i
$366$	10.0273	+	16.6429i	0.524133	+	0.869938i
$367$	17.7537			0.926735			0.463368	−	0.886166i	$-0.346641\pi$
$367$	17.7537			0.926735			0.463368	+	0.886166i	$0.346641\pi$
$368$	3.32215	+	5.75413i	0.173179	+	0.299955i
$369$	−18.3961	+	5.67255i	−0.957662	+	0.295301i
$370$	−10.4252	+	2.79344i	−0.541983	+	0.145224i
$371$	14.7083	−	2.29680i	0.763619	−	0.119244i
$372$	−0.697136	+	1.26123i	−0.0361448	+	0.0653918i
$373$	15.8312			0.819710			0.409855	−	0.912151i	$-0.365579\pi$
$373$	15.8312			0.819710			0.409855	+	0.912151i	$0.365579\pi$
$374$	8.99632			0.465189
$375$	−18.3097	−	10.1205i	−0.945508	−	0.522622i
$376$	−9.98523	+	5.76497i	−0.514949	+	0.297306i
$377$	6.62811	+	31.8414i	0.341365	+	1.63991i
$378$	−13.4432	+	2.87747i	−0.691445	+	0.148001i
$379$	−1.80495	+	6.73617i	−0.0927141	+	0.346014i	−0.996663	−	0.0816269i	$-0.973988\pi$
$379$	−1.80495	+	6.73617i	−0.0927141	+	0.346014i	0.903949	+	0.427641i	$0.140655\pi$
$380$	−10.3603	−	5.98154i	−0.531474	−	0.306847i
$381$	−15.4047	+	15.9904i	−0.789208	+	0.819213i
$382$	9.56413	−	2.56270i	0.489344	−	0.131119i
$383$	23.7318	−	23.7318i	1.21264	−	1.21264i	0.242483	−	0.970156i	$-0.422038\pi$
$383$	23.7318	−	23.7318i	1.21264	−	1.21264i	0.970156	−	0.242483i	$-0.0779617\pi$
$384$	1.48359	−	0.893853i	0.0757089	−	0.0456142i
$385$	−17.1119	−	6.61135i	−0.872101	−	0.336946i
$386$	−3.38008	−	1.95149i	−0.172042	−	0.0993284i
$387$	−15.3212	+	0.571838i	−0.778823	+	0.0290682i
$388$	−5.09054	+	5.09054i	−0.258433	+	0.258433i
$389$	15.1589	−	26.2560i	0.768587	−	1.33123i	−0.169743	−	0.985488i	$-0.554294\pi$
$389$	15.1589	−	26.2560i	0.768587	−	1.33123i	0.938329	−	0.345743i	$-0.112373\pi$
$390$	12.1979	+	0.462727i	0.617662	+	0.0234311i
$391$	16.8507			0.852175
$392$	5.88722	−	3.78691i	0.297349	−	0.191268i
$393$	−6.64586	+	6.89854i	−0.335240	+	0.347985i
$394$		−	4.81087i		−	0.242368i
$395$	5.97363	+	22.2939i	0.300566	+	1.12173i
$396$	10.1694	−	3.13579i	0.511030	−	0.157579i
$397$	12.6321	−	12.6321i	0.633985	−	0.633985i	−0.315080	−	0.949065i	$-0.602031\pi$
$397$	12.6321	−	12.6321i	0.633985	−	0.633985i	0.949065	+	0.315080i	$0.102031\pi$
$398$	−6.21129	−	6.21129i	−0.311344	−	0.311344i
$399$	27.6258	−	4.84342i	1.38302	−	0.242474i
$400$	−1.02143	+	0.589721i	−0.0510713	+	0.0294860i
$401$	0.953278	−	0.255430i	0.0476044	−	0.0127556i	−0.234938	−	0.972010i	$-0.575489\pi$
$401$	0.953278	−	0.255430i	0.0476044	−	0.0127556i	0.282543	+	0.959255i	$0.408822\pi$
$402$	−4.96738	+	20.0254i	−0.247751	+	0.998776i
$403$	−0.169610	+	2.99504i	−0.00844888	+	0.149194i
$404$	−4.70732	+	2.71777i	−0.234198	+	0.135214i
$405$	11.4773	−	13.3318i	0.570312	−	0.662462i
$406$	−23.7298	−	2.54628i	−1.17769	−	0.126370i
$407$	−9.79368	+	16.9631i	−0.485455	+	0.840832i
$408$	−0.0819316	−	4.39191i	−0.00405622	−	0.217432i
$409$	−1.66504	+	6.21402i	−0.0823310	+	0.307263i	−0.994795	−	0.101893i	$-0.967510\pi$
$409$	−1.66504	+	6.21402i	−0.0823310	+	0.307263i	0.912464	+	0.409156i	$0.134177\pi$
$410$	−3.24629	+	12.1153i	−0.160323	+	0.598333i
$411$	0.406614	+	21.7964i	0.0200568	+	1.07514i
$412$	−6.08387	+	10.5376i	−0.299731	+	0.519149i
$413$	10.8461	+	24.5040i	0.533703	+	1.20577i
$414$	19.0479	−	5.87353i	0.936152	−	0.288668i
$415$	−2.05805	+	1.18821i	−0.101026	+	0.0583271i
$416$	1.97644	−	3.01558i	0.0969028	−	0.147851i
$417$	−4.26326	+	17.1868i	−0.208773	+	0.841642i
$418$	−20.9710	+	5.61917i	−1.02573	+	0.274843i
$419$	−4.14630	+	2.39387i	−0.202560	+	0.116948i	−0.597849	−	0.801609i	$-0.703978\pi$
$419$	−4.14630	+	2.39387i	−0.202560	+	0.116948i	0.395289	+	0.918557i	$0.370644\pi$
$420$	−3.07175	+	8.41404i	−0.149886	+	0.410563i
$421$	−0.472730	−	0.472730i	−0.0230395	−	0.0230395i	0.695493	−	0.718533i	$-0.255186\pi$
$421$	−0.472730	−	0.472730i	−0.0230395	−	0.0230395i	−0.718533	+	0.695493i	$0.755186\pi$
$422$	−12.2051	+	12.2051i	−0.594137	+	0.594137i
$423$	10.1924	+	33.0541i	0.495573	+	1.60714i
$424$	1.45627	+	5.43488i	0.0707228	+	0.263941i
$425$			2.99119i			0.145094i
$426$	−7.08012	+	7.34931i	−0.343033	+	0.356075i
$427$	−23.1063	+	18.6281i	−1.11819	+	0.901476i
$428$	−7.08782			−0.342602
$429$	16.2469	−	15.0593i	0.784410	−	0.727072i
$430$	−4.99469	+	8.65106i	−0.240865	+	0.417191i
$431$	2.79639	−	2.79639i	0.134698	−	0.134698i	−0.636543	−	0.771241i	$-0.719636\pi$
$431$	2.79639	−	2.79639i	0.134698	−	0.134698i	0.771241	+	0.636543i	$0.219636\pi$
$432$	−1.62347	−	4.93602i	−0.0781095	−	0.237485i
$433$	19.3037	+	11.1450i	0.927677	+	0.535595i	0.886076	−	0.463540i	$-0.153421\pi$
$433$	19.3037	+	11.1450i	0.927677	+	0.535595i	0.0416011	+	0.999134i	$0.486754\pi$
$434$	−2.05335	−	0.793336i	−0.0985642	−	0.0380813i
$435$	26.1582	−	15.7602i	1.25419	−	0.755641i
$436$	5.84190	−	5.84190i	0.279776	−	0.279776i
$437$	−39.2801	+	10.5251i	−1.87902	+	0.503482i
$438$	12.8909	−	13.3810i	0.615950	−	0.639368i
$439$	−13.3071	−	7.68284i	−0.635112	−	0.366682i	0.147617	−	0.989045i	$-0.452840\pi$
$439$	−13.3071	−	7.68284i	−0.635112	−	0.366682i	−0.782729	+	0.622362i	$0.786173\pi$
$440$	1.79455	−	6.69736i	0.0855519	−	0.319284i
$441$	−7.14394	−	19.7475i	−0.340188	−	0.940358i
$442$	−4.11699	−	8.16484i	−0.195825	−	0.388362i
$443$	−21.4724	+	12.3971i	−1.02018	+	0.589004i	−0.914157	−	0.405359i	$-0.867146\pi$
$443$	−21.4724	+	12.3971i	−1.02018	+	0.589004i	−0.106027	+	0.994363i	$0.533813\pi$
$444$	8.37043	+	4.62668i	0.397243	+	0.219573i
$445$	5.50990			0.261194
$446$	15.4648			0.732278
$447$	−17.7141	+	32.0477i	−0.837849	+	1.51580i
$448$	1.66055	+	2.05975i	0.0784536	+	0.0973141i
$449$	−25.1155	+	6.72968i	−1.18527	+	0.317593i	−0.797016	−	0.603958i	$-0.793589\pi$
$449$	−25.1155	+	6.72968i	−1.18527	+	0.317593i	−0.388257	+	0.921551i	$0.626923\pi$
$450$	1.04262	+	3.38122i	0.0491496	+	0.159392i
$451$	11.3814	+	19.7131i	0.535928	+	0.928254i
$452$	−10.9216			−0.513711
$453$	−2.13248	−	3.53941i	−0.100192	−	0.166296i
$454$			19.4382i			0.912278i
$455$	1.83060	+	18.5559i	0.0858199	+	0.869912i
$456$	2.93421	+	10.1867i	0.137407	+	0.477034i
$457$	17.1694	−	4.60052i	0.803150	−	0.215203i	0.166183	−	0.986095i	$-0.446856\pi$
$457$	17.1694	−	4.60052i	0.803150	−	0.215203i	0.636966	+	0.770892i	$0.280189\pi$
$458$		−	5.34353i		−	0.249687i
$459$	−12.8998	−	2.69346i	−0.602112	−	0.125720i
$460$	3.36131	−	12.5446i	0.156722	−	0.584894i
$461$	−7.94677	−	29.6577i	−0.370118	−	1.38130i	−0.860349	−	0.509706i	$-0.829754\pi$
$461$	−7.94677	−	29.6577i	−0.370118	−	1.38130i	0.490231	−	0.871593i	$-0.336912\pi$
$462$	6.85560	+	14.7394i	0.318951	+	0.685738i
$463$	4.70860	−	4.70860i	0.218827	−	0.218827i	−0.589177	−	0.808004i	$-0.700548\pi$
$463$	4.70860	−	4.70860i	0.218827	−	0.218827i	0.808004	+	0.589177i	$0.200548\pi$
$464$		−	9.02051i		−	0.418767i
$465$	2.70672	−	0.779654i	0.125521	−	0.0361556i
$466$	3.77987	−	3.77987i	0.175099	−	0.175099i
$467$	12.7798	+	22.1352i	0.591377	+	1.02430i	0.994047	+	0.108950i	$0.0347489\pi$
$467$	12.7798	+	22.1352i	0.591377	+	1.02430i	−0.402670	+	0.915345i	$0.631918\pi$
$468$	−7.49978	−	7.79444i	−0.346677	−	0.360298i
$469$	−31.3365	−	3.36250i	−1.44698	−	0.155266i
$470$	21.7688	+	5.83293i	1.00412	+	0.269053i
$471$	4.56386	−	18.3987i	0.210292	−	0.847765i
$472$	−8.77142	+	5.06418i	−0.403737	+	0.233098i
$473$	4.69211	+	17.5112i	0.215743	+	0.805165i
$474$	9.89394	−	17.8997i	0.454444	−	0.822162i
$475$	−1.86832	−	6.97268i	−0.0857245	−	0.319928i
$476$	6.62958	−	1.03525i	0.303866	−	0.0474506i
$477$	16.8681	−	0.629571i	0.772336	−	0.0288261i
$478$	2.17760	+	1.25724i	0.0996011	+	0.0575047i
$479$	5.95801	+	5.95801i	0.272228	+	0.272228i	0.829997	−	0.557768i	$-0.188342\pi$
$479$	5.95801	+	5.95801i	0.272228	+	0.272228i	−0.557768	+	0.829997i	$0.688342\pi$
$480$	−3.28593	−	0.815088i	−0.149981	−	0.0372035i
$481$	19.8772	+	1.12565i	0.906323	+	0.0513253i
$482$			0.765776i			0.0348802i
$483$	12.8410	+	27.6078i	0.584284	+	1.25620i
$484$	−0.791629	−	1.37114i	−0.0359831	−	0.0623246i
$485$	14.0716			0.638957
$486$	−15.5207	+	1.45175i	−0.704034	+	0.0658526i
$487$	4.87821	−	18.2057i	0.221053	−	0.824980i	−0.762895	−	0.646523i	$-0.776223\pi$
$487$	4.87821	−	18.2057i	0.221053	−	0.824980i	0.983948	−	0.178458i	$-0.0571107\pi$
$488$	−7.93234	−	7.93234i	−0.359080	−	0.359080i
$489$	−17.1141	+	30.9622i	−0.773925	+	1.40016i
$490$	−13.3709	−	2.90290i	−0.604035	−	0.131140i
$491$	−7.87704	−	13.6434i	−0.355486	−	0.615719i	0.631715	−	0.775200i	$-0.282351\pi$
$491$	−7.87704	−	13.6434i	−0.355486	−	0.615719i	−0.987201	+	0.159481i	$0.949018\pi$
$492$	9.52008	−	5.73580i	0.429198	−	0.258590i
$493$	−19.8121	−	11.4385i	−0.892291	−	0.515165i
$494$	14.6968	+	16.4613i	0.661240	+	0.740629i
$495$	−18.3894	−	9.72132i	−0.826544	−	0.436941i
$496$	0.215339	−	0.803657i	0.00966901	−	0.0360853i
$497$	−12.5912	−	9.18996i	−0.564794	−	0.412226i
$498$	2.04388	+	0.506993i	0.0915885	+	0.0227189i
$499$	−3.30313	+	12.3274i	−0.147868	+	0.551852i	0.851743	+	0.523960i	$0.175546\pi$
$499$	−3.30313	+	12.3274i	−0.147868	+	0.551852i	−0.999611	+	0.0278916i	$0.991121\pi$
$500$	11.6669	+	3.12614i	0.521761	+	0.139805i
$501$	0.0873791	+	4.68392i	0.00390381	+	0.209262i
$502$	−8.12040	−	2.17585i	−0.362431	−	0.0971131i
$503$	−16.2100	−	9.35887i	−0.722770	−	0.417291i	0.0930013	−	0.995666i	$-0.470354\pi$
$503$	−16.2100	−	9.35887i	−0.722770	−	0.417291i	−0.815771	+	0.578374i	$0.803687\pi$
$504$	7.13317	−	3.48107i	0.317737	−	0.155059i
$505$	10.2624	+	2.74981i	0.456673	+	0.122365i
$506$	−11.7846	−	20.4115i	−0.523890	−	0.907404i
$507$	−21.1026	−	7.85372i	−0.937199	−	0.348796i
$508$	6.40962	−	11.1018i	0.284381	−	0.492562i
$509$	−0.624087	−	2.32912i	−0.0276622	−	0.103237i	0.950715	−	0.310068i	$-0.100352\pi$
$509$	−0.624087	−	2.32912i	−0.0276622	−	0.103237i	−0.978377	+	0.206831i	$0.933685\pi$
$510$	−5.95694	+	6.18342i	−0.263778	+	0.273807i
$511$	22.9250	+	16.7323i	1.01414	+	0.740193i
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	31.7527	−	1.77870i	1.40192	−	0.0785317i
$514$	−6.03617	−	1.61739i	−0.266244	−	0.0713399i
$515$	22.9730	−	6.15558i	1.01231	−	0.271247i
$516$	8.50604	−	2.45012i	0.374458	−	0.107860i
$517$	35.4205	−	20.4500i	1.55779	−	0.899391i
$518$	−5.26514	+	13.6275i	−0.231337	+	0.598758i
$519$	14.2827	−	4.11405i	0.626941	−	0.180587i
$520$	−6.89960	+	1.43622i	−0.302568	+	0.0629826i
$521$	−26.5738	−	15.3424i	−1.16422	−	0.672163i	−0.211909	−	0.977289i	$-0.567968\pi$
$521$	−26.5738	−	15.3424i	−1.16422	−	0.672163i	−0.952312	+	0.305126i	$0.901301\pi$
$522$	−26.3825	−	6.02424i	−1.15473	−	0.263674i
$523$	−8.73505	+	15.1295i	−0.381957	+	0.661569i	−0.991342	−	0.131306i	$-0.958083\pi$
$523$	−8.73505	+	15.1295i	−0.381957	+	0.661569i	0.609385	+	0.792875i	$0.291416\pi$
$524$	2.76522	−	4.78950i	0.120799	−	0.209230i
$525$	−4.90071	+	2.27942i	−0.213884	+	0.0994822i
$526$	−28.6882	+	7.68697i	−1.25086	+	0.335168i
$527$	−1.49204	−	1.49204i	−0.0649942	−	0.0649942i
$528$	−5.26271	+	3.17075i	−0.229030	+	0.137989i
$529$	−10.5733	−	18.3135i	−0.459709	−	0.796240i
$530$	5.49895	−	9.52446i	0.238859	−	0.413716i
$531$	8.95344	+	29.0360i	0.388546	+	1.26006i
$532$	−14.8074	+	6.55412i	−0.641981	+	0.284157i
$533$	12.6827	−	19.3508i	0.549348	−	0.838175i
$534$	−3.51623	−	3.38744i	−0.152162	−	0.146589i
$535$	9.79627	+	9.79627i	0.423530	+	0.423530i
$536$		−	11.9121i		−	0.514523i
$537$	3.39635	−	0.978299i	0.146563	−	0.0422167i
$538$	−17.5242	−	17.5242i	−0.755524	−	0.755524i
$539$	−20.8837	+	13.4333i	−0.899523	+	0.578611i
$540$	−4.57837	+	9.06607i	−0.197022	+	0.390142i
$541$	−12.1954	−	3.26775i	−0.524322	−	0.140492i	−0.0130571	−	0.999915i	$-0.504156\pi$
$541$	−12.1954	−	3.26775i	−0.524322	−	0.140492i	−0.511265	+	0.859423i	$0.670823\pi$
$542$	−23.1231	+	13.3501i	−0.993223	+	0.573438i
$543$	−1.81070	−	6.28618i	−0.0777045	−	0.269766i
$544$	0.656394	+	2.44970i	0.0281427	+	0.105030i
$545$	−16.1485			−0.691726
$546$	10.2398	−	12.9672i	0.438222	−	0.554943i
$547$	3.08215			0.131783			0.0658917	−	0.997827i	$-0.479011\pi$
$547$	3.08215			0.131783			0.0658917	+	0.997827i	$0.479011\pi$
$548$	−3.25759	−	12.1575i	−0.139157	−	0.519342i
$549$	−28.4974	+	17.9024i	−1.21624	+	0.764054i
$550$	3.62329	−	2.09191i	0.154498	−	0.0891993i
$551$	53.3279	+	14.2892i	2.27184	+	0.608739i
$552$	−9.85738	+	5.93902i	−0.419558	+	0.252781i
$553$	29.1417	+	11.2592i	1.23923	+	0.478791i
$554$	−9.04685	−	9.04685i	−0.384364	−	0.384364i
$555$	−5.17433	−	17.9637i	−0.219638	−	0.762516i
$556$		−	10.2235i		−	0.433574i
$557$	30.7907	+	30.7907i	1.30464	+	1.30464i	0.925226	+	0.379416i	$0.123875\pi$
$557$	30.7907	+	30.7907i	1.30464	+	1.30464i	0.379416	+	0.925226i	$0.376125\pi$
$558$	−2.20666	−	1.16652i	−0.0934154	−	0.0493827i
$559$	13.7455	−	12.2721i	0.581371	−	0.519054i
$560$	0.551746	−	5.14193i	0.0233155	−	0.217286i
$561$	0.290635	+	15.5794i	0.0122706	+	0.657762i
$562$	−4.42364	+	7.66198i	−0.186600	+	0.323201i
$563$	2.39146	+	4.14212i	0.100788	+	0.174570i	0.912009	−	0.410169i	$-0.134530\pi$
$563$	2.39146	+	4.14212i	0.100788	+	0.174570i	−0.811222	+	0.584739i	$0.801197\pi$
$564$	−10.3061	−	17.1057i	−0.433964	−	0.720278i
$565$	15.0951	+	15.0951i	0.635056	+	0.635056i
$566$	13.2273	−	3.54424i	0.555985	−	0.148976i
$567$	−5.41735	−	23.1873i	−0.227507	−	0.973776i
$568$	2.94591	−	5.10246i	0.123608	−	0.214094i
$569$	16.5875	−	28.7305i	0.695386	−	1.20444i	−0.274665	−	0.961540i	$-0.588567\pi$
$569$	16.5875	−	28.7305i	0.695386	−	1.20444i	0.970050	−	0.242903i	$-0.0780998\pi$
$570$	10.0238	−	18.1347i	0.419852	−	0.759581i
$571$	−6.52137	−	3.76512i	−0.272911	−	0.157565i	0.357299	−	0.933990i	$-0.383698\pi$
$571$	−6.52137	−	3.76512i	−0.272911	−	0.157565i	−0.630210	+	0.776425i	$0.717031\pi$
$572$	−7.01099	+	10.6971i	−0.293144	+	0.447269i
$573$	4.74694	+	16.4799i	0.198306	+	0.688457i
$574$	10.6557	+	13.2173i	0.444758	+	0.551679i
$575$	6.78665	−	3.91828i	0.283023	−	0.163403i
$576$	1.59586	+	2.54032i	0.0664941	+	0.105847i
$577$	−13.8622	+	3.71436i	−0.577090	+	0.154631i	−0.535546	−	0.844506i	$-0.679894\pi$
$577$	−13.8622	+	3.71436i	−0.577090	+	0.154631i	−0.0415436	+	0.999137i	$0.513228\pi$
$578$	−10.2080	−	2.73524i	−0.424598	−	0.113771i
$579$	3.27030	−	5.91651i	0.135909	−	0.245882i
$580$	−12.4675	+	12.4675i	−0.517685	+	0.517685i
$581$	−0.343192	+	3.19834i	−0.0142380	+	0.132689i
$582$	−8.97999	−	8.65108i	−0.372233	−	0.358599i
$583$	−5.16582	−	19.2791i	−0.213946	−	0.798459i
$584$	−5.36365	+	9.29012i	−0.221950	+	0.384428i
$585$	−0.407263	+	21.1386i	−0.0168382	+	0.873973i
$586$	−2.29708	−	3.97867i	−0.0948916	−	0.164357i
$587$	34.5575	+	9.25966i	1.42634	+	0.382187i	0.887729	−	0.460367i	$-0.152282\pi$
$587$	34.5575	+	9.25966i	1.42634	+	0.382187i	0.538612	+	0.842554i	$0.318949\pi$
$588$	6.74817	+	10.0728i	0.278290	+	0.415397i
$589$	4.40998	+	2.54611i	0.181710	+	0.104910i
$590$	19.1226	+	5.12388i	0.787264	+	0.210947i
$591$	8.33122	−	0.155420i	0.342701	−	0.00639312i
$592$	−5.33363	−	1.42914i	−0.219211	−	0.0587374i
$593$	7.73655	−	28.8732i	0.317702	−	1.18568i	−0.603745	−	0.797177i	$-0.706326\pi$
$593$	7.73655	−	28.8732i	0.317702	−	1.18568i	0.921447	−	0.388503i	$-0.127008\pi$
$594$	5.75893	+	17.5095i	0.236292	+	0.718424i
$595$	−10.5938	−	7.73208i	−0.434302	−	0.316984i
$596$	5.47173	−	20.4208i	0.224131	−	0.836468i
$597$	10.5557	−	10.9571i	0.432017	−	0.448443i
$598$	−13.1320	+	20.0364i	−0.537008	+	0.819348i
$599$	28.4385	+	16.4190i	1.16196	+	0.670861i	0.951774	−	0.306800i	$-0.0992581\pi$
$599$	28.4385	+	16.4190i	1.16196	+	0.670861i	0.210191	+	0.977660i	$0.432591\pi$
$600$	−1.05425	−	1.74980i	−0.0430394	−	0.0714354i
$601$	−10.4847	−	18.1600i	−0.427680	−	0.740764i	0.568986	−	0.822347i	$-0.307336\pi$
$601$	−10.4847	−	18.1600i	−0.427680	−	0.740764i	−0.996667	+	0.0815832i	$0.974002\pi$
$602$	5.47281	+	12.3644i	0.223055	+	0.503936i
$603$	−34.8395	−	7.95533i	−1.41877	−	0.323966i
$604$	1.68695	+	1.68695i	0.0686412	+	0.0686412i
$605$	−0.800961	+	2.98923i	−0.0325637	+	0.121529i
$606$	−4.85858	−	8.06411i	−0.197366	−	0.327582i
$607$	9.62375			0.390616			0.195308	−	0.980742i	$-0.437429\pi$
$607$	9.62375			0.390616			0.195308	+	0.980742i	$0.437429\pi$
$608$	−3.06020	−	5.30042i	−0.124107	−	0.214960i
$609$	3.64291	−	41.1763i	0.147618	−	1.66855i
$610$			21.9270i			0.887799i
$611$	−34.7694	−	22.7882i	−1.40662	−	0.921912i
$612$	7.60304	−	0.283770i	0.307335	−	0.0114707i
$613$	−1.34949	−	1.34949i	−0.0545053	−	0.0545053i	0.679329	−	0.733834i	$-0.262271\pi$
$613$	−1.34949	−	1.34949i	−0.0545053	−	0.0545053i	−0.733834	+	0.679329i	$0.762271\pi$
$614$	6.64580	+	3.83695i	0.268203	+	0.154847i
$615$	−21.0856	−	5.23037i	−0.850253	−	0.210909i
$616$	−5.89045	−	7.30653i	−0.237333	−	0.294388i
$617$	2.19996	+	8.21036i	0.0885670	+	0.330536i	0.995966	−	0.0897342i	$-0.0286018\pi$
$617$	2.19996	+	8.21036i	0.0885670	+	0.330536i	−0.907399	+	0.420271i	$0.861935\pi$
$618$	−18.4450	−	10.1953i	−0.741965	−	0.410115i
$619$	−5.67669	−	21.1857i	−0.228165	−	0.851524i	−0.981112	−	0.193443i	$-0.938035\pi$
$619$	−5.67669	−	21.1857i	−0.228165	−	0.851524i	0.752946	−	0.658082i	$-0.228632\pi$
$620$	−1.40838	+	0.813130i	−0.0565620	+	0.0326561i
$621$	10.7868	+	32.7964i	0.432861	+	1.31607i
$622$	−14.2666	−	3.82271i	−0.572037	−	0.153277i
$623$	4.39688	−	6.02420i	0.176157	−	0.241354i
$624$	5.28607	+	3.32527i	0.211612	+	0.133117i
$625$	−8.85586	−	15.3388i	−0.354234	−	0.613552i
$626$	−12.8907	+	12.8907i	−0.515216	+	0.515216i
$627$	−10.4085	−	36.1350i	−0.415675	−	1.44309i
$628$			10.9444i			0.436729i
$629$	−9.90222	+	9.90222i	−0.394827	+	0.394827i
$630$	−14.6702	−	5.04768i	−0.584477	−	0.201104i
$631$	1.95596	+	7.29974i	0.0778655	+	0.290598i	0.993868	−	0.110575i	$-0.0352692\pi$
$631$	1.95596	+	7.29974i	0.0778655	+	0.290598i	−0.916002	+	0.401173i	$0.868603\pi$
$632$	−3.05615	+	11.4057i	−0.121567	+	0.453695i
$633$	−21.5305	−	20.7419i	−0.855762	−	0.824418i
$634$			25.2327i			1.00212i
$635$	−24.2030	+	6.48518i	−0.960467	+	0.257356i
$636$	−9.36481	+	2.69748i	−0.371339	+	0.106962i
$637$	21.7487	+	12.8060i	0.861714	+	0.507394i
$638$			31.9984i			1.26683i
$639$	−12.9559	−	12.0236i	−0.512527	−	0.475645i
$640$	1.95463			0.0772633
$641$	−3.97489	−	6.88471i	−0.156999	−	0.271930i	0.776786	−	0.629764i	$-0.216848\pi$
$641$	−3.97489	−	6.88471i	−0.156999	−	0.271930i	−0.933785	+	0.357835i	$0.883515\pi$
$642$	−0.228979	−	12.2743i	−0.00903708	−	0.484429i
$643$	24.7126	−	6.62172i	0.974570	−	0.261135i	0.263814	−	0.964574i	$-0.415020\pi$
$643$	24.7126	−	6.62172i	0.974570	−	0.261135i	0.710756	+	0.703438i	$0.248353\pi$
$644$	−11.0332	−	13.6856i	−0.434768	−	0.539288i
$645$	−15.1428	−	8.37007i	−0.596248	−	0.329571i
$646$	−15.5220			−0.610705
$647$	−16.5116			−0.649138			−0.324569	−	0.945862i	$-0.605219\pi$
$647$	−16.5116			−0.649138			−0.324569	+	0.945862i	$0.605219\pi$
$648$	8.49551	−	2.97091i	0.333735	−	0.116709i
$649$	31.1148	−	17.9641i	1.22136	−	0.705153i
$650$	−3.55669	−	2.33109i	−0.139505	−	0.0914329i
$651$	1.30752	−	3.58152i	0.0512459	−	0.140371i
$652$	5.28639	−	19.7291i	0.207031	−	0.772650i
$653$	−12.5981	−	7.27353i	−0.493003	−	0.284635i	0.232817	−	0.972521i	$-0.425206\pi$
$653$	−12.5981	−	7.27353i	−0.493003	−	0.284635i	−0.725819	+	0.687885i	$0.758539\pi$
$654$	10.3054	+	9.92797i	0.402974	+	0.388214i
$655$	−10.4416	+	2.79782i	−0.407987	+	0.109320i
$656$	−4.53746	+	4.53746i	−0.177158	+	0.177158i
$657$	23.5890	+	21.8915i	0.920293	+	0.854068i
$658$	23.7488	−	19.1461i	0.925825	−	0.746391i
$659$	22.4966	+	12.9884i	0.876342	+	0.505956i	0.869451	−	0.494020i	$-0.164473\pi$
$659$	22.4966	+	12.9884i	0.876342	+	0.505956i	0.00689143	+	0.999976i	$0.497806\pi$
$660$	11.6561	+	2.89135i	0.453714	+	0.112546i
$661$	14.7223	−	14.7223i	0.572629	−	0.572629i	−0.360233	−	0.932862i	$-0.617303\pi$
$661$	14.7223	−	14.7223i	0.572629	−	0.572629i	0.932862	+	0.360233i	$0.117303\pi$
$662$	9.73136	−	16.8552i	0.378220	−	0.655097i
$663$	14.0065	−	7.39337i	0.543966	−	0.287135i
$664$	−1.21580			−0.0471821
$665$	29.5243	+	11.4070i	1.14490	+	0.442346i
$666$	−7.74184	+	14.6449i	−0.299990	+	0.567480i
$667$			59.9349i			2.32069i
$668$	−0.700037	−	2.61257i	−0.0270852	−	0.101083i
$669$	0.499605	+	26.7811i	0.0193158	+	1.03542i
$670$	−16.4640	+	16.4640i	−0.636060	+	0.636060i
$671$	28.1383	+	28.1383i	1.08627	+	1.08627i
$672$	−3.51333	+	2.94220i	−0.135530	+	0.113498i
$673$	−42.3938	+	24.4761i	−1.63416	+	0.943484i	−0.651372	+	0.758758i	$0.725806\pi$
$673$	−42.3938	+	24.4761i	−1.63416	+	0.943484i	−0.982790	+	0.184726i	$0.940860\pi$
$674$	−4.48631	+	1.20210i	−0.172806	+	0.0463033i
$675$	−5.82175	+	1.91479i	−0.224079	+	0.0737004i
$676$	12.9169	+	1.46768i	0.496803	+	0.0564492i
$677$	−25.5319	+	14.7409i	−0.981273	+	0.566538i	−0.902654	−	0.430367i	$-0.858384\pi$
$677$	−25.5319	+	14.7409i	−0.981273	+	0.566538i	−0.0786184	+	0.996905i	$0.525051\pi$
$678$	−0.352835	−	18.9136i	−0.0135505	−	0.726371i
$679$	11.2291	−	15.3850i	0.430932	−	0.590423i
$680$	2.47857	−	4.29302i	0.0950490	−	0.164630i
$681$	−33.6620	+	0.627969i	−1.28993	+	0.0240638i
$682$	−0.763870	+	2.85080i	−0.0292501	+	0.109163i
$683$	−10.2730	+	38.3393i	−0.393085	+	1.46701i	0.431934	+	0.901905i	$0.357831\pi$
$683$	−10.2730	+	38.3393i	−0.393085	+	1.46701i	−0.825018	+	0.565106i	$0.808835\pi$
$684$	−17.5460	+	5.41041i	−0.670887	+	0.206872i
$685$	−12.3008	+	21.3056i	−0.469989	+	0.814045i
$686$	−13.8438	+	12.3024i	−0.528558	+	0.469709i
$687$	9.25366	−	0.172628i	0.353049	−	0.00658617i
$688$	−4.42594	+	2.55532i	−0.168737	+	0.0974206i
$689$	−15.1332	+	13.5111i	−0.576529	+	0.514731i
$690$	21.8327	+	5.41568i	0.831155	+	0.206171i
$691$	−22.5909	+	6.05320i	−0.859396	+	0.230275i	−0.661497	−	0.749948i	$-0.730079\pi$
$691$	−22.5909	+	6.05320i	−0.859396	+	0.230275i	−0.197899	+	0.980222i	$0.563412\pi$
$692$	−7.43170	+	4.29069i	−0.282511	+	0.163108i
$693$	−25.3034	+	12.3484i	−0.961198	+	0.469075i
$694$	11.4809	+	11.4809i	0.435809	+	0.435809i
$695$	−14.1302	+	14.1302i	−0.535991	+	0.535991i
$696$	15.6213	−	0.291416i	0.592122	−	0.0110461i
$697$	4.21204	+	15.7195i	0.159542	+	0.595420i
$698$		−	8.59758i		−	0.325423i
$699$	6.66791	+	6.42368i	0.252203	+	0.242966i
$700$	2.42935	−	1.95852i	0.0918210	−	0.0740251i
$701$	14.3867			0.543379			0.271689	−	0.962385i	$-0.412418\pi$
$701$	14.3867			0.543379			0.271689	+	0.962385i	$0.412418\pi$
$702$	13.2557	−	13.2395i	0.500305	−	0.499694i
$703$	16.8977	−	29.2678i	0.637311	−	1.10385i
$704$	2.50831	−	2.50831i	0.0945356	−	0.0945356i
$705$	−9.39791	+	37.8865i	−0.353946	+	1.42689i
$706$	−23.9457	−	13.8250i	−0.901207	−	0.520312i
$707$	11.1959	−	9.02600i	0.421064	−	0.339458i
$708$	−9.05327	−	15.0263i	−0.340243	−	0.564723i
$709$	25.8555	−	25.8555i	0.971025	−	0.971025i	−0.0285670	−	0.999592i	$-0.509094\pi$
$709$	25.8555	−	25.8555i	0.971025	−	0.971025i	0.999592	+	0.0285670i	$0.00909440\pi$
$710$	−11.1239	+	2.98063i	−0.417472	+	0.111861i
$711$	31.3175	+	16.5555i	1.17450	+	0.620882i
$712$	2.44124	+	1.40945i	0.0914894	+	0.0528215i
$713$	−1.43078	+	5.33973i	−0.0535830	+	0.199974i
$714$	2.00697	+	11.4473i	0.0751089	+	0.428405i
$715$	24.4749	−	5.09470i	0.915309	−	0.190531i
$716$	−1.76722	+	1.02031i	−0.0660441	+	0.0381306i
$717$	−2.10687	+	3.81167i	−0.0786826	+	0.142350i
$718$	−6.52681			−0.243578
$719$	−19.1730			−0.715034			−0.357517	−	0.933907i	$-0.616377\pi$
$719$	−19.1730			−0.715034			−0.357517	+	0.933907i	$0.616377\pi$
$720$	1.30537	−	5.71673i	0.0486484	−	0.213050i
$721$	11.6022	−	30.0294i	0.432088	−	1.11835i
$722$	17.8303	−	4.77761i	0.663574	−	0.177804i
$723$	−1.32613	+	0.0247392i	−0.0493194	+	0.000920059i
$724$	1.88845	+	3.27088i	0.0701835	+	0.121561i
$725$	−10.6392			−0.395128
$726$	2.34890	−	1.41520i	0.0871758	−	0.0525230i
$727$		−	50.2236i		−	1.86269i	−0.364138	−	0.931345i	$-0.618636\pi$
$727$		−	50.2236i		−	1.86269i	0.364138	−	0.931345i	$-0.381364\pi$
$728$	−3.93558	+	8.68972i	−0.145862	+	0.322062i
$729$	−3.01547	−	26.8311i	−0.111684	−	0.993744i
$730$	20.2534	−	5.42688i	0.749612	−	0.200858i
$731$			12.9611i			0.479385i
$732$	13.4806	−	13.9931i	0.498256	−	0.517199i
$733$	−7.69817	+	28.7300i	−0.284338	+	1.06117i	0.664983	+	0.746858i	$0.268439\pi$
$733$	−7.69817	+	28.7300i	−0.284338	+	1.06117i	−0.949321	+	0.314307i	$0.898228\pi$
$734$	−4.59499	−	17.1488i	−0.169604	−	0.632972i
$735$	4.59514	−	23.2488i	0.169494	−	0.857545i
$736$	4.69822	−	4.69822i	0.173179	−	0.173179i
$737$			42.2555i			1.55650i
$738$	10.2405	+	16.3011i	0.376959	+	0.600052i
$739$	15.2737	−	15.2737i	0.561853	−	0.561853i	−0.367980	−	0.929834i	$-0.619951\pi$
$739$	15.2737	−	15.2737i	0.561853	−	0.561853i	0.929834	+	0.367980i	$0.119951\pi$
$740$	5.39651	+	9.34702i	0.198380	+	0.343603i
$741$	−28.0320	+	25.9830i	−1.02978	+	0.954509i
$742$	−6.02534	−	13.6127i	−0.221197	−	0.499738i
$743$	−35.6490	−	9.55213i	−1.30784	−	0.350434i	−0.463428	−	0.886134i	$-0.653381\pi$
$743$	−35.6490	−	9.55213i	−1.30784	−	0.350434i	−0.844408	+	0.535701i	$0.820048\pi$
$744$	1.39869	+	0.346951i	0.0512784	+	0.0127198i
$745$	−35.7868	+	20.6615i	−1.31113	+	0.756979i
$746$	−4.09742	−	15.2918i	−0.150017	−	0.559872i
$747$	−0.811955	+	3.55587i	−0.0297079	+	0.130102i
$748$	−2.32842	−	8.68978i	−0.0851354	−	0.317730i
$749$	18.5281	−	2.89327i	0.677000	−	0.105718i
$750$	−5.03679	+	20.3052i	−0.183917	+	0.741441i
$751$	12.7984	+	7.38914i	0.467019	+	0.269633i	0.714991	−	0.699134i	$-0.246431\pi$
$751$	12.7984	+	7.38914i	0.467019	+	0.269633i	−0.247972	+	0.968767i	$0.579764\pi$
$752$	8.15290	+	8.15290i	0.297306	+	0.297306i
$753$	3.50570	−	14.1328i	0.127755	−	0.515027i
$754$	29.0409	−	14.6434i	1.05761	−	0.533282i
$755$		−	4.66318i		−	0.169710i
$756$	6.25878	+	12.2404i	0.227630	+	0.445179i
$757$	10.7098	+	18.5499i	0.389255	+	0.674209i	0.992349	−	0.123461i	$-0.0393993\pi$
$757$	10.7098	+	18.5499i	0.389255	+	0.674209i	−0.603095	+	0.797669i	$0.706066\pi$
$758$	6.97379			0.253300
$759$	34.9670	−	21.0674i	1.26922	−	0.764699i
$760$	−3.09627	+	11.5554i	−0.112314	+	0.419160i
$761$	21.5002	+	21.5002i	0.779382	+	0.779382i	0.979726	−	0.200343i	$-0.0642058\pi$
$761$	21.5002	+	21.5002i	0.779382	+	0.779382i	−0.200343	+	0.979726i	$0.564206\pi$
$762$	19.4326	+	10.7412i	0.703968	+	0.389113i
$763$	−12.8864	+	17.6558i	−0.466521	+	0.639183i
$764$	−4.95076	−	8.57497i	−0.179112	−	0.310231i
$765$	−10.9006	−	10.1162i	−0.394112	−	0.365751i
$766$	−29.0654	−	16.7809i	−1.05018	−	0.606319i
$767$	−30.5429	−	20.0181i	−1.10284	−	0.722811i
$768$	−1.24738	−	1.20169i	−0.0450108	−	0.0433622i
$769$	−4.68811	+	17.4963i	−0.169058	+	0.630931i	0.828430	+	0.560092i	$0.189234\pi$
$769$	−4.68811	+	17.4963i	−0.169058	+	0.630931i	−0.997488	+	0.0708390i	$0.977432\pi$
$770$	−1.95720	+	18.2399i	−0.0705327	+	0.657321i
$771$	2.60591	−	10.5054i	0.0938494	−	0.378342i
$772$	−1.01017	+	3.76999i	−0.0363567	+	0.135685i
$773$	−26.1562	−	7.00854i	−0.940774	−	0.252080i	−0.244331	−	0.969692i	$-0.578568\pi$
$773$	−26.1562	−	7.00854i	−0.940774	−	0.252080i	−0.696443	+	0.717612i	$0.745235\pi$
$774$	4.51778	+	14.6512i	0.162388	+	0.526626i
$775$	−0.947866	−	0.253980i	−0.0340483	−	0.00912323i
$776$	6.23461	+	3.59956i	0.223810	+	0.129217i
$777$	−23.7695	−	8.67765i	−0.852727	−	0.311309i
$778$	−29.2847	−	7.84682i	−1.04991	−	0.281322i
$779$	−19.6371	−	34.0125i	−0.703572	−	1.21862i
$780$	−2.71008	−	11.9020i	−0.0970363	−	0.426159i
$781$	−10.4500	+	18.0999i	−0.373930	+	0.647665i
$782$	−4.36127	−	16.2765i	−0.155959	−	0.582046i
$783$	9.58016	−	45.8825i	0.342367	−	1.63971i
$784$	−5.18160	−	4.70649i	−0.185057	−	0.168089i
$785$	15.1266	−	15.1266i	0.539890	−	0.539890i
$786$	8.38355	+	4.63394i	0.299031	+	0.165287i
$787$	−29.7095	−	7.96064i	−1.05903	−	0.283766i	−0.313051	−	0.949736i	$-0.601351\pi$
$787$	−29.7095	−	7.96064i	−1.05903	−	0.283766i	−0.745979	+	0.665970i	$0.768018\pi$
$788$	−4.64694	+	1.24514i	−0.165540	+	0.0443564i
$789$	−14.2387	−	49.4324i	−0.506911	−	1.75984i
$790$	19.9881	−	11.5402i	0.711146	−	0.410581i
$791$	28.5500	−	4.45826i	1.01512	−	0.158517i
$792$	−5.66097	−	9.01126i	−0.201154	−	0.320201i
$793$	12.6607	−	38.4146i	0.449594	−	1.36414i
$794$	−15.4711	−	8.93222i	−0.549047	−	0.316992i
$795$	16.6716	+	9.21511i	0.591282	+	0.326826i
$796$	−4.39204	+	7.60724i	−0.155672	+	0.269632i
$797$	10.7972	−	18.7014i	0.382458	−	0.662436i	−0.608955	−	0.793205i	$-0.708411\pi$
$797$	10.7972	−	18.7014i	0.382458	−	0.662436i	0.991413	+	0.130768i	$0.0417444\pi$
$798$	−11.8285	−	25.4309i	−0.418723	−	0.900245i
$799$	28.2449	−	7.56819i	0.999231	−	0.267743i
$800$	0.833991	+	0.833991i	0.0294860	+	0.0294860i
$801$	5.75261	−	6.19867i	0.203258	−	0.219019i
$802$	−0.493453	−	0.854685i	−0.0174244	−	0.0301800i
$803$	19.0264	−	32.9547i	0.671428	−	1.16295i
$804$	20.6287	−	0.384831i	0.727518	−	0.0135719i
$805$	−3.66596	+	34.1645i	−0.129208	+	1.20414i
$806$	2.93689	−	0.611344i	0.103447	−	0.0215337i
$807$	29.7815	−	30.9137i	1.04836	−	1.08822i
$808$	3.84351	+	3.84351i	0.135214	+	0.135214i
$809$		−	44.1849i		−	1.55346i	−0.629835	−	0.776729i	$-0.716877\pi$
$809$		−	44.1849i		−	1.55346i	0.629835	−	0.776729i	$-0.283123\pi$
$810$	−15.8481	−	7.63570i	−0.556844	−	0.268291i
$811$	13.8741	+	13.8741i	0.487184	+	0.487184i	0.907416	−	0.420233i	$-0.138051\pi$
$811$	13.8741	+	13.8741i	0.487184	+	0.487184i	−0.420233	+	0.907416i	$0.638051\pi$
$812$	3.68220	+	23.5803i	0.129220	+	0.827505i
$813$	−23.8661	−	39.6122i	−0.837021	−	1.38926i
$814$	18.9199	+	5.06958i	0.663143	+	0.177689i
$815$	−34.5746	+	19.9616i	−1.21109	+	0.699226i
$816$	−4.22105	+	1.21585i	−0.147766	+	0.0425633i
$817$	−8.09563	−	30.2133i	−0.283230	−	1.05703i
$818$	6.43323			0.224932
$819$	22.7867	+	17.3138i	0.796231	+	0.604993i
$820$	12.5427			0.438010
$821$	2.07667	+	7.75025i	0.0724764	+	0.270486i	0.992649	−	0.121027i	$-0.0386187\pi$
$821$	2.07667	+	7.75025i	0.0724764	+	0.270486i	−0.920173	+	0.391512i	$0.871952\pi$
$822$	20.9485	−	6.03408i	0.730661	−	0.210463i
$823$	27.9738	−	16.1507i	0.975107	−	0.562978i	0.0743177	−	0.997235i	$-0.476322\pi$
$823$	27.9738	−	16.1507i	0.975107	−	0.562978i	0.900789	+	0.434256i	$0.142989\pi$
$824$	11.7531	+	3.14924i	0.409440	+	0.109709i
$825$	3.73972	+	6.20705i	0.130200	+	0.216102i
$826$	20.8619	−	16.8187i	0.725879	−	0.585196i
$827$	−10.5632	−	10.5632i	−0.367318	−	0.367318i	0.499180	−	0.866498i	$-0.333635\pi$
$827$	−10.5632	−	10.5632i	−0.367318	−	0.367318i	−0.866498	+	0.499180i	$0.833635\pi$
$828$	−10.6033	−	16.8786i	−0.368492	−	0.586573i
$829$			7.22444i			0.250915i	0.992099	+	0.125458i	$0.0400399\pi$
$829$			7.22444i			0.250915i	−0.992099	+	0.125458i	$0.959960\pi$
$830$	1.68039	+	1.68039i	0.0583271	+	0.0583271i
$831$	15.3746	−	15.9592i	0.533340	−	0.553617i
$832$	−3.42436	−	1.12860i	−0.118718	−	0.0391273i
$833$	−16.9076	+	5.41243i	−0.585813	+	0.187530i
$834$	17.7046	−	0.330281i	0.613060	−	0.0114367i
$835$	−2.64337	+	4.57845i	−0.0914776	+	0.158444i
$836$	10.8554	+	18.8021i	0.375442	+	0.650285i
$837$	1.94883	−	3.85907i	0.0673614	−	0.133389i
$838$	3.38544	+	3.38544i	0.116948	+	0.116948i
$839$	43.2150	−	11.5794i	1.49195	−	0.399766i	0.581554	−	0.813508i	$-0.302445\pi$
$839$	43.2150	−	11.5794i	1.49195	−	0.399766i	0.910395	+	0.413741i	$0.135778\pi$
$840$	8.92237	+	0.789370i	0.307851	+	0.0272359i
$841$	26.1848	−	45.3534i	0.902924	−	1.56391i
$842$	−0.334271	+	0.578974i	−0.0115197	+	0.0199528i
$843$	−13.4115	−	7.41311i	−0.461918	−	0.255321i
$844$	14.9482	+	8.63034i	0.514538	+	0.297068i
$845$	−15.8243	−	19.8813i	−0.544372	−	0.683938i
$846$	29.2898	−	18.4001i	1.00700	−	0.632610i
$847$	2.62908	+	3.26112i	0.0903362	+	0.112053i
$848$	4.87278	−	2.81330i	0.167332	−	0.0966092i
$849$	6.56506	+	22.7919i	0.225312	+	0.782215i
$850$	2.88927	−	0.774178i	0.0991012	−	0.0265541i
$851$	35.4382	+	9.49564i	1.21481	+	0.325506i
$852$	8.93135	+	4.93673i	0.305983	+	0.169130i
$853$	−28.3574	+	28.3574i	−0.970940	+	0.970940i	−0.999590	−	0.0286493i	$-0.990879\pi$
$853$	−28.3574	+	28.3574i	−0.970940	+	0.970940i	0.0286493	+	0.999590i	$0.490879\pi$
$854$	23.9737	+	17.4977i	0.820363	+	0.598759i
$855$	31.7287	+	16.7729i	1.08510	+	0.573621i
$856$	1.83446	+	6.84630i	0.0627006	+	0.234002i
$857$	−2.28469	+	3.95720i	−0.0780435	+	0.135175i	−0.902406	−	0.430887i	$-0.858201\pi$
$857$	−2.28469	+	3.95720i	−0.0780435	+	0.135175i	0.824362	+	0.566063i	$0.191534\pi$
$858$	−18.7512	−	11.7957i	−0.640156	−	0.402699i
$859$	22.8984	+	39.6613i	0.781285	+	1.35322i	0.931194	+	0.364525i	$0.118769\pi$
$859$	22.8984	+	39.6613i	0.781285	+	1.35322i	−0.149909	+	0.988700i	$0.547898\pi$
$860$	9.64900	+	2.58544i	0.329028	+	0.0881628i
$861$	−22.5448	+	18.8799i	−0.768325	+	0.643426i
$862$	−3.42487	−	1.97735i	−0.116651	−	0.0673488i
$863$	24.9390	+	6.68238i	0.848933	+	0.227471i	0.656956	−	0.753929i	$-0.271844\pi$
$863$	24.9390	+	6.68238i	0.848933	+	0.227471i	0.191976	+	0.981400i	$0.438510\pi$
$864$	−4.34765	+	2.84569i	−0.147910	+	0.0968124i
$865$	16.2019	+	4.34128i	0.550880	+	0.147608i
$866$	5.76908	−	21.5305i	0.196041	−	0.731636i
$867$	4.40696	−	17.7661i	0.149668	−	0.603369i
$868$	−0.234856	+	2.18872i	−0.00797155	+	0.0742899i
$869$	10.8410	−	40.4593i	0.367757	−	1.37249i
$870$	−21.9934	−	21.1878i	−0.745645	−	0.718334i
$871$	38.3501	−	19.3374i	1.29944	−	0.655223i
$872$	−7.15483	−	4.13084i	−0.242293	−	0.139888i
$873$	14.6914	−	15.8306i	0.497229	−	0.535784i
$874$	20.3329	+	35.2175i	0.687769	+	1.19125i
$875$	−31.7743	−	3.40948i	−1.07417	−	0.115261i
$876$	−16.2614	−	8.98838i	−0.549423	−	0.303689i
$877$	−6.46471	−	6.46471i	−0.218298	−	0.218298i	0.589483	−	0.807781i	$-0.299332\pi$
$877$	−6.46471	−	6.46471i	−0.218298	−	0.218298i	−0.807781	+	0.589483i	$0.799332\pi$
$878$	−3.97693	+	14.8421i	−0.134215	+	0.500897i
$879$	6.81584	−	4.10651i	0.229893	−	0.138509i
$880$	−6.93362			−0.233732
$881$	−9.57090	−	16.5773i	−0.322452	−	0.558503i	0.658542	−	0.752544i	$-0.271174\pi$
$881$	−9.57090	−	16.5773i	−0.322452	−	0.558503i	−0.980993	+	0.194042i	$0.937840\pi$
$882$	−17.2256	+	12.0115i	−0.580018	+	0.404450i
$883$			40.2359i			1.35405i	0.735962	+	0.677023i	$0.236730\pi$
$883$			40.2359i			1.35405i	−0.735962	+	0.677023i	$0.763270\pi$
$884$	−6.82107	+	6.08992i	−0.229418	+	0.204826i
$885$	−8.25551	+	33.2811i	−0.277506	+	1.11873i
$886$	17.5321	+	17.5321i	0.589004	+	0.589004i
$887$	14.8553	+	8.57674i	0.498794	+	0.287979i	0.728215	−	0.685348i	$-0.240350\pi$
$887$	14.8553	+	8.57674i	0.498794	+	0.287979i	−0.229422	+	0.973327i	$0.573683\pi$
$888$	2.30261	−	9.28268i	0.0772705	−	0.311506i
$889$	−12.2234	+	31.6373i	−0.409960	+	1.06108i
$890$	−1.42607	−	5.32216i	−0.0478019	−	0.178399i
$891$	−30.1360	+	10.5387i	−1.00959	+	0.353059i
$892$	−4.00258	−	14.9378i	−0.134016	−	0.500155i
$893$	−61.1135	+	35.2839i	−2.04509	+	1.18073i
$894$	35.5405	+	8.81596i	1.18865	+	0.294850i
$895$	3.85272	+	1.03233i	0.128782	+	0.0345071i
$896$	1.55978	−	2.13707i	0.0521087	−	0.0713945i
$897$	−35.1222	−	22.0941i	−1.17270	−	0.737700i
$898$	13.0007	+	22.5179i	0.433840	+	0.751433i
$899$	5.30692	−	5.30692i	0.176996	−	0.176996i
$900$	2.99616	−	1.88222i	0.0998720	−	0.0627407i
$901$		−	14.2697i		−	0.475392i
$902$	16.0957	−	16.0957i	0.535928	−	0.535928i
$903$	−21.2353	+	9.87698i	−0.706665	+	0.328685i
$904$	2.82673	+	10.5495i	0.0940156	+	0.350871i
$905$	1.91071	−	7.13086i	0.0635141	−	0.237038i
$906$	−2.86688	+	2.97588i	−0.0952458	+	0.0988670i
$907$		−	7.66628i		−	0.254555i	−0.991867	−	0.127277i	$-0.959376\pi$
$907$		−	7.66628i		−	0.254555i	0.991867	−	0.127277i	$-0.0406238\pi$
$908$	18.7758	−	5.03096i	0.623097	−	0.166958i
$909$	13.8080	−	8.67436i	0.457984	−	0.287710i
$910$	17.4498	−	6.57083i	0.578455	−	0.217821i
$911$		−	57.7098i		−	1.91201i	−0.293347	−	0.956006i	$-0.594769\pi$
$911$		−	57.7098i		−	1.91201i	0.293347	−	0.956006i	$-0.405231\pi$
$912$	9.08013	−	5.47073i	0.300673	−	0.181154i
$913$	4.31278			0.142732
$914$	−8.88752	−	15.3936i	−0.293973	−	0.509177i
$915$	−37.9721	+	0.708374i	−1.25532	+	0.0234181i
$916$	−5.16146	+	1.38301i	−0.170539	+	0.0456959i
$917$	−5.27339	+	13.6489i	−0.174143	+	0.450726i
$918$	0.737042	+	13.1574i	0.0243260	+	0.434259i
$919$	−8.40333			−0.277200			−0.138600	−	0.990348i	$-0.544260\pi$
$919$	−8.40333			−0.277200			−0.138600	+	0.990348i	$0.544260\pi$
$920$	−12.9871			−0.428172
$921$	−6.42994	+	11.6328i	−0.211874	+	0.383314i
$922$	−26.5904	+	15.3520i	−0.875708	+	0.505590i
$923$	21.2093	+	1.20109i	0.698111	+	0.0395342i
$924$	12.4628	−	10.4368i	0.409995	−	0.343347i
$925$	−1.68559	+	6.29070i	−0.0554218	+	0.206837i
$926$	−5.76684	−	3.32948i	−0.189510	−	0.109414i
$927$	17.0598	−	32.2714i	0.560318	−	1.05993i
$928$	−8.71314	+	2.33468i	−0.286023	+	0.0766396i
$929$	−25.8682	+	25.8682i	−0.848708	+	0.848708i	−0.989972	−	0.141264i	$-0.954883\pi$
$929$	−25.8682	+	25.8682i	−0.848708	+	0.848708i	0.141264	+	0.989972i	$0.454883\pi$
$930$	−1.45364	−	2.41270i	−0.0476667	−	0.0791155i
$931$	36.0321	−	23.1774i	1.18090	−	0.759608i
$932$	−4.62938	−	2.67277i	−0.151640	−	0.0875496i
$933$	6.15909	−	24.8296i	0.201640	−	0.812885i
$934$	18.0733	−	18.0733i	0.591377	−	0.591377i
$935$	−8.79222	+	15.2286i	−0.287536	+	0.498027i
$936$	−5.58777	+	9.26158i	−0.182642	+	0.302724i
$937$	−28.6653			−0.936453			−0.468227	−	0.883608i	$-0.655107\pi$
$937$	−28.6653			−0.936453			−0.468227	+	0.883608i	$0.655107\pi$
$938$	4.86255	+	31.1390i	0.158768	+	1.01672i
$939$	−22.7399	−	21.9070i	−0.742089	−	0.714908i
$940$		−	22.5367i		−	0.735067i
$941$	9.55863	+	35.6733i	0.311602	+	1.16292i	0.927111	+	0.374786i	$0.122284\pi$
$941$	9.55863	+	35.6733i	0.311602	+	1.16292i	−0.615509	+	0.788130i	$0.711050\pi$
$942$	−18.9530	+	0.353569i	−0.617521	+	0.0115199i
$943$	30.1482	−	30.1482i	0.981761	−	0.981761i
$944$	7.16184	+	7.16184i	0.233098	+	0.233098i
$945$	8.26738	−	25.5683i	0.268938	−	0.831736i
$946$	15.7001	−	9.06445i	0.510454	−	0.294711i
$947$	3.12253	−	0.836680i	0.101469	−	0.0271884i	−0.207727	−	0.978187i	$-0.566607\pi$
$947$	3.12253	−	0.836680i	0.101469	−	0.0271884i	0.309196	+	0.950998i	$0.399940\pi$
$948$	−19.8506	−	4.92401i	−0.644716	−	0.159925i
$949$	−38.6160	−	2.18683i	−1.25353	−	0.0709876i
$950$	−6.25153	+	3.60932i	−0.202826	+	0.117102i
$951$	−43.6968	+	0.815168i	−1.41696	+	0.0264336i
$952$	−2.71584	−	6.13574i	−0.0880207	−	0.198860i
$953$	−22.8899	+	39.6465i	−0.741477	+	1.28428i	0.210346	+	0.977627i	$0.432541\pi$
$953$	−22.8899	+	39.6465i	−0.741477	+	1.28428i	−0.951823	+	0.306649i	$0.900792\pi$
$954$	−4.97390	−	16.1304i	−0.161036	−	0.522240i
$955$	−5.00912	+	18.6943i	−0.162091	+	0.604933i
$956$	0.650794	−	2.42880i	0.0210482	−	0.0785529i
$957$	−55.4131	+	1.03374i	−1.79125	+	0.0334160i
$958$	4.21295	−	7.29704i	0.136114	−	0.235757i
$959$	13.4783	+	30.4507i	0.435237	+	0.983306i
$960$	0.0631461	+	3.38492i	0.00203803	+	0.109248i
$961$	−26.2473	+	15.1539i	−0.846687	+	0.488835i
$962$	−4.05731	−	19.4913i	−0.130813	−	0.628423i
$963$	21.2487	−	0.793068i	0.684728	−	0.0255563i
$964$	0.739683	−	0.198197i	0.0238236	−	0.00638351i
$965$	6.60680	−	3.81444i	0.212680	−	0.122791i
$966$	23.3436	−	19.5488i	0.751067	−	0.628973i
$967$	11.8127	+	11.8127i	0.379871	+	0.379871i	0.871055	−	0.491185i	$-0.163436\pi$
$967$	11.8127	+	11.8127i	0.379871	+	0.379871i	−0.491185	+	0.871055i	$0.663436\pi$
$968$	−1.11953	+	1.11953i	−0.0359831	+	0.0359831i
$969$	−0.501454	−	26.8802i	−0.0161090	−	0.863517i
$970$	−3.64199	−	13.5921i	−0.116937	−	0.436416i
$971$		−	6.23460i		−	0.200078i	−0.994984	−	0.100039i	$-0.968103\pi$
$971$		−	6.23460i		−	0.200078i	0.994984	−	0.100039i	$-0.0318967\pi$
$972$	5.41934	+	14.6161i	0.173825	+	0.468812i
$973$	4.17328	+	26.7250i	0.133789	+	0.856766i
$974$	−18.8480			−0.603927
$975$	3.92196	−	6.23461i	0.125603	−	0.199667i
$976$	−5.60901	+	9.71509i	−0.179540	+	0.310972i
$977$	−3.69824	+	3.69824i	−0.118317	+	0.118317i	−0.763786	−	0.645469i	$-0.776662\pi$
$977$	−3.69824	+	3.69824i	−0.118317	+	0.118317i	0.645469	+	0.763786i	$0.276662\pi$
$978$	34.3366	+	8.51734i	1.09796	+	0.272354i
$979$	−8.65979	−	4.99973i	−0.276768	−	0.159792i
$980$	0.656653	+	13.6666i	0.0209760	+	0.436564i
$981$	−16.8598	+	18.1672i	−0.538293	+	0.580033i
$982$	−11.1398	+	11.1398i	−0.355486	+	0.355486i
$983$	−5.49935	+	1.47355i	−0.175402	+	0.0469988i	−0.345451	−	0.938437i	$-0.612274\pi$
$983$	−5.49935	+	1.47355i	−0.175402	+	0.0469988i	0.170049	+	0.985436i	$0.445607\pi$
$984$	−8.00433	−	7.71116i	−0.255169	−	0.245823i
$985$	8.14362	+	4.70172i	0.259477	+	0.149809i
$986$	−5.92101	+	22.0975i	−0.188563	+	0.703728i
$987$	33.9234	+	40.5085i	1.07979	+	1.28940i
$988$	12.0966	−	18.4565i	0.384843	−	0.587180i
$989$	29.4073	−	16.9783i	0.935096	−	0.539878i
$990$	−4.63053	+	20.2789i	−0.147168	+	0.644506i
$991$	−40.2728			−1.27931			−0.639653	−	0.768663i	$-0.720922\pi$
$991$	−40.2728			−1.27931			−0.639653	+	0.768663i	$0.720922\pi$
$992$	−0.832007			−0.0264162
$993$	29.5034	+	16.3078i	0.936262	+	0.517511i
$994$	−5.61797	+	14.5407i	−0.178191	+	0.461204i
$995$	16.5846	−	4.44382i	0.525766	−	0.140879i
$996$	−0.0392775	−	2.10546i	−0.00124456	−	0.0667139i
$997$	−0.675765	−	1.17046i	−0.0214017	−	0.0370688i	0.855126	−	0.518420i	$-0.173480\pi$
$997$	−0.675765	−	1.17046i	−0.0214017	−	0.0370688i	−0.876528	+	0.481351i	$0.840146\pi$
$998$	12.7623			0.403984
$999$	−25.6115	−	12.9338i	−0.810312	−	0.409208i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	546.2.bw.a.11.18	✓	152
3.2	odd	2	inner	546.2.bw.a.11.37	yes	152
7.2	even	3		546.2.ch.a.401.8	yes	152
13.6	odd	12		546.2.ch.a.305.25	yes	152
21.2	odd	6		546.2.ch.a.401.25	yes	152
39.32	even	12		546.2.ch.a.305.8	yes	152
91.58	odd	12	inner	546.2.bw.a.149.37	yes	152
273.149	even	12	inner	546.2.bw.a.149.18	yes	152

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
546.2.bw.a.11.18	✓	152	1.1	even	1	trivial
546.2.bw.a.11.37	yes	152	3.2	odd	2	inner
546.2.bw.a.149.18	yes	152	273.149	even	12	inner
546.2.bw.a.149.37	yes	152	91.58	odd	12	inner
546.2.ch.a.305.8	yes	152	39.32	even	12
546.2.ch.a.305.25	yes	152	13.6	odd	12
546.2.ch.a.401.8	yes	152	7.2	even	3
546.2.ch.a.401.25	yes	152	21.2	odd	6

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:	\( N \)	\(=\)	\( 546 = 2 \cdot 3 \cdot 7 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	546.bw (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.66438 - 0.479415i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.88802 + 0.505894i) q^{5} +(-0.893853 - 1.48359i) q^{6} +(2.05975 - 1.66055i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.54032 - 1.59586i) q^{9} +O(q^{10})\)	\(q+(-0.258819 - 0.965926i) q^{2} +(1.66438 - 0.479415i) q^{3} +(-0.866025 + 0.500000i) q^{4} +(1.88802 + 0.505894i) q^{5} +(-0.893853 - 1.48359i) q^{6} +(2.05975 - 1.66055i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.54032 - 1.59586i) q^{9} -1.95463i q^{10} +(-2.50831 - 2.50831i) q^{11} +(-1.20169 + 1.24738i) q^{12} +(-1.12860 + 3.42436i) q^{13} +(-2.13707 - 1.55978i) q^{14} +(3.38492 - 0.0631461i) q^{15} +(0.500000 - 0.866025i) q^{16} +(-1.26806 - 2.19634i) q^{17} +(-2.19896 - 2.04072i) q^{18} +(4.32777 + 4.32777i) q^{19} +(-1.88802 + 0.505894i) q^{20} +(2.63212 - 3.75126i) q^{21} +(-1.77364 + 3.07204i) q^{22} +(-3.32215 + 5.75413i) q^{23} +(1.51589 + 0.837897i) q^{24} +(-1.02143 - 0.589721i) q^{25} +(3.59978 + 0.203857i) q^{26} +(3.46298 - 3.87398i) q^{27} +(-0.953521 + 2.46795i) q^{28} +(7.81199 - 4.51025i) q^{29} +(-0.937076 - 3.25324i) q^{30} +(0.803657 - 0.215339i) q^{31} +(-0.965926 - 0.258819i) q^{32} +(-5.37731 - 2.97226i) q^{33} +(-1.79330 + 1.79330i) q^{34} +(4.72892 - 2.09314i) q^{35} +(-1.40206 + 2.65221i) q^{36} +(-1.42914 - 5.33363i) q^{37} +(3.06020 - 5.30042i) q^{38} +(-0.236734 + 6.24051i) q^{39} +(0.977313 + 1.69275i) q^{40} +(-6.19829 - 1.66083i) q^{41} +(-4.30468 - 1.57153i) q^{42} +(-4.42594 - 2.55532i) q^{43} +(3.42642 + 0.918106i) q^{44} +(5.60352 - 1.72788i) q^{45} +(6.41789 + 1.71967i) q^{46} +(-2.98417 + 11.1371i) q^{47} +(0.417005 - 1.68110i) q^{48} +(1.48514 - 6.84064i) q^{49} +(-0.305262 + 1.13925i) q^{50} +(-3.16348 - 3.04761i) q^{51} +(-0.734782 - 3.52989i) q^{52} +(4.87278 + 2.81330i) q^{53} +(-4.63827 - 2.34233i) q^{54} +(-3.46681 - 6.00469i) q^{55} +(2.63065 + 0.282277i) q^{56} +(9.27786 + 5.12826i) q^{57} +(-6.37846 - 6.37846i) q^{58} +(-2.62141 + 9.78325i) q^{59} +(-2.89985 + 1.74715i) q^{60} -11.2180 q^{61} +(-0.416003 - 0.720539i) q^{62} +(2.58243 - 7.50540i) q^{63} +1.00000i q^{64} +(-3.86319 + 5.89432i) q^{65} +(-1.47924 + 5.96336i) q^{66} +(-8.42310 - 8.42310i) q^{67} +(2.19634 + 1.26806i) q^{68} +(-2.77070 + 11.1697i) q^{69} +(-3.24575 - 4.02604i) q^{70} +(-1.52491 - 5.69106i) q^{71} +(2.92472 + 0.667838i) q^{72} +(2.77643 + 10.3618i) q^{73} +(-4.78200 + 2.76089i) q^{74} +(-1.98276 - 0.491832i) q^{75} +(-5.91185 - 1.58408i) q^{76} +(-9.33168 - 1.00132i) q^{77} +(6.08914 - 1.38649i) q^{78} +(5.90403 + 10.2261i) q^{79} +(1.38213 - 1.38213i) q^{80} +(3.90648 - 8.10799i) q^{81} +6.41694i q^{82} +(-0.859699 + 0.859699i) q^{83} +(-0.403847 + 4.56475i) q^{84} +(-1.28300 - 4.78824i) q^{85} +(-1.32273 + 4.93650i) q^{86} +(10.8398 - 11.2520i) q^{87} -3.54729i q^{88} +(2.72285 - 0.729586i) q^{89} +(-3.11930 - 4.96538i) q^{90} +(3.36169 + 8.92743i) q^{91} -6.64429i q^{92} +(1.23435 - 0.743691i) q^{93} +11.5299 q^{94} +(5.98154 + 10.3603i) q^{95} +(-1.73175 + 0.0323060i) q^{96} +(6.95381 - 1.86327i) q^{97} +(-6.99193 + 0.335948i) q^{98} +(-10.3748 - 2.36901i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 152 q + 12 q^{7}+O(q^{10}) \) 152 * q + 12 * q^7	\( 152 q + 12 q^{7} + 76 q^{16} - 8 q^{18} + 12 q^{19} + 8 q^{21} + 24 q^{27} + 16 q^{28} - 12 q^{31} - 48 q^{33} + 24 q^{36} - 36 q^{37} - 8 q^{39} + 84 q^{43} - 40 q^{45} - 16 q^{46} - 28 q^{49} + 4 q^{52} + 24 q^{54} + 16 q^{55} - 8 q^{57} - 16 q^{58} + 64 q^{61} - 100 q^{63} + 16 q^{66} - 112 q^{67} + 84 q^{69} + 16 q^{72} - 120 q^{73} - 48 q^{76} - 8 q^{78} + 32 q^{79} + 48 q^{81} - 8 q^{84} - 152 q^{85} + 48 q^{87} + 16 q^{91} - 12 q^{93} - 64 q^{94} - 100 q^{97} + 16 q^{99}+O(q^{100}) \) 152 * q + 12 * q^7 + 76 * q^16 - 8 * q^18 + 12 * q^19 + 8 * q^21 + 24 * q^27 + 16 * q^28 - 12 * q^31 - 48 * q^33 + 24 * q^36 - 36 * q^37 - 8 * q^39 + 84 * q^43 - 40 * q^45 - 16 * q^46 - 28 * q^49 + 4 * q^52 + 24 * q^54 + 16 * q^55 - 8 * q^57 - 16 * q^58 + 64 * q^61 - 100 * q^63 + 16 * q^66 - 112 * q^67 + 84 * q^69 + 16 * q^72 - 120 * q^73 - 48 * q^76 - 8 * q^78 + 32 * q^79 + 48 * q^81 - 8 * q^84 - 152 * q^85 + 48 * q^87 + 16 * q^91 - 12 * q^93 - 64 * q^94 - 100 * q^97 + 16 * q^99

Introduction

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