LMFDB - Embedded newform 930.2.z.d.349.11

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(109,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 5, 2]))

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

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

chi := DirichletCharacter("930.109");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.z (of order $10$, 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:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$72$
Relative dimension:	$18$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			349.11
Character	$\chi$	$=$	930.349
Dual form			930.2.z.d.469.11

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.16020 - 0.577517i) q^{5} +1.00000 q^{6} +(-2.84298 + 3.91303i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.16020 - 0.577517i) q^{5} +1.00000 q^{6} +(-2.84298 + 3.91303i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-1.87601 - 1.21679i) q^{10} +(-4.06169 - 2.95099i) q^{11} +(0.951057 + 0.309017i) q^{12} +(-3.01750 + 0.980445i) q^{13} +(-3.91303 + 2.84298i) q^{14} +(-2.23294 + 0.118288i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.37230 - 3.26519i) q^{17} +(0.951057 - 0.309017i) q^{18} +(-2.13430 + 6.56870i) q^{19} +(-1.40818 - 1.73696i) q^{20} +(-1.49464 + 4.60004i) q^{21} +(-2.95099 - 4.06169i) q^{22} +(2.30085 + 3.16685i) q^{23} +(0.809017 + 0.587785i) q^{24} +(4.33295 + 2.49511i) q^{25} -3.17279 q^{26} +(0.587785 - 0.809017i) q^{27} +(-4.60004 + 1.49464i) q^{28} +(-0.619555 + 1.90680i) q^{29} +(-2.16020 - 0.577517i) q^{30} +(-5.14971 - 2.11671i) q^{31} +1.00000i q^{32} +(-4.77480 - 1.55143i) q^{33} +(-1.24719 - 3.83847i) q^{34} +(8.40126 - 6.81106i) q^{35} +1.00000 q^{36} -3.60356i q^{37} +(-4.05968 + 5.58767i) q^{38} +(-2.56684 + 1.86492i) q^{39} +(-0.802514 - 2.08710i) q^{40} +(2.28478 - 7.03185i) q^{41} +(-2.84298 + 3.91303i) q^{42} +(11.4334 + 3.71495i) q^{43} +(-1.55143 - 4.77480i) q^{44} +(-2.08710 + 0.802514i) q^{45} +(1.20963 + 3.72285i) q^{46} +(-1.46040 + 0.474514i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-5.06613 - 15.5920i) q^{49} +(3.34985 + 3.71194i) q^{50} +(-3.26519 - 2.37230i) q^{51} +(-3.01750 - 0.980445i) q^{52} +(6.36945 + 8.76680i) q^{53} +(0.809017 - 0.587785i) q^{54} +(7.06982 + 8.72043i) q^{55} -4.83677 q^{56} +6.90674i q^{57} +(-1.17846 + 1.62202i) q^{58} +(0.287936 + 0.886175i) q^{59} +(-1.87601 - 1.21679i) q^{60} -11.1468 q^{61} +(-4.24357 - 3.60446i) q^{62} +4.83677i q^{63} +(-0.309017 + 0.951057i) q^{64} +(7.08464 - 0.375301i) q^{65} +(-4.06169 - 2.95099i) q^{66} +3.35915i q^{67} -4.03600i q^{68} +(3.16685 + 2.30085i) q^{69} +(10.0948 - 3.88157i) q^{70} +(-9.12291 + 6.62818i) q^{71} +(0.951057 + 0.309017i) q^{72} +(-1.44366 + 1.98703i) q^{73} +(1.11356 - 3.42719i) q^{74} +(4.89191 + 1.03404i) q^{75} +(-5.58767 + 4.05968i) q^{76} +(23.0946 - 7.50390i) q^{77} +(-3.01750 + 0.980445i) q^{78} +(-6.66791 + 4.84452i) q^{79} +(-0.118288 - 2.23294i) q^{80} +(0.309017 - 0.951057i) q^{81} +(4.34592 - 5.98164i) q^{82} +(-6.20586 - 2.01641i) q^{83} +(-3.91303 + 2.84298i) q^{84} +(3.23895 + 8.42353i) q^{85} +(9.72586 + 7.06625i) q^{86} +2.00492i q^{87} -5.02052i q^{88} +(13.9569 + 10.1403i) q^{89} +(-2.23294 + 0.118288i) q^{90} +(4.74219 - 14.5950i) q^{91} +3.91444i q^{92} +(-5.55177 - 0.421763i) q^{93} -1.53556 q^{94} +(8.40406 - 12.9571i) q^{95} +(0.309017 + 0.951057i) q^{96} +(0.0295729 - 0.0407037i) q^{97} -16.3944i q^{98} -5.02052 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	$ 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) $ 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/930\mathbb{Z}\right)^\times$.

$n$	$187$	$311$	$871$
$\chi(n)$	$-1$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$2$	0.951057	+	0.309017i	0.672499	+	0.218508i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$3$	0.951057	−	0.309017i	0.549093	−	0.178411i
$4$	0.809017	+	0.587785i	0.404508	+	0.293893i
$5$	−2.16020	−	0.577517i	−0.966072	−	0.258274i
$5$	−2.16020	−	0.577517i	−0.966072	−	0.258274i
$6$	1.00000			0.408248
$7$	−2.84298	+	3.91303i	−1.07455	+	1.47899i	−0.209160	+	0.977881i	$0.567073\pi$
$7$	−2.84298	+	3.91303i	−1.07455	+	1.47899i	−0.865387	+	0.501105i	$0.832927\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	−1.87601	−	1.21679i	−0.593247	−	0.384783i
$11$	−4.06169	−	2.95099i	−1.22464	−	0.889757i	−0.228168	−	0.973622i	$-0.573274\pi$
$11$	−4.06169	−	2.95099i	−1.22464	−	0.889757i	−0.996477	+	0.0838651i	$0.973274\pi$
$12$	0.951057	+	0.309017i	0.274546	+	0.0892055i
$13$	−3.01750	+	0.980445i	−0.836904	+	0.271927i	−0.695951	−	0.718090i	$-0.745017\pi$
$13$	−3.01750	+	0.980445i	−0.836904	+	0.271927i	−0.140953	+	0.990016i	$0.545017\pi$
$14$	−3.91303	+	2.84298i	−1.04580	+	0.759819i
$15$	−2.23294	+	0.118288i	−0.576542	+	0.0305417i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	−2.37230	−	3.26519i	−0.575368	−	0.791926i	0.417810	−	0.908534i	$-0.362798\pi$
$17$	−2.37230	−	3.26519i	−0.575368	−	0.791926i	−0.993178	+	0.116608i	$0.962798\pi$
$18$	0.951057	−	0.309017i	0.224166	−	0.0728360i
$19$	−2.13430	+	6.56870i	−0.489642	+	1.50696i	0.335501	+	0.942040i	$0.391095\pi$
$19$	−2.13430	+	6.56870i	−0.489642	+	1.50696i	−0.825143	+	0.564924i	$0.808905\pi$
$20$	−1.40818	−	1.73696i	−0.314880	−	0.388395i
$21$	−1.49464	+	4.60004i	−0.326158	+	1.00381i
$22$	−2.95099	−	4.06169i	−0.629153	−	0.865955i
$23$	2.30085	+	3.16685i	0.479760	+	0.660334i	0.978459	−	0.206442i	$-0.0661885\pi$
$23$	2.30085	+	3.16685i	0.479760	+	0.660334i	−0.498698	+	0.866776i	$0.666188\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	4.33295	+	2.49511i	0.866589	+	0.499022i
$26$	−3.17279			−0.622235
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−4.60004	+	1.49464i	−0.869326	+	0.282461i
$29$	−0.619555	+	1.90680i	−0.115049	+	0.354083i	−0.991957	−	0.126574i	$-0.959602\pi$
$29$	−0.619555	+	1.90680i	−0.115049	+	0.354083i	0.876909	+	0.480657i	$0.159602\pi$
$30$	−2.16020	−	0.577517i	−0.394397	−	0.105440i
$31$	−5.14971	−	2.11671i	−0.924916	−	0.380172i
$31$	−5.14971	−	2.11671i	−0.924916	−	0.380172i
$32$			1.00000i			0.176777i
$33$	−4.77480	−	1.55143i	−0.831186	−	0.270069i
$34$	−1.24719	−	3.83847i	−0.213892	−	0.658292i
$35$	8.40126	−	6.81106i	1.42007	−	1.15128i
$36$	1.00000			0.166667
$37$		−	3.60356i		−	0.592421i	−0.955123	−	0.296211i	$-0.904277\pi$
$37$		−	3.60356i		−	0.592421i	0.955123	−	0.296211i	$-0.0957230\pi$
$38$	−4.05968	+	5.58767i	−0.658567	+	0.906440i
$39$	−2.56684	+	1.86492i	−0.411023	+	0.298626i
$40$	−0.802514	−	2.08710i	−0.126889	−	0.329999i
$41$	2.28478	−	7.03185i	0.356823	−	1.09819i	−0.598121	−	0.801406i	$-0.704086\pi$
$41$	2.28478	−	7.03185i	0.356823	−	1.09819i	0.954945	−	0.296784i	$-0.0959141\pi$
$42$	−2.84298	+	3.91303i	−0.438682	+	0.603794i
$43$	11.4334	+	3.71495i	1.74358	+	0.566524i	0.995299	−	0.0968550i	$-0.0308783\pi$
$43$	11.4334	+	3.71495i	1.74358	+	0.566524i	0.748283	+	0.663379i	$0.230878\pi$
$44$	−1.55143	−	4.77480i	−0.233886	−	0.719828i
$45$	−2.08710	+	0.802514i	−0.311126	+	0.119632i
$46$	1.20963	+	3.72285i	0.178350	+	0.548905i
$47$	−1.46040	+	0.474514i	−0.213022	+	0.0692149i	−0.413584	−	0.910466i	$-0.635723\pi$
$47$	−1.46040	+	0.474514i	−0.213022	+	0.0692149i	0.200562	+	0.979681i	$0.435723\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	−5.06613	−	15.5920i	−0.723733	−	2.22742i
$50$	3.34985	+	3.71194i	0.473740	+	0.524948i
$51$	−3.26519	−	2.37230i	−0.457219	−	0.332189i
$52$	−3.01750	−	0.980445i	−0.418452	−	0.135963i
$53$	6.36945	+	8.76680i	0.874912	+	1.20421i	0.977804	+	0.209520i	$0.0671902\pi$
$53$	6.36945	+	8.76680i	0.874912	+	1.20421i	−0.102893	+	0.994692i	$0.532810\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	7.06982	+	8.72043i	0.953294	+	1.17586i
$56$	−4.83677			−0.646341
$57$			6.90674i			0.914821i
$58$	−1.17846	+	1.62202i	−0.154740	+	0.212981i
$59$	0.287936	+	0.886175i	0.0374861	+	0.115370i	0.968049	−	0.250763i	$-0.0806815\pi$
$59$	0.287936	+	0.886175i	0.0374861	+	0.115370i	−0.930562	+	0.366133i	$0.880681\pi$
$60$	−1.87601	−	1.21679i	−0.242192	−	0.157087i
$61$	−11.1468			−1.42720			−0.713601	−	0.700552i	$-0.752937\pi$
$61$	−11.1468			−1.42720			−0.713601	+	0.700552i	$0.752937\pi$
$62$	−4.24357	−	3.60446i	−0.538934	−	0.457767i
$63$			4.83677i			0.609376i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	7.08464	−	0.375301i	0.878741	−	0.0465504i
$66$	−4.06169	−	2.95099i	−0.499959	−	0.363242i
$67$			3.35915i			0.410385i	0.978722	+	0.205193i	$0.0657821\pi$
$67$			3.35915i			0.410385i	−0.978722	+	0.205193i	$0.934218\pi$
$68$		−	4.03600i		−	0.489437i
$69$	3.16685	+	2.30085i	0.381244	+	0.276990i
$70$	10.0948	−	3.88157i	1.20656	−	0.463937i
$71$	−9.12291	+	6.62818i	−1.08269	+	0.786620i	−0.978150	−	0.207900i	$-0.933337\pi$
$71$	−9.12291	+	6.62818i	−1.08269	+	0.786620i	−0.104540	+	0.994521i	$0.533337\pi$
$72$	0.951057	+	0.309017i	0.112083	+	0.0364180i
$73$	−1.44366	+	1.98703i	−0.168968	+	0.232564i	−0.885101	−	0.465400i	$-0.845911\pi$
$73$	−1.44366	+	1.98703i	−0.168968	+	0.232564i	0.716133	+	0.697964i	$0.245911\pi$
$74$	1.11356	−	3.42719i	0.129449	−	0.398402i
$75$	4.89191	+	1.03404i	0.564869	+	0.119400i
$76$	−5.58767	+	4.05968i	−0.640950	+	0.465677i
$77$	23.0946	−	7.50390i	2.63188	−	0.855148i
$78$	−3.01750	+	0.980445i	−0.341665	+	0.111014i
$79$	−6.66791	+	4.84452i	−0.750198	+	0.545051i	−0.895888	−	0.444280i	$-0.853460\pi$
$79$	−6.66791	+	4.84452i	−0.750198	+	0.545051i	0.145690	+	0.989330i	$0.453460\pi$
$80$	−0.118288	−	2.23294i	−0.0132249	−	0.249650i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	4.34592	−	5.98164i	0.479927	−	0.660562i
$83$	−6.20586	−	2.01641i	−0.681182	−	0.221329i	−0.0520689	−	0.998643i	$-0.516582\pi$
$83$	−6.20586	−	2.01641i	−0.681182	−	0.221329i	−0.629113	+	0.777314i	$0.716582\pi$
$84$	−3.91303	+	2.84298i	−0.426947	+	0.310195i
$85$	3.23895	+	8.42353i	0.351313	+	0.913660i
$86$	9.72586	+	7.06625i	1.04877	+	0.761973i
$87$			2.00492i			0.214950i
$88$		−	5.02052i		−	0.535189i
$89$	13.9569	+	10.1403i	1.47943	+	1.07487i	0.977741	+	0.209814i	$0.0672859\pi$
$89$	13.9569	+	10.1403i	1.47943	+	1.07487i	0.501684	+	0.865051i	$0.332714\pi$
$90$	−2.23294	+	0.118288i	−0.235372	+	0.0124686i
$91$	4.74219	−	14.5950i	0.497117	−	1.52997i
$92$			3.91444i			0.408109i
$93$	−5.55177	−	0.421763i	−0.575691	−	0.0437348i
$94$	−1.53556			−0.158381
$95$	8.40406	−	12.9571i	0.862239	−	1.32937i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	0.0295729	−	0.0407037i	0.00300268	−	0.00413283i	−0.807513	−	0.589850i	$-0.799187\pi$
$97$	0.0295729	−	0.0407037i	0.00300268	−	0.00413283i	0.810516	+	0.585717i	$0.199187\pi$
$98$		−	16.3944i		−	1.65608i
$99$	−5.02052			−0.504581
$100$	2.03884	+	4.56543i	0.203884	+	0.456543i
$101$	−3.16788	+	2.30160i	−0.315216	+	0.229018i	−0.734131	−	0.679007i	$-0.762410\pi$
$101$	−3.16788	+	2.30160i	−0.315216	+	0.229018i	0.418915	+	0.908025i	$0.362410\pi$
$102$	−2.37230	−	3.26519i	−0.234893	−	0.323302i
$103$	7.54614	+	2.45189i	0.743544	+	0.241592i	0.656201	−	0.754586i	$-0.272162\pi$
$103$	7.54614	+	2.45189i	0.743544	+	0.241592i	0.0873429	+	0.996178i	$0.472162\pi$
$104$	−2.56684	−	1.86492i	−0.251699	−	0.182870i
$105$	5.88534	−	9.07384i	0.574350	−	0.885516i
$106$	3.34862	+	10.3060i	0.325247	+	1.00101i
$107$	2.51753	+	3.46508i	0.243379	+	0.334982i	0.913179	−	0.407560i	$-0.133620\pi$
$107$	2.51753	+	3.46508i	0.243379	+	0.334982i	−0.669800	+	0.742542i	$0.733620\pi$
$108$	0.951057	−	0.309017i	0.0915155	−	0.0297352i
$109$	−2.35215	−	7.23917i	−0.225295	−	0.693386i	−0.998262	−	0.0589397i	$-0.981228\pi$
$109$	−2.35215	−	7.23917i	−0.225295	−	0.693386i	0.772967	−	0.634447i	$-0.218772\pi$
$110$	4.02904	+	10.4783i	0.384154	+	0.999068i
$111$	−1.11356	−	3.42719i	−0.105694	−	0.325294i
$112$	−4.60004	−	1.49464i	−0.434663	−	0.141231i
$113$	0.384475	−	0.529184i	0.0361683	−	0.0497814i	−0.790550	−	0.612398i	$-0.790205\pi$
$113$	0.384475	−	0.529184i	0.0361683	−	0.0497814i	0.826718	+	0.562616i	$0.190205\pi$
$114$	−2.13430	+	6.56870i	−0.199896	+	0.615215i
$115$	−3.14139	−	8.16981i	−0.292936	−	0.761839i
$116$	−1.62202	+	1.17846i	−0.150601	+	0.109418i
$117$	−1.86492	+	2.56684i	−0.172412	+	0.237304i
$118$			0.931780i			0.0857773i
$119$	19.5212			1.78951
$120$	−1.40818	−	1.73696i	−0.128549	−	0.158562i
$121$	4.38979	+	13.5104i	0.399071	+	1.22822i
$122$	−10.6012	−	3.44455i	−0.959792	−	0.311855i
$123$		−	7.39372i		−	0.666669i
$124$	−2.92203	−	4.73938i	−0.262406	−	0.425609i
$125$	−7.91907	−	7.89229i	−0.708303	−	0.705908i
$126$	−1.49464	+	4.60004i	−0.133154	+	0.409804i
$127$	4.78294	−	1.55407i	0.424417	−	0.137902i	−0.0890176	−	0.996030i	$-0.528373\pi$
$127$	4.78294	−	1.55407i	0.424417	−	0.137902i	0.513435	+	0.858128i	$0.328373\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	12.0218			1.05846
$130$	6.85386	+	1.83234i	0.601124	+	0.160707i
$131$	−14.5644	−	10.5816i	−1.27250	−	0.924522i	−0.273197	−	0.961958i	$-0.588081\pi$
$131$	−14.5644	−	10.5816i	−1.27250	−	0.924522i	−0.999299	+	0.0374359i	$0.988081\pi$
$132$	−2.95099	−	4.06169i	−0.256851	−	0.353525i
$133$	−19.6358	−	27.0263i	−1.70264	−	2.34348i
$134$	−1.03803	+	3.19474i	−0.0896725	+	0.275983i
$135$	−1.73696	+	1.40818i	−0.149493	+	0.121197i
$136$	1.24719	−	3.83847i	0.106946	−	0.329146i
$137$	−1.35038	+	0.438766i	−0.115371	+	0.0374863i	−0.366134	−	0.930562i	$-0.619319\pi$
$137$	−1.35038	+	0.438766i	−0.115371	+	0.0374863i	0.250763	+	0.968049i	$0.419319\pi$
$138$	2.30085	+	3.16685i	0.195861	+	0.269580i
$139$	−0.326451	−	1.00471i	−0.0276892	−	0.0852187i	0.936257	−	0.351316i	$-0.114266\pi$
$139$	−0.326451	−	1.00471i	−0.0276892	−	0.0852187i	−0.963946	+	0.266097i	$0.914266\pi$
$140$	10.8002	−	0.572130i	0.912784	−	0.0483538i
$141$	−1.24229	+	0.902579i	−0.104620	+	0.0760108i
$142$	−10.7246	+	3.48464i	−0.899990	+	0.292425i
$143$	15.1494	+	4.92235i	1.26686	+	0.411627i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	2.43957	−	3.76126i	0.202595	−	0.312356i
$146$	−1.98703	+	1.44366i	−0.164448	+	0.119478i
$147$	−9.63636	−	13.2633i	−0.794794	−	1.09394i
$148$	2.11812	−	2.91534i	0.174108	−	0.239639i
$149$	−1.55255			−0.127190			−0.0635950	−	0.997976i	$-0.520257\pi$
$149$	−1.55255			−0.127190			−0.0635950	+	0.997976i	$0.520257\pi$
$150$	4.33295	+	2.49511i	0.353784	+	0.203725i
$151$	−5.97239	−	4.33919i	−0.486026	−	0.353119i	0.317628	−	0.948215i	$-0.397114\pi$
$151$	−5.97239	−	4.33919i	−0.486026	−	0.353119i	−0.803654	+	0.595097i	$0.797114\pi$
$152$	−6.56870	+	2.13430i	−0.532792	+	0.173115i
$153$	−3.83847	−	1.24719i	−0.310322	−	0.100830i
$154$	24.2831			1.95679
$155$	9.90198	+	7.54657i	0.795346	+	0.606155i
$156$	−3.17279			−0.254026
$157$	6.71392	+	2.18149i	0.535830	+	0.174102i	0.564417	−	0.825490i	$-0.309101\pi$
$157$	6.71392	+	2.18149i	0.535830	+	0.174102i	−0.0285876	+	0.999591i	$0.509101\pi$
$158$	−7.83859	+	2.54691i	−0.623605	+	0.202622i
$159$	8.76680	+	6.36945i	0.695253	+	0.505131i
$160$	0.577517	−	2.16020i	0.0456568	−	0.170779i
$161$	−18.9333			−1.49215
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	−9.90438	−	13.6322i	−0.775771	−	1.06776i	−0.995736	−	0.0922492i	$-0.970594\pi$
$163$	−9.90438	−	13.6322i	−0.775771	−	1.06776i	0.219965	−	0.975508i	$-0.429406\pi$
$164$	5.98164	−	4.34592i	0.467088	−	0.339359i
$165$	9.41856	+	6.10893i	0.733234	+	0.475579i
$166$	−5.27902	−	3.83543i	−0.409731	−	0.297687i
$167$	22.6794	+	7.36899i	1.75499	+	0.570229i	0.996661	−	0.0816482i	$-0.0260184\pi$
$167$	22.6794	+	7.36899i	1.75499	+	0.570229i	0.758324	+	0.651878i	$0.226018\pi$
$168$	−4.60004	+	1.49464i	−0.354901	+	0.115314i
$169$	−2.37318	+	1.72422i	−0.182553	+	0.132632i
$170$	0.477409	+	9.01214i	0.0366156	+	0.691200i
$171$	2.13430	+	6.56870i	0.163214	+	0.502321i
$172$	7.06625	+	9.72586i	0.538796	+	0.741590i
$173$	−14.4925	+	4.70890i	−1.10185	+	0.358011i	−0.802812	−	0.596232i	$-0.796664\pi$
$173$	−14.4925	+	4.70890i	−1.10185	+	0.358011i	−0.299033	+	0.954243i	$0.596664\pi$
$174$	−0.619555	+	1.90680i	−0.0469684	+	0.144554i
$175$	−22.0819	+	9.86140i	−1.66924	+	0.745452i
$176$	1.55143	−	4.77480i	0.116943	−	0.359914i
$177$	0.547687	+	0.753826i	0.0411666	+	0.0566610i
$178$	10.1403	+	13.9569i	0.760045	+	1.04611i
$179$	−5.58006	−	4.05415i	−0.417073	−	0.303021i	0.359386	−	0.933189i	$-0.382986\pi$
$179$	−5.58006	−	4.05415i	−0.417073	−	0.303021i	−0.776459	+	0.630168i	$0.782986\pi$
$180$	−2.16020	−	0.577517i	−0.161012	−	0.0430456i
$181$	4.82036			0.358295			0.179147	−	0.983822i	$-0.442666\pi$
$181$	4.82036			0.358295			0.179147	+	0.983822i	$0.442666\pi$
$182$	9.02018	−	12.4152i	0.668620	−	0.920277i
$183$	−10.6012	+	3.44455i	−0.783667	+	0.254629i
$184$	−1.20963	+	3.72285i	−0.0891750	+	0.274452i
$185$	−2.08112	+	7.78441i	−0.153007	+	0.572321i
$186$	−5.14971	−	2.11671i	−0.377595	−	0.155205i
$187$			20.2628i			1.48177i
$188$	−1.46040	−	0.474514i	−0.106511	−	0.0346075i
$189$	1.49464	+	4.60004i	0.108719	+	0.334604i
$190$	11.9967	−	9.72597i	0.870333	−	0.705596i
$191$	−3.93520			−0.284741			−0.142371	−	0.989813i	$-0.545472\pi$
$191$	−3.93520			−0.284741			−0.142371	+	0.989813i	$0.545472\pi$
$192$			1.00000i			0.0721688i
$193$	−4.83823	+	6.65925i	−0.348263	+	0.479343i	−0.946832	−	0.321728i	$-0.895736\pi$
$193$	−4.83823	+	6.65925i	−0.348263	+	0.479343i	0.598569	+	0.801071i	$0.295736\pi$
$194$	0.0407037	−	0.0295729i	0.00292235	−	0.00212321i
$195$	6.62191	−	2.54621i	0.474205	−	0.182338i
$196$	5.06613	−	15.5920i	0.361867	−	1.11371i
$197$	5.02036	−	6.90993i	0.357686	−	0.492312i	−0.591816	−	0.806073i	$-0.701589\pi$
$197$	5.02036	−	6.90993i	0.357686	−	0.492312i	0.949502	+	0.313761i	$0.101589\pi$
$198$	−4.77480	−	1.55143i	−0.339330	−	0.110255i
$199$	3.12724	+	9.62465i	0.221684	+	0.682273i	0.998611	+	0.0526830i	$0.0167773\pi$
$199$	3.12724	+	9.62465i	0.221684	+	0.682273i	−0.776927	+	0.629590i	$0.783223\pi$
$200$	0.528257	+	4.97202i	0.0373534	+	0.351575i
$201$	1.03803	+	3.19474i	0.0732173	+	0.225340i
$202$	−3.72407	+	1.21002i	−0.262025	+	0.0851369i
$203$	−5.69996	−	7.84533i	−0.400059	−	0.550634i
$204$	−1.24719	−	3.83847i	−0.0873210	−	0.268746i
$205$	−8.99661	+	13.8707i	−0.628351	+	0.968772i
$206$	6.41913	+	4.66377i	0.447242	+	0.324941i
$207$	3.72285	+	1.20963i	0.258756	+	0.0840750i
$208$	−1.86492	−	2.56684i	−0.129309	−	0.177978i
$209$	28.0530	−	20.3817i	1.94047	−	1.40983i
$210$	8.40126	−	6.81106i	0.579742	−	0.470008i
$211$	21.8889			1.50689			0.753446	−	0.657510i	$-0.228390\pi$
$211$	21.8889			1.50689			0.753446	+	0.657510i	$0.228390\pi$
$212$			10.8364i			0.744244i
$213$	−6.62818	+	9.12291i	−0.454155	+	0.625091i
$214$	1.32354	+	4.07344i	0.0904755	+	0.278455i
$215$	−22.5531	−	14.6280i	−1.53811	−	0.997624i
$216$	1.00000			0.0680414
$217$	22.9233	−	14.1332i	1.55613	−	0.959425i
$218$		−	7.61171i		−	0.515530i
$219$	−0.758978	+	2.33590i	−0.0512870	+	0.157845i
$220$	0.593865	+	11.2105i	0.0400384	+	0.755812i
$221$	10.3598	+	7.52681i	0.696874	+	0.506308i
$222$		−	3.60356i		−	0.241855i
$223$			23.0876i			1.54606i	0.634368	+	0.773031i	$0.281260\pi$
$223$			23.0876i			1.54606i	−0.634368	+	0.773031i	$0.718740\pi$
$224$	−3.91303	−	2.84298i	−0.261450	−	0.189955i
$225$	4.97202	−	0.528257i	0.331468	−	0.0352171i
$226$	0.529184	−	0.384475i	0.0352008	−	0.0255749i
$227$	1.28927	+	0.418908i	0.0855716	+	0.0278039i	0.351490	−	0.936192i	$-0.385675\pi$
$227$	1.28927	+	0.418908i	0.0855716	+	0.0278039i	−0.265918	+	0.963996i	$0.585675\pi$
$228$	−4.05968	+	5.58767i	−0.268859	+	0.370053i
$229$	−4.07177	+	12.5316i	−0.269070	+	0.828113i	0.721658	+	0.692250i	$0.243381\pi$
$229$	−4.07177	+	12.5316i	−0.269070	+	0.828113i	−0.990728	+	0.135862i	$0.956619\pi$
$230$	−0.463029	−	8.74070i	−0.0305313	−	0.576345i
$231$	19.6455	−	14.2733i	1.29258	−	0.939111i
$232$	−1.90680	+	0.619555i	−0.125187	+	0.0406758i
$233$	−1.28916	+	0.418873i	−0.0844557	+	0.0274413i	−0.350940	−	0.936398i	$-0.614138\pi$
$233$	−1.28916	+	0.418873i	−0.0844557	+	0.0274413i	0.266484	+	0.963839i	$0.414138\pi$
$234$	−2.56684	+	1.86492i	−0.167800	+	0.121914i
$235$	3.42881	−	0.181637i	0.223671	−	0.0118487i
$236$	−0.287936	+	0.886175i	−0.0187430	+	0.0576851i
$237$	−4.84452	+	6.66791i	−0.314685	+	0.433127i
$238$	18.5658	+	6.03239i	1.20344	+	0.391022i
$239$	14.0630	−	10.2174i	0.909660	−	0.660906i	−0.0312691	−	0.999511i	$-0.509955\pi$
$239$	14.0630	−	10.2174i	0.909660	−	0.660906i	0.940929	+	0.338605i	$0.109955\pi$
$240$	−0.802514	−	2.08710i	−0.0518020	−	0.134722i
$241$	−0.213214	−	0.154909i	−0.0137343	−	0.00997858i	0.580897	−	0.813977i	$-0.302702\pi$
$241$	−0.213214	−	0.154909i	−0.0137343	−	0.00997858i	−0.594631	+	0.803999i	$0.702702\pi$
$242$			14.2056i			0.913173i
$243$		−	1.00000i		−	0.0641500i
$244$	−9.01796	−	6.55193i	−0.577316	−	0.419444i
$245$	1.93925	+	36.6076i	0.123894	+	2.33877i
$246$	2.28478	−	7.03185i	0.145673	−	0.448334i
$247$		−	21.9136i		−	1.39433i
$248$	−1.31447	−	5.41038i	−0.0834689	−	0.343559i
$249$	−6.52523			−0.413519
$250$	−5.09263	−	9.95314i	−0.322086	−	0.629492i
$251$	−1.54053	−	4.74125i	−0.0972372	−	0.299265i	0.890593	−	0.454801i	$-0.150290\pi$
$251$	−1.54053	−	4.74125i	−0.0972372	−	0.299265i	−0.987830	+	0.155536i	$0.950290\pi$
$252$	−2.84298	+	3.91303i	−0.179091	+	0.246498i
$253$		−	19.6525i		−	1.23554i
$254$	5.02908			0.315553
$255$	5.68343	+	7.01036i	0.355910	+	0.439006i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−13.9876	−	19.2523i	−0.872521	−	1.20092i	−0.978437	−	0.206547i	$-0.933777\pi$
$257$	−13.9876	−	19.2523i	−0.872521	−	1.20092i	0.105915	−	0.994375i	$-0.466223\pi$
$258$	11.4334	+	3.71495i	0.711814	+	0.231283i
$259$	14.1008	+	10.2449i	0.876183	+	0.636584i
$260$	5.95219	+	3.86062i	0.369139	+	0.239425i
$261$	0.619555	+	1.90680i	0.0383495	+	0.118028i
$262$	−10.5816	−	14.5644i	−0.653736	−	0.899790i
$263$	−5.44937	+	1.77061i	−0.336023	+	0.109180i	−0.472168	−	0.881508i	$-0.656529\pi$
$263$	−5.44937	+	1.77061i	−0.336023	+	0.109180i	0.136146	+	0.990689i	$0.456529\pi$
$264$	−1.55143	−	4.77480i	−0.0954837	−	0.293869i
$265$	−8.69633	−	22.6165i	−0.534211	−	1.38932i
$266$	−10.3231	−	31.7713i	−0.632952	−	1.94802i
$267$	16.4073	+	5.33105i	1.00411	+	0.326255i
$268$	−1.97446	+	2.71761i	−0.120609	+	0.166004i
$269$	9.23580	−	28.4249i	0.563116	−	1.73309i	−0.110366	−	0.993891i	$-0.535202\pi$
$269$	9.23580	−	28.4249i	0.563116	−	1.73309i	0.673482	−	0.739203i	$-0.264798\pi$
$270$	−2.08710	+	0.802514i	−0.127017	+	0.0488394i
$271$	−10.0355	+	7.29125i	−0.609616	+	0.442912i	−0.849279	−	0.527944i	$-0.822963\pi$
$271$	−10.0355	+	7.29125i	−0.609616	+	0.442912i	0.239663	+	0.970856i	$0.422963\pi$
$272$	2.37230	−	3.26519i	0.143842	−	0.197982i
$273$		−	15.3460i		−	0.928785i
$274$	−1.41988			−0.0857779
$275$	−10.2360	−	22.9208i	−0.617256	−	1.38218i
$276$	1.20963	+	3.72285i	0.0728111	+	0.224089i
$277$	−17.3531	−	5.63836i	−1.04265	−	0.338776i	−0.262868	−	0.964832i	$-0.584668\pi$
$277$	−17.3531	−	5.63836i	−1.04265	−	0.338776i	−0.779779	+	0.626055i	$0.784668\pi$
$278$		−	1.05642i		−	0.0633597i
$279$	−5.41038	+	1.31447i	−0.323911	+	0.0786953i
$280$	10.4484	+	2.79332i	0.624412	+	0.166933i
$281$	−7.85441	+	24.1734i	−0.468555	+	1.44206i	0.385901	+	0.922540i	$0.373891\pi$
$281$	−7.85441	+	24.1734i	−0.468555	+	1.44206i	−0.854456	+	0.519524i	$0.826109\pi$
$282$	−1.46040	+	0.474514i	−0.0869657	+	0.0282569i
$283$	−15.5895	+	21.4571i	−0.926698	+	1.27549i	0.0344358	+	0.999407i	$0.489037\pi$
$283$	−15.5895	+	21.4571i	−0.926698	+	1.27549i	−0.961134	+	0.276083i	$0.910963\pi$
$284$	−11.2765			−0.669139
$285$	3.98876	−	14.9200i	0.236274	−	0.883782i
$286$	12.8869	+	9.36286i	0.762017	+	0.553638i
$287$	21.0202	+	28.9318i	1.24078	+	1.70779i
$288$	0.587785	+	0.809017i	0.0346356	+	0.0476718i
$289$	0.219613	−	0.675900i	0.0129184	−	0.0397588i
$290$	3.48246	−	2.82330i	0.204497	−	0.165790i
$291$	0.0155474	−	0.0478500i	0.000911405	−	0.00280502i
$292$	−2.33590	+	0.758978i	−0.136698	+	0.0444159i
$293$	−14.6983	−	20.2305i	−0.858686	−	1.18188i	−0.981881	−	0.189498i	$-0.939314\pi$
$293$	−14.6983	−	20.2305i	−0.858686	−	1.18188i	0.123195	−	0.992383i	$-0.460686\pi$
$294$	−5.06613	−	15.5920i	−0.295463	−	0.909341i
$295$	−0.110218	−	2.08061i	−0.00641714	−	0.121138i
$296$	2.91534	−	2.11812i	0.169451	−	0.123113i
$297$	−4.77480	+	1.55143i	−0.277062	+	0.0900229i
$298$	−1.47656	−	0.479765i	−0.0855351	−	0.0277920i
$299$	−10.0477	−	7.30011i	−0.581076	−	0.422176i
$300$	3.34985	+	3.71194i	0.193403	+	0.214309i
$301$	−47.0417	+	34.1778i	−2.71144	+	1.96998i
$302$	−4.33919	−	5.97239i	−0.249693	−	0.343672i
$303$	−2.30160	+	3.16788i	−0.132224	+	0.181990i
$304$	−6.90674			−0.396129
$305$	24.0794	+	6.43748i	1.37878	+	0.368609i
$306$	−3.26519	−	2.37230i	−0.186659	−	0.135616i
$307$	−12.4820	+	4.05564i	−0.712385	+	0.231468i	−0.642718	−	0.766103i	$-0.722193\pi$
$307$	−12.4820	+	4.05564i	−0.712385	+	0.231468i	−0.0696663	+	0.997570i	$0.522193\pi$
$308$	23.0946	+	7.50390i	1.31594	+	0.427574i
$309$	7.93449			0.451377
$310$	7.08533	+	10.2371i	0.402419	+	0.581428i
$311$	23.7348			1.34588			0.672939	−	0.739698i	$-0.265032\pi$
$311$	23.7348			1.34588			0.672939	+	0.739698i	$0.265032\pi$
$312$	−3.01750	−	0.980445i	−0.170832	−	0.0555068i
$313$	20.6315	−	6.70357i	1.16616	−	0.378908i	0.338952	−	0.940804i	$-0.389928\pi$
$313$	20.6315	−	6.70357i	1.16616	−	0.378908i	0.827208	+	0.561895i	$0.189928\pi$
$314$	5.71121	+	4.14943i	0.322302	+	0.234166i
$315$	2.79332	−	10.4484i	0.157386	−	0.588701i
$316$	−8.24198			−0.463648
$317$	−3.59021	+	4.94151i	−0.201647	+	0.277543i	−0.897850	−	0.440302i	$-0.854871\pi$
$317$	−3.59021	+	4.94151i	−0.201647	+	0.277543i	0.696203	+	0.717845i	$0.254871\pi$
$318$	6.36945	+	8.76680i	0.357181	+	0.491618i
$319$	8.14337	−	5.91651i	0.455941	−	0.331261i
$320$	1.21679	−	1.87601i	0.0680207	−	0.104872i
$321$	3.46508	+	2.51753i	0.193402	+	0.140515i
$322$	−18.0066	−	5.85070i	−1.00347	−	0.326047i
$323$	26.5113	−	8.61405i	1.47513	−	0.479298i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	−15.5210	−	3.28077i	−0.860950	−	0.181985i
$326$	−5.20704	−	16.0256i	−0.288391	−	0.887577i
$327$	−4.47405	−	6.15800i	−0.247416	−	0.340538i
$328$	7.03185	−	2.28478i	0.388269	−	0.126156i
$329$	2.29511	−	7.06364i	0.126534	−	0.389431i
$330$	7.06982	+	8.72043i	0.389181	+	0.480044i
$331$	−0.0792598	+	0.243937i	−0.00435651	+	0.0134080i	−0.953211	−	0.302305i	$-0.902244\pi$
$331$	−0.0792598	+	0.243937i	−0.00435651	+	0.0134080i	0.948855	+	0.315713i	$0.102244\pi$
$332$	−3.83543	−	5.27902i	−0.210497	−	0.289724i
$333$	−2.11812	−	2.91534i	−0.116072	−	0.159760i
$334$	19.2923	+	14.0166i	1.05563	+	0.766957i
$335$	1.93997	−	7.25644i	0.105992	−	0.396462i
$336$	−4.83677			−0.263867
$337$	−15.2533	+	20.9944i	−0.830901	+	1.14364i	0.156853	+	0.987622i	$0.449865\pi$
$337$	−15.2533	+	20.9944i	−0.830901	+	1.14364i	−0.987755	+	0.156015i	$0.950135\pi$
$338$	−2.78984	+	0.906475i	−0.151748	+	0.0493058i
$339$	0.202130	−	0.622093i	0.0109782	−	0.0337875i
$340$	−2.33086	+	8.71858i	−0.126409	+	0.472831i
$341$	14.6701	+	23.7942i	0.794432	+	1.28853i
$342$			6.90674i			0.373474i
$343$	43.2144	+	14.0412i	2.33336	+	0.758155i
$344$	3.71495	+	11.4334i	0.200297	+	0.616449i
$345$	−5.51225	−	6.79921i	−0.296770	−	0.366057i
$346$	−15.2383			−0.819218
$347$		−	2.05115i		−	0.110112i	−0.998483	−	0.0550559i	$-0.982466\pi$
$347$		−	2.05115i		−	0.110112i	0.998483	−	0.0550559i	$-0.0175337\pi$
$348$	−1.17846	+	1.62202i	−0.0631723	+	0.0869492i
$349$	−23.2482	+	16.8908i	−1.24445	+	0.904143i	−0.997886	−	0.0649841i	$-0.979300\pi$
$349$	−23.2482	+	16.8908i	−1.24445	+	0.904143i	−0.246560	+	0.969127i	$0.579300\pi$
$350$	−24.0485	+	2.55506i	−1.28545	+	0.136574i
$351$	−0.980445	+	3.01750i	−0.0523323	+	0.161062i
$352$	2.95099	−	4.06169i	0.157288	−	0.216489i
$353$	17.3261	+	5.62958i	0.922173	+	0.299632i	0.731358	−	0.681994i	$-0.238887\pi$
$353$	17.3261	+	5.62958i	0.922173	+	0.299632i	0.190815	+	0.981626i	$0.438887\pi$
$354$	0.287936	+	0.886175i	0.0153036	+	0.0470997i
$355$	23.5352	−	9.04957i	1.24912	−	0.480301i
$356$	5.33105	+	16.4073i	0.282545	+	0.869584i
$357$	18.5658	−	6.03239i	0.982605	−	0.319268i
$358$	−4.05415	−	5.58006i	−0.214268	−	0.294915i
$359$	6.70489	+	20.6355i	0.353871	+	1.08910i	0.956661	+	0.291203i	$0.0940554\pi$
$359$	6.70489	+	20.6355i	0.353871	+	1.08910i	−0.602791	+	0.797899i	$0.705945\pi$
$360$	−1.87601	−	1.21679i	−0.0988745	−	0.0641305i
$361$	−23.2213	−	16.8713i	−1.22217	−	0.887961i
$362$	4.58444	+	1.48957i	0.240953	+	0.0782903i
$363$	8.34987	+	11.4926i	0.438254	+	0.603205i
$364$	12.4152	−	9.02018i	0.650734	−	0.472786i
$365$	4.26615	−	3.45865i	0.223300	−	0.181034i
$366$	−11.1468			−0.582653
$367$			18.1506i			0.947456i	0.880671	+	0.473728i	$0.157092\pi$
$367$			18.1506i			0.947456i	−0.880671	+	0.473728i	$0.842908\pi$
$368$	−2.30085	+	3.16685i	−0.119940	+	0.165083i
$369$	−2.28478	−	7.03185i	−0.118941	−	0.366063i
$370$	−4.38478	+	6.76032i	−0.227954	+	0.351452i
$371$	−52.4130			−2.72115
$372$	−4.24357	−	3.60446i	−0.220019	−	0.186883i
$373$			13.4651i			0.697199i	0.937272	+	0.348599i	$0.113343\pi$
$373$			13.4651i			0.697199i	−0.937272	+	0.348599i	$0.886657\pi$
$374$	−6.26156	+	19.2711i	−0.323778	+	0.996485i
$375$	−9.97034	−	5.05889i	−0.514866	−	0.261240i
$376$	−1.24229	−	0.902579i	−0.0640664	−	0.0465469i
$377$		−	6.36120i		−	0.327618i
$378$			4.83677i			0.248777i
$379$	6.32693	+	4.59678i	0.324992	+	0.236121i	0.738303	−	0.674469i	$-0.235628\pi$
$379$	6.32693	+	4.59678i	0.324992	+	0.236121i	−0.413310	+	0.910590i	$0.635628\pi$
$380$	14.4150	−	5.54276i	0.739476	−	0.284337i
$381$	4.06861	−	2.95602i	0.208441	−	0.151442i
$382$	−3.74260	−	1.21604i	−0.191488	−	0.0622182i
$383$	−8.29971	+	11.4236i	−0.424096	+	0.583717i	−0.966585	−	0.256345i	$-0.917482\pi$
$383$	−8.29971	+	11.4236i	−0.424096	+	0.583717i	0.542490	+	0.840062i	$0.317482\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	−54.2227	+	2.87239i	−2.76344	+	0.146391i
$386$	−6.65925	+	4.83823i	−0.338947	+	0.246259i
$387$	11.4334	−	3.71495i	0.581194	−	0.188841i
$388$	0.0478500	−	0.0155474i	0.00242922	−	0.000789300i
$389$	−16.8728	+	12.2588i	−0.855484	+	0.621546i	−0.926653	−	0.375919i	$-0.877327\pi$
$389$	−16.8728	+	12.2588i	−0.855484	+	0.621546i	0.0711684	+	0.997464i	$0.477327\pi$
$390$	7.08464	−	0.375301i	0.358744	−	0.0190041i
$391$	4.88206	−	15.0254i	0.246897	−	0.759870i
$392$	9.63636	−	13.2633i	0.486710	−	0.669898i
$393$	−17.1215	−	5.56310i	−0.863663	−	0.280621i
$394$	6.90993	−	5.02036i	0.348117	−	0.252922i
$395$	17.2018	−	6.61430i	0.865517	−	0.332802i
$396$	−4.06169	−	2.95099i	−0.204107	−	0.148293i
$397$			22.2027i			1.11432i	0.830404	+	0.557161i	$0.188110\pi$
$397$			22.2027i			1.11432i	−0.830404	+	0.557161i	$0.811890\pi$
$398$			10.1200i			0.507268i
$399$	−27.0263	−	19.6358i	−1.35301	−	0.983017i
$400$	−1.03404	+	4.89191i	−0.0517018	+	0.244595i
$401$	0.628608	−	1.93466i	0.0313912	−	0.0966121i	−0.934133	−	0.356924i	$-0.883825\pi$
$401$	0.628608	−	1.93466i	0.0313912	−	0.0966121i	0.965525	+	0.260312i	$0.0838255\pi$
$402$			3.35915i			0.167539i
$403$	17.6146	+	1.33816i	0.877445	+	0.0666587i
$404$	−3.91572			−0.194814
$405$	−1.21679	+	1.87601i	−0.0604628	+	0.0932198i
$406$	−2.99665	−	9.22273i	−0.148721	−	0.457717i
$407$	−10.6341	+	14.6365i	−0.527111	+	0.725506i
$408$		−	4.03600i		−	0.199812i
$409$	−32.6350			−1.61370			−0.806848	−	0.590759i	$-0.798828\pi$
$409$	−32.6350			−1.61370			−0.806848	+	0.590759i	$0.798828\pi$
$410$	−12.8426	+	10.4117i	−0.634249	+	0.514198i
$411$	−1.14870	+	0.834583i	−0.0566614	+	0.0411669i
$412$	4.66377	+	6.41913i	0.229768	+	0.316248i
$413$	−4.28623	−	1.39268i	−0.210911	−	0.0685293i
$414$	3.16685	+	2.30085i	0.155642	+	0.113081i
$415$	12.2414	+	7.93984i	0.600907	+	0.389751i
$416$	−0.980445	−	3.01750i	−0.0480703	−	0.147945i
$417$	−0.620947	−	0.854660i	−0.0304079	−	0.0418529i
$418$	32.9783	−	10.7153i	1.61302	−	0.524103i
$419$	−7.50362	−	23.0938i	−0.366576	−	1.12820i	−0.948988	−	0.315311i	$-0.897891\pi$
$419$	−7.50362	−	23.0938i	−0.366576	−	1.12820i	0.582412	−	0.812894i	$-0.302109\pi$
$420$	10.0948	−	3.88157i	0.492576	−	0.189401i
$421$	−4.30083	−	13.2366i	−0.209610	−	0.645112i	−0.999493	−	0.0318546i	$-0.989859\pi$
$421$	−4.30083	−	13.2366i	−0.209610	−	0.645112i	0.789883	−	0.613258i	$-0.210141\pi$
$422$	20.8175	+	6.76403i	1.01338	+	0.329268i
$423$	−0.902579	+	1.24229i	−0.0438849	+	0.0604024i
$424$	−3.34862	+	10.3060i	−0.162623	+	0.500503i
$425$	−2.13205	−	20.0671i	−0.103419	−	0.973396i
$426$	−9.12291	+	6.62818i	−0.442006	+	0.321136i
$427$	31.6902	−	43.6178i	1.53360	−	2.11081i
$428$			4.28307i			0.207030i
$429$	15.9291			0.769062
$430$	−16.9289	−	20.8814i	−0.816386	−	1.00699i
$431$	2.27320	+	6.99620i	0.109496	+	0.336995i	0.990759	−	0.135631i	$-0.0433062\pi$
$431$	2.27320	+	6.99620i	0.109496	+	0.336995i	−0.881263	+	0.472626i	$0.843306\pi$
$432$	0.951057	+	0.309017i	0.0457577	+	0.0148676i
$433$		−	20.1227i		−	0.967035i	−0.875335	−	0.483518i	$-0.839359\pi$
$433$		−	20.1227i		−	0.967035i	0.875335	−	0.483518i	$-0.160641\pi$
$434$	26.1688	−	6.35779i	1.25614	−	0.305184i
$435$	1.15788	−	4.33104i	0.0555160	−	0.207657i
$436$	2.35215	−	7.23917i	0.112647	−	0.346693i
$437$	−25.7128	+	8.35459i	−1.23001	+	0.399654i
$438$	−1.44366	+	1.98703i	−0.0689809	+	0.0949440i
$439$	38.4539			1.83531			0.917653	−	0.397383i	$-0.130082\pi$
$439$	38.4539			1.83531			0.917653	+	0.397383i	$0.130082\pi$
$440$	−2.89944	+	10.8453i	−0.138225	+	0.517031i
$441$	−13.2633	−	9.63636i	−0.631586	−	0.458874i
$442$	7.52681	+	10.3598i	0.358014	+	0.492764i
$443$	6.38389	+	8.78666i	0.303308	+	0.417467i	0.933280	−	0.359151i	$-0.116934\pi$
$443$	6.38389	+	8.78666i	0.303308	+	0.417467i	−0.629972	+	0.776618i	$0.716934\pi$
$444$	1.11356	−	3.42719i	0.0528472	−	0.162647i
$445$	−24.2935	−	29.9653i	−1.15162	−	1.42049i
$446$	−7.13447	+	21.9576i	−0.337827	+	1.03972i
$447$	−1.47656	+	0.479765i	−0.0698391	+	0.0226921i
$448$	−2.84298	−	3.91303i	−0.134318	−	0.184873i
$449$	−3.12522	−	9.61843i	−0.147488	−	0.453922i	0.849834	−	0.527050i	$-0.176702\pi$
$449$	−3.12522	−	9.61843i	−0.147488	−	0.453922i	−0.997323	+	0.0731280i	$0.976702\pi$
$450$	4.89191	+	1.03404i	0.230607	+	0.0487449i
$451$	−30.0310	+	21.8188i	−1.41410	+	1.02741i
$452$	0.622093	−	0.202130i	0.0292608	−	0.00950741i
$453$	−7.02096	−	2.28125i	−0.329874	−	0.107182i
$454$	1.09671	+	0.796810i	0.0514714	+	0.0373961i
$455$	−18.6729	+	28.7894i	−0.875401	+	1.34967i
$456$	−5.58767	+	4.05968i	−0.261667	+	0.190112i
$457$	10.5416	+	14.5092i	0.493114	+	0.678714i	0.980959	−	0.194217i	$-0.0622166\pi$
$457$	10.5416	+	14.5092i	0.493114	+	0.678714i	−0.487844	+	0.872931i	$0.662217\pi$
$458$	−7.74497	+	10.6600i	−0.361899	+	0.498111i
$459$	−4.03600			−0.188384
$460$	2.26066	−	8.45598i	0.105404	−	0.394262i
$461$	−15.0249	−	10.9162i	−0.699779	−	0.508419i	0.180081	−	0.983652i	$-0.442364\pi$
$461$	−15.0249	−	10.9162i	−0.699779	−	0.508419i	−0.879860	+	0.475232i	$0.842364\pi$
$462$	23.0946	−	7.50390i	1.07446	−	0.349113i
$463$	21.7593	+	7.07002i	1.01124	+	0.328572i	0.767348	−	0.641231i	$-0.221576\pi$
$463$	21.7593	+	7.07002i	1.01124	+	0.328572i	0.243892	+	0.969802i	$0.421576\pi$
$464$	−2.00492			−0.0930762
$465$	11.7494	+	4.11734i	0.544864	+	0.190937i
$466$	−1.35550			−0.0627924
$467$	−33.9004	−	11.0149i	−1.56873	−	0.509710i	−0.609604	−	0.792706i	$-0.708672\pi$
$467$	−33.9004	−	11.0149i	−1.56873	−	0.509710i	−0.959121	+	0.282996i	$0.908672\pi$
$468$	−3.01750	+	0.980445i	−0.139484	+	0.0453211i
$469$	−13.1444	−	9.55000i	−0.606954	−	0.440978i
$470$	3.31712	+	0.886812i	0.153007	+	0.0409056i
$471$	7.05944			0.325282
$472$	−0.547687	+	0.753826i	−0.0252093	+	0.0346976i
$473$	−35.4763	−	48.8289i	−1.63120	−	2.24515i
$474$	−6.66791	+	4.84452i	−0.306267	+	0.222516i
$475$	−25.6374	+	23.1365i	−1.17633	+	1.06158i
$476$	15.7930	+	11.4743i	0.723871	+	0.525923i
$477$	10.3060	+	3.34862i	0.471879	+	0.153323i
$478$	16.5320	−	5.37159i	0.756158	−	0.245691i
$479$	−4.73419	+	3.43959i	−0.216311	+	0.157159i	−0.690664	−	0.723175i	$-0.742682\pi$
$479$	−4.73419	+	3.43959i	−0.216311	+	0.157159i	0.474354	+	0.880334i	$0.342682\pi$
$480$	−0.118288	−	2.23294i	−0.00539906	−	0.101919i
$481$	3.53309	+	10.8737i	0.161095	+	0.495800i
$482$	−0.154909	−	0.213214i	−0.00705592	−	0.00971165i
$483$	−18.0066	+	5.85070i	−0.819328	+	0.266216i
$484$	−4.38979	+	13.5104i	−0.199536	+	0.614108i
$485$	−0.0873906	+	0.0708492i	−0.00396820	+	0.00321710i
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	−0.767491	−	1.05636i	−0.0347783	−	0.0478683i	0.791274	−	0.611462i	$-0.209418\pi$
$487$	−0.767491	−	1.05636i	−0.0347783	−	0.0478683i	−0.826052	+	0.563594i	$0.809418\pi$
$488$	−6.55193	−	9.01796i	−0.296592	−	0.408224i
$489$	−13.6322	−	9.90438i	−0.616470	−	0.447891i
$490$	−9.46803	+	35.4151i	−0.427722	+	1.59989i
$491$	1.02194			0.0461193			0.0230597	−	0.999734i	$-0.492659\pi$
$491$	1.02194			0.0461193			0.0230597	+	0.999734i	$0.492659\pi$
$492$	4.34592	−	5.98164i	0.195929	−	0.269673i
$493$	7.69583	−	2.50053i	0.346603	−	0.112618i
$494$	6.77169	−	20.8411i	0.304673	−	0.937686i
$495$	10.8453	+	2.89944i	0.487462	+	0.130320i
$496$	0.421763	−	5.55177i	0.0189377	−	0.249282i
$497$		−	54.5420i		−	2.44654i
$498$	−6.20586	−	2.01641i	−0.278091	−	0.0903573i
$499$	9.43293	+	29.0316i	0.422276	+	1.29963i	0.905579	+	0.424178i	$0.139437\pi$
$499$	9.43293	+	29.0316i	0.422276	+	1.29963i	−0.483303	+	0.875453i	$0.660563\pi$
$500$	−1.76769	−	11.0397i	−0.0790536	−	0.493711i
$501$	23.8465			1.06538
$502$		−	4.98525i		−	0.222502i
$503$	−19.1788	+	26.3973i	−0.855139	+	1.17700i	0.127568	+	0.991830i	$0.459283\pi$
$503$	−19.1788	+	26.3973i	−0.855139	+	1.17700i	−0.982707	+	0.185168i	$0.940717\pi$
$504$	−3.91303	+	2.84298i	−0.174300	+	0.126637i
$505$	8.17248	−	3.14242i	0.363671	−	0.139836i
$506$	6.07297	−	18.6907i	0.269976	−	0.830902i
$507$	−1.72422	+	2.37318i	−0.0765752	+	0.105397i
$508$	4.78294	+	1.55407i	0.212209	+	0.0689508i
$509$	−2.59770	−	7.99490i	−0.115141	−	0.354368i	0.876835	−	0.480791i	$-0.159650\pi$
$509$	−2.59770	−	7.99490i	−0.115141	−	0.354368i	−0.991976	+	0.126423i	$0.959650\pi$
$510$	3.23895	+	8.42353i	0.143423	+	0.373000i
$511$	−3.67100	−	11.2982i	−0.162396	−	0.499803i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	4.05968	+	5.58767i	0.179239	+	0.246702i
$514$	−7.35371	−	22.6324i	−0.324358	−	0.998271i
$515$	−14.8852	−	9.65461i	−0.655920	−	0.425433i
$516$	9.72586	+	7.06625i	0.428157	+	0.311074i
$517$	7.33199	+	2.38231i	0.322460	+	0.104774i
$518$	10.2449	+	14.1008i	0.450133	+	0.619555i
$519$	−12.3281	+	8.95687i	−0.541142	+	0.393163i
$520$	4.46787	+	5.51099i	0.195929	+	0.241673i
$521$	−22.9937			−1.00737			−0.503685	−	0.863887i	$-0.668023\pi$
$521$	−22.9937			−1.00737			−0.503685	+	0.863887i	$0.668023\pi$
$522$			2.00492i			0.0877531i
$523$	1.18170	−	1.62647i	0.0516722	−	0.0711206i	−0.782399	−	0.622777i	$-0.786004\pi$
$523$	1.18170	−	1.62647i	0.0516722	−	0.0711206i	0.834071	+	0.551657i	$0.186004\pi$
$524$	−5.56310	−	17.1215i	−0.243025	−	0.747954i
$525$	−17.9538	+	16.2024i	−0.783569	+	0.707133i
$526$	−5.72981			−0.249831
$527$	5.30520	+	21.8363i	0.231098	+	0.951204i
$528$		−	5.02052i		−	0.218490i
$529$	2.37237	−	7.30141i	0.103147	−	0.317453i
$530$	−1.28181	−	24.1969i	−0.0556781	−	1.05105i
$531$	0.753826	+	0.547687i	0.0327133	+	0.0237676i
$532$		−	33.4063i		−	1.44835i
$533$			23.4587i			1.01611i
$534$	13.9569	+	10.1403i	0.603973	+	0.438812i
$535$	−3.43722	−	8.93919i	−0.148604	−	0.386475i
$536$	−2.71761	+	1.97446i	−0.117383	+	0.0852836i
$537$	−6.55975	−	2.13139i	−0.283074	−	0.0919764i
$538$	17.5675	−	24.1796i	0.757390	−	1.04246i
$539$	−25.4346	+	78.2798i	−1.09555	+	3.37175i
$540$	−2.23294	+	0.118288i	−0.0960903	+	0.00509028i
$541$	28.0150	−	20.3541i	1.20446	−	0.875091i	0.209744	−	0.977756i	$-0.432737\pi$
$541$	28.0150	−	20.3541i	1.20446	−	0.875091i	0.994716	+	0.102665i	$0.0327371\pi$
$542$	−11.7975	+	3.83324i	−0.506746	+	0.164652i
$543$	4.58444	−	1.48957i	0.196737	−	0.0639237i
$544$	3.26519	−	2.37230i	0.139994	−	0.101712i
$545$	0.900370	+	16.9965i	0.0385676	+	0.728049i
$546$	4.74219	−	14.5950i	0.202947	−	0.624607i
$547$	−12.1848	+	16.7710i	−0.520985	+	0.717075i	−0.985723	−	0.168374i	$-0.946149\pi$
$547$	−12.1848	+	16.7710i	−0.520985	+	0.717075i	0.464738	+	0.885448i	$0.346149\pi$
$548$	−1.35038	−	0.438766i	−0.0576855	−	0.0187432i
$549$	−9.01796	+	6.55193i	−0.384877	+	0.279630i
$550$	−2.65213	−	24.9621i	−0.113087	−	1.06439i
$551$	−11.2029	−	8.13935i	−0.477258	−	0.346748i
$552$			3.91444i			0.166610i
$553$		−	39.8646i		−	1.69521i
$554$	−14.7614	−	10.7248i	−0.627153	−	0.455653i
$555$	0.426256	+	8.04652i	0.0180935	+	0.341556i
$556$	0.326451	−	1.00471i	0.0138446	−	0.0426093i
$557$			29.5661i			1.25276i	0.779519	+	0.626378i	$0.215463\pi$
$557$			29.5661i			1.25276i	−0.779519	+	0.626378i	$0.784537\pi$
$558$	−5.55177	−	0.421763i	−0.235025	−	0.0178546i
$559$	−38.1427			−1.61326
$560$	9.07384	+	5.88534i	0.383440	+	0.248701i
$561$	6.26156	+	19.2711i	0.264363	+	0.813627i
$562$	−14.9400	+	20.5631i	−0.630205	+	0.867403i
$563$			10.7216i			0.451862i	0.974143	+	0.225931i	$0.0725424\pi$
$563$			10.7216i			0.451862i	−0.974143	+	0.225931i	$0.927458\pi$
$564$	−1.53556			−0.0646587
$565$	−1.13616	+	0.921103i	−0.0477984	+	0.0387511i
$566$	−21.4571	+	15.5895i	−0.901908	+	0.655274i
$567$	2.84298	+	3.91303i	0.119394	+	0.164332i
$568$	−10.7246	−	3.48464i	−0.449995	−	0.146212i
$569$	29.2100	+	21.2223i	1.22455	+	0.889685i	0.996469	−	0.0839587i	$-0.0267564\pi$
$569$	29.2100	+	21.2223i	1.22455	+	0.889685i	0.228076	+	0.973643i	$0.426756\pi$
$570$	8.40406	−	12.9571i	0.352007	−	0.542715i
$571$	1.19933	+	3.69114i	0.0501902	+	0.154470i	0.973010	−	0.230762i	$-0.0741217\pi$
$571$	1.19933	+	3.69114i	0.0501902	+	0.154470i	−0.922820	+	0.385231i	$0.874122\pi$
$572$	9.36286	+	12.8869i	0.391481	+	0.538827i
$573$	−3.74260	+	1.21604i	−0.156349	+	0.0508009i
$574$	11.0510	+	34.0114i	0.461259	+	1.41961i
$575$	2.06783	+	19.4627i	0.0862345	+	0.811649i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	−36.6093	−	11.8951i	−1.52407	−	0.495199i	−0.577138	−	0.816647i	$-0.695831\pi$
$577$	−36.6093	−	11.8951i	−1.52407	−	0.495199i	−0.946927	+	0.321448i	$0.895831\pi$
$578$	0.417729	−	0.574955i	0.0173752	−	0.0239150i
$579$	−2.54361	+	7.82842i	−0.105709	+	0.325338i
$580$	4.18447	−	1.60898i	0.173751	−	0.0668092i
$581$	25.5334	−	18.5511i	1.05930	−	0.769630i
$582$	0.0295729	−	0.0407037i	0.00122584	−	0.00168722i
$583$		−	54.4042i		−	2.25319i
$584$	−2.45611			−0.101634
$585$	5.51099	−	4.46787i	0.227852	−	0.184724i
$586$	−7.72738	−	23.7824i	−0.319215	−	0.982443i
$587$	17.7717	+	5.77438i	0.733517	+	0.238334i	0.651874	−	0.758327i	$-0.273983\pi$
$587$	17.7717	+	5.77438i	0.733517	+	0.238334i	0.0816433	+	0.996662i	$0.473983\pi$
$588$		−	16.3944i		−	0.676092i
$589$	24.8951	−	29.3092i	1.02578	−	1.20767i
$590$	0.538119	−	2.01283i	0.0221540	−	0.0828670i
$591$	2.63936	−	8.12311i	0.108569	−	0.334140i
$592$	3.42719	−	1.11356i	0.140856	−	0.0457670i
$593$	−10.7199	+	14.7546i	−0.440212	+	0.605900i	−0.970259	−	0.242068i	$-0.922174\pi$
$593$	−10.7199	+	14.7546i	−0.440212	+	0.605900i	0.530047	+	0.847968i	$0.322174\pi$
$594$	−5.02052			−0.205995
$595$	−42.1698	−	11.2738i	−1.72879	−	0.462183i
$596$	−1.25604	−	0.912567i	−0.0514494	−	0.0373802i
$597$	5.94836	+	8.18722i	0.243450	+	0.335081i
$598$	−7.30011	−	10.0477i	−0.298524	−	0.410883i
$599$	13.7642	−	42.3620i	0.562391	−	1.73086i	−0.113187	−	0.993574i	$-0.536106\pi$
$599$	13.7642	−	42.3620i	0.562391	−	1.73086i	0.675578	−	0.737289i	$-0.263894\pi$
$600$	2.03884	+	4.56543i	0.0832353	+	0.186383i
$601$	7.60698	−	23.4119i	0.310295	−	0.954991i	−0.667353	−	0.744742i	$-0.732573\pi$
$601$	7.60698	−	23.4119i	0.310295	−	0.954991i	0.977648	−	0.210249i	$-0.0674274\pi$
$602$	−55.3009	+	17.9683i	−2.25390	+	0.732335i
$603$	1.97446	+	2.71761i	0.0804061	+	0.110670i
$604$	−2.28125	−	7.02096i	−0.0928227	−	0.285679i
$605$	−1.68035	−	31.7203i	−0.0683160	−	1.28961i
$606$	−3.16788	+	2.30160i	−0.128686	+	0.0934961i
$607$	38.7171	−	12.5799i	1.57148	−	0.510604i	0.611634	−	0.791141i	$-0.290513\pi$
$607$	38.7171	−	12.5799i	1.57148	−	0.510604i	0.959843	+	0.280537i	$0.0905127\pi$
$608$	−6.56870	−	2.13430i	−0.266396	−	0.0865573i
$609$	−7.84533	−	5.69996i	−0.317909	−	0.230974i
$610$	20.9115	+	13.5633i	0.846684	+	0.549164i
$611$	3.94153	−	2.86369i	0.159457	−	0.115853i
$612$	−2.37230	−	3.26519i	−0.0958947	−	0.131988i
$613$	0.639002	−	0.879511i	0.0258091	−	0.0355231i	−0.795917	−	0.605405i	$-0.793011\pi$
$613$	0.639002	−	0.879511i	0.0258091	−	0.0355231i	0.821727	+	0.569882i	$0.193011\pi$
$614$	−13.1243			−0.529655
$615$	−4.27000	+	15.9719i	−0.172183	+	0.644050i
$616$	19.6455	+	14.2733i	0.791538	+	0.575086i
$617$	5.52574	−	1.79542i	0.222458	−	0.0722810i	−0.195667	−	0.980670i	$-0.562687\pi$
$617$	5.52574	−	1.79542i	0.222458	−	0.0722810i	0.418125	+	0.908389i	$0.362687\pi$
$618$	7.54614	+	2.45189i	0.303550	+	0.0986295i
$619$	25.9541			1.04318			0.521592	−	0.853195i	$-0.325338\pi$
$619$	25.9541			1.04318			0.521592	+	0.853195i	$0.325338\pi$
$620$	3.57511	+	11.9255i	0.143580	+	0.478941i
$621$	3.91444			0.157081
$622$	22.5732	+	7.33446i	0.905101	+	0.294085i
$623$	−79.3583	+	25.7851i	−3.17942	+	1.03306i
$624$	−2.56684	−	1.86492i	−0.102756	−	0.0746565i
$625$	12.5489	+	21.6223i	0.501955	+	0.864894i
$626$	21.6932			0.867035
$627$	20.3817	−	28.0530i	0.813968	−	1.12033i
$628$	4.14943	+	5.71121i	0.165580	+	0.227902i
$629$	−11.7663	+	8.54873i	−0.469154	+	0.340860i
$630$	5.88534	−	9.07384i	0.234478	−	0.361510i
$631$	24.4831	+	17.7880i	0.974658	+	0.708130i	0.956508	−	0.291705i	$-0.0942225\pi$
$631$	24.4831	+	17.7880i	0.974658	+	0.708130i	0.0181495	+	0.999835i	$0.494223\pi$
$632$	−7.83859	−	2.54691i	−0.311802	−	0.101311i
$633$	20.8175	−	6.76403i	0.827423	−	0.268846i
$634$	−4.94151	+	3.59021i	−0.196252	+	0.142586i
$635$	−11.2296	+	0.594878i	−0.445634	+	0.0236070i
$636$	3.34862	+	10.3060i	0.132781	+	0.408659i
$637$	30.5741	+	42.0817i	1.21139	+	1.66734i
$638$	9.57311	−	3.11049i	0.379003	−	0.123146i
$639$	−3.48464	+	10.7246i	−0.137850	+	0.424259i
$640$	1.73696	−	1.40818i	0.0686592	−	0.0556634i
$641$	−6.13239	+	18.8735i	−0.242215	+	0.745460i	0.753867	+	0.657027i	$0.228186\pi$
$641$	−6.13239	+	18.8735i	−0.242215	+	0.745460i	−0.996082	+	0.0884336i	$0.971814\pi$
$642$	2.51753	+	3.46508i	0.0993589	+	0.136756i
$643$	−9.72671	−	13.3877i	−0.383584	−	0.527958i	0.572946	−	0.819593i	$-0.305801\pi$
$643$	−9.72671	−	13.3877i	−0.383584	−	0.527958i	−0.956530	+	0.291635i	$0.905801\pi$
$644$	−15.3173	−	11.1287i	−0.603587	−	0.438532i
$645$	−25.9696	−	6.94281i	−1.02255	−	0.273373i
$646$	27.8756			1.09675
$647$	−4.22855	+	5.82010i	−0.166241	+	0.228812i	−0.884008	−	0.467473i	$-0.845165\pi$
$647$	−4.22855	+	5.82010i	−0.166241	+	0.228812i	0.717766	+	0.696284i	$0.245165\pi$
$648$	0.951057	−	0.309017i	0.0373610	−	0.0121393i
$649$	1.44559	−	4.44906i	0.0567443	−	0.174641i
$650$	−13.7475	−	7.91645i	−0.539222	−	0.310509i
$651$	17.4339	−	20.5252i	0.683290	−	0.804445i
$652$		−	16.8503i		−	0.659910i
$653$	0.131088	+	0.0425932i	0.00512989	+	0.00166680i	0.311581	−	0.950220i	$-0.399142\pi$
$653$	0.131088	+	0.0425932i	0.00512989	+	0.00166680i	−0.306451	+	0.951886i	$0.599142\pi$
$654$	−2.35215	−	7.23917i	−0.0919762	−	0.283074i
$655$	25.3509	+	31.2697i	0.990543	+	1.22181i
$656$	7.39372			0.288676
$657$			2.45611i			0.0958218i
$658$	4.36557	−	6.00869i	0.170188	−	0.234243i
$659$	−0.914232	+	0.664228i	−0.0356134	+	0.0258747i	−0.605450	−	0.795884i	$-0.707007\pi$
$659$	−0.914232	+	0.664228i	−0.0356134	+	0.0258747i	0.569836	+	0.821758i	$0.307007\pi$
$660$	4.02904	+	10.4783i	0.156830	+	0.407868i
$661$	14.4827	−	44.5733i	0.563313	−	1.73370i	−0.109598	−	0.993976i	$-0.534956\pi$
$661$	14.4827	−	44.5733i	0.563313	−	1.73370i	0.672911	−	0.739723i	$-0.265044\pi$
$662$	−0.150761	+	0.207505i	−0.00585950	+	0.00806491i
$663$	12.1786	+	3.95708i	0.472979	+	0.153680i
$664$	−2.01641	−	6.20586i	−0.0782517	−	0.240834i
$665$	26.8090	+	69.7223i	1.03961	+	2.70371i
$666$	−1.11356	−	3.42719i	−0.0431496	−	0.132801i
$667$	−7.46404	+	2.42521i	−0.289009	+	0.0939046i
$668$	14.0166	+	19.2923i	0.542320	+	0.746440i
$669$	7.13447	+	21.9576i	0.275835	+	0.848932i
$670$	4.08738	−	6.30180i	0.157909	−	0.243460i
$671$	45.2749	+	32.8941i	1.74782	+	1.26986i
$672$	−4.60004	−	1.49464i	−0.177450	−	0.0576572i
$673$	24.9083	+	34.2833i	0.960145	+	1.32153i	0.946871	+	0.321614i	$0.104225\pi$
$673$	24.9083	+	34.2833i	0.960145	+	1.32153i	0.0132736	+	0.999912i	$0.495775\pi$
$674$	−20.9944	+	15.2533i	−0.808674	+	0.587536i
$675$	4.56543	−	2.03884i	0.175723	−	0.0784750i
$676$	−2.93342			−0.112824
$677$			8.98736i			0.345412i	0.984973	+	0.172706i	$0.0552511\pi$
$677$			8.98736i			0.345412i	−0.984973	+	0.172706i	$0.944749\pi$
$678$	0.384475	−	0.529184i	0.0147657	−	0.0203232i
$679$	0.0751993	+	0.231440i	0.00288588	+	0.00888184i
$680$	−4.91097	+	7.57159i	−0.188327	+	0.290357i
$681$	1.35561			0.0519472
$682$	6.59933	+	27.1629i	0.252701	+	1.04012i
$683$		−	39.4695i		−	1.51026i	−0.655576	−	0.755129i	$-0.727574\pi$
$683$		−	39.4695i		−	1.51026i	0.655576	−	0.755129i	$-0.272426\pi$
$684$	−2.13430	+	6.56870i	−0.0816070	+	0.251161i
$685$	3.17050	−	0.167954i	0.121138	−	0.00641718i
$686$	36.7604	+	26.7080i	1.40352	+	1.01972i
$687$			13.1765i			0.502716i
$688$			12.0218i			0.458328i
$689$	−27.8152	−	20.2089i	−1.05967	−	0.769899i
$690$	−3.14139	−	8.16981i	−0.119591	−	0.311020i
$691$	−32.4296	+	23.5615i	−1.23368	+	0.896320i	−0.997160	−	0.0753065i	$-0.976006\pi$
$691$	−32.4296	+	23.5615i	−1.23368	+	0.896320i	−0.236519	+	0.971627i	$0.576006\pi$
$692$	−14.4925	−	4.70890i	−0.550923	−	0.179006i
$693$	14.2733	−	19.6455i	0.542196	−	0.746269i
$694$	0.633841	−	1.95076i	0.0240603	−	0.0740500i
$695$	0.124961	+	2.35891i	0.00474004	+	0.0894787i
$696$	−1.62202	+	1.17846i	−0.0614824	+	0.0446696i
$697$	−28.3805	+	9.22140i	−1.07499	+	0.349285i
$698$	−27.3299	+	8.88001i	−1.03445	+	0.336114i
$699$	−1.09662	+	0.796744i	−0.0414782	+	0.0301356i
$700$	−23.6610	−	5.00139i	−0.894303	−	0.189035i
$701$	5.77633	−	17.7777i	0.218169	−	0.671455i	−0.780744	−	0.624851i	$-0.785160\pi$
$701$	5.77633	−	17.7777i	0.218169	−	0.671455i	0.998913	−	0.0466048i	$-0.0148402\pi$
$702$	−1.86492	+	2.56684i	−0.0703868	+	0.0968791i
$703$	23.6707	+	7.69108i	0.892757	+	0.290074i
$704$	4.06169	−	2.95099i	0.153081	−	0.111220i
$705$	3.20486	−	1.23231i	0.120702	−	0.0464114i
$706$	14.7384	+	10.7081i	0.554688	+	0.403004i
$707$		−	18.9394i		−	0.712291i
$708$			0.931780i			0.0350184i
$709$	−13.4452	−	9.76852i	−0.504945	−	0.366864i	0.305957	−	0.952045i	$-0.401023\pi$
$709$	−13.4452	−	9.76852i	−0.504945	−	0.366864i	−0.810903	+	0.585181i	$0.801023\pi$
$710$	25.1798	−	1.33387i	0.944981	−	0.0500594i
$711$	−2.54691	+	7.83859i	−0.0955167	+	0.293970i
$712$			17.2516i			0.646532i
$713$	−5.14541	−	21.1786i	−0.192697	−	0.793145i
$714$	19.5212			0.730563
$715$	−29.8831	−	19.3823i	−1.11756	−	0.724858i
$716$	−2.13139	−	6.55975i	−0.0796539	−	0.245149i
$717$	10.2174	−	14.0630i	0.381575	−	0.525192i
$718$			21.6975i			0.809743i
$719$	−24.3557			−0.908316			−0.454158	−	0.890921i	$-0.650060\pi$
$719$	−24.3557			−0.908316			−0.454158	+	0.890921i	$0.650060\pi$
$720$	−1.40818	−	1.73696i	−0.0524799	−	0.0647325i
$721$	−31.0479	+	22.5576i	−1.15628	+	0.840089i
$722$	−16.8713	−	23.2213i	−0.627884	−	0.864208i
$723$	−0.250648	−	0.0814406i	−0.00932172	−	0.00302881i
$724$	3.89975	+	2.83334i	0.144933	+	0.105300i
$725$	−7.44216	+	6.71619i	−0.276395	+	0.249433i
$726$	4.38979	+	13.5104i	0.162920	+	0.501417i
$727$	−0.726360	−	0.999748i	−0.0269392	−	0.0370786i	0.795335	−	0.606170i	$-0.207295\pi$
$727$	−0.726360	−	0.999748i	−0.0269392	−	0.0370786i	−0.822274	+	0.569092i	$0.807295\pi$
$728$	14.5950	−	4.74219i	0.540925	−	0.175757i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	5.12613	−	1.97106i	0.189727	−	0.0729521i
$731$	−14.9935	−	46.1454i	−0.554556	−	1.70675i
$732$	−10.6012	−	3.44455i	−0.391833	−	0.127314i
$733$	20.9947	−	28.8968i	0.775458	−	1.06733i	−0.220311	−	0.975430i	$-0.570707\pi$
$733$	20.9947	−	28.8968i	0.775458	−	1.06733i	0.995769	−	0.0918965i	$-0.0292929\pi$
$734$	−5.60886	+	17.2623i	−0.207027	+	0.637163i
$735$	13.1567	+	34.2166i	0.485292	+	1.26210i
$736$	−3.16685	+	2.30085i	−0.116732	+	0.0848105i
$737$	9.91281	−	13.6438i	0.365143	−	0.502576i
$738$		−	7.39372i		−	0.272167i
$739$	−26.6317			−0.979664			−0.489832	−	0.871817i	$-0.662942\pi$
$739$	−26.6317			−0.979664			−0.489832	+	0.871817i	$0.662942\pi$
$740$	−6.25922	+	5.07447i	−0.230094	+	0.186541i
$741$	−6.77169	−	20.8411i	−0.248764	−	0.765617i
$742$	−49.8477	−	16.1965i	−1.82997	−	0.594592i
$743$			37.7845i			1.38618i	0.720851	+	0.693090i	$0.243751\pi$
$743$			37.7845i			1.38618i	−0.720851	+	0.693090i	$0.756249\pi$
$744$	−2.92203	−	4.73938i	−0.107127	−	0.173754i
$745$	3.35383	+	0.896626i	0.122875	+	0.0328498i
$746$	−4.16096	+	12.8061i	−0.152343	+	0.468865i
$747$	−6.20586	+	2.01641i	−0.227061	+	0.0737764i
$748$	−11.9102	+	16.3930i	−0.435480	+	0.599387i
$749$	−20.7162			−0.756955
$750$	−7.91907	−	7.89229i	−0.289164	−	0.288186i
$751$	6.62034	+	4.80996i	0.241580	+	0.175518i	0.701987	−	0.712190i	$-0.252297\pi$
$751$	6.62034	+	4.80996i	0.241580	+	0.175518i	−0.460407	+	0.887708i	$0.652297\pi$
$752$	−0.902579	−	1.24229i	−0.0329137	−	0.0453018i
$753$	−2.93025	−	4.03315i	−0.106784	−	0.146976i
$754$	1.96572	−	6.04986i	0.0715872	−	0.220323i
$755$	10.3956	+	12.8227i	0.378335	+	0.466666i
$756$	−1.49464	+	4.60004i	−0.0543597	+	0.167302i
$757$	25.3344	−	8.23166i	0.920796	−	0.299185i	0.190003	−	0.981784i	$-0.439150\pi$
$757$	25.3344	−	8.23166i	0.920796	−	0.299185i	0.730793	+	0.682599i	$0.239150\pi$
$758$	4.59678	+	6.32693i	0.166963	+	0.229804i
$759$	−6.07297	−	18.6907i	−0.220435	−	0.678428i
$760$	15.4223	−	0.816981i	0.559427	−	0.0296350i
$761$	27.5264	−	19.9991i	0.997833	−	0.724968i	0.0362105	−	0.999344i	$-0.488471\pi$
$761$	27.5264	−	19.9991i	0.997833	−	0.724968i	0.961622	+	0.274376i	$0.0884713\pi$
$762$	4.78294	−	1.55407i	0.173268	−	0.0562981i
$763$	35.0142	+	11.3768i	1.26760	+	0.411868i
$764$	−3.18364	−	2.31305i	−0.115180	−	0.0836833i
$765$	7.57159	+	4.91097i	0.273751	+	0.177557i
$766$	−11.4236	+	8.29971i	−0.412751	+	0.299881i
$767$	−1.73769	−	2.39173i	−0.0627445	−	0.0863604i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	−22.3633			−0.806442			−0.403221	−	0.915103i	$-0.632109\pi$
$769$	−22.3633			−0.806442			−0.403221	+	0.915103i	$0.632109\pi$
$770$	−52.4564	−	14.0239i	−1.89040	−	0.505387i
$771$	−19.2523	−	13.9876i	−0.693353	−	0.503750i
$772$	−7.82842	+	2.54361i	−0.281751	+	0.0915464i
$773$	−23.5530	−	7.65282i	−0.847141	−	0.275253i	−0.146893	−	0.989152i	$-0.546927\pi$
$773$	−23.5530	−	7.65282i	−0.847141	−	0.275253i	−0.700248	+	0.713900i	$0.746927\pi$
$774$	12.0218			0.432115
$775$	−17.0320	−	22.0207i	−0.611808	−	0.791006i
$776$	0.0503125			0.00180611
$777$	16.5765	+	5.38604i	0.594679	+	0.193223i
$778$	−19.8352	+	6.44483i	−0.711125	+	0.231058i
$779$	41.3137	+	30.0162i	1.48022	+	1.07544i
$780$	6.85386	+	1.83234i	0.245408	+	0.0656083i
$781$	56.6141			2.02581
$782$	9.28624	−	12.7814i	0.332075	−	0.457062i
$783$	1.17846	+	1.62202i	0.0421149	+	0.0579662i
$784$	13.2633	−	9.63636i	0.473690	−	0.344156i
$785$	−13.2436	−	8.58986i	−0.472684	−	0.306585i
$786$	−14.5644	−	10.5816i	−0.519494	−	0.377435i
$787$	−3.54629	−	1.15226i	−0.126411	−	0.0410736i	0.245128	−	0.969491i	$-0.421170\pi$
$787$	−3.54629	−	1.15226i	−0.126411	−	0.0410736i	−0.371540	+	0.928417i	$0.621170\pi$
$788$	8.12311	−	2.63936i	0.289374	−	0.0940232i
$789$	−4.63551	+	3.36790i	−0.165029	+	0.119900i
$790$	18.4038	−	0.974924i	0.654779	−	0.0346862i
$791$	0.977658	+	3.00892i	0.0347615	+	0.106985i
$792$	−2.95099	−	4.06169i	−0.104859	−	0.144326i
$793$	33.6355	−	10.9288i	1.19443	−	0.388094i
$794$	−6.86102	+	21.1160i	−0.243488	+	0.749380i
$795$	−15.2596	−	18.8223i	−0.541202	−	0.667558i
$796$	−3.12724	+	9.62465i	−0.110842	+	0.341137i
$797$	−19.1070	−	26.2986i	−0.676806	−	0.931544i	0.323084	−	0.946370i	$-0.395280\pi$
$797$	−19.1070	−	26.2986i	−0.676806	−	0.931544i	−0.999890	+	0.0148263i	$0.995280\pi$
$798$	−19.6358	−	27.0263i	−0.695098	−	0.956721i
$799$	5.01390	+	3.64281i	0.177379	+	0.128873i
$800$	−2.49511	+	4.33295i	−0.0882154	+	0.153193i
$801$	17.2516			0.609557
$802$	1.19568	−	1.64572i	0.0422210	−	0.0581123i
$803$	11.7274	−	3.81047i	0.413851	−	0.134468i
$804$	−1.03803	+	3.19474i	−0.0366086	+	0.112670i
$805$	40.8997	+	10.9343i	1.44152	+	0.385383i
$806$	16.3389	+	6.71587i	0.575515	+	0.236557i
$807$		−	29.8877i		−	1.05210i
$808$	−3.72407	−	1.21002i	−0.131012	−	0.0425685i
$809$	6.73331	+	20.7230i	0.236730	+	0.728581i	0.996887	+	0.0788415i	$0.0251221\pi$
$809$	6.73331	+	20.7230i	0.236730	+	0.728581i	−0.760157	+	0.649740i	$0.774878\pi$
$810$	−1.73696	+	1.40818i	−0.0610304	+	0.0494785i
$811$	29.1603			1.02396			0.511978	−	0.858999i	$-0.328913\pi$
$811$	29.1603			1.02396			0.511978	+	0.858999i	$0.328913\pi$
$812$		−	9.69736i		−	0.340310i
$813$	−7.29125	+	10.0355i	−0.255715	+	0.351962i
$814$	−14.6365	+	10.6341i	−0.513010	+	0.372724i
$815$	13.5226	+	35.1683i	0.473677	+	1.23189i
$816$	1.24719	−	3.83847i	0.0436605	−	0.134373i
$817$	−48.8048	+	67.1740i	−1.70746	+	2.35012i
$818$	−31.0377	−	10.0848i	−1.08521	−	0.352606i
$819$	−4.74219	−	14.5950i	−0.165706	−	0.509989i
$820$	−15.4314	+	5.93356i	−0.538888	+	0.207209i
$821$	−0.143488	−	0.441611i	−0.00500777	−	0.0154123i	0.948521	−	0.316713i	$-0.102579\pi$
$821$	−0.143488	−	0.441611i	−0.00500777	−	0.0154123i	−0.953529	+	0.301301i	$0.902579\pi$
$822$	−1.35038	+	0.438766i	−0.0471000	+	0.0153037i
$823$	−32.1619	−	44.2671i	−1.12109	−	1.54305i	−0.803969	−	0.594671i	$-0.797282\pi$
$823$	−32.1619	−	44.2671i	−1.12109	−	1.54305i	−0.317126	−	0.948384i	$-0.602718\pi$
$824$	2.45189	+	7.54614i	0.0854157	+	0.262882i
$825$	−16.8180	−	18.6359i	−0.585527	−	0.648819i
$826$	−3.64608	−	2.64903i	−0.126863	−	0.0921717i
$827$	−0.0605903	−	0.0196870i	−0.00210693	−	0.000684583i	0.307963	−	0.951398i	$-0.400353\pi$
$827$	−0.0605903	−	0.0196870i	−0.00210693	−	0.000684583i	−0.310070	+	0.950714i	$0.600353\pi$
$828$	2.30085	+	3.16685i	0.0799601	+	0.110056i
$829$	−10.4226	+	7.57249i	−0.361993	+	0.263003i	−0.753883	−	0.657009i	$-0.771821\pi$
$829$	−10.4226	+	7.57249i	−0.361993	+	0.263003i	0.391890	+	0.920012i	$0.371821\pi$
$830$	9.18872	+	11.3340i	0.318945	+	0.393410i
$831$	−18.2461			−0.632951
$832$		−	3.17279i		−	0.109997i
$833$	−38.8924	+	53.5308i	−1.34754	+	1.85473i
$834$	−0.326451	−	1.00471i	−0.0113041	−	0.0347904i
$835$	−44.7364	−	29.0163i	−1.54817	−	1.00415i
$836$	34.6755			1.19928
$837$	−4.73938	+	2.92203i	−0.163817	+	0.101000i
$838$		−	24.2822i		−	0.838816i
$839$	12.3447	−	37.9930i	0.426185	−	1.31166i	−0.475669	−	0.879624i	$-0.657794\pi$
$839$	12.3447	−	37.9930i	0.426185	−	1.31166i	0.901855	−	0.432039i	$-0.142206\pi$
$840$	10.8002	−	0.572130i	0.372642	−	0.0197403i
$841$	20.2095	+	14.6830i	0.696878	+	0.506312i
$842$		−	13.9178i		−	0.479639i
$843$			25.4174i			0.875422i
$844$	17.7085	+	12.8659i	0.609550	+	0.442864i
$845$	6.12232	−	2.35411i	0.210614	−	0.0809837i
$846$	−1.24229	+	0.902579i	−0.0427109	+	0.0310313i
$847$	−65.3466	−	21.2324i	−2.24533	−	0.729554i
$848$	−6.36945	+	8.76680i	−0.218728	+	0.301053i
$849$	−8.19587	+	25.2243i	−0.281282	+	0.865696i
$850$	4.17337	−	19.7438i	0.143145	−	0.677205i
$851$	11.4119	−	8.29124i	0.391196	−	0.284220i
$852$	−10.7246	+	3.48464i	−0.367419	+	0.119382i
$853$	−33.6984	+	10.9493i	−1.15381	+	0.374896i	−0.822577	−	0.568653i	$-0.807465\pi$
$853$	−33.6984	+	10.9493i	−1.15381	+	0.374896i	−0.331233	+	0.943549i	$0.607465\pi$
$854$	43.6178	−	31.6902i	1.49257	−	1.08442i
$855$	−0.816981	−	15.4223i	−0.0279402	−	0.527432i
$856$	−1.32354	+	4.07344i	−0.0452377	+	0.139227i
$857$	−14.8304	+	20.4123i	−0.506598	+	0.697272i	−0.983341	−	0.181771i	$-0.941817\pi$
$857$	−14.8304	+	20.4123i	−0.506598	+	0.697272i	0.476743	+	0.879043i	$0.341817\pi$
$858$	15.1494	+	4.92235i	0.517193	+	0.168046i
$859$	37.3194	−	27.1142i	1.27332	−	0.925123i	0.273993	−	0.961732i	$-0.411655\pi$
$859$	37.3194	−	27.1142i	1.27332	−	0.925123i	0.999330	+	0.0366085i	$0.0116555\pi$
$860$	−9.64768	−	25.0907i	−0.328983	−	0.855586i
$861$	28.9318	+	21.0202i	0.985995	+	0.716367i
$862$			7.35624i			0.250554i
$863$		−	43.3873i		−	1.47692i	−0.674297	−	0.738461i	$-0.735553\pi$
$863$		−	43.3873i		−	1.47692i	0.674297	−	0.738461i	$-0.264447\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	34.0262	−	1.80250i	1.15693	−	0.0612870i
$866$	6.21826	−	19.1378i	0.211305	−	0.650330i
$867$		−	0.710683i		−	0.0241361i
$868$	26.8526	+	2.03997i	0.911438	+	0.0692411i
$869$	41.3791			1.40369
$870$	2.43957	−	3.76126i	0.0827093	−	0.127519i
$871$	−3.29346	−	10.1362i	−0.111595	−	0.343453i
$872$	4.47405	−	6.15800i	0.151510	−	0.208536i
$873$		−	0.0503125i		−	0.00170282i
$874$	−27.0360			−0.914508
$875$	53.3966	−	8.54992i	1.80513	−	0.289040i
$876$	−1.98703	+	1.44366i	−0.0671356	+	0.0487768i
$877$	−7.99283	−	11.0012i	−0.269899	−	0.371484i	0.652457	−	0.757826i	$-0.273738\pi$
$877$	−7.99283	−	11.0012i	−0.269899	−	0.371484i	−0.922356	+	0.386342i	$0.873738\pi$
$878$	36.5718	+	11.8829i	1.23424	+	0.401029i
$879$	−20.2305	−	14.6983i	−0.682359	−	0.495763i
$880$	−6.10893	+	9.41856i	−0.205932	+	0.317500i
$881$	2.37397	+	7.30632i	0.0799810	+	0.246156i	0.983049	−	0.183340i	$-0.0586910\pi$
$881$	2.37397	+	7.30632i	0.0799810	+	0.246156i	−0.903069	+	0.429497i	$0.858691\pi$
$882$	−9.63636	−	13.2633i	−0.324473	−	0.446599i
$883$	29.9000	−	9.71509i	1.00621	−	0.326939i	0.240868	−	0.970558i	$-0.422568\pi$
$883$	29.9000	−	9.71509i	1.00621	−	0.326939i	0.765346	+	0.643619i	$0.222568\pi$
$884$	3.95708	+	12.1786i	0.133091	+	0.409612i
$885$	−0.747766	−	1.94471i	−0.0251359	−	0.0653709i
$886$	3.35621	+	10.3293i	0.112754	+	0.347021i
$887$	48.0551	+	15.6140i	1.61353	+	0.524268i	0.970403	−	0.241490i	$-0.0776361\pi$
$887$	48.0551	+	15.6140i	1.61353	+	0.524268i	0.643129	+	0.765758i	$0.277636\pi$
$888$	2.11812	−	2.91534i	0.0710794	−	0.0978324i
$889$	−7.51669	+	23.1340i	−0.252102	+	0.775889i
$890$	−13.8447	−	36.0058i	−0.464075	−	1.20692i
$891$	−4.06169	+	2.95099i	−0.136072	+	0.0988619i
$892$	−13.5706	+	18.6783i	−0.454376	+	0.625395i
$893$		−	10.6057i		−	0.354907i
$894$	−1.55255			−0.0519251
$895$	9.71271	+	11.9804i	0.324660	+	0.400459i
$896$	−1.49464	−	4.60004i	−0.0499326	−	0.153677i
$897$	−11.8118	−	3.83789i	−0.394385	−	0.128144i
$898$		−	10.1134i		−	0.337489i
$899$	7.22667	−	8.50803i	0.241023	−	0.283759i
$900$	4.33295	+	2.49511i	0.144432	+	0.0831703i
$901$	13.5150	−	41.5950i	0.450251	−	1.38573i
$902$	−35.3035	+	11.4708i	−1.17548	+	0.381936i
$903$	−34.1778	+	47.0417i	−1.13737	+	1.56545i
$904$	0.654107			0.0217553
$905$	−10.4130	−	2.78384i	−0.346138	−	0.0925381i
$906$	−5.97239	−	4.33919i	−0.198419	−	0.144160i
$907$	−8.89723	−	12.2460i	−0.295428	−	0.406621i	0.635340	−	0.772233i	$-0.280860\pi$
$907$	−8.89723	−	12.2460i	−0.295428	−	0.406621i	−0.930768	+	0.365611i	$0.880860\pi$
$908$	0.796810	+	1.09671i	0.0264431	+	0.0363958i
$909$	−1.21002	+	3.72407i	−0.0401339	+	0.123520i
$910$	−26.6554	+	21.6101i	−0.883619	+	0.716367i
$911$	−3.42393	+	10.5378i	−0.113440	+	0.349132i	−0.991618	−	0.129201i	$-0.958759\pi$
$911$	−3.42393	+	10.5378i	−0.113440	+	0.349132i	0.878179	+	0.478333i	$0.158759\pi$
$912$	−6.56870	+	2.13430i	−0.217512	+	0.0706738i
$913$	19.2559	+	26.5034i	0.637276	+	0.877136i
$914$	5.54204	+	17.0566i	0.183314	+	0.564183i
$915$	24.8901	−	1.31853i	0.822842	−	0.0435892i
$916$	−10.6600	+	7.74497i	−0.352217	+	0.255901i
$917$	82.8126	−	26.9074i	2.73471	−	0.888562i
$918$	−3.83847	−	1.24719i	−0.126688	−	0.0411635i
$919$	19.7015	+	14.3140i	0.649892	+	0.472174i	0.863234	−	0.504803i	$-0.168435\pi$
$919$	19.7015	+	14.3140i	0.649892	+	0.472174i	−0.213342	+	0.976978i	$0.568435\pi$
$920$	4.76306	−	7.34354i	0.157033	−	0.242109i
$921$	−10.6178	+	7.71429i	−0.349869	+	0.254195i
$922$	−10.9162	−	15.0249i	−0.359507	−	0.494819i
$923$	21.0298	−	28.9450i	0.692205	−	0.952738i
$924$	24.2831			0.798856
$925$	8.99127	−	15.6140i	0.295631	−	0.513386i
$926$	18.5096	+	13.4480i	0.608262	+	0.441928i
$927$	7.54614	−	2.45189i	0.247848	−	0.0805307i
$928$	−1.90680	−	0.619555i	−0.0625936	−	0.0203379i
$929$	54.4637			1.78690			0.893448	−	0.449166i	$-0.148279\pi$
$929$	54.4637			1.78690			0.893448	+	0.449166i	$0.148279\pi$
$930$	9.90198	+	7.54657i	0.324699	+	0.247462i
$931$	113.232			3.71102
$932$	−1.28916	−	0.418873i	−0.0422278	−	0.0137207i
$933$	22.5732	−	7.33446i	0.739012	−	0.240120i
$934$	−28.8374	−	20.9516i	−0.943590	−	0.685558i
$935$	11.7021	−	43.7718i	0.382701	−	1.43149i
$936$	−3.17279			−0.103706
$937$	29.0020	−	39.9178i	0.947453	−	1.30406i	−0.00519674	−	0.999986i	$-0.501654\pi$
$937$	29.0020	−	39.9178i	0.947453	−	1.30406i	0.952650	−	0.304070i	$-0.0983458\pi$
$938$	−9.55000	−	13.1444i	−0.311819	−	0.429181i
$939$	17.5502	−	12.7510i	0.572729	−	0.416112i
$940$	2.88073	+	1.86845i	0.0939589	+	0.0609422i
$941$	4.10778	+	2.98448i	0.133910	+	0.0972912i	0.652724	−	0.757596i	$-0.273626\pi$
$941$	4.10778	+	2.98448i	0.133910	+	0.0972912i	−0.518814	+	0.854887i	$0.673626\pi$
$942$	6.71392	+	2.18149i	0.218751	+	0.0710767i
$943$	27.5257	−	8.94365i	0.896361	−	0.291245i
$944$	−0.753826	+	0.547687i	−0.0245349	+	0.0178257i
$945$	−0.572130	−	10.8002i	−0.0186114	−	0.351331i
$946$	−18.6510	−	57.4018i	−0.606396	−	1.86629i
$947$	25.4186	+	34.9857i	0.825994	+	1.13688i	0.988655	+	0.150202i	$0.0479923\pi$
$947$	25.4186	+	34.9857i	0.825994	+	1.13688i	−0.162661	+	0.986682i	$0.552008\pi$
$948$	−7.83859	+	2.54691i	−0.254586	+	0.0827199i
$949$	2.40808	−	7.41130i	0.0781695	−	0.240581i
$950$	−31.5322	+	14.0817i	−1.02304	+	0.456872i
$951$	−1.88749	+	5.80909i	−0.0612060	+	0.188373i
$952$	11.4743	+	15.7930i	0.371884	+	0.511854i
$953$	17.9540	+	24.7115i	0.581586	+	0.800484i	0.993868	−	0.110572i	$-0.0352682\pi$
$953$	17.9540	+	24.7115i	0.581586	+	0.800484i	−0.412282	+	0.911056i	$0.635268\pi$
$954$	8.76680	+	6.36945i	0.283836	+	0.206219i
$955$	8.50083	+	2.27265i	0.275080	+	0.0735411i
$956$	17.3828			0.562201
$957$	5.91651	−	8.14337i	0.191254	−	0.263238i
$958$	−5.56538	+	1.80830i	−0.179809	+	0.0584236i
$959$	2.12221	−	6.53150i	0.0685298	−	0.210913i
$960$	0.577517	−	2.16020i	0.0186393	−	0.0697202i
$961$	22.0391	+	21.8009i	0.710938	+	0.703255i
$962$			11.4333i			0.368625i
$963$	4.07344	+	1.32354i	0.131265	+	0.0426506i
$964$	−0.0814406	−	0.250648i	−0.00262303	−	0.00807284i
$965$	14.2974	−	11.5912i	0.460249	−	0.373133i
$966$	−18.9333			−0.609167
$967$		−	27.8388i		−	0.895234i	−0.894225	−	0.447617i	$-0.852273\pi$
$967$		−	27.8388i		−	0.895234i	0.894225	−	0.447617i	$-0.147727\pi$
$968$	−8.34987	+	11.4926i	−0.268375	+	0.369386i
$969$	22.5519	−	16.3849i	0.724470	−	0.526358i
$970$	−0.105007	+	0.0403765i	−0.00337157	+	0.00129641i
$971$	−3.19329	+	9.82793i	−0.102478	+	0.315393i	−0.989130	−	0.147043i	$-0.953025\pi$
$971$	−3.19329	+	9.82793i	−0.102478	+	0.315393i	0.886653	+	0.462436i	$0.153025\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	4.85957	+	1.57897i	0.155791	+	0.0506194i
$974$	−0.403494	−	1.24183i	−0.0129288	−	0.0397907i
$975$	−15.7752	+	1.67605i	−0.505209	+	0.0536765i
$976$	−3.44455	−	10.6012i	−0.110257	−	0.339338i
$977$	24.3030	−	7.89654i	0.777523	−	0.252633i	0.106741	−	0.994287i	$-0.465958\pi$
$977$	24.3030	−	7.89654i	0.777523	−	0.252633i	0.670782	+	0.741654i	$0.265958\pi$
$978$	−9.90438	−	13.6322i	−0.316707	−	0.435910i
$979$	−26.7647	−	82.3731i	−0.855402	−	2.63266i
$980$	−19.9485	+	30.7560i	−0.637231	+	0.982464i
$981$	−6.15800	−	4.47405i	−0.196610	−	0.142845i
$982$	0.971918	+	0.315795i	0.0310152	+	0.0100774i
$983$	14.3548	+	19.7577i	0.457847	+	0.630173i	0.974061	−	0.226287i	$-0.0726588\pi$
$983$	14.3548	+	19.7577i	0.457847	+	0.630173i	−0.516213	+	0.856460i	$0.672659\pi$
$984$	5.98164	−	4.34592i	0.190688	−	0.138543i
$985$	−14.8356	+	12.0275i	−0.472701	+	0.383228i
$986$	8.09188			0.257698
$987$		−	7.42715i		−	0.236409i
$988$	12.8805	−	17.7285i	0.409784	−	0.564019i
$989$	14.5419	+	44.7555i	0.462407	+	1.42314i
$990$	9.41856	+	6.10893i	0.299341	+	0.194154i
$991$	37.2588			1.18356			0.591782	−	0.806098i	$-0.298425\pi$
$991$	37.2588			1.18356			0.591782	+	0.806098i	$0.298425\pi$
$992$	2.11671	−	5.14971i	0.0672056	−	0.163504i
$993$			0.256490i			0.00813947i
$994$	16.8544	−	51.8725i	0.534589	−	1.64530i
$995$	−1.19706	−	22.5972i	−0.0379495	−	0.716380i
$996$	−5.27902	−	3.83543i	−0.167272	−	0.121530i
$997$			9.74144i			0.308514i	0.988031	+	0.154257i	$0.0492984\pi$
$997$			9.74144i			0.308514i	−0.988031	+	0.154257i	$0.950702\pi$
$998$			30.5256i			0.966271i
$999$	−2.91534	−	2.11812i	−0.0922372	−	0.0670143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.349.11	yes	72
5.4	even	2	inner	930.2.z.d.349.2	✓	72
31.4	even	5	inner	930.2.z.d.469.2	yes	72
155.4	even	10	inner	930.2.z.d.469.11	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.349.2	✓	72	5.4	even	2	inner
930.2.z.d.349.11	yes	72	1.1	even	1	trivial
930.2.z.d.469.2	yes	72	31.4	even	5	inner
930.2.z.d.469.11	yes	72	155.4	even	10	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:	\( N \)	\(=\)	\( 930 = 2 \cdot 3 \cdot 5 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	930.z (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.16020 - 0.577517i) q^{5} +1.00000 q^{6} +(-2.84298 + 3.91303i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(-2.16020 - 0.577517i) q^{5} +1.00000 q^{6} +(-2.84298 + 3.91303i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(-1.87601 - 1.21679i) q^{10} +(-4.06169 - 2.95099i) q^{11} +(0.951057 + 0.309017i) q^{12} +(-3.01750 + 0.980445i) q^{13} +(-3.91303 + 2.84298i) q^{14} +(-2.23294 + 0.118288i) q^{15} +(0.309017 + 0.951057i) q^{16} +(-2.37230 - 3.26519i) q^{17} +(0.951057 - 0.309017i) q^{18} +(-2.13430 + 6.56870i) q^{19} +(-1.40818 - 1.73696i) q^{20} +(-1.49464 + 4.60004i) q^{21} +(-2.95099 - 4.06169i) q^{22} +(2.30085 + 3.16685i) q^{23} +(0.809017 + 0.587785i) q^{24} +(4.33295 + 2.49511i) q^{25} -3.17279 q^{26} +(0.587785 - 0.809017i) q^{27} +(-4.60004 + 1.49464i) q^{28} +(-0.619555 + 1.90680i) q^{29} +(-2.16020 - 0.577517i) q^{30} +(-5.14971 - 2.11671i) q^{31} +1.00000i q^{32} +(-4.77480 - 1.55143i) q^{33} +(-1.24719 - 3.83847i) q^{34} +(8.40126 - 6.81106i) q^{35} +1.00000 q^{36} -3.60356i q^{37} +(-4.05968 + 5.58767i) q^{38} +(-2.56684 + 1.86492i) q^{39} +(-0.802514 - 2.08710i) q^{40} +(2.28478 - 7.03185i) q^{41} +(-2.84298 + 3.91303i) q^{42} +(11.4334 + 3.71495i) q^{43} +(-1.55143 - 4.77480i) q^{44} +(-2.08710 + 0.802514i) q^{45} +(1.20963 + 3.72285i) q^{46} +(-1.46040 + 0.474514i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-5.06613 - 15.5920i) q^{49} +(3.34985 + 3.71194i) q^{50} +(-3.26519 - 2.37230i) q^{51} +(-3.01750 - 0.980445i) q^{52} +(6.36945 + 8.76680i) q^{53} +(0.809017 - 0.587785i) q^{54} +(7.06982 + 8.72043i) q^{55} -4.83677 q^{56} +6.90674i q^{57} +(-1.17846 + 1.62202i) q^{58} +(0.287936 + 0.886175i) q^{59} +(-1.87601 - 1.21679i) q^{60} -11.1468 q^{61} +(-4.24357 - 3.60446i) q^{62} +4.83677i q^{63} +(-0.309017 + 0.951057i) q^{64} +(7.08464 - 0.375301i) q^{65} +(-4.06169 - 2.95099i) q^{66} +3.35915i q^{67} -4.03600i q^{68} +(3.16685 + 2.30085i) q^{69} +(10.0948 - 3.88157i) q^{70} +(-9.12291 + 6.62818i) q^{71} +(0.951057 + 0.309017i) q^{72} +(-1.44366 + 1.98703i) q^{73} +(1.11356 - 3.42719i) q^{74} +(4.89191 + 1.03404i) q^{75} +(-5.58767 + 4.05968i) q^{76} +(23.0946 - 7.50390i) q^{77} +(-3.01750 + 0.980445i) q^{78} +(-6.66791 + 4.84452i) q^{79} +(-0.118288 - 2.23294i) q^{80} +(0.309017 - 0.951057i) q^{81} +(4.34592 - 5.98164i) q^{82} +(-6.20586 - 2.01641i) q^{83} +(-3.91303 + 2.84298i) q^{84} +(3.23895 + 8.42353i) q^{85} +(9.72586 + 7.06625i) q^{86} +2.00492i q^{87} -5.02052i q^{88} +(13.9569 + 10.1403i) q^{89} +(-2.23294 + 0.118288i) q^{90} +(4.74219 - 14.5950i) q^{91} +3.91444i q^{92} +(-5.55177 - 0.421763i) q^{93} -1.53556 q^{94} +(8.40406 - 12.9571i) q^{95} +(0.309017 + 0.951057i) q^{96} +(0.0295729 - 0.0407037i) q^{97} -16.3944i q^{98} -5.02052 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9}+O(q^{10}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9	\( 72 q + 18 q^{4} + 4 q^{5} + 72 q^{6} + 18 q^{9} - 6 q^{11} - 4 q^{14} - 18 q^{16} + 12 q^{19} - 4 q^{20} - 16 q^{21} + 18 q^{24} - 4 q^{25} + 12 q^{26} + 24 q^{29} + 4 q^{30} + 22 q^{31} + 14 q^{34} - 22 q^{35} + 72 q^{36} + 8 q^{39} - 28 q^{41} - 4 q^{44} - 4 q^{45} - 22 q^{46} + 42 q^{49} - 32 q^{50} - 4 q^{51} + 18 q^{54} + 14 q^{55} + 24 q^{56} - 28 q^{59} + 56 q^{61} + 18 q^{64} + 46 q^{65} - 6 q^{66} - 8 q^{69} + 46 q^{70} - 68 q^{71} + 8 q^{74} + 32 q^{75} - 12 q^{76} + 26 q^{79} - 6 q^{80} - 18 q^{81} - 4 q^{84} - 32 q^{85} + 80 q^{86} + 32 q^{89} - 44 q^{91} + 12 q^{94} + 74 q^{95} - 18 q^{96} - 4 q^{99}+O(q^{100}) \) 72 * q + 18 * q^4 + 4 * q^5 + 72 * q^6 + 18 * q^9 - 6 * q^11 - 4 * q^14 - 18 * q^16 + 12 * q^19 - 4 * q^20 - 16 * q^21 + 18 * q^24 - 4 * q^25 + 12 * q^26 + 24 * q^29 + 4 * q^30 + 22 * q^31 + 14 * q^34 - 22 * q^35 + 72 * q^36 + 8 * q^39 - 28 * q^41 - 4 * q^44 - 4 * q^45 - 22 * q^46 + 42 * q^49 - 32 * q^50 - 4 * q^51 + 18 * q^54 + 14 * q^55 + 24 * q^56 - 28 * q^59 + 56 * q^61 + 18 * q^64 + 46 * q^65 - 6 * q^66 - 8 * q^69 + 46 * q^70 - 68 * q^71 + 8 * q^74 + 32 * q^75 - 12 * q^76 + 26 * q^79 - 6 * q^80 - 18 * q^81 - 4 * q^84 - 32 * q^85 + 80 * q^86 + 32 * q^89 - 44 * q^91 + 12 * q^94 + 74 * q^95 - 18 * q^96 - 4 * q^99

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