LMFDB - Embedded newform 930.2.z.d.349.15

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			349.15
Character	$\chi$	$=$	930.349
Dual form			930.2.z.d.469.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.951057 + 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.756872 + 2.10408i) q^{5} +1.00000 q^{6} +(-2.15407 + 2.96482i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})$	\(q+(0.951057 + 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.756872 + 2.10408i) q^{5} +1.00000 q^{6} +(-2.15407 + 2.96482i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.0696317 + 2.23498i) q^{10} +(-1.06683 - 0.775098i) q^{11} +(0.951057 + 0.309017i) q^{12} +(-1.40500 + 0.456511i) q^{13} +(-2.96482 + 2.15407i) q^{14} +(1.37002 + 1.76721i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.66664 + 5.04670i) q^{17} +(0.951057 - 0.309017i) q^{18} +(1.42011 - 4.37065i) q^{19} +(-0.624424 + 2.14711i) q^{20} +(-1.13246 + 3.48536i) q^{21} +(-0.775098 - 1.06683i) q^{22} +(-2.34583 - 3.22876i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-3.85429 + 3.18503i) q^{25} -1.47730 q^{26} +(0.587785 - 0.809017i) q^{27} +(-3.48536 + 1.13246i) q^{28} +(-2.50015 + 7.69466i) q^{29} +(0.756872 + 2.10408i) q^{30} +(4.26078 + 3.58410i) q^{31} +1.00000i q^{32} +(-1.25414 - 0.407493i) q^{33} +(1.92767 + 5.93275i) q^{34} +(-7.86858 - 2.28834i) q^{35} +1.00000 q^{36} -5.13435i q^{37} +(2.70121 - 3.71790i) q^{38} +(-1.19516 + 0.868336i) q^{39} +(-1.25736 + 1.84907i) q^{40} +(0.894708 - 2.75363i) q^{41} +(-2.15407 + 2.96482i) q^{42} +(2.33014 + 0.757109i) q^{43} +(-0.407493 - 1.25414i) q^{44} +(1.84907 + 1.25736i) q^{45} +(-1.23328 - 3.79564i) q^{46} +(9.06957 - 2.94688i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-1.98704 - 6.11548i) q^{49} +(-4.64988 + 1.83811i) q^{50} +(5.04670 + 3.66664i) q^{51} +(-1.40500 - 0.456511i) q^{52} +(-0.0546022 - 0.0751534i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.823413 - 2.83135i) q^{55} -3.66472 q^{56} -4.59558i q^{57} +(-4.75556 + 6.54547i) q^{58} +(-3.99601 - 12.2985i) q^{59} +(0.0696317 + 2.23498i) q^{60} -0.469606 q^{61} +(2.94469 + 4.72534i) q^{62} +3.66472i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.02394 - 2.61070i) q^{65} +(-1.06683 - 0.775098i) q^{66} +15.6857i q^{67} +6.23806i q^{68} +(-3.22876 - 2.34583i) q^{69} +(-6.77632 - 4.60787i) q^{70} +(11.5879 - 8.41913i) q^{71} +(0.951057 + 0.309017i) q^{72} +(2.20955 - 3.04119i) q^{73} +(1.58660 - 4.88306i) q^{74} +(-2.68142 + 4.22019i) q^{75} +(3.71790 - 2.70121i) q^{76} +(4.59606 - 1.49335i) q^{77} +(-1.40500 + 0.456511i) q^{78} +(5.46961 - 3.97390i) q^{79} +(-1.76721 + 1.37002i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.70184 - 2.34238i) q^{82} +(13.0165 + 4.22932i) q^{83} +(-2.96482 + 2.15407i) q^{84} +(-7.84347 + 11.5346i) q^{85} +(1.98214 + 1.44011i) q^{86} +8.09064i q^{87} -1.31868i q^{88} +(-7.27261 - 5.28386i) q^{89} +(1.37002 + 1.76721i) q^{90} +(1.67299 - 5.14892i) q^{91} -3.99097i q^{92} +(5.15979 + 2.09203i) q^{93} +9.53631 q^{94} +(10.2710 - 0.319998i) q^{95} +(0.309017 + 0.951057i) q^{96} +(0.729409 - 1.00395i) q^{97} -6.43020i q^{98} -1.31868 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
$5$	0.756872	+	2.10408i	0.338483	+	0.940972i
$5$	0.756872	+	2.10408i	0.338483	+	0.940972i
$6$	1.00000			0.408248
$7$	−2.15407	+	2.96482i	−0.814162	+	1.12060i	0.176506	+	0.984300i	$0.443521\pi$
$7$	−2.15407	+	2.96482i	−0.814162	+	1.12060i	−0.990668	+	0.136298i	$0.956479\pi$
$8$	0.587785	+	0.809017i	0.207813	+	0.286031i
$9$	0.809017	−	0.587785i	0.269672	−	0.195928i
$10$	0.0696317	+	2.23498i	0.0220195	+	0.706764i
$11$	−1.06683	−	0.775098i	−0.321662	−	0.233701i	0.415223	−	0.909720i	$-0.363704\pi$
$11$	−1.06683	−	0.775098i	−0.321662	−	0.233701i	−0.736884	+	0.676019i	$0.763704\pi$
$12$	0.951057	+	0.309017i	0.274546	+	0.0892055i
$13$	−1.40500	+	0.456511i	−0.389676	+	0.126613i	−0.497301	−	0.867578i	$-0.665675\pi$
$13$	−1.40500	+	0.456511i	−0.389676	+	0.126613i	0.107625	+	0.994192i	$0.465675\pi$
$14$	−2.96482	+	2.15407i	−0.792382	+	0.575700i
$15$	1.37002	+	1.76721i	0.353739	+	0.456292i
$16$	0.309017	+	0.951057i	0.0772542	+	0.237764i
$17$	3.66664	+	5.04670i	0.889291	+	1.22400i	0.973760	+	0.227578i	$0.0730808\pi$
$17$	3.66664	+	5.04670i	0.889291	+	1.22400i	−0.0844685	+	0.996426i	$0.526919\pi$
$18$	0.951057	−	0.309017i	0.224166	−	0.0728360i
$19$	1.42011	−	4.37065i	0.325796	−	1.00270i	−0.645284	−	0.763943i	$-0.723261\pi$
$19$	1.42011	−	4.37065i	0.325796	−	1.00270i	0.971080	−	0.238754i	$-0.0767390\pi$
$20$	−0.624424	+	2.14711i	−0.139626	+	0.480109i
$21$	−1.13246	+	3.48536i	−0.247123	+	0.760568i
$22$	−0.775098	−	1.06683i	−0.165251	−	0.227449i
$23$	−2.34583	−	3.22876i	−0.489140	−	0.673244i	0.491089	−	0.871109i	$-0.336599\pi$
$23$	−2.34583	−	3.22876i	−0.489140	−	0.673244i	−0.980229	+	0.197866i	$0.936599\pi$
$24$	0.809017	+	0.587785i	0.165140	+	0.119981i
$25$	−3.85429	+	3.18503i	−0.770858	+	0.637007i
$26$	−1.47730			−0.289723
$27$	0.587785	−	0.809017i	0.113119	−	0.155695i
$28$	−3.48536	+	1.13246i	−0.658671	+	0.214015i
$29$	−2.50015	+	7.69466i	−0.464265	+	1.42886i	0.395639	+	0.918406i	$0.370523\pi$
$29$	−2.50015	+	7.69466i	−0.464265	+	1.42886i	−0.859904	+	0.510456i	$0.829477\pi$
$30$	0.756872	+	2.10408i	0.138185	+	0.384150i
$31$	4.26078	+	3.58410i	0.765258	+	0.643724i
$31$	4.26078	+	3.58410i	0.765258	+	0.643724i
$32$			1.00000i			0.176777i
$33$	−1.25414	−	0.407493i	−0.218317	−	0.0709355i
$34$	1.92767	+	5.93275i	0.330592	+	1.01746i
$35$	−7.86858	−	2.28834i	−1.33003	−	0.386800i
$36$	1.00000			0.166667
$37$		−	5.13435i		−	0.844083i	−0.906577	−	0.422041i	$-0.861314\pi$
$37$		−	5.13435i		−	0.844083i	0.906577	−	0.422041i	$-0.138686\pi$
$38$	2.70121	−	3.71790i	0.438195	−	0.603123i
$39$	−1.19516	+	0.868336i	−0.191379	+	0.139045i
$40$	−1.25736	+	1.84907i	−0.198806	+	0.292363i
$41$	0.894708	−	2.75363i	0.139730	−	0.430045i	−0.856566	−	0.516038i	$-0.827406\pi$
$41$	0.894708	−	2.75363i	0.139730	−	0.430045i	0.996296	+	0.0859933i	$0.0274064\pi$
$42$	−2.15407	+	2.96482i	−0.332380	+	0.457482i
$43$	2.33014	+	0.757109i	0.355343	+	0.115458i	0.481248	−	0.876584i	$-0.340184\pi$
$43$	2.33014	+	0.757109i	0.355343	+	0.115458i	−0.125905	+	0.992042i	$0.540184\pi$
$44$	−0.407493	−	1.25414i	−0.0614319	−	0.189068i
$45$	1.84907	+	1.25736i	0.275643	+	0.187436i
$46$	−1.23328	−	3.79564i	−0.181837	−	0.559637i
$47$	9.06957	−	2.94688i	1.32293	−	0.429847i	0.439432	−	0.898276i	$-0.355180\pi$
$47$	9.06957	−	2.94688i	1.32293	−	0.429847i	0.883501	+	0.468429i	$0.155180\pi$
$48$	0.587785	+	0.809017i	0.0848395	+	0.116772i
$49$	−1.98704	−	6.11548i	−0.283863	−	0.873641i
$50$	−4.64988	+	1.83811i	−0.657592	+	0.259947i
$51$	5.04670	+	3.66664i	0.706679	+	0.513433i
$52$	−1.40500	−	0.456511i	−0.194838	−	0.0633067i
$53$	−0.0546022	−	0.0751534i	−0.00750018	−	0.0103231i	0.805250	−	0.592935i	$-0.202031\pi$
$53$	−0.0546022	−	0.0751534i	−0.00750018	−	0.0103231i	−0.812751	+	0.582612i	$0.802031\pi$
$54$	0.809017	−	0.587785i	0.110093	−	0.0799874i
$55$	0.823413	−	2.83135i	0.111029	−	0.381779i
$56$	−3.66472			−0.489719
$57$		−	4.59558i		−	0.608699i
$58$	−4.75556	+	6.54547i	−0.624436	+	0.859462i
$59$	−3.99601	−	12.2985i	−0.520237	−	1.60112i	−0.773547	−	0.633739i	$-0.781519\pi$
$59$	−3.99601	−	12.2985i	−0.520237	−	1.60112i	0.253310	−	0.967385i	$-0.418481\pi$
$60$	0.0696317	+	2.23498i	0.00898941	+	0.288535i
$61$	−0.469606			−0.0601269			−0.0300634	−	0.999548i	$-0.509571\pi$
$61$	−0.469606			−0.0601269			−0.0300634	+	0.999548i	$0.509571\pi$
$62$	2.94469	+	4.72534i	0.373976	+	0.600118i
$63$			3.66472i			0.461712i
$64$	−0.309017	+	0.951057i	−0.0386271	+	0.118882i
$65$	−2.02394	−	2.61070i	−0.251039	−	0.323818i
$66$	−1.06683	−	0.775098i	−0.131318	−	0.0954080i
$67$			15.6857i			1.91632i	0.286241	+	0.958158i	$0.407594\pi$
$67$			15.6857i			1.91632i	−0.286241	+	0.958158i	$0.592406\pi$
$68$			6.23806i			0.756476i
$69$	−3.22876	−	2.34583i	−0.388698	−	0.282405i
$70$	−6.77632	−	4.60787i	−0.809926	−	0.550745i
$71$	11.5879	−	8.41913i	1.37523	−	0.999167i	0.377927	−	0.925835i	$-0.376637\pi$
$71$	11.5879	−	8.41913i	1.37523	−	0.999167i	0.997308	−	0.0733311i	$-0.0233630\pi$
$72$	0.951057	+	0.309017i	0.112083	+	0.0364180i
$73$	2.20955	−	3.04119i	0.258609	−	0.355944i	−0.659894	−	0.751358i	$-0.729399\pi$
$73$	2.20955	−	3.04119i	0.258609	−	0.355944i	0.918503	+	0.395414i	$0.129399\pi$
$74$	1.58660	−	4.88306i	0.184439	−	0.567644i
$75$	−2.68142	+	4.22019i	−0.309624	+	0.487305i
$76$	3.71790	−	2.70121i	0.426472	−	0.309850i
$77$	4.59606	−	1.49335i	0.523769	−	0.170183i
$78$	−1.40500	+	0.456511i	−0.159085	+	0.0516897i
$79$	5.46961	−	3.97390i	0.615379	−	0.447099i	−0.235925	−	0.971771i	$-0.575812\pi$
$79$	5.46961	−	3.97390i	0.615379	−	0.447099i	0.851304	+	0.524672i	$0.175812\pi$
$80$	−1.76721	+	1.37002i	−0.197580	+	0.153173i
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	1.70184	−	2.34238i	0.187936	−	0.258672i
$83$	13.0165	+	4.22932i	1.42875	+	0.464228i	0.918370	−	0.395722i	$-0.129506\pi$
$83$	13.0165	+	4.22932i	1.42875	+	0.464228i	0.510378	+	0.859950i	$0.329506\pi$
$84$	−2.96482	+	2.15407i	−0.323489	+	0.235028i
$85$	−7.84347	+	11.5346i	−0.850744	+	1.25110i
$86$	1.98214	+	1.44011i	0.213739	+	0.155291i
$87$			8.09064i			0.867408i
$88$		−	1.31868i		−	0.140571i
$89$	−7.27261	−	5.28386i	−0.770896	−	0.560088i	0.131337	−	0.991338i	$-0.458073\pi$
$89$	−7.27261	−	5.28386i	−0.770896	−	0.560088i	−0.902233	+	0.431249i	$0.858073\pi$
$90$	1.37002	+	1.76721i	0.144413	+	0.186280i
$91$	1.67299	−	5.14892i	0.175377	−	0.539754i
$92$		−	3.99097i		−	0.416088i
$93$	5.15979	+	2.09203i	0.535045	+	0.216934i
$94$	9.53631			0.983596
$95$	10.2710	−	0.319998i	1.05379	−	0.0328311i
$96$	0.309017	+	0.951057i	0.0315389	+	0.0970668i
$97$	0.729409	−	1.00395i	0.0740602	−	0.101935i	−0.770380	−	0.637585i	$-0.779933\pi$
$97$	0.729409	−	1.00395i	0.0740602	−	0.101935i	0.844440	+	0.535650i	$0.179933\pi$
$98$		−	6.43020i		−	0.649548i
$99$	−1.31868			−0.132532
$100$	−4.99030	+	0.311251i	−0.499030	+	0.0311251i
$101$	5.80233	−	4.21564i	0.577353	−	0.419472i	−0.260416	−	0.965497i	$-0.583860\pi$
$101$	5.80233	−	4.21564i	0.577353	−	0.419472i	0.837769	+	0.546025i	$0.183860\pi$
$102$	3.66664	+	5.04670i	0.363052	+	0.499698i
$103$	−1.81758	−	0.590567i	−0.179091	−	0.0581903i	0.218099	−	0.975927i	$-0.430015\pi$
$103$	−1.81758	−	0.590567i	−0.179091	−	0.0581903i	−0.397190	+	0.917736i	$0.630015\pi$
$104$	−1.19516	−	0.868336i	−0.117195	−	0.0851473i
$105$	−8.19060	+	0.255181i	−0.799320	+	0.0249031i
$106$	−0.0287061	−	0.0883482i	−0.00278818	−	0.00858113i
$107$	−6.73023	−	9.26337i	−0.650636	−	0.895524i	0.348490	−	0.937312i	$-0.386694\pi$
$107$	−6.73023	−	9.26337i	−0.650636	−	0.895524i	−0.999126	+	0.0417883i	$0.986694\pi$
$108$	0.951057	−	0.309017i	0.0915155	−	0.0297352i
$109$	5.40207	+	16.6259i	0.517425	+	1.59247i	0.778827	+	0.627239i	$0.215815\pi$
$109$	5.40207	+	16.6259i	0.517425	+	1.59247i	−0.261402	+	0.965230i	$0.584185\pi$
$110$	1.65805	−	2.43832i	0.158089	−	0.232485i
$111$	−1.58660	−	4.88306i	−0.150594	−	0.463480i
$112$	−3.48536	−	1.13246i	−0.329336	−	0.107008i
$113$	7.44465	−	10.2467i	0.700334	−	0.963927i	−0.299617	−	0.954060i	$-0.596859\pi$
$113$	7.44465	−	10.2467i	0.700334	−	0.963927i	0.999951	−	0.00986782i	$-0.00314108\pi$
$114$	1.42011	−	4.37065i	0.133006	−	0.409349i
$115$	5.01808	−	7.37958i	0.467938	−	0.688149i
$116$	−6.54547	+	4.75556i	−0.607731	+	0.441543i
$117$	−0.868336	+	1.19516i	−0.0802777	+	0.110493i
$118$		−	12.9314i		−	1.19043i
$119$	−22.8608			−2.09564
$120$	−0.624424	+	2.14711i	−0.0570019	+	0.196004i
$121$	−2.86184	−	8.80782i	−0.260167	−	0.800711i
$122$	−0.446622	−	0.145116i	−0.0404352	−	0.0131382i
$123$		−	2.89534i		−	0.261064i
$124$	1.34036	+	5.40402i	0.120368	+	0.485295i
$125$	−9.61876	−	5.69907i	−0.860328	−	0.509740i
$126$	−1.13246	+	3.48536i	−0.100888	+	0.310500i
$127$	−4.49246	+	1.45969i	−0.398641	+	0.129526i	−0.501475	−	0.865172i	$-0.667209\pi$
$127$	−4.49246	+	1.45969i	−0.398641	+	0.129526i	0.102834	+	0.994699i	$0.467209\pi$
$128$	−0.587785	+	0.809017i	−0.0519534	+	0.0715077i
$129$	2.45006			0.215715
$130$	−1.11813	−	3.10836i	−0.0980662	−	0.272621i
$131$	−9.15152	−	6.64897i	−0.799572	−	0.580923i	0.111216	−	0.993796i	$-0.464525\pi$
$131$	−9.15152	−	6.64897i	−0.799572	−	0.580923i	−0.910789	+	0.412873i	$0.864525\pi$
$132$	−0.775098	−	1.06683i	−0.0674636	−	0.0928557i
$133$	9.89920	+	13.6251i	0.858369	+	1.18144i
$134$	−4.84715	+	14.9180i	−0.418730	+	1.28872i
$135$	2.14711	+	0.624424i	0.184794	+	0.0537419i
$136$	−1.92767	+	5.93275i	−0.165296	+	0.508729i
$137$	−17.9823	+	5.84280i	−1.53633	+	0.499184i	−0.950361	−	0.311150i	$-0.899286\pi$
$137$	−17.9823	+	5.84280i	−1.53633	+	0.499184i	−0.585969	+	0.810334i	$0.699286\pi$
$138$	−2.34583	−	3.22876i	−0.199691	−	0.274851i
$139$	2.18005	+	6.70950i	0.184909	+	0.569092i	0.999947	−	0.0103160i	$-0.00328375\pi$
$139$	2.18005	+	6.70950i	0.184909	+	0.569092i	−0.815038	+	0.579408i	$0.803284\pi$
$140$	−5.02076	−	6.47634i	−0.424331	−	0.547351i
$141$	7.71504	−	5.60530i	0.649724	−	0.472052i
$142$	13.6224	−	4.42620i	1.14317	−	0.371438i
$143$	1.85274	+	0.601990i	0.154933	+	0.0503409i
$144$	0.809017	+	0.587785i	0.0674181	+	0.0489821i
$145$	−18.0824	+	0.563365i	−1.50167	+	0.0467849i
$146$	3.04119	−	2.20955i	0.251691	−	0.182864i
$147$	−3.77958	−	5.20214i	−0.311734	−	0.429065i
$148$	3.01790	−	4.15378i	0.248070	−	0.341439i
$149$	9.48205			0.776799			0.388400	−	0.921491i	$-0.373028\pi$
$149$	9.48205			0.776799			0.388400	+	0.921491i	$0.373028\pi$
$150$	−3.85429	+	3.18503i	−0.314702	+	0.260057i
$151$	13.1149	+	9.52856i	1.06728	+	0.775423i	0.975421	−	0.220349i	$-0.0707197\pi$
$151$	13.1149	+	9.52856i	1.06728	+	0.775423i	0.0918570	+	0.995772i	$0.470720\pi$
$152$	4.37065	−	1.42011i	0.354507	−	0.115186i
$153$	5.93275	+	1.92767i	0.479635	+	0.155843i
$154$	4.83258			0.389421
$155$	−4.31637	+	11.6777i	−0.346699	+	0.937976i
$156$	−1.47730			−0.118279
$157$	7.22110	+	2.34628i	0.576307	+	0.187253i	0.582645	−	0.812726i	$-0.302018\pi$
$157$	7.22110	+	2.34628i	0.576307	+	0.187253i	−0.00633859	+	0.999980i	$0.502018\pi$
$158$	6.42991	−	2.08920i	0.511536	−	0.166208i
$159$	−0.0751534	−	0.0546022i	−0.00596006	−	0.00433023i
$160$	−2.10408	+	0.756872i	−0.166342	+	0.0598359i
$161$	14.6258			1.15268
$162$	0.587785	−	0.809017i	0.0461808	−	0.0635624i
$163$	−8.43000	−	11.6029i	−0.660289	−	0.908809i	0.339202	−	0.940713i	$-0.389843\pi$
$163$	−8.43000	−	11.6029i	−0.660289	−	0.908809i	−0.999491	+	0.0319040i	$0.989843\pi$
$164$	2.34238	−	1.70184i	0.182909	−	0.132891i
$165$	−0.0918216	−	2.94722i	−0.00714830	−	0.229441i
$166$	11.0725	+	8.04465i	0.859393	+	0.624386i
$167$	−12.9256	−	4.19978i	−1.00021	−	0.324989i	−0.237262	−	0.971446i	$-0.576250\pi$
$167$	−12.9256	−	4.19978i	−1.00021	−	0.324989i	−0.762951	+	0.646457i	$0.776250\pi$
$168$	−3.48536	+	1.13246i	−0.268901	+	0.0873713i
$169$	−8.75161	+	6.35842i	−0.673201	+	0.489109i
$170$	−11.0240	+	8.54629i	−0.845500	+	0.655471i
$171$	−1.42011	−	4.37065i	−0.108599	−	0.334232i
$172$	1.44011	+	1.98214i	0.109807	+	0.151136i
$173$	2.44715	−	0.795126i	0.186053	−	0.0604523i	−0.214509	−	0.976722i	$-0.568815\pi$
$173$	2.44715	−	0.795126i	0.186053	−	0.0604523i	0.400562	+	0.916270i	$0.368815\pi$
$174$	−2.50015	+	7.69466i	−0.189536	+	0.583330i
$175$	−1.14065	−	18.2881i	−0.0862250	−	1.38245i
$176$	0.407493	−	1.25414i	0.0307160	−	0.0945340i
$177$	−7.60087	−	10.4617i	−0.571316	−	0.786349i
$178$	−5.28386	−	7.27261i	−0.396042	−	0.545105i
$179$	−14.2123	−	10.3258i	−1.06228	−	0.771788i	−0.0877671	−	0.996141i	$-0.527973\pi$
$179$	−14.2123	−	10.3258i	−1.06228	−	0.771788i	−0.974508	+	0.224353i	$0.927973\pi$
$180$	0.756872	+	2.10408i	0.0564139	+	0.156829i
$181$	−12.5598			−0.933562			−0.466781	−	0.884373i	$-0.654586\pi$
$181$	−12.5598			−0.933562			−0.466781	+	0.884373i	$0.654586\pi$
$182$	3.18221	−	4.37994i	0.235881	−	0.324663i
$183$	−0.446622	+	0.145116i	−0.0330152	+	0.0107273i
$184$	1.23328	−	3.79564i	0.0909185	−	0.279818i
$185$	10.8031	−	3.88605i	0.794258	−	0.285708i
$186$	4.26078	+	3.58410i	0.312415	+	0.262799i
$187$		−	8.22598i		−	0.601543i
$188$	9.06957	+	2.94688i	0.661467	+	0.214924i
$189$	1.13246	+	3.48536i	0.0823745	+	0.253523i
$190$	9.86722	+	2.86959i	0.715844	+	0.208182i
$191$	18.7735			1.35840			0.679200	−	0.733953i	$-0.262327\pi$
$191$	18.7735			1.35840			0.679200	+	0.733953i	$0.262327\pi$
$192$			1.00000i			0.0721688i
$193$	3.22014	−	4.43214i	0.231791	−	0.319032i	−0.677240	−	0.735763i	$-0.736824\pi$
$193$	3.22014	−	4.43214i	0.231791	−	0.319032i	0.909030	+	0.416730i	$0.136824\pi$
$194$	1.00395	−	0.729409i	0.0720791	−	0.0523685i
$195$	−2.73163	−	1.85750i	−0.195616	−	0.133018i
$196$	1.98704	−	6.11548i	0.141932	−	0.436820i
$197$	−1.69833	+	2.33756i	−0.121001	+	0.166544i	−0.865221	−	0.501391i	$-0.832822\pi$
$197$	−1.69833	+	2.33756i	−0.121001	+	0.166544i	0.744219	+	0.667935i	$0.232822\pi$
$198$	−1.25414	−	0.407493i	−0.0891275	−	0.0289593i
$199$	−8.17671	−	25.1653i	−0.579632	−	1.78392i	−0.619837	−	0.784731i	$-0.712801\pi$
$199$	−8.17671	−	25.1653i	−0.579632	−	1.78392i	0.0402050	−	0.999191i	$-0.487199\pi$
$200$	−4.84224	−	1.24607i	−0.342398	−	0.0881105i
$201$	4.84715	+	14.9180i	0.341892	+	1.05223i
$202$	6.82104	−	2.21629i	0.479927	−	0.155938i
$203$	−17.4278	−	23.9873i	−1.22319	−	1.68358i
$204$	1.92767	+	5.93275i	0.134964	+	0.415376i
$205$	6.47103	−	0.201607i	0.451956	−	0.0140809i
$206$	−1.54613	−	1.12333i	−0.107724	−	0.0782658i
$207$	−3.79564	−	1.23328i	−0.263815	−	0.0857188i
$208$	−0.868336	−	1.19516i	−0.0602083	−	0.0828695i
$209$	−4.90270	+	3.56202i	−0.339127	+	0.246390i
$210$	−7.86858	−	2.28834i	−0.542983	−	0.157911i
$211$	17.5899			1.21094			0.605469	−	0.795869i	$-0.292986\pi$
$211$	17.5899			1.21094			0.605469	+	0.795869i	$0.292986\pi$
$212$		−	0.0928948i		−	0.00638004i
$213$	8.41913	−	11.5879i	0.576869	−	0.793992i
$214$	−3.53829	−	10.8897i	−0.241873	−	0.744408i
$215$	0.170601	+	5.47583i	0.0116349	+	0.373449i
$216$	1.00000			0.0680414
$217$	−19.8042	+	4.91204i	−1.34440	+	0.333451i
$218$			17.4815i			1.18399i
$219$	1.16163	−	3.57513i	0.0784957	−	0.241585i
$220$	2.33038	−	1.80662i	0.157114	−	0.121802i
$221$	−7.45549	−	5.41673i	−0.501511	−	0.364369i
$222$		−	5.13435i		−	0.344595i
$223$			25.4777i			1.70612i	0.521817	+	0.853058i	$0.325255\pi$
$223$			25.4777i			1.70612i	−0.521817	+	0.853058i	$0.674745\pi$
$224$	−2.96482	−	2.15407i	−0.198096	−	0.143925i
$225$	−1.24607	+	4.84224i	−0.0830714	+	0.322816i
$226$	10.2467	−	7.44465i	0.681600	−	0.495211i
$227$	−9.59276	−	3.11688i	−0.636694	−	0.206874i	−0.0271557	−	0.999631i	$-0.508645\pi$
$227$	−9.59276	−	3.11688i	−0.636694	−	0.206874i	−0.609538	+	0.792757i	$0.708645\pi$
$228$	2.70121	−	3.71790i	0.178892	−	0.246224i
$229$	−3.83365	+	11.7988i	−0.253335	+	0.779684i	0.740818	+	0.671705i	$0.234438\pi$
$229$	−3.83365	+	11.7988i	−0.253335	+	0.779684i	−0.994153	+	0.107979i	$0.965562\pi$
$230$	7.05289	−	5.46773i	0.465054	−	0.360531i
$231$	3.90964	−	2.84052i	0.257235	−	0.186893i
$232$	−7.69466	+	2.50015i	−0.505179	+	0.164143i
$233$	14.2955	−	4.64488i	0.936527	−	0.304296i	0.199298	−	0.979939i	$-0.436134\pi$
$233$	14.2955	−	4.64488i	0.936527	−	0.304296i	0.737229	+	0.675643i	$0.236134\pi$
$234$	−1.19516	+	0.868336i	−0.0781302	+	0.0567649i
$235$	13.0650	+	16.8527i	0.852265	+	1.09935i
$236$	3.99601	−	12.2985i	0.260118	−	0.800562i
$237$	3.97390	−	5.46961i	0.258133	−	0.355289i
$238$	−21.7419	−	7.06437i	−1.40932	−	0.457915i
$239$	10.8264	−	7.86585i	0.700302	−	0.508799i	−0.179728	−	0.983716i	$-0.557522\pi$
$239$	10.8264	−	7.86585i	0.700302	−	0.508799i	0.880031	+	0.474917i	$0.157522\pi$
$240$	−1.25736	+	1.84907i	−0.0811621	+	0.119357i
$241$	0.769975	+	0.559420i	0.0495984	+	0.0360354i	0.612308	−	0.790619i	$-0.290241\pi$
$241$	0.769975	+	0.559420i	0.0495984	+	0.0360354i	−0.562710	+	0.826655i	$0.690241\pi$
$242$		−	9.26109i		−	0.595326i
$243$		−	1.00000i		−	0.0641500i
$244$	−0.379919	−	0.276027i	−0.0243218	−	0.0176708i
$245$	11.3635	−	8.80953i	0.725989	−	0.562820i
$246$	0.894708	−	2.75363i	0.0570445	−	0.175565i
$247$			6.78905i			0.431977i
$248$	−0.395178	+	5.55372i	−0.0250938	+	0.352662i
$249$	13.6864			0.867339
$250$	−7.38688	−	8.39250i	−0.467187	−	0.530788i
$251$	0.360490	+	1.10947i	0.0227539	+	0.0700293i	0.961789	−	0.273793i	$-0.0882783\pi$
$251$	0.360490	+	1.10947i	0.0227539	+	0.0700293i	−0.939035	+	0.343822i	$0.888278\pi$
$252$	−2.15407	+	2.96482i	−0.135694	+	0.186766i
$253$			5.26280i			0.330869i
$254$	−4.72365			−0.296388
$255$	−3.89520	+	13.3938i	−0.243927	+	0.838754i
$256$	−0.809017	+	0.587785i	−0.0505636	+	0.0367366i
$257$	−3.44043	−	4.73534i	−0.214608	−	0.295383i	0.688118	−	0.725599i	$-0.258437\pi$
$257$	−3.44043	−	4.73534i	−0.214608	−	0.295383i	−0.902726	+	0.430216i	$0.858437\pi$
$258$	2.33014	+	0.757109i	0.145068	+	0.0471355i
$259$	15.2225	+	11.0598i	0.945877	+	0.687220i
$260$	−0.102867	−	3.30174i	−0.00637954	−	0.204765i
$261$	2.50015	+	7.69466i	0.154755	+	0.476287i
$262$	−6.64897	−	9.15152i	−0.410775	−	0.565383i
$263$	−3.32632	+	1.08079i	−0.205110	+	0.0666442i	−0.409770	−	0.912189i	$-0.634391\pi$
$263$	−3.32632	+	1.08079i	−0.205110	+	0.0666442i	0.204660	+	0.978833i	$0.434391\pi$
$264$	−0.407493	−	1.25414i	−0.0250795	−	0.0771867i
$265$	0.116802	−	0.171769i	0.00717508	−	0.0105517i
$266$	5.20432	+	16.0172i	0.319097	+	0.982080i
$267$	−8.54947	−	2.77789i	−0.523219	−	0.170004i
$268$	−9.21983	+	12.6900i	−0.563191	+	0.775166i
$269$	−4.80340	+	14.7833i	−0.292868	+	0.901356i	0.691061	+	0.722796i	$0.257144\pi$
$269$	−4.80340	+	14.7833i	−0.292868	+	0.901356i	−0.983929	+	0.178559i	$0.942856\pi$
$270$	1.84907	+	1.25736i	0.112531	+	0.0765203i
$271$	−1.67432	+	1.21646i	−0.101708	+	0.0738949i	−0.637477	−	0.770470i	$-0.720022\pi$
$271$	−1.67432	+	1.21646i	−0.101708	+	0.0738949i	0.535769	+	0.844365i	$0.320022\pi$
$272$	−3.66664	+	5.04670i	−0.222323	+	0.306001i
$273$		−	5.41390i		−	0.327664i
$274$	−18.9077			−1.14226
$275$	6.58059	−	0.410439i	0.396825	−	0.0247504i
$276$	−1.23328	−	3.79564i	−0.0742346	−	0.228471i
$277$	−7.85252	−	2.55144i	−0.471812	−	0.153301i	0.0634537	−	0.997985i	$-0.479788\pi$
$277$	−7.85252	−	2.55144i	−0.471812	−	0.153301i	−0.535266	+	0.844684i	$0.679788\pi$
$278$			7.05478i			0.423118i
$279$	5.55372	+	0.395178i	0.332493	+	0.0236587i
$280$	−2.77373	−	7.71087i	−0.165762	−	0.460812i
$281$	4.03646	−	12.4229i	0.240795	−	0.741091i	−0.755505	−	0.655143i	$-0.772608\pi$
$281$	4.03646	−	12.4229i	0.240795	−	0.741091i	0.996300	−	0.0859475i	$-0.0273917\pi$
$282$	9.06957	−	2.94688i	0.540085	−	0.175484i
$283$	−10.8387	+	14.9181i	−0.644291	+	0.886791i	−0.998835	−	0.0482487i	$-0.984636\pi$
$283$	−10.8387	+	14.9181i	−0.644291	+	0.886791i	0.354544	+	0.935039i	$0.384636\pi$
$284$	14.3235			0.849942
$285$	9.66946	−	3.47826i	0.572769	−	0.206034i
$286$	1.57603	+	1.14505i	0.0931926	+	0.0677084i
$287$	6.23676	+	8.58416i	0.368144	+	0.506707i
$288$	0.587785	+	0.809017i	0.0346356	+	0.0476718i
$289$	−6.77163	+	20.8409i	−0.398331	+	1.22594i
$290$	−17.3715	−	5.05199i	−1.02009	−	0.296663i
$291$	0.383473	−	1.18021i	0.0224796	−	0.0691850i
$292$	3.57513	−	1.16163i	0.209219	−	0.0679793i
$293$	−15.9969	−	22.0178i	−0.934548	−	1.28630i	−0.958059	−	0.286572i	$-0.907484\pi$
$293$	−15.9969	−	22.0178i	−0.934548	−	1.28630i	0.0235103	−	0.999724i	$-0.492516\pi$
$294$	−1.98704	−	6.11548i	−0.115887	−	0.356662i
$295$	22.8525	−	17.7163i	1.33052	−	1.03148i
$296$	4.15378	−	3.01790i	0.241434	−	0.175412i
$297$	−1.25414	+	0.407493i	−0.0727723	+	0.0236452i
$298$	9.01796	+	2.93011i	0.522396	+	0.169737i
$299$	4.76986	+	3.46550i	0.275848	+	0.200415i
$300$	−4.64988	+	1.83811i	−0.268461	+	0.106123i
$301$	−7.26398	+	5.27759i	−0.418689	+	0.304195i
$302$	9.52856	+	13.1149i	0.548307	+	0.754680i
$303$	4.21564	−	5.80233i	0.242182	−	0.333335i
$304$	4.59558			0.263574
$305$	−0.355431	−	0.988087i	−0.0203519	−	0.0565777i
$306$	5.04670	+	3.66664i	0.288501	+	0.209608i
$307$	20.4530	−	6.64560i	1.16732	−	0.379284i	0.339676	−	0.940542i	$-0.389682\pi$
$307$	20.4530	−	6.64560i	1.16732	−	0.379284i	0.827641	+	0.561258i	$0.189682\pi$
$308$	4.59606	+	1.49335i	0.261885	+	0.0850915i
$309$	−1.91112			−0.108720
$310$	−7.71372	+	9.77233i	−0.438110	+	0.555031i
$311$	13.9543			0.791278			0.395639	−	0.918406i	$-0.370523\pi$
$311$	13.9543			0.791278			0.395639	+	0.918406i	$0.370523\pi$
$312$	−1.40500	−	0.456511i	−0.0795423	−	0.0258449i
$313$	−5.36962	+	1.74469i	−0.303509	+	0.0986160i	−0.456812	−	0.889563i	$-0.651009\pi$
$313$	−5.36962	+	1.74469i	−0.303509	+	0.0986160i	0.153303	+	0.988179i	$0.451009\pi$
$314$	6.14264	+	4.46289i	0.346649	+	0.251855i
$315$	−7.71087	+	2.77373i	−0.434458	+	0.156282i
$316$	6.76081			0.380325
$317$	−0.507483	+	0.698490i	−0.0285031	+	0.0392311i	−0.823031	−	0.567997i	$-0.807719\pi$
$317$	−0.507483	+	0.698490i	−0.0285031	+	0.0392311i	0.794528	+	0.607228i	$0.207719\pi$
$318$	−0.0546022	−	0.0751534i	−0.00306194	−	0.00421440i
$319$	8.63135	−	6.27104i	0.483263	−	0.351111i
$320$	−2.23498	+	0.0696317i	−0.124939	+	0.00389253i
$321$	−9.26337	−	6.73023i	−0.517031	−	0.375645i
$322$	13.9100	+	4.51962i	0.775172	+	0.251869i
$323$	27.2644	−	8.85875i	1.51703	−	0.492914i
$324$	0.809017	−	0.587785i	0.0449454	−	0.0326547i
$325$	3.96126	−	6.23449i	0.219731	−	0.345827i
$326$	−4.43191	−	13.6400i	−0.245461	−	0.755451i
$327$	10.2753	+	14.1428i	0.568228	+	0.782099i
$328$	2.75363	−	0.894708i	0.152044	−	0.0494020i
$329$	−10.7995	+	33.2375i	−0.595396	+	1.83244i
$330$	0.823413	−	2.83135i	0.0453274	−	0.155860i
$331$	−1.65658	+	5.09842i	−0.0910537	+	0.280234i	−0.986205	−	0.165528i	$-0.947067\pi$
$331$	−1.65658	+	5.09842i	−0.0910537	+	0.280234i	0.895151	+	0.445762i	$0.147067\pi$
$332$	8.04465	+	11.0725i	0.441507	+	0.607683i
$333$	−3.01790	−	4.15378i	−0.165380	−	0.227626i
$334$	−10.9952	−	7.98846i	−0.601629	−	0.437109i
$335$	−33.0040	+	11.8721i	−1.80320	+	0.648641i
$336$	−3.66472			−0.199927
$337$	1.78641	−	2.45879i	0.0973122	−	0.133939i	−0.757584	−	0.652737i	$-0.773621\pi$
$337$	1.78641	−	2.45879i	0.0973122	−	0.133939i	0.854897	+	0.518799i	$0.173621\pi$
$338$	−10.2881	+	3.34282i	−0.559601	+	0.181825i
$339$	3.91389	−	12.0457i	0.212573	−	0.654233i
$340$	−13.1254	+	4.72141i	−0.711823	+	0.256055i
$341$	−1.76750	−	7.12615i	−0.0957154	−	0.385903i
$342$		−	4.59558i		−	0.248500i
$343$	−1.98596	−	0.645276i	−0.107232	−	0.0348417i
$344$	0.757109	+	2.33014i	0.0408206	+	0.125633i
$345$	2.49206	−	8.56907i	0.134168	−	0.461343i
$346$	2.57308			0.138330
$347$		−	26.8726i		−	1.44260i	−0.692624	−	0.721299i	$-0.743546\pi$
$347$		−	26.8726i		−	1.44260i	0.692624	−	0.721299i	$-0.256454\pi$
$348$	−4.75556	+	6.54547i	−0.254925	+	0.350874i
$349$	12.1817	−	8.85051i	0.652071	−	0.473757i	−0.211905	−	0.977290i	$-0.567967\pi$
$349$	12.1817	−	8.85051i	0.652071	−	0.473757i	0.863976	+	0.503533i	$0.167967\pi$
$350$	4.56651	−	17.7455i	0.244090	−	0.948536i
$351$	−0.456511	+	1.40500i	−0.0243668	+	0.0749932i
$352$	0.775098	−	1.06683i	0.0413129	−	0.0568623i
$353$	−34.0897	−	11.0764i	−1.81441	−	0.589538i	−0.999957	−	0.00931204i	$-0.997036\pi$
$353$	−34.0897	−	11.0764i	−1.81441	−	0.589538i	−0.814455	−	0.580226i	$-0.802964\pi$
$354$	−3.99601	−	12.2985i	−0.212386	−	0.653656i
$355$	26.4851	+	18.0097i	1.40568	+	0.955857i
$356$	−2.77789	−	8.54947i	−0.147228	−	0.453121i
$357$	−21.7419	+	7.06437i	−1.15070	+	0.373886i
$358$	−10.3258	−	14.2123i	−0.545737	−	0.751142i
$359$	5.82807	+	17.9370i	0.307594	+	0.946677i	0.978697	+	0.205312i	$0.0658210\pi$
$359$	5.82807	+	17.9370i	0.307594	+	0.946677i	−0.671103	+	0.741364i	$0.734179\pi$
$360$	0.0696317	+	2.23498i	0.00366991	+	0.117794i
$361$	−1.71458	−	1.24571i	−0.0902409	−	0.0655638i
$362$	−11.9451	−	3.88119i	−0.627819	−	0.203991i
$363$	−5.44353	−	7.49238i	−0.285711	−	0.393248i
$364$	4.37994	−	3.18221i	0.229571	−	0.166793i
$365$	8.07125	+	2.34728i	0.422468	+	0.122862i
$366$	−0.469606			−0.0245467
$367$			15.0665i			0.786465i	0.919439	+	0.393232i	$0.128643\pi$
$367$			15.0665i			0.786465i	−0.919439	+	0.393232i	$0.871357\pi$
$368$	2.34583	−	3.22876i	0.122285	−	0.168311i
$369$	−0.894708	−	2.75363i	−0.0465766	−	0.143348i
$370$	11.4752	−	0.357514i	0.596567	−	0.0185862i
$371$	0.340434			0.0176744
$372$	2.94469	+	4.72534i	0.152675	+	0.244997i
$373$			32.6657i			1.69136i	0.533686	+	0.845682i	$0.320806\pi$
$373$			32.6657i			1.69136i	−0.533686	+	0.845682i	$0.679194\pi$
$374$	2.54197	−	7.82337i	0.131442	−	0.404537i
$375$	−10.9091	−	2.44777i	−0.563343	−	0.126403i
$376$	7.71504	+	5.60530i	0.397873	+	0.289072i
$377$		−	11.9523i		−	0.615575i
$378$			3.66472i			0.188493i
$379$	−17.8261	−	12.9514i	−0.915664	−	0.665269i	0.0267769	−	0.999641i	$-0.491476\pi$
$379$	−17.8261	−	12.9514i	−0.915664	−	0.665269i	−0.942441	+	0.334373i	$0.891476\pi$
$380$	8.49754	+	5.77828i	0.435914	+	0.296420i
$381$	−3.82151	+	2.77649i	−0.195782	+	0.142244i
$382$	17.8546	+	5.80132i	0.913522	+	0.296821i
$383$	−18.0768	+	24.8806i	−0.923681	+	1.27134i	0.0385923	+	0.999255i	$0.487713\pi$
$383$	−18.0768	+	24.8806i	−0.923681	+	1.27134i	−0.962274	+	0.272083i	$0.912287\pi$
$384$	−0.309017	+	0.951057i	−0.0157695	+	0.0485334i
$385$	6.62075	+	8.54019i	0.337425	+	0.435249i
$386$	4.43214	−	3.22014i	0.225590	−	0.163901i
$387$	2.33014	−	0.757109i	0.118448	−	0.0384860i
$388$	1.18021	−	0.383473i	0.0599160	−	0.0194679i
$389$	−22.6724	+	16.4725i	−1.14954	+	0.835187i	−0.988419	−	0.151749i	$-0.951510\pi$
$389$	−22.6724	+	16.4725i	−1.14954	+	0.835187i	−0.161117	+	0.986935i	$0.551510\pi$
$390$	−2.02394	−	2.61070i	−0.102486	−	0.132198i
$391$	7.69327	−	23.6774i	0.389065	−	1.19742i
$392$	3.77958	−	5.20214i	0.190897	−	0.262748i
$393$	−10.7583	−	3.49557i	−0.542683	−	0.176328i
$394$	−2.33756	+	1.69833i	−0.117764	+	0.0855608i
$395$	12.5012	+	8.50075i	0.629003	+	0.427719i
$396$	−1.06683	−	0.775098i	−0.0536103	−	0.0389501i
$397$			10.1396i			0.508893i	0.967087	+	0.254447i	$0.0818933\pi$
$397$			10.1396i			0.508893i	−0.967087	+	0.254447i	$0.918107\pi$
$398$		−	26.4604i		−	1.32634i
$399$	13.6251	+	9.89920i	0.682107	+	0.495580i
$400$	−4.22019	−	2.68142i	−0.211009	−	0.134071i
$401$	6.26322	−	19.2762i	0.312770	−	0.962608i	−0.663892	−	0.747828i	$-0.731097\pi$
$401$	6.26322	−	19.2762i	0.312770	−	0.962608i	0.976663	−	0.214780i	$-0.0689033\pi$
$402$			15.6857i			0.782332i
$403$	−7.62256	−	3.09056i	−0.379707	−	0.153952i
$404$	7.17207			0.356824
$405$	2.23498	−	0.0696317i	0.111057	−	0.00346003i
$406$	−9.16234	−	28.1988i	−0.454719	−	1.39948i
$407$	−3.97963	+	5.47749i	−0.197263	+	0.271509i
$408$			6.23806i			0.308830i
$409$	−3.98554			−0.197072			−0.0985361	−	0.995133i	$-0.531416\pi$
$409$	−3.98554			−0.197072			−0.0985361	+	0.995133i	$0.531416\pi$
$410$	6.21661	+	1.80792i	0.307017	+	0.0892867i
$411$	−15.2966	+	11.1137i	−0.754528	+	0.548196i
$412$	−1.12333	−	1.54613i	−0.0553423	−	0.0761721i
$413$	45.0705	+	14.6443i	2.21777	+	0.720598i
$414$	−3.22876	−	2.34583i	−0.158685	−	0.115291i
$415$	0.953005	+	30.5888i	0.0467812	+	1.50155i
$416$	−0.456511	−	1.40500i	−0.0223823	−	0.0688856i
$417$	4.14670	+	5.70744i	0.203065	+	0.279494i
$418$	−5.76348	+	1.87267i	−0.281901	+	0.0915951i
$419$	3.33583	+	10.2666i	0.162966	+	0.501558i	0.998881	−	0.0473017i	$-0.0150622\pi$
$419$	3.33583	+	10.2666i	0.162966	+	0.501558i	−0.835915	+	0.548859i	$0.815062\pi$
$420$	−6.77632	−	4.60787i	−0.330651	−	0.224841i
$421$	3.99911	+	12.3080i	0.194905	+	0.599855i	0.999978	+	0.00667928i	$0.00212610\pi$
$421$	3.99911	+	12.3080i	0.194905	+	0.599855i	−0.805073	+	0.593176i	$0.797874\pi$
$422$	16.7290	+	5.43557i	0.814354	+	0.264600i
$423$	5.60530	−	7.71504i	0.272539	−	0.375118i
$424$	0.0287061	−	0.0883482i	0.00139409	−	0.00429057i
$425$	−30.2062	−	7.77307i	−1.46522	−	0.377049i
$426$	11.5879	−	8.41913i	0.561437	−	0.407908i
$427$	1.01156	−	1.39230i	0.0489530	−	0.0673780i
$428$		−	11.4502i		−	0.553464i
$429$	1.94808			0.0940542
$430$	−1.52987	+	5.26055i	−0.0737771	+	0.253686i
$431$	−0.347925	−	1.07080i	−0.0167589	−	0.0515787i	0.942327	−	0.334693i	$-0.108633\pi$
$431$	−0.347925	−	1.07080i	−0.0167589	−	0.0515787i	−0.959086	+	0.283114i	$0.908633\pi$
$432$	0.951057	+	0.309017i	0.0457577	+	0.0148676i
$433$			26.2586i			1.26191i	0.775820	+	0.630954i	$0.217336\pi$
$433$			26.2586i			1.26191i	−0.775820	+	0.630954i	$0.782664\pi$
$434$	−20.3529	−	1.44822i	−0.976968	−	0.0695167i
$435$	−17.0233	+	6.12358i	−0.816207	+	0.293603i
$436$	−5.40207	+	16.6259i	−0.258712	+	0.796234i
$437$	−17.4432	+	5.66763i	−0.834419	+	0.271119i
$438$	2.20955	−	3.04119i	0.105577	−	0.145314i
$439$	−19.4449			−0.928055			−0.464027	−	0.885821i	$-0.653596\pi$
$439$	−19.4449			−0.928055			−0.464027	+	0.885821i	$0.653596\pi$
$440$	2.77460	−	0.998068i	0.132274	−	0.0475810i
$441$	−5.20214	−	3.77958i	−0.247721	−	0.179980i
$442$	−5.41673	−	7.45549i	−0.257648	−	0.354622i
$443$	−1.38399	−	1.90490i	−0.0657553	−	0.0905044i	0.774873	−	0.632117i	$-0.217814\pi$
$443$	−1.38399	−	1.90490i	−0.0657553	−	0.0905044i	−0.840628	+	0.541613i	$0.817814\pi$
$444$	1.58660	−	4.88306i	0.0752968	−	0.231740i
$445$	5.61323	−	19.3014i	0.266093	−	0.914972i
$446$	−7.87305	+	24.2308i	−0.372800	+	1.14736i
$447$	9.01796	−	2.93011i	0.426535	−	0.138590i
$448$	−2.15407	−	2.96482i	−0.101770	−	0.140075i
$449$	1.57147	+	4.83650i	0.0741624	+	0.228248i	0.981266	−	0.192660i	$-0.0617114\pi$
$449$	1.57147	+	4.83650i	0.0741624	+	0.228248i	−0.907103	+	0.420908i	$0.861711\pi$
$450$	−2.68142	+	4.22019i	−0.126403	+	0.198942i
$451$	−3.08883	+	2.24417i	−0.145448	+	0.105674i
$452$	12.0457	−	3.91389i	0.566582	−	0.184094i
$453$	15.4175	+	5.00946i	0.724379	+	0.235365i
$454$	−8.16009	−	5.92865i	−0.382972	−	0.278245i
$455$	12.1000	−	0.376979i	0.567256	−	0.0176730i
$456$	3.71790	−	2.70121i	0.174107	−	0.126496i
$457$	−8.04352	−	11.0710i	−0.376260	−	0.517878i	0.578329	−	0.815804i	$-0.303705\pi$
$457$	−8.04352	−	11.0710i	−0.376260	−	0.517878i	−0.954589	+	0.297926i	$0.903705\pi$
$458$	−7.29204	+	10.0366i	−0.340735	+	0.468981i
$459$	6.23806			0.291168
$460$	8.39732	−	3.02065i	0.391527	−	0.140839i
$461$	16.5115	+	11.9963i	0.769017	+	0.558723i	0.901663	−	0.432440i	$-0.142347\pi$
$461$	16.5115	+	11.9963i	0.769017	+	0.558723i	−0.132646	+	0.991163i	$0.542347\pi$
$462$	4.59606	−	1.49335i	0.213828	−	0.0694769i
$463$	10.7037	+	3.47784i	0.497442	+	0.161629i	0.546984	−	0.837143i	$-0.315776\pi$
$463$	10.7037	+	3.47784i	0.497442	+	0.161629i	−0.0495413	+	0.998772i	$0.515776\pi$
$464$	−8.09064			−0.375599
$465$	−0.496501	+	12.4400i	−0.0230247	+	0.576891i
$466$	15.0311			0.696304
$467$	−15.4743	−	5.02791i	−0.716065	−	0.232664i	−0.0717489	−	0.997423i	$-0.522858\pi$
$467$	−15.4743	−	5.02791i	−0.716065	−	0.232664i	−0.644316	+	0.764759i	$0.722858\pi$
$468$	−1.40500	+	0.456511i	−0.0649460	+	0.0211022i
$469$	−46.5054	−	33.7881i	−2.14742	−	1.56019i
$470$	7.21776	+	20.0652i	0.332931	+	0.925536i
$471$	7.59272			0.349854
$472$	7.60087	−	10.4617i	0.349858	−	0.481539i
$473$	−1.89903	−	2.61380i	−0.0873176	−	0.120182i
$474$	5.46961	−	3.97390i	0.251227	−	0.182527i
$475$	8.44716	+	21.3689i	0.387582	+	0.980471i
$476$	−18.4948	−	13.4372i	−0.847706	−	0.615894i
$477$	−0.0883482	−	0.0287061i	−0.00404518	−	0.00131436i
$478$	12.7272	−	4.13532i	0.582129	−	0.189145i
$479$	2.96001	−	2.15058i	0.135246	−	0.0982623i	−0.518105	−	0.855317i	$-0.673362\pi$
$479$	2.96001	−	2.15058i	0.135246	−	0.0982623i	0.653352	+	0.757055i	$0.273362\pi$
$480$	−1.76721	+	1.37002i	−0.0806618	+	0.0625327i
$481$	2.34389	+	7.21375i	0.106872	+	0.328919i
$482$	0.559420	+	0.769975i	0.0254809	+	0.0350714i
$483$	13.9100	−	4.51962i	0.632926	−	0.205650i
$484$	2.86184	−	8.80782i	0.130083	−	0.400356i
$485$	2.66445	+	0.774876i	0.120986	+	0.0351853i
$486$	0.309017	−	0.951057i	0.0140173	−	0.0431408i
$487$	−13.6070	−	18.7284i	−0.616592	−	0.848666i	0.380508	−	0.924778i	$-0.375749\pi$
$487$	−13.6070	−	18.7284i	−0.616592	−	0.848666i	−0.997099	+	0.0761121i	$0.975749\pi$
$488$	−0.276027	−	0.379919i	−0.0124952	−	0.0171981i
$489$	−11.6029	−	8.43000i	−0.524701	−	0.381218i
$490$	13.5296	−	4.86684i	0.611207	−	0.219861i
$491$	4.82567			0.217779			0.108890	−	0.994054i	$-0.465270\pi$
$491$	4.82567			0.217779			0.108890	+	0.994054i	$0.465270\pi$
$492$	1.70184	−	2.34238i	0.0767247	−	0.105602i
$493$	−47.9998	+	15.5961i	−2.16180	+	0.702412i
$494$	−2.09793	+	6.45677i	−0.0943904	+	0.290504i
$495$	−0.998068	−	2.77460i	−0.0448598	−	0.124709i
$496$	−2.09203	+	5.15979i	−0.0939350	+	0.231681i
$497$			52.4916i			2.35457i
$498$	13.0165	+	4.22932i	0.583284	+	0.189520i
$499$	−1.71802	−	5.28753i	−0.0769092	−	0.236702i	0.905209	−	0.424966i	$-0.139714\pi$
$499$	−1.71802	−	5.28753i	−0.0769092	−	0.236702i	−0.982118	+	0.188264i	$0.939714\pi$
$500$	−4.43192	−	10.2644i	−0.198201	−	0.459038i
$501$	−13.5908			−0.607191
$502$			1.16657i			0.0520665i
$503$	0.874847	−	1.20412i	0.0390075	−	0.0536892i	−0.789068	−	0.614306i	$-0.789436\pi$
$503$	0.874847	−	1.20412i	0.0390075	−	0.0536892i	0.828075	+	0.560617i	$0.189436\pi$
$504$	−2.96482	+	2.15407i	−0.132064	+	0.0959499i
$505$	13.2616	+	9.01785i	0.590136	+	0.401289i
$506$	−1.62629	+	5.00522i	−0.0722976	+	0.222509i
$507$	−6.35842	+	8.75161i	−0.282387	+	0.388673i
$508$	−4.49246	−	1.45969i	−0.199321	−	0.0647632i
$509$	8.12437	+	25.0042i	0.360106	+	1.10829i	0.952989	+	0.303005i	$0.0979898\pi$
$509$	8.12437	+	25.0042i	0.360106	+	1.10829i	−0.592883	+	0.805289i	$0.702010\pi$
$510$	−7.84347	+	11.5346i	−0.347315	+	0.510761i
$511$	4.25706	+	13.1019i	0.188321	+	0.579593i
$512$	−0.951057	+	0.309017i	−0.0420312	+	0.0136568i
$513$	−2.70121	−	3.71790i	−0.119261	−	0.164149i
$514$	−1.80874	−	5.56673i	−0.0797801	−	0.245538i
$515$	−0.133074	−	4.27131i	−0.00586395	−	0.188217i
$516$	1.98214	+	1.44011i	0.0872587	+	0.0633971i
$517$	−11.9598	−	3.88598i	−0.525993	−	0.170905i
$518$	11.0598	+	15.2225i	0.485938	+	0.668836i
$519$	2.08167	−	1.51242i	0.0913751	−	0.0663879i
$520$	0.922463	−	3.17193i	0.0404527	−	0.139098i
$521$	25.8710			1.13343			0.566715	−	0.823914i	$-0.308214\pi$
$521$	25.8710			1.13343			0.566715	+	0.823914i	$0.308214\pi$
$522$			8.09064i			0.354118i
$523$	16.4052	−	22.5798i	0.717350	−	0.987347i	−0.282258	−	0.959339i	$-0.591083\pi$
$523$	16.4052	−	22.5798i	0.717350	−	0.987347i	0.999608	−	0.0280085i	$-0.00891655\pi$
$524$	−3.49557	−	10.7583i	−0.152705	−	0.469977i
$525$	−6.73615	−	17.0405i	−0.293990	−	0.743709i
$526$	−3.49750			−0.152498
$527$	−2.46515	+	34.6445i	−0.107383	+	1.50914i
$528$		−	1.31868i		−	0.0573880i
$529$	2.18541	−	6.72601i	0.0950179	−	0.292435i
$530$	0.164165	−	0.127268i	0.00713086	−	0.00552817i
$531$	−10.4617	−	7.60087i	−0.453999	−	0.329850i
$532$			16.8415i			0.730173i
$533$			4.27728i			0.185270i
$534$	−7.27261	−	5.28386i	−0.314717	−	0.228655i
$535$	14.3969	−	21.1721i	0.622434	−	0.915351i
$536$	−12.6900	+	9.21983i	−0.548125	+	0.398236i
$537$	−16.7075	−	5.42860i	−0.720983	−	0.234262i
$538$	−9.13660	+	12.5755i	−0.393907	+	0.542166i
$539$	−2.62026	+	8.06434i	−0.112863	+	0.347356i
$540$	1.37002	+	1.76721i	0.0589564	+	0.0760487i
$541$	−24.7967	+	18.0159i	−1.06609	+	0.774563i	−0.975206	−	0.221298i	$-0.928971\pi$
$541$	−24.7967	+	18.0159i	−1.06609	+	0.774563i	−0.0908883	+	0.995861i	$0.528971\pi$
$542$	−1.96828	+	0.639533i	−0.0845449	+	0.0274703i
$543$	−11.9451	+	3.88119i	−0.512612	+	0.166558i
$544$	−5.04670	+	3.66664i	−0.216375	+	0.157206i
$545$	−30.8934	+	23.9500i	−1.32333	+	1.02591i
$546$	1.67299	−	5.14892i	0.0715972	−	0.220354i
$547$	3.43534	−	4.72834i	0.146885	−	0.202169i	−0.729235	−	0.684264i	$-0.760124\pi$
$547$	3.43534	−	4.72834i	0.146885	−	0.202169i	0.876119	+	0.482094i	$0.160124\pi$
$548$	−17.9823	−	5.84280i	−0.768165	−	0.249592i
$549$	−0.379919	+	0.276027i	−0.0162145	+	0.0117806i
$550$	6.38535	+	1.64316i	0.272272	+	0.0700647i
$551$	30.0802	+	21.8545i	1.28146	+	0.931035i
$552$		−	3.99097i		−	0.169867i
$553$			24.7765i			1.05360i
$554$	−6.67975	−	4.85312i	−0.283795	−	0.206189i
$555$	9.07349	−	7.03419i	0.385148	−	0.298585i
$556$	−2.18005	+	6.70950i	−0.0924546	+	0.284546i
$557$		−	26.9810i		−	1.14322i	−0.820524	−	0.571611i	$-0.806318\pi$
$557$		−	26.9810i		−	1.14322i	0.820524	−	0.571611i	$-0.193682\pi$
$558$	5.15979	+	2.09203i	0.218431	+	0.0885627i
$559$	−3.61947			−0.153087
$560$	−0.255181	−	8.19060i	−0.0107834	−	0.346116i
$561$	−2.54197	−	7.82337i	−0.107322	−	0.330303i
$562$	7.67780	−	10.5676i	0.323869	−	0.445767i
$563$			41.4756i			1.74799i	0.485935	+	0.873995i	$0.338479\pi$
$563$			41.4756i			1.74799i	−0.485935	+	0.873995i	$0.661521\pi$
$564$	9.53631			0.401551
$565$	27.1945	+	7.90871i	1.14408	+	0.332722i
$566$	−14.9181	+	10.8387i	−0.627056	+	0.455583i
$567$	2.15407	+	2.96482i	0.0904625	+	0.124511i
$568$	13.6224	+	4.42620i	0.571585	+	0.185719i
$569$	20.6290	+	14.9878i	0.864811	+	0.628322i	0.929190	−	0.369603i	$-0.120506\pi$
$569$	20.6290	+	14.9878i	0.864811	+	0.628322i	−0.0643783	+	0.997926i	$0.520506\pi$
$570$	10.2710	−	0.319998i	0.430207	−	0.0134032i
$571$	−2.18614	−	6.72824i	−0.0914870	−	0.281568i	0.894835	−	0.446397i	$-0.147293\pi$
$571$	−2.18614	−	6.72824i	−0.0914870	−	0.281568i	−0.986322	+	0.164829i	$0.947293\pi$
$572$	1.14505	+	1.57603i	0.0478771	+	0.0658971i
$573$	17.8546	−	5.80132i	0.745887	−	0.242353i
$574$	3.27886	+	10.0913i	0.136857	+	0.421202i
$575$	19.3253	+	4.97303i	0.805919	+	0.207390i
$576$	0.309017	+	0.951057i	0.0128757	+	0.0396274i
$577$	18.2137	+	5.91799i	0.758246	+	0.246369i	0.662526	−	0.749039i	$-0.269485\pi$
$577$	18.2137	+	5.91799i	0.758246	+	0.246369i	0.0957201	+	0.995408i	$0.469485\pi$
$578$	−12.8804	+	17.7283i	−0.535754	+	0.737402i
$579$	1.69293	−	5.21029i	0.0703556	−	0.216532i
$580$	−14.9601	−	10.1728i	−0.621186	−	0.422404i
$581$	−40.5777	+	29.4814i	−1.68345	+	1.22310i
$582$	0.729409	−	1.00395i	0.0302350	−	0.0416149i
$583$			0.122498i			0.00507335i
$584$	3.75912			0.155553
$585$	−3.17193	−	0.922463i	−0.131143	−	0.0381391i
$586$	−8.41006	−	25.8835i	−0.347417	−	1.06924i
$587$	30.3863	+	9.87310i	1.25418	+	0.407507i	0.859416	−	0.511277i	$-0.170828\pi$
$587$	30.3863	+	9.87310i	1.25418	+	0.407507i	0.394761	+	0.918784i	$0.370828\pi$
$588$		−	6.43020i		−	0.265177i
$589$	21.7156	−	13.5326i	0.894778	−	0.557599i
$590$	27.2086	−	9.78739i	1.12016	−	0.402940i
$591$	−0.892867	+	2.74796i	−0.0367276	+	0.113036i
$592$	4.88306	−	1.58660i	0.200693	−	0.0652090i
$593$	−22.7503	+	31.3131i	−0.934243	+	1.28588i	0.0239381	+	0.999713i	$0.492380\pi$
$593$	−22.7503	+	31.3131i	−0.934243	+	1.28588i	−0.958181	+	0.286162i	$0.907620\pi$
$594$	−1.31868			−0.0541059
$595$	−17.3027	−	48.1009i	−0.709341	−	1.97194i
$596$	7.67114	+	5.57341i	0.314222	+	0.228296i
$597$	−15.5530	−	21.4069i	−0.636543	−	0.876126i
$598$	3.46550	+	4.76986i	0.141715	+	0.195054i
$599$	11.7127	−	36.0479i	0.478567	−	1.47288i	−0.362519	−	0.931977i	$-0.618083\pi$
$599$	11.7127	−	36.0479i	0.478567	−	1.47288i	0.841086	−	0.540902i	$-0.181917\pi$
$600$	−4.99030	+	0.311251i	−0.203728	+	0.0127068i
$601$	5.82415	−	17.9249i	0.237572	−	0.731171i	−0.759198	−	0.650860i	$-0.774409\pi$
$601$	5.82415	−	17.9249i	0.237572	−	0.731171i	0.996770	−	0.0803114i	$-0.0255915\pi$
$602$	−8.53932	+	2.77459i	−0.348037	+	0.113084i
$603$	9.21983	+	12.6900i	0.375461	+	0.516777i
$604$	5.00946	+	15.4175i	0.203832	+	0.627330i
$605$	16.3663	−	12.6879i	0.665385	−	0.515837i
$606$	5.80233	−	4.21564i	0.235703	−	0.171249i
$607$	5.63497	−	1.83091i	0.228716	−	0.0743145i	−0.192417	−	0.981313i	$-0.561633\pi$
$607$	5.63497	−	1.83091i	0.228716	−	0.0743145i	0.421133	+	0.906999i	$0.361633\pi$
$608$	4.37065	+	1.42011i	0.177253	+	0.0575931i
$609$	−23.9873	−	17.4278i	−0.972015	−	0.706211i
$610$	−0.0326994	−	1.04956i	−0.00132396	−	0.0424955i
$611$	−11.3974	+	8.28072i	−0.461091	+	0.335002i
$612$	3.66664	+	5.04670i	0.148215	+	0.204001i
$613$	−18.1222	+	24.9431i	−0.731948	+	1.00744i	0.267093	+	0.963671i	$0.413937\pi$
$613$	−18.1222	+	24.9431i	−0.731948	+	1.00744i	−0.999042	+	0.0437700i	$0.986063\pi$
$614$	21.5056			0.867896
$615$	6.09201	−	2.19140i	0.245654	−	0.0883657i
$616$	3.90964	+	2.84052i	0.157524	+	0.114448i
$617$	−38.8594	+	12.6262i	−1.56442	+	0.508310i	−0.957984	−	0.286823i	$-0.907401\pi$
$617$	−38.8594	+	12.6262i	−1.56442	+	0.508310i	−0.606435	+	0.795133i	$0.707401\pi$
$618$	−1.81758	−	0.590567i	−0.0731138	−	0.0237561i
$619$	33.2297			1.33561			0.667807	−	0.744334i	$-0.267233\pi$
$619$	33.2297			1.33561			0.667807	+	0.744334i	$0.267233\pi$
$620$	−10.3560	+	6.91037i	−0.415907	+	0.277527i
$621$	−3.99097			−0.160152
$622$	13.2714	+	4.31213i	0.532133	+	0.172901i
$623$	31.3314	−	10.1802i	1.25527	−	0.407861i
$624$	−1.19516	−	0.868336i	−0.0478448	−	0.0347612i
$625$	4.71112	−	24.5521i	0.188445	−	0.982084i
$626$	−5.64595			−0.225658
$627$	−3.56202	+	4.90270i	−0.142254	+	0.195795i
$628$	4.46289	+	6.14264i	0.178089	+	0.245118i
$629$	25.9115	−	18.8258i	1.03316	−	0.750635i
$630$	−8.19060	+	0.255181i	−0.326321	+	0.0101666i
$631$	−12.9081	−	9.37827i	−0.513863	−	0.373343i	0.300424	−	0.953806i	$-0.402872\pi$
$631$	−12.9081	−	9.37827i	−0.513863	−	0.373343i	−0.814287	+	0.580463i	$0.802872\pi$
$632$	6.42991	+	2.08920i	0.255768	+	0.0831041i
$633$	16.7290	−	5.43557i	0.664917	−	0.216045i
$634$	−0.698490	+	0.507483i	−0.0277406	+	0.0201547i
$635$	−6.47151	−	8.34769i	−0.256814	−	0.331268i
$636$	−0.0287061	−	0.0883482i	−0.00113827	−	0.00350323i
$637$	5.58357	+	7.68513i	0.221229	+	0.304496i
$638$	10.1468	−	3.29688i	0.401714	−	0.130525i
$639$	4.42620	−	13.6224i	0.175098	−	0.538895i
$640$	−2.14711	−	0.624424i	−0.0848721	−	0.0246825i
$641$	4.00625	−	12.3300i	0.158237	−	0.487004i	−0.840237	−	0.542219i	$-0.817584\pi$
$641$	4.00625	−	12.3300i	0.158237	−	0.487004i	0.998475	+	0.0552147i	$0.0175843\pi$
$642$	−6.73023	−	9.26337i	−0.265621	−	0.365596i
$643$	−15.1154	−	20.8046i	−0.596095	−	0.820454i	0.399249	−	0.916843i	$-0.369271\pi$
$643$	−15.1154	−	20.8046i	−0.596095	−	0.820454i	−0.995344	+	0.0963882i	$0.969271\pi$
$644$	11.8325	+	8.59684i	0.466267	+	0.338763i
$645$	1.85438	+	5.15511i	0.0730160	+	0.202982i
$646$	28.6675			1.12791
$647$	11.1007	−	15.2788i	0.436415	−	0.600673i	−0.532996	−	0.846118i	$-0.678934\pi$
$647$	11.1007	−	15.2788i	0.436415	−	0.600673i	0.969411	+	0.245444i	$0.0789339\pi$
$648$	0.951057	−	0.309017i	0.0373610	−	0.0121393i
$649$	−5.26945	+	16.2177i	−0.206844	+	0.636600i
$650$	5.69395	−	4.70525i	0.223335	−	0.184555i
$651$	−17.3171	+	10.7915i	−0.678709	+	0.422951i
$652$		−	14.3420i		−	0.561675i
$653$	18.5594	+	6.03030i	0.726284	+	0.235984i	0.648746	−	0.761005i	$-0.275294\pi$
$653$	18.5594	+	6.03030i	0.726284	+	0.235984i	0.0775384	+	0.996989i	$0.475294\pi$
$654$	5.40207	+	16.6259i	0.211238	+	0.650123i
$655$	7.06343	−	24.2879i	0.275991	−	0.949008i
$656$	2.89534			0.113044
$657$		−	3.75912i		−	0.146657i
$658$	−20.5419	+	28.2735i	−0.800806	+	1.10222i
$659$	−1.82403	+	1.32523i	−0.0710540	+	0.0516237i	−0.622745	−	0.782425i	$-0.713983\pi$
$659$	−1.82403	+	1.32523i	−0.0710540	+	0.0516237i	0.551691	+	0.834048i	$0.313983\pi$
$660$	1.65805	−	2.43832i	0.0645394	−	0.0949115i
$661$	−3.89995	+	12.0028i	−0.151691	+	0.466856i	−0.997811	−	0.0661368i	$-0.978933\pi$
$661$	−3.89995	+	12.0028i	−0.151691	+	0.466856i	0.846120	+	0.532992i	$0.178933\pi$
$662$	−3.15100	+	4.33697i	−0.122467	+	0.168561i
$663$	−8.76446	−	2.84775i	−0.340383	−	0.110597i
$664$	4.22932	+	13.0165i	0.164130	+	0.505139i
$665$	−21.1758	+	31.1411i	−0.821163	+	1.20760i
$666$	−1.58660	−	4.88306i	−0.0614796	−	0.189215i
$667$	30.7092	−	9.97801i	1.18906	−	0.386350i
$668$	−7.98846	−	10.9952i	−0.309083	−	0.425416i
$669$	7.87305	+	24.2308i	0.304390	+	0.936816i
$670$	−35.0573	+	1.09222i	−1.35438	+	0.0421962i
$671$	0.500990	+	0.363991i	0.0193405	+	0.0140517i
$672$	−3.48536	−	1.13246i	−0.134451	−	0.0436857i
$673$	11.0435	+	15.2001i	0.425695	+	0.585919i	0.966958	−	0.254934i	$-0.0820538\pi$
$673$	11.0435	+	15.2001i	0.425695	+	0.585919i	−0.541263	+	0.840853i	$0.682054\pi$
$674$	2.45879	−	1.78641i	0.0947090	−	0.0688101i
$675$	0.311251	+	4.99030i	0.0119801	+	0.192077i
$676$	−10.8176			−0.416061
$677$			4.71206i			0.181099i	0.995892	+	0.0905497i	$0.0288624\pi$
$677$			4.71206i			0.181099i	−0.995892	+	0.0905497i	$0.971138\pi$
$678$	7.44465	−	10.2467i	0.285910	−	0.393522i
$679$	1.40532	+	4.32514i	0.0539313	+	0.165984i
$680$	−13.9420	+	0.434367i	−0.534650	+	0.0166572i
$681$	−10.0864			−0.386512
$682$	0.521112	−	7.32356i	0.0199544	−	0.280434i
$683$			3.31087i			0.126687i	0.997992	+	0.0633435i	$0.0201764\pi$
$683$			3.31087i			0.126687i	−0.997992	+	0.0633435i	$0.979824\pi$
$684$	1.42011	−	4.37065i	0.0542993	−	0.167116i
$685$	−25.9040	−	33.4139i	−0.989740	−	1.27668i
$686$	−1.68936	−	1.22739i	−0.0644999	−	0.0468619i
$687$			12.4060i			0.473317i
$688$			2.45006i			0.0934075i
$689$	0.111024	+	0.0806638i	0.00422969	+	0.00307305i
$690$	5.01808	−	7.37958i	0.191035	−	0.280936i
$691$	−11.0343	+	8.01691i	−0.419766	+	0.304978i	−0.777543	−	0.628829i	$-0.783534\pi$
$691$	−11.0343	+	8.01691i	−0.419766	+	0.304978i	0.357778	+	0.933807i	$0.383534\pi$
$692$	2.44715	+	0.795126i	0.0930266	+	0.0302262i
$693$	2.84052	−	3.90964i	0.107902	−	0.148515i
$694$	8.30409	−	25.5574i	0.315219	−	0.970144i
$695$	−12.4673	+	9.66522i	−0.472911	+	0.366623i
$696$	−6.54547	+	4.75556i	−0.248105	+	0.180259i
$697$	17.1773	−	5.58125i	0.650637	−	0.211405i
$698$	14.3204	−	4.65299i	0.542036	−	0.176118i
$699$	12.1604	−	8.83508i	0.459950	−	0.334173i
$700$	9.82666	−	15.4658i	0.371413	−	0.584553i
$701$	2.38408	−	7.33745i	0.0900455	−	0.277132i	−0.895885	−	0.444285i	$-0.853458\pi$
$701$	2.38408	−	7.33745i	0.0900455	−	0.277132i	0.985931	+	0.167154i	$0.0534576\pi$
$702$	−0.868336	+	1.19516i	−0.0327732	+	0.0451085i
$703$	−22.4405	−	7.29136i	−0.846359	−	0.274999i
$704$	1.06683	−	0.775098i	0.0402077	−	0.0292126i
$705$	17.6333	+	11.9906i	0.664108	+	0.451590i
$706$	−28.9984	−	21.0686i	−1.09137	−	0.792927i
$707$			26.2837i			0.988499i
$708$		−	12.9314i		−	0.485991i
$709$	9.61136	+	6.98307i	0.360962	+	0.262255i	0.753453	−	0.657501i	$-0.228387\pi$
$709$	9.61136	+	6.98307i	0.360962	+	0.262255i	−0.392491	+	0.919756i	$0.628387\pi$
$710$	19.6235	+	25.3126i	0.736457	+	0.949965i
$711$	2.08920	−	6.42991i	0.0783513	−	0.241140i
$712$		−	8.98945i		−	0.336894i
$713$	1.57714	−	22.1648i	0.0590645	−	0.830076i
$714$	−22.8608			−0.855543
$715$	0.135648	+	4.35393i	0.00507295	+	0.162828i
$716$	−5.42860	−	16.7075i	−0.202876	−	0.624390i
$717$	7.86585	−	10.8264i	0.293756	−	0.404320i
$718$			18.8600i			0.703850i
$719$	23.7055			0.884065			0.442033	−	0.896999i	$-0.354257\pi$
$719$	23.7055			0.884065			0.442033	+	0.896999i	$0.354257\pi$
$720$	−0.624424	+	2.14711i	−0.0232709	+	0.0800182i
$721$	5.66612	−	4.11668i	0.211017	−	0.153313i
$722$	−1.24571	−	1.71458i	−0.0463606	−	0.0638099i
$723$	0.905160	+	0.294104i	0.0336633	+	0.0109379i
$724$	−10.1611	−	7.38246i	−0.377634	−	0.274367i
$725$	−14.8715	−	37.6205i	−0.552312	−	1.39719i
$726$	−2.86184	−	8.80782i	−0.106213	−	0.326889i
$727$	−17.4459	−	24.0122i	−0.647032	−	0.890563i	0.351935	−	0.936025i	$-0.385524\pi$
$727$	−17.4459	−	24.0122i	−0.647032	−	0.890563i	−0.998966	+	0.0454621i	$0.985524\pi$
$728$	5.14892	−	1.67299i	0.190832	−	0.0620050i
$729$	−0.309017	−	0.951057i	−0.0114451	−	0.0352243i
$730$	6.95086	+	4.72655i	0.257263	+	0.174938i
$731$	4.72289	+	14.5356i	0.174682	+	0.537617i
$732$	−0.446622	−	0.145116i	−0.0165076	−	0.00536365i
$733$	18.1005	−	24.9132i	0.668559	−	0.920192i	−0.331168	−	0.943572i	$-0.607443\pi$
$733$	18.1005	−	24.9132i	0.668559	−	0.920192i	0.999727	+	0.0233799i	$0.00744274\pi$
$734$	−4.65580	+	14.3291i	−0.171849	+	0.528897i
$735$	8.08506	−	11.8899i	0.298222	−	0.438565i
$736$	3.22876	−	2.34583i	0.119014	−	0.0864686i
$737$	12.1580	−	16.7340i	0.447845	−	0.616405i
$738$		−	2.89534i		−	0.106579i
$739$	−27.6817			−1.01829			−0.509144	−	0.860682i	$-0.670038\pi$
$739$	−27.6817			−1.01829			−0.509144	+	0.860682i	$0.670038\pi$
$740$	11.0240	+	3.20602i	0.405252	+	0.117855i
$741$	2.09793	+	6.45677i	0.0770695	+	0.237195i
$742$	0.323772	+	0.105200i	0.0118860	+	0.00386201i
$743$		−	28.6124i		−	1.04969i	−0.851198	−	0.524844i	$-0.824124\pi$
$743$		−	28.6124i		−	1.04969i	0.851198	−	0.524844i	$-0.175876\pi$
$744$	1.34036	+	5.40402i	0.0491399	+	0.198121i
$745$	7.17669	+	19.9510i	0.262934	+	0.730947i
$746$	−10.0943	+	31.0669i	−0.369577	+	1.13744i
$747$	13.0165	−	4.22932i	0.476249	−	0.154743i
$748$	4.83511	−	6.65496i	0.176789	−	0.243329i
$749$	41.9617			1.53325
$750$	−9.61876	−	5.69907i	−0.351228	−	0.208101i
$751$	7.14322	+	5.18985i	0.260660	+	0.189380i	0.710438	−	0.703760i	$-0.248497\pi$
$751$	7.14322	+	5.18985i	0.260660	+	0.189380i	−0.449778	+	0.893140i	$0.648497\pi$
$752$	5.60530	+	7.71504i	0.204404	+	0.281339i
$753$	0.685692	+	0.943774i	0.0249880	+	0.0343930i
$754$	3.69347	−	11.3673i	0.134508	−	0.413974i
$755$	−10.1225	+	34.8067i	−0.368396	+	1.26675i
$756$	−1.13246	+	3.48536i	−0.0411872	+	0.126761i
$757$	−15.9576	+	5.18495i	−0.579990	+	0.188450i	−0.584296	−	0.811541i	$-0.698629\pi$
$757$	−15.9576	+	5.18495i	−0.579990	+	0.188450i	0.00430627	+	0.999991i	$0.498629\pi$
$758$	−12.9514	−	17.8261i	−0.470416	−	0.647472i
$759$	1.62629	+	5.00522i	0.0590307	+	0.181678i
$760$	6.29605	+	8.12136i	0.228382	+	0.294593i
$761$	−13.8710	+	10.0779i	−0.502822	+	0.365322i	−0.810094	−	0.586300i	$-0.800584\pi$
$761$	−13.8710	+	10.0779i	−0.502822	+	0.365322i	0.307272	+	0.951622i	$0.400584\pi$
$762$	−4.49246	+	1.45969i	−0.162745	+	0.0528789i
$763$	−60.9292	−	19.7971i	−2.20579	−	0.716703i
$764$	15.1880	+	11.0348i	0.549484	+	0.399224i
$765$	0.434367	+	13.9420i	0.0157046	+	0.504073i
$766$	−24.8806	+	18.0768i	−0.898972	+	0.653141i
$767$	11.2288	+	15.4551i	0.405447	+	0.558051i
$768$	−0.587785	+	0.809017i	−0.0212099	+	0.0291929i
$769$	−29.2266			−1.05394			−0.526970	−	0.849884i	$-0.676672\pi$
$769$	−29.2266			−1.05394			−0.526970	+	0.849884i	$0.676672\pi$
$770$	3.65764	+	10.1681i	0.131812	+	0.366434i
$771$	−4.73534	−	3.44043i	−0.170539	−	0.123904i
$772$	5.21029	−	1.69293i	0.187523	−	0.0609298i
$773$	25.4272	+	8.26179i	0.914552	+	0.297156i	0.728230	−	0.685333i	$-0.240343\pi$
$773$	25.4272	+	8.26179i	0.914552	+	0.297156i	0.186322	+	0.982489i	$0.440343\pi$
$774$	2.45006			0.0880654
$775$	−27.8378	−	0.243455i	−0.999962	−	0.00874515i
$776$	1.24094			0.0445473
$777$	17.8951	+	5.81446i	0.641982	+	0.208593i
$778$	−26.6530	+	8.66008i	−0.955556	+	0.310479i
$779$	−10.7646	−	7.82092i	−0.385681	−	0.280214i
$780$	−1.11813	−	3.10836i	−0.0400354	−	0.111297i
$781$	−18.8880			−0.675866
$782$	14.6335	−	20.1412i	0.523292	−	0.720249i
$783$	4.75556	+	6.54547i	0.169950	+	0.233916i
$784$	5.20214	−	3.77958i	0.185791	−	0.134985i
$785$	0.528694	+	16.9696i	0.0188699	+	0.605671i
$786$	−9.15152	−	6.64897i	−0.326424	−	0.237161i
$787$	−48.2500	−	15.6774i	−1.71993	−	0.558838i	−0.727992	−	0.685586i	$-0.759546\pi$
$787$	−48.2500	−	15.6774i	−1.71993	−	0.558838i	−0.991935	+	0.126748i	$0.959546\pi$
$788$	−2.74796	+	0.892867i	−0.0978921	+	0.0318071i
$789$	−2.82954	+	2.05578i	−0.100734	+	0.0731877i
$790$	9.26246	+	11.9478i	0.329544	+	0.425083i
$791$	14.3433	+	44.1442i	0.509990	+	1.56959i
$792$	−0.775098	−	1.06683i	−0.0275419	−	0.0379082i
$793$	0.659795	−	0.214380i	0.0234300	−	0.00761287i
$794$	−3.13332	+	9.64336i	−0.111197	+	0.342230i
$795$	0.0580057	−	0.199456i	0.00205725	−	0.00707396i
$796$	8.17671	−	25.1653i	0.289816	−	0.891961i
$797$	−9.08984	−	12.5111i	−0.321979	−	0.443166i	0.617091	−	0.786892i	$-0.288311\pi$
$797$	−9.08984	−	12.5111i	−0.321979	−	0.443166i	−0.939070	+	0.343726i	$0.888311\pi$
$798$	9.89920	+	13.6251i	0.350428	+	0.482323i
$799$	48.1269	+	34.9662i	1.70261	+	1.23702i
$800$	−3.18503	−	3.85429i	−0.112608	−	0.136270i
$801$	−8.98945			−0.317626
$802$	11.9134	−	16.3973i	0.420675	−	0.579009i
$803$	−4.71444	+	1.53181i	−0.166369	+	0.0540566i
$804$	−4.84715	+	14.9180i	−0.170946	+	0.526117i
$805$	11.0699	+	30.7739i	0.390161	+	1.08464i
$806$	−6.29445	−	5.29480i	−0.221713	−	0.186501i
$807$			15.5441i			0.547179i
$808$	6.82104	+	2.21629i	0.239964	+	0.0779689i
$809$	−11.2447	−	34.6075i	−0.395341	−	1.21673i	−0.928696	−	0.370843i	$-0.879069\pi$
$809$	−11.2447	−	34.6075i	−0.395341	−	1.21673i	0.533355	−	0.845892i	$-0.320931\pi$
$810$	2.14711	+	0.624424i	0.0754419	+	0.0219400i
$811$	−22.2031			−0.779657			−0.389829	−	0.920887i	$-0.627466\pi$
$811$	−22.2031			−0.779657			−0.389829	+	0.920887i	$0.627466\pi$
$812$		−	29.6500i		−	1.04051i
$813$	−1.21646	+	1.67432i	−0.0426633	+	0.0587209i
$814$	−5.47749	+	3.97963i	−0.191986	+	0.139486i
$815$	18.0330	−	26.5193i	0.631668	−	0.928930i
$816$	−1.92767	+	5.93275i	−0.0674819	+	0.207688i
$817$	6.61812	−	9.10906i	0.231539	−	0.318686i
$818$	−3.79047	−	1.23160i	−0.132531	−	0.0430618i
$819$	−1.67299	−	5.14892i	−0.0584589	−	0.179918i
$820$	5.35367	+	3.64047i	0.186958	+	0.127131i
$821$	−0.158730	−	0.488520i	−0.00553971	−	0.0170495i	0.948248	−	0.317529i	$-0.102853\pi$
$821$	−0.158730	−	0.488520i	−0.00553971	−	0.0170495i	−0.953788	+	0.300480i	$0.902853\pi$
$822$	−17.9823	+	5.84280i	−0.627204	+	0.203791i
$823$	−8.15832	−	11.2290i	−0.284381	−	0.391417i	0.642798	−	0.766036i	$-0.277774\pi$
$823$	−8.15832	−	11.2290i	−0.284381	−	0.391417i	−0.927179	+	0.374619i	$0.877774\pi$
$824$	−0.590567	−	1.81758i	−0.0205734	−	0.0633184i
$825$	6.13168	−	2.42387i	0.213478	−	0.0843882i
$826$	38.3392	+	27.8551i	1.33399	+	0.969202i
$827$	−30.0117	−	9.75141i	−1.04361	−	0.339090i	−0.263453	−	0.964672i	$-0.584861\pi$
$827$	−30.0117	−	9.75141i	−1.04361	−	0.339090i	−0.780158	+	0.625583i	$0.784861\pi$
$828$	−2.34583	−	3.22876i	−0.0815234	−	0.112207i
$829$	36.4314	−	26.4689i	1.26531	−	0.919304i	0.266308	−	0.963888i	$-0.414196\pi$
$829$	36.4314	−	26.4689i	1.26531	−	0.919304i	0.999006	+	0.0445836i	$0.0141961\pi$
$830$	−8.54610	+	29.3862i	−0.296640	+	1.02001i
$831$	−8.25662			−0.286419
$832$		−	1.47730i		−	0.0512162i
$833$	23.5772	−	32.4513i	0.816903	−	1.12437i
$834$	2.18005	+	6.70950i	0.0754889	+	0.232331i
$835$	−0.946349	−	30.3752i	−0.0327497	−	1.05118i
$836$	−6.06008			−0.209592
$837$	5.40402	−	1.34036i	0.186790	−	0.0463296i
$838$			10.7950i			0.372906i
$839$	−10.9288	+	33.6355i	−0.377306	+	1.16123i	0.564604	+	0.825362i	$0.309029\pi$
$839$	−10.9288	+	33.6355i	−0.377306	+	1.16123i	−0.941910	+	0.335866i	$0.890971\pi$
$840$	−5.02076	−	6.47634i	−0.173233	−	0.223455i
$841$	−29.4955	−	21.4298i	−1.01709	−	0.738957i
$842$			12.9414i			0.445990i
$843$		−	13.0623i		−	0.449888i
$844$	14.2305	+	10.3391i	0.489835	+	0.355886i
$845$	−20.0024	−	13.6016i	−0.688105	−	0.467908i
$846$	7.71504	−	5.60530i	0.265249	−	0.192714i
$847$	32.2782	+	10.4878i	1.10909	+	0.360366i
$848$	0.0546022	−	0.0751534i	0.00187505	−	0.00258078i
$849$	−5.69822	+	17.5373i	−0.195562	+	0.601879i
$850$	−26.3258	−	16.7269i	−0.902968	−	0.573727i
$851$	−16.5776	+	12.0443i	−0.568273	+	0.412875i
$852$	13.6224	−	4.42620i	0.466697	−	0.151639i
$853$	−29.4780	+	9.57799i	−1.00931	+	0.327944i	−0.766579	−	0.642150i	$-0.778043\pi$
$853$	−29.4780	+	9.57799i	−1.00931	+	0.327944i	−0.242729	+	0.970094i	$0.578043\pi$
$854$	1.39230	−	1.01156i	0.0476435	−	0.0346150i
$855$	8.12136	−	6.29605i	0.277745	−	0.215320i
$856$	3.53829	−	10.8897i	0.120936	−	0.372204i
$857$	8.55293	−	11.7721i	0.292162	−	0.402127i	−0.637553	−	0.770407i	$-0.720053\pi$
$857$	8.55293	−	11.7721i	0.292162	−	0.402127i	0.929715	+	0.368280i	$0.120053\pi$
$858$	1.85274	+	0.601990i	0.0632513	+	0.0205516i
$859$	31.3241	−	22.7583i	1.06877	−	0.776504i	0.0930758	−	0.995659i	$-0.470330\pi$
$859$	31.3241	−	22.7583i	1.06877	−	0.776504i	0.975690	+	0.219155i	$0.0703301\pi$
$860$	−3.08059	+	4.53032i	−0.105047	+	0.154483i
$861$	8.58416	+	6.23676i	0.292547	+	0.212548i
$862$		−	1.12591i		−	0.0383486i
$863$		−	18.8389i		−	0.641283i	−0.947201	−	0.320641i	$-0.896102\pi$
$863$		−	18.8389i		−	0.641283i	0.947201	−	0.320641i	$-0.103898\pi$
$864$	0.809017	+	0.587785i	0.0275233	+	0.0199969i
$865$	3.52518	+	4.54718i	0.119860	+	0.154609i
$866$	−8.11435	+	24.9734i	−0.275737	+	0.848631i
$867$			21.9134i			0.744219i
$868$	−18.9092	−	7.66672i	−0.641820	−	0.260225i
$869$	−8.91531			−0.302431
$870$	−18.0824	+	0.563365i	−0.613052	+	0.0190999i
$871$	−7.16070	−	22.0384i	−0.242631	−	0.746742i
$872$	−10.2753	+	14.1428i	−0.347967	+	0.478936i
$873$		−	1.24094i		−	0.0419996i
$874$	−18.3408			−0.620388
$875$	37.6162	−	16.2417i	1.27166	−	0.549071i
$876$	3.04119	−	2.20955i	0.102752	−	0.0746539i
$877$	−5.14294	−	7.07865i	−0.173665	−	0.239029i	0.713308	−	0.700851i	$-0.247196\pi$
$877$	−5.14294	−	7.07865i	−0.173665	−	0.239029i	−0.886973	+	0.461822i	$0.847196\pi$
$878$	−18.4932	−	6.00881i	−0.624115	−	0.202787i
$879$	−22.0178	−	15.9969i	−0.742643	−	0.539562i
$880$	2.94722	−	0.0918216i	0.0993507	−	0.00309531i
$881$	13.9461	+	42.9217i	0.469856	+	1.44607i	0.852771	+	0.522285i	$0.174920\pi$
$881$	13.9461	+	42.9217i	0.469856	+	1.44607i	−0.382915	+	0.923784i	$0.625080\pi$
$882$	−3.77958	−	5.20214i	−0.127265	−	0.175165i
$883$	−3.13437	+	1.01842i	−0.105480	+	0.0342725i	−0.361281	−	0.932457i	$-0.617661\pi$
$883$	−3.13437	+	1.01842i	−0.105480	+	0.0342725i	0.255801	+	0.966729i	$0.417661\pi$
$884$	−2.84775	−	8.76446i	−0.0957800	−	0.294781i
$885$	16.2594	−	23.9110i	0.546552	−	0.803759i
$886$	−0.727606	−	2.23934i	−0.0244444	−	0.0752321i
$887$	−43.1862	−	14.0320i	−1.45005	−	0.471150i	−0.525035	−	0.851080i	$-0.675948\pi$
$887$	−43.1862	−	14.0320i	−1.45005	−	0.471150i	−0.925015	+	0.379931i	$0.875948\pi$
$888$	3.01790	−	4.15378i	0.101274	−	0.139392i
$889$	5.34935	−	16.4636i	0.179412	−	0.552172i
$890$	11.3029	−	16.6221i	0.378876	−	0.557174i
$891$	−1.06683	+	0.775098i	−0.0357402	+	0.0259668i
$892$	−14.9754	+	20.6119i	−0.501415	+	0.690138i
$893$		−	43.8249i		−	1.46654i
$894$	9.48205			0.317127
$895$	10.9695	−	37.7191i	0.366669	−	1.26081i
$896$	−1.13246	−	3.48536i	−0.0378329	−	0.116438i
$897$	5.60730	+	1.82192i	0.187222	+	0.0608322i
$898$			5.08540i			0.169702i
$899$	−38.2310	+	23.8244i	−1.27508	+	0.794589i
$900$	−3.85429	+	3.18503i	−0.128476	+	0.106168i
$901$	0.179070	−	0.551121i	0.00596569	−	0.0183605i
$902$	−3.63114	+	1.17983i	−0.120904	+	0.0392840i
$903$	−5.27759	+	7.26398i	−0.175627	+	0.241730i
$904$	12.6656			0.421252
$905$	−9.50615	−	26.4268i	−0.315995	−	0.878456i
$906$	13.1149	+	9.52856i	0.435714	+	0.316565i
$907$	−1.72622	−	2.37594i	−0.0573183	−	0.0788918i	0.779396	−	0.626532i	$-0.215526\pi$
$907$	−1.72622	−	2.37594i	−0.0573183	−	0.0788918i	−0.836714	+	0.547640i	$0.815526\pi$
$908$	−5.92865	−	8.16009i	−0.196749	−	0.270802i
$909$	2.21629	−	6.82104i	0.0735098	−	0.226240i
$910$	11.6243	+	3.38057i	0.385340	+	0.112065i
$911$	15.1915	−	46.7547i	0.503318	−	1.54905i	−0.300262	−	0.953857i	$-0.597074\pi$
$911$	15.1915	−	46.7547i	0.503318	−	1.54905i	0.803580	−	0.595197i	$-0.202926\pi$
$912$	4.37065	−	1.42011i	0.144727	−	0.0470246i
$913$	−10.6083	−	14.6010i	−0.351083	−	0.483224i
$914$	−4.22873	−	13.0147i	−0.139874	−	0.430488i
$915$	−0.643371	−	0.829893i	−0.0212692	−	0.0274354i
$916$	−10.0366	+	7.29204i	−0.331620	+	0.240936i
$917$	39.4261	−	12.8103i	1.30196	−	0.423033i
$918$	5.93275	+	1.92767i	0.195810	+	0.0636225i
$919$	17.9217	+	13.0209i	0.591183	+	0.429519i	0.842738	−	0.538324i	$-0.180942\pi$
$919$	17.9217	+	13.0209i	0.591183	+	0.429519i	−0.251556	+	0.967843i	$0.580942\pi$
$920$	8.91976	−	0.277898i	0.294076	−	0.00916203i
$921$	17.3984	−	12.6407i	0.573297	−	0.416525i
$922$	11.9963	+	16.5115i	0.395077	+	0.543777i
$923$	−12.4376	+	17.1189i	−0.409388	+	0.563474i
$924$	4.83258			0.158980
$925$	16.3531	+	19.7893i	0.537686	+	0.650668i
$926$	9.10510	+	6.61524i	0.299212	+	0.217390i
$927$	−1.81758	+	0.590567i	−0.0596971	+	0.0193968i
$928$	−7.69466	−	2.50015i	−0.252589	−	0.0820713i
$929$	−19.0690			−0.625633			−0.312816	−	0.949814i	$-0.601272\pi$
$929$	−19.0690			−0.625633			−0.312816	+	0.949814i	$0.601272\pi$
$930$	−4.31637	+	11.6777i	−0.141539	+	0.382927i
$931$	−29.5505			−0.968478
$932$	14.2955	+	4.64488i	0.468263	+	0.152148i
$933$	13.2714	−	4.31213i	0.434485	−	0.141173i
$934$	−13.1632	−	9.56365i	−0.430714	−	0.312932i
$935$	17.3081	−	6.22601i	0.566036	−	0.203612i
$936$	−1.47730			−0.0482871
$937$	34.9936	−	48.1645i	1.14319	−	1.57347i	0.383022	−	0.923739i	$-0.374883\pi$
$937$	34.9936	−	48.1645i	1.14319	−	1.57347i	0.760168	−	0.649726i	$-0.225117\pi$
$938$	−33.7881	−	46.5054i	−1.10322	−	1.51845i
$939$	−4.56767	+	3.31861i	−0.149060	+	0.108299i
$940$	0.664029	+	21.3135i	0.0216583	+	0.695170i
$941$	6.14889	+	4.46743i	0.200448	+	0.145634i	0.683481	−	0.729968i	$-0.260465\pi$
$941$	6.14889	+	4.46743i	0.200448	+	0.145634i	−0.483033	+	0.875602i	$0.660465\pi$
$942$	7.22110	+	2.34628i	0.235276	+	0.0764459i
$943$	−10.9897	+	3.57076i	−0.357872	+	0.116280i
$944$	10.4617	−	7.60087i	0.340499	−	0.247387i
$945$	−6.47634	+	5.02076i	−0.210675	+	0.163325i
$946$	−0.998381	−	3.07270i	−0.0324602	−	0.0999021i
$947$	−8.19115	−	11.2742i	−0.266177	−	0.366361i	0.654918	−	0.755700i	$-0.272703\pi$
$947$	−8.19115	−	11.2742i	−0.266177	−	0.366361i	−0.921094	+	0.389339i	$0.872703\pi$
$948$	6.42991	−	2.08920i	0.208834	−	0.0678542i
$949$	−1.71608	+	5.28155i	−0.0557063	+	0.171446i
$950$	1.43038	+	22.9333i	0.0464076	+	0.744055i
$951$	−0.266800	+	0.821125i	−0.00865157	+	0.0266268i
$952$	−13.4372	−	18.4948i	−0.435503	−	0.599419i
$953$	20.3310	+	27.9833i	0.658587	+	0.906467i	0.999434	−	0.0336516i	$-0.0107137\pi$
$953$	20.3310	+	27.9833i	0.658587	+	0.906467i	−0.340847	+	0.940119i	$0.610714\pi$
$954$	−0.0751534	−	0.0546022i	−0.00243318	−	0.00176781i
$955$	14.2091	+	39.5008i	0.459796	+	1.27822i
$956$	13.3822			0.432811
$957$	6.27104	−	8.63135i	0.202714	−	0.279012i
$958$	3.47970	−	1.13062i	0.112424	−	0.0365288i
$959$	21.4122	−	65.9001i	0.691437	−	2.12802i
$960$	−2.10408	+	0.756872i	−0.0679088	+	0.0244279i
$961$	5.30843	+	30.5421i	0.171240	+	0.985229i
$962$			7.58499i			0.244550i
$963$	−10.8897	−	3.53829i	−0.350917	−	0.114020i
$964$	0.294104	+	0.905160i	0.00947246	+	0.0291532i
$965$	11.7628	+	3.42086i	0.378658	+	0.110121i
$966$	14.6258			0.470578
$967$		−	40.3235i		−	1.29671i	−0.761336	−	0.648357i	$-0.775456\pi$
$967$		−	40.3235i		−	1.29671i	0.761336	−	0.648357i	$-0.224544\pi$
$968$	5.44353	−	7.49238i	0.174962	−	0.240814i
$969$	23.1925	−	16.8503i	0.745050	−	0.541311i
$970$	2.29459	+	1.56031i	0.0736749	+	0.0500985i
$971$	15.8279	−	48.7133i	0.507942	−	1.56328i	−0.287827	−	0.957682i	$-0.592933\pi$
$971$	15.8279	−	48.7133i	0.507942	−	1.56328i	0.795769	−	0.605601i	$-0.207067\pi$
$972$	0.587785	−	0.809017i	0.0188532	−	0.0259492i
$973$	−24.5885	−	7.98927i	−0.788270	−	0.256124i
$974$	−7.15362	−	22.0166i	−0.229217	−	0.705457i
$975$	1.84082	−	7.15345i	0.0589535	−	0.229094i
$976$	−0.145116	−	0.446622i	−0.00464505	−	0.0142960i
$977$	0.684423	−	0.222383i	0.0218966	−	0.00711465i	−0.298048	−	0.954551i	$-0.596336\pi$
$977$	0.684423	−	0.222383i	0.0218966	−	0.00711465i	0.319945	+	0.947436i	$0.396336\pi$
$978$	−8.43000	−	11.6029i	−0.269562	−	0.371020i
$979$	3.66314	+	11.2740i	0.117074	+	0.360318i
$980$	14.3714	−	0.447746i	0.459077	−	0.0143027i
$981$	14.1428	+	10.2753i	0.451545	+	0.328067i
$982$	4.58948	+	1.49121i	0.146456	+	0.0475865i
$983$	0.898643	+	1.23688i	0.0286623	+	0.0394502i	0.823108	−	0.567885i	$-0.192238\pi$
$983$	0.898643	+	1.23688i	0.0286623	+	0.0394502i	−0.794445	+	0.607336i	$0.792238\pi$
$984$	2.34238	−	1.70184i	0.0746722	−	0.0542526i
$985$	−6.20382	−	1.80420i	−0.197670	−	0.0574865i
$986$	−50.4699			−1.60729
$987$			34.9480i			1.11241i
$988$	−3.99050	+	5.49246i	−0.126955	+	0.174738i
$989$	−3.02160	−	9.29953i	−0.0960813	−	0.295708i
$990$	−0.0918216	−	2.94722i	−0.00291828	−	0.0936687i
$991$	−53.8217			−1.70970			−0.854851	−	0.518874i	$-0.826351\pi$
$991$	−53.8217			−1.70970			−0.854851	+	0.518874i	$0.826351\pi$
$992$	−3.58410	+	4.26078i	−0.113795	+	0.135280i
$993$			5.36079i			0.170120i
$994$	−16.2208	+	49.9225i	−0.514492	+	1.58344i
$995$	46.7611	−	36.2514i	1.48243	−	1.14925i
$996$	11.0725	+	8.04465i	0.350846	+	0.254904i
$997$			25.7150i			0.814401i	0.913339	+	0.407201i	$0.133495\pi$
$997$			25.7150i			0.814401i	−0.913339	+	0.407201i	$0.866505\pi$
$998$		−	5.55963i		−	0.175987i
$999$	−4.15378	−	3.01790i	−0.131420	−	0.0954821i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.z.d.349.15	yes	72
5.4	even	2	inner	930.2.z.d.349.6	✓	72
31.4	even	5	inner	930.2.z.d.469.6	yes	72
155.4	even	10	inner	930.2.z.d.469.15	yes	72

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.z.d.349.6	✓	72	5.4	even	2	inner
930.2.z.d.349.15	yes	72	1.1	even	1	trivial
930.2.z.d.469.6	yes	72	31.4	even	5	inner
930.2.z.d.469.15	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)

\(f(q)\)	\(=\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.756872 + 2.10408i) q^{5} +1.00000 q^{6} +(-2.15407 + 2.96482i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +O(q^{10})\)	\(q+(0.951057 + 0.309017i) q^{2} +(0.951057 - 0.309017i) q^{3} +(0.809017 + 0.587785i) q^{4} +(0.756872 + 2.10408i) q^{5} +1.00000 q^{6} +(-2.15407 + 2.96482i) q^{7} +(0.587785 + 0.809017i) q^{8} +(0.809017 - 0.587785i) q^{9} +(0.0696317 + 2.23498i) q^{10} +(-1.06683 - 0.775098i) q^{11} +(0.951057 + 0.309017i) q^{12} +(-1.40500 + 0.456511i) q^{13} +(-2.96482 + 2.15407i) q^{14} +(1.37002 + 1.76721i) q^{15} +(0.309017 + 0.951057i) q^{16} +(3.66664 + 5.04670i) q^{17} +(0.951057 - 0.309017i) q^{18} +(1.42011 - 4.37065i) q^{19} +(-0.624424 + 2.14711i) q^{20} +(-1.13246 + 3.48536i) q^{21} +(-0.775098 - 1.06683i) q^{22} +(-2.34583 - 3.22876i) q^{23} +(0.809017 + 0.587785i) q^{24} +(-3.85429 + 3.18503i) q^{25} -1.47730 q^{26} +(0.587785 - 0.809017i) q^{27} +(-3.48536 + 1.13246i) q^{28} +(-2.50015 + 7.69466i) q^{29} +(0.756872 + 2.10408i) q^{30} +(4.26078 + 3.58410i) q^{31} +1.00000i q^{32} +(-1.25414 - 0.407493i) q^{33} +(1.92767 + 5.93275i) q^{34} +(-7.86858 - 2.28834i) q^{35} +1.00000 q^{36} -5.13435i q^{37} +(2.70121 - 3.71790i) q^{38} +(-1.19516 + 0.868336i) q^{39} +(-1.25736 + 1.84907i) q^{40} +(0.894708 - 2.75363i) q^{41} +(-2.15407 + 2.96482i) q^{42} +(2.33014 + 0.757109i) q^{43} +(-0.407493 - 1.25414i) q^{44} +(1.84907 + 1.25736i) q^{45} +(-1.23328 - 3.79564i) q^{46} +(9.06957 - 2.94688i) q^{47} +(0.587785 + 0.809017i) q^{48} +(-1.98704 - 6.11548i) q^{49} +(-4.64988 + 1.83811i) q^{50} +(5.04670 + 3.66664i) q^{51} +(-1.40500 - 0.456511i) q^{52} +(-0.0546022 - 0.0751534i) q^{53} +(0.809017 - 0.587785i) q^{54} +(0.823413 - 2.83135i) q^{55} -3.66472 q^{56} -4.59558i q^{57} +(-4.75556 + 6.54547i) q^{58} +(-3.99601 - 12.2985i) q^{59} +(0.0696317 + 2.23498i) q^{60} -0.469606 q^{61} +(2.94469 + 4.72534i) q^{62} +3.66472i q^{63} +(-0.309017 + 0.951057i) q^{64} +(-2.02394 - 2.61070i) q^{65} +(-1.06683 - 0.775098i) q^{66} +15.6857i q^{67} +6.23806i q^{68} +(-3.22876 - 2.34583i) q^{69} +(-6.77632 - 4.60787i) q^{70} +(11.5879 - 8.41913i) q^{71} +(0.951057 + 0.309017i) q^{72} +(2.20955 - 3.04119i) q^{73} +(1.58660 - 4.88306i) q^{74} +(-2.68142 + 4.22019i) q^{75} +(3.71790 - 2.70121i) q^{76} +(4.59606 - 1.49335i) q^{77} +(-1.40500 + 0.456511i) q^{78} +(5.46961 - 3.97390i) q^{79} +(-1.76721 + 1.37002i) q^{80} +(0.309017 - 0.951057i) q^{81} +(1.70184 - 2.34238i) q^{82} +(13.0165 + 4.22932i) q^{83} +(-2.96482 + 2.15407i) q^{84} +(-7.84347 + 11.5346i) q^{85} +(1.98214 + 1.44011i) q^{86} +8.09064i q^{87} -1.31868i q^{88} +(-7.27261 - 5.28386i) q^{89} +(1.37002 + 1.76721i) q^{90} +(1.67299 - 5.14892i) q^{91} -3.99097i q^{92} +(5.15979 + 2.09203i) q^{93} +9.53631 q^{94} +(10.2710 - 0.319998i) q^{95} +(0.309017 + 0.951057i) q^{96} +(0.729409 - 1.00395i) q^{97} -6.43020i q^{98} -1.31868 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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