LMFDB - Embedded newform 930.2.bf.a.377.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(377,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([6, 3, 8]))

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

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

chi := DirichletCharacter("930.377");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.bf (of order $12$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$7.42608738798$
Analytic rank:	$0$
Dimension:	$256$
Relative dimension:	$64$ over $\Q(\zeta_{12})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			377.2
Character	$\chi$	$=$	930.377
Dual form			930.2.bf.a.893.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.707107 + 0.707107i) q^{2} +(-1.70669 + 0.295334i) q^{3} -1.00000i q^{4} +(2.22324 + 0.239148i) q^{5} +(0.997976 - 1.41564i) q^{6} +(-3.38718 + 0.907593i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82556 - 1.00809i) q^{9} +O(q^{10})$	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.70669 + 0.295334i) q^{3} -1.00000i q^{4} +(2.22324 + 0.239148i) q^{5} +(0.997976 - 1.41564i) q^{6} +(-3.38718 + 0.907593i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82556 - 1.00809i) q^{9} +(-1.74117 + 1.40297i) q^{10} +(3.85884 - 2.22790i) q^{11} +(0.295334 + 1.70669i) q^{12} +(-2.44386 - 0.654831i) q^{13} +(1.75334 - 3.03687i) q^{14} +(-3.86501 + 0.248450i) q^{15} -1.00000 q^{16} +(0.252355 + 0.941802i) q^{17} +(-1.28514 + 2.71079i) q^{18} +(-5.23678 - 3.02346i) q^{19} +(0.239148 - 2.22324i) q^{20} +(5.51282 - 2.54933i) q^{21} +(-1.15325 + 4.30398i) q^{22} +(-0.257923 - 0.257923i) q^{23} +(-1.41564 - 0.997976i) q^{24} +(4.88562 + 1.06337i) q^{25} +(2.19111 - 1.26504i) q^{26} +(-4.52461 + 2.55497i) q^{27} +(0.907593 + 3.38718i) q^{28} +0.619287 q^{29} +(2.55729 - 2.90865i) q^{30} +(0.0974819 - 5.56691i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.92786 + 4.94198i) q^{33} +(-0.844397 - 0.487513i) q^{34} +(-7.74758 + 1.20776i) q^{35} +(-1.00809 - 2.82556i) q^{36} +(3.05592 - 0.818831i) q^{37} +(5.84087 - 1.56506i) q^{38} +(4.36430 + 0.395834i) q^{39} +(1.40297 + 1.74117i) q^{40} +(-3.75707 + 2.16914i) q^{41} +(-2.09550 + 5.70080i) q^{42} +(-1.39197 - 5.19490i) q^{43} +(-2.22790 - 3.85884i) q^{44} +(6.52298 - 1.56549i) q^{45} +0.364758 q^{46} +(5.64302 - 5.64302i) q^{47} +(1.70669 - 0.295334i) q^{48} +(4.58712 - 2.64837i) q^{49} +(-4.20657 + 2.70274i) q^{50} +(-0.708838 - 1.53283i) q^{51} +(-0.654831 + 2.44386i) q^{52} +(3.24089 - 12.0951i) q^{53} +(1.39275 - 5.00602i) q^{54} +(9.11194 - 4.03034i) q^{55} +(-3.03687 - 1.75334i) q^{56} +(9.83047 + 3.61349i) q^{57} +(-0.437902 + 0.437902i) q^{58} +(-2.32199 + 4.02181i) q^{59} +(0.248450 + 3.86501i) q^{60} +6.04358 q^{61} +(3.86747 + 4.00533i) q^{62} +(-8.65575 + 5.97903i) q^{63} +1.00000i q^{64} +(-5.27670 - 2.04029i) q^{65} +(0.697119 - 7.68614i) q^{66} +(3.00222 - 11.2044i) q^{67} +(0.941802 - 0.252355i) q^{68} +(0.516368 + 0.364020i) q^{69} +(4.62435 - 6.33239i) q^{70} +(8.97996 - 5.18458i) q^{71} +(2.71079 + 1.28514i) q^{72} +(10.7698 + 2.88575i) q^{73} +(-1.58186 + 2.73986i) q^{74} +(-8.65226 - 0.371944i) q^{75} +(-3.02346 + 5.23678i) q^{76} +(-11.0486 + 11.0486i) q^{77} +(-3.36592 + 2.80613i) q^{78} +(-4.35275 - 2.51306i) q^{79} +(-2.22324 - 0.239148i) q^{80} +(6.96752 - 5.69681i) q^{81} +(1.12283 - 4.19046i) q^{82} +(-3.01187 + 11.2405i) q^{83} +(-2.54933 - 5.51282i) q^{84} +(0.335817 + 2.15420i) q^{85} +(4.65762 + 2.68908i) q^{86} +(-1.05693 + 0.182897i) q^{87} +(4.30398 + 1.15325i) q^{88} +14.0530 q^{89} +(-3.50547 + 5.71941i) q^{90} +8.87214 q^{91} +(-0.257923 + 0.257923i) q^{92} +(1.47773 + 9.52976i) q^{93} +7.98043i q^{94} +(-10.9196 - 7.97424i) q^{95} +(-0.997976 + 1.41564i) q^{96} +(-9.72908 - 9.72908i) q^{97} +(-1.37090 + 5.11627i) q^{98} +(8.65746 - 10.1851i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) $ 256 * q + 8 * q^3 - 4 * q^7	$ 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) $ 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Display 100 coefficients 10 coefficients

Character values

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

$n$	$187$	$311$	$871$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$-1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$2$	−0.707107	+	0.707107i	−0.500000	+	0.500000i
$3$	−1.70669	+	0.295334i	−0.985356	+	0.170511i
$3$	−1.70669	+	0.295334i	−0.985356	+	0.170511i
$4$		−	1.00000i		−	0.500000i
$5$	2.22324	+	0.239148i	0.994264	+	0.106950i
$5$	2.22324	+	0.239148i	0.994264	+	0.106950i
$6$	0.997976	−	1.41564i	0.407422	−	0.577934i
$7$	−3.38718	+	0.907593i	−1.28024	+	0.343038i	−0.833944	−	0.551849i	$-0.813922\pi$
$7$	−3.38718	+	0.907593i	−1.28024	+	0.343038i	−0.446292	+	0.894888i	$0.647256\pi$
$8$	0.707107	+	0.707107i	0.250000	+	0.250000i
$9$	2.82556	−	1.00809i	0.941852	−	0.336029i
$10$	−1.74117	+	1.40297i	−0.550607	+	0.443657i
$11$	3.85884	−	2.22790i	1.16349	−	0.671738i	0.211348	−	0.977411i	$-0.432215\pi$
$11$	3.85884	−	2.22790i	1.16349	−	0.671738i	0.952137	+	0.305672i	$0.0988812\pi$
$12$	0.295334	+	1.70669i	0.0852557	+	0.492678i
$13$	−2.44386	−	0.654831i	−0.677806	−	0.181617i	−0.0965373	−	0.995329i	$-0.530777\pi$
$13$	−2.44386	−	0.654831i	−0.677806	−	0.181617i	−0.581268	+	0.813712i	$0.697443\pi$
$14$	1.75334	−	3.03687i	0.468599	−	0.811637i
$15$	−3.86501	+	0.248450i	−0.997940	+	0.0641494i
$16$	−1.00000			−0.250000
$17$	0.252355	+	0.941802i	0.0612051	+	0.228421i	0.989753	−	0.142793i	$-0.0456084\pi$
$17$	0.252355	+	0.941802i	0.0612051	+	0.228421i	−0.928547	+	0.371214i	$0.878942\pi$
$18$	−1.28514	+	2.71079i	−0.302912	+	0.638940i
$19$	−5.23678	−	3.02346i	−1.20140	−	0.693629i	−0.240534	−	0.970641i	$-0.577322\pi$
$19$	−5.23678	−	3.02346i	−1.20140	−	0.693629i	−0.960866	+	0.277012i	$0.910656\pi$
$20$	0.239148	−	2.22324i	0.0534751	−	0.497132i
$21$	5.51282	−	2.54933i	1.20300	−	0.556309i
$22$	−1.15325	+	4.30398i	−0.245873	+	0.917612i
$23$	−0.257923	−	0.257923i	−0.0537807	−	0.0537807i	0.679705	−	0.733486i	$-0.262108\pi$
$23$	−0.257923	−	0.257923i	−0.0537807	−	0.0537807i	−0.733486	+	0.679705i	$0.762108\pi$
$24$	−1.41564	−	0.997976i	−0.288967	−	0.203711i
$25$	4.88562	+	1.06337i	0.977123	+	0.212673i
$26$	2.19111	−	1.26504i	0.429712	−	0.248094i
$27$	−4.52461	+	2.55497i	−0.870762	+	0.491704i
$28$	0.907593	+	3.38718i	0.171519	+	0.640118i
$29$	0.619287			0.114999			0.0574994	−	0.998346i	$-0.481687\pi$
$29$	0.619287			0.114999			0.0574994	+	0.998346i	$0.481687\pi$
$30$	2.55729	−	2.90865i	0.466895	−	0.531045i
$31$	0.0974819	−	5.56691i	0.0175083	−	0.999847i
$31$	0.0974819	−	5.56691i	0.0175083	−	0.999847i
$32$	0.707107	−	0.707107i	0.125000	−	0.125000i
$33$	−5.92786	+	4.94198i	−1.03191	+	0.860289i
$34$	−0.844397	−	0.487513i	−0.144813	−	0.0836077i
$35$	−7.74758	+	1.20776i	−1.30958	+	0.204149i
$36$	−1.00809	−	2.82556i	−0.168014	−	0.470926i
$37$	3.05592	−	0.818831i	0.502390	−	0.134615i	0.00128107	−	0.999999i	$-0.499592\pi$
$37$	3.05592	−	0.818831i	0.502390	−	0.134615i	0.501109	+	0.865384i	$0.332926\pi$
$38$	5.84087	−	1.56506i	0.947514	−	0.253886i
$39$	4.36430	+	0.395834i	0.698848	+	0.0633842i
$40$	1.40297	+	1.74117i	0.221829	+	0.275304i
$41$	−3.75707	+	2.16914i	−0.586755	+	0.338763i	−0.763813	−	0.645437i	$-0.776675\pi$
$41$	−3.75707	+	2.16914i	−0.586755	+	0.338763i	0.177058	+	0.984200i	$0.443342\pi$
$42$	−2.09550	+	5.70080i	−0.323343	+	0.879652i
$43$	−1.39197	−	5.19490i	−0.212273	−	0.792215i	−0.987109	−	0.160052i	$-0.948834\pi$
$43$	−1.39197	−	5.19490i	−0.212273	−	0.792215i	0.774835	−	0.632163i	$-0.217833\pi$
$44$	−2.22790	−	3.85884i	−0.335869	−	0.581743i
$45$	6.52298	−	1.56549i	0.972388	−	0.233370i
$46$	0.364758			0.0537807
$47$	5.64302	−	5.64302i	0.823119	−	0.823119i	−0.163435	−	0.986554i	$-0.552257\pi$
$47$	5.64302	−	5.64302i	0.823119	−	0.823119i	0.986554	+	0.163435i	$0.0522575\pi$
$48$	1.70669	−	0.295334i	0.246339	−	0.0426278i
$49$	4.58712	−	2.64837i	0.655303	−	0.378339i
$50$	−4.20657	+	2.70274i	−0.594898	+	0.382225i
$51$	−0.708838	−	1.53283i	−0.0992571	−	0.214639i
$52$	−0.654831	+	2.44386i	−0.0908087	+	0.338903i
$53$	3.24089	−	12.0951i	0.445170	−	1.66140i	−0.270318	−	0.962771i	$-0.587129\pi$
$53$	3.24089	−	12.0951i	0.445170	−	1.66140i	0.715488	−	0.698625i	$-0.246205\pi$
$54$	1.39275	−	5.00602i	0.189529	−	0.681233i
$55$	9.11194	−	4.03034i	1.22865	−	0.543451i
$56$	−3.03687	−	1.75334i	−0.405818	−	0.234299i
$57$	9.83047	+	3.61349i	1.30208	+	0.478619i
$58$	−0.437902	+	0.437902i	−0.0574994	+	0.0574994i
$59$	−2.32199	+	4.02181i	−0.302298	+	0.523595i	−0.976656	−	0.214809i	$-0.931087\pi$
$59$	−2.32199	+	4.02181i	−0.302298	+	0.523595i	0.674358	+	0.738404i	$0.264420\pi$
$60$	0.248450	+	3.86501i	0.0320747	+	0.498970i
$61$	6.04358			0.773801			0.386901	−	0.922121i	$-0.373546\pi$
$61$	6.04358			0.773801			0.386901	+	0.922121i	$0.373546\pi$
$62$	3.86747	+	4.00533i	0.491169	+	0.508677i
$63$	−8.65575	+	5.97903i	−1.09052	+	0.753287i
$64$			1.00000i			0.125000i
$65$	−5.27670	−	2.04029i	−0.654494	−	0.253067i
$66$	0.697119	−	7.68614i	0.0858094	−	0.946098i
$67$	3.00222	−	11.2044i	0.366780	−	1.36884i	−0.498213	−	0.867055i	$-0.666010\pi$
$67$	3.00222	−	11.2044i	0.366780	−	1.36884i	0.864992	−	0.501785i	$-0.167323\pi$
$68$	0.941802	−	0.252355i	0.114210	−	0.0306026i
$69$	0.516368	+	0.364020i	0.0621633	+	0.0438229i
$70$	4.62435	−	6.33239i	0.552716	−	0.756865i
$71$	8.97996	−	5.18458i	1.06572	−	0.615297i	0.138715	−	0.990332i	$-0.455703\pi$
$71$	8.97996	−	5.18458i	1.06572	−	0.615297i	0.927010	+	0.375036i	$0.122370\pi$
$72$	2.71079	+	1.28514i	0.319470	+	0.151456i
$73$	10.7698	+	2.88575i	1.26050	+	0.337751i	0.826386	−	0.563105i	$-0.190393\pi$
$73$	10.7698	+	2.88575i	1.26050	+	0.337751i	0.434118	+	0.900856i	$0.357060\pi$
$74$	−1.58186	+	2.73986i	−0.183888	+	0.318503i
$75$	−8.65226	−	0.371944i	−0.999077	−	0.0429484i
$76$	−3.02346	+	5.23678i	−0.346814	+	0.600700i
$77$	−11.0486	+	11.0486i	−1.25910	+	1.25910i
$78$	−3.36592	+	2.80613i	−0.381116	+	0.317732i
$79$	−4.35275	−	2.51306i	−0.489723	−	0.282742i	0.234737	−	0.972059i	$-0.424577\pi$
$79$	−4.35275	−	2.51306i	−0.489723	−	0.282742i	−0.724459	+	0.689317i	$0.757911\pi$
$80$	−2.22324	−	0.239148i	−0.248566	−	0.0267375i
$81$	6.96752	−	5.69681i	0.774169	−	0.632978i
$82$	1.12283	−	4.19046i	0.123996	−	0.462759i
$83$	−3.01187	+	11.2405i	−0.330596	+	1.23380i	0.577970	+	0.816058i	$0.303845\pi$
$83$	−3.01187	+	11.2405i	−0.330596	+	1.23380i	−0.908566	+	0.417742i	$0.862822\pi$
$84$	−2.54933	−	5.51282i	−0.278155	−	0.601498i
$85$	0.335817	+	2.15420i	0.0364244	+	0.233656i
$86$	4.65762	+	2.68908i	0.502244	+	0.289971i
$87$	−1.05693	+	0.182897i	−0.113315	+	0.0196086i
$88$	4.30398	+	1.15325i	0.458806	+	0.122937i
$89$	14.0530			1.48961			0.744806	−	0.667281i	$-0.232542\pi$
$89$	14.0530			1.48961			0.744806	+	0.667281i	$0.232542\pi$
$90$	−3.50547	+	5.71941i	−0.369509	+	0.602879i
$91$	8.87214			0.930053
$92$	−0.257923	+	0.257923i	−0.0268904	+	0.0268904i
$93$	1.47773	+	9.52976i	0.153233	+	0.988190i
$94$			7.98043i			0.823119i
$95$	−10.9196	−	7.97424i	−1.12033	−	0.818140i
$96$	−0.997976	+	1.41564i	−0.101856	+	0.144483i
$97$	−9.72908	−	9.72908i	−0.987839	−	0.987839i	0.0120883	−	0.999927i	$-0.496152\pi$
$97$	−9.72908	−	9.72908i	−0.987839	−	0.987839i	−0.999927	+	0.0120883i	$0.996152\pi$
$98$	−1.37090	+	5.11627i	−0.138482	+	0.516821i
$99$	8.65746	−	10.1851i	0.870107	−	1.02364i
$100$	1.06337	−	4.88562i	0.106337	−	0.488562i
$101$			4.11113i			0.409073i	0.978859	+	0.204536i	$0.0655687\pi$
$101$			4.11113i			0.409073i	−0.978859	+	0.204536i	$0.934431\pi$
$102$	1.58510	+	0.582652i	0.156948	+	0.0576911i
$103$	18.0950	+	4.84855i	1.78296	+	0.477742i	0.991118	−	0.132987i	$-0.0424569\pi$
$103$	18.0950	+	4.84855i	1.78296	+	0.477742i	0.791840	+	0.610729i	$0.209124\pi$
$104$	−1.26504	−	2.19111i	−0.124047	−	0.214856i
$105$	12.8660	−	4.34940i	1.25559	−	0.424458i
$106$	6.26091	+	10.8442i	0.608113	+	1.05328i
$107$	−0.865914	−	3.23164i	−0.0837111	−	0.312414i	0.911356	−	0.411619i	$-0.135037\pi$
$107$	−0.865914	−	3.23164i	−0.0837111	−	0.312414i	−0.995067	+	0.0992052i	$0.968370\pi$
$108$	2.55497	+	4.52461i	0.245852	+	0.435381i
$109$		−	4.28521i		−	0.410449i	−0.978715	−	0.205225i	$-0.934208\pi$
$109$		−	4.28521i		−	0.410449i	0.978715	−	0.205225i	$-0.0657925\pi$
$110$	−3.59324	+	9.29300i	−0.342602	+	0.886053i
$111$	−4.97367	+	2.30001i	−0.472080	+	0.218307i
$112$	3.38718	−	0.907593i	0.320059	−	0.0857595i
$113$	5.07782	−	18.9507i	0.477681	−	1.78273i	−0.133288	−	0.991077i	$-0.542554\pi$
$113$	5.07782	−	18.9507i	0.477681	−	1.78273i	0.610970	−	0.791654i	$-0.290780\pi$
$114$	−9.50632	+	4.39607i	−0.890348	+	0.411730i
$115$	−0.511744	−	0.635108i	−0.0477204	−	0.0592241i
$116$		−	0.619287i		−	0.0574994i
$117$	−7.56540	+	0.613363i	−0.699421	+	0.0567054i
$118$	−1.20195	−	4.48574i	−0.110649	−	0.412946i
$119$	−1.70955	−	2.96102i	−0.156714	−	0.271436i
$120$	−2.90865	−	2.55729i	−0.265522	−	0.233448i
$121$	4.42712	−	7.66799i	0.402465	−	0.697090i
$122$	−4.27346	+	4.27346i	−0.386901	+	0.386901i
$123$	5.77151	−	4.81164i	0.520399	−	0.433851i
$124$	−5.56691	−	0.0974819i	−0.499923	−	0.00875414i
$125$	10.6076	+	3.53251i	0.948773	+	0.315957i
$126$	1.89272	−	10.3483i	0.168617	−	0.921904i
$127$	−9.56503	+	2.56294i	−0.848759	+	0.227424i	−0.656881	−	0.753994i	$-0.728125\pi$
$127$	−9.56503	+	2.56294i	−0.848759	+	0.227424i	−0.191878	+	0.981419i	$0.561458\pi$
$128$	−0.707107	−	0.707107i	−0.0625000	−	0.0625000i
$129$	3.90989	+	8.45497i	0.344246	+	0.744418i
$130$	5.17390	−	2.28848i	0.453781	−	0.200713i
$131$	2.00335	+	1.15663i	0.175033	+	0.101056i	0.584957	−	0.811064i	$-0.301111\pi$
$131$	2.00335	+	1.15663i	0.175033	+	0.101056i	−0.409924	+	0.912120i	$0.634445\pi$
$132$	4.94198	+	5.92786i	0.430144	+	0.515954i
$133$	20.4820	+	5.48814i	1.77602	+	0.475882i
$134$	5.79984	+	10.0456i	0.501030	+	0.867810i
$135$	−10.6703	+	4.59827i	−0.918356	+	0.395756i
$136$	−0.487513	+	0.844397i	−0.0418039	+	0.0724064i
$137$	−1.24268	−	0.332975i	−0.106169	−	0.0284480i	0.205343	−	0.978690i	$-0.434169\pi$
$137$	−1.24268	−	0.332975i	−0.106169	−	0.0284480i	−0.311512	+	0.950242i	$0.600836\pi$
$138$	−0.622528	+	0.107726i	−0.0529931	+	0.00917022i
$139$		−	6.31234i		−	0.535405i	−0.963502	−	0.267703i	$-0.913736\pi$
$139$		−	6.31234i		−	0.535405i	0.963502	−	0.267703i	$-0.0862645\pi$
$140$	1.20776	+	7.74758i	0.102075	+	0.654790i
$141$	−7.96428	+	11.2974i	−0.670714	+	0.951416i
$142$	−2.68374	+	10.0158i	−0.225214	+	0.840511i
$143$	−10.8894	+	2.91780i	−0.910616	+	0.243999i
$144$	−2.82556	+	1.00809i	−0.235463	+	0.0840072i
$145$	1.37683	+	0.148101i	0.114339	+	0.0122991i
$146$	−9.65589	+	5.57483i	−0.799127	+	0.461376i
$147$	−7.04661	+	5.87468i	−0.581195	+	0.484535i
$148$	−0.818831	−	3.05592i	−0.0673075	−	0.251195i
$149$	−1.42392	+	2.46630i	−0.116652	+	0.202047i	−0.918439	−	0.395563i	$-0.870550\pi$
$149$	−1.42392	+	2.46630i	−0.116652	+	0.202047i	0.801787	+	0.597610i	$0.203883\pi$
$150$	6.38108	−	5.85507i	0.521013	−	0.478064i
$151$	−20.2687			−1.64944			−0.824722	−	0.565539i	$-0.808668\pi$
$151$	−20.2687			−1.64944			−0.824722	+	0.565539i	$0.808668\pi$
$152$	−1.56506	−	5.84087i	−0.126943	−	0.473757i
$153$	1.66246	+	2.40672i	0.134402	+	0.194572i
$154$		−	15.6251i		−	1.25910i
$155$	1.54804	−	12.3533i	0.124342	−	0.992239i
$156$	0.395834	−	4.36430i	0.0316921	−	0.349424i
$157$	−12.4345	−	12.4345i	−0.992381	−	0.992381i	0.00759043	−	0.999971i	$-0.497584\pi$
$157$	−12.4345	−	12.4345i	−0.992381	−	0.992381i	−0.999971	+	0.00759043i	$0.997584\pi$
$158$	4.85486	−	1.30086i	0.386232	−	0.103491i
$159$	−1.95906	+	21.5998i	−0.155364	+	1.71297i
$160$	1.74117	−	1.40297i	0.137652	−	0.110914i
$161$	1.10772	+	0.639544i	0.0873008	+	0.0504031i
$162$	−0.898533	+	8.95503i	−0.0705954	+	0.703574i
$163$	−7.45568	+	7.45568i	−0.583974	+	0.583974i	−0.935993	−	0.352019i	$-0.885495\pi$
$163$	−7.45568	+	7.45568i	−0.583974	+	0.583974i	0.352019	+	0.935993i	$0.385495\pi$
$164$	2.16914	+	3.75707i	0.169382	+	0.293377i
$165$	−14.3609	+	9.56959i	−1.11800	+	0.744992i
$166$	−5.81849	−	10.0779i	−0.451602	−	0.782198i
$167$	−2.53851	−	9.47384i	−0.196436	−	0.733108i	−0.991891	−	0.127095i	$-0.959435\pi$
$167$	−2.53851	−	9.47384i	−0.196436	−	0.733108i	0.795455	−	0.606013i	$-0.207232\pi$
$168$	5.70080	+	2.09550i	0.439826	+	0.161672i
$169$	−5.71467	−	3.29936i	−0.439590	−	0.253797i
$170$	−1.76071	−	1.28579i	−0.135040	−	0.0986159i
$171$	−17.8447	−	3.26382i	−1.36462	−	0.249590i
$172$	−5.19490	+	1.39197i	−0.396107	+	0.106137i
$173$	−5.36339	+	20.0164i	−0.407771	+	1.52182i	0.391117	+	0.920341i	$0.372089\pi$
$173$	−5.36339	+	20.0164i	−0.407771	+	1.52182i	−0.798888	+	0.601480i	$0.794578\pi$
$174$	0.618034	−	0.876689i	0.0468530	−	0.0664616i
$175$	−17.5136	+	0.832331i	−1.32390	+	0.0629183i
$176$	−3.85884	+	2.22790i	−0.290871	+	0.167935i
$177$	2.77513	−	7.54973i	0.208592	−	0.567472i
$178$	−9.93696	+	9.93696i	−0.744806	+	0.744806i
$179$	1.45384	−	2.51812i	0.108665	−	0.188213i	−0.806565	−	0.591146i	$-0.798676\pi$
$179$	1.45384	−	2.51812i	0.108665	−	0.188213i	0.915230	+	0.402933i	$0.132009\pi$
$180$	−1.56549	−	6.52298i	−0.116685	−	0.486194i
$181$	5.15576	+	8.93004i	0.383225	+	0.663764i	0.991521	−	0.129945i	$-0.0414802\pi$
$181$	5.15576	+	8.93004i	0.383225	+	0.663764i	−0.608297	+	0.793710i	$0.708147\pi$
$182$	−6.27355	+	6.27355i	−0.465026	+	0.465026i
$183$	−10.3145	+	1.78488i	−0.762469	+	0.131942i
$184$		−	0.364758i		−	0.0268904i
$185$	6.98987	−	1.08964i	0.513906	−	0.0801122i
$186$	−7.78347	−	5.69365i	−0.570712	−	0.417478i
$187$	3.07204	+	3.07204i	0.224650	+	0.224650i
$188$	−5.64302	−	5.64302i	−0.411559	−	0.411559i
$189$	13.0068	−	12.7607i	0.946108	−	0.928202i
$190$	13.3600	−	2.08267i	0.969233	−	0.151093i
$191$	−9.51628	+	5.49423i	−0.688574	+	0.397548i	−0.803078	−	0.595874i	$-0.796806\pi$
$191$	−9.51628	+	5.49423i	−0.688574	+	0.397548i	0.114504	+	0.993423i	$0.463472\pi$
$192$	−0.295334	−	1.70669i	−0.0213139	−	0.123169i
$193$	0.597524	+	2.22999i	0.0430107	+	0.160518i	0.984091	−	0.177665i	$-0.0568543\pi$
$193$	0.597524	+	2.22999i	0.0430107	+	0.160518i	−0.941080	+	0.338183i	$0.890188\pi$
$194$	13.7590			0.987839
$195$	9.60824	+	1.92375i	0.688060	+	0.137763i
$196$	−2.64837	−	4.58712i	−0.189170	−	0.327651i
$197$	−8.32183	−	2.22983i	−0.592906	−	0.158869i	−0.0501247	−	0.998743i	$-0.515962\pi$
$197$	−8.32183	−	2.22983i	−0.592906	−	0.158869i	−0.542781	+	0.839874i	$0.682629\pi$
$198$	1.08022	+	13.3237i	0.0767677	+	0.946875i
$199$	−21.6415	+	12.4947i	−1.53412	+	0.885727i	−0.534958	+	0.844878i	$0.679673\pi$
$199$	−21.6415	+	12.4947i	−1.53412	+	0.885727i	−0.999165	+	0.0408483i	$0.986994\pi$
$200$	2.70274	+	4.20657i	0.191112	+	0.297449i
$201$	−1.81479	+	20.0091i	−0.128006	+	1.41133i
$202$	−2.90701	−	2.90701i	−0.204536	−	0.204536i
$203$	−2.09764	+	0.562061i	−0.147225	+	0.0394489i
$204$	−1.53283	+	0.708838i	−0.107320	+	0.0496286i
$205$	−8.87161	+	3.92404i	−0.619620	+	0.274067i
$206$	−16.2236	+	9.36668i	−1.13035	+	0.652608i
$207$	−0.988785	−	0.468767i	−0.0687253	−	0.0325816i
$208$	2.44386	+	0.654831i	0.169451	+	0.0454044i
$209$	−26.9439			−1.86375
$210$	−6.02215	+	12.1731i	−0.415568	+	0.840025i
$211$	13.5189	−	23.4154i	0.930678	−	1.61198i	0.148513	−	0.988910i	$-0.452551\pi$
$211$	13.5189	−	23.4154i	0.930678	−	1.61198i	0.782165	−	0.623071i	$-0.214115\pi$
$212$	−12.0951	−	3.24089i	−0.830698	−	0.222585i
$213$	−13.7948	+	11.5005i	−0.945203	+	0.788004i
$214$	2.89741	+	1.67282i	0.198063	+	0.114351i
$215$	−1.85234	−	11.8824i	−0.126328	−	0.810374i
$216$	−5.00602	−	1.39275i	−0.340617	−	0.0947645i
$217$	4.72230	+	18.9446i	0.320571	+	1.28605i
$218$	3.03010	+	3.03010i	0.205225	+	0.205225i
$219$	−19.2328	−	1.74439i	−1.29964	−	0.117875i
$220$	−4.03034	−	9.11194i	−0.271725	−	0.614327i
$221$		−	2.46689i		−	0.165941i
$222$	1.89056	−	5.14326i	0.126886	−	0.345193i
$223$	2.46398	+	9.19572i	0.165001	+	0.615791i	0.998040	+	0.0625772i	$0.0199320\pi$
$223$	2.46398	+	9.19572i	0.165001	+	0.615791i	−0.833040	+	0.553214i	$0.813401\pi$
$224$	−1.75334	+	3.03687i	−0.117150	+	0.202909i
$225$	14.8765	−	1.92052i	0.991770	−	0.128035i
$226$	9.80960	+	16.9907i	0.652525	+	1.13021i
$227$	2.56119	+	0.686268i	0.169992	+	0.0455492i	0.342811	−	0.939404i	$-0.388621\pi$
$227$	2.56119	+	0.686268i	0.169992	+	0.0455492i	−0.172819	+	0.984954i	$0.555288\pi$
$228$	3.61349	−	9.83047i	0.239309	−	0.651039i
$229$	−9.38013	−	5.41562i	−0.619857	−	0.357874i	0.156956	−	0.987606i	$-0.449832\pi$
$229$	−9.38013	−	5.41562i	−0.619857	−	0.357874i	−0.776813	+	0.629731i	$0.783165\pi$
$230$	0.810947	+	0.0872312i	0.0534722	+	0.00575186i
$231$	15.5934	−	22.1195i	1.02597	−	1.45536i
$232$	0.437902	+	0.437902i	0.0287497	+	0.0287497i
$233$	−12.7374	−	12.7374i	−0.834455	−	0.834455i	0.153667	−	0.988123i	$-0.450892\pi$
$233$	−12.7374	−	12.7374i	−0.834455	−	0.834455i	−0.988123	+	0.153667i	$0.950892\pi$
$234$	4.91583	−	5.78326i	0.321358	−	0.378063i
$235$	13.8953	−	11.1963i	0.906430	−	0.730365i
$236$	4.02181	+	2.32199i	0.261797	+	0.151149i
$237$	8.17097	+	3.00349i	0.530762	+	0.195098i
$238$	3.30259	+	0.884927i	0.214075	+	0.0573613i
$239$	10.4632	+	18.1227i	0.676806	+	1.17226i	0.975937	+	0.218051i	$0.0699698\pi$
$239$	10.4632	+	18.1227i	0.676806	+	1.17226i	−0.299131	+	0.954212i	$0.596697\pi$
$240$	3.86501	−	0.248450i	0.249485	−	0.0160374i
$241$	3.11180	−	5.38979i	0.200448	−	0.347187i	−0.748225	−	0.663446i	$-0.769093\pi$
$241$	3.11180	−	5.38979i	0.200448	−	0.347187i	0.948673	+	0.316259i	$0.102427\pi$
$242$	2.29164	+	8.55253i	0.147312	+	0.549778i
$243$	−10.2089	+	11.7804i	−0.654902	+	0.755714i
$244$		−	6.04358i		−	0.386901i
$245$	10.8316	−	4.79098i	0.692007	−	0.306084i
$246$	−0.678732	+	7.48341i	−0.0432744	+	0.477125i
$247$	10.8181	+	10.8181i	0.688341	+	0.688341i
$248$	4.00533	−	3.86747i	0.254339	−	0.245585i
$249$	1.82063	−	20.0734i	0.115377	−	1.27210i
$250$	−9.99857	+	5.00285i	−0.632365	+	0.316408i
$251$	−3.81845	−	2.20458i	−0.241018	−	0.139152i	0.374626	−	0.927176i	$-0.377771\pi$
$251$	−3.81845	−	2.20458i	−0.241018	−	0.139152i	−0.615645	+	0.788024i	$0.711104\pi$
$252$	5.97903	+	8.65575i	0.376643	+	0.545261i
$253$	−1.56991	−	0.420657i	−0.0986996	−	0.0264465i
$254$	4.95122	−	8.57577i	0.310667	−	0.538092i
$255$	−1.20934	−	3.57737i	−0.0757321	−	0.224024i
$256$	1.00000			0.0625000
$257$	−2.95193	−	0.790966i	−0.184136	−	0.0493391i	0.165573	−	0.986198i	$-0.447053\pi$
$257$	−2.95193	−	0.790966i	−0.184136	−	0.0493391i	−0.349709	+	0.936858i	$0.613719\pi$
$258$	−8.74327	−	3.21386i	−0.544332	−	0.200086i
$259$	−9.60780	+	5.54707i	−0.597000	+	0.344678i
$260$	−2.04029	+	5.27670i	−0.126534	+	0.327247i
$261$	1.74983	−	0.624295i	0.108312	−	0.0386429i
$262$	−2.23444	+	0.598718i	−0.138044	+	0.0369889i
$263$	18.4700	+	18.4700i	1.13891	+	1.13891i	0.988646	+	0.150266i	$0.0480129\pi$
$263$	18.4700	+	18.4700i	1.13891	+	1.13891i	0.150266	+	0.988646i	$0.451987\pi$
$264$	−7.68614	−	0.697119i	−0.473049	−	0.0429047i
$265$	10.0978	−	26.1154i	0.620303	−	1.60426i
$266$	−18.3637	+	10.6023i	−1.12595	+	0.650067i
$267$	−23.9840	+	4.15033i	−1.46780	+	0.253996i
$268$	−11.2044	−	3.00222i	−0.684420	−	0.183390i
$269$	−10.0277	−	17.3685i	−0.611399	−	1.05897i	−0.991005	−	0.133826i	$-0.957274\pi$
$269$	−10.0277	−	17.3685i	−0.611399	−	1.05897i	0.379606	−	0.925148i	$-0.376060\pi$
$270$	4.29360	−	10.7965i	0.261300	−	0.657056i
$271$	12.3008			0.747219			0.373609	−	0.927586i	$-0.378120\pi$
$271$	12.3008			0.747219			0.373609	+	0.927586i	$0.378120\pi$
$272$	−0.252355	−	0.941802i	−0.0153013	−	0.0571051i
$273$	−15.1420	+	2.62025i	−0.916433	+	0.158585i
$274$	1.11416	−	0.643258i	0.0673086	−	0.0388606i
$275$	21.2219	−	6.78132i	1.27973	−	0.408929i
$276$	0.364020	−	0.516368i	0.0219114	−	0.0310817i
$277$	0.498413	+	0.498413i	0.0299467	+	0.0299467i	0.721922	−	0.691975i	$-0.243259\pi$
$277$	0.498413	+	0.498413i	0.0299467	+	0.0299467i	−0.691975	+	0.721922i	$0.743259\pi$
$278$	4.46350	+	4.46350i	0.267703	+	0.267703i
$279$	−5.33649	−	15.8279i	−0.319487	−	0.947591i
$280$	−6.33239	−	4.62435i	−0.378432	−	0.276358i
$281$		−	9.48258i		−	0.565683i	−0.959167	−	0.282842i	$-0.908723\pi$
$281$		−	9.48258i		−	0.565683i	0.959167	−	0.282842i	$-0.0912771\pi$
$282$	−2.35690	−	13.6201i	−0.140351	−	0.811065i
$283$	−0.0883063	+	0.0883063i	−0.00524927	+	0.00524927i	−0.709727	−	0.704477i	$-0.751182\pi$
$283$	−0.0883063	+	0.0883063i	−0.00524927	+	0.00524927i	0.704477	+	0.709727i	$0.251182\pi$
$284$	−5.18458	−	8.97996i	−0.307648	−	0.532862i
$285$	20.9914	+	10.3846i	1.24342	+	0.615131i
$286$	5.63676	−	9.76316i	0.333309	−	0.577308i
$287$	10.7572	−	10.7572i	0.634976	−	0.634976i
$288$	1.28514	−	2.71079i	0.0757279	−	0.159735i
$289$	13.8991	−	8.02466i	0.817596	−	0.472039i
$290$	−1.07829	+	0.868839i	−0.0633191	+	0.0510200i
$291$	19.4778	+	13.7312i	1.14181	+	0.804935i
$292$	2.88575	−	10.7698i	0.168876	−	0.630252i
$293$	6.84962	−	1.83535i	0.400159	−	0.107222i	−0.0531263	−	0.998588i	$-0.516919\pi$
$293$	6.84962	−	1.83535i	0.400159	−	0.107222i	0.453285	+	0.891366i	$0.350252\pi$
$294$	0.828686	−	9.13673i	0.0483299	−	0.532865i
$295$	−6.12416	+	8.38616i	−0.356562	+	0.488261i
$296$	2.73986	+	1.58186i	0.159251	+	0.0919438i
$297$	−11.7675	+	19.9396i	−0.682822	+	1.15702i
$298$	−0.737075	−	2.75080i	−0.0426976	−	0.159350i
$299$	0.461433	+	0.799225i	0.0266853	+	0.0462204i
$300$	−0.371944	+	8.65226i	−0.0214742	+	0.499539i
$301$	9.42971	+	16.3327i	0.543520	+	0.941404i
$302$	14.3321	−	14.3321i	0.824722	−	0.824722i
$303$	−1.21416	−	7.01641i	−0.0697516	−	0.403082i
$304$	5.23678	+	3.02346i	0.300350	+	0.173407i
$305$	13.4363	+	1.44531i	0.769363	+	0.0827582i
$306$	−2.87734	−	0.526269i	−0.164487	−	0.0300848i
$307$	30.7280	−	8.23353i	1.75374	−	0.469913i	0.768320	−	0.640066i	$-0.221093\pi$
$307$	30.7280	−	8.23353i	1.75374	−	0.469913i	0.985418	+	0.170153i	$0.0544262\pi$
$308$	11.0486	+	11.0486i	0.629552	+	0.629552i
$309$	−32.3145	−	2.93087i	−1.83831	−	0.166731i
$310$	7.64046	+	9.82972i	0.433949	+	0.558291i
$311$			25.1695i			1.42723i	0.700537	+	0.713616i	$0.252944\pi$
$311$			25.1695i			1.42723i	−0.700537	+	0.713616i	$0.747056\pi$
$312$	2.80613	+	3.36592i	0.158866	+	0.190558i
$313$	8.51441	+	31.7762i	0.481263	+	1.79610i	0.596329	+	0.802740i	$0.296625\pi$
$313$	8.51441	+	31.7762i	0.481263	+	1.79610i	−0.115066	+	0.993358i	$0.536708\pi$
$314$	17.5850			0.992381
$315$	−20.6737	+	11.2228i	−1.16483	+	0.632335i
$316$	−2.51306	+	4.35275i	−0.141371	+	0.244861i
$317$	−5.21366	−	19.4576i	−0.292828	−	1.09285i	−0.942927	−	0.333000i	$-0.891939\pi$
$317$	−5.21366	−	19.4576i	−0.292828	−	1.09285i	0.650099	−	0.759850i	$-0.274727\pi$
$318$	−13.8881	−	16.6586i	−0.778805	−	0.934168i
$319$	2.38973	−	1.37971i	0.133799	−	0.0772490i
$320$	−0.239148	+	2.22324i	−0.0133688	+	0.124283i
$321$	2.43226	+	5.25965i	0.135755	+	0.293565i
$322$	−1.23550	+	0.331052i	−0.0688520	+	0.0184488i
$323$	1.52597	−	5.69500i	0.0849072	−	0.316878i
$324$	−5.69681	−	6.96752i	−0.316489	−	0.387085i
$325$	−11.2435	−	5.79798i	−0.623675	−	0.321614i
$326$		−	10.5439i		−	0.583974i
$327$	1.26557	+	7.31352i	0.0699862	+	0.404438i
$328$	−4.19046	−	1.12283i	−0.231380	−	0.0619980i
$329$	−13.9924	+	24.2355i	−0.771425	+	1.33615i
$330$	3.38799	−	16.9214i	0.186503	−	0.931494i
$331$	1.08900	+	1.88620i	0.0598567	+	0.103675i	0.894401	−	0.447266i	$-0.147602\pi$
$331$	1.08900	+	1.88620i	0.0598567	+	0.103675i	−0.834544	+	0.550941i	$0.814269\pi$
$332$	11.2405	+	3.01187i	0.616900	+	0.165298i
$333$	7.80922	−	5.39428i	0.427942	−	0.295605i
$334$	8.49401	+	4.90402i	0.464772	+	0.268336i
$335$	9.35418	−	24.1922i	0.511074	−	1.32176i
$336$	−5.51282	+	2.54933i	−0.300749	+	0.139077i
$337$	−14.2101	−	14.2101i	−0.774076	−	0.774076i	0.204741	−	0.978816i	$-0.434365\pi$
$337$	−14.2101	−	14.2101i	−0.774076	−	0.774076i	−0.978816	+	0.204741i	$0.934365\pi$
$338$	6.37388	−	1.70788i	0.346694	−	0.0928962i
$339$	−3.06946	+	33.8425i	−0.166710	+	1.83807i
$340$	2.15420	−	0.335817i	0.116828	−	0.0182122i
$341$	−12.0264	−	21.6990i	−0.651265	−	1.17507i
$342$	14.9260	−	10.3103i	0.807105	−	0.557515i
$343$	4.22337	−	4.22337i	0.228041	−	0.228041i
$344$	2.68908	−	4.65762i	0.144985	−	0.251122i
$345$	1.06096	+	0.932794i	0.0571199	+	0.0502199i
$346$	−10.3613	−	17.9462i	−0.557025	−	0.964796i
$347$	4.27720	+	15.9627i	0.229612	+	0.856923i	0.980504	+	0.196498i	$0.0629571\pi$
$347$	4.27720	+	15.9627i	0.229612	+	0.856923i	−0.750892	+	0.660425i	$0.770376\pi$
$348$	0.182897	+	1.05693i	0.00980429	+	0.0566573i
$349$		−	23.5590i		−	1.26109i	−0.776154	−	0.630543i	$-0.782832\pi$
$349$		−	23.5590i		−	1.26109i	0.776154	−	0.630543i	$-0.217168\pi$
$350$	11.7954	−	12.9725i	0.630492	−	0.693411i
$351$	12.7306	−	3.28114i	0.679510	−	0.175134i
$352$	1.15325	−	4.30398i	0.0614683	−	0.229403i
$353$	−23.6668	+	6.34149i	−1.25966	+	0.337524i	−0.826059	−	0.563584i	$-0.809422\pi$
$353$	−23.6668	+	6.34149i	−1.25966	+	0.337524i	−0.433596	+	0.901107i	$0.642756\pi$
$354$	3.37615	+	7.30078i	0.179440	+	0.388032i
$355$	21.2045	−	9.37905i	1.12542	−	0.497788i
$356$		−	14.0530i		−	0.744806i
$357$	3.79215	+	4.54865i	0.200702	+	0.240740i
$358$	0.752562	+	2.80860i	0.0397741	+	0.148439i
$359$	11.6009	+	20.0933i	0.612272	+	1.06049i	0.990857	+	0.134919i	$0.0430775\pi$
$359$	11.6009	+	20.0933i	0.612272	+	1.06049i	−0.378585	+	0.925567i	$0.623589\pi$
$360$	5.71941	+	3.50547i	0.301440	+	0.184754i
$361$	8.78258	+	15.2119i	0.462241	+	0.800625i
$362$	−9.96016	−	2.66882i	−0.523495	−	0.140270i
$363$	−5.29108	+	14.3943i	−0.277709	+	0.755506i
$364$		−	8.87214i		−	0.465026i
$365$	23.2536	+	8.99128i	1.21715	+	0.470625i
$366$	6.03135	−	8.55555i	0.315264	−	0.447206i
$367$	−2.39621	+	8.94276i	−0.125081	+	0.466808i	−0.999843	−	0.0177452i	$-0.994351\pi$
$367$	−2.39621	+	8.94276i	−0.125081	+	0.466808i	0.874762	+	0.484553i	$0.161018\pi$
$368$	0.257923	+	0.257923i	0.0134452	+	0.0134452i
$369$	−8.42911	+	9.91648i	−0.438802	+	0.516231i
$370$	−4.17209	+	5.71308i	−0.216897	+	0.297009i
$371$			43.9099i			2.27969i
$372$	9.52976	−	1.47773i	0.494095	−	0.0766167i
$373$	−20.7498	+	20.7498i	−1.07439	+	1.07439i	−0.0773844	+	0.997001i	$0.524657\pi$
$373$	−20.7498	+	20.7498i	−1.07439	+	1.07439i	−0.997001	+	0.0773844i	$0.975343\pi$
$374$	−4.34453			−0.224650
$375$	−19.1471	−	2.89609i	−0.988754	−	0.149554i
$376$	7.98043			0.411559
$377$	−1.51345	−	0.405528i	−0.0779468	−	0.0208858i
$378$	−0.174062	+	18.2204i	−0.00895280	+	0.937155i
$379$	−19.7005	−	11.3741i	−1.01195	−	0.584249i	−0.100187	−	0.994969i	$-0.531944\pi$
$379$	−19.7005	−	11.3741i	−1.01195	−	0.584249i	−0.911762	+	0.410719i	$0.865278\pi$
$380$	−7.97424	+	10.9196i	−0.409070	+	0.560163i
$381$	15.5676	−	7.19902i	0.797551	−	0.368817i
$382$	2.84402	−	10.6140i	0.145513	−	0.543061i
$383$	6.54620	−	24.4308i	0.334495	−	1.24835i	−0.569920	−	0.821700i	$-0.693026\pi$
$383$	6.54620	−	24.4308i	0.334495	−	1.24835i	0.904415	−	0.426653i	$-0.140308\pi$
$384$	1.41564	+	0.997976i	0.0722417	+	0.0509278i
$385$	−27.2059	+	21.9214i	−1.38654	+	1.11722i
$386$	−1.99935	−	1.15433i	−0.101764	−	0.0587537i
$387$	−9.16999	−	13.2753i	−0.466137	−	0.674819i
$388$	−9.72908	+	9.72908i	−0.493919	+	0.493919i
$389$	−15.0546	+	26.0753i	−0.763299	+	1.32207i	0.177842	+	0.984059i	$0.443088\pi$
$389$	−15.0546	+	26.0753i	−0.763299	+	1.32207i	−0.941141	+	0.338014i	$0.890245\pi$
$390$	−8.15435	+	5.43375i	−0.412911	+	0.275149i
$391$	0.177824	−	0.308001i	0.00899296	−	0.0155763i
$392$	5.11627	+	1.37090i	0.258410	+	0.0692409i
$393$	−3.76068	−	1.38235i	−0.189701	−	0.0697305i
$394$	7.46114	−	4.30769i	0.375887	−	0.217018i
$395$	−9.07623	−	6.62810i	−0.456675	−	0.333496i
$396$	−10.1851	−	8.65746i	−0.511821	−	0.435054i
$397$	−14.7407	+	3.94975i	−0.739812	+	0.198232i	−0.608995	−	0.793174i	$-0.708427\pi$
$397$	−14.7407	+	3.94975i	−0.739812	+	0.198232i	−0.130818	+	0.991406i	$0.541760\pi$
$398$	6.46774	−	24.1379i	0.324198	−	1.20993i
$399$	−36.5772	−	3.31749i	−1.83115	−	0.166082i
$400$	−4.88562	−	1.06337i	−0.244281	−	0.0531684i
$401$			4.85335i			0.242365i	0.992630	+	0.121182i	$0.0386686\pi$
$401$			4.85335i			0.242365i	−0.992630	+	0.121182i	$0.961331\pi$
$402$	−12.8653	−	15.4318i	−0.641664	−	0.769670i
$403$	−3.88362	+	13.5409i	−0.193457	+	0.674522i
$404$	4.11113			0.204536
$405$	16.8529	−	10.9991i	0.837426	−	0.546550i
$406$	1.08582	−	1.88069i	0.0538882	−	0.0933372i
$407$	9.96804	−	9.96804i	0.494097	−	0.494097i
$408$	0.582652	−	1.58510i	0.0288456	−	0.0784741i
$409$	8.11640	+	4.68600i	0.401330	+	0.231708i	0.687058	−	0.726603i	$-0.258902\pi$
$409$	8.11640	+	4.68600i	0.401330	+	0.231708i	−0.285728	+	0.958311i	$0.592235\pi$
$410$	3.49847	−	9.04789i	0.172777	−	0.446843i
$411$	2.21920	+	0.201278i	0.109465	+	0.00992829i
$412$	4.84855	−	18.0950i	0.238871	−	0.891479i
$413$	4.21485	−	15.7300i	0.207399	−	0.774024i
$414$	1.03065	−	0.367708i	0.0506534	−	0.0180719i
$415$	−9.38425	+	24.2700i	−0.460655	+	1.19137i
$416$	−2.19111	+	1.26504i	−0.107428	+	0.0620235i
$417$	1.86425	+	10.7732i	0.0912927	+	0.527565i
$418$	19.0522	−	19.0522i	0.931874	−	0.931874i
$419$	20.1816			0.985937			0.492969	−	0.870047i	$-0.335912\pi$
$419$	20.1816			0.985937			0.492969	+	0.870047i	$0.335912\pi$
$420$	−4.34940	−	12.8660i	−0.212229	−	0.627796i
$421$	13.2979	+	23.0326i	0.648100	+	1.12254i	0.983576	+	0.180494i	$0.0577695\pi$
$421$	13.2979	+	23.0326i	0.648100	+	1.12254i	−0.335476	+	0.942049i	$0.608897\pi$
$422$	6.99789	+	26.1165i	0.340652	+	1.27133i
$423$	10.2560	−	21.6333i	0.498664	−	1.05185i
$424$	10.8442	−	6.26091i	0.526642	−	0.304057i
$425$	0.231429	+	4.86963i	0.0112259	+	0.236212i
$426$	1.62227	−	17.8865i	0.0785994	−	0.866604i
$427$	−20.4707	+	5.48511i	−0.990648	+	0.265443i
$428$	−3.23164	+	0.865914i	−0.156207	+	0.0418555i
$429$	17.7230	−	8.19578i	0.855676	−	0.395696i
$430$	9.71193	+	7.09233i	0.468351	+	0.342023i
$431$	−1.42240	−	0.821225i	−0.0685148	−	0.0395570i	0.465351	−	0.885126i	$-0.345928\pi$
$431$	−1.42240	−	0.821225i	−0.0685148	−	0.0395570i	−0.533866	+	0.845569i	$0.679261\pi$
$432$	4.52461	−	2.55497i	0.217691	−	0.122926i
$433$	−6.94052	+	6.94052i	−0.333540	+	0.333540i	−0.853929	−	0.520389i	$-0.825787\pi$
$433$	−6.94052	+	6.94052i	−0.333540	+	0.333540i	0.520389	+	0.853929i	$0.325787\pi$
$434$	−16.7350	−	10.0567i	−0.803308	−	0.482737i
$435$	−2.39355	+	0.153862i	−0.114762	+	0.00737710i
$436$	−4.28521			−0.205225
$437$	0.570868	+	2.13051i	0.0273083	+	0.101916i
$438$	14.8331	−	12.3662i	0.708755	−	0.590880i
$439$	−11.4549	+	6.61351i	−0.546714	+	0.315645i	−0.747796	−	0.663929i	$-0.768888\pi$
$439$	−11.4549	+	6.61351i	−0.546714	+	0.315645i	0.201082	+	0.979574i	$0.435554\pi$
$440$	9.29300	+	3.59324i	0.443026	+	0.171301i
$441$	10.2914	−	12.1073i	0.490065	−	0.576540i
$442$	1.74435	+	1.74435i	0.0829703	+	0.0829703i
$443$	3.53746	−	13.2020i	0.168070	−	0.627245i	−0.829559	−	0.558419i	$-0.811408\pi$
$443$	3.53746	−	13.2020i	0.168070	−	0.627245i	0.997629	−	0.0688259i	$-0.0219253\pi$
$444$	2.30001	+	4.97367i	0.109153	+	0.236040i
$445$	31.2432	+	3.36074i	1.48107	+	0.159314i
$446$	−8.24465	−	4.76005i	−0.390396	−	0.225395i
$447$	1.70180	−	4.62973i	0.0804924	−	0.218979i
$448$	−0.907593	−	3.38718i	−0.0428798	−	0.160029i
$449$	15.0495			0.710228			0.355114	−	0.934823i	$-0.384442\pi$
$449$	15.0495			0.710228			0.355114	+	0.934823i	$0.384442\pi$
$450$	−9.16129	+	11.8773i	−0.431868	+	0.559902i
$451$	−9.66528	+	16.7408i	−0.455120	+	0.788292i
$452$	−18.9507	−	5.07782i	−0.891366	−	0.238841i
$453$	34.5923	−	5.98604i	1.62529	−	0.281249i
$454$	−2.29630	+	1.32577i	−0.107771	+	0.0622214i
$455$	19.7249	+	2.12175i	0.924718	+	0.0994693i
$456$	4.39607	+	9.50632i	0.205865	+	0.445174i
$457$	15.5923	+	15.5923i	0.729378	+	0.729378i	0.970496	−	0.241117i	$-0.0775139\pi$
$457$	15.5923	+	15.5923i	0.729378	+	0.729378i	−0.241117	+	0.970496i	$0.577514\pi$
$458$	10.4622	−	2.80333i	0.488866	−	0.130991i
$459$	−3.54809	−	3.61653i	−0.165610	−	0.168805i
$460$	−0.635108	+	0.511744i	−0.0296120	+	0.0238602i
$461$		−	15.1177i		−	0.704100i	−0.935981	−	0.352050i	$-0.885485\pi$
$461$		−	15.1177i		−	0.704100i	0.935981	−	0.352050i	$-0.114515\pi$
$462$	4.61462	+	26.6671i	0.214691	+	1.24066i
$463$	−2.27924	+	2.27924i	−0.105925	+	0.105925i	−0.758083	−	0.652158i	$-0.773864\pi$
$463$	−2.27924	+	2.27924i	−0.105925	+	0.105925i	0.652158	+	0.758083i	$0.273864\pi$
$464$	−0.619287			−0.0287497
$465$	1.00633	+	21.5404i	0.0466674	+	0.998910i
$466$	18.0134			0.834455
$467$	20.6242	−	20.6242i	0.954373	−	0.954373i	−0.0446302	−	0.999004i	$-0.514211\pi$
$467$	20.6242	−	20.6242i	0.954373	−	0.954373i	0.999004	+	0.0446302i	$0.0142110\pi$
$468$	0.613363	+	7.56540i	0.0283527	+	0.349711i
$469$			40.6763i			1.87826i
$470$	−1.90850	+	17.7424i	−0.0880327	+	0.818398i
$471$	24.8941	+	17.5494i	1.14706	+	0.808636i
$472$	−4.48574	+	1.20195i	−0.206473	+	0.0553243i
$473$	−16.9451	−	16.9451i	−0.779138	−	0.779138i
$474$	−7.90154	+	3.65396i	−0.362930	+	0.167832i
$475$	−22.3699	−	20.3401i	−1.02640	−	0.933267i
$476$	−2.96102	+	1.70955i	−0.135718	+	0.0783570i
$477$	−3.03565	−	37.4426i	−0.138993	−	1.71438i
$478$	−20.2133	−	5.41613i	−0.924534	−	0.247728i
$479$	−3.44372	+	5.96470i	−0.157348	+	0.272534i	−0.933911	−	0.357505i	$-0.883628\pi$
$479$	−3.44372	+	5.96470i	−0.157348	+	0.272534i	0.776564	+	0.630039i	$0.216961\pi$
$480$	−2.55729	+	2.90865i	−0.116724	+	0.132761i
$481$	−8.00445			−0.364971
$482$	1.61078	+	6.01153i	0.0733692	+	0.273818i
$483$	−2.07941	−	0.764352i	−0.0946166	−	0.0347792i
$484$	−7.66799	−	4.42712i	−0.348545	−	0.201233i
$485$	−19.3034	−	23.9568i	−0.876523	−	1.08782i
$486$	−1.11122	−	15.5488i	−0.0504057	−	0.705308i
$487$	−4.25370	+	15.8750i	−0.192754	+	0.719366i	0.800083	+	0.599889i	$0.204788\pi$
$487$	−4.25370	+	15.8750i	−0.192754	+	0.719366i	−0.992837	+	0.119477i	$0.961878\pi$
$488$	4.27346	+	4.27346i	0.193450	+	0.193450i
$489$	10.5226	−	14.9264i	0.475848	−	0.674996i
$490$	−4.27139	+	11.0469i	−0.192962	+	0.499046i
$491$	25.5873	−	14.7728i	1.15474	−	0.666689i	0.204701	−	0.978824i	$-0.434378\pi$
$491$	25.5873	−	14.7728i	1.15474	−	0.666689i	0.950038	+	0.312136i	$0.101044\pi$
$492$	−4.81164	−	5.77151i	−0.216925	−	0.260200i
$493$	0.156280	+	0.583246i	0.00703851	+	0.0262681i
$494$	−15.2991			−0.688341
$495$	21.6834	−	20.5736i	0.974595	−	0.924713i
$496$	−0.0974819	+	5.56691i	−0.00437707	+	0.249962i
$497$	−25.7113	+	25.7113i	−1.15331	+	1.15331i
$498$	12.9067	+	15.4814i	0.578363	+	0.693740i
$499$	−12.0315	−	6.94636i	−0.538602	−	0.310962i	0.205910	−	0.978571i	$-0.433985\pi$
$499$	−12.0315	−	6.94636i	−0.538602	−	0.310962i	−0.744512	+	0.667609i	$0.767318\pi$
$500$	3.53251	−	10.6076i	0.157979	−	0.474387i
$501$	7.13038	+	15.4192i	0.318562	+	0.688877i
$502$	4.25893	−	1.14118i	0.190085	−	0.0509332i
$503$	−20.3067	+	5.44116i	−0.905431	+	0.242610i	−0.681347	−	0.731960i	$-0.738606\pi$
$503$	−20.3067	+	5.44116i	−0.905431	+	0.242610i	−0.224084	+	0.974570i	$0.571939\pi$
$504$	−10.3483	−	1.89272i	−0.460952	−	0.0843086i
$505$	−0.983168	+	9.14004i	−0.0437504	+	0.406726i
$506$	1.40755	−	0.812647i	0.0625730	−	0.0361266i
$507$	10.7276	+	3.94324i	0.476428	+	0.175126i
$508$	2.56294	+	9.56503i	0.113712	+	0.424379i
$509$	12.4306	+	21.5303i	0.550975	+	0.954316i	0.998205	+	0.0598970i	$0.0190772\pi$
$509$	12.4306	+	21.5303i	0.550975	+	0.954316i	−0.447230	+	0.894419i	$0.647589\pi$
$510$	3.38472	+	1.67445i	0.149878	+	0.0741459i
$511$	−39.0982			−1.72960
$512$	−0.707107	+	0.707107i	−0.0312500	+	0.0312500i
$513$	31.4193	+	0.300153i	1.38719	+	0.0132521i
$514$	2.64662	−	1.52803i	0.116738	−	0.0673985i
$515$	39.0701	+	15.1069i	1.72164	+	0.665689i
$516$	8.45497	−	3.90989i	0.372209	−	0.172123i
$517$	9.20342	−	34.3476i	0.404766	−	1.51061i
$518$	2.87137	−	10.7161i	0.126161	−	0.470839i
$519$	3.24208	−	35.7458i	0.142311	−	1.56906i
$520$	−2.28848	−	5.17390i	−0.100357	−	0.226890i
$521$	−1.38146	−	0.797584i	−0.0605227	−	0.0349428i	0.469433	−	0.882968i	$-0.344458\pi$
$521$	−1.38146	−	0.797584i	−0.0605227	−	0.0349428i	−0.529956	+	0.848025i	$0.677792\pi$
$522$	−0.795873	+	1.67876i	−0.0348344	+	0.0734773i
$523$	6.19788	−	6.19788i	0.271014	−	0.271014i	−0.558494	−	0.829508i	$-0.688621\pi$
$523$	6.19788	−	6.19788i	0.271014	−	0.271014i	0.829508	+	0.558494i	$0.188621\pi$
$524$	1.15663	−	2.00335i	0.0505278	−	0.0875167i
$525$	29.6444	−	6.59289i	1.29379	−	0.287738i
$526$	−26.1206			−1.13891
$527$	5.26753	−	1.31303i	0.229457	−	0.0571965i
$528$	5.92786	−	4.94198i	0.257977	−	0.215072i
$529$		−	22.8670i		−	0.994215i
$530$	11.3262	+	25.6066i	0.491977	+	1.11228i
$531$	−2.50659	+	13.7046i	−0.108777	+	0.594729i
$532$	5.48814	−	20.4820i	0.237941	−	0.888008i
$533$	10.6022	−	2.84084i	0.459231	−	0.123051i
$534$	14.0245	−	19.8940i	0.606901	−	0.860897i
$535$	−1.15230	−	7.39179i	−0.0498182	−	0.319575i
$536$	10.0456	−	5.79984i	0.433905	−	0.250515i
$537$	−1.73756	+	4.72701i	−0.0749811	+	0.203986i
$538$	19.3720	+	5.19071i	0.835187	+	0.223788i
$539$	11.8006	−	20.4393i	0.508290	−	0.880384i
$540$	4.59827	+	10.6703i	0.197878	+	0.459178i
$541$	3.69391	−	6.39804i	0.158814	−	0.275073i	−0.775628	−	0.631191i	$-0.782566\pi$
$541$	3.69391	−	6.39804i	0.158814	−	0.275073i	0.934441	+	0.356118i	$0.115900\pi$
$542$	−8.69796	+	8.69796i	−0.373609	+	0.373609i
$543$	−11.4366	−	13.7181i	−0.490792	−	0.588700i
$544$	0.844397	+	0.487513i	0.0362032	+	0.0209019i
$545$	1.02480	−	9.52707i	0.0438976	−	0.408095i
$546$	8.85418	−	12.5598i	0.378924	−	0.537509i
$547$	3.00865	−	11.2284i	0.128641	−	0.480093i	−0.871303	−	0.490746i	$-0.836724\pi$
$547$	3.00865	−	11.2284i	0.128641	−	0.480093i	0.999943	+	0.0106529i	$0.00339100\pi$
$548$	−0.332975	+	1.24268i	−0.0142240	+	0.0530846i
$549$	17.0765	−	6.09245i	0.728806	−	0.260019i
$550$	−10.2110	+	19.8013i	−0.435400	+	0.844329i
$551$	−3.24307	−	1.87239i	−0.138159	−	0.0797664i
$552$	0.107726	+	0.622528i	0.00458511	+	0.0264966i
$553$	17.0244	+	4.56168i	0.723952	+	0.193982i
$554$	−0.704862			−0.0299467
$555$	−11.6077	+	3.92403i	−0.492720	+	0.166566i
$556$	−6.31234			−0.267703
$557$	6.46185	−	6.46185i	0.273797	−	0.273797i	−0.556829	−	0.830627i	$-0.687982\pi$
$557$	6.46185	−	6.46185i	0.273797	−	0.273797i	0.830627	+	0.556829i	$0.187982\pi$
$558$	14.9655	+	7.41854i	0.633539	+	0.314052i
$559$			13.6071i			0.575520i
$560$	7.74758	−	1.20776i	0.327395	−	0.0510373i
$561$	−6.15029	−	4.33573i	−0.259666	−	0.183055i
$562$	6.70520	+	6.70520i	0.282842	+	0.282842i
$563$	4.10461	−	15.3186i	0.172989	−	0.645603i	−0.823897	−	0.566740i	$-0.808204\pi$
$563$	4.10461	−	15.3186i	0.172989	−	0.645603i	0.996885	−	0.0788628i	$-0.0251289\pi$
$564$	11.2974	+	7.96428i	0.475708	+	0.335357i
$565$	15.8213	−	40.9176i	0.665605	−	1.72142i
$566$		−	0.124884i		−	0.00524927i
$567$	−18.4299	+	25.6198i	−0.773983	+	1.07593i
$568$	10.0158	+	2.68374i	0.420255	+	0.112607i
$569$	12.7268	+	22.0434i	0.533534	+	0.924108i	0.999233	+	0.0391649i	$0.0124698\pi$
$569$	12.7268	+	22.0434i	0.533534	+	0.924108i	−0.465699	+	0.884943i	$0.654197\pi$
$570$	−22.1862	+	7.50012i	−0.929276	+	0.314145i
$571$	−13.4006	−	23.2105i	−0.560797	−	0.971328i	−0.997427	−	0.0716875i	$-0.977162\pi$
$571$	−13.4006	−	23.2105i	−0.560797	−	0.971328i	0.436630	−	0.899641i	$-0.356172\pi$
$572$	2.91780	+	10.8894i	0.121999	+	0.455308i
$573$	14.6187	−	12.1874i	0.610704	−	0.509136i
$574$			15.2129i			0.634976i
$575$	−0.985847	−	1.53438i	−0.0411126	−	0.0639881i
$576$	1.00809	+	2.82556i	0.0420036	+	0.117731i
$577$	−9.56199	+	2.56213i	−0.398071	+	0.106663i	−0.452300	−	0.891866i	$-0.649396\pi$
$577$	−9.56199	+	2.56213i	−0.398071	+	0.106663i	0.0542293	+	0.998529i	$0.482730\pi$
$578$	−4.15387	+	15.5025i	−0.172778	+	0.644817i
$579$	−1.67838	−	3.62942i	−0.0697510	−	0.150834i
$580$	0.148101	−	1.37683i	0.00614957	−	0.0571696i
$581$		−	40.8071i		−	1.69296i
$582$	−23.4823	+	4.06351i	−0.973372	+	0.168438i
$583$	−14.4408	−	53.8937i	−0.598075	−	2.23205i
$584$	5.57483	+	9.65589i	0.230688	+	0.399564i
$585$	−16.9664	−	0.445593i	−0.701474	−	0.0184230i
$586$	−3.54562	+	6.14120i	−0.146468	+	0.253691i
$587$	−10.1110	+	10.1110i	−0.417325	+	0.417325i	−0.884281	−	0.466956i	$-0.845351\pi$
$587$	−10.1110	+	10.1110i	−0.417325	+	0.417325i	0.466956	+	0.884281i	$0.345351\pi$
$588$	5.87468	+	7.04661i	0.242268	+	0.290597i
$589$	−17.3418	+	28.8580i	−0.714557	+	1.18907i
$590$	−1.59947	−	10.2603i	−0.0658493	−	0.422412i
$591$	14.8613	+	1.34789i	0.611312	+	0.0554449i
$592$	−3.05592	+	0.818831i	−0.125598	+	0.0336538i
$593$	−22.7359	−	22.7359i	−0.933651	−	0.933651i	0.0642806	−	0.997932i	$-0.479525\pi$
$593$	−22.7359	−	22.7359i	−0.933651	−	0.933651i	−0.997932	+	0.0642806i	$0.979525\pi$
$594$	−5.77854	−	22.4204i	−0.237096	−	0.919919i
$595$	−3.09262	−	6.99191i	−0.126785	−	0.286640i
$596$	2.46630	+	1.42392i	0.101024	+	0.0583260i
$597$	33.2451	−	27.7160i	1.36063	−	1.13434i
$598$	−0.891420	−	0.238855i	−0.0364529	−	0.00976752i
$599$	−8.48154	−	14.6905i	−0.346546	−	0.600236i	0.639087	−	0.769134i	$-0.279312\pi$
$599$	−8.48154	−	14.6905i	−0.346546	−	0.600236i	−0.985633	+	0.168899i	$0.945979\pi$
$600$	−5.85507	−	6.38108i	−0.239032	−	0.260506i
$601$	6.72319	−	11.6449i	0.274244	−	0.475005i	−0.695700	−	0.718333i	$-0.744906\pi$
$601$	6.72319	−	11.6449i	0.274244	−	0.475005i	0.969944	+	0.243327i	$0.0782389\pi$
$602$	−18.2168	−	4.88118i	−0.742462	−	0.198942i
$603$	−2.81210	−	34.6853i	−0.114518	−	1.41249i
$604$			20.2687i			0.824722i
$605$	11.6763	−	15.9891i	0.474711	−	0.650048i
$606$	5.81989	+	4.10281i	0.236417	+	0.166665i
$607$	−5.71898	+	21.3435i	−0.232126	+	0.866307i	0.747297	+	0.664490i	$0.231351\pi$
$607$	−5.71898	+	21.3435i	−0.232126	+	0.866307i	−0.979423	+	0.201817i	$0.935315\pi$
$608$	−5.84087	+	1.56506i	−0.236879	+	0.0634714i
$609$	3.41402	−	1.57877i	0.138343	−	0.0639748i
$610$	−10.5229	+	8.47894i	−0.426061	+	0.343302i
$611$	−17.4860	+	10.0955i	−0.707407	+	0.408422i
$612$	2.40672	−	1.66246i	0.0972858	−	0.0672010i
$613$	−4.98101	−	18.5894i	−0.201181	−	0.750819i	−0.990580	−	0.136938i	$-0.956274\pi$
$613$	−4.98101	−	18.5894i	−0.201181	−	0.750819i	0.789398	−	0.613881i	$-0.210393\pi$
$614$	−15.9060	+	27.5499i	−0.641913	+	1.11183i
$615$	13.9822	−	9.31719i	0.563815	−	0.375705i
$616$	−15.6251			−0.629552
$617$	−3.01569	−	11.2547i	−0.121407	−	0.453097i	0.878279	−	0.478148i	$-0.158692\pi$
$617$	−3.01569	−	11.2547i	−0.121407	−	0.453097i	−0.999686	+	0.0250512i	$0.992025\pi$
$618$	24.9222	−	20.7774i	1.00252	−	0.835788i
$619$			14.5015i			0.582865i	0.956591	+	0.291433i	$0.0941319\pi$
$619$			14.5015i			0.582865i	−0.956591	+	0.291433i	$0.905868\pi$
$620$	−12.3533	−	1.54804i	−0.496120	−	0.0621708i
$621$	1.82599	+	0.508017i	0.0732744	+	0.0203860i
$622$	−17.7975	−	17.7975i	−0.713616	−	0.713616i
$623$	−47.6000	+	12.7544i	−1.90706	+	0.510994i
$624$	−4.36430	−	0.395834i	−0.174712	−	0.0158461i
$625$	22.7385	+	10.3904i	0.909540	+	0.415616i
$626$	−28.4898	−	16.4486i	−1.13868	−	0.657417i
$627$	45.9848	−	7.95746i	1.83645	−	0.317790i
$628$	−12.4345	+	12.4345i	−0.496190	+	0.496190i
$629$	1.54235	+	2.67144i	0.0614977	+	0.106517i
$630$	6.68277	−	22.5543i	0.266248	−	0.898583i
$631$	18.8121	+	32.5835i	0.748899	+	1.29713i	0.948351	+	0.317223i	$0.102750\pi$
$631$	18.8121	+	32.5835i	0.748899	+	1.29713i	−0.199452	+	0.979908i	$0.563916\pi$
$632$	−1.30086	−	4.85486i	−0.0517453	−	0.193116i
$633$	−16.1571	+	43.9553i	−0.642188	+	1.74707i
$634$	17.4452	+	10.0720i	0.692839	+	0.400011i
$635$	−21.8783	+	3.41059i	−0.868214	+	0.135345i
$636$	21.5998	+	1.95906i	0.856487	+	0.0776818i
$637$	−12.9445	+	3.46848i	−0.512881	+	0.137426i
$638$	−0.714192	+	2.66540i	−0.0282751	+	0.105524i
$639$	20.1469	−	23.7019i	0.796998	−	0.937632i
$640$	−1.40297	−	1.74117i	−0.0554571	−	0.0688259i
$641$	−28.7660	+	16.6081i	−1.13619	+	0.655980i	−0.945484	−	0.325668i	$-0.894411\pi$
$641$	−28.7660	+	16.6081i	−1.13619	+	0.655980i	−0.190706	+	0.981647i	$0.561078\pi$
$642$	−5.43900	−	1.99927i	−0.214660	−	0.0789049i
$643$	−11.6586	+	11.6586i	−0.459770	+	0.459770i	−0.898580	−	0.438810i	$-0.855400\pi$
$643$	−11.6586	+	11.6586i	−0.459770	+	0.459770i	0.438810	+	0.898580i	$0.355400\pi$
$644$	0.639544	−	1.10772i	0.0252016	−	0.0436504i
$645$	6.67064	+	19.7325i	0.262656	+	0.776966i
$646$	2.94795	+	5.10599i	0.115985	+	0.200893i
$647$	−11.9820	+	11.9820i	−0.471061	+	0.471061i	−0.902258	−	0.431197i	$-0.858092\pi$
$647$	−11.9820	+	11.9820i	−0.471061	+	0.471061i	0.431197	+	0.902258i	$0.358092\pi$
$648$	8.95503	+	0.898533i	0.351787	+	0.0352977i
$649$			20.6927i			0.812260i
$650$	12.0501	−	3.85053i	0.472644	−	0.151030i
$651$	−13.6545	−	30.9379i	−0.535162	−	1.21255i
$652$	7.45568	+	7.45568i	0.291987	+	0.291987i
$653$	31.7366	+	31.7366i	1.24195	+	1.24195i	0.959192	+	0.282756i	$0.0912488\pi$
$653$	31.7366	+	31.7366i	1.24195	+	1.24195i	0.282756	+	0.959192i	$0.408751\pi$
$654$	−6.06633	−	4.27654i	−0.237212	−	0.167226i
$655$	4.17732	+	3.05057i	0.163222	+	0.119196i
$656$	3.75707	−	2.16914i	0.146689	−	0.0846908i
$657$	33.3396	−	2.70300i	1.30070	−	0.105454i
$658$	−7.24299	−	27.0312i	−0.282361	−	1.05379i
$659$	−23.8353			−0.928492			−0.464246	−	0.885706i	$-0.653675\pi$
$659$	−23.8353			−0.928492			−0.464246	+	0.885706i	$0.653675\pi$
$660$	9.56959	+	14.3609i	0.372496	+	0.558999i
$661$	−12.6115	−	21.8438i	−0.490532	−	0.849627i	0.509408	−	0.860525i	$-0.329864\pi$
$661$	−12.6115	−	21.8438i	−0.490532	−	0.849627i	−0.999941	+	0.0108981i	$0.996531\pi$
$662$	−2.10378	−	0.563706i	−0.0817657	−	0.0219091i
$663$	0.728556	+	4.21020i	0.0282948	+	0.163511i
$664$	−10.0779	+	5.81849i	−0.391099	+	0.225801i
$665$	44.2240	+	17.0997i	1.71493	+	0.663098i
$666$	−1.70762	+	9.33628i	−0.0661688	+	0.361774i
$667$	−0.159728	−	0.159728i	−0.00618471	−	0.00618471i
$668$	−9.47384	+	2.53851i	−0.366554	+	0.0982178i
$669$	−6.92106	−	14.9665i	−0.267584	−	0.578638i
$670$	10.4921	+	23.7209i	0.405344	+	0.916418i
$671$	23.3212	−	13.4645i	0.900306	−	0.519792i
$672$	2.09550	−	5.70080i	0.0808358	−	0.219913i
$673$	24.8919	+	6.66976i	0.959511	+	0.257100i	0.704393	−	0.709810i	$-0.251219\pi$
$673$	24.8919	+	6.66976i	0.959511	+	0.257100i	0.255118	+	0.966910i	$0.417886\pi$
$674$	20.0962			0.774076
$675$	−24.8224	+	7.67128i	−0.955415	+	0.295268i
$676$	−3.29936	+	5.71467i	−0.126899	+	0.219795i
$677$	−35.0644	−	9.39548i	−1.34764	−	0.361098i	−0.488374	−	0.872635i	$-0.662410\pi$
$677$	−35.0644	−	9.39548i	−1.34764	−	0.361098i	−0.859261	+	0.511537i	$0.829076\pi$
$678$	−21.7599	−	26.1007i	−0.835682	−	1.00239i
$679$	41.7843	+	24.1241i	1.60353	+	0.925800i
$680$	−1.28579	+	1.76071i	−0.0493080	+	0.0675202i
$681$	−4.57382	−	0.414837i	−0.175269	−	0.0158966i
$682$	23.8475	+	6.83959i	0.913166	+	0.261901i
$683$	−9.60893	−	9.60893i	−0.367675	−	0.367675i	0.498953	−	0.866629i	$-0.333718\pi$
$683$	−9.60893	−	9.60893i	−0.367675	−	0.367675i	−0.866629	+	0.498953i	$0.833718\pi$
$684$	−3.26382	+	17.8447i	−0.124795	+	0.682310i
$685$	−2.68315	−	1.03747i	−0.102518	−	0.0396396i
$686$			5.97275i			0.228041i
$687$	17.6084	+	6.47249i	0.671801	+	0.246941i
$688$	1.39197	+	5.19490i	0.0530683	+	0.198054i
$689$	−15.8406	+	27.4367i	−0.603477	+	1.04525i
$690$	−1.40979	+	0.0906241i	−0.0536699	+	0.00345000i
$691$	−16.4747	−	28.5350i	−0.626727	−	1.08552i	−0.988204	−	0.153141i	$-0.951061\pi$
$691$	−16.4747	−	28.5350i	−0.626727	−	1.08552i	0.361478	−	0.932381i	$-0.382272\pi$
$692$	20.0164	+	5.36339i	0.760911	+	0.203885i
$693$	−20.0805	+	42.3563i	−0.762794	+	1.60898i
$694$	−14.3118	−	8.26291i	−0.543268	−	0.313656i
$695$	1.50958	−	14.0339i	0.0572617	−	0.532335i
$696$	−0.876689	−	0.618034i	−0.0332308	−	0.0234265i
$697$	−2.99102	−	2.99102i	−0.113293	−	0.113293i
$698$	16.6588	+	16.6588i	0.630543	+	0.630543i
$699$	25.5006	+	17.9770i	0.964519	+	0.679951i
$700$	0.832331	+	17.5136i	0.0314592	+	0.661952i
$701$	28.2268	+	16.2968i	1.06611	+	0.615520i	0.927117	−	0.374773i	$-0.122279\pi$
$701$	28.2268	+	16.2968i	1.06611	+	0.615520i	0.138996	+	0.990293i	$0.455613\pi$
$702$	−6.68178	+	11.3220i	−0.252188	+	0.427322i
$703$	−18.4789	−	4.95140i	−0.696944	−	0.186746i
$704$	2.22790	+	3.85884i	0.0839673	+	0.145436i
$705$	−20.4083	+	23.2123i	−0.768621	+	0.874226i
$706$	12.2508	−	21.2190i	0.461066	−	0.798589i
$707$	−3.73123	−	13.9252i	−0.140328	−	0.523709i
$708$	−7.54973	−	2.77513i	−0.283736	−	0.104296i
$709$			31.1791i			1.17096i	0.810688	+	0.585479i	$0.199093\pi$
$709$			31.1791i			1.17096i	−0.810688	+	0.585479i	$0.800907\pi$
$710$	−8.36187	+	21.6258i	−0.313815	+	0.811603i
$711$	−14.8323	−	2.71285i	−0.556256	−	0.101740i
$712$	9.93696	+	9.93696i	0.372403	+	0.372403i
$713$	−1.46098	+	1.41069i	−0.0547141	+	0.0528309i
$714$	−5.89784	−	0.534923i	−0.220721	−	0.0200190i
$715$	−24.9075	+	3.88281i	−0.931489	+	0.145209i
$716$	−2.51812	−	1.45384i	−0.0941066	−	0.0543325i
$717$	−23.2096	−	27.8397i	−0.866779	−	1.03969i
$718$	−22.4112	−	6.00506i	−0.836379	−	0.224107i
$719$	−11.2760	+	19.5306i	−0.420525	+	0.728370i	−0.995991	−	0.0894554i	$-0.971487\pi$
$719$	−11.2760	+	19.5306i	−0.420525	+	0.728370i	0.575466	+	0.817826i	$0.304821\pi$
$720$	−6.52298	+	1.56549i	−0.243097	+	0.0583425i
$721$	−65.6918			−2.44649
$722$	−16.9667	−	4.54620i	−0.631433	−	0.169192i
$723$	−3.71907	+	10.1177i	−0.138314	+	0.376281i
$724$	8.93004	−	5.15576i	0.331882	−	0.191612i
$725$	3.02560	+	0.658530i	0.112368	+	0.0244572i
$726$	−6.43697	−	13.9197i	−0.238898	−	0.516608i
$727$	−19.4544	+	5.21280i	−0.721525	+	0.193332i	−0.600852	−	0.799360i	$-0.705172\pi$
$727$	−19.4544	+	5.21280i	−0.721525	+	0.193332i	−0.120673	+	0.992692i	$0.538505\pi$
$728$	6.27355	+	6.27355i	0.232513	+	0.232513i
$729$	13.9443	−	23.1205i	0.516454	−	0.856315i
$730$	−22.8006	+	10.0850i	−0.843888	+	0.373263i
$731$	4.54130	−	2.62192i	0.167966	−	0.0969752i
$732$	1.78488	+	10.3145i	0.0659710	+	0.381235i
$733$	−17.3109	−	4.63845i	−0.639394	−	0.171325i	−0.0754650	−	0.997148i	$-0.524044\pi$
$733$	−17.3109	−	4.63845i	−0.639394	−	0.171325i	−0.563929	+	0.825823i	$0.690711\pi$
$734$	−4.62911	−	8.01786i	−0.170864	−	0.295945i
$735$	−17.0713	+	11.3756i	−0.629683	+	0.419597i
$736$	−0.364758			−0.0134452
$737$	−13.3773	−	49.9248i	−0.492760	−	1.83901i
$738$	−1.05173	−	12.9723i	−0.0387146	−	0.477517i
$739$	−30.8189	+	17.7933i	−1.13369	+	0.654538i	−0.944861	−	0.327471i	$-0.893803\pi$
$739$	−30.8189	+	17.7933i	−1.13369	+	0.654538i	−0.188832	+	0.982009i	$0.560470\pi$
$740$	−1.08964	−	6.98987i	−0.0400561	−	0.256953i
$741$	−21.6581	−	15.2682i	−0.795630	−	0.560890i
$742$	−31.0490	−	31.0490i	−1.13984	−	1.13984i
$743$	26.6031	+	26.6031i	0.975972	+	0.975972i	0.999718	−	0.0237457i	$-0.00755920\pi$
$743$	26.6031	+	26.6031i	0.975972	+	0.975972i	−0.0237457	+	0.999718i	$0.507559\pi$
$744$	−5.69365	+	7.78347i	−0.208739	+	0.285356i
$745$	−3.75553	+	5.14266i	−0.137592	+	0.188412i
$746$		−	29.3447i		−	1.07439i
$747$	2.82114	+	34.7968i	0.103220	+	1.27315i
$748$	3.07204	−	3.07204i	0.112325	−	0.112325i
$749$	5.86602	+	10.1602i	0.214340	+	0.371247i
$750$	15.5869	−	11.4912i	0.569154	−	0.419600i
$751$	−4.78656	+	8.29057i	−0.174664	+	0.302527i	−0.940045	−	0.341050i	$-0.889217\pi$
$751$	−4.78656	+	8.29057i	−0.174664	+	0.302527i	0.765381	+	0.643578i	$0.222551\pi$
$752$	−5.64302	+	5.64302i	−0.205780	+	0.205780i
$753$	7.16798	+	2.63481i	0.261216	+	0.0960178i
$754$	1.35692	−	0.783421i	0.0494163	−	0.0285305i
$755$	−45.0622	−	4.84722i	−1.63998	−	0.176408i
$756$	−12.7607	−	13.0068i	−0.464101	−	0.473054i
$757$	2.20270	−	8.22059i	0.0800585	−	0.298782i	−0.914274	−	0.405096i	$-0.867238\pi$
$757$	2.20270	−	8.22059i	0.0800585	−	0.298782i	0.994333	+	0.106314i	$0.0339047\pi$
$758$	21.9731	−	5.88768i	0.798099	−	0.213850i
$759$	2.80358	+	0.254280i	0.101764	+	0.00922978i
$760$	−2.08267	−	13.3600i	−0.0755463	−	0.484616i
$761$	4.50451	+	2.60068i	0.163288	+	0.0942745i	0.579417	−	0.815031i	$-0.303280\pi$
$761$	4.50451	+	2.60068i	0.163288	+	0.0942745i	−0.416129	+	0.909306i	$0.636614\pi$
$762$	−5.91746	+	16.0984i	−0.214367	+	0.583184i
$763$	3.88923	+	14.5148i	0.140800	+	0.525472i
$764$	5.49423	+	9.51628i	0.198774	+	0.344287i
$765$	3.12049	+	5.74829i	0.112822	+	0.207830i
$766$	12.6463	+	21.9040i	0.456929	+	0.791424i
$767$	8.30824	−	8.30824i	0.299993	−	0.299993i
$768$	−1.70669	+	0.295334i	−0.0615847	+	0.0106570i
$769$	30.3279	+	17.5098i	1.09365	+	0.631421i	0.934547	−	0.355840i	$-0.115805\pi$
$769$	30.3279	+	17.5098i	1.09365	+	0.631421i	0.159107	+	0.987261i	$0.449139\pi$
$770$	3.73670	−	34.7383i	0.134661	−	1.25188i
$771$	5.27161	+	0.478126i	0.189852	+	0.0172193i
$772$	2.22999	−	0.597524i	0.0802591	−	0.0215054i
$773$	12.0507	+	12.0507i	0.433434	+	0.433434i	0.889795	−	0.456361i	$-0.150847\pi$
$773$	12.0507	+	12.0507i	0.433434	+	0.433434i	−0.456361	+	0.889795i	$0.650847\pi$
$774$	15.8712	+	2.90286i	0.570478	+	0.104341i
$775$	6.39593	−	27.0941i	0.229749	−	0.973250i
$776$		−	13.7590i		−	0.493919i
$777$	14.7593	−	12.3046i	0.529485	−	0.441426i
$778$	−7.79284	−	29.0833i	−0.279387	−	1.04269i
$779$	26.2332			0.939903
$780$	1.92375	−	9.60824i	0.0688813	−	0.344030i
$781$	23.1015	−	40.0130i	0.826637	−	1.43178i
$782$	0.0920487	+	0.343530i	0.00329165	+	0.0122846i
$783$	−2.80203	+	1.58226i	−0.100137	+	0.0565454i
$784$	−4.58712	+	2.64837i	−0.163826	+	0.0945848i
$785$	−24.6712	−	30.6186i	−0.880554	−	1.09282i
$786$	3.63667	−	1.68173i	0.129716	−	0.0599854i
$787$	51.3430	−	13.7573i	1.83018	−	0.490396i	0.832233	−	0.554426i	$-0.187062\pi$
$787$	51.3430	−	13.7573i	1.83018	−	0.490396i	0.997948	+	0.0640301i	$0.0203954\pi$
$788$	−2.22983	+	8.32183i	−0.0794343	+	0.296453i
$789$	−36.9774	−	26.0677i	−1.31643	−	0.928035i
$790$	11.1046	−	1.73109i	0.395085	−	0.0615894i
$791$			68.7981i			2.44618i
$792$	13.3237	−	1.08022i	0.473437	−	0.0383838i
$793$	−14.7697	−	3.95753i	−0.524487	−	0.140536i
$794$	7.63033	−	13.2161i	0.270790	−	0.469022i
$795$	−9.52101	+	47.5530i	−0.337675	+	1.68653i
$796$	12.4947	+	21.6415i	0.442863	+	0.767062i
$797$	−22.6029	−	6.05643i	−0.800636	−	0.214530i	−0.164773	−	0.986332i	$-0.552689\pi$
$797$	−22.6029	−	6.05643i	−0.800636	−	0.214530i	−0.635863	+	0.771802i	$0.719356\pi$
$798$	28.2098	−	23.5182i	0.998616	−	0.832534i
$799$	6.73865	+	3.89056i	0.238396	+	0.137638i
$800$	4.20657	−	2.70274i	0.148725	−	0.0955562i
$801$	39.7075	−	14.1666i	1.40299	−	0.500553i
$802$	−3.43184	−	3.43184i	−0.121182	−	0.121182i
$803$	47.9879	−	12.8583i	1.69346	−	0.453761i
$804$	20.0091	+	1.81479i	0.705667	+	0.0640028i
$805$	2.30979	+	1.68677i	0.0814094	+	0.0594509i
$806$	−6.82875	−	12.3210i	−0.240533	−	0.433989i
$807$	22.2436	+	26.6810i	0.783013	+	0.939216i
$808$	−2.90701	+	2.90701i	−0.102268	+	0.102268i
$809$	−2.48091	+	4.29707i	−0.0872242	+	0.151077i	−0.906337	−	0.422556i	$-0.861133\pi$
$809$	−2.48091	+	4.29707i	−0.0872242	+	0.151077i	0.819113	+	0.573633i	$0.194466\pi$
$810$	−4.13923	+	19.6943i	−0.145438	+	0.691988i
$811$	−6.60601	−	11.4419i	−0.231968	−	0.401781i	0.726419	−	0.687252i	$-0.241183\pi$
$811$	−6.60601	−	11.4419i	−0.231968	−	0.401781i	−0.958387	+	0.285471i	$0.907850\pi$
$812$	0.562061	+	2.09764i	0.0197245	+	0.0736127i
$813$	−20.9936	+	3.63284i	−0.736276	+	0.127409i
$814$			14.0969i			0.494097i
$815$	−18.3588	+	14.7928i	−0.643081	+	0.518168i
$816$	0.708838	+	1.53283i	0.0248143	+	0.0536598i
$817$	−8.41712	+	31.4131i	−0.294478	+	1.09901i
$818$	−9.05266	+	2.42565i	−0.316519	+	0.0848110i
$819$	25.0687	−	8.94388i	0.875972	−	0.312524i
$820$	3.92404	+	8.87161i	0.137033	+	0.309810i
$821$			29.5798i			1.03234i	0.856486	+	0.516171i	$0.172643\pi$
$821$			29.5798i			1.03234i	−0.856486	+	0.516171i	$0.827357\pi$
$822$	−1.71154	+	1.42689i	−0.0596967	+	0.0497684i
$823$	−10.1901	−	38.0298i	−0.355203	−	1.32564i	−0.880228	−	0.474550i	$-0.842611\pi$
$823$	−10.1901	−	38.0298i	−0.355203	−	1.32564i	0.525025	−	0.851087i	$-0.324056\pi$
$824$	9.36668	+	16.2236i	0.326304	+	0.565175i
$825$	−34.2164	+	17.8411i	−1.19126	+	0.621149i
$826$	8.14246	+	14.1032i	0.283313	+	0.490712i
$827$	−18.4891	−	4.95414i	−0.642930	−	0.172272i	−0.0773995	−	0.997000i	$-0.524662\pi$
$827$	−18.4891	−	4.95414i	−0.642930	−	0.172272i	−0.565530	+	0.824728i	$0.691328\pi$
$828$	−0.468767	+	0.988785i	−0.0162908	+	0.0343627i
$829$		−	23.2699i		−	0.808198i	−0.914715	−	0.404099i	$-0.867585\pi$
$829$		−	23.2699i		−	0.808198i	0.914715	−	0.404099i	$-0.132415\pi$
$830$	−10.5258	−	23.7971i	−0.365356	−	0.826011i
$831$	−0.997833	−	0.703436i	−0.0346144	−	0.0244019i
$832$	0.654831	−	2.44386i	0.0227022	−	0.0847257i
$833$	3.65183	+	3.65183i	0.126528	+	0.126528i
$834$	−8.93601	−	6.29956i	−0.309429	−	0.218136i
$835$	−3.37807	−	21.6697i	−0.116903	−	0.749912i
$836$			26.9439i			0.931874i
$837$	13.7822	+	25.4372i	0.476383	+	0.879238i
$838$	−14.2706	+	14.2706i	−0.492969	+	0.492969i
$839$	50.9140			1.75775			0.878874	−	0.477054i	$-0.158295\pi$
$839$	50.9140			1.75775			0.878874	+	0.477054i	$0.158295\pi$
$840$	12.1731	+	6.02215i	0.420013	+	0.207784i
$841$	−28.6165			−0.986775
$842$	−25.6896	−	6.88350i	−0.885321	−	0.237221i
$843$	2.80053	+	16.1838i	0.0964554	+	0.557399i
$844$	−23.4154	−	13.5189i	−0.805991	−	0.465339i
$845$	−11.9161	−	8.70194i	−0.409925	−	0.299356i
$846$	8.04496	+	22.5492i	0.276592	+	0.775256i
$847$	−8.03604	+	29.9909i	−0.276122	+	1.03050i
$848$	−3.24089	+	12.0951i	−0.111292	+	0.415349i
$849$	0.124631	−	0.176791i	0.00427734	−	0.00606746i
$850$	−3.60699	−	3.27970i	−0.123719	−	0.112493i
$851$	−0.999388	−	0.576997i	−0.0342586	−	0.0197792i
$852$	11.5005	+	13.7948i	0.394002	+	0.472602i
$853$	37.6947	−	37.6947i	1.29064	−	1.29064i	0.356255	−	0.934389i	$-0.384054\pi$
$853$	37.6947	−	37.6947i	1.29064	−	1.29064i	0.934389	−	0.356255i	$-0.115946\pi$
$854$	10.5964	−	18.3536i	0.362602	−	0.628046i
$855$	−38.8926	−	11.5238i	−1.33010	−	0.394105i
$856$	1.67282	−	2.89741i	0.0571757	−	0.0990313i
$857$	48.3864	+	12.9651i	1.65285	+	0.442879i	0.960408	−	0.278596i	$-0.0898690\pi$
$857$	48.3864	+	12.9651i	1.65285	+	0.442879i	0.692440	+	0.721475i	$0.256536\pi$
$858$	−6.73679	+	18.3274i	−0.229990	+	0.625686i
$859$	32.8709	−	18.9780i	1.12154	−	0.647521i	0.179746	−	0.983713i	$-0.442472\pi$
$859$	32.8709	−	18.9780i	1.12154	−	0.647521i	0.941794	+	0.336192i	$0.109139\pi$
$860$	−11.8824	+	1.85234i	−0.405187	+	0.0631641i
$861$	−15.1822	+	21.5361i	−0.517407	+	0.733948i
$862$	1.58649	−	0.425098i	0.0540359	−	0.0144789i
$863$	9.55504	−	35.6599i	0.325257	−	1.21388i	−0.588796	−	0.808282i	$-0.700398\pi$
$863$	9.55504	−	35.6599i	0.325257	−	1.21388i	0.914053	−	0.405595i	$-0.132936\pi$
$864$	−1.39275	+	5.00602i	−0.0473822	+	0.170308i
$865$	−16.7110	+	43.2188i	−0.568191	+	1.46948i
$866$		−	9.81538i		−	0.333540i
$867$	−21.3515	+	17.8005i	−0.725134	+	0.604536i
$868$	18.9446	−	4.72230i	0.643023	−	0.160285i
$869$	−22.3954			−0.759714
$870$	1.58370	−	1.80129i	0.0536924	−	0.0610695i
$871$	−14.6740	+	25.4162i	−0.497211	+	0.861194i
$872$	3.03010	−	3.03010i	0.102612	−	0.102612i
$873$	−37.2978	−	17.6823i	−1.26234	−	0.598455i
$874$	−1.91016	−	1.10283i	−0.0646121	−	0.0373038i
$875$	−39.1360	−	2.33786i	−1.32304	−	0.0790342i
$876$	−1.74439	+	19.2328i	−0.0589373	+	0.649818i
$877$	12.6031	−	47.0355i	0.425577	−	1.58828i	−0.337082	−	0.941475i	$-0.609440\pi$
$877$	12.6031	−	47.0355i	0.425577	−	1.58828i	0.762659	−	0.646801i	$-0.223893\pi$
$878$	3.42340	−	12.7763i	0.115534	−	0.431180i
$879$	−11.1481	+	5.15529i	−0.376016	+	0.173884i
$880$	−9.11194	+	4.03034i	−0.307164	+	0.135863i
$881$	−23.4692	+	13.5500i	−0.790699	+	0.456510i	−0.840209	−	0.542263i	$-0.817567\pi$
$881$	−23.4692	+	13.5500i	−0.790699	+	0.456510i	0.0495096	+	0.998774i	$0.484234\pi$
$882$	1.28409	+	15.8383i	0.0432374	+	0.533302i
$883$	33.2613	−	33.2613i	1.11933	−	1.11933i	0.127491	−	0.991840i	$-0.459308\pi$
$883$	33.2613	−	33.2613i	1.11933	−	1.11933i	0.991840	−	0.127491i	$-0.0406925\pi$
$884$	−2.46689			−0.0829703
$885$	7.97530	−	16.1212i	0.268087	−	0.541909i
$886$	6.83385	+	11.8366i	0.229588	+	0.397658i
$887$	3.66961	+	13.6952i	0.123213	+	0.459839i	0.999770	−	0.0214608i	$-0.00683170\pi$
$887$	3.66961	+	13.6952i	0.123213	+	0.459839i	−0.876556	+	0.481299i	$0.840165\pi$
$888$	−5.14326	−	1.89056i	−0.172597	−	0.0634432i
$889$	30.0724	−	17.3623i	1.00860	−	0.582313i
$890$	−24.4687	+	19.7159i	−0.820192	+	0.660877i
$891$	14.1946	−	37.5061i	0.475539	−	1.25650i
$892$	9.19572	−	2.46398i	0.307895	−	0.0825003i
$893$	−46.6127	+	12.4898i	−1.55983	+	0.417956i
$894$	2.07036	+	4.47707i	0.0692432	+	0.149736i
$895$	3.83444	−	5.25071i	0.128171	−	0.175512i
$896$	3.03687	+	1.75334i	0.101455	+	0.0585748i
$897$	−1.02356	−	1.22775i	−0.0341757	−	0.0409934i
$898$	−10.6416	+	10.6416i	−0.355114	+	0.355114i
$899$	0.0603693	−	3.44752i	0.00201343	−	0.114981i
$900$	−1.92052	−	14.8765i	−0.0640173	−	0.495885i
$901$	12.2091			0.406744
$902$	−5.00312	−	18.6719i	−0.166586	−	0.621706i
$903$	−20.9172	−	25.0899i	−0.696080	−	0.834941i
$904$	16.9907	−	9.80960i	0.565103	−	0.326262i
$905$	9.32691	+	21.0866i	0.310037	+	0.700943i
$906$	−20.2277	+	28.6932i	−0.672020	+	0.953269i
$907$	29.5255	+	29.5255i	0.980379	+	0.980379i	0.999811	−	0.0194322i	$-0.00618585\pi$
$907$	29.5255	+	29.5255i	0.980379	+	0.980379i	−0.0194322	+	0.999811i	$0.506186\pi$
$908$	0.686268	−	2.56119i	0.0227746	−	0.0849960i
$909$	4.14437	+	11.6162i	0.137460	+	0.385286i
$910$	−15.4479	+	12.4473i	−0.512094	+	0.412624i
$911$	−44.1112	−	25.4676i	−1.46147	−	0.843780i	−0.462390	−	0.886677i	$-0.653008\pi$
$911$	−44.1112	−	25.4676i	−1.46147	−	0.843780i	−0.999080	+	0.0428969i	$0.986341\pi$
$912$	−9.83047	−	3.61349i	−0.325519	−	0.119655i
$913$	13.4203	+	50.0853i	0.444148	+	1.65758i
$914$	−22.0509			−0.729378
$915$	−23.3585	+	1.50153i	−0.772207	+	0.0496389i
$916$	−5.41562	+	9.38013i	−0.178937	+	0.309928i
$917$	−7.83547	−	2.09951i	−0.258750	−	0.0693318i
$918$	5.06615	+	0.0483978i	0.167208	+	0.00159736i
$919$	0.316589	−	0.182783i	0.0104433	−	0.00602944i	−0.494769	−	0.869024i	$-0.664747\pi$
$919$	0.316589	−	0.182783i	0.0104433	−	0.00602944i	0.505213	+	0.862995i	$0.331414\pi$
$920$	0.0872312	−	0.810947i	0.00287593	−	0.0267361i
$921$	−50.0114	+	23.1271i	−1.64793	+	0.762063i
$922$	10.6898	+	10.6898i	0.352050	+	0.352050i
$923$	−25.3408	+	6.79005i	−0.834103	+	0.223497i
$924$	−22.1195	−	15.5934i	−0.727678	−	0.512987i
$925$	15.8008	−	0.750930i	0.519526	−	0.0246904i
$926$		−	3.22334i		−	0.105925i
$927$	56.0163	−	4.54151i	1.83982	−	0.149163i
$928$	0.437902	−	0.437902i	0.0143748	−	0.0143748i
$929$	−35.3097			−1.15847			−0.579237	−	0.815159i	$-0.696649\pi$
$929$	−35.3097			−1.15847			−0.579237	+	0.815159i	$0.696649\pi$
$930$	−15.9429	−	14.5198i	−0.522789	−	0.476122i
$931$	−32.0290			−1.04971
$932$	−12.7374	+	12.7374i	−0.417228	+	0.417228i
$933$	−7.43342	−	42.9565i	−0.243359	−	1.40633i
$934$			29.1670i			0.954373i
$935$	6.09523	+	7.56457i	0.199335	+	0.247388i
$936$	−5.78326	−	4.91583i	−0.189032	−	0.160679i
$937$	15.4937	−	4.15154i	0.506159	−	0.135625i	0.00330190	−	0.999995i	$-0.498949\pi$
$937$	15.4937	−	4.15154i	0.506159	−	0.135625i	0.502857	+	0.864370i	$0.332282\pi$
$938$	−28.7625	−	28.7625i	−0.939129	−	0.939129i
$939$	−23.9160	−	51.7174i	−0.780470	−	1.68773i
$940$	−11.1963	−	13.8953i	−0.365183	−	0.453215i
$941$	−29.6497	+	17.1183i	−0.966553	+	0.558040i	−0.898184	−	0.439620i	$-0.855113\pi$
$941$	−29.6497	+	17.1183i	−0.966553	+	0.558040i	−0.0683693	+	0.997660i	$0.521780\pi$
$942$	−30.0121	+	5.19346i	−0.977848	+	0.169212i
$943$	1.52851	+	0.409562i	0.0497750	+	0.0133372i
$944$	2.32199	−	4.02181i	0.0755744	−	0.130899i
$945$	31.9690	−	25.2595i	1.03995	−	0.821692i
$946$	23.9640			0.779138
$947$	−0.450854	−	1.68261i	−0.0146508	−	0.0546775i	0.958213	−	0.286054i	$-0.0923437\pi$
$947$	−0.450854	−	1.68261i	−0.0146508	−	0.0546775i	−0.972864	+	0.231377i	$0.925677\pi$
$948$	3.00349	−	8.17097i	0.0975489	−	0.265381i
$949$	−24.4301	−	14.1047i	−0.793035	−	0.457859i
$950$	30.2005	−	1.43527i	0.979833	−	0.0465665i
$951$	14.6446	+	31.6683i	0.474883	+	1.02691i
$952$	0.884927	−	3.30259i	0.0286806	−	0.107038i
$953$	6.11440	+	6.11440i	0.198065	+	0.198065i	0.799170	−	0.601105i	$-0.205273\pi$
$953$	6.11440	+	6.11440i	0.198065	+	0.198065i	−0.601105	+	0.799170i	$0.705273\pi$
$954$	28.6224	+	24.3294i	0.926686	+	0.787693i
$955$	−22.4709	+	9.93920i	−0.727142	+	0.321625i
$956$	18.1227	−	10.4632i	0.586131	−	0.338403i
$957$	−3.67105	+	3.06051i	−0.118668	+	0.0989321i
$958$	−1.78260	−	6.65275i	−0.0575932	−	0.214941i
$959$	4.51139			0.145680
$960$	−0.248450	−	3.86501i	−0.00801868	−	0.124743i
$961$	−30.9810	−	1.08535i	−0.999387	−	0.0350112i
$962$	5.66000	−	5.66000i	0.182486	−	0.182486i
$963$	−5.70446	−	8.25825i	−0.183823	−	0.266118i
$964$	−5.38979	−	3.11180i	−0.173593	−	0.100224i
$965$	0.795144	+	5.10071i	0.0255966	+	0.164198i
$966$	2.01085	−	0.929889i	0.0646979	−	0.0299187i
$967$	−40.6604	+	10.8949i	−1.30755	+	0.350357i	−0.844300	−	0.535871i	$-0.819983\pi$
$967$	−40.6604	+	10.8949i	−1.30755	+	0.350357i	−0.463249	+	0.886228i	$0.653317\pi$
$968$	8.55253	−	2.29164i	0.274889	−	0.0736562i
$969$	−0.922423	+	10.1702i	−0.0296325	+	0.326715i
$970$	30.5896	+	3.29044i	0.982173	+	0.105650i
$971$	6.17547	−	3.56541i	0.198180	−	0.114419i	−0.397626	−	0.917547i	$-0.630166\pi$
$971$	6.17547	−	3.56541i	0.198180	−	0.114419i	0.595806	+	0.803128i	$0.296833\pi$
$972$	11.7804	+	10.2089i	0.377857	+	0.327451i
$973$	5.72904	+	21.3811i	0.183664	+	0.685445i
$974$	−8.21752	−	14.2332i	−0.263306	−	0.456060i
$975$	20.9014	+	6.57475i	0.669380	+	0.210561i
$976$	−6.04358			−0.193450
$977$	−2.27858	+	2.27858i	−0.0728982	+	0.0728982i	−0.742616	−	0.669718i	$-0.766415\pi$
$977$	−2.27858	+	2.27858i	−0.0728982	+	0.0728982i	0.669718	+	0.742616i	$0.266415\pi$
$978$	3.11398	+	17.9952i	0.0995742	+	0.575422i
$979$	54.2282	−	31.3087i	1.73314	−	1.00063i
$980$	−4.79098	−	10.8316i	−0.153042	−	0.346004i
$981$	−4.31987	−	12.1081i	−0.137923	−	0.386582i
$982$	−7.64698	+	28.5389i	−0.244025	+	0.910714i
$983$	−13.9949	+	52.2297i	−0.446368	+	1.66587i	0.265930	+	0.963992i	$0.414321\pi$
$983$	−13.9949	+	52.2297i	−0.446368	+	1.66587i	−0.712299	+	0.701877i	$0.752346\pi$
$984$	7.48341	+	0.678732i	0.238563	+	0.0216372i
$985$	−17.9682	−	6.94759i	−0.572514	−	0.221369i
$986$	−0.522924	−	0.301910i	−0.0166533	−	0.00961478i
$987$	16.7230	−	45.4948i	0.532300	−	1.44812i
$988$	10.8181	−	10.8181i	0.344170	−	0.344170i
$989$	−0.980864	+	1.69891i	−0.0311897	+	0.0540221i
$990$	−0.784751	+	29.8802i	−0.0249410	+	0.949654i
$991$	51.2962			1.62948			0.814739	−	0.579828i	$-0.196880\pi$
$991$	51.2962			1.62948			0.814739	+	0.579828i	$0.196880\pi$
$992$	−3.86747	−	4.00533i	−0.122792	−	0.127169i
$993$	−2.41563	−	2.89753i	−0.0766579	−	0.0919503i
$994$		−	36.3613i		−	1.15331i
$995$	−51.1023	+	22.6033i	−1.62005	+	0.716572i
$996$	−20.0734	−	1.82063i	−0.636051	−	0.0576887i
$997$	−6.83600	+	25.5123i	−0.216498	+	0.807982i	0.769136	+	0.639086i	$0.220687\pi$
$997$	−6.83600	+	25.5123i	−0.216498	+	0.807982i	−0.985634	+	0.168897i	$0.945980\pi$
$998$	13.4193	−	3.59570i	0.424782	−	0.113820i
$999$	−11.7348	+	11.5127i	−0.371272	+	0.364245i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.bf.a.377.2	✓	256
3.2	odd	2	inner	930.2.bf.a.377.61	yes	256
5.3	odd	4	inner	930.2.bf.a.563.45	yes	256
15.8	even	4	inner	930.2.bf.a.563.19	yes	256
31.25	even	3	inner	930.2.bf.a.707.19	yes	256
93.56	odd	6	inner	930.2.bf.a.707.45	yes	256
155.118	odd	12	inner	930.2.bf.a.893.61	yes	256
465.428	even	12	inner	930.2.bf.a.893.2	yes	256

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.bf.a.377.2	✓	256	1.1	even	1	trivial
930.2.bf.a.377.61	yes	256	3.2	odd	2	inner
930.2.bf.a.563.19	yes	256	15.8	even	4	inner
930.2.bf.a.563.45	yes	256	5.3	odd	4	inner
930.2.bf.a.707.19	yes	256	31.25	even	3	inner
930.2.bf.a.707.45	yes	256	93.56	odd	6	inner
930.2.bf.a.893.2	yes	256	465.428	even	12	inner
930.2.bf.a.893.61	yes	256	155.118	odd	12	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.bf (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.70669 + 0.295334i) q^{3} -1.00000i q^{4} +(2.22324 + 0.239148i) q^{5} +(0.997976 - 1.41564i) q^{6} +(-3.38718 + 0.907593i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82556 - 1.00809i) q^{9} +O(q^{10})\)	\(q+(-0.707107 + 0.707107i) q^{2} +(-1.70669 + 0.295334i) q^{3} -1.00000i q^{4} +(2.22324 + 0.239148i) q^{5} +(0.997976 - 1.41564i) q^{6} +(-3.38718 + 0.907593i) q^{7} +(0.707107 + 0.707107i) q^{8} +(2.82556 - 1.00809i) q^{9} +(-1.74117 + 1.40297i) q^{10} +(3.85884 - 2.22790i) q^{11} +(0.295334 + 1.70669i) q^{12} +(-2.44386 - 0.654831i) q^{13} +(1.75334 - 3.03687i) q^{14} +(-3.86501 + 0.248450i) q^{15} -1.00000 q^{16} +(0.252355 + 0.941802i) q^{17} +(-1.28514 + 2.71079i) q^{18} +(-5.23678 - 3.02346i) q^{19} +(0.239148 - 2.22324i) q^{20} +(5.51282 - 2.54933i) q^{21} +(-1.15325 + 4.30398i) q^{22} +(-0.257923 - 0.257923i) q^{23} +(-1.41564 - 0.997976i) q^{24} +(4.88562 + 1.06337i) q^{25} +(2.19111 - 1.26504i) q^{26} +(-4.52461 + 2.55497i) q^{27} +(0.907593 + 3.38718i) q^{28} +0.619287 q^{29} +(2.55729 - 2.90865i) q^{30} +(0.0974819 - 5.56691i) q^{31} +(0.707107 - 0.707107i) q^{32} +(-5.92786 + 4.94198i) q^{33} +(-0.844397 - 0.487513i) q^{34} +(-7.74758 + 1.20776i) q^{35} +(-1.00809 - 2.82556i) q^{36} +(3.05592 - 0.818831i) q^{37} +(5.84087 - 1.56506i) q^{38} +(4.36430 + 0.395834i) q^{39} +(1.40297 + 1.74117i) q^{40} +(-3.75707 + 2.16914i) q^{41} +(-2.09550 + 5.70080i) q^{42} +(-1.39197 - 5.19490i) q^{43} +(-2.22790 - 3.85884i) q^{44} +(6.52298 - 1.56549i) q^{45} +0.364758 q^{46} +(5.64302 - 5.64302i) q^{47} +(1.70669 - 0.295334i) q^{48} +(4.58712 - 2.64837i) q^{49} +(-4.20657 + 2.70274i) q^{50} +(-0.708838 - 1.53283i) q^{51} +(-0.654831 + 2.44386i) q^{52} +(3.24089 - 12.0951i) q^{53} +(1.39275 - 5.00602i) q^{54} +(9.11194 - 4.03034i) q^{55} +(-3.03687 - 1.75334i) q^{56} +(9.83047 + 3.61349i) q^{57} +(-0.437902 + 0.437902i) q^{58} +(-2.32199 + 4.02181i) q^{59} +(0.248450 + 3.86501i) q^{60} +6.04358 q^{61} +(3.86747 + 4.00533i) q^{62} +(-8.65575 + 5.97903i) q^{63} +1.00000i q^{64} +(-5.27670 - 2.04029i) q^{65} +(0.697119 - 7.68614i) q^{66} +(3.00222 - 11.2044i) q^{67} +(0.941802 - 0.252355i) q^{68} +(0.516368 + 0.364020i) q^{69} +(4.62435 - 6.33239i) q^{70} +(8.97996 - 5.18458i) q^{71} +(2.71079 + 1.28514i) q^{72} +(10.7698 + 2.88575i) q^{73} +(-1.58186 + 2.73986i) q^{74} +(-8.65226 - 0.371944i) q^{75} +(-3.02346 + 5.23678i) q^{76} +(-11.0486 + 11.0486i) q^{77} +(-3.36592 + 2.80613i) q^{78} +(-4.35275 - 2.51306i) q^{79} +(-2.22324 - 0.239148i) q^{80} +(6.96752 - 5.69681i) q^{81} +(1.12283 - 4.19046i) q^{82} +(-3.01187 + 11.2405i) q^{83} +(-2.54933 - 5.51282i) q^{84} +(0.335817 + 2.15420i) q^{85} +(4.65762 + 2.68908i) q^{86} +(-1.05693 + 0.182897i) q^{87} +(4.30398 + 1.15325i) q^{88} +14.0530 q^{89} +(-3.50547 + 5.71941i) q^{90} +8.87214 q^{91} +(-0.257923 + 0.257923i) q^{92} +(1.47773 + 9.52976i) q^{93} +7.98043i q^{94} +(-10.9196 - 7.97424i) q^{95} +(-0.997976 + 1.41564i) q^{96} +(-9.72908 - 9.72908i) q^{97} +(-1.37090 + 5.11627i) q^{98} +(8.65746 - 10.1851i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 256 q + 8 q^{3} - 4 q^{7}+O(q^{10}) \) 256 * q + 8 * q^3 - 4 * q^7	\( 256 q + 8 q^{3} - 4 q^{7} - 8 q^{10} - 8 q^{12} + 8 q^{15} - 256 q^{16} - 4 q^{22} - 16 q^{25} - 40 q^{27} - 4 q^{28} - 48 q^{30} + 32 q^{31} - 8 q^{33} + 8 q^{37} - 12 q^{42} - 40 q^{45} + 16 q^{46} - 8 q^{48} - 16 q^{51} + 20 q^{55} + 40 q^{57} + 56 q^{58} - 8 q^{60} - 32 q^{61} + 56 q^{63} + 32 q^{66} - 24 q^{67} + 24 q^{70} + 8 q^{73} - 4 q^{75} + 16 q^{76} - 88 q^{78} - 48 q^{81} + 64 q^{85} - 20 q^{87} - 4 q^{88} - 8 q^{90} - 68 q^{93} + 152 q^{97}+O(q^{100}) \) 256 * q + 8 * q^3 - 4 * q^7 - 8 * q^10 - 8 * q^12 + 8 * q^15 - 256 * q^16 - 4 * q^22 - 16 * q^25 - 40 * q^27 - 4 * q^28 - 48 * q^30 + 32 * q^31 - 8 * q^33 + 8 * q^37 - 12 * q^42 - 40 * q^45 + 16 * q^46 - 8 * q^48 - 16 * q^51 + 20 * q^55 + 40 * q^57 + 56 * q^58 - 8 * q^60 - 32 * q^61 + 56 * q^63 + 32 * q^66 - 24 * q^67 + 24 * q^70 + 8 * q^73 - 4 * q^75 + 16 * q^76 - 88 * q^78 - 48 * q^81 + 64 * q^85 - 20 * q^87 - 4 * q^88 - 8 * q^90 - 68 * q^93 + 152 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more