LMFDB - Embedded newform 390.2.bd.a.253.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [390,2,Mod(7,390)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(390, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 11]))

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

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

chi := DirichletCharacter("390.7");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 390 = 2 \cdot 3 \cdot 5 \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	390.bd (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:	$3.11416567883$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{12})$
Coefficient field:	$\Q(\zeta_{24})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{4} + 1 $ x^8 - x^4 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			253.1
Root			$-0.258819 + 0.965926i$ of defining polynomial
Character	$\chi$	$=$	390.253
Dual form			390.2.bd.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.866025 - 0.500000i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12132 - 0.707107i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.56583 - 2.71209i) q^{7} -1.00000i q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})$	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12132 - 0.707107i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.56583 - 2.71209i) q^{7} -1.00000i q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.19067 - 0.448288i) q^{10} +(-3.99087 + 1.06935i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.53553 + 0.707107i) q^{13} +3.13165i q^{14} +(-1.86603 + 1.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.66925 - 6.22973i) q^{17} -1.00000 q^{18} +(-0.560842 + 2.09309i) q^{19} +(1.67303 + 1.48356i) q^{20} +(2.21441 + 2.21441i) q^{21} +(3.99087 + 1.06935i) q^{22} +(-1.49465 - 5.57812i) q^{23} +(0.258819 + 0.965926i) q^{24} +(4.00000 - 3.00000i) q^{25} +(-2.70831 - 2.38014i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.56583 - 2.71209i) q^{28} +(-7.51179 - 4.33694i) q^{29} +(2.23205 - 0.133975i) q^{30} +(4.54757 - 4.54757i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.57812 - 2.06583i) q^{33} +(-4.56048 + 4.56048i) q^{34} +(-5.23936 - 4.64601i) q^{35} +(0.866025 + 0.500000i) q^{36} +(0.351911 - 0.609528i) q^{37} +(1.53225 - 1.53225i) q^{38} +(-3.59808 + 0.232051i) q^{39} +(-0.707107 - 2.12132i) q^{40} +(-0.133352 - 0.497678i) q^{41} +(-0.810531 - 3.02494i) q^{42} +(-3.38014 - 0.905706i) q^{43} +(-2.92152 - 2.92152i) q^{44} +(1.48356 - 1.67303i) q^{45} +(-1.49465 + 5.57812i) q^{46} +4.69677 q^{47} +(0.258819 - 0.965926i) q^{48} +(-1.40362 + 2.43115i) q^{49} +(-4.96410 + 0.598076i) q^{50} +6.44949i q^{51} +(1.15539 + 3.41542i) q^{52} +(-8.92820 - 8.92820i) q^{53} +(0.965926 - 0.258819i) q^{54} +(-7.70977 + 5.09041i) q^{55} +(-2.71209 + 1.56583i) q^{56} -2.16693i q^{57} +(4.33694 + 7.51179i) q^{58} +(9.64444 + 2.58422i) q^{59} +(-2.00000 - 1.00000i) q^{60} +(4.20648 + 7.28585i) q^{61} +(-6.21209 + 1.66452i) q^{62} +(-2.71209 - 1.56583i) q^{63} -1.00000 q^{64} +(8.00000 - 1.00000i) q^{65} -4.13165 q^{66} +(7.13834 + 4.12132i) q^{67} +(6.22973 - 1.66925i) q^{68} +(2.88745 + 5.00120i) q^{69} +(2.21441 + 6.64324i) q^{70} +(6.47772 + 1.73570i) q^{71} +(-0.500000 - 0.866025i) q^{72} +11.5240i q^{73} +(-0.609528 + 0.351911i) q^{74} +(-3.08725 + 3.93305i) q^{75} +(-2.09309 + 0.560842i) q^{76} +(9.14918 + 9.14918i) q^{77} +(3.23205 + 1.59808i) q^{78} -10.6203i q^{79} +(-0.448288 + 2.19067i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.133352 + 0.497678i) q^{82} -13.1003 q^{83} +(-0.810531 + 3.02494i) q^{84} +(-0.864068 - 14.3956i) q^{85} +(2.47443 + 2.47443i) q^{86} +(8.37832 + 2.24496i) q^{87} +(1.06935 + 3.99087i) q^{88} +(4.02993 + 15.0399i) q^{89} +(-2.12132 + 0.707107i) q^{90} +(-3.61829 - 10.6959i) q^{91} +(4.08346 - 4.08346i) q^{92} +(-3.21561 + 5.56961i) q^{93} +(-4.06753 - 2.34839i) q^{94} +(0.290313 + 4.83669i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-3.60867 + 2.08346i) q^{97} +(2.43115 - 1.40362i) q^{98} +(-2.92152 + 2.92152i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) $ 8 * q + 4 * q^4 - 4 * q^7	$ 8 q + 4 q^{4} - 4 q^{7} - 16 q^{11} - 8 q^{15} - 4 q^{16} + 12 q^{17} - 8 q^{18} - 24 q^{19} + 8 q^{21} + 16 q^{22} + 16 q^{23} + 32 q^{25} + 4 q^{28} - 24 q^{29} + 4 q^{30} - 4 q^{31} - 12 q^{33} - 24 q^{35} + 8 q^{37} - 8 q^{39} + 28 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} + 16 q^{46} + 32 q^{47} - 20 q^{49} - 12 q^{50} - 16 q^{53} - 4 q^{55} + 12 q^{56} - 8 q^{58} + 32 q^{59} - 16 q^{60} - 8 q^{61} - 16 q^{62} + 12 q^{63} - 8 q^{64} + 64 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{70} + 8 q^{71} - 4 q^{72} - 24 q^{74} - 24 q^{76} - 24 q^{77} + 12 q^{78} + 4 q^{81} + 28 q^{82} - 32 q^{83} - 8 q^{84} - 32 q^{85} - 8 q^{86} + 28 q^{87} + 8 q^{88} - 4 q^{89} - 8 q^{91} + 20 q^{92} - 12 q^{94} + 4 q^{95} + 12 q^{97} + 24 q^{98} - 8 q^{99}+O(q^{100}) $ 8 * q + 4 * q^4 - 4 * q^7 - 16 * q^11 - 8 * q^15 - 4 * q^16 + 12 * q^17 - 8 * q^18 - 24 * q^19 + 8 * q^21 + 16 * q^22 + 16 * q^23 + 32 * q^25 + 4 * q^28 - 24 * q^29 + 4 * q^30 - 4 * q^31 - 12 * q^33 - 24 * q^35 + 8 * q^37 - 8 * q^39 + 28 * q^41 - 8 * q^42 - 8 * q^43 - 8 * q^44 + 16 * q^46 + 32 * q^47 - 20 * q^49 - 12 * q^50 - 16 * q^53 - 4 * q^55 + 12 * q^56 - 8 * q^58 + 32 * q^59 - 16 * q^60 - 8 * q^61 - 16 * q^62 + 12 * q^63 - 8 * q^64 + 64 * q^65 - 16 * q^66 + 12 * q^68 + 8 * q^70 + 8 * q^71 - 4 * q^72 - 24 * q^74 - 24 * q^76 - 24 * q^77 + 12 * q^78 + 4 * q^81 + 28 * q^82 - 32 * q^83 - 8 * q^84 - 32 * q^85 - 8 * q^86 + 28 * q^87 + 8 * q^88 - 4 * q^89 - 8 * q^91 + 20 * q^92 - 12 * q^94 + 4 * q^95 + 12 * q^97 + 24 * q^98 - 8 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/390\mathbb{Z}\right)^\times$.

$n$	$131$	$157$	$301$
$\chi(n)$	$1$	$e\left(\frac{3}{4}\right)$	$e\left(\frac{5}{12}\right)$

Coefficient data

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

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

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

$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$2$	−0.866025	−	0.500000i	−0.612372	−	0.353553i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$3$	−0.965926	+	0.258819i	−0.557678	+	0.149429i
$4$	0.500000	+	0.866025i	0.250000	+	0.433013i
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$5$	2.12132	−	0.707107i	0.948683	−	0.316228i
$6$	0.965926	+	0.258819i	0.394338	+	0.105662i
$7$	−1.56583	−	2.71209i	−0.591827	−	1.02507i	−0.993986	−	0.109504i	$-0.965074\pi$
$7$	−1.56583	−	2.71209i	−0.591827	−	1.02507i	0.402160	−	0.915570i	$-0.368260\pi$
$8$		−	1.00000i		−	0.353553i
$9$	0.866025	−	0.500000i	0.288675	−	0.166667i
$10$	−2.19067	−	0.448288i	−0.692751	−	0.141761i
$11$	−3.99087	+	1.06935i	−1.20329	+	0.322421i	−0.804127	−	0.594458i	$-0.797367\pi$
$11$	−3.99087	+	1.06935i	−1.20329	+	0.322421i	−0.399166	+	0.916879i	$0.630700\pi$
$12$	−0.707107	−	0.707107i	−0.204124	−	0.204124i
$13$	3.53553	+	0.707107i	0.980581	+	0.196116i
$13$	3.53553	+	0.707107i	0.980581	+	0.196116i
$14$			3.13165i			0.836969i
$15$	−1.86603	+	1.23205i	−0.481806	+	0.318114i
$16$	−0.500000	+	0.866025i	−0.125000	+	0.216506i
$17$	1.66925	−	6.22973i	0.404853	−	1.51093i	−0.399474	−	0.916744i	$-0.630807\pi$
$17$	1.66925	−	6.22973i	0.404853	−	1.51093i	0.804327	−	0.594187i	$-0.202526\pi$
$18$	−1.00000			−0.235702
$19$	−0.560842	+	2.09309i	−0.128666	+	0.480188i	−0.999944	−	0.0106020i	$-0.996625\pi$
$19$	−0.560842	+	2.09309i	−0.128666	+	0.480188i	0.871278	+	0.490790i	$0.163292\pi$
$20$	1.67303	+	1.48356i	0.374101	+	0.331735i
$21$	2.21441	+	2.21441i	0.483224	+	0.483224i
$22$	3.99087	+	1.06935i	0.850856	+	0.227986i
$23$	−1.49465	−	5.57812i	−0.311656	−	1.16312i	−0.927062	−	0.374907i	$-0.877675\pi$
$23$	−1.49465	−	5.57812i	−0.311656	−	1.16312i	0.615406	−	0.788210i	$-0.288992\pi$
$24$	0.258819	+	0.965926i	0.0528312	+	0.197169i
$25$	4.00000	−	3.00000i	0.800000	−	0.600000i
$26$	−2.70831	−	2.38014i	−0.531143	−	0.466784i
$27$	−0.707107	+	0.707107i	−0.136083	+	0.136083i
$28$	1.56583	−	2.71209i	0.295913	−	0.512537i
$29$	−7.51179	−	4.33694i	−1.39490	−	0.805349i	−0.401052	−	0.916055i	$-0.631355\pi$
$29$	−7.51179	−	4.33694i	−1.39490	−	0.805349i	−0.993853	+	0.110707i	$0.964689\pi$
$30$	2.23205	−	0.133975i	0.407515	−	0.0244603i
$31$	4.54757	−	4.54757i	0.816767	−	0.816767i	−0.168871	−	0.985638i	$-0.554012\pi$
$31$	4.54757	−	4.54757i	0.816767	−	0.816767i	0.985638	+	0.168871i	$0.0540122\pi$
$32$	0.866025	−	0.500000i	0.153093	−	0.0883883i
$33$	3.57812	−	2.06583i	0.622870	−	0.359614i
$34$	−4.56048	+	4.56048i	−0.782116	+	0.782116i
$35$	−5.23936	−	4.64601i	−0.885613	−	0.785318i
$36$	0.866025	+	0.500000i	0.144338	+	0.0833333i
$37$	0.351911	−	0.609528i	0.0578539	−	0.100206i	−0.835648	−	0.549265i	$-0.814908\pi$
$37$	0.351911	−	0.609528i	0.0578539	−	0.100206i	0.893502	+	0.449060i	$0.148241\pi$
$38$	1.53225	−	1.53225i	0.248564	−	0.248564i
$39$	−3.59808	+	0.232051i	−0.576153	+	0.0371579i
$40$	−0.707107	−	2.12132i	−0.111803	−	0.335410i
$41$	−0.133352	−	0.497678i	−0.0208261	−	0.0777242i	0.954731	−	0.297472i	$-0.0961434\pi$
$41$	−0.133352	−	0.497678i	−0.0208261	−	0.0777242i	−0.975557	+	0.219747i	$0.929477\pi$
$42$	−0.810531	−	3.02494i	−0.125068	−	0.466759i
$43$	−3.38014	−	0.905706i	−0.515466	−	0.138119i	−0.00829766	−	0.999966i	$-0.502641\pi$
$43$	−3.38014	−	0.905706i	−0.515466	−	0.138119i	−0.507169	+	0.861847i	$0.669308\pi$
$44$	−2.92152	−	2.92152i	−0.440436	−	0.440436i
$45$	1.48356	−	1.67303i	0.221157	−	0.249401i
$46$	−1.49465	+	5.57812i	−0.220374	+	0.822448i
$47$	4.69677			0.685095			0.342547	−	0.939501i	$-0.388710\pi$
$47$	4.69677			0.685095			0.342547	+	0.939501i	$0.388710\pi$
$48$	0.258819	−	0.965926i	0.0373573	−	0.139419i
$49$	−1.40362	+	2.43115i	−0.200518	+	0.347307i
$50$	−4.96410	+	0.598076i	−0.702030	+	0.0845807i
$51$			6.44949i			0.903109i
$52$	1.15539	+	3.41542i	0.160224	+	0.473633i
$53$	−8.92820	−	8.92820i	−1.22638	−	1.22638i	−0.965322	−	0.261061i	$-0.915928\pi$
$53$	−8.92820	−	8.92820i	−1.22638	−	1.22638i	−0.261061	−	0.965322i	$-0.584072\pi$
$54$	0.965926	−	0.258819i	0.131446	−	0.0352208i
$55$	−7.70977	+	5.09041i	−1.03958	+	0.686390i
$56$	−2.71209	+	1.56583i	−0.362418	+	0.209242i
$57$		−	2.16693i		−	0.287017i
$58$	4.33694	+	7.51179i	0.569467	+	0.986347i
$59$	9.64444	+	2.58422i	1.25560	+	0.336437i	0.824497	−	0.565866i	$-0.191458\pi$
$59$	9.64444	+	2.58422i	1.25560	+	0.336437i	0.431102	+	0.902303i	$0.358125\pi$
$60$	−2.00000	−	1.00000i	−0.258199	−	0.129099i
$61$	4.20648	+	7.28585i	0.538585	+	0.932857i	0.998981	+	0.0451429i	$0.0143743\pi$
$61$	4.20648	+	7.28585i	0.538585	+	0.932857i	−0.460395	+	0.887714i	$0.652292\pi$
$62$	−6.21209	+	1.66452i	−0.788936	+	0.211395i
$63$	−2.71209	−	1.56583i	−0.341691	−	0.197276i
$64$	−1.00000			−0.125000
$65$	8.00000	−	1.00000i	0.992278	−	0.124035i
$66$	−4.13165			−0.508571
$67$	7.13834	+	4.12132i	0.872087	+	0.503499i	0.868041	−	0.496492i	$-0.165379\pi$
$67$	7.13834	+	4.12132i	0.872087	+	0.503499i	0.00404550	+	0.999992i	$0.498712\pi$
$68$	6.22973	−	1.66925i	0.755466	−	0.202426i
$69$	2.88745	+	5.00120i	0.347608	+	0.602074i
$70$	2.21441	+	6.64324i	0.264673	+	0.794019i
$71$	6.47772	+	1.73570i	0.768764	+	0.205990i	0.621825	−	0.783156i	$-0.286391\pi$
$71$	6.47772	+	1.73570i	0.768764	+	0.205990i	0.146938	+	0.989146i	$0.453058\pi$
$72$	−0.500000	−	0.866025i	−0.0589256	−	0.102062i
$73$			11.5240i			1.34878i	0.738377	+	0.674389i	$0.235593\pi$
$73$			11.5240i			1.34878i	−0.738377	+	0.674389i	$0.764407\pi$
$74$	−0.609528	+	0.351911i	−0.0708562	+	0.0409089i
$75$	−3.08725	+	3.93305i	−0.356484	+	0.454150i
$76$	−2.09309	+	0.560842i	−0.240094	+	0.0643330i
$77$	9.14918	+	9.14918i	1.04265	+	1.04265i
$78$	3.23205	+	1.59808i	0.365958	+	0.180946i
$79$		−	10.6203i		−	1.19488i	−0.801913	−	0.597440i	$-0.796184\pi$
$79$		−	10.6203i		−	1.19488i	0.801913	−	0.597440i	$-0.203816\pi$
$80$	−0.448288	+	2.19067i	−0.0501201	+	0.244924i
$81$	0.500000	−	0.866025i	0.0555556	−	0.0962250i
$82$	−0.133352	+	0.497678i	−0.0147263	+	0.0549593i
$83$	−13.1003			−1.43794			−0.718972	−	0.695039i	$-0.755387\pi$
$83$	−13.1003			−1.43794			−0.718972	+	0.695039i	$0.755387\pi$
$84$	−0.810531	+	3.02494i	−0.0884362	+	0.330048i
$85$	−0.864068	−	14.3956i	−0.0937213	−	1.56142i
$86$	2.47443	+	2.47443i	0.266825	+	0.266825i
$87$	8.37832	+	2.24496i	0.898250	+	0.240685i
$88$	1.06935	+	3.99087i	0.113993	+	0.425428i
$89$	4.02993	+	15.0399i	0.427171	+	1.59423i	0.759135	+	0.650933i	$0.225622\pi$
$89$	4.02993	+	15.0399i	0.427171	+	1.59423i	−0.331963	+	0.943292i	$0.607711\pi$
$90$	−2.12132	+	0.707107i	−0.223607	+	0.0745356i
$91$	−3.61829	−	10.6959i	−0.379300	−	1.12123i
$92$	4.08346	−	4.08346i	0.425731	−	0.425731i
$93$	−3.21561	+	5.56961i	−0.333444	+	0.577541i
$94$	−4.06753	−	2.34839i	−0.419533	−	0.242218i
$95$	0.290313	+	4.83669i	0.0297855	+	0.496234i
$96$	−0.707107	+	0.707107i	−0.0721688	+	0.0721688i
$97$	−3.60867	+	2.08346i	−0.366405	+	0.211544i	−0.671887	−	0.740654i	$-0.734516\pi$
$97$	−3.60867	+	2.08346i	−0.366405	+	0.211544i	0.305482	+	0.952198i	$0.401182\pi$
$98$	2.43115	−	1.40362i	0.245583	−	0.141787i
$99$	−2.92152	+	2.92152i	−0.293624	+	0.293624i
$100$	4.59808	+	1.96410i	0.459808	+	0.196410i
$101$	−0.0748321	−	0.0432043i	−0.00744607	−	0.00429899i	0.496272	−	0.868167i	$-0.334702\pi$
$101$	−0.0748321	−	0.0432043i	−0.00744607	−	0.00429899i	−0.503718	+	0.863868i	$0.668035\pi$
$102$	3.22474	−	5.58542i	0.319297	−	0.553039i
$103$	2.91824	−	2.91824i	0.287542	−	0.287542i	−0.548565	−	0.836108i	$-0.684826\pi$
$103$	2.91824	−	2.91824i	0.287542	−	0.287542i	0.836108	+	0.548565i	$0.184826\pi$
$104$	0.707107	−	3.53553i	0.0693375	−	0.346688i
$105$	6.26330	+	3.13165i	0.611236	+	0.305618i
$106$	3.26795	+	12.1962i	0.317411	+	1.18460i
$107$	4.01033	+	14.9668i	0.387693	+	1.44689i	0.833877	+	0.551950i	$0.186116\pi$
$107$	4.01033	+	14.9668i	0.387693	+	1.44689i	−0.446184	+	0.894941i	$0.647217\pi$
$108$	−0.965926	−	0.258819i	−0.0929463	−	0.0249049i
$109$	1.94182	+	1.94182i	0.185993	+	0.185993i	0.793961	−	0.607969i	$-0.208015\pi$
$109$	1.94182	+	1.94182i	0.185993	+	0.185993i	−0.607969	+	0.793961i	$0.708015\pi$
$110$	9.22206	−	0.553536i	0.879289	−	0.0527776i
$111$	−0.182163	+	0.679841i	−0.0172901	+	0.0645276i
$112$	3.13165			0.295913
$113$	−1.45956	+	5.44717i	−0.137304	+	0.512426i	0.862674	+	0.505761i	$0.168788\pi$
$113$	−1.45956	+	5.44717i	−0.137304	+	0.512426i	−0.999978	+	0.00666525i	$0.997878\pi$
$114$	−1.08346	+	1.87662i	−0.101476	+	0.175761i
$115$	−7.11496	−	10.7761i	−0.663473	−	1.00488i
$116$		−	8.67387i		−	0.805349i
$117$	3.41542	−	1.15539i	0.315755	−	0.106816i
$118$	−7.06022	−	7.06022i	−0.649946	−	0.649946i
$119$	−19.5093	+	5.22751i	−1.78842	+	0.479205i
$120$	1.23205	+	1.86603i	0.112470	+	0.170344i
$121$	5.25725	−	3.03528i	0.477932	−	0.275934i
$122$		−	8.41297i		−	0.761674i
$123$	0.257617	+	0.446206i	0.0232285	+	0.0402330i
$124$	6.21209	+	1.66452i	0.557862	+	0.149479i
$125$	6.36396	−	9.19239i	0.569210	−	0.822192i
$126$	1.56583	+	2.71209i	0.139495	+	0.241612i
$127$	−3.79555	+	1.01702i	−0.336801	+	0.0902456i	−0.423256	−	0.906010i	$-0.639113\pi$
$127$	−3.79555	+	1.01702i	−0.336801	+	0.0902456i	0.0864548	+	0.996256i	$0.472446\pi$
$128$	0.866025	+	0.500000i	0.0765466	+	0.0441942i
$129$	3.49938			0.308103
$130$	−7.42820	−	3.13397i	−0.651497	−	0.274868i
$131$	3.87540			0.338595			0.169297	−	0.985565i	$-0.445850\pi$
$131$	3.87540			0.338595			0.169297	+	0.985565i	$0.445850\pi$
$132$	3.57812	+	2.06583i	0.311435	+	0.179807i
$133$	6.55484	−	1.75636i	0.568377	−	0.152296i
$134$	−4.12132	−	7.13834i	−0.356028	−	0.616658i
$135$	−1.00000	+	2.00000i	−0.0860663	+	0.172133i
$136$	−6.22973	−	1.66925i	−0.534195	−	0.143137i
$137$	−3.98307	−	6.89887i	−0.340296	−	0.589410i	0.644191	−	0.764864i	$-0.277194\pi$
$137$	−3.98307	−	6.89887i	−0.340296	−	0.589410i	−0.984488	+	0.175454i	$0.943861\pi$
$138$		−	5.77489i		−	0.491591i
$139$	−9.27123	+	5.35275i	−0.786376	+	0.454014i	−0.838685	−	0.544617i	$-0.816675\pi$
$139$	−9.27123	+	5.35275i	−0.786376	+	0.454014i	0.0523093	+	0.998631i	$0.483342\pi$
$140$	1.40388	−	6.86042i	0.118650	−	0.579811i
$141$	−4.53674	+	1.21561i	−0.382062	+	0.102373i
$142$	−4.74202	−	4.74202i	−0.397941	−	0.397941i
$143$	−14.8660	+	0.958753i	−1.24316	+	0.0801750i
$144$			1.00000i			0.0833333i
$145$	−19.0016	−	3.88839i	−1.57800	−	0.322913i
$146$	5.76198	−	9.98004i	0.476865	−	0.825954i
$147$	0.726569	−	2.71159i	0.0599264	−	0.223648i
$148$	0.703823			0.0578539
$149$	−3.69886	+	13.8043i	−0.303022	+	1.13089i	0.631612	+	0.775284i	$0.282393\pi$
$149$	−3.69886	+	13.8043i	−0.303022	+	1.13089i	−0.934635	+	0.355610i	$0.884273\pi$
$150$	4.64016	−	1.86250i	0.378868	−	0.152073i
$151$	15.7919	+	15.7919i	1.28513	+	1.28513i	0.937711	+	0.347416i	$0.112941\pi$
$151$	15.7919	+	15.7919i	1.28513	+	1.28513i	0.347416	+	0.937711i	$0.387059\pi$
$152$	2.09309	+	0.560842i	0.169772	+	0.0454903i
$153$	−1.66925	−	6.22973i	−0.134951	−	0.503644i
$154$	−3.34883	−	12.4980i	−0.269857	−	1.00712i
$155$	6.43123	−	12.8625i	0.516569	−	1.03314i
$156$	−2.00000	−	3.00000i	−0.160128	−	0.240192i
$157$	−0.584907	+	0.584907i	−0.0466806	+	0.0466806i	−0.730062	−	0.683381i	$-0.760509\pi$
$157$	−0.584907	+	0.584907i	−0.0466806	+	0.0466806i	0.683381	+	0.730062i	$0.260509\pi$
$158$	−5.31017	+	9.19748i	−0.422454	+	0.731712i
$159$	10.9348	+	6.31319i	0.867184	+	0.500669i
$160$	1.48356	−	1.67303i	0.117286	−	0.132265i
$161$	−12.7880	+	12.7880i	−1.00783	+	1.00783i
$162$	−0.866025	+	0.500000i	−0.0680414	+	0.0392837i
$163$	7.61193	−	4.39475i	0.596213	−	0.344223i	−0.171338	−	0.985212i	$-0.554809\pi$
$163$	7.61193	−	4.39475i	0.596213	−	0.344223i	0.767550	+	0.640989i	$0.221476\pi$
$164$	0.364326	−	0.364326i	0.0284490	−	0.0284490i
$165$	6.12957	−	6.91239i	0.477186	−	0.538129i
$166$	11.3452	+	6.55015i	0.880557	+	0.508390i
$167$	3.16390	−	5.48004i	0.244830	−	0.424058i	−0.717254	−	0.696812i	$-0.754601\pi$
$167$	3.16390	−	5.48004i	0.244830	−	0.424058i	0.962084	+	0.272754i	$0.0879345\pi$
$168$	2.21441	−	2.21441i	0.170846	−	0.170846i
$169$	12.0000	+	5.00000i	0.923077	+	0.384615i
$170$	−6.44949	+	12.8990i	−0.494653	+	0.989307i
$171$	0.560842	+	2.09309i	0.0428887	+	0.160063i
$172$	−0.905706	−	3.38014i	−0.0690594	−	0.257733i
$173$	18.4605	+	4.94646i	1.40352	+	0.376073i	0.879608	−	0.475699i	$-0.157805\pi$
$173$	18.4605	+	4.94646i	1.40352	+	0.376073i	0.523914	+	0.851771i	$0.324471\pi$
$174$	−6.13335	−	6.13335i	−0.464968	−	0.464968i
$175$	−14.3996	−	6.15088i	−1.08851	−	0.464963i
$176$	1.06935	−	3.99087i	0.0806053	−	0.300823i
$177$	−9.98466			−0.750493
$178$	4.02993	−	15.0399i	0.302056	−	1.12729i
$179$	−3.85217	+	6.67215i	−0.287925	+	0.498700i	−0.973314	−	0.229476i	$-0.926299\pi$
$179$	−3.85217	+	6.67215i	−0.287925	+	0.498700i	0.685390	+	0.728177i	$0.259632\pi$
$180$	2.19067	+	0.448288i	0.163283	+	0.0334134i
$181$		−	9.94938i		−	0.739532i	−0.929125	−	0.369766i	$-0.879438\pi$
$181$		−	9.94938i		−	0.739532i	0.929125	−	0.369766i	$-0.120562\pi$
$182$	−2.21441	+	11.0721i	−0.164143	+	0.820716i
$183$	−5.94887	−	5.94887i	−0.439753	−	0.439753i
$184$	−5.57812	+	1.49465i	−0.411224	+	0.110187i
$185$	0.315515	−	1.54184i	0.0231971	−	0.113359i
$186$	5.56961	−	3.21561i	0.408383	−	0.235780i
$187$			26.6471i			1.94863i
$188$	2.34839	+	4.06753i	0.171274	+	0.296655i
$189$	3.02494	+	0.810531i	0.220032	+	0.0589575i
$190$	2.16693	−	4.33386i	0.157206	−	0.314411i
$191$	−7.12871	−	12.3473i	−0.515815	−	0.893418i	−0.999831	−	0.0183592i	$-0.994156\pi$
$191$	−7.12871	−	12.3473i	−0.515815	−	0.893418i	0.484016	−	0.875059i	$-0.339178\pi$
$192$	0.965926	−	0.258819i	0.0697097	−	0.0186787i
$193$	−17.6472	−	10.1886i	−1.27027	−	0.733391i	−0.295231	−	0.955426i	$-0.595397\pi$
$193$	−17.6472	−	10.1886i	−1.27027	−	0.733391i	−0.975039	+	0.222035i	$0.928730\pi$
$194$	4.16693			0.299168
$195$	−7.46859	+	3.03648i	−0.534837	+	0.217447i
$196$	−2.80725			−0.200518
$197$	−0.853371	−	0.492694i	−0.0608002	−	0.0351030i	0.469292	−	0.883043i	$-0.344509\pi$
$197$	−0.853371	−	0.492694i	−0.0608002	−	0.0351030i	−0.530092	+	0.847940i	$0.677843\pi$
$198$	3.99087	−	1.06935i	0.283619	−	0.0759954i
$199$	−1.47480	−	2.55443i	−0.104546	−	0.181078i	0.809007	−	0.587799i	$-0.200006\pi$
$199$	−1.47480	−	2.55443i	−0.104546	−	0.181078i	−0.913552	+	0.406721i	$0.866672\pi$
$200$	−3.00000	−	4.00000i	−0.212132	−	0.282843i
$201$	−7.96178	−	2.13335i	−0.561581	−	0.150475i
$202$	0.0432043	+	0.0748321i	0.00303985	+	0.00526517i
$203$			27.1635i			1.90651i
$204$	−5.58542	+	3.22474i	−0.391058	+	0.225777i
$205$	−0.634795	−	0.961440i	−0.0443360	−	0.0671499i
$206$	−3.98638	+	1.06815i	−0.277745	+	0.0744214i
$207$	−4.08346	−	4.08346i	−0.283820	−	0.283820i
$208$	−2.38014	+	2.70831i	−0.165033	+	0.187787i
$209$		−	8.95300i		−	0.619292i
$210$	−3.85835	−	5.84374i	−0.266252	−	0.403257i
$211$	4.82755	−	8.36156i	0.332342	−	0.575633i	−0.650629	−	0.759396i	$-0.725494\pi$
$211$	4.82755	−	8.36156i	0.332342	−	0.575633i	0.982971	+	0.183763i	$0.0588278\pi$
$212$	3.26795	−	12.1962i	0.224444	−	0.837635i
$213$	−6.70623			−0.459503
$214$	4.01033	−	14.9668i	0.274141	−	1.02311i
$215$	−7.81079	+	0.468828i	−0.532691	+	0.0319738i
$216$	0.707107	+	0.707107i	0.0481125	+	0.0481125i
$217$	−19.4541	−	5.21271i	−1.32063	−	0.353862i
$218$	−0.710755	−	2.65257i	−0.0481384	−	0.179655i
$219$	−2.98262	−	11.1313i	−0.201547	−	0.752183i
$220$	−8.26330	−	4.13165i	−0.557112	−	0.278556i
$221$	10.3068	−	20.8451i	0.693309	−	1.40219i
$222$	0.497678	−	0.497678i	0.0334020	−	0.0334020i
$223$	8.21441	−	14.2278i	0.550078	−	0.952763i	−0.448191	−	0.893938i	$-0.647931\pi$
$223$	8.21441	−	14.2278i	0.550078	−	0.952763i	0.998268	−	0.0588246i	$-0.0187353\pi$
$224$	−2.71209	−	1.56583i	−0.181209	−	0.104621i
$225$	1.96410	−	4.59808i	0.130940	−	0.306538i
$226$	3.98760	−	3.98760i	0.265251	−	0.265251i
$227$	9.55620	−	5.51727i	0.634267	−	0.366194i	−0.148136	−	0.988967i	$-0.547327\pi$
$227$	9.55620	−	5.51727i	0.634267	−	0.366194i	0.782403	+	0.622773i	$0.213994\pi$
$228$	1.87662	−	1.08346i	0.124282	−	0.0717542i
$229$	12.5558	−	12.5558i	0.829713	−	0.829713i	−0.157764	−	0.987477i	$-0.550429\pi$
$229$	12.5558	−	12.5558i	0.829713	−	0.829713i	0.987477	+	0.157764i	$0.0504285\pi$
$230$	0.773689	+	12.8898i	0.0510155	+	0.849931i
$231$	−11.2054	−	6.46945i	−0.737262	−	0.425659i
$232$	−4.33694	+	7.51179i	−0.284734	+	0.493173i
$233$	20.1134	−	20.1134i	1.31767	−	1.31767i	0.402055	−	0.915616i	$-0.368296\pi$
$233$	20.1134	−	20.1134i	1.31767	−	1.31767i	0.915616	−	0.402055i	$-0.131704\pi$
$234$	−3.53553	−	0.707107i	−0.231125	−	0.0462250i
$235$	9.96336	−	3.32112i	0.649938	−	0.216646i
$236$	2.58422	+	9.64444i	0.168218	+	0.627800i
$237$	2.74874	+	10.2585i	0.178550	+	0.666358i
$238$	19.5093	+	5.22751i	1.26460	+	0.338849i
$239$	6.54927	+	6.54927i	0.423637	+	0.423637i	0.886454	−	0.462817i	$-0.153161\pi$
$239$	6.54927	+	6.54927i	0.423637	+	0.423637i	−0.462817	+	0.886454i	$0.653161\pi$
$240$	−0.133975	−	2.23205i	−0.00864802	−	0.144078i
$241$	1.88839	−	7.04757i	0.121642	−	0.453974i	−0.878056	−	0.478558i	$-0.841160\pi$
$241$	1.88839	−	7.04757i	0.121642	−	0.453974i	0.999698	+	0.0245845i	$0.00782627\pi$
$242$	−6.07055			−0.390230
$243$	−0.258819	+	0.965926i	−0.0166032	+	0.0619642i
$244$	−4.20648	+	7.28585i	−0.269293	+	0.466428i
$245$	−1.25845	+	6.14975i	−0.0803997	+	0.392893i
$246$		−	0.515234i		−	0.0328501i
$247$	−3.46292	+	7.00362i	−0.220340	+	0.445630i
$248$	−4.54757	−	4.54757i	−0.288771	−	0.288771i
$249$	12.6539	−	3.39060i	0.801909	−	0.214871i
$250$	−10.1075	+	4.77886i	−0.639257	+	0.302242i
$251$	6.28768	−	3.63019i	0.396875	−	0.229136i	−0.288260	−	0.957552i	$-0.593077\pi$
$251$	6.28768	−	3.63019i	0.396875	−	0.229136i	0.685135	+	0.728416i	$0.259743\pi$
$252$		−	3.13165i		−	0.197276i
$253$	11.9299	+	20.6632i	0.750028	+	1.29909i
$254$	3.79555	+	1.01702i	0.238154	+	0.0638133i
$255$	4.56048	+	13.6814i	0.285588	+	0.856765i
$256$	−0.500000	−	0.866025i	−0.0312500	−	0.0541266i
$257$	12.3238	−	3.30215i	0.768736	−	0.205982i	0.146923	−	0.989148i	$-0.453063\pi$
$257$	12.3238	−	3.30215i	0.768736	−	0.205982i	0.621813	+	0.783166i	$0.286396\pi$
$258$	−3.03055	−	1.74969i	−0.188674	−	0.108931i
$259$	−2.20413			−0.136958
$260$	4.86603	+	6.42820i	0.301778	+	0.398660i
$261$	−8.67387			−0.536899
$262$	−3.35619	−	1.93770i	−0.207346	−	0.119711i
$263$	−11.7261	+	3.14199i	−0.723061	+	0.193744i	−0.601537	−	0.798845i	$-0.705445\pi$
$263$	−11.7261	+	3.14199i	−0.723061	+	0.193744i	−0.121524	+	0.992588i	$0.538778\pi$
$264$	−2.06583	−	3.57812i	−0.127143	−	0.220218i
$265$	−25.2528	−	12.6264i	−1.55127	−	0.775633i
$266$	−6.55484	−	1.75636i	−0.401903	−	0.107690i
$267$	−7.78522	−	13.4844i	−0.476448	−	0.825232i
$268$			8.24264i			0.503499i
$269$	4.11892	−	2.37806i	0.251135	−	0.144993i	−0.369149	−	0.929370i	$-0.620351\pi$
$269$	4.11892	−	2.37806i	0.251135	−	0.144993i	0.620284	+	0.784378i	$0.287017\pi$
$270$	1.86603	−	1.23205i	0.113563	−	0.0749802i
$271$	13.7404	−	3.68173i	0.834670	−	0.223649i	0.183920	−	0.982941i	$-0.441121\pi$
$271$	13.7404	−	3.68173i	0.834670	−	0.223649i	0.650750	+	0.759292i	$0.274455\pi$
$272$	4.56048	+	4.56048i	0.276520	+	0.276520i
$273$	6.26330	+	9.39496i	0.379072	+	0.568609i
$274$			7.96613i			0.481252i
$275$	−12.7554	+	16.2500i	−0.769181	+	0.979913i
$276$	−2.88745	+	5.00120i	−0.173804	+	0.301037i
$277$	−7.71864	+	28.8064i	−0.463768	+	1.73081i	0.197173	+	0.980369i	$0.436824\pi$
$277$	−7.71864	+	28.8064i	−0.463768	+	1.73081i	−0.660941	+	0.750438i	$0.729843\pi$
$278$	10.7055			0.642073
$279$	1.66452	−	6.21209i	0.0996525	−	0.371908i
$280$	−4.64601	+	5.23936i	−0.277652	+	0.313111i
$281$	11.8878	+	11.8878i	0.709165	+	0.709165i	0.966360	−	0.257195i	$-0.0827982\pi$
$281$	11.8878	+	11.8878i	0.709165	+	0.709165i	−0.257195	+	0.966360i	$0.582798\pi$
$282$	4.53674	+	1.21561i	0.270159	+	0.0723888i
$283$	−0.572643	−	2.13713i	−0.0340401	−	0.127039i	0.946815	−	0.321779i	$-0.104281\pi$
$283$	−0.572643	−	2.13713i	−0.0340401	−	0.127039i	−0.980855	+	0.194739i	$0.937614\pi$
$284$	1.73570	+	6.47772i	0.102995	+	0.384382i
$285$	−1.53225	−	4.59675i	−0.0907627	−	0.272288i
$286$	13.3537	+	6.60270i	0.789621	+	0.390426i
$287$	−1.14094	+	1.14094i	−0.0673476	+	0.0673476i
$288$	0.500000	−	0.866025i	0.0294628	−	0.0510310i
$289$	−21.3007	−	12.2980i	−1.25298	−	0.723409i
$290$	14.5117	+	12.8682i	0.852154	+	0.755649i
$291$	2.94646	−	2.94646i	0.172725	−	0.172725i
$292$	−9.98004	+	5.76198i	−0.584038	+	0.337194i
$293$	−9.15320	+	5.28460i	−0.534735	+	0.308730i	−0.742943	−	0.669355i	$-0.766571\pi$
$293$	−9.15320	+	5.28460i	−0.534735	+	0.308730i	0.208207	+	0.978085i	$0.433237\pi$
$294$	−1.98502	+	1.98502i	−0.115769	+	0.115769i
$295$	22.2863	−	1.33769i	1.29756	−	0.0778834i
$296$	−0.609528	−	0.351911i	−0.0354281	−	0.0204544i
$297$	2.06583	−	3.57812i	0.119871	−	0.207623i
$298$	10.1055	−	10.1055i	0.585394	−	0.585394i
$299$	−1.34007	−	20.7785i	−0.0774981	−	1.20165i
$300$	−4.94975	−	0.707107i	−0.285774	−	0.0408248i
$301$	2.83636	+	10.5854i	0.163485	+	0.610134i
$302$	−5.78024	−	21.5721i	−0.332615	−	1.24134i
$303$	0.0834643	+	0.0223642i	0.00479490	+	0.00128479i
$304$	−1.53225	−	1.53225i	−0.0878806	−	0.0878806i
$305$	14.0752	+	12.4812i	0.805942	+	0.714670i
$306$	−1.66925	+	6.22973i	−0.0954247	+	0.356130i
$307$	−16.4767			−0.940376			−0.470188	−	0.882566i	$-0.655814\pi$
$307$	−16.4767			−0.940376			−0.470188	+	0.882566i	$0.655814\pi$
$308$	−3.34883	+	12.4980i	−0.190818	+	0.712141i
$309$	−2.06350	+	3.57409i	−0.117389	+	0.203323i
$310$	−12.0008	+	7.92360i	−0.681602	+	0.450030i
$311$		−	1.66274i		−	0.0942855i	−0.998888	−	0.0471427i	$-0.984988\pi$
$311$		−	1.66274i		−	0.0942855i	0.998888	−	0.0471427i	$-0.0150116\pi$
$312$	0.232051	+	3.59808i	0.0131373	+	0.203701i
$313$	9.47871	+	9.47871i	0.535769	+	0.535769i	0.922283	−	0.386515i	$-0.126321\pi$
$313$	9.47871	+	9.47871i	0.535769	+	0.535769i	−0.386515	+	0.922283i	$0.626321\pi$
$314$	0.798997	−	0.214091i	0.0450900	−	0.0120818i
$315$	−6.86042	−	1.40388i	−0.386541	−	0.0790998i
$316$	9.19748	−	5.31017i	0.517399	−	0.298720i
$317$			16.6556i			0.935472i	0.883868	+	0.467736i	$0.154930\pi$
$317$			16.6556i			0.935472i	−0.883868	+	0.467736i	$0.845070\pi$
$318$	−6.31319	−	10.9348i	−0.354026	−	0.613192i
$319$	34.6163	+	9.27541i	1.93814	+	0.519323i
$320$	−2.12132	+	0.707107i	−0.118585	+	0.0395285i
$321$	−7.74737	−	13.4188i	−0.432416	−	0.748966i
$322$	17.4687	−	4.68073i	0.973494	−	0.260847i
$323$	12.1032	+	6.98779i	0.673441	+	0.388811i
$324$	1.00000			0.0555556
$325$	16.2635	−	7.77817i	0.902134	−	0.431455i
$326$	−8.78950			−0.486806
$327$	−2.37823	−	1.37307i	−0.131517	−	0.0759311i
$328$	−0.497678	+	0.133352i	−0.0274797	+	0.00736315i
$329$	−7.35433	−	12.7381i	−0.405458	−	0.702273i
$330$	−8.76456	+	2.92152i	−0.482473	+	0.160824i
$331$	−28.6759	−	7.68369i	−1.57617	−	0.422334i	−0.638433	−	0.769678i	$-0.720417\pi$
$331$	−28.6759	−	7.68369i	−1.57617	−	0.422334i	−0.937738	+	0.347344i	$0.887084\pi$
$332$	−6.55015	−	11.3452i	−0.359486	−	0.622648i
$333$		−	0.703823i		−	0.0385693i
$334$	−5.48004	+	3.16390i	−0.299854	+	0.173121i
$335$	18.0569	+	3.69507i	0.986554	+	0.201883i
$336$	−3.02494	+	0.810531i	−0.165024	+	0.0442181i
$337$	−11.8379	−	11.8379i	−0.644850	−	0.644850i	0.306893	−	0.951744i	$-0.400710\pi$
$337$	−11.8379	−	11.8379i	−0.644850	−	0.644850i	−0.951744	+	0.306893i	$0.900710\pi$
$338$	−7.89230	−	10.3301i	−0.429285	−	0.561885i
$339$		−	5.63932i		−	0.306286i
$340$	12.0349	−	7.94610i	0.652685	−	0.430938i
$341$	−13.2858	+	23.0117i	−0.719467	+	1.24615i
$342$	0.560842	−	2.09309i	0.0303269	−	0.113181i
$343$	−13.1302			−0.708967
$344$	−0.905706	+	3.38014i	−0.0488324	+	0.182245i
$345$	9.66158	+	8.56742i	0.520162	+	0.461254i
$346$	−13.5140	−	13.5140i	−0.726517	−	0.726517i
$347$	10.1891	+	2.73016i	0.546980	+	0.146563i	0.521718	−	0.853118i	$-0.325291\pi$
$347$	10.1891	+	2.73016i	0.546980	+	0.146563i	0.0252619	+	0.999681i	$0.491958\pi$
$348$	2.24496	+	8.37832i	0.120343	+	0.449125i
$349$	−1.55923	−	5.81914i	−0.0834639	−	0.311491i	0.911555	−	0.411178i	$-0.134883\pi$
$349$	−1.55923	−	5.81914i	−0.0834639	−	0.311491i	−0.995019	+	0.0996868i	$0.968216\pi$
$350$	9.39496	+	12.5266i	0.502182	+	0.669575i
$351$	−3.00000	+	2.00000i	−0.160128	+	0.106752i
$352$	−2.92152	+	2.92152i	−0.155718	+	0.155718i
$353$	−9.15623	+	15.8591i	−0.487337	+	0.844093i	−0.999894	−	0.0145607i	$-0.995365\pi$
$353$	−9.15623	+	15.8591i	−0.487337	+	0.844093i	0.512557	+	0.858653i	$0.328698\pi$
$354$	8.64697	+	4.99233i	0.459581	+	0.265339i
$355$	14.9686	−	0.898464i	0.794453	−	0.0476855i
$356$	−11.0100	+	11.0100i	−0.583527	+	0.583527i
$357$	17.4916	−	10.0988i	0.925754	−	0.534484i
$358$	6.67215	−	3.85217i	0.352634	−	0.203593i
$359$	−19.1263	+	19.1263i	−1.00945	+	1.00945i	−0.00949146	+	0.999955i	$0.503021\pi$
$359$	−19.1263	+	19.1263i	−1.00945	+	1.00945i	−0.999955	+	0.00949146i	$0.996979\pi$
$360$	−1.67303	−	1.48356i	−0.0881766	−	0.0781907i
$361$	12.3880	+	7.15221i	0.652000	+	0.376432i
$362$	−4.97469	+	8.61642i	−0.261464	+	0.452869i
$363$	−4.29253	+	4.29253i	−0.225299	+	0.225299i
$364$	7.45377	−	8.48148i	0.390684	−	0.444550i
$365$	8.14867	+	24.4460i	0.426521	+	1.27956i
$366$	2.17744	+	8.12630i	0.113816	+	0.424769i
$367$	7.09397	+	26.4751i	0.370302	+	1.38199i	0.860089	+	0.510145i	$0.170408\pi$
$367$	7.09397	+	26.4751i	0.370302	+	1.38199i	−0.489786	+	0.871843i	$0.662925\pi$
$368$	5.57812	+	1.49465i	0.290779	+	0.0779141i
$369$	−0.364326	−	0.364326i	−0.0189660	−	0.0189660i
$370$	−1.04417	+	1.17752i	−0.0542836	+	0.0612163i
$371$	−10.2341	+	38.1941i	−0.531327	+	1.98294i
$372$	−6.43123			−0.333444
$373$	−6.06381	+	22.6305i	−0.313972	+	1.17176i	0.610970	+	0.791654i	$0.290780\pi$
$373$	−6.06381	+	22.6305i	−0.313972	+	1.17176i	−0.924942	+	0.380107i	$0.875887\pi$
$374$	13.3235	−	23.0770i	0.688943	−	1.19328i
$375$	−3.76795	+	10.5263i	−0.194576	+	0.543575i
$376$		−	4.69677i		−	0.242218i
$377$	−23.4915	−	20.6450i	−1.20987	−	1.06327i
$378$	−2.21441	−	2.21441i	−0.113897	−	0.113897i
$379$	19.7078	−	5.28069i	1.01232	−	0.271251i	0.285722	−	0.958313i	$-0.407767\pi$
$379$	19.7078	−	5.28069i	1.01232	−	0.271251i	0.726599	+	0.687062i	$0.241100\pi$
$380$	−4.04354	+	2.66977i	−0.207429	+	0.136956i
$381$	3.40300	−	1.96472i	0.174341	−	0.100656i
$382$			14.2574i			0.729473i
$383$	−10.6392	−	18.4277i	−0.543639	−	0.941610i	−0.998691	−	0.0511451i	$-0.983713\pi$
$383$	−10.6392	−	18.4277i	−0.543639	−	0.941610i	0.455053	−	0.890465i	$-0.349620\pi$
$384$	−0.965926	−	0.258819i	−0.0492922	−	0.0132078i
$385$	25.8778	+	12.9389i	1.31885	+	0.659427i
$386$	10.1886	+	17.6472i	0.518586	+	0.898216i
$387$	−3.38014	+	0.905706i	−0.171822	+	0.0460396i
$388$	−3.60867	−	2.08346i	−0.183202	−	0.105772i
$389$	17.7570			0.900318			0.450159	−	0.892948i	$-0.351367\pi$
$389$	17.7570			0.900318			0.450159	+	0.892948i	$0.351367\pi$
$390$	7.98623	+	1.10463i	0.404398	+	0.0559349i
$391$	−37.2451			−1.88357
$392$	2.43115	+	1.40362i	0.122791	+	0.0708937i
$393$	−3.74334	+	1.00303i	−0.188827	+	0.0505960i
$394$	0.492694	+	0.853371i	0.0248216	+	0.0429922i
$395$	−7.50971	−	22.5291i	−0.377855	−	1.13356i
$396$	−3.99087	−	1.06935i	−0.200549	−	0.0537369i
$397$	−9.82270	−	17.0134i	−0.492987	−	0.853879i	0.506980	−	0.861958i	$-0.330762\pi$
$397$	−9.82270	−	17.0134i	−0.492987	−	0.853879i	−0.999967	+	0.00807905i	$0.997428\pi$
$398$			2.94960i			0.147850i
$399$	−5.87691	+	3.39303i	−0.294213	+	0.169864i
$400$	0.598076	+	4.96410i	0.0299038	+	0.248205i
$401$	34.7009	−	9.29807i	1.73288	−	0.464323i	0.752035	−	0.659123i	$-0.229072\pi$
$401$	34.7009	−	9.29807i	1.73288	−	0.464323i	0.980843	+	0.194800i	$0.0624058\pi$
$402$	5.82843	+	5.82843i	0.290696	+	0.290696i
$403$	19.2937	−	12.8625i	0.961087	−	0.640725i
$404$		−	0.0864086i		−	0.00429899i
$405$	0.448288	−	2.19067i	0.0222756	−	0.108855i
$406$	13.5818	−	23.5243i	0.674052	−	1.16749i
$407$	−0.752633	+	2.80887i	−0.0373066	+	0.139230i
$408$	6.44949			0.319297
$409$	−2.37032	+	8.84615i	−0.117205	+	0.437414i	−0.999442	−	0.0333904i	$-0.989370\pi$
$409$	−2.37032	+	8.84615i	−0.117205	+	0.437414i	0.882238	+	0.470804i	$0.156036\pi$
$410$	0.0690283	+	1.15003i	0.00340906	+	0.0567959i
$411$	5.63291	+	5.63291i	0.277851	+	0.277851i
$412$	3.98638	+	1.06815i	0.196395	+	0.0526239i
$413$	−8.09288	−	30.2030i	−0.398225	−	1.48619i
$414$	1.49465	+	5.57812i	0.0734581	+	0.274149i
$415$	−27.7899	+	9.26330i	−1.36415	+	0.454718i
$416$	3.41542	−	1.15539i	0.167455	−	0.0566479i
$417$	7.56993	−	7.56993i	0.370701	−	0.370701i
$418$	−4.47650	+	7.75352i	−0.218953	+	0.379237i
$419$	4.69474	+	2.71051i	0.229353	+	0.132417i	0.610273	−	0.792191i	$-0.291060\pi$
$419$	4.69474	+	2.71051i	0.229353	+	0.132417i	−0.380921	+	0.924608i	$0.624393\pi$
$420$	0.419562	+	6.99001i	0.0204725	+	0.341077i
$421$	−5.60456	+	5.60456i	−0.273150	+	0.273150i	−0.830367	−	0.557217i	$-0.811869\pi$
$421$	−5.60456	+	5.60456i	−0.273150	+	0.273150i	0.557217	+	0.830367i	$0.311869\pi$
$422$	−8.36156	+	4.82755i	−0.407034	+	0.235001i
$423$	4.06753	−	2.34839i	0.197770	−	0.114182i
$424$	−8.92820	+	8.92820i	−0.433592	+	0.433592i
$425$	−12.0122	−	29.9267i	−0.582676	−	1.45166i
$426$	5.80776	+	3.35311i	0.281387	+	0.162459i
$427$	13.1732	−	22.8167i	0.637498	−	1.10418i
$428$	−10.9564	+	10.9564i	−0.529599	+	0.529599i
$429$	14.1113	−	4.77369i	0.681300	−	0.230476i
$430$	6.99876	+	3.49938i	0.337510	+	0.168755i
$431$	−8.63808	−	32.2377i	−0.416082	−	1.55284i	−0.782659	−	0.622450i	$-0.786137\pi$
$431$	−8.63808	−	32.2377i	−0.416082	−	1.55284i	0.366578	−	0.930387i	$-0.380529\pi$
$432$	−0.258819	−	0.965926i	−0.0124524	−	0.0464731i
$433$	−21.1652	−	5.67120i	−1.01713	−	0.272540i	−0.288527	−	0.957472i	$-0.593166\pi$
$433$	−21.1652	−	5.67120i	−1.01713	−	0.272540i	−0.728608	+	0.684931i	$0.759832\pi$
$434$	14.2414	+	14.2414i	0.683609	+	0.683609i
$435$	19.3605	−	1.16208i	0.928266	−	0.0557174i
$436$	−0.710755	+	2.65257i	−0.0340390	+	0.127035i
$437$	12.5138			0.598615
$438$	−2.98262	+	11.1313i	−0.142515	+	0.531874i
$439$	8.07571	−	13.9875i	0.385433	−	0.667589i	−0.606396	−	0.795162i	$-0.707386\pi$
$439$	8.07571	−	13.9875i	0.385433	−	0.667589i	0.991829	+	0.127573i	$0.0407189\pi$
$440$	5.09041	+	7.70977i	0.242676	+	0.367549i
$441$			2.80725i			0.133678i
$442$	−19.3485	+	12.8990i	−0.920313	+	0.613542i
$443$	5.67511	+	5.67511i	0.269633	+	0.269633i	0.828952	−	0.559319i	$-0.188937\pi$
$443$	5.67511	+	5.67511i	0.269633	+	0.269633i	−0.559319	+	0.828952i	$0.688937\pi$
$444$	−0.679841	+	0.182163i	−0.0322638	+	0.00864506i
$445$	19.1836	+	29.0548i	0.909389	+	1.37733i
$446$	−14.2278	+	8.21441i	−0.673705	+	0.388964i
$447$		−	14.2913i		−	0.675955i
$448$	1.56583	+	2.71209i	0.0739783	+	0.128134i
$449$	−14.3730	−	3.85125i	−0.678306	−	0.181752i	−0.0968126	−	0.995303i	$-0.530865\pi$
$449$	−14.3730	−	3.85125i	−0.678306	−	0.181752i	−0.581493	+	0.813551i	$0.697531\pi$
$450$	−4.00000	+	3.00000i	−0.188562	+	0.141421i
$451$	1.06438	+	1.84357i	0.0501199	+	0.0868102i
$452$	−5.44717	+	1.45956i	−0.256213	+	0.0686521i
$453$	−19.3411	−	11.1666i	−0.908722	−	0.524651i
$454$	−11.0345			−0.517877
$455$	−15.2387	−	20.1309i	−0.714401	−	0.943751i
$456$	−2.16693			−0.101476
$457$	−1.60508	−	0.926692i	−0.0750824	−	0.0433488i	0.461989	−	0.886886i	$-0.347136\pi$
$457$	−1.60508	−	0.926692i	−0.0750824	−	0.0433488i	−0.537071	+	0.843537i	$0.680469\pi$
$458$	−17.1516	+	4.59575i	−0.801441	+	0.214745i
$459$	3.22474	+	5.58542i	0.150518	+	0.260705i
$460$	5.77489	−	11.5498i	0.269256	−	0.538511i
$461$	−12.1452	−	3.25429i	−0.565657	−	0.151567i	−0.0353532	−	0.999375i	$-0.511256\pi$
$461$	−12.1452	−	3.25429i	−0.565657	−	0.151567i	−0.530304	+	0.847807i	$0.677922\pi$
$462$	6.46945	+	11.2054i	0.300986	+	0.521323i
$463$			21.0119i			0.976505i	0.872702	+	0.488253i	$0.162366\pi$
$463$			21.0119i			0.976505i	−0.872702	+	0.488253i	$0.837634\pi$
$464$	7.51179	−	4.33694i	0.348726	−	0.201337i
$465$	−2.88304	+	14.0887i	−0.133698	+	0.653348i
$466$	−27.4754	+	7.36200i	−1.27277	+	0.341038i
$467$	19.0053	+	19.0053i	0.879461	+	0.879461i	0.993479	−	0.114017i	$-0.0363719\pi$
$467$	19.0053	+	19.0053i	0.879461	+	0.879461i	−0.114017	+	0.993479i	$0.536372\pi$
$468$	2.70831	+	2.38014i	0.125192	+	0.110022i
$469$		−	25.8131i		−	1.19194i
$470$	−10.2891	−	2.10551i	−0.474600	−	0.0971198i
$471$	0.413591	−	0.716361i	0.0190573	−	0.0330082i
$472$	2.58422	−	9.64444i	0.118948	−	0.443921i
$473$	14.4582			0.664789
$474$	2.74874	−	10.2585i	0.126254	−	0.471186i
$475$	4.03591	+	10.0549i	0.185180	+	0.461350i
$476$	−14.2818	−	14.2818i	−0.654607	−	0.654607i
$477$	−12.1962	−	3.26795i	−0.558423	−	0.149629i
$478$	−2.39720	−	8.94646i	−0.109645	−	0.409202i
$479$	0.706287	+	2.63590i	0.0322711	+	0.120437i	0.980182	−	0.198097i	$-0.0634761\pi$
$479$	0.706287	+	2.63590i	0.0322711	+	0.120437i	−0.947911	+	0.318534i	$0.896809\pi$
$480$	−1.00000	+	2.00000i	−0.0456435	+	0.0912871i
$481$	1.67520	−	1.90617i	0.0763824	−	0.0869139i
$482$	−5.15918	+	5.15918i	−0.234994	+	0.234994i
$483$	9.04248	−	15.6620i	0.411447	−	0.712647i
$484$	5.25725	+	3.03528i	0.238966	+	0.137967i
$485$	−6.18191	+	6.97141i	−0.280706	+	0.316555i
$486$	0.707107	−	0.707107i	0.0320750	−	0.0320750i
$487$	27.9172	−	16.1180i	1.26505	−	0.730377i	0.291003	−	0.956722i	$-0.406011\pi$
$487$	27.9172	−	16.1180i	1.26505	−	0.730377i	0.974047	+	0.226345i	$0.0726778\pi$
$488$	7.28585	−	4.20648i	0.329815	−	0.190419i
$489$	−6.21512	+	6.21512i	−0.281057	+	0.281057i
$490$	4.16473	−	4.69662i	0.188143	−	0.212172i
$491$	−21.9402	−	12.6672i	−0.990148	−	0.571662i	−0.0848294	−	0.996395i	$-0.527035\pi$
$491$	−21.9402	−	12.6672i	−0.990148	−	0.571662i	−0.905318	+	0.424733i	$0.860368\pi$
$492$	−0.257617	+	0.446206i	−0.0116143	+	0.0201165i
$493$	−39.5570	+	39.5570i	−1.78156	+	1.78156i
$494$	6.50079	−	4.33386i	0.292484	−	0.194989i
$495$	−4.13165	+	8.26330i	−0.185704	+	0.371408i
$496$	1.66452	+	6.21209i	0.0747394	+	0.278931i
$497$	−5.43561	−	20.2860i	−0.243820	−	0.909950i
$498$	−12.6539	−	3.39060i	−0.567035	−	0.151937i
$499$	−6.07571	−	6.07571i	−0.271986	−	0.271986i	0.557913	−	0.829899i	$-0.311602\pi$
$499$	−6.07571	−	6.07571i	−0.271986	−	0.271986i	−0.829899	+	0.557913i	$0.811602\pi$
$500$	11.1428	+	0.915158i	0.498322	+	0.0409271i
$501$	−1.63776	+	6.11219i	−0.0731696	+	0.273073i
$502$	−7.26039			−0.324047
$503$	1.19016	−	4.44174i	0.0530666	−	0.198047i	−0.934303	−	0.356479i	$-0.883977\pi$
$503$	1.19016	−	4.44174i	0.0530666	−	0.198047i	0.987370	+	0.158432i	$0.0506438\pi$
$504$	−1.56583	+	2.71209i	−0.0697474	+	0.120806i
$505$	−0.189293	−	0.0387359i	−0.00842342	−	0.00172373i
$506$		−	23.8598i		−	1.06070i
$507$	−12.8852	−	1.72380i	−0.572252	−	0.0765567i
$508$	−2.77854	−	2.77854i	−0.123278	−	0.123278i
$509$	27.8585	−	7.46466i	1.23481	−	0.330865i	0.418357	−	0.908283i	$-0.362606\pi$
$509$	27.8585	−	7.46466i	1.23481	−	0.330865i	0.816449	+	0.577418i	$0.195940\pi$
$510$	2.89123	−	14.1287i	0.128026	−	0.625630i
$511$	31.2540	−	18.0445i	1.38260	−	0.798242i
$512$			1.00000i			0.0441942i
$513$	−1.08346	−	1.87662i	−0.0478361	−	0.0828546i
$514$	−12.3238	−	3.30215i	−0.543579	−	0.145651i
$515$	4.12701	−	8.25402i	0.181858	−	0.363715i
$516$	1.74969	+	3.03055i	0.0770258	+	0.133413i
$517$	−18.7442	+	5.02250i	−0.824370	+	0.220889i
$518$	1.90883	+	1.10206i	0.0838692	+	0.0484219i
$519$	−19.1117			−0.838909
$520$	−1.00000	−	8.00000i	−0.0438529	−	0.350823i
$521$	−29.1375			−1.27654			−0.638268	−	0.769814i	$-0.720349\pi$
$521$	−29.1375			−1.27654			−0.638268	+	0.769814i	$0.720349\pi$
$522$	7.51179	+	4.33694i	0.328782	+	0.189822i
$523$	16.7269	−	4.48196i	0.731416	−	0.195982i	0.126156	−	0.992010i	$-0.459736\pi$
$523$	16.7269	−	4.48196i	0.731416	−	0.195982i	0.605260	+	0.796028i	$0.293069\pi$
$524$	1.93770	+	3.35619i	0.0846487	+	0.146616i
$525$	15.5009	+	2.21441i	0.676514	+	0.0966449i
$526$	11.7261	+	3.14199i	0.511281	+	0.136997i
$527$	−20.7391	−	35.9211i	−0.903408	−	1.56475i
$528$			4.13165i			0.179807i
$529$	−8.96281	+	5.17468i	−0.389687	+	0.224986i
$530$	15.5563	+	23.5612i	0.675725	+	1.02343i
$531$	9.64444	−	2.58422i	0.418533	−	0.112146i
$532$	4.79847	+	4.79847i	0.208040	+	0.208040i
$533$	−0.119560	−	1.85385i	−0.00517874	−	0.0802992i
$534$			15.5704i			0.673799i
$535$	19.0903	+	28.9136i	0.825346	+	1.25004i
$536$	4.12132	−	7.13834i	0.178014	−	0.308329i
$537$	1.99403	−	7.44182i	0.0860487	−	0.321138i
$538$	−4.75611			−0.205051
$539$	3.00193	−	11.2034i	0.129302	−	0.482563i
$540$	−2.23205	+	0.133975i	−0.0960522	+	0.00576535i
$541$	−3.79216	−	3.79216i	−0.163037	−	0.163037i	0.620873	−	0.783911i	$-0.286778\pi$
$541$	−3.79216	−	3.79216i	−0.163037	−	0.163037i	−0.783911	+	0.620873i	$0.786778\pi$
$542$	−13.7404	−	3.68173i	−0.590201	−	0.158144i
$543$	2.57509	+	9.61037i	0.110508	+	0.412420i
$544$	−1.66925	−	6.22973i	−0.0715685	−	0.267097i
$545$	5.49229	+	2.74615i	0.235264	+	0.117632i
$546$	−0.726702	−	11.2679i	−0.0311000	−	0.482223i
$547$	16.1356	−	16.1356i	0.689907	−	0.689907i	−0.272304	−	0.962211i	$-0.587786\pi$
$547$	16.1356	−	16.1356i	0.689907	−	0.689907i	0.962211	+	0.272304i	$0.0877857\pi$
$548$	3.98307	−	6.89887i	0.170148	−	0.294705i
$549$	7.28585	+	4.20648i	0.310952	+	0.179528i
$550$	19.1715	−	7.69521i	0.817477	−	0.328125i
$551$	13.2905	−	13.2905i	0.566196	−	0.566196i
$552$	5.00120	−	2.88745i	0.212865	−	0.122898i
$553$	−28.8033	+	16.6296i	−1.22484	+	0.707162i
$554$	21.0877	−	21.0877i	0.895931	−	0.895931i
$555$	0.0942944	+	1.57097i	0.00400257	+	0.0666839i
$556$	−9.27123	−	5.35275i	−0.393188	−	0.227007i
$557$	−7.08228	+	12.2669i	−0.300086	+	0.519764i	−0.976155	−	0.217074i	$-0.930349\pi$
$557$	−7.08228	+	12.2669i	−0.300086	+	0.519764i	0.676069	+	0.736838i	$0.263682\pi$
$558$	−4.54757	+	4.54757i	−0.192514	+	0.192514i
$559$	−11.3102	−	5.59227i	−0.478369	−	0.236528i
$560$	6.64324	−	2.21441i	0.280728	−	0.0935760i
$561$	−6.89676	−	25.7391i	−0.291182	−	1.08670i
$562$	−4.35122	−	16.2390i	−0.183545	−	0.685001i
$563$	27.2447	+	7.30019i	1.14823	+	0.307666i	0.782254	−	0.622959i	$-0.214070\pi$
$563$	27.2447	+	7.30019i	1.14823	+	0.307666i	0.365972	+	0.930626i	$0.380737\pi$
$564$	−3.32112	−	3.32112i	−0.139844	−	0.139844i
$565$	0.755526	+	12.5873i	0.0317852	+	0.529550i
$566$	−0.572643	+	2.13713i	−0.0240700	+	0.0898305i
$567$	−3.13165			−0.131517
$568$	1.73570	−	6.47772i	0.0728283	−	0.271799i
$569$	5.17914	−	8.97053i	0.217121	−	0.376064i	−0.736806	−	0.676104i	$-0.763667\pi$
$569$	5.17914	−	8.97053i	0.217121	−	0.376064i	0.953927	+	0.300040i	$0.0970001\pi$
$570$	−0.971408	+	4.74703i	−0.0406878	+	0.198831i
$571$		−	35.4765i		−	1.48465i	−0.670042	−	0.742323i	$-0.733724\pi$
$571$		−	35.4765i		−	1.48465i	0.670042	−	0.742323i	$-0.266276\pi$
$572$	−8.26330	−	12.3950i	−0.345506	−	0.518259i
$573$	10.0815	+	10.0815i	0.421161	+	0.421161i
$574$	1.55855	−	0.417613i	0.0650528	−	0.0174308i
$575$	−22.7130	−	17.8285i	−0.947196	−	0.743500i
$576$	−0.866025	+	0.500000i	−0.0360844	+	0.0208333i
$577$			5.58381i			0.232457i	0.993222	+	0.116229i	$0.0370805\pi$
$577$			5.58381i			0.232457i	−0.993222	+	0.116229i	$0.962919\pi$
$578$	12.2980	+	21.3007i	0.511528	+	0.885992i
$579$	19.6828	+	5.27400i	0.817991	+	0.219180i
$580$	−6.13335	−	18.4001i	−0.254674	−	0.764021i
$581$	20.5128	+	35.5292i	0.851014	+	1.47400i
$582$	−4.02494	+	1.07848i	−0.166839	+	0.0447045i
$583$	45.1787	+	26.0839i	1.87111	+	1.08029i
$584$	11.5240			0.476865
$585$	6.42820	−	4.86603i	0.265773	−	0.201185i
$586$	10.5692			0.436610
$587$	−2.09538	−	1.20977i	−0.0864856	−	0.0499325i	0.456133	−	0.889911i	$-0.349234\pi$
$587$	−2.09538	−	1.20977i	−0.0864856	−	0.0499325i	−0.542619	+	0.839979i	$0.682567\pi$
$588$	2.71159	−	0.726569i	0.111824	−	0.0299632i
$589$	6.96801	+	12.0689i	0.287112	+	0.497292i
$590$	−19.9693	−	9.98466i	−0.822124	−	0.411062i
$591$	0.951812	+	0.255037i	0.0391523	+	0.0104908i
$592$	0.351911	+	0.609528i	0.0144635	+	0.0250515i
$593$		−	34.8515i		−	1.43118i	−0.698520	−	0.715591i	$-0.746158\pi$
$593$		−	34.8515i		−	1.43118i	0.698520	−	0.715591i	$-0.253842\pi$
$594$	−3.57812	+	2.06583i	−0.146812	+	0.0847619i
$595$	−37.6892	+	24.8844i	−1.54510	+	1.02016i
$596$	−13.8043	+	3.69886i	−0.565447	+	0.151511i
$597$	2.08568	+	2.08568i	0.0853612	+	0.0853612i
$598$	−9.22872	+	18.6647i	−0.377390	+	0.763258i
$599$			45.1749i			1.84580i	0.385043	+	0.922899i	$0.374187\pi$
$599$			45.1749i			1.84580i	−0.385043	+	0.922899i	$0.625813\pi$
$600$	3.93305	+	3.08725i	0.160566	+	0.126036i
$601$	−9.74604	+	16.8806i	−0.397549	+	0.688576i	−0.993423	−	0.114503i	$-0.963473\pi$
$601$	−9.74604	+	16.8806i	−0.397549	+	0.688576i	0.595874	+	0.803078i	$0.296806\pi$
$602$	2.83636	−	10.5854i	0.115601	−	0.431430i
$603$	8.24264			0.335666
$604$	−5.78024	+	21.5721i	−0.235195	+	0.877758i
$605$	9.00605	−	10.1562i	0.366148	−	0.412910i
$606$	−0.0611001	−	0.0611001i	−0.00248202	−	0.00248202i
$607$	−17.7121	−	4.74593i	−0.718911	−	0.192632i	−0.119225	−	0.992867i	$-0.538041\pi$
$607$	−17.7121	−	4.74593i	−0.718911	−	0.192632i	−0.599686	+	0.800236i	$0.704708\pi$
$608$	0.560842	+	2.09309i	0.0227452	+	0.0848861i
$609$	−7.03044	−	26.2380i	−0.284888	−	1.06322i
$610$	−5.94887	−	17.8466i	−0.240863	−	0.722588i
$611$	16.6056	+	3.32112i	0.671791	+	0.134358i
$612$	4.56048	−	4.56048i	0.184346	−	0.184346i
$613$	6.99415	−	12.1142i	0.282491	−	0.489289i	−0.689506	−	0.724280i	$-0.742173\pi$
$613$	6.99415	−	12.1142i	0.282491	−	0.489289i	0.971998	+	0.234990i	$0.0755059\pi$
$614$	14.2693	+	8.23836i	0.575860	+	0.332473i
$615$	0.862003	+	0.764383i	0.0347593	+	0.0308229i
$616$	9.14918	−	9.14918i	0.368631	−	0.368631i
$617$	−19.6020	+	11.3172i	−0.789146	+	0.455614i	−0.839662	−	0.543109i	$-0.817247\pi$
$617$	−19.6020	+	11.3172i	−0.789146	+	0.455614i	0.0505155	+	0.998723i	$0.483914\pi$
$618$	3.57409	−	2.06350i	0.143771	−	0.0830063i
$619$	7.11480	−	7.11480i	0.285968	−	0.285968i	−0.549516	−	0.835484i	$-0.685188\pi$
$619$	7.11480	−	7.11480i	0.285968	−	0.285968i	0.835484	+	0.549516i	$0.185188\pi$
$620$	14.3548	−	0.861621i	0.576504	−	0.0346035i
$621$	5.00120	+	2.88745i	0.200691	+	0.115869i
$622$	−0.831371	+	1.43998i	−0.0333350	+	0.0577378i
$623$	34.4794	−	34.4794i	1.38139	−	1.38139i
$624$	1.59808	−	3.23205i	0.0639742	−	0.129386i
$625$	7.00000	−	24.0000i	0.280000	−	0.960000i
$626$	−3.46945	−	12.9482i	−0.138667	−	0.517513i
$627$	2.31721	+	8.64793i	0.0925403	+	0.345365i
$628$	−0.798997	−	0.214091i	−0.0318835	−	0.00854315i
$629$	−3.20977	−	3.20977i	−0.127982	−	0.127982i
$630$	5.23936	+	4.64601i	0.208741	+	0.185101i
$631$	−1.15350	+	4.30493i	−0.0459202	+	0.171376i	−0.985078	−	0.172110i	$-0.944941\pi$
$631$	−1.15350	+	4.30493i	−0.0459202	+	0.171376i	0.939157	+	0.343487i	$0.111608\pi$
$632$	−10.6203			−0.422454
$633$	−2.49892	+	9.32611i	−0.0993232	+	0.370679i
$634$	8.32780	−	14.4242i	0.330739	−	0.572857i
$635$	−7.33245	+	4.84128i	−0.290979	+	0.192120i
$636$			12.6264i			0.500669i
$637$	−6.68164	+	7.60289i	−0.264736	+	0.301238i
$638$	−25.3409	−	25.3409i	−1.00326	−	1.00326i
$639$	6.47772	−	1.73570i	0.256255	−	0.0686632i
$640$	2.19067	+	0.448288i	0.0865939	+	0.0177201i
$641$	−5.18600	+	2.99414i	−0.204835	+	0.118261i	−0.598909	−	0.800817i	$-0.704399\pi$
$641$	−5.18600	+	2.99414i	−0.204835	+	0.118261i	0.394074	+	0.919079i	$0.371065\pi$
$642$			15.4947i			0.611528i
$643$	−15.5207	−	26.8826i	−0.612076	−	1.06015i	−0.990890	−	0.134673i	$-0.957001\pi$
$643$	−15.5207	−	26.8826i	−0.612076	−	1.06015i	0.378814	−	0.925473i	$-0.376332\pi$
$644$	−17.4687	−	4.68073i	−0.688364	−	0.184447i
$645$	7.42330	−	2.47443i	0.292292	−	0.0974307i
$646$	−6.98779	−	12.1032i	−0.274931	−	0.476194i
$647$	−1.66268	+	0.445515i	−0.0653668	+	0.0175150i	−0.291354	−	0.956615i	$-0.594106\pi$
$647$	−1.66268	+	0.445515i	−0.0653668	+	0.0175150i	0.225987	+	0.974130i	$0.427439\pi$
$648$	−0.866025	−	0.500000i	−0.0340207	−	0.0196419i
$649$	−41.2531			−1.61933
$650$	−17.9737	−	1.39563i	−0.704985	−	0.0547412i
$651$	20.1404			0.789364
$652$	7.61193	+	4.39475i	0.298106	+	0.172112i
$653$	−19.2230	+	5.15079i	−0.752255	+	0.201566i	−0.614518	−	0.788903i	$-0.710649\pi$
$653$	−19.2230	+	5.15079i	−0.752255	+	0.201566i	−0.137737	+	0.990469i	$0.543983\pi$
$654$	1.37307	+	2.37823i	0.0536914	+	0.0929963i
$655$	8.22096	−	2.74032i	0.321219	−	0.107073i
$656$	0.497678	+	0.133352i	0.0194311	+	0.00520654i
$657$	5.76198	+	9.98004i	0.224796	+	0.389358i
$658$			14.7087i			0.573403i
$659$	−17.8129	+	10.2843i	−0.693892	+	0.400619i	−0.805068	−	0.593182i	$-0.797871\pi$
$659$	−17.8129	+	10.2843i	−0.693892	+	0.400619i	0.111177	+	0.993801i	$0.464538\pi$
$660$	9.05109	+	1.85217i	0.352313	+	0.0720956i
$661$	2.22010	−	0.594874i	0.0863519	−	0.0231379i	−0.215384	−	0.976529i	$-0.569100\pi$
$661$	2.22010	−	0.594874i	0.0863519	−	0.0231379i	0.301736	+	0.953391i	$0.402434\pi$
$662$	20.9922	+	20.9922i	0.815886	+	0.815886i
$663$	−4.56048	+	22.8024i	−0.177114	+	0.885571i
$664$			13.1003i			0.508390i
$665$	12.6630	−	8.36078i	0.491049	−	0.324217i
$666$	−0.351911	+	0.609528i	−0.0136363	+	0.0236187i
$667$	−12.9644	+	48.3839i	−0.501984	+	1.87343i
$668$	6.32780			0.244830
$669$	−4.25209	+	15.8690i	−0.164395	+	0.613532i
$670$	−13.7902	−	12.2285i	−0.532762	−	0.472428i
$671$	−24.5787	−	24.5787i	−0.948848	−	0.948848i
$672$	3.02494	+	0.810531i	0.116690	+	0.0312669i
$673$	−12.6768	−	47.3105i	−0.488655	−	1.82369i	−0.563004	−	0.826454i	$-0.690355\pi$
$673$	−12.6768	−	47.3105i	−0.488655	−	1.82369i	0.0743489	−	0.997232i	$-0.476312\pi$
$674$	4.33296	+	16.1708i	0.166900	+	0.622878i
$675$	−0.707107	+	4.94975i	−0.0272166	+	0.190516i
$676$	1.66987	+	12.8923i	0.0642259	+	0.495858i
$677$	21.8321	−	21.8321i	0.839075	−	0.839075i	−0.149662	−	0.988737i	$-0.547819\pi$
$677$	21.8321	−	21.8321i	0.839075	−	0.839075i	0.988737	+	0.149662i	$0.0478187\pi$
$678$	−2.81966	+	4.88380i	−0.108288	+	0.187561i
$679$	11.3011	+	6.52469i	0.433696	+	0.250394i
$680$	−14.3956	+	0.864068i	−0.552046	+	0.0331355i
$681$	−7.80260	+	7.80260i	−0.298996	+	0.298996i
$682$	23.0117	−	13.2858i	0.881163	−	0.508740i
$683$	3.96489	−	2.28913i	0.151712	−	0.0875911i	−0.422222	−	0.906492i	$-0.638750\pi$
$683$	3.96489	−	2.28913i	0.151712	−	0.0875911i	0.573934	+	0.818901i	$0.305416\pi$
$684$	−1.53225	+	1.53225i	−0.0585870	+	0.0585870i
$685$	−13.3276	−	11.8183i	−0.509221	−	0.451553i
$686$	11.3711	+	6.56512i	0.434152	+	0.250658i
$687$	−8.87832	+	15.3777i	−0.338729	+	0.586696i
$688$	2.47443	−	2.47443i	0.0943369	−	0.0943369i
$689$	−25.2528	−	37.8792i	−0.962054	−	1.44308i
$690$	−4.08346	−	12.2504i	−0.155455	−	0.466364i
$691$	−0.487899	−	1.82086i	−0.0185605	−	0.0692689i	0.956024	−	0.293287i	$-0.0947492\pi$
$691$	−0.487899	−	1.82086i	−0.0185605	−	0.0692689i	−0.974585	+	0.224018i	$0.928083\pi$
$692$	4.94646	+	18.4605i	0.188036	+	0.701761i
$693$	12.4980	+	3.34883i	0.474760	+	0.127212i
$694$	−7.45894	−	7.45894i	−0.283138	−	0.283138i
$695$	−15.8823	+	17.9106i	−0.602450	+	0.679390i
$696$	2.24496	−	8.37832i	0.0850951	−	0.317579i
$697$	−3.32300			−0.125867
$698$	−1.55923	+	5.81914i	−0.0590179	+	0.220258i
$699$	−14.2223	+	24.6337i	−0.537937	+	0.931734i
$700$	−1.87297	−	15.5458i	−0.0707915	−	0.587578i
$701$			19.3315i			0.730140i	0.930980	+	0.365070i	$0.118955\pi$
$701$			19.3315i			0.730140i	−0.930980	+	0.365070i	$0.881045\pi$
$702$	3.59808	−	0.232051i	0.135801	−	0.00875819i
$703$	1.07843	+	1.07843i	0.0406739	+	0.0406739i
$704$	3.99087	−	1.06935i	0.150412	−	0.0403027i
$705$	−8.76430	+	5.78666i	−0.330083	+	0.217938i
$706$	15.8591	−	9.15623i	0.596864	−	0.344599i
$707$			0.270602i			0.0101770i
$708$	−4.99233	−	8.64697i	−0.187623	−	0.324973i
$709$	47.6526	+	12.7685i	1.78963	+	0.479531i	0.992284	−	0.123988i	$-0.0395685\pi$
$709$	47.6526	+	12.7685i	1.78963	+	0.479531i	0.797349	+	0.603519i	$0.206235\pi$
$710$	−13.4125	−	6.70623i	−0.503360	−	0.251680i
$711$	−5.31017	−	9.19748i	−0.199147	−	0.344932i
$712$	15.0399	−	4.02993i	0.563644	−	0.151028i
$713$	−32.1639	−	18.5698i	−1.20455	−	0.695445i
$714$	−20.1976			−0.755875
$715$	−30.8576	+	12.5457i	−1.15401	+	0.469182i
$716$	−7.70434			−0.287925
$717$	−8.02118	−	4.63103i	−0.299556	−	0.172949i
$718$	26.1270	−	7.00070i	0.975050	−	0.261264i
$719$	1.82789	+	3.16599i	0.0681687	+	0.118072i	0.898095	−	0.439801i	$-0.144951\pi$
$719$	1.82789	+	3.16599i	0.0681687	+	0.118072i	−0.829927	+	0.557873i	$0.811618\pi$
$720$	0.707107	+	2.12132i	0.0263523	+	0.0790569i
$721$	−12.4840	−	3.34507i	−0.464927	−	0.124577i
$722$	−7.15221	−	12.3880i	−0.266178	−	0.461033i
$723$			7.29618i			0.271348i
$724$	8.61642	−	4.97469i	0.320227	−	0.184883i
$725$	−43.0580	+	5.18764i	−1.59913	+	0.192664i
$726$	5.86370	−	1.57117i	0.217622	−	0.0583118i
$727$	37.4846	+	37.4846i	1.39023	+	1.39023i	0.824799	+	0.565426i	$0.191288\pi$
$727$	37.4846	+	37.4846i	1.39023	+	1.39023i	0.565426	+	0.824799i	$0.308712\pi$
$728$	−10.6959	+	3.61829i	−0.396416	+	0.134103i
$729$		−	1.00000i		−	0.0370370i
$730$	5.16605	−	25.2452i	0.191204	−	0.934367i
$731$	−11.2846	+	19.5455i	−0.417376	+	0.722916i
$732$	2.17744	−	8.12630i	0.0804804	−	0.300357i
$733$	23.6692			0.874242			0.437121	−	0.899403i	$-0.355998\pi$
$733$	23.6692			0.874242			0.437121	+	0.899403i	$0.355998\pi$
$734$	7.09397	−	26.4751i	0.261843	−	0.977212i
$735$	−0.376100	−	6.26592i	−0.0138727	−	0.231122i
$736$	−4.08346	−	4.08346i	−0.150518	−	0.150518i
$737$	−32.8953	−	8.81427i	−1.21171	−	0.324678i
$738$	0.133352	+	0.497678i	0.00490877	+	0.0183198i
$739$	3.49448	+	13.0416i	0.128547	+	0.479743i	0.999941	−	0.0108400i	$-0.00345056\pi$
$739$	3.49448	+	13.0416i	0.128547	+	0.479743i	−0.871395	+	0.490583i	$0.836784\pi$
$740$	1.49303	−	0.497678i	0.0548850	−	0.0182950i
$741$	1.53225	−	7.66125i	0.0562886	−	0.281443i
$742$	27.9600	−	27.9600i	1.02644	−	1.02644i
$743$	−8.75456	+	15.1633i	−0.321174	+	0.556289i	−0.980730	−	0.195366i	$-0.937411\pi$
$743$	−8.75456	+	15.1633i	−0.321174	+	0.556289i	0.659557	+	0.751655i	$0.270744\pi$
$744$	5.56961	+	3.21561i	0.204192	+	0.117890i
$745$	1.91467	+	31.8989i	0.0701480	+	1.16868i
$746$	16.5666	−	16.5666i	0.606548	−	0.606548i
$747$	−11.3452	+	6.55015i	−0.415099	+	0.239657i
$748$	−23.0770	+	13.3235i	−0.843780	+	0.487156i
$749$	34.3117	−	34.3117i	1.25372	−	1.25372i
$750$	8.52628	−	7.23205i	0.311336	−	0.264077i
$751$	41.3055	+	23.8478i	1.50726	+	0.870217i	0.999964	+	0.00844558i	$0.00268834\pi$
$751$	41.3055	+	23.8478i	1.50726	+	0.870217i	0.507296	+	0.861772i	$0.330645\pi$
$752$	−2.34839	+	4.06753i	−0.0856369	+	0.148327i
$753$	−5.13387	+	5.13387i	−0.187089	+	0.187089i
$754$	10.0217	+	29.6249i	0.364970	+	1.07887i
$755$	44.6663	+	22.3331i	1.62557	+	0.812786i
$756$	0.810531	+	3.02494i	0.0294787	+	0.110016i
$757$	−3.91699	−	14.6184i	−0.142365	−	0.531315i	−0.999859	−	0.0168196i	$-0.994646\pi$
$757$	−3.91699	−	14.6184i	−0.142365	−	0.531315i	0.857493	−	0.514496i	$-0.172021\pi$
$758$	−19.7078	−	5.28069i	−0.715819	−	0.191803i
$759$	−16.8715	−	16.8715i	−0.612395	−	0.612395i
$760$	4.83669	−	0.290313i	0.175445	−	0.0105308i
$761$	−8.03025	+	29.9693i	−0.291097	+	1.08639i	0.653172	+	0.757210i	$0.273438\pi$
$761$	−8.03025	+	29.9693i	−0.291097	+	1.08639i	−0.944268	+	0.329177i	$0.893229\pi$
$762$	−3.92945			−0.142349
$763$	2.22584	−	8.30694i	0.0805808	−	0.300731i
$764$	7.12871	−	12.3473i	0.257908	−	0.446709i
$765$	−7.94610	−	12.0349i	−0.287292	−	0.435123i
$766$			21.2784i			0.768821i
$767$	32.2709	+	15.9562i	1.16524	+	0.576147i
$768$	0.707107	+	0.707107i	0.0255155	+	0.0255155i
$769$	−35.7577	+	9.58125i	−1.28946	+	0.345509i	−0.837454	−	0.546508i	$-0.815957\pi$
$769$	−35.7577	+	9.58125i	−1.28946	+	0.345509i	−0.452002	+	0.892017i	$0.649290\pi$
$770$	−15.9414	−	24.1443i	−0.574488	−	0.870101i
$771$	−11.0492	+	6.37926i	−0.397927	+	0.229743i
$772$		−	20.3772i		−	0.733391i
$773$	11.2290	+	19.4492i	0.403880	+	0.699541i	0.994190	−	0.107636i	$-0.0343280\pi$
$773$	11.2290	+	19.4492i	0.403880	+	0.699541i	−0.590310	+	0.807176i	$0.700995\pi$
$774$	3.38014	+	0.905706i	0.121497	+	0.0325549i
$775$	4.54757	−	31.8330i	0.163353	−	1.14347i
$776$	2.08346	+	3.60867i	0.0747920	+	0.129544i
$777$	2.12902	−	0.570470i	0.0763783	−	0.0204655i
$778$	−15.3781	−	8.87852i	−0.551330	−	0.318310i
$779$	1.11648			0.0400019
$780$	−6.36396	−	4.94975i	−0.227866	−	0.177229i
$781$	−27.7078			−0.991463
$782$	32.2552	+	18.6225i	1.15344	+	0.665941i
$783$	8.37832	−	2.24496i	0.299417	−	0.0802284i
$784$	−1.40362	−	2.43115i	−0.0501294	−	0.0868267i
$785$	−0.827183	+	1.65437i	−0.0295234	+	0.0590468i
$786$	3.74334	+	1.00303i	0.133521	+	0.0357768i
$787$	−17.1466	−	29.6988i	−0.611211	−	1.05865i	−0.991037	−	0.133590i	$-0.957349\pi$
$787$	−17.1466	−	29.6988i	−0.611211	−	1.05865i	0.379826	−	0.925058i	$-0.375984\pi$
$788$		−	0.985388i		−	0.0351030i
$789$	10.5133	−	6.06987i	0.374284	−	0.216093i
$790$	−4.76097	+	23.2657i	−0.169388	+	0.827755i
$791$	17.0586	−	4.57085i	0.606535	−	0.162521i
$792$	2.92152	+	2.92152i	0.103812	+	0.103812i
$793$	9.72030	+	28.7338i	0.345178	+	1.02037i
$794$			19.6454i			0.697189i
$795$	27.6603	+	5.66025i	0.981008	+	0.200749i
$796$	1.47480	−	2.55443i	0.0522728	−	0.0905392i
$797$	−2.32379	+	8.67251i	−0.0823129	+	0.307196i	−0.994792	−	0.101928i	$-0.967499\pi$
$797$	−2.32379	+	8.67251i	−0.0823129	+	0.307196i	0.912479	+	0.409124i	$0.134166\pi$
$798$	6.78607			0.240224
$799$	7.84009	−	29.2596i	0.277363	−	1.03513i
$800$	1.96410	−	4.59808i	0.0694415	−	0.162567i
$801$	11.0100	+	11.0100i	0.389018	+	0.389018i
$802$	−34.7009	−	9.29807i	−1.22533	−	0.328326i
$803$	−12.3231	−	45.9906i	−0.434874	−	1.62297i
$804$	−2.13335	−	7.96178i	−0.0752375	−	0.280790i
$805$	−18.0850	+	36.1699i	−0.637411	+	1.27482i
$806$	−23.1401	+	1.49237i	−0.815074	+	0.0525666i
$807$	−3.36308	+	3.36308i	−0.118386	+	0.118386i
$808$	−0.0432043	+	0.0748321i	−0.00151992	+	0.00263258i
$809$	3.15982	+	1.82432i	0.111093	+	0.0641398i	0.554517	−	0.832172i	$-0.312903\pi$
$809$	3.15982	+	1.82432i	0.111093	+	0.0641398i	−0.443424	+	0.896312i	$0.646236\pi$
$810$	−1.48356	+	1.67303i	−0.0521271	+	0.0587844i
$811$	−12.5110	+	12.5110i	−0.439321	+	0.439321i	−0.891784	−	0.452462i	$-0.850546\pi$
$811$	−12.5110	+	12.5110i	−0.439321	+	0.439321i	0.452462	+	0.891784i	$0.350546\pi$
$812$	−23.5243	+	13.5818i	−0.825542	+	0.476627i
$813$	−12.3193	+	7.11255i	−0.432057	+	0.249448i
$814$	2.05623	−	2.05623i	0.0720709	−	0.0720709i
$815$	13.0398	−	14.7051i	0.456764	−	0.515098i
$816$	−5.58542	−	3.22474i	−0.195529	−	0.112889i
$817$	3.79145	−	6.56699i	0.132646	−	0.229750i
$818$	6.47583	−	6.47583i	0.226422	−	0.226422i
$819$	−8.48148	−	7.45377i	−0.296367	−	0.260456i
$820$	0.515234	−	1.03047i	0.0179928	−	0.0359855i
$821$	4.52479	+	16.8868i	0.157916	+	0.589352i	0.998838	+	0.0481950i	$0.0153469\pi$
$821$	4.52479	+	16.8868i	0.157916	+	0.589352i	−0.840922	+	0.541157i	$0.817986\pi$
$822$	−2.06179	−	7.69469i	−0.0719131	−	0.268383i
$823$	−17.8126	−	4.77286i	−0.620907	−	0.166372i	−0.0653670	−	0.997861i	$-0.520822\pi$
$823$	−17.8126	−	4.77286i	−0.620907	−	0.166372i	−0.555540	+	0.831490i	$0.687488\pi$
$824$	−2.91824	−	2.91824i	−0.101662	−	0.101662i
$825$	8.11499	−	18.9977i	0.282528	−	0.661413i
$826$	−8.09288	+	30.2030i	−0.281587	+	1.05090i
$827$	37.3071			1.29730			0.648648	−	0.761088i	$-0.275335\pi$
$827$	37.3071			1.29730			0.648648	+	0.761088i	$0.275335\pi$
$828$	1.49465	−	5.57812i	0.0519427	−	0.193853i
$829$	3.93285	−	6.81189i	0.136593	−	0.236587i	−0.789612	−	0.613607i	$-0.789718\pi$
$829$	3.93285	−	6.81189i	0.136593	−	0.236587i	0.926205	+	0.377020i	$0.123051\pi$
$830$	28.6984	+	5.87270i	0.996137	+	0.203844i
$831$		−	29.8225i		−	1.03453i
$832$	−3.53553	−	0.707107i	−0.122573	−	0.0245145i
$833$	12.8024	+	12.8024i	0.443577	+	0.443577i
$834$	−10.3407	+	2.77079i	−0.358070	+	0.0959445i
$835$	2.83668	−	13.8621i	0.0981673	−	0.479719i
$836$	7.75352	−	4.47650i	0.268161	−	0.154823i
$837$			6.43123i			0.222296i
$838$	−2.71051	−	4.69474i	−0.0936329	−	0.162177i
$839$	−23.3587	−	6.25895i	−0.806433	−	0.216083i	−0.168026	−	0.985782i	$-0.553739\pi$
$839$	−23.3587	−	6.25895i	−0.806433	−	0.216083i	−0.638406	+	0.769699i	$0.720406\pi$
$840$	3.13165	−	6.26330i	0.108052	−	0.216105i
$841$	23.1180	+	40.0416i	0.797173	+	1.38074i
$842$	7.65597	−	2.05141i	0.263842	−	0.0706963i
$843$	−14.5595	−	8.40592i	−0.501455	−	0.289515i
$844$	9.65509			0.332342
$845$	28.9914	+	2.12132i	0.997334	+	0.0729756i
$846$	−4.69677			−0.161478
$847$	−16.4639	−	9.50543i	−0.565706	−	0.326610i
$848$	12.1962	−	3.26795i	0.418818	−	0.112222i
$849$	1.10626	+	1.91610i	0.0379668	+	0.0657605i
$850$	−4.56048	+	31.9233i	−0.156423	+	1.09496i
$851$	−3.92601	−	1.05197i	−0.134582	−	0.0360611i
$852$	−3.35311	−	5.80776i	−0.114876	−	0.198971i
$853$			25.7188i			0.880594i	0.897852	+	0.440297i	$0.145127\pi$
$853$			25.7188i			0.880594i	−0.897852	+	0.440297i	$0.854873\pi$
$854$	−22.8167	+	13.1732i	−0.780773	+	0.450779i
$855$	2.66977	+	4.04354i	0.0913041	+	0.138286i
$856$	14.9668	−	4.01033i	0.511553	−	0.137070i
$857$	−35.8169	−	35.8169i	−1.22348	−	1.22348i	−0.966385	−	0.257098i	$-0.917234\pi$
$857$	−35.8169	−	35.8169i	−1.22348	−	1.22348i	−0.257098	−	0.966385i	$-0.582766\pi$
$858$	−14.6076	−	2.92152i	−0.498695	−	0.0997390i
$859$			16.2706i			0.555146i	0.960705	+	0.277573i	$0.0895300\pi$
$859$			16.2706i			0.555146i	−0.960705	+	0.277573i	$0.910470\pi$
$860$	−4.31141	−	6.52993i	−0.147018	−	0.222669i
$861$	0.806767	−	1.39736i	0.0274945	−	0.0476220i
$862$	−8.63808	+	32.2377i	−0.294214	+	1.09802i
$863$	35.4102			1.20538			0.602689	−	0.797976i	$-0.294096\pi$
$863$	35.4102			1.20538			0.602689	+	0.797976i	$0.294096\pi$
$864$	−0.258819	+	0.965926i	−0.00880520	+	0.0328615i
$865$	42.6582	−	2.56048i	1.45042	−	0.0870589i
$866$	15.4940	+	15.4940i	0.526508	+	0.526508i
$867$	23.7578	+	6.36589i	0.806858	+	0.216197i
$868$	−5.21271	−	19.4541i	−0.176931	−	0.660315i
$869$	11.3569	+	42.3844i	0.385255	+	1.43779i
$870$	−17.3477	−	8.67387i	−0.588143	−	0.294072i
$871$	22.3236	+	19.6186i	0.756407	+	0.664752i
$872$	1.94182	−	1.94182i	0.0657583	−	0.0657583i
$873$	−2.08346	+	3.60867i	−0.0705146	+	0.122135i
$874$	−10.8372	−	6.25689i	−0.366575	−	0.211642i
$875$	−34.8954	−	2.86596i	−1.17968	−	0.0968870i
$876$	8.14867	−	8.14867i	0.275318	−	0.275318i
$877$	16.9687	−	9.79691i	0.572994	−	0.330818i	−0.185350	−	0.982672i	$-0.559342\pi$
$877$	16.9687	−	9.79691i	0.572994	−	0.330818i	0.758344	+	0.651854i	$0.226009\pi$
$878$	−13.9875	+	8.07571i	−0.472057	+	0.272542i
$879$	7.47355	−	7.47355i	0.252077	−	0.252077i
$880$	−0.553536	−	9.22206i	−0.0186597	−	0.310876i
$881$	15.0999	+	8.71795i	0.508730	+	0.293715i	0.732311	−	0.680970i	$-0.238442\pi$
$881$	15.0999	+	8.71795i	0.508730	+	0.293715i	−0.223582	+	0.974685i	$0.571775\pi$
$882$	1.40362	−	2.43115i	0.0472625	−	0.0818610i
$883$	−0.0146247	+	0.0146247i	−0.000492161	+	0.000492161i	−0.707353	−	0.706861i	$-0.750111\pi$
$883$	−0.0146247	+	0.0146247i	−0.000492161	+	0.000492161i	0.706861	+	0.707353i	$0.250111\pi$
$884$	23.2058	−	1.49661i	0.780494	−	0.0503364i
$885$	−21.1807	+	7.06022i	−0.711980	+	0.237327i
$886$	−2.07724	−	7.75235i	−0.0697861	−	0.260445i
$887$	7.19696	+	26.8594i	0.241650	+	0.901851i	0.975038	+	0.222040i	$0.0712716\pi$
$887$	7.19696	+	26.8594i	0.241650	+	0.901851i	−0.733387	+	0.679811i	$0.762062\pi$
$888$	0.679841	+	0.182163i	0.0228140	+	0.00611298i
$889$	8.70142	+	8.70142i	0.291836	+	0.291836i
$890$	−2.08604	−	34.7540i	−0.0699244	−	1.16496i
$891$	−1.06935	+	3.99087i	−0.0358246	+	0.133699i
$892$	16.4288			0.550078
$893$	−2.63415	+	9.83078i	−0.0881485	+	0.328975i
$894$	−7.14564	+	12.3766i	−0.238986	+	0.413936i
$895$	−3.45376	+	16.8777i	−0.115446	+	0.564158i
$896$		−	3.13165i		−	0.104621i
$897$	6.67228	+	19.7237i	0.222781	+	0.658554i
$898$	10.5218	+	10.5218i	0.351117	+	0.351117i
$899$	−53.8829	+	14.4379i	−1.79709	+	0.481530i
$900$	4.96410	−	0.598076i	0.165470	−	0.0199359i
$901$	−70.5237	+	40.7169i	−2.34948	+	1.35648i
$902$		−	2.12877i		−	0.0708802i
$903$	−5.47942	−	9.49063i	−0.182344	−	0.315828i
$904$	5.44717	+	1.45956i	0.181170	+	0.0485444i
$905$	−7.03528	−	21.1058i	−0.233860	−	0.701581i
$906$	11.1666	+	19.3411i	0.370984	+	0.642564i
$907$	−1.57473	+	0.421948i	−0.0522881	+	0.0140106i	−0.284868	−	0.958567i	$-0.591950\pi$
$907$	−1.57473	+	0.421948i	−0.0522881	+	0.0140106i	0.232580	+	0.972577i	$0.425283\pi$
$908$	9.55620	+	5.51727i	0.317134	+	0.183097i
$909$	−0.0864086			−0.00286599
$910$	3.13165	+	25.0532i	0.103813	+	0.830506i
$911$	8.17584			0.270878			0.135439	−	0.990786i	$-0.456756\pi$
$911$	8.17584			0.270878			0.135439	+	0.990786i	$0.456756\pi$
$912$	1.87662	+	1.08346i	0.0621409	+	0.0358771i
$913$	52.2816	−	14.0088i	1.73027	−	0.463624i
$914$	0.926692	+	1.60508i	0.0306522	+	0.0530912i
$915$	−16.8259	−	8.41297i	−0.556248	−	0.278124i
$916$	17.1516	+	4.59575i	0.566704	+	0.151848i
$917$	−6.06820	−	10.5104i	−0.200389	−	0.347085i
$918$		−	6.44949i		−	0.212865i
$919$	25.7515	−	14.8676i	0.849463	−	0.490437i	−0.0110069	−	0.999939i	$-0.503504\pi$
$919$	25.7515	−	14.8676i	0.849463	−	0.490437i	0.860470	+	0.509502i	$0.170170\pi$
$920$	−10.7761	+	7.11496i	−0.355277	+	0.234573i
$921$	15.9153	−	4.26449i	0.524427	−	0.140520i
$922$	8.89089	+	8.89089i	0.292806	+	0.292806i
$923$	21.6749	+	10.7171i	0.713437	+	0.352756i
$924$		−	12.9389i		−	0.425659i
$925$	−0.420940	−	3.49385i	−0.0138404	−	0.114877i
$926$	10.5059	−	18.1968i	0.345247	−	0.597985i
$927$	1.06815	−	3.98638i	0.0350826	−	0.130930i
$928$	−8.67387			−0.284734
$929$	−12.3875	+	46.2307i	−0.406420	+	1.51678i	0.395002	+	0.918680i	$0.370744\pi$
$929$	−12.3875	+	46.2307i	−0.406420	+	1.51678i	−0.801422	+	0.598099i	$0.795923\pi$
$930$	9.54114	−	10.7597i	0.312866	−	0.352823i
$931$	−4.30140	−	4.30140i	−0.140973	−	0.140973i
$932$	27.4754	+	7.36200i	0.899986	+	0.241150i
$933$	0.430350	+	1.60609i	0.0140890	+	0.0525809i
$934$	−6.95643	−	25.9618i	−0.227621	−	0.849495i
$935$	18.8423	+	56.5269i	0.616209	+	1.84863i
$936$	−1.15539	−	3.41542i	−0.0377653	−	0.111636i
$937$	19.0807	−	19.0807i	0.623339	−	0.623339i	−0.323045	−	0.946384i	$-0.604706\pi$
$937$	19.0807	−	19.0807i	0.623339	−	0.623339i	0.946384	+	0.323045i	$0.104706\pi$
$938$	−12.9065	+	22.3548i	−0.421414	+	0.729910i
$939$	−11.6090	−	6.70246i	−0.378846	−	0.218727i
$940$	7.85786	+	6.96797i	0.256295	+	0.227270i
$941$	15.0121	−	15.0121i	0.489381	−	0.489381i	−0.418730	−	0.908111i	$-0.637525\pi$
$941$	15.0121	−	15.0121i	0.489381	−	0.489381i	0.908111	+	0.418730i	$0.137525\pi$
$942$	−0.716361	+	0.413591i	−0.0233403	+	0.0134755i
$943$	−2.57679	+	1.48771i	−0.0839118	+	0.0484465i
$944$	−7.06022	+	7.06022i	−0.229791	+	0.229791i
$945$	6.99001	−	0.419562i	0.227385	−	0.0136483i
$946$	−12.5212	−	7.22911i	−0.407099	−	0.235039i
$947$	−23.8717	+	41.3470i	−0.775726	+	1.34360i	0.158660	+	0.987333i	$0.449283\pi$
$947$	−23.8717	+	41.3470i	−0.775726	+	1.34360i	−0.934386	+	0.356263i	$0.884051\pi$
$948$	−7.50971	+	7.50971i	−0.243904	+	0.243904i
$949$	−8.14867	+	40.7433i	−0.264517	+	1.32258i
$950$	1.53225	−	10.7257i	0.0497128	−	0.347989i
$951$	−4.31079	−	16.0881i	−0.139787	−	0.521692i
$952$	5.22751	+	19.5093i	0.169425	+	0.632302i
$953$	−46.7550	−	12.5280i	−1.51454	−	0.405820i	−0.596602	−	0.802538i	$-0.703483\pi$
$953$	−46.7550	−	12.5280i	−1.51454	−	0.405820i	−0.917941	+	0.396717i	$0.870149\pi$
$954$	8.92820	+	8.92820i	0.289061	+	0.289061i
$955$	−23.8531	−	21.1518i	−0.771869	−	0.684456i
$956$	−2.39720	+	8.94646i	−0.0775309	+	0.289349i
$957$	−35.8374			−1.15846
$958$	0.706287	−	2.63590i	0.0228191	−	0.0851620i
$959$	−12.4736	+	21.6049i	−0.402793	+	0.697658i
$960$	1.86603	−	1.23205i	0.0602257	−	0.0397643i
$961$		−	10.3607i		−	0.334217i
$962$	−2.40385	+	0.813193i	−0.0775032	+	0.0262184i
$963$	10.9564	+	10.9564i	0.353066	+	0.353066i
$964$	7.04757	−	1.88839i	0.226987	−	0.0608209i
$965$	−44.6397	−	9.13484i	−1.43700	−	0.294061i
$966$	−15.6620	+	9.04248i	−0.503917	+	0.290937i
$967$			37.2490i			1.19785i	0.800806	+	0.598923i	$0.204405\pi$
$967$			37.2490i			1.19785i	−0.800806	+	0.598923i	$0.795595\pi$
$968$	−3.03528	−	5.25725i	−0.0975575	−	0.168974i
$969$	−13.4994	−	3.61715i	−0.433662	−	0.116200i
$970$	8.83939	−	2.94646i	0.283816	−	0.0946052i
$971$	−1.94923	−	3.37617i	−0.0625538	−	0.108346i	0.833052	−	0.553194i	$-0.186591\pi$
$971$	−1.94923	−	3.37617i	−0.0625538	−	0.108346i	−0.895606	+	0.444848i	$0.853258\pi$
$972$	−0.965926	+	0.258819i	−0.0309821	+	0.00830162i
$973$	29.0343	+	16.7629i	0.930796	+	0.537395i
$974$	−32.2360			−1.03291
$975$	−13.6962	+	11.7224i	−0.438628	+	0.375418i
$976$	−8.41297			−0.269293
$977$	−1.50804	−	0.870670i	−0.0482466	−	0.0278552i	0.475683	−	0.879617i	$-0.342201\pi$
$977$	−1.50804	−	0.870670i	−0.0482466	−	0.0278552i	−0.523929	+	0.851762i	$0.675534\pi$
$978$	8.49001	−	2.27489i	0.271481	−	0.0727430i
$979$	−32.1658	−	55.7129i	−1.02802	−	1.78059i
$980$	−5.95507	+	1.98502i	−0.190228	+	0.0634093i
$981$	2.65257	+	0.710755i	0.0846902	+	0.0226927i
$982$	12.6672	+	21.9402i	0.404226	+	0.700140i
$983$			20.0098i			0.638213i	0.947719	+	0.319106i	$0.103383\pi$
$983$			20.0098i			0.638213i	−0.947719	+	0.319106i	$0.896617\pi$
$984$	0.446206	−	0.257617i	0.0142245	−	0.00821253i
$985$	−2.15866	−	0.441737i	−0.0687807	−	0.0140749i
$986$	54.0359	−	14.4789i	1.72085	−	0.461101i
$987$	10.4006	+	10.4006i	0.331055	+	0.331055i
$988$	−7.79677	+	0.502838i	−0.248048	+	0.0159974i
$989$			20.2085i			0.642594i
$990$	7.70977	−	5.09041i	0.245033	−	0.161784i
$991$	25.3482	−	43.9043i	0.805211	−	1.39467i	−0.110937	−	0.993827i	$-0.535385\pi$
$991$	25.3482	−	43.9043i	0.805211	−	1.39467i	0.916148	−	0.400839i	$-0.131281\pi$
$992$	1.66452	−	6.21209i	0.0528487	−	0.197234i
$993$	29.6875			0.942104
$994$	−5.43561	+	20.2860i	−0.172407	+	0.643432i
$995$	−4.93477	−	4.37591i	−0.156443	−	0.138726i
$996$	9.26330	+	9.26330i	0.293519	+	0.293519i
$997$	42.8975	+	11.4944i	1.35858	+	0.364030i	0.863294	−	0.504701i	$-0.168397\pi$
$997$	42.8975	+	11.4944i	1.35858	+	0.364030i	0.495284	+	0.868731i	$0.335064\pi$
$998$	2.22386	+	8.29958i	0.0703952	+	0.262719i
$999$	0.182163	+	0.679841i	0.00576337	+	0.0215092i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	390.2.bd.a.253.1	yes	8
5.2	odd	4		390.2.bn.a.97.2	yes	8
13.11	odd	12		390.2.bn.a.193.2	yes	8
65.37	even	12	inner	390.2.bd.a.37.1	✓	8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
390.2.bd.a.37.1	✓	8	65.37	even	12	inner
390.2.bd.a.253.1	yes	8	1.1	even	1	trivial
390.2.bn.a.97.2	yes	8	5.2	odd	4
390.2.bn.a.193.2	yes	8	13.11	odd	12

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:	\( N \)	\(=\)	\( 390 = 2 \cdot 3 \cdot 5 \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	390.bd (of order \(12\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12132 - 0.707107i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.56583 - 2.71209i) q^{7} -1.00000i q^{8} +(0.866025 - 0.500000i) q^{9} +O(q^{10})\)	\(q+(-0.866025 - 0.500000i) q^{2} +(-0.965926 + 0.258819i) q^{3} +(0.500000 + 0.866025i) q^{4} +(2.12132 - 0.707107i) q^{5} +(0.965926 + 0.258819i) q^{6} +(-1.56583 - 2.71209i) q^{7} -1.00000i q^{8} +(0.866025 - 0.500000i) q^{9} +(-2.19067 - 0.448288i) q^{10} +(-3.99087 + 1.06935i) q^{11} +(-0.707107 - 0.707107i) q^{12} +(3.53553 + 0.707107i) q^{13} +3.13165i q^{14} +(-1.86603 + 1.23205i) q^{15} +(-0.500000 + 0.866025i) q^{16} +(1.66925 - 6.22973i) q^{17} -1.00000 q^{18} +(-0.560842 + 2.09309i) q^{19} +(1.67303 + 1.48356i) q^{20} +(2.21441 + 2.21441i) q^{21} +(3.99087 + 1.06935i) q^{22} +(-1.49465 - 5.57812i) q^{23} +(0.258819 + 0.965926i) q^{24} +(4.00000 - 3.00000i) q^{25} +(-2.70831 - 2.38014i) q^{26} +(-0.707107 + 0.707107i) q^{27} +(1.56583 - 2.71209i) q^{28} +(-7.51179 - 4.33694i) q^{29} +(2.23205 - 0.133975i) q^{30} +(4.54757 - 4.54757i) q^{31} +(0.866025 - 0.500000i) q^{32} +(3.57812 - 2.06583i) q^{33} +(-4.56048 + 4.56048i) q^{34} +(-5.23936 - 4.64601i) q^{35} +(0.866025 + 0.500000i) q^{36} +(0.351911 - 0.609528i) q^{37} +(1.53225 - 1.53225i) q^{38} +(-3.59808 + 0.232051i) q^{39} +(-0.707107 - 2.12132i) q^{40} +(-0.133352 - 0.497678i) q^{41} +(-0.810531 - 3.02494i) q^{42} +(-3.38014 - 0.905706i) q^{43} +(-2.92152 - 2.92152i) q^{44} +(1.48356 - 1.67303i) q^{45} +(-1.49465 + 5.57812i) q^{46} +4.69677 q^{47} +(0.258819 - 0.965926i) q^{48} +(-1.40362 + 2.43115i) q^{49} +(-4.96410 + 0.598076i) q^{50} +6.44949i q^{51} +(1.15539 + 3.41542i) q^{52} +(-8.92820 - 8.92820i) q^{53} +(0.965926 - 0.258819i) q^{54} +(-7.70977 + 5.09041i) q^{55} +(-2.71209 + 1.56583i) q^{56} -2.16693i q^{57} +(4.33694 + 7.51179i) q^{58} +(9.64444 + 2.58422i) q^{59} +(-2.00000 - 1.00000i) q^{60} +(4.20648 + 7.28585i) q^{61} +(-6.21209 + 1.66452i) q^{62} +(-2.71209 - 1.56583i) q^{63} -1.00000 q^{64} +(8.00000 - 1.00000i) q^{65} -4.13165 q^{66} +(7.13834 + 4.12132i) q^{67} +(6.22973 - 1.66925i) q^{68} +(2.88745 + 5.00120i) q^{69} +(2.21441 + 6.64324i) q^{70} +(6.47772 + 1.73570i) q^{71} +(-0.500000 - 0.866025i) q^{72} +11.5240i q^{73} +(-0.609528 + 0.351911i) q^{74} +(-3.08725 + 3.93305i) q^{75} +(-2.09309 + 0.560842i) q^{76} +(9.14918 + 9.14918i) q^{77} +(3.23205 + 1.59808i) q^{78} -10.6203i q^{79} +(-0.448288 + 2.19067i) q^{80} +(0.500000 - 0.866025i) q^{81} +(-0.133352 + 0.497678i) q^{82} -13.1003 q^{83} +(-0.810531 + 3.02494i) q^{84} +(-0.864068 - 14.3956i) q^{85} +(2.47443 + 2.47443i) q^{86} +(8.37832 + 2.24496i) q^{87} +(1.06935 + 3.99087i) q^{88} +(4.02993 + 15.0399i) q^{89} +(-2.12132 + 0.707107i) q^{90} +(-3.61829 - 10.6959i) q^{91} +(4.08346 - 4.08346i) q^{92} +(-3.21561 + 5.56961i) q^{93} +(-4.06753 - 2.34839i) q^{94} +(0.290313 + 4.83669i) q^{95} +(-0.707107 + 0.707107i) q^{96} +(-3.60867 + 2.08346i) q^{97} +(2.43115 - 1.40362i) q^{98} +(-2.92152 + 2.92152i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q + 4 q^{4} - 4 q^{7}+O(q^{10}) \) 8 * q + 4 * q^4 - 4 * q^7	\( 8 q + 4 q^{4} - 4 q^{7} - 16 q^{11} - 8 q^{15} - 4 q^{16} + 12 q^{17} - 8 q^{18} - 24 q^{19} + 8 q^{21} + 16 q^{22} + 16 q^{23} + 32 q^{25} + 4 q^{28} - 24 q^{29} + 4 q^{30} - 4 q^{31} - 12 q^{33} - 24 q^{35} + 8 q^{37} - 8 q^{39} + 28 q^{41} - 8 q^{42} - 8 q^{43} - 8 q^{44} + 16 q^{46} + 32 q^{47} - 20 q^{49} - 12 q^{50} - 16 q^{53} - 4 q^{55} + 12 q^{56} - 8 q^{58} + 32 q^{59} - 16 q^{60} - 8 q^{61} - 16 q^{62} + 12 q^{63} - 8 q^{64} + 64 q^{65} - 16 q^{66} + 12 q^{68} + 8 q^{70} + 8 q^{71} - 4 q^{72} - 24 q^{74} - 24 q^{76} - 24 q^{77} + 12 q^{78} + 4 q^{81} + 28 q^{82} - 32 q^{83} - 8 q^{84} - 32 q^{85} - 8 q^{86} + 28 q^{87} + 8 q^{88} - 4 q^{89} - 8 q^{91} + 20 q^{92} - 12 q^{94} + 4 q^{95} + 12 q^{97} + 24 q^{98} - 8 q^{99}+O(q^{100}) \) 8 * q + 4 * q^4 - 4 * q^7 - 16 * q^11 - 8 * q^15 - 4 * q^16 + 12 * q^17 - 8 * q^18 - 24 * q^19 + 8 * q^21 + 16 * q^22 + 16 * q^23 + 32 * q^25 + 4 * q^28 - 24 * q^29 + 4 * q^30 - 4 * q^31 - 12 * q^33 - 24 * q^35 + 8 * q^37 - 8 * q^39 + 28 * q^41 - 8 * q^42 - 8 * q^43 - 8 * q^44 + 16 * q^46 + 32 * q^47 - 20 * q^49 - 12 * q^50 - 16 * q^53 - 4 * q^55 + 12 * q^56 - 8 * q^58 + 32 * q^59 - 16 * q^60 - 8 * q^61 - 16 * q^62 + 12 * q^63 - 8 * q^64 + 64 * q^65 - 16 * q^66 + 12 * q^68 + 8 * q^70 + 8 * q^71 - 4 * q^72 - 24 * q^74 - 24 * q^76 - 24 * q^77 + 12 * q^78 + 4 * q^81 + 28 * q^82 - 32 * q^83 - 8 * q^84 - 32 * q^85 - 8 * q^86 + 28 * q^87 + 8 * q^88 - 4 * q^89 - 8 * q^91 + 20 * q^92 - 12 * q^94 + 4 * q^95 + 12 * q^97 + 24 * q^98 - 8 * q^99

Introduction

L-functions

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