LMFDB - Embedded newform 930.2.i.l.211.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [930,2,Mod(211,930)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(930, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("930.211");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 930 = 2 \cdot 3 \cdot 5 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	930.i (of order $3$, degree $2$, 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:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{5})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 2x^{2} + x + 1 $ x^4 - x^3 + 2*x^2 + x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			211.1
Root			$-0.309017 + 0.535233i$ of defining polynomial
Character	$\chi$	$=$	930.211
Dual form			930.2.i.l.811.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.118034 - 0.204441i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.118034 - 0.204441i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.11803 - 3.66854i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.118034 - 0.204441i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-2.85410 - 4.94345i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.61803 + 2.80252i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.118034 + 0.204441i) q^{21} +(2.11803 - 3.66854i) q^{22} -1.23607 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(-0.118034 - 0.204441i) q^{28} +3.00000 q^{29} -1.00000 q^{30} +(1.35410 - 5.40059i) q^{31} +1.00000 q^{32} -4.23607 q^{33} +(-2.85410 - 4.94345i) q^{34} -0.236068 q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.618034 + 1.07047i) q^{37} +(1.61803 + 2.80252i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-0.618034 + 1.07047i) q^{41} +(-0.118034 + 0.204441i) q^{42} +(-0.763932 - 1.32317i) q^{43} +(2.11803 - 3.66854i) q^{44} +(0.500000 + 0.866025i) q^{45} -1.23607 q^{46} +0.763932 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.47214 - 6.01392i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-2.85410 + 4.94345i) q^{51} +(3.73607 - 6.47106i) q^{53} +1.00000 q^{54} +(-2.11803 - 3.66854i) q^{55} +(-0.118034 - 0.204441i) q^{56} +(1.61803 - 2.80252i) q^{57} +3.00000 q^{58} +(3.11803 + 5.40059i) q^{59} -1.00000 q^{60} -14.1803 q^{61} +(1.35410 - 5.40059i) q^{62} +0.236068 q^{63} +1.00000 q^{64} -4.23607 q^{66} +(-2.61803 + 4.53457i) q^{67} +(-2.85410 - 4.94345i) q^{68} +(0.618034 + 1.07047i) q^{69} -0.236068 q^{70} +(1.23607 - 2.14093i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-1.47214 + 2.54981i) q^{73} +(0.618034 + 1.07047i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(1.61803 + 2.80252i) q^{76} -1.00000 q^{77} +(5.23607 + 9.06914i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.618034 + 1.07047i) q^{82} +(-2.35410 + 4.07742i) q^{83} +(-0.118034 + 0.204441i) q^{84} -5.70820 q^{85} +(-0.763932 - 1.32317i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(2.11803 - 3.66854i) q^{88} +10.9443 q^{89} +(0.500000 + 0.866025i) q^{90} -1.23607 q^{92} +(-5.35410 + 1.52761i) q^{93} +0.763932 q^{94} +3.23607 q^{95} +(-0.500000 - 0.866025i) q^{96} +1.47214 q^{97} +(3.47214 - 6.01392i) q^{98} +(2.11803 + 3.66854i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 - 2 * q^9	$ 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 4 q^{14} - 4 q^{15} + 4 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 4 q^{21} + 4 q^{22} + 4 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{27} + 4 q^{28} + 12 q^{29} - 4 q^{30} - 8 q^{31} + 4 q^{32} - 8 q^{33} + 2 q^{34} + 8 q^{35} - 2 q^{36} - 2 q^{37} + 2 q^{38} + 2 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} + 4 q^{44} + 2 q^{45} + 4 q^{46} + 12 q^{47} - 2 q^{48} - 4 q^{49} - 2 q^{50} + 2 q^{51} + 6 q^{53} + 4 q^{54} - 4 q^{55} + 4 q^{56} + 2 q^{57} + 12 q^{58} + 8 q^{59} - 4 q^{60} - 12 q^{61} - 8 q^{62} - 8 q^{63} + 4 q^{64} - 8 q^{66} - 6 q^{67} + 2 q^{68} - 2 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} + 12 q^{73} - 2 q^{74} - 2 q^{75} + 2 q^{76} - 4 q^{77} + 12 q^{79} + 2 q^{80} - 2 q^{81} + 2 q^{82} + 4 q^{83} + 4 q^{84} + 4 q^{85} - 12 q^{86} - 6 q^{87} + 4 q^{88} + 8 q^{89} + 2 q^{90} + 4 q^{92} - 8 q^{93} + 12 q^{94} + 4 q^{95} - 2 q^{96} - 12 q^{97} - 4 q^{98} + 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 + 4 * q^14 - 4 * q^15 + 4 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 4 * q^21 + 4 * q^22 + 4 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^27 + 4 * q^28 + 12 * q^29 - 4 * q^30 - 8 * q^31 + 4 * q^32 - 8 * q^33 + 2 * q^34 + 8 * q^35 - 2 * q^36 - 2 * q^37 + 2 * q^38 + 2 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 + 4 * q^44 + 2 * q^45 + 4 * q^46 + 12 * q^47 - 2 * q^48 - 4 * q^49 - 2 * q^50 + 2 * q^51 + 6 * q^53 + 4 * q^54 - 4 * q^55 + 4 * q^56 + 2 * q^57 + 12 * q^58 + 8 * q^59 - 4 * q^60 - 12 * q^61 - 8 * q^62 - 8 * q^63 + 4 * q^64 - 8 * q^66 - 6 * q^67 + 2 * q^68 - 2 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 + 12 * q^73 - 2 * q^74 - 2 * q^75 + 2 * q^76 - 4 * q^77 + 12 * q^79 + 2 * q^80 - 2 * q^81 + 2 * q^82 + 4 * q^83 + 4 * q^84 + 4 * q^85 - 12 * q^86 - 6 * q^87 + 4 * q^88 + 8 * q^89 + 2 * q^90 + 4 * q^92 - 8 * q^93 + 12 * q^94 + 4 * q^95 - 2 * q^96 - 12 * q^97 - 4 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

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

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

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 $

$2$	1.00000			0.707107
$2$	1.00000			0.707107
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$3$	−0.500000	−	0.866025i	−0.288675	−	0.500000i
$4$	1.00000			0.500000
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$5$	0.500000	−	0.866025i	0.223607	−	0.387298i
$6$	−0.500000	−	0.866025i	−0.204124	−	0.353553i
$7$	−0.118034	−	0.204441i	−0.0446127	−	0.0772714i	0.842857	−	0.538138i	$-0.180872\pi$
$7$	−0.118034	−	0.204441i	−0.0446127	−	0.0772714i	−0.887469	+	0.460866i	$0.847539\pi$
$8$	1.00000			0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	0.500000	−	0.866025i	0.158114	−	0.273861i
$11$	2.11803	−	3.66854i	0.638611	−	1.10611i	−0.347126	−	0.937818i	$-0.612843\pi$
$11$	2.11803	−	3.66854i	0.638611	−	1.10611i	0.985738	−	0.168289i	$-0.0538241\pi$
$12$	−0.500000	−	0.866025i	−0.144338	−	0.250000i
$13$		0			0		−0.866025	−	0.500000i	$-0.833333\pi$
$13$		0			0		0.866025	+	0.500000i	$0.166667\pi$
$14$	−0.118034	−	0.204441i	−0.0315459	−	0.0546391i
$15$	−1.00000			−0.258199
$16$	1.00000			0.250000
$17$	−2.85410	−	4.94345i	−0.692221	−	1.19896i	−0.971108	−	0.238639i	$-0.923299\pi$
$17$	−2.85410	−	4.94345i	−0.692221	−	1.19896i	0.278887	−	0.960324i	$-0.410035\pi$
$18$	−0.500000	+	0.866025i	−0.117851	+	0.204124i
$19$	1.61803	+	2.80252i	0.371202	+	0.642942i	0.989751	−	0.142805i	$-0.0456123\pi$
$19$	1.61803	+	2.80252i	0.371202	+	0.642942i	−0.618548	+	0.785747i	$0.712279\pi$
$20$	0.500000	−	0.866025i	0.111803	−	0.193649i
$21$	−0.118034	+	0.204441i	−0.0257571	+	0.0446127i
$22$	2.11803	−	3.66854i	0.451566	−	0.782136i
$23$	−1.23607			−0.257738			−0.128869	−	0.991662i	$-0.541135\pi$
$23$	−1.23607			−0.257738			−0.128869	+	0.991662i	$0.541135\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	−0.500000	−	0.866025i	−0.100000	−	0.173205i
$26$		0			0
$27$	1.00000			0.192450
$28$	−0.118034	−	0.204441i	−0.0223063	−	0.0386357i
$29$	3.00000			0.557086			0.278543	−	0.960424i	$-0.410149\pi$
$29$	3.00000			0.557086			0.278543	+	0.960424i	$0.410149\pi$
$30$	−1.00000			−0.182574
$31$	1.35410	−	5.40059i	0.243204	−	0.969975i
$31$	1.35410	−	5.40059i	0.243204	−	0.969975i
$32$	1.00000			0.176777
$33$	−4.23607			−0.737405
$34$	−2.85410	−	4.94345i	−0.489474	−	0.847795i
$35$	−0.236068			−0.0399028
$36$	−0.500000	+	0.866025i	−0.0833333	+	0.144338i
$37$	0.618034	+	1.07047i	0.101604	+	0.175984i	0.912346	−	0.409421i	$-0.134269\pi$
$37$	0.618034	+	1.07047i	0.101604	+	0.175984i	−0.810742	+	0.585404i	$0.800936\pi$
$38$	1.61803	+	2.80252i	0.262480	+	0.454628i
$39$		0			0
$40$	0.500000	−	0.866025i	0.0790569	−	0.136931i
$41$	−0.618034	+	1.07047i	−0.0965207	+	0.167179i	−0.910242	−	0.414076i	$-0.864105\pi$
$41$	−0.618034	+	1.07047i	−0.0965207	+	0.167179i	0.813722	+	0.581255i	$0.197438\pi$
$42$	−0.118034	+	0.204441i	−0.0182130	+	0.0315459i
$43$	−0.763932	−	1.32317i	−0.116499	−	0.201781i	0.801879	−	0.597486i	$-0.203834\pi$
$43$	−0.763932	−	1.32317i	−0.116499	−	0.201781i	−0.918378	+	0.395705i	$0.870500\pi$
$44$	2.11803	−	3.66854i	0.319306	−	0.553054i
$45$	0.500000	+	0.866025i	0.0745356	+	0.129099i
$46$	−1.23607			−0.182248
$47$	0.763932			0.111431			0.0557155	−	0.998447i	$-0.482256\pi$
$47$	0.763932			0.111431			0.0557155	+	0.998447i	$0.482256\pi$
$48$	−0.500000	−	0.866025i	−0.0721688	−	0.125000i
$49$	3.47214	−	6.01392i	0.496019	−	0.859131i
$50$	−0.500000	−	0.866025i	−0.0707107	−	0.122474i
$51$	−2.85410	+	4.94345i	−0.399654	+	0.692221i
$52$		0			0
$53$	3.73607	−	6.47106i	0.513188	−	0.888868i	−0.486695	−	0.873572i	$-0.661798\pi$
$53$	3.73607	−	6.47106i	0.513188	−	0.888868i	0.999883	−	0.0152962i	$-0.00486912\pi$
$54$	1.00000			0.136083
$55$	−2.11803	−	3.66854i	−0.285596	−	0.494666i
$56$	−0.118034	−	0.204441i	−0.0157730	−	0.0273196i
$57$	1.61803	−	2.80252i	0.214314	−	0.371202i
$58$	3.00000			0.393919
$59$	3.11803	+	5.40059i	0.405933	+	0.703097i	0.994430	−	0.105403i	$-0.0336131\pi$
$59$	3.11803	+	5.40059i	0.405933	+	0.703097i	−0.588496	+	0.808500i	$0.700280\pi$
$60$	−1.00000			−0.129099
$61$	−14.1803			−1.81561			−0.907803	−	0.419396i	$-0.862242\pi$
$61$	−14.1803			−1.81561			−0.907803	+	0.419396i	$0.862242\pi$
$62$	1.35410	−	5.40059i	0.171971	−	0.685876i
$63$	0.236068			0.0297418
$64$	1.00000			0.125000
$65$		0			0
$66$	−4.23607			−0.521424
$67$	−2.61803	+	4.53457i	−0.319844	+	0.553986i	−0.980455	−	0.196742i	$-0.936964\pi$
$67$	−2.61803	+	4.53457i	−0.319844	+	0.553986i	0.660611	+	0.750728i	$0.270297\pi$
$68$	−2.85410	−	4.94345i	−0.346111	−	0.599481i
$69$	0.618034	+	1.07047i	0.0744025	+	0.128869i
$70$	−0.236068			−0.0282155
$71$	1.23607	−	2.14093i	0.146694	−	0.254082i	−0.783309	−	0.621632i	$-0.786470\pi$
$71$	1.23607	−	2.14093i	0.146694	−	0.254082i	0.930004	+	0.367550i	$0.119803\pi$
$72$	−0.500000	+	0.866025i	−0.0589256	+	0.102062i
$73$	−1.47214	+	2.54981i	−0.172300	+	0.298433i	−0.939224	−	0.343306i	$-0.888453\pi$
$73$	−1.47214	+	2.54981i	−0.172300	+	0.298433i	0.766923	+	0.641739i	$0.221787\pi$
$74$	0.618034	+	1.07047i	0.0718450	+	0.124439i
$75$	−0.500000	+	0.866025i	−0.0577350	+	0.100000i
$76$	1.61803	+	2.80252i	0.185601	+	0.321471i
$77$	−1.00000			−0.113961
$78$		0			0
$79$	5.23607	+	9.06914i	0.589104	+	1.02036i	0.994350	+	0.106150i	$0.0338524\pi$
$79$	5.23607	+	9.06914i	0.589104	+	1.02036i	−0.405246	+	0.914207i	$0.632814\pi$
$80$	0.500000	−	0.866025i	0.0559017	−	0.0968246i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−0.618034	+	1.07047i	−0.0682504	+	0.118213i
$83$	−2.35410	+	4.07742i	−0.258396	+	0.447555i	−0.965812	−	0.259242i	$-0.916527\pi$
$83$	−2.35410	+	4.07742i	−0.258396	+	0.447555i	0.707416	+	0.706797i	$0.249861\pi$
$84$	−0.118034	+	0.204441i	−0.0128786	+	0.0223063i
$85$	−5.70820			−0.619142
$86$	−0.763932	−	1.32317i	−0.0823769	−	0.142681i
$87$	−1.50000	−	2.59808i	−0.160817	−	0.278543i
$88$	2.11803	−	3.66854i	0.225783	−	0.391068i
$89$	10.9443			1.16009			0.580045	−	0.814584i	$-0.303035\pi$
$89$	10.9443			1.16009			0.580045	+	0.814584i	$0.303035\pi$
$90$	0.500000	+	0.866025i	0.0527046	+	0.0912871i
$91$		0			0
$92$	−1.23607			−0.128869
$93$	−5.35410	+	1.52761i	−0.555195	+	0.158406i
$94$	0.763932			0.0787936
$95$	3.23607			0.332014
$96$	−0.500000	−	0.866025i	−0.0510310	−	0.0883883i
$97$	1.47214			0.149473			0.0747364	−	0.997203i	$-0.476188\pi$
$97$	1.47214			0.149473			0.0747364	+	0.997203i	$0.476188\pi$
$98$	3.47214	−	6.01392i	0.350739	−	0.607497i
$99$	2.11803	+	3.66854i	0.212870	+	0.368702i
$100$	−0.500000	−	0.866025i	−0.0500000	−	0.0866025i
$101$	1.47214			0.146483			0.0732415	−	0.997314i	$-0.476666\pi$
$101$	1.47214			0.146483			0.0732415	+	0.997314i	$0.476666\pi$
$102$	−2.85410	+	4.94345i	−0.282598	+	0.489474i
$103$	−9.35410	+	16.2018i	−0.921687	+	1.59641i	−0.124883	+	0.992172i	$0.539855\pi$
$103$	−9.35410	+	16.2018i	−0.921687	+	1.59641i	−0.796804	+	0.604237i	$0.793478\pi$
$104$		0			0
$105$	0.118034	+	0.204441i	0.0115189	+	0.0199514i
$106$	3.73607	−	6.47106i	0.362879	−	0.628525i
$107$	5.35410	+	9.27358i	0.517601	+	0.896510i	0.999791	+	0.0204441i	$0.00650800\pi$
$107$	5.35410	+	9.27358i	0.517601	+	0.896510i	−0.482190	+	0.876066i	$0.660159\pi$
$108$	1.00000			0.0962250
$109$	3.23607			0.309959			0.154980	−	0.987918i	$-0.450469\pi$
$109$	3.23607			0.309959			0.154980	+	0.987918i	$0.450469\pi$
$110$	−2.11803	−	3.66854i	−0.201947	−	0.349782i
$111$	0.618034	−	1.07047i	0.0586612	−	0.101604i
$112$	−0.118034	−	0.204441i	−0.0111532	−	0.0193178i
$113$	3.70820	−	6.42280i	0.348838	−	0.604206i	−0.637205	−	0.770694i	$-0.719910\pi$
$113$	3.70820	−	6.42280i	0.348838	−	0.604206i	0.986043	+	0.166488i	$0.0532428\pi$
$114$	1.61803	−	2.80252i	0.151543	−	0.262480i
$115$	−0.618034	+	1.07047i	−0.0576320	+	0.0998215i
$116$	3.00000			0.278543
$117$		0			0
$118$	3.11803	+	5.40059i	0.287038	+	0.497165i
$119$	−0.673762	+	1.16699i	−0.0617637	+	0.106978i
$120$	−1.00000			−0.0912871
$121$	−3.47214	−	6.01392i	−0.315649	−	0.546720i
$122$	−14.1803			−1.28383
$123$	1.23607			0.111452
$124$	1.35410	−	5.40059i	0.121602	−	0.484988i
$125$	−1.00000			−0.0894427
$126$	0.236068			0.0210306
$127$	4.59017	+	7.95041i	0.407312	+	0.705485i	0.994588	−	0.103902i	$-0.0331329\pi$
$127$	4.59017	+	7.95041i	0.407312	+	0.705485i	−0.587276	+	0.809387i	$0.699800\pi$
$128$	1.00000			0.0883883
$129$	−0.763932	+	1.32317i	−0.0672605	+	0.116499i
$130$		0			0
$131$	6.47214	+	11.2101i	0.565473	+	0.979428i	0.997005	+	0.0773308i	$0.0246397\pi$
$131$	6.47214	+	11.2101i	0.565473	+	0.979428i	−0.431532	+	0.902097i	$0.642027\pi$
$132$	−4.23607			−0.368702
$133$	0.381966	−	0.661585i	0.0331207	−	0.0573667i
$134$	−2.61803	+	4.53457i	−0.226164	+	0.391727i
$135$	0.500000	−	0.866025i	0.0430331	−	0.0745356i
$136$	−2.85410	−	4.94345i	−0.244737	−	0.423897i
$137$	0.381966	−	0.661585i	0.0326336	−	0.0565230i	−0.849247	−	0.527995i	$-0.822944\pi$
$137$	0.381966	−	0.661585i	0.0326336	−	0.0565230i	0.881881	+	0.471472i	$0.156277\pi$
$138$	0.618034	+	1.07047i	0.0526105	+	0.0911241i
$139$	17.1246			1.45249			0.726245	−	0.687436i	$-0.241264\pi$
$139$	17.1246			1.45249			0.726245	+	0.687436i	$0.241264\pi$
$140$	−0.236068			−0.0199514
$141$	−0.381966	−	0.661585i	−0.0321673	−	0.0557155i
$142$	1.23607	−	2.14093i	0.103729	−	0.179663i
$143$		0			0
$144$	−0.500000	+	0.866025i	−0.0416667	+	0.0721688i
$145$	1.50000	−	2.59808i	0.124568	−	0.215758i
$146$	−1.47214	+	2.54981i	−0.121835	+	0.211024i
$147$	−6.94427			−0.572754
$148$	0.618034	+	1.07047i	0.0508021	+	0.0879918i
$149$	8.73607	+	15.1313i	0.715687	+	1.23961i	0.962694	+	0.270592i	$0.0872194\pi$
$149$	8.73607	+	15.1313i	0.715687	+	1.23961i	−0.247008	+	0.969014i	$0.579447\pi$
$150$	−0.500000	+	0.866025i	−0.0408248	+	0.0707107i
$151$	9.18034			0.747085			0.373543	−	0.927613i	$-0.378143\pi$
$151$	9.18034			0.747085			0.373543	+	0.927613i	$0.378143\pi$
$152$	1.61803	+	2.80252i	0.131240	+	0.227314i
$153$	5.70820			0.461481
$154$	−1.00000			−0.0805823
$155$	−4.00000	−	3.87298i	−0.321288	−	0.311086i
$156$		0			0
$157$	−22.1803			−1.77018			−0.885092	−	0.465416i	$-0.845905\pi$
$157$	−22.1803			−1.77018			−0.885092	+	0.465416i	$0.845905\pi$
$158$	5.23607	+	9.06914i	0.416559	+	0.721502i
$159$	−7.47214			−0.592579
$160$	0.500000	−	0.866025i	0.0395285	−	0.0684653i
$161$	0.145898	+	0.252703i	0.0114984	+	0.0199158i
$162$	−0.500000	−	0.866025i	−0.0392837	−	0.0680414i
$163$	−18.7639			−1.46970			−0.734852	−	0.678227i	$-0.762749\pi$
$163$	−18.7639			−1.46970			−0.734852	+	0.678227i	$0.762749\pi$
$164$	−0.618034	+	1.07047i	−0.0482603	+	0.0835894i
$165$	−2.11803	+	3.66854i	−0.164889	+	0.285596i
$166$	−2.35410	+	4.07742i	−0.182714	+	0.316469i
$167$	−2.14590	−	3.71680i	−0.166055	−	0.287615i	0.770975	−	0.636866i	$-0.219769\pi$
$167$	−2.14590	−	3.71680i	−0.166055	−	0.287615i	−0.937029	+	0.349251i	$0.886436\pi$
$168$	−0.118034	+	0.204441i	−0.00910652	+	0.0157730i
$169$	6.50000	+	11.2583i	0.500000	+	0.866025i
$170$	−5.70820			−0.437799
$171$	−3.23607			−0.247468
$172$	−0.763932	−	1.32317i	−0.0582493	−	0.100891i
$173$	3.50000	−	6.06218i	0.266100	−	0.460899i	−0.701751	−	0.712422i	$-0.747598\pi$
$173$	3.50000	−	6.06218i	0.266100	−	0.460899i	0.967851	+	0.251523i	$0.0809315\pi$
$174$	−1.50000	−	2.59808i	−0.113715	−	0.196960i
$175$	−0.118034	+	0.204441i	−0.00892253	+	0.0154543i
$176$	2.11803	−	3.66854i	0.159653	−	0.276527i
$177$	3.11803	−	5.40059i	0.234366	−	0.405933i
$178$	10.9443			0.820308
$179$	3.11803	+	5.40059i	0.233053	+	0.403659i	0.958705	−	0.284402i	$-0.0917952\pi$
$179$	3.11803	+	5.40059i	0.233053	+	0.403659i	−0.725652	+	0.688062i	$0.758462\pi$
$180$	0.500000	+	0.866025i	0.0372678	+	0.0645497i
$181$	−2.70820	+	4.69075i	−0.201299	+	0.348660i	−0.948947	−	0.315435i	$-0.897850\pi$
$181$	−2.70820	+	4.69075i	−0.201299	+	0.348660i	0.747648	+	0.664095i	$0.231183\pi$
$182$		0			0
$183$	7.09017	+	12.2805i	0.524120	+	0.907803i
$184$	−1.23607			−0.0911241
$185$	1.23607			0.0908775
$186$	−5.35410	+	1.52761i	−0.392582	+	0.112010i
$187$	−24.1803			−1.76824
$188$	0.763932			0.0557155
$189$	−0.118034	−	0.204441i	−0.00858571	−	0.0148709i
$190$	3.23607			0.234769
$191$	−9.85410	+	17.0678i	−0.713018	+	1.23498i	0.250701	+	0.968064i	$0.419339\pi$
$191$	−9.85410	+	17.0678i	−0.713018	+	1.23498i	−0.963719	+	0.266919i	$0.913995\pi$
$192$	−0.500000	−	0.866025i	−0.0360844	−	0.0625000i
$193$	7.20820	+	12.4850i	0.518858	+	0.898688i	0.999760	+	0.0219138i	$0.00697595\pi$
$193$	7.20820	+	12.4850i	0.518858	+	0.898688i	−0.480902	+	0.876774i	$0.659691\pi$
$194$	1.47214			0.105693
$195$		0			0
$196$	3.47214	−	6.01392i	0.248010	−	0.429565i
$197$	9.00000	−	15.5885i	0.641223	−	1.11063i	−0.343937	−	0.938993i	$-0.611761\pi$
$197$	9.00000	−	15.5885i	0.641223	−	1.11063i	0.985160	−	0.171639i	$-0.0549062\pi$
$198$	2.11803	+	3.66854i	0.150522	+	0.260712i
$199$	−13.8262	+	23.9477i	−0.980116	+	1.69761i	−0.318217	+	0.948018i	$0.603084\pi$
$199$	−13.8262	+	23.9477i	−0.980116	+	1.69761i	−0.661899	+	0.749593i	$0.730249\pi$
$200$	−0.500000	−	0.866025i	−0.0353553	−	0.0612372i
$201$	5.23607			0.369324
$202$	1.47214			0.103579
$203$	−0.354102	−	0.613323i	−0.0248531	−	0.0430468i
$204$	−2.85410	+	4.94345i	−0.199827	+	0.346111i
$205$	0.618034	+	1.07047i	0.0431654	+	0.0747646i
$206$	−9.35410	+	16.2018i	−0.651731	+	1.12883i
$207$	0.618034	−	1.07047i	0.0429563	−	0.0744025i
$208$		0			0
$209$	13.7082			0.948216
$210$	0.118034	+	0.204441i	0.00814512	+	0.0141078i
$211$	−8.56231	−	14.8303i	−0.589453	−	1.02096i	−0.994304	−	0.106580i	$-0.966010\pi$
$211$	−8.56231	−	14.8303i	−0.589453	−	1.02096i	0.404851	−	0.914383i	$-0.367324\pi$
$212$	3.73607	−	6.47106i	0.256594	−	0.444434i
$213$	−2.47214			−0.169388
$214$	5.35410	+	9.27358i	0.365999	+	0.633929i
$215$	−1.52786			−0.104199
$216$	1.00000			0.0680414
$217$	−1.26393	+	0.360620i	−0.0858013	+	0.0244805i
$218$	3.23607			0.219174
$219$	2.94427			0.198955
$220$	−2.11803	−	3.66854i	−0.142798	−	0.247333i
$221$		0			0
$222$	0.618034	−	1.07047i	0.0414797	−	0.0718450i
$223$	8.35410	+	14.4697i	0.559432	+	0.968965i	0.997544	+	0.0700443i	$0.0223141\pi$
$223$	8.35410	+	14.4697i	0.559432	+	0.968965i	−0.438112	+	0.898920i	$0.644353\pi$
$224$	−0.118034	−	0.204441i	−0.00788648	−	0.0136598i
$225$	1.00000			0.0666667
$226$	3.70820	−	6.42280i	0.246666	−	0.427238i
$227$	4.59017	−	7.95041i	0.304660	−	0.527687i	−0.672525	−	0.740074i	$-0.734790\pi$
$227$	4.59017	−	7.95041i	0.304660	−	0.527687i	0.977186	+	0.212387i	$0.0681237\pi$
$228$	1.61803	−	2.80252i	0.107157	−	0.185601i
$229$	−2.14590	−	3.71680i	−0.141805	−	0.245613i	0.786371	−	0.617754i	$-0.211957\pi$
$229$	−2.14590	−	3.71680i	−0.141805	−	0.245613i	−0.928176	+	0.372141i	$0.878624\pi$
$230$	−0.618034	+	1.07047i	−0.0407520	+	0.0705845i
$231$	0.500000	+	0.866025i	0.0328976	+	0.0569803i
$232$	3.00000			0.196960
$233$	1.81966			0.119210			0.0596049	−	0.998222i	$-0.481016\pi$
$233$	1.81966			0.119210			0.0596049	+	0.998222i	$0.481016\pi$
$234$		0			0
$235$	0.381966	−	0.661585i	0.0249167	−	0.0431570i
$236$	3.11803	+	5.40059i	0.202967	+	0.351549i
$237$	5.23607	−	9.06914i	0.340119	−	0.589104i
$238$	−0.673762	+	1.16699i	−0.0436735	+	0.0756447i
$239$	1.70820	−	2.95870i	0.110495	−	0.191382i	−0.805475	−	0.592629i	$-0.798090\pi$
$239$	1.70820	−	2.95870i	0.110495	−	0.191382i	0.915970	+	0.401247i	$0.131423\pi$
$240$	−1.00000			−0.0645497
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	0.632709	−	0.774389i	$-0.281943\pi$
$241$	−5.50000	−	9.52628i	−0.354286	−	0.613642i	−0.986996	+	0.160748i	$0.948609\pi$
$242$	−3.47214	−	6.01392i	−0.223197	−	0.386589i
$243$	−0.500000	+	0.866025i	−0.0320750	+	0.0555556i
$244$	−14.1803			−0.907803
$245$	−3.47214	−	6.01392i	−0.221827	−	0.384215i
$246$	1.23607			0.0788088
$247$		0			0
$248$	1.35410	−	5.40059i	0.0859856	−	0.342938i
$249$	4.70820			0.298370
$250$	−1.00000			−0.0632456
$251$	3.23607	+	5.60503i	0.204259	+	0.353787i	0.949896	−	0.312565i	$-0.101188\pi$
$251$	3.23607	+	5.60503i	0.204259	+	0.353787i	−0.745638	+	0.666352i	$0.767855\pi$
$252$	0.236068			0.0148709
$253$	−2.61803	+	4.53457i	−0.164594	+	0.285086i
$254$	4.59017	+	7.95041i	0.288013	+	0.498853i
$255$	2.85410	+	4.94345i	0.178731	+	0.309571i
$256$	1.00000			0.0625000
$257$	−6.32624	+	10.9574i	−0.394620	+	0.683502i	−0.993053	−	0.117671i	$-0.962457\pi$
$257$	−6.32624	+	10.9574i	−0.394620	+	0.683502i	0.598433	+	0.801173i	$0.295790\pi$
$258$	−0.763932	+	1.32317i	−0.0475603	+	0.0823769i
$259$	0.145898	−	0.252703i	0.00906566	−	0.0157022i
$260$		0			0
$261$	−1.50000	+	2.59808i	−0.0928477	+	0.160817i
$262$	6.47214	+	11.2101i	0.399850	+	0.692560i
$263$	4.47214			0.275764			0.137882	−	0.990449i	$-0.455971\pi$
$263$	4.47214			0.275764			0.137882	+	0.990449i	$0.455971\pi$
$264$	−4.23607			−0.260712
$265$	−3.73607	−	6.47106i	−0.229505	−	0.397514i
$266$	0.381966	−	0.661585i	0.0234198	−	0.0405644i
$267$	−5.47214	−	9.47802i	−0.334889	−	0.580045i
$268$	−2.61803	+	4.53457i	−0.159922	+	0.276993i
$269$	11.0000	−	19.0526i	0.670682	−	1.16166i	−0.307029	−	0.951700i	$-0.599335\pi$
$269$	11.0000	−	19.0526i	0.670682	−	1.16166i	0.977711	−	0.209955i	$-0.0673317\pi$
$270$	0.500000	−	0.866025i	0.0304290	−	0.0527046i
$271$	1.76393			0.107151			0.0535756	−	0.998564i	$-0.482938\pi$
$271$	1.76393			0.107151			0.0535756	+	0.998564i	$0.482938\pi$
$272$	−2.85410	−	4.94345i	−0.173055	−	0.299741i
$273$		0			0
$274$	0.381966	−	0.661585i	0.0230754	−	0.0399678i
$275$	−4.23607			−0.255445
$276$	0.618034	+	1.07047i	0.0372013	+	0.0644345i
$277$	−10.6525			−0.640045			−0.320023	−	0.947410i	$-0.603691\pi$
$277$	−10.6525			−0.640045			−0.320023	+	0.947410i	$0.603691\pi$
$278$	17.1246			1.02707
$279$	4.00000	+	3.87298i	0.239474	+	0.231869i
$280$	−0.236068			−0.0141078
$281$	−0.472136			−0.0281653			−0.0140826	−	0.999901i	$-0.504483\pi$
$281$	−0.472136			−0.0281653			−0.0140826	+	0.999901i	$0.504483\pi$
$282$	−0.381966	−	0.661585i	−0.0227457	−	0.0393968i
$283$	7.41641			0.440860			0.220430	−	0.975403i	$-0.429254\pi$
$283$	7.41641			0.440860			0.220430	+	0.975403i	$0.429254\pi$
$284$	1.23607	−	2.14093i	0.0733471	−	0.127041i
$285$	−1.61803	−	2.80252i	−0.0958441	−	0.166007i
$286$		0			0
$287$	0.291796			0.0172242
$288$	−0.500000	+	0.866025i	−0.0294628	+	0.0510310i
$289$	−7.79180	+	13.4958i	−0.458341	+	0.793870i
$290$	1.50000	−	2.59808i	0.0880830	−	0.152564i
$291$	−0.736068	−	1.27491i	−0.0431491	−	0.0747364i
$292$	−1.47214	+	2.54981i	−0.0861502	+	0.149217i
$293$	−1.20820	−	2.09267i	−0.0705840	−	0.122255i	0.828573	−	0.559880i	$-0.189153\pi$
$293$	−1.20820	−	2.09267i	−0.0705840	−	0.122255i	−0.899157	+	0.437625i	$0.855820\pi$
$294$	−6.94427			−0.404998
$295$	6.23607			0.363078
$296$	0.618034	+	1.07047i	0.0359225	+	0.0622196i
$297$	2.11803	−	3.66854i	0.122901	−	0.212870i
$298$	8.73607	+	15.1313i	0.506067	+	0.876533i
$299$		0			0
$300$	−0.500000	+	0.866025i	−0.0288675	+	0.0500000i
$301$	−0.180340	+	0.312358i	−0.0103946	+	0.0180040i
$302$	9.18034			0.528269
$303$	−0.736068	−	1.27491i	−0.0422860	−	0.0732415i
$304$	1.61803	+	2.80252i	0.0928006	+	0.160735i
$305$	−7.09017	+	12.2805i	−0.405982	+	0.703181i
$306$	5.70820			0.326316
$307$	−7.61803	−	13.1948i	−0.434784	−	0.753068i	0.562494	−	0.826801i	$-0.309842\pi$
$307$	−7.61803	−	13.1948i	−0.434784	−	0.753068i	−0.997278	+	0.0737332i	$0.976509\pi$
$308$	−1.00000			−0.0569803
$309$	18.7082			1.06427
$310$	−4.00000	−	3.87298i	−0.227185	−	0.219971i
$311$	−0.583592			−0.0330925			−0.0165462	−	0.999863i	$-0.505267\pi$
$311$	−0.583592			−0.0330925			−0.0165462	+	0.999863i	$0.505267\pi$
$312$		0			0
$313$	−9.44427	−	16.3580i	−0.533822	−	0.924606i	−0.999219	−	0.0395048i	$-0.987422\pi$
$313$	−9.44427	−	16.3580i	−0.533822	−	0.924606i	0.465398	−	0.885102i	$-0.345911\pi$
$314$	−22.1803			−1.25171
$315$	0.118034	−	0.204441i	0.00665046	−	0.0115189i
$316$	5.23607	+	9.06914i	0.294552	+	0.510179i
$317$	−10.4443	−	18.0900i	−0.586609	−	1.01604i	−0.994673	−	0.103083i	$-0.967129\pi$
$317$	−10.4443	−	18.0900i	−0.586609	−	1.01604i	0.408064	−	0.912953i	$-0.366204\pi$
$318$	−7.47214			−0.419017
$319$	6.35410	−	11.0056i	0.355761	−	0.616197i
$320$	0.500000	−	0.866025i	0.0279508	−	0.0484123i
$321$	5.35410	−	9.27358i	0.298837	−	0.517601i
$322$	0.145898	+	0.252703i	0.00813058	+	0.0140826i
$323$	9.23607	−	15.9973i	0.513909	−	0.890116i
$324$	−0.500000	−	0.866025i	−0.0277778	−	0.0481125i
$325$		0			0
$326$	−18.7639			−1.03924
$327$	−1.61803	−	2.80252i	−0.0894775	−	0.154980i
$328$	−0.618034	+	1.07047i	−0.0341252	+	0.0591066i
$329$	−0.0901699	−	0.156179i	−0.00497123	−	0.00861042i
$330$	−2.11803	+	3.66854i	−0.116594	+	0.201947i
$331$	8.61803	−	14.9269i	0.473690	−	0.820455i	−0.525856	−	0.850573i	$-0.676255\pi$
$331$	8.61803	−	14.9269i	0.473690	−	0.820455i	0.999546	+	0.0301183i	$0.00958839\pi$
$332$	−2.35410	+	4.07742i	−0.129198	+	0.223778i
$333$	−1.23607			−0.0677361
$334$	−2.14590	−	3.71680i	−0.117418	−	0.203374i
$335$	2.61803	+	4.53457i	0.143038	+	0.247750i
$336$	−0.118034	+	0.204441i	−0.00643928	+	0.0111532i
$337$	−26.4164			−1.43899			−0.719497	−	0.694496i	$-0.755627\pi$
$337$	−26.4164			−1.43899			−0.719497	+	0.694496i	$0.755627\pi$
$338$	6.50000	+	11.2583i	0.353553	+	0.612372i
$339$	−7.41641			−0.402804
$340$	−5.70820			−0.309571
$341$	−16.9443	−	16.4062i	−0.917584	−	0.888447i
$342$	−3.23607			−0.174987
$343$	−3.29180			−0.177740
$344$	−0.763932	−	1.32317i	−0.0411885	−	0.0713405i
$345$	1.23607			0.0665477
$346$	3.50000	−	6.06218i	0.188161	−	0.325905i
$347$	7.11803	+	12.3288i	0.382116	+	0.661844i	0.991365	−	0.131135i	$-0.0418621\pi$
$347$	7.11803	+	12.3288i	0.382116	+	0.661844i	−0.609248	+	0.792979i	$0.708529\pi$
$348$	−1.50000	−	2.59808i	−0.0804084	−	0.139272i
$349$	−27.2361			−1.45791			−0.728957	−	0.684560i	$-0.759994\pi$
$349$	−27.2361			−1.45791			−0.728957	+	0.684560i	$0.759994\pi$
$350$	−0.118034	+	0.204441i	−0.00630918	+	0.0109278i
$351$		0			0
$352$	2.11803	−	3.66854i	0.112892	−	0.195534i
$353$	−11.1803	−	19.3649i	−0.595069	−	1.03069i	−0.993537	−	0.113508i	$-0.963791\pi$
$353$	−11.1803	−	19.3649i	−0.595069	−	1.03069i	0.398468	−	0.917182i	$-0.369542\pi$
$354$	3.11803	−	5.40059i	0.165722	−	0.287038i
$355$	−1.23607	−	2.14093i	−0.0656037	−	0.113629i
$356$	10.9443			0.580045
$357$	1.34752			0.0713185
$358$	3.11803	+	5.40059i	0.164793	+	0.285430i
$359$	3.38197	−	5.85774i	0.178493	−	0.309160i	−0.762871	−	0.646550i	$-0.776211\pi$
$359$	3.38197	−	5.85774i	0.178493	−	0.309160i	0.941365	+	0.337391i	$0.109544\pi$
$360$	0.500000	+	0.866025i	0.0263523	+	0.0456435i
$361$	4.26393	−	7.38535i	0.224417	−	0.388702i
$362$	−2.70820	+	4.69075i	−0.142340	+	0.246540i
$363$	−3.47214	+	6.01392i	−0.182240	+	0.315649i
$364$		0			0
$365$	1.47214	+	2.54981i	0.0770551	+	0.133463i
$366$	7.09017	+	12.2805i	0.370609	+	0.641914i
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	−0.578101	−	0.815966i	$-0.696206\pi$
$367$	8.00000	−	13.8564i	0.417597	−	0.723299i	0.995697	+	0.0926670i	$0.0295392\pi$
$368$	−1.23607			−0.0644345
$369$	−0.618034	−	1.07047i	−0.0321736	−	0.0557262i
$370$	1.23607			0.0642601
$371$	−1.76393			−0.0915788
$372$	−5.35410	+	1.52761i	−0.277597	+	0.0792029i
$373$	7.23607			0.374669			0.187335	−	0.982296i	$-0.440015\pi$
$373$	7.23607			0.374669			0.187335	+	0.982296i	$0.440015\pi$
$374$	−24.1803			−1.25034
$375$	0.500000	+	0.866025i	0.0258199	+	0.0447214i
$376$	0.763932			0.0393968
$377$		0			0
$378$	−0.118034	−	0.204441i	−0.00607101	−	0.0105153i
$379$	5.00000	+	8.66025i	0.256833	+	0.444847i	0.965392	−	0.260804i	$-0.0839877\pi$
$379$	5.00000	+	8.66025i	0.256833	+	0.444847i	−0.708559	+	0.705652i	$0.750654\pi$
$380$	3.23607			0.166007
$381$	4.59017	−	7.95041i	0.235162	−	0.407312i
$382$	−9.85410	+	17.0678i	−0.504180	+	0.873265i
$383$	6.90983	−	11.9682i	0.353076	−	0.611545i	−0.633711	−	0.773570i	$-0.718469\pi$
$383$	6.90983	−	11.9682i	0.353076	−	0.611545i	0.986787	+	0.162025i	$0.0518024\pi$
$384$	−0.500000	−	0.866025i	−0.0255155	−	0.0441942i
$385$	−0.500000	+	0.866025i	−0.0254824	+	0.0441367i
$386$	7.20820	+	12.4850i	0.366888	+	0.635469i
$387$	1.52786			0.0776657
$388$	1.47214			0.0747364
$389$	1.76393	+	3.05522i	0.0894349	+	0.154906i	0.907272	−	0.420543i	$-0.138161\pi$
$389$	1.76393	+	3.05522i	0.0894349	+	0.154906i	−0.817838	+	0.575449i	$0.804827\pi$
$390$		0			0
$391$	3.52786	+	6.11044i	0.178412	+	0.309018i
$392$	3.47214	−	6.01392i	0.175369	−	0.303749i
$393$	6.47214	−	11.2101i	0.326476	−	0.565473i
$394$	9.00000	−	15.5885i	0.453413	−	0.785335i
$395$	10.4721			0.526910
$396$	2.11803	+	3.66854i	0.106435	+	0.184351i
$397$	7.18034	+	12.4367i	0.360371	+	0.624181i	0.988022	−	0.154314i	$-0.0493168\pi$
$397$	7.18034	+	12.4367i	0.360371	+	0.624181i	−0.627651	+	0.778495i	$0.715983\pi$
$398$	−13.8262	+	23.9477i	−0.693047	+	1.20039i
$399$	−0.763932			−0.0382444
$400$	−0.500000	−	0.866025i	−0.0250000	−	0.0433013i
$401$	29.3050			1.46342			0.731710	−	0.681616i	$-0.238723\pi$
$401$	29.3050			1.46342			0.731710	+	0.681616i	$0.238723\pi$
$402$	5.23607			0.261151
$403$		0			0
$404$	1.47214			0.0732415
$405$	−1.00000			−0.0496904
$406$	−0.354102	−	0.613323i	−0.0175738	−	0.0304387i
$407$	5.23607			0.259542
$408$	−2.85410	+	4.94345i	−0.141299	+	0.244737i
$409$	5.73607	+	9.93516i	0.283630	+	0.491262i	0.972276	−	0.233836i	$-0.0751278\pi$
$409$	5.73607	+	9.93516i	0.283630	+	0.491262i	−0.688646	+	0.725098i	$0.741794\pi$
$410$	0.618034	+	1.07047i	0.0305225	+	0.0528666i
$411$	−0.763932			−0.0376820
$412$	−9.35410	+	16.2018i	−0.460844	+	0.798204i
$413$	0.736068	−	1.27491i	0.0362195	−	0.0627341i
$414$	0.618034	−	1.07047i	0.0303747	−	0.0526105i
$415$	2.35410	+	4.07742i	0.115558	+	0.200153i
$416$		0			0
$417$	−8.56231	−	14.8303i	−0.419298	−	0.726245i
$418$	13.7082			0.670490
$419$	0.708204			0.0345980			0.0172990	−	0.999850i	$-0.494493\pi$
$419$	0.708204			0.0345980			0.0172990	+	0.999850i	$0.494493\pi$
$420$	0.118034	+	0.204441i	0.00575947	+	0.00997569i
$421$	14.6180	−	25.3192i	0.712439	−	1.23398i	−0.251499	−	0.967857i	$-0.580924\pi$
$421$	14.6180	−	25.3192i	0.712439	−	1.23398i	0.963939	−	0.266124i	$-0.0857430\pi$
$422$	−8.56231	−	14.8303i	−0.416807	−	0.721930i
$423$	−0.381966	+	0.661585i	−0.0185718	+	0.0321673i
$424$	3.73607	−	6.47106i	0.181440	−	0.314262i
$425$	−2.85410	+	4.94345i	−0.138444	+	0.239793i
$426$	−2.47214			−0.119775
$427$	1.67376	+	2.89904i	0.0809990	+	0.140294i
$428$	5.35410	+	9.27358i	0.258800	+	0.448255i
$429$		0			0
$430$	−1.52786			−0.0736801
$431$	10.8541	+	18.7999i	0.522824	+	0.905557i	0.999647	+	0.0265582i	$0.00845473\pi$
$431$	10.8541	+	18.7999i	0.522824	+	0.905557i	−0.476824	+	0.878999i	$0.658212\pi$
$432$	1.00000			0.0481125
$433$	6.00000			0.288342			0.144171	−	0.989553i	$-0.453949\pi$
$433$	6.00000			0.288342			0.144171	+	0.989553i	$0.453949\pi$
$434$	−1.26393	+	0.360620i	−0.0606707	+	0.0173103i
$435$	−3.00000			−0.143839
$436$	3.23607			0.154980
$437$	−2.00000	−	3.46410i	−0.0956730	−	0.165710i
$438$	2.94427			0.140683
$439$	−10.5902	+	18.3427i	−0.505441	+	0.875450i	0.494539	+	0.869155i	$0.335337\pi$
$439$	−10.5902	+	18.3427i	−0.505441	+	0.875450i	−0.999980	+	0.00629443i	$0.997996\pi$
$440$	−2.11803	−	3.66854i	−0.100973	−	0.174891i
$441$	3.47214	+	6.01392i	0.165340	+	0.286377i
$442$		0			0
$443$	16.0000	−	27.7128i	0.760183	−	1.31668i	−0.182573	−	0.983192i	$-0.558443\pi$
$443$	16.0000	−	27.7128i	0.760183	−	1.31668i	0.942756	−	0.333483i	$-0.108224\pi$
$444$	0.618034	−	1.07047i	0.0293306	−	0.0508021i
$445$	5.47214	−	9.47802i	0.259404	−	0.449301i
$446$	8.35410	+	14.4697i	0.395578	+	0.685162i
$447$	8.73607	−	15.1313i	0.413202	−	0.715687i
$448$	−0.118034	−	0.204441i	−0.00557658	−	0.00965892i
$449$	0.111456			0.00525994			0.00262997	−	0.999997i	$-0.499163\pi$
$449$	0.111456			0.00525994			0.00262997	+	0.999997i	$0.499163\pi$
$450$	1.00000			0.0471405
$451$	2.61803	+	4.53457i	0.123278	+	0.213524i
$452$	3.70820	−	6.42280i	0.174419	−	0.302103i
$453$	−4.59017	−	7.95041i	−0.215665	−	0.373543i
$454$	4.59017	−	7.95041i	0.215427	−	0.373131i
$455$		0			0
$456$	1.61803	−	2.80252i	0.0757714	−	0.131240i
$457$	19.8885			0.930347			0.465173	−	0.885220i	$-0.345992\pi$
$457$	19.8885			0.930347			0.465173	+	0.885220i	$0.345992\pi$
$458$	−2.14590	−	3.71680i	−0.100271	−	0.173675i
$459$	−2.85410	−	4.94345i	−0.133218	−	0.230740i
$460$	−0.618034	+	1.07047i	−0.0288160	+	0.0499107i
$461$	−27.0000			−1.25752			−0.628758	−	0.777601i	$-0.716436\pi$
$461$	−27.0000			−1.25752			−0.628758	+	0.777601i	$0.716436\pi$
$462$	0.500000	+	0.866025i	0.0232621	+	0.0402911i
$463$	−14.7082			−0.683548			−0.341774	−	0.939782i	$-0.611028\pi$
$463$	−14.7082			−0.683548			−0.341774	+	0.939782i	$0.611028\pi$
$464$	3.00000			0.139272
$465$	−1.35410	+	5.40059i	−0.0627950	+	0.250447i
$466$	1.81966			0.0842941
$467$	−36.5967			−1.69350			−0.846748	−	0.531995i	$-0.821443\pi$
$467$	−36.5967			−1.69350			−0.846748	+	0.531995i	$0.821443\pi$
$468$		0			0
$469$	1.23607			0.0570763
$470$	0.381966	−	0.661585i	0.0176188	−	0.0305166i
$471$	11.0902	+	19.2087i	0.511008	+	0.885092i
$472$	3.11803	+	5.40059i	0.143519	+	0.248582i
$473$	−6.47214			−0.297589
$474$	5.23607	−	9.06914i	0.240501	−	0.416559i
$475$	1.61803	−	2.80252i	0.0742405	−	0.128588i
$476$	−0.673762	+	1.16699i	−0.0308818	+	0.0534889i
$477$	3.73607	+	6.47106i	0.171063	+	0.296289i
$478$	1.70820	−	2.95870i	0.0781314	−	0.135328i
$479$	5.32624	+	9.22531i	0.243362	+	0.421515i	0.961670	−	0.274210i	$-0.0884164\pi$
$479$	5.32624	+	9.22531i	0.243362	+	0.421515i	−0.718308	+	0.695725i	$0.755083\pi$
$480$	−1.00000			−0.0456435
$481$		0			0
$482$	−5.50000	−	9.52628i	−0.250518	−	0.433910i
$483$	0.145898	−	0.252703i	0.00663859	−	0.0114984i
$484$	−3.47214	−	6.01392i	−0.157824	−	0.273360i
$485$	0.736068	−	1.27491i	0.0334231	−	0.0578906i
$486$	−0.500000	+	0.866025i	−0.0226805	+	0.0392837i
$487$	−0.409830	+	0.709846i	−0.0185712	+	0.0321662i	−0.875162	−	0.483831i	$-0.839245\pi$
$487$	−0.409830	+	0.709846i	−0.0185712	+	0.0321662i	0.856590	+	0.515997i	$0.172578\pi$
$488$	−14.1803			−0.641914
$489$	9.38197	+	16.2500i	0.424267	+	0.734852i
$490$	−3.47214	−	6.01392i	−0.156855	−	0.271681i
$491$	−14.6459	+	25.3674i	−0.660960	+	1.14482i	0.319404	+	0.947619i	$0.396517\pi$
$491$	−14.6459	+	25.3674i	−0.660960	+	1.14482i	−0.980364	+	0.197198i	$0.936816\pi$
$492$	1.23607			0.0557262
$493$	−8.56231	−	14.8303i	−0.385627	−	0.667925i
$494$		0			0
$495$	4.23607			0.190397
$496$	1.35410	−	5.40059i	0.0608010	−	0.242494i
$497$	−0.583592			−0.0261777
$498$	4.70820			0.210980
$499$	4.32624	+	7.49326i	0.193669	+	0.335445i	0.946463	−	0.322811i	$-0.104628\pi$
$499$	4.32624	+	7.49326i	0.193669	+	0.335445i	−0.752794	+	0.658256i	$0.771295\pi$
$500$	−1.00000			−0.0447214
$501$	−2.14590	+	3.71680i	−0.0958717	+	0.166055i
$502$	3.23607	+	5.60503i	0.144433	+	0.250165i
$503$	−3.85410	−	6.67550i	−0.171846	−	0.297646i	0.767219	−	0.641385i	$-0.221640\pi$
$503$	−3.85410	−	6.67550i	−0.171846	−	0.297646i	−0.939065	+	0.343739i	$0.888306\pi$
$504$	0.236068			0.0105153
$505$	0.736068	−	1.27491i	0.0327546	−	0.0567326i
$506$	−2.61803	+	4.53457i	−0.116386	+	0.201586i
$507$	6.50000	−	11.2583i	0.288675	−	0.500000i
$508$	4.59017	+	7.95041i	0.203656	+	0.352742i
$509$	10.6803	−	18.4989i	0.473398	−	0.819949i	−0.526139	−	0.850399i	$-0.676361\pi$
$509$	10.6803	−	18.4989i	0.473398	−	0.819949i	0.999536	+	0.0304499i	$0.00969401\pi$
$510$	2.85410	+	4.94345i	0.126382	+	0.218900i
$511$	0.695048			0.0307471
$512$	1.00000			0.0441942
$513$	1.61803	+	2.80252i	0.0714379	+	0.123734i
$514$	−6.32624	+	10.9574i	−0.279038	+	0.483309i
$515$	9.35410	+	16.2018i	0.412191	+	0.713936i
$516$	−0.763932	+	1.32317i	−0.0336302	+	0.0582493i
$517$	1.61803	−	2.80252i	0.0711611	−	0.123255i
$518$	0.145898	−	0.252703i	0.00641039	−	0.0111031i
$519$	−7.00000			−0.307266
$520$		0			0
$521$	−6.47214	−	11.2101i	−0.283549	−	0.491122i	0.688707	−	0.725040i	$-0.258179\pi$
$521$	−6.47214	−	11.2101i	−0.283549	−	0.491122i	−0.972256	+	0.233918i	$0.924845\pi$
$522$	−1.50000	+	2.59808i	−0.0656532	+	0.113715i
$523$	−23.4164			−1.02393			−0.511964	−	0.859007i	$-0.671082\pi$
$523$	−23.4164			−1.02393			−0.511964	+	0.859007i	$0.671082\pi$
$524$	6.47214	+	11.2101i	0.282737	+	0.489714i
$525$	0.236068			0.0103029
$526$	4.47214			0.194994
$527$	−30.5623	+	8.71991i	−1.33131	+	0.379845i
$528$	−4.23607			−0.184351
$529$	−21.4721			−0.933571
$530$	−3.73607	−	6.47106i	−0.162284	−	0.281085i
$531$	−6.23607			−0.270622
$532$	0.381966	−	0.661585i	0.0165603	−	0.0286833i
$533$		0			0
$534$	−5.47214	−	9.47802i	−0.236802	−	0.410154i
$535$	10.7082			0.462956
$536$	−2.61803	+	4.53457i	−0.113082	+	0.195864i
$537$	3.11803	−	5.40059i	0.134553	−	0.233053i
$538$	11.0000	−	19.0526i	0.474244	−	0.821414i
$539$	−14.7082	−	25.4754i	−0.633527	−	1.09730i
$540$	0.500000	−	0.866025i	0.0215166	−	0.0372678i
$541$	−0.326238	−	0.565061i	−0.0140261	−	0.0242939i	0.858927	−	0.512098i	$-0.171131\pi$
$541$	−0.326238	−	0.565061i	−0.0140261	−	0.0242939i	−0.872953	+	0.487804i	$0.837798\pi$
$542$	1.76393			0.0757674
$543$	5.41641			0.232440
$544$	−2.85410	−	4.94345i	−0.122369	−	0.211949i
$545$	1.61803	−	2.80252i	0.0693090	−	0.120047i
$546$		0			0
$547$	8.70820	−	15.0831i	0.372336	−	0.644905i	−0.617589	−	0.786501i	$-0.711890\pi$
$547$	8.70820	−	15.0831i	0.372336	−	0.644905i	0.989924	+	0.141597i	$0.0452236\pi$
$548$	0.381966	−	0.661585i	0.0163168	−	0.0282615i
$549$	7.09017	−	12.2805i	0.302601	−	0.524120i
$550$	−4.23607			−0.180627
$551$	4.85410	+	8.40755i	0.206792	+	0.358174i
$552$	0.618034	+	1.07047i	0.0263053	+	0.0455621i
$553$	1.23607	−	2.14093i	0.0525630	−	0.0910417i
$554$	−10.6525			−0.452580
$555$	−0.618034	−	1.07047i	−0.0262341	−	0.0454388i
$556$	17.1246			0.726245
$557$	24.4164			1.03456			0.517278	−	0.855817i	$-0.326945\pi$
$557$	24.4164			1.03456			0.517278	+	0.855817i	$0.326945\pi$
$558$	4.00000	+	3.87298i	0.169334	+	0.163956i
$559$		0			0
$560$	−0.236068			−0.00997569
$561$	12.0902	+	20.9408i	0.510447	+	0.884121i
$562$	−0.472136			−0.0199159
$563$	0.937694	−	1.62413i	0.0395191	−	0.0684491i	−0.845589	−	0.533834i	$-0.820751\pi$
$563$	0.937694	−	1.62413i	0.0395191	−	0.0684491i	0.885108	+	0.465385i	$0.154084\pi$
$564$	−0.381966	−	0.661585i	−0.0160837	−	0.0278577i
$565$	−3.70820	−	6.42280i	−0.156005	−	0.270209i
$566$	7.41641			0.311735
$567$	−0.118034	+	0.204441i	−0.00495696	+	0.00858571i
$568$	1.23607	−	2.14093i	0.0518643	−	0.0898315i
$569$	−4.47214	+	7.74597i	−0.187482	+	0.324728i	−0.944410	−	0.328770i	$-0.893366\pi$
$569$	−4.47214	+	7.74597i	−0.187482	+	0.324728i	0.756928	+	0.653498i	$0.226699\pi$
$570$	−1.61803	−	2.80252i	−0.0677720	−	0.117385i
$571$	19.1803	−	33.2213i	0.802672	−	1.39027i	−0.115179	−	0.993345i	$-0.536744\pi$
$571$	19.1803	−	33.2213i	0.802672	−	1.39027i	0.917851	−	0.396924i	$-0.129922\pi$
$572$		0			0
$573$	19.7082			0.823322
$574$	0.291796			0.0121793
$575$	0.618034	+	1.07047i	0.0257738	+	0.0446415i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	14.4164	+	24.9700i	0.600163	+	1.03951i	0.992796	+	0.119817i	$0.0382309\pi$
$577$	14.4164	+	24.9700i	0.600163	+	1.03951i	−0.392633	+	0.919695i	$0.628436\pi$
$578$	−7.79180	+	13.4958i	−0.324096	+	0.561351i
$579$	7.20820	−	12.4850i	0.299563	−	0.518858i
$580$	1.50000	−	2.59808i	0.0622841	−	0.107879i
$581$	1.11146			0.0461110
$582$	−0.736068	−	1.27491i	−0.0305110	−	0.0528466i
$583$	−15.8262	−	27.4118i	−0.655456	−	1.13528i
$584$	−1.47214	+	2.54981i	−0.0609174	+	0.105512i
$585$		0			0
$586$	−1.20820	−	2.09267i	−0.0499104	−	0.0864474i
$587$	−9.65248			−0.398400			−0.199200	−	0.979959i	$-0.563834\pi$
$587$	−9.65248			−0.398400			−0.199200	+	0.979959i	$0.563834\pi$
$588$	−6.94427			−0.286377
$589$	17.3262	−	4.94345i	0.713915	−	0.203691i
$590$	6.23607			0.256735
$591$	−18.0000			−0.740421
$592$	0.618034	+	1.07047i	0.0254010	+	0.0439959i
$593$	−20.5410			−0.843519			−0.421759	−	0.906708i	$-0.638587\pi$
$593$	−20.5410			−0.843519			−0.421759	+	0.906708i	$0.638587\pi$
$594$	2.11803	−	3.66854i	0.0869040	−	0.150522i
$595$	0.673762	+	1.16699i	0.0276216	+	0.0478419i
$596$	8.73607	+	15.1313i	0.357843	+	0.619803i
$597$	27.6525			1.13174
$598$		0			0
$599$	−13.4164	+	23.2379i	−0.548180	+	0.949475i	0.450220	+	0.892918i	$0.351346\pi$
$599$	−13.4164	+	23.2379i	−0.548180	+	0.949475i	−0.998399	+	0.0565571i	$0.981988\pi$
$600$	−0.500000	+	0.866025i	−0.0204124	+	0.0353553i
$601$	−20.1246	−	34.8569i	−0.820900	−	1.42184i	−0.905013	−	0.425384i	$-0.860139\pi$
$601$	−20.1246	−	34.8569i	−0.820900	−	1.42184i	0.0841128	−	0.996456i	$-0.473194\pi$
$602$	−0.180340	+	0.312358i	−0.00735011	+	0.0127308i
$603$	−2.61803	−	4.53457i	−0.106615	−	0.184662i
$604$	9.18034			0.373543
$605$	−6.94427			−0.282325
$606$	−0.736068	−	1.27491i	−0.0299007	−	0.0517896i
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	−0.0998457	−	0.995003i	$-0.531835\pi$
$607$	20.0000	−	34.6410i	0.811775	−	1.40604i	0.911621	−	0.411033i	$-0.134832\pi$
$608$	1.61803	+	2.80252i	0.0656199	+	0.113657i
$609$	−0.354102	+	0.613323i	−0.0143489	+	0.0248531i
$610$	−7.09017	+	12.2805i	−0.287073	+	0.497224i
$611$		0			0
$612$	5.70820			0.230740
$613$	3.70820	+	6.42280i	0.149773	+	0.259414i	0.931143	−	0.364653i	$-0.118812\pi$
$613$	3.70820	+	6.42280i	0.149773	+	0.259414i	−0.781371	+	0.624067i	$0.785479\pi$
$614$	−7.61803	−	13.1948i	−0.307439	−	0.532500i
$615$	0.618034	−	1.07047i	0.0249215	−	0.0431654i
$616$	−1.00000			−0.0402911
$617$	−0.145898	−	0.252703i	−0.00587363	−	0.0101734i	0.863074	−	0.505078i	$-0.168536\pi$
$617$	−0.145898	−	0.252703i	−0.00587363	−	0.0101734i	−0.868947	+	0.494905i	$0.835203\pi$
$618$	18.7082			0.752554
$619$	26.0000			1.04503			0.522514	−	0.852631i	$-0.324994\pi$
$619$	26.0000			1.04503			0.522514	+	0.852631i	$0.324994\pi$
$620$	−4.00000	−	3.87298i	−0.160644	−	0.155543i
$621$	−1.23607			−0.0496017
$622$	−0.583592			−0.0233999
$623$	−1.29180	−	2.23746i	−0.0517547	−	0.0896418i
$624$		0			0
$625$	−0.500000	+	0.866025i	−0.0200000	+	0.0346410i
$626$	−9.44427	−	16.3580i	−0.377469	−	0.653796i
$627$	−6.85410	−	11.8717i	−0.273726	−	0.474108i
$628$	−22.1803			−0.885092
$629$	3.52786	−	6.11044i	0.140665	−	0.243639i
$630$	0.118034	−	0.204441i	0.00470259	−	0.00814512i
$631$	3.29837	−	5.71295i	0.131306	−	0.227429i	−0.792874	−	0.609385i	$-0.791416\pi$
$631$	3.29837	−	5.71295i	0.131306	−	0.227429i	0.924180	+	0.381956i	$0.124750\pi$
$632$	5.23607	+	9.06914i	0.208280	+	0.360751i
$633$	−8.56231	+	14.8303i	−0.340321	+	0.589453i
$634$	−10.4443	−	18.0900i	−0.414795	−	0.718446i
$635$	9.18034			0.364311
$636$	−7.47214			−0.296289
$637$		0			0
$638$	6.35410	−	11.0056i	0.251561	−	0.435717i
$639$	1.23607	+	2.14093i	0.0488981	+	0.0846940i
$640$	0.500000	−	0.866025i	0.0197642	−	0.0342327i
$641$	12.1459	−	21.0373i	0.479734	−	0.830924i	−0.519996	−	0.854169i	$-0.674066\pi$
$641$	12.1459	−	21.0373i	0.479734	−	0.830924i	0.999730	+	0.0232450i	$0.00739978\pi$
$642$	5.35410	−	9.27358i	0.211310	−	0.365999i
$643$	16.2918			0.642486			0.321243	−	0.946997i	$-0.395899\pi$
$643$	16.2918			0.642486			0.321243	+	0.946997i	$0.395899\pi$
$644$	0.145898	+	0.252703i	0.00574919	+	0.00995789i
$645$	0.763932	+	1.32317i	0.0300798	+	0.0520997i
$646$	9.23607	−	15.9973i	0.363388	−	0.629407i
$647$	−36.1803			−1.42240			−0.711198	−	0.702992i	$-0.751847\pi$
$647$	−36.1803			−1.42240			−0.711198	+	0.702992i	$0.751847\pi$
$648$	−0.500000	−	0.866025i	−0.0196419	−	0.0340207i
$649$	26.4164			1.03693
$650$		0			0
$651$	0.944272	+	0.914287i	0.0370089	+	0.0358337i
$652$	−18.7639			−0.734852
$653$	13.3607			0.522844			0.261422	−	0.965225i	$-0.415809\pi$
$653$	13.3607			0.522844			0.261422	+	0.965225i	$0.415809\pi$
$654$	−1.61803	−	2.80252i	−0.0632701	−	0.109587i
$655$	12.9443			0.505775
$656$	−0.618034	+	1.07047i	−0.0241302	+	0.0417947i
$657$	−1.47214	−	2.54981i	−0.0574335	−	0.0994777i
$658$	−0.0901699	−	0.156179i	−0.00351519	−	0.00608849i
$659$	−16.1246			−0.628126			−0.314063	−	0.949402i	$-0.601690\pi$
$659$	−16.1246			−0.628126			−0.314063	+	0.949402i	$0.601690\pi$
$660$	−2.11803	+	3.66854i	−0.0824444	+	0.142798i
$661$	0.145898	−	0.252703i	0.00567478	−	0.00982900i	−0.863174	−	0.504906i	$-0.831527\pi$
$661$	0.145898	−	0.252703i	0.00567478	−	0.00982900i	0.868849	+	0.495077i	$0.164860\pi$
$662$	8.61803	−	14.9269i	0.334949	−	0.580149i
$663$		0			0
$664$	−2.35410	+	4.07742i	−0.0913569	+	0.158235i
$665$	−0.381966	−	0.661585i	−0.0148120	−	0.0256551i
$666$	−1.23607			−0.0478967
$667$	−3.70820			−0.143582
$668$	−2.14590	−	3.71680i	−0.0830273	−	0.143807i
$669$	8.35410	−	14.4697i	0.322988	−	0.559432i
$670$	2.61803	+	4.53457i	0.101143	+	0.175186i
$671$	−30.0344	+	52.0212i	−1.15947	+	2.00826i
$672$	−0.118034	+	0.204441i	−0.00455326	+	0.00788648i
$673$	17.6803	−	30.6232i	0.681527	−	1.18044i	−0.292988	−	0.956116i	$-0.594650\pi$
$673$	17.6803	−	30.6232i	0.681527	−	1.18044i	0.974515	−	0.224323i	$-0.0720171\pi$
$674$	−26.4164			−1.01752
$675$	−0.500000	−	0.866025i	−0.0192450	−	0.0333333i
$676$	6.50000	+	11.2583i	0.250000	+	0.433013i
$677$	−4.79180	+	8.29963i	−0.184164	+	0.318981i	−0.943294	−	0.331957i	$-0.892291\pi$
$677$	−4.79180	+	8.29963i	−0.184164	+	0.318981i	0.759131	+	0.650938i	$0.225624\pi$
$678$	−7.41641			−0.284825
$679$	−0.173762	−	0.300965i	−0.00666838	−	0.0115500i
$680$	−5.70820			−0.218900
$681$	−9.18034			−0.351791
$682$	−16.9443	−	16.4062i	−0.648830	−	0.628227i
$683$	−38.5967			−1.47686			−0.738432	−	0.674328i	$-0.764433\pi$
$683$	−38.5967			−1.47686			−0.738432	+	0.674328i	$0.764433\pi$
$684$	−3.23607			−0.123734
$685$	−0.381966	−	0.661585i	−0.0145942	−	0.0252778i
$686$	−3.29180			−0.125681
$687$	−2.14590	+	3.71680i	−0.0818711	+	0.141805i
$688$	−0.763932	−	1.32317i	−0.0291246	−	0.0504453i
$689$		0			0
$690$	1.23607			0.0470563
$691$	9.61803	−	16.6589i	0.365887	−	0.633735i	−0.623031	−	0.782197i	$-0.714099\pi$
$691$	9.61803	−	16.6589i	0.365887	−	0.633735i	0.988918	+	0.148462i	$0.0474322\pi$
$692$	3.50000	−	6.06218i	0.133050	−	0.230449i
$693$	0.500000	−	0.866025i	0.0189934	−	0.0328976i
$694$	7.11803	+	12.3288i	0.270197	+	0.467995i
$695$	8.56231	−	14.8303i	0.324787	−	0.562547i
$696$	−1.50000	−	2.59808i	−0.0568574	−	0.0984798i
$697$	7.05573			0.267255
$698$	−27.2361			−1.03090
$699$	−0.909830	−	1.57587i	−0.0344129	−	0.0596049i
$700$	−0.118034	+	0.204441i	−0.00446127	+	0.00772714i
$701$	14.6803	+	25.4271i	0.554469	+	0.960368i	0.997945	+	0.0640818i	$0.0204119\pi$
$701$	14.6803	+	25.4271i	0.554469	+	0.960368i	−0.443476	+	0.896286i	$0.646255\pi$
$702$		0			0
$703$	−2.00000	+	3.46410i	−0.0754314	+	0.130651i
$704$	2.11803	−	3.66854i	0.0798264	−	0.138263i
$705$	−0.763932			−0.0287713
$706$	−11.1803	−	19.3649i	−0.420778	−	0.728808i
$707$	−0.173762	−	0.300965i	−0.00653500	−	0.0113189i
$708$	3.11803	−	5.40059i	0.117183	−	0.202967i
$709$	11.1246			0.417794			0.208897	−	0.977938i	$-0.433013\pi$
$709$	11.1246			0.417794			0.208897	+	0.977938i	$0.433013\pi$
$710$	−1.23607	−	2.14093i	−0.0463888	−	0.0803478i
$711$	−10.4721			−0.392736
$712$	10.9443			0.410154
$713$	−1.67376	+	6.67550i	−0.0626829	+	0.249999i
$714$	1.34752			0.0504298
$715$		0			0
$716$	3.11803	+	5.40059i	0.116526	+	0.201830i
$717$	−3.41641			−0.127588
$718$	3.38197	−	5.85774i	0.126214	−	0.218609i
$719$	−20.5623	−	35.6150i	−0.766845	−	1.32821i	−0.939266	−	0.343191i	$-0.888492\pi$
$719$	−20.5623	−	35.6150i	−0.766845	−	1.32821i	0.172421	−	0.985023i	$-0.444841\pi$
$720$	0.500000	+	0.866025i	0.0186339	+	0.0322749i
$721$	4.41641			0.164476
$722$	4.26393	−	7.38535i	0.158687	−	0.274854i
$723$	−5.50000	+	9.52628i	−0.204547	+	0.354286i
$724$	−2.70820	+	4.69075i	−0.100650	+	0.174330i
$725$	−1.50000	−	2.59808i	−0.0557086	−	0.0964901i
$726$	−3.47214	+	6.01392i	−0.128863	+	0.223197i
$727$	20.8820	+	36.1686i	0.774469	+	1.34142i	0.935092	+	0.354404i	$0.115316\pi$
$727$	20.8820	+	36.1686i	0.774469	+	1.34142i	−0.160623	+	0.987016i	$0.551350\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	1.47214	+	2.54981i	0.0544862	+	0.0943729i
$731$	−4.36068	+	7.55292i	−0.161286	+	0.279355i
$732$	7.09017	+	12.2805i	0.262060	+	0.453902i
$733$	−14.8885	+	25.7877i	−0.549921	+	0.952491i	0.448358	+	0.893854i	$0.352009\pi$
$733$	−14.8885	+	25.7877i	−0.549921	+	0.952491i	−0.998279	+	0.0586371i	$0.981325\pi$
$734$	8.00000	−	13.8564i	0.295285	−	0.511449i
$735$	−3.47214	+	6.01392i	−0.128072	+	0.221827i
$736$	−1.23607			−0.0455621
$737$	11.0902	+	19.2087i	0.408512	+	0.707563i
$738$	−0.618034	−	1.07047i	−0.0227501	−	0.0394044i
$739$	−13.1459	+	22.7694i	−0.483580	+	0.837585i	−0.999822	−	0.0188579i	$-0.993997\pi$
$739$	−13.1459	+	22.7694i	−0.483580	+	0.837585i	0.516242	+	0.856442i	$0.327330\pi$
$740$	1.23607			0.0454388
$741$		0			0
$742$	−1.76393			−0.0647560
$743$	−38.3607			−1.40732			−0.703658	−	0.710538i	$-0.748451\pi$
$743$	−38.3607			−1.40732			−0.703658	+	0.710538i	$0.748451\pi$
$744$	−5.35410	+	1.52761i	−0.196291	+	0.0560049i
$745$	17.4721			0.640130
$746$	7.23607			0.264931
$747$	−2.35410	−	4.07742i	−0.0861321	−	0.149185i
$748$	−24.1803			−0.884121
$749$	1.26393	−	2.18919i	0.0461831	−	0.0799914i
$750$	0.500000	+	0.866025i	0.0182574	+	0.0316228i
$751$	22.8262	+	39.5362i	0.832941	+	1.44270i	0.895696	+	0.444668i	$0.146678\pi$
$751$	22.8262	+	39.5362i	0.832941	+	1.44270i	−0.0627544	+	0.998029i	$0.519988\pi$
$752$	0.763932			0.0278577
$753$	3.23607	−	5.60503i	0.117929	−	0.204259i
$754$		0			0
$755$	4.59017	−	7.95041i	0.167053	−	0.289345i
$756$	−0.118034	−	0.204441i	−0.00429285	−	0.00743544i
$757$	−6.29180	+	10.8977i	−0.228679	+	0.396084i	−0.957417	−	0.288709i	$-0.906774\pi$
$757$	−6.29180	+	10.8977i	−0.228679	+	0.396084i	0.728738	+	0.684793i	$0.240107\pi$
$758$	5.00000	+	8.66025i	0.181608	+	0.314555i
$759$	5.23607			0.190057
$760$	3.23607			0.117385
$761$	−18.8541	−	32.6563i	−0.683461	−	1.18379i	−0.973918	−	0.226901i	$-0.927141\pi$
$761$	−18.8541	−	32.6563i	−0.683461	−	1.18379i	0.290457	−	0.956888i	$-0.406193\pi$
$762$	4.59017	−	7.95041i	0.166284	−	0.288013i
$763$	−0.381966	−	0.661585i	−0.0138281	−	0.0239510i
$764$	−9.85410	+	17.0678i	−0.356509	+	0.617492i
$765$	2.85410	−	4.94345i	0.103190	−	0.178731i
$766$	6.90983	−	11.9682i	0.249662	−	0.432428i
$767$		0			0
$768$	−0.500000	−	0.866025i	−0.0180422	−	0.0312500i
$769$	17.2082	+	29.8055i	0.620544	+	1.07481i	0.989385	+	0.145321i	$0.0464214\pi$
$769$	17.2082	+	29.8055i	0.620544	+	1.07481i	−0.368841	+	0.929493i	$0.620245\pi$
$770$	−0.500000	+	0.866025i	−0.0180187	+	0.0312094i
$771$	12.6525			0.455668
$772$	7.20820	+	12.4850i	0.259429	+	0.449344i
$773$	−6.94427			−0.249768			−0.124884	−	0.992171i	$-0.539856\pi$
$773$	−6.94427			−0.249768			−0.124884	+	0.992171i	$0.539856\pi$
$774$	1.52786			0.0549179
$775$	−5.35410	+	1.52761i	−0.192325	+	0.0548734i
$776$	1.47214			0.0528466
$777$	−0.291796			−0.0104681
$778$	1.76393	+	3.05522i	0.0632400	+	0.109535i
$779$	−4.00000			−0.143315
$780$		0			0
$781$	−5.23607	−	9.06914i	−0.187361	−	0.324519i
$782$	3.52786	+	6.11044i	0.126156	+	0.218509i
$783$	3.00000			0.107211
$784$	3.47214	−	6.01392i	0.124005	−	0.214783i
$785$	−11.0902	+	19.2087i	−0.395825	+	0.685589i
$786$	6.47214	−	11.2101i	0.230853	−	0.399850i
$787$	10.5066	+	18.1979i	0.374519	+	0.648686i	0.990255	−	0.139267i	$-0.0444745\pi$
$787$	10.5066	+	18.1979i	0.374519	+	0.648686i	−0.615736	+	0.787953i	$0.711141\pi$
$788$	9.00000	−	15.5885i	0.320612	−	0.555316i
$789$	−2.23607	−	3.87298i	−0.0796061	−	0.137882i
$790$	10.4721			0.372582
$791$	−1.75078			−0.0622504
$792$	2.11803	+	3.66854i	0.0752611	+	0.130356i
$793$		0			0
$794$	7.18034	+	12.4367i	0.254821	+	0.441362i
$795$	−3.73607	+	6.47106i	−0.132505	+	0.229505i
$796$	−13.8262	+	23.9477i	−0.490058	+	0.848805i
$797$	−16.0279	+	27.7611i	−0.567736	+	0.983348i	0.429053	+	0.903279i	$0.358847\pi$
$797$	−16.0279	+	27.7611i	−0.567736	+	0.983348i	−0.996789	+	0.0800685i	$0.974486\pi$
$798$	−0.763932			−0.0270429
$799$	−2.18034	−	3.77646i	−0.0771349	−	0.133602i
$800$	−0.500000	−	0.866025i	−0.0176777	−	0.0306186i
$801$	−5.47214	+	9.47802i	−0.193348	+	0.334889i
$802$	29.3050			1.03479
$803$	6.23607	+	10.8012i	0.220066	+	0.381166i
$804$	5.23607			0.184662
$805$	0.291796			0.0102845
$806$		0			0
$807$	−22.0000			−0.774437
$808$	1.47214			0.0517896
$809$	−22.2705	−	38.5737i	−0.782989	−	1.35618i	−0.930193	−	0.367071i	$-0.880361\pi$
$809$	−22.2705	−	38.5737i	−0.782989	−	1.35618i	0.147203	−	0.989106i	$-0.452973\pi$
$810$	−1.00000			−0.0351364
$811$	8.41641	−	14.5776i	0.295540	−	0.511890i	−0.679570	−	0.733610i	$-0.737834\pi$
$811$	8.41641	−	14.5776i	0.295540	−	0.511890i	0.975110	+	0.221720i	$0.0711671\pi$
$812$	−0.354102	−	0.613323i	−0.0124265	−	0.0215234i
$813$	−0.881966	−	1.52761i	−0.0309319	−	0.0535756i
$814$	5.23607			0.183524
$815$	−9.38197	+	16.2500i	−0.328636	+	0.569214i
$816$	−2.85410	+	4.94345i	−0.0999136	+	0.173055i
$817$	2.47214	−	4.28187i	0.0864891	−	0.149803i
$818$	5.73607	+	9.93516i	0.200557	+	0.347375i
$819$		0			0
$820$	0.618034	+	1.07047i	0.0215827	+	0.0373823i
$821$	40.8885			1.42702			0.713510	−	0.700645i	$-0.247104\pi$
$821$	40.8885			1.42702			0.713510	+	0.700645i	$0.247104\pi$
$822$	−0.763932			−0.0266452
$823$	12.4098	+	21.4945i	0.432579	+	0.749250i	0.997095	−	0.0761731i	$-0.0242702\pi$
$823$	12.4098	+	21.4945i	0.432579	+	0.749250i	−0.564515	+	0.825423i	$0.690937\pi$
$824$	−9.35410	+	16.2018i	−0.325866	+	0.564416i
$825$	2.11803	+	3.66854i	0.0737405	+	0.127722i
$826$	0.736068	−	1.27491i	0.0256111	−	0.0443597i
$827$	9.41641	−	16.3097i	0.327441	−	0.567144i	−0.654563	−	0.756008i	$-0.727147\pi$
$827$	9.41641	−	16.3097i	0.327441	−	0.567144i	0.982003	+	0.188864i	$0.0604805\pi$
$828$	0.618034	−	1.07047i	0.0214782	−	0.0372013i
$829$	−36.7639			−1.27686			−0.638432	−	0.769678i	$-0.720417\pi$
$829$	−36.7639			−1.27686			−0.638432	+	0.769678i	$0.720417\pi$
$830$	2.35410	+	4.07742i	0.0817121	+	0.141529i
$831$	5.32624	+	9.22531i	0.184765	+	0.320023i
$832$		0			0
$833$	−39.6393			−1.37342
$834$	−8.56231	−	14.8303i	−0.296488	−	0.513533i
$835$	−4.29180			−0.148524
$836$	13.7082			0.474108
$837$	1.35410	−	5.40059i	0.0468046	−	0.186672i
$838$	0.708204			0.0244645
$839$	−17.3475			−0.598903			−0.299452	−	0.954112i	$-0.596804\pi$
$839$	−17.3475			−0.598903			−0.299452	+	0.954112i	$0.596804\pi$
$840$	0.118034	+	0.204441i	0.00407256	+	0.00705388i
$841$	−20.0000			−0.689655
$842$	14.6180	−	25.3192i	0.503771	−	0.872556i
$843$	0.236068	+	0.408882i	0.00813061	+	0.0140826i
$844$	−8.56231	−	14.8303i	−0.294727	−	0.510482i
$845$	13.0000			0.447214
$846$	−0.381966	+	0.661585i	−0.0131323	+	0.0227457i
$847$	−0.819660	+	1.41969i	−0.0281639	+	0.0487812i
$848$	3.73607	−	6.47106i	0.128297	−	0.222217i
$849$	−3.70820	−	6.42280i	−0.127265	−	0.220430i
$850$	−2.85410	+	4.94345i	−0.0978949	+	0.169559i
$851$	−0.763932	−	1.32317i	−0.0261873	−	0.0453577i
$852$	−2.47214			−0.0846940
$853$	14.4721			0.495516			0.247758	−	0.968822i	$-0.420306\pi$
$853$	14.4721			0.495516			0.247758	+	0.968822i	$0.420306\pi$
$854$	1.67376	+	2.89904i	0.0572750	+	0.0992031i
$855$	−1.61803	+	2.80252i	−0.0553356	+	0.0958441i
$856$	5.35410	+	9.27358i	0.182999	+	0.316964i
$857$	−22.0000	+	38.1051i	−0.751506	+	1.30165i	0.195587	+	0.980686i	$0.437339\pi$
$857$	−22.0000	+	38.1051i	−0.751506	+	1.30165i	−0.947093	+	0.320960i	$0.895995\pi$
$858$		0			0
$859$	8.61803	−	14.9269i	0.294044	−	0.509298i	−0.680718	−	0.732545i	$-0.738332\pi$
$859$	8.61803	−	14.9269i	0.294044	−	0.509298i	0.974762	+	0.223247i	$0.0716656\pi$
$860$	−1.52786			−0.0520997
$861$	−0.145898	−	0.252703i	−0.00497219	−	0.00861209i
$862$	10.8541	+	18.7999i	0.369692	+	0.640326i
$863$	−22.4721	+	38.9229i	−0.764960	+	1.32495i	0.175307	+	0.984514i	$0.443908\pi$
$863$	−22.4721	+	38.9229i	−0.764960	+	1.32495i	−0.940268	+	0.340436i	$0.889425\pi$
$864$	1.00000			0.0340207
$865$	−3.50000	−	6.06218i	−0.119004	−	0.206120i
$866$	6.00000			0.203888
$867$	15.5836			0.529247
$868$	−1.26393	+	0.360620i	−0.0429006	+	0.0122402i
$869$	44.3607			1.50483
$870$	−3.00000			−0.101710
$871$		0			0
$872$	3.23607			0.109587
$873$	−0.736068	+	1.27491i	−0.0249121	+	0.0431491i
$874$	−2.00000	−	3.46410i	−0.0676510	−	0.117175i
$875$	0.118034	+	0.204441i	0.00399028	+	0.00691136i
$876$	2.94427			0.0994777
$877$	−28.6180	+	49.5679i	−0.966362	+	1.67379i	−0.260453	+	0.965487i	$0.583872\pi$
$877$	−28.6180	+	49.5679i	−0.966362	+	1.67379i	−0.705909	+	0.708302i	$0.749461\pi$
$878$	−10.5902	+	18.3427i	−0.357401	+	0.619037i
$879$	−1.20820	+	2.09267i	−0.0407517	+	0.0705840i
$880$	−2.11803	−	3.66854i	−0.0713989	−	0.123667i
$881$	−4.32624	+	7.49326i	−0.145755	+	0.252454i	−0.929654	−	0.368433i	$-0.879894\pi$
$881$	−4.32624	+	7.49326i	−0.145755	+	0.252454i	0.783900	+	0.620888i	$0.213228\pi$
$882$	3.47214	+	6.01392i	0.116913	+	0.202499i
$883$	33.2361			1.11848			0.559241	−	0.829005i	$-0.311093\pi$
$883$	33.2361			1.11848			0.559241	+	0.829005i	$0.311093\pi$
$884$		0			0
$885$	−3.11803	−	5.40059i	−0.104812	−	0.181539i
$886$	16.0000	−	27.7128i	0.537531	−	0.931030i
$887$	22.1246	+	38.3210i	0.742872	+	1.28669i	0.951183	+	0.308629i	$0.0998701\pi$
$887$	22.1246	+	38.3210i	0.742872	+	1.28669i	−0.208311	+	0.978063i	$0.566797\pi$
$888$	0.618034	−	1.07047i	0.0207399	−	0.0359225i
$889$	1.08359	−	1.87684i	0.0363425	−	0.0629471i
$890$	5.47214	−	9.47802i	0.183426	−	0.317704i
$891$	−4.23607			−0.141914
$892$	8.35410	+	14.4697i	0.279716	+	0.484482i
$893$	1.23607	+	2.14093i	0.0413634	+	0.0716436i
$894$	8.73607	−	15.1313i	0.292178	−	0.506067i
$895$	6.23607			0.208449
$896$	−0.118034	−	0.204441i	−0.00394324	−	0.00682989i
$897$		0			0
$898$	0.111456			0.00371934
$899$	4.06231	−	16.2018i	0.135485	−	0.540360i
$900$	1.00000			0.0333333
$901$	−42.6525			−1.42096
$902$	2.61803	+	4.53457i	0.0871710	+	0.150985i
$903$	0.360680			0.0120027
$904$	3.70820	−	6.42280i	0.123333	−	0.213619i
$905$	2.70820	+	4.69075i	0.0900237	+	0.155926i
$906$	−4.59017	−	7.95041i	−0.152498	−	0.264135i
$907$	1.52786			0.0507319			0.0253659	−	0.999678i	$-0.491925\pi$
$907$	1.52786			0.0507319			0.0253659	+	0.999678i	$0.491925\pi$
$908$	4.59017	−	7.95041i	0.152330	−	0.263844i
$909$	−0.736068	+	1.27491i	−0.0244138	+	0.0422860i
$910$		0			0
$911$	8.27051	+	14.3249i	0.274014	+	0.474607i	0.969886	−	0.243560i	$-0.0783151\pi$
$911$	8.27051	+	14.3249i	0.274014	+	0.474607i	−0.695872	+	0.718166i	$0.744982\pi$
$912$	1.61803	−	2.80252i	0.0535785	−	0.0928006i
$913$	9.97214	+	17.2722i	0.330030	+	0.571628i
$914$	19.8885			0.657855
$915$	14.1803			0.468788
$916$	−2.14590	−	3.71680i	−0.0709025	−	0.122807i
$917$	1.52786	−	2.64634i	0.0504545	−	0.0873898i
$918$	−2.85410	−	4.94345i	−0.0941994	−	0.163158i
$919$	−1.59017	+	2.75426i	−0.0524549	+	0.0908545i	−0.891061	−	0.453884i	$-0.850038\pi$
$919$	−1.59017	+	2.75426i	−0.0524549	+	0.0908545i	0.838606	+	0.544739i	$0.183371\pi$
$920$	−0.618034	+	1.07047i	−0.0203760	+	0.0352922i
$921$	−7.61803	+	13.1948i	−0.251023	+	0.434784i
$922$	−27.0000			−0.889198
$923$		0			0
$924$	0.500000	+	0.866025i	0.0164488	+	0.0284901i
$925$	0.618034	−	1.07047i	0.0203208	−	0.0351967i
$926$	−14.7082			−0.483342
$927$	−9.35410	−	16.2018i	−0.307229	−	0.532136i
$928$	3.00000			0.0984798
$929$	12.7639			0.418771			0.209386	−	0.977833i	$-0.432854\pi$
$929$	12.7639			0.418771			0.209386	+	0.977833i	$0.432854\pi$
$930$	−1.35410	+	5.40059i	−0.0444028	+	0.177092i
$931$	22.4721			0.736495
$932$	1.81966			0.0596049
$933$	0.291796	+	0.505406i	0.00955297	+	0.0165462i
$934$	−36.5967			−1.19748
$935$	−12.0902	+	20.9408i	−0.395391	+	0.684837i
$936$		0			0
$937$	27.9443	+	48.4009i	0.912900	+	1.58119i	0.809948	+	0.586502i	$0.199495\pi$
$937$	27.9443	+	48.4009i	0.912900	+	1.58119i	0.102952	+	0.994686i	$0.467171\pi$
$938$	1.23607			0.0403591
$939$	−9.44427	+	16.3580i	−0.308202	+	0.533822i
$940$	0.381966	−	0.661585i	0.0124584	−	0.0215785i
$941$	−30.3885	+	52.6345i	−0.990638	+	1.71584i	−0.377095	+	0.926175i	$0.623077\pi$
$941$	−30.3885	+	52.6345i	−0.990638	+	1.71584i	−0.613543	+	0.789661i	$0.710256\pi$
$942$	11.0902	+	19.2087i	0.361337	+	0.625854i
$943$	0.763932	−	1.32317i	0.0248770	−	0.0430883i
$944$	3.11803	+	5.40059i	0.101483	+	0.175774i
$945$	−0.236068			−0.00767929
$946$	−6.47214			−0.210427
$947$	0.763932	+	1.32317i	0.0248245	+	0.0429972i	0.878171	−	0.478347i	$-0.158764\pi$
$947$	0.763932	+	1.32317i	0.0248245	+	0.0429972i	−0.853346	+	0.521345i	$0.825431\pi$
$948$	5.23607	−	9.06914i	0.170060	−	0.294552i
$949$		0			0
$950$	1.61803	−	2.80252i	0.0524960	−	0.0909257i
$951$	−10.4443	+	18.0900i	−0.338679	+	0.586609i
$952$	−0.673762	+	1.16699i	−0.0218368	+	0.0378224i
$953$	47.4853			1.53820			0.769100	−	0.639129i	$-0.220705\pi$
$953$	47.4853			1.53820			0.769100	+	0.639129i	$0.220705\pi$
$954$	3.73607	+	6.47106i	0.120960	+	0.209508i
$955$	9.85410	+	17.0678i	0.318871	+	0.552301i
$956$	1.70820	−	2.95870i	0.0552473	−	0.0956911i
$957$	−12.7082			−0.410798
$958$	5.32624	+	9.22531i	0.172083	+	0.298056i
$959$	−0.180340			−0.00582348
$960$	−1.00000			−0.0322749
$961$	−27.3328	−	14.6259i	−0.881704	−	0.471803i
$962$		0			0
$963$	−10.7082			−0.345067
$964$	−5.50000	−	9.52628i	−0.177143	−	0.306821i
$965$	14.4164			0.464081
$966$	0.145898	−	0.252703i	0.00469419	−	0.00813058i
$967$	14.9443	+	25.8842i	0.480575	+	0.832381i	0.999752	−	0.0222862i	$-0.00709451\pi$
$967$	14.9443	+	25.8842i	0.480575	+	0.832381i	−0.519176	+	0.854667i	$0.673761\pi$
$968$	−3.47214	−	6.01392i	−0.111599	−	0.193295i
$969$	−18.4721			−0.593411
$970$	0.736068	−	1.27491i	0.0236337	−	0.0409348i
$971$	−1.06231	+	1.83997i	−0.0340910	+	0.0590474i	−0.882568	−	0.470186i	$-0.844187\pi$
$971$	−1.06231	+	1.83997i	−0.0340910	+	0.0590474i	0.848477	+	0.529233i	$0.177520\pi$
$972$	−0.500000	+	0.866025i	−0.0160375	+	0.0277778i
$973$	−2.02129	−	3.50097i	−0.0647995	−	0.112236i
$974$	−0.409830	+	0.709846i	−0.0131318	+	0.0227449i
$975$		0			0
$976$	−14.1803			−0.453902
$977$	38.2492			1.22370			0.611851	−	0.790973i	$-0.290425\pi$
$977$	38.2492			1.22370			0.611851	+	0.790973i	$0.290425\pi$
$978$	9.38197	+	16.2500i	0.300002	+	0.519619i
$979$	23.1803	−	40.1495i	0.740847	−	1.28318i
$980$	−3.47214	−	6.01392i	−0.110913	−	0.192107i
$981$	−1.61803	+	2.80252i	−0.0516598	+	0.0894775i
$982$	−14.6459	+	25.3674i	−0.467369	+	0.809508i
$983$	17.1803	−	29.7572i	0.547968	−	0.949108i	−0.450446	−	0.892804i	$-0.648735\pi$
$983$	17.1803	−	29.7572i	0.547968	−	0.949108i	0.998414	−	0.0563043i	$-0.0179317\pi$
$984$	1.23607			0.0394044
$985$	−9.00000	−	15.5885i	−0.286764	−	0.496690i
$986$	−8.56231	−	14.8303i	−0.272679	−	0.472295i
$987$	−0.0901699	+	0.156179i	−0.00287014	+	0.00497123i
$988$		0			0
$989$	0.944272	+	1.63553i	0.0300261	+	0.0520067i
$990$	4.23607			0.134631
$991$	−7.63932			−0.242671			−0.121336	−	0.992612i	$-0.538718\pi$
$991$	−7.63932			−0.242671			−0.121336	+	0.992612i	$0.538718\pi$
$992$	1.35410	−	5.40059i	0.0429928	−	0.171469i
$993$	−17.2361			−0.546970
$994$	−0.583592			−0.0185104
$995$	13.8262	+	23.9477i	0.438321	+	0.759195i
$996$	4.70820			0.149185
$997$	4.03444	−	6.98786i	0.127772	−	0.221308i	−0.795041	−	0.606556i	$-0.792551\pi$
$997$	4.03444	−	6.98786i	0.127772	−	0.221308i	0.922813	+	0.385248i	$0.125884\pi$
$998$	4.32624	+	7.49326i	0.136945	+	0.237195i
$999$	0.618034	+	1.07047i	0.0195537	+	0.0338681i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	930.2.i.l.211.1	✓	4
31.5	even	3	inner	930.2.i.l.811.1	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
930.2.i.l.211.1	✓	4	1.1	even	1	trivial
930.2.i.l.811.1	yes	4	31.5	even	3	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.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.118034 - 0.204441i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+1.00000 q^{2} +(-0.500000 - 0.866025i) q^{3} +1.00000 q^{4} +(0.500000 - 0.866025i) q^{5} +(-0.500000 - 0.866025i) q^{6} +(-0.118034 - 0.204441i) q^{7} +1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(0.500000 - 0.866025i) q^{10} +(2.11803 - 3.66854i) q^{11} +(-0.500000 - 0.866025i) q^{12} +(-0.118034 - 0.204441i) q^{14} -1.00000 q^{15} +1.00000 q^{16} +(-2.85410 - 4.94345i) q^{17} +(-0.500000 + 0.866025i) q^{18} +(1.61803 + 2.80252i) q^{19} +(0.500000 - 0.866025i) q^{20} +(-0.118034 + 0.204441i) q^{21} +(2.11803 - 3.66854i) q^{22} -1.23607 q^{23} +(-0.500000 - 0.866025i) q^{24} +(-0.500000 - 0.866025i) q^{25} +1.00000 q^{27} +(-0.118034 - 0.204441i) q^{28} +3.00000 q^{29} -1.00000 q^{30} +(1.35410 - 5.40059i) q^{31} +1.00000 q^{32} -4.23607 q^{33} +(-2.85410 - 4.94345i) q^{34} -0.236068 q^{35} +(-0.500000 + 0.866025i) q^{36} +(0.618034 + 1.07047i) q^{37} +(1.61803 + 2.80252i) q^{38} +(0.500000 - 0.866025i) q^{40} +(-0.618034 + 1.07047i) q^{41} +(-0.118034 + 0.204441i) q^{42} +(-0.763932 - 1.32317i) q^{43} +(2.11803 - 3.66854i) q^{44} +(0.500000 + 0.866025i) q^{45} -1.23607 q^{46} +0.763932 q^{47} +(-0.500000 - 0.866025i) q^{48} +(3.47214 - 6.01392i) q^{49} +(-0.500000 - 0.866025i) q^{50} +(-2.85410 + 4.94345i) q^{51} +(3.73607 - 6.47106i) q^{53} +1.00000 q^{54} +(-2.11803 - 3.66854i) q^{55} +(-0.118034 - 0.204441i) q^{56} +(1.61803 - 2.80252i) q^{57} +3.00000 q^{58} +(3.11803 + 5.40059i) q^{59} -1.00000 q^{60} -14.1803 q^{61} +(1.35410 - 5.40059i) q^{62} +0.236068 q^{63} +1.00000 q^{64} -4.23607 q^{66} +(-2.61803 + 4.53457i) q^{67} +(-2.85410 - 4.94345i) q^{68} +(0.618034 + 1.07047i) q^{69} -0.236068 q^{70} +(1.23607 - 2.14093i) q^{71} +(-0.500000 + 0.866025i) q^{72} +(-1.47214 + 2.54981i) q^{73} +(0.618034 + 1.07047i) q^{74} +(-0.500000 + 0.866025i) q^{75} +(1.61803 + 2.80252i) q^{76} -1.00000 q^{77} +(5.23607 + 9.06914i) q^{79} +(0.500000 - 0.866025i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-0.618034 + 1.07047i) q^{82} +(-2.35410 + 4.07742i) q^{83} +(-0.118034 + 0.204441i) q^{84} -5.70820 q^{85} +(-0.763932 - 1.32317i) q^{86} +(-1.50000 - 2.59808i) q^{87} +(2.11803 - 3.66854i) q^{88} +10.9443 q^{89} +(0.500000 + 0.866025i) q^{90} -1.23607 q^{92} +(-5.35410 + 1.52761i) q^{93} +0.763932 q^{94} +3.23607 q^{95} +(-0.500000 - 0.866025i) q^{96} +1.47214 q^{97} +(3.47214 - 6.01392i) q^{98} +(2.11803 + 3.66854i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} - 2 q^{9}+O(q^{10}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 - 2 * q^9	\( 4 q + 4 q^{2} - 2 q^{3} + 4 q^{4} + 2 q^{5} - 2 q^{6} + 4 q^{7} + 4 q^{8} - 2 q^{9} + 2 q^{10} + 4 q^{11} - 2 q^{12} + 4 q^{14} - 4 q^{15} + 4 q^{16} + 2 q^{17} - 2 q^{18} + 2 q^{19} + 2 q^{20} + 4 q^{21} + 4 q^{22} + 4 q^{23} - 2 q^{24} - 2 q^{25} + 4 q^{27} + 4 q^{28} + 12 q^{29} - 4 q^{30} - 8 q^{31} + 4 q^{32} - 8 q^{33} + 2 q^{34} + 8 q^{35} - 2 q^{36} - 2 q^{37} + 2 q^{38} + 2 q^{40} + 2 q^{41} + 4 q^{42} - 12 q^{43} + 4 q^{44} + 2 q^{45} + 4 q^{46} + 12 q^{47} - 2 q^{48} - 4 q^{49} - 2 q^{50} + 2 q^{51} + 6 q^{53} + 4 q^{54} - 4 q^{55} + 4 q^{56} + 2 q^{57} + 12 q^{58} + 8 q^{59} - 4 q^{60} - 12 q^{61} - 8 q^{62} - 8 q^{63} + 4 q^{64} - 8 q^{66} - 6 q^{67} + 2 q^{68} - 2 q^{69} + 8 q^{70} - 4 q^{71} - 2 q^{72} + 12 q^{73} - 2 q^{74} - 2 q^{75} + 2 q^{76} - 4 q^{77} + 12 q^{79} + 2 q^{80} - 2 q^{81} + 2 q^{82} + 4 q^{83} + 4 q^{84} + 4 q^{85} - 12 q^{86} - 6 q^{87} + 4 q^{88} + 8 q^{89} + 2 q^{90} + 4 q^{92} - 8 q^{93} + 12 q^{94} + 4 q^{95} - 2 q^{96} - 12 q^{97} - 4 q^{98} + 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^2 - 2 * q^3 + 4 * q^4 + 2 * q^5 - 2 * q^6 + 4 * q^7 + 4 * q^8 - 2 * q^9 + 2 * q^10 + 4 * q^11 - 2 * q^12 + 4 * q^14 - 4 * q^15 + 4 * q^16 + 2 * q^17 - 2 * q^18 + 2 * q^19 + 2 * q^20 + 4 * q^21 + 4 * q^22 + 4 * q^23 - 2 * q^24 - 2 * q^25 + 4 * q^27 + 4 * q^28 + 12 * q^29 - 4 * q^30 - 8 * q^31 + 4 * q^32 - 8 * q^33 + 2 * q^34 + 8 * q^35 - 2 * q^36 - 2 * q^37 + 2 * q^38 + 2 * q^40 + 2 * q^41 + 4 * q^42 - 12 * q^43 + 4 * q^44 + 2 * q^45 + 4 * q^46 + 12 * q^47 - 2 * q^48 - 4 * q^49 - 2 * q^50 + 2 * q^51 + 6 * q^53 + 4 * q^54 - 4 * q^55 + 4 * q^56 + 2 * q^57 + 12 * q^58 + 8 * q^59 - 4 * q^60 - 12 * q^61 - 8 * q^62 - 8 * q^63 + 4 * q^64 - 8 * q^66 - 6 * q^67 + 2 * q^68 - 2 * q^69 + 8 * q^70 - 4 * q^71 - 2 * q^72 + 12 * q^73 - 2 * q^74 - 2 * q^75 + 2 * q^76 - 4 * q^77 + 12 * q^79 + 2 * q^80 - 2 * q^81 + 2 * q^82 + 4 * q^83 + 4 * q^84 + 4 * q^85 - 12 * q^86 - 6 * q^87 + 4 * q^88 + 8 * q^89 + 2 * q^90 + 4 * q^92 - 8 * q^93 + 12 * q^94 + 4 * q^95 - 2 * q^96 - 12 * q^97 - 4 * q^98 + 4 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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