LMFDB - Embedded newform 1014.2.e.n.991.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1014,2,Mod(529,1014)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1014, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("1014.529");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1014 = 2 \cdot 3 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1014.e (of order $3$, degree $2$, not 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:	$8.09683076496$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.64827.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - x^{5} + 3x^{4} + 5x^{2} - 2x + 1 $ x^6 - x^5 + 3x^4 + 5x^2 - 2*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			991.1
Root			$0.900969 - 1.56052i$ of defining polynomial
Character	$\chi$	$=$	1014.991
Dual form			1014.2.e.n.529.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.15883 q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.34601 - 4.06341i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})$	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.15883 q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.34601 - 4.06341i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.57942 - 2.73563i) q^{10} +(-0.0685317 - 0.118700i) q^{11} -1.00000 q^{12} +4.69202 q^{14} +(-1.57942 - 2.73563i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.80194 - 4.85310i) q^{17} -1.00000 q^{18} +(2.49396 - 4.31966i) q^{19} +(1.57942 - 2.73563i) q^{20} +4.69202 q^{21} +(0.0685317 - 0.118700i) q^{22} +(3.04892 + 5.28088i) q^{23} +(-0.500000 - 0.866025i) q^{24} +4.97823 q^{25} -1.00000 q^{27} +(2.34601 + 4.06341i) q^{28} +(0.425428 + 0.736862i) q^{29} +(1.57942 - 2.73563i) q^{30} +6.23490 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.0685317 - 0.118700i) q^{33} +5.60388 q^{34} +(-7.41066 + 12.8356i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.85086 - 10.1340i) q^{37} +4.98792 q^{38} +3.15883 q^{40} +(2.13706 + 3.70150i) q^{41} +(2.34601 + 4.06341i) q^{42} +(1.04892 - 1.81678i) q^{43} +0.137063 q^{44} +(1.57942 - 2.73563i) q^{45} +(-3.04892 + 5.28088i) q^{46} +4.98792 q^{47} +(0.500000 - 0.866025i) q^{48} +(-7.50753 - 13.0034i) q^{49} +(2.48911 + 4.31127i) q^{50} +5.60388 q^{51} -1.82908 q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.216480 + 0.374955i) q^{55} +(-2.34601 + 4.06341i) q^{56} +4.98792 q^{57} +(-0.425428 + 0.736862i) q^{58} +(2.94989 - 5.10935i) q^{59} +3.15883 q^{60} +(-2.19806 + 3.80716i) q^{61} +(3.11745 + 5.39958i) q^{62} +(2.34601 + 4.06341i) q^{63} +1.00000 q^{64} +0.137063 q^{66} +(2.35690 + 4.08226i) q^{67} +(2.80194 + 4.85310i) q^{68} +(-3.04892 + 5.28088i) q^{69} -14.8213 q^{70} +(0.0489173 - 0.0847273i) q^{71} +(0.500000 - 0.866025i) q^{72} -2.32304 q^{73} +(5.85086 - 10.1340i) q^{74} +(2.48911 + 4.31127i) q^{75} +(2.49396 + 4.31966i) q^{76} -0.643104 q^{77} +14.5157 q^{79} +(1.57942 + 2.73563i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.13706 + 3.70150i) q^{82} -9.85623 q^{83} +(-2.34601 + 4.06341i) q^{84} +(-8.85086 + 15.3301i) q^{85} +2.09783 q^{86} +(-0.425428 + 0.736862i) q^{87} +(0.0685317 + 0.118700i) q^{88} +(-8.54288 - 14.7967i) q^{89} +3.15883 q^{90} -6.09783 q^{92} +(3.11745 + 5.39958i) q^{93} +(2.49396 + 4.31966i) q^{94} +(-7.87800 + 13.6451i) q^{95} +1.00000 q^{96} +(-1.06369 + 1.84236i) q^{97} +(7.50753 - 13.0034i) q^{98} +0.137063 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9	$ 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 5 q^{11} - 6 q^{12} + 18 q^{14} - q^{15} - 3 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + q^{20} + 18 q^{21} - 5 q^{22} - 3 q^{24} + 36 q^{25} - 6 q^{27} + 9 q^{28} - 11 q^{29} + q^{30} - 10 q^{31} + 3 q^{32} - 5 q^{33} + 16 q^{34} + 4 q^{35} - 3 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{40} + 2 q^{41} + 9 q^{42} - 12 q^{43} - 10 q^{44} + q^{45} - 8 q^{47} + 3 q^{48} - 20 q^{49} + 18 q^{50} + 16 q^{51} + 10 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 8 q^{57} + 11 q^{58} - 5 q^{59} + 2 q^{60} - 22 q^{61} - 5 q^{62} + 9 q^{63} + 6 q^{64} - 10 q^{66} + 6 q^{67} + 8 q^{68} + 8 q^{70} - 18 q^{71} + 3 q^{72} + 26 q^{73} + 8 q^{74} + 18 q^{75} - 4 q^{76} - 12 q^{77} + 62 q^{79} + q^{80} - 3 q^{81} - 2 q^{82} - 26 q^{83} - 9 q^{84} - 26 q^{85} - 24 q^{86} + 11 q^{87} - 5 q^{88} - 14 q^{89} + 2 q^{90} - 5 q^{93} - 4 q^{94} - 8 q^{95} + 6 q^{96} - 23 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) $ 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 5 * q^11 - 6 * q^12 + 18 * q^14 - q^15 - 3 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + q^20 + 18 * q^21 - 5 * q^22 - 3 * q^24 + 36 * q^25 - 6 * q^27 + 9 * q^28 - 11 * q^29 + q^30 - 10 * q^31 + 3 * q^32 - 5 * q^33 + 16 * q^34 + 4 * q^35 - 3 * q^36 - 8 * q^37 - 8 * q^38 + 2 * q^40 + 2 * q^41 + 9 * q^42 - 12 * q^43 - 10 * q^44 + q^45 - 8 * q^47 + 3 * q^48 - 20 * q^49 + 18 * q^50 + 16 * q^51 + 10 * q^53 - 3 * q^54 - 18 * q^55 - 9 * q^56 - 8 * q^57 + 11 * q^58 - 5 * q^59 + 2 * q^60 - 22 * q^61 - 5 * q^62 + 9 * q^63 + 6 * q^64 - 10 * q^66 + 6 * q^67 + 8 * q^68 + 8 * q^70 - 18 * q^71 + 3 * q^72 + 26 * q^73 + 8 * q^74 + 18 * q^75 - 4 * q^76 - 12 * q^77 + 62 * q^79 + q^80 - 3 * q^81 - 2 * q^82 - 26 * q^83 - 9 * q^84 - 26 * q^85 - 24 * q^86 + 11 * q^87 - 5 * q^88 - 14 * q^89 + 2 * q^90 - 5 * q^93 - 4 * q^94 - 8 * q^95 + 6 * q^96 - 23 * q^97 + 20 * q^98 - 10 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1014\mathbb{Z}\right)^\times$.

$n$	$677$	$847$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

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 $

$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$2$	0.500000	+	0.866025i	0.353553	+	0.612372i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$3$	0.500000	+	0.866025i	0.288675	+	0.500000i
$4$	−0.500000	+	0.866025i	−0.250000	+	0.433013i
$5$	−3.15883			−1.41267			−0.706337	−	0.707876i	$-0.749654\pi$
$5$	−3.15883			−1.41267			−0.706337	+	0.707876i	$0.749654\pi$
$6$	−0.500000	+	0.866025i	−0.204124	+	0.353553i
$7$	2.34601	−	4.06341i	0.886709	−	1.53582i	0.0429661	−	0.999077i	$-0.486319\pi$
$7$	2.34601	−	4.06341i	0.886709	−	1.53582i	0.843743	−	0.536748i	$-0.180347\pi$
$8$	−1.00000			−0.353553
$9$	−0.500000	+	0.866025i	−0.166667	+	0.288675i
$10$	−1.57942	−	2.73563i	−0.499455	−	0.865082i
$11$	−0.0685317	−	0.118700i	−0.0206631	−	0.0357895i	0.855509	−	0.517788i	$-0.173244\pi$
$11$	−0.0685317	−	0.118700i	−0.0206631	−	0.0357895i	−0.876172	+	0.481998i	$0.839911\pi$
$12$	−1.00000			−0.288675
$13$		0			0
$13$		0			0
$14$	4.69202			1.25400
$15$	−1.57942	−	2.73563i	−0.407804	−	0.706337i
$16$	−0.500000	−	0.866025i	−0.125000	−	0.216506i
$17$	2.80194	−	4.85310i	0.679570	−	1.17705i	−0.295541	−	0.955330i	$-0.595500\pi$
$17$	2.80194	−	4.85310i	0.679570	−	1.17705i	0.975111	−	0.221719i	$-0.0711668\pi$
$18$	−1.00000			−0.235702
$19$	2.49396	−	4.31966i	0.572153	−	0.990999i	−0.424191	−	0.905573i	$-0.639441\pi$
$19$	2.49396	−	4.31966i	0.572153	−	0.990999i	0.996345	−	0.0854262i	$-0.0272252\pi$
$20$	1.57942	−	2.73563i	0.353168	−	0.611705i
$21$	4.69202			1.02388
$22$	0.0685317	−	0.118700i	0.0146110	−	0.0253070i
$23$	3.04892	+	5.28088i	0.635743	+	1.10114i	0.986357	+	0.164619i	$0.0526396\pi$
$23$	3.04892	+	5.28088i	0.635743	+	1.10114i	−0.350614	+	0.936520i	$0.614027\pi$
$24$	−0.500000	−	0.866025i	−0.102062	−	0.176777i
$25$	4.97823			0.995646
$26$		0			0
$27$	−1.00000			−0.192450
$28$	2.34601	+	4.06341i	0.443354	+	0.767912i
$29$	0.425428	+	0.736862i	0.0789999	+	0.136832i	0.902819	−	0.430021i	$-0.141494\pi$
$29$	0.425428	+	0.736862i	0.0789999	+	0.136832i	−0.823819	+	0.566853i	$0.808161\pi$
$30$	1.57942	−	2.73563i	0.288361	−	0.499455i
$31$	6.23490			1.11982			0.559910	−	0.828553i	$-0.310836\pi$
$31$	6.23490			1.11982			0.559910	+	0.828553i	$0.310836\pi$
$32$	0.500000	−	0.866025i	0.0883883	−	0.153093i
$33$	0.0685317	−	0.118700i	0.0119298	−	0.0206631i
$34$	5.60388			0.961057
$35$	−7.41066	+	12.8356i	−1.25263	+	2.16962i
$36$	−0.500000	−	0.866025i	−0.0833333	−	0.144338i
$37$	−5.85086	−	10.1340i	−0.961875	−	1.66602i	−0.717787	−	0.696263i	$-0.754845\pi$
$37$	−5.85086	−	10.1340i	−0.961875	−	1.66602i	−0.244087	−	0.969753i	$-0.578488\pi$
$38$	4.98792			0.809147
$39$		0			0
$40$	3.15883			0.499455
$41$	2.13706	+	3.70150i	0.333753	+	0.578078i	0.983245	−	0.182291i	$-0.0583514\pi$
$41$	2.13706	+	3.70150i	0.333753	+	0.578078i	−0.649491	+	0.760369i	$0.725018\pi$
$42$	2.34601	+	4.06341i	0.361997	+	0.626998i
$43$	1.04892	−	1.81678i	0.159958	−	0.277056i	−0.774895	−	0.632090i	$-0.782197\pi$
$43$	1.04892	−	1.81678i	0.159958	−	0.277056i	0.934853	+	0.355034i	$0.115531\pi$
$44$	0.137063			0.0206631
$45$	1.57942	−	2.73563i	0.235446	−	0.407804i
$46$	−3.04892	+	5.28088i	−0.449538	+	0.778623i
$47$	4.98792			0.727563			0.363781	−	0.931484i	$-0.381486\pi$
$47$	4.98792			0.727563			0.363781	+	0.931484i	$0.381486\pi$
$48$	0.500000	−	0.866025i	0.0721688	−	0.125000i
$49$	−7.50753	−	13.0034i	−1.07250	−	1.85763i
$50$	2.48911	+	4.31127i	0.352014	+	0.609706i
$51$	5.60388			0.784700
$52$		0			0
$53$	−1.82908			−0.251244			−0.125622	−	0.992078i	$-0.540093\pi$
$53$	−1.82908			−0.251244			−0.125622	+	0.992078i	$0.540093\pi$
$54$	−0.500000	−	0.866025i	−0.0680414	−	0.117851i
$55$	0.216480	+	0.374955i	0.0291902	+	0.0505589i
$56$	−2.34601	+	4.06341i	−0.313499	+	0.542996i
$57$	4.98792			0.660666
$58$	−0.425428	+	0.736862i	−0.0558614	+	0.0967547i
$59$	2.94989	−	5.10935i	0.384042	−	0.665181i	−0.607593	−	0.794248i	$-0.707865\pi$
$59$	2.94989	−	5.10935i	0.384042	−	0.665181i	0.991636	+	0.129067i	$0.0411983\pi$
$60$	3.15883			0.407804
$61$	−2.19806	+	3.80716i	−0.281433	+	0.487456i	−0.971738	−	0.236062i	$-0.924143\pi$
$61$	−2.19806	+	3.80716i	−0.281433	+	0.487456i	0.690305	+	0.723519i	$0.257476\pi$
$62$	3.11745	+	5.39958i	0.395916	+	0.685747i
$63$	2.34601	+	4.06341i	0.295570	+	0.511942i
$64$	1.00000			0.125000
$65$		0			0
$66$	0.137063			0.0168713
$67$	2.35690	+	4.08226i	0.287941	+	0.498728i	0.973318	−	0.229460i	$-0.0736961\pi$
$67$	2.35690	+	4.08226i	0.287941	+	0.498728i	−0.685377	+	0.728188i	$0.740363\pi$
$68$	2.80194	+	4.85310i	0.339785	+	0.588525i
$69$	−3.04892	+	5.28088i	−0.367047	+	0.635743i
$70$	−14.8213			−1.77149
$71$	0.0489173	−	0.0847273i	0.00580542	−	0.0100553i	−0.863108	−	0.505019i	$-0.831485\pi$
$71$	0.0489173	−	0.0847273i	0.00580542	−	0.0100553i	0.868914	+	0.494964i	$0.164819\pi$
$72$	0.500000	−	0.866025i	0.0589256	−	0.102062i
$73$	−2.32304			−0.271892			−0.135946	−	0.990716i	$-0.543407\pi$
$73$	−2.32304			−0.271892			−0.135946	+	0.990716i	$0.543407\pi$
$74$	5.85086	−	10.1340i	0.680148	−	1.17805i
$75$	2.48911	+	4.31127i	0.287418	+	0.497823i
$76$	2.49396	+	4.31966i	0.286077	+	0.495499i
$77$	−0.643104			−0.0732885
$78$		0			0
$79$	14.5157			1.63315			0.816574	−	0.577241i	$-0.195871\pi$
$79$	14.5157			1.63315			0.816574	+	0.577241i	$0.195871\pi$
$80$	1.57942	+	2.73563i	0.176584	+	0.305853i
$81$	−0.500000	−	0.866025i	−0.0555556	−	0.0962250i
$82$	−2.13706	+	3.70150i	−0.235999	+	0.408763i
$83$	−9.85623			−1.08186			−0.540931	−	0.841067i	$-0.681928\pi$
$83$	−9.85623			−1.08186			−0.540931	+	0.841067i	$0.681928\pi$
$84$	−2.34601	+	4.06341i	−0.255971	+	0.443354i
$85$	−8.85086	+	15.3301i	−0.960010	+	1.66279i
$86$	2.09783			0.226215
$87$	−0.425428	+	0.736862i	−0.0456106	+	0.0789999i
$88$	0.0685317	+	0.118700i	0.00730550	+	0.0126535i
$89$	−8.54288	−	14.7967i	−0.905543	−	1.56845i	−0.820187	−	0.572096i	$-0.806130\pi$
$89$	−8.54288	−	14.7967i	−0.905543	−	1.56845i	−0.0853566	−	0.996350i	$-0.527203\pi$
$90$	3.15883			0.332970
$91$		0			0
$92$	−6.09783			−0.635743
$93$	3.11745	+	5.39958i	0.323264	+	0.559910i
$94$	2.49396	+	4.31966i	0.257232	+	0.445539i
$95$	−7.87800	+	13.6451i	−0.808266	+	1.39996i
$96$	1.00000			0.102062
$97$	−1.06369	+	1.84236i	−0.108001	+	0.187063i	−0.914960	−	0.403544i	$-0.867778\pi$
$97$	−1.06369	+	1.84236i	−0.108001	+	0.187063i	0.806959	+	0.590607i	$0.201112\pi$
$98$	7.50753	−	13.0034i	0.758375	−	1.31354i
$99$	0.137063			0.0137754
$100$	−2.48911	+	4.31127i	−0.248911	+	0.431127i
$101$	4.59299	+	7.95529i	0.457020	+	0.791581i	0.998802	−	0.0489377i	$-0.0155836\pi$
$101$	4.59299	+	7.95529i	0.457020	+	0.791581i	−0.541782	+	0.840519i	$0.682250\pi$
$102$	2.80194	+	4.85310i	0.277433	+	0.480528i
$103$	0.225209			0.0221905			0.0110953	−	0.999938i	$-0.496468\pi$
$103$	0.225209			0.0221905			0.0110953	+	0.999938i	$0.496468\pi$
$104$		0			0
$105$	−14.8213			−1.44641
$106$	−0.914542	−	1.58403i	−0.0888282	−	0.153855i
$107$	−5.64191	−	9.77207i	−0.545424	−	0.944702i	−0.998580	−	0.0532707i	$-0.983035\pi$
$107$	−5.64191	−	9.77207i	−0.545424	−	0.944702i	0.453156	−	0.891431i	$-0.350298\pi$
$108$	0.500000	−	0.866025i	0.0481125	−	0.0833333i
$109$	−0.195669			−0.0187417			−0.00937086	−	0.999956i	$-0.502983\pi$
$109$	−0.195669			−0.0187417			−0.00937086	+	0.999956i	$0.502983\pi$
$110$	−0.216480	+	0.374955i	−0.0206406	+	0.0357505i
$111$	5.85086	−	10.1340i	0.555339	−	0.961875i
$112$	−4.69202			−0.443354
$113$	0.219833	−	0.380761i	0.0206801	−	0.0358190i	−0.855500	−	0.517803i	$-0.826750\pi$
$113$	0.219833	−	0.380761i	0.0206801	−	0.0358190i	0.876180	+	0.481984i	$0.160084\pi$
$114$	2.49396	+	4.31966i	0.233581	+	0.404574i
$115$	−9.63102	−	16.6814i	−0.898097	−	1.55555i
$116$	−0.850855			−0.0789999
$117$		0			0
$118$	5.89977			0.543118
$119$	−13.1468	−	22.7708i	−1.20516	−	2.08740i
$120$	1.57942	+	2.73563i	0.144180	+	0.249728i
$121$	5.49061	−	9.51001i	0.499146	−	0.864546i
$122$	−4.39612			−0.398006
$123$	−2.13706	+	3.70150i	−0.192693	+	0.333753i
$124$	−3.11745	+	5.39958i	−0.279955	+	0.484897i
$125$	0.0687686			0.00615085
$126$	−2.34601	+	4.06341i	−0.208999	+	0.361997i
$127$	3.93631	+	6.81789i	0.349291	+	0.604990i	0.986124	−	0.166012i	$-0.0530890\pi$
$127$	3.93631	+	6.81789i	0.349291	+	0.604990i	−0.636832	+	0.771002i	$0.719756\pi$
$128$	0.500000	+	0.866025i	0.0441942	+	0.0765466i
$129$	2.09783			0.184704
$130$		0			0
$131$	−0.621334			−0.0542862			−0.0271431	−	0.999632i	$-0.508641\pi$
$131$	−0.621334			−0.0542862			−0.0271431	+	0.999632i	$0.508641\pi$
$132$	0.0685317	+	0.118700i	0.00596492	+	0.0103315i
$133$	−11.7017	−	20.2680i	−1.01467	−	1.75745i
$134$	−2.35690	+	4.08226i	−0.203605	+	0.352654i
$135$	3.15883			0.271869
$136$	−2.80194	+	4.85310i	−0.240264	+	0.416150i
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	−0.938725	−	0.344668i	$-0.887992\pi$
$137$	−2.00000	+	3.46410i	−0.170872	+	0.295958i	0.767853	+	0.640626i	$0.221325\pi$
$138$	−6.09783			−0.519082
$139$	6.82908	−	11.8283i	0.579235	−	1.00327i	−0.416332	−	0.909213i	$-0.636685\pi$
$139$	6.82908	−	11.8283i	0.579235	−	1.00327i	0.995567	−	0.0940524i	$-0.0299821\pi$
$140$	−7.41066	−	12.8356i	−0.626315	−	1.08481i
$141$	2.49396	+	4.31966i	0.210029	+	0.363781i
$142$	0.0978347			0.00821010
$143$		0			0
$144$	1.00000			0.0833333
$145$	−1.34385	−	2.32762i	−0.111601	−	0.193299i
$146$	−1.16152	−	2.01182i	−0.0961282	−	0.166499i
$147$	7.50753	−	13.0034i	0.619211	−	1.07250i
$148$	11.7017			0.961875
$149$	−8.02930	+	13.9072i	−0.657786	+	1.13932i	0.323401	+	0.946262i	$0.395174\pi$
$149$	−8.02930	+	13.9072i	−0.657786	+	1.13932i	−0.981188	+	0.193057i	$0.938160\pi$
$150$	−2.48911	+	4.31127i	−0.203235	+	0.352014i
$151$	−21.8823			−1.78076			−0.890379	−	0.455221i	$-0.849560\pi$
$151$	−21.8823			−1.78076			−0.890379	+	0.455221i	$0.849560\pi$
$152$	−2.49396	+	4.31966i	−0.202287	+	0.350371i
$153$	2.80194	+	4.85310i	0.226523	+	0.392350i
$154$	−0.321552	−	0.556945i	−0.0259114	−	0.0448799i
$155$	−19.6950			−1.58194
$156$		0			0
$157$	−7.90217			−0.630661			−0.315331	−	0.948982i	$-0.602115\pi$
$157$	−7.90217			−0.630661			−0.315331	+	0.948982i	$0.602115\pi$
$158$	7.25786	+	12.5710i	0.577405	+	1.00009i
$159$	−0.914542	−	1.58403i	−0.0725279	−	0.125622i
$160$	−1.57942	+	2.73563i	−0.124864	+	0.216271i
$161$	28.6112			2.25488
$162$	0.500000	−	0.866025i	0.0392837	−	0.0680414i
$163$	−4.00969	+	6.94498i	−0.314063	+	0.543973i	−0.979238	−	0.202714i	$-0.935024\pi$
$163$	−4.00969	+	6.94498i	−0.314063	+	0.543973i	0.665175	+	0.746688i	$0.268357\pi$
$164$	−4.27413			−0.333753
$165$	−0.216480	+	0.374955i	−0.0168530	+	0.0291902i
$166$	−4.92812	−	8.53575i	−0.382496	−	0.662502i
$167$	8.54288	+	14.7967i	0.661068	+	1.14500i	0.980335	+	0.197338i	$0.0632297\pi$
$167$	8.54288	+	14.7967i	0.661068	+	1.14500i	−0.319268	+	0.947665i	$0.603437\pi$
$168$	−4.69202			−0.361997
$169$		0			0
$170$	−17.7017			−1.35766
$171$	2.49396	+	4.31966i	0.190718	+	0.330333i
$172$	1.04892	+	1.81678i	0.0799792	+	0.138528i
$173$	7.67241	−	13.2890i	0.583322	−	1.01034i	−0.411760	−	0.911292i	$-0.635086\pi$
$173$	7.67241	−	13.2890i	0.583322	−	1.01034i	0.995082	−	0.0990516i	$-0.0315809\pi$
$174$	−0.850855			−0.0645032
$175$	11.6790	−	20.2286i	0.882848	−	1.52914i
$176$	−0.0685317	+	0.118700i	−0.00516577	+	0.00894737i
$177$	5.89977			0.443454
$178$	8.54288	−	14.7967i	0.640316	−	1.10906i
$179$	−0.261750	−	0.453364i	−0.0195641	−	0.0338860i	0.856078	−	0.516847i	$-0.172895\pi$
$179$	−0.261750	−	0.453364i	−0.0195641	−	0.0338860i	−0.875642	+	0.482961i	$0.839561\pi$
$180$	1.57942	+	2.73563i	0.117723	+	0.203902i
$181$	8.89008			0.660795			0.330397	−	0.943842i	$-0.392817\pi$
$181$	8.89008			0.660795			0.330397	+	0.943842i	$0.392817\pi$
$182$		0			0
$183$	−4.39612			−0.324971
$184$	−3.04892	−	5.28088i	−0.224769	−	0.389312i
$185$	18.4819	+	32.0116i	1.35881	+	2.35354i
$186$	−3.11745	+	5.39958i	−0.228582	+	0.395916i
$187$	−0.768086			−0.0561680
$188$	−2.49396	+	4.31966i	−0.181891	+	0.315044i
$189$	−2.34601	+	4.06341i	−0.170647	+	0.295570i
$190$	−15.7560			−1.14306
$191$	3.51573	−	6.08942i	0.254389	−	0.440615i	−0.710340	−	0.703859i	$-0.751459\pi$
$191$	3.51573	−	6.08942i	0.254389	−	0.440615i	0.964729	+	0.263243i	$0.0847922\pi$
$192$	0.500000	+	0.866025i	0.0360844	+	0.0625000i
$193$	8.87800	+	15.3772i	0.639053	+	1.10687i	0.985641	+	0.168854i	$0.0540067\pi$
$193$	8.87800	+	15.3772i	0.639053	+	1.10687i	−0.346588	+	0.938017i	$0.612660\pi$
$194$	−2.12737			−0.152737
$195$		0			0
$196$	15.0151			1.07250
$197$	−9.32855	−	16.1575i	−0.664632	−	1.15118i	−0.979385	−	0.202003i	$-0.935255\pi$
$197$	−9.32855	−	16.1575i	−0.664632	−	1.15118i	0.314753	−	0.949174i	$-0.398078\pi$
$198$	0.0685317	+	0.118700i	0.00487033	+	0.00843567i
$199$	−3.83124	+	6.63590i	−0.271589	+	0.470407i	−0.969269	−	0.246003i	$-0.920883\pi$
$199$	−3.83124	+	6.63590i	−0.271589	+	0.470407i	0.697680	+	0.716410i	$0.254216\pi$
$200$	−4.97823			−0.352014
$201$	−2.35690	+	4.08226i	−0.166243	+	0.287941i
$202$	−4.59299	+	7.95529i	−0.323162	+	0.559732i
$203$	3.99223			0.280200
$204$	−2.80194	+	4.85310i	−0.196175	+	0.339785i
$205$	−6.75063	−	11.6924i	−0.471484	−	0.816635i
$206$	0.112605	+	0.195037i	0.00784554	+	0.0135889i
$207$	−6.09783			−0.423829
$208$		0			0
$209$	−0.683661			−0.0472898
$210$	−7.41066	−	12.8356i	−0.511384	−	0.885743i
$211$	−5.58211	−	9.66849i	−0.384288	−	0.665606i	0.607382	−	0.794410i	$-0.292220\pi$
$211$	−5.58211	−	9.66849i	−0.384288	−	0.665606i	−0.991670	+	0.128803i	$0.958886\pi$
$212$	0.914542	−	1.58403i	0.0628110	−	0.108792i
$213$	0.0978347			0.00670352
$214$	5.64191	−	9.77207i	0.385673	−	0.668005i
$215$	−3.31336	+	5.73890i	−0.225969	+	0.391390i
$216$	1.00000			0.0680414
$217$	14.6271	−	25.3349i	0.992955	−	1.71985i
$218$	−0.0978347	−	0.169455i	−0.00662620	−	0.0114769i
$219$	−1.16152	−	2.01182i	−0.0784884	−	0.135946i
$220$	−0.432960			−0.0291902
$221$		0			0
$222$	11.7017			0.785367
$223$	12.3177	+	21.3348i	0.824852	+	1.42869i	0.902032	+	0.431668i	$0.142075\pi$
$223$	12.3177	+	21.3348i	0.824852	+	1.42869i	−0.0771803	+	0.997017i	$0.524592\pi$
$224$	−2.34601	−	4.06341i	−0.156749	−	0.271498i
$225$	−2.48911	+	4.31127i	−0.165941	+	0.287418i
$226$	0.439665			0.0292461
$227$	−3.73825	+	6.47484i	−0.248116	+	0.429750i	−0.963003	−	0.269490i	$-0.913145\pi$
$227$	−3.73825	+	6.47484i	−0.248116	+	0.429750i	0.714887	+	0.699240i	$0.246478\pi$
$228$	−2.49396	+	4.31966i	−0.165166	+	0.286077i
$229$	19.2271			1.27056			0.635282	−	0.772280i	$-0.280884\pi$
$229$	19.2271			1.27056			0.635282	+	0.772280i	$0.280884\pi$
$230$	9.63102	−	16.6814i	0.635051	−	1.09994i
$231$	−0.321552	−	0.556945i	−0.0211566	−	0.0366443i
$232$	−0.425428	−	0.736862i	−0.0279307	−	0.0483774i
$233$	3.70171			0.242507			0.121254	−	0.992622i	$-0.461309\pi$
$233$	3.70171			0.242507			0.121254	+	0.992622i	$0.461309\pi$
$234$		0			0
$235$	−15.7560			−1.02781
$236$	2.94989	+	5.10935i	0.192021	+	0.332591i
$237$	7.25786	+	12.5710i	0.471449	+	0.816574i
$238$	13.1468	−	22.7708i	0.852177	−	1.47601i
$239$	−8.51334			−0.550682			−0.275341	−	0.961347i	$-0.588791\pi$
$239$	−8.51334			−0.550682			−0.275341	+	0.961347i	$0.588791\pi$
$240$	−1.57942	+	2.73563i	−0.101951	+	0.176584i
$241$	8.71648	−	15.0974i	0.561478	−	0.972508i	−0.435890	−	0.900000i	$-0.643566\pi$
$241$	8.71648	−	15.0974i	0.561478	−	0.972508i	0.997368	−	0.0725082i	$-0.0231003\pi$
$242$	10.9812			0.705899
$243$	0.500000	−	0.866025i	0.0320750	−	0.0555556i
$244$	−2.19806	−	3.80716i	−0.140717	−	0.243728i
$245$	23.7150	+	41.0757i	1.51510	+	2.62423i
$246$	−4.27413			−0.272508
$247$		0			0
$248$	−6.23490			−0.395916
$249$	−4.92812	−	8.53575i	−0.312307	−	0.540931i
$250$	0.0343843	+	0.0595554i	0.00217466	+	0.00376661i
$251$	1.74214	−	3.01747i	0.109963	−	0.190461i	−0.805792	−	0.592198i	$-0.798260\pi$
$251$	1.74214	−	3.01747i	0.109963	−	0.190461i	0.915755	+	0.401737i	$0.131594\pi$
$252$	−4.69202			−0.295570
$253$	0.417895	−	0.723815i	0.0262728	−	0.0455059i
$254$	−3.93631	+	6.81789i	−0.246986	+	0.427793i
$255$	−17.7017			−1.10852
$256$	−0.500000	+	0.866025i	−0.0312500	+	0.0541266i
$257$	6.80194	+	11.7813i	0.424293	+	0.734897i	0.996354	−	0.0853137i	$-0.0271893\pi$
$257$	6.80194	+	11.7813i	0.424293	+	0.734897i	−0.572061	+	0.820211i	$0.693856\pi$
$258$	1.04892	+	1.81678i	0.0653027	+	0.113108i
$259$	−54.9047			−3.41161
$260$		0			0
$261$	−0.850855			−0.0526666
$262$	−0.310667	−	0.538091i	−0.0191931	−	0.0332434i
$263$	−5.72886	−	9.92267i	−0.353256	−	0.611858i	0.633561	−	0.773692i	$-0.281592\pi$
$263$	−5.72886	−	9.92267i	−0.353256	−	0.611858i	−0.986818	+	0.161834i	$0.948259\pi$
$264$	−0.0685317	+	0.118700i	−0.00421783	+	0.00730550i
$265$	5.77777			0.354926
$266$	11.7017	−	20.2680i	0.717478	−	1.24271i
$267$	8.54288	−	14.7967i	0.522816	−	0.905543i
$268$	−4.71379			−0.287941
$269$	−11.1833	+	19.3700i	−0.681857	+	1.18101i	0.292556	+	0.956248i	$0.405494\pi$
$269$	−11.1833	+	19.3700i	−0.681857	+	1.18101i	−0.974413	+	0.224763i	$0.927839\pi$
$270$	1.57942	+	2.73563i	0.0961202	+	0.166485i
$271$	−1.93631	−	3.35379i	−0.117623	−	0.203728i	0.801202	−	0.598393i	$-0.204194\pi$
$271$	−1.93631	−	3.35379i	−0.117623	−	0.203728i	−0.918825	+	0.394665i	$0.870861\pi$
$272$	−5.60388			−0.339785
$273$		0			0
$274$	−4.00000			−0.241649
$275$	−0.341166	−	0.590918i	−0.0205731	−	0.0356337i
$276$	−3.04892	−	5.28088i	−0.183523	−	0.317872i
$277$	−14.3545	+	24.8627i	−0.862478	+	1.49386i	0.00705077	+	0.999975i	$0.497756\pi$
$277$	−14.3545	+	24.8627i	−0.862478	+	1.49386i	−0.869529	+	0.493881i	$0.835578\pi$
$278$	13.6582			0.819163
$279$	−3.11745	+	5.39958i	−0.186637	+	0.323264i
$280$	7.41066	−	12.8356i	0.442871	−	0.767076i
$281$	−29.0858			−1.73511			−0.867555	−	0.497341i	$-0.834310\pi$
$281$	−29.0858			−1.73511			−0.867555	+	0.497341i	$0.834310\pi$
$282$	−2.49396	+	4.31966i	−0.148513	+	0.257232i
$283$	−6.87800	−	11.9130i	−0.408855	−	0.708157i	0.585907	−	0.810378i	$-0.300738\pi$
$283$	−6.87800	−	11.9130i	−0.408855	−	0.708157i	−0.994762	+	0.102221i	$0.967405\pi$
$284$	0.0489173	+	0.0847273i	0.00290271	+	0.00502764i
$285$	−15.7560			−0.933305
$286$		0			0
$287$	20.0543			1.18377
$288$	0.500000	+	0.866025i	0.0294628	+	0.0510310i
$289$	−7.20171	−	12.4737i	−0.423630	−	0.733749i
$290$	1.34385	−	2.32762i	0.0789139	−	0.136683i
$291$	−2.12737			−0.124709
$292$	1.16152	−	2.01182i	0.0679729	−	0.117733i
$293$	−13.8681	+	24.0202i	−0.810182	+	1.40328i	0.102555	+	0.994727i	$0.467298\pi$
$293$	−13.8681	+	24.0202i	−0.810182	+	1.40328i	−0.912737	+	0.408548i	$0.866035\pi$
$294$	15.0151			0.875696
$295$	−9.31820	+	16.1396i	−0.542527	+	0.939684i
$296$	5.85086	+	10.1340i	0.340074	+	0.589026i
$297$	0.0685317	+	0.118700i	0.00397661	+	0.00688769i
$298$	−16.0586			−0.930250
$299$		0			0
$300$	−4.97823			−0.287418
$301$	−4.92154	−	8.52436i	−0.283673	−	0.491336i
$302$	−10.9412	−	18.9506i	−0.629593	−	1.09049i
$303$	−4.59299	+	7.95529i	−0.263860	+	0.457020i
$304$	−4.98792			−0.286077
$305$	6.94331	−	12.0262i	0.397573	−	0.688617i
$306$	−2.80194	+	4.85310i	−0.160176	+	0.277433i
$307$	−12.4590			−0.711075			−0.355538	−	0.934662i	$-0.615702\pi$
$307$	−12.4590			−0.711075			−0.355538	+	0.934662i	$0.615702\pi$
$308$	0.321552	−	0.556945i	0.0183221	−	0.0317349i
$309$	0.112605	+	0.195037i	0.00640586	+	0.0110953i
$310$	−9.84750	−	17.0564i	−0.559301	−	0.968737i
$311$	−6.09783			−0.345776			−0.172888	−	0.984941i	$-0.555310\pi$
$311$	−6.09783			−0.345776			−0.172888	+	0.984941i	$0.555310\pi$
$312$		0			0
$313$	−12.7385			−0.720025			−0.360013	−	0.932947i	$-0.617228\pi$
$313$	−12.7385			−0.720025			−0.360013	+	0.932947i	$0.617228\pi$
$314$	−3.95108	−	6.84348i	−0.222972	−	0.386200i
$315$	−7.41066	−	12.8356i	−0.417543	−	0.723206i
$316$	−7.25786	+	12.5710i	−0.408287	+	0.707173i
$317$	14.8140			0.832038			0.416019	−	0.909356i	$-0.363425\pi$
$317$	14.8140			0.832038			0.416019	+	0.909356i	$0.363425\pi$
$318$	0.914542	−	1.58403i	0.0512850	−	0.0888282i
$319$	0.0583105	−	0.100997i	0.00326476	−	0.00565473i
$320$	−3.15883			−0.176584
$321$	5.64191	−	9.77207i	0.314901	−	0.545424i
$322$	14.3056	+	24.7780i	0.797219	+	1.38082i
$323$	−13.9758	−	24.2069i	−0.777636	−	1.34691i
$324$	1.00000			0.0555556
$325$		0			0
$326$	−8.01938			−0.444152
$327$	−0.0978347	−	0.169455i	−0.00541027	−	0.00937086i
$328$	−2.13706	−	3.70150i	−0.118000	−	0.204381i
$329$	11.7017	−	20.2680i	0.645136	−	1.11741i
$330$	−0.432960			−0.0238337
$331$	−3.85086	+	6.66988i	−0.211662	+	0.366610i	−0.952235	−	0.305367i	$-0.901221\pi$
$331$	−3.85086	+	6.66988i	−0.211662	+	0.366610i	0.740573	+	0.671976i	$0.234554\pi$
$332$	4.92812	−	8.53575i	0.270465	−	0.468460i
$333$	11.7017			0.641250
$334$	−8.54288	+	14.7967i	−0.467445	+	0.809639i
$335$	−7.44504	−	12.8952i	−0.406766	−	0.704540i
$336$	−2.34601	−	4.06341i	−0.127985	−	0.221677i
$337$	26.5961			1.44878			0.724391	−	0.689389i	$-0.242121\pi$
$337$	26.5961			1.44878			0.724391	+	0.689389i	$0.242121\pi$
$338$		0			0
$339$	0.439665			0.0238793
$340$	−8.85086	−	15.3301i	−0.480005	−	0.831393i
$341$	−0.427288	−	0.740084i	−0.0231389	−	0.0400778i
$342$	−2.49396	+	4.31966i	−0.134858	+	0.233581i
$343$	−37.6069			−2.03058
$344$	−1.04892	+	1.81678i	−0.0565538	+	0.0979541i
$345$	9.63102	−	16.6814i	0.518517	−	0.898097i
$346$	15.3448			0.824942
$347$	−0.455927	+	0.789689i	−0.0244754	+	0.0423927i	−0.878004	−	0.478654i	$-0.841125\pi$
$347$	−0.455927	+	0.789689i	−0.0244754	+	0.0423927i	0.853528	+	0.521047i	$0.174458\pi$
$348$	−0.425428	−	0.736862i	−0.0228053	−	0.0395000i
$349$	8.86054	+	15.3469i	0.474294	+	0.821501i	0.999567	−	0.0294326i	$-0.00937003\pi$
$349$	8.86054	+	15.3469i	0.474294	+	0.821501i	−0.525273	+	0.850934i	$0.676037\pi$
$350$	23.3580			1.24854
$351$		0			0
$352$	−0.137063			−0.00730550
$353$	13.2174	+	22.8933i	0.703493	+	1.21849i	0.967233	+	0.253892i	$0.0817108\pi$
$353$	13.2174	+	22.8933i	0.703493	+	1.21849i	−0.263739	+	0.964594i	$0.584956\pi$
$354$	2.94989	+	5.10935i	0.156785	+	0.271559i
$355$	−0.154522	+	0.267639i	−0.00820116	+	0.0142048i
$356$	17.0858			0.905543
$357$	13.1468	−	22.7708i	0.695800	−	1.20516i
$358$	0.261750	−	0.453364i	0.0138339	−	0.0239610i
$359$	7.76941			0.410054			0.205027	−	0.978756i	$-0.434272\pi$
$359$	7.76941			0.410054			0.205027	+	0.978756i	$0.434272\pi$
$360$	−1.57942	+	2.73563i	−0.0832426	+	0.144180i
$361$	−2.93967	−	5.09165i	−0.154719	−	0.267982i
$362$	4.44504	+	7.69904i	0.233626	+	0.404652i
$363$	10.9812			0.576364
$364$		0			0
$365$	7.33811			0.384094
$366$	−2.19806	−	3.80716i	−0.114895	−	0.199003i
$367$	6.66368	+	11.5418i	0.347841	+	0.602479i	0.985866	−	0.167537i	$-0.0535815\pi$
$367$	6.66368	+	11.5418i	0.347841	+	0.602479i	−0.638025	+	0.770016i	$0.720248\pi$
$368$	3.04892	−	5.28088i	0.158936	−	0.275285i
$369$	−4.27413			−0.222502
$370$	−18.4819	+	32.0116i	−0.960827	+	1.66420i
$371$	−4.29105	+	7.43232i	−0.222780	+	0.385867i
$372$	−6.23490			−0.323264
$373$	−3.35152	+	5.80500i	−0.173535	+	0.300572i	−0.939653	−	0.342128i	$-0.888852\pi$
$373$	−3.35152	+	5.80500i	−0.173535	+	0.300572i	0.766118	+	0.642700i	$0.222186\pi$
$374$	−0.384043	−	0.665182i	−0.0198584	−	0.0343957i
$375$	0.0343843	+	0.0595554i	0.00177560	+	0.00307543i
$376$	−4.98792			−0.257232
$377$		0			0
$378$	−4.69202			−0.241332
$379$	−1.20775	−	2.09189i	−0.0620380	−	0.107453i	0.833338	−	0.552763i	$-0.186427\pi$
$379$	−1.20775	−	2.09189i	−0.0620380	−	0.107453i	−0.895376	+	0.445310i	$0.853093\pi$
$380$	−7.87800	−	13.6451i	−0.404133	−	0.699979i
$381$	−3.93631	+	6.81789i	−0.201663	+	0.349291i
$382$	7.03146			0.359761
$383$	−5.04892	+	8.74498i	−0.257988	+	0.446848i	−0.965703	−	0.259650i	$-0.916393\pi$
$383$	−5.04892	+	8.74498i	−0.257988	+	0.446848i	0.707715	+	0.706498i	$0.249726\pi$
$384$	−0.500000	+	0.866025i	−0.0255155	+	0.0441942i
$385$	2.03146			0.103533
$386$	−8.87800	+	15.3772i	−0.451878	+	0.782676i
$387$	1.04892	+	1.81678i	0.0533195	+	0.0923520i
$388$	−1.06369	−	1.84236i	−0.0540005	−	0.0935317i
$389$	25.1336			1.27432			0.637162	−	0.770730i	$-0.280108\pi$
$389$	25.1336			1.27432			0.637162	+	0.770730i	$0.280108\pi$
$390$		0			0
$391$	34.1715			1.72813
$392$	7.50753	+	13.0034i	0.379188	+	0.656772i
$393$	−0.310667	−	0.538091i	−0.0156711	−	0.0271431i
$394$	9.32855	−	16.1575i	0.469966	−	0.814004i
$395$	−45.8528			−2.30710
$396$	−0.0685317	+	0.118700i	−0.00344385	+	0.00596492i
$397$	−10.4179	+	18.0443i	−0.522859	+	0.905619i	0.476787	+	0.879019i	$0.341801\pi$
$397$	−10.4179	+	18.0443i	−0.522859	+	0.905619i	−0.999646	+	0.0265998i	$0.991532\pi$
$398$	−7.66248			−0.384085
$399$	11.7017	−	20.2680i	0.585818	−	1.01467i
$400$	−2.48911	−	4.31127i	−0.124456	−	0.215564i
$401$	2.97823	+	5.15845i	0.148726	+	0.257600i	0.930757	−	0.365639i	$-0.119150\pi$
$401$	2.97823	+	5.15845i	0.148726	+	0.257600i	−0.782031	+	0.623239i	$0.785816\pi$
$402$	−4.71379			−0.235103
$403$		0			0
$404$	−9.18598			−0.457020
$405$	1.57942	+	2.73563i	0.0784819	+	0.135935i
$406$	1.99612	+	3.45737i	0.0990655	+	0.171587i
$407$	−0.801938	+	1.38900i	−0.0397506	+	0.0688500i
$408$	−5.60388			−0.277433
$409$	0.900969	−	1.56052i	0.0445500	−	0.0771629i	−0.842891	−	0.538085i	$-0.819148\pi$
$409$	0.900969	−	1.56052i	0.0445500	−	0.0771629i	0.887441	+	0.460922i	$0.152481\pi$
$410$	6.75063	−	11.6924i	0.333390	−	0.577448i
$411$	−4.00000			−0.197305
$412$	−0.112605	+	0.195037i	−0.00554763	+	0.00960878i
$413$	−13.8409	−	23.9732i	−0.681068	−	1.17964i
$414$	−3.04892	−	5.28088i	−0.149846	−	0.259541i
$415$	31.1342			1.52832
$416$		0			0
$417$	13.6582			0.668843
$418$	−0.341830	−	0.592068i	−0.0167195	−	0.0289590i
$419$	14.2250	+	24.6384i	0.694935	+	1.20366i	0.970202	+	0.242296i	$0.0779004\pi$
$419$	14.2250	+	24.6384i	0.694935	+	1.20366i	−0.275267	+	0.961368i	$0.588766\pi$
$420$	7.41066	−	12.8356i	0.361603	−	0.626315i
$421$	13.9323			0.679019			0.339509	−	0.940603i	$-0.389739\pi$
$421$	13.9323			0.679019			0.339509	+	0.940603i	$0.389739\pi$
$422$	5.58211	−	9.66849i	0.271733	−	0.470655i
$423$	−2.49396	+	4.31966i	−0.121260	+	0.210029i
$424$	1.82908			0.0888282
$425$	13.9487	−	24.1598i	0.676611	−	1.17192i
$426$	0.0489173	+	0.0847273i	0.00237005	+	0.00410505i
$427$	10.3134	+	17.8633i	0.499098	+	0.864464i
$428$	11.2838			0.545424
$429$		0			0
$430$	−6.62671			−0.319568
$431$	7.95108	+	13.7717i	0.382990	+	0.663358i	0.991488	−	0.130197i	$-0.0415610\pi$
$431$	7.95108	+	13.7717i	0.382990	+	0.663358i	−0.608498	+	0.793555i	$0.708228\pi$
$432$	0.500000	+	0.866025i	0.0240563	+	0.0416667i
$433$	−2.38859	+	4.13716i	−0.114788	+	0.198819i	−0.917695	−	0.397285i	$-0.869952\pi$
$433$	−2.38859	+	4.13716i	−0.114788	+	0.198819i	0.802907	+	0.596105i	$0.203286\pi$
$434$	29.2543			1.40425
$435$	1.34385	−	2.32762i	0.0644329	−	0.111601i
$436$	0.0978347	−	0.169455i	0.00468543	−	0.00811541i
$437$	30.4155			1.45497
$438$	1.16152	−	2.01182i	0.0554997	−	0.0961282i
$439$	16.8158	+	29.1258i	0.802575	+	1.39010i	0.917916	+	0.396774i	$0.129870\pi$
$439$	16.8158	+	29.1258i	0.802575	+	1.39010i	−0.115342	+	0.993326i	$0.536796\pi$
$440$	−0.216480	−	0.374955i	−0.0103203	−	0.0178753i
$441$	15.0151			0.715003
$442$		0			0
$443$	−35.3749			−1.68071			−0.840357	−	0.542033i	$-0.817655\pi$
$443$	−35.3749			−1.68071			−0.840357	+	0.542033i	$0.817655\pi$
$444$	5.85086	+	10.1340i	0.277669	+	0.480937i
$445$	26.9855	+	46.7403i	1.27924	+	2.21570i
$446$	−12.3177	+	21.3348i	−0.583258	+	1.01023i
$447$	−16.0586			−0.759546
$448$	2.34601	−	4.06341i	0.110839	−	0.191978i
$449$	−9.03146	+	15.6429i	−0.426221	+	0.738236i	−0.996534	−	0.0831914i	$-0.973489\pi$
$449$	−9.03146	+	15.6429i	−0.426221	+	0.738236i	0.570313	+	0.821428i	$0.306822\pi$
$450$	−4.97823			−0.234676
$451$	0.292913	−	0.507340i	0.0137927	−	0.0238897i
$452$	0.219833	+	0.380761i	0.0103401	+	0.0179095i
$453$	−10.9412	−	18.9506i	−0.514060	−	0.890379i
$454$	−7.47650			−0.350890
$455$		0			0
$456$	−4.98792			−0.233581
$457$	−7.73341	−	13.3947i	−0.361753	−	0.626575i	0.626496	−	0.779425i	$-0.284488\pi$
$457$	−7.73341	−	13.3947i	−0.361753	−	0.626575i	−0.988250	+	0.152849i	$0.951155\pi$
$458$	9.61356	+	16.6512i	0.449212	+	0.778059i
$459$	−2.80194	+	4.85310i	−0.130783	+	0.226523i
$460$	19.2620			0.898097
$461$	−9.40462	+	16.2893i	−0.438017	+	0.758667i	−0.997536	−	0.0701499i	$-0.977652\pi$
$461$	−9.40462	+	16.2893i	−0.438017	+	0.758667i	0.559520	+	0.828817i	$0.310986\pi$
$462$	0.321552	−	0.556945i	0.0149600	−	0.0259114i
$463$	15.8431			0.736291			0.368145	−	0.929768i	$-0.379993\pi$
$463$	15.8431			0.736291			0.368145	+	0.929768i	$0.379993\pi$
$464$	0.425428	−	0.736862i	0.0197500	−	0.0342080i
$465$	−9.84750	−	17.0564i	−0.456667	−	0.790970i
$466$	1.85086	+	3.20578i	0.0857392	+	0.148505i
$467$	22.0006			1.01807			0.509033	−	0.860747i	$-0.330003\pi$
$467$	22.0006			1.01807			0.509033	+	0.860747i	$0.330003\pi$
$468$		0			0
$469$	22.1172			1.02128
$470$	−7.87800	−	13.6451i	−0.363385	−	0.629402i
$471$	−3.95108	−	6.84348i	−0.182056	−	0.315331i
$472$	−2.94989	+	5.10935i	−0.135780	+	0.235177i
$473$	−0.287536			−0.0132209
$474$	−7.25786	+	12.5710i	−0.333365	+	0.577405i
$475$	12.4155	−	21.5043i	0.569662	−	0.986684i
$476$	26.2935			1.20516
$477$	0.914542	−	1.58403i	0.0418740	−	0.0725279i
$478$	−4.25667	−	7.37277i	−0.194695	−	0.337222i
$479$	−10.6746	−	18.4889i	−0.487733	−	0.844779i	0.512167	−	0.858886i	$-0.328843\pi$
$479$	−10.6746	−	18.4889i	−0.487733	−	0.844779i	−0.999900	+	0.0141070i	$0.995509\pi$
$480$	−3.15883			−0.144180
$481$		0			0
$482$	17.4330			0.794050
$483$	14.3056	+	24.7780i	0.650927	+	1.12744i
$484$	5.49061	+	9.51001i	0.249573	+	0.432273i
$485$	3.36001	−	5.81971i	0.152570	−	0.264259i
$486$	1.00000			0.0453609
$487$	−15.8197	+	27.4005i	−0.716859	+	1.24164i	0.245380	+	0.969427i	$0.421087\pi$
$487$	−15.8197	+	27.4005i	−0.716859	+	1.24164i	−0.962238	+	0.272209i	$0.912246\pi$
$488$	2.19806	−	3.80716i	0.0995016	−	0.172342i
$489$	−8.01938			−0.362649
$490$	−23.7150	+	41.0757i	−1.07134	+	1.85561i
$491$	0.699554	+	1.21166i	0.0315704	+	0.0546816i	0.881379	−	0.472410i	$-0.156616\pi$
$491$	0.699554	+	1.21166i	0.0315704	+	0.0546816i	−0.849808	+	0.527092i	$0.823282\pi$
$492$	−2.13706	−	3.70150i	−0.0963463	−	0.166877i
$493$	4.76809			0.214744
$494$		0			0
$495$	−0.432960			−0.0194601
$496$	−3.11745	−	5.39958i	−0.139978	−	0.242448i
$497$	−0.229521	−	0.397542i	−0.0102954	−	0.0178322i
$498$	4.92812	−	8.53575i	0.220834	−	0.382496i
$499$		0			0			−	1.00000i	$-0.5\pi$
$499$		0			0				1.00000i	$0.5\pi$
$500$	−0.0343843	+	0.0595554i	−0.00153771	+	0.00266340i
$501$	−8.54288	+	14.7967i	−0.381668	+	0.661068i
$502$	3.48427			0.155511
$503$	9.19136	−	15.9199i	0.409822	−	0.709833i	−0.585047	−	0.810999i	$-0.698924\pi$
$503$	9.19136	−	15.9199i	0.409822	−	0.709833i	0.994870	+	0.101166i	$0.0322573\pi$
$504$	−2.34601	−	4.06341i	−0.104500	−	0.180999i
$505$	−14.5085	−	25.1294i	−0.645619	−	1.11825i
$506$	0.835790			0.0371554
$507$		0			0
$508$	−7.87263			−0.349291
$509$	0.0663757	+	0.114966i	0.00294205	+	0.00509578i	0.867493	−	0.497450i	$-0.165730\pi$
$509$	0.0663757	+	0.114966i	0.00294205	+	0.00509578i	−0.864551	+	0.502546i	$0.832397\pi$
$510$	−8.85086	−	15.3301i	−0.391922	−	0.678830i
$511$	−5.44989	+	9.43948i	−0.241089	+	0.417578i
$512$	−1.00000			−0.0441942
$513$	−2.49396	+	4.31966i	−0.110111	+	0.190718i
$514$	−6.80194	+	11.7813i	−0.300021	+	0.519651i
$515$	−0.711399			−0.0313480
$516$	−1.04892	+	1.81678i	−0.0461760	+	0.0799792i
$517$	−0.341830	−	0.592068i	−0.0150337	−	0.0260391i
$518$	−27.4523	−	47.5488i	−1.20619	−	2.08918i
$519$	15.3448			0.673563
$520$		0			0
$521$	37.0508			1.62323			0.811613	−	0.584195i	$-0.198590\pi$
$521$	37.0508			1.62323			0.811613	+	0.584195i	$0.198590\pi$
$522$	−0.425428	−	0.736862i	−0.0186205	−	0.0322516i
$523$	1.57673	+	2.73097i	0.0689455	+	0.119417i	0.898437	−	0.439102i	$-0.144703\pi$
$523$	1.57673	+	2.73097i	0.0689455	+	0.119417i	−0.829492	+	0.558519i	$0.811370\pi$
$524$	0.310667	−	0.538091i	0.0135715	−	0.0235066i
$525$	23.3580			1.01942
$526$	5.72886	−	9.92267i	0.249790	−	0.432649i
$527$	17.4698	−	30.2586i	0.760996	−	1.31808i
$528$	−0.137063			−0.00596492
$529$	−7.09179	+	12.2833i	−0.308339	+	0.534059i
$530$	2.88889	+	5.00370i	0.125485	+	0.217347i
$531$	2.94989	+	5.10935i	0.128014	+	0.221727i
$532$	23.4034			1.01467
$533$		0			0
$534$	17.0858			0.739373
$535$	17.8218	+	30.8683i	0.770506	+	1.33455i
$536$	−2.35690	−	4.08226i	−0.101802	−	0.176327i
$537$	0.261750	−	0.453364i	0.0112953	−	0.0195641i
$538$	−22.3666			−0.964292
$539$	−1.02901	+	1.78229i	−0.0443225	+	0.0767688i
$540$	−1.57942	+	2.73563i	−0.0679673	+	0.117723i
$541$	4.07846			0.175347			0.0876733	−	0.996149i	$-0.472057\pi$
$541$	4.07846			0.175347			0.0876733	+	0.996149i	$0.472057\pi$
$542$	1.93631	−	3.35379i	0.0831718	−	0.144058i
$543$	4.44504	+	7.69904i	0.190755	+	0.330397i
$544$	−2.80194	−	4.85310i	−0.120132	−	0.208075i
$545$	0.618087			0.0264759
$546$		0			0
$547$	−23.0508			−0.985583			−0.492791	−	0.870148i	$-0.664023\pi$
$547$	−23.0508			−0.985583			−0.492791	+	0.870148i	$0.664023\pi$
$548$	−2.00000	−	3.46410i	−0.0854358	−	0.147979i
$549$	−2.19806	−	3.80716i	−0.0938110	−	0.162485i
$550$	0.341166	−	0.590918i	0.0145474	−	0.0251968i
$551$	4.24400			0.180800
$552$	3.04892	−	5.28088i	0.129771	−	0.224769i
$553$	34.0541	−	58.9834i	1.44813	−	2.50823i
$554$	−28.7090			−1.21973
$555$	−18.4819	+	32.0116i	−0.784512	+	1.35881i
$556$	6.82908	+	11.8283i	0.289618	+	0.501633i
$557$	−10.2078	−	17.6803i	−0.432516	−	0.749140i	0.564573	−	0.825383i	$-0.309041\pi$
$557$	−10.2078	−	17.6803i	−0.432516	−	0.749140i	−0.997089	+	0.0762430i	$0.975708\pi$
$558$	−6.23490			−0.263944
$559$		0			0
$560$	14.8213			0.626315
$561$	−0.384043	−	0.665182i	−0.0162143	−	0.0280840i
$562$	−14.5429	−	25.1890i	−0.613454	−	1.06253i
$563$	−10.7805	+	18.6723i	−0.454342	+	0.786944i	−0.998650	−	0.0519416i	$-0.983459\pi$
$563$	−10.7805	+	18.6723i	−0.454342	+	0.786944i	0.544308	+	0.838886i	$0.316792\pi$
$564$	−4.98792			−0.210029
$565$	−0.694414	+	1.20276i	−0.0292142	+	0.0506005i
$566$	6.87800	−	11.9130i	0.289104	−	0.500743i
$567$	−4.69202			−0.197046
$568$	−0.0489173	+	0.0847273i	−0.00205253	+	0.00355508i
$569$	−4.49396	−	7.78377i	−0.188397	−	0.326312i	0.756319	−	0.654203i	$-0.226996\pi$
$569$	−4.49396	−	7.78377i	−0.188397	−	0.326312i	−0.944716	+	0.327890i	$0.893662\pi$
$570$	−7.87800	−	13.6451i	−0.329973	−	0.571530i
$571$	13.5603			0.567482			0.283741	−	0.958901i	$-0.408424\pi$
$571$	13.5603			0.567482			0.283741	+	0.958901i	$0.408424\pi$
$572$		0			0
$573$	7.03146			0.293743
$574$	10.0271	+	17.3675i	0.418525	+	0.724907i
$575$	15.1782	+	26.2894i	0.632975	+	1.09635i
$576$	−0.500000	+	0.866025i	−0.0208333	+	0.0360844i
$577$	16.2825			0.677849			0.338924	−	0.940814i	$-0.389937\pi$
$577$	16.2825			0.677849			0.338924	+	0.940814i	$0.389937\pi$
$578$	7.20171	−	12.4737i	0.299552	−	0.518839i
$579$	−8.87800	+	15.3772i	−0.368957	+	0.639053i
$580$	2.68771			0.111601
$581$	−23.1228	+	40.0499i	−0.959296	+	1.66155i
$582$	−1.06369	−	1.84236i	−0.0440913	−	0.0763683i
$583$	0.125350	+	0.217113i	0.00519148	+	0.00899190i
$584$	2.32304			0.0961282
$585$		0			0
$586$	−27.7362			−1.14577
$587$	−23.7853	−	41.1974i	−0.981725	−	1.70040i	−0.655673	−	0.755045i	$-0.727615\pi$
$587$	−23.7853	−	41.1974i	−0.981725	−	1.70040i	−0.326052	−	0.945352i	$-0.605718\pi$
$588$	7.50753	+	13.0034i	0.309605	+	0.536252i
$589$	15.5496	−	26.9327i	0.640709	−	1.10974i
$590$	−18.6364			−0.767248
$591$	9.32855	−	16.1575i	0.383725	−	0.664632i
$592$	−5.85086	+	10.1340i	−0.240469	+	0.416504i
$593$	31.0267			1.27411			0.637056	−	0.770817i	$-0.280152\pi$
$593$	31.0267			1.27411			0.637056	+	0.770817i	$0.280152\pi$
$594$	−0.0685317	+	0.118700i	−0.00281189	+	0.00487033i
$595$	41.5284	+	71.9293i	1.70250	+	2.94881i
$596$	−8.02930	−	13.9072i	−0.328893	−	0.569660i
$597$	−7.66248			−0.313604
$598$		0			0
$599$	22.3263			0.912228			0.456114	−	0.889921i	$-0.349241\pi$
$599$	22.3263			0.912228			0.456114	+	0.889921i	$0.349241\pi$
$600$	−2.48911	−	4.31127i	−0.101618	−	0.176007i
$601$	4.09030	+	7.08461i	0.166847	+	0.288987i	0.937310	−	0.348498i	$-0.113308\pi$
$601$	4.09030	+	7.08461i	0.166847	+	0.288987i	−0.770463	+	0.637485i	$0.779975\pi$
$602$	4.92154	−	8.52436i	0.200587	−	0.347427i
$603$	−4.71379			−0.191960
$604$	10.9412	−	18.9506i	0.445189	−	0.771091i
$605$	−17.3439	+	30.0405i	−0.705130	+	1.22132i
$606$	−9.18598			−0.373155
$607$	−1.65399	+	2.86479i	−0.0671334	+	0.116278i	−0.897638	−	0.440733i	$-0.854719\pi$
$607$	−1.65399	+	2.86479i	−0.0671334	+	0.116278i	0.830505	+	0.557011i	$0.188052\pi$
$608$	−2.49396	−	4.31966i	−0.101143	−	0.175186i
$609$	1.99612	+	3.45737i	0.0808867	+	0.140100i
$610$	13.8866			0.562253
$611$		0			0
$612$	−5.60388			−0.226523
$613$	5.44265	+	9.42694i	0.219827	+	0.380751i	0.954755	−	0.297394i	$-0.0961175\pi$
$613$	5.44265	+	9.42694i	0.219827	+	0.380751i	−0.734928	+	0.678145i	$0.762784\pi$
$614$	−6.22952	−	10.7898i	−0.251403	−	0.435443i
$615$	6.75063	−	11.6924i	0.272212	−	0.471484i
$616$	0.643104			0.0259114
$617$	17.2838	−	29.9364i	0.695820	−	1.20520i	−0.274083	−	0.961706i	$-0.588374\pi$
$617$	17.2838	−	29.9364i	0.695820	−	1.20520i	0.969903	−	0.243490i	$-0.0782923\pi$
$618$	−0.112605	+	0.195037i	−0.00452962	+	0.00784554i
$619$	2.86592			0.115191			0.0575955	−	0.998340i	$-0.481657\pi$
$619$	2.86592			0.115191			0.0575955	+	0.998340i	$0.481657\pi$
$620$	9.84750	−	17.0564i	0.395485	−	0.685001i
$621$	−3.04892	−	5.28088i	−0.122349	−	0.211914i
$622$	−3.04892	−	5.28088i	−0.122250	−	0.211744i
$623$	−80.1667			−3.21181
$624$		0			0
$625$	−25.1084			−1.00434
$626$	−6.36927	−	11.0319i	−0.254567	−	0.440924i
$627$	−0.341830	−	0.592068i	−0.0136514	−	0.0236449i
$628$	3.95108	−	6.84348i	0.157665	−	0.273084i
$629$	−65.5749			−2.61464
$630$	7.41066	−	12.8356i	0.295248	−	0.511384i
$631$	21.3315	−	36.9473i	0.849195	−	1.47085i	−0.0327326	−	0.999464i	$-0.510421\pi$
$631$	21.3315	−	36.9473i	0.849195	−	1.47085i	0.881928	−	0.471385i	$-0.156246\pi$
$632$	−14.5157			−0.577405
$633$	5.58211	−	9.66849i	0.221869	−	0.384288i
$634$	7.40701	+	12.8293i	0.294170	+	0.509517i
$635$	−12.4342	−	21.5366i	−0.493434	−	0.854654i
$636$	1.82908			0.0725279
$637$		0			0
$638$	0.116621			0.00461707
$639$	0.0489173	+	0.0847273i	0.00193514	+	0.00335176i
$640$	−1.57942	−	2.73563i	−0.0624319	−	0.108135i
$641$	−20.6963	+	35.8471i	−0.817456	+	1.41588i	0.0900948	+	0.995933i	$0.471283\pi$
$641$	−20.6963	+	35.8471i	−0.817456	+	1.41588i	−0.907551	+	0.419942i	$0.862050\pi$
$642$	11.2838			0.445337
$643$	−6.85623	+	11.8753i	−0.270383	+	0.468318i	−0.968960	−	0.247217i	$-0.920484\pi$
$643$	−6.85623	+	11.8753i	−0.270383	+	0.468318i	0.698577	+	0.715535i	$0.253817\pi$
$644$	−14.3056	+	24.7780i	−0.563719	+	0.976390i
$645$	−6.62671			−0.260926
$646$	13.9758	−	24.2069i	0.549872	−	0.952406i
$647$	−9.00431	−	15.5959i	−0.353996	−	0.613139i	0.632950	−	0.774193i	$-0.281844\pi$
$647$	−9.00431	−	15.5959i	−0.353996	−	0.613139i	−0.986946	+	0.161054i	$0.948511\pi$
$648$	0.500000	+	0.866025i	0.0196419	+	0.0340207i
$649$	−0.808643			−0.0317420
$650$		0			0
$651$	29.2543			1.14657
$652$	−4.00969	−	6.94498i	−0.157032	−	0.271987i
$653$	−23.2826	−	40.3267i	−0.911119	−	1.57810i	−0.812486	−	0.582981i	$-0.801886\pi$
$653$	−23.2826	−	40.3267i	−0.911119	−	1.57810i	−0.0986335	−	0.995124i	$-0.531447\pi$
$654$	0.0978347	−	0.169455i	0.00382564	−	0.00662620i
$655$	1.96269			0.0766887
$656$	2.13706	−	3.70150i	0.0834383	−	0.144519i
$657$	1.16152	−	2.01182i	0.0453153	−	0.0784884i
$658$	23.4034			0.912360
$659$	−6.92812	+	11.9998i	−0.269881	+	0.467448i	−0.968831	−	0.247723i	$-0.920318\pi$
$659$	−6.92812	+	11.9998i	−0.269881	+	0.467448i	0.698950	+	0.715171i	$0.253651\pi$
$660$	−0.216480	−	0.374955i	−0.00842648	−	0.0145951i
$661$	21.5526	+	37.3301i	0.838298	+	1.45197i	0.891317	+	0.453381i	$0.149782\pi$
$661$	21.5526	+	37.3301i	0.838298	+	1.45197i	−0.0530194	+	0.998593i	$0.516885\pi$
$662$	−7.70171			−0.299335
$663$		0			0
$664$	9.85623			0.382496
$665$	36.9638	+	64.0231i	1.43339	+	2.48271i
$666$	5.85086	+	10.1340i	0.226716	+	0.392684i
$667$	−2.59419	+	4.49326i	−0.100447	+	0.173980i
$668$	−17.0858			−0.661068
$669$	−12.3177	+	21.3348i	−0.476229	+	0.824852i
$670$	7.44504	−	12.8952i	0.287627	−	0.498185i
$671$	0.602548			0.0232611
$672$	2.34601	−	4.06341i	0.0904993	−	0.156749i
$673$	−15.3708	−	26.6229i	−0.592499	−	1.02624i	−0.993895	−	0.110334i	$-0.964808\pi$
$673$	−15.3708	−	26.6229i	−0.592499	−	1.02624i	0.401395	−	0.915905i	$-0.368525\pi$
$674$	13.2981	+	23.0329i	0.512222	+	0.887194i
$675$	−4.97823			−0.191612
$676$		0			0
$677$	16.5894			0.637582			0.318791	−	0.947825i	$-0.396723\pi$
$677$	16.5894			0.637582			0.318791	+	0.947825i	$0.396723\pi$
$678$	0.219833	+	0.380761i	0.00844262	+	0.0146230i
$679$	4.99084	+	8.64440i	0.191531	+	0.331741i
$680$	8.85086	−	15.3301i	0.339415	−	0.587884i
$681$	−7.47650			−0.286500
$682$	0.427288	−	0.740084i	0.0163617	−	0.0283393i
$683$	17.4943	−	30.3009i	0.669399	−	1.15943i	−0.308673	−	0.951168i	$-0.599885\pi$
$683$	17.4943	−	30.3009i	0.669399	−	1.15943i	0.978072	−	0.208265i	$-0.0667817\pi$
$684$	−4.98792			−0.190718
$685$	6.31767	−	10.9425i	0.241386	−	0.418092i
$686$	−18.8034	−	32.5685i	−0.717918	−	1.24347i
$687$	9.61356	+	16.6512i	0.366780	+	0.635282i
$688$	−2.09783			−0.0799792
$689$		0			0
$690$	19.2620			0.733294
$691$	−7.04354	−	12.1998i	−0.267949	−	0.464101i	0.700383	−	0.713767i	$-0.253013\pi$
$691$	−7.04354	−	12.1998i	−0.267949	−	0.464101i	−0.968332	+	0.249666i	$0.919679\pi$
$692$	7.67241	+	13.2890i	0.291661	+	0.505172i
$693$	0.321552	−	0.556945i	0.0122148	−	0.0211566i
$694$	−0.911854			−0.0346135
$695$	−21.5719	+	37.3637i	−0.818270	+	1.41729i
$696$	0.425428	−	0.736862i	0.0161258	−	0.0279307i
$697$	23.9517			0.907234
$698$	−8.86054	+	15.3469i	−0.335377	+	0.580889i
$699$	1.85086	+	3.20578i	0.0700058	+	0.121254i
$700$	11.6790	+	20.2286i	0.441424	+	0.764569i
$701$	48.6112			1.83602			0.918009	−	0.396559i	$-0.129796\pi$
$701$	48.6112			1.83602			0.918009	+	0.396559i	$0.129796\pi$
$702$		0			0
$703$	−58.3672			−2.20136
$704$	−0.0685317	−	0.118700i	−0.00258288	−	0.00447369i
$705$	−7.87800	−	13.6451i	−0.296703	−	0.513904i
$706$	−13.2174	+	22.8933i	−0.497445	+	0.861600i
$707$	43.1008			1.62097
$708$	−2.94989	+	5.10935i	−0.110864	+	0.192021i
$709$	−8.64310	+	14.9703i	−0.324599	+	0.562221i	−0.981431	−	0.191815i	$-0.938563\pi$
$709$	−8.64310	+	14.9703i	−0.324599	+	0.562221i	0.656832	+	0.754037i	$0.271896\pi$
$710$	−0.309043			−0.0115982
$711$	−7.25786	+	12.5710i	−0.272191	+	0.471449i
$712$	8.54288	+	14.7967i	0.320158	+	0.554530i
$713$	19.0097	+	32.9257i	0.711918	+	1.23308i
$714$	26.2935			0.984010
$715$		0			0
$716$	0.523499			0.0195641
$717$	−4.25667	−	7.37277i	−0.158968	−	0.275341i
$718$	3.88471	+	6.72851i	0.144976	+	0.251106i
$719$	−14.5603	+	25.2192i	−0.543009	+	0.940519i	0.455720	+	0.890123i	$0.349382\pi$
$719$	−14.5603	+	25.2192i	−0.543009	+	0.940519i	−0.998729	+	0.0503960i	$0.983952\pi$
$720$	−3.15883			−0.117723
$721$	0.528344	−	0.915118i	0.0196765	−	0.0340808i
$722$	2.93967	−	5.09165i	0.109403	−	0.189492i
$723$	17.4330			0.648339
$724$	−4.44504	+	7.69904i	−0.165199	+	0.286133i
$725$	2.11788	+	3.66827i	0.0786559	+	0.136236i
$726$	5.49061	+	9.51001i	0.203776	+	0.352950i
$727$	45.5666			1.68997			0.844985	−	0.534790i	$-0.179609\pi$
$727$	45.5666			1.68997			0.844985	+	0.534790i	$0.179609\pi$
$728$		0			0
$729$	1.00000			0.0370370
$730$	3.66905	+	6.35499i	0.135798	+	0.235209i
$731$	−5.87800	−	10.1810i	−0.217406	−	0.376558i
$732$	2.19806	−	3.80716i	0.0812427	−	0.140717i
$733$	−21.7995			−0.805185			−0.402592	−	0.915379i	$-0.631891\pi$
$733$	−21.7995			−0.805185			−0.402592	+	0.915379i	$0.631891\pi$
$734$	−6.66368	+	11.5418i	−0.245961	+	0.426017i
$735$	−23.7150	+	41.0757i	−0.874743	+	1.51510i
$736$	6.09783			0.224769
$737$	0.323044	−	0.559529i	0.0118995	−	0.0206105i
$738$	−2.13706	−	3.70150i	−0.0786664	−	0.136254i
$739$	20.7832	+	35.9975i	0.764521	+	1.32419i	0.940500	+	0.339795i	$0.110358\pi$
$739$	20.7832	+	35.9975i	0.764521	+	1.32419i	−0.175979	+	0.984394i	$0.556309\pi$
$740$	−36.9638			−1.35881
$741$		0			0
$742$	−8.58211			−0.315059
$743$	−14.4112	−	24.9609i	−0.528695	−	0.915727i	−0.999440	−	0.0334577i	$-0.989348\pi$
$743$	−14.4112	−	24.9609i	−0.528695	−	0.915727i	0.470745	−	0.882269i	$-0.343985\pi$
$744$	−3.11745	−	5.39958i	−0.114291	−	0.197958i
$745$	25.3632	−	43.9304i	0.929237	−	1.60949i
$746$	−6.70304			−0.245416
$747$	4.92812	−	8.53575i	0.180310	−	0.312307i
$748$	0.384043	−	0.665182i	0.0140420	−	0.0243215i
$749$	−52.9439			−1.93453
$750$	−0.0343843	+	0.0595554i	−0.00125554	+	0.00217466i
$751$	−8.31013	−	14.3936i	−0.303241	−	0.525229i	0.673627	−	0.739071i	$-0.264735\pi$
$751$	−8.31013	−	14.3936i	−0.303241	−	0.525229i	−0.976868	+	0.213842i	$0.931402\pi$
$752$	−2.49396	−	4.31966i	−0.0909453	−	0.157522i
$753$	3.48427			0.126974
$754$		0			0
$755$	69.1226			2.51563
$756$	−2.34601	−	4.06341i	−0.0853236	−	0.147785i
$757$	20.1957	+	34.9799i	0.734024	+	1.27137i	0.955150	+	0.296122i	$0.0956934\pi$
$757$	20.1957	+	34.9799i	0.734024	+	1.27137i	−0.221126	+	0.975245i	$0.570973\pi$
$758$	1.20775	−	2.09189i	0.0438675	−	0.0759807i
$759$	0.835790			0.0303372
$760$	7.87800	−	13.6451i	0.285765	−	0.494960i
$761$	1.64742	−	2.85341i	0.0597188	−	0.103436i	−0.834620	−	0.550826i	$-0.814313\pi$
$761$	1.64742	−	2.85341i	0.0597188	−	0.103436i	0.894339	+	0.447390i	$0.147646\pi$
$762$	−7.87263			−0.285195
$763$	−0.459042	+	0.795085i	−0.0166185	+	0.0287840i
$764$	3.51573	+	6.08942i	0.127195	+	0.220308i
$765$	−8.85086	−	15.3301i	−0.320003	−	0.554262i
$766$	−10.0978			−0.364850
$767$		0			0
$768$	−1.00000			−0.0360844
$769$	1.17629	+	2.03740i	0.0424182	+	0.0734704i	0.886455	−	0.462815i	$-0.153160\pi$
$769$	1.17629	+	2.03740i	0.0424182	+	0.0734704i	−0.844037	+	0.536285i	$0.819827\pi$
$770$	1.01573	+	1.75930i	0.0366043	+	0.0634006i
$771$	−6.80194	+	11.7813i	−0.244966	+	0.424293i
$772$	−17.7560			−0.639053
$773$	10.1969	−	17.6615i	0.366756	−	0.635240i	−0.622300	−	0.782778i	$-0.713802\pi$
$773$	10.1969	−	17.6615i	0.366756	−	0.635240i	0.989056	+	0.147539i	$0.0471351\pi$
$774$	−1.04892	+	1.81678i	−0.0377026	+	0.0653027i
$775$	31.0388			1.11494
$776$	1.06369	−	1.84236i	0.0381841	−	0.0661369i
$777$	−27.4523	−	47.5488i	−0.984847	−	1.70581i
$778$	12.5668	+	21.7663i	0.450542	+	0.780361i
$779$	21.3190			0.763832
$780$		0			0
$781$	−0.0134095			−0.000479831
$782$	17.0858	+	29.5934i	0.610985	+	1.05826i
$783$	−0.425428	−	0.736862i	−0.0152035	−	0.0263333i
$784$	−7.50753	+	13.0034i	−0.268126	+	0.464408i
$785$	24.9616			0.890919
$786$	0.310667	−	0.538091i	0.0110811	−	0.0191931i
$787$	−9.83877	+	17.0413i	−0.350714	+	0.607455i	−0.986375	−	0.164514i	$-0.947395\pi$
$787$	−9.83877	+	17.0413i	−0.350714	+	0.607455i	0.635660	+	0.771969i	$0.280728\pi$
$788$	18.6571			0.664632
$789$	5.72886	−	9.92267i	0.203953	−	0.353256i
$790$	−22.9264	−	39.7097i	−0.815684	−	1.41281i
$791$	−1.03146	−	1.78654i	−0.0366745	−	0.0635220i
$792$	−0.137063			−0.00487033
$793$		0			0
$794$	−20.8358			−0.739435
$795$	2.88889	+	5.00370i	0.102458	+	0.177463i
$796$	−3.83124	−	6.63590i	−0.135795	−	0.235203i
$797$	22.9345	−	39.7236i	0.812380	−	1.40708i	−0.0988140	−	0.995106i	$-0.531505\pi$
$797$	22.9345	−	39.7236i	0.812380	−	1.40708i	0.911194	−	0.411977i	$-0.135162\pi$
$798$	23.4034			0.828472
$799$	13.9758	−	24.2069i	0.494430	−	0.856377i
$800$	2.48911	−	4.31127i	0.0880035	−	0.152427i
$801$	17.0858			0.603695
$802$	−2.97823	+	5.15845i	−0.105165	+	0.182151i
$803$	0.159202	+	0.275746i	0.00561812	+	0.00973087i
$804$	−2.35690	−	4.08226i	−0.0831213	−	0.143970i
$805$	−90.3779			−3.18540
$806$		0			0
$807$	−22.3666			−0.787341
$808$	−4.59299	−	7.95529i	−0.161581	−	0.279866i
$809$	−19.0707	−	33.0314i	−0.670490	−	1.16132i	−0.977765	−	0.209702i	$-0.932751\pi$
$809$	−19.0707	−	33.0314i	−0.670490	−	1.16132i	0.307276	−	0.951621i	$-0.400583\pi$
$810$	−1.57942	+	2.73563i	−0.0554950	+	0.0961202i
$811$	46.6983			1.63980			0.819899	−	0.572509i	$-0.194030\pi$
$811$	46.6983			1.63980			0.819899	+	0.572509i	$0.194030\pi$
$812$	−1.99612	+	3.45737i	−0.0700499	+	0.121330i
$813$	1.93631	−	3.35379i	0.0679095	−	0.117623i
$814$	−1.60388			−0.0562158
$815$	12.6659	−	21.9381i	0.443669	−	0.768456i
$816$	−2.80194	−	4.85310i	−0.0980874	−	0.169892i
$817$	−5.23191	−	9.06194i	−0.183042	−	0.317037i
$818$	1.80194			0.0630033
$819$		0			0
$820$	13.5013			0.471484
$821$	−16.3475	−	28.3147i	−0.570532	−	0.988190i	−0.996511	−	0.0834572i	$-0.973404\pi$
$821$	−16.3475	−	28.3147i	−0.570532	−	0.988190i	0.425980	−	0.904733i	$-0.359930\pi$
$822$	−2.00000	−	3.46410i	−0.0697580	−	0.120824i
$823$	10.8400	−	18.7754i	0.377858	−	0.654469i	−0.612893	−	0.790166i	$-0.709994\pi$
$823$	10.8400	−	18.7754i	0.377858	−	0.654469i	0.990750	+	0.135698i	$0.0433276\pi$
$824$	−0.225209			−0.00784554
$825$	0.341166	−	0.590918i	0.0118779	−	0.0205731i
$826$	13.8409	−	23.9732i	0.481588	−	0.834134i
$827$	−13.9172			−0.483950			−0.241975	−	0.970283i	$-0.577795\pi$
$827$	−13.9172			−0.483950			−0.241975	+	0.970283i	$0.577795\pi$
$828$	3.04892	−	5.28088i	0.105957	−	0.183523i
$829$	8.20237	+	14.2069i	0.284880	+	0.493427i	0.972580	−	0.232568i	$-0.0747128\pi$
$829$	8.20237	+	14.2069i	0.284880	+	0.493427i	−0.687700	+	0.725995i	$0.741380\pi$
$830$	15.5671	+	26.9630i	0.540342	+	0.935900i
$831$	−28.7090			−0.995904
$832$		0			0
$833$	−84.1426			−2.91537
$834$	6.82908	+	11.8283i	0.236472	+	0.409581i
$835$	−26.9855	−	46.7403i	−0.933873	−	1.61751i
$836$	0.341830	−	0.592068i	0.0118225	−	0.0204771i
$837$	−6.23490			−0.215510
$838$	−14.2250	+	24.6384i	−0.491394	+	0.851119i
$839$	−5.80731	+	10.0586i	−0.200491	+	0.347260i	−0.948687	−	0.316218i	$-0.897587\pi$
$839$	−5.80731	+	10.0586i	−0.200491	+	0.347260i	0.748196	+	0.663478i	$0.230920\pi$
$840$	14.8213			0.511384
$841$	14.1380	−	24.4878i	0.487518	−	0.844406i
$842$	6.96615	+	12.0657i	0.240069	+	0.415812i
$843$	−14.5429	−	25.1890i	−0.500883	−	0.867555i
$844$	11.1642			0.384288
$845$		0			0
$846$	−4.98792			−0.171488
$847$	−25.7620	−	44.6212i	−0.885194	−	1.53320i
$848$	0.914542	+	1.58403i	0.0314055	+	0.0543959i
$849$	6.87800	−	11.9130i	0.236052	−	0.408855i
$850$	27.8974			0.956872
$851$	35.6775	−	61.7953i	1.22301	−	2.11832i
$852$	−0.0489173	+	0.0847273i	−0.00167588	+	0.00290271i
$853$	26.2983			0.900436			0.450218	−	0.892919i	$-0.351346\pi$
$853$	26.2983			0.900436			0.450218	+	0.892919i	$0.351346\pi$
$854$	−10.3134	+	17.8633i	−0.352916	+	0.611268i
$855$	−7.87800	−	13.6451i	−0.269422	−	0.466653i
$856$	5.64191	+	9.77207i	0.192836	+	0.334003i
$857$	−48.6305			−1.66119			−0.830594	−	0.556879i	$-0.811999\pi$
$857$	−48.6305			−1.66119			−0.830594	+	0.556879i	$0.811999\pi$
$858$		0			0
$859$	33.6185			1.14705			0.573524	−	0.819189i	$-0.305576\pi$
$859$	33.6185			1.14705			0.573524	+	0.819189i	$0.305576\pi$
$860$	−3.31336	−	5.73890i	−0.112984	−	0.195695i
$861$	10.0271	+	17.3675i	0.341724	+	0.591884i
$862$	−7.95108	+	13.7717i	−0.270815	+	0.469065i
$863$	−5.78879			−0.197053			−0.0985264	−	0.995134i	$-0.531413\pi$
$863$	−5.78879			−0.197053			−0.0985264	+	0.995134i	$0.531413\pi$
$864$	−0.500000	+	0.866025i	−0.0170103	+	0.0294628i
$865$	−24.2359	+	41.9777i	−0.824044	+	1.42729i
$866$	−4.77718			−0.162335
$867$	7.20171	−	12.4737i	0.244583	−	0.423630i
$868$	14.6271	+	25.3349i	0.496477	+	0.859924i
$869$	−0.994787	−	1.72302i	−0.0337458	−	0.0584495i
$870$	2.68771			0.0911219
$871$		0			0
$872$	0.195669			0.00662620
$873$	−1.06369	−	1.84236i	−0.0360004	−	0.0623545i
$874$	15.2078	+	26.3406i	0.514410	+	0.890984i
$875$	0.161332	−	0.279435i	0.00545402	−	0.00944663i
$876$	2.32304			0.0784884
$877$	−4.75302	+	8.23247i	−0.160498	+	0.277991i	−0.935047	−	0.354523i	$-0.884643\pi$
$877$	−4.75302	+	8.23247i	−0.160498	+	0.277991i	0.774549	+	0.632514i	$0.217977\pi$
$878$	−16.8158	+	29.1258i	−0.567506	+	0.982949i
$879$	−27.7362			−0.935517
$880$	0.216480	−	0.374955i	0.00729754	−	0.0126397i
$881$	23.3937	+	40.5191i	0.788155	+	1.36512i	0.927096	+	0.374824i	$0.122297\pi$
$881$	23.3937	+	40.5191i	0.788155	+	1.36512i	−0.138941	+	0.990301i	$0.544370\pi$
$882$	7.50753	+	13.0034i	0.252792	+	0.437848i
$883$	3.03146			0.102017			0.0510084	−	0.998698i	$-0.483756\pi$
$883$	3.03146			0.102017			0.0510084	+	0.998698i	$0.483756\pi$
$884$		0			0
$885$	−18.6364			−0.626456
$886$	−17.6875	−	30.6356i	−0.594222	−	1.02922i
$887$	−18.5090	−	32.0586i	−0.621472	−	1.07642i	−0.989212	−	0.146493i	$-0.953202\pi$
$887$	−18.5090	−	32.0586i	−0.621472	−	1.07642i	0.367740	−	0.929929i	$-0.380132\pi$
$888$	−5.85086	+	10.1340i	−0.196342	+	0.340074i
$889$	36.9385			1.23888
$890$	−26.9855	+	46.7403i	−0.904557	+	1.56674i
$891$	−0.0685317	+	0.118700i	−0.00229590	+	0.00397661i
$892$	−24.6353			−0.824852
$893$	12.4397	−	21.5461i	0.416278	−	0.721014i
$894$	−8.02930	−	13.9072i	−0.268540	−	0.465125i
$895$	0.826823	+	1.43210i	0.0276377	+	0.0478698i
$896$	4.69202			0.156749
$897$		0			0
$898$	−18.0629			−0.602767
$899$	2.65250	+	4.59426i	0.0884657	+	0.153227i
$900$	−2.48911	−	4.31127i	−0.0829705	−	0.143709i
$901$	−5.12498	+	8.87673i	−0.170738	+	0.295727i
$902$	0.585826			0.0195059
$903$	4.92154	−	8.52436i	0.163779	−	0.283673i
$904$	−0.219833	+	0.380761i	−0.00731152	+	0.0126639i
$905$	−28.0823			−0.933487
$906$	10.9412	−	18.9506i	0.363496	−	0.629593i
$907$	−9.54825	−	16.5381i	−0.317045	−	0.549137i	0.662825	−	0.748774i	$-0.269357\pi$
$907$	−9.54825	−	16.5381i	−0.317045	−	0.549137i	−0.979870	+	0.199637i	$0.936024\pi$
$908$	−3.73825	−	6.47484i	−0.124058	−	0.214875i
$909$	−9.18598			−0.304680
$910$		0			0
$911$	−31.3142			−1.03749			−0.518743	−	0.854930i	$-0.673600\pi$
$911$	−31.3142			−1.03749			−0.518743	+	0.854930i	$0.673600\pi$
$912$	−2.49396	−	4.31966i	−0.0825832	−	0.143038i
$913$	0.675464	+	1.16994i	0.0223546	+	0.0387193i
$914$	7.73341	−	13.3947i	0.255798	−	0.443056i
$915$	13.8866			0.459078
$916$	−9.61356	+	16.6512i	−0.317641	+	0.550171i
$917$	−1.45766	+	2.52473i	−0.0481360	+	0.0833741i
$918$	−5.60388			−0.184955
$919$	−15.1984	+	26.3243i	−0.501348	+	0.868359i	0.498651	+	0.866803i	$0.333829\pi$
$919$	−15.1984	+	26.3243i	−0.501348	+	0.868359i	−0.999999	+	0.00155673i	$0.999504\pi$
$920$	9.63102	+	16.6814i	0.317525	+	0.549970i
$921$	−6.22952	−	10.7898i	−0.205270	−	0.355538i
$922$	−18.8092			−0.619449
$923$		0			0
$924$	0.643104			0.0211566
$925$	−29.1269	−	50.4493i	−0.957687	−	1.65876i
$926$	7.92154	+	13.7205i	0.260318	+	0.450884i
$927$	−0.112605	+	0.195037i	−0.00369842	+	0.00640586i
$928$	0.850855			0.0279307
$929$	20.2905	−	35.1442i	0.665710	−	1.15304i	−0.313382	−	0.949627i	$-0.601462\pi$
$929$	20.2905	−	35.1442i	0.665710	−	1.15304i	0.979092	−	0.203417i	$-0.0652047\pi$
$930$	9.84750	−	17.0564i	0.322912	−	0.559301i
$931$	−74.8939			−2.45455
$932$	−1.85086	+	3.20578i	−0.0606268	+	0.105009i
$933$	−3.04892	−	5.28088i	−0.0998171	−	0.172888i
$934$	11.0003	+	19.0531i	0.359941	+	0.623436i
$935$	2.42626			0.0793470
$936$		0			0
$937$	−18.7047			−0.611056			−0.305528	−	0.952183i	$-0.598833\pi$
$937$	−18.7047			−0.611056			−0.305528	+	0.952183i	$0.598833\pi$
$938$	11.0586	+	19.1541i	0.361076	+	0.625402i
$939$	−6.36927	−	11.0319i	−0.207853	−	0.360013i
$940$	7.87800	−	13.6451i	0.256952	−	0.445054i
$941$	−4.04998			−0.132026			−0.0660128	−	0.997819i	$-0.521028\pi$
$941$	−4.04998			−0.132026			−0.0660128	+	0.997819i	$0.521028\pi$
$942$	3.95108	−	6.84348i	0.128733	−	0.222972i
$943$	−13.0315	+	22.5711i	−0.424363	+	0.735018i
$944$	−5.89977			−0.192021
$945$	7.41066	−	12.8356i	0.241069	−	0.417543i
$946$	−0.143768	−	0.249014i	−0.00467430	−	0.00809613i
$947$	−5.76779	−	9.99011i	−0.187428	−	0.324635i	0.756964	−	0.653457i	$-0.226682\pi$
$947$	−5.76779	−	9.99011i	−0.187428	−	0.324635i	−0.944392	+	0.328822i	$0.893348\pi$
$948$	−14.5157			−0.471449
$949$		0			0
$950$	24.8310			0.805624
$951$	7.40701	+	12.8293i	0.240189	+	0.416019i
$952$	13.1468	+	22.7708i	0.426089	+	0.738007i
$953$	4.78554	−	8.28881i	0.155019	−	0.268501i	−0.778047	−	0.628206i	$-0.783789\pi$
$953$	4.78554	−	8.28881i	0.155019	−	0.268501i	0.933066	+	0.359705i	$0.117123\pi$
$954$	1.82908			0.0592188
$955$	−11.1056	+	19.2355i	−0.359369	+	0.622445i
$956$	4.25667	−	7.37277i	0.137670	−	0.238452i
$957$	0.116621			0.00376982
$958$	10.6746	−	18.4889i	0.344879	−	0.597349i
$959$	9.38404	+	16.2536i	0.303027	+	0.524857i
$960$	−1.57942	−	2.73563i	−0.0509755	−	0.0882921i
$961$	7.87395			0.253998
$962$		0			0
$963$	11.2838			0.363616
$964$	8.71648	+	15.0974i	0.280739	+	0.486254i
$965$	−28.0441	−	48.5739i	−0.902773	−	1.56365i
$966$	−14.3056	+	24.7780i	−0.460275	+	0.797219i
$967$	−61.2073			−1.96829			−0.984147	−	0.177357i	$-0.943245\pi$
$967$	−61.2073			−1.96829			−0.984147	+	0.177357i	$0.943245\pi$
$968$	−5.49061	+	9.51001i	−0.176475	+	0.305663i
$969$	13.9758	−	24.2069i	0.448969	−	0.777636i
$970$	6.72002			0.215767
$971$	14.4297	−	24.9930i	0.463072	−	0.802065i	−0.536040	−	0.844193i	$-0.680080\pi$
$971$	14.4297	−	24.9930i	0.463072	−	0.802065i	0.999112	+	0.0421278i	$0.0134137\pi$
$972$	0.500000	+	0.866025i	0.0160375	+	0.0277778i
$973$	−32.0422	−	55.4987i	−1.02723	−	1.77921i
$974$	−31.6394			−1.01379
$975$		0			0
$976$	4.39612			0.140717
$977$	23.3153	+	40.3832i	0.745922	+	1.29197i	0.949763	+	0.312970i	$0.101324\pi$
$977$	23.3153	+	40.3832i	0.745922	+	1.29197i	−0.203841	+	0.979004i	$0.565343\pi$
$978$	−4.00969	−	6.94498i	−0.128216	−	0.222076i
$979$	−1.17092	+	2.02808i	−0.0374226	+	0.0648179i
$980$	−47.4301			−1.51510
$981$	0.0978347	−	0.169455i	0.00312362	−	0.00541027i
$982$	−0.699554	+	1.21166i	−0.0223237	+	0.0386657i
$983$	−55.6883			−1.77618			−0.888090	−	0.459669i	$-0.847968\pi$
$983$	−55.6883			−1.77618			−0.888090	+	0.459669i	$0.847968\pi$
$984$	2.13706	−	3.70150i	0.0681271	−	0.118000i
$985$	29.4673	+	51.0389i	0.938908	+	1.62624i
$986$	2.38404	+	4.12928i	0.0759234	+	0.131503i
$987$	23.4034			0.744939
$988$		0			0
$989$	12.7922			0.406770
$990$	−0.216480	−	0.374955i	−0.00688019	−	0.0119168i
$991$	4.66086	+	8.07284i	0.148057	+	0.256442i	0.930509	−	0.366268i	$-0.119365\pi$
$991$	4.66086	+	8.07284i	0.148057	+	0.256442i	−0.782452	+	0.622711i	$0.786031\pi$
$992$	3.11745	−	5.39958i	0.0989791	−	0.171437i
$993$	−7.70171			−0.244406
$994$	0.229521	−	0.397542i	0.00727997	−	0.0126093i
$995$	12.1023	−	20.9617i	0.383667	−	0.664531i
$996$	9.85623			0.312307
$997$	−23.0127	+	39.8591i	−0.728819	+	1.26235i	0.228564	+	0.973529i	$0.426597\pi$
$997$	−23.0127	+	39.8591i	−0.728819	+	1.26235i	−0.957383	+	0.288822i	$0.906736\pi$
$998$		0			0
$999$	5.85086	+	10.1340i	0.185113	+	0.320625i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1014.2.e.n.991.1		6
13.2	odd	12		1014.2.b.f.337.6		6
13.3	even	3		1014.2.a.l.1.1	✓	3
13.4	even	6		1014.2.e.l.529.3		6
13.5	odd	4		1014.2.i.h.361.6		12
13.6	odd	12		1014.2.i.h.823.3		12
13.7	odd	12		1014.2.i.h.823.4		12
13.8	odd	4		1014.2.i.h.361.1		12
13.9	even	3	inner	1014.2.e.n.529.1		6
13.10	even	6		1014.2.a.n.1.3	yes	3
13.11	odd	12		1014.2.b.f.337.1		6
13.12	even	2		1014.2.e.l.991.3		6
39.2	even	12		3042.2.b.o.1351.1		6
39.11	even	12		3042.2.b.o.1351.6		6
39.23	odd	6		3042.2.a.ba.1.1		3
39.29	odd	6		3042.2.a.bh.1.3		3
52.3	odd	6		8112.2.a.cj.1.1		3
52.23	odd	6		8112.2.a.cm.1.3		3

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1014.2.a.l.1.1	✓	3	13.3	even	3
1014.2.a.n.1.3	yes	3	13.10	even	6
1014.2.b.f.337.1		6	13.11	odd	12
1014.2.b.f.337.6		6	13.2	odd	12
1014.2.e.l.529.3		6	13.4	even	6
1014.2.e.l.991.3		6	13.12	even	2
1014.2.e.n.529.1		6	13.9	even	3	inner
1014.2.e.n.991.1		6	1.1	even	1	trivial
1014.2.i.h.361.1		12	13.8	odd	4
1014.2.i.h.361.6		12	13.5	odd	4
1014.2.i.h.823.3		12	13.6	odd	12
1014.2.i.h.823.4		12	13.7	odd	12
3042.2.a.ba.1.1		3	39.23	odd	6
3042.2.a.bh.1.3		3	39.29	odd	6
3042.2.b.o.1351.1		6	39.2	even	12
3042.2.b.o.1351.6		6	39.11	even	12
8112.2.a.cj.1.1		3	52.3	odd	6
8112.2.a.cm.1.3		3	52.23	odd	6

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:	\( N \)	\(=\)	\( 1014 = 2 \cdot 3 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1014.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.15883 q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.34601 - 4.06341i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +O(q^{10})\)	\(q+(0.500000 + 0.866025i) q^{2} +(0.500000 + 0.866025i) q^{3} +(-0.500000 + 0.866025i) q^{4} -3.15883 q^{5} +(-0.500000 + 0.866025i) q^{6} +(2.34601 - 4.06341i) q^{7} -1.00000 q^{8} +(-0.500000 + 0.866025i) q^{9} +(-1.57942 - 2.73563i) q^{10} +(-0.0685317 - 0.118700i) q^{11} -1.00000 q^{12} +4.69202 q^{14} +(-1.57942 - 2.73563i) q^{15} +(-0.500000 - 0.866025i) q^{16} +(2.80194 - 4.85310i) q^{17} -1.00000 q^{18} +(2.49396 - 4.31966i) q^{19} +(1.57942 - 2.73563i) q^{20} +4.69202 q^{21} +(0.0685317 - 0.118700i) q^{22} +(3.04892 + 5.28088i) q^{23} +(-0.500000 - 0.866025i) q^{24} +4.97823 q^{25} -1.00000 q^{27} +(2.34601 + 4.06341i) q^{28} +(0.425428 + 0.736862i) q^{29} +(1.57942 - 2.73563i) q^{30} +6.23490 q^{31} +(0.500000 - 0.866025i) q^{32} +(0.0685317 - 0.118700i) q^{33} +5.60388 q^{34} +(-7.41066 + 12.8356i) q^{35} +(-0.500000 - 0.866025i) q^{36} +(-5.85086 - 10.1340i) q^{37} +4.98792 q^{38} +3.15883 q^{40} +(2.13706 + 3.70150i) q^{41} +(2.34601 + 4.06341i) q^{42} +(1.04892 - 1.81678i) q^{43} +0.137063 q^{44} +(1.57942 - 2.73563i) q^{45} +(-3.04892 + 5.28088i) q^{46} +4.98792 q^{47} +(0.500000 - 0.866025i) q^{48} +(-7.50753 - 13.0034i) q^{49} +(2.48911 + 4.31127i) q^{50} +5.60388 q^{51} -1.82908 q^{53} +(-0.500000 - 0.866025i) q^{54} +(0.216480 + 0.374955i) q^{55} +(-2.34601 + 4.06341i) q^{56} +4.98792 q^{57} +(-0.425428 + 0.736862i) q^{58} +(2.94989 - 5.10935i) q^{59} +3.15883 q^{60} +(-2.19806 + 3.80716i) q^{61} +(3.11745 + 5.39958i) q^{62} +(2.34601 + 4.06341i) q^{63} +1.00000 q^{64} +0.137063 q^{66} +(2.35690 + 4.08226i) q^{67} +(2.80194 + 4.85310i) q^{68} +(-3.04892 + 5.28088i) q^{69} -14.8213 q^{70} +(0.0489173 - 0.0847273i) q^{71} +(0.500000 - 0.866025i) q^{72} -2.32304 q^{73} +(5.85086 - 10.1340i) q^{74} +(2.48911 + 4.31127i) q^{75} +(2.49396 + 4.31966i) q^{76} -0.643104 q^{77} +14.5157 q^{79} +(1.57942 + 2.73563i) q^{80} +(-0.500000 - 0.866025i) q^{81} +(-2.13706 + 3.70150i) q^{82} -9.85623 q^{83} +(-2.34601 + 4.06341i) q^{84} +(-8.85086 + 15.3301i) q^{85} +2.09783 q^{86} +(-0.425428 + 0.736862i) q^{87} +(0.0685317 + 0.118700i) q^{88} +(-8.54288 - 14.7967i) q^{89} +3.15883 q^{90} -6.09783 q^{92} +(3.11745 + 5.39958i) q^{93} +(2.49396 + 4.31966i) q^{94} +(-7.87800 + 13.6451i) q^{95} +1.00000 q^{96} +(-1.06369 + 1.84236i) q^{97} +(7.50753 - 13.0034i) q^{98} +0.137063 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9}+O(q^{10}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9	\( 6 q + 3 q^{2} + 3 q^{3} - 3 q^{4} - 2 q^{5} - 3 q^{6} + 9 q^{7} - 6 q^{8} - 3 q^{9} - q^{10} + 5 q^{11} - 6 q^{12} + 18 q^{14} - q^{15} - 3 q^{16} + 8 q^{17} - 6 q^{18} - 4 q^{19} + q^{20} + 18 q^{21} - 5 q^{22} - 3 q^{24} + 36 q^{25} - 6 q^{27} + 9 q^{28} - 11 q^{29} + q^{30} - 10 q^{31} + 3 q^{32} - 5 q^{33} + 16 q^{34} + 4 q^{35} - 3 q^{36} - 8 q^{37} - 8 q^{38} + 2 q^{40} + 2 q^{41} + 9 q^{42} - 12 q^{43} - 10 q^{44} + q^{45} - 8 q^{47} + 3 q^{48} - 20 q^{49} + 18 q^{50} + 16 q^{51} + 10 q^{53} - 3 q^{54} - 18 q^{55} - 9 q^{56} - 8 q^{57} + 11 q^{58} - 5 q^{59} + 2 q^{60} - 22 q^{61} - 5 q^{62} + 9 q^{63} + 6 q^{64} - 10 q^{66} + 6 q^{67} + 8 q^{68} + 8 q^{70} - 18 q^{71} + 3 q^{72} + 26 q^{73} + 8 q^{74} + 18 q^{75} - 4 q^{76} - 12 q^{77} + 62 q^{79} + q^{80} - 3 q^{81} - 2 q^{82} - 26 q^{83} - 9 q^{84} - 26 q^{85} - 24 q^{86} + 11 q^{87} - 5 q^{88} - 14 q^{89} + 2 q^{90} - 5 q^{93} - 4 q^{94} - 8 q^{95} + 6 q^{96} - 23 q^{97} + 20 q^{98} - 10 q^{99}+O(q^{100}) \) 6 * q + 3 * q^2 + 3 * q^3 - 3 * q^4 - 2 * q^5 - 3 * q^6 + 9 * q^7 - 6 * q^8 - 3 * q^9 - q^10 + 5 * q^11 - 6 * q^12 + 18 * q^14 - q^15 - 3 * q^16 + 8 * q^17 - 6 * q^18 - 4 * q^19 + q^20 + 18 * q^21 - 5 * q^22 - 3 * q^24 + 36 * q^25 - 6 * q^27 + 9 * q^28 - 11 * q^29 + q^30 - 10 * q^31 + 3 * q^32 - 5 * q^33 + 16 * q^34 + 4 * q^35 - 3 * q^36 - 8 * q^37 - 8 * q^38 + 2 * q^40 + 2 * q^41 + 9 * q^42 - 12 * q^43 - 10 * q^44 + q^45 - 8 * q^47 + 3 * q^48 - 20 * q^49 + 18 * q^50 + 16 * q^51 + 10 * q^53 - 3 * q^54 - 18 * q^55 - 9 * q^56 - 8 * q^57 + 11 * q^58 - 5 * q^59 + 2 * q^60 - 22 * q^61 - 5 * q^62 + 9 * q^63 + 6 * q^64 - 10 * q^66 + 6 * q^67 + 8 * q^68 + 8 * q^70 - 18 * q^71 + 3 * q^72 + 26 * q^73 + 8 * q^74 + 18 * q^75 - 4 * q^76 - 12 * q^77 + 62 * q^79 + q^80 - 3 * q^81 - 2 * q^82 - 26 * q^83 - 9 * q^84 - 26 * q^85 - 24 * q^86 + 11 * q^87 - 5 * q^88 - 14 * q^89 + 2 * q^90 - 5 * q^93 - 4 * q^94 - 8 * q^95 + 6 * q^96 - 23 * q^97 + 20 * q^98 - 10 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more