LMFDB - Embedded newform 966.2.q.d.463.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(85,966)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(966, base_ring=CyclotomicField(22))

chi = DirichletCharacter(H, H._module([0, 0, 8]))

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

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

chi := DirichletCharacter("966.85");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.q (of order $11$, degree $10$, 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:	$7.71354883526$
Analytic rank:	$0$
Dimension:	$20$
Relative dimension:	$2$ over $\Q(\zeta_{11})$
Coefficient field:	$\mathbb{Q}[x]/(x^{20} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{20} - 6 x^{19} + 10 x^{18} - 14 x^{17} + 77 x^{16} + 12 x^{15} - 226 x^{14} - 793 x^{13} + \cdots + 1849 $ x^20 - 6x^19 + 10x^18 - 14x^17 + 77x^16 + 12x^15 - 226x^14 - 793x^13 + 690x^12 + 6105x^11 + 13883x^10 + 24365x^9 + 36461x^8 + 41912x^7 + 45709x^6 + 33023x^5 + 25949x^4 + 12217x^3 + 2895x^2 - 172*x + 1849
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{11}]$

Embedding invariants

Embedding label			463.2
Root			$-1.18676 - 1.36960i$ of defining polynomial
Character	$\chi$	$=$	966.463
Dual form			966.2.q.d.169.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.04445 - 2.35942i) q^{5} +(0.959493 + 0.281733i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})$	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.04445 - 2.35942i) q^{5} +(0.959493 + 0.281733i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-2.62636 - 1.68786i) q^{10} +(0.406117 - 2.82461i) q^{11} +(0.142315 - 0.989821i) q^{12} +(-4.31364 - 2.77221i) q^{13} +(-0.654861 - 0.755750i) q^{14} +(1.29691 + 2.83983i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-1.82582 - 0.536110i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(0.139665 - 0.0410093i) q^{19} +(-1.29691 + 2.83983i) q^{20} +(0.142315 + 0.989821i) q^{21} -2.85365 q^{22} +(2.89539 + 3.82318i) q^{23} -1.00000 q^{24} +(-0.675513 - 4.69830i) q^{25} +(-2.13010 + 4.66426i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-0.654861 + 0.755750i) q^{28} +(-1.77600 - 0.521480i) q^{29} +(2.62636 - 1.68786i) q^{30} +(-1.12110 - 2.45487i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(2.40065 + 1.54280i) q^{33} +(-0.270811 + 1.88353i) q^{34} +(0.444301 - 3.09018i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-4.68468 - 5.40640i) q^{37} +(-0.0604683 - 0.132407i) q^{38} +(4.31364 - 2.77221i) q^{39} +(2.99549 + 0.879557i) q^{40} +(-0.716308 + 0.826664i) q^{41} +(0.959493 - 0.281733i) q^{42} +(0.771732 - 1.68986i) q^{43} +(0.406117 + 2.82461i) q^{44} -3.12196 q^{45} +(3.37221 - 3.41002i) q^{46} +7.90904 q^{47} +(0.142315 + 0.989821i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-4.55434 + 1.33727i) q^{50} +(1.24614 - 1.43812i) q^{51} +(4.91993 + 1.44462i) q^{52} +(1.40543 - 0.903213i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-5.83414 - 6.73296i) q^{55} +(0.841254 + 0.540641i) q^{56} +(-0.0207155 + 0.144079i) q^{57} +(-0.263421 + 1.83213i) q^{58} +(-12.1055 - 7.77975i) q^{59} +(-2.04445 - 2.35942i) q^{60} +(2.58676 + 5.66422i) q^{61} +(-2.27033 + 1.45906i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-15.3598 + 4.51004i) q^{65} +(1.18545 - 2.59577i) q^{66} +(-1.57879 - 10.9807i) q^{67} +1.90290 q^{68} +(-4.68048 + 1.04553i) q^{69} -3.12196 q^{70} +(0.615750 + 4.28264i) q^{71} +(0.415415 - 0.909632i) q^{72} +(6.57502 - 1.93060i) q^{73} +(-4.68468 + 5.40640i) q^{74} +(4.55434 + 1.33727i) q^{75} +(-0.122454 + 0.0786963i) q^{76} +(-1.18545 - 2.59577i) q^{77} +(-3.35789 - 3.87521i) q^{78} +(-0.496731 - 0.319229i) q^{79} +(0.444301 - 3.09018i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(0.920191 + 0.591371i) q^{82} +(-6.12492 - 7.06853i) q^{83} +(-0.415415 - 0.909632i) q^{84} +(-4.99770 + 3.21183i) q^{85} +(-1.78249 - 0.523385i) q^{86} +(1.21213 - 1.39887i) q^{87} +(2.73806 - 0.803967i) q^{88} +(-2.83474 + 6.20721i) q^{89} +(0.444301 + 3.09018i) q^{90} -5.12763 q^{91} +(-3.85522 - 2.85259i) q^{92} +2.69875 q^{93} +(-1.12557 - 7.82853i) q^{94} +(0.188779 - 0.413369i) q^{95} +(0.959493 - 0.281733i) q^{96} +(1.94704 - 2.24701i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(-2.40065 + 1.54280i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) $ 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/966\mathbb{Z}\right)^\times$.

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$1$	$e\left(\frac{8}{11}\right)$

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 $

$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$2$	−0.142315	−	0.989821i	−0.100632	−	0.699909i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$3$	−0.415415	+	0.909632i	−0.239840	+	0.525176i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	2.04445	−	2.35942i	0.914304	−	1.05516i	−0.0839717	−	0.996468i	$-0.526761\pi$
$5$	2.04445	−	2.35942i	0.914304	−	1.05516i	0.998276	−	0.0586952i	$-0.0186940\pi$
$6$	0.959493	+	0.281733i	0.391711	+	0.115017i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$7$	0.841254	−	0.540641i	0.317964	−	0.204343i
$8$	0.415415	+	0.909632i	0.146871	+	0.321603i
$9$	−0.654861	−	0.755750i	−0.218287	−	0.251917i
$10$	−2.62636	−	1.68786i	−0.830527	−	0.533747i
$11$	0.406117	−	2.82461i	0.122449	−	0.851651i	−0.832319	−	0.554298i	$-0.812987\pi$
$11$	0.406117	−	2.82461i	0.122449	−	0.851651i	0.954767	−	0.297353i	$-0.0961040\pi$
$12$	0.142315	−	0.989821i	0.0410828	−	0.285737i
$13$	−4.31364	−	2.77221i	−1.19639	−	0.768872i	−0.218061	−	0.975935i	$-0.569973\pi$
$13$	−4.31364	−	2.77221i	−1.19639	−	0.768872i	−0.978328	+	0.207063i	$0.933609\pi$
$14$	−0.654861	−	0.755750i	−0.175019	−	0.201983i
$15$	1.29691	+	2.83983i	0.334860	+	0.733241i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−1.82582	−	0.536110i	−0.442827	−	0.130026i	0.0527153	−	0.998610i	$-0.483212\pi$
$17$	−1.82582	−	0.536110i	−0.442827	−	0.130026i	−0.495542	+	0.868584i	$0.665031\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	0.139665	−	0.0410093i	0.0320413	−	0.00940818i	−0.265673	−	0.964063i	$-0.585594\pi$
$19$	0.139665	−	0.0410093i	0.0320413	−	0.00940818i	0.297714	+	0.954655i	$0.403776\pi$
$20$	−1.29691	+	2.83983i	−0.289997	+	0.635006i
$21$	0.142315	+	0.989821i	0.0310556	+	0.215997i
$22$	−2.85365			−0.608401
$23$	2.89539	+	3.82318i	0.603731	+	0.797188i
$23$	2.89539	+	3.82318i	0.603731	+	0.797188i
$24$	−1.00000			−0.204124
$25$	−0.675513	−	4.69830i	−0.135103	−	0.939659i
$26$	−2.13010	+	4.66426i	−0.417746	+	0.914736i
$27$	0.959493	−	0.281733i	0.184655	−	0.0542195i
$28$	−0.654861	+	0.755750i	−0.123757	+	0.142823i
$29$	−1.77600	−	0.521480i	−0.329794	−	0.0968364i	0.112644	−	0.993635i	$-0.464068\pi$
$29$	−1.77600	−	0.521480i	−0.329794	−	0.0968364i	−0.442438	+	0.896799i	$0.645886\pi$
$30$	2.62636	−	1.68786i	0.479505	−	0.308159i
$31$	−1.12110	−	2.45487i	−0.201356	−	0.440908i	0.781836	−	0.623484i	$-0.214284\pi$
$31$	−1.12110	−	2.45487i	−0.201356	−	0.440908i	−0.983192	+	0.182577i	$0.941556\pi$
$32$	−0.654861	−	0.755750i	−0.115764	−	0.133599i
$33$	2.40065	+	1.54280i	0.417899	+	0.268567i
$34$	−0.270811	+	1.88353i	−0.0464438	+	0.323023i
$35$	0.444301	−	3.09018i	0.0751005	−	0.522336i
$36$	0.841254	+	0.540641i	0.140209	+	0.0901068i
$37$	−4.68468	−	5.40640i	−0.770156	−	0.888807i	0.226202	−	0.974080i	$-0.427369\pi$
$37$	−4.68468	−	5.40640i	−0.770156	−	0.888807i	−0.996358	+	0.0852732i	$0.972824\pi$
$38$	−0.0604683	−	0.132407i	−0.00980925	−	0.0214793i
$39$	4.31364	−	2.77221i	0.690735	−	0.443908i
$40$	2.99549	+	0.879557i	0.473629	+	0.139070i
$41$	−0.716308	+	0.826664i	−0.111869	+	0.129103i	−0.808922	−	0.587916i	$-0.799949\pi$
$41$	−0.716308	+	0.826664i	−0.111869	+	0.129103i	0.697053	+	0.717019i	$0.254494\pi$
$42$	0.959493	−	0.281733i	0.148053	−	0.0434723i
$43$	0.771732	−	1.68986i	0.117688	−	0.257701i	−0.841616	−	0.540077i	$-0.818395\pi$
$43$	0.771732	−	1.68986i	0.117688	−	0.257701i	0.959304	+	0.282376i	$0.0911225\pi$
$44$	0.406117	+	2.82461i	0.0612245	+	0.425826i
$45$	−3.12196			−0.465394
$46$	3.37221	−	3.41002i	0.497205	−	0.502779i
$47$	7.90904			1.15365			0.576826	−	0.816867i	$-0.304291\pi$
$47$	7.90904			1.15365			0.576826	+	0.816867i	$0.304291\pi$
$48$	0.142315	+	0.989821i	0.0205414	+	0.142868i
$49$	0.415415	−	0.909632i	0.0593450	−	0.129947i
$50$	−4.55434	+	1.33727i	−0.644081	+	0.189119i
$51$	1.24614	−	1.43812i	0.174494	−	0.201377i
$52$	4.91993	+	1.44462i	0.682271	+	0.200333i
$53$	1.40543	−	0.903213i	0.193050	−	0.124066i	−0.440545	−	0.897730i	$-0.645215\pi$
$53$	1.40543	−	0.903213i	0.193050	−	0.124066i	0.633595	+	0.773665i	$0.281578\pi$
$54$	−0.415415	−	0.909632i	−0.0565308	−	0.123785i
$55$	−5.83414	−	6.73296i	−0.786675	−	0.907872i
$56$	0.841254	+	0.540641i	0.112417	+	0.0722462i
$57$	−0.0207155	+	0.144079i	−0.00274384	+	0.0190838i
$58$	−0.263421	+	1.83213i	−0.0345889	+	0.240571i
$59$	−12.1055	−	7.77975i	−1.57601	−	1.01284i	−0.977298	−	0.211870i	$-0.932045\pi$
$59$	−12.1055	−	7.77975i	−1.57601	−	1.01284i	−0.598708	−	0.800967i	$-0.704319\pi$
$60$	−2.04445	−	2.35942i	−0.263937	−	0.304599i
$61$	2.58676	+	5.66422i	0.331201	+	0.725229i	0.999831	−	0.0183662i	$-0.00584648\pi$
$61$	2.58676	+	5.66422i	0.331201	+	0.725229i	−0.668631	+	0.743595i	$0.733119\pi$
$62$	−2.27033	+	1.45906i	−0.288333	+	0.185300i
$63$	−0.959493	−	0.281733i	−0.120885	−	0.0354950i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−15.3598	+	4.51004i	−1.90515	+	0.559402i
$66$	1.18545	−	2.59577i	0.145919	−	0.319518i
$67$	−1.57879	−	10.9807i	−0.192879	−	1.34150i	−0.824339	−	0.566096i	$-0.808453\pi$
$67$	−1.57879	−	10.9807i	−0.192879	−	1.34150i	0.631460	−	0.775409i	$-0.282456\pi$
$68$	1.90290			0.230761
$69$	−4.68048	+	1.04553i	−0.563463	+	0.125868i
$70$	−3.12196			−0.373145
$71$	0.615750	+	4.28264i	0.0730761	+	0.508256i	0.993181	+	0.116583i	$0.0371942\pi$
$71$	0.615750	+	4.28264i	0.0730761	+	0.508256i	−0.920105	+	0.391672i	$0.871897\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	6.57502	−	1.93060i	0.769548	−	0.225960i	0.126687	−	0.991943i	$-0.459566\pi$
$73$	6.57502	−	1.93060i	0.769548	−	0.225960i	0.642861	+	0.765983i	$0.277747\pi$
$74$	−4.68468	+	5.40640i	−0.544582	+	0.628482i
$75$	4.55434	+	1.33727i	0.525890	+	0.154415i
$76$	−0.122454	+	0.0786963i	−0.0140464	+	0.00902708i
$77$	−1.18545	−	2.59577i	−0.135095	−	0.295816i
$78$	−3.35789	−	3.87521i	−0.380206	−	0.438781i
$79$	−0.496731	−	0.319229i	−0.0558866	−	0.0359161i	0.512399	−	0.858747i	$-0.328757\pi$
$79$	−0.496731	−	0.319229i	−0.0558866	−	0.0359161i	−0.568286	+	0.822831i	$0.692393\pi$
$80$	0.444301	−	3.09018i	0.0496743	−	0.345493i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	0.920191	+	0.591371i	0.101618	+	0.0653060i
$83$	−6.12492	−	7.06853i	−0.672297	−	0.775872i	0.312437	−	0.949939i	$-0.398855\pi$
$83$	−6.12492	−	7.06853i	−0.672297	−	0.775872i	−0.984734	+	0.174066i	$0.944309\pi$
$84$	−0.415415	−	0.909632i	−0.0453255	−	0.0992490i
$85$	−4.99770	+	3.21183i	−0.542077	+	0.348372i
$86$	−1.78249	−	0.523385i	−0.192210	−	0.0564381i
$87$	1.21213	−	1.39887i	0.129954	−	0.149975i
$88$	2.73806	−	0.803967i	0.291878	−	0.0857032i
$89$	−2.83474	+	6.20721i	−0.300481	+	0.657962i	−0.998298	−	0.0583137i	$-0.981428\pi$
$89$	−2.83474	+	6.20721i	−0.300481	+	0.657962i	0.697817	+	0.716276i	$0.254155\pi$
$90$	0.444301	+	3.09018i	0.0468334	+	0.325733i
$91$	−5.12763			−0.537522
$92$	−3.85522	−	2.85259i	−0.401935	−	0.297403i
$93$	2.69875			0.279847
$94$	−1.12557	−	7.82853i	−0.116094	−	0.807452i
$95$	0.188779	−	0.413369i	0.0193683	−	0.0424108i
$96$	0.959493	−	0.281733i	0.0979278	−	0.0287542i
$97$	1.94704	−	2.24701i	0.197692	−	0.228149i	−0.648244	−	0.761432i	$-0.724496\pi$
$97$	1.94704	−	2.24701i	0.197692	−	0.228149i	0.845937	+	0.533283i	$0.179042\pi$
$98$	−0.959493	−	0.281733i	−0.0969234	−	0.0284593i
$99$	−2.40065	+	1.54280i	−0.241274	+	0.155057i
$100$	1.97181	+	4.31767i	0.197181	+	0.431767i
$101$	−6.48644	−	7.48575i	−0.645425	−	0.744860i	0.334899	−	0.942254i	$-0.391298\pi$
$101$	−6.48644	−	7.48575i	−0.645425	−	0.744860i	−0.980324	+	0.197394i	$0.936752\pi$
$102$	−1.60082	−	1.02879i	−0.158505	−	0.101865i
$103$	2.03958	−	14.1856i	0.200966	−	1.39775i	−0.600461	−	0.799654i	$-0.705016\pi$
$103$	2.03958	−	14.1856i	0.200966	−	1.39775i	0.801427	−	0.598093i	$-0.204075\pi$
$104$	0.729738	−	5.07544i	0.0715567	−	0.497688i
$105$	2.62636	+	1.68786i	0.256306	+	0.164718i
$106$	−1.09403	−	1.26258i	−0.106262	−	0.122633i
$107$	6.74815	+	14.7764i	0.652368	+	1.42849i	0.889466	+	0.457001i	$0.151077\pi$
$107$	6.74815	+	14.7764i	0.652368	+	1.42849i	−0.237098	+	0.971486i	$0.576196\pi$
$108$	−0.841254	+	0.540641i	−0.0809497	+	0.0520232i
$109$	0.136085	+	0.0399583i	0.0130346	+	0.00382731i	0.288243	−	0.957557i	$-0.406929\pi$
$109$	0.136085	+	0.0399583i	0.0130346	+	0.00382731i	−0.275209	+	0.961384i	$0.588747\pi$
$110$	−5.83414	+	6.73296i	−0.556264	+	0.641962i
$111$	6.86392	−	2.01543i	0.651495	−	0.191296i
$112$	0.415415	−	0.909632i	0.0392530	−	0.0859521i
$113$	0.732577	+	5.09518i	0.0689150	+	0.479315i	0.994828	+	0.101577i	$0.0323888\pi$
$113$	0.732577	+	5.09518i	0.0689150	+	0.479315i	−0.925913	+	0.377738i	$0.876702\pi$
$114$	0.145561			0.0136330
$115$	14.9399	+	0.984849i	1.39316	+	0.0918377i
$116$	1.85097			0.171859
$117$	0.729738	+	5.07544i	0.0674643	+	0.469225i
$118$	−5.97777	+	13.0895i	−0.550298	+	1.20499i
$119$	−1.82582	+	0.536110i	−0.167373	+	0.0491451i
$120$	−2.04445	+	2.35942i	−0.186632	+	0.215384i
$121$	2.74095	+	0.804815i	0.249177	+	0.0731650i
$122$	5.23843	−	3.36653i	0.474265	−	0.304792i
$123$	−0.454395	−	0.994985i	−0.0409714	−	0.0897148i
$124$	1.76731	+	2.03958i	0.158709	+	0.183160i
$125$	0.665496	+	0.427688i	0.0595237	+	0.0382536i
$126$	−0.142315	+	0.989821i	−0.0126784	+	0.0881803i
$127$	2.26355	−	15.7433i	0.200857	−	1.39699i	−0.600891	−	0.799331i	$-0.705187\pi$
$127$	2.26355	−	15.7433i	0.200857	−	1.39699i	0.801748	−	0.597662i	$-0.203903\pi$
$128$	0.841254	+	0.540641i	0.0743570	+	0.0477863i
$129$	1.21656	+	1.40398i	0.107112	+	0.123614i
$130$	6.65006	+	14.5616i	0.583249	+	1.27714i
$131$	17.0556	−	10.9610i	1.49016	−	0.957666i	0.494057	−	0.869429i	$-0.335513\pi$
$131$	17.0556	−	10.9610i	1.49016	−	0.957666i	0.996100	−	0.0882365i	$-0.0281231\pi$
$132$	−2.73806	−	0.803967i	−0.238318	−	0.0699764i
$133$	0.0953222	−	0.110008i	0.00826549	−	0.00953888i
$134$	−10.6442	+	3.12543i	−0.919522	+	0.269996i
$135$	1.29691	−	2.83983i	0.111620	−	0.244414i
$136$	−0.270811	−	1.88353i	−0.0232219	−	0.161512i
$137$	0.274615			0.0234619			0.0117310	−	0.999931i	$-0.496266\pi$
$137$	0.274615			0.0234619			0.0117310	+	0.999931i	$0.496266\pi$
$138$	1.70099	+	4.48404i	0.144798	+	0.381707i
$139$	12.8339			1.08856			0.544279	−	0.838904i	$-0.316803\pi$
$139$	12.8339			1.08856			0.544279	+	0.838904i	$0.316803\pi$
$140$	0.444301	+	3.09018i	0.0375503	+	0.261168i
$141$	−3.28553	+	7.19431i	−0.276692	+	0.605870i
$142$	4.15142	−	1.21897i	0.348379	−	0.102293i
$143$	−9.58224	+	11.0585i	−0.801307	+	0.924758i
$144$	−0.959493	−	0.281733i	−0.0799577	−	0.0234777i
$145$	−4.86132	+	3.12418i	−0.403711	+	0.259449i
$146$	−2.84667	−	6.23334i	−0.235592	−	0.515875i
$147$	0.654861	+	0.755750i	0.0540120	+	0.0623332i
$148$	6.01807	+	3.86758i	0.494683	+	0.317913i
$149$	−2.91589	+	20.2804i	−0.238879	+	1.66144i	0.418755	+	0.908099i	$0.362467\pi$
$149$	−2.91589	+	20.2804i	−0.238879	+	1.66144i	−0.657633	+	0.753338i	$0.728442\pi$
$150$	0.675513	−	4.69830i	0.0551554	−	0.383614i
$151$	14.5196	+	9.33118i	1.18159	+	0.759361i	0.975678	−	0.219210i	$-0.0703480\pi$
$151$	14.5196	+	9.33118i	1.18159	+	0.759361i	0.205911	+	0.978571i	$0.433984\pi$
$152$	0.0953222	+	0.110008i	0.00773165	+	0.00892281i
$153$	0.790495	+	1.73094i	0.0639077	+	0.139938i
$154$	−2.40065	+	1.54280i	−0.193450	+	0.124322i
$155$	−8.08410	−	2.37370i	−0.649330	−	0.190661i
$156$	−3.35789	+	3.87521i	−0.268846	+	0.310265i
$157$	−5.21709	+	1.53188i	−0.416370	+	0.122257i	−0.483206	−	0.875507i	$-0.660528\pi$
$157$	−5.21709	+	1.53188i	−0.416370	+	0.122257i	0.0668362	+	0.997764i	$0.478710\pi$
$158$	−0.245288	+	0.537106i	−0.0195141	+	0.0427299i
$159$	0.237756	+	1.65363i	0.0188553	+	0.131141i
$160$	−3.12196			−0.246812
$161$	4.50273	+	1.65090i	0.354865	+	0.130109i
$162$	1.00000			0.0785674
$163$	0.201986	+	1.40485i	0.0158208	+	0.110036i	0.996202	−	0.0870768i	$-0.0277526\pi$
$163$	0.201986	+	1.40485i	0.0158208	+	0.110036i	−0.980381	+	0.197113i	$0.936843\pi$
$164$	0.454395	−	0.994985i	0.0354823	−	0.0776953i
$165$	8.54810	−	2.50995i	0.665469	−	0.195399i
$166$	−6.12492	+	7.06853i	−0.475386	+	0.548624i
$167$	11.0130	+	3.23371i	0.852211	+	0.250232i	0.678532	−	0.734571i	$-0.262616\pi$
$167$	11.0130	+	3.23371i	0.852211	+	0.250232i	0.173679	+	0.984802i	$0.444435\pi$
$168$	−0.841254	+	0.540641i	−0.0649041	+	0.0417113i
$169$	5.52195	+	12.0914i	0.424766	+	0.930107i
$170$	3.89038	+	4.48974i	0.298379	+	0.344347i
$171$	−0.122454	−	0.0786963i	−0.00936427	−	0.00601805i
$172$	−0.264384	+	1.83883i	−0.0201591	+	0.140209i
$173$	0.176302	−	1.22621i	0.0134040	−	0.0932270i	−0.982021	−	0.188770i	$-0.939550\pi$
$173$	0.176302	−	1.22621i	0.0134040	−	0.0932270i	0.995425	+	0.0955435i	$0.0304589\pi$
$174$	−1.55714	−	1.00071i	−0.118046	−	0.0758638i
$175$	−3.10837	−	3.58725i	−0.234971	−	0.271170i
$176$	−1.18545	−	2.59577i	−0.0893567	−	0.195664i
$177$	12.1055	−	7.77975i	0.909907	−	0.584762i
$178$	6.54745	+	1.92250i	0.490752	+	0.144098i
$179$	−5.27058	+	6.08257i	−0.393941	+	0.454632i	−0.917724	−	0.397220i	$-0.869975\pi$
$179$	−5.27058	+	6.08257i	−0.393941	+	0.454632i	0.523782	+	0.851852i	$0.324521\pi$
$180$	2.99549	−	0.879557i	0.223271	−	0.0655583i
$181$	−4.96274	+	10.8669i	−0.368878	+	0.807730i	0.630622	+	0.776090i	$0.282800\pi$
$181$	−4.96274	+	10.8669i	−0.368878	+	0.807730i	−0.999499	+	0.0316391i	$0.989927\pi$
$182$	0.729738	+	5.07544i	0.0540918	+	0.376217i
$183$	−6.22693			−0.460308
$184$	−2.27490	+	4.22195i	−0.167708	+	0.311246i
$185$	−22.3335			−1.64199
$186$	−0.384072	−	2.67128i	−0.0281616	−	0.195868i
$187$	−2.25580	+	4.93951i	−0.164960	+	0.361213i
$188$	−7.58867	+	2.22823i	−0.553460	+	0.162511i
$189$	0.654861	−	0.755750i	0.0476341	−	0.0549727i
$190$	−0.436027	−	0.128029i	−0.0316328	−	0.00928822i
$191$	5.81746	−	3.73865i	0.420936	−	0.270519i	−0.312979	−	0.949760i	$-0.601327\pi$
$191$	5.81746	−	3.73865i	0.420936	−	0.270519i	0.733916	+	0.679241i	$0.237691\pi$
$192$	−0.415415	−	0.909632i	−0.0299800	−	0.0656470i
$193$	11.9231	+	13.7600i	0.858246	+	0.990469i	1.00000		0.000566869i	$0.000180440\pi$
$193$	11.9231	+	13.7600i	0.858246	+	0.990469i	−0.141754	+	0.989902i	$0.545274\pi$
$194$	−2.50123	−	1.60744i	−0.179578	−	0.115408i
$195$	2.27821	−	15.8453i	0.163146	−	1.13471i
$196$	−0.142315	+	0.989821i	−0.0101653	+	0.0707015i
$197$	−0.221859	−	0.142580i	−0.0158068	−	0.0101584i	0.532714	−	0.846296i	$-0.321172\pi$
$197$	−0.221859	−	0.142580i	−0.0158068	−	0.0101584i	−0.548520	+	0.836137i	$0.684809\pi$
$198$	1.86875	+	2.15665i	0.132806	+	0.153266i
$199$	5.92165	+	12.9666i	0.419775	+	0.919179i	0.994877	+	0.101097i	$0.0322352\pi$
$199$	5.92165	+	12.9666i	0.419775	+	0.919179i	−0.575102	+	0.818082i	$0.695038\pi$
$200$	3.99310	−	2.56621i	0.282355	−	0.181458i
$201$	10.6442	+	3.12543i	0.750787	+	0.220451i
$202$	−6.48644	+	7.48575i	−0.456384	+	0.526696i
$203$	−1.77600	+	0.521480i	−0.124651	+	0.0366007i
$204$	−0.790495	+	1.73094i	−0.0553457	+	0.121190i
$205$	0.485991	+	3.38014i	0.0339431	+	0.236079i
$206$	−14.3315			−0.998520
$207$	0.993288	−	4.69184i	0.0690383	−	0.326106i
$208$	−5.12763			−0.355537
$209$	−0.0591149	−	0.411153i	−0.00408906	−	0.0284400i
$210$	1.29691	−	2.83983i	0.0894951	−	0.195967i
$211$	23.7123	−	6.96255i	1.63242	−	0.479321i	0.668101	−	0.744070i	$-0.267107\pi$
$211$	23.7123	−	6.96255i	1.63242	−	0.479321i	0.964317	+	0.264749i	$0.0852890\pi$
$212$	−1.09403	+	1.26258i	−0.0751385	+	0.0867144i
$213$	−4.15142	−	1.21897i	−0.284450	−	0.0835222i
$214$	13.6656	−	8.78236i	0.934163	−	0.600350i
$215$	−2.40931	−	5.27566i	−0.164314	−	0.359797i
$216$	0.654861	+	0.755750i	0.0445576	+	0.0514222i
$217$	−2.27033	−	1.45906i	−0.154120	−	0.0990471i
$218$	0.0201846	−	0.140387i	0.00136707	−	0.00950820i
$219$	−0.975227	+	6.78285i	−0.0658997	+	0.458342i
$220$	7.49471	+	4.81656i	0.505293	+	0.324732i
$221$	6.38973	+	7.37414i	0.429820	+	0.496039i
$222$	−2.97175	−	6.50723i	−0.199451	−	0.436737i
$223$	−7.71394	+	4.95745i	−0.516564	+	0.331975i	−0.772811	−	0.634636i	$-0.781150\pi$
$223$	−7.71394	+	4.95745i	−0.516564	+	0.331975i	0.256248	+	0.966611i	$0.417514\pi$
$224$	−0.959493	−	0.281733i	−0.0641088	−	0.0188240i
$225$	−3.10837	+	3.58725i	−0.207225	+	0.239150i
$226$	4.93907	−	1.45024i	0.328542	−	0.0964686i
$227$	−3.09954	+	6.78705i	−0.205724	+	0.450472i	−0.984167	−	0.177242i	$-0.943282\pi$
$227$	−3.09954	+	6.78705i	−0.205724	+	0.450472i	0.778443	+	0.627715i	$0.216010\pi$
$228$	−0.0207155	−	0.144079i	−0.00137192	−	0.00954190i
$229$	−20.1907			−1.33424			−0.667119	−	0.744951i	$-0.732473\pi$
$229$	−20.1907			−1.33424			−0.667119	+	0.744951i	$0.732473\pi$
$230$	−1.15135	−	14.9280i	−0.0759179	−	0.984326i
$231$	2.85365			0.187757
$232$	−0.263421	−	1.83213i	−0.0172944	−	0.120286i
$233$	−4.67393	+	10.2345i	−0.306199	+	0.670483i	−0.998702	−	0.0509321i	$-0.983781\pi$
$233$	−4.67393	+	10.2345i	−0.306199	+	0.670483i	0.692503	+	0.721415i	$0.256508\pi$
$234$	4.91993	−	1.44462i	0.321626	−	0.0944378i
$235$	16.1696	−	18.6607i	1.05479	−	1.21729i
$236$	13.8070	+	4.05410i	0.898758	+	0.263899i
$237$	0.496731	−	0.319229i	0.0322661	−	0.0207362i
$238$	0.790495	+	1.73094i	0.0512402	+	0.112200i
$239$	3.83673	+	4.42782i	0.248178	+	0.286412i	0.866146	−	0.499790i	$-0.166590\pi$
$239$	3.83673	+	4.42782i	0.248178	+	0.286412i	−0.617969	+	0.786203i	$0.712044\pi$
$240$	2.62636	+	1.68786i	0.169531	+	0.108951i
$241$	2.95878	−	20.5788i	0.190592	−	1.32560i	−0.639853	−	0.768497i	$-0.721005\pi$
$241$	2.95878	−	20.5788i	0.190592	−	1.32560i	0.830445	−	0.557100i	$-0.188086\pi$
$242$	0.406545	−	2.82759i	0.0261337	−	0.181764i
$243$	−0.841254	−	0.540641i	−0.0539664	−	0.0346821i
$244$	−4.07777	−	4.70600i	−0.261053	−	0.301271i
$245$	−1.29691	−	2.83983i	−0.0828564	−	0.181430i
$246$	−0.920191	+	0.591371i	−0.0586692	+	0.0377044i
$247$	−0.716150	−	0.210281i	−0.0455675	−	0.0133798i
$248$	1.76731	−	2.03958i	0.112224	−	0.129513i
$249$	8.97414	−	2.63505i	0.568713	−	0.166989i
$250$	0.328625	−	0.719588i	0.0207841	−	0.0455107i
$251$	1.64832	+	11.4643i	0.104041	+	0.723622i	0.973345	+	0.229344i	$0.0736582\pi$
$251$	1.64832	+	11.4643i	0.104041	+	0.723622i	−0.869304	+	0.494277i	$0.835433\pi$
$252$	1.00000			0.0629941
$253$	11.9749	−	6.62569i	0.752852	−	0.416553i
$254$	−15.9052			−0.997981
$255$	−0.845461	−	5.88031i	−0.0529448	−	0.368239i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	29.1952	−	8.57249i	1.82115	−	0.534737i	0.821763	−	0.569829i	$-0.192991\pi$
$257$	29.1952	−	8.57249i	1.82115	−	0.534737i	0.999384	+	0.0350919i	$0.0111724\pi$
$258$	1.21656	−	1.40398i	0.0757397	−	0.0874083i
$259$	−6.86392	−	2.01543i	−0.426503	−	0.125233i
$260$	13.4670	−	8.65471i	0.835187	−	0.536742i
$261$	0.768923	+	1.68371i	0.0475951	+	0.104219i
$262$	−13.2767	−	15.3221i	−0.820236	−	0.946603i
$263$	23.2378	+	14.9340i	1.43290	+	0.920871i	0.999809	+	0.0195215i	$0.00621429\pi$
$263$	23.2378	+	14.9340i	1.43290	+	0.920871i	0.433093	+	0.901349i	$0.357422\pi$
$264$	−0.406117	+	2.82461i	−0.0249948	+	0.173843i
$265$	0.742264	−	5.16256i	0.0455969	−	0.317133i
$266$	−0.122454	−	0.0786963i	−0.00750812	−	0.00482518i
$267$	−4.46868	−	5.15713i	−0.273479	−	0.315611i
$268$	4.60845	+	10.0911i	0.281506	+	0.616412i
$269$	−8.06947	+	5.18593i	−0.492004	+	0.316192i	−0.763011	−	0.646386i	$-0.776280\pi$
$269$	−8.06947	+	5.18593i	−0.492004	+	0.316192i	0.271007	+	0.962577i	$0.412643\pi$
$270$	−2.99549	−	0.879557i	−0.182300	−	0.0535281i
$271$	17.4552	−	20.1443i	1.06033	−	1.22368i	0.0865309	−	0.996249i	$-0.472422\pi$
$271$	17.4552	−	20.1443i	1.06033	−	1.22368i	0.973794	−	0.227431i	$-0.0730327\pi$
$272$	−1.82582	+	0.536110i	−0.110707	+	0.0325064i
$273$	2.13010	−	4.66426i	0.128919	−	0.282294i
$274$	−0.0390817	−	0.271819i	−0.00236101	−	0.0164212i
$275$	−13.5452			−0.816805
$276$	4.19632	−	2.32183i	0.252589	−	0.139757i
$277$	19.4124			1.16638			0.583190	−	0.812336i	$-0.301804\pi$
$277$	19.4124			1.16638			0.583190	+	0.812336i	$0.301804\pi$
$278$	−1.82645	−	12.7033i	−0.109543	−	0.761892i
$279$	−1.12110	+	2.45487i	−0.0671186	+	0.146969i
$280$	2.99549	−	0.879557i	0.179015	−	0.0525636i
$281$	1.10630	−	1.27674i	0.0659963	−	0.0761638i	−0.721791	−	0.692111i	$-0.756681\pi$
$281$	1.10630	−	1.27674i	0.0659963	−	0.0761638i	0.787788	+	0.615947i	$0.211226\pi$
$282$	7.58867	+	2.22823i	0.451898	+	0.132689i
$283$	−2.63185	+	1.69139i	−0.156447	+	0.100542i	−0.616522	−	0.787338i	$-0.711459\pi$
$283$	−2.63185	+	1.69139i	−0.156447	+	0.100542i	0.460075	+	0.887880i	$0.347823\pi$
$284$	−1.79737	−	3.93568i	−0.106654	−	0.233540i
$285$	0.297592	+	0.343439i	0.0176278	+	0.0203436i
$286$	12.3096	+	7.91092i	0.727884	+	0.467782i
$287$	−0.155669	+	1.08270i	−0.00918883	+	0.0639097i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	−11.2551	−	7.23321i	−0.662065	−	0.425483i
$290$	3.78422	+	4.36722i	0.222217	+	0.256452i
$291$	1.23512	+	2.70454i	0.0724040	+	0.158543i
$292$	−5.76477	+	3.70479i	−0.337358	+	0.216807i
$293$	−20.9349	−	6.14704i	−1.22303	−	0.359114i	−0.394414	−	0.918933i	$-0.629053\pi$
$293$	−20.9349	−	6.14704i	−1.22303	−	0.359114i	−0.828615	+	0.559819i	$0.810871\pi$
$294$	0.654861	−	0.755750i	0.0381923	−	0.0440762i
$295$	−43.1048	+	12.6567i	−2.50966	+	0.736902i
$296$	2.97175	−	6.50723i	0.172730	−	0.378225i
$297$	−0.406117	−	2.82461i	−0.0235653	−	0.163900i
$298$	20.4890			1.18689
$299$	−1.89103	−	24.5184i	−0.109361	−	1.41794i
$300$	−4.74661			−0.274046
$301$	−0.264384	−	1.83883i	−0.0152388	−	0.105988i
$302$	7.16985	−	15.6998i	0.412578	−	0.903421i
$303$	9.50384	−	2.79058i	0.545982	−	0.160315i
$304$	0.0953222	−	0.110008i	0.00546711	−	0.00630938i
$305$	18.6527	+	5.47694i	1.06805	+	0.313609i
$306$	1.60082	−	1.02879i	0.0915130	−	0.0588118i
$307$	−1.27408	−	2.78985i	−0.0727157	−	0.159225i	0.869784	−	0.493433i	$-0.164258\pi$
$307$	−1.27408	−	2.78985i	−0.0727157	−	0.159225i	−0.942499	+	0.334208i	$0.891531\pi$
$308$	1.86875	+	2.15665i	0.106482	+	0.122886i
$309$	12.0564	+	7.74817i	0.685864	+	0.440778i
$310$	−1.19906	+	8.33962i	−0.0681019	+	0.473659i
$311$	−3.05309	+	21.2347i	−0.173125	+	1.20411i	0.699107	+	0.715017i	$0.253581\pi$
$311$	−3.05309	+	21.2347i	−0.173125	+	1.20411i	−0.872232	+	0.489092i	$0.837328\pi$
$312$	4.31364	+	2.77221i	0.244212	+	0.156945i
$313$	−9.46957	−	10.9285i	−0.535252	−	0.617713i	0.422131	−	0.906535i	$-0.361282\pi$
$313$	−9.46957	−	10.9285i	−0.535252	−	0.617713i	−0.957383	+	0.288821i	$0.906737\pi$
$314$	2.25875	+	4.94598i	0.127469	+	0.279118i
$315$	−2.62636	+	1.68786i	−0.147978	+	0.0951000i
$316$	0.566547	+	0.166353i	0.0318708	+	0.00935810i
$317$	17.4072	−	20.0890i	0.977685	−	1.12831i	−0.0140367	−	0.999901i	$-0.504468\pi$
$317$	17.4072	−	20.0890i	0.977685	−	1.12831i	0.991722	−	0.128407i	$-0.0409864\pi$
$318$	1.60296	−	0.470672i	0.0898896	−	0.0263940i
$319$	−2.19424	+	4.80471i	−0.122854	+	0.269012i
$320$	0.444301	+	3.09018i	0.0248372	+	0.172746i
$321$	−16.2444			−0.906672
$322$	0.993288	−	4.69184i	0.0553538	−	0.261466i
$323$	−0.276989			−0.0154121
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−10.1107	+	22.1394i	−0.560842	+	1.22807i
$326$	1.36180	−	0.399861i	0.0754231	−	0.0221462i
$327$	−0.0928793	+	0.107188i	−0.00513624	+	0.00592753i
$328$	−1.04952	−	0.308168i	−0.0579503	−	0.0170157i
$329$	6.65351	−	4.27595i	0.366820	−	0.235741i
$330$	−3.70092	−	8.10389i	−0.203729	−	0.446105i
$331$	0.697362	+	0.804798i	0.0383305	+	0.0442357i	0.774591	−	0.632462i	$-0.217956\pi$
$331$	0.697362	+	0.804798i	0.0383305	+	0.0442357i	−0.736261	+	0.676698i	$0.763410\pi$
$332$	7.86825	+	5.05662i	0.431826	+	0.277518i
$333$	−1.01808	+	7.08088i	−0.0557903	+	0.388030i
$334$	1.63348	−	11.3611i	0.0893800	−	0.621652i
$335$	−29.1358	−	18.7244i	−1.59186	−	1.02302i
$336$	0.654861	+	0.755750i	0.0357256	+	0.0412295i
$337$	3.30570	+	7.23847i	0.180073	+	0.394304i	0.978046	−	0.208388i	$-0.0668218\pi$
$337$	3.30570	+	7.23847i	0.180073	+	0.394304i	−0.797973	+	0.602693i	$0.794094\pi$
$338$	11.1825	−	7.18653i	0.608246	−	0.390896i
$339$	−4.93907	−	1.45024i	−0.268253	−	0.0787663i
$340$	3.89038	−	4.48974i	0.210986	−	0.243490i
$341$	−7.38934	+	2.16971i	−0.400155	+	0.117496i
$342$	−0.0604683	+	0.132407i	−0.00326975	+	0.00715975i
$343$	−0.142315	−	0.989821i	−0.00768428	−	0.0534453i
$344$	1.85774			0.100163
$345$	−7.10213	+	13.1807i	−0.382366	+	0.709627i
$346$	−1.23882			−0.0665993
$347$	2.84161	+	19.7638i	0.152546	+	1.06098i	0.911933	+	0.410339i	$0.134590\pi$
$347$	2.84161	+	19.7638i	0.152546	+	1.06098i	−0.759387	+	0.650639i	$0.774501\pi$
$348$	−0.768923	+	1.68371i	−0.0412186	+	0.0902561i
$349$	−11.2156	+	3.29320i	−0.600357	+	0.176281i	−0.567769	−	0.823188i	$-0.692193\pi$
$349$	−11.2156	+	3.29320i	−0.600357	+	0.176281i	−0.0325883	+	0.999469i	$0.510375\pi$
$350$	−3.10837	+	3.58725i	−0.166149	+	0.191746i
$351$	−4.91993	−	1.44462i	−0.262606	−	0.0771082i
$352$	−2.40065	+	1.54280i	−0.127955	+	0.0822316i
$353$	7.16663	+	15.6927i	0.381441	+	0.835240i	0.998820	+	0.0485735i	$0.0154675\pi$
$353$	7.16663	+	15.6927i	0.381441	+	0.835240i	−0.617378	+	0.786666i	$0.711805\pi$
$354$	−9.42336	−	10.8751i	−0.500846	−	0.578007i
$355$	11.3634	+	7.30281i	0.603106	+	0.387593i
$356$	0.971137	−	6.75441i	0.0514702	−	0.357983i
$357$	0.270811	−	1.88353i	0.0143329	−	0.0996872i
$358$	6.77074	+	4.35129i	0.357845	+	0.229973i
$359$	7.90975	+	9.12833i	0.417460	+	0.481775i	0.925062	−	0.379817i	$-0.124013\pi$
$359$	7.90975	+	9.12833i	0.417460	+	0.481775i	−0.507601	+	0.861592i	$0.669468\pi$
$360$	−1.29691	−	2.83983i	−0.0683530	−	0.149672i
$361$	−15.9660	+	10.2607i	−0.840315	+	0.540038i
$362$	11.4626	+	3.36571i	0.602458	+	0.176898i
$363$	−1.87072	+	2.15892i	−0.0981871	+	0.113314i
$364$	4.91993	−	1.44462i	0.257874	−	0.0757187i
$365$	8.88719	−	19.4602i	0.465177	−	1.01859i
$366$	0.886185	+	6.16355i	0.0463216	+	0.322174i
$367$	−31.7307			−1.65633			−0.828164	−	0.560485i	$-0.810615\pi$
$367$	−31.7307			−1.65633			−0.828164	+	0.560485i	$0.810615\pi$
$368$	4.50273	+	1.65090i	0.234721	+	0.0860589i
$369$	1.09383			0.0569427
$370$	3.17839	+	22.1062i	0.165237	+	1.14925i
$371$	0.694006	−	1.51966i	0.0360310	−	0.0788969i
$372$	−2.58943	+	0.760326i	−0.134256	+	0.0394211i
$373$	5.54694	−	6.40151i	0.287209	−	0.331457i	−0.593750	−	0.804650i	$-0.702353\pi$
$373$	5.54694	−	6.40151i	0.287209	−	0.331457i	0.880959	+	0.473192i	$0.156898\pi$
$374$	5.21026	+	1.52987i	0.269416	+	0.0791078i
$375$	−0.665496	+	0.427688i	−0.0343660	+	0.0220857i
$376$	3.28553	+	7.19431i	0.169438	+	0.371018i
$377$	6.21536	+	7.17291i	0.320107	+	0.369424i
$378$	−0.841254	−	0.540641i	−0.0432694	−	0.0278076i
$379$	0.0999625	−	0.695254i	0.00513473	−	0.0357128i	−0.987093	−	0.160148i	$-0.948803\pi$
$379$	0.0999625	−	0.695254i	0.00513473	−	0.0357128i	0.992228	+	0.124435i	$0.0397119\pi$
$380$	−0.0646729	+	0.449810i	−0.00331765	+	0.0230748i
$381$	13.3803	+	8.59900i	0.685494	+	0.440540i
$382$	−4.52851	−	5.22618i	−0.231699	−	0.267395i
$383$	−14.3883	−	31.5059i	−0.735206	−	1.60988i	−0.791284	−	0.611449i	$-0.790587\pi$
$383$	−14.3883	−	31.5059i	−0.735206	−	1.60988i	0.0560781	−	0.998426i	$-0.482140\pi$
$384$	−0.841254	+	0.540641i	−0.0429300	+	0.0275895i
$385$	−8.54810	−	2.50995i	−0.435652	−	0.127919i
$386$	11.9231	−	13.7600i	0.606872	−	0.700367i
$387$	−1.78249	+	0.523385i	−0.0906089	+	0.0266052i
$388$	−1.23512	+	2.70454i	−0.0627037	+	0.137302i
$389$	2.12997	+	14.8143i	0.107994	+	0.751114i	0.969804	+	0.243884i	$0.0784216\pi$
$389$	2.12997	+	14.8143i	0.107994	+	0.751114i	−0.861810	+	0.507230i	$0.830669\pi$
$390$	−16.0082			−0.810609
$391$	−3.23683	−	8.53270i	−0.163693	−	0.431517i
$392$	1.00000			0.0505076
$393$	2.88530	+	20.0677i	0.145544	+	1.01228i
$394$	−0.109555	+	0.239892i	−0.00551931	+	0.0120856i
$395$	−1.76873	+	0.519347i	−0.0889947	+	0.0261312i
$396$	1.86875	−	2.15665i	0.0939080	−	0.108376i
$397$	−34.9538	−	10.2634i	−1.75428	−	0.515103i	−0.762946	−	0.646462i	$-0.776248\pi$
$397$	−34.9538	−	10.2634i	−1.75428	−	0.515103i	−0.991335	+	0.131359i	$0.958066\pi$
$398$	11.9919	−	7.70672i	0.601099	−	0.386303i
$399$	0.0604683	+	0.132407i	0.00302720	+	0.00662864i
$400$	−3.10837	−	3.58725i	−0.155418	−	0.179362i
$401$	30.9538	+	19.8928i	1.54576	+	0.993398i	0.986379	+	0.164486i	$0.0525964\pi$
$401$	30.9538	+	19.8928i	1.54576	+	0.993398i	0.559378	+	0.828913i	$0.311040\pi$
$402$	1.57879	−	10.9807i	0.0787426	−	0.547667i
$403$	−1.96938	+	13.6974i	−0.0981019	+	0.682314i
$404$	8.33268	+	5.35509i	0.414566	+	0.266425i
$405$	2.04445	+	2.35942i	0.101589	+	0.117240i
$406$	0.768923	+	1.68371i	0.0381610	+	0.0835609i
$407$	−17.1735	+	11.0367i	−0.851259	+	0.547071i
$408$	1.82582	+	0.536110i	0.0903917	+	0.0265414i
$409$	9.79195	−	11.3005i	0.484181	−	0.558774i	−0.460121	−	0.887856i	$-0.652194\pi$
$409$	9.79195	−	11.3005i	0.484181	−	0.558774i	0.944301	+	0.329082i	$0.106739\pi$
$410$	3.27657	−	0.962088i	0.161818	−	0.0475141i
$411$	−0.114079	+	0.249798i	−0.00562710	+	0.0123216i
$412$	2.03958	+	14.1856i	0.100483	+	0.698873i
$413$	−14.3899			−0.708079
$414$	−4.78545	−	0.315459i	−0.235192	−	0.0155040i
$415$	−29.1997			−1.43336
$416$	0.729738	+	5.07544i	0.0357784	+	0.248844i
$417$	−5.33140	+	11.6741i	−0.261080	+	0.571685i
$418$	−0.398555	+	0.117026i	−0.0194940	+	0.00572394i
$419$	17.9560	−	20.7223i	0.877206	−	1.01235i	−0.122596	−	0.992457i	$-0.539122\pi$
$419$	17.9560	−	20.7223i	0.877206	−	1.01235i	0.999802	−	0.0198933i	$-0.00633266\pi$
$420$	−2.99549	−	0.879557i	−0.146165	−	0.0429180i
$421$	−19.6282	+	12.6143i	−0.956619	+	0.614782i	−0.923060	−	0.384655i	$-0.874320\pi$
$421$	−19.6282	+	12.6143i	−0.956619	+	0.614782i	−0.0335587	+	0.999437i	$0.510684\pi$
$422$	−10.2663	−	22.4800i	−0.499755	−	1.09431i
$423$	−5.17932	−	5.97725i	−0.251827	−	0.290624i
$424$	1.40543	+	0.903213i	0.0682536	+	0.0438639i
$425$	−1.28544	+	8.94040i	−0.0623528	+	0.433673i
$426$	−0.615750	+	4.28264i	−0.0298332	+	0.207494i
$427$	5.23843	+	3.36653i	0.253505	+	0.162918i
$428$	−10.6378	−	12.2767i	−0.514197	−	0.593415i
$429$	−6.07855	−	13.3102i	−0.293475	−	0.642621i
$430$	−4.87908	+	3.13560i	−0.235290	+	0.151212i
$431$	−19.4757	−	5.71857i	−0.938110	−	0.275454i	−0.223282	−	0.974754i	$-0.571677\pi$
$431$	−19.4757	−	5.71857i	−0.938110	−	0.275454i	−0.714828	+	0.699300i	$0.753495\pi$
$432$	0.654861	−	0.755750i	0.0315070	−	0.0363610i
$433$	−20.4471	+	6.00381i	−0.982625	+	0.288525i	−0.733308	−	0.679897i	$-0.762024\pi$
$433$	−20.4471	+	6.00381i	−0.982625	+	0.288525i	−0.249318	+	0.968422i	$0.580206\pi$
$434$	−1.12110	+	2.45487i	−0.0538146	+	0.117838i
$435$	−0.822389	−	5.71984i	−0.0394305	−	0.274245i
$436$	−0.141831			−0.00679245
$437$	0.561170	+	0.415226i	0.0268444	+	0.0198629i
$438$	6.85260			0.327430
$439$	−1.11507	−	7.75548i	−0.0532194	−	0.370149i	−0.998975	−	0.0452694i	$-0.985585\pi$
$439$	−1.11507	−	7.75548i	−0.0532194	−	0.370149i	0.945755	−	0.324879i	$-0.105324\pi$
$440$	3.70092	−	8.10389i	0.176435	−	0.386338i
$441$	−0.959493	+	0.281733i	−0.0456901	+	0.0134158i
$442$	6.38973	−	7.37414i	0.303929	−	0.350752i
$443$	−10.1689	−	2.98586i	−0.483139	−	0.141862i	0.0310878	−	0.999517i	$-0.490103\pi$
$443$	−10.1689	−	2.98586i	−0.483139	−	0.141862i	−0.514227	+	0.857654i	$0.671921\pi$
$444$	−6.01807	+	3.86758i	−0.285605	+	0.183547i
$445$	8.84992	+	19.3786i	0.419526	+	0.918635i
$446$	6.00480	+	6.92991i	0.284335	+	0.328141i
$447$	−17.2364	−	11.0772i	−0.815255	−	0.523933i
$448$	−0.142315	+	0.989821i	−0.00672374	+	0.0467647i
$449$	−1.19512	+	8.31225i	−0.0564013	+	0.392279i	0.941993	+	0.335632i	$0.108950\pi$
$449$	−1.19512	+	8.31225i	−0.0564013	+	0.392279i	−0.998394	+	0.0566469i	$0.981959\pi$
$450$	3.99310	+	2.56621i	0.188237	+	0.120972i
$451$	2.04410	+	2.35901i	0.0962527	+	0.111082i
$452$	−2.13838	−	4.68240i	−0.100581	−	0.220242i
$453$	−14.5196	+	9.33118i	−0.682190	+	0.438417i
$454$	7.15908	+	2.10210i	0.335992	+	0.0986562i
$455$	−10.4832	+	12.0982i	−0.491459	+	0.567173i
$456$	−0.139665	+	0.0410093i	−0.00654041	+	0.00192044i
$457$	14.9723	−	32.7847i	0.700372	−	1.53360i	−0.139147	−	0.990272i	$-0.544436\pi$
$457$	14.9723	−	32.7847i	0.700372	−	1.53360i	0.839519	−	0.543330i	$-0.182837\pi$
$458$	2.87343	+	19.9852i	0.134267	+	0.933846i
$459$	−1.90290			−0.0888199
$460$	−14.6122	+	3.26411i	−0.681299	+	0.152190i
$461$	−12.8121			−0.596719			−0.298359	−	0.954454i	$-0.596439\pi$
$461$	−12.8121			−0.596719			−0.298359	+	0.954454i	$0.596439\pi$
$462$	−0.406117	−	2.82461i	−0.0188943	−	0.131413i
$463$	−1.07591	+	2.35591i	−0.0500018	+	0.109489i	−0.932984	−	0.359918i	$-0.882805\pi$
$463$	−1.07591	+	2.35591i	−0.0500018	+	0.109489i	0.882982	+	0.469406i	$0.155532\pi$
$464$	−1.77600	+	0.521480i	−0.0824486	+	0.0242091i
$465$	5.51745	−	6.36748i	0.255866	−	0.295285i
$466$	10.7955	+	3.16984i	0.500091	+	0.146840i
$467$	25.9963	−	16.7068i	1.20297	−	0.773100i	0.223500	−	0.974704i	$-0.428252\pi$
$467$	25.9963	−	16.7068i	1.20297	−	0.773100i	0.979467	+	0.201604i	$0.0646154\pi$
$468$	−2.13010	−	4.66426i	−0.0984637	−	0.215605i
$469$	−7.26477	−	8.38399i	−0.335456	−	0.387137i
$470$	−20.7720	−	13.3493i	−0.958139	−	0.615758i
$471$	0.773815	−	5.38200i	0.0356555	−	0.247990i
$472$	2.04789	−	14.2434i	0.0942619	−	0.655606i
$473$	−4.45977	−	2.86612i	−0.205061	−	0.131784i
$474$	−0.386672	−	0.446244i	−0.0177604	−	0.0204967i
$475$	−0.287019	−	0.628484i	−0.0131693	−	0.0288368i
$476$	1.60082	−	1.02879i	0.0733737	−	0.0471544i
$477$	−1.60296	−	0.470672i	−0.0733946	−	0.0215506i
$478$	3.83673	−	4.42782i	0.175488	−	0.202524i
$479$	1.64839	−	0.484010i	0.0753167	−	0.0221150i	−0.243857	−	0.969811i	$-0.578413\pi$
$479$	1.64839	−	0.484010i	0.0753167	−	0.0221150i	0.319174	+	0.947696i	$0.396595\pi$
$480$	1.29691	−	2.83983i	0.0591955	−	0.129620i
$481$	5.22033	+	36.3082i	0.238026	+	1.65551i
$482$	−20.7904			−0.946978
$483$	−3.37221	+	3.41002i	−0.153441	+	0.155161i
$484$	−2.85666			−0.129848
$485$	−1.32100	−	9.18778i	−0.0599837	−	0.417196i
$486$	−0.415415	+	0.909632i	−0.0188436	+	0.0412617i
$487$	−10.1142	+	2.96980i	−0.458319	+	0.134575i	−0.502739	−	0.864438i	$-0.667674\pi$
$487$	−10.1142	+	2.96980i	−0.458319	+	0.134575i	0.0444198	+	0.999013i	$0.485856\pi$
$488$	−4.07777	+	4.70600i	−0.184592	+	0.213031i
$489$	−1.36180	−	0.399861i	−0.0615827	−	0.0180823i
$490$	−2.62636	+	1.68786i	−0.118647	+	0.0762496i
$491$	17.6346	+	38.6143i	0.795837	+	1.74264i	0.659130	+	0.752029i	$0.270925\pi$
$491$	17.6346	+	38.6143i	0.795837	+	1.74264i	0.136707	+	0.990612i	$0.456348\pi$
$492$	0.716308	+	0.826664i	0.0322937	+	0.0372689i
$493$	2.96308	+	1.90426i	0.133451	+	0.0857635i
$494$	−0.106221	+	0.738787i	−0.00477913	+	0.0332396i
$495$	−1.26788	+	8.81830i	−0.0569870	+	0.396353i
$496$	−2.27033	−	1.45906i	−0.101941	−	0.0655135i
$497$	2.83337	+	3.26988i	0.127094	+	0.146674i
$498$	−3.88538	−	8.50779i	−0.174108	−	0.381243i
$499$	−6.78863	+	4.36278i	−0.303901	+	0.195305i	−0.683699	−	0.729764i	$-0.739630\pi$
$499$	−6.78863	+	4.36278i	−0.303901	+	0.195305i	0.379798	+	0.925069i	$0.375993\pi$
$500$	−0.759032	−	0.222872i	−0.0339449	−	0.00996713i
$501$	−7.51645	+	8.67444i	−0.335810	+	0.387545i
$502$	11.1131	−	3.26309i	0.496000	−	0.145639i
$503$	−12.9537	+	28.3647i	−0.577578	+	1.26472i	0.365085	+	0.930974i	$0.381040\pi$
$503$	−12.9537	+	28.3647i	−0.577578	+	1.26472i	−0.942663	+	0.333746i	$0.891687\pi$
$504$	−0.142315	−	0.989821i	−0.00633921	−	0.0440902i
$505$	−30.9232			−1.37606
$506$	−8.26245	−	10.9100i	−0.367311	−	0.485010i
$507$	−13.2926			−0.590346
$508$	2.26355	+	15.7433i	0.100429	+	0.698496i
$509$	4.19851	−	9.19346i	0.186096	−	0.407493i	−0.793472	−	0.608607i	$-0.791729\pi$
$509$	4.19851	−	9.19346i	0.186096	−	0.407493i	0.979568	+	0.201114i	$0.0644560\pi$
$510$	−5.70014	+	1.67371i	−0.252406	+	0.0741132i
$511$	4.48750	−	5.17885i	0.198515	−	0.229099i
$512$	−0.959493	−	0.281733i	−0.0424040	−	0.0124509i
$513$	0.122454	−	0.0786963i	0.00540647	−	0.00347453i
$514$	−12.6401	−	27.6781i	−0.557533	−	1.22083i
$515$	−29.2999	−	33.8139i	−1.29111	−	1.49002i
$516$	−1.56283	−	1.00437i	−0.0687997	−	0.0442149i
$517$	3.21200	−	22.3399i	0.141263	−	0.982509i
$518$	−1.01808	+	7.08088i	−0.0447317	+	0.311116i
$519$	1.04216	+	0.669756i	0.0457458	+	0.0293990i
$520$	−10.4832	−	12.0982i	−0.459717	−	0.530542i
$521$	4.55311	+	9.96991i	0.199475	+	0.436790i	0.982763	−	0.184869i	$-0.0591862\pi$
$521$	4.55311	+	9.96991i	0.199475	+	0.436790i	−0.783288	+	0.621659i	$0.786459\pi$
$522$	1.55714	−	1.00071i	0.0681541	−	0.0438000i
$523$	24.0103	+	7.05006i	1.04990	+	0.308277i	0.760775	−	0.649015i	$-0.224819\pi$
$523$	24.0103	+	7.05006i	1.04990	+	0.308277i	0.289121	+	0.957293i	$0.406637\pi$
$524$	−13.2767	+	15.3221i	−0.579995	+	0.669350i
$525$	4.55434	−	1.33727i	0.198768	−	0.0583634i
$526$	11.4749	−	25.1266i	0.500331	−	1.09557i
$527$	0.730852	+	5.08319i	0.0318364	+	0.221427i
$528$	2.85365			0.124189
$529$	−6.23341	+	22.1392i	−0.271018	+	0.962574i
$530$	−5.21565			−0.226553
$531$	2.04789	+	14.2434i	0.0888710	+	0.618111i
$532$	−0.0604683	+	0.132407i	−0.00262163	+	0.00574057i
$533$	5.38158	−	1.58017i	0.233102	−	0.0684449i
$534$	−4.46868	+	5.15713i	−0.193379	+	0.223171i
$535$	48.6599	+	14.2878i	2.10375	+	0.617717i
$536$	9.33254	−	5.99766i	0.403104	−	0.259059i
$537$	−3.34342	−	7.32107i	−0.144279	−	0.315928i
$538$	6.28155	+	7.24930i	0.270817	+	0.312539i
$539$	−2.40065	−	1.54280i	−0.103403	−	0.0664532i
$540$	−0.444301	+	3.09018i	−0.0191197	+	0.132980i
$541$	2.80486	−	19.5082i	0.120590	−	0.838723i	−0.836300	−	0.548272i	$-0.815286\pi$
$541$	2.80486	−	19.5082i	0.120590	−	0.838723i	0.956890	−	0.290451i	$-0.0938052\pi$
$542$	−22.4234	−	14.4106i	−0.963168	−	0.618990i
$543$	−7.82327	−	9.02854i	−0.335729	−	0.387452i
$544$	0.790495	+	1.73094i	0.0338922	+	0.0742135i
$545$	0.372498	−	0.239390i	0.0159560	−	0.0102543i
$546$	−4.91993	−	1.44462i	−0.210553	−	0.0618241i
$547$	−11.9796	+	13.8252i	−0.512212	+	0.591124i	−0.951664	−	0.307142i	$-0.900627\pi$
$547$	−11.9796	+	13.8252i	−0.512212	+	0.591124i	0.439452	+	0.898266i	$0.355173\pi$
$548$	−0.263491	+	0.0773679i	−0.0112558	+	0.00330499i
$549$	2.58676	−	5.66422i	0.110400	−	0.241743i
$550$	1.92768	+	13.4073i	0.0821965	+	0.571689i
$551$	−0.269430			−0.0114781
$552$	−2.89539	−	3.82318i	−0.123236	−	0.162725i
$553$	−0.590465			−0.0251091
$554$	−2.76268	−	19.2148i	−0.117375	−	0.816361i
$555$	9.27768	−	20.3153i	0.393816	−	0.862336i
$556$	−12.3140	+	3.61573i	−0.522232	+	0.153341i
$557$	22.8093	−	26.3233i	0.966459	−	1.11535i	−0.0268233	−	0.999640i	$-0.508539\pi$
$557$	22.8093	−	26.3233i	0.966459	−	1.11535i	0.993283	−	0.115713i	$-0.0369154\pi$
$558$	2.58943	+	0.760326i	0.109619	+	0.0321872i
$559$	−8.01361	+	5.15004i	−0.338940	+	0.217823i
$560$	−1.29691	−	2.83983i	−0.0548043	−	0.120005i
$561$	−3.55604	−	4.10389i	−0.150136	−	0.173266i
$562$	−1.42119	−	0.913340i	−0.0599491	−	0.0385269i
$563$	5.53420	−	38.4912i	0.233239	−	1.62221i	−0.450702	−	0.892674i	$-0.648826\pi$
$563$	5.53420	−	38.4912i	0.233239	−	1.62221i	0.683941	−	0.729537i	$-0.260265\pi$
$564$	1.12557	−	7.82853i	0.0473952	−	0.329641i
$565$	13.5194	+	8.68838i	0.568765	+	0.365523i
$566$	2.04872	+	2.36435i	0.0861142	+	0.0993811i
$567$	0.415415	+	0.909632i	0.0174458	+	0.0382010i
$568$	−3.63983	+	2.33918i	−0.152724	+	0.0981497i
$569$	−4.80090	−	1.40967i	−0.201264	−	0.0590965i	0.179547	−	0.983749i	$-0.442537\pi$
$569$	−4.80090	−	1.40967i	−0.201264	−	0.0590965i	−0.380811	+	0.924653i	$0.624355\pi$
$570$	0.297592	−	0.343439i	0.0124648	−	0.0143851i
$571$	31.7312	−	9.31711i	1.32791	−	0.389909i	0.460568	−	0.887625i	$-0.347646\pi$
$571$	31.7312	−	9.31711i	1.32791	−	0.389909i	0.867340	+	0.497716i	$0.165828\pi$
$572$	6.07855	−	13.3102i	0.254157	−	0.556527i
$573$	0.984139	+	6.84484i	0.0411130	+	0.285947i
$574$	1.09383			0.0456557
$575$	16.0066	−	16.1860i	0.667519	−	0.675003i
$576$	1.00000			0.0416667
$577$	−5.74373	−	39.9485i	−0.239115	−	1.66308i	−0.656482	−	0.754341i	$-0.727956\pi$
$577$	−5.74373	−	39.9485i	−0.239115	−	1.66308i	0.417368	−	0.908738i	$-0.362953\pi$
$578$	−5.55782	+	12.1699i	−0.231175	+	0.506202i
$579$	−17.4696	+	5.12954i	−0.726012	+	0.213176i
$580$	3.78422	−	4.36722i	0.157131	−	0.181339i
$581$	−8.97414	−	2.63505i	−0.372310	−	0.109320i
$582$	2.50123	−	1.60744i	0.103679	−	0.0666307i
$583$	−1.98045	−	4.33659i	−0.0820220	−	0.179603i
$584$	4.48750	+	5.17885i	0.185694	+	0.214302i
$585$	13.4670	+	8.65471i	0.556792	+	0.357828i
$586$	−3.10513	+	21.5966i	−0.128272	+	0.892148i
$587$	4.29015	−	29.8387i	0.177073	−	1.23157i	−0.686417	−	0.727208i	$-0.740818\pi$
$587$	4.29015	−	29.8387i	0.177073	−	1.23157i	0.863491	−	0.504365i	$-0.168273\pi$
$588$	−0.841254	−	0.540641i	−0.0346927	−	0.0222957i
$589$	−0.257251	−	0.296884i	−0.0105998	−	0.0122329i
$590$	18.6623	+	40.8648i	0.768316	+	1.68238i
$591$	0.221859	−	0.142580i	0.00912607	−	0.00586497i
$592$	−6.86392	−	2.01543i	−0.282105	−	0.0828336i
$593$	15.1461	−	17.4796i	0.621977	−	0.717800i	−0.354104	−	0.935206i	$-0.615214\pi$
$593$	15.1461	−	17.4796i	0.621977	−	0.717800i	0.976081	+	0.217406i	$0.0697596\pi$
$594$	−2.73806	+	0.803967i	−0.112344	+	0.0329872i
$595$	−2.46789	+	5.40392i	−0.101174	+	0.221539i
$596$	−2.91589	−	20.2804i	−0.119439	−	0.830719i
$597$	−14.2548			−0.583410
$598$	−23.9998	+	5.36112i	−0.981423	+	0.219232i
$599$	−10.8634			−0.443868			−0.221934	−	0.975062i	$-0.571237\pi$
$599$	−10.8634			−0.443868			−0.221934	+	0.975062i	$0.571237\pi$
$600$	0.675513	+	4.69830i	0.0275777	+	0.191807i
$601$	−12.6603	+	27.7221i	−0.516423	+	1.13081i	0.454353	+	0.890822i	$0.349870\pi$
$601$	−12.6603	+	27.7221i	−0.516423	+	1.13081i	−0.970776	+	0.239987i	$0.922857\pi$
$602$	−1.78249	+	0.523385i	−0.0726487	+	0.0213316i
$603$	−7.26477	+	8.38399i	−0.295844	+	0.341422i
$604$	−16.5604	−	4.86256i	−0.673831	−	0.197855i
$605$	7.50261	−	4.82164i	0.305025	−	0.196027i
$606$	−4.11471	−	9.00997i	−0.167149	−	0.366005i
$607$	9.13956	+	10.5476i	0.370963	+	0.428115i	0.910283	−	0.413987i	$-0.135864\pi$
$607$	9.13956	+	10.5476i	0.370963	+	0.428115i	−0.539320	+	0.842101i	$0.681319\pi$
$608$	−0.122454	−	0.0786963i	−0.00496616	−	0.00319156i
$609$	0.263421	−	1.83213i	0.0106744	−	0.0742418i
$610$	2.76663	−	19.2423i	0.112018	−	0.779099i
$611$	−34.1167	−	21.9255i	−1.38022	−	0.887010i
$612$	−1.24614	−	1.43812i	−0.0503721	−	0.0581325i
$613$	−3.29698	−	7.21939i	−0.133164	−	0.291588i	0.831290	−	0.555839i	$-0.187603\pi$
$613$	−3.29698	−	7.21939i	−0.133164	−	0.291588i	−0.964454	+	0.264250i	$0.914875\pi$
$614$	−2.58013	+	1.65815i	−0.104126	+	0.0669175i
$615$	−3.27657	−	0.962088i	−0.132124	−	0.0387951i
$616$	1.86875	−	2.15665i	0.0752939	−	0.0868938i
$617$	5.36240	−	1.57454i	0.215882	−	0.0633887i	−0.172003	−	0.985096i	$-0.555024\pi$
$617$	5.36240	−	1.57454i	0.215882	−	0.0633887i	0.387885	+	0.921708i	$0.373206\pi$
$618$	5.95350	−	13.0364i	0.239485	−	0.524399i
$619$	2.00359	+	13.9353i	0.0805309	+	0.560105i	0.989643	+	0.143553i	$0.0458526\pi$
$619$	2.00359	+	13.9353i	0.0805309	+	0.560105i	−0.909112	+	0.416552i	$0.863238\pi$
$620$	8.42538			0.338371
$621$	3.85522	+	2.85259i	0.154705	+	0.114470i
$622$	21.4531			0.860189
$623$	0.971137	+	6.75441i	0.0389078	+	0.270610i
$624$	2.13010	−	4.66426i	0.0852721	−	0.186720i
$625$	25.1414	−	7.38217i	1.00565	−	0.295287i
$626$	−9.46957	+	10.9285i	−0.378480	+	0.436789i
$627$	0.398555	+	0.117026i	0.0159168	+	0.00467358i
$628$	4.57419	−	2.93965i	0.182530	−	0.117305i
$629$	5.65496	+	12.3826i	0.225478	+	0.493728i
$630$	2.04445	+	2.35942i	0.0814527	+	0.0940014i
$631$	−25.7520	−	16.5498i	−1.02517	−	0.658836i	−0.0838934	−	0.996475i	$-0.526736\pi$
$631$	−25.7520	−	16.5498i	−1.02517	−	0.658836i	−0.941276	+	0.337638i	$0.890372\pi$
$632$	0.0840319	−	0.584455i	0.00334261	−	0.0232484i
$633$	−3.51707	+	24.4618i	−0.139791	+	0.972268i
$634$	−22.3618	−	14.3710i	−0.888100	−	0.570747i
$635$	−32.5173	−	37.5270i	−1.29041	−	1.48921i
$636$	−0.694006	−	1.51966i	−0.0275191	−	0.0602585i
$637$	−4.31364	+	2.77221i	−0.170913	+	0.109839i
$638$	5.06808	+	1.48812i	0.200647	+	0.0589153i
$639$	2.83337	−	3.26988i	0.112086	−	0.129355i
$640$	2.99549	−	0.879557i	0.118407	−	0.0347675i
$641$	3.80608	−	8.33415i	0.150331	−	0.329179i	−0.819452	−	0.573148i	$-0.805722\pi$
$641$	3.80608	−	8.33415i	0.150331	−	0.329179i	0.969783	+	0.243969i	$0.0784494\pi$
$642$	2.31181	+	16.0790i	0.0912400	+	0.634588i
$643$	32.0047			1.26214			0.631071	−	0.775725i	$-0.282616\pi$
$643$	32.0047			1.26214			0.631071	+	0.775725i	$0.282616\pi$
$644$	−4.78545	−	0.315459i	−0.188573	−	0.0124308i
$645$	5.79978			0.228366
$646$	0.0394196	+	0.274169i	0.00155094	+	0.0107870i
$647$	4.26147	−	9.33131i	0.167536	−	0.366852i	−0.807179	−	0.590307i	$-0.799007\pi$
$647$	4.26147	−	9.33131i	0.167536	−	0.366852i	0.974714	+	0.223456i	$0.0717338\pi$
$648$	−0.959493	+	0.281733i	−0.0376924	+	0.0110675i
$649$	−26.8910	+	31.0339i	−1.05556	+	1.21819i
$650$	23.3530	+	6.85705i	0.915979	+	0.268956i
$651$	2.27033	−	1.45906i	0.0889814	−	0.0571849i
$652$	−0.589595	−	1.29103i	−0.0230903	−	0.0505608i
$653$	24.4979	+	28.2721i	0.958676	+	1.10637i	0.994259	+	0.107004i	$0.0341259\pi$
$653$	24.4979	+	28.2721i	0.958676	+	1.10637i	−0.0355826	+	0.999367i	$0.511329\pi$
$654$	0.119315	+	0.0766794i	0.00466560	+	0.00299840i
$655$	9.00778	−	62.6505i	0.351963	−	2.44796i
$656$	−0.155669	+	1.08270i	−0.00607784	+	0.0422723i
$657$	−5.76477	−	3.70479i	−0.224905	−	0.144538i
$658$	−5.17932	−	5.97725i	−0.201911	−	0.233018i
$659$	7.93923	+	17.3845i	0.309269	+	0.677204i	0.998897	−	0.0469598i	$-0.0149533\pi$
$659$	7.93923	+	17.3845i	0.309269	+	0.677204i	−0.689628	+	0.724164i	$0.742226\pi$
$660$	−7.49471	+	4.81656i	−0.291731	+	0.187484i
$661$	−16.7961	−	4.93178i	−0.653293	−	0.191824i	−0.0617427	−	0.998092i	$-0.519666\pi$
$661$	−16.7961	−	4.93178i	−0.653293	−	0.191824i	−0.591551	+	0.806268i	$0.701484\pi$
$662$	0.697362	−	0.804798i	0.0271037	−	0.0312794i
$663$	−9.36215	+	2.74897i	−0.363596	+	0.106761i
$664$	3.88538	−	8.50779i	0.150782	−	0.330166i
$665$	−0.0646729	−	0.449810i	−0.00250791	−	0.0174429i
$666$	7.15370			0.277200
$667$	−3.14850	−	8.29984i	−0.121910	−	0.321371i
$668$	−11.4779			−0.444094
$669$	−1.30497	−	9.07625i	−0.0504530	−	0.350908i
$670$	−14.3874	+	31.5040i	−0.555833	+	1.21710i
$671$	17.0497	−	5.00625i	0.658197	−	0.193264i
$672$	0.654861	−	0.755750i	0.0252618	−	0.0291537i
$673$	−39.1418	−	11.4931i	−1.50880	−	0.443025i	−0.580318	−	0.814390i	$-0.697072\pi$
$673$	−39.1418	−	11.4931i	−1.50880	−	0.443025i	−0.928487	+	0.371365i	$0.878890\pi$
$674$	6.69434	−	4.30219i	0.257856	−	0.165714i
$675$	−1.97181	−	4.31767i	−0.0758951	−	0.166187i
$676$	−8.70481	−	10.0459i	−0.334801	−	0.386380i
$677$	36.2881	+	23.3210i	1.39467	+	0.896298i	0.999749	−	0.0224188i	$-0.00713674\pi$
$677$	36.2881	+	23.3210i	1.39467	+	0.896298i	0.394918	+	0.918716i	$0.370773\pi$
$678$	−0.732577	+	5.09518i	−0.0281344	+	0.195679i
$679$	0.423133	−	2.94296i	0.0162384	−	0.112940i
$680$	−4.99770	−	3.21183i	−0.191653	−	0.123168i
$681$	−4.88612	−	5.63889i	−0.187237	−	0.216083i
$682$	3.19924	+	7.00535i	0.122505	+	0.268249i
$683$	−20.6203	+	13.2518i	−0.789012	+	0.507067i	−0.872013	−	0.489482i	$-0.837186\pi$
$683$	−20.6203	+	13.2518i	−0.789012	+	0.507067i	0.0830012	+	0.996549i	$0.473549\pi$
$684$	0.139665	+	0.0410093i	0.00534022	+	0.00156803i
$685$	0.561435	−	0.647930i	0.0214513	−	0.0247561i
$686$	−0.959493	+	0.281733i	−0.0366336	+	0.0107566i
$687$	8.38752	−	18.3661i	0.320004	−	0.700710i
$688$	−0.264384	−	1.83883i	−0.0100795	−	0.0701047i
$689$	−8.56640			−0.326354
$690$	14.0573	+	5.15403i	0.535153	+	0.196210i
$691$	24.0323			0.914231			0.457116	−	0.889407i	$-0.348883\pi$
$691$	24.0323			0.914231			0.457116	+	0.889407i	$0.348883\pi$
$692$	0.176302	+	1.22621i	0.00670201	+	0.0466135i
$693$	−1.18545	+	2.59577i	−0.0450315	+	0.0986053i
$694$	19.1583	−	5.62538i	0.727238	−	0.213536i
$695$	26.2382	−	30.2805i	0.995273	−	1.14861i
$696$	1.77600	+	0.521480i	0.0673190	+	0.0197666i
$697$	1.75103	−	1.12532i	0.0663251	−	0.0426246i
$698$	4.85582	+	10.6328i	0.183796	+	0.402456i
$699$	−7.36799	−	8.50311i	−0.278683	−	0.321617i
$700$	3.99310	+	2.56621i	0.150925	+	0.0969936i
$701$	−0.646018	+	4.49315i	−0.0243998	+	0.169704i	−0.998378	−	0.0569389i	$-0.981866\pi$
$701$	−0.646018	+	4.49315i	−0.0243998	+	0.169704i	0.973978	+	0.226643i	$0.0727751\pi$
$702$	−0.729738	+	5.07544i	−0.0275422	+	0.191560i
$703$	−0.875997	−	0.562969i	−0.0330389	−	0.0212328i
$704$	1.86875	+	2.15665i	0.0704310	+	0.0812817i
$705$	10.2573	+	22.4603i	0.386312	+	0.845905i
$706$	14.5131	−	9.32699i	0.546207	−	0.351026i
$707$	−9.50384	−	2.79058i	−0.357429	−	0.104951i
$708$	−9.42336	+	10.8751i	−0.354152	+	0.408713i
$709$	26.5549	−	7.79721i	0.997288	−	0.292830i	0.257946	−	0.966159i	$-0.416954\pi$
$709$	26.5549	−	7.79721i	0.997288	−	0.292830i	0.739343	+	0.673329i	$0.235136\pi$
$710$	5.61130	−	12.2870i	0.210588	−	0.461124i
$711$	0.0840319	+	0.584455i	0.00315144	+	0.0219188i
$712$	−6.82386			−0.255735
$713$	6.13938	−	11.3940i	0.229922	−	0.426708i
$714$	−1.90290			−0.0712144
$715$	6.50122	+	45.2170i	0.243132	+	1.69102i
$716$	3.34342	−	7.32107i	0.124950	−	0.273601i
$717$	−5.62153	+	1.65063i	−0.209940	+	0.0616439i
$718$	7.90975	−	9.12833i	0.295189	−	0.340666i
$719$	25.3536	+	7.44450i	0.945531	+	0.277633i	0.717925	−	0.696120i	$-0.245092\pi$
$719$	25.3536	+	7.44450i	0.945531	+	0.277633i	0.227606	+	0.973753i	$0.426910\pi$
$720$	−2.62636	+	1.68786i	−0.0978785	+	0.0629027i
$721$	−5.95350	−	13.0364i	−0.221720	−	0.485499i
$722$	12.4285	+	14.3432i	0.462540	+	0.533800i
$723$	17.4900	+	11.2401i	0.650461	+	0.418026i
$724$	1.70016	−	11.8249i	0.0631859	−	0.439468i
$725$	−1.25036	+	8.69642i	−0.0464371	+	0.322977i
$726$	2.40318	+	1.54443i	0.0891903	+	0.0573191i
$727$	11.8994	+	13.7327i	0.441325	+	0.509316i	0.932215	−	0.361905i	$-0.117874\pi$
$727$	11.8994	+	13.7327i	0.441325	+	0.509316i	−0.490890	+	0.871222i	$0.663328\pi$
$728$	−2.13010	−	4.66426i	−0.0789466	−	0.172869i
$729$	0.841254	−	0.540641i	0.0311575	−	0.0200237i
$730$	−20.5269	−	6.02725i	−0.759736	−	0.223078i
$731$	−2.31500	+	2.67165i	−0.0856232	+	0.0988144i
$732$	5.97470	−	1.75433i	0.220831	−	0.0648419i
$733$	8.59605	−	18.8227i	0.317502	−	0.695233i	−0.681840	−	0.731502i	$-0.738820\pi$
$733$	8.59605	−	18.8227i	0.317502	−	0.695233i	0.999342	+	0.0362684i	$0.0115471\pi$
$734$	4.51575	+	31.4077i	0.166679	+	1.15928i
$735$	3.12196			0.115155
$736$	0.993288	−	4.69184i	0.0366131	−	0.172944i
$737$	−31.6573			−1.16611
$738$	−0.155669	−	1.08270i	−0.00573024	−	0.0398547i
$739$	−11.3574	+	24.8693i	−0.417790	+	0.914831i	0.577363	+	0.816488i	$0.304082\pi$
$739$	−11.3574	+	24.8693i	−0.417790	+	0.914831i	−0.995152	+	0.0983439i	$0.968645\pi$
$740$	21.4289	−	6.29208i	0.787741	−	0.231302i
$741$	0.488777	−	0.564079i	0.0179557	−	0.0207220i
$742$	−1.60296	−	0.470672i	−0.0588466	−	0.0172789i
$743$	40.5070	−	26.0323i	1.48606	−	0.955031i	0.489511	−	0.871997i	$-0.337175\pi$
$743$	40.5070	−	26.0323i	1.48606	−	0.955031i	0.996547	−	0.0830346i	$-0.0264612\pi$
$744$	1.12110	+	2.45487i	0.0411016	+	0.0899999i
$745$	41.8886	+	48.3420i	1.53468	+	1.77112i
$746$	−7.12576	−	4.57945i	−0.260893	−	0.167665i
$747$	−1.33107	+	9.25781i	−0.0487014	+	0.338725i
$748$	0.772802	−	5.37495i	0.0282564	−	0.196528i
$749$	13.6656	+	8.78236i	0.499331	+	0.320901i
$750$	0.518045	+	0.597855i	0.0189163	+	0.0218306i
$751$	−5.08021	−	11.1241i	−0.185380	−	0.405925i	0.794010	−	0.607905i	$-0.207990\pi$
$751$	−5.08021	−	11.1241i	−0.185380	−	0.405925i	−0.979390	+	0.201980i	$0.935262\pi$
$752$	6.65351	−	4.27595i	0.242628	−	0.155928i
$753$	−11.1131	−	3.26309i	−0.404982	−	0.118913i
$754$	6.21536	−	7.17291i	0.226350	−	0.261222i
$755$	51.7007	−	15.1807i	1.88158	−	0.552482i
$756$	−0.415415	+	0.909632i	−0.0151085	+	0.0330830i
$757$	0.535398	+	3.72378i	0.0194594	+	0.135343i	0.997235	−	0.0743104i	$-0.0236755\pi$
$757$	0.535398	+	3.72378i	0.0194594	+	0.135343i	−0.977776	+	0.209653i	$0.932766\pi$
$758$	−0.702404			−0.0255125
$759$	1.05240	+	13.6451i	0.0381998	+	0.495286i
$760$	0.454435			0.0164841
$761$	1.69807	+	11.8103i	0.0615550	+	0.428124i	0.997175	+	0.0751151i	$0.0239324\pi$
$761$	1.69807	+	11.8103i	0.0615550	+	0.428124i	−0.935620	+	0.353009i	$0.885158\pi$
$762$	6.60726	−	14.4679i	0.239356	−	0.524116i
$763$	0.136085	−	0.0399583i	0.00492662	−	0.00144659i
$764$	−4.52851	+	5.22618i	−0.163836	+	0.189076i
$765$	5.70014	+	1.67371i	0.206089	+	0.0605132i
$766$	−29.1375	+	18.7256i	−1.05278	+	0.676582i
$767$	30.6518	+	67.1181i	1.10677	+	2.42349i
$768$	0.654861	+	0.755750i	0.0236303	+	0.0272708i
$769$	−7.79336	−	5.00849i	−0.281036	−	0.180611i	0.392528	−	0.919740i	$-0.371601\pi$
$769$	−7.79336	−	5.00849i	−0.281036	−	0.180611i	−0.673563	+	0.739130i	$0.735237\pi$
$770$	−1.26788	+	8.81830i	−0.0456912	+	0.317789i
$771$	−4.33032	+	30.1180i	−0.155953	+	1.08467i
$772$	−15.3168	−	9.84352i	−0.551264	−	0.354276i
$773$	−2.53398	−	2.92437i	−0.0911410	−	0.105182i	0.708347	−	0.705864i	$-0.249441\pi$
$773$	−2.53398	−	2.92437i	−0.0911410	−	0.105182i	−0.799488	+	0.600682i	$0.794896\pi$
$774$	0.771732	+	1.68986i	0.0277393	+	0.0607407i
$775$	−10.7764	+	6.92556i	−0.387099	+	0.248774i
$776$	2.85278	+	0.837653i	0.102409	+	0.0300700i
$777$	4.68468	−	5.40640i	0.168062	−	0.193954i
$778$	14.3604	−	4.21659i	0.514844	−	0.151172i
$779$	−0.0661422	+	0.144831i	−0.00236979	+	0.00518911i
$780$	2.27821	+	15.8453i	0.0815730	+	0.567353i
$781$	12.3468			0.441805
$782$	−7.98520	+	4.41821i	−0.285550	+	0.157995i
$783$	−1.85097			−0.0661484
$784$	−0.142315	−	0.989821i	−0.00508267	−	0.0353508i
$785$	−7.05173	+	15.4411i	−0.251687	+	0.551118i
$786$	19.4528	−	5.71186i	0.693859	−	0.203735i
$787$	−4.79092	+	5.52902i	−0.170778	+	0.197088i	−0.834686	−	0.550726i	$-0.814351\pi$
$787$	−4.79092	+	5.52902i	−0.170778	+	0.197088i	0.663908	+	0.747814i	$0.268897\pi$
$788$	0.253042	+	0.0742998i	0.00901424	+	0.00264682i
$789$	−23.2378	+	14.9340i	−0.827287	+	0.531665i
$790$	0.765778	+	1.67682i	0.0272452	+	0.0596586i
$791$	3.37095	+	3.89028i	0.119857	+	0.138322i
$792$	−2.40065	−	1.54280i	−0.0853032	−	0.0548211i
$793$	4.54403	−	31.6044i	0.161363	−	1.12231i
$794$	−5.18445	+	36.0586i	−0.183989	+	1.27967i
$795$	4.38768	+	2.81979i	0.155615	+	0.100008i
$796$	−9.33490	−	10.7730i	−0.330867	−	0.381841i
$797$	−15.3513	−	33.6146i	−0.543770	−	1.19069i	−0.959631	−	0.281262i	$-0.909247\pi$
$797$	−15.3513	−	33.6146i	−0.543770	−	1.19069i	0.415861	−	0.909428i	$-0.363480\pi$
$798$	0.122454	−	0.0786963i	0.00433482	−	0.00278582i
$799$	−14.4405	−	4.24011i	−0.510868	−	0.150004i
$800$	−3.10837	+	3.58725i	−0.109897	+	0.126828i
$801$	6.54745	−	1.92250i	0.231343	−	0.0679284i
$802$	15.2851	−	33.4697i	0.539736	−	1.18186i
$803$	−2.78296	−	19.3559i	−0.0982085	−	0.683055i
$804$	−11.0936			−0.391241
$805$	13.1007	−	7.24864i	0.461740	−	0.255481i
$806$	13.8382			0.487430
$807$	−1.36511	−	9.49456i	−0.0480542	−	0.334224i
$808$	4.11471	−	9.00997i	0.144755	−	0.316970i
$809$	−21.5462	+	6.32652i	−0.757522	+	0.222429i	−0.637614	−	0.770356i	$-0.720078\pi$
$809$	−21.5462	+	6.32652i	−0.757522	+	0.222429i	−0.119909	+	0.992785i	$0.538260\pi$
$810$	2.04445	−	2.35942i	0.0718345	−	0.0829015i
$811$	16.7590	+	4.92089i	0.588488	+	0.172796i	0.562402	−	0.826864i	$-0.309877\pi$
$811$	16.7590	+	4.92089i	0.588488	+	0.172796i	0.0260862	+	0.999660i	$0.491696\pi$
$812$	1.55714	−	1.00071i	0.0546449	−	0.0351181i
$813$	11.0728	+	24.2460i	0.388340	+	0.850345i
$814$	13.3684	+	15.4280i	0.468564	+	0.540751i
$815$	3.72757	+	2.39556i	0.130571	+	0.0839128i
$816$	0.270811	−	1.88353i	0.00948029	−	0.0659369i
$817$	0.0384840	−	0.267662i	0.00134638	−	0.00936431i
$818$	−12.5790	−	8.08405i	−0.439815	−	0.282652i
$819$	3.35789	+	3.87521i	0.117334	+	0.135411i
$820$	−1.41860	−	3.10630i	−0.0495397	−	0.108477i
$821$	−38.7393	+	24.8962i	−1.35201	+	0.868884i	−0.997801	−	0.0662822i	$-0.978886\pi$
$821$	−38.7393	+	24.8962i	−1.35201	+	0.868884i	−0.354209	+	0.935166i	$0.615250\pi$
$822$	0.263491	+	0.0773679i	0.00919029	+	0.00269851i
$823$	−14.1775	+	16.3617i	−0.494197	+	0.570333i	−0.946982	−	0.321286i	$-0.895885\pi$
$823$	−14.1775	+	16.3617i	−0.494197	+	0.570333i	0.452786	+	0.891619i	$0.350430\pi$
$824$	13.7509	−	4.03764i	0.479036	−	0.140658i
$825$	5.62687	−	12.3211i	0.195902	−	0.428967i
$826$	2.04789	+	14.2434i	0.0712553	+	0.495591i
$827$	29.7842			1.03570			0.517848	−	0.855472i	$-0.326733\pi$
$827$	29.7842			1.03570			0.517848	+	0.855472i	$0.326733\pi$
$828$	0.368792	+	4.78163i	0.0128164	+	0.166173i
$829$	−30.7447			−1.06781			−0.533904	−	0.845545i	$-0.679276\pi$
$829$	−30.7447			−1.06781			−0.533904	+	0.845545i	$0.679276\pi$
$830$	4.15555	+	28.9025i	0.144241	+	1.00322i
$831$	−8.06422	+	17.6582i	−0.279745	+	0.612555i
$832$	4.91993	−	1.44462i	0.170568	−	0.0500832i
$833$	−1.24614	+	1.43812i	−0.0431761	+	0.0498278i
$834$	12.3140	+	3.61573i	0.426400	+	0.125202i
$835$	30.1451	−	19.3731i	1.04322	−	0.670434i
$836$	0.172555	+	0.377844i	0.00596796	+	0.0130680i
$837$	−1.76731	−	2.03958i	−0.0610870	−	0.0704982i
$838$	−23.0668	−	14.8241i	−0.796828	−	0.512090i
$839$	−1.86241	+	12.9533i	−0.0642974	+	0.447198i	0.932087	+	0.362235i	$0.117986\pi$
$839$	−1.86241	+	12.9533i	−0.0642974	+	0.447198i	−0.996384	+	0.0849630i	$0.972923\pi$
$840$	−0.444301	+	3.09018i	−0.0153298	+	0.106621i
$841$	−21.5141	−	13.8263i	−0.741866	−	0.476769i
$842$	15.2793	+	17.6332i	0.526558	+	0.607680i
$843$	0.701788	+	1.53670i	0.0241709	+	0.0529268i
$844$	−20.7902	+	13.3610i	−0.715627	+	0.459906i
$845$	39.8180	+	11.6916i	1.36978	+	0.402204i
$846$	−5.17932	+	5.97725i	−0.178069	+	0.205502i
$847$	2.74095	−	0.804815i	0.0941801	−	0.0276538i
$848$	0.694006	−	1.51966i	0.0238323	−	0.0521854i
$849$	−0.445230	−	3.09664i	−0.0152802	−	0.106276i
$850$	9.03234			0.309807
$851$	7.10568	−	33.5640i	0.243580	−	1.15056i
$852$	4.32668			0.148230
$853$	−6.75613	−	46.9899i	−0.231325	−	1.60890i	−0.692381	−	0.721532i	$-0.743438\pi$
$853$	−6.75613	−	46.9899i	−0.231325	−	1.60890i	0.461056	−	0.887371i	$-0.347471\pi$
$854$	2.58676	−	5.66422i	0.0885171	−	0.193825i
$855$	−0.436027	+	0.128029i	−0.0149118	+	0.00437851i
$856$	−10.6378	+	12.2767i	−0.363592	+	0.419608i
$857$	10.1738	+	2.98731i	0.347531	+	0.102044i	0.450840	−	0.892605i	$-0.351125\pi$
$857$	10.1738	+	2.98731i	0.347531	+	0.102044i	−0.103308	+	0.994649i	$0.532943\pi$
$858$	−12.3096	+	7.91092i	−0.420244	+	0.270074i
$859$	13.0134	+	28.4953i	0.444010	+	0.972246i	0.990845	+	0.135005i	$0.0431052\pi$
$859$	13.0134	+	28.4953i	0.444010	+	0.972246i	−0.546835	+	0.837240i	$0.684168\pi$
$860$	3.79805	+	4.38318i	0.129512	+	0.149465i
$861$	−0.920191	−	0.591371i	−0.0313600	−	0.0201539i
$862$	−2.88869	+	20.0913i	−0.0983891	+	0.684311i
$863$	2.74265	−	19.0756i	0.0933610	−	0.649340i	−0.888379	−	0.459111i	$-0.848168\pi$
$863$	2.74265	−	19.0756i	0.0933610	−	0.649340i	0.981740	−	0.190229i	$-0.0609230\pi$
$864$	−0.841254	−	0.540641i	−0.0286200	−	0.0183930i
$865$	−2.53270	−	2.92289i	−0.0861143	−	0.0993812i
$866$	8.85263	+	19.3846i	0.300825	+	0.658714i
$867$	11.2551	−	7.23321i	0.382243	−	0.245653i
$868$	2.58943	+	0.760326i	0.0878911	+	0.0258071i
$869$	−1.10343	+	1.27342i	−0.0374313	+	0.0431980i
$870$	−5.54458	+	1.62804i	−0.187979	+	0.0551956i
$871$	−23.6304	+	51.7435i	−0.800687	+	1.75326i
$872$	0.0201846	+	0.140387i	0.000683537	+	0.00475410i
$873$	−2.97322			−0.100628
$874$	0.331137	−	0.614551i	0.0112009	−	0.0207875i
$875$	0.791076			0.0267433
$876$	−0.975227	−	6.78285i	−0.0329499	−	0.229171i
$877$	19.3250	−	42.3159i	0.652559	−	1.42891i	−0.236737	−	0.971574i	$-0.576078\pi$
$877$	19.3250	−	42.3159i	0.652559	−	1.42891i	0.889296	−	0.457332i	$-0.151195\pi$
$878$	−7.51785	+	2.20744i	−0.253715	+	0.0744975i
$879$	14.2882	−	16.4895i	0.481929	−	0.556176i
$880$	−8.54810	−	2.50995i	−0.288157	−	0.0846104i
$881$	−8.76336	+	5.63187i	−0.295245	+	0.189742i	−0.679874	−	0.733329i	$-0.737966\pi$
$881$	−8.76336	+	5.63187i	−0.295245	+	0.189742i	0.384629	+	0.923071i	$0.374329\pi$
$882$	0.415415	+	0.909632i	0.0139878	+	0.0306289i
$883$	−20.5207	−	23.6821i	−0.690575	−	0.796966i	0.296872	−	0.954917i	$-0.404057\pi$
$883$	−20.5207	−	23.6821i	−0.690575	−	0.796966i	−0.987447	+	0.157951i	$0.949511\pi$
$884$	−8.20844	−	5.27524i	−0.276080	−	0.177426i
$885$	6.39343	−	44.4673i	0.214913	−	1.49475i
$886$	−1.50828	+	10.4903i	−0.0506717	+	0.352429i
$887$	−48.4371	−	31.1286i	−1.62636	−	1.04520i	−0.951683	−	0.307082i	$-0.900647\pi$
$887$	−48.4371	−	31.1286i	−1.62636	−	1.04520i	−0.674675	−	0.738115i	$-0.735716\pi$
$888$	4.68468	+	5.40640i	0.157207	+	0.181427i
$889$	−6.60726	−	14.4679i	−0.221600	−	0.485237i
$890$	17.9219	−	11.5177i	0.600743	−	0.386074i
$891$	2.73806	+	0.803967i	0.0917285	+	0.0269339i
$892$	6.00480	−	6.92991i	0.201056	−	0.232030i
$893$	1.10461	−	0.324344i	0.0369645	−	0.0108538i
$894$	−8.51143	+	18.6374i	−0.284665	+	0.623329i
$895$	3.57591	+	24.8710i	0.119529	+	0.831345i
$896$	1.00000			0.0334077
$897$	23.0883	+	8.46519i	0.770897	+	0.282644i
$898$	8.39773			0.280236
$899$	0.710908	+	4.94447i	0.0237101	+	0.164907i
$900$	1.97181	−	4.31767i	0.0657271	−	0.143922i
$901$	−3.05028	+	0.895643i	−0.101620	+	0.0298382i
$902$	2.04410	−	2.35901i	0.0680609	−	0.0785465i
$903$	1.78249	+	0.523385i	0.0593174	+	0.0174172i
$904$	−4.33042	+	2.78299i	−0.144028	+	0.0925609i
$905$	15.4935	+	33.9259i	0.515020	+	1.12774i
$906$	11.3026	+	13.0438i	0.375502	+	0.433353i
$907$	−36.1704	−	23.2453i	−1.20102	−	0.771848i	−0.221887	−	0.975072i	$-0.571222\pi$
$907$	−36.1704	−	23.2453i	−1.20102	−	0.771848i	−0.979132	+	0.203224i	$0.934858\pi$
$908$	1.06186	−	7.38537i	0.0352389	−	0.245092i
$909$	−1.40964	+	9.80425i	−0.0467548	+	0.325186i
$910$	13.4670	+	8.65471i	0.446426	+	0.286901i
$911$	9.98412	+	11.5223i	0.330789	+	0.381750i	0.896643	−	0.442755i	$-0.145999\pi$
$911$	9.98412	+	11.5223i	0.330789	+	0.381750i	−0.565854	+	0.824505i	$0.691453\pi$
$912$	0.0604683	+	0.132407i	0.00200230	+	0.00438443i
$913$	−22.4533	+	14.4298i	−0.743094	+	0.477558i
$914$	−34.5817	−	10.1541i	−1.14386	−	0.335868i
$915$	−12.7306	+	14.6919i	−0.420862	+	0.485700i
$916$	19.3728	−	5.68837i	0.640096	−	0.187949i
$917$	8.42215	−	18.4419i	0.278124	−	0.609006i
$918$	0.270811	+	1.88353i	0.00893811	+	0.0621659i
$919$	−28.2691			−0.932510			−0.466255	−	0.884650i	$-0.654397\pi$
$919$	−28.2691			−0.932510			−0.466255	+	0.884650i	$0.654397\pi$
$920$	5.31043	+	13.9990i	0.175080	+	0.461533i
$921$	3.06701			0.101061
$922$	1.82335	+	12.6817i	0.0600489	+	0.417649i
$923$	9.21624	−	20.1807i	0.303356	−	0.664257i
$924$	−2.73806	+	0.803967i	−0.0900756	+	0.0264486i
$925$	−22.2363	+	25.6621i	−0.731126	+	0.843764i
$926$	2.48505	+	0.729677i	0.0816639	+	0.0239787i
$927$	−12.0564	+	7.74817i	−0.395984	+	0.254483i
$928$	0.768923	+	1.68371i	0.0252411	+	0.0552703i
$929$	18.9492	+	21.8685i	0.621702	+	0.717482i	0.976029	−	0.217639i	$-0.0698356\pi$
$929$	18.9492	+	21.8685i	0.621702	+	0.717482i	−0.354327	+	0.935121i	$0.615290\pi$
$930$	−7.08788	−	4.55511i	−0.232421	−	0.149368i
$931$	0.0207155	−	0.144079i	0.000678923	−	0.00472201i
$932$	1.60122	−	11.1367i	0.0524496	−	0.364795i
$933$	−18.0475	−	11.5984i	−0.590847	−	0.379714i
$934$	−20.2364	−	23.3541i	−0.662157	−	0.764170i
$935$	7.04250	+	15.4209i	0.230314	+	0.504318i
$936$	−4.31364	+	2.77221i	−0.140996	+	0.0906124i
$937$	−18.8255	−	5.52768i	−0.615004	−	0.180581i	−0.0406295	−	0.999174i	$-0.512936\pi$
$937$	−18.8255	−	5.52768i	−0.615004	−	0.180581i	−0.574374	+	0.818593i	$0.694755\pi$
$938$	−7.26477	+	8.38399i	−0.237203	+	0.273747i
$939$	13.8747	−	4.07397i	0.452783	−	0.132949i
$940$	−10.2573	+	22.4603i	−0.334556	+	0.732575i
$941$	−6.71258	−	46.6870i	−0.218824	−	1.52195i	−0.742390	−	0.669968i	$-0.766308\pi$
$941$	−6.71258	−	46.6870i	−0.218824	−	1.52195i	0.523567	−	0.851985i	$-0.324601\pi$
$942$	−5.43735			−0.177158
$943$	−5.23448	−	0.345059i	−0.170458	−	0.0112367i
$944$	−14.3899			−0.468350
$945$	−0.444301	−	3.09018i	−0.0144531	−	0.100524i
$946$	−2.20226	+	4.82227i	−0.0716015	+	0.156785i
$947$	−33.4760	+	9.82945i	−1.08783	+	0.319414i	−0.776005	−	0.630727i	$-0.782757\pi$
$947$	−33.4760	+	9.82945i	−1.08783	+	0.319414i	−0.311820	+	0.950141i	$0.600939\pi$
$948$	−0.386672	+	0.446244i	−0.0125585	+	0.0144933i
$949$	−33.7143	−	9.89941i	−1.09441	−	0.321348i
$950$	−0.581240	+	0.373540i	−0.0188579	+	0.0121193i
$951$	11.0424	+	24.1794i	0.358073	+	0.784070i
$952$	−1.24614	−	1.43812i	−0.0403875	−	0.0466097i
$953$	−37.2703	−	23.9522i	−1.20730	−	0.775887i	−0.227098	−	0.973872i	$-0.572924\pi$
$953$	−37.2703	−	23.9522i	−1.20730	−	0.775887i	−0.980205	+	0.197985i	$0.936560\pi$
$954$	−0.237756	+	1.65363i	−0.00769763	+	0.0535382i
$955$	3.07244	−	21.3693i	0.0994218	−	0.691494i
$956$	−4.92878	−	3.16753i	−0.159408	−	0.102445i
$957$	−3.45900	−	3.99190i	−0.111814	−	0.129040i
$958$	−0.713673	−	1.56273i	−0.0230577	−	0.0504894i
$959$	0.231020	−	0.148468i	0.00746004	−	0.00479428i
$960$	−2.99549	−	0.879557i	−0.0966792	−	0.0283876i
$961$	15.5312	−	17.9239i	0.501005	−	0.578191i
$962$	35.1957	−	10.3344i	1.13475	−	0.333194i
$963$	6.74815	−	14.7764i	0.217456	−	0.476162i
$964$	2.95878	+	20.5788i	0.0952960	+	0.662799i
$965$	56.8419			1.82980
$966$	3.85522	+	2.85259i	0.124040	+	0.0917805i
$967$	38.7466			1.24601			0.623003	−	0.782219i	$-0.285912\pi$
$967$	38.7466			1.24601			0.623003	+	0.782219i	$0.285912\pi$
$968$	0.406545	+	2.82759i	0.0130669	+	0.0908820i
$969$	0.115065	−	0.251958i	0.00369643	−	0.00809405i
$970$	−8.90626	+	2.61511i	−0.285963	+	0.0839663i
$971$	9.09541	−	10.4967i	0.291885	−	0.336854i	−0.590800	−	0.806818i	$-0.701188\pi$
$971$	9.09541	−	10.4967i	0.291885	−	0.336854i	0.882685	+	0.469964i	$0.155733\pi$
$972$	0.959493	+	0.281733i	0.0307758	+	0.00903658i
$973$	10.7966	−	6.93853i	0.346122	−	0.222439i
$974$	4.37898	+	9.58862i	0.140312	+	0.307239i
$975$	−15.9386	−	18.3941i	−0.510443	−	0.589082i
$976$	5.23843	+	3.36653i	0.167678	+	0.107760i
$977$	−7.77956	+	54.1081i	−0.248890	+	1.73107i	0.355759	+	0.934578i	$0.384223\pi$
$977$	−7.77956	+	54.1081i	−0.248890	+	1.73107i	−0.604649	+	0.796492i	$0.706687\pi$
$978$	−0.201986	+	1.40485i	−0.00645881	+	0.0449220i
$979$	16.3817	+	10.5279i	0.523561	+	0.336472i
$980$	2.04445	+	2.35942i	0.0653074	+	0.0753688i
$981$	−0.0589186	−	0.129014i	−0.00188112	−	0.00411909i
$982$	35.7116	−	22.9505i	1.13960	−	0.732379i
$983$	26.9389	+	7.90999i	0.859219	+	0.252289i	0.681524	−	0.731796i	$-0.261318\pi$
$983$	26.9389	+	7.90999i	0.859219	+	0.252289i	0.177695	+	0.984086i	$0.443136\pi$
$984$	0.716308	−	0.826664i	0.0228351	−	0.0263531i
$985$	−0.789986	+	0.231961i	−0.0251710	+	0.00739088i
$986$	1.46319	−	3.20393i	0.0465973	−	0.102034i
$987$	1.12557	+	7.82853i	0.0358274	+	0.249185i
$988$	0.746384			0.0237456
$989$	8.69510	−	1.94233i	0.276488	−	0.0617625i
$990$	8.90898			0.283146
$991$	0.590426	+	4.10650i	0.0187555	+	0.130447i	0.997048	−	0.0767819i	$-0.0244645\pi$
$991$	0.590426	+	4.10650i	0.0187555	+	0.130447i	−0.978292	+	0.207229i	$0.933555\pi$
$992$	−1.12110	+	2.45487i	−0.0355950	+	0.0779422i
$993$	−1.02176	+	0.300017i	−0.0324247	+	0.00952076i
$994$	2.83337	−	3.26988i	0.0898691	−	0.103714i
$995$	42.7001	+	12.5379i	1.35369	+	0.397478i
$996$	−7.86825	+	5.05662i	−0.249315	+	0.160225i
$997$	4.77050	+	10.4459i	0.151083	+	0.330826i	0.970007	−	0.243076i	$-0.0781564\pi$
$997$	4.77050	+	10.4459i	0.151083	+	0.330826i	−0.818924	+	0.573902i	$0.805429\pi$
$998$	5.28450	+	6.09864i	0.167278	+	0.193049i
$999$	−6.01807	−	3.86758i	−0.190403	−	0.122365i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.q.d.463.2	yes	20
23.8	even	11	inner	966.2.q.d.169.2	✓	20

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.q.d.169.2	✓	20	23.8	even	11	inner
966.2.q.d.463.2	yes	20	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.q (of order \(11\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.04445 - 2.35942i) q^{5} +(0.959493 + 0.281733i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +O(q^{10})\)	\(q+(-0.142315 - 0.989821i) q^{2} +(-0.415415 + 0.909632i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.04445 - 2.35942i) q^{5} +(0.959493 + 0.281733i) q^{6} +(0.841254 - 0.540641i) q^{7} +(0.415415 + 0.909632i) q^{8} +(-0.654861 - 0.755750i) q^{9} +(-2.62636 - 1.68786i) q^{10} +(0.406117 - 2.82461i) q^{11} +(0.142315 - 0.989821i) q^{12} +(-4.31364 - 2.77221i) q^{13} +(-0.654861 - 0.755750i) q^{14} +(1.29691 + 2.83983i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-1.82582 - 0.536110i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(0.139665 - 0.0410093i) q^{19} +(-1.29691 + 2.83983i) q^{20} +(0.142315 + 0.989821i) q^{21} -2.85365 q^{22} +(2.89539 + 3.82318i) q^{23} -1.00000 q^{24} +(-0.675513 - 4.69830i) q^{25} +(-2.13010 + 4.66426i) q^{26} +(0.959493 - 0.281733i) q^{27} +(-0.654861 + 0.755750i) q^{28} +(-1.77600 - 0.521480i) q^{29} +(2.62636 - 1.68786i) q^{30} +(-1.12110 - 2.45487i) q^{31} +(-0.654861 - 0.755750i) q^{32} +(2.40065 + 1.54280i) q^{33} +(-0.270811 + 1.88353i) q^{34} +(0.444301 - 3.09018i) q^{35} +(0.841254 + 0.540641i) q^{36} +(-4.68468 - 5.40640i) q^{37} +(-0.0604683 - 0.132407i) q^{38} +(4.31364 - 2.77221i) q^{39} +(2.99549 + 0.879557i) q^{40} +(-0.716308 + 0.826664i) q^{41} +(0.959493 - 0.281733i) q^{42} +(0.771732 - 1.68986i) q^{43} +(0.406117 + 2.82461i) q^{44} -3.12196 q^{45} +(3.37221 - 3.41002i) q^{46} +7.90904 q^{47} +(0.142315 + 0.989821i) q^{48} +(0.415415 - 0.909632i) q^{49} +(-4.55434 + 1.33727i) q^{50} +(1.24614 - 1.43812i) q^{51} +(4.91993 + 1.44462i) q^{52} +(1.40543 - 0.903213i) q^{53} +(-0.415415 - 0.909632i) q^{54} +(-5.83414 - 6.73296i) q^{55} +(0.841254 + 0.540641i) q^{56} +(-0.0207155 + 0.144079i) q^{57} +(-0.263421 + 1.83213i) q^{58} +(-12.1055 - 7.77975i) q^{59} +(-2.04445 - 2.35942i) q^{60} +(2.58676 + 5.66422i) q^{61} +(-2.27033 + 1.45906i) q^{62} +(-0.959493 - 0.281733i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-15.3598 + 4.51004i) q^{65} +(1.18545 - 2.59577i) q^{66} +(-1.57879 - 10.9807i) q^{67} +1.90290 q^{68} +(-4.68048 + 1.04553i) q^{69} -3.12196 q^{70} +(0.615750 + 4.28264i) q^{71} +(0.415415 - 0.909632i) q^{72} +(6.57502 - 1.93060i) q^{73} +(-4.68468 + 5.40640i) q^{74} +(4.55434 + 1.33727i) q^{75} +(-0.122454 + 0.0786963i) q^{76} +(-1.18545 - 2.59577i) q^{77} +(-3.35789 - 3.87521i) q^{78} +(-0.496731 - 0.319229i) q^{79} +(0.444301 - 3.09018i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(0.920191 + 0.591371i) q^{82} +(-6.12492 - 7.06853i) q^{83} +(-0.415415 - 0.909632i) q^{84} +(-4.99770 + 3.21183i) q^{85} +(-1.78249 - 0.523385i) q^{86} +(1.21213 - 1.39887i) q^{87} +(2.73806 - 0.803967i) q^{88} +(-2.83474 + 6.20721i) q^{89} +(0.444301 + 3.09018i) q^{90} -5.12763 q^{91} +(-3.85522 - 2.85259i) q^{92} +2.69875 q^{93} +(-1.12557 - 7.82853i) q^{94} +(0.188779 - 0.413369i) q^{95} +(0.959493 - 0.281733i) q^{96} +(1.94704 - 2.24701i) q^{97} +(-0.959493 - 0.281733i) q^{98} +(-2.40065 + 1.54280i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9}+O(q^{10}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9	\( 20 q - 2 q^{2} + 2 q^{3} - 2 q^{4} + 12 q^{5} + 2 q^{6} - 2 q^{7} - 2 q^{8} - 2 q^{9} - 10 q^{10} - 7 q^{11} + 2 q^{12} - 8 q^{13} - 2 q^{14} - q^{15} - 2 q^{16} + 13 q^{17} - 2 q^{18} - 8 q^{19} + q^{20} + 2 q^{21} + 4 q^{22} - 20 q^{24} + 16 q^{25} - 8 q^{26} + 2 q^{27} - 2 q^{28} + 3 q^{29} + 10 q^{30} + 9 q^{31} - 2 q^{32} - 4 q^{33} - 9 q^{34} + q^{35} - 2 q^{36} - q^{37} + 3 q^{38} + 8 q^{39} + q^{40} + 10 q^{41} + 2 q^{42} - 15 q^{43} - 7 q^{44} - 10 q^{45} - 28 q^{47} + 2 q^{48} - 2 q^{49} + 5 q^{50} - 2 q^{51} + 3 q^{52} + 38 q^{53} + 2 q^{54} - 8 q^{55} - 2 q^{56} - 14 q^{57} - 19 q^{58} - 10 q^{59} - 12 q^{60} - 6 q^{61} + 20 q^{62} - 2 q^{63} - 2 q^{64} - 36 q^{65} - 4 q^{66} + 36 q^{67} - 20 q^{68} + 11 q^{69} - 10 q^{70} - q^{71} - 2 q^{72} + 65 q^{73} - q^{74} - 5 q^{75} + 14 q^{76} + 4 q^{77} - 14 q^{78} + 10 q^{79} + q^{80} - 2 q^{81} + 10 q^{82} - 14 q^{83} + 2 q^{84} - 5 q^{85} + 51 q^{86} - 3 q^{87} - 7 q^{88} - 18 q^{89} + q^{90} - 30 q^{91} - 11 q^{92} + 2 q^{93} + 38 q^{94} - 73 q^{95} + 2 q^{96} - 20 q^{97} - 2 q^{98} + 4 q^{99}+O(q^{100}) \) 20 * q - 2 * q^2 + 2 * q^3 - 2 * q^4 + 12 * q^5 + 2 * q^6 - 2 * q^7 - 2 * q^8 - 2 * q^9 - 10 * q^10 - 7 * q^11 + 2 * q^12 - 8 * q^13 - 2 * q^14 - q^15 - 2 * q^16 + 13 * q^17 - 2 * q^18 - 8 * q^19 + q^20 + 2 * q^21 + 4 * q^22 - 20 * q^24 + 16 * q^25 - 8 * q^26 + 2 * q^27 - 2 * q^28 + 3 * q^29 + 10 * q^30 + 9 * q^31 - 2 * q^32 - 4 * q^33 - 9 * q^34 + q^35 - 2 * q^36 - q^37 + 3 * q^38 + 8 * q^39 + q^40 + 10 * q^41 + 2 * q^42 - 15 * q^43 - 7 * q^44 - 10 * q^45 - 28 * q^47 + 2 * q^48 - 2 * q^49 + 5 * q^50 - 2 * q^51 + 3 * q^52 + 38 * q^53 + 2 * q^54 - 8 * q^55 - 2 * q^56 - 14 * q^57 - 19 * q^58 - 10 * q^59 - 12 * q^60 - 6 * q^61 + 20 * q^62 - 2 * q^63 - 2 * q^64 - 36 * q^65 - 4 * q^66 + 36 * q^67 - 20 * q^68 + 11 * q^69 - 10 * q^70 - q^71 - 2 * q^72 + 65 * q^73 - q^74 - 5 * q^75 + 14 * q^76 + 4 * q^77 - 14 * q^78 + 10 * q^79 + q^80 - 2 * q^81 + 10 * q^82 - 14 * q^83 + 2 * q^84 - 5 * q^85 + 51 * q^86 - 3 * q^87 - 7 * q^88 - 18 * q^89 + q^90 - 30 * q^91 - 11 * q^92 + 2 * q^93 + 38 * q^94 - 73 * q^95 + 2 * q^96 - 20 * q^97 - 2 * q^98 + 4 * q^99

Introduction

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