LMFDB - Embedded newform 693.2.j.h.232.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [693,2,Mod(232,693)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(693, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("693.232");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 693 = 3^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	693.j (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$5.53363286007$
Analytic rank:	$0$
Dimension:	$28$
Relative dimension:	$14$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			232.6
Character	$\chi$	$=$	693.232
Dual form			693.2.j.h.463.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.313556 + 0.543094i) q^{2} +(-0.395002 - 1.68641i) q^{3} +(0.803366 + 1.39147i) q^{4} +(-0.166433 - 0.288270i) q^{5} +(1.03973 + 0.314260i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.26182 q^{8} +(-2.68795 + 1.33227i) q^{9} +O(q^{10})$	\(q+(-0.313556 + 0.543094i) q^{2} +(-0.395002 - 1.68641i) q^{3} +(0.803366 + 1.39147i) q^{4} +(-0.166433 - 0.288270i) q^{5} +(1.03973 + 0.314260i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.26182 q^{8} +(-2.68795 + 1.33227i) q^{9} +0.208744 q^{10} +(-0.500000 + 0.866025i) q^{11} +(2.02926 - 1.90444i) q^{12} +(3.15916 + 5.47182i) q^{13} +(0.313556 + 0.543094i) q^{14} +(-0.420400 + 0.394541i) q^{15} +(-0.897524 + 1.55456i) q^{16} +2.34305 q^{17} +(0.119274 - 1.87755i) q^{18} +2.12294 q^{19} +(0.267413 - 0.463173i) q^{20} +(-1.65797 - 0.501123i) q^{21} +(-0.313556 - 0.543094i) q^{22} +(1.69528 + 2.93632i) q^{23} +(0.893424 + 3.81436i) q^{24} +(2.44460 - 4.23417i) q^{25} -3.96229 q^{26} +(3.30849 + 4.00673i) q^{27} +1.60673 q^{28} +(1.13523 - 1.96628i) q^{29} +(-0.0824543 - 0.352028i) q^{30} +(3.58266 + 6.20535i) q^{31} +(-2.82467 - 4.89247i) q^{32} +(1.65797 + 0.501123i) q^{33} +(-0.734676 + 1.27250i) q^{34} -0.332866 q^{35} +(-4.01322 - 2.66990i) q^{36} +0.952833 q^{37} +(-0.665659 + 1.15296i) q^{38} +(7.97985 - 7.48901i) q^{39} +(0.376442 + 0.652017i) q^{40} +(-1.75268 - 3.03573i) q^{41} +(0.792024 - 0.743306i) q^{42} +(-2.05881 + 3.56597i) q^{43} -1.60673 q^{44} +(0.831417 + 0.553122i) q^{45} -2.12626 q^{46} +(-2.17286 + 3.76350i) q^{47} +(2.97614 + 0.899539i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.53304 + 2.65530i) q^{50} +(-0.925507 - 3.95133i) q^{51} +(-5.07592 + 8.79174i) q^{52} +5.73180 q^{53} +(-3.21343 + 0.540491i) q^{54} +0.332866 q^{55} +(-1.13091 + 1.95880i) q^{56} +(-0.838564 - 3.58014i) q^{57} +(0.711918 + 1.23308i) q^{58} +(1.11240 + 1.92674i) q^{59} +(-0.886728 - 0.268014i) q^{60} +(2.29783 - 3.97995i) q^{61} -4.49346 q^{62} +(-0.190195 + 2.99396i) q^{63} -0.0473285 q^{64} +(1.05158 - 1.82138i) q^{65} +(-0.792024 + 0.743306i) q^{66} +(4.70378 + 8.14718i) q^{67} +(1.88232 + 3.26028i) q^{68} +(4.28219 - 4.01879i) q^{69} +(0.104372 - 0.180778i) q^{70} +11.2832 q^{71} +(6.07966 - 3.01335i) q^{72} +8.83632 q^{73} +(-0.298766 + 0.517478i) q^{74} +(-8.10616 - 2.45009i) q^{75} +(1.70549 + 2.95400i) q^{76} +(0.500000 + 0.866025i) q^{77} +(1.56511 + 6.68204i) q^{78} +(-0.819734 + 1.41982i) q^{79} +0.597510 q^{80} +(5.45012 - 7.16213i) q^{81} +2.19825 q^{82} +(-5.05135 + 8.74919i) q^{83} +(-0.634662 - 2.70961i) q^{84} +(-0.389960 - 0.675431i) q^{85} +(-1.29111 - 2.23626i) q^{86} +(-3.76437 - 1.13778i) q^{87} +(1.13091 - 1.95880i) q^{88} -13.3337 q^{89} +(-0.561093 + 0.278103i) q^{90} +6.31831 q^{91} +(-2.72387 + 4.71787i) q^{92} +(9.04960 - 8.49295i) q^{93} +(-1.36263 - 2.36014i) q^{94} +(-0.353327 - 0.611980i) q^{95} +(-7.13496 + 6.69608i) q^{96} +(-5.53540 + 9.58759i) q^{97} +0.627112 q^{98} +(0.190195 - 2.99396i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q - q^{2} - 2 q^{3} - 17 q^{4} - 4 q^{5} + q^{6} + 14 q^{7} + 24 q^{8} + 2 q^{9}+O(q^{10}) $ 28 * q - q^2 - 2 * q^3 - 17 * q^4 - 4 * q^5 + q^6 + 14 * q^7 + 24 * q^8 + 2 * q^9	\( 28 q - q^{2} - 2 q^{3} - 17 q^{4} - 4 q^{5} + q^{6} + 14 q^{7} + 24 q^{8} + 2 q^{9} + 20 q^{10} - 14 q^{11} + 20 q^{12} - 9 q^{13} + q^{14} - 5 q^{15} - 19 q^{16} + 24 q^{17} - 13 q^{18} + 32 q^{19} - 8 q^{20} - q^{21} - q^{22} + 12 q^{23} - 42 q^{24} - 16 q^{25} - 10 q^{26} - 26 q^{27} - 34 q^{28} - 8 q^{29} + 73 q^{30} - 15 q^{31} - 10 q^{32} + q^{33} - 14 q^{34} - 8 q^{35} - 17 q^{36} - 2 q^{37} + 14 q^{38} + 22 q^{39} + 3 q^{40} - 20 q^{41} - 13 q^{42} - 39 q^{43} + 34 q^{44} - 13 q^{45} + 8 q^{46} - 29 q^{47} + 38 q^{48} - 14 q^{49} - 7 q^{50} - 29 q^{51} - 59 q^{52} + 24 q^{53} + q^{54} + 8 q^{55} + 12 q^{56} + 6 q^{57} - 23 q^{58} - 3 q^{59} - q^{60} - 26 q^{61} - 8 q^{62} - 5 q^{63} + 36 q^{64} - 8 q^{65} + 13 q^{66} - 35 q^{67} + 16 q^{68} + 41 q^{69} + 10 q^{70} - 28 q^{71} + 21 q^{72} + 48 q^{73} - q^{74} + 23 q^{75} - 55 q^{76} + 14 q^{77} - 71 q^{78} + 15 q^{79} + 170 q^{80} - 10 q^{81} + 30 q^{82} - 6 q^{83} + 13 q^{84} + 28 q^{85} - 6 q^{86} - 12 q^{88} - 76 q^{89} - 19 q^{90} - 18 q^{91} + 94 q^{92} + 7 q^{93} - 32 q^{94} - 8 q^{95} + 65 q^{96} - 25 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 28 * q - q^2 - 2 * q^3 - 17 * q^4 - 4 * q^5 + q^6 + 14 * q^7 + 24 * q^8 + 2 * q^9 + 20 * q^10 - 14 * q^11 + 20 * q^12 - 9 * q^13 + q^14 - 5 * q^15 - 19 * q^16 + 24 * q^17 - 13 * q^18 + 32 * q^19 - 8 * q^20 - q^21 - q^22 + 12 * q^23 - 42 * q^24 - 16 * q^25 - 10 * q^26 - 26 * q^27 - 34 * q^28 - 8 * q^29 + 73 * q^30 - 15 * q^31 - 10 * q^32 + q^33 - 14 * q^34 - 8 * q^35 - 17 * q^36 - 2 * q^37 + 14 * q^38 + 22 * q^39 + 3 * q^40 - 20 * q^41 - 13 * q^42 - 39 * q^43 + 34 * q^44 - 13 * q^45 + 8 * q^46 - 29 * q^47 + 38 * q^48 - 14 * q^49 - 7 * q^50 - 29 * q^51 - 59 * q^52 + 24 * q^53 + q^54 + 8 * q^55 + 12 * q^56 + 6 * q^57 - 23 * q^58 - 3 * q^59 - q^60 - 26 * q^61 - 8 * q^62 - 5 * q^63 + 36 * q^64 - 8 * q^65 + 13 * q^66 - 35 * q^67 + 16 * q^68 + 41 * q^69 + 10 * q^70 - 28 * q^71 + 21 * q^72 + 48 * q^73 - q^74 + 23 * q^75 - 55 * q^76 + 14 * q^77 - 71 * q^78 + 15 * q^79 + 170 * q^80 - 10 * q^81 + 30 * q^82 - 6 * q^83 + 13 * q^84 + 28 * q^85 - 6 * q^86 - 12 * q^88 - 76 * q^89 - 19 * q^90 - 18 * q^91 + 94 * q^92 + 7 * q^93 - 32 * q^94 - 8 * q^95 + 65 * q^96 - 25 * q^97 + 2 * q^98 + 5 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/693\mathbb{Z}\right)^\times$.

$n$	$155$	$199$	$442$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$1$	$1$

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 $

$2$	−0.313556	+	0.543094i	−0.221717	+	0.384026i	−0.955330	−	0.295543i	$-0.904500\pi$
$2$	−0.313556	+	0.543094i	−0.221717	+	0.384026i	0.733612	+	0.679568i	$0.237833\pi$
$3$	−0.395002	−	1.68641i	−0.228054	−	0.973648i
$3$	−0.395002	−	1.68641i	−0.228054	−	0.973648i
$4$	0.803366	+	1.39147i	0.401683	+	0.695735i
$5$	−0.166433	−	0.288270i	−0.0744311	−	0.128918i	0.826408	−	0.563072i	$-0.190381\pi$
$5$	−0.166433	−	0.288270i	−0.0744311	−	0.128918i	−0.900839	+	0.434154i	$0.857047\pi$
$6$	1.03973	+	0.314260i	0.424470	+	0.128296i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$7$	0.500000	−	0.866025i	0.188982	−	0.327327i
$8$	−2.26182			−0.799675
$9$	−2.68795	+	1.33227i	−0.895982	+	0.444089i
$10$	0.208744			0.0660107
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$11$	−0.500000	+	0.866025i	−0.150756	+	0.261116i
$12$	2.02926	−	1.90444i	0.585796	−	0.549763i
$13$	3.15916	+	5.47182i	0.876193	+	1.51761i	0.855487	+	0.517824i	$0.173258\pi$
$13$	3.15916	+	5.47182i	0.876193	+	1.51761i	0.0207056	+	0.999786i	$0.493409\pi$
$14$	0.313556	+	0.543094i	0.0838013	+	0.145148i
$15$	−0.420400	+	0.394541i	−0.108547	+	0.101870i
$16$	−0.897524	+	1.55456i	−0.224381	+	0.388639i
$17$	2.34305			0.568272			0.284136	−	0.958784i	$-0.408293\pi$
$17$	2.34305			0.568272			0.284136	+	0.958784i	$0.408293\pi$
$18$	0.119274	−	1.87755i	0.0281131	−	0.442543i
$19$	2.12294			0.487035			0.243518	−	0.969896i	$-0.421699\pi$
$19$	2.12294			0.487035			0.243518	+	0.969896i	$0.421699\pi$
$20$	0.267413	−	0.463173i	0.0597954	−	0.103569i
$21$	−1.65797	−	0.501123i	−0.361799	−	0.109354i
$22$	−0.313556	−	0.543094i	−0.0668503	−	0.115788i
$23$	1.69528	+	2.93632i	0.353491	+	0.612265i	0.986859	−	0.161587i	$-0.0516611\pi$
$23$	1.69528	+	2.93632i	0.353491	+	0.612265i	−0.633367	+	0.773851i	$0.718328\pi$
$24$	0.893424	+	3.81436i	0.182369	+	0.778602i
$25$	2.44460	−	4.23417i	0.488920	−	0.846834i
$26$	−3.96229			−0.777069
$27$	3.30849	+	4.00673i	0.636720	+	0.771095i
$28$	1.60673			0.303644
$29$	1.13523	−	1.96628i	0.210807	−	0.365129i	−0.741160	−	0.671328i	$-0.765724\pi$
$29$	1.13523	−	1.96628i	0.210807	−	0.365129i	0.951967	+	0.306199i	$0.0990574\pi$
$30$	−0.0824543	−	0.352028i	−0.0150540	−	0.0642712i
$31$	3.58266	+	6.20535i	0.643465	+	1.11451i	0.984654	+	0.174519i	$0.0558370\pi$
$31$	3.58266	+	6.20535i	0.643465	+	1.11451i	−0.341189	+	0.939995i	$0.610830\pi$
$32$	−2.82467	−	4.89247i	−0.499336	−	0.864875i
$33$	1.65797	+	0.501123i	0.288616	+	0.0872343i
$34$	−0.734676	+	1.27250i	−0.125996	+	0.218231i
$35$	−0.332866			−0.0562646
$36$	−4.01322	−	2.66990i	−0.668869	−	0.444983i
$37$	0.952833			0.156645			0.0783224	−	0.996928i	$-0.475044\pi$
$37$	0.952833			0.156645			0.0783224	+	0.996928i	$0.475044\pi$
$38$	−0.665659	+	1.15296i	−0.107984	+	0.187034i
$39$	7.97985	−	7.48901i	1.27780	−	1.19920i
$40$	0.376442	+	0.652017i	0.0595207	+	0.103093i
$41$	−1.75268	−	3.03573i	−0.273723	−	0.474102i	0.696089	−	0.717955i	$-0.254922\pi$
$41$	−1.75268	−	3.03573i	−0.273723	−	0.474102i	−0.969812	+	0.243853i	$0.921588\pi$
$42$	0.792024	−	0.743306i	0.122212	−	0.114695i
$43$	−2.05881	+	3.56597i	−0.313966	+	0.543806i	−0.979217	−	0.202814i	$-0.934991\pi$
$43$	−2.05881	+	3.56597i	−0.313966	+	0.543806i	0.665251	+	0.746620i	$0.268325\pi$
$44$	−1.60673			−0.242224
$45$	0.831417	+	0.553122i	0.123940	+	0.0824546i
$46$	−2.12626			−0.313501
$47$	−2.17286	+	3.76350i	−0.316944	+	0.548963i	−0.979849	−	0.199740i	$-0.935990\pi$
$47$	−2.17286	+	3.76350i	−0.316944	+	0.548963i	0.662905	+	0.748704i	$0.269323\pi$
$48$	2.97614	+	0.899539i	0.429569	+	0.129837i
$49$	−0.500000	−	0.866025i	−0.0714286	−	0.123718i
$50$	1.53304	+	2.65530i	0.216804	+	0.375516i
$51$	−0.925507	−	3.95133i	−0.129597	−	0.553297i
$52$	−5.07592	+	8.79174i	−0.703903	+	1.21920i
$53$	5.73180			0.787324			0.393662	−	0.919255i	$-0.371208\pi$
$53$	5.73180			0.787324			0.393662	+	0.919255i	$0.371208\pi$
$54$	−3.21343	+	0.540491i	−0.437292	+	0.0735515i
$55$	0.332866			0.0448836
$56$	−1.13091	+	1.95880i	−0.151124	+	0.261755i
$57$	−0.838564	−	3.58014i	−0.111070	−	0.474201i
$58$	0.711918	+	1.23308i	0.0934794	+	0.161911i
$59$	1.11240	+	1.92674i	0.144823	+	0.250840i	0.929307	−	0.369309i	$-0.120406\pi$
$59$	1.11240	+	1.92674i	0.144823	+	0.250840i	−0.784484	+	0.620149i	$0.787072\pi$
$60$	−0.886728	−	0.268014i	−0.114476	−	0.0346004i
$61$	2.29783	−	3.97995i	0.294206	−	0.509580i	−0.680594	−	0.732661i	$-0.738278\pi$
$61$	2.29783	−	3.97995i	0.294206	−	0.509580i	0.974800	+	0.223081i	$0.0716114\pi$
$62$	−4.49346			−0.570669
$63$	−0.190195	+	2.99396i	−0.0239624	+	0.377204i
$64$	−0.0473285			−0.00591606
$65$	1.05158	−	1.82138i	0.130432	−	0.225915i
$66$	−0.792024	+	0.743306i	−0.0974914	+	0.0914947i
$67$	4.70378	+	8.14718i	0.574658	+	0.995336i	0.996079	+	0.0884712i	$0.0281981\pi$
$67$	4.70378	+	8.14718i	0.574658	+	0.995336i	−0.421421	+	0.906865i	$0.638469\pi$
$68$	1.88232	+	3.26028i	0.228265	+	0.395367i
$69$	4.28219	−	4.01879i	0.515515	−	0.483806i
$70$	0.104372	−	0.180778i	0.0124748	−	0.0216071i
$71$	11.2832			1.33907			0.669534	−	0.742782i	$-0.266494\pi$
$71$	11.2832			1.33907			0.669534	+	0.742782i	$0.266494\pi$
$72$	6.07966	−	3.01335i	0.716495	−	0.355127i
$73$	8.83632			1.03421			0.517106	−	0.855921i	$-0.327009\pi$
$73$	8.83632			1.03421			0.517106	+	0.855921i	$0.327009\pi$
$74$	−0.298766	+	0.517478i	−0.0347309	+	0.0601556i
$75$	−8.10616	−	2.45009i	−0.936019	−	0.282912i
$76$	1.70549	+	2.95400i	0.195634	+	0.338847i
$77$	0.500000	+	0.866025i	0.0569803	+	0.0986928i
$78$	1.56511	+	6.68204i	0.177214	+	0.756592i
$79$	−0.819734	+	1.41982i	−0.0922273	+	0.159742i	−0.908448	−	0.417998i	$-0.862732\pi$
$79$	−0.819734	+	1.41982i	−0.0922273	+	0.159742i	0.816221	+	0.577740i	$0.196065\pi$
$80$	0.597510			0.0668037
$81$	5.45012	−	7.16213i	0.605569	−	0.795793i
$82$	2.19825			0.242756
$83$	−5.05135	+	8.74919i	−0.554458	+	0.960349i	0.443488	+	0.896280i	$0.353741\pi$
$83$	−5.05135	+	8.74919i	−0.554458	+	0.960349i	−0.997946	+	0.0640683i	$0.979592\pi$
$84$	−0.634662	−	2.70961i	−0.0692472	−	0.295642i
$85$	−0.389960	−	0.675431i	−0.0422971	−	0.0732608i
$86$	−1.29111	−	2.23626i	−0.139224	−	0.241142i
$87$	−3.76437	−	1.13778i	−0.403583	−	0.121983i
$88$	1.13091	−	1.95880i	0.120556	−	0.208808i
$89$	−13.3337			−1.41337			−0.706686	−	0.707528i	$-0.749811\pi$
$89$	−13.3337			−1.41337			−0.706686	+	0.707528i	$0.749811\pi$
$90$	−0.561093	+	0.278103i	−0.0591444	+	0.0293147i
$91$	6.31831			0.662339
$92$	−2.72387	+	4.71787i	−0.283983	+	0.491872i
$93$	9.04960	−	8.49295i	0.938400	−	0.880678i
$94$	−1.36263	−	2.36014i	−0.140544	−	0.243429i
$95$	−0.353327	−	0.611980i	−0.0362506	−	0.0627878i
$96$	−7.13496	+	6.69608i	−0.728208	+	0.683416i
$97$	−5.53540	+	9.58759i	−0.562035	+	0.973473i	0.435284	+	0.900293i	$0.356648\pi$
$97$	−5.53540	+	9.58759i	−0.562035	+	0.973473i	−0.997319	+	0.0731796i	$0.976685\pi$
$98$	0.627112			0.0633478
$99$	0.190195	−	2.99396i	0.0191154	−	0.300905i
$100$	7.85563			0.785563
$101$	2.18944	−	3.79223i	0.217858	−	0.377341i	−0.736295	−	0.676661i	$-0.763426\pi$
$101$	2.18944	−	3.79223i	0.217858	−	0.377341i	0.954153	+	0.299320i	$0.0967598\pi$
$102$	2.43615	+	0.736325i	0.241214	+	0.0729071i
$103$	−3.34578	−	5.79506i	−0.329669	−	0.571004i	0.652777	−	0.757550i	$-0.273604\pi$
$103$	−3.34578	−	5.79506i	−0.329669	−	0.571004i	−0.982446	+	0.186546i	$0.940271\pi$
$104$	−7.14545	−	12.3763i	−0.700669	−	1.21359i
$105$	0.131483	+	0.561348i	0.0128314	+	0.0547820i
$106$	−1.79724	+	3.11291i	−0.174563	+	0.302353i
$107$	−12.8252			−1.23986			−0.619929	−	0.784658i	$-0.712839\pi$
$107$	−12.8252			−1.23986			−0.619929	+	0.784658i	$0.712839\pi$
$108$	−2.91731	+	7.82254i	−0.280719	+	0.752724i
$109$	−6.85420			−0.656514			−0.328257	−	0.944589i	$-0.606461\pi$
$109$	−6.85420			−0.656514			−0.328257	+	0.944589i	$0.606461\pi$
$110$	−0.104372	+	0.180778i	−0.00995149	+	0.0172365i
$111$	−0.376371	−	1.60687i	−0.0357235	−	0.152517i
$112$	0.897524	+	1.55456i	0.0848080	+	0.146892i
$113$	−9.52689	−	16.5010i	−0.896214	−	1.55229i	−0.832295	−	0.554333i	$-0.812973\pi$
$113$	−9.52689	−	16.5010i	−0.896214	−	1.55229i	−0.0639191	−	0.997955i	$-0.520360\pi$
$114$	2.20729	+	0.667154i	0.206732	+	0.0624847i
$115$	0.564302	−	0.977401i	0.0526215	−	0.0911431i
$116$	3.64803			0.338711
$117$	−15.7816	−	10.4991i	−1.45901	−	0.970644i
$118$	−1.39520			−0.128439
$119$	1.17152	−	2.02914i	0.107393	−	0.186011i
$120$	0.950871	−	0.892383i	0.0868023	−	0.0814630i
$121$	−0.500000	−	0.866025i	−0.0454545	−	0.0787296i
$122$	1.44099	+	2.49587i	0.130461	+	0.225966i
$123$	−4.42717	+	4.15485i	−0.399185	+	0.374631i
$124$	−5.75637	+	9.97033i	−0.516937	+	0.895362i
$125$	−3.29178			−0.294426
$126$	−1.56637	−	1.04207i	−0.139543	−	0.0928349i
$127$	−16.4474			−1.45947			−0.729735	−	0.683730i	$-0.760357\pi$
$127$	−16.4474			−1.45947			−0.729735	+	0.683730i	$0.760357\pi$
$128$	5.66418	−	9.81065i	0.500648	−	0.867147i
$129$	6.82692	+	2.06344i	0.601077	+	0.181676i
$130$	0.659455	+	1.14221i	0.0578381	+	0.100178i
$131$	−1.07621	−	1.86406i	−0.0940293	−	0.162864i	0.815174	−	0.579216i	$-0.196641\pi$
$131$	−1.07621	−	1.86406i	−0.0940293	−	0.162864i	−0.909203	+	0.416353i	$0.863308\pi$
$132$	0.634662	+	2.70961i	0.0552402	+	0.235841i
$133$	1.06147	−	1.83852i	0.0920410	−	0.159420i
$134$	−5.89958			−0.509646
$135$	0.604379	−	1.62059i	0.0520167	−	0.139478i
$136$	−5.29956			−0.454433
$137$	6.19047	−	10.7222i	0.528888	−	0.916060i	−0.470545	−	0.882376i	$-0.655943\pi$
$137$	6.19047	−	10.7222i	0.528888	−	0.916060i	0.999433	−	0.0336842i	$-0.0107240\pi$
$138$	0.839878	+	3.58575i	0.0714952	+	0.305239i
$139$	−3.08220	−	5.33853i	−0.261429	−	0.452808i	0.705193	−	0.709016i	$-0.250860\pi$
$139$	−3.08220	−	5.33853i	−0.261429	−	0.452808i	−0.966622	+	0.256207i	$0.917527\pi$
$140$	−0.267413	−	0.463173i	−0.0226005	−	0.0391453i
$141$	7.20509	+	2.17774i	0.606778	+	0.183399i
$142$	−3.53791	+	6.12783i	−0.296895	+	0.514236i
$143$	−6.31831			−0.528364
$144$	0.341410	−	5.37431i	0.0284508	−	0.447859i
$145$	−0.755761			−0.0627625
$146$	−2.77068	+	4.79896i	−0.229303	+	0.397164i
$147$	−1.26297	+	1.18529i	−0.104168	+	0.0977607i
$148$	0.765473	+	1.32584i	0.0629215	+	0.108983i
$149$	−8.81642	−	15.2705i	−0.722269	−	1.25101i	−0.960088	−	0.279697i	$-0.909766\pi$
$149$	−8.81642	−	15.2705i	−0.722269	−	1.25101i	0.237819	−	0.971309i	$-0.423567\pi$
$150$	3.87236	−	3.63417i	0.316177	−	0.296729i
$151$	4.46158	−	7.72769i	0.363079	−	0.628870i	−0.625387	−	0.780314i	$-0.715059\pi$
$151$	4.46158	−	7.72769i	0.363079	−	0.628870i	0.988466	+	0.151444i	$0.0483923\pi$
$152$	−4.80171			−0.389470
$153$	−6.29799	+	3.12157i	−0.509162	+	0.252364i
$154$	−0.627112			−0.0505341
$155$	1.19255	−	2.06555i	0.0957876	−	0.165909i
$156$	16.8315	+	5.08731i	1.34760	+	0.407311i
$157$	−4.59268	−	7.95476i	−0.366536	−	0.634859i	0.622485	−	0.782631i	$-0.286123\pi$
$157$	−4.59268	−	7.95476i	−0.366536	−	0.634859i	−0.989021	+	0.147773i	$0.952790\pi$
$158$	−0.514065	−	0.890386i	−0.0408968	−	0.0708353i
$159$	−2.26407	−	9.66616i	−0.179553	−	0.766576i
$160$	−0.940237	+	1.62854i	−0.0743322	+	0.128747i
$161$	3.39057			0.267214
$162$	2.18080	+	5.20566i	0.171340	+	0.408995i
$163$	7.78639			0.609877			0.304939	−	0.952372i	$-0.401364\pi$
$163$	7.78639			0.609877			0.304939	+	0.952372i	$0.401364\pi$
$164$	2.81609	−	4.87761i	0.219899	−	0.380877i
$165$	−0.131483	−	0.561348i	−0.0102359	−	0.0437009i
$166$	−3.16776	−	5.48672i	−0.245866	−	0.425852i
$167$	5.39638	+	9.34680i	0.417584	+	0.723277i	0.995696	−	0.0926804i	$-0.0295435\pi$
$167$	5.39638	+	9.34680i	0.417584	+	0.723277i	−0.578112	+	0.815958i	$0.696210\pi$
$168$	3.75004	+	1.13345i	0.289322	+	0.0874476i
$169$	−13.4605	+	23.3144i	−1.03543	+	1.79341i
$170$	0.489097			0.0375120
$171$	−5.70634	+	2.82832i	−0.436375	+	0.216287i
$172$	−6.61592			−0.504459
$173$	−9.27120	+	16.0582i	−0.704877	+	1.22088i	0.261859	+	0.965106i	$0.415664\pi$
$173$	−9.27120	+	16.0582i	−0.704877	+	1.22088i	−0.966736	+	0.255776i	$0.917669\pi$
$174$	1.79826	−	1.68765i	0.136326	−	0.127941i
$175$	−2.44460	−	4.23417i	−0.184794	−	0.320073i
$176$	−0.897524	−	1.55456i	−0.0676534	−	0.117179i
$177$	2.80987	−	2.63703i	0.211203	−	0.198212i
$178$	4.18086	−	7.24147i	0.313369	−	0.542771i
$179$	14.3776			1.07463			0.537314	−	0.843382i	$-0.319439\pi$
$179$	14.3776			1.07463			0.537314	+	0.843382i	$0.319439\pi$
$180$	−0.101721	+	1.60125i	−0.00758187	+	0.119350i
$181$	25.5325			1.89782			0.948908	−	0.315554i	$-0.102190\pi$
$181$	25.5325			1.89782			0.948908	+	0.315554i	$0.102190\pi$
$182$	−1.98114	+	3.43144i	−0.146852	+	0.254355i
$183$	−7.61947	−	2.30298i	−0.563247	−	0.170242i
$184$	−3.83443	−	6.64143i	−0.282678	−	0.489613i
$185$	−0.158583	−	0.274674i	−0.0116592	−	0.0201944i
$186$	1.77492	+	7.57780i	0.130144	+	0.555631i
$187$	−1.17152	+	2.02914i	−0.0856703	+	0.148385i
$188$	−6.98240			−0.509244
$189$	5.12418	−	0.861874i	0.372729	−	0.0626921i
$190$	0.443151			0.0321495
$191$	−6.20241	+	10.7429i	−0.448790	+	0.777328i	−0.998308	−	0.0581546i	$-0.981478\pi$
$191$	−6.20241	+	10.7429i	−0.448790	+	0.777328i	0.549517	+	0.835482i	$0.314812\pi$
$192$	0.0186948	+	0.0798151i	0.00134918	+	0.00576016i
$193$	−6.06714	−	10.5086i	−0.436723	−	0.756426i	0.560712	−	0.828011i	$-0.310528\pi$
$193$	−6.06714	−	10.5086i	−0.436723	−	0.756426i	−0.997434	+	0.0715853i	$0.977194\pi$
$194$	−3.47131	−	6.01249i	−0.249226	−	0.431672i
$195$	−3.48697	−	1.05394i	−0.249707	−	0.0754740i
$196$	0.803366	−	1.39147i	0.0573833	−	0.0993907i
$197$	−6.15684			−0.438656			−0.219328	−	0.975651i	$-0.570387\pi$
$197$	−6.15684			−0.438656			−0.219328	+	0.975651i	$0.570387\pi$
$198$	1.56637	+	1.04207i	0.111317	+	0.0740566i
$199$	17.7386			1.25746			0.628729	−	0.777625i	$-0.283576\pi$
$199$	17.7386			1.25746			0.628729	+	0.777625i	$0.283576\pi$
$200$	−5.52925	+	9.57695i	−0.390977	+	0.677192i
$201$	11.8815	−	11.1506i	0.838054	−	0.786505i
$202$	1.37302	+	2.37815i	0.0966057	+	0.167326i
$203$	−1.13523	−	1.96628i	−0.0796777	−	0.138006i
$204$	4.75464	−	4.46218i	0.332892	−	0.312415i
$205$	−0.583408	+	1.01049i	−0.0407470	+	0.0705758i
$206$	4.19635			0.292374
$207$	−8.46880	−	5.63409i	−0.588622	−	0.391597i
$208$	−11.3417			−0.786404
$209$	−1.06147	+	1.83852i	−0.0734233	+	0.127173i
$210$	−0.346092	−	0.104606i	−0.0238826	−	0.00721853i
$211$	−13.2899	−	23.0188i	−0.914916	−	1.58468i	−0.807024	−	0.590518i	$-0.798923\pi$
$211$	−13.2899	−	23.0188i	−0.914916	−	1.58468i	−0.107892	−	0.994163i	$-0.534410\pi$
$212$	4.60473	+	7.97563i	0.316254	+	0.547769i
$213$	−4.45688	−	19.0281i	−0.305380	−	1.30378i
$214$	4.02141	−	6.96529i	0.274898	−	0.476138i
$215$	1.37062			0.0934754
$216$	−7.48322	−	9.06251i	−0.509169	−	0.616626i
$217$	7.16532			0.486414
$218$	2.14917	−	3.72248i	0.145560	−	0.252118i
$219$	−3.49036	−	14.9016i	−0.235857	−	1.00696i
$220$	0.267413	+	0.463173i	0.0180290	+	0.0312271i
$221$	7.40205	+	12.8207i	0.497916	+	0.862416i
$222$	0.990693	+	0.299437i	0.0664910	+	0.0200969i
$223$	5.89487	−	10.2102i	0.394749	−	0.683726i	−0.598320	−	0.801257i	$-0.704165\pi$
$223$	5.89487	−	10.2102i	0.394749	−	0.683726i	0.993069	+	0.117531i	$0.0374981\pi$
$224$	−5.64934			−0.377462
$225$	−0.929903	+	14.6381i	−0.0619935	+	0.975873i
$226$	11.9488			0.794825
$227$	−0.438458	+	0.759431i	−0.0291015	+	0.0504052i	−0.880209	−	0.474586i	$-0.842598\pi$
$227$	−0.438458	+	0.759431i	−0.0291015	+	0.0504052i	0.851108	+	0.524991i	$0.175931\pi$
$228$	4.30798	−	4.04300i	0.285303	−	0.267754i
$229$	−1.99647	−	3.45798i	−0.131930	−	0.228510i	0.792490	−	0.609884i	$-0.208784\pi$
$229$	−1.99647	−	3.45798i	−0.131930	−	0.228510i	−0.924421	+	0.381375i	$0.875451\pi$
$230$	0.353881	+	0.612939i	0.0233342	+	0.0404160i
$231$	1.26297	−	1.18529i	0.0830974	−	0.0779861i
$232$	−2.56770	+	4.44738i	−0.168577	+	0.291985i
$233$	12.5760			0.823882			0.411941	−	0.911211i	$-0.364851\pi$
$233$	12.5760			0.823882			0.411941	+	0.911211i	$0.364851\pi$
$234$	10.6504	−	5.27883i	0.696240	−	0.345088i
$235$	1.44654			0.0943620
$236$	−1.78733	+	3.09575i	−0.116346	+	0.201516i
$237$	2.71819	+	0.821575i	0.176566	+	0.0533670i
$238$	0.734676	+	1.27250i	0.0476220	+	0.0824836i
$239$	−12.4415	−	21.5493i	−0.804773	−	1.39391i	−0.916444	−	0.400163i	$-0.868954\pi$
$239$	−12.4415	−	21.5493i	−0.804773	−	1.39391i	0.111671	−	0.993745i	$-0.464380\pi$
$240$	−0.236018	−	1.00765i	−0.0152349	−	0.0650433i
$241$	3.81868	−	6.61415i	0.245983	−	0.426055i	−0.716425	−	0.697665i	$-0.754223\pi$
$241$	3.81868	−	6.61415i	0.245983	−	0.426055i	0.962408	+	0.271610i	$0.0875559\pi$
$242$	0.627112			0.0403123
$243$	−14.2311	−	6.36208i	−0.912925	−	0.408127i
$244$	7.38397			0.472711
$245$	−0.166433	+	0.288270i	−0.0106330	+	0.0184169i
$246$	−0.868313	−	3.70715i	−0.0553616	−	0.236359i
$247$	6.70669	+	11.6163i	0.426737	+	0.739130i
$248$	−8.10334	−	14.0354i	−0.514563	−	0.891249i
$249$	16.7500	+	5.06269i	1.06149	+	0.320835i
$250$	1.03216	−	1.78775i	0.0652793	−	0.113067i
$251$	1.81219			0.114384			0.0571922	−	0.998363i	$-0.481785\pi$
$251$	1.81219			0.114384			0.0571922	+	0.998363i	$0.481785\pi$
$252$	−4.31881	+	2.14060i	−0.272059	+	0.134845i
$253$	−3.39057			−0.213163
$254$	5.15718	−	8.93249i	0.323590	−	0.560474i
$255$	−0.985018	+	0.924429i	−0.0616842	+	0.0578900i
$256$	3.50474	+	6.07039i	0.219047	+	0.379400i
$257$	5.29331	+	9.16828i	0.330187	+	0.571901i	0.982548	−	0.186007i	$-0.0595547\pi$
$257$	5.29331	+	9.16828i	0.330187	+	0.571901i	−0.652361	+	0.757908i	$0.726221\pi$
$258$	−3.26126	+	3.06066i	−0.203037	+	0.190548i
$259$	0.476416	−	0.825177i	0.0296031	−	0.0512740i
$260$	3.37920			0.209569
$261$	−0.431832	+	6.79769i	−0.0267297	+	0.420767i
$262$	1.34981			0.0833917
$263$	−9.82544	+	17.0182i	−0.605863	+	1.04938i	0.386052	+	0.922477i	$0.373839\pi$
$263$	−9.82544	+	17.0182i	−0.605863	+	1.04938i	−0.991915	+	0.126908i	$0.959495\pi$
$264$	−3.75004	−	1.13345i	−0.230799	−	0.0697591i
$265$	−0.953961	−	1.65231i	−0.0586014	−	0.101501i
$266$	0.665659	+	1.15296i	0.0408142	+	0.0706922i
$267$	5.26684	+	22.4861i	0.322325	+	1.37613i
$268$	−7.55770	+	13.0903i	−0.461660	+	0.799619i
$269$	19.8823			1.21224			0.606122	−	0.795372i	$-0.292724\pi$
$269$	19.8823			1.21224			0.606122	+	0.795372i	$0.292724\pi$
$270$	0.690628	+	0.836381i	0.0420303	+	0.0509005i
$271$	3.99534			0.242700			0.121350	−	0.992610i	$-0.461278\pi$
$271$	3.99534			0.242700			0.121350	+	0.992610i	$0.461278\pi$
$272$	−2.10294	+	3.64240i	−0.127509	+	0.220853i
$273$	−2.49574	−	10.6553i	−0.151049	−	0.644886i
$274$	3.88212	+	6.72402i	0.234527	+	0.406213i
$275$	2.44460	+	4.23417i	0.147415	+	0.255330i
$276$	9.03219	+	2.72998i	0.543674	+	0.164326i
$277$	3.21341	−	5.56579i	0.193075	−	0.334416i	−0.753193	−	0.657800i	$-0.771487\pi$
$277$	3.21341	−	5.56579i	0.193075	−	0.334416i	0.946268	+	0.323384i	$0.104821\pi$
$278$	3.86577			0.231853
$279$	−17.8972	−	11.9066i	−1.07148	−	0.712829i
$280$	0.752884			0.0449934
$281$	4.62012	−	8.00229i	0.275614	−	0.477377i	−0.694676	−	0.719323i	$-0.744452\pi$
$281$	4.62012	−	8.00229i	0.275614	−	0.477377i	0.970290	+	0.241946i	$0.0777857\pi$
$282$	−3.44191	+	3.23020i	−0.204963	+	0.192356i
$283$	−11.6174	−	20.1220i	−0.690585	−	1.19613i	−0.971647	−	0.236438i	$-0.924020\pi$
$283$	−11.6174	−	20.1220i	−0.690585	−	1.19613i	0.281062	−	0.959690i	$-0.409313\pi$
$284$	9.06452	+	15.7002i	0.537880	+	0.931636i
$285$	−0.892484	+	0.837587i	−0.0528662	+	0.0496143i
$286$	1.98114	−	3.43144i	0.117147	−	0.202905i
$287$	−3.50536			−0.206915
$288$	14.1107	+	9.38749i	0.831478	+	0.553163i
$289$	−11.5101			−0.677067
$290$	0.236973	−	0.410450i	0.0139155	−	0.0241024i
$291$	18.3551	+	5.54783i	1.07599	+	0.325220i
$292$	7.09879	+	12.2955i	0.415426	+	0.719538i
$293$	12.8140	+	22.1945i	0.748602	+	1.29662i	0.948493	+	0.316799i	$0.102608\pi$
$293$	12.8140	+	22.1945i	0.748602	+	1.29662i	−0.199891	+	0.979818i	$0.564059\pi$
$294$	−0.247710	−	1.05757i	−0.0144467	−	0.0616785i
$295$	0.370281	−	0.641346i	0.0215586	−	0.0373406i
$296$	−2.15514			−0.125265
$297$	−5.12418	+	0.861874i	−0.297335	+	0.0500110i
$298$	11.0578			0.640559
$299$	−10.7113	+	18.5526i	−0.619453	+	1.07292i
$300$	−3.10299	−	13.2478i	−0.179151	−	0.764862i
$301$	2.05881	+	3.56597i	0.118668	+	0.205539i
$302$	2.79791	+	4.84612i	0.161002	+	0.278863i
$303$	−7.26008	−	2.19436i	−0.417080	−	0.126063i
$304$	−1.90539	+	3.30023i	−0.109281	+	0.189281i
$305$	−1.52974			−0.0875924
$306$	0.279464	−	4.39919i	0.0159759	−	0.251485i
$307$	−15.8591			−0.905128			−0.452564	−	0.891732i	$-0.649491\pi$
$307$	−15.8591			−0.905128			−0.452564	+	0.891732i	$0.649491\pi$
$308$	−0.803366	+	1.39147i	−0.0457760	+	0.0792864i
$309$	−8.45125	+	7.93141i	−0.480775	+	0.451202i
$310$	0.747859	+	1.29533i	0.0424756	+	0.0735698i
$311$	11.4704	+	19.8674i	0.650429	+	1.12658i	0.983019	+	0.183505i	$0.0587444\pi$
$311$	11.4704	+	19.8674i	0.650429	+	1.12658i	−0.332589	+	0.943072i	$0.607922\pi$
$312$	−18.0490	+	16.9388i	−1.02182	+	0.958971i
$313$	−11.1997	+	19.3985i	−0.633046	+	1.09647i	0.353879	+	0.935291i	$0.384862\pi$
$313$	−11.1997	+	19.3985i	−0.633046	+	1.09647i	−0.986925	+	0.161177i	$0.948471\pi$
$314$	5.76025			0.325070
$315$	0.894726	−	0.443467i	0.0504121	−	0.0249865i
$316$	−2.63418			−0.148184
$317$	3.87828	−	6.71737i	0.217826	−	0.377285i	−0.736317	−	0.676636i	$-0.763437\pi$
$317$	3.87828	−	6.71737i	0.217826	−	0.377285i	0.954143	+	0.299351i	$0.0967702\pi$
$318$	5.95955	+	1.80128i	0.334195	+	0.101011i
$319$	1.13523	+	1.96628i	0.0635608	+	0.110091i
$320$	0.00787702	+	0.0136434i	0.000440339	+	0.000762689i
$321$	5.06598	+	21.6285i	0.282755	+	1.20719i
$322$	−1.06313	+	1.84140i	−0.0592460	+	0.102617i
$323$	4.97414			0.276769
$324$	14.3443	+	1.82987i	0.796908	+	0.101659i
$325$	30.8915			1.71355
$326$	−2.44147	+	4.22875i	−0.135220	+	0.234209i
$327$	2.70742	+	11.5590i	0.149721	+	0.639213i
$328$	3.96425	+	6.86629i	0.218889	+	0.379127i
$329$	2.17286	+	3.76350i	0.119794	+	0.207489i
$330$	0.346092	+	0.104606i	0.0190517	+	0.00575839i
$331$	4.35411	−	7.54154i	0.239324	−	0.414521i	−0.721197	−	0.692730i	$-0.756408\pi$
$331$	4.35411	−	7.54154i	0.239324	−	0.414521i	0.960520	+	0.278210i	$0.0897410\pi$
$332$	−16.2323			−0.890864
$333$	−2.56116	+	1.26943i	−0.140351	+	0.0695643i
$334$	−6.76826			−0.370343
$335$	1.56573	−	2.71192i	0.0855448	−	0.148168i
$336$	2.26709	−	2.12764i	0.123680	−	0.116072i
$337$	−14.1718	−	24.5464i	−0.771989	−	1.33712i	−0.936471	−	0.350745i	$-0.885928\pi$
$337$	−14.1718	−	24.5464i	−0.771989	−	1.33712i	0.164482	−	0.986380i	$-0.447405\pi$
$338$	−8.44126	−	14.6207i	−0.459144	−	0.795261i
$339$	−24.0644	+	22.5842i	−1.30700	+	1.22660i
$340$	0.626561	−	1.08524i	0.0339801	−	0.0588552i
$341$	−7.16532			−0.388024
$342$	0.253211	−	3.98592i	0.0136921	−	0.215534i
$343$	−1.00000			−0.0539949
$344$	4.65667	−	8.06560i	0.251071	−	0.434868i
$345$	−1.87120	−	0.565570i	−0.100742	−	0.0304492i
$346$	−5.81408	−	10.0703i	−0.312567	−	0.541382i
$347$	15.1006	+	26.1550i	0.810641	+	1.40407i	0.912416	+	0.409264i	$0.134215\pi$
$347$	15.1006	+	26.1550i	0.810641	+	1.40407i	−0.101775	+	0.994807i	$0.532452\pi$
$348$	−1.44098	−	6.15207i	−0.0772445	−	0.329785i
$349$	8.94111	−	15.4865i	0.478607	−	0.828971i	−0.521092	−	0.853500i	$-0.674475\pi$
$349$	8.94111	−	15.4865i	0.478607	−	0.828971i	0.999699	+	0.0245292i	$0.00780867\pi$
$350$	3.06607			0.163889
$351$	−11.4721	+	30.7614i	−0.612333	+	1.64192i
$352$	5.64934			0.301111
$353$	13.3120	−	23.0571i	0.708527	−	1.22720i	−0.256877	−	0.966444i	$-0.582694\pi$
$353$	13.3120	−	23.0571i	0.708527	−	1.22720i	0.965404	−	0.260760i	$-0.0839731\pi$
$354$	0.551107	+	2.35288i	0.0292910	+	0.125054i
$355$	−1.87789	−	3.25261i	−0.0996683	−	0.172630i
$356$	−10.7119	−	18.5535i	−0.567727	−	0.983332i
$357$	−3.88471	−	1.17415i	−0.205601	−	0.0621428i
$358$	−4.50816	+	7.80837i	−0.238264	+	0.412685i
$359$	−6.81672			−0.359773			−0.179886	−	0.983687i	$-0.557573\pi$
$359$	−6.81672			−0.359773			−0.179886	+	0.983687i	$0.557573\pi$
$360$	−1.88052	−	1.25106i	−0.0991120	−	0.0659369i
$361$	−14.4931			−0.762797
$362$	−8.00586	+	13.8666i	−0.420779	+	0.728810i
$363$	−1.26297	+	1.18529i	−0.0662888	+	0.0622114i
$364$	5.07592	+	8.79174i	0.266050	+	0.460813i
$365$	−1.47066	−	2.54725i	−0.0769776	−	0.133329i
$366$	3.63987	−	3.41598i	0.190259	−	0.178556i
$367$	−17.0879	+	29.5971i	−0.891979	+	1.54495i	−0.0544806	+	0.998515i	$0.517350\pi$
$367$	−17.0879	+	29.5971i	−0.891979	+	1.54495i	−0.837499	+	0.546439i	$0.815983\pi$
$368$	−6.08623			−0.317267
$369$	8.75552	+	5.82485i	0.455794	+	0.303229i
$370$	0.198898			0.0103402
$371$	2.86590	−	4.96389i	0.148790	−	0.257712i
$372$	19.0878	+	5.76930i	0.989658	+	0.299124i
$373$	−10.6613	−	18.4659i	−0.552020	−	0.956126i	−0.998129	−	0.0611478i	$-0.980524\pi$
$373$	−10.6613	−	18.4659i	−0.552020	−	0.956126i	0.446109	−	0.894979i	$-0.352809\pi$
$374$	−0.734676	−	1.27250i	−0.0379892	−	0.0657992i
$375$	1.30026	+	5.55128i	0.0671450	+	0.286667i
$376$	4.91462	−	8.51238i	0.253452	−	0.438992i
$377$	14.3455			0.738832
$378$	−1.13864	+	3.05316i	−0.0585651	+	0.157037i
$379$	9.54931			0.490515			0.245258	−	0.969458i	$-0.421127\pi$
$379$	9.54931			0.490515			0.245258	+	0.969458i	$0.421127\pi$
$380$	0.567701	−	0.983287i	0.0291225	−	0.0504416i
$381$	6.49675	+	27.7370i	0.332839	+	1.42101i
$382$	−3.88960	−	6.73699i	−0.199009	−	0.344694i
$383$	8.74931	+	15.1543i	0.447069	+	0.774346i	0.998194	−	0.0600765i	$-0.0191345\pi$
$383$	8.74931	+	15.1543i	0.447069	+	0.774346i	−0.551125	+	0.834423i	$0.685801\pi$
$384$	−18.7821	−	5.67690i	−0.958471	−	0.289698i
$385$	0.166433	−	0.288270i	0.00848221	−	0.0146916i
$386$	7.60955			0.387316
$387$	0.783154	−	12.3280i	0.0398100	−	0.626669i
$388$	−17.7878			−0.903039
$389$	11.1271	−	19.2727i	0.564166	−	0.977165i	−0.432960	−	0.901413i	$-0.642531\pi$
$389$	11.1271	−	19.2727i	0.564166	−	0.977165i	0.997127	−	0.0757517i	$-0.0241356\pi$
$390$	1.66575	−	1.56329i	0.0843484	−	0.0791601i
$391$	3.97213	+	6.87993i	0.200879	+	0.347933i
$392$	1.13091	+	1.95880i	0.0571196	+	0.0989341i
$393$	−2.71846	+	2.55124i	−0.137128	+	0.128693i
$394$	1.93051	−	3.34374i	0.0972578	−	0.168455i
$395$	0.545723			0.0274583
$396$	4.31881	−	2.14060i	0.217028	−	0.107569i
$397$	22.7276			1.14067			0.570333	−	0.821414i	$-0.306814\pi$
$397$	22.7276			1.14067			0.570333	+	0.821414i	$0.306814\pi$
$398$	−5.56204	+	9.63374i	−0.278800	+	0.482896i
$399$	−3.51977	−	1.06385i	−0.176209	−	0.0532592i
$400$	4.38817	+	7.60054i	0.219409	+	0.380027i
$401$	18.5616	+	32.1497i	0.926924	+	1.60548i	0.788438	+	0.615114i	$0.210890\pi$
$401$	18.5616	+	32.1497i	0.926924	+	1.60548i	0.138486	+	0.990364i	$0.455776\pi$
$402$	2.33035	+	9.94911i	0.116227	+	0.496216i
$403$	−22.6364	+	39.2073i	−1.12760	+	1.95306i
$404$	7.03569			0.350039
$405$	−2.97171	−	0.379093i	−0.147666	−	0.0188373i
$406$	1.42384			0.0706638
$407$	−0.476416	+	0.825177i	−0.0236151	+	0.0409025i
$408$	2.09333	+	8.93722i	0.103635	+	0.442458i
$409$	−12.7331	−	22.0544i	−0.629612	−	1.09052i	−0.987630	−	0.156805i	$-0.949881\pi$
$409$	−12.7331	−	22.0544i	−0.629612	−	1.09052i	0.358018	−	0.933715i	$-0.383453\pi$
$410$	−0.365862	−	0.633691i	−0.0180686	−	0.0312958i
$411$	−20.5273	−	6.20437i	−1.01254	−	0.306039i
$412$	5.37577	−	9.31110i	0.264845	−	0.458725i
$413$	2.22481			0.109476
$414$	5.71529	−	2.83275i	0.280891	−	0.139222i
$415$	3.36284			0.165076
$416$	17.8472	−	30.9122i	0.875029	−	1.51559i
$417$	−7.78547	+	7.30658i	−0.381256	+	0.357805i
$418$	−0.665659	−	1.15296i	−0.0325585	−	0.0563929i
$419$	−13.0672	−	22.6330i	−0.638374	−	1.10570i	−0.985790	−	0.167985i	$-0.946274\pi$
$419$	−13.0672	−	22.6330i	−0.638374	−	1.10570i	0.347415	−	0.937711i	$-0.387059\pi$
$420$	−0.675470	+	0.633922i	−0.0329596	+	0.0309322i
$421$	2.64196	−	4.57600i	0.128761	−	0.223021i	−0.794436	−	0.607348i	$-0.792233\pi$
$421$	2.64196	−	4.57600i	0.128761	−	0.223021i	0.923197	+	0.384328i	$0.125567\pi$
$422$	16.6685			0.811411
$423$	0.826536	−	13.0109i	0.0401875	−	0.632613i
$424$	−12.9643			−0.629603
$425$	5.72781	−	9.92086i	0.277840	−	0.481232i
$426$	11.7315	+	3.54585i	0.568394	+	0.171797i
$427$	−2.29783	−	3.97995i	−0.111200	−	0.192603i
$428$	−10.3033	−	17.8459i	−0.498030	−	0.862613i
$429$	2.49574	+	10.6553i	0.120496	+	0.514441i
$430$	−0.429765	+	0.744376i	−0.0207251	+	0.0358970i
$431$	6.16102			0.296766			0.148383	−	0.988930i	$-0.452593\pi$
$431$	6.16102			0.296766			0.148383	+	0.988930i	$0.452593\pi$
$432$	−9.19814	+	1.54710i	−0.442546	+	0.0744351i
$433$	14.9612			0.718990			0.359495	−	0.933147i	$-0.382949\pi$
$433$	14.9612			0.718990			0.359495	+	0.933147i	$0.382949\pi$
$434$	−2.24673	+	3.89145i	−0.107846	+	0.186795i
$435$	0.298527	+	1.27452i	0.0143133	+	0.0611086i
$436$	−5.50643	−	9.53742i	−0.263710	−	0.456759i
$437$	3.59898	+	6.23362i	0.172163	+	0.298194i
$438$	9.18742	+	2.77690i	0.438992	+	0.132685i
$439$	−0.759476	+	1.31545i	−0.0362478	+	0.0627831i	−0.883580	−	0.468280i	$-0.844874\pi$
$439$	−0.759476	+	1.31545i	−0.0362478	+	0.0627831i	0.847332	+	0.531063i	$0.178207\pi$
$440$	−0.752884			−0.0358923
$441$	2.49775	+	1.66170i	0.118941	+	0.0791284i
$442$	−9.28382			−0.441587
$443$	−8.27210	+	14.3277i	−0.393019	+	0.680729i	−0.992846	−	0.119401i	$-0.961903\pi$
$443$	−8.27210	+	14.3277i	−0.393019	+	0.680729i	0.599827	+	0.800130i	$0.295236\pi$
$444$	1.93354	−	1.81461i	0.0917618	−	0.0861175i
$445$	2.21917	+	3.84372i	0.105199	+	0.182210i
$446$	3.69674	+	6.40294i	0.175046	+	0.303188i
$447$	−22.2698	+	20.9000i	−1.05332	+	0.988534i
$448$	−0.0236642	+	0.0409877i	−0.00111803	+	0.00193648i
$449$	9.34500			0.441018			0.220509	−	0.975385i	$-0.429228\pi$
$449$	9.34500			0.441018			0.220509	+	0.975385i	$0.429228\pi$
$450$	−7.65829	−	5.09488i	−0.361015	−	0.240175i
$451$	3.50536			0.165061
$452$	15.3071	−	26.5128i	0.719987	−	1.24705i
$453$	−14.7944	−	4.47160i	−0.695100	−	0.210094i
$454$	−0.274962	−	0.476248i	−0.0129046	−	0.0223514i
$455$	−1.05158	−	1.82138i	−0.0492986	−	0.0853878i
$456$	1.89668	+	8.09764i	0.0888203	+	0.379207i
$457$	−4.42964	+	7.67237i	−0.207210	+	0.358898i	−0.950835	−	0.309699i	$-0.899772\pi$
$457$	−4.42964	+	7.67237i	−0.207210	+	0.358898i	0.743625	+	0.668597i	$0.233105\pi$
$458$	2.50401			0.117005
$459$	7.75195	+	9.38795i	0.361830	+	0.438192i
$460$	1.81336			0.0845486
$461$	−1.10017	+	1.90556i	−0.0512402	+	0.0887507i	−0.890508	−	0.454968i	$-0.849651\pi$
$461$	−1.10017	+	1.90556i	−0.0512402	+	0.0887507i	0.839268	+	0.543719i	$0.182984\pi$
$462$	0.247710	+	1.05757i	0.0115245	+	0.0492024i
$463$	−12.7857	−	22.1454i	−0.594201	−	1.02919i	−0.993659	−	0.112435i	$-0.964135\pi$
$463$	−12.7857	−	22.1454i	−0.594201	−	1.02919i	0.399458	−	0.916751i	$-0.369198\pi$
$464$	2.03780	+	3.52957i	0.0946023	+	0.163856i
$465$	−3.95442	−	1.19522i	−0.183382	−	0.0554272i
$466$	−3.94328	+	6.82996i	−0.182669	+	0.316392i
$467$	0.378642			0.0175215			0.00876074	−	0.999962i	$-0.497211\pi$
$467$	0.378642			0.0175215			0.00876074	+	0.999962i	$0.497211\pi$
$468$	1.93083	−	30.3942i	0.0892527	−	1.40497i
$469$	9.40755			0.434400
$470$	−0.453572	+	0.785609i	−0.0209217	+	0.0362374i
$471$	−11.6009	+	10.8873i	−0.534539	+	0.501659i
$472$	−2.51606	−	4.35794i	−0.115811	−	0.200591i
$473$	−2.05881	−	3.56597i	−0.0946644	−	0.163964i
$474$	−1.29850	+	1.21863i	−0.0596420	+	0.0559734i
$475$	5.18973	−	8.98888i	0.238121	−	0.412438i
$476$	3.76465			0.172552
$477$	−15.4068	+	7.63630i	−0.705428	+	0.349642i
$478$	15.6044			0.713729
$479$	10.9958	−	19.0452i	0.502409	−	0.870199i	−0.497587	−	0.867414i	$-0.665780\pi$
$479$	10.9958	−	19.0452i	0.502409	−	0.870199i	0.999996	−	0.00278433i	$-0.000886281\pi$
$480$	3.11777	+	0.942348i	0.142306	+	0.0430121i
$481$	3.01015	+	5.21373i	0.137251	+	0.237726i
$482$	2.39474	+	4.14781i	0.109077	+	0.188928i
$483$	−1.33928	−	5.71788i	−0.0609394	−	0.260173i
$484$	0.803366	−	1.39147i	0.0365166	−	0.0632486i
$485$	3.68509			0.167331
$486$	7.91745	−	5.73396i	0.359143	−	0.260098i
$487$	12.1617			0.551098			0.275549	−	0.961287i	$-0.411140\pi$
$487$	12.1617			0.551098			0.275549	+	0.961287i	$0.411140\pi$
$488$	−5.19727	+	9.00194i	−0.235269	+	0.407499i
$489$	−3.07564	−	13.1310i	−0.139085	−	0.593806i
$490$	−0.104372	−	0.180778i	−0.00471505	−	0.00816670i
$491$	13.3141	+	23.0607i	0.600858	+	1.04072i	0.992691	+	0.120681i	$0.0385077\pi$
$491$	13.3141	+	23.0607i	0.600858	+	1.04072i	−0.391833	+	0.920036i	$0.628159\pi$
$492$	−9.33799	−	2.82241i	−0.420989	−	0.127244i
$493$	2.65990	−	4.60709i	0.119796	−	0.207493i
$494$	−8.41169			−0.378460
$495$	−0.894726	+	0.443467i	−0.0402150	+	0.0199324i
$496$	−12.8621			−0.577525
$497$	5.64159	−	9.77152i	0.253060	−	0.438313i
$498$	−8.00158	+	7.50940i	−0.358559	+	0.336504i
$499$	7.12034	+	12.3328i	0.318750	+	0.552091i	0.980228	−	0.197874i	$-0.0634036\pi$
$499$	7.12034	+	12.3328i	0.318750	+	0.552091i	−0.661477	+	0.749965i	$0.730070\pi$
$500$	−2.64450	−	4.58041i	−0.118266	−	0.204842i
$501$	13.6309	−	12.7925i	0.608986	−	0.571527i
$502$	−0.568222	+	0.984190i	−0.0253610	+	0.0439266i
$503$	−25.5095			−1.13741			−0.568705	−	0.822541i	$-0.692555\pi$
$503$	−25.5095			−1.13741			−0.568705	+	0.822541i	$0.692555\pi$
$504$	0.430188	−	6.77182i	0.0191621	−	0.301641i
$505$	−1.45758			−0.0648616
$506$	1.06313	−	1.84140i	0.0472620	−	0.0818602i
$507$	44.6345	+	13.4908i	1.98229	+	0.599146i
$508$	−13.2133	−	22.8861i	−0.586244	−	1.01540i
$509$	2.56424	+	4.44139i	0.113658	+	0.196861i	0.917242	−	0.398329i	$-0.130410\pi$
$509$	2.56424	+	4.44139i	0.113658	+	0.196861i	−0.803585	+	0.595191i	$0.797077\pi$
$510$	−0.193194	−	0.824818i	−0.00855478	−	0.0365235i
$511$	4.41816	−	7.65248i	0.195448	−	0.338526i
$512$	18.2610			0.807029
$513$	7.02372	+	8.50603i	0.310105	+	0.375551i
$514$	−6.63899			−0.292833
$515$	−1.11370	+	1.92898i	−0.0490753	+	0.0850009i
$516$	2.61330	+	11.1571i	0.115044	+	0.491166i
$517$	−2.17286	−	3.76350i	−0.0955623	−	0.165519i
$518$	0.298766	+	0.517478i	0.0131270	+	0.0227367i
$519$	30.7428	+	9.29202i	1.34946	+	0.407875i
$520$	−2.37848	+	4.11965i	−0.104303	+	0.180658i
$521$	12.4413			0.545065			0.272533	−	0.962147i	$-0.412139\pi$
$521$	12.4413			0.545065			0.272533	+	0.962147i	$0.412139\pi$
$522$	−3.55639	−	2.36598i	−0.155659	−	0.103556i
$523$	35.2797			1.54267			0.771336	−	0.636428i	$-0.219589\pi$
$523$	35.2797			1.54267			0.771336	+	0.636428i	$0.219589\pi$
$524$	1.72919	−	2.99504i	0.0755399	−	0.130839i
$525$	−6.17492	+	5.79510i	−0.269496	+	0.252919i
$526$	−6.16165	−	10.6723i	−0.268661	−	0.465334i
$527$	8.39434	+	14.5394i	0.365663	+	0.633347i
$528$	−2.26709	+	2.12764i	−0.0986626	+	0.0925938i
$529$	5.75202	−	9.96280i	0.250088	−	0.433165i
$530$	1.19648			0.0519718
$531$	−5.55702	−	3.69695i	−0.241154	−	0.160434i
$532$	3.41099			0.147885
$533$	11.0740	−	19.1807i	0.479668	−	0.830809i
$534$	−13.8635	−	4.19025i	−0.599933	−	0.181330i
$535$	2.13454	+	3.69713i	0.0922841	+	0.159841i
$536$	−10.6391	−	18.4275i	−0.459539	−	0.795946i
$537$	−5.67916	−	24.2464i	−0.245074	−	1.04631i
$538$	−6.23420	+	10.7979i	−0.268775	+	0.465533i
$539$	1.00000			0.0430730
$540$	2.74054	−	0.460953i	0.117934	−	0.0198363i
$541$	22.0722			0.948959			0.474479	−	0.880267i	$-0.342636\pi$
$541$	22.0722			0.948959			0.474479	+	0.880267i	$0.342636\pi$
$542$	−1.25276	+	2.16985i	−0.0538107	+	0.0932029i
$543$	−10.0854	−	43.0582i	−0.432805	−	1.84781i
$544$	−6.61833	−	11.4633i	−0.283759	−	0.491485i
$545$	1.14077	+	1.97586i	0.0488650	+	0.0846367i
$546$	6.56937	+	1.98559i	0.281143	+	0.0849755i
$547$	16.7083	−	28.9397i	0.714397	−	1.23737i	−0.248794	−	0.968556i	$-0.580034\pi$
$547$	16.7083	−	28.9397i	0.714397	−	1.23737i	0.963192	−	0.268816i	$-0.0866323\pi$
$548$	19.8928			0.849780
$549$	−0.874071	+	13.7592i	−0.0373045	+	0.587229i
$550$	−3.06607			−0.130738
$551$	2.41003	−	4.17429i	0.102671	−	0.177831i
$552$	−9.68556	+	9.08979i	−0.412245	+	0.386887i
$553$	0.819734	+	1.41982i	0.0348586	+	0.0603769i
$554$	2.01517	+	3.49037i	0.0856163	+	0.148292i
$555$	−0.400571	+	0.375932i	−0.0170033	+	0.0159574i
$556$	4.95227	−	8.57759i	0.210023	−	0.363771i
$557$	33.5112			1.41992			0.709958	−	0.704244i	$-0.248714\pi$
$557$	33.5112			1.41992			0.709958	+	0.704244i	$0.248714\pi$
$558$	12.0782	−	5.98649i	0.511310	−	0.253428i
$559$	−26.0165			−1.10038
$560$	0.298755	−	0.517459i	0.0126247	−	0.0218666i
$561$	3.88471	+	1.17415i	0.164013	+	0.0495728i
$562$	2.89733	+	5.01833i	0.122217	+	0.211685i
$563$	−11.4207	−	19.7813i	−0.481326	−	0.833680i	0.518445	−	0.855111i	$-0.326511\pi$
$563$	−11.4207	−	19.7813i	−0.481326	−	0.833680i	−0.999770	+	0.0214308i	$0.993178\pi$
$564$	2.75806	+	11.7752i	0.116135	+	0.495825i
$565$	−3.17118	+	5.49264i	−0.133412	+	0.231077i
$566$	14.5709			0.612459
$567$	−3.47753	−	8.30101i	−0.146043	−	0.348610i
$568$	−25.5206			−1.07082
$569$	−21.7255	+	37.6296i	−0.910778	+	1.57751i	−0.0978111	+	0.995205i	$0.531184\pi$
$569$	−21.7255	+	37.6296i	−0.910778	+	1.57751i	−0.812967	+	0.582309i	$0.802149\pi$
$570$	−0.175045	−	0.747333i	−0.00733184	−	0.0313023i
$571$	−0.127217	−	0.220347i	−0.00532388	−	0.00922123i	0.863351	−	0.504604i	$-0.168361\pi$
$571$	−0.127217	−	0.220347i	−0.00532388	−	0.00922123i	−0.868675	+	0.495382i	$0.835028\pi$
$572$	−5.07592	−	8.79174i	−0.212235	−	0.367601i
$573$	20.5669	+	6.21633i	0.859193	+	0.259691i
$574$	1.09913	−	1.90374i	0.0458766	−	0.0794607i
$575$	16.5772			0.691316
$576$	0.127216	−	0.0630542i	0.00530068	−	0.00262726i
$577$	−22.8344			−0.950610			−0.475305	−	0.879821i	$-0.657662\pi$
$577$	−22.8344			−0.950610			−0.475305	+	0.879821i	$0.657662\pi$
$578$	3.60907	−	6.25109i	0.150117	−	0.260011i
$579$	−15.3253	+	14.3826i	−0.636896	+	0.597720i
$580$	−0.607152	−	1.05162i	−0.0252106	−	0.0436661i
$581$	5.05135	+	8.74919i	0.209565	+	0.362978i
$582$	−8.76834	+	8.22900i	−0.363459	+	0.341103i
$583$	−2.86590	+	4.96389i	−0.118693	+	0.205583i
$584$	−19.9862			−0.827034
$585$	−0.400010	+	6.29676i	−0.0165384	+	0.260339i
$586$	−16.0716			−0.663912
$587$	9.63121	−	16.6817i	0.397523	−	0.688529i	−0.595897	−	0.803061i	$-0.703203\pi$
$587$	9.63121	−	16.6817i	0.397523	−	0.688529i	0.993420	+	0.114532i	$0.0365367\pi$
$588$	−2.66392	−	0.805170i	−0.109858	−	0.0332046i
$589$	7.60576	+	13.1736i	0.313390	+	0.542807i
$590$	0.232208	+	0.402196i	0.00955984	+	0.0165581i
$591$	2.43196	+	10.3829i	0.100037	+	0.427097i
$592$	−0.855190	+	1.48123i	−0.0351481	+	0.0608783i
$593$	23.6776			0.972322			0.486161	−	0.873869i	$-0.338397\pi$
$593$	23.6776			0.972322			0.486161	+	0.873869i	$0.338397\pi$
$594$	1.13864	−	3.05316i	0.0467188	−	0.125273i
$595$	−0.779921			−0.0319736
$596$	14.1656	−	24.5356i	0.580246	−	1.00502i
$597$	−7.00678	−	29.9146i	−0.286769	−	1.22432i
$598$	−6.71720	−	11.6345i	−0.274687	−	0.475772i
$599$	−17.0378	−	29.5103i	−0.696144	−	1.20576i	−0.969794	−	0.243927i	$-0.921564\pi$
$599$	−17.0378	−	29.5103i	−0.696144	−	1.20576i	0.273650	−	0.961829i	$-0.411769\pi$
$600$	18.3347	+	5.54167i	0.748511	+	0.226238i
$601$	−10.4992	+	18.1851i	−0.428271	+	0.741787i	−0.996720	−	0.0809316i	$-0.974210\pi$
$601$	−10.4992	+	18.1851i	−0.428271	+	0.741787i	0.568449	+	0.822719i	$0.307544\pi$
$602$	−2.58221			−0.105243
$603$	−23.4977	−	15.6325i	−0.956902	−	0.636604i
$604$	14.3371			0.583370
$605$	−0.166433	+	0.288270i	−0.00676646	+	0.0117199i
$606$	3.46818	−	3.25485i	0.140885	−	0.132219i
$607$	−17.6355	−	30.5456i	−0.715803	−	1.23981i	−0.962649	−	0.270753i	$-0.912727\pi$
$607$	−17.6355	−	30.5456i	−0.715803	−	1.23981i	0.246846	−	0.969055i	$-0.420606\pi$
$608$	−5.99660	−	10.3864i	−0.243194	−	0.421225i
$609$	−2.86753	+	2.69115i	−0.116198	+	0.109051i
$610$	0.479657	−	0.830791i	0.0194208	−	0.0336377i
$611$	−27.4576			−1.11082
$612$	−9.40315	−	6.25570i	−0.380100	−	0.252872i
$613$	−5.85526			−0.236492			−0.118246	−	0.992984i	$-0.537727\pi$
$613$	−5.85526			−0.236492			−0.118246	+	0.992984i	$0.537727\pi$
$614$	4.97272	−	8.61300i	0.200683	−	0.347593i
$615$	1.93455	+	0.584718i	0.0780086	+	0.0235781i
$616$	−1.13091	−	1.95880i	−0.0455657	−	0.0789221i
$617$	−15.4053	−	26.6828i	−0.620194	−	1.07421i	−0.989449	−	0.144880i	$-0.953720\pi$
$617$	−15.4053	−	26.6828i	−0.620194	−	1.07421i	0.369255	−	0.929328i	$-0.379613\pi$
$618$	−1.65757	−	7.07676i	−0.0666771	−	0.284669i
$619$	−13.2177	+	22.8937i	−0.531264	+	0.920176i	0.468070	+	0.883691i	$0.344949\pi$
$619$	−13.2177	+	22.8937i	−0.531264	+	0.920176i	−0.999334	+	0.0364847i	$0.988384\pi$
$620$	3.83220			0.153905
$621$	−6.15620	+	16.5073i	−0.247040	+	0.662416i
$622$	−14.3865			−0.576846
$623$	−6.66686	+	11.5473i	−0.267102	+	0.462634i
$624$	4.47998	+	19.1267i	0.179343	+	0.765681i
$625$	−11.6751	−	20.2219i	−0.467006	−	0.808877i
$626$	−7.02348	−	12.1650i	−0.280715	−	0.486212i
$627$	3.51977	+	1.06385i	0.140566	+	0.0424862i
$628$	7.37920	−	12.7812i	0.294462	−	0.510024i
$629$	2.23253			0.0890169
$630$	−0.0397022	+	0.624973i	−0.00158177	+	0.0248995i
$631$	−35.3771			−1.40834			−0.704170	−	0.710032i	$-0.748681\pi$
$631$	−35.3771			−1.40834			−0.704170	+	0.710032i	$0.748681\pi$
$632$	1.85409	−	3.21138i	0.0737519	−	0.127742i
$633$	−33.5696	+	31.5047i	−1.33427	+	1.25220i
$634$	2.43211	+	4.21254i	0.0965915	+	0.167301i
$635$	2.73739	+	4.74130i	0.108630	+	0.188153i
$636$	11.6313	−	10.9158i	0.461211	−	0.432842i
$637$	3.15916	−	5.47182i	0.125170	−	0.216801i
$638$	−1.42384			−0.0563702
$639$	−30.3286	+	15.0322i	−1.19978	+	0.594666i
$640$	−3.77083			−0.149055
$641$	9.95654	−	17.2452i	0.393260	−	0.681146i	−0.599618	−	0.800287i	$-0.704681\pi$
$641$	9.95654	−	17.2452i	0.393260	−	0.681146i	0.992877	+	0.119141i	$0.0380140\pi$
$642$	−13.3348	−	4.03044i	−0.526282	−	0.159069i
$643$	15.2899	+	26.4828i	0.602973	+	1.04438i	0.992368	+	0.123309i	$0.0393508\pi$
$643$	15.2899	+	26.4828i	0.602973	+	1.04438i	−0.389395	+	0.921071i	$0.627316\pi$
$644$	2.72387	+	4.71787i	0.107335	+	0.185910i
$645$	−0.541397	−	2.31142i	−0.0213175	−	0.0910122i
$646$	−1.55967	+	2.70143i	−0.0613644	+	0.106286i
$647$	−40.0863			−1.57595			−0.787977	−	0.615705i	$-0.788871\pi$
$647$	−40.0863			−1.57595			−0.787977	+	0.615705i	$0.788871\pi$
$648$	−12.3272	+	16.1995i	−0.484258	+	0.636376i
$649$	−2.22481			−0.0873313
$650$	−9.68621	+	16.7770i	−0.379924	+	0.658048i
$651$	−2.83031	−	12.0837i	−0.110929	−	0.473596i
$652$	6.25532	+	10.8345i	0.244977	+	0.424313i
$653$	10.7966	+	18.7003i	0.422505	+	0.731800i	0.996184	−	0.0872804i	$-0.0278176\pi$
$653$	10.7966	+	18.7003i	0.422505	+	0.731800i	−0.573679	+	0.819080i	$0.694484\pi$
$654$	−7.12655	−	2.15400i	−0.278670	−	0.0842281i
$655$	−0.358235	+	0.620482i	−0.0139974	+	0.0242442i
$656$	6.29229			0.245673
$657$	−23.7516	+	11.7723i	−0.926637	+	0.459283i
$658$	−2.72525			−0.106241
$659$	10.2125	−	17.6886i	0.397823	−	0.689050i	−0.595634	−	0.803256i	$-0.703099\pi$
$659$	10.2125	−	17.6886i	0.397823	−	0.689050i	0.993457	+	0.114206i	$0.0364325\pi$
$660$	0.675470	−	0.633922i	0.0262926	−	0.0246754i
$661$	−11.7249	−	20.3081i	−0.456044	−	0.789892i	0.542703	−	0.839925i	$-0.317401\pi$
$661$	−11.7249	−	20.3081i	−0.456044	−	0.789892i	−0.998748	+	0.0500325i	$0.984068\pi$
$662$	2.73051	+	4.72939i	0.106124	+	0.183813i
$663$	18.6972	−	17.5471i	0.726138	−	0.681473i
$664$	11.4253	−	19.7891i	0.443386	−	0.767967i
$665$	−0.706654			−0.0274029
$666$	0.113648	−	1.78899i	0.00440377	−	0.0693220i
$667$	7.69817			0.298074
$668$	−8.67053	+	15.0178i	−0.335473	+	0.581056i
$669$	−19.5471	−	5.90810i	−0.755733	−	0.228420i
$670$	0.981886	+	1.70068i	0.0379335	+	0.0657028i
$671$	2.29783	+	3.97995i	0.0887066	+	0.153644i
$672$	2.23150	+	9.52710i	0.0860819	+	0.367516i
$673$	3.32474	−	5.75863i	0.128159	−	0.221979i	−0.794804	−	0.606866i	$-0.792426\pi$
$673$	3.32474	−	5.75863i	0.128159	−	0.221979i	0.922964	+	0.384887i	$0.125760\pi$
$674$	17.7747			0.684654
$675$	25.0531	−	4.21388i	0.964295	−	0.162192i
$676$	−43.2550			−1.66365
$677$	−17.6512	+	30.5728i	−0.678392	+	1.17501i	0.297073	+	0.954855i	$0.403989\pi$
$677$	−17.6512	+	30.5728i	−0.678392	+	1.17501i	−0.975465	+	0.220154i	$0.929344\pi$
$678$	−4.71981	−	20.1506i	−0.181263	−	0.773880i
$679$	5.53540	+	9.58759i	0.212429	+	0.367938i
$680$	0.882021	+	1.52771i	0.0338240	+	0.0585848i
$681$	1.45390	+	0.439442i	0.0557137	+	0.0168395i
$682$	2.24673	−	3.89145i	0.0860316	−	0.149011i
$683$	−34.6423			−1.32555			−0.662775	−	0.748818i	$-0.730622\pi$
$683$	−34.6423			−1.32555			−0.662775	+	0.748818i	$0.730622\pi$
$684$	−8.51981	−	5.66803i	−0.325763	−	0.216723i
$685$	−4.12120			−0.157463
$686$	0.313556	−	0.543094i	0.0119716	−	0.0207354i
$687$	−5.04296	+	4.73276i	−0.192401	+	0.180566i
$688$	−3.69567	−	6.40109i	−0.140896	−	0.244039i
$689$	18.1077	+	31.3634i	0.689847	+	1.19485i
$690$	0.893882	−	0.838899i	0.0340295	−	0.0319363i
$691$	−4.84461	+	8.39111i	−0.184298	+	0.319213i	−0.943340	−	0.331829i	$-0.892334\pi$
$691$	−4.84461	+	8.39111i	−0.184298	+	0.319213i	0.759042	+	0.651042i	$0.225668\pi$
$692$	−29.7927			−1.13255
$693$	−2.49775	−	1.66170i	−0.0948818	−	0.0631226i
$694$	−18.9395			−0.718933
$695$	−1.02596	+	1.77702i	−0.0389169	+	0.0674061i
$696$	8.51434	+	2.57346i	0.322735	+	0.0975468i
$697$	−4.10661	−	7.11286i	−0.155549	−	0.269419i
$698$	5.60707	+	9.71174i	0.212231	+	0.367595i
$699$	−4.96755	−	21.2083i	−0.187890	−	0.802171i
$700$	3.92782	−	6.80318i	0.148457	−	0.257136i
$701$	1.71944			0.0649424			0.0324712	−	0.999473i	$-0.489662\pi$
$701$	1.71944			0.0649424			0.0324712	+	0.999473i	$0.489662\pi$
$702$	−13.1092	−	15.8758i	−0.494775	−	0.599194i
$703$	2.02280			0.0762915
$704$	0.0236642	−	0.0409877i	0.000891879	−	0.00154478i
$705$	−0.571387	−	2.43946i	−0.0215197	−	0.0918754i
$706$	8.34811	+	14.4594i	0.314185	+	0.544185i
$707$	−2.18944	−	3.79223i	−0.0823425	−	0.142621i
$708$	5.92670	+	1.79135i	0.222739	+	0.0673230i
$709$	11.4192	−	19.7787i	0.428859	−	0.742805i	−0.567913	−	0.823088i	$-0.692249\pi$
$709$	11.4192	−	19.7787i	0.428859	−	0.742805i	0.996772	+	0.0802831i	$0.0255824\pi$
$710$	2.35530			0.0883928
$711$	0.311819	−	4.90851i	0.0116941	−	0.184084i
$712$	30.1585			1.13024
$713$	−12.1473	+	21.0397i	−0.454918	+	0.787941i
$714$	1.85575	−	1.74160i	0.0694497	−	0.0651778i
$715$	1.05158	+	1.82138i	0.0393267	+	0.0681159i
$716$	11.5504	+	20.0059i	0.431660	+	0.747657i
$717$	−31.4265	+	29.4934i	−1.17364	+	1.10145i
$718$	2.13742	−	3.70212i	0.0797679	−	0.138162i
$719$	−28.4305			−1.06028			−0.530140	−	0.847910i	$-0.677861\pi$
$719$	−28.4305			−1.06028			−0.530140	+	0.847910i	$0.677861\pi$
$720$	−1.60608	+	0.796044i	−0.0598549	+	0.0296668i
$721$	−6.69156			−0.249207
$722$	4.54441	−	7.87114i	0.169125	−	0.292934i
$723$	−12.6626	−	3.82726i	−0.470925	−	0.142337i
$724$	20.5119	+	35.5277i	0.762320	+	1.32038i
$725$	−5.55038	−	9.61354i	−0.206136	−	0.357038i
$726$	−0.247710	−	1.05757i	−0.00919338	−	0.0392500i
$727$	24.4743	−	42.3907i	0.907700	−	1.57218i	0.0904492	−	0.995901i	$-0.471170\pi$
$727$	24.4743	−	42.3907i	0.907700	−	1.57218i	0.817251	−	0.576282i	$-0.195497\pi$
$728$	−14.2909			−0.529656
$729$	−5.10775	+	26.5125i	−0.189176	+	0.981943i
$730$	1.84453			0.0682691
$731$	−4.82390	+	8.35524i	−0.178418	+	0.309030i
$732$	−2.91668	−	12.4524i	−0.107804	−	0.460254i
$733$	12.7023	+	22.0011i	0.469171	+	0.812629i	0.999379	−	0.0352393i	$-0.0112193\pi$
$733$	12.7023	+	22.0011i	0.469171	+	0.812629i	−0.530208	+	0.847868i	$0.677886\pi$
$734$	−10.7160	−	18.5607i	−0.395535	−	0.685086i
$735$	0.551883	+	0.166807i	0.0203565	+	0.00615276i
$736$	9.57724	−	16.5883i	0.353022	−	0.611451i
$737$	−9.40755			−0.346532
$738$	−5.90879	+	2.92866i	−0.217505	+	0.107806i
$739$	17.8673			0.657259			0.328630	−	0.944459i	$-0.393413\pi$
$739$	17.8673			0.657259			0.328630	+	0.944459i	$0.393413\pi$
$740$	0.254800	−	0.441327i	0.00936663	−	0.0162235i
$741$	16.9407	−	15.8987i	0.622333	−	0.584053i
$742$	1.79724	+	3.11291i	0.0659787	+	0.114279i
$743$	15.9974	+	27.7084i	0.586889	+	1.01652i	0.994637	+	0.103427i	$0.0329807\pi$
$743$	15.9974	+	27.7084i	0.586889	+	1.01652i	−0.407749	+	0.913094i	$0.633686\pi$
$744$	−20.4686	+	19.2096i	−0.750415	+	0.704256i
$745$	−2.93469	+	5.08303i	−0.107519	+	0.186228i
$746$	13.3716			0.489570
$747$	1.92149	−	30.2471i	0.0703035	−	1.10668i
$748$	−3.76465			−0.137649
$749$	−6.41260	+	11.1069i	−0.234311	+	0.405839i
$750$	−3.42258	−	1.03447i	−0.124975	−	0.0377736i
$751$	−7.05725	−	12.2235i	−0.257523	−	0.446043i	0.708055	−	0.706157i	$-0.249573\pi$
$751$	−7.05725	−	12.2235i	−0.257523	−	0.446043i	−0.965578	+	0.260115i	$0.916240\pi$
$752$	−3.90039	−	6.75567i	−0.142232	−	0.246354i
$753$	−0.715818	−	3.05609i	−0.0260859	−	0.111370i
$754$	−4.49812	+	7.79097i	−0.163812	+	0.283730i
$755$	−2.97022			−0.108097
$756$	5.31586	+	6.43774i	0.193336	+	0.234138i
$757$	−47.3440			−1.72075			−0.860373	−	0.509665i	$-0.829769\pi$
$757$	−47.3440			−1.72075			−0.860373	+	0.509665i	$0.829769\pi$
$758$	−2.99424	+	5.18618i	−0.108756	+	0.188370i
$759$	1.33928	+	5.71788i	0.0486128	+	0.207546i
$760$	0.799163	+	1.38419i	0.0289887	+	0.0502099i
$761$	−25.8586	−	44.7883i	−0.937372	−	1.62358i	−0.770349	−	0.637623i	$-0.779918\pi$
$761$	−25.8586	−	44.7883i	−0.937372	−	1.62358i	−0.167023	−	0.985953i	$-0.553415\pi$
$762$	−17.1009	−	5.16876i	−0.619501	−	0.187244i
$763$	−3.42710	+	5.93591i	−0.124069	+	0.214895i
$764$	−19.9312			−0.721086
$765$	1.94805	+	1.29599i	0.0704318	+	0.0468567i
$766$	−10.9736			−0.396492
$767$	−7.02852	+	12.1737i	−0.253785	+	0.439569i
$768$	8.85279	−	8.30825i	0.319447	−	0.299798i
$769$	18.9550	+	32.8311i	0.683536	+	1.18392i	0.973895	+	0.227001i	$0.0728920\pi$
$769$	18.9550	+	32.8311i	0.683536	+	1.18392i	−0.290359	+	0.956918i	$0.593775\pi$
$770$	0.104372	+	0.180778i	0.00376131	+	0.00651478i
$771$	13.3706	−	12.5482i	0.481530	−	0.451911i
$772$	9.74827	−	16.8845i	0.350848	−	0.607686i
$773$	30.1901			1.08586			0.542931	−	0.839777i	$-0.317315\pi$
$773$	30.1901			1.08586			0.542931	+	0.839777i	$0.317315\pi$
$774$	6.44973	+	4.29085i	0.231831	+	0.154232i
$775$	35.0327			1.25841
$776$	12.5201	−	21.6854i	0.449445	−	0.778462i
$777$	−1.57977	−	0.477486i	−0.0566740	−	0.0171297i
$778$	6.97793	+	12.0861i	0.250171	+	0.433309i
$779$	−3.72083	−	6.44467i	−0.133313	−	0.230904i
$780$	−1.33479	−	5.69871i	−0.0477931	−	0.204047i
$781$	−5.64159	+	9.77152i	−0.201872	+	0.349653i
$782$	−4.98194			−0.178154
$783$	11.6343	−	1.95686i	0.415775	−	0.0699323i
$784$	1.79505			0.0641088
$785$	−1.52875	+	2.64787i	−0.0545633	+	0.0945065i
$786$	−0.533178	−	2.27634i	−0.0190178	−	0.0811942i
$787$	19.9957	+	34.6337i	0.712771	+	1.23456i	0.963813	+	0.266580i	$0.0858937\pi$
$787$	19.9957	+	34.6337i	0.712771	+	1.23456i	−0.251041	+	0.967976i	$0.580773\pi$
$788$	−4.94619	−	8.56705i	−0.176201	−	0.305189i
$789$	32.5806	+	9.84750i	1.15990	+	0.350580i
$790$	−0.171115	+	0.296379i	−0.00608799	+	0.0105447i
$791$	−19.0538			−0.677474
$792$	−0.430188	+	6.77182i	−0.0152861	+	0.240626i
$793$	29.0368			1.03113
$794$	−7.12637	+	12.3432i	−0.252906	+	0.438045i
$795$	−2.40965	+	2.26143i	−0.0854615	+	0.0802048i
$796$	14.2506	+	24.6827i	0.505099	+	0.874857i
$797$	22.7481	+	39.4008i	0.805778	+	1.39565i	0.915765	+	0.401715i	$0.131586\pi$
$797$	22.7481	+	39.4008i	0.805778	+	1.39565i	−0.109987	+	0.993933i	$0.535081\pi$
$798$	1.68142	−	1.57799i	0.0595215	−	0.0558603i
$799$	−5.09111	+	8.81806i	−0.180111	+	0.311961i
$800$	−27.6208			−0.976541
$801$	35.8403	−	17.7641i	1.26636	−	0.627663i
$802$	−23.2804			−0.822060
$803$	−4.41816	+	7.65248i	−0.155913	+	0.270050i
$804$	25.0609	+	7.57467i	0.883831	+	0.267138i
$805$	−0.564302	−	0.977401i	−0.0198890	−	0.0344488i
$806$	−14.1955	−	24.5874i	−0.500016	−	0.866054i
$807$	−7.85353	−	33.5296i	−0.276457	−	1.18030i
$808$	−4.95213	+	8.57734i	−0.174215	+	0.301750i
$809$	−53.7432			−1.88951			−0.944755	−	0.327778i	$-0.893700\pi$
$809$	−53.7432			−1.88951			−0.944755	+	0.327778i	$0.893700\pi$
$810$	1.13768	−	1.49505i	0.0399740	−	0.0525308i
$811$	49.4404			1.73609			0.868044	−	0.496487i	$-0.165377\pi$
$811$	49.4404			1.73609			0.868044	+	0.496487i	$0.165377\pi$
$812$	1.82401	−	3.15928i	0.0640103	−	0.110869i
$813$	−1.57817	−	6.73778i	−0.0553487	−	0.236304i
$814$	−0.298766	−	0.517478i	−0.0104718	−	0.0181376i
$815$	−1.29591	−	2.24459i	−0.0453938	−	0.0786244i
$816$	6.97324	+	2.10766i	0.244112	+	0.0737829i
$817$	−4.37073	+	7.57033i	−0.152913	+	0.264852i
$818$	15.9702			0.558383
$819$	−16.9833	+	8.41769i	−0.593444	+	0.294138i
$820$	−1.87476			−0.0654694
$821$	21.8654	−	37.8719i	0.763106	−	1.32174i	−0.178136	−	0.984006i	$-0.557007\pi$
$821$	21.8654	−	37.8719i	0.763106	−	1.32174i	0.941242	−	0.337733i	$-0.109660\pi$
$822$	9.80600	−	9.20283i	0.342024	−	0.320986i
$823$	−8.36662	−	14.4914i	−0.291642	−	0.505139i	0.682556	−	0.730833i	$-0.260868\pi$
$823$	−8.36662	−	14.4914i	−0.291642	−	0.505139i	−0.974198	+	0.225694i	$0.927535\pi$
$824$	7.56756	+	13.1074i	0.263628	+	0.456618i
$825$	6.17492	−	5.79510i	0.214983	−	0.201759i
$826$	−0.697601	+	1.20828i	−0.0242727	+	0.0420415i
$827$	47.2494			1.64302			0.821511	−	0.570193i	$-0.193132\pi$
$827$	47.2494			1.64302			0.821511	+	0.570193i	$0.193132\pi$
$828$	1.03613	−	16.3103i	0.0360081	−	0.566823i
$829$	−42.1657			−1.46447			−0.732237	−	0.681050i	$-0.761524\pi$
$829$	−42.1657			−1.46447			−0.732237	+	0.681050i	$0.761524\pi$
$830$	−1.05444	+	1.82634i	−0.0366001	+	0.0633933i
$831$	−10.6555	−	3.22063i	−0.369635	−	0.111722i
$832$	−0.149518	−	0.258973i	−0.00518361	−	0.00897827i
$833$	−1.17152	−	2.02914i	−0.0405909	−	0.0703055i
$834$	−1.52699	−	6.51927i	−0.0528752	−	0.225744i
$835$	1.79627	−	3.11123i	0.0621625	−	0.107669i
$836$	−3.41099			−0.117972
$837$	−13.0099	+	34.8851i	−0.449690	+	1.20581i
$838$	16.3892			0.566155
$839$	−11.2518	+	19.4887i	−0.388455	+	0.672824i	−0.992242	−	0.124322i	$-0.960325\pi$
$839$	−11.2518	+	19.4887i	−0.388455	+	0.672824i	0.603787	+	0.797146i	$0.293658\pi$
$840$	−0.297390	−	1.26967i	−0.0102609	−	0.0438078i
$841$	11.9225	+	20.6504i	0.411120	+	0.712082i
$842$	1.65680	+	2.86966i	0.0570971	+	0.0988951i
$843$	−15.3201	−	4.63050i	−0.527652	−	0.159483i
$844$	21.3533	−	36.9851i	0.735012	−	1.27308i
$845$	8.96112			0.308272
$846$	6.80700	+	4.52854i	0.234029	+	0.155694i
$847$	−1.00000			−0.0343604
$848$	−5.14443	+	8.91041i	−0.176660	+	0.305985i
$849$	−29.3450	+	27.5400i	−1.00712	+	0.945169i
$850$	3.59198	+	6.22149i	0.123204	+	0.213395i
$851$	1.61532	+	2.79782i	0.0553725	+	0.0959080i
$852$	22.8965	−	21.4881i	0.784420	−	0.736170i
$853$	26.7887	−	46.3995i	0.917229	−	1.58869i	0.113624	−	0.993524i	$-0.463754\pi$
$853$	26.7887	−	46.3995i	0.917229	−	1.58869i	0.803605	−	0.595163i	$-0.202913\pi$
$854$	2.88199			0.0986195
$855$	1.76505	+	1.17424i	0.0603633	+	0.0401583i
$856$	29.0083			0.991484
$857$	1.29494	−	2.24290i	0.0442343	−	0.0766161i	−0.843061	−	0.537819i	$-0.819249\pi$
$857$	1.29494	−	2.24290i	0.0442343	−	0.0766161i	0.887295	+	0.461203i	$0.152582\pi$
$858$	−6.56937	−	1.98559i	−0.224275	−	0.0677870i
$859$	−4.47568	−	7.75211i	−0.152708	−	0.264498i	0.779514	−	0.626385i	$-0.215466\pi$
$859$	−4.47568	−	7.75211i	−0.152708	−	0.264498i	−0.932222	+	0.361886i	$0.882133\pi$
$860$	1.10111	+	1.90718i	0.0375475	+	0.0650341i
$861$	1.38462	+	5.91147i	0.0471878	+	0.201462i
$862$	−1.93182	+	3.34602i	−0.0657982	+	0.113966i
$863$	−32.7780			−1.11578			−0.557889	−	0.829916i	$-0.688388\pi$
$863$	−32.7780			−1.11578			−0.557889	+	0.829916i	$0.688388\pi$
$864$	10.2574	−	27.5044i	0.348964	−	0.935719i
$865$	6.17214			0.209859
$866$	−4.69117	+	8.12535i	−0.159413	+	0.276111i
$867$	4.54652	+	19.4108i	0.154408	+	0.659225i
$868$	5.75637	+	9.97033i	0.195384	+	0.338415i
$869$	−0.819734	−	1.41982i	−0.0278076	−	0.0481641i
$870$	−0.785790	−	0.237505i	−0.0266408	−	0.00805218i
$871$	−29.7199	+	51.4764i	−1.00702	+	1.74421i
$872$	15.5030			0.524998
$873$	2.10561	−	33.1456i	0.0712643	−	1.12181i
$874$	−4.51393			−0.152686
$875$	−1.64589	+	2.85076i	−0.0556412	+	0.0963734i
$876$	17.9312	−	16.8282i	0.605838	−	0.568572i
$877$	−24.9187	−	43.1604i	−0.841443	−	1.45742i	−0.888674	−	0.458539i	$-0.848373\pi$
$877$	−24.9187	−	43.1604i	−0.841443	−	1.45742i	0.0472310	−	0.998884i	$-0.484960\pi$
$878$	−0.476276	−	0.824935i	−0.0160735	−	0.0278402i
$879$	32.3674	−	30.3765i	1.09173	−	1.02457i
$880$	−0.298755	+	0.517459i	−0.0100710	+	0.0174435i
$881$	−10.4600			−0.352408			−0.176204	−	0.984354i	$-0.556382\pi$
$881$	−10.4600			−0.352408			−0.176204	+	0.984354i	$0.556382\pi$
$882$	−1.68564	+	0.835481i	−0.0567585	+	0.0281321i
$883$	46.8773			1.57755			0.788773	−	0.614685i	$-0.210717\pi$
$883$	46.8773			1.57755			0.788773	+	0.614685i	$0.210717\pi$
$884$	−11.8931	+	20.5995i	−0.400009	+	0.692835i
$885$	−1.22783	−	0.371113i	−0.0412732	−	0.0124748i
$886$	−5.18753	−	8.98506i	−0.174278	−	0.301859i
$887$	−22.0725	−	38.2307i	−0.741123	−	1.28366i	−0.951984	−	0.306147i	$-0.900960\pi$
$887$	−22.0725	−	38.2307i	−0.741123	−	1.28366i	0.210861	−	0.977516i	$-0.432373\pi$
$888$	0.851284	+	3.63444i	0.0285672	+	0.121964i
$889$	−8.22370	+	14.2439i	−0.275814	+	0.477724i
$890$	−2.78334			−0.0932976
$891$	3.47753	+	8.30101i	0.116502	+	0.278094i
$892$	18.9429			0.634256
$893$	−4.61284	+	7.98968i	−0.154363	+	0.267365i
$894$	−4.36783	−	18.6479i	−0.146082	−	0.623679i
$895$	−2.39290	−	4.14462i	−0.0799858	−	0.138539i
$896$	−5.66418	−	9.81065i	−0.189227	−	0.327751i
$897$	35.5182	+	10.7354i	1.18592	+	0.358444i
$898$	−2.93018	+	5.07522i	−0.0977813	+	0.169362i
$899$	16.2686			0.542589
$900$	−21.1155	+	10.4658i	−0.703851	+	0.348860i
$901$	13.4299			0.447414
$902$	−1.09913	+	1.90374i	−0.0365969	+	0.0633877i
$903$	5.20045	−	4.88057i	0.173060	−	0.162415i
$904$	21.5481	+	37.3224i	0.716680	+	1.24133i
$905$	−4.24945	−	7.36026i	−0.141257	−	0.244663i
$906$	7.06736	−	6.63265i	0.234797	−	0.220355i
$907$	−0.849219	+	1.47089i	−0.0281978	+	0.0488401i	−0.879780	−	0.475381i	$-0.842310\pi$
$907$	−0.849219	+	1.47089i	−0.0281978	+	0.0488401i	0.851582	+	0.524221i	$0.175644\pi$
$908$	−1.40897			−0.0467582
$909$	−0.832844	+	13.1102i	−0.0276237	+	0.434839i
$910$	1.31891			0.0437215
$911$	23.0305	−	39.8900i	0.763036	−	1.32162i	−0.178243	−	0.983986i	$-0.557041\pi$
$911$	23.0305	−	39.8900i	0.763036	−	1.32162i	0.941279	−	0.337630i	$-0.109625\pi$
$912$	6.31816	+	1.90967i	0.209215	+	0.0632353i
$913$	−5.05135	−	8.74919i	−0.167175	−	0.289556i
$914$	−2.77788	−	4.81143i	−0.0918841	−	0.159148i
$915$	0.604248	+	2.57976i	0.0199758	+	0.0852842i
$916$	3.20778	−	5.55604i	0.105988	−	0.183577i
$917$	−2.15243			−0.0710795
$918$	−7.52921	+	1.26640i	−0.248501	+	0.0417973i
$919$	−43.8015			−1.44488			−0.722438	−	0.691435i	$-0.756979\pi$
$919$	−43.8015			−1.44488			−0.722438	+	0.691435i	$0.756979\pi$
$920$	−1.27635	+	2.21071i	−0.0420801	+	0.0728848i
$921$	6.26438	+	26.7450i	0.206418	+	0.881277i
$922$	−0.689932	−	1.19500i	−0.0227217	−	0.0393552i
$923$	35.6453	+	61.7395i	1.17328	+	2.03218i
$924$	2.66392	+	0.805170i	0.0876365	+	0.0264881i
$925$	2.32930	−	4.03446i	0.0765868	−	0.132652i
$926$	16.0361			0.526979
$927$	16.7138	+	11.1193i	0.548955	+	0.365207i
$928$	−12.8266			−0.421055
$929$	−2.88290	+	4.99333i	−0.0945850	+	0.163826i	−0.909435	−	0.415845i	$-0.863486\pi$
$929$	−2.88290	+	4.99333i	−0.0945850	+	0.163826i	0.814850	+	0.579671i	$0.196819\pi$
$930$	1.88905	−	1.77285i	0.0619444	−	0.0581342i
$931$	−1.06147	−	1.83852i	−0.0347882	−	0.0602550i
$932$	10.1031	+	17.4991i	0.330939	+	0.573204i
$933$	28.9737	−	27.1915i	0.948557	−	0.890210i
$934$	−0.118725	+	0.205639i	−0.00388482	+	0.00672870i
$935$	0.779921			0.0255061
$936$	35.6951	+	23.7471i	1.16673	+	0.776200i
$937$	−13.2027			−0.431314			−0.215657	−	0.976469i	$-0.569189\pi$
$937$	−13.2027			−0.431314			−0.215657	+	0.976469i	$0.569189\pi$
$938$	−2.94979	+	5.10919i	−0.0963141	+	0.166821i
$939$	37.1377	+	11.2249i	1.21194	+	0.366310i
$940$	1.16210	+	2.01282i	0.0379036	+	0.0656510i
$941$	−23.8017	−	41.2257i	−0.775913	−	1.34392i	−0.934280	−	0.356540i	$-0.883956\pi$
$941$	−23.8017	−	41.2257i	−0.775913	−	1.34392i	0.158368	−	0.987380i	$-0.449377\pi$
$942$	−2.27531	−	9.71413i	−0.0741335	−	0.316503i
$943$	5.94258	−	10.2929i	0.193517	−	0.335181i
$944$	−3.99363			−0.129982
$945$	−1.10128	−	1.33370i	−0.0358248	−	0.0433854i
$946$	2.58221			0.0839550
$947$	−24.8875	+	43.1065i	−0.808736	+	1.40077i	0.105004	+	0.994472i	$0.466514\pi$
$947$	−24.8875	+	43.1065i	−0.808736	+	1.40077i	−0.913740	+	0.406300i	$0.866819\pi$
$948$	1.04051	+	4.44231i	0.0337941	+	0.144280i
$949$	27.9153	+	48.3508i	0.906170	+	1.56953i
$950$	3.25454	+	5.63703i	0.105591	+	0.182889i
$951$	−12.8602	−	3.88698i	−0.417019	−	0.126044i
$952$	−2.64978	+	4.58955i	−0.0858798	+	0.148748i
$953$	27.4003			0.887583			0.443792	−	0.896130i	$-0.353633\pi$
$953$	27.4003			0.887583			0.443792	+	0.896130i	$0.353633\pi$
$954$	0.683653	−	10.7617i	0.0221341	−	0.348424i
$955$	4.12914			0.133616
$956$	19.9901	−	34.6239i	0.646527	−	1.11982i
$957$	2.86753	−	2.69115i	0.0926942	−	0.0869925i
$958$	6.89557	+	11.9435i	0.222786	+	0.385876i
$959$	−6.19047	−	10.7222i	−0.199901	−	0.346238i
$960$	0.0198969	−	0.0186730i	0.000642170	−	0.000602670i
$961$	−10.1709	+	17.6165i	−0.328094	+	0.568275i
$962$	−3.77540			−0.121724
$963$	34.4735	−	17.0866i	1.11089	−	0.550608i
$964$	12.2712			0.395229
$965$	−2.01955	+	3.49796i	−0.0650115	+	0.112603i
$966$	3.52529	+	1.06552i	0.113424	+	0.0342825i
$967$	−15.3792	−	26.6375i	−0.494561	−	0.856604i	0.505420	−	0.862874i	$-0.331338\pi$
$967$	−15.3792	−	26.6375i	−0.494561	−	0.856604i	−0.999980	+	0.00626935i	$0.998004\pi$
$968$	1.13091	+	1.95880i	0.0363489	+	0.0629581i
$969$	−1.96479	−	8.38843i	−0.0631183	−	0.269475i
$970$	−1.15548	+	2.00135i	−0.0371003	+	0.0642596i
$971$	50.4500			1.61902			0.809509	−	0.587108i	$-0.199733\pi$
$971$	50.4500			1.61902			0.809509	+	0.587108i	$0.199733\pi$
$972$	−2.58013	−	24.9132i	−0.0827578	−	0.799092i
$973$	−6.16441			−0.197622
$974$	−3.81337	+	6.60494i	−0.122188	+	0.211636i
$975$	−12.2022	−	52.0957i	−0.390783	−	1.66840i
$976$	4.12470	+	7.14420i	0.132029	+	0.228680i
$977$	20.9072	+	36.2124i	0.668882	+	1.15854i	0.978217	+	0.207584i	$0.0665601\pi$
$977$	20.9072	+	36.2124i	0.668882	+	1.15854i	−0.309335	+	0.950953i	$0.600107\pi$
$978$	8.09578	+	2.44695i	0.258874	+	0.0782448i
$979$	6.66686	−	11.5473i	0.213074	−	0.369055i
$980$	−0.534826			−0.0170844
$981$	18.4237	−	9.13164i	0.588225	−	0.291551i
$982$	−16.6989			−0.532883
$983$	−2.22174	+	3.84817i	−0.0708625	+	0.122737i	−0.899280	−	0.437374i	$-0.855908\pi$
$983$	−2.22174	+	3.84817i	−0.0708625	+	0.122737i	0.828417	+	0.560112i	$0.189242\pi$
$984$	10.0135	−	9.39754i	0.319218	−	0.299583i
$985$	1.02470	+	1.77483i	0.0326497	+	0.0565509i
$986$	1.66806	+	2.88916i	0.0531217	+	0.0920095i
$987$	5.48852	−	5.15092i	0.174702	−	0.163956i
$988$	−10.7759	+	18.6643i	−0.342826	+	0.593791i
$989$	−13.9611			−0.443937
$990$	0.0397022	−	0.624973i	0.00126182	−	0.0198629i
$991$	−7.10930			−0.225834			−0.112917	−	0.993604i	$-0.536019\pi$
$991$	−7.10930			−0.225834			−0.112917	+	0.993604i	$0.536019\pi$
$992$	20.2397	−	35.0561i	0.642610	−	1.11303i
$993$	−14.4380	−	4.36389i	−0.458176	−	0.138484i
$994$	3.53791	+	6.12783i	0.112216	+	0.194363i
$995$	−2.95229	−	5.11352i	−0.0935939	−	0.162109i
$996$	6.41179	+	27.3743i	0.203165	+	0.867388i
$997$	−2.20532	+	3.81973i	−0.0698432	+	0.120972i	−0.898832	−	0.438293i	$-0.855583\pi$
$997$	−2.20532	+	3.81973i	−0.0698432	+	0.120972i	0.828989	+	0.559265i	$0.188917\pi$
$998$	−8.93049			−0.282690
$999$	3.15244	+	3.81774i	0.0997388	+	0.120788i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	693.2.j.h.232.6	✓	28
9.2	odd	6		6237.2.a.be.1.6		14
9.4	even	3	inner	693.2.j.h.463.6	yes	28
9.7	even	3		6237.2.a.bf.1.9		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
693.2.j.h.232.6	✓	28	1.1	even	1	trivial
693.2.j.h.463.6	yes	28	9.4	even	3	inner
6237.2.a.be.1.6		14	9.2	odd	6
6237.2.a.bf.1.9		14	9.7	even	3

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:	\( N \)	\(=\)	\( 693 = 3^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	693.j (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.313556 + 0.543094i) q^{2} +(-0.395002 - 1.68641i) q^{3} +(0.803366 + 1.39147i) q^{4} +(-0.166433 - 0.288270i) q^{5} +(1.03973 + 0.314260i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.26182 q^{8} +(-2.68795 + 1.33227i) q^{9} +O(q^{10})\)	\(q+(-0.313556 + 0.543094i) q^{2} +(-0.395002 - 1.68641i) q^{3} +(0.803366 + 1.39147i) q^{4} +(-0.166433 - 0.288270i) q^{5} +(1.03973 + 0.314260i) q^{6} +(0.500000 - 0.866025i) q^{7} -2.26182 q^{8} +(-2.68795 + 1.33227i) q^{9} +0.208744 q^{10} +(-0.500000 + 0.866025i) q^{11} +(2.02926 - 1.90444i) q^{12} +(3.15916 + 5.47182i) q^{13} +(0.313556 + 0.543094i) q^{14} +(-0.420400 + 0.394541i) q^{15} +(-0.897524 + 1.55456i) q^{16} +2.34305 q^{17} +(0.119274 - 1.87755i) q^{18} +2.12294 q^{19} +(0.267413 - 0.463173i) q^{20} +(-1.65797 - 0.501123i) q^{21} +(-0.313556 - 0.543094i) q^{22} +(1.69528 + 2.93632i) q^{23} +(0.893424 + 3.81436i) q^{24} +(2.44460 - 4.23417i) q^{25} -3.96229 q^{26} +(3.30849 + 4.00673i) q^{27} +1.60673 q^{28} +(1.13523 - 1.96628i) q^{29} +(-0.0824543 - 0.352028i) q^{30} +(3.58266 + 6.20535i) q^{31} +(-2.82467 - 4.89247i) q^{32} +(1.65797 + 0.501123i) q^{33} +(-0.734676 + 1.27250i) q^{34} -0.332866 q^{35} +(-4.01322 - 2.66990i) q^{36} +0.952833 q^{37} +(-0.665659 + 1.15296i) q^{38} +(7.97985 - 7.48901i) q^{39} +(0.376442 + 0.652017i) q^{40} +(-1.75268 - 3.03573i) q^{41} +(0.792024 - 0.743306i) q^{42} +(-2.05881 + 3.56597i) q^{43} -1.60673 q^{44} +(0.831417 + 0.553122i) q^{45} -2.12626 q^{46} +(-2.17286 + 3.76350i) q^{47} +(2.97614 + 0.899539i) q^{48} +(-0.500000 - 0.866025i) q^{49} +(1.53304 + 2.65530i) q^{50} +(-0.925507 - 3.95133i) q^{51} +(-5.07592 + 8.79174i) q^{52} +5.73180 q^{53} +(-3.21343 + 0.540491i) q^{54} +0.332866 q^{55} +(-1.13091 + 1.95880i) q^{56} +(-0.838564 - 3.58014i) q^{57} +(0.711918 + 1.23308i) q^{58} +(1.11240 + 1.92674i) q^{59} +(-0.886728 - 0.268014i) q^{60} +(2.29783 - 3.97995i) q^{61} -4.49346 q^{62} +(-0.190195 + 2.99396i) q^{63} -0.0473285 q^{64} +(1.05158 - 1.82138i) q^{65} +(-0.792024 + 0.743306i) q^{66} +(4.70378 + 8.14718i) q^{67} +(1.88232 + 3.26028i) q^{68} +(4.28219 - 4.01879i) q^{69} +(0.104372 - 0.180778i) q^{70} +11.2832 q^{71} +(6.07966 - 3.01335i) q^{72} +8.83632 q^{73} +(-0.298766 + 0.517478i) q^{74} +(-8.10616 - 2.45009i) q^{75} +(1.70549 + 2.95400i) q^{76} +(0.500000 + 0.866025i) q^{77} +(1.56511 + 6.68204i) q^{78} +(-0.819734 + 1.41982i) q^{79} +0.597510 q^{80} +(5.45012 - 7.16213i) q^{81} +2.19825 q^{82} +(-5.05135 + 8.74919i) q^{83} +(-0.634662 - 2.70961i) q^{84} +(-0.389960 - 0.675431i) q^{85} +(-1.29111 - 2.23626i) q^{86} +(-3.76437 - 1.13778i) q^{87} +(1.13091 - 1.95880i) q^{88} -13.3337 q^{89} +(-0.561093 + 0.278103i) q^{90} +6.31831 q^{91} +(-2.72387 + 4.71787i) q^{92} +(9.04960 - 8.49295i) q^{93} +(-1.36263 - 2.36014i) q^{94} +(-0.353327 - 0.611980i) q^{95} +(-7.13496 + 6.69608i) q^{96} +(-5.53540 + 9.58759i) q^{97} +0.627112 q^{98} +(0.190195 - 2.99396i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q - q^{2} - 2 q^{3} - 17 q^{4} - 4 q^{5} + q^{6} + 14 q^{7} + 24 q^{8} + 2 q^{9}+O(q^{10}) \) 28 * q - q^2 - 2 * q^3 - 17 * q^4 - 4 * q^5 + q^6 + 14 * q^7 + 24 * q^8 + 2 * q^9	\( 28 q - q^{2} - 2 q^{3} - 17 q^{4} - 4 q^{5} + q^{6} + 14 q^{7} + 24 q^{8} + 2 q^{9} + 20 q^{10} - 14 q^{11} + 20 q^{12} - 9 q^{13} + q^{14} - 5 q^{15} - 19 q^{16} + 24 q^{17} - 13 q^{18} + 32 q^{19} - 8 q^{20} - q^{21} - q^{22} + 12 q^{23} - 42 q^{24} - 16 q^{25} - 10 q^{26} - 26 q^{27} - 34 q^{28} - 8 q^{29} + 73 q^{30} - 15 q^{31} - 10 q^{32} + q^{33} - 14 q^{34} - 8 q^{35} - 17 q^{36} - 2 q^{37} + 14 q^{38} + 22 q^{39} + 3 q^{40} - 20 q^{41} - 13 q^{42} - 39 q^{43} + 34 q^{44} - 13 q^{45} + 8 q^{46} - 29 q^{47} + 38 q^{48} - 14 q^{49} - 7 q^{50} - 29 q^{51} - 59 q^{52} + 24 q^{53} + q^{54} + 8 q^{55} + 12 q^{56} + 6 q^{57} - 23 q^{58} - 3 q^{59} - q^{60} - 26 q^{61} - 8 q^{62} - 5 q^{63} + 36 q^{64} - 8 q^{65} + 13 q^{66} - 35 q^{67} + 16 q^{68} + 41 q^{69} + 10 q^{70} - 28 q^{71} + 21 q^{72} + 48 q^{73} - q^{74} + 23 q^{75} - 55 q^{76} + 14 q^{77} - 71 q^{78} + 15 q^{79} + 170 q^{80} - 10 q^{81} + 30 q^{82} - 6 q^{83} + 13 q^{84} + 28 q^{85} - 6 q^{86} - 12 q^{88} - 76 q^{89} - 19 q^{90} - 18 q^{91} + 94 q^{92} + 7 q^{93} - 32 q^{94} - 8 q^{95} + 65 q^{96} - 25 q^{97} + 2 q^{98} + 5 q^{99}+O(q^{100}) \) 28 * q - q^2 - 2 * q^3 - 17 * q^4 - 4 * q^5 + q^6 + 14 * q^7 + 24 * q^8 + 2 * q^9 + 20 * q^10 - 14 * q^11 + 20 * q^12 - 9 * q^13 + q^14 - 5 * q^15 - 19 * q^16 + 24 * q^17 - 13 * q^18 + 32 * q^19 - 8 * q^20 - q^21 - q^22 + 12 * q^23 - 42 * q^24 - 16 * q^25 - 10 * q^26 - 26 * q^27 - 34 * q^28 - 8 * q^29 + 73 * q^30 - 15 * q^31 - 10 * q^32 + q^33 - 14 * q^34 - 8 * q^35 - 17 * q^36 - 2 * q^37 + 14 * q^38 + 22 * q^39 + 3 * q^40 - 20 * q^41 - 13 * q^42 - 39 * q^43 + 34 * q^44 - 13 * q^45 + 8 * q^46 - 29 * q^47 + 38 * q^48 - 14 * q^49 - 7 * q^50 - 29 * q^51 - 59 * q^52 + 24 * q^53 + q^54 + 8 * q^55 + 12 * q^56 + 6 * q^57 - 23 * q^58 - 3 * q^59 - q^60 - 26 * q^61 - 8 * q^62 - 5 * q^63 + 36 * q^64 - 8 * q^65 + 13 * q^66 - 35 * q^67 + 16 * q^68 + 41 * q^69 + 10 * q^70 - 28 * q^71 + 21 * q^72 + 48 * q^73 - q^74 + 23 * q^75 - 55 * q^76 + 14 * q^77 - 71 * q^78 + 15 * q^79 + 170 * q^80 - 10 * q^81 + 30 * q^82 - 6 * q^83 + 13 * q^84 + 28 * q^85 - 6 * q^86 - 12 * q^88 - 76 * q^89 - 19 * q^90 - 18 * q^91 + 94 * q^92 + 7 * q^93 - 32 * q^94 - 8 * q^95 + 65 * q^96 - 25 * q^97 + 2 * q^98 + 5 * q^99

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