LMFDB - Embedded newform 966.2.s.b.181.15

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [966,2,Mod(97,966)]

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, 11, 1]))

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

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

chi := DirichletCharacter("966.97");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 966 = 2 \cdot 3 \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	966.s (of order $22$, 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:	$160$
Relative dimension:	$16$ over $\Q(\zeta_{22})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{22}]$

Embedding invariants

Embedding label			181.15
Character	$\chi$	$=$	966.181
Dual form			966.2.s.b.475.15

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.30682 - 2.66222i) q^{5} +(-0.281733 + 0.959493i) q^{6} +(1.52570 + 2.16153i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(q+(0.142315 + 0.989821i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.30682 - 2.66222i) q^{5} +(-0.281733 + 0.959493i) q^{6} +(1.52570 + 2.16153i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +(2.96342 + 1.90447i) q^{10} +(3.55357 + 0.510926i) q^{11} +(-0.989821 - 0.142315i) q^{12} +(3.07793 - 4.78935i) q^{13} +(-1.92240 + 1.81779i) q^{14} +(3.20429 - 1.46335i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-6.14743 - 1.80505i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(0.796653 - 0.233918i) q^{19} +(-1.46335 + 3.20429i) q^{20} +(0.489895 + 2.60000i) q^{21} +3.59011i q^{22} +(-3.28405 - 3.49500i) q^{23} -1.00000i q^{24} +(-1.05439 - 7.33343i) q^{25} +(5.17864 + 2.36501i) q^{26} +(0.281733 + 0.959493i) q^{27} +(-2.07288 - 1.64414i) q^{28} +(-4.72570 - 1.38759i) q^{29} +(1.90447 + 2.96342i) q^{30} +(2.72145 - 1.24284i) q^{31} +(0.654861 + 0.755750i) q^{32} +(3.02019 + 1.94096i) q^{33} +(0.911804 - 6.34174i) q^{34} +(9.27400 + 0.924526i) q^{35} +(-0.841254 - 0.540641i) q^{36} +(-6.97851 + 6.04691i) q^{37} +(0.344913 + 0.755254i) q^{38} +(4.78935 - 3.07793i) q^{39} +(-3.37993 - 0.992436i) q^{40} +(5.97516 + 5.17751i) q^{41} +(-2.50382 + 0.854927i) q^{42} +(6.37214 + 2.91006i) q^{43} +(-3.55357 + 0.510926i) q^{44} +3.52262 q^{45} +(2.99205 - 3.74802i) q^{46} +7.07236i q^{47} +(0.989821 - 0.142315i) q^{48} +(-2.34446 + 6.59572i) q^{49} +(7.10873 - 2.08731i) q^{50} +(-4.84205 - 4.19566i) q^{51} +(-1.60394 + 5.46251i) q^{52} +(2.34381 + 3.64704i) q^{53} +(-0.909632 + 0.415415i) q^{54} +(9.55766 - 8.28176i) q^{55} +(1.33240 - 2.28576i) q^{56} +(0.821834 + 0.118162i) q^{57} +(0.700930 - 4.87507i) q^{58} +(-1.74175 + 2.71022i) q^{59} +(-2.66222 + 2.30682i) q^{60} +(-0.467439 - 1.02355i) q^{61} +(1.61750 + 2.51687i) q^{62} +(-0.634455 + 2.56855i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-5.65006 - 19.2423i) q^{65} +(-1.49139 + 3.26568i) q^{66} +(5.21182 - 0.749346i) q^{67} +6.40695 q^{68} +(-1.53541 - 4.54340i) q^{69} +(0.404713 + 9.31118i) q^{70} +(-1.25825 - 8.75133i) q^{71} +(0.415415 - 0.909632i) q^{72} +(2.33325 + 7.94631i) q^{73} +(-6.97851 - 6.04691i) q^{74} +(2.08731 - 7.10873i) q^{75} +(-0.698480 + 0.448886i) q^{76} +(4.31731 + 8.46068i) q^{77} +(3.72820 + 4.30257i) q^{78} +(-5.15697 + 8.02440i) q^{79} +(0.501321 - 3.48676i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-4.27445 + 6.65118i) q^{82} +(-6.24299 - 7.20479i) q^{83} +(-1.20256 - 2.35666i) q^{84} +(-18.9865 + 12.2019i) q^{85} +(-1.97359 + 6.72142i) q^{86} +(-3.72222 - 3.22532i) q^{87} +(-1.01145 - 3.44469i) q^{88} +(5.51664 - 12.0797i) q^{89} +(0.501321 + 3.48676i) q^{90} +(15.0484 - 0.654080i) q^{91} +(4.13568 + 2.42820i) q^{92} +2.99181 q^{93} +(-7.00038 + 1.00650i) q^{94} +(1.21500 - 2.66047i) q^{95} +(0.281733 + 0.959493i) q^{96} +(-3.40095 + 3.92491i) q^{97} +(-6.86224 - 1.38193i) q^{98} +(1.94096 + 3.02019i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9}+O(q^{10}) $ 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9	$ 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9} + 22 q^{14} - 16 q^{16} - 16 q^{18} - 52 q^{23} - 48 q^{25} + 22 q^{28} - 12 q^{29} + 16 q^{32} + 22 q^{35} + 16 q^{36} + 22 q^{37} - 4 q^{39} + 154 q^{43} + 8 q^{46} + 4 q^{50} + 22 q^{51} + 88 q^{53} + 22 q^{57} + 56 q^{58} - 16 q^{64} + 16 q^{71} - 16 q^{72} + 22 q^{74} - 72 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} - 22 q^{84} - 68 q^{85} - 44 q^{86} + 44 q^{88} - 8 q^{92} - 8 q^{93} - 66 q^{95} + 66 q^{98} - 66 q^{99}+O(q^{100}) $ 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9 + 22 * q^14 - 16 * q^16 - 16 * q^18 - 52 * q^23 - 48 * q^25 + 22 * q^28 - 12 * q^29 + 16 * q^32 + 22 * q^35 + 16 * q^36 + 22 * q^37 - 4 * q^39 + 154 * q^43 + 8 * q^46 + 4 * q^50 + 22 * q^51 + 88 * q^53 + 22 * q^57 + 56 * q^58 - 16 * q^64 + 16 * q^71 - 16 * q^72 + 22 * q^74 - 72 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 - 22 * q^84 - 68 * q^85 - 44 * q^86 + 44 * q^88 - 8 * q^92 - 8 * q^93 - 66 * q^95 + 66 * q^98 - 66 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$323$	$829$	$925$
$\chi(n)$	$1$	$-1$	$e\left(\frac{5}{22}\right)$

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
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$3$	0.909632	+	0.415415i	0.525176	+	0.239840i
$4$	−0.959493	+	0.281733i	−0.479746	+	0.140866i
$5$	2.30682	−	2.66222i	1.03164	−	1.19058i	0.0502175	−	0.998738i	$-0.484009\pi$
$5$	2.30682	−	2.66222i	1.03164	−	1.19058i	0.981426	−	0.191842i	$-0.0614460\pi$
$6$	−0.281733	+	0.959493i	−0.115017	+	0.391711i
$7$	1.52570	+	2.16153i	0.576662	+	0.816983i
$7$	1.52570	+	2.16153i	0.576662	+	0.816983i
$8$	−0.415415	−	0.909632i	−0.146871	−	0.321603i
$9$	0.654861	+	0.755750i	0.218287	+	0.251917i
$10$	2.96342	+	1.90447i	0.937114	+	0.602247i
$11$	3.55357	+	0.510926i	1.07144	+	0.154050i	0.655390	−	0.755291i	$-0.272504\pi$
$11$	3.55357	+	0.510926i	1.07144	+	0.154050i	0.416052	+	0.909341i	$0.363414\pi$
$12$	−0.989821	−	0.142315i	−0.285737	−	0.0410828i
$13$	3.07793	−	4.78935i	0.853665	−	1.32833i	−0.0894949	−	0.995987i	$-0.528525\pi$
$13$	3.07793	−	4.78935i	0.853665	−	1.32833i	0.943159	−	0.332341i	$-0.107838\pi$
$14$	−1.92240	+	1.81779i	−0.513784	+	0.485825i
$15$	3.20429	−	1.46335i	0.827343	−	0.377835i
$16$	0.841254	−	0.540641i	0.210313	−	0.135160i
$17$	−6.14743	−	1.80505i	−1.49097	−	0.437788i	−0.568119	−	0.822946i	$-0.692329\pi$
$17$	−6.14743	−	1.80505i	−1.49097	−	0.437788i	−0.922851	+	0.385158i	$0.874147\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	0.796653	−	0.233918i	0.182765	−	0.0536645i	−0.189070	−	0.981964i	$-0.560547\pi$
$19$	0.796653	−	0.233918i	0.182765	−	0.0536645i	0.371834	+	0.928299i	$0.378729\pi$
$20$	−1.46335	+	3.20429i	−0.327215	+	0.716500i
$21$	0.489895	+	2.60000i	0.106904	+	0.567367i
$22$			3.59011i			0.765414i
$23$	−3.28405	−	3.49500i	−0.684772	−	0.728757i
$23$	−3.28405	−	3.49500i	−0.684772	−	0.728757i
$24$		−	1.00000i		−	0.204124i
$25$	−1.05439	−	7.33343i	−0.210878	−	1.46669i
$26$	5.17864	+	2.36501i	1.01562	+	0.463816i
$27$	0.281733	+	0.959493i	0.0542195	+	0.184655i
$28$	−2.07288	−	1.64414i	−0.391737	−	0.310713i
$29$	−4.72570	−	1.38759i	−0.877540	−	0.257669i	−0.188221	−	0.982127i	$-0.560272\pi$
$29$	−4.72570	−	1.38759i	−0.877540	−	0.257669i	−0.689319	+	0.724458i	$0.742090\pi$
$30$	1.90447	+	2.96342i	0.347707	+	0.541043i
$31$	2.72145	−	1.24284i	0.488787	−	0.223221i	−0.155747	−	0.987797i	$-0.549779\pi$
$31$	2.72145	−	1.24284i	0.488787	−	0.223221i	0.644534	+	0.764575i	$0.277051\pi$
$32$	0.654861	+	0.755750i	0.115764	+	0.133599i
$33$	3.02019	+	1.94096i	0.525748	+	0.337878i
$34$	0.911804	−	6.34174i	0.156373	−	1.08760i
$35$	9.27400	+	0.924526i	1.56759	+	0.156273i
$36$	−0.841254	−	0.540641i	−0.140209	−	0.0901068i
$37$	−6.97851	+	6.04691i	−1.14726	+	0.994106i	−0.147273	+	0.989096i	$0.547049\pi$
$37$	−6.97851	+	6.04691i	−1.14726	+	0.994106i	−0.999987	+	0.00501050i	$0.998405\pi$
$38$	0.344913	+	0.755254i	0.0559522	+	0.122518i
$39$	4.78935	−	3.07793i	0.766911	−	0.492863i
$40$	−3.37993	−	0.992436i	−0.534414	−	0.156918i
$41$	5.97516	+	5.17751i	0.933164	+	0.808591i	0.981740	−	0.190229i	$-0.0609229\pi$
$41$	5.97516	+	5.17751i	0.933164	+	0.808591i	−0.0485762	+	0.998819i	$0.515468\pi$
$42$	−2.50382	+	0.854927i	−0.386347	+	0.131918i
$43$	6.37214	+	2.91006i	0.971742	+	0.443780i	0.837061	−	0.547110i	$-0.184272\pi$
$43$	6.37214	+	2.91006i	0.971742	+	0.443780i	0.134681	+	0.990889i	$0.456999\pi$
$44$	−3.55357	+	0.510926i	−0.535721	+	0.0770250i
$45$	3.52262			0.525121
$46$	2.99205	−	3.74802i	0.441154	−	0.552615i
$47$			7.07236i			1.03161i	0.856706	+	0.515805i	$0.172507\pi$
$47$			7.07236i			1.03161i	−0.856706	+	0.515805i	$0.827493\pi$
$48$	0.989821	−	0.142315i	0.142868	−	0.0205414i
$49$	−2.34446	+	6.59572i	−0.334923	+	0.942246i
$50$	7.10873	−	2.08731i	1.00533	−	0.295191i
$51$	−4.84205	−	4.19566i	−0.678023	−	0.587510i
$52$	−1.60394	+	5.46251i	−0.222426	+	0.757513i
$53$	2.34381	+	3.64704i	0.321947	+	0.500960i	0.964072	−	0.265640i	$-0.0855833\pi$
$53$	2.34381	+	3.64704i	0.321947	+	0.500960i	−0.642125	+	0.766600i	$0.721947\pi$
$54$	−0.909632	+	0.415415i	−0.123785	+	0.0565308i
$55$	9.55766	−	8.28176i	1.28875	−	1.11671i
$56$	1.33240	−	2.28576i	0.178050	−	0.305448i
$57$	0.821834	+	0.118162i	0.108855	+	0.0156509i
$58$	0.700930	−	4.87507i	0.0920366	−	0.640129i
$59$	−1.74175	+	2.71022i	−0.226757	+	0.352841i	−0.935925	−	0.352198i	$-0.885434\pi$
$59$	−1.74175	+	2.71022i	−0.226757	+	0.352841i	0.709168	+	0.705039i	$0.249071\pi$
$60$	−2.66222	+	2.30682i	−0.343691	+	0.297810i
$61$	−0.467439	−	1.02355i	−0.0598495	−	0.131052i	0.877344	−	0.479862i	$-0.159313\pi$
$61$	−0.467439	−	1.02355i	−0.0598495	−	0.131052i	−0.937194	+	0.348810i	$0.886586\pi$
$62$	1.61750	+	2.51687i	0.205422	+	0.319643i
$63$	−0.634455	+	2.56855i	−0.0799339	+	0.323607i
$64$	−0.654861	+	0.755750i	−0.0818576	+	0.0944687i
$65$	−5.65006	−	19.2423i	−0.700803	−	2.38672i
$66$	−1.49139	+	3.26568i	−0.183577	+	0.401977i
$67$	5.21182	−	0.749346i	0.636725	−	0.0915472i	0.183610	−	0.982999i	$-0.441222\pi$
$67$	5.21182	−	0.749346i	0.636725	−	0.0915472i	0.453115	+	0.891452i	$0.350313\pi$
$68$	6.40695			0.776957
$69$	−1.53541	−	4.54340i	−0.184841	−	0.546962i
$70$	0.404713	+	9.31118i	0.0483724	+	1.11290i
$71$	−1.25825	−	8.75133i	−0.149327	−	1.03859i	−0.917325	−	0.398140i	$-0.869656\pi$
$71$	−1.25825	−	8.75133i	−0.149327	−	1.03859i	0.767998	−	0.640453i	$-0.221253\pi$
$72$	0.415415	−	0.909632i	0.0489571	−	0.107201i
$73$	2.33325	+	7.94631i	0.273086	+	0.930045i	0.975817	+	0.218589i	$0.0701455\pi$
$73$	2.33325	+	7.94631i	0.273086	+	0.930045i	−0.702731	+	0.711456i	$0.748036\pi$
$74$	−6.97851	−	6.04691i	−0.811235	−	0.702939i
$75$	2.08731	−	7.10873i	0.241022	−	0.820846i
$76$	−0.698480	+	0.448886i	−0.0801212	+	0.0514907i
$77$	4.31731	+	8.46068i	0.492003	+	0.964184i
$78$	3.72820	+	4.30257i	0.422135	+	0.487170i
$79$	−5.15697	+	8.02440i	−0.580204	+	0.902815i	−0.999988	−	0.00480859i	$-0.998469\pi$
$79$	−5.15697	+	8.02440i	−0.580204	+	0.902815i	0.419784	+	0.907624i	$0.362106\pi$
$80$	0.501321	−	3.48676i	0.0560494	−	0.389832i
$81$	−0.142315	+	0.989821i	−0.0158128	+	0.109980i
$82$	−4.27445	+	6.65118i	−0.472035	+	0.734500i
$83$	−6.24299	−	7.20479i	−0.685257	−	0.790828i	0.301425	−	0.953490i	$-0.402538\pi$
$83$	−6.24299	−	7.20479i	−0.685257	−	0.790828i	−0.986682	+	0.162661i	$0.947992\pi$
$84$	−1.20256	−	2.35666i	−0.131210	−	0.257133i
$85$	−18.9865	+	12.2019i	−2.05937	+	1.32348i
$86$	−1.97359	+	6.72142i	−0.212817	+	0.724789i
$87$	−3.72222	−	3.22532i	−0.399064	−	0.345791i
$88$	−1.01145	−	3.44469i	−0.107821	−	0.367205i
$89$	5.51664	−	12.0797i	0.584762	−	1.28045i	−0.353794	−	0.935323i	$-0.615108\pi$
$89$	5.51664	−	12.0797i	0.584762	−	1.28045i	0.938556	−	0.345127i	$-0.112164\pi$
$90$	0.501321	+	3.48676i	0.0528439	+	0.367537i
$91$	15.0484	−	0.654080i	1.57750	−	0.0685663i
$92$	4.13568	+	2.42820i	0.431174	+	0.253157i
$93$	2.99181			0.310237
$94$	−7.00038	+	1.00650i	−0.722034	+	0.103813i
$95$	1.21500	−	2.66047i	0.124656	−	0.272959i
$96$	0.281733	+	0.959493i	0.0287542	+	0.0979278i
$97$	−3.40095	+	3.92491i	−0.345314	+	0.398514i	−0.901666	−	0.432433i	$-0.857655\pi$
$97$	−3.40095	+	3.92491i	−0.345314	+	0.398514i	0.556352	+	0.830947i	$0.312201\pi$
$98$	−6.86224	−	1.38193i	−0.693190	−	0.139596i
$99$	1.94096	+	3.02019i	0.195074	+	0.303541i
$100$	3.07774	+	6.73932i	0.307774	+	0.673932i
$101$	−11.8294	+	10.2503i	−1.17707	+	1.01994i	−0.177715	+	0.984082i	$0.556870\pi$
$101$	−11.8294	+	10.2503i	−1.17707	+	1.01994i	−0.999357	+	0.0358564i	$0.988584\pi$
$102$	3.46386	−	5.38987i	0.342973	−	0.533677i
$103$	−1.69261	+	11.7724i	−0.166778	+	1.15997i	0.718713	+	0.695307i	$0.244732\pi$
$103$	−1.69261	+	11.7724i	−0.166778	+	1.15997i	−0.885490	+	0.464658i	$0.846177\pi$
$104$	−5.63517	−	0.810215i	−0.552574	−	0.0794481i
$105$	8.05187	+	4.69354i	0.785782	+	0.458043i
$106$	−3.27636	+	2.83898i	−0.318228	+	0.275746i
$107$	−3.66168	+	1.67223i	−0.353988	+	0.161661i	−0.584469	−	0.811416i	$-0.698697\pi$
$107$	−3.66168	+	1.67223i	−0.353988	+	0.161661i	0.230481	+	0.973077i	$0.425970\pi$
$108$	−0.540641	−	0.841254i	−0.0520232	−	0.0809497i
$109$	−2.37144	+	8.07637i	−0.227142	+	0.773576i	0.764507	+	0.644615i	$0.222982\pi$
$109$	−2.37144	+	8.07637i	−0.227142	+	0.773576i	−0.991650	+	0.128961i	$0.958836\pi$
$110$	9.55766	+	8.28176i	0.911287	+	0.789635i
$111$	−8.85985	+	2.60149i	−0.840940	+	0.246922i
$112$	2.45212	+	0.993541i	0.231703	+	0.0938808i
$113$	1.55627	−	0.223758i	0.146401	−	0.0210493i	−0.0687245	−	0.997636i	$-0.521893\pi$
$113$	1.55627	−	0.223758i	0.146401	−	0.0210493i	0.215126	+	0.976586i	$0.430984\pi$
$114$			0.830285i			0.0777633i
$115$	−16.8802	+	0.680521i	−1.57408	+	0.0634589i
$116$	4.92521			0.457294
$117$	5.63517	−	0.810215i	0.520972	−	0.0749044i
$118$	−2.93051	−	1.33832i	−0.269776	−	0.123202i
$119$	−5.47748	−	16.0418i	−0.502119	−	1.47055i
$120$	−2.66222	−	2.30682i	−0.243026	−	0.210583i
$121$	1.81238	+	0.532163i	0.164762	+	0.0483785i
$122$	0.946608	−	0.608348i	0.0857018	−	0.0550772i
$123$	3.28438	+	7.19180i	0.296143	+	0.648463i
$124$	−2.26106	+	1.95922i	−0.203049	+	0.175943i
$125$	−7.13841	−	4.58757i	−0.638478	−	0.410325i
$126$	−2.63270	−	0.262454i	−0.234540	−	0.0233813i
$127$	−1.47484	+	10.2577i	−0.130871	+	0.910228i	0.813551	+	0.581493i	$0.197531\pi$
$127$	−1.47484	+	10.2577i	−0.130871	+	0.910228i	−0.944422	+	0.328735i	$0.893378\pi$
$128$	−0.841254	−	0.540641i	−0.0743570	−	0.0477863i
$129$	4.58742	+	5.29416i	0.403900	+	0.466125i
$130$	18.2424	−	8.33102i	1.59996	−	0.730678i
$131$	1.33535	+	2.07785i	0.116670	+	0.181543i	0.894677	−	0.446713i	$-0.147406\pi$
$131$	1.33535	+	2.07785i	0.116670	+	0.181543i	−0.778007	+	0.628256i	$0.783769\pi$
$132$	−3.44469	−	1.01145i	−0.299821	−	0.0880355i
$133$	1.72108	+	1.36510i	0.149236	+	0.118369i
$134$	1.48344	+	5.05213i	0.128150	+	0.436437i
$135$	3.20429	+	1.46335i	0.275781	+	0.125945i
$136$	0.911804	+	6.34174i	0.0781866	+	0.543800i
$137$		−	19.4799i		−	1.66428i	−0.554563	−	0.832142i	$-0.687115\pi$
$137$		−	19.4799i		−	1.66428i	0.554563	−	0.832142i	$-0.312885\pi$
$138$	4.27865	−	2.16637i	0.364223	−	0.184414i
$139$		−	13.4542i		−	1.14117i	−0.821239	−	0.570584i	$-0.806717\pi$
$139$		−	13.4542i		−	1.14117i	0.821239	−	0.570584i	$-0.193283\pi$
$140$	−9.15881	+	1.72571i	−0.774061	+	0.145849i
$141$	−2.93797	+	6.43325i	−0.247421	+	0.541777i
$142$	8.48319	−	2.49089i	0.711894	−	0.209031i
$143$	13.3846	−	15.4467i	1.11928	−	1.29172i
$144$	0.959493	+	0.281733i	0.0799577	+	0.0234777i
$145$	−14.5954	+	9.37991i	−1.21208	+	0.778959i
$146$	−7.53337	+	3.44038i	−0.623466	+	0.284727i
$147$	−4.87256	+	5.02575i	−0.401882	+	0.414517i
$148$	4.99222	−	7.76804i	0.410358	−	0.638529i
$149$	13.8138	+	1.98612i	1.13167	+	0.162710i	0.682604	−	0.730789i	$-0.260848\pi$
$149$	13.8138	+	1.98612i	1.13167	+	0.162710i	0.449067	+	0.893498i	$0.351757\pi$
$150$	7.33343	+	1.05439i	0.598772	+	0.0860905i
$151$	−11.7555	−	7.55480i	−0.956649	−	0.614801i	−0.0335802	−	0.999436i	$-0.510691\pi$
$151$	−11.7555	−	7.55480i	−0.956649	−	0.614801i	−0.923069	+	0.384635i	$0.874327\pi$
$152$	−0.543721	−	0.627487i	−0.0441016	−	0.0508960i
$153$	−2.66154	−	5.82797i	−0.215173	−	0.471163i
$154$	−7.76015	+	5.47744i	−0.625330	+	0.441385i
$155$	2.96918	−	10.1121i	0.238491	−	0.812225i
$156$	−3.72820	+	4.30257i	−0.298495	+	0.344481i
$157$	−4.77063	+	1.40078i	−0.380737	+	0.111795i	−0.466500	−	0.884521i	$-0.654485\pi$
$157$	−4.77063	+	1.40078i	−0.380737	+	0.111795i	0.0857631	+	0.996316i	$0.472667\pi$
$158$	−8.67663	−	3.96249i	−0.690276	−	0.315238i
$159$	0.616970	+	4.29112i	0.0489289	+	0.340308i
$160$	3.52262			0.278487
$161$	2.54406	−	12.4309i	0.200500	−	0.979694i
$162$	−1.00000			−0.0785674
$163$	1.61952	+	11.2640i	0.126850	+	0.882263i	0.949512	+	0.313731i	$0.101579\pi$
$163$	1.61952	+	11.2640i	0.126850	+	0.882263i	−0.822662	+	0.568531i	$0.807512\pi$
$164$	−7.19180	−	3.28438i	−0.561585	−	0.256467i
$165$	12.1343	−	3.56296i	0.944655	−	0.277376i
$166$	6.24299	−	7.20479i	0.484550	−	0.559200i
$167$	4.67915	−	15.9357i	0.362084	−	1.23314i	−0.554122	−	0.832435i	$-0.686946\pi$
$167$	4.67915	−	15.9357i	0.362084	−	1.23314i	0.916206	−	0.400708i	$-0.131236\pi$
$168$	2.16153	−	1.52570i	0.166766	−	0.117711i
$169$	−8.06386	−	17.6574i	−0.620297	−	1.35826i
$170$	−14.7797	−	17.0567i	−1.13355	−	1.30819i
$171$	0.698480	+	0.448886i	0.0534141	+	0.0343272i
$172$	−6.93388	−	0.996941i	−0.528703	−	0.0760160i
$173$	−20.1978	−	2.90400i	−1.53561	−	0.220787i	−0.677989	−	0.735072i	$-0.737149\pi$
$173$	−20.1978	−	2.90400i	−1.53561	−	0.220787i	−0.857620	+	0.514284i	$0.828058\pi$
$174$	2.66277	−	4.14335i	0.201864	−	0.314106i
$175$	14.2428	−	13.4677i	1.07665	−	1.01807i
$176$	3.26568	−	1.49139i	0.246160	−	0.112417i
$177$	−2.71022	+	1.74175i	−0.203713	+	0.130918i
$178$	12.7419	+	3.74136i	0.955045	+	0.280427i
$179$	−12.8236	+	14.7992i	−0.958478	+	1.10614i	0.0358046	+	0.999359i	$0.488601\pi$
$179$	−12.8236	+	14.7992i	−0.958478	+	1.10614i	−0.994282	+	0.106783i	$0.965945\pi$
$180$	−3.37993	+	0.992436i	−0.251925	+	0.0739718i
$181$	−0.281535	+	0.616477i	−0.0209264	+	0.0458223i	−0.919807	−	0.392372i	$-0.871655\pi$
$181$	−0.281535	+	0.616477i	−0.0209264	+	0.0458223i	0.898880	+	0.438194i	$0.144382\pi$
$182$	2.78903	+	14.8021i	0.206737	+	1.09721i
$183$		−	1.12523i		−	0.0831797i
$184$	−1.81492	+	4.43915i	−0.133797	+	0.327259i
$185$			32.5275i			2.39147i
$186$	0.425779	+	2.96136i	0.0312197	+	0.217138i
$187$	−20.9231	−	9.55524i	−1.53005	−	0.698748i
$188$	−1.99251	−	6.78588i	−0.145319	−	0.494911i
$189$	−1.64414	+	2.07288i	−0.119593	+	0.150780i
$190$	2.80630	+	0.824005i	0.203591	+	0.0597796i
$191$	4.54982	+	7.07966i	0.329213	+	0.512266i	0.965920	−	0.258840i	$-0.0833402\pi$
$191$	4.54982	+	7.07966i	0.329213	+	0.512266i	−0.636707	+	0.771106i	$0.719704\pi$
$192$	−0.909632	+	0.415415i	−0.0656470	+	0.0299800i
$193$	15.3872	+	17.7578i	1.10760	+	1.27823i	0.957143	+	0.289617i	$0.0935278\pi$
$193$	15.3872	+	17.7578i	1.10760	+	1.27823i	0.150453	+	0.988617i	$0.451927\pi$
$194$	−4.36896	−	2.80776i	−0.313673	−	0.201586i
$195$	2.85408	−	19.8506i	0.204385	−	1.42153i
$196$	0.391263	−	6.98906i	0.0279474	−	0.499218i
$197$	−20.2882	−	13.0384i	−1.44547	−	0.928950i	−0.999424	−	0.0339429i	$-0.989194\pi$
$197$	−20.2882	−	13.0384i	−1.44547	−	0.928950i	−0.446051	−	0.895007i	$-0.647170\pi$
$198$	−2.71322	+	2.35102i	−0.192820	+	0.167080i
$199$	−1.87014	−	4.09504i	−0.132571	−	0.290290i	0.831692	−	0.555237i	$-0.187373\pi$
$199$	−1.87014	−	4.09504i	−0.132571	−	0.290290i	−0.964263	+	0.264948i	$0.914645\pi$
$200$	−6.23272	+	4.00552i	−0.440720	+	0.283233i
$201$	5.05213	+	1.48344i	0.356349	+	0.104634i
$202$	−11.8294	−	10.2503i	−0.832315	−	0.721205i
$203$	−4.21069	−	12.3318i	−0.295533	−	0.865524i
$204$	5.82797	+	2.66154i	0.408039	+	0.186345i
$205$	27.5673	−	3.96358i	1.92538	−	0.276828i
$206$	−11.8934			−0.828654
$207$	0.490744	−	4.77066i	0.0341091	−	0.331584i
$208$		−	5.69312i		−	0.394747i
$209$	2.95047	−	0.424214i	0.204089	−	0.0293435i
$210$	−3.49987	+	8.63787i	−0.241514	+	0.596070i
$211$	9.15646	−	2.68858i	0.630357	−	0.185089i	0.0490792	−	0.998795i	$-0.484371\pi$
$211$	9.15646	−	2.68858i	0.630357	−	0.185089i	0.581277	+	0.813706i	$0.302553\pi$
$212$	−3.27636	−	2.83898i	−0.225021	−	0.194982i
$213$	2.49089	−	8.48319i	0.170673	−	0.581259i
$214$	−2.17633	−	3.38643i	−0.148771	−	0.231491i
$215$	22.4466	−	10.2510i	1.53085	−	0.699114i
$216$	0.755750	−	0.654861i	0.0514222	−	0.0445576i
$217$	6.83857	+	3.98629i	0.464233	+	0.270607i
$218$	−8.33165	−	1.19791i	−0.564291	−	0.0811328i
$219$	−1.17862	+	8.19748i	−0.0796438	+	0.553934i
$220$	−6.83726	+	10.6390i	−0.460968	+	0.717281i
$221$	−27.5664	+	23.8864i	−1.85431	+	1.60677i
$222$	−3.83590	−	8.39944i	−0.257449	−	0.563734i
$223$	−9.74102	−	15.1573i	−0.652307	−	1.01501i	−0.997083	−	0.0763243i	$-0.975682\pi$
$223$	−9.74102	−	15.1573i	−0.652307	−	1.01501i	0.344776	−	0.938685i	$-0.387955\pi$
$224$	−0.634455	+	2.56855i	−0.0423913	+	0.171619i
$225$	4.85176	−	5.59923i	0.323451	−	0.373282i
$226$	0.442960	+	1.50858i	0.0294653	+	0.100349i
$227$	0.113088	−	0.247627i	0.00750588	−	0.0164356i	−0.905842	−	0.423616i	$-0.860761\pi$
$227$	0.113088	−	0.247627i	0.00750588	−	0.0164356i	0.913348	+	0.407180i	$0.133488\pi$
$228$	−0.821834	+	0.118162i	−0.0544273	+	0.00782546i
$229$	19.5567			1.29234			0.646172	−	0.763192i	$-0.276369\pi$
$229$	19.5567			1.29234			0.646172	+	0.763192i	$0.276369\pi$
$230$	−3.07589	−	16.6115i	−0.202818	−	1.09533i
$231$	0.412467	+	9.48958i	0.0271383	+	0.624369i
$232$	0.700930	+	4.87507i	0.0460183	+	0.320064i
$233$	11.8999	−	26.0571i	0.779587	−	1.70706i	0.0752782	−	0.997163i	$-0.476016\pi$
$233$	11.8999	−	26.0571i	0.779587	−	1.70706i	0.704308	−	0.709894i	$-0.251257\pi$
$234$	1.60394	+	5.46251i	0.104853	+	0.357095i
$235$	18.8282	+	16.3147i	1.22821	+	1.06425i
$236$	0.907643	−	3.09115i	0.0590825	−	0.201217i
$237$	−8.02440	+	5.15697i	−0.521241	+	0.334981i
$238$	15.0990	−	7.70471i	0.978725	−	0.499422i
$239$	9.23628	+	10.6592i	0.597445	+	0.689489i	0.971262	−	0.238014i	$-0.0764964\pi$
$239$	9.23628	+	10.6592i	0.597445	+	0.689489i	−0.373816	+	0.927503i	$0.621951\pi$
$240$	1.90447	−	2.96342i	0.122933	−	0.191288i
$241$	2.09117	−	14.5444i	0.134704	−	0.936888i	−0.804604	−	0.593812i	$-0.797622\pi$
$241$	2.09117	−	14.5444i	0.134704	−	0.936888i	0.939308	−	0.343076i	$-0.111469\pi$
$242$	−0.268818	+	1.86967i	−0.0172803	+	0.120187i
$243$	−0.540641	+	0.841254i	−0.0346821	+	0.0539664i
$244$	0.736872	+	0.850396i	0.0471734	+	0.0544410i
$245$	12.1510	+	21.4566i	0.776298	+	1.37081i
$246$	−6.65118	+	4.27445i	−0.424064	+	0.272529i
$247$	1.33172	−	4.53544i	0.0847356	−	0.288583i
$248$	−2.26106	−	1.95922i	−0.143578	−	0.124411i
$249$	−2.68584	−	9.14714i	−0.170208	−	0.579676i
$250$	3.52498	−	7.71863i	0.222939	−	0.488169i
$251$	−1.69864	−	11.8143i	−0.107217	−	0.745713i	−0.970519	−	0.241025i	$-0.922517\pi$
$251$	−1.69864	−	11.8143i	−0.107217	−	0.745713i	0.863302	−	0.504688i	$-0.168393\pi$
$252$	−0.114890	−	2.64326i	−0.00723737	−	0.166509i
$253$	−9.88442	−	14.0976i	−0.621428	−	0.886310i
$254$	−10.3632			−0.650247
$255$	−22.3395	+	3.21194i	−1.39896	+	0.201139i
$256$	0.415415	−	0.909632i	0.0259634	−	0.0568520i
$257$	−4.97936	−	16.9581i	−0.310604	−	1.05782i	−0.955853	−	0.293847i	$-0.905064\pi$
$257$	−4.97936	−	16.9581i	−0.310604	−	1.05782i	0.645249	−	0.763973i	$-0.276754\pi$
$258$	−4.58742	+	5.29416i	−0.285600	+	0.329600i
$259$	−23.7177	−	5.85849i	−1.47375	−	0.364029i
$260$	10.8424	+	16.8711i	0.672416	+	1.04630i
$261$	−2.04600	−	4.48012i	−0.126644	−	0.277313i
$262$	−1.86666	+	1.61747i	−0.115323	+	0.0999277i
$263$	−12.3291	+	19.1844i	−0.760245	+	1.18296i	0.218089	+	0.975929i	$0.430018\pi$
$263$	−12.3291	+	19.1844i	−0.760245	+	1.18296i	−0.978334	+	0.207035i	$0.933619\pi$
$264$	0.510926	−	3.55357i	0.0314453	−	0.218707i
$265$	15.1160	+	2.17335i	0.928567	+	0.133508i
$266$	−1.10627	+	1.89783i	−0.0678299	+	0.116364i
$267$	10.0362	−	8.69643i	0.614207	−	0.532213i
$268$	−4.78959	+	2.18733i	−0.292571	+	0.133613i
$269$	6.57398	+	10.2293i	0.400823	+	0.623692i	0.981730	−	0.190277i	$-0.0609387\pi$
$269$	6.57398	+	10.2293i	0.400823	+	0.623692i	−0.580908	+	0.813969i	$0.697302\pi$
$270$	−0.992436	+	3.37993i	−0.0603978	+	0.205696i
$271$	−11.3934	−	9.87244i	−0.692100	−	0.599708i	0.236127	−	0.971722i	$-0.424122\pi$
$271$	−11.3934	−	9.87244i	−0.692100	−	0.599708i	−0.928227	+	0.372014i	$0.878667\pi$
$272$	−6.14743	+	1.80505i	−0.372742	+	0.109447i
$273$	13.9602	+	5.65634i	0.844909	+	0.342337i
$274$	19.2817	−	2.77228i	1.16485	−	0.167480i
$275$		−	26.5986i		−	1.60395i
$276$	2.75324	+	3.92679i	0.165725	+	0.236365i
$277$	−21.5134			−1.29261			−0.646306	−	0.763078i	$-0.723687\pi$
$277$	−21.5134			−1.29261			−0.646306	+	0.763078i	$0.723687\pi$
$278$	13.3172	−	1.91473i	0.798715	−	0.114838i
$279$	2.72145	+	1.24284i	0.162929	+	0.0744071i
$280$	−3.01158	−	8.81999i	−0.179976	−	0.527095i
$281$	6.69972	+	5.80534i	0.399672	+	0.346317i	0.831388	−	0.555692i	$-0.187547\pi$
$281$	6.69972	+	5.80534i	0.399672	+	0.346317i	−0.431717	+	0.902009i	$0.642092\pi$
$282$	−6.78588	−	1.99251i	−0.404093	−	0.118653i
$283$	−21.0246	+	13.5117i	−1.24978	+	0.803188i	−0.986852	−	0.161627i	$-0.948326\pi$
$283$	−21.0246	+	13.5117i	−1.24978	+	0.803188i	−0.262932	+	0.964814i	$0.584690\pi$
$284$	3.67282	+	8.04235i	0.217942	+	0.477226i
$285$	2.21040	−	1.91532i	0.130933	−	0.113454i
$286$	17.1943	+	11.0501i	1.01672	+	0.653407i
$287$	−2.07503	+	20.8149i	−0.122485	+	1.22866i
$288$	−0.142315	+	0.989821i	−0.00838598	+	0.0583258i
$289$	20.2313	+	13.0019i	1.19008	+	0.764817i
$290$	−11.3616	−	13.1120i	−0.667175	−	0.769961i
$291$	−4.72408	+	2.15742i	−0.276931	+	0.126470i
$292$	−4.47747	−	6.96708i	−0.262024	−	0.407717i
$293$	1.30502	+	0.383188i	0.0762400	+	0.0223861i	0.319630	−	0.947542i	$-0.396441\pi$
$293$	1.30502	+	0.383188i	0.0762400	+	0.0223861i	−0.243390	+	0.969928i	$0.578260\pi$
$294$	−5.66804	−	4.10772i	−0.330567	−	0.239567i
$295$	3.19728	+	10.8889i	0.186153	+	0.633978i
$296$	8.39944	+	3.83590i	0.488208	+	0.222957i
$297$	0.510926	+	3.55357i	0.0296469	+	0.206199i
$298$			13.9558i			0.808440i
$299$	−26.8469	+	4.97114i	−1.55259	+	0.287488i
$300$			7.40884i			0.427750i
$301$	3.43180	+	18.2135i	0.197806	+	1.04981i
$302$	5.80492	−	12.7110i	0.334036	−	0.731436i
$303$	−15.0185	+	4.40984i	−0.862792	+	0.253339i
$304$	0.543721	−	0.627487i	0.0311845	−	0.0359889i
$305$	−3.80321	−	1.11672i	−0.217771	−	0.0639434i
$306$	5.38987	−	3.46386i	0.308118	−	0.198016i
$307$	13.1197	−	5.99156i	0.748781	−	0.341957i	−0.00420723	−	0.999991i	$-0.501339\pi$
$307$	13.1197	−	5.99156i	0.748781	−	0.341957i	0.752988	+	0.658035i	$0.228612\pi$
$308$	−6.52608	−	6.90164i	−0.371858	−	0.393257i
$309$	−6.43007	+	10.0054i	−0.365794	+	0.569186i
$310$	10.4317	+	1.49986i	0.592483	+	0.0851863i
$311$	24.9371	+	3.58542i	1.41405	+	0.203310i	0.806625	−	0.591063i	$-0.201292\pi$
$311$	24.9371	+	3.58542i	1.41405	+	0.203310i	0.607430	+	0.794374i	$0.292201\pi$
$312$	−4.78935	−	3.07793i	−0.271144	−	0.174254i
$313$	2.56939	+	2.96524i	0.145231	+	0.167605i	0.823704	−	0.567020i	$-0.191904\pi$
$313$	2.56939	+	2.96524i	0.145231	+	0.167605i	−0.678474	+	0.734625i	$0.737358\pi$
$314$	−2.06545	−	4.52271i	−0.116560	−	0.255232i
$315$	5.37447	+	7.61426i	0.302817	+	0.429015i
$316$	2.68734	−	9.15224i	0.151175	−	0.514854i
$317$	−4.44271	+	5.12716i	−0.249528	+	0.287970i	−0.866671	−	0.498881i	$-0.833745\pi$
$317$	−4.44271	+	5.12716i	−0.249528	+	0.287970i	0.617143	+	0.786851i	$0.288290\pi$
$318$	−4.15964	+	1.22138i	−0.233261	+	0.0684916i
$319$	−16.0841	−	7.34538i	−0.900539	−	0.411262i
$320$	0.501321	+	3.48676i	0.0280247	+	0.194916i
$321$	−4.02545			−0.224679
$322$	12.6664	+	0.749063i	0.705874	+	0.0417436i
$323$	−5.31960			−0.295990
$324$	−0.142315	−	0.989821i	−0.00790638	−	0.0549901i
$325$	−38.3677	−	17.5220i	−2.12826	−	0.971944i
$326$	−10.9188	+	3.20606i	−0.604739	+	0.177567i
$327$	−5.51218	+	6.36139i	−0.304824	+	0.351786i
$328$	2.22745	−	7.58601i	0.122991	−	0.418868i
$329$	−15.2872	+	10.7903i	−0.842808	+	0.594890i
$330$	5.25358	+	11.5037i	0.289200	+	0.633260i
$331$	−1.43559	−	1.65675i	−0.0789069	−	0.0910634i	0.714923	−	0.699203i	$-0.246462\pi$
$331$	−1.43559	−	1.65675i	−0.0789069	−	0.0910634i	−0.793830	+	0.608139i	$0.791916\pi$
$332$	8.01992	+	5.15409i	0.440151	+	0.282868i
$333$	−9.13990	−	1.31412i	−0.500864	−	0.0720133i
$334$	16.4394	+	2.36363i	0.899526	+	0.129332i
$335$	10.0278	−	15.6036i	0.547879	−	0.852516i
$336$	1.81779	+	1.92240i	0.0991687	+	0.104876i
$337$	0.604506	−	0.276068i	0.0329295	−	0.0150384i	−0.398882	−	0.917002i	$-0.630602\pi$
$337$	0.604506	−	0.276068i	0.0329295	−	0.0150384i	0.431812	+	0.901964i	$0.357874\pi$
$338$	16.3301	−	10.4947i	0.888238	−	0.570836i
$339$	1.50858	+	0.442960i	0.0819350	+	0.0240583i
$340$	14.7797	−	17.0567i	0.801543	−	0.925029i
$341$	10.3059	−	3.02607i	0.558094	−	0.163871i
$342$	−0.344913	+	0.755254i	−0.0186507	+	0.0408394i
$343$	−17.8338	+	4.99548i	−0.962936	+	0.269731i
$344$		−	7.00518i		−	0.377694i
$345$	−15.6374	−	6.39325i	−0.841892	−	0.344201i
$346$		−	20.4055i		−	1.09701i
$347$	4.28190	+	29.7813i	0.229865	+	1.59874i	0.698672	+	0.715442i	$0.253775\pi$
$347$	4.28190	+	29.7813i	0.229865	+	1.59874i	−0.468807	+	0.883301i	$0.655316\pi$
$348$	4.48012	+	2.04600i	0.240160	+	0.109677i
$349$	−4.10450	−	13.9786i	−0.219709	−	0.748259i	−0.993401	−	0.114697i	$-0.963410\pi$
$349$	−4.10450	−	13.9786i	−0.219709	−	0.748259i	0.773692	−	0.633562i	$-0.218408\pi$
$350$	15.3576	+	12.1812i	0.820899	+	0.651110i
$351$	5.46251	+	1.60394i	0.291567	+	0.0856118i
$352$	1.94096	+	3.02019i	0.103454	+	0.160977i
$353$	7.02985	−	3.21042i	0.374161	−	0.170874i	−0.219454	−	0.975623i	$-0.570428\pi$
$353$	7.02985	−	3.21042i	0.374161	−	0.170874i	0.593615	+	0.804749i	$0.297700\pi$
$354$	−2.10973	−	2.43476i	−0.112131	−	0.129406i
$355$	−26.2005	−	16.8381i	−1.39058	−	0.893671i
$356$	−1.88992	+	13.1446i	−0.100165	+	0.696665i
$357$	1.68153	−	16.8676i	0.0889961	−	0.892728i
$358$	−16.4735	−	10.5869i	−0.870653	−	0.559535i
$359$	13.1291	−	11.3765i	0.692930	−	0.600427i	−0.235527	−	0.971868i	$-0.575682\pi$
$359$	13.1291	−	11.3765i	0.692930	−	0.600427i	0.928457	+	0.371441i	$0.121136\pi$
$360$	−1.46335	−	3.20429i	−0.0771253	−	0.168881i
$361$	−15.4039	+	9.89947i	−0.810731	+	0.521025i
$362$	−0.650268	−	0.190936i	−0.0341774	−	0.0100354i
$363$	1.42753	+	1.23696i	0.0749260	+	0.0649238i
$364$	−14.2545	+	4.86720i	−0.747140	+	0.255111i
$365$	26.5372	+	12.1191i	1.38902	+	0.634344i
$366$	1.11378	−	0.160138i	0.0582183	−	0.00837053i
$367$	11.0216			0.575325			0.287663	−	0.957732i	$-0.407122\pi$
$367$	11.0216			0.575325			0.287663	+	0.957732i	$0.407122\pi$
$368$	−4.65226	−	1.16468i	−0.242516	−	0.0607134i
$369$			7.90627i			0.411584i
$370$	−32.1964	+	4.62914i	−1.67381	+	0.240658i
$371$	−4.30724	+	10.6305i	−0.223621	+	0.551910i
$372$	−2.87062	+	0.842891i	−0.148835	+	0.0437019i
$373$	−20.5794	−	17.8321i	−1.06556	−	0.923313i	−0.0683280	−	0.997663i	$-0.521766\pi$
$373$	−20.5794	−	17.8321i	−1.06556	−	0.923313i	−0.997232	+	0.0743498i	$0.976312\pi$
$374$	6.48032	−	22.0699i	0.335089	−	1.14121i
$375$	−4.58757	−	7.13841i	−0.236901	−	0.368626i
$376$	6.43325	−	2.93797i	0.331769	−	0.151514i
$377$	−21.1910	+	18.3621i	−1.09139	+	0.945699i
$378$	−2.28576	−	1.33240i	−0.117567	−	0.0685313i
$379$	14.9026	+	2.14267i	0.765495	+	0.110062i	0.513992	−	0.857795i	$-0.328166\pi$
$379$	14.9026	+	2.14267i	0.765495	+	0.110062i	0.251503	+	0.967856i	$0.419075\pi$
$380$	−0.416239	+	2.89501i	−0.0213526	+	0.148511i
$381$	−5.60278	+	8.71810i	−0.287039	+	0.446642i
$382$	−6.36009	+	5.51105i	−0.325410	+	0.281970i
$383$	−9.66821	−	21.1704i	−0.494023	−	1.08176i	−0.978366	−	0.206881i	$-0.933669\pi$
$383$	−9.66821	−	21.1704i	−0.494023	−	1.08176i	0.484344	−	0.874878i	$-0.339058\pi$
$384$	−0.540641	−	0.841254i	−0.0275895	−	0.0429300i
$385$	32.4834	+	8.02370i	1.65551	+	0.408926i
$386$	−15.3872	+	17.7578i	−0.783189	+	0.903848i
$387$	1.97359	+	6.72142i	0.100323	+	0.341669i
$388$	2.15742	−	4.72408i	0.109526	−	0.239829i
$389$	6.67494	−	0.959712i	0.338433	−	0.0486593i	0.0289967	−	0.999580i	$-0.490769\pi$
$389$	6.67494	−	0.959712i	0.338433	−	0.0486593i	0.309436	+	0.950920i	$0.399860\pi$
$390$	20.0547			1.01551
$391$	13.8798	+	27.4131i	0.701934	+	1.38634i
$392$	6.97360	−	0.607366i	0.352220	−	0.0306766i
$393$	0.351510	+	2.44481i	0.0177313	+	0.123324i
$394$	10.0184	−	21.9373i	0.504720	−	1.10518i
$395$	9.46647	+	32.2399i	0.476310	+	1.62216i
$396$	−2.71322	−	2.35102i	−0.136345	−	0.118143i
$397$	−5.82777	+	19.8476i	−0.292488	+	0.996121i	0.673855	+	0.738863i	$0.264637\pi$
$397$	−5.82777	+	19.8476i	−0.292488	+	0.996121i	−0.966343	+	0.257258i	$0.917181\pi$
$398$	3.78721	−	2.43389i	0.189836	−	0.122000i
$399$	0.998464	+	1.95670i	0.0499857	+	0.0979576i
$400$	−4.85176	−	5.59923i	−0.242588	−	0.279962i
$401$	−0.0591851	+	0.0920937i	−0.00295556	+	0.00459894i	−0.842728	−	0.538339i	$-0.819052\pi$
$401$	−0.0591851	+	0.0920937i	−0.00295556	+	0.00459894i	0.839773	+	0.542938i	$0.182688\pi$
$402$	−0.749346	+	5.21182i	−0.0373740	+	0.259942i
$403$	2.42401	−	16.8594i	0.120749	−	0.839825i
$404$	8.46242	−	13.1678i	0.421021	−	0.655122i
$405$	2.30682	+	2.66222i	0.114627	+	0.132287i
$406$	11.6070	−	5.92283i	0.576048	−	0.293945i
$407$	−27.8881	+	17.9226i	−1.38236	+	0.888391i
$408$	−1.80505	+	6.14743i	−0.0893631	+	0.304343i
$409$	13.2863	+	11.5126i	0.656965	+	0.569264i	0.918251	−	0.395998i	$-0.129601\pi$
$409$	13.2863	+	11.5126i	0.656965	+	0.569264i	−0.261286	+	0.965261i	$0.584147\pi$
$410$	7.84647	+	26.7226i	0.387510	+	1.31974i
$411$	8.09226	−	17.7196i	0.399162	−	0.874042i
$412$	−1.69261	−	11.7724i	−0.0833889	−	0.579983i
$413$	−8.51563	+	0.370134i	−0.419027	+	0.0182131i
$414$	4.79194	−	0.193186i	0.235511	−	0.00949458i
$415$	−33.5822			−1.64848
$416$	5.63517	−	0.810215i	0.276287	−	0.0397241i
$417$	5.58907	−	12.2384i	0.273698	−	0.599315i
$418$	0.839793	+	2.86007i	0.0410756	+	0.139891i
$419$	9.04672	−	10.4405i	0.441961	−	0.510051i	−0.490440	−	0.871475i	$-0.663164\pi$
$419$	9.04672	−	10.4405i	0.441961	−	0.510051i	0.932401	+	0.361424i	$0.117709\pi$
$420$	−9.04803	−	2.23494i	−0.441499	−	0.109054i
$421$	−7.11120	−	11.0652i	−0.346579	−	0.539287i	0.623579	−	0.781760i	$-0.285678\pi$
$421$	−7.11120	−	11.0652i	−0.346579	−	0.539287i	−0.970158	+	0.242473i	$0.922041\pi$
$422$	3.96431	+	8.68063i	0.192980	+	0.422567i
$423$	−5.34493	+	4.63141i	−0.259880	+	0.225187i
$424$	2.34381	−	3.64704i	0.113826	−	0.177116i
$425$	−6.75542	+	46.9849i	−0.327686	+	2.27910i
$426$	8.75133	+	1.25825i	0.424004	+	0.0609625i
$427$	1.49926	−	2.57202i	0.0725544	−	0.124469i
$428$	3.04224	−	2.63611i	0.147052	−	0.127421i
$429$	18.5919	−	8.49063i	0.897625	−	0.409932i
$430$	13.3412	+	20.7593i	0.643368	+	1.00110i
$431$	9.03681	−	30.7765i	0.435288	−	1.48245i	−0.391626	−	0.920125i	$-0.628087\pi$
$431$	9.03681	−	30.7765i	0.435288	−	1.48245i	0.826913	−	0.562329i	$-0.190095\pi$
$432$	0.755750	+	0.654861i	0.0363610	+	0.0315070i
$433$	5.50728	−	1.61708i	0.264663	−	0.0777121i	−0.146709	−	0.989180i	$-0.546868\pi$
$433$	5.50728	−	1.61708i	0.264663	−	0.0777121i	0.411372	+	0.911468i	$0.365050\pi$
$434$	−2.97249	+	7.33628i	−0.142684	+	0.352153i
$435$	−17.1730	+	2.46911i	−0.823384	+	0.118385i
$436$		−	8.41733i		−	0.403117i
$437$	−3.43379	−	2.01610i	−0.164261	−	0.0964430i
$438$	−8.28178			−0.395719
$439$	12.6009	−	1.81173i	0.601406	−	0.0864691i	0.165114	−	0.986274i	$-0.447201\pi$
$439$	12.6009	−	1.81173i	0.601406	−	0.0864691i	0.436292	+	0.899805i	$0.356292\pi$
$440$	−11.5037	−	5.25358i	−0.548420	−	0.250455i
$441$	−6.52001	+	2.54745i	−0.310476	+	0.121307i
$442$	−27.5664	−	23.8864i	−1.31120	−	1.13616i
$443$	−15.5415	−	4.56340i	−0.738400	−	0.216814i	−0.109159	−	0.994024i	$-0.534816\pi$
$443$	−15.5415	−	4.56340i	−0.738400	−	0.216814i	−0.629241	+	0.777210i	$0.716634\pi$
$444$	7.76804	−	4.99222i	0.368655	−	0.236920i
$445$	−19.4330	−	42.5523i	−0.921213	−	2.01717i
$446$	13.6167	−	11.7990i	0.644772	−	0.558698i
$447$	11.7404	+	7.54510i	0.555302	+	0.356871i
$448$	−2.63270	−	0.262454i	−0.124383	−	0.0123998i
$449$	0.145926	−	1.01494i	0.00688668	−	0.0478979i	−0.986088	−	0.166222i	$-0.946843\pi$
$449$	0.145926	−	1.01494i	0.00688668	−	0.0478979i	0.992975	+	0.118324i	$0.0377522\pi$
$450$	6.23272	+	4.00552i	0.293813	+	0.188822i
$451$	18.5878	+	21.4515i	0.875267	+	1.01011i
$452$	−1.43019	+	0.653145i	−0.0672704	+	0.0307214i
$453$	−7.55480	−	11.7555i	−0.354955	−	0.552321i
$454$	0.261201	+	0.0766954i	0.0122588	+	0.00359950i
$455$	32.9726	−	41.5709i	1.54578	−	1.94887i
$456$	−0.233918	−	0.796653i	−0.0109542	−	0.0373067i
$457$	34.6255	+	15.8129i	1.61971	+	0.739697i	0.999016	−	0.0443541i	$-0.0141230\pi$
$457$	34.6255	+	15.8129i	1.61971	+	0.739697i	0.620696	+	0.784052i	$0.286850\pi$
$458$	2.78321	+	19.3577i	0.130051	+	0.904524i
$459$		−	6.40695i		−	0.299051i
$460$	16.0047	−	5.40865i	0.746222	−	0.252180i
$461$		−	13.3795i		−	0.623146i	−0.950222	−	0.311573i	$-0.899144\pi$
$461$		−	13.3795i		−	0.623146i	0.950222	−	0.311573i	$-0.100856\pi$
$462$	−9.33429	+	1.75878i	−0.434270	+	0.0818257i
$463$	8.24468	−	18.0533i	0.383163	−	0.839009i	−0.615541	−	0.788105i	$-0.711062\pi$
$463$	8.24468	−	18.0533i	0.383163	−	0.839009i	0.998704	−	0.0509041i	$-0.0162103\pi$
$464$	−4.72570	+	1.38759i	−0.219385	+	0.0644173i
$465$	6.90159	−	7.96486i	0.320054	−	0.369361i
$466$	27.4854	+	8.07044i	1.27324	+	0.373856i
$467$	11.2055	−	7.20131i	0.518527	−	0.333237i	−0.255062	−	0.966925i	$-0.582096\pi$
$467$	11.2055	−	7.20131i	0.518527	−	0.333237i	0.773589	+	0.633688i	$0.218460\pi$
$468$	−5.17864	+	2.36501i	−0.239383	+	0.109322i
$469$	9.57142	+	10.1222i	0.441967	+	0.467402i
$470$	−13.4691	+	20.9583i	−0.621284	+	0.966737i
$471$	−4.92142	−	0.707593i	−0.226767	−	0.0326042i
$472$	3.18885	+	0.458488i	0.146779	+	0.0211036i
$473$	21.1570	+	13.5968i	0.972800	+	0.625180i
$474$	−6.24647	−	7.20881i	−0.286910	−	0.331112i
$475$	−2.55541	−	5.59556i	−0.117250	−	0.256742i
$476$	9.77511	+	13.8488i	0.448041	+	0.634761i
$477$	−1.22138	+	4.15964i	−0.0559232	+	0.190457i
$478$	−9.23628	+	10.6592i	−0.422458	+	0.487542i
$479$	−17.3895	+	5.10602i	−0.794547	+	0.233300i	−0.653723	−	0.756734i	$-0.726794\pi$
$479$	−17.3895	+	5.10602i	−0.794547	+	0.233300i	−0.140825	+	0.990035i	$0.544975\pi$
$480$	3.20429	+	1.46335i	0.146255	+	0.0667924i
$481$	7.48144	+	52.0345i	0.341124	+	2.37257i
$482$	14.6940			0.669292
$483$	7.47815	−	10.2507i	0.340268	−	0.466424i
$484$	−1.88890			−0.0858589
$485$	2.60356	+	18.1082i	0.118222	+	0.822249i
$486$	−0.909632	−	0.415415i	−0.0412617	−	0.0188436i
$487$	32.0796	−	9.41942i	1.45367	−	0.426835i	0.542914	−	0.839788i	$-0.317321\pi$
$487$	32.0796	−	9.41942i	1.45367	−	0.426835i	0.910752	+	0.412954i	$0.135503\pi$
$488$	−0.736872	+	0.850396i	−0.0333566	+	0.0384956i
$489$	−3.20606	+	10.9188i	−0.144983	+	0.493767i
$490$	−19.5090	+	15.0809i	−0.881325	+	0.681286i
$491$	−1.37684	−	3.01487i	−0.0621361	−	0.136059i	0.876017	−	0.482281i	$-0.160192\pi$
$491$	−1.37684	−	3.01487i	−0.0621361	−	0.136059i	−0.938153	+	0.346222i	$0.887464\pi$
$492$	−5.17751	−	5.97516i	−0.233420	−	0.269381i
$493$	26.5462	+	17.0602i	1.19558	+	0.768354i
$494$	4.67880	+	0.672709i	0.210509	+	0.0302666i
$495$	12.5179	+	1.79980i	0.562636	+	0.0808949i
$496$	1.61750	−	2.51687i	0.0726277	−	0.113011i
$497$	16.9966	−	16.0717i	0.762401	−	0.720914i
$498$	8.67180	−	3.96028i	0.388593	−	0.177464i
$499$	20.4036	−	13.1126i	0.913390	−	0.587000i	0.00265702	−	0.999996i	$-0.499154\pi$
$499$	20.4036	−	13.1126i	0.913390	−	0.587000i	0.910733	+	0.412997i	$0.135518\pi$
$500$	8.14172	+	2.39062i	0.364109	+	0.106912i
$501$	10.8762	−	12.5519i	0.485915	−	0.560776i
$502$	11.4523	−	3.36270i	0.511142	−	0.150085i
$503$	1.22191	−	2.67560i	0.0544821	−	0.119299i	−0.880433	−	0.474170i	$-0.842748\pi$
$503$	1.22191	−	2.67560i	0.0544821	−	0.119299i	0.934915	+	0.354871i	$0.115475\pi$
$504$	2.60000	−	0.489895i	0.115813	−	0.0218216i
$505$			55.1380i			2.45361i
$506$	12.5474	−	11.7901i	0.557801	−	0.524135i
$507$		−	19.4116i		−	0.862098i
$508$	−1.47484	−	10.2577i	−0.0654355	−	0.455114i
$509$	−39.8751	−	18.2104i	−1.76743	−	0.807160i	−0.982169	−	0.188000i	$-0.939799\pi$
$509$	−39.8751	−	18.2104i	−1.76743	−	0.807160i	−0.785265	−	0.619160i	$-0.787473\pi$
$510$	−6.35849	−	21.6550i	−0.281559	−	0.958901i
$511$	−13.6164	+	17.1671i	−0.602353	+	0.759428i
$512$	0.959493	+	0.281733i	0.0424040	+	0.0124509i
$513$	0.448886	+	0.698480i	0.0198188	+	0.0308386i
$514$	16.0769	−	7.34207i	0.709121	−	0.323845i
$515$	27.4360	+	31.6629i	1.20898	+	1.39523i
$516$	−5.89313	−	3.78729i	−0.259431	−	0.166726i
$517$	−3.61345	+	25.1321i	−0.158920	+	1.10531i
$518$	2.42347	−	24.3101i	0.106481	−	1.06812i
$519$	−17.1662	−	11.0320i	−0.753512	−	0.484253i
$520$	−15.1563	+	13.1330i	−0.664648	+	0.575921i
$521$	15.5619	+	34.0759i	0.681781	+	1.49289i	0.860745	+	0.509037i	$0.169998\pi$
$521$	15.5619	+	34.0759i	0.681781	+	1.49289i	−0.178964	+	0.983856i	$0.557274\pi$
$522$	4.14335	−	2.66277i	0.181349	−	0.116546i
$523$	−13.1372	−	3.85743i	−0.574449	−	0.168674i	−0.0184114	−	0.999830i	$-0.505861\pi$
$523$	−13.1372	−	3.85743i	−0.574449	−	0.168674i	−0.556038	+	0.831157i	$0.687679\pi$
$524$	−1.86666	−	1.61747i	−0.0815454	−	0.0706595i
$525$	18.5504	−	6.33402i	0.809605	−	0.276439i
$526$	−20.7438	−	9.47337i	−0.904472	−	0.413059i
$527$	−18.9733	+	2.72795i	−0.826490	+	0.118831i
$528$	3.59011			0.156240
$529$	−1.42999	+	22.9555i	−0.0621735	+	0.998065i
$530$			15.2714i			0.663348i
$531$	−3.18885	+	0.458488i	−0.138384	+	0.0198967i
$532$	−2.03596	−	0.824922i	−0.0882699	−	0.0357649i
$533$	43.1881	−	12.6812i	1.87068	−	0.549282i
$534$	10.0362	+	8.69643i	0.434310	+	0.376331i
$535$	−3.99501	+	13.6057i	−0.172719	+	0.588228i
$536$	−2.84670	−	4.42955i	−0.122959	−	0.191327i
$537$	−17.8125	+	8.13470i	−0.768667	+	0.351038i
$538$	−9.18962	+	7.96285i	−0.396193	+	0.343303i
$539$	−11.7011	+	22.2405i	−0.504003	+	0.957966i
$540$	−3.48676	−	0.501321i	−0.150046	−	0.0215734i
$541$	−4.85352	+	33.7570i	−0.208669	+	1.45133i	0.568837	+	0.822451i	$0.307394\pi$
$541$	−4.85352	+	33.7570i	−0.208669	+	1.45133i	−0.777506	+	0.628876i	$0.783515\pi$
$542$	8.15050	−	12.6824i	0.350094	−	0.544757i
$543$	−0.512187	+	0.443813i	−0.0219801	+	0.0190458i
$544$	−2.66154	−	5.82797i	−0.114113	−	0.249872i
$545$	16.0306	+	24.9440i	0.686674	+	1.06849i
$546$	−3.61203	+	14.6231i	−0.154581	+	0.625810i
$547$	4.07387	−	4.70150i	0.174186	−	0.201021i	−0.661943	−	0.749554i	$-0.730268\pi$
$547$	4.07387	−	4.70150i	0.174186	−	0.201021i	0.836129	+	0.548533i	$0.184813\pi$
$548$	5.48813	+	18.6909i	0.234441	+	0.798434i
$549$	0.467439	−	1.02355i	0.0199498	−	0.0436840i
$550$	26.3278	−	3.78537i	1.12262	−	0.161409i
$551$	−4.08932			−0.174211
$552$	−3.49500	+	3.28405i	−0.148757	+	0.139779i
$553$	−25.2130	+	1.09589i	−1.07217	+	0.0466019i
$554$	−3.06167	−	21.2944i	−0.130078	−	0.904711i
$555$	−13.5124	+	29.5880i	−0.573570	+	1.25594i
$556$	3.79048	+	12.9092i	0.160752	+	0.547472i
$557$	4.03813	+	3.49906i	0.171101	+	0.148260i	0.736202	−	0.676762i	$-0.236617\pi$
$557$	4.03813	+	3.49906i	0.171101	+	0.148260i	−0.565101	+	0.825022i	$0.691163\pi$
$558$	−0.842891	+	2.87062i	−0.0356824	+	0.121523i
$559$	33.5503	−	21.5615i	1.41903	−	0.911953i
$560$	8.30163	−	4.23614i	0.350808	−	0.179010i
$561$	−15.0629	−	17.3835i	−0.635956	−	0.733932i
$562$	−4.79278	+	7.45771i	−0.202171	+	0.314585i
$563$	−2.35138	+	16.3542i	−0.0990987	+	0.689247i	0.878341	+	0.478034i	$0.158650\pi$
$563$	−2.35138	+	16.3542i	−0.0990987	+	0.689247i	−0.977440	+	0.211213i	$0.932259\pi$
$564$	1.00650	−	7.00038i	0.0423814	−	0.294769i
$565$	2.99435	−	4.65929i	0.125973	−	0.196018i
$566$	−16.3663	−	18.8877i	−0.687927	−	0.793910i
$567$	−2.35666	+	1.20256i	−0.0989705	+	0.0505026i
$568$	−7.43780	+	4.77998i	−0.312083	+	0.200564i
$569$	−12.0782	+	41.1346i	−0.506345	+	1.72445i	0.167768	+	0.985826i	$0.446344\pi$
$569$	−12.0782	+	41.1346i	−0.506345	+	1.72445i	−0.674114	+	0.738628i	$0.735474\pi$
$570$	2.21040	+	1.91532i	0.0925834	+	0.0802240i
$571$	2.83789	+	9.66496i	0.118762	+	0.404466i	0.997319	−	0.0731706i	$-0.0233117\pi$
$571$	2.83789	+	9.66496i	0.118762	+	0.404466i	−0.878558	+	0.477637i	$0.841494\pi$
$572$	−8.49063	+	18.5919i	−0.355011	+	0.777366i
$573$	1.19767	+	8.32994i	0.0500332	+	0.347988i
$574$	−20.8983	+	0.908349i	−0.872278	+	0.0379138i
$575$	−22.1676	+	27.7685i	−0.924455	+	1.15803i
$576$	−1.00000			−0.0416667
$577$	−34.0180	+	4.89105i	−1.41619	+	0.203617i	−0.807535	−	0.589820i	$-0.799199\pi$
$577$	−34.0180	+	4.89105i	−1.41619	+	0.203617i	−0.608652	+	0.793437i	$0.708289\pi$
$578$	−9.99033	+	21.8758i	−0.415543	+	0.909912i
$579$	6.61985	+	22.5451i	0.275112	+	0.936944i
$580$	11.3616	−	13.1120i	0.471764	−	0.544445i
$581$	6.04845	−	24.4868i	0.250932	−	1.01588i
$582$	−2.80776	−	4.36896i	−0.116386	−	0.181099i
$583$	6.46553	+	14.1575i	0.267775	+	0.586345i
$584$	6.25895	−	5.42341i	0.258997	−	0.224422i
$585$	10.8424	−	16.8711i	0.448277	−	0.697533i
$586$	−0.193564	+	1.34627i	−0.00799606	+	0.0556138i
$587$	8.49008	+	1.22069i	0.350423	+	0.0503832i	0.315279	−	0.948999i	$-0.397902\pi$
$587$	8.49008	+	1.22069i	0.350423	+	0.0503832i	0.0351441	+	0.999382i	$0.488811\pi$
$588$	3.25926	−	6.19493i	0.134410	−	0.255475i
$589$	1.87733	−	1.62671i	0.0773538	−	0.0670275i
$590$	−10.3231	+	4.71439i	−0.424994	+	0.194088i
$591$	−13.0384	−	20.2882i	−0.536330	−	0.834545i
$592$	−2.60149	+	8.85985i	−0.106921	+	0.364138i
$593$	−16.6994	−	14.4701i	−0.685761	−	0.594215i	0.240703	−	0.970599i	$-0.422622\pi$
$593$	−16.6994	−	14.4701i	−0.685761	−	0.594215i	−0.926464	+	0.376384i	$0.877168\pi$
$594$	−3.44469	+	1.01145i	−0.141337	+	0.0415003i
$595$	−55.3424	−	22.4235i	−2.26882	−	0.919273i
$596$	−13.8138	+	1.98612i	−0.565835	+	0.0813548i
$597$		−	4.50187i		−	0.184249i
$598$	−8.74125	−	25.8661i	−0.357456	−	1.05774i
$599$	−3.81829			−0.156011			−0.0780055	−	0.996953i	$-0.524855\pi$
$599$	−3.81829			−0.156011			−0.0780055	+	0.996953i	$0.524855\pi$
$600$	−7.33343	+	1.05439i	−0.299386	+	0.0430452i
$601$	−35.0404	−	16.0024i	−1.42933	−	0.652752i	−0.457665	−	0.889125i	$-0.651314\pi$
$601$	−35.0404	−	16.0024i	−1.42933	−	0.652752i	−0.971662	+	0.236373i	$0.924041\pi$
$602$	−17.5397	+	5.98892i	−0.714864	+	0.244090i
$603$	3.97933	+	3.44811i	0.162051	+	0.140418i
$604$	13.4078	+	3.93687i	0.545554	+	0.160189i
$605$	5.59758	−	3.59735i	0.227574	−	0.146253i
$606$	−6.50231	−	14.2381i	−0.264138	−	0.578382i
$607$	−2.25275	+	1.95202i	−0.0914363	+	0.0792300i	−0.699380	−	0.714750i	$-0.746540\pi$
$607$	−2.25275	+	1.95202i	−0.0914363	+	0.0792300i	0.607943	+	0.793980i	$0.291995\pi$
$608$	0.698480	+	0.448886i	0.0283271	+	0.0182047i
$609$	1.29264	−	12.9666i	0.0523805	−	0.525433i
$610$	0.564104	−	3.92343i	0.0228399	−	0.158855i
$611$	33.8721	+	21.7682i	1.37032	+	0.880649i
$612$	4.19566	+	4.84205i	0.169600	+	0.195728i
$613$	−6.19287	+	2.82819i	−0.250128	+	0.114229i	−0.536534	−	0.843879i	$-0.680267\pi$
$613$	−6.19287	+	2.82819i	−0.250128	+	0.114229i	0.286406	+	0.958108i	$0.407539\pi$
$614$	7.79771	+	12.1335i	0.314690	+	0.489667i
$615$	26.7226	+	7.84647i	1.07756	+	0.316400i
$616$	5.90263	−	7.44185i	0.237824	−	0.299841i
$617$	−2.48805	−	8.47354i	−0.100165	−	0.341132i	0.894128	−	0.447811i	$-0.147796\pi$
$617$	−2.48805	−	8.47354i	−0.100165	−	0.341132i	−0.994293	+	0.106679i	$0.965978\pi$
$618$	−10.8186	−	4.94070i	−0.435189	−	0.198744i
$619$	0.556405	+	3.86988i	0.0223638	+	0.155544i	0.997943	−	0.0641031i	$-0.0204186\pi$
$619$	0.556405	+	3.86988i	0.0223638	+	0.155544i	−0.975579	+	0.219647i	$0.929510\pi$
$620$			10.5390i			0.423257i
$621$	2.42820	−	4.13568i	0.0974403	−	0.165959i
$622$			25.1936i			1.01017i
$623$	34.5275	−	6.50571i	1.38332	−	0.260646i
$624$	2.36501	−	5.17864i	0.0946760	−	0.207312i
$625$	6.86350	−	2.01530i	0.274540	−	0.0806122i
$626$	−2.56939	+	2.96524i	−0.102694	+	0.118515i
$627$	2.86007	+	0.839793i	0.114220	+	0.0335381i
$628$	4.18274	−	2.68808i	0.166909	−	0.107266i
$629$	53.8148	−	24.5764i	2.14574	−	0.979926i
$630$	−6.77189	+	6.40339i	−0.269799	+	0.255117i
$631$	2.19909	−	3.42185i	0.0875443	−	0.136222i	−0.794720	−	0.606977i	$-0.792382\pi$
$631$	2.19909	−	3.42185i	0.0875443	−	0.136222i	0.882264	+	0.470755i	$0.156018\pi$
$632$	9.44153	+	1.35749i	0.375564	+	0.0539979i
$633$	9.44588	+	1.35811i	0.375440	+	0.0539801i
$634$	−5.70724	−	3.66782i	−0.226664	−	0.145668i
$635$	23.9061	+	27.5892i	0.948687	+	1.09484i
$636$	−1.80093	−	3.94348i	−0.0714114	−	0.156369i
$637$	24.3732	+	31.5296i	0.965699	+	1.24925i
$638$	4.98160	−	16.9658i	0.197224	−	0.671682i
$639$	5.78984	−	6.68183i	0.229042	−	0.264329i
$640$	−3.37993	+	0.992436i	−0.133603	+	0.0392295i
$641$	−41.2459	−	18.8364i	−1.62912	−	0.743992i	−0.629657	−	0.776874i	$-0.716804\pi$
$641$	−41.2459	−	18.8364i	−1.62912	−	0.743992i	−0.999459	+	0.0328813i	$0.989532\pi$
$642$	−0.572882	−	3.98448i	−0.0226098	−	0.157255i
$643$	38.1202			1.50331			0.751656	−	0.659555i	$-0.229255\pi$
$643$	38.1202			1.50331			0.751656	+	0.659555i	$0.229255\pi$
$644$	1.06118	+	12.6441i	0.0418165	+	0.498248i
$645$	24.6766			0.971639
$646$	−0.757057	−	5.26545i	−0.0297860	−	0.207166i
$647$	−29.7387	−	13.5812i	−1.16915	−	0.533932i	−0.266300	−	0.963890i	$-0.585801\pi$
$647$	−29.7387	−	13.5812i	−1.16915	−	0.533932i	−0.902849	+	0.429958i	$0.858528\pi$
$648$	0.959493	−	0.281733i	0.0376924	−	0.0110675i
$649$	−7.57416	+	8.74105i	−0.297312	+	0.343116i
$650$	11.8833	−	40.4709i	0.466102	−	1.58740i
$651$	4.56462	+	6.46691i	0.178902	+	0.253458i
$652$	−4.72734	−	10.3514i	−0.185137	−	0.405393i
$653$	−10.7138	−	12.3643i	−0.419262	−	0.483854i	0.506350	−	0.862328i	$-0.330994\pi$
$653$	−10.7138	−	12.3643i	−0.419262	−	0.483854i	−0.925612	+	0.378474i	$0.876449\pi$
$654$	−7.08111	−	4.55075i	−0.276893	−	0.177948i
$655$	8.61212	+	1.23824i	0.336503	+	0.0483819i
$656$	7.82580	+	1.12518i	0.305546	+	0.0439309i
$657$	−4.47747	+	6.96708i	−0.174683	+	0.271811i
$658$	−12.8561	−	13.5959i	−0.501182	−	0.530024i
$659$	9.75207	−	4.45362i	0.379887	−	0.173488i	−0.216314	−	0.976324i	$-0.569403\pi$
$659$	9.75207	−	4.45362i	0.379887	−	0.173488i	0.596201	+	0.802835i	$0.296676\pi$
$660$	−10.6390	+	6.83726i	−0.414122	+	0.266140i
$661$	43.8535	+	12.8765i	1.70570	+	0.500839i	0.981937	−	0.189207i	$-0.0605918\pi$
$661$	43.8535	+	12.8765i	1.70570	+	0.500839i	0.723765	+	0.690047i	$0.242410\pi$
$662$	1.43559	−	1.65675i	0.0557956	−	0.0643916i
$663$	−34.9980	+	10.2763i	−1.35921	+	0.399100i
$664$	−3.96028	+	8.67180i	−0.153689	+	0.336531i
$665$	7.60442	−	1.43283i	0.294887	−	0.0555629i
$666$		−	9.23389i		−	0.357806i
$667$	10.6698	+	21.0732i	0.413137	+	0.815958i
$668$			16.6085i			0.642602i
$669$	−2.56416	−	17.8341i	−0.0991363	−	0.689508i
$670$	16.8719	+	7.70513i	0.651818	+	0.297675i
$671$	−1.13812	−	3.87608i	−0.0439366	−	0.149634i
$672$	−1.64414	+	2.07288i	−0.0634239	+	0.0799629i
$673$	12.2064	+	3.58412i	0.470521	+	0.138158i	0.508393	−	0.861125i	$-0.330240\pi$
$673$	12.2064	+	3.58412i	0.470521	+	0.138158i	−0.0378719	+	0.999283i	$0.512058\pi$
$674$	0.359289	+	0.559064i	0.0138393	+	0.0215343i
$675$	6.73932	−	3.07774i	0.259397	−	0.118462i
$676$	12.7119	+	14.6703i	0.488918	+	0.564242i
$677$	11.4887	+	7.38334i	0.441547	+	0.283765i	0.742465	−	0.669885i	$-0.233657\pi$
$677$	11.4887	+	7.38334i	0.441547	+	0.283765i	−0.300918	+	0.953650i	$0.597293\pi$
$678$	−0.223758	+	1.55627i	−0.00859336	+	0.0597681i
$679$	−13.6727	−	1.36303i	−0.524709	−	0.0523083i
$680$	18.9865	+	12.2019i	0.728098	+	0.467920i
$681$	0.205736	−	0.178271i	0.00788382	−	0.00683137i
$682$	4.46195	+	9.77030i	0.170857	+	0.374124i
$683$	27.6488	−	17.7688i	1.05795	−	0.679905i	0.108590	−	0.994087i	$-0.465367\pi$
$683$	27.6488	−	17.7688i	1.05795	−	0.679905i	0.949363	+	0.314182i	$0.101730\pi$
$684$	−0.796653	−	0.233918i	−0.0304608	−	0.00894409i
$685$	−51.8598	−	44.9368i	−1.98146	−	1.71695i
$686$	−7.48265	−	16.9414i	−0.285689	−	0.646824i
$687$	17.7894	+	8.12416i	0.678709	+	0.309956i
$688$	6.93388	−	0.996941i	0.264352	−	0.0380080i
$689$	24.6811			0.940274
$690$	4.10274	−	16.3881i	0.156189	−	0.623886i
$691$		−	16.5351i		−	0.629024i	−0.949254	−	0.314512i	$-0.898159\pi$
$691$		−	16.5351i		−	0.629024i	0.949254	−	0.314512i	$-0.101841\pi$
$692$	20.1978	−	2.90400i	0.767805	−	0.110394i
$693$	−3.56692	+	8.80337i	−0.135496	+	0.334412i
$694$	−28.8688	+	8.47664i	−1.09584	+	0.321769i
$695$	−35.8180	−	31.0364i	−1.35865	−	1.17728i
$696$	−1.38759	+	4.72570i	−0.0525965	+	0.179127i
$697$	−27.3862	−	42.6138i	−1.03733	−	1.61411i
$698$	13.2522	−	6.05209i	0.501604	−	0.229075i
$699$	21.6490	−	18.7590i	0.818841	−	0.709530i
$700$	−9.87155	+	16.9349i	−0.373109	+	0.640077i
$701$	19.2805	+	2.77212i	0.728216	+	0.104702i	0.496444	−	0.868069i	$-0.334639\pi$
$701$	19.2805	+	2.77212i	0.728216	+	0.104702i	0.231772	+	0.972770i	$0.425548\pi$
$702$	−0.810215	+	5.63517i	−0.0305796	+	0.212686i
$703$	−4.14496	+	6.44969i	−0.156330	+	0.243255i
$704$	−2.71322	+	2.35102i	−0.102259	+	0.0886075i
$705$	10.3493	+	22.6619i	0.389778	+	0.853496i
$706$	4.17820	+	6.50140i	0.157249	+	0.244684i
$707$	−40.2045	−	9.93086i	−1.51204	−	0.373488i
$708$	2.10973	−	2.43476i	0.0792885	−	0.0915038i
$709$	7.47733	+	25.4654i	0.280817	+	0.956375i	0.972252	+	0.233936i	$0.0751607\pi$
$709$	7.47733	+	25.4654i	0.280817	+	0.956375i	−0.691435	+	0.722439i	$0.743021\pi$
$710$	12.9379	−	28.3301i	0.485552	−	1.06321i
$711$	−9.44153	+	1.35749i	−0.354085	+	0.0509097i
$712$	−13.2798			−0.497682
$713$	−13.2811	−	5.42989i	−0.497382	−	0.203351i
$714$	16.9352	−	0.736093i	0.633784	−	0.0275476i
$715$	−10.2465	−	71.2657i	−0.383196	−	2.66519i
$716$	8.13470	−	17.8125i	0.304008	−	0.665685i
$717$	3.97361	+	13.5329i	0.148397	+	0.505394i
$718$	13.1291	+	11.3765i	0.489975	+	0.424566i
$719$	7.68721	−	26.1802i	0.286684	−	0.976358i	−0.682677	−	0.730720i	$-0.739184\pi$
$719$	7.68721	−	26.1802i	0.286684	−	0.976358i	0.969362	−	0.245638i	$-0.0789973\pi$
$720$	2.96342	−	1.90447i	0.110440	−	0.0709755i
$721$	−28.0288	+	14.3025i	−1.04385	+	0.532653i
$722$	−11.9909	−	13.8382i	−0.446255	−	0.515006i
$723$	7.94416	−	12.3614i	0.295447	−	0.459724i
$724$	0.0964497	−	0.670823i	0.00358453	−	0.0249309i
$725$	−5.19308	+	36.1187i	−0.192866	+	1.34141i
$726$	−1.02121	+	1.58904i	−0.0379008	+	0.0589748i
$727$	−13.3490	−	15.4055i	−0.495086	−	0.571359i	0.452132	−	0.891951i	$-0.350664\pi$
$727$	−13.3490	−	15.4055i	−0.495086	−	0.571359i	−0.947217	+	0.320592i	$0.896118\pi$
$728$	−6.84629	−	13.4168i	−0.253740	−	0.497258i
$729$	−0.841254	+	0.540641i	−0.0311575	+	0.0200237i
$730$	−8.21914	+	27.9918i	−0.304204	+	1.03602i
$731$	−33.9194	−	29.3914i	−1.25456	−	1.08708i
$732$	0.317015	+	1.07965i	0.0117172	+	0.0399052i
$733$	19.1634	−	41.9619i	0.707815	−	1.54990i	−0.122415	−	0.992479i	$-0.539064\pi$
$733$	19.1634	−	41.9619i	0.707815	−	1.54990i	0.830231	−	0.557420i	$-0.188209\pi$
$734$	1.56854	+	10.9095i	0.0578960	+	0.402676i
$735$	2.13952	+	24.5653i	0.0789173	+	0.906106i
$736$	0.490744	−	4.77066i	0.0180891	−	0.175849i
$737$	18.9034			0.696316
$738$	−7.82580	+	1.12518i	−0.288072	+	0.0414184i
$739$	8.19167	−	17.9373i	0.301335	−	0.659833i	−0.697027	−	0.717045i	$-0.745494\pi$
$739$	8.19167	−	17.9373i	0.301335	−	0.659833i	0.998362	+	0.0572127i	$0.0182213\pi$
$740$	−9.16405	−	31.2099i	−0.336877	−	1.14730i
$741$	3.09547	−	3.57236i	0.113715	−	0.131234i
$742$	−11.1353	−	2.75052i	−0.408790	−	0.100975i
$743$	19.8176	+	30.8368i	0.727039	+	1.13129i	0.986216	+	0.165464i	$0.0529123\pi$
$743$	19.8176	+	30.8368i	0.727039	+	1.13129i	−0.259177	+	0.965830i	$0.583451\pi$
$744$	−1.24284	−	2.72145i	−0.0455649	−	0.0997732i
$745$	37.1535	−	32.1937i	1.36120	−	1.17949i
$746$	14.7219	−	22.9077i	0.539006	−	0.838710i
$747$	1.35673	−	9.43627i	0.0496402	−	0.345255i
$748$	22.7675	+	3.27348i	0.832464	+	0.119690i
$749$	−9.20123	−	5.36352i	−0.336206	−	0.195979i
$750$	6.41287	−	5.55678i	0.234165	−	0.202905i
$751$	−13.1102	+	5.98724i	−0.478399	+	0.218477i	−0.639994	−	0.768380i	$-0.721063\pi$
$751$	−13.1102	+	5.98724i	−0.478399	+	0.218477i	0.161595	+	0.986857i	$0.448336\pi$
$752$	3.82361	+	5.94965i	0.139433	+	0.216961i
$753$	3.36270	−	11.4523i	0.122544	−	0.417346i
$754$	−21.1910	−	18.3621i	−0.771732	−	0.668710i
$755$	−47.2304	+	13.8681i	−1.71889	+	0.504712i
$756$	0.993541	−	2.45212i	0.0361347	−	0.0891826i
$757$	−43.0981	+	6.19657i	−1.56643	+	0.225218i	−0.870234	−	0.492638i	$-0.836033\pi$
$757$	−43.0981	+	6.19657i	−1.56643	+	0.225218i	−0.696192	+	0.717856i	$0.745124\pi$
$758$			15.0558i			0.546853i
$759$	−3.13483	−	16.9298i	−0.113787	−	0.614512i
$760$	−2.92478			−0.106093
$761$	−21.1462	+	3.04036i	−0.766548	+	0.110213i	−0.514487	−	0.857498i	$-0.672018\pi$
$761$	−21.1462	+	3.04036i	−0.766548	+	0.110213i	−0.252061	+	0.967711i	$0.581108\pi$
$762$	−9.42672	−	4.30504i	−0.341494	−	0.155955i
$763$	−21.0755	+	7.19620i	−0.762983	+	0.260520i
$764$	−6.36009	−	5.51105i	−0.230100	−	0.199383i
$765$	−21.6550	−	6.35849i	−0.782939	−	0.229892i
$766$	19.5790	−	12.5827i	0.707419	−	0.454630i
$767$	7.61921	+	16.6837i	0.275114	+	0.602415i
$768$	0.755750	−	0.654861i	0.0272708	−	0.0236303i
$769$	−4.96991	−	3.19397i	−0.179220	−	0.115177i	0.447955	−	0.894056i	$-0.352152\pi$
$769$	−4.96991	−	3.19397i	−0.179220	−	0.115177i	−0.627175	+	0.778879i	$0.715789\pi$
$770$	−3.31915	+	33.2947i	−0.119614	+	1.19986i
$771$	2.51528	−	17.4942i	0.0905856	−	0.630037i
$772$	−19.7669	−	12.7034i	−0.711425	−	0.457205i
$773$	−16.5194	−	19.0644i	−0.594162	−	0.685700i	0.376426	−	0.926447i	$-0.377153\pi$
$773$	−16.5194	−	19.0644i	−0.594162	−	0.685700i	−0.970588	+	0.240747i	$0.922608\pi$
$774$	−6.37214	+	2.91006i	−0.229042	+	0.104600i
$775$	−11.9838	−	18.6471i	−0.430470	−	0.669824i
$776$	4.98303	+	1.46315i	0.178880	+	0.0525240i
$777$	−19.1407	−	15.1818i	−0.686669	−	0.544643i
$778$	1.89989	+	6.47042i	0.0681142	+	0.231976i
$779$	5.97124	+	2.72698i	0.213942	+	0.0977040i
$780$	2.85408	+	19.8506i	0.102192	+	0.710764i
$781$		−	31.7413i		−	1.13579i
$782$	−25.1588	+	17.6399i	−0.899676	+	0.630800i
$783$		−	4.92521i		−	0.176012i
$784$	1.59363	+	6.81618i	0.0569154	+	0.243435i
$785$	−7.27581	+	15.9318i	−0.259685	+	0.568630i
$786$	−2.36990	+	0.695864i	−0.0845314	+	0.0248206i
$787$	15.2904	−	17.6461i	0.545045	−	0.629016i	−0.414676	−	0.909969i	$-0.636105\pi$
$787$	15.2904	−	17.6461i	0.545045	−	0.629016i	0.959721	+	0.280953i	$0.0906506\pi$
$788$	23.1397	+	6.79444i	0.824319	+	0.242042i
$789$	−19.1844	+	12.3291i	−0.682984	+	0.438927i
$790$	−30.5645	+	13.9583i	−1.08744	+	0.496615i
$791$	2.85806	+	3.02254i	0.101621	+	0.107469i
$792$	1.94096	−	3.02019i	0.0689690	−	0.107318i
$793$	−6.34089	−	0.911682i	−0.225172	−	0.0323748i
$794$	−20.4749	−	2.94385i	−0.726628	−	0.104473i
$795$	12.8471	+	8.25635i	0.455641	+	0.292823i
$796$	2.94810	+	3.40228i	0.104492	+	0.120591i
$797$	7.31728	+	16.0226i	0.259191	+	0.567550i	0.993831	−	0.110908i	$-0.0353759\pi$
$797$	7.31728	+	16.0226i	0.259191	+	0.567550i	−0.734639	+	0.678458i	$0.762649\pi$
$798$	−1.79469	+	1.26677i	−0.0635313	+	0.0448431i
$799$	12.7659	−	43.4768i	0.451627	−	1.53810i
$800$	4.85176	−	5.59923i	0.171536	−	0.197963i
$801$	12.7419	−	3.74136i	0.450213	−	0.132194i
$802$	−0.0995793	−	0.0454763i	−0.00351627	−	0.00160583i
$803$	4.23138	+	29.4299i	0.149322	+	1.03856i
$804$	−5.26541			−0.185697
$805$	−27.2251	−	35.4488i	−0.959559	−	1.24941i
$806$	17.0327			0.599953
$807$	1.73049	+	12.0358i	0.0609162	+	0.423682i
$808$	14.2381	+	6.50231i	0.500894	+	0.228751i
$809$	−43.2395	+	12.6963i	−1.52022	+	0.446377i	−0.932041	−	0.362354i	$-0.881973\pi$
$809$	−43.2395	+	12.6963i	−1.52022	+	0.446377i	−0.588179	+	0.808731i	$0.700155\pi$
$810$	−2.30682	+	2.66222i	−0.0810536	+	0.0935408i
$811$	8.28462	−	28.2148i	0.290912	−	0.990756i	−0.676266	−	0.736657i	$-0.736403\pi$
$811$	8.28462	−	28.2148i	0.290912	−	0.990756i	0.967178	−	0.254099i	$-0.0817788\pi$
$812$	7.51440	+	10.6460i	0.263704	+	0.373601i
$813$	−6.26265	−	13.7133i	−0.219641	−	0.480946i
$814$	−21.7091	−	25.0536i	−0.760903	−	0.878129i
$815$	33.7231	+	21.6725i	1.18127	+	0.759155i
$816$	−6.34174	−	0.911804i	−0.222005	−	0.0319195i
$817$	5.75709	+	0.827745i	0.201415	+	0.0289591i
$818$	−9.50462	+	14.7895i	−0.332321	+	0.517102i
$819$	10.3489	+	10.9445i	0.361620	+	0.382430i
$820$	−25.3340	+	11.5696i	−0.884701	+	0.404029i
$821$	35.5601	−	22.8531i	1.24105	−	0.797578i	0.255480	−	0.966814i	$-0.417767\pi$
$821$	35.5601	−	22.8531i	1.24105	−	0.797578i	0.985575	+	0.169237i	$0.0541303\pi$
$822$	18.6909	+	5.48813i	0.651919	+	0.191421i
$823$	16.1180	−	18.6011i	0.561837	−	0.648395i	−0.401762	−	0.915744i	$-0.631602\pi$
$823$	16.1180	−	18.6011i	0.561837	−	0.648395i	0.963600	+	0.267349i	$0.0861477\pi$
$824$	11.4117	−	3.35076i	0.397544	−	0.116729i
$825$	11.0494	−	24.1949i	0.384692	−	0.842359i
$826$	−1.57827	−	8.37628i	−0.0549150	−	0.291448i
$827$			35.1860i			1.22354i	0.791036	+	0.611769i	$0.209542\pi$
$827$			35.1860i			1.22354i	−0.791036	+	0.611769i	$0.790458\pi$
$828$	0.873184	+	4.71567i	0.0303452	+	0.163881i
$829$			18.7620i			0.651631i	0.945433	+	0.325816i	$0.105639\pi$
$829$			18.7620i			0.651631i	−0.945433	+	0.325816i	$0.894361\pi$
$830$	−4.77924	−	33.2404i	−0.165890	−	1.15379i
$831$	−19.5692	−	8.93697i	−0.678849	−	0.310020i
$832$	1.60394	+	5.46251i	0.0556065	+	0.189378i
$833$	26.3180	−	36.3148i	0.911864	−	1.25823i
$834$	12.9092	+	3.79048i	0.447009	+	0.131254i
$835$	−31.6304	−	49.2179i	−1.09461	−	1.70325i
$836$	−2.71144	+	1.23828i	−0.0937773	+	0.0428266i
$837$	1.95922	+	2.26106i	0.0677206	+	0.0781537i
$838$	11.6217	+	7.46881i	0.401465	+	0.258006i
$839$	−2.82190	+	19.6267i	−0.0974228	+	0.677590i	0.881323	+	0.472514i	$0.156653\pi$
$839$	−2.82190	+	19.6267i	−0.0974228	+	0.677590i	−0.978746	+	0.205076i	$0.934256\pi$
$840$	0.924526	−	9.27400i	0.0318992	−	0.319984i
$841$	−3.98952	−	2.56391i	−0.137570	−	0.0884106i
$842$	9.94059	−	8.61357i	0.342575	−	0.296843i
$843$	3.68265	+	8.06389i	0.126837	+	0.277735i
$844$	−8.02810	+	5.15934i	−0.276338	+	0.177592i
$845$	−65.6097	−	19.2648i	−2.25704	−	0.662728i
$846$	−5.34493	−	4.63141i	−0.183763	−	0.159231i
$847$	1.61487	+	4.72945i	0.0554875	+	0.162506i
$848$	3.94348	+	1.80093i	0.135420	+	0.0618441i
$849$	−24.7376	+	3.55674i	−0.848994	+	0.122067i
$850$	−47.4681			−1.62814
$851$	44.0517	+	4.53148i	1.51007	+	0.155337i
$852$			8.84133i			0.302899i
$853$	−44.5756	+	6.40900i	−1.52624	+	0.219440i	−0.853756	−	0.520673i	$-0.825681\pi$
$853$	−44.5756	+	6.40900i	−1.52624	+	0.219440i	−0.672482	+	0.740113i	$0.734772\pi$
$854$	2.75921	+	1.11797i	0.0944181	+	0.0382560i
$855$	2.80630	−	0.824005i	0.0959735	−	0.0281804i
$856$	3.04224	+	2.63611i	0.103981	+	0.0901005i
$857$	−3.35203	+	11.4160i	−0.114503	+	0.389962i	−0.996724	−	0.0808730i	$-0.974229\pi$
$857$	−3.35203	+	11.4160i	−0.114503	+	0.389962i	0.882221	+	0.470835i	$0.156047\pi$
$858$	11.0501	+	17.1943i	0.377245	+	0.587004i
$859$	49.6655	−	22.6815i	1.69456	−	0.773881i	0.696131	−	0.717915i	$-0.254903\pi$
$859$	49.6655	−	22.6815i	1.69456	−	0.773881i	0.998433	−	0.0559662i	$-0.0178239\pi$
$860$	−18.6493	+	16.1597i	−0.635936	+	0.551042i
$861$	−10.5343	+	18.0719i	−0.359009	+	0.615887i
$862$	31.7494	+	4.56487i	1.08139	+	0.155480i
$863$	6.16707	−	42.8929i	0.209930	−	1.46009i	−0.563450	−	0.826150i	$-0.690526\pi$
$863$	6.16707	−	42.8929i	0.209930	−	1.46009i	0.773380	−	0.633943i	$-0.218565\pi$
$864$	−0.540641	+	0.841254i	−0.0183930	+	0.0286200i
$865$	−54.3238	+	47.0719i	−1.84707	+	1.60049i
$866$	2.38439	+	5.22109i	0.0810249	+	0.177420i
$867$	13.0019	+	20.2313i	0.441567	+	0.687092i
$868$	−7.68463	−	1.89817i	−0.260833	−	0.0644282i
$869$	−22.4255	+	25.8804i	−0.760733	+	0.877933i
$870$	−4.88795	−	16.6468i	−0.165717	−	0.564381i
$871$	12.4527	−	27.2677i	0.421945	−	0.923930i
$872$	8.33165	−	1.19791i	0.282145	−	0.0405664i
$873$	−5.19340			−0.175770
$874$	1.50690	−	3.68576i	0.0509715	−	0.124673i
$875$	−0.974889	−	22.4292i	−0.0329573	−	0.758245i
$876$	−1.17862	−	8.19748i	−0.0398219	−	0.276967i
$877$	−16.8620	+	36.9226i	−0.569389	+	1.24679i	0.377733	+	0.925915i	$0.376704\pi$
$877$	−16.8620	+	36.9226i	−0.569389	+	1.24679i	−0.947122	+	0.320874i	$0.896023\pi$
$878$	3.58658	+	12.2148i	0.121041	+	0.412228i
$879$	1.02790	+	0.890684i	0.0346704	+	0.0300420i
$880$	3.56296	−	12.1343i	0.120107	−	0.409048i
$881$	−10.1688	+	6.53508i	−0.342595	+	0.220173i	−0.700612	−	0.713543i	$-0.747089\pi$
$881$	−10.1688	+	6.53508i	−0.342595	+	0.220173i	0.358017	+	0.933715i	$0.383453\pi$
$882$	−3.44942	−	6.09110i	−0.116148	−	0.205098i
$883$	4.34865	+	5.01861i	0.146344	+	0.168890i	0.824189	−	0.566315i	$-0.191631\pi$
$883$	4.34865	+	5.01861i	0.146344	+	0.168890i	−0.677845	+	0.735205i	$0.737086\pi$
$884$	19.7202	−	30.6852i	0.663261	−	1.03205i
$885$	−1.61508	+	11.2331i	−0.0542903	+	0.377597i
$886$	2.30516	−	16.0328i	0.0774435	−	0.538631i
$887$	−31.8027	+	49.4860i	−1.06783	+	1.66158i	−0.401631	+	0.915801i	$0.631557\pi$
$887$	−31.8027	+	49.4860i	−1.06783	+	1.66158i	−0.666199	+	0.745774i	$0.732080\pi$
$888$	6.04691	+	6.97851i	0.202921	+	0.234183i
$889$	−24.4226	+	12.4624i	−0.819109	+	0.417974i
$890$	39.3536	−	25.2910i	1.31914	−	0.847757i
$891$	−1.01145	+	3.44469i	−0.0338849	+	0.115401i
$892$	13.6167	+	11.7990i	0.455922	+	0.395059i
$893$	1.65435	+	5.63422i	0.0553609	+	0.188542i
$894$	−5.79747	+	12.6947i	−0.193896	+	0.424574i
$895$	9.81692	+	68.2782i	0.328144	+	2.28229i
$896$	−0.114890	−	2.64326i	−0.00383820	−	0.0883050i
$897$	−26.4859	−	6.63068i	−0.884337	−	0.221392i
$898$	1.02538			0.0342172
$899$	−14.5853	+	2.09705i	−0.486447	+	0.0699406i
$900$	−3.07774	+	6.73932i	−0.102591	+	0.224644i
$901$	−7.82532	−	26.6506i	−0.260699	−	0.887860i
$902$	−18.5878	+	21.4515i	−0.618907	+	0.714257i
$903$	−4.44447	+	17.9932i	−0.147903	+	0.598775i
$904$	−0.850034	−	1.32268i	−0.0282717	−	0.0439916i
$905$	0.991742	+	2.17161i	0.0329666	+	0.0721868i
$906$	10.5607	−	9.15088i	0.350855	−	0.304018i
$907$	25.1883	−	39.1937i	0.836363	−	1.30141i	−0.115010	−	0.993364i	$-0.536690\pi$
$907$	25.1883	−	39.1937i	0.836363	−	1.30141i	0.951373	−	0.308041i	$-0.0996735\pi$
$908$	−0.0387421	+	0.269457i	−0.00128570	+	0.00894224i
$909$	−15.4933	−	2.22759i	−0.513879	−	0.0738846i
$910$	45.8402	+	26.7209i	1.51959	+	0.885788i
$911$	39.2481	−	34.0086i	1.30035	−	1.12676i	0.316335	−	0.948647i	$-0.397548\pi$
$911$	39.2481	−	34.0086i	1.30035	−	1.12676i	0.984011	−	0.178109i	$-0.0569979\pi$
$912$	0.755254	−	0.344913i	0.0250089	−	0.0114212i
$913$	−18.5038	−	28.7924i	−0.612385	−	0.952890i
$914$	−10.7243	+	36.5235i	−0.354727	+	1.20809i
$915$	−2.99562	−	2.59572i	−0.0990321	−	0.0858118i
$916$	−18.7645	+	5.50977i	−0.619998	+	0.182048i
$917$	−2.45399	+	6.05659i	−0.0810379	+	0.200006i
$918$	6.34174	−	0.911804i	0.209309	−	0.0300940i
$919$			27.6518i			0.912148i	0.889942	+	0.456074i	$0.150745\pi$
$919$			27.6518i			0.912148i	−0.889942	+	0.456074i	$0.849255\pi$
$920$	7.63130	+	15.0720i	0.251597	+	0.496911i
$921$	14.4231			0.475257
$922$	13.2433	−	1.90410i	0.436146	−	0.0627083i
$923$	−45.7861	−	20.9098i	−1.50707	−	0.688254i
$924$	−3.06928	−	8.98898i	−0.100972	−	0.295716i
$925$	51.7027	+	44.8006i	1.69997	+	1.47304i
$926$	19.0429	+	5.59150i	0.625789	+	0.183748i
$927$	−10.0054	+	6.43007i	−0.328620	+	0.211191i
$928$	−2.04600	−	4.48012i	−0.0671634	−	0.147067i
$929$	19.6712	−	17.0452i	0.645391	−	0.559234i	−0.269467	−	0.963010i	$-0.586848\pi$
$929$	19.6712	−	17.0452i	0.645391	−	0.559234i	0.914858	+	0.403775i	$0.132302\pi$
$930$	8.86599	+	5.69782i	0.290727	+	0.186839i
$931$	−0.324860	+	5.80291i	−0.0106469	+	0.190183i
$932$	−4.07672	+	28.3542i	−0.133537	+	0.928772i
$933$	21.1942	+	13.6207i	0.693866	+	0.445921i
$934$	8.72272	+	10.0666i	0.285416	+	0.329388i
$935$	−73.7039	+	33.6595i	−2.41038	+	1.10078i
$936$	−3.07793	−	4.78935i	−0.100605	−	0.156545i
$937$	7.89570	+	2.31839i	0.257941	+	0.0757384i	0.408146	−	0.912916i	$-0.366175\pi$
$937$	7.89570	+	2.31839i	0.257941	+	0.0757384i	−0.150205	+	0.988655i	$0.547993\pi$
$938$	−8.65706	+	10.9145i	−0.282663	+	0.356373i
$939$	1.10540	+	3.76464i	0.0360733	+	0.122854i
$940$	−22.6619	−	10.3493i	−0.739149	−	0.337558i
$941$	−5.27054	−	36.6574i	−0.171815	−	1.19500i	−0.875047	−	0.484037i	$-0.839170\pi$
$941$	−5.27054	−	36.6574i	−0.171815	−	1.19500i	0.703233	−	0.710960i	$-0.251739\pi$
$942$		−	4.97203i		−	0.161997i
$943$	−1.52738	−	37.8864i	−0.0497384	−	1.23375i
$944$			3.22165i			0.104856i
$945$	1.72571	+	9.15881i	0.0561374	+	0.297936i
$946$	−10.4474	+	22.8767i	−0.339675	+	0.743785i
$947$	−9.17372	+	2.69365i	−0.298106	+	0.0875318i	−0.427365	−	0.904079i	$-0.640558\pi$
$947$	−9.17372	+	2.69365i	−0.298106	+	0.0875318i	0.129259	+	0.991611i	$0.458740\pi$
$948$	6.24647	−	7.20881i	0.202876	−	0.234131i
$949$	45.2393	+	13.2834i	1.46853	+	0.431199i
$950$	5.17493	−	3.32573i	0.167897	−	0.107901i
$951$	−6.17114	+	2.81826i	−0.200113	+	0.0913884i
$952$	−12.3167	+	11.6465i	−0.399188	+	0.377465i
$953$	−3.21850	+	5.00809i	−0.104258	+	0.162228i	−0.889463	−	0.457008i	$-0.848921\pi$
$953$	−3.21850	+	5.00809i	−0.104258	+	0.162228i	0.785205	+	0.619236i	$0.212557\pi$
$954$	−4.29112	−	0.616970i	−0.138930	−	0.0199751i
$955$	29.3432	+	4.21892i	0.949524	+	0.136521i
$956$	−11.8652	−	7.62530i	−0.383748	−	0.246620i
$957$	−11.5793	−	13.3632i	−0.374305	−	0.431971i
$958$	−7.52884	−	16.4859i	−0.243246	−	0.532634i
$959$	42.1065	−	29.7206i	1.35969	−	0.959728i
$960$	−0.992436	+	3.37993i	−0.0320307	+	0.109087i
$961$	−14.4391	+	16.6636i	−0.465776	+	0.537534i
$962$	−50.4402	+	14.8106i	−1.62626	+	0.477512i
$963$	−3.66168	−	1.67223i	−0.117996	−	0.0538870i
$964$	2.09117	+	14.5444i	0.0673521	+	0.468444i
$965$	82.7707			2.66448
$966$	11.2106	+	5.94320i	0.360696	+	0.191219i
$967$	47.6295			1.53166			0.765830	−	0.643043i	$-0.222328\pi$
$967$	47.6295			1.53166			0.765830	+	0.643043i	$0.222328\pi$
$968$	−0.268818	−	1.86967i	−0.00864014	−	0.0600935i
$969$	−4.83887	−	2.20984i	−0.155447	−	0.0709903i
$970$	−17.5533	+	5.15412i	−0.563603	+	0.165489i
$971$	−7.41641	+	8.55900i	−0.238004	+	0.274671i	−0.862168	−	0.506622i	$-0.830894\pi$
$971$	−7.41641	+	8.55900i	−0.238004	+	0.274671i	0.624164	+	0.781293i	$0.285440\pi$
$972$	0.281733	−	0.959493i	0.00903658	−	0.0307758i
$973$	29.0817	−	20.5271i	0.932315	−	0.658068i
$974$	13.8890	+	30.4126i	0.445031	+	0.974481i
$975$	−27.6216	−	31.8771i	−0.884600	−	1.02088i
$976$	−0.946608	−	0.608348i	−0.0303002	−	0.0194727i
$977$	−14.7221	−	2.11671i	−0.471001	−	0.0677197i	−0.0972722	−	0.995258i	$-0.531012\pi$
$977$	−14.7221	−	2.11671i	−0.471001	−	0.0677197i	−0.373729	+	0.927538i	$0.621921\pi$
$978$	−11.2640	−	1.61952i	−0.360182	−	0.0517864i
$979$	25.7756	−	40.1076i	0.823792	−	1.28185i
$980$	−17.7038	−	17.1642i	−0.565528	−	0.548289i
$981$	−7.65667	+	3.49669i	−0.244459	+	0.111641i
$982$	2.78823	−	1.79189i	0.0889761	−	0.0571815i
$983$	−41.3444	−	12.1398i	−1.31868	−	0.387199i	−0.454664	−	0.890663i	$-0.650241\pi$
$983$	−41.3444	−	12.1398i	−1.31868	−	0.387199i	−0.864016	+	0.503464i	$0.832059\pi$
$984$	5.17751	−	5.97516i	0.165053	−	0.190481i
$985$	−81.5125	+	23.9342i	−2.59720	+	0.762608i
$986$	−13.1087	+	28.7039i	−0.417464	+	0.914120i
$987$	−18.3881	+	3.46471i	−0.585301	+	0.110283i
$988$			4.72691i			0.150383i
$989$	−10.7558	−	31.8274i	−0.342014	−	1.01205i
$990$			12.6466i			0.401935i
$991$	−4.24102	−	29.4970i	−0.134721	−	0.937002i	−0.939285	−	0.343137i	$-0.888510\pi$
$991$	−4.24102	−	29.4970i	−0.134721	−	0.937002i	0.804565	−	0.593865i	$-0.202399\pi$
$992$	2.72145	+	1.24284i	0.0864061	+	0.0394603i
$993$	−0.617614	−	2.10340i	−0.0195994	−	0.0667494i
$994$	18.3270	+	14.5363i	0.581296	+	0.461065i
$995$	−15.2160	−	4.46782i	−0.482379	−	0.141639i
$996$	5.15409	+	8.01992i	0.163314	+	0.254121i
$997$	−39.5281	+	18.0519i	−1.25187	+	0.571708i	−0.927358	−	0.374174i	$-0.877926\pi$
$997$	−39.5281	+	18.0519i	−1.25187	+	0.571708i	−0.324508	+	0.945883i	$0.605199\pi$
$998$	15.8828	+	18.3298i	0.502763	+	0.580219i
$999$	−7.76804	−	4.99222i	−0.245770	−	0.157947i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	966.2.s.b.181.15	yes	160
7.6	odd	2	inner	966.2.s.b.181.2	✓	160
23.15	odd	22	inner	966.2.s.b.475.2	yes	160
161.153	even	22	inner	966.2.s.b.475.15	yes	160

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
966.2.s.b.181.2	✓	160	7.6	odd	2	inner
966.2.s.b.181.15	yes	160	1.1	even	1	trivial
966.2.s.b.475.2	yes	160	23.15	odd	22	inner
966.2.s.b.475.15	yes	160	161.153	even	22	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 966 = 2 \cdot 3 \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	966.s (of order \(22\), degree \(10\), minimal)

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.30682 - 2.66222i) q^{5} +(-0.281733 + 0.959493i) q^{6} +(1.52570 + 2.16153i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(q+(0.142315 + 0.989821i) q^{2} +(0.909632 + 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(2.30682 - 2.66222i) q^{5} +(-0.281733 + 0.959493i) q^{6} +(1.52570 + 2.16153i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +(2.96342 + 1.90447i) q^{10} +(3.55357 + 0.510926i) q^{11} +(-0.989821 - 0.142315i) q^{12} +(3.07793 - 4.78935i) q^{13} +(-1.92240 + 1.81779i) q^{14} +(3.20429 - 1.46335i) q^{15} +(0.841254 - 0.540641i) q^{16} +(-6.14743 - 1.80505i) q^{17} +(-0.654861 + 0.755750i) q^{18} +(0.796653 - 0.233918i) q^{19} +(-1.46335 + 3.20429i) q^{20} +(0.489895 + 2.60000i) q^{21} +3.59011i q^{22} +(-3.28405 - 3.49500i) q^{23} -1.00000i q^{24} +(-1.05439 - 7.33343i) q^{25} +(5.17864 + 2.36501i) q^{26} +(0.281733 + 0.959493i) q^{27} +(-2.07288 - 1.64414i) q^{28} +(-4.72570 - 1.38759i) q^{29} +(1.90447 + 2.96342i) q^{30} +(2.72145 - 1.24284i) q^{31} +(0.654861 + 0.755750i) q^{32} +(3.02019 + 1.94096i) q^{33} +(0.911804 - 6.34174i) q^{34} +(9.27400 + 0.924526i) q^{35} +(-0.841254 - 0.540641i) q^{36} +(-6.97851 + 6.04691i) q^{37} +(0.344913 + 0.755254i) q^{38} +(4.78935 - 3.07793i) q^{39} +(-3.37993 - 0.992436i) q^{40} +(5.97516 + 5.17751i) q^{41} +(-2.50382 + 0.854927i) q^{42} +(6.37214 + 2.91006i) q^{43} +(-3.55357 + 0.510926i) q^{44} +3.52262 q^{45} +(2.99205 - 3.74802i) q^{46} +7.07236i q^{47} +(0.989821 - 0.142315i) q^{48} +(-2.34446 + 6.59572i) q^{49} +(7.10873 - 2.08731i) q^{50} +(-4.84205 - 4.19566i) q^{51} +(-1.60394 + 5.46251i) q^{52} +(2.34381 + 3.64704i) q^{53} +(-0.909632 + 0.415415i) q^{54} +(9.55766 - 8.28176i) q^{55} +(1.33240 - 2.28576i) q^{56} +(0.821834 + 0.118162i) q^{57} +(0.700930 - 4.87507i) q^{58} +(-1.74175 + 2.71022i) q^{59} +(-2.66222 + 2.30682i) q^{60} +(-0.467439 - 1.02355i) q^{61} +(1.61750 + 2.51687i) q^{62} +(-0.634455 + 2.56855i) q^{63} +(-0.654861 + 0.755750i) q^{64} +(-5.65006 - 19.2423i) q^{65} +(-1.49139 + 3.26568i) q^{66} +(5.21182 - 0.749346i) q^{67} +6.40695 q^{68} +(-1.53541 - 4.54340i) q^{69} +(0.404713 + 9.31118i) q^{70} +(-1.25825 - 8.75133i) q^{71} +(0.415415 - 0.909632i) q^{72} +(2.33325 + 7.94631i) q^{73} +(-6.97851 - 6.04691i) q^{74} +(2.08731 - 7.10873i) q^{75} +(-0.698480 + 0.448886i) q^{76} +(4.31731 + 8.46068i) q^{77} +(3.72820 + 4.30257i) q^{78} +(-5.15697 + 8.02440i) q^{79} +(0.501321 - 3.48676i) q^{80} +(-0.142315 + 0.989821i) q^{81} +(-4.27445 + 6.65118i) q^{82} +(-6.24299 - 7.20479i) q^{83} +(-1.20256 - 2.35666i) q^{84} +(-18.9865 + 12.2019i) q^{85} +(-1.97359 + 6.72142i) q^{86} +(-3.72222 - 3.22532i) q^{87} +(-1.01145 - 3.44469i) q^{88} +(5.51664 - 12.0797i) q^{89} +(0.501321 + 3.48676i) q^{90} +(15.0484 - 0.654080i) q^{91} +(4.13568 + 2.42820i) q^{92} +2.99181 q^{93} +(-7.00038 + 1.00650i) q^{94} +(1.21500 - 2.66047i) q^{95} +(0.281733 + 0.959493i) q^{96} +(-3.40095 + 3.92491i) q^{97} +(-6.86224 - 1.38193i) q^{98} +(1.94096 + 3.02019i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9}+O(q^{10}) \) 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9	\( 160 q + 16 q^{2} - 16 q^{4} + 16 q^{8} + 16 q^{9} + 22 q^{14} - 16 q^{16} - 16 q^{18} - 52 q^{23} - 48 q^{25} + 22 q^{28} - 12 q^{29} + 16 q^{32} + 22 q^{35} + 16 q^{36} + 22 q^{37} - 4 q^{39} + 154 q^{43} + 8 q^{46} + 4 q^{50} + 22 q^{51} + 88 q^{53} + 22 q^{57} + 56 q^{58} - 16 q^{64} + 16 q^{71} - 16 q^{72} + 22 q^{74} - 72 q^{77} + 4 q^{78} + 88 q^{79} - 16 q^{81} - 22 q^{84} - 68 q^{85} - 44 q^{86} + 44 q^{88} - 8 q^{92} - 8 q^{93} - 66 q^{95} + 66 q^{98} - 66 q^{99}+O(q^{100}) \) 160 * q + 16 * q^2 - 16 * q^4 + 16 * q^8 + 16 * q^9 + 22 * q^14 - 16 * q^16 - 16 * q^18 - 52 * q^23 - 48 * q^25 + 22 * q^28 - 12 * q^29 + 16 * q^32 + 22 * q^35 + 16 * q^36 + 22 * q^37 - 4 * q^39 + 154 * q^43 + 8 * q^46 + 4 * q^50 + 22 * q^51 + 88 * q^53 + 22 * q^57 + 56 * q^58 - 16 * q^64 + 16 * q^71 - 16 * q^72 + 22 * q^74 - 72 * q^77 + 4 * q^78 + 88 * q^79 - 16 * q^81 - 22 * q^84 - 68 * q^85 - 44 * q^86 + 44 * q^88 - 8 * q^92 - 8 * q^93 - 66 * q^95 + 66 * q^98 - 66 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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