LMFDB - Embedded newform 966.2.s.b.181.2

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			181.2
Character	$\chi$	$=$	966.181
Dual form			966.2.s.b.475.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.142315 + 0.989821i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.30682 + 2.66222i) q^{5} +(0.281733 - 0.959493i) q^{6} +(1.33240 + 2.28576i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})$	\(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} +(1.33240 + 2.28576i) 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} +(-2.07288 + 1.64414i) 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} +(-0.262454 - 2.63270i) 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} +(-1.92240 - 1.81779i) 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} +(-9.15881 - 1.72571i) 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} +(2.56855 - 0.634455i) 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} +(-3.44942 + 6.09110i) 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} +(1.52570 - 2.16153i) 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} +(-0.854927 + 2.50382i) 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} +(3.56692 + 8.80337i) 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} +(0.993541 + 2.45212i) 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} +(-6.52001 - 2.54745i) 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	$0.515991\pi$
$5$	−2.30682	+	2.66222i	−1.03164	+	1.19058i	−0.981426	+	0.191842i	$0.938554\pi$
$6$	0.281733	−	0.959493i	0.115017	−	0.391711i
$7$	1.33240	+	2.28576i	0.503600	+	0.863937i
$7$	1.33240	+	2.28576i	0.503600	+	0.863937i
$8$	−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	$0.471475\pi$
$13$	−3.07793	+	4.78935i	−0.853665	+	1.32833i	−0.943159	+	0.332341i	$0.892162\pi$
$14$	−2.07288	+	1.64414i	−0.553999	+	0.439414i
$15$	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	0.922851	−	0.385158i	$-0.125853\pi$
$17$	6.14743	+	1.80505i	1.49097	+	0.437788i	0.568119	+	0.822946i	$0.307671\pi$
$18$	−0.654861	+	0.755750i	−0.154352	+	0.178132i
$19$	−0.796653	+	0.233918i	−0.182765	+	0.0536645i	−0.371834	−	0.928299i	$-0.621271\pi$
$19$	−0.796653	+	0.233918i	−0.182765	+	0.0536645i	0.189070	+	0.981964i	$0.439453\pi$
$20$	1.46335	−	3.20429i	0.327215	−	0.716500i
$21$	−0.262454	−	2.63270i	−0.0572722	−	0.574503i
$22$			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
$28$	−1.92240	−	1.81779i	−0.363300	−	0.343530i
$29$	−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	−0.644534	−	0.764575i	$-0.722949\pi$
$31$	−2.72145	+	1.24284i	−0.488787	+	0.223221i	0.155747	+	0.987797i	$0.450221\pi$
$32$	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
$35$	−9.15881	−	1.72571i	−1.54812	−	0.291699i
$36$	−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	0.0485762	−	0.998819i	$-0.484532\pi$
$41$	−5.97516	−	5.17751i	−0.933164	−	0.808591i	−0.981740	+	0.190229i	$0.939077\pi$
$42$	2.56855	−	0.634455i	0.396336	−	0.0978986i
$43$	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	$-0.827493\pi$
$47$		−	7.07236i		−	1.03161i	0.856706	−	0.515805i	$-0.172507\pi$
$48$	−0.989821	+	0.142315i	−0.142868	+	0.0205414i
$49$	−3.44942	+	6.09110i	−0.492774	+	0.870157i
$50$	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
$56$	1.52570	−	2.16153i	0.203881	−	0.288847i
$57$	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	−0.709168	−	0.705039i	$-0.750929\pi$
$59$	1.74175	−	2.71022i	0.226757	−	0.352841i	0.935925	+	0.352198i	$0.114566\pi$
$60$	−2.66222	+	2.30682i	−0.343691	+	0.297810i
$61$	0.467439	+	1.02355i	0.0598495	+	0.131052i	0.937194	−	0.348810i	$-0.113414\pi$
$61$	0.467439	+	1.02355i	0.0598495	+	0.131052i	−0.877344	+	0.479862i	$0.840687\pi$
$62$	−1.61750	−	2.51687i	−0.205422	−	0.319643i
$63$	−0.854927	+	2.50382i	−0.107711	+	0.315451i
$64$	−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	$-0.929854\pi$
$73$	−2.33325	−	7.94631i	−0.273086	−	0.930045i	0.702731	−	0.711456i	$-0.251964\pi$
$74$	−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
$77$	3.56692	+	8.80337i	0.406488	+	1.00324i
$78$	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	0.986682	−	0.162661i	$-0.0520078\pi$
$83$	6.24299	+	7.20479i	0.685257	+	0.790828i	−0.301425	+	0.953490i	$0.597462\pi$
$84$	0.993541	+	2.45212i	0.108404	+	0.267548i
$85$	−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	$0.384892\pi$
$89$	−5.51664	+	12.0797i	−0.584762	+	1.28045i	−0.938556	+	0.345127i	$0.887836\pi$
$90$	−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	−0.556352	−	0.830947i	$-0.687799\pi$
$97$	3.40095	−	3.92491i	0.345314	−	0.398514i	0.901666	+	0.432433i	$0.142345\pi$
$98$	−6.52001	−	2.54745i	−0.658620	−	0.257332i
$99$	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	$-0.443130\pi$
$101$	11.8294	−	10.2503i	1.17707	−	1.01994i	0.999357	−	0.0358564i	$-0.0114159\pi$
$102$	3.46386	−	5.38987i	0.342973	−	0.533677i
$103$	1.69261	−	11.7724i	0.166778	−	1.15997i	−0.718713	−	0.695307i	$-0.755268\pi$
$103$	1.69261	−	11.7724i	0.166778	−	1.15997i	0.885490	−	0.464658i	$-0.153823\pi$
$104$	5.63517	+	0.810215i	0.552574	+	0.0794481i
$105$	7.61426	+	5.37447i	0.743076	+	0.524495i
$106$	−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
$112$	2.35666	+	1.20256i	0.222684	+	0.113631i
$113$	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
$119$	4.06492	+	16.4566i	0.372631	+	1.50857i
$120$	−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
$126$	−2.60000	−	0.489895i	−0.231626	−	0.0436433i
$127$	−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	0.778007	−	0.628256i	$-0.216231\pi$
$131$	−1.33535	−	2.07785i	−0.116670	−	0.181543i	−0.894677	+	0.446713i	$0.852594\pi$
$132$	3.44469	+	1.01145i	0.299821	+	0.0880355i
$133$	−1.59614	−	1.50929i	−0.138403	−	0.130872i
$134$	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	$0.193283\pi$
$139$			13.4542i			1.14117i	−0.821239	+	0.570584i	$0.806717\pi$
$140$	9.27400	−	0.924526i	0.783796	−	0.0781367i
$141$	−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
$147$	5.66804	−	4.10772i	0.467492	−	0.338799i
$148$	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
$154$	−8.20614	+	4.78347i	−0.661270	+	0.385463i
$155$	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	−0.0857631	−	0.996316i	$-0.527333\pi$
$157$	4.77063	−	1.40078i	0.380737	−	0.111795i	0.466500	+	0.884521i	$0.345515\pi$
$158$	−8.67663	−	3.96249i	−0.690276	−	0.315238i
$159$	−0.616970	−	4.29112i	−0.0489289	−	0.340308i
$160$	−3.52262			−0.278487
$161$	3.61306	−	12.1633i	0.284749	−	0.958602i
$162$	−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	$0.313054\pi$
$167$	−4.67915	+	15.9357i	−0.362084	+	1.23314i	−0.916206	+	0.400708i	$0.868764\pi$
$168$	−2.28576	+	1.33240i	−0.176350	+	0.102797i
$169$	−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	0.857620	−	0.514284i	$-0.171942\pi$
$173$	20.1978	+	2.90400i	1.53561	+	0.220787i	0.677989	+	0.735072i	$0.262851\pi$
$174$	−2.66277	+	4.14335i	−0.201864	+	0.314106i
$175$	15.3576	−	12.1812i	1.16093	−	0.920808i
$176$	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	−0.898880	−	0.438194i	$-0.855618\pi$
$181$	0.281535	−	0.616477i	0.0209264	−	0.0458223i	0.919807	+	0.392372i	$0.128345\pi$
$182$	−1.49418	−	14.9883i	−0.110756	−	1.11101i
$183$		−	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
$189$	1.81779	−	1.92240i	0.132225	−	0.139834i
$190$	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
$196$	1.59363	−	6.81618i	0.113831	−	0.486870i
$197$	−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	0.964263	−	0.264948i	$-0.0853547\pi$
$199$	1.87014	+	4.09504i	0.132571	+	0.290290i	−0.831692	+	0.555237i	$0.812627\pi$
$200$	−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
$203$	−3.12482	−	12.6507i	−0.219320	−	0.887902i
$204$	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
$210$	−4.23614	+	8.30163i	−0.292322	+	0.572867i
$211$	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
$217$	−6.46691	−	4.56462i	−0.439002	−	0.309867i
$218$	−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	$0.0243184\pi$
$223$	9.74102	+	15.1573i	0.652307	+	1.01501i	−0.344776	+	0.938685i	$0.612045\pi$
$224$	−0.854927	+	2.50382i	−0.0571222	+	0.167293i
$225$	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	−0.913348	−	0.407180i	$-0.866512\pi$
$227$	−0.113088	+	0.247627i	−0.00750588	+	0.0164356i	0.905842	+	0.423616i	$0.139239\pi$
$228$	−0.821834	+	0.118162i	−0.0544273	+	0.00782546i
$229$	−19.5567			−1.29234			−0.646172	−	0.763192i	$-0.723631\pi$
$229$	−19.5567			−1.29234			−0.646172	+	0.763192i	$0.723631\pi$
$230$	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
$238$	−15.7106	+	6.36557i	−1.01837	+	0.412618i
$239$	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	$0.202378\pi$
$241$	−2.09117	+	14.5444i	−0.134704	+	0.936888i	−0.939308	+	0.343076i	$0.888531\pi$
$242$	−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
$245$	−8.25864	−	23.2342i	−0.527625	−	1.48438i
$246$	−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	$0.0774835\pi$
$251$	1.69864	+	11.8143i	0.107217	+	0.745713i	−0.863302	+	0.504688i	$0.831607\pi$
$252$	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	$0.0949355\pi$
$257$	4.97936	+	16.9581i	0.310604	+	1.05782i	−0.645249	+	0.763973i	$0.723246\pi$
$258$	4.58742	−	5.29416i	0.285600	−	0.329600i
$259$	−23.1200	−	7.89430i	−1.43661	−	0.490528i
$260$	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
$266$	1.26677	−	1.79469i	0.0776706	−	0.110039i
$267$	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	0.580908	−	0.813969i	$-0.302698\pi$
$269$	−6.57398	−	10.2293i	−0.400823	−	0.623692i	−0.981730	+	0.190277i	$0.939061\pi$
$270$	−0.992436	+	3.37993i	−0.0603978	+	0.205696i
$271$	11.3934	+	9.87244i	0.692100	+	0.599708i	0.928227	−	0.372014i	$-0.121333\pi$
$271$	11.3934	+	9.87244i	0.692100	+	0.599708i	−0.236127	+	0.971722i	$0.575878\pi$
$272$	6.14743	−	1.80505i	0.372742	−	0.109447i
$273$	13.4168	+	6.84629i	0.812019	+	0.414356i
$274$	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
$280$	2.23494	+	9.04803i	0.133563	+	0.540723i
$281$	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	0.262932	−	0.964814i	$-0.415310\pi$
$283$	21.0246	−	13.5117i	1.24978	−	0.803188i	0.986852	+	0.161627i	$0.0516740\pi$
$284$	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
$287$	3.87324	−	20.5563i	0.228630	−	1.21340i
$288$	−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	0.243390	−	0.969928i	$-0.421740\pi$
$293$	−1.30502	−	0.383188i	−0.0762400	−	0.0223861i	−0.319630	+	0.947542i	$0.603559\pi$
$294$	4.87256	+	5.02575i	0.284173	+	0.293108i
$295$	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
$301$	1.83854	+	18.4425i	0.105972	+	1.06301i
$302$	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	−0.752988	−	0.658035i	$-0.771388\pi$
$307$	−13.1197	+	5.99156i	−0.748781	+	0.341957i	0.00420723	+	0.999991i	$0.498661\pi$
$308$	−5.90263	−	7.44185i	−0.336334	−	0.424039i
$309$	−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	−0.607430	−	0.794374i	$-0.707799\pi$
$311$	−24.9371	−	3.58542i	−1.41405	−	0.203310i	−0.806625	+	0.591063i	$0.798708\pi$
$312$	−4.78935	−	3.07793i	−0.271144	−	0.174254i
$313$	−2.56939	−	2.96524i	−0.145231	−	0.167605i	0.678474	−	0.734625i	$-0.262642\pi$
$313$	−2.56939	−	2.96524i	−0.145231	−	0.167605i	−0.823704	+	0.567020i	$0.808096\pi$
$314$	2.06545	+	4.52271i	0.116560	+	0.255232i
$315$	−4.69354	−	8.05187i	−0.264451	−	0.453671i
$316$	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
$322$	12.5537	+	1.84526i	0.699590	+	0.102832i
$323$	−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
$329$	16.1657	−	9.42322i	0.891246	−	0.519519i
$330$	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
$336$	−1.64414	−	2.07288i	−0.0896950	−	0.113085i
$337$	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
$343$	−18.5188	+	0.231238i	−0.999922	+	0.0124857i
$344$		−	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	$0.0365898\pi$
$349$	4.10450	+	13.9786i	0.219709	+	0.748259i	−0.773692	+	0.633562i	$0.781592\pi$
$350$	14.2428	+	13.4677i	0.761309	+	0.719881i
$351$	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	−0.593615	−	0.804749i	$-0.702300\pi$
$353$	−7.02985	+	3.21042i	−0.374161	+	0.170874i	0.219454	+	0.975623i	$0.429572\pi$
$354$	−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
$357$	3.13873	−	16.6581i	0.166119	−	0.881639i
$358$	−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
$364$	14.6231	−	3.61203i	0.766457	−	0.189322i
$365$	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	$-0.592878\pi$
$367$	−11.0216			−0.575325			−0.287663	+	0.957732i	$0.592878\pi$
$368$	−4.65226	−	1.16468i	−0.242516	−	0.0607134i
$369$		−	7.90627i		−	0.411584i
$370$	32.1964	−	4.62914i	1.67381	−	0.240658i
$371$	−5.21337	+	10.2167i	−0.270665	+	0.530425i
$372$	−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
$378$	2.16153	+	1.52570i	0.111177	+	0.0784737i
$379$	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	$0.0663312\pi$
$383$	9.66821	+	21.1704i	0.494023	+	1.08176i	−0.484344	+	0.874878i	$0.660942\pi$
$384$	0.540641	+	0.841254i	0.0275895	+	0.0429300i
$385$	−31.6648	−	10.8119i	−1.61379	−	0.551026i
$386$	−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	$-0.735363\pi$
$397$	5.82777	−	19.8476i	0.292488	−	0.996121i	0.966343	−	0.257258i	$-0.0828189\pi$
$398$	−3.78721	+	2.43389i	−0.189836	+	0.122000i
$399$	0.824922	+	2.03596i	0.0412977	+	0.101925i
$400$	−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
$406$	12.0772	−	4.89339i	0.599380	−	0.242855i
$407$	−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	0.261286	−	0.965261i	$-0.415853\pi$
$409$	−13.2863	−	11.5126i	−0.656965	−	0.569264i	−0.918251	+	0.395998i	$0.870399\pi$
$410$	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	−0.932401	−	0.361424i	$-0.882291\pi$
$419$	−9.04672	+	10.4405i	−0.441961	+	0.510051i	0.490440	+	0.871475i	$0.336836\pi$
$420$	−8.81999	−	3.01158i	−0.430372	−	0.146950i
$421$	−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
$427$	−1.71677	+	2.43223i	−0.0830805	+	0.117704i
$428$	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	−0.411372	−	0.911468i	$-0.634950\pi$
$433$	−5.50728	+	1.61708i	−0.264663	+	0.0777121i	0.146709	+	0.989180i	$0.453132\pi$
$434$	3.59782	−	7.05070i	0.172701	−	0.338444i
$435$	−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	−0.436292	−	0.899805i	$-0.643708\pi$
$439$	−12.6009	+	1.81173i	−0.601406	+	0.0864691i	−0.165114	+	0.986274i	$0.552799\pi$
$440$	11.5037	+	5.25358i	0.548420	+	0.250455i
$441$	−6.86224	+	1.38193i	−0.326773	+	0.0658061i
$442$	−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
$448$	−2.60000	−	0.489895i	−0.122838	−	0.0231454i
$449$	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
$455$	36.4552	−	38.5532i	1.70905	−	1.80740i
$456$	−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	$0.100856\pi$
$461$			13.3795i			0.623146i	−0.950222	+	0.311573i	$0.899144\pi$
$462$	9.45169	−	0.942240i	0.439732	−	0.0438370i
$463$	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	−0.773589	−	0.633688i	$-0.781540\pi$
$467$	−11.2055	+	7.20131i	−0.518527	+	0.333237i	0.255062	+	0.966925i	$0.417904\pi$
$468$	5.17864	−	2.36501i	0.239383	−	0.109322i
$469$	8.65706	+	10.9145i	0.399746	+	0.503987i
$470$	−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
$476$	−8.53663	−	14.6448i	−0.391276	−	0.671242i
$477$	−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	0.140825	−	0.990035i	$-0.455025\pi$
$479$	17.3895	−	5.10602i	0.794547	−	0.233300i	0.653723	+	0.756734i	$0.273206\pi$
$480$	3.20429	+	1.46335i	0.146255	+	0.0667924i
$481$	−7.48144	−	52.0345i	−0.341124	−	2.37257i
$482$	−14.6940			−0.669292
$483$	−8.33937	+	9.56321i	−0.379454	+	0.435141i
$484$	−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
$490$	21.8224	−	11.4811i	0.985835	−	0.518665i
$491$	−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
$497$	18.3270	−	14.5363i	0.822077	−	0.652044i
$498$	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	−0.934915	−	0.354871i	$-0.884525\pi$
$503$	−1.22191	+	2.67560i	−0.0544821	+	0.119299i	0.880433	+	0.474170i	$0.157252\pi$
$504$	2.63270	−	0.262454i	0.117270	−	0.0116906i
$505$			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	$0.0602005\pi$
$509$	39.8751	+	18.2104i	1.76743	+	0.807160i	0.785265	+	0.619160i	$0.212527\pi$
$510$	6.35849	+	21.6550i	0.281559	+	0.958901i
$511$	15.0546	−	15.9209i	0.665974	−	0.704300i
$512$	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
$518$	4.52364	−	24.0081i	0.198757	−	1.05486i
$519$	−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	$-0.830002\pi$
$521$	−15.5619	−	34.0759i	−0.681781	−	1.49289i	0.178964	−	0.983856i	$-0.442726\pi$
$522$	4.14335	−	2.66277i	0.181349	−	0.116546i
$523$	13.1372	+	3.85743i	0.574449	+	0.168674i	0.556038	−	0.831157i	$-0.312321\pi$
$523$	13.1372	+	3.85743i	0.574449	+	0.168674i	0.0184114	+	0.999830i	$0.494139\pi$
$524$	1.86666	+	1.61747i	0.0815454	+	0.0706595i
$525$	−19.0300	+	4.70058i	−0.830538	+	0.205150i
$526$	−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
$532$	1.95670	+	0.998464i	0.0848338	+	0.0432889i
$533$	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
$539$	−15.3698	+	19.8828i	−0.662026	+	0.856411i
$540$	−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
$546$	−4.86720	+	14.2545i	−0.208297	+	0.610037i
$547$	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
$560$	−8.63787	+	3.49987i	−0.365017	+	0.147896i
$561$	−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	$-0.841350\pi$
$563$	2.35138	−	16.3542i	0.0990987	−	0.689247i	0.977440	−	0.211213i	$-0.0677413\pi$
$564$	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
$567$	−2.45212	+	0.993541i	−0.102979	+	0.0417248i
$568$	−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	0.608652	−	0.793437i	$-0.291711\pi$
$577$	34.0180	−	4.89105i	1.41619	−	0.203617i	0.807535	+	0.589820i	$0.200801\pi$
$578$	−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
$581$	−8.15028	+	23.8696i	−0.338131	+	0.990280i
$582$	−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	−0.0351441	−	0.999382i	$-0.511189\pi$
$587$	−8.49008	−	1.22069i	−0.350423	−	0.0503832i	−0.315279	+	0.948999i	$0.602098\pi$
$588$	−4.28116	+	5.53820i	−0.176552	+	0.228392i
$589$	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	0.926464	−	0.376384i	$-0.122832\pi$
$593$	16.6994	+	14.4701i	0.685761	+	0.594215i	−0.240703	+	0.970599i	$0.577378\pi$
$594$	3.44469	−	1.01145i	0.141337	−	0.0415003i
$595$	−53.1881	−	27.1408i	−2.18050	−	1.11266i
$596$	−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	0.971662	−	0.236373i	$-0.0759587\pi$
$601$	35.0404	+	16.0024i	1.42933	+	0.652752i	0.457665	+	0.889125i	$0.348686\pi$
$602$	−17.9932	+	4.44447i	−0.733347	+	0.181143i
$603$	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	−0.607943	−	0.793980i	$-0.708005\pi$
$607$	2.25275	−	1.95202i	0.0914363	−	0.0792300i	0.699380	+	0.714750i	$0.253460\pi$
$608$	−0.698480	−	0.448886i	−0.0283271	−	0.0182047i
$609$	−2.41283	+	12.8055i	−0.0977729	+	0.518907i
$610$	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
$616$	6.52608	−	6.90164i	0.262943	−	0.278075i
$617$	−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	0.975579	−	0.219647i	$-0.0704905\pi$
$619$	−0.556405	−	3.86988i	−0.0223638	−	0.155544i	−0.997943	+	0.0641031i	$0.979581\pi$
$620$			10.5390i			0.423257i
$621$	−2.42820	+	4.13568i	−0.0974403	+	0.165959i
$622$		−	25.1936i		−	1.01017i
$623$	−34.9618	+	3.48534i	−1.40071	+	0.139637i
$624$	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
$630$	7.30195	−	5.79167i	0.290917	−	0.230746i
$631$	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
$637$	−18.5554	−	35.2685i	−0.735191	−	1.39739i
$638$	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	$-0.770745\pi$
$643$	−38.1202			−1.50331			−0.751656	+	0.659555i	$0.770745\pi$
$644$	−0.0399039	+	12.6885i	−0.00157243	+	0.499998i
$645$	24.6766			0.971639
$646$	−0.757057	−	5.26545i	−0.0297860	−	0.207166i
$647$	29.7387	+	13.5812i	1.16915	+	0.533932i	0.902849	−	0.429958i	$-0.141472\pi$
$647$	29.7387	+	13.5812i	1.16915	+	0.533932i	0.266300	+	0.963890i	$0.414199\pi$
$648$	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
$651$	3.98629	+	6.83857i	0.156235	+	0.268025i
$652$	−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
$658$	11.6279	+	14.6601i	0.453304	+	0.571511i
$659$	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	−0.723765	−	0.690047i	$-0.757590\pi$
$661$	−43.8535	−	12.8765i	−1.70570	−	0.500839i	−0.981937	+	0.189207i	$0.939408\pi$
$662$	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
$665$	7.70007	−	0.767620i	0.298596	−	0.0297670i
$666$		−	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
$672$	1.81779	−	1.92240i	0.0701229	−	0.0741583i
$673$	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	0.300918	−	0.953650i	$-0.402707\pi$
$677$	−11.4887	−	7.38334i	−0.441547	−	0.283765i	−0.742465	+	0.669885i	$0.766343\pi$
$678$	0.223758	−	1.55627i	0.00859336	−	0.0597681i
$679$	13.5028	+	2.54422i	0.518191	+	0.0976382i
$680$	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
$686$	−2.86439	−	18.2974i	−0.109363	−	0.698598i
$687$	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	$0.101841\pi$
$691$			16.5351i			0.629024i	−0.949254	+	0.314512i	$0.898159\pi$
$692$	−20.1978	+	2.90400i	−0.767805	+	0.110394i
$693$	−4.31731	+	8.46068i	−0.164001	+	0.321395i
$694$	−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
$700$	−11.3037	+	16.0145i	−0.427240	+	0.605290i
$701$	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
$707$	39.1912	+	13.3818i	1.47394	+	0.503275i
$708$	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	$0.260816\pi$
$719$	−7.68721	+	26.1802i	−0.286684	+	0.976358i	−0.969362	+	0.245638i	$0.921003\pi$
$720$	−2.96342	+	1.90447i	−0.110440	+	0.0709755i
$721$	29.1640	−	11.8166i	1.08613	−	0.440073i
$722$	−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	0.947217	−	0.320592i	$-0.103882\pi$
$727$	13.3490	+	15.4055i	0.495086	+	0.571359i	−0.452132	+	0.891951i	$0.649336\pi$
$728$	5.65634	+	13.9602i	0.209638	+	0.517399i
$729$	−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	$0.460936\pi$
$733$	−19.1634	+	41.9619i	−0.707815	+	1.54990i	−0.830231	+	0.557420i	$0.811791\pi$
$734$	−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
$742$	−10.8547	−	3.70632i	−0.398487	−	0.136063i
$743$	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
$749$	−8.70116	−	6.14165i	−0.317933	−	0.224411i
$750$	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
$756$	−1.20256	+	2.35666i	−0.0437365	+	0.0857110i
$757$	−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	0.252061	−	0.967711i	$-0.418892\pi$
$761$	21.1462	−	3.04036i	0.766548	−	0.110213i	0.514487	+	0.857498i	$0.327982\pi$
$762$	9.42672	+	4.30504i	0.341494	+	0.155955i
$763$	−21.6204	+	5.34042i	−0.782710	+	0.193336i
$764$	−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	0.627175	−	0.778879i	$-0.284211\pi$
$769$	4.96991	+	3.19397i	0.179220	+	0.115177i	−0.447955	+	0.894056i	$0.647848\pi$
$770$	6.19550	−	32.8811i	0.223270	−	1.18495i
$771$	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	0.970588	−	0.240747i	$-0.0773924\pi$
$773$	16.5194	+	19.0644i	0.594162	+	0.685700i	−0.376426	+	0.926447i	$0.622847\pi$
$774$	−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
$777$	17.7513	+	16.7853i	0.636823	+	0.602169i
$778$	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
$784$	0.391263	+	6.98906i	0.0139737	+	0.249609i
$785$	−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	−0.959721	−	0.280953i	$-0.909349\pi$
$787$	−15.2904	+	17.6461i	−0.545045	+	0.629016i	0.414676	+	0.909969i	$0.363895\pi$
$788$	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
$791$	2.58503	+	3.25912i	0.0919130	+	0.115881i
$792$	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	0.734639	−	0.678458i	$-0.237351\pi$
$797$	−7.31728	−	16.0226i	−0.259191	−	0.567550i	−0.993831	+	0.110908i	$0.964624\pi$
$798$	−1.89783	+	1.10627i	−0.0671826	+	0.0391616i
$799$	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
$805$	24.0467	+	37.6773i	0.847534	+	1.32795i
$806$	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	$0.263597\pi$
$811$	−8.28462	+	28.2148i	−0.290912	+	0.990756i	−0.967178	+	0.254099i	$0.918221\pi$
$812$	6.56235	+	11.2578i	0.230293	+	0.395073i
$813$	−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
$819$	−9.36026	−	11.8011i	−0.327074	−	0.412365i
$820$	−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
$826$	0.845535	+	8.48163i	0.0294199	+	0.295114i
$827$			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	$-0.894361\pi$
$829$		−	18.7620i		−	0.651631i	0.945433	−	0.325816i	$-0.105639\pi$
$830$	−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
$833$	−32.1998	+	31.2182i	−1.11566	+	1.08165i
$834$	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	$-0.843347\pi$
$839$	2.82190	−	19.6267i	0.0974228	−	0.677590i	0.978746	−	0.205076i	$-0.0657443\pi$
$840$	1.72571	−	9.15881i	0.0595427	−	0.316009i
$841$	−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
$847$	1.19842	+	4.85173i	0.0411782	+	0.166707i
$848$	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	0.672482	−	0.740113i	$-0.265228\pi$
$853$	44.5756	−	6.40900i	1.52624	−	0.219440i	0.853756	+	0.520673i	$0.174319\pi$
$854$	−2.65180	−	1.35316i	−0.0907427	−	0.0463041i
$855$	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	−0.882221	−	0.470835i	$-0.843953\pi$
$857$	3.35203	−	11.4160i	0.114503	−	0.389962i	0.996724	+	0.0808730i	$0.0257708\pi$
$858$	11.0501	+	17.1943i	0.377245	+	0.587004i
$859$	−49.6655	+	22.6815i	−1.69456	+	0.773881i	−0.696131	+	0.717915i	$0.745097\pi$
$859$	−49.6655	+	22.6815i	−1.69456	+	0.773881i	−0.998433	+	0.0559662i	$0.982176\pi$
$860$	18.6493	−	16.1597i	0.635936	−	0.551042i
$861$	−12.0626	+	17.0897i	−0.411093	+	0.582415i
$862$	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
$868$	7.49095	+	2.55778i	0.254260	+	0.0868168i
$869$	−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	−0.358017	−	0.933715i	$-0.616547\pi$
$881$	10.1688	−	6.53508i	0.342595	−	0.220173i	0.700612	+	0.713543i	$0.252911\pi$
$882$	−2.34446	−	6.59572i	−0.0789420	−	0.222089i
$883$	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	$-0.368443\pi$
$887$	31.8027	−	49.4860i	1.06783	−	1.66158i	0.666199	−	0.745774i	$-0.267920\pi$
$888$	−6.04691	−	6.97851i	−0.202921	−	0.234183i
$889$	−25.4118	+	10.2963i	−0.852286	+	0.345326i
$890$	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
$903$	5.98892	−	17.5397i	0.199299	−	0.583684i
$904$	−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
$910$	43.3489	+	30.5975i	1.43700	+	1.01430i
$911$	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
$917$	2.97025	−	5.82083i	0.0980862	−	0.192221i
$918$	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
$924$	2.27776	+	9.22139i	0.0749330	+	0.303362i
$925$	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	−0.914858	−	0.403775i	$-0.867698\pi$
$929$	−19.6712	+	17.0452i	−0.645391	+	0.559234i	0.269467	+	0.963010i	$0.413152\pi$
$930$	−8.86599	−	5.69782i	−0.290727	−	0.186839i
$931$	1.32317	−	5.65937i	0.0433651	−	0.185478i
$932$	−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	0.150205	−	0.988655i	$-0.452007\pi$
$937$	−7.89570	−	2.31839i	−0.257941	−	0.0757384i	−0.408146	+	0.912916i	$0.633825\pi$
$938$	−9.57142	+	10.1222i	−0.312518	+	0.330503i
$939$	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	$0.160830\pi$
$941$	5.27054	+	36.6574i	0.171815	+	1.19500i	−0.703233	+	0.710960i	$0.748261\pi$
$942$		−	4.97203i		−	0.161997i
$943$	1.52738	+	37.8864i	0.0497384	+	1.23375i
$944$		−	3.22165i		−	0.104856i
$945$	0.924526	+	9.27400i	0.0300748	+	0.301683i
$946$	−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
$952$	13.2808	−	10.5339i	0.430434	−	0.341406i
$953$	−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
$959$	44.5265	−	25.9551i	1.43784	−	0.838133i
$960$	−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
$966$	−10.6527	−	6.89350i	−0.342744	−	0.221795i
$967$	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	−0.624164	−	0.781293i	$-0.714560\pi$
$971$	7.41641	−	8.55900i	0.238004	−	0.274671i	0.862168	+	0.506622i	$0.169106\pi$
$972$	−0.281733	+	0.959493i	−0.00903658	+	0.0307758i
$973$	−30.7531	+	17.9264i	−0.985898	+	0.574693i
$974$	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
$980$	14.4699	+	19.9663i	0.462225	+	0.637801i
$981$	−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	0.864016	−	0.503464i	$-0.167941\pi$
$983$	41.3444	+	12.1398i	1.31868	+	0.387199i	0.454664	+	0.890663i	$0.349759\pi$
$984$	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
$987$	−18.6194	+	1.85617i	−0.592663	+	0.0590826i
$988$			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
$994$	16.9966	+	16.0717i	0.539099	+	0.509763i
$995$	−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	0.324508	−	0.945883i	$-0.394801\pi$
$997$	39.5281	−	18.0519i	1.25187	−	0.571708i	0.927358	+	0.374174i	$0.122074\pi$
$998$	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.181.2	✓	160
7.6	odd	2	inner	966.2.s.b.181.15	yes	160
23.15	odd	22	inner	966.2.s.b.475.15	yes	160
161.153	even	22	inner	966.2.s.b.475.2	yes	160

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

\(f(q)\)	\(=\)	\(q+(0.142315 + 0.989821i) q^{2} +(-0.909632 - 0.415415i) q^{3} +(-0.959493 + 0.281733i) q^{4} +(-2.30682 + 2.66222i) q^{5} +(0.281733 - 0.959493i) q^{6} +(1.33240 + 2.28576i) q^{7} +(-0.415415 - 0.909632i) q^{8} +(0.654861 + 0.755750i) q^{9} +O(q^{10})\)	\(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} +(1.33240 + 2.28576i) 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} +(-2.07288 + 1.64414i) 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} +(-0.262454 - 2.63270i) 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} +(-1.92240 - 1.81779i) 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} +(-9.15881 - 1.72571i) 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} +(2.56855 - 0.634455i) 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} +(-3.44942 + 6.09110i) 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} +(1.52570 - 2.16153i) 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} +(-0.854927 + 2.50382i) 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} +(3.56692 + 8.80337i) 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} +(0.993541 + 2.45212i) 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} +(-6.52001 - 2.54745i) 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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