LMFDB - Embedded newform 403.2.k.e.287.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [403,2,Mod(66,403)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(403, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 6]))

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

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

chi := DirichletCharacter("403.66");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 403 = 13 \cdot 31 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	403.k (of order $5$, degree $4$, 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:	$3.21797120146$
Analytic rank:	$0$
Dimension:	$68$
Relative dimension:	$17$ over $\Q(\zeta_{5})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			287.1
Character	$\chi$	$=$	403.287
Dual form			403.2.k.e.66.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.831221 + 2.55823i) q^{2} +(-0.796905 - 2.45262i) q^{3} +(-4.23560 - 3.07735i) q^{4} -0.866460 q^{5} +6.93679 q^{6} +(1.08832 + 0.790714i) q^{7} +(7.04097 - 5.11556i) q^{8} +(-2.95324 + 2.14566i) q^{9} +O(q^{10})$	\(q+(-0.831221 + 2.55823i) q^{2} +(-0.796905 - 2.45262i) q^{3} +(-4.23560 - 3.07735i) q^{4} -0.866460 q^{5} +6.93679 q^{6} +(1.08832 + 0.790714i) q^{7} +(7.04097 - 5.11556i) q^{8} +(-2.95324 + 2.14566i) q^{9} +(0.720220 - 2.21661i) q^{10} +(-0.806312 - 0.585820i) q^{11} +(-4.17219 + 12.8407i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-2.92747 + 2.12693i) q^{14} +(0.690486 + 2.12510i) q^{15} +(3.99850 + 12.3061i) q^{16} +(-4.93920 + 3.58854i) q^{17} +(-3.03430 - 9.33861i) q^{18} +(-0.793078 + 2.44084i) q^{19} +(3.66998 + 2.66640i) q^{20} +(1.07203 - 3.29937i) q^{21} +(2.16889 - 1.57579i) q^{22} +(0.357550 - 0.259775i) q^{23} +(-18.1575 - 13.1922i) q^{24} -4.24925 q^{25} -2.68989 q^{26} +(1.35697 + 0.985896i) q^{27} +(-2.17641 - 6.69830i) q^{28} +(-2.71553 + 8.35753i) q^{29} -6.01045 q^{30} +(-0.833293 - 5.50505i) q^{31} -17.3993 q^{32} +(-0.794240 + 2.44442i) q^{33} +(-5.07476 - 15.6185i) q^{34} +(-0.942990 - 0.685122i) q^{35} +19.1117 q^{36} +2.91856 q^{37} +(-5.58503 - 4.05776i) q^{38} +(2.08632 - 1.51580i) q^{39} +(-6.10071 + 4.43243i) q^{40} +(-3.33326 + 10.2587i) q^{41} +(7.54948 + 5.48502i) q^{42} +(-2.49495 + 7.67867i) q^{43} +(1.61245 + 4.96260i) q^{44} +(2.55887 - 1.85913i) q^{45} +(0.367363 + 1.13063i) q^{46} +(2.69197 + 8.28503i) q^{47} +(26.9958 - 19.6136i) q^{48} +(-1.60390 - 4.93629i) q^{49} +(3.53206 - 10.8706i) q^{50} +(12.7374 + 9.25426i) q^{51} +(1.61786 - 4.97925i) q^{52} +(6.09781 - 4.43032i) q^{53} +(-3.65009 + 2.65195i) q^{54} +(0.698637 + 0.507589i) q^{55} +11.7078 q^{56} +6.61847 q^{57} +(-19.1233 - 13.8939i) q^{58} +(0.0998181 + 0.307209i) q^{59} +(3.61504 - 11.1259i) q^{60} +4.77967 q^{61} +(14.7759 + 2.44416i) q^{62} -4.91069 q^{63} +(6.46568 - 19.8993i) q^{64} +(-0.267751 - 0.824052i) q^{65} +(-5.59321 - 4.06371i) q^{66} -3.10226 q^{67} +31.9636 q^{68} +(-0.922063 - 0.669918i) q^{69} +(2.53654 - 1.84290i) q^{70} +(-8.58190 + 6.23511i) q^{71} +(-9.81745 + 30.2150i) q^{72} +(-9.25387 - 6.72333i) q^{73} +(-2.42597 + 7.46637i) q^{74} +(3.38625 + 10.4218i) q^{75} +(10.8705 - 7.89787i) q^{76} +(-0.414313 - 1.27512i) q^{77} +(2.14358 + 6.59728i) q^{78} +(5.44156 - 3.95353i) q^{79} +(-3.46454 - 10.6627i) q^{80} +(-2.04746 + 6.30144i) q^{81} +(-23.4735 - 17.0545i) q^{82} +(0.611921 - 1.88330i) q^{83} +(-14.6940 + 10.6758i) q^{84} +(4.27962 - 3.10932i) q^{85} +(-17.5700 - 12.7653i) q^{86} +22.6619 q^{87} -8.67401 q^{88} +(2.96544 + 2.15452i) q^{89} +(2.62910 + 8.09153i) q^{90} +(-0.415703 + 1.27940i) q^{91} -2.31386 q^{92} +(-12.8378 + 6.43076i) q^{93} -23.4327 q^{94} +(0.687170 - 2.11489i) q^{95} +(13.8656 + 42.6739i) q^{96} +(4.50908 + 3.27604i) q^{97} +13.9614 q^{98} +3.63820 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) $ 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/403\mathbb{Z}\right)^\times$.

$n$	$249$	$313$
$\chi(n)$	$1$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.831221	+	2.55823i	−0.587762	+	1.80895i	0.000122172		1.00000i	$0.499961\pi$
$2$	−0.831221	+	2.55823i	−0.587762	+	1.80895i	−0.587884	+	0.808945i	$0.700039\pi$
$3$	−0.796905	−	2.45262i	−0.460093	−	1.41602i	−0.865050	−	0.501686i	$-0.832713\pi$
$3$	−0.796905	−	2.45262i	−0.460093	−	1.41602i	0.404956	−	0.914336i	$-0.367287\pi$
$4$	−4.23560	−	3.07735i	−2.11780	−	1.53867i
$5$	−0.866460			−0.387493			−0.193746	−	0.981052i	$-0.562064\pi$
$5$	−0.866460			−0.387493			−0.193746	+	0.981052i	$0.562064\pi$
$6$	6.93679			2.83193
$7$	1.08832	+	0.790714i	0.411348	+	0.298862i	0.774147	−	0.633005i	$-0.218179\pi$
$7$	1.08832	+	0.790714i	0.411348	+	0.298862i	−0.362799	+	0.931867i	$0.618179\pi$
$8$	7.04097	−	5.11556i	2.48936	−	1.80862i
$9$	−2.95324	+	2.14566i	−0.984415	+	0.715219i
$10$	0.720220	−	2.21661i	0.227753	−	0.700953i
$11$	−0.806312	−	0.585820i	−0.243112	−	0.176631i	0.459557	−	0.888149i	$-0.348008\pi$
$11$	−0.806312	−	0.585820i	−0.243112	−	0.176631i	−0.702669	+	0.711517i	$0.748008\pi$
$12$	−4.17219	+	12.8407i	−1.20441	+	3.70679i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$13$	0.309017	+	0.951057i	0.0857059	+	0.263776i
$14$	−2.92747	+	2.12693i	−0.782400	+	0.568447i
$15$	0.690486	+	2.12510i	0.178283	+	0.548698i
$16$	3.99850	+	12.3061i	0.999624	+	3.07653i
$17$	−4.93920	+	3.58854i	−1.19793	+	0.870348i	−0.994080	−	0.108654i	$-0.965346\pi$
$17$	−4.93920	+	3.58854i	−1.19793	+	0.870348i	−0.203852	+	0.979002i	$0.565346\pi$
$18$	−3.03430	−	9.33861i	−0.715191	−	2.20113i
$19$	−0.793078	+	2.44084i	−0.181945	+	0.559968i	−0.999882	−	0.0153389i	$-0.995117\pi$
$19$	−0.793078	+	2.44084i	−0.181945	+	0.559968i	0.817938	+	0.575307i	$0.195117\pi$
$20$	3.66998	+	2.66640i	0.820633	+	0.596224i
$21$	1.07203	−	3.29937i	0.233936	−	0.719982i
$22$	2.16889	−	1.57579i	0.462408	−	0.335959i
$23$	0.357550	−	0.259775i	0.0745543	−	0.0541668i	−0.549884	−	0.835241i	$-0.685328\pi$
$23$	0.357550	−	0.259775i	0.0745543	−	0.0541668i	0.624438	+	0.781074i	$0.285328\pi$
$24$	−18.1575	−	13.1922i	−3.70639	−	2.69285i
$25$	−4.24925			−0.849849
$26$	−2.68989			−0.527530
$27$	1.35697	+	0.985896i	0.261149	+	0.189736i
$28$	−2.17641	−	6.69830i	−0.411303	−	1.26586i
$29$	−2.71553	+	8.35753i	−0.504260	+	1.55195i	0.297750	+	0.954644i	$0.403764\pi$
$29$	−2.71553	+	8.35753i	−0.504260	+	1.55195i	−0.802011	+	0.597310i	$0.796236\pi$
$30$	−6.01045			−1.09735
$31$	−0.833293	−	5.50505i	−0.149664	−	0.988737i
$31$	−0.833293	−	5.50505i	−0.149664	−	0.988737i
$32$	−17.3993			−3.07579
$33$	−0.794240	+	2.44442i	−0.138259	+	0.425519i
$34$	−5.07476	−	15.6185i	−0.870314	−	2.67855i
$35$	−0.942990	−	0.685122i	−0.159394	−	0.115807i
$36$	19.1117			3.18528
$37$	2.91856			0.479809			0.239904	−	0.970797i	$-0.422884\pi$
$37$	2.91856			0.479809			0.239904	+	0.970797i	$0.422884\pi$
$38$	−5.58503	−	4.05776i	−0.906011	−	0.658255i
$39$	2.08632	−	1.51580i	0.334079	−	0.242723i
$40$	−6.10071	+	4.43243i	−0.964608	+	0.700829i
$41$	−3.33326	+	10.2587i	−0.520567	+	1.60214i	0.252351	+	0.967636i	$0.418796\pi$
$41$	−3.33326	+	10.2587i	−0.520567	+	1.60214i	−0.772918	+	0.634505i	$0.781204\pi$
$42$	7.54948	+	5.48502i	1.16491	+	0.846356i
$43$	−2.49495	+	7.67867i	−0.380476	+	1.17099i	0.559233	+	0.829011i	$0.311096\pi$
$43$	−2.49495	+	7.67867i	−0.380476	+	1.17099i	−0.939709	+	0.341975i	$0.888904\pi$
$44$	1.61245	+	4.96260i	0.243085	+	0.748140i
$45$	2.55887	−	1.85913i	0.381454	−	0.277142i
$46$	0.367363	+	1.13063i	0.0541647	+	0.166702i
$47$	2.69197	+	8.28503i	0.392664	+	1.20850i	0.930766	+	0.365616i	$0.119142\pi$
$47$	2.69197	+	8.28503i	0.392664	+	1.20850i	−0.538102	+	0.842880i	$0.680858\pi$
$48$	26.9958	−	19.6136i	3.89651	−	2.83098i
$49$	−1.60390	−	4.93629i	−0.229128	−	0.705184i
$50$	3.53206	−	10.8706i	0.499509	−	1.53733i
$51$	12.7374	+	9.25426i	1.78359	+	1.29586i
$52$	1.61786	−	4.97925i	0.224356	−	0.690498i
$53$	6.09781	−	4.43032i	0.837599	−	0.608551i	−0.0841000	−	0.996457i	$-0.526802\pi$
$53$	6.09781	−	4.43032i	0.837599	−	0.608551i	0.921699	+	0.387906i	$0.126802\pi$
$54$	−3.65009	+	2.65195i	−0.496715	+	0.360885i
$55$	0.698637	+	0.507589i	0.0942042	+	0.0684433i
$56$	11.7078			1.56452
$57$	6.61847			0.876638
$58$	−19.1233	−	13.8939i	−2.51101	−	1.82436i
$59$	0.0998181	+	0.307209i	0.0129952	+	0.0399952i	0.957344	−	0.288951i	$-0.0933065\pi$
$59$	0.0998181	+	0.307209i	0.0129952	+	0.0399952i	−0.944349	+	0.328946i	$0.893307\pi$
$60$	3.61504	−	11.1259i	0.466699	−	1.43635i
$61$	4.77967			0.611974			0.305987	−	0.952036i	$-0.401014\pi$
$61$	4.77967			0.611974			0.305987	+	0.952036i	$0.401014\pi$
$62$	14.7759	+	2.44416i	1.87654	+	0.310408i
$63$	−4.91069			−0.618689
$64$	6.46568	−	19.8993i	0.808210	−	2.48742i
$65$	−0.267751	−	0.824052i	−0.0332104	−	0.102211i
$66$	−5.59321	−	4.06371i	−0.688477	−	0.500208i
$67$	−3.10226			−0.379002			−0.189501	−	0.981881i	$-0.560687\pi$
$67$	−3.10226			−0.379002			−0.189501	+	0.981881i	$0.560687\pi$
$68$	31.9636			3.87616
$69$	−0.922063	−	0.669918i	−0.111003	−	0.0806487i
$70$	2.53654	−	1.84290i	0.303174	−	0.220269i
$71$	−8.58190	+	6.23511i	−1.01848	+	0.739972i	−0.965971	−	0.258649i	$-0.916723\pi$
$71$	−8.58190	+	6.23511i	−1.01848	+	0.739972i	−0.0525122	+	0.998620i	$0.516723\pi$
$72$	−9.81745	+	30.2150i	−1.15700	+	3.56087i
$73$	−9.25387	−	6.72333i	−1.08308	−	0.786906i	−0.104866	−	0.994486i	$-0.533441\pi$
$73$	−9.25387	−	6.72333i	−1.08308	−	0.786906i	−0.978218	+	0.207580i	$0.933441\pi$
$74$	−2.42597	+	7.46637i	−0.282013	+	0.867948i
$75$	3.38625	+	10.4218i	0.391010	+	1.20341i
$76$	10.8705	−	7.89787i	1.24693	−	0.905947i
$77$	−0.414313	−	1.27512i	−0.0472154	−	0.145314i
$78$	2.14358	+	6.59728i	0.242713	+	0.746994i
$79$	5.44156	−	3.95353i	0.612224	−	0.444807i	−0.237973	−	0.971272i	$-0.576483\pi$
$79$	5.44156	−	3.95353i	0.612224	−	0.444807i	0.850197	+	0.526465i	$0.176483\pi$
$80$	−3.46454	−	10.6627i	−0.387347	−	1.19213i
$81$	−2.04746	+	6.30144i	−0.227496	+	0.700160i
$82$	−23.4735	−	17.0545i	−2.59222	−	1.88335i
$83$	0.611921	−	1.88330i	0.0671670	−	0.206719i	−0.911840	−	0.410546i	$-0.865338\pi$
$83$	0.611921	−	1.88330i	0.0671670	−	0.206719i	0.979007	+	0.203827i	$0.0653381\pi$
$84$	−14.6940	+	10.6758i	−1.60325	+	1.16483i
$85$	4.27962	−	3.10932i	0.464190	−	0.337253i
$86$	−17.5700	−	12.7653i	−1.89462	−	1.37652i
$87$	22.6619			2.42961
$88$	−8.67401			−0.924652
$89$	2.96544	+	2.15452i	0.314336	+	0.228379i	0.733755	−	0.679414i	$-0.237766\pi$
$89$	2.96544	+	2.15452i	0.314336	+	0.228379i	−0.419419	+	0.907793i	$0.637766\pi$
$90$	2.62910	+	8.09153i	0.277131	+	0.852922i
$91$	−0.415703	+	1.27940i	−0.0435775	+	0.134118i
$92$	−2.31386			−0.241236
$93$	−12.8378	+	6.43076i	−1.33121	+	0.666839i
$94$	−23.4327			−2.41690
$95$	0.687170	−	2.11489i	0.0705022	−	0.216983i
$96$	13.8656	+	42.6739i	1.41515	+	4.35539i
$97$	4.50908	+	3.27604i	0.457828	+	0.332632i	0.792679	−	0.609640i	$-0.208686\pi$
$97$	4.50908	+	3.27604i	0.457828	+	0.332632i	−0.334851	+	0.942271i	$0.608686\pi$
$98$	13.9614			1.41031
$99$	3.63820			0.365653
$100$	17.9981	+	13.0764i	1.79981	+	1.30764i
$101$	−12.5186	+	9.09532i	−1.24565	+	0.905018i	−0.997961	−	0.0638219i	$-0.979671\pi$
$101$	−12.5186	+	9.09532i	−1.24565	+	0.905018i	−0.247689	+	0.968840i	$0.579671\pi$
$102$	−34.2622	+	24.8929i	−3.39246	+	2.46477i
$103$	0.0884967	−	0.272365i	0.00871984	−	0.0268369i	−0.946602	−	0.322405i	$-0.895509\pi$
$103$	0.0884967	−	0.272365i	0.00871984	−	0.0268369i	0.955322	+	0.295568i	$0.0955088\pi$
$104$	7.04097	+	5.11556i	0.690424	+	0.501622i
$105$	−0.928872	+	2.85878i	−0.0906487	+	0.278988i
$106$	6.26517	+	19.2822i	0.608527	+	1.87285i
$107$	6.43819	−	4.67762i	0.622403	−	0.452202i	−0.231357	−	0.972869i	$-0.574317\pi$
$107$	6.43819	−	4.67762i	0.622403	−	0.452202i	0.853760	+	0.520667i	$0.174317\pi$
$108$	−2.71364	−	8.35173i	−0.261120	−	0.803645i
$109$	−5.48692	−	16.8870i	−0.525552	−	1.61748i	−0.763222	−	0.646136i	$-0.776384\pi$
$109$	−5.48692	−	16.8870i	−0.525552	−	1.61748i	0.237670	−	0.971346i	$-0.423616\pi$
$110$	−1.87925	+	1.36536i	−0.179180	+	0.130182i
$111$	−2.32582	−	7.15813i	−0.220757	−	0.679420i
$112$	−5.37895	+	16.5547i	−0.508263	+	1.56427i
$113$	−17.1550	−	12.4639i	−1.61381	−	1.17250i	−0.849346	−	0.527837i	$-0.823003\pi$
$113$	−17.1550	−	12.4639i	−1.61381	−	1.17250i	−0.764465	−	0.644665i	$-0.776997\pi$
$114$	−5.50141	+	16.9316i	−0.515254	+	1.58579i
$115$	−0.309803	+	0.225085i	−0.0288892	+	0.0209893i
$116$	37.2209	−	27.0426i	3.45587	−	2.51084i
$117$	−2.95324	−	2.14566i	−0.273028	−	0.198366i
$118$	−0.868883			−0.0799871
$119$	−8.21296			−0.752881
$120$	15.7328	+	11.4305i	1.43620	+	1.04346i
$121$	−3.09223	−	9.51692i	−0.281112	−	0.865174i
$122$	−3.97296	+	12.2275i	−0.359695	+	1.10703i
$123$	27.8170			2.50818
$124$	−13.4115	+	25.8816i	−1.20438	+	2.32423i
$125$	8.01410			0.716803
$126$	4.08187	−	12.5627i	0.363642	−	1.11917i
$127$	−3.57799	−	11.0119i	−0.317495	−	0.977150i	−0.974715	−	0.223451i	$-0.928268\pi$
$127$	−3.57799	−	11.0119i	−0.317495	−	0.977150i	0.657220	−	0.753699i	$-0.271732\pi$
$128$	17.3800	+	12.6273i	1.53619	+	1.11611i
$129$	20.8211			1.83320
$130$	2.33068			0.204414
$131$	3.54130	+	2.57291i	0.309405	+	0.224796i	0.731641	−	0.681690i	$-0.238755\pi$
$131$	3.54130	+	2.57291i	0.309405	+	0.224796i	−0.422236	+	0.906486i	$0.638755\pi$
$132$	10.8864	−	7.90944i	0.947541	−	0.688429i
$133$	−2.79314	+	2.02933i	−0.242196	+	0.175965i
$134$	2.57867	−	7.93632i	0.222763	−	0.685593i
$135$	−1.17576	−	0.854239i	−0.101193	−	0.0735212i
$136$	−16.4193	+	50.5335i	−1.40795	+	4.33321i
$137$	−4.71268	−	14.5041i	−0.402631	−	1.23917i	−0.922857	−	0.385143i	$-0.874152\pi$
$137$	−4.71268	−	14.5041i	−0.402631	−	1.23917i	0.520226	−	0.854029i	$-0.325848\pi$
$138$	2.48025	−	1.80200i	0.211133	−	0.153397i
$139$	4.86798	+	14.9821i	0.412897	+	1.27077i	0.914119	+	0.405447i	$0.132884\pi$
$139$	4.86798	+	14.9821i	0.412897	+	1.27077i	−0.501222	+	0.865319i	$0.667116\pi$
$140$	1.88577	+	5.80381i	0.159377	+	0.490512i
$141$	18.1748	−	13.2048i	1.53059	−	1.11204i
$142$	−8.81743	−	27.1373i	−0.739942	−	2.27731i
$143$	0.307984	−	0.947876i	0.0257549	−	0.0792654i
$144$	−38.2132	−	27.7635i	−3.18444	−	2.31363i
$145$	2.35289	−	7.24146i	0.195397	−	0.601371i
$146$	24.8919	−	18.0850i	2.06007	−	1.49673i
$147$	−10.8287	+	7.86751i	−0.893135	+	0.648901i
$148$	−12.3619	−	8.98143i	−1.01614	−	0.738269i
$149$	2.19851			0.180109			0.0900545	−	0.995937i	$-0.471296\pi$
$149$	2.19851			0.180109			0.0900545	+	0.995937i	$0.471296\pi$
$150$	−29.4761			−2.40672
$151$	12.5305	+	9.10391i	1.01971	+	0.740866i	0.966224	−	0.257702i	$-0.0829654\pi$
$151$	12.5305	+	9.10391i	1.01971	+	0.740866i	0.0534903	+	0.998568i	$0.482965\pi$
$152$	6.90225	+	21.2429i	0.559846	+	1.72303i
$153$	6.88689	−	21.1957i	0.556772	−	1.71357i
$154$	3.60645			0.290616
$155$	0.722015	+	4.76991i	0.0579936	+	0.383128i
$156$	−13.5015			−1.08098
$157$	1.62291	−	4.99479i	0.129522	−	0.398628i	−0.865176	−	0.501469i	$-0.832793\pi$
$157$	1.62291	−	4.99479i	0.129522	−	0.398628i	0.994698	+	0.102841i	$0.0327933\pi$
$158$	5.59091	+	17.2071i	0.444789	+	1.36892i
$159$	−15.7253	−	11.4251i	−1.24710	−	0.906068i
$160$	15.0758			1.19185
$161$	0.594538			0.0468562
$162$	−14.4187	−	10.4758i	−1.13284	−	0.823055i
$163$	−5.62795	+	4.08895i	−0.440815	+	0.320271i	−0.785959	−	0.618279i	$-0.787830\pi$
$163$	−5.62795	+	4.08895i	−0.440815	+	0.320271i	0.345144	+	0.938550i	$0.387830\pi$
$164$	45.6879	−	33.1942i	3.56763	−	2.59203i
$165$	0.688177	−	2.11799i	0.0535745	−	0.164885i
$166$	4.30928	+	3.13087i	0.334465	+	0.243003i
$167$	2.38569	−	7.34241i	0.184611	−	0.568173i	−0.815331	−	0.578995i	$-0.803445\pi$
$167$	2.38569	−	7.34241i	0.184611	−	0.568173i	0.999941	+	0.0108224i	$0.00344494\pi$
$168$	−9.33001	−	28.7148i	−0.719826	−	2.21540i
$169$	−0.809017	+	0.587785i	−0.0622321	+	0.0452143i
$170$	4.39707	+	13.5328i	0.337240	+	1.03792i
$171$	−2.89506	−	8.91008i	−0.221391	−	0.681371i
$172$	34.1975	−	24.8460i	2.60754	−	1.89449i
$173$	5.82324	+	17.9221i	0.442733	+	1.36259i	0.884951	+	0.465684i	$0.154192\pi$
$173$	5.82324	+	17.9221i	0.442733	+	1.36259i	−0.442219	+	0.896907i	$0.645808\pi$
$174$	−18.8370	+	57.9744i	−1.42803	+	4.39503i
$175$	−4.62456	−	3.35994i	−0.349584	−	0.253988i
$176$	3.98512	−	12.2650i	0.300390	−	0.924506i
$177$	0.673921	−	0.489632i	0.0506550	−	0.0368030i
$178$	−7.97670	+	5.79541i	−0.597879	+	0.434385i
$179$	20.0231	+	14.5477i	1.49660	+	1.08734i	0.971711	+	0.236173i	$0.0758932\pi$
$179$	20.0231	+	14.5477i	1.49660	+	1.08734i	0.524889	+	0.851171i	$0.324107\pi$
$180$	−16.5595			−1.23427
$181$	−10.0741			−0.748802			−0.374401	−	0.927267i	$-0.622152\pi$
$181$	−10.0741			−0.748802			−0.374401	+	0.927267i	$0.622152\pi$
$182$	−2.92747	−	2.12693i	−0.216999	−	0.157659i
$183$	−3.80894	−	11.7227i	−0.281565	−	0.866569i
$184$	1.18860	−	3.65813i	0.0876248	−	0.269681i
$185$	−2.52882			−0.185922
$186$	−5.78038	−	38.1874i	−0.423838	−	2.80004i
$187$	6.08477			0.444962
$188$	14.0938	−	43.3762i	1.02790	−	3.16354i
$189$	0.697262	+	2.14595i	0.0507183	+	0.156095i
$190$	4.83920	+	3.51589i	0.351073	+	0.255069i
$191$	−21.3591			−1.54549			−0.772747	−	0.634715i	$-0.781118\pi$
$191$	−21.3591			−1.54549			−0.772747	+	0.634715i	$0.781118\pi$
$192$	−53.9580			−3.89409
$193$	−5.62600	−	4.08753i	−0.404969	−	0.294227i	0.366593	−	0.930381i	$-0.380524\pi$
$193$	−5.62600	−	4.08753i	−0.404969	−	0.294227i	−0.771562	+	0.636154i	$0.780524\pi$
$194$	−12.1289	+	8.81218i	−0.870806	+	0.632678i
$195$	−1.80772	+	1.31338i	−0.129453	+	0.0940533i
$196$	−8.39719	+	25.8439i	−0.599799	+	1.84599i
$197$	−15.2806	−	11.1020i	−1.08870	−	0.790986i	−0.109519	−	0.993985i	$-0.534931\pi$
$197$	−15.2806	−	11.1020i	−1.08870	−	0.790986i	−0.979179	+	0.202999i	$0.934931\pi$
$198$	−3.02415	+	9.30738i	−0.214917	+	0.661447i
$199$	7.26049	+	22.3455i	0.514683	+	1.58403i	0.783859	+	0.620939i	$0.213249\pi$
$199$	7.26049	+	22.3455i	0.514683	+	1.58403i	−0.269176	+	0.963091i	$0.586751\pi$
$200$	−29.9188	+	21.7373i	−2.11558	+	1.53706i
$201$	2.47221	+	7.60868i	0.174376	+	0.536675i
$202$	−12.8622	−	39.5858i	−0.904982	−	2.78525i
$203$	−9.56379	+	6.94850i	−0.671246	+	0.487689i
$204$	−25.4720	−	78.3947i	−1.78340	−	5.48873i
$205$	2.88813	−	8.88876i	0.201716	−	0.620818i
$206$	0.623213	+	0.452791i	0.0434213	+	0.0315474i
$207$	−0.498543	+	1.53436i	−0.0346512	+	0.106645i
$208$	−10.4682	+	7.60559i	−0.725839	+	0.527353i
$209$	2.06936	−	1.50348i	0.143141	−	0.103998i
$210$	−6.54132	−	4.75255i	−0.451394	−	0.327957i
$211$	−12.2487			−0.843235			−0.421618	−	0.906774i	$-0.638537\pi$
$211$	−12.2487			−0.843235			−0.421618	+	0.906774i	$0.638537\pi$
$212$	−39.4615			−2.71023
$213$	22.1313	+	16.0794i	1.51641	+	1.10174i
$214$	6.61489	+	20.3585i	0.452184	+	1.39168i
$215$	2.16177	−	6.65326i	0.147432	−	0.453749i
$216$	14.5978			0.993254
$217$	3.44603	−	6.65018i	0.233932	−	0.451444i
$218$	47.7618			3.23484
$219$	−9.11533	+	28.0541i	−0.615957	+	1.89572i
$220$	−1.39712	−	4.29989i	−0.0941938	−	0.289899i
$221$	−4.93920	−	3.58854i	−0.332246	−	0.241391i
$222$	20.2454			1.35879
$223$	0.654097			0.0438016			0.0219008	−	0.999760i	$-0.493028\pi$
$223$	0.654097			0.0438016			0.0219008	+	0.999760i	$0.493028\pi$
$224$	−18.9361	−	13.7579i	−1.26522	−	0.919238i
$225$	12.5491	−	9.11743i	0.836605	−	0.607829i
$226$	46.1451	−	33.5264i	3.06953	−	2.23014i
$227$	7.33822	−	22.5847i	0.487055	−	1.49900i	−0.341928	−	0.939726i	$-0.611080\pi$
$227$	7.33822	−	22.5847i	0.487055	−	1.49900i	0.828983	−	0.559274i	$-0.188920\pi$
$228$	−28.0332	−	20.3673i	−1.85655	−	1.34886i
$229$	0.543390	−	1.67238i	0.0359082	−	0.110514i	−0.931496	−	0.363752i	$-0.881496\pi$
$229$	0.543390	−	1.67238i	0.0359082	−	0.110514i	0.967404	+	0.253238i	$0.0814956\pi$
$230$	−0.318305	−	0.979643i	−0.0209884	−	0.0645957i
$231$	−2.79723	+	2.03231i	−0.184044	+	0.133716i
$232$	23.6335	+	72.7365i	1.55162	+	4.77538i
$233$	−2.75217	−	8.47030i	−0.180300	−	0.554908i	0.819535	−	0.573029i	$-0.194232\pi$
$233$	−2.75217	−	8.47030i	−0.180300	−	0.554908i	−0.999836	+	0.0181209i	$0.994232\pi$
$234$	7.94390	−	5.77158i	0.519309	−	0.377300i
$235$	−2.33248	−	7.17865i	−0.152154	−	0.468283i
$236$	0.522597	−	1.60839i	0.0340182	−	0.104697i
$237$	−14.0329	−	10.1955i	−0.911536	−	0.662270i
$238$	6.82678	−	21.0107i	0.442515	−	1.36192i
$239$	−7.60809	+	5.52760i	−0.492126	+	0.357551i	−0.806001	−	0.591914i	$-0.798373\pi$
$239$	−7.60809	+	5.52760i	−0.492126	+	0.357551i	0.313875	+	0.949464i	$0.398373\pi$
$240$	−23.3908	+	16.9944i	−1.50987	+	1.09698i
$241$	3.13553	+	2.27809i	0.201977	+	0.146745i	0.684176	−	0.729317i	$-0.260162\pi$
$241$	3.13553	+	2.27809i	0.201977	+	0.146745i	−0.482199	+	0.876062i	$0.660162\pi$
$242$	26.9168			1.73028
$243$	22.1186			1.41891
$244$	−20.2448	−	14.7087i	−1.29604	−	0.941628i
$245$	1.38971	+	4.27710i	0.0887855	+	0.273254i
$246$	−23.1221	+	71.1625i	−1.47421	+	4.53715i
$247$	−2.56645			−0.163300
$248$	−34.0286	−	34.4981i	−2.16082	−	2.19063i
$249$	−5.10666			−0.323621
$250$	−6.66149	+	20.5020i	−0.421310	+	1.29666i
$251$	6.95841	+	21.4158i	0.439211	+	1.35175i	0.888709	+	0.458471i	$0.151603\pi$
$251$	6.95841	+	21.4158i	0.439211	+	1.35175i	−0.449498	+	0.893281i	$0.648397\pi$
$252$	20.7997	+	15.1119i	1.31026	+	0.951960i
$253$	−0.440478			−0.0276926
$254$	31.1452			1.95422
$255$	−11.0364	−	8.01845i	−0.691129	−	0.502135i
$256$	−12.8956	+	9.36921i	−0.805976	+	0.585576i
$257$	−8.82663	+	6.41292i	−0.550590	+	0.400027i	−0.828003	−	0.560724i	$-0.810523\pi$
$257$	−8.82663	+	6.41292i	−0.550590	+	0.400027i	0.277413	+	0.960751i	$0.410523\pi$
$258$	−17.3069	+	53.2653i	−1.07748	+	3.31615i
$259$	3.17635	+	2.30775i	0.197368	+	0.143397i
$260$	−1.40181	+	4.31432i	−0.0869364	+	0.267563i
$261$	−9.91278	−	30.5084i	−0.613586	−	1.88842i
$262$	−9.52570	+	6.92083i	−0.588500	+	0.427570i
$263$	−1.37899	−	4.24410i	−0.0850324	−	0.261703i	0.899496	−	0.436930i	$-0.143934\pi$
$263$	−1.37899	−	4.24410i	−0.0850324	−	0.261703i	−0.984528	+	0.175227i	$0.943934\pi$
$264$	6.91236	+	21.2741i	0.425426	+	1.30933i
$265$	−5.28351	+	3.83869i	−0.324563	+	0.235809i
$266$	−2.86979	−	8.83232i	−0.175958	−	0.541544i
$267$	2.92104	−	8.99005i	0.178765	−	0.550182i
$268$	13.1400	+	9.54674i	0.802651	+	0.583160i
$269$	−4.05612	+	12.4834i	−0.247306	+	0.761129i	0.747943	+	0.663763i	$0.231042\pi$
$269$	−4.05612	+	12.4834i	−0.247306	+	0.761129i	−0.995249	+	0.0973659i	$0.968958\pi$
$270$	3.16266	−	2.29781i	0.192473	−	0.139840i
$271$	15.7234	−	11.4237i	0.955130	−	0.693942i	0.00311511	−	0.999995i	$-0.499008\pi$
$271$	15.7234	−	11.4237i	0.955130	−	0.693942i	0.952015	+	0.306053i	$0.0990084\pi$
$272$	−63.9103	−	46.4335i	−3.87513	−	2.81545i
$273$	3.46917			0.209964
$274$	41.0223			2.47825
$275$	3.42622	+	2.48929i	0.206609	+	0.150110i
$276$	1.84392	+	5.67501i	0.110991	+	0.341596i
$277$	−4.30331	+	13.2442i	−0.258561	+	0.795768i	0.734547	+	0.678558i	$0.237395\pi$
$277$	−4.30331	+	13.2442i	−0.258561	+	0.795768i	−0.993107	+	0.117209i	$0.962605\pi$
$278$	−42.3741			−2.54143
$279$	14.2729	+	14.4698i	0.854495	+	0.866285i
$280$	−10.1443			−0.606241
$281$	2.19908	−	6.76806i	0.131186	−	0.403749i	−0.863791	−	0.503850i	$-0.831917\pi$
$281$	2.19908	−	6.76806i	0.131186	−	0.403749i	0.994977	+	0.100101i	$0.0319166\pi$
$282$	18.6736	+	57.4715i	1.11200	+	3.42238i
$283$	8.99557	+	6.53566i	0.534731	+	0.388505i	0.822124	−	0.569308i	$-0.192789\pi$
$283$	8.99557	+	6.53566i	0.534731	+	0.388505i	−0.287394	+	0.957813i	$0.592789\pi$
$284$	55.5371			3.29552
$285$	−5.73464			−0.339691
$286$	2.16889	+	1.57579i	0.128249	+	0.0931784i
$287$	−11.7394	+	8.52915i	−0.692953	+	0.503460i
$288$	51.3844	−	37.3330i	3.02786	−	2.19987i
$289$	6.26478	−	19.2810i	0.368517	−	1.13418i
$290$	16.5696	+	12.0385i	0.973000	+	0.706926i
$291$	4.44158	−	13.6698i	0.260370	−	0.801336i
$292$	18.5057	+	56.9547i	1.08296	+	3.33302i
$293$	8.81748	−	6.40627i	0.515123	−	0.374259i	−0.299641	−	0.954052i	$-0.596867\pi$
$293$	8.81748	−	6.40627i	0.515123	−	0.374259i	0.814763	+	0.579794i	$0.196867\pi$
$294$	−11.1259	−	34.2420i	−0.648875	−	1.99703i
$295$	−0.0864884	−	0.266184i	−0.00503555	−	0.0154978i
$296$	20.5495	−	14.9301i	1.19442	−	0.867794i
$297$	−0.516583	−	1.58988i	−0.0299752	−	0.0922541i
$298$	−1.82745	+	5.62430i	−0.105861	+	0.325807i
$299$	0.357550	+	0.259775i	0.0206776	+	0.0150232i
$300$	17.7287	−	54.5632i	1.02357	−	3.15021i
$301$	−8.78695	+	6.38409i	−0.506471	+	0.367973i
$302$	−33.7055	+	24.4885i	−1.93954	+	1.40916i
$303$	32.2835	+	23.4554i	1.85464	+	1.34748i
$304$	−33.2084			−1.90463
$305$	−4.14139			−0.237136
$306$	48.4989	+	35.2365i	2.77250	+	2.01434i
$307$	1.07743	+	3.31599i	0.0614921	+	0.189253i	0.977083	−	0.212857i	$-0.0682768\pi$
$307$	1.07743	+	3.31599i	0.0614921	+	0.189253i	−0.915591	+	0.402110i	$0.868277\pi$
$308$	−2.16913	+	6.67591i	−0.123598	+	0.380395i
$309$	−0.738532			−0.0420136
$310$	−12.8027	−	2.11776i	−0.727145	−	0.120281i
$311$	−17.1505			−0.972515			−0.486258	−	0.873816i	$-0.661638\pi$
$311$	−17.1505			−0.972515			−0.486258	+	0.873816i	$0.661638\pi$
$312$	6.93555	−	21.3454i	0.392648	−	1.20845i
$313$	−7.63295	−	23.4918i	−0.431440	−	1.32784i	−0.896691	−	0.442657i	$-0.854036\pi$
$313$	−7.63295	−	23.4918i	−0.431440	−	1.32784i	0.465251	−	0.885179i	$-0.345964\pi$
$314$	11.4289	+	8.30355i	0.644967	+	0.468596i
$315$	4.25492			0.239737
$316$	−35.2147			−1.98098
$317$	−2.73068	−	1.98396i	−0.153371	−	0.111430i	0.508453	−	0.861089i	$-0.330217\pi$
$317$	−2.73068	−	1.98396i	−0.153371	−	0.111430i	−0.661824	+	0.749659i	$0.730217\pi$
$318$	42.2992	−	30.7322i	2.37202	−	1.72338i
$319$	7.08556	−	5.14796i	0.396715	−	0.288231i
$320$	−5.60225	+	17.2420i	−0.313175	+	0.963855i
$321$	−16.6031	−	12.0628i	−0.926692	−	0.673281i
$322$	−0.494193	+	1.52097i	−0.0275403	+	0.0847602i
$323$	−4.84189	−	14.9018i	−0.269410	−	0.829158i
$324$	28.0640	−	20.3897i	1.55911	−	1.13276i
$325$	−1.31309	−	4.04127i	−0.0728371	−	0.224170i
$326$	−5.78241	−	17.7964i	−0.320258	−	0.985654i
$327$	−37.0449	+	26.9147i	−2.04859	+	1.48839i
$328$	29.0097	+	89.2827i	1.60179	+	4.92981i
$329$	−3.62136	+	11.1454i	−0.199652	+	0.614465i
$330$	4.84629	+	3.52104i	0.266780	+	0.193827i
$331$	1.23970	−	3.81539i	0.0681398	−	0.209713i	−0.911189	−	0.411990i	$-0.864834\pi$
$331$	1.23970	−	3.81539i	0.0681398	−	0.209713i	0.979328	+	0.202277i	$0.0648340\pi$
$332$	−8.38741	+	6.09381i	−0.460319	+	0.334441i
$333$	−8.61923	+	6.26224i	−0.472331	+	0.343169i
$334$	16.8006	+	12.2063i	0.919287	+	0.667901i
$335$	2.68799			0.146860
$336$	44.8890			2.44889
$337$	26.3317	+	19.1311i	1.43438	+	1.04214i	0.989180	+	0.146706i	$0.0468671\pi$
$337$	26.3317	+	19.1311i	1.43438	+	1.04214i	0.445199	+	0.895432i	$0.353133\pi$
$338$	−0.831221	−	2.55823i	−0.0452125	−	0.139150i
$339$	−16.8982	+	52.0074i	−0.917785	+	2.82465i
$340$	−27.6952			−1.50198
$341$	−2.55308	+	4.92695i	−0.138257	+	0.266809i
$342$	25.2005			1.36269
$343$	5.06755	−	15.5963i	0.273622	−	0.842123i
$344$	21.7138	+	66.8283i	1.17073	+	3.60314i
$345$	0.798931	+	0.580457i	0.0430130	+	0.0312508i
$346$	−50.6893			−2.72507
$347$	4.09449			0.219804			0.109902	−	0.993942i	$-0.464946\pi$
$347$	4.09449			0.219804			0.109902	+	0.993942i	$0.464946\pi$
$348$	−95.9867	−	69.7384i	−5.14543	−	3.73837i
$349$	−27.8274	+	20.2178i	−1.48957	+	1.08223i	−0.515255	+	0.857037i	$0.672303\pi$
$349$	−27.8274	+	20.2178i	−1.48957	+	1.08223i	−0.974313	+	0.225198i	$0.927697\pi$
$350$	12.4395	−	9.03786i	0.664922	−	0.483094i
$351$	−0.518316	+	1.59521i	−0.0276657	+	0.0851462i
$352$	14.0293	+	10.1929i	0.747763	+	0.543281i
$353$	−1.21596	+	3.74235i	−0.0647192	+	0.199185i	−0.978187	−	0.207725i	$-0.933394\pi$
$353$	−1.21596	+	3.74235i	−0.0647192	+	0.199185i	0.913468	+	0.406911i	$0.133394\pi$
$354$	0.692417	+	2.13104i	0.0368016	+	0.113264i
$355$	7.43587	−	5.40248i	0.394655	−	0.286734i
$356$	−5.93023	−	18.2514i	−0.314302	−	0.967321i
$357$	6.54495	+	20.1433i	0.346395	+	1.06610i
$358$	−53.8600	+	39.1316i	−2.84659	+	2.06817i
$359$	−3.42976	−	10.5557i	−0.181016	−	0.557109i	0.818841	−	0.574020i	$-0.194617\pi$
$359$	−3.42976	−	10.5557i	−0.181016	−	0.557109i	−0.999857	+	0.0169111i	$0.994617\pi$
$360$	8.50643	−	26.1801i	0.448328	−	1.37981i
$361$	10.0426	+	7.29636i	0.528557	+	0.384019i
$362$	8.37380	−	25.7719i	0.440117	−	1.35454i
$363$	−20.8772	+	15.1682i	−1.09577	+	0.796122i
$364$	5.69792	−	4.13978i	0.298652	−	0.216983i
$365$	8.01811	+	5.82550i	0.419687	+	0.304920i
$366$	33.1556			1.73307
$367$	−37.7348			−1.96974			−0.984869	−	0.173299i	$-0.944557\pi$
$367$	−37.7348			−1.96974			−0.984869	+	0.173299i	$0.944557\pi$
$368$	4.62648	+	3.36133i	0.241172	+	0.175222i
$369$	−12.1678	−	37.4485i	−0.633428	−	1.94949i
$370$	2.10201	−	6.46931i	0.109278	−	0.336323i
$371$	10.1395			0.526418
$372$	74.1653	+	12.2681i	3.84529	+	0.636071i
$373$	−15.0425			−0.778873			−0.389437	−	0.921053i	$-0.627330\pi$
$373$	−15.0425			−0.778873			−0.389437	+	0.921053i	$0.627330\pi$
$374$	−5.05779	+	15.5663i	−0.261532	+	0.804912i
$375$	−6.38648	−	19.6556i	−0.329796	−	1.01501i
$376$	61.3367	+	44.5637i	3.16320	+	2.29820i
$377$	−8.78762			−0.452586
$378$	−6.06942			−0.312177
$379$	−19.8957	−	14.4551i	−1.02197	−	0.742508i	−0.0552881	−	0.998470i	$-0.517608\pi$
$379$	−19.8957	−	14.4551i	−1.02197	−	0.742508i	−0.966687	+	0.255962i	$0.917608\pi$
$380$	−9.41883	+	6.84318i	−0.483176	+	0.351048i
$381$	−24.1567	+	17.5509i	−1.23759	+	0.899160i
$382$	17.7542	−	54.6417i	0.908382	−	2.79571i
$383$	−7.48884	−	5.44096i	−0.382662	−	0.278020i	0.379780	−	0.925077i	$-0.376000\pi$
$383$	−7.48884	−	5.44096i	−0.382662	−	0.278020i	−0.762442	+	0.647057i	$0.776000\pi$
$384$	17.1198	−	52.6895i	0.873643	−	2.68880i
$385$	0.358986	+	1.10484i	0.0182956	+	0.0563081i
$386$	15.1333	−	10.9950i	0.770265	−	0.559631i
$387$	−9.10760	−	28.0303i	−0.462965	−	1.42486i
$388$	−9.01718	−	27.7520i	−0.457778	−	1.40890i
$389$	7.28054	−	5.28962i	0.369138	−	0.268194i	−0.387715	−	0.921779i	$-0.626736\pi$
$389$	7.28054	−	5.28962i	0.369138	−	0.268194i	0.756853	+	0.653585i	$0.226736\pi$
$390$	−1.85733	−	5.71628i	−0.0940496	−	0.289455i
$391$	−0.833796	+	2.56616i	−0.0421669	+	0.129776i
$392$	−36.5449	−	26.5514i	−1.84579	−	1.34105i
$393$	3.48829	−	10.7358i	0.175961	−	0.541551i
$394$	41.1031	−	29.8632i	2.07074	−	1.50448i
$395$	−4.71490	+	3.42557i	−0.237232	+	0.172359i
$396$	−15.4100	−	11.1960i	−0.774381	−	0.562621i
$397$	7.23963			0.363347			0.181673	−	0.983359i	$-0.441849\pi$
$397$	7.23963			0.363347			0.181673	+	0.983359i	$0.441849\pi$
$398$	−63.2001			−3.16793
$399$	7.20305	+	5.23332i	0.360603	+	0.261994i
$400$	−16.9906	−	52.2917i	−0.849530	−	2.61458i
$401$	−7.34593	+	22.6085i	−0.366838	+	1.12901i	0.581983	+	0.813201i	$0.302277\pi$
$401$	−7.34593	+	22.6085i	−0.366838	+	1.12901i	−0.948822	+	0.315812i	$0.897723\pi$
$402$	−21.5197			−1.07331
$403$	4.97812	−	2.49366i	0.247978	−	0.124218i
$404$	81.0134			4.03057
$405$	1.77404	−	5.45995i	0.0881530	−	0.271307i
$406$	−9.82627	−	30.2422i	−0.487670	−	1.50089i
$407$	−2.35327	−	1.70975i	−0.116647	−	0.0847492i
$408$	137.024			6.78371
$409$	19.4742			0.962935			0.481467	−	0.876464i	$-0.340104\pi$
$409$	19.4742			0.962935			0.481467	+	0.876464i	$0.340104\pi$
$410$	20.3389	+	14.7770i	1.00446	+	0.729786i
$411$	−31.8176	+	23.1168i	−1.56945	+	1.14027i
$412$	−1.21300	+	0.881295i	−0.0597601	+	0.0434183i
$413$	−0.134280	+	0.413270i	−0.00660747	+	0.0203357i
$414$	−3.51085	−	2.55078i	−0.172549	−	0.125364i
$415$	−0.530205	+	1.63180i	−0.0260267	+	0.0801020i
$416$	−5.37668	−	16.5477i	−0.263614	−	0.811319i
$417$	32.8661	−	23.8786i	1.60946	−	1.16934i
$418$	2.12616	+	6.54364i	0.103994	+	0.320060i
$419$	6.39853	+	19.6927i	0.312589	+	0.962049i	0.976736	+	0.214447i	$0.0687950\pi$
$419$	6.39853	+	19.6927i	0.312589	+	0.962049i	−0.664147	+	0.747602i	$0.731205\pi$
$420$	12.7318	−	9.25018i	0.621247	−	0.451362i
$421$	9.81464	+	30.2064i	0.478336	+	1.47217i	0.841405	+	0.540405i	$0.181729\pi$
$421$	9.81464	+	30.2064i	0.478336	+	1.47217i	−0.363068	+	0.931762i	$0.618271\pi$
$422$	10.1814	−	31.3350i	0.495621	−	1.52537i
$423$	−25.7269	−	18.6917i	−1.25088	−	0.908821i
$424$	20.2709	−	62.3875i	0.984443	−	3.02980i
$425$	20.9879	−	15.2486i	1.01806	−	0.739665i
$426$	−59.5308	+	43.2516i	−2.88428	+	2.09555i
$427$	5.20184	+	3.77935i	0.251734	+	0.182896i
$428$	−41.6643			−2.01392
$429$	−2.57022			−0.124091
$430$	15.2237	+	11.0607i	0.734151	+	0.533392i
$431$	−6.76673	−	20.8259i	−0.325942	−	1.00315i	−0.971014	−	0.239024i	$-0.923172\pi$
$431$	−6.76673	−	20.8259i	−0.325942	−	1.00315i	0.645071	−	0.764122i	$-0.276828\pi$
$432$	−6.70670	+	20.6411i	−0.322676	+	0.993096i
$433$	−21.1031			−1.01415			−0.507076	−	0.861901i	$-0.669274\pi$
$433$	−21.1031			−1.01415			−0.507076	+	0.861901i	$0.669274\pi$
$434$	14.1483	+	14.3435i	0.679141	+	0.688512i
$435$	−19.6356			−0.941455
$436$	−28.7267	+	88.4118i	−1.37576	+	4.23416i
$437$	0.350505	+	1.07874i	0.0167669	+	0.0516033i
$438$	−64.1921	−	46.6383i	−3.06722	−	2.22846i
$439$	5.96677			0.284778			0.142389	−	0.989811i	$-0.454522\pi$
$439$	5.96677			0.284778			0.142389	+	0.989811i	$0.454522\pi$
$440$	7.51568			0.358296
$441$	15.3283	+	11.1367i	0.729918	+	0.530317i
$442$	13.2859	−	9.65276i	0.631945	−	0.459135i
$443$	−25.3384	+	18.4094i	−1.20386	+	0.874658i	−0.994659	−	0.103214i	$-0.967087\pi$
$443$	−25.3384	+	18.4094i	−1.20386	+	0.874658i	−0.209205	+	0.977872i	$0.567087\pi$
$444$	−12.1768	+	37.4763i	−0.577886	+	1.77855i
$445$	−2.56944	−	1.86680i	−0.121803	−	0.0884950i
$446$	−0.543699	+	1.67333i	−0.0257449	+	0.0792347i
$447$	−1.75200	−	5.39211i	−0.0828669	−	0.255038i
$448$	22.7714	−	16.5444i	1.07585	−	0.781650i
$449$	−3.29468	−	10.1400i	−0.155485	−	0.478535i	0.842724	−	0.538345i	$-0.180950\pi$
$449$	−3.29468	−	10.1400i	−0.155485	−	0.478535i	−0.998210	+	0.0598103i	$0.980950\pi$
$450$	12.8935	+	39.6821i	0.607805	+	1.87063i
$451$	8.69740	−	6.31903i	0.409544	−	0.297551i
$452$	34.3063	+	105.584i	1.61363	+	4.96625i
$453$	12.3429	−	37.9874i	0.579919	−	1.78481i
$454$	51.6773	+	37.5458i	2.42534	+	1.76211i
$455$	0.360190	−	1.10855i	0.0168860	−	0.0519697i
$456$	46.6004	−	33.8572i	2.18227	−	1.58551i
$457$	21.1289	−	15.3511i	0.988370	−	0.718093i	0.0288062	−	0.999585i	$-0.490829\pi$
$457$	21.1289	−	15.3511i	0.988370	−	0.718093i	0.959563	+	0.281492i	$0.0908294\pi$
$458$	3.82667	+	2.78024i	0.178808	+	0.129912i
$459$	−10.2403			−0.477975
$460$	2.00486			0.0934773
$461$	29.5226	+	21.4494i	1.37500	+	0.998998i	0.997328	+	0.0730594i	$0.0232763\pi$
$461$	29.5226	+	21.4494i	1.37500	+	0.998998i	0.377675	+	0.925938i	$0.376724\pi$
$462$	−2.87400	−	8.84527i	−0.133711	−	0.411519i
$463$	1.30408	−	4.01354i	0.0606056	−	0.186525i	−0.916170	−	0.400790i	$-0.868736\pi$
$463$	1.30408	−	4.01354i	0.0606056	−	0.186525i	0.976776	+	0.214265i	$0.0687357\pi$
$464$	−113.707			−5.27870
$465$	11.1234	−	5.57199i	0.515836	−	0.258395i
$466$	23.9567			1.10977
$467$	5.08450	−	15.6485i	0.235283	−	0.724126i	−0.761801	−	0.647811i	$-0.775685\pi$
$467$	5.08450	−	15.6485i	0.235283	−	0.724126i	0.997084	−	0.0763148i	$-0.0243154\pi$
$468$	5.90584	+	18.1763i	0.272998	+	0.840200i
$469$	−3.37627	−	2.45300i	−0.155902	−	0.113269i
$470$	20.3035			0.936530
$471$	−13.5436			−0.624058
$472$	2.27436	+	1.65242i	0.104686	+	0.0760588i
$473$	6.51002	−	4.72981i	0.299331	−	0.217477i
$474$	37.7470	−	27.4248i	1.73378	−	1.25966i
$475$	3.36998	−	10.3717i	0.154625	−	0.475888i
$476$	34.7868	+	25.2741i	1.59445	+	1.15844i
$477$	−8.50238	+	26.1676i	−0.389297	+	1.19813i
$478$	−7.81689	−	24.0579i	−0.357536	−	1.10038i
$479$	−17.9908	+	13.0711i	−0.822022	+	0.597234i	−0.917291	−	0.398217i	$-0.869629\pi$
$479$	−17.9908	+	13.0711i	−0.822022	+	0.597234i	0.0952688	+	0.995452i	$0.469629\pi$
$480$	−12.0140	−	36.9753i	−0.548361	−	1.68768i
$481$	0.901886	+	2.77572i	0.0411224	+	0.126562i
$482$	−8.43421	+	6.12781i	−0.384168	+	0.279114i
$483$	−0.473791	−	1.45818i	−0.0215582	−	0.0663494i
$484$	−16.1894	+	49.8257i	−0.735880	+	2.26481i
$485$	−3.90694	−	2.83856i	−0.177405	−	0.128892i
$486$	−18.3855	+	56.5846i	−0.833981	+	2.56673i
$487$	16.4603	−	11.9591i	0.745887	−	0.541919i	−0.148662	−	0.988888i	$-0.547497\pi$
$487$	16.4603	−	11.9591i	0.745887	−	0.541919i	0.894549	+	0.446969i	$0.147497\pi$
$488$	33.6535	−	24.4507i	1.52342	−	1.10683i
$489$	14.5136	+	10.5447i	0.656327	+	0.476849i
$490$	−12.0970			−0.546485
$491$	7.04178			0.317791			0.158896	−	0.987295i	$-0.449207\pi$
$491$	7.04178			0.317791			0.158896	+	0.987295i	$0.449207\pi$
$492$	−117.822	−	85.6026i	−5.31182	−	3.85926i
$493$	−16.5788	−	51.0242i	−0.746671	−	2.29802i
$494$	2.13329	−	6.56559i	0.0959813	−	0.295400i
$495$	−3.15236			−0.141688
$496$	64.4139	−	32.2665i	2.89227	−	1.44881i
$497$	−14.2701			−0.640101
$498$	4.24476	−	13.0640i	0.190212	−	0.585413i
$499$	3.65903	+	11.2613i	0.163801	+	0.504126i	0.998946	−	0.0459030i	$-0.0146165\pi$
$499$	3.65903	+	11.2613i	0.163801	+	0.504126i	−0.835145	+	0.550029i	$0.814617\pi$
$500$	−33.9446	−	24.6622i	−1.51805	−	1.10293i
$501$	−19.9093			−0.889483
$502$	−60.5706			−2.70340
$503$	21.4788	+	15.6053i	0.957692	+	0.695804i	0.952614	−	0.304183i	$-0.0983834\pi$
$503$	21.4788	+	15.6053i	0.957692	+	0.695804i	0.00507864	+	0.999987i	$0.498383\pi$
$504$	−34.5760	+	25.1209i	−1.54014	+	1.11898i
$505$	10.8469	−	7.88073i	0.482680	−	0.350688i
$506$	0.366134	−	1.12685i	0.0162767	−	0.0500944i
$507$	2.08632	+	1.51580i	0.0926569	+	0.0673192i
$508$	−18.7325	+	57.6528i	−0.831122	+	2.55793i
$509$	−2.98816	−	9.19661i	−0.132448	−	0.407633i	0.862736	−	0.505654i	$-0.168749\pi$
$509$	−2.98816	−	9.19661i	−0.132448	−	0.407633i	−0.995184	+	0.0980211i	$0.968749\pi$
$510$	29.6868	−	21.5687i	1.31455	−	0.955079i
$511$	−4.75498	−	14.6343i	−0.210348	−	0.647385i
$512$	0.0276340	+	0.0850486i	0.00122126	+	0.00375865i
$513$	−3.48260	+	2.53026i	−0.153761	+	0.111714i
$514$	−9.06888	−	27.9111i	−0.400011	−	1.23111i
$515$	−0.0766789	+	0.235993i	−0.00337887	+	0.0103991i
$516$	−88.1900	−	64.0738i	−3.88235	−	2.82069i
$517$	2.68297	−	8.25733i	0.117997	−	0.363157i
$518$	−8.54401	+	6.20759i	−0.375402	+	0.272746i
$519$	39.3155	−	28.5644i	1.72576	−	1.25384i
$520$	−6.10071	−	4.43243i	−0.267534	−	0.194375i
$521$	−7.26662			−0.318357			−0.159178	−	0.987250i	$-0.550884\pi$
$521$	−7.26662			−0.318357			−0.159178	+	0.987250i	$0.550884\pi$
$522$	86.2874			3.77670
$523$	0.779595	+	0.566409i	0.0340893	+	0.0247673i	0.604699	−	0.796454i	$-0.293293\pi$
$523$	0.779595	+	0.566409i	0.0340893	+	0.0247673i	−0.570610	+	0.821221i	$0.693293\pi$
$524$	−7.08183	−	21.7956i	−0.309371	−	0.952146i
$525$	−4.55533	+	14.0199i	−0.198811	+	0.611877i
$526$	12.0037			0.523385
$527$	23.8709	+	24.2002i	1.03983	+	1.05418i
$528$	−33.2571			−1.44733
$529$	−7.04703	+	21.6885i	−0.306393	+	0.942980i
$530$	−5.42852	−	16.7073i	−0.235800	−	0.725717i
$531$	−0.953952	−	0.693087i	−0.0413980	−	0.0300774i
$532$	18.0756			0.783675
$533$	−10.7866			−0.467221
$534$	20.5706	+	14.9454i	0.890178	+	0.646752i
$535$	−5.57843	+	4.05297i	−0.241177	+	0.175225i
$536$	−21.8429	+	15.8698i	−0.943471	+	0.685472i
$537$	19.7234	−	60.7023i	0.851126	−	2.61950i
$538$	−28.5641	−	20.7530i	−1.23148	−	0.894725i
$539$	−1.59853	+	4.91978i	−0.0688537	+	0.211910i
$540$	2.35126	+	7.23644i	0.101182	+	0.311407i
$541$	−10.4011	+	7.55685i	−0.447178	+	0.324894i	−0.788481	−	0.615059i	$-0.789132\pi$
$541$	−10.4011	+	7.55685i	−0.447178	+	0.324894i	0.341302	+	0.939954i	$0.389132\pi$
$542$	16.1550	+	49.7198i	0.693915	+	2.13565i
$543$	8.02810	+	24.7080i	0.344519	+	1.06032i
$544$	85.9386	−	62.4381i	3.68459	−	2.67701i
$545$	4.75420	+	14.6319i	0.203647	+	0.626762i
$546$	−2.88364	+	8.87494i	−0.123409	+	0.379813i
$547$	4.35891	+	3.16693i	0.186373	+	0.135408i	0.677060	−	0.735928i	$-0.263254\pi$
$547$	4.35891	+	3.16693i	0.186373	+	0.135408i	−0.490686	+	0.871336i	$0.663254\pi$
$548$	−24.6732	+	75.9363i	−1.05399	+	3.24384i
$549$	−14.1155	+	10.2555i	−0.602437	+	0.437696i
$550$	−9.21614	+	6.69592i	−0.392977	+	0.285515i
$551$	−18.2458	−	13.2563i	−0.777297	−	0.564739i
$552$	−9.91922			−0.422190
$553$	9.04830			0.384773
$554$	−30.3048	−	22.0177i	−1.28753	−	0.935444i
$555$	2.01523	+	6.20223i	0.0855417	+	0.263270i
$556$	25.4863	−	78.4387i	1.08086	−	3.32654i
$557$	−3.53822			−0.149919			−0.0749595	−	0.997187i	$-0.523883\pi$
$557$	−3.53822			−0.149919			−0.0749595	+	0.997187i	$0.523883\pi$
$558$	−48.8811	+	24.4858i	−2.06930	+	1.03657i
$559$	−8.07383			−0.341487
$560$	4.66065	−	14.3440i	0.196948	−	0.606144i
$561$	−4.84898	−	14.9236i	−0.204724	−	0.630076i
$562$	15.4864	+	11.2515i	0.653253	+	0.474616i
$563$	17.5165			0.738231			0.369115	−	0.929384i	$-0.379661\pi$
$563$	17.5165			0.738231			0.369115	+	0.929384i	$0.379661\pi$
$564$	−117.617			−4.95257
$565$	14.8642	+	10.7994i	0.625340	+	0.454336i
$566$	−24.1971	+	17.5802i	−1.01708	+	0.738951i
$567$	−7.21095	+	5.23906i	−0.302831	+	0.220020i
$568$	−28.5287	+	87.8024i	−1.19704	+	3.68411i
$569$	9.19636	+	6.68154i	0.385531	+	0.280105i	0.763622	−	0.645664i	$-0.223419\pi$
$569$	9.19636	+	6.68154i	0.385531	+	0.280105i	−0.378091	+	0.925769i	$0.623419\pi$
$570$	4.76675	−	14.6706i	0.199657	−	0.614482i
$571$	−6.03931	−	18.5871i	−0.252737	−	0.777845i	−0.994267	−	0.106925i	$-0.965899\pi$
$571$	−6.03931	−	18.5871i	−0.252737	−	0.777845i	0.741530	−	0.670920i	$-0.234101\pi$
$572$	−4.22144	+	3.06706i	−0.176507	+	0.128240i
$573$	17.0212	+	52.3859i	0.711071	+	2.18845i
$574$	−12.0616	−	37.1217i	−0.503440	−	1.54943i
$575$	−1.51932	+	1.10385i	−0.0633599	+	0.0460337i
$576$	23.6024	+	72.6407i	0.983433	+	3.02670i
$577$	−8.10995	+	24.9598i	−0.337621	+	1.03909i	0.627795	+	0.778379i	$0.283958\pi$
$577$	−8.10995	+	24.9598i	−0.337621	+	1.03909i	−0.965416	+	0.260713i	$0.916042\pi$
$578$	44.1180	+	32.0536i	1.83507	+	1.33325i
$579$	−5.54178	+	17.0558i	−0.230308	+	0.708816i
$580$	−32.2504	+	23.4313i	−1.33913	+	0.972931i
$581$	2.15512	−	1.56579i	0.0894094	−	0.0649597i
$582$	31.2786	+	22.7252i	1.29654	+	0.941990i
$583$	−7.51211			−0.311120
$584$	−99.5498			−4.11940
$585$	2.55887	+	1.85913i	0.105796	+	0.0768654i
$586$	9.05948	+	27.8822i	0.374244	+	1.15180i
$587$	6.85145	−	21.0866i	0.282790	−	0.870337i	−0.704263	−	0.709939i	$-0.748722\pi$
$587$	6.85145	−	21.0866i	0.282790	−	0.870337i	0.987052	−	0.160398i	$-0.0512777\pi$
$588$	70.0771			2.88993
$589$	14.0978	+	2.33200i	0.580891	+	0.0960884i
$590$	0.752852			0.0309944
$591$	−15.0518	+	46.3248i	−0.619150	+	1.90555i
$592$	11.6699	+	35.9161i	0.479628	+	1.47614i
$593$	19.3473	+	14.0566i	0.794498	+	0.577237i	0.909295	−	0.416152i	$-0.136622\pi$
$593$	19.3473	+	14.0566i	0.794498	+	0.577237i	−0.114797	+	0.993389i	$0.536622\pi$
$594$	4.49668			0.184501
$595$	7.11620			0.291736
$596$	−9.31202	−	6.76558i	−0.381435	−	0.277129i
$597$	49.0191	−	35.6145i	2.00622	−	1.45760i
$598$	−0.961768	+	0.698766i	−0.0393296	+	0.0285747i
$599$	−2.51000	+	7.72499i	−0.102556	+	0.315635i	−0.989149	−	0.146915i	$-0.953065\pi$
$599$	−2.51000	+	7.72499i	−0.102556	+	0.315635i	0.886593	+	0.462550i	$0.153065\pi$
$600$	77.1558	+	56.0570i	3.14987	+	2.28852i
$601$	−7.62635	+	23.4715i	−0.311085	+	0.957422i	0.666251	+	0.745728i	$0.267898\pi$
$601$	−7.62635	+	23.4715i	−0.311085	+	0.957422i	−0.977336	+	0.211694i	$0.932102\pi$
$602$	−9.02811	−	27.7857i	−0.367958	−	1.13246i
$603$	9.16174	−	6.65640i	0.373095	−	0.271069i
$604$	−25.0582	−	77.1211i	−1.01960	−	3.13801i
$605$	2.67930	+	8.24603i	0.108929	+	0.335249i
$606$	−86.8391	+	63.0923i	−3.52760	+	2.56295i
$607$	0.711366	+	2.18936i	0.0288735	+	0.0888634i	0.964455	−	0.264248i	$-0.0851237\pi$
$607$	0.711366	+	2.18936i	0.0288735	+	0.0888634i	−0.935581	+	0.353111i	$0.885124\pi$
$608$	13.7990	−	42.4690i	0.559624	−	1.72234i
$609$	24.6635	+	17.9191i	0.999414	+	0.726117i
$610$	3.44241	−	10.5947i	0.139379	−	0.428965i
$611$	−7.04767	+	5.12043i	−0.285118	+	0.207150i
$612$	−94.3965	+	68.5831i	−3.81575	+	2.77231i
$613$	9.16646	+	6.65982i	0.370230	+	0.268988i	0.757306	−	0.653060i	$-0.226515\pi$
$613$	9.16646	+	6.65982i	0.370230	+	0.268988i	−0.387076	+	0.922048i	$0.626515\pi$
$614$	−9.37865			−0.378492
$615$	−24.1023			−0.971900
$616$	−9.44014	−	6.85866i	−0.380354	−	0.276343i
$617$	2.93343	+	9.02817i	0.118095	+	0.363460i	0.992580	−	0.121593i	$-0.0388002\pi$
$617$	2.93343	+	9.02817i	0.118095	+	0.363460i	−0.874485	+	0.485053i	$0.838800\pi$
$618$	0.613883	−	1.88934i	0.0246940	−	0.0760003i
$619$	38.2803			1.53861			0.769307	−	0.638879i	$-0.220602\pi$
$619$	38.2803			1.53861			0.769307	+	0.638879i	$0.220602\pi$
$620$	11.6205	−	22.4253i	0.466690	−	0.900623i
$621$	0.741295			0.0297472
$622$	14.2558	−	43.8750i	0.571607	−	1.75923i
$623$	1.52375	+	4.68963i	0.0610479	+	0.187886i
$624$	26.9958	+	19.6136i	1.08070	+	0.785172i
$625$	14.3023			0.572094
$626$	66.4422			2.65557
$627$	−5.33655	−	3.87723i	−0.213121	−	0.154842i
$628$	−22.2447	+	16.1617i	−0.887659	+	0.644922i
$629$	−14.4154	+	10.4734i	−0.574778	+	0.417601i
$630$	−3.53678	+	10.8851i	−0.140909	+	0.433672i
$631$	2.14511	+	1.55852i	0.0853956	+	0.0620435i	0.629664	−	0.776868i	$-0.283193\pi$
$631$	2.14511	+	1.55852i	0.0853956	+	0.0620435i	−0.544268	+	0.838911i	$0.683193\pi$
$632$	18.0894	−	55.6733i	0.719556	−	2.21457i
$633$	9.76105	+	30.0414i	0.387967	+	1.19404i
$634$	7.34523	−	5.33662i	0.291716	−	0.211944i
$635$	3.10018	+	9.54138i	0.123027	+	0.378638i
$636$	31.4471	+	96.7842i	1.24696	+	3.83774i
$637$	4.19906	−	3.05079i	0.166373	−	0.120877i
$638$	7.28003	+	22.4056i	0.288219	+	0.887047i
$639$	11.9660	−	36.8276i	0.473369	−	1.45688i
$640$	−15.0591	−	10.9411i	−0.595264	−	0.432484i
$641$	10.6802	−	32.8702i	0.421841	−	1.29829i	−0.484146	−	0.874987i	$-0.660870\pi$
$641$	10.6802	−	32.8702i	0.421841	−	1.29829i	0.905987	−	0.423306i	$-0.139130\pi$
$642$	44.6603	−	32.4476i	1.76260	−	1.28061i
$643$	16.3158	−	11.8541i	0.643432	−	0.467481i	−0.217596	−	0.976039i	$-0.569821\pi$
$643$	16.3158	−	11.8541i	0.643432	−	0.467481i	0.861028	+	0.508558i	$0.169821\pi$
$644$	−2.51823	−	1.82960i	−0.0992321	−	0.0720963i
$645$	−18.0407			−0.710350
$646$	42.1470			1.65825
$647$	−8.33558	−	6.05615i	−0.327705	−	0.238092i	0.411751	−	0.911296i	$-0.364917\pi$
$647$	−8.33558	−	6.05615i	−0.327705	−	0.238092i	−0.739456	+	0.673204i	$0.764917\pi$
$648$	17.8193	+	54.8422i	0.700008	+	2.15440i
$649$	0.0994843	−	0.306181i	0.00390510	−	0.0120187i
$650$	11.4300			0.448321
$651$	−19.0565	−	3.15225i	−0.746885	−	0.123546i
$652$	36.4209			1.42635
$653$	2.92788	−	9.01108i	0.114577	−	0.352631i	−0.877282	−	0.479976i	$-0.840645\pi$
$653$	2.92788	−	9.01108i	0.114577	−	0.352631i	0.991859	+	0.127345i	$0.0406455\pi$
$654$	−38.0616	−	117.142i	−1.48833	−	4.58060i
$655$	−3.06840	−	2.22932i	−0.119892	−	0.0871068i
$656$	−139.573			−5.44940
$657$	41.7549			1.62901
$658$	−25.5024	−	18.5286i	−0.994186	−	0.722318i
$659$	19.6011	−	14.2410i	0.763549	−	0.554751i	−0.136448	−	0.990647i	$-0.543569\pi$
$659$	19.6011	−	14.2410i	0.763549	−	0.554751i	0.899997	+	0.435897i	$0.143569\pi$
$660$	−9.43264	+	6.85321i	−0.367165	+	0.266761i
$661$	−1.03806	+	3.19484i	−0.0403760	+	0.124265i	−0.969213	−	0.246224i	$-0.920810\pi$
$661$	−1.03806	+	3.19484i	−0.0403760	+	0.124265i	0.928837	+	0.370489i	$0.120810\pi$
$662$	8.73020	+	6.34286i	0.339309	+	0.246522i
$663$	−4.86525	+	14.9737i	−0.188951	+	0.581531i
$664$	−5.32561	−	16.3906i	−0.206674	−	0.636077i
$665$	2.42014	−	1.75833i	0.0938490	−	0.0681853i
$666$	−8.85579	−	27.2553i	−0.343155	−	1.05612i
$667$	1.20014	+	3.69366i	0.0464697	+	0.143019i
$668$	−32.7000	+	23.7579i	−1.26520	+	0.919222i
$669$	−0.521254	−	1.60425i	−0.0201528	−	0.0620240i
$670$	−2.23431	+	6.87650i	−0.0863190	+	0.265662i
$671$	−3.85390	−	2.80003i	−0.148778	−	0.108094i
$672$	−18.6526	+	57.4068i	−0.719540	+	2.21452i
$673$	15.8051	−	11.4830i	0.609240	−	0.442639i	−0.239906	−	0.970796i	$-0.577117\pi$
$673$	15.8051	−	11.4830i	0.609240	−	0.442639i	0.849147	+	0.528157i	$0.177117\pi$
$674$	−70.8293	+	51.4605i	−2.72824	+	1.98218i
$675$	−5.76610	−	4.18932i	−0.221937	−	0.161247i
$676$	5.23549			0.201365
$677$	−32.4238			−1.24615			−0.623073	−	0.782164i	$-0.714116\pi$
$677$	−32.4238			−1.24615			−0.623073	+	0.782164i	$0.714116\pi$
$678$	−119.001	−	86.4592i	−4.57020	−	3.32045i
$679$	2.31694	+	7.13080i	0.0889158	+	0.273655i
$680$	14.2267	−	43.7853i	0.545569	−	1.67909i
$681$	−61.2396			−2.34671
$682$	−10.4821	−	10.6267i	−0.401381	−	0.406919i
$683$	18.0982			0.692507			0.346254	−	0.938141i	$-0.387454\pi$
$683$	18.0982			0.692507			0.346254	+	0.938141i	$0.387454\pi$
$684$	−15.1571	+	46.6487i	−0.579545	+	1.78366i
$685$	4.08335	+	12.5673i	0.156017	+	0.480170i
$686$	35.6868	+	25.9280i	1.36253	+	0.989935i
$687$	−4.53475			−0.173012
$688$	−104.471			−3.98290
$689$	6.09781	+	4.43032i	0.232308	+	0.168782i
$690$	−2.14903	+	1.56136i	−0.0818123	+	0.0594401i
$691$	21.3287	−	15.4962i	0.811383	−	0.589504i	−0.102848	−	0.994697i	$-0.532796\pi$
$691$	21.3287	−	15.4962i	0.811383	−	0.589504i	0.914231	+	0.405193i	$0.132796\pi$
$692$	30.4875	−	93.8310i	1.15896	−	3.56692i
$693$	3.95955	+	2.87678i	0.150411	+	0.109280i
$694$	−3.40343	+	10.4747i	−0.129192	+	0.397613i
$695$	−4.21791	−	12.9814i	−0.159994	−	0.492412i
$696$	159.561	−	115.928i	6.04816	−	4.39425i
$697$	−20.3501	−	62.6313i	−0.770817	−	2.37233i
$698$	−28.5912	−	87.9946i	−1.08219	−	3.33064i
$699$	−18.5812	+	13.5000i	−0.702806	+	0.510619i
$700$	9.24811	+	28.4628i	0.349546	+	1.07579i
$701$	−8.03893	+	24.7413i	−0.303626	+	0.934465i	0.676560	+	0.736387i	$0.263470\pi$
$701$	−8.03893	+	24.7413i	−0.303626	+	0.934465i	−0.980186	+	0.198078i	$0.936530\pi$
$702$	−3.65009	−	2.65195i	−0.137764	−	0.100091i
$703$	−2.31465	+	7.12375i	−0.0872986	+	0.268677i
$704$	−16.8708	+	12.2573i	−0.635841	+	0.461966i
$705$	−15.7477	+	11.4414i	−0.593094	+	0.430908i
$706$	−8.56308	−	6.22144i	−0.322276	−	0.234147i
$707$	−20.8161			−0.782871
$708$	−4.36123			−0.163905
$709$	−7.96865	−	5.78957i	−0.299269	−	0.217432i	0.428009	−	0.903774i	$-0.359215\pi$
$709$	−7.96865	−	5.78957i	−0.299269	−	0.217432i	−0.727278	+	0.686343i	$0.759215\pi$
$710$	7.63995	+	23.5133i	0.286722	+	0.882440i
$711$	−7.58735	+	23.3515i	−0.284548	+	0.875749i
$712$	31.9011			1.19555
$713$	−1.72802	−	1.75186i	−0.0647148	−	0.0656077i
$714$	−56.9715			−2.13211
$715$	−0.266855	+	0.821297i	−0.00997983	+	0.0307148i
$716$	−40.0419	−	123.236i	−1.49644	−	4.60556i
$717$	19.6200	+	14.2548i	0.732723	+	0.532355i
$718$	29.8549			1.11417
$719$	−35.9525			−1.34080			−0.670401	−	0.741999i	$-0.733878\pi$
$719$	−35.9525			−1.34080			−0.670401	+	0.741999i	$0.733878\pi$
$720$	33.1102	+	24.0560i	1.23395	+	0.896514i
$721$	0.311676	−	0.226446i	0.0116074	−	0.00843329i
$722$	−27.0134	+	19.6264i	−1.00534	+	0.730419i
$723$	3.08858	−	9.50569i	0.114866	−	0.353520i
$724$	42.6699	+	31.0015i	1.58581	+	1.15216i
$725$	11.5389	−	35.5132i	0.428545	−	1.31893i
$726$	−21.4502	−	66.0168i	−0.796090	−	2.45011i
$727$	10.6011	−	7.70211i	0.393171	−	0.285656i	−0.373583	−	0.927597i	$-0.621871\pi$
$727$	10.6011	−	7.70211i	0.393171	−	0.285656i	0.766754	+	0.641941i	$0.221871\pi$
$728$	3.61791	+	11.1348i	0.134089	+	0.412683i
$729$	−11.4840	−	35.3443i	−0.425335	−	1.30905i
$730$	−21.5678	+	15.6699i	−0.798260	+	0.579970i
$731$	−15.2321	−	46.8797i	−0.563381	−	1.73391i
$732$	−19.9417	+	61.3743i	−0.737067	+	2.26846i
$733$	15.7881	+	11.4707i	0.583145	+	0.423680i	0.839857	−	0.542808i	$-0.182639\pi$
$733$	15.7881	+	11.4707i	0.583145	+	0.423680i	−0.256711	+	0.966488i	$0.582639\pi$
$734$	31.3659	−	96.5344i	1.15774	−	3.56315i
$735$	9.38263	−	6.81688i	0.346083	−	0.251444i
$736$	−6.22112	+	4.51991i	−0.229314	+	0.166606i
$737$	2.50139	+	1.81737i	0.0921399	+	0.0669436i
$738$	105.916			3.89883
$739$	49.2886			1.81311			0.906556	−	0.422085i	$-0.138702\pi$
$739$	49.2886			1.81311			0.906556	+	0.422085i	$0.138702\pi$
$740$	10.7111	+	7.78205i	0.393747	+	0.286074i
$741$	2.04522	+	6.29454i	0.0751330	+	0.231236i
$742$	−8.42818	+	25.9393i	−0.309408	+	0.952261i
$743$	23.8803			0.876083			0.438042	−	0.898955i	$-0.355672\pi$
$743$	23.8803			0.876083			0.438042	+	0.898955i	$0.355672\pi$
$744$	−57.4933	+	110.951i	−2.10781	+	4.06766i
$745$	−1.90492			−0.0697909
$746$	12.5037	−	38.4823i	0.457792	−	1.40894i
$747$	2.23376	+	6.87481i	0.0817291	+	0.251536i
$748$	−25.7727	−	18.7249i	−0.942342	−	0.684651i
$749$	10.7055			0.391170
$750$	55.5921			2.02994
$751$	21.6807	+	15.7519i	0.791138	+	0.574796i	0.908301	−	0.418317i	$-0.137380\pi$
$751$	21.6807	+	15.7519i	0.791138	+	0.574796i	−0.117163	+	0.993113i	$0.537380\pi$
$752$	−91.1926	+	66.2553i	−3.32545	+	2.41608i
$753$	46.9796	−	34.1327i	1.71203	−	1.24386i
$754$	7.30446	−	22.4808i	0.266013	−	0.818703i
$755$	−10.8571	−	7.88818i	−0.395132	−	0.287080i
$756$	3.65051	−	11.2351i	0.132768	−	0.408617i
$757$	−3.03566	−	9.34281i	−0.110333	−	0.339570i	0.880612	−	0.473838i	$-0.157132\pi$
$757$	−3.03566	−	9.34281i	−0.110333	−	0.339570i	−0.990945	+	0.134268i	$0.957132\pi$
$758$	53.5173	−	38.8826i	1.94383	−	1.41228i
$759$	0.351019	+	1.08033i	0.0127412	+	0.0392133i
$760$	−5.98052	−	18.4061i	−0.216936	−	0.667661i
$761$	−8.30309	+	6.03255i	−0.300987	+	0.218680i	−0.728019	−	0.685556i	$-0.759559\pi$
$761$	−8.30309	+	6.03255i	−0.300987	+	0.218680i	0.427033	+	0.904236i	$0.359559\pi$
$762$	−24.8197	−	76.3873i	−0.899124	−	2.76722i
$763$	7.38125	−	22.7171i	0.267219	−	0.822416i
$764$	90.4689	+	65.7295i	3.27305	+	2.37801i
$765$	−5.96721	+	18.3652i	−0.215745	+	0.663995i
$766$	20.1441	−	14.6356i	0.727837	−	0.528805i
$767$	−0.261327	+	0.189865i	−0.00943598	+	0.00685564i
$768$	33.2557	+	24.1617i	1.20001	+	0.871860i
$769$	−36.8695			−1.32955			−0.664774	−	0.747045i	$-0.731472\pi$
$769$	−36.8695			−1.32955			−0.664774	+	0.747045i	$0.731472\pi$
$770$	−3.12485			−0.112612
$771$	22.7625	+	16.5379i	0.819770	+	0.595598i
$772$	11.2508	+	34.6263i	0.404924	+	1.24623i
$773$	−11.5063	+	35.4129i	−0.413855	+	1.27371i	0.499417	+	0.866362i	$0.333548\pi$
$773$	−11.5063	+	35.4129i	−0.413855	+	1.27371i	−0.913271	+	0.407352i	$0.866452\pi$
$774$	79.2785			2.84961
$775$	3.54087	+	23.3923i	0.127192	+	0.840278i
$776$	48.5071			1.74130
$777$	3.12879	−	9.62943i	0.112245	−	0.345454i
$778$	7.48036	+	23.0222i	0.268184	+	0.825385i
$779$	−22.3964	−	16.2719i	−0.802433	−	0.583002i
$780$	11.6985			0.418874
$781$	10.5723			0.378308
$782$	−5.87177	−	4.26609i	−0.209974	−	0.152555i
$783$	−11.9245	+	8.66368i	−0.426148	+	0.309615i
$784$	54.3333	−	39.4754i	1.94047	−	1.40984i
$785$	−1.40618	+	4.32778i	−0.0501888	+	0.154465i
$786$	24.5653	+	17.8477i	0.876214	+	0.636607i
$787$	−13.8970	+	42.7707i	−0.495376	+	1.52461i	0.320993	+	0.947081i	$0.395983\pi$
$787$	−13.8970	+	42.7707i	−0.495376	+	1.52461i	−0.816370	+	0.577530i	$0.804017\pi$
$788$	30.5579	+	94.0474i	1.08858	+	3.35030i
$789$	−9.31026	+	6.76430i	−0.331454	+	0.240815i
$790$	−4.84430	−	14.9092i	−0.172352	−	0.530446i
$791$	−8.81490	−	27.1295i	−0.313422	−	0.964613i
$792$	25.6165	−	18.6115i	0.910242	−	0.661329i
$793$	1.47700	+	4.54574i	0.0524498	+	0.161424i
$794$	−6.01773	+	18.5207i	−0.213561	+	0.657274i
$795$	13.6253	+	9.89938i	0.483240	+	0.351095i
$796$	38.0122	−	116.990i	1.34731	−	4.14659i
$797$	18.3849	−	13.3574i	0.651228	−	0.473145i	−0.212461	−	0.977169i	$-0.568148\pi$
$797$	18.3849	−	13.3574i	0.651228	−	0.473145i	0.863689	+	0.504025i	$0.168148\pi$
$798$	−19.3754	+	14.0770i	−0.685881	+	0.498322i
$799$	−43.0273	−	31.2612i	−1.52220	−	1.10594i
$800$	73.9340			2.61396
$801$	−13.3805			−0.472778
$802$	−51.7316	−	37.5852i	−1.82671	−	1.32718i
$803$	3.52284	+	10.8422i	0.124318	+	0.382613i
$804$	12.9432	−	39.8352i	0.456473	−	1.40488i
$805$	−0.515144			−0.0181564
$806$	2.24146	+	14.8080i	0.0789522	+	0.521589i
$807$	33.8495			1.19156
$808$	−41.6156	+	128.080i	−1.46403	+	4.50583i
$809$	6.86307	+	21.1223i	0.241293	+	0.742622i	0.996224	+	0.0868186i	$0.0276701\pi$
$809$	6.86307	+	21.1223i	0.241293	+	0.742622i	−0.754932	+	0.655804i	$0.772330\pi$
$810$	12.4932	+	9.07685i	0.438967	+	0.318928i
$811$	−5.11160			−0.179492			−0.0897462	−	0.995965i	$-0.528606\pi$
$811$	−5.11160			−0.179492			−0.0897462	+	0.995965i	$0.528606\pi$
$812$	61.8914			2.17196
$813$	−40.5482	−	29.4600i	−1.42209	−	1.03321i
$814$	6.33003	−	4.59904i	0.221868	−	0.161196i
$815$	4.87639	−	3.54291i	0.170813	−	0.124103i
$816$	−62.9535	+	193.751i	−2.20381	+	6.78264i
$817$	−16.7637	−	12.1796i	−0.586489	−	0.426109i
$818$	−16.1873	+	49.8195i	−0.565976	+	1.74190i
$819$	−1.51749	−	4.67035i	−0.0530253	−	0.163195i
$820$	−39.5868	+	28.7615i	−1.38243	+	1.00439i
$821$	−5.94726	−	18.3038i	−0.207561	−	0.638806i	−0.999599	−	0.0283343i	$-0.990980\pi$
$821$	−5.94726	−	18.3038i	−0.207561	−	0.638806i	0.792038	−	0.610472i	$-0.209020\pi$
$822$	−32.6908	−	100.612i	−1.14022	−	3.50925i
$823$	−19.3284	+	14.0429i	−0.673746	+	0.489505i	−0.871277	−	0.490791i	$-0.836708\pi$
$823$	−19.3284	+	14.0429i	−0.673746	+	0.489505i	0.197531	+	0.980297i	$0.436708\pi$
$824$	−0.770197	−	2.37042i	−0.0268311	−	0.0825776i
$825$	3.37492	−	10.3869i	0.117500	−	0.361627i
$826$	−0.945627	−	0.687038i	−0.0329026	−	0.0239051i
$827$	−13.6416	+	41.9844i	−0.474364	+	1.45994i	0.372450	+	0.928052i	$0.378518\pi$
$827$	−13.6416	+	41.9844i	−0.474364	+	1.45994i	−0.846814	+	0.531889i	$0.821482\pi$
$828$	6.83338	−	4.96474i	0.237477	−	0.172537i
$829$	−17.3209	+	12.5844i	−0.601581	+	0.437074i	−0.846440	−	0.532484i	$-0.821258\pi$
$829$	−17.3209	+	12.5844i	−0.601581	+	0.437074i	0.244859	+	0.969559i	$0.421258\pi$
$830$	−3.73382	−	2.71278i	−0.129603	−	0.0941618i
$831$	35.9124			1.24579
$832$	20.9234			0.725388
$833$	25.6360	+	18.6257i	0.888235	+	0.645341i
$834$	33.7681	+	103.928i	1.16929	+	3.59872i
$835$	−2.06711	+	6.36191i	−0.0715352	+	0.220163i
$836$	−13.3917			−0.463162
$837$	4.29666	−	8.29173i	0.148514	−	0.286604i
$838$	−55.6970			−1.92402
$839$	16.7588	−	51.5781i	0.578576	−	1.78067i	−0.0450884	−	0.998983i	$-0.514357\pi$
$839$	16.7588	−	51.5781i	0.578576	−	1.78067i	0.623665	−	0.781692i	$-0.285643\pi$
$840$	8.08408	+	24.8802i	0.278927	+	0.858450i
$841$	−39.0127	−	28.3444i	−1.34526	−	0.977392i
$842$	−85.4331			−2.94422
$843$	−18.3519			−0.632074
$844$	51.8806	+	37.6935i	1.78580	+	1.29746i
$845$	0.700981	−	0.509292i	0.0241145	−	0.0175202i
$846$	69.2024	−	50.2785i	2.37923	−	1.72861i
$847$	4.15981	−	12.8026i	0.142933	−	0.439901i
$848$	78.9021	+	57.3257i	2.70951	+	1.96857i
$849$	8.86089	−	27.2710i	0.304105	−	0.935939i
$850$	21.5639	+	66.3668i	0.739635	+	2.27636i
$851$	1.04353	−	0.758170i	0.0357718	−	0.0259897i
$852$	−44.2578	−	136.212i	−1.51625	−	4.66653i
$853$	−4.64658	−	14.3007i	−0.159096	−	0.489646i	0.839457	−	0.543426i	$-0.182873\pi$
$853$	−4.64658	−	14.3007i	−0.159096	−	0.489646i	−0.998553	+	0.0537797i	$0.982873\pi$
$854$	−13.9924	+	10.1660i	−0.478808	+	0.347875i
$855$	2.50845	+	7.72023i	0.0857873	+	0.264026i
$856$	21.4024	−	65.8699i	0.731520	−	2.25139i
$857$	−16.0507	−	11.6615i	−0.548281	−	0.398349i	0.278870	−	0.960329i	$-0.410040\pi$
$857$	−16.0507	−	11.6615i	−0.548281	−	0.398349i	−0.827151	+	0.561979i	$0.810040\pi$
$858$	2.13642	−	6.57521i	0.0729361	−	0.224474i
$859$	4.34949	−	3.16009i	0.148403	−	0.107821i	−0.511106	−	0.859517i	$-0.670764\pi$
$859$	4.34949	−	3.16009i	0.148403	−	0.107821i	0.659509	+	0.751697i	$0.270764\pi$
$860$	−29.6308	+	21.5280i	−1.01040	+	0.734100i
$861$	30.2740	+	21.9953i	1.03173	+	0.749598i
$862$	58.9021			2.00621
$863$	46.6463			1.58786			0.793930	−	0.608010i	$-0.208032\pi$
$863$	46.6463			1.58786			0.793930	+	0.608010i	$0.208032\pi$
$864$	−23.6103	−	17.1539i	−0.803240	−	0.583588i
$865$	−5.04560	−	15.5288i	−0.171556	−	0.527994i
$866$	17.5414	−	53.9868i	0.596080	−	1.83454i
$867$	−52.2815			−1.77557
$868$	−35.0609	+	17.5629i	−1.19005	+	0.596124i
$869$	−6.70365			−0.227406
$870$	16.3215	−	50.2325i	0.553351	−	1.70304i
$871$	−0.958652	−	2.95043i	−0.0324827	−	0.0999714i
$872$	−125.020	−	90.8322i	−4.23370	−	3.07597i
$873$	−20.3457			−0.688597
$874$	−3.05103			−0.103203
$875$	8.72195	+	6.33687i	0.294856	+	0.214225i
$876$	124.941	−	90.7750i	4.22137	−	3.06700i
$877$	1.50235	−	1.09152i	0.0507308	−	0.0368581i	−0.562131	−	0.827048i	$-0.690018\pi$
$877$	1.50235	−	1.09152i	0.0507308	−	0.0368581i	0.612862	+	0.790190i	$0.290018\pi$
$878$	−4.95970	+	15.2644i	−0.167382	+	0.515148i
$879$	−22.7389	−	16.5208i	−0.766963	−	0.557231i
$880$	−3.45295	+	10.6271i	−0.116399	+	0.358239i
$881$	4.82818	+	14.8596i	0.162665	+	0.500633i	0.998857	−	0.0478053i	$-0.0152227\pi$
$881$	4.82818	+	14.8596i	0.162665	+	0.500633i	−0.836191	+	0.548438i	$0.815223\pi$
$882$	−41.2314	+	29.9563i	−1.38833	+	1.00868i
$883$	5.14871	+	15.8461i	0.173268	+	0.533264i	0.999550	−	0.0299926i	$-0.00954837\pi$
$883$	5.14871	+	15.8461i	0.173268	+	0.533264i	−0.826282	+	0.563256i	$0.809548\pi$
$884$	9.87731	+	30.3992i	0.332210	+	1.02244i
$885$	−0.583926	+	0.424247i	−0.0196284	+	0.0142609i
$886$	−26.0338	−	80.1239i	−0.874624	−	2.69181i
$887$	11.1662	−	34.3661i	0.374925	−	1.15390i	−0.568604	−	0.822611i	$-0.692516\pi$
$887$	11.1662	−	34.3661i	0.374925	−	1.15390i	0.943529	−	0.331289i	$-0.107484\pi$
$888$	−52.9939	−	38.5023i	−1.77836	−	1.29205i
$889$	4.81327	−	14.8137i	0.161432	−	0.496836i
$890$	6.91149	−	5.02149i	0.231674	−	0.168321i
$891$	5.34240	−	3.88148i	0.178977	−	0.130035i
$892$	−2.77050	−	2.01288i	−0.0927631	−	0.0673963i
$893$	−22.3574			−0.748162
$894$	15.2506			0.510056
$895$	−17.3493	−	12.6050i	−0.579922	−	0.421338i
$896$	8.93052	+	27.4853i	0.298348	+	0.918219i
$897$	0.352197	−	1.08395i	0.0117595	−	0.0361920i
$898$	28.6790			0.957032
$899$	48.2715	+	7.98484i	1.60994	+	0.266309i
$900$	−81.2104			−2.70701
$901$	−14.2199	+	43.7645i	−0.473735	+	1.45801i
$902$	8.93610	+	27.5025i	0.297540	+	0.915733i
$903$	22.6601	+	16.4636i	0.754082	+	0.547873i
$904$	−184.548			−6.13797
$905$	8.72880			0.290155
$906$	86.9212	+	63.1519i	2.88776	+	2.09808i
$907$	−38.1022	+	27.6829i	−1.26516	+	0.919195i	−0.998999	−	0.0447333i	$-0.985756\pi$
$907$	−38.1022	+	27.6829i	−1.26516	+	0.919195i	−0.266164	+	0.963928i	$0.585756\pi$
$908$	−100.583	+	73.0776i	−3.33796	+	2.42517i
$909$	17.4551	−	53.7214i	0.578950	−	1.78183i
$910$	2.53654	+	1.84290i	0.0840854	+	0.0610916i
$911$	3.91461	−	12.0479i	0.129697	−	0.399165i	−0.865031	−	0.501719i	$-0.832701\pi$
$911$	3.91461	−	12.0479i	0.129697	−	0.399165i	0.994727	+	0.102553i	$0.0327013\pi$
$912$	26.4639	+	81.4476i	0.876308	+	2.69700i
$913$	−1.59667	+	1.16005i	−0.0528421	+	0.0383920i
$914$	21.7088	+	66.8129i	0.718064	+	2.20997i
$915$	3.30030	+	10.1573i	0.109104	+	0.335789i
$916$	−7.44808	+	5.41135i	−0.246092	+	0.178796i
$917$	1.81965	+	5.60032i	0.0600903	+	0.184939i
$918$	8.51192	−	26.1970i	0.280935	−	0.864630i
$919$	−13.9695	−	10.1495i	−0.460812	−	0.334800i	0.333038	−	0.942914i	$-0.391926\pi$
$919$	−13.9695	−	10.1495i	−0.460812	−	0.334800i	−0.793850	+	0.608114i	$0.791926\pi$
$920$	−1.02987	+	3.16963i	−0.0339540	+	0.104500i
$921$	7.27425	−	5.28505i	0.239695	−	0.174148i
$922$	−79.4123	+	57.6964i	−2.61531	+	1.90013i
$923$	−8.58190	−	6.23511i	−0.282477	−	0.205231i
$924$	18.1021			0.595514
$925$	−12.4017			−0.407765
$926$	9.18359	+	6.67227i	0.301792	+	0.219264i
$927$	0.323049	+	0.994244i	0.0106103	+	0.0326553i
$928$	47.2483	−	145.415i	1.55100	−	4.77349i
$929$	−21.4238			−0.702893			−0.351447	−	0.936208i	$-0.614310\pi$
$929$	−21.4238			−0.702893			−0.351447	+	0.936208i	$0.614310\pi$
$930$	5.00846	+	33.0878i	0.164234	+	1.08499i
$931$	13.3207			0.436569
$932$	−14.4090	+	44.3462i	−0.471981	+	1.45261i
$933$	13.6673	+	42.0637i	0.447448	+	1.37710i
$934$	35.8062	+	26.0147i	1.17161	+	0.851227i
$935$	−5.27221			−0.172420
$936$	−31.7699			−1.03843
$937$	18.3850	+	13.3575i	0.600612	+	0.436370i	0.846096	−	0.533030i	$-0.178947\pi$
$937$	18.3850	+	13.3575i	0.600612	+	0.436370i	−0.245484	+	0.969401i	$0.578947\pi$
$938$	9.08179	−	6.59830i	0.296531	−	0.215442i
$939$	−51.5338	+	37.4415i	−1.68174	+	1.22186i
$940$	−12.2117	+	37.5838i	−0.398302	+	1.22585i
$941$	17.4742	+	12.6958i	0.569644	+	0.413870i	0.834976	−	0.550287i	$-0.185482\pi$
$941$	17.4742	+	12.6958i	0.569644	+	0.413870i	−0.265332	+	0.964157i	$0.585482\pi$
$942$	11.2577	−	34.6478i	0.366797	−	1.12889i
$943$	1.47315	+	4.53390i	0.0479724	+	0.147644i
$944$	−3.38142	+	2.45675i	−0.110056	+	0.0799602i
$945$	−0.604149	−	1.85938i	−0.0196530	−	0.0604856i
$946$	6.68869	+	20.5857i	0.217468	+	0.669298i
$947$	18.4996	−	13.4407i	0.601156	−	0.436765i	−0.245133	−	0.969489i	$-0.578832\pi$
$947$	18.4996	−	13.4407i	0.601156	−	0.436765i	0.846289	+	0.532724i	$0.178832\pi$
$948$	28.0628	+	86.3683i	0.911436	+	2.80511i
$949$	3.53466	−	10.8786i	0.114740	−	0.353134i
$950$	23.7322	+	17.2424i	0.769973	+	0.559418i
$951$	−2.68980	+	8.27836i	−0.0872228	+	0.268444i
$952$	−57.8272	+	42.0139i	−1.87419	+	1.36168i
$953$	−10.3791	+	7.54086i	−0.336212	+	0.244272i	−0.743062	−	0.669223i	$-0.766627\pi$
$953$	−10.3791	+	7.54086i	−0.336212	+	0.244272i	0.406850	+	0.913495i	$0.366627\pi$
$954$	−59.8756	−	43.5022i	−1.93854	−	1.40844i
$955$	18.5068			0.598867
$956$	49.2352			1.59238
$957$	−18.2725	−	13.2758i	−0.590667	−	0.429145i
$958$	−18.4846	−	56.8898i	−0.597210	−	1.83802i
$959$	6.33970	−	19.5116i	0.204720	−	0.630062i
$960$	46.7525			1.50893
$961$	−29.6112	+	9.17465i	−0.955201	+	0.295956i
$962$	−7.85061			−0.253114
$963$	−8.97698	+	27.6283i	−0.289279	+	0.890310i
$964$	−6.27037	−	19.2982i	−0.201955	−	0.621553i
$965$	4.87471	+	3.54168i	0.156922	+	0.114011i
$966$	4.12418			0.132693
$967$	11.6770			0.375508			0.187754	−	0.982216i	$-0.439879\pi$
$967$	11.6770			0.375508			0.187754	+	0.982216i	$0.439879\pi$
$968$	−70.4567	−	51.1898i	−2.26456	−	1.64530i
$969$	−32.6899	+	23.7506i	−1.05015	+	0.762980i
$970$	10.5092	−	7.63540i	0.337431	−	0.245158i
$971$	−0.0418491	+	0.128798i	−0.00134300	+	0.00413333i	−0.951726	−	0.306950i	$-0.900692\pi$
$971$	−0.0418491	+	0.128798i	−0.00134300	+	0.00413333i	0.950383	+	0.311083i	$0.100692\pi$
$972$	−93.6857	−	68.0666i	−3.00497	−	2.18324i
$973$	−6.54862	+	20.1546i	−0.209939	+	0.646126i
$974$	16.9121	+	52.0499i	0.541897	+	1.66779i
$975$	−8.86531	+	6.44102i	−0.283917	+	0.206278i
$976$	19.1115	+	58.8191i	0.611744	+	1.88275i
$977$	12.3793	+	38.0996i	0.396050	+	1.21892i	0.928141	+	0.372228i	$0.121406\pi$
$977$	12.3793	+	38.0996i	0.396050	+	1.21892i	−0.532092	+	0.846687i	$0.678594\pi$
$978$	−39.0399	+	28.3641i	−1.24836	+	0.906985i
$979$	−1.12891	−	3.47443i	−0.0360801	−	0.111043i
$980$	7.27583	−	22.3927i	0.232418	−	0.715309i
$981$	52.4380	+	38.0984i	1.67422	+	1.21639i
$982$	−5.85328	+	18.0145i	−0.186786	+	0.574867i
$983$	−42.3375	+	30.7600i	−1.35036	+	0.981093i	−0.351365	+	0.936239i	$0.614282\pi$
$983$	−42.3375	+	30.7600i	−1.35036	+	0.981093i	−0.998994	+	0.0448539i	$0.985718\pi$
$984$	195.859	−	142.300i	6.24375	−	4.53635i
$985$	13.2400	+	9.61945i	0.421863	+	0.306501i
$986$	144.313			4.59585
$987$	30.2213			0.961954
$988$	10.8705	+	7.89787i	0.345836	+	0.251265i
$989$	1.10266	+	3.39363i	0.0350625	+	0.107911i
$990$	2.62031	−	8.06447i	0.0832788	−	0.256306i
$991$	14.1347			0.449002			0.224501	−	0.974474i	$-0.427925\pi$
$991$	14.1347			0.449002			0.224501	+	0.974474i	$0.427925\pi$
$992$	14.4987	+	95.7842i	0.460335	+	3.04115i
$993$	−10.3456			−0.328309
$994$	11.8616	−	36.5062i	0.376227	−	1.15791i
$995$	−6.29092	−	19.3615i	−0.199436	−	0.613800i
$996$	21.6298	+	15.7150i	0.685366	+	0.497947i
$997$	26.4077			0.836339			0.418169	−	0.908369i	$-0.362672\pi$
$997$	26.4077			0.836339			0.418169	+	0.908369i	$0.362672\pi$
$998$	−31.8506			−1.00821
$999$	3.96040	+	2.87740i	0.125302	+	0.0910369i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	403.2.k.e.287.1	yes	68
31.4	even	5	inner	403.2.k.e.66.1	✓	68

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
403.2.k.e.66.1	✓	68	31.4	even	5	inner
403.2.k.e.287.1	yes	68	1.1	even	1	trivial

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 403 = 13 \cdot 31 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	403.k (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.831221 + 2.55823i) q^{2} +(-0.796905 - 2.45262i) q^{3} +(-4.23560 - 3.07735i) q^{4} -0.866460 q^{5} +6.93679 q^{6} +(1.08832 + 0.790714i) q^{7} +(7.04097 - 5.11556i) q^{8} +(-2.95324 + 2.14566i) q^{9} +O(q^{10})\)	\(q+(-0.831221 + 2.55823i) q^{2} +(-0.796905 - 2.45262i) q^{3} +(-4.23560 - 3.07735i) q^{4} -0.866460 q^{5} +6.93679 q^{6} +(1.08832 + 0.790714i) q^{7} +(7.04097 - 5.11556i) q^{8} +(-2.95324 + 2.14566i) q^{9} +(0.720220 - 2.21661i) q^{10} +(-0.806312 - 0.585820i) q^{11} +(-4.17219 + 12.8407i) q^{12} +(0.309017 + 0.951057i) q^{13} +(-2.92747 + 2.12693i) q^{14} +(0.690486 + 2.12510i) q^{15} +(3.99850 + 12.3061i) q^{16} +(-4.93920 + 3.58854i) q^{17} +(-3.03430 - 9.33861i) q^{18} +(-0.793078 + 2.44084i) q^{19} +(3.66998 + 2.66640i) q^{20} +(1.07203 - 3.29937i) q^{21} +(2.16889 - 1.57579i) q^{22} +(0.357550 - 0.259775i) q^{23} +(-18.1575 - 13.1922i) q^{24} -4.24925 q^{25} -2.68989 q^{26} +(1.35697 + 0.985896i) q^{27} +(-2.17641 - 6.69830i) q^{28} +(-2.71553 + 8.35753i) q^{29} -6.01045 q^{30} +(-0.833293 - 5.50505i) q^{31} -17.3993 q^{32} +(-0.794240 + 2.44442i) q^{33} +(-5.07476 - 15.6185i) q^{34} +(-0.942990 - 0.685122i) q^{35} +19.1117 q^{36} +2.91856 q^{37} +(-5.58503 - 4.05776i) q^{38} +(2.08632 - 1.51580i) q^{39} +(-6.10071 + 4.43243i) q^{40} +(-3.33326 + 10.2587i) q^{41} +(7.54948 + 5.48502i) q^{42} +(-2.49495 + 7.67867i) q^{43} +(1.61245 + 4.96260i) q^{44} +(2.55887 - 1.85913i) q^{45} +(0.367363 + 1.13063i) q^{46} +(2.69197 + 8.28503i) q^{47} +(26.9958 - 19.6136i) q^{48} +(-1.60390 - 4.93629i) q^{49} +(3.53206 - 10.8706i) q^{50} +(12.7374 + 9.25426i) q^{51} +(1.61786 - 4.97925i) q^{52} +(6.09781 - 4.43032i) q^{53} +(-3.65009 + 2.65195i) q^{54} +(0.698637 + 0.507589i) q^{55} +11.7078 q^{56} +6.61847 q^{57} +(-19.1233 - 13.8939i) q^{58} +(0.0998181 + 0.307209i) q^{59} +(3.61504 - 11.1259i) q^{60} +4.77967 q^{61} +(14.7759 + 2.44416i) q^{62} -4.91069 q^{63} +(6.46568 - 19.8993i) q^{64} +(-0.267751 - 0.824052i) q^{65} +(-5.59321 - 4.06371i) q^{66} -3.10226 q^{67} +31.9636 q^{68} +(-0.922063 - 0.669918i) q^{69} +(2.53654 - 1.84290i) q^{70} +(-8.58190 + 6.23511i) q^{71} +(-9.81745 + 30.2150i) q^{72} +(-9.25387 - 6.72333i) q^{73} +(-2.42597 + 7.46637i) q^{74} +(3.38625 + 10.4218i) q^{75} +(10.8705 - 7.89787i) q^{76} +(-0.414313 - 1.27512i) q^{77} +(2.14358 + 6.59728i) q^{78} +(5.44156 - 3.95353i) q^{79} +(-3.46454 - 10.6627i) q^{80} +(-2.04746 + 6.30144i) q^{81} +(-23.4735 - 17.0545i) q^{82} +(0.611921 - 1.88330i) q^{83} +(-14.6940 + 10.6758i) q^{84} +(4.27962 - 3.10932i) q^{85} +(-17.5700 - 12.7653i) q^{86} +22.6619 q^{87} -8.67401 q^{88} +(2.96544 + 2.15452i) q^{89} +(2.62910 + 8.09153i) q^{90} +(-0.415703 + 1.27940i) q^{91} -2.31386 q^{92} +(-12.8378 + 6.43076i) q^{93} -23.4327 q^{94} +(0.687170 - 2.11489i) q^{95} +(13.8656 + 42.6739i) q^{96} +(4.50908 + 3.27604i) q^{97} +13.9614 q^{98} +3.63820 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9}+O(q^{10}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9	\( 68 q - 3 q^{2} - 2 q^{3} - 23 q^{4} + 12 q^{5} + 4 q^{6} + 2 q^{7} - 3 q^{8} - 23 q^{9} - 13 q^{10} - 5 q^{11} - 28 q^{12} - 17 q^{13} - 3 q^{14} - 14 q^{15} + 9 q^{16} + 12 q^{17} - 19 q^{18} - 4 q^{19} - 53 q^{20} - 13 q^{21} - 14 q^{22} - 9 q^{23} + 2 q^{24} + 96 q^{25} + 12 q^{26} + 25 q^{27} - 25 q^{28} - 78 q^{30} - 2 q^{31} + 76 q^{32} + 29 q^{33} - 15 q^{34} - 36 q^{35} + 52 q^{36} + 24 q^{37} - 19 q^{38} + 3 q^{39} - 12 q^{40} - 40 q^{41} + 11 q^{42} - 22 q^{43} + 4 q^{44} + 63 q^{45} - 24 q^{46} + 3 q^{47} + 68 q^{48} + 33 q^{49} - 76 q^{50} - 59 q^{51} - 13 q^{52} - q^{53} + 18 q^{54} - 22 q^{55} + 78 q^{56} - 16 q^{57} + 5 q^{58} - 18 q^{59} + 43 q^{60} - 32 q^{61} - 39 q^{62} + 20 q^{63} + 23 q^{64} + 2 q^{65} + 11 q^{66} + 114 q^{67} + 98 q^{68} - 46 q^{69} + 32 q^{70} - 2 q^{71} + 28 q^{72} + 10 q^{73} - 43 q^{74} - 12 q^{75} - 35 q^{76} - 3 q^{77} - 6 q^{78} - 10 q^{79} + 68 q^{80} - 54 q^{81} - 80 q^{82} - 22 q^{83} - 14 q^{84} - 50 q^{85} - 66 q^{86} + 76 q^{87} - 34 q^{88} - 10 q^{89} - 63 q^{90} - 8 q^{91} - 64 q^{92} - 16 q^{93} + 30 q^{94} + 15 q^{95} + 34 q^{96} - 7 q^{97} + 138 q^{98} - 48 q^{99}+O(q^{100}) \) 68 * q - 3 * q^2 - 2 * q^3 - 23 * q^4 + 12 * q^5 + 4 * q^6 + 2 * q^7 - 3 * q^8 - 23 * q^9 - 13 * q^10 - 5 * q^11 - 28 * q^12 - 17 * q^13 - 3 * q^14 - 14 * q^15 + 9 * q^16 + 12 * q^17 - 19 * q^18 - 4 * q^19 - 53 * q^20 - 13 * q^21 - 14 * q^22 - 9 * q^23 + 2 * q^24 + 96 * q^25 + 12 * q^26 + 25 * q^27 - 25 * q^28 - 78 * q^30 - 2 * q^31 + 76 * q^32 + 29 * q^33 - 15 * q^34 - 36 * q^35 + 52 * q^36 + 24 * q^37 - 19 * q^38 + 3 * q^39 - 12 * q^40 - 40 * q^41 + 11 * q^42 - 22 * q^43 + 4 * q^44 + 63 * q^45 - 24 * q^46 + 3 * q^47 + 68 * q^48 + 33 * q^49 - 76 * q^50 - 59 * q^51 - 13 * q^52 - q^53 + 18 * q^54 - 22 * q^55 + 78 * q^56 - 16 * q^57 + 5 * q^58 - 18 * q^59 + 43 * q^60 - 32 * q^61 - 39 * q^62 + 20 * q^63 + 23 * q^64 + 2 * q^65 + 11 * q^66 + 114 * q^67 + 98 * q^68 - 46 * q^69 + 32 * q^70 - 2 * q^71 + 28 * q^72 + 10 * q^73 - 43 * q^74 - 12 * q^75 - 35 * q^76 - 3 * q^77 - 6 * q^78 - 10 * q^79 + 68 * q^80 - 54 * q^81 - 80 * q^82 - 22 * q^83 - 14 * q^84 - 50 * q^85 - 66 * q^86 + 76 * q^87 - 34 * q^88 - 10 * q^89 - 63 * q^90 - 8 * q^91 - 64 * q^92 - 16 * q^93 + 30 * q^94 + 15 * q^95 + 34 * q^96 - 7 * q^97 + 138 * q^98 - 48 * q^99

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