LMFDB - Embedded newform 625.2.d.p.251.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [625,2,Mod(126,625)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(625, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("625.126");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 625 = 5^{4} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	625.d (of order $5$, degree $4$, not 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:	$4.99065012633$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 25x^{14} + 239x^{12} + 1165x^{10} + 3166x^{8} + 4820x^{6} + 3809x^{4} + 1205x^{2} + 1 $ x^16 + 25x^14 + 239x^12 + 1165x^10 + 3166x^8 + 4820x^6 + 3809x^4 + 1205*x^2 + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			251.2
Root			$-2.04679i$ of defining polynomial
Character	$\chi$	$=$	625.251
Dual form			625.2.d.p.376.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.264347 + 0.192059i) q^{2} +(0.530081 - 1.63142i) q^{3} +(-0.585041 + 1.80057i) q^{4} +(0.173205 + 0.533069i) q^{6} -3.42409 q^{7} +(-0.393106 - 1.20986i) q^{8} +(0.0465016 + 0.0337854i) q^{9} +O(q^{10})$	\(q+(-0.264347 + 0.192059i) q^{2} +(0.530081 - 1.63142i) q^{3} +(-0.585041 + 1.80057i) q^{4} +(0.173205 + 0.533069i) q^{6} -3.42409 q^{7} +(-0.393106 - 1.20986i) q^{8} +(0.0465016 + 0.0337854i) q^{9} +(4.32105 - 3.13943i) q^{11} +(2.62737 + 1.90890i) q^{12} +(-2.84866 - 2.06967i) q^{13} +(0.905150 - 0.657630i) q^{14} +(-2.72704 - 1.98131i) q^{16} +(-0.790426 - 2.43268i) q^{17} -0.0187814 q^{18} +(-0.626004 - 1.92664i) q^{19} +(-1.81505 + 5.58614i) q^{21} +(-0.539301 + 1.65980i) q^{22} +(6.12492 - 4.45002i) q^{23} -2.18216 q^{24} +1.15054 q^{26} +(4.24308 - 3.08278i) q^{27} +(2.00324 - 6.16533i) q^{28} +(1.46557 - 4.51057i) q^{29} +(0.501908 + 1.54471i) q^{31} +3.64565 q^{32} +(-2.83122 - 8.71361i) q^{33} +(0.676166 + 0.491264i) q^{34} +(-0.0880383 + 0.0639636i) q^{36} +(-0.0108643 - 0.00789335i) q^{37} +(0.535512 + 0.389072i) q^{38} +(-4.88653 + 3.55027i) q^{39} +(-7.82918 - 5.68823i) q^{41} +(-0.593069 - 1.82528i) q^{42} -2.32645 q^{43} +(3.12477 + 9.61706i) q^{44} +(-0.764438 + 2.35270i) q^{46} +(-2.14658 + 6.60649i) q^{47} +(-4.67790 + 3.39869i) q^{48} +4.72443 q^{49} -4.38772 q^{51} +(5.39318 - 3.91837i) q^{52} +(-0.532270 + 1.63816i) q^{53} +(-0.529569 + 1.62985i) q^{54} +(1.34603 + 4.14266i) q^{56} -3.47500 q^{57} +(0.478878 + 1.47384i) q^{58} +(0.0179464 + 0.0130388i) q^{59} +(-3.16947 + 2.30275i) q^{61} +(-0.429355 - 0.311944i) q^{62} +(-0.159226 - 0.115684i) q^{63} +(4.49035 - 3.26243i) q^{64} +(2.42196 + 1.75965i) q^{66} +(-1.27263 - 3.91676i) q^{67} +4.84265 q^{68} +(-4.01315 - 12.3512i) q^{69} +(0.722772 - 2.22446i) q^{71} +(0.0225954 - 0.0695415i) q^{72} +(1.22463 - 0.889748i) q^{73} +0.00438793 q^{74} +3.83530 q^{76} +(-14.7957 + 10.7497i) q^{77} +(0.609877 - 1.87701i) q^{78} +(0.131898 - 0.405940i) q^{79} +(-2.72685 - 8.39237i) q^{81} +3.16210 q^{82} +(1.86704 + 5.74616i) q^{83} +(-8.99637 - 6.53625i) q^{84} +(0.614990 - 0.446817i) q^{86} +(-6.58177 - 4.78194i) q^{87} +(-5.49689 - 3.99372i) q^{88} +(4.92984 - 3.58174i) q^{89} +(9.75408 + 7.08676i) q^{91} +(4.42924 + 13.6318i) q^{92} +2.78613 q^{93} +(-0.701397 - 2.15868i) q^{94} +(1.93249 - 5.94759i) q^{96} +(4.94484 - 15.2186i) q^{97} +(-1.24889 + 0.907371i) q^{98} +0.307002 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) $ 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9	$ 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9} + 2 q^{11} + 25 q^{12} + 5 q^{13} + 9 q^{14} - 14 q^{16} - 10 q^{17} + 10 q^{18} + 7 q^{21} - 40 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} + 20 q^{27} + 30 q^{28} - 10 q^{29} + 17 q^{31} - 60 q^{32} + 5 q^{33} - q^{34} - 4 q^{36} - 15 q^{37} - 15 q^{38} - 9 q^{39} + 12 q^{41} - 45 q^{42} + 49 q^{44} - 33 q^{46} + 25 q^{47} - 20 q^{48} - 8 q^{49} - 28 q^{51} + 20 q^{52} - 30 q^{54} - 35 q^{56} + 20 q^{57} + 5 q^{58} + 20 q^{59} - 23 q^{61} + 15 q^{62} + 10 q^{63} - 28 q^{64} - 26 q^{66} - 80 q^{68} + 6 q^{69} + 22 q^{71} + 5 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 40 q^{77} - 25 q^{78} + 75 q^{79} + 11 q^{81} + 90 q^{82} + 25 q^{83} - 31 q^{84} + 17 q^{86} - 20 q^{87} + 5 q^{89} + 22 q^{91} + 60 q^{92} + 80 q^{93} - 51 q^{94} - 28 q^{96} + 40 q^{97} + 15 q^{98} - 44 q^{99}+O(q^{100}) $ 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9 + 2 * q^11 + 25 * q^12 + 5 * q^13 + 9 * q^14 - 14 * q^16 - 10 * q^17 + 10 * q^18 + 7 * q^21 - 40 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 + 20 * q^27 + 30 * q^28 - 10 * q^29 + 17 * q^31 - 60 * q^32 + 5 * q^33 - q^34 - 4 * q^36 - 15 * q^37 - 15 * q^38 - 9 * q^39 + 12 * q^41 - 45 * q^42 + 49 * q^44 - 33 * q^46 + 25 * q^47 - 20 * q^48 - 8 * q^49 - 28 * q^51 + 20 * q^52 - 30 * q^54 - 35 * q^56 + 20 * q^57 + 5 * q^58 + 20 * q^59 - 23 * q^61 + 15 * q^62 + 10 * q^63 - 28 * q^64 - 26 * q^66 - 80 * q^68 + 6 * q^69 + 22 * q^71 + 5 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 40 * q^77 - 25 * q^78 + 75 * q^79 + 11 * q^81 + 90 * q^82 + 25 * q^83 - 31 * q^84 + 17 * q^86 - 20 * q^87 + 5 * q^89 + 22 * q^91 + 60 * q^92 + 80 * q^93 - 51 * q^94 - 28 * q^96 + 40 * q^97 + 15 * q^98 - 44 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/625\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−0.264347	+	0.192059i	−0.186922	+	0.135807i	−0.677311	−	0.735697i	$-0.736855\pi$
$2$	−0.264347	+	0.192059i	−0.186922	+	0.135807i	0.490389	+	0.871504i	$0.336855\pi$
$3$	0.530081	−	1.63142i	0.306042	−	0.941901i	−0.673244	−	0.739421i	$-0.735100\pi$
$3$	0.530081	−	1.63142i	0.306042	−	0.941901i	0.979286	−	0.202481i	$-0.0649004\pi$
$4$	−0.585041	+	1.80057i	−0.292521	+	0.900286i
$5$		0			0
$5$		0			0
$6$	0.173205	+	0.533069i	0.0707104	+	0.217624i
$7$	−3.42409			−1.29419			−0.647093	−	0.762411i	$-0.724016\pi$
$7$	−3.42409			−1.29419			−0.647093	+	0.762411i	$0.724016\pi$
$8$	−0.393106	−	1.20986i	−0.138984	−	0.427749i
$9$	0.0465016	+	0.0337854i	0.0155005	+	0.0112618i
$10$		0			0
$11$	4.32105	−	3.13943i	1.30285	−	0.946573i	0.302867	−	0.953033i	$-0.402056\pi$
$11$	4.32105	−	3.13943i	1.30285	−	0.946573i	0.999979	+	0.00645946i	$0.00205613\pi$
$12$	2.62737	+	1.90890i	0.758457	+	0.551051i
$13$	−2.84866	−	2.06967i	−0.790076	−	0.574024i	0.117910	−	0.993024i	$-0.462381\pi$
$13$	−2.84866	−	2.06967i	−0.790076	−	0.574024i	−0.907986	+	0.419000i	$0.862381\pi$
$14$	0.905150	−	0.657630i	0.241911	−	0.175759i
$15$		0			0
$16$	−2.72704	−	1.98131i	−0.681759	−	0.495327i
$17$	−0.790426	−	2.43268i	−0.191706	−	0.590012i	−0.999999	−	0.00123106i	$-0.999608\pi$
$17$	−0.790426	−	2.43268i	−0.191706	−	0.590012i	0.808293	−	0.588781i	$-0.200392\pi$
$18$	−0.0187814			−0.00442681
$19$	−0.626004	−	1.92664i	−0.143615	−	0.442002i	0.853215	−	0.521559i	$-0.174649\pi$
$19$	−0.626004	−	1.92664i	−0.143615	−	0.442002i	−0.996830	+	0.0795572i	$0.974649\pi$
$20$		0			0
$21$	−1.81505	+	5.58614i	−0.396076	+	1.21900i
$22$	−0.539301	+	1.65980i	−0.114979	+	0.353870i
$23$	6.12492	−	4.45002i	1.27714	−	0.927893i	0.277673	−	0.960676i	$-0.410437\pi$
$23$	6.12492	−	4.45002i	1.27714	−	0.927893i	0.999462	+	0.0327828i	$0.0104370\pi$
$24$	−2.18216			−0.445432
$25$		0			0
$26$	1.15054			0.225639
$27$	4.24308	−	3.08278i	0.816581	−	0.593281i
$28$	2.00324	−	6.16533i	0.378576	−	1.16514i
$29$	1.46557	−	4.51057i	0.272150	−	0.837593i	−0.717809	−	0.696240i	$-0.754855\pi$
$29$	1.46557	−	4.51057i	0.272150	−	0.837593i	0.989959	−	0.141352i	$-0.0451451\pi$
$30$		0			0
$31$	0.501908	+	1.54471i	0.0901453	+	0.277439i	0.985958	−	0.166993i	$-0.0534057\pi$
$31$	0.501908	+	1.54471i	0.0901453	+	0.277439i	−0.895813	+	0.444432i	$0.853406\pi$
$32$	3.64565			0.644466
$33$	−2.83122	−	8.71361i	−0.492853	−	1.51684i
$34$	0.676166	+	0.491264i	0.115962	+	0.0842510i
$35$		0			0
$36$	−0.0880383	+	0.0639636i	−0.0146731	+	0.0106606i
$37$	−0.0108643	−	0.00789335i	−0.00178607	−	0.00129766i	0.586892	−	0.809665i	$-0.300351\pi$
$37$	−0.0108643	−	0.00789335i	−0.00178607	−	0.00129766i	−0.588678	+	0.808368i	$0.700351\pi$
$38$	0.535512	+	0.389072i	0.0868715	+	0.0631159i
$39$	−4.88653	+	3.55027i	−0.782471	+	0.568498i
$40$		0			0
$41$	−7.82918	−	5.68823i	−1.22271	−	0.888353i	−0.226390	−	0.974037i	$-0.572693\pi$
$41$	−7.82918	−	5.68823i	−1.22271	−	0.888353i	−0.996322	+	0.0856838i	$0.972693\pi$
$42$	−0.593069	−	1.82528i	−0.0915125	−	0.281646i
$43$	−2.32645			−0.354780			−0.177390	−	0.984141i	$-0.556765\pi$
$43$	−2.32645			−0.354780			−0.177390	+	0.984141i	$0.556765\pi$
$44$	3.12477	+	9.61706i	0.471077	+	1.44983i
$45$		0			0
$46$	−0.764438	+	2.35270i	−0.112710	+	0.346887i
$47$	−2.14658	+	6.60649i	−0.313111	+	0.963656i	0.663414	+	0.748252i	$0.269107\pi$
$47$	−2.14658	+	6.60649i	−0.313111	+	0.963656i	−0.976525	+	0.215403i	$0.930893\pi$
$48$	−4.67790	+	3.39869i	−0.675196	+	0.490559i
$49$	4.72443			0.674918
$50$		0			0
$51$	−4.38772			−0.614403
$52$	5.39318	−	3.91837i	0.747899	−	0.543381i
$53$	−0.532270	+	1.63816i	−0.0731129	+	0.225018i	−0.980935	−	0.194338i	$-0.937744\pi$
$53$	−0.532270	+	1.63816i	−0.0731129	+	0.225018i	0.907822	+	0.419356i	$0.137744\pi$
$54$	−0.529569	+	1.62985i	−0.0720652	+	0.221794i
$55$		0			0
$56$	1.34603	+	4.14266i	0.179871	+	0.553587i
$57$	−3.47500			−0.460275
$58$	0.478878	+	1.47384i	0.0628798	+	0.193524i
$59$	0.0179464	+	0.0130388i	0.00233642	+	0.00169751i	0.588953	−	0.808167i	$-0.299540\pi$
$59$	0.0179464	+	0.0130388i	0.00233642	+	0.00169751i	−0.586616	+	0.809865i	$0.699540\pi$
$60$		0			0
$61$	−3.16947	+	2.30275i	−0.405809	+	0.294837i	−0.771903	−	0.635740i	$-0.780695\pi$
$61$	−3.16947	+	2.30275i	−0.405809	+	0.294837i	0.366094	+	0.930578i	$0.380695\pi$
$62$	−0.429355	−	0.311944i	−0.0545281	−	0.0396170i
$63$	−0.159226	−	0.115684i	−0.0200606	−	0.0145749i
$64$	4.49035	−	3.26243i	0.561294	−	0.407804i
$65$		0			0
$66$	2.42196	+	1.75965i	0.298122	+	0.216599i
$67$	−1.27263	−	3.91676i	−0.155477	−	0.478508i	0.842732	−	0.538333i	$-0.180946\pi$
$67$	−1.27263	−	3.91676i	−0.155477	−	0.478508i	−0.998209	+	0.0598251i	$0.980946\pi$
$68$	4.84265			0.587258
$69$	−4.01315	−	12.3512i	−0.483126	−	1.48691i
$70$		0			0
$71$	0.722772	−	2.22446i	0.0857772	−	0.263995i	−0.898963	−	0.438024i	$-0.855679\pi$
$71$	0.722772	−	2.22446i	0.0857772	−	0.263995i	0.984741	+	0.174029i	$0.0556785\pi$
$72$	0.0225954	−	0.0695415i	0.00266289	−	0.00819554i
$73$	1.22463	−	0.889748i	0.143332	−	0.104137i	−0.513808	−	0.857905i	$-0.671766\pi$
$73$	1.22463	−	0.889748i	0.143332	−	0.104137i	0.657141	+	0.753768i	$0.271766\pi$
$74$	0.00438793			0.000510086
$75$		0			0
$76$	3.83530			0.439939
$77$	−14.7957	+	10.7497i	−1.68613	+	1.22504i
$78$	0.609877	−	1.87701i	0.0690550	−	0.212529i
$79$	0.131898	−	0.405940i	0.0148397	−	0.0456719i	−0.943362	−	0.331764i	$-0.892356\pi$
$79$	0.131898	−	0.405940i	0.0148397	−	0.0456719i	0.958202	+	0.286092i	$0.0923563\pi$
$80$		0			0
$81$	−2.72685	−	8.39237i	−0.302983	−	0.932485i
$82$	3.16210			0.349196
$83$	1.86704	+	5.74616i	0.204934	+	0.630723i	0.999716	+	0.0238275i	$0.00758524\pi$
$83$	1.86704	+	5.74616i	0.204934	+	0.630723i	−0.794782	+	0.606895i	$0.792415\pi$
$84$	−8.99637	−	6.53625i	−0.981585	−	0.713163i
$85$		0			0
$86$	0.614990	−	0.446817i	0.0663161	−	0.0481815i
$87$	−6.58177	−	4.78194i	−0.705640	−	0.512678i
$88$	−5.49689	−	3.99372i	−0.585970	−	0.425732i
$89$	4.92984	−	3.58174i	0.522562	−	0.379663i	−0.295006	−	0.955495i	$-0.595322\pi$
$89$	4.92984	−	3.58174i	0.522562	−	0.379663i	0.817568	+	0.575832i	$0.195322\pi$
$90$		0			0
$91$	9.75408	+	7.08676i	1.02251	+	0.742894i
$92$	4.42924	+	13.6318i	0.461781	+	1.42121i
$93$	2.78613			0.288908
$94$	−0.701397	−	2.15868i	−0.0723436	−	0.222651i
$95$		0			0
$96$	1.93249	−	5.94759i	0.197234	−	0.607023i
$97$	4.94484	−	15.2186i	0.502072	−	1.54522i	−0.303565	−	0.952811i	$-0.598177\pi$
$97$	4.94484	−	15.2186i	0.502072	−	1.54522i	0.805638	−	0.592409i	$-0.201823\pi$
$98$	−1.24889	+	0.907371i	−0.126157	+	0.0916583i
$99$	0.307002			0.0308549
$100$		0			0
$101$	1.44418			0.143701			0.0718505	−	0.997415i	$-0.477110\pi$
$101$	1.44418			0.143701			0.0718505	+	0.997415i	$0.477110\pi$
$102$	1.15988	−	0.842703i	0.114845	−	0.0834400i
$103$	−4.53196	+	13.9479i	−0.446547	+	1.37433i	0.434231	+	0.900802i	$0.357020\pi$
$103$	−4.53196	+	13.9479i	−0.446547	+	1.37433i	−0.880778	+	0.473530i	$0.842980\pi$
$104$	−1.38418	+	4.26007i	−0.135730	+	0.417734i
$105$		0			0
$106$	−0.173920	−	0.535270i	−0.0168926	−	0.0519900i
$107$	−12.2169			−1.18106			−0.590528	−	0.807017i	$-0.701081\pi$
$107$	−12.2169			−1.18106			−0.590528	+	0.807017i	$0.701081\pi$
$108$	3.06839	+	9.44352i	0.295255	+	0.908703i
$109$	12.4197	+	9.02343i	1.18959	+	0.864287i	0.993221	−	0.116243i	$-0.0370850\pi$
$109$	12.4197	+	9.02343i	1.18959	+	0.864287i	0.196369	+	0.980530i	$0.437085\pi$
$110$		0			0
$111$	−0.0186363	+	0.0135401i	−0.00176888	+	0.00128517i
$112$	9.33763	+	6.78418i	0.882323	+	0.641045i
$113$	15.0108	+	10.9060i	1.41210	+	1.02595i	0.993013	+	0.118007i	$0.0376505\pi$
$113$	15.0108	+	10.9060i	1.41210	+	1.02595i	0.419089	+	0.907945i	$0.362350\pi$
$114$	0.918606	−	0.667406i	0.0860353	−	0.0625083i
$115$		0			0
$116$	7.26419	+	5.27774i	0.674463	+	0.490026i
$117$	−0.0625425	−	0.192486i	−0.00578206	−	0.0177953i
$118$	−0.00724831			−0.000667261
$119$	2.70649	+	8.32973i	0.248104	+	0.763585i
$120$		0			0
$121$	5.41630	−	16.6696i	0.492391	−	1.51542i
$122$	0.395575	−	1.21745i	0.0358136	−	0.110223i
$123$	−13.4300	+	9.75747i	−1.21094	+	0.879801i
$124$	−3.07500			−0.276144
$125$		0			0
$126$	0.0643092			0.00572911
$127$	0.548435	−	0.398461i	0.0486657	−	0.0353577i	−0.563186	−	0.826330i	$-0.690425\pi$
$127$	0.548435	−	0.398461i	0.0486657	−	0.0353577i	0.611852	+	0.790972i	$0.290425\pi$
$128$	−2.81357	+	8.65927i	−0.248687	+	0.765378i
$129$	−1.23321	+	3.79542i	−0.108578	+	0.334168i
$130$		0			0
$131$	2.17875	+	6.70550i	0.190358	+	0.585863i	0.999999	−	0.00106268i	$-0.000338260\pi$
$131$	2.17875	+	6.70550i	0.190358	+	0.585863i	−0.809641	+	0.586925i	$0.800338\pi$
$132$	17.3459			1.50976
$133$	2.14350	+	6.59700i	0.185865	+	0.572033i
$134$	1.08867	+	0.790962i	0.0940465	+	0.0683288i
$135$		0			0
$136$	−2.63247	+	1.91260i	−0.225733	+	0.164004i
$137$	−8.83331	−	6.41778i	−0.754681	−	0.548308i	0.142593	−	0.989781i	$-0.454456\pi$
$137$	−8.83331	−	6.41778i	−0.754681	−	0.548308i	−0.897274	+	0.441474i	$0.854456\pi$
$138$	3.43303	+	2.49424i	0.292239	+	0.212324i
$139$	−15.7841	+	11.4678i	−1.33879	+	0.972686i	−0.339300	+	0.940678i	$0.610190\pi$
$139$	−15.7841	+	11.4678i	−1.33879	+	0.972686i	−0.999488	+	0.0320076i	$0.989810\pi$
$140$		0			0
$141$	9.64011	+	7.00395i	0.811843	+	0.589839i
$142$	0.236166	+	0.726846i	0.0198186	+	0.0609955i
$143$	−18.8068			−1.57270
$144$	−0.0598722	−	0.184268i	−0.00498935	−	0.0153556i
$145$		0			0
$146$	−0.152844	+	0.470405i	−0.0126494	+	0.0389310i
$147$	2.50433	−	7.70753i	0.206553	−	0.635706i
$148$	0.0205686	−	0.0149440i	0.00169073	−	0.00122839i
$149$	−12.7945			−1.04817			−0.524085	−	0.851666i	$-0.675593\pi$
$149$	−12.7945			−1.04817			−0.524085	+	0.851666i	$0.675593\pi$
$150$		0			0
$151$	2.15617			0.175466			0.0877331	−	0.996144i	$-0.472038\pi$
$151$	2.15617			0.175466			0.0877331	+	0.996144i	$0.472038\pi$
$152$	−2.08487	+	1.51475i	−0.169106	+	0.122862i
$153$	0.0454330	−	0.139828i	0.00367304	−	0.0113044i
$154$	1.84662	−	5.68331i	0.148805	−	0.457974i
$155$		0			0
$156$	−3.53370	−	10.8756i	−0.282922	−	0.870745i
$157$	15.7474			1.25678			0.628389	−	0.777899i	$-0.283715\pi$
$157$	15.7474			1.25678			0.628389	+	0.777899i	$0.283715\pi$
$158$	0.0430978	+	0.132641i	0.00342868	+	0.0105524i
$159$	2.39038	+	1.73671i	0.189569	+	0.137730i
$160$		0			0
$161$	−20.9723	+	15.2373i	−1.65285	+	1.20087i
$162$	2.33267	+	1.69478i	0.183272	+	0.133155i
$163$	5.98040	+	4.34502i	0.468421	+	0.340328i	0.796826	−	0.604209i	$-0.206511\pi$
$163$	5.98040	+	4.34502i	0.468421	+	0.340328i	−0.328404	+	0.944537i	$0.606511\pi$
$164$	14.8225	−	10.7692i	1.15744	−	0.840930i
$165$		0			0
$166$	−1.59715	−	1.16040i	−0.123963	−	0.0900643i
$167$	3.34249	+	10.2871i	0.258649	+	0.796041i	0.993089	+	0.117367i	$0.0374453\pi$
$167$	3.34249	+	10.2871i	0.258649	+	0.796041i	−0.734439	+	0.678675i	$0.762555\pi$
$168$	7.47194			0.576472
$169$	−0.185902	−	0.572147i	−0.0143001	−	0.0440113i
$170$		0			0
$171$	0.0359821	−	0.110742i	0.00275162	−	0.00846862i
$172$	1.36107	−	4.18894i	0.103781	−	0.319404i
$173$	12.1339	−	8.81577i	0.922521	−	0.670251i	−0.0216293	−	0.999766i	$-0.506885\pi$
$173$	12.1339	−	8.81577i	0.922521	−	0.670251i	0.944150	+	0.329515i	$0.106885\pi$
$174$	2.65829			0.201524
$175$		0			0
$176$	−18.0038			−1.35709
$177$	0.0307849	−	0.0223665i	0.00231393	−	0.00168117i
$178$	−0.615282	+	1.89364i	−0.0461174	+	0.141935i
$179$	2.28624	−	7.03631i	0.170881	−	0.525919i	−0.828540	−	0.559930i	$-0.810828\pi$
$179$	2.28624	−	7.03631i	0.170881	−	0.525919i	0.999421	+	0.0340111i	$0.0108282\pi$
$180$		0			0
$181$	−3.37374	−	10.3833i	−0.250768	−	0.771785i	−0.994634	−	0.103456i	$-0.967010\pi$
$181$	−3.37374	−	10.3833i	−0.250768	−	0.771785i	0.743866	−	0.668329i	$-0.232990\pi$
$182$	−3.93954			−0.292018
$183$	2.07669	+	6.39139i	0.153513	+	0.472465i
$184$	−7.79163	−	5.66095i	−0.574407	−	0.417331i
$185$		0			0
$186$	−0.736505	+	0.535102i	−0.0540032	+	0.0392356i
$187$	−11.0527	−	8.03026i	−0.808253	−	0.587231i
$188$	−10.6396	−	7.73014i	−0.775974	−	0.563778i
$189$	−14.5287	+	10.5557i	−1.05681	+	0.767815i
$190$		0			0
$191$	1.41693	+	1.02946i	0.102525	+	0.0744891i	0.637867	−	0.770147i	$-0.279817\pi$
$191$	1.41693	+	1.02946i	0.102525	+	0.0744891i	−0.535341	+	0.844636i	$0.679817\pi$
$192$	−2.94215	−	9.05501i	−0.212332	−	0.653489i
$193$	9.53146			0.686089			0.343045	−	0.939319i	$-0.388542\pi$
$193$	9.53146			0.686089			0.343045	+	0.939319i	$0.388542\pi$
$194$	1.61573	+	4.97271i	0.116003	+	0.357020i
$195$		0			0
$196$	−2.76398	+	8.50667i	−0.197427	+	0.607619i
$197$	−7.39073	+	22.7463i	−0.526567	+	1.62061i	0.234628	+	0.972085i	$0.424613\pi$
$197$	−7.39073	+	22.7463i	−0.526567	+	1.62061i	−0.761195	+	0.648523i	$0.775387\pi$
$198$	−0.0811552	+	0.0589627i	−0.00576745	+	0.00419030i
$199$	23.8281			1.68913			0.844566	−	0.535451i	$-0.179858\pi$
$199$	23.8281			1.68913			0.844566	+	0.535451i	$0.179858\pi$
$200$		0			0
$201$	−7.06448			−0.498290
$202$	−0.381764	+	0.277368i	−0.0268608	+	0.0195155i
$203$	−5.01827	+	15.4446i	−0.352213	+	1.08400i
$204$	2.56700	−	7.90040i	0.179726	−	0.553139i
$205$		0			0
$206$	−1.48082	−	4.55750i	−0.103174	−	0.317536i
$207$	0.435164			0.0302460
$208$	3.66774	+	11.2881i	0.254312	+	0.782692i
$209$	−8.75355	−	6.35982i	−0.605496	−	0.439918i
$210$		0			0
$211$	12.4527	−	9.04738i	0.857276	−	0.622847i	−0.0698666	−	0.997556i	$-0.522257\pi$
$211$	12.4527	−	9.04738i	0.857276	−	0.622847i	0.927142	+	0.374709i	$0.122257\pi$
$212$	−2.63822	−	1.91678i	−0.181194	−	0.131645i
$213$	−3.24591	−	2.35829i	−0.222406	−	0.161587i
$214$	3.22951	−	2.34638i	0.220765	−	0.160395i
$215$		0			0
$216$	−5.39770	−	3.92166i	−0.367267	−	0.266835i
$217$	−1.71858	−	5.28924i	−0.116665	−	0.359057i
$218$	−5.01614			−0.339736
$219$	−0.802399	−	2.46953i	−0.0542211	−	0.166875i
$220$		0			0
$221$	−2.78320	+	8.56580i	−0.187218	+	0.576198i
$222$	0.00232596	−	0.00715856i	0.000156108	−	0.000480451i
$223$	−15.8367	+	11.5061i	−1.06051	+	0.770503i	−0.974182	−	0.225764i	$-0.927512\pi$
$223$	−15.8367	+	11.5061i	−1.06051	+	0.770503i	−0.0863242	+	0.996267i	$0.527512\pi$
$224$	−12.4831			−0.834059
$225$		0			0
$226$	−6.06268			−0.403283
$227$	1.08575	−	0.788847i	0.0720640	−	0.0523576i	−0.551170	−	0.834393i	$-0.685818\pi$
$227$	1.08575	−	0.788847i	0.0720640	−	0.0523576i	0.623234	+	0.782035i	$0.285818\pi$
$228$	2.03302	−	6.25698i	0.134640	−	0.414379i
$229$	−6.91278	+	21.2753i	−0.456809	+	1.40591i	0.412189	+	0.911098i	$0.364764\pi$
$229$	−6.91278	+	21.2753i	−0.456809	+	1.40591i	−0.868998	+	0.494815i	$0.835236\pi$
$230$		0			0
$231$	9.69438	+	29.8362i	0.637843	+	1.96308i
$232$	−6.03327			−0.396104
$233$	−5.67512	−	17.4662i	−0.371789	−	1.14425i	−0.945619	−	0.325276i	$-0.894543\pi$
$233$	−5.67512	−	17.4662i	−0.371789	−	1.14425i	0.573830	−	0.818975i	$-0.305457\pi$
$234$	0.0535017	+	0.0388713i	0.00349752	+	0.00254109i
$235$		0			0
$236$	−0.0339768	+	0.0246856i	−0.00221170	+	0.00160689i
$237$	−0.592343	−	0.430362i	−0.0384768	−	0.0279550i
$238$	−2.31526	−	1.68213i	−0.150076	−	0.109037i
$239$	9.71123	−	7.05562i	0.628168	−	0.456390i	−0.227597	−	0.973755i	$-0.573087\pi$
$239$	9.71123	−	7.05562i	0.628168	−	0.456390i	0.855765	+	0.517365i	$0.173087\pi$
$240$		0			0
$241$	−8.18481	−	5.94661i	−0.527230	−	0.383055i	0.292091	−	0.956391i	$-0.405649\pi$
$241$	−8.18481	−	5.94661i	−0.527230	−	0.383055i	−0.819321	+	0.573336i	$0.805649\pi$
$242$	1.76978	+	5.44683i	0.113766	+	0.350135i
$243$	0.597258			0.0383141
$244$	−2.29200	−	7.05406i	−0.146731	−	0.451590i
$245$		0			0
$246$	1.67617	−	5.15872i	0.106869	−	0.328908i
$247$	−2.20425	+	6.78397i	−0.140253	+	0.431654i
$248$	1.67158	−	1.21447i	0.106145	−	0.0771191i
$249$	10.3641			0.656797
$250$		0			0
$251$	16.7258			1.05573			0.527863	−	0.849330i	$-0.322994\pi$
$251$	16.7258			1.05573			0.527863	+	0.849330i	$0.322994\pi$
$252$	0.301452	−	0.219017i	0.0189897	−	0.0137968i
$253$	12.4956	−	38.4575i	0.785592	−	2.41780i
$254$	−0.0684489	+	0.210664i	−0.00429487	+	0.0132182i
$255$		0			0
$256$	2.51099	+	7.72803i	0.156937	+	0.483002i
$257$	−15.0170			−0.936732			−0.468366	−	0.883535i	$-0.655157\pi$
$257$	−15.0170			−0.936732			−0.468366	+	0.883535i	$0.655157\pi$
$258$	−0.402952	−	1.24016i	−0.0250867	−	0.0772088i
$259$	0.0372003	+	0.0270276i	0.00231151	+	0.00167941i
$260$		0			0
$261$	0.220543	−	0.160234i	0.0136513	−	0.00991822i
$262$	−1.86380	−	1.35413i	−0.115146	−	0.0836585i
$263$	4.99311	+	3.62771i	0.307888	+	0.223694i	0.730990	−	0.682388i	$-0.239059\pi$
$263$	4.99311	+	3.62771i	0.307888	+	0.223694i	−0.423102	+	0.906082i	$0.639059\pi$
$264$	−9.42924	+	6.85075i	−0.580330	+	0.421634i
$265$		0			0
$266$	−1.83364	−	1.33222i	−0.112428	−	0.0816837i
$267$	−3.23011	−	9.94126i	−0.197679	−	0.608395i
$268$	7.79694			0.476274
$269$	3.43171	+	10.5617i	0.209235	+	0.643959i	0.999513	+	0.0312102i	$0.00993614\pi$
$269$	3.43171	+	10.5617i	0.209235	+	0.643959i	−0.790278	+	0.612749i	$0.790064\pi$
$270$		0			0
$271$	−0.358920	+	1.10464i	−0.0218028	+	0.0671022i	−0.961366	−	0.275274i	$-0.911232\pi$
$271$	−0.358920	+	1.10464i	−0.0218028	+	0.0671022i	0.939563	+	0.342376i	$0.111232\pi$
$272$	−2.66437	+	8.20008i	−0.161551	+	0.497203i
$273$	16.7319	−	12.1565i	1.01266	−	0.735743i
$274$	3.56766			0.215530
$275$		0			0
$276$	24.5871			1.47997
$277$	−1.75950	+	1.27835i	−0.105718	+	0.0768087i	−0.639388	−	0.768884i	$-0.720812\pi$
$277$	−1.75950	+	1.27835i	−0.105718	+	0.0768087i	0.533670	+	0.845693i	$0.320812\pi$
$278$	1.96998	−	6.06296i	0.118151	−	0.363632i
$279$	−0.0288492	+	0.0887887i	−0.00172716	+	0.00531564i
$280$		0			0
$281$	−7.45277	−	22.9373i	−0.444595	−	1.36832i	−0.882927	−	0.469510i	$-0.844431\pi$
$281$	−7.45277	−	22.9373i	−0.444595	−	1.36832i	0.438332	−	0.898813i	$-0.355569\pi$
$282$	−3.89351			−0.231855
$283$	−5.01052	−	15.4208i	−0.297845	−	0.916672i	−0.982251	−	0.187571i	$-0.939939\pi$
$283$	−5.01052	−	15.4208i	−0.297845	−	0.916672i	0.684406	−	0.729101i	$-0.260061\pi$
$284$	3.58245	+	2.60281i	0.212580	+	0.154448i
$285$		0			0
$286$	4.97152	−	3.61202i	0.293972	−	0.213583i
$287$	26.8079	+	19.4771i	1.58242	+	1.14969i
$288$	0.169528	+	0.123170i	0.00998956	+	0.00725784i
$289$	8.46013	−	6.14664i	0.497654	−	0.361567i
$290$		0			0
$291$	−22.2069	−	16.1342i	−1.30179	−	0.945805i
$292$	0.885595	+	2.72558i	0.0518255	+	0.159503i
$293$	−3.48929			−0.203846			−0.101923	−	0.994792i	$-0.532500\pi$
$293$	−3.48929			−0.203846			−0.101923	+	0.994792i	$0.532500\pi$
$294$	0.818292	+	2.51844i	0.0477238	+	0.146879i
$295$		0			0
$296$	−0.00527901	+	0.0162471i	−0.000306836	+	0.000944345i
$297$	8.65640	−	26.6417i	0.502296	−	1.54591i
$298$	3.38220	−	2.45731i	0.195926	−	0.142348i
$299$	−26.6579			−1.54167
$300$		0			0
$301$	7.96599			0.459152
$302$	−0.569976	+	0.414112i	−0.0327984	+	0.0238295i
$303$	0.765530	−	2.35606i	0.0439786	−	0.135352i
$304$	−2.11013	+	6.49433i	−0.121025	+	0.372475i
$305$		0			0
$306$	0.0148453	+	0.0456891i	0.000848648	+	0.00261187i
$307$	−8.92690			−0.509485			−0.254742	−	0.967009i	$-0.581991\pi$
$307$	−8.92690			−0.509485			−0.254742	+	0.967009i	$0.581991\pi$
$308$	−10.6995	−	32.9297i	−0.609662	−	1.87635i
$309$	20.3527	+	14.7871i	1.15782	+	0.841207i
$310$		0			0
$311$	21.9325	−	15.9349i	1.24368	−	0.903585i	0.245840	−	0.969310i	$-0.420936\pi$
$311$	21.9325	−	15.9349i	1.24368	−	0.903585i	0.997838	+	0.0657255i	$0.0209362\pi$
$312$	6.21624	+	4.51636i	0.351925	+	0.255689i
$313$	−16.2672	−	11.8188i	−0.919475	−	0.668038i	0.0239180	−	0.999714i	$-0.492386\pi$
$313$	−16.2672	−	11.8188i	−0.919475	−	0.668038i	−0.943393	+	0.331676i	$0.892386\pi$
$314$	−4.16278	+	3.02443i	−0.234919	+	0.170679i
$315$		0			0
$316$	0.653759	+	0.474984i	0.0367768	+	0.0267199i
$317$	−2.99126	−	9.20616i	−0.168006	−	0.517070i	0.831239	−	0.555915i	$-0.187632\pi$
$317$	−2.99126	−	9.20616i	−0.168006	−	0.517070i	−0.999245	+	0.0388454i	$0.987632\pi$
$318$	−0.965442			−0.0541393
$319$	−7.82780	−	24.0915i	−0.438273	−	1.34886i
$320$		0			0
$321$	−6.47597	+	19.9310i	−0.361453	+	1.11244i
$322$	2.61751	−	8.05587i	0.145868	−	0.448936i
$323$	−4.19209	+	3.04573i	−0.233254	+	0.169469i
$324$	16.7064			0.928132
$325$		0			0
$326$	−2.41540			−0.133777
$327$	21.3044	−	15.4786i	1.17814	−	0.855968i
$328$	−3.80425	+	11.7083i	−0.210054	+	0.646481i
$329$	7.35009	−	22.6212i	0.405224	−	1.24715i
$330$		0			0
$331$	6.08018	+	18.7129i	0.334197	+	1.02855i	0.967116	+	0.254334i	$0.0818564\pi$
$331$	6.08018	+	18.7129i	0.334197	+	1.02855i	−0.632919	+	0.774218i	$0.718144\pi$
$332$	−11.4387			−0.627778
$333$	−0.000238526	0	0.000734106i	−1.30711e−5	0	4.02288e-5i
$334$	−2.85932	−	2.07741i	−0.156455	−	0.113671i
$335$		0			0
$336$	16.0176	−	11.6374i	0.873830	−	0.634874i
$337$	15.2542	+	11.0828i	0.830948	+	0.603719i	0.919827	−	0.392323i	$-0.128329\pi$
$337$	15.2542	+	11.0828i	0.830948	+	0.603719i	−0.0888795	+	0.996042i	$0.528329\pi$
$338$	0.159029	+	0.115541i	0.00865003	+	0.00628462i
$339$	25.7493	−	18.7079i	1.39851	−	1.01608i
$340$		0			0
$341$	7.01828	+	5.09908i	0.380061	+	0.276131i
$342$	0.0117572	+	0.0361849i	0.000635757	+	0.00195666i
$343$	7.79178			0.420717
$344$	0.914542	+	2.81467i	0.0493088	+	0.151757i
$345$		0			0
$346$	−1.51440	+	4.66085i	−0.0814147	+	0.250569i
$347$	−8.02679	+	24.7039i	−0.430901	+	1.32618i	0.466328	+	0.884612i	$0.345577\pi$
$347$	−8.02679	+	24.7039i	−0.430901	+	1.32618i	−0.897229	+	0.441565i	$0.854423\pi$
$348$	12.4608	−	9.05333i	0.667971	−	0.485309i
$349$	−26.1490			−1.39972			−0.699861	−	0.714279i	$-0.746755\pi$
$349$	−26.1490			−1.39972			−0.699861	+	0.714279i	$0.746755\pi$
$350$		0			0
$351$	−18.4674			−0.985718
$352$	15.7530	−	11.4453i	0.839640	−	0.610034i
$353$	1.64673	−	5.06811i	0.0876465	−	0.269748i	−0.897621	−	0.440768i	$-0.854706\pi$
$353$	1.64673	−	5.06811i	0.0876465	−	0.269748i	0.985268	+	0.171020i	$0.0547062\pi$
$354$	−0.00384219	+	0.0118251i	−0.000204210	+	0.000628495i
$355$		0			0
$356$	3.56502	+	10.9720i	0.188946	+	0.581515i
$357$	15.0240			0.795152
$358$	0.747030	+	2.29912i	0.0394818	+	0.121512i
$359$	−8.00869	−	5.81866i	−0.422683	−	0.307097i	0.356034	−	0.934473i	$-0.384129\pi$
$359$	−8.00869	−	5.81866i	−0.422683	−	0.307097i	−0.778716	+	0.627376i	$0.784129\pi$
$360$		0			0
$361$	12.0513	−	8.75575i	0.634277	−	0.460829i
$362$	2.88605	+	2.09684i	0.151688	+	0.110207i
$363$	−24.3241	−	17.6725i	−1.27669	−	0.927567i
$364$	−18.4668	+	13.4169i	−0.967921	+	0.703236i
$365$		0			0
$366$	−1.77649	−	1.29070i	−0.0928587	−	0.0674658i
$367$	−5.07999	−	15.6346i	−0.265173	−	0.816119i	−0.991653	−	0.128932i	$-0.958845\pi$
$367$	−5.07999	−	15.6346i	−0.265173	−	0.816119i	0.726480	−	0.687187i	$-0.241155\pi$
$368$	−25.5197			−1.33031
$369$	−0.171890	−	0.529024i	−0.00894824	−	0.0275399i
$370$		0			0
$371$	1.82254	−	5.60921i	0.0946217	−	0.291216i
$372$	−1.63000	+	5.01663i	−0.0845116	+	0.260100i
$373$	18.6019	−	13.5151i	0.963172	−	0.699785i	0.00928655	−	0.999957i	$-0.497044\pi$
$373$	18.6019	−	13.5151i	0.963172	−	0.699785i	0.953885	+	0.300172i	$0.0970440\pi$
$374$	4.46404			0.230830
$375$		0			0
$376$	8.83674			0.455720
$377$	−13.5103	+	9.81583i	−0.695818	+	0.505541i
$378$	1.81330	−	5.58075i	0.0932658	−	0.287043i
$379$	5.07547	−	15.6207i	0.260710	−	0.802382i	−0.731941	−	0.681368i	$-0.761385\pi$
$379$	5.07547	−	15.6207i	0.260710	−	0.802382i	0.992651	−	0.121014i	$-0.0386146\pi$
$380$		0			0
$381$	−0.359343	−	1.10594i	−0.0184097	−	0.0566593i
$382$	−0.572279			−0.0292803
$383$	−1.45393	−	4.47475i	−0.0742926	−	0.228649i	0.907014	−	0.421101i	$-0.138356\pi$
$383$	−1.45393	−	4.47475i	−0.0742926	−	0.228649i	−0.981306	+	0.192452i	$0.938356\pi$
$384$	12.6355	+	9.18023i	0.644802	+	0.468476i
$385$		0			0
$386$	−2.51961	+	1.83061i	−0.128245	+	0.0931754i
$387$	−0.108184	−	0.0786000i	−0.00549928	−	0.00399546i
$388$	24.5093	+	17.8071i	1.24427	+	0.904017i
$389$	−2.86283	+	2.07997i	−0.145151	+	0.105458i	−0.657991	−	0.753026i	$-0.728593\pi$
$389$	−2.86283	+	2.07997i	−0.145151	+	0.105458i	0.512840	+	0.858484i	$0.328593\pi$
$390$		0			0
$391$	−15.6668	−	11.3826i	−0.792303	−	0.575642i
$392$	−1.85720	−	5.71588i	−0.0938028	−	0.288695i
$393$	12.0944			0.610082
$394$	−2.41493	−	7.43238i	−0.121662	−	0.374438i
$395$		0			0
$396$	−0.179609	+	0.552780i	−0.00902570	+	0.0277782i
$397$	2.70814	−	8.33481i	0.135918	−	0.418312i	−0.859814	−	0.510608i	$-0.829420\pi$
$397$	2.70814	−	8.33481i	0.135918	−	0.418312i	0.995732	+	0.0922956i	$0.0294205\pi$
$398$	−6.29890	+	4.57642i	−0.315735	+	0.229395i
$399$	11.8987			0.595681
$400$		0			0
$401$	22.7677			1.13697			0.568483	−	0.822695i	$-0.307531\pi$
$401$	22.7677			1.13697			0.568483	+	0.822695i	$0.307531\pi$
$402$	1.86747	−	1.35680i	0.0931412	−	0.0676710i
$403$	1.76729	−	5.43915i	0.0880348	−	0.270943i
$404$	−0.844903	+	2.60034i	−0.0420355	+	0.129372i
$405$		0			0
$406$	−1.63972	−	5.04655i	−0.0813781	−	0.250456i
$407$	−0.0717256			−0.00355531
$408$	1.72484	+	5.30851i	0.0853922	+	0.262810i
$409$	−22.6870	−	16.4830i	−1.12180	−	0.815034i	−0.137318	−	0.990527i	$-0.543848\pi$
$409$	−22.6870	−	16.4830i	−1.12180	−	0.815034i	−0.984481	+	0.175493i	$0.943848\pi$
$410$		0			0
$411$	−15.1525	+	11.0089i	−0.747416	+	0.543030i
$412$	−22.4629	−	16.3202i	−1.10667	−	0.804041i
$413$	−0.0614502	−	0.0446462i	−0.00302377	−	0.00219690i
$414$	−0.115034	+	0.0835774i	−0.00565363	+	0.00410760i
$415$		0			0
$416$	−10.3852	−	7.54530i	−0.509177	−	0.369939i
$417$	10.3420	+	31.8293i	0.506449	+	1.55869i
$418$	3.53544			0.172924
$419$	10.5344	+	32.4216i	0.514640	+	1.58390i	0.783936	+	0.620842i	$0.213209\pi$
$419$	10.5344	+	32.4216i	0.514640	+	1.58390i	−0.269296	+	0.963057i	$0.586791\pi$
$420$		0			0
$421$	−9.93150	+	30.5660i	−0.484032	+	1.48970i	0.349347	+	0.936993i	$0.386403\pi$
$421$	−9.93150	+	30.5660i	−0.484032	+	1.48970i	−0.833379	+	0.552703i	$0.813597\pi$
$422$	−1.55419	+	4.78330i	−0.0756567	+	0.232847i
$423$	−0.323022	+	0.234689i	−0.0157059	+	0.0114110i
$424$	2.19117			0.106413
$425$		0			0
$426$	1.31098			0.0635171
$427$	10.8526	−	7.88485i	0.525192	−	0.381575i
$428$	7.14742	−	21.9975i	0.345483	−	1.06329i
$429$	−9.96912	+	30.6818i	−0.481314	+	1.48133i
$430$		0			0
$431$	−5.48656	−	16.8859i	−0.264278	−	0.813364i	−0.991859	−	0.127342i	$-0.959355\pi$
$431$	−5.48656	−	16.8859i	−0.264278	−	0.813364i	0.727581	−	0.686022i	$-0.240645\pi$
$432$	−17.6789			−0.850579
$433$	−0.947953	−	2.91750i	−0.0455557	−	0.140206i	0.925691	−	0.378279i	$-0.123484\pi$
$433$	−0.947953	−	2.91750i	−0.0455557	−	0.140206i	−0.971247	+	0.238073i	$0.923484\pi$
$434$	1.47015	+	1.06813i	0.0705695	+	0.0512717i
$435$		0			0
$436$	−23.5134	+	17.0835i	−1.12609	+	0.818149i
$437$	−12.4078	−	9.01481i	−0.593546	−	0.431237i
$438$	0.686409	+	0.498705i	0.0327979	+	0.0238291i
$439$	−11.9310	+	8.66838i	−0.569436	+	0.413719i	−0.834900	−	0.550401i	$-0.814475\pi$
$439$	−11.9310	+	8.66838i	−0.569436	+	0.413719i	0.265464	+	0.964121i	$0.414475\pi$
$440$		0			0
$441$	0.219693	+	0.159616i	0.0104616	+	0.00760078i
$442$	−0.909413	−	2.79889i	−0.0432564	−	0.133129i
$443$	10.1857			0.483935			0.241968	−	0.970284i	$-0.422207\pi$
$443$	10.1857			0.483935			0.241968	+	0.970284i	$0.422207\pi$
$444$	−0.0134769	−	0.0414775i	−0.000639584	−	0.00196844i
$445$		0			0
$446$	1.97655	−	6.08319i	0.0935923	−	0.288047i
$447$	−6.78214	+	20.8733i	−0.320784	+	0.987273i
$448$	−15.3754	+	11.1709i	−0.726419	+	0.527774i
$449$	18.9484			0.894230			0.447115	−	0.894477i	$-0.352451\pi$
$449$	18.9484			0.894230			0.447115	+	0.894477i	$0.352451\pi$
$450$		0			0
$451$	−51.6881			−2.43390
$452$	−28.4190	+	20.6476i	−1.33672	+	0.971183i
$453$	1.14294	−	3.51761i	0.0537001	−	0.165272i
$454$	−0.135511	+	0.417059i	−0.00635983	+	0.0195735i
$455$		0			0
$456$	1.36604	+	4.20425i	0.0639708	+	0.196882i
$457$	30.4392			1.42389			0.711943	−	0.702237i	$-0.247815\pi$
$457$	30.4392			1.42389			0.711943	+	0.702237i	$0.247815\pi$
$458$	−2.25876	−	6.95174i	−0.105545	−	0.324833i
$459$	−10.8532	−	7.88535i	−0.506586	−	0.368056i
$460$		0			0
$461$	−1.91714	+	1.39289i	−0.0892903	+	0.0648732i	−0.631535	−	0.775348i	$-0.717575\pi$
$461$	−1.91714	+	1.39289i	−0.0892903	+	0.0648732i	0.542244	+	0.840221i	$0.317575\pi$
$462$	−8.29301	−	6.02522i	−0.385826	−	0.280319i
$463$	0.259680	+	0.188669i	0.0120684	+	0.00876817i	0.593803	−	0.804610i	$-0.297626\pi$
$463$	0.259680	+	0.188669i	0.0120684	+	0.00876817i	−0.581735	+	0.813379i	$0.697626\pi$
$464$	−12.9335	+	9.39674i	−0.600423	+	0.436233i
$465$		0			0
$466$	4.85475	+	3.52719i	0.224892	+	0.163394i
$467$	−3.95762	−	12.1803i	−0.183137	−	0.563637i	0.816774	−	0.576957i	$-0.195760\pi$
$467$	−3.95762	−	12.1803i	−0.183137	−	0.563637i	−0.999911	+	0.0133197i	$0.995760\pi$
$468$	0.383175			0.0177123
$469$	4.35761	+	13.4113i	0.201216	+	0.619278i
$470$		0			0
$471$	8.34739	−	25.6906i	0.384627	−	1.18376i
$472$	0.00872027	−	0.0268382i	0.000401383	−	0.00123533i
$473$	−10.0527	+	7.30372i	−0.462224	+	0.335826i
$474$	0.239239			0.0109886
$475$		0			0
$476$	−16.5817			−0.760021
$477$	−0.0800972	+	0.0581940i	−0.00366740	+	0.00266452i
$478$	−1.21204	+	3.73027i	−0.0554373	+	0.170619i
$479$	−6.28683	+	19.3489i	−0.287253	+	0.884072i	0.698462	+	0.715647i	$0.253868\pi$
$479$	−6.28683	+	19.3489i	−0.287253	+	0.884072i	−0.985714	+	0.168425i	$0.946132\pi$
$480$		0			0
$481$	0.0146119	+	0.0449709i	0.000666247	+	0.00205050i
$482$	3.30573			0.150572
$483$	13.7414	+	42.2917i	0.625255	+	1.92434i
$484$	26.8461	+	19.5049i	1.22028	+	0.886585i
$485$		0			0
$486$	−0.157883	+	0.114709i	−0.00716173	+	0.00520330i
$487$	12.5332	+	9.10589i	0.567933	+	0.412627i	0.834354	−	0.551230i	$-0.185841\pi$
$487$	12.5332	+	9.10589i	0.567933	+	0.412627i	−0.266421	+	0.963857i	$0.585841\pi$
$488$	4.03194	+	2.92938i	0.182517	+	0.132607i
$489$	10.2587	−	7.45335i	0.463912	−	0.337052i
$490$		0			0
$491$	22.2549	+	16.1691i	1.00435	+	0.729702i	0.963016	−	0.269443i	$-0.0868397\pi$
$491$	22.2549	+	16.1691i	1.00435	+	0.729702i	0.0413326	+	0.999145i	$0.486840\pi$
$492$	−9.71192	−	29.8902i	−0.437847	−	1.34756i
$493$	−12.1312			−0.546362
$494$	−0.720240	−	2.21667i	−0.0324051	−	0.0997327i
$495$		0			0
$496$	1.69183	−	5.20692i	0.0759655	−	0.233798i
$497$	−2.47484	+	7.61677i	−0.111012	+	0.341659i
$498$	−2.73972	+	1.99052i	−0.122770	+	0.0891974i
$499$	4.91044			0.219821			0.109911	−	0.993941i	$-0.464943\pi$
$499$	4.91044			0.219821			0.109911	+	0.993941i	$0.464943\pi$
$500$		0			0
$501$	18.5544			0.828950
$502$	−4.42143	+	3.21235i	−0.197338	+	0.143374i
$503$	−12.6837	+	39.0365i	−0.565539	+	1.74055i	0.100805	+	0.994906i	$0.467858\pi$
$503$	−12.6837	+	39.0365i	−0.565539	+	1.74055i	−0.666344	+	0.745644i	$0.732142\pi$
$504$	−0.0773688	+	0.238117i	−0.00344628	+	0.0106066i
$505$		0			0
$506$	4.08295	+	12.5660i	0.181509	+	0.558629i
$507$	−1.03196			−0.0458308
$508$	0.396601	+	1.22061i	0.0175963	+	0.0541559i
$509$	−33.5260	−	24.3581i	−1.48601	−	1.07965i	−0.975556	−	0.219750i	$-0.929476\pi$
$509$	−33.5260	−	24.3581i	−1.48601	−	1.07965i	−0.510458	−	0.859903i	$-0.670524\pi$
$510$		0			0
$511$	−4.19326	+	3.04658i	−0.185499	+	0.134773i
$512$	−16.8800	−	12.2641i	−0.745999	−	0.542000i
$513$	−8.59559	−	6.24506i	−0.379504	−	0.275726i
$514$	3.96969	−	2.88415i	0.175095	−	0.127214i
$515$		0			0
$516$	−6.11245	−	4.44096i	−0.269086	−	0.195502i
$517$	11.4651	+	35.2860i	0.504235	+	1.55188i
$518$	−0.0150247			−0.000660147
$519$	−7.95030	−	24.4685i	−0.348980	−	1.07405i
$520$		0			0
$521$	−0.501988	+	1.54496i	−0.0219925	+	0.0676859i	−0.961450	−	0.274978i	$-0.911329\pi$
$521$	−0.501988	+	1.54496i	−0.0219925	+	0.0676859i	0.939458	+	0.342664i	$0.111329\pi$
$522$	−0.0275255	+	0.0847147i	−0.00120476	+	0.00370786i
$523$	−15.3721	+	11.1685i	−0.672174	+	0.488363i	−0.870752	−	0.491722i	$-0.836368\pi$
$523$	−15.3721	+	11.1685i	−0.672174	+	0.488363i	0.198578	+	0.980085i	$0.436368\pi$
$524$	−13.3484			−0.583128
$525$		0			0
$526$	−2.01665			−0.0879301
$527$	3.36107	−	2.44196i	0.146411	−	0.106374i
$528$	−9.54349	+	29.3718i	−0.415327	+	1.27825i
$529$	10.6046	−	32.6378i	0.461072	−	1.41903i
$530$		0			0
$531$	0.000394015		0.00121265i	1.70988e−5		5.26246e-5i
$532$	−13.1324			−0.569362
$533$	10.5299	+	32.4077i	0.456100	+	1.40373i
$534$	2.76318	+	2.00757i	0.119575	+	0.0868760i
$535$		0			0
$536$	−4.23843	+	3.07940i	−0.183072	+	0.133010i
$537$	−10.2673	−	7.45963i	−0.443067	−	0.321907i
$538$	−2.93564	−	2.13287i	−0.126564	−	0.0919544i
$539$	20.4145	−	14.8320i	0.879314	−	0.638859i
$540$		0			0
$541$	27.1179	+	19.7023i	1.16589	+	0.847067i	0.990511	−	0.137434i	$-0.0438856\pi$
$541$	27.1179	+	19.7023i	1.16589	+	0.847067i	0.175377	+	0.984501i	$0.443886\pi$
$542$	−0.117277	−	0.360943i	−0.00503750	−	0.0155038i
$543$	−18.7279			−0.803691
$544$	−2.88162	−	8.86870i	−0.123548	−	0.380243i
$545$		0			0
$546$	−2.08828	+	6.42705i	−0.0893700	+	0.275053i
$547$	5.38486	−	16.5729i	0.230240	−	0.708606i	−0.767477	−	0.641076i	$-0.778488\pi$
$547$	5.38486	−	16.5729i	0.230240	−	0.708606i	0.997717	−	0.0675298i	$-0.0215118\pi$
$548$	16.7235	−	12.1504i	0.714394	−	0.519037i
$549$	−0.225185			−0.00961065
$550$		0			0
$551$	−9.60771			−0.409302
$552$	−13.3656	+	9.71067i	−0.568877	+	0.413313i
$553$	−0.451631	+	1.38998i	−0.0192053	+	0.0591079i
$554$	0.219599	−	0.675857i	0.00932988	−	0.0287144i
$555$		0			0
$556$	−11.4143	−	35.1295i	−0.484073	−	1.48982i
$557$	16.2929			0.690351			0.345175	−	0.938538i	$-0.387819\pi$
$557$	16.2929			0.690351			0.345175	+	0.938538i	$0.387819\pi$
$558$	−0.00942651	−	0.0290118i	−0.000399056	−	0.00122817i
$559$	6.62726	+	4.81499i	0.280303	+	0.203652i
$560$		0			0
$561$	−18.9596	+	13.7749i	−0.800473	+	0.581578i
$562$	6.37544	+	4.63203i	0.268932	+	0.195390i
$563$	18.6882	+	13.5778i	0.787615	+	0.572236i	0.907255	−	0.420582i	$-0.138174\pi$
$563$	18.6882	+	13.5778i	0.787615	+	0.572236i	−0.119640	+	0.992817i	$0.538174\pi$
$564$	−18.2510	+	13.2601i	−0.768505	+	0.558351i
$565$		0			0
$566$	4.28623	+	3.11413i	0.180164	+	0.130897i
$567$	9.33698	+	28.7363i	0.392116	+	1.20681i
$568$	−2.97541			−0.124845
$569$	−2.86871	−	8.82898i	−0.120263	−	0.370130i	0.872746	−	0.488175i	$-0.162337\pi$
$569$	−2.86871	−	8.82898i	−0.120263	−	0.370130i	−0.993008	+	0.118045i	$0.962337\pi$
$570$		0			0
$571$	6.86460	−	21.1271i	0.287275	−	0.884140i	−0.698433	−	0.715675i	$-0.746119\pi$
$571$	6.86460	−	21.1271i	0.287275	−	0.884140i	0.985708	−	0.168465i	$-0.0538809\pi$
$572$	11.0028	−	33.8630i	0.460048	−	1.41588i
$573$	2.43057	−	1.76591i	0.101539	−	0.0737721i
$574$	−10.8273			−0.451924
$575$		0			0
$576$	0.319031			0.0132930
$577$	11.8191	−	8.58711i	0.492037	−	0.357486i	−0.313930	−	0.949446i	$-0.601646\pi$
$577$	11.8191	−	8.58711i	0.492037	−	0.357486i	0.805967	+	0.591960i	$0.201646\pi$
$578$	−1.05589	+	3.24969i	−0.0439192	+	0.135169i
$579$	5.05244	−	15.5498i	0.209972	−	0.646229i
$580$		0			0
$581$	−6.39292	−	19.6754i	−0.265223	−	0.816273i
$582$	8.96905			0.371779
$583$	2.84291	+	8.74959i	0.117741	+	0.362371i
$584$	−1.55788	−	1.13186i	−0.0644655	−	0.0468369i
$585$		0			0
$586$	0.922384	−	0.670151i	0.0381033	−	0.0276837i
$587$	18.8853	+	13.7210i	0.779479	+	0.566325i	0.904823	−	0.425789i	$-0.140003\pi$
$587$	18.8853	+	13.7210i	0.779479	+	0.566325i	−0.125344	+	0.992113i	$0.540003\pi$
$588$	12.4128	+	9.01845i	0.511896	+	0.371914i
$589$	2.66191	−	1.93399i	0.109682	−	0.0796888i
$590$		0			0
$591$	33.1911	+	24.1148i	1.36530	+	0.991949i
$592$	0.0139881	+	0.0430509i	0.000574907	+	0.00176938i
$593$	41.9815			1.72397			0.861986	−	0.506932i	$-0.169220\pi$
$593$	41.9815			1.72397			0.861986	+	0.506932i	$0.169220\pi$
$594$	2.82849	+	8.70520i	0.116054	+	0.357179i
$595$		0			0
$596$	7.48534	−	23.0375i	0.306611	−	0.943653i
$597$	12.6308	−	38.8737i	0.516946	−	1.59100i
$598$	7.04694	−	5.11990i	0.288171	−	0.209368i
$599$	−25.4160			−1.03847			−0.519236	−	0.854631i	$-0.673783\pi$
$599$	−25.4160			−1.03847			−0.519236	+	0.854631i	$0.673783\pi$
$600$		0			0
$601$	37.1379			1.51489			0.757444	−	0.652900i	$-0.226448\pi$
$601$	37.1379			1.51489			0.757444	+	0.652900i	$0.226448\pi$
$602$	−2.10579	+	1.52994i	−0.0858254	+	0.0623558i
$603$	0.0731497	−	0.225132i	0.00297889	−	0.00916807i
$604$	−1.26145	+	3.88233i	−0.0513275	+	0.157970i
$605$		0			0
$606$	0.250138	+	0.769845i	0.0101612	+	0.0312728i
$607$	18.9242			0.768109			0.384054	−	0.923310i	$-0.374527\pi$
$607$	18.9242			0.768109			0.384054	+	0.923310i	$0.374527\pi$
$608$	−2.28219	−	7.02386i	−0.0925550	−	0.284855i
$609$	22.5366	+	16.3738i	0.913230	+	0.663500i
$610$		0			0
$611$	19.7881	−	14.3769i	0.800543	−	0.581628i
$612$	0.225191	+	0.163611i	0.00910280	+	0.00661357i
$613$	7.44552	+	5.40949i	0.300722	+	0.218487i	0.727905	−	0.685678i	$-0.240494\pi$
$613$	7.44552	+	5.40949i	0.300722	+	0.218487i	−0.427183	+	0.904165i	$0.640494\pi$
$614$	2.35980	−	1.71450i	0.0952338	−	0.0691914i
$615$		0			0
$616$	18.8219	+	13.6749i	0.758355	+	0.550977i
$617$	10.1164	+	31.1352i	0.407273	+	1.25346i	0.918982	+	0.394298i	$0.129012\pi$
$617$	10.1164	+	31.1352i	0.407273	+	1.25346i	−0.511710	+	0.859158i	$0.670988\pi$
$618$	−8.22017			−0.330664
$619$	11.2467	+	34.6139i	0.452045	+	1.39125i	0.874570	+	0.484900i	$0.161144\pi$
$619$	11.2467	+	34.6139i	0.452045	+	1.39125i	−0.422525	+	0.906351i	$0.638856\pi$
$620$		0			0
$621$	12.2701	−	37.7635i	0.492383	−	1.51540i
$622$	−2.73735	+	8.42469i	−0.109758	+	0.337799i
$623$	−16.8802	+	12.2642i	−0.676292	+	0.491355i
$624$	20.3599			0.815049
$625$		0			0
$626$	6.57010			0.262594
$627$	−15.0156	+	10.9095i	−0.599667	+	0.435684i
$628$	−9.21287	+	28.3543i	−0.367634	+	1.13146i
$629$	−0.0106146	+	0.0326684i	−0.000423232	+	0.00130257i
$630$		0			0
$631$	3.74167	+	11.5157i	0.148953	+	0.458432i	0.997498	−	0.0706920i	$-0.0225207\pi$
$631$	3.74167	+	11.5157i	0.148953	+	0.458432i	−0.848545	+	0.529124i	$0.822521\pi$
$632$	−0.542980			−0.0215986
$633$	−8.15918	−	25.1114i	−0.324298	−	0.998087i
$634$	2.55886	+	1.85912i	0.101625	+	0.0738352i
$635$		0			0
$636$	−4.52555	+	3.28800i	−0.179450	+	0.130378i
$637$	−13.4583	−	9.77801i	−0.533237	−	0.387419i
$638$	6.69626	+	4.86512i	0.265107	+	0.192612i
$639$	0.108764	−	0.0790219i	0.00430265	−	0.00312606i
$640$		0			0
$641$	−7.88935	−	5.73195i	−0.311610	−	0.226398i	0.420977	−	0.907071i	$-0.361687\pi$
$641$	−7.88935	−	5.73195i	−0.311610	−	0.226398i	−0.732587	+	0.680673i	$0.761687\pi$
$642$	−2.11603	−	6.51247i	−0.0835130	−	0.257027i
$643$	−6.77862			−0.267323			−0.133661	−	0.991027i	$-0.542673\pi$
$643$	−6.77862			−0.267323			−0.133661	+	0.991027i	$0.542673\pi$
$644$	−15.1662	−	46.6766i	−0.597630	−	1.83932i
$645$		0			0
$646$	0.523206	−	1.61026i	0.0205853	−	0.0633549i
$647$	12.3974	−	38.1552i	0.487392	−	1.50004i	−0.341096	−	0.940029i	$-0.610798\pi$
$647$	12.3974	−	38.1552i	0.487392	−	1.50004i	0.828487	−	0.560008i	$-0.189202\pi$
$648$	−9.08162	+	6.59818i	−0.356760	+	0.259201i
$649$	0.118482			0.00465082
$650$		0			0
$651$	−9.53997			−0.373901
$652$	−11.3223	+	8.22613i	−0.443416	+	0.322160i
$653$	−1.89801	+	5.84148i	−0.0742750	+	0.228595i	−0.981301	−	0.192480i	$-0.938347\pi$
$653$	−1.89801	+	5.84148i	−0.0742750	+	0.228595i	0.907026	+	0.421075i	$0.138347\pi$
$654$	−2.65896	+	8.18344i	−0.103974	+	0.319998i
$655$		0			0
$656$	10.0803	+	31.0240i	0.393570	+	1.21128i
$657$	0.0870078			0.00339450
$658$	2.40165	+	7.39152i	0.0936260	+	0.288151i
$659$	35.7298	+	25.9592i	1.39184	+	1.01123i	0.995661	+	0.0930526i	$0.0296625\pi$
$659$	35.7298	+	25.9592i	1.39184	+	1.01123i	0.396175	+	0.918175i	$0.370338\pi$
$660$		0			0
$661$	−22.4460	+	16.3079i	−0.873047	+	0.634306i	−0.931403	−	0.363990i	$-0.881414\pi$
$661$	−22.4460	+	16.3079i	−0.873047	+	0.634306i	0.0583560	+	0.998296i	$0.481414\pi$
$662$	−5.20126	−	3.77894i	−0.202153	−	0.146873i
$663$	12.4991	+	9.08114i	0.485425	+	0.352682i
$664$	6.21808	−	4.51770i	0.241308	−	0.175321i
$665$		0			0
$666$	0.000204046	0	0.000148248i	7.90661e−6	0	5.74449e-6i
$667$	−11.0956	−	34.1488i	−0.429624	−	1.32225i
$668$	−20.4782			−0.792325
$669$	10.3765	+	31.9355i	0.401178	+	1.23470i
$670$		0			0
$671$	−6.46611	+	19.9006i	−0.249621	+	0.768256i
$672$	−6.61703	+	20.3651i	−0.255257	+	0.785601i
$673$	−33.8431	+	24.5884i	−1.30456	+	0.947815i	−0.999989	−	0.00467644i	$-0.998511\pi$
$673$	−33.8431	+	24.5884i	−1.30456	+	0.947815i	−0.304566	+	0.952491i	$0.598511\pi$
$674$	−6.16096			−0.237311
$675$		0			0
$676$	1.13895			0.0438059
$677$	18.3060	−	13.3001i	0.703556	−	0.511163i	−0.177533	−	0.984115i	$-0.556812\pi$
$677$	18.3060	−	13.3001i	0.703556	−	0.511163i	0.881088	+	0.472952i	$0.156812\pi$
$678$	−3.21371	+	9.89078i	−0.123422	+	0.379853i
$679$	−16.9316	+	52.1101i	−0.649775	+	1.99980i
$680$		0			0
$681$	−0.711404	−	2.18947i	−0.0272610	−	0.0839009i
$682$	−2.83459			−0.108542
$683$	15.1426	+	46.6040i	0.579414	+	1.78325i	0.620630	+	0.784104i	$0.286877\pi$
$683$	15.1426	+	46.6040i	0.579414	+	1.78325i	−0.0412155	+	0.999150i	$0.513123\pi$
$684$	0.178347	+	0.129577i	0.00681928	+	0.00495449i
$685$		0			0
$686$	−2.05974	+	1.49649i	−0.0786411	+	0.0571361i
$687$	31.0447	+	22.5553i	1.18443	+	0.860538i
$688$	6.34431	+	4.60941i	0.241875	+	0.175732i
$689$	4.90671	−	3.56493i	0.186931	−	0.135813i
$690$		0			0
$691$	−29.3336	−	21.3121i	−1.11590	−	0.810750i	−0.132319	−	0.991207i	$-0.542242\pi$
$691$	−29.3336	−	21.3121i	−1.11590	−	0.810750i	−0.983583	+	0.180457i	$0.942242\pi$
$692$	8.77462	+	27.0055i	0.333561	+	1.02659i
$693$	−1.05121			−0.0399320
$694$	−2.62276	−	8.07204i	−0.0995588	−	0.306410i
$695$		0			0
$696$	−3.19812	+	9.84281i	−0.121225	+	0.373091i
$697$	−7.64927	+	23.5420i	−0.289737	+	0.891718i
$698$	6.91241	−	5.02216i	0.261639	−	0.190091i
$699$	−31.5030			−1.19155
$700$		0			0
$701$	−8.32362			−0.314379			−0.157189	−	0.987568i	$-0.550243\pi$
$701$	−8.32362			−0.314379			−0.157189	+	0.987568i	$0.550243\pi$
$702$	4.88181	−	3.54684i	0.184252	−	0.133867i
$703$	−0.00840658	+	0.0258728i	−0.000317060	+	0.000975811i
$704$	9.16088	−	28.1943i	0.345264	−	1.06261i
$705$		0			0
$706$	0.538070	+	1.65601i	0.0202505	+	0.0623247i
$707$	−4.94500			−0.185976
$708$	0.0222621	+	0.0685157i	0.000836661	+	0.00257498i
$709$	−30.1841	−	21.9301i	−1.13359	−	0.823601i	−0.147376	−	0.989081i	$-0.547083\pi$
$709$	−30.1841	−	21.9301i	−1.13359	−	0.823601i	−0.986213	+	0.165480i	$0.947083\pi$
$710$		0			0
$711$	0.0198483	−	0.0144206i	0.000744370	−	0.000540816i
$712$	−6.27134	−	4.55639i	−0.235028	−	0.170758i
$713$	9.94815	+	7.22775i	0.372561	+	0.270681i
$714$	−3.97154	+	2.88549i	−0.148631	+	0.107987i
$715$		0			0
$716$	11.3318	+	8.23307i	0.423491	+	0.307684i
$717$	−6.36296	−	19.5832i	−0.237629	−	0.731347i
$718$	3.23460			0.120714
$719$	−2.36869	−	7.29008i	−0.0883373	−	0.271874i	0.897123	−	0.441781i	$-0.145653\pi$
$719$	−2.36869	−	7.29008i	−0.0883373	−	0.271874i	−0.985460	+	0.169907i	$0.945653\pi$
$720$		0			0
$721$	15.5179	−	47.7591i	0.577915	−	1.77864i
$722$	−1.50409	+	4.62912i	−0.0559765	+	0.172278i
$723$	−14.0400	+	10.2007i	−0.522155	+	0.379368i
$724$	20.6697			0.768183
$725$		0			0
$726$	9.82419			0.364610
$727$	−37.1411	+	26.9846i	−1.37749	+	1.00080i	−0.380377	+	0.924832i	$0.624206\pi$
$727$	−37.1411	+	26.9846i	−1.37749	+	1.00080i	−0.997110	+	0.0759713i	$0.975794\pi$
$728$	4.73957	−	14.5869i	0.175660	−	0.540626i
$729$	8.49713	−	26.1515i	0.314709	−	0.968574i
$730$		0			0
$731$	1.83889	+	5.65951i	0.0680137	+	0.209325i
$732$	−12.7231			−0.470259
$733$	−7.32776	−	22.5525i	−0.270657	−	0.832996i	−0.990336	−	0.138689i	$-0.955711\pi$
$733$	−7.32776	−	22.5525i	−0.270657	−	0.832996i	0.719679	−	0.694307i	$-0.244289\pi$
$734$	4.34565	+	3.15730i	0.160401	+	0.116538i
$735$		0			0
$736$	22.3293	−	16.2232i	0.823070	−	0.597995i
$737$	−17.7955	−	12.9292i	−0.655505	−	0.476252i
$738$	0.147043	+	0.106833i	0.00541272	+	0.00393257i
$739$	2.86135	−	2.07890i	0.105257	−	0.0764734i	−0.533912	−	0.845540i	$-0.679279\pi$
$739$	2.86135	−	2.07890i	0.105257	−	0.0764734i	0.639169	+	0.769067i	$0.279279\pi$
$740$		0			0
$741$	9.89908	+	7.19210i	0.363652	+	0.264209i
$742$	0.595518	+	1.83282i	0.0218621	+	0.0672848i
$743$	15.7201			0.576715			0.288358	−	0.957523i	$-0.406891\pi$
$743$	15.7201			0.576715			0.288358	+	0.957523i	$0.406891\pi$
$744$	−1.09524	−	3.37082i	−0.0401536	−	0.123580i
$745$		0			0
$746$	−2.32167	+	7.14536i	−0.0850023	+	0.261610i
$747$	−0.107316	+	0.330284i	−0.00392648	+	0.0120845i
$748$	20.9253	−	15.2032i	0.765106	−	0.555882i
$749$	41.8320			1.52851
$750$		0			0
$751$	−14.1856			−0.517642			−0.258821	−	0.965925i	$-0.583334\pi$
$751$	−14.1856			−0.517642			−0.258821	+	0.965925i	$0.583334\pi$
$752$	18.9433	−	13.7631i	0.690790	−	0.501889i
$753$	8.86604	−	27.2869i	0.323097	−	0.994389i
$754$	1.68620	−	5.18958i	0.0614076	−	0.188993i
$755$		0			0
$756$	−10.5064	−	32.3355i	−0.382116	−	1.17603i
$757$	−12.7388			−0.463000			−0.231500	−	0.972835i	$-0.574363\pi$
$757$	−12.7388			−0.463000			−0.231500	+	0.972835i	$0.574363\pi$
$758$	1.65842	+	5.10408i	0.0602364	+	0.185389i
$759$	−56.1167	−	40.7712i	−2.03691	−	1.47990i
$760$		0			0
$761$	−26.0746	+	18.9443i	−0.945203	+	0.686730i	−0.949667	−	0.313260i	$-0.898579\pi$
$761$	−26.0746	+	18.9443i	−0.945203	+	0.686730i	0.00446471	+	0.999990i	$0.498579\pi$
$762$	0.307398	+	0.223338i	0.0111359	+	0.00809068i
$763$	−42.5262	−	30.8971i	−1.53955	−	1.11855i
$764$	−2.68258	+	1.94901i	−0.0970523	+	0.0705127i
$765$		0			0
$766$	1.24376	+	0.903646i	0.0449389	+	0.0326500i
$767$	−0.0241371	−	0.0742864i	−0.000871541	−	0.00268233i
$768$	13.9387			0.502969
$769$	−3.51312	−	10.8123i	−0.126686	−	0.389900i	0.867518	−	0.497405i	$-0.165714\pi$
$769$	−3.51312	−	10.8123i	−0.126686	−	0.389900i	−0.994205	+	0.107505i	$0.965714\pi$
$770$		0			0
$771$	−7.96020	+	24.4990i	−0.286680	+	0.882309i
$772$	−5.57630	+	17.1621i	−0.200695	+	0.617677i
$773$	22.0048	−	15.9874i	0.791457	−	0.575027i	−0.116938	−	0.993139i	$-0.537308\pi$
$773$	22.0048	−	15.9874i	0.791457	−	0.575027i	0.908396	+	0.418112i	$0.137308\pi$
$774$	0.0436939			0.00157054
$775$		0			0
$776$	−20.3562			−0.730746
$777$	0.0638125	−	0.0463625i	0.00228926	−	0.00166325i
$778$	0.357303	−	1.09967i	0.0128099	−	0.0394249i
$779$	−6.05809	+	18.6449i	−0.217054	+	0.668022i
$780$		0			0
$781$	−3.86041	−	11.8811i	−0.138136	−	0.425140i
$782$	6.32760			0.226275
$783$	−7.68654	−	23.6568i	−0.274695	−	0.845423i
$784$	−12.8837	−	9.36054i	−0.460131	−	0.334305i
$785$		0			0
$786$	−3.19712	+	2.32285i	−0.114038	+	0.0828532i
$787$	−20.8133	−	15.1217i	−0.741912	−	0.539031i	0.151397	−	0.988473i	$-0.451623\pi$
$787$	−20.8133	−	15.1217i	−0.741912	−	0.539031i	−0.893309	+	0.449442i	$0.851623\pi$
$788$	−36.6325	−	26.6151i	−1.30498	−	0.948123i
$789$	8.56507	−	6.22289i	0.304925	−	0.221541i
$790$		0			0
$791$	−51.3986	−	37.3432i	−1.82752	−	1.32777i
$792$	−0.120685	−	0.371429i	−0.00428834	−	0.0131982i
$793$	13.7947			0.489864
$794$	0.884889	+	2.72341i	0.0314035	+	0.0966501i
$795$		0			0
$796$	−13.9404	+	42.9043i	−0.494106	+	1.52070i
$797$	−5.46074	+	16.8064i	−0.193429	+	0.595314i	0.806562	+	0.591150i	$0.201326\pi$
$797$	−5.46074	+	16.8064i	−0.193429	+	0.595314i	−0.999991	+	0.00416480i	$0.998674\pi$
$798$	−3.14539	+	2.28526i	−0.111346	+	0.0808974i
$799$	17.7682			0.628593
$800$		0			0
$801$	0.350256			0.0123757
$802$	−6.01858	+	4.37276i	−0.212524	+	0.154407i
$803$	2.49840	−	7.68930i	0.0881668	−	0.271349i
$804$	4.13301	−	12.7201i	0.145760	−	0.448603i
$805$		0			0
$806$	0.577463	+	1.77725i	0.0203403	+	0.0626009i
$807$	19.0497			0.670580
$808$	−0.567715	−	1.74725i	−0.0199721	−	0.0614679i
$809$	33.0545	+	24.0155i	1.16213	+	0.844339i	0.990046	−	0.140743i	$-0.0449491\pi$
$809$	33.0545	+	24.0155i	1.16213	+	0.844339i	0.172087	+	0.985082i	$0.444949\pi$
$810$		0			0
$811$	−13.4470	+	9.76981i	−0.472188	+	0.343064i	−0.798293	−	0.602269i	$-0.794263\pi$
$811$	−13.4470	+	9.76981i	−0.472188	+	0.343064i	0.326106	+	0.945333i	$0.394263\pi$
$812$	−24.8733	−	18.0715i	−0.872881	−	0.634185i
$813$	1.61188	+	1.17110i	0.0565311	+	0.0410722i
$814$	0.0189605	−	0.0137756i	0.000664564	−	0.000482834i
$815$		0			0
$816$	11.9655	+	8.69342i	0.418875	+	0.304330i
$817$	1.45637	+	4.48223i	0.0509518	+	0.156814i
$818$	9.16296			0.320375
$819$	0.214151	+	0.659090i	0.00748306	+	0.0230305i
$820$		0			0
$821$	−13.5653	+	41.7498i	−0.473433	+	1.45708i	0.374626	+	0.927176i	$0.377771\pi$
$821$	−13.5653	+	41.7498i	−0.473433	+	1.45708i	−0.848059	+	0.529902i	$0.822229\pi$
$822$	1.89115	−	5.82035i	0.0659613	−	0.203008i
$823$	21.1932	−	15.3977i	0.738748	−	0.536732i	−0.153571	−	0.988138i	$-0.549077\pi$
$823$	21.1932	−	15.3977i	0.738748	−	0.536732i	0.892319	+	0.451406i	$0.149077\pi$
$824$	18.6565			0.649932
$825$		0			0
$826$	0.0248189			0.000863561
$827$	18.1079	−	13.1562i	0.629675	−	0.457486i	−0.226613	−	0.973985i	$-0.572765\pi$
$827$	18.1079	−	13.1562i	0.629675	−	0.457486i	0.856288	+	0.516499i	$0.172765\pi$
$828$	−0.254589	+	0.783544i	−0.00884758	+	0.0272300i
$829$	0.259970	−	0.800106i	0.00902914	−	0.0277888i	−0.946440	−	0.322878i	$-0.895349\pi$
$829$	0.259970	−	0.800106i	0.00902914	−	0.0277888i	0.955470	+	0.295090i	$0.0953495\pi$
$830$		0			0
$831$	1.15285	+	3.54812i	0.0399920	+	0.123083i
$832$	−19.5437			−0.677554
$833$	−3.73431	−	11.4930i	−0.129386	−	0.398210i
$834$	−8.84700	−	6.42772i	−0.306346	−	0.222574i
$835$		0			0
$836$	16.5725	−	12.0406i	0.573172	−	0.416434i
$837$	6.89164	+	5.00707i	0.238210	+	0.173070i
$838$	−9.01162	−	6.54733i	−0.311301	−	0.226174i
$839$	−28.7628	+	20.8974i	−0.993003	+	0.721459i	−0.960577	−	0.278015i	$-0.910323\pi$
$839$	−28.7628	+	20.8974i	−0.993003	+	0.721459i	−0.0324264	+	0.999474i	$0.510323\pi$
$840$		0			0
$841$	5.26412	+	3.82461i	0.181521	+	0.131883i
$842$	−3.24513	−	9.98748i	−0.111834	−	0.344191i
$843$	−41.3709			−1.42489
$844$	9.00515	+	27.7150i	0.309970	+	0.953989i
$845$		0			0
$846$	0.0403157	−	0.124079i	0.00138608	−	0.00426592i
$847$	−18.5459	+	57.0785i	−0.637245	+	1.96124i
$848$	4.69721	−	3.41273i	0.161303	−	0.117193i
$849$	−27.8138			−0.954567
$850$		0			0
$851$	−0.101668			−0.00348515
$852$	6.14526	−	4.46479i	0.210533	−	0.152961i
$853$	6.03838	−	18.5842i	0.206750	−	0.636312i	−0.792887	−	0.609369i	$-0.791423\pi$
$853$	6.03838	−	18.5842i	0.206750	−	0.636312i	0.999637	−	0.0269427i	$-0.00857717\pi$
$854$	−1.35448	+	4.16868i	−0.0463495	+	0.142649i
$855$		0			0
$856$	4.80256	+	14.7807i	0.164148	+	0.505196i
$857$	0.570622			0.0194921			0.00974604	−	0.999953i	$-0.496898\pi$
$857$	0.570622			0.0194921			0.00974604	+	0.999953i	$0.496898\pi$
$858$	−3.25742	−	10.0253i	−0.111207	−	0.342259i
$859$	16.2598	+	11.8135i	0.554778	+	0.403070i	0.829544	−	0.558441i	$-0.188600\pi$
$859$	16.2598	+	11.8135i	0.554778	+	0.403070i	−0.274766	+	0.961511i	$0.588600\pi$
$860$		0			0
$861$	45.9856	−	33.4105i	1.56719	−	1.13863i
$862$	4.69345	+	3.40999i	0.159860	+	0.116145i
$863$	11.2975	+	8.20815i	0.384573	+	0.279409i	0.763228	−	0.646129i	$-0.223613\pi$
$863$	11.2975	+	8.20815i	0.384573	+	0.279409i	−0.378655	+	0.925538i	$0.623613\pi$
$864$	15.4688	−	11.2387i	0.526258	−	0.382349i
$865$		0			0
$866$	0.810922	+	0.589170i	0.0275563	+	0.0200208i
$867$	−5.54321	−	17.0602i	−0.188257	−	0.579396i
$868$	10.5291			0.357381
$869$	−0.704482	−	2.16817i	−0.0238979	−	0.0735503i
$870$		0			0
$871$	−4.48111	+	13.7914i	−0.151837	+	0.467305i
$872$	6.03480	−	18.5732i	0.204364	−	0.628968i
$873$	0.744110	−	0.540628i	0.0251843	−	0.0182975i
$874$	5.01135			0.169511
$875$		0			0
$876$	4.91601			0.166096
$877$	18.9724	−	13.7843i	0.640653	−	0.465462i	−0.219421	−	0.975630i	$-0.570417\pi$
$877$	18.9724	−	13.7843i	0.640653	−	0.465462i	0.860075	+	0.510168i	$0.170417\pi$
$878$	1.48908	−	4.58293i	0.0502541	−	0.154666i
$879$	−1.84961	+	5.69250i	−0.0623857	+	0.192003i
$880$		0			0
$881$	13.7424	+	42.2948i	0.462994	+	1.42495i	0.861488	+	0.507777i	$0.169533\pi$
$881$	13.7424	+	42.2948i	0.462994	+	1.42495i	−0.398495	+	0.917171i	$0.630467\pi$
$882$	−0.0887311			−0.00298773
$883$	0.234287	+	0.721061i	0.00788439	+	0.0242656i	0.954921	−	0.296859i	$-0.0959391\pi$
$883$	0.234287	+	0.721061i	0.00788439	+	0.0242656i	−0.947037	+	0.321125i	$0.895939\pi$
$884$	−13.7951	−	10.0227i	−0.463978	−	0.337100i
$885$		0			0
$886$	−2.69255	+	1.95625i	−0.0904580	+	0.0657216i
$887$	44.8758	+	32.6041i	1.50678	+	1.09474i	0.967581	+	0.252562i	$0.0812733\pi$
$887$	44.8758	+	32.6041i	1.50678	+	1.09474i	0.539200	+	0.842178i	$0.318727\pi$
$888$	0.0237076	+	0.0172246i	0.000795575	+	0.000578019i
$889$	−1.87789	+	1.36437i	−0.0629825	+	0.0457595i
$890$		0			0
$891$	−38.1301	−	27.7031i	−1.27741	−	0.928090i
$892$	−11.4523	−	35.2467i	−0.383453	−	1.18015i
$893$	14.0721			0.470905
$894$	−2.21607	−	6.82037i	−0.0741166	−	0.228107i
$895$		0			0
$896$	9.63392	−	29.6502i	0.321847	−	0.990542i
$897$	−14.1308	+	43.4903i	−0.471815	+	1.45210i
$898$	−5.00895	+	3.63922i	−0.167151	+	0.121442i
$899$	7.70312			0.256914
$900$		0			0
$901$	4.40584			0.146780
$902$	13.6636	−	9.92719i	0.454948	−	0.330539i
$903$	4.22262	−	12.9959i	0.140520	−	0.432476i
$904$	7.29386	−	22.4482i	0.242590	−	0.746616i
$905$		0			0
$906$	0.373458	+	1.14938i	0.0124073	+	0.0381857i
$907$	−15.8193			−0.525271			−0.262636	−	0.964895i	$-0.584592\pi$
$907$	−15.8193			−0.525271			−0.262636	+	0.964895i	$0.584592\pi$
$908$	0.785164	+	2.41649i	0.0260566	+	0.0801939i
$909$	0.0671565	+	0.0487920i	0.00222744	+	0.00161833i
$910$		0			0
$911$	6.49164	−	4.71646i	0.215078	−	0.156263i	−0.475030	−	0.879969i	$-0.657563\pi$
$911$	6.49164	−	4.71646i	0.215078	−	0.156263i	0.690108	+	0.723706i	$0.257563\pi$
$912$	9.47644	+	6.88504i	0.313796	+	0.227986i
$913$	26.1072	+	18.9680i	0.864023	+	0.627750i
$914$	−8.04652	+	5.84614i	−0.266155	+	0.193373i
$915$		0			0
$916$	−34.2635	−	24.8939i	−1.13210	−	0.822518i
$917$	−7.46025	−	22.9603i	−0.246359	−	0.758215i
$918$	4.38348			0.144676
$919$	7.05800	+	21.7223i	0.232822	+	0.716552i	0.997403	+	0.0720245i	$0.0229460\pi$
$919$	7.05800	+	21.7223i	0.232822	+	0.716552i	−0.764581	+	0.644528i	$0.777054\pi$
$920$		0			0
$921$	−4.73198	+	14.5635i	−0.155924	+	0.479885i
$922$	0.239274	−	0.736411i	0.00788008	−	0.0242524i
$923$	−6.66284	+	4.84084i	−0.219310	+	0.159338i
$924$	−59.3939			−1.95392
$925$		0			0
$926$	−0.104881			−0.00344661
$927$	−0.681979	+	0.495487i	−0.0223991	+	0.0162739i
$928$	5.34297	−	16.4440i	0.175392	−	0.539800i
$929$	−12.2766	+	37.7834i	−0.402781	+	1.23963i	0.519953	+	0.854195i	$0.325950\pi$
$929$	−12.2766	+	37.7834i	−0.402781	+	1.23963i	−0.922734	+	0.385438i	$0.874050\pi$
$930$		0			0
$931$	−2.95751	−	9.10227i	−0.0969284	−	0.298315i
$932$	34.7694			1.13891
$933$	−14.3705	−	44.2279i	−0.470470	−	1.44796i
$934$	3.38553	+	2.45973i	0.110778	+	0.0804849i
$935$		0			0
$936$	−0.208295	+	0.151335i	−0.00680832	+	0.00494654i
$937$	24.6238	+	17.8903i	0.804426	+	0.584449i	0.912209	−	0.409725i	$-0.134375\pi$
$937$	24.6238	+	17.8903i	0.804426	+	0.584449i	−0.107784	+	0.994174i	$0.534375\pi$
$938$	−3.72770	−	2.70833i	−0.121714	−	0.0884301i
$939$	−27.9044	+	20.2737i	−0.910624	+	0.661607i
$940$		0			0
$941$	−20.7203	−	15.0542i	−0.675461	−	0.490752i	0.196387	−	0.980526i	$-0.437079\pi$
$941$	−20.7203	−	15.0542i	−0.675461	−	0.490752i	−0.871849	+	0.489775i	$0.837079\pi$
$942$	2.72752	+	8.39444i	0.0888674	+	0.273506i
$943$	−73.2659			−2.38587
$944$	−0.0231066	−	0.0711147i	−0.000752055	−	0.00231459i
$945$		0			0
$946$	1.25466	−	3.86144i	0.0407924	−	0.125546i
$947$	17.9459	−	55.2318i	0.583163	−	1.79479i	−0.0233616	−	0.999727i	$-0.507437\pi$
$947$	17.9459	−	55.2318i	0.583163	−	1.79479i	0.606525	−	0.795065i	$-0.292563\pi$
$948$	1.12144	−	0.814777i	0.0364228	−	0.0264627i
$949$	−5.33005			−0.173021
$950$		0			0
$951$	−16.6047			−0.538446
$952$	9.01384	−	6.54894i	0.292140	−	0.212252i
$953$	14.0979	−	43.3888i	0.456675	−	1.40550i	−0.412483	−	0.910965i	$-0.635339\pi$
$953$	14.0979	−	43.3888i	0.456675	−	1.40550i	0.869158	−	0.494535i	$-0.164661\pi$
$954$	0.00999675	−	0.0307668i	0.000323657	−	0.000996113i
$955$		0			0
$956$	7.02269	+	21.6136i	0.227130	+	0.699034i
$957$	−43.4527			−1.40463
$958$	−2.05423	−	6.32226i	−0.0663691	−	0.204263i
$959$	30.2461	+	21.9751i	0.976698	+	0.709612i
$960$		0			0
$961$	22.9453	−	16.6707i	0.740171	−	0.537766i
$962$	−0.0124997	−	0.00908158i	−0.000403007	−	0.000292802i
$963$	−0.568107	−	0.412754i	−0.0183070	−	0.0133008i
$964$	15.4958	−	11.2583i	0.499085	−	0.362606i
$965$		0			0
$966$	−11.7550	−	8.54052i	−0.378212	−	0.274787i
$967$	13.1162	+	40.3675i	0.421788	+	1.29813i	0.906036	+	0.423200i	$0.139093\pi$
$967$	13.1162	+	40.3675i	0.421788	+	1.29813i	−0.484248	+	0.874931i	$0.660907\pi$
$968$	−22.2971			−0.716655
$969$	2.74673	+	8.45356i	0.0882376	+	0.271567i
$970$		0			0
$971$	−4.46009	+	13.7268i	−0.143131	+	0.440512i	−0.996766	−	0.0803596i	$-0.974393\pi$
$971$	−4.46009	+	13.7268i	−0.143131	+	0.440512i	0.853635	+	0.520872i	$0.174393\pi$
$972$	−0.349420	+	1.07541i	−0.0112077	+	0.0344936i
$973$	54.0462	−	39.2668i	1.73264	−	1.25884i
$974$	−5.06198			−0.162196
$975$		0			0
$976$	13.2057			0.422705
$977$	13.4093	−	9.74244i	0.429002	−	0.311688i	−0.352248	−	0.935907i	$-0.614583\pi$
$977$	13.4093	−	9.74244i	0.429002	−	0.311688i	0.781250	+	0.624219i	$0.214583\pi$
$978$	−1.28036	+	3.94054i	−0.0409414	+	0.126005i
$979$	10.0575	−	30.9538i	0.321439	−	0.989286i
$980$		0			0
$981$	0.272675	+	0.839207i	0.00870584	+	0.0267938i
$982$	−8.98845			−0.286833
$983$	−10.2956	−	31.6867i	−0.328380	−	1.01065i	−0.969892	−	0.243537i	$-0.921692\pi$
$983$	−10.2956	−	31.6867i	−0.328380	−	1.01065i	0.641512	−	0.767113i	$-0.278308\pi$
$984$	17.0846	+	12.4127i	0.544636	+	0.395701i
$985$		0			0
$986$	3.20685	−	2.32992i	0.102127	−	0.0741996i
$987$	−33.0086	−	23.9822i	−1.05068	−	0.763361i
$988$	−10.9255	−	7.93781i	−0.347585	−	0.252535i
$989$	−14.2493	+	10.3527i	−0.453102	+	0.329198i
$990$		0			0
$991$	19.8178	+	14.3985i	0.629534	+	0.457383i	0.856239	−	0.516580i	$-0.172795\pi$
$991$	19.8178	+	14.3985i	0.629534	+	0.457383i	−0.226705	+	0.973963i	$0.572795\pi$
$992$	1.82978	+	5.63148i	0.0580956	+	0.178800i
$993$	33.7516			1.07107
$994$	−0.808656	−	2.48879i	−0.0256490	−	0.0789396i
$995$		0			0
$996$	−6.06342	+	18.6613i	−0.192127	+	0.591305i
$997$	18.4970	−	56.9279i	0.585806	−	1.80292i	−0.0102041	−	0.999948i	$-0.503248\pi$
$997$	18.4970	−	56.9279i	0.585806	−	1.80292i	0.596010	−	0.802977i	$-0.296752\pi$
$998$	−1.29806	+	0.943097i	−0.0410894	+	0.0298532i
$999$	−0.0704313			−0.00222835

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	625.2.d.p.251.2		16
5.2	odd	4		625.2.e.k.374.4		32
5.3	odd	4		625.2.e.k.374.5		32
5.4	even	2		625.2.d.n.251.3		16
25.2	odd	20		625.2.e.j.499.4		32
25.3	odd	20		625.2.b.d.624.8		16
25.4	even	10		625.2.a.g.1.3	yes	8
25.6	even	5		625.2.d.q.501.3		16
25.8	odd	20		625.2.e.j.124.4		32
25.9	even	10		625.2.d.n.376.3		16
25.11	even	5		625.2.d.q.126.3		16
25.12	odd	20		625.2.e.k.249.5		32
25.13	odd	20		625.2.e.k.249.4		32
25.14	even	10		625.2.d.m.126.2		16
25.16	even	5	inner	625.2.d.p.376.2		16
25.17	odd	20		625.2.e.j.124.5		32
25.19	even	10		625.2.d.m.501.2		16
25.21	even	5		625.2.a.e.1.6	✓	8
25.22	odd	20		625.2.b.d.624.9		16
25.23	odd	20		625.2.e.j.499.5		32
75.29	odd	10		5625.2.a.s.1.6		8
75.71	odd	10		5625.2.a.be.1.3		8
100.71	odd	10		10000.2.a.bn.1.2		8
100.79	odd	10		10000.2.a.be.1.7		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
625.2.a.e.1.6	✓	8	25.21	even	5
625.2.a.g.1.3	yes	8	25.4	even	10
625.2.b.d.624.8		16	25.3	odd	20
625.2.b.d.624.9		16	25.22	odd	20
625.2.d.m.126.2		16	25.14	even	10
625.2.d.m.501.2		16	25.19	even	10
625.2.d.n.251.3		16	5.4	even	2
625.2.d.n.376.3		16	25.9	even	10
625.2.d.p.251.2		16	1.1	even	1	trivial
625.2.d.p.376.2		16	25.16	even	5	inner
625.2.d.q.126.3		16	25.11	even	5
625.2.d.q.501.3		16	25.6	even	5
625.2.e.j.124.4		32	25.8	odd	20
625.2.e.j.124.5		32	25.17	odd	20
625.2.e.j.499.4		32	25.2	odd	20
625.2.e.j.499.5		32	25.23	odd	20
625.2.e.k.249.4		32	25.13	odd	20
625.2.e.k.249.5		32	25.12	odd	20
625.2.e.k.374.4		32	5.2	odd	4
625.2.e.k.374.5		32	5.3	odd	4
5625.2.a.s.1.6		8	75.29	odd	10
5625.2.a.be.1.3		8	75.71	odd	10
10000.2.a.be.1.7		8	100.79	odd	10
10000.2.a.bn.1.2		8	100.71	odd	10

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:	\( N \)	\(=\)	\( 625 = 5^{4} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	625.d (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.264347 + 0.192059i) q^{2} +(0.530081 - 1.63142i) q^{3} +(-0.585041 + 1.80057i) q^{4} +(0.173205 + 0.533069i) q^{6} -3.42409 q^{7} +(-0.393106 - 1.20986i) q^{8} +(0.0465016 + 0.0337854i) q^{9} +O(q^{10})\)	\(q+(-0.264347 + 0.192059i) q^{2} +(0.530081 - 1.63142i) q^{3} +(-0.585041 + 1.80057i) q^{4} +(0.173205 + 0.533069i) q^{6} -3.42409 q^{7} +(-0.393106 - 1.20986i) q^{8} +(0.0465016 + 0.0337854i) q^{9} +(4.32105 - 3.13943i) q^{11} +(2.62737 + 1.90890i) q^{12} +(-2.84866 - 2.06967i) q^{13} +(0.905150 - 0.657630i) q^{14} +(-2.72704 - 1.98131i) q^{16} +(-0.790426 - 2.43268i) q^{17} -0.0187814 q^{18} +(-0.626004 - 1.92664i) q^{19} +(-1.81505 + 5.58614i) q^{21} +(-0.539301 + 1.65980i) q^{22} +(6.12492 - 4.45002i) q^{23} -2.18216 q^{24} +1.15054 q^{26} +(4.24308 - 3.08278i) q^{27} +(2.00324 - 6.16533i) q^{28} +(1.46557 - 4.51057i) q^{29} +(0.501908 + 1.54471i) q^{31} +3.64565 q^{32} +(-2.83122 - 8.71361i) q^{33} +(0.676166 + 0.491264i) q^{34} +(-0.0880383 + 0.0639636i) q^{36} +(-0.0108643 - 0.00789335i) q^{37} +(0.535512 + 0.389072i) q^{38} +(-4.88653 + 3.55027i) q^{39} +(-7.82918 - 5.68823i) q^{41} +(-0.593069 - 1.82528i) q^{42} -2.32645 q^{43} +(3.12477 + 9.61706i) q^{44} +(-0.764438 + 2.35270i) q^{46} +(-2.14658 + 6.60649i) q^{47} +(-4.67790 + 3.39869i) q^{48} +4.72443 q^{49} -4.38772 q^{51} +(5.39318 - 3.91837i) q^{52} +(-0.532270 + 1.63816i) q^{53} +(-0.529569 + 1.62985i) q^{54} +(1.34603 + 4.14266i) q^{56} -3.47500 q^{57} +(0.478878 + 1.47384i) q^{58} +(0.0179464 + 0.0130388i) q^{59} +(-3.16947 + 2.30275i) q^{61} +(-0.429355 - 0.311944i) q^{62} +(-0.159226 - 0.115684i) q^{63} +(4.49035 - 3.26243i) q^{64} +(2.42196 + 1.75965i) q^{66} +(-1.27263 - 3.91676i) q^{67} +4.84265 q^{68} +(-4.01315 - 12.3512i) q^{69} +(0.722772 - 2.22446i) q^{71} +(0.0225954 - 0.0695415i) q^{72} +(1.22463 - 0.889748i) q^{73} +0.00438793 q^{74} +3.83530 q^{76} +(-14.7957 + 10.7497i) q^{77} +(0.609877 - 1.87701i) q^{78} +(0.131898 - 0.405940i) q^{79} +(-2.72685 - 8.39237i) q^{81} +3.16210 q^{82} +(1.86704 + 5.74616i) q^{83} +(-8.99637 - 6.53625i) q^{84} +(0.614990 - 0.446817i) q^{86} +(-6.58177 - 4.78194i) q^{87} +(-5.49689 - 3.99372i) q^{88} +(4.92984 - 3.58174i) q^{89} +(9.75408 + 7.08676i) q^{91} +(4.42924 + 13.6318i) q^{92} +2.78613 q^{93} +(-0.701397 - 2.15868i) q^{94} +(1.93249 - 5.94759i) q^{96} +(4.94484 - 15.2186i) q^{97} +(-1.24889 + 0.907371i) q^{98} +0.307002 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9}+O(q^{10}) \) 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9	\( 16 q + 5 q^{3} - 8 q^{4} - 3 q^{6} - 20 q^{7} + 10 q^{8} + 3 q^{9} + 2 q^{11} + 25 q^{12} + 5 q^{13} + 9 q^{14} - 14 q^{16} - 10 q^{17} + 10 q^{18} + 7 q^{21} - 40 q^{22} + 15 q^{23} + 10 q^{24} + 22 q^{26} + 20 q^{27} + 30 q^{28} - 10 q^{29} + 17 q^{31} - 60 q^{32} + 5 q^{33} - q^{34} - 4 q^{36} - 15 q^{37} - 15 q^{38} - 9 q^{39} + 12 q^{41} - 45 q^{42} + 49 q^{44} - 33 q^{46} + 25 q^{47} - 20 q^{48} - 8 q^{49} - 28 q^{51} + 20 q^{52} - 30 q^{54} - 35 q^{56} + 20 q^{57} + 5 q^{58} + 20 q^{59} - 23 q^{61} + 15 q^{62} + 10 q^{63} - 28 q^{64} - 26 q^{66} - 80 q^{68} + 6 q^{69} + 22 q^{71} + 5 q^{72} + 40 q^{73} - 36 q^{74} - 20 q^{76} - 40 q^{77} - 25 q^{78} + 75 q^{79} + 11 q^{81} + 90 q^{82} + 25 q^{83} - 31 q^{84} + 17 q^{86} - 20 q^{87} + 5 q^{89} + 22 q^{91} + 60 q^{92} + 80 q^{93} - 51 q^{94} - 28 q^{96} + 40 q^{97} + 15 q^{98} - 44 q^{99}+O(q^{100}) \) 16 * q + 5 * q^3 - 8 * q^4 - 3 * q^6 - 20 * q^7 + 10 * q^8 + 3 * q^9 + 2 * q^11 + 25 * q^12 + 5 * q^13 + 9 * q^14 - 14 * q^16 - 10 * q^17 + 10 * q^18 + 7 * q^21 - 40 * q^22 + 15 * q^23 + 10 * q^24 + 22 * q^26 + 20 * q^27 + 30 * q^28 - 10 * q^29 + 17 * q^31 - 60 * q^32 + 5 * q^33 - q^34 - 4 * q^36 - 15 * q^37 - 15 * q^38 - 9 * q^39 + 12 * q^41 - 45 * q^42 + 49 * q^44 - 33 * q^46 + 25 * q^47 - 20 * q^48 - 8 * q^49 - 28 * q^51 + 20 * q^52 - 30 * q^54 - 35 * q^56 + 20 * q^57 + 5 * q^58 + 20 * q^59 - 23 * q^61 + 15 * q^62 + 10 * q^63 - 28 * q^64 - 26 * q^66 - 80 * q^68 + 6 * q^69 + 22 * q^71 + 5 * q^72 + 40 * q^73 - 36 * q^74 - 20 * q^76 - 40 * q^77 - 25 * q^78 + 75 * q^79 + 11 * q^81 + 90 * q^82 + 25 * q^83 - 31 * q^84 + 17 * q^86 - 20 * q^87 + 5 * q^89 + 22 * q^91 + 60 * q^92 + 80 * q^93 - 51 * q^94 - 28 * q^96 + 40 * q^97 + 15 * q^98 - 44 * q^99

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