LMFDB - Embedded newform 375.2.g.c.76.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(76,375)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(375, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 2]))

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

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

chi := DirichletCharacter("375.76");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.g (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:	$2.99439007580$
Analytic rank:	$0$
Dimension:	$12$
Relative dimension:	$3$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} + 3x^{10} - 2x^{9} + 34x^{8} - 22x^{7} + 236x^{6} - 179x^{5} + 877x^{4} - 409x^{3} + 96x^{2} - 11x + 1 $ x^12 + 3x^10 - 2x^9 + 34x^8 - 22x^7 + 236x^6 - 179x^5 + 877x^4 - 409x^3 + 96x^2 - 11x + 1
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 5 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			76.2
Root			$0.0437845 + 0.134755i$ of defining polynomial
Character	$\chi$	$=$	375.76
Dual form			375.2.g.c.301.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.114629 - 0.0832830i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.611830 - 1.88302i) q^{4} +(0.0437845 - 0.134755i) q^{6} +0.858311 q^{7} +(-0.174259 + 0.536314i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.114629 - 0.0832830i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.611830 - 1.88302i) q^{4} +(0.0437845 - 0.134755i) q^{6} +0.858311 q^{7} +(-0.174259 + 0.536314i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(2.97713 + 2.16301i) q^{11} +(1.60179 - 1.16377i) q^{12} +(3.70638 - 2.69285i) q^{13} +(-0.0983875 - 0.0714827i) q^{14} +(-3.13894 + 2.28058i) q^{16} +(1.63996 - 5.04728i) q^{17} +0.141689 q^{18} +(1.96804 - 6.05699i) q^{19} +(0.265233 + 0.816302i) q^{21} +(-0.161124 - 0.495888i) q^{22} +(2.76990 + 2.01245i) q^{23} -0.563913 q^{24} -0.649128 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.525140 - 1.61622i) q^{28} +(1.15388 + 3.55129i) q^{29} +(0.387167 - 1.19158i) q^{31} +1.67757 q^{32} +(-1.13716 + 3.49982i) q^{33} +(-0.608340 + 0.441985i) q^{34} +(1.60179 + 1.16377i) q^{36} +(-6.02772 + 4.37939i) q^{37} +(-0.730039 + 0.530404i) q^{38} +(3.70638 + 2.69285i) q^{39} +(2.04817 - 1.48808i) q^{41} +(0.0375807 - 0.115661i) q^{42} +3.37972 q^{43} +(2.25149 - 6.92938i) q^{44} +(-0.149909 - 0.461371i) q^{46} +(2.62645 + 8.08338i) q^{47} +(-3.13894 - 2.28058i) q^{48} -6.26330 q^{49} +5.30702 q^{51} +(-7.33836 - 5.33163i) q^{52} +(0.725656 + 2.23334i) q^{53} +(0.0437845 + 0.134755i) q^{54} +(-0.149568 + 0.460324i) q^{56} +6.36870 q^{57} +(0.163493 - 0.503181i) q^{58} +(-10.6195 + 7.71550i) q^{59} +(-8.37141 - 6.08218i) q^{61} +(-0.143619 + 0.104345i) q^{62} +(-0.694388 + 0.504502i) q^{63} +(6.08559 + 4.42144i) q^{64} +(0.421827 - 0.306475i) q^{66} +(-1.03412 + 3.18270i) q^{67} -10.5075 q^{68} +(-1.05801 + 3.25621i) q^{69} +(-1.33585 - 4.11131i) q^{71} +(-0.174259 - 0.536314i) q^{72} +(-7.34593 - 5.33713i) q^{73} +1.05568 q^{74} -12.6095 q^{76} +(2.55530 + 1.85653i) q^{77} +(-0.200592 - 0.617357i) q^{78} +(-1.00347 - 3.08837i) q^{79} +(0.309017 - 0.951057i) q^{81} -0.358712 q^{82} +(2.28447 - 7.03087i) q^{83} +(1.37484 - 0.998876i) q^{84} +(-0.387414 - 0.281473i) q^{86} +(-3.02091 + 2.19482i) q^{87} +(-1.67884 + 1.21975i) q^{88} +(12.5378 + 9.10921i) q^{89} +(3.18123 - 2.31130i) q^{91} +(2.09478 - 6.44705i) q^{92} +1.25290 q^{93} +(0.372140 - 1.14533i) q^{94} +(0.518399 + 1.59547i) q^{96} +(3.10209 + 9.54725i) q^{97} +(0.717957 + 0.521627i) q^{98} -3.67993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	$ 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) $ 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/375\mathbb{Z}\right)^\times$.

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{1}{5}\right)$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$	−0.114629	−	0.0832830i	−0.0810551	−	0.0588900i	0.546520	−	0.837446i	$-0.315952\pi$
$2$	−0.114629	−	0.0832830i	−0.0810551	−	0.0588900i	−0.627575	+	0.778556i	$0.715952\pi$
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$3$	0.309017	+	0.951057i	0.178411	+	0.549093i
$4$	−0.611830	−	1.88302i	−0.305915	−	0.941510i
$5$		0			0
$5$		0			0
$6$	0.0437845	−	0.134755i	0.0178749	−	0.0550134i
$7$	0.858311			0.324411			0.162205	−	0.986757i	$-0.448139\pi$
$7$	0.858311			0.324411			0.162205	+	0.986757i	$0.448139\pi$
$8$	−0.174259	+	0.536314i	−0.0616098	+	0.189615i
$9$	−0.809017	+	0.587785i	−0.269672	+	0.195928i
$10$		0			0
$11$	2.97713	+	2.16301i	0.897637	+	0.652171i	0.937858	−	0.347019i	$-0.112806\pi$
$11$	2.97713	+	2.16301i	0.897637	+	0.652171i	−0.0402210	+	0.999191i	$0.512806\pi$
$12$	1.60179	−	1.16377i	0.462398	−	0.335952i
$13$	3.70638	−	2.69285i	1.02797	−	0.746861i	0.0600653	−	0.998194i	$-0.480869\pi$
$13$	3.70638	−	2.69285i	1.02797	−	0.746861i	0.967901	+	0.251334i	$0.0808691\pi$
$14$	−0.0983875	−	0.0714827i	−0.0262952	−	0.0191045i
$15$		0			0
$16$	−3.13894	+	2.28058i	−0.784736	+	0.570144i
$17$	1.63996	−	5.04728i	0.397749	−	1.22414i	−0.529052	−	0.848590i	$-0.677452\pi$
$17$	1.63996	−	5.04728i	0.397749	−	1.22414i	0.926800	−	0.375555i	$-0.122548\pi$
$18$	0.141689			0.0333965
$19$	1.96804	−	6.05699i	0.451499	−	1.38957i	−0.423699	−	0.905803i	$-0.639268\pi$
$19$	1.96804	−	6.05699i	0.451499	−	1.38957i	0.875197	−	0.483766i	$-0.160732\pi$
$20$		0			0
$21$	0.265233	+	0.816302i	0.0578785	+	0.178132i
$22$	−0.161124	−	0.495888i	−0.0343517	−	0.105724i
$23$	2.76990	+	2.01245i	0.577564	+	0.419625i	0.837845	−	0.545908i	$-0.183815\pi$
$23$	2.76990	+	2.01245i	0.577564	+	0.419625i	−0.260281	+	0.965533i	$0.583815\pi$
$24$	−0.563913			−0.115108
$25$		0			0
$26$	−0.649128			−0.127304
$27$	−0.809017	−	0.587785i	−0.155695	−	0.113119i
$28$	−0.525140	−	1.61622i	−0.0992422	−	0.305436i
$29$	1.15388	+	3.55129i	0.214271	+	0.659458i	0.999205	+	0.0398784i	$0.0126971\pi$
$29$	1.15388	+	3.55129i	0.214271	+	0.659458i	−0.784934	+	0.619580i	$0.787303\pi$
$30$		0			0
$31$	0.387167	−	1.19158i	0.0695373	−	0.214014i	−0.910249	−	0.414062i	$-0.864110\pi$
$31$	0.387167	−	1.19158i	0.0695373	−	0.214014i	0.979786	+	0.200048i	$0.0641098\pi$
$32$	1.67757			0.296556
$33$	−1.13716	+	3.49982i	−0.197954	+	0.609241i
$34$	−0.608340	+	0.441985i	−0.104329	+	0.0757997i
$35$		0			0
$36$	1.60179	+	1.16377i	0.266965	+	0.193962i
$37$	−6.02772	+	4.37939i	−0.990951	+	0.719968i	−0.960129	−	0.279557i	$-0.909812\pi$
$37$	−6.02772	+	4.37939i	−0.990951	+	0.719968i	−0.0308218	+	0.999525i	$0.509812\pi$
$38$	−0.730039	+	0.530404i	−0.118428	+	0.0860430i
$39$	3.70638	+	2.69285i	0.593496	+	0.431200i
$40$		0			0
$41$	2.04817	−	1.48808i	0.319870	−	0.232399i	−0.416250	−	0.909250i	$-0.636656\pi$
$41$	2.04817	−	1.48808i	0.319870	−	0.232399i	0.736120	+	0.676851i	$0.236656\pi$
$42$	0.0375807	−	0.115661i	0.00579882	−	0.0178469i
$43$	3.37972			0.515402			0.257701	−	0.966225i	$-0.417035\pi$
$43$	3.37972			0.515402			0.257701	+	0.966225i	$0.417035\pi$
$44$	2.25149	−	6.92938i	0.339425	−	1.04464i
$45$		0			0
$46$	−0.149909	−	0.461371i	−0.0221028	−	0.0680255i
$47$	2.62645	+	8.08338i	0.383107	+	1.17908i	0.937844	+	0.347057i	$0.112819\pi$
$47$	2.62645	+	8.08338i	0.383107	+	1.17908i	−0.554737	+	0.832026i	$0.687181\pi$
$48$	−3.13894	−	2.28058i	−0.453067	−	0.329173i
$49$	−6.26330			−0.894758
$50$		0			0
$51$	5.30702			0.743132
$52$	−7.33836	−	5.33163i	−1.01765	−	0.739364i
$53$	0.725656	+	2.23334i	0.0996765	+	0.306773i	0.988444	−	0.151585i	$-0.0484378\pi$
$53$	0.725656	+	2.23334i	0.0996765	+	0.306773i	−0.888768	+	0.458358i	$0.848438\pi$
$54$	0.0437845	+	0.134755i	0.00595831	+	0.0183378i
$55$		0			0
$56$	−0.149568	+	0.460324i	−0.0199869	+	0.0615133i
$57$	6.36870			0.843555
$58$	0.163493	−	0.503181i	0.0214677	−	0.0660709i
$59$	−10.6195	+	7.71550i	−1.38254	+	1.00447i	−0.385900	+	0.922541i	$0.626109\pi$
$59$	−10.6195	+	7.71550i	−1.38254	+	1.00447i	−0.996638	+	0.0819317i	$0.973891\pi$
$60$		0			0
$61$	−8.37141	−	6.08218i	−1.07185	−	0.778744i	−0.0956052	−	0.995419i	$-0.530479\pi$
$61$	−8.37141	−	6.08218i	−1.07185	−	0.778744i	−0.976244	+	0.216676i	$0.930479\pi$
$62$	−0.143619	+	0.104345i	−0.0182396	+	0.0132519i
$63$	−0.694388	+	0.504502i	−0.0874846	+	0.0635613i
$64$	6.08559	+	4.42144i	0.760698	+	0.552680i
$65$		0			0
$66$	0.421827	−	0.306475i	0.0519234	−	0.0377245i
$67$	−1.03412	+	3.18270i	−0.126338	+	0.388828i	−0.994142	−	0.108077i	$-0.965531\pi$
$67$	−1.03412	+	3.18270i	−0.126338	+	0.388828i	0.867805	+	0.496906i	$0.165531\pi$
$68$	−10.5075			−1.27422
$69$	−1.05801	+	3.25621i	−0.127369	+	0.392002i
$70$		0			0
$71$	−1.33585	−	4.11131i	−0.158536	−	0.487923i	0.839966	−	0.542639i	$-0.182575\pi$
$71$	−1.33585	−	4.11131i	−0.158536	−	0.487923i	−0.998502	+	0.0547158i	$0.982575\pi$
$72$	−0.174259	−	0.536314i	−0.0205366	−	0.0632052i
$73$	−7.34593	−	5.33713i	−0.859776	−	0.624664i	0.0680477	−	0.997682i	$-0.478323\pi$
$73$	−7.34593	−	5.33713i	−0.859776	−	0.624664i	−0.927824	+	0.373018i	$0.878323\pi$
$74$	1.05568			0.122721
$75$		0			0
$76$	−12.6095			−1.44641
$77$	2.55530	+	1.85653i	0.291203	+	0.211572i
$78$	−0.200592	−	0.617357i	−0.0227125	−	0.0699020i
$79$	−1.00347	−	3.08837i	−0.112899	−	0.347469i	0.878604	−	0.477552i	$-0.158476\pi$
$79$	−1.00347	−	3.08837i	−0.112899	−	0.347469i	−0.991503	+	0.130083i	$0.958476\pi$
$80$		0			0
$81$	0.309017	−	0.951057i	0.0343352	−	0.105673i
$82$	−0.358712			−0.0396131
$83$	2.28447	−	7.03087i	0.250753	−	0.771738i	−0.743884	−	0.668309i	$-0.767019\pi$
$83$	2.28447	−	7.03087i	0.250753	−	0.771738i	0.994637	−	0.103429i	$-0.0329815\pi$
$84$	1.37484	−	0.998876i	0.150007	−	0.108986i
$85$		0			0
$86$	−0.387414	−	0.281473i	−0.0417760	−	0.0303520i
$87$	−3.02091	+	2.19482i	−0.323875	+	0.235309i
$88$	−1.67884	+	1.21975i	−0.178965	+	0.130026i
$89$	12.5378	+	9.10921i	1.32900	+	0.965575i	0.999773	+	0.0213236i	$0.00678803\pi$
$89$	12.5378	+	9.10921i	1.32900	+	0.965575i	0.329227	+	0.944251i	$0.393212\pi$
$90$		0			0
$91$	3.18123	−	2.31130i	0.333483	−	0.242290i
$92$	2.09478	−	6.44705i	0.218395	−	0.672152i
$93$	1.25290			0.129920
$94$	0.372140	−	1.14533i	0.0383833	−	0.118132i
$95$		0			0
$96$	0.518399	+	1.59547i	0.0529089	+	0.162837i
$97$	3.10209	+	9.54725i	0.314970	+	0.969377i	0.975767	+	0.218812i	$0.0702182\pi$
$97$	3.10209	+	9.54725i	0.314970	+	0.969377i	−0.660797	+	0.750564i	$0.729782\pi$
$98$	0.717957	+	0.521627i	0.0725247	+	0.0526922i
$99$	−3.67993			−0.369847
$100$		0			0
$101$	−0.714616			−0.0711070			−0.0355535	−	0.999368i	$-0.511319\pi$
$101$	−0.714616			−0.0711070			−0.0355535	+	0.999368i	$0.511319\pi$
$102$	−0.608340	−	0.441985i	−0.0602346	−	0.0437630i
$103$	−0.241269	−	0.742551i	−0.0237730	−	0.0731657i	0.938466	−	0.345371i	$-0.112247\pi$
$103$	−0.241269	−	0.742551i	−0.0237730	−	0.0731657i	−0.962239	+	0.272205i	$0.912247\pi$
$104$	0.798339	+	2.45704i	0.0782836	+	0.240932i
$105$		0			0
$106$	0.102818	−	0.316441i	0.00998655	−	0.0307354i
$107$	−11.9601			−1.15623			−0.578113	−	0.815957i	$-0.696211\pi$
$107$	−11.9601			−1.15623			−0.578113	+	0.815957i	$0.696211\pi$
$108$	−0.611830	+	1.88302i	−0.0588734	+	0.181194i
$109$	−1.96902	+	1.43057i	−0.188598	+	0.137024i	−0.678078	−	0.734990i	$-0.737187\pi$
$109$	−1.96902	+	1.43057i	−0.188598	+	0.137024i	0.489480	+	0.872015i	$0.337187\pi$
$110$		0			0
$111$	−6.02772	−	4.37939i	−0.572126	−	0.415674i
$112$	−2.69419	+	1.95744i	−0.254577	+	0.184961i
$113$	−12.9729	+	9.42535i	−1.22039	+	0.886662i	−0.996132	−	0.0878685i	$-0.971994\pi$
$113$	−12.9729	+	9.42535i	−1.22039	+	0.886662i	−0.224254	+	0.974531i	$0.571994\pi$
$114$	−0.730039	−	0.530404i	−0.0683744	−	0.0496769i
$115$		0			0
$116$	5.98117	−	4.34558i	0.555338	−	0.403477i
$117$	−1.41571	+	4.35712i	−0.130883	+	0.402815i
$118$	1.85987			0.171215
$119$	1.40759	−	4.33213i	0.129034	−	0.397126i
$120$		0			0
$121$	0.785483	+	2.41747i	0.0714076	+	0.219770i
$122$	0.453065	+	1.39439i	0.0410186	+	0.126242i
$123$	2.04817	+	1.48808i	0.184677	+	0.134176i
$124$	−2.48065			−0.222769
$125$		0			0
$126$	0.121614			0.0108342
$127$	−3.10539	−	2.25620i	−0.275559	−	0.200205i	0.441419	−	0.897301i	$-0.354475\pi$
$127$	−3.10539	−	2.25620i	−0.275559	−	0.200205i	−0.716978	+	0.697096i	$0.754475\pi$
$128$	−1.36615	−	4.20459i	−0.120752	−	0.371637i
$129$	1.04439	+	3.21430i	0.0919534	+	0.283004i
$130$		0			0
$131$	−3.84709	+	11.8401i	−0.336122	+	1.03448i	0.630044	+	0.776559i	$0.283037\pi$
$131$	−3.84709	+	11.8401i	−0.336122	+	1.03448i	−0.966167	+	0.257919i	$0.916963\pi$
$132$	7.28598			0.634163
$133$	1.68919	−	5.19878i	0.146471	−	0.450791i
$134$	0.383605	−	0.278705i	0.0331384	−	0.0240765i
$135$		0			0
$136$	2.42115	+	1.75907i	0.207611	+	0.150839i
$137$	−9.59406	+	6.97049i	−0.819676	+	0.595529i	−0.916620	−	0.399761i	$-0.869093\pi$
$137$	−9.59406	+	6.97049i	−0.819676	+	0.595529i	0.0969439	+	0.995290i	$0.469093\pi$
$138$	0.392466	−	0.285143i	0.0334089	−	0.0242730i
$139$	3.77074	+	2.73960i	0.319830	+	0.232370i	0.736103	−	0.676870i	$-0.236664\pi$
$139$	3.77074	+	2.73960i	0.319830	+	0.232370i	−0.416273	+	0.909240i	$0.636664\pi$
$140$		0			0
$141$	−6.87614	+	4.99580i	−0.579075	+	0.420723i
$142$	−0.189275	+	0.582530i	−0.0158836	+	0.0488848i
$143$	16.8590			1.40982
$144$	1.19897	−	3.69005i	0.0999141	−	0.307504i
$145$		0			0
$146$	0.397566	+	1.22358i	0.0329028	+	0.101264i
$147$	−1.93547	−	5.95676i	−0.159635	−	0.491305i
$148$	11.9344	+	8.67087i	0.981004	+	0.712741i
$149$	−11.5480			−0.946053			−0.473026	−	0.881048i	$-0.656838\pi$
$149$	−11.5480			−0.946053			−0.473026	+	0.881048i	$0.656838\pi$
$150$		0			0
$151$	24.4694			1.99129			0.995646	−	0.0932103i	$-0.0297129\pi$
$151$	24.4694			1.99129			0.995646	+	0.0932103i	$0.0297129\pi$
$152$	2.90550	+	2.11097i	0.235667	+	0.171222i
$153$	1.63996	+	5.04728i	0.132583	+	0.408048i
$154$	−0.138294	−	0.425626i	−0.0111441	−	0.0342979i
$155$		0			0
$156$	2.80300	−	8.62676i	0.224420	−	0.690693i
$157$	22.3660			1.78500			0.892501	−	0.451045i	$-0.148948\pi$
$157$	22.3660			1.78500			0.892501	+	0.451045i	$0.148948\pi$
$158$	−0.142181	+	0.437589i	−0.0113113	+	0.0348127i
$159$	−1.89979	+	1.38028i	−0.150663	+	0.109463i
$160$		0			0
$161$	2.37743	+	1.72731i	0.187368	+	0.136131i
$162$	−0.114629	+	0.0832830i	−0.00900612	+	0.00654333i
$163$	−0.658095	+	0.478134i	−0.0515460	+	0.0374503i	−0.613260	−	0.789881i	$-0.710142\pi$
$163$	−0.658095	+	0.478134i	−0.0515460	+	0.0374503i	0.561714	+	0.827332i	$0.310142\pi$
$164$	−4.05522	−	2.94629i	−0.316659	−	0.230067i
$165$		0			0
$166$	−0.847418	+	0.615685i	−0.0657724	+	0.0477865i
$167$	7.77671	−	23.9343i	0.601780	−	1.85209i	0.0842082	−	0.996448i	$-0.473164\pi$
$167$	7.77671	−	23.9343i	0.601780	−	1.85209i	0.517572	−	0.855640i	$-0.326836\pi$
$168$	−0.484013			−0.0373424
$169$	2.46864	−	7.59770i	0.189896	−	0.584438i
$170$		0			0
$171$	1.96804	+	6.05699i	0.150500	+	0.463190i
$172$	−2.06781	−	6.36408i	−0.157669	−	0.485256i
$173$	0.332462	+	0.241548i	0.0252766	+	0.0183645i	0.600352	−	0.799736i	$-0.295027\pi$
$173$	0.332462	+	0.241548i	0.0252766	+	0.0183645i	−0.575075	+	0.818101i	$0.695027\pi$
$174$	0.529076			0.0401091
$175$		0			0
$176$	−14.2779			−1.07624
$177$	−10.6195	−	7.71550i	−0.798208	−	0.579932i
$178$	−0.678550	−	2.08836i	−0.0508595	−	0.156529i
$179$	−4.58896	−	14.1234i	−0.342995	−	1.05563i	−0.962648	−	0.270755i	$-0.912727\pi$
$179$	−4.58896	−	14.1234i	−0.342995	−	1.05563i	0.619653	−	0.784876i	$-0.287273\pi$
$180$		0			0
$181$	0.228432	−	0.703043i	0.0169792	−	0.0522568i	−0.942208	−	0.335029i	$-0.891254\pi$
$181$	0.228432	−	0.703043i	0.0169792	−	0.0522568i	0.959187	+	0.282772i	$0.0912540\pi$
$182$	−0.557153			−0.0412990
$183$	3.19759	−	9.84118i	0.236373	−	0.727481i
$184$	−1.56198	+	1.13485i	−0.115151	+	0.0836621i
$185$		0			0
$186$	−0.143619	−	0.104345i	−0.0105307	−	0.00765097i
$187$	15.7997	−	11.4791i	1.15539	−	0.839437i
$188$	13.6142	−	9.89131i	0.992920	−	0.721398i
$189$	−0.694388	−	0.504502i	−0.0505093	−	0.0366971i
$190$		0			0
$191$	2.20462	−	1.60175i	0.159521	−	0.115899i	−0.505161	−	0.863025i	$-0.668567\pi$
$191$	2.20462	−	1.60175i	0.159521	−	0.115899i	0.664682	+	0.747126i	$0.268567\pi$
$192$	−2.32449	+	7.15404i	−0.167755	+	0.516298i
$193$	−14.2040			−1.02243			−0.511215	−	0.859453i	$-0.670804\pi$
$193$	−14.2040			−1.02243			−0.511215	+	0.859453i	$0.670804\pi$
$194$	0.439534	−	1.35275i	0.0315567	−	0.0971215i
$195$		0			0
$196$	3.83208	+	11.7939i	0.273720	+	0.842423i
$197$	1.71378	+	5.27447i	0.122102	+	0.375791i	0.993362	−	0.115031i	$-0.0366967\pi$
$197$	1.71378	+	5.27447i	0.122102	+	0.375791i	−0.871260	+	0.490821i	$0.836697\pi$
$198$	0.421827	+	0.306475i	0.0299780	+	0.0217803i
$199$	5.96371			0.422756			0.211378	−	0.977404i	$-0.432205\pi$
$199$	5.96371			0.422756			0.211378	+	0.977404i	$0.432205\pi$
$200$		0			0
$201$	−3.34649			−0.236043
$202$	0.0819159	+	0.0595154i	0.00576358	+	0.00418749i
$203$	0.990391	+	3.04811i	0.0695119	+	0.213935i
$204$	−3.24700	−	9.99322i	−0.227335	−	0.699666i
$205$		0			0
$206$	−0.0341853	+	0.105212i	−0.00238181	+	0.00733044i
$207$	−3.42379			−0.237970
$208$	−5.49289	+	16.9054i	−0.380863	+	1.17218i
$209$	18.9604	−	13.7755i	1.31152	−	0.952875i
$210$		0			0
$211$	11.0983	+	8.06342i	0.764042	+	0.555109i	0.900147	−	0.435586i	$-0.143459\pi$
$211$	11.0983	+	8.06342i	0.764042	+	0.555109i	−0.136106	+	0.990694i	$0.543459\pi$
$212$	3.76144	−	2.73285i	0.258337	−	0.187693i
$213$	3.49729	−	2.54093i	0.239630	−	0.174102i
$214$	1.37098	+	0.996073i	0.0937180	+	0.0680901i
$215$		0			0
$216$	0.456216	−	0.331460i	0.0310415	−	0.0225530i
$217$	0.332310	−	1.02274i	0.0225587	−	0.0694284i
$218$	0.344849			0.0233561
$219$	2.80590	−	8.63566i	0.189605	−	0.583544i
$220$		0			0
$221$	−7.51322	−	23.1233i	−0.505394	−	1.55544i
$222$	0.326224	+	1.00401i	0.0218947	+	0.0673849i
$223$	2.62259	+	1.90543i	0.175622	+	0.127597i	0.672124	−	0.740439i	$-0.265382\pi$
$223$	2.62259	+	1.90543i	0.175622	+	0.127597i	−0.496502	+	0.868036i	$0.665382\pi$
$224$	1.43988			0.0962060
$225$		0			0
$226$	2.27204			0.151134
$227$	10.6627	+	7.74694i	0.707711	+	0.514182i	0.882434	−	0.470435i	$-0.155903\pi$
$227$	10.6627	+	7.74694i	0.707711	+	0.514182i	−0.174723	+	0.984618i	$0.555903\pi$
$228$	−3.89656	−	11.9924i	−0.258056	−	0.794215i
$229$	1.80407	+	5.55236i	0.119216	+	0.366911i	0.992803	−	0.119758i	$-0.0382119\pi$
$229$	1.80407	+	5.55236i	0.119216	+	0.366911i	−0.873587	+	0.486669i	$0.838212\pi$
$230$		0			0
$231$	−0.976037	+	3.00393i	−0.0642185	+	0.197644i
$232$	−2.10568			−0.138245
$233$	−2.88453	+	8.87767i	−0.188972	+	0.581595i	−0.999994	−	0.00341975i	$-0.998911\pi$
$233$	−2.88453	+	8.87767i	−0.188972	+	0.581595i	0.811022	+	0.585015i	$0.198911\pi$
$234$	0.525156	−	0.381548i	0.0343305	−	0.0249426i
$235$		0			0
$236$	21.0258	+	15.2761i	1.36866	+	0.994390i
$237$	2.62712	−	1.90872i	0.170650	−	0.123984i
$238$	−0.522144	+	0.379360i	−0.0338456	+	0.0245903i
$239$	−13.8748	−	10.0806i	−0.897485	−	0.652061i	0.0403340	−	0.999186i	$-0.487158\pi$
$239$	−13.8748	−	10.0806i	−0.897485	−	0.652061i	−0.937819	+	0.347125i	$0.887158\pi$
$240$		0			0
$241$	−5.84169	+	4.24424i	−0.376296	+	0.273395i	−0.759817	−	0.650137i	$-0.774711\pi$
$241$	−5.84169	+	4.24424i	−0.376296	+	0.273395i	0.383521	+	0.923532i	$0.374711\pi$
$242$	0.111295	−	0.342530i	0.00715430	−	0.0220187i
$243$	1.00000			0.0641500
$244$	−6.33099	+	19.4848i	−0.405300	+	1.24739i
$245$		0			0
$246$	−0.110848	−	0.341155i	−0.00706742	−	0.0217513i
$247$	−9.01625	−	27.7492i	−0.573690	−	1.76564i
$248$	0.571593	+	0.415286i	0.0362962	+	0.0263707i
$249$	7.39269			0.468493
$250$		0			0
$251$	−5.75708			−0.363383			−0.181692	−	0.983356i	$-0.558157\pi$
$251$	−5.75708			−0.363383			−0.181692	+	0.983356i	$0.558157\pi$
$252$	1.37484	+	0.998876i	0.0866065	+	0.0629233i
$253$	3.89339	+	11.9826i	0.244776	+	0.753342i
$254$	0.168066	+	0.517253i	0.0105454	+	0.0324553i
$255$		0			0
$256$	4.45541	−	13.7123i	0.278463	−	0.857021i
$257$	−26.9602			−1.68173			−0.840867	−	0.541242i	$-0.817954\pi$
$257$	−26.9602			−1.68173			−0.840867	+	0.541242i	$0.817954\pi$
$258$	0.147979	−	0.455433i	0.00921278	−	0.0283540i
$259$	−5.17365	+	3.75888i	−0.321475	+	0.233565i
$260$		0			0
$261$	−3.02091	−	2.19482i	−0.186990	−	0.135856i
$262$	1.42707	−	1.03683i	0.0881648	−	0.0640555i
$263$	16.7202	−	12.1479i	1.03101	−	0.749073i	0.0625002	−	0.998045i	$-0.480093\pi$
$263$	16.7202	−	12.1479i	1.03101	−	0.749073i	0.968511	+	0.248972i	$0.0800926\pi$
$264$	−1.67884	−	1.21975i	−0.103326	−	0.0750704i
$265$		0			0
$266$	−0.626600	+	0.455252i	−0.0384193	+	0.0279133i
$267$	−4.78900	+	14.7390i	−0.293082	+	0.902013i
$268$	6.62579			0.404734
$269$	−4.24699	+	13.0709i	−0.258943	+	0.796946i	0.734084	+	0.679059i	$0.237612\pi$
$269$	−4.24699	+	13.0709i	−0.258943	+	0.796946i	−0.993027	+	0.117887i	$0.962388\pi$
$270$		0			0
$271$	1.03333	+	3.18025i	0.0627701	+	0.193187i	0.977524	−	0.210826i	$-0.0676153\pi$
$271$	1.03333	+	3.18025i	0.0627701	+	0.193187i	−0.914754	+	0.404012i	$0.867615\pi$
$272$	6.36296	+	19.5832i	0.385811	+	1.18740i
$273$	3.18123	+	2.31130i	0.192537	+	0.139886i
$274$	1.68028			0.101510
$275$		0			0
$276$	6.77883			0.408038
$277$	7.20791	+	5.23685i	0.433081	+	0.314652i	0.782880	−	0.622173i	$-0.213750\pi$
$277$	7.20791	+	5.23685i	0.433081	+	0.314652i	−0.349799	+	0.936825i	$0.613750\pi$
$278$	−0.204075	−	0.628077i	−0.0122396	−	0.0376696i
$279$	0.387167	+	1.19158i	0.0231791	+	0.0713380i
$280$		0			0
$281$	−6.95019	+	21.3905i	−0.414613	+	1.27605i	0.497983	+	0.867187i	$0.334074\pi$
$281$	−6.95019	+	21.3905i	−0.414613	+	1.27605i	−0.912596	+	0.408862i	$0.865926\pi$
$282$	1.20427			0.0717133
$283$	−0.403866	+	1.24297i	−0.0240073	+	0.0738870i	−0.962342	−	0.271840i	$-0.912368\pi$
$283$	−0.403866	+	1.24297i	−0.0240073	+	0.0738870i	0.938335	+	0.345727i	$0.112368\pi$
$284$	−6.92437	+	5.03085i	−0.410886	+	0.298526i
$285$		0			0
$286$	−1.93254	−	1.40407i	−0.114273	−	0.0830243i
$287$	1.75797	−	1.27724i	0.103769	−	0.0753929i
$288$	−1.35719	+	0.986054i	−0.0799730	+	0.0581038i
$289$	−9.03225	−	6.56231i	−0.531309	−	0.386018i
$290$		0			0
$291$	−8.12138	+	5.90053i	−0.476084	+	0.345895i
$292$	−5.55546	+	17.0980i	−0.325109	+	1.00058i
$293$	−1.97058			−0.115123			−0.0575613	−	0.998342i	$-0.518332\pi$
$293$	−1.97058			−0.115123			−0.0575613	+	0.998342i	$0.518332\pi$
$294$	−0.274235	+	0.844010i	−0.0159937	+	0.0492236i
$295$		0			0
$296$	−1.29835	−	3.99590i	−0.0754648	−	0.232257i
$297$	−1.13716	−	3.49982i	−0.0659847	−	0.203080i
$298$	1.32374	+	0.961756i	0.0766824	+	0.0557130i
$299$	15.6855			0.907118
$300$		0			0
$301$	2.90085			0.167202
$302$	−2.80491	−	2.03789i	−0.161404	−	0.117267i
$303$	−0.220829	−	0.679640i	−0.0126863	−	0.0390443i
$304$	7.63588	+	23.5008i	0.437948	+	1.34786i
$305$		0			0
$306$	0.232365	−	0.715146i	0.0132834	−	0.0408822i
$307$	15.2544			0.870617			0.435308	−	0.900281i	$-0.356639\pi$
$307$	15.2544			0.870617			0.435308	+	0.900281i	$0.356639\pi$
$308$	1.93248	−	5.94756i	0.110113	−	0.338894i
$309$	0.631652	−	0.458922i	0.0359334	−	0.0261071i
$310$		0			0
$311$	−14.3562	−	10.4304i	−0.814065	−	0.591453i	0.100941	−	0.994892i	$-0.467815\pi$
$311$	−14.3562	−	10.4304i	−0.814065	−	0.591453i	−0.915006	+	0.403439i	$0.867815\pi$
$312$	−2.09008	+	1.51853i	−0.118327	+	0.0859699i
$313$	−22.1565	+	16.0976i	−1.25236	+	0.909890i	−0.998356	−	0.0573136i	$-0.981747\pi$
$313$	−22.1565	+	16.0976i	−1.25236	+	0.909890i	−0.254001	+	0.967204i	$0.581747\pi$
$314$	−2.56380	−	1.86271i	−0.144684	−	0.105119i
$315$		0			0
$316$	−5.20150	+	3.77911i	−0.292607	+	0.212592i
$317$	−2.67165	+	8.22248i	−0.150055	+	0.461821i	−0.997626	−	0.0688603i	$-0.978064\pi$
$317$	−2.67165	+	8.22248i	−0.150055	+	0.461821i	0.847572	+	0.530681i	$0.178064\pi$
$318$	0.332725			0.0186583
$319$	−4.24621	+	13.0685i	−0.237742	+	0.731696i
$320$		0			0
$321$	−3.69587	−	11.3747i	−0.206283	−	0.634875i
$322$	−0.128668	−	0.396000i	−0.00717039	−	0.0220682i
$323$	−27.3438	−	19.8664i	−1.52145	−	1.10540i
$324$	−1.97992			−0.109996
$325$		0			0
$326$	0.115257			0.00638351
$327$	−1.96902	−	1.43057i	−0.108887	−	0.0791109i
$328$	0.441167	+	1.35777i	0.0243594	+	0.0749704i
$329$	2.25431	+	6.93805i	0.124284	+	0.382507i
$330$		0			0
$331$	1.53353	−	4.71971i	0.0842903	−	0.259419i	−0.900025	−	0.435839i	$-0.856452\pi$
$331$	1.53353	−	4.71971i	0.0842903	−	0.259419i	0.984315	+	0.176420i	$0.0564517\pi$
$332$	−14.6370			−0.803308
$333$	2.30238	−	7.08601i	0.126170	−	0.388311i
$334$	−2.88475	+	2.09590i	−0.157847	+	0.114682i
$335$		0			0
$336$	−2.69419	−	1.95744i	−0.146980	−	0.106787i
$337$	−5.91011	+	4.29394i	−0.321944	+	0.233906i	−0.737005	−	0.675888i	$-0.763760\pi$
$337$	−5.91011	+	4.29394i	−0.321944	+	0.233906i	0.415061	+	0.909794i	$0.363760\pi$
$338$	−0.915738	+	0.665322i	−0.0498096	+	0.0361888i
$339$	−12.9729	−	9.42535i	−0.704590	−	0.511915i
$340$		0			0
$341$	3.73004	−	2.71003i	0.201993	−	0.146757i
$342$	0.278850	−	0.858212i	0.0150785	−	0.0464068i
$343$	−11.3840			−0.614680
$344$	−0.588946	+	1.81259i	−0.0317538	+	0.0977282i
$345$		0			0
$346$	−0.0179930	−	0.0553768i	−0.000967311	−	0.00297708i
$347$	−4.92493	−	15.1574i	−0.264384	−	0.813691i	−0.991835	−	0.127531i	$-0.959295\pi$
$347$	−4.92493	−	15.1574i	−0.264384	−	0.813691i	0.727450	−	0.686160i	$-0.240705\pi$
$348$	5.98117	+	4.34558i	0.320624	+	0.232947i
$349$	16.5844			0.887743			0.443871	−	0.896091i	$-0.353605\pi$
$349$	16.5844			0.887743			0.443871	+	0.896091i	$0.353605\pi$
$350$		0			0
$351$	−4.58134			−0.244534
$352$	4.99435	+	3.62861i	0.266200	+	0.193405i
$353$	−4.00768	−	12.3344i	−0.213307	−	0.656492i	−0.999269	−	0.0382177i	$-0.987832\pi$
$353$	−4.00768	−	12.3344i	−0.213307	−	0.656492i	0.785962	−	0.618275i	$-0.212168\pi$
$354$	0.574732	+	1.76884i	0.0305467	+	0.0940129i
$355$		0			0
$356$	9.48185	−	29.1821i	0.502537	−	1.54665i
$357$	4.55507			0.241080
$358$	−0.650208	+	2.00113i	−0.0343646	+	0.105763i
$359$	10.9153	−	7.93042i	0.576087	−	0.418551i	−0.261225	−	0.965278i	$-0.584126\pi$
$359$	10.9153	−	7.93042i	0.576087	−	0.418551i	0.837311	+	0.546727i	$0.184126\pi$
$360$		0			0
$361$	−17.4427	−	12.6728i	−0.918036	−	0.666992i
$362$	−0.0847365	+	0.0615647i	−0.00445365	+	0.00323577i
$363$	−2.05642	+	1.49408i	−0.107934	+	0.0784188i
$364$	−6.29859	−	4.57619i	−0.330136	−	0.239858i
$365$		0			0
$366$	−1.18614	+	0.861781i	−0.0620006	+	0.0450460i
$367$	−1.41364	+	4.35073i	−0.0737913	+	0.227106i	−0.981149	−	0.193253i	$-0.938096\pi$
$367$	−1.41364	+	4.35073i	−0.0737913	+	0.227106i	0.907358	+	0.420360i	$0.138096\pi$
$368$	−13.2841			−0.692482
$369$	−0.782331	+	2.40777i	−0.0407265	+	0.125343i
$370$		0			0
$371$	0.622838	+	1.91690i	0.0323361	+	0.0995204i
$372$	−0.766562	−	2.35924i	−0.0397444	−	0.122321i
$373$	−16.7841	−	12.1944i	−0.869048	−	0.631401i	0.0612830	−	0.998120i	$-0.480481\pi$
$373$	−16.7841	−	12.1944i	−0.869048	−	0.631401i	−0.930331	+	0.366720i	$0.880481\pi$
$374$	−2.76712			−0.143084
$375$		0			0
$376$	−4.79291			−0.247175
$377$	13.8398	+	10.0552i	0.712787	+	0.517870i
$378$	0.0375807	+	0.115661i	0.00193294	+	0.00594898i
$379$	−1.78662	−	5.49865i	−0.0917725	−	0.282447i	0.894627	−	0.446815i	$-0.147442\pi$
$379$	−1.78662	−	5.49865i	−0.0917725	−	0.282447i	−0.986399	+	0.164368i	$0.947442\pi$
$380$		0			0
$381$	1.18615	−	3.65061i	0.0607686	−	0.187026i
$382$	−0.386113			−0.0197553
$383$	−7.97647	+	24.5491i	−0.407579	+	1.25440i	0.511144	+	0.859495i	$0.329222\pi$
$383$	−7.97647	+	24.5491i	−0.407579	+	1.25440i	−0.918723	+	0.394903i	$0.870778\pi$
$384$	3.57664	−	2.59858i	0.182519	−	0.132608i
$385$		0			0
$386$	1.62820	+	1.18295i	0.0828731	+	0.0602108i
$387$	−2.73425	+	1.98655i	−0.138990	+	0.100982i
$388$	16.0797	−	11.6826i	0.816324	−	0.593094i
$389$	12.7053	+	9.23092i	0.644183	+	0.468026i	0.861285	−	0.508123i	$-0.169660\pi$
$389$	12.7053	+	9.23092i	0.644183	+	0.468026i	−0.217102	+	0.976149i	$0.569660\pi$
$390$		0			0
$391$	14.6999	−	10.6801i	0.743407	−	0.540117i
$392$	1.09144	−	3.35909i	0.0551258	−	0.169660i
$393$	−12.4495			−0.627992
$394$	0.242825	−	0.747337i	0.0122333	−	0.0376503i
$395$		0			0
$396$	2.25149	+	6.92938i	0.113142	+	0.348214i
$397$	6.05796	+	18.6445i	0.304040	+	0.935740i	0.980034	+	0.198832i	$0.0637148\pi$
$397$	6.05796	+	18.6445i	0.304040	+	0.935740i	−0.675993	+	0.736908i	$0.736285\pi$
$398$	−0.683615	−	0.496675i	−0.0342665	−	0.0248961i
$399$	5.46632			0.273658
$400$		0			0
$401$	−14.4239			−0.720297			−0.360148	−	0.932895i	$-0.617274\pi$
$401$	−14.4239			−0.720297			−0.360148	+	0.932895i	$0.617274\pi$
$402$	0.383605	+	0.278705i	0.0191325	+	0.0139006i
$403$	−1.77375	−	5.45903i	−0.0883566	−	0.271934i
$404$	0.437224	+	1.34564i	0.0217527	+	0.0669479i
$405$		0			0
$406$	0.140328	−	0.431885i	0.00696436	−	0.0214341i
$407$	−27.4179			−1.35906
$408$	−0.924795	+	2.84623i	−0.0457842	+	0.140909i
$409$	22.5507	−	16.3841i	1.11506	−	0.810140i	0.131609	−	0.991302i	$-0.457986\pi$
$409$	22.5507	−	16.3841i	1.11506	−	0.810140i	0.983453	+	0.181162i	$0.0579858\pi$
$410$		0			0
$411$	−9.59406	−	6.97049i	−0.473240	−	0.343829i
$412$	−1.25062	+	0.908630i	−0.0616137	+	0.0447650i
$413$	−9.11481	+	6.62229i	−0.448510	+	0.325862i
$414$	0.392466	+	0.285143i	0.0192886	+	0.0140140i
$415$		0			0
$416$	6.21773	−	4.51745i	0.304850	−	0.221486i
$417$	−1.44030	+	4.43277i	−0.0705316	+	0.217074i
$418$	−3.32069			−0.162420
$419$	−11.2137	+	34.5121i	−0.547823	+	1.68603i	0.166359	+	0.986065i	$0.446799\pi$
$419$	−11.2137	+	34.5121i	−0.547823	+	1.68603i	−0.714182	+	0.699960i	$0.753201\pi$
$420$		0			0
$421$	−1.04324	−	3.21077i	−0.0508445	−	0.156483i	0.922410	−	0.386211i	$-0.126216\pi$
$421$	−1.04324	−	3.21077i	−0.0508445	−	0.156483i	−0.973255	+	0.229728i	$0.926216\pi$
$422$	−0.600649	−	1.84861i	−0.0292391	−	0.0899888i
$423$	−6.87614	−	4.99580i	−0.334329	−	0.242904i
$424$	−1.32422			−0.0643099
$425$		0			0
$426$	−0.612508			−0.0296761
$427$	−7.18527	−	5.22040i	−0.347719	−	0.252633i
$428$	7.31755	+	22.5211i	0.353707	+	1.08860i
$429$	5.20972	+	16.0339i	0.251528	+	0.774123i
$430$		0			0
$431$	−7.93015	+	24.4065i	−0.381982	+	1.17562i	0.556665	+	0.830737i	$0.312081\pi$
$431$	−7.93015	+	24.4065i	−0.381982	+	1.17562i	−0.938646	+	0.344881i	$0.887919\pi$
$432$	3.87995			0.186674
$433$	12.3010	−	37.8587i	0.591150	−	1.81937i	0.0181229	−	0.999836i	$-0.494231\pi$
$433$	12.3010	−	37.8587i	0.591150	−	1.81937i	0.573027	−	0.819536i	$-0.305769\pi$
$434$	−0.123270	+	0.0895606i	−0.00591713	+	0.00429905i
$435$		0			0
$436$	3.89850	+	2.83243i	0.186704	+	0.135649i
$437$	17.6407	−	12.8167i	0.843867	−	0.613106i
$438$	−1.04084	+	0.756216i	−0.0497333	+	0.0361334i
$439$	−27.4402	−	19.9365i	−1.30965	−	0.951516i	−1.00000		0.000665125i	$-0.999788\pi$
$439$	−27.4402	−	19.9365i	−1.30965	−	0.951516i	−0.309649	−	0.950851i	$-0.600212\pi$
$440$		0			0
$441$	5.06712	−	3.68148i	0.241291	−	0.175308i
$442$	−1.06454	+	3.27633i	−0.0506352	+	0.155839i
$443$	28.9300			1.37451			0.687253	−	0.726418i	$-0.258816\pi$
$443$	28.9300			1.37451			0.687253	+	0.726418i	$0.258816\pi$
$444$	−4.55855	+	14.0298i	−0.216339	+	0.665823i
$445$		0			0
$446$	−0.141936	−	0.436835i	−0.00672088	−	0.0206847i
$447$	−3.56854	−	10.9828i	−0.168786	−	0.519471i
$448$	5.22332	+	3.79497i	0.246779	+	0.179295i
$449$	−10.2089			−0.481788			−0.240894	−	0.970551i	$-0.577441\pi$
$449$	−10.2089			−0.481788			−0.240894	+	0.970551i	$0.577441\pi$
$450$		0			0
$451$	9.31639			0.438692
$452$	25.6853	+	18.6615i	1.20814	+	0.877762i
$453$	7.56147	+	23.2718i	0.355269	+	1.09340i
$454$	−0.577074	−	1.77605i	−0.0270834	−	0.0833542i
$455$		0			0
$456$	−1.10980	+	3.41562i	−0.0519712	+	0.159951i
$457$	−32.4952			−1.52006			−0.760030	−	0.649888i	$-0.774816\pi$
$457$	−32.4952			−1.52006			−0.760030	+	0.649888i	$0.774816\pi$
$458$	0.255618	−	0.786712i	0.0119442	−	0.0367606i
$459$	−4.29347	+	3.11939i	−0.200402	+	0.145601i
$460$		0			0
$461$	0.566772	+	0.411784i	0.0263972	+	0.0191787i	0.600906	−	0.799320i	$-0.294807\pi$
$461$	0.566772	+	0.411784i	0.0263972	+	0.0191787i	−0.574508	+	0.818499i	$0.694807\pi$
$462$	0.362059	−	0.263051i	0.0168445	−	0.0122382i
$463$	1.75659	−	1.27623i	0.0816355	−	0.0593117i	−0.546219	−	0.837642i	$-0.683933\pi$
$463$	1.75659	−	1.27623i	0.0816355	−	0.0593117i	0.627854	+	0.778331i	$0.283933\pi$
$464$	−11.7210	−	8.51578i	−0.544132	−	0.395335i
$465$		0			0
$466$	1.07001	−	0.777408i	0.0495673	−	0.0360127i
$467$	1.19809	−	3.68734i	0.0554410	−	0.170630i	−0.919502	−	0.393086i	$-0.871407\pi$
$467$	1.19809	−	3.68734i	0.0554410	−	0.170630i	0.974943	+	0.222456i	$0.0714075\pi$
$468$	9.07071			0.419294
$469$	−0.887597	+	2.73174i	−0.0409854	+	0.126140i
$470$		0			0
$471$	6.91148	+	21.2714i	0.318464	+	0.980132i
$472$	−2.28739	−	7.03986i	−0.105286	−	0.324036i
$473$	10.0618	+	7.31036i	0.462644	+	0.336131i
$474$	−0.460109			−0.0211335
$475$		0			0
$476$	−9.01870			−0.413371
$477$	−1.89979	−	1.38028i	−0.0869855	−	0.0631986i
$478$	0.750911	+	2.31107i	0.0343459	+	0.105706i
$479$	−6.79817	−	20.9226i	−0.310617	−	0.955979i	−0.977521	−	0.210836i	$-0.932381\pi$
$479$	−6.79817	−	20.9226i	−0.310617	−	0.955979i	0.666905	−	0.745143i	$-0.267619\pi$
$480$		0			0
$481$	−10.5480	+	32.4634i	−0.480948	+	1.48020i
$482$	1.02310			0.0466010
$483$	−0.908099	+	2.79484i	−0.0413199	+	0.127170i
$484$	4.07156	−	2.95816i	0.185071	−	0.134462i
$485$		0			0
$486$	−0.114629	−	0.0832830i	−0.00519969	−	0.00377779i
$487$	22.9759	−	16.6929i	1.04114	−	0.756430i	0.0706291	−	0.997503i	$-0.477499\pi$
$487$	22.9759	−	16.6929i	1.04114	−	0.756430i	0.970507	+	0.241073i	$0.0774993\pi$
$488$	4.72075	−	3.42982i	0.213698	−	0.155261i
$489$	−0.658095	−	0.478134i	−0.0297601	−	0.0216220i
$490$		0			0
$491$	11.3641	−	8.25653i	0.512856	−	0.372612i	−0.301050	−	0.953608i	$-0.597337\pi$
$491$	11.3641	−	8.25653i	0.512856	−	0.372612i	0.813906	+	0.580997i	$0.197337\pi$
$492$	1.54896	−	4.76720i	0.0698323	−	0.214922i
$493$	19.8167			0.892498
$494$	−1.27751	+	3.93176i	−0.0574778	+	0.176898i
$495$		0			0
$496$	1.50219	+	4.62326i	0.0674503	+	0.207591i
$497$	−1.14657	−	3.52878i	−0.0514307	−	0.158287i
$498$	−0.847418	−	0.615685i	−0.0379737	−	0.0275895i
$499$	13.0842			0.585731			0.292866	−	0.956154i	$-0.405391\pi$
$499$	13.0842			0.585731			0.292866	+	0.956154i	$0.405391\pi$
$500$		0			0
$501$	25.1660			1.12433
$502$	0.659929	+	0.479467i	0.0294541	+	0.0213996i
$503$	−3.80226	−	11.7022i	−0.169534	−	0.521773i	0.829807	−	0.558050i	$-0.188450\pi$
$503$	−3.80226	−	11.7022i	−0.169534	−	0.521773i	−0.999342	+	0.0362767i	$0.988450\pi$
$504$	−0.149568	−	0.460324i	−0.00666230	−	0.0205044i
$505$		0			0
$506$	0.551653	−	1.69781i	0.0245240	−	0.0754770i
$507$	7.98869			0.354790
$508$	−2.34850	+	7.22793i	−0.104198	+	0.320688i
$509$	−0.0634186	+	0.0460763i	−0.00281098	+	0.00204230i	−0.589190	−	0.807995i	$-0.700553\pi$
$509$	−0.0634186	+	0.0460763i	−0.00281098	+	0.00204230i	0.586379	+	0.810037i	$0.300553\pi$
$510$		0			0
$511$	−6.30509	−	4.58092i	−0.278921	−	0.202648i
$512$	−8.80600	+	6.39793i	−0.389174	+	0.282751i
$513$	−5.15239	+	3.74343i	−0.227483	+	0.165276i
$514$	3.09043	+	2.24533i	0.136313	+	0.0990372i
$515$		0			0
$516$	5.41361	−	3.93321i	0.238321	−	0.173150i
$517$	−9.66515	+	29.7463i	−0.425073	+	1.30824i
$518$	0.906103			0.0398119
$519$	−0.126989	+	0.390832i	−0.00557420	+	0.0171556i
$520$		0			0
$521$	5.59919	+	17.2325i	0.245305	+	0.754971i	0.995586	+	0.0938524i	$0.0299182\pi$
$521$	5.59919	+	17.2325i	0.245305	+	0.754971i	−0.750281	+	0.661119i	$0.770082\pi$
$522$	0.163493	+	0.503181i	0.00715591	+	0.0220236i
$523$	9.40913	+	6.83613i	0.411432	+	0.298923i	0.774181	−	0.632964i	$-0.218162\pi$
$523$	9.40913	+	6.83613i	0.411432	+	0.298923i	−0.362749	+	0.931887i	$0.618162\pi$
$524$	24.6490			1.07680
$525$		0			0
$526$	−2.92834			−0.127682
$527$	−5.37929	−	3.90828i	−0.234326	−	0.170247i
$528$	−4.41212	−	13.5791i	−0.192013	−	0.590955i
$529$	−3.48500	−	10.7257i	−0.151522	−	0.466336i
$530$		0			0
$531$	4.05628	−	12.4839i	0.176027	−	0.541757i
$532$	−10.8229			−0.469232
$533$	3.58413	−	11.0308i	0.155246	−	0.477797i
$534$	1.77647	−	1.29068i	0.0768753	−	0.0558532i
$535$		0			0
$536$	−1.52672	−	1.10923i	−0.0659442	−	0.0479113i
$537$	12.0141	−	8.72873i	0.518445	−	0.376672i
$538$	1.57541	−	1.14460i	0.0679208	−	0.0493473i
$539$	−18.6466	−	13.5476i	−0.803167	−	0.583535i
$540$		0			0
$541$	−23.6812	+	17.2054i	−1.01814	+	0.739719i	−0.965900	−	0.258916i	$-0.916635\pi$
$541$	−23.6812	+	17.2054i	−1.01814	+	0.739719i	−0.0522359	+	0.998635i	$0.516635\pi$
$542$	0.146412	−	0.450608i	0.00628891	−	0.0193553i
$543$	0.739223			0.0317231
$544$	2.75115	−	8.46718i	0.117955	−	0.363027i
$545$		0			0
$546$	−0.172170	−	0.529884i	−0.00736819	−	0.0226770i
$547$	−3.72908	−	11.4769i	−0.159444	−	0.490717i	0.839140	−	0.543915i	$-0.183059\pi$
$547$	−3.72908	−	11.4769i	−0.159444	−	0.490717i	−0.998584	+	0.0531977i	$0.983059\pi$
$548$	18.9955	+	13.8010i	0.811448	+	0.589551i
$549$	10.3476			0.441626
$550$		0			0
$551$	23.7810			1.01311
$552$	−1.56198	−	1.13485i	−0.0664825	−	0.0483023i
$553$	−0.861290	−	2.65078i	−0.0366258	−	0.112723i
$554$	−0.390096	−	1.20059i	−0.0165736	−	0.0510083i
$555$		0			0
$556$	2.85168	−	8.77655i	0.120938	−	0.372209i
$557$	41.4154			1.75483			0.877413	−	0.479737i	$-0.159268\pi$
$557$	41.4154			1.75483			0.877413	+	0.479737i	$0.159268\pi$
$558$	0.0548576	−	0.168834i	0.00232231	−	0.00714732i
$559$	12.5265	−	9.10106i	0.529816	−	0.384934i
$560$		0			0
$561$	15.7997	+	11.4791i	0.667062	+	0.484649i
$562$	2.57816	−	1.87314i	0.108753	−	0.0790137i
$563$	−26.0072	+	18.8954i	−1.09607	+	0.796345i	−0.980415	−	0.196944i	$-0.936898\pi$
$563$	−26.0072	+	18.8954i	−1.09607	+	0.796345i	−0.115660	+	0.993289i	$0.536898\pi$
$564$	13.6142	+	9.89131i	0.573262	+	0.416499i
$565$		0			0
$566$	0.149813	−	0.108846i	0.00629712	−	0.00457513i
$567$	0.265233	−	0.816302i	0.0111387	−	0.0342815i
$568$	2.43773			0.102285
$569$	6.52273	−	20.0749i	0.273447	−	0.841583i	−0.716179	−	0.697916i	$-0.754111\pi$
$569$	6.52273	−	20.0749i	0.273447	−	0.841583i	0.989626	−	0.143667i	$-0.0458893\pi$
$570$		0			0
$571$	−7.64795	−	23.5380i	−0.320057	−	0.985034i	−0.973623	−	0.228164i	$-0.926728\pi$
$571$	−7.64795	−	23.5380i	−0.320057	−	0.985034i	0.653566	−	0.756870i	$-0.273272\pi$
$572$	−10.3149	−	31.7459i	−0.431286	−	1.32736i
$573$	2.20462	+	1.60175i	0.0920994	+	0.0669142i
$574$	−0.307886			−0.0128509
$575$		0			0
$576$	−7.52220			−0.313425
$577$	−15.1861	−	11.0333i	−0.632205	−	0.459324i	0.224959	−	0.974368i	$-0.427775\pi$
$577$	−15.1861	−	11.0333i	−0.632205	−	0.459324i	−0.857163	+	0.515045i	$0.827775\pi$
$578$	0.488830	+	1.50446i	0.0203327	+	0.0625775i
$579$	−4.38929	−	13.5088i	−0.182413	−	0.561408i
$580$		0			0
$581$	1.96078	−	6.03467i	0.0813470	−	0.250360i
$582$	1.42236			0.0589587
$583$	−2.67036	+	8.21853i	−0.110595	+	0.340377i
$584$	4.14247	−	3.00968i	0.171417	−	0.124541i
$585$		0			0
$586$	0.225886	+	0.164116i	0.00933127	+	0.00677956i
$587$	11.9388	−	8.67406i	0.492768	−	0.358017i	−0.313480	−	0.949595i	$-0.601495\pi$
$587$	11.9388	−	8.67406i	0.492768	−	0.358017i	0.806248	+	0.591578i	$0.201495\pi$
$588$	−10.0325	+	7.28905i	−0.413734	+	0.300595i
$589$	−6.45543	−	4.69014i	−0.265991	−	0.193254i
$590$		0			0
$591$	−4.48673	+	3.25980i	−0.184560	+	0.134090i
$592$	8.93313	−	27.4933i	0.367149	−	1.12997i
$593$	−8.01859			−0.329284			−0.164642	−	0.986353i	$-0.552647\pi$
$593$	−8.01859			−0.329284			−0.164642	+	0.986353i	$0.552647\pi$
$594$	−0.161124	+	0.495888i	−0.00661099	+	0.0203465i
$595$		0			0
$596$	7.06544	+	21.7452i	0.289412	+	0.890718i
$597$	1.84289	+	5.67182i	0.0754243	+	0.232132i
$598$	−1.79802	−	1.30634i	−0.0735265	−	0.0534201i
$599$	−1.28951			−0.0526878			−0.0263439	−	0.999653i	$-0.508386\pi$
$599$	−1.28951			−0.0526878			−0.0263439	+	0.999653i	$0.508386\pi$
$600$		0			0
$601$	−16.8813			−0.688603			−0.344302	−	0.938859i	$-0.611884\pi$
$601$	−16.8813			−0.688603			−0.344302	+	0.938859i	$0.611884\pi$
$602$	−0.332522	−	0.241591i	−0.0135526	−	0.00984652i
$603$	−1.03412	−	3.18270i	−0.0421127	−	0.129609i
$604$	−14.9711	−	46.0764i	−0.609167	−	1.87482i
$605$		0			0
$606$	−0.0312891	+	0.0962979i	−0.00127103	+	0.00391184i
$607$	0.499318			0.0202667			0.0101334	−	0.999949i	$-0.496774\pi$
$607$	0.499318			0.0202667			0.0101334	+	0.999949i	$0.496774\pi$
$608$	3.30153	−	10.1611i	0.133895	−	0.412085i
$609$	−2.59288	+	1.88384i	−0.105069	+	0.0763369i
$610$		0			0
$611$	31.5019	+	22.8875i	1.27443	+	0.925929i
$612$	8.50074	−	6.17615i	0.343622	−	0.249656i
$613$	22.1866	−	16.1195i	0.896108	−	0.651061i	−0.0413552	−	0.999145i	$-0.513168\pi$
$613$	22.1866	−	16.1195i	0.896108	−	0.651061i	0.937463	+	0.348084i	$0.113168\pi$
$614$	−1.74860	−	1.27043i	−0.0705679	−	0.0512706i
$615$		0			0
$616$	−1.44097	+	1.04692i	−0.0580582	+	0.0421818i
$617$	8.75151	−	26.9344i	0.352323	−	1.08434i	−0.605223	−	0.796056i	$-0.706916\pi$
$617$	8.75151	−	26.9344i	0.352323	−	1.08434i	0.957546	−	0.288282i	$-0.0930840\pi$
$618$	−0.110626			−0.00445003
$619$	−0.114894	+	0.353606i	−0.00461796	+	0.0142126i	−0.953339	−	0.301902i	$-0.902378\pi$
$619$	−0.114894	+	0.353606i	−0.00461796	+	0.0142126i	0.948721	+	0.316115i	$0.102378\pi$
$620$		0			0
$621$	−1.05801	−	3.25621i	−0.0424564	−	0.130667i
$622$	0.776966	+	2.39125i	0.0311535	+	0.0958806i
$623$	10.7613	+	7.81853i	0.431142	+	0.313243i
$624$	−17.7754			−0.711584
$625$		0			0
$626$	3.88043			0.155093
$627$	18.9604	+	13.7755i	0.757206	+	0.550142i
$628$	−13.6842	−	42.1157i	−0.546059	−	1.68060i
$629$	12.2188	+	37.6056i	0.487195	+	1.49943i
$630$		0			0
$631$	5.08354	−	15.6455i	0.202373	−	0.622839i	−0.797438	−	0.603400i	$-0.793812\pi$
$631$	5.08354	−	15.6455i	0.202373	−	0.622839i	0.999811	−	0.0194386i	$-0.00618787\pi$
$632$	1.83120			0.0728411
$633$	−4.23919	+	13.0469i	−0.168493	+	0.518567i
$634$	0.991042	−	0.720034i	0.0393593	−	0.0285962i
$635$		0			0
$636$	3.76144	+	2.73285i	0.149151	+	0.108364i
$637$	−23.2142	+	16.8661i	−0.919780	+	0.668259i
$638$	1.57512	−	1.14439i	0.0623598	−	0.0453070i
$639$	3.49729	+	2.54093i	0.138351	+	0.100518i
$640$		0			0
$641$	1.63910	−	1.19088i	0.0647407	−	0.0470368i	−0.554944	−	0.831888i	$-0.687260\pi$
$641$	1.63910	−	1.19088i	0.0647407	−	0.0470368i	0.619685	+	0.784851i	$0.287260\pi$
$642$	−0.523666	+	1.61168i	−0.0206675	+	0.0636079i
$643$	33.2034			1.30941			0.654706	−	0.755883i	$-0.272792\pi$
$643$	33.2034			1.30941			0.654706	+	0.755883i	$0.272792\pi$
$644$	1.79797	−	5.53357i	0.0708498	−	0.218053i
$645$		0			0
$646$	1.47986	+	4.55455i	0.0582244	+	0.179196i
$647$	12.5398	+	38.5936i	0.492992	+	1.51727i	0.820064	+	0.572273i	$0.193938\pi$
$647$	12.5398	+	38.5936i	0.492992	+	1.51727i	−0.327072	+	0.944999i	$0.606062\pi$
$648$	0.456216	+	0.331460i	0.0179218	+	0.0130210i
$649$	−48.3042			−1.89611
$650$		0			0
$651$	1.07538			0.0421474
$652$	1.30298	+	0.946669i	0.0510286	+	0.0370744i
$653$	2.87297	+	8.84208i	0.112428	+	0.346017i	0.991402	−	0.130852i	$-0.0417714\pi$
$653$	2.87297	+	8.84208i	0.112428	+	0.346017i	−0.878974	+	0.476870i	$0.841771\pi$
$654$	0.106564	+	0.327971i	0.00416699	+	0.0128247i
$655$		0			0
$656$	−3.03540	+	9.34201i	−0.118513	+	0.364744i
$657$	9.08007			0.354247
$658$	0.319412	−	0.983049i	0.0124520	−	0.0383232i
$659$	2.81185	−	2.04293i	0.109534	−	0.0795811i	−0.531670	−	0.846952i	$-0.678435\pi$
$659$	2.81185	−	2.04293i	0.109534	−	0.0795811i	0.641204	+	0.767371i	$0.278435\pi$
$660$		0			0
$661$	−3.29515	−	2.39407i	−0.128166	−	0.0931184i	0.521855	−	0.853034i	$-0.325240\pi$
$661$	−3.29515	−	2.39407i	−0.128166	−	0.0931184i	−0.650022	+	0.759916i	$0.725240\pi$
$662$	−0.568859	+	0.413300i	−0.0221093	+	0.0160634i
$663$	19.6699	−	14.2910i	0.763914	−	0.555016i
$664$	3.37266	+	2.45038i	0.130885	+	0.0950932i
$665$		0			0
$666$	−0.854064	+	0.620514i	−0.0330943	+	0.0240444i
$667$	−3.95065	+	12.1589i	−0.152970	+	0.470793i
$668$	−49.8267			−1.92785
$669$	−1.00174	+	3.08304i	−0.0387296	+	0.119197i
$670$		0			0
$671$	−11.7669	−	36.2148i	−0.454257	−	1.39806i
$672$	0.444947	+	1.36941i	0.0171642	+	0.0528260i
$673$	17.3003	+	12.5694i	0.666877	+	0.484514i	0.868978	−	0.494850i	$-0.164777\pi$
$673$	17.3003	+	12.5694i	0.666877	+	0.484514i	−0.202102	+	0.979365i	$0.564777\pi$
$674$	1.03508			0.0398699
$675$		0			0
$676$	−15.8170			−0.608346
$677$	−16.4438	−	11.9472i	−0.631988	−	0.459166i	0.225100	−	0.974336i	$-0.427729\pi$
$677$	−16.4438	−	11.9472i	−0.631988	−	0.459166i	−0.857088	+	0.515169i	$0.827729\pi$
$678$	0.702100	+	2.16084i	0.0269640	+	0.0829866i
$679$	2.66256	+	8.19451i	0.102180	+	0.314476i
$680$		0			0
$681$	−4.07281	+	12.5348i	−0.156070	+	0.480335i
$682$	−0.653271			−0.0250150
$683$	5.85868	−	18.0312i	0.224176	−	0.689943i	−0.774198	−	0.632943i	$-0.781847\pi$
$683$	5.85868	−	18.0312i	0.224176	−	0.689943i	0.998374	−	0.0569998i	$-0.0181535\pi$
$684$	10.2013	−	7.41170i	0.390058	−	0.283394i
$685$		0			0
$686$	1.30494	+	0.948096i	0.0498229	+	0.0361985i
$687$	−4.72312	+	3.43155i	−0.180198	+	0.130922i
$688$	−10.6087	+	7.70770i	−0.404455	+	0.293853i
$689$	8.70359	+	6.32353i	0.331580	+	0.240907i
$690$		0			0
$691$	−11.9893	+	8.71071i	−0.456093	+	0.331371i	−0.791997	−	0.610525i	$-0.790958\pi$
$691$	−11.9893	+	8.71071i	−0.456093	+	0.331371i	0.335904	+	0.941896i	$0.390958\pi$
$692$	0.251429	−	0.773818i	0.00955789	−	0.0294162i
$693$	−3.15852			−0.119982
$694$	−0.697811	+	2.14764i	−0.0264885	+	0.0815234i
$695$		0			0
$696$	−0.650691	−	2.00262i	−0.0246644	−	0.0759092i
$697$	−4.15185	−	12.7781i	−0.157262	−	0.484004i
$698$	−1.90106	−	1.38120i	−0.0719560	−	0.0522791i
$699$	−9.33453			−0.353064
$700$		0			0
$701$	31.3996			1.18595			0.592973	−	0.805222i	$-0.297954\pi$
$701$	31.3996			1.18595			0.592973	+	0.805222i	$0.297954\pi$
$702$	0.525156	+	0.381548i	0.0198207	+	0.0144006i
$703$	14.6632	+	45.1287i	0.553033	+	1.70206i
$704$	8.55395	+	26.3264i	0.322389	+	0.992212i
$705$		0			0
$706$	−0.567846	+	1.74765i	−0.0213712	+	0.0657737i
$707$	−0.613363			−0.0230679
$708$	−8.03112	+	24.7173i	−0.301828	+	0.928931i
$709$	−20.4944	+	14.8900i	−0.769682	+	0.559207i	−0.901865	−	0.432019i	$-0.857801\pi$
$709$	−20.4944	+	14.8900i	−0.769682	+	0.559207i	0.132183	+	0.991225i	$0.457801\pi$
$710$		0			0
$711$	2.62712	+	1.90872i	0.0985248	+	0.0715825i
$712$	−7.07021	+	5.13681i	−0.264967	+	0.192510i
$713$	3.47041	−	2.52140i	0.129968	−	0.0944272i
$714$	−0.522144	−	0.379360i	−0.0195408	−	0.0141972i
$715$		0			0
$716$	−23.7869	+	17.2822i	−0.888959	+	0.645867i
$717$	5.29969	−	16.3108i	0.197921	−	0.609137i
$718$	−1.91168			−0.0713432
$719$	−1.27535	+	3.92511i	−0.0475624	+	0.146382i	−0.972017	−	0.234910i	$-0.924521\pi$
$719$	−1.27535	+	3.92511i	−0.0475624	+	0.146382i	0.924455	+	0.381292i	$0.124521\pi$
$720$		0			0
$721$	−0.207084	−	0.637339i	−0.00771221	−	0.0237358i
$722$	0.944008	+	2.90536i	0.0351323	+	0.108126i
$723$	−5.84169	−	4.24424i	−0.217255	−	0.157845i
$724$	−1.46361			−0.0543945
$725$		0			0
$726$	0.360157			0.0133667
$727$	18.6106	+	13.5214i	0.690227	+	0.501479i	0.876735	−	0.480974i	$-0.159717\pi$
$727$	18.6106	+	13.5214i	0.690227	+	0.501479i	−0.186508	+	0.982454i	$0.559717\pi$
$728$	0.685223	+	2.10890i	0.0253961	+	0.0781610i
$729$	0.309017	+	0.951057i	0.0114451	+	0.0352243i
$730$		0			0
$731$	5.54260	−	17.0584i	0.205000	−	0.630927i
$732$	−20.4875			−0.757240
$733$	2.89145	−	8.89896i	0.106798	−	0.328690i	−0.883350	−	0.468714i	$-0.844718\pi$
$733$	2.89145	−	8.89896i	0.106798	−	0.328690i	0.990148	+	0.140023i	$0.0447177\pi$
$734$	0.524386	−	0.380989i	0.0193554	−	0.0140625i
$735$		0			0
$736$	4.64671	+	3.37604i	0.171280	+	0.124442i
$737$	−9.96291	+	7.23847i	−0.366988	+	0.266633i
$738$	0.290204	−	0.210846i	0.0106826	−	0.00776133i
$739$	38.1657	+	27.7290i	1.40395	+	1.02003i	0.994168	+	0.107844i	$0.0343948\pi$
$739$	38.1657	+	27.7290i	1.40395	+	1.02003i	0.409781	+	0.912184i	$0.365605\pi$
$740$		0			0
$741$	23.6048	−	17.1499i	0.867146	−	0.630018i
$742$	0.0882496	−	0.271604i	0.00323974	−	0.00997091i
$743$	−2.39450			−0.0878455			−0.0439228	−	0.999035i	$-0.513986\pi$
$743$	−2.39450			−0.0878455			−0.0439228	+	0.999035i	$0.513986\pi$
$744$	−0.218329	+	0.671947i	−0.00800433	+	0.0246348i
$745$		0			0
$746$	0.908366	+	2.79566i	0.0332576	+	0.102356i
$747$	2.28447	+	7.03087i	0.0835843	+	0.257246i
$748$	−31.2821	−	22.7278i	−1.14379	−	0.831011i
$749$	−10.2655			−0.375092
$750$		0			0
$751$	−7.21632			−0.263327			−0.131664	−	0.991294i	$-0.542032\pi$
$751$	−7.21632			−0.263327			−0.131664	+	0.991294i	$0.542032\pi$
$752$	−26.6790	−	19.3835i	−0.972885	−	0.706842i
$753$	−1.77903	−	5.47530i	−0.0648316	−	0.199531i
$754$	−0.749019	−	2.30524i	−0.0272777	−	0.0839520i
$755$		0			0
$756$	−0.525140	+	1.61622i	−0.0190992	+	0.0587812i
$757$	−13.3742			−0.486094			−0.243047	−	0.970015i	$-0.578147\pi$
$757$	−13.3742			−0.486094			−0.243047	+	0.970015i	$0.578147\pi$
$758$	−0.253145	+	0.779101i	−0.00919465	+	0.0282982i
$759$	−10.1930	+	7.40567i	−0.369984	+	0.268809i
$760$		0			0
$761$	−17.5994	−	12.7867i	−0.637978	−	0.463518i	0.221177	−	0.975234i	$-0.429010\pi$
$761$	−17.5994	−	12.7867i	−0.637978	−	0.463518i	−0.859155	+	0.511716i	$0.829010\pi$
$762$	−0.440002	+	0.319680i	−0.0159396	+	0.0115808i
$763$	−1.69003	+	1.22788i	−0.0611831	+	0.0444521i
$764$	−4.36499	−	3.17135i	−0.157920	−	0.114735i
$765$		0			0
$766$	2.95886	−	2.14973i	0.106908	−	0.0776730i
$767$	−18.5832	+	57.1932i	−0.671000	+	2.06513i
$768$	14.4180			0.520265
$769$	4.38814	−	13.5053i	0.158240	−	0.487014i	−0.840234	−	0.542223i	$-0.817583\pi$
$769$	4.38814	−	13.5053i	0.158240	−	0.487014i	0.998475	+	0.0552094i	$0.0175826\pi$
$770$		0			0
$771$	−8.33117	−	25.6407i	−0.300040	−	0.923427i
$772$	8.69046	+	26.7465i	0.312777	+	0.962627i
$773$	18.4752	+	13.4230i	0.664505	+	0.482791i	0.868181	−	0.496247i	$-0.165289\pi$
$773$	18.4752	+	13.4230i	0.664505	+	0.482791i	−0.203676	+	0.979038i	$0.565289\pi$
$774$	0.478870			0.0172126
$775$		0			0
$776$	−5.66089			−0.203214
$777$	−5.17365	−	3.75888i	−0.185604	−	0.134849i
$778$	−0.687616	−	2.11627i	−0.0246522	−	0.0758718i
$779$	−4.98243	−	15.3343i	−0.178514	−	0.549410i
$780$		0			0
$781$	4.91582	−	15.1293i	0.175902	−	0.541370i
$782$	−2.57451			−0.0920644
$783$	1.15388	−	3.55129i	0.0412365	−	0.126913i
$784$	19.6602	−	14.2839i	0.702148	−	0.510141i
$785$		0			0
$786$	1.42707	+	1.03683i	0.0509020	+	0.0369824i
$787$	−31.1279	+	22.6157i	−1.10959	+	0.806163i	−0.982599	−	0.185741i	$-0.940531\pi$
$787$	−31.1279	+	22.6157i	−1.10959	+	0.806163i	−0.126990	+	0.991904i	$0.540531\pi$
$788$	8.88339	−	6.45416i	0.316458	−	0.229920i
$789$	16.7202	+	12.1479i	0.595254	+	0.432478i
$790$		0			0
$791$	−11.1348	+	8.08988i	−0.395906	+	0.287643i
$792$	0.641260	−	1.97360i	0.0227862	−	0.0701287i
$793$	−47.4060			−1.68344
$794$	0.858349	−	2.64173i	0.0304617	−	0.0937514i
$795$		0			0
$796$	−3.64878	−	11.2298i	−0.129327	−	0.398029i
$797$	0.577055	+	1.77599i	0.0204404	+	0.0629089i	0.960756	−	0.277393i	$-0.0894706\pi$
$797$	0.577055	+	1.77599i	0.0204404	+	0.0629089i	−0.940316	+	0.340302i	$0.889471\pi$
$798$	−0.626600	−	0.455252i	−0.0221814	−	0.0161157i
$799$	45.1063			1.59575
$800$		0			0
$801$	−15.4975			−0.547578
$802$	1.65340	+	1.20127i	0.0583837	+	0.0424182i
$803$	−10.3255	−	31.7786i	−0.364379	−	1.12144i
$804$	2.04748	+	6.30150i	0.0722091	+	0.222237i
$805$		0			0
$806$	−0.251321	+	0.773487i	−0.00885241	+	0.0272449i
$807$	−13.7435			−0.483796
$808$	0.124528	−	0.383258i	0.00438089	−	0.0134830i
$809$	−28.4381	+	20.6615i	−0.999831	+	0.726420i	−0.962052	−	0.272866i	$-0.912028\pi$
$809$	−28.4381	+	20.6615i	−0.999831	+	0.726420i	−0.0377789	+	0.999286i	$0.512028\pi$
$810$		0			0
$811$	5.33270	+	3.87443i	0.187256	+	0.136050i	0.677464	−	0.735556i	$-0.263079\pi$
$811$	5.33270	+	3.87443i	0.187256	+	0.136050i	−0.490208	+	0.871606i	$0.663079\pi$
$812$	5.13370	−	3.72985i	0.180158	−	0.130892i
$813$	−2.70528	+	1.96550i	−0.0948785	+	0.0689332i
$814$	3.14290	+	2.28345i	0.110158	+	0.0800348i
$815$		0			0
$816$	−16.6584	+	12.1031i	−0.583162	+	0.423692i
$817$	6.65141	−	20.4709i	0.232703	−	0.716187i
$818$	−3.94949			−0.138091
$819$	−1.21512	+	3.73976i	−0.0424598	+	0.130678i
$820$		0			0
$821$	1.62463	+	5.00011i	0.0567001	+	0.174505i	0.975396	−	0.220461i	$-0.0707563\pi$
$821$	1.62463	+	5.00011i	0.0567001	+	0.174505i	−0.918696	+	0.394966i	$0.870756\pi$
$822$	0.519236	+	1.59804i	0.0181104	+	0.0557382i
$823$	−17.9536	−	13.0440i	−0.625823	−	0.454687i	0.229128	−	0.973396i	$-0.426413\pi$
$823$	−17.9536	−	13.0440i	−0.625823	−	0.454687i	−0.854951	+	0.518709i	$0.826413\pi$
$824$	0.440283			0.0153380
$825$		0			0
$826$	1.59635			0.0555440
$827$	−5.30922	−	3.85738i	−0.184620	−	0.134134i	0.491637	−	0.870800i	$-0.336399\pi$
$827$	−5.30922	−	3.85738i	−0.184620	−	0.134134i	−0.676256	+	0.736666i	$0.736399\pi$
$828$	2.09478	+	6.44705i	0.0727985	+	0.224051i
$829$	7.74316	+	23.8310i	0.268931	+	0.827685i	0.990762	+	0.135615i	$0.0433010\pi$
$829$	7.74316	+	23.8310i	0.268931	+	0.827685i	−0.721831	+	0.692070i	$0.756699\pi$
$830$		0			0
$831$	−2.75318	+	8.47340i	−0.0955066	+	0.293939i
$832$	34.4618			1.19475
$833$	−10.2716	+	31.6126i	−0.355889	+	1.09531i
$834$	0.534274	−	0.388173i	0.0185004	−	0.0134413i
$835$		0			0
$836$	−37.5402	−	27.2745i	−1.29835	−	0.943310i
$837$	−1.01362	+	0.736436i	−0.0350357	+	0.0254550i
$838$	4.15968	−	3.02219i	0.143694	−	0.104400i
$839$	34.0989	+	24.7743i	1.17722	+	0.855303i	0.991856	−	0.127366i	$-0.0406524\pi$
$839$	34.0989	+	24.7743i	1.17722	+	0.855303i	0.185368	+	0.982669i	$0.440652\pi$
$840$		0			0
$841$	12.1813	−	8.85021i	0.420044	−	0.305180i
$842$	−0.147816	+	0.454932i	−0.00509409	+	0.0156780i
$843$	−22.4913			−0.774641
$844$	8.39327	−	25.8318i	0.288908	−	0.889169i
$845$		0			0
$846$	0.372140	+	1.14533i	0.0127944	+	0.0393773i
$847$	0.674189	+	2.07494i	0.0231654	+	0.0712957i
$848$	−7.37109	−	5.35541i	−0.253124	−	0.183906i
$849$	−1.30694			−0.0448540
$850$		0			0
$851$	−25.5095			−0.874454
$852$	−6.92437	−	5.03085i	−0.237225	−	0.172354i
$853$	−13.3641	−	41.1306i	−0.457580	−	1.40829i	−0.868080	−	0.496425i	$-0.834646\pi$
$853$	−13.3641	−	41.1306i	−0.457580	−	1.40829i	0.410500	−	0.911861i	$-0.365354\pi$
$854$	0.388871	+	1.19682i	0.0133069	+	0.0409544i
$855$		0			0
$856$	2.08415	−	6.41436i	0.0712349	−	0.219238i
$857$	39.2430			1.34052			0.670258	−	0.742128i	$-0.266183\pi$
$857$	39.2430			1.34052			0.670258	+	0.742128i	$0.266183\pi$
$858$	0.738163	−	2.27183i	0.0252005	−	0.0775590i
$859$	−42.5617	+	30.9229i	−1.45219	+	1.05508i	−0.466872	+	0.884325i	$0.654619\pi$
$859$	−42.5617	+	30.9229i	−1.45219	+	1.05508i	−0.985314	+	0.170750i	$0.945381\pi$
$860$		0			0
$861$	1.75797	+	1.27724i	0.0599113	+	0.0435281i
$862$	2.94167	−	2.13725i	0.100194	−	0.0727950i
$863$	−34.6861	+	25.2009i	−1.18073	+	0.857850i	−0.992254	−	0.124228i	$-0.960355\pi$
$863$	−34.6861	+	25.2009i	−1.18073	+	0.857850i	−0.188476	+	0.982078i	$0.560355\pi$
$864$	−1.35719	−	0.986054i	−0.0461724	−	0.0335462i
$865$		0			0
$866$	−4.56304	+	3.31524i	−0.155058	+	0.112657i
$867$	3.45001	−	10.6180i	0.117169	−	0.360608i
$868$	−2.12917			−0.0722686
$869$	3.69270	−	11.3650i	0.125266	−	0.385530i
$870$		0			0
$871$	4.73766	+	14.5810i	0.160530	+	0.494059i
$872$	−0.424118	−	1.30530i	−0.0143624	−	0.0442031i
$873$	−8.12138	−	5.90053i	−0.274867	−	0.199703i
$874$	−3.08955			−0.104506
$875$		0			0
$876$	−17.9779			−0.607415
$877$	−0.315771	−	0.229421i	−0.0106628	−	0.00774700i	0.582441	−	0.812873i	$-0.302098\pi$
$877$	−0.315771	−	0.229421i	−0.0106628	−	0.00774700i	−0.593104	+	0.805126i	$0.702098\pi$
$878$	1.48508	+	4.57060i	0.0501190	+	0.154250i
$879$	−0.608943	−	1.87413i	−0.0205391	−	0.0632129i
$880$		0			0
$881$	13.8131	−	42.5124i	0.465376	−	1.43228i	−0.393133	−	0.919481i	$-0.628609\pi$
$881$	13.8131	−	42.5124i	0.465376	−	1.43228i	0.858509	−	0.512798i	$-0.171391\pi$
$882$	−0.887444			−0.0298818
$883$	−10.1224	+	31.1534i	−0.340645	+	1.04840i	0.623230	+	0.782039i	$0.285820\pi$
$883$	−10.1224	+	31.1534i	−0.340645	+	1.04840i	−0.963874	+	0.266358i	$0.914180\pi$
$884$	−38.9448	+	28.2951i	−1.30986	+	0.951666i
$885$		0			0
$886$	−3.31622	−	2.40938i	−0.111411	−	0.0809446i
$887$	−12.7121	+	9.23588i	−0.426830	+	0.310110i	−0.780380	−	0.625305i	$-0.784974\pi$
$887$	−12.7121	+	9.23588i	−0.426830	+	0.310110i	0.353550	+	0.935416i	$0.384974\pi$
$888$	3.39911	−	2.46960i	0.114067	−	0.0828743i
$889$	−2.66539	−	1.93652i	−0.0893944	−	0.0649488i
$890$		0			0
$891$	2.97713	−	2.16301i	0.0997374	−	0.0724635i
$892$	1.98337	−	6.10419i	0.0664082	−	0.204383i
$893$	54.1299			1.81139
$894$	−0.505625	+	1.55615i	−0.0169106	+	0.0520456i
$895$		0			0
$896$	−1.17258	−	3.60884i	−0.0391733	−	0.120563i
$897$	4.84710	+	14.9178i	0.161840	+	0.498092i
$898$	1.17024	+	0.850228i	0.0390514	+	0.0283725i
$899$	4.67839			0.156033
$900$		0			0
$901$	12.4623			0.415180
$902$	−1.06793	−	0.775897i	−0.0355582	−	0.0258345i
$903$	0.896411	+	2.75887i	0.0298307	+	0.0918094i
$904$	−2.79430	−	8.59998i	−0.0929372	−	0.286031i
$905$		0			0
$906$	1.07138	−	3.29737i	0.0355942	−	0.109548i
$907$	1.50466			0.0499613			0.0249806	−	0.999688i	$-0.492048\pi$
$907$	1.50466			0.0499613			0.0249806	+	0.999688i	$0.492048\pi$
$908$	8.06385	−	24.8180i	0.267608	−	0.823613i
$909$	0.578137	−	0.420041i	0.0191756	−	0.0139319i
$910$		0			0
$911$	−9.26400	−	6.73069i	−0.306930	−	0.222998i	0.423648	−	0.905827i	$-0.360749\pi$
$911$	−9.26400	−	6.73069i	−0.306930	−	0.222998i	−0.730578	+	0.682829i	$0.760749\pi$
$912$	−19.9910	+	14.5243i	−0.661968	+	0.480948i
$913$	22.0090	−	15.9904i	0.728390	−	0.529207i
$914$	3.72489	+	2.70629i	0.123209	+	0.0895162i
$915$		0			0
$916$	9.35142	−	6.79421i	0.308980	−	0.224487i
$917$	−3.30200	+	10.1625i	−0.109042	+	0.335596i
$918$	0.751949			0.0248180
$919$	−6.73660	+	20.7331i	−0.222220	+	0.683923i	0.776342	+	0.630312i	$0.217073\pi$
$919$	−6.73660	+	20.7331i	−0.222220	+	0.683923i	−0.998562	+	0.0536108i	$0.982927\pi$
$920$		0			0
$921$	4.71388	+	14.5078i	0.155328	+	0.478049i
$922$	−0.0306740	−	0.0944049i	−0.00101019	−	0.00310906i
$923$	−16.0223	−	11.6409i	−0.527380	−	0.383164i
$924$	6.25363			0.205729
$925$		0			0
$926$	−0.307645			−0.0101098
$927$	0.631652	+	0.458922i	0.0207462	+	0.0150730i
$928$	1.93573	+	5.95756i	0.0635434	+	0.195566i
$929$	−9.50249	−	29.2457i	−0.311767	−	0.959519i	−0.977065	−	0.212941i	$-0.931696\pi$
$929$	−9.50249	−	29.2457i	−0.311767	−	0.959519i	0.665298	−	0.746578i	$-0.268304\pi$
$930$		0			0
$931$	−12.3264	+	37.9368i	−0.403982	+	1.24333i
$932$	18.4817			0.605387
$933$	5.48358	−	16.8767i	0.179524	−	0.552519i
$934$	−0.444429	+	0.322896i	−0.0145421	+	0.0105655i
$935$		0			0
$936$	−2.09008	−	1.51853i	−0.0683164	−	0.0496348i
$937$	−3.08284	+	2.23982i	−0.100712	+	0.0731716i	−0.637002	−	0.770862i	$-0.719826\pi$
$937$	−3.08284	+	2.23982i	−0.100712	+	0.0731716i	0.536289	+	0.844034i	$0.319826\pi$
$938$	0.329252	−	0.239216i	0.0107505	−	0.00781067i
$939$	−22.1565	−	16.0976i	−0.723049	−	0.525326i
$940$		0			0
$941$	16.7501	−	12.1697i	0.546037	−	0.396719i	−0.280285	−	0.959917i	$-0.590429\pi$
$941$	16.7501	−	12.1697i	0.546037	−	0.396719i	0.826322	+	0.563197i	$0.190429\pi$
$942$	0.979284	−	3.01393i	0.0319068	−	0.0981990i
$943$	8.66792			0.282266
$944$	15.7381	−	48.4370i	0.512233	−	1.57649i
$945$		0			0
$946$	−0.544553	−	1.67596i	−0.0177049	−	0.0544902i
$947$	−4.84640	−	14.9157i	−0.157487	−	0.484695i	0.840917	−	0.541163i	$-0.182016\pi$
$947$	−4.84640	−	14.9157i	−0.157487	−	0.484695i	−0.998404	+	0.0564684i	$0.982016\pi$
$948$	−5.20150	−	3.77911i	−0.168937	−	0.122740i
$949$	−41.5989			−1.35036
$950$		0			0
$951$	−8.64563			−0.280354
$952$	2.07809	+	1.50982i	0.0673514	+	0.0489337i
$953$	2.39552	+	7.37266i	0.0775985	+	0.238824i	0.982330	−	0.187160i	$-0.0599282\pi$
$953$	2.39552	+	7.37266i	0.0775985	+	0.238824i	−0.904731	+	0.425983i	$0.859928\pi$
$954$	0.102818	+	0.316441i	0.00332885	+	0.0102451i
$955$		0			0
$956$	−10.4930	+	32.2941i	−0.339368	+	1.04447i
$957$	−13.7410			−0.444185
$958$	−0.963230	+	2.96452i	−0.0311205	+	0.0957792i
$959$	−8.23468	+	5.98285i	−0.265912	+	0.193196i
$960$		0			0
$961$	23.8096	+	17.2987i	0.768050	+	0.558021i
$962$	3.91276	−	2.84279i	0.126152	−	0.0916551i
$963$	9.67592	−	7.02997i	0.311802	−	0.226538i
$964$	11.5661	+	8.40326i	0.372519	+	0.270651i
$965$		0			0
$966$	0.336857	−	0.244741i	0.0108382	−	0.00787442i
$967$	14.9649	−	46.0571i	0.481238	−	1.48110i	−0.356119	−	0.934441i	$-0.615900\pi$
$967$	14.9649	−	46.0571i	0.481238	−	1.48110i	0.837357	−	0.546657i	$-0.184100\pi$
$968$	−1.43340			−0.0460712
$969$	10.4444	−	32.1446i	0.335523	−	1.03263i
$970$		0			0
$971$	7.82895	+	24.0950i	0.251243	+	0.773246i	0.994547	+	0.104292i	$0.0332577\pi$
$971$	7.82895	+	24.0950i	0.251243	+	0.773246i	−0.743304	+	0.668954i	$0.766742\pi$
$972$	−0.611830	−	1.88302i	−0.0196245	−	0.0603979i
$973$	3.23647	+	2.35143i	0.103756	+	0.0753834i
$974$	−4.02394			−0.128936
$975$		0			0
$976$	40.1483			1.28511
$977$	−0.945620	−	0.687033i	−0.0302531	−	0.0219801i	0.572556	−	0.819866i	$-0.305952\pi$
$977$	−0.945620	−	0.687033i	−0.0302531	−	0.0219801i	−0.602809	+	0.797885i	$0.705952\pi$
$978$	0.0356165	+	0.109616i	0.00113889	+	0.00350514i
$979$	17.6232	+	54.2385i	0.563239	+	1.73347i
$980$		0			0
$981$	0.752097	−	2.31472i	0.0240126	−	0.0739033i
$982$	−1.99029			−0.0635127
$983$	7.41464	−	22.8199i	0.236490	−	0.727842i	−0.760430	−	0.649420i	$-0.775012\pi$
$983$	7.41464	−	22.8199i	0.236490	−	0.727842i	0.996920	−	0.0784223i	$-0.0249882\pi$
$984$	−1.15499	+	0.839150i	−0.0368197	+	0.0267511i
$985$		0			0
$986$	−2.27157	−	1.65039i	−0.0723415	−	0.0525592i
$987$	−5.90186	+	4.28795i	−0.187858	+	0.136487i
$988$	−46.7358	+	33.9555i	−1.48686	+	1.08027i
$989$	9.36148	+	6.80151i	0.297678	+	0.216276i
$990$		0			0
$991$	29.6688	−	21.5556i	0.942459	−	0.684737i	−0.00655196	−	0.999979i	$-0.502086\pi$
$991$	29.6688	−	21.5556i	0.942459	−	0.684737i	0.949011	+	0.315242i	$0.102086\pi$
$992$	0.649502	−	1.99896i	0.0206217	−	0.0634671i
$993$	4.96260			0.157483
$994$	−0.162457	+	0.499991i	−0.00515282	+	0.0158588i
$995$		0			0
$996$	−4.52307	−	13.9206i	−0.143319	−	0.441091i
$997$	17.6202	+	54.2295i	0.558038	+	1.71747i	0.687782	+	0.725918i	$0.258585\pi$
$997$	17.6202	+	54.2295i	0.558038	+	1.71747i	−0.129743	+	0.991548i	$0.541415\pi$
$998$	−1.49984	−	1.08970i	−0.0474765	−	0.0344937i
$999$	7.45067			0.235729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.g.c.76.2		12
5.2	odd	4		375.2.i.d.49.4		24
5.3	odd	4		375.2.i.d.49.3		24
5.4	even	2		75.2.g.c.16.2	✓	12
15.14	odd	2		225.2.h.d.91.2		12
25.2	odd	20		375.2.i.d.199.3		24
25.6	even	5		1875.2.a.k.1.4		6
25.8	odd	20		1875.2.b.f.1249.6		12
25.11	even	5	inner	375.2.g.c.301.2		12
25.14	even	10		75.2.g.c.61.2	yes	12
25.17	odd	20		1875.2.b.f.1249.7		12
25.19	even	10		1875.2.a.j.1.3		6
25.23	odd	20		375.2.i.d.199.4		24
75.14	odd	10		225.2.h.d.136.2		12
75.44	odd	10		5625.2.a.p.1.4		6
75.56	odd	10		5625.2.a.q.1.3		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.2	✓	12	5.4	even	2
75.2.g.c.61.2	yes	12	25.14	even	10
225.2.h.d.91.2		12	15.14	odd	2
225.2.h.d.136.2		12	75.14	odd	10
375.2.g.c.76.2		12	1.1	even	1	trivial
375.2.g.c.301.2		12	25.11	even	5	inner
375.2.i.d.49.3		24	5.3	odd	4
375.2.i.d.49.4		24	5.2	odd	4
375.2.i.d.199.3		24	25.2	odd	20
375.2.i.d.199.4		24	25.23	odd	20
1875.2.a.j.1.3		6	25.19	even	10
1875.2.a.k.1.4		6	25.6	even	5
1875.2.b.f.1249.6		12	25.8	odd	20
1875.2.b.f.1249.7		12	25.17	odd	20
5625.2.a.p.1.4		6	75.44	odd	10
5625.2.a.q.1.3		6	75.56	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:	\( N \)	\(=\)	\( 375 = 3 \cdot 5^{3} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	375.g (of order \(5\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.114629 - 0.0832830i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.611830 - 1.88302i) q^{4} +(0.0437845 - 0.134755i) q^{6} +0.858311 q^{7} +(-0.174259 + 0.536314i) q^{8} +(-0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.114629 - 0.0832830i) q^{2} +(0.309017 + 0.951057i) q^{3} +(-0.611830 - 1.88302i) q^{4} +(0.0437845 - 0.134755i) q^{6} +0.858311 q^{7} +(-0.174259 + 0.536314i) q^{8} +(-0.809017 + 0.587785i) q^{9} +(2.97713 + 2.16301i) q^{11} +(1.60179 - 1.16377i) q^{12} +(3.70638 - 2.69285i) q^{13} +(-0.0983875 - 0.0714827i) q^{14} +(-3.13894 + 2.28058i) q^{16} +(1.63996 - 5.04728i) q^{17} +0.141689 q^{18} +(1.96804 - 6.05699i) q^{19} +(0.265233 + 0.816302i) q^{21} +(-0.161124 - 0.495888i) q^{22} +(2.76990 + 2.01245i) q^{23} -0.563913 q^{24} -0.649128 q^{26} +(-0.809017 - 0.587785i) q^{27} +(-0.525140 - 1.61622i) q^{28} +(1.15388 + 3.55129i) q^{29} +(0.387167 - 1.19158i) q^{31} +1.67757 q^{32} +(-1.13716 + 3.49982i) q^{33} +(-0.608340 + 0.441985i) q^{34} +(1.60179 + 1.16377i) q^{36} +(-6.02772 + 4.37939i) q^{37} +(-0.730039 + 0.530404i) q^{38} +(3.70638 + 2.69285i) q^{39} +(2.04817 - 1.48808i) q^{41} +(0.0375807 - 0.115661i) q^{42} +3.37972 q^{43} +(2.25149 - 6.92938i) q^{44} +(-0.149909 - 0.461371i) q^{46} +(2.62645 + 8.08338i) q^{47} +(-3.13894 - 2.28058i) q^{48} -6.26330 q^{49} +5.30702 q^{51} +(-7.33836 - 5.33163i) q^{52} +(0.725656 + 2.23334i) q^{53} +(0.0437845 + 0.134755i) q^{54} +(-0.149568 + 0.460324i) q^{56} +6.36870 q^{57} +(0.163493 - 0.503181i) q^{58} +(-10.6195 + 7.71550i) q^{59} +(-8.37141 - 6.08218i) q^{61} +(-0.143619 + 0.104345i) q^{62} +(-0.694388 + 0.504502i) q^{63} +(6.08559 + 4.42144i) q^{64} +(0.421827 - 0.306475i) q^{66} +(-1.03412 + 3.18270i) q^{67} -10.5075 q^{68} +(-1.05801 + 3.25621i) q^{69} +(-1.33585 - 4.11131i) q^{71} +(-0.174259 - 0.536314i) q^{72} +(-7.34593 - 5.33713i) q^{73} +1.05568 q^{74} -12.6095 q^{76} +(2.55530 + 1.85653i) q^{77} +(-0.200592 - 0.617357i) q^{78} +(-1.00347 - 3.08837i) q^{79} +(0.309017 - 0.951057i) q^{81} -0.358712 q^{82} +(2.28447 - 7.03087i) q^{83} +(1.37484 - 0.998876i) q^{84} +(-0.387414 - 0.281473i) q^{86} +(-3.02091 + 2.19482i) q^{87} +(-1.67884 + 1.21975i) q^{88} +(12.5378 + 9.10921i) q^{89} +(3.18123 - 2.31130i) q^{91} +(2.09478 - 6.44705i) q^{92} +1.25290 q^{93} +(0.372140 - 1.14533i) q^{94} +(0.518399 + 1.59547i) q^{96} +(3.10209 + 9.54725i) q^{97} +(0.717957 + 0.521627i) q^{98} -3.67993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9}+O(q^{10}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9	\( 12 q - 3 q^{3} - 10 q^{4} + 12 q^{7} - 9 q^{8} - 3 q^{9} - 4 q^{11} + 2 q^{13} + 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 3 q^{21} - 13 q^{22} - 19 q^{23} + 6 q^{24} - 56 q^{26} - 3 q^{27} - q^{28} - q^{29} + 13 q^{31} + 32 q^{32} + q^{33} - 25 q^{34} - 8 q^{37} + 22 q^{38} + 2 q^{39} + 8 q^{41} + 16 q^{42} + 4 q^{43} + 33 q^{44} - 22 q^{46} + 13 q^{47} + 16 q^{48} - 28 q^{49} + 26 q^{51} - 44 q^{52} - 44 q^{53} + 45 q^{56} + 22 q^{57} - 41 q^{58} - 22 q^{59} - 8 q^{61} - 41 q^{62} - 3 q^{63} + 49 q^{64} - 3 q^{66} + 6 q^{67} + 100 q^{68} + 6 q^{69} - 21 q^{71} - 9 q^{72} + 16 q^{73} - 44 q^{74} - 52 q^{76} - q^{77} + 19 q^{78} + 10 q^{79} - 3 q^{81} - 26 q^{82} + 10 q^{83} - 6 q^{84} + 56 q^{86} + 4 q^{87} + 16 q^{88} + 57 q^{89} - 7 q^{91} - 3 q^{92} - 22 q^{93} - 23 q^{94} - 23 q^{96} - 4 q^{97} + 18 q^{98} + 6 q^{99}+O(q^{100}) \) 12 * q - 3 * q^3 - 10 * q^4 + 12 * q^7 - 9 * q^8 - 3 * q^9 - 4 * q^11 + 2 * q^13 + 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 3 * q^21 - 13 * q^22 - 19 * q^23 + 6 * q^24 - 56 * q^26 - 3 * q^27 - q^28 - q^29 + 13 * q^31 + 32 * q^32 + q^33 - 25 * q^34 - 8 * q^37 + 22 * q^38 + 2 * q^39 + 8 * q^41 + 16 * q^42 + 4 * q^43 + 33 * q^44 - 22 * q^46 + 13 * q^47 + 16 * q^48 - 28 * q^49 + 26 * q^51 - 44 * q^52 - 44 * q^53 + 45 * q^56 + 22 * q^57 - 41 * q^58 - 22 * q^59 - 8 * q^61 - 41 * q^62 - 3 * q^63 + 49 * q^64 - 3 * q^66 + 6 * q^67 + 100 * q^68 + 6 * q^69 - 21 * q^71 - 9 * q^72 + 16 * q^73 - 44 * q^74 - 52 * q^76 - q^77 + 19 * q^78 + 10 * q^79 - 3 * q^81 - 26 * q^82 + 10 * q^83 - 6 * q^84 + 56 * q^86 + 4 * q^87 + 16 * q^88 + 57 * q^89 - 7 * q^91 - 3 * q^92 - 22 * q^93 - 23 * q^94 - 23 * q^96 - 4 * q^97 + 18 * q^98 + 6 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more