LMFDB - Embedded newform 375.2.i.d.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [375,2,Mod(49,375)]

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, 7]))

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

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

chi := DirichletCharacter("375.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 375 = 3 \cdot 5^{3} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	375.i (of order $10$, 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:	$24$
Relative dimension:	$6$ over $\Q(\zeta_{10})$
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			199.3
Character	$\chi$	$=$	375.199
Dual form			375.2.i.d.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0832830 - 0.114629i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.611830 - 1.88302i) q^{4} +(0.0437845 + 0.134755i) q^{6} +0.858311i q^{7} +(-0.536314 + 0.174259i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})$	\(q+(-0.0832830 - 0.114629i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.611830 - 1.88302i) q^{4} +(0.0437845 + 0.134755i) q^{6} +0.858311i q^{7} +(-0.536314 + 0.174259i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.97713 - 2.16301i) q^{11} +(-1.16377 + 1.60179i) q^{12} +(2.69285 - 3.70638i) q^{13} +(0.0983875 - 0.0714827i) q^{14} +(-3.13894 - 2.28058i) q^{16} +(-5.04728 + 1.63996i) q^{17} -0.141689i q^{18} +(-1.96804 - 6.05699i) q^{19} +(0.265233 - 0.816302i) q^{21} +(-0.495888 - 0.161124i) q^{22} +(-2.01245 - 2.76990i) q^{23} +0.563913 q^{24} -0.649128 q^{26} +(-0.587785 - 0.809017i) q^{27} +(1.61622 + 0.525140i) q^{28} +(-1.15388 + 3.55129i) q^{29} +(0.387167 + 1.19158i) q^{31} +1.67757i q^{32} +(-3.49982 + 1.13716i) q^{33} +(0.608340 + 0.441985i) q^{34} +(1.60179 - 1.16377i) q^{36} +(4.37939 - 6.02772i) q^{37} +(-0.530404 + 0.730039i) q^{38} +(-3.70638 + 2.69285i) q^{39} +(2.04817 + 1.48808i) q^{41} +(-0.115661 + 0.0375807i) q^{42} -3.37972i q^{43} +(-2.25149 - 6.92938i) q^{44} +(-0.149909 + 0.461371i) q^{46} +(8.08338 + 2.62645i) q^{47} +(2.28058 + 3.13894i) q^{48} +6.26330 q^{49} +5.30702 q^{51} +(-5.33163 - 7.33836i) q^{52} +(-2.23334 - 0.725656i) q^{53} +(-0.0437845 + 0.134755i) q^{54} +(-0.149568 - 0.460324i) q^{56} +6.36870i q^{57} +(0.503181 - 0.163493i) q^{58} +(10.6195 + 7.71550i) q^{59} +(-8.37141 + 6.08218i) q^{61} +(0.104345 - 0.143619i) q^{62} +(-0.504502 + 0.694388i) q^{63} +(-6.08559 + 4.42144i) q^{64} +(0.421827 + 0.306475i) q^{66} +(3.18270 - 1.03412i) q^{67} +10.5075i q^{68} +(1.05801 + 3.25621i) q^{69} +(-1.33585 + 4.11131i) q^{71} +(-0.536314 - 0.174259i) q^{72} +(5.33713 + 7.34593i) q^{73} -1.05568 q^{74} -12.6095 q^{76} +(1.85653 + 2.55530i) q^{77} +(0.617357 + 0.200592i) q^{78} +(1.00347 - 3.08837i) q^{79} +(0.309017 + 0.951057i) q^{81} -0.358712i q^{82} +(7.03087 - 2.28447i) q^{83} +(-1.37484 - 0.998876i) q^{84} +(-0.387414 + 0.281473i) q^{86} +(2.19482 - 3.02091i) q^{87} +(-1.21975 + 1.67884i) q^{88} +(-12.5378 + 9.10921i) q^{89} +(3.18123 + 2.31130i) q^{91} +(-6.44705 + 2.09478i) q^{92} -1.25290i q^{93} +(-0.372140 - 1.14533i) q^{94} +(0.518399 - 1.59547i) q^{96} +(9.54725 + 3.10209i) q^{97} +(-0.521627 - 0.717957i) q^{98} +3.67993 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) $ 24 * q + 20 * q^4 + 6 * q^9	$ 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) $ 24 * q + 20 * q^4 + 6 * q^9 - 8 * q^11 - 12 * q^14 + 32 * q^16 - 14 * q^19 - 6 * q^21 - 12 * q^24 - 112 * q^26 + 2 * q^29 + 26 * q^31 + 50 * q^34 - 4 * q^39 + 16 * q^41 - 66 * q^44 - 44 * q^46 + 56 * q^49 + 52 * q^51 + 90 * q^56 + 44 * q^59 - 16 * q^61 - 98 * q^64 - 6 * q^66 - 12 * q^69 - 42 * q^71 + 88 * q^74 - 104 * q^76 - 20 * q^79 - 6 * q^81 + 12 * q^84 + 112 * q^86 - 114 * q^89 - 14 * q^91 + 46 * q^94 - 46 * q^96 - 12 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$127$	$251$
$\chi(n)$	$e\left(\frac{3}{10}\right)$	$1$

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 $

$2$	−0.0832830	−	0.114629i	−0.0588900	−	0.0810551i	0.778556	−	0.627575i	$-0.215952\pi$
$2$	−0.0832830	−	0.114629i	−0.0588900	−	0.0810551i	−0.837446	+	0.546520i	$0.815952\pi$
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$3$	−0.951057	−	0.309017i	−0.549093	−	0.178411i
$4$	0.611830	−	1.88302i	0.305915	−	0.941510i
$5$		0			0
$5$		0			0
$6$	0.0437845	+	0.134755i	0.0178749	+	0.0550134i
$7$			0.858311i			0.324411i	0.986757	+	0.162205i	$0.0518607\pi$
$7$			0.858311i			0.324411i	−0.986757	+	0.162205i	$0.948139\pi$
$8$	−0.536314	+	0.174259i	−0.189615	+	0.0616098i
$9$	0.809017	+	0.587785i	0.269672	+	0.195928i
$10$		0			0
$11$	2.97713	−	2.16301i	0.897637	−	0.652171i	−0.0402210	−	0.999191i	$-0.512806\pi$
$11$	2.97713	−	2.16301i	0.897637	−	0.652171i	0.937858	+	0.347019i	$0.112806\pi$
$12$	−1.16377	+	1.60179i	−0.335952	+	0.462398i
$13$	2.69285	−	3.70638i	0.746861	−	1.02797i	−0.251334	−	0.967901i	$-0.580869\pi$
$13$	2.69285	−	3.70638i	0.746861	−	1.02797i	0.998194	−	0.0600653i	$-0.0191309\pi$
$14$	0.0983875	−	0.0714827i	0.0262952	−	0.0191045i
$15$		0			0
$16$	−3.13894	−	2.28058i	−0.784736	−	0.570144i
$17$	−5.04728	+	1.63996i	−1.22414	+	0.397749i	−0.848590	−	0.529052i	$-0.822548\pi$
$17$	−5.04728	+	1.63996i	−1.22414	+	0.397749i	−0.375555	+	0.926800i	$0.622548\pi$
$18$		−	0.141689i		−	0.0333965i
$19$	−1.96804	−	6.05699i	−0.451499	−	1.38957i	−0.875197	−	0.483766i	$-0.839268\pi$
$19$	−1.96804	−	6.05699i	−0.451499	−	1.38957i	0.423699	−	0.905803i	$-0.360732\pi$
$20$		0			0
$21$	0.265233	−	0.816302i	0.0578785	−	0.178132i
$22$	−0.495888	−	0.161124i	−0.105724	−	0.0343517i
$23$	−2.01245	−	2.76990i	−0.419625	−	0.577564i	0.545908	−	0.837845i	$-0.316185\pi$
$23$	−2.01245	−	2.76990i	−0.419625	−	0.577564i	−0.965533	+	0.260281i	$0.916185\pi$
$24$	0.563913			0.115108
$25$		0			0
$26$	−0.649128			−0.127304
$27$	−0.587785	−	0.809017i	−0.113119	−	0.155695i
$28$	1.61622	+	0.525140i	0.305436	+	0.0992422i
$29$	−1.15388	+	3.55129i	−0.214271	+	0.659458i	0.784934	+	0.619580i	$0.212697\pi$
$29$	−1.15388	+	3.55129i	−0.214271	+	0.659458i	−0.999205	+	0.0398784i	$0.987303\pi$
$30$		0			0
$31$	0.387167	+	1.19158i	0.0695373	+	0.214014i	0.979786	−	0.200048i	$-0.0641098\pi$
$31$	0.387167	+	1.19158i	0.0695373	+	0.214014i	−0.910249	+	0.414062i	$0.864110\pi$
$32$			1.67757i			0.296556i
$33$	−3.49982	+	1.13716i	−0.609241	+	0.197954i
$34$	0.608340	+	0.441985i	0.104329	+	0.0757997i
$35$		0			0
$36$	1.60179	−	1.16377i	0.266965	−	0.193962i
$37$	4.37939	−	6.02772i	0.719968	−	0.990951i	−0.279557	−	0.960129i	$-0.590188\pi$
$37$	4.37939	−	6.02772i	0.719968	−	0.990951i	0.999525	−	0.0308218i	$-0.00981244\pi$
$38$	−0.530404	+	0.730039i	−0.0860430	+	0.118428i
$39$	−3.70638	+	2.69285i	−0.593496	+	0.431200i
$40$		0			0
$41$	2.04817	+	1.48808i	0.319870	+	0.232399i	0.736120	−	0.676851i	$-0.236656\pi$
$41$	2.04817	+	1.48808i	0.319870	+	0.232399i	−0.416250	+	0.909250i	$0.636656\pi$
$42$	−0.115661	+	0.0375807i	−0.0178469	+	0.00579882i
$43$		−	3.37972i		−	0.515402i	−0.966225	−	0.257701i	$-0.917035\pi$
$43$		−	3.37972i		−	0.515402i	0.966225	−	0.257701i	$-0.0829650\pi$
$44$	−2.25149	−	6.92938i	−0.339425	−	1.04464i
$45$		0			0
$46$	−0.149909	+	0.461371i	−0.0221028	+	0.0680255i
$47$	8.08338	+	2.62645i	1.17908	+	0.383107i	0.832026	−	0.554737i	$-0.187181\pi$
$47$	8.08338	+	2.62645i	1.17908	+	0.383107i	0.347057	+	0.937844i	$0.387181\pi$
$48$	2.28058	+	3.13894i	0.329173	+	0.453067i
$49$	6.26330			0.894758
$50$		0			0
$51$	5.30702			0.743132
$52$	−5.33163	−	7.33836i	−0.739364	−	1.01765i
$53$	−2.23334	−	0.725656i	−0.306773	−	0.0996765i	0.151585	−	0.988444i	$-0.451562\pi$
$53$	−2.23334	−	0.725656i	−0.306773	−	0.0996765i	−0.458358	+	0.888768i	$0.651562\pi$
$54$	−0.0437845	+	0.134755i	−0.00595831	+	0.0183378i
$55$		0			0
$56$	−0.149568	−	0.460324i	−0.0199869	−	0.0615133i
$57$			6.36870i			0.843555i
$58$	0.503181	−	0.163493i	0.0660709	−	0.0214677i
$59$	10.6195	+	7.71550i	1.38254	+	1.00447i	0.996638	+	0.0819317i	$0.0261089\pi$
$59$	10.6195	+	7.71550i	1.38254	+	1.00447i	0.385900	+	0.922541i	$0.373891\pi$
$60$		0			0
$61$	−8.37141	+	6.08218i	−1.07185	+	0.778744i	−0.976244	−	0.216676i	$-0.930479\pi$
$61$	−8.37141	+	6.08218i	−1.07185	+	0.778744i	−0.0956052	+	0.995419i	$0.530479\pi$
$62$	0.104345	−	0.143619i	0.0132519	−	0.0182396i
$63$	−0.504502	+	0.694388i	−0.0635613	+	0.0874846i
$64$	−6.08559	+	4.42144i	−0.760698	+	0.552680i
$65$		0			0
$66$	0.421827	+	0.306475i	0.0519234	+	0.0377245i
$67$	3.18270	−	1.03412i	0.388828	−	0.126338i	−0.108077	−	0.994142i	$-0.534469\pi$
$67$	3.18270	−	1.03412i	0.388828	−	0.126338i	0.496906	+	0.867805i	$0.334469\pi$
$68$			10.5075i			1.27422i
$69$	1.05801	+	3.25621i	0.127369	+	0.392002i
$70$		0			0
$71$	−1.33585	+	4.11131i	−0.158536	+	0.487923i	−0.998502	−	0.0547158i	$-0.982575\pi$
$71$	−1.33585	+	4.11131i	−0.158536	+	0.487923i	0.839966	+	0.542639i	$0.182575\pi$
$72$	−0.536314	−	0.174259i	−0.0632052	−	0.0205366i
$73$	5.33713	+	7.34593i	0.624664	+	0.859776i	0.997682	−	0.0680477i	$-0.0216770\pi$
$73$	5.33713	+	7.34593i	0.624664	+	0.859776i	−0.373018	+	0.927824i	$0.621677\pi$
$74$	−1.05568			−0.122721
$75$		0			0
$76$	−12.6095			−1.44641
$77$	1.85653	+	2.55530i	0.211572	+	0.291203i
$78$	0.617357	+	0.200592i	0.0699020	+	0.0227125i
$79$	1.00347	−	3.08837i	0.112899	−	0.347469i	−0.878604	−	0.477552i	$-0.841524\pi$
$79$	1.00347	−	3.08837i	0.112899	−	0.347469i	0.991503	+	0.130083i	$0.0415244\pi$
$80$		0			0
$81$	0.309017	+	0.951057i	0.0343352	+	0.105673i
$82$		−	0.358712i		−	0.0396131i
$83$	7.03087	−	2.28447i	0.771738	−	0.250753i	0.103429	−	0.994637i	$-0.467019\pi$
$83$	7.03087	−	2.28447i	0.771738	−	0.250753i	0.668309	+	0.743884i	$0.267019\pi$
$84$	−1.37484	−	0.998876i	−0.150007	−	0.108986i
$85$		0			0
$86$	−0.387414	+	0.281473i	−0.0417760	+	0.0303520i
$87$	2.19482	−	3.02091i	0.235309	−	0.323875i
$88$	−1.21975	+	1.67884i	−0.130026	+	0.178965i
$89$	−12.5378	+	9.10921i	−1.32900	+	0.965575i	−0.329227	+	0.944251i	$0.606788\pi$
$89$	−12.5378	+	9.10921i	−1.32900	+	0.965575i	−0.999773	+	0.0213236i	$0.993212\pi$
$90$		0			0
$91$	3.18123	+	2.31130i	0.333483	+	0.242290i
$92$	−6.44705	+	2.09478i	−0.672152	+	0.218395i
$93$		−	1.25290i		−	0.129920i
$94$	−0.372140	−	1.14533i	−0.0383833	−	0.118132i
$95$		0			0
$96$	0.518399	−	1.59547i	0.0529089	−	0.162837i
$97$	9.54725	+	3.10209i	0.969377	+	0.314970i	0.750564	−	0.660797i	$-0.229782\pi$
$97$	9.54725	+	3.10209i	0.969377	+	0.314970i	0.218812	+	0.975767i	$0.429782\pi$
$98$	−0.521627	−	0.717957i	−0.0526922	−	0.0725247i
$99$	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	$0.511319\pi$
$102$	−0.441985	−	0.608340i	−0.0437630	−	0.0602346i
$103$	0.742551	+	0.241269i	0.0731657	+	0.0237730i	0.345371	−	0.938466i	$-0.387753\pi$
$103$	0.742551	+	0.241269i	0.0731657	+	0.0237730i	−0.272205	+	0.962239i	$0.587753\pi$
$104$	−0.798339	+	2.45704i	−0.0782836	+	0.240932i
$105$		0			0
$106$	0.102818	+	0.316441i	0.00998655	+	0.0307354i
$107$		−	11.9601i		−	1.15623i	−0.815957	−	0.578113i	$-0.803789\pi$
$107$		−	11.9601i		−	1.15623i	0.815957	−	0.578113i	$-0.196211\pi$
$108$	−1.88302	+	0.611830i	−0.181194	+	0.0588734i
$109$	1.96902	+	1.43057i	0.188598	+	0.137024i	0.678078	−	0.734990i	$-0.262813\pi$
$109$	1.96902	+	1.43057i	0.188598	+	0.137024i	−0.489480	+	0.872015i	$0.662813\pi$
$110$		0			0
$111$	−6.02772	+	4.37939i	−0.572126	+	0.415674i
$112$	1.95744	−	2.69419i	0.184961	−	0.254577i
$113$	−9.42535	+	12.9729i	−0.886662	+	1.22039i	0.0878685	+	0.996132i	$0.471994\pi$
$113$	−9.42535	+	12.9729i	−0.886662	+	1.22039i	−0.974531	+	0.224254i	$0.928006\pi$
$114$	0.730039	−	0.530404i	0.0683744	−	0.0496769i
$115$		0			0
$116$	5.98117	+	4.34558i	0.555338	+	0.403477i
$117$	4.35712	−	1.41571i	0.402815	−	0.130883i
$118$		−	1.85987i		−	0.171215i
$119$	−1.40759	−	4.33213i	−0.129034	−	0.397126i
$120$		0			0
$121$	0.785483	−	2.41747i	0.0714076	−	0.219770i
$122$	1.39439	+	0.453065i	0.126242	+	0.0410186i
$123$	−1.48808	−	2.04817i	−0.134176	−	0.184677i
$124$	2.48065			0.222769
$125$		0			0
$126$	0.121614			0.0108342
$127$	−2.25620	−	3.10539i	−0.200205	−	0.275559i	0.697096	−	0.716978i	$-0.254475\pi$
$127$	−2.25620	−	3.10539i	−0.200205	−	0.275559i	−0.897301	+	0.441419i	$0.854475\pi$
$128$	4.20459	+	1.36615i	0.371637	+	0.120752i
$129$	−1.04439	+	3.21430i	−0.0919534	+	0.283004i
$130$		0			0
$131$	−3.84709	−	11.8401i	−0.336122	−	1.03448i	−0.966167	−	0.257919i	$-0.916963\pi$
$131$	−3.84709	−	11.8401i	−0.336122	−	1.03448i	0.630044	−	0.776559i	$-0.283037\pi$
$132$			7.28598i			0.634163i
$133$	5.19878	−	1.68919i	0.450791	−	0.146471i
$134$	−0.383605	−	0.278705i	−0.0331384	−	0.0240765i
$135$		0			0
$136$	2.42115	−	1.75907i	0.207611	−	0.150839i
$137$	6.97049	−	9.59406i	0.595529	−	0.819676i	−0.399761	−	0.916620i	$-0.630907\pi$
$137$	6.97049	−	9.59406i	0.595529	−	0.819676i	0.995290	+	0.0969439i	$0.0309068\pi$
$138$	0.285143	−	0.392466i	0.0242730	−	0.0334089i
$139$	−3.77074	+	2.73960i	−0.319830	+	0.232370i	−0.736103	−	0.676870i	$-0.763336\pi$
$139$	−3.77074	+	2.73960i	−0.319830	+	0.232370i	0.416273	+	0.909240i	$0.363336\pi$
$140$		0			0
$141$	−6.87614	−	4.99580i	−0.579075	−	0.420723i
$142$	0.582530	−	0.189275i	0.0488848	−	0.0158836i
$143$		−	16.8590i		−	1.40982i
$144$	−1.19897	−	3.69005i	−0.0999141	−	0.307504i
$145$		0			0
$146$	0.397566	−	1.22358i	0.0329028	−	0.101264i
$147$	−5.95676	−	1.93547i	−0.491305	−	0.159635i
$148$	−8.67087	−	11.9344i	−0.712741	−	0.981004i
$149$	11.5480			0.946053			0.473026	−	0.881048i	$-0.343162\pi$
$149$	11.5480			0.946053			0.473026	+	0.881048i	$0.343162\pi$
$150$		0			0
$151$	24.4694			1.99129			0.995646	−	0.0932103i	$-0.0297129\pi$
$151$	24.4694			1.99129			0.995646	+	0.0932103i	$0.0297129\pi$
$152$	2.11097	+	2.90550i	0.171222	+	0.235667i
$153$	−5.04728	−	1.63996i	−0.408048	−	0.132583i
$154$	0.138294	−	0.425626i	0.0111441	−	0.0342979i
$155$		0			0
$156$	2.80300	+	8.62676i	0.224420	+	0.690693i
$157$			22.3660i			1.78500i	0.451045	+	0.892501i	$0.351052\pi$
$157$			22.3660i			1.78500i	−0.451045	+	0.892501i	$0.648948\pi$
$158$	−0.437589	+	0.142181i	−0.0348127	+	0.0113113i
$159$	1.89979	+	1.38028i	0.150663	+	0.109463i
$160$		0			0
$161$	2.37743	−	1.72731i	0.187368	−	0.136131i
$162$	0.0832830	−	0.114629i	0.00654333	−	0.00900612i
$163$	−0.478134	+	0.658095i	−0.0374503	+	0.0515460i	−0.827332	−	0.561714i	$-0.810142\pi$
$163$	−0.478134	+	0.658095i	−0.0374503	+	0.0515460i	0.789881	+	0.613260i	$0.210142\pi$
$164$	4.05522	−	2.94629i	0.316659	−	0.230067i
$165$		0			0
$166$	−0.847418	−	0.615685i	−0.0657724	−	0.0477865i
$167$	−23.9343	+	7.77671i	−1.85209	+	0.601780i	−0.855640	+	0.517572i	$0.826836\pi$
$167$	−23.9343	+	7.77671i	−1.85209	+	0.601780i	−0.996448	+	0.0842082i	$0.973164\pi$
$168$			0.484013i			0.0373424i
$169$	−2.46864	−	7.59770i	−0.189896	−	0.584438i
$170$		0			0
$171$	1.96804	−	6.05699i	0.150500	−	0.463190i
$172$	−6.36408	−	2.06781i	−0.485256	−	0.157669i
$173$	−0.241548	−	0.332462i	−0.0183645	−	0.0252766i	0.799736	−	0.600352i	$-0.204973\pi$
$173$	−0.241548	−	0.332462i	−0.0183645	−	0.0252766i	−0.818101	+	0.575075i	$0.804973\pi$
$174$	−0.529076			−0.0401091
$175$		0			0
$176$	−14.2779			−1.07624
$177$	−7.71550	−	10.6195i	−0.579932	−	0.798208i
$178$	2.08836	+	0.678550i	0.156529	+	0.0508595i
$179$	4.58896	−	14.1234i	0.342995	−	1.05563i	−0.619653	−	0.784876i	$-0.712727\pi$
$179$	4.58896	−	14.1234i	0.342995	−	1.05563i	0.962648	−	0.270755i	$-0.0872733\pi$
$180$		0			0
$181$	0.228432	+	0.703043i	0.0169792	+	0.0522568i	0.959187	−	0.282772i	$-0.0912540\pi$
$181$	0.228432	+	0.703043i	0.0169792	+	0.0522568i	−0.942208	+	0.335029i	$0.891254\pi$
$182$		−	0.557153i		−	0.0412990i
$183$	9.84118	−	3.19759i	0.727481	−	0.236373i
$184$	1.56198	+	1.13485i	0.115151	+	0.0836621i
$185$		0			0
$186$	−0.143619	+	0.104345i	−0.0105307	+	0.00765097i
$187$	−11.4791	+	15.7997i	−0.839437	+	1.15539i
$188$	9.89131	−	13.6142i	0.721398	−	0.992920i
$189$	0.694388	−	0.504502i	0.0505093	−	0.0366971i
$190$		0			0
$191$	2.20462	+	1.60175i	0.159521	+	0.115899i	0.664682	−	0.747126i	$-0.268567\pi$
$191$	2.20462	+	1.60175i	0.159521	+	0.115899i	−0.505161	+	0.863025i	$0.668567\pi$
$192$	7.15404	−	2.32449i	0.516298	−	0.167755i
$193$			14.2040i			1.02243i	0.859453	+	0.511215i	$0.170804\pi$
$193$			14.2040i			1.02243i	−0.859453	+	0.511215i	$0.829196\pi$
$194$	−0.439534	−	1.35275i	−0.0315567	−	0.0971215i
$195$		0			0
$196$	3.83208	−	11.7939i	0.273720	−	0.842423i
$197$	5.27447	+	1.71378i	0.375791	+	0.122102i	0.490821	−	0.871260i	$-0.336697\pi$
$197$	5.27447	+	1.71378i	0.375791	+	0.122102i	−0.115031	+	0.993362i	$0.536697\pi$
$198$	−0.306475	−	0.421827i	−0.0217803	−	0.0299780i
$199$	−5.96371			−0.422756			−0.211378	−	0.977404i	$-0.567795\pi$
$199$	−5.96371			−0.422756			−0.211378	+	0.977404i	$0.567795\pi$
$200$		0			0
$201$	−3.34649			−0.236043
$202$	0.0595154	+	0.0819159i	0.00418749	+	0.00576358i
$203$	−3.04811	−	0.990391i	−0.213935	−	0.0695119i
$204$	3.24700	−	9.99322i	0.227335	−	0.699666i
$205$		0			0
$206$	−0.0341853	−	0.105212i	−0.00238181	−	0.00733044i
$207$		−	3.42379i		−	0.237970i
$208$	−16.9054	+	5.49289i	−1.17218	+	0.380863i
$209$	−18.9604	−	13.7755i	−1.31152	−	0.952875i
$210$		0			0
$211$	11.0983	−	8.06342i	0.764042	−	0.555109i	−0.136106	−	0.990694i	$-0.543459\pi$
$211$	11.0983	−	8.06342i	0.764042	−	0.555109i	0.900147	+	0.435586i	$0.143459\pi$
$212$	−2.73285	+	3.76144i	−0.187693	+	0.258337i
$213$	2.54093	−	3.49729i	0.174102	−	0.239630i
$214$	−1.37098	+	0.996073i	−0.0937180	+	0.0680901i
$215$		0			0
$216$	0.456216	+	0.331460i	0.0310415	+	0.0225530i
$217$	−1.02274	+	0.332310i	−0.0694284	+	0.0225587i
$218$		−	0.344849i		−	0.0233561i
$219$	−2.80590	−	8.63566i	−0.189605	−	0.583544i
$220$		0			0
$221$	−7.51322	+	23.1233i	−0.505394	+	1.55544i
$222$	1.00401	+	0.326224i	0.0673849	+	0.0218947i
$223$	−1.90543	−	2.62259i	−0.127597	−	0.175622i	0.740439	−	0.672124i	$-0.234618\pi$
$223$	−1.90543	−	2.62259i	−0.127597	−	0.175622i	−0.868036	+	0.496502i	$0.834618\pi$
$224$	−1.43988			−0.0962060
$225$		0			0
$226$	2.27204			0.151134
$227$	7.74694	+	10.6627i	0.514182	+	0.707711i	0.984618	−	0.174723i	$-0.0559031\pi$
$227$	7.74694	+	10.6627i	0.514182	+	0.707711i	−0.470435	+	0.882434i	$0.655903\pi$
$228$	11.9924	+	3.89656i	0.794215	+	0.258056i
$229$	−1.80407	+	5.55236i	−0.119216	+	0.366911i	−0.992803	−	0.119758i	$-0.961788\pi$
$229$	−1.80407	+	5.55236i	−0.119216	+	0.366911i	0.873587	+	0.486669i	$0.161788\pi$
$230$		0			0
$231$	−0.976037	−	3.00393i	−0.0642185	−	0.197644i
$232$		−	2.10568i		−	0.138245i
$233$	−8.87767	+	2.88453i	−0.581595	+	0.188972i	−0.585015	−	0.811022i	$-0.698911\pi$
$233$	−8.87767	+	2.88453i	−0.581595	+	0.188972i	0.00341975	+	0.999994i	$0.498911\pi$
$234$	−0.525156	−	0.381548i	−0.0343305	−	0.0249426i
$235$		0			0
$236$	21.0258	−	15.2761i	1.36866	−	0.994390i
$237$	−1.90872	+	2.62712i	−0.123984	+	0.170650i
$238$	−0.379360	+	0.522144i	−0.0245903	+	0.0338456i
$239$	13.8748	−	10.0806i	0.897485	−	0.652061i	−0.0403340	−	0.999186i	$-0.512842\pi$
$239$	13.8748	−	10.0806i	0.897485	−	0.652061i	0.937819	+	0.347125i	$0.112842\pi$
$240$		0			0
$241$	−5.84169	−	4.24424i	−0.376296	−	0.273395i	0.383521	−	0.923532i	$-0.374711\pi$
$241$	−5.84169	−	4.24424i	−0.376296	−	0.273395i	−0.759817	+	0.650137i	$0.774711\pi$
$242$	−0.342530	+	0.111295i	−0.0220187	+	0.00715430i
$243$		−	1.00000i		−	0.0641500i
$244$	6.33099	+	19.4848i	0.405300	+	1.24739i
$245$		0			0
$246$	−0.110848	+	0.341155i	−0.00706742	+	0.0217513i
$247$	−27.7492	−	9.01625i	−1.76564	−	0.573690i
$248$	−0.415286	−	0.571593i	−0.0263707	−	0.0362962i
$249$	−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	$0.558157\pi$
$252$	0.998876	+	1.37484i	0.0629233	+	0.0866065i
$253$	−11.9826	−	3.89339i	−0.753342	−	0.244776i
$254$	−0.168066	+	0.517253i	−0.0105454	+	0.0324553i
$255$		0			0
$256$	4.45541	+	13.7123i	0.278463	+	0.857021i
$257$		−	26.9602i		−	1.68173i	−0.541242	−	0.840867i	$-0.682046\pi$
$257$		−	26.9602i		−	1.68173i	0.541242	−	0.840867i	$-0.317954\pi$
$258$	0.455433	−	0.147979i	0.0283540	−	0.00921278i
$259$	5.17365	+	3.75888i	0.321475	+	0.233565i
$260$		0			0
$261$	−3.02091	+	2.19482i	−0.186990	+	0.135856i
$262$	−1.03683	+	1.42707i	−0.0640555	+	0.0881648i
$263$	12.1479	−	16.7202i	0.749073	−	1.03101i	−0.248972	−	0.968511i	$-0.580093\pi$
$263$	12.1479	−	16.7202i	0.749073	−	1.03101i	0.998045	−	0.0625002i	$-0.0199074\pi$
$264$	1.67884	−	1.21975i	0.103326	−	0.0750704i
$265$		0			0
$266$	−0.626600	−	0.455252i	−0.0384193	−	0.0279133i
$267$	14.7390	−	4.78900i	0.902013	−	0.293082i
$268$		−	6.62579i		−	0.404734i
$269$	4.24699	+	13.0709i	0.258943	+	0.796946i	0.993027	+	0.117887i	$0.0376120\pi$
$269$	4.24699	+	13.0709i	0.258943	+	0.796946i	−0.734084	+	0.679059i	$0.762388\pi$
$270$		0			0
$271$	1.03333	−	3.18025i	0.0627701	−	0.193187i	−0.914754	−	0.404012i	$-0.867615\pi$
$271$	1.03333	−	3.18025i	0.0627701	−	0.193187i	0.977524	+	0.210826i	$0.0676153\pi$
$272$	19.5832	+	6.36296i	1.18740	+	0.385811i
$273$	−2.31130	−	3.18123i	−0.139886	−	0.192537i
$274$	−1.68028			−0.101510
$275$		0			0
$276$	6.77883			0.408038
$277$	5.23685	+	7.20791i	0.314652	+	0.433081i	0.936825	−	0.349799i	$-0.113750\pi$
$277$	5.23685	+	7.20791i	0.314652	+	0.433081i	−0.622173	+	0.782880i	$0.713750\pi$
$278$	0.628077	+	0.204075i	0.0376696	+	0.0122396i
$279$	−0.387167	+	1.19158i	−0.0231791	+	0.0713380i
$280$		0			0
$281$	−6.95019	−	21.3905i	−0.414613	−	1.27605i	−0.912596	−	0.408862i	$-0.865926\pi$
$281$	−6.95019	−	21.3905i	−0.414613	−	1.27605i	0.497983	−	0.867187i	$-0.334074\pi$
$282$			1.20427i			0.0717133i
$283$	−1.24297	+	0.403866i	−0.0738870	+	0.0240073i	−0.345727	−	0.938335i	$-0.612368\pi$
$283$	−1.24297	+	0.403866i	−0.0738870	+	0.0240073i	0.271840	+	0.962342i	$0.412368\pi$
$284$	6.92437	+	5.03085i	0.410886	+	0.298526i
$285$		0			0
$286$	−1.93254	+	1.40407i	−0.114273	+	0.0830243i
$287$	−1.27724	+	1.75797i	−0.0753929	+	0.103769i
$288$	−0.986054	+	1.35719i	−0.0581038	+	0.0799730i
$289$	9.03225	−	6.56231i	0.531309	−	0.386018i
$290$		0			0
$291$	−8.12138	−	5.90053i	−0.476084	−	0.345895i
$292$	17.0980	−	5.55546i	1.00058	−	0.325109i
$293$			1.97058i			0.115123i	0.998342	+	0.0575613i	$0.0183325\pi$
$293$			1.97058i			0.115123i	−0.998342	+	0.0575613i	$0.981668\pi$
$294$	0.274235	+	0.844010i	0.0159937	+	0.0492236i
$295$		0			0
$296$	−1.29835	+	3.99590i	−0.0754648	+	0.232257i
$297$	−3.49982	−	1.13716i	−0.203080	−	0.0659847i
$298$	−0.961756	−	1.32374i	−0.0557130	−	0.0766824i
$299$	−15.6855			−0.907118
$300$		0			0
$301$	2.90085			0.167202
$302$	−2.03789	−	2.80491i	−0.117267	−	0.161404i
$303$	0.679640	+	0.220829i	0.0390443	+	0.0126863i
$304$	−7.63588	+	23.5008i	−0.437948	+	1.34786i
$305$		0			0
$306$	0.232365	+	0.715146i	0.0132834	+	0.0408822i
$307$			15.2544i			0.870617i	0.900281	+	0.435308i	$0.143361\pi$
$307$			15.2544i			0.870617i	−0.900281	+	0.435308i	$0.856639\pi$
$308$	5.94756	−	1.93248i	0.338894	−	0.110113i
$309$	−0.631652	−	0.458922i	−0.0359334	−	0.0261071i
$310$		0			0
$311$	−14.3562	+	10.4304i	−0.814065	+	0.591453i	−0.915006	−	0.403439i	$-0.867815\pi$
$311$	−14.3562	+	10.4304i	−0.814065	+	0.591453i	0.100941	+	0.994892i	$0.467815\pi$
$312$	1.51853	−	2.09008i	0.0859699	−	0.118327i
$313$	−16.0976	+	22.1565i	−0.909890	+	1.25236i	0.0573136	+	0.998356i	$0.481747\pi$
$313$	−16.0976	+	22.1565i	−0.909890	+	1.25236i	−0.967204	+	0.254001i	$0.918253\pi$
$314$	2.56380	−	1.86271i	0.144684	−	0.105119i
$315$		0			0
$316$	−5.20150	−	3.77911i	−0.292607	−	0.212592i
$317$	8.22248	−	2.67165i	0.461821	−	0.150055i	−0.0688603	−	0.997626i	$-0.521936\pi$
$317$	8.22248	−	2.67165i	0.461821	−	0.150055i	0.530681	+	0.847572i	$0.321936\pi$
$318$		−	0.332725i		−	0.0186583i
$319$	4.24621	+	13.0685i	0.237742	+	0.731696i
$320$		0			0
$321$	−3.69587	+	11.3747i	−0.206283	+	0.634875i
$322$	−0.396000	−	0.128668i	−0.0220682	−	0.00717039i
$323$	19.8664	+	27.3438i	1.10540	+	1.52145i
$324$	1.97992			0.109996
$325$		0			0
$326$	0.115257			0.00638351
$327$	−1.43057	−	1.96902i	−0.0791109	−	0.108887i
$328$	−1.35777	−	0.441167i	−0.0749704	−	0.0243594i
$329$	−2.25431	+	6.93805i	−0.124284	+	0.382507i
$330$		0			0
$331$	1.53353	+	4.71971i	0.0842903	+	0.259419i	0.984315	−	0.176420i	$-0.0564517\pi$
$331$	1.53353	+	4.71971i	0.0842903	+	0.259419i	−0.900025	+	0.435839i	$0.856452\pi$
$332$		−	14.6370i		−	0.803308i
$333$	7.08601	−	2.30238i	0.388311	−	0.126170i
$334$	2.88475	+	2.09590i	0.157847	+	0.114682i
$335$		0			0
$336$	−2.69419	+	1.95744i	−0.146980	+	0.106787i
$337$	4.29394	−	5.91011i	0.233906	−	0.321944i	−0.675888	−	0.737005i	$-0.736240\pi$
$337$	4.29394	−	5.91011i	0.233906	−	0.321944i	0.909794	+	0.415061i	$0.136240\pi$
$338$	−0.665322	+	0.915738i	−0.0361888	+	0.0498096i
$339$	12.9729	−	9.42535i	0.704590	−	0.511915i
$340$		0			0
$341$	3.73004	+	2.71003i	0.201993	+	0.146757i
$342$	−0.858212	+	0.278850i	−0.0464068	+	0.0150785i
$343$			11.3840i			0.614680i
$344$	0.588946	+	1.81259i	0.0317538	+	0.0977282i
$345$		0			0
$346$	−0.0179930	+	0.0553768i	−0.000967311	+	0.00297708i
$347$	−15.1574	−	4.92493i	−0.813691	−	0.264384i	−0.127531	−	0.991835i	$-0.540705\pi$
$347$	−15.1574	−	4.92493i	−0.813691	−	0.264384i	−0.686160	+	0.727450i	$0.740705\pi$
$348$	−4.34558	−	5.98117i	−0.232947	−	0.320624i
$349$	−16.5844			−0.887743			−0.443871	−	0.896091i	$-0.646395\pi$
$349$	−16.5844			−0.887743			−0.443871	+	0.896091i	$0.646395\pi$
$350$		0			0
$351$	−4.58134			−0.244534
$352$	3.62861	+	4.99435i	0.193405	+	0.266200i
$353$	12.3344	+	4.00768i	0.656492	+	0.213307i	0.618275	−	0.785962i	$-0.287832\pi$
$353$	12.3344	+	4.00768i	0.656492	+	0.213307i	0.0382177	+	0.999269i	$0.487832\pi$
$354$	−0.574732	+	1.76884i	−0.0305467	+	0.0940129i
$355$		0			0
$356$	9.48185	+	29.1821i	0.502537	+	1.54665i
$357$			4.55507i			0.241080i
$358$	−2.00113	+	0.650208i	−0.105763	+	0.0343646i
$359$	−10.9153	−	7.93042i	−0.576087	−	0.418551i	0.261225	−	0.965278i	$-0.415874\pi$
$359$	−10.9153	−	7.93042i	−0.576087	−	0.418551i	−0.837311	+	0.546727i	$0.815874\pi$
$360$		0			0
$361$	−17.4427	+	12.6728i	−0.918036	+	0.666992i
$362$	0.0615647	−	0.0847365i	0.00323577	−	0.00445365i
$363$	−1.49408	+	2.05642i	−0.0784188	+	0.107934i
$364$	6.29859	−	4.57619i	0.330136	−	0.239858i
$365$		0			0
$366$	−1.18614	−	0.861781i	−0.0620006	−	0.0450460i
$367$	4.35073	−	1.41364i	0.227106	−	0.0737913i	−0.193253	−	0.981149i	$-0.561904\pi$
$367$	4.35073	−	1.41364i	0.227106	−	0.0737913i	0.420360	+	0.907358i	$0.361904\pi$
$368$			13.2841i			0.692482i
$369$	0.782331	+	2.40777i	0.0407265	+	0.125343i
$370$		0			0
$371$	0.622838	−	1.91690i	0.0323361	−	0.0995204i
$372$	−2.35924	−	0.766562i	−0.122321	−	0.0397444i
$373$	12.1944	+	16.7841i	0.631401	+	0.869048i	0.998120	−	0.0612830i	$-0.0195192\pi$
$373$	12.1944	+	16.7841i	0.631401	+	0.869048i	−0.366720	+	0.930331i	$0.619519\pi$
$374$	2.76712			0.143084
$375$		0			0
$376$	−4.79291			−0.247175
$377$	10.0552	+	13.8398i	0.517870	+	0.712787i
$378$	−0.115661	−	0.0375807i	−0.00594898	−	0.00193294i
$379$	1.78662	−	5.49865i	0.0917725	−	0.282447i	−0.894627	−	0.446815i	$-0.852558\pi$
$379$	1.78662	−	5.49865i	0.0917725	−	0.282447i	0.986399	+	0.164368i	$0.0525584\pi$
$380$		0			0
$381$	1.18615	+	3.65061i	0.0607686	+	0.187026i
$382$		−	0.386113i		−	0.0197553i
$383$	−24.5491	+	7.97647i	−1.25440	+	0.407579i	−0.859495	−	0.511144i	$-0.829222\pi$
$383$	−24.5491	+	7.97647i	−1.25440	+	0.407579i	−0.394903	+	0.918723i	$0.629222\pi$
$384$	−3.57664	−	2.59858i	−0.182519	−	0.132608i
$385$		0			0
$386$	1.62820	−	1.18295i	0.0828731	−	0.0602108i
$387$	1.98655	−	2.73425i	0.100982	−	0.138990i
$388$	11.6826	−	16.0797i	0.593094	−	0.816324i
$389$	−12.7053	+	9.23092i	−0.644183	+	0.468026i	−0.861285	−	0.508123i	$-0.830340\pi$
$389$	−12.7053	+	9.23092i	−0.644183	+	0.468026i	0.217102	+	0.976149i	$0.430340\pi$
$390$		0			0
$391$	14.6999	+	10.6801i	0.743407	+	0.540117i
$392$	−3.35909	+	1.09144i	−0.169660	+	0.0551258i
$393$			12.4495i			0.627992i
$394$	−0.242825	−	0.747337i	−0.0122333	−	0.0376503i
$395$		0			0
$396$	2.25149	−	6.92938i	0.113142	−	0.348214i
$397$	18.6445	+	6.05796i	0.935740	+	0.304040i	0.736908	−	0.675993i	$-0.236285\pi$
$397$	18.6445	+	6.05796i	0.935740	+	0.304040i	0.198832	+	0.980034i	$0.436285\pi$
$398$	0.496675	+	0.683615i	0.0248961	+	0.0342665i
$399$	−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	$0.617274\pi$
$402$	0.278705	+	0.383605i	0.0139006	+	0.0191325i
$403$	5.45903	+	1.77375i	0.271934	+	0.0883566i
$404$	−0.437224	+	1.34564i	−0.0217527	+	0.0669479i
$405$		0			0
$406$	0.140328	+	0.431885i	0.00696436	+	0.0214341i
$407$		−	27.4179i		−	1.35906i
$408$	−2.84623	+	0.924795i	−0.140909	+	0.0457842i
$409$	−22.5507	−	16.3841i	−1.11506	−	0.810140i	−0.131609	−	0.991302i	$-0.542014\pi$
$409$	−22.5507	−	16.3841i	−1.11506	−	0.810140i	−0.983453	+	0.181162i	$0.942014\pi$
$410$		0			0
$411$	−9.59406	+	6.97049i	−0.473240	+	0.343829i
$412$	0.908630	−	1.25062i	0.0447650	−	0.0616137i
$413$	−6.62229	+	9.11481i	−0.325862	+	0.448510i
$414$	−0.392466	+	0.285143i	−0.0192886	+	0.0140140i
$415$		0			0
$416$	6.21773	+	4.51745i	0.304850	+	0.221486i
$417$	4.43277	−	1.44030i	0.217074	−	0.0705316i
$418$			3.32069i			0.162420i
$419$	11.2137	+	34.5121i	0.547823	+	1.68603i	0.714182	+	0.699960i	$0.246799\pi$
$419$	11.2137	+	34.5121i	0.547823	+	1.68603i	−0.166359	+	0.986065i	$0.553201\pi$
$420$		0			0
$421$	−1.04324	+	3.21077i	−0.0508445	+	0.156483i	−0.973255	−	0.229728i	$-0.926216\pi$
$421$	−1.04324	+	3.21077i	−0.0508445	+	0.156483i	0.922410	+	0.386211i	$0.126216\pi$
$422$	−1.84861	−	0.600649i	−0.0899888	−	0.0292391i
$423$	4.99580	+	6.87614i	0.242904	+	0.334329i
$424$	1.32422			0.0643099
$425$		0			0
$426$	−0.612508			−0.0296761
$427$	−5.22040	−	7.18527i	−0.252633	−	0.347719i
$428$	−22.5211	−	7.31755i	−1.08860	−	0.353707i
$429$	−5.20972	+	16.0339i	−0.251528	+	0.774123i
$430$		0			0
$431$	−7.93015	−	24.4065i	−0.381982	−	1.17562i	−0.938646	−	0.344881i	$-0.887919\pi$
$431$	−7.93015	−	24.4065i	−0.381982	−	1.17562i	0.556665	−	0.830737i	$-0.312081\pi$
$432$			3.87995i			0.186674i
$433$	37.8587	−	12.3010i	1.81937	−	0.591150i	0.819536	−	0.573027i	$-0.194231\pi$
$433$	37.8587	−	12.3010i	1.81937	−	0.591150i	0.999836	−	0.0181229i	$-0.00576900\pi$
$434$	0.123270	+	0.0895606i	0.00591713	+	0.00429905i
$435$		0			0
$436$	3.89850	−	2.83243i	0.186704	−	0.135649i
$437$	−12.8167	+	17.6407i	−0.613106	+	0.843867i
$438$	−0.756216	+	1.04084i	−0.0361334	+	0.0497333i
$439$	27.4402	−	19.9365i	1.30965	−	0.951516i	0.309649	−	0.950851i	$-0.399788\pi$
$439$	27.4402	−	19.9365i	1.30965	−	0.951516i	1.00000		0.000665125i	$-0.000211716\pi$
$440$		0			0
$441$	5.06712	+	3.68148i	0.241291	+	0.175308i
$442$	3.27633	−	1.06454i	0.155839	−	0.0506352i
$443$		−	28.9300i		−	1.37451i	−0.726418	−	0.687253i	$-0.758816\pi$
$443$		−	28.9300i		−	1.37451i	0.726418	−	0.687253i	$-0.241184\pi$
$444$	4.55855	+	14.0298i	0.216339	+	0.665823i
$445$		0			0
$446$	−0.141936	+	0.436835i	−0.00672088	+	0.0206847i
$447$	−10.9828	−	3.56854i	−0.519471	−	0.168786i
$448$	−3.79497	−	5.22332i	−0.179295	−	0.246779i
$449$	10.2089			0.481788			0.240894	−	0.970551i	$-0.422559\pi$
$449$	10.2089			0.481788			0.240894	+	0.970551i	$0.422559\pi$
$450$		0			0
$451$	9.31639			0.438692
$452$	18.6615	+	25.6853i	0.877762	+	1.20814i
$453$	−23.2718	−	7.56147i	−1.09340	−	0.355269i
$454$	0.577074	−	1.77605i	0.0270834	−	0.0833542i
$455$		0			0
$456$	−1.10980	−	3.41562i	−0.0519712	−	0.159951i
$457$		−	32.4952i		−	1.52006i	−0.649888	−	0.760030i	$-0.725184\pi$
$457$		−	32.4952i		−	1.52006i	0.649888	−	0.760030i	$-0.274816\pi$
$458$	0.786712	−	0.255618i	0.0367606	−	0.0119442i
$459$	4.29347	+	3.11939i	0.200402	+	0.145601i
$460$		0			0
$461$	0.566772	−	0.411784i	0.0263972	−	0.0191787i	−0.574508	−	0.818499i	$-0.694807\pi$
$461$	0.566772	−	0.411784i	0.0263972	−	0.0191787i	0.600906	+	0.799320i	$0.294807\pi$
$462$	−0.263051	+	0.362059i	−0.0122382	+	0.0168445i
$463$	1.27623	−	1.75659i	0.0593117	−	0.0816355i	−0.778331	−	0.627854i	$-0.783933\pi$
$463$	1.27623	−	1.75659i	0.0593117	−	0.0816355i	0.837642	+	0.546219i	$0.183933\pi$
$464$	11.7210	−	8.51578i	0.544132	−	0.395335i
$465$		0			0
$466$	1.07001	+	0.777408i	0.0495673	+	0.0360127i
$467$	−3.68734	+	1.19809i	−0.170630	+	0.0554410i	−0.393086	−	0.919502i	$-0.628593\pi$
$467$	−3.68734	+	1.19809i	−0.170630	+	0.0554410i	0.222456	+	0.974943i	$0.428593\pi$
$468$		−	9.07071i		−	0.419294i
$469$	0.887597	+	2.73174i	0.0409854	+	0.126140i
$470$		0			0
$471$	6.91148	−	21.2714i	0.318464	−	0.980132i
$472$	−7.03986	−	2.28739i	−0.324036	−	0.105286i
$473$	−7.31036	−	10.0618i	−0.336131	−	0.462644i
$474$	0.460109			0.0211335
$475$		0			0
$476$	−9.01870			−0.413371
$477$	−1.38028	−	1.89979i	−0.0631986	−	0.0869855i
$478$	−2.31107	−	0.750911i	−0.105706	−	0.0343459i
$479$	6.79817	−	20.9226i	0.310617	−	0.955979i	−0.666905	−	0.745143i	$-0.732381\pi$
$479$	6.79817	−	20.9226i	0.310617	−	0.955979i	0.977521	−	0.210836i	$-0.0676187\pi$
$480$		0			0
$481$	−10.5480	−	32.4634i	−0.480948	−	1.48020i
$482$			1.02310i			0.0466010i
$483$	−2.79484	+	0.908099i	−0.127170	+	0.0413199i
$484$	−4.07156	−	2.95816i	−0.185071	−	0.134462i
$485$		0			0
$486$	−0.114629	+	0.0832830i	−0.00519969	+	0.00377779i
$487$	−16.6929	+	22.9759i	−0.756430	+	1.04114i	0.241073	+	0.970507i	$0.422501\pi$
$487$	−16.6929	+	22.9759i	−0.756430	+	1.04114i	−0.997503	+	0.0706291i	$0.977499\pi$
$488$	3.42982	−	4.72075i	0.155261	−	0.213698i
$489$	0.658095	−	0.478134i	0.0297601	−	0.0216220i
$490$		0			0
$491$	11.3641	+	8.25653i	0.512856	+	0.372612i	0.813906	−	0.580997i	$-0.197337\pi$
$491$	11.3641	+	8.25653i	0.512856	+	0.372612i	−0.301050	+	0.953608i	$0.597337\pi$
$492$	−4.76720	+	1.54896i	−0.214922	+	0.0698323i
$493$		−	19.8167i		−	0.892498i
$494$	1.27751	+	3.93176i	0.0574778	+	0.176898i
$495$		0			0
$496$	1.50219	−	4.62326i	0.0674503	−	0.207591i
$497$	−3.52878	−	1.14657i	−0.158287	−	0.0514307i
$498$	0.615685	+	0.847418i	0.0275895	+	0.0379737i
$499$	−13.0842			−0.585731			−0.292866	−	0.956154i	$-0.594609\pi$
$499$	−13.0842			−0.585731			−0.292866	+	0.956154i	$0.594609\pi$
$500$		0			0
$501$	25.1660			1.12433
$502$	0.479467	+	0.659929i	0.0213996	+	0.0294541i
$503$	11.7022	+	3.80226i	0.521773	+	0.169534i	0.558050	−	0.829807i	$-0.311550\pi$
$503$	11.7022	+	3.80226i	0.521773	+	0.169534i	−0.0362767	+	0.999342i	$0.511550\pi$
$504$	0.149568	−	0.460324i	0.00666230	−	0.0205044i
$505$		0			0
$506$	0.551653	+	1.69781i	0.0245240	+	0.0754770i
$507$			7.98869i			0.354790i
$508$	−7.22793	+	2.34850i	−0.320688	+	0.104198i
$509$	0.0634186	+	0.0460763i	0.00281098	+	0.00204230i	0.589190	−	0.807995i	$-0.299447\pi$
$509$	0.0634186	+	0.0460763i	0.00281098	+	0.00204230i	−0.586379	+	0.810037i	$0.699447\pi$
$510$		0			0
$511$	−6.30509	+	4.58092i	−0.278921	+	0.202648i
$512$	6.39793	−	8.80600i	0.282751	−	0.389174i
$513$	−3.74343	+	5.15239i	−0.165276	+	0.227483i
$514$	−3.09043	+	2.24533i	−0.136313	+	0.0990372i
$515$		0			0
$516$	5.41361	+	3.93321i	0.238321	+	0.173150i
$517$	29.7463	−	9.66515i	1.30824	−	0.425073i
$518$		−	0.906103i		−	0.0398119i
$519$	0.126989	+	0.390832i	0.00557420	+	0.0171556i
$520$		0			0
$521$	5.59919	−	17.2325i	0.245305	−	0.754971i	−0.750281	−	0.661119i	$-0.770082\pi$
$521$	5.59919	−	17.2325i	0.245305	−	0.754971i	0.995586	−	0.0938524i	$-0.0299182\pi$
$522$	0.503181	+	0.163493i	0.0220236	+	0.00715591i
$523$	−6.83613	−	9.40913i	−0.298923	−	0.411432i	0.632964	−	0.774181i	$-0.281838\pi$
$523$	−6.83613	−	9.40913i	−0.298923	−	0.411432i	−0.931887	+	0.362749i	$0.881838\pi$
$524$	−24.6490			−1.07680
$525$		0			0
$526$	−2.92834			−0.127682
$527$	−3.90828	−	5.37929i	−0.170247	−	0.234326i
$528$	13.5791	+	4.41212i	0.590955	+	0.192013i
$529$	3.48500	−	10.7257i	0.151522	−	0.466336i
$530$		0			0
$531$	4.05628	+	12.4839i	0.176027	+	0.541757i
$532$		−	10.8229i		−	0.469232i
$533$	11.0308	−	3.58413i	0.477797	−	0.155246i
$534$	−1.77647	−	1.29068i	−0.0768753	−	0.0558532i
$535$		0			0
$536$	−1.52672	+	1.10923i	−0.0659442	+	0.0479113i
$537$	−8.72873	+	12.0141i	−0.376672	+	0.518445i
$538$	1.14460	−	1.57541i	0.0493473	−	0.0679208i
$539$	18.6466	−	13.5476i	0.803167	−	0.583535i
$540$		0			0
$541$	−23.6812	−	17.2054i	−1.01814	−	0.739719i	−0.0522359	−	0.998635i	$-0.516635\pi$
$541$	−23.6812	−	17.2054i	−1.01814	−	0.739719i	−0.965900	+	0.258916i	$0.916635\pi$
$542$	−0.450608	+	0.146412i	−0.0193553	+	0.00628891i
$543$		−	0.739223i		−	0.0317231i
$544$	−2.75115	−	8.46718i	−0.117955	−	0.363027i
$545$		0			0
$546$	−0.172170	+	0.529884i	−0.00736819	+	0.0226770i
$547$	−11.4769	−	3.72908i	−0.490717	−	0.159444i	0.0531977	−	0.998584i	$-0.483059\pi$
$547$	−11.4769	−	3.72908i	−0.490717	−	0.159444i	−0.543915	+	0.839140i	$0.683059\pi$
$548$	−13.8010	−	18.9955i	−0.589551	−	0.811448i
$549$	−10.3476			−0.441626
$550$		0			0
$551$	23.7810			1.01311
$552$	−1.13485	−	1.56198i	−0.0483023	−	0.0664825i
$553$	2.65078	+	0.861290i	0.112723	+	0.0366258i
$554$	0.390096	−	1.20059i	0.0165736	−	0.0510083i
$555$		0			0
$556$	2.85168	+	8.77655i	0.120938	+	0.372209i
$557$			41.4154i			1.75483i	0.479737	+	0.877413i	$0.340732\pi$
$557$			41.4154i			1.75483i	−0.479737	+	0.877413i	$0.659268\pi$
$558$	0.168834	−	0.0548576i	0.00714732	−	0.00232231i
$559$	−12.5265	−	9.10106i	−0.529816	−	0.384934i
$560$		0			0
$561$	15.7997	−	11.4791i	0.667062	−	0.484649i
$562$	−1.87314	+	2.57816i	−0.0790137	+	0.108753i
$563$	−18.8954	+	26.0072i	−0.796345	+	1.09607i	0.196944	+	0.980415i	$0.436898\pi$
$563$	−18.8954	+	26.0072i	−0.796345	+	1.09607i	−0.993289	+	0.115660i	$0.963102\pi$
$564$	−13.6142	+	9.89131i	−0.573262	+	0.416499i
$565$		0			0
$566$	0.149813	+	0.108846i	0.00629712	+	0.00457513i
$567$	−0.816302	+	0.265233i	−0.0342815	+	0.0111387i
$568$		−	2.43773i		−	0.102285i
$569$	−6.52273	−	20.0749i	−0.273447	−	0.841583i	−0.989626	−	0.143667i	$-0.954111\pi$
$569$	−6.52273	−	20.0749i	−0.273447	−	0.841583i	0.716179	−	0.697916i	$-0.245889\pi$
$570$		0			0
$571$	−7.64795	+	23.5380i	−0.320057	+	0.985034i	0.653566	+	0.756870i	$0.273272\pi$
$571$	−7.64795	+	23.5380i	−0.320057	+	0.985034i	−0.973623	+	0.228164i	$0.926728\pi$
$572$	−31.7459	−	10.3149i	−1.32736	−	0.431286i
$573$	−1.60175	−	2.20462i	−0.0669142	−	0.0920994i
$574$	0.307886			0.0128509
$575$		0			0
$576$	−7.52220			−0.313425
$577$	−11.0333	−	15.1861i	−0.459324	−	0.632205i	0.515045	−	0.857163i	$-0.327775\pi$
$577$	−11.0333	−	15.1861i	−0.459324	−	0.632205i	−0.974368	+	0.224959i	$0.927775\pi$
$578$	−1.50446	−	0.488830i	−0.0625775	−	0.0203327i
$579$	4.38929	−	13.5088i	0.182413	−	0.561408i
$580$		0			0
$581$	1.96078	+	6.03467i	0.0813470	+	0.250360i
$582$			1.42236i			0.0589587i
$583$	−8.21853	+	2.67036i	−0.340377	+	0.110595i
$584$	−4.14247	−	3.00968i	−0.171417	−	0.124541i
$585$		0			0
$586$	0.225886	−	0.164116i	0.00933127	−	0.00677956i
$587$	−8.67406	+	11.9388i	−0.358017	+	0.492768i	−0.949595	−	0.313480i	$-0.898505\pi$
$587$	−8.67406	+	11.9388i	−0.358017	+	0.492768i	0.591578	+	0.806248i	$0.298505\pi$
$588$	−7.28905	+	10.0325i	−0.300595	+	0.413734i
$589$	6.45543	−	4.69014i	0.265991	−	0.193254i
$590$		0			0
$591$	−4.48673	−	3.25980i	−0.184560	−	0.134090i
$592$	−27.4933	+	8.93313i	−1.12997	+	0.367149i
$593$			8.01859i			0.329284i	0.986353	+	0.164642i	$0.0526469\pi$
$593$			8.01859i			0.329284i	−0.986353	+	0.164642i	$0.947353\pi$
$594$	0.161124	+	0.495888i	0.00661099	+	0.0203465i
$595$		0			0
$596$	7.06544	−	21.7452i	0.289412	−	0.890718i
$597$	5.67182	+	1.84289i	0.232132	+	0.0754243i
$598$	1.30634	+	1.79802i	0.0534201	+	0.0735265i
$599$	1.28951			0.0526878			0.0263439	−	0.999653i	$-0.491614\pi$
$599$	1.28951			0.0526878			0.0263439	+	0.999653i	$0.491614\pi$
$600$		0			0
$601$	−16.8813			−0.688603			−0.344302	−	0.938859i	$-0.611884\pi$
$601$	−16.8813			−0.688603			−0.344302	+	0.938859i	$0.611884\pi$
$602$	−0.241591	−	0.332522i	−0.00984652	−	0.0135526i
$603$	3.18270	+	1.03412i	0.129609	+	0.0421127i
$604$	14.9711	−	46.0764i	0.609167	−	1.87482i
$605$		0			0
$606$	−0.0312891	−	0.0962979i	−0.00127103	−	0.00391184i
$607$			0.499318i			0.0202667i	0.999949	+	0.0101334i	$0.00322560\pi$
$607$			0.499318i			0.0202667i	−0.999949	+	0.0101334i	$0.996774\pi$
$608$	10.1611	−	3.30153i	0.412085	−	0.133895i
$609$	2.59288	+	1.88384i	0.105069	+	0.0763369i
$610$		0			0
$611$	31.5019	−	22.8875i	1.27443	−	0.925929i
$612$	−6.17615	+	8.50074i	−0.249656	+	0.343622i
$613$	16.1195	−	22.1866i	0.651061	−	0.896108i	−0.348084	−	0.937463i	$-0.613168\pi$
$613$	16.1195	−	22.1866i	0.651061	−	0.896108i	0.999145	+	0.0413552i	$0.0131675\pi$
$614$	1.74860	−	1.27043i	0.0705679	−	0.0512706i
$615$		0			0
$616$	−1.44097	−	1.04692i	−0.0580582	−	0.0421818i
$617$	−26.9344	+	8.75151i	−1.08434	+	0.352323i	−0.796056	−	0.605223i	$-0.793084\pi$
$617$	−26.9344	+	8.75151i	−1.08434	+	0.352323i	−0.288282	+	0.957546i	$0.593084\pi$
$618$			0.110626i			0.00445003i
$619$	0.114894	+	0.353606i	0.00461796	+	0.0142126i	0.953339	−	0.301902i	$-0.0976216\pi$
$619$	0.114894	+	0.353606i	0.00461796	+	0.0142126i	−0.948721	+	0.316115i	$0.897622\pi$
$620$		0			0
$621$	−1.05801	+	3.25621i	−0.0424564	+	0.130667i
$622$	2.39125	+	0.776966i	0.0958806	+	0.0311535i
$623$	−7.81853	−	10.7613i	−0.313243	−	0.431142i
$624$	17.7754			0.711584
$625$		0			0
$626$	3.88043			0.155093
$627$	13.7755	+	18.9604i	0.550142	+	0.757206i
$628$	42.1157	+	13.6842i	1.68060	+	0.546059i
$629$	−12.2188	+	37.6056i	−0.487195	+	1.49943i
$630$		0			0
$631$	5.08354	+	15.6455i	0.202373	+	0.622839i	0.999811	+	0.0194386i	$0.00618787\pi$
$631$	5.08354	+	15.6455i	0.202373	+	0.622839i	−0.797438	+	0.603400i	$0.793812\pi$
$632$			1.83120i			0.0728411i
$633$	−13.0469	+	4.23919i	−0.518567	+	0.168493i
$634$	−0.991042	−	0.720034i	−0.0393593	−	0.0285962i
$635$		0			0
$636$	3.76144	−	2.73285i	0.149151	−	0.108364i
$637$	16.8661	−	23.2142i	0.668259	−	0.919780i
$638$	1.14439	−	1.57512i	0.0453070	−	0.0623598i
$639$	−3.49729	+	2.54093i	−0.138351	+	0.100518i
$640$		0			0
$641$	1.63910	+	1.19088i	0.0647407	+	0.0470368i	0.619685	−	0.784851i	$-0.287260\pi$
$641$	1.63910	+	1.19088i	0.0647407	+	0.0470368i	−0.554944	+	0.831888i	$0.687260\pi$
$642$	1.61168	−	0.523666i	0.0636079	−	0.0206675i
$643$		−	33.2034i		−	1.30941i	−0.755883	−	0.654706i	$-0.772792\pi$
$643$		−	33.2034i		−	1.30941i	0.755883	−	0.654706i	$-0.227208\pi$
$644$	−1.79797	−	5.53357i	−0.0708498	−	0.218053i
$645$		0			0
$646$	1.47986	−	4.55455i	0.0582244	−	0.179196i
$647$	38.5936	+	12.5398i	1.51727	+	0.492992i	0.944999	−	0.327072i	$-0.106062\pi$
$647$	38.5936	+	12.5398i	1.51727	+	0.492992i	0.572273	+	0.820064i	$0.306062\pi$
$648$	−0.331460	−	0.456216i	−0.0130210	−	0.0179218i
$649$	48.3042			1.89611
$650$		0			0
$651$	1.07538			0.0421474
$652$	0.946669	+	1.30298i	0.0370744	+	0.0510286i
$653$	−8.84208	−	2.87297i	−0.346017	−	0.112428i	0.130852	−	0.991402i	$-0.458229\pi$
$653$	−8.84208	−	2.87297i	−0.346017	−	0.112428i	−0.476870	+	0.878974i	$0.658229\pi$
$654$	−0.106564	+	0.327971i	−0.00416699	+	0.0128247i
$655$		0			0
$656$	−3.03540	−	9.34201i	−0.118513	−	0.364744i
$657$			9.08007i			0.354247i
$658$	0.983049	−	0.319412i	0.0383232	−	0.0124520i
$659$	−2.81185	−	2.04293i	−0.109534	−	0.0795811i	0.531670	−	0.846952i	$-0.321565\pi$
$659$	−2.81185	−	2.04293i	−0.109534	−	0.0795811i	−0.641204	+	0.767371i	$0.721565\pi$
$660$		0			0
$661$	−3.29515	+	2.39407i	−0.128166	+	0.0931184i	−0.650022	−	0.759916i	$-0.725240\pi$
$661$	−3.29515	+	2.39407i	−0.128166	+	0.0931184i	0.521855	+	0.853034i	$0.325240\pi$
$662$	0.413300	−	0.568859i	0.0160634	−	0.0221093i
$663$	14.2910	−	19.6699i	0.555016	−	0.763914i
$664$	−3.37266	+	2.45038i	−0.130885	+	0.0950932i
$665$		0			0
$666$	−0.854064	−	0.620514i	−0.0330943	−	0.0240444i
$667$	12.1589	−	3.95065i	0.470793	−	0.152970i
$668$			49.8267i			1.92785i
$669$	1.00174	+	3.08304i	0.0387296	+	0.119197i
$670$		0			0
$671$	−11.7669	+	36.2148i	−0.454257	+	1.39806i
$672$	1.36941	+	0.444947i	0.0528260	+	0.0171642i
$673$	−12.5694	−	17.3003i	−0.484514	−	0.666877i	0.494850	−	0.868978i	$-0.335223\pi$
$673$	−12.5694	−	17.3003i	−0.484514	−	0.666877i	−0.979365	+	0.202102i	$0.935223\pi$
$674$	−1.03508			−0.0398699
$675$		0			0
$676$	−15.8170			−0.608346
$677$	−11.9472	−	16.4438i	−0.459166	−	0.631988i	0.515169	−	0.857088i	$-0.327729\pi$
$677$	−11.9472	−	16.4438i	−0.459166	−	0.631988i	−0.974336	+	0.225100i	$0.927729\pi$
$678$	−2.16084	−	0.702100i	−0.0829866	−	0.0269640i
$679$	−2.66256	+	8.19451i	−0.102180	+	0.314476i
$680$		0			0
$681$	−4.07281	−	12.5348i	−0.156070	−	0.480335i
$682$		−	0.653271i		−	0.0250150i
$683$	18.0312	−	5.85868i	0.689943	−	0.224176i	0.0569998	−	0.998374i	$-0.481847\pi$
$683$	18.0312	−	5.85868i	0.689943	−	0.224176i	0.632943	+	0.774198i	$0.281847\pi$
$684$	−10.2013	−	7.41170i	−0.390058	−	0.283394i
$685$		0			0
$686$	1.30494	−	0.948096i	0.0498229	−	0.0361985i
$687$	3.43155	−	4.72312i	0.130922	−	0.180198i
$688$	−7.70770	+	10.6087i	−0.293853	+	0.404455i
$689$	−8.70359	+	6.32353i	−0.331580	+	0.240907i
$690$		0			0
$691$	−11.9893	−	8.71071i	−0.456093	−	0.331371i	0.335904	−	0.941896i	$-0.390958\pi$
$691$	−11.9893	−	8.71071i	−0.456093	−	0.331371i	−0.791997	+	0.610525i	$0.790958\pi$
$692$	−0.773818	+	0.251429i	−0.0294162	+	0.00955789i
$693$			3.15852i			0.119982i
$694$	0.697811	+	2.14764i	0.0264885	+	0.0815234i
$695$		0			0
$696$	−0.650691	+	2.00262i	−0.0246644	+	0.0759092i
$697$	−12.7781	−	4.15185i	−0.484004	−	0.157262i
$698$	1.38120	+	1.90106i	0.0522791	+	0.0719560i
$699$	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	$0.297954\pi$
$702$	0.381548	+	0.525156i	0.0144006	+	0.0198207i
$703$	−45.1287	−	14.6632i	−1.70206	−	0.553033i
$704$	−8.55395	+	26.3264i	−0.322389	+	0.992212i
$705$		0			0
$706$	−0.567846	−	1.74765i	−0.0213712	−	0.0657737i
$707$		−	0.613363i		−	0.0230679i
$708$	−24.7173	+	8.03112i	−0.928931	+	0.301828i
$709$	20.4944	+	14.8900i	0.769682	+	0.559207i	0.901865	−	0.432019i	$-0.142199\pi$
$709$	20.4944	+	14.8900i	0.769682	+	0.559207i	−0.132183	+	0.991225i	$0.542199\pi$
$710$		0			0
$711$	2.62712	−	1.90872i	0.0985248	−	0.0715825i
$712$	5.13681	−	7.07021i	0.192510	−	0.264967i
$713$	2.52140	−	3.47041i	0.0944272	−	0.129968i
$714$	0.522144	−	0.379360i	0.0195408	−	0.0141972i
$715$		0			0
$716$	−23.7869	−	17.2822i	−0.888959	−	0.645867i
$717$	−16.3108	+	5.29969i	−0.609137	+	0.197921i
$718$			1.91168i			0.0713432i
$719$	1.27535	+	3.92511i	0.0475624	+	0.146382i	0.972017	−	0.234910i	$-0.0754794\pi$
$719$	1.27535	+	3.92511i	0.0475624	+	0.146382i	−0.924455	+	0.381292i	$0.875479\pi$
$720$		0			0
$721$	−0.207084	+	0.637339i	−0.00771221	+	0.0237358i
$722$	2.90536	+	0.944008i	0.108126	+	0.0351323i
$723$	4.24424	+	5.84169i	0.157845	+	0.217255i
$724$	1.46361			0.0543945
$725$		0			0
$726$	0.360157			0.0133667
$727$	13.5214	+	18.6106i	0.501479	+	0.690227i	0.982454	−	0.186508i	$-0.0597169\pi$
$727$	13.5214	+	18.6106i	0.501479	+	0.690227i	−0.480974	+	0.876735i	$0.659717\pi$
$728$	−2.10890	−	0.685223i	−0.0781610	−	0.0253961i
$729$	−0.309017	+	0.951057i	−0.0114451	+	0.0352243i
$730$		0			0
$731$	5.54260	+	17.0584i	0.205000	+	0.630927i
$732$		−	20.4875i		−	0.757240i
$733$	8.89896	−	2.89145i	0.328690	−	0.106798i	−0.140023	−	0.990148i	$-0.544718\pi$
$733$	8.89896	−	2.89145i	0.328690	−	0.106798i	0.468714	+	0.883350i	$0.344718\pi$
$734$	−0.524386	−	0.380989i	−0.0193554	−	0.0140625i
$735$		0			0
$736$	4.64671	−	3.37604i	0.171280	−	0.124442i
$737$	7.23847	−	9.96291i	0.266633	−	0.366988i
$738$	0.210846	−	0.290204i	0.00776133	−	0.0106826i
$739$	−38.1657	+	27.7290i	−1.40395	+	1.02003i	−0.409781	+	0.912184i	$0.634395\pi$
$739$	−38.1657	+	27.7290i	−1.40395	+	1.02003i	−0.994168	+	0.107844i	$0.965605\pi$
$740$		0			0
$741$	23.6048	+	17.1499i	0.867146	+	0.630018i
$742$	−0.271604	+	0.0882496i	−0.00997091	+	0.00323974i
$743$			2.39450i			0.0878455i	0.999035	+	0.0439228i	$0.0139855\pi$
$743$			2.39450i			0.0878455i	−0.999035	+	0.0439228i	$0.986014\pi$
$744$	0.218329	+	0.671947i	0.00800433	+	0.0246348i
$745$		0			0
$746$	0.908366	−	2.79566i	0.0332576	−	0.102356i
$747$	7.03087	+	2.28447i	0.257246	+	0.0835843i
$748$	22.7278	+	31.2821i	0.831011	+	1.14379i
$749$	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	$0.542032\pi$
$752$	−19.3835	−	26.6790i	−0.706842	−	0.972885i
$753$	5.47530	+	1.77903i	0.199531	+	0.0648316i
$754$	0.749019	−	2.30524i	0.0272777	−	0.0839520i
$755$		0			0
$756$	−0.525140	−	1.61622i	−0.0190992	−	0.0587812i
$757$		−	13.3742i		−	0.486094i	−0.970015	−	0.243047i	$-0.921853\pi$
$757$		−	13.3742i		−	0.486094i	0.970015	−	0.243047i	$-0.0781469\pi$
$758$	−0.779101	+	0.253145i	−0.0282982	+	0.00919465i
$759$	10.1930	+	7.40567i	0.369984	+	0.268809i
$760$		0			0
$761$	−17.5994	+	12.7867i	−0.637978	+	0.463518i	−0.859155	−	0.511716i	$-0.829010\pi$
$761$	−17.5994	+	12.7867i	−0.637978	+	0.463518i	0.221177	+	0.975234i	$0.429010\pi$
$762$	0.319680	−	0.440002i	0.0115808	−	0.0159396i
$763$	−1.22788	+	1.69003i	−0.0444521	+	0.0611831i
$764$	4.36499	−	3.17135i	0.157920	−	0.114735i
$765$		0			0
$766$	2.95886	+	2.14973i	0.106908	+	0.0776730i
$767$	57.1932	−	18.5832i	2.06513	−	0.671000i
$768$		−	14.4180i		−	0.520265i
$769$	−4.38814	−	13.5053i	−0.158240	−	0.487014i	0.840234	−	0.542223i	$-0.182417\pi$
$769$	−4.38814	−	13.5053i	−0.158240	−	0.487014i	−0.998475	+	0.0552094i	$0.982417\pi$
$770$		0			0
$771$	−8.33117	+	25.6407i	−0.300040	+	0.923427i
$772$	26.7465	+	8.69046i	0.962627	+	0.312777i
$773$	−13.4230	−	18.4752i	−0.482791	−	0.664505i	0.496247	−	0.868181i	$-0.334711\pi$
$773$	−13.4230	−	18.4752i	−0.482791	−	0.664505i	−0.979038	+	0.203676i	$0.934711\pi$
$774$	−0.478870			−0.0172126
$775$		0			0
$776$	−5.66089			−0.203214
$777$	−3.75888	−	5.17365i	−0.134849	−	0.185604i
$778$	2.11627	+	0.687616i	0.0758718	+	0.0246522i
$779$	4.98243	−	15.3343i	0.178514	−	0.549410i
$780$		0			0
$781$	4.91582	+	15.1293i	0.175902	+	0.541370i
$782$		−	2.57451i		−	0.0920644i
$783$	3.55129	−	1.15388i	0.126913	−	0.0412365i
$784$	−19.6602	−	14.2839i	−0.702148	−	0.510141i
$785$		0			0
$786$	1.42707	−	1.03683i	0.0509020	−	0.0369824i
$787$	22.6157	−	31.1279i	0.806163	−	1.10959i	−0.185741	−	0.982599i	$-0.559469\pi$
$787$	22.6157	−	31.1279i	0.806163	−	1.10959i	0.991904	−	0.126990i	$-0.0405315\pi$
$788$	6.45416	−	8.88339i	0.229920	−	0.316458i
$789$	−16.7202	+	12.1479i	−0.595254	+	0.432478i
$790$		0			0
$791$	−11.1348	−	8.08988i	−0.395906	−	0.287643i
$792$	−1.97360	+	0.641260i	−0.0701287	+	0.0227862i
$793$			47.4060i			1.68344i
$794$	−0.858349	−	2.64173i	−0.0304617	−	0.0937514i
$795$		0			0
$796$	−3.64878	+	11.2298i	−0.129327	+	0.398029i
$797$	1.77599	+	0.577055i	0.0629089	+	0.0204404i	0.340302	−	0.940316i	$-0.389471\pi$
$797$	1.77599	+	0.577055i	0.0629089	+	0.0204404i	−0.277393	+	0.960756i	$0.589471\pi$
$798$	0.455252	+	0.626600i	0.0161157	+	0.0221814i
$799$	−45.1063			−1.59575
$800$		0			0
$801$	−15.4975			−0.547578
$802$	1.20127	+	1.65340i	0.0424182	+	0.0583837i
$803$	31.7786	+	10.3255i	1.12144	+	0.364379i
$804$	−2.04748	+	6.30150i	−0.0722091	+	0.222237i
$805$		0			0
$806$	−0.251321	−	0.773487i	−0.00885241	−	0.0272449i
$807$		−	13.7435i		−	0.483796i
$808$	0.383258	−	0.124528i	0.0134830	−	0.00438089i
$809$	28.4381	+	20.6615i	0.999831	+	0.726420i	0.962052	−	0.272866i	$-0.0879717\pi$
$809$	28.4381	+	20.6615i	0.999831	+	0.726420i	0.0377789	+	0.999286i	$0.487972\pi$
$810$		0			0
$811$	5.33270	−	3.87443i	0.187256	−	0.136050i	−0.490208	−	0.871606i	$-0.663079\pi$
$811$	5.33270	−	3.87443i	0.187256	−	0.136050i	0.677464	+	0.735556i	$0.263079\pi$
$812$	−3.72985	+	5.13370i	−0.130892	+	0.180158i
$813$	−1.96550	+	2.70528i	−0.0689332	+	0.0948785i
$814$	−3.14290	+	2.28345i	−0.110158	+	0.0800348i
$815$		0			0
$816$	−16.6584	−	12.1031i	−0.583162	−	0.423692i
$817$	−20.4709	+	6.65141i	−0.716187	+	0.232703i
$818$			3.94949i			0.138091i
$819$	1.21512	+	3.73976i	0.0424598	+	0.130678i
$820$		0			0
$821$	1.62463	−	5.00011i	0.0567001	−	0.174505i	−0.918696	−	0.394966i	$-0.870756\pi$
$821$	1.62463	−	5.00011i	0.0567001	−	0.174505i	0.975396	+	0.220461i	$0.0707563\pi$
$822$	1.59804	+	0.519236i	0.0557382	+	0.0181104i
$823$	13.0440	+	17.9536i	0.454687	+	0.625823i	0.973396	−	0.229128i	$-0.0735874\pi$
$823$	13.0440	+	17.9536i	0.454687	+	0.625823i	−0.518709	+	0.854951i	$0.673587\pi$
$824$	−0.440283			−0.0153380
$825$		0			0
$826$	1.59635			0.0555440
$827$	−3.85738	−	5.30922i	−0.134134	−	0.184620i	0.736666	−	0.676256i	$-0.236399\pi$
$827$	−3.85738	−	5.30922i	−0.134134	−	0.184620i	−0.870800	+	0.491637i	$0.836399\pi$
$828$	−6.44705	−	2.09478i	−0.224051	−	0.0727985i
$829$	−7.74316	+	23.8310i	−0.268931	+	0.827685i	0.721831	+	0.692070i	$0.243301\pi$
$829$	−7.74316	+	23.8310i	−0.268931	+	0.827685i	−0.990762	+	0.135615i	$0.956699\pi$
$830$		0			0
$831$	−2.75318	−	8.47340i	−0.0955066	−	0.293939i
$832$			34.4618i			1.19475i
$833$	−31.6126	+	10.2716i	−1.09531	+	0.355889i
$834$	−0.534274	−	0.388173i	−0.0185004	−	0.0134413i
$835$		0			0
$836$	−37.5402	+	27.2745i	−1.29835	+	0.943310i
$837$	0.736436	−	1.01362i	0.0254550	−	0.0350357i
$838$	3.02219	−	4.15968i	0.104400	−	0.143694i
$839$	−34.0989	+	24.7743i	−1.17722	+	0.855303i	−0.991856	−	0.127366i	$-0.959348\pi$
$839$	−34.0989	+	24.7743i	−1.17722	+	0.855303i	−0.185368	+	0.982669i	$0.559348\pi$
$840$		0			0
$841$	12.1813	+	8.85021i	0.420044	+	0.305180i
$842$	0.454932	−	0.147816i	0.0156780	−	0.00509409i
$843$			22.4913i			0.774641i
$844$	−8.39327	−	25.8318i	−0.288908	−	0.889169i
$845$		0			0
$846$	0.372140	−	1.14533i	0.0127944	−	0.0393773i
$847$	2.07494	+	0.674189i	0.0712957	+	0.0231654i
$848$	5.35541	+	7.37109i	0.183906	+	0.253124i
$849$	1.30694			0.0448540
$850$		0			0
$851$	−25.5095			−0.874454
$852$	−5.03085	−	6.92437i	−0.172354	−	0.237225i
$853$	41.1306	+	13.3641i	1.40829	+	0.457580i	0.911861	−	0.410500i	$-0.134646\pi$
$853$	41.1306	+	13.3641i	1.40829	+	0.457580i	0.496425	+	0.868080i	$0.334646\pi$
$854$	−0.388871	+	1.19682i	−0.0133069	+	0.0409544i
$855$		0			0
$856$	2.08415	+	6.41436i	0.0712349	+	0.219238i
$857$			39.2430i			1.34052i	0.742128	+	0.670258i	$0.233817\pi$
$857$			39.2430i			1.34052i	−0.742128	+	0.670258i	$0.766183\pi$
$858$	2.27183	−	0.738163i	0.0775590	−	0.0252005i
$859$	42.5617	+	30.9229i	1.45219	+	1.05508i	0.985314	+	0.170750i	$0.0546192\pi$
$859$	42.5617	+	30.9229i	1.45219	+	1.05508i	0.466872	+	0.884325i	$0.345381\pi$
$860$		0			0
$861$	1.75797	−	1.27724i	0.0599113	−	0.0435281i
$862$	−2.13725	+	2.94167i	−0.0727950	+	0.100194i
$863$	−25.2009	+	34.6861i	−0.857850	+	1.18073i	0.124228	+	0.992254i	$0.460355\pi$
$863$	−25.2009	+	34.6861i	−0.857850	+	1.18073i	−0.982078	+	0.188476i	$0.939645\pi$
$864$	1.35719	−	0.986054i	0.0461724	−	0.0335462i
$865$		0			0
$866$	−4.56304	−	3.31524i	−0.155058	−	0.112657i
$867$	−10.6180	+	3.45001i	−0.360608	+	0.117169i
$868$			2.12917i			0.0722686i
$869$	−3.69270	−	11.3650i	−0.125266	−	0.385530i
$870$		0			0
$871$	4.73766	−	14.5810i	0.160530	−	0.494059i
$872$	−1.30530	−	0.424118i	−0.0442031	−	0.0143624i
$873$	5.90053	+	8.12138i	0.199703	+	0.274867i
$874$	3.08955			0.104506
$875$		0			0
$876$	−17.9779			−0.607415
$877$	−0.229421	−	0.315771i	−0.00774700	−	0.0106628i	0.805126	−	0.593104i	$-0.202098\pi$
$877$	−0.229421	−	0.315771i	−0.00774700	−	0.0106628i	−0.812873	+	0.582441i	$0.802098\pi$
$878$	−4.57060	−	1.48508i	−0.154250	−	0.0501190i
$879$	0.608943	−	1.87413i	0.0205391	−	0.0632129i
$880$		0			0
$881$	13.8131	+	42.5124i	0.465376	+	1.43228i	0.858509	+	0.512798i	$0.171391\pi$
$881$	13.8131	+	42.5124i	0.465376	+	1.43228i	−0.393133	+	0.919481i	$0.628609\pi$
$882$		−	0.887444i		−	0.0298818i
$883$	−31.1534	+	10.1224i	−1.04840	+	0.340645i	−0.782039	−	0.623230i	$-0.785820\pi$
$883$	−31.1534	+	10.1224i	−1.04840	+	0.340645i	−0.266358	+	0.963874i	$0.585820\pi$
$884$	38.9448	+	28.2951i	1.30986	+	0.951666i
$885$		0			0
$886$	−3.31622	+	2.40938i	−0.111411	+	0.0809446i
$887$	9.23588	−	12.7121i	0.310110	−	0.426830i	−0.625305	−	0.780380i	$-0.715026\pi$
$887$	9.23588	−	12.7121i	0.310110	−	0.426830i	0.935416	+	0.353550i	$0.115026\pi$
$888$	2.46960	−	3.39911i	0.0828743	−	0.114067i
$889$	2.66539	−	1.93652i	0.0893944	−	0.0649488i
$890$		0			0
$891$	2.97713	+	2.16301i	0.0997374	+	0.0724635i
$892$	−6.10419	+	1.98337i	−0.204383	+	0.0664082i
$893$		−	54.1299i		−	1.81139i
$894$	0.505625	+	1.55615i	0.0169106	+	0.0520456i
$895$		0			0
$896$	−1.17258	+	3.60884i	−0.0391733	+	0.120563i
$897$	14.9178	+	4.84710i	0.498092	+	0.161840i
$898$	−0.850228	−	1.17024i	−0.0283725	−	0.0390514i
$899$	−4.67839			−0.156033
$900$		0			0
$901$	12.4623			0.415180
$902$	−0.775897	−	1.06793i	−0.0258345	−	0.0355582i
$903$	−2.75887	−	0.896411i	−0.0918094	−	0.0298307i
$904$	2.79430	−	8.59998i	0.0929372	−	0.286031i
$905$		0			0
$906$	1.07138	+	3.29737i	0.0355942	+	0.109548i
$907$			1.50466i			0.0499613i	0.999688	+	0.0249806i	$0.00795241\pi$
$907$			1.50466i			0.0499613i	−0.999688	+	0.0249806i	$0.992048\pi$
$908$	24.8180	−	8.06385i	0.823613	−	0.267608i
$909$	−0.578137	−	0.420041i	−0.0191756	−	0.0139319i
$910$		0			0
$911$	−9.26400	+	6.73069i	−0.306930	+	0.222998i	−0.730578	−	0.682829i	$-0.760749\pi$
$911$	−9.26400	+	6.73069i	−0.306930	+	0.222998i	0.423648	+	0.905827i	$0.360749\pi$
$912$	14.5243	−	19.9910i	0.480948	−	0.661968i
$913$	15.9904	−	22.0090i	0.529207	−	0.728390i
$914$	−3.72489	+	2.70629i	−0.123209	+	0.0895162i
$915$		0			0
$916$	9.35142	+	6.79421i	0.308980	+	0.224487i
$917$	10.1625	−	3.30200i	0.335596	−	0.109042i
$918$		−	0.751949i		−	0.0248180i
$919$	6.73660	+	20.7331i	0.222220	+	0.683923i	0.998562	+	0.0536108i	$0.0170730\pi$
$919$	6.73660	+	20.7331i	0.222220	+	0.683923i	−0.776342	+	0.630312i	$0.782927\pi$
$920$		0			0
$921$	4.71388	−	14.5078i	0.155328	−	0.478049i
$922$	−0.0944049	−	0.0306740i	−0.00310906	−	0.00101019i
$923$	11.6409	+	16.0223i	0.383164	+	0.527380i
$924$	−6.25363			−0.205729
$925$		0			0
$926$	−0.307645			−0.0101098
$927$	0.458922	+	0.631652i	0.0150730	+	0.0207462i
$928$	−5.95756	−	1.93573i	−0.195566	−	0.0635434i
$929$	9.50249	−	29.2457i	0.311767	−	0.959519i	−0.665298	−	0.746578i	$-0.731696\pi$
$929$	9.50249	−	29.2457i	0.311767	−	0.959519i	0.977065	−	0.212941i	$-0.0683043\pi$
$930$		0			0
$931$	−12.3264	−	37.9368i	−0.403982	−	1.24333i
$932$			18.4817i			0.605387i
$933$	16.8767	−	5.48358i	0.552519	−	0.179524i
$934$	0.444429	+	0.322896i	0.0145421	+	0.0105655i
$935$		0			0
$936$	−2.09008	+	1.51853i	−0.0683164	+	0.0496348i
$937$	2.23982	−	3.08284i	0.0731716	−	0.100712i	−0.770862	−	0.637002i	$-0.780174\pi$
$937$	2.23982	−	3.08284i	0.0731716	−	0.100712i	0.844034	+	0.536289i	$0.180174\pi$
$938$	0.239216	−	0.329252i	0.00781067	−	0.0107505i
$939$	22.1565	−	16.0976i	0.723049	−	0.525326i
$940$		0			0
$941$	16.7501	+	12.1697i	0.546037	+	0.396719i	0.826322	−	0.563197i	$-0.190429\pi$
$941$	16.7501	+	12.1697i	0.546037	+	0.396719i	−0.280285	+	0.959917i	$0.590429\pi$
$942$	−3.01393	+	0.979284i	−0.0981990	+	0.0319068i
$943$		−	8.66792i		−	0.282266i
$944$	−15.7381	−	48.4370i	−0.512233	−	1.57649i
$945$		0			0
$946$	−0.544553	+	1.67596i	−0.0177049	+	0.0544902i
$947$	−14.9157	−	4.84640i	−0.484695	−	0.157487i	0.0564684	−	0.998404i	$-0.482016\pi$
$947$	−14.9157	−	4.84640i	−0.484695	−	0.157487i	−0.541163	+	0.840917i	$0.682016\pi$
$948$	3.77911	+	5.20150i	0.122740	+	0.168937i
$949$	41.5989			1.35036
$950$		0			0
$951$	−8.64563			−0.280354
$952$	1.50982	+	2.07809i	0.0489337	+	0.0673514i
$953$	−7.37266	−	2.39552i	−0.238824	−	0.0775985i	0.187160	−	0.982330i	$-0.440072\pi$
$953$	−7.37266	−	2.39552i	−0.238824	−	0.0775985i	−0.425983	+	0.904731i	$0.640072\pi$
$954$	−0.102818	+	0.316441i	−0.00332885	+	0.0102451i
$955$		0			0
$956$	−10.4930	−	32.2941i	−0.339368	−	1.04447i
$957$		−	13.7410i		−	0.444185i
$958$	−2.96452	+	0.963230i	−0.0957792	+	0.0311205i
$959$	8.23468	+	5.98285i	0.265912	+	0.193196i
$960$		0			0
$961$	23.8096	−	17.2987i	0.768050	−	0.558021i
$962$	−2.84279	+	3.91276i	−0.0916551	+	0.126152i
$963$	7.02997	−	9.67592i	0.226538	−	0.311802i
$964$	−11.5661	+	8.40326i	−0.372519	+	0.270651i
$965$		0			0
$966$	0.336857	+	0.244741i	0.0108382	+	0.00787442i
$967$	−46.0571	+	14.9649i	−1.48110	+	0.481238i	−0.934441	−	0.356119i	$-0.884100\pi$
$967$	−46.0571	+	14.9649i	−1.48110	+	0.481238i	−0.546657	+	0.837357i	$0.684100\pi$
$968$			1.43340i			0.0460712i
$969$	−10.4444	−	32.1446i	−0.335523	−	1.03263i
$970$		0			0
$971$	7.82895	−	24.0950i	0.251243	−	0.773246i	−0.743304	−	0.668954i	$-0.766742\pi$
$971$	7.82895	−	24.0950i	0.251243	−	0.773246i	0.994547	−	0.104292i	$-0.0332577\pi$
$972$	−1.88302	−	0.611830i	−0.0603979	−	0.0196245i
$973$	−2.35143	−	3.23647i	−0.0753834	−	0.103756i
$974$	4.02394			0.128936
$975$		0			0
$976$	40.1483			1.28511
$977$	−0.687033	−	0.945620i	−0.0219801	−	0.0302531i	0.797885	−	0.602809i	$-0.205952\pi$
$977$	−0.687033	−	0.945620i	−0.0219801	−	0.0302531i	−0.819866	+	0.572556i	$0.805952\pi$
$978$	−0.109616	−	0.0356165i	−0.00350514	−	0.00113889i
$979$	−17.6232	+	54.2385i	−0.563239	+	1.73347i
$980$		0			0
$981$	0.752097	+	2.31472i	0.0240126	+	0.0739033i
$982$		−	1.99029i		−	0.0635127i
$983$	22.8199	−	7.41464i	0.727842	−	0.236490i	0.0784223	−	0.996920i	$-0.475012\pi$
$983$	22.8199	−	7.41464i	0.727842	−	0.236490i	0.649420	+	0.760430i	$0.275012\pi$
$984$	1.15499	+	0.839150i	0.0368197	+	0.0267511i
$985$		0			0
$986$	−2.27157	+	1.65039i	−0.0723415	+	0.0525592i
$987$	4.28795	−	5.90186i	0.136487	−	0.187858i
$988$	−33.9555	+	46.7358i	−1.08027	+	1.48686i
$989$	−9.36148	+	6.80151i	−0.297678	+	0.216276i
$990$		0			0
$991$	29.6688	+	21.5556i	0.942459	+	0.684737i	0.949011	−	0.315242i	$-0.102086\pi$
$991$	29.6688	+	21.5556i	0.942459	+	0.684737i	−0.00655196	+	0.999979i	$0.502086\pi$
$992$	−1.99896	+	0.649502i	−0.0634671	+	0.0206217i
$993$		−	4.96260i		−	0.157483i
$994$	0.162457	+	0.499991i	0.00515282	+	0.0158588i
$995$		0			0
$996$	−4.52307	+	13.9206i	−0.143319	+	0.441091i
$997$	54.2295	+	17.6202i	1.71747	+	0.558038i	0.991548	−	0.129743i	$-0.0414153\pi$
$997$	54.2295	+	17.6202i	1.71747	+	0.558038i	0.725918	+	0.687782i	$0.241415\pi$
$998$	1.08970	+	1.49984i	0.0344937	+	0.0474765i
$999$	−7.45067			−0.235729

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	375.2.i.d.199.3		24
5.2	odd	4		75.2.g.c.61.2	yes	12
5.3	odd	4		375.2.g.c.301.2		12
5.4	even	2	inner	375.2.i.d.199.4		24
15.2	even	4		225.2.h.d.136.2		12
25.3	odd	20		1875.2.a.k.1.4		6
25.4	even	10		1875.2.b.f.1249.6		12
25.9	even	10	inner	375.2.i.d.49.3		24
25.12	odd	20		75.2.g.c.16.2	✓	12
25.13	odd	20		375.2.g.c.76.2		12
25.16	even	5	inner	375.2.i.d.49.4		24
25.21	even	5		1875.2.b.f.1249.7		12
25.22	odd	20		1875.2.a.j.1.3		6
75.47	even	20		5625.2.a.p.1.4		6
75.53	even	20		5625.2.a.q.1.3		6
75.62	even	20		225.2.h.d.91.2		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.2	✓	12	25.12	odd	20
75.2.g.c.61.2	yes	12	5.2	odd	4
225.2.h.d.91.2		12	75.62	even	20
225.2.h.d.136.2		12	15.2	even	4
375.2.g.c.76.2		12	25.13	odd	20
375.2.g.c.301.2		12	5.3	odd	4
375.2.i.d.49.3		24	25.9	even	10	inner
375.2.i.d.49.4		24	25.16	even	5	inner
375.2.i.d.199.3		24	1.1	even	1	trivial
375.2.i.d.199.4		24	5.4	even	2	inner
1875.2.a.j.1.3		6	25.22	odd	20
1875.2.a.k.1.4		6	25.3	odd	20
1875.2.b.f.1249.6		12	25.4	even	10
1875.2.b.f.1249.7		12	25.21	even	5
5625.2.a.p.1.4		6	75.47	even	20
5625.2.a.q.1.3		6	75.53	even	20

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.i (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.0832830 - 0.114629i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.611830 - 1.88302i) q^{4} +(0.0437845 + 0.134755i) q^{6} +0.858311i q^{7} +(-0.536314 + 0.174259i) q^{8} +(0.809017 + 0.587785i) q^{9} +O(q^{10})\)	\(q+(-0.0832830 - 0.114629i) q^{2} +(-0.951057 - 0.309017i) q^{3} +(0.611830 - 1.88302i) q^{4} +(0.0437845 + 0.134755i) q^{6} +0.858311i q^{7} +(-0.536314 + 0.174259i) q^{8} +(0.809017 + 0.587785i) q^{9} +(2.97713 - 2.16301i) q^{11} +(-1.16377 + 1.60179i) q^{12} +(2.69285 - 3.70638i) q^{13} +(0.0983875 - 0.0714827i) q^{14} +(-3.13894 - 2.28058i) q^{16} +(-5.04728 + 1.63996i) q^{17} -0.141689i q^{18} +(-1.96804 - 6.05699i) q^{19} +(0.265233 - 0.816302i) q^{21} +(-0.495888 - 0.161124i) q^{22} +(-2.01245 - 2.76990i) q^{23} +0.563913 q^{24} -0.649128 q^{26} +(-0.587785 - 0.809017i) q^{27} +(1.61622 + 0.525140i) q^{28} +(-1.15388 + 3.55129i) q^{29} +(0.387167 + 1.19158i) q^{31} +1.67757i q^{32} +(-3.49982 + 1.13716i) q^{33} +(0.608340 + 0.441985i) q^{34} +(1.60179 - 1.16377i) q^{36} +(4.37939 - 6.02772i) q^{37} +(-0.530404 + 0.730039i) q^{38} +(-3.70638 + 2.69285i) q^{39} +(2.04817 + 1.48808i) q^{41} +(-0.115661 + 0.0375807i) q^{42} -3.37972i q^{43} +(-2.25149 - 6.92938i) q^{44} +(-0.149909 + 0.461371i) q^{46} +(8.08338 + 2.62645i) q^{47} +(2.28058 + 3.13894i) q^{48} +6.26330 q^{49} +5.30702 q^{51} +(-5.33163 - 7.33836i) q^{52} +(-2.23334 - 0.725656i) q^{53} +(-0.0437845 + 0.134755i) q^{54} +(-0.149568 - 0.460324i) q^{56} +6.36870i q^{57} +(0.503181 - 0.163493i) q^{58} +(10.6195 + 7.71550i) q^{59} +(-8.37141 + 6.08218i) q^{61} +(0.104345 - 0.143619i) q^{62} +(-0.504502 + 0.694388i) q^{63} +(-6.08559 + 4.42144i) q^{64} +(0.421827 + 0.306475i) q^{66} +(3.18270 - 1.03412i) q^{67} +10.5075i q^{68} +(1.05801 + 3.25621i) q^{69} +(-1.33585 + 4.11131i) q^{71} +(-0.536314 - 0.174259i) q^{72} +(5.33713 + 7.34593i) q^{73} -1.05568 q^{74} -12.6095 q^{76} +(1.85653 + 2.55530i) q^{77} +(0.617357 + 0.200592i) q^{78} +(1.00347 - 3.08837i) q^{79} +(0.309017 + 0.951057i) q^{81} -0.358712i q^{82} +(7.03087 - 2.28447i) q^{83} +(-1.37484 - 0.998876i) q^{84} +(-0.387414 + 0.281473i) q^{86} +(2.19482 - 3.02091i) q^{87} +(-1.21975 + 1.67884i) q^{88} +(-12.5378 + 9.10921i) q^{89} +(3.18123 + 2.31130i) q^{91} +(-6.44705 + 2.09478i) q^{92} -1.25290i q^{93} +(-0.372140 - 1.14533i) q^{94} +(0.518399 - 1.59547i) q^{96} +(9.54725 + 3.10209i) q^{97} +(-0.521627 - 0.717957i) q^{98} +3.67993 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q + 20 q^{4} + 6 q^{9}+O(q^{10}) \) 24 * q + 20 * q^4 + 6 * q^9	\( 24 q + 20 q^{4} + 6 q^{9} - 8 q^{11} - 12 q^{14} + 32 q^{16} - 14 q^{19} - 6 q^{21} - 12 q^{24} - 112 q^{26} + 2 q^{29} + 26 q^{31} + 50 q^{34} - 4 q^{39} + 16 q^{41} - 66 q^{44} - 44 q^{46} + 56 q^{49} + 52 q^{51} + 90 q^{56} + 44 q^{59} - 16 q^{61} - 98 q^{64} - 6 q^{66} - 12 q^{69} - 42 q^{71} + 88 q^{74} - 104 q^{76} - 20 q^{79} - 6 q^{81} + 12 q^{84} + 112 q^{86} - 114 q^{89} - 14 q^{91} + 46 q^{94} - 46 q^{96} - 12 q^{99}+O(q^{100}) \) 24 * q + 20 * q^4 + 6 * q^9 - 8 * q^11 - 12 * q^14 + 32 * q^16 - 14 * q^19 - 6 * q^21 - 12 * q^24 - 112 * q^26 + 2 * q^29 + 26 * q^31 + 50 * q^34 - 4 * q^39 + 16 * q^41 - 66 * q^44 - 44 * q^46 + 56 * q^49 + 52 * q^51 + 90 * q^56 + 44 * q^59 - 16 * q^61 - 98 * q^64 - 6 * q^66 - 12 * q^69 - 42 * q^71 + 88 * q^74 - 104 * q^76 - 20 * q^79 - 6 * q^81 + 12 * q^84 + 112 * q^86 - 114 * q^89 - 14 * q^91 + 46 * q^94 - 46 * q^96 - 12 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

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Database

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