LMFDB - Embedded newform 225.2.h.d.91.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [225,2,Mod(46,225)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(225, base_ring=CyclotomicField(10))

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

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

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

chi := DirichletCharacter("225.46");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 225 = 3^{2} \cdot 5^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	225.h (of order $5$, degree $4$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$1.79663404548$
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:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 75)
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			91.2
Root			$0.0437845 + 0.134755i$ of defining polynomial
Character	$\chi$	$=$	225.91
Dual form			225.2.h.d.136.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.114629 - 0.0832830i) q^{2} +(-0.611830 - 1.88302i) q^{4} +(-2.14898 - 0.617963i) q^{5} -0.858311 q^{7} +(-0.174259 + 0.536314i) q^{8} +O(q^{10})$	\(q+(-0.114629 - 0.0832830i) q^{2} +(-0.611830 - 1.88302i) q^{4} +(-2.14898 - 0.617963i) q^{5} -0.858311 q^{7} +(-0.174259 + 0.536314i) q^{8} +(0.194870 + 0.249810i) q^{10} +(-2.97713 - 2.16301i) q^{11} +(-3.70638 + 2.69285i) q^{13} +(0.0983875 + 0.0714827i) q^{14} +(-3.13894 + 2.28058i) q^{16} +(1.63996 - 5.04728i) q^{17} +(1.96804 - 6.05699i) q^{19} +(0.151175 + 4.42466i) q^{20} +(0.161124 + 0.495888i) q^{22} +(2.76990 + 2.01245i) q^{23} +(4.23624 + 2.65598i) q^{25} +0.649128 q^{26} +(0.525140 + 1.61622i) q^{28} +(-1.15388 - 3.55129i) q^{29} +(0.387167 - 1.19158i) q^{31} +1.67757 q^{32} +(-0.608340 + 0.441985i) q^{34} +(1.84449 + 0.530404i) q^{35} +(6.02772 - 4.37939i) q^{37} +(-0.730039 + 0.530404i) q^{38} +(0.705901 - 1.04484i) q^{40} +(-2.04817 + 1.48808i) q^{41} -3.37972 q^{43} +(-2.25149 + 6.92938i) q^{44} +(-0.149909 - 0.461371i) q^{46} +(2.62645 + 8.08338i) q^{47} -6.26330 q^{49} +(-0.264399 - 0.657260i) q^{50} +(7.33836 + 5.33163i) q^{52} +(0.725656 + 2.23334i) q^{53} +(5.06113 + 6.48802i) q^{55} +(0.149568 - 0.460324i) q^{56} +(-0.163493 + 0.503181i) q^{58} +(10.6195 - 7.71550i) q^{59} +(-8.37141 - 6.08218i) q^{61} +(-0.143619 + 0.104345i) q^{62} +(6.08559 + 4.42144i) q^{64} +(9.62903 - 3.49647i) q^{65} +(1.03412 - 3.18270i) q^{67} -10.5075 q^{68} +(-0.167259 - 0.214415i) q^{70} +(1.33585 + 4.11131i) q^{71} +(7.34593 + 5.33713i) q^{73} -1.05568 q^{74} -12.6095 q^{76} +(2.55530 + 1.85653i) q^{77} +(-1.00347 - 3.08837i) q^{79} +(8.15484 - 2.96116i) q^{80} +0.358712 q^{82} +(2.28447 - 7.03087i) q^{83} +(-6.64327 + 9.83307i) q^{85} +(0.387414 + 0.281473i) q^{86} +(1.67884 - 1.21975i) q^{88} +(-12.5378 - 9.10921i) q^{89} +(3.18123 - 2.31130i) q^{91} +(2.09478 - 6.44705i) q^{92} +(0.372140 - 1.14533i) q^{94} +(-7.97227 + 11.8002i) q^{95} +(-3.10209 - 9.54725i) q^{97} +(0.717957 + 0.521627i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8	$ 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29} + 13 q^{31} + 32 q^{32} - 25 q^{34} + 10 q^{35} + 8 q^{37} + 22 q^{38} - 28 q^{40} - 8 q^{41} - 4 q^{43} - 33 q^{44} - 22 q^{46} + 13 q^{47} - 28 q^{49} - 81 q^{50} + 44 q^{52} - 44 q^{53} + 9 q^{55} - 45 q^{56} + 41 q^{58} + 22 q^{59} - 8 q^{61} - 41 q^{62} + 49 q^{64} + 38 q^{65} - 6 q^{67} + 100 q^{68} - 45 q^{70} + 21 q^{71} - 16 q^{73} + 44 q^{74} - 52 q^{76} - q^{77} + 10 q^{79} + 99 q^{80} + 26 q^{82} + 10 q^{83} + 23 q^{85} - 56 q^{86} - 16 q^{88} - 57 q^{89} - 7 q^{91} - 3 q^{92} - 23 q^{94} - 21 q^{95} + 4 q^{97} + 18 q^{98}+O(q^{100}) $ 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{1}{5}\right)$

Coefficient data

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

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

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

$2$	−0.114629	−	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			0
$3$		0			0
$4$	−0.611830	−	1.88302i	−0.305915	−	0.941510i
$5$	−2.14898	−	0.617963i	−0.961054	−	0.276362i
$5$	−2.14898	−	0.617963i	−0.961054	−	0.276362i
$6$		0			0
$7$	−0.858311			−0.324411			−0.162205	−	0.986757i	$-0.551861\pi$
$7$	−0.858311			−0.324411			−0.162205	+	0.986757i	$0.551861\pi$
$8$	−0.174259	+	0.536314i	−0.0616098	+	0.189615i
$9$		0			0
$10$	0.194870	+	0.249810i	0.0616234	+	0.0789969i
$11$	−2.97713	−	2.16301i	−0.897637	−	0.652171i	0.0402210	−	0.999191i	$-0.487194\pi$
$11$	−2.97713	−	2.16301i	−0.897637	−	0.652171i	−0.937858	+	0.347019i	$0.887194\pi$
$12$		0			0
$13$	−3.70638	+	2.69285i	−1.02797	+	0.746861i	−0.967901	−	0.251334i	$-0.919131\pi$
$13$	−3.70638	+	2.69285i	−1.02797	+	0.746861i	−0.0600653	+	0.998194i	$0.519131\pi$
$14$	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			0
$19$	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	$-0.160732\pi$
$20$	0.151175	+	4.42466i	0.0338037	+	0.989385i
$21$		0			0
$22$	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			0
$25$	4.23624	+	2.65598i	0.847249	+	0.531197i
$26$	0.649128			0.127304
$27$		0			0
$28$	0.525140	+	1.61622i	0.0992422	+	0.305436i
$29$	−1.15388	−	3.55129i	−0.214271	−	0.659458i	−0.999205	−	0.0398784i	$-0.987303\pi$
$29$	−1.15388	−	3.55129i	−0.214271	−	0.659458i	0.784934	−	0.619580i	$-0.212697\pi$
$30$		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
$33$		0			0
$34$	−0.608340	+	0.441985i	−0.104329	+	0.0757997i
$35$	1.84449	+	0.530404i	0.311776	+	0.0896547i
$36$		0			0
$37$	6.02772	−	4.37939i	0.990951	−	0.719968i	0.0308218	−	0.999525i	$-0.490188\pi$
$37$	6.02772	−	4.37939i	0.990951	−	0.719968i	0.960129	+	0.279557i	$0.0901876\pi$
$38$	−0.730039	+	0.530404i	−0.118428	+	0.0860430i
$39$		0			0
$40$	0.705901	−	1.04484i	0.111613	−	0.165204i
$41$	−2.04817	+	1.48808i	−0.319870	+	0.232399i	−0.736120	−	0.676851i	$-0.763344\pi$
$41$	−2.04817	+	1.48808i	−0.319870	+	0.232399i	0.416250	+	0.909250i	$0.363344\pi$
$42$		0			0
$43$	−3.37972			−0.515402			−0.257701	−	0.966225i	$-0.582965\pi$
$43$	−3.37972			−0.515402			−0.257701	+	0.966225i	$0.582965\pi$
$44$	−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	$0.687181\pi$
$48$		0			0
$49$	−6.26330			−0.894758
$50$	−0.264399	−	0.657260i	−0.0373917	−	0.0929506i
$51$		0			0
$52$	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			0
$55$	5.06113	+	6.48802i	0.682442	+	0.874844i
$56$	0.149568	−	0.460324i	0.0199869	−	0.0615133i
$57$		0			0
$58$	−0.163493	+	0.503181i	−0.0214677	+	0.0660709i
$59$	10.6195	−	7.71550i	1.38254	−	1.00447i	0.385900	−	0.922541i	$-0.373891\pi$
$59$	10.6195	−	7.71550i	1.38254	−	1.00447i	0.996638	−	0.0819317i	$-0.0261089\pi$
$60$		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			0
$64$	6.08559	+	4.42144i	0.760698	+	0.552680i
$65$	9.62903	−	3.49647i	1.19433	−	0.433683i
$66$		0			0
$67$	1.03412	−	3.18270i	0.126338	−	0.388828i	−0.867805	−	0.496906i	$-0.834469\pi$
$67$	1.03412	−	3.18270i	0.126338	−	0.388828i	0.994142	+	0.108077i	$0.0344695\pi$
$68$	−10.5075			−1.27422
$69$		0			0
$70$	−0.167259	−	0.214415i	−0.0199913	−	0.0256275i
$71$	1.33585	+	4.11131i	0.158536	+	0.487923i	0.998502	−	0.0547158i	$-0.0174253\pi$
$71$	1.33585	+	4.11131i	0.158536	+	0.487923i	−0.839966	+	0.542639i	$0.817425\pi$
$72$		0			0
$73$	7.34593	+	5.33713i	0.859776	+	0.624664i	0.927824	−	0.373018i	$-0.121677\pi$
$73$	7.34593	+	5.33713i	0.859776	+	0.624664i	−0.0680477	+	0.997682i	$0.521677\pi$
$74$	−1.05568			−0.122721
$75$		0			0
$76$	−12.6095			−1.44641
$77$	2.55530	+	1.85653i	0.291203	+	0.211572i
$78$		0			0
$79$	−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	$0.958476\pi$
$80$	8.15484	−	2.96116i	0.911739	−	0.331068i
$81$		0			0
$82$	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	$-0.0329815\pi$
$84$		0			0
$85$	−6.64327	+	9.83307i	−0.720564	+	1.06655i
$86$	0.387414	+	0.281473i	0.0417760	+	0.0303520i
$87$		0			0
$88$	1.67884	−	1.21975i	0.178965	−	0.130026i
$89$	−12.5378	−	9.10921i	−1.32900	−	0.965575i	−0.999773	−	0.0213236i	$-0.993212\pi$
$89$	−12.5378	−	9.10921i	−1.32900	−	0.965575i	−0.329227	−	0.944251i	$-0.606788\pi$
$90$		0			0
$91$	3.18123	−	2.31130i	0.333483	−	0.242290i
$92$	2.09478	−	6.44705i	0.218395	−	0.672152i
$93$		0			0
$94$	0.372140	−	1.14533i	0.0383833	−	0.118132i
$95$	−7.97227	+	11.8002i	−0.817938	+	1.21067i
$96$		0			0
$97$	−3.10209	−	9.54725i	−0.314970	−	0.969377i	−0.975767	−	0.218812i	$-0.929782\pi$
$97$	−3.10209	−	9.54725i	−0.314970	−	0.969377i	0.660797	−	0.750564i	$-0.270218\pi$
$98$	0.717957	+	0.521627i	0.0725247	+	0.0526922i
$99$		0			0
$100$	2.40941	−	9.60194i	0.240941	−	0.960194i
$101$	0.714616			0.0711070			0.0355535	−	0.999368i	$-0.488681\pi$
$101$	0.714616			0.0711070			0.0355535	+	0.999368i	$0.488681\pi$
$102$		0			0
$103$	0.241269	+	0.742551i	0.0237730	+	0.0731657i	0.962239	−	0.272205i	$-0.0877530\pi$
$103$	0.241269	+	0.742551i	0.0237730	+	0.0731657i	−0.938466	+	0.345371i	$0.887753\pi$
$104$	−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			0
$109$	−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	$0.337187\pi$
$110$	−0.0398114	−	1.16522i	−0.00379587	−	0.111100i
$111$		0			0
$112$	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			0
$115$	−4.70884	−	6.03642i	−0.439102	−	0.562899i
$116$	−5.98117	+	4.34558i	−0.555338	+	0.403477i
$117$		0			0
$118$	−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
$123$		0			0
$124$	−2.48065			−0.222769
$125$	−7.46231	−	8.32550i	−0.667449	−	0.744655i
$126$		0			0
$127$	3.10539	+	2.25620i	0.275559	+	0.200205i	0.716978	−	0.697096i	$-0.245525\pi$
$127$	3.10539	+	2.25620i	0.275559	+	0.200205i	−0.441419	+	0.897301i	$0.645525\pi$
$128$	−1.36615	−	4.20459i	−0.120752	−	0.371637i
$129$		0			0
$130$	−1.39496	−	0.401137i	−0.122346	−	0.0351821i
$131$	3.84709	−	11.8401i	0.336122	−	1.03448i	−0.630044	−	0.776559i	$-0.716963\pi$
$131$	3.84709	−	11.8401i	0.336122	−	1.03448i	0.966167	−	0.257919i	$-0.0830367\pi$
$132$		0			0
$133$	−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			0
$139$	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	$0.636664\pi$
$140$	−0.129755	−	3.79773i	−0.0109663	−	0.320967i
$141$		0			0
$142$	0.189275	−	0.582530i	0.0158836	−	0.0488848i
$143$	16.8590			1.40982
$144$		0			0
$145$	0.285109	+	8.34472i	0.0236770	+	0.692991i
$146$	−0.397566	−	1.22358i	−0.0329028	−	0.101264i
$147$		0			0
$148$	−11.9344	−	8.67087i	−0.981004	−	0.712741i
$149$	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	$0.0297129\pi$
$152$	2.90550	+	2.11097i	0.235667	+	0.171222i
$153$		0			0
$154$	−0.138294	−	0.425626i	−0.0111441	−	0.0342979i
$155$	−1.56837	+	2.32143i	−0.125974	+	0.186461i
$156$		0			0
$157$	−22.3660			−1.78500			−0.892501	−	0.451045i	$-0.851052\pi$
$157$	−22.3660			−1.78500			−0.892501	+	0.451045i	$0.851052\pi$
$158$	−0.142181	+	0.437589i	−0.0113113	+	0.0348127i
$159$		0			0
$160$	−3.60508	−	1.03668i	−0.285006	−	0.0819567i
$161$	−2.37743	−	1.72731i	−0.187368	−	0.136131i
$162$		0			0
$163$	0.658095	−	0.478134i	0.0515460	−	0.0374503i	−0.561714	−	0.827332i	$-0.689858\pi$
$163$	0.658095	−	0.478134i	0.0515460	−	0.0374503i	0.613260	+	0.789881i	$0.289858\pi$
$164$	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			0
$169$	2.46864	−	7.59770i	0.189896	−	0.584438i
$170$	1.58044	−	0.573885i	0.121214	−	0.0440150i
$171$		0			0
$172$	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			0
$175$	−3.63601	−	2.27966i	−0.274857	−	0.172326i
$176$	14.2779			1.07624
$177$		0			0
$178$	0.678550	+	2.08836i	0.0508595	+	0.156529i
$179$	4.58896	+	14.1234i	0.342995	+	1.05563i	0.962648	+	0.270755i	$0.0872733\pi$
$179$	4.58896	+	14.1234i	0.342995	+	1.05563i	−0.619653	+	0.784876i	$0.712727\pi$
$180$		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
$183$		0			0
$184$	−1.56198	+	1.13485i	−0.115151	+	0.0836621i
$185$	−15.6598	+	5.68633i	−1.15133	+	0.418067i
$186$		0			0
$187$	−15.7997	+	11.4791i	−1.15539	+	0.839437i
$188$	13.6142	−	9.89131i	0.992920	−	0.721398i
$189$		0			0
$190$	1.89661	−	0.688692i	0.137595	−	0.0499630i
$191$	−2.20462	+	1.60175i	−0.159521	+	0.115899i	−0.664682	−	0.747126i	$-0.731433\pi$
$191$	−2.20462	+	1.60175i	−0.159521	+	0.115899i	0.505161	+	0.863025i	$0.331433\pi$
$192$		0			0
$193$	14.2040			1.02243			0.511215	−	0.859453i	$-0.329196\pi$
$193$	14.2040			1.02243			0.511215	+	0.859453i	$0.329196\pi$
$194$	−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			0
$199$	5.96371			0.422756			0.211378	−	0.977404i	$-0.432205\pi$
$199$	5.96371			0.422756			0.211378	+	0.977404i	$0.432205\pi$
$200$	−2.16264	+	1.80913i	−0.152922	+	0.127925i
$201$		0			0
$202$	−0.0819159	−	0.0595154i	−0.00576358	−	0.00418749i
$203$	0.990391	+	3.04811i	0.0695119	+	0.213935i
$204$		0			0
$205$	5.32106	−	1.93217i	0.371639	−	0.134948i
$206$	0.0341853	−	0.105212i	0.00238181	−	0.00733044i
$207$		0			0
$208$	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
$213$		0			0
$214$	1.37098	+	0.996073i	0.0937180	+	0.0680901i
$215$	7.26295	+	2.08854i	0.495329	+	0.142437i
$216$		0			0
$217$	−0.332310	+	1.02274i	−0.0225587	+	0.0694284i
$218$	0.344849			0.0233561
$219$		0			0
$220$	9.12052	−	13.4998i	0.614905	−	0.910154i
$221$	7.51322	+	23.1233i	0.505394	+	1.55544i
$222$		0			0
$223$	−2.62259	−	1.90543i	−0.175622	−	0.127597i	0.496502	−	0.868036i	$-0.334618\pi$
$223$	−2.62259	−	1.90543i	−0.175622	−	0.127597i	−0.672124	+	0.740439i	$0.734618\pi$
$224$	−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	$0.555903\pi$
$228$		0			0
$229$	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	$0.838212\pi$
$230$	0.0370403	+	1.08412i	0.00244237	+	0.0714845i
$231$		0			0
$232$	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			0
$235$	−0.648959	−	18.9941i	−0.0423334	−	1.23904i
$236$	−21.0258	−	15.2761i	−1.36866	−	0.994390i
$237$		0			0
$238$	0.522144	−	0.379360i	0.0338456	−	0.0245903i
$239$	13.8748	+	10.0806i	0.897485	+	0.652061i	0.937819	−	0.347125i	$-0.112842\pi$
$239$	13.8748	+	10.0806i	0.897485	+	0.652061i	−0.0403340	+	0.999186i	$0.512842\pi$
$240$		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
$243$		0			0
$244$	−6.33099	+	19.4848i	−0.405300	+	1.24739i
$245$	13.4597	+	3.87049i	0.859910	+	0.247277i
$246$		0			0
$247$	9.01625	+	27.7492i	0.573690	+	1.76564i
$248$	0.571593	+	0.415286i	0.0362962	+	0.0263707i
$249$		0			0
$250$	0.162026	+	1.57583i	0.0102474	+	0.0996642i
$251$	5.75708			0.363383			0.181692	−	0.983356i	$-0.441843\pi$
$251$	5.75708			0.363383			0.181692	+	0.983356i	$0.441843\pi$
$252$		0			0
$253$	−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			0
$259$	−5.17365	+	3.75888i	−0.321475	+	0.233565i
$260$	−12.4752	−	15.9924i	−0.773682	−	0.991807i
$261$		0			0
$262$	−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	$0.0800926\pi$
$264$		0			0
$265$	−0.179299	−	5.24783i	−0.0110143	−	0.322372i
$266$	0.626600	−	0.455252i	0.0384193	−	0.0279133i
$267$		0			0
$268$	−6.62579			−0.404734
$269$	4.24699	−	13.0709i	0.258943	−	0.796946i	−0.734084	−	0.679059i	$-0.762388\pi$
$269$	4.24699	−	13.0709i	0.258943	−	0.796946i	0.993027	−	0.117887i	$-0.0376120\pi$
$270$		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
$273$		0			0
$274$	1.68028			0.101510
$275$	−6.86691	−	17.0702i	−0.414090	−	1.02937i
$276$		0			0
$277$	−7.20791	−	5.23685i	−0.433081	−	0.314652i	0.349799	−	0.936825i	$-0.386250\pi$
$277$	−7.20791	−	5.23685i	−0.433081	−	0.314652i	−0.782880	+	0.622173i	$0.786250\pi$
$278$	−0.204075	−	0.628077i	−0.0122396	−	0.0376696i
$279$		0			0
$280$	−0.605882	+	0.896799i	−0.0362084	+	0.0535940i
$281$	6.95019	−	21.3905i	0.414613	−	1.27605i	−0.497983	−	0.867187i	$-0.665926\pi$
$281$	6.95019	−	21.3905i	0.414613	−	1.27605i	0.912596	−	0.408862i	$-0.134074\pi$
$282$		0			0
$283$	0.403866	−	1.24297i	0.0240073	−	0.0738870i	−0.938335	−	0.345727i	$-0.887632\pi$
$283$	0.403866	−	1.24297i	0.0240073	−	0.0738870i	0.962342	+	0.271840i	$0.0876322\pi$
$284$	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
$288$		0			0
$289$	−9.03225	−	6.56231i	−0.531309	−	0.386018i
$290$	0.662291	−	0.980293i	0.0388911	−	0.0575648i
$291$		0			0
$292$	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			0
$295$	−27.5889	+	10.0180i	−1.60629	+	0.583272i
$296$	1.29835	+	3.99590i	0.0754648	+	0.232257i
$297$		0			0
$298$	−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			0
$304$	7.63588	+	23.5008i	0.437948	+	1.34786i
$305$	14.2314	+	18.2437i	0.814889	+	1.04463i
$306$		0			0
$307$	−15.2544			−0.870617			−0.435308	−	0.900281i	$-0.643361\pi$
$307$	−15.2544			−0.870617			−0.435308	+	0.900281i	$0.643361\pi$
$308$	1.93248	−	5.94756i	0.110113	−	0.338894i
$309$		0			0
$310$	0.373116	−	0.135485i	0.0211916	−	0.00769502i
$311$	14.3562	+	10.4304i	0.814065	+	0.591453i	0.915006	−	0.403439i	$-0.132185\pi$
$311$	14.3562	+	10.4304i	0.814065	+	0.591453i	−0.100941	+	0.994892i	$0.532185\pi$
$312$		0			0
$313$	22.1565	−	16.0976i	1.25236	−	0.909890i	0.254001	−	0.967204i	$-0.418253\pi$
$313$	22.1565	−	16.0976i	1.25236	−	0.909890i	0.998356	+	0.0573136i	$0.0182535\pi$
$314$	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			0
$319$	−4.24621	+	13.0685i	−0.237742	+	0.731696i
$320$	−10.3455	−	13.2623i	−0.578333	−	0.741383i
$321$		0			0
$322$	0.128668	+	0.396000i	0.00717039	+	0.0220682i
$323$	−27.3438	−	19.8664i	−1.52145	−	1.10540i
$324$		0			0
$325$	−22.8533	+	1.56345i	−1.26767	+	0.0867248i
$326$	−0.115257			−0.00638351
$327$		0			0
$328$	−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
$333$		0			0
$334$	−2.88475	+	2.09590i	−0.157847	+	0.114682i
$335$	−4.18910	+	6.20051i	−0.228875	+	0.338770i
$336$		0			0
$337$	5.91011	−	4.29394i	0.321944	−	0.233906i	−0.415061	−	0.909794i	$-0.636240\pi$
$337$	5.91011	−	4.29394i	0.321944	−	0.233906i	0.737005	+	0.675888i	$0.236240\pi$
$338$	−0.915738	+	0.665322i	−0.0498096	+	0.0361888i
$339$		0			0
$340$	22.5804	+	6.49325i	1.22460	+	0.352146i
$341$	−3.73004	+	2.71003i	−0.201993	+	0.146757i
$342$		0			0
$343$	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	$-0.240705\pi$
$348$		0			0
$349$	16.5844			0.887743			0.443871	−	0.896091i	$-0.353605\pi$
$349$	16.5844			0.887743			0.443871	+	0.896091i	$0.353605\pi$
$350$	0.226936	+	0.564133i	0.0121303	+	0.0301542i
$351$		0			0
$352$	−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			0
$355$	−0.330069	−	9.66063i	−0.0175182	−	0.512733i
$356$	−9.48185	+	29.1821i	−0.502537	+	1.54665i
$357$		0			0
$358$	0.650208	−	2.00113i	0.0343646	−	0.105763i
$359$	−10.9153	+	7.93042i	−0.576087	+	0.418551i	−0.837311	−	0.546727i	$-0.815874\pi$
$359$	−10.9153	+	7.93042i	−0.576087	+	0.418551i	0.261225	+	0.965278i	$0.415874\pi$
$360$		0			0
$361$	−17.4427	−	12.6728i	−0.918036	−	0.666992i
$362$	−0.0847365	+	0.0615647i	−0.00445365	+	0.00323577i
$363$		0			0
$364$	−6.29859	−	4.57619i	−0.330136	−	0.239858i
$365$	−12.4881	−	16.0089i	−0.653658	−	0.837945i
$366$		0			0
$367$	1.41364	−	4.35073i	0.0737913	−	0.227106i	−0.907358	−	0.420360i	$-0.861904\pi$
$367$	1.41364	−	4.35073i	0.0737913	−	0.227106i	0.981149	+	0.193253i	$0.0619039\pi$
$368$	−13.2841			−0.692482
$369$		0			0
$370$	2.26864	+	0.652373i	0.117941	+	0.0339152i
$371$	−0.622838	−	1.91690i	−0.0323361	−	0.0995204i
$372$		0			0
$373$	16.7841	+	12.1944i	0.869048	+	0.631401i	0.930331	−	0.366720i	$-0.119519\pi$
$373$	16.7841	+	12.1944i	0.869048	+	0.631401i	−0.0612830	+	0.998120i	$0.519519\pi$
$374$	2.76712			0.143084
$375$		0			0
$376$	−4.79291			−0.247175
$377$	13.8398	+	10.0552i	0.712787	+	0.517870i
$378$		0			0
$379$	−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	$0.947442\pi$
$380$	27.0977	+	7.79223i	1.39008	+	0.399733i
$381$		0			0
$382$	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	$0.870778\pi$
$384$		0			0
$385$	−4.34402	−	5.56873i	−0.221392	−	0.283809i
$386$	−1.62820	−	1.18295i	−0.0828731	−	0.0602108i
$387$		0			0
$388$	−16.0797	+	11.6826i	−0.816324	+	0.593094i
$389$	−12.7053	−	9.23092i	−0.644183	−	0.468026i	0.217102	−	0.976149i	$-0.430340\pi$
$389$	−12.7053	−	9.23092i	−0.644183	−	0.468026i	−0.861285	+	0.508123i	$0.830340\pi$
$390$		0			0
$391$	14.6999	−	10.6801i	0.743407	−	0.540117i
$392$	1.09144	−	3.35909i	0.0551258	−	0.169660i
$393$		0			0
$394$	0.242825	−	0.747337i	0.0122333	−	0.0376503i
$395$	0.247944	+	7.25695i	0.0124754	+	0.365137i
$396$		0			0
$397$	−6.05796	−	18.6445i	−0.304040	−	0.935740i	−0.980034	−	0.198832i	$-0.936285\pi$
$397$	−6.05796	−	18.6445i	−0.304040	−	0.935740i	0.675993	−	0.736908i	$-0.263715\pi$
$398$	−0.683615	−	0.496675i	−0.0342665	−	0.0248961i
$399$		0			0
$400$	−19.3545	+	1.32409i	−0.967725	+	0.0662046i
$401$	14.4239			0.720297			0.360148	−	0.932895i	$-0.382726\pi$
$401$	14.4239			0.720297			0.360148	+	0.932895i	$0.382726\pi$
$402$		0			0
$403$	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			0
$409$	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	$0.0579858\pi$
$410$	−0.770865	−	0.221671i	−0.0380703	−	0.0109475i
$411$		0			0
$412$	1.25062	−	0.908630i	0.0616137	−	0.0447650i
$413$	−9.11481	+	6.62229i	−0.448510	+	0.325862i
$414$		0			0
$415$	−9.25410	+	13.6975i	−0.454266	+	0.672383i
$416$	−6.21773	+	4.51745i	−0.304850	+	0.221486i
$417$		0			0
$418$	3.32069			0.162420
$419$	11.2137	−	34.5121i	0.547823	−	1.68603i	−0.166359	−	0.986065i	$-0.553201\pi$
$419$	11.2137	−	34.5121i	0.547823	−	1.68603i	0.714182	−	0.699960i	$-0.246799\pi$
$420$		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
$423$		0			0
$424$	−1.32422			−0.0643099
$425$	20.3527	−	17.0258i	0.987253	−	0.825872i
$426$		0			0
$427$	7.18527	+	5.22040i	0.347719	+	0.252633i
$428$	7.31755	+	22.5211i	0.353707	+	1.08860i
$429$		0			0
$430$	−0.658606	−	0.844288i	−0.0317608	−	0.0407152i
$431$	7.93015	−	24.4065i	0.381982	−	1.17562i	−0.556665	−	0.830737i	$-0.687919\pi$
$431$	7.93015	−	24.4065i	0.381982	−	1.17562i	0.938646	−	0.344881i	$-0.112081\pi$
$432$		0			0
$433$	−12.3010	+	37.8587i	−0.591150	+	1.81937i	−0.0181229	+	0.999836i	$0.505769\pi$
$433$	−12.3010	+	37.8587i	−0.591150	+	1.81937i	−0.573027	+	0.819536i	$0.694231\pi$
$434$	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
$438$		0			0
$439$	−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	$-0.600212\pi$
$440$	−4.36156	+	1.58376i	−0.207929	+	0.0755026i
$441$		0			0
$442$	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	$0.258816\pi$
$444$		0			0
$445$	21.3142	+	27.3234i	1.01039	+	1.29525i
$446$	0.141936	+	0.436835i	0.00672088	+	0.0206847i
$447$		0			0
$448$	−5.22332	−	3.79497i	−0.246779	−	0.179295i
$449$	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
$452$	25.6853	+	18.6615i	1.20814	+	0.877762i
$453$		0			0
$454$	−0.577074	−	1.77605i	−0.0270834	−	0.0833542i
$455$	−8.26470	+	3.00105i	−0.387455	+	0.140692i
$456$		0			0
$457$	32.4952			1.52006			0.760030	−	0.649888i	$-0.225184\pi$
$457$	32.4952			1.52006			0.760030	+	0.649888i	$0.225184\pi$
$458$	0.255618	−	0.786712i	0.0119442	−	0.0367606i
$459$		0			0
$460$	−8.48568	+	12.5601i	−0.395647	+	0.585618i
$461$	−0.566772	−	0.411784i	−0.0263972	−	0.0191787i	0.574508	−	0.818499i	$-0.305193\pi$
$461$	−0.566772	−	0.411784i	−0.0263972	−	0.0191787i	−0.600906	+	0.799320i	$0.705193\pi$
$462$		0			0
$463$	−1.75659	+	1.27623i	−0.0816355	+	0.0593117i	−0.627854	−	0.778331i	$-0.716067\pi$
$463$	−1.75659	+	1.27623i	−0.0816355	+	0.0593117i	0.546219	+	0.837642i	$0.316067\pi$
$464$	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	$0.0714075\pi$
$468$		0			0
$469$	−0.887597	+	2.73174i	−0.0409854	+	0.126140i
$470$	−1.50749	+	2.23132i	−0.0695356	+	0.102923i
$471$		0			0
$472$	2.28739	+	7.03986i	0.105286	+	0.324036i
$473$	10.0618	+	7.31036i	0.462644	+	0.336131i
$474$		0			0
$475$	24.4244	−	20.4318i	1.12067	−	0.937476i
$476$	9.01870			0.413371
$477$		0			0
$478$	−0.750911	−	2.31107i	−0.0343459	−	0.105706i
$479$	6.79817	+	20.9226i	0.310617	+	0.955979i	0.977521	+	0.210836i	$0.0676187\pi$
$479$	6.79817	+	20.9226i	0.310617	+	0.955979i	−0.666905	+	0.745143i	$0.732381\pi$
$480$		0			0
$481$	−10.5480	+	32.4634i	−0.480948	+	1.48020i
$482$	1.02310			0.0466010
$483$		0			0
$484$	4.07156	−	2.95816i	0.185071	−	0.134462i
$485$	0.766483	+	22.4338i	0.0348042	+	1.01867i
$486$		0			0
$487$	−22.9759	+	16.6929i	−1.04114	+	0.756430i	−0.970507	−	0.241073i	$-0.922501\pi$
$487$	−22.9759	+	16.6929i	−1.04114	+	0.756430i	−0.0706291	+	0.997503i	$0.522501\pi$
$488$	4.72075	−	3.42982i	0.213698	−	0.155261i
$489$		0			0
$490$	−1.22053	−	1.56464i	−0.0551380	−	0.0706831i
$491$	−11.3641	+	8.25653i	−0.512856	+	0.372612i	−0.813906	−	0.580997i	$-0.802663\pi$
$491$	−11.3641	+	8.25653i	−0.512856	+	0.372612i	0.301050	+	0.953608i	$0.402663\pi$
$492$		0			0
$493$	−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			0
$499$	13.0842			0.585731			0.292866	−	0.956154i	$-0.405391\pi$
$499$	13.0842			0.585731			0.292866	+	0.956154i	$0.405391\pi$
$500$	−11.1114	+	19.1455i	−0.496918	+	0.856211i
$501$		0			0
$502$	−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			0
$505$	−1.53570	−	0.441607i	−0.0683376	−	0.0196512i
$506$	−0.551653	+	1.69781i	−0.0245240	+	0.0754770i
$507$		0			0
$508$	2.34850	−	7.22793i	0.104198	−	0.320688i
$509$	0.0634186	−	0.0460763i	0.00281098	−	0.00204230i	−0.586379	−	0.810037i	$-0.699447\pi$
$509$	0.0634186	−	0.0460763i	0.00281098	−	0.00204230i	0.589190	+	0.807995i	$0.299447\pi$
$510$		0			0
$511$	−6.30509	−	4.58092i	−0.278921	−	0.202648i
$512$	−8.80600	+	6.39793i	−0.389174	+	0.282751i
$513$		0			0
$514$	3.09043	+	2.24533i	0.136313	+	0.0990372i
$515$	−0.0596143	−	1.74482i	−0.00262692	−	0.0768861i
$516$		0			0
$517$	9.66515	−	29.7463i	0.425073	−	1.30824i
$518$	0.906103			0.0398119
$519$		0			0
$520$	0.197259	+	5.77347i	0.00865036	+	0.253183i
$521$	−5.59919	−	17.2325i	−0.245305	−	0.754971i	−0.995586	−	0.0938524i	$-0.970082\pi$
$521$	−5.59919	−	17.2325i	−0.245305	−	0.754971i	0.750281	−	0.661119i	$-0.229918\pi$
$522$		0			0
$523$	−9.40913	−	6.83613i	−0.411432	−	0.298923i	0.362749	−	0.931887i	$-0.381838\pi$
$523$	−9.40913	−	6.83613i	−0.411432	−	0.298923i	−0.774181	+	0.632964i	$0.781838\pi$
$524$	−24.6490			−1.07680
$525$		0			0
$526$	−2.92834			−0.127682
$527$	−5.37929	−	3.90828i	−0.234326	−	0.170247i
$528$		0			0
$529$	−3.48500	−	10.7257i	−0.151522	−	0.466336i
$530$	−0.416502	+	0.616487i	−0.0180917	+	0.0267785i
$531$		0			0
$532$	10.8229			0.469232
$533$	3.58413	−	11.0308i	0.155246	−	0.477797i
$534$		0			0
$535$	25.7020	+	7.39090i	1.11120	+	0.319536i
$536$	1.52672	+	1.10923i	0.0659442	+	0.0479113i
$537$		0			0
$538$	−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			0
$544$	2.75115	−	8.46718i	0.117955	−	0.363027i
$545$	5.11542	−	1.85750i	0.219121	−	0.0795665i
$546$		0			0
$547$	3.72908	+	11.4769i	0.159444	+	0.490717i	0.998584	−	0.0531977i	$-0.0169413\pi$
$547$	3.72908	+	11.4769i	0.159444	+	0.490717i	−0.839140	+	0.543915i	$0.816941\pi$
$548$	18.9955	+	13.8010i	0.811448	+	0.589551i
$549$		0			0
$550$	−0.634510	+	2.52864i	−0.0270556	+	0.107822i
$551$	−23.7810			−1.01311
$552$		0			0
$553$	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			0
$559$	12.5265	−	9.10106i	0.529816	−	0.384934i
$560$	−6.99939	+	2.54160i	−0.295778	+	0.107402i
$561$		0			0
$562$	−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	$0.536898\pi$
$564$		0			0
$565$	33.7030	−	12.2381i	1.41790	−	0.514862i
$566$	−0.149813	+	0.108846i	−0.00629712	+	0.00457513i
$567$		0			0
$568$	−2.43773			−0.102285
$569$	−6.52273	+	20.0749i	−0.273447	+	0.841583i	0.716179	+	0.697916i	$0.245889\pi$
$569$	−6.52273	+	20.0749i	−0.273447	+	0.841583i	−0.989626	+	0.143667i	$0.954111\pi$
$570$		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
$573$		0			0
$574$	−0.307886			−0.0128509
$575$	6.38894	+	15.8820i	0.266437	+	0.662327i
$576$		0			0
$577$	15.1861	+	11.0333i	0.632205	+	0.459324i	0.857163	−	0.515045i	$-0.172225\pi$
$577$	15.1861	+	11.0333i	0.632205	+	0.459324i	−0.224959	+	0.974368i	$0.572225\pi$
$578$	0.488830	+	1.50446i	0.0203327	+	0.0625775i
$579$		0			0
$580$	15.5388	−	5.64242i	0.645215	−	0.234289i
$581$	−1.96078	+	6.03467i	−0.0813470	+	0.250360i
$582$		0			0
$583$	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	$0.201495\pi$
$588$		0			0
$589$	−6.45543	−	4.69014i	−0.265991	−	0.193254i
$590$	3.99683	+	1.14933i	0.164547	+	0.0473173i
$591$		0			0
$592$	−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			0
$595$	5.70199	−	8.43983i	0.233759	−	0.345999i
$596$	−7.06544	−	21.7452i	−0.289412	−	0.890718i
$597$		0			0
$598$	1.79802	+	1.30634i	0.0735265	+	0.0534201i
$599$	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	$0.611884\pi$
$602$	−0.332522	−	0.241591i	−0.0135526	−	0.00984652i
$603$		0			0
$604$	−14.9711	−	46.0764i	−0.609167	−	1.87482i
$605$	−0.194082	−	5.68050i	−0.00789055	−	0.230945i
$606$		0			0
$607$	−0.499318			−0.0202667			−0.0101334	−	0.999949i	$-0.503226\pi$
$607$	−0.499318			−0.0202667			−0.0101334	+	0.999949i	$0.503226\pi$
$608$	3.30153	−	10.1611i	0.133895	−	0.412085i
$609$		0			0
$610$	−0.111946	−	3.27650i	−0.00453257	−	0.132662i
$611$	−31.5019	−	22.8875i	−1.27443	−	0.925929i
$612$		0			0
$613$	−22.1866	+	16.1195i	−0.896108	+	0.651061i	−0.937463	−	0.348084i	$-0.886832\pi$
$613$	−22.1866	+	16.1195i	−0.896108	+	0.651061i	0.0413552	+	0.999145i	$0.486832\pi$
$614$	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			0
$619$	−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	$0.102378\pi$
$620$	5.33087	+	1.53295i	0.214093	+	0.0615647i
$621$		0			0
$622$	−0.776966	−	2.39125i	−0.0311535	−	0.0958806i
$623$	10.7613	+	7.81853i	0.431142	+	0.313243i
$624$		0			0
$625$	10.8915	+	22.5028i	0.435660	+	0.900111i
$626$	−3.88043			−0.155093
$627$		0			0
$628$	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
$633$		0			0
$634$	0.991042	−	0.720034i	0.0393593	−	0.0285962i
$635$	−5.27919	−	6.76755i	−0.209498	−	0.268562i
$636$		0			0
$637$	23.2142	−	16.8661i	0.919780	−	0.668259i
$638$	1.57512	−	1.14439i	0.0623598	−	0.0453070i
$639$		0			0
$640$	0.337558	+	9.87982i	0.0133431	+	0.390534i
$641$	−1.63910	+	1.19088i	−0.0647407	+	0.0470368i	−0.619685	−	0.784851i	$-0.712740\pi$
$641$	−1.63910	+	1.19088i	−0.0647407	+	0.0470368i	0.554944	+	0.831888i	$0.312740\pi$
$642$		0			0
$643$	−33.2034			−1.30941			−0.654706	−	0.755883i	$-0.727208\pi$
$643$	−33.2034			−1.30941			−0.654706	+	0.755883i	$0.727208\pi$
$644$	−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			0
$649$	−48.3042			−1.89611
$650$	2.74986	+	1.72407i	0.107859	+	0.0676237i
$651$		0			0
$652$	−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			0
$655$	−15.5841	+	23.0669i	−0.608921	+	0.901297i
$656$	3.03540	−	9.34201i	0.118513	−	0.364744i
$657$		0			0
$658$	−0.319412	+	0.983049i	−0.0124520	+	0.0383232i
$659$	−2.81185	+	2.04293i	−0.109534	+	0.0795811i	−0.641204	−	0.767371i	$-0.721565\pi$
$659$	−2.81185	+	2.04293i	−0.109534	+	0.0795811i	0.531670	+	0.846952i	$0.321565\pi$
$660$		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
$663$		0			0
$664$	3.37266	+	2.45038i	0.130885	+	0.0950932i
$665$	6.84269	−	10.1282i	0.265348	−	0.392756i
$666$		0			0
$667$	3.95065	−	12.1589i	0.152970	−	0.470793i
$668$	−49.8267			−1.92785
$669$		0			0
$670$	0.996590	−	0.361879i	0.0385016	−	0.0139806i
$671$	11.7669	+	36.2148i	0.454257	+	1.39806i
$672$		0			0
$673$	−17.3003	−	12.5694i	−0.666877	−	0.484514i	0.202102	−	0.979365i	$-0.435223\pi$
$673$	−17.3003	−	12.5694i	−0.666877	−	0.484514i	−0.868978	+	0.494850i	$0.835223\pi$
$674$	−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			0
$679$	2.66256	+	8.19451i	0.102180	+	0.314476i
$680$	−4.11596	−	5.27638i	−0.157840	−	0.202340i
$681$		0			0
$682$	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	$-0.0181535\pi$
$684$		0			0
$685$	24.9250	−	9.05068i	0.952334	−	0.345809i
$686$	−1.30494	−	0.948096i	−0.0498229	−	0.0361985i
$687$		0			0
$688$	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
$693$		0			0
$694$	−0.697811	+	2.14764i	−0.0264885	+	0.0815234i
$695$	−6.41028	−	8.21754i	−0.243156	−	0.311709i
$696$		0			0
$697$	4.15185	+	12.7781i	0.157262	+	0.484004i
$698$	−1.90106	−	1.38120i	−0.0719560	−	0.0522791i
$699$		0			0
$700$	−2.06802	+	8.24145i	−0.0781638	+	0.311497i
$701$	−31.3996			−1.18595			−0.592973	−	0.805222i	$-0.702046\pi$
$701$	−31.3996			−1.18595			−0.592973	+	0.805222i	$0.702046\pi$
$702$		0			0
$703$	−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
$708$		0			0
$709$	−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	$0.457801\pi$
$710$	−0.766731	+	1.13488i	−0.0287749	+	0.0425913i
$711$		0			0
$712$	7.07021	−	5.13681i	0.264967	−	0.192510i
$713$	3.47041	−	2.52140i	0.129968	−	0.0944272i
$714$		0			0
$715$	−36.2297	−	10.4183i	−1.35491	−	0.389620i
$716$	23.7869	−	17.2822i	0.888959	−	0.645867i
$717$		0			0
$718$	1.91168			0.0713432
$719$	1.27535	−	3.92511i	0.0475624	−	0.146382i	−0.924455	−	0.381292i	$-0.875479\pi$
$719$	1.27535	−	3.92511i	0.0475624	−	0.146382i	0.972017	+	0.234910i	$0.0754794\pi$
$720$		0			0
$721$	−0.207084	−	0.637339i	−0.00771221	−	0.0237358i
$722$	0.944008	+	2.90536i	0.0351323	+	0.108126i
$723$		0			0
$724$	−1.46361			−0.0543945
$725$	4.54404	−	18.1088i	0.168761	−	0.672545i
$726$		0			0
$727$	−18.6106	−	13.5214i	−0.690227	−	0.501479i	0.186508	−	0.982454i	$-0.440283\pi$
$727$	−18.6106	−	13.5214i	−0.690227	−	0.501479i	−0.876735	+	0.480974i	$0.840283\pi$
$728$	0.685223	+	2.10890i	0.0253961	+	0.0781610i
$729$		0			0
$730$	0.0982330	+	2.87514i	0.00363577	+	0.106414i
$731$	−5.54260	+	17.0584i	−0.205000	+	0.630927i
$732$		0			0
$733$	−2.89145	+	8.89896i	−0.106798	+	0.328690i	−0.990148	−	0.140023i	$-0.955282\pi$
$733$	−2.89145	+	8.89896i	−0.106798	+	0.328690i	0.883350	+	0.468714i	$0.155282\pi$
$734$	−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			0
$739$	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	$0.365605\pi$
$740$	20.2886	+	26.0086i	0.745823	+	0.956094i
$741$		0			0
$742$	−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			0
$745$	−24.8165	−	7.13627i	−0.909208	−	0.261453i
$746$	−0.908366	−	2.79566i	−0.0332576	−	0.102356i
$747$		0			0
$748$	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
$753$		0			0
$754$	−0.749019	−	2.30524i	−0.0272777	−	0.0839520i
$755$	−52.5843	−	15.1212i	−1.91374	−	0.550317i
$756$		0			0
$757$	13.3742			0.486094			0.243047	−	0.970015i	$-0.421853\pi$
$757$	13.3742			0.486094			0.243047	+	0.970015i	$0.421853\pi$
$758$	−0.253145	+	0.779101i	−0.00919465	+	0.0282982i
$759$		0			0
$760$	−4.93936	−	6.33193i	−0.179170	−	0.229683i
$761$	17.5994	+	12.7867i	0.637978	+	0.463518i	0.859155	−	0.511716i	$-0.170990\pi$
$761$	17.5994	+	12.7867i	0.637978	+	0.463518i	−0.221177	+	0.975234i	$0.570990\pi$
$762$		0			0
$763$	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
$768$		0			0
$769$	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	$0.0175826\pi$
$770$	0.0341706	+	1.00012i	0.00123142	+	0.0360419i
$771$		0			0
$772$	−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			0
$775$	4.80495	−	4.01951i	0.172599	−	0.144385i
$776$	5.66089			0.203214
$777$		0			0
$778$	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
$783$		0			0
$784$	19.6602	−	14.2839i	0.702148	−	0.510141i
$785$	48.0642	+	13.8214i	1.71548	+	0.493306i
$786$		0			0
$787$	31.1279	−	22.6157i	1.10959	−	0.806163i	0.126990	−	0.991904i	$-0.459469\pi$
$787$	31.1279	−	22.6157i	1.10959	−	0.806163i	0.982599	+	0.185741i	$0.0594685\pi$
$788$	8.88339	−	6.45416i	0.316458	−	0.229920i
$789$		0			0
$790$	0.575959	−	0.852508i	0.0204917	−	0.0303309i
$791$	11.1348	−	8.08988i	0.395906	−	0.287643i
$792$		0			0
$793$	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			0
$799$	45.1063			1.59575
$800$	7.10661	+	4.45561i	0.251257	+	0.157530i
$801$		0			0
$802$	−1.65340	−	1.20127i	−0.0583837	−	0.0424182i
$803$	−10.3255	−	31.7786i	−0.364379	−	1.12144i
$804$		0			0
$805$	4.04165	+	5.18112i	0.142449	+	0.182610i
$806$	0.251321	−	0.773487i	0.00885241	−	0.0272449i
$807$		0			0
$808$	−0.124528	+	0.383258i	−0.00438089	+	0.0134830i
$809$	28.4381	−	20.6615i	0.999831	−	0.726420i	0.0377789	−	0.999286i	$-0.487972\pi$
$809$	28.4381	−	20.6615i	0.999831	−	0.726420i	0.962052	+	0.272866i	$0.0879717\pi$
$810$		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
$813$		0			0
$814$	3.14290	+	2.28345i	0.110158	+	0.0800348i
$815$	−1.70970	+	0.620822i	−0.0598883	+	0.0217465i
$816$		0			0
$817$	−6.65141	+	20.4709i	−0.232703	+	0.716187i
$818$	−3.94949			−0.138091
$819$		0			0
$820$	−6.89389	−	8.83750i	−0.240745	−	0.308619i
$821$	−1.62463	−	5.00011i	−0.0567001	−	0.174505i	0.918696	−	0.394966i	$-0.129244\pi$
$821$	−1.62463	−	5.00011i	−0.0567001	−	0.174505i	−0.975396	+	0.220461i	$0.929244\pi$
$822$		0			0
$823$	17.9536	+	13.0440i	0.625823	+	0.454687i	0.854951	−	0.518709i	$-0.173587\pi$
$823$	17.9536	+	13.0440i	0.625823	+	0.454687i	−0.229128	+	0.973396i	$0.573587\pi$
$824$	−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	$0.736399\pi$
$828$		0			0
$829$	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	$0.756699\pi$
$830$	2.20156	−	0.799423i	0.0764172	−	0.0277484i
$831$		0			0
$832$	−34.4618			−1.19475
$833$	−10.2716	+	31.6126i	−0.355889	+	1.09531i
$834$		0			0
$835$	−31.5025	+	46.6285i	−1.09019	+	1.61365i
$836$	37.5402	+	27.2745i	1.29835	+	0.943310i
$837$		0			0
$838$	−4.15968	+	3.02219i	−0.143694	+	0.104400i
$839$	−34.0989	−	24.7743i	−1.17722	−	0.855303i	−0.185368	−	0.982669i	$-0.559348\pi$
$839$	−34.0989	−	24.7743i	−1.17722	−	0.855303i	−0.991856	+	0.127366i	$0.959348\pi$
$840$		0			0
$841$	12.1813	−	8.85021i	0.420044	−	0.305180i
$842$	−0.147816	+	0.454932i	−0.00509409	+	0.0156780i
$843$		0			0
$844$	8.39327	−	25.8318i	0.288908	−	0.889169i
$845$	−10.0002	+	14.8018i	−0.344016	+	0.509197i
$846$		0			0
$847$	−0.674189	−	2.07494i	−0.0231654	−	0.0712957i
$848$	−7.37109	−	5.35541i	−0.253124	−	0.183906i
$849$		0			0
$850$	−3.75098	+	0.256614i	−0.128657	+	0.00880180i
$851$	25.5095			0.874454
$852$		0			0
$853$	13.3641	+	41.1306i	0.457580	+	1.40829i	0.868080	+	0.496425i	$0.165354\pi$
$853$	13.3641	+	41.1306i	0.457580	+	1.40829i	−0.410500	+	0.911861i	$0.634646\pi$
$854$	−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			0
$859$	−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	$0.945381\pi$
$860$	−0.510928	−	14.9541i	−0.0174225	−	0.509931i
$861$		0			0
$862$	−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	$0.560355\pi$
$864$		0			0
$865$	−0.565187	−	0.724530i	−0.0192169	−	0.0246348i
$866$	4.56304	−	3.31524i	0.155058	−	0.112657i
$867$		0			0
$868$	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
$873$		0			0
$874$	−3.08955			−0.104506
$875$	6.40498	+	7.14587i	0.216528	+	0.241574i
$876$		0			0
$877$	0.315771	+	0.229421i	0.0106628	+	0.00774700i	0.593104	−	0.805126i	$-0.297902\pi$
$877$	0.315771	+	0.229421i	0.0106628	+	0.00774700i	−0.582441	+	0.812873i	$0.697902\pi$
$878$	1.48508	+	4.57060i	0.0501190	+	0.154250i
$879$		0			0
$880$	−30.6830	−	8.82324i	−1.03432	−	0.297431i
$881$	−13.8131	+	42.5124i	−0.465376	+	1.43228i	0.393133	+	0.919481i	$0.371391\pi$
$881$	−13.8131	+	42.5124i	−0.465376	+	1.43228i	−0.858509	+	0.512798i	$0.828609\pi$
$882$		0			0
$883$	10.1224	−	31.1534i	0.340645	−	1.04840i	−0.623230	−	0.782039i	$-0.714180\pi$
$883$	10.1224	−	31.1534i	0.340645	−	1.04840i	0.963874	−	0.266358i	$-0.0858202\pi$
$884$	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	$0.384974\pi$
$888$		0			0
$889$	−2.66539	−	1.93652i	−0.0893944	−	0.0649488i
$890$	−0.167660	−	4.90717i	−0.00561999	−	0.164489i
$891$		0			0
$892$	−1.98337	+	6.10419i	−0.0664082	+	0.204383i
$893$	54.1299			1.81139
$894$		0			0
$895$	−1.13387	−	33.1867i	−0.0379011	−	1.10931i
$896$	1.17258	+	3.60884i	0.0391733	+	0.120563i
$897$		0			0
$898$	−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			0
$904$	−2.79430	−	8.59998i	−0.0929372	−	0.286031i
$905$	−0.925352	+	1.36966i	−0.0307597	+	0.0455291i
$906$		0			0
$907$	−1.50466			−0.0499613			−0.0249806	−	0.999688i	$-0.507952\pi$
$907$	−1.50466			−0.0499613			−0.0249806	+	0.999688i	$0.507952\pi$
$908$	8.06385	−	24.8180i	0.267608	−	0.823613i
$909$		0			0
$910$	1.19731	+	0.344300i	0.0396905	+	0.0114134i
$911$	9.26400	+	6.73069i	0.306930	+	0.222998i	0.730578	−	0.682829i	$-0.239251\pi$
$911$	9.26400	+	6.73069i	0.306930	+	0.222998i	−0.423648	+	0.905827i	$0.639251\pi$
$912$		0			0
$913$	−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			0
$919$	−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	$0.982927\pi$
$920$	4.05797	−	1.47352i	0.133787	−	0.0485805i
$921$		0			0
$922$	0.0306740	+	0.0944049i	0.00101019	+	0.00310906i
$923$	−16.0223	−	11.6409i	−0.527380	−	0.383164i
$924$		0			0
$925$	37.1665	−	2.54266i	1.22203	−	0.0836020i
$926$	0.307645			0.0101098
$927$		0			0
$928$	−1.93573	−	5.95756i	−0.0635434	−	0.195566i
$929$	9.50249	+	29.2457i	0.311767	+	0.959519i	0.977065	+	0.212941i	$0.0683043\pi$
$929$	9.50249	+	29.2457i	0.311767	+	0.959519i	−0.665298	+	0.746578i	$0.731696\pi$
$930$		0			0
$931$	−12.3264	+	37.9368i	−0.403982	+	1.24333i
$932$	18.4817			0.605387
$933$		0			0
$934$	−0.444429	+	0.322896i	−0.0145421	+	0.0105655i
$935$	41.0469	−	14.9048i	1.34238	−	0.487440i
$936$		0			0
$937$	3.08284	−	2.23982i	0.100712	−	0.0731716i	−0.536289	−	0.844034i	$-0.680174\pi$
$937$	3.08284	−	2.23982i	0.100712	−	0.0731716i	0.637002	+	0.770862i	$0.280174\pi$
$938$	0.329252	−	0.239216i	0.0107505	−	0.00781067i
$939$		0			0
$940$	−35.3692	+	12.8432i	−1.15362	+	0.418898i
$941$	−16.7501	+	12.1697i	−0.546037	+	0.396719i	−0.826322	−	0.563197i	$-0.809571\pi$
$941$	−16.7501	+	12.1697i	−0.546037	+	0.396719i	0.280285	+	0.959917i	$0.409571\pi$
$942$		0			0
$943$	−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	$0.982016\pi$
$948$		0			0
$949$	−41.5989			−1.35036
$950$	−4.50137	+	0.307950i	−0.146044	+	0.00999123i
$951$		0			0
$952$	−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			0
$955$	5.72752	−	2.07976i	0.185338	−	0.0672994i
$956$	10.4930	−	32.2941i	0.339368	−	1.04447i
$957$		0			0
$958$	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
$963$		0			0
$964$	11.5661	+	8.40326i	0.372519	+	0.270651i
$965$	−30.5242	−	8.77758i	−0.982609	−	0.282560i
$966$		0			0
$967$	−14.9649	+	46.0571i	−0.481238	+	1.48110i	0.356119	+	0.934441i	$0.384100\pi$
$967$	−14.9649	+	46.0571i	−0.481238	+	1.48110i	−0.837357	+	0.546657i	$0.815900\pi$
$968$	−1.43340			−0.0460712
$969$		0			0
$970$	1.78050	−	2.63541i	0.0571683	−	0.0846179i
$971$	−7.82895	−	24.0950i	−0.251243	−	0.773246i	−0.994547	−	0.104292i	$-0.966742\pi$
$971$	−7.82895	−	24.0950i	−0.251243	−	0.773246i	0.743304	−	0.668954i	$-0.233258\pi$
$972$		0			0
$973$	−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			0
$979$	17.6232	+	54.2385i	0.563239	+	1.73347i
$980$	−0.946853	−	27.7130i	−0.0302461	−	0.885259i
$981$		0			0
$982$	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	$-0.0249882\pi$
$984$		0			0
$985$	−0.423451	−	12.3938i	−0.0134923	−	0.394899i
$986$	2.27157	+	1.65039i	0.0723415	+	0.0525592i
$987$		0			0
$988$	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
$993$		0			0
$994$	−0.162457	+	0.499991i	−0.00515282	+	0.0158588i
$995$	−12.8159	−	3.68535i	−0.406291	−	0.116834i
$996$		0			0
$997$	−17.6202	−	54.2295i	−0.558038	−	1.71747i	−0.687782	−	0.725918i	$-0.741415\pi$
$997$	−17.6202	−	54.2295i	−0.558038	−	1.71747i	0.129743	−	0.991548i	$-0.458585\pi$
$998$	−1.49984	−	1.08970i	−0.0474765	−	0.0344937i
$999$		0			0

Twists

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

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.16.2	✓	12	3.2	odd	2
75.2.g.c.61.2	yes	12	75.11	odd	10
225.2.h.d.91.2		12	1.1	even	1	trivial
225.2.h.d.136.2		12	25.11	even	5	inner
375.2.g.c.76.2		12	15.14	odd	2
375.2.g.c.301.2		12	75.14	odd	10
375.2.i.d.49.3		24	15.2	even	4
375.2.i.d.49.4		24	15.8	even	4
375.2.i.d.199.3		24	75.23	even	20
375.2.i.d.199.4		24	75.2	even	20
1875.2.a.j.1.3		6	75.56	odd	10
1875.2.a.k.1.4		6	75.44	odd	10
1875.2.b.f.1249.6		12	75.17	even	20
1875.2.b.f.1249.7		12	75.8	even	20
5625.2.a.p.1.4		6	25.6	even	5
5625.2.a.q.1.3		6	25.19	even	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:	\( N \)	\(=\)	\( 225 = 3^{2} \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	225.h (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.114629 - 0.0832830i) q^{2} +(-0.611830 - 1.88302i) q^{4} +(-2.14898 - 0.617963i) q^{5} -0.858311 q^{7} +(-0.174259 + 0.536314i) q^{8} +O(q^{10})\)	\(q+(-0.114629 - 0.0832830i) q^{2} +(-0.611830 - 1.88302i) q^{4} +(-2.14898 - 0.617963i) q^{5} -0.858311 q^{7} +(-0.174259 + 0.536314i) q^{8} +(0.194870 + 0.249810i) q^{10} +(-2.97713 - 2.16301i) q^{11} +(-3.70638 + 2.69285i) q^{13} +(0.0983875 + 0.0714827i) q^{14} +(-3.13894 + 2.28058i) q^{16} +(1.63996 - 5.04728i) q^{17} +(1.96804 - 6.05699i) q^{19} +(0.151175 + 4.42466i) q^{20} +(0.161124 + 0.495888i) q^{22} +(2.76990 + 2.01245i) q^{23} +(4.23624 + 2.65598i) q^{25} +0.649128 q^{26} +(0.525140 + 1.61622i) q^{28} +(-1.15388 - 3.55129i) q^{29} +(0.387167 - 1.19158i) q^{31} +1.67757 q^{32} +(-0.608340 + 0.441985i) q^{34} +(1.84449 + 0.530404i) q^{35} +(6.02772 - 4.37939i) q^{37} +(-0.730039 + 0.530404i) q^{38} +(0.705901 - 1.04484i) q^{40} +(-2.04817 + 1.48808i) q^{41} -3.37972 q^{43} +(-2.25149 + 6.92938i) q^{44} +(-0.149909 - 0.461371i) q^{46} +(2.62645 + 8.08338i) q^{47} -6.26330 q^{49} +(-0.264399 - 0.657260i) q^{50} +(7.33836 + 5.33163i) q^{52} +(0.725656 + 2.23334i) q^{53} +(5.06113 + 6.48802i) q^{55} +(0.149568 - 0.460324i) q^{56} +(-0.163493 + 0.503181i) q^{58} +(10.6195 - 7.71550i) q^{59} +(-8.37141 - 6.08218i) q^{61} +(-0.143619 + 0.104345i) q^{62} +(6.08559 + 4.42144i) q^{64} +(9.62903 - 3.49647i) q^{65} +(1.03412 - 3.18270i) q^{67} -10.5075 q^{68} +(-0.167259 - 0.214415i) q^{70} +(1.33585 + 4.11131i) q^{71} +(7.34593 + 5.33713i) q^{73} -1.05568 q^{74} -12.6095 q^{76} +(2.55530 + 1.85653i) q^{77} +(-1.00347 - 3.08837i) q^{79} +(8.15484 - 2.96116i) q^{80} +0.358712 q^{82} +(2.28447 - 7.03087i) q^{83} +(-6.64327 + 9.83307i) q^{85} +(0.387414 + 0.281473i) q^{86} +(1.67884 - 1.21975i) q^{88} +(-12.5378 - 9.10921i) q^{89} +(3.18123 - 2.31130i) q^{91} +(2.09478 - 6.44705i) q^{92} +(0.372140 - 1.14533i) q^{94} +(-7.97227 + 11.8002i) q^{95} +(-3.10209 - 9.54725i) q^{97} +(0.717957 + 0.521627i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8} - 9 q^{10} + 4 q^{11} - 2 q^{13} - 6 q^{14} + 16 q^{16} + q^{17} + 7 q^{19} - 26 q^{20} + 13 q^{22} - 19 q^{23} + 4 q^{25} + 56 q^{26} + q^{28} + q^{29} + 13 q^{31} + 32 q^{32} - 25 q^{34} + 10 q^{35} + 8 q^{37} + 22 q^{38} - 28 q^{40} - 8 q^{41} - 4 q^{43} - 33 q^{44} - 22 q^{46} + 13 q^{47} - 28 q^{49} - 81 q^{50} + 44 q^{52} - 44 q^{53} + 9 q^{55} - 45 q^{56} + 41 q^{58} + 22 q^{59} - 8 q^{61} - 41 q^{62} + 49 q^{64} + 38 q^{65} - 6 q^{67} + 100 q^{68} - 45 q^{70} + 21 q^{71} - 16 q^{73} + 44 q^{74} - 52 q^{76} - q^{77} + 10 q^{79} + 99 q^{80} + 26 q^{82} + 10 q^{83} + 23 q^{85} - 56 q^{86} - 16 q^{88} - 57 q^{89} - 7 q^{91} - 3 q^{92} - 23 q^{94} - 21 q^{95} + 4 q^{97} + 18 q^{98}+O(q^{100}) \) 12 * q - 10 * q^4 + 6 * q^5 - 12 * q^7 - 9 * q^8 - 9 * q^10 + 4 * q^11 - 2 * q^13 - 6 * q^14 + 16 * q^16 + q^17 + 7 * q^19 - 26 * q^20 + 13 * q^22 - 19 * q^23 + 4 * q^25 + 56 * q^26 + q^28 + q^29 + 13 * q^31 + 32 * q^32 - 25 * q^34 + 10 * q^35 + 8 * q^37 + 22 * q^38 - 28 * q^40 - 8 * q^41 - 4 * q^43 - 33 * q^44 - 22 * q^46 + 13 * q^47 - 28 * q^49 - 81 * q^50 + 44 * q^52 - 44 * q^53 + 9 * q^55 - 45 * q^56 + 41 * q^58 + 22 * q^59 - 8 * q^61 - 41 * q^62 + 49 * q^64 + 38 * q^65 - 6 * q^67 + 100 * q^68 - 45 * q^70 + 21 * q^71 - 16 * q^73 + 44 * q^74 - 52 * q^76 - q^77 + 10 * q^79 + 99 * q^80 + 26 * q^82 + 10 * q^83 + 23 * q^85 - 56 * q^86 - 16 * q^88 - 57 * q^89 - 7 * q^91 - 3 * q^92 - 23 * q^94 - 21 * q^95 + 4 * q^97 + 18 * q^98

Introduction

L-functions

Modular forms

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Database

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