LMFDB - Embedded newform 225.2.h.d.46.2

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			46.2
Root			$0.199632 + 0.145041i$ of defining polynomial
Character	$\chi$	$=$	225.46
Dual form			225.2.h.d.181.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0762527 + 0.234682i) q^{2} +(1.56877 + 1.13978i) q^{4} +(2.09387 + 0.784664i) q^{5} -1.24676 q^{7} +(-0.786373 + 0.571334i) q^{8} +O(q^{10})$	\(q+(-0.0762527 + 0.234682i) q^{2} +(1.56877 + 1.13978i) q^{4} +(2.09387 + 0.784664i) q^{5} -1.24676 q^{7} +(-0.786373 + 0.571334i) q^{8} +(-0.343810 + 0.431561i) q^{10} +(-0.794084 + 2.44394i) q^{11} +(-1.44659 - 4.45215i) q^{13} +(0.0950687 - 0.292592i) q^{14} +(1.12432 + 3.46029i) q^{16} +(4.72397 - 3.43216i) q^{17} +(-3.37244 + 2.45022i) q^{19} +(2.39047 + 3.61751i) q^{20} +(-0.512997 - 0.372714i) q^{22} +(-0.496117 + 1.52689i) q^{23} +(3.76860 + 3.28597i) q^{25} +1.15514 q^{26} +(-1.95588 - 1.42103i) q^{28} +(-2.60158 - 1.89016i) q^{29} +(7.43739 - 5.40358i) q^{31} -2.84182 q^{32} +(0.445250 + 1.37034i) q^{34} +(-2.61055 - 0.978287i) q^{35} +(-0.394857 - 1.21524i) q^{37} +(-0.317865 - 0.978287i) q^{38} +(-2.09487 + 0.579261i) q^{40} +(-2.68719 - 8.27031i) q^{41} -3.88086 q^{43} +(-4.03129 + 2.92891i) q^{44} +(-0.320503 - 0.232859i) q^{46} +(-2.59656 - 1.88651i) q^{47} -5.44559 q^{49} +(-1.05852 + 0.633858i) q^{50} +(2.80510 - 8.63320i) q^{52} +(-10.7877 - 7.83770i) q^{53} +(-3.58038 + 4.49421i) q^{55} +(0.980418 - 0.712315i) q^{56} +(0.641964 - 0.466414i) q^{58} +(1.97548 + 6.07990i) q^{59} +(1.18258 - 3.63961i) q^{61} +(0.701000 + 2.15746i) q^{62} +(-2.03194 + 6.25366i) q^{64} +(0.464465 - 10.4573i) q^{65} +(8.19034 - 5.95063i) q^{67} +11.3227 q^{68} +(0.428648 - 0.538052i) q^{70} +(11.2284 + 8.15794i) q^{71} +(-3.51704 + 10.8243i) q^{73} +0.315305 q^{74} -8.08332 q^{76} +(0.990032 - 3.04700i) q^{77} +(-9.29008 - 6.74964i) q^{79} +(-0.360991 + 8.12762i) q^{80} +2.14580 q^{82} +(-2.29137 + 1.66478i) q^{83} +(12.5845 - 3.47978i) q^{85} +(0.295926 - 0.910766i) q^{86} +(-0.771858 - 2.37554i) q^{88} +(0.426682 - 1.31319i) q^{89} +(1.80355 + 5.55075i) q^{91} +(-2.51861 + 1.82988i) q^{92} +(0.640724 - 0.465513i) q^{94} +(-8.98407 + 2.48422i) q^{95} +(-0.0246815 - 0.0179322i) q^{97} +(0.415241 - 1.27798i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/225\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{3}{5}\right)$

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 $

$2$	−0.0762527	+	0.234682i	−0.0539188	+	0.165945i	−0.974390	−	0.224866i	$-0.927805\pi$
$2$	−0.0762527	+	0.234682i	−0.0539188	+	0.165945i	0.920471	+	0.390811i	$0.127805\pi$
$3$		0			0
$3$		0			0
$4$	1.56877	+	1.13978i	0.784386	+	0.569890i
$5$	2.09387	+	0.784664i	0.936408	+	0.350913i
$5$	2.09387	+	0.784664i	0.936408	+	0.350913i
$6$		0			0
$7$	−1.24676			−0.471231			−0.235615	−	0.971846i	$-0.575711\pi$
$7$	−1.24676			−0.471231			−0.235615	+	0.971846i	$0.575711\pi$
$8$	−0.786373	+	0.571334i	−0.278025	+	0.201997i
$9$		0			0
$10$	−0.343810	+	0.431561i	−0.108722	+	0.136472i
$11$	−0.794084	+	2.44394i	−0.239425	+	0.736876i	0.757078	+	0.653324i	$0.226626\pi$
$11$	−0.794084	+	2.44394i	−0.239425	+	0.736876i	−0.996503	+	0.0835513i	$0.973374\pi$
$12$		0			0
$13$	−1.44659	−	4.45215i	−0.401212	−	1.23480i	−0.924017	−	0.382351i	$-0.875115\pi$
$13$	−1.44659	−	4.45215i	−0.401212	−	1.23480i	0.522805	−	0.852452i	$-0.324885\pi$
$14$	0.0950687	−	0.292592i	0.0254082	−	0.0781984i
$15$		0			0
$16$	1.12432	+	3.46029i	0.281079	+	0.865073i
$17$	4.72397	−	3.43216i	1.14573	−	0.832422i	0.157823	−	0.987467i	$-0.449553\pi$
$17$	4.72397	−	3.43216i	1.14573	−	0.832422i	0.987907	+	0.155046i	$0.0495526\pi$
$18$		0			0
$19$	−3.37244	+	2.45022i	−0.773692	+	0.562120i	−0.903079	−	0.429474i	$-0.858699\pi$
$19$	−3.37244	+	2.45022i	−0.773692	+	0.562120i	0.129387	+	0.991594i	$0.458699\pi$
$20$	2.39047	+	3.61751i	0.534524	+	0.808901i
$21$		0			0
$22$	−0.512997	−	0.372714i	−0.109371	−	0.0794629i
$23$	−0.496117	+	1.52689i	−0.103447	+	0.318379i	−0.989363	−	0.145468i	$-0.953531\pi$
$23$	−0.496117	+	1.52689i	−0.103447	+	0.318379i	0.885915	+	0.463847i	$0.153531\pi$
$24$		0			0
$25$	3.76860	+	3.28597i	0.753721	+	0.657195i
$26$	1.15514			0.226542
$27$		0			0
$28$	−1.95588	−	1.42103i	−0.369627	−	0.268550i
$29$	−2.60158	−	1.89016i	−0.483102	−	0.350994i	0.319423	−	0.947612i	$-0.396511\pi$
$29$	−2.60158	−	1.89016i	−0.483102	−	0.350994i	−0.802525	+	0.596618i	$0.796511\pi$
$30$		0			0
$31$	7.43739	−	5.40358i	1.33579	−	0.970512i	0.336207	−	0.941788i	$-0.390856\pi$
$31$	7.43739	−	5.40358i	1.33579	−	0.970512i	0.999587	−	0.0287236i	$-0.00914425\pi$
$32$	−2.84182			−0.502368
$33$		0			0
$34$	0.445250	+	1.37034i	0.0763598	+	0.235011i
$35$	−2.61055	−	0.978287i	−0.441264	−	0.165361i
$36$		0			0
$37$	−0.394857	−	1.21524i	−0.0649141	−	0.199785i	0.913339	−	0.407200i	$-0.133495\pi$
$37$	−0.394857	−	1.21524i	−0.0649141	−	0.199785i	−0.978253	+	0.207415i	$0.933495\pi$
$38$	−0.317865	−	0.978287i	−0.0515645	−	0.158699i
$39$		0			0
$40$	−2.09487	+	0.579261i	−0.331228	+	0.0915891i
$41$	−2.68719	−	8.27031i	−0.419668	−	1.29161i	−0.908008	−	0.418953i	$-0.862397\pi$
$41$	−2.68719	−	8.27031i	−0.419668	−	1.29161i	0.488340	−	0.872654i	$-0.337603\pi$
$42$		0			0
$43$	−3.88086			−0.591825			−0.295913	−	0.955215i	$-0.595624\pi$
$43$	−3.88086			−0.591825			−0.295913	+	0.955215i	$0.595624\pi$
$44$	−4.03129	+	2.92891i	−0.607740	+	0.441549i
$45$		0			0
$46$	−0.320503	−	0.232859i	−0.0472556	−	0.0343332i
$47$	−2.59656	−	1.88651i	−0.378747	−	0.275176i	0.382082	−	0.924129i	$-0.375207\pi$
$47$	−2.59656	−	1.88651i	−0.378747	−	0.275176i	−0.760829	+	0.648953i	$0.775207\pi$
$48$		0			0
$49$	−5.44559			−0.777942
$50$	−1.05852	+	0.633858i	−0.149698	+	0.0896411i
$51$		0			0
$52$	2.80510	−	8.63320i	0.388997	−	1.19721i
$53$	−10.7877	−	7.83770i	−1.48180	−	1.07659i	−0.976971	−	0.213371i	$-0.931556\pi$
$53$	−10.7877	−	7.83770i	−1.48180	−	1.07659i	−0.504829	−	0.863219i	$-0.668444\pi$
$54$		0			0
$55$	−3.58038	+	4.49421i	−0.482779	+	0.605999i
$56$	0.980418	−	0.712315i	0.131014	−	0.0951871i
$57$		0			0
$58$	0.641964	−	0.466414i	0.0842940	−	0.0612432i
$59$	1.97548	+	6.07990i	0.257186	+	0.791536i	0.993391	+	0.114778i	$0.0366157\pi$
$59$	1.97548	+	6.07990i	0.257186	+	0.791536i	−0.736206	+	0.676758i	$0.763384\pi$
$60$		0			0
$61$	1.18258	−	3.63961i	0.151414	−	0.466005i	−0.846366	−	0.532602i	$-0.821214\pi$
$61$	1.18258	−	3.63961i	0.151414	−	0.466005i	0.997780	+	0.0665973i	$0.0212143\pi$
$62$	0.701000	+	2.15746i	0.0890271	+	0.273997i
$63$		0			0
$64$	−2.03194	+	6.25366i	−0.253992	+	0.781708i
$65$	0.464465	−	10.4573i	0.0576098	−	1.29707i
$66$		0			0
$67$	8.19034	−	5.95063i	1.00061	−	0.726985i	0.0383907	−	0.999263i	$-0.487777\pi$
$67$	8.19034	−	5.95063i	1.00061	−	0.726985i	0.962219	+	0.272277i	$0.0877768\pi$
$68$	11.3227			1.37308
$69$		0			0
$70$	0.428648	−	0.538052i	0.0512332	−	0.0643095i
$71$	11.2284	+	8.15794i	1.33257	+	0.968169i	0.999682	+	0.0252028i	$0.00802316\pi$
$71$	11.2284	+	8.15794i	1.33257	+	0.968169i	0.332888	+	0.942966i	$0.391977\pi$
$72$		0			0
$73$	−3.51704	+	10.8243i	−0.411638	+	1.26689i	0.503585	+	0.863946i	$0.332014\pi$
$73$	−3.51704	+	10.8243i	−0.411638	+	1.26689i	−0.915223	+	0.402947i	$0.867986\pi$
$74$	0.315305			0.0366534
$75$		0			0
$76$	−8.08332			−0.927220
$77$	0.990032	−	3.04700i	0.112825	−	0.347238i
$78$		0			0
$79$	−9.29008	−	6.74964i	−1.04522	−	0.759394i	−0.0739188	−	0.997264i	$-0.523551\pi$
$79$	−9.29008	−	6.74964i	−1.04522	−	0.759394i	−0.971297	+	0.237871i	$0.923551\pi$
$80$	−0.360991	+	8.12762i	−0.0403601	+	0.908696i
$81$		0			0
$82$	2.14580			0.236964
$83$	−2.29137	+	1.66478i	−0.251511	+	0.182733i	−0.706396	−	0.707817i	$-0.749680\pi$
$83$	−2.29137	+	1.66478i	−0.251511	+	0.182733i	0.454885	+	0.890550i	$0.349680\pi$
$84$		0			0
$85$	12.5845	−	3.47978i	1.36498	−	0.377435i
$86$	0.295926	−	0.910766i	0.0319105	−	0.0982105i
$87$		0			0
$88$	−0.771858	−	2.37554i	−0.0822804	−	0.253233i
$89$	0.426682	−	1.31319i	0.0452282	−	0.139198i	−0.925892	−	0.377788i	$-0.876685\pi$
$89$	0.426682	−	1.31319i	0.0452282	−	0.139198i	0.971121	+	0.238589i	$0.0766850\pi$
$90$		0			0
$91$	1.80355	+	5.55075i	0.189063	+	0.581877i
$92$	−2.51861	+	1.82988i	−0.262584	+	0.190778i
$93$		0			0
$94$	0.640724	−	0.465513i	0.0660857	−	0.0480140i
$95$	−8.98407	+	2.48422i	−0.921746	+	0.254876i
$96$		0			0
$97$	−0.0246815	−	0.0179322i	−0.00250603	−	0.00182074i	0.586532	−	0.809926i	$-0.300493\pi$
$97$	−0.0246815	−	0.0179322i	−0.00250603	−	0.00182074i	−0.589038	+	0.808106i	$0.700493\pi$
$98$	0.415241	−	1.27798i	0.0419457	−	0.129096i
$99$		0			0
$100$	2.16680	+	9.45033i	0.216680	+	0.945033i
$101$	11.2308			1.11750			0.558751	−	0.829336i	$-0.311281\pi$
$101$	11.2308			1.11750			0.558751	+	0.829336i	$0.311281\pi$
$102$		0			0
$103$	0.583288	+	0.423783i	0.0574730	+	0.0417566i	0.616151	−	0.787628i	$-0.288691\pi$
$103$	0.583288	+	0.423783i	0.0574730	+	0.0417566i	−0.558678	+	0.829385i	$0.688691\pi$
$104$	3.68122	+	2.67456i	0.360973	+	0.262262i
$105$		0			0
$106$	2.66195	−	1.93402i	0.258552	−	0.187849i
$107$	−2.11668			−0.204627			−0.102313	−	0.994752i	$-0.532624\pi$
$107$	−2.11668			−0.204627			−0.102313	+	0.994752i	$0.532624\pi$
$108$		0			0
$109$	0.690602	+	2.12545i	0.0661477	+	0.203582i	0.978667	−	0.205451i	$-0.0658662\pi$
$109$	0.690602	+	2.12545i	0.0661477	+	0.203582i	−0.912520	+	0.409033i	$0.865866\pi$
$110$	−0.781695	−	1.18295i	−0.0745317	−	0.112790i
$111$		0			0
$112$	−1.40175	−	4.31415i	−0.132453	−	0.407649i
$113$	0.973217	+	2.99525i	0.0915526	+	0.281770i	0.986340	−	0.164723i	$-0.0526729\pi$
$113$	0.973217	+	2.99525i	0.0915526	+	0.281770i	−0.894787	+	0.446493i	$0.852673\pi$
$114$		0			0
$115$	−2.23690	+	2.80783i	−0.208592	+	0.261831i
$116$	−1.92693	−	5.93047i	−0.178911	−	0.550630i
$117$		0			0
$118$	−1.57748			−0.145219
$119$	−5.88965	+	4.27908i	−0.539903	+	0.392262i
$120$		0			0
$121$	3.55691	+	2.58425i	0.323356	+	0.234932i
$122$	0.763975	+	0.555061i	0.0691671	+	0.0502528i
$123$		0			0
$124$	17.8265			1.60086
$125$	5.31259	+	9.83750i	0.475172	+	0.879893i
$126$		0			0
$127$	−4.83929	+	14.8938i	−0.429418	+	1.32161i	0.469282	+	0.883048i	$0.344513\pi$
$127$	−4.83929	+	14.8938i	−0.429418	+	1.32161i	−0.898700	+	0.438564i	$0.855487\pi$
$128$	−5.91084	−	4.29448i	−0.522450	−	0.379582i
$129$		0			0
$130$	2.41872	+	0.906400i	0.212136	+	0.0794965i
$131$	−12.1000	+	8.79116i	−1.05718	+	0.768087i	−0.973565	−	0.228411i	$-0.926647\pi$
$131$	−12.1000	+	8.79116i	−1.05718	+	0.768087i	−0.0836161	+	0.996498i	$0.526647\pi$
$132$		0			0
$133$	4.20463	−	3.05484i	0.364587	−	0.264888i
$134$	0.771969	+	2.37588i	0.0666879	+	0.205244i
$135$		0			0
$136$	−1.75389	+	5.39792i	−0.150395	+	0.462868i
$137$	3.24300	+	9.98092i	0.277068	+	0.852727i	0.988665	+	0.150139i	$0.0479723\pi$
$137$	3.24300	+	9.98092i	0.277068	+	0.852727i	−0.711597	+	0.702588i	$0.752028\pi$
$138$		0			0
$139$	3.84749	−	11.8414i	0.326340	−	1.00437i	−0.644492	−	0.764611i	$-0.722931\pi$
$139$	3.84749	−	11.8414i	0.326340	−	1.00437i	0.970832	−	0.239761i	$-0.0770690\pi$
$140$	−2.98033	−	4.51017i	−0.251884	−	0.381179i
$141$		0			0
$142$	−2.77072	+	2.01304i	−0.232513	+	0.168931i
$143$	12.0295			1.00596
$144$		0			0
$145$	−3.96424	−	5.99913i	−0.329212	−	0.498200i
$146$	−2.27209	−	1.65077i	−0.188039	−	0.136619i
$147$		0			0
$148$	0.765671	−	2.35649i	0.0629378	−	0.193703i
$149$	17.0680			1.39826			0.699131	−	0.714994i	$-0.253570\pi$
$149$	17.0680			1.39826			0.699131	+	0.714994i	$0.253570\pi$
$150$		0			0
$151$	−1.57516			−0.128185			−0.0640923	−	0.997944i	$-0.520415\pi$
$151$	−1.57516			−0.128185			−0.0640923	+	0.997944i	$0.520415\pi$
$152$	1.25210	−	3.85358i	0.101559	−	0.312567i
$153$		0			0
$154$	0.639584	+	0.464685i	0.0515391	+	0.0374454i
$155$	19.8129	−	5.47855i	1.59141	−	0.440048i
$156$		0			0
$157$	−9.20058			−0.734286			−0.367143	−	0.930164i	$-0.619664\pi$
$157$	−9.20058			−0.734286			−0.367143	+	0.930164i	$0.619664\pi$
$158$	2.29241	−	1.66553i	0.182374	−	0.132503i
$159$		0			0
$160$	−5.95041	−	2.22988i	−0.470421	−	0.176287i
$161$	0.618538	−	1.90366i	0.0487476	−	0.150030i
$162$		0			0
$163$	−1.41553	−	4.35656i	−0.110873	−	0.341232i	0.880191	−	0.474620i	$-0.157414\pi$
$163$	−1.41553	−	4.35656i	−0.110873	−	0.341232i	−0.991064	+	0.133388i	$0.957414\pi$
$164$	5.21075	−	16.0370i	0.406891	−	1.25228i
$165$		0			0
$166$	−0.215970	−	0.664687i	−0.0167625	−	0.0515897i
$167$	0.115310	−	0.0837776i	0.00892296	−	0.00648291i	−0.583315	−	0.812246i	$-0.698245\pi$
$167$	0.115310	−	0.0837776i	0.00892296	−	0.00648291i	0.592238	+	0.805763i	$0.298245\pi$
$168$		0			0
$169$	−7.21176	+	5.23965i	−0.554751	+	0.403050i
$170$	−0.142959	+	3.21869i	−0.0109645	+	0.246862i
$171$		0			0
$172$	−6.08819	−	4.42333i	−0.464220	−	0.337275i
$173$	−7.60885	+	23.4176i	−0.578490	+	1.78041i	0.0454831	+	0.998965i	$0.485517\pi$
$173$	−7.60885	+	23.4176i	−0.578490	+	1.78041i	−0.623974	+	0.781445i	$0.714483\pi$
$174$		0			0
$175$	−4.69854	−	4.09682i	−0.355176	−	0.309690i
$176$	−9.34955			−0.704749
$177$		0			0
$178$	0.275647	+	0.200269i	0.0206606	+	0.0150108i
$179$	−19.5420	−	14.1981i	−1.46064	−	1.06122i	−0.983195	−	0.182557i	$-0.941563\pi$
$179$	−19.5420	−	14.1981i	−1.46064	−	1.06122i	−0.477446	−	0.878661i	$-0.658437\pi$
$180$		0			0
$181$	−1.59218	+	1.15679i	−0.118346	+	0.0859834i	−0.645384	−	0.763858i	$-0.723303\pi$
$181$	−1.59218	+	1.15679i	−0.118346	+	0.0859834i	0.527038	+	0.849842i	$0.323303\pi$
$182$	−1.44019			−0.106754
$183$		0			0
$184$	−0.482231	−	1.48415i	−0.0355505	−	0.109413i
$185$	0.126779	−	2.85440i	0.00932098	−	0.209859i
$186$		0			0
$187$	4.63677	+	14.2705i	0.339074	+	1.04356i
$188$	−1.92320	−	5.91901i	−0.140264	−	0.431689i
$189$		0			0
$190$	0.102059	−	2.29783i	0.00740412	−	0.166702i
$191$	2.40061	+	7.38832i	0.173702	+	0.534600i	0.999572	−	0.0292607i	$-0.00931531\pi$
$191$	2.40061	+	7.38832i	0.173702	+	0.534600i	−0.825870	+	0.563861i	$0.809315\pi$
$192$		0			0
$193$	14.3458			1.03264			0.516318	−	0.856397i	$-0.327302\pi$
$193$	14.3458			1.03264			0.516318	+	0.856397i	$0.327302\pi$
$194$	0.00609039	−	0.00442493i	0.000437265	−	0.000317691i
$195$		0			0
$196$	−8.54290	−	6.20678i	−0.610207	−	0.443341i
$197$	0.132307	+	0.0961264i	0.00942645	+	0.00684872i	0.592489	−	0.805579i	$-0.298146\pi$
$197$	0.132307	+	0.0961264i	0.00942645	+	0.00684872i	−0.583062	+	0.812428i	$0.698146\pi$
$198$		0			0
$199$	4.96974			0.352295			0.176148	−	0.984364i	$-0.443636\pi$
$199$	4.96974			0.352295			0.176148	+	0.984364i	$0.443636\pi$
$200$	−4.84092	−	0.430872i	−0.342304	−	0.0304673i
$201$		0			0
$202$	−0.856375	+	2.63565i	−0.0602543	+	0.185444i
$203$	3.24355	+	2.35658i	0.227652	+	0.165399i
$204$		0			0
$205$	0.862792	−	19.4255i	0.0602600	−	1.35674i
$206$	−0.143931	+	0.104572i	−0.0100282	+	0.00728590i
$207$		0			0
$208$	13.7793	−	10.0112i	0.955423	−	0.694155i
$209$	−3.31020	−	10.1877i	−0.228971	−	0.704701i
$210$		0			0
$211$	1.01784	−	3.13260i	0.0700713	−	0.215657i	−0.909888	−	0.414853i	$-0.863833\pi$
$211$	1.01784	−	3.13260i	0.0700713	−	0.215657i	0.979960	+	0.199196i	$0.0638330\pi$
$212$	−7.99015	−	24.5911i	−0.548766	−	1.68893i
$213$		0			0
$214$	0.161402	−	0.496745i	0.0110332	−	0.0339568i
$215$	−8.12602	−	3.04517i	−0.554190	−	0.207679i
$216$		0			0
$217$	−9.27263	+	6.73696i	−0.629467	+	0.457335i
$218$	−0.551465			−0.0373500
$219$		0			0
$220$	−10.7392	+	2.96954i	−0.724038	+	0.200207i
$221$	−22.1141	−	16.0669i	−1.48756	−	1.08077i
$222$		0			0
$223$	−4.87419	+	15.0012i	−0.326400	+	1.00456i	0.644404	+	0.764685i	$0.277105\pi$
$223$	−4.87419	+	15.0012i	−0.326400	+	1.00456i	−0.970805	+	0.239872i	$0.922895\pi$
$224$	3.54307			0.236731
$225$		0			0
$226$	−0.777142			−0.0516947
$227$	−4.18427	+	12.8779i	−0.277720	+	0.854734i	0.710767	+	0.703428i	$0.248348\pi$
$227$	−4.18427	+	12.8779i	−0.277720	+	0.854734i	−0.988487	+	0.151307i	$0.951652\pi$
$228$		0			0
$229$	11.9596	+	8.68915i	0.790312	+	0.574195i	0.908056	−	0.418849i	$-0.137566\pi$
$229$	11.9596	+	8.68915i	0.790312	+	0.574195i	−0.117744	+	0.993044i	$0.537566\pi$
$230$	−0.488376	−	0.739064i	−0.0322026	−	0.0487325i
$231$		0			0
$232$	3.12573			0.205214
$233$	0.419864	−	0.305049i	0.0275062	−	0.0199844i	−0.573947	−	0.818892i	$-0.694589\pi$
$233$	0.419864	−	0.305049i	0.0275062	−	0.0199844i	0.601453	+	0.798908i	$0.294589\pi$
$234$		0			0
$235$	−3.95659	−	5.98754i	−0.258099	−	0.390584i
$236$	−3.83067	+	11.7896i	−0.249356	+	0.767438i
$237$		0			0
$238$	−0.555120	−	1.70848i	−0.0359831	−	0.110745i
$239$	−2.54331	+	7.82750i	−0.164513	+	0.506319i	−0.999000	−	0.0447086i	$-0.985764\pi$
$239$	−2.54331	+	7.82750i	−0.164513	+	0.506319i	0.834487	+	0.551027i	$0.185764\pi$
$240$		0			0
$241$	−0.395906	−	1.21847i	−0.0255025	−	0.0784888i	0.937495	−	0.347998i	$-0.113138\pi$
$241$	−0.395906	−	1.21847i	−0.0255025	−	0.0784888i	−0.962998	+	0.269509i	$0.913138\pi$
$242$	−0.877700	+	0.637686i	−0.0564207	+	0.0409920i
$243$		0			0
$244$	6.00356	−	4.36184i	0.384339	−	0.279238i
$245$	−11.4024	−	4.27296i	−0.728471	−	0.272990i
$246$		0			0
$247$	15.7873	+	11.4701i	1.00452	+	0.729828i
$248$	−2.76132	+	8.49846i	−0.175344	+	0.539653i
$249$		0			0
$250$	−2.71378	+	0.496631i	−0.171635	+	0.0314097i
$251$	−4.63494			−0.292555			−0.146277	−	0.989244i	$-0.546729\pi$
$251$	−4.63494			−0.292555			−0.146277	+	0.989244i	$0.546729\pi$
$252$		0			0
$253$	−3.33767	−	2.42496i	−0.209837	−	0.152456i
$254$	−3.12630	−	2.27139i	−0.196161	−	0.142519i
$255$		0			0
$256$	−9.18081	+	6.67025i	−0.573801	+	0.416891i
$257$	18.3001			1.14153			0.570766	−	0.821113i	$-0.306647\pi$
$257$	18.3001			1.14153			0.570766	+	0.821113i	$0.306647\pi$
$258$		0			0
$259$	0.492291	+	1.51512i	0.0305895	+	0.0941448i
$260$	12.6477	−	15.8758i	0.784376	−	0.984573i
$261$		0			0
$262$	−1.14047	−	3.51000i	−0.0704583	−	0.216848i
$263$	−5.15027	−	15.8509i	−0.317579	−	0.977409i	−0.974680	−	0.223606i	$-0.928217\pi$
$263$	−5.15027	−	15.8509i	−0.317579	−	0.977409i	0.657100	−	0.753803i	$-0.271783\pi$
$264$		0			0
$265$	−16.4380	−	24.8758i	−1.00978	−	1.52811i
$266$	0.396301	+	1.21969i	0.0242988	+	0.0747839i
$267$		0			0
$268$	19.6312			1.19917
$269$	2.12942	−	1.54712i	0.129833	−	0.0943294i	−0.520973	−	0.853573i	$-0.674431\pi$
$269$	2.12942	−	1.54712i	0.129833	−	0.0943294i	0.650807	+	0.759244i	$0.274431\pi$
$270$		0			0
$271$	−3.69192	−	2.68233i	−0.224268	−	0.162940i	0.469978	−	0.882678i	$-0.344262\pi$
$271$	−3.69192	−	2.68233i	−0.224268	−	0.162940i	−0.694246	+	0.719738i	$0.744262\pi$
$272$	17.1875	+	12.4875i	1.04215	+	0.757164i
$273$		0			0
$274$	−2.58963			−0.156445
$275$	−11.0233	+	6.60090i	−0.664731	+	0.398049i
$276$		0			0
$277$	0.389132	−	1.19762i	0.0233807	−	0.0719583i	−0.938685	−	0.344775i	$-0.887955\pi$
$277$	0.389132	−	1.19762i	0.0233807	−	0.0719583i	0.962066	+	0.272817i	$0.0879552\pi$
$278$	2.48557	+	1.80587i	0.149075	+	0.108309i
$279$		0			0
$280$	2.61180	−	0.722198i	0.156085	−	0.0431596i
$281$	10.8543	−	7.88611i	0.647513	−	0.470446i	−0.214910	−	0.976634i	$-0.568946\pi$
$281$	10.8543	−	7.88611i	0.647513	−	0.470446i	0.862423	+	0.506188i	$0.168946\pi$
$282$		0			0
$283$	−19.4884	+	14.1591i	−1.15846	+	0.841674i	−0.989583	−	0.143962i	$-0.954016\pi$
$283$	−19.4884	+	14.1591i	−1.15846	+	0.841674i	−0.168882	+	0.985636i	$0.554016\pi$
$284$	8.31661	+	25.5959i	0.493500	+	1.51884i
$285$		0			0
$286$	−0.917281	+	2.82310i	−0.0542400	+	0.166934i
$287$	3.35028	+	10.3111i	0.197761	+	0.608644i
$288$		0			0
$289$	5.28283	−	16.2589i	0.310754	−	0.956404i
$290$	1.71017	−	0.472886i	0.100425	−	0.0277688i
$291$		0			0
$292$	−17.8548	+	12.9723i	−1.04487	+	0.759145i
$293$	32.1727			1.87955			0.939776	−	0.341792i	$-0.111034\pi$
$293$	32.1727			1.87955			0.939776	+	0.341792i	$0.111034\pi$
$294$		0			0
$295$	−0.634279	+	14.2806i	−0.0369292	+	0.831450i
$296$	1.00481	+	0.730041i	0.0584037	+	0.0424328i
$297$		0			0
$298$	−1.30148	+	4.00554i	−0.0753926	+	0.232035i
$299$	7.51561			0.434639
$300$		0			0
$301$	4.83849			0.278886
$302$	0.120110	−	0.369661i	0.00691156	−	0.0212716i
$303$		0			0
$304$	−12.2702	−	8.91482i	−0.703744	−	0.511300i
$305$	5.33205	−	6.69296i	0.305312	−	0.383237i
$306$		0			0
$307$	20.2962			1.15837			0.579183	−	0.815198i	$-0.303372\pi$
$307$	20.2962			1.15837			0.579183	+	0.815198i	$0.303372\pi$
$308$	5.02605	−	3.65164i	0.286386	−	0.208071i
$309$		0			0
$310$	−0.225074	+	5.06749i	−0.0127834	+	0.287814i
$311$	5.78554	−	17.8061i	0.328068	−	1.00969i	−0.641969	−	0.766731i	$-0.721882\pi$
$311$	5.78554	−	17.8061i	0.328068	−	1.00969i	0.970037	−	0.242959i	$-0.0781180\pi$
$312$		0			0
$313$	7.68955	+	23.6660i	0.434639	+	1.33768i	0.893456	+	0.449151i	$0.148274\pi$
$313$	7.68955	+	23.6660i	0.434639	+	1.33768i	−0.458817	+	0.888531i	$0.651726\pi$
$314$	0.701569	−	2.15921i	0.0395919	−	0.121851i
$315$		0			0
$316$	−6.88092	−	21.1773i	−0.387082	−	1.19132i
$317$	−20.3775	+	14.8052i	−1.14452	+	0.831540i	−0.987742	−	0.156094i	$-0.950110\pi$
$317$	−20.3775	+	14.8052i	−1.14452	+	0.831540i	−0.156775	+	0.987634i	$0.550110\pi$
$318$		0			0
$319$	6.68532	−	4.85717i	0.374306	−	0.271949i
$320$	−9.16165	+	11.5000i	−0.512152	+	0.642869i
$321$		0			0
$322$	0.399590	+	0.290319i	0.0222683	+	0.0161788i
$323$	−7.52174	+	23.1496i	−0.418521	+	1.28808i
$324$		0			0
$325$	9.17801	−	21.5318i	0.509104	−	1.19437i
$326$	1.13034			0.0626039
$327$		0			0
$328$	6.83824	+	4.96827i	0.377579	+	0.274327i
$329$	3.23728	+	2.35202i	0.178477	+	0.129671i
$330$		0			0
$331$	−24.6097	+	17.8800i	−1.35267	+	0.982773i	−0.353797	+	0.935322i	$0.615110\pi$
$331$	−24.6097	+	17.8800i	−1.35267	+	0.982773i	−0.998874	+	0.0474508i	$0.984890\pi$
$332$	−5.49212			−0.301419
$333$		0			0
$334$	0.0108684	+	0.0334494i	0.000594691	+	0.00183027i
$335$	21.8188	−	6.03319i	1.19209	−	0.329629i
$336$		0			0
$337$	−1.41361	−	4.35066i	−0.0770045	−	0.236995i	0.905143	−	0.425107i	$-0.139763\pi$
$337$	−1.41361	−	4.35066i	−0.0770045	−	0.236995i	−0.982148	+	0.188111i	$0.939763\pi$
$338$	−0.679734	−	2.09200i	−0.0369726	−	0.113790i
$339$		0			0
$340$	23.7084	+	8.88455i	1.28577	+	0.481832i
$341$	7.30011	+	22.4674i	0.395323	+	1.21668i
$342$		0			0
$343$	15.5167			0.837821
$344$	3.05180	−	2.21726i	0.164542	−	0.119547i
$345$		0			0
$346$	−4.91550	−	3.57132i	−0.264259	−	0.191995i
$347$	−13.6038	−	9.88377i	−0.730293	−	0.530589i	0.159363	−	0.987220i	$-0.449056\pi$
$347$	−13.6038	−	9.88377i	−0.730293	−	0.530589i	−0.889656	+	0.456631i	$0.849056\pi$
$348$		0			0
$349$	0.373581			0.0199973			0.00999866	−	0.999950i	$-0.496817\pi$
$349$	0.373581			0.0199973			0.00999866	+	0.999950i	$0.496817\pi$
$350$	1.31972	−	0.790268i	0.0705422	−	0.0422416i
$351$		0			0
$352$	2.25665	−	6.94524i	0.120280	−	0.370183i
$353$	−19.3909	−	14.0883i	−1.03208	−	0.749847i	−0.0633526	−	0.997991i	$-0.520179\pi$
$353$	−19.3909	−	14.0883i	−1.03208	−	0.749847i	−0.968723	+	0.248144i	$0.920179\pi$
$354$		0			0
$355$	17.1097	+	25.8922i	0.908087	+	1.37422i
$356$	2.16612	−	1.57378i	0.114804	−	0.0834101i
$357$		0			0
$358$	4.82218	−	3.50352i	0.254860	−	0.185167i
$359$	1.46789	+	4.51771i	0.0774724	+	0.238435i	0.982291	−	0.187362i	$-0.0599937\pi$
$359$	1.46789	+	4.51771i	0.0774724	+	0.238435i	−0.904819	+	0.425797i	$0.859994\pi$
$360$		0			0
$361$	−0.501540	+	1.54358i	−0.0263969	+	0.0812412i
$362$	−0.150069	−	0.461865i	−0.00788744	−	0.0242751i
$363$		0			0
$364$	−3.49728	+	10.7635i	−0.183307	+	0.564162i
$365$	−15.8577	+	19.9051i	−0.830030	+	1.04188i
$366$		0			0
$367$	14.0526	−	10.2098i	0.733540	−	0.532948i	−0.157141	−	0.987576i	$-0.550228\pi$
$367$	14.0526	−	10.2098i	0.733540	−	0.532948i	0.890681	+	0.454628i	$0.150228\pi$
$368$	−5.84128			−0.304498
$369$		0			0
$370$	0.660208	+	0.247408i	0.0343226	+	0.0128621i
$371$	13.4496	+	9.77172i	0.698270	+	0.507323i
$372$		0			0
$373$	0.651645	−	2.00556i	0.0337409	−	0.103844i	−0.932768	−	0.360478i	$-0.882614\pi$
$373$	0.651645	−	2.00556i	0.0337409	−	0.103844i	0.966509	+	0.256634i	$0.0826136\pi$
$374$	−3.70260			−0.191457
$375$		0			0
$376$	3.11969			0.160886
$377$	−4.65185	+	14.3169i	−0.239582	+	0.737359i
$378$		0			0
$379$	−10.0391	−	7.29380i	−0.515671	−	0.374657i	0.299299	−	0.954159i	$-0.403247\pi$
$379$	−10.0391	−	7.29380i	−0.515671	−	0.374657i	−0.814971	+	0.579502i	$0.803247\pi$
$380$	−16.9254	−	6.34269i	−0.868256	−	0.325373i
$381$		0			0
$382$	−1.91696			−0.0980801
$383$	26.9448	−	19.5766i	1.37682	−	1.00032i	0.379646	−	0.925132i	$-0.376046\pi$
$383$	26.9448	−	19.5766i	1.37682	−	1.00032i	0.997170	−	0.0751836i	$-0.0239543\pi$
$384$		0			0
$385$	4.46388	−	5.60320i	0.227500	−	0.285565i
$386$	−1.09391	+	3.36671i	−0.0556785	+	0.171361i
$387$		0			0
$388$	−0.0182810	−	0.0562631i	−0.000928076	−	0.00285633i
$389$	5.24639	−	16.1467i	0.266002	−	0.818671i	−0.725459	−	0.688266i	$-0.758372\pi$
$389$	5.24639	−	16.1467i	0.266002	−	0.818671i	0.991461	−	0.130405i	$-0.0416278\pi$
$390$		0			0
$391$	2.89690	+	8.91573i	0.146502	+	0.450888i
$392$	4.28227	−	3.11125i	0.216287	−	0.157142i
$393$		0			0
$394$	−0.0326478	+	0.0237200i	−0.00164477	+	0.00119500i
$395$	−14.1560	−	21.4225i	−0.712268	−	1.07788i
$396$		0			0
$397$	0.701070	+	0.509357i	0.0351857	+	0.0255639i	0.605239	−	0.796044i	$-0.293078\pi$
$397$	0.701070	+	0.509357i	0.0351857	+	0.0255639i	−0.570053	+	0.821608i	$0.693078\pi$
$398$	−0.378956	+	1.16631i	−0.0189953	+	0.0584617i
$399$		0			0
$400$	−7.13333	+	16.7350i	−0.356666	+	0.836748i
$401$	−9.68680			−0.483736			−0.241868	−	0.970309i	$-0.577760\pi$
$401$	−9.68680			−0.483736			−0.241868	+	0.970309i	$0.577760\pi$
$402$		0			0
$403$	−34.8164	−	25.2956i	−1.73433	−	1.26006i
$404$	17.6185	+	12.8006i	0.876553	+	0.636853i
$405$		0			0
$406$	−0.800374	+	0.581506i	−0.0397219	+	0.0288597i
$407$	3.28353			0.162759
$408$		0			0
$409$	0.469043	+	1.44357i	0.0231927	+	0.0713797i	0.961983	−	0.273109i	$-0.0880521\pi$
$409$	0.469043	+	1.44357i	0.0231927	+	0.0713797i	−0.938790	+	0.344489i	$0.888052\pi$
$410$	4.49302	+	1.68373i	0.221895	+	0.0831535i
$411$		0			0
$412$	0.432026	+	1.32964i	0.0212844	+	0.0655066i
$413$	−2.46295	−	7.58017i	−0.121194	−	0.372996i
$414$		0			0
$415$	−6.10413	+	1.68788i	−0.299640	+	0.0828546i
$416$	4.11095	+	12.6522i	0.201556	+	0.620325i
$417$		0			0
$418$	2.64329			0.129287
$419$	−24.7252	+	17.9639i	−1.20790	+	0.877594i	−0.995039	−	0.0994875i	$-0.968280\pi$
$419$	−24.7252	+	17.9639i	−1.20790	+	0.877594i	−0.212866	+	0.977081i	$0.568280\pi$
$420$		0			0
$421$	5.64016	+	4.09782i	0.274885	+	0.199715i	0.716683	−	0.697399i	$-0.245659\pi$
$421$	5.64016	+	4.09782i	0.274885	+	0.199715i	−0.441799	+	0.897114i	$0.645659\pi$
$422$	0.657551	+	0.477739i	0.0320091	+	0.0232560i
$423$		0			0
$424$	12.9611			0.629445
$425$	29.0807	+	2.58837i	1.41062	+	0.125554i
$426$		0			0
$427$	−1.47439	+	4.53772i	−0.0713510	+	0.219596i
$428$	−3.32058	−	2.41255i	−0.160506	−	0.116615i
$429$		0			0
$430$	1.33428	−	1.67483i	0.0643446	−	0.0807673i
$431$	8.85650	−	6.43463i	0.426603	−	0.309945i	−0.353686	−	0.935364i	$-0.615072\pi$
$431$	8.85650	−	6.43463i	0.426603	−	0.309945i	0.780289	+	0.625419i	$0.215072\pi$
$432$		0			0
$433$	−8.44561	+	6.13609i	−0.405870	+	0.294882i	−0.771928	−	0.635710i	$-0.780707\pi$
$433$	−8.44561	+	6.13609i	−0.405870	+	0.294882i	0.366058	+	0.930592i	$0.380707\pi$
$434$	−0.873978	−	2.68983i	−0.0419523	−	0.129116i
$435$		0			0
$436$	−1.33915	+	4.12149i	−0.0641338	+	0.197384i
$437$	−2.06810	−	6.36495i	−0.0989305	−	0.304477i
$438$		0			0
$439$	4.76917	−	14.6780i	0.227620	−	0.700543i	−0.770395	−	0.637567i	$-0.779941\pi$
$439$	4.76917	−	14.6780i	0.227620	−	0.700543i	0.998015	−	0.0629758i	$-0.0200591\pi$
$440$	0.247825	−	5.57972i	0.0118146	−	0.266003i
$441$		0			0
$442$	5.45686	−	3.96464i	0.259556	−	0.188579i
$443$	−18.9105			−0.898463			−0.449231	−	0.893415i	$-0.648302\pi$
$443$	−18.9105			−0.898463			−0.449231	+	0.893415i	$0.648302\pi$
$444$		0			0
$445$	1.92383	−	2.41486i	0.0911985	−	0.114475i
$446$	−3.14884	−	2.28777i	−0.149102	−	0.108329i
$447$		0			0
$448$	2.53334	−	7.79681i	0.119689	−	0.368365i
$449$	11.4152			0.538714			0.269357	−	0.963040i	$-0.413189\pi$
$449$	11.4152			0.538714			0.269357	+	0.963040i	$0.413189\pi$
$450$		0			0
$451$	22.3460			1.05223
$452$	−1.88717	+	5.80813i	−0.0887652	+	0.273191i
$453$		0			0
$454$	−2.70314	−	1.96395i	−0.126865	−	0.0921725i
$455$	−0.579076	+	13.0377i	−0.0271475	+	0.611219i
$456$		0			0
$457$	−33.9739			−1.58923			−0.794616	−	0.607112i	$-0.792328\pi$
$457$	−33.9739			−1.58923			−0.794616	+	0.607112i	$0.792328\pi$
$458$	−2.95114	+	2.14413i	−0.137898	+	0.100188i
$459$		0			0
$460$	−6.70950	+	1.85527i	−0.312832	+	0.0865023i
$461$	7.62985	−	23.4823i	0.355358	−	1.09368i	−0.600444	−	0.799667i	$-0.705009\pi$
$461$	7.62985	−	23.4823i	0.355358	−	1.09368i	0.955802	−	0.294012i	$-0.0949905\pi$
$462$		0			0
$463$	−4.21237	−	12.9643i	−0.195765	−	0.602504i	−0.999967	−	0.00814689i	$-0.997407\pi$
$463$	−4.21237	−	12.9643i	−0.195765	−	0.602504i	0.804202	−	0.594357i	$-0.202593\pi$
$464$	3.61551	−	11.1274i	0.167846	−	0.516576i
$465$		0			0
$466$	0.0395737	+	0.121795i	0.00183321	+	0.00564205i
$467$	7.66232	−	5.56700i	0.354570	−	0.257610i	−0.396214	−	0.918158i	$-0.629676\pi$
$467$	7.66232	−	5.56700i	0.354570	−	0.257610i	0.750784	+	0.660548i	$0.229676\pi$
$468$		0			0
$469$	−10.2114	+	7.41900i	−0.471518	+	0.342578i
$470$	1.70687	−	0.471972i	0.0787319	−	0.0217705i
$471$		0			0
$472$	−5.02712	−	3.65241i	−0.231392	−	0.168116i
$473$	3.08173	−	9.48459i	0.141698	−	0.436102i
$474$		0			0
$475$	−20.7608	−	1.84784i	−0.952570	−	0.0847847i
$476$	−14.1167			−0.647039
$477$		0			0
$478$	−1.64304	−	1.19374i	−0.0751508	−	0.0546002i
$479$	−20.8149	−	15.1229i	−0.951055	−	0.690982i	1.08775e−6	−	1.00000i	$-0.500000\pi$
$479$	−20.8149	−	15.1229i	−0.951055	−	0.690982i	−0.951056	+	0.309018i	$0.900000\pi$
$480$		0			0
$481$	−4.83925	+	3.51592i	−0.220651	+	0.160312i
$482$	0.316142			0.0143999
$483$		0			0
$484$	2.63451	+	8.10820i	0.119751	+	0.368554i
$485$	−0.0376093	−	0.0569145i	−0.00170775	−	0.00258435i
$486$		0			0
$487$	−8.77751	−	27.0144i	−0.397747	−	1.22414i	−0.926802	−	0.375551i	$-0.877453\pi$
$487$	−8.77751	−	27.0144i	−0.397747	−	1.22414i	0.529055	−	0.848588i	$-0.322547\pi$
$488$	1.14948	+	3.53774i	0.0520346	+	0.160146i
$489$		0			0
$490$	1.87225	−	2.35010i	0.0845795	−	0.106167i
$491$	1.88593	+	5.80429i	0.0851107	+	0.261944i	0.984551	−	0.175101i	$-0.0560251\pi$
$491$	1.88593	+	5.80429i	0.0851107	+	0.261944i	−0.899440	+	0.437045i	$0.856025\pi$
$492$		0			0
$493$	−18.7771			−0.845679
$494$	−3.89566	+	2.83036i	−0.175274	+	0.127344i
$495$		0			0
$496$	27.0600	+	19.6602i	1.21503	+	0.882770i
$497$	−13.9992	−	10.1710i	−0.627948	−	0.456231i
$498$		0			0
$499$	−20.3163			−0.909481			−0.454740	−	0.890624i	$-0.650268\pi$
$499$	−20.3163			−0.909481			−0.454740	+	0.890624i	$0.650268\pi$
$500$	−2.87834	+	21.4880i	−0.128723	+	0.960972i
$501$		0			0
$502$	0.353426	−	1.08773i	0.0157742	−	0.0485480i
$503$	11.8332	+	8.59734i	0.527617	+	0.383336i	0.819466	−	0.573128i	$-0.194270\pi$
$503$	11.8332	+	8.59734i	0.527617	+	0.383336i	−0.291848	+	0.956465i	$0.594270\pi$
$504$		0			0
$505$	23.5158	+	8.81237i	1.04644	+	0.392145i
$506$	0.823600	−	0.598380i	0.0366135	−	0.0266012i
$507$		0			0
$508$	−24.5674	+	17.8493i	−1.09000	+	0.791934i
$509$	1.33058	+	4.09510i	0.0589768	+	0.181512i	0.976205	−	0.216851i	$-0.0695785\pi$
$509$	1.33058	+	4.09510i	0.0589768	+	0.181512i	−0.917228	+	0.398363i	$0.869578\pi$
$510$		0			0
$511$	4.38490	−	13.4953i	0.193977	−	0.596999i
$512$	−5.38081	−	16.5604i	−0.237800	−	0.731874i
$513$		0			0
$514$	−1.39543	+	4.29471i	−0.0615500	+	0.189431i
$515$	0.888802	+	1.34503i	0.0391653	+	0.0592692i
$516$		0			0
$517$	6.67241	−	4.84779i	0.293452	−	0.213205i
$518$	−0.393109			−0.0172722
$519$		0			0
$520$	5.60937	+	8.48871i	0.245987	+	0.372255i
$521$	−32.0705	−	23.3006i	−1.40503	−	1.02082i	−0.994021	−	0.109186i	$-0.965176\pi$
$521$	−32.0705	−	23.3006i	−1.40503	−	1.02082i	−0.411011	−	0.911630i	$-0.634824\pi$
$522$		0			0
$523$	11.2134	−	34.5114i	0.490329	−	1.50908i	−0.333782	−	0.942650i	$-0.608325\pi$
$523$	11.2134	−	34.5114i	0.490329	−	1.50908i	0.824111	−	0.566428i	$-0.191675\pi$
$524$	−29.0021			−1.26696
$525$		0			0
$526$	4.11264			0.179320
$527$	16.5880	−	51.0526i	0.722585	−	2.22389i
$528$		0			0
$529$	16.5221	+	12.0040i	0.718353	+	0.521914i
$530$	7.09135	−	1.96086i	0.308029	−	0.0851742i
$531$		0			0
$532$	10.0779			0.436934
$533$	−32.9334	+	23.9275i	−1.42650	+	1.03642i
$534$		0			0
$535$	−4.43205	−	1.66088i	−0.191614	−	0.0718061i
$536$	−3.04087	+	9.35883i	−0.131346	+	0.404240i
$537$		0			0
$538$	0.200706	+	0.617709i	0.00865304	+	0.0266313i
$539$	4.32426	−	13.3087i	0.186259	−	0.573246i
$540$		0			0
$541$	−11.9294	−	36.7150i	−0.512886	−	1.57850i	−0.787096	−	0.616830i	$-0.788417\pi$
$541$	−11.9294	−	36.7150i	−0.512886	−	1.57850i	0.274211	−	0.961670i	$-0.411583\pi$
$542$	0.911014	−	0.661890i	0.0391314	−	0.0284306i
$543$		0			0
$544$	−13.4247	+	9.75359i	−0.575578	+	0.418182i
$545$	−0.221736	+	4.99232i	−0.00949812	+	0.213848i
$546$		0			0
$547$	−8.38303	−	6.09063i	−0.358433	−	0.260416i	0.393965	−	0.919125i	$-0.371103\pi$
$547$	−8.38303	−	6.09063i	−0.358433	−	0.260416i	−0.752398	+	0.658709i	$0.771103\pi$
$548$	−6.28853	+	19.3541i	−0.268633	+	0.826766i
$549$		0			0
$550$	−0.708553	−	3.09031i	−0.0302128	−	0.131771i
$551$	13.4050			0.571073
$552$		0			0
$553$	11.5825	+	8.41517i	0.492538	+	0.357850i
$554$	0.251388	+	0.182644i	0.0106805	+	0.00775981i
$555$		0			0
$556$	19.5324	−	14.1911i	0.828359	−	0.601838i
$557$	−12.6830			−0.537398			−0.268699	−	0.963224i	$-0.586594\pi$
$557$	−12.6830			−0.537398			−0.268699	+	0.963224i	$0.586594\pi$
$558$		0			0
$559$	5.61401	+	17.2781i	0.237447	+	0.730788i
$560$	0.450069	−	10.1332i	0.0190189	−	0.428205i
$561$		0			0
$562$	1.02306	+	3.14864i	0.0431550	+	0.132817i
$563$	−4.04480	−	12.4486i	−0.170468	−	0.524646i	0.828930	−	0.559353i	$-0.188950\pi$
$563$	−4.04480	−	12.4486i	−0.170468	−	0.524646i	−0.999398	+	0.0347068i	$0.988950\pi$
$564$		0			0
$565$	−0.312477	+	7.03533i	−0.0131460	+	0.295978i
$566$	−1.83685	−	5.65324i	−0.0772086	−	0.237624i
$567$		0			0
$568$	−13.4906			−0.566055
$569$	−2.09376	+	1.52120i	−0.0877748	+	0.0637721i	−0.630807	−	0.775940i	$-0.717276\pi$
$569$	−2.09376	+	1.52120i	−0.0877748	+	0.0637721i	0.543032	+	0.839712i	$0.317276\pi$
$570$		0			0
$571$	8.55571	+	6.21609i	0.358045	+	0.260135i	0.752236	−	0.658893i	$-0.228975\pi$
$571$	8.55571	+	6.21609i	0.358045	+	0.260135i	−0.394191	+	0.919029i	$0.628975\pi$
$572$	18.8715	+	13.7110i	0.789059	+	0.573285i
$573$		0			0
$574$	−2.67529			−0.111665
$575$	−6.88699	+	4.12402i	−0.287207	+	0.171983i
$576$		0			0
$577$	−0.00441597	+	0.0135910i	−0.000183839	+	0.000565800i	−0.951148	−	0.308734i	$-0.900095\pi$
$577$	−0.00441597	+	0.0135910i	−0.000183839	+	0.000565800i	0.950965	+	0.309300i	$0.100095\pi$
$578$	3.41283	+	2.47957i	0.141955	+	0.103136i
$579$		0			0
$580$	0.618690	−	13.9296i	0.0256897	−	0.578397i
$581$	2.85679	−	2.07558i	0.118519	−	0.0861094i
$582$		0			0
$583$	27.7212	−	20.1406i	1.14809	−	0.834139i
$584$	−3.41860	−	10.5214i	−0.141463	−	0.435377i
$585$		0			0
$586$	−2.45326	+	7.55035i	−0.101343	+	0.311902i
$587$	6.99581	+	21.5309i	0.288748	+	0.888675i	0.985250	+	0.171120i	$0.0547387\pi$
$587$	6.99581	+	21.5309i	0.288748	+	0.888675i	−0.696502	+	0.717555i	$0.745261\pi$
$588$		0			0
$589$	−11.8422	+	36.4465i	−0.487949	+	1.50175i
$590$	−3.30304	−	1.23779i	−0.135984	−	0.0509590i
$591$		0			0
$592$	3.76116	−	2.73264i	0.154583	−	0.112311i
$593$	−12.7423			−0.523264			−0.261632	−	0.965168i	$-0.584261\pi$
$593$	−12.7423			−0.523264			−0.261632	+	0.965168i	$0.584261\pi$
$594$		0			0
$595$	−15.6898	+	4.33845i	−0.643219	+	0.177859i
$596$	26.7758	+	19.4537i	1.09678	+	0.796856i
$597$		0			0
$598$	−0.573086	+	1.76378i	−0.0234352	+	0.0721262i
$599$	6.83599			0.279311			0.139656	−	0.990200i	$-0.455400\pi$
$599$	6.83599			0.279311			0.139656	+	0.990200i	$0.455400\pi$
$600$		0			0
$601$	31.8422			1.29887			0.649435	−	0.760417i	$-0.275005\pi$
$601$	31.8422			1.29887			0.649435	+	0.760417i	$0.275005\pi$
$602$	−0.368948	+	1.13551i	−0.0150372	+	0.0462798i
$603$		0			0
$604$	−2.47107	−	1.79534i	−0.100546	−	0.0730511i
$605$	5.41995	+	8.20207i	0.220352	+	0.333462i
$606$		0			0
$607$	27.7763			1.12741			0.563703	−	0.825977i	$-0.309376\pi$
$607$	27.7763			1.12741			0.563703	+	0.825977i	$0.309376\pi$
$608$	9.58388	−	6.96310i	0.388678	−	0.282391i
$609$		0			0
$610$	1.16413	+	1.76169i	0.0471343	+	0.0713288i
$611$	−4.64286	+	14.2893i	−0.187830	+	0.578082i
$612$		0			0
$613$	−1.11769	−	3.43991i	−0.0451433	−	0.138937i	0.925944	−	0.377660i	$-0.123271\pi$
$613$	−1.11769	−	3.43991i	−0.0451433	−	0.138937i	−0.971088	+	0.238723i	$0.923271\pi$
$614$	−1.54764	+	4.76315i	−0.0624577	+	0.192225i
$615$		0			0
$616$	0.962321	+	2.96172i	0.0387730	+	0.119331i
$617$	36.1166	−	26.2402i	1.45400	−	1.05639i	0.469122	−	0.883133i	$-0.344570\pi$
$617$	36.1166	−	26.2402i	1.45400	−	1.05639i	0.984876	−	0.173259i	$-0.0554297\pi$
$618$		0			0
$619$	−16.5917	+	12.0546i	−0.666878	+	0.484515i	−0.868979	−	0.494850i	$-0.835223\pi$
$619$	−16.5917	+	12.0546i	−0.666878	+	0.484515i	0.202101	+	0.979365i	$0.435223\pi$
$620$	37.3264	+	13.9878i	1.49906	+	0.561763i
$621$		0			0
$622$	3.73760	+	2.71552i	0.149864	+	0.108883i
$623$	−0.531970	+	1.63724i	−0.0213129	+	0.0655945i
$624$		0			0
$625$	3.40475	+	24.7671i	0.136190	+	0.990683i
$626$	−6.14033			−0.245417
$627$		0			0
$628$	−14.4336	−	10.4866i	−0.575964	−	0.418463i
$629$	−6.03621	−	4.38556i	−0.240679	−	0.174864i
$630$		0			0
$631$	30.5288	−	22.1805i	1.21533	−	0.882991i	0.219629	−	0.975583i	$-0.429515\pi$
$631$	30.5288	−	22.1805i	1.21533	−	0.882991i	0.995704	+	0.0925923i	$0.0295153\pi$
$632$	11.1618			0.443991
$633$		0			0
$634$	−1.92066	−	5.91117i	−0.0762790	−	0.234763i
$635$	−21.8195	+	27.3885i	−0.865881	+	1.08688i
$636$		0			0
$637$	7.87754	+	24.2446i	0.312119	+	0.960605i
$638$	0.630115	+	1.93929i	0.0249465	+	0.0767774i
$639$		0			0
$640$	−9.00683	−	13.6301i	−0.356026	−	0.538778i
$641$	2.83865	+	8.73646i	0.112120	+	0.345070i	0.991335	−	0.131355i	$-0.0419327\pi$
$641$	2.83865	+	8.73646i	0.112120	+	0.345070i	−0.879216	+	0.476424i	$0.841933\pi$
$642$		0			0
$643$	3.42111			0.134915			0.0674577	−	0.997722i	$-0.478511\pi$
$643$	3.42111			0.134915			0.0674577	+	0.997722i	$0.478511\pi$
$644$	3.14010	−	2.28142i	0.123737	−	0.0899005i
$645$		0			0
$646$	−4.85922	−	3.53043i	−0.191184	−	0.138903i
$647$	2.64334	+	1.92050i	0.103920	+	0.0755027i	0.638532	−	0.769595i	$-0.279542\pi$
$647$	2.64334	+	1.92050i	0.103920	+	0.0755027i	−0.534611	+	0.845098i	$0.679542\pi$
$648$		0			0
$649$	−16.4276			−0.644840
$650$	4.35328	+	3.79577i	0.170750	+	0.148882i
$651$		0			0
$652$	2.74487	−	8.44785i	0.107498	−	0.330843i
$653$	10.2229	+	7.42740i	0.400054	+	0.290656i	0.769563	−	0.638571i	$-0.220474\pi$
$653$	10.2229	+	7.42740i	0.400054	+	0.290656i	−0.369509	+	0.929227i	$0.620474\pi$
$654$		0			0
$655$	−32.2339	+	8.91313i	−1.25948	+	0.348265i
$656$	25.5965	−	18.5969i	0.999374	−	0.726088i
$657$		0			0
$658$	−0.798829	+	0.580383i	−0.0311416	+	0.0226257i
$659$	2.82719	+	8.70118i	0.110131	+	0.338950i	0.990901	−	0.134596i	$-0.0429737\pi$
$659$	2.82719	+	8.70118i	0.110131	+	0.338950i	−0.880769	+	0.473546i	$0.842974\pi$
$660$		0			0
$661$	1.97487	−	6.07804i	0.0768137	−	0.236408i	−0.905275	−	0.424825i	$-0.860336\pi$
$661$	1.97487	−	6.07804i	0.0768137	−	0.236408i	0.982089	+	0.188417i	$0.0603356\pi$
$662$	−2.31955	−	7.13884i	−0.0901519	−	0.277459i
$663$		0			0
$664$	0.850729	−	2.61827i	0.0330147	−	0.101609i
$665$	11.2010	−	3.09722i	0.434355	−	0.120105i
$666$		0			0
$667$	4.17676	−	3.03459i	0.161725	−	0.117500i
$668$	0.276383			0.0106936
$669$		0			0
$670$	−0.247861	+	5.58052i	−0.00957569	+	0.215594i
$671$	7.95593	+	5.78032i	0.307135	+	0.223147i
$672$		0			0
$673$	−10.4158	+	32.0566i	−0.401500	+	1.23569i	0.522282	+	0.852773i	$0.325081\pi$
$673$	−10.4158	+	32.0566i	−0.401500	+	1.23569i	−0.923782	+	0.382918i	$0.874919\pi$
$674$	1.12881			0.0434802
$675$		0			0
$676$	−17.2857			−0.664833
$677$	−2.84401	+	8.75295i	−0.109304	+	0.336403i	−0.990716	−	0.135944i	$-0.956593\pi$
$677$	−2.84401	+	8.75295i	−0.109304	+	0.336403i	0.881412	+	0.472347i	$0.156593\pi$
$678$		0			0
$679$	0.0307719	+	0.0223571i	0.00118092	+	0.000857988i
$680$	−7.90798	+	9.92634i	−0.303257	+	0.380658i
$681$		0			0
$682$	−5.82935			−0.223217
$683$	22.0227	−	16.0005i	0.842677	−	0.612241i	−0.0804402	−	0.996759i	$-0.525633\pi$
$683$	22.0227	−	16.0005i	0.842677	−	0.612241i	0.923117	+	0.384519i	$0.125633\pi$
$684$		0			0
$685$	−1.04125	+	23.4434i	−0.0397841	+	0.895728i
$686$	−1.18319	+	3.64147i	−0.0451743	+	0.139032i
$687$		0			0
$688$	−4.36332	−	13.4289i	−0.166350	−	0.511972i
$689$	−19.2892	+	59.3662i	−0.734862	+	2.26167i
$690$		0			0
$691$	9.21607	+	28.3642i	0.350596	+	1.07902i	0.958519	+	0.285028i	$0.0920028\pi$
$691$	9.21607	+	28.3642i	0.350596	+	1.07902i	−0.607923	+	0.793996i	$0.707997\pi$
$692$	−38.6275	+	28.0645i	−1.46840	+	1.06685i
$693$		0			0
$694$	3.35687	−	2.43891i	0.127425	−	0.0925797i
$695$	17.3477	−	21.7753i	0.658034	−	0.825985i
$696$		0			0
$697$	−41.0792	−	29.8458i	−1.55599	−	1.13049i
$698$	−0.0284865	+	0.0876726i	−0.00107823	+	0.00331846i
$699$		0			0
$700$	−2.70147	−	11.7823i	−0.102106	−	0.445328i
$701$	19.1081			0.721704			0.360852	−	0.932623i	$-0.382486\pi$
$701$	19.1081			0.721704			0.360852	+	0.932623i	$0.382486\pi$
$702$		0			0
$703$	4.30925	+	3.13086i	0.162527	+	0.118082i
$704$	−13.6700	−	9.93187i	−0.515209	−	0.374322i
$705$		0			0
$706$	4.78489	−	3.47642i	0.180082	−	0.130837i
$707$	−14.0020			−0.526601
$708$		0			0
$709$	4.48525	+	13.8042i	0.168447	+	0.518427i	0.999274	−	0.0381042i	$-0.0121319\pi$
$709$	4.48525	+	13.8042i	0.168447	+	0.518427i	−0.830827	+	0.556531i	$0.812132\pi$
$710$	−7.38109	+	2.04097i	−0.277008	+	0.0765964i
$711$		0			0
$712$	0.414740	+	1.27644i	0.0155430	+	0.0478365i
$713$	4.56086	+	14.0369i	0.170806	+	0.525685i
$714$		0			0
$715$	25.1882	+	9.43911i	0.941986	+	0.353003i
$716$	−14.4743	−	44.5473i	−0.540930	−	1.66481i
$717$		0			0
$718$	−1.17215			−0.0437444
$719$	28.1139	−	20.4260i	1.04847	−	0.761760i	0.0765512	−	0.997066i	$-0.475609\pi$
$719$	28.1139	−	20.4260i	1.04847	−	0.761760i	0.971921	+	0.235306i	$0.0756091\pi$
$720$		0			0
$721$	−0.727219	−	0.528356i	−0.0270831	−	0.0196770i
$722$	−0.324007	−	0.235405i	−0.0120583	−	0.00876086i
$723$		0			0
$724$	−3.81626			−0.141830
$725$	−3.59332	−	15.6720i	−0.133452	−	0.582044i
$726$		0			0
$727$	13.1727	−	40.5415i	0.488550	−	1.50360i	−0.338223	−	0.941066i	$-0.609826\pi$
$727$	13.1727	−	40.5415i	0.488550	−	1.50360i	0.826773	−	0.562536i	$-0.190174\pi$
$728$	−4.58959	−	3.33453i	−0.170102	−	0.123586i
$729$		0			0
$730$	−3.46217	−	5.23933i	−0.128141	−	0.193916i
$731$	−18.3330	+	13.3197i	−0.678072	+	0.492648i
$732$		0			0
$733$	−1.58754	+	1.15341i	−0.0586370	+	0.0426023i	−0.616718	−	0.787184i	$-0.711538\pi$
$733$	−1.58754	+	1.15341i	−0.0586370	+	0.0426023i	0.558081	+	0.829787i	$0.311538\pi$
$734$	1.32451	+	4.07642i	0.0488885	+	0.150463i
$735$		0			0
$736$	1.40987	−	4.33915i	0.0519687	−	0.159943i
$737$	8.03917	+	24.7420i	0.296127	+	0.911384i
$738$		0			0
$739$	3.81947	−	11.7551i	0.140501	−	0.432419i	−0.855904	−	0.517135i	$-0.826998\pi$
$739$	3.81947	−	11.7551i	0.140501	−	0.432419i	0.996405	+	0.0847164i	$0.0269984\pi$
$740$	3.45227	−	4.33340i	0.126908	−	0.159299i
$741$		0			0
$742$	−3.31881	+	2.41126i	−0.121838	+	0.0885201i
$743$	−8.63742			−0.316876			−0.158438	−	0.987369i	$-0.550646\pi$
$743$	−8.63742			−0.316876			−0.158438	+	0.987369i	$0.550646\pi$
$744$		0			0
$745$	35.7381	+	13.3926i	1.30934	+	0.490668i
$746$	0.420978	+	0.305858i	0.0154131	+	0.0111983i
$747$		0			0
$748$	−8.99121	+	27.6721i	−0.328751	+	1.01179i
$749$	2.63898			0.0964264
$750$		0			0
$751$	−24.3654			−0.889105			−0.444552	−	0.895753i	$-0.646637\pi$
$751$	−24.3654			−0.889105			−0.444552	+	0.895753i	$0.646637\pi$
$752$	3.60852	−	11.1059i	0.131589	−	0.404990i
$753$		0			0
$754$	−3.00520	−	2.18341i	−0.109443	−	0.0795150i
$755$	−3.29818	−	1.23597i	−0.120033	−	0.0449816i
$756$		0			0
$757$	−5.18352			−0.188398			−0.0941991	−	0.995553i	$-0.530029\pi$
$757$	−5.18352			−0.188398			−0.0941991	+	0.995553i	$0.530029\pi$
$758$	2.47723	−	1.79981i	0.0899769	−	0.0653720i
$759$		0			0
$760$	5.64551	−	7.08643i	0.204784	−	0.257052i
$761$	−9.66099	+	29.7335i	−0.350211	+	1.07784i	0.608524	+	0.793535i	$0.291762\pi$
$761$	−9.66099	+	29.7335i	−0.350211	+	1.07784i	−0.958735	+	0.284302i	$0.908238\pi$
$762$		0			0
$763$	−0.861014	−	2.64993i	−0.0311708	−	0.0959339i
$764$	−4.65505	+	14.3268i	−0.168414	+	0.518324i
$765$		0			0
$766$	2.53964	+	7.81622i	0.0917611	+	0.282412i
$767$	24.2109	−	17.5903i	0.874205	−	0.635147i
$768$		0			0
$769$	35.7497	−	25.9737i	1.28917	−	0.936636i	0.289380	−	0.957214i	$-0.406551\pi$
$769$	35.7497	−	25.9737i	1.28917	−	0.936636i	0.999788	+	0.0205786i	$0.00655083\pi$
$770$	0.974585	+	1.47485i	0.0351216	+	0.0531499i
$771$		0			0
$772$	22.5054	+	16.3511i	0.809986	+	0.588489i
$773$	6.67110	−	20.5315i	0.239943	−	0.738468i	−0.756484	−	0.654012i	$-0.773085\pi$
$773$	6.67110	−	20.5315i	0.239943	−	0.738468i	0.996427	−	0.0844563i	$-0.0269153\pi$
$774$		0			0
$775$	45.7846	+	4.07512i	1.64463	+	0.146383i
$776$	0.0296542			0.00106452
$777$		0			0
$778$	3.38929	+	2.46246i	0.121512	+	0.0882835i
$779$	29.3265	+	21.3070i	1.05073	+	0.763401i
$780$		0			0
$781$	−28.8538	+	20.9635i	−1.03247	+	0.750135i
$782$	−2.31325			−0.0827218
$783$		0			0
$784$	−6.12257	−	18.8433i	−0.218663	−	0.672977i
$785$	−19.2648	−	7.21937i	−0.687592	−	0.257670i
$786$		0			0
$787$	4.45638	+	13.7153i	0.158853	+	0.488899i	0.998531	−	0.0541857i	$-0.0172563\pi$
$787$	4.45638	+	13.7153i	0.158853	+	0.488899i	−0.839678	+	0.543085i	$0.817256\pi$
$788$	0.0979961	+	0.301601i	0.00349097	+	0.0107441i
$789$		0			0
$790$	6.10690	−	1.68864i	0.217274	−	0.0600792i
$791$	−1.21337	−	3.73436i	−0.0431424	−	0.132779i
$792$		0			0
$793$	−17.9148			−0.636173
$794$	−0.172995	+	0.125688i	−0.00613937	+	0.00446052i
$795$		0			0
$796$	7.79639	+	5.66441i	0.276336	+	0.200770i
$797$	−31.9211	−	23.1921i	−1.13070	−	0.821505i	−0.144907	−	0.989445i	$-0.546288\pi$
$797$	−31.9211	−	23.1921i	−1.13070	−	0.821505i	−0.985797	+	0.167941i	$0.946288\pi$
$798$		0			0
$799$	−18.7409			−0.663004
$800$	−10.7097	−	9.33815i	−0.378645	−	0.330153i
$801$		0			0
$802$	0.738645	−	2.27332i	0.0260825	−	0.0802736i
$803$	−23.6612	−	17.1909i	−0.834986	−	0.606653i
$804$		0			0
$805$	2.78888	−	3.50068i	0.0982950	−	0.123383i
$806$	8.59125	−	6.24191i	0.302614	−	0.219862i
$807$		0			0
$808$	−8.83156	+	6.41650i	−0.310693	+	0.225732i
$809$	1.84237	+	5.67024i	0.0647744	+	0.199355i	0.978206	−	0.207638i	$-0.0665775\pi$
$809$	1.84237	+	5.67024i	0.0647744	+	0.199355i	−0.913431	+	0.406993i	$0.866577\pi$
$810$		0			0
$811$	−12.1062	+	37.2590i	−0.425105	+	1.30834i	0.477788	+	0.878475i	$0.341439\pi$
$811$	−12.1062	+	37.2590i	−0.425105	+	1.30834i	−0.902893	+	0.429865i	$0.858561\pi$
$812$	2.40241	+	7.39386i	0.0843081	+	0.259474i
$813$		0			0
$814$	−0.250378	+	0.770586i	−0.00877576	+	0.0270090i
$815$	0.454493	−	10.2328i	0.0159202	−	0.358439i
$816$		0			0
$817$	13.0880	−	9.50897i	0.457890	−	0.332677i
$818$	−0.374544			−0.0130956
$819$		0			0
$820$	23.4944	−	29.4908i	0.820458	−	1.02986i
$821$	16.6923	+	12.1277i	0.582567	+	0.423260i	0.839649	−	0.543130i	$-0.182761\pi$
$821$	16.6923	+	12.1277i	0.582567	+	0.423260i	−0.257082	+	0.966390i	$0.582761\pi$
$822$		0			0
$823$	12.0567	−	37.1066i	0.420269	−	1.29345i	−0.487183	−	0.873300i	$-0.661976\pi$
$823$	12.0567	−	37.1066i	0.420269	−	1.29345i	0.907452	−	0.420155i	$-0.138024\pi$
$824$	−0.700803			−0.0244136
$825$		0			0
$826$	1.96673			0.0684314
$827$	−6.05598	+	18.6384i	−0.210587	+	0.648120i	0.788850	+	0.614585i	$0.210677\pi$
$827$	−6.05598	+	18.6384i	−0.210587	+	0.648120i	−0.999438	+	0.0335352i	$0.989323\pi$
$828$		0			0
$829$	7.01831	+	5.09910i	0.243756	+	0.177099i	0.702955	−	0.711234i	$-0.251864\pi$
$829$	7.01831	+	5.09910i	0.243756	+	0.177099i	−0.459199	+	0.888333i	$0.651864\pi$
$830$	0.0693427	−	1.56123i	0.00240692	−	0.0541912i
$831$		0			0
$832$	30.7816			1.06716
$833$	−25.7248	+	18.6902i	−0.891311	+	0.647575i
$834$		0			0
$835$	0.307182	−	0.0849400i	0.0106305	−	0.00293947i
$836$	6.41884	−	19.7551i	0.222000	−	0.683246i
$837$		0			0
$838$	−2.33044	−	7.17235i	−0.0805036	−	0.247765i
$839$	1.19256	−	3.67033i	0.0411718	−	0.126714i	−0.928358	−	0.371687i	$-0.878779\pi$
$839$	1.19256	−	3.67033i	0.0411718	−	0.126714i	0.969530	+	0.244974i	$0.0787793\pi$
$840$		0			0
$841$	−5.76596	−	17.7458i	−0.198826	−	0.611925i
$842$	−1.39176	+	1.01117i	−0.0479632	+	0.0348473i
$843$		0			0
$844$	5.16724	−	3.75422i	0.177864	−	0.129226i
$845$	−19.2119	+	5.31235i	−0.660908	+	0.182750i
$846$		0			0
$847$	−4.43461	−	3.22193i	−0.152375	−	0.110707i
$848$	14.9920	−	46.1406i	0.514827	−	1.58447i
$849$		0			0
$850$	−2.82493	+	6.62735i	−0.0968943	+	0.227316i
$851$	2.05144			0.0703224
$852$		0			0
$853$	24.1004	+	17.5100i	0.825183	+	0.599531i	0.918192	−	0.396135i	$-0.129649\pi$
$853$	24.1004	+	17.5100i	0.825183	+	0.599531i	−0.0930093	+	0.995665i	$0.529649\pi$
$854$	−0.952493	−	0.692027i	−0.0325936	−	0.0236807i
$855$		0			0
$856$	1.66450	−	1.20933i	0.0568913	−	0.0413340i
$857$	−36.2041			−1.23671			−0.618354	−	0.785899i	$-0.712200\pi$
$857$	−36.2041			−1.23671			−0.618354	+	0.785899i	$0.712200\pi$
$858$		0			0
$859$	−11.6355	−	35.8104i	−0.396998	−	1.22184i	−0.927394	−	0.374086i	$-0.877957\pi$
$859$	−11.6355	−	35.8104i	−0.396998	−	1.22184i	0.530396	−	0.847750i	$-0.322043\pi$
$860$	−9.27706	−	14.0391i	−0.316345	−	0.478728i
$861$		0			0
$862$	0.834757	+	2.56912i	0.0284319	+	0.0875045i
$863$	0.772275	+	2.37682i	0.0262885	+	0.0809078i	0.963340	−	0.268283i	$-0.0864564\pi$
$863$	0.772275	+	2.37682i	0.0262885	+	0.0809078i	−0.937051	+	0.349191i	$0.886456\pi$
$864$		0			0
$865$	−34.3070	+	43.0632i	−1.16647	+	1.46419i
$866$	−0.796028	−	2.44992i	−0.0270501	−	0.0832518i
$867$		0			0
$868$	−22.2253			−0.754376
$869$	23.8728	−	17.3446i	0.809830	−	0.588376i
$870$		0			0
$871$	−38.3411	−	27.8565i	−1.29914	−	0.943881i
$872$	−1.75741	−	1.27684i	−0.0595136	−	0.0432391i
$873$		0			0
$874$	1.65143			0.0558606
$875$	−6.62352	−	12.2650i	−0.223916	−	0.414632i
$876$		0			0
$877$	−10.0273	+	30.8609i	−0.338599	+	1.04210i	0.626323	+	0.779563i	$0.284559\pi$
$877$	−10.0273	+	30.8609i	−0.338599	+	1.04210i	−0.964922	+	0.262537i	$0.915441\pi$
$878$	3.08100	+	2.23847i	0.103979	+	0.0755449i
$879$		0			0
$880$	−19.5768	−	7.33626i	−0.659933	−	0.247305i
$881$	−26.9099	+	19.5512i	−0.906619	+	0.658697i	−0.940157	−	0.340740i	$-0.889322\pi$
$881$	−26.9099	+	19.5512i	−0.906619	+	0.658697i	0.0335388	+	0.999437i	$0.489322\pi$
$882$		0			0
$883$	8.87730	−	6.44974i	0.298745	−	0.217051i	−0.428307	−	0.903633i	$-0.640890\pi$
$883$	8.87730	−	6.44974i	0.298745	−	0.217051i	0.727052	+	0.686582i	$0.240890\pi$
$884$	−16.3794	−	50.4105i	−0.550897	−	1.69549i
$885$		0			0
$886$	1.44197	−	4.43794i	0.0484440	−	0.149095i
$887$	8.03604	+	24.7324i	0.269824	+	0.830432i	0.990543	+	0.137205i	$0.0438118\pi$
$887$	8.03604	+	24.7324i	0.269824	+	0.830432i	−0.720719	+	0.693227i	$0.756188\pi$
$888$		0			0
$889$	6.03343	−	18.5690i	0.202355	−	0.622784i
$890$	0.420025	+	0.635628i	0.0140793	+	0.0213063i
$891$		0			0
$892$	−24.7446	+	17.9780i	−0.828511	+	0.601948i
$893$	13.3791			0.447715
$894$		0			0
$895$	−29.7778	−	45.0630i	−0.995362	−	1.50629i
$896$	7.36940	+	5.35418i	0.246194	+	0.178871i
$897$		0			0
$898$	−0.870436	+	2.67893i	−0.0290468	+	0.0893970i
$899$	−29.5626			−0.985969
$900$		0			0
$901$	−77.8608			−2.59392
$902$	−1.70394	+	5.24420i	−0.0567351	+	0.174613i
$903$		0			0
$904$	−2.47660	−	1.79936i	−0.0823705	−	0.0598457i
$905$	−4.24152	+	1.17284i	−0.140993	+	0.0389865i
$906$		0			0
$907$	−55.0108			−1.82660			−0.913302	−	0.407283i	$-0.866476\pi$
$907$	−55.0108			−1.82660			−0.913302	+	0.407283i	$0.866476\pi$
$908$	−21.2421	+	15.4333i	−0.704944	+	0.512172i
$909$		0			0
$910$	−3.01556	−	1.13006i	−0.0999650	−	0.0374612i
$911$	3.74142	−	11.5149i	0.123959	−	0.381506i	−0.869751	−	0.493490i	$-0.835721\pi$
$911$	3.74142	−	11.5149i	0.123959	−	0.381506i	0.993710	+	0.111985i	$0.0357208\pi$
$912$		0			0
$913$	−2.24908	−	6.92195i	−0.0744336	−	0.229083i
$914$	2.59060	−	7.97306i	0.0856895	−	0.263725i
$915$		0			0
$916$	8.85816	+	27.2626i	0.292682	+	0.900782i
$917$	15.0858	−	10.9605i	0.498176	−	0.361946i
$918$		0			0
$919$	−4.83138	+	3.51020i	−0.159372	+	0.115791i	−0.664613	−	0.747188i	$-0.731404\pi$
$919$	−4.83138	+	3.51020i	−0.159372	+	0.115791i	0.505241	+	0.862978i	$0.331404\pi$
$920$	0.154833	−	3.48602i	0.00510468	−	0.114931i
$921$		0			0
$922$	4.92906	+	3.58117i	0.162330	+	0.117940i
$923$	20.0774	−	61.7918i	0.660855	−	2.03390i
$924$		0			0
$925$	2.50520	−	5.87726i	0.0823706	−	0.193243i
$926$	3.36370			0.110538
$927$		0			0
$928$	7.39324	+	5.37150i	0.242695	+	0.176328i
$929$	37.9232	+	27.5528i	1.24422	+	0.903979i	0.997872	−	0.0652030i	$-0.0207695\pi$
$929$	37.9232	+	27.5528i	1.24422	+	0.903979i	0.246348	+	0.969182i	$0.420770\pi$
$930$		0			0
$931$	18.3650	−	13.3429i	0.601887	−	0.437297i
$932$	1.00636			0.0329644
$933$		0			0
$934$	0.722201	+	2.22271i	0.0236311	+	0.0727291i
$935$	−1.48876	+	33.5189i	−0.0486875	+	1.09619i
$936$		0			0
$937$	−6.00528	−	18.4823i	−0.196184	−	0.603792i	−0.999961	−	0.00886093i	$-0.997179\pi$
$937$	−6.00528	−	18.4823i	−0.196184	−	0.603792i	0.803777	−	0.594931i	$-0.202821\pi$
$938$	−0.962459	−	2.96214i	−0.0314254	−	0.0967174i
$939$		0			0
$940$	0.617495	−	13.9027i	0.0201405	−	0.453457i
$941$	−6.70867	−	20.6472i	−0.218696	−	0.673078i	−0.998870	−	0.0475159i	$-0.984870\pi$
$941$	−6.70867	−	20.6472i	−0.218696	−	0.673078i	0.780174	−	0.625563i	$-0.215130\pi$
$942$		0			0
$943$	13.9610			0.454633
$944$	−18.8172	+	13.6715i	−0.612447	+	0.444969i
$945$		0			0
$946$	1.99087	+	1.44645i	0.0647287	+	0.0470282i
$947$	−5.10943	−	3.71222i	−0.166034	−	0.120631i	0.501665	−	0.865062i	$-0.332721\pi$
$947$	−5.10943	−	3.71222i	−0.166034	−	0.120631i	−0.667699	+	0.744431i	$0.732721\pi$
$948$		0			0
$949$	53.2792			1.72952
$950$	2.01672	−	4.73127i	0.0654310	−	0.153503i
$951$		0			0
$952$	2.18668	−	6.72990i	0.0708707	−	0.218117i
$953$	17.6380	+	12.8147i	0.571350	+	0.415110i	0.835595	−	0.549345i	$-0.185123\pi$
$953$	17.6380	+	12.8147i	0.571350	+	0.415110i	−0.264245	+	0.964455i	$0.585123\pi$
$954$		0			0
$955$	−0.770779	+	17.3539i	−0.0249418	+	0.561558i
$956$	−12.9115	+	9.38076i	−0.417588	+	0.303395i
$957$		0			0
$958$	5.13625	−	3.73171i	0.165945	−	0.120566i
$959$	−4.04324	−	12.4438i	−0.130563	−	0.401831i
$960$		0			0
$961$	16.5366	−	50.8943i	0.533437	−	1.64175i
$962$	−0.456116	−	1.40378i	−0.0147058	−	0.0452597i
$963$		0			0
$964$	0.767705	−	2.36275i	0.0247261	−	0.0760992i
$965$	30.0384	+	11.2567i	0.966969	+	0.362365i
$966$		0			0
$967$	5.67338	−	4.12195i	0.182444	−	0.132553i	−0.492815	−	0.870134i	$-0.664032\pi$
$967$	5.67338	−	4.12195i	0.182444	−	0.132553i	0.675259	+	0.737581i	$0.264032\pi$
$968$	−4.27353			−0.137356
$969$		0			0
$970$	0.0162246	−	0.00448632i	0.000520940	−	0.000144047i
$971$	5.99504	+	4.35565i	0.192390	+	0.139779i	0.679810	−	0.733388i	$-0.262062\pi$
$971$	5.99504	+	4.35565i	0.192390	+	0.139779i	−0.487420	+	0.873167i	$0.662062\pi$
$972$		0			0
$973$	−4.79690	+	14.7633i	−0.153781	+	0.473291i
$974$	7.00909			0.224586
$975$		0			0
$976$	13.9237			0.445688
$977$	−12.1315	+	37.3370i	−0.388122	+	1.19452i	0.546068	+	0.837741i	$0.316124\pi$
$977$	−12.1315	+	37.3370i	−0.388122	+	1.19452i	−0.934190	+	0.356776i	$0.883876\pi$
$978$		0			0
$979$	2.87054	+	2.08557i	0.0917430	+	0.0666552i
$980$	−13.0175	−	19.6995i	−0.415829	−	0.629278i
$981$		0			0
$982$	−1.50597			−0.0480573
$983$	−14.8719	+	10.8051i	−0.474341	+	0.344629i	−0.799131	−	0.601158i	$-0.794706\pi$
$983$	−14.8719	+	10.8051i	−0.474341	+	0.344629i	0.324790	+	0.945786i	$0.394706\pi$
$984$		0			0
$985$	0.201606	+	0.305093i	0.00642371	+	0.00972106i
$986$	1.43181	−	4.40665i	0.0455980	−	0.140336i
$987$		0			0
$988$	11.6932	+	35.9881i	0.372012	+	1.14493i
$989$	1.92536	−	5.92564i	0.0612228	−	0.188424i
$990$		0			0
$991$	16.2128	+	49.8980i	0.515018	+	1.58506i	0.783250	+	0.621707i	$0.213560\pi$
$991$	16.2128	+	49.8980i	0.515018	+	1.58506i	−0.268233	+	0.963354i	$0.586440\pi$
$992$	−21.1357	+	15.3560i	−0.671060	+	0.487554i
$993$		0			0
$994$	3.45442	−	2.50978i	0.109567	−	0.0796054i
$995$	10.4060	+	3.89958i	0.329892	+	0.123625i
$996$		0			0
$997$	29.4256	+	21.3789i	0.931917	+	0.677077i	0.946461	−	0.322817i	$-0.104630\pi$
$997$	29.4256	+	21.3789i	0.931917	+	0.677077i	−0.0145444	+	0.999894i	$0.504630\pi$
$998$	1.54917	−	4.76785i	0.0490381	−	0.150924i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	225.2.h.d.46.2		12
3.2	odd	2		75.2.g.c.46.2	yes	12
15.2	even	4		375.2.i.d.274.4		24
15.8	even	4		375.2.i.d.274.3		24
15.14	odd	2		375.2.g.c.226.2		12
25.6	even	5	inner	225.2.h.d.181.2		12
25.9	even	10		5625.2.a.q.1.4		6
25.16	even	5		5625.2.a.p.1.3		6
75.8	even	20		375.2.i.d.349.4		24
75.17	even	20		375.2.i.d.349.3		24
75.38	even	20		1875.2.b.f.1249.5		12
75.41	odd	10		1875.2.a.j.1.4		6
75.44	odd	10		375.2.g.c.151.2		12
75.56	odd	10		75.2.g.c.31.2	✓	12
75.59	odd	10		1875.2.a.k.1.3		6
75.62	even	20		1875.2.b.f.1249.8		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
75.2.g.c.31.2	✓	12	75.56	odd	10
75.2.g.c.46.2	yes	12	3.2	odd	2
225.2.h.d.46.2		12	1.1	even	1	trivial
225.2.h.d.181.2		12	25.6	even	5	inner
375.2.g.c.151.2		12	75.44	odd	10
375.2.g.c.226.2		12	15.14	odd	2
375.2.i.d.274.3		24	15.8	even	4
375.2.i.d.274.4		24	15.2	even	4
375.2.i.d.349.3		24	75.17	even	20
375.2.i.d.349.4		24	75.8	even	20
1875.2.a.j.1.4		6	75.41	odd	10
1875.2.a.k.1.3		6	75.59	odd	10
1875.2.b.f.1249.5		12	75.38	even	20
1875.2.b.f.1249.8		12	75.62	even	20
5625.2.a.p.1.3		6	25.16	even	5
5625.2.a.q.1.4		6	25.9	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)

\(f(q)\)	\(=\)	\(q+(-0.0762527 + 0.234682i) q^{2} +(1.56877 + 1.13978i) q^{4} +(2.09387 + 0.784664i) q^{5} -1.24676 q^{7} +(-0.786373 + 0.571334i) q^{8} +O(q^{10})\)	\(q+(-0.0762527 + 0.234682i) q^{2} +(1.56877 + 1.13978i) q^{4} +(2.09387 + 0.784664i) q^{5} -1.24676 q^{7} +(-0.786373 + 0.571334i) q^{8} +(-0.343810 + 0.431561i) q^{10} +(-0.794084 + 2.44394i) q^{11} +(-1.44659 - 4.45215i) q^{13} +(0.0950687 - 0.292592i) q^{14} +(1.12432 + 3.46029i) q^{16} +(4.72397 - 3.43216i) q^{17} +(-3.37244 + 2.45022i) q^{19} +(2.39047 + 3.61751i) q^{20} +(-0.512997 - 0.372714i) q^{22} +(-0.496117 + 1.52689i) q^{23} +(3.76860 + 3.28597i) q^{25} +1.15514 q^{26} +(-1.95588 - 1.42103i) q^{28} +(-2.60158 - 1.89016i) q^{29} +(7.43739 - 5.40358i) q^{31} -2.84182 q^{32} +(0.445250 + 1.37034i) q^{34} +(-2.61055 - 0.978287i) q^{35} +(-0.394857 - 1.21524i) q^{37} +(-0.317865 - 0.978287i) q^{38} +(-2.09487 + 0.579261i) q^{40} +(-2.68719 - 8.27031i) q^{41} -3.88086 q^{43} +(-4.03129 + 2.92891i) q^{44} +(-0.320503 - 0.232859i) q^{46} +(-2.59656 - 1.88651i) q^{47} -5.44559 q^{49} +(-1.05852 + 0.633858i) q^{50} +(2.80510 - 8.63320i) q^{52} +(-10.7877 - 7.83770i) q^{53} +(-3.58038 + 4.49421i) q^{55} +(0.980418 - 0.712315i) q^{56} +(0.641964 - 0.466414i) q^{58} +(1.97548 + 6.07990i) q^{59} +(1.18258 - 3.63961i) q^{61} +(0.701000 + 2.15746i) q^{62} +(-2.03194 + 6.25366i) q^{64} +(0.464465 - 10.4573i) q^{65} +(8.19034 - 5.95063i) q^{67} +11.3227 q^{68} +(0.428648 - 0.538052i) q^{70} +(11.2284 + 8.15794i) q^{71} +(-3.51704 + 10.8243i) q^{73} +0.315305 q^{74} -8.08332 q^{76} +(0.990032 - 3.04700i) q^{77} +(-9.29008 - 6.74964i) q^{79} +(-0.360991 + 8.12762i) q^{80} +2.14580 q^{82} +(-2.29137 + 1.66478i) q^{83} +(12.5845 - 3.47978i) q^{85} +(0.295926 - 0.910766i) q^{86} +(-0.771858 - 2.37554i) q^{88} +(0.426682 - 1.31319i) q^{89} +(1.80355 + 5.55075i) q^{91} +(-2.51861 + 1.82988i) q^{92} +(0.640724 - 0.465513i) q^{94} +(-8.98407 + 2.48422i) q^{95} +(-0.0246815 - 0.0179322i) q^{97} +(0.415241 - 1.27798i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q - 10 q^{4} + 6 q^{5} - 12 q^{7} - 9 q^{8}+O(q^{10}) \) 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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