LMFDB - Embedded newform 725.2.e.b.157.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(157,725)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(725, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([1, 1]))

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

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

chi := DirichletCharacter("725.157");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.e (of order $4$, degree $2$, 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:	$5.78915414654$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 28x^{14} + 288x^{12} + 1372x^{10} + 3184x^{8} + 3696x^{6} + 2076x^{4} + 504x^{2} + 36 $ x^16 + 28x^14 + 288x^12 + 1372x^10 + 3184x^8 + 3696x^6 + 2076x^4 + 504*x^2 + 36
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			157.5
Root			$-0.807187i$ of defining polynomial
Character	$\chi$	$=$	725.157
Dual form			725.2.e.b.568.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.192813i q^{2} -1.87822 q^{3} +1.96282 q^{4} -0.362145i q^{6} +(-1.55767 - 1.55767i) q^{7} +0.764084i q^{8} +0.527707 q^{9} +(1.15301 + 1.15301i) q^{11} -3.68661 q^{12} +(2.73688 + 2.73688i) q^{13} +(0.300339 - 0.300339i) q^{14} +3.77832 q^{16} -2.15844i q^{17} +0.101749i q^{18} +(2.15301 - 2.15301i) q^{19} +(2.92565 + 2.92565i) q^{21} +(-0.222316 + 0.222316i) q^{22} +(1.84506 - 1.84506i) q^{23} -1.43512i q^{24} +(-0.527707 + 0.527707i) q^{26} +4.64351 q^{27} +(-3.05743 - 3.05743i) q^{28} +(-1.79087 - 5.07866i) q^{29} +(5.11584 + 5.11584i) q^{31} +2.25668i q^{32} +(-2.16561 - 2.16561i) q^{33} +0.416176 q^{34} +1.03579 q^{36} -2.48506 q^{37} +(0.415129 + 0.415129i) q^{38} +(-5.14047 - 5.14047i) q^{39} +(-0.490530 + 0.490530i) q^{41} +(-0.564103 + 0.564103i) q^{42} +9.89254 q^{43} +(2.26316 + 2.26316i) q^{44} +(0.355752 + 0.355752i) q^{46} +9.44060 q^{47} -7.09651 q^{48} -2.14733i q^{49} +4.05403i q^{51} +(5.37202 + 5.37202i) q^{52} +(-1.29978 + 1.29978i) q^{53} +0.895329i q^{54} +(1.19019 - 1.19019i) q^{56} +(-4.04383 + 4.04383i) q^{57} +(0.979232 - 0.345303i) q^{58} -2.43441i q^{59} +(3.32497 + 3.32497i) q^{61} +(-0.986400 + 0.986400i) q^{62} +(-0.821993 - 0.821993i) q^{63} +7.12153 q^{64} +(0.417558 - 0.417558i) q^{66} +(4.68018 - 4.68018i) q^{67} -4.23664i q^{68} +(-3.46543 + 3.46543i) q^{69} +0.803417i q^{71} +0.403212i q^{72} +11.4797i q^{73} -0.479153i q^{74} +(4.22599 - 4.22599i) q^{76} -3.59203i q^{77} +(0.991149 - 0.991149i) q^{78} +(2.09760 - 2.09760i) q^{79} -10.3046 q^{81} +(-0.0945805 - 0.0945805i) q^{82} +(7.41355 - 7.41355i) q^{83} +(5.74253 + 5.74253i) q^{84} +1.90741i q^{86} +(3.36364 + 9.53884i) q^{87} +(-0.880999 + 0.880999i) q^{88} +(-3.83444 + 3.83444i) q^{89} -8.52632i q^{91} +(3.62153 - 3.62153i) q^{92} +(-9.60866 - 9.60866i) q^{93} +1.82027i q^{94} -4.23853i q^{96} -11.2386 q^{97} +0.414032 q^{98} +(0.608453 + 0.608453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{4} + 40 q^{9} - 4 q^{11} - 20 q^{14} - 16 q^{16} + 12 q^{19} - 32 q^{21} - 40 q^{26} + 4 q^{29} + 20 q^{31} - 80 q^{34} - 104 q^{36} - 16 q^{39} - 28 q^{44} + 44 q^{46} + 36 q^{56} + 24 q^{61}+ \cdots + 92 q^{99}+O(q^{100}) $ 16 * q - 8 * q^4 + 40 * q^9 - 4 * q^11 - 20 * q^14 - 16 * q^16 + 12 * q^19 - 32 * q^21 - 40 * q^26 + 4 * q^29 + 20 * q^31 - 80 * q^34 - 104 * q^36 - 16 * q^39 - 28 * q^44 + 44 * q^46 + 36 * q^56 + 24 * q^61 + 32 * q^64 + 80 * q^66 + 40 * q^69 - 36 * q^76 - 52 * q^79 + 40 * q^81 + 136 * q^84 - 40 * q^89 + 92 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{1}{4}\right)$

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 $

$2$			0.192813i			0.136339i	0.997674	+	0.0681697i	$0.0217159\pi$
$2$			0.192813i			0.136339i	−0.997674	+	0.0681697i	$0.978284\pi$
$3$	−1.87822			−1.08439			−0.542195	−	0.840253i	$-0.682407\pi$
$3$	−1.87822			−1.08439			−0.542195	+	0.840253i	$0.682407\pi$
$4$	1.96282			0.981412
$5$		0			0
$5$		0			0
$6$		−	0.362145i		−	0.147845i
$7$	−1.55767	−	1.55767i	−0.588744	−	0.588744i	0.348547	−	0.937291i	$-0.386675\pi$
$7$	−1.55767	−	1.55767i	−0.588744	−	0.588744i	−0.937291	+	0.348547i	$0.886675\pi$
$8$			0.764084i			0.270144i
$9$	0.527707			0.175902
$10$		0			0
$11$	1.15301	+	1.15301i	0.347647	+	0.347647i	0.859232	−	0.511586i	$-0.170942\pi$
$11$	1.15301	+	1.15301i	0.347647	+	0.347647i	−0.511586	+	0.859232i	$0.670942\pi$
$12$	−3.68661			−1.06423
$13$	2.73688	+	2.73688i	0.759075	+	0.759075i	0.976154	−	0.217079i	$-0.0696530\pi$
$13$	2.73688	+	2.73688i	0.759075	+	0.759075i	−0.217079	+	0.976154i	$0.569653\pi$
$14$	0.300339	−	0.300339i	0.0802690	−	0.0802690i
$15$		0			0
$16$	3.77832			0.944580
$17$		−	2.15844i		−	0.523500i	−0.965136	−	0.261750i	$-0.915700\pi$
$17$		−	2.15844i		−	0.523500i	0.965136	−	0.261750i	$-0.0842995\pi$
$18$			0.101749i			0.0239824i
$19$	2.15301	−	2.15301i	0.493935	−	0.493935i	−0.415608	−	0.909544i	$-0.636431\pi$
$19$	2.15301	−	2.15301i	0.493935	−	0.493935i	0.909544	+	0.415608i	$0.136431\pi$
$20$		0			0
$21$	2.92565	+	2.92565i	0.638428	+	0.638428i
$22$	−0.222316	+	0.222316i	−0.0473979	+	0.0473979i
$23$	1.84506	−	1.84506i	0.384722	−	0.384722i	−0.488078	−	0.872800i	$-0.662302\pi$
$23$	1.84506	−	1.84506i	0.384722	−	0.384722i	0.872800	+	0.488078i	$0.162302\pi$
$24$		−	1.43512i		−	0.292942i
$25$		0			0
$26$	−0.527707	+	0.527707i	−0.103492	+	0.103492i
$27$	4.64351			0.893644
$28$	−3.05743	−	3.05743i	−0.577800	−	0.577800i
$29$	−1.79087	−	5.07866i	−0.332556	−	0.943084i
$29$	−1.79087	−	5.07866i	−0.332556	−	0.943084i
$30$		0			0
$31$	5.11584	+	5.11584i	0.918831	+	0.918831i	0.996945	−	0.0781131i	$-0.0248895\pi$
$31$	5.11584	+	5.11584i	0.918831	+	0.918831i	−0.0781131	+	0.996945i	$0.524890\pi$
$32$			2.25668i			0.398928i
$33$	−2.16561	−	2.16561i	−0.376985	−	0.376985i
$34$	0.416176			0.0713736
$35$		0			0
$36$	1.03579			0.172632
$37$	−2.48506			−0.408542			−0.204271	−	0.978914i	$-0.565482\pi$
$37$	−2.48506			−0.408542			−0.204271	+	0.978914i	$0.565482\pi$
$38$	0.415129	+	0.415129i	0.0673428	+	0.0673428i
$39$	−5.14047	−	5.14047i	−0.823133	−	0.823133i
$40$		0			0
$41$	−0.490530	+	0.490530i	−0.0766079	+	0.0766079i	−0.744372	−	0.667765i	$-0.767251\pi$
$41$	−0.490530	+	0.490530i	−0.0766079	+	0.0766079i	0.667765	+	0.744372i	$0.267251\pi$
$42$	−0.564103	+	0.564103i	−0.0870429	+	0.0870429i
$43$	9.89254			1.50860			0.754299	−	0.656531i	$-0.227977\pi$
$43$	9.89254			1.50860			0.754299	+	0.656531i	$0.227977\pi$
$44$	2.26316	+	2.26316i	0.341185	+	0.341185i
$45$		0			0
$46$	0.355752	+	0.355752i	0.0524528	+	0.0524528i
$47$	9.44060			1.37705			0.688527	−	0.725211i	$-0.258258\pi$
$47$	9.44060			1.37705			0.688527	+	0.725211i	$0.258258\pi$
$48$	−7.09651			−1.02429
$49$		−	2.14733i		−	0.306761i
$50$		0			0
$51$			4.05403i			0.567678i
$52$	5.37202	+	5.37202i	0.744965	+	0.744965i
$53$	−1.29978	+	1.29978i	−0.178539	+	0.178539i	−0.790718	−	0.612180i	$-0.790293\pi$
$53$	−1.29978	+	1.29978i	−0.178539	+	0.178539i	0.612180	+	0.790718i	$0.290293\pi$
$54$			0.895329i			0.121839i
$55$		0			0
$56$	1.19019	−	1.19019i	0.159046	−	0.159046i
$57$	−4.04383	+	4.04383i	−0.535619	+	0.535619i
$58$	0.979232	−	0.345303i	0.128579	−	0.0453405i
$59$		−	2.43441i		−	0.316934i	−0.987364	−	0.158467i	$-0.949345\pi$
$59$		−	2.43441i		−	0.316934i	0.987364	−	0.158467i	$-0.0506551\pi$
$60$		0			0
$61$	3.32497	+	3.32497i	0.425719	+	0.425719i	0.887167	−	0.461448i	$-0.152670\pi$
$61$	3.32497	+	3.32497i	0.425719	+	0.425719i	−0.461448	+	0.887167i	$0.652670\pi$
$62$	−0.986400	+	0.986400i	−0.125273	+	0.125273i
$63$	−0.821993	−	0.821993i	−0.103561	−	0.103561i
$64$	7.12153			0.890191
$65$		0			0
$66$	0.417558	−	0.417558i	0.0513979	−	0.0513979i
$67$	4.68018	−	4.68018i	0.571775	−	0.571775i	−0.360849	−	0.932624i	$-0.617513\pi$
$67$	4.68018	−	4.68018i	0.571775	−	0.571775i	0.932624	+	0.360849i	$0.117513\pi$
$68$		−	4.23664i		−	0.513769i
$69$	−3.46543	+	3.46543i	−0.417189	+	0.417189i
$70$		0			0
$71$			0.803417i			0.0953480i	0.998863	+	0.0476740i	$0.0151809\pi$
$71$			0.803417i			0.0953480i	−0.998863	+	0.0476740i	$0.984819\pi$
$72$			0.403212i			0.0475190i
$73$			11.4797i			1.34360i	0.740733	+	0.671799i	$0.234478\pi$
$73$			11.4797i			1.34360i	−0.740733	+	0.671799i	$0.765522\pi$
$74$		−	0.479153i		−	0.0557004i
$75$		0			0
$76$	4.22599	−	4.22599i	0.484754	−	0.484754i
$77$		−	3.59203i		−	0.409350i
$78$	0.991149	−	0.991149i	0.112225	−	0.112225i
$79$	2.09760	−	2.09760i	0.235999	−	0.235999i	−0.579192	−	0.815191i	$-0.696632\pi$
$79$	2.09760	−	2.09760i	0.235999	−	0.235999i	0.815191	+	0.579192i	$0.196632\pi$
$80$		0			0
$81$	−10.3046			−1.14496
$82$	−0.0945805	−	0.0945805i	−0.0104447	−	0.0104447i
$83$	7.41355	−	7.41355i	0.813742	−	0.813742i	−0.171450	−	0.985193i	$-0.554845\pi$
$83$	7.41355	−	7.41355i	0.813742	−	0.813742i	0.985193	+	0.171450i	$0.0548453\pi$
$84$	5.74253	+	5.74253i	0.626561	+	0.626561i
$85$		0			0
$86$			1.90741i			0.205681i
$87$	3.36364	+	9.53884i	0.360620	+	1.02267i
$88$	−0.880999	+	0.880999i	−0.0939148	+	0.0939148i
$89$	−3.83444	+	3.83444i	−0.406450	+	0.406450i	−0.880499	−	0.474049i	$-0.842792\pi$
$89$	−3.83444	+	3.83444i	−0.406450	+	0.406450i	0.474049	+	0.880499i	$0.342792\pi$
$90$		0			0
$91$		−	8.52632i		−	0.893802i
$92$	3.62153	−	3.62153i	0.377571	−	0.377571i
$93$	−9.60866	−	9.60866i	−0.996372	−	0.996372i
$94$			1.82027i			0.187747i
$95$		0			0
$96$		−	4.23853i		−	0.432593i
$97$	−11.2386			−1.14110			−0.570552	−	0.821261i	$-0.693271\pi$
$97$	−11.2386			−1.14110			−0.570552	+	0.821261i	$0.693271\pi$
$98$	0.414032			0.0418236
$99$	0.608453	+	0.608453i	0.0611518	+	0.0611518i
$100$		0			0
$101$	−3.61891	−	3.61891i	−0.360095	−	0.360095i	0.503753	−	0.863848i	$-0.331952\pi$
$101$	−3.61891	−	3.61891i	−0.360095	−	0.360095i	−0.863848	+	0.503753i	$0.831952\pi$
$102$	−0.781670			−0.0773968
$103$	−3.90893	+	3.90893i	−0.385158	+	0.385158i	−0.872956	−	0.487798i	$-0.837800\pi$
$103$	−3.90893	+	3.90893i	−0.385158	+	0.385158i	0.487798	+	0.872956i	$0.337800\pi$
$104$	−2.09121	+	2.09121i	−0.205060	+	0.205060i
$105$		0			0
$106$	−0.250614	−	0.250614i	−0.0243418	−	0.0243418i
$107$	−11.2646	−	11.2646i	−1.08899	−	1.08899i	−0.995633	−	0.0933536i	$-0.970241\pi$
$107$	−11.2646	−	11.2646i	−1.08899	−	1.08899i	−0.0933536	−	0.995633i	$-0.529759\pi$
$108$	9.11439			0.877032
$109$	6.52155			0.624651			0.312326	−	0.949975i	$-0.398892\pi$
$109$	6.52155			0.624651			0.312326	+	0.949975i	$0.398892\pi$
$110$		0			0
$111$	4.66749			0.443019
$112$	−5.88538	−	5.88538i	−0.556116	−	0.556116i
$113$			19.0637i			1.79337i	0.442674	+	0.896683i	$0.354030\pi$
$113$			19.0637i			1.79337i	−0.442674	+	0.896683i	$0.645970\pi$
$114$	−0.779703	−	0.779703i	−0.0730259	−	0.0730259i
$115$		0			0
$116$	−3.51516	−	9.96851i	−0.326374	−	0.925553i
$117$	1.44427	+	1.44427i	0.133523	+	0.133523i
$118$	0.469386			0.0432105
$119$	−3.36214	+	3.36214i	−0.308207	+	0.308207i
$120$		0			0
$121$		−	8.34112i		−	0.758283i
$122$	−0.641097	+	0.641097i	−0.0580422	+	0.0580422i
$123$	0.921322	−	0.921322i	0.0830728	−	0.0830728i
$124$	10.0415	+	10.0415i	0.901752	+	0.901752i
$125$		0			0
$126$	0.158491	−	0.158491i	0.0141195	−	0.0141195i
$127$			6.13610i			0.544491i	0.962228	+	0.272245i	$0.0877663\pi$
$127$			6.13610i			0.544491i	−0.962228	+	0.272245i	$0.912234\pi$
$128$			5.88648i			0.520296i
$129$	−18.5804			−1.63591
$130$		0			0
$131$	−15.6914	+	15.6914i	−1.37097	+	1.37097i	−0.511951	+	0.859015i	$0.671077\pi$
$131$	−15.6914	+	15.6914i	−1.37097	+	1.37097i	−0.859015	+	0.511951i	$0.828923\pi$
$132$	−4.25071	−	4.25071i	−0.369977	−	0.369977i
$133$	−6.70737			−0.581603
$134$	0.902399	+	0.902399i	0.0779554	+	0.0779554i
$135$		0			0
$136$	1.64923			0.141420
$137$		−	12.4600i		−	1.06453i	−0.846577	−	0.532267i	$-0.821340\pi$
$137$		−	12.4600i		−	1.06453i	0.846577	−	0.532267i	$-0.178660\pi$
$138$	−0.668181	−	0.668181i	−0.0568793	−	0.0568793i
$139$			1.85129i			0.157025i	0.996913	+	0.0785123i	$0.0250170\pi$
$139$			1.85129i			0.157025i	−0.996913	+	0.0785123i	$0.974983\pi$
$140$		0			0
$141$	−17.7315			−1.49326
$142$	−0.154909			−0.0129997
$143$			6.31133i			0.527780i
$144$	1.99384			0.166154
$145$		0			0
$146$	−2.21344			−0.183185
$147$			4.03315i			0.332648i
$148$	−4.87774			−0.400948
$149$	−16.4633			−1.34873			−0.674365	−	0.738398i	$-0.735583\pi$
$149$	−16.4633			−1.34873			−0.674365	+	0.738398i	$0.735583\pi$
$150$		0			0
$151$		−	2.77832i		−	0.226097i	−0.993589	−	0.113048i	$-0.963939\pi$
$151$		−	2.77832i		−	0.226097i	0.993589	−	0.113048i	$-0.0360615\pi$
$152$	1.64508	+	1.64508i	0.133434	+	0.133434i
$153$		−	1.13903i		−	0.0920847i
$154$	0.692590			0.0558105
$155$		0			0
$156$	−10.0898	−	10.0898i	−0.807833	−	0.807833i
$157$	0.932142			0.0743931			0.0371965	−	0.999308i	$-0.488157\pi$
$157$	0.932142			0.0743931			0.0371965	+	0.999308i	$0.488157\pi$
$158$	0.404445	+	0.404445i	0.0321759	+	0.0321759i
$159$	2.44127	−	2.44127i	0.193605	−	0.193605i
$160$		0			0
$161$	−5.74800			−0.453006
$162$		−	1.98687i		−	0.156103i
$163$		−	12.6956i		−	0.994396i	−0.867637	−	0.497198i	$-0.834362\pi$
$163$		−	12.6956i		−	0.994396i	0.867637	−	0.497198i	$-0.165638\pi$
$164$	−0.962823	+	0.962823i	−0.0751839	+	0.0751839i
$165$		0			0
$166$	1.42943	+	1.42943i	0.110945	+	0.110945i
$167$	−11.0826	+	11.0826i	−0.857595	+	0.857595i	−0.991054	−	0.133459i	$-0.957392\pi$
$167$	−11.0826	+	11.0826i	−0.857595	+	0.857595i	0.133459	+	0.991054i	$0.457392\pi$
$168$	−2.23544	+	2.23544i	−0.172468	+	0.172468i
$169$			1.98106i			0.152389i
$170$		0			0
$171$	1.13616	−	1.13616i	0.0868843	−	0.0868843i
$172$	19.4173			1.48056
$173$	−12.8849	−	12.8849i	−0.979620	−	0.979620i	0.0201761	−	0.999796i	$-0.493577\pi$
$173$	−12.8849	−	12.8849i	−0.979620	−	0.979620i	−0.999796	+	0.0201761i	$0.993577\pi$
$174$	−1.83921	+	0.648554i	−0.139430	+	0.0491668i
$175$		0			0
$176$	4.35646	+	4.35646i	0.328380	+	0.328380i
$177$			4.57236i			0.343680i
$178$	−0.739329	−	0.739329i	−0.0554151	−	0.0554151i
$179$	−21.1019			−1.57723			−0.788615	−	0.614887i	$-0.789202\pi$
$179$	−21.1019			−1.57723			−0.788615	+	0.614887i	$0.789202\pi$
$180$		0			0
$181$	−12.7532			−0.947940			−0.473970	−	0.880541i	$-0.657179\pi$
$181$	−12.7532			−0.947940			−0.473970	+	0.880541i	$0.657179\pi$
$182$	1.64399			0.121860
$183$	−6.24502	−	6.24502i	−0.461645	−	0.461645i
$184$	1.40978	+	1.40978i	0.103931	+	0.103931i
$185$		0			0
$186$	1.85267	−	1.85267i	0.135845	−	0.135845i
$187$	2.48872	−	2.48872i	0.181993	−	0.181993i
$188$	18.5302			1.35146
$189$	−7.23306	−	7.23306i	−0.526127	−	0.526127i
$190$		0			0
$191$	−4.60637	−	4.60637i	−0.333305	−	0.333305i	0.520535	−	0.853840i	$-0.325732\pi$
$191$	−4.60637	−	4.60637i	−0.333305	−	0.333305i	−0.853840	+	0.520535i	$0.825732\pi$
$192$	−13.3758			−0.965314
$193$	6.03773			0.434606			0.217303	−	0.976104i	$-0.430274\pi$
$193$	6.03773			0.434606			0.217303	+	0.976104i	$0.430274\pi$
$194$		−	2.16694i		−	0.155577i
$195$		0			0
$196$		−	4.21482i		−	0.301059i
$197$	7.10733	+	7.10733i	0.506377	+	0.506377i	0.913412	−	0.407036i	$-0.133438\pi$
$197$	7.10733	+	7.10733i	0.506377	+	0.506377i	−0.407036	+	0.913412i	$0.633438\pi$
$198$	−0.117318	+	0.117318i	−0.00833740	+	0.00833740i
$199$			20.8864i			1.48060i	0.672279	+	0.740298i	$0.265316\pi$
$199$			20.8864i			1.48060i	−0.672279	+	0.740298i	$0.734684\pi$
$200$		0			0
$201$	−8.79040	+	8.79040i	−0.620027	+	0.620027i
$202$	0.697774	−	0.697774i	0.0490952	−	0.0490952i
$203$	−5.12130	+	10.7005i	−0.359444	+	0.751025i
$204$			7.95735i			0.557126i
$205$		0			0
$206$	−0.753692	−	0.753692i	−0.0525122	−	0.0525122i
$207$	0.973652	−	0.973652i	0.0676735	−	0.0676735i
$208$	10.3408	+	10.3408i	0.717007	+	0.717007i
$209$	4.96491			0.343430
$210$		0			0
$211$	1.14164	−	1.14164i	0.0785935	−	0.0785935i	−0.666717	−	0.745311i	$-0.732301\pi$
$211$	1.14164	−	1.14164i	0.0785935	−	0.0785935i	0.745311	+	0.666717i	$0.232301\pi$
$212$	−2.55124	+	2.55124i	−0.175220	+	0.175220i
$213$		−	1.50899i		−	0.103394i
$214$	2.17195	−	2.17195i	0.148472	−	0.148472i
$215$		0			0
$216$			3.54803i			0.241413i
$217$		−	15.9376i		−	1.08191i
$218$			1.25744i			0.0851646i
$219$		−	21.5614i		−	1.45699i
$220$		0			0
$221$	5.90741	−	5.90741i	0.397375	−	0.397375i
$222$			0.899954i			0.0604009i
$223$	18.4792	−	18.4792i	1.23746	−	1.23746i	0.276425	−	0.961035i	$-0.410850\pi$
$223$	18.4792	−	18.4792i	1.23746	−	1.23746i	0.961035	−	0.276425i	$-0.0891498\pi$
$224$	3.51516	−	3.51516i	0.234866	−	0.234866i
$225$		0			0
$226$	−3.67574			−0.244506
$227$	18.5773	+	18.5773i	1.23302	+	1.23302i	0.962798	+	0.270222i	$0.0870972\pi$
$227$	18.5773	+	18.5773i	1.23302	+	1.23302i	0.270222	+	0.962798i	$0.412903\pi$
$228$	−7.93733	+	7.93733i	−0.525662	+	0.525662i
$229$	17.2134	+	17.2134i	1.13750	+	1.13750i	0.988898	+	0.148598i	$0.0474762\pi$
$229$	17.2134	+	17.2134i	1.13750	+	1.13750i	0.148598	+	0.988898i	$0.452524\pi$
$230$		0			0
$231$			6.74662i			0.443895i
$232$	3.88052	−	1.36837i	0.254769	−	0.0898381i
$233$	20.2653	−	20.2653i	1.32762	−	1.32762i	0.420184	−	0.907439i	$-0.361965\pi$
$233$	20.2653	−	20.2653i	1.32762	−	1.32762i	0.907439	−	0.420184i	$-0.138035\pi$
$234$	−0.278474	+	0.278474i	−0.0182044	+	0.0182044i
$235$		0			0
$236$		−	4.77832i		−	0.311042i
$237$	−3.93975	+	3.93975i	−0.255914	+	0.255914i
$238$	−0.648265	−	0.648265i	−0.0420208	−	0.0420208i
$239$		−	22.5302i		−	1.45736i	−0.684857	−	0.728678i	$-0.740135\pi$
$239$		−	22.5302i		−	1.45736i	0.684857	−	0.728678i	$-0.259865\pi$
$240$		0			0
$241$		−	21.5188i		−	1.38615i	−0.720868	−	0.693073i	$-0.756257\pi$
$241$		−	21.5188i		−	1.38615i	0.720868	−	0.693073i	$-0.243743\pi$
$242$	1.60828			0.103384
$243$	5.42386			0.347941
$244$	6.52632	+	6.52632i	0.417805	+	0.417805i
$245$		0			0
$246$	0.177643	+	0.177643i	0.0113261	+	0.0113261i
$247$	11.7851			0.749868
$248$	−3.90893	+	3.90893i	−0.248217	+	0.248217i
$249$	−13.9243	+	13.9243i	−0.882414	+	0.882414i
$250$		0			0
$251$	16.3764	+	16.3764i	1.03367	+	1.03367i	0.999413	+	0.0342592i	$0.0109072\pi$
$251$	16.3764	+	16.3764i	1.03367	+	1.03367i	0.0342592	+	0.999413i	$0.489093\pi$
$252$	−1.61343	−	1.61343i	−0.101636	−	0.101636i
$253$	4.25477			0.267495
$254$	−1.18312			−0.0742356
$255$		0			0
$256$	13.1081			0.819254
$257$	−2.66706	−	2.66706i	−0.166366	−	0.166366i	0.619014	−	0.785380i	$-0.287533\pi$
$257$	−2.66706	−	2.66706i	−0.166366	−	0.166366i	−0.785380	+	0.619014i	$0.787533\pi$
$258$		−	3.58253i		−	0.223039i
$259$	3.87091	+	3.87091i	0.240527	+	0.240527i
$260$		0			0
$261$	−0.945053	−	2.68004i	−0.0584973	−	0.165890i
$262$	−3.02551	−	3.02551i	−0.186917	−	0.186917i
$263$	−21.3510			−1.31656			−0.658280	−	0.752773i	$-0.728716\pi$
$263$	−21.3510			−1.31656			−0.658280	+	0.752773i	$0.728716\pi$
$264$	1.65471	−	1.65471i	0.101840	−	0.101840i
$265$		0			0
$266$		−	1.29327i		−	0.0792954i
$267$	7.20192	−	7.20192i	0.440750	−	0.440750i
$268$	9.18637	−	9.18637i	0.561147	−	0.561147i
$269$	7.49123	+	7.49123i	0.456749	+	0.456749i	0.897587	−	0.440838i	$-0.145319\pi$
$269$	7.49123	+	7.49123i	0.456749	+	0.456749i	−0.440838	+	0.897587i	$0.645319\pi$
$270$		0			0
$271$	8.14477	−	8.14477i	0.494760	−	0.494760i	−0.415042	−	0.909802i	$-0.636233\pi$
$271$	8.14477	−	8.14477i	0.494760	−	0.494760i	0.909802	+	0.415042i	$0.136233\pi$
$272$		−	8.15530i		−	0.494487i
$273$			16.0143i			0.969230i
$274$	2.40246			0.145138
$275$		0			0
$276$	−6.80203	+	6.80203i	−0.409434	+	0.409434i
$277$	2.29225	+	2.29225i	0.137728	+	0.137728i	0.772610	−	0.634882i	$-0.218951\pi$
$277$	2.29225	+	2.29225i	0.137728	+	0.137728i	−0.634882	+	0.772610i	$0.718951\pi$
$278$	−0.356953			−0.0214086
$279$	2.69966	+	2.69966i	0.161624	+	0.161624i
$280$		0			0
$281$	−16.0403			−0.956885			−0.478442	−	0.878119i	$-0.658798\pi$
$281$	−16.0403			−0.956885			−0.478442	+	0.878119i	$0.658798\pi$
$282$		−	3.41887i		−	0.203591i
$283$	−10.1149	−	10.1149i	−0.601266	−	0.601266i	0.339383	−	0.940648i	$-0.389782\pi$
$283$	−10.1149	−	10.1149i	−0.601266	−	0.601266i	−0.940648	+	0.339383i	$0.889782\pi$
$284$			1.57696i			0.0935756i
$285$		0			0
$286$	−1.21691			−0.0719572
$287$	1.52817			0.0902049
$288$			1.19086i			0.0701723i
$289$	12.3411			0.725948
$290$		0			0
$291$	21.1085			1.23740
$292$			22.5326i			1.31862i
$293$	−21.8078			−1.27402			−0.637012	−	0.770854i	$-0.719830\pi$
$293$	−21.8078			−1.27402			−0.637012	+	0.770854i	$0.719830\pi$
$294$	−0.777643			−0.0453531
$295$		0			0
$296$		−	1.89880i		−	0.110365i
$297$	5.35403	+	5.35403i	0.310672	+	0.310672i
$298$		−	3.17435i		−	0.183885i
$299$	10.0994			0.584066
$300$		0			0
$301$	−15.4093	−	15.4093i	−0.888178	−	0.888178i
$302$	0.535696			0.0308259
$303$	6.79711	+	6.79711i	0.390484	+	0.390484i
$304$	8.13478	−	8.13478i	0.466561	−	0.466561i
$305$		0			0
$306$	0.219619			0.0125548
$307$			6.59288i			0.376275i	0.982143	+	0.188138i	$0.0602451\pi$
$307$			6.59288i			0.376275i	−0.982143	+	0.188138i	$0.939755\pi$
$308$		−	7.05052i		−	0.401741i
$309$	7.34182	−	7.34182i	0.417662	−	0.417662i
$310$		0			0
$311$	22.7805	+	22.7805i	1.29177	+	1.29177i	0.933694	+	0.358072i	$0.116566\pi$
$311$	22.7805	+	22.7805i	1.29177	+	1.29177i	0.358072	+	0.933694i	$0.383434\pi$
$312$	3.92775	−	3.92775i	0.222365	−	0.222365i
$313$	−20.4117	+	20.4117i	−1.15374	+	1.15374i	−0.167941	+	0.985797i	$0.553712\pi$
$313$	−20.4117	+	20.4117i	−1.15374	+	1.15374i	−0.985797	+	0.167941i	$0.946288\pi$
$314$			0.179729i			0.0101427i
$315$		0			0
$316$	4.11722	−	4.11722i	0.231612	−	0.231612i
$317$	−24.2946			−1.36452			−0.682262	−	0.731108i	$-0.739003\pi$
$317$	−24.2946			−1.36452			−0.682262	+	0.731108i	$0.739003\pi$
$318$	0.470709	+	0.470709i	0.0263960	+	0.0263960i
$319$	3.79087	−	7.92066i	0.212248	−	0.443472i
$320$		0			0
$321$	21.1573	+	21.1573i	1.18089	+	1.18089i
$322$		−	1.10829i		−	0.0617626i
$323$	−4.64716	−	4.64716i	−0.258575	−	0.258575i
$324$	−20.2262			−1.12368
$325$		0			0
$326$	2.44788			0.135575
$327$	−12.2489			−0.677366
$328$	−0.374806	−	0.374806i	−0.0206952	−	0.0206952i
$329$	−14.7053	−	14.7053i	−0.810732	−	0.810732i
$330$		0			0
$331$	8.62531	−	8.62531i	0.474090	−	0.474090i	−0.429146	−	0.903235i	$-0.641185\pi$
$331$	8.62531	−	8.62531i	0.474090	−	0.474090i	0.903235	+	0.429146i	$0.141185\pi$
$332$	14.5515	−	14.5515i	0.798616	−	0.798616i
$333$	−1.31138			−0.0718634
$334$	−2.13686	−	2.13686i	−0.116924	−	0.116924i
$335$		0			0
$336$	11.0540	+	11.0540i	0.603047	+	0.603047i
$337$	−26.7563			−1.45751			−0.728754	−	0.684776i	$-0.759900\pi$
$337$	−26.7563			−1.45751			−0.728754	+	0.684776i	$0.759900\pi$
$338$	−0.381974			−0.0207766
$339$		−	35.8059i		−	1.94471i
$340$		0			0
$341$			11.7973i			0.638858i
$342$	0.219066	+	0.219066i	0.0118457	+	0.0118457i
$343$	−14.2485	+	14.2485i	−0.769348	+	0.769348i
$344$			7.55873i			0.407539i
$345$		0			0
$346$	2.48437	−	2.48437i	0.133561	−	0.133561i
$347$	−18.4521	+	18.4521i	−0.990563	+	0.990563i	−0.999956	−	0.00939290i	$-0.997010\pi$
$347$	−18.4521	+	18.4521i	−0.990563	+	0.990563i	0.00939290	+	0.999956i	$0.497010\pi$
$348$	6.60224	+	18.7230i	0.353917	+	1.00366i
$349$			24.2654i			1.29890i	0.760406	+	0.649448i	$0.225000\pi$
$349$			24.2654i			1.29890i	−0.760406	+	0.649448i	$0.775000\pi$
$350$		0			0
$351$	12.7087	+	12.7087i	0.678342	+	0.678342i
$352$	−2.60198	+	2.60198i	−0.138686	+	0.138686i
$353$	21.7308	+	21.7308i	1.15661	+	1.15661i	0.985199	+	0.171415i	$0.0548337\pi$
$353$	21.7308	+	21.7308i	1.15661	+	1.15661i	0.171415	+	0.985199i	$0.445166\pi$
$354$	−0.881610			−0.0468571
$355$		0			0
$356$	−7.52632	+	7.52632i	−0.398894	+	0.398894i
$357$	6.31484	−	6.31484i	0.334217	−	0.334217i
$358$		−	4.06872i		−	0.215039i
$359$	22.6346	−	22.6346i	1.19461	−	1.19461i	0.218850	−	0.975759i	$-0.429770\pi$
$359$	22.6346	−	22.6346i	1.19461	−	1.19461i	0.975759	−	0.218850i	$-0.0702305\pi$
$360$		0			0
$361$			9.72906i			0.512056i
$362$		−	2.45899i		−	0.129242i
$363$			15.6664i			0.822275i
$364$		−	16.7357i		−	0.877187i
$365$		0			0
$366$	1.20412	−	1.20412i	0.0629404	−	0.0629404i
$367$		−	9.52855i		−	0.497386i	−0.968582	−	0.248693i	$-0.919999\pi$
$367$		−	9.52855i		−	0.497386i	0.968582	−	0.248693i	$-0.0800011\pi$
$368$	6.97124	−	6.97124i	0.363401	−	0.363401i
$369$	−0.258856	+	0.258856i	−0.0134755	+	0.0134755i
$370$		0			0
$371$	4.04926			0.210227
$372$	−18.8601	−	18.8601i	−0.977851	−	0.977851i
$373$	14.0936	−	14.0936i	0.729739	−	0.729739i	−0.240828	−	0.970568i	$-0.577419\pi$
$373$	14.0936	−	14.0936i	0.729739	−	0.729739i	0.970568	+	0.240828i	$0.0774191\pi$
$374$	0.479857	+	0.479857i	0.0248128	+	0.0248128i
$375$		0			0
$376$			7.21341i			0.372003i
$377$	8.99830	−	18.8011i	0.463436	−	0.968306i
$378$	1.39463	−	1.39463i	0.0717319	−	0.0717319i
$379$	−10.9031	+	10.9031i	−0.560055	+	0.560055i	−0.929323	−	0.369268i	$-0.879608\pi$
$379$	−10.9031	+	10.9031i	−0.560055	+	0.560055i	0.369268	+	0.929323i	$0.379608\pi$
$380$		0			0
$381$		−	11.5249i		−	0.590441i
$382$	0.888167	−	0.888167i	0.0454426	−	0.0454426i
$383$	0.989916	+	0.989916i	0.0505823	+	0.0505823i	0.731946	−	0.681363i	$-0.238613\pi$
$383$	0.989916	+	0.989916i	0.0505823	+	0.0505823i	−0.681363	+	0.731946i	$0.738613\pi$
$384$		−	11.0561i		−	0.564204i
$385$		0			0
$386$			1.16415i			0.0592538i
$387$	5.22036			0.265366
$388$	−22.0593			−1.11989
$389$	3.15870	+	3.15870i	0.160153	+	0.160153i	0.782634	−	0.622482i	$-0.213876\pi$
$389$	3.15870	+	3.15870i	0.160153	+	0.160153i	−0.622482	+	0.782634i	$0.713876\pi$
$390$		0			0
$391$	−3.98247	−	3.98247i	−0.201402	−	0.201402i
$392$	1.64074			0.0828697
$393$	29.4719	−	29.4719i	1.48666	−	1.48666i
$394$	−1.37039	+	1.37039i	−0.0690391	+	0.0690391i
$395$		0			0
$396$	1.19429	+	1.19429i	0.0600151	+	0.0600151i
$397$	1.80109	+	1.80109i	0.0903941	+	0.0903941i	0.750858	−	0.660464i	$-0.229640\pi$
$397$	1.80109	+	1.80109i	0.0903941	+	0.0903941i	−0.660464	+	0.750858i	$0.729640\pi$
$398$	−4.02717			−0.201864
$399$	12.5979			0.630685
$400$		0			0
$401$	10.4344			0.521070			0.260535	−	0.965464i	$-0.416101\pi$
$401$	10.4344			0.521070			0.260535	+	0.965464i	$0.416101\pi$
$402$	−1.69490	−	1.69490i	−0.0845341	−	0.0845341i
$403$			28.0029i			1.39492i
$404$	−7.10329	−	7.10329i	−0.353402	−	0.353402i
$405$		0			0
$406$	−2.06319	−	0.987452i	−0.102394	−	0.0490064i
$407$	−2.86531	−	2.86531i	−0.142028	−	0.142028i
$408$	−3.09762			−0.153355
$409$	−10.1466	+	10.1466i	−0.501718	+	0.501718i	−0.911972	−	0.410253i	$-0.865440\pi$
$409$	−10.1466	+	10.1466i	−0.501718	+	0.501718i	0.410253	+	0.911972i	$0.365440\pi$
$410$		0			0
$411$			23.4027i			1.15437i
$412$	−7.67253	+	7.67253i	−0.377999	+	0.377999i
$413$	−3.79201	+	3.79201i	−0.186593	+	0.186593i
$414$	0.187733	+	0.187733i	0.00922656	+	0.00922656i
$415$		0			0
$416$	−6.17626	+	6.17626i	−0.302816	+	0.302816i
$417$		−	3.47713i		−	0.170276i
$418$			0.957299i			0.0468230i
$419$	−29.5026			−1.44130			−0.720648	−	0.693301i	$-0.756156\pi$
$419$	−29.5026			−1.44130			−0.720648	+	0.693301i	$0.756156\pi$
$420$		0			0
$421$	−12.2513	+	12.2513i	−0.597093	+	0.597093i	−0.939538	−	0.342445i	$-0.888745\pi$
$421$	−12.2513	+	12.2513i	−0.597093	+	0.597093i	0.342445	+	0.939538i	$0.388745\pi$
$422$	0.220122	+	0.220122i	0.0107154	+	0.0107154i
$423$	4.98187			0.242227
$424$	−0.993141	−	0.993141i	−0.0482312	−	0.0482312i
$425$		0			0
$426$	0.290953			0.0140967
$427$		−	10.3584i		−	0.501279i
$428$	−22.1103	−	22.1103i	−1.06874	−	1.06874i
$429$		−	11.8541i		−	0.572319i
$430$		0			0
$431$	19.8262			0.954994			0.477497	−	0.878633i	$-0.341544\pi$
$431$	19.8262			0.954994			0.477497	+	0.878633i	$0.341544\pi$
$432$	17.5447			0.844118
$433$		−	1.79930i		−	0.0864687i	−0.999065	−	0.0432344i	$-0.986234\pi$
$433$		−	1.79930i		−	0.0864687i	0.999065	−	0.0432344i	$-0.0137662\pi$
$434$	3.07297			0.147507
$435$		0			0
$436$	12.8007			0.613040
$437$		−	7.94490i		−	0.380056i
$438$	4.15732			0.198644
$439$	24.7983			1.18356			0.591779	−	0.806100i	$-0.298426\pi$
$439$	24.7983			1.18356			0.591779	+	0.806100i	$0.298426\pi$
$440$		0			0
$441$		−	1.13316i		−	0.0539599i
$442$	1.13903	+	1.13903i	0.0541779	+	0.0541779i
$443$		−	15.9290i		−	0.756807i	−0.925641	−	0.378404i	$-0.876473\pi$
$443$		−	15.9290i		−	0.756807i	0.925641	−	0.378404i	$-0.123527\pi$
$444$	9.16147			0.434784
$445$		0			0
$446$	3.56303	+	3.56303i	0.168715	+	0.168715i
$447$	30.9218			1.46255
$448$	−11.0930	−	11.0930i	−0.524095	−	0.524095i
$449$	7.98176	−	7.98176i	0.376683	−	0.376683i	−0.493221	−	0.869904i	$-0.664181\pi$
$449$	7.98176	−	7.98176i	0.376683	−	0.376683i	0.869904	+	0.493221i	$0.164181\pi$
$450$		0			0
$451$	−1.13118			−0.0532650
$452$			37.4187i			1.76003i
$453$			5.21830i			0.245177i
$454$	−3.58195	+	3.58195i	−0.168109	+	0.168109i
$455$		0			0
$456$	−3.08983	−	3.08983i	−0.144694	−	0.144694i
$457$	−21.3938	+	21.3938i	−1.00076	+	1.00076i	−0.000758030		1.00000i	$0.500241\pi$
$457$	−21.3938	+	21.3938i	−1.00076	+	1.00076i	−1.00000		0.000758030i	$0.999759\pi$
$458$	−3.31897	+	3.31897i	−0.155085	+	0.155085i
$459$		−	10.0228i		−	0.467822i
$460$		0			0
$461$	15.1101	−	15.1101i	0.703750	−	0.703750i	−0.261464	−	0.965213i	$-0.584205\pi$
$461$	15.1101	−	15.1101i	0.703750	−	0.703750i	0.965213	+	0.261464i	$0.0842051\pi$
$462$	−1.30084			−0.0605204
$463$	−3.82517	−	3.82517i	−0.177771	−	0.177771i	0.612613	−	0.790383i	$-0.290119\pi$
$463$	−3.82517	−	3.82517i	−0.177771	−	0.177771i	−0.790383	+	0.612613i	$0.790119\pi$
$464$	−6.76648	−	19.1888i	−0.314126	−	0.890818i
$465$		0			0
$466$	3.90741	+	3.90741i	0.181007	+	0.181007i
$467$		−	5.88766i		−	0.272449i	−0.990678	−	0.136224i	$-0.956503\pi$
$467$		−	5.88766i		−	0.272449i	0.990678	−	0.136224i	$-0.0434968\pi$
$468$	2.83485	+	2.83485i	0.131041	+	0.131041i
$469$	−14.5804			−0.673258
$470$		0			0
$471$	−1.75077			−0.0806711
$472$	1.86009			0.0856178
$473$	11.4062	+	11.4062i	0.524459	+	0.524459i
$474$	−0.759636	−	0.759636i	−0.0348912	−	0.0348912i
$475$		0			0
$476$	−6.59930	+	6.59930i	−0.302478	+	0.302478i
$477$	−0.685903	+	0.685903i	−0.0314053	+	0.0314053i
$478$	4.34411			0.198695
$479$	6.77715	+	6.77715i	0.309656	+	0.309656i	0.844776	−	0.535120i	$-0.179734\pi$
$479$	6.77715	+	6.77715i	0.309656	+	0.309656i	−0.535120	+	0.844776i	$0.679734\pi$
$480$		0			0
$481$	−6.80133	−	6.80133i	−0.310114	−	0.310114i
$482$	4.14910			0.188986
$483$	10.7960			0.491235
$484$		−	16.3721i		−	0.744188i
$485$		0			0
$486$			1.04579i			0.0474380i
$487$	−7.92933	−	7.92933i	−0.359312	−	0.359312i	0.504247	−	0.863559i	$-0.331770\pi$
$487$	−7.92933	−	7.92933i	−0.359312	−	0.359312i	−0.863559	+	0.504247i	$0.831770\pi$
$488$	−2.54055	+	2.54055i	−0.115005	+	0.115005i
$489$			23.8451i			1.07831i
$490$		0			0
$491$	0.661102	−	0.661102i	0.0298351	−	0.0298351i	−0.692032	−	0.721867i	$-0.743284\pi$
$491$	0.661102	−	0.661102i	0.0298351	−	0.0298351i	0.721867	+	0.692032i	$0.243284\pi$
$492$	1.80839	−	1.80839i	0.0815286	−	0.0815286i
$493$	−10.9620	+	3.86549i	−0.493704	+	0.174093i
$494$			2.27232i			0.102236i
$495$		0			0
$496$	19.3293	+	19.3293i	0.867910	+	0.867910i
$497$	1.25146	−	1.25146i	0.0561356	−	0.0561356i
$498$	−2.68478	−	2.68478i	−0.120308	−	0.120308i
$499$	25.7405			1.15230			0.576151	−	0.817343i	$-0.304554\pi$
$499$	25.7405			1.15230			0.576151	+	0.817343i	$0.304554\pi$
$500$		0			0
$501$	20.8155	−	20.8155i	0.929968	−	0.929968i
$502$	−3.15759	+	3.15759i	−0.140930	+	0.140930i
$503$		−	6.69875i		−	0.298682i	−0.988786	−	0.149341i	$-0.952285\pi$
$503$		−	6.69875i		−	0.298682i	0.988786	−	0.149341i	$-0.0477153\pi$
$504$	0.628071	−	0.628071i	0.0279765	−	0.0279765i
$505$		0			0
$506$			0.820375i			0.0364701i
$507$		−	3.72086i		−	0.165249i
$508$			12.0441i			0.534370i
$509$		−	29.5491i		−	1.30974i	−0.755741	−	0.654871i	$-0.772723\pi$
$509$		−	29.5491i		−	1.30974i	0.755741	−	0.654871i	$-0.227277\pi$
$510$		0			0
$511$	17.8816	−	17.8816i	0.791036	−	0.791036i
$512$			14.3004i			0.631992i
$513$	9.99754	−	9.99754i	0.441402	−	0.441402i
$514$	0.514243	−	0.514243i	0.0226823	−	0.0226823i
$515$		0			0
$516$	−36.4700			−1.60550
$517$	10.8851	+	10.8851i	0.478728	+	0.478728i
$518$	−0.746362	+	0.746362i	−0.0327933	+	0.0327933i
$519$	24.2007	+	24.2007i	1.06229	+	1.06229i
$520$		0			0
$521$		−	9.69781i		−	0.424869i	−0.977175	−	0.212434i	$-0.931861\pi$
$521$		−	9.69781i		−	0.424869i	0.977175	−	0.212434i	$-0.0681392\pi$
$522$	0.516747	−	0.182219i	0.0226174	−	0.00797549i
$523$	10.4806	−	10.4806i	0.458283	−	0.458283i	−0.439808	−	0.898092i	$-0.644954\pi$
$523$	10.4806	−	10.4806i	0.458283	−	0.458283i	0.898092	+	0.439808i	$0.144954\pi$
$524$	−30.7995	+	30.7995i	−1.34548	+	1.34548i
$525$		0			0
$526$		−	4.11675i		−	0.179499i
$527$	11.0422	−	11.0422i	0.481008	−	0.481008i
$528$	−8.18238	−	8.18238i	−0.356092	−	0.356092i
$529$			16.1915i			0.703977i
$530$		0			0
$531$		−	1.28466i		−	0.0557493i
$532$	−13.1654			−0.570792
$533$	−2.68505			−0.116302
$534$	1.38862	+	1.38862i	0.0600916	+	0.0600916i
$535$		0			0
$536$	3.57605	+	3.57605i	0.154462	+	0.154462i
$537$	39.6340			1.71033
$538$	−1.44441	+	1.44441i	−0.0622728	+	0.0622728i
$539$	2.47590	−	2.47590i	0.106644	−	0.106644i
$540$		0			0
$541$	−20.2464	−	20.2464i	−0.870463	−	0.870463i	0.122060	−	0.992523i	$-0.461050\pi$
$541$	−20.2464	−	20.2464i	−0.870463	−	0.870463i	−0.992523	+	0.122060i	$0.961050\pi$
$542$	1.57042	+	1.57042i	0.0674552	+	0.0674552i
$543$	23.9534			1.02794
$544$	4.87091			0.208839
$545$		0			0
$546$	−3.08777			−0.132144
$547$	20.1591	+	20.1591i	0.861939	+	0.861939i	0.991563	−	0.129624i	$-0.0413771\pi$
$547$	20.1591	+	20.1591i	0.861939	+	0.861939i	−0.129624	+	0.991563i	$0.541377\pi$
$548$		−	24.4569i		−	1.04475i
$549$	1.75461	+	1.75461i	0.0748848	+	0.0748848i
$550$		0			0
$551$	−14.7902	−	7.07866i	−0.630083	−	0.301561i
$552$	−2.64788	−	2.64788i	−0.112701	−	0.112701i
$553$	−6.53474			−0.277885
$554$	−0.441976	+	0.441976i	−0.0187778	+	0.0187778i
$555$		0			0
$556$			3.63376i			0.154106i
$557$	−10.2070	+	10.2070i	−0.432485	+	0.432485i	−0.889473	−	0.456988i	$-0.848928\pi$
$557$	−10.2070	+	10.2070i	−0.432485	+	0.432485i	0.456988	+	0.889473i	$0.348928\pi$
$558$	−0.520530	+	0.520530i	−0.0220358	+	0.0220358i
$559$	27.0747	+	27.0747i	1.14514	+	1.14514i
$560$		0			0
$561$	−4.67435	+	4.67435i	−0.197351	+	0.197351i
$562$		−	3.09278i		−	0.130461i
$563$		−	9.06228i		−	0.381930i	−0.981597	−	0.190965i	$-0.938838\pi$
$563$		−	9.06228i		−	0.381930i	0.981597	−	0.190965i	$-0.0611616\pi$
$564$	−34.8038			−1.46551
$565$		0			0
$566$	1.95028	−	1.95028i	0.0819762	−	0.0819762i
$567$	16.0512	+	16.0512i	0.674089	+	0.674089i
$568$	−0.613878			−0.0257577
$569$	26.3160	+	26.3160i	1.10323	+	1.10323i	0.994019	+	0.109207i	$0.0348312\pi$
$569$	26.3160	+	26.3160i	1.10323	+	1.10323i	0.109207	+	0.994019i	$0.465169\pi$
$570$		0			0
$571$	−7.28850			−0.305014			−0.152507	−	0.988302i	$-0.548735\pi$
$571$	−7.28850			−0.305014			−0.152507	+	0.988302i	$0.548735\pi$
$572$			12.3880i			0.517969i
$573$	8.65177	+	8.65177i	0.361433	+	0.361433i
$574$			0.294651i			0.0122985i
$575$		0			0
$576$	3.75808			0.156587
$577$	14.8536			0.618365			0.309183	−	0.951003i	$-0.399945\pi$
$577$	14.8536			0.618365			0.309183	+	0.951003i	$0.399945\pi$
$578$			2.37953i			0.0989753i
$579$	−11.3402			−0.471282
$580$		0			0
$581$	−23.0957			−0.958172
$582$			4.06999i			0.168707i
$583$	−2.99733			−0.124137
$584$	−8.77146			−0.362966
$585$		0			0
$586$		−	4.20482i		−	0.173700i
$587$	−20.8980	−	20.8980i	−0.862552	−	0.862552i	0.129082	−	0.991634i	$-0.458797\pi$
$587$	−20.8980	−	20.8980i	−0.862552	−	0.862552i	−0.991634	+	0.129082i	$0.958797\pi$
$588$			7.91635i			0.326465i
$589$	22.0289			0.907686
$590$		0			0
$591$	−13.3491	−	13.3491i	−0.549110	−	0.549110i
$592$	−9.38937			−0.385901
$593$	9.91716	+	9.91716i	0.407249	+	0.407249i	0.880778	−	0.473529i	$-0.157020\pi$
$593$	9.91716	+	9.91716i	0.407249	+	0.407249i	−0.473529	+	0.880778i	$0.657020\pi$
$594$	−1.03233	+	1.03233i	−0.0423569	+	0.0423569i
$595$		0			0
$596$	−32.3146			−1.32366
$597$		−	39.2292i		−	1.60554i
$598$			1.94730i			0.0796312i
$599$	−16.5929	+	16.5929i	−0.677968	+	0.677968i	−0.959540	−	0.281572i	$-0.909144\pi$
$599$	−16.5929	+	16.5929i	−0.677968	+	0.677968i	0.281572	+	0.959540i	$0.409144\pi$
$600$		0			0
$601$	−11.6957	−	11.6957i	−0.477079	−	0.477079i	0.427118	−	0.904196i	$-0.359529\pi$
$601$	−11.6957	−	11.6957i	−0.477079	−	0.477079i	−0.904196	+	0.427118i	$0.859529\pi$
$602$	2.97112	−	2.97112i	0.121094	−	0.121094i
$603$	2.46976	−	2.46976i	0.100576	−	0.100576i
$604$		−	5.45335i		−	0.221894i
$605$		0			0
$606$	−1.31057	+	1.31057i	−0.0532383	+	0.0532383i
$607$	−11.6762			−0.473921			−0.236961	−	0.971519i	$-0.576151\pi$
$607$	−11.6762			−0.473921			−0.236961	+	0.971519i	$0.576151\pi$
$608$	4.85866	+	4.85866i	0.197045	+	0.197045i
$609$	9.61891	−	20.0978i	0.389778	−	0.814404i
$610$		0			0
$611$	25.8378	+	25.8378i	1.04529	+	1.04529i
$612$		−	2.23571i		−	0.0903730i
$613$	−18.8812	−	18.8812i	−0.762605	−	0.762605i	0.214188	−	0.976793i	$-0.431290\pi$
$613$	−18.8812	−	18.8812i	−0.762605	−	0.762605i	−0.976793	+	0.214188i	$0.931290\pi$
$614$	−1.27119			−0.0513011
$615$		0			0
$616$	2.74461			0.110584
$617$	11.3496			0.456916			0.228458	−	0.973554i	$-0.426632\pi$
$617$	11.3496			0.456916			0.228458	+	0.973554i	$0.426632\pi$
$618$	1.41560	+	1.41560i	0.0569437	+	0.0569437i
$619$	−6.62460	−	6.62460i	−0.266265	−	0.266265i	0.561328	−	0.827593i	$-0.310291\pi$
$619$	−6.62460	−	6.62460i	−0.266265	−	0.266265i	−0.827593	+	0.561328i	$0.810291\pi$
$620$		0			0
$621$	8.56757	−	8.56757i	0.343805	−	0.343805i
$622$	−4.39238	+	4.39238i	−0.176119	+	0.176119i
$623$	11.9456			0.478590
$624$	−19.4223	−	19.4223i	−0.777516	−	0.777516i
$625$		0			0
$626$	−3.93564	−	3.93564i	−0.157300	−	0.157300i
$627$	−9.32519			−0.372412
$628$	1.82963			0.0730102
$629$			5.36387i			0.213872i
$630$		0			0
$631$		−	16.5965i		−	0.660696i	−0.943859	−	0.330348i	$-0.892834\pi$
$631$		−	16.5965i		−	0.660696i	0.943859	−	0.330348i	$-0.107166\pi$
$632$	1.60274	+	1.60274i	0.0637537	+	0.0637537i
$633$	−2.14424	+	2.14424i	−0.0852260	+	0.0852260i
$634$		−	4.68432i		−	0.186038i
$635$		0			0
$636$	4.79178	−	4.79178i	0.190007	−	0.190007i
$637$	5.87698	−	5.87698i	0.232854	−	0.232854i
$638$	1.52721	+	0.730929i	0.0604627	+	0.0289377i
$639$			0.423968i			0.0167719i
$640$		0			0
$641$	−23.3026	−	23.3026i	−0.920396	−	0.920396i	0.0766614	−	0.997057i	$-0.475574\pi$
$641$	−23.3026	−	23.3026i	−0.920396	−	0.920396i	−0.997057	+	0.0766614i	$0.975574\pi$
$642$	−4.07941	+	4.07941i	−0.161001	+	0.161001i
$643$	−15.9279	−	15.9279i	−0.628133	−	0.628133i	0.319465	−	0.947598i	$-0.396497\pi$
$643$	−15.9279	−	15.9279i	−0.628133	−	0.628133i	−0.947598	+	0.319465i	$0.896497\pi$
$644$	−11.2823			−0.444585
$645$		0			0
$646$	0.896033	−	0.896033i	0.0352539	−	0.0352539i
$647$	−22.0404	+	22.0404i	−0.866497	+	0.866497i	−0.992083	−	0.125586i	$-0.959919\pi$
$647$	−22.0404	+	22.0404i	−0.866497	+	0.866497i	0.125586	+	0.992083i	$0.459919\pi$
$648$		−	7.87361i		−	0.309305i
$649$	2.80691	−	2.80691i	0.110181	−	0.110181i
$650$		0			0
$651$			29.9343i			1.17322i
$652$		−	24.9192i		−	0.975912i
$653$		−	27.2009i		−	1.06445i	−0.846602	−	0.532227i	$-0.821355\pi$
$653$		−	27.2009i		−	1.06445i	0.846602	−	0.532227i	$-0.178645\pi$
$654$		−	2.36175i		−	0.0923516i
$655$		0			0
$656$	−1.85338	+	1.85338i	−0.0723623	+	0.0723623i
$657$			6.05792i			0.236342i
$658$	2.83538	−	2.83538i	0.110535	−	0.110535i
$659$	−4.67457	+	4.67457i	−0.182095	+	0.182095i	−0.792268	−	0.610173i	$-0.791100\pi$
$659$	−4.67457	+	4.67457i	−0.182095	+	0.182095i	0.610173	+	0.792268i	$0.291100\pi$
$660$		0			0
$661$	0.289878			0.0112749			0.00563747	−	0.999984i	$-0.498206\pi$
$661$	0.289878			0.0112749			0.00563747	+	0.999984i	$0.498206\pi$
$662$	1.66307	+	1.66307i	0.0646371	+	0.0646371i
$663$	−11.0954	+	11.0954i	−0.430910	+	0.430910i
$664$	5.66457	+	5.66457i	0.219828	+	0.219828i
$665$		0			0
$666$		−	0.252852i		−	0.00979782i
$667$	−12.6747	−	6.06619i	−0.490767	−	0.234884i
$668$	−21.7531	+	21.7531i	−0.841654	+	0.841654i
$669$	−34.7080	+	34.7080i	−1.34189	+	1.34189i
$670$		0			0
$671$			7.66747i			0.295999i
$672$	−6.60224	+	6.60224i	−0.254687	+	0.254687i
$673$	12.7489	+	12.7489i	0.491434	+	0.491434i	0.908758	−	0.417324i	$-0.137032\pi$
$673$	12.7489	+	12.7489i	0.491434	+	0.491434i	−0.417324	+	0.908758i	$0.637032\pi$
$674$		−	5.15896i		−	0.198716i
$675$		0			0
$676$			3.88847i			0.149557i
$677$	4.24368			0.163098			0.0815489	−	0.996669i	$-0.474013\pi$
$677$	4.24368			0.163098			0.0815489	+	0.996669i	$0.474013\pi$
$678$	6.90384			0.265140
$679$	17.5060	+	17.5060i	0.671819	+	0.671819i
$680$		0			0
$681$	−34.8923	−	34.8923i	−1.33708	−	1.33708i
$682$	−2.27467			−0.0871014
$683$	−31.3545	+	31.3545i	−1.19975	+	1.19975i	−0.225504	+	0.974242i	$0.572403\pi$
$683$	−31.3545	+	31.3545i	−1.19975	+	1.19975i	−0.974242	+	0.225504i	$0.927597\pi$
$684$	2.23008	−	2.23008i	0.0852693	−	0.0852693i
$685$		0			0
$686$	−2.74730	−	2.74730i	−0.104892	−	0.104892i
$687$	−32.3306	−	32.3306i	−1.23349	−	1.23349i
$688$	37.3772			1.42499
$689$	−7.11469			−0.271048
$690$		0			0
$691$	−29.5226			−1.12309			−0.561546	−	0.827445i	$-0.689793\pi$
$691$	−29.5226			−1.12309			−0.561546	+	0.827445i	$0.689793\pi$
$692$	−25.2908	−	25.2908i	−0.961411	−	0.961411i
$693$		−	1.89554i		−	0.0720056i
$694$	−3.55781	−	3.55781i	−0.135053	−	0.135053i
$695$		0			0
$696$	−7.28847	+	2.57011i	−0.276269	+	0.0974196i
$697$	1.05878	+	1.05878i	0.0401042	+	0.0401042i
$698$	−4.67868			−0.177091
$699$	−38.0626	+	38.0626i	−1.43966	+	1.43966i
$700$		0			0
$701$			19.9925i			0.755105i	0.925988	+	0.377552i	$0.123234\pi$
$701$			19.9925i			0.755105i	−0.925988	+	0.377552i	$0.876766\pi$
$702$	−2.45041	+	2.45041i	−0.0924848	+	0.0924848i
$703$	−5.35038	+	5.35038i	−0.201793	+	0.201793i
$704$	8.21122	+	8.21122i	0.309472	+	0.309472i
$705$		0			0
$706$	−4.18998	+	4.18998i	−0.157692	+	0.157692i
$707$			11.2742i			0.424008i
$708$			8.97473i			0.337291i
$709$	−52.1626			−1.95901			−0.979503	−	0.201429i	$-0.935442\pi$
$709$	−52.1626			−1.95901			−0.979503	+	0.201429i	$0.935442\pi$
$710$		0			0
$711$	1.10692	−	1.10692i	0.0415127	−	0.0415127i
$712$	−2.92983	−	2.92983i	−0.109800	−	0.109800i
$713$	18.8781			0.706990
$714$	1.21758	+	1.21758i	0.0455669	+	0.0455669i
$715$		0			0
$716$	−41.4193			−1.54791
$717$			42.3166i			1.58034i
$718$	4.36424	+	4.36424i	0.162872	+	0.162872i
$719$		−	40.9120i		−	1.52576i	−0.646541	−	0.762879i	$-0.723785\pi$
$719$		−	40.9120i		−	1.52576i	0.646541	−	0.762879i	$-0.276215\pi$
$720$		0			0
$721$	12.1776			0.453519
$722$	−1.87589			−0.0698134
$723$			40.4169i			1.50312i
$724$	−25.0323			−0.930319
$725$		0			0
$726$	−3.02069			−0.112108
$727$		−	53.5853i		−	1.98737i	−0.112209	−	0.993685i	$-0.535793\pi$
$727$		−	53.5853i		−	1.98737i	0.112209	−	0.993685i	$-0.464207\pi$
$728$	6.51483			0.241456
$729$	20.7267			0.767657
$730$		0			0
$731$		−	21.3525i		−	0.789751i
$732$	−12.2579	−	12.2579i	−0.453064	−	0.453064i
$733$			25.8493i			0.954765i	0.878695	+	0.477383i	$0.158414\pi$
$733$			25.8493i			0.954765i	−0.878695	+	0.477383i	$0.841586\pi$
$734$	1.83723			0.0678134
$735$		0			0
$736$	4.16371	+	4.16371i	0.153476	+	0.153476i
$737$	10.7926			0.397551
$738$	−0.0499108	−	0.0499108i	−0.00183724	−	0.00183724i
$739$	16.3056	−	16.3056i	0.599810	−	0.599810i	−0.340452	−	0.940262i	$-0.610580\pi$
$739$	16.3056	−	16.3056i	0.599810	−	0.599810i	0.940262	+	0.340452i	$0.110580\pi$
$740$		0			0
$741$	−22.1350			−0.813149
$742$			0.780750i			0.0286622i
$743$		−	4.30076i		−	0.157780i	−0.996883	−	0.0788898i	$-0.974862\pi$
$743$		−	4.30076i		−	0.157780i	0.996883	−	0.0788898i	$-0.0251375\pi$
$744$	7.34182	−	7.34182i	0.269164	−	0.269164i
$745$		0			0
$746$	2.71743	+	2.71743i	0.0994922	+	0.0994922i
$747$	3.91218	−	3.91218i	0.143139	−	0.143139i
$748$	4.88491	−	4.88491i	0.178610	−	0.178610i
$749$			35.0930i			1.28227i
$750$		0			0
$751$	20.6415	−	20.6415i	0.753217	−	0.753217i	−0.221861	−	0.975078i	$-0.571213\pi$
$751$	20.6415	−	20.6415i	0.753217	−	0.753217i	0.975078	+	0.221861i	$0.0712131\pi$
$752$	35.6696			1.30074
$753$	−30.7586	−	30.7586i	−1.12090	−	1.12090i
$754$	3.62510	+	1.73499i	0.132018	+	0.0631846i
$755$		0			0
$756$	−14.1972	−	14.1972i	−0.516348	−	0.516348i
$757$			42.3352i			1.53870i	0.638829	+	0.769349i	$0.279419\pi$
$757$			42.3352i			1.53870i	−0.638829	+	0.769349i	$0.720581\pi$
$758$	−2.10226	−	2.10226i	−0.0763575	−	0.0763575i
$759$	−7.99139			−0.290069
$760$		0			0
$761$	−21.6547			−0.784984			−0.392492	−	0.919756i	$-0.628387\pi$
$761$	−21.6547			−0.784984			−0.392492	+	0.919756i	$0.628387\pi$
$762$	2.22216			0.0805003
$763$	−10.1584	−	10.1584i	−0.367760	−	0.367760i
$764$	−9.04148	−	9.04148i	−0.327109	−	0.327109i
$765$		0			0
$766$	−0.190869	+	0.190869i	−0.00689636	+	0.00689636i
$767$	6.66270	−	6.66270i	0.240576	−	0.240576i
$768$	−24.6198			−0.888391
$769$	−26.0688	−	26.0688i	−0.940065	−	0.940065i	0.0582378	−	0.998303i	$-0.481452\pi$
$769$	−26.0688	−	26.0688i	−0.940065	−	0.940065i	−0.998303	+	0.0582378i	$0.981452\pi$
$770$		0			0
$771$	5.00932	+	5.00932i	0.180406	+	0.180406i
$772$	11.8510			0.426527
$773$	−21.7119			−0.780922			−0.390461	−	0.920619i	$-0.627684\pi$
$773$	−21.7119			−0.780922			−0.390461	+	0.920619i	$0.627684\pi$
$774$			1.00655i			0.0361798i
$775$		0			0
$776$		−	8.58721i		−	0.308263i
$777$	−7.27042	−	7.27042i	−0.260825	−	0.260825i
$778$	−0.609039	+	0.609039i	−0.0218351	+	0.0218351i
$779$			2.11223i			0.0756787i
$780$		0			0
$781$	−0.926350	+	0.926350i	−0.0331474	+	0.0331474i
$782$	0.767871	−	0.767871i	0.0274590	−	0.0274590i
$783$	−8.31591	−	23.5828i	−0.297187	−	0.842781i
$784$		−	8.11328i		−	0.289760i
$785$		0			0
$786$	5.68257	+	5.68257i	0.202691	+	0.202691i
$787$	−2.90929	+	2.90929i	−0.103705	+	0.103705i	−0.757056	−	0.653351i	$-0.773363\pi$
$787$	−2.90929	+	2.90929i	−0.103705	+	0.103705i	0.653351	+	0.757056i	$0.273363\pi$
$788$	13.9504	+	13.9504i	0.496964	+	0.496964i
$789$	40.1019			1.42766
$790$		0			0
$791$	29.6950	−	29.6950i	1.05583	−	1.05583i
$792$	−0.464909	+	0.464909i	−0.0165198	+	0.0165198i
$793$			18.2001i			0.646304i
$794$	−0.347273	+	0.347273i	−0.0123243	+	0.0123243i
$795$		0			0
$796$			40.9963i			1.45307i
$797$			6.97586i			0.247098i	0.992339	+	0.123549i	$0.0394275\pi$
$797$			6.97586i			0.247098i	−0.992339	+	0.123549i	$0.960572\pi$
$798$			2.42904i			0.0859871i
$799$		−	20.3770i		−	0.720887i
$800$		0			0
$801$	−2.02346	+	2.02346i	−0.0714954	+	0.0714954i
$802$			2.01189i			0.0710423i
$803$	−13.2363	+	13.2363i	−0.467098	+	0.467098i
$804$	−17.2540	+	17.2540i	−0.608502	+	0.608502i
$805$		0			0
$806$	−5.39932			−0.190183
$807$	−14.0702	−	14.0702i	−0.495294	−	0.495294i
$808$	2.76515	−	2.76515i	0.0972778	−	0.0972778i
$809$	26.8378	+	26.8378i	0.943568	+	0.943568i	0.998491	−	0.0549228i	$-0.0174913\pi$
$809$	26.8378	+	26.8378i	0.943568	+	0.943568i	−0.0549228	+	0.998491i	$0.517491\pi$
$810$		0			0
$811$			15.8850i			0.557798i	0.960320	+	0.278899i	$0.0899694\pi$
$811$			15.8850i			0.557798i	−0.960320	+	0.278899i	$0.910031\pi$
$812$	−10.0522	+	21.0031i	−0.352763	+	0.737065i
$813$	−15.2977	+	15.2977i	−0.536513	+	0.536513i
$814$	0.552470	−	0.552470i	0.0193640	−	0.0193640i
$815$		0			0
$816$			15.3174i			0.536217i
$817$	21.2988	−	21.2988i	0.745150	−	0.745150i
$818$	−1.95640	−	1.95640i	−0.0684039	−	0.0684039i
$819$		−	4.49940i		−	0.157222i
$820$		0			0
$821$		−	31.4307i		−	1.09694i	−0.836171	−	0.548469i	$-0.815211\pi$
$821$		−	31.4307i		−	1.09694i	0.836171	−	0.548469i	$-0.184789\pi$
$822$	−4.51234			−0.157386
$823$	16.4642			0.573905			0.286953	−	0.957945i	$-0.407358\pi$
$823$	16.4642			0.573905			0.286953	+	0.957945i	$0.407358\pi$
$824$	−2.98675	−	2.98675i	−0.104048	−	0.104048i
$825$		0			0
$826$	−0.731149	−	0.731149i	−0.0254399	−	0.0254399i
$827$	−40.2890			−1.40099			−0.700493	−	0.713659i	$-0.747037\pi$
$827$	−40.2890			−1.40099			−0.700493	+	0.713659i	$0.747037\pi$
$828$	1.91111	−	1.91111i	0.0664156	−	0.0664156i
$829$	−32.5842	+	32.5842i	−1.13170	+	1.13170i	−0.141801	+	0.989895i	$0.545289\pi$
$829$	−32.5842	+	32.5842i	−1.13170	+	1.13170i	−0.989895	+	0.141801i	$0.954711\pi$
$830$		0			0
$831$	−4.30535	−	4.30535i	−0.149351	−	0.149351i
$832$	19.4908	+	19.4908i	0.675721	+	0.675721i
$833$	−4.63488			−0.160589
$834$	0.670436			0.0232153
$835$		0			0
$836$	9.74524			0.337046
$837$	23.7554	+	23.7554i	0.821108	+	0.821108i
$838$		−	5.68849i		−	0.196505i
$839$	21.8745	+	21.8745i	0.755193	+	0.755193i	0.975443	−	0.220250i	$-0.0706874\pi$
$839$	21.8745	+	21.8745i	0.755193	+	0.755193i	−0.220250	+	0.975443i	$0.570687\pi$
$840$		0			0
$841$	−22.5856	+	18.1904i	−0.778813	+	0.627256i
$842$	−2.36221	−	2.36221i	−0.0814072	−	0.0814072i
$843$	30.1272			1.03764
$844$	2.24083	−	2.24083i	0.0771326	−	0.0771326i
$845$		0			0
$846$			0.960569i			0.0330250i
$847$	−12.9927	+	12.9927i	−0.446435	+	0.446435i
$848$	−4.91099	+	4.91099i	−0.168644	+	0.168644i
$849$	18.9979	+	18.9979i	0.652007	+	0.652007i
$850$		0			0
$851$	−4.58510	+	4.58510i	−0.157175	+	0.157175i
$852$		−	2.96189i		−	0.101473i
$853$		−	42.3889i		−	1.45137i	−0.688028	−	0.725684i	$-0.741524\pi$
$853$		−	42.3889i		−	1.45137i	0.688028	−	0.725684i	$-0.258476\pi$
$854$	1.99724			0.0683440
$855$		0			0
$856$	8.60707	−	8.60707i	0.294184	−	0.294184i
$857$	0.623109	+	0.623109i	0.0212850	+	0.0212850i	0.717669	−	0.696384i	$-0.245209\pi$
$857$	0.623109	+	0.623109i	0.0212850	+	0.0212850i	−0.696384	+	0.717669i	$0.745209\pi$
$858$	2.28562			0.0780296
$859$	1.31996	+	1.31996i	0.0450364	+	0.0450364i	0.729266	−	0.684230i	$-0.239862\pi$
$859$	1.31996	+	1.31996i	0.0450364	+	0.0450364i	−0.684230	+	0.729266i	$0.739862\pi$
$860$		0			0
$861$	−2.87023			−0.0978173
$862$			3.82275i			0.130203i
$863$	2.30417	+	2.30417i	0.0784348	+	0.0784348i	0.745236	−	0.666801i	$-0.232337\pi$
$863$	2.30417	+	2.30417i	0.0784348	+	0.0784348i	−0.666801	+	0.745236i	$0.732337\pi$
$864$			10.4789i			0.356499i
$865$		0			0
$866$	0.346928			0.0117891
$867$	−23.1793			−0.787211
$868$		−	31.2826i		−	1.06180i
$869$	4.83713			0.164088
$870$		0			0
$871$	25.6182			0.868040
$872$			4.98301i			0.168746i
$873$	−5.93067			−0.200723
$874$	1.53188			0.0518166
$875$		0			0
$876$		−	42.3212i		−	1.42990i
$877$	4.53313	+	4.53313i	0.153073	+	0.153073i	0.779489	−	0.626416i	$-0.215479\pi$
$877$	4.53313	+	4.53313i	0.153073	+	0.153073i	−0.626416	+	0.779489i	$0.715479\pi$
$878$			4.78144i			0.161366i
$879$	40.9598			1.38154
$880$		0			0
$881$	11.8964	+	11.8964i	0.400799	+	0.400799i	0.878515	−	0.477715i	$-0.158535\pi$
$881$	11.8964	+	11.8964i	0.400799	+	0.400799i	−0.477715	+	0.878515i	$0.658535\pi$
$882$	0.218488			0.00735686
$883$	−8.01660	−	8.01660i	−0.269780	−	0.269780i	0.559231	−	0.829012i	$-0.311096\pi$
$883$	−8.01660	−	8.01660i	−0.269780	−	0.269780i	−0.829012	+	0.559231i	$0.811096\pi$
$884$	11.5952	−	11.5952i	0.389989	−	0.389989i
$885$		0			0
$886$	3.07131			0.103183
$887$			25.8619i			0.868358i	0.900827	+	0.434179i	$0.142961\pi$
$887$			25.8619i			0.868358i	−0.900827	+	0.434179i	$0.857039\pi$
$888$			3.56636i			0.119679i
$889$	9.55802	−	9.55802i	0.320566	−	0.320566i
$890$		0			0
$891$	−11.8814	−	11.8814i	−0.398042	−	0.398042i
$892$	36.2715	−	36.2715i	1.21446	−	1.21446i
$893$	20.3257	−	20.3257i	0.680175	−	0.680175i
$894$			5.96212i			0.199403i
$895$		0			0
$896$	9.16919	−	9.16919i	0.306321	−	0.306321i
$897$	−18.9690			−0.633356
$898$	1.53899	+	1.53899i	0.0513567	+	0.0513567i
$899$	16.8198	−	35.1434i	0.560972	−	1.17210i
$900$		0			0
$901$	2.80550	+	2.80550i	0.0934649	+	0.0934649i
$902$		−	0.218105i		−	0.00726211i
$903$	28.9421	+	28.9421i	0.963132	+	0.963132i
$904$	−14.5663			−0.484468
$905$		0			0
$906$	−1.00616			−0.0334273
$907$	2.91928			0.0969330			0.0484665	−	0.998825i	$-0.484567\pi$
$907$	2.91928			0.0969330			0.0484665	+	0.998825i	$0.484567\pi$
$908$	36.4640	+	36.4640i	1.21010	+	1.21010i
$909$	−1.90973	−	1.90973i	−0.0633416	−	0.0633416i
$910$		0			0
$911$	9.89240	−	9.89240i	0.327750	−	0.327750i	−0.523980	−	0.851730i	$-0.675553\pi$
$911$	9.89240	−	9.89240i	0.327750	−	0.327750i	0.851730	+	0.523980i	$0.175553\pi$
$912$	−15.2789	+	15.2789i	−0.505935	+	0.505935i
$913$	17.0958			0.565790
$914$	−4.12499	−	4.12499i	−0.136443	−	0.136443i
$915$		0			0
$916$	33.7869	+	33.7869i	1.11635	+	1.11635i
$917$	48.8841			1.61430
$918$	1.93252			0.0637826
$919$		−	41.5614i		−	1.37098i	−0.728080	−	0.685492i	$-0.759587\pi$
$919$		−	41.5614i		−	1.37098i	0.728080	−	0.685492i	$-0.240413\pi$
$920$		0			0
$921$		−	12.3829i		−	0.408029i
$922$	2.91343	+	2.91343i	0.0959488	+	0.0959488i
$923$	−2.19886	+	2.19886i	−0.0723763	+	0.0723763i
$924$			13.2424i			0.435644i
$925$		0			0
$926$	0.737542	−	0.737542i	0.0242371	−	0.0242371i
$927$	−2.06277	+	2.06277i	−0.0677502	+	0.0677502i
$928$	11.4609	−	4.04141i	0.376222	−	0.132666i
$929$			38.2809i			1.25596i	0.778231	+	0.627978i	$0.216117\pi$
$929$			38.2809i			1.25596i	−0.778231	+	0.627978i	$0.783883\pi$
$930$		0			0
$931$	−4.62322	−	4.62322i	−0.151520	−	0.151520i
$932$	39.7772	−	39.7772i	1.30294	−	1.30294i
$933$	−42.7868	−	42.7868i	−1.40078	−	1.40078i
$934$	1.13522			0.0371455
$935$		0			0
$936$	−1.10354	+	1.10354i	−0.0360705	+	0.0360705i
$937$	21.8574	−	21.8574i	0.714051	−	0.714051i	−0.253329	−	0.967380i	$-0.581526\pi$
$937$	21.8574	−	21.8574i	0.714051	−	0.714051i	0.967380	+	0.253329i	$0.0815255\pi$
$938$		−	2.81128i		−	0.0917916i
$939$	38.3376	−	38.3376i	1.25110	−	1.25110i
$940$		0			0
$941$			18.5149i			0.603570i	0.953376	+	0.301785i	$0.0975825\pi$
$941$			18.5149i			0.603570i	−0.953376	+	0.301785i	$0.902418\pi$
$942$		−	0.337571i		−	0.0109986i
$943$			1.81012i			0.0589455i
$944$		−	9.19799i		−	0.299369i
$945$		0			0
$946$	−2.19927	+	2.19927i	−0.0715044	+	0.0715044i
$947$		−	19.9673i		−	0.648851i	−0.945911	−	0.324426i	$-0.894829\pi$
$947$		−	19.9673i		−	0.648851i	0.945911	−	0.324426i	$-0.105171\pi$
$948$	−7.73304	+	7.73304i	−0.251157	+	0.251157i
$949$	−31.4186	+	31.4186i	−1.01989	+	1.01989i
$950$		0			0
$951$	45.6307			1.47968
$952$	−2.56896	−	2.56896i	−0.0832605	−	0.0832605i
$953$	29.4327	−	29.4327i	0.953419	−	0.953419i	−0.0455438	−	0.998962i	$-0.514502\pi$
$953$	29.4327	−	29.4327i	0.953419	−	0.953419i	0.998962	+	0.0455438i	$0.0145021\pi$
$954$	−0.132251	−	0.132251i	−0.00428178	−	0.00428178i
$955$		0			0
$956$		−	44.2227i		−	1.43027i
$957$	−7.12008	+	14.8767i	−0.230160	+	0.480897i
$958$	−1.30672	+	1.30672i	−0.0422183	+	0.0422183i
$959$	−19.4086	+	19.4086i	−0.626738	+	0.626738i
$960$		0			0
$961$			21.3436i			0.688502i
$962$	1.31138	−	1.31138i	0.0422807	−	0.0422807i
$963$	−5.94439	−	5.94439i	−0.191555	−	0.191555i
$964$		−	42.2375i		−	1.36038i
$965$		0			0
$966$			2.08161i			0.0669747i
$967$	−3.89596			−0.125286			−0.0626428	−	0.998036i	$-0.519953\pi$
$967$	−3.89596			−0.125286			−0.0626428	+	0.998036i	$0.519953\pi$
$968$	6.37331			0.204846
$969$	8.72838	+	8.72838i	0.280396	+	0.280396i
$970$		0			0
$971$	19.4738	+	19.4738i	0.624944	+	0.624944i	0.946792	−	0.321847i	$-0.104304\pi$
$971$	19.4738	+	19.4738i	0.624944	+	0.624944i	−0.321847	+	0.946792i	$0.604304\pi$
$972$	10.6461			0.341473
$973$	2.88370	−	2.88370i	0.0924473	−	0.0924473i
$974$	1.52888	−	1.52888i	0.0489884	−	0.0489884i
$975$		0			0
$976$	12.5628	+	12.5628i	0.402125	+	0.402125i
$977$	5.83126	+	5.83126i	0.186558	+	0.186558i	0.794206	−	0.607648i	$-0.207887\pi$
$977$	5.83126	+	5.83126i	0.186558	+	0.186558i	−0.607648	+	0.794206i	$0.707887\pi$
$978$	−4.59765			−0.147017
$979$	−8.84232			−0.282602
$980$		0			0
$981$	3.44147			0.109878
$982$	0.127469	+	0.127469i	0.00406770	+	0.00406770i
$983$		−	0.962476i		−	0.0306982i	−0.999882	−	0.0153491i	$-0.995114\pi$
$983$		−	0.962476i		−	0.0306982i	0.999882	−	0.0153491i	$-0.00488596\pi$
$984$	0.703967	+	0.703967i	0.0224417	+	0.0224417i
$985$		0			0
$986$	−0.745317	−	2.11362i	−0.0237357	−	0.0673113i
$987$	27.6199	+	27.6199i	0.879150	+	0.879150i
$988$	23.1321			0.735929
$989$	18.2524	−	18.2524i	0.580392	−	0.580392i
$990$		0			0
$991$			49.5984i			1.57554i	0.615967	+	0.787772i	$0.288765\pi$
$991$			49.5984i			1.57554i	−0.615967	+	0.787772i	$0.711235\pi$
$992$	−11.5448	+	11.5448i	−0.366547	+	0.366547i
$993$	−16.2002	+	16.2002i	−0.514098	+	0.514098i
$994$	0.241297	+	0.241297i	0.00765349	+	0.00765349i
$995$		0			0
$996$	−27.3309	+	27.3309i	−0.866012	+	0.866012i
$997$			21.7128i			0.687651i	0.939033	+	0.343826i	$0.111723\pi$
$997$			21.7128i			0.687651i	−0.939033	+	0.343826i	$0.888277\pi$
$998$			4.96310i			0.157104i
$999$	−11.5394			−0.365091

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	725.2.e.b.157.5	yes	16
5.2	odd	4		725.2.j.b.418.4	yes	16
5.3	odd	4		725.2.j.b.418.5	yes	16
5.4	even	2	inner	725.2.e.b.157.4	✓	16
29.17	odd	4		725.2.j.b.307.5	yes	16
145.17	even	4	inner	725.2.e.b.568.5	yes	16
145.104	odd	4		725.2.j.b.307.4	yes	16
145.133	even	4	inner	725.2.e.b.568.4	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
725.2.e.b.157.4	✓	16	5.4	even	2	inner
725.2.e.b.157.5	yes	16	1.1	even	1	trivial
725.2.e.b.568.4	yes	16	145.133	even	4	inner
725.2.e.b.568.5	yes	16	145.17	even	4	inner
725.2.j.b.307.4	yes	16	145.104	odd	4
725.2.j.b.307.5	yes	16	29.17	odd	4
725.2.j.b.418.4	yes	16	5.2	odd	4
725.2.j.b.418.5	yes	16	5.3	odd	4

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:	\( N \)	\(=\)	\( 725 = 5^{2} \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	725.e (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+0.192813i q^{2} -1.87822 q^{3} +1.96282 q^{4} -0.362145i q^{6} +(-1.55767 - 1.55767i) q^{7} +0.764084i q^{8} +0.527707 q^{9} +(1.15301 + 1.15301i) q^{11} -3.68661 q^{12} +(2.73688 + 2.73688i) q^{13} +(0.300339 - 0.300339i) q^{14} +3.77832 q^{16} -2.15844i q^{17} +0.101749i q^{18} +(2.15301 - 2.15301i) q^{19} +(2.92565 + 2.92565i) q^{21} +(-0.222316 + 0.222316i) q^{22} +(1.84506 - 1.84506i) q^{23} -1.43512i q^{24} +(-0.527707 + 0.527707i) q^{26} +4.64351 q^{27} +(-3.05743 - 3.05743i) q^{28} +(-1.79087 - 5.07866i) q^{29} +(5.11584 + 5.11584i) q^{31} +2.25668i q^{32} +(-2.16561 - 2.16561i) q^{33} +0.416176 q^{34} +1.03579 q^{36} -2.48506 q^{37} +(0.415129 + 0.415129i) q^{38} +(-5.14047 - 5.14047i) q^{39} +(-0.490530 + 0.490530i) q^{41} +(-0.564103 + 0.564103i) q^{42} +9.89254 q^{43} +(2.26316 + 2.26316i) q^{44} +(0.355752 + 0.355752i) q^{46} +9.44060 q^{47} -7.09651 q^{48} -2.14733i q^{49} +4.05403i q^{51} +(5.37202 + 5.37202i) q^{52} +(-1.29978 + 1.29978i) q^{53} +0.895329i q^{54} +(1.19019 - 1.19019i) q^{56} +(-4.04383 + 4.04383i) q^{57} +(0.979232 - 0.345303i) q^{58} -2.43441i q^{59} +(3.32497 + 3.32497i) q^{61} +(-0.986400 + 0.986400i) q^{62} +(-0.821993 - 0.821993i) q^{63} +7.12153 q^{64} +(0.417558 - 0.417558i) q^{66} +(4.68018 - 4.68018i) q^{67} -4.23664i q^{68} +(-3.46543 + 3.46543i) q^{69} +0.803417i q^{71} +0.403212i q^{72} +11.4797i q^{73} -0.479153i q^{74} +(4.22599 - 4.22599i) q^{76} -3.59203i q^{77} +(0.991149 - 0.991149i) q^{78} +(2.09760 - 2.09760i) q^{79} -10.3046 q^{81} +(-0.0945805 - 0.0945805i) q^{82} +(7.41355 - 7.41355i) q^{83} +(5.74253 + 5.74253i) q^{84} +1.90741i q^{86} +(3.36364 + 9.53884i) q^{87} +(-0.880999 + 0.880999i) q^{88} +(-3.83444 + 3.83444i) q^{89} -8.52632i q^{91} +(3.62153 - 3.62153i) q^{92} +(-9.60866 - 9.60866i) q^{93} +1.82027i q^{94} -4.23853i q^{96} -11.2386 q^{97} +0.414032 q^{98} +(0.608453 + 0.608453i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{4} + 40 q^{9} - 4 q^{11} - 20 q^{14} - 16 q^{16} + 12 q^{19} - 32 q^{21} - 40 q^{26} + 4 q^{29} + 20 q^{31} - 80 q^{34} - 104 q^{36} - 16 q^{39} - 28 q^{44} + 44 q^{46} + 36 q^{56} + 24 q^{61}+ \cdots + 92 q^{99}+O(q^{100}) \) 16 * q - 8 * q^4 + 40 * q^9 - 4 * q^11 - 20 * q^14 - 16 * q^16 + 12 * q^19 - 32 * q^21 - 40 * q^26 + 4 * q^29 + 20 * q^31 - 80 * q^34 - 104 * q^36 - 16 * q^39 - 28 * q^44 + 44 * q^46 + 36 * q^56 + 24 * q^61 + 32 * q^64 + 80 * q^66 + 40 * q^69 - 36 * q^76 - 52 * q^79 + 40 * q^81 + 136 * q^84 - 40 * q^89 + 92 * q^99

Introduction

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