LMFDB - Embedded newform 725.2.j.b.418.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [725,2,Mod(307,725)]

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, 3]))

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

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

chi := DirichletCharacter("725.307");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 725 = 5^{2} \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	725.j (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			418.5
Root			$-0.807187i$ of defining polynomial
Character	$\chi$	$=$	725.418
Dual form			725.2.j.b.307.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+0.192813 q^{2} -1.87822i q^{3} -1.96282 q^{4} -0.362145i q^{6} +(-1.55767 + 1.55767i) q^{7} -0.764084 q^{8} -0.527707 q^{9} +(1.15301 + 1.15301i) q^{11} +3.68661i q^{12} +(-2.73688 + 2.73688i) q^{13} +(-0.300339 + 0.300339i) q^{14} +3.77832 q^{16} -2.15844 q^{17} -0.101749 q^{18} +(-2.15301 + 2.15301i) q^{19} +(2.92565 + 2.92565i) q^{21} +(0.222316 + 0.222316i) q^{22} +(1.84506 + 1.84506i) q^{23} +1.43512i q^{24} +(-0.527707 + 0.527707i) q^{26} -4.64351i q^{27} +(3.05743 - 3.05743i) q^{28} +(1.79087 + 5.07866i) q^{29} +(5.11584 + 5.11584i) q^{31} +2.25668 q^{32} +(2.16561 - 2.16561i) q^{33} -0.416176 q^{34} +1.03579 q^{36} +2.48506i q^{37} +(-0.415129 + 0.415129i) q^{38} +(5.14047 + 5.14047i) q^{39} +(-0.490530 + 0.490530i) q^{41} +(0.564103 + 0.564103i) q^{42} +9.89254i q^{43} +(-2.26316 - 2.26316i) q^{44} +(0.355752 + 0.355752i) q^{46} -9.44060i q^{47} -7.09651i q^{48} +2.14733i q^{49} +4.05403i q^{51} +(5.37202 - 5.37202i) q^{52} +(-1.29978 - 1.29978i) q^{53} -0.895329i q^{54} +(1.19019 - 1.19019i) q^{56} +(4.04383 + 4.04383i) q^{57} +(0.345303 + 0.979232i) q^{58} +2.43441i q^{59} +(3.32497 + 3.32497i) q^{61} +(0.986400 + 0.986400i) q^{62} +(0.821993 - 0.821993i) q^{63} -7.12153 q^{64} +(0.417558 - 0.417558i) q^{66} +(-4.68018 - 4.68018i) q^{67} +4.23664 q^{68} +(3.46543 - 3.46543i) q^{69} +0.803417i q^{71} +0.403212 q^{72} -11.4797 q^{73} +0.479153i q^{74} +(4.22599 - 4.22599i) q^{76} -3.59203 q^{77} +(0.991149 + 0.991149i) q^{78} +(-2.09760 + 2.09760i) q^{79} -10.3046 q^{81} +(-0.0945805 + 0.0945805i) q^{82} +(7.41355 + 7.41355i) q^{83} +(-5.74253 - 5.74253i) q^{84} +1.90741i q^{86} +(9.53884 - 3.36364i) q^{87} +(-0.880999 - 0.880999i) q^{88} +(3.83444 - 3.83444i) q^{89} -8.52632i q^{91} +(-3.62153 - 3.62153i) q^{92} +(9.60866 - 9.60866i) q^{93} -1.82027i q^{94} -4.23853i q^{96} +11.2386i q^{97} +0.414032i q^{98} +(-0.608453 - 0.608453i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/725\mathbb{Z}\right)^\times$.

$n$	$176$	$552$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$e\left(\frac{3}{4}\right)$

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 $

$2$	0.192813			0.136339			0.0681697	−	0.997674i	$-0.478284\pi$
$2$	0.192813			0.136339			0.0681697	+	0.997674i	$0.478284\pi$
$3$		−	1.87822i		−	1.08439i	−0.840253	−	0.542195i	$-0.817593\pi$
$3$		−	1.87822i		−	1.08439i	0.840253	−	0.542195i	$-0.182407\pi$
$4$	−1.96282			−0.981412
$5$		0			0
$5$		0			0
$6$		−	0.362145i		−	0.147845i
$7$	−1.55767	+	1.55767i	−0.588744	+	0.588744i	−0.937291	−	0.348547i	$-0.886675\pi$
$7$	−1.55767	+	1.55767i	−0.588744	+	0.588744i	0.348547	+	0.937291i	$0.386675\pi$
$8$	−0.764084			−0.270144
$9$	−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	$0.670942\pi$
$12$			3.68661i			1.06423i
$13$	−2.73688	+	2.73688i	−0.759075	+	0.759075i	−0.976154	−	0.217079i	$-0.930347\pi$
$13$	−2.73688	+	2.73688i	−0.759075	+	0.759075i	0.217079	+	0.976154i	$0.430347\pi$
$14$	−0.300339	+	0.300339i	−0.0802690	+	0.0802690i
$15$		0			0
$16$	3.77832			0.944580
$17$	−2.15844			−0.523500			−0.261750	−	0.965136i	$-0.584300\pi$
$17$	−2.15844			−0.523500			−0.261750	+	0.965136i	$0.584300\pi$
$18$	−0.101749			−0.0239824
$19$	−2.15301	+	2.15301i	−0.493935	+	0.493935i	−0.909544	−	0.415608i	$-0.863569\pi$
$19$	−2.15301	+	2.15301i	−0.493935	+	0.493935i	0.415608	+	0.909544i	$0.363569\pi$
$20$		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	0.872800	−	0.488078i	$-0.162302\pi$
$23$	1.84506	+	1.84506i	0.384722	+	0.384722i	−0.488078	+	0.872800i	$0.662302\pi$
$24$			1.43512i			0.292942i
$25$		0			0
$26$	−0.527707	+	0.527707i	−0.103492	+	0.103492i
$27$		−	4.64351i		−	0.893644i
$28$	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	$0.524890\pi$
$32$	2.25668			0.398928
$33$	2.16561	−	2.16561i	0.376985	−	0.376985i
$34$	−0.416176			−0.0713736
$35$		0			0
$36$	1.03579			0.172632
$37$			2.48506i			0.408542i	0.978914	+	0.204271i	$0.0654824\pi$
$37$			2.48506i			0.408542i	−0.978914	+	0.204271i	$0.934518\pi$
$38$	−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
$43$			9.89254i			1.50860i	0.656531	+	0.754299i	$0.272023\pi$
$43$			9.89254i			1.50860i	−0.656531	+	0.754299i	$0.727977\pi$
$44$	−2.26316	−	2.26316i	−0.341185	−	0.341185i
$45$		0			0
$46$	0.355752	+	0.355752i	0.0524528	+	0.0524528i
$47$		−	9.44060i		−	1.37705i	−0.725211	−	0.688527i	$-0.758258\pi$
$47$		−	9.44060i		−	1.37705i	0.725211	−	0.688527i	$-0.241742\pi$
$48$		−	7.09651i		−	1.02429i
$49$			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	0.612180	−	0.790718i	$-0.290293\pi$
$53$	−1.29978	−	1.29978i	−0.178539	−	0.178539i	−0.790718	+	0.612180i	$0.790293\pi$
$54$		−	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
$58$	0.345303	+	0.979232i	0.0453405	+	0.128579i
$59$			2.43441i			0.316934i	0.987364	+	0.158467i	$0.0506551\pi$
$59$			2.43441i			0.316934i	−0.987364	+	0.158467i	$0.949345\pi$
$60$		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	$-0.382487\pi$
$67$	−4.68018	−	4.68018i	−0.571775	−	0.571775i	−0.932624	+	0.360849i	$0.882487\pi$
$68$	4.23664			0.513769
$69$	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	$0.984819\pi$
$72$	0.403212			0.0475190
$73$	−11.4797			−1.34360			−0.671799	−	0.740733i	$-0.734478\pi$
$73$	−11.4797			−1.34360			−0.671799	+	0.740733i	$0.734478\pi$
$74$			0.479153i			0.0557004i
$75$		0			0
$76$	4.22599	−	4.22599i	0.484754	−	0.484754i
$77$	−3.59203			−0.409350
$78$	0.991149	+	0.991149i	0.112225	+	0.112225i
$79$	−2.09760	+	2.09760i	−0.235999	+	0.235999i	−0.815191	−	0.579192i	$-0.803368\pi$
$79$	−2.09760	+	2.09760i	−0.235999	+	0.235999i	0.579192	+	0.815191i	$0.303368\pi$
$80$		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	0.985193	−	0.171450i	$-0.0548453\pi$
$83$	7.41355	+	7.41355i	0.813742	+	0.813742i	−0.171450	+	0.985193i	$0.554845\pi$
$84$	−5.74253	−	5.74253i	−0.626561	−	0.626561i
$85$		0			0
$86$			1.90741i			0.205681i
$87$	9.53884	−	3.36364i	1.02267	−	0.360620i
$88$	−0.880999	−	0.880999i	−0.0939148	−	0.0939148i
$89$	3.83444	−	3.83444i	0.406450	−	0.406450i	−0.474049	−	0.880499i	$-0.657208\pi$
$89$	3.83444	−	3.83444i	0.406450	−	0.406450i	0.880499	+	0.474049i	$0.157208\pi$
$90$		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
$97$			11.2386i			1.14110i	0.821261	+	0.570552i	$0.193271\pi$
$97$			11.2386i			1.14110i	−0.821261	+	0.570552i	$0.806729\pi$
$98$			0.414032i			0.0418236i
$99$	−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	$0.831952\pi$
$102$			0.781670i			0.0773968i
$103$	−3.90893	−	3.90893i	−0.385158	−	0.385158i	0.487798	−	0.872956i	$-0.337800\pi$
$103$	−3.90893	−	3.90893i	−0.385158	−	0.385158i	−0.872956	+	0.487798i	$0.837800\pi$
$104$	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	−0.0933536	+	0.995633i	$0.529759\pi$
$107$	−11.2646	+	11.2646i	−1.08899	+	1.08899i	−0.995633	+	0.0933536i	$0.970241\pi$
$108$			9.11439i			0.877032i
$109$	−6.52155			−0.624651			−0.312326	−	0.949975i	$-0.601108\pi$
$109$	−6.52155			−0.624651			−0.312326	+	0.949975i	$0.601108\pi$
$110$		0			0
$111$	4.66749			0.443019
$112$	−5.88538	+	5.88538i	−0.556116	+	0.556116i
$113$	−19.0637			−1.79337			−0.896683	−	0.442674i	$-0.854030\pi$
$113$	−19.0637			−1.79337			−0.896683	+	0.442674i	$0.854030\pi$
$114$	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
$118$			0.469386i			0.0432105i
$119$	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
$127$	6.13610			0.544491			0.272245	−	0.962228i	$-0.412234\pi$
$127$	6.13610			0.544491			0.272245	+	0.962228i	$0.412234\pi$
$128$	−5.88648			−0.520296
$129$	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
$133$		−	6.70737i		−	0.581603i
$134$	−0.902399	−	0.902399i	−0.0779554	−	0.0779554i
$135$		0			0
$136$	1.64923			0.141420
$137$	−12.4600			−1.06453			−0.532267	−	0.846577i	$-0.678660\pi$
$137$	−12.4600			−1.06453			−0.532267	+	0.846577i	$0.678660\pi$
$138$	0.668181	−	0.668181i	0.0568793	−	0.0568793i
$139$		−	1.85129i		−	0.157025i	−0.996913	−	0.0785123i	$-0.974983\pi$
$139$		−	1.85129i		−	0.157025i	0.996913	−	0.0785123i	$-0.0250170\pi$
$140$		0			0
$141$	−17.7315			−1.49326
$142$			0.154909i			0.0129997i
$143$	−6.31133			−0.527780
$144$	−1.99384			−0.166154
$145$		0			0
$146$	−2.21344			−0.183185
$147$	4.03315			0.332648
$148$		−	4.87774i		−	0.400948i
$149$	16.4633			1.34873			0.674365	−	0.738398i	$-0.264417\pi$
$149$	16.4633			1.34873			0.674365	+	0.738398i	$0.264417\pi$
$150$		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
$153$	1.13903			0.0920847
$154$	−0.692590			−0.0558105
$155$		0			0
$156$	−10.0898	−	10.0898i	−0.807833	−	0.807833i
$157$		−	0.932142i		−	0.0743931i	−0.999308	−	0.0371965i	$-0.988157\pi$
$157$		−	0.932142i		−	0.0743931i	0.999308	−	0.0371965i	$-0.0118428\pi$
$158$	−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
$162$	−1.98687			−0.156103
$163$	12.6956			0.994396			0.497198	−	0.867637i	$-0.334362\pi$
$163$	12.6956			0.994396			0.497198	+	0.867637i	$0.334362\pi$
$164$	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	$-0.0426085\pi$
$167$	11.0826	+	11.0826i	0.857595	+	0.857595i	−0.133459	+	0.991054i	$0.542608\pi$
$168$	−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
$172$		−	19.4173i		−	1.48056i
$173$	12.8849	−	12.8849i	0.979620	−	0.979620i	−0.0201761	−	0.999796i	$-0.506423\pi$
$173$	12.8849	−	12.8849i	0.979620	−	0.979620i	0.999796	+	0.0201761i	$0.00642269\pi$
$174$	1.83921	−	0.648554i	0.139430	−	0.0491668i
$175$		0			0
$176$	4.35646	+	4.35646i	0.328380	+	0.328380i
$177$	4.57236			0.343680
$178$	0.739329	−	0.739329i	0.0554151	−	0.0554151i
$179$	21.1019			1.57723			0.788615	−	0.614887i	$-0.210798\pi$
$179$	21.1019			1.57723			0.788615	+	0.614887i	$0.210798\pi$
$180$		0			0
$181$	−12.7532			−0.947940			−0.473970	−	0.880541i	$-0.657179\pi$
$181$	−12.7532			−0.947940			−0.473970	+	0.880541i	$0.657179\pi$
$182$		−	1.64399i		−	0.121860i
$183$	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
$188$			18.5302i			1.35146i
$189$	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	$0.825732\pi$
$192$			13.3758i			0.965314i
$193$			6.03773i			0.434606i	0.976104	+	0.217303i	$0.0697259\pi$
$193$			6.03773i			0.434606i	−0.976104	+	0.217303i	$0.930274\pi$
$194$			2.16694i			0.155577i
$195$		0			0
$196$		−	4.21482i		−	0.301059i
$197$	7.10733	−	7.10733i	0.506377	−	0.506377i	−0.407036	−	0.913412i	$-0.633438\pi$
$197$	7.10733	−	7.10733i	0.506377	−	0.506377i	0.913412	+	0.407036i	$0.133438\pi$
$198$	−0.117318	−	0.117318i	−0.00833740	−	0.00833740i
$199$		−	20.8864i		−	1.48060i	−0.672279	−	0.740298i	$-0.734684\pi$
$199$		−	20.8864i		−	1.48060i	0.672279	−	0.740298i	$-0.265316\pi$
$200$		0			0
$201$	−8.79040	+	8.79040i	−0.620027	+	0.620027i
$202$	−0.697774	−	0.697774i	−0.0490952	−	0.0490952i
$203$	−10.7005	−	5.12130i	−0.751025	−	0.359444i
$204$		−	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
$213$	1.50899			0.103394
$214$	−2.17195	+	2.17195i	−0.148472	+	0.148472i
$215$		0			0
$216$			3.54803i			0.241413i
$217$	−15.9376			−1.08191
$218$	−1.25744			−0.0851646
$219$			21.5614i			1.45699i
$220$		0			0
$221$	5.90741	−	5.90741i	0.397375	−	0.397375i
$222$	0.899954			0.0604009
$223$	18.4792	+	18.4792i	1.23746	+	1.23746i	0.961035	+	0.276425i	$0.0891498\pi$
$223$	18.4792	+	18.4792i	1.23746	+	1.23746i	0.276425	+	0.961035i	$0.410850\pi$
$224$	−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	0.270222	−	0.962798i	$-0.412903\pi$
$227$	18.5773	−	18.5773i	1.23302	−	1.23302i	0.962798	−	0.270222i	$-0.0870972\pi$
$228$	−7.93733	−	7.93733i	−0.525662	−	0.525662i
$229$	−17.2134	−	17.2134i	−1.13750	−	1.13750i	−0.988898	−	0.148598i	$-0.952524\pi$
$229$	−17.2134	−	17.2134i	−1.13750	−	1.13750i	−0.148598	−	0.988898i	$-0.547476\pi$
$230$		0			0
$231$			6.74662i			0.443895i
$232$	−1.36837	−	3.88052i	−0.0898381	−	0.254769i
$233$	20.2653	+	20.2653i	1.32762	+	1.32762i	0.907439	+	0.420184i	$0.138035\pi$
$233$	20.2653	+	20.2653i	1.32762	+	1.32762i	0.420184	+	0.907439i	$0.361965\pi$
$234$	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	$0.259865\pi$
$239$			22.5302i			1.45736i	−0.684857	+	0.728678i	$0.740135\pi$
$240$		0			0
$241$		−	21.5188i		−	1.38615i	−0.720868	−	0.693073i	$-0.756257\pi$
$241$		−	21.5188i		−	1.38615i	0.720868	−	0.693073i	$-0.243743\pi$
$242$		−	1.60828i		−	0.103384i
$243$			5.42386i			0.347941i
$244$	−6.52632	−	6.52632i	−0.417805	−	0.417805i
$245$		0			0
$246$	0.177643	+	0.177643i	0.0113261	+	0.0113261i
$247$		−	11.7851i		−	0.749868i
$248$	−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
$253$			4.25477i			0.267495i
$254$	1.18312			0.0742356
$255$		0			0
$256$	13.1081			0.819254
$257$	−2.66706	+	2.66706i	−0.166366	+	0.166366i	−0.785380	−	0.619014i	$-0.787533\pi$
$257$	−2.66706	+	2.66706i	−0.166366	+	0.166366i	0.619014	+	0.785380i	$0.287533\pi$
$258$	3.58253			0.223039
$259$	−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
$263$		−	21.3510i		−	1.31656i	−0.752773	−	0.658280i	$-0.771284\pi$
$263$		−	21.3510i		−	1.31656i	0.752773	−	0.658280i	$-0.228716\pi$
$264$	−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	0.440838	−	0.897587i	$-0.354681\pi$
$269$	−7.49123	−	7.49123i	−0.456749	−	0.456749i	−0.897587	+	0.440838i	$0.854681\pi$
$270$		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	$0.136233\pi$
$272$	−8.15530			−0.494487
$273$	−16.0143			−0.969230
$274$	−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	−0.634882	−	0.772610i	$-0.718951\pi$
$277$	2.29225	−	2.29225i	0.137728	−	0.137728i	0.772610	+	0.634882i	$0.218951\pi$
$278$		−	0.356953i		−	0.0214086i
$279$	−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	$0.658798\pi$
$282$	−3.41887			−0.203591
$283$	10.1149	−	10.1149i	0.601266	−	0.601266i	−0.339383	−	0.940648i	$-0.610218\pi$
$283$	10.1149	−	10.1149i	0.601266	−	0.601266i	0.940648	+	0.339383i	$0.110218\pi$
$284$		−	1.57696i		−	0.0935756i
$285$		0			0
$286$	−1.21691			−0.0719572
$287$		−	1.52817i		−	0.0902049i
$288$	−1.19086			−0.0701723
$289$	−12.3411			−0.725948
$290$		0			0
$291$	21.1085			1.23740
$292$	22.5326			1.31862
$293$		−	21.8078i		−	1.27402i	−0.770854	−	0.637012i	$-0.780170\pi$
$293$		−	21.8078i		−	1.27402i	0.770854	−	0.637012i	$-0.219830\pi$
$294$	0.777643			0.0453531
$295$		0			0
$296$		−	1.89880i		−	0.110365i
$297$	5.35403	−	5.35403i	0.310672	−	0.310672i
$298$	3.17435			0.183885
$299$	−10.0994			−0.584066
$300$		0			0
$301$	−15.4093	−	15.4093i	−0.888178	−	0.888178i
$302$		−	0.535696i		−	0.0308259i
$303$	−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
$307$	6.59288			0.376275			0.188138	−	0.982143i	$-0.439755\pi$
$307$	6.59288			0.376275			0.188138	+	0.982143i	$0.439755\pi$
$308$	7.05052			0.401741
$309$	−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	−0.985797	−	0.167941i	$-0.946288\pi$
$313$	−20.4117	−	20.4117i	−1.15374	−	1.15374i	−0.167941	−	0.985797i	$-0.553712\pi$
$314$		−	0.179729i		−	0.0101427i
$315$		0			0
$316$	4.11722	−	4.11722i	0.231612	−	0.231612i
$317$			24.2946i			1.36452i	0.731108	+	0.682262i	$0.239003\pi$
$317$			24.2946i			1.36452i	−0.731108	+	0.682262i	$0.760997\pi$
$318$	−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
$322$	−1.10829			−0.0617626
$323$	4.64716	−	4.64716i	0.258575	−	0.258575i
$324$	20.2262			1.12368
$325$		0			0
$326$	2.44788			0.135575
$327$			12.2489i			0.677366i
$328$	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
$333$		−	1.31138i		−	0.0718634i
$334$	2.13686	+	2.13686i	0.116924	+	0.116924i
$335$		0			0
$336$	11.0540	+	11.0540i	0.603047	+	0.603047i
$337$			26.7563i			1.45751i	0.684776	+	0.728754i	$0.259900\pi$
$337$			26.7563i			1.45751i	−0.684776	+	0.728754i	$0.740100\pi$
$338$		−	0.381974i		−	0.0207766i
$339$			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	$-0.00298990\pi$
$347$	18.4521	+	18.4521i	0.990563	+	0.990563i	−0.00939290	+	0.999956i	$0.502990\pi$
$348$	−18.7230	+	6.60224i	−1.00366	+	0.353917i
$349$		−	24.2654i		−	1.29890i	−0.760406	−	0.649448i	$-0.775000\pi$
$349$		−	24.2654i		−	1.29890i	0.760406	−	0.649448i	$-0.225000\pi$
$350$		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	−0.171415	+	0.985199i	$0.554834\pi$
$353$	−21.7308	+	21.7308i	−1.15661	+	1.15661i	−0.985199	+	0.171415i	$0.945166\pi$
$354$	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
$358$	4.06872			0.215039
$359$	−22.6346	+	22.6346i	−1.19461	+	1.19461i	−0.218850	+	0.975759i	$0.570230\pi$
$359$	−22.6346	+	22.6346i	−1.19461	+	1.19461i	−0.975759	+	0.218850i	$0.929770\pi$
$360$		0			0
$361$			9.72906i			0.512056i
$362$	−2.45899			−0.129242
$363$	−15.6664			−0.822275
$364$			16.7357i			0.877187i
$365$		0			0
$366$	1.20412	−	1.20412i	0.0629404	−	0.0629404i
$367$	−9.52855			−0.497386			−0.248693	−	0.968582i	$-0.580001\pi$
$367$	−9.52855			−0.497386			−0.248693	+	0.968582i	$0.580001\pi$
$368$	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	0.970568	−	0.240828i	$-0.0774191\pi$
$373$	14.0936	+	14.0936i	0.729739	+	0.729739i	−0.240828	+	0.970568i	$0.577419\pi$
$374$	−0.479857	−	0.479857i	−0.0248128	−	0.0248128i
$375$		0			0
$376$			7.21341i			0.372003i
$377$	−18.8011	−	8.99830i	−0.968306	−	0.463436i
$378$	1.39463	+	1.39463i	0.0717319	+	0.0717319i
$379$	10.9031	−	10.9031i	0.560055	−	0.560055i	−0.369268	−	0.929323i	$-0.620392\pi$
$379$	10.9031	−	10.9031i	0.560055	−	0.560055i	0.929323	+	0.369268i	$0.120392\pi$
$380$		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	$-0.761387\pi$
$383$	−0.989916	+	0.989916i	−0.0505823	+	0.0505823i	0.681363	+	0.731946i	$0.261387\pi$
$384$			11.0561i			0.564204i
$385$		0			0
$386$			1.16415i			0.0592538i
$387$		−	5.22036i		−	0.265366i
$388$		−	22.0593i		−	1.11989i
$389$	−3.15870	−	3.15870i	−0.160153	−	0.160153i	0.622482	−	0.782634i	$-0.286124\pi$
$389$	−3.15870	−	3.15870i	−0.160153	−	0.160153i	−0.782634	+	0.622482i	$0.786124\pi$
$390$		0			0
$391$	−3.98247	−	3.98247i	−0.201402	−	0.201402i
$392$		−	1.64074i		−	0.0828697i
$393$	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	−0.660464	−	0.750858i	$-0.729640\pi$
$397$	1.80109	−	1.80109i	0.0903941	−	0.0903941i	0.750858	+	0.660464i	$0.229640\pi$
$398$		−	4.02717i		−	0.201864i
$399$	−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
$403$	−28.0029			−1.39492
$404$	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
$408$		−	3.09762i		−	0.153355i
$409$	10.1466	−	10.1466i	0.501718	−	0.501718i	−0.410253	−	0.911972i	$-0.634560\pi$
$409$	10.1466	−	10.1466i	0.501718	−	0.501718i	0.911972	+	0.410253i	$0.134560\pi$
$410$		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
$417$	−3.47713			−0.170276
$418$	−0.957299			−0.0468230
$419$	29.5026			1.44130			0.720648	−	0.693301i	$-0.243844\pi$
$419$	29.5026			1.44130			0.720648	+	0.693301i	$0.243844\pi$
$420$		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
$423$			4.98187i			0.242227i
$424$	0.993141	+	0.993141i	0.0482312	+	0.0482312i
$425$		0			0
$426$	0.290953			0.0140967
$427$	−10.3584			−0.501279
$428$	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	$0.341544\pi$
$432$		−	17.5447i		−	0.844118i
$433$	1.79930			0.0864687			0.0432344	−	0.999065i	$-0.486234\pi$
$433$	1.79930			0.0864687			0.0432344	+	0.999065i	$0.486234\pi$
$434$	−3.07297			−0.147507
$435$		0			0
$436$	12.8007			0.613040
$437$	−7.94490			−0.380056
$438$			4.15732i			0.198644i
$439$	−24.7983			−1.18356			−0.591779	−	0.806100i	$-0.701574\pi$
$439$	−24.7983			−1.18356			−0.591779	+	0.806100i	$0.701574\pi$
$440$		0			0
$441$		−	1.13316i		−	0.0539599i
$442$	1.13903	−	1.13903i	0.0541779	−	0.0541779i
$443$	15.9290			0.756807			0.378404	−	0.925641i	$-0.376473\pi$
$443$	15.9290			0.756807			0.378404	+	0.925641i	$0.376473\pi$
$444$	−9.16147			−0.434784
$445$		0			0
$446$	3.56303	+	3.56303i	0.168715	+	0.168715i
$447$		−	30.9218i		−	1.46255i
$448$	11.0930	−	11.0930i	0.524095	−	0.524095i
$449$	−7.98176	+	7.98176i	−0.376683	+	0.376683i	−0.869904	−	0.493221i	$-0.835819\pi$
$449$	−7.98176	+	7.98176i	−0.376683	+	0.376683i	0.493221	+	0.869904i	$0.335819\pi$
$450$		0			0
$451$	−1.13118			−0.0532650
$452$	37.4187			1.76003
$453$	−5.21830			−0.245177
$454$	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	1.00000		0.000758030i	$0.000241289\pi$
$457$	21.3938	+	21.3938i	1.00076	+	1.00076i	0.000758030		1.00000i	$0.499759\pi$
$458$	−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	$0.0842051\pi$
$462$			1.30084i			0.0605204i
$463$	3.82517	−	3.82517i	0.177771	−	0.177771i	−0.612613	−	0.790383i	$-0.709881\pi$
$463$	3.82517	−	3.82517i	0.177771	−	0.177771i	0.790383	+	0.612613i	$0.209881\pi$
$464$	6.76648	+	19.1888i	0.314126	+	0.890818i
$465$		0			0
$466$	3.90741	+	3.90741i	0.181007	+	0.181007i
$467$	−5.88766			−0.272449			−0.136224	−	0.990678i	$-0.543497\pi$
$467$	−5.88766			−0.272449			−0.136224	+	0.990678i	$0.543497\pi$
$468$	−2.83485	+	2.83485i	−0.131041	+	0.131041i
$469$	14.5804			0.673258
$470$		0			0
$471$	−1.75077			−0.0806711
$472$		−	1.86009i		−	0.0856178i
$473$	−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
$478$			4.34411i			0.198695i
$479$	−6.77715	−	6.77715i	−0.309656	−	0.309656i	0.535120	−	0.844776i	$-0.320266\pi$
$479$	−6.77715	−	6.77715i	−0.309656	−	0.309656i	−0.844776	+	0.535120i	$0.820266\pi$
$480$		0			0
$481$	−6.80133	−	6.80133i	−0.310114	−	0.310114i
$482$		−	4.14910i		−	0.188986i
$483$			10.7960i			0.491235i
$484$			16.3721i			0.744188i
$485$		0			0
$486$			1.04579i			0.0474380i
$487$	−7.92933	+	7.92933i	−0.359312	+	0.359312i	−0.863559	−	0.504247i	$-0.831770\pi$
$487$	−7.92933	+	7.92933i	−0.359312	+	0.359312i	0.504247	+	0.863559i	$0.331770\pi$
$488$	−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
$493$	−3.86549	−	10.9620i	−0.174093	−	0.493704i
$494$		−	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	$-0.695446\pi$
$499$	−25.7405			−1.15230			−0.576151	+	0.817343i	$0.695446\pi$
$500$		0			0
$501$	20.8155	−	20.8155i	0.929968	−	0.929968i
$502$	3.15759	+	3.15759i	0.140930	+	0.140930i
$503$	6.69875			0.298682			0.149341	−	0.988786i	$-0.452285\pi$
$503$	6.69875			0.298682			0.149341	+	0.988786i	$0.452285\pi$
$504$	−0.628071	+	0.628071i	−0.0279765	+	0.0279765i
$505$		0			0
$506$			0.820375i			0.0364701i
$507$	−3.72086			−0.165249
$508$	−12.0441			−0.534370
$509$			29.5491i			1.30974i	0.755741	+	0.654871i	$0.227277\pi$
$509$			29.5491i			1.30974i	−0.755741	+	0.654871i	$0.772723\pi$
$510$		0			0
$511$	17.8816	−	17.8816i	0.791036	−	0.791036i
$512$	14.3004			0.631992
$513$	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	$-0.0681392\pi$
$522$	−0.182219	−	0.516747i	−0.00797549	−	0.0226174i
$523$	10.4806	+	10.4806i	0.458283	+	0.458283i	0.898092	−	0.439808i	$-0.144954\pi$
$523$	10.4806	+	10.4806i	0.458283	+	0.458283i	−0.439808	+	0.898092i	$0.644954\pi$
$524$	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
$532$			13.1654i			0.570792i
$533$		−	2.68505i		−	0.116302i
$534$	−1.38862	−	1.38862i	−0.0600916	−	0.0600916i
$535$		0			0
$536$	3.57605	+	3.57605i	0.154462	+	0.154462i
$537$		−	39.6340i		−	1.71033i
$538$	−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
$543$			23.9534i			1.02794i
$544$	−4.87091			−0.208839
$545$		0			0
$546$	−3.08777			−0.132144
$547$	20.1591	−	20.1591i	0.861939	−	0.861939i	−0.129624	−	0.991563i	$-0.541377\pi$
$547$	20.1591	−	20.1591i	0.861939	−	0.861939i	0.991563	+	0.129624i	$0.0413771\pi$
$548$	24.4569			1.04475
$549$	−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
$553$		−	6.53474i		−	0.277885i
$554$	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	$-0.151072\pi$
$557$	10.2070	+	10.2070i	0.432485	+	0.432485i	−0.456988	+	0.889473i	$0.651072\pi$
$558$	−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
$562$	−3.09278			−0.130461
$563$	9.06228			0.381930			0.190965	−	0.981597i	$-0.438838\pi$
$563$	9.06228			0.381930			0.190965	+	0.981597i	$0.438838\pi$
$564$	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
$568$		−	0.613878i		−	0.0257577i
$569$	−26.3160	−	26.3160i	−1.10323	−	1.10323i	−0.994019	−	0.109207i	$-0.965169\pi$
$569$	−26.3160	−	26.3160i	−1.10323	−	1.10323i	−0.109207	−	0.994019i	$-0.534831\pi$
$570$		0			0
$571$	−7.28850			−0.305014			−0.152507	−	0.988302i	$-0.548735\pi$
$571$	−7.28850			−0.305014			−0.152507	+	0.988302i	$0.548735\pi$
$572$	12.3880			0.517969
$573$	−8.65177	+	8.65177i	−0.361433	+	0.361433i
$574$		−	0.294651i		−	0.0122985i
$575$		0			0
$576$	3.75808			0.156587
$577$		−	14.8536i		−	0.618365i	−0.951003	−	0.309183i	$-0.899945\pi$
$577$		−	14.8536i		−	0.618365i	0.951003	−	0.309183i	$-0.100055\pi$
$578$	−2.37953			−0.0989753
$579$	11.3402			0.471282
$580$		0			0
$581$	−23.0957			−0.958172
$582$	4.06999			0.168707
$583$		−	2.99733i		−	0.124137i
$584$	8.77146			0.362966
$585$		0			0
$586$		−	4.20482i		−	0.173700i
$587$	−20.8980	+	20.8980i	−0.862552	+	0.862552i	−0.991634	−	0.129082i	$-0.958797\pi$
$587$	−20.8980	+	20.8980i	−0.862552	+	0.862552i	0.129082	+	0.991634i	$0.458797\pi$
$588$	−7.91635			−0.326465
$589$	−22.0289			−0.907686
$590$		0			0
$591$	−13.3491	−	13.3491i	−0.549110	−	0.549110i
$592$			9.38937i			0.385901i
$593$	−9.91716	+	9.91716i	−0.407249	+	0.407249i	−0.880778	−	0.473529i	$-0.842980\pi$
$593$	−9.91716	+	9.91716i	−0.407249	+	0.407249i	0.473529	+	0.880778i	$0.342980\pi$
$594$	1.03233	−	1.03233i	0.0423569	−	0.0423569i
$595$		0			0
$596$	−32.3146			−1.32366
$597$	−39.2292			−1.60554
$598$	−1.94730			−0.0796312
$599$	16.5929	−	16.5929i	0.677968	−	0.677968i	−0.281572	−	0.959540i	$-0.590856\pi$
$599$	16.5929	−	16.5929i	0.677968	−	0.677968i	0.959540	+	0.281572i	$0.0908559\pi$
$600$		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
$607$			11.6762i			0.473921i	0.971519	+	0.236961i	$0.0761513\pi$
$607$			11.6762i			0.473921i	−0.971519	+	0.236961i	$0.923849\pi$
$608$	−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
$612$	−2.23571			−0.0903730
$613$	18.8812	−	18.8812i	0.762605	−	0.762605i	−0.214188	−	0.976793i	$-0.568710\pi$
$613$	18.8812	−	18.8812i	0.762605	−	0.762605i	0.976793	+	0.214188i	$0.0687104\pi$
$614$	1.27119			0.0513011
$615$		0			0
$616$	2.74461			0.110584
$617$		−	11.3496i		−	0.456916i	−0.973554	−	0.228458i	$-0.926632\pi$
$617$		−	11.3496i		−	0.456916i	0.973554	−	0.228458i	$-0.0733684\pi$
$618$	−1.41560	+	1.41560i	−0.0569437	+	0.0569437i
$619$	6.62460	+	6.62460i	0.266265	+	0.266265i	0.827593	−	0.561328i	$-0.189709\pi$
$619$	6.62460	+	6.62460i	0.266265	+	0.266265i	−0.561328	+	0.827593i	$0.689709\pi$
$620$		0			0
$621$	8.56757	−	8.56757i	0.343805	−	0.343805i
$622$	4.39238	+	4.39238i	0.176119	+	0.176119i
$623$			11.9456i			0.478590i
$624$	19.4223	+	19.4223i	0.777516	+	0.777516i
$625$		0			0
$626$	−3.93564	−	3.93564i	−0.157300	−	0.157300i
$627$			9.32519i			0.372412i
$628$			1.82963i			0.0730102i
$629$		−	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
$638$	−0.730929	+	1.52721i	−0.0289377	+	0.0604627i
$639$		−	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	$-0.603503\pi$
$643$	15.9279	−	15.9279i	0.628133	−	0.628133i	0.947598	+	0.319465i	$0.103503\pi$
$644$	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	$-0.0400810\pi$
$647$	22.0404	+	22.0404i	0.866497	+	0.866497i	−0.125586	+	0.992083i	$0.540081\pi$
$648$	7.87361			0.309305
$649$	−2.80691	+	2.80691i	−0.110181	+	0.110181i
$650$		0			0
$651$			29.9343i			1.17322i
$652$	−24.9192			−0.975912
$653$	27.2009			1.06445			0.532227	−	0.846602i	$-0.321355\pi$
$653$	27.2009			1.06445			0.532227	+	0.846602i	$0.321355\pi$
$654$			2.36175i			0.0923516i
$655$		0			0
$656$	−1.85338	+	1.85338i	−0.0723623	+	0.0723623i
$657$	6.05792			0.236342
$658$	2.83538	+	2.83538i	0.110535	+	0.110535i
$659$	4.67457	−	4.67457i	0.182095	−	0.182095i	−0.610173	−	0.792268i	$-0.708900\pi$
$659$	4.67457	−	4.67457i	0.182095	−	0.182095i	0.792268	+	0.610173i	$0.208900\pi$
$660$		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
$667$	−6.06619	+	12.6747i	−0.234884	+	0.490767i
$668$	−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	$-0.862968\pi$
$673$	−12.7489	+	12.7489i	−0.491434	+	0.491434i	0.417324	+	0.908758i	$0.362968\pi$
$674$			5.15896i			0.198716i
$675$		0			0
$676$			3.88847i			0.149557i
$677$		−	4.24368i		−	0.163098i	−0.996669	−	0.0815489i	$-0.974013\pi$
$677$		−	4.24368i		−	0.163098i	0.996669	−	0.0815489i	$-0.0259867\pi$
$678$			6.90384i			0.265140i
$679$	−17.5060	−	17.5060i	−0.671819	−	0.671819i
$680$		0			0
$681$	−34.8923	−	34.8923i	−1.33708	−	1.33708i
$682$			2.27467i			0.0871014i
$683$	−31.3545	−	31.3545i	−1.19975	−	1.19975i	−0.974242	−	0.225504i	$-0.927597\pi$
$683$	−31.3545	−	31.3545i	−1.19975	−	1.19975i	−0.225504	−	0.974242i	$-0.572403\pi$
$684$	−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
$688$			37.3772i			1.42499i
$689$	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
$693$	1.89554			0.0720056
$694$	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
$698$		−	4.67868i		−	0.177091i
$699$	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
$707$	11.2742			0.424008
$708$	−8.97473			−0.337291
$709$	52.1626			1.95901			0.979503	−	0.201429i	$-0.0645584\pi$
$709$	52.1626			1.95901			0.979503	+	0.201429i	$0.0645584\pi$
$710$		0			0
$711$	1.10692	−	1.10692i	0.0415127	−	0.0415127i
$712$	−2.92983	+	2.92983i	−0.109800	+	0.109800i
$713$			18.8781i			0.706990i
$714$	−1.21758	−	1.21758i	−0.0455669	−	0.0455669i
$715$		0			0
$716$	−41.4193			−1.54791
$717$	42.3166			1.58034
$718$	−4.36424	+	4.36424i	−0.162872	+	0.162872i
$719$			40.9120i			1.52576i	0.646541	+	0.762879i	$0.276215\pi$
$719$			40.9120i			1.52576i	−0.646541	+	0.762879i	$0.723785\pi$
$720$		0			0
$721$	12.1776			0.453519
$722$			1.87589i			0.0698134i
$723$	−40.4169			−1.50312
$724$	25.0323			0.930319
$725$		0			0
$726$	−3.02069			−0.112108
$727$	−53.5853			−1.98737			−0.993685	−	0.112209i	$-0.964207\pi$
$727$	−53.5853			−1.98737			−0.993685	+	0.112209i	$0.964207\pi$
$728$			6.51483i			0.241456i
$729$	−20.7267			−0.767657
$730$		0			0
$731$		−	21.3525i		−	0.789751i
$732$	−12.2579	+	12.2579i	−0.453064	+	0.453064i
$733$	−25.8493			−0.954765			−0.477383	−	0.878695i	$-0.658414\pi$
$733$	−25.8493			−0.954765			−0.477383	+	0.878695i	$0.658414\pi$
$734$	−1.83723			−0.0678134
$735$		0			0
$736$	4.16371	+	4.16371i	0.153476	+	0.153476i
$737$		−	10.7926i		−	0.397551i
$738$	0.0499108	−	0.0499108i	0.00183724	−	0.00183724i
$739$	−16.3056	+	16.3056i	−0.599810	+	0.599810i	−0.940262	−	0.340452i	$-0.889420\pi$
$739$	−16.3056	+	16.3056i	−0.599810	+	0.599810i	0.340452	+	0.940262i	$0.389420\pi$
$740$		0			0
$741$	−22.1350			−0.813149
$742$	0.780750			0.0286622
$743$	4.30076			0.157780			0.0788898	−	0.996883i	$-0.474862\pi$
$743$	4.30076			0.157780			0.0788898	+	0.996883i	$0.474862\pi$
$744$	−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	$0.0712131\pi$
$752$		−	35.6696i		−	1.30074i
$753$	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
$757$	42.3352			1.53870			0.769349	−	0.638829i	$-0.220581\pi$
$757$	42.3352			1.53870			0.769349	+	0.638829i	$0.220581\pi$
$758$	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	$0.628387\pi$
$762$		−	2.22216i		−	0.0805003i
$763$	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
$768$		−	24.6198i		−	0.888391i
$769$	26.0688	+	26.0688i	0.940065	+	0.940065i	0.998303	−	0.0582378i	$-0.0185482\pi$
$769$	26.0688	+	26.0688i	0.940065	+	0.940065i	−0.0582378	+	0.998303i	$0.518548\pi$
$770$		0			0
$771$	5.00932	+	5.00932i	0.180406	+	0.180406i
$772$		−	11.8510i		−	0.426527i
$773$		−	21.7119i		−	0.780922i	−0.920619	−	0.390461i	$-0.872316\pi$
$773$		−	21.7119i		−	0.780922i	0.920619	−	0.390461i	$-0.127684\pi$
$774$		−	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
$783$	23.5828	−	8.31591i	0.842781	−	0.297187i
$784$			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	$-0.226637\pi$
$787$	2.90929	+	2.90929i	0.103705	+	0.103705i	−0.653351	+	0.757056i	$0.726637\pi$
$788$	−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
$793$	−18.2001			−0.646304
$794$	0.347273	−	0.347273i	0.0123243	−	0.0123243i
$795$		0			0
$796$			40.9963i			1.45307i
$797$	6.97586			0.247098			0.123549	−	0.992339i	$-0.460572\pi$
$797$	6.97586			0.247098			0.123549	+	0.992339i	$0.460572\pi$
$798$	−2.42904			−0.0859871
$799$			20.3770i			0.720887i
$800$		0			0
$801$	−2.02346	+	2.02346i	−0.0714954	+	0.0714954i
$802$	2.01189			0.0710423
$803$	−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	0.0549228	−	0.998491i	$-0.482509\pi$
$809$	−26.8378	−	26.8378i	−0.943568	−	0.943568i	−0.998491	+	0.0549228i	$0.982509\pi$
$810$		0			0
$811$			15.8850i			0.557798i	0.960320	+	0.278899i	$0.0899694\pi$
$811$			15.8850i			0.557798i	−0.960320	+	0.278899i	$0.910031\pi$
$812$	21.0031	+	10.0522i	0.737065	+	0.352763i
$813$	−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	$-0.184789\pi$
$822$			4.51234i			0.157386i
$823$			16.4642i			0.573905i	0.957945	+	0.286953i	$0.0926422\pi$
$823$			16.4642i			0.573905i	−0.957945	+	0.286953i	$0.907358\pi$
$824$	2.98675	+	2.98675i	0.104048	+	0.104048i
$825$		0			0
$826$	−0.731149	−	0.731149i	−0.0254399	−	0.0254399i
$827$			40.2890i			1.40099i	0.713659	+	0.700493i	$0.247037\pi$
$827$			40.2890i			1.40099i	−0.713659	+	0.700493i	$0.752963\pi$
$828$	1.91111	+	1.91111i	0.0664156	+	0.0664156i
$829$	32.5842	−	32.5842i	1.13170	−	1.13170i	0.141801	−	0.989895i	$-0.454711\pi$
$829$	32.5842	−	32.5842i	1.13170	−	1.13170i	0.989895	−	0.141801i	$-0.0452892\pi$
$830$		0			0
$831$	−4.30535	−	4.30535i	−0.149351	−	0.149351i
$832$	19.4908	−	19.4908i	0.675721	−	0.675721i
$833$		−	4.63488i		−	0.160589i
$834$	−0.670436			−0.0232153
$835$		0			0
$836$	9.74524			0.337046
$837$	23.7554	−	23.7554i	0.821108	−	0.821108i
$838$	5.68849			0.196505
$839$	−21.8745	−	21.8745i	−0.755193	−	0.755193i	0.220250	−	0.975443i	$-0.429313\pi$
$839$	−21.8745	−	21.8745i	−0.755193	−	0.755193i	−0.975443	+	0.220250i	$0.929313\pi$
$840$		0			0
$841$	−22.5856	+	18.1904i	−0.778813	+	0.627256i
$842$	−2.36221	+	2.36221i	−0.0814072	+	0.0814072i
$843$			30.1272i			1.03764i
$844$	−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
$852$	−2.96189			−0.101473
$853$	42.3889			1.45137			0.725684	−	0.688028i	$-0.241524\pi$
$853$	42.3889			1.45137			0.725684	+	0.688028i	$0.241524\pi$
$854$	−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	−0.696384	−	0.717669i	$-0.745209\pi$
$857$	0.623109	−	0.623109i	0.0212850	−	0.0212850i	0.717669	+	0.696384i	$0.245209\pi$
$858$			2.28562i			0.0780296i
$859$	−1.31996	−	1.31996i	−0.0450364	−	0.0450364i	0.684230	−	0.729266i	$-0.260138\pi$
$859$	−1.31996	−	1.31996i	−0.0450364	−	0.0450364i	−0.729266	+	0.684230i	$0.760138\pi$
$860$		0			0
$861$	−2.87023			−0.0978173
$862$	3.82275			0.130203
$863$	−2.30417	+	2.30417i	−0.0784348	+	0.0784348i	−0.745236	−	0.666801i	$-0.767663\pi$
$863$	−2.30417	+	2.30417i	−0.0784348	+	0.0784348i	0.666801	+	0.745236i	$0.267663\pi$
$864$		−	10.4789i		−	0.356499i
$865$		0			0
$866$	0.346928			0.0117891
$867$			23.1793i			0.787211i
$868$	31.2826			1.06180
$869$	−4.83713			−0.164088
$870$		0			0
$871$	25.6182			0.868040
$872$	4.98301			0.168746
$873$		−	5.93067i		−	0.200723i
$874$	−1.53188			−0.0518166
$875$		0			0
$876$		−	42.3212i		−	1.42990i
$877$	4.53313	−	4.53313i	0.153073	−	0.153073i	−0.626416	−	0.779489i	$-0.715479\pi$
$877$	4.53313	−	4.53313i	0.153073	−	0.153073i	0.779489	+	0.626416i	$0.215479\pi$
$878$	−4.78144			−0.161366
$879$	−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	$0.658535\pi$
$882$		−	0.218488i		−	0.00735686i
$883$	8.01660	−	8.01660i	0.269780	−	0.269780i	−0.559231	−	0.829012i	$-0.688904\pi$
$883$	8.01660	−	8.01660i	0.269780	−	0.269780i	0.829012	+	0.559231i	$0.188904\pi$
$884$	−11.5952	+	11.5952i	−0.389989	+	0.389989i
$885$		0			0
$886$	3.07131			0.103183
$887$	25.8619			0.868358			0.434179	−	0.900827i	$-0.357039\pi$
$887$	25.8619			0.868358			0.434179	+	0.900827i	$0.357039\pi$
$888$	−3.56636			−0.119679
$889$	−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
$897$			18.9690i			0.633356i
$898$	−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
$902$	−0.218105			−0.00726211
$903$	−28.9421	+	28.9421i	−0.963132	+	0.963132i
$904$	14.5663			0.484468
$905$		0			0
$906$	−1.00616			−0.0334273
$907$		−	2.91928i		−	0.0969330i	−0.998825	−	0.0484665i	$-0.984567\pi$
$907$		−	2.91928i		−	0.0969330i	0.998825	−	0.0484665i	$-0.0154334\pi$
$908$	−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
$913$			17.0958i			0.565790i
$914$	4.12499	+	4.12499i	0.136443	+	0.136443i
$915$		0			0
$916$	33.7869	+	33.7869i	1.11635	+	1.11635i
$917$		−	48.8841i		−	1.61430i
$918$			1.93252i			0.0637826i
$919$			41.5614i			1.37098i	0.728080	+	0.685492i	$0.240413\pi$
$919$			41.5614i			1.37098i	−0.728080	+	0.685492i	$0.759587\pi$
$920$		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
$928$	4.04141	+	11.4609i	0.132666	+	0.376222i
$929$		−	38.2809i		−	1.25596i	−0.778231	−	0.627978i	$-0.783883\pi$
$929$		−	38.2809i		−	1.25596i	0.778231	−	0.627978i	$-0.216117\pi$
$930$		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	$-0.418474\pi$
$937$	−21.8574	−	21.8574i	−0.714051	−	0.714051i	−0.967380	+	0.253329i	$0.918474\pi$
$938$	2.81128			0.0917916
$939$	−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	$0.902418\pi$
$942$	−0.337571			−0.0109986
$943$	−1.81012			−0.0589455
$944$			9.19799i			0.299369i
$945$		0			0
$946$	−2.19927	+	2.19927i	−0.0715044	+	0.0715044i
$947$	−19.9673			−0.648851			−0.324426	−	0.945911i	$-0.605171\pi$
$947$	−19.9673			−0.648851			−0.324426	+	0.945911i	$0.605171\pi$
$948$	−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	0.998962	−	0.0455438i	$-0.0145021\pi$
$953$	29.4327	+	29.4327i	0.953419	+	0.953419i	−0.0455438	+	0.998962i	$0.514502\pi$
$954$	0.132251	+	0.132251i	0.00428178	+	0.00428178i
$955$		0			0
$956$		−	44.2227i		−	1.43027i
$957$	14.8767	+	7.12008i	0.480897	+	0.230160i
$958$	−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
$967$			3.89596i			0.125286i	0.998036	+	0.0626428i	$0.0199529\pi$
$967$			3.89596i			0.125286i	−0.998036	+	0.0626428i	$0.980047\pi$
$968$			6.37331i			0.204846i
$969$	−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	$0.604304\pi$
$972$		−	10.6461i		−	0.341473i
$973$	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	−0.607648	−	0.794206i	$-0.707887\pi$
$977$	5.83126	−	5.83126i	0.186558	−	0.186558i	0.794206	+	0.607648i	$0.207887\pi$
$978$		−	4.59765i		−	0.147017i
$979$	8.84232			0.282602
$980$		0			0
$981$	3.44147			0.109878
$982$	0.127469	−	0.127469i	0.00406770	−	0.00406770i
$983$	0.962476			0.0306982			0.0153491	−	0.999882i	$-0.495114\pi$
$983$	0.962476			0.0306982			0.0153491	+	0.999882i	$0.495114\pi$
$984$	−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
$988$			23.1321i			0.735929i
$989$	−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
$997$	21.7128			0.687651			0.343826	−	0.939033i	$-0.388277\pi$
$997$	21.7128			0.687651			0.343826	+	0.939033i	$0.388277\pi$
$998$	−4.96310			−0.157104
$999$	11.5394			0.365091

Twists

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

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

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.j (of order \(4\), degree \(2\), minimal)

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