LMFDB - Embedded newform 325.2.m.b.199.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [325,2,Mod(49,325)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(325, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 5]))

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

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

chi := DirichletCharacter("325.49");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 325 = 5^{2} \cdot 13 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	325.m (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.59513806569$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$4$ over $\Q(\zeta_{6})$
Coefficient field:	8.0.22581504.2
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - 4x^{7} + 5x^{6} + 2x^{5} - 11x^{4} + 4x^{3} + 20x^{2} - 32x + 16 $ x^8 - 4x^7 + 5x^6 + 2x^5 - 11x^4 + 4x^3 + 20x^2 - 32*x + 16
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 65)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			199.3
Root			$-1.27597 - 0.609843i$ of defining polynomial
Character	$\chi$	$=$	325.199
Dual form			325.2.m.b.49.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.109843 - 0.190254i) q^{2} +(-1.38581 - 0.800098i) q^{3} +(0.975869 + 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(-0.166123 - 0.287734i) q^{7} +0.868145 q^{8} +(-0.219687 - 0.380509i) q^{9} +O(q^{10})$	\(q+(0.109843 - 0.190254i) q^{2} +(-1.38581 - 0.800098i) q^{3} +(0.975869 + 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(-0.166123 - 0.287734i) q^{7} +0.868145 q^{8} +(-0.219687 - 0.380509i) q^{9} +(4.65213 + 2.68591i) q^{11} -3.12316i q^{12} +(0.619491 + 3.55193i) q^{13} -0.0729902 q^{14} +(-1.85638 + 3.21534i) q^{16} +(4.38581 - 2.53215i) q^{17} -0.0965246 q^{18} +(1.96410 - 1.13397i) q^{19} +0.531659i q^{21} +(1.02201 - 0.590059i) q^{22} +(2.45880 + 1.41959i) q^{23} +(-1.20308 - 0.694601i) q^{24} +(0.743818 + 0.272296i) q^{26} +5.50367i q^{27} +(0.324229 - 0.561581i) q^{28} +(-1.45174 + 2.51448i) q^{29} -5.46410i q^{31} +(1.27597 + 2.21004i) q^{32} +(-4.29798 - 7.44432i) q^{33} -1.11256i q^{34} +(0.428771 - 0.742653i) q^{36} +(2.98601 - 5.17191i) q^{37} -0.498239i q^{38} +(1.98340 - 5.41796i) q^{39} +(3.23205 + 1.86603i) q^{41} +(0.101151 + 0.0583993i) q^{42} +(-4.38581 + 2.53215i) q^{43} +10.4844i q^{44} +(0.540166 - 0.311865i) q^{46} -8.34285 q^{47} +(5.14517 - 2.97057i) q^{48} +(3.44481 - 5.96658i) q^{49} -8.10387 q^{51} +(-5.39913 + 4.51332i) q^{52} +1.56063i q^{53} +(1.04710 + 0.604542i) q^{54} +(-0.144219 - 0.249795i) q^{56} -3.62916 q^{57} +(0.318928 + 0.552399i) q^{58} +(-2.34461 + 1.35366i) q^{59} +(-7.05193 - 12.2143i) q^{61} +(-1.03957 - 0.600196i) q^{62} +(-0.0729902 + 0.126423i) q^{63} -6.86488 q^{64} -1.88842 q^{66} +(-5.16612 + 8.94799i) q^{67} +(8.55995 + 4.94209i) q^{68} +(-2.27162 - 3.93456i) q^{69} +(-11.0828 + 6.39866i) q^{71} +(-0.190720 - 0.330337i) q^{72} -9.68922 q^{73} +(-0.655986 - 1.13620i) q^{74} +(3.83341 + 2.21322i) q^{76} -1.78477i q^{77} +(-0.812927 - 0.972477i) q^{78} -4.51851 q^{79} +(3.74441 - 6.48552i) q^{81} +(0.710039 - 0.409941i) q^{82} +4.26371 q^{83} +(-0.898640 + 0.518830i) q^{84} +1.11256i q^{86} +(4.02367 - 2.32306i) q^{87} +(4.03872 + 2.33176i) q^{88} +(2.79366 + 1.61292i) q^{89} +(0.919100 - 0.768307i) q^{91} +5.54133i q^{92} +(-4.37182 + 7.57221i) q^{93} +(-0.916407 + 1.58726i) q^{94} -4.08359i q^{96} +(1.25396 + 2.17191i) q^{97} +(-0.756779 - 1.31078i) q^{98} -2.36023i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) $ 8 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 18 * q^6 + 10 * q^7 + 12 * q^8 + 4 * q^9	$ 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9} + 8 q^{13} - 4 q^{14} - 2 q^{16} + 18 q^{17} - 40 q^{18} - 12 q^{19} + 6 q^{22} + 6 q^{23} + 12 q^{24} + 10 q^{26} + 8 q^{28} + 8 q^{29} - 4 q^{32} - 18 q^{33} + 20 q^{36} - 2 q^{37} + 12 q^{41} - 42 q^{42} - 18 q^{43} - 42 q^{46} - 16 q^{47} - 6 q^{48} - 12 q^{49} - 8 q^{51} + 16 q^{52} - 18 q^{54} + 12 q^{56} - 28 q^{57} + 22 q^{58} + 12 q^{59} - 28 q^{61} + 12 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} + 12 q^{68} + 16 q^{69} + 12 q^{72} - 16 q^{73} - 10 q^{74} + 54 q^{76} + 18 q^{78} + 16 q^{79} + 8 q^{81} - 6 q^{82} + 24 q^{83} + 30 q^{84} + 54 q^{87} + 42 q^{88} - 24 q^{89} + 28 q^{91} + 8 q^{93} - 32 q^{94} - 2 q^{97} + 24 q^{98}+O(q^{100}) $ 8 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 18 * q^6 + 10 * q^7 + 12 * q^8 + 4 * q^9 + 8 * q^13 - 4 * q^14 - 2 * q^16 + 18 * q^17 - 40 * q^18 - 12 * q^19 + 6 * q^22 + 6 * q^23 + 12 * q^24 + 10 * q^26 + 8 * q^28 + 8 * q^29 - 4 * q^32 - 18 * q^33 + 20 * q^36 - 2 * q^37 + 12 * q^41 - 42 * q^42 - 18 * q^43 - 42 * q^46 - 16 * q^47 - 6 * q^48 - 12 * q^49 - 8 * q^51 + 16 * q^52 - 18 * q^54 + 12 * q^56 - 28 * q^57 + 22 * q^58 + 12 * q^59 - 28 * q^61 + 12 * q^62 - 4 * q^63 + 8 * q^64 + 12 * q^66 - 30 * q^67 + 12 * q^68 + 16 * q^69 + 12 * q^72 - 16 * q^73 - 10 * q^74 + 54 * q^76 + 18 * q^78 + 16 * q^79 + 8 * q^81 - 6 * q^82 + 24 * q^83 + 30 * q^84 + 54 * q^87 + 42 * q^88 - 24 * q^89 + 28 * q^91 + 8 * q^93 - 32 * q^94 - 2 * q^97 + 24 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/325\mathbb{Z}\right)^\times$.

$n$	$27$	$301$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.109843	−	0.190254i	0.0776710	−	0.134530i	−0.824574	−	0.565755i	$-0.808585\pi$
$2$	0.109843	−	0.190254i	0.0776710	−	0.134530i	0.902245	+	0.431224i	$0.141918\pi$
$3$	−1.38581	−	0.800098i	−0.800098	−	0.461937i	0.0434075	−	0.999057i	$-0.486179\pi$
$3$	−1.38581	−	0.800098i	−0.800098	−	0.461937i	−0.843505	+	0.537121i	$0.819512\pi$
$4$	0.975869	+	1.69025i	0.487934	+	0.845127i
$5$		0			0
$5$		0			0
$6$	−0.304444	+	0.175771i	−0.124289	+	0.0717582i
$7$	−0.166123	−	0.287734i	−0.0627887	−	0.108753i	0.832922	−	0.553390i	$-0.186666\pi$
$7$	−0.166123	−	0.287734i	−0.0627887	−	0.108753i	−0.895711	+	0.444637i	$0.853333\pi$
$8$	0.868145			0.306936
$9$	−0.219687	−	0.380509i	−0.0732290	−	0.126836i
$10$		0			0
$11$	4.65213	+	2.68591i	1.40267	+	0.809832i	0.994666	−	0.103149i	$-0.0328917\pi$
$11$	4.65213	+	2.68591i	1.40267	+	0.809832i	0.408004	+	0.912980i	$0.366225\pi$
$12$		−	3.12316i		−	0.901579i
$13$	0.619491	+	3.55193i	0.171816	+	0.985129i
$13$	0.619491	+	3.55193i	0.171816	+	0.985129i
$14$	−0.0729902			−0.0195074
$15$		0			0
$16$	−1.85638	+	3.21534i	−0.464094	+	0.803835i
$17$	4.38581	−	2.53215i	1.06372	−	0.614136i	0.137258	−	0.990535i	$-0.456171\pi$
$17$	4.38581	−	2.53215i	1.06372	−	0.614136i	0.926458	+	0.376399i	$0.122838\pi$
$18$	−0.0965246			−0.0227511
$19$	1.96410	−	1.13397i	0.450596	−	0.260152i	−0.257486	−	0.966282i	$-0.582894\pi$
$19$	1.96410	−	1.13397i	0.450596	−	0.260152i	0.708082	+	0.706130i	$0.249561\pi$
$20$		0			0
$21$			0.531659i			0.116018i
$22$	1.02201	−	0.590059i	0.217894	−	0.125801i
$23$	2.45880	+	1.41959i	0.512695	+	0.296005i	0.733941	−	0.679213i	$-0.237679\pi$
$23$	2.45880	+	1.41959i	0.512695	+	0.296005i	−0.221246	+	0.975218i	$0.571012\pi$
$24$	−1.20308	−	0.694601i	−0.245578	−	0.141785i
$25$		0			0
$26$	0.743818	+	0.272296i	0.145875	+	0.0534016i
$27$			5.50367i			1.05918i
$28$	0.324229	−	0.561581i	0.0612735	−	0.106129i
$29$	−1.45174	+	2.51448i	−0.269581	+	0.466928i	−0.968754	−	0.248025i	$-0.920219\pi$
$29$	−1.45174	+	2.51448i	−0.269581	+	0.466928i	0.699173	+	0.714953i	$0.253552\pi$
$30$		0			0
$31$		−	5.46410i		−	0.981382i	−0.871334	−	0.490691i	$-0.836744\pi$
$31$		−	5.46410i		−	0.981382i	0.871334	−	0.490691i	$-0.163256\pi$
$32$	1.27597	+	2.21004i	0.225561	+	0.390683i
$33$	−4.29798	−	7.44432i	−0.748182	−	1.29589i
$34$		−	1.11256i		−	0.190802i
$35$		0			0
$36$	0.428771	−	0.742653i	0.0714619	−	0.123776i
$37$	2.98601	−	5.17191i	0.490896	−	0.850257i	−0.509049	−	0.860738i	$-0.670003\pi$
$37$	2.98601	−	5.17191i	0.490896	−	0.850257i	0.999945	+	0.0104803i	$0.00333604\pi$
$38$		−	0.498239i		−	0.0808250i
$39$	1.98340	−	5.41796i	0.317598	−	0.867568i
$40$		0			0
$41$	3.23205	+	1.86603i	0.504762	+	0.291424i	0.730678	−	0.682723i	$-0.239204\pi$
$41$	3.23205	+	1.86603i	0.504762	+	0.291424i	−0.225916	+	0.974147i	$0.572538\pi$
$42$	0.101151	+	0.0583993i	0.0156079	+	0.00901121i
$43$	−4.38581	+	2.53215i	−0.668830	+	0.386149i	−0.795633	−	0.605779i	$-0.792862\pi$
$43$	−4.38581	+	2.53215i	−0.668830	+	0.386149i	0.126803	+	0.991928i	$0.459528\pi$
$44$			10.4844i			1.58058i
$45$		0			0
$46$	0.540166	−	0.311865i	0.0796432	−	0.0459820i
$47$	−8.34285			−1.21693			−0.608465	−	0.793581i	$-0.708214\pi$
$47$	−8.34285			−1.21693			−0.608465	+	0.793581i	$0.708214\pi$
$48$	5.14517	−	2.97057i	0.742642	−	0.428764i
$49$	3.44481	−	5.96658i	0.492115	−	0.852368i
$50$		0			0
$51$	−8.10387			−1.13477
$52$	−5.39913	+	4.51332i	−0.748724	+	0.625885i
$53$			1.56063i			0.214369i	0.994239	+	0.107184i	$0.0341835\pi$
$53$			1.56063i			0.214369i	−0.994239	+	0.107184i	$0.965817\pi$
$54$	1.04710	+	0.604542i	0.142492	+	0.0822678i
$55$		0			0
$56$	−0.144219	−	0.249795i	−0.0192721	−	0.0333802i
$57$	−3.62916			−0.480694
$58$	0.318928	+	0.552399i	0.0418773	+	0.0725335i
$59$	−2.34461	+	1.35366i	−0.305242	+	0.176232i	−0.644795	−	0.764355i	$-0.723057\pi$
$59$	−2.34461	+	1.35366i	−0.305242	+	0.176232i	0.339553	+	0.940587i	$0.389724\pi$
$60$		0			0
$61$	−7.05193	−	12.2143i	−0.902908	−	1.56388i	−0.823702	−	0.567023i	$-0.808095\pi$
$61$	−7.05193	−	12.2143i	−0.902908	−	1.56388i	−0.0792059	−	0.996858i	$-0.525238\pi$
$62$	−1.03957	−	0.600196i	−0.132025	−	0.0762249i
$63$	−0.0729902	+	0.126423i	−0.00919590	+	0.0159278i
$64$	−6.86488			−0.858111
$65$		0			0
$66$	−1.88842			−0.232448
$67$	−5.16612	+	8.94799i	−0.631142	+	1.09317i	0.356176	+	0.934419i	$0.384080\pi$
$67$	−5.16612	+	8.94799i	−0.631142	+	1.09317i	−0.987319	+	0.158752i	$0.949253\pi$
$68$	8.55995	+	4.94209i	1.03805	+	0.599316i
$69$	−2.27162	−	3.93456i	−0.273471	−	0.473666i
$70$		0			0
$71$	−11.0828	+	6.39866i	−1.31529	+	0.759382i	−0.982967	−	0.183785i	$-0.941165\pi$
$71$	−11.0828	+	6.39866i	−1.31529	+	0.759382i	−0.332321	+	0.943166i	$0.607832\pi$
$72$	−0.190720	−	0.330337i	−0.0224766	−	0.0389306i
$73$	−9.68922			−1.13404			−0.567019	−	0.823705i	$-0.691903\pi$
$73$	−9.68922			−1.13404			−0.567019	+	0.823705i	$0.691903\pi$
$74$	−0.655986	−	1.13620i	−0.0762569	−	0.132081i
$75$		0			0
$76$	3.83341	+	2.21322i	0.439722	+	0.253874i
$77$		−	1.78477i		−	0.203393i
$78$	−0.812927	−	0.972477i	−0.0920459	−	0.110111i
$79$	−4.51851			−0.508372			−0.254186	−	0.967155i	$-0.581808\pi$
$79$	−4.51851			−0.508372			−0.254186	+	0.967155i	$0.581808\pi$
$80$		0			0
$81$	3.74441	−	6.48552i	0.416046	−	0.720613i
$82$	0.710039	−	0.409941i	0.0784107	−	0.0452704i
$83$	4.26371			0.468003			0.234001	−	0.972236i	$-0.424818\pi$
$83$	4.26371			0.468003			0.234001	+	0.972236i	$0.424818\pi$
$84$	−0.898640	+	0.518830i	−0.0980496	+	0.0566090i
$85$		0			0
$86$			1.11256i			0.119970i
$87$	4.02367	−	2.32306i	0.431382	−	0.249059i
$88$	4.03872	+	2.33176i	0.430529	+	0.248566i
$89$	2.79366	+	1.61292i	0.296127	+	0.170969i	0.640702	−	0.767790i	$-0.278644\pi$
$89$	2.79366	+	1.61292i	0.296127	+	0.170969i	−0.344575	+	0.938759i	$0.611977\pi$
$90$		0			0
$91$	0.919100	−	0.768307i	0.0963478	−	0.0805405i
$92$			5.54133i			0.577724i
$93$	−4.37182	+	7.57221i	−0.453336	+	0.785201i
$94$	−0.916407	+	1.58726i	−0.0945202	+	0.163714i
$95$		0			0
$96$		−	4.08359i		−	0.416780i
$97$	1.25396	+	2.17191i	0.127320	+	0.220524i	0.922637	−	0.385669i	$-0.126029\pi$
$97$	1.25396	+	2.17191i	0.127320	+	0.220524i	−0.795318	+	0.606193i	$0.792696\pi$
$98$	−0.756779	−	1.31078i	−0.0764462	−	0.132409i
$99$		−	2.36023i		−	0.237213i
$100$		0			0
$101$	6.22336	−	10.7792i	0.619247	−	1.07257i	−0.370376	−	0.928882i	$-0.620771\pi$
$101$	6.22336	−	10.7792i	0.619247	−	1.07257i	0.989623	−	0.143686i	$-0.0458955\pi$
$102$	−0.890157	+	1.54180i	−0.0881386	+	0.152661i
$103$		−	15.0247i		−	1.48043i	−0.672370	−	0.740215i	$-0.734724\pi$
$103$		−	15.0247i		−	1.48043i	0.672370	−	0.740215i	$-0.265276\pi$
$104$	0.537808	+	3.08359i	0.0527364	+	0.302371i
$105$		0			0
$106$	0.296916	+	0.171425i	0.0288390	+	0.0166502i
$107$	11.3140	+	6.53215i	1.09377	+	0.631487i	0.934577	−	0.355761i	$-0.115778\pi$
$107$	11.3140	+	6.53215i	1.09377	+	0.631487i	0.159190	+	0.987248i	$0.449112\pi$
$108$	−9.30260	+	5.37086i	−0.895144	+	0.516811i
$109$		−	11.2325i		−	1.07587i	−0.842985	−	0.537937i	$-0.819204\pi$
$109$		−	11.2325i		−	1.07587i	0.842985	−	0.537937i	$-0.180796\pi$
$110$		0			0
$111$	−8.27607	+	4.77819i	−0.785530	+	0.453526i
$112$	1.23355			0.116560
$113$	15.8862	−	9.17191i	1.49445	−	0.862821i	0.494470	−	0.869195i	$-0.335362\pi$
$113$	15.8862	−	9.17191i	1.49445	−	0.862821i	0.999980	+	0.00637349i	$0.00202876\pi$
$114$	−0.398640	+	0.690464i	−0.0373360	+	0.0646679i
$115$		0			0
$116$	−5.66682			−0.526151
$117$	1.21545	−	1.01603i	0.112368	−	0.0939325i
$118$			0.594763i			0.0547524i
$119$	−1.45717	−	0.841298i	−0.133579	−	0.0771216i
$120$		0			0
$121$	8.92820	+	15.4641i	0.811655	+	1.40583i
$122$	−3.09843			−0.280519
$123$	−2.98601	−	5.17191i	−0.269239	−	0.466336i
$124$	9.23572	−	5.33225i	0.829392	−	0.478850i
$125$		0			0
$126$	0.0160350	+	0.0277734i	0.00142851	+	0.00247425i
$127$	2.80589	+	1.61998i	0.248982	+	0.143750i	0.619298	−	0.785156i	$-0.287417\pi$
$127$	2.80589	+	1.61998i	0.248982	+	0.143750i	−0.370316	+	0.928906i	$0.620751\pi$
$128$	−3.30600	+	5.72615i	−0.292212	+	0.506125i
$129$	8.10387			0.713506
$130$		0			0
$131$	0.175664			0.0153478			0.00767390	−	0.999971i	$-0.497557\pi$
$131$	0.175664			0.0153478			0.00767390	+	0.999971i	$0.497557\pi$
$132$	8.38853	−	14.5294i	0.730127	−	1.26462i
$133$	−0.652566	−	0.376759i	−0.0565846	−	0.0326692i
$134$	1.13493	+	1.96576i	0.0980430	+	0.169815i
$135$		0			0
$136$	3.80752	−	2.19827i	0.326492	−	0.188500i
$137$	−8.99144	−	15.5736i	−0.768190	−	1.33054i	−0.938543	−	0.345162i	$-0.887824\pi$
$137$	−8.99144	−	15.5736i	−0.768190	−	1.33054i	0.170353	−	0.985383i	$-0.445509\pi$
$138$	−0.998090			−0.0849631
$139$	5.99307	+	10.3803i	0.508325	+	0.880445i	0.999954	+	0.00964021i	$0.00306862\pi$
$139$	5.99307	+	10.3803i	0.508325	+	0.880445i	−0.491628	+	0.870805i	$0.663598\pi$
$140$		0			0
$141$	11.5616	+	6.67510i	0.973663	+	0.562144i
$142$			2.81140i			0.235928i
$143$	−6.65821	+	18.1879i	−0.556788	+	1.52095i
$144$	1.63129			0.135941
$145$		0			0
$146$	−1.06430	+	1.84342i	−0.0880819	+	0.152562i
$147$	−9.54769	+	5.51236i	−0.787481	+	0.454652i
$148$	11.6558			0.958101
$149$	−2.95350	+	1.70520i	−0.241960	+	0.139696i	−0.616077	−	0.787686i	$-0.711279\pi$
$149$	−2.95350	+	1.70520i	−0.241960	+	0.139696i	0.374117	+	0.927381i	$0.377946\pi$
$150$		0			0
$151$			7.96141i			0.647890i	0.946076	+	0.323945i	$0.105009\pi$
$151$			7.96141i			0.647890i	−0.946076	+	0.323945i	$0.894991\pi$
$152$	1.70512	−	0.984454i	0.138304	−	0.0798498i
$153$	−1.92701	−	1.11256i	−0.155790	−	0.0899451i
$154$	−0.339560	−	0.196045i	−0.0273625	−	0.0157978i
$155$		0			0
$156$	11.0933	−	1.93477i	0.888172	−	0.154906i
$157$		−	16.4329i		−	1.31148i	−0.754985	−	0.655742i	$-0.772356\pi$
$157$		−	16.4329i		−	1.31148i	0.754985	−	0.655742i	$-0.227644\pi$
$158$	−0.496329	+	0.859667i	−0.0394858	+	0.0683914i
$159$	1.24865	−	2.16273i	0.0990247	−	0.171516i
$160$		0			0
$161$		−	0.943307i		−	0.0743430i
$162$	−0.822599	−	1.42478i	−0.0646295	−	0.111942i
$163$	−8.90361	−	15.4215i	−0.697384	−	1.20791i	−0.969370	−	0.245604i	$-0.921014\pi$
$163$	−8.90361	−	15.4215i	−0.697384	−	1.20791i	0.271986	−	0.962301i	$-0.412320\pi$
$164$			7.28398i			0.568784i
$165$		0			0
$166$	0.468341	−	0.811190i	0.0363503	−	0.0629605i
$167$	−3.14683	+	5.45047i	−0.243509	+	0.421770i	−0.961711	−	0.274064i	$-0.911632\pi$
$167$	−3.14683	+	5.45047i	−0.243509	+	0.421770i	0.718202	+	0.695834i	$0.244965\pi$
$168$			0.461557i			0.0356099i
$169$	−12.2325	+	4.40078i	−0.940959	+	0.338522i
$170$		0			0
$171$	−0.862975	−	0.498239i	−0.0659933	−	0.0381013i
$172$	−8.55995	−	4.94209i	−0.652690	−	0.376831i
$173$	13.8349	−	7.98756i	1.05184	−	0.607283i	0.128679	−	0.991686i	$-0.458926\pi$
$173$	13.8349	−	7.98756i	1.05184	−	0.607283i	0.923165	+	0.384404i	$0.125593\pi$
$174$		−	1.02069i		−	0.0773786i
$175$		0			0
$176$	−17.2722	+	9.97212i	−1.30194	+	0.751677i
$177$	4.33225			0.325632
$178$	0.613729	−	0.354337i	0.0460010	−	0.0265587i
$179$	−11.8087	+	20.4533i	−0.882625	+	1.52875i	−0.0342123	+	0.999415i	$0.510892\pi$
$179$	−11.8087	+	20.4533i	−0.882625	+	1.52875i	−0.848412	+	0.529336i	$0.822441\pi$
$180$		0			0
$181$	2.62590			0.195182			0.0975909	−	0.995227i	$-0.468886\pi$
$181$	2.62590			0.195182			0.0975909	+	0.995227i	$0.468886\pi$
$182$	−0.0452168	−	0.259256i	−0.00335169	−	0.0192174i
$183$			22.5689i			1.66834i
$184$	2.13459	+	1.23241i	0.157364	+	0.0908544i
$185$		0			0
$186$	0.960431	+	1.66351i	0.0704222	+	0.121975i
$187$	27.2045			1.98939
$188$	−8.14153	−	14.1015i	−0.593782	−	1.02846i
$189$	1.58359	−	0.914288i	0.115189	−	0.0665046i
$190$		0			0
$191$	1.00791	+	1.74575i	0.0729298	+	0.126318i	0.900184	−	0.435509i	$-0.143432\pi$
$191$	1.00791	+	1.74575i	0.0729298	+	0.126318i	−0.827254	+	0.561828i	$0.810098\pi$
$192$	9.51343	+	5.49258i	0.686572	+	0.396393i
$193$	−11.4105	+	19.7636i	−0.821348	+	1.42262i	0.0833298	+	0.996522i	$0.473445\pi$
$193$	−11.4105	+	19.7636i	−0.821348	+	1.42262i	−0.904678	+	0.426095i	$0.859889\pi$
$194$	0.550955			0.0395563
$195$		0			0
$196$	13.4467			0.960480
$197$	0.321513	−	0.556877i	0.0229068	−	0.0396758i	−0.854345	−	0.519707i	$-0.826041\pi$
$197$	0.321513	−	0.556877i	0.0229068	−	0.0396758i	0.877252	+	0.480031i	$0.159375\pi$
$198$	−0.449045	−	0.259256i	−0.0319122	−	0.0184245i
$199$	−1.53342	−	2.65596i	−0.108701	−	0.188276i	0.806543	−	0.591175i	$-0.201336\pi$
$199$	−1.53342	−	2.65596i	−0.108701	−	0.188276i	−0.915244	+	0.402899i	$0.868003\pi$
$200$		0			0
$201$	14.3185	−	8.26681i	1.00995	−	0.583096i
$202$	−1.36719	−	2.36804i	−0.0961952	−	0.166615i
$203$	0.964670			0.0677065
$204$	−7.90831	−	13.6976i	−0.553693	−	0.959024i
$205$		0			0
$206$	−2.85852	−	1.65037i	−0.199163	−	0.114987i
$207$		−	1.24746i		−	0.0867045i
$208$	−12.5707	−	4.60185i	−0.871620	−	0.319081i
$209$	12.1830			0.842716
$210$		0			0
$211$	4.10020	−	7.10175i	0.282269	−	0.488904i	−0.689674	−	0.724120i	$-0.742246\pi$
$211$	4.10020	−	7.10175i	0.282269	−	0.488904i	0.971943	+	0.235215i	$0.0755796\pi$
$212$	−2.63786	+	1.52297i	−0.181169	+	0.104598i
$213$	20.4782			1.40314
$214$	2.48554	−	1.43503i	0.169908	−	0.0980964i
$215$		0			0
$216$			4.77798i			0.325101i
$217$	−1.57221	+	0.907714i	−0.106728	+	0.0616197i
$218$	−2.13703	−	1.23381i	−0.144738	−	0.0835643i
$219$	13.4274	+	7.75232i	0.907341	+	0.523854i
$220$		0			0
$221$	11.7110	+	14.0095i	0.787767	+	0.942378i
$222$			2.09941i			0.140903i
$223$	5.12210	−	8.87174i	0.343001	−	0.594095i	−0.641987	−	0.766715i	$-0.721890\pi$
$223$	5.12210	−	8.87174i	0.343001	−	0.594095i	0.984989	+	0.172620i	$0.0552232\pi$
$224$	0.423935	−	0.734278i	0.0283254	−	0.0490610i
$225$		0			0
$226$		−	4.02990i		−	0.268065i
$227$	−3.52190	−	6.10012i	−0.233757	−	0.404879i	0.725154	−	0.688587i	$-0.241769\pi$
$227$	−3.52190	−	6.10012i	−0.233757	−	0.404879i	−0.958911	+	0.283708i	$0.908435\pi$
$228$	−3.54159	−	6.13421i	−0.234547	−	0.406248i
$229$		−	1.32899i		−	0.0878219i	−0.999035	−	0.0439109i	$-0.986018\pi$
$229$		−	1.32899i		−	0.0878219i	0.999035	−	0.0439109i	$-0.0139818\pi$
$230$		0			0
$231$	−1.42799	+	2.47335i	−0.0939547	+	0.162734i
$232$	−1.26032	+	2.18294i	−0.0827440	+	0.143317i
$233$		−	1.24746i		−	0.0817238i	−0.999165	−	0.0408619i	$-0.986990\pi$
$233$		−	1.24746i		−	0.0817238i	0.999165	−	0.0408619i	$-0.0130104\pi$
$234$	−0.0597962	−	0.342849i	−0.00390900	−	0.0224127i
$235$		0			0
$236$	−4.57606	−	2.64199i	−0.297876	−	0.171979i
$237$	6.26180	+	3.61525i	0.406748	+	0.234836i
$238$	−0.320121	+	0.184822i	−0.0207504	+	0.0119802i
$239$		−	9.94207i		−	0.643099i	−0.946893	−	0.321549i	$-0.895796\pi$
$239$		−	9.94207i		−	0.643099i	0.946893	−	0.321549i	$-0.104204\pi$
$240$		0			0
$241$	−19.5608	+	11.2934i	−1.26002	+	0.727475i	−0.973079	−	0.230472i	$-0.925973\pi$
$241$	−19.5608	+	11.2934i	−1.26002	+	0.727475i	−0.286944	+	0.957947i	$0.592640\pi$
$242$	3.92282			0.252168
$243$	3.92086	−	2.26371i	0.251523	−	0.145217i
$244$	13.7635	−	23.8391i	0.881119	−	1.52614i
$245$		0			0
$246$	−1.31197			−0.0836483
$247$	5.24455	+	6.27387i	0.333702	+	0.399197i
$248$		−	4.74363i		−	0.301221i
$249$	−5.90869	−	3.41139i	−0.374448	−	0.216188i
$250$		0			0
$251$	−3.38418	−	5.86157i	−0.213608	−	0.369979i	0.739233	−	0.673449i	$-0.235188\pi$
$251$	−3.38418	−	5.86157i	−0.213608	−	0.369979i	−0.952841	+	0.303470i	$0.901855\pi$
$252$	−0.284915			−0.0179480
$253$	7.62577	+	13.2082i	0.479428	+	0.830394i
$254$	0.616417	−	0.355888i	0.0386774	−	0.0223304i
$255$		0			0
$256$	−6.13860	−	10.6324i	−0.383663	−	0.664523i
$257$	−8.88007	−	5.12691i	−0.553924	−	0.319808i	0.196779	−	0.980448i	$-0.436952\pi$
$257$	−8.88007	−	5.12691i	−0.553924	−	0.319808i	−0.750703	+	0.660640i	$0.770285\pi$
$258$	0.890157	−	1.54180i	0.0554187	−	0.0959881i
$259$	−1.98418			−0.123291
$260$		0			0
$261$	1.27571			0.0789645
$262$	0.0192955	−	0.0334208i	0.00119208	−	0.00206474i
$263$	16.1574	+	9.32850i	0.996310	+	0.575220i	0.907154	−	0.420798i	$-0.138250\pi$
$263$	16.1574	+	9.32850i	0.996310	+	0.575220i	0.0891555	+	0.996018i	$0.471583\pi$
$264$	−3.73127	−	6.46275i	−0.229644	−	0.397754i
$265$		0			0
$266$	−0.143360	+	0.0827690i	−0.00878998	+	0.00507489i
$267$	−2.58098	−	4.47040i	−0.157954	−	0.273584i
$268$	−20.1658			−1.23182
$269$	8.97894	+	15.5520i	0.547456	+	0.948221i	0.998448	+	0.0556934i	$0.0177369\pi$
$269$	8.97894	+	15.5520i	0.547456	+	0.948221i	−0.450992	+	0.892528i	$0.648930\pi$
$270$		0			0
$271$	−26.7582	−	15.4488i	−1.62544	−	0.938450i	−0.985429	−	0.170086i	$-0.945595\pi$
$271$	−26.7582	−	15.4488i	−1.62544	−	0.938450i	−0.640014	−	0.768363i	$-0.721071\pi$
$272$			18.8025i			1.14007i
$273$	−1.88842	+	0.329358i	−0.114292	+	0.0199337i
$274$	−3.95060			−0.238665
$275$		0			0
$276$	4.43361	−	7.67923i	0.266872	−	0.462235i
$277$	−22.9536	+	13.2522i	−1.37915	+	0.796250i	−0.992057	−	0.125792i	$-0.959853\pi$
$277$	−22.9536	+	13.2522i	−1.37915	+	0.796250i	−0.387089	+	0.922042i	$0.626519\pi$
$278$	2.63320			0.157929
$279$	−2.07914	+	1.20039i	−0.124475	+	0.0718656i
$280$		0			0
$281$			4.97766i			0.296942i	0.988917	+	0.148471i	$0.0474352\pi$
$281$			4.97766i			0.296942i	−0.988917	+	0.148471i	$0.952565\pi$
$282$	2.53993	−	1.46643i	0.151251	−	0.0873247i
$283$	10.9001	+	6.29317i	0.647943	+	0.374090i	0.787668	−	0.616100i	$-0.211288\pi$
$283$	10.9001	+	6.29317i	0.647943	+	0.374090i	−0.139725	+	0.990190i	$0.544622\pi$
$284$	−21.6307	−	12.4885i	−1.28355	−	0.741057i
$285$		0			0
$286$	2.72898	+	3.26458i	0.161368	+	0.193039i
$287$		−	1.23996i		−	0.0731926i
$288$	0.560626	−	0.971033i	0.0330352	−	0.0572187i
$289$	4.32355	−	7.48861i	0.254327	−	0.440507i
$290$		0			0
$291$		−	4.01315i		−	0.235255i
$292$	−9.45541	−	16.3772i	−0.553336	−	0.958406i
$293$	−8.45880	−	14.6511i	−0.494168	−	0.855925i	0.505809	−	0.862645i	$-0.331194\pi$
$293$	−8.45880	−	14.6511i	−0.494168	−	0.855925i	−0.999977	+	0.00672072i	$0.997861\pi$
$294$			2.42199i			0.141253i
$295$		0			0
$296$	2.59229	−	4.48997i	0.150674	−	0.260974i
$297$	−14.7824	+	25.6038i	−0.857759	+	1.48568i
$298$			0.749222i			0.0434012i
$299$	−3.51908	+	9.61292i	−0.203514	+	0.555929i
$300$		0			0
$301$	1.45717	+	0.841298i	0.0839899	+	0.0484916i
$302$	1.51469	+	0.874509i	0.0871608	+	0.0503223i
$303$	−17.2488	+	9.95859i	−0.990917	+	0.572106i
$304$			8.42034i			0.482940i
$305$		0			0
$306$	−0.423339	+	0.244415i	−0.0242007	+	0.0139723i
$307$	4.30426			0.245657			0.122828	−	0.992428i	$-0.460803\pi$
$307$	4.30426			0.245657			0.122828	+	0.992428i	$0.460803\pi$
$308$	3.01671	−	1.74170i	0.171893	−	0.0992425i
$309$	−12.0213	+	20.8214i	−0.683865	+	1.18449i
$310$		0			0
$311$	2.22512			0.126175			0.0630875	−	0.998008i	$-0.479905\pi$
$311$	2.22512			0.126175			0.0630875	+	0.998008i	$0.479905\pi$
$312$	1.72188	−	4.70357i	0.0974820	−	0.266287i
$313$		−	7.20887i		−	0.407469i	−0.979026	−	0.203735i	$-0.934692\pi$
$313$		−	7.20887i		−	0.407469i	0.979026	−	0.203735i	$-0.0653080\pi$
$314$	−3.12642	−	1.80504i	−0.176434	−	0.101864i
$315$		0			0
$316$	−4.40948	−	7.63744i	−0.248052	−	0.429639i
$317$	−0.321644			−0.0180653			−0.00903266	−	0.999959i	$-0.502875\pi$
$317$	−0.321644			−0.0180653			−0.00903266	+	0.999959i	$0.502875\pi$
$318$	−0.274313	−	0.475124i	−0.0153827	−	0.0266436i
$319$	−13.5073	+	7.79847i	−0.756266	+	0.436630i
$320$		0			0
$321$	−10.4527	−	18.1046i	−0.583414	−	1.01050i
$322$	−0.179468	−	0.103616i	−0.0100014	−	0.00577430i
$323$	5.74278	−	9.94679i	0.319537	−	0.553454i
$324$	14.6162			0.812013
$325$		0			0
$326$	−3.91201			−0.216666
$327$	−8.98707	+	15.5661i	−0.496986	+	0.860805i
$328$	2.80589	+	1.61998i	0.154929	+	0.0894485i
$329$	1.38594	+	2.40052i	0.0764094	+	0.132345i
$330$		0			0
$331$	−14.4037	+	8.31600i	−0.791701	+	0.457089i	−0.840561	−	0.541717i	$-0.817775\pi$
$331$	−14.4037	+	8.31600i	−0.791701	+	0.457089i	0.0488600	+	0.998806i	$0.484441\pi$
$332$	4.16082	+	7.20676i	0.228355	+	0.395522i
$333$	−2.62395			−0.143791
$334$	0.691317	+	1.19740i	0.0378272	+	0.0655186i
$335$		0			0
$336$	−1.70947	−	0.986961i	−0.0932590	−	0.0538431i
$337$		−	24.2186i		−	1.31927i	−0.751586	−	0.659636i	$-0.770711\pi$
$337$		−	24.2186i		−	1.31927i	0.751586	−	0.659636i	$-0.229289\pi$
$338$	−0.506387	+	2.81068i	−0.0275438	+	0.152881i
$339$	−29.3537			−1.59427
$340$		0			0
$341$	14.6761	−	25.4197i	0.794754	−	1.37655i
$342$	−0.189584	+	0.109456i	−0.0102515	+	0.00591873i
$343$	−4.61478			−0.249174
$344$	−3.80752	+	2.19827i	−0.205288	+	0.118523i
$345$		0			0
$346$		−	3.50952i		−	0.188673i
$347$	−5.43309	+	3.13680i	−0.291664	+	0.168392i	−0.638692	−	0.769463i	$-0.720524\pi$
$347$	−5.43309	+	3.13680i	−0.291664	+	0.168392i	0.347028	+	0.937855i	$0.387191\pi$
$348$	7.85314	+	4.53401i	0.420972	+	0.243049i
$349$	6.12275	+	3.53497i	0.327743	+	0.189223i	0.654839	−	0.755769i	$-0.272737\pi$
$349$	6.12275	+	3.53497i	0.327743	+	0.189223i	−0.327095	+	0.944991i	$0.606070\pi$
$350$		0			0
$351$	−19.5487	+	3.40948i	−1.04343	+	0.181984i
$352$			13.7085i			0.730666i
$353$	−10.8949	+	18.8705i	−0.579878	+	1.00438i	0.415615	+	0.909541i	$0.363566\pi$
$353$	−10.8949	+	18.8705i	−0.579878	+	1.00438i	−0.995493	+	0.0948371i	$0.969767\pi$
$354$	0.475869	−	0.824229i	0.0252921	−	0.0438073i
$355$		0			0
$356$			6.29598i			0.333687i
$357$	1.34624	+	2.33176i	0.0712506	+	0.123410i
$358$	2.59422	+	4.49332i	0.137109	+	0.237479i
$359$		−	23.9737i		−	1.26528i	−0.774444	−	0.632642i	$-0.781971\pi$
$359$		−	23.9737i		−	1.26528i	0.774444	−	0.632642i	$-0.218029\pi$
$360$		0			0
$361$	−6.92820	+	12.0000i	−0.364642	+	0.631579i
$362$	0.288438	−	0.499589i	0.0151600	−	0.0262578i
$363$		−	28.5737i		−	1.49973i
$364$	2.19556	+	0.803745i	0.115078	+	0.0421277i
$365$		0			0
$366$	4.29384	+	2.47905i	0.224443	+	0.129582i
$367$	−5.53505	−	3.19566i	−0.288927	−	0.166812i	0.348531	−	0.937297i	$-0.386681\pi$
$367$	−5.53505	−	3.19566i	−0.288927	−	0.166812i	−0.637458	+	0.770485i	$0.720014\pi$
$368$	−9.12892	+	5.27059i	−0.475878	+	0.274748i
$369$		−	1.63977i		−	0.0853628i
$370$		0			0
$371$	0.449045	−	0.259256i	0.0233133	−	0.0134599i
$372$	−17.0653			−0.884793
$373$	17.3899	−	10.0401i	0.900414	−	0.519855i	0.0230798	−	0.999734i	$-0.492653\pi$
$373$	17.3899	−	10.0401i	0.900414	−	0.519855i	0.877335	+	0.479879i	$0.159319\pi$
$374$	2.98823	−	5.17577i	0.154518	−	0.267633i
$375$		0			0
$376$	−7.24280			−0.373519
$377$	−9.83062	−	3.59878i	−0.506302	−	0.185346i
$378$		−	0.401714i		−	0.0206619i
$379$	4.73007	+	2.73091i	0.242968	+	0.140277i	0.616540	−	0.787324i	$-0.288534\pi$
$379$	4.73007	+	2.73091i	0.242968	+	0.140277i	−0.373572	+	0.927601i	$0.621867\pi$
$380$		0			0
$381$	−2.59229	−	4.48997i	−0.132807	−	0.230028i
$382$	0.442849			0.0226581
$383$	−2.83388	−	4.90842i	−0.144804	−	0.250808i	0.784496	−	0.620134i	$-0.212922\pi$
$383$	−2.83388	−	4.90842i	−0.144804	−	0.250808i	−0.929300	+	0.369326i	$0.879589\pi$
$384$	9.16297	−	5.29024i	0.467596	−	0.269966i
$385$		0			0
$386$	2.50675	+	4.34181i	0.127590	+	0.220992i
$387$	1.92701	+	1.11256i	0.0979554	+	0.0565546i
$388$	−2.44739	+	4.23901i	−0.124247	+	0.215203i
$389$	10.6174			0.538325			0.269162	−	0.963095i	$-0.413253\pi$
$389$	10.6174			0.538325			0.269162	+	0.963095i	$0.413253\pi$
$390$		0			0
$391$	14.3784			0.727149
$392$	2.99059	−	5.17986i	0.151048	−	0.261622i
$393$	−0.243436	−	0.140548i	−0.0122797	−	0.00708971i
$394$	−0.0706321	−	0.122338i	−0.00355840	−	0.00616332i
$395$		0			0
$396$	3.98940	−	2.30328i	0.200475	−	0.115744i
$397$	14.0169	+	24.2780i	0.703487	+	1.21848i	0.967235	+	0.253884i	$0.0817081\pi$
$397$	14.0169	+	24.2780i	0.703487	+	1.21848i	−0.263748	+	0.964592i	$0.584959\pi$
$398$	−0.673745			−0.0337718
$399$	0.602888	+	1.04423i	0.0301822	+	0.0522770i
$400$		0			0
$401$	19.4979	+	11.2571i	0.973680	+	0.562155i	0.900356	−	0.435154i	$-0.143306\pi$
$401$	19.4979	+	11.2571i	0.973680	+	0.562155i	0.0733241	+	0.997308i	$0.476639\pi$
$402$		−	3.63222i		−	0.181159i
$403$	19.4081	−	3.38496i	0.966788	−	0.168617i
$404$	24.2927			1.20861
$405$		0			0
$406$	0.105963	−	0.183533i	0.00525884	−	0.00910857i
$407$	27.7826	−	16.0403i	1.37713	−	0.795087i
$408$	−7.03533			−0.348301
$409$	3.71328	−	2.14386i	0.183610	−	0.106007i	−0.405378	−	0.914149i	$-0.632860\pi$
$409$	3.71328	−	2.14386i	0.183610	−	0.106007i	0.588988	+	0.808142i	$0.299527\pi$
$410$		0			0
$411$			28.7761i			1.41942i
$412$	25.3956	−	14.6622i	1.25115	−	0.722353i
$413$	0.778989	+	0.449749i	0.0383315	+	0.0221307i
$414$	−0.237335	−	0.137025i	−0.0116644	−	0.00673443i
$415$		0			0
$416$	−7.05946	+	5.90125i	−0.346119	+	0.289333i
$417$		−	19.1802i		−	0.939257i
$418$	1.33822	−	2.31787i	0.0654546	−	0.113371i
$419$	8.85578	−	15.3387i	0.432633	−	0.749343i	−0.564466	−	0.825456i	$-0.690918\pi$
$419$	8.85578	−	15.3387i	0.432633	−	0.749343i	0.997099	+	0.0761137i	$0.0242512\pi$
$420$		0			0
$421$		−	12.8787i		−	0.627672i	−0.949477	−	0.313836i	$-0.898386\pi$
$421$		−	12.8787i		−	0.627672i	0.949477	−	0.313836i	$-0.101614\pi$
$422$	−0.900759	−	1.56016i	−0.0438483	−	0.0759474i
$423$	1.83281	+	3.17453i	0.0891145	+	0.154351i
$424$			1.35485i			0.0657973i
$425$		0			0
$426$	2.24940	−	3.89607i	0.108984	−	0.188765i
$427$	−2.34298	+	4.05816i	−0.113385	+	0.196388i
$428$			25.4981i			1.23250i
$429$	23.7792	−	19.8778i	1.14807	−	0.959710i
$430$		0			0
$431$	8.22590	+	4.74923i	0.396228	+	0.228762i	0.684855	−	0.728679i	$-0.259866\pi$
$431$	8.22590	+	4.74923i	0.396228	+	0.228762i	−0.288627	+	0.957442i	$0.593199\pi$
$432$	−17.6962	−	10.2169i	−0.851408	−	0.491560i
$433$	−1.20922	+	0.698141i	−0.0581112	+	0.0335505i	−0.528774	−	0.848763i	$-0.677348\pi$
$433$	−1.20922	+	0.698141i	−0.0581112	+	0.0335505i	0.470663	+	0.882313i	$0.344015\pi$
$434$			0.398826i			0.0191443i
$435$		0			0
$436$	18.9857	−	10.9614i	0.909251	−	0.524956i
$437$	6.43911			0.308024
$438$	2.94983	−	1.70308i	0.140948	−	0.0813765i
$439$	−2.08090	+	3.60422i	−0.0993159	+	0.172020i	−0.911402	−	0.411518i	$-0.864999\pi$
$439$	−2.08090	+	3.60422i	−0.0993159	+	0.172020i	0.812086	+	0.583538i	$0.198332\pi$
$440$		0			0
$441$	−3.02711			−0.144148
$442$	3.95174	−	0.689221i	0.187965	−	0.0327829i
$443$		−	9.54563i		−	0.453526i	−0.973950	−	0.226763i	$-0.927186\pi$
$443$		−	9.54563i		−	0.453526i	0.973950	−	0.226763i	$-0.0728144\pi$
$444$	−16.1527	−	9.32578i	−0.766574	−	0.442582i
$445$		0			0
$446$	−1.12526	−	1.94900i	−0.0532825	−	0.0922880i
$447$	5.45732			0.258122
$448$	1.14042	+	1.97526i	0.0538796	+	0.0933223i
$449$	−18.8075	+	10.8585i	−0.887582	+	0.512446i	−0.873151	−	0.487450i	$-0.837927\pi$
$449$	−18.8075	+	10.8585i	−0.887582	+	0.512446i	−0.0144310	+	0.999896i	$0.504594\pi$
$450$		0			0
$451$	10.0239	+	17.3620i	0.472009	+	0.817544i
$452$	31.0057	+	17.9012i	1.45839	+	0.842000i
$453$	6.36991	−	11.0330i	0.299284	−	0.518376i
$454$	−1.54743			−0.0726246
$455$		0			0
$456$	−3.15064			−0.147542
$457$	−2.36130	+	4.08989i	−0.110457	+	0.191317i	−0.915955	−	0.401282i	$-0.868565\pi$
$457$	−2.36130	+	4.08989i	−0.110457	+	0.191317i	0.805498	+	0.592599i	$0.201898\pi$
$458$	−0.252845	−	0.145980i	−0.0118147	−	0.00682122i
$459$	13.9361	+	24.1381i	0.650482	+	1.12667i
$460$		0			0
$461$	1.54283	−	0.890753i	0.0718568	−	0.0414865i	−0.463641	−	0.886023i	$-0.653457\pi$
$461$	1.54283	−	0.890753i	0.0718568	−	0.0414865i	0.535498	+	0.844537i	$0.320124\pi$
$462$	0.313710	+	0.543362i	0.0145951	+	0.0252795i
$463$	6.80200			0.316116			0.158058	−	0.987430i	$-0.449477\pi$
$463$	6.80200			0.316116			0.158058	+	0.987430i	$0.449477\pi$
$464$	−5.38995	−	9.33566i	−0.250222	−	0.433397i
$465$		0			0
$466$	−0.237335	−	0.137025i	−0.0109943	−	0.00634758i
$467$		−	18.2374i		−	0.843927i	−0.906613	−	0.421963i	$-0.861341\pi$
$467$		−	18.2374i		−	0.843927i	0.906613	−	0.421963i	$-0.138659\pi$
$468$	2.90348	+	1.06290i	0.134213	+	0.0491325i
$469$	3.43285			0.158514
$470$		0			0
$471$	−13.1479	+	22.7728i	−0.605823	+	1.04932i
$472$	−2.03546	+	1.17517i	−0.0936897	+	0.0540918i
$473$	−27.2045			−1.25086
$474$	1.37564	−	0.794223i	0.0631850	−	0.0364799i
$475$		0			0
$476$		−	3.28398i		−	0.150521i
$477$	0.593832	−	0.342849i	0.0271897	−	0.0156980i
$478$	−1.89152	−	1.09207i	−0.0865162	−	0.0499502i
$479$	−30.4674	−	17.5904i	−1.39209	−	0.803724i	−0.398544	−	0.917149i	$-0.630485\pi$
$479$	−30.4674	−	17.5904i	−1.39209	−	0.803724i	−0.993547	+	0.113425i	$0.963818\pi$
$480$		0			0
$481$	20.2201	+	7.40214i	0.921957	+	0.337508i
$482$			4.96204i			0.226015i
$483$	−0.754738	+	1.30724i	−0.0343418	+	0.0594817i
$484$	−17.4255	+	30.1819i	−0.792069	+	1.37190i
$485$		0			0
$486$		−	0.994615i		−	0.0451166i
$487$	5.15200	+	8.92352i	0.233459	+	0.404363i	0.958824	−	0.284002i	$-0.0916621\pi$
$487$	5.15200	+	8.92352i	0.233459	+	0.404363i	−0.725364	+	0.688365i	$0.758329\pi$
$488$	−6.12210	−	10.6038i	−0.277134	−	0.480011i
$489$			28.4950i			1.28859i
$490$		0			0
$491$	4.66599	−	8.08174i	0.210573	−	0.364724i	−0.741321	−	0.671151i	$-0.765800\pi$
$491$	4.66599	−	8.08174i	0.210573	−	0.364724i	0.951894	+	0.306427i	$0.0991336\pi$
$492$	5.82790	−	10.0942i	0.262742	−	0.455083i
$493$			14.7041i			0.662238i
$494$	1.76971	−	0.308654i	0.0796230	−	0.0138870i
$495$		0			0
$496$	17.5689	+	10.1434i	0.788869	+	0.455454i
$497$	3.68222	+	2.12593i	0.165170	+	0.0953611i
$498$	−1.29806	+	0.749437i	−0.0581676	+	0.0335831i
$499$			23.9421i			1.07179i	0.844283	+	0.535897i	$0.180026\pi$
$499$			23.9421i			1.07179i	−0.844283	+	0.535897i	$0.819974\pi$
$500$		0			0
$501$	8.72181	−	5.03554i	0.389662	−	0.224971i
$502$	−1.48692			−0.0663645
$503$	−36.4980	+	21.0721i	−1.62737	+	0.939560i	−0.642490	+	0.766294i	$0.722099\pi$
$503$	−36.4980	+	21.0721i	−1.62737	+	0.939560i	−0.984875	+	0.173266i	$0.944568\pi$
$504$	−0.0633661	+	0.109753i	−0.00282255	+	0.00488880i
$505$		0			0
$506$	3.35056			0.148951
$507$	20.4729	+	3.68852i	0.909235	+	0.163813i
$508$			6.32355i			0.280562i
$509$	29.0640	+	16.7801i	1.28824	+	0.743765i	0.978340	−	0.207005i	$-0.0663715\pi$
$509$	29.0640	+	16.7801i	1.28824	+	0.743765i	0.309899	+	0.950770i	$0.399705\pi$
$510$		0			0
$511$	1.60960	+	2.78792i	0.0712047	+	0.123330i
$512$	−15.9211			−0.703621
$513$	6.24102	+	10.8098i	0.275548	+	0.477263i
$514$	−1.95084	+	1.12632i	−0.0860477	+	0.0496796i
$515$		0			0
$516$	7.90831	+	13.6976i	0.348144	+	0.603003i
$517$	−38.8120	−	22.4081i	−1.70695	−	0.985508i
$518$	−0.217949	+	0.377499i	−0.00957614	+	0.0165864i
$519$	−25.5633			−1.12210
$520$		0			0
$521$	12.4649			0.546098			0.273049	−	0.962000i	$-0.411968\pi$
$521$	12.4649			0.546098			0.273049	+	0.962000i	$0.411968\pi$
$522$	0.140128	−	0.242710i	0.00613326	−	0.0106231i
$523$	−4.90132	−	2.82978i	−0.214320	−	0.123738i	0.388998	−	0.921239i	$-0.372821\pi$
$523$	−4.90132	−	2.82978i	−0.214320	−	0.123738i	−0.603317	+	0.797501i	$0.706155\pi$
$524$	0.171425	+	0.296916i	0.00748872	+	0.0129708i
$525$		0			0
$526$	3.54958	−	2.04935i	0.154769	−	0.0893558i
$527$	−13.8359	−	23.9645i	−0.602702	−	1.04391i
$528$	31.9147			1.38891
$529$	−7.46953	−	12.9376i	−0.324762	−	0.562505i
$530$		0			0
$531$	1.03016	+	0.594763i	0.0447051	+	0.0258105i
$532$		−	1.47067i		−	0.0637616i
$533$	−4.62577	+	12.6360i	−0.200364	+	0.547327i
$534$	−1.13402			−0.0490737
$535$		0			0
$536$	−4.48494	+	7.76815i	−0.193720	+	0.335533i
$537$	32.7293	−	18.8963i	1.41237	−	0.815433i
$538$	3.94511			0.170086
$539$	32.0514	−	18.5049i	1.38055	−	0.797061i
$540$		0			0
$541$		−	15.4750i		−	0.665321i	−0.943047	−	0.332660i	$-0.892054\pi$
$541$		−	15.4750i		−	0.665321i	0.943047	−	0.332660i	$-0.107946\pi$
$542$	−5.87842	+	3.39391i	−0.252500	+	0.145781i
$543$	−3.63900	−	2.10098i	−0.156165	−	0.0901616i
$544$	11.1923	+	6.46187i	0.479866	+	0.277051i
$545$		0			0
$546$	−0.144769	+	0.395458i	−0.00619552	+	0.0169240i
$547$			25.1765i			1.07647i	0.842795	+	0.538234i	$0.180908\pi$
$547$			25.1765i			1.07647i	−0.842795	+	0.538234i	$0.819092\pi$
$548$	17.5489	−	30.3956i	0.749653	−	1.29844i
$549$	−3.09843	+	5.36665i	−0.132238	+	0.229043i
$550$		0			0
$551$			6.58493i			0.280528i
$552$	−1.97210	−	3.41577i	−0.0839380	−	0.145385i
$553$	0.750630	+	1.30013i	0.0319200	+	0.0552871i
$554$			5.82269i			0.247382i
$555$		0			0
$556$	−11.6969	+	20.2596i	−0.496059	+	0.859199i
$557$	21.1744	−	36.6752i	0.897190	−	1.55398i	0.0661194	−	0.997812i	$-0.478938\pi$
$557$	21.1744	−	36.6752i	0.897190	−	1.55398i	0.831071	−	0.556167i	$-0.187728\pi$
$558$			0.527420i			0.0223275i
$559$	−11.7110	−	14.0095i	−0.495322	−	0.592537i
$560$		0			0
$561$	−37.7002	−	21.7662i	−1.59171	−	0.918971i
$562$	0.947022	+	0.546763i	0.0399477	+	0.0230638i
$563$	20.6032	−	11.8953i	0.868322	−	0.501326i	0.00153173	−	0.999999i	$-0.499512\pi$
$563$	20.6032	−	11.8953i	0.868322	−	0.501326i	0.866790	+	0.498673i	$0.166179\pi$
$564$			26.0561i			1.09716i
$565$		0			0
$566$	2.39461	−	1.38253i	0.100653	−	0.0581119i
$567$	−2.48814			−0.104492
$568$	−9.62148	+	5.55497i	−0.403709	+	0.233081i
$569$	13.3710	−	23.1593i	0.560543	−	0.970889i	−0.436906	−	0.899507i	$-0.643926\pi$
$569$	13.3710	−	23.1593i	0.560543	−	0.970889i	0.997449	−	0.0713817i	$-0.0227408\pi$
$570$		0			0
$571$	16.7159			0.699539			0.349769	−	0.936836i	$-0.386260\pi$
$571$	16.7159			0.699539			0.349769	+	0.936836i	$0.386260\pi$
$572$	−37.2398	+	6.49498i	−1.55707	+	0.271569i
$573$		−	3.22571i		−	0.134756i
$574$	−0.235908	−	0.136202i	−0.00984661	−	0.00568494i
$575$		0			0
$576$	1.50812	+	2.61215i	0.0628385	+	0.108840i
$577$	−20.6768			−0.860786			−0.430393	−	0.902642i	$-0.641625\pi$
$577$	−20.6768			−0.860786			−0.430393	+	0.902642i	$0.641625\pi$
$578$	−0.949828	−	1.64515i	−0.0395076	−	0.0684292i
$579$	31.6257	−	18.2591i	1.31432	−	0.758822i
$580$		0			0
$581$	−0.708301	−	1.22681i	−0.0293853	−	0.0508968i
$582$	−0.763519	−	0.440818i	−0.0316489	−	0.0182725i
$583$	−4.19170	+	7.26023i	−0.173602	+	0.300688i
$584$	−8.41165			−0.348076
$585$		0			0
$586$	−3.71657			−0.153530
$587$	−10.3986	+	18.0109i	−0.429196	+	0.743388i	−0.996802	−	0.0799116i	$-0.974536\pi$
$587$	−10.3986	+	18.0109i	−0.429196	+	0.743388i	0.567606	+	0.823300i	$0.307870\pi$
$588$	−18.6346	−	10.7587i	−0.768478	−	0.443681i
$589$	−6.19615	−	10.7321i	−0.255308	−	0.442206i
$590$		0			0
$591$	−0.891111	+	0.514483i	−0.0366554	+	0.0211630i
$592$	11.0863	+	19.2021i	0.455644	+	0.789199i
$593$	−21.8475			−0.897169			−0.448585	−	0.893740i	$-0.648072\pi$
$593$	−21.8475			−0.897169			−0.448585	+	0.893740i	$0.648072\pi$
$594$	3.24749	+	5.62482i	0.133246	+	0.230789i
$595$		0			0
$596$	−5.76446	−	3.32811i	−0.236121	−	0.136325i
$597$			4.90755i			0.200853i
$598$	1.44235	+	1.72544i	0.0589822	+	0.0705583i
$599$	3.58040			0.146291			0.0731456	−	0.997321i	$-0.476696\pi$
$599$	3.58040			0.146291			0.0731456	+	0.997321i	$0.476696\pi$
$600$		0			0
$601$	−10.6743	+	18.4885i	−0.435414	+	0.754160i	−0.997329	−	0.0730352i	$-0.976731\pi$
$601$	−10.6743	+	18.4885i	−0.435414	+	0.754160i	0.561915	+	0.827195i	$0.310065\pi$
$602$	0.320121	−	0.184822i	0.0130472	−	0.00753278i
$603$	4.53972			0.184872
$604$	−13.4568	+	7.76929i	−0.547550	+	0.316128i
$605$		0			0
$606$			4.37554i			0.177744i
$607$	−2.85767	+	1.64988i	−0.115989	+	0.0669665i	−0.556872	−	0.830598i	$-0.687999\pi$
$607$	−2.85767	+	1.64988i	−0.115989	+	0.0669665i	0.440883	+	0.897565i	$0.354665\pi$
$608$	5.01226	+	2.89383i	0.203274	+	0.117360i
$609$	−1.33685	−	0.771830i	−0.0541718	−	0.0312761i
$610$		0			0
$611$	−5.16832	−	29.6332i	−0.209088	−	1.19883i
$612$		−	4.34285i		−	0.175549i
$613$	4.94318	−	8.56183i	0.199653	−	0.345809i	−0.748763	−	0.662838i	$-0.769352\pi$
$613$	4.94318	−	8.56183i	0.199653	−	0.345809i	0.948416	+	0.317029i	$0.102685\pi$
$614$	0.472795	−	0.818904i	0.0190804	−	0.0330483i
$615$		0			0
$616$		−	1.54944i		−	0.0624286i
$617$	22.8584	+	39.5920i	0.920246	+	1.59391i	0.799033	+	0.601287i	$0.205345\pi$
$617$	22.8584	+	39.5920i	0.920246	+	1.59391i	0.121213	+	0.992626i	$0.461321\pi$
$618$	2.64091	+	4.57419i	0.106233	+	0.184001i
$619$		−	19.9143i		−	0.800425i	−0.916422	−	0.400212i	$-0.868936\pi$
$619$		−	19.9143i		−	0.800425i	0.916422	−	0.400212i	$-0.131064\pi$
$620$		0			0
$621$	−7.81295	+	13.5324i	−0.313523	+	0.543038i
$622$	0.244415	−	0.423339i	0.00980014	−	0.0169743i
$623$		−	1.07177i		−	0.0429397i
$624$	13.7386	+	16.4351i	0.549986	+	0.657930i
$625$		0			0
$626$	−1.37152	−	0.791847i	−0.0548169	−	0.0316486i
$627$	−16.8833	−	9.74760i	−0.674255	−	0.389282i
$628$	27.7757	−	16.0363i	1.10837	−	0.639918i
$629$		−	30.2440i		−	1.20591i
$630$		0			0
$631$	12.6403	−	7.29790i	0.503204	−	0.290525i	−0.226832	−	0.973934i	$-0.572837\pi$
$631$	12.6403	−	7.29790i	0.503204	−	0.290525i	0.730036	+	0.683409i	$0.239503\pi$
$632$	−3.92272			−0.156038
$633$	−11.3642	+	6.56112i	−0.451686	+	0.260781i
$634$	−0.0353305	+	0.0611942i	−0.00140315	+	0.00243033i
$635$		0			0
$636$	4.87409			0.193270
$637$	23.3269	+	8.53948i	0.924246	+	0.338346i
$638$			3.42644i			0.135654i
$639$	4.86950	+	2.81140i	0.192634	+	0.111217i
$640$		0			0
$641$	−7.08183	−	12.2661i	−0.279716	−	0.484482i	0.691598	−	0.722282i	$-0.256907\pi$
$641$	−7.08183	−	12.2661i	−0.279716	−	0.484482i	−0.971314	+	0.237801i	$0.923573\pi$
$642$	−4.59265			−0.181257
$643$	8.38581	+	14.5246i	0.330704	+	0.572796i	0.982650	−	0.185469i	$-0.0593805\pi$
$643$	8.38581	+	14.5246i	0.330704	+	0.572796i	−0.651946	+	0.758265i	$0.726047\pi$
$644$	1.59443	−	0.920544i	0.0628293	−	0.0362745i
$645$		0			0
$646$	−1.26161	−	2.18518i	−0.0496376	−	0.0859748i
$647$	−2.59087	−	1.49584i	−0.101858	−	0.0588075i	0.448206	−	0.893930i	$-0.352063\pi$
$647$	−2.59087	−	1.49584i	−0.101858	−	0.0588075i	−0.550063	+	0.835123i	$0.685396\pi$
$648$	3.25069	−	5.63037i	0.127699	−	0.221182i
$649$	−14.5432			−0.570872
$650$		0			0
$651$	2.90504			0.113858
$652$	17.3775	−	30.0987i	0.680556	−	1.17876i
$653$	−10.1016	−	5.83217i	−0.395307	−	0.228230i	0.289150	−	0.957284i	$-0.406627\pi$
$653$	−10.1016	−	5.83217i	−0.395307	−	0.228230i	−0.684457	+	0.729053i	$0.739961\pi$
$654$	1.97434	+	3.41966i	0.0772028	+	0.133719i
$655$		0			0
$656$	−11.9998	+	6.92810i	−0.468514	+	0.270497i
$657$	2.12859	+	3.68683i	0.0830444	+	0.143837i
$658$	0.608946			0.0237392
$659$	−0.905237	−	1.56792i	−0.0352630	−	0.0610773i	0.847855	−	0.530228i	$-0.177894\pi$
$659$	−0.905237	−	1.56792i	−0.0352630	−	0.0610773i	−0.883118	+	0.469150i	$0.844560\pi$
$660$		0			0
$661$	10.6872	+	6.17028i	0.415686	+	0.239996i	0.693230	−	0.720717i	$-0.256187\pi$
$661$	10.6872	+	6.17028i	0.415686	+	0.239996i	−0.277544	+	0.960713i	$0.589520\pi$
$662$			3.65383i			0.142010i
$663$	−5.02027	−	28.7844i	−0.194971	−	1.11789i
$664$	3.70152			0.143647
$665$		0			0
$666$	−0.288223	+	0.499217i	−0.0111684	+	0.0193443i
$667$	−7.13907	+	4.12174i	−0.276426	+	0.159594i
$668$	−12.2836			−0.475265
$669$	−14.1965	+	8.19636i	−0.548869	+	0.316890i
$670$		0			0
$671$		−	75.7634i		−	2.92481i
$672$	−1.17499	+	0.678380i	−0.0453262	+	0.0261691i
$673$	−8.02481	−	4.63313i	−0.309334	−	0.178594i	0.337295	−	0.941399i	$-0.390488\pi$
$673$	−8.02481	−	4.63313i	−0.309334	−	0.178594i	−0.646628	+	0.762805i	$0.723822\pi$
$674$	−4.60770	−	2.66025i	−0.177482	−	0.102469i
$675$		0			0
$676$	−19.3757	−	16.3814i	−0.745220	−	0.630053i
$677$			13.8984i			0.534158i	0.963675	+	0.267079i	$0.0860585\pi$
$677$			13.8984i			0.534158i	−0.963675	+	0.267079i	$0.913941\pi$
$678$	−3.22431	+	5.58467i	−0.123829	+	0.214478i
$679$	0.416622	−	0.721611i	0.0159885	−	0.0276929i
$680$		0			0
$681$			11.2715i			0.431924i
$682$	−3.22414	−	5.58438i	−0.123459	−	0.213837i
$683$	18.8756	+	32.6935i	0.722255	+	1.25098i	0.960094	+	0.279678i	$0.0902278\pi$
$683$	18.8756	+	32.6935i	0.722255	+	1.25098i	−0.237838	+	0.971305i	$0.576439\pi$
$684$		−	1.94486i		−	0.0743637i
$685$		0			0
$686$	−0.506903	+	0.877981i	−0.0193536	+	0.0335215i
$687$	−1.06332	+	1.84172i	−0.0405681	+	0.0702661i
$688$		−	18.8025i		−	0.716838i
$689$	−5.54324	+	0.966794i	−0.211181	+	0.0368319i
$690$		0			0
$691$	−1.43146	−	0.826456i	−0.0544554	−	0.0314399i	0.472525	−	0.881317i	$-0.343343\pi$
$691$	−1.43146	−	0.826456i	−0.0544554	−	0.0314399i	−0.526981	+	0.849877i	$0.676676\pi$
$692$	27.0020	+	15.5896i	1.02646	+	0.592628i
$693$	−0.679120	+	0.392090i	−0.0257976	+	0.0148943i
$694$			1.37823i			0.0523168i
$695$		0			0
$696$	3.49312	−	2.01676i	0.132407	−	0.0764450i
$697$	18.9002			0.715897
$698$	1.34509	−	0.776587i	0.0509123	−	0.0293943i
$699$	−0.998090	+	1.72874i	−0.0377512	+	0.0653871i
$700$		0			0
$701$	−20.4819			−0.773590			−0.386795	−	0.922166i	$-0.626418\pi$
$701$	−20.4819			−0.773590			−0.386795	+	0.922166i	$0.626418\pi$
$702$	−1.49863	+	4.09373i	−0.0565620	+	0.154508i
$703$		−	13.5442i		−	0.510830i
$704$	−31.9363	−	18.4384i	−1.20365	−	0.694925i
$705$		0			0
$706$	2.39347	+	4.14561i	0.0900794	+	0.156022i
$707$	−4.13538			−0.155527
$708$	4.22770	+	7.32260i	0.158887	+	0.275200i
$709$	−19.0021	+	10.9709i	−0.713639	+	0.412020i	−0.812407	−	0.583091i	$-0.801843\pi$
$709$	−19.0021	+	10.9709i	−0.713639	+	0.412020i	0.0987679	+	0.995110i	$0.468510\pi$
$710$		0			0
$711$	0.992658	+	1.71933i	0.0372276	+	0.0644801i
$712$	2.42530	+	1.40025i	0.0908919	+	0.0524764i
$713$	7.75678	−	13.4351i	0.290494	−	0.503150i
$714$	0.591503			0.0221364
$715$		0			0
$716$	−46.0950			−1.72265
$717$	−7.95463	+	13.7778i	−0.297071	+	0.514542i
$718$	−4.56110	−	2.63335i	−0.170219	−	0.0982759i
$719$	−19.4237	−	33.6429i	−0.724384	−	1.25467i	−0.959227	−	0.282636i	$-0.908791\pi$
$719$	−19.4237	−	33.6429i	−0.724384	−	1.25467i	0.234844	−	0.972033i	$-0.424542\pi$
$720$		0			0
$721$	−4.32312	+	2.49596i	−0.161002	+	0.0929543i
$722$	1.52204	+	2.63624i	0.0566443	+	0.0981108i
$723$	36.1434			1.34419
$724$	2.56254	+	4.43844i	0.0952359	+	0.164953i
$725$		0			0
$726$	−5.43628	−	3.13864i	−0.201759	−	0.116486i
$727$			30.6598i			1.13711i	0.822645	+	0.568555i	$0.192497\pi$
$727$			30.6598i			1.13711i	−0.822645	+	0.568555i	$0.807503\pi$
$728$	0.797912	−	0.667002i	0.0295726	−	0.0247207i
$729$	−29.7112			−1.10042
$730$		0			0
$731$	−12.8236	+	22.2110i	−0.474296	+	0.821505i
$732$	−38.1473	+	22.0243i	−1.40996	+	0.814043i
$733$	−24.3858			−0.900709			−0.450355	−	0.892850i	$-0.648702\pi$
$733$	−24.3858			−0.900709			−0.450355	+	0.892850i	$0.648702\pi$
$734$	−1.21598	+	0.702045i	−0.0448826	+	0.0259130i
$735$		0			0
$736$			7.24539i			0.267069i
$737$	−48.0669	+	27.7515i	−1.77057	+	1.02224i
$738$	−0.311973	−	0.180117i	−0.0114839	−	0.00663021i
$739$	33.1504	+	19.1394i	1.21946	+	0.704054i	0.964802	−	0.262977i	$-0.0847044\pi$
$739$	33.1504	+	19.1394i	1.21946	+	0.704054i	0.254656	+	0.967032i	$0.418038\pi$
$740$		0			0
$741$	−2.24823	−	12.8905i	−0.0825909	−	0.473546i
$742$		−	0.113910i		−	0.00418178i
$743$	−20.0040	+	34.6479i	−0.733874	+	1.27111i	0.221342	+	0.975196i	$0.428956\pi$
$743$	−20.0040	+	34.6479i	−0.733874	+	1.27111i	−0.955216	+	0.295910i	$0.904377\pi$
$744$	−3.79537	+	6.57377i	−0.139145	+	0.241006i
$745$		0			0
$746$		−	4.41134i		−	0.161511i
$747$	−0.936681	−	1.62238i	−0.0342714	−	0.0593598i
$748$	26.5480	+	45.9825i	0.970691	+	1.68129i
$749$		−	4.34057i		−	0.158601i
$750$		0			0
$751$	12.8010	−	22.1720i	0.467115	−	0.809067i	−0.532179	−	0.846632i	$-0.678627\pi$
$751$	12.8010	−	22.1720i	0.467115	−	0.809067i	0.999294	+	0.0375648i	$0.0119601\pi$
$752$	15.4875	−	26.8251i	0.564770	−	0.978211i
$753$			10.8307i			0.394693i
$754$	−1.76451	+	1.47502i	−0.0642597	+	0.0537169i
$755$		0			0
$756$	3.09076	+	1.78445i	0.112410	+	0.0648998i
$757$	1.60083	+	0.924239i	0.0581831	+	0.0335920i	0.528809	−	0.848741i	$-0.322639\pi$
$757$	1.60083	+	0.924239i	0.0581831	+	0.0335920i	−0.470626	+	0.882333i	$0.655972\pi$
$758$	1.03914	−	0.599945i	0.0377431	−	0.0217910i
$759$		−	24.4055i		−	0.885862i
$760$		0			0
$761$	22.7006	−	13.1062i	0.822896	−	0.475099i	−0.0285179	−	0.999593i	$-0.509079\pi$
$761$	22.7006	−	13.1062i	0.822896	−	0.475099i	0.851414	+	0.524494i	$0.175745\pi$
$762$	−1.13898			−0.0412610
$763$	−3.23196	+	1.86597i	−0.117005	+	0.0675528i
$764$	−1.96718	+	3.40725i	−0.0711699	+	0.123270i
$765$		0			0
$766$	−1.24513			−0.0449884
$767$	−6.26058	−	7.48932i	−0.226056	−	0.270424i
$768$			19.6459i			0.708911i
$769$	38.4078	+	22.1747i	1.38502	+	0.799641i	0.992749	−	0.120208i	$-0.0383562\pi$
$769$	38.4078	+	22.1747i	1.38502	+	0.799641i	0.392271	+	0.919850i	$0.371690\pi$
$770$		0			0
$771$	8.20406	+	14.2099i	0.295462	+	0.511755i
$772$	−44.5408			−1.60306
$773$	−11.6319	−	20.1471i	−0.418371	−	0.724640i	0.577405	−	0.816458i	$-0.304065\pi$
$773$	−11.6319	−	20.1471i	−0.418371	−	0.724640i	−0.995776	+	0.0918181i	$0.970732\pi$
$774$	0.423339	−	0.244415i	0.0152166	−	0.00878531i
$775$		0			0
$776$	1.08861	+	1.88554i	0.0390790	+	0.0676868i
$777$	2.74970	+	1.58754i	0.0986448	+	0.0569526i
$778$	1.16625	−	2.02001i	0.0418122	−	0.0724209i
$779$	8.46410			0.303258
$780$		0			0
$781$	−68.7449			−2.45989
$782$	1.57938	−	2.73556i	0.0564784	−	0.0978235i
$783$	−13.8389	−	7.98989i	−0.494562	−	0.285535i
$784$	12.7897	+	22.1524i	0.456776	+	0.791159i
$785$		0			0
$786$	−0.0534798	+	0.0308766i	−0.00190756	+	0.00110133i
$787$	−23.9567	−	41.4942i	−0.853963	−	1.47911i	−0.877604	−	0.479387i	$-0.840859\pi$
$787$	−23.9567	−	41.4942i	−0.853963	−	1.47911i	0.0236408	−	0.999721i	$-0.492474\pi$
$788$	1.25502			0.0447081
$789$	−14.9274	−	25.8551i	−0.531430	−	0.920464i
$790$		0			0
$791$	−5.27814	−	3.04734i	−0.187669	−	0.108351i
$792$		−	2.04903i		−	0.0728090i
$793$	39.0158	−	32.6147i	1.38549	−	1.15818i
$794$	6.15865			0.218562
$795$		0			0
$796$	2.99284	−	5.18374i	0.106078	−	0.183733i
$797$	17.9225	−	10.3476i	0.634849	−	0.366530i	−0.147779	−	0.989020i	$-0.547212\pi$
$797$	17.9225	−	10.3476i	0.634849	−	0.366530i	0.782627	+	0.622490i	$0.213879\pi$
$798$	0.264893			0.00937712
$799$	−36.5902	+	21.1253i	−1.29447	+	0.747361i
$800$		0			0
$801$		−	1.41735i		−	0.0500795i
$802$	4.28344	−	2.47305i	0.151254	−	0.0873263i
$803$	−45.0755	−	26.0244i	−1.59068	−	0.918380i
$804$	27.9460	+	16.1346i	0.985580	+	0.569025i
$805$		0			0
$806$	1.48785	−	4.06430i	0.0524073	−	0.143159i
$807$		−	28.7361i		−	1.01156i
$808$	5.40278	−	9.35788i	0.190069	−	0.329209i
$809$	7.94574	−	13.7624i	0.279357	−	0.483861i	−0.691868	−	0.722024i	$-0.743212\pi$
$809$	7.94574	−	13.7624i	0.279357	−	0.483861i	0.971225	+	0.238163i	$0.0765453\pi$
$810$		0			0
$811$			23.8796i			0.838525i	0.907865	+	0.419263i	$0.137711\pi$
$811$			23.8796i			0.838525i	−0.907865	+	0.419263i	$0.862289\pi$
$812$	0.941391	+	1.63054i	0.0330363	+	0.0572206i
$813$	24.7212	+	42.8183i	0.867009	+	1.50170i
$814$		−	7.04768i		−	0.247021i
$815$		0			0
$816$	15.0438	−	26.0567i	0.526640	−	0.912167i
$817$	−5.74278	+	9.94679i	−0.200915	+	0.347994i
$818$		−	0.941956i		−	0.0329347i
$819$	−0.494262	−	0.180939i	−0.0172709	−	0.00632250i
$820$		0			0
$821$	13.7782	+	7.95484i	0.480862	+	0.277626i	0.720776	−	0.693169i	$-0.243786\pi$
$821$	13.7782	+	7.95484i	0.480862	+	0.277626i	−0.239914	+	0.970794i	$0.577119\pi$
$822$	5.47478	+	3.16087i	0.190955	+	0.110248i
$823$	−12.8271	+	7.40573i	−0.447124	+	0.258147i	−0.706615	−	0.707598i	$-0.749779\pi$
$823$	−12.8271	+	7.40573i	−0.447124	+	0.258147i	0.259491	+	0.965746i	$0.416445\pi$
$824$		−	13.0436i		−	0.454397i
$825$		0			0
$826$	0.171134	−	0.0988040i	0.00595450	−	0.00343783i
$827$	−33.9498			−1.18055			−0.590275	−	0.807202i	$-0.700981\pi$
$827$	−33.9498			−1.18055			−0.590275	+	0.807202i	$0.700981\pi$
$828$	2.10853	−	1.21736i	0.0732763	−	0.0423061i
$829$	−11.6573	+	20.1910i	−0.404875	+	0.701264i	−0.994307	−	0.106554i	$-0.966018\pi$
$829$	−11.6573	+	20.1910i	−0.404875	+	0.701264i	0.589432	+	0.807818i	$0.299352\pi$
$830$		0			0
$831$	42.4124			1.47127
$832$	−4.25274	−	24.3836i	−0.147437	−	0.845350i
$833$		−	34.8910i		−	1.20890i
$834$	−3.64911	−	2.10682i	−0.126358	−	0.0729530i
$835$		0			0
$836$	11.8890	+	20.5924i	0.411190	+	0.712202i
$837$	30.0726			1.03946
$838$	−1.94550	−	3.36970i	−0.0672061	−	0.116404i
$839$	12.8111	−	7.39649i	0.442288	−	0.255355i	−0.262280	−	0.964992i	$-0.584474\pi$
$839$	12.8111	−	7.39649i	0.442288	−	0.255355i	0.704568	+	0.709637i	$0.251141\pi$
$840$		0			0
$841$	10.2849	+	17.8140i	0.354652	+	0.614276i
$842$	−2.45024	−	1.41465i	−0.0844408	−	0.0487519i
$843$	3.98261	−	6.89809i	0.137169	−	0.237583i
$844$	16.0050			0.550915
$845$		0			0
$846$	0.805291			0.0276865
$847$	2.96636	−	5.13789i	0.101925	−	0.176540i
$848$	−5.01794	−	2.89711i	−0.172317	−	0.0994872i
$849$	−10.0703	−	17.4423i	−0.345612	−	0.598617i
$850$		0			0
$851$	14.6840	−	8.47780i	0.503360	−	0.290615i
$852$	19.9841	+	34.6134i	0.684643	+	1.18584i
$853$	−16.3452			−0.559650			−0.279825	−	0.960051i	$-0.590276\pi$
$853$	−16.3452			−0.559650			−0.279825	+	0.960051i	$0.590276\pi$
$854$	0.514722	+	0.891525i	0.0176134	+	0.0305073i
$855$		0			0
$856$	9.82220	+	5.67085i	0.335716	+	0.193826i
$857$			34.1418i			1.16626i	0.812378	+	0.583132i	$0.198173\pi$
$857$			34.1418i			1.16626i	−0.812378	+	0.583132i	$0.801827\pi$
$858$	−1.16986	−	6.70754i	−0.0399383	−	0.228992i
$859$	45.1996			1.54219			0.771096	−	0.636719i	$-0.219709\pi$
$859$	45.1996			1.54219			0.771096	+	0.636719i	$0.219709\pi$
$860$		0			0
$861$	−0.992090	+	1.71835i	−0.0338103	+	0.0585612i
$862$	1.80712	−	1.04334i	0.0615508	−	0.0355364i
$863$	−4.75058			−0.161712			−0.0808559	−	0.996726i	$-0.525765\pi$
$863$	−4.75058			−0.161712			−0.0808559	+	0.996726i	$0.525765\pi$
$864$	−12.1633	+	7.02250i	−0.413805	+	0.238910i
$865$		0			0
$866$			0.306745i			0.0104236i
$867$	−11.9832	+	6.91853i	−0.406972	+	0.234966i
$868$	−3.06854	−	1.77162i	−0.104153	−	0.0601327i
$869$	−21.0207	−	12.1363i	−0.713079	−	0.411696i
$870$		0			0
$871$	−34.9830	−	12.8065i	−1.18535	−	0.433933i
$872$		−	9.75140i		−	0.330224i
$873$	0.550955	−	0.954282i	0.0186470	−	0.0322975i
$874$	0.707294	−	1.22507i	0.0239246	−	0.0414386i
$875$		0			0
$876$			30.2610i			1.02242i
$877$	−1.12753	−	1.95294i	−0.0380741	−	0.0659462i	0.846360	−	0.532611i	$-0.178789\pi$
$877$	−1.12753	−	1.95294i	−0.0380741	−	0.0659462i	−0.884434	+	0.466664i	$0.845456\pi$
$878$	0.457146	+	0.791801i	0.0154279	+	0.0267220i
$879$			27.0715i			0.913098i
$880$		0			0
$881$	−1.49152	+	2.58339i	−0.0502507	+	0.0870367i	−0.890057	−	0.455850i	$-0.849335\pi$
$881$	−1.49152	+	2.58339i	−0.0502507	+	0.0870367i	0.839806	+	0.542887i	$0.182669\pi$
$882$	−0.332509	+	0.575922i	−0.0111961	+	0.0193923i
$883$			28.2874i			0.951947i	0.879460	+	0.475973i	$0.157904\pi$
$883$			28.2874i			0.951947i	−0.879460	+	0.475973i	$0.842096\pi$
$884$	−12.2512	+	33.4660i	−0.412051	+	1.12558i
$885$		0			0
$886$	−1.81610	−	1.04852i	−0.0610130	−	0.0352259i
$887$	24.2328	+	13.9908i	0.813658	+	0.469766i	0.848225	−	0.529637i	$-0.177672\pi$
$887$	24.2328	+	13.9908i	0.813658	+	0.469766i	−0.0345665	+	0.999402i	$0.511005\pi$
$888$	−7.18483	+	4.14816i	−0.241107	+	0.139203i
$889$		−	1.07647i		−	0.0361035i
$890$		0			0
$891$	34.8390	−	20.1143i	1.16715	−	0.673855i
$892$	19.9940			0.669448
$893$	−16.3862	+	9.46058i	−0.548343	+	0.316586i
$894$	0.599451	−	1.03828i	0.0200486	−	0.0347252i
$895$		0			0
$896$	2.19681			0.0733903
$897$	12.5681	−	10.5061i	0.419635	−	0.350787i
$898$			4.77095i			0.159209i
$899$	13.7394	+	7.93244i	0.458234	+	0.264562i
$900$		0			0
$901$	3.95174	+	6.84461i	0.131651	+	0.228027i
$902$	4.40426			0.146646
$903$	−1.34624	−	2.33176i	−0.0448001	−	0.0775960i
$904$	13.7915	−	7.96255i	0.458700	−	0.264830i
$905$		0			0
$906$	−1.39938	−	2.42381i	−0.0464914	−	0.0805255i
$907$	14.3344	+	8.27600i	0.475967	+	0.274800i	0.718734	−	0.695285i	$-0.244722\pi$
$907$	14.3344	+	8.27600i	0.475967	+	0.274800i	−0.242767	+	0.970085i	$0.578055\pi$
$908$	6.87383	−	11.9058i	0.228116	−	0.395109i
$909$	−5.46876			−0.181387
$910$		0			0
$911$	7.04863			0.233532			0.116766	−	0.993159i	$-0.462747\pi$
$911$	7.04863			0.233532			0.116766	+	0.993159i	$0.462747\pi$
$912$	6.73710	−	11.6690i	0.223088	−	0.386399i
$913$	19.8353	+	11.4519i	0.656454	+	0.379004i
$914$	0.518746	+	0.898494i	0.0171586	+	0.0297196i
$915$		0			0
$916$	2.24632	−	1.29692i	0.0742206	−	0.0428513i
$917$	−0.0291818	−	0.0505443i	−0.000963668	−	0.00166912i
$918$	6.12316			0.202094
$919$	8.27188	+	14.3273i	0.272864	+	0.472615i	0.969594	−	0.244719i	$-0.0786957\pi$
$919$	8.27188	+	14.3273i	0.272864	+	0.472615i	−0.696730	+	0.717334i	$0.745362\pi$
$920$		0			0
$921$	−5.96488	−	3.44383i	−0.196550	−	0.113478i
$922$		−	0.391374i		−	0.0128892i
$923$	−29.5933	−	35.4015i	−0.974076	−	1.16525i
$924$	−5.57412			−0.183375
$925$		0			0
$926$	0.747155	−	1.29411i	0.0245530	−	0.0425271i
$927$	−5.71704	+	3.30074i	−0.187772	+	0.108410i
$928$	−7.40948			−0.243228
$929$	29.3035	−	16.9184i	0.961416	−	0.555074i	0.0648073	−	0.997898i	$-0.479357\pi$
$929$	29.3035	−	16.9184i	0.961416	−	0.555074i	0.896609	+	0.442824i	$0.146023\pi$
$930$		0			0
$931$		−	15.6253i		−	0.512098i
$932$	2.10853	−	1.21736i	0.0690670	−	0.0398759i
$933$	−3.08359	−	1.78031i	−0.100952	−	0.0582848i
$934$	−3.46975	−	2.00326i	−0.113534	−	0.0655487i
$935$		0			0
$936$	1.05518	−	0.882066i	0.0344898	−	0.0288312i
$937$		−	30.4606i		−	0.995104i	−0.867434	−	0.497552i	$-0.834232\pi$
$937$		−	30.4606i		−	0.995104i	0.867434	−	0.497552i	$-0.165768\pi$
$938$	0.377076	−	0.653115i	0.0123120	−	0.0213250i
$939$	−5.76780	+	9.99012i	−0.188225	+	0.326015i
$940$		0			0
$941$			38.2101i			1.24561i	0.782375	+	0.622807i	$0.214008\pi$
$941$			38.2101i			1.24561i	−0.782375	+	0.622807i	$0.785992\pi$
$942$	2.88842	+	5.00289i	0.0941098	+	0.163003i
$943$	5.29798	+	9.17637i	0.172526	+	0.298824i
$944$		−	10.0516i		−	0.327153i
$945$		0			0
$946$	−2.98823	+	5.17577i	−0.0971558	+	0.168279i
$947$	26.2241	−	45.4215i	0.852169	−	1.47600i	−0.0270773	−	0.999633i	$-0.508620\pi$
$947$	26.2241	−	45.4215i	0.852169	−	1.47600i	0.879247	−	0.476367i	$-0.158047\pi$
$948$			14.1120i			0.458338i
$949$	−6.00239	−	34.4155i	−0.194846	−	1.11717i
$950$		0			0
$951$	0.445737	+	0.257347i	0.0144540	+	0.00834504i
$952$	−1.26503	−	0.730368i	−0.0410000	−	0.0236714i
$953$	34.4245	−	19.8750i	1.11512	−	0.643814i	0.174969	−	0.984574i	$-0.444018\pi$
$953$	34.4245	−	19.8750i	1.11512	−	0.643814i	0.940150	+	0.340760i	$0.110684\pi$
$954$		−	0.150639i		−	0.00487711i
$955$		0			0
$956$	16.8046	−	9.70215i	0.543500	−	0.313790i
$957$	24.9581			0.806782
$958$	−6.69329	+	3.86437i	−0.216250	+	0.124852i
$959$	−2.98737	+	5.17428i	−0.0964673	+	0.167086i
$960$		0			0
$961$	1.14359			0.0368901
$962$	3.62933	−	3.03389i	0.117014	−	0.0978164i
$963$		−	5.74011i		−	0.184972i
$964$	−38.1776	−	22.0418i	−1.22962	−	0.709920i
$965$		0			0
$966$	0.165806	+	0.287184i	0.00533472	+	0.00924001i
$967$	25.7857			0.829214			0.414607	−	0.910001i	$-0.363919\pi$
$967$	25.7857			0.829214			0.414607	+	0.910001i	$0.363919\pi$
$968$	7.75097	+	13.4251i	0.249126	+	0.431498i
$969$	−15.9168	+	9.18958i	−0.511322	+	0.295212i
$970$		0			0
$971$	27.7626	+	48.0863i	0.890945	+	1.54316i	0.838744	+	0.544525i	$0.183290\pi$
$971$	27.7626	+	48.0863i	0.890945	+	1.54316i	0.0522005	+	0.998637i	$0.483377\pi$
$972$	7.65249	+	4.41817i	0.245454	+	0.141713i
$973$	1.99118	−	3.44882i	0.0638342	−	0.110564i
$974$	2.26365			0.0725321
$975$		0			0
$976$	52.3642			1.67614
$977$	20.2580	−	35.0879i	0.648112	−	1.12256i	−0.335461	−	0.942054i	$-0.608892\pi$
$977$	20.2580	−	35.0879i	0.648112	−	1.12256i	0.983573	−	0.180509i	$-0.0577745\pi$
$978$	5.42130	+	3.12999i	0.173354	+	0.100086i
$979$	8.66430	+	15.0070i	0.276912	+	0.479626i
$980$		0			0
$981$	−4.27405	+	2.46762i	−0.136460	+	0.0787852i
$982$	−1.02506	−	1.77545i	−0.0327109	−	0.0566569i
$983$	34.8059			1.11014			0.555068	−	0.831805i	$-0.312692\pi$
$983$	34.8059			1.11014			0.555068	+	0.831805i	$0.312692\pi$
$984$	−2.59229	−	4.48997i	−0.0826390	−	0.143135i
$985$		0			0
$986$	2.79751	+	1.61514i	0.0890910	+	0.0514367i
$987$		−	4.43555i		−	0.141185i
$988$	−5.48645	+	14.9871i	−0.174547	+	0.476803i
$989$	−14.3784			−0.457208
$990$		0			0
$991$	−21.9427	+	38.0059i	−0.697034	+	1.20730i	0.272456	+	0.962168i	$0.412164\pi$
$991$	−21.9427	+	38.0059i	−0.697034	+	1.20730i	−0.969490	+	0.245130i	$0.921169\pi$
$992$	12.0759	−	6.97201i	0.383410	−	0.221362i
$993$	26.6145			0.844584
$994$	0.808936	−	0.467040i	0.0256579	−	0.0148136i
$995$		0			0
$996$		−	13.3163i		−	0.421942i
$997$	−4.75567	+	2.74569i	−0.150614	+	0.0869568i	−0.573413	−	0.819267i	$-0.694381\pi$
$997$	−4.75567	+	2.74569i	−0.150614	+	0.0869568i	0.422799	+	0.906223i	$0.361048\pi$
$998$	4.55508	+	2.62988i	0.144189	+	0.0832474i
$999$	28.4645	+	16.4340i	0.900577	+	0.519949i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	325.2.m.b.199.3		8
5.2	odd	4		325.2.n.d.251.3		8
5.3	odd	4		65.2.m.a.56.2	yes	8
5.4	even	2		325.2.m.c.199.2		8
13.10	even	6		325.2.m.c.49.2		8
15.8	even	4		585.2.bu.c.316.3		8
20.3	even	4		1040.2.da.b.641.2		8
65.3	odd	12		845.2.m.g.361.3		8
65.7	even	12		4225.2.a.bi.1.3		4
65.8	even	4		845.2.e.m.191.3		8
65.18	even	4		845.2.e.n.191.2		8
65.23	odd	12		65.2.m.a.36.2	✓	8
65.28	even	12		845.2.e.n.146.2		8
65.32	even	12		4225.2.a.bl.1.2		4
65.33	even	12		845.2.a.m.1.2		4
65.38	odd	4		845.2.m.g.316.3		8
65.43	odd	12		845.2.c.g.506.4		8
65.48	odd	12		845.2.c.g.506.5		8
65.49	even	6	inner	325.2.m.b.49.3		8
65.58	even	12		845.2.a.l.1.3		4
65.62	odd	12		325.2.n.d.101.3		8
65.63	even	12		845.2.e.m.146.3		8
195.23	even	12		585.2.bu.c.361.3		8
195.98	odd	12		7605.2.a.cf.1.3		4
195.188	odd	12		7605.2.a.cj.1.2		4
260.23	even	12		1040.2.da.b.881.2		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
65.2.m.a.36.2	✓	8	65.23	odd	12
65.2.m.a.56.2	yes	8	5.3	odd	4
325.2.m.b.49.3		8	65.49	even	6	inner
325.2.m.b.199.3		8	1.1	even	1	trivial
325.2.m.c.49.2		8	13.10	even	6
325.2.m.c.199.2		8	5.4	even	2
325.2.n.d.101.3		8	65.62	odd	12
325.2.n.d.251.3		8	5.2	odd	4
585.2.bu.c.316.3		8	15.8	even	4
585.2.bu.c.361.3		8	195.23	even	12
845.2.a.l.1.3		4	65.58	even	12
845.2.a.m.1.2		4	65.33	even	12
845.2.c.g.506.4		8	65.43	odd	12
845.2.c.g.506.5		8	65.48	odd	12
845.2.e.m.146.3		8	65.63	even	12
845.2.e.m.191.3		8	65.8	even	4
845.2.e.n.146.2		8	65.28	even	12
845.2.e.n.191.2		8	65.18	even	4
845.2.m.g.316.3		8	65.38	odd	4
845.2.m.g.361.3		8	65.3	odd	12
1040.2.da.b.641.2		8	20.3	even	4
1040.2.da.b.881.2		8	260.23	even	12
4225.2.a.bi.1.3		4	65.7	even	12
4225.2.a.bl.1.2		4	65.32	even	12
7605.2.a.cf.1.3		4	195.98	odd	12
7605.2.a.cj.1.2		4	195.188	odd	12

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:	\( N \)	\(=\)	\( 325 = 5^{2} \cdot 13 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	325.m (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(0.109843 - 0.190254i) q^{2} +(-1.38581 - 0.800098i) q^{3} +(0.975869 + 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(-0.166123 - 0.287734i) q^{7} +0.868145 q^{8} +(-0.219687 - 0.380509i) q^{9} +O(q^{10})\)	\(q+(0.109843 - 0.190254i) q^{2} +(-1.38581 - 0.800098i) q^{3} +(0.975869 + 1.69025i) q^{4} +(-0.304444 + 0.175771i) q^{6} +(-0.166123 - 0.287734i) q^{7} +0.868145 q^{8} +(-0.219687 - 0.380509i) q^{9} +(4.65213 + 2.68591i) q^{11} -3.12316i q^{12} +(0.619491 + 3.55193i) q^{13} -0.0729902 q^{14} +(-1.85638 + 3.21534i) q^{16} +(4.38581 - 2.53215i) q^{17} -0.0965246 q^{18} +(1.96410 - 1.13397i) q^{19} +0.531659i q^{21} +(1.02201 - 0.590059i) q^{22} +(2.45880 + 1.41959i) q^{23} +(-1.20308 - 0.694601i) q^{24} +(0.743818 + 0.272296i) q^{26} +5.50367i q^{27} +(0.324229 - 0.561581i) q^{28} +(-1.45174 + 2.51448i) q^{29} -5.46410i q^{31} +(1.27597 + 2.21004i) q^{32} +(-4.29798 - 7.44432i) q^{33} -1.11256i q^{34} +(0.428771 - 0.742653i) q^{36} +(2.98601 - 5.17191i) q^{37} -0.498239i q^{38} +(1.98340 - 5.41796i) q^{39} +(3.23205 + 1.86603i) q^{41} +(0.101151 + 0.0583993i) q^{42} +(-4.38581 + 2.53215i) q^{43} +10.4844i q^{44} +(0.540166 - 0.311865i) q^{46} -8.34285 q^{47} +(5.14517 - 2.97057i) q^{48} +(3.44481 - 5.96658i) q^{49} -8.10387 q^{51} +(-5.39913 + 4.51332i) q^{52} +1.56063i q^{53} +(1.04710 + 0.604542i) q^{54} +(-0.144219 - 0.249795i) q^{56} -3.62916 q^{57} +(0.318928 + 0.552399i) q^{58} +(-2.34461 + 1.35366i) q^{59} +(-7.05193 - 12.2143i) q^{61} +(-1.03957 - 0.600196i) q^{62} +(-0.0729902 + 0.126423i) q^{63} -6.86488 q^{64} -1.88842 q^{66} +(-5.16612 + 8.94799i) q^{67} +(8.55995 + 4.94209i) q^{68} +(-2.27162 - 3.93456i) q^{69} +(-11.0828 + 6.39866i) q^{71} +(-0.190720 - 0.330337i) q^{72} -9.68922 q^{73} +(-0.655986 - 1.13620i) q^{74} +(3.83341 + 2.21322i) q^{76} -1.78477i q^{77} +(-0.812927 - 0.972477i) q^{78} -4.51851 q^{79} +(3.74441 - 6.48552i) q^{81} +(0.710039 - 0.409941i) q^{82} +4.26371 q^{83} +(-0.898640 + 0.518830i) q^{84} +1.11256i q^{86} +(4.02367 - 2.32306i) q^{87} +(4.03872 + 2.33176i) q^{88} +(2.79366 + 1.61292i) q^{89} +(0.919100 - 0.768307i) q^{91} +5.54133i q^{92} +(-4.37182 + 7.57221i) q^{93} +(-0.916407 + 1.58726i) q^{94} -4.08359i q^{96} +(1.25396 + 2.17191i) q^{97} +(-0.756779 - 1.31078i) q^{98} -2.36023i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9}+O(q^{10}) \) 8 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 18 * q^6 + 10 * q^7 + 12 * q^8 + 4 * q^9	\( 8 q - 2 q^{2} + 6 q^{3} - 2 q^{4} - 18 q^{6} + 10 q^{7} + 12 q^{8} + 4 q^{9} + 8 q^{13} - 4 q^{14} - 2 q^{16} + 18 q^{17} - 40 q^{18} - 12 q^{19} + 6 q^{22} + 6 q^{23} + 12 q^{24} + 10 q^{26} + 8 q^{28} + 8 q^{29} - 4 q^{32} - 18 q^{33} + 20 q^{36} - 2 q^{37} + 12 q^{41} - 42 q^{42} - 18 q^{43} - 42 q^{46} - 16 q^{47} - 6 q^{48} - 12 q^{49} - 8 q^{51} + 16 q^{52} - 18 q^{54} + 12 q^{56} - 28 q^{57} + 22 q^{58} + 12 q^{59} - 28 q^{61} + 12 q^{62} - 4 q^{63} + 8 q^{64} + 12 q^{66} - 30 q^{67} + 12 q^{68} + 16 q^{69} + 12 q^{72} - 16 q^{73} - 10 q^{74} + 54 q^{76} + 18 q^{78} + 16 q^{79} + 8 q^{81} - 6 q^{82} + 24 q^{83} + 30 q^{84} + 54 q^{87} + 42 q^{88} - 24 q^{89} + 28 q^{91} + 8 q^{93} - 32 q^{94} - 2 q^{97} + 24 q^{98}+O(q^{100}) \) 8 * q - 2 * q^2 + 6 * q^3 - 2 * q^4 - 18 * q^6 + 10 * q^7 + 12 * q^8 + 4 * q^9 + 8 * q^13 - 4 * q^14 - 2 * q^16 + 18 * q^17 - 40 * q^18 - 12 * q^19 + 6 * q^22 + 6 * q^23 + 12 * q^24 + 10 * q^26 + 8 * q^28 + 8 * q^29 - 4 * q^32 - 18 * q^33 + 20 * q^36 - 2 * q^37 + 12 * q^41 - 42 * q^42 - 18 * q^43 - 42 * q^46 - 16 * q^47 - 6 * q^48 - 12 * q^49 - 8 * q^51 + 16 * q^52 - 18 * q^54 + 12 * q^56 - 28 * q^57 + 22 * q^58 + 12 * q^59 - 28 * q^61 + 12 * q^62 - 4 * q^63 + 8 * q^64 + 12 * q^66 - 30 * q^67 + 12 * q^68 + 16 * q^69 + 12 * q^72 - 16 * q^73 - 10 * q^74 + 54 * q^76 + 18 * q^78 + 16 * q^79 + 8 * q^81 - 6 * q^82 + 24 * q^83 + 30 * q^84 + 54 * q^87 + 42 * q^88 - 24 * q^89 + 28 * q^91 + 8 * q^93 - 32 * q^94 - 2 * q^97 + 24 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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