LMFDB - Embedded newform 435.2.f.f.289.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [435,2,Mod(289,435)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(435, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 1]))

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

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

chi := DirichletCharacter("435.289");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 435 = 3 \cdot 5 \cdot 29 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	435.f (of order $2$, degree $1$, 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:	$3.47349248793$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{12} - x^{11} - 11 x^{9} + 55 x^{8} - 66 x^{7} + 328 x^{6} - 214 x^{5} + 207 x^{4} + 383 x^{3} + \cdots + 209 $ x^12 - x^11 - 11x^9 + 55x^8 - 66x^7 + 328x^6 - 214x^5 + 207x^4 + 383x^3 + 16x^2 - 107*x + 209
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{6} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			289.5
Root			$-2.21342 + 2.00212i$ of defining polynomial
Character	$\chi$	$=$	435.289
Dual form			435.2.f.f.289.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.334522 q^{2} +1.00000 q^{3} -1.88809 q^{4} +(1.95387 - 1.08739i) q^{5} -0.334522 q^{6} +0.275019i q^{7} +1.30066 q^{8} +1.00000 q^{9} +O(q^{10})$	\(q-0.334522 q^{2} +1.00000 q^{3} -1.88809 q^{4} +(1.95387 - 1.08739i) q^{5} -0.334522 q^{6} +0.275019i q^{7} +1.30066 q^{8} +1.00000 q^{9} +(-0.653612 + 0.363756i) q^{10} -0.541705i q^{11} -1.88809 q^{12} -5.03697i q^{13} -0.0920000i q^{14} +(1.95387 - 1.08739i) q^{15} +3.34109 q^{16} +3.32386 q^{17} -0.334522 q^{18} +6.31271i q^{19} +(-3.68908 + 2.05309i) q^{20} +0.275019i q^{21} +0.181212i q^{22} -6.93673i q^{23} +1.30066 q^{24} +(2.63518 - 4.24922i) q^{25} +1.68498i q^{26} +1.00000 q^{27} -0.519262i q^{28} +(2.25292 + 4.89125i) q^{29} +(-0.653612 + 0.363756i) q^{30} -10.1057i q^{31} -3.71898 q^{32} -0.541705i q^{33} -1.11191 q^{34} +(0.299052 + 0.537350i) q^{35} -1.88809 q^{36} +4.07094 q^{37} -2.11174i q^{38} -5.03697i q^{39} +(2.54130 - 1.41432i) q^{40} +8.49843i q^{41} -0.0920000i q^{42} +5.97627 q^{43} +1.02279i q^{44} +(1.95387 - 1.08739i) q^{45} +2.32049i q^{46} -12.4310 q^{47} +3.34109 q^{48} +6.92436 q^{49} +(-0.881526 + 1.42146i) q^{50} +3.32386 q^{51} +9.51028i q^{52} +3.98569i q^{53} -0.334522 q^{54} +(-0.589043 - 1.05842i) q^{55} +0.357705i q^{56} +6.31271i q^{57} +(-0.753651 - 1.63623i) q^{58} -8.01554 q^{59} +(-3.68908 + 2.05309i) q^{60} -4.84022i q^{61} +3.38058i q^{62} +0.275019i q^{63} -5.43810 q^{64} +(-5.47714 - 9.84156i) q^{65} +0.181212i q^{66} +12.1664i q^{67} -6.27576 q^{68} -6.93673i q^{69} +(-0.100040 - 0.179756i) q^{70} -7.20182 q^{71} +1.30066 q^{72} +1.23869 q^{73} -1.36182 q^{74} +(2.63518 - 4.24922i) q^{75} -11.9190i q^{76} +0.148979 q^{77} +1.68498i q^{78} -2.36972i q^{79} +(6.52804 - 3.63306i) q^{80} +1.00000 q^{81} -2.84292i q^{82} +10.3724i q^{83} -0.519262i q^{84} +(6.49437 - 3.61432i) q^{85} -1.99920 q^{86} +(2.25292 + 4.89125i) q^{87} -0.704571i q^{88} +2.50630i q^{89} +(-0.653612 + 0.363756i) q^{90} +1.38526 q^{91} +13.0972i q^{92} -10.1057i q^{93} +4.15845 q^{94} +(6.86436 + 12.3342i) q^{95} -3.71898 q^{96} -17.8627 q^{97} -2.31636 q^{98} -0.541705i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 12 q^{3} + 16 q^{4} - 6 q^{5} + 12 q^{9}+O(q^{10}) $ 12 * q + 12 * q^3 + 16 * q^4 - 6 * q^5 + 12 * q^9	$ 12 q + 12 q^{3} + 16 q^{4} - 6 q^{5} + 12 q^{9} + 2 q^{10} + 16 q^{12} - 6 q^{15} + 32 q^{16} - 8 q^{17} - 20 q^{20} + 12 q^{25} + 12 q^{27} + 8 q^{29} + 2 q^{30} - 40 q^{32} - 52 q^{34} + 14 q^{35} + 16 q^{36} + 20 q^{37} - 22 q^{40} + 44 q^{43} - 6 q^{45} - 32 q^{47} + 32 q^{48} - 4 q^{49} + 24 q^{50} - 8 q^{51} + 42 q^{55} - 24 q^{58} - 28 q^{59} - 20 q^{60} - 4 q^{64} + 22 q^{65} + 16 q^{68} - 26 q^{70} - 16 q^{71} - 36 q^{73} - 28 q^{74} + 12 q^{75} - 22 q^{80} + 12 q^{81} + 30 q^{85} - 16 q^{86} + 8 q^{87} + 2 q^{90} + 24 q^{91} - 28 q^{94} + 16 q^{95} - 40 q^{96} - 40 q^{97} - 112 q^{98}+O(q^{100}) $ 12 * q + 12 * q^3 + 16 * q^4 - 6 * q^5 + 12 * q^9 + 2 * q^10 + 16 * q^12 - 6 * q^15 + 32 * q^16 - 8 * q^17 - 20 * q^20 + 12 * q^25 + 12 * q^27 + 8 * q^29 + 2 * q^30 - 40 * q^32 - 52 * q^34 + 14 * q^35 + 16 * q^36 + 20 * q^37 - 22 * q^40 + 44 * q^43 - 6 * q^45 - 32 * q^47 + 32 * q^48 - 4 * q^49 + 24 * q^50 - 8 * q^51 + 42 * q^55 - 24 * q^58 - 28 * q^59 - 20 * q^60 - 4 * q^64 + 22 * q^65 + 16 * q^68 - 26 * q^70 - 16 * q^71 - 36 * q^73 - 28 * q^74 + 12 * q^75 - 22 * q^80 + 12 * q^81 + 30 * q^85 - 16 * q^86 + 8 * q^87 + 2 * q^90 + 24 * q^91 - 28 * q^94 + 16 * q^95 - 40 * q^96 - 40 * q^97 - 112 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/435\mathbb{Z}\right)^\times$.

$n$	$31$	$146$	$262$
$\chi(n)$	$-1$	$1$	$-1$

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 $

$2$	−0.334522			−0.236543			−0.118272	−	0.992981i	$-0.537735\pi$
$2$	−0.334522			−0.236543			−0.118272	+	0.992981i	$0.537735\pi$
$3$	1.00000			0.577350
$3$	1.00000			0.577350
$4$	−1.88809			−0.944047
$5$	1.95387	−	1.08739i	0.873795	−	0.486294i
$5$	1.95387	−	1.08739i	0.873795	−	0.486294i
$6$	−0.334522			−0.136568
$7$			0.275019i			0.103947i	0.998648	+	0.0519737i	$0.0165512\pi$
$7$			0.275019i			0.103947i	−0.998648	+	0.0519737i	$0.983449\pi$
$8$	1.30066			0.459851
$9$	1.00000			0.333333
$10$	−0.653612	+	0.363756i	−0.206690	+	0.115030i
$11$		−	0.541705i		−	0.163330i	−0.996660	−	0.0816650i	$-0.973976\pi$
$11$		−	0.541705i		−	0.163330i	0.996660	−	0.0816650i	$-0.0260238\pi$
$12$	−1.88809			−0.545046
$13$		−	5.03697i		−	1.39700i	−0.715608	−	0.698502i	$-0.753850\pi$
$13$		−	5.03697i		−	1.39700i	0.715608	−	0.698502i	$-0.246150\pi$
$14$		−	0.0920000i		−	0.0245880i
$15$	1.95387	−	1.08739i	0.504486	−	0.280762i
$16$	3.34109			0.835273
$17$	3.32386			0.806154			0.403077	−	0.915166i	$-0.367941\pi$
$17$	3.32386			0.806154			0.403077	+	0.915166i	$0.367941\pi$
$18$	−0.334522			−0.0788477
$19$			6.31271i			1.44824i	0.689676	+	0.724118i	$0.257753\pi$
$19$			6.31271i			1.44824i	−0.689676	+	0.724118i	$0.742247\pi$
$20$	−3.68908	+	2.05309i	−0.824904	+	0.459085i
$21$			0.275019i			0.0600140i
$22$			0.181212i			0.0386346i
$23$		−	6.93673i		−	1.44641i	−0.690635	−	0.723204i	$-0.742669\pi$
$23$		−	6.93673i		−	1.44641i	0.690635	−	0.723204i	$-0.257331\pi$
$24$	1.30066			0.265495
$25$	2.63518	−	4.24922i	0.527036	−	0.849843i
$26$			1.68498i			0.330452i
$27$	1.00000			0.192450
$28$		−	0.519262i		−	0.0981312i
$29$	2.25292	+	4.89125i	0.418356	+	0.908283i
$29$	2.25292	+	4.89125i	0.418356	+	0.908283i
$30$	−0.653612	+	0.363756i	−0.119333	+	0.0664124i
$31$		−	10.1057i		−	1.81504i	−0.420012	−	0.907518i	$-0.637974\pi$
$31$		−	10.1057i		−	1.81504i	0.420012	−	0.907518i	$-0.362026\pi$
$32$	−3.71898			−0.657429
$33$		−	0.541705i		−	0.0942987i
$34$	−1.11191			−0.190690
$35$	0.299052	+	0.537350i	0.0505490	+	0.0908287i
$36$	−1.88809			−0.314682
$37$	4.07094			0.669259			0.334629	−	0.942350i	$-0.391389\pi$
$37$	4.07094			0.669259			0.334629	+	0.942350i	$0.391389\pi$
$38$		−	2.11174i		−	0.342570i
$39$		−	5.03697i		−	0.806561i
$40$	2.54130	−	1.41432i	0.401816	−	0.223623i
$41$			8.49843i			1.32723i	0.748073	+	0.663616i	$0.230979\pi$
$41$			8.49843i			1.32723i	−0.748073	+	0.663616i	$0.769021\pi$
$42$		−	0.0920000i		−	0.0141959i
$43$	5.97627			0.911372			0.455686	−	0.890140i	$-0.349394\pi$
$43$	5.97627			0.911372			0.455686	+	0.890140i	$0.349394\pi$
$44$			1.02279i			0.154191i
$45$	1.95387	−	1.08739i	0.291265	−	0.162098i
$46$			2.32049i			0.342138i
$47$	−12.4310			−1.81325			−0.906624	−	0.421939i	$-0.861349\pi$
$47$	−12.4310			−1.81325			−0.906624	+	0.421939i	$0.861349\pi$
$48$	3.34109			0.482245
$49$	6.92436			0.989195
$50$	−0.881526	+	1.42146i	−0.124667	+	0.201025i
$51$	3.32386			0.465433
$52$			9.51028i			1.31884i
$53$			3.98569i			0.547477i	0.961804	+	0.273739i	$0.0882603\pi$
$53$			3.98569i			0.547477i	−0.961804	+	0.273739i	$0.911740\pi$
$54$	−0.334522			−0.0455227
$55$	−0.589043	−	1.05842i	−0.0794265	−	0.142717i
$56$			0.357705i			0.0478003i
$57$			6.31271i			0.836139i
$58$	−0.753651	−	1.63623i	−0.0989593	−	0.214848i
$59$	−8.01554			−1.04353			−0.521767	−	0.853088i	$-0.674727\pi$
$59$	−8.01554			−1.04353			−0.521767	+	0.853088i	$0.674727\pi$
$60$	−3.68908	+	2.05309i	−0.476258	+	0.265053i
$61$		−	4.84022i		−	0.619726i	−0.950781	−	0.309863i	$-0.899717\pi$
$61$		−	4.84022i		−	0.619726i	0.950781	−	0.309863i	$-0.100283\pi$
$62$			3.38058i			0.429334i
$63$			0.275019i			0.0346491i
$64$	−5.43810			−0.679762
$65$	−5.47714	−	9.84156i	−0.679355	−	1.22070i
$66$			0.181212i			0.0223057i
$67$			12.1664i			1.48636i	0.669090	+	0.743182i	$0.266684\pi$
$67$			12.1664i			1.48636i	−0.669090	+	0.743182i	$0.733316\pi$
$68$	−6.27576			−0.761048
$69$		−	6.93673i		−	0.835084i
$70$	−0.100040	−	0.179756i	−0.0119570	−	0.0214849i
$71$	−7.20182			−0.854698			−0.427349	−	0.904087i	$-0.640553\pi$
$71$	−7.20182			−0.854698			−0.427349	+	0.904087i	$0.640553\pi$
$72$	1.30066			0.153284
$73$	1.23869			0.144977			0.0724886	−	0.997369i	$-0.476906\pi$
$73$	1.23869			0.144977			0.0724886	+	0.997369i	$0.476906\pi$
$74$	−1.36182			−0.158309
$75$	2.63518	−	4.24922i	0.304284	−	0.490657i
$76$		−	11.9190i		−	1.36720i
$77$	0.148979			0.0169777
$78$			1.68498i			0.190786i
$79$		−	2.36972i		−	0.266614i	−0.991075	−	0.133307i	$-0.957440\pi$
$79$		−	2.36972i		−	0.266614i	0.991075	−	0.133307i	$-0.0425597\pi$
$80$	6.52804	−	3.63306i	0.729857	−	0.406188i
$81$	1.00000			0.111111
$82$		−	2.84292i		−	0.313948i
$83$			10.3724i			1.13852i	0.822159	+	0.569258i	$0.192770\pi$
$83$			10.3724i			1.13852i	−0.822159	+	0.569258i	$0.807230\pi$
$84$		−	0.519262i		−	0.0566561i
$85$	6.49437	−	3.61432i	0.704413	−	0.392028i
$86$	−1.99920			−0.215579
$87$	2.25292	+	4.89125i	0.241538	+	0.524397i
$88$		−	0.704571i		−	0.0751075i
$89$			2.50630i			0.265667i	0.991138	+	0.132833i	$0.0424076\pi$
$89$			2.50630i			0.265667i	−0.991138	+	0.132833i	$0.957592\pi$
$90$	−0.653612	+	0.363756i	−0.0688967	+	0.0383432i
$91$	1.38526			0.145215
$92$			13.0972i			1.36548i
$93$		−	10.1057i		−	1.04791i
$94$	4.15845			0.428911
$95$	6.86436	+	12.3342i	0.704269	+	1.26546i
$96$	−3.71898			−0.379567
$97$	−17.8627			−1.81368			−0.906840	−	0.421476i	$-0.861512\pi$
$97$	−17.8627			−1.81368			−0.906840	+	0.421476i	$0.861512\pi$
$98$	−2.31636			−0.233987
$99$		−	0.541705i		−	0.0544434i
$100$	−4.97546	+	8.02292i	−0.497546	+	0.802292i
$101$			13.6767i			1.36088i	0.732803	+	0.680441i	$0.238212\pi$
$101$			13.6767i			1.36088i	−0.732803	+	0.680441i	$0.761788\pi$
$102$	−1.11191			−0.110095
$103$			10.6870i			1.05302i	0.850168	+	0.526511i	$0.176500\pi$
$103$			10.6870i			1.05302i	−0.850168	+	0.526511i	$0.823500\pi$
$104$		−	6.55136i		−	0.642414i
$105$	0.299052	+	0.537350i	0.0291845	+	0.0524400i
$106$		−	1.33330i		−	0.129502i
$107$		−	4.59224i		−	0.443948i	−0.975053	−	0.221974i	$-0.928750\pi$
$107$		−	4.59224i		−	0.443948i	0.975053	−	0.221974i	$-0.0712501\pi$
$108$	−1.88809			−0.181682
$109$	−13.1473			−1.25928			−0.629639	−	0.776888i	$-0.716797\pi$
$109$	−13.1473			−1.25928			−0.629639	+	0.776888i	$0.716797\pi$
$110$	0.197048	+	0.354065i	0.0187878	+	0.0337587i
$111$	4.07094			0.386397
$112$			0.918863i			0.0868244i
$113$	−12.4441			−1.17065			−0.585323	−	0.810800i	$-0.699032\pi$
$113$	−12.4441			−1.17065			−0.585323	+	0.810800i	$0.699032\pi$
$114$		−	2.11174i		−	0.197783i
$115$	−7.54291	−	13.5534i	−0.703380	−	1.26386i
$116$	−4.25372	−	9.23515i	−0.394948	−	0.857462i
$117$		−	5.03697i		−	0.465668i
$118$	2.68138			0.246841
$119$			0.914124i			0.0837976i
$120$	2.54130	−	1.41432i	0.231988	−	0.129109i
$121$	10.7066			0.973323
$122$			1.61916i			0.146592i
$123$			8.49843i			0.766278i
$124$			19.0805i			1.71348i
$125$	0.528238	−	11.1679i	0.0472470	−	0.998883i
$126$		−	0.0920000i		−	0.00819601i
$127$	−10.3846			−0.921487			−0.460744	−	0.887533i	$-0.652417\pi$
$127$	−10.3846			−0.921487			−0.460744	+	0.887533i	$0.652417\pi$
$128$	9.25713			0.818222
$129$	5.97627			0.526181
$130$	1.83223	+	3.29222i	0.160697	+	0.288747i
$131$			3.80784i			0.332693i	0.986067	+	0.166346i	$0.0531970\pi$
$131$			3.80784i			0.332693i	−0.986067	+	0.166346i	$0.946803\pi$
$132$			1.02279i			0.0890224i
$133$	−1.73611			−0.150540
$134$		−	4.06994i		−	0.351589i
$135$	1.95387	−	1.08739i	0.168162	−	0.0935874i
$136$	4.32319			0.370711
$137$	9.05968			0.774021			0.387010	−	0.922075i	$-0.373508\pi$
$137$	9.05968			0.774021			0.387010	+	0.922075i	$0.373508\pi$
$138$			2.32049i			0.197533i
$139$	1.41853			0.120318			0.0601591	−	0.998189i	$-0.480839\pi$
$139$	1.41853			0.120318			0.0601591	+	0.998189i	$0.480839\pi$
$140$	−0.564638	−	1.01457i	−0.0477207	−	0.0857466i
$141$	−12.4310			−1.04688
$142$	2.40917			0.202173
$143$	−2.72855			−0.228173
$144$	3.34109			0.278424
$145$	9.72058	+	7.10706i	0.807251	+	0.590209i
$146$	−0.414368			−0.0342933
$147$	6.92436			0.571112
$148$	−7.68632			−0.631812
$149$	4.70591			0.385523			0.192762	−	0.981246i	$-0.438256\pi$
$149$	4.70591			0.385523			0.192762	+	0.981246i	$0.438256\pi$
$150$	−0.881526	+	1.42146i	−0.0719763	+	0.116062i
$151$	−5.99181			−0.487606			−0.243803	−	0.969825i	$-0.578395\pi$
$151$	−5.99181			−0.487606			−0.243803	+	0.969825i	$0.578395\pi$
$152$			8.21066i			0.665973i
$153$	3.32386			0.268718
$154$	−0.0498368			−0.00401596
$155$	−10.9888	−	19.7452i	−0.882642	−	1.58597i
$156$			9.51028i			0.761432i
$157$	11.2728			0.899664			0.449832	−	0.893113i	$-0.351484\pi$
$157$	11.2728			0.899664			0.449832	+	0.893113i	$0.351484\pi$
$158$			0.792725i			0.0630658i
$159$			3.98569i			0.316086i
$160$	−7.26639	+	4.04397i	−0.574458	+	0.319704i
$161$	1.90773			0.150350
$162$	−0.334522			−0.0262826
$163$	−11.2859			−0.883980			−0.441990	−	0.897020i	$-0.645727\pi$
$163$	−11.2859			−0.883980			−0.441990	+	0.897020i	$0.645727\pi$
$164$		−	16.0458i		−	1.25297i
$165$	−0.589043	−	1.05842i	−0.0458569	−	0.0823977i
$166$		−	3.46980i		−	0.269308i
$167$			9.11150i			0.705069i	0.935799	+	0.352535i	$0.114680\pi$
$167$			9.11150i			0.705069i	−0.935799	+	0.352535i	$0.885320\pi$
$168$			0.357705i			0.0275975i
$169$	−12.3711			−0.951621
$170$	−2.17251	+	1.20907i	−0.166624	+	0.0927316i
$171$			6.31271i			0.482745i
$172$	−11.2838			−0.860379
$173$		−	6.68099i		−	0.507946i	−0.967211	−	0.253973i	$-0.918263\pi$
$173$		−	6.68099i		−	0.507946i	0.967211	−	0.253973i	$-0.0817374\pi$
$174$	−0.753651	−	1.63623i	−0.0571342	−	0.124043i
$175$	1.16861	+	0.724723i	0.0883389	+	0.0547839i
$176$		−	1.80988i		−	0.136425i
$177$	−8.01554			−0.602485
$178$		−	0.838413i		−	0.0628417i
$179$	17.6127			1.31644			0.658218	−	0.752827i	$-0.271310\pi$
$179$	17.6127			1.31644			0.658218	+	0.752827i	$0.271310\pi$
$180$	−3.68908	+	2.05309i	−0.274968	+	0.153028i
$181$	0.799278			0.0594099			0.0297049	−	0.999559i	$-0.490543\pi$
$181$	0.799278			0.0594099			0.0297049	+	0.999559i	$0.490543\pi$
$182$	−0.463401			−0.0343496
$183$		−	4.84022i		−	0.357799i
$184$		−	9.02229i		−	0.665132i
$185$	7.95407	−	4.42669i	0.584795	−	0.325457i
$186$			3.38058i			0.247876i
$187$		−	1.80055i		−	0.131669i
$188$	23.4709			1.71179
$189$			0.275019i			0.0200047i
$190$	−2.29628	−	4.12606i	−0.166590	−	0.299336i
$191$			14.0344i			1.01549i	0.861506	+	0.507747i	$0.169522\pi$
$191$			14.0344i			1.01549i	−0.861506	+	0.507747i	$0.830478\pi$
$192$	−5.43810			−0.392461
$193$	22.3693			1.61018			0.805089	−	0.593154i	$-0.202117\pi$
$193$	22.3693			1.61018			0.805089	+	0.593154i	$0.202117\pi$
$194$	5.97546			0.429013
$195$	−5.47714	−	9.84156i	−0.392226	−	0.704769i
$196$	−13.0739			−0.933847
$197$			4.66274i			0.332207i	0.986108	+	0.166103i	$0.0531186\pi$
$197$			4.66274i			0.332207i	−0.986108	+	0.166103i	$0.946881\pi$
$198$			0.181212i			0.0128782i
$199$	14.9769			1.06169			0.530843	−	0.847470i	$-0.321876\pi$
$199$	14.9769			1.06169			0.530843	+	0.847470i	$0.321876\pi$
$200$	3.42746	−	5.52676i	0.242358	−	0.390801i
$201$			12.1664i			0.858152i
$202$		−	4.57516i		−	0.321907i
$203$	−1.34519	+	0.619595i	−0.0944136	+	0.0434870i
$204$	−6.27576			−0.439391
$205$	9.24109	+	16.6048i	0.645426	+	1.15973i
$206$		−	3.57504i		−	0.249085i
$207$		−	6.93673i		−	0.482136i
$208$		−	16.8290i		−	1.16688i
$209$	3.41963			0.236540
$210$	−0.100040	−	0.179756i	−0.00690339	−	0.0124043i
$211$		−	15.8960i		−	1.09432i	−0.837027	−	0.547162i	$-0.815708\pi$
$211$		−	15.8960i		−	1.09432i	0.837027	−	0.547162i	$-0.184292\pi$
$212$		−	7.52537i		−	0.516844i
$213$	−7.20182			−0.493460
$214$			1.53621i			0.105013i
$215$	11.6768	−	6.49852i	0.796353	−	0.443195i
$216$	1.30066			0.0884984
$217$	2.77926			0.188668
$218$	4.39805			0.297874
$219$	1.23869			0.0837026
$220$	1.11217	+	1.99839i	0.0749824	+	0.134732i
$221$		−	16.7422i		−	1.12620i
$222$	−1.36182			−0.0913995
$223$			7.51910i			0.503516i	0.967790	+	0.251758i	$0.0810087\pi$
$223$			7.51910i			0.503516i	−0.967790	+	0.251758i	$0.918991\pi$
$224$		−	1.02279i		−	0.0683380i
$225$	2.63518	−	4.24922i	0.175679	−	0.283281i
$226$	4.16284			0.276908
$227$		−	14.9639i		−	0.993187i	−0.867983	−	0.496594i	$-0.834584\pi$
$227$		−	14.9639i		−	0.993187i	0.867983	−	0.496594i	$-0.165416\pi$
$228$		−	11.9190i		−	0.789355i
$229$		−	12.3067i		−	0.813247i	−0.913596	−	0.406623i	$-0.866706\pi$
$229$		−	12.3067i		−	0.813247i	0.913596	−	0.406623i	$-0.133294\pi$
$230$	2.52327	+	4.53393i	0.166380	+	0.298958i
$231$	0.148979			0.00980210
$232$	2.93027	+	6.36183i	0.192382	+	0.417675i
$233$		−	10.7500i		−	0.704258i	−0.935951	−	0.352129i	$-0.885458\pi$
$233$		−	10.7500i		−	0.704258i	0.935951	−	0.352129i	$-0.114542\pi$
$234$			1.68498i			0.110151i
$235$	−24.2885	+	13.5173i	−1.58441	+	0.881772i
$236$	15.1341			0.985146
$237$		−	2.36972i		−	0.153930i
$238$		−	0.305795i		−	0.0198217i
$239$	−6.04481			−0.391006			−0.195503	−	0.980703i	$-0.562634\pi$
$239$	−6.04481			−0.391006			−0.195503	+	0.980703i	$0.562634\pi$
$240$	6.52804	−	3.63306i	0.421383	−	0.234513i
$241$	24.1998			1.55885			0.779423	−	0.626498i	$-0.215512\pi$
$241$	24.1998			1.55885			0.779423	+	0.626498i	$0.215512\pi$
$242$	−3.58158			−0.230233
$243$	1.00000			0.0641500
$244$			9.13879i			0.585051i
$245$	13.5293	−	7.52947i	0.864354	−	0.481040i
$246$		−	2.84292i		−	0.181258i
$247$	31.7969			2.02319
$248$		−	13.1440i		−	0.834647i
$249$			10.3724i			0.657323i
$250$	−0.176707	+	3.73590i	−0.0111760	+	0.236279i
$251$			26.0151i			1.64206i	0.570886	+	0.821030i	$0.306600\pi$
$251$			26.0151i			1.64206i	−0.570886	+	0.821030i	$0.693400\pi$
$252$		−	0.519262i		−	0.0327104i
$253$	−3.75766			−0.236242
$254$	3.47389			0.217971
$255$	6.49437	−	3.61432i	0.406693	−	0.226338i
$256$	7.77948			0.486218
$257$		−	3.58709i		−	0.223757i	−0.993722	−	0.111878i	$-0.964313\pi$
$257$		−	3.58709i		−	0.223757i	0.993722	−	0.111878i	$-0.0356867\pi$
$258$	−1.99920			−0.124465
$259$			1.11959i			0.0695677i
$260$	10.3414	+	18.5818i	0.641344	+	1.15239i
$261$	2.25292	+	4.89125i	0.139452	+	0.302761i
$262$		−	1.27381i		−	0.0786962i
$263$	3.92407			0.241969			0.120984	−	0.992654i	$-0.461395\pi$
$263$	3.92407			0.241969			0.120984	+	0.992654i	$0.461395\pi$
$264$		−	0.704571i		−	0.0433633i
$265$	4.33399	+	7.78751i	0.266235	+	0.478383i
$266$	0.580769			0.0356093
$267$			2.50630i			0.153383i
$268$		−	22.9713i		−	1.40320i
$269$		−	13.8826i		−	0.846437i	−0.906028	−	0.423218i	$-0.860900\pi$
$269$		−	13.8826i		−	0.846437i	0.906028	−	0.423218i	$-0.139100\pi$
$270$	−0.653612	+	0.363756i	−0.0397775	+	0.0221375i
$271$		−	13.3880i		−	0.813265i	−0.913592	−	0.406632i	$-0.866703\pi$
$271$		−	13.3880i		−	0.813265i	0.913592	−	0.406632i	$-0.133297\pi$
$272$	11.1053			0.673358
$273$	1.38526			0.0838398
$274$	−3.03067			−0.183089
$275$	−2.30182	−	1.42749i	−0.138805	−	0.0860808i
$276$			13.0972i			0.788359i
$277$		−	9.91356i		−	0.595648i	−0.954621	−	0.297824i	$-0.903739\pi$
$277$		−	9.91356i		−	0.595648i	0.954621	−	0.297824i	$-0.0962609\pi$
$278$	−0.474530			−0.0284604
$279$		−	10.1057i		−	0.605012i
$280$	0.388963	+	0.698907i	0.0232450	+	0.0417677i
$281$	−18.7167			−1.11654			−0.558271	−	0.829658i	$-0.688535\pi$
$281$	−18.7167			−1.11654			−0.558271	+	0.829658i	$0.688535\pi$
$282$	4.15845			0.247632
$283$		−	18.9462i		−	1.12624i	−0.826377	−	0.563118i	$-0.809602\pi$
$283$		−	18.9462i		−	1.12624i	0.826377	−	0.563118i	$-0.190398\pi$
$284$	13.5977			0.806876
$285$	6.86436	+	12.3342i	0.406610	+	0.730614i
$286$	0.912761			0.0539727
$287$	−2.33723			−0.137962
$288$	−3.71898			−0.219143
$289$	−5.95197			−0.350116
$290$	−3.25175	−	2.37747i	−0.190950	−	0.139610i
$291$	−17.8627			−1.04713
$292$	−2.33875			−0.136865
$293$	−7.13932			−0.417083			−0.208542	−	0.978013i	$-0.566872\pi$
$293$	−7.13932			−0.417083			−0.208542	+	0.978013i	$0.566872\pi$
$294$	−2.31636			−0.135093
$295$	−15.6613	+	8.71600i	−0.911835	+	0.507465i
$296$	5.29489			0.307759
$297$		−	0.541705i		−	0.0314329i
$298$	−1.57423			−0.0911929
$299$	−34.9401			−2.02064
$300$	−4.97546	+	8.02292i	−0.287259	+	0.463204i
$301$			1.64359i			0.0947347i
$302$	2.00439			0.115340
$303$			13.6767i			0.785706i
$304$			21.0913i			1.20967i
$305$	−5.26319	−	9.45713i	−0.301369	−	0.541514i
$306$	−1.11191			−0.0635634
$307$	10.0637			0.574368			0.287184	−	0.957875i	$-0.407281\pi$
$307$	10.0637			0.574368			0.287184	+	0.957875i	$0.407281\pi$
$308$	−0.281286			−0.0160278
$309$			10.6870i			0.607963i
$310$	3.67600	+	6.60520i	0.208783	+	0.375150i
$311$		−	16.2493i		−	0.921412i	−0.887553	−	0.460706i	$-0.847596\pi$
$311$		−	16.2493i		−	0.921412i	0.887553	−	0.460706i	$-0.152404\pi$
$312$		−	6.55136i		−	0.370898i
$313$			21.4838i			1.21434i	0.794573	+	0.607168i	$0.207695\pi$
$313$			21.4838i			1.21434i	−0.794573	+	0.607168i	$0.792305\pi$
$314$	−3.77099			−0.212809
$315$	0.299052	+	0.537350i	0.0168497	+	0.0302762i
$316$			4.47426i			0.251697i
$317$	−24.4204			−1.37159			−0.685794	−	0.727796i	$-0.740545\pi$
$317$	−24.4204			−1.37159			−0.685794	+	0.727796i	$0.740545\pi$
$318$		−	1.33330i		−	0.0747680i
$319$	2.64961	−	1.22042i	0.148350	−	0.0683302i
$320$	−10.6253	+	5.91332i	−0.593973	+	0.330565i
$321$		−	4.59224i		−	0.256314i
$322$	−0.638179			−0.0355643
$323$			20.9826i			1.16750i
$324$	−1.88809			−0.104894
$325$	−21.4032	−	13.2733i	−1.18723	−	0.736271i
$326$	3.77539			0.209099
$327$	−13.1473			−0.727045
$328$			11.0535i			0.610329i
$329$		−	3.41876i		−	0.188482i
$330$	0.197048	+	0.354065i	0.0108471	+	0.0194906i
$331$			0.627675i			0.0345001i	0.999851	+	0.0172501i	$0.00549114\pi$
$331$			0.627675i			0.0345001i	−0.999851	+	0.0172501i	$0.994509\pi$
$332$		−	19.5840i		−	1.07481i
$333$	4.07094			0.223086
$334$		−	3.04800i		−	0.166779i
$335$	13.2296	+	23.7715i	0.722810	+	1.29878i
$336$			0.918863i			0.0501281i
$337$	−27.2068			−1.48205			−0.741024	−	0.671479i	$-0.765659\pi$
$337$	−27.2068			−1.48205			−0.741024	+	0.671479i	$0.765659\pi$
$338$	4.13840			0.225099
$339$	−12.4441			−0.675873
$340$	−12.2620	+	6.82418i	−0.665000	+	0.370093i
$341$	−5.47430			−0.296450
$342$		−	2.11174i		−	0.114190i
$343$			3.82946i			0.206772i
$344$	7.77306			0.419096
$345$	−7.54291	−	13.5534i	−0.406097	−	0.729692i
$346$			2.23494i			0.120151i
$347$			13.0161i			0.698739i	0.936985	+	0.349369i	$0.113604\pi$
$347$			13.0161i			0.698739i	−0.936985	+	0.349369i	$0.886396\pi$
$348$	−4.25372	−	9.23515i	−0.228023	−	0.495056i
$349$	23.2480			1.24444			0.622218	−	0.782844i	$-0.286232\pi$
$349$	23.2480			1.24444			0.622218	+	0.782844i	$0.286232\pi$
$350$	−0.390928	−	0.242436i	−0.0208960	−	0.0129588i
$351$		−	5.03697i		−	0.268854i
$352$			2.01459i			0.107378i
$353$			33.0268i			1.75784i	0.476969	+	0.878920i	$0.341735\pi$
$353$			33.0268i			1.75784i	−0.476969	+	0.878920i	$0.658265\pi$
$354$	2.68138			0.142514
$355$	−14.0714	+	7.83116i	−0.746831	+	0.415635i
$356$		−	4.73213i		−	0.250802i
$357$			0.914124i			0.0483805i
$358$	−5.89185			−0.311394
$359$			30.0802i			1.58757i	0.608195	+	0.793787i	$0.291894\pi$
$359$			30.0802i			1.58757i	−0.608195	+	0.793787i	$0.708106\pi$
$360$	2.54130	−	1.41432i	0.133939	−	0.0745410i
$361$	−20.8503			−1.09739
$362$	−0.267376			−0.0140530
$363$	10.7066			0.561948
$364$	−2.61551			−0.137090
$365$	2.42022	−	1.34693i	0.126680	−	0.0705016i
$366$			1.61916i			0.0846349i
$367$	−3.89299			−0.203213			−0.101606	−	0.994825i	$-0.532398\pi$
$367$	−3.89299			−0.203213			−0.101606	+	0.994825i	$0.532398\pi$
$368$		−	23.1762i		−	1.20814i
$369$			8.49843i			0.442411i
$370$	−2.66082	+	1.48083i	−0.138329	+	0.0769845i
$371$	−1.09614			−0.0569088
$372$			19.0805i			0.989279i
$373$		−	1.78697i		−	0.0925260i	−0.998929	−	0.0462630i	$-0.985269\pi$
$373$		−	1.78697i		−	0.0925260i	0.998929	−	0.0462630i	$-0.0147312\pi$
$374$			0.602324i			0.0311454i
$375$	0.528238	−	11.1679i	0.0272781	−	0.576706i
$376$	−16.1684			−0.833824
$377$	24.6371	−	11.3479i	1.26888	−	0.584445i
$378$		−	0.0920000i		−	0.00473197i
$379$			18.4165i			0.945993i	0.881064	+	0.472996i	$0.156828\pi$
$379$			18.4165i			0.945993i	−0.881064	+	0.472996i	$0.843172\pi$
$380$	−12.9606	−	23.2881i	−0.664863	−	1.19466i
$381$	−10.3846			−0.532021
$382$		−	4.69482i		−	0.240208i
$383$			28.3971i			1.45102i	0.688210	+	0.725512i	$0.258397\pi$
$383$			28.3971i			1.45102i	−0.688210	+	0.725512i	$0.741603\pi$
$384$	9.25713			0.472401
$385$	0.291085	−	0.161998i	0.0148351	−	0.00825617i
$386$	−7.48304			−0.380877
$387$	5.97627			0.303791
$388$	33.7264			1.71220
$389$			8.49677i			0.430803i	0.976526	+	0.215402i	$0.0691061\pi$
$389$			8.49677i			0.430803i	−0.976526	+	0.215402i	$0.930894\pi$
$390$	1.83223	+	3.29222i	0.0927784	+	0.166708i
$391$		−	23.0567i		−	1.16603i
$392$	9.00621			0.454882
$393$			3.80784i			0.192080i
$394$		−	1.55979i		−	0.0785812i
$395$	−2.57680	−	4.63011i	−0.129653	−	0.232966i
$396$			1.02279i			0.0513971i
$397$			1.07708i			0.0540571i	0.999635	+	0.0270286i	$0.00860451\pi$
$397$			1.07708i			0.0540571i	−0.999635	+	0.0270286i	$0.991395\pi$
$398$	−5.01011			−0.251134
$399$	−1.73611			−0.0869144
$400$	8.80437	−	14.1970i	0.440218	−	0.709851i
$401$	18.2009			0.908910			0.454455	−	0.890770i	$-0.349834\pi$
$401$	18.2009			0.908910			0.454455	+	0.890770i	$0.349834\pi$
$402$		−	4.06994i		−	0.202990i
$403$	−50.9021			−2.53561
$404$		−	25.8229i		−	1.28474i
$405$	1.95387	−	1.08739i	0.0970883	−	0.0540327i
$406$	0.449995	−	0.207268i	0.0223329	−	0.0102866i
$407$		−	2.20525i		−	0.109310i
$408$	4.32319			0.214030
$409$		−	29.4035i		−	1.45391i	−0.686684	−	0.726956i	$-0.740934\pi$
$409$		−	29.4035i		−	1.45391i	0.686684	−	0.726956i	$-0.259066\pi$
$410$	−3.09135	−	5.55468i	−0.152671	−	0.274326i
$411$	9.05968			0.446881
$412$		−	20.1781i		−	0.994103i
$413$		−	2.20442i		−	0.108473i
$414$			2.32049i			0.114046i
$415$	11.2788	+	20.2662i	0.553654	+	0.994830i
$416$			18.7324i			0.918431i
$417$	1.41853			0.0694657
$418$	−1.14394			−0.0559520
$419$	−7.33375			−0.358277			−0.179139	−	0.983824i	$-0.557331\pi$
$419$	−7.33375			−0.358277			−0.179139	+	0.983824i	$0.557331\pi$
$420$	−0.564638	−	1.01457i	−0.0275515	−	0.0495058i
$421$			21.0761i			1.02718i	0.858034	+	0.513592i	$0.171686\pi$
$421$			21.0761i			1.02718i	−0.858034	+	0.513592i	$0.828314\pi$
$422$			5.31756i			0.258855i
$423$	−12.4310			−0.604416
$424$			5.18401i			0.251758i
$425$	8.75896	−	14.1238i	0.424872	−	0.685105i
$426$	2.40917			0.116725
$427$	1.33115			0.0644189
$428$			8.67058i			0.419108i
$429$	−2.72855			−0.131736
$430$	−3.90616	+	2.17390i	−0.188372	+	0.104835i
$431$	−10.6334			−0.512195			−0.256098	−	0.966651i	$-0.582437\pi$
$431$	−10.6334			−0.512195			−0.256098	+	0.966651i	$0.582437\pi$
$432$	3.34109			0.160748
$433$	−12.7281			−0.611674			−0.305837	−	0.952084i	$-0.598936\pi$
$433$	−12.7281			−0.611674			−0.305837	+	0.952084i	$0.598936\pi$
$434$	−0.929724			−0.0446282
$435$	9.72058	+	7.10706i	0.466066	+	0.340757i
$436$	24.8233			1.18882
$437$	43.7896			2.09474
$438$	−0.414368			−0.0197993
$439$	−4.48366			−0.213994			−0.106997	−	0.994259i	$-0.534123\pi$
$439$	−4.48366			−0.213994			−0.106997	+	0.994259i	$0.534123\pi$
$440$	−0.766141	−	1.37664i	−0.0365244	−	0.0656286i
$441$	6.92436			0.329732
$442$			5.60063i			0.266395i
$443$	−12.8049			−0.608379			−0.304189	−	0.952612i	$-0.598386\pi$
$443$	−12.8049			−0.608379			−0.304189	+	0.952612i	$0.598386\pi$
$444$	−7.68632			−0.364777
$445$	2.72532	+	4.89697i	0.129192	+	0.232138i
$446$		−	2.51531i		−	0.119103i
$447$	4.70591			0.222582
$448$		−	1.49558i		−	0.0706595i
$449$		−	22.1787i		−	1.04668i	−0.852124	−	0.523340i	$-0.824686\pi$
$449$		−	22.1787i		−	1.04668i	0.852124	−	0.523340i	$-0.175314\pi$
$450$	−0.881526	+	1.42146i	−0.0415555	+	0.0670082i
$451$	4.60364			0.216777
$452$	23.4957			1.10515
$453$	−5.99181			−0.281520
$454$			5.00575i			0.234932i
$455$	2.70661	−	1.50632i	0.126888	−	0.0706172i
$456$			8.21066i			0.384499i
$457$		−	12.2239i		−	0.571808i	−0.958258	−	0.285904i	$-0.907706\pi$
$457$		−	12.2239i		−	0.571808i	0.958258	−	0.285904i	$-0.0922939\pi$
$458$			4.11685i			0.192368i
$459$	3.32386			0.155144
$460$	14.2417	+	25.5902i	0.664024	+	1.19315i
$461$		−	26.1495i		−	1.21790i	−0.793207	−	0.608952i	$-0.791590\pi$
$461$		−	26.1495i		−	1.21790i	0.793207	−	0.608952i	$-0.208410\pi$
$462$	−0.0498368			−0.00231862
$463$			23.5519i			1.09455i	0.836953	+	0.547275i	$0.184335\pi$
$463$			23.5519i			1.09455i	−0.836953	+	0.547275i	$0.815665\pi$
$464$	7.52720	+	16.3421i	0.349442	+	0.758664i
$465$	−10.9888	−	19.7452i	−0.509594	−	0.915660i
$466$			3.59613i			0.166587i
$467$	−12.7060			−0.587963			−0.293981	−	0.955811i	$-0.594980\pi$
$467$	−12.7060			−0.587963			−0.293981	+	0.955811i	$0.594980\pi$
$468$			9.51028i			0.439613i
$469$	−3.34599			−0.154503
$470$	8.12505	−	4.52185i	0.374781	−	0.208577i
$471$	11.2728			0.519421
$472$	−10.4255			−0.479870
$473$		−	3.23737i		−	0.148855i
$474$			0.792725i			0.0364111i
$475$	26.8241	+	16.6351i	1.23077	+	0.763272i
$476$		−	1.72595i		−	0.0791089i
$477$			3.98569i			0.182492i
$478$	2.02212			0.0924898
$479$			14.2867i			0.652775i	0.945236	+	0.326388i	$0.105831\pi$
$479$			14.2867i			0.652775i	−0.945236	+	0.326388i	$0.894169\pi$
$480$	−7.26639	+	4.04397i	−0.331664	+	0.184581i
$481$		−	20.5052i		−	0.934957i
$482$	−8.09538			−0.368734
$483$	1.90773			0.0868047
$484$	−20.2150			−0.918863
$485$	−34.9012	+	19.4236i	−1.58478	+	0.881982i
$486$	−0.334522			−0.0151742
$487$		−	34.4239i		−	1.55990i	−0.625844	−	0.779948i	$-0.715246\pi$
$487$		−	34.4239i		−	1.55990i	0.625844	−	0.779948i	$-0.284754\pi$
$488$		−	6.29545i		−	0.284982i
$489$	−11.2859			−0.510366
$490$	−4.52585	+	2.51878i	−0.204457	+	0.113787i
$491$		−	20.5793i		−	0.928733i	−0.885643	−	0.464366i	$-0.846282\pi$
$491$		−	20.5793i		−	0.928733i	0.885643	−	0.464366i	$-0.153718\pi$
$492$		−	16.0458i		−	0.723403i
$493$	7.48838	+	16.2578i	0.337260	+	0.732216i
$494$	−10.6368			−0.478572
$495$	−0.589043	−	1.05842i	−0.0264755	−	0.0475723i
$496$		−	33.7641i		−	1.51605i
$497$		−	1.98064i		−	0.0888436i
$498$		−	3.46980i		−	0.155485i
$499$	−19.5569			−0.875487			−0.437743	−	0.899100i	$-0.644222\pi$
$499$	−19.5569			−0.875487			−0.437743	+	0.899100i	$0.644222\pi$
$500$	−0.997363	+	21.0860i	−0.0446034	+	0.942993i
$501$			9.11150i			0.407072i
$502$		−	8.70264i		−	0.388418i
$503$	−38.5345			−1.71817			−0.859084	−	0.511835i	$-0.828966\pi$
$503$	−38.5345			−1.71817			−0.859084	+	0.511835i	$0.828966\pi$
$504$			0.357705i			0.0159334i
$505$	14.8719	+	26.7224i	0.661790	+	1.18913i
$506$	1.25702			0.0558814
$507$	−12.3711			−0.549418
$508$	19.6072			0.869928
$509$	9.66065			0.428201			0.214100	−	0.976812i	$-0.431318\pi$
$509$	9.66065			0.428201			0.214100	+	0.976812i	$0.431318\pi$
$510$	−2.17251	+	1.20907i	−0.0962005	+	0.0535386i
$511$			0.340662i			0.0150700i
$512$	−21.1167			−0.933234
$513$			6.31271i			0.278713i
$514$			1.19996i			0.0529281i
$515$	11.6209	+	20.8810i	0.512079	+	0.920126i
$516$	−11.2838			−0.496740
$517$			6.73393i			0.296158i
$518$		−	0.374527i		−	0.0164557i
$519$		−	6.68099i		−	0.293263i
$520$	−7.12387	−	12.8005i	−0.312402	−	0.561338i
$521$	20.3242			0.890421			0.445211	−	0.895426i	$-0.353129\pi$
$521$	20.3242			0.890421			0.445211	+	0.895426i	$0.353129\pi$
$522$	−0.753651	−	1.63623i	−0.0329864	−	0.0716160i
$523$			40.6870i			1.77912i	0.456820	+	0.889559i	$0.348988\pi$
$523$			40.6870i			1.77912i	−0.456820	+	0.889559i	$0.651012\pi$
$524$		−	7.18957i		−	0.314078i
$525$	1.16861	+	0.724723i	0.0510025	+	0.0316295i
$526$	−1.31269			−0.0572360
$527$		−	33.5899i		−	1.46320i
$528$		−	1.80988i		−	0.0787651i
$529$	−25.1182			−1.09209
$530$	−1.44982	−	2.60510i	−0.0629761	−	0.113158i
$531$	−8.01554			−0.347845
$532$	3.27795			0.142117
$533$	42.8064			1.85415
$534$		−	0.838413i		−	0.0362817i
$535$	−4.99354	−	8.97261i	−0.215890	−	0.387920i
$536$			15.8243i			0.683506i
$537$	17.6127			0.760045
$538$			4.64404i			0.200219i
$539$		−	3.75096i		−	0.161565i
$540$	−3.68908	+	2.05309i	−0.158753	+	0.0883509i
$541$		−	5.02402i		−	0.216000i	−0.994151	−	0.108000i	$-0.965555\pi$
$541$		−	5.02402i		−	0.216000i	0.994151	−	0.108000i	$-0.0344446\pi$
$542$			4.47860i			0.192372i
$543$	0.799278			0.0343003
$544$	−12.3614			−0.529989
$545$	−25.6880	+	14.2962i	−1.10035	+	0.612380i
$546$	−0.463401			−0.0198317
$547$			8.61344i			0.368284i	0.982900	+	0.184142i	$0.0589506\pi$
$547$			8.61344i			0.368284i	−0.982900	+	0.184142i	$0.941049\pi$
$548$	−17.1055			−0.730712
$549$		−	4.84022i		−	0.206575i
$550$	0.770011	+	0.477527i	0.0328334	+	0.0203618i
$551$	−30.8771	+	14.2220i	−1.31541	+	0.605878i
$552$		−	9.02229i		−	0.384014i
$553$	0.651718			0.0277139
$554$			3.31631i			0.140896i
$555$	7.95407	−	4.42669i	0.337631	−	0.187903i
$556$	−2.67832			−0.113586
$557$		−	0.455853i		−	0.0193151i	−0.999953	−	0.00965755i	$-0.996926\pi$
$557$		−	0.455853i		−	0.0193151i	0.999953	−	0.00965755i	$-0.00307414\pi$
$558$			3.38058i			0.143111i
$559$		−	30.1023i		−	1.27319i
$560$	0.999160	+	1.79533i	0.0422222	+	0.0758667i
$561$		−	1.80055i		−	0.0760192i
$562$	6.26114			0.264110
$563$	0.120515			0.00507911			0.00253956	−	0.999997i	$-0.499192\pi$
$563$	0.120515			0.00507911			0.00253956	+	0.999997i	$0.499192\pi$
$564$	23.4709			0.988304
$565$	−24.3142	+	13.5316i	−1.02290	+	0.569279i
$566$			6.33794i			0.266403i
$567$			0.275019i			0.0115497i
$568$	−9.36708			−0.393034
$569$			22.7315i			0.952954i	0.879187	+	0.476477i	$0.158086\pi$
$569$			22.7315i			0.952954i	−0.879187	+	0.476477i	$0.841914\pi$
$570$	−2.29628	−	4.12606i	−0.0961808	−	0.172822i
$571$	26.7167			1.11806			0.559030	−	0.829147i	$-0.311174\pi$
$571$	26.7167			1.11806			0.559030	+	0.829147i	$0.311174\pi$
$572$	5.15176			0.215406
$573$			14.0344i			0.586296i
$574$	0.781856			0.0326340
$575$	−29.4756	−	18.2795i	−1.22922	−	0.762308i
$576$	−5.43810			−0.226587
$577$	15.3024			0.637049			0.318524	−	0.947915i	$-0.396813\pi$
$577$	15.3024			0.637049			0.318524	+	0.947915i	$0.396813\pi$
$578$	1.99107			0.0828175
$579$	22.3693			0.929637
$580$	−18.3534	−	13.4188i	−0.762083	−	0.557185i
$581$	−2.85260			−0.118346
$582$	5.97546			0.247691
$583$	2.15907			0.0894195
$584$	1.61110			0.0666679
$585$	−5.47714	−	9.84156i	−0.226452	−	0.406898i
$586$	2.38826			0.0986582
$587$		−	41.6229i		−	1.71796i	−0.512009	−	0.858980i	$-0.671098\pi$
$587$		−	41.6229i		−	1.71796i	0.512009	−	0.858980i	$-0.328902\pi$
$588$	−13.0739			−0.539157
$589$	63.7944			2.62860
$590$	5.23905	−	2.91570i	0.215688	−	0.120037i
$591$			4.66274i			0.191800i
$592$	13.6014			0.559013
$593$			11.7493i			0.482487i	0.970465	+	0.241244i	$0.0775553\pi$
$593$			11.7493i			0.482487i	−0.970465	+	0.241244i	$0.922445\pi$
$594$			0.181212i			0.00743523i
$595$	0.994006	+	1.78607i	0.0407503	+	0.0732219i
$596$	−8.88521			−0.363952
$597$	14.9769			0.612964
$598$	11.6882			0.477968
$599$			8.86844i			0.362354i	0.983450	+	0.181177i	$0.0579908\pi$
$599$			8.86844i			0.362354i	−0.983450	+	0.181177i	$0.942009\pi$
$600$	3.42746	−	5.52676i	0.139925	−	0.225629i
$601$		−	0.339050i		−	0.0138301i	−0.999976	−	0.00691506i	$-0.997799\pi$
$601$		−	0.339050i		−	0.0138301i	0.999976	−	0.00691506i	$-0.00220115\pi$
$602$		−	0.549817i		−	0.0224089i
$603$			12.1664i			0.495454i
$604$	11.3131			0.460324
$605$	20.9192	−	11.6422i	0.850485	−	0.473322i
$606$		−	4.57516i		−	0.185853i
$607$	−8.27856			−0.336017			−0.168008	−	0.985786i	$-0.553734\pi$
$607$	−8.27856			−0.336017			−0.168008	+	0.985786i	$0.553734\pi$
$608$		−	23.4769i		−	0.952112i
$609$	−1.34519	+	0.619595i	−0.0545097	+	0.0251072i
$610$	1.76066	+	3.16362i	0.0712869	+	0.128091i
$611$			62.6146i			2.53312i
$612$	−6.27576			−0.253683
$613$		−	42.0873i		−	1.69989i	−0.526870	−	0.849946i	$-0.676635\pi$
$613$		−	42.0873i		−	1.69989i	0.526870	−	0.849946i	$-0.323365\pi$
$614$	−3.36655			−0.135863
$615$	9.24109	+	16.6048i	0.372637	+	0.669570i
$616$	0.193770			0.00780723
$617$	−28.7087			−1.15577			−0.577884	−	0.816119i	$-0.696121\pi$
$617$	−28.7087			−1.15577			−0.577884	+	0.816119i	$0.696121\pi$
$618$		−	3.57504i		−	0.143809i
$619$			8.90716i			0.358009i	0.983848	+	0.179005i	$0.0572877\pi$
$619$			8.90716i			0.358009i	−0.983848	+	0.179005i	$0.942712\pi$
$620$	20.7479	+	37.2807i	0.833256	+	1.49723i
$621$		−	6.93673i		−	0.278361i
$622$			5.43575i			0.217954i
$623$	−0.689279			−0.0276154
$624$		−	16.8290i		−	0.673698i
$625$	−11.1117	−	22.3949i	−0.444467	−	0.895795i
$626$		−	7.18681i		−	0.287243i
$627$	3.41963			0.136567
$628$	−21.2840			−0.849325
$629$	13.5312			0.539525
$630$	−0.100040	−	0.179756i	−0.00398567	−	0.00716163i
$631$	17.9351			0.713986			0.356993	−	0.934107i	$-0.383802\pi$
$631$	17.9351			0.713986			0.356993	+	0.934107i	$0.383802\pi$
$632$		−	3.08219i		−	0.122603i
$633$		−	15.8960i		−	0.631809i
$634$	8.16918			0.324440
$635$	−20.2902	+	11.2921i	−0.805191	+	0.448114i
$636$		−	7.52537i		−	0.298400i
$637$		−	34.8778i		−	1.38191i
$638$	−0.886356	+	0.408256i	−0.0350912	+	0.0161630i
$639$	−7.20182			−0.284899
$640$	18.0872	−	10.0661i	0.714958	−	0.397897i
$641$			0.220741i			0.00871875i	0.999990	+	0.00435938i	$0.00138764\pi$
$641$			0.220741i			0.00871875i	−0.999990	+	0.00435938i	$0.998612\pi$
$642$			1.53621i			0.0606292i
$643$			6.25440i			0.246650i	0.992366	+	0.123325i	$0.0393557\pi$
$643$			6.25440i			0.246650i	−0.992366	+	0.123325i	$0.960644\pi$
$644$	−3.60198			−0.141938
$645$	11.6768	−	6.49852i	0.459774	−	0.255879i
$646$		−	7.01914i		−	0.276164i
$647$		−	24.3697i		−	0.958071i	−0.877796	−	0.479035i	$-0.840987\pi$
$647$		−	24.3697i		−	0.958071i	0.877796	−	0.479035i	$-0.159013\pi$
$648$	1.30066			0.0510946
$649$			4.34205i			0.170441i
$650$	7.15984	+	4.44022i	0.280832	+	0.174160i
$651$	2.77926			0.108928
$652$	21.3088			0.834519
$653$	41.1834			1.61163			0.805815	−	0.592167i	$-0.201727\pi$
$653$	41.1834			1.61163			0.805815	+	0.592167i	$0.201727\pi$
$654$	4.39805			0.171977
$655$	4.14060	+	7.44001i	0.161787	+	0.290705i
$656$			28.3940i			1.10860i
$657$	1.23869			0.0483257
$658$			1.14365i			0.0445842i
$659$			4.18021i			0.162838i	0.996680	+	0.0814190i	$0.0259452\pi$
$659$			4.18021i			0.162838i	−0.996680	+	0.0814190i	$0.974055\pi$
$660$	1.11217	+	1.99839i	0.0432911	+	0.0777873i
$661$	−8.11965			−0.315818			−0.157909	−	0.987454i	$-0.550475\pi$
$661$	−8.11965			−0.315818			−0.157909	+	0.987454i	$0.550475\pi$
$662$		−	0.209971i		−	0.00816077i
$663$		−	16.7422i		−	0.650212i
$664$			13.4909i			0.523548i
$665$	−3.39213	+	1.88783i	−0.131541	+	0.0732069i
$666$	−1.36182			−0.0527695
$667$	33.9293	−	15.6279i	1.31375	−	0.605113i
$668$		−	17.2034i		−	0.665619i
$669$			7.51910i			0.290705i
$670$	−4.42560	−	7.95211i	−0.170976	−	0.307217i
$671$	−2.62197			−0.101220
$672$		−	1.02279i		−	0.0394550i
$673$		−	33.1749i		−	1.27880i	−0.768875	−	0.639399i	$-0.779183\pi$
$673$		−	33.1749i		−	1.27880i	0.768875	−	0.639399i	$-0.220817\pi$
$674$	9.10128			0.350568
$675$	2.63518	−	4.24922i	0.101428	−	0.163552i
$676$	23.3577			0.898375
$677$	−14.7844			−0.568212			−0.284106	−	0.958793i	$-0.591697\pi$
$677$	−14.7844			−0.568212			−0.284106	+	0.958793i	$0.591697\pi$
$678$	4.16284			0.159873
$679$		−	4.91257i		−	0.188527i
$680$	8.44694	−	4.70099i	0.323925	−	0.180275i
$681$		−	14.9639i		−	0.573417i
$682$	1.83128			0.0701232
$683$		−	33.5573i		−	1.28404i	−0.766690	−	0.642018i	$-0.778098\pi$
$683$		−	33.5573i		−	1.28404i	0.766690	−	0.642018i	$-0.221902\pi$
$684$		−	11.9190i		−	0.455734i
$685$	17.7014	−	9.85138i	0.676336	−	0.376402i
$686$		−	1.28104i		−	0.0489104i
$687$		−	12.3067i		−	0.469528i
$688$	19.9673			0.761245
$689$	20.0758			0.764828
$690$	2.52327	+	4.53393i	0.0960593	+	0.172604i
$691$	−11.4767			−0.436596			−0.218298	−	0.975882i	$-0.570050\pi$
$691$	−11.4767			−0.436596			−0.218298	+	0.975882i	$0.570050\pi$
$692$			12.6143i			0.479525i
$693$	0.148979			0.00565924
$694$		−	4.35417i		−	0.165282i
$695$	2.77162	−	1.54249i	0.105133	−	0.0585101i
$696$	2.93027	+	6.36183i	0.111072	+	0.241145i
$697$			28.2476i			1.06995i
$698$	−7.77697			−0.294363
$699$		−	10.7500i		−	0.406604i
$700$	−2.20645	−	1.36835i	−0.0833962	−	0.0517186i
$701$	11.0065			0.415711			0.207855	−	0.978160i	$-0.433352\pi$
$701$	11.0065			0.415711			0.207855	+	0.978160i	$0.433352\pi$
$702$			1.68498i			0.0635955i
$703$			25.6987i			0.969244i
$704$			2.94584i			0.111026i
$705$	−24.2885	+	13.5173i	−0.914758	+	0.509092i
$706$		−	11.0482i		−	0.415805i
$707$	−3.76135			−0.141460
$708$	15.1341			0.568774
$709$	21.4248			0.804624			0.402312	−	0.915503i	$-0.368207\pi$
$709$	21.4248			0.804624			0.402312	+	0.915503i	$0.368207\pi$
$710$	4.70719	−	2.61970i	0.176658	−	0.0983156i
$711$		−	2.36972i		−	0.0888715i
$712$			3.25983i			0.122167i
$713$	−70.1005			−2.62528
$714$		−	0.305795i		−	0.0114441i
$715$	−5.33122	+	2.96699i	−0.199376	+	0.110959i
$716$	−33.2545			−1.24278
$717$	−6.04481			−0.225747
$718$		−	10.0625i		−	0.375530i
$719$	−21.8797			−0.815977			−0.407988	−	0.912987i	$-0.633770\pi$
$719$	−21.8797			−0.815977			−0.407988	+	0.912987i	$0.633770\pi$
$720$	6.52804	−	3.63306i	0.243286	−	0.135396i
$721$	−2.93913			−0.109459
$722$	6.97491			0.259579
$723$	24.1998			0.900000
$724$	−1.50911			−0.0560857
$725$	26.7208	+	3.31619i	0.992387	+	0.123160i
$726$	−3.58158			−0.132925
$727$	36.6219			1.35823			0.679115	−	0.734032i	$-0.262364\pi$
$727$	36.6219			1.35823			0.679115	+	0.734032i	$0.262364\pi$
$728$	1.80175			0.0667772
$729$	1.00000			0.0370370
$730$	−0.809619	+	0.450579i	−0.0299654	+	0.0166767i
$731$	19.8643			0.734707
$732$			9.13879i			0.337779i
$733$	−7.68719			−0.283933			−0.141966	−	0.989871i	$-0.545342\pi$
$733$	−7.68719			−0.283933			−0.141966	+	0.989871i	$0.545342\pi$
$734$	1.30229			0.0480686
$735$	13.5293	−	7.52947i	0.499035	−	0.277729i
$736$			25.7975i			0.950910i
$737$	6.59060			0.242768
$738$		−	2.84292i		−	0.104649i
$739$		−	26.2160i		−	0.964371i	−0.876069	−	0.482186i	$-0.839843\pi$
$739$		−	26.2160i		−	0.964371i	0.876069	−	0.482186i	$-0.160157\pi$
$740$	−15.0180	+	8.35801i	−0.552074	+	0.307247i
$741$	31.7969			1.16809
$742$	0.366684			0.0134614
$743$	7.62063			0.279574			0.139787	−	0.990182i	$-0.455358\pi$
$743$	7.62063			0.279574			0.139787	+	0.990182i	$0.455358\pi$
$744$		−	13.1440i		−	0.481883i
$745$	9.19472	−	5.11715i	0.336868	−	0.187478i
$746$			0.597783i			0.0218864i
$747$			10.3724i			0.379506i
$748$			3.39961i			0.124302i
$749$	1.26295			0.0461472
$750$	−0.176707	+	3.73590i	−0.00645244	+	0.136416i
$751$		−	28.5397i		−	1.04143i	−0.853731	−	0.520714i	$-0.825666\pi$
$751$		−	28.5397i		−	1.04143i	0.853731	−	0.520714i	$-0.174334\pi$
$752$	−41.5331			−1.51456
$753$			26.0151i			0.948043i
$754$	−8.24166	+	3.79612i	−0.300144	+	0.138247i
$755$	−11.7072	+	6.51542i	−0.426068	+	0.237120i
$756$		−	0.519262i		−	0.0188854i
$757$	−19.8761			−0.722408			−0.361204	−	0.932487i	$-0.617634\pi$
$757$	−19.8761			−0.722408			−0.361204	+	0.932487i	$0.617634\pi$
$758$		−	6.16074i		−	0.223768i
$759$	−3.75766			−0.136394
$760$	8.92817	+	16.0425i	0.323859	+	0.581924i
$761$	33.8887			1.22847			0.614233	−	0.789125i	$-0.289465\pi$
$761$	33.8887			1.22847			0.614233	+	0.789125i	$0.289465\pi$
$762$	3.47389			0.125846
$763$		−	3.61574i		−	0.130899i
$764$		−	26.4983i		−	0.958674i
$765$	6.49437	−	3.61432i	0.234804	−	0.130676i
$766$		−	9.49947i		−	0.343230i
$767$			40.3740i			1.45782i
$768$	7.77948			0.280718
$769$			37.6604i			1.35807i	0.734107	+	0.679034i	$0.237601\pi$
$769$			37.6604i			1.35807i	−0.734107	+	0.679034i	$0.762399\pi$
$770$	−0.0973744	+	0.0541919i	−0.00350913	+	0.00195294i
$771$		−	3.58709i		−	0.129186i
$772$	−42.2354			−1.52008
$773$	23.1391			0.832255			0.416127	−	0.909306i	$-0.363387\pi$
$773$	23.1391			0.832255			0.416127	+	0.909306i	$0.363387\pi$
$774$	−1.99920			−0.0718596
$775$	−42.9413	−	26.6303i	−1.54250	−	0.956589i
$776$	−23.2332			−0.834022
$777$			1.11959i			0.0401649i
$778$		−	2.84236i		−	0.101904i
$779$	−53.6482			−1.92214
$780$	10.3414	+	18.5818i	0.370280	+	0.665335i
$781$			3.90126i			0.139598i
$782$			7.71298i			0.275816i
$783$	2.25292	+	4.89125i	0.0805127	+	0.174799i
$784$	23.1349			0.826248
$785$	22.0254	−	12.2579i	0.786122	−	0.437502i
$786$		−	1.27381i		−	0.0454353i
$787$		−	11.0598i		−	0.394238i	−0.980380	−	0.197119i	$-0.936841\pi$
$787$		−	11.0598i		−	0.394238i	0.980380	−	0.197119i	$-0.0631586\pi$
$788$		−	8.80370i		−	0.313619i
$789$	3.92407			0.139701
$790$	0.861999	+	1.54888i	0.0306685	+	0.0551066i
$791$		−	3.42237i		−	0.121686i
$792$		−	0.704571i		−	0.0250358i
$793$	−24.3800			−0.865760
$794$		−	0.360308i		−	0.0127868i
$795$	4.33399	+	7.78751i	0.153711	+	0.276195i
$796$	−28.2778			−1.00228
$797$	−11.5108			−0.407733			−0.203866	−	0.978999i	$-0.565351\pi$
$797$	−11.5108			−0.407733			−0.203866	+	0.978999i	$0.565351\pi$
$798$	0.580769			0.0205590
$799$	−41.3189			−1.46176
$800$	−9.80017	+	15.8028i	−0.346488	+	0.558712i
$801$			2.50630i			0.0885557i
$802$	−6.08861			−0.214996
$803$		−	0.671001i		−	0.0236791i
$804$		−	22.9713i		−	0.810136i
$805$	3.72745	−	2.07444i	0.131375	−	0.0731145i
$806$	17.0279			0.599782
$807$		−	13.8826i		−	0.488690i
$808$			17.7887i			0.625803i
$809$		−	26.4897i		−	0.931330i	−0.884961	−	0.465665i	$-0.845815\pi$
$809$		−	26.4897i		−	0.931330i	0.884961	−	0.465665i	$-0.154185\pi$
$810$	−0.653612	+	0.363756i	−0.0229656	+	0.0127811i
$811$	−40.5686			−1.42455			−0.712277	−	0.701898i	$-0.752336\pi$
$811$	−40.5686			−1.42455			−0.712277	+	0.701898i	$0.752336\pi$
$812$	2.53984	−	1.16985i	0.0891309	−	0.0410538i
$813$		−	13.3880i		−	0.469539i
$814$			0.737705i			0.0258565i
$815$	−22.0511	+	12.2721i	−0.772417	+	0.429874i
$816$	11.1053			0.388764
$817$			37.7265i			1.31988i
$818$			9.83615i			0.343913i
$819$	1.38526			0.0484050
$820$	−17.4480	−	31.3514i	−0.609312	−	1.09484i
$821$	−34.6649			−1.20981			−0.604906	−	0.796297i	$-0.706789\pi$
$821$	−34.6649			−1.20981			−0.604906	+	0.796297i	$0.706789\pi$
$822$	−3.03067			−0.105707
$823$	37.6231			1.31146			0.655729	−	0.754996i	$-0.272361\pi$
$823$	37.6231			1.31146			0.655729	+	0.754996i	$0.272361\pi$
$824$			13.9001i			0.484233i
$825$	−2.30182	−	1.42749i	−0.0801391	−	0.0496987i
$826$			0.737429i			0.0256585i
$827$	45.0238			1.56563			0.782816	−	0.622253i	$-0.213783\pi$
$827$	45.0238			1.56563			0.782816	+	0.622253i	$0.213783\pi$
$828$			13.0972i			0.455159i
$829$			12.5148i			0.434656i	0.976099	+	0.217328i	$0.0697341\pi$
$829$			12.5148i			0.434656i	−0.976099	+	0.217328i	$0.930266\pi$
$830$	−3.77301	−	6.77951i	−0.130963	−	0.235320i
$831$		−	9.91356i		−	0.343898i
$832$			27.3915i			0.949631i
$833$	23.0156			0.797443
$834$	−0.474530			−0.0164316
$835$	9.90773	+	17.8026i	0.342871	+	0.616086i
$836$	−6.45658			−0.223305
$837$		−	10.1057i		−	0.349304i
$838$	2.45330			0.0847480
$839$			35.4253i			1.22302i	0.791238	+	0.611508i	$0.209437\pi$
$839$			35.4253i			1.22302i	−0.791238	+	0.611508i	$0.790563\pi$
$840$	0.388963	+	0.698907i	0.0134205	+	0.0241146i
$841$	−18.8487	+	22.0392i	−0.649956	+	0.759972i
$842$		−	7.05042i		−	0.242973i
$843$	−18.7167			−0.644636
$844$			30.0131i			1.03309i
$845$	−24.1714	+	13.4521i	−0.831521	+	0.462768i
$846$	4.15845			0.142970
$847$			2.94450i			0.101174i
$848$			13.3166i			0.457293i
$849$		−	18.9462i		−	0.650233i
$850$	−2.93007	+	4.72473i	−0.100501	+	0.162057i
$851$		−	28.2390i		−	0.968021i
$852$	13.5977			0.465850
$853$	−4.63924			−0.158844			−0.0794222	−	0.996841i	$-0.525308\pi$
$853$	−4.63924			−0.158844			−0.0794222	+	0.996841i	$0.525308\pi$
$854$	−0.445300			−0.0152379
$855$	6.86436	+	12.3342i	0.234756	+	0.421820i
$856$		−	5.97292i		−	0.204150i
$857$			52.9487i			1.80869i	0.426800	+	0.904346i	$0.359641\pi$
$857$			52.9487i			1.80869i	−0.426800	+	0.904346i	$0.640359\pi$
$858$	0.912761			0.0311612
$859$		−	37.3538i		−	1.27450i	−0.770658	−	0.637248i	$-0.780073\pi$
$859$		−	37.3538i		−	1.27450i	0.770658	−	0.637248i	$-0.219927\pi$
$860$	−22.0469	+	12.2698i	−0.751795	+	0.418397i
$861$	−2.33723			−0.0796525
$862$	3.55713			0.121156
$863$		−	10.2002i		−	0.347219i	−0.984815	−	0.173609i	$-0.944457\pi$
$863$		−	10.2002i		−	0.347219i	0.984815	−	0.173609i	$-0.0555431\pi$
$864$	−3.71898			−0.126522
$865$	−7.26482	−	13.0537i	−0.247011	−	0.443841i
$866$	4.25784			0.144687
$867$	−5.95197			−0.202139
$868$	−5.24750			−0.178112
$869$	−1.28369			−0.0435461
$870$	−3.25175	−	2.37747i	−0.110245	−	0.0806038i
$871$	61.2818			2.07646
$872$	−17.1000			−0.579081
$873$	−17.8627			−0.604560
$874$	−14.6486			−0.495496
$875$	3.07137	+	0.145275i	0.103831	+	0.00491120i
$876$	−2.33875			−0.0790192
$877$		−	8.25649i		−	0.278802i	−0.990236	−	0.139401i	$-0.955482\pi$
$877$		−	8.25649i		−	0.278802i	0.990236	−	0.139401i	$-0.0445177\pi$
$878$	1.49989			0.0506187
$879$	−7.13932			−0.240803
$880$	−1.96805	−	3.53627i	−0.0663428	−	0.119208i
$881$		−	4.94367i		−	0.166556i	−0.996526	−	0.0832782i	$-0.973461\pi$
$881$		−	4.94367i		−	0.166556i	0.996526	−	0.0832782i	$-0.0265390\pi$
$882$	−2.31636			−0.0779958
$883$		−	35.6378i		−	1.19931i	−0.800259	−	0.599654i	$-0.795305\pi$
$883$		−	35.6378i		−	1.19931i	0.800259	−	0.599654i	$-0.204695\pi$
$884$			31.6108i			1.06319i
$885$	−15.6613	+	8.71600i	−0.526448	+	0.292985i
$886$	4.28352			0.143908
$887$	2.14284			0.0719497			0.0359748	−	0.999353i	$-0.488546\pi$
$887$	2.14284			0.0719497			0.0359748	+	0.999353i	$0.488546\pi$
$888$	5.29489			0.177685
$889$		−	2.85597i		−	0.0957862i
$890$	−0.911679	−	1.63815i	−0.0305596	−	0.0549108i
$891$		−	0.541705i		−	0.0181478i
$892$		−	14.1968i		−	0.475343i
$893$		−	78.4733i		−	2.62601i
$894$	−1.57423			−0.0526503
$895$	34.4129	−	19.1519i	1.15030	−	0.640176i
$896$			2.54588i			0.0850520i
$897$	−34.9401			−1.16662
$898$			7.41929i			0.247585i
$899$	49.4295	−	22.7673i	1.64857	−	0.759332i
$900$	−4.97546	+	8.02292i	−0.165849	+	0.267431i
$901$			13.2479i			0.441351i
$902$	−1.54002			−0.0512771
$903$			1.64359i			0.0546951i
$904$	−16.1855			−0.538323
$905$	1.56168	−	0.869125i	0.0519120	−	0.0288907i
$906$	2.00439			0.0665916
$907$	−27.7834			−0.922533			−0.461266	−	0.887262i	$-0.652605\pi$
$907$	−27.7834			−0.922533			−0.461266	+	0.887262i	$0.652605\pi$
$908$			28.2532i			0.937616i
$909$			13.6767i			0.453627i
$910$	−0.905423	+	0.503897i	−0.0300145	+	0.0167040i
$911$			7.92701i			0.262634i	0.991340	+	0.131317i	$0.0419205\pi$
$911$			7.92701i			0.262634i	−0.991340	+	0.131317i	$0.958080\pi$
$912$			21.0913i			0.698404i
$913$	5.61877			0.185954
$914$			4.08916i			0.135257i
$915$	−5.26319	−	9.45713i	−0.173996	−	0.312643i
$916$			23.2361i			0.767743i
$917$	−1.04723			−0.0345825
$918$	−1.11191			−0.0366983
$919$	24.5480			0.809764			0.404882	−	0.914369i	$-0.367313\pi$
$919$	24.5480			0.809764			0.404882	+	0.914369i	$0.367313\pi$
$920$	−9.81072	−	17.6283i	−0.323450	−	0.581189i
$921$	10.0637			0.331612
$922$			8.74760i			0.288087i
$923$			36.2753i			1.19402i
$924$	−0.281286			−0.00925364
$925$	10.7277	−	17.2983i	0.352723	−	0.568765i
$926$		−	7.87864i		−	0.258908i
$927$			10.6870i			0.351007i
$928$	−8.37855	−	18.1905i	−0.275040	−	0.597132i
$929$	2.45572			0.0805695			0.0402847	−	0.999188i	$-0.487173\pi$
$929$	2.45572			0.0805695			0.0402847	+	0.999188i	$0.487173\pi$
$930$	3.67600	+	6.60520i	0.120541	+	0.216593i
$931$			43.7115i			1.43259i
$932$			20.2971i			0.664853i
$933$		−	16.2493i		−	0.531977i
$934$	4.25044			0.139079
$935$	−1.95789	−	3.51803i	−0.0640300	−	0.115052i
$936$		−	6.55136i		−	0.214138i
$937$			39.7814i			1.29960i	0.760104	+	0.649801i	$0.225148\pi$
$937$			39.7814i			1.29960i	−0.760104	+	0.649801i	$0.774852\pi$
$938$	1.11931			0.0365467
$939$			21.4838i			0.701097i
$940$	45.8590	−	25.5220i	1.49576	−	0.832435i
$941$	33.7621			1.10061			0.550306	−	0.834963i	$-0.314511\pi$
$941$	33.7621			1.10061			0.550306	+	0.834963i	$0.314511\pi$
$942$	−3.77099			−0.122866
$943$	58.9513			1.91972
$944$	−26.7806			−0.871636
$945$	0.299052	+	0.537350i	0.00972816	+	0.0174800i
$946$			1.08297i			0.0352105i
$947$	−1.32780			−0.0431476			−0.0215738	−	0.999767i	$-0.506868\pi$
$947$	−1.32780			−0.0431476			−0.0215738	+	0.999767i	$0.506868\pi$
$948$			4.47426i			0.145317i
$949$		−	6.23922i		−	0.202534i
$950$	−8.97326	−	5.56482i	−0.291131	−	0.180547i
$951$	−24.4204			−0.791887
$952$			1.18896i			0.0385344i
$953$			21.2315i			0.687755i	0.939014	+	0.343878i	$0.111741\pi$
$953$			21.2315i			0.687755i	−0.939014	+	0.343878i	$0.888259\pi$
$954$		−	1.33330i		−	0.0431673i
$955$	15.2608	+	27.4213i	0.493829	+	0.887333i
$956$	11.4132			0.369128
$957$	2.64961	−	1.22042i	0.0856499	−	0.0394504i
$958$		−	4.77922i		−	0.154409i
$959$			2.49158i			0.0804574i
$960$	−10.6253	+	5.91332i	−0.342930	+	0.190852i
$961$	−71.1251			−2.29436
$962$			6.85945i			0.221158i
$963$		−	4.59224i		−	0.147983i
$964$	−45.6915			−1.47162
$965$	43.7066	−	24.3241i	1.40697	−	0.783021i
$966$	−0.638179			−0.0205331
$967$	−8.54151			−0.274677			−0.137338	−	0.990524i	$-0.543855\pi$
$967$	−8.54151			−0.274677			−0.137338	+	0.990524i	$0.543855\pi$
$968$	13.9255			0.447584
$969$			20.9826i			0.674057i
$970$	11.6753	−	6.49764i	0.374870	−	0.208627i
$971$		−	18.0454i		−	0.579104i	−0.957162	−	0.289552i	$-0.906494\pi$
$971$		−	18.0454i		−	0.579104i	0.957162	−	0.289552i	$-0.0935063\pi$
$972$	−1.88809			−0.0605607
$973$			0.390123i			0.0125068i
$974$			11.5156i			0.368983i
$975$	−21.4032	−	13.2733i	−0.685450	−	0.425086i
$976$		−	16.1716i		−	0.517641i
$977$			15.2948i			0.489324i	0.969608	+	0.244662i	$0.0786770\pi$
$977$			15.2948i			0.489324i	−0.969608	+	0.244662i	$0.921323\pi$
$978$	3.77539			0.120724
$979$	1.35767			0.0433914
$980$	−25.5446	+	14.2163i	−0.815991	+	0.454124i
$981$	−13.1473			−0.419760
$982$			6.88425i			0.219685i
$983$	−38.2643			−1.22044			−0.610221	−	0.792231i	$-0.708919\pi$
$983$	−38.2643			−1.22044			−0.610221	+	0.792231i	$0.708919\pi$
$984$			11.0535i			0.352374i
$985$	5.07021	+	9.11037i	0.161550	+	0.290281i
$986$	−2.50503	−	5.43861i	−0.0797764	−	0.173201i
$987$		−	3.41876i		−	0.108820i
$988$	−60.0356			−1.90999
$989$		−	41.4557i		−	1.31822i
$990$	0.197048	+	0.354065i	0.00626260	+	0.0112529i
$991$	22.5768			0.717174			0.358587	−	0.933496i	$-0.383259\pi$
$991$	22.5768			0.717174			0.358587	+	0.933496i	$0.383259\pi$
$992$			37.5829i			1.19326i
$993$			0.627675i			0.0199187i
$994$			0.662567i			0.0210153i
$995$	29.2629	−	16.2857i	0.927695	−	0.516292i
$996$		−	19.5840i		−	0.620544i
$997$	−28.4370			−0.900608			−0.450304	−	0.892875i	$-0.648684\pi$
$997$	−28.4370			−0.900608			−0.450304	+	0.892875i	$0.648684\pi$
$998$	6.54222			0.207090
$999$	4.07094			0.128799

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	435.2.f.f.289.5	yes	12
3.2	odd	2		1305.2.f.l.289.8		12
5.2	odd	4		2175.2.d.j.376.13		24
5.3	odd	4		2175.2.d.j.376.12		24
5.4	even	2		435.2.f.e.289.8	yes	12
15.14	odd	2		1305.2.f.k.289.5		12
29.28	even	2		435.2.f.e.289.7	✓	12
87.86	odd	2		1305.2.f.k.289.6		12
145.28	odd	4		2175.2.d.j.376.11		24
145.57	odd	4		2175.2.d.j.376.14		24
145.144	even	2	inner	435.2.f.f.289.6	yes	12
435.434	odd	2		1305.2.f.l.289.7		12

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
435.2.f.e.289.7	✓	12	29.28	even	2
435.2.f.e.289.8	yes	12	5.4	even	2
435.2.f.f.289.5	yes	12	1.1	even	1	trivial
435.2.f.f.289.6	yes	12	145.144	even	2	inner
1305.2.f.k.289.5		12	15.14	odd	2
1305.2.f.k.289.6		12	87.86	odd	2
1305.2.f.l.289.7		12	435.434	odd	2
1305.2.f.l.289.8		12	3.2	odd	2
2175.2.d.j.376.11		24	145.28	odd	4
2175.2.d.j.376.12		24	5.3	odd	4
2175.2.d.j.376.13		24	5.2	odd	4
2175.2.d.j.376.14		24	145.57	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 435 = 3 \cdot 5 \cdot 29 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	435.f (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.334522 q^{2} +1.00000 q^{3} -1.88809 q^{4} +(1.95387 - 1.08739i) q^{5} -0.334522 q^{6} +0.275019i q^{7} +1.30066 q^{8} +1.00000 q^{9} +O(q^{10})\)	\(q-0.334522 q^{2} +1.00000 q^{3} -1.88809 q^{4} +(1.95387 - 1.08739i) q^{5} -0.334522 q^{6} +0.275019i q^{7} +1.30066 q^{8} +1.00000 q^{9} +(-0.653612 + 0.363756i) q^{10} -0.541705i q^{11} -1.88809 q^{12} -5.03697i q^{13} -0.0920000i q^{14} +(1.95387 - 1.08739i) q^{15} +3.34109 q^{16} +3.32386 q^{17} -0.334522 q^{18} +6.31271i q^{19} +(-3.68908 + 2.05309i) q^{20} +0.275019i q^{21} +0.181212i q^{22} -6.93673i q^{23} +1.30066 q^{24} +(2.63518 - 4.24922i) q^{25} +1.68498i q^{26} +1.00000 q^{27} -0.519262i q^{28} +(2.25292 + 4.89125i) q^{29} +(-0.653612 + 0.363756i) q^{30} -10.1057i q^{31} -3.71898 q^{32} -0.541705i q^{33} -1.11191 q^{34} +(0.299052 + 0.537350i) q^{35} -1.88809 q^{36} +4.07094 q^{37} -2.11174i q^{38} -5.03697i q^{39} +(2.54130 - 1.41432i) q^{40} +8.49843i q^{41} -0.0920000i q^{42} +5.97627 q^{43} +1.02279i q^{44} +(1.95387 - 1.08739i) q^{45} +2.32049i q^{46} -12.4310 q^{47} +3.34109 q^{48} +6.92436 q^{49} +(-0.881526 + 1.42146i) q^{50} +3.32386 q^{51} +9.51028i q^{52} +3.98569i q^{53} -0.334522 q^{54} +(-0.589043 - 1.05842i) q^{55} +0.357705i q^{56} +6.31271i q^{57} +(-0.753651 - 1.63623i) q^{58} -8.01554 q^{59} +(-3.68908 + 2.05309i) q^{60} -4.84022i q^{61} +3.38058i q^{62} +0.275019i q^{63} -5.43810 q^{64} +(-5.47714 - 9.84156i) q^{65} +0.181212i q^{66} +12.1664i q^{67} -6.27576 q^{68} -6.93673i q^{69} +(-0.100040 - 0.179756i) q^{70} -7.20182 q^{71} +1.30066 q^{72} +1.23869 q^{73} -1.36182 q^{74} +(2.63518 - 4.24922i) q^{75} -11.9190i q^{76} +0.148979 q^{77} +1.68498i q^{78} -2.36972i q^{79} +(6.52804 - 3.63306i) q^{80} +1.00000 q^{81} -2.84292i q^{82} +10.3724i q^{83} -0.519262i q^{84} +(6.49437 - 3.61432i) q^{85} -1.99920 q^{86} +(2.25292 + 4.89125i) q^{87} -0.704571i q^{88} +2.50630i q^{89} +(-0.653612 + 0.363756i) q^{90} +1.38526 q^{91} +13.0972i q^{92} -10.1057i q^{93} +4.15845 q^{94} +(6.86436 + 12.3342i) q^{95} -3.71898 q^{96} -17.8627 q^{97} -2.31636 q^{98} -0.541705i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 12 q^{3} + 16 q^{4} - 6 q^{5} + 12 q^{9}+O(q^{10}) \) 12 * q + 12 * q^3 + 16 * q^4 - 6 * q^5 + 12 * q^9	\( 12 q + 12 q^{3} + 16 q^{4} - 6 q^{5} + 12 q^{9} + 2 q^{10} + 16 q^{12} - 6 q^{15} + 32 q^{16} - 8 q^{17} - 20 q^{20} + 12 q^{25} + 12 q^{27} + 8 q^{29} + 2 q^{30} - 40 q^{32} - 52 q^{34} + 14 q^{35} + 16 q^{36} + 20 q^{37} - 22 q^{40} + 44 q^{43} - 6 q^{45} - 32 q^{47} + 32 q^{48} - 4 q^{49} + 24 q^{50} - 8 q^{51} + 42 q^{55} - 24 q^{58} - 28 q^{59} - 20 q^{60} - 4 q^{64} + 22 q^{65} + 16 q^{68} - 26 q^{70} - 16 q^{71} - 36 q^{73} - 28 q^{74} + 12 q^{75} - 22 q^{80} + 12 q^{81} + 30 q^{85} - 16 q^{86} + 8 q^{87} + 2 q^{90} + 24 q^{91} - 28 q^{94} + 16 q^{95} - 40 q^{96} - 40 q^{97} - 112 q^{98}+O(q^{100}) \) 12 * q + 12 * q^3 + 16 * q^4 - 6 * q^5 + 12 * q^9 + 2 * q^10 + 16 * q^12 - 6 * q^15 + 32 * q^16 - 8 * q^17 - 20 * q^20 + 12 * q^25 + 12 * q^27 + 8 * q^29 + 2 * q^30 - 40 * q^32 - 52 * q^34 + 14 * q^35 + 16 * q^36 + 20 * q^37 - 22 * q^40 + 44 * q^43 - 6 * q^45 - 32 * q^47 + 32 * q^48 - 4 * q^49 + 24 * q^50 - 8 * q^51 + 42 * q^55 - 24 * q^58 - 28 * q^59 - 20 * q^60 - 4 * q^64 + 22 * q^65 + 16 * q^68 - 26 * q^70 - 16 * q^71 - 36 * q^73 - 28 * q^74 + 12 * q^75 - 22 * q^80 + 12 * q^81 + 30 * q^85 - 16 * q^86 + 8 * q^87 + 2 * q^90 + 24 * q^91 - 28 * q^94 + 16 * q^95 - 40 * q^96 - 40 * q^97 - 112 * q^98

Introduction

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