LMFDB - Embedded newform 136.2.n.b.49.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,2,Mod(9,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(8))

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

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

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

chi := DirichletCharacter("136.9");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	136.n (of order $8$, degree $4$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$1.08596546749$
Analytic rank:	$0$
Dimension:	$4$
Coefficient field:	$\Q(\zeta_{8})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} + 1 $ x^4 + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			49.1
Root			$-0.707107 + 0.707107i$ of defining polynomial
Character	$\chi$	$=$	136.49
Dual form			136.2.n.b.25.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 + 2.41421i) q^{3} +(-2.70711 + 1.12132i) q^{5} +(1.00000 + 0.414214i) q^{7} +(-2.70711 + 2.70711i) q^{9} +O(q^{10})$	\(q+(1.00000 + 2.41421i) q^{3} +(-2.70711 + 1.12132i) q^{5} +(1.00000 + 0.414214i) q^{7} +(-2.70711 + 2.70711i) q^{9} +(1.58579 - 3.82843i) q^{11} +2.58579i q^{13} +(-5.41421 - 5.41421i) q^{15} +(2.82843 - 3.00000i) q^{17} +(5.41421 + 5.41421i) q^{19} +2.82843i q^{21} +(2.41421 - 5.82843i) q^{23} +(2.53553 - 2.53553i) q^{25} +(-2.00000 - 0.828427i) q^{27} +(-5.12132 + 2.12132i) q^{29} +(-0.414214 - 1.00000i) q^{31} +10.8284 q^{33} -3.17157 q^{35} +(-4.12132 - 9.94975i) q^{37} +(-6.24264 + 2.58579i) q^{39} +(-8.53553 - 3.53553i) q^{41} +(0.242641 - 0.242641i) q^{43} +(4.29289 - 10.3640i) q^{45} -1.17157i q^{47} +(-4.12132 - 4.12132i) q^{49} +(10.0711 + 3.82843i) q^{51} +(5.82843 + 5.82843i) q^{53} +12.1421i q^{55} +(-7.65685 + 18.4853i) q^{57} +(-5.07107 + 5.07107i) q^{59} +(4.12132 + 1.70711i) q^{61} +(-3.82843 + 1.58579i) q^{63} +(-2.89949 - 7.00000i) q^{65} -2.82843 q^{67} +16.4853 q^{69} +(3.48528 + 8.41421i) q^{71} +(7.36396 - 3.05025i) q^{73} +(8.65685 + 3.58579i) q^{75} +(3.17157 - 3.17157i) q^{77} +(1.58579 - 3.82843i) q^{79} +5.82843i q^{81} +(-9.07107 - 9.07107i) q^{83} +(-4.29289 + 11.2929i) q^{85} +(-10.2426 - 10.2426i) q^{87} +4.24264i q^{89} +(-1.07107 + 2.58579i) q^{91} +(2.00000 - 2.00000i) q^{93} +(-20.7279 - 8.58579i) q^{95} +(-4.12132 + 1.70711i) q^{97} +(6.07107 + 14.6569i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + 4 q^{3} - 8 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) $ 4 * q + 4 * q^3 - 8 * q^5 + 4 * q^7 - 8 * q^9	$ 4 q + 4 q^{3} - 8 q^{5} + 4 q^{7} - 8 q^{9} + 12 q^{11} - 16 q^{15} + 16 q^{19} + 4 q^{23} - 4 q^{25} - 8 q^{27} - 12 q^{29} + 4 q^{31} + 32 q^{33} - 24 q^{35} - 8 q^{37} - 8 q^{39} - 20 q^{41} - 16 q^{43} + 20 q^{45} - 8 q^{49} + 12 q^{51} + 12 q^{53} - 8 q^{57} + 8 q^{59} + 8 q^{61} - 4 q^{63} + 28 q^{65} + 32 q^{69} - 20 q^{71} + 4 q^{73} + 12 q^{75} + 24 q^{77} + 12 q^{79} - 8 q^{83} - 20 q^{85} - 24 q^{87} + 24 q^{91} + 8 q^{93} - 32 q^{95} - 8 q^{97} - 4 q^{99}+O(q^{100}) $ 4 * q + 4 * q^3 - 8 * q^5 + 4 * q^7 - 8 * q^9 + 12 * q^11 - 16 * q^15 + 16 * q^19 + 4 * q^23 - 4 * q^25 - 8 * q^27 - 12 * q^29 + 4 * q^31 + 32 * q^33 - 24 * q^35 - 8 * q^37 - 8 * q^39 - 20 * q^41 - 16 * q^43 + 20 * q^45 - 8 * q^49 + 12 * q^51 + 12 * q^53 - 8 * q^57 + 8 * q^59 + 8 * q^61 - 4 * q^63 + 28 * q^65 + 32 * q^69 - 20 * q^71 + 4 * q^73 + 12 * q^75 + 24 * q^77 + 12 * q^79 - 8 * q^83 - 20 * q^85 - 24 * q^87 + 24 * q^91 + 8 * q^93 - 32 * q^95 - 8 * q^97 - 4 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{8}\right)$

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			0
$2$		0			0
$3$	1.00000	+	2.41421i	0.577350	+	1.39385i	0.895182	+	0.445700i	$0.147045\pi$
$3$	1.00000	+	2.41421i	0.577350	+	1.39385i	−0.317832	+	0.948147i	$0.602955\pi$
$4$		0			0
$5$	−2.70711	+	1.12132i	−1.21065	+	0.501470i	−0.894427	−	0.447214i	$-0.852416\pi$
$5$	−2.70711	+	1.12132i	−1.21065	+	0.501470i	−0.316228	+	0.948683i	$0.602416\pi$
$6$		0			0
$7$	1.00000	+	0.414214i	0.377964	+	0.156558i	0.563574	−	0.826066i	$-0.309426\pi$
$7$	1.00000	+	0.414214i	0.377964	+	0.156558i	−0.185610	+	0.982624i	$0.559426\pi$
$8$		0			0
$9$	−2.70711	+	2.70711i	−0.902369	+	0.902369i
$10$		0			0
$11$	1.58579	−	3.82843i	0.478133	−	1.15431i	−0.482351	−	0.875978i	$-0.660217\pi$
$11$	1.58579	−	3.82843i	0.478133	−	1.15431i	0.960484	−	0.278336i	$-0.0897829\pi$
$12$		0			0
$13$			2.58579i			0.717168i	0.933497	+	0.358584i	$0.116740\pi$
$13$			2.58579i			0.717168i	−0.933497	+	0.358584i	$0.883260\pi$
$14$		0			0
$15$	−5.41421	−	5.41421i	−1.39794	−	1.39794i
$16$		0			0
$17$	2.82843	−	3.00000i	0.685994	−	0.727607i
$17$	2.82843	−	3.00000i	0.685994	−	0.727607i
$18$		0			0
$19$	5.41421	+	5.41421i	1.24211	+	1.24211i	0.959126	+	0.282980i	$0.0913230\pi$
$19$	5.41421	+	5.41421i	1.24211	+	1.24211i	0.282980	+	0.959126i	$0.408677\pi$
$20$		0			0
$21$			2.82843i			0.617213i
$22$		0			0
$23$	2.41421	−	5.82843i	0.503398	−	1.21531i	−0.444223	−	0.895916i	$-0.646520\pi$
$23$	2.41421	−	5.82843i	0.503398	−	1.21531i	0.947622	−	0.319395i	$-0.103480\pi$
$24$		0			0
$25$	2.53553	−	2.53553i	0.507107	−	0.507107i
$26$		0			0
$27$	−2.00000	−	0.828427i	−0.384900	−	0.159431i
$28$		0			0
$29$	−5.12132	+	2.12132i	−0.951005	+	0.393919i	−0.803609	−	0.595158i	$-0.797089\pi$
$29$	−5.12132	+	2.12132i	−0.951005	+	0.393919i	−0.147397	+	0.989077i	$0.547089\pi$
$30$		0			0
$31$	−0.414214	−	1.00000i	−0.0743950	−	0.179605i	0.882307	−	0.470674i	$-0.155989\pi$
$31$	−0.414214	−	1.00000i	−0.0743950	−	0.179605i	−0.956702	+	0.291069i	$0.905989\pi$
$32$		0			0
$33$	10.8284			1.88499
$34$		0			0
$35$	−3.17157			−0.536094
$36$		0			0
$37$	−4.12132	−	9.94975i	−0.677541	−	1.63573i	−0.768481	−	0.639872i	$-0.778987\pi$
$37$	−4.12132	−	9.94975i	−0.677541	−	1.63573i	0.0909405	−	0.995856i	$-0.471013\pi$
$38$		0			0
$39$	−6.24264	+	2.58579i	−0.999623	+	0.414057i
$40$		0			0
$41$	−8.53553	−	3.53553i	−1.33303	−	0.552158i	−0.401509	−	0.915855i	$-0.631514\pi$
$41$	−8.53553	−	3.53553i	−1.33303	−	0.552158i	−0.931517	+	0.363697i	$0.881514\pi$
$42$		0			0
$43$	0.242641	−	0.242641i	0.0370024	−	0.0370024i	−0.688364	−	0.725366i	$-0.741671\pi$
$43$	0.242641	−	0.242641i	0.0370024	−	0.0370024i	0.725366	+	0.688364i	$0.241671\pi$
$44$		0			0
$45$	4.29289	−	10.3640i	0.639947	−	1.54497i
$46$		0			0
$47$		−	1.17157i		−	0.170891i	−0.996343	−	0.0854457i	$-0.972769\pi$
$47$		−	1.17157i		−	0.170891i	0.996343	−	0.0854457i	$-0.0272314\pi$
$48$		0			0
$49$	−4.12132	−	4.12132i	−0.588760	−	0.588760i
$50$		0			0
$51$	10.0711	+	3.82843i	1.41023	+	0.536087i
$52$		0			0
$53$	5.82843	+	5.82843i	0.800596	+	0.800596i	0.983189	−	0.182593i	$-0.0584489\pi$
$53$	5.82843	+	5.82843i	0.800596	+	0.800596i	−0.182593	+	0.983189i	$0.558449\pi$
$54$		0			0
$55$			12.1421i			1.63725i
$56$		0			0
$57$	−7.65685	+	18.4853i	−1.01418	+	2.44844i
$58$		0			0
$59$	−5.07107	+	5.07107i	−0.660197	+	0.660197i	−0.955426	−	0.295230i	$-0.904604\pi$
$59$	−5.07107	+	5.07107i	−0.660197	+	0.660197i	0.295230	+	0.955426i	$0.404604\pi$
$60$		0			0
$61$	4.12132	+	1.70711i	0.527681	+	0.218573i	0.630587	−	0.776118i	$-0.282814\pi$
$61$	4.12132	+	1.70711i	0.527681	+	0.218573i	−0.102906	+	0.994691i	$0.532814\pi$
$62$		0			0
$63$	−3.82843	+	1.58579i	−0.482336	+	0.199790i
$64$		0			0
$65$	−2.89949	−	7.00000i	−0.359638	−	0.868243i
$66$		0			0
$67$	−2.82843			−0.345547			−0.172774	−	0.984962i	$-0.555273\pi$
$67$	−2.82843			−0.345547			−0.172774	+	0.984962i	$0.555273\pi$
$68$		0			0
$69$	16.4853			1.98459
$70$		0			0
$71$	3.48528	+	8.41421i	0.413627	+	0.998583i	0.984156	+	0.177306i	$0.0567382\pi$
$71$	3.48528	+	8.41421i	0.413627	+	0.998583i	−0.570529	+	0.821277i	$0.693262\pi$
$72$		0			0
$73$	7.36396	−	3.05025i	0.861886	−	0.357005i	0.0924414	−	0.995718i	$-0.470533\pi$
$73$	7.36396	−	3.05025i	0.861886	−	0.357005i	0.769445	+	0.638713i	$0.220533\pi$
$74$		0			0
$75$	8.65685	+	3.58579i	0.999607	+	0.414051i
$76$		0			0
$77$	3.17157	−	3.17157i	0.361434	−	0.361434i
$78$		0			0
$79$	1.58579	−	3.82843i	0.178415	−	0.430732i	−0.809219	−	0.587506i	$-0.800110\pi$
$79$	1.58579	−	3.82843i	0.178415	−	0.430732i	0.987634	+	0.156775i	$0.0501097\pi$
$80$		0			0
$81$			5.82843i			0.647603i
$82$		0			0
$83$	−9.07107	−	9.07107i	−0.995679	−	0.995679i	0.00431166	−	0.999991i	$-0.498628\pi$
$83$	−9.07107	−	9.07107i	−0.995679	−	0.995679i	−0.999991	+	0.00431166i	$0.998628\pi$
$84$		0			0
$85$	−4.29289	+	11.2929i	−0.465630	+	1.22489i
$86$		0			0
$87$	−10.2426	−	10.2426i	−1.09813	−	1.09813i
$88$		0			0
$89$			4.24264i			0.449719i	0.974391	+	0.224860i	$0.0721923\pi$
$89$			4.24264i			0.449719i	−0.974391	+	0.224860i	$0.927808\pi$
$90$		0			0
$91$	−1.07107	+	2.58579i	−0.112278	+	0.271064i
$92$		0			0
$93$	2.00000	−	2.00000i	0.207390	−	0.207390i
$94$		0			0
$95$	−20.7279	−	8.58579i	−2.12664	−	0.880883i
$96$		0			0
$97$	−4.12132	+	1.70711i	−0.418457	+	0.173330i	−0.581969	−	0.813211i	$-0.697718\pi$
$97$	−4.12132	+	1.70711i	−0.418457	+	0.173330i	0.163513	+	0.986541i	$0.447718\pi$
$98$		0			0
$99$	6.07107	+	14.6569i	0.610165	+	1.47307i
$100$		0			0
$101$	−6.58579			−0.655310			−0.327655	−	0.944797i	$-0.606258\pi$
$101$	−6.58579			−0.655310			−0.327655	+	0.944797i	$0.606258\pi$
$102$		0			0
$103$	2.82843			0.278693			0.139347	−	0.990244i	$-0.455500\pi$
$103$	2.82843			0.278693			0.139347	+	0.990244i	$0.455500\pi$
$104$		0			0
$105$	−3.17157	−	7.65685i	−0.309514	−	0.747232i
$106$		0			0
$107$	6.65685	−	2.75736i	0.643542	−	0.266564i	−0.0369523	−	0.999317i	$-0.511765\pi$
$107$	6.65685	−	2.75736i	0.643542	−	0.266564i	0.680495	+	0.732753i	$0.261765\pi$
$108$		0			0
$109$	−5.29289	−	2.19239i	−0.506967	−	0.209993i	0.114514	−	0.993422i	$-0.463469\pi$
$109$	−5.29289	−	2.19239i	−0.506967	−	0.209993i	−0.621481	+	0.783429i	$0.713469\pi$
$110$		0			0
$111$	19.8995	−	19.8995i	1.88878	−	1.88878i
$112$		0			0
$113$	−1.29289	+	3.12132i	−0.121625	+	0.293629i	−0.972952	−	0.231006i	$-0.925798\pi$
$113$	−1.29289	+	3.12132i	−0.121625	+	0.293629i	0.851327	+	0.524635i	$0.175798\pi$
$114$		0			0
$115$			18.4853i			1.72376i
$116$		0			0
$117$	−7.00000	−	7.00000i	−0.647150	−	0.647150i
$118$		0			0
$119$	4.07107	−	1.82843i	0.373194	−	0.167612i
$120$		0			0
$121$	−4.36396	−	4.36396i	−0.396724	−	0.396724i
$122$		0			0
$123$		−	24.1421i		−	2.17682i
$124$		0			0
$125$	1.58579	−	3.82843i	0.141837	−	0.342425i
$126$		0			0
$127$	0.585786	−	0.585786i	0.0519801	−	0.0519801i	−0.680639	−	0.732619i	$-0.738298\pi$
$127$	0.585786	−	0.585786i	0.0519801	−	0.0519801i	0.732619	+	0.680639i	$0.238298\pi$
$128$		0			0
$129$	0.828427	+	0.343146i	0.0729389	+	0.0302123i
$130$		0			0
$131$	3.00000	−	1.24264i	0.262111	−	0.108570i	−0.247758	−	0.968822i	$-0.579694\pi$
$131$	3.00000	−	1.24264i	0.262111	−	0.108570i	0.509869	+	0.860252i	$0.329694\pi$
$132$		0			0
$133$	3.17157	+	7.65685i	0.275010	+	0.663933i
$134$		0			0
$135$	6.34315			0.545931
$136$		0			0
$137$	−7.75736			−0.662756			−0.331378	−	0.943498i	$-0.607514\pi$
$137$	−7.75736			−0.662756			−0.331378	+	0.943498i	$0.607514\pi$
$138$		0			0
$139$	1.92893	+	4.65685i	0.163610	+	0.394989i	0.984329	−	0.176343i	$-0.0564268\pi$
$139$	1.92893	+	4.65685i	0.163610	+	0.394989i	−0.820719	+	0.571332i	$0.806427\pi$
$140$		0			0
$141$	2.82843	−	1.17157i	0.238197	−	0.0986642i
$142$		0			0
$143$	9.89949	+	4.10051i	0.827837	+	0.342901i
$144$		0			0
$145$	11.4853	−	11.4853i	0.953801	−	0.953801i
$146$		0			0
$147$	5.82843	−	14.0711i	0.480721	−	1.16056i
$148$		0			0
$149$		−	3.31371i		−	0.271470i	−0.990745	−	0.135735i	$-0.956660\pi$
$149$		−	3.31371i		−	0.271470i	0.990745	−	0.135735i	$-0.0433395\pi$
$150$		0			0
$151$	0.242641	+	0.242641i	0.0197458	+	0.0197458i	0.716911	−	0.697165i	$-0.245555\pi$
$151$	0.242641	+	0.242641i	0.0197458	+	0.0197458i	−0.697165	+	0.716911i	$0.745555\pi$
$152$		0			0
$153$	0.464466	+	15.7782i	0.0375499	+	1.27559i
$154$		0			0
$155$	2.24264	+	2.24264i	0.180133	+	0.180133i
$156$		0			0
$157$		−	20.0000i		−	1.59617i	−0.602542	−	0.798087i	$-0.705846\pi$
$157$		−	20.0000i		−	1.59617i	0.602542	−	0.798087i	$-0.294154\pi$
$158$		0			0
$159$	−8.24264	+	19.8995i	−0.653684	+	1.57813i
$160$		0			0
$161$	4.82843	−	4.82843i	0.380533	−	0.380533i
$162$		0			0
$163$	−9.24264	−	3.82843i	−0.723939	−	0.299866i	−0.00988059	−	0.999951i	$-0.503145\pi$
$163$	−9.24264	−	3.82843i	−0.723939	−	0.299866i	−0.714059	+	0.700086i	$0.753145\pi$
$164$		0			0
$165$	−29.3137	+	12.1421i	−2.28207	+	0.945264i
$166$		0			0
$167$	−2.65685	−	6.41421i	−0.205594	−	0.496347i	0.787126	−	0.616792i	$-0.211568\pi$
$167$	−2.65685	−	6.41421i	−0.205594	−	0.496347i	−0.992720	+	0.120445i	$0.961568\pi$
$168$		0			0
$169$	6.31371			0.485670
$170$		0			0
$171$	−29.3137			−2.24168
$172$		0			0
$173$	8.29289	+	20.0208i	0.630497	+	1.52215i	0.838999	+	0.544133i	$0.183141\pi$
$173$	8.29289	+	20.0208i	0.630497	+	1.52215i	−0.208502	+	0.978022i	$0.566859\pi$
$174$		0			0
$175$	3.58579	−	1.48528i	0.271060	−	0.112277i
$176$		0			0
$177$	−17.3137	−	7.17157i	−1.30138	−	0.539048i
$178$		0			0
$179$	7.41421	−	7.41421i	0.554164	−	0.554164i	−0.373476	−	0.927640i	$-0.621834\pi$
$179$	7.41421	−	7.41421i	0.554164	−	0.554164i	0.927640	+	0.373476i	$0.121834\pi$
$180$		0			0
$181$	−6.46447	+	15.6066i	−0.480500	+	1.16003i	0.478872	+	0.877885i	$0.341046\pi$
$181$	−6.46447	+	15.6066i	−0.480500	+	1.16003i	−0.959372	+	0.282145i	$0.908954\pi$
$182$		0			0
$183$			11.6569i			0.861699i
$184$		0			0
$185$	22.3137	+	22.3137i	1.64054	+	1.64054i
$186$		0			0
$187$	−7.00000	−	15.5858i	−0.511891	−	1.13975i
$188$		0			0
$189$	−1.65685	−	1.65685i	−0.120518	−	0.120518i
$190$		0			0
$191$			17.6569i			1.27761i	0.769371	+	0.638803i	$0.220570\pi$
$191$			17.6569i			1.27761i	−0.769371	+	0.638803i	$0.779430\pi$
$192$		0			0
$193$	−0.778175	+	1.87868i	−0.0560142	+	0.135230i	−0.949409	−	0.314042i	$-0.898317\pi$
$193$	−0.778175	+	1.87868i	−0.0560142	+	0.135230i	0.893395	+	0.449272i	$0.148317\pi$
$194$		0			0
$195$	14.0000	−	14.0000i	1.00256	−	1.00256i
$196$		0			0
$197$	−18.7782	−	7.77817i	−1.33789	−	0.554172i	−0.404994	−	0.914319i	$-0.632726\pi$
$197$	−18.7782	−	7.77817i	−1.33789	−	0.554172i	−0.932895	+	0.360147i	$0.882726\pi$
$198$		0			0
$199$	13.2426	−	5.48528i	0.938746	−	0.388841i	0.139756	−	0.990186i	$-0.455368\pi$
$199$	13.2426	−	5.48528i	0.938746	−	0.388841i	0.798990	+	0.601345i	$0.205368\pi$
$200$		0			0
$201$	−2.82843	−	6.82843i	−0.199502	−	0.481640i
$202$		0			0
$203$	−6.00000			−0.421117
$204$		0			0
$205$	27.0711			1.89073
$206$		0			0
$207$	9.24264	+	22.3137i	0.642408	+	1.55091i
$208$		0			0
$209$	29.3137	−	12.1421i	2.02767	−	0.839889i
$210$		0			0
$211$	−25.9706	−	10.7574i	−1.78789	−	0.740567i	−0.990570	−	0.137007i	$-0.956252\pi$
$211$	−25.9706	−	10.7574i	−1.78789	−	0.740567i	−0.797317	−	0.603561i	$-0.793748\pi$
$212$		0			0
$213$	−16.8284	+	16.8284i	−1.15306	+	1.15306i
$214$		0			0
$215$	−0.384776	+	0.928932i	−0.0262415	+	0.0633526i
$216$		0			0
$217$		−	1.17157i		−	0.0795315i
$218$		0			0
$219$	14.7279	+	14.7279i	0.995221	+	0.995221i
$220$		0			0
$221$	7.75736	+	7.31371i	0.521816	+	0.491973i
$222$		0			0
$223$	1.89949	+	1.89949i	0.127200	+	0.127200i	0.767841	−	0.640641i	$-0.221331\pi$
$223$	1.89949	+	1.89949i	0.127200	+	0.127200i	−0.640641	+	0.767841i	$0.721331\pi$
$224$		0			0
$225$			13.7279i			0.915195i
$226$		0			0
$227$	−1.58579	+	3.82843i	−0.105252	+	0.254102i	−0.967728	−	0.251997i	$-0.918913\pi$
$227$	−1.58579	+	3.82843i	−0.105252	+	0.254102i	0.862476	+	0.506098i	$0.168913\pi$
$228$		0			0
$229$	−8.82843	+	8.82843i	−0.583399	+	0.583399i	−0.935836	−	0.352437i	$-0.885353\pi$
$229$	−8.82843	+	8.82843i	−0.583399	+	0.583399i	0.352437	+	0.935836i	$0.385353\pi$
$230$		0			0
$231$	10.8284	+	4.48528i	0.712458	+	0.295110i
$232$		0			0
$233$	−3.87868	+	1.60660i	−0.254101	+	0.105252i	−0.506098	−	0.862476i	$-0.668913\pi$
$233$	−3.87868	+	1.60660i	−0.254101	+	0.105252i	0.251997	+	0.967728i	$0.418913\pi$
$234$		0			0
$235$	1.31371	+	3.17157i	0.0856969	+	0.206891i
$236$		0			0
$237$	10.8284			0.703382
$238$		0			0
$239$	16.4853			1.06634			0.533172	−	0.846007i	$-0.321000\pi$
$239$	16.4853			1.06634			0.533172	+	0.846007i	$0.321000\pi$
$240$		0			0
$241$	−5.36396	−	12.9497i	−0.345523	−	0.834167i	−0.997137	−	0.0756158i	$-0.975908\pi$
$241$	−5.36396	−	12.9497i	−0.345523	−	0.834167i	0.651614	−	0.758551i	$-0.274092\pi$
$242$		0			0
$243$	−20.0711	+	8.31371i	−1.28756	+	0.533325i
$244$		0			0
$245$	15.7782	+	6.53553i	1.00803	+	0.417540i
$246$		0			0
$247$	−14.0000	+	14.0000i	−0.890799	+	0.890799i
$248$		0			0
$249$	12.8284	−	30.9706i	0.812969	−	1.96268i
$250$		0			0
$251$			7.51472i			0.474325i	0.971470	+	0.237162i	$0.0762174\pi$
$251$			7.51472i			0.474325i	−0.971470	+	0.237162i	$0.923783\pi$
$252$		0			0
$253$	−18.4853	−	18.4853i	−1.16216	−	1.16216i
$254$		0			0
$255$	−31.5563	+	0.928932i	−1.97614	+	0.0581720i
$256$		0			0
$257$	10.0000	+	10.0000i	0.623783	+	0.623783i	0.946497	−	0.322714i	$-0.104595\pi$
$257$	10.0000	+	10.0000i	0.623783	+	0.623783i	−0.322714	+	0.946497i	$0.604595\pi$
$258$		0			0
$259$		−	11.6569i		−	0.724322i
$260$		0			0
$261$	8.12132	−	19.6066i	0.502697	−	1.21362i
$262$		0			0
$263$	3.07107	−	3.07107i	0.189370	−	0.189370i	−0.606054	−	0.795424i	$-0.707248\pi$
$263$	3.07107	−	3.07107i	0.189370	−	0.189370i	0.795424	+	0.606054i	$0.207248\pi$
$264$		0			0
$265$	−22.3137	−	9.24264i	−1.37072	−	0.567771i
$266$		0			0
$267$	−10.2426	+	4.24264i	−0.626839	+	0.259645i
$268$		0			0
$269$	0.121320	+	0.292893i	0.00739703	+	0.0178580i	0.927535	−	0.373737i	$-0.121924\pi$
$269$	0.121320	+	0.292893i	0.00739703	+	0.0178580i	−0.920138	+	0.391595i	$0.871924\pi$
$270$		0			0
$271$	26.1421			1.58802			0.794011	−	0.607904i	$-0.207989\pi$
$271$	26.1421			1.58802			0.794011	+	0.607904i	$0.207989\pi$
$272$		0			0
$273$	−7.31371			−0.442646
$274$		0			0
$275$	−5.68629	−	13.7279i	−0.342896	−	0.827825i
$276$		0			0
$277$	21.0208	−	8.70711i	1.26302	−	0.523159i	0.352184	−	0.935931i	$-0.385439\pi$
$277$	21.0208	−	8.70711i	1.26302	−	0.523159i	0.910835	+	0.412772i	$0.135439\pi$
$278$		0			0
$279$	3.82843	+	1.58579i	0.229202	+	0.0949386i
$280$		0			0
$281$	−12.6569	+	12.6569i	−0.755045	+	0.755045i	−0.975416	−	0.220371i	$-0.929273\pi$
$281$	−12.6569	+	12.6569i	−0.755045	+	0.755045i	0.220371	+	0.975416i	$0.429273\pi$
$282$		0			0
$283$	−10.8995	+	26.3137i	−0.647908	+	1.56419i	0.167862	+	0.985811i	$0.446314\pi$
$283$	−10.8995	+	26.3137i	−0.647908	+	1.56419i	−0.815770	+	0.578377i	$0.803686\pi$
$284$		0			0
$285$		−	58.6274i		−	3.47279i
$286$		0			0
$287$	−7.07107	−	7.07107i	−0.417392	−	0.417392i
$288$		0			0
$289$	−1.00000	−	16.9706i	−0.0588235	−	0.998268i
$290$		0			0
$291$	−8.24264	−	8.24264i	−0.483192	−	0.483192i
$292$		0			0
$293$		−	10.9706i		−	0.640907i	−0.947264	−	0.320454i	$-0.896165\pi$
$293$		−	10.9706i		−	0.640907i	0.947264	−	0.320454i	$-0.103835\pi$
$294$		0			0
$295$	8.04163	−	19.4142i	0.468202	−	1.13034i
$296$		0			0
$297$	−6.34315	+	6.34315i	−0.368067	+	0.368067i
$298$		0			0
$299$	15.0711	+	6.24264i	0.871582	+	0.361021i
$300$		0			0
$301$	0.343146	−	0.142136i	0.0197786	−	0.00819256i
$302$		0			0
$303$	−6.58579	−	15.8995i	−0.378344	−	0.913402i
$304$		0			0
$305$	−13.0711			−0.748447
$306$		0			0
$307$	−14.1421			−0.807134			−0.403567	−	0.914950i	$-0.632230\pi$
$307$	−14.1421			−0.807134			−0.403567	+	0.914950i	$0.632230\pi$
$308$		0			0
$309$	2.82843	+	6.82843i	0.160904	+	0.388456i
$310$		0			0
$311$	−21.1421	+	8.75736i	−1.19886	+	0.496584i	−0.890631	−	0.454728i	$-0.849737\pi$
$311$	−21.1421	+	8.75736i	−1.19886	+	0.496584i	−0.308230	+	0.951312i	$0.599737\pi$
$312$		0			0
$313$	8.53553	+	3.53553i	0.482457	+	0.199840i	0.610637	−	0.791911i	$-0.290914\pi$
$313$	8.53553	+	3.53553i	0.482457	+	0.199840i	−0.128180	+	0.991751i	$0.540914\pi$
$314$		0			0
$315$	8.58579	−	8.58579i	0.483754	−	0.483754i
$316$		0			0
$317$	−7.12132	+	17.1924i	−0.399973	+	0.965621i	0.587698	+	0.809080i	$0.300034\pi$
$317$	−7.12132	+	17.1924i	−0.399973	+	0.965621i	−0.987672	+	0.156541i	$0.949966\pi$
$318$		0			0
$319$			22.9706i			1.28610i
$320$		0			0
$321$	13.3137	+	13.3137i	0.743099	+	0.743099i
$322$		0			0
$323$	31.5563	−	0.928932i	1.75584	−	0.0516872i
$324$		0			0
$325$	6.55635	+	6.55635i	0.363681	+	0.363681i
$326$		0			0
$327$		−	14.9706i		−	0.827874i
$328$		0			0
$329$	0.485281	−	1.17157i	0.0267544	−	0.0645909i
$330$		0			0
$331$	13.4142	−	13.4142i	0.737312	−	0.737312i	−0.234745	−	0.972057i	$-0.575426\pi$
$331$	13.4142	−	13.4142i	0.737312	−	0.737312i	0.972057	+	0.234745i	$0.0754255\pi$
$332$		0			0
$333$	38.0919	+	15.7782i	2.08742	+	0.864639i
$334$		0			0
$335$	7.65685	−	3.17157i	0.418339	−	0.173282i
$336$		0			0
$337$	4.87868	+	11.7782i	0.265759	+	0.641598i	0.999275	−	0.0380738i	$-0.0121222\pi$
$337$	4.87868	+	11.7782i	0.265759	+	0.641598i	−0.733516	+	0.679672i	$0.762122\pi$
$338$		0			0
$339$	−8.82843			−0.479494
$340$		0			0
$341$	−4.48528			−0.242892
$342$		0			0
$343$	−5.31371	−	12.8284i	−0.286913	−	0.692670i
$344$		0			0
$345$	−44.6274	+	18.4853i	−2.40266	+	0.995214i
$346$		0			0
$347$	18.0711	+	7.48528i	0.970106	+	0.401831i	0.810751	−	0.585391i	$-0.199059\pi$
$347$	18.0711	+	7.48528i	0.970106	+	0.401831i	0.159354	+	0.987221i	$0.449059\pi$
$348$		0			0
$349$	−1.48528	+	1.48528i	−0.0795053	+	0.0795053i	−0.745741	−	0.666236i	$-0.767904\pi$
$349$	−1.48528	+	1.48528i	−0.0795053	+	0.0795053i	0.666236	+	0.745741i	$0.267904\pi$
$350$		0			0
$351$	2.14214	−	5.17157i	0.114339	−	0.276038i
$352$		0			0
$353$		−	21.3137i		−	1.13441i	−0.823575	−	0.567207i	$-0.808024\pi$
$353$		−	21.3137i		−	1.13441i	0.823575	−	0.567207i	$-0.191976\pi$
$354$		0			0
$355$	−18.8701	−	18.8701i	−1.00152	−	1.00152i
$356$		0			0
$357$	8.48528	+	8.00000i	0.449089	+	0.423405i
$358$		0			0
$359$	3.75736	+	3.75736i	0.198306	+	0.198306i	0.799273	−	0.600968i	$-0.205218\pi$
$359$	3.75736	+	3.75736i	0.198306	+	0.198306i	−0.600968	+	0.799273i	$0.705218\pi$
$360$		0			0
$361$			39.6274i			2.08565i
$362$		0			0
$363$	6.17157	−	14.8995i	0.323924	−	0.782021i
$364$		0			0
$365$	−16.5147	+	16.5147i	−0.864420	+	0.864420i
$366$		0			0
$367$	24.3137	+	10.0711i	1.26917	+	0.525705i	0.912710	−	0.408607i	$-0.133985\pi$
$367$	24.3137	+	10.0711i	1.26917	+	0.525705i	0.356455	+	0.934313i	$0.383985\pi$
$368$		0			0
$369$	32.6777	−	13.5355i	1.70113	−	0.704632i
$370$		0			0
$371$	3.41421	+	8.24264i	0.177257	+	0.427937i
$372$		0			0
$373$	−29.6985			−1.53773			−0.768865	−	0.639412i	$-0.779178\pi$
$373$	−29.6985			−1.53773			−0.768865	+	0.639412i	$0.779178\pi$
$374$		0			0
$375$	10.8284			0.559178
$376$		0			0
$377$	−5.48528	−	13.2426i	−0.282506	−	0.682031i
$378$		0			0
$379$	−21.1421	+	8.75736i	−1.08600	+	0.449835i	−0.852610	−	0.522548i	$-0.824981\pi$
$379$	−21.1421	+	8.75736i	−1.08600	+	0.449835i	−0.233389	+	0.972383i	$0.574981\pi$
$380$		0			0
$381$	2.00000	+	0.828427i	0.102463	+	0.0424416i
$382$		0			0
$383$	0.928932	−	0.928932i	0.0474662	−	0.0474662i	−0.682975	−	0.730441i	$-0.739314\pi$
$383$	0.928932	−	0.928932i	0.0474662	−	0.0474662i	0.730441	+	0.682975i	$0.239314\pi$
$384$		0			0
$385$	−5.02944	+	12.1421i	−0.256324	+	0.618821i
$386$		0			0
$387$			1.31371i			0.0667796i
$388$		0			0
$389$	3.41421	+	3.41421i	0.173107	+	0.173107i	0.788343	−	0.615236i	$-0.210939\pi$
$389$	3.41421	+	3.41421i	0.173107	+	0.173107i	−0.615236	+	0.788343i	$0.710939\pi$
$390$		0			0
$391$	−10.6569	−	23.7279i	−0.538940	−	1.19997i
$392$		0			0
$393$	6.00000	+	6.00000i	0.302660	+	0.302660i
$394$		0			0
$395$			12.1421i			0.610937i
$396$		0			0
$397$	4.12132	−	9.94975i	0.206843	−	0.499364i	−0.786080	−	0.618125i	$-0.787892\pi$
$397$	4.12132	−	9.94975i	0.206843	−	0.499364i	0.992923	+	0.118762i	$0.0378925\pi$
$398$		0			0
$399$	−15.3137	+	15.3137i	−0.766644	+	0.766644i
$400$		0			0
$401$	1.12132	+	0.464466i	0.0559961	+	0.0231943i	0.410506	−	0.911858i	$-0.365352\pi$
$401$	1.12132	+	0.464466i	0.0559961	+	0.0231943i	−0.354510	+	0.935052i	$0.615352\pi$
$402$		0			0
$403$	2.58579	−	1.07107i	0.128807	−	0.0533537i
$404$		0			0
$405$	−6.53553	−	15.7782i	−0.324753	−	0.784024i
$406$		0			0
$407$	−44.6274			−2.21210
$408$		0			0
$409$	−24.0000			−1.18672			−0.593362	−	0.804936i	$-0.702200\pi$
$409$	−24.0000			−1.18672			−0.593362	+	0.804936i	$0.702200\pi$
$410$		0			0
$411$	−7.75736	−	18.7279i	−0.382642	−	0.923780i
$412$		0			0
$413$	−7.17157	+	2.97056i	−0.352890	+	0.146172i
$414$		0			0
$415$	34.7279	+	14.3848i	1.70473	+	0.706121i
$416$		0			0
$417$	−9.31371	+	9.31371i	−0.456094	+	0.456094i
$418$		0			0
$419$	−1.68629	+	4.07107i	−0.0823807	+	0.198885i	−0.959703	−	0.281018i	$-0.909328\pi$
$419$	−1.68629	+	4.07107i	−0.0823807	+	0.198885i	0.877322	+	0.479903i	$0.159328\pi$
$420$		0			0
$421$			36.0416i			1.75656i	0.478145	+	0.878281i	$0.341309\pi$
$421$			36.0416i			1.75656i	−0.478145	+	0.878281i	$0.658691\pi$
$422$		0			0
$423$	3.17157	+	3.17157i	0.154207	+	0.154207i
$424$		0			0
$425$	−0.435029	−	14.7782i	−0.0211020	−	0.716847i
$426$		0			0
$427$	3.41421	+	3.41421i	0.165225	+	0.165225i
$428$		0			0
$429$			28.0000i			1.35185i
$430$		0			0
$431$	−12.0711	+	29.1421i	−0.581443	+	1.40373i	0.310062	+	0.950716i	$0.399650\pi$
$431$	−12.0711	+	29.1421i	−0.581443	+	1.40373i	−0.891505	+	0.453011i	$0.850350\pi$
$432$		0			0
$433$	−15.2132	+	15.2132i	−0.731100	+	0.731100i	−0.970838	−	0.239738i	$-0.922939\pi$
$433$	−15.2132	+	15.2132i	−0.731100	+	0.731100i	0.239738	+	0.970838i	$0.422939\pi$
$434$		0			0
$435$	39.2132	+	16.2426i	1.88013	+	0.778775i
$436$		0			0
$437$	44.6274	−	18.4853i	2.13482	−	0.884271i
$438$		0			0
$439$	−2.31371	−	5.58579i	−0.110427	−	0.266595i	0.858999	−	0.511977i	$-0.171087\pi$
$439$	−2.31371	−	5.58579i	−0.110427	−	0.266595i	−0.969427	+	0.245382i	$0.921087\pi$
$440$		0			0
$441$	22.3137			1.06256
$442$		0			0
$443$	22.1421			1.05200			0.526002	−	0.850483i	$-0.323690\pi$
$443$	22.1421			1.05200			0.526002	+	0.850483i	$0.323690\pi$
$444$		0			0
$445$	−4.75736	−	11.4853i	−0.225520	−	0.544455i
$446$		0			0
$447$	8.00000	−	3.31371i	0.378387	−	0.156733i
$448$		0			0
$449$	−33.0919	−	13.7071i	−1.56170	−	0.646878i	−0.576318	−	0.817225i	$-0.695511\pi$
$449$	−33.0919	−	13.7071i	−1.56170	−	0.646878i	−0.985384	+	0.170347i	$0.945511\pi$
$450$		0			0
$451$	−27.0711	+	27.0711i	−1.27473	+	1.27473i
$452$		0			0
$453$	−0.343146	+	0.828427i	−0.0161224	+	0.0389229i
$454$		0			0
$455$		−	8.20101i		−	0.384469i
$456$		0			0
$457$	12.3431	+	12.3431i	0.577388	+	0.577388i	0.934183	−	0.356795i	$-0.116130\pi$
$457$	12.3431	+	12.3431i	0.577388	+	0.577388i	−0.356795	+	0.934183i	$0.616130\pi$
$458$		0			0
$459$	−8.14214	+	3.65685i	−0.380042	+	0.170687i
$460$		0			0
$461$	−17.1421	−	17.1421i	−0.798389	−	0.798389i	0.184453	−	0.982841i	$-0.440949\pi$
$461$	−17.1421	−	17.1421i	−0.798389	−	0.798389i	−0.982841	+	0.184453i	$0.940949\pi$
$462$		0			0
$463$		−	6.62742i		−	0.308002i	−0.988071	−	0.154001i	$-0.950784\pi$
$463$		−	6.62742i		−	0.308002i	0.988071	−	0.154001i	$-0.0492159\pi$
$464$		0			0
$465$	−3.17157	+	7.65685i	−0.147078	+	0.355078i
$466$		0			0
$467$	−6.24264	+	6.24264i	−0.288875	+	0.288875i	−0.836635	−	0.547760i	$-0.815481\pi$
$467$	−6.24264	+	6.24264i	−0.288875	+	0.288875i	0.547760	+	0.836635i	$0.315481\pi$
$468$		0			0
$469$	−2.82843	−	1.17157i	−0.130605	−	0.0540982i
$470$		0			0
$471$	48.2843	−	20.0000i	2.22482	−	0.921551i
$472$		0			0
$473$	−0.544156	−	1.31371i	−0.0250203	−	0.0604044i
$474$		0			0
$475$	27.4558			1.25976
$476$		0			0
$477$	−31.5563			−1.44487
$478$		0			0
$479$	−1.38478	−	3.34315i	−0.0632720	−	0.152752i	0.889081	−	0.457750i	$-0.151344\pi$
$479$	−1.38478	−	3.34315i	−0.0632720	−	0.152752i	−0.952353	+	0.304997i	$0.901344\pi$
$480$		0			0
$481$	25.7279	−	10.6569i	1.17309	−	0.485911i
$482$		0			0
$483$	16.4853	+	6.82843i	0.750106	+	0.310704i
$484$		0			0
$485$	9.24264	−	9.24264i	0.419687	−	0.419687i
$486$		0			0
$487$	11.1421	−	26.8995i	0.504898	−	1.21893i	−0.441888	−	0.897070i	$-0.645691\pi$
$487$	11.1421	−	26.8995i	0.504898	−	1.21893i	0.946786	−	0.321862i	$-0.104309\pi$
$488$		0			0
$489$		−	26.1421i		−	1.18219i
$490$		0			0
$491$	3.75736	+	3.75736i	0.169567	+	0.169567i	0.786789	−	0.617222i	$-0.211742\pi$
$491$	3.75736	+	3.75736i	0.169567	+	0.169567i	−0.617222	+	0.786789i	$0.711742\pi$
$492$		0			0
$493$	−8.12132	+	21.3640i	−0.365766	+	0.962184i
$494$		0			0
$495$	−32.8701	−	32.8701i	−1.47740	−	1.47740i
$496$		0			0
$497$			9.85786i			0.442186i
$498$		0			0
$499$	15.4853	−	37.3848i	0.693216	−	1.67357i	−0.0449811	−	0.998988i	$-0.514323\pi$
$499$	15.4853	−	37.3848i	0.693216	−	1.67357i	0.738198	−	0.674585i	$-0.235677\pi$
$500$		0			0
$501$	12.8284	−	12.8284i	0.573132	−	0.573132i
$502$		0			0
$503$	9.82843	+	4.07107i	0.438228	+	0.181520i	0.590879	−	0.806760i	$-0.298781\pi$
$503$	9.82843	+	4.07107i	0.438228	+	0.181520i	−0.152651	+	0.988280i	$0.548781\pi$
$504$		0			0
$505$	17.8284	−	7.38478i	0.793355	−	0.328618i
$506$		0			0
$507$	6.31371	+	15.2426i	0.280402	+	0.676949i
$508$		0			0
$509$	−20.0000			−0.886484			−0.443242	−	0.896402i	$-0.646172\pi$
$509$	−20.0000			−0.886484			−0.443242	+	0.896402i	$0.646172\pi$
$510$		0			0
$511$	8.62742			0.381654
$512$		0			0
$513$	−6.34315	−	15.3137i	−0.280057	−	0.676117i
$514$		0			0
$515$	−7.65685	+	3.17157i	−0.337401	+	0.139756i
$516$		0			0
$517$	−4.48528	−	1.85786i	−0.197262	−	0.0817088i
$518$		0			0
$519$	−40.0416	+	40.0416i	−1.75763	+	1.75763i
$520$		0			0
$521$	−2.53553	+	6.12132i	−0.111084	+	0.268180i	−0.969639	−	0.244541i	$-0.921363\pi$
$521$	−2.53553	+	6.12132i	−0.111084	+	0.268180i	0.858555	+	0.512721i	$0.171363\pi$
$522$		0			0
$523$		−	39.1127i		−	1.71028i	−0.518398	−	0.855139i	$-0.673471\pi$
$523$		−	39.1127i		−	1.71028i	0.518398	−	0.855139i	$-0.326529\pi$
$524$		0			0
$525$	7.17157	+	7.17157i	0.312993	+	0.312993i
$526$		0			0
$527$	−4.17157	−	1.58579i	−0.181717	−	0.0690779i
$528$		0			0
$529$	−11.8787	−	11.8787i	−0.516464	−	0.516464i
$530$		0			0
$531$		−	27.4558i		−	1.19148i
$532$		0			0
$533$	9.14214	−	22.0711i	0.395990	−	0.956004i
$534$		0			0
$535$	−14.9289	+	14.9289i	−0.645434	+	0.645434i
$536$		0			0
$537$	25.3137	+	10.4853i	1.09237	+	0.452473i
$538$		0			0
$539$	−22.3137	+	9.24264i	−0.961119	+	0.398109i
$540$		0			0
$541$	2.94975	+	7.12132i	0.126820	+	0.306169i	0.974518	−	0.224309i	$-0.0720124\pi$
$541$	2.94975	+	7.12132i	0.126820	+	0.306169i	−0.847699	+	0.530478i	$0.822012\pi$
$542$		0			0
$543$	−44.1421			−1.89432
$544$		0			0
$545$	16.7868			0.719067
$546$		0			0
$547$	−10.1716	−	24.5563i	−0.434905	−	1.04995i	−0.977685	−	0.210078i	$-0.932628\pi$
$547$	−10.1716	−	24.5563i	−0.434905	−	1.04995i	0.542779	−	0.839875i	$-0.317372\pi$
$548$		0			0
$549$	−15.7782	+	6.53553i	−0.673396	+	0.278930i
$550$		0			0
$551$	−39.2132	−	16.2426i	−1.67054	−	0.691960i
$552$		0			0
$553$	3.17157	−	3.17157i	0.134869	−	0.134869i
$554$		0			0
$555$	−31.5563	+	76.1838i	−1.33949	+	3.23382i
$556$		0			0
$557$		−	8.24264i		−	0.349252i	−0.984635	−	0.174626i	$-0.944128\pi$
$557$		−	8.24264i		−	0.349252i	0.984635	−	0.174626i	$-0.0558716\pi$
$558$		0			0
$559$	0.627417	+	0.627417i	0.0265369	+	0.0265369i
$560$		0			0
$561$	30.6274	−	32.4853i	1.29309	−	1.37153i
$562$		0			0
$563$	22.3848	+	22.3848i	0.943406	+	0.943406i	0.998482	−	0.0550763i	$-0.0175402\pi$
$563$	22.3848	+	22.3848i	0.943406	+	0.943406i	−0.0550763	+	0.998482i	$0.517540\pi$
$564$		0			0
$565$		−	9.89949i		−	0.416475i
$566$		0			0
$567$	−2.41421	+	5.82843i	−0.101387	+	0.244771i
$568$		0			0
$569$	11.8284	−	11.8284i	0.495873	−	0.495873i	−0.414277	−	0.910151i	$-0.635966\pi$
$569$	11.8284	−	11.8284i	0.495873	−	0.495873i	0.910151	+	0.414277i	$0.135966\pi$
$570$		0			0
$571$	−25.4853	−	10.5563i	−1.06653	−	0.441769i	−0.220762	−	0.975328i	$-0.570855\pi$
$571$	−25.4853	−	10.5563i	−1.06653	−	0.441769i	−0.845763	+	0.533558i	$0.820855\pi$
$572$		0			0
$573$	−42.6274	+	17.6569i	−1.78079	+	0.737626i
$574$		0			0
$575$	−8.65685	−	20.8995i	−0.361016	−	0.871569i
$576$		0			0
$577$	17.2132			0.716595			0.358298	−	0.933607i	$-0.383357\pi$
$577$	17.2132			0.716595			0.358298	+	0.933607i	$0.383357\pi$
$578$		0			0
$579$	−5.31371			−0.220830
$580$		0			0
$581$	−5.31371	−	12.8284i	−0.220450	−	0.532213i
$582$		0			0
$583$	31.5563	−	13.0711i	1.30693	−	0.541348i
$584$		0			0
$585$	26.7990	+	11.1005i	1.10800	+	0.458949i
$586$		0			0
$587$	30.0416	−	30.0416i	1.23995	−	1.23995i	0.279931	−	0.960020i	$-0.409689\pi$
$587$	30.0416	−	30.0416i	1.23995	−	1.23995i	0.960020	−	0.279931i	$-0.0903114\pi$
$588$		0			0
$589$	3.17157	−	7.65685i	0.130682	−	0.315495i
$590$		0			0
$591$		−	53.1127i		−	2.18476i
$592$		0			0
$593$	3.48528	+	3.48528i	0.143123	+	0.143123i	0.775038	−	0.631915i	$-0.217731\pi$
$593$	3.48528	+	3.48528i	0.143123	+	0.143123i	−0.631915	+	0.775038i	$0.717731\pi$
$594$		0			0
$595$	−8.97056	+	9.51472i	−0.367757	+	0.390065i
$596$		0			0
$597$	26.4853	+	26.4853i	1.08397	+	1.08397i
$598$		0			0
$599$		−	9.65685i		−	0.394568i	−0.980346	−	0.197284i	$-0.936788\pi$
$599$		−	9.65685i		−	0.394568i	0.980346	−	0.197284i	$-0.0632122\pi$
$600$		0			0
$601$	−0.878680	+	2.12132i	−0.0358421	+	0.0865305i	−0.940787	−	0.338998i	$-0.889912\pi$
$601$	−0.878680	+	2.12132i	−0.0358421	+	0.0865305i	0.904945	+	0.425529i	$0.139912\pi$
$602$		0			0
$603$	7.65685	−	7.65685i	0.311811	−	0.311811i
$604$		0			0
$605$	16.7071	+	6.92031i	0.679240	+	0.281351i
$606$		0			0
$607$	−8.89949	+	3.68629i	−0.361219	+	0.149622i	−0.555909	−	0.831243i	$-0.687630\pi$
$607$	−8.89949	+	3.68629i	−0.361219	+	0.149622i	0.194690	+	0.980865i	$0.437630\pi$
$608$		0			0
$609$	−6.00000	−	14.4853i	−0.243132	−	0.586973i
$610$		0			0
$611$	3.02944			0.122558
$612$		0			0
$613$	−1.31371			−0.0530602			−0.0265301	−	0.999648i	$-0.508446\pi$
$613$	−1.31371			−0.0530602			−0.0265301	+	0.999648i	$0.508446\pi$
$614$		0			0
$615$	27.0711	+	65.3553i	1.09161	+	2.63538i
$616$		0			0
$617$	−4.36396	+	1.80761i	−0.175686	+	0.0727717i	−0.468793	−	0.883308i	$-0.655311\pi$
$617$	−4.36396	+	1.80761i	−0.175686	+	0.0727717i	0.293106	+	0.956080i	$0.405311\pi$
$618$		0			0
$619$	5.58579	+	2.31371i	0.224512	+	0.0929958i	0.492104	−	0.870536i	$-0.336228\pi$
$619$	5.58579	+	2.31371i	0.224512	+	0.0929958i	−0.267592	+	0.963532i	$0.586228\pi$
$620$		0			0
$621$	−9.65685	+	9.65685i	−0.387516	+	0.387516i
$622$		0			0
$623$	−1.75736	+	4.24264i	−0.0704071	+	0.169978i
$624$		0			0
$625$			30.0711i			1.20284i
$626$		0			0
$627$	58.6274	+	58.6274i	2.34135	+	2.34135i
$628$		0			0
$629$	−41.5061	−	15.7782i	−1.65496	−	0.629117i
$630$		0			0
$631$	15.2132	+	15.2132i	0.605628	+	0.605628i	0.941800	−	0.336172i	$-0.109132\pi$
$631$	15.2132	+	15.2132i	0.605628	+	0.605628i	−0.336172	+	0.941800i	$0.609132\pi$
$632$		0			0
$633$		−	73.4558i		−	2.91961i
$634$		0			0
$635$	−0.928932	+	2.24264i	−0.0368635	+	0.0889965i
$636$		0			0
$637$	10.6569	−	10.6569i	0.422240	−	0.422240i
$638$		0			0
$639$	−32.2132	−	13.3431i	−1.27433	−	0.527847i
$640$		0			0
$641$	−18.9497	+	7.84924i	−0.748470	+	0.310026i	−0.724117	−	0.689677i	$-0.757753\pi$
$641$	−18.9497	+	7.84924i	−0.748470	+	0.310026i	−0.0243529	+	0.999703i	$0.507753\pi$
$642$		0			0
$643$	16.3137	+	39.3848i	0.643350	+	1.55318i	0.822133	+	0.569295i	$0.192784\pi$
$643$	16.3137	+	39.3848i	0.643350	+	1.55318i	−0.178783	+	0.983889i	$0.557216\pi$
$644$		0			0
$645$	−2.62742			−0.103454
$646$		0			0
$647$	−6.82843			−0.268453			−0.134227	−	0.990951i	$-0.542855\pi$
$647$	−6.82843			−0.268453			−0.134227	+	0.990951i	$0.542855\pi$
$648$		0			0
$649$	11.3726	+	27.4558i	0.446413	+	1.07774i
$650$		0			0
$651$	2.82843	−	1.17157i	0.110855	−	0.0459176i
$652$		0			0
$653$	29.6066	+	12.2635i	1.15860	+	0.479906i	0.877407	−	0.479746i	$-0.159271\pi$
$653$	29.6066	+	12.2635i	1.15860	+	0.479906i	0.281189	+	0.959653i	$0.409271\pi$
$654$		0			0
$655$	−6.72792	+	6.72792i	−0.262882	+	0.262882i
$656$		0			0
$657$	−11.6777	+	28.1924i	−0.455589	+	1.09989i
$658$		0			0
$659$			10.1421i			0.395082i	0.980295	+	0.197541i	$0.0632955\pi$
$659$			10.1421i			0.395082i	−0.980295	+	0.197541i	$0.936705\pi$
$660$		0			0
$661$	32.6569	+	32.6569i	1.27020	+	1.27020i	0.945980	+	0.324224i	$0.105103\pi$
$661$	32.6569	+	32.6569i	1.27020	+	1.27020i	0.324224	+	0.945980i	$0.394897\pi$
$662$		0			0
$663$	−9.89949	+	26.0416i	−0.384465	+	1.01137i
$664$		0			0
$665$	−17.1716	−	17.1716i	−0.665885	−	0.665885i
$666$		0			0
$667$			34.9706i			1.35407i
$668$		0			0
$669$	−2.68629	+	6.48528i	−0.103858	+	0.250735i
$670$		0			0
$671$	13.0711	−	13.0711i	0.504603	−	0.504603i
$672$		0			0
$673$	9.77817	+	4.05025i	0.376921	+	0.156126i	0.563097	−	0.826391i	$-0.309610\pi$
$673$	9.77817	+	4.05025i	0.376921	+	0.156126i	−0.186176	+	0.982516i	$0.559610\pi$
$674$		0			0
$675$	−7.17157	+	2.97056i	−0.276034	+	0.114337i
$676$		0			0
$677$	−10.1508	−	24.5061i	−0.390125	−	0.941846i	−0.989912	−	0.141686i	$-0.954748\pi$
$677$	−10.1508	−	24.5061i	−0.390125	−	0.941846i	0.599786	−	0.800160i	$-0.295252\pi$
$678$		0			0
$679$	−4.82843			−0.185298
$680$		0			0
$681$	−10.8284			−0.414946
$682$		0			0
$683$	2.31371	+	5.58579i	0.0885316	+	0.213734i	0.961944	−	0.273248i	$-0.0880978\pi$
$683$	2.31371	+	5.58579i	0.0885316	+	0.213734i	−0.873412	+	0.486982i	$0.838098\pi$
$684$		0			0
$685$	21.0000	−	8.69848i	0.802369	−	0.332352i
$686$		0			0
$687$	−30.1421	−	12.4853i	−1.14999	−	0.476343i
$688$		0			0
$689$	−15.0711	+	15.0711i	−0.574162	+	0.574162i
$690$		0			0
$691$	−8.07107	+	19.4853i	−0.307038	+	0.741255i	0.692760	+	0.721168i	$0.256394\pi$
$691$	−8.07107	+	19.4853i	−0.307038	+	0.741255i	−0.999798	+	0.0200872i	$0.993606\pi$
$692$		0			0
$693$			17.1716i			0.652294i
$694$		0			0
$695$	−10.4437	−	10.4437i	−0.396150	−	0.396150i
$696$		0			0
$697$	−34.7487	+	15.6066i	−1.31620	+	0.591142i
$698$		0			0
$699$	−7.75736	−	7.75736i	−0.293410	−	0.293410i
$700$		0			0
$701$		−	40.2426i		−	1.51994i	−0.649956	−	0.759972i	$-0.725213\pi$
$701$		−	40.2426i		−	1.51994i	0.649956	−	0.759972i	$-0.274787\pi$
$702$		0			0
$703$	31.5563	−	76.1838i	1.19017	−	2.87333i
$704$		0			0
$705$	−6.34315	+	6.34315i	−0.238897	+	0.238897i
$706$		0			0
$707$	−6.58579	−	2.72792i	−0.247684	−	0.102594i
$708$		0			0
$709$	24.9203	−	10.3223i	0.935902	−	0.387663i	0.137987	−	0.990434i	$-0.455937\pi$
$709$	24.9203	−	10.3223i	0.935902	−	0.387663i	0.797914	+	0.602771i	$0.205937\pi$
$710$		0			0
$711$	6.07107	+	14.6569i	0.227683	+	0.549675i
$712$		0			0
$713$	−6.82843			−0.255727
$714$		0			0
$715$	−31.3970			−1.17418
$716$		0			0
$717$	16.4853	+	39.7990i	0.615654	+	1.48632i
$718$		0			0
$719$	2.65685	−	1.10051i	0.0990839	−	0.0410419i	−0.332591	−	0.943071i	$-0.607923\pi$
$719$	2.65685	−	1.10051i	0.0990839	−	0.0410419i	0.431675	+	0.902029i	$0.357923\pi$
$720$		0			0
$721$	2.82843	+	1.17157i	0.105336	+	0.0436317i
$722$		0			0
$723$	25.8995	−	25.8995i	0.963213	−	0.963213i
$724$		0			0
$725$	−7.60660	+	18.3640i	−0.282502	+	0.682020i
$726$		0			0
$727$			31.5147i			1.16882i	0.811460	+	0.584408i	$0.198673\pi$
$727$			31.5147i			1.16882i	−0.811460	+	0.584408i	$0.801327\pi$
$728$		0			0
$729$	−27.7782	−	27.7782i	−1.02882	−	1.02882i
$730$		0			0
$731$	−0.0416306	−	1.41421i	−0.00153976	−	0.0523066i
$732$		0			0
$733$	−26.6569	−	26.6569i	−0.984593	−	0.984593i	0.0152897	−	0.999883i	$-0.495133\pi$
$733$	−26.6569	−	26.6569i	−0.984593	−	0.984593i	−0.999883	+	0.0152897i	$0.995133\pi$
$734$		0			0
$735$			44.6274i			1.64611i
$736$		0			0
$737$	−4.48528	+	10.8284i	−0.165217	+	0.398870i
$738$		0			0
$739$	−14.9289	+	14.9289i	−0.549170	+	0.549170i	−0.926201	−	0.377031i	$-0.876945\pi$
$739$	−14.9289	+	14.9289i	−0.549170	+	0.549170i	0.377031	+	0.926201i	$0.376945\pi$
$740$		0			0
$741$	−47.7990	−	19.7990i	−1.75594	−	0.727334i
$742$		0			0
$743$	−7.24264	+	3.00000i	−0.265707	+	0.110059i	−0.511560	−	0.859248i	$-0.670932\pi$
$743$	−7.24264	+	3.00000i	−0.265707	+	0.110059i	0.245853	+	0.969307i	$0.420932\pi$
$744$		0			0
$745$	3.71573	+	8.97056i	0.136134	+	0.328656i
$746$		0			0
$747$	49.1127			1.79694
$748$		0			0
$749$	7.79899			0.284969
$750$		0			0
$751$	0.857864	+	2.07107i	0.0313039	+	0.0755743i	0.938758	−	0.344576i	$-0.111977\pi$
$751$	0.857864	+	2.07107i	0.0313039	+	0.0755743i	−0.907454	+	0.420150i	$0.861977\pi$
$752$		0			0
$753$	−18.1421	+	7.51472i	−0.661136	+	0.273852i
$754$		0			0
$755$	−0.928932	−	0.384776i	−0.0338073	−	0.0140034i
$756$		0			0
$757$	8.14214	−	8.14214i	0.295931	−	0.295931i	−0.543487	−	0.839418i	$-0.682896\pi$
$757$	8.14214	−	8.14214i	0.295931	−	0.295931i	0.839418	+	0.543487i	$0.182896\pi$
$758$		0			0
$759$	26.1421	−	63.1127i	0.948899	−	2.29085i
$760$		0			0
$761$			24.5269i			0.889100i	0.895754	+	0.444550i	$0.146636\pi$
$761$			24.5269i			0.889100i	−0.895754	+	0.444550i	$0.853364\pi$
$762$		0			0
$763$	−4.38478	−	4.38478i	−0.158740	−	0.158740i
$764$		0			0
$765$	−18.9497	−	42.1924i	−0.685130	−	1.52547i
$766$		0			0
$767$	−13.1127	−	13.1127i	−0.473472	−	0.473472i
$768$		0			0
$769$			11.7574i			0.423981i	0.977272	+	0.211991i	$0.0679946\pi$
$769$			11.7574i			0.423981i	−0.977272	+	0.211991i	$0.932005\pi$
$770$		0			0
$771$	−14.1421	+	34.1421i	−0.509317	+	1.22960i
$772$		0			0
$773$	27.4142	−	27.4142i	0.986021	−	0.986021i	−0.0138829	−	0.999904i	$-0.504419\pi$
$773$	27.4142	−	27.4142i	0.986021	−	0.986021i	0.999904	+	0.0138829i	$0.00441921\pi$
$774$		0			0
$775$	−3.58579	−	1.48528i	−0.128805	−	0.0533529i
$776$		0			0
$777$	28.1421	−	11.6569i	1.00959	−	0.418187i
$778$		0			0
$779$	−27.0711	−	65.3553i	−0.969922	−	2.34160i
$780$		0			0
$781$	37.7401			1.35045
$782$		0			0
$783$	12.0000			0.428845
$784$		0			0
$785$	22.4264	+	54.1421i	0.800433	+	1.93242i
$786$		0			0
$787$	33.0416	−	13.6863i	1.17781	−	0.487864i	0.294041	−	0.955793i	$-0.405000\pi$
$787$	33.0416	−	13.6863i	1.17781	−	0.487864i	0.883766	+	0.467929i	$0.155000\pi$
$788$		0			0
$789$	10.4853	+	4.34315i	0.373286	+	0.154620i
$790$		0			0
$791$	−2.58579	+	2.58579i	−0.0919400	+	0.0919400i
$792$		0			0
$793$	−4.41421	+	10.6569i	−0.156753	+	0.378436i
$794$		0			0
$795$		−	63.1127i		−	2.23838i
$796$		0			0
$797$	21.9706	+	21.9706i	0.778237	+	0.778237i	0.979531	−	0.201294i	$-0.0645146\pi$
$797$	21.9706	+	21.9706i	0.778237	+	0.778237i	−0.201294	+	0.979531i	$0.564515\pi$
$798$		0			0
$799$	−3.51472	−	3.31371i	−0.124342	−	0.117231i
$800$		0			0
$801$	−11.4853	−	11.4853i	−0.405812	−	0.405812i
$802$		0			0
$803$		−	33.0294i		−	1.16558i
$804$		0			0
$805$	−7.65685	+	18.4853i	−0.269869	+	0.651521i
$806$		0			0
$807$	−0.585786	+	0.585786i	−0.0206207	+	0.0206207i
$808$		0			0
$809$	18.7071	+	7.74874i	0.657707	+	0.272431i	0.686473	−	0.727155i	$-0.259158\pi$
$809$	18.7071	+	7.74874i	0.657707	+	0.272431i	−0.0287664	+	0.999586i	$0.509158\pi$
$810$		0			0
$811$	−0.757359	+	0.313708i	−0.0265945	+	0.0110158i	−0.395941	−	0.918276i	$-0.629582\pi$
$811$	−0.757359	+	0.313708i	−0.0265945	+	0.0110158i	0.369347	+	0.929292i	$0.379582\pi$
$812$		0			0
$813$	26.1421	+	63.1127i	0.916845	+	2.21346i
$814$		0			0
$815$	29.3137			1.02681
$816$		0			0
$817$	2.62742			0.0919217
$818$		0			0
$819$	−4.10051	−	9.89949i	−0.143283	−	0.345916i
$820$		0			0
$821$	−28.9203	+	11.9792i	−1.00933	+	0.418076i	−0.825209	−	0.564828i	$-0.808943\pi$
$821$	−28.9203	+	11.9792i	−1.00933	+	0.418076i	−0.184117	+	0.982904i	$0.558943\pi$
$822$		0			0
$823$	−35.0416	−	14.5147i	−1.22147	−	0.505951i	−0.323596	−	0.946195i	$-0.604892\pi$
$823$	−35.0416	−	14.5147i	−1.22147	−	0.505951i	−0.897878	+	0.440244i	$0.854892\pi$
$824$		0			0
$825$	27.4558	−	27.4558i	0.955890	−	0.955890i
$826$		0			0
$827$	10.6569	−	25.7279i	0.370575	−	0.894648i	−0.623078	−	0.782160i	$-0.714118\pi$
$827$	10.6569	−	25.7279i	0.370575	−	0.894648i	0.993653	−	0.112488i	$-0.0358819\pi$
$828$		0			0
$829$			28.9706i			1.00619i	0.864231	+	0.503095i	$0.167805\pi$
$829$			28.9706i			1.00619i	−0.864231	+	0.503095i	$0.832195\pi$
$830$		0			0
$831$	42.0416	+	42.0416i	1.45841	+	1.45841i
$832$		0			0
$833$	−24.0208	+	0.707107i	−0.832272	+	0.0244998i
$834$		0			0
$835$	14.3848	+	14.3848i	0.497806	+	0.497806i
$836$		0			0
$837$			2.34315i			0.0809910i
$838$		0			0
$839$	−15.2843	+	36.8995i	−0.527672	+	1.27391i	0.405373	+	0.914151i	$0.367142\pi$
$839$	−15.2843	+	36.8995i	−0.527672	+	1.27391i	−0.933045	+	0.359761i	$0.882858\pi$
$840$		0			0
$841$	1.22183	−	1.22183i	0.0421319	−	0.0421319i
$842$		0			0
$843$	−43.2132	−	17.8995i	−1.48834	−	0.616491i
$844$		0			0
$845$	−17.0919	+	7.07969i	−0.587979	+	0.243549i
$846$		0			0
$847$	−2.55635	−	6.17157i	−0.0878372	−	0.212058i
$848$		0			0
$849$	−74.4264			−2.55431
$850$		0			0
$851$	−67.9411			−2.32899
$852$		0			0
$853$	−13.0503	−	31.5061i	−0.446832	−	1.07875i	−0.973502	−	0.228678i	$-0.926560\pi$
$853$	−13.0503	−	31.5061i	−0.446832	−	1.07875i	0.526670	−	0.850070i	$-0.323440\pi$
$854$		0			0
$855$	79.3553	−	32.8701i	2.71390	−	1.12413i
$856$		0			0
$857$	1.12132	+	0.464466i	0.0383036	+	0.0158659i	0.401753	−	0.915748i	$-0.368401\pi$
$857$	1.12132	+	0.464466i	0.0383036	+	0.0158659i	−0.363449	+	0.931614i	$0.618401\pi$
$858$		0			0
$859$	14.7279	−	14.7279i	0.502510	−	0.502510i	−0.409707	−	0.912217i	$-0.634369\pi$
$859$	14.7279	−	14.7279i	0.502510	−	0.502510i	0.912217	+	0.409707i	$0.134369\pi$
$860$		0			0
$861$	10.0000	−	24.1421i	0.340799	−	0.822762i
$862$		0			0
$863$			6.34315i			0.215923i	0.994155	+	0.107962i	$0.0344324\pi$
$863$			6.34315i			0.215923i	−0.994155	+	0.107962i	$0.965568\pi$
$864$		0			0
$865$	−44.8995	−	44.8995i	−1.52663	−	1.52663i
$866$		0			0
$867$	39.9706	−	19.3848i	1.35747	−	0.658342i
$868$		0			0
$869$	−12.1421	−	12.1421i	−0.411894	−	0.411894i
$870$		0			0
$871$		−	7.31371i		−	0.247816i
$872$		0			0
$873$	6.53553	−	15.7782i	0.221194	−	0.534010i
$874$		0			0
$875$	3.17157	−	3.17157i	0.107219	−	0.107219i
$876$		0			0
$877$	−21.5355	−	8.92031i	−0.727203	−	0.301217i	−0.0118011	−	0.999930i	$-0.503756\pi$
$877$	−21.5355	−	8.92031i	−0.727203	−	0.301217i	−0.715402	+	0.698713i	$0.753756\pi$
$878$		0			0
$879$	26.4853	−	10.9706i	0.893326	−	0.370028i
$880$		0			0
$881$	−2.15076	−	5.19239i	−0.0724609	−	0.174936i	0.883499	−	0.468433i	$-0.155181\pi$
$881$	−2.15076	−	5.19239i	−0.0724609	−	0.174936i	−0.955960	+	0.293497i	$0.905181\pi$
$882$		0			0
$883$	−26.3431			−0.886517			−0.443259	−	0.896394i	$-0.646178\pi$
$883$	−26.3431			−0.886517			−0.443259	+	0.896394i	$0.646178\pi$
$884$		0			0
$885$	54.9117			1.84584
$886$		0			0
$887$	−3.38478	−	8.17157i	−0.113650	−	0.274375i	0.856812	−	0.515628i	$-0.172441\pi$
$887$	−3.38478	−	8.17157i	−0.113650	−	0.274375i	−0.970462	+	0.241254i	$0.922441\pi$
$888$		0			0
$889$	0.828427	−	0.343146i	0.0277846	−	0.0115087i
$890$		0			0
$891$	22.3137	+	9.24264i	0.747537	+	0.309640i
$892$		0			0
$893$	6.34315	−	6.34315i	0.212265	−	0.212265i
$894$		0			0
$895$	−11.7574	+	28.3848i	−0.393005	+	0.948798i
$896$		0			0
$897$			42.6274i			1.42329i
$898$		0			0
$899$	4.24264	+	4.24264i	0.141500	+	0.141500i
$900$		0			0
$901$	33.9706	−	1.00000i	1.13172	−	0.0333148i
$902$		0			0
$903$	0.686292	+	0.686292i	0.0228384	+	0.0228384i
$904$		0			0
$905$		−	49.4975i		−	1.64535i
$906$		0			0
$907$	−5.24264	+	12.6569i	−0.174079	+	0.420264i	−0.986705	−	0.162522i	$-0.948037\pi$
$907$	−5.24264	+	12.6569i	−0.174079	+	0.420264i	0.812626	+	0.582786i	$0.198037\pi$
$908$		0			0
$909$	17.8284	−	17.8284i	0.591332	−	0.591332i
$910$		0			0
$911$	15.4853	+	6.41421i	0.513050	+	0.212512i	0.624161	−	0.781296i	$-0.285441\pi$
$911$	15.4853	+	6.41421i	0.513050	+	0.212512i	−0.111111	+	0.993808i	$0.535441\pi$
$912$		0			0
$913$	−49.1127	+	20.3431i	−1.62539	+	0.673260i
$914$		0			0
$915$	−13.0711	−	31.5563i	−0.432116	−	1.04322i
$916$		0			0
$917$	3.51472			0.116066
$918$		0			0
$919$	19.3137			0.637100			0.318550	−	0.947906i	$-0.396804\pi$
$919$	19.3137			0.637100			0.318550	+	0.947906i	$0.396804\pi$
$920$		0			0
$921$	−14.1421	−	34.1421i	−0.465999	−	1.12502i
$922$		0			0
$923$	−21.7574	+	9.01219i	−0.716152	+	0.296640i
$924$		0			0
$925$	−35.6777	−	14.7782i	−1.17307	−	0.485903i
$926$		0			0
$927$	−7.65685	+	7.65685i	−0.251484	+	0.251484i
$928$		0			0
$929$	−10.0503	+	24.2635i	−0.329738	+	0.796058i	0.668873	+	0.743376i	$0.266777\pi$
$929$	−10.0503	+	24.2635i	−0.329738	+	0.796058i	−0.998611	+	0.0526817i	$0.983223\pi$
$930$		0			0
$931$		−	44.6274i		−	1.46260i
$932$		0			0
$933$	−42.2843	−	42.2843i	−1.38432	−	1.38432i
$934$		0			0
$935$	36.4264	+	34.3431i	1.19127	+	1.12314i
$936$		0			0
$937$	9.14214	+	9.14214i	0.298661	+	0.298661i	0.840489	−	0.541829i	$-0.182268\pi$
$937$	9.14214	+	9.14214i	0.298661	+	0.298661i	−0.541829	+	0.840489i	$0.682268\pi$
$938$		0			0
$939$			24.1421i			0.787849i
$940$		0			0
$941$	−18.4350	+	44.5061i	−0.600965	+	1.45086i	0.271625	+	0.962403i	$0.412439\pi$
$941$	−18.4350	+	44.5061i	−0.600965	+	1.45086i	−0.872590	+	0.488454i	$0.837561\pi$
$942$		0			0
$943$	−41.2132	+	41.2132i	−1.34209	+	1.34209i
$944$		0			0
$945$	6.34315	+	2.62742i	0.206343	+	0.0854699i
$946$		0			0
$947$	−42.5563	+	17.6274i	−1.38290	+	0.572814i	−0.945254	−	0.326335i	$-0.894186\pi$
$947$	−42.5563	+	17.6274i	−1.38290	+	0.572814i	−0.437642	+	0.899150i	$0.644186\pi$
$948$		0			0
$949$	7.88730	+	19.0416i	0.256033	+	0.618117i
$950$		0			0
$951$	−48.6274			−1.57685
$952$		0			0
$953$	24.7279			0.801016			0.400508	−	0.916293i	$-0.368834\pi$
$953$	24.7279			0.801016			0.400508	+	0.916293i	$0.368834\pi$
$954$		0			0
$955$	−19.7990	−	47.7990i	−0.640680	−	1.54674i
$956$		0			0
$957$	−55.4558	+	22.9706i	−1.79263	+	0.742533i
$958$		0			0
$959$	−7.75736	−	3.21320i	−0.250498	−	0.103760i
$960$		0			0
$961$	21.0919	−	21.0919i	0.680383	−	0.680383i
$962$		0			0
$963$	−10.5563	+	25.4853i	−0.340174	+	0.821252i
$964$		0			0
$965$		−	5.95837i		−	0.191807i
$966$		0			0
$967$	9.07107	+	9.07107i	0.291706	+	0.291706i	0.837754	−	0.546048i	$-0.183868\pi$
$967$	9.07107	+	9.07107i	0.291706	+	0.291706i	−0.546048	+	0.837754i	$0.683868\pi$
$968$		0			0
$969$	33.7990	+	75.2548i	1.08578	+	2.41753i
$970$		0			0
$971$	36.2426	+	36.2426i	1.16308	+	1.16308i	0.983797	+	0.179284i	$0.0573782\pi$
$971$	36.2426	+	36.2426i	1.16308	+	1.16308i	0.179284	+	0.983797i	$0.442622\pi$
$972$		0			0
$973$			5.45584i			0.174906i
$974$		0			0
$975$	−9.27208	+	22.3848i	−0.296944	+	0.716887i
$976$		0			0
$977$	43.4853	−	43.4853i	1.39122	−	1.39122i	0.568611	−	0.822607i	$-0.307481\pi$
$977$	43.4853	−	43.4853i	1.39122	−	1.39122i	0.822607	−	0.568611i	$-0.192519\pi$
$978$		0			0
$979$	16.2426	+	6.72792i	0.519117	+	0.215025i
$980$		0			0
$981$	20.2635	−	8.39340i	0.646962	−	0.267981i
$982$		0			0
$983$	20.7990	+	50.2132i	0.663385	+	1.60155i	0.792464	+	0.609918i	$0.208798\pi$
$983$	20.7990	+	50.2132i	0.663385	+	1.60155i	−0.129080	+	0.991634i	$0.541202\pi$
$984$		0			0
$985$	59.5563			1.89762
$986$		0			0
$987$	3.31371			0.105477
$988$		0			0
$989$	−0.828427	−	2.00000i	−0.0263425	−	0.0635963i
$990$		0			0
$991$	10.3137	−	4.27208i	0.327626	−	0.135707i	−0.212807	−	0.977094i	$-0.568261\pi$
$991$	10.3137	−	4.27208i	0.327626	−	0.135707i	0.540433	+	0.841387i	$0.318261\pi$
$992$		0			0
$993$	45.7990	+	18.9706i	1.45339	+	0.602013i
$994$		0			0
$995$	−29.6985	+	29.6985i	−0.941505	+	0.941505i
$996$		0			0
$997$	10.6360	−	25.6777i	0.336847	−	0.813220i	−0.661168	−	0.750238i	$-0.729939\pi$
$997$	10.6360	−	25.6777i	0.336847	−	0.813220i	0.998015	−	0.0629820i	$-0.0200611\pi$
$998$		0			0
$999$			23.3137i			0.737613i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.2.n.b.49.1	yes	4
3.2	odd	2		1224.2.bq.b.865.1		4
4.3	odd	2		272.2.v.a.49.1		4
17.3	odd	16		2312.2.b.i.577.4		4
17.5	odd	16		2312.2.a.t.1.1		4
17.8	even	8	inner	136.2.n.b.25.1	✓	4
17.12	odd	16		2312.2.a.t.1.4		4
17.14	odd	16		2312.2.b.i.577.1		4
51.8	odd	8		1224.2.bq.b.433.1		4
68.39	even	16		4624.2.a.bo.1.4		4
68.59	odd	8		272.2.v.a.161.1		4
68.63	even	16		4624.2.a.bo.1.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.2.n.b.25.1	✓	4	17.8	even	8	inner
136.2.n.b.49.1	yes	4	1.1	even	1	trivial
272.2.v.a.49.1		4	4.3	odd	2
272.2.v.a.161.1		4	68.59	odd	8
1224.2.bq.b.433.1		4	51.8	odd	8
1224.2.bq.b.865.1		4	3.2	odd	2
2312.2.a.t.1.1		4	17.5	odd	16
2312.2.a.t.1.4		4	17.12	odd	16
2312.2.b.i.577.1		4	17.14	odd	16
2312.2.b.i.577.4		4	17.3	odd	16
4624.2.a.bo.1.1		4	68.63	even	16
4624.2.a.bo.1.4		4	68.39	even	16

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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	136.n (of order \(8\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 + 2.41421i) q^{3} +(-2.70711 + 1.12132i) q^{5} +(1.00000 + 0.414214i) q^{7} +(-2.70711 + 2.70711i) q^{9} +O(q^{10})\)	\(q+(1.00000 + 2.41421i) q^{3} +(-2.70711 + 1.12132i) q^{5} +(1.00000 + 0.414214i) q^{7} +(-2.70711 + 2.70711i) q^{9} +(1.58579 - 3.82843i) q^{11} +2.58579i q^{13} +(-5.41421 - 5.41421i) q^{15} +(2.82843 - 3.00000i) q^{17} +(5.41421 + 5.41421i) q^{19} +2.82843i q^{21} +(2.41421 - 5.82843i) q^{23} +(2.53553 - 2.53553i) q^{25} +(-2.00000 - 0.828427i) q^{27} +(-5.12132 + 2.12132i) q^{29} +(-0.414214 - 1.00000i) q^{31} +10.8284 q^{33} -3.17157 q^{35} +(-4.12132 - 9.94975i) q^{37} +(-6.24264 + 2.58579i) q^{39} +(-8.53553 - 3.53553i) q^{41} +(0.242641 - 0.242641i) q^{43} +(4.29289 - 10.3640i) q^{45} -1.17157i q^{47} +(-4.12132 - 4.12132i) q^{49} +(10.0711 + 3.82843i) q^{51} +(5.82843 + 5.82843i) q^{53} +12.1421i q^{55} +(-7.65685 + 18.4853i) q^{57} +(-5.07107 + 5.07107i) q^{59} +(4.12132 + 1.70711i) q^{61} +(-3.82843 + 1.58579i) q^{63} +(-2.89949 - 7.00000i) q^{65} -2.82843 q^{67} +16.4853 q^{69} +(3.48528 + 8.41421i) q^{71} +(7.36396 - 3.05025i) q^{73} +(8.65685 + 3.58579i) q^{75} +(3.17157 - 3.17157i) q^{77} +(1.58579 - 3.82843i) q^{79} +5.82843i q^{81} +(-9.07107 - 9.07107i) q^{83} +(-4.29289 + 11.2929i) q^{85} +(-10.2426 - 10.2426i) q^{87} +4.24264i q^{89} +(-1.07107 + 2.58579i) q^{91} +(2.00000 - 2.00000i) q^{93} +(-20.7279 - 8.58579i) q^{95} +(-4.12132 + 1.70711i) q^{97} +(6.07107 + 14.6569i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + 4 q^{3} - 8 q^{5} + 4 q^{7} - 8 q^{9}+O(q^{10}) \) 4 * q + 4 * q^3 - 8 * q^5 + 4 * q^7 - 8 * q^9	\( 4 q + 4 q^{3} - 8 q^{5} + 4 q^{7} - 8 q^{9} + 12 q^{11} - 16 q^{15} + 16 q^{19} + 4 q^{23} - 4 q^{25} - 8 q^{27} - 12 q^{29} + 4 q^{31} + 32 q^{33} - 24 q^{35} - 8 q^{37} - 8 q^{39} - 20 q^{41} - 16 q^{43} + 20 q^{45} - 8 q^{49} + 12 q^{51} + 12 q^{53} - 8 q^{57} + 8 q^{59} + 8 q^{61} - 4 q^{63} + 28 q^{65} + 32 q^{69} - 20 q^{71} + 4 q^{73} + 12 q^{75} + 24 q^{77} + 12 q^{79} - 8 q^{83} - 20 q^{85} - 24 q^{87} + 24 q^{91} + 8 q^{93} - 32 q^{95} - 8 q^{97} - 4 q^{99}+O(q^{100}) \) 4 * q + 4 * q^3 - 8 * q^5 + 4 * q^7 - 8 * q^9 + 12 * q^11 - 16 * q^15 + 16 * q^19 + 4 * q^23 - 4 * q^25 - 8 * q^27 - 12 * q^29 + 4 * q^31 + 32 * q^33 - 24 * q^35 - 8 * q^37 - 8 * q^39 - 20 * q^41 - 16 * q^43 + 20 * q^45 - 8 * q^49 + 12 * q^51 + 12 * q^53 - 8 * q^57 + 8 * q^59 + 8 * q^61 - 4 * q^63 + 28 * q^65 + 32 * q^69 - 20 * q^71 + 4 * q^73 + 12 * q^75 + 24 * q^77 + 12 * q^79 - 8 * q^83 - 20 * q^85 - 24 * q^87 + 24 * q^91 + 8 * q^93 - 32 * q^95 - 8 * q^97 - 4 * q^99

Introduction

L-functions

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