LMFDB - Embedded newform 136.4.k.b.81.6

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,4,Mod(81,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(4))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("136.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

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

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$8.02425976078$
Analytic rank:	$0$
Dimension:	$14$
Relative dimension:	$7$ over $\Q(i)$
Coefficient field:	$\mathbb{Q}[x]/(x^{14} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{14} + 119x^{12} + 5319x^{10} + 112122x^{8} + 1120191x^{6} + 4382607x^{4} + 1699337x^{2} + 2704 $ x^14 + 119x^12 + 5319x^10 + 112122x^8 + 1120191x^6 + 4382607x^4 + 1699337x^2 + 2704
Coefficient ring:	$\Z[a_1, \ldots, a_{9}]$
Coefficient ring index:	$ 2^{15}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			81.6
Root			$-3.80701i$ of defining polynomial
Character	$\chi$	$=$	136.81
Dual form			136.4.k.b.89.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(3.80701 + 3.80701i) q^{3} +(2.78003 + 2.78003i) q^{5} +(25.7370 - 25.7370i) q^{7} +1.98658i q^{9} +O(q^{10})$	\(q+(3.80701 + 3.80701i) q^{3} +(2.78003 + 2.78003i) q^{5} +(25.7370 - 25.7370i) q^{7} +1.98658i q^{9} +(-17.1786 + 17.1786i) q^{11} +71.6546 q^{13} +21.1672i q^{15} +(-34.3358 + 61.1069i) q^{17} +72.2853i q^{19} +195.962 q^{21} +(-90.8809 + 90.8809i) q^{23} -109.543i q^{25} +(95.2262 - 95.2262i) q^{27} +(-82.0612 - 82.0612i) q^{29} +(35.2724 + 35.2724i) q^{31} -130.798 q^{33} +143.099 q^{35} +(69.5253 + 69.5253i) q^{37} +(272.789 + 272.789i) q^{39} +(196.536 - 196.536i) q^{41} +344.162i q^{43} +(-5.52277 + 5.52277i) q^{45} -626.172 q^{47} -981.785i q^{49} +(-363.351 + 101.918i) q^{51} -145.329i q^{53} -95.5140 q^{55} +(-275.191 + 275.191i) q^{57} -454.009i q^{59} +(-179.197 + 179.197i) q^{61} +(51.1287 + 51.1287i) q^{63} +(199.202 + 199.202i) q^{65} -874.562 q^{67} -691.968 q^{69} +(58.6994 + 58.6994i) q^{71} +(-275.870 - 275.870i) q^{73} +(417.030 - 417.030i) q^{75} +884.249i q^{77} +(-464.841 + 464.841i) q^{79} +778.691 q^{81} +163.049i q^{83} +(-265.334 + 74.4246i) q^{85} -624.815i q^{87} -418.761 q^{89} +(1844.17 - 1844.17i) q^{91} +268.564i q^{93} +(-200.956 + 200.956i) q^{95} +(162.634 + 162.634i) q^{97} +(-34.1267 - 34.1267i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7}+O(q^{10}) $ 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7	$ 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7} - 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} - 162 q^{23} - 204 q^{27} + 158 q^{29} - 350 q^{31} + 116 q^{33} + 236 q^{35} + 582 q^{37} - 320 q^{39} + 878 q^{41} - 26 q^{45} - 448 q^{47} - 590 q^{51} + 1460 q^{55} + 292 q^{57} - 1130 q^{61} + 114 q^{63} + 20 q^{65} - 64 q^{67} + 2076 q^{69} - 3274 q^{71} - 1426 q^{73} + 946 q^{75} + 1718 q^{79} + 166 q^{81} - 2018 q^{85} + 476 q^{89} + 2128 q^{91} - 2444 q^{95} + 1926 q^{97} + 3870 q^{99}+O(q^{100}) $ 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7 - 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 - 162 * q^23 - 204 * q^27 + 158 * q^29 - 350 * q^31 + 116 * q^33 + 236 * q^35 + 582 * q^37 - 320 * q^39 + 878 * q^41 - 26 * q^45 - 448 * q^47 - 590 * q^51 + 1460 * q^55 + 292 * q^57 - 1130 * q^61 + 114 * q^63 + 20 * q^65 - 64 * q^67 + 2076 * q^69 - 3274 * q^71 - 1426 * q^73 + 946 * q^75 + 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 + 2128 * q^91 - 2444 * q^95 + 1926 * q^97 + 3870 * q^99

Display 100 coefficients 10 coefficients

Character values

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

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{1}{4}\right)$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		0			0
$2$		0			0
$3$	3.80701	+	3.80701i	0.732659	+	0.732659i	0.971146	−	0.238487i	$-0.0766515\pi$
$3$	3.80701	+	3.80701i	0.732659	+	0.732659i	−0.238487	+	0.971146i	$0.576651\pi$
$4$		0			0
$5$	2.78003	+	2.78003i	0.248654	+	0.248654i	0.820418	−	0.571764i	$-0.193741\pi$
$5$	2.78003	+	2.78003i	0.248654	+	0.248654i	−0.571764	+	0.820418i	$0.693741\pi$
$6$		0			0
$7$	25.7370	−	25.7370i	1.38967	−	1.38967i	0.563660	−	0.826007i	$-0.309393\pi$
$7$	25.7370	−	25.7370i	1.38967	−	1.38967i	0.826007	−	0.563660i	$-0.190607\pi$
$8$		0			0
$9$			1.98658i			0.0735772i
$10$		0			0
$11$	−17.1786	+	17.1786i	−0.470867	+	0.470867i	−0.902195	−	0.431328i	$-0.858045\pi$
$11$	−17.1786	+	17.1786i	−0.470867	+	0.470867i	0.431328	+	0.902195i	$0.358045\pi$
$12$		0			0
$13$	71.6546			1.52872			0.764362	−	0.644787i	$-0.223054\pi$
$13$	71.6546			1.52872			0.764362	+	0.644787i	$0.223054\pi$
$14$		0			0
$15$			21.1672i			0.364357i
$16$		0			0
$17$	−34.3358	+	61.1069i	−0.489862	+	0.871800i
$17$	−34.3358	+	61.1069i	−0.489862	+	0.871800i
$18$		0			0
$19$			72.2853i			0.872810i	0.899750	+	0.436405i	$0.143749\pi$
$19$			72.2853i			0.872810i	−0.899750	+	0.436405i	$0.856251\pi$
$20$		0			0
$21$	195.962			2.03630
$22$		0			0
$23$	−90.8809	+	90.8809i	−0.823912	+	0.823912i	−0.986667	−	0.162755i	$-0.947962\pi$
$23$	−90.8809	+	90.8809i	−0.823912	+	0.823912i	0.162755	+	0.986667i	$0.447962\pi$
$24$		0			0
$25$		−	109.543i		−	0.876343i
$26$		0			0
$27$	95.2262	−	95.2262i	0.678752	−	0.678752i
$28$		0			0
$29$	−82.0612	−	82.0612i	−0.525461	−	0.525461i	0.393754	−	0.919216i	$-0.371176\pi$
$29$	−82.0612	−	82.0612i	−0.525461	−	0.525461i	−0.919216	+	0.393754i	$0.871176\pi$
$30$		0			0
$31$	35.2724	+	35.2724i	0.204358	+	0.204358i	0.801864	−	0.597506i	$-0.203842\pi$
$31$	35.2724	+	35.2724i	0.204358	+	0.204358i	−0.597506	+	0.801864i	$0.703842\pi$
$32$		0			0
$33$	−130.798			−0.689969
$34$		0			0
$35$	143.099			0.691092
$36$		0			0
$37$	69.5253	+	69.5253i	0.308916	+	0.308916i	0.844489	−	0.535573i	$-0.179904\pi$
$37$	69.5253	+	69.5253i	0.308916	+	0.308916i	−0.535573	+	0.844489i	$0.679904\pi$
$38$		0			0
$39$	272.789	+	272.789i	1.12003	+	1.12003i
$40$		0			0
$41$	196.536	−	196.536i	0.748628	−	0.748628i	−0.225594	−	0.974221i	$-0.572432\pi$
$41$	196.536	−	196.536i	0.748628	−	0.748628i	0.974221	+	0.225594i	$0.0724322\pi$
$42$		0			0
$43$			344.162i			1.22056i	0.792185	+	0.610281i	$0.208943\pi$
$43$			344.162i			1.22056i	−0.792185	+	0.610281i	$0.791057\pi$
$44$		0			0
$45$	−5.52277	+	5.52277i	−0.0182953	+	0.0182953i
$46$		0			0
$47$	−626.172			−1.94333			−0.971665	−	0.236362i	$-0.924045\pi$
$47$	−626.172			−1.94333			−0.971665	+	0.236362i	$0.924045\pi$
$48$		0			0
$49$		−	981.785i		−	2.86235i
$50$		0			0
$51$	−363.351	+	101.918i	−0.997633	+	0.279830i
$52$		0			0
$53$		−	145.329i		−	0.376651i	−0.982107	−	0.188326i	$-0.939694\pi$
$53$		−	145.329i		−	0.376651i	0.982107	−	0.188326i	$-0.0603060\pi$
$54$		0			0
$55$	−95.5140			−0.234166
$56$		0			0
$57$	−275.191	+	275.191i	−0.639472	+	0.639472i
$58$		0			0
$59$		−	454.009i		−	1.00181i	−0.865502	−	0.500906i	$-0.833000\pi$
$59$		−	454.009i		−	1.00181i	0.865502	−	0.500906i	$-0.167000\pi$
$60$		0			0
$61$	−179.197	+	179.197i	−0.376129	+	0.376129i	−0.869703	−	0.493575i	$-0.835690\pi$
$61$	−179.197	+	179.197i	−0.376129	+	0.376129i	0.493575	+	0.869703i	$0.335690\pi$
$62$		0			0
$63$	51.1287	+	51.1287i	0.102248	+	0.102248i
$64$		0			0
$65$	199.202	+	199.202i	0.380123	+	0.380123i
$66$		0			0
$67$	−874.562			−1.59470			−0.797349	−	0.603518i	$-0.793765\pi$
$67$	−874.562			−1.59470			−0.797349	+	0.603518i	$0.793765\pi$
$68$		0			0
$69$	−691.968			−1.20729
$70$		0			0
$71$	58.6994	+	58.6994i	0.0981174	+	0.0981174i	0.754462	−	0.656344i	$-0.227898\pi$
$71$	58.6994	+	58.6994i	0.0981174	+	0.0981174i	−0.656344	+	0.754462i	$0.727898\pi$
$72$		0			0
$73$	−275.870	−	275.870i	−0.442303	−	0.442303i	0.450482	−	0.892785i	$-0.351252\pi$
$73$	−275.870	−	275.870i	−0.442303	−	0.442303i	−0.892785	+	0.450482i	$0.851252\pi$
$74$		0			0
$75$	417.030	−	417.030i	0.642060	−	0.642060i
$76$		0			0
$77$			884.249i			1.30870i
$78$		0			0
$79$	−464.841	+	464.841i	−0.662009	+	0.662009i	−0.955853	−	0.293844i	$-0.905065\pi$
$79$	−464.841	+	464.841i	−0.662009	+	0.662009i	0.293844	+	0.955853i	$0.405065\pi$
$80$		0			0
$81$	778.691			1.06816
$82$		0			0
$83$			163.049i			0.215626i	0.994171	+	0.107813i	$0.0343848\pi$
$83$			163.049i			0.215626i	−0.994171	+	0.107813i	$0.965615\pi$
$84$		0			0
$85$	−265.334	+	74.4246i	−0.338582	+	0.0949703i
$86$		0			0
$87$		−	624.815i		−	0.769968i
$88$		0			0
$89$	−418.761			−0.498748			−0.249374	−	0.968407i	$-0.580225\pi$
$89$	−418.761			−0.498748			−0.249374	+	0.968407i	$0.580225\pi$
$90$		0			0
$91$	1844.17	−	1844.17i	2.12442	−	2.12442i
$92$		0			0
$93$			268.564i			0.299450i
$94$		0			0
$95$	−200.956	+	200.956i	−0.217028	+	0.217028i
$96$		0			0
$97$	162.634	+	162.634i	0.170237	+	0.170237i	0.787084	−	0.616846i	$-0.211590\pi$
$97$	162.634	+	162.634i	0.170237	+	0.170237i	−0.616846	+	0.787084i	$0.711590\pi$
$98$		0			0
$99$	−34.1267	−	34.1267i	−0.0346451	−	0.0346451i
$100$		0			0
$101$	1060.55			1.04484			0.522420	−	0.852689i	$-0.325029\pi$
$101$	1060.55			1.04484			0.522420	+	0.852689i	$0.325029\pi$
$102$		0			0
$103$	671.076			0.641972			0.320986	−	0.947084i	$-0.395986\pi$
$103$	671.076			0.641972			0.320986	+	0.947084i	$0.395986\pi$
$104$		0			0
$105$	544.780	+	544.780i	0.506334	+	0.506334i
$106$		0			0
$107$	−175.136	−	175.136i	−0.158234	−	0.158234i	0.623550	−	0.781784i	$-0.285690\pi$
$107$	−175.136	−	175.136i	−0.158234	−	0.158234i	−0.781784	+	0.623550i	$0.785690\pi$
$108$		0			0
$109$	509.552	−	509.552i	0.447764	−	0.447764i	−0.446847	−	0.894611i	$-0.647453\pi$
$109$	509.552	−	509.552i	0.447764	−	0.447764i	0.894611	+	0.446847i	$0.147453\pi$
$110$		0			0
$111$			529.366i			0.452660i
$112$		0			0
$113$	−208.993	+	208.993i	−0.173986	+	0.173986i	−0.788728	−	0.614742i	$-0.789260\pi$
$113$	−208.993	+	208.993i	−0.173986	+	0.173986i	0.614742	+	0.788728i	$0.289260\pi$
$114$		0			0
$115$	−505.304			−0.409738
$116$		0			0
$117$			142.348i			0.112479i
$118$		0			0
$119$	689.008	+	2456.41i	0.530767	+	1.89226i
$120$		0			0
$121$			740.793i			0.556569i
$122$		0			0
$123$	1496.43			1.09698
$124$		0			0
$125$	652.037	−	652.037i	0.466560	−	0.466560i
$126$		0			0
$127$		−	450.551i		−	0.314803i	−0.987535	−	0.157401i	$-0.949688\pi$
$127$		−	450.551i		−	0.314803i	0.987535	−	0.157401i	$-0.0503117\pi$
$128$		0			0
$129$	−1310.22	+	1310.22i	−0.894255	+	0.894255i
$130$		0			0
$131$	562.452	+	562.452i	0.375127	+	0.375127i	0.869341	−	0.494213i	$-0.164544\pi$
$131$	562.452	+	562.452i	0.375127	+	0.375127i	−0.494213	+	0.869341i	$0.664544\pi$
$132$		0			0
$133$	1860.41	+	1860.41i	1.21292	+	1.21292i
$134$		0			0
$135$	529.464			0.337548
$136$		0			0
$137$	−1480.25			−0.923109			−0.461555	−	0.887112i	$-0.652708\pi$
$137$	−1480.25			−0.923109			−0.461555	+	0.887112i	$0.652708\pi$
$138$		0			0
$139$	−2213.66	−	2213.66i	−1.35079	−	1.35079i	−0.884776	−	0.466017i	$-0.845689\pi$
$139$	−2213.66	−	2213.66i	−1.35079	−	1.35079i	−0.466017	−	0.884776i	$-0.654311\pi$
$140$		0			0
$141$	−2383.84	−	2383.84i	−1.42380	−	1.42380i
$142$		0			0
$143$	−1230.92	+	1230.92i	−0.719825	+	0.719825i
$144$		0			0
$145$		−	456.266i		−	0.261316i
$146$		0			0
$147$	3737.66	−	3737.66i	2.09712	−	2.09712i
$148$		0			0
$149$	−2885.80			−1.58667			−0.793336	−	0.608784i	$-0.791658\pi$
$149$	−2885.80			−1.58667			−0.793336	+	0.608784i	$0.791658\pi$
$150$		0			0
$151$			1037.68i			0.559239i	0.960111	+	0.279619i	$0.0902083\pi$
$151$			1037.68i			0.559239i	−0.960111	+	0.279619i	$0.909792\pi$
$152$		0			0
$153$	−121.394	−	68.2110i	−0.0641446	−	0.0360427i
$154$		0			0
$155$			196.117i			0.101629i
$156$		0			0
$157$	3420.64			1.73883			0.869415	−	0.494082i	$-0.164496\pi$
$157$	3420.64			1.73883			0.869415	+	0.494082i	$0.164496\pi$
$158$		0			0
$159$	553.269	−	553.269i	0.275957	−	0.275957i
$160$		0			0
$161$			4678.00i			2.28993i
$162$		0			0
$163$	−57.4644	+	57.4644i	−0.0276132	+	0.0276132i	−0.720779	−	0.693165i	$-0.756216\pi$
$163$	−57.4644	+	57.4644i	−0.0276132	+	0.0276132i	0.693165	+	0.720779i	$0.256216\pi$
$164$		0			0
$165$	−363.622	−	363.622i	−0.171563	−	0.171563i
$166$		0			0
$167$	857.266	+	857.266i	0.397229	+	0.397229i	0.877255	−	0.480025i	$-0.159373\pi$
$167$	857.266	+	857.266i	0.397229	+	0.397229i	−0.480025	+	0.877255i	$0.659373\pi$
$168$		0			0
$169$	2937.38			1.33700
$170$		0			0
$171$	−143.601			−0.0642189
$172$		0			0
$173$	−1010.59	−	1010.59i	−0.444127	−	0.444127i	0.449269	−	0.893396i	$-0.351684\pi$
$173$	−1010.59	−	1010.59i	−0.444127	−	0.444127i	−0.893396	+	0.449269i	$0.851684\pi$
$174$		0			0
$175$	−2819.30	−	2819.30i	−1.21782	−	1.21782i
$176$		0			0
$177$	1728.41	−	1728.41i	0.733986	−	0.733986i
$178$		0			0
$179$			1950.92i			0.814629i	0.913288	+	0.407315i	$0.133535\pi$
$179$			1950.92i			0.814629i	−0.913288	+	0.407315i	$0.866465\pi$
$180$		0			0
$181$	−1850.30	+	1850.30i	−0.759844	+	0.759844i	−0.976294	−	0.216449i	$-0.930552\pi$
$181$	−1850.30	+	1850.30i	−0.759844	+	0.759844i	0.216449	+	0.976294i	$0.430552\pi$
$182$		0			0
$183$	−1364.41			−0.551148
$184$		0			0
$185$			386.565i			0.153626i
$186$		0			0
$187$	−459.889	−	1639.57i	−0.179842	−	0.641161i
$188$		0			0
$189$		−	4901.67i		−	1.88648i
$190$		0			0
$191$	−2192.73			−0.830683			−0.415342	−	0.909665i	$-0.636338\pi$
$191$	−2192.73			−0.830683			−0.415342	+	0.909665i	$0.636338\pi$
$192$		0			0
$193$	70.8011	−	70.8011i	0.0264061	−	0.0264061i	−0.693780	−	0.720187i	$-0.744056\pi$
$193$	70.8011	−	70.8011i	0.0264061	−	0.0264061i	0.720187	+	0.693780i	$0.244056\pi$
$194$		0			0
$195$			1516.73i			0.557001i
$196$		0			0
$197$	−566.472	+	566.472i	−0.204870	+	0.204870i	−0.802083	−	0.597213i	$-0.796275\pi$
$197$	−566.472	+	566.472i	−0.204870	+	0.204870i	0.597213	+	0.802083i	$0.296275\pi$
$198$		0			0
$199$	−790.293	−	790.293i	−0.281519	−	0.281519i	0.552195	−	0.833715i	$-0.313790\pi$
$199$	−790.293	−	790.293i	−0.281519	−	0.281519i	−0.833715	+	0.552195i	$0.813790\pi$
$200$		0			0
$201$	−3329.46	−	3329.46i	−1.16837	−	1.16837i
$202$		0			0
$203$	−4224.02			−1.46043
$204$		0			0
$205$	1092.75			0.372298
$206$		0			0
$207$	−180.543	−	180.543i	−0.0606211	−	0.0606211i
$208$		0			0
$209$	−1241.76	−	1241.76i	−0.410977	−	0.410977i
$210$		0			0
$211$	399.006	−	399.006i	0.130183	−	0.130183i	−0.639013	−	0.769196i	$-0.720657\pi$
$211$	399.006	−	399.006i	0.130183	−	0.130183i	0.769196	+	0.639013i	$0.220657\pi$
$212$		0			0
$213$			446.938i			0.143773i
$214$		0			0
$215$	−956.781	+	956.781i	−0.303497	+	0.303497i
$216$		0			0
$217$	1815.61			0.567980
$218$		0			0
$219$		−	2100.48i		−	0.648114i
$220$		0			0
$221$	−2460.32	+	4378.59i	−0.748864	+	1.33274i
$222$		0			0
$223$			5051.79i			1.51701i	0.651667	+	0.758505i	$0.274070\pi$
$223$			5051.79i			1.51701i	−0.651667	+	0.758505i	$0.725930\pi$
$224$		0			0
$225$	217.616			0.0644788
$226$		0			0
$227$	202.315	−	202.315i	0.0591547	−	0.0591547i	−0.676911	−	0.736065i	$-0.736682\pi$
$227$	202.315	−	202.315i	0.0591547	−	0.0591547i	0.736065	+	0.676911i	$0.236682\pi$
$228$		0			0
$229$		−	2265.18i		−	0.653657i	−0.945084	−	0.326828i	$-0.894020\pi$
$229$		−	2265.18i		−	0.653657i	0.945084	−	0.326828i	$-0.105980\pi$
$230$		0			0
$231$	−3366.34	+	3366.34i	−0.958827	+	0.958827i
$232$		0			0
$233$	3776.51	+	3776.51i	1.06184	+	1.06184i	0.997958	+	0.0638776i	$0.0203467\pi$
$233$	3776.51	+	3776.51i	1.06184	+	1.06184i	0.0638776	+	0.997958i	$0.479653\pi$
$234$		0			0
$235$	−1740.78	−	1740.78i	−0.483216	−	0.483216i
$236$		0			0
$237$	−3539.31			−0.970053
$238$		0			0
$239$	7017.70			1.89932			0.949660	−	0.313284i	$-0.101429\pi$
$239$	7017.70			1.89932			0.949660	+	0.313284i	$0.101429\pi$
$240$		0			0
$241$	−3368.64	−	3368.64i	−0.900386	−	0.900386i	0.0950830	−	0.995469i	$-0.469688\pi$
$241$	−3368.64	−	3368.64i	−0.900386	−	0.900386i	−0.995469	+	0.0950830i	$0.969688\pi$
$242$		0			0
$243$	393.374	+	393.374i	0.103848	+	0.103848i
$244$		0			0
$245$	2729.40	−	2729.40i	0.711734	−	0.711734i
$246$		0			0
$247$			5179.58i			1.33429i
$248$		0			0
$249$	−620.729	+	620.729i	−0.157980	+	0.157980i
$250$		0			0
$251$	6592.92			1.65793			0.828967	−	0.559298i	$-0.188929\pi$
$251$	6592.92			1.65793			0.828967	+	0.559298i	$0.188929\pi$
$252$		0			0
$253$		−	3122.41i		−	0.775905i
$254$		0			0
$255$	−1293.46	−	726.793i	−0.317646	−	0.178484i
$256$		0			0
$257$		−	6128.40i		−	1.48747i	−0.668476	−	0.743734i	$-0.733053\pi$
$257$		−	6128.40i		−	1.48747i	0.668476	−	0.743734i	$-0.266947\pi$
$258$		0			0
$259$	3578.74			0.858580
$260$		0			0
$261$	163.022	−	163.022i	0.0386620	−	0.0386620i
$262$		0			0
$263$			6142.19i			1.44009i	0.693927	+	0.720045i	$0.255879\pi$
$263$			6142.19i			1.44009i	−0.693927	+	0.720045i	$0.744121\pi$
$264$		0			0
$265$	404.020	−	404.020i	0.0936557	−	0.0936557i
$266$		0			0
$267$	−1594.22	−	1594.22i	−0.365412	−	0.365412i
$268$		0			0
$269$	831.758	+	831.758i	0.188525	+	0.188525i	0.795058	−	0.606533i	$-0.207440\pi$
$269$	831.758	+	831.758i	0.188525	+	0.188525i	−0.606533	+	0.795058i	$0.707440\pi$
$270$		0			0
$271$	−2498.30			−0.560004			−0.280002	−	0.959999i	$-0.590335\pi$
$271$	−2498.30			−0.560004			−0.280002	+	0.959999i	$0.590335\pi$
$272$		0			0
$273$	14041.6			3.11294
$274$		0			0
$275$	1881.79	+	1881.79i	0.412641	+	0.412641i
$276$		0			0
$277$	3640.10	+	3640.10i	0.789576	+	0.789576i	0.981425	−	0.191848i	$-0.0614482\pi$
$277$	3640.10	+	3640.10i	0.789576	+	0.789576i	−0.191848	+	0.981425i	$0.561448\pi$
$278$		0			0
$279$	−70.0716	+	70.0716i	−0.0150361	+	0.0150361i
$280$		0			0
$281$		−	3355.18i		−	0.712290i	−0.934431	−	0.356145i	$-0.884091\pi$
$281$		−	3355.18i		−	0.712290i	0.934431	−	0.356145i	$-0.115909\pi$
$282$		0			0
$283$	−1847.55	+	1847.55i	−0.388076	+	0.388076i	−0.874001	−	0.485925i	$-0.838483\pi$
$283$	−1847.55	+	1847.55i	−0.388076	+	0.388076i	0.485925	+	0.874001i	$0.338483\pi$
$284$		0			0
$285$	−1530.08			−0.318014
$286$		0			0
$287$		−	10116.5i		−	2.08069i
$288$		0			0
$289$	−2555.11	−	4196.31i	−0.520070	−	0.854123i
$290$		0			0
$291$			1238.30i			0.249452i
$292$		0			0
$293$	−1683.63			−0.335695			−0.167848	−	0.985813i	$-0.553682\pi$
$293$	−1683.63			−0.335695			−0.167848	+	0.985813i	$0.553682\pi$
$294$		0			0
$295$	1262.16	−	1262.16i	0.249104	−	0.249104i
$296$		0			0
$297$			3271.70i			0.639203i
$298$		0			0
$299$	−6512.03	+	6512.03i	−1.25953	+	1.25953i
$300$		0			0
$301$	8857.68	+	8857.68i	1.69617	+	1.69617i
$302$		0			0
$303$	4037.52	+	4037.52i	0.765511	+	0.765511i
$304$		0			0
$305$	−996.348			−0.187052
$306$		0			0
$307$	5864.67			1.09028			0.545138	−	0.838346i	$-0.316477\pi$
$307$	5864.67			1.09028			0.545138	+	0.838346i	$0.316477\pi$
$308$		0			0
$309$	2554.79	+	2554.79i	0.470346	+	0.470346i
$310$		0			0
$311$	4507.41	+	4507.41i	0.821838	+	0.821838i	0.986371	−	0.164534i	$-0.0526119\pi$
$311$	4507.41	+	4507.41i	0.821838	+	0.821838i	−0.164534	+	0.986371i	$0.552612\pi$
$312$		0			0
$313$	−2339.52	+	2339.52i	−0.422484	+	0.422484i	−0.886058	−	0.463574i	$-0.846567\pi$
$313$	−2339.52	+	2339.52i	−0.422484	+	0.422484i	0.463574	+	0.886058i	$0.346567\pi$
$314$		0			0
$315$			284.279i			0.0508486i
$316$		0			0
$317$	5257.60	−	5257.60i	0.931534	−	0.931534i	−0.0662682	−	0.997802i	$-0.521109\pi$
$317$	5257.60	−	5257.60i	0.931534	−	0.931534i	0.997802	+	0.0662682i	$0.0211093\pi$
$318$		0			0
$319$	2819.39			0.494845
$320$		0			0
$321$		−	1333.49i		−	0.231863i
$322$		0			0
$323$	−4417.13	−	2481.97i	−0.760916	−	0.427556i
$324$		0			0
$325$		−	7849.25i		−	1.33969i
$326$		0			0
$327$	3879.74			0.656116
$328$		0			0
$329$	−16115.8	+	16115.8i	−2.70058	+	2.70058i
$330$		0			0
$331$			953.626i			0.158356i	0.996860	+	0.0791782i	$0.0252296\pi$
$331$			953.626i			0.158356i	−0.996860	+	0.0791782i	$0.974770\pi$
$332$		0			0
$333$	−138.118	+	138.118i	−0.0227292	+	0.0227292i
$334$		0			0
$335$	−2431.31	−	2431.31i	−0.396528	−	0.396528i
$336$		0			0
$337$	−6649.51	−	6649.51i	−1.07484	−	1.07484i	−0.996963	−	0.0778798i	$-0.975185\pi$
$337$	−6649.51	−	6649.51i	−1.07484	−	1.07484i	−0.0778798	−	0.996963i	$-0.524815\pi$
$338$		0			0
$339$	−1591.27			−0.254944
$340$		0			0
$341$	−1211.86			−0.192451
$342$		0			0
$343$	−16440.4	−	16440.4i	−2.58804	−	2.58804i
$344$		0			0
$345$	−1923.69	−	1923.69i	−0.300198	−	0.300198i
$346$		0			0
$347$	7319.13	−	7319.13i	1.13231	−	1.13231i	0.142518	−	0.989792i	$-0.454480\pi$
$347$	7319.13	−	7319.13i	1.13231	−	1.13231i	0.989792	−	0.142518i	$-0.0455200\pi$
$348$		0			0
$349$			9266.42i			1.42126i	0.703566	+	0.710630i	$0.251590\pi$
$349$			9266.42i			1.42126i	−0.703566	+	0.710630i	$0.748410\pi$
$350$		0			0
$351$	6823.40	−	6823.40i	1.03762	−	1.03762i
$352$		0			0
$353$	3315.92			0.499968			0.249984	−	0.968250i	$-0.419575\pi$
$353$	3315.92			0.499968			0.249984	+	0.968250i	$0.419575\pi$
$354$		0			0
$355$			326.373i			0.0487945i
$356$		0			0
$357$	−6728.50	+	11974.6i	−0.997507	+	1.77525i
$358$		0			0
$359$			5654.75i			0.831327i	0.909518	+	0.415664i	$0.136451\pi$
$359$			5654.75i			0.831327i	−0.909518	+	0.415664i	$0.863549\pi$
$360$		0			0
$361$	1633.83			0.238203
$362$		0			0
$363$	−2820.21	+	2820.21i	−0.407775	+	0.407775i
$364$		0			0
$365$		−	1533.85i		−	0.219961i
$366$		0			0
$367$	−9.03278	+	9.03278i	−0.00128476	+	0.00128476i	−0.707749	−	0.706464i	$-0.750289\pi$
$367$	−9.03278	+	9.03278i	−0.00128476	+	0.00128476i	0.706464	+	0.707749i	$0.250289\pi$
$368$		0			0
$369$	390.435	+	390.435i	0.0550820	+	0.0550820i
$370$		0			0
$371$	−3740.34	−	3740.34i	−0.523419	−	0.523419i
$372$		0			0
$373$	2955.39			0.410252			0.205126	−	0.978736i	$-0.434240\pi$
$373$	2955.39			0.410252			0.205126	+	0.978736i	$0.434240\pi$
$374$		0			0
$375$	4964.62			0.683658
$376$		0			0
$377$	−5880.06	−	5880.06i	−0.803286	−	0.803286i
$378$		0			0
$379$	−3054.12	−	3054.12i	−0.413931	−	0.413931i	0.469175	−	0.883105i	$-0.344552\pi$
$379$	−3054.12	−	3054.12i	−0.413931	−	0.413931i	−0.883105	+	0.469175i	$0.844552\pi$
$380$		0			0
$381$	1715.25	−	1715.25i	0.230643	−	0.230643i
$382$		0			0
$383$		−	5788.94i		−	0.772326i	−0.922431	−	0.386163i	$-0.873800\pi$
$383$		−	5788.94i		−	0.772326i	0.922431	−	0.386163i	$-0.126200\pi$
$384$		0			0
$385$	−2458.24	+	2458.24i	−0.325412	+	0.325412i
$386$		0			0
$387$	−683.706			−0.0898055
$388$		0			0
$389$			10329.9i			1.34640i	0.739462	+	0.673198i	$0.235080\pi$
$389$			10329.9i			1.34640i	−0.739462	+	0.673198i	$0.764920\pi$
$390$		0			0
$391$	−2432.98	−	8673.92i	−0.314683	−	1.12189i
$392$		0			0
$393$			4282.51i			0.549680i
$394$		0			0
$395$	−2584.55			−0.329222
$396$		0			0
$397$	7727.58	−	7727.58i	0.976917	−	0.976917i	−0.0228226	−	0.999740i	$-0.507265\pi$
$397$	7727.58	−	7727.58i	0.976917	−	0.976917i	0.999740	+	0.0228226i	$0.00726530\pi$
$398$		0			0
$399$			14165.2i			1.77731i
$400$		0			0
$401$	−4285.93	+	4285.93i	−0.533739	+	0.533739i	−0.921683	−	0.387944i	$-0.873185\pi$
$401$	−4285.93	+	4285.93i	−0.533739	+	0.533739i	0.387944	+	0.921683i	$0.373185\pi$
$402$		0			0
$403$	2527.43	+	2527.43i	0.312407	+	0.312407i
$404$		0			0
$405$	2164.79	+	2164.79i	0.265603	+	0.265603i
$406$		0			0
$407$	−2388.69			−0.290916
$408$		0			0
$409$	12598.8			1.52316			0.761580	−	0.648071i	$-0.224424\pi$
$409$	12598.8			1.52316			0.761580	+	0.648071i	$0.224424\pi$
$410$		0			0
$411$	−5635.31	−	5635.31i	−0.676324	−	0.676324i
$412$		0			0
$413$	−11684.8	−	11684.8i	−1.39219	−	1.39219i
$414$		0			0
$415$	−453.282	+	453.282i	−0.0536162	+	0.0536162i
$416$		0			0
$417$		−	16854.8i		−	1.97934i
$418$		0			0
$419$	1462.63	−	1462.63i	0.170536	−	0.170536i	−0.616679	−	0.787215i	$-0.711522\pi$
$419$	1462.63	−	1462.63i	0.170536	−	0.170536i	0.787215	+	0.616679i	$0.211522\pi$
$420$		0			0
$421$	−7194.58			−0.832880			−0.416440	−	0.909163i	$-0.636722\pi$
$421$	−7194.58			−0.832880			−0.416440	+	0.909163i	$0.636722\pi$
$422$		0			0
$423$		−	1243.94i		−	0.142985i
$424$		0			0
$425$	6693.82	+	3761.24i	0.763995	+	0.429287i
$426$		0			0
$427$			9223.99i			1.04539i
$428$		0			0
$429$	−9372.27			−1.05477
$430$		0			0
$431$	9683.60	−	9683.60i	1.08223	−	1.08223i	0.0859325	−	0.996301i	$-0.472613\pi$
$431$	9683.60	−	9683.60i	1.08223	−	1.08223i	0.996301	−	0.0859325i	$-0.0273869\pi$
$432$		0			0
$433$			12504.4i			1.38782i	0.720063	+	0.693909i	$0.244113\pi$
$433$			12504.4i			1.38782i	−0.720063	+	0.693909i	$0.755887\pi$
$434$		0			0
$435$	1737.01	−	1737.01i	0.191455	−	0.191455i
$436$		0			0
$437$	−6569.35	−	6569.35i	−0.719119	−	0.719119i
$438$		0			0
$439$	−9878.38	−	9878.38i	−1.07396	−	1.07396i	−0.997037	−	0.0769257i	$-0.975490\pi$
$439$	−9878.38	−	9878.38i	−1.07396	−	1.07396i	−0.0769257	−	0.997037i	$-0.524510\pi$
$440$		0			0
$441$	1950.40			0.210604
$442$		0			0
$443$	829.809			0.0889964			0.0444982	−	0.999009i	$-0.485831\pi$
$443$	829.809			0.0889964			0.0444982	+	0.999009i	$0.485831\pi$
$444$		0			0
$445$	−1164.17	−	1164.17i	−0.124016	−	0.124016i
$446$		0			0
$447$	−10986.3	−	10986.3i	−1.16249	−	1.16249i
$448$		0			0
$449$	5937.37	−	5937.37i	0.624057	−	0.624057i	−0.322509	−	0.946566i	$-0.604526\pi$
$449$	5937.37	−	5937.37i	0.624057	−	0.624057i	0.946566	+	0.322509i	$0.104526\pi$
$450$		0			0
$451$			6752.41i			0.705008i
$452$		0			0
$453$	−3950.45	+	3950.45i	−0.409731	+	0.409731i
$454$		0			0
$455$	10253.7			1.05649
$456$		0			0
$457$			4013.92i			0.410861i	0.978672	+	0.205430i	$0.0658594\pi$
$457$			4013.92i			0.410861i	−0.978672	+	0.205430i	$0.934141\pi$
$458$		0			0
$459$	2549.31	+	9088.65i	0.259241	+	0.924230i
$460$		0			0
$461$		−	9576.45i		−	0.967505i	−0.875205	−	0.483753i	$-0.839273\pi$
$461$		−	9576.45i		−	0.967505i	0.875205	−	0.483753i	$-0.160727\pi$
$462$		0			0
$463$	8366.78			0.839822			0.419911	−	0.907565i	$-0.362061\pi$
$463$	8366.78			0.839822			0.419911	+	0.907565i	$0.362061\pi$
$464$		0			0
$465$	−746.618	+	746.618i	−0.0744593	+	0.0744593i
$466$		0			0
$467$			8324.94i			0.824909i	0.910978	+	0.412454i	$0.135328\pi$
$467$			8324.94i			0.824909i	−0.910978	+	0.412454i	$0.864672\pi$
$468$		0			0
$469$	−22508.6	+	22508.6i	−2.21610	+	2.21610i
$470$		0			0
$471$	13022.4	+	13022.4i	1.27397	+	1.27397i
$472$		0			0
$473$	−5912.20	−	5912.20i	−0.574722	−	0.574722i
$474$		0			0
$475$	7918.34			0.764881
$476$		0			0
$477$	288.709			0.0277129
$478$		0			0
$479$	−619.058	−	619.058i	−0.0590511	−	0.0590511i	0.676965	−	0.736016i	$-0.263295\pi$
$479$	−619.058	−	619.058i	−0.0590511	−	0.0590511i	−0.736016	+	0.676965i	$0.763295\pi$
$480$		0			0
$481$	4981.81	+	4981.81i	0.472247	+	0.472247i
$482$		0			0
$483$	−17809.2	+	17809.2i	−1.67773	+	1.67773i
$484$		0			0
$485$			904.258i			0.0846603i
$486$		0			0
$487$	2801.50	−	2801.50i	0.260674	−	0.260674i	−0.564654	−	0.825328i	$-0.690990\pi$
$487$	2801.50	−	2801.50i	0.260674	−	0.260674i	0.825328	+	0.564654i	$0.190990\pi$
$488$		0			0
$489$	−437.534			−0.0404621
$490$		0			0
$491$		−	5348.65i		−	0.491611i	−0.969319	−	0.245806i	$-0.920947\pi$
$491$		−	5348.65i		−	0.491611i	0.969319	−	0.245806i	$-0.0790525\pi$
$492$		0			0
$493$	7832.14	−	2196.87i	0.715501	−	0.200694i
$494$		0			0
$495$		−	189.747i		−	0.0172293i
$496$		0			0
$497$	3021.49			0.272701
$498$		0			0
$499$	−2291.68	+	2291.68i	−0.205591	+	0.205591i	−0.802390	−	0.596800i	$-0.796439\pi$
$499$	−2291.68	+	2291.68i	−0.205591	+	0.205591i	0.596800	+	0.802390i	$0.296439\pi$
$500$		0			0
$501$			6527.23i			0.582067i
$502$		0			0
$503$	12161.4	−	12161.4i	1.07803	−	1.07803i	0.0813446	−	0.996686i	$-0.474079\pi$
$503$	12161.4	−	12161.4i	1.07803	−	1.07803i	0.996686	−	0.0813446i	$-0.0259214\pi$
$504$		0			0
$505$	2948.37	+	2948.37i	0.259803	+	0.259803i
$506$		0			0
$507$	11182.6	+	11182.6i	0.979562	+	0.979562i
$508$		0			0
$509$	19542.7			1.70179			0.850897	−	0.525333i	$-0.176059\pi$
$509$	19542.7			1.70179			0.850897	+	0.525333i	$0.176059\pi$
$510$		0			0
$511$	−14200.1			−1.22931
$512$		0			0
$513$	6883.46	+	6883.46i	0.592421	+	0.592421i
$514$		0			0
$515$	1865.61	+	1865.61i	0.159629	+	0.159629i
$516$		0			0
$517$	10756.7	−	10756.7i	0.915049	−	0.915049i
$518$		0			0
$519$		−	7694.67i		−	0.650787i
$520$		0			0
$521$	13819.8	−	13819.8i	1.16211	−	1.16211i	0.178093	−	0.984014i	$-0.443007\pi$
$521$	13819.8	−	13819.8i	1.16211	−	1.16211i	0.984014	−	0.178093i	$-0.0569926\pi$
$522$		0			0
$523$	−13396.9			−1.12009			−0.560044	−	0.828463i	$-0.689216\pi$
$523$	−13396.9			−1.12009			−0.560044	+	0.828463i	$0.689216\pi$
$524$		0			0
$525$		−	21466.2i		−	1.78450i
$526$		0			0
$527$	−3366.49	+	944.281i	−0.278267	+	0.0780522i
$528$		0			0
$529$		−	4351.67i		−	0.357662i
$530$		0			0
$531$	901.927			0.0737106
$532$		0			0
$533$	14082.7	−	14082.7i	1.14445	−	1.14445i
$534$		0			0
$535$		−	973.770i		−	0.0786911i
$536$		0			0
$537$	−7427.16	+	7427.16i	−0.596845	+	0.596845i
$538$		0			0
$539$	16865.7	+	16865.7i	1.34778	+	1.34778i
$540$		0			0
$541$	7739.88	+	7739.88i	0.615090	+	0.615090i	0.944268	−	0.329178i	$-0.106772\pi$
$541$	7739.88	+	7739.88i	0.615090	+	0.615090i	−0.329178	+	0.944268i	$0.606772\pi$
$542$		0			0
$543$	−14088.2			−1.11341
$544$		0			0
$545$	2833.15			0.222676
$546$		0			0
$547$	−8933.89	−	8933.89i	−0.698328	−	0.698328i	0.265722	−	0.964050i	$-0.414390\pi$
$547$	−8933.89	−	8933.89i	−0.698328	−	0.698328i	−0.964050	+	0.265722i	$0.914390\pi$
$548$		0			0
$549$	−355.990	−	355.990i	−0.0276745	−	0.0276745i
$550$		0			0
$551$	5931.82	−	5931.82i	0.458628	−	0.458628i
$552$		0			0
$553$			23927.2i			1.83994i
$554$		0			0
$555$	−1471.66	+	1471.66i	−0.112556	+	0.112556i
$556$		0			0
$557$	3440.59			0.261728			0.130864	−	0.991400i	$-0.458225\pi$
$557$	3440.59			0.261728			0.130864	+	0.991400i	$0.458225\pi$
$558$		0			0
$559$			24660.8i			1.86590i
$560$		0			0
$561$	4491.05	−	7992.65i	0.337990	−	0.601515i
$562$		0			0
$563$		−	11973.1i		−	0.896278i	−0.893964	−	0.448139i	$-0.852087\pi$
$563$		−	11973.1i		−	0.896278i	0.893964	−	0.448139i	$-0.147913\pi$
$564$		0			0
$565$	−1162.01			−0.0865243
$566$		0			0
$567$	20041.2	−	20041.2i	1.48439	−	1.48439i
$568$		0			0
$569$			12536.9i			0.923680i	0.886963	+	0.461840i	$0.152811\pi$
$569$			12536.9i			0.923680i	−0.886963	+	0.461840i	$0.847189\pi$
$570$		0			0
$571$	2485.78	−	2485.78i	0.182183	−	0.182183i	−0.610123	−	0.792306i	$-0.708880\pi$
$571$	2485.78	−	2485.78i	0.182183	−	0.182183i	0.792306	+	0.610123i	$0.208880\pi$
$572$		0			0
$573$	−8347.74	−	8347.74i	−0.608607	−	0.608607i
$574$		0			0
$575$	9955.35	+	9955.35i	0.722029	+	0.722029i
$576$		0			0
$577$	15196.0			1.09639			0.548195	−	0.836350i	$-0.315315\pi$
$577$	15196.0			1.09639			0.548195	+	0.836350i	$0.315315\pi$
$578$		0			0
$579$	539.080			0.0386933
$580$		0			0
$581$	4196.39	+	4196.39i	0.299648	+	0.299648i
$582$		0			0
$583$	2496.55	+	2496.55i	0.177352	+	0.177352i
$584$		0			0
$585$	−395.732	+	395.732i	−0.0279684	+	0.0279684i
$586$		0			0
$587$			11409.2i			0.802230i	0.916028	+	0.401115i	$0.131377\pi$
$587$			11409.2i			0.802230i	−0.916028	+	0.401115i	$0.868623\pi$
$588$		0			0
$589$	−2549.68	+	2549.68i	−0.178366	+	0.178366i
$590$		0			0
$591$	−4313.12			−0.300200
$592$		0			0
$593$		−	3295.58i		−	0.228218i	−0.993468	−	0.114109i	$-0.963599\pi$
$593$		−	3295.58i		−	0.228218i	0.993468	−	0.114109i	$-0.0364013\pi$
$594$		0			0
$595$	−4913.43	+	8744.36i	−0.338540	+	0.602494i
$596$		0			0
$597$		−	6017.30i		−	0.412515i
$598$		0			0
$599$	−1426.99			−0.0973378			−0.0486689	−	0.998815i	$-0.515498\pi$
$599$	−1426.99			−0.0973378			−0.0486689	+	0.998815i	$0.515498\pi$
$600$		0			0
$601$	−20369.5	+	20369.5i	−1.38251	+	1.38251i	−0.542376	+	0.840136i	$0.682475\pi$
$601$	−20369.5	+	20369.5i	−1.38251	+	1.38251i	−0.840136	+	0.542376i	$0.817525\pi$
$602$		0			0
$603$		−	1737.39i		−	0.117333i
$604$		0			0
$605$	−2059.43	+	2059.43i	−0.138393	+	0.138393i
$606$		0			0
$607$	−2322.12	−	2322.12i	−0.155275	−	0.155275i	0.625194	−	0.780469i	$-0.285020\pi$
$607$	−2322.12	−	2322.12i	−0.155275	−	0.155275i	−0.780469	+	0.625194i	$0.785020\pi$
$608$		0			0
$609$	−16080.9	−	16080.9i	−1.07000	−	1.07000i
$610$		0			0
$611$	−44868.1			−2.97082
$612$		0			0
$613$	15397.0			1.01449			0.507244	−	0.861803i	$-0.330664\pi$
$613$	15397.0			1.01449			0.507244	+	0.861803i	$0.330664\pi$
$614$		0			0
$615$	4160.12	+	4160.12i	0.272768	+	0.272768i
$616$		0			0
$617$	−20796.5	−	20796.5i	−1.35695	−	1.35695i	−0.877655	−	0.479293i	$-0.840893\pi$
$617$	−20796.5	−	20796.5i	−1.35695	−	1.35695i	−0.479293	−	0.877655i	$-0.659107\pi$
$618$		0			0
$619$	−1841.95	+	1841.95i	−0.119603	+	0.119603i	−0.764375	−	0.644772i	$-0.776952\pi$
$619$	−1841.95	+	1841.95i	−0.119603	+	0.119603i	0.644772	+	0.764375i	$0.276952\pi$
$620$		0			0
$621$			17308.5i			1.11846i
$622$		0			0
$623$	−10777.6	+	10777.6i	−0.693093	+	0.693093i
$624$		0			0
$625$	−10067.5			−0.644319
$626$		0			0
$627$		−	9454.76i		−	0.602212i
$628$		0			0
$629$	−6635.68	+	1861.27i	−0.420639	+	0.117987i
$630$		0			0
$631$		−	6384.47i		−	0.402792i	−0.979510	−	0.201396i	$-0.935452\pi$
$631$		−	6384.47i		−	0.402792i	0.979510	−	0.201396i	$-0.0645478\pi$
$632$		0			0
$633$	3038.03			0.190760
$634$		0			0
$635$	1252.55	−	1252.55i	0.0782769	−	0.0782769i
$636$		0			0
$637$		−	70349.4i		−	4.37574i
$638$		0			0
$639$	−116.611	+	116.611i	−0.00721920	+	0.00721920i
$640$		0			0
$641$	−21042.7	−	21042.7i	−1.29663	−	1.29663i	−0.930607	−	0.366021i	$-0.880720\pi$
$641$	−21042.7	−	21042.7i	−1.29663	−	1.29663i	−0.366021	−	0.930607i	$-0.619280\pi$
$642$		0			0
$643$	11224.9	+	11224.9i	0.688442	+	0.688442i	0.961888	−	0.273445i	$-0.0881632\pi$
$643$	11224.9	+	11224.9i	0.688442	+	0.688442i	−0.273445	+	0.961888i	$0.588163\pi$
$644$		0			0
$645$	−7284.94			−0.444720
$646$		0			0
$647$	−19644.7			−1.19368			−0.596842	−	0.802359i	$-0.703578\pi$
$647$	−19644.7			−1.19368			−0.596842	+	0.802359i	$0.703578\pi$
$648$		0			0
$649$	7799.22	+	7799.22i	0.471720	+	0.471720i
$650$		0			0
$651$	6912.04	+	6912.04i	0.416135	+	0.416135i
$652$		0			0
$653$	−3999.32	+	3999.32i	−0.239672	+	0.239672i	−0.816714	−	0.577043i	$-0.804207\pi$
$653$	−3999.32	+	3999.32i	−0.239672	+	0.239672i	0.577043	+	0.816714i	$0.304207\pi$
$654$		0			0
$655$			3127.27i			0.186554i
$656$		0			0
$657$	548.039	−	548.039i	0.0325434	−	0.0325434i
$658$		0			0
$659$	22818.1			1.34881			0.674407	−	0.738360i	$-0.264400\pi$
$659$	22818.1			1.34881			0.674407	+	0.738360i	$0.264400\pi$
$660$		0			0
$661$			5851.00i			0.344293i	0.985071	+	0.172146i	$0.0550702\pi$
$661$			5851.00i			0.344293i	−0.985071	+	0.172146i	$0.944930\pi$
$662$		0			0
$663$	−26035.8	+	7302.88i	−1.52511	+	0.427783i
$664$		0			0
$665$			10344.0i			0.603192i
$666$		0			0
$667$	14915.6			0.865868
$668$		0			0
$669$	−19232.2	+	19232.2i	−1.11145	+	1.11145i
$670$		0			0
$671$		−	6156.70i		−	0.354213i
$672$		0			0
$673$	8905.21	−	8905.21i	0.510060	−	0.510060i	−0.404484	−	0.914545i	$-0.632549\pi$
$673$	8905.21	−	8905.21i	0.510060	−	0.510060i	0.914545	+	0.404484i	$0.132549\pi$
$674$		0			0
$675$	−10431.3	−	10431.3i	−0.594819	−	0.594819i
$676$		0			0
$677$	17965.5	+	17965.5i	1.01990	+	1.01990i	0.999798	+	0.0200980i	$0.00639784\pi$
$677$	17965.5	+	17965.5i	1.01990	+	1.01990i	0.0200980	+	0.999798i	$0.493602\pi$
$678$		0			0
$679$	8371.43			0.473146
$680$		0			0
$681$	1540.43			0.0866804
$682$		0			0
$683$	−14089.4	−	14089.4i	−0.789338	−	0.789338i	0.192048	−	0.981386i	$-0.438487\pi$
$683$	−14089.4	−	14089.4i	−0.789338	−	0.789338i	−0.981386	+	0.192048i	$0.938487\pi$
$684$		0			0
$685$	−4115.13	−	4115.13i	−0.229535	−	0.229535i
$686$		0			0
$687$	8623.56	−	8623.56i	0.478907	−	0.478907i
$688$		0			0
$689$		−	10413.5i		−	0.575795i
$690$		0			0
$691$	−18417.0	+	18417.0i	−1.01391	+	1.01391i	−0.0140112	+	0.999902i	$0.504460\pi$
$691$	−18417.0	+	18417.0i	−1.01391	+	1.01391i	−0.999902	+	0.0140112i	$0.995540\pi$
$692$		0			0
$693$	−1756.64			−0.0962902
$694$		0			0
$695$		−	12308.1i		−	0.671759i
$696$		0			0
$697$	5261.48	+	18757.9i	0.285929	+	1.01938i
$698$		0			0
$699$			28754.4i			1.55593i
$700$		0			0
$701$	8521.04			0.459109			0.229554	−	0.973296i	$-0.426273\pi$
$701$	8521.04			0.459109			0.229554	+	0.973296i	$0.426273\pi$
$702$		0			0
$703$	−5025.66	+	5025.66i	−0.269625	+	0.269625i
$704$		0			0
$705$		−	13254.3i		−	0.708065i
$706$		0			0
$707$	27295.4	−	27295.4i	1.45198	−	1.45198i
$708$		0			0
$709$	−19634.5	−	19634.5i	−1.04004	−	1.04004i	−0.999164	−	0.0408774i	$-0.986985\pi$
$709$	−19634.5	−	19634.5i	−1.04004	−	1.04004i	−0.0408774	−	0.999164i	$-0.513015\pi$
$710$		0			0
$711$	−923.446	−	923.446i	−0.0487088	−	0.0487088i
$712$		0			0
$713$	−6411.17			−0.336746
$714$		0			0
$715$	−6844.02			−0.357975
$716$		0			0
$717$	26716.4	+	26716.4i	1.39155	+	1.39155i
$718$		0			0
$719$	20219.0	+	20219.0i	1.04874	+	1.04874i	0.998750	+	0.0499880i	$0.0159183\pi$
$719$	20219.0	+	20219.0i	1.04874	+	1.04874i	0.0499880	+	0.998750i	$0.484082\pi$
$720$		0			0
$721$	17271.5	−	17271.5i	0.892127	−	0.892127i
$722$		0			0
$723$		−	25648.9i		−	1.31935i
$724$		0			0
$725$	−8989.22	+	8989.22i	−0.460484	+	0.460484i
$726$		0			0
$727$	−22672.4			−1.15663			−0.578317	−	0.815812i	$-0.696290\pi$
$727$	−22672.4			−1.15663			−0.578317	+	0.815812i	$0.696290\pi$
$728$		0			0
$729$		−	18029.5i		−	0.915994i
$730$		0			0
$731$	−21030.6	−	11817.1i	−1.06409	−	0.597907i
$732$		0			0
$733$		−	3241.83i		−	0.163356i	−0.996659	−	0.0816779i	$-0.973972\pi$
$733$		−	3241.83i		−	0.163356i	0.996659	−	0.0816779i	$-0.0260279\pi$
$734$		0			0
$735$	20781.7			1.04292
$736$		0			0
$737$	15023.7	−	15023.7i	0.750890	−	0.750890i
$738$		0			0
$739$			8977.81i			0.446893i	0.974716	+	0.223447i	$0.0717309\pi$
$739$			8977.81i			0.446893i	−0.974716	+	0.223447i	$0.928269\pi$
$740$		0			0
$741$	−19718.7	+	19718.7i	−0.977576	+	0.977576i
$742$		0			0
$743$	−3759.91	−	3759.91i	−0.185650	−	0.185650i	0.608163	−	0.793812i	$-0.291907\pi$
$743$	−3759.91	−	3759.91i	−0.185650	−	0.185650i	−0.793812	+	0.608163i	$0.791907\pi$
$744$		0			0
$745$	−8022.63	−	8022.63i	−0.394532	−	0.394532i
$746$		0			0
$747$	−323.911			−0.0158652
$748$		0			0
$749$	−9014.96			−0.439786
$750$		0			0
$751$	13408.0	+	13408.0i	0.651485	+	0.651485i	0.953351	−	0.301865i	$-0.0976093\pi$
$751$	13408.0	+	13408.0i	0.651485	+	0.651485i	−0.301865	+	0.953351i	$0.597609\pi$
$752$		0			0
$753$	25099.3	+	25099.3i	1.21470	+	1.21470i
$754$		0			0
$755$	−2884.78	+	2884.78i	−0.139057	+	0.139057i
$756$		0			0
$757$			28601.5i			1.37324i	0.727018	+	0.686619i	$0.240906\pi$
$757$			28601.5i			1.37324i	−0.727018	+	0.686619i	$0.759094\pi$
$758$		0			0
$759$	11887.0	−	11887.0i	0.568474	−	0.568474i
$760$		0			0
$761$	−23710.9			−1.12946			−0.564730	−	0.825276i	$-0.691020\pi$
$761$	−23710.9			−1.12946			−0.564730	+	0.825276i	$0.691020\pi$
$762$		0			0
$763$		−	26228.7i		−	1.24449i
$764$		0			0
$765$	−147.851	−	527.108i	−0.00698765	−	0.0249120i
$766$		0			0
$767$		−	32531.8i		−	1.53149i
$768$		0			0
$769$	−3392.20			−0.159071			−0.0795357	−	0.996832i	$-0.525344\pi$
$769$	−3392.20			−0.159071			−0.0795357	+	0.996832i	$0.525344\pi$
$770$		0			0
$771$	23330.9	−	23330.9i	1.08981	−	1.08981i
$772$		0			0
$773$			10444.4i			0.485977i	0.970029	+	0.242988i	$0.0781277\pi$
$773$			10444.4i			0.485977i	−0.970029	+	0.242988i	$0.921872\pi$
$774$		0			0
$775$	3863.84	−	3863.84i	0.179088	−	0.179088i
$776$		0			0
$777$	13624.3	+	13624.3i	0.629046	+	0.629046i
$778$		0			0
$779$	14206.7	+	14206.7i	0.653410	+	0.653410i
$780$		0			0
$781$	−2016.74			−0.0924004
$782$		0			0
$783$	−15628.8			−0.713316
$784$		0			0
$785$	9509.48	+	9509.48i	0.432367	+	0.432367i
$786$		0			0
$787$	−8973.36	−	8973.36i	−0.406437	−	0.406437i	0.474057	−	0.880494i	$-0.342789\pi$
$787$	−8973.36	−	8973.36i	−0.406437	−	0.406437i	−0.880494	+	0.474057i	$0.842789\pi$
$788$		0			0
$789$	−23383.4	+	23383.4i	−1.05509	+	1.05509i
$790$		0			0
$791$			10757.7i			0.483564i
$792$		0			0
$793$	−12840.3	+	12840.3i	−0.574997	+	0.574997i
$794$		0			0
$795$	3076.21			0.137235
$796$		0			0
$797$			31949.2i			1.41995i	0.704228	+	0.709974i	$0.251293\pi$
$797$			31949.2i			1.41995i	−0.704228	+	0.709974i	$0.748707\pi$
$798$		0			0
$799$	21500.1	−	38263.4i	0.951964	−	1.69420i
$800$		0			0
$801$		−	831.904i		−	0.0366965i
$802$		0			0
$803$	9478.10			0.416531
$804$		0			0
$805$	−13005.0	+	13005.0i	−0.569399	+	0.569399i
$806$		0			0
$807$			6333.02i			0.276249i
$808$		0			0
$809$	13072.2	−	13072.2i	0.568101	−	0.568101i	−0.363495	−	0.931596i	$-0.618417\pi$
$809$	13072.2	−	13072.2i	0.568101	−	0.568101i	0.931596	+	0.363495i	$0.118417\pi$
$810$		0			0
$811$	15766.6	+	15766.6i	0.682665	+	0.682665i	0.960600	−	0.277935i	$-0.0896500\pi$
$811$	15766.6	+	15766.6i	0.682665	+	0.682665i	−0.277935	+	0.960600i	$0.589650\pi$
$812$		0			0
$813$	−9511.05	−	9511.05i	−0.410292	−	0.410292i
$814$		0			0
$815$	−319.506			−0.0137323
$816$		0			0
$817$	−24877.8			−1.06532
$818$		0			0
$819$	3663.61	+	3663.61i	0.156309	+	0.156309i
$820$		0			0
$821$	13357.5	+	13357.5i	0.567818	+	0.567818i	0.931517	−	0.363699i	$-0.118486\pi$
$821$	13357.5	+	13357.5i	0.567818	+	0.567818i	−0.363699	+	0.931517i	$0.618486\pi$
$822$		0			0
$823$	5642.25	−	5642.25i	0.238975	−	0.238975i	−0.577451	−	0.816426i	$-0.695952\pi$
$823$	5642.25	−	5642.25i	0.238975	−	0.238975i	0.816426	+	0.577451i	$0.195952\pi$
$824$		0			0
$825$			14328.0i			0.604649i
$826$		0			0
$827$	−3153.39	+	3153.39i	−0.132593	+	0.132593i	−0.770288	−	0.637696i	$-0.779888\pi$
$827$	−3153.39	+	3153.39i	−0.132593	+	0.132593i	0.637696	+	0.770288i	$0.279888\pi$
$828$		0			0
$829$	19686.3			0.824769			0.412384	−	0.911010i	$-0.364696\pi$
$829$	19686.3			0.824769			0.412384	+	0.911010i	$0.364696\pi$
$830$		0			0
$831$			27715.8i			1.15698i
$832$		0			0
$833$	59993.8	+	33710.4i	2.49539	+	1.40216i
$834$		0			0
$835$			4766.46i			0.197545i
$836$		0			0
$837$	6717.71			0.277417
$838$		0			0
$839$	−20299.7	+	20299.7i	−0.835307	+	0.835307i	−0.988237	−	0.152930i	$-0.951129\pi$
$839$	−20299.7	+	20299.7i	−0.835307	+	0.835307i	0.152930	+	0.988237i	$0.451129\pi$
$840$		0			0
$841$		−	10920.9i		−	0.447780i
$842$		0			0
$843$	12773.2	−	12773.2i	0.521865	−	0.521865i
$844$		0			0
$845$	8166.02	+	8166.02i	0.332449	+	0.332449i
$846$		0			0
$847$	19065.8	+	19065.8i	0.773446	+	0.773446i
$848$		0			0
$849$	−14067.3			−0.568654
$850$		0			0
$851$	−12637.0			−0.509039
$852$		0			0
$853$	5307.45	+	5307.45i	0.213040	+	0.213040i	0.805558	−	0.592517i	$-0.201866\pi$
$853$	5307.45	+	5307.45i	0.213040	+	0.213040i	−0.592517	+	0.805558i	$0.701866\pi$
$854$		0			0
$855$	−399.215	−	399.215i	−0.0159683	−	0.0159683i
$856$		0			0
$857$	−55.7082	+	55.7082i	−0.00222048	+	0.00222048i	−0.708216	−	0.705996i	$-0.750500\pi$
$857$	−55.7082	+	55.7082i	−0.00222048	+	0.00222048i	0.705996	+	0.708216i	$0.250500\pi$
$858$		0			0
$859$		−	5441.53i		−	0.216138i	−0.994143	−	0.108069i	$-0.965533\pi$
$859$		−	5441.53i		−	0.216138i	0.994143	−	0.108069i	$-0.0344668\pi$
$860$		0			0
$861$	38513.5	−	38513.5i	1.52443	−	1.52443i
$862$		0			0
$863$	7156.86			0.282297			0.141148	−	0.989988i	$-0.454921\pi$
$863$	7156.86			0.282297			0.141148	+	0.989988i	$0.454921\pi$
$864$		0			0
$865$		−	5618.97i		−	0.220868i
$866$		0			0
$867$	6248.06	−	25702.7i	0.244747	−	1.00681i
$868$		0			0
$869$		−	15970.6i		−	0.623436i
$870$		0			0
$871$	−62666.4			−2.43785
$872$		0			0
$873$	−323.087	+	323.087i	−0.0125256	+	0.0125256i
$874$		0			0
$875$		−	33562.9i		−	1.29673i
$876$		0			0
$877$	10284.2	−	10284.2i	0.395979	−	0.395979i	−0.480833	−	0.876812i	$-0.659666\pi$
$877$	10284.2	−	10284.2i	0.395979	−	0.395979i	0.876812	+	0.480833i	$0.159666\pi$
$878$		0			0
$879$	−6409.59	−	6409.59i	−0.245950	−	0.245950i
$880$		0			0
$881$	−15872.5	−	15872.5i	−0.606990	−	0.606990i	0.335168	−	0.942158i	$-0.391207\pi$
$881$	−15872.5	−	15872.5i	−0.606990	−	0.606990i	−0.942158	+	0.335168i	$0.891207\pi$
$882$		0			0
$883$	34760.2			1.32477			0.662385	−	0.749163i	$-0.269544\pi$
$883$	34760.2			1.32477			0.662385	+	0.749163i	$0.269544\pi$
$884$		0			0
$885$	9610.10			0.365017
$886$		0			0
$887$	4228.29	+	4228.29i	0.160059	+	0.160059i	0.782593	−	0.622534i	$-0.213897\pi$
$887$	4228.29	+	4228.29i	0.160059	+	0.160059i	−0.622534	+	0.782593i	$0.713897\pi$
$888$		0			0
$889$	−11595.8	−	11595.8i	−0.437471	−	0.437471i
$890$		0			0
$891$	−13376.8	+	13376.8i	−0.502963	+	0.502963i
$892$		0			0
$893$		−	45263.0i		−	1.69616i
$894$		0			0
$895$	−5423.62	+	5423.62i	−0.202561	+	0.202561i
$896$		0			0
$897$	−49582.7			−1.84562
$898$		0			0
$899$		−	5788.99i		−	0.214765i
$900$		0			0
$901$	8880.62	+	4989.99i	0.328364	+	0.184507i
$902$		0			0
$903$			67442.5i			2.48543i
$904$		0			0
$905$	−10287.8			−0.377876
$906$		0			0
$907$	26461.5	−	26461.5i	0.968731	−	0.968731i	−0.0307949	−	0.999526i	$-0.509804\pi$
$907$	26461.5	−	26461.5i	0.968731	−	0.968731i	0.999526	+	0.0307949i	$0.00980387\pi$
$908$		0			0
$909$			2106.87i			0.0768764i
$910$		0			0
$911$	−18.0094	+	18.0094i	−0.000654970	+	0.000654970i	−0.707434	−	0.706779i	$-0.750147\pi$
$911$	−18.0094	+	18.0094i	−0.000654970	+	0.000654970i	0.706779	+	0.707434i	$0.250147\pi$
$912$		0			0
$913$	−2800.95	−	2800.95i	−0.101531	−	0.101531i
$914$		0			0
$915$	−3793.10	−	3793.10i	−0.137045	−	0.137045i
$916$		0			0
$917$	28951.6			1.04260
$918$		0			0
$919$	−11502.6			−0.412878			−0.206439	−	0.978459i	$-0.566188\pi$
$919$	−11502.6			−0.412878			−0.206439	+	0.978459i	$0.566188\pi$
$920$		0			0
$921$	22326.8	+	22326.8i	0.798800	+	0.798800i
$922$		0			0
$923$	4206.08	+	4206.08i	0.149994	+	0.149994i
$924$		0			0
$925$	7616.00	−	7616.00i	0.270716	−	0.270716i
$926$		0			0
$927$			1333.15i			0.0472345i
$928$		0			0
$929$	−26325.7	+	26325.7i	−0.929729	+	0.929729i	−0.997688	−	0.0679592i	$-0.978351\pi$
$929$	−26325.7	+	26325.7i	−0.929729	+	0.929729i	0.0679592	+	0.997688i	$0.478351\pi$
$930$		0			0
$931$	70968.7			2.49829
$932$		0			0
$933$			34319.4i			1.20425i
$934$		0			0
$935$	3279.55	−	5836.57i	0.114709	−	0.204146i
$936$		0			0
$937$			72.1695i			0.00251619i	0.999999	+	0.00125810i	$0.000400465\pi$
$937$			72.1695i			0.00251619i	−0.999999	+	0.00125810i	$0.999600\pi$
$938$		0			0
$939$	−17813.1			−0.619072
$940$		0			0
$941$	6951.94	−	6951.94i	0.240836	−	0.240836i	−0.576360	−	0.817196i	$-0.695527\pi$
$941$	6951.94	−	6951.94i	0.240836	−	0.240836i	0.817196	+	0.576360i	$0.195527\pi$
$942$		0			0
$943$			35722.7i			1.23361i
$944$		0			0
$945$	13626.8	−	13626.8i	0.469080	−	0.469080i
$946$		0			0
$947$	−14532.5	−	14532.5i	−0.498671	−	0.498671i	0.412353	−	0.911024i	$-0.364707\pi$
$947$	−14532.5	−	14532.5i	−0.498671	−	0.498671i	−0.911024	+	0.412353i	$0.864707\pi$
$948$		0			0
$949$	−19767.3	−	19767.3i	−0.676159	−	0.676159i
$950$		0			0
$951$	40031.4			1.36499
$952$		0			0
$953$	−2360.48			−0.0802345			−0.0401172	−	0.999195i	$-0.512773\pi$
$953$	−2360.48			−0.0802345			−0.0401172	+	0.999195i	$0.512773\pi$
$954$		0			0
$955$	−6095.87	−	6095.87i	−0.206553	−	0.206553i
$956$		0			0
$957$	10733.4	+	10733.4i	0.362552	+	0.362552i
$958$		0			0
$959$	−38097.1	+	38097.1i	−1.28281	+	1.28281i
$960$		0			0
$961$		−	27302.7i		−	0.916475i
$962$		0			0
$963$	347.923	−	347.923i	0.0116424	−	0.0116424i
$964$		0			0
$965$	393.659			0.0131319
$966$		0			0
$967$			9395.70i			0.312456i	0.987721	+	0.156228i	$0.0499335\pi$
$967$			9395.70i			0.312456i	−0.987721	+	0.156228i	$0.950066\pi$
$968$		0			0
$969$	−7367.16	−	26264.9i	−0.244239	−	0.870744i
$970$		0			0
$971$			24081.5i			0.795893i	0.917409	+	0.397947i	$0.130277\pi$
$971$			24081.5i			0.795893i	−0.917409	+	0.397947i	$0.869723\pi$
$972$		0			0
$973$	−113946.			−3.75430
$974$		0			0
$975$	29882.1	−	29882.1i	0.981532	−	0.981532i
$976$		0			0
$977$		−	7503.29i		−	0.245703i	−0.992425	−	0.122851i	$-0.960796\pi$
$977$		−	7503.29i		−	0.245703i	0.992425	−	0.122851i	$-0.0392038\pi$
$978$		0			0
$979$	7193.71	−	7193.71i	0.234844	−	0.234844i
$980$		0			0
$981$	1012.27	+	1012.27i	0.0329452	+	0.0329452i
$982$		0			0
$983$	−9334.52	−	9334.52i	−0.302874	−	0.302874i	0.539263	−	0.842137i	$-0.318703\pi$
$983$	−9334.52	−	9334.52i	−0.302874	−	0.302874i	−0.842137	+	0.539263i	$0.818703\pi$
$984$		0			0
$985$	−3149.62			−0.101884
$986$		0			0
$987$	−122706.			−3.95721
$988$		0			0
$989$	−31277.7	−	31277.7i	−1.00564	−	1.00564i
$990$		0			0
$991$	−27451.4	−	27451.4i	−0.879940	−	0.879940i	0.113588	−	0.993528i	$-0.463766\pi$
$991$	−27451.4	−	27451.4i	−0.879940	−	0.879940i	−0.993528	+	0.113588i	$0.963766\pi$
$992$		0			0
$993$	−3630.46	+	3630.46i	−0.116021	+	0.116021i
$994$		0			0
$995$		−	4394.08i		−	0.140002i
$996$		0			0
$997$	14656.5	−	14656.5i	0.465573	−	0.465573i	−0.434904	−	0.900477i	$-0.643218\pi$
$997$	14656.5	−	14656.5i	0.465573	−	0.465573i	0.900477	+	0.434904i	$0.143218\pi$
$998$		0			0
$999$	13241.3			0.419354

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.4.k.b.81.6	✓	14
4.3	odd	2		272.4.o.f.81.2		14
17.2	even	8		2312.4.a.l.1.11		14
17.4	even	4	inner	136.4.k.b.89.6	yes	14
17.15	even	8		2312.4.a.l.1.4		14
68.55	odd	4		272.4.o.f.225.2		14

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.4.k.b.81.6	✓	14	1.1	even	1	trivial
136.4.k.b.89.6	yes	14	17.4	even	4	inner
272.4.o.f.81.2		14	4.3	odd	2
272.4.o.f.225.2		14	68.55	odd	4
2312.4.a.l.1.4		14	17.15	even	8
2312.4.a.l.1.11		14	17.2	even	8

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:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	136.k (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(3.80701 + 3.80701i) q^{3} +(2.78003 + 2.78003i) q^{5} +(25.7370 - 25.7370i) q^{7} +1.98658i q^{9} +O(q^{10})\)	\(q+(3.80701 + 3.80701i) q^{3} +(2.78003 + 2.78003i) q^{5} +(25.7370 - 25.7370i) q^{7} +1.98658i q^{9} +(-17.1786 + 17.1786i) q^{11} +71.6546 q^{13} +21.1672i q^{15} +(-34.3358 + 61.1069i) q^{17} +72.2853i q^{19} +195.962 q^{21} +(-90.8809 + 90.8809i) q^{23} -109.543i q^{25} +(95.2262 - 95.2262i) q^{27} +(-82.0612 - 82.0612i) q^{29} +(35.2724 + 35.2724i) q^{31} -130.798 q^{33} +143.099 q^{35} +(69.5253 + 69.5253i) q^{37} +(272.789 + 272.789i) q^{39} +(196.536 - 196.536i) q^{41} +344.162i q^{43} +(-5.52277 + 5.52277i) q^{45} -626.172 q^{47} -981.785i q^{49} +(-363.351 + 101.918i) q^{51} -145.329i q^{53} -95.5140 q^{55} +(-275.191 + 275.191i) q^{57} -454.009i q^{59} +(-179.197 + 179.197i) q^{61} +(51.1287 + 51.1287i) q^{63} +(199.202 + 199.202i) q^{65} -874.562 q^{67} -691.968 q^{69} +(58.6994 + 58.6994i) q^{71} +(-275.870 - 275.870i) q^{73} +(417.030 - 417.030i) q^{75} +884.249i q^{77} +(-464.841 + 464.841i) q^{79} +778.691 q^{81} +163.049i q^{83} +(-265.334 + 74.4246i) q^{85} -624.815i q^{87} -418.761 q^{89} +(1844.17 - 1844.17i) q^{91} +268.564i q^{93} +(-200.956 + 200.956i) q^{95} +(162.634 + 162.634i) q^{97} +(-34.1267 - 34.1267i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7}+O(q^{10}) \) 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7	\( 14 q + 6 q^{3} + 6 q^{5} + 10 q^{7} - 66 q^{11} - 124 q^{13} + 130 q^{17} - 148 q^{21} - 162 q^{23} - 204 q^{27} + 158 q^{29} - 350 q^{31} + 116 q^{33} + 236 q^{35} + 582 q^{37} - 320 q^{39} + 878 q^{41} - 26 q^{45} - 448 q^{47} - 590 q^{51} + 1460 q^{55} + 292 q^{57} - 1130 q^{61} + 114 q^{63} + 20 q^{65} - 64 q^{67} + 2076 q^{69} - 3274 q^{71} - 1426 q^{73} + 946 q^{75} + 1718 q^{79} + 166 q^{81} - 2018 q^{85} + 476 q^{89} + 2128 q^{91} - 2444 q^{95} + 1926 q^{97} + 3870 q^{99}+O(q^{100}) \) 14 * q + 6 * q^3 + 6 * q^5 + 10 * q^7 - 66 * q^11 - 124 * q^13 + 130 * q^17 - 148 * q^21 - 162 * q^23 - 204 * q^27 + 158 * q^29 - 350 * q^31 + 116 * q^33 + 236 * q^35 + 582 * q^37 - 320 * q^39 + 878 * q^41 - 26 * q^45 - 448 * q^47 - 590 * q^51 + 1460 * q^55 + 292 * q^57 - 1130 * q^61 + 114 * q^63 + 20 * q^65 - 64 * q^67 + 2076 * q^69 - 3274 * q^71 - 1426 * q^73 + 946 * q^75 + 1718 * q^79 + 166 * q^81 - 2018 * q^85 + 476 * q^89 + 2128 * q^91 - 2444 * q^95 + 1926 * q^97 + 3870 * q^99

Introduction

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