LMFDB - Embedded newform 896.2.q.c.703.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [896,2,Mod(703,896)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(896, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 3, 1]))

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

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

chi := DirichletCharacter("896.703");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 896 = 2^{7} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	896.q (of order $6$, 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:	$7.15459602111$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$8$ over $\Q(\zeta_{6})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 4 x^{14} - 24 x^{13} + 104 x^{12} - 196 x^{11} + 312 x^{10} - 236 x^{9} + 31 x^{8} + \cdots + 1 $ x^16 - 4x^15 + 4x^14 - 24x^13 + 104x^12 - 196x^11 + 312x^10 - 236x^9 + 31x^8 + 236x^7 + 312x^6 + 196x^5 + 104x^4 + 24x^3 + 4x^2 + 4*x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			703.8
Root			$2.92664 + 0.385299i$ of defining polynomial
Character	$\chi$	$=$	896.703
Dual form			896.2.q.c.831.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.63287 + 1.52009i) q^{3} +(0.866025 + 1.50000i) q^{5} +(2.14973 - 1.54230i) q^{7} +(3.12132 + 5.40629i) q^{9} +O(q^{10})$	\(q+(2.63287 + 1.52009i) q^{3} +(0.866025 + 1.50000i) q^{5} +(2.14973 - 1.54230i) q^{7} +(3.12132 + 5.40629i) q^{9} +(-1.09057 + 1.88892i) q^{11} -5.91359 q^{13} +5.26573i q^{15} +(3.62132 + 2.09077i) q^{17} +(-3.27171 + 1.88892i) q^{19} +(8.00436 - 0.792893i) q^{21} +(-1.88892 + 1.09057i) q^{23} +(1.00000 - 1.73205i) q^{25} +9.85818i q^{27} -7.41421i q^{29} +(4.03865 - 6.99514i) q^{31} +(-5.74264 + 3.31552i) q^{33} +(4.17516 + 1.88892i) q^{35} +(1.07616 - 0.621320i) q^{37} +(-15.5697 - 8.98916i) q^{39} -7.34847i q^{41} +6.16919 q^{43} +(-5.40629 + 9.36396i) q^{45} +(4.56026 + 7.89860i) q^{47} +(2.24264 - 6.63103i) q^{49} +(6.35630 + 11.0094i) q^{51} +(1.37333 + 0.792893i) q^{53} -3.77784 q^{55} -11.4853 q^{57} +(2.63287 + 1.52009i) q^{59} +(-1.07616 - 1.86396i) q^{61} +(15.0481 + 6.80803i) q^{63} +(-5.12132 - 8.87039i) q^{65} +(-4.81400 + 8.33810i) q^{67} -6.63103 q^{69} +8.72455i q^{71} +(-11.7426 - 6.77962i) q^{73} +(5.26573 - 3.04017i) q^{75} +(0.568852 + 5.74264i) q^{77} +(-7.23159 + 4.17516i) q^{79} +(-5.62132 + 9.73641i) q^{81} -12.1607i q^{83} +7.24264i q^{85} +(11.2702 - 19.5206i) q^{87} +(9.98528 - 5.76500i) q^{89} +(-12.7126 + 9.12051i) q^{91} +(21.2664 - 12.2782i) q^{93} +(-5.66676 - 3.27171i) q^{95} -5.91359i q^{97} -13.6161 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 16 q^{9}+O(q^{10}) $ 16 * q + 16 * q^9	$ 16 q + 16 q^{9} + 24 q^{17} + 16 q^{25} - 24 q^{33} - 32 q^{49} - 48 q^{57} - 48 q^{65} - 120 q^{73} - 56 q^{81} + 24 q^{89}+O(q^{100}) $ 16 * q + 16 * q^9 + 24 * q^17 + 16 * q^25 - 24 * q^33 - 32 * q^49 - 48 * q^57 - 48 * q^65 - 120 * q^73 - 56 * q^81 + 24 * q^89

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/896\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$645$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	2.63287	+	1.52009i	1.52009	+	0.877622i	0.999720	+	0.0236785i	$0.00753779\pi$
$3$	2.63287	+	1.52009i	1.52009	+	0.877622i	0.520366	+	0.853943i	$0.325796\pi$
$4$		0			0
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	0.992085	−	0.125567i	$-0.0400750\pi$
$5$	0.866025	+	1.50000i	0.387298	+	0.670820i	−0.604787	+	0.796387i	$0.706742\pi$
$6$		0			0
$7$	2.14973	−	1.54230i	0.812520	−	0.582933i
$7$	2.14973	−	1.54230i	0.812520	−	0.582933i
$8$		0			0
$9$	3.12132	+	5.40629i	1.04044	+	1.80210i
$10$		0			0
$11$	−1.09057	+	1.88892i	−0.328819	+	0.569531i	−0.982278	−	0.187431i	$-0.939984\pi$
$11$	−1.09057	+	1.88892i	−0.328819	+	0.569531i	0.653459	+	0.756962i	$0.273317\pi$
$12$		0			0
$13$	−5.91359			−1.64014			−0.820068	−	0.572267i	$-0.806064\pi$
$13$	−5.91359			−1.64014			−0.820068	+	0.572267i	$0.806064\pi$
$14$		0			0
$15$			5.26573i			1.35961i
$16$		0			0
$17$	3.62132	+	2.09077i	0.878299	+	0.507086i	0.870097	−	0.492880i	$-0.164056\pi$
$17$	3.62132	+	2.09077i	0.878299	+	0.507086i	0.00820195	+	0.999966i	$0.497389\pi$
$18$		0			0
$19$	−3.27171	+	1.88892i	−0.750581	+	0.433348i	−0.825904	−	0.563811i	$-0.809335\pi$
$19$	−3.27171	+	1.88892i	−0.750581	+	0.433348i	0.0753229	+	0.997159i	$0.476001\pi$
$20$		0			0
$21$	8.00436	−	0.792893i	1.74669	−	0.173023i
$22$		0			0
$23$	−1.88892	+	1.09057i	−0.393867	+	0.227399i	−0.683834	−	0.729637i	$-0.739689\pi$
$23$	−1.88892	+	1.09057i	−0.393867	+	0.227399i	0.289967	+	0.957037i	$0.406356\pi$
$24$		0			0
$25$	1.00000	−	1.73205i	0.200000	−	0.346410i
$26$		0			0
$27$			9.85818i			1.89721i
$28$		0			0
$29$		−	7.41421i		−	1.37678i	−0.725338	−	0.688392i	$-0.758317\pi$
$29$		−	7.41421i		−	1.37678i	0.725338	−	0.688392i	$-0.241683\pi$
$30$		0			0
$31$	4.03865	−	6.99514i	0.725362	−	1.25636i	−0.233463	−	0.972366i	$-0.575006\pi$
$31$	4.03865	−	6.99514i	0.725362	−	1.25636i	0.958825	−	0.283998i	$-0.0916610\pi$
$32$		0			0
$33$	−5.74264	+	3.31552i	−0.999665	+	0.577157i
$34$		0			0
$35$	4.17516	+	1.88892i	0.705731	+	0.319286i
$36$		0			0
$37$	1.07616	−	0.621320i	0.176919	−	0.102144i	−0.408925	−	0.912568i	$-0.634096\pi$
$37$	1.07616	−	0.621320i	0.176919	−	0.102144i	0.585844	+	0.810424i	$0.300763\pi$
$38$		0			0
$39$	−15.5697	−	8.98916i	−2.49315	−	1.43942i
$40$		0			0
$41$		−	7.34847i		−	1.14764i	−0.818982	−	0.573819i	$-0.805461\pi$
$41$		−	7.34847i		−	1.14764i	0.818982	−	0.573819i	$-0.194539\pi$
$42$		0			0
$43$	6.16919			0.940792			0.470396	−	0.882455i	$-0.344111\pi$
$43$	6.16919			0.940792			0.470396	+	0.882455i	$0.344111\pi$
$44$		0			0
$45$	−5.40629	+	9.36396i	−0.805921	+	1.39590i
$46$		0			0
$47$	4.56026	+	7.89860i	0.665182	+	1.15213i	0.979236	+	0.202724i	$0.0649793\pi$
$47$	4.56026	+	7.89860i	0.665182	+	1.15213i	−0.314054	+	0.949405i	$0.601687\pi$
$48$		0			0
$49$	2.24264	−	6.63103i	0.320377	−	0.947290i
$50$		0			0
$51$	6.35630	+	11.0094i	0.890060	+	1.54163i
$52$		0			0
$53$	1.37333	+	0.792893i	0.188642	+	0.108912i	0.591346	−	0.806418i	$-0.298597\pi$
$53$	1.37333	+	0.792893i	0.188642	+	0.108912i	−0.402705	+	0.915330i	$0.631930\pi$
$54$		0			0
$55$	−3.77784			−0.509404
$56$		0			0
$57$	−11.4853			−1.52126
$58$		0			0
$59$	2.63287	+	1.52009i	0.342770	+	0.197898i	0.661496	−	0.749948i	$-0.269922\pi$
$59$	2.63287	+	1.52009i	0.342770	+	0.197898i	−0.318726	+	0.947847i	$0.603255\pi$
$60$		0			0
$61$	−1.07616	−	1.86396i	−0.137788	−	0.238656i	0.788871	−	0.614559i	$-0.210666\pi$
$61$	−1.07616	−	1.86396i	−0.137788	−	0.238656i	−0.926659	+	0.375903i	$0.877333\pi$
$62$		0			0
$63$	15.0481	+	6.80803i	1.89588	+	0.857731i
$64$		0			0
$65$	−5.12132	−	8.87039i	−0.635222	−	1.10024i
$66$		0			0
$67$	−4.81400	+	8.33810i	−0.588124	+	1.01866i	0.406354	+	0.913716i	$0.366800\pi$
$67$	−4.81400	+	8.33810i	−0.588124	+	1.01866i	−0.994478	+	0.104945i	$0.966533\pi$
$68$		0			0
$69$	−6.63103			−0.798282
$70$		0			0
$71$			8.72455i			1.03541i	0.855558	+	0.517707i	$0.173214\pi$
$71$			8.72455i			1.03541i	−0.855558	+	0.517707i	$0.826786\pi$
$72$		0			0
$73$	−11.7426	−	6.77962i	−1.37437	−	0.793494i	−0.382897	−	0.923791i	$-0.625074\pi$
$73$	−11.7426	−	6.77962i	−1.37437	−	0.793494i	−0.991475	+	0.130297i	$0.958407\pi$
$74$		0			0
$75$	5.26573	−	3.04017i	0.608034	−	0.351049i
$76$		0			0
$77$	0.568852	+	5.74264i	0.0648268	+	0.654435i
$78$		0			0
$79$	−7.23159	+	4.17516i	−0.813618	+	0.469742i	−0.848211	−	0.529659i	$-0.822320\pi$
$79$	−7.23159	+	4.17516i	−0.813618	+	0.469742i	0.0345928	+	0.999401i	$0.488987\pi$
$80$		0			0
$81$	−5.62132	+	9.73641i	−0.624591	+	1.08182i
$82$		0			0
$83$		−	12.1607i		−	1.33481i	−0.744696	−	0.667404i	$-0.767405\pi$
$83$		−	12.1607i		−	1.33481i	0.744696	−	0.667404i	$-0.232595\pi$
$84$		0			0
$85$			7.24264i			0.785575i
$86$		0			0
$87$	11.2702	−	19.5206i	1.20830	−	2.09283i
$88$		0			0
$89$	9.98528	−	5.76500i	1.05844	−	0.611089i	0.133438	−	0.991057i	$-0.457398\pi$
$89$	9.98528	−	5.76500i	1.05844	−	0.611089i	0.925000	+	0.379968i	$0.124065\pi$
$90$		0			0
$91$	−12.7126	+	9.12051i	−1.33264	+	0.956090i
$92$		0			0
$93$	21.2664	−	12.2782i	2.20523	−	1.27319i
$94$		0			0
$95$	−5.66676	−	3.27171i	−0.581397	−	0.335670i
$96$		0			0
$97$		−	5.91359i		−	0.600434i	−0.953871	−	0.300217i	$-0.902941\pi$
$97$		−	5.91359i		−	0.600434i	0.953871	−	0.300217i	$-0.0970591\pi$
$98$		0			0
$99$	−13.6161			−1.36847
$100$		0			0
$101$	−4.03295	+	6.98528i	−0.401294	+	0.695061i	−0.993882	−	0.110444i	$-0.964773\pi$
$101$	−4.03295	+	6.98528i	−0.401294	+	0.695061i	0.592588	+	0.805505i	$0.298106\pi$
$102$		0			0
$103$	−2.93214	−	5.07862i	−0.288913	−	0.500411i	0.684638	−	0.728883i	$-0.259960\pi$
$103$	−2.93214	−	5.07862i	−0.288913	−	0.500411i	−0.973550	+	0.228472i	$0.926627\pi$
$104$		0			0
$105$	8.12132	+	11.3199i	0.792560	+	1.10471i
$106$		0			0
$107$	−4.17516	−	7.23159i	−0.403628	−	0.699105i	0.590533	−	0.807014i	$-0.298918\pi$
$107$	−4.17516	−	7.23159i	−0.403628	−	0.699105i	−0.994161	+	0.107909i	$0.965584\pi$
$108$		0			0
$109$	−2.59808	−	1.50000i	−0.248851	−	0.143674i	0.370387	−	0.928877i	$-0.379225\pi$
$109$	−2.59808	−	1.50000i	−0.248851	−	0.143674i	−0.619238	+	0.785203i	$0.712558\pi$
$110$		0			0
$111$	3.77784			0.358577
$112$		0			0
$113$	−4.24264			−0.399114			−0.199557	−	0.979886i	$-0.563950\pi$
$113$	−4.24264			−0.399114			−0.199557	+	0.979886i	$0.563950\pi$
$114$		0			0
$115$	−3.27171	−	1.88892i	−0.305088	−	0.176143i
$116$		0			0
$117$	−18.4582	−	31.9706i	−1.70646	−	2.95568i
$118$		0			0
$119$	11.0094	−	1.09057i	1.00923	−	0.0999723i
$120$		0			0
$121$	3.12132	+	5.40629i	0.283756	+	0.491480i
$122$		0			0
$123$	11.1703	−	19.3475i	1.00719	−	1.74451i
$124$		0			0
$125$	12.1244			1.08444
$126$		0			0
$127$			21.0629i			1.86903i	0.355921	+	0.934516i	$0.384167\pi$
$127$			21.0629i			1.86903i	−0.355921	+	0.934516i	$0.615833\pi$
$128$		0			0
$129$	16.2426	+	9.37769i	1.43008	+	0.825660i
$130$		0			0
$131$	3.91055	−	2.25775i	0.341666	−	0.197261i	−0.319343	−	0.947639i	$-0.603462\pi$
$131$	3.91055	−	2.25775i	0.341666	−	0.197261i	0.661009	+	0.750378i	$0.270129\pi$
$132$		0			0
$133$	−4.11999	+	9.10660i	−0.357249	+	0.789643i
$134$		0			0
$135$	−14.7873	+	8.53744i	−1.27269	+	0.734786i
$136$		0			0
$137$	2.37868	−	4.11999i	0.203224	−	0.351995i	−0.746341	−	0.665564i	$-0.768191\pi$
$137$	2.37868	−	4.11999i	0.203224	−	0.351995i	0.949566	+	0.313569i	$0.101525\pi$
$138$		0			0
$139$			10.6853i			0.906319i	0.891429	+	0.453160i	$0.149703\pi$
$139$			10.6853i			0.906319i	−0.891429	+	0.453160i	$0.850297\pi$
$140$		0			0
$141$			27.7279i			2.33511i
$142$		0			0
$143$	6.44918	−	11.1703i	0.539307	−	0.934108i
$144$		0			0
$145$	11.1213	−	6.42090i	0.923575	−	0.533226i
$146$		0			0
$147$	15.9843	−	14.0496i	1.31836	−	1.15879i
$148$		0			0
$149$	4.45322	−	2.57107i	0.364822	−	0.210630i	−0.306372	−	0.951912i	$-0.599115\pi$
$149$	4.45322	−	2.57107i	0.364822	−	0.210630i	0.671194	+	0.741282i	$0.265782\pi$
$150$		0			0
$151$	−2.99542	−	1.72941i	−0.243764	−	0.140737i	0.373141	−	0.927774i	$-0.378281\pi$
$151$	−2.99542	−	1.72941i	−0.243764	−	0.140737i	−0.616906	+	0.787037i	$0.711614\pi$
$152$		0			0
$153$			26.1039i			2.11037i
$154$		0			0
$155$	13.9903			1.12373
$156$		0			0
$157$	4.83743	−	8.37868i	0.386069	−	0.668691i	−0.605848	−	0.795581i	$-0.707166\pi$
$157$	4.83743	−	8.37868i	0.386069	−	0.668691i	0.991917	+	0.126889i	$0.0404993\pi$
$158$		0			0
$159$	2.41053	+	4.17516i	0.191168	+	0.331112i
$160$		0			0
$161$	−2.37868	+	5.25770i	−0.187466	+	0.414365i
$162$		0			0
$163$	−1.72941	−	2.99542i	−0.135458	−	0.234620i	0.790314	−	0.612701i	$-0.209917\pi$
$163$	−1.72941	−	2.99542i	−0.135458	−	0.234620i	−0.925772	+	0.378082i	$0.876584\pi$
$164$		0			0
$165$	−9.94655	−	5.74264i	−0.774338	−	0.447064i
$166$		0			0
$167$	−23.5837			−1.82496			−0.912481	−	0.409120i	$-0.865836\pi$
$167$	−23.5837			−1.82496			−0.912481	+	0.409120i	$0.865836\pi$
$168$		0			0
$169$	21.9706			1.69004
$170$		0			0
$171$	−20.4241	−	11.7919i	−1.56187	−	0.901745i
$172$		0			0
$173$	−7.70719	−	13.3492i	−0.585967	−	1.01492i	−0.994754	−	0.102294i	$-0.967382\pi$
$173$	−7.70719	−	13.3492i	−0.585967	−	1.01492i	0.408787	−	0.912630i	$-0.365952\pi$
$174$		0			0
$175$	−0.521611	−	5.26573i	−0.0394301	−	0.398052i
$176$		0			0
$177$	4.62132	+	8.00436i	0.347360	+	0.601645i
$178$		0			0
$179$	0.187112	−	0.324087i	0.0139854	−	0.0242234i	−0.858948	−	0.512063i	$-0.828881\pi$
$179$	0.187112	−	0.324087i	0.0139854	−	0.0242234i	0.872933	+	0.487839i	$0.162215\pi$
$180$		0			0
$181$	8.95743			0.665800			0.332900	−	0.942962i	$-0.391973\pi$
$181$	8.95743			0.665800			0.332900	+	0.942962i	$0.391973\pi$
$182$		0			0
$183$		−	6.54341i		−	0.483703i
$184$		0			0
$185$	1.86396	+	1.07616i	0.137041	+	0.0791207i
$186$		0			0
$187$	−7.89860	+	4.56026i	−0.577603	+	0.333479i
$188$		0			0
$189$	15.2042	+	21.1924i	1.10595	+	1.54152i
$190$		0			0
$191$	13.6808	−	7.89860i	0.989906	−	0.571522i	0.0846597	−	0.996410i	$-0.473020\pi$
$191$	13.6808	−	7.89860i	0.989906	−	0.571522i	0.905246	+	0.424888i	$0.139686\pi$
$192$		0			0
$193$	−4.37868	+	7.58410i	−0.315184	+	0.545915i	−0.979477	−	0.201558i	$-0.935400\pi$
$193$	−4.37868	+	7.58410i	−0.315184	+	0.545915i	0.664292	+	0.747473i	$0.268733\pi$
$194$		0			0
$195$		−	31.1394i		−	2.22994i
$196$		0			0
$197$			13.0711i			0.931275i	0.884976	+	0.465638i	$0.154175\pi$
$197$			13.0711i			0.931275i	−0.884976	+	0.465638i	$0.845825\pi$
$198$		0			0
$199$	0.260805	−	0.451728i	0.0184880	−	0.0320222i	−0.856633	−	0.515926i	$-0.827448\pi$
$199$	0.260805	−	0.451728i	0.0184880	−	0.0320222i	0.875121	+	0.483903i	$0.160781\pi$
$200$		0			0
$201$	−25.3492	+	14.6354i	−1.78800	+	1.03230i
$202$		0			0
$203$	−11.4349	−	15.9385i	−0.802574	−	1.11867i
$204$		0			0
$205$	11.0227	−	6.36396i	0.769859	−	0.444478i
$206$		0			0
$207$	−11.7919	−	6.80803i	−0.819590	−	0.473191i
$208$		0			0
$209$		−	8.23999i		−	0.569972i
$210$		0			0
$211$	−25.4252			−1.75034			−0.875171	−	0.483813i	$-0.839251\pi$
$211$	−25.4252			−1.75034			−0.875171	+	0.483813i	$0.839251\pi$
$212$		0			0
$213$	−13.2621	+	22.9706i	−0.908701	+	1.57392i
$214$		0			0
$215$	5.34267	+	9.25378i	0.364367	+	0.631103i
$216$		0			0
$217$	−2.10660	−	21.2664i	−0.143005	−	1.44366i
$218$		0			0
$219$	−20.6112	−	35.6996i	−1.39278	−	2.41236i
$220$		0			0
$221$	−21.4150	−	12.3640i	−1.44053	−	0.831690i
$222$		0			0
$223$	1.04322			0.0698593			0.0349296	−	0.999390i	$-0.488879\pi$
$223$	1.04322			0.0698593			0.0349296	+	0.999390i	$0.488879\pi$
$224$		0			0
$225$	12.4853			0.832352
$226$		0			0
$227$	15.0808	+	8.70693i	1.00095	+	0.577899i	0.908530	−	0.417821i	$-0.137206\pi$
$227$	15.0808	+	8.70693i	1.00095	+	0.577899i	0.0924215	+	0.995720i	$0.470539\pi$
$228$		0			0
$229$	−4.75039	−	8.22792i	−0.313915	−	0.543716i	0.665291	−	0.746584i	$-0.268307\pi$
$229$	−4.75039	−	8.22792i	−0.313915	−	0.543716i	−0.979206	+	0.202867i	$0.934974\pi$
$230$		0			0
$231$	−7.23159	+	15.9843i	−0.475804	+	1.05169i
$232$		0			0
$233$	−9.10660	−	15.7731i	−0.596593	−	1.03333i	−0.993320	−	0.115393i	$-0.963187\pi$
$233$	−9.10660	−	15.7731i	−0.596593	−	1.03333i	0.396727	−	0.917937i	$-0.370146\pi$
$234$		0			0
$235$	−7.89860	+	13.6808i	−0.515248	+	0.892435i
$236$		0			0
$237$	−25.3864			−1.64902
$238$		0			0
$239$		−	9.25378i		−	0.598577i	−0.954163	−	0.299289i	$-0.903251\pi$
$239$		−	9.25378i		−	0.598577i	0.954163	−	0.299289i	$-0.0967494\pi$
$240$		0			0
$241$	−11.2279	−	6.48244i	−0.723254	−	0.417571i	0.0926951	−	0.995695i	$-0.470452\pi$
$241$	−11.2279	−	6.48244i	−0.723254	−	0.417571i	−0.815949	+	0.578124i	$0.803785\pi$
$242$		0			0
$243$	−3.98805	+	2.30250i	−0.255834	+	0.147706i
$244$		0			0
$245$	11.8887	−	2.37868i	0.759543	−	0.151968i
$246$		0			0
$247$	19.3475	−	11.1703i	1.23105	−	0.710749i
$248$		0			0
$249$	18.4853	−	32.0174i	1.17146	−	2.02902i
$250$		0			0
$251$		−	0.737669i		−	0.0465613i	−0.999729	−	0.0232806i	$-0.992589\pi$
$251$		−	0.737669i		−	0.0465613i	0.999729	−	0.0232806i	$-0.00741113\pi$
$252$		0			0
$253$		−	4.75736i		−	0.299093i
$254$		0			0
$255$	−11.0094	+	19.0689i	−0.689437	+	1.19414i
$256$		0			0
$257$	1.86396	−	1.07616i	0.116271	−	0.0671289i	−0.440737	−	0.897636i	$-0.645283\pi$
$257$	1.86396	−	1.07616i	0.116271	−	0.0671289i	0.557008	+	0.830507i	$0.311949\pi$
$258$		0			0
$259$	1.35518	−	2.99542i	0.0842071	−	0.186127i
$260$		0			0
$261$	40.0834	−	23.1421i	2.48110	−	1.43246i
$262$		0			0
$263$	13.2224	+	7.63398i	0.815331	+	0.470731i	0.848804	−	0.528708i	$-0.177323\pi$
$263$	13.2224	+	7.63398i	0.815331	+	0.470731i	−0.0334730	+	0.999440i	$0.510657\pi$
$264$		0			0
$265$			2.74666i			0.168726i
$266$		0			0
$267$	35.0532			2.14522
$268$		0			0
$269$	−5.97514	+	10.3492i	−0.364311	+	0.631004i	−0.988665	−	0.150137i	$-0.952029\pi$
$269$	−5.97514	+	10.3492i	−0.364311	+	0.631004i	0.624355	+	0.781141i	$0.285362\pi$
$270$		0			0
$271$	−2.93214	−	5.07862i	−0.178115	−	0.308504i	0.763120	−	0.646257i	$-0.223667\pi$
$271$	−2.93214	−	5.07862i	−0.178115	−	0.308504i	−0.941235	+	0.337753i	$0.890333\pi$
$272$		0			0
$273$	−47.3345	+	4.68885i	−2.86482	+	0.283782i
$274$		0			0
$275$	2.18114	+	3.77784i	0.131528	+	0.227812i
$276$		0			0
$277$	24.0131	+	13.8640i	1.44281	+	0.833005i	0.998036	−	0.0626400i	$-0.0199520\pi$
$277$	24.0131	+	13.8640i	1.44281	+	0.833005i	0.444770	+	0.895645i	$0.353285\pi$
$278$		0			0
$279$	50.4236			3.01878
$280$		0			0
$281$	−16.2426			−0.968955			−0.484477	−	0.874804i	$-0.660990\pi$
$281$	−16.2426			−0.968955			−0.484477	+	0.874804i	$0.660990\pi$
$282$		0			0
$283$	5.98208	+	3.45375i	0.355597	+	0.205304i	0.667148	−	0.744925i	$-0.267515\pi$
$283$	5.98208	+	3.45375i	0.355597	+	0.205304i	−0.311550	+	0.950230i	$0.600848\pi$
$284$		0			0
$285$	−9.94655	−	17.2279i	−0.589183	−	1.02049i
$286$		0			0
$287$	−11.3335	−	15.7972i	−0.668997	−	0.932479i
$288$		0			0
$289$	0.242641	+	0.420266i	0.0142730	+	0.0247215i
$290$		0			0
$291$	8.98916	−	15.5697i	0.526954	−	0.912711i
$292$		0			0
$293$	−15.2913			−0.893326			−0.446663	−	0.894702i	$-0.647388\pi$
$293$	−15.2913			−0.893326			−0.446663	+	0.894702i	$0.647388\pi$
$294$		0			0
$295$			5.26573i			0.306583i
$296$		0			0
$297$	−18.6213	−	10.7510i	−1.08052	−	0.623838i
$298$		0			0
$299$	11.1703	−	6.44918i	0.645995	−	0.372966i
$300$		0			0
$301$	13.2621	−	9.51472i	0.764412	−	0.548419i
$302$		0			0
$303$	−21.2365	+	12.2609i	−1.22000	+	0.704369i
$304$		0			0
$305$	1.86396	−	3.22848i	0.106730	−	0.184862i
$306$		0			0
$307$			7.55568i			0.431225i	0.976479	+	0.215613i	$0.0691749\pi$
$307$			7.55568i			0.431225i	−0.976479	+	0.215613i	$0.930825\pi$
$308$		0			0
$309$		−	17.8284i		−	1.01422i
$310$		0			0
$311$	−12.5743	+	21.7793i	−0.713021	+	1.23499i	0.250697	+	0.968066i	$0.419340\pi$
$311$	−12.5743	+	21.7793i	−0.713021	+	1.23499i	−0.963718	+	0.266923i	$0.913993\pi$
$312$		0			0
$313$	−17.7426	+	10.2437i	−1.00287	+	0.579009i	−0.909097	−	0.416584i	$-0.863227\pi$
$313$	−17.7426	+	10.2437i	−1.00287	+	0.579009i	−0.0937762	+	0.995593i	$0.529894\pi$
$314$		0			0
$315$	2.81998	+	28.4680i	0.158888	+	1.60399i
$316$		0			0
$317$	−9.61332	+	5.55025i	−0.539938	+	0.311733i	−0.745054	−	0.667004i	$-0.767576\pi$
$317$	−9.61332	+	5.55025i	−0.539938	+	0.311733i	0.205116	+	0.978738i	$0.434243\pi$
$318$		0			0
$319$	14.0049	+	8.08571i	0.784121	+	0.452713i
$320$		0			0
$321$		−	25.3864i		−	1.41693i
$322$		0			0
$323$	−15.7972			−0.878979
$324$		0			0
$325$	−5.91359	+	10.2426i	−0.328027	+	0.568159i
$326$		0			0
$327$	−4.56026	−	7.89860i	−0.252183	−	0.436793i
$328$		0			0
$329$	21.9853	+	9.94655i	1.21209	+	0.548371i
$330$		0			0
$331$	10.9832	+	19.0234i	0.603691	+	1.04562i	0.992257	+	0.124202i	$0.0396371\pi$
$331$	10.9832	+	19.0234i	0.603691	+	1.04562i	−0.388566	+	0.921421i	$0.627030\pi$
$332$		0			0
$333$	6.71807	+	3.87868i	0.368148	+	0.212550i
$334$		0			0
$335$	−16.6762			−0.911118
$336$		0			0
$337$	2.24264			0.122164			0.0610822	−	0.998133i	$-0.480545\pi$
$337$	2.24264			0.122164			0.0610822	+	0.998133i	$0.480545\pi$
$338$		0			0
$339$	−11.1703	−	6.44918i	−0.606688	−	0.350271i
$340$		0			0
$341$	8.80884	+	15.2574i	0.477025	+	0.826232i
$342$		0			0
$343$	−5.40596	−	17.7137i	−0.291894	−	0.956451i
$344$		0			0
$345$	−5.74264	−	9.94655i	−0.309173	−	0.535504i
$346$		0			0
$347$	14.0678	−	24.3661i	0.755198	−	1.30804i	−0.190078	−	0.981769i	$-0.560874\pi$
$347$	14.0678	−	24.3661i	0.755198	−	1.30804i	0.945276	−	0.326273i	$-0.105793\pi$
$348$		0			0
$349$	−33.8726			−1.81316			−0.906579	−	0.422036i	$-0.861316\pi$
$349$	−33.8726			−1.81316			−0.906579	+	0.422036i	$0.861316\pi$
$350$		0			0
$351$		−	58.2973i		−	3.11168i
$352$		0			0
$353$	1.65076	+	0.953065i	0.0878610	+	0.0507265i	0.543287	−	0.839547i	$-0.317180\pi$
$353$	1.65076	+	0.953065i	0.0878610	+	0.0507265i	−0.455426	+	0.890274i	$0.650513\pi$
$354$		0			0
$355$	−13.0868	+	7.55568i	−0.694576	+	0.401014i
$356$		0			0
$357$	30.6441	+	13.8640i	1.62186	+	0.733759i
$358$		0			0
$359$	1.43059	−	0.825952i	0.0755037	−	0.0435921i	−0.461773	−	0.886998i	$-0.652786\pi$
$359$	1.43059	−	0.825952i	0.0755037	−	0.0435921i	0.537277	+	0.843406i	$0.319453\pi$
$360$		0			0
$361$	−2.36396	+	4.09450i	−0.124419	+	0.215500i
$362$		0			0
$363$			18.9787i			0.996123i
$364$		0			0
$365$		−	23.4853i		−	1.22928i
$366$		0			0
$367$	−9.96621	+	17.2620i	−0.520232	+	0.901068i	0.479491	+	0.877547i	$0.340821\pi$
$367$	−9.96621	+	17.2620i	−0.520232	+	0.901068i	−0.999723	+	0.0235217i	$0.992512\pi$
$368$		0			0
$369$	39.7279	−	22.9369i	2.06815	−	1.19405i
$370$		0			0
$371$	4.17516	−	0.413582i	0.216764	−	0.0214721i
$372$		0			0
$373$	−4.11999	+	2.37868i	−0.213325	+	0.123163i	−0.602856	−	0.797850i	$-0.705971\pi$
$373$	−4.11999	+	2.37868i	−0.213325	+	0.123163i	0.389531	+	0.921014i	$0.372637\pi$
$374$		0			0
$375$	31.9218	+	18.4301i	1.64843	+	0.951724i
$376$		0			0
$377$			43.8446i			2.25811i
$378$		0			0
$379$	−35.4274			−1.81978			−0.909892	−	0.414844i	$-0.863836\pi$
$379$	−35.4274			−1.81978			−0.909892	+	0.414844i	$0.863836\pi$
$380$		0			0
$381$	−32.0174	+	55.4558i	−1.64030	+	2.84109i
$382$		0			0
$383$	−17.4586	−	30.2392i	−0.892093	−	1.54515i	−0.837361	−	0.546650i	$-0.815903\pi$
$383$	−17.4586	−	30.2392i	−0.892093	−	1.54515i	−0.0547321	−	0.998501i	$-0.517430\pi$
$384$		0			0
$385$	−8.12132	+	5.82655i	−0.413901	+	0.296949i
$386$		0			0
$387$	19.2560	+	33.3524i	0.978838	+	1.69540i
$388$		0			0
$389$	0.148586	+	0.0857864i	0.00753363	+	0.00434955i	0.503762	−	0.863842i	$-0.331949\pi$
$389$	0.148586	+	0.0857864i	0.00753363	+	0.00434955i	−0.496228	+	0.868192i	$0.665282\pi$
$390$		0			0
$391$	−9.12051			−0.461244
$392$		0			0
$393$	13.7279			0.692482
$394$		0			0
$395$	−12.5255	−	7.23159i	−0.630226	−	0.363861i
$396$		0			0
$397$	−4.75039	−	8.22792i	−0.238415	−	0.412948i	0.721844	−	0.692055i	$-0.243295\pi$
$397$	−4.75039	−	8.22792i	−0.238415	−	0.412948i	−0.960260	+	0.279108i	$0.909961\pi$
$398$		0			0
$399$	−24.6902	+	17.7137i	−1.23606	+	0.886795i
$400$		0			0
$401$	2.37868	+	4.11999i	0.118786	+	0.205743i	0.919287	−	0.393589i	$-0.128767\pi$
$401$	2.37868	+	4.11999i	0.118786	+	0.205743i	−0.800501	+	0.599331i	$0.795433\pi$
$402$		0			0
$403$	−23.8829	+	41.3664i	−1.18969	+	2.06061i
$404$		0			0
$405$	−19.4728			−0.967612
$406$		0			0
$407$			2.71037i			0.134348i
$408$		0			0
$409$	10.3492	+	5.97514i	0.511737	+	0.295452i	0.733547	−	0.679638i	$-0.237863\pi$
$409$	10.3492	+	5.97514i	0.511737	+	0.295452i	−0.221810	+	0.975090i	$0.571197\pi$
$410$		0			0
$411$	12.5255	−	7.23159i	0.617837	−	0.356708i
$412$		0			0
$413$	8.00436	−	0.792893i	0.393869	−	0.0390157i
$414$		0			0
$415$	18.2410	−	10.5315i	0.895417	−	0.516969i
$416$		0			0
$417$	−16.2426	+	28.1331i	−0.795406	+	1.37768i
$418$		0			0
$419$			6.08034i			0.297044i	0.988909	+	0.148522i	$0.0474516\pi$
$419$			6.08034i			0.297044i	−0.988909	+	0.148522i	$0.952548\pi$
$420$		0			0
$421$		−	16.2426i		−	0.791618i	−0.918333	−	0.395809i	$-0.870464\pi$
$421$		−	16.2426i		−	0.791618i	0.918333	−	0.395809i	$-0.129536\pi$
$422$		0			0
$423$	−28.4680	+	49.3081i	−1.38416	+	2.39744i
$424$		0			0
$425$	7.24264	−	4.18154i	0.351320	−	0.202835i
$426$		0			0
$427$	−5.18823	−	2.34725i	−0.251076	−	0.113591i
$428$		0			0
$429$	33.9596	−	19.6066i	1.63959	−	0.946616i
$430$		0			0
$431$	13.6808	+	7.89860i	0.658980	+	0.380462i	0.791888	−	0.610666i	$-0.209098\pi$
$431$	13.6808	+	7.89860i	0.658980	+	0.380462i	−0.132909	+	0.991128i	$0.542432\pi$
$432$		0			0
$433$			13.6823i			0.657531i	0.944412	+	0.328765i	$0.106633\pi$
$433$			13.6823i			0.657531i	−0.944412	+	0.328765i	$0.893367\pi$
$434$		0			0
$435$	39.0413			1.87188
$436$		0			0
$437$	4.11999	−	7.13604i	0.197086	−	0.341363i
$438$		0			0
$439$	10.4245	+	18.0558i	0.497536	+	0.861758i	0.999996	−	0.00284264i	$-0.000904841\pi$
$439$	10.4245	+	18.0558i	0.497536	+	0.861758i	−0.502460	+	0.864601i	$0.667572\pi$
$440$		0			0
$441$	42.8492	−	8.57321i	2.04044	−	0.408248i
$442$		0			0
$443$	8.53744	+	14.7873i	0.405626	+	0.702565i	0.994394	−	0.105737i	$-0.0337203\pi$
$443$	8.53744	+	14.7873i	0.405626	+	0.702565i	−0.588768	+	0.808302i	$0.700387\pi$
$444$		0			0
$445$	17.2950	+	9.98528i	0.819862	+	0.473348i
$446$		0			0
$447$	15.6330			0.739414
$448$		0			0
$449$	13.7574			0.649250			0.324625	−	0.945843i	$-0.394762\pi$
$449$	13.7574			0.649250			0.324625	+	0.945843i	$0.394762\pi$
$450$		0			0
$451$	13.8807	+	8.01401i	0.653615	+	0.377365i
$452$		0			0
$453$	−5.25770	−	9.10660i	−0.247028	−	0.427865i
$454$		0			0
$455$	−24.6902	−	11.1703i	−1.15749	−	0.523672i
$456$		0			0
$457$	9.74264	+	16.8747i	0.455742	+	0.789367i	0.998731	−	0.0503724i	$-0.0160408\pi$
$457$	9.74264	+	16.8747i	0.455742	+	0.789367i	−0.542989	+	0.839740i	$0.682707\pi$
$458$		0			0
$459$	−20.6112	+	35.6996i	−0.962048	+	1.66632i
$460$		0			0
$461$	19.1757			0.893099			0.446550	−	0.894759i	$-0.352653\pi$
$461$	19.1757			0.893099			0.446550	+	0.894759i	$0.352653\pi$
$462$		0			0
$463$			4.36227i			0.202732i	0.994849	+	0.101366i	$0.0323213\pi$
$463$			4.36227i			0.202732i	−0.994849	+	0.101366i	$0.967679\pi$
$464$		0			0
$465$	36.8345	+	21.2664i	1.70816	+	0.986207i
$466$		0			0
$467$	27.6838	−	15.9833i	1.28106	−	0.739618i	0.304014	−	0.952668i	$-0.401673\pi$
$467$	27.6838	−	15.9833i	1.28106	−	0.739618i	0.977041	+	0.213050i	$0.0683397\pi$
$468$		0			0
$469$	2.51104	+	25.3492i	0.115949	+	1.17052i
$470$		0			0
$471$	25.4726	−	14.7066i	1.17372	−	0.677645i
$472$		0			0
$473$	−6.72792	+	11.6531i	−0.309350	+	0.535810i
$474$		0			0
$475$			7.55568i			0.346678i
$476$		0			0
$477$			9.89949i			0.453267i
$478$		0			0
$479$	8.79643	−	15.2359i	0.401919	−	0.696144i	−0.592039	−	0.805910i	$-0.701677\pi$
$479$	8.79643	−	15.2359i	0.401919	−	0.696144i	0.993958	+	0.109766i	$0.0350100\pi$
$480$		0			0
$481$	−6.36396	+	3.67423i	−0.290172	+	0.167531i
$482$		0			0
$483$	−14.2549	+	10.2270i	−0.648620	+	0.465345i
$484$		0			0
$485$	8.87039	−	5.12132i	0.402784	−	0.232547i
$486$		0			0
$487$	18.5651	+	10.7186i	0.841266	+	0.485705i	0.857694	−	0.514160i	$-0.171896\pi$
$487$	18.5651	+	10.7186i	0.841266	+	0.485705i	−0.0164286	+	0.999865i	$0.505230\pi$
$488$		0			0
$489$		−	10.5154i		−	0.475523i
$490$		0			0
$491$	24.1475			1.08976			0.544881	−	0.838513i	$-0.316575\pi$
$491$	24.1475			1.08976			0.544881	+	0.838513i	$0.316575\pi$
$492$		0			0
$493$	15.5014	−	26.8492i	0.698149	−	1.20923i
$494$		0			0
$495$	−11.7919	−	20.4241i	−0.530004	−	0.917994i
$496$		0			0
$497$	13.4558	+	18.7554i	0.603577	+	0.841294i
$498$		0			0
$499$	1.35518	+	2.34725i	0.0606664	+	0.105077i	0.894763	−	0.446540i	$-0.147344\pi$
$499$	1.35518	+	2.34725i	0.0606664	+	0.105077i	−0.834097	+	0.551618i	$0.814011\pi$
$500$		0			0
$501$	−62.0927	−	35.8492i	−2.77410	−	1.60163i
$502$		0			0
$503$	−3.12967			−0.139545			−0.0697724	−	0.997563i	$-0.522227\pi$
$503$	−3.12967			−0.139545			−0.0697724	+	0.997563i	$0.522227\pi$
$504$		0			0
$505$	−13.9706			−0.621682
$506$		0			0
$507$	57.8455	+	33.3971i	2.56901	+	1.48322i
$508$		0			0
$509$	−3.61269	−	6.25736i	−0.160130	−	0.277353i	0.774785	−	0.632224i	$-0.217858\pi$
$509$	−3.61269	−	6.25736i	−0.160130	−	0.277353i	−0.934915	+	0.354872i	$0.884525\pi$
$510$		0			0
$511$	−35.6996	+	3.53632i	−1.57926	+	0.156438i
$512$		0			0
$513$	−18.6213	−	32.2531i	−0.822151	−	1.42401i
$514$		0			0
$515$	5.07862	−	8.79643i	0.223791	−	0.387617i
$516$		0			0
$517$	−19.8931			−0.874897
$518$		0			0
$519$		−	46.8623i		−	2.05703i
$520$		0			0
$521$	−20.7426	−	11.9758i	−0.908752	−	0.524668i	−0.0287223	−	0.999587i	$-0.509144\pi$
$521$	−20.7426	−	11.9758i	−0.908752	−	0.524668i	−0.880029	+	0.474919i	$0.842477\pi$
$522$		0			0
$523$	−25.6123	+	14.7873i	−1.11995	+	0.646602i	−0.941388	−	0.337327i	$-0.890477\pi$
$523$	−25.6123	+	14.7873i	−1.11995	+	0.646602i	−0.178560	+	0.983929i	$0.557144\pi$
$524$		0			0
$525$	6.63103	−	14.6569i	0.289402	−	0.639678i
$526$		0			0
$527$	29.2505	−	16.8878i	1.27417	−	0.735642i
$528$		0			0
$529$	−9.12132	+	15.7986i	−0.396579	+	0.686895i
$530$		0			0
$531$			18.9787i			0.823605i
$532$		0			0
$533$			43.4558i			1.88228i
$534$		0			0
$535$	7.23159	−	12.5255i	0.312649	−	0.541524i
$536$		0			0
$537$	0.985281	−	0.568852i	0.0425180	−	0.0245478i
$538$		0			0
$539$	10.0797	+	11.4678i	0.434165	+	0.493952i
$540$		0			0
$541$	−18.1865	+	10.5000i	−0.781900	+	0.451430i	−0.837103	−	0.547045i	$-0.815753\pi$
$541$	−18.1865	+	10.5000i	−0.781900	+	0.451430i	0.0552031	+	0.998475i	$0.482419\pi$
$542$		0			0
$543$	23.5837	+	13.6161i	1.01207	+	0.584321i
$544$		0			0
$545$		−	5.19615i		−	0.222579i
$546$		0			0
$547$	9.25378			0.395663			0.197832	−	0.980236i	$-0.436610\pi$
$547$	9.25378			0.395663			0.197832	+	0.980236i	$0.436610\pi$
$548$		0			0
$549$	6.71807	−	11.6360i	0.286720	−	0.496614i
$550$		0			0
$551$	14.0049	+	24.2571i	0.596627	+	1.03339i
$552$		0			0
$553$	−9.10660	+	20.1287i	−0.387252	+	0.855960i
$554$		0			0
$555$	3.27171	+	5.66676i	0.138876	+	0.240541i
$556$		0			0
$557$	23.6799	+	13.6716i	1.00335	+	0.579283i	0.909237	−	0.416279i	$-0.136666\pi$
$557$	23.6799	+	13.6716i	1.00335	+	0.579283i	0.0941107	+	0.995562i	$0.469999\pi$
$558$		0			0
$559$	−36.4821			−1.54303
$560$		0			0
$561$	−27.7279			−1.17067
$562$		0			0
$563$	−13.1643	−	7.60043i	−0.554810	−	0.320320i	0.196250	−	0.980554i	$-0.437124\pi$
$563$	−13.1643	−	7.60043i	−0.554810	−	0.320320i	−0.751060	+	0.660234i	$0.770457\pi$
$564$		0			0
$565$	−3.67423	−	6.36396i	−0.154576	−	0.267734i
$566$		0			0
$567$	2.93214	+	29.6004i	0.123138	+	1.24310i
$568$		0			0
$569$	5.74264	+	9.94655i	0.240744	+	0.416981i	0.960926	−	0.276804i	$-0.0892752\pi$
$569$	5.74264	+	9.94655i	0.240744	+	0.416981i	−0.720182	+	0.693785i	$0.755942\pi$
$570$		0			0
$571$	9.44089	−	16.3521i	0.395089	−	0.684314i	−0.598023	−	0.801479i	$-0.704047\pi$
$571$	9.44089	−	16.3521i	0.395089	−	0.684314i	0.993113	+	0.117164i	$0.0373804\pi$
$572$		0			0
$573$	48.0262			2.00632
$574$		0			0
$575$			4.36227i			0.181919i
$576$		0			0
$577$	25.5000	+	14.7224i	1.06158	+	0.612903i	0.925869	−	0.377846i	$-0.123335\pi$
$577$	25.5000	+	14.7224i	1.06158	+	0.612903i	0.135710	+	0.990749i	$0.456668\pi$
$578$		0			0
$579$	−23.0569	+	13.3119i	−0.958214	+	0.553225i
$580$		0			0
$581$	−18.7554	−	26.1421i	−0.778105	−	1.08456i
$582$		0			0
$583$	−2.99542	+	1.72941i	−0.124058	+	0.0716248i
$584$		0			0
$585$	31.9706	−	55.3746i	1.32182	−	2.28946i
$586$		0			0
$587$		−	1.65433i		−	0.0682814i	−0.999417	−	0.0341407i	$-0.989131\pi$
$587$		−	1.65433i		−	0.0682814i	0.999417	−	0.0341407i	$-0.0108694\pi$
$588$		0			0
$589$			30.5147i			1.25734i
$590$		0			0
$591$	−19.8691	+	34.4144i	−0.817307	+	1.41562i
$592$		0			0
$593$	−1.86396	+	1.07616i	−0.0765437	+	0.0441925i	−0.537783	−	0.843083i	$-0.680738\pi$
$593$	−1.86396	+	1.07616i	−0.0765437	+	0.0441925i	0.461240	+	0.887276i	$0.347405\pi$
$594$		0			0
$595$	11.1703	+	15.5697i	0.457938	+	0.638295i
$596$		0			0
$597$	1.37333	−	0.792893i	0.0562067	−	0.0324510i
$598$		0			0
$599$	25.4726	+	14.7066i	1.04078	+	0.600896i	0.920055	−	0.391789i	$-0.128144\pi$
$599$	25.4726	+	14.7066i	1.04078	+	0.600896i	0.120728	+	0.992686i	$0.461477\pi$
$600$		0			0
$601$		−	21.4511i		−	0.875007i	−0.899217	−	0.437504i	$-0.855863\pi$
$601$		−	21.4511i		−	0.875007i	0.899217	−	0.437504i	$-0.144137\pi$
$602$		0			0
$603$	−60.1042			−2.44763
$604$		0			0
$605$	−5.40629	+	9.36396i	−0.219797	+	0.380699i
$606$		0			0
$607$	9.38132	+	16.2489i	0.380776	+	0.659523i	0.991173	−	0.132572i	$-0.0423236\pi$
$607$	9.38132	+	16.2489i	0.380776	+	0.659523i	−0.610397	+	0.792095i	$0.708990\pi$
$608$		0			0
$609$	−5.87868	−	59.3460i	−0.238216	−	2.40482i
$610$		0			0
$611$	−26.9675	−	46.7091i	−1.09099	−	1.88965i
$612$		0			0
$613$	−5.64191	−	3.25736i	−0.227875	−	0.131564i	0.381717	−	0.924279i	$-0.375333\pi$
$613$	−5.64191	−	3.25736i	−0.227875	−	0.131564i	−0.609591	+	0.792716i	$0.708666\pi$
$614$		0			0
$615$	38.6951			1.56034
$616$		0			0
$617$	−39.2132			−1.57866			−0.789332	−	0.613967i	$-0.789573\pi$
$617$	−39.2132			−1.57866			−0.789332	+	0.613967i	$0.789573\pi$
$618$		0			0
$619$	−36.7826	−	21.2365i	−1.47842	−	0.853565i	−0.478716	−	0.877970i	$-0.658898\pi$
$619$	−36.7826	−	21.2365i	−1.47842	−	0.853565i	−0.999702	+	0.0244049i	$0.992231\pi$
$620$		0			0
$621$	−10.7510	−	18.6213i	−0.431424	−	0.747248i
$622$		0			0
$623$	12.5743	−	27.7934i	0.503777	−	1.11352i
$624$		0			0
$625$	5.50000	+	9.52628i	0.220000	+	0.381051i
$626$		0			0
$627$	12.5255	−	21.6948i	0.500220	−	0.866406i
$628$		0			0
$629$	5.19615			0.207184
$630$		0			0
$631$		−	6.16919i		−	0.245591i	−0.992432	−	0.122796i	$-0.960814\pi$
$631$		−	6.16919i		−	0.245591i	0.992432	−	0.122796i	$-0.0391860\pi$
$632$		0			0
$633$	−66.9411	−	38.6485i	−2.66067	−	1.53614i
$634$		0			0
$635$	−31.5944	+	18.2410i	−1.25378	+	0.723873i
$636$		0			0
$637$	−13.2621	+	39.2132i	−0.525462	+	1.55368i
$638$		0			0
$639$	−47.1674	+	27.2321i	−1.86591	+	1.07729i
$640$		0			0
$641$	−21.9853	+	38.0796i	−0.868366	+	1.50405i	−0.00470114	+	0.999989i	$0.501496\pi$
$641$	−21.9853	+	38.0796i	−0.868366	+	1.50405i	−0.863665	+	0.504066i	$0.831837\pi$
$642$		0			0
$643$			28.9264i			1.14074i	0.821386	+	0.570372i	$0.193201\pi$
$643$			28.9264i			1.14074i	−0.821386	+	0.570372i	$0.806799\pi$
$644$		0			0
$645$			32.4853i			1.27911i
$646$		0			0
$647$	−1.88892	+	3.27171i	−0.0742611	+	0.128624i	−0.900765	−	0.434307i	$-0.856993\pi$
$647$	−1.88892	+	3.27171i	−0.0742611	+	0.128624i	0.826504	+	0.562931i	$0.190326\pi$
$648$		0			0
$649$	−5.74264	+	3.31552i	−0.225418	+	0.130145i
$650$		0			0
$651$	26.7804	−	59.1938i	1.04961	−	2.31999i
$652$		0			0
$653$	21.5636	−	12.4497i	0.843849	−	0.487196i	−0.0147219	−	0.999892i	$-0.504686\pi$
$653$	21.5636	−	12.4497i	0.843849	−	0.487196i	0.858571	+	0.512695i	$0.171353\pi$
$654$		0			0
$655$	6.77326	+	3.91055i	0.264653	+	0.152798i
$656$		0			0
$657$		−	84.6454i		−	3.30233i
$658$		0			0
$659$	19.2560			0.750108			0.375054	−	0.927003i	$-0.377624\pi$
$659$	19.2560			0.750108			0.375054	+	0.927003i	$0.377624\pi$
$660$		0			0
$661$	3.22848	−	5.59188i	0.125573	−	0.217499i	−0.796384	−	0.604792i	$-0.793256\pi$
$661$	3.22848	−	5.59188i	0.125573	−	0.217499i	0.921957	+	0.387293i	$0.126590\pi$
$662$		0			0
$663$	−37.5886	−	65.1053i	−1.45982	−	2.52848i
$664$		0			0
$665$	−17.2279	+	1.70656i	−0.668070	+	0.0661775i
$666$		0			0
$667$	8.08571	+	14.0049i	0.313080	+	0.542270i
$668$		0			0
$669$	2.74666	+	1.58579i	0.106192	+	0.0613100i
$670$		0			0
$671$	4.69450			0.181229
$672$		0			0
$673$	−2.24264			−0.0864474			−0.0432237	−	0.999065i	$-0.513763\pi$
$673$	−2.24264			−0.0864474			−0.0432237	+	0.999065i	$0.513763\pi$
$674$		0			0
$675$	17.0749	+	9.85818i	0.657212	+	0.379442i
$676$		0			0
$677$	−10.2437	−	17.7426i	−0.393698	−	0.681905i	0.599236	−	0.800572i	$-0.295471\pi$
$677$	−10.2437	−	17.7426i	−0.393698	−	0.681905i	−0.992934	+	0.118667i	$0.962138\pi$
$678$		0			0
$679$	−9.12051	−	12.7126i	−0.350013	−	0.487865i
$680$		0			0
$681$	26.4706	+	45.8484i	1.01435	+	1.75691i
$682$		0			0
$683$	−11.2478	+	19.4818i	−0.430385	+	0.745449i	−0.996906	−	0.0785980i	$-0.974956\pi$
$683$	−11.2478	+	19.4818i	−0.430385	+	0.745449i	0.566521	+	0.824047i	$0.308289\pi$
$684$		0			0
$685$	8.23999			0.314834
$686$		0			0
$687$		−	28.8840i		−	1.10199i
$688$		0			0
$689$	−8.12132	−	4.68885i	−0.309398	−	0.178631i
$690$		0			0
$691$	−7.89860	+	4.56026i	−0.300477	+	0.173480i	−0.642657	−	0.766154i	$-0.722168\pi$
$691$	−7.89860	+	4.56026i	−0.300477	+	0.173480i	0.342180	+	0.939634i	$0.388835\pi$
$692$		0			0
$693$	−29.2708	+	21.0000i	−1.11191	+	0.797724i
$694$		0			0
$695$	−16.0280	+	9.25378i	−0.607977	+	0.351016i
$696$		0			0
$697$	15.3640	−	26.6112i	0.581952	−	1.00797i
$698$		0			0
$699$		−	55.3713i		−	2.09433i
$700$		0			0
$701$			14.1421i			0.534141i	0.963677	+	0.267071i	$0.0860557\pi$
$701$			14.1421i			0.534141i	−0.963677	+	0.267071i	$0.913944\pi$
$702$		0			0
$703$	−2.34725	+	4.06555i	−0.0885282	+	0.153335i
$704$		0			0
$705$	−41.5919	+	24.0131i	−1.56644	+	0.904385i
$706$		0			0
$707$	2.10363	+	21.2365i	0.0791153	+	0.798679i
$708$		0			0
$709$	−10.5769	+	6.10660i	−0.397225	+	0.229338i	−0.685286	−	0.728274i	$-0.740323\pi$
$709$	−10.5769	+	6.10660i	−0.397225	+	0.229338i	0.288061	+	0.957612i	$0.406990\pi$
$710$		0			0
$711$	−45.1442	−	26.0640i	−1.69304	−	0.977478i
$712$		0			0
$713$			17.6177i			0.659787i
$714$		0			0
$715$	22.3406			0.835491
$716$		0			0
$717$	14.0665	−	24.3640i	0.525325	−	0.909889i
$718$		0			0
$719$	−1.88892	−	3.27171i	−0.0704448	−	0.122014i	0.828651	−	0.559765i	$-0.189109\pi$
$719$	−1.88892	−	3.27171i	−0.0704448	−	0.122014i	−0.899096	+	0.437751i	$0.855775\pi$
$720$		0			0
$721$	−14.1360	−	6.39540i	−0.526454	−	0.238177i
$722$		0			0
$723$	−19.7077	−	34.1348i	−0.732939	−	1.26949i
$724$		0			0
$725$	−12.8418	−	7.41421i	−0.476932	−	0.275357i
$726$		0			0
$727$	−31.2659			−1.15959			−0.579795	−	0.814762i	$-0.696867\pi$
$727$	−31.2659			−1.15959			−0.579795	+	0.814762i	$0.696867\pi$
$728$		0			0
$729$	19.7279			0.730664
$730$		0			0
$731$	22.3406	+	12.8984i	0.826297	+	0.477063i
$732$		0			0
$733$	−12.1859	−	21.1066i	−0.450097	−	0.779590i	0.548295	−	0.836285i	$-0.315277\pi$
$733$	−12.1859	−	21.1066i	−0.450097	−	0.779590i	−0.998392	+	0.0566949i	$0.981944\pi$
$734$		0			0
$735$	34.9172	+	11.8091i	1.28794	+	0.435587i
$736$		0			0
$737$	−10.5000	−	18.1865i	−0.386772	−	0.669910i
$738$		0			0
$739$	9.81512	−	17.0003i	0.361055	−	0.625365i	−0.627080	−	0.778955i	$-0.715750\pi$
$739$	9.81512	−	17.0003i	0.361055	−	0.625365i	0.988135	+	0.153590i	$0.0490834\pi$
$740$		0			0
$741$	67.9193			2.49508
$742$		0			0
$743$			53.4058i			1.95927i	0.200793	+	0.979634i	$0.435648\pi$
$743$			53.4058i			1.95927i	−0.200793	+	0.979634i	$0.564352\pi$
$744$		0			0
$745$	7.71320	+	4.45322i	0.282590	+	0.163153i
$746$		0			0
$747$	65.7441	−	37.9574i	2.40545	−	1.38879i
$748$		0			0
$749$	−20.1287	−	9.10660i	−0.735487	−	0.332748i
$750$		0			0
$751$	34.1348	−	19.7077i	1.24560	−	0.719146i	0.275369	−	0.961339i	$-0.411200\pi$
$751$	34.1348	−	19.7077i	1.24560	−	0.719146i	0.970228	+	0.242193i	$0.0778668\pi$
$752$		0			0
$753$	1.12132	−	1.94218i	0.0408632	−	0.0707771i
$754$		0			0
$755$		−	5.99085i		−	0.218029i
$756$		0			0
$757$		−	51.2132i		−	1.86138i	−0.365815	−	0.930688i	$-0.619210\pi$
$757$		−	51.2132i		−	1.86138i	0.365815	−	0.930688i	$-0.380790\pi$
$758$		0			0
$759$	7.23159	−	12.5255i	0.262490	−	0.454646i
$760$		0			0
$761$	0.106602	−	0.0615465i	0.00386431	−	0.00223106i	−0.498067	−	0.867139i	$-0.665956\pi$
$761$	0.106602	−	0.0615465i	0.00386431	−	0.00223106i	0.501931	+	0.864908i	$0.332623\pi$
$762$		0			0
$763$	−7.89860	+	0.782416i	−0.285948	+	0.0283254i
$764$		0			0
$765$	−39.1558	+	22.6066i	−1.41568	+	0.817343i
$766$		0			0
$767$	−15.5697	−	8.98916i	−0.562189	−	0.324580i
$768$		0			0
$769$			19.1757i			0.691492i	0.938328	+	0.345746i	$0.112374\pi$
$769$			19.1757i			0.691492i	−0.938328	+	0.345746i	$0.887626\pi$
$770$		0			0
$771$	6.54341			0.235655
$772$		0			0
$773$	−2.59808	+	4.50000i	−0.0934463	+	0.161854i	−0.908959	−	0.416885i	$-0.863122\pi$
$773$	−2.59808	+	4.50000i	−0.0934463	+	0.161854i	0.815513	+	0.578739i	$0.196455\pi$
$774$		0			0
$775$	−8.07729	−	13.9903i	−0.290145	−	0.502546i
$776$		0			0
$777$	8.12132	−	5.82655i	0.291351	−	0.209026i
$778$		0			0
$779$	13.8807	+	24.0420i	0.497327	+	0.861395i
$780$		0			0
$781$	−16.4800	−	9.51472i	−0.589700	−	0.340463i
$782$		0			0
$783$	73.0907			2.61205
$784$		0			0
$785$	16.7574			0.598096
$786$		0			0
$787$	−26.4062	−	15.2456i	−0.941278	−	0.543447i	−0.0509172	−	0.998703i	$-0.516214\pi$
$787$	−26.4062	−	15.2456i	−0.941278	−	0.543447i	−0.890361	+	0.455256i	$0.849548\pi$
$788$		0			0
$789$	23.2086	+	40.1985i	0.826248	+	1.43110i
$790$		0			0
$791$	−9.12051	+	6.54341i	−0.324288	+	0.232657i
$792$		0			0
$793$	6.36396	+	11.0227i	0.225991	+	0.391428i
$794$		0			0
$795$	−4.17516	+	7.23159i	−0.148078	+	0.256478i
$796$		0			0
$797$	−11.4069			−0.404054			−0.202027	−	0.979380i	$-0.564753\pi$
$797$	−11.4069			−0.404054			−0.202027	+	0.979380i	$0.564753\pi$
$798$		0			0
$799$			38.1378i			1.34922i
$800$		0			0
$801$	62.3345	+	35.9889i	2.20248	+	1.27160i
$802$		0			0
$803$	25.6123	−	14.7873i	0.903839	−	0.521832i
$804$		0			0
$805$	−9.94655	+	0.985281i	−0.350570	+	0.0347266i
$806$		0			0
$807$	−31.4635	+	18.1654i	−1.10757	+	0.639454i
$808$		0			0
$809$	−5.22792	+	9.05503i	−0.183804	+	0.318358i	−0.943173	−	0.332303i	$-0.892174\pi$
$809$	−5.22792	+	9.05503i	−0.183804	+	0.318358i	0.759369	+	0.650660i	$0.225508\pi$
$810$		0			0
$811$		−	33.3524i		−	1.17116i	−0.810614	−	0.585580i	$-0.800867\pi$
$811$		−	33.3524i		−	1.17116i	0.810614	−	0.585580i	$-0.199133\pi$
$812$		0			0
$813$		−	17.8284i		−	0.625270i
$814$		0			0
$815$	2.99542	−	5.18823i	0.104925	−	0.181736i
$816$		0			0
$817$	−20.1838	+	11.6531i	−0.706141	+	0.407690i
$818$		0			0
$819$	−88.9882	−	40.2599i	−3.10950	−	1.40679i
$820$		0			0
$821$	40.8263	−	23.5711i	1.42485	−	0.822636i	0.428139	−	0.903713i	$-0.359169\pi$
$821$	40.8263	−	23.5711i	1.42485	−	0.822636i	0.996708	+	0.0810768i	$0.0258359\pi$
$822$		0			0
$823$	−14.1391	−	8.16321i	−0.492858	−	0.284552i	0.232901	−	0.972500i	$-0.425178\pi$
$823$	−14.1391	−	8.16321i	−0.492858	−	0.284552i	−0.725759	+	0.687949i	$0.758511\pi$
$824$		0			0
$825$			13.2621i			0.461726i
$826$		0			0
$827$	−39.5705			−1.37600			−0.688000	−	0.725710i	$-0.741511\pi$
$827$	−39.5705			−1.37600			−0.688000	+	0.725710i	$0.741511\pi$
$828$		0			0
$829$	17.2950	−	29.9558i	0.600681	−	1.04041i	−0.392037	−	0.919949i	$-0.628230\pi$
$829$	17.2950	−	29.9558i	0.600681	−	1.04041i	0.992718	−	0.120460i	$-0.0384370\pi$
$830$		0			0
$831$	42.1488	+	73.0039i	1.46213	+	2.53248i
$832$		0			0
$833$	21.9853	−	19.3242i	0.761745	−	0.669545i
$834$		0			0
$835$	−20.4241	−	35.3756i	−0.706805	−	1.22422i
$836$		0			0
$837$	68.9594	+	39.8137i	2.38358	+	1.37616i
$838$		0			0
$839$	−40.9081			−1.41230			−0.706152	−	0.708061i	$-0.749570\pi$
$839$	−40.9081			−1.41230			−0.706152	+	0.708061i	$0.749570\pi$
$840$		0			0
$841$	−25.9706			−0.895537
$842$		0			0
$843$	−42.7647	−	24.6902i	−1.47289	−	0.850376i
$844$		0			0
$845$	19.0271	+	32.9558i	0.654551	+	1.13372i
$846$		0			0
$847$	15.0481	+	6.80803i	0.517058	+	0.233927i
$848$		0			0
$849$	10.5000	+	18.1865i	0.360359	+	0.624160i
$850$		0			0
$851$	−1.35518	+	2.34725i	−0.0464551	+	0.0804627i
$852$		0			0
$853$	−5.91359			−0.202478			−0.101239	−	0.994862i	$-0.532281\pi$
$853$	−5.91359			−0.202478			−0.101239	+	0.994862i	$0.532281\pi$
$854$		0			0
$855$		−	40.8482i		−	1.39698i
$856$		0			0
$857$	20.7426	+	11.9758i	0.708555	+	0.409084i	0.810526	−	0.585703i	$-0.199181\pi$
$857$	20.7426	+	11.9758i	0.708555	+	0.409084i	−0.101971	+	0.994787i	$0.532515\pi$
$858$		0			0
$859$	−15.2359	+	8.79643i	−0.519841	+	0.300130i	−0.736869	−	0.676035i	$-0.763697\pi$
$859$	−15.2359	+	8.79643i	−0.519841	+	0.300130i	0.217029	+	0.976165i	$0.430363\pi$
$860$		0			0
$861$	−5.82655	−	58.8198i	−0.198568	−	2.00457i
$862$		0			0
$863$	6.58342	−	3.80094i	0.224102	−	0.129385i	−0.383746	−	0.923439i	$-0.625366\pi$
$863$	6.58342	−	3.80094i	0.224102	−	0.129385i	0.607848	+	0.794053i	$0.292033\pi$
$864$		0			0
$865$	13.3492	−	23.1216i	0.453888	−	0.786157i
$866$		0			0
$867$			1.47534i			0.0501051i
$868$		0			0
$869$		−	18.2132i		−	0.617841i
$870$		0			0
$871$	28.4680	−	49.3081i	0.964603	−	1.67074i
$872$		0			0
$873$	31.9706	−	18.4582i	1.08204	−	0.624716i
$874$		0			0
$875$	26.0640	−	18.6994i	0.881125	−	0.632154i
$876$		0			0
$877$	−26.7958	+	15.4706i	−0.904830	+	0.522404i	−0.878764	−	0.477256i	$-0.841631\pi$
$877$	−26.7958	+	15.4706i	−0.904830	+	0.522404i	−0.0260658	+	0.999660i	$0.508298\pi$
$878$		0			0
$879$	−40.2599	−	23.2441i	−1.35793	−	0.784003i
$880$		0			0
$881$			0.246186i			0.00829422i	0.999991	+	0.00414711i	$0.00132007\pi$
$881$			0.246186i			0.00829422i	−0.999991	+	0.00414711i	$0.998680\pi$
$882$		0			0
$883$	25.4252			0.855626			0.427813	−	0.903867i	$-0.359284\pi$
$883$	25.4252			0.855626			0.427813	+	0.903867i	$0.359284\pi$
$884$		0			0
$885$	−8.00436	+	13.8640i	−0.269064	+	0.466032i
$886$		0			0
$887$	19.6716	+	34.0722i	0.660508	+	1.14403i	0.980482	+	0.196608i	$0.0629925\pi$
$887$	19.6716	+	34.0722i	0.660508	+	1.14403i	−0.319974	+	0.947426i	$0.603674\pi$
$888$		0			0
$889$	32.4853	+	45.2795i	1.08952	+	1.51863i
$890$		0			0
$891$	−12.2609	−	21.2365i	−0.410755	−	0.711448i
$892$		0			0
$893$	−29.8396	−	17.2279i	−0.998545	−	0.576510i
$894$		0			0
$895$	0.648175			0.0216661
$896$		0			0
$897$	39.2132			1.30929
$898$		0			0
$899$	−51.8635	−	29.9434i	−1.72974	−	0.998668i
$900$		0			0
$901$	3.31552	+	5.74264i	0.110456	+	0.191315i
$902$		0			0
$903$	49.3804	−	4.89151i	1.64328	−	0.162779i
$904$		0			0
$905$	7.75736	+	13.4361i	0.257863	+	0.446632i
$906$		0			0
$907$	7.89860	−	13.6808i	0.262269	−	0.454263i	−0.704576	−	0.709629i	$-0.748863\pi$
$907$	7.89860	−	13.6808i	0.262269	−	0.454263i	0.966844	+	0.255366i	$0.0821960\pi$
$908$		0			0
$909$	−50.3526			−1.67009
$910$		0			0
$911$			50.1019i			1.65995i	0.557799	+	0.829976i	$0.311646\pi$
$911$			50.1019i			1.65995i	−0.557799	+	0.829976i	$0.688354\pi$
$912$		0			0
$913$	22.9706	+	13.2621i	0.760215	+	0.438910i
$914$		0			0
$915$	9.81512	−	5.66676i	0.324478	−	0.187337i
$916$		0			0
$917$	4.92447	−	10.8848i	0.162620	−	0.359447i
$918$		0			0
$919$	25.9309	−	14.9712i	0.855383	−	0.493856i	−0.00708041	−	0.999975i	$-0.502254\pi$
$919$	25.9309	−	14.9712i	0.855383	−	0.493856i	0.862463	+	0.506119i	$0.168920\pi$
$920$		0			0
$921$	−11.4853	+	19.8931i	−0.378453	+	0.655500i
$922$		0			0
$923$		−	51.5934i		−	1.69822i
$924$		0			0
$925$		−	2.48528i		−	0.0817155i
$926$		0			0
$927$	18.3043	−	31.7040i	0.601192	−	1.04130i
$928$		0			0
$929$	11.9558	−	6.90271i	0.392259	−	0.226471i	−0.290880	−	0.956760i	$-0.593948\pi$
$929$	11.9558	−	6.90271i	0.392259	−	0.226471i	0.683138	+	0.730289i	$0.260615\pi$
$930$		0			0
$931$	5.18823	+	25.9309i	0.170037	+	0.849853i
$932$		0			0
$933$	−66.2127	+	38.2279i	−2.16771	+	1.25153i
$934$		0			0
$935$	−13.6808	−	7.89860i	−0.447409	−	0.258312i
$936$		0			0
$937$			24.4949i			0.800213i	0.916469	+	0.400107i	$0.131027\pi$
$937$			24.4949i			0.800213i	−0.916469	+	0.400107i	$0.868973\pi$
$938$		0			0
$939$	−62.2853			−2.03260
$940$		0			0
$941$	−26.0423	+	45.1066i	−0.848955	+	1.47043i	0.0331867	+	0.999449i	$0.489434\pi$
$941$	−26.0423	+	45.1066i	−0.848955	+	1.47043i	−0.882142	+	0.470984i	$0.843899\pi$
$942$		0			0
$943$	8.01401	+	13.8807i	0.260972	+	0.452017i
$944$		0			0
$945$	−18.6213	+	41.1595i	−0.605752	+	1.33892i
$946$		0			0
$947$	17.9008	+	31.0051i	0.581699	+	1.00753i	0.995278	+	0.0970636i	$0.0309450\pi$
$947$	17.9008	+	31.0051i	0.581699	+	1.00753i	−0.413580	+	0.910468i	$0.635722\pi$
$948$		0			0
$949$	69.4412	+	40.0919i	2.25416	+	1.30144i
$950$		0			0
$951$	−33.7474			−1.09434
$952$		0			0
$953$	50.1838			1.62561			0.812806	−	0.582535i	$-0.197939\pi$
$953$	50.1838			1.62561			0.812806	+	0.582535i	$0.197939\pi$
$954$		0			0
$955$	23.6958	+	13.6808i	0.766778	+	0.442699i
$956$		0			0
$957$	24.5819	+	42.5772i	0.794621	+	1.37632i
$958$		0			0
$959$	−1.24075	−	12.5255i	−0.0400658	−	0.404469i
$960$		0			0
$961$	−17.1213	−	29.6550i	−0.552301	−	0.956613i
$962$		0			0
$963$	26.0640	−	45.1442i	0.839902	−	1.45475i
$964$		0			0
$965$	−15.1682			−0.488281
$966$		0			0
$967$			2.55536i			0.0821749i	0.999156	+	0.0410874i	$0.0130822\pi$
$967$			2.55536i			0.0821749i	−0.999156	+	0.0410874i	$0.986918\pi$
$968$		0			0
$969$	−41.5919	−	24.0131i	−1.33612	−	0.771411i
$970$		0			0
$971$	−28.9615	+	16.7209i	−0.929419	+	0.536601i	−0.886628	−	0.462483i	$-0.846958\pi$
$971$	−28.9615	+	16.7209i	−0.929419	+	0.536601i	−0.0427915	+	0.999084i	$0.513625\pi$
$972$		0			0
$973$	16.4800	+	22.9706i	0.528324	+	0.736402i
$974$		0			0
$975$	−31.1394	+	17.9783i	−0.997258	+	0.575767i
$976$		0			0
$977$	−25.3492	+	43.9062i	−0.810994	+	1.40468i	0.101175	+	0.994869i	$0.467740\pi$
$977$	−25.3492	+	43.9062i	−0.810994	+	1.40468i	−0.912169	+	0.409814i	$0.865593\pi$
$978$		0			0
$979$			25.1485i			0.803751i
$980$		0			0
$981$		−	18.7279i		−	0.597937i
$982$		0			0
$983$	0.782416	−	1.35518i	0.0249552	−	0.0432237i	−0.853278	−	0.521456i	$-0.825389\pi$
$983$	0.782416	−	1.35518i	0.0249552	−	0.0432237i	0.878233	+	0.478232i	$0.158722\pi$
$984$		0			0
$985$	−19.6066	+	11.3199i	−0.624718	+	0.360681i
$986$		0			0
$987$	42.7647	+	59.6074i	1.36122	+	1.89733i
$988$		0			0
$989$	−11.6531	+	6.72792i	−0.370547	+	0.213935i
$990$		0			0
$991$	−26.1208	−	15.0808i	−0.829754	−	0.479059i	0.0240142	−	0.999712i	$-0.492355\pi$
$991$	−26.1208	−	15.0808i	−0.829754	−	0.479059i	−0.853769	+	0.520653i	$0.825689\pi$
$992$		0			0
$993$			66.7816i			2.11925i
$994$		0			0
$995$	0.903457			0.0286415
$996$		0			0
$997$	16.4905	−	28.5624i	0.522261	−	0.904582i	−0.477404	−	0.878684i	$-0.658422\pi$
$997$	16.4905	−	28.5624i	0.522261	−	0.904582i	0.999665	−	0.0258979i	$-0.00824447\pi$
$998$		0			0
$999$	6.12509	+	10.6090i	0.193789	+	0.335653i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	896.2.q.c.703.8	yes	16
4.3	odd	2	inner	896.2.q.c.703.2	yes	16
7.5	odd	6	inner	896.2.q.c.831.7	yes	16
8.3	odd	2	inner	896.2.q.c.703.7	yes	16
8.5	even	2	inner	896.2.q.c.703.1	✓	16
28.19	even	6	inner	896.2.q.c.831.1	yes	16
56.5	odd	6	inner	896.2.q.c.831.2	yes	16
56.19	even	6	inner	896.2.q.c.831.8	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
896.2.q.c.703.1	✓	16	8.5	even	2	inner
896.2.q.c.703.2	yes	16	4.3	odd	2	inner
896.2.q.c.703.7	yes	16	8.3	odd	2	inner
896.2.q.c.703.8	yes	16	1.1	even	1	trivial
896.2.q.c.831.1	yes	16	28.19	even	6	inner
896.2.q.c.831.2	yes	16	56.5	odd	6	inner
896.2.q.c.831.7	yes	16	7.5	odd	6	inner
896.2.q.c.831.8	yes	16	56.19	even	6	inner

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:	\( N \)	\(=\)	\( 896 = 2^{7} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	896.q (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.63287 + 1.52009i) q^{3} +(0.866025 + 1.50000i) q^{5} +(2.14973 - 1.54230i) q^{7} +(3.12132 + 5.40629i) q^{9} +O(q^{10})\)	\(q+(2.63287 + 1.52009i) q^{3} +(0.866025 + 1.50000i) q^{5} +(2.14973 - 1.54230i) q^{7} +(3.12132 + 5.40629i) q^{9} +(-1.09057 + 1.88892i) q^{11} -5.91359 q^{13} +5.26573i q^{15} +(3.62132 + 2.09077i) q^{17} +(-3.27171 + 1.88892i) q^{19} +(8.00436 - 0.792893i) q^{21} +(-1.88892 + 1.09057i) q^{23} +(1.00000 - 1.73205i) q^{25} +9.85818i q^{27} -7.41421i q^{29} +(4.03865 - 6.99514i) q^{31} +(-5.74264 + 3.31552i) q^{33} +(4.17516 + 1.88892i) q^{35} +(1.07616 - 0.621320i) q^{37} +(-15.5697 - 8.98916i) q^{39} -7.34847i q^{41} +6.16919 q^{43} +(-5.40629 + 9.36396i) q^{45} +(4.56026 + 7.89860i) q^{47} +(2.24264 - 6.63103i) q^{49} +(6.35630 + 11.0094i) q^{51} +(1.37333 + 0.792893i) q^{53} -3.77784 q^{55} -11.4853 q^{57} +(2.63287 + 1.52009i) q^{59} +(-1.07616 - 1.86396i) q^{61} +(15.0481 + 6.80803i) q^{63} +(-5.12132 - 8.87039i) q^{65} +(-4.81400 + 8.33810i) q^{67} -6.63103 q^{69} +8.72455i q^{71} +(-11.7426 - 6.77962i) q^{73} +(5.26573 - 3.04017i) q^{75} +(0.568852 + 5.74264i) q^{77} +(-7.23159 + 4.17516i) q^{79} +(-5.62132 + 9.73641i) q^{81} -12.1607i q^{83} +7.24264i q^{85} +(11.2702 - 19.5206i) q^{87} +(9.98528 - 5.76500i) q^{89} +(-12.7126 + 9.12051i) q^{91} +(21.2664 - 12.2782i) q^{93} +(-5.66676 - 3.27171i) q^{95} -5.91359i q^{97} -13.6161 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 16 q^{9}+O(q^{10}) \) 16 * q + 16 * q^9	\( 16 q + 16 q^{9} + 24 q^{17} + 16 q^{25} - 24 q^{33} - 32 q^{49} - 48 q^{57} - 48 q^{65} - 120 q^{73} - 56 q^{81} + 24 q^{89}+O(q^{100}) \) 16 * q + 16 * q^9 + 24 * q^17 + 16 * q^25 - 24 * q^33 - 32 * q^49 - 48 * q^57 - 48 * q^65 - 120 * q^73 - 56 * q^81 + 24 * q^89

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more