LMFDB - Embedded newform 1008.2.v.e.323.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1008,2,Mod(323,1008)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1008, base_ring=CyclotomicField(4))

chi = DirichletCharacter(H, H._module([2, 3, 2, 0]))

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

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

chi := DirichletCharacter("1008.323");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1008 = 2^{4} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1008.v (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:	$8.04892052375$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$20$ over $\Q(i)$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{4}]$

Embedding invariants

Embedding label			323.12
Character	$\chi$	$=$	1008.323
Dual form			1008.2.v.e.827.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.351970 + 1.36971i) q^{2} +(-1.75223 + 0.964197i) q^{4} +(-2.96859 - 2.96859i) q^{5} +1.00000 q^{7} +(-1.93741 - 2.06069i) q^{8} +O(q^{10})$	\(q+(0.351970 + 1.36971i) q^{2} +(-1.75223 + 0.964197i) q^{4} +(-2.96859 - 2.96859i) q^{5} +1.00000 q^{7} +(-1.93741 - 2.06069i) q^{8} +(3.02127 - 5.11098i) q^{10} +(0.569860 - 0.569860i) q^{11} +(2.53650 + 2.53650i) q^{13} +(0.351970 + 1.36971i) q^{14} +(2.14065 - 3.37900i) q^{16} +1.03528i q^{17} +(-5.23568 + 5.23568i) q^{19} +(8.06398 + 2.33936i) q^{20} +(0.981119 + 0.579972i) q^{22} +8.71217i q^{23} +12.6251i q^{25} +(-2.58151 + 4.36705i) q^{26} +(-1.75223 + 0.964197i) q^{28} +(6.05233 - 6.05233i) q^{29} +3.00413i q^{31} +(5.38170 + 1.74277i) q^{32} +(-1.41804 + 0.364388i) q^{34} +(-2.96859 - 2.96859i) q^{35} +(-0.149739 + 0.149739i) q^{37} +(-9.01419 - 5.32858i) q^{38} +(-0.365980 + 11.8687i) q^{40} -8.63459 q^{41} +(1.73121 + 1.73121i) q^{43} +(-0.449071 + 1.54798i) q^{44} +(-11.9332 + 3.06642i) q^{46} -4.10865 q^{47} +1.00000 q^{49} +(-17.2928 + 4.44366i) q^{50} +(-6.89022 - 1.99886i) q^{52} +(6.04092 + 6.04092i) q^{53} -3.38337 q^{55} +(-1.93741 - 2.06069i) q^{56} +(10.4202 + 6.15973i) q^{58} +(6.05121 - 6.05121i) q^{59} +(5.81897 + 5.81897i) q^{61} +(-4.11480 + 1.05736i) q^{62} +(-0.492902 + 7.98480i) q^{64} -15.0597i q^{65} +(0.0256948 - 0.0256948i) q^{67} +(-0.998214 - 1.81405i) q^{68} +(3.02127 - 5.11098i) q^{70} +14.5257i q^{71} -5.38496i q^{73} +(-0.257803 - 0.152396i) q^{74} +(4.12591 - 14.2224i) q^{76} +(0.569860 - 0.569860i) q^{77} +3.89876i q^{79} +(-16.3856 + 3.67615i) q^{80} +(-3.03912 - 11.8269i) q^{82} +(1.40691 + 1.40691i) q^{83} +(3.07333 - 3.07333i) q^{85} +(-1.76193 + 2.98060i) q^{86} +(-2.27836 - 0.0702547i) q^{88} -17.0358 q^{89} +(2.53650 + 2.53650i) q^{91} +(-8.40025 - 15.2658i) q^{92} +(-1.44612 - 5.62767i) q^{94} +31.0852 q^{95} +3.75210 q^{97} +(0.351970 + 1.36971i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 40 q^{7}+O(q^{10}) $ 40 * q + 40 * q^7	$ 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) $ 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times$.

$n$	$127$	$577$	$757$	$785$
$\chi(n)$	$-1$	$1$	$e\left(\frac{3}{4}\right)$	$-1$

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 $

$2$	0.351970	+	1.36971i	0.248880	+	0.968534i
$2$	0.351970	+	1.36971i	0.248880	+	0.968534i
$3$		0			0
$3$		0			0
$4$	−1.75223	+	0.964197i	−0.876117	+	0.482098i
$5$	−2.96859	−	2.96859i	−1.32760	−	1.32760i	−0.907463	−	0.420133i	$-0.861983\pi$
$5$	−2.96859	−	2.96859i	−1.32760	−	1.32760i	−0.420133	−	0.907463i	$-0.638017\pi$
$6$		0			0
$7$	1.00000			0.377964
$7$	1.00000			0.377964
$8$	−1.93741	−	2.06069i	−0.684977	−	0.728565i
$9$		0			0
$10$	3.02127	−	5.11098i	0.955409	−	1.61623i
$11$	0.569860	−	0.569860i	0.171819	−	0.171819i	−0.615959	−	0.787778i	$-0.711231\pi$
$11$	0.569860	−	0.569860i	0.171819	−	0.171819i	0.787778	+	0.615959i	$0.211231\pi$
$12$		0			0
$13$	2.53650	+	2.53650i	0.703498	+	0.703498i	0.965160	−	0.261661i	$-0.0842704\pi$
$13$	2.53650	+	2.53650i	0.703498	+	0.703498i	−0.261661	+	0.965160i	$0.584270\pi$
$14$	0.351970	+	1.36971i	0.0940679	+	0.366072i
$15$		0			0
$16$	2.14065	−	3.37900i	0.535162	−	0.844749i
$17$			1.03528i			0.251092i	0.992088	+	0.125546i	$0.0400683\pi$
$17$			1.03528i			0.251092i	−0.992088	+	0.125546i	$0.959932\pi$
$18$		0			0
$19$	−5.23568	+	5.23568i	−1.20115	+	1.20115i	−0.227329	+	0.973818i	$0.572999\pi$
$19$	−5.23568	+	5.23568i	−1.20115	+	1.20115i	−0.973818	+	0.227329i	$0.927001\pi$
$20$	8.06398	+	2.33936i	1.80316	+	0.523098i
$21$		0			0
$22$	0.981119	+	0.579972i	0.209175	+	0.123650i
$23$			8.71217i			1.81661i	0.418304	+	0.908307i	$0.362625\pi$
$23$			8.71217i			1.81661i	−0.418304	+	0.908307i	$0.637375\pi$
$24$		0			0
$25$			12.6251i			2.52502i
$26$	−2.58151	+	4.36705i	−0.506275	+	0.856449i
$27$		0			0
$28$	−1.75223	+	0.964197i	−0.331141	+	0.182216i
$29$	6.05233	−	6.05233i	1.12389	−	1.12389i	0.132739	−	0.991151i	$-0.457623\pi$
$29$	6.05233	−	6.05233i	1.12389	−	1.12389i	0.991151	−	0.132739i	$-0.0423772\pi$
$30$		0			0
$31$			3.00413i			0.539558i	0.962922	+	0.269779i	$0.0869506\pi$
$31$			3.00413i			0.539558i	−0.962922	+	0.269779i	$0.913049\pi$
$32$	5.38170	+	1.74277i	0.951360	+	0.308082i
$33$		0			0
$34$	−1.41804	+	0.364388i	−0.243192	+	0.0624920i
$35$	−2.96859	−	2.96859i	−0.501784	−	0.501784i
$36$		0			0
$37$	−0.149739	+	0.149739i	−0.0246169	+	0.0246169i	−0.719308	−	0.694691i	$-0.755541\pi$
$37$	−0.149739	+	0.149739i	−0.0246169	+	0.0246169i	0.694691	+	0.719308i	$0.255541\pi$
$38$	−9.01419	−	5.32858i	−1.46229	−	0.864410i
$39$		0			0
$40$	−0.365980	+	11.8687i	−0.0578666	+	1.87661i
$41$	−8.63459			−1.34850			−0.674248	−	0.738505i	$-0.735532\pi$
$41$	−8.63459			−1.34850			−0.674248	+	0.738505i	$0.735532\pi$
$42$		0			0
$43$	1.73121	+	1.73121i	0.264007	+	0.264007i	0.826680	−	0.562673i	$-0.190227\pi$
$43$	1.73121	+	1.73121i	0.264007	+	0.264007i	−0.562673	+	0.826680i	$0.690227\pi$
$44$	−0.449071	+	1.54798i	−0.0677000	+	0.233368i
$45$		0			0
$46$	−11.9332	+	3.06642i	−1.75945	+	0.452120i
$47$	−4.10865			−0.599308			−0.299654	−	0.954048i	$-0.596871\pi$
$47$	−4.10865			−0.599308			−0.299654	+	0.954048i	$0.596871\pi$
$48$		0			0
$49$	1.00000			0.142857
$50$	−17.2928	+	4.44366i	−2.44557	+	0.628428i
$51$		0			0
$52$	−6.89022	−	1.99886i	−0.955502	−	0.277192i
$53$	6.04092	+	6.04092i	0.829783	+	0.829783i	0.987487	−	0.157703i	$-0.0504089\pi$
$53$	6.04092	+	6.04092i	0.829783	+	0.829783i	−0.157703	+	0.987487i	$0.550409\pi$
$54$		0			0
$55$	−3.38337			−0.456213
$56$	−1.93741	−	2.06069i	−0.258897	−	0.275372i
$57$		0			0
$58$	10.4202	+	6.15973i	1.36824	+	0.808812i
$59$	6.05121	−	6.05121i	0.787800	−	0.787800i	−0.193333	−	0.981133i	$-0.561930\pi$
$59$	6.05121	−	6.05121i	0.787800	−	0.787800i	0.981133	+	0.193333i	$0.0619298\pi$
$60$		0			0
$61$	5.81897	+	5.81897i	0.745042	+	0.745042i	0.973544	−	0.228501i	$-0.0733826\pi$
$61$	5.81897	+	5.81897i	0.745042	+	0.745042i	−0.228501	+	0.973544i	$0.573383\pi$
$62$	−4.11480	+	1.05736i	−0.522580	+	0.134285i
$63$		0			0
$64$	−0.492902	+	7.98480i	−0.0616128	+	0.998100i
$65$		−	15.0597i		−	1.86792i
$66$		0			0
$67$	0.0256948	−	0.0256948i	0.00313912	−	0.00313912i	−0.705535	−	0.708675i	$-0.749293\pi$
$67$	0.0256948	−	0.0256948i	0.00313912	−	0.00313912i	0.708675	+	0.705535i	$0.249293\pi$
$68$	−0.998214	−	1.81405i	−0.121051	−	0.219986i
$69$		0			0
$70$	3.02127	−	5.11098i	0.361111	−	0.610879i
$71$			14.5257i			1.72388i	0.507008	+	0.861941i	$0.330752\pi$
$71$			14.5257i			1.72388i	−0.507008	+	0.861941i	$0.669248\pi$
$72$		0			0
$73$		−	5.38496i		−	0.630261i	−0.949048	−	0.315131i	$-0.897952\pi$
$73$		−	5.38496i		−	0.630261i	0.949048	−	0.315131i	$-0.102048\pi$
$74$	−0.257803	−	0.152396i	−0.0299690	−	0.0177156i
$75$		0			0
$76$	4.12591	−	14.2224i	0.473275	−	1.63142i
$77$	0.569860	−	0.569860i	0.0649416	−	0.0649416i
$78$		0			0
$79$			3.89876i			0.438645i	0.975652	+	0.219322i	$0.0703846\pi$
$79$			3.89876i			0.438645i	−0.975652	+	0.219322i	$0.929615\pi$
$80$	−16.3856	+	3.67615i	−1.83196	+	0.411006i
$81$		0			0
$82$	−3.03912	−	11.8269i	−0.335614	−	1.30606i
$83$	1.40691	+	1.40691i	0.154428	+	0.154428i	0.780092	−	0.625664i	$-0.215172\pi$
$83$	1.40691	+	1.40691i	0.154428	+	0.154428i	−0.625664	+	0.780092i	$0.715172\pi$
$84$		0			0
$85$	3.07333	−	3.07333i	0.333349	−	0.333349i
$86$	−1.76193	+	2.98060i	−0.189994	+	0.321406i
$87$		0			0
$88$	−2.27836	−	0.0702547i	−0.242874	−	0.00748917i
$89$	−17.0358			−1.80579			−0.902897	−	0.429856i	$-0.858564\pi$
$89$	−17.0358			−1.80579			−0.902897	+	0.429856i	$0.858564\pi$
$90$		0			0
$91$	2.53650	+	2.53650i	0.265897	+	0.265897i
$92$	−8.40025	−	15.2658i	−0.875786	−	1.59157i
$93$		0			0
$94$	−1.44612	−	5.62767i	−0.149156	−	0.580450i
$95$	31.0852			3.18928
$96$		0			0
$97$	3.75210			0.380968			0.190484	−	0.981690i	$-0.438994\pi$
$97$	3.75210			0.380968			0.190484	+	0.981690i	$0.438994\pi$
$98$	0.351970	+	1.36971i	0.0355543	+	0.138362i
$99$		0			0
$100$	−12.1731	−	22.1221i	−1.21731	−	2.21221i
$101$	−1.23327	−	1.23327i	−0.122715	−	0.122715i	0.643082	−	0.765797i	$-0.277655\pi$
$101$	−1.23327	−	1.23327i	−0.122715	−	0.122715i	−0.765797	+	0.643082i	$0.777655\pi$
$102$		0			0
$103$	14.3330			1.41227			0.706134	−	0.708078i	$-0.250438\pi$
$103$	14.3330			1.41227			0.706134	+	0.708078i	$0.250438\pi$
$104$	0.312710	−	10.1412i	0.0306637	−	0.994424i
$105$		0			0
$106$	−6.14811	+	10.4005i	−0.597157	+	1.01019i
$107$	−7.33395	+	7.33395i	−0.709000	+	0.709000i	−0.966325	−	0.257325i	$-0.917159\pi$
$107$	−7.33395	+	7.33395i	−0.709000	+	0.709000i	0.257325	+	0.966325i	$0.417159\pi$
$108$		0			0
$109$	−4.12218	−	4.12218i	−0.394833	−	0.394833i	0.481573	−	0.876406i	$-0.340066\pi$
$109$	−4.12218	−	4.12218i	−0.394833	−	0.394833i	−0.876406	+	0.481573i	$0.840066\pi$
$110$	−1.19084	−	4.63424i	−0.113542	−	0.441858i
$111$		0			0
$112$	2.14065	−	3.37900i	0.202272	−	0.319285i
$113$			12.1524i			1.14320i	0.820533	+	0.571599i	$0.193677\pi$
$113$			12.1524i			1.14320i	−0.820533	+	0.571599i	$0.806323\pi$
$114$		0			0
$115$	25.8629	−	25.8629i	2.41173	−	2.41173i
$116$	−4.76947	+	16.4407i	−0.442834	+	1.52648i
$117$		0			0
$118$	10.4183	+	6.15858i	0.959080	+	0.566943i
$119$			1.03528i			0.0949040i
$120$		0			0
$121$			10.3505i			0.940956i
$122$	−5.92222	+	10.0184i	−0.536172	+	0.907025i
$123$		0			0
$124$	−2.89657	−	5.26394i	−0.260120	−	0.472716i
$125$	22.6358	−	22.6358i	2.02461	−	2.02461i
$126$		0			0
$127$			1.32089i			0.117210i	0.998281	+	0.0586052i	$0.0186653\pi$
$127$			1.32089i			0.117210i	−0.998281	+	0.0586052i	$0.981335\pi$
$128$	−11.1104	+	2.13528i	−0.982028	+	0.188733i
$129$		0			0
$130$	20.6274	−	5.30055i	1.80915	−	0.464889i
$131$	−1.67723	−	1.67723i	−0.146540	−	0.146540i	0.630030	−	0.776571i	$-0.283043\pi$
$131$	−1.67723	−	1.67723i	−0.146540	−	0.146540i	−0.776571	+	0.630030i	$0.783043\pi$
$132$		0			0
$133$	−5.23568	+	5.23568i	−0.453991	+	0.453991i
$134$	0.0442383	+	0.0261507i	0.00382161	+	0.00225908i
$135$		0			0
$136$	2.13339	−	2.00576i	0.182937	−	0.171993i
$137$	8.49554			0.725823			0.362911	−	0.931824i	$-0.381783\pi$
$137$	8.49554			0.725823			0.362911	+	0.931824i	$0.381783\pi$
$138$		0			0
$139$	−7.80995	−	7.80995i	−0.662432	−	0.662432i	0.293521	−	0.955953i	$-0.405173\pi$
$139$	−7.80995	−	7.80995i	−0.662432	−	0.662432i	−0.955953	+	0.293521i	$0.905173\pi$
$140$	8.06398	+	2.33936i	0.681531	+	0.197712i
$141$		0			0
$142$	−19.8961	+	5.11261i	−1.66964	+	0.429041i
$143$	2.89090			0.241749
$144$		0			0
$145$	−35.9338			−2.98414
$146$	7.37585	−	1.89534i	0.610430	−	0.156860i
$147$		0			0
$148$	0.118000	−	0.406755i	0.00969952	−	0.0334350i
$149$	−13.1113	−	13.1113i	−1.07412	−	1.07412i	−0.997024	−	0.0770980i	$-0.975435\pi$
$149$	−13.1113	−	13.1113i	−1.07412	−	1.07412i	−0.0770980	−	0.997024i	$-0.524565\pi$
$150$		0			0
$151$	13.4389			1.09364			0.546822	−	0.837249i	$-0.315838\pi$
$151$	13.4389			1.09364			0.546822	+	0.837249i	$0.315838\pi$
$152$	20.9328	+	0.645476i	1.69787	+	0.0523550i
$153$		0			0
$154$	0.981119	+	0.579972i	0.0790608	+	0.0467354i
$155$	8.91804	−	8.91804i	0.716314	−	0.716314i
$156$		0			0
$157$	−5.92492	−	5.92492i	−0.472860	−	0.472860i	0.429979	−	0.902839i	$-0.358521\pi$
$157$	−5.92492	−	5.92492i	−0.472860	−	0.472860i	−0.902839	+	0.429979i	$0.858521\pi$
$158$	−5.34018	+	1.37225i	−0.424842	+	0.109170i
$159$		0			0
$160$	−10.8025	−	21.1497i	−0.854013	−	1.67203i
$161$			8.71217i			0.686615i
$162$		0			0
$163$	−1.82469	+	1.82469i	−0.142921	+	0.142921i	−0.774947	−	0.632026i	$-0.782224\pi$
$163$	−1.82469	+	1.82469i	−0.142921	+	0.142921i	0.632026	+	0.774947i	$0.282224\pi$
$164$	15.1298	−	8.32544i	1.18144	−	0.650108i
$165$		0			0
$166$	−1.43187	+	2.42225i	−0.111135	+	0.188003i
$167$			5.49283i			0.425048i	0.977156	+	0.212524i	$0.0681683\pi$
$167$			5.49283i			0.425048i	−0.977156	+	0.212524i	$0.931832\pi$
$168$		0			0
$169$		−	0.132347i		−	0.0101805i
$170$	5.29130	+	3.12786i	0.405824	+	0.239896i
$171$		0			0
$172$	−4.70271	−	1.36426i	−0.358579	−	0.104024i
$173$	−11.4180	+	11.4180i	−0.868093	+	0.868093i	−0.992261	−	0.124168i	$-0.960374\pi$
$173$	−11.4180	+	11.4180i	−0.868093	+	0.868093i	0.124168	+	0.992261i	$0.460374\pi$
$174$		0			0
$175$			12.6251i			0.954368i
$176$	−0.705684	−	3.14543i	−0.0531930	−	0.237095i
$177$		0			0
$178$	−5.99610	−	23.3342i	−0.449427	−	1.74897i
$179$	−5.47860	−	5.47860i	−0.409490	−	0.409490i	0.472071	−	0.881561i	$-0.343507\pi$
$179$	−5.47860	−	5.47860i	−0.409490	−	0.409490i	−0.881561	+	0.472071i	$0.843507\pi$
$180$		0			0
$181$	−9.42734	+	9.42734i	−0.700728	+	0.700728i	−0.964567	−	0.263838i	$-0.915011\pi$
$181$	−9.42734	+	9.42734i	−0.700728	+	0.700728i	0.263838	+	0.964567i	$0.415011\pi$
$182$	−2.58151	+	4.36705i	−0.191354	+	0.323707i
$183$		0			0
$184$	17.9531	−	16.8790i	1.32352	−	1.24434i
$185$	0.889027			0.0653625
$186$		0			0
$187$	0.589965	+	0.589965i	0.0431425	+	0.0431425i
$188$	7.19931	−	3.96154i	0.525064	−	0.288925i
$189$		0			0
$190$	10.9411	+	42.5779i	0.793748	+	3.08892i
$191$	10.1433			0.733946			0.366973	−	0.930232i	$-0.380394\pi$
$191$	10.1433			0.733946			0.366973	+	0.930232i	$0.380394\pi$
$192$		0			0
$193$	−12.6529			−0.910774			−0.455387	−	0.890294i	$-0.650499\pi$
$193$	−12.6529			−0.910774			−0.455387	+	0.890294i	$0.650499\pi$
$194$	1.32063	+	5.13931i	0.0948156	+	0.368981i
$195$		0			0
$196$	−1.75223	+	0.964197i	−0.125160	+	0.0688712i
$197$	−4.32030	−	4.32030i	−0.307808	−	0.307808i	0.536250	−	0.844059i	$-0.319840\pi$
$197$	−4.32030	−	4.32030i	−0.307808	−	0.307808i	−0.844059	+	0.536250i	$0.819840\pi$
$198$		0			0
$199$	7.22338			0.512052			0.256026	−	0.966670i	$-0.417587\pi$
$199$	7.22338			0.512052			0.256026	+	0.966670i	$0.417587\pi$
$200$	26.0164	−	24.4600i	1.83964	−	1.72958i
$201$		0			0
$202$	1.25516	−	2.12331i	0.0883125	−	0.149395i
$203$	6.05233	−	6.05233i	0.424790	−	0.424790i
$204$		0			0
$205$	25.6326	+	25.6326i	1.79026	+	1.79026i
$206$	5.04477	+	19.6320i	0.351486	+	1.36783i
$207$		0			0
$208$	14.0006	−	3.14107i	0.970765	−	0.217794i
$209$			5.96721i			0.412760i
$210$		0			0
$211$	9.51875	−	9.51875i	0.655298	−	0.655298i	−0.298966	−	0.954264i	$-0.596642\pi$
$211$	9.51875	−	9.51875i	0.655298	−	0.655298i	0.954264	+	0.298966i	$0.0966417\pi$
$212$	−16.4097	−	4.76047i	−1.12702	−	0.326950i
$213$		0			0
$214$	−12.6268	−	7.46409i	−0.863147	−	0.510235i
$215$		−	10.2785i		−	0.700989i
$216$		0			0
$217$			3.00413i			0.203934i
$218$	4.19533	−	7.09709i	0.284143	−	0.480676i
$219$		0			0
$220$	5.92845	−	3.26223i	0.399696	−	0.219939i
$221$	−2.62599	+	2.62599i	−0.176643	+	0.176643i
$222$		0			0
$223$			16.0637i			1.07571i	0.843038	+	0.537853i	$0.180765\pi$
$223$			16.0637i			1.07571i	−0.843038	+	0.537853i	$0.819235\pi$
$224$	5.38170	+	1.74277i	0.359580	+	0.116444i
$225$		0			0
$226$	−16.6453	+	4.27727i	−1.10723	+	0.284520i
$227$	11.5695	+	11.5695i	0.767894	+	0.767894i	0.977735	−	0.209842i	$-0.0672949\pi$
$227$	11.5695	+	11.5695i	0.767894	+	0.767894i	−0.209842	+	0.977735i	$0.567295\pi$
$228$		0			0
$229$	−4.50533	+	4.50533i	−0.297721	+	0.297721i	−0.840121	−	0.542400i	$-0.817516\pi$
$229$	−4.50533	+	4.50533i	−0.297721	+	0.297721i	0.542400	+	0.840121i	$0.317516\pi$
$230$	44.5278	+	26.3218i	2.93607	+	1.73561i
$231$		0			0
$232$	−24.1978	−	0.746156i	−1.58867	−	0.0489876i
$233$	−16.2560			−1.06496			−0.532482	−	0.846442i	$-0.678740\pi$
$233$	−16.2560			−1.06496			−0.532482	+	0.846442i	$0.678740\pi$
$234$		0			0
$235$	12.1969	+	12.1969i	0.795638	+	0.795638i
$236$	−4.76858	+	16.4377i	−0.310408	+	1.07000i
$237$		0			0
$238$	−1.41804	+	0.364388i	−0.0919178	+	0.0236197i
$239$	4.55597			0.294701			0.147351	−	0.989084i	$-0.452925\pi$
$239$	4.55597			0.294701			0.147351	+	0.989084i	$0.452925\pi$
$240$		0			0
$241$	−22.0079			−1.41765			−0.708827	−	0.705382i	$-0.750775\pi$
$241$	−22.0079			−1.41765			−0.708827	+	0.705382i	$0.750775\pi$
$242$	−14.1773	+	3.64307i	−0.911348	+	0.234186i
$243$		0			0
$244$	−15.8068	−	4.58556i	−1.01193	−	0.293561i
$245$	−2.96859	−	2.96859i	−0.189657	−	0.189657i
$246$		0			0
$247$	−26.5606			−1.69001
$248$	6.19058	−	5.82022i	0.393103	−	0.369585i
$249$		0			0
$250$	38.9717	+	23.0375i	2.46479	+	1.45702i
$251$	3.15767	−	3.15767i	0.199311	−	0.199311i	−0.600394	−	0.799704i	$-0.704990\pi$
$251$	3.15767	−	3.15767i	0.199311	−	0.199311i	0.799704	+	0.600394i	$0.204990\pi$
$252$		0			0
$253$	4.96472	+	4.96472i	0.312129	+	0.312129i
$254$	−1.80925	+	0.464915i	−0.113522	+	0.0291714i
$255$		0			0
$256$	−6.83524	−	14.4665i	−0.427202	−	0.904156i
$257$		−	0.930640i		−	0.0580517i	−0.999579	−	0.0290259i	$-0.990759\pi$
$257$		−	0.930640i		−	0.0580517i	0.999579	−	0.0290259i	$-0.00924052\pi$
$258$		0			0
$259$	−0.149739	+	0.149739i	−0.00930431	+	0.00930431i
$260$	14.5205	+	26.3881i	0.900522	+	1.63652i
$261$		0			0
$262$	1.70699	−	2.88766i	0.105458	−	0.178401i
$263$		−	14.8926i		−	0.918319i	−0.888354	−	0.459160i	$-0.848151\pi$
$263$		−	14.8926i		−	0.918319i	0.888354	−	0.459160i	$-0.151849\pi$
$264$		0			0
$265$		−	35.8660i		−	2.20323i
$266$	−9.01419	−	5.32858i	−0.552695	−	0.326716i
$267$		0			0
$268$	−0.0202485	+	0.0697981i	−0.00123687	+	0.00426360i
$269$	7.20537	−	7.20537i	0.439319	−	0.439319i	−0.452464	−	0.891783i	$-0.649455\pi$
$269$	7.20537	−	7.20537i	0.439319	−	0.439319i	0.891783	+	0.452464i	$0.149455\pi$
$270$		0			0
$271$		−	25.2262i		−	1.53238i	−0.642611	−	0.766192i	$-0.722149\pi$
$271$		−	25.2262i		−	1.53238i	0.642611	−	0.766192i	$-0.277851\pi$
$272$	3.49821	+	2.21617i	0.212110	+	0.134375i
$273$		0			0
$274$	2.99017	+	11.6365i	0.180643	+	0.702984i
$275$	7.19454	+	7.19454i	0.433847	+	0.433847i
$276$		0			0
$277$	10.1502	−	10.1502i	0.609866	−	0.609866i	−0.333045	−	0.942911i	$-0.608076\pi$
$277$	10.1502	−	10.1502i	0.609866	−	0.609866i	0.942911	+	0.333045i	$0.108076\pi$
$278$	7.94853	−	13.4463i	0.476721	−	0.806454i
$279$		0			0
$280$	−0.365980	+	11.8687i	−0.0218715	+	0.709293i
$281$	9.47979			0.565517			0.282758	−	0.959191i	$-0.408751\pi$
$281$	9.47979			0.565517			0.282758	+	0.959191i	$0.408751\pi$
$282$		0			0
$283$	2.74974	+	2.74974i	0.163455	+	0.163455i	0.784095	−	0.620640i	$-0.213127\pi$
$283$	2.74974	+	2.74974i	0.163455	+	0.163455i	−0.620640	+	0.784095i	$0.713127\pi$
$284$	−14.0056	−	25.4524i	−0.831081	−	1.51032i
$285$		0			0
$286$	1.01751	+	3.95970i	0.0601666	+	0.234142i
$287$	−8.63459			−0.509683
$288$		0			0
$289$	15.9282			0.936953
$290$	−12.6476	−	49.2191i	−0.742695	−	2.89024i
$291$		0			0
$292$	5.19216	+	9.43570i	0.303848	+	0.552183i
$293$	−0.497276	−	0.497276i	−0.0290512	−	0.0290512i	0.692432	−	0.721483i	$-0.256539\pi$
$293$	−0.497276	−	0.497276i	−0.0290512	−	0.0290512i	−0.721483	+	0.692432i	$0.756539\pi$
$294$		0			0
$295$	−35.9272			−2.09176
$296$	0.598670	+	0.0184604i	0.0347970	+	0.00107299i
$297$		0			0
$298$	13.3440	−	22.5736i	0.772996	−	1.30765i
$299$	−22.0984	+	22.0984i	−1.27798	+	1.27798i
$300$		0			0
$301$	1.73121	+	1.73121i	0.0997853	+	0.0997853i
$302$	4.73009	+	18.4075i	0.272186	+	1.05923i
$303$		0			0
$304$	6.48359	+	28.8991i	0.371859	+	1.65748i
$305$		−	34.5483i		−	1.97823i
$306$		0			0
$307$	11.0456	−	11.0456i	0.630408	−	0.630408i	−0.317762	−	0.948170i	$-0.602931\pi$
$307$	11.0456	−	11.0456i	0.630408	−	0.630408i	0.948170	+	0.317762i	$0.102931\pi$
$308$	−0.449071	+	1.54798i	−0.0255882	+	0.0882046i
$309$		0			0
$310$	15.3540	+	9.07628i	0.872051	+	0.515498i
$311$			24.7421i			1.40299i	0.712672	+	0.701497i	$0.247485\pi$
$311$			24.7421i			1.40299i	−0.712672	+	0.701497i	$0.752515\pi$
$312$		0			0
$313$		−	20.1653i		−	1.13981i	−0.821710	−	0.569906i	$-0.806980\pi$
$313$		−	20.1653i		−	1.13981i	0.821710	−	0.569906i	$-0.193020\pi$
$314$	6.03005	−	10.2008i	0.340296	−	0.575667i
$315$		0			0
$316$	−3.75917	−	6.83154i	−0.211470	−	0.384304i
$317$	8.70522	−	8.70522i	0.488934	−	0.488934i	−0.419036	−	0.907970i	$-0.637632\pi$
$317$	8.70522	−	8.70522i	0.488934	−	0.488934i	0.907970	+	0.419036i	$0.137632\pi$
$318$		0			0
$319$		−	6.89796i		−	0.386212i
$320$	25.1669	−	22.2404i	1.40687	−	1.24328i
$321$		0			0
$322$	−11.9332	+	3.06642i	−0.665011	+	0.170885i
$323$	−5.42040	−	5.42040i	−0.301599	−	0.301599i
$324$		0			0
$325$	−32.0235	+	32.0235i	−1.77635	+	1.77635i
$326$	−3.14155	−	1.85707i	−0.173994	−	0.102854i
$327$		0			0
$328$	16.7287	+	17.7932i	0.923689	+	0.982466i
$329$	−4.10865			−0.226517
$330$		0			0
$331$	−2.78793	−	2.78793i	−0.153239	−	0.153239i	0.626324	−	0.779563i	$-0.284559\pi$
$331$	−2.78793	−	2.78793i	−0.153239	−	0.153239i	−0.779563	+	0.626324i	$0.784559\pi$
$332$	−3.82177	−	1.10870i	−0.209747	−	0.0608476i
$333$		0			0
$334$	−7.52360	+	1.93331i	−0.411673	+	0.105786i
$335$	−0.152555			−0.00833496
$336$		0			0
$337$	−0.465376			−0.0253506			−0.0126753	−	0.999920i	$-0.504035\pi$
$337$	−0.465376			−0.0253506			−0.0126753	+	0.999920i	$0.504035\pi$
$338$	0.181278	−	0.0465822i	0.00986021	−	0.00253374i
$339$		0			0
$340$	−2.42190	+	8.34848i	−0.131346	+	0.452760i
$341$	1.71193	+	1.71193i	0.0927064	+	0.0927064i
$342$		0			0
$343$	1.00000			0.0539949
$344$	0.213431	−	6.92155i	0.0115074	−	0.373185i
$345$		0			0
$346$	−19.6582	−	11.6206i	−1.05683	−	0.624727i
$347$	−21.3262	+	21.3262i	−1.14485	+	1.14485i	−0.157299	+	0.987551i	$0.550279\pi$
$347$	−21.3262	+	21.3262i	−1.14485	+	1.14485i	−0.987551	+	0.157299i	$0.949721\pi$
$348$		0			0
$349$	5.11124	+	5.11124i	0.273598	+	0.273598i	0.830547	−	0.556949i	$-0.188028\pi$
$349$	5.11124	+	5.11124i	0.273598	+	0.273598i	−0.556949	+	0.830547i	$0.688028\pi$
$350$	−17.2928	+	4.44366i	−0.924338	+	0.237523i
$351$		0			0
$352$	4.05995	−	2.07368i	0.216396	−	0.110528i
$353$			10.2227i			0.544102i	0.962283	+	0.272051i	$0.0877019\pi$
$353$			10.2227i			0.544102i	−0.962283	+	0.272051i	$0.912298\pi$
$354$		0			0
$355$	43.1209	−	43.1209i	2.28862	−	2.28862i
$356$	29.8508	−	16.4259i	1.58209	−	0.870571i
$357$		0			0
$358$	5.57581	−	9.43241i	0.294691	−	0.498519i
$359$			5.90071i			0.311427i	0.987802	+	0.155714i	$0.0497677\pi$
$359$			5.90071i			0.311427i	−0.987802	+	0.155714i	$0.950232\pi$
$360$		0			0
$361$		−	35.8247i		−	1.88551i
$362$	−16.2309	−	9.59462i	−0.853077	−	0.504282i
$363$		0			0
$364$	−6.89022	−	1.99886i	−0.361146	−	0.104769i
$365$	−15.9857	+	15.9857i	−0.836732	+	0.836732i
$366$		0			0
$367$			14.1762i			0.739994i	0.929033	+	0.369997i	$0.120641\pi$
$367$			14.1762i			0.739994i	−0.929033	+	0.369997i	$0.879359\pi$
$368$	29.4384	+	18.6497i	1.53458	+	0.972183i
$369$		0			0
$370$	0.312911	+	1.21771i	0.0162675	+	0.0633059i
$371$	6.04092	+	6.04092i	0.313629	+	0.313629i
$372$		0			0
$373$	21.5106	−	21.5106i	1.11378	−	1.11378i	0.121141	−	0.992635i	$-0.461345\pi$
$373$	21.5106	−	21.5106i	1.11378	−	1.11378i	0.992635	−	0.121141i	$-0.0386553\pi$
$374$	−0.600433	+	1.01573i	−0.0310477	+	0.0525223i
$375$		0			0
$376$	7.96012	+	8.46665i	0.410512	+	0.436634i
$377$	30.7035			1.58131
$378$		0			0
$379$	−8.15510	−	8.15510i	−0.418900	−	0.418900i	0.465925	−	0.884824i	$-0.345722\pi$
$379$	−8.15510	−	8.15510i	−0.418900	−	0.418900i	−0.884824	+	0.465925i	$0.845722\pi$
$380$	−54.4686	+	29.9723i	−2.79418	+	1.53754i
$381$		0			0
$382$	3.57015	+	13.8935i	0.182665	+	0.710852i
$383$	9.06121			0.463006			0.231503	−	0.972834i	$-0.425636\pi$
$383$	9.06121			0.463006			0.231503	+	0.972834i	$0.425636\pi$
$384$		0			0
$385$	−3.38337			−0.172432
$386$	−4.45343	−	17.3308i	−0.226674	−	0.882116i
$387$		0			0
$388$	−6.57456	+	3.61777i	−0.333773	+	0.183664i
$389$	22.1084	+	22.1084i	1.12094	+	1.12094i	0.991600	+	0.129339i	$0.0412855\pi$
$389$	22.1084	+	22.1084i	1.12094	+	1.12094i	0.129339	+	0.991600i	$0.458715\pi$
$390$		0			0
$391$	−9.01954			−0.456138
$392$	−1.93741	−	2.06069i	−0.0978539	−	0.104081i
$393$		0			0
$394$	4.39696	−	7.43819i	0.221515	−	0.374730i
$395$	11.5738	−	11.5738i	0.582343	−	0.582343i
$396$		0			0
$397$	−25.1321	−	25.1321i	−1.26134	−	1.26134i	−0.950443	−	0.310899i	$-0.899370\pi$
$397$	−25.1321	−	25.1321i	−1.26134	−	1.26134i	−0.310899	−	0.950443i	$-0.600630\pi$
$398$	2.54241	+	9.89397i	0.127440	+	0.495940i
$399$		0			0
$400$	42.6602	+	27.0259i	2.13301	+	1.35130i
$401$			1.54588i			0.0771975i	0.999255	+	0.0385987i	$0.0122894\pi$
$401$			1.54588i			0.0771975i	−0.999255	+	0.0385987i	$0.987711\pi$
$402$		0			0
$403$	−7.61997	+	7.61997i	−0.379578	+	0.379578i
$404$	3.35010	+	0.971865i	0.166674	+	0.0483521i
$405$		0			0
$406$	10.4202	+	6.15973i	0.517146	+	0.305702i
$407$			0.170660i			0.00845931i
$408$		0			0
$409$		−	5.72850i		−	0.283256i	−0.989920	−	0.141628i	$-0.954766\pi$
$409$		−	5.72850i		−	0.283256i	0.989920	−	0.141628i	$-0.0452337\pi$
$410$	−26.0874	+	44.1312i	−1.28837	+	2.17948i
$411$		0			0
$412$	−25.1147	+	13.8198i	−1.23731	+	0.680852i
$413$	6.05121	−	6.05121i	0.297761	−	0.297761i
$414$		0			0
$415$		−	8.35307i		−	0.410036i
$416$	9.23015	+	18.0712i	0.452545	+	0.886015i
$417$		0			0
$418$	−8.17337	+	2.10028i	−0.399773	+	0.102728i
$419$	26.2299	+	26.2299i	1.28141	+	1.28141i	0.939863	+	0.341551i	$0.110952\pi$
$419$	26.2299	+	26.2299i	1.28141	+	1.28141i	0.341551	+	0.939863i	$0.389048\pi$
$420$		0			0
$421$	9.38496	−	9.38496i	0.457395	−	0.457395i	−0.440404	−	0.897800i	$-0.645165\pi$
$421$	9.38496	−	9.38496i	0.457395	−	0.457395i	0.897800	+	0.440404i	$0.145165\pi$
$422$	16.3883	+	9.68765i	0.797769	+	0.471588i
$423$		0			0
$424$	0.744749	−	24.1522i	0.0361682	−	1.17293i
$425$	−13.0705			−0.634013
$426$		0			0
$427$	5.81897	+	5.81897i	0.281599	+	0.281599i
$428$	5.77943	−	19.9222i	0.279359	−	0.962975i
$429$		0			0
$430$	14.0786	−	3.61773i	0.678932	−	0.174463i
$431$	15.9406			0.767830			0.383915	−	0.923368i	$-0.374576\pi$
$431$	15.9406			0.767830			0.383915	+	0.923368i	$0.374576\pi$
$432$		0			0
$433$	25.0062			1.20172			0.600862	−	0.799353i	$-0.294824\pi$
$433$	25.0062			1.20172			0.600862	+	0.799353i	$0.294824\pi$
$434$	−4.11480	+	1.05736i	−0.197517	+	0.0507551i
$435$		0			0
$436$	11.1976	+	3.24843i	0.536269	+	0.155572i
$437$	−45.6141	−	45.6141i	−2.18202	−	2.18202i
$438$		0			0
$439$	−35.0522			−1.67295			−0.836474	−	0.548007i	$-0.815387\pi$
$439$	−35.0522			−1.67295			−0.836474	+	0.548007i	$0.815387\pi$
$440$	6.55496	+	6.97207i	0.312495	+	0.332381i
$441$		0			0
$442$	−4.52112	−	2.67258i	−0.215048	−	0.127122i
$443$	−17.1307	+	17.1307i	−0.813904	+	0.813904i	−0.985217	−	0.171313i	$-0.945199\pi$
$443$	−17.1307	+	17.1307i	−0.813904	+	0.813904i	0.171313	+	0.985217i	$0.445199\pi$
$444$		0			0
$445$	50.5725	+	50.5725i	2.39737	+	2.39737i
$446$	−22.0027	+	5.65395i	−1.04186	+	0.267722i
$447$		0			0
$448$	−0.492902	+	7.98480i	−0.0232874	+	0.377246i
$449$			14.7964i			0.698286i	0.937070	+	0.349143i	$0.113527\pi$
$449$			14.7964i			0.698286i	−0.937070	+	0.349143i	$0.886473\pi$
$450$		0			0
$451$	−4.92050	+	4.92050i	−0.231697	+	0.231697i
$452$	−11.7173	−	21.2938i	−0.551134	−	1.00158i
$453$		0			0
$454$	−11.7748	+	19.9190i	−0.552618	+	0.934845i
$455$		−	15.0597i		−	0.706008i
$456$		0			0
$457$			11.9903i			0.560883i	0.959871	+	0.280442i	$0.0904809\pi$
$457$			11.9903i			0.560883i	−0.959871	+	0.280442i	$0.909519\pi$
$458$	−7.75676	−	4.58528i	−0.362450	−	0.214256i
$459$		0			0
$460$	−20.3809	+	70.2548i	−0.950266	+	3.27565i
$461$	−14.9493	+	14.9493i	−0.696260	+	0.696260i	−0.963602	−	0.267342i	$-0.913855\pi$
$461$	−14.9493	+	14.9493i	−0.696260	+	0.696260i	0.267342	+	0.963602i	$0.413855\pi$
$462$		0			0
$463$			31.4696i			1.46252i	0.682101	+	0.731258i	$0.261067\pi$
$463$			31.4696i			1.46252i	−0.682101	+	0.731258i	$0.738933\pi$
$464$	−7.49489	−	33.4067i	−0.347941	−	1.55087i
$465$		0			0
$466$	−5.72161	−	22.2660i	−0.265048	−	1.03145i
$467$	−24.7699	−	24.7699i	−1.14621	−	1.14621i	−0.987291	−	0.158922i	$-0.949198\pi$
$467$	−24.7699	−	24.7699i	−1.14621	−	1.14621i	−0.158922	−	0.987291i	$-0.550802\pi$
$468$		0			0
$469$	0.0256948	−	0.0256948i	0.00118647	−	0.00118647i
$470$	−12.4133	+	20.9992i	−0.572584	+	0.968622i
$471$		0			0
$472$	−24.1933	−	0.746018i	−1.11359	−	0.0343383i
$473$	1.97310			0.0907230
$474$		0			0
$475$	−66.1010	−	66.1010i	−3.03292	−	3.03292i
$476$	−0.998214	−	1.81405i	−0.0457531	−	0.0831470i
$477$		0			0
$478$	1.60356	+	6.24038i	0.0733453	+	0.285428i
$479$	17.7194			0.809620			0.404810	−	0.914401i	$-0.367338\pi$
$479$	17.7194			0.809620			0.404810	+	0.914401i	$0.367338\pi$
$480$		0			0
$481$	−0.759624			−0.0346359
$482$	−7.74612	−	30.1445i	−0.352826	−	1.37305i
$483$		0			0
$484$	−9.97994	−	18.1365i	−0.453633	−	0.824388i
$485$	−11.1385	−	11.1385i	−0.505772	−	0.505772i
$486$		0			0
$487$	−33.8639			−1.53452			−0.767260	−	0.641336i	$-0.778381\pi$
$487$	−33.8639			−1.53452			−0.767260	+	0.641336i	$0.778381\pi$
$488$	0.717386	−	23.2648i	0.0324745	−	1.05315i
$489$		0			0
$490$	3.02127	−	5.11098i	0.136487	−	0.230891i
$491$	−25.3486	+	25.3486i	−1.14397	+	1.14397i	−0.156248	+	0.987718i	$0.549940\pi$
$491$	−25.3486	+	25.3486i	−1.14397	+	1.14397i	−0.987718	+	0.156248i	$0.950060\pi$
$492$		0			0
$493$	6.26586	+	6.26586i	0.282200	+	0.282200i
$494$	−9.34853	−	36.3804i	−0.420610	−	1.63683i
$495$		0			0
$496$	10.1509	+	6.43079i	0.455791	+	0.288751i
$497$			14.5257i			0.651566i
$498$		0			0
$499$	−7.26690	+	7.26690i	−0.325311	+	0.325311i	−0.850800	−	0.525489i	$-0.823882\pi$
$499$	−7.26690	+	7.26690i	−0.325311	+	0.325311i	0.525489	+	0.850800i	$0.323882\pi$
$500$	−17.8379	+	61.4886i	−0.797734	+	2.74986i
$501$		0			0
$502$	5.43652	+	3.21370i	0.242644	+	0.143435i
$503$		−	12.3031i		−	0.548567i	−0.961649	−	0.274284i	$-0.911559\pi$
$503$		−	12.3031i		−	0.548567i	0.961649	−	0.274284i	$-0.0884407\pi$
$504$		0			0
$505$			7.32217i			0.325832i
$506$	−5.05281	+	8.54768i	−0.224625	+	0.379991i
$507$		0			0
$508$	−1.27360	−	2.31452i	−0.0565069	−	0.102690i
$509$	−14.0082	+	14.0082i	−0.620901	+	0.620901i	−0.945762	−	0.324861i	$-0.894682\pi$
$509$	−14.0082	+	14.0082i	−0.620901	+	0.620901i	0.324861	+	0.945762i	$0.394682\pi$
$510$		0			0
$511$		−	5.38496i		−	0.238216i
$512$	17.4092	−	14.4541i	0.769384	−	0.638787i
$513$		0			0
$514$	1.27471	−	0.327557i	0.0562251	−	0.0144479i
$515$	−42.5487	−	42.5487i	−1.87492	−	1.87492i
$516$		0			0
$517$	−2.34135	+	2.34135i	−0.102973	+	0.102973i
$518$	−0.257803	−	0.152396i	−0.0113272	−	0.00669588i
$519$		0			0
$520$	−31.0333	+	29.1767i	−1.36090	+	1.27948i
$521$	−36.8204			−1.61313			−0.806566	−	0.591144i	$-0.798677\pi$
$521$	−36.8204			−1.61313			−0.806566	+	0.591144i	$0.798677\pi$
$522$		0			0
$523$	2.49783	+	2.49783i	0.109222	+	0.109222i	0.759606	−	0.650384i	$-0.225392\pi$
$523$	2.49783	+	2.49783i	0.109222	+	0.109222i	−0.650384	+	0.759606i	$0.725392\pi$
$524$	4.55609	+	1.32172i	0.199034	+	0.0577397i
$525$		0			0
$526$	20.3987	−	5.24176i	0.889424	−	0.228552i
$527$	−3.11012			−0.135479
$528$		0			0
$529$	−52.9020			−2.30009
$530$	49.1262	−	12.6238i	2.13391	−	0.548342i
$531$		0			0
$532$	4.12591	−	14.2224i	0.178881	−	0.616618i
$533$	−21.9016	−	21.9016i	−0.948664	−	0.948664i
$534$		0			0
$535$	43.5431			1.88253
$536$	−0.102730	−	0.00316776i	−0.00443727	−	0.000136826i
$537$		0			0
$538$	12.4054	+	7.33322i	0.534833	+	0.316158i
$539$	0.569860	−	0.569860i	0.0245456	−	0.0245456i
$540$		0			0
$541$	14.5049	+	14.5049i	0.623613	+	0.623613i	0.946453	−	0.322841i	$-0.104638\pi$
$541$	14.5049	+	14.5049i	0.623613	+	0.623613i	−0.322841	+	0.946453i	$0.604638\pi$
$542$	34.5527	−	8.87888i	1.48417	−	0.381380i
$543$		0			0
$544$	−1.80426	+	5.57157i	−0.0773570	+	0.238879i
$545$			24.4742i			1.04836i
$546$		0			0
$547$	10.3072	−	10.3072i	0.440704	−	0.440704i	−0.451545	−	0.892249i	$-0.649127\pi$
$547$	10.3072	−	10.3072i	0.440704	−	0.440704i	0.892249	+	0.451545i	$0.149127\pi$
$548$	−14.8862	+	8.19137i	−0.635906	+	0.349918i
$549$		0			0
$550$	−7.32220	+	12.3867i	−0.312220	+	0.528172i
$551$			63.3761i			2.69991i
$552$		0			0
$553$			3.89876i			0.165792i
$554$	17.4754	+	10.3303i	0.742460	+	0.438892i
$555$		0			0
$556$	21.2152	+	6.15454i	0.899725	+	0.261010i
$557$	−8.62884	+	8.62884i	−0.365616	+	0.365616i	−0.865875	−	0.500260i	$-0.833238\pi$
$557$	−8.62884	+	8.62884i	−0.365616	+	0.365616i	0.500260	+	0.865875i	$0.333238\pi$
$558$		0			0
$559$			8.78243i			0.371457i
$560$	−16.3856	+	3.67615i	−0.692417	+	0.155346i
$561$		0			0
$562$	3.33660	+	12.9846i	0.140746	+	0.547722i
$563$	10.3155	+	10.3155i	0.434748	+	0.434748i	0.890240	−	0.455492i	$-0.150537\pi$
$563$	10.3155	+	10.3155i	0.434748	+	0.434748i	−0.455492	+	0.890240i	$0.650537\pi$
$564$		0			0
$565$	36.0755	−	36.0755i	1.51771	−	1.51771i
$566$	−2.79853	+	4.73419i	−0.117631	+	0.198993i
$567$		0			0
$568$	29.9330	−	28.1422i	1.25596	−	1.18082i
$569$	3.23614			0.135666			0.0678330	−	0.997697i	$-0.478391\pi$
$569$	3.23614			0.135666			0.0678330	+	0.997697i	$0.478391\pi$
$570$		0			0
$571$	27.7822	+	27.7822i	1.16265	+	1.16265i	0.983893	+	0.178757i	$0.0572078\pi$
$571$	27.7822	+	27.7822i	1.16265	+	1.16265i	0.178757	+	0.983893i	$0.442792\pi$
$572$	−5.06553	+	2.78739i	−0.211800	+	0.116547i
$573$		0			0
$574$	−3.03912	−	11.8269i	−0.126850	−	0.493646i
$575$	−109.992			−4.58699
$576$		0			0
$577$	22.0528			0.918072			0.459036	−	0.888418i	$-0.348195\pi$
$577$	22.0528			0.918072			0.459036	+	0.888418i	$0.348195\pi$
$578$	5.60625	+	21.8171i	0.233189	+	0.907471i
$579$		0			0
$580$	62.9645	−	34.6473i	2.61446	−	1.43865i
$581$	1.40691	+	1.40691i	0.0583684	+	0.0583684i
$582$		0			0
$583$	6.88495			0.285146
$584$	−11.0967	+	10.4329i	−0.459186	+	0.431715i
$585$		0			0
$586$	0.506100	−	0.856153i	0.0209068	−	0.0353673i
$587$	16.9242	−	16.9242i	0.698538	−	0.698538i	−0.265557	−	0.964095i	$-0.585556\pi$
$587$	16.9242	−	16.9242i	0.698538	−	0.698538i	0.964095	+	0.265557i	$0.0855560\pi$
$588$		0			0
$589$	−15.7287	−	15.7287i	−0.648088	−	0.648088i
$590$	−12.6453	−	49.2099i	−0.520598	−	2.02594i
$591$		0			0
$592$	0.185428	+	0.826504i	0.00762106	+	0.0339691i
$593$		−	9.14027i		−	0.375346i	−0.982232	−	0.187673i	$-0.939905\pi$
$593$		−	9.14027i		−	0.375346i	0.982232	−	0.187673i	$-0.0600945\pi$
$594$		0			0
$595$	3.07333	−	3.07333i	0.125994	−	0.125994i
$596$	35.6160	+	10.3322i	1.45889	+	0.423224i
$597$		0			0
$598$	−38.0465	−	22.4905i	−1.55584	−	0.919707i
$599$		−	26.4441i		−	1.08047i	−0.841513	−	0.540237i	$-0.818334\pi$
$599$		−	26.4441i		−	1.08047i	0.841513	−	0.540237i	$-0.181666\pi$
$600$		0			0
$601$		−	28.3857i		−	1.15788i	−0.815371	−	0.578938i	$-0.803467\pi$
$601$		−	28.3857i		−	1.15788i	0.815371	−	0.578938i	$-0.196533\pi$
$602$	−1.76193	+	2.98060i	−0.0718109	+	0.121480i
$603$		0			0
$604$	−23.5481	+	12.9578i	−0.958160	+	0.527244i
$605$	30.7265	−	30.7265i	1.24921	−	1.24921i
$606$		0			0
$607$			9.53246i			0.386911i	0.981109	+	0.193455i	$0.0619695\pi$
$607$			9.53246i			0.386911i	−0.981109	+	0.193455i	$0.938031\pi$
$608$	−37.3015	+	19.0523i	−1.51277	+	0.772672i
$609$		0			0
$610$	47.3213	−	12.1600i	1.91598	−	0.492342i
$611$	−10.4216	−	10.4216i	−0.421612	−	0.421612i
$612$		0			0
$613$	1.07498	−	1.07498i	0.0434181	−	0.0434181i	−0.685064	−	0.728483i	$-0.740226\pi$
$613$	1.07498	−	1.07498i	0.0434181	−	0.0434181i	0.728483	+	0.685064i	$0.240226\pi$
$614$	19.0171	+	11.2416i	0.767468	+	0.453676i
$615$		0			0
$616$	−2.27836	−	0.0702547i	−0.0917976	−	0.00283064i
$617$	−35.3828			−1.42446			−0.712229	−	0.701948i	$-0.752314\pi$
$617$	−35.3828			−1.42446			−0.712229	+	0.701948i	$0.752314\pi$
$618$		0			0
$619$	−3.97297	−	3.97297i	−0.159687	−	0.159687i	0.622741	−	0.782428i	$-0.286019\pi$
$619$	−3.97297	−	3.97297i	−0.159687	−	0.159687i	−0.782428	+	0.622741i	$0.786019\pi$
$620$	−7.02775	+	24.2252i	−0.282241	+	0.972909i
$621$		0			0
$622$	−33.8896	+	8.70847i	−1.35885	+	0.349178i
$623$	−17.0358			−0.682526
$624$		0			0
$625$	−71.2676			−2.85070
$626$	27.6207	−	7.09759i	1.10395	−	0.283677i
$627$		0			0
$628$	16.0946	+	4.66906i	0.642246	+	0.186316i
$629$	−0.155022	−	0.155022i	−0.00618111	−	0.00618111i
$630$		0			0
$631$	−25.6289			−1.02027			−0.510135	−	0.860095i	$-0.670404\pi$
$631$	−25.6289			−1.02027			−0.510135	+	0.860095i	$0.670404\pi$
$632$	8.03414	−	7.55348i	0.319581	−	0.300461i
$633$		0			0
$634$	14.9876	+	8.85968i	0.595235	+	0.351863i
$635$	3.92120	−	3.92120i	0.155608	−	0.155608i
$636$		0			0
$637$	2.53650	+	2.53650i	0.100500	+	0.100500i
$638$	9.44824	−	2.42788i	0.374059	−	0.0961205i
$639$		0			0
$640$	39.3210	+	26.6434i	1.55430	+	1.05317i
$641$			10.5770i			0.417766i	0.977941	+	0.208883i	$0.0669829\pi$
$641$			10.5770i			0.417766i	−0.977941	+	0.208883i	$0.933017\pi$
$642$		0			0
$643$	8.26445	−	8.26445i	0.325918	−	0.325918i	−0.525114	−	0.851032i	$-0.675977\pi$
$643$	8.26445	−	8.26445i	0.325918	−	0.325918i	0.851032	+	0.525114i	$0.175977\pi$
$644$	−8.40025	−	15.2658i	−0.331016	−	0.601556i
$645$		0			0
$646$	5.51658	−	9.33221i	0.217047	−	0.367171i
$647$		−	23.2954i		−	0.915835i	−0.888995	−	0.457917i	$-0.848596\pi$
$647$		−	23.2954i		−	0.915835i	0.888995	−	0.457917i	$-0.151404\pi$
$648$		0			0
$649$		−	6.89668i		−	0.270718i
$650$	−55.1344	−	32.5918i	−2.16255	−	1.27835i
$651$		0			0
$652$	1.43793	−	4.95666i	0.0563136	−	0.194118i
$653$	20.0365	−	20.0365i	0.784090	−	0.784090i	−0.196429	−	0.980518i	$-0.562934\pi$
$653$	20.0365	−	20.0365i	0.784090	−	0.784090i	0.980518	+	0.196429i	$0.0629344\pi$
$654$		0			0
$655$			9.95804i			0.389093i
$656$	−18.4836	+	29.1762i	−0.721664	+	1.13914i
$657$		0			0
$658$	−1.44612	−	5.62767i	−0.0563756	−	0.219389i
$659$	−24.7397	−	24.7397i	−0.963723	−	0.963723i	0.0356416	−	0.999365i	$-0.488653\pi$
$659$	−24.7397	−	24.7397i	−0.963723	−	0.963723i	−0.999365	+	0.0356416i	$0.988653\pi$
$660$		0			0
$661$	−6.31446	+	6.31446i	−0.245604	+	0.245604i	−0.819164	−	0.573560i	$-0.805562\pi$
$661$	−6.31446	+	6.31446i	−0.245604	+	0.245604i	0.573560	+	0.819164i	$0.305562\pi$
$662$	2.83740	−	4.79994i	0.110279	−	0.186555i
$663$		0			0
$664$	0.173449	−	5.62496i	0.00673114	−	0.218291i
$665$	31.0852			1.20543
$666$		0			0
$667$	52.7290	+	52.7290i	2.04167	+	2.04167i
$668$	−5.29617	−	9.62472i	−0.204915	−	0.372392i
$669$		0			0
$670$	−0.0536947	−	0.208956i	−0.00207441	−	0.00807269i
$671$	6.63199			0.256025
$672$		0			0
$673$	2.32930			0.0897877			0.0448939	−	0.998992i	$-0.485705\pi$
$673$	2.32930			0.0897877			0.0448939	+	0.998992i	$0.485705\pi$
$674$	−0.163798	−	0.637431i	−0.00630927	−	0.0245529i
$675$		0			0
$676$	0.127609	+	0.231903i	0.00490802	+	0.00891935i
$677$	17.0208	+	17.0208i	0.654163	+	0.654163i	0.953993	−	0.299830i	$-0.0969300\pi$
$677$	17.0208	+	17.0208i	0.654163	+	0.654163i	−0.299830	+	0.953993i	$0.596930\pi$
$678$		0			0
$679$	3.75210			0.143993
$680$	−12.2875	−	0.378892i	−0.471203	−	0.0145299i
$681$		0			0
$682$	−1.74231	+	2.94741i	−0.0667165	+	0.112862i
$683$	5.18231	−	5.18231i	0.198296	−	0.198296i	−0.600973	−	0.799269i	$-0.705220\pi$
$683$	5.18231	−	5.18231i	0.198296	−	0.198296i	0.799269	+	0.600973i	$0.205220\pi$
$684$		0			0
$685$	−25.2198	−	25.2198i	−0.963599	−	0.963599i
$686$	0.351970	+	1.36971i	0.0134383	+	0.0522959i
$687$		0			0
$688$	9.55567	−	2.14384i	0.364307	−	0.0817331i
$689$			30.6455i			1.16750i
$690$		0			0
$691$	−23.6472	+	23.6472i	−0.899582	+	0.899582i	−0.995399	−	0.0958169i	$-0.969454\pi$
$691$	−23.6472	+	23.6472i	−0.899582	+	0.899582i	0.0958169	+	0.995399i	$0.469454\pi$
$692$	8.99780	−	31.0162i	0.342045	−	1.17906i
$693$		0			0
$694$	−36.7170	−	21.7046i	−1.39376	−	0.823896i
$695$			46.3692i			1.75888i
$696$		0			0
$697$		−	8.93922i		−	0.338597i
$698$	−5.20193	+	8.79993i	−0.196896	+	0.333082i
$699$		0			0
$700$	−12.1731	−	22.1221i	−0.460099	−	0.836138i
$701$	4.62771	−	4.62771i	0.174786	−	0.174786i	−0.614292	−	0.789078i	$-0.710558\pi$
$701$	4.62771	−	4.62771i	0.174786	−	0.174786i	0.789078	+	0.614292i	$0.210558\pi$
$702$		0			0
$703$		−	1.56797i		−	0.0591370i
$704$	4.26933	+	4.83110i	0.160907	+	0.182079i
$705$		0			0
$706$	−14.0022	+	3.59810i	−0.526981	+	0.135416i
$707$	−1.23327	−	1.23327i	−0.0463820	−	0.0463820i
$708$		0			0
$709$	−27.1441	+	27.1441i	−1.01942	+	1.01942i	−0.0196099	+	0.999808i	$0.506242\pi$
$709$	−27.1441	+	27.1441i	−1.01942	+	1.01942i	−0.999808	+	0.0196099i	$0.993758\pi$
$710$	74.2406	+	43.8860i	2.78620	+	1.64701i
$711$		0			0
$712$	33.0054	+	35.1056i	1.23693	+	1.31564i
$713$	−26.1725			−0.980168
$714$		0			0
$715$	−8.58190	−	8.58190i	−0.320945	−	0.320945i
$716$	14.8822	+	4.31734i	0.556175	+	0.161347i
$717$		0			0
$718$	−8.08228	+	2.07687i	−0.301628	+	0.0775082i
$719$	39.3061			1.46587			0.732934	−	0.680299i	$-0.238150\pi$
$719$	39.3061			1.46587			0.732934	+	0.680299i	$0.238150\pi$
$720$		0			0
$721$	14.3330			0.533787
$722$	49.0696	−	12.6092i	1.82618	−	0.469266i
$723$		0			0
$724$	7.42910	−	25.6087i	0.276100	−	0.951740i
$725$	76.4113	+	76.4113i	2.83784	+	2.83784i
$726$		0			0
$727$	36.1990			1.34255			0.671274	−	0.741209i	$-0.265747\pi$
$727$	36.1990			1.34255			0.671274	+	0.741209i	$0.265747\pi$
$728$	0.312710	−	10.1412i	0.0115898	−	0.375857i
$729$		0			0
$730$	−27.5224	−	16.2694i	−1.01865	−	0.602157i
$731$	−1.79229	+	1.79229i	−0.0662902	+	0.0662902i
$732$		0			0
$733$	−3.85554	−	3.85554i	−0.142408	−	0.142408i	0.632309	−	0.774716i	$-0.282107\pi$
$733$	−3.85554	−	3.85554i	−0.142408	−	0.142408i	−0.774716	+	0.632309i	$0.782107\pi$
$734$	−19.4174	+	4.98961i	−0.716709	+	0.184170i
$735$		0			0
$736$	−15.1833	+	46.8863i	−0.559665	+	1.72825i
$737$		−	0.0292849i		−	0.00107872i
$738$		0			0
$739$	−20.1965	+	20.1965i	−0.742942	+	0.742942i	−0.973143	−	0.230201i	$-0.926061\pi$
$739$	−20.1965	+	20.1965i	−0.742942	+	0.742942i	0.230201	+	0.973143i	$0.426061\pi$
$740$	−1.55778	+	0.857196i	−0.0572652	+	0.0315112i
$741$		0			0
$742$	−6.14811	+	10.4005i	−0.225704	+	0.381816i
$743$		−	38.9110i		−	1.42751i	−0.700398	−	0.713753i	$-0.746994\pi$
$743$		−	38.9110i		−	1.42751i	0.700398	−	0.713753i	$-0.253006\pi$
$744$		0			0
$745$			77.8444i			2.85200i
$746$	37.0344	+	21.8923i	1.35593	+	0.801533i
$747$		0			0
$748$	−1.60260	−	0.464914i	−0.0585968	−	0.0169990i
$749$	−7.33395	+	7.33395i	−0.267977	+	0.267977i
$750$		0			0
$751$			1.20106i			0.0438274i	0.999760	+	0.0219137i	$0.00697590\pi$
$751$			1.20106i			0.0438274i	−0.999760	+	0.0219137i	$0.993024\pi$
$752$	−8.79517	+	13.8831i	−0.320727	+	0.506265i
$753$		0			0
$754$	10.8067	+	42.0550i	0.393557	+	1.53155i
$755$	−39.8947	−	39.8947i	−1.45192	−	1.45192i
$756$		0			0
$757$	12.9836	−	12.9836i	0.471896	−	0.471896i	−0.430632	−	0.902528i	$-0.641709\pi$
$757$	12.9836	−	12.9836i	0.471896	−	0.471896i	0.902528	+	0.430632i	$0.141709\pi$
$758$	8.29981	−	14.0405i	0.301463	−	0.509974i
$759$		0			0
$760$	−60.2247	−	64.0570i	−2.18458	−	2.32359i
$761$	16.4747			0.597208			0.298604	−	0.954377i	$-0.403479\pi$
$761$	16.4747			0.597208			0.298604	+	0.954377i	$0.403479\pi$
$762$		0			0
$763$	−4.12218	−	4.12218i	−0.149233	−	0.149233i
$764$	−17.7735	+	9.78017i	−0.643023	+	0.353834i
$765$		0			0
$766$	3.18927	+	12.4113i	0.115233	+	0.448437i
$767$	30.6978			1.10843
$768$		0			0
$769$	33.6226			1.21246			0.606231	−	0.795289i	$-0.292681\pi$
$769$	33.6226			1.21246			0.606231	+	0.795289i	$0.292681\pi$
$770$	−1.19084	−	4.63424i	−0.0429150	−	0.167007i
$771$		0			0
$772$	22.1708	−	12.1999i	0.797945	−	0.439083i
$773$	20.0820	+	20.0820i	0.722299	+	0.722299i	0.969073	−	0.246774i	$-0.0793707\pi$
$773$	20.0820	+	20.0820i	0.722299	+	0.722299i	−0.246774	+	0.969073i	$0.579371\pi$
$774$		0			0
$775$	−37.9274			−1.36239
$776$	−7.26935	−	7.73193i	−0.260955	−	0.277560i
$777$		0			0
$778$	−22.5007	+	38.0636i	−0.806688	+	1.36465i
$779$	45.2079	−	45.2079i	1.61974	−	1.61974i
$780$		0			0
$781$	8.27761	+	8.27761i	0.296196	+	0.296196i
$782$	−3.17461	−	12.3542i	−0.113524	−	0.441785i
$783$		0			0
$784$	2.14065	−	3.37900i	0.0764518	−	0.120678i
$785$			35.1774i			1.25553i
$786$		0			0
$787$	−1.75329	+	1.75329i	−0.0624980	+	0.0624980i	−0.737665	−	0.675167i	$-0.764072\pi$
$787$	−1.75329	+	1.75329i	−0.0624980	+	0.0624980i	0.675167	+	0.737665i	$0.264072\pi$
$788$	11.7358	+	3.40456i	0.418070	+	0.121282i
$789$		0			0
$790$	19.9265	+	11.7792i	0.708952	+	0.419085i
$791$			12.1524i			0.432089i
$792$		0			0
$793$			29.5196i			1.04827i
$794$	25.5780	−	43.2695i	0.907730	−	1.53558i
$795$		0			0
$796$	−12.6571	+	6.96476i	−0.448617	+	0.246859i
$797$	16.1165	−	16.1165i	0.570876	−	0.570876i	−0.361497	−	0.932373i	$-0.617734\pi$
$797$	16.1165	−	16.1165i	0.570876	−	0.570876i	0.932373	+	0.361497i	$0.117734\pi$
$798$		0			0
$799$		−	4.25360i		−	0.150482i
$800$	−22.0027	+	67.9445i	−0.777912	+	2.40220i
$801$		0			0
$802$	−2.11741	+	0.544103i	−0.0747684	+	0.0192129i
$803$	−3.06867	−	3.06867i	−0.108291	−	0.108291i
$804$		0			0
$805$	25.8629	−	25.8629i	0.911548	−	0.911548i
$806$	−13.1192	−	7.75518i	−0.462104	−	0.273165i
$807$		0			0
$808$	−0.152043	+	4.93075i	−0.00534885	+	0.173463i
$809$	−30.3586			−1.06735			−0.533676	−	0.845689i	$-0.679190\pi$
$809$	−30.3586			−1.06735			−0.533676	+	0.845689i	$0.679190\pi$
$810$		0			0
$811$	20.3645	+	20.3645i	0.715095	+	0.715095i	0.967596	−	0.252502i	$-0.0812534\pi$
$811$	20.3645	+	20.3645i	0.715095	+	0.715095i	−0.252502	+	0.967596i	$0.581253\pi$
$812$	−4.76947	+	16.4407i	−0.167375	+	0.576957i
$813$		0			0
$814$	−0.233756	+	0.0600672i	−0.00819313	+	0.00210536i
$815$	10.8336			0.379483
$816$		0			0
$817$	−18.1281			−0.634223
$818$	7.84641	−	2.01626i	0.274343	−	0.0704969i
$819$		0			0
$820$	−69.6291	−	20.1994i	−2.43155	−	0.705395i
$821$	35.3970	+	35.3970i	1.23536	+	1.23536i	0.961876	+	0.273487i	$0.0881770\pi$
$821$	35.3970	+	35.3970i	1.23536	+	1.23536i	0.273487	+	0.961876i	$0.411823\pi$
$822$		0			0
$823$	24.6885			0.860587			0.430294	−	0.902689i	$-0.358410\pi$
$823$	24.6885			0.860587			0.430294	+	0.902689i	$0.358410\pi$
$824$	−27.7688	−	29.5358i	−0.967371	−	1.02893i
$825$		0			0
$826$	10.4183	+	6.15858i	0.362498	+	0.214284i
$827$	37.8496	−	37.8496i	1.31616	−	1.31616i	0.399369	−	0.916790i	$-0.369229\pi$
$827$	37.8496	−	37.8496i	1.31616	−	1.31616i	0.916790	−	0.399369i	$-0.130771\pi$
$828$		0			0
$829$	−5.82230	−	5.82230i	−0.202217	−	0.202217i	0.598732	−	0.800949i	$-0.295671\pi$
$829$	−5.82230	−	5.82230i	−0.202217	−	0.202217i	−0.800949	+	0.598732i	$0.795671\pi$
$830$	11.4413	−	2.94003i	0.397134	−	0.102050i
$831$		0			0
$832$	−21.5037	+	19.0032i	−0.745506	+	0.658817i
$833$			1.03528i			0.0358703i
$834$		0			0
$835$	16.3060	−	16.3060i	0.564291	−	0.564291i
$836$	−5.75356	−	10.4559i	−0.198991	−	0.361626i
$837$		0			0
$838$	−26.6953	+	45.1596i	−0.922175	+	1.56001i
$839$		−	24.7552i		−	0.854645i	−0.904099	−	0.427323i	$-0.859457\pi$
$839$		−	24.7552i		−	0.854645i	0.904099	−	0.427323i	$-0.140543\pi$
$840$		0			0
$841$		−	44.2615i		−	1.52626i
$842$	16.1579	+	9.55149i	0.556840	+	0.329166i
$843$		0			0
$844$	−7.50113	+	25.8570i	−0.258200	+	0.890036i
$845$	−0.392885	+	0.392885i	−0.0135156	+	0.0135156i
$846$		0			0
$847$			10.3505i			0.355648i
$848$	33.3437	−	7.48075i	1.14503	−	0.256890i
$849$		0			0
$850$	−4.60043	−	17.9029i	−0.157793	−	0.614064i
$851$	−1.30455	−	1.30455i	−0.0447194	−	0.0447194i
$852$		0			0
$853$	9.64611	−	9.64611i	0.330276	−	0.330276i	−0.522415	−	0.852691i	$-0.674969\pi$
$853$	9.64611	−	9.64611i	0.330276	−	0.330276i	0.852691	+	0.522415i	$0.174969\pi$
$854$	−5.92222	+	10.0184i	−0.202654	+	0.342823i
$855$		0			0
$856$	29.3219	+	0.904160i	1.00220	+	0.0309036i
$857$	2.92127			0.0997886			0.0498943	−	0.998755i	$-0.484112\pi$
$857$	2.92127			0.0997886			0.0498943	+	0.998755i	$0.484112\pi$
$858$		0			0
$859$	−1.63800	−	1.63800i	−0.0558880	−	0.0558880i	0.678610	−	0.734498i	$-0.262582\pi$
$859$	−1.63800	−	1.63800i	−0.0558880	−	0.0558880i	−0.734498	+	0.678610i	$0.762582\pi$
$860$	9.91052	+	18.0104i	0.337946	+	0.614149i
$861$		0			0
$862$	5.61060	+	21.8340i	0.191098	+	0.743670i
$863$	54.6506			1.86033			0.930164	−	0.367145i	$-0.119665\pi$
$863$	54.6506			1.86033			0.930164	+	0.367145i	$0.119665\pi$
$864$		0			0
$865$	67.7907			2.30495
$866$	8.80145	+	34.2514i	0.299085	+	1.16391i
$867$		0			0
$868$	−2.89657	−	5.26394i	−0.0983160	−	0.178670i
$869$	2.22175	+	2.22175i	0.0753676	+	0.0753676i
$870$		0			0
$871$	0.130350			0.00441673
$872$	−0.508199	+	16.4809i	−0.0172098	+	0.558113i
$873$		0			0
$874$	46.4235	−	78.5332i	1.57030	−	2.65642i
$875$	22.6358	−	22.6358i	0.765230	−	0.765230i
$876$		0			0
$877$	−28.8847	−	28.8847i	−0.975368	−	0.975368i	0.0243360	−	0.999704i	$-0.492253\pi$
$877$	−28.8847	−	28.8847i	−0.975368	−	0.975368i	−0.999704	+	0.0243360i	$0.992253\pi$
$878$	−12.3373	−	48.0114i	−0.416364	−	1.62031i
$879$		0			0
$880$	−7.24260	+	11.4324i	−0.244148	+	0.385385i
$881$			22.1474i			0.746166i	0.927798	+	0.373083i	$0.121699\pi$
$881$			22.1474i			0.746166i	−0.927798	+	0.373083i	$0.878301\pi$
$882$		0			0
$883$	−34.6797	+	34.6797i	−1.16706	+	1.16706i	−0.184169	+	0.982895i	$0.558959\pi$
$883$	−34.6797	+	34.6797i	−1.16706	+	1.16706i	−0.982895	+	0.184169i	$0.941041\pi$
$884$	2.06938	−	7.13331i	0.0696007	−	0.239919i
$885$		0			0
$886$	−29.4936	−	17.4347i	−0.990858	−	0.585729i
$887$		−	21.6236i		−	0.726050i	−0.931779	−	0.363025i	$-0.881744\pi$
$887$		−	21.6236i		−	0.726050i	0.931779	−	0.363025i	$-0.118256\pi$
$888$		0			0
$889$			1.32089i			0.0443014i
$890$	−51.4698	+	87.0698i	−1.72527	+	2.91859i
$891$		0			0
$892$	−15.4886	−	28.1474i	−0.518596	−	0.942445i
$893$	21.5116	−	21.5116i	0.719857	−	0.719857i
$894$		0			0
$895$			32.5275i			1.08727i
$896$	−11.1104	+	2.13528i	−0.371172	+	0.0713345i
$897$		0			0
$898$	−20.2668	+	5.20789i	−0.676313	+	0.173790i
$899$	18.1820	+	18.1820i	0.606403	+	0.606403i
$900$		0			0
$901$	−6.25404	+	6.25404i	−0.208352	+	0.208352i
$902$	−8.47155	−	5.00781i	−0.282072	−	0.166742i
$903$		0			0
$904$	25.0423	−	23.5441i	0.832894	−	0.783065i
$905$	55.9719			1.86057
$906$		0			0
$907$	−37.3334	−	37.3334i	−1.23963	−	1.23963i	−0.960150	−	0.279485i	$-0.909836\pi$
$907$	−37.3334	−	37.3334i	−1.23963	−	1.23963i	−0.279485	−	0.960150i	$-0.590164\pi$
$908$	−31.4277	−	9.11719i	−1.04297	−	0.302565i
$909$		0			0
$910$	20.6274	−	5.30055i	0.683793	−	0.175712i
$911$	22.0091			0.729194			0.364597	−	0.931165i	$-0.381207\pi$
$911$	22.0091			0.729194			0.364597	+	0.931165i	$0.381207\pi$
$912$		0			0
$913$	1.60348			0.0530674
$914$	−16.4233	+	4.22023i	−0.543235	+	0.139593i
$915$		0			0
$916$	3.55037	−	12.2384i	0.117308	−	0.404369i
$917$	−1.67723	−	1.67723i	−0.0553871	−	0.0553871i
$918$		0			0
$919$	35.8652			1.18308			0.591542	−	0.806274i	$-0.298519\pi$
$919$	35.8652			1.18308			0.591542	+	0.806274i	$0.298519\pi$
$920$	−103.402	−	3.18849i	−3.40908	−	0.105121i
$921$		0			0
$922$	−25.7380	−	15.2146i	−0.847637	−	0.501066i
$923$	−36.8444	+	36.8444i	−1.21275	+	1.21275i
$924$		0			0
$925$	−1.89047	−	1.89047i	−0.0621581	−	0.0621581i
$926$	−43.1044	+	11.0764i	−1.41650	+	0.363992i
$927$		0			0
$928$	43.1197	−	22.0240i	1.41547	−	0.722974i
$929$			16.1094i			0.528531i	0.964450	+	0.264265i	$0.0851295\pi$
$929$			16.1094i			0.528531i	−0.964450	+	0.264265i	$0.914870\pi$
$930$		0			0
$931$	−5.23568	+	5.23568i	−0.171592	+	0.171592i
$932$	28.4842	−	15.6739i	0.933032	−	0.513417i
$933$		0			0
$934$	25.2094	−	42.6459i	0.824877	−	1.39542i
$935$		−	3.50273i		−	0.114552i
$936$		0			0
$937$		−	17.5529i		−	0.573429i	−0.958016	−	0.286714i	$-0.907437\pi$
$937$		−	17.5529i		−	0.573429i	0.958016	−	0.286714i	$-0.0925630\pi$
$938$	0.0442383	+	0.0261507i	0.00144443	+	0.000853851i
$939$		0			0
$940$	−33.1320	−	9.61162i	−1.08065	−	0.313496i
$941$	6.41436	−	6.41436i	0.209102	−	0.209102i	−0.594784	−	0.803886i	$-0.702762\pi$
$941$	6.41436	−	6.41436i	0.209102	−	0.209102i	0.803886	+	0.594784i	$0.202762\pi$
$942$		0			0
$943$		−	75.2260i		−	2.44970i
$944$	−7.49350	−	33.4005i	−0.243893	−	1.08709i
$945$		0			0
$946$	0.694470	+	2.70258i	0.0225792	+	0.0878683i
$947$	7.95690	+	7.95690i	0.258564	+	0.258564i	0.824470	−	0.565906i	$-0.191473\pi$
$947$	7.95690	+	7.95690i	0.258564	+	0.258564i	−0.565906	+	0.824470i	$0.691473\pi$
$948$		0			0
$949$	13.6589	−	13.6589i	0.443388	−	0.443388i
$950$	67.2739	−	113.805i	2.18265	−	3.69232i
$951$		0			0
$952$	2.13339	−	2.00576i	0.0691437	−	0.0650071i
$953$	45.4471			1.47217			0.736087	−	0.676887i	$-0.236671\pi$
$953$	45.4471			1.47217			0.736087	+	0.676887i	$0.236671\pi$
$954$		0			0
$955$	−30.1114	−	30.1114i	−0.974383	−	0.974383i
$956$	−7.98313	+	4.39285i	−0.258193	+	0.142075i
$957$		0			0
$958$	6.23670	+	24.2705i	0.201499	+	0.784145i
$959$	8.49554			0.274335
$960$		0			0
$961$	21.9752			0.708878
$962$	−0.267365	−	1.04047i	−0.00862019	−	0.0335460i
$963$		0			0
$964$	38.5630	−	21.2200i	1.24203	−	0.683449i
$965$	37.5612	+	37.5612i	1.20914	+	1.20914i
$966$		0			0
$967$	62.0308			1.99478			0.997389	−	0.0722214i	$-0.0230088\pi$
$967$	62.0308			1.99478			0.997389	+	0.0722214i	$0.0230088\pi$
$968$	21.3292	−	20.0532i	0.685547	−	0.644534i
$969$		0			0
$970$	11.3361	−	19.1769i	0.363981	−	0.615734i
$971$	−11.5203	+	11.5203i	−0.369704	+	0.369704i	−0.867369	−	0.497665i	$-0.834191\pi$
$971$	−11.5203	+	11.5203i	−0.369704	+	0.369704i	0.497665	+	0.867369i	$0.334191\pi$
$972$		0			0
$973$	−7.80995	−	7.80995i	−0.250376	−	0.250376i
$974$	−11.9191	−	46.3839i	−0.381912	−	1.48624i
$975$		0			0
$976$	32.1186	−	7.20590i	1.02809	−	0.230655i
$977$		−	30.9755i		−	0.990995i	−0.868609	−	0.495498i	$-0.834986\pi$
$977$		−	30.9755i		−	0.990995i	0.868609	−	0.495498i	$-0.165014\pi$
$978$		0			0
$979$	−9.70804	+	9.70804i	−0.310270	+	0.310270i
$980$	8.06398	+	2.33936i	0.257594	+	0.0747282i
$981$		0			0
$982$	−43.6423	−	25.7984i	−1.39268	−	0.823260i
$983$			39.7177i			1.26680i	0.773825	+	0.633399i	$0.218341\pi$
$983$			39.7177i			1.26680i	−0.773825	+	0.633399i	$0.781659\pi$
$984$		0			0
$985$			25.6504i			0.817290i
$986$	−6.37704	+	10.7878i	−0.203086	+	0.343555i
$987$		0			0
$988$	46.5404	−	25.6096i	1.48065	−	0.814751i
$989$	−15.0826	+	15.0826i	−0.479599	+	0.479599i
$990$		0			0
$991$			44.2359i			1.40520i	0.711585	+	0.702600i	$0.247978\pi$
$991$			44.2359i			1.40520i	−0.711585	+	0.702600i	$0.752022\pi$
$992$	−5.23551	+	16.1673i	−0.166228	+	0.513313i
$993$		0			0
$994$	−19.8961	+	5.11261i	−0.631064	+	0.162162i
$995$	−21.4433	−	21.4433i	−0.679798	−	0.679798i
$996$		0			0
$997$	−19.7318	+	19.7318i	−0.624913	+	0.624913i	−0.946784	−	0.321871i	$-0.895688\pi$
$997$	−19.7318	+	19.7318i	−0.624913	+	0.624913i	0.321871	+	0.946784i	$0.395688\pi$
$998$	−12.5113	−	7.39585i	−0.396039	−	0.234111i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1008.2.v.e.323.12	yes	40
3.2	odd	2	inner	1008.2.v.e.323.9	✓	40
4.3	odd	2		4032.2.v.e.1583.1		40
12.11	even	2		4032.2.v.e.1583.20		40
16.5	even	4		4032.2.v.e.3599.20		40
16.11	odd	4	inner	1008.2.v.e.827.9	yes	40
48.5	odd	4		4032.2.v.e.3599.1		40
48.11	even	4	inner	1008.2.v.e.827.12	yes	40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1008.2.v.e.323.9	✓	40	3.2	odd	2	inner
1008.2.v.e.323.12	yes	40	1.1	even	1	trivial
1008.2.v.e.827.9	yes	40	16.11	odd	4	inner
1008.2.v.e.827.12	yes	40	48.11	even	4	inner
4032.2.v.e.1583.1		40	4.3	odd	2
4032.2.v.e.1583.20		40	12.11	even	2
4032.2.v.e.3599.1		40	48.5	odd	4
4032.2.v.e.3599.20		40	16.5	even	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1008.v (of order \(4\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.351970 + 1.36971i) q^{2} +(-1.75223 + 0.964197i) q^{4} +(-2.96859 - 2.96859i) q^{5} +1.00000 q^{7} +(-1.93741 - 2.06069i) q^{8} +O(q^{10})\)	\(q+(0.351970 + 1.36971i) q^{2} +(-1.75223 + 0.964197i) q^{4} +(-2.96859 - 2.96859i) q^{5} +1.00000 q^{7} +(-1.93741 - 2.06069i) q^{8} +(3.02127 - 5.11098i) q^{10} +(0.569860 - 0.569860i) q^{11} +(2.53650 + 2.53650i) q^{13} +(0.351970 + 1.36971i) q^{14} +(2.14065 - 3.37900i) q^{16} +1.03528i q^{17} +(-5.23568 + 5.23568i) q^{19} +(8.06398 + 2.33936i) q^{20} +(0.981119 + 0.579972i) q^{22} +8.71217i q^{23} +12.6251i q^{25} +(-2.58151 + 4.36705i) q^{26} +(-1.75223 + 0.964197i) q^{28} +(6.05233 - 6.05233i) q^{29} +3.00413i q^{31} +(5.38170 + 1.74277i) q^{32} +(-1.41804 + 0.364388i) q^{34} +(-2.96859 - 2.96859i) q^{35} +(-0.149739 + 0.149739i) q^{37} +(-9.01419 - 5.32858i) q^{38} +(-0.365980 + 11.8687i) q^{40} -8.63459 q^{41} +(1.73121 + 1.73121i) q^{43} +(-0.449071 + 1.54798i) q^{44} +(-11.9332 + 3.06642i) q^{46} -4.10865 q^{47} +1.00000 q^{49} +(-17.2928 + 4.44366i) q^{50} +(-6.89022 - 1.99886i) q^{52} +(6.04092 + 6.04092i) q^{53} -3.38337 q^{55} +(-1.93741 - 2.06069i) q^{56} +(10.4202 + 6.15973i) q^{58} +(6.05121 - 6.05121i) q^{59} +(5.81897 + 5.81897i) q^{61} +(-4.11480 + 1.05736i) q^{62} +(-0.492902 + 7.98480i) q^{64} -15.0597i q^{65} +(0.0256948 - 0.0256948i) q^{67} +(-0.998214 - 1.81405i) q^{68} +(3.02127 - 5.11098i) q^{70} +14.5257i q^{71} -5.38496i q^{73} +(-0.257803 - 0.152396i) q^{74} +(4.12591 - 14.2224i) q^{76} +(0.569860 - 0.569860i) q^{77} +3.89876i q^{79} +(-16.3856 + 3.67615i) q^{80} +(-3.03912 - 11.8269i) q^{82} +(1.40691 + 1.40691i) q^{83} +(3.07333 - 3.07333i) q^{85} +(-1.76193 + 2.98060i) q^{86} +(-2.27836 - 0.0702547i) q^{88} -17.0358 q^{89} +(2.53650 + 2.53650i) q^{91} +(-8.40025 - 15.2658i) q^{92} +(-1.44612 - 5.62767i) q^{94} +31.0852 q^{95} +3.75210 q^{97} +(0.351970 + 1.36971i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 40 q^{7}+O(q^{10}) \) 40 * q + 40 * q^7	\( 40 q + 40 q^{7} + 48 q^{10} - 24 q^{13} + 12 q^{16} - 32 q^{19} - 8 q^{22} - 56 q^{34} - 8 q^{37} + 32 q^{43} - 52 q^{46} + 40 q^{49} - 8 q^{52} + 48 q^{55} + 56 q^{58} - 24 q^{61} + 48 q^{64} + 48 q^{70} - 24 q^{76} - 64 q^{82} + 64 q^{85} - 120 q^{88} - 24 q^{91} - 128 q^{94} + 64 q^{97}+O(q^{100}) \) 40 * q + 40 * q^7 + 48 * q^10 - 24 * q^13 + 12 * q^16 - 32 * q^19 - 8 * q^22 - 56 * q^34 - 8 * q^37 + 32 * q^43 - 52 * q^46 + 40 * q^49 - 8 * q^52 + 48 * q^55 + 56 * q^58 - 24 * q^61 + 48 * q^64 + 48 * q^70 - 24 * q^76 - 64 * q^82 + 64 * q^85 - 120 * q^88 - 24 * q^91 - 128 * q^94 + 64 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

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