LMFDB - Embedded newform 784.2.x.o.165.12

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [784,2,Mod(165,784)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(784, base_ring=CyclotomicField(12))

chi = DirichletCharacter(H, H._module([0, 3, 8]))

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

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

chi := DirichletCharacter("784.165");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 784 = 2^{4} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	784.x (of order $12$, degree $4$, not 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:	$6.26027151847$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{12})$
Twist minimal:	no (minimal twist has level 112)
Sato-Tate group:	$\mathrm{SU}(2)[C_{12}]$

Embedding invariants

Embedding label			165.12
Character	$\chi$	$=$	784.165
Dual form			784.2.x.o.765.12

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.40944 - 0.116052i) q^{2} +(0.312249 + 1.16533i) q^{3} +(1.97306 - 0.327139i) q^{4} +(0.262843 - 0.980942i) q^{5} +(0.575337 + 1.60623i) q^{6} +(2.74296 - 0.690063i) q^{8} +(1.33758 - 0.772254i) q^{9} +(0.256621 - 1.41309i) q^{10} +(-2.36993 + 0.635020i) q^{11} +(0.997312 + 2.19712i) q^{12} +(2.65786 - 2.65786i) q^{13} +1.22519 q^{15} +(3.78596 - 1.29093i) q^{16} +(0.509128 - 0.881836i) q^{17} +(1.79563 - 1.24368i) q^{18} +(-0.0936561 - 0.0250951i) q^{19} +(0.197701 - 2.02145i) q^{20} +(-3.26658 + 1.17006i) q^{22} +(-1.67238 + 0.965551i) q^{23} +(1.66064 + 2.98098i) q^{24} +(3.43697 + 1.98433i) q^{25} +(3.43765 - 4.05455i) q^{26} +(3.87683 + 3.87683i) q^{27} +(-5.05325 + 5.05325i) q^{29} +(1.72684 - 0.142187i) q^{30} +(-4.28249 + 7.41749i) q^{31} +(5.18628 - 2.25887i) q^{32} +(-1.48001 - 2.56346i) q^{33} +(0.615248 - 1.30198i) q^{34} +(2.38650 - 1.96128i) q^{36} +(2.06704 - 7.71428i) q^{37} +(-0.134915 - 0.0245011i) q^{38} +(3.92719 + 2.26737i) q^{39} +(0.0440545 - 2.87206i) q^{40} +8.51782i q^{41} +(-4.47950 - 4.47950i) q^{43} +(-4.46828 + 2.02823i) q^{44} +(-0.405963 - 1.51507i) q^{45} +(-2.24507 + 1.55497i) q^{46} +(-6.02995 - 10.4442i) q^{47} +(2.68652 + 4.00880i) q^{48} +(5.07450 + 2.39794i) q^{50} +(1.18660 + 0.317949i) q^{51} +(4.37464 - 6.11361i) q^{52} +(-1.42191 + 0.381000i) q^{53} +(5.91409 + 5.01426i) q^{54} +2.49167i q^{55} -0.116976i q^{57} +(-6.53583 + 7.70871i) q^{58} +(-6.96158 + 1.86535i) q^{59} +(2.41738 - 0.400808i) q^{60} +(-4.42654 - 1.18609i) q^{61} +(-5.17511 + 10.9515i) q^{62} +(7.04763 - 3.78563i) q^{64} +(-1.90861 - 3.30580i) q^{65} +(-2.38349 - 3.44129i) q^{66} +(0.907543 + 3.38700i) q^{67} +(0.716059 - 1.90647i) q^{68} +(-1.64738 - 1.64738i) q^{69} +5.43131i q^{71} +(3.13603 - 3.04128i) q^{72} +(7.34303 + 4.23950i) q^{73} +(2.01811 - 11.1127i) q^{74} +(-1.23921 + 4.62480i) q^{75} +(-0.192999 - 0.0188756i) q^{76} +(5.79829 + 2.73996i) q^{78} +(-0.433595 - 0.751008i) q^{79} +(-0.271217 - 4.05312i) q^{80} +(-0.990483 + 1.71557i) q^{81} +(0.988514 + 12.0054i) q^{82} +(5.44318 - 5.44318i) q^{83} +(-0.731209 - 0.731209i) q^{85} +(-6.83345 - 5.79374i) q^{86} +(-7.46657 - 4.31083i) q^{87} +(-6.06240 + 3.37723i) q^{88} +(3.93155 - 2.26988i) q^{89} +(-0.748010 - 2.08830i) q^{90} +(-2.98385 + 2.45219i) q^{92} +(-9.98102 - 2.67441i) q^{93} +(-9.71095 - 14.0207i) q^{94} +(-0.0492336 + 0.0852752i) q^{95} +(4.25173 + 5.33840i) q^{96} -16.4025 q^{97} +(-2.67958 + 2.67958i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27}+ \cdots - 24 q^{99}+O(q^{100}) $ 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/784\mathbb{Z}\right)^\times$.

$n$	$197$	$687$	$689$
$\chi(n)$	$e\left(\frac{1}{4}\right)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	1.40944	−	0.116052i	0.996627	−	0.0820615i
$2$	1.40944	−	0.116052i	0.996627	−	0.0820615i
$3$	0.312249	+	1.16533i	0.180277	+	0.672803i	0.995592	+	0.0937859i	$0.0298969\pi$
$3$	0.312249	+	1.16533i	0.180277	+	0.672803i	−0.815315	+	0.579017i	$0.803436\pi$
$4$	1.97306	−	0.327139i	0.986532	−	0.163569i
$5$	0.262843	−	0.980942i	0.117547	−	0.438691i	−0.881918	−	0.471403i	$-0.843748\pi$
$5$	0.262843	−	0.980942i	0.117547	−	0.438691i	0.999465	+	0.0327122i	$0.0104145\pi$
$6$	0.575337	+	1.60623i	0.234880	+	0.655740i
$7$		0			0
$7$		0			0
$8$	2.74296	−	0.690063i	0.969782	−	0.243974i
$9$	1.33758	−	0.772254i	0.445861	−	0.257418i
$10$	0.256621	−	1.41309i	0.0811507	−	0.446857i
$11$	−2.36993	+	0.635020i	−0.714560	+	0.191466i	−0.597743	−	0.801688i	$-0.703936\pi$
$11$	−2.36993	+	0.635020i	−0.714560	+	0.191466i	−0.116817	+	0.993153i	$0.537269\pi$
$12$	0.997312	+	2.19712i	0.287899	+	0.634254i
$13$	2.65786	−	2.65786i	0.737157	−	0.737157i	−0.234870	−	0.972027i	$-0.575466\pi$
$13$	2.65786	−	2.65786i	0.737157	−	0.737157i	0.972027	+	0.234870i	$0.0754663\pi$
$14$		0			0
$15$	1.22519			0.316343
$16$	3.78596	−	1.29093i	0.946490	−	0.322733i
$17$	0.509128	−	0.881836i	0.123482	−	0.213877i	−0.797657	−	0.603112i	$-0.793927\pi$
$17$	0.509128	−	0.881836i	0.123482	−	0.213877i	0.921138	+	0.389235i	$0.127261\pi$
$18$	1.79563	−	1.24368i	0.423233	−	0.293138i
$19$	−0.0936561	−	0.0250951i	−0.0214862	−	0.00575721i	0.248060	−	0.968745i	$-0.420207\pi$
$19$	−0.0936561	−	0.0250951i	−0.0214862	−	0.00575721i	−0.269546	+	0.962987i	$0.586874\pi$
$20$	0.197701	−	2.02145i	0.0442073	−	0.452009i
$21$		0			0
$22$	−3.26658	+	1.17006i	−0.696438	+	0.249458i
$23$	−1.67238	+	0.965551i	−0.348716	+	0.201331i	−0.664120	−	0.747626i	$-0.731193\pi$
$23$	−1.67238	+	0.965551i	−0.348716	+	0.201331i	0.315404	+	0.948958i	$0.397860\pi$
$24$	1.66064	+	2.98098i	0.338976	+	0.608489i
$25$	3.43697	+	1.98433i	0.687393	+	0.396867i
$26$	3.43765	−	4.05455i	0.674179	−	0.795163i
$27$	3.87683	+	3.87683i	0.746096	+	0.746096i
$28$		0			0
$29$	−5.05325	+	5.05325i	−0.938365	+	0.938365i	−0.998208	−	0.0598432i	$-0.980940\pi$
$29$	−5.05325	+	5.05325i	−0.938365	+	0.938365i	0.0598432	+	0.998208i	$0.480940\pi$
$30$	1.72684	−	0.142187i	0.315276	−	0.0259596i
$31$	−4.28249	+	7.41749i	−0.769158	+	1.33222i	0.168862	+	0.985640i	$0.445991\pi$
$31$	−4.28249	+	7.41749i	−0.769158	+	1.33222i	−0.938020	+	0.346581i	$0.887343\pi$
$32$	5.18628	−	2.25887i	0.916814	−	0.399315i
$33$	−1.48001	−	2.56346i	−0.257637	−	0.446241i
$34$	0.615248	−	1.30198i	0.105514	−	0.223288i
$35$		0			0
$36$	2.38650	−	1.96128i	0.397751	−	0.326880i
$37$	2.06704	−	7.71428i	0.339818	−	1.26822i	−0.558732	−	0.829349i	$-0.688712\pi$
$37$	2.06704	−	7.71428i	0.339818	−	1.26822i	0.898550	−	0.438871i	$-0.144622\pi$
$38$	−0.134915	−	0.0245011i	−0.0218862	−	0.00397460i
$39$	3.92719	+	2.26737i	0.628854	+	0.363069i
$40$	0.0440545	−	2.87206i	0.00696562	−	0.454113i
$41$			8.51782i			1.33026i	0.746728	+	0.665130i	$0.231624\pi$
$41$			8.51782i			1.33026i	−0.746728	+	0.665130i	$0.768376\pi$
$42$		0			0
$43$	−4.47950	−	4.47950i	−0.683117	−	0.683117i	0.277584	−	0.960701i	$-0.410466\pi$
$43$	−4.47950	−	4.47950i	−0.683117	−	0.683117i	−0.960701	+	0.277584i	$0.910466\pi$
$44$	−4.46828	+	2.02823i	−0.673618	+	0.305767i
$45$	−0.405963	−	1.51507i	−0.0605174	−	0.225854i
$46$	−2.24507	+	1.55497i	−0.331018	+	0.229268i
$47$	−6.02995	−	10.4442i	−0.879559	−	1.52344i	−0.851826	−	0.523825i	$-0.824505\pi$
$47$	−6.02995	−	10.4442i	−0.879559	−	1.52344i	−0.0277324	−	0.999615i	$-0.508829\pi$
$48$	2.68652	+	4.00880i	0.387766	+	0.578620i
$49$		0			0
$50$	5.07450	+	2.39794i	0.717642	+	0.339120i
$51$	1.18660	+	0.317949i	0.166158	+	0.0445218i
$52$	4.37464	−	6.11361i	0.606653	−	0.847806i
$53$	−1.42191	+	0.381000i	−0.195315	+	0.0523344i	−0.355150	−	0.934809i	$-0.615570\pi$
$53$	−1.42191	+	0.381000i	−0.195315	+	0.0523344i	0.159836	+	0.987144i	$0.448904\pi$
$54$	5.91409	+	5.01426i	0.804806	+	0.682354i
$55$			2.49167i			0.335977i
$56$		0			0
$57$		−	0.116976i		−	0.0154939i
$58$	−6.53583	+	7.70871i	−0.858196	+	1.01220i
$59$	−6.96158	+	1.86535i	−0.906320	+	0.242848i	−0.681729	−	0.731605i	$-0.738771\pi$
$59$	−6.96158	+	1.86535i	−0.906320	+	0.242848i	−0.224592	+	0.974453i	$0.572105\pi$
$60$	2.41738	−	0.400808i	0.312083	−	0.0517441i
$61$	−4.42654	−	1.18609i	−0.566760	−	0.151863i	−0.0359500	−	0.999354i	$-0.511446\pi$
$61$	−4.42654	−	1.18609i	−0.566760	−	0.151863i	−0.530810	+	0.847491i	$0.678112\pi$
$62$	−5.17511	+	10.9515i	−0.657240	+	1.39085i
$63$		0			0
$64$	7.04763	−	3.78563i	0.880953	−	0.473203i
$65$	−1.90861	−	3.30580i	−0.236734	−	0.410034i
$66$	−2.38349	−	3.44129i	−0.293388	−	0.423594i
$67$	0.907543	+	3.38700i	0.110874	+	0.413787i	0.998945	−	0.0459185i	$-0.0146215\pi$
$67$	0.907543	+	3.38700i	0.110874	+	0.413787i	−0.888071	+	0.459706i	$0.847955\pi$
$68$	0.716059	−	1.90647i	0.0868350	−	0.231194i
$69$	−1.64738	−	1.64738i	−0.198322	−	0.198322i
$70$		0			0
$71$			5.43131i			0.644578i	0.946641	+	0.322289i	$0.104452\pi$
$71$			5.43131i			0.644578i	−0.946641	+	0.322289i	$0.895548\pi$
$72$	3.13603	−	3.04128i	0.369585	−	0.358418i
$73$	7.34303	+	4.23950i	0.859436	+	0.496196i	0.863824	−	0.503795i	$-0.168063\pi$
$73$	7.34303	+	4.23950i	0.859436	+	0.496196i	−0.00438712	+	0.999990i	$0.501396\pi$
$74$	2.01811	−	11.1127i	0.234600	−	1.29183i
$75$	−1.23921	+	4.62480i	−0.143092	+	0.534026i
$76$	−0.192999	−	0.0188756i	−0.0221385	−	0.00216518i
$77$		0			0
$78$	5.79829	+	2.73996i	0.656527	+	0.310240i
$79$	−0.433595	−	0.751008i	−0.0487832	−	0.0844950i	0.840603	−	0.541652i	$-0.182201\pi$
$79$	−0.433595	−	0.751008i	−0.0487832	−	0.0844950i	−0.889386	+	0.457157i	$0.848868\pi$
$80$	−0.271217	−	4.05312i	−0.0303230	−	0.453153i
$81$	−0.990483	+	1.71557i	−0.110054	+	0.190619i
$82$	0.988514	+	12.0054i	0.109163	+	1.32577i
$83$	5.44318	−	5.44318i	0.597466	−	0.597466i	−0.342171	−	0.939638i	$-0.611162\pi$
$83$	5.44318	−	5.44318i	0.597466	−	0.597466i	0.939638	+	0.342171i	$0.111162\pi$
$84$		0			0
$85$	−0.731209	−	0.731209i	−0.0793108	−	0.0793108i
$86$	−6.83345	−	5.79374i	−0.736870	−	0.624755i
$87$	−7.46657	−	4.31083i	−0.800500	−	0.462169i
$88$	−6.06240	+	3.37723i	−0.646254	+	0.360014i
$89$	3.93155	−	2.26988i	0.416744	−	0.240607i	−0.276939	−	0.960887i	$-0.589320\pi$
$89$	3.93155	−	2.26988i	0.416744	−	0.240607i	0.693683	+	0.720280i	$0.255987\pi$
$90$	−0.748010	−	2.08830i	−0.0788471	−	0.220126i
$91$		0			0
$92$	−2.98385	+	2.45219i	−0.311088	+	0.255659i
$93$	−9.98102	−	2.67441i	−1.03498	−	0.277323i
$94$	−9.71095	−	14.0207i	−1.00161	−	1.44612i
$95$	−0.0492336	+	0.0852752i	−0.00505126	+	0.00874905i
$96$	4.25173	+	5.33840i	0.433941	+	0.544848i
$97$	−16.4025			−1.66542			−0.832712	−	0.553706i	$-0.813213\pi$
$97$	−16.4025			−1.66542			−0.832712	+	0.553706i	$0.813213\pi$
$98$		0			0
$99$	−2.67958	+	2.67958i	−0.269308	+	0.269308i
$100$	7.43051	+	2.79085i	0.743051	+	0.279085i
$101$	8.88412	−	2.38049i	0.884003	−	0.236868i	0.211870	−	0.977298i	$-0.432045\pi$
$101$	8.88412	−	2.38049i	0.884003	−	0.236868i	0.672134	+	0.740430i	$0.265378\pi$
$102$	1.70935	+	0.310424i	0.169251	+	0.0307365i
$103$	6.69469	−	3.86518i	0.659647	−	0.380848i	−0.132495	−	0.991184i	$-0.542299\pi$
$103$	6.69469	−	3.86518i	0.659647	−	0.380848i	0.792143	+	0.610336i	$0.208966\pi$
$104$	5.45630	−	9.12448i	0.535034	−	0.894729i
$105$		0			0
$106$	−1.95989	+	0.702015i	−0.190361	+	0.0681857i
$107$	−4.89154	+	18.2555i	−0.472883	+	1.76482i	0.156449	+	0.987686i	$0.449995\pi$
$107$	−4.89154	+	18.2555i	−0.472883	+	1.76482i	−0.629332	+	0.777137i	$0.716671\pi$
$108$	8.91749	+	6.38097i	0.858086	+	0.614009i
$109$	−4.23429	−	15.8026i	−0.405571	−	1.51361i	−0.802999	−	0.595980i	$-0.796764\pi$
$109$	−4.23429	−	15.8026i	−0.405571	−	1.51361i	0.397428	−	0.917633i	$-0.369903\pi$
$110$	0.289165	+	3.51187i	0.0275708	+	0.334844i
$111$	9.63510			0.914524
$112$		0			0
$113$	−20.1152			−1.89228			−0.946138	−	0.323765i	$-0.895051\pi$
$113$	−20.1152			−1.89228			−0.946138	+	0.323765i	$0.895051\pi$
$114$	−0.0135754	−	0.164871i	−0.00127145	−	0.0154416i
$115$	0.507576	+	1.89430i	0.0473317	+	0.176644i
$116$	−8.31727	+	11.6235i	−0.772239	+	1.07921i
$117$	1.50257	−	5.60765i	0.138912	−	0.518428i
$118$	−9.59547	+	3.43701i	−0.883335	+	0.316403i
$119$		0			0
$120$	3.36065	−	0.845460i	0.306784	−	0.0771796i
$121$	−4.31298	+	2.49010i	−0.392089	+	0.226373i
$122$	−6.37661	−	1.15801i	−0.577311	−	0.104842i
$123$	−9.92606	+	2.65968i	−0.895003	+	0.239815i
$124$	−6.02308	+	16.0361i	−0.540888	+	1.44009i
$125$	6.44039	−	6.44039i	0.576046	−	0.576046i
$126$		0			0
$127$	−0.988901			−0.0877508			−0.0438754	−	0.999037i	$-0.513970\pi$
$127$	−0.988901			−0.0877508			−0.0438754	+	0.999037i	$0.513970\pi$
$128$	9.49390	−	6.15352i	0.839150	−	0.543899i
$129$	3.82137	−	6.61880i	0.336453	−	0.582753i
$130$	−3.07372	−	4.43785i	−0.269583	−	0.389225i
$131$	−7.60883	−	2.03878i	−0.664786	−	0.178129i	−0.0893811	−	0.995998i	$-0.528489\pi$
$131$	−7.60883	−	2.03878i	−0.664786	−	0.178129i	−0.575405	+	0.817869i	$0.695156\pi$
$132$	−3.75877	−	4.57370i	−0.327159	−	0.398089i
$133$		0			0
$134$	1.67220	+	4.66846i	0.144456	+	0.403293i
$135$	4.82194	−	2.78395i	0.415007	−	0.239604i
$136$	0.787994	−	2.77017i	0.0675700	−	0.237540i
$137$	9.57893	+	5.53040i	0.818383	+	0.472494i	0.849859	−	0.527011i	$-0.176687\pi$
$137$	9.57893	+	5.53040i	0.818383	+	0.472494i	−0.0314753	+	0.999505i	$0.510021\pi$
$138$	−2.51308	−	2.13071i	−0.213927	−	0.181378i
$139$	−12.4154	−	12.4154i	−1.05306	−	1.05306i	−0.998511	−	0.0545473i	$-0.982628\pi$
$139$	−12.4154	−	12.4154i	−1.05306	−	1.05306i	−0.0545473	−	0.998511i	$-0.517372\pi$
$140$		0			0
$141$	10.2881	−	10.2881i	0.866411	−	0.866411i
$142$	0.630317	+	7.65513i	0.0528951	+	0.642404i
$143$	−4.61114	+	7.98672i	−0.385603	+	0.667883i
$144$	4.06711	−	4.65045i	0.338926	−	0.387538i
$145$	3.62873	+	6.28515i	0.301350	+	0.521954i
$146$	10.8416	+	5.12316i	0.897256	+	0.423996i
$147$		0			0
$148$	1.55475	−	15.8970i	0.127800	−	1.30672i
$149$	1.35622	−	5.06147i	0.111106	−	0.414652i	−0.887861	−	0.460113i	$-0.847809\pi$
$149$	1.35622	−	5.06147i	0.111106	−	0.414652i	0.998966	+	0.0454610i	$0.0144757\pi$
$150$	−1.20988	+	6.66221i	−0.0987863	+	0.543967i
$151$	−1.18073	−	0.681693i	−0.0960862	−	0.0554754i	0.451187	−	0.892429i	$-0.351001\pi$
$151$	−1.18073	−	0.681693i	−0.0960862	−	0.0554754i	−0.547273	+	0.836954i	$0.684334\pi$
$152$	−0.274212	−	0.00420613i	−0.0222415	−	0.000341162i
$153$		−	1.57271i		−	0.127146i
$154$		0			0
$155$	6.15051	+	6.15051i	0.494021	+	0.494021i
$156$	8.49035	+	3.18892i	0.679772	+	0.255318i
$157$	0.0822524	+	0.306970i	0.00656446	+	0.0244989i	0.969130	−	0.246549i	$-0.0792966\pi$
$157$	0.0822524	+	0.306970i	0.00656446	+	0.0244989i	−0.962566	+	0.271048i	$0.912630\pi$
$158$	−0.698284	−	1.00818i	−0.0555525	−	0.0802068i
$159$	−0.887981	−	1.53803i	−0.0704215	−	0.121974i
$160$	−0.852640	−	5.68117i	−0.0674071	−	0.449136i
$161$		0			0
$162$	−1.19693	+	2.53294i	−0.0940400	+	0.199007i
$163$	14.3376	+	3.84175i	1.12301	+	0.300909i	0.772100	−	0.635501i	$-0.219206\pi$
$163$	14.3376	+	3.84175i	1.12301	+	0.300909i	0.350907	+	0.936410i	$0.385873\pi$
$164$	2.78651	+	16.8062i	0.217590	+	1.31234i
$165$	−2.90362	+	0.778022i	−0.226046	+	0.0605689i
$166$	7.04016	−	8.30354i	0.546422	−	0.644480i
$167$			14.5986i			1.12967i	0.825204	+	0.564836i	$0.191060\pi$
$167$			14.5986i			1.12967i	−0.825204	+	0.564836i	$0.808940\pi$
$168$		0			0
$169$		−	1.12842i		−	0.0868018i
$170$	−1.11546	−	0.945740i	−0.0855516	−	0.0725349i
$171$	−0.144653	+	0.0387596i	−0.0110619	+	0.00296402i
$172$	−10.3037	−	7.37291i	−0.785653	−	0.562179i
$173$	−11.9299	−	3.19660i	−0.907011	−	0.243033i	−0.224986	−	0.974362i	$-0.572234\pi$
$173$	−11.9299	−	3.19660i	−0.907011	−	0.243033i	−0.682025	+	0.731329i	$0.738900\pi$
$174$	−11.0240	−	5.20935i	−0.835727	−	0.394920i
$175$		0			0
$176$	−8.15268	+	5.46357i	−0.614531	+	0.411832i
$177$	−4.34749	−	7.53008i	−0.326777	−	0.565995i
$178$	5.27788	−	3.65554i	0.395594	−	0.273994i
$179$	−0.122083	−	0.455619i	−0.00912489	−	0.0340545i	0.961213	−	0.275806i	$-0.0889448\pi$
$179$	−0.122083	−	0.455619i	−0.00912489	−	0.0340545i	−0.970338	+	0.241752i	$0.922278\pi$
$180$	−1.29663	−	2.85653i	−0.0966451	−	0.212913i
$181$	−15.4654	−	15.4654i	−1.14953	−	1.14953i	−0.986645	−	0.162887i	$-0.947919\pi$
$181$	−15.4654	−	15.4654i	−1.14953	−	1.14953i	−0.162887	−	0.986645i	$-0.552081\pi$
$182$		0			0
$183$		−	5.52873i		−	0.408696i
$184$	−3.92098	+	3.80251i	−0.289059	+	0.280325i
$185$	−7.02396	−	4.05528i	−0.516412	−	0.298150i
$186$	−14.3781	−	2.61110i	−1.05425	−	0.191455i
$187$	−0.646613	+	2.41319i	−0.0472850	+	0.176470i
$188$	−15.3142	−	18.6344i	−1.11690	−	1.35905i
$189$		0			0
$190$	−0.0594956	+	0.125904i	−0.00431627	+	0.00913405i
$191$	−3.04108	−	5.26731i	−0.220045	−	0.381129i	0.734776	−	0.678309i	$-0.237287\pi$
$191$	−3.04108	−	5.26731i	−0.220045	−	0.381129i	−0.954821	+	0.297180i	$0.903954\pi$
$192$	6.61211	+	7.03075i	0.477188	+	0.507400i
$193$	−5.03089	+	8.71375i	−0.362131	+	0.627229i	−0.988311	−	0.152449i	$-0.951284\pi$
$193$	−5.03089	+	8.71375i	−0.362131	+	0.627229i	0.626180	+	0.779678i	$0.284617\pi$
$194$	−23.1184	+	1.90355i	−1.65981	+	0.136667i
$195$	3.25639	−	3.25639i	0.233195	−	0.233195i
$196$		0			0
$197$	−10.0837	−	10.0837i	−0.718432	−	0.718432i	0.249852	−	0.968284i	$-0.419618\pi$
$197$	−10.0837	−	10.0837i	−0.718432	−	0.718432i	−0.968284	+	0.249852i	$0.919618\pi$
$198$	−3.46574	+	4.08769i	−0.246300	+	0.290499i
$199$	10.0980	+	5.83005i	0.715825	+	0.413282i	0.813214	−	0.581965i	$-0.197716\pi$
$199$	10.0980	+	5.83005i	0.715825	+	0.413282i	−0.0973893	+	0.995246i	$0.531049\pi$
$200$	10.7968	+	3.07122i	0.763447	+	0.217168i
$201$	−3.66359	+	2.11517i	−0.258409	+	0.149193i
$202$	12.2454	−	4.38620i	0.861584	−	0.308612i
$203$		0			0
$204$	2.44526	+	0.239150i	0.171202	+	0.0167439i
$205$	8.35549	+	2.23885i	0.583572	+	0.156368i
$206$	8.98723	−	6.22469i	0.626170	−	0.433695i
$207$	−1.49130	+	2.58301i	−0.103653	+	0.179532i
$208$	6.63143	−	13.4937i	0.459807	−	0.935617i
$209$	0.237894			0.0164555
$210$		0			0
$211$	6.53423	−	6.53423i	0.449835	−	0.449835i	−0.445465	−	0.895300i	$-0.646962\pi$
$211$	6.53423	−	6.53423i	0.449835	−	0.449835i	0.895300	+	0.445465i	$0.146962\pi$
$212$	−2.68088	+	1.21690i	−0.184124	+	0.0835771i
$213$	−6.32927	+	1.69592i	−0.433674	+	0.116203i
$214$	−4.77576	+	26.2977i	−0.326464	+	1.79768i
$215$	−5.57153	+	3.21672i	−0.379975	+	0.219379i
$216$	13.3092	+	7.95872i	0.905579	+	0.541522i
$217$		0			0
$218$	−7.80192	−	21.7815i	−0.528413	−	1.47523i
$219$	−2.64756	+	9.88082i	−0.178905	+	0.667684i
$220$	0.815122	+	4.91622i	0.0549555	+	0.331452i
$221$	−0.990604	−	3.69698i	−0.0666352	−	0.248686i
$222$	13.5801	−	1.11818i	0.911439	−	0.0750472i
$223$	23.3350			1.56263			0.781315	−	0.624137i	$-0.214549\pi$
$223$	23.3350			1.56263			0.781315	+	0.624137i	$0.214549\pi$
$224$		0			0
$225$	6.12964			0.408643
$226$	−28.3512	+	2.33441i	−1.88589	+	0.155283i
$227$	4.05036	+	15.1161i	0.268832	+	1.00329i	0.959863	+	0.280468i	$0.0904898\pi$
$227$	4.05036	+	15.1161i	0.268832	+	1.00329i	−0.691032	+	0.722824i	$0.742844\pi$
$228$	−0.0382674	−	0.230801i	−0.00253432	−	0.0152852i
$229$	−6.92092	+	25.8292i	−0.457347	+	1.70684i	0.223747	+	0.974647i	$0.428171\pi$
$229$	−6.92092	+	25.8292i	−0.457347	+	1.70684i	−0.681094	+	0.732196i	$0.738496\pi$
$230$	0.935237	+	2.61100i	0.0616677	+	0.172164i
$231$		0			0
$232$	−10.3738	+	17.3479i	−0.681072	+	1.13895i
$233$	11.0402	−	6.37405i	0.723267	−	0.417578i	−0.0926872	−	0.995695i	$-0.529546\pi$
$233$	11.0402	−	6.37405i	0.723267	−	0.417578i	0.815954	+	0.578117i	$0.196212\pi$
$234$	1.46700	−	8.07805i	0.0959008	−	0.528078i
$235$	−11.8301	+	3.16986i	−0.771708	+	0.206779i
$236$	−13.1254	+	5.95786i	−0.854391	+	0.387823i
$237$	0.739782	−	0.739782i	0.0480540	−	0.0480540i
$238$		0			0
$239$	14.9688			0.968253			0.484127	−	0.874998i	$-0.339137\pi$
$239$	14.9688			0.968253			0.484127	+	0.874998i	$0.339137\pi$
$240$	4.63853	−	1.58164i	0.299416	−	0.102094i
$241$	9.90526	−	17.1564i	0.638054	−	1.10514i	−0.347805	−	0.937567i	$-0.613073\pi$
$241$	9.90526	−	17.1564i	0.638054	−	1.10514i	0.985859	−	0.167575i	$-0.0535937\pi$
$242$	−5.78992	+	4.01019i	−0.372190	+	0.257785i
$243$	13.5791	+	3.63850i	0.871098	+	0.233410i
$244$	−9.12186	−	0.892134i	−0.583967	−	0.0571130i
$245$		0			0
$246$	−13.6816	+	4.90061i	−0.872305	+	0.312452i
$247$	−0.315624	+	0.182226i	−0.0200827	+	0.0115947i
$248$	−6.62815	+	23.3010i	−0.420888	+	1.47962i
$249$	8.04272	+	4.64346i	0.509686	+	0.294268i
$250$	8.32995	−	9.82480i	0.526832	−	0.621375i
$251$	−9.23966	−	9.23966i	−0.583202	−	0.583202i	0.352580	−	0.935782i	$-0.385305\pi$
$251$	−9.23966	−	9.23966i	−0.583202	−	0.583202i	−0.935782	+	0.352580i	$0.885305\pi$
$252$		0			0
$253$	3.35028	−	3.35028i	0.210630	−	0.210630i
$254$	−1.39380	+	0.114764i	−0.0874548	+	0.00720096i
$255$	0.623780	−	1.08042i	0.0390626	−	0.0676584i
$256$	12.6670	−	9.77483i	0.791687	−	0.610927i
$257$	11.6109	+	20.1107i	0.724271	+	1.25447i	0.959273	+	0.282479i	$0.0911568\pi$
$257$	11.6109	+	20.1107i	0.724271	+	1.25447i	−0.235003	+	0.971995i	$0.575510\pi$
$258$	4.61788	−	9.77231i	0.287496	−	0.608398i
$259$		0			0
$260$	−4.84726	−	5.89818i	−0.300614	−	0.365790i
$261$	−2.85675	+	10.6615i	−0.176828	+	0.659933i
$262$	−10.9608	−	1.99052i	−0.677162	−	0.122975i
$263$	3.91454	+	2.26006i	0.241381	+	0.139361i	0.615811	−	0.787894i	$-0.288828\pi$
$263$	3.91454	+	2.26006i	0.241381	+	0.139361i	−0.374430	+	0.927255i	$0.622162\pi$
$264$	−5.82856	−	6.01016i	−0.358723	−	0.369900i
$265$			1.49496i			0.0918345i
$266$		0			0
$267$	3.87278	+	3.87278i	0.237011	+	0.237011i
$268$	2.89866	+	6.38587i	0.177064	+	0.390079i
$269$	−0.103258	−	0.385363i	−0.00629574	−	0.0234960i	0.962707	−	0.270548i	$-0.0872049\pi$
$269$	−0.103258	−	0.385363i	−0.00629574	−	0.0234960i	−0.969002	+	0.247052i	$0.920538\pi$
$270$	6.47317	−	4.48342i	0.393945	−	0.272852i
$271$	5.31084	+	9.19864i	0.322611	+	0.558778i	0.981026	−	0.193877i	$-0.0621063\pi$
$271$	5.31084	+	9.19864i	0.322611	+	0.558778i	−0.658415	+	0.752655i	$0.728773\pi$
$272$	0.789149	−	3.99584i	0.0478492	−	0.242284i
$273$		0			0
$274$	14.1428	+	6.68313i	0.854397	+	0.403742i
$275$	−9.40545	−	2.52018i	−0.567170	−	0.151973i
$276$	−3.78932	−	2.71147i	−0.228090	−	0.163211i
$277$	11.1219	−	2.98011i	0.668252	−	0.179058i	0.0912848	−	0.995825i	$-0.470903\pi$
$277$	11.1219	−	2.98011i	0.668252	−	0.179058i	0.576967	+	0.816767i	$0.304236\pi$
$278$	−18.9396	−	16.0579i	−1.13592	−	0.963091i
$279$			13.2287i			0.791981i
$280$		0			0
$281$			18.6360i			1.11173i	0.831272	+	0.555866i	$0.187613\pi$
$281$			18.6360i			1.11173i	−0.831272	+	0.555866i	$0.812387\pi$
$282$	13.3065	−	15.6944i	0.792390	−	0.934588i
$283$	8.77861	−	2.35222i	0.521834	−	0.139825i	0.0117192	−	0.999931i	$-0.496270\pi$
$283$	8.77861	−	2.35222i	0.521834	−	0.139825i	0.510115	+	0.860106i	$0.329603\pi$
$284$	1.77679	+	10.7163i	0.105433	+	0.635897i
$285$	−0.114747	−	0.0307463i	−0.00679701	−	0.00182125i
$286$	−5.57226	+	11.7920i	−0.329495	+	0.697274i
$287$		0			0
$288$	5.19267	−	7.02655i	0.305981	−	0.414044i
$289$	7.98158	+	13.8245i	0.469505	+	0.813206i
$290$	5.84390	+	8.43745i	0.343166	+	0.495464i
$291$	−5.12167	−	19.1143i	−0.300238	−	1.12050i
$292$	15.8752	+	5.96261i	0.929024	+	0.348935i
$293$	12.0193	+	12.0193i	0.702174	+	0.702174i	0.964877	−	0.262703i	$-0.0846138\pi$
$293$	12.0193	+	12.0193i	0.702174	+	0.702174i	−0.262703	+	0.964877i	$0.584614\pi$
$294$		0			0
$295$			7.31920i			0.426140i
$296$	0.346451	−	22.5863i	0.0201371	−	1.31280i
$297$	−11.6497	−	6.72594i	−0.675982	−	0.390278i
$298$	1.32411	−	7.29125i	0.0767039	−	0.422371i
$299$	−1.87866	+	7.01125i	−0.108646	+	0.405471i
$300$	−0.932092	+	9.53042i	−0.0538143	+	0.550239i
$301$		0			0
$302$	−1.74328	−	0.823782i	−0.100315	−	0.0474033i
$303$	5.54812	+	9.60962i	0.318731	+	0.552058i
$304$	−0.386974	+	0.0258947i	−0.0221945	+	0.00148516i
$305$	−2.32697	+	4.03043i	−0.133242	+	0.230781i
$306$	−0.182516	−	2.21664i	−0.0104338	−	0.126717i
$307$	−17.8339	+	17.8339i	−1.01784	+	1.01784i	−0.0179975	+	0.999838i	$0.505729\pi$
$307$	−17.8339	+	17.8339i	−1.01784	+	1.01784i	−0.999838	+	0.0179975i	$0.994271\pi$
$308$		0			0
$309$	6.59462	+	6.59462i	0.375155	+	0.375155i
$310$	9.38257	+	7.95501i	0.532894	+	0.451814i
$311$	−5.66778	−	3.27229i	−0.321390	−	0.185555i	0.330622	−	0.943763i	$-0.392742\pi$
$311$	−5.66778	−	3.27229i	−0.321390	−	0.185555i	−0.652012	+	0.758209i	$0.726075\pi$
$312$	12.3367	+	3.50928i	0.698431	+	0.198674i
$313$	16.6047	−	9.58671i	0.938551	−	0.541873i	0.0490453	−	0.998797i	$-0.484382\pi$
$313$	16.6047	−	9.58671i	0.938551	−	0.541873i	0.889506	+	0.456924i	$0.151049\pi$
$314$	0.151555	+	0.423112i	0.00855274	+	0.0238776i
$315$		0			0
$316$	−1.10119	−	1.33994i	−0.0619470	−	0.0753776i
$317$	−18.1794	−	4.87115i	−1.02106	−	0.273591i	−0.290814	−	0.956780i	$-0.593926\pi$
$317$	−18.1794	−	4.87115i	−1.02106	−	0.273591i	−0.730242	+	0.683189i	$0.760593\pi$
$318$	−1.43005	−	2.06471i	−0.0801933	−	0.115783i
$319$	8.76691	−	15.1847i	0.490853	−	0.850182i
$320$	−1.86106	−	7.90834i	−0.104037	−	0.442089i
$321$	−22.8010			−1.27263
$322$		0			0
$323$	−0.0698127	+	0.0698127i	−0.00388448	+	0.00388448i
$324$	−1.39306	+	3.70895i	−0.0773921	+	0.206053i
$325$	14.4090	−	3.86089i	0.799270	−	0.214164i
$326$	20.6539	+	3.75081i	1.14391	+	0.207738i
$327$	17.0931	−	9.86868i	0.945248	−	0.545739i
$328$	5.87783	+	23.3640i	0.324549	+	1.29006i
$329$		0			0
$330$	−4.00219	+	1.43355i	−0.220313	+	0.0789143i
$331$	2.53476	−	9.45985i	0.139323	−	0.519960i	−0.860620	−	0.509248i	$-0.829924\pi$
$331$	2.53476	−	9.45985i	0.139323	−	0.519960i	0.999943	−	0.0107120i	$-0.00340981\pi$
$332$	8.95906	−	12.5204i	0.491692	−	0.687147i
$333$	−3.19255	−	11.9148i	−0.174951	−	0.652926i
$334$	1.69420	+	20.5759i	0.0927025	+	1.12586i
$335$	3.56099			0.194558
$336$		0			0
$337$	4.91600			0.267792			0.133896	−	0.990995i	$-0.457251\pi$
$337$	4.91600			0.267792			0.133896	+	0.990995i	$0.457251\pi$
$338$	−0.130956	−	1.59045i	−0.00712308	−	0.0865090i
$339$	−6.28094	−	23.4408i	−0.341134	−	1.27313i
$340$	−1.68193	−	1.20352i	−0.0912154	−	0.0652698i
$341$	5.43893	−	20.2984i	0.294535	−	1.09922i
$342$	−0.199382	+	0.0714167i	−0.0107813	+	0.00386178i
$343$		0			0
$344$	−15.3782	−	9.19593i	−0.829137	−	0.495811i
$345$	−2.04899	+	1.18299i	−0.110314	+	0.0636898i
$346$	−17.1854	−	3.12093i	−0.923895	−	0.167782i
$347$	−9.03438	+	2.42076i	−0.484991	+	0.129953i	−0.493026	−	0.870015i	$-0.664109\pi$
$347$	−9.03438	+	2.42076i	−0.484991	+	0.129953i	0.00803463	+	0.999968i	$0.497442\pi$
$348$	−16.1423	−	6.06293i	−0.865316	−	0.325007i
$349$	17.2061	−	17.2061i	0.921021	−	0.921021i	−0.0760810	−	0.997102i	$-0.524241\pi$
$349$	17.2061	−	17.2061i	0.921021	−	0.921021i	0.997102	+	0.0760810i	$0.0242407\pi$
$350$		0			0
$351$	20.6081			1.09998
$352$	−10.8567	+	8.64674i	−0.578663	+	0.460873i
$353$	−4.08472	+	7.07494i	−0.217408	+	0.376561i	−0.954015	−	0.299760i	$-0.903093\pi$
$353$	−4.08472	+	7.07494i	−0.217408	+	0.376561i	0.736607	+	0.676321i	$0.236427\pi$
$354$	−7.00143	−	10.1087i	−0.372122	−	0.537270i
$355$	5.32780	+	1.42758i	0.282771	+	0.0757681i
$356$	7.01464	−	5.76479i	0.371775	−	0.305533i
$357$		0			0
$358$	−0.224944	−	0.628001i	−0.0118887	−	0.0331909i
$359$	10.0193	−	5.78465i	0.528799	−	0.305302i	−0.211728	−	0.977329i	$-0.567909\pi$
$359$	10.0193	−	5.78465i	0.528799	−	0.305302i	0.740527	+	0.672027i	$0.234576\pi$
$360$	−2.15903	−	3.87564i	−0.113791	−	0.204264i
$361$	−16.4463	−	9.49530i	−0.865597	−	0.499753i
$362$	−23.5924	−	20.0028i	−1.23999	−	1.05132i
$363$	−4.24851	−	4.24851i	−0.222989	−	0.222989i
$364$		0			0
$365$	6.08876	−	6.08876i	0.318700	−	0.318700i
$366$	−0.641623	−	7.79244i	−0.0335382	−	0.407317i
$367$	4.25356	−	7.36738i	0.222034	−	0.384574i	−0.733392	−	0.679807i	$-0.762064\pi$
$367$	4.25356	−	7.36738i	0.222034	−	0.384574i	0.955425	+	0.295232i	$0.0953971\pi$
$368$	−5.08511	+	5.81447i	−0.265080	+	0.303100i
$369$	6.57792	+	11.3933i	0.342433	+	0.593111i
$370$	−10.3705	−	4.90055i	−0.539136	−	0.254767i
$371$		0			0
$372$	−20.5681	−	2.01159i	−1.06641	−	0.104296i
$373$	1.35756	−	5.06649i	0.0702919	−	0.262333i	−0.921833	−	0.387588i	$-0.873308\pi$
$373$	1.35756	−	5.06649i	0.0702919	−	0.262333i	0.992125	+	0.125255i	$0.0399749\pi$
$374$	−0.631308	+	3.47630i	−0.0326441	+	0.179755i
$375$	9.51618	+	5.49417i	0.491414	+	0.283718i
$376$	−23.7470	−	24.4869i	−1.22466	−	1.26281i
$377$			26.8616i			1.38344i
$378$		0			0
$379$	−3.62966	−	3.62966i	−0.186443	−	0.186443i	0.607713	−	0.794156i	$-0.292087\pi$
$379$	−3.62966	−	3.62966i	−0.186443	−	0.186443i	−0.794156	+	0.607713i	$0.792087\pi$
$380$	−0.0692443	+	0.184360i	−0.00355216	+	0.00945745i
$381$	−0.308783	−	1.15239i	−0.0158194	−	0.0590390i
$382$	−4.89752	−	7.07105i	−0.250579	−	0.361786i
$383$	−3.48127	−	6.02973i	−0.177884	−	0.308105i	0.763271	−	0.646078i	$-0.223592\pi$
$383$	−3.48127	−	6.02973i	−0.177884	−	0.308105i	−0.941156	+	0.337973i	$0.890259\pi$
$384$	10.1353	+	9.14209i	0.517217	+	0.466530i
$385$		0			0
$386$	−6.07950	+	12.8654i	−0.309438	+	0.654831i
$387$	−9.45101	−	2.53239i	−0.480422	−	0.128729i
$388$	−32.3632	+	5.36590i	−1.64299	+	0.272412i
$389$	12.7317	−	3.41145i	0.645523	−	0.172967i	0.0788190	−	0.996889i	$-0.474885\pi$
$389$	12.7317	−	3.41145i	0.645523	−	0.172967i	0.566704	+	0.823922i	$0.308218\pi$
$390$	4.21178	−	4.96761i	0.213272	−	0.251545i
$391$			1.96636i			0.0994429i
$392$		0			0
$393$		−	9.50339i		−	0.479383i
$394$	−15.3826	−	13.0421i	−0.774964	−	0.657053i
$395$	−0.850663	+	0.227934i	−0.0428015	+	0.0114686i
$396$	−4.41038	+	6.16357i	−0.221630	+	0.309731i
$397$	6.02928	+	1.61554i	0.302601	+	0.0810817i	0.406925	−	0.913462i	$-0.366601\pi$
$397$	6.02928	+	1.61554i	0.302601	+	0.0810817i	−0.104324	+	0.994543i	$0.533268\pi$
$398$	14.9091	+	7.04524i	0.747325	+	0.353146i
$399$		0			0
$400$	15.5739	+	3.07572i	0.778693	+	0.153786i
$401$	7.95077	+	13.7711i	0.397042	+	0.687697i	0.993360	−	0.115051i	$-0.0367033\pi$
$401$	7.95077	+	13.7711i	0.397042	+	0.687697i	−0.596317	+	0.802749i	$0.703370\pi$
$402$	−4.91815	+	3.40638i	−0.245295	+	0.169895i
$403$	8.33239	+	31.0969i	0.415066	+	1.54905i
$404$	16.7502	−	7.60321i	0.833353	−	0.378274i
$405$	1.42253	+	1.42253i	0.0706861	+	0.0706861i
$406$		0			0
$407$			19.5949i			0.971282i
$408$	3.47421	+	0.0532908i	0.171999	+	0.00263829i
$409$	4.93864	+	2.85133i	0.244200	+	0.140989i	0.617106	−	0.786880i	$-0.288305\pi$
$409$	4.93864	+	2.85133i	0.244200	+	0.140989i	−0.372906	+	0.927869i	$0.621638\pi$
$410$	12.0364	+	2.18585i	0.594436	+	0.107952i
$411$	−3.45372	+	12.8895i	−0.170360	+	0.635791i
$412$	11.9446	−	9.81634i	0.588468	−	0.483616i
$413$		0			0
$414$	−1.80214	+	3.81368i	−0.0885704	+	0.187432i
$415$	−3.90874	−	6.77014i	−0.191873	−	0.332333i
$416$	7.78066	−	19.7881i	0.381478	−	0.970194i
$417$	10.5913	−	18.3447i	0.518659	−	0.898343i
$418$	0.335298	−	0.0276082i	0.0164000	−	0.00135036i
$419$	4.57142	−	4.57142i	0.223328	−	0.223328i	−0.586570	−	0.809898i	$-0.699522\pi$
$419$	4.57142	−	4.57142i	0.223328	−	0.223328i	0.809898	+	0.586570i	$0.199522\pi$
$420$		0			0
$421$	0.421252	+	0.421252i	0.0205306	+	0.0205306i	0.717298	−	0.696767i	$-0.245379\pi$
$421$	0.421252	+	0.421252i	0.0205306	+	0.0205306i	−0.696767	+	0.717298i	$0.745379\pi$
$422$	8.45131	−	9.96794i	0.411404	−	0.485232i
$423$	−16.1311	−	9.31331i	−0.784322	−	0.452829i
$424$	−3.63733	+	2.02628i	−0.176644	+	0.0984047i
$425$	3.49971	−	2.02056i	0.169761	−	0.0980115i
$426$	−8.72393	+	3.12483i	−0.422676	+	0.151399i
$427$		0			0
$428$	−3.67924	+	37.6194i	−0.177843	+	1.81840i
$429$	−10.7470	−	2.87964i	−0.518869	−	0.139031i
$430$	−7.47945	+	5.18038i	−0.360691	+	0.249820i
$431$	10.5518	−	18.2762i	0.508262	−	0.880336i	−0.491692	−	0.870769i	$-0.663621\pi$
$431$	10.5518	−	18.2762i	0.508262	−	0.880336i	0.999954	−	0.00956658i	$-0.00304518\pi$
$432$	19.6822	+	9.67280i	0.946963	+	0.465383i
$433$	13.9717			0.671436			0.335718	−	0.941962i	$-0.391021\pi$
$433$	13.9717			0.671436			0.335718	+	0.941962i	$0.391021\pi$
$434$		0			0
$435$	−6.19120	+	6.19120i	−0.296845	+	0.296845i
$436$	−13.5242	−	29.7943i	−0.647690	−	1.42689i
$437$	0.180859	−	0.0484611i	0.00865168	−	0.00231821i
$438$	−2.58489	+	14.2337i	−0.123511	+	0.680113i
$439$	4.69322	−	2.70963i	0.223995	−	0.129324i	−0.383804	−	0.923415i	$-0.625386\pi$
$439$	4.69322	−	2.70963i	0.223995	−	0.129324i	0.607799	+	0.794091i	$0.292053\pi$
$440$	1.71941	+	6.83455i	0.0819696	+	0.325824i
$441$		0			0
$442$	−1.82525	−	5.09573i	−0.0868181	−	0.242379i
$443$	1.56401	−	5.83698i	0.0743085	−	0.277323i	−0.918767	−	0.394800i	$-0.870814\pi$
$443$	1.56401	−	5.83698i	0.0743085	−	0.277323i	0.993076	+	0.117477i	$0.0374806\pi$
$444$	19.0107	−	3.15202i	0.902207	−	0.149588i
$445$	−1.19324	−	4.45325i	−0.0565652	−	0.211104i
$446$	32.8894	−	2.70809i	1.55736	−	0.128232i
$447$	6.32175			0.299009
$448$		0			0
$449$	18.4262			0.869587			0.434794	−	0.900530i	$-0.356821\pi$
$449$	18.4262			0.869587			0.434794	+	0.900530i	$0.356821\pi$
$450$	8.63938	−	0.711360i	0.407264	−	0.0335338i
$451$	−5.40898	−	20.1866i	−0.254699	−	0.950550i
$452$	−39.6885	+	6.58045i	−1.86679	+	0.309518i
$453$	0.425716	−	1.58879i	0.0200019	−	0.0746480i
$454$	7.46301	+	20.8353i	0.350257	+	0.977848i
$455$		0			0
$456$	−0.0807208	−	0.320860i	−0.00378010	−	0.0150257i
$457$	31.1530	−	17.9862i	1.45728	−	0.841358i	0.458399	−	0.888747i	$-0.348423\pi$
$457$	31.1530	−	17.9862i	1.45728	−	0.841358i	0.998877	+	0.0473884i	$0.0150898\pi$
$458$	−6.75710	+	37.2080i	−0.315739	+	1.73862i
$459$	5.39253	−	1.44492i	0.251702	−	0.0674433i
$460$	1.62118	+	3.57152i	0.0755878	+	0.166523i
$461$	0.903879	−	0.903879i	0.0420978	−	0.0420978i	−0.685745	−	0.727842i	$-0.740523\pi$
$461$	0.903879	−	0.903879i	0.0420978	−	0.0420978i	0.727842	+	0.685745i	$0.240523\pi$
$462$		0			0
$463$	−12.5999			−0.585565			−0.292782	−	0.956179i	$-0.594581\pi$
$463$	−12.5999			−0.585565			−0.292782	+	0.956179i	$0.594581\pi$
$464$	−12.6080	+	25.6548i	−0.585312	+	1.19099i
$465$	−5.24687	+	9.08785i	−0.243318	+	0.421439i
$466$	14.8208	−	10.2651i	0.686560	−	0.475522i
$467$	−8.00668	−	2.14538i	−0.370505	−	0.0992765i	0.0687620	−	0.997633i	$-0.478095\pi$
$467$	−8.00668	−	2.14538i	−0.370505	−	0.0992765i	−0.439267	+	0.898357i	$0.644762\pi$
$468$	1.13018	−	11.5558i	0.0522424	−	0.534167i
$469$		0			0
$470$	−16.3059	+	5.84064i	−0.752137	+	0.269409i
$471$	−0.332038	+	0.191702i	−0.0152995	+	0.00883318i
$472$	−17.8081	+	9.92050i	−0.819684	+	0.456628i
$473$	13.4606	+	7.77151i	0.618921	+	0.357334i
$474$	0.956828	−	1.12854i	0.0439486	−	0.0518353i
$475$	−0.272096	−	0.272096i	−0.0124846	−	0.0124846i
$476$		0			0
$477$	−1.60770	+	1.60770i	−0.0736114	+	0.0736114i
$478$	21.0977	−	1.73717i	0.964987	−	0.0794563i
$479$	4.63918	−	8.03529i	0.211969	−	0.367142i	−0.740361	−	0.672209i	$-0.765346\pi$
$479$	4.63918	−	8.03529i	0.211969	−	0.367142i	0.952331	+	0.305067i	$0.0986789\pi$
$480$	6.35419	−	2.76755i	0.290028	−	0.126321i
$481$	−15.0096	−	25.9974i	−0.684378	−	1.18538i
$482$	11.9699	−	25.3305i	0.545212	−	1.15377i
$483$		0			0
$484$	−7.69517	+	6.32407i	−0.349781	+	0.287458i
$485$	−4.31128	+	16.0899i	−0.195765	+	0.730606i
$486$	19.5612	+	3.55238i	0.887314	+	0.161139i
$487$	33.5037	+	19.3434i	1.51820	+	0.876533i	0.999771	+	0.0214118i	$0.00681612\pi$
$487$	33.5037	+	19.3434i	1.51820	+	0.876533i	0.518429	+	0.855121i	$0.326517\pi$
$488$	−12.9603	−	0.198798i	−0.586685	−	0.00899914i
$489$			17.9076i			0.809810i
$490$		0			0
$491$	−29.8086	−	29.8086i	−1.34524	−	1.34524i	−0.890750	−	0.454494i	$-0.849820\pi$
$491$	−29.8086	−	29.8086i	−1.34524	−	1.34524i	−0.454494	−	0.890750i	$-0.650180\pi$
$492$	−18.7147	+	8.49492i	−0.843722	+	0.382980i
$493$	1.88338	+	7.02889i	0.0848234	+	0.316565i
$494$	−0.423706	+	0.293466i	−0.0190635	+	0.0132036i
$495$	1.92420	+	3.33282i	0.0864865	+	0.149799i
$496$	−6.63786	+	33.6107i	−0.298049	+	1.50917i
$497$		0			0
$498$	11.8746	+	5.61132i	0.532115	+	0.251449i
$499$	10.7993	+	2.89367i	0.483444	+	0.129538i	0.492306	−	0.870422i	$-0.336154\pi$
$499$	10.7993	+	2.89367i	0.483444	+	0.129538i	−0.00886191	+	0.999961i	$0.502821\pi$
$500$	10.6004	−	14.8142i	0.474064	−	0.662512i
$501$	−17.0121	+	4.55839i	−0.760046	+	0.203654i
$502$	−14.0951	−	11.9505i	−0.629093	−	0.533377i
$503$		−	18.1532i		−	0.809409i	−0.914448	−	0.404704i	$-0.867374\pi$
$503$		−	18.1532i		−	0.809409i	0.914448	−	0.404704i	$-0.132626\pi$
$504$		0			0
$505$		−	9.34050i		−	0.415647i
$506$	4.33322	−	5.11084i	0.192635	−	0.227205i
$507$	1.31498	−	0.352349i	0.0584005	−	0.0156484i
$508$	−1.95116	+	0.323508i	−0.0865689	+	0.0143533i
$509$	1.97895	+	0.530258i	0.0877154	+	0.0235033i	0.302410	−	0.953178i	$-0.402209\pi$
$509$	1.97895	+	0.530258i	0.0877154	+	0.0235033i	−0.214694	+	0.976681i	$0.568876\pi$
$510$	0.753798	−	1.59518i	0.0333787	−	0.0706358i
$511$		0			0
$512$	16.7190	−	15.2471i	0.738883	−	0.673834i
$513$	−0.265799	−	0.460378i	−0.0117353	−	0.0203262i
$514$	18.6989	+	26.9975i	0.824772	+	1.19081i
$515$	−2.03187	−	7.58304i	−0.0895348	−	0.334149i
$516$	5.37454	−	14.3094i	0.236601	−	0.629938i
$517$	20.9228	+	20.9228i	0.920183	+	0.920183i
$518$		0			0
$519$		−	14.9004i		−	0.654053i
$520$	−7.51644	−	7.75062i	−0.329618	−	0.339887i
$521$	−2.51905	−	1.45437i	−0.110361	−	0.0637172i	0.443803	−	0.896124i	$-0.353629\pi$
$521$	−2.51905	−	1.45437i	−0.110361	−	0.0637172i	−0.554165	+	0.832407i	$0.686962\pi$
$522$	−2.78913	+	15.3584i	−0.122077	+	0.672218i
$523$	−4.28781	+	16.0023i	−0.187493	+	0.699732i	0.806590	+	0.591111i	$0.201310\pi$
$523$	−4.28781	+	16.0023i	−0.187493	+	0.699732i	−0.994083	+	0.108622i	$0.965356\pi$
$524$	−15.6797	−	1.53350i	−0.684969	−	0.0669911i
$525$		0			0
$526$	5.77962	+	2.73114i	0.252003	+	0.119083i
$527$	4.36067	+	7.55290i	0.189954	+	0.329010i
$528$	−8.91253	−	7.79456i	−0.387868	−	0.339215i
$529$	−9.63542	+	16.6890i	−0.418931	+	0.725611i
$530$	0.173493	+	2.10706i	0.00753607	+	0.0915247i
$531$	−7.87117	+	7.87117i	−0.341580	+	0.341580i
$532$		0			0
$533$	22.6392	+	22.6392i	0.980611	+	0.980611i
$534$	5.90792	+	5.00903i	0.255661	+	0.216762i
$535$	16.6219	+	9.59663i	0.718625	+	0.414899i
$536$	4.82659	+	8.66412i	0.208477	+	0.374233i
$537$	0.492826	−	0.284533i	0.0212670	−	0.0122785i
$538$	−0.190258	−	0.531165i	−0.00820262	−	0.0229001i
$539$		0			0
$540$	8.60326	−	7.07035i	0.370225	−	0.304260i
$541$	−7.01543	−	1.87978i	−0.301617	−	0.0808180i	0.104837	−	0.994489i	$-0.466568\pi$
$541$	−7.01543	−	1.87978i	−0.301617	−	0.0808180i	−0.406453	+	0.913671i	$0.633235\pi$
$542$	8.55285	+	12.3486i	0.367377	+	0.530419i
$543$	13.1932	−	22.8513i	0.566174	−	0.980643i
$544$	0.648534	−	5.72350i	0.0278057	−	0.245393i
$545$	−16.6144			−0.711682
$546$		0			0
$547$	18.2712	−	18.2712i	0.781218	−	0.781218i	−0.198818	−	0.980036i	$-0.563710\pi$
$547$	18.2712	−	18.2712i	0.781218	−	0.781218i	0.980036	+	0.198818i	$0.0637103\pi$
$548$	20.7090	+	7.77819i	0.884647	+	0.332268i
$549$	−6.83683	+	1.83192i	−0.291789	+	0.0781846i
$550$	−13.5489	−	2.46053i	−0.577728	−	0.104917i
$551$	0.600079	−	0.346456i	0.0255642	−	0.0147595i
$552$	−5.65550	−	3.38190i	−0.240714	−	0.143943i
$553$		0			0
$554$	15.3299	−	5.49103i	0.651305	−	0.233291i
$555$	2.53252	−	9.45148i	0.107499	−	0.401193i
$556$	−28.5579	−	20.4348i	−1.21112	−	0.866627i
$557$	1.28251	+	4.78640i	0.0543418	+	0.202806i	0.987759	−	0.155986i	$-0.0498554\pi$
$557$	1.28251	+	4.78640i	0.0543418	+	0.202806i	−0.933417	+	0.358792i	$0.883189\pi$
$558$	1.53522	+	18.6451i	0.0649911	+	0.789310i
$559$	−23.8117			−1.00713
$560$		0			0
$561$	−3.01407			−0.127254
$562$	2.16276	+	26.2664i	0.0912303	+	1.10798i
$563$	6.29301	+	23.4858i	0.265219	+	0.989809i	0.962116	+	0.272639i	$0.0878964\pi$
$563$	6.29301	+	23.4858i	0.265219	+	0.989809i	−0.696898	+	0.717170i	$0.745437\pi$
$564$	16.9334	−	23.6646i	0.713024	−	0.996460i
$565$	−5.28712	+	19.7318i	−0.222431	+	0.830123i
$566$	12.1000	−	4.33410i	0.508600	−	0.182176i
$567$		0			0
$568$	3.74795	+	14.8979i	0.157260	+	0.625100i
$569$	−2.33865	+	1.35022i	−0.0980412	+	0.0566041i	−0.548219	−	0.836335i	$-0.684694\pi$
$569$	−2.33865	+	1.35022i	−0.0980412	+	0.0566041i	0.450178	+	0.892939i	$0.351361\pi$
$570$	−0.165297	−	0.0300185i	−0.00692354	−	0.00125734i
$571$	12.8196	−	3.43500i	0.536484	−	0.143750i	0.0196030	−	0.999808i	$-0.493760\pi$
$571$	12.8196	−	3.43500i	0.536484	−	0.143750i	0.516881	+	0.856058i	$0.327093\pi$
$572$	−6.48530	+	17.2668i	−0.271164	+	0.721961i
$573$	5.18857	−	5.18857i	0.216756	−	0.216756i
$574$		0			0
$575$	−7.66390			−0.319607
$576$	6.50333	−	10.5062i	0.270972	−	0.437756i
$577$	−12.4461	+	21.5572i	−0.518137	+	0.897439i	0.481641	+	0.876369i	$0.340041\pi$
$577$	−12.4461	+	21.5572i	−0.518137	+	0.897439i	−0.999778	+	0.0210709i	$0.993292\pi$
$578$	12.8540	+	18.5586i	0.534654	+	0.771935i
$579$	−11.7253	−	3.14178i	−0.487286	−	0.130568i
$580$	9.21584	+	11.2139i	0.382667	+	0.465632i
$581$		0			0
$582$	−9.43697	−	26.3462i	−0.391175	−	1.09209i
$583$	3.12788	−	1.80589i	0.129544	−	0.0747921i
$584$	23.0671	+	6.56161i	0.954525	+	0.271522i
$585$	−5.10584	−	2.94786i	−0.211101	−	0.121879i
$586$	18.3354	+	15.5456i	0.757427	+	0.642185i
$587$	−23.9315	−	23.9315i	−0.987758	−	0.987758i	0.0121684	−	0.999926i	$-0.496127\pi$
$587$	−23.9315	−	23.9315i	−0.987758	−	0.987758i	−0.999926	+	0.0121684i	$0.996127\pi$
$588$		0			0
$589$	0.587224	−	0.587224i	0.0241961	−	0.0241961i
$590$	0.849411	+	10.3160i	0.0349697	+	0.424703i
$591$	8.60218	−	14.8994i	0.353846	−	0.612880i
$592$	−2.13290	−	31.8744i	−0.0876615	−	1.31003i
$593$	0.895084	+	1.55033i	0.0367567	+	0.0636645i	0.883819	−	0.467830i	$-0.154964\pi$
$593$	0.895084	+	1.55033i	0.0367567	+	0.0636645i	−0.847062	+	0.531494i	$0.821631\pi$
$594$	−17.2001	−	8.12786i	−0.705729	−	0.333490i
$595$		0			0
$596$	1.02010	−	10.4303i	0.0417849	−	0.427241i
$597$	−3.64086	+	13.5879i	−0.149010	+	0.556114i
$598$	−1.83419	+	10.1000i	−0.0750057	+	0.413019i
$599$	−37.3788	−	21.5806i	−1.52726	−	0.881761i	−0.999476	−	0.0323796i	$-0.989691\pi$
$599$	−37.3788	−	21.5806i	−1.52726	−	0.881761i	−0.527779	−	0.849381i	$-0.676975\pi$
$600$	−0.207702	+	13.5408i	−0.00847938	+	0.552800i
$601$		−	27.6564i		−	1.12813i	−0.825730	−	0.564065i	$-0.809237\pi$
$601$		−	27.6564i		−	1.12813i	0.825730	−	0.564065i	$-0.190763\pi$
$602$		0			0
$603$	3.82954	+	3.82954i	0.155951	+	0.155951i
$604$	−2.55266	−	0.958762i	−0.103866	−	0.0390115i
$605$	1.30901	+	4.88529i	0.0532188	+	0.198615i
$606$	8.93498	+	12.9003i	0.362959	+	0.524041i
$607$	−10.7968	−	18.7006i	−0.438228	−	0.759032i	0.559325	−	0.828948i	$-0.311060\pi$
$607$	−10.7968	−	18.7006i	−0.438228	−	0.759032i	−0.997553	+	0.0699158i	$0.977727\pi$
$608$	−0.542413	+	0.0814064i	−0.0219978	+	0.00330147i
$609$		0			0
$610$	−2.81199	+	5.95071i	−0.113854	+	0.240937i
$611$	−43.7859	−	11.7324i	−1.77139	−	0.474642i
$612$	−0.514493	−	3.10305i	−0.0207972	−	0.125433i
$613$	9.58708	−	2.56885i	0.387219	−	0.103755i	−0.0599573	−	0.998201i	$-0.519096\pi$
$613$	9.58708	−	2.56885i	0.387219	−	0.103755i	0.447176	+	0.894446i	$0.352430\pi$
$614$	−23.0662	+	27.2056i	−0.930878	+	1.09793i
$615$			10.4360i			0.420819i
$616$		0			0
$617$			14.2458i			0.573515i	0.958003	+	0.286758i	$0.0925774\pi$
$617$			14.2458i			0.573515i	−0.958003	+	0.286758i	$0.907423\pi$
$618$	10.0601	+	8.52942i	0.404675	+	0.343104i
$619$	35.2895	−	9.45579i	1.41840	−	0.380060i	0.533487	−	0.845808i	$-0.320881\pi$
$619$	35.2895	−	9.45579i	1.41840	−	0.380060i	0.884917	+	0.465748i	$0.154215\pi$
$620$	14.1474	+	10.1233i	0.568174	+	0.406560i
$621$	−10.2268	−	2.74027i	−0.410388	−	0.109963i
$622$	−8.36817	−	3.95435i	−0.335533	−	0.158555i
$623$		0			0
$624$	17.7952	+	3.51442i	0.712379	+	0.140689i
$625$	5.29682	+	9.17437i	0.211873	+	0.366975i
$626$	22.2908	−	15.4389i	0.890919	−	0.617064i
$627$	0.0742821	+	0.277225i	0.00296654	+	0.0110713i
$628$	0.262711	+	0.578764i	0.0104833	+	0.0230952i
$629$	−5.75034	−	5.75034i	−0.229281	−	0.229281i
$630$		0			0
$631$		−	4.87006i		−	0.193874i	−0.995291	−	0.0969370i	$-0.969095\pi$
$631$		−	4.87006i		−	0.193874i	0.995291	−	0.0969370i	$-0.0309045\pi$
$632$	−1.70758	−	1.76078i	−0.0679237	−	0.0700399i
$633$	9.65483	+	5.57422i	0.383745	+	0.221555i
$634$	−26.1881	−	4.75585i	−1.04006	−	0.188879i
$635$	−0.259925	+	0.970054i	−0.0103148	+	0.0384954i
$636$	−2.25519	−	2.74414i	−0.0894242	−	0.108812i
$637$		0			0
$638$	10.5942	−	22.4195i	0.419430	−	0.887595i
$639$	4.19436	+	7.26484i	0.165926	+	0.287393i
$640$	−3.54084	−	10.9304i	−0.139964	−	0.432061i
$641$	−17.1939	+	29.7808i	−0.679120	+	1.17627i	0.296126	+	0.955149i	$0.404305\pi$
$641$	−17.1939	+	29.7808i	−0.679120	+	1.17627i	−0.975246	+	0.221121i	$0.929028\pi$
$642$	−32.1367	+	2.64611i	−1.26834	+	0.104434i
$643$	11.9018	−	11.9018i	0.469361	−	0.469361i	−0.432346	−	0.901708i	$-0.642314\pi$
$643$	11.9018	−	11.9018i	0.469361	−	0.469361i	0.901708	+	0.432346i	$0.142314\pi$
$644$		0			0
$645$	−5.48825	−	5.48825i	−0.216099	−	0.216099i
$646$	−0.0902951	+	0.106499i	−0.00355261	+	0.00419015i
$647$	−4.56190	−	2.63381i	−0.179347	−	0.103546i	0.407639	−	0.913143i	$-0.366352\pi$
$647$	−4.56190	−	2.63381i	−0.179347	−	0.103546i	−0.586986	+	0.809597i	$0.699686\pi$
$648$	−1.53300	+	5.38922i	−0.0602221	+	0.211709i
$649$	15.3139	−	8.84148i	0.601123	−	0.347058i
$650$	19.8607	−	7.11392i	0.779000	−	0.279031i
$651$		0			0
$652$	29.5458	+	2.88963i	1.15710	+	0.113167i
$653$	33.1336	+	8.87812i	1.29662	+	0.347427i	0.840170	−	0.542323i	$-0.182455\pi$
$653$	33.1336	+	8.87812i	1.29662	+	0.347427i	0.456447	+	0.889751i	$0.349122\pi$
$654$	22.9464	−	15.8930i	0.897276	−	0.621467i
$655$	−3.99985	+	6.92794i	−0.156287	+	0.270697i
$656$	10.9959	+	32.2481i	0.429319	+	1.25908i
$657$	13.0959			0.510919
$658$		0			0
$659$	−14.4817	+	14.4817i	−0.564126	+	0.564126i	−0.930477	−	0.366351i	$-0.880607\pi$
$659$	−14.4817	+	14.4817i	−0.564126	+	0.564126i	0.366351	+	0.930477i	$0.380607\pi$
$660$	−5.47450	+	2.48497i	−0.213095	+	0.0967274i
$661$	−15.3347	+	4.10893i	−0.596452	+	0.159819i	−0.544400	−	0.838826i	$-0.683243\pi$
$661$	−15.3347	+	4.10893i	−0.596452	+	0.159819i	−0.0520518	+	0.998644i	$0.516576\pi$
$662$	2.47476	−	13.6273i	0.0961843	−	0.529640i
$663$	3.99889	−	2.30876i	0.155304	−	0.0896648i
$664$	11.1743	−	18.6865i	0.433646	−	0.725178i
$665$		0			0
$666$	−5.88246	−	16.4227i	−0.227941	−	0.636367i
$667$	3.57180	−	13.3301i	0.138301	−	0.516145i
$668$	4.77576	+	28.8039i	0.184780	+	1.11446i
$669$	7.28634	+	27.1930i	0.281706	+	1.05134i
$670$	5.01901	−	0.413261i	0.193901	−	0.0159657i
$671$	11.2438			0.434061
$672$		0			0
$673$	−8.09831			−0.312167			−0.156083	−	0.987744i	$-0.549887\pi$
$673$	−8.09831			−0.312167			−0.156083	+	0.987744i	$0.549887\pi$
$674$	6.92883	−	0.570514i	0.266889	−	0.0219754i
$675$	5.63161	+	21.0175i	0.216761	+	0.808962i
$676$	−0.369151	−	2.22645i	−0.0141981	−	0.0856327i
$677$	5.86138	−	21.8750i	0.225271	−	0.840724i	−0.757025	−	0.653386i	$-0.773348\pi$
$677$	5.86138	−	21.8750i	0.225271	−	0.840724i	0.982296	−	0.187337i	$-0.0599857\pi$
$678$	−11.5730	−	32.3095i	−0.444458	−	1.24084i
$679$		0			0
$680$	−2.51026	−	1.50110i	−0.0962639	−	0.0575644i
$681$	−16.3505	+	9.43999i	−0.626554	+	0.361741i
$682$	5.31019	−	29.2406i	0.203338	−	1.11968i
$683$	−36.8038	+	9.86156i	−1.40826	+	0.377342i	−0.881304	−	0.472550i	$-0.843334\pi$
$683$	−36.8038	+	9.86156i	−1.40826	+	0.377342i	−0.526956	+	0.849892i	$0.676667\pi$
$684$	−0.272729	+	0.123797i	−0.0104281	+	0.00473348i
$685$	7.94275	−	7.94275i	0.303477	−	0.303477i
$686$		0			0
$687$	−32.2606			−1.23082
$688$	−22.7419	−	11.1765i	−0.867027	−	0.426099i
$689$	−2.76660	+	4.79189i	−0.105399	+	0.182556i
$690$	−2.75065	+	1.90514i	−0.104715	+	0.0725275i
$691$	23.8952	+	6.40271i	0.909018	+	0.243571i	0.682885	−	0.730526i	$-0.260725\pi$
$691$	23.8952	+	6.40271i	0.909018	+	0.243571i	0.226133	+	0.974096i	$0.427392\pi$
$692$	−24.5841	−	2.40437i	−0.934548	−	0.0914004i
$693$		0			0
$694$	−12.4525	+	4.46038i	−0.472691	+	0.169314i
$695$	−15.4421	+	8.91547i	−0.585750	+	0.338183i
$696$	−23.4552	−	6.67201i	−0.889068	−	0.252902i
$697$	7.51132	+	4.33666i	0.284511	+	0.164263i
$698$	22.2542	−	26.2478i	0.842334	−	0.993495i
$699$	10.8752	+	10.8752i	0.411336	+	0.411336i
$700$		0			0
$701$	−10.6300	+	10.6300i	−0.401489	+	0.401489i	−0.878757	−	0.477269i	$-0.841627\pi$
$701$	−10.6300	+	10.6300i	−0.401489	+	0.401489i	0.477269	+	0.878757i	$0.341627\pi$
$702$	29.0460	−	2.39162i	1.09627	−	0.0902660i
$703$	−0.387181	+	0.670617i	−0.0146028	+	0.0252928i
$704$	−14.2984	+	13.4470i	−0.538892	+	0.506804i
$705$	−7.38785	−	12.7961i	−0.278242	−	0.481930i
$706$	−4.93612	+	10.4458i	−0.185773	+	0.393132i
$707$		0			0
$708$	−11.0413	−	13.4351i	−0.414956	−	0.504921i
$709$	−0.916878	+	3.42184i	−0.0344341	+	0.128510i	−0.981003	−	0.193991i	$-0.937857\pi$
$709$	−0.916878	+	3.42184i	−0.0344341	+	0.128510i	0.946569	+	0.322501i	$0.104523\pi$
$710$	7.67492	+	1.39379i	0.288034	+	0.0523080i
$711$	−1.15994	−	0.669691i	−0.0435011	−	0.0251154i
$712$	9.21772	−	8.93921i	0.345449	−	0.335011i
$713$		−	16.5398i		−	0.619422i
$714$		0			0
$715$	6.62251	+	6.62251i	0.247668	+	0.247668i
$716$	−0.389927	−	0.859027i	−0.0145723	−	0.0321033i
$717$	4.67400	+	17.4436i	0.174554	+	0.651444i
$718$	13.4503	−	9.31590i	0.501962	−	0.347666i
$719$	8.10598	+	14.0400i	0.302302	+	0.523603i	0.976657	−	0.214805i	$-0.0689115\pi$
$719$	8.10598	+	14.0400i	0.302302	+	0.523603i	−0.674355	+	0.738407i	$0.735578\pi$
$720$	−3.49282	−	5.21194i	−0.130170	−	0.194237i
$721$		0			0
$722$	−24.2821	−	11.4745i	−0.903688	−	0.427035i
$723$	23.0858	+	6.18582i	0.858569	+	0.230053i
$724$	−35.5735	−	25.4548i	−1.32208	−	0.946022i
$725$	−27.3952	+	7.34051i	−1.01743	+	0.272620i
$726$	−6.48108	−	5.49498i	−0.240536	−	0.203938i
$727$		−	14.2822i		−	0.529699i	−0.964290	−	0.264849i	$-0.914678\pi$
$727$		−	14.2822i		−	0.529699i	0.964290	−	0.264849i	$-0.0853223\pi$
$728$		0			0
$729$			22.9031i			0.848263i
$730$	7.87515	−	9.28839i	0.291473	−	0.343779i
$731$	−6.23082	+	1.66954i	−0.230455	+	0.0617503i
$732$	−1.80866	−	10.9085i	−0.0668501	−	0.403191i
$733$	−33.2603	−	8.91206i	−1.22850	−	0.329175i	−0.414502	−	0.910048i	$-0.636044\pi$
$733$	−33.2603	−	8.91206i	−1.22850	−	0.329175i	−0.813994	+	0.580874i	$0.802711\pi$
$734$	5.14015	−	10.8775i	0.189726	−	0.401497i
$735$		0			0
$736$	−6.49240	+	8.78531i	−0.239313	+	0.323831i
$737$	−4.30162	−	7.45062i	−0.158452	−	0.274447i
$738$	10.5934	+	15.2948i	0.389950	+	0.563010i
$739$	−5.40009	−	20.1534i	−0.198646	−	0.741356i	−0.991293	−	0.131675i	$-0.957964\pi$
$739$	−5.40009	−	20.1534i	−0.198646	−	0.741356i	0.792647	−	0.609681i	$-0.208702\pi$
$740$	−15.1854	−	5.70352i	−0.558225	−	0.209666i
$741$	−0.310906	−	0.310906i	−0.0114214	−	0.0114214i
$742$		0			0
$743$		−	30.1201i		−	1.10500i	−0.833513	−	0.552500i	$-0.813674\pi$
$743$		−	30.1201i		−	1.10500i	0.833513	−	0.552500i	$-0.186326\pi$
$744$	−29.2230	−	0.448251i	−1.07137	−	0.0164337i
$745$	−4.60854	−	2.66074i	−0.168844	−	0.0974820i
$746$	1.32543	−	7.29848i	0.0485274	−	0.267216i
$747$	3.07719	−	11.4842i	0.112588	−	0.420186i
$748$	−0.486359	+	4.97291i	−0.0177831	+	0.181828i
$749$		0			0
$750$	14.0501	+	6.63935i	0.513039	+	0.242435i
$751$	−22.6093	−	39.1605i	−0.825026	−	1.42899i	−0.901900	−	0.431946i	$-0.857827\pi$
$751$	−22.6093	−	39.1605i	−0.825026	−	1.42899i	0.0768741	−	0.997041i	$-0.475506\pi$
$752$	−36.3119	−	31.7570i	−1.32416	−	1.15806i
$753$	7.88217	−	13.6523i	0.287242	−	0.497518i
$754$	3.11736	+	37.8600i	0.113528	+	1.37878i
$755$	−0.979047	+	0.979047i	−0.0356312	+	0.0356312i
$756$		0			0
$757$	−10.1353	−	10.1353i	−0.368375	−	0.368375i	0.498509	−	0.866884i	$-0.333881\pi$
$757$	−10.1353	−	10.1353i	−0.368375	−	0.368375i	−0.866884	+	0.498509i	$0.833881\pi$
$758$	−5.53703	−	4.69457i	−0.201114	−	0.170515i
$759$	4.95030	+	2.85806i	0.179684	+	0.103741i
$760$	−0.0762005	+	0.267880i	−0.00276408	+	0.00971704i
$761$	−17.0843	+	9.86363i	−0.619306	+	0.357556i	−0.776599	−	0.629996i	$-0.783057\pi$
$761$	−17.0843	+	9.86363i	−0.619306	+	0.357556i	0.157293	+	0.987552i	$0.449723\pi$
$762$	−0.568951	−	1.58840i	−0.0206109	−	0.0575417i
$763$		0			0
$764$	−7.72339	−	9.39788i	−0.279422	−	0.340003i
$765$	−1.54273	−	0.413374i	−0.0557776	−	0.0149456i
$766$	−5.60641	−	8.09456i	−0.202568	−	0.292468i
$767$	−13.5451	+	23.4607i	−0.489084	+	0.847118i
$768$	15.3462	+	11.7090i	0.553756	+	0.422513i
$769$	41.2736			1.48837			0.744183	−	0.667976i	$-0.232839\pi$
$769$	41.2736			1.48837			0.744183	+	0.667976i	$0.232839\pi$
$770$		0			0
$771$	−19.8101	+	19.8101i	−0.713444	+	0.713444i
$772$	−7.07565	+	18.8386i	−0.254658	+	0.678015i
$773$	−51.5773	+	13.8201i	−1.85511	+	0.497074i	−0.999779	−	0.0210159i	$-0.993310\pi$
$773$	−51.5773	+	13.8201i	−1.85511	+	0.497074i	−0.855326	+	0.518090i	$0.826643\pi$
$774$	−13.6146	−	2.47245i	−0.489365	−	0.0888704i
$775$	−29.4375	+	16.9958i	−1.05743	+	0.610506i
$776$	−44.9914	+	11.3188i	−1.61510	+	0.406320i
$777$		0			0
$778$	17.5487	−	6.28579i	0.629152	−	0.225356i
$779$	0.213755	−	0.797746i	0.00765858	−	0.0285822i
$780$	5.35977	−	7.49035i	0.191911	−	0.268198i
$781$	−3.44899	−	12.8718i	−0.123415	−	0.460590i
$782$	0.228200	+	2.77147i	0.00816043	+	0.0991075i
$783$	−39.1812			−1.40022
$784$		0			0
$785$	0.322740			0.0115191
$786$	−1.10289	−	13.3945i	−0.0393389	−	0.477766i
$787$	0.132467	+	0.494375i	0.00472196	+	0.0176226i	0.968247	−	0.249997i	$-0.0804296\pi$
$787$	0.132467	+	0.494375i	0.00472196	+	0.0176226i	−0.963525	+	0.267620i	$0.913763\pi$
$788$	−23.1945	−	16.5970i	−0.826269	−	0.591242i
$789$	−1.41140	+	5.26743i	−0.0502473	+	0.187526i
$790$	−1.17251	+	0.419982i	−0.0417160	+	0.0149423i
$791$		0			0
$792$	−5.50089	+	9.19905i	−0.195466	+	0.326874i
$793$	−14.9176	+	8.61266i	−0.529739	+	0.305845i
$794$	8.68542	+	1.57730i	0.308234	+	0.0559763i
$795$	−1.74212	+	0.466799i	−0.0617865	+	0.0165556i
$796$	21.8311	+	8.19964i	0.773784	+	0.290628i
$797$	−35.5605	+	35.5605i	−1.25962	+	1.25962i	−0.308341	+	0.951276i	$0.599774\pi$
$797$	−35.5605	+	35.5605i	−1.25962	+	1.25962i	−0.951276	+	0.308341i	$0.900226\pi$
$798$		0			0
$799$	−12.2801			−0.434438
$800$	22.3074	+	2.52767i	0.788686	+	0.0893666i
$801$	3.50586	−	6.07232i	0.123873	−	0.214555i
$802$	12.8043	+	18.4869i	0.452137	+	0.652796i
$803$	−20.0946	−	5.38433i	−0.709123	−	0.190009i
$804$	−6.53653	+	5.37187i	−0.230526	+	0.189451i
$805$		0			0
$806$	15.3529	+	42.8623i	0.540783	+	1.50976i
$807$	0.416833	−	0.240659i	0.0146732	−	0.00847158i
$808$	22.7261	−	12.6602i	0.799501	−	0.445384i
$809$	1.17802	+	0.680131i	0.0414170	+	0.0239121i	0.520566	−	0.853822i	$-0.325721\pi$
$809$	1.17802	+	0.680131i	0.0414170	+	0.0239121i	−0.479149	+	0.877734i	$0.659054\pi$
$810$	2.17006	+	1.83989i	0.0762483	+	0.0646471i
$811$	−12.4370	−	12.4370i	−0.436722	−	0.436722i	0.454186	−	0.890907i	$-0.349930\pi$
$811$	−12.4370	−	12.4370i	−0.436722	−	0.436722i	−0.890907	+	0.454186i	$0.849930\pi$
$812$		0			0
$813$	−9.06114	+	9.06114i	−0.317788	+	0.317788i
$814$	2.27403	+	27.6179i	0.0797049	+	0.968006i
$815$	7.53706	−	13.0546i	0.264012	−	0.457282i
$816$	4.90288	−	0.328080i	0.171635	−	0.0114851i
$817$	0.307119	+	0.531945i	0.0107447	+	0.0186104i
$818$	7.29164	+	3.44564i	0.254946	+	0.120474i
$819$		0			0
$820$	17.2183	+	1.68398i	0.601290	+	0.0588072i
$821$	−1.42969	+	5.33567i	−0.0498965	+	0.186216i	−0.986376	−	0.164506i	$-0.947397\pi$
$821$	−1.42969	+	5.33567i	−0.0498965	+	0.186216i	0.936480	+	0.350722i	$0.114064\pi$
$822$	−3.37197	+	18.5678i	−0.117611	+	0.647626i
$823$	−16.5082	−	9.53100i	−0.575439	−	0.332230i	0.183880	−	0.982949i	$-0.441134\pi$
$823$	−16.5082	−	9.53100i	−0.575439	−	0.332230i	−0.759319	+	0.650719i	$0.774468\pi$
$824$	15.6960	−	15.2218i	0.546797	−	0.530276i
$825$		−	11.7474i		−	0.408991i
$826$		0			0
$827$	3.94521	+	3.94521i	0.137188	+	0.137188i	0.772366	−	0.635178i	$-0.219073\pi$
$827$	3.94521	+	3.94521i	0.137188	+	0.137188i	−0.635178	+	0.772366i	$0.719073\pi$
$828$	−2.09743	+	5.58431i	−0.0728907	+	0.194068i
$829$	6.94085	+	25.9036i	0.241066	+	0.899669i	0.975320	+	0.220795i	$0.0708652\pi$
$829$	6.94085	+	25.9036i	0.241066	+	0.899669i	−0.734255	+	0.678874i	$0.762468\pi$
$830$	−6.29484	−	9.08851i	−0.218497	−	0.315467i
$831$	6.94562	+	12.0302i	0.240941	+	0.417322i
$832$	8.66994	−	28.7932i	0.300576	−	0.998226i
$833$		0			0
$834$	12.7989	−	27.0850i	0.443190	−	0.937875i
$835$	14.3203	+	3.83713i	0.495576	+	0.132789i
$836$	0.469380	−	0.0778244i	0.0162338	−	0.00269161i
$837$	−45.3588	+	12.1539i	−1.56783	+	0.420099i
$838$	5.91263	−	6.97368i	0.204249	−	0.240902i
$839$			5.34140i			0.184406i	0.995740	+	0.0922028i	$0.0293908\pi$
$839$			5.34140i			0.184406i	−0.995740	+	0.0922028i	$0.970609\pi$
$840$		0			0
$841$		−	22.0706i		−	0.761056i
$842$	0.642619	+	0.544844i	0.0221461	+	0.0187766i
$843$	−21.7171	+	5.81908i	−0.747976	+	0.200420i
$844$	10.7548	−	15.0300i	0.370197	−	0.517356i
$845$	−1.10692	−	0.296598i	−0.0380791	−	0.0102033i
$846$	−23.8167	−	11.2545i	−0.818837	−	0.386939i
$847$		0			0
$848$	−4.89146	+	3.27804i	−0.167973	+	0.112568i
$849$	5.48222	+	9.49549i	0.188149	+	0.325884i
$850$	4.69816	−	3.25402i	0.161145	−	0.111612i
$851$	3.99165	+	14.8971i	0.136832	+	0.510664i
$852$	−11.9332	+	5.41671i	−0.408826	+	0.185574i
$853$	−1.42841	−	1.42841i	−0.0489078	−	0.0489078i	0.682230	−	0.731138i	$-0.261010\pi$
$853$	−1.42841	−	1.42841i	−0.0489078	−	0.0489078i	−0.731138	+	0.682230i	$0.761010\pi$
$854$		0			0
$855$			0.152084i			0.00520115i
$856$	−0.819860	+	53.4494i	−0.0280222	+	1.82686i
$857$	−22.1543	−	12.7908i	−0.756778	−	0.436926i	0.0713599	−	0.997451i	$-0.477266\pi$
$857$	−22.1543	−	12.7908i	−0.756778	−	0.436926i	−0.828138	+	0.560525i	$0.810599\pi$
$858$	−15.4815	−	2.81148i	−0.528528	−	0.0959825i
$859$	11.7968	−	44.0264i	0.402503	−	1.50216i	−0.406113	−	0.913823i	$-0.633116\pi$
$859$	11.7968	−	44.0264i	0.402503	−	1.50216i	0.808616	−	0.588337i	$-0.200217\pi$
$860$	−9.94066	+	8.16946i	−0.338974	+	0.278576i
$861$		0			0
$862$	12.7512	−	26.9839i	0.434306	−	0.919075i
$863$	−19.7223	−	34.1601i	−0.671356	−	1.16282i	−0.977520	−	0.210843i	$-0.932379\pi$
$863$	−19.7223	−	34.1601i	−0.671356	−	1.16282i	0.306164	−	0.951979i	$-0.400954\pi$
$864$	28.8636	+	11.3491i	0.981959	+	0.386104i
$865$	−6.27135	+	10.8623i	−0.213232	+	0.369329i
$866$	19.6923	−	1.62145i	0.669172	−	0.0550991i
$867$	−13.6178	+	13.6178i	−0.462486	+	0.462486i
$868$		0			0
$869$	1.50449	+	1.50449i	0.0510364	+	0.0510364i
$870$	−8.00765	+	9.44466i	−0.271485	+	0.320204i
$871$	11.4143	+	6.59004i	0.386758	+	0.223295i
$872$	−22.5193	−	40.4239i	−0.762598	−	1.36893i
$873$	−21.9398	+	12.6669i	−0.742548	+	0.428710i
$874$	0.249287	−	0.0892924i	0.00843226	−	0.00302036i
$875$		0			0
$876$	−1.99140	+	20.3616i	−0.0672832	+	0.687955i
$877$	10.1823	+	2.72833i	0.343831	+	0.0921292i	0.426602	−	0.904439i	$-0.359710\pi$
$877$	10.1823	+	2.72833i	0.343831	+	0.0921292i	−0.0827714	+	0.996569i	$0.526377\pi$
$878$	6.30037	−	4.36373i	0.212627	−	0.147269i
$879$	−10.2534	+	17.7594i	−0.345839	+	0.599011i
$880$	3.21658	+	9.43337i	0.108431	+	0.317999i
$881$	15.4426			0.520274			0.260137	−	0.965572i	$-0.416232\pi$
$881$	15.4426			0.520274			0.260137	+	0.965572i	$0.416232\pi$
$882$		0			0
$883$	10.0224	−	10.0224i	0.337280	−	0.337280i	−0.518063	−	0.855343i	$-0.673347\pi$
$883$	10.0224	−	10.0224i	0.337280	−	0.337280i	0.855343	+	0.518063i	$0.173347\pi$
$884$	−3.16395	−	6.97032i	−0.106415	−	0.234437i
$885$	−8.52927	+	2.28541i	−0.286708	+	0.0768233i
$886$	1.52699	−	8.40840i	0.0513004	−	0.282486i
$887$	−37.9027	+	21.8831i	−1.27265	+	0.734763i	−0.975485	−	0.220064i	$-0.929373\pi$
$887$	−37.9027	+	21.8831i	−1.27265	+	0.734763i	−0.297162	+	0.954827i	$0.596040\pi$
$888$	26.4287	−	6.64883i	0.886888	−	0.223120i
$889$		0			0
$890$	−2.19862	−	6.13812i	−0.0736979	−	0.205750i
$891$	1.25795	−	4.69474i	0.0421430	−	0.157280i
$892$	46.0415	−	7.63380i	1.54158	−	0.255598i
$893$	0.302644	+	1.12948i	0.0101276	+	0.0377967i
$894$	8.91016	−	0.733655i	0.298000	−	0.0245371i
$895$	−0.479024			−0.0160120
$896$		0			0
$897$	−8.75703			−0.292389
$898$	25.9707	−	2.13841i	0.866655	−	0.0713596i
$899$	−15.8419	−	59.1229i	−0.528358	−	1.97186i
$900$	12.0942	−	2.00524i	0.403139	−	0.0668415i
$901$	−0.387956	+	1.44787i	−0.0129247	+	0.0482356i
$902$	−9.96636	−	27.8242i	−0.331844	−	0.926443i
$903$		0			0
$904$	−55.1750	+	13.8807i	−1.83509	+	0.461666i
$905$	−19.2356	+	11.1057i	−0.639413	+	0.369165i
$906$	0.415639	−	2.28872i	0.0138087	−	0.0760377i
$907$	46.8743	−	12.5599i	1.55643	−	0.417045i	0.624902	−	0.780703i	$-0.285139\pi$
$907$	46.8743	−	12.5599i	1.55643	−	0.417045i	0.931533	+	0.363658i	$0.118472\pi$
$908$	12.9367	+	28.5001i	0.429319	+	0.945808i
$909$	10.0449	−	10.0449i	0.333169	−	0.333169i
$910$		0			0
$911$	−35.2525			−1.16797			−0.583983	−	0.811766i	$-0.698507\pi$
$911$	−35.2525			−1.16797			−0.583983	+	0.811766i	$0.698507\pi$
$912$	−0.151008	−	0.442867i	−0.00500038	−	0.0146648i
$913$	−9.44340	+	16.3564i	−0.312531	+	0.541319i
$914$	41.8210	−	28.9659i	1.38332	−	0.958107i
$915$	−5.42336	−	1.45319i	−0.179291	−	0.0480409i
$916$	−5.20567	+	53.2268i	−0.172000	+	1.75866i
$917$		0			0
$918$	7.43278	−	2.66236i	0.245318	−	0.0878708i
$919$	22.1228	−	12.7726i	0.729763	−	0.421329i	−0.0885726	−	0.996070i	$-0.528231\pi$
$919$	22.1228	−	12.7726i	0.729763	−	0.421329i	0.818335	+	0.574741i	$0.194897\pi$
$920$	2.69944	+	4.84572i	0.0889980	+	0.159759i
$921$	−26.3510	−	15.2138i	−0.868295	−	0.501310i
$922$	1.16907	−	1.37886i	0.0385012	−	0.0454105i
$923$	14.4357	+	14.4357i	0.475156	+	0.475156i
$924$		0			0
$925$	22.4120	−	22.4120i	0.736903	−	0.736903i
$926$	−17.7588	+	1.46224i	−0.583590	+	0.0480523i
$927$	5.96981	−	10.3400i	0.196074	−	0.339610i
$928$	−14.7930	+	37.6222i	−0.485603	+	1.23501i
$929$	1.98515	+	3.43838i	0.0651306	+	0.112810i	0.896752	−	0.442534i	$-0.145920\pi$
$929$	1.98515	+	3.43838i	0.0651306	+	0.112810i	−0.831621	+	0.555343i	$0.812587\pi$
$930$	−6.34051	+	13.4177i	−0.207913	+	0.439985i
$931$		0			0
$932$	19.6978	−	16.1881i	0.645222	−	0.530258i
$933$	2.04354	−	7.62660i	0.0669025	−	0.249684i
$934$	−11.5339	−	2.09460i	−0.377402	−	0.0685375i
$935$	2.19724	+	1.26858i	0.0718576	+	0.0414870i
$936$	0.251842	−	16.4184i	0.00823170	−	0.536653i
$937$		−	18.3326i		−	0.598899i	−0.954112	−	0.299450i	$-0.903197\pi$
$937$		−	18.3326i		−	0.598899i	0.954112	−	0.299450i	$-0.0968031\pi$
$938$		0			0
$939$	16.3565	+	16.3565i	0.533773	+	0.533773i
$940$	−22.3045	+	10.1244i	−0.727492	+	0.330221i
$941$	−7.71512	−	28.7932i	−0.251506	−	0.938632i	−0.970001	−	0.243100i	$-0.921836\pi$
$941$	−7.71512	−	28.7932i	−0.251506	−	0.938632i	0.718496	−	0.695531i	$-0.244831\pi$
$942$	−0.445742	+	0.308728i	−0.0145230	+	0.0100589i
$943$	−8.22438	−	14.2451i	−0.267823	−	0.463883i
$944$	−23.9482	+	16.0491i	−0.779448	+	0.522352i
$945$		0			0
$946$	19.8739	+	9.39136i	0.646157	+	0.305339i
$947$	−27.1840	−	7.28394i	−0.883362	−	0.236696i	−0.211505	−	0.977377i	$-0.567837\pi$
$947$	−27.1840	−	7.28394i	−0.883362	−	0.236696i	−0.671857	+	0.740681i	$0.734503\pi$
$948$	1.21763	−	1.70165i	0.0395467	−	0.0552670i
$949$	30.7847	−	8.24874i	0.999314	−	0.267765i
$950$	−0.415081	−	0.351926i	−0.0134670	−	0.0114180i
$951$		−	22.7060i		−	0.736291i
$952$		0			0
$953$		−	9.54510i		−	0.309196i	−0.987977	−	0.154598i	$-0.950592\pi$
$953$		−	9.54510i		−	0.309196i	0.987977	−	0.154598i	$-0.0494083\pi$
$954$	−2.07938	+	2.45254i	−0.0673225	+	0.0794038i
$955$	−5.96625	+	1.59865i	−0.193063	+	0.0517311i
$956$	29.5345	−	4.89689i	0.955212	−	0.158377i
$957$	20.4327	+	5.47492i	0.660495	+	0.176979i
$958$	5.60615	−	11.8637i	0.181126	−	0.383298i
$959$		0			0
$960$	8.63470	−	4.63812i	0.278684	−	0.149695i
$961$	−21.1794	−	36.6839i	−0.683208	−	1.18335i
$962$	−24.1722	−	34.8999i	−0.779343	−	1.12522i
$963$	7.55502	+	28.1957i	0.243457	+	0.908595i
$964$	13.9312	−	37.0911i	0.448693	−	1.19462i
$965$	7.22535	+	7.22535i	0.232592	+	0.232592i
$966$		0			0
$967$			54.0255i			1.73734i	0.495388	+	0.868672i	$0.335026\pi$
$967$			54.0255i			1.73734i	−0.495388	+	0.868672i	$0.664974\pi$
$968$	−10.1120	+	9.80646i	−0.325012	+	0.315192i
$969$	−0.103154	−	0.0595558i	−0.00331377	−	0.00191321i
$970$	−4.20923	+	23.1782i	−0.135150	+	0.744207i
$971$	−1.54187	+	5.75433i	−0.0494809	+	0.184665i	−0.986243	−	0.165301i	$-0.947140\pi$
$971$	−1.54187	+	5.75433i	−0.0494809	+	0.184665i	0.936762	+	0.349966i	$0.113807\pi$
$972$	27.9827	+	2.73675i	0.897544	+	0.0877813i
$973$		0			0
$974$	49.4665	+	23.3752i	1.58501	+	0.748991i
$975$	8.99842	+	15.5857i	0.288180	+	0.499143i
$976$	−18.2899	+	1.22388i	−0.585444	+	0.0391754i
$977$	14.6499	−	25.3743i	0.468690	−	0.811795i	−0.530669	−	0.847579i	$-0.678059\pi$
$977$	14.6499	−	25.3743i	0.468690	−	0.811795i	0.999360	+	0.0357835i	$0.0113927\pi$
$978$	2.07822	+	25.2398i	0.0664542	+	0.807078i
$979$	−7.87607	+	7.87607i	−0.251720	+	0.251720i
$980$		0			0
$981$	−17.8673	−	17.8673i	−0.570460	−	0.570460i
$982$	−45.4729	−	38.5542i	−1.45110	−	1.23031i
$983$	13.8442	+	7.99296i	0.441562	+	0.254936i	0.704260	−	0.709942i	$-0.251279\pi$
$983$	13.8442	+	7.99296i	0.441562	+	0.254936i	−0.262698	+	0.964878i	$0.584612\pi$
$984$	−25.3914	+	14.1450i	−0.809449	+	0.450926i
$985$	−12.5419	+	7.24108i	−0.399619	+	0.230720i
$986$	3.47024	+	9.68825i	0.110515	+	0.308537i
$987$		0			0
$988$	−0.563133	+	0.462795i	−0.0179156	+	0.0147235i
$989$	11.8166	+	3.16625i	0.375746	+	0.100681i
$990$	3.09884	+	4.47411i	0.0984876	+	0.142197i
$991$	−10.3826	+	17.9832i	−0.329814	+	0.571255i	−0.982475	−	0.186396i	$-0.940319\pi$
$991$	−10.3826	+	17.9832i	−0.329814	+	0.571255i	0.652661	+	0.757650i	$0.273653\pi$
$992$	−5.45509	+	48.1428i	−0.173199	+	1.52853i
$993$	11.8153			0.374948
$994$		0			0
$995$	8.37312	−	8.37312i	0.265446	−	0.265446i
$996$	17.3878	+	6.53077i	0.550955	+	0.206935i
$997$	48.0242	−	12.8681i	1.52094	−	0.407535i	0.600890	−	0.799331i	$-0.294813\pi$
$997$	48.0242	−	12.8681i	1.52094	−	0.407535i	0.920052	+	0.391796i	$0.128146\pi$
$998$	15.5568	+	2.82518i	0.492443	+	0.0894294i
$999$	37.9205	−	21.8934i	1.19975	−	0.692677i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	784.2.x.o.165.12		48
7.2	even	3	inner	784.2.x.o.373.5		48
7.3	odd	6		784.2.m.j.197.5		24
7.4	even	3		784.2.m.k.197.5		24
7.5	odd	6		112.2.w.c.37.5	✓	48
7.6	odd	2		112.2.w.c.53.12	yes	48
16.13	even	4	inner	784.2.x.o.557.5		48
28.19	even	6		448.2.ba.c.177.4		48
28.27	even	2		448.2.ba.c.305.9		48
56.5	odd	6		896.2.ba.f.737.4		48
56.13	odd	2		896.2.ba.f.865.9		48
56.19	even	6		896.2.ba.e.737.9		48
56.27	even	2		896.2.ba.e.865.4		48
112.5	odd	12		896.2.ba.f.289.9		48
112.13	odd	4		112.2.w.c.109.5	yes	48
112.19	even	12		448.2.ba.c.401.9		48
112.27	even	4		896.2.ba.e.417.9		48
112.45	odd	12		784.2.m.j.589.5		24
112.61	odd	12		112.2.w.c.93.12	yes	48
112.69	odd	4		896.2.ba.f.417.4		48
112.75	even	12		896.2.ba.e.289.4		48
112.83	even	4		448.2.ba.c.81.4		48
112.93	even	12	inner	784.2.x.o.765.12		48
112.109	even	12		784.2.m.k.589.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
112.2.w.c.37.5	✓	48	7.5	odd	6
112.2.w.c.53.12	yes	48	7.6	odd	2
112.2.w.c.93.12	yes	48	112.61	odd	12
112.2.w.c.109.5	yes	48	112.13	odd	4
448.2.ba.c.81.4		48	112.83	even	4
448.2.ba.c.177.4		48	28.19	even	6
448.2.ba.c.305.9		48	28.27	even	2
448.2.ba.c.401.9		48	112.19	even	12
784.2.m.j.197.5		24	7.3	odd	6
784.2.m.j.589.5		24	112.45	odd	12
784.2.m.k.197.5		24	7.4	even	3
784.2.m.k.589.5		24	112.109	even	12
784.2.x.o.165.12		48	1.1	even	1	trivial
784.2.x.o.373.5		48	7.2	even	3	inner
784.2.x.o.557.5		48	16.13	even	4	inner
784.2.x.o.765.12		48	112.93	even	12	inner
896.2.ba.e.289.4		48	112.75	even	12
896.2.ba.e.417.9		48	112.27	even	4
896.2.ba.e.737.9		48	56.19	even	6
896.2.ba.e.865.4		48	56.27	even	2
896.2.ba.f.289.9		48	112.5	odd	12
896.2.ba.f.417.4		48	112.69	odd	4
896.2.ba.f.737.4		48	56.5	odd	6
896.2.ba.f.865.9		48	56.13	odd	2

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:	\( N \)	\(=\)	\( 784 = 2^{4} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	784.x (of order \(12\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.40944 - 0.116052i) q^{2} +(0.312249 + 1.16533i) q^{3} +(1.97306 - 0.327139i) q^{4} +(0.262843 - 0.980942i) q^{5} +(0.575337 + 1.60623i) q^{6} +(2.74296 - 0.690063i) q^{8} +(1.33758 - 0.772254i) q^{9} +(0.256621 - 1.41309i) q^{10} +(-2.36993 + 0.635020i) q^{11} +(0.997312 + 2.19712i) q^{12} +(2.65786 - 2.65786i) q^{13} +1.22519 q^{15} +(3.78596 - 1.29093i) q^{16} +(0.509128 - 0.881836i) q^{17} +(1.79563 - 1.24368i) q^{18} +(-0.0936561 - 0.0250951i) q^{19} +(0.197701 - 2.02145i) q^{20} +(-3.26658 + 1.17006i) q^{22} +(-1.67238 + 0.965551i) q^{23} +(1.66064 + 2.98098i) q^{24} +(3.43697 + 1.98433i) q^{25} +(3.43765 - 4.05455i) q^{26} +(3.87683 + 3.87683i) q^{27} +(-5.05325 + 5.05325i) q^{29} +(1.72684 - 0.142187i) q^{30} +(-4.28249 + 7.41749i) q^{31} +(5.18628 - 2.25887i) q^{32} +(-1.48001 - 2.56346i) q^{33} +(0.615248 - 1.30198i) q^{34} +(2.38650 - 1.96128i) q^{36} +(2.06704 - 7.71428i) q^{37} +(-0.134915 - 0.0245011i) q^{38} +(3.92719 + 2.26737i) q^{39} +(0.0440545 - 2.87206i) q^{40} +8.51782i q^{41} +(-4.47950 - 4.47950i) q^{43} +(-4.46828 + 2.02823i) q^{44} +(-0.405963 - 1.51507i) q^{45} +(-2.24507 + 1.55497i) q^{46} +(-6.02995 - 10.4442i) q^{47} +(2.68652 + 4.00880i) q^{48} +(5.07450 + 2.39794i) q^{50} +(1.18660 + 0.317949i) q^{51} +(4.37464 - 6.11361i) q^{52} +(-1.42191 + 0.381000i) q^{53} +(5.91409 + 5.01426i) q^{54} +2.49167i q^{55} -0.116976i q^{57} +(-6.53583 + 7.70871i) q^{58} +(-6.96158 + 1.86535i) q^{59} +(2.41738 - 0.400808i) q^{60} +(-4.42654 - 1.18609i) q^{61} +(-5.17511 + 10.9515i) q^{62} +(7.04763 - 3.78563i) q^{64} +(-1.90861 - 3.30580i) q^{65} +(-2.38349 - 3.44129i) q^{66} +(0.907543 + 3.38700i) q^{67} +(0.716059 - 1.90647i) q^{68} +(-1.64738 - 1.64738i) q^{69} +5.43131i q^{71} +(3.13603 - 3.04128i) q^{72} +(7.34303 + 4.23950i) q^{73} +(2.01811 - 11.1127i) q^{74} +(-1.23921 + 4.62480i) q^{75} +(-0.192999 - 0.0188756i) q^{76} +(5.79829 + 2.73996i) q^{78} +(-0.433595 - 0.751008i) q^{79} +(-0.271217 - 4.05312i) q^{80} +(-0.990483 + 1.71557i) q^{81} +(0.988514 + 12.0054i) q^{82} +(5.44318 - 5.44318i) q^{83} +(-0.731209 - 0.731209i) q^{85} +(-6.83345 - 5.79374i) q^{86} +(-7.46657 - 4.31083i) q^{87} +(-6.06240 + 3.37723i) q^{88} +(3.93155 - 2.26988i) q^{89} +(-0.748010 - 2.08830i) q^{90} +(-2.98385 + 2.45219i) q^{92} +(-9.98102 - 2.67441i) q^{93} +(-9.71095 - 14.0207i) q^{94} +(-0.0492336 + 0.0852752i) q^{95} +(4.25173 + 5.33840i) q^{96} -16.4025 q^{97} +(-2.67958 + 2.67958i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q - 4 q^{2} - 4 q^{4} - 4 q^{5} + 4 q^{6} - 4 q^{8} + 2 q^{10} - 4 q^{11} - 2 q^{12} + 24 q^{13} - 40 q^{15} + 16 q^{16} - 8 q^{17} + 18 q^{18} + 4 q^{19} + 16 q^{20} - 18 q^{24} + 10 q^{26} + 24 q^{27}+ \cdots - 24 q^{99}+O(q^{100}) \) 48 * q - 4 * q^2 - 4 * q^4 - 4 * q^5 + 4 * q^6 - 4 * q^8 + 2 * q^10 - 4 * q^11 - 2 * q^12 + 24 * q^13 - 40 * q^15 + 16 * q^16 - 8 * q^17 + 18 * q^18 + 4 * q^19 + 16 * q^20 - 18 * q^24 + 10 * q^26 + 24 * q^27 + 24 * q^29 - 4 * q^30 - 28 * q^31 + 16 * q^32 - 16 * q^33 + 44 * q^34 - 72 * q^36 - 24 * q^37 - 20 * q^38 - 26 * q^40 - 40 * q^43 + 6 * q^44 + 28 * q^45 - 14 * q^46 + 20 * q^47 - 56 * q^48 + 56 * q^50 + 24 * q^51 + 16 * q^52 - 16 * q^53 - 64 * q^54 - 6 * q^58 + 20 * q^59 + 46 * q^60 - 8 * q^61 - 24 * q^62 + 80 * q^64 + 8 * q^65 + 20 * q^66 + 48 * q^67 + 40 * q^69 - 32 * q^72 - 8 * q^74 + 4 * q^75 + 36 * q^76 + 116 * q^78 - 36 * q^79 + 28 * q^80 - 2 * q^82 + 8 * q^83 - 20 * q^86 - 42 * q^88 + 20 * q^90 + 76 * q^92 + 8 * q^93 + 72 * q^94 - 4 * q^95 + 120 * q^96 + 48 * q^97 - 24 * q^99

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