LMFDB - Embedded newform 128.5.h.a.15.14

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [128,5,Mod(15,128)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(128, base_ring=CyclotomicField(8))

chi = DirichletCharacter(H, H._module([4, 1]))

N = Newforms(chi, 5, names="a")

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

chi := DirichletCharacter("128.15");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 128 = 2^{7} $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	128.h (of order $8$, 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:	$13.2313552747$
Analytic rank:	$0$
Dimension:	$60$
Relative dimension:	$15$ over $\Q(\zeta_{8})$
Twist minimal:	no (minimal twist has level 32)
Sato-Tate group:	$\mathrm{SU}(2)[C_{8}]$

Embedding invariants

Embedding label			15.14
Character	$\chi$	$=$	128.15
Dual form			128.5.h.a.111.14

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(12.3801 - 5.12803i) q^{3} +(-36.8127 - 15.2483i) q^{5} +(-16.3058 + 16.3058i) q^{7} +(69.6958 - 69.6958i) q^{9} +O(q^{10})$	\(q+(12.3801 - 5.12803i) q^{3} +(-36.8127 - 15.2483i) q^{5} +(-16.3058 + 16.3058i) q^{7} +(69.6958 - 69.6958i) q^{9} +(-135.158 - 55.9844i) q^{11} +(-177.746 + 73.6249i) q^{13} -533.940 q^{15} -418.220i q^{17} +(93.8220 + 226.506i) q^{19} +(-118.251 + 285.484i) q^{21} +(226.375 + 226.375i) q^{23} +(680.721 + 680.721i) q^{25} +(90.0723 - 217.454i) q^{27} +(-199.899 - 482.599i) q^{29} -1011.07i q^{31} -1960.37 q^{33} +(848.895 - 351.624i) q^{35} +(-1014.43 - 420.191i) q^{37} +(-1822.97 + 1822.97i) q^{39} +(777.292 - 777.292i) q^{41} +(-1947.97 - 806.874i) q^{43} +(-3628.43 + 1502.95i) q^{45} +991.052 q^{47} +1869.24i q^{49} +(-2144.64 - 5177.63i) q^{51} +(1653.39 - 3991.63i) q^{53} +(4121.87 + 4121.87i) q^{55} +(2323.06 + 2323.06i) q^{57} +(629.109 - 1518.80i) q^{59} +(-604.682 - 1459.83i) q^{61} +2272.89i q^{63} +7665.97 q^{65} +(-138.463 + 57.3534i) q^{67} +(3963.41 + 1641.70i) q^{69} +(-4552.60 + 4552.60i) q^{71} +(4813.22 - 4813.22i) q^{73} +(11918.2 + 4936.67i) q^{75} +(3116.73 - 1290.99i) q^{77} +5010.95 q^{79} +4829.74i q^{81} +(1268.41 + 3062.22i) q^{83} +(-6377.15 + 15395.8i) q^{85} +(-4949.56 - 4949.56i) q^{87} +(-3481.14 - 3481.14i) q^{89} +(1697.78 - 4098.80i) q^{91} +(-5184.80 - 12517.2i) q^{93} -9768.94i q^{95} -9319.15 q^{97} +(-13321.8 + 5518.09i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) $ 60 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	$ 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 1156 q^{23} - 4 q^{25} - 3644 q^{27} - 4 q^{29} - 8 q^{33} + 5188 q^{35} - 4 q^{37} + 2692 q^{39} - 4 q^{41} - 5564 q^{43} - 328 q^{45} + 8 q^{47} - 8384 q^{51} + 956 q^{53} + 11780 q^{55} - 4 q^{57} + 13060 q^{59} + 7548 q^{61} - 8 q^{65} - 18876 q^{67} - 19588 q^{69} - 19964 q^{71} - 4 q^{73} + 200 q^{75} + 9404 q^{77} + 50184 q^{79} - 10556 q^{83} + 2496 q^{85} - 49276 q^{87} - 4 q^{89} - 31868 q^{91} + 320 q^{93} - 8 q^{97} + 46920 q^{99}+O(q^{100}) $ 60 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 1156 * q^23 - 4 * q^25 - 3644 * q^27 - 4 * q^29 - 8 * q^33 + 5188 * q^35 - 4 * q^37 + 2692 * q^39 - 4 * q^41 - 5564 * q^43 - 328 * q^45 + 8 * q^47 - 8384 * q^51 + 956 * q^53 + 11780 * q^55 - 4 * q^57 + 13060 * q^59 + 7548 * q^61 - 8 * q^65 - 18876 * q^67 - 19588 * q^69 - 19964 * q^71 - 4 * q^73 + 200 * q^75 + 9404 * q^77 + 50184 * q^79 - 10556 * q^83 + 2496 * q^85 - 49276 * q^87 - 4 * q^89 - 31868 * q^91 + 320 * q^93 - 8 * q^97 + 46920 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/128\mathbb{Z}\right)^\times$.

$n$	$5$	$127$
$\chi(n)$	$e\left(\frac{1}{8}\right)$	$-1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	12.3801	−	5.12803i	1.37557	−	0.569781i	0.432278	−	0.901740i	$-0.357710\pi$
$3$	12.3801	−	5.12803i	1.37557	−	0.569781i	0.943294	+	0.331960i	$0.107710\pi$
$4$		0			0
$5$	−36.8127	−	15.2483i	−1.47251	−	0.609932i	−0.505078	−	0.863074i	$-0.668536\pi$
$5$	−36.8127	−	15.2483i	−1.47251	−	0.609932i	−0.967429	+	0.253141i	$0.918536\pi$
$6$		0			0
$7$	−16.3058	+	16.3058i	−0.332771	+	0.332771i	−0.853638	−	0.520867i	$-0.825609\pi$
$7$	−16.3058	+	16.3058i	−0.332771	+	0.332771i	0.520867	+	0.853638i	$0.325609\pi$
$8$		0			0
$9$	69.6958	−	69.6958i	0.860442	−	0.860442i
$10$		0			0
$11$	−135.158	−	55.9844i	−1.11701	−	0.462681i	−0.253664	−	0.967292i	$-0.581636\pi$
$11$	−135.158	−	55.9844i	−1.11701	−	0.462681i	−0.863347	+	0.504612i	$0.831636\pi$
$12$		0			0
$13$	−177.746	+	73.6249i	−1.05175	+	0.435650i	−0.840517	−	0.541785i	$-0.817749\pi$
$13$	−177.746	+	73.6249i	−1.05175	+	0.435650i	−0.211236	+	0.977435i	$0.567749\pi$
$14$		0			0
$15$	−533.940			−2.37307
$16$		0			0
$17$		−	418.220i		−	1.44713i	−0.690257	−	0.723565i	$-0.742502\pi$
$17$		−	418.220i		−	1.44713i	0.690257	−	0.723565i	$-0.257498\pi$
$18$		0			0
$19$	93.8220	+	226.506i	0.259895	+	0.627442i	0.998931	−	0.0462240i	$-0.0147188\pi$
$19$	93.8220	+	226.506i	0.259895	+	0.627442i	−0.739036	+	0.673666i	$0.764719\pi$
$20$		0			0
$21$	−118.251	+	285.484i	−0.268144	+	0.647357i
$22$		0			0
$23$	226.375	+	226.375i	0.427929	+	0.427929i	0.887922	−	0.459993i	$-0.152148\pi$
$23$	226.375	+	226.375i	0.427929	+	0.427929i	−0.459993	+	0.887922i	$0.652148\pi$
$24$		0			0
$25$	680.721	+	680.721i	1.08915	+	1.08915i
$26$		0			0
$27$	90.0723	−	217.454i	0.123556	−	0.298291i
$28$		0			0
$29$	−199.899	−	482.599i	−0.237692	−	0.573839i	0.759351	−	0.650681i	$-0.225516\pi$
$29$	−199.899	−	482.599i	−0.237692	−	0.573839i	−0.997043	+	0.0768416i	$0.975516\pi$
$30$		0			0
$31$		−	1011.07i		−	1.05210i	−0.850452	−	0.526052i	$-0.823672\pi$
$31$		−	1011.07i		−	1.05210i	0.850452	−	0.526052i	$-0.176328\pi$
$32$		0			0
$33$	−1960.37			−1.80015
$34$		0			0
$35$	848.895	−	351.624i	0.692975	−	0.287040i
$36$		0			0
$37$	−1014.43	−	420.191i	−0.741001	−	0.306933i	−0.0199372	−	0.999801i	$-0.506347\pi$
$37$	−1014.43	−	420.191i	−0.741001	−	0.306933i	−0.721064	+	0.692868i	$0.756347\pi$
$38$		0			0
$39$	−1822.97	+	1822.97i	−1.19854	+	1.19854i
$40$		0			0
$41$	777.292	−	777.292i	0.462399	−	0.462399i	−0.437042	−	0.899441i	$-0.643974\pi$
$41$	777.292	−	777.292i	0.462399	−	0.462399i	0.899441	+	0.437042i	$0.143974\pi$
$42$		0			0
$43$	−1947.97	−	806.874i	−1.05352	−	0.436384i	−0.212376	−	0.977188i	$-0.568120\pi$
$43$	−1947.97	−	806.874i	−1.05352	−	0.436384i	−0.841149	+	0.540804i	$0.818120\pi$
$44$		0			0
$45$	−3628.43	+	1502.95i	−1.79182	+	0.742195i
$46$		0			0
$47$	991.052			0.448643			0.224321	−	0.974515i	$-0.427983\pi$
$47$	991.052			0.448643			0.224321	+	0.974515i	$0.427983\pi$
$48$		0			0
$49$			1869.24i			0.778527i
$50$		0			0
$51$	−2144.64	−	5177.63i	−0.824546	−	1.99063i
$52$		0			0
$53$	1653.39	−	3991.63i	0.588603	−	1.42101i	−0.296235	−	0.955115i	$-0.595731\pi$
$53$	1653.39	−	3991.63i	0.588603	−	1.42101i	0.884838	−	0.465899i	$-0.154269\pi$
$54$		0			0
$55$	4121.87	+	4121.87i	1.36260	+	1.36260i
$56$		0			0
$57$	2323.06	+	2323.06i	0.715008	+	0.715008i
$58$		0			0
$59$	629.109	−	1518.80i	0.180727	−	0.436313i	−0.807390	−	0.590018i	$-0.799121\pi$
$59$	629.109	−	1518.80i	0.180727	−	0.436313i	0.988117	+	0.153705i	$0.0491206\pi$
$60$		0			0
$61$	−604.682	−	1459.83i	−0.162505	−	0.392323i	0.821562	−	0.570119i	$-0.193103\pi$
$61$	−604.682	−	1459.83i	−0.162505	−	0.392323i	−0.984067	+	0.177797i	$0.943103\pi$
$62$		0			0
$63$			2272.89i			0.572660i
$64$		0			0
$65$	7665.97			1.81443
$66$		0			0
$67$	−138.463	+	57.3534i	−0.0308450	+	0.0127764i	−0.398053	−	0.917363i	$-0.630314\pi$
$67$	−138.463	+	57.3534i	−0.0308450	+	0.0127764i	0.367208	+	0.930139i	$0.380314\pi$
$68$		0			0
$69$	3963.41	+	1641.70i	0.832474	+	0.344822i
$70$		0			0
$71$	−4552.60	+	4552.60i	−0.903115	+	0.903115i	−0.995704	−	0.0925892i	$-0.970486\pi$
$71$	−4552.60	+	4552.60i	−0.903115	+	0.903115i	0.0925892	+	0.995704i	$0.470486\pi$
$72$		0			0
$73$	4813.22	−	4813.22i	0.903213	−	0.903213i	−0.0924998	−	0.995713i	$-0.529486\pi$
$73$	4813.22	−	4813.22i	0.903213	−	0.903213i	0.995713	+	0.0924998i	$0.0294858\pi$
$74$		0			0
$75$	11918.2	+	4936.67i	2.11879	+	0.877630i
$76$		0			0
$77$	3116.73	−	1290.99i	0.525675	−	0.217742i
$78$		0			0
$79$	5010.95			0.802909			0.401454	−	0.915879i	$-0.368505\pi$
$79$	5010.95			0.802909			0.401454	+	0.915879i	$0.368505\pi$
$80$		0			0
$81$			4829.74i			0.736128i
$82$		0			0
$83$	1268.41	+	3062.22i	0.184121	+	0.444508i	0.988808	−	0.149191i	$-0.0476670\pi$
$83$	1268.41	+	3062.22i	0.184121	+	0.444508i	−0.804687	+	0.593699i	$0.797667\pi$
$84$		0			0
$85$	−6377.15	+	15395.8i	−0.882651	+	2.13091i
$86$		0			0
$87$	−4949.56	−	4949.56i	−0.653925	−	0.653925i
$88$		0			0
$89$	−3481.14	−	3481.14i	−0.439482	−	0.439482i	0.452356	−	0.891838i	$-0.350584\pi$
$89$	−3481.14	−	3481.14i	−0.439482	−	0.439482i	−0.891838	+	0.452356i	$0.850584\pi$
$90$		0			0
$91$	1697.78	−	4098.80i	0.205021	−	0.494964i
$92$		0			0
$93$	−5184.80	−	12517.2i	−0.599469	−	1.44725i
$94$		0			0
$95$		−	9768.94i		−	1.08243i
$96$		0			0
$97$	−9319.15			−0.990450			−0.495225	−	0.868765i	$-0.664914\pi$
$97$	−9319.15			−0.990450			−0.495225	+	0.868765i	$0.664914\pi$
$98$		0			0
$99$	−13321.8	+	5518.09i	−1.35923	+	0.563012i
$100$		0			0
$101$	5896.31	+	2442.33i	0.578013	+	0.239421i	0.652484	−	0.757802i	$-0.273727\pi$
$101$	5896.31	+	2442.33i	0.578013	+	0.239421i	−0.0744713	+	0.997223i	$0.523727\pi$
$102$		0			0
$103$	5644.16	−	5644.16i	0.532016	−	0.532016i	−0.389156	−	0.921172i	$-0.627233\pi$
$103$	5644.16	−	5644.16i	0.532016	−	0.532016i	0.921172	+	0.389156i	$0.127233\pi$
$104$		0			0
$105$	8706.31	−	8706.31i	0.789688	−	0.789688i
$106$		0			0
$107$	15127.2	+	6265.88i	1.32127	+	0.547286i	0.928151	−	0.372203i	$-0.121398\pi$
$107$	15127.2	+	6265.88i	1.32127	+	0.547286i	0.393114	+	0.919490i	$0.371398\pi$
$108$		0			0
$109$	2544.85	−	1054.11i	0.214195	−	0.0887226i	−0.273006	−	0.962012i	$-0.588018\pi$
$109$	2544.85	−	1054.11i	0.214195	−	0.0887226i	0.487201	+	0.873290i	$0.338018\pi$
$110$		0			0
$111$	−14713.6			−1.19418
$112$		0			0
$113$			741.348i			0.0580584i	0.999579	+	0.0290292i	$0.00924158\pi$
$113$			741.348i			0.0580584i	−0.999579	+	0.0290292i	$0.990758\pi$
$114$		0			0
$115$	−4881.63	−	11785.3i	−0.369121	−	0.891137i
$116$		0			0
$117$	−7256.82	+	17519.5i	−0.530120	+	1.27982i
$118$		0			0
$119$	6819.41	+	6819.41i	0.481563	+	0.481563i
$120$		0			0
$121$	4780.76	+	4780.76i	0.326532	+	0.326532i
$122$		0			0
$123$	5637.02	−	13609.0i	0.372597	−	0.899528i
$124$		0			0
$125$	−5149.11	−	12431.1i	−0.329543	−	0.795588i
$126$		0			0
$127$			3501.89i			0.217118i	0.994090	+	0.108559i	$0.0346236\pi$
$127$			3501.89i			0.217118i	−0.994090	+	0.108559i	$0.965376\pi$
$128$		0			0
$129$	−28253.8			−1.69784
$130$		0			0
$131$	−21054.5	+	8721.05i	−1.22688	+	0.508190i	−0.899591	−	0.436734i	$-0.856135\pi$
$131$	−21054.5	+	8721.05i	−1.22688	+	0.508190i	−0.327289	+	0.944924i	$0.606135\pi$
$132$		0			0
$133$	−5223.20	−	2163.52i	−0.295280	−	0.122309i
$134$		0			0
$135$	−6631.61	+	6631.61i	−0.363874	+	0.363874i
$136$		0			0
$137$	−9885.25	+	9885.25i	−0.526680	+	0.526680i	−0.919581	−	0.392901i	$-0.871471\pi$
$137$	−9885.25	+	9885.25i	−0.526680	+	0.526680i	0.392901	+	0.919581i	$0.371471\pi$
$138$		0			0
$139$	−20486.7	−	8485.87i	−1.06033	−	0.439204i	−0.216764	−	0.976224i	$-0.569550\pi$
$139$	−20486.7	−	8485.87i	−1.06033	−	0.439204i	−0.843570	+	0.537020i	$0.819550\pi$
$140$		0			0
$141$	12269.4	−	5082.14i	0.617140	−	0.255628i
$142$		0			0
$143$	28145.7			1.37639
$144$		0			0
$145$			20813.9i			0.989959i
$146$		0			0
$147$	9585.53	+	23141.5i	0.443590	+	1.07092i
$148$		0			0
$149$	11796.8	−	28480.0i	0.531363	−	1.28282i	−0.399257	−	0.916839i	$-0.630732\pi$
$149$	11796.8	−	28480.0i	0.531363	−	1.28282i	0.930620	−	0.365986i	$-0.119268\pi$
$150$		0			0
$151$	−322.194	−	322.194i	−0.0141307	−	0.0141307i	0.700006	−	0.714137i	$-0.253181\pi$
$151$	−322.194	−	322.194i	−0.0141307	−	0.0141307i	−0.714137	+	0.700006i	$0.753181\pi$
$152$		0			0
$153$	−29148.2	−	29148.2i	−1.24517	−	1.24517i
$154$		0			0
$155$	−15417.1	+	37220.3i	−0.641713	+	1.54923i
$156$		0			0
$157$	3713.05	+	8964.09i	0.150637	+	0.363670i	0.981127	−	0.193364i	$-0.0619397\pi$
$157$	3713.05	+	8964.09i	0.150637	+	0.363670i	−0.830490	+	0.557033i	$0.811940\pi$
$158$		0			0
$159$		−	57895.6i		−	2.29008i
$160$		0			0
$161$	−7382.43			−0.284805
$162$		0			0
$163$	−22447.6	+	9298.11i	−0.844880	+	0.349961i	−0.762776	−	0.646663i	$-0.776164\pi$
$163$	−22447.6	+	9298.11i	−0.844880	+	0.349961i	−0.0821042	+	0.996624i	$0.526164\pi$
$164$		0			0
$165$	72166.4	+	29892.3i	2.65074	+	1.09797i
$166$		0			0
$167$	−13704.4	+	13704.4i	−0.491392	+	0.491392i	−0.908745	−	0.417352i	$-0.862958\pi$
$167$	−13704.4	+	13704.4i	−0.491392	+	0.491392i	0.417352	+	0.908745i	$0.362958\pi$
$168$		0			0
$169$	5977.42	−	5977.42i	0.209286	−	0.209286i
$170$		0			0
$171$	22325.5	+	9247.54i	0.763501	+	0.316253i
$172$		0			0
$173$	−22173.8	+	9184.67i	−0.740879	+	0.306882i	−0.721014	−	0.692921i	$-0.756324\pi$
$173$	−22173.8	+	9184.67i	−0.740879	+	0.306882i	−0.0198648	+	0.999803i	$0.506324\pi$
$174$		0			0
$175$	−22199.4			−0.724877
$176$		0			0
$177$		−	22029.1i		−	0.703154i
$178$		0			0
$179$	−22936.8	−	55374.3i	−0.715858	−	1.72823i	−0.684817	−	0.728715i	$-0.740118\pi$
$179$	−22936.8	−	55374.3i	−0.715858	−	1.72823i	−0.0310412	−	0.999518i	$-0.509882\pi$
$180$		0			0
$181$	17838.8	−	43066.6i	0.544512	−	1.31457i	−0.376998	−	0.926214i	$-0.623044\pi$
$181$	17838.8	−	43066.6i	0.544512	−	1.31457i	0.921510	−	0.388354i	$-0.126956\pi$
$182$		0			0
$183$	−14972.1	−	14972.1i	−0.447076	−	0.447076i
$184$		0			0
$185$	30936.7	+	30936.7i	0.903921	+	0.903921i
$186$		0			0
$187$	−23413.8	+	56525.9i	−0.669559	+	1.61646i
$188$		0			0
$189$	2077.05	+	5014.45i	0.0581466	+	0.140378i
$190$		0			0
$191$		−	21269.5i		−	0.583030i	−0.956566	−	0.291515i	$-0.905841\pi$
$191$		−	21269.5i		−	0.583030i	0.956566	−	0.291515i	$-0.0941593\pi$
$192$		0			0
$193$	−46955.0			−1.26057			−0.630285	−	0.776364i	$-0.717062\pi$
$193$	−46955.0			−1.26057			−0.630285	+	0.776364i	$0.717062\pi$
$194$		0			0
$195$	94905.8	−	39311.3i	2.49588	−	1.03383i
$196$		0			0
$197$	−51034.7	−	21139.2i	−1.31502	−	0.544700i	−0.388676	−	0.921375i	$-0.627067\pi$
$197$	−51034.7	−	21139.2i	−1.31502	−	0.544700i	−0.926345	+	0.376675i	$0.877067\pi$
$198$		0			0
$199$	−5766.67	+	5766.67i	−0.145619	+	0.145619i	−0.776158	−	0.630539i	$-0.782834\pi$
$199$	−5766.67	+	5766.67i	−0.145619	+	0.145619i	0.630539	+	0.776158i	$0.282834\pi$
$200$		0			0
$201$	−1420.09	+	1420.09i	−0.0351498	+	0.0351498i
$202$		0			0
$203$	11128.7	+	4609.64i	0.270054	+	0.111860i
$204$		0			0
$205$	−40466.6	+	16761.8i	−0.962917	+	0.398853i
$206$		0			0
$207$	31554.7			0.736417
$208$		0			0
$209$		−	35866.8i		−	0.821107i
$210$		0			0
$211$	27079.1	+	65374.7i	0.608231	+	1.46840i	0.864922	+	0.501907i	$0.167368\pi$
$211$	27079.1	+	65374.7i	0.608231	+	1.46840i	−0.256690	+	0.966494i	$0.582632\pi$
$212$		0			0
$213$	−33016.0	+	79707.8i	−0.727723	+	1.75688i
$214$		0			0
$215$	59406.4	+	59406.4i	1.28516	+	1.28516i
$216$		0			0
$217$	16486.3	+	16486.3i	0.350110	+	0.350110i
$218$		0			0
$219$	34906.1	−	84270.7i	0.727801	−	1.75707i
$220$		0			0
$221$	30791.4	+	74337.1i	0.630442	+	1.52202i
$222$		0			0
$223$			1531.57i			0.0307983i	0.999881	+	0.0153992i	$0.00490190\pi$
$223$			1531.57i			0.0307983i	−0.999881	+	0.0153992i	$0.995098\pi$
$224$		0			0
$225$	94886.7			1.87431
$226$		0			0
$227$	−10427.0	+	4319.02i	−0.202353	+	0.0838172i	−0.481558	−	0.876414i	$-0.659929\pi$
$227$	−10427.0	+	4319.02i	−0.202353	+	0.0838172i	0.279205	+	0.960231i	$0.409929\pi$
$228$		0			0
$229$	−6003.50	−	2486.73i	−0.114481	−	0.0474196i	0.324708	−	0.945814i	$-0.394734\pi$
$229$	−6003.50	−	2486.73i	−0.114481	−	0.0474196i	−0.439189	+	0.898395i	$0.644734\pi$
$230$		0			0
$231$	31965.3	−	31965.3i	0.599039	−	0.599039i
$232$		0			0
$233$	57796.3	−	57796.3i	1.06461	−	1.06461i	0.0668415	−	0.997764i	$-0.478708\pi$
$233$	57796.3	−	57796.3i	1.06461	−	1.06461i	0.997764	−	0.0668415i	$-0.0212922\pi$
$234$		0			0
$235$	−36483.3	−	15111.9i	−0.660630	−	0.273642i
$236$		0			0
$237$	62036.3	−	25696.3i	1.10446	−	0.457482i
$238$		0			0
$239$	−16773.4			−0.293646			−0.146823	−	0.989163i	$-0.546905\pi$
$239$	−16773.4			−0.293646			−0.146823	+	0.989163i	$0.546905\pi$
$240$		0			0
$241$			45067.0i			0.775933i	0.921673	+	0.387967i	$0.126822\pi$
$241$			45067.0i			0.775933i	−0.921673	+	0.387967i	$0.873178\pi$
$242$		0			0
$243$	32062.9	+	77406.6i	0.542988	+	1.31089i
$244$		0			0
$245$	28502.8	−	68811.9i	0.474849	−	1.14639i
$246$		0			0
$247$	−33353.0	−	33353.0i	−0.546690	−	0.546690i
$248$		0			0
$249$	31406.2	+	31406.2i	0.506544	+	0.506544i
$250$		0			0
$251$	30548.0	−	73749.4i	0.484881	−	1.17061i	−0.472383	−	0.881393i	$-0.656606\pi$
$251$	30548.0	−	73749.4i	0.484881	−	1.17061i	0.957265	−	0.289214i	$-0.0933939\pi$
$252$		0			0
$253$	−17923.0	−	43269.9i	−0.280007	−	0.675996i
$254$		0			0
$255$			223305.i			3.43414i
$256$		0			0
$257$	95099.7			1.43983			0.719917	−	0.694060i	$-0.244180\pi$
$257$	95099.7			1.43983			0.719917	+	0.694060i	$0.244180\pi$
$258$		0			0
$259$	23392.6	−	9689.54i	0.348722	−	0.144445i
$260$		0			0
$261$	−47567.2	−	19703.0i	−0.698275	−	0.289235i
$262$		0			0
$263$	54332.1	−	54332.1i	0.785498	−	0.785498i	−0.195254	−	0.980753i	$-0.562553\pi$
$263$	54332.1	−	54332.1i	0.785498	−	0.785498i	0.980753	+	0.195254i	$0.0625533\pi$
$264$		0			0
$265$	−121731.	+	121731.i	−1.73344	+	1.73344i
$266$		0			0
$267$	−60948.3	−	25245.6i	−0.854947	−	0.354131i
$268$		0			0
$269$	26442.2	−	10952.7i	0.365421	−	0.151362i	−0.192415	−	0.981314i	$-0.561632\pi$
$269$	26442.2	−	10952.7i	0.365421	−	0.151362i	0.557836	+	0.829951i	$0.311632\pi$
$270$		0			0
$271$	−98455.5			−1.34061			−0.670303	−	0.742087i	$-0.733836\pi$
$271$	−98455.5			−1.34061			−0.670303	+	0.742087i	$0.733836\pi$
$272$		0			0
$273$		−	59450.0i		−	0.797676i
$274$		0			0
$275$	−53895.3	−	130115.i	−0.712665	−	1.72053i
$276$		0			0
$277$	−29781.0	+	71897.6i	−0.388132	+	0.937033i	0.602204	+	0.798342i	$0.294289\pi$
$277$	−29781.0	+	71897.6i	−0.388132	+	0.937033i	−0.990336	+	0.138691i	$0.955711\pi$
$278$		0			0
$279$	−70467.5	−	70467.5i	−0.905274	−	0.905274i
$280$		0			0
$281$	−78358.3	−	78358.3i	−0.992368	−	0.992368i	0.00760335	−	0.999971i	$-0.497580\pi$
$281$	−78358.3	−	78358.3i	−0.992368	−	0.992368i	−0.999971	+	0.00760335i	$0.997580\pi$
$282$		0			0
$283$	−32370.2	+	78148.7i	−0.404178	+	0.975773i	0.582462	+	0.812858i	$0.302090\pi$
$283$	−32370.2	+	78148.7i	−0.404178	+	0.975773i	−0.986640	+	0.162915i	$0.947910\pi$
$284$		0			0
$285$	−50095.3	−	120941.i	−0.616748	−	1.48896i
$286$		0			0
$287$			25348.7i			0.307746i
$288$		0			0
$289$	−91387.3			−1.09418
$290$		0			0
$291$	−115372.	+	47788.8i	−1.36244	+	0.564339i
$292$		0			0
$293$	−93442.7	−	38705.2i	−1.08845	−	0.450852i	−0.234987	−	0.971999i	$-0.575505\pi$
$293$	−93442.7	−	38705.2i	−1.08845	−	0.450852i	−0.853467	+	0.521146i	$0.825505\pi$
$294$		0			0
$295$	−46318.4	+	46318.4i	−0.532242	+	0.532242i
$296$		0			0
$297$	−24348.0	+	24348.0i	−0.276027	+	0.276027i
$298$		0			0
$299$	−56904.0	−	23570.4i	−0.636503	−	0.263648i
$300$		0			0
$301$	44919.8	−	18606.4i	0.495798	−	0.205366i
$302$		0			0
$303$	85521.5			0.931515
$304$		0			0
$305$			62960.7i			0.676815i
$306$		0			0
$307$	−18027.1	−	43521.3i	−0.191271	−	0.461769i	0.798929	−	0.601425i	$-0.205400\pi$
$307$	−18027.1	−	43521.3i	−0.191271	−	0.461769i	−0.990200	+	0.139656i	$0.955400\pi$
$308$		0			0
$309$	40932.1	−	98818.9i	0.428694	−	1.03496i
$310$		0			0
$311$	37400.0	+	37400.0i	0.386679	+	0.386679i	0.873501	−	0.486822i	$-0.161844\pi$
$311$	37400.0	+	37400.0i	0.386679	+	0.386679i	−0.486822	+	0.873501i	$0.661844\pi$
$312$		0			0
$313$	18300.2	+	18300.2i	0.186796	+	0.186796i	0.794309	−	0.607513i	$-0.207833\pi$
$313$	18300.2	+	18300.2i	0.186796	+	0.186796i	−0.607513	+	0.794309i	$0.707833\pi$
$314$		0			0
$315$	34657.7	−	83671.1i	0.349284	−	0.843246i
$316$		0			0
$317$	58606.2	+	141488.i	0.583210	+	1.40799i	0.889888	+	0.456180i	$0.150783\pi$
$317$	58606.2	+	141488.i	0.583210	+	1.40799i	−0.306678	+	0.951813i	$0.599217\pi$
$318$		0			0
$319$			76418.4i			0.750960i
$320$		0			0
$321$	219408.			2.12933
$322$		0			0
$323$	94729.6	−	39238.3i	0.907989	−	0.376101i
$324$		0			0
$325$	−171113.	−	70877.5i	−1.62001	−	0.671030i
$326$		0			0
$327$	26100.1	−	26100.1i	0.244089	−	0.244089i
$328$		0			0
$329$	−16159.9	+	16159.9i	−0.149295	+	0.149295i
$330$		0			0
$331$	11038.4	+	4572.25i	0.100751	+	0.0417325i	0.432490	−	0.901639i	$-0.357635\pi$
$331$	11038.4	+	4572.25i	0.100751	+	0.0417325i	−0.331739	+	0.943371i	$0.607635\pi$
$332$		0			0
$333$	−99987.1	+	41416.0i	−0.901686	+	0.373491i
$334$		0			0
$335$	5971.75			0.0532123
$336$		0			0
$337$		−	3639.07i		−	0.0320428i	−0.999872	−	0.0160214i	$-0.994900\pi$
$337$		−	3639.07i		−	0.0320428i	0.999872	−	0.0160214i	$-0.00509999\pi$
$338$		0			0
$339$	3801.65	+	9178.00i	0.0330806	+	0.0798635i
$340$		0			0
$341$	−56604.3	+	136655.i	−0.486789	+	1.17521i
$342$		0			0
$343$	−69629.6	−	69629.6i	−0.591842	−	0.591842i
$344$		0			0
$345$	−120871.	−	120871.i	−1.01551	−	1.01551i
$346$		0			0
$347$	−25855.6	+	62420.8i	−0.214731	+	0.518407i	−0.994139	−	0.108110i	$-0.965520\pi$
$347$	−25855.6	+	62420.8i	−0.214731	+	0.518407i	0.779408	+	0.626517i	$0.215520\pi$
$348$		0			0
$349$	47656.2	+	115052.i	0.391263	+	0.944592i	0.989665	+	0.143396i	$0.0458023\pi$
$349$	47656.2	+	115052.i	0.391263	+	0.944592i	−0.598403	+	0.801196i	$0.704198\pi$
$350$		0			0
$351$			45283.2i			0.367555i
$352$		0			0
$353$	130506.			1.04732			0.523661	−	0.851927i	$-0.324566\pi$
$353$	130506.			1.04732			0.523661	+	0.851927i	$0.324566\pi$
$354$		0			0
$355$	237013.	−	98174.0i	1.88068	−	0.779004i
$356$		0			0
$357$	119395.	+	49455.2i	0.936809	+	0.388039i
$358$		0			0
$359$	−23242.9	+	23242.9i	−0.180344	+	0.180344i	−0.791506	−	0.611162i	$-0.790702\pi$
$359$	−23242.9	+	23242.9i	−0.180344	+	0.180344i	0.611162	+	0.791506i	$0.290702\pi$
$360$		0			0
$361$	49648.3	−	49648.3i	0.380969	−	0.380969i
$362$		0			0
$363$	83702.3	+	34670.6i	0.635220	+	0.263117i
$364$		0			0
$365$	−250581.	+	103794.i	−1.88089	+	0.779089i
$366$		0			0
$367$	−27798.5			−0.206391			−0.103195	−	0.994661i	$-0.532907\pi$
$367$	−27798.5			−0.206391			−0.103195	+	0.994661i	$0.532907\pi$
$368$		0			0
$369$		−	108348.i		−	0.795734i
$370$		0			0
$371$	38126.8	+	92046.3i	0.277002	+	0.668742i
$372$		0			0
$373$	68701.6	−	165860.i	0.493798	−	1.19213i	−0.458975	−	0.888449i	$-0.651783\pi$
$373$	68701.6	−	165860.i	0.493798	−	1.19213i	0.952773	−	0.303684i	$-0.0982166\pi$
$374$		0			0
$375$	−127494.	−	127494.i	−0.906621	−	0.906621i
$376$		0			0
$377$	71062.6	+	71062.6i	0.499986	+	0.499986i
$378$		0			0
$379$	−30582.0	+	73831.5i	−0.212906	+	0.514000i	−0.993867	−	0.110579i	$-0.964730\pi$
$379$	−30582.0	+	73831.5i	−0.212906	+	0.514000i	0.780961	+	0.624579i	$0.214730\pi$
$380$		0			0
$381$	17957.8	+	43354.0i	0.123709	+	0.298661i
$382$		0			0
$383$		−	151316.i		−	1.03154i	−0.856727	−	0.515770i	$-0.827506\pi$
$383$		−	151316.i		−	1.03154i	0.856727	−	0.515770i	$-0.172494\pi$
$384$		0			0
$385$	−134421.			−0.906869
$386$		0			0
$387$	−192001.	+	79529.3i	−1.28198	+	0.531013i
$388$		0			0
$389$	44293.8	+	18347.1i	0.292714	+	0.121246i	0.524208	−	0.851590i	$-0.324361\pi$
$389$	44293.8	+	18347.1i	0.292714	+	0.121246i	−0.231494	+	0.972836i	$0.574361\pi$
$390$		0			0
$391$	94674.5	−	94674.5i	0.619269	−	0.619269i
$392$		0			0
$393$	−215936.	+	215936.i	−1.39810	+	1.39810i
$394$		0			0
$395$	−184467.	−	76408.6i	−1.18229	−	0.489720i
$396$		0			0
$397$	213580.	−	88467.7i	1.35512	−	0.561311i	0.417411	−	0.908718i	$-0.362938\pi$
$397$	213580.	−	88467.7i	1.35512	−	0.561311i	0.937714	+	0.347407i	$0.112938\pi$
$398$		0			0
$399$	−75758.6			−0.475868
$400$		0			0
$401$		−	56323.0i		−	0.350265i	−0.984545	−	0.175133i	$-0.943965\pi$
$401$		−	56323.0i		−	0.350265i	0.984545	−	0.175133i	$-0.0560354\pi$
$402$		0			0
$403$	74440.1	+	179714.i	0.458350	+	1.10655i
$404$		0			0
$405$	73645.4	−	177796.i	0.448989	−	1.08395i
$406$		0			0
$407$	113585.	+	113585.i	0.685694	+	0.685694i
$408$		0			0
$409$	33902.3	+	33902.3i	0.202667	+	0.202667i	0.801142	−	0.598475i	$-0.204226\pi$
$409$	33902.3	+	33902.3i	0.202667	+	0.202667i	−0.598475	+	0.801142i	$0.704226\pi$
$410$		0			0
$411$	−71689.0	+	173073.i	−0.424394	+	1.02458i
$412$		0			0
$413$	14507.2	+	35023.4i	0.0850516	+	0.205333i
$414$		0			0
$415$		−	132069.i		−	0.766843i
$416$		0			0
$417$	−297144.			−1.70881
$418$		0			0
$419$	196155.	−	81250.0i	1.11730	−	0.462802i	0.253857	−	0.967242i	$-0.418301\pi$
$419$	196155.	−	81250.0i	1.11730	−	0.462802i	0.863447	+	0.504440i	$0.168301\pi$
$420$		0			0
$421$	204610.	+	84752.3i	1.15442	+	0.478175i	0.876012	−	0.482288i	$-0.160194\pi$
$421$	204610.	+	84752.3i	1.15442	+	0.478175i	0.278405	+	0.960464i	$0.410194\pi$
$422$		0			0
$423$	69072.1	−	69072.1i	0.386031	−	0.386031i
$424$		0			0
$425$	284691.	−	284691.i	1.57615	−	1.57615i
$426$		0			0
$427$	33663.5	+	13943.9i	0.184631	+	0.0764765i
$428$		0			0
$429$	348448.	−	144332.i	1.89332	−	0.784238i
$430$		0			0
$431$	137568.			0.740565			0.370282	−	0.928919i	$-0.379261\pi$
$431$	137568.			0.740565			0.370282	+	0.928919i	$0.379261\pi$
$432$		0			0
$433$		−	260727.i		−	1.39063i	−0.718707	−	0.695313i	$-0.755266\pi$
$433$		−	260727.i		−	1.39063i	0.718707	−	0.695313i	$-0.244734\pi$
$434$		0			0
$435$	106734.	+	257679.i	0.564059	+	1.36176i
$436$		0			0
$437$	−30036.4	+	72514.2i	−0.157284	+	0.379717i
$438$		0			0
$439$	251147.	+	251147.i	1.30316	+	1.30316i	0.926249	+	0.376912i	$0.123014\pi$
$439$	251147.	+	251147.i	1.30316	+	1.30316i	0.376912	+	0.926249i	$0.376986\pi$
$440$		0			0
$441$	130278.	+	130278.i	0.669877	+	0.669877i
$442$		0			0
$443$	75747.5	−	182871.i	0.385977	−	0.931830i	−0.604807	−	0.796372i	$-0.706750\pi$
$443$	75747.5	−	182871.i	0.385977	−	0.931830i	0.990783	−	0.135458i	$-0.0432504\pi$
$444$		0			0
$445$	75068.5	+	181231.i	0.379086	+	0.915194i
$446$		0			0
$447$		−	413081.i		−	2.06738i
$448$		0			0
$449$	−381454.			−1.89212			−0.946061	−	0.323987i	$-0.894976\pi$
$449$	−381454.			−1.89212			−0.946061	+	0.323987i	$0.894976\pi$
$450$		0			0
$451$	−148574.	+	61541.2i	−0.730447	+	0.302561i
$452$		0			0
$453$	−5641.03	−	2336.59i	−0.0274892	−	0.0113864i
$454$		0			0
$455$	−125000.	+	125000.i	−0.603790	+	0.603790i
$456$		0			0
$457$	44442.2	−	44442.2i	0.212796	−	0.212796i	−0.592658	−	0.805454i	$-0.701921\pi$
$457$	44442.2	−	44442.2i	0.212796	−	0.212796i	0.805454	+	0.592658i	$0.201921\pi$
$458$		0			0
$459$	−90943.6	−	37670.1i	−0.431665	−	0.178802i
$460$		0			0
$461$	38697.8	−	16029.1i	0.182089	−	0.0754238i	−0.289776	−	0.957094i	$-0.593581\pi$
$461$	38697.8	−	16029.1i	0.182089	−	0.0754238i	0.471865	+	0.881671i	$0.343581\pi$
$462$		0			0
$463$	−242418.			−1.13085			−0.565423	−	0.824801i	$-0.691287\pi$
$463$	−242418.			−1.13085			−0.565423	+	0.824801i	$0.691287\pi$
$464$		0			0
$465$			539852.i			2.49671i
$466$		0			0
$467$	−91180.2	−	220128.i	−0.418087	−	1.00935i	−0.982901	−	0.184133i	$-0.941052\pi$
$467$	−91180.2	−	220128.i	−0.418087	−	1.00935i	0.564814	−	0.825218i	$-0.308948\pi$
$468$		0			0
$469$	1322.56	−	3192.94i	0.00601271	−	0.0145160i
$470$		0			0
$471$	91936.2	+	91936.2i	0.414424	+	0.414424i
$472$		0			0
$473$	218111.	+	218111.i	0.974891	+	0.974891i
$474$		0			0
$475$	−90321.0	+	218054.i	−0.400315	+	0.966445i
$476$		0			0
$477$	−162966.	−	393434.i	−0.716241	−	1.72916i
$478$		0			0
$479$			288697.i			1.25826i	0.777299	+	0.629131i	$0.216589\pi$
$479$			288697.i			1.25826i	−0.777299	+	0.629131i	$0.783411\pi$
$480$		0			0
$481$	211248.			0.913065
$482$		0			0
$483$	−91395.6	+	37857.3i	−0.391770	+	0.162276i
$484$		0			0
$485$	343063.	+	142101.i	1.45844	+	0.604108i
$486$		0			0
$487$	121674.	−	121674.i	0.513026	−	0.513026i	−0.402426	−	0.915452i	$-0.631833\pi$
$487$	121674.	−	121674.i	0.513026	−	0.513026i	0.915452	+	0.402426i	$0.131833\pi$
$488$		0			0
$489$	−230224.	+	230224.i	−0.962793	+	0.962793i
$490$		0			0
$491$	244513.	+	101280.i	1.01423	+	0.420110i	0.826998	−	0.562205i	$-0.190047\pi$
$491$	244513.	+	101280.i	1.01423	+	0.420110i	0.187237	+	0.982315i	$0.440047\pi$
$492$		0			0
$493$	−201833.	+	83601.8i	−0.830420	+	0.343971i
$494$		0			0
$495$	574554.			2.34488
$496$		0			0
$497$		−	148467.i		−	0.601061i
$498$		0			0
$499$	−153204.	−	369867.i	−0.615275	−	1.48540i	−0.857134	−	0.515093i	$-0.827757\pi$
$499$	−153204.	−	369867.i	−0.615275	−	1.48540i	0.241859	−	0.970311i	$-0.422243\pi$
$500$		0			0
$501$	−99386.3	+	239940.i	−0.395960	+	0.955932i
$502$		0			0
$503$	−22792.5	−	22792.5i	−0.0900857	−	0.0900857i	0.660628	−	0.750714i	$-0.270290\pi$
$503$	−22792.5	−	22792.5i	−0.0900857	−	0.0900857i	−0.750714	+	0.660628i	$0.770290\pi$
$504$		0			0
$505$	−179817.	−	179817.i	−0.705097	−	0.705097i
$506$		0			0
$507$	43349.0	−	104654.i	0.168641	−	0.407135i
$508$		0			0
$509$	−155453.	−	375296.i	−0.600016	−	1.44857i	−0.873565	−	0.486708i	$-0.838198\pi$
$509$	−155453.	−	375296.i	−0.600016	−	1.44857i	0.273549	−	0.961858i	$-0.411802\pi$
$510$		0			0
$511$			156967.i			0.601126i
$512$		0			0
$513$	57705.5			0.219271
$514$		0			0
$515$	−293840.	+	121713.i	−1.10789	+	0.458903i
$516$		0			0
$517$	−133949.	−	55483.4i	−0.501139	−	0.207578i
$518$		0			0
$519$	−227415.	+	227415.i	−0.844277	+	0.844277i
$520$		0			0
$521$	154254.	−	154254.i	0.568279	−	0.568279i	−0.363367	−	0.931646i	$-0.618373\pi$
$521$	154254.	−	154254.i	0.568279	−	0.568279i	0.931646	+	0.363367i	$0.118373\pi$
$522$		0			0
$523$	147061.	+	60914.8i	0.537644	+	0.222700i	0.634948	−	0.772555i	$-0.281022\pi$
$523$	147061.	+	60914.8i	0.537644	+	0.222700i	−0.0973032	+	0.995255i	$0.531022\pi$
$524$		0			0
$525$	−274831.	+	113839.i	−0.997120	+	0.413021i
$526$		0			0
$527$	−422851.			−1.52253
$528$		0			0
$529$		−	177350.i		−	0.633753i
$530$		0			0
$531$	−62008.0	−	149701.i	−0.219917	−	0.530926i
$532$		0			0
$533$	−80932.7	+	195389.i	−0.284885	+	0.687773i
$534$		0			0
$535$	−461328.	−	461328.i	−1.61177	−	1.61177i
$536$		0			0
$537$	−567922.	−	567922.i	−1.96943	−	1.96943i
$538$		0			0
$539$	104648.	−	252644.i	0.360210	−	0.869623i
$540$		0			0
$541$	130723.	+	315593.i	0.446640	+	1.07828i	0.973573	+	0.228377i	$0.0733418\pi$
$541$	130723.	+	315593.i	0.446640	+	1.07828i	−0.526933	+	0.849907i	$0.676658\pi$
$542$		0			0
$543$		−	624648.i		−	2.11854i
$544$		0			0
$545$	−109756.			−0.369519
$546$		0			0
$547$	78375.9	−	32464.4i	0.261944	−	0.108501i	−0.247847	−	0.968799i	$-0.579723\pi$
$547$	78375.9	−	32464.4i	0.261944	−	0.108501i	0.509790	+	0.860299i	$0.329723\pi$
$548$		0			0
$549$	−143888.	−	59600.3i	−0.477397	−	0.197744i
$550$		0			0
$551$	90556.8	−	90556.8i	0.298276	−	0.298276i
$552$		0			0
$553$	−81707.5	+	81707.5i	−0.267185	+	0.267185i
$554$		0			0
$555$	541645.	+	224357.i	1.75845	+	0.728372i
$556$		0			0
$557$	−161400.	+	66854.2i	−0.520228	+	0.215486i	−0.627317	−	0.778764i	$-0.715847\pi$
$557$	−161400.	+	66854.2i	−0.520228	+	0.215486i	0.107089	+	0.994249i	$0.465847\pi$
$558$		0			0
$559$	405650.			1.29816
$560$		0			0
$561$			819866.i			2.60506i
$562$		0			0
$563$	130682.	+	315495.i	0.412287	+	0.995350i	0.984522	+	0.175260i	$0.0560766\pi$
$563$	130682.	+	315495.i	0.412287	+	0.995350i	−0.572235	+	0.820090i	$0.693923\pi$
$564$		0			0
$565$	11304.3	−	27291.0i	0.0354117	−	0.0854914i
$566$		0			0
$567$	−78752.6	−	78752.6i	−0.244962	−	0.244962i
$568$		0			0
$569$	−290588.	−	290588.i	−0.897537	−	0.897537i	0.0976805	−	0.995218i	$-0.468858\pi$
$569$	−290588.	−	290588.i	−0.897537	−	0.897537i	−0.995218	+	0.0976805i	$0.968858\pi$
$570$		0			0
$571$	2140.61	−	5167.90i	0.00656547	−	0.0158505i	−0.920563	−	0.390595i	$-0.872269\pi$
$571$	2140.61	−	5167.90i	0.00656547	−	0.0158505i	0.927128	+	0.374744i	$0.122269\pi$
$572$		0			0
$573$	−109071.	−	263320.i	−0.332199	−	0.801999i
$574$		0			0
$575$			308196.i			0.932161i
$576$		0			0
$577$	154494.			0.464046			0.232023	−	0.972710i	$-0.425466\pi$
$577$	154494.			0.464046			0.232023	+	0.972710i	$0.425466\pi$
$578$		0			0
$579$	−581310.	+	240786.i	−1.73401	+	0.718249i
$580$		0			0
$581$	−70614.2	−	29249.4i	−0.209190	−	0.0866491i
$582$		0			0
$583$	−446938.	+	446938.i	−1.31495	+	1.31495i
$584$		0			0
$585$	534286.	−	534286.i	1.56121	−	1.56121i
$586$		0			0
$587$	−297544.	−	123247.i	−0.863525	−	0.357684i	−0.0934400	−	0.995625i	$-0.529786\pi$
$587$	−297544.	−	123247.i	−0.863525	−	0.357684i	−0.770085	+	0.637941i	$0.779786\pi$
$588$		0			0
$589$	229014.	−	94860.9i	0.660134	−	0.273436i
$590$		0			0
$591$	−740219.			−2.11927
$592$		0			0
$593$		−	60087.1i		−	0.170872i	−0.996344	−	0.0854362i	$-0.972772\pi$
$593$		−	60087.1i		−	0.170872i	0.996344	−	0.0854362i	$-0.0272284\pi$
$594$		0			0
$595$	−147056.	−	355025.i	−0.415384	−	1.00283i
$596$		0			0
$597$	−41820.6	+	100964.i	−0.117339	+	0.283281i
$598$		0			0
$599$	204917.	+	204917.i	0.571117	+	0.571117i	0.932440	−	0.361324i	$-0.117675\pi$
$599$	204917.	+	204917.i	0.571117	+	0.571117i	−0.361324	+	0.932440i	$0.617675\pi$
$600$		0			0
$601$	465471.	+	465471.i	1.28868	+	1.28868i	0.935591	+	0.353085i	$0.114867\pi$
$601$	465471.	+	465471.i	1.28868	+	1.28868i	0.353085	+	0.935591i	$0.385133\pi$
$602$		0			0
$603$	−5653.02	+	13647.6i	−0.0155470	+	0.0375337i
$604$		0			0
$605$	−103094.	−	248891.i	−0.281658	−	0.679983i
$606$		0			0
$607$		−	177108.i		−	0.480684i	−0.970688	−	0.240342i	$-0.922740\pi$
$607$		−	177108.i		−	0.480684i	0.970688	−	0.240342i	$-0.0772596\pi$
$608$		0			0
$609$	161413.			0.435214
$610$		0			0
$611$	−176156.	+	72966.1i	−0.471861	+	0.195451i
$612$		0			0
$613$	−371444.	−	153857.i	−0.988492	−	0.409447i	−0.170927	−	0.985284i	$-0.554676\pi$
$613$	−371444.	−	153857.i	−0.988492	−	0.409447i	−0.817564	+	0.575837i	$0.804676\pi$
$614$		0			0
$615$	−415027.	+	415027.i	−1.09730	+	1.09730i
$616$		0			0
$617$	272431.	−	272431.i	0.715627	−	0.715627i	−0.252080	−	0.967706i	$-0.581114\pi$
$617$	272431.	−	272431.i	0.715627	−	0.715627i	0.967706	+	0.252080i	$0.0811145\pi$
$618$		0			0
$619$	456310.	+	189010.i	1.19091	+	0.493291i	0.888051	−	0.459745i	$-0.152059\pi$
$619$	456310.	+	189010.i	1.19091	+	0.493291i	0.302858	+	0.953036i	$0.402059\pi$
$620$		0			0
$621$	69616.1	−	28835.9i	0.180521	−	0.0747741i
$622$		0			0
$623$	113525.			0.292494
$624$		0			0
$625$		−	65541.8i		−	0.167787i
$626$		0			0
$627$	−183926.	−	444036.i	−0.467851	−	1.12949i
$628$		0			0
$629$	−175732.	+	424256.i	−0.444171	+	1.07232i
$630$		0			0
$631$	−82866.7	−	82866.7i	−0.208124	−	0.208124i	0.595346	−	0.803470i	$-0.297015\pi$
$631$	−82866.7	−	82866.7i	−0.208124	−	0.208124i	−0.803470	+	0.595346i	$0.797015\pi$
$632$		0			0
$633$	670486.	+	670486.i	1.67333	+	1.67333i
$634$		0			0
$635$	53397.9	−	128914.i	0.132427	−	0.319707i
$636$		0			0
$637$	−137623.	−	332251.i	−0.339166	−	0.818818i
$638$		0			0
$639$			634595.i			1.55416i
$640$		0			0
$641$	188338.			0.458375			0.229188	−	0.973382i	$-0.426393\pi$
$641$	188338.			0.458375			0.229188	+	0.973382i	$0.426393\pi$
$642$		0			0
$643$	624590.	−	258714.i	1.51068	−	0.625745i	0.534984	−	0.844862i	$-0.320318\pi$
$643$	624590.	−	258714.i	1.51068	−	0.625745i	0.975699	+	0.219117i	$0.0703175\pi$
$644$		0			0
$645$	1.04010e6	+	430822.i	2.50008	+	1.03557i
$646$		0			0
$647$	370379.	−	370379.i	0.884786	−	0.884786i	−0.109230	−	0.994016i	$-0.534839\pi$
$647$	370379.	−	370379.i	0.884786	−	0.884786i	0.994016	+	0.109230i	$0.0348386\pi$
$648$		0			0
$649$	−170059.	+	170059.i	−0.403747	+	0.403747i
$650$		0			0
$651$	288645.	+	119561.i	0.681087	+	0.282115i
$652$		0			0
$653$	−409913.	+	169792.i	−0.961315	+	0.398190i	−0.807472	−	0.589906i	$-0.799165\pi$
$653$	−409913.	+	169792.i	−0.961315	+	0.398190i	−0.153843	+	0.988095i	$0.549165\pi$
$654$		0			0
$655$	908053.			2.11655
$656$		0			0
$657$		−	670922.i		−	1.55432i
$658$		0			0
$659$	−75158.6	−	181449.i	−0.173064	−	0.417815i	0.813418	−	0.581679i	$-0.197604\pi$
$659$	−75158.6	−	181449.i	−0.173064	−	0.417815i	−0.986483	+	0.163864i	$0.947604\pi$
$660$		0			0
$661$	−9304.81	+	22463.8i	−0.0212963	+	0.0514139i	−0.934170	−	0.356828i	$-0.883858\pi$
$661$	−9304.81	+	22463.8i	−0.0212963	+	0.0514139i	0.912874	+	0.408242i	$0.133858\pi$
$662$		0			0
$663$	762405.	+	762405.i	1.73444	+	1.73444i
$664$		0			0
$665$	159290.	+	159290.i	0.360201	+	0.360201i
$666$		0			0
$667$	63996.1	−	154500.i	0.143847	−	0.347278i
$668$		0			0
$669$	7853.94	+	18961.1i	0.0175483	+	0.0423653i
$670$		0			0
$671$			231161.i			0.513417i
$672$		0			0
$673$	−204886.			−0.452357			−0.226179	−	0.974086i	$-0.572623\pi$
$673$	−204886.			−0.452357			−0.226179	+	0.974086i	$0.572623\pi$
$674$		0			0
$675$	209339.	−	86711.2i	0.459455	−	0.190313i
$676$		0			0
$677$	−583755.	−	241799.i	−1.27366	−	0.527567i	−0.359585	−	0.933112i	$-0.617082\pi$
$677$	−583755.	−	241799.i	−1.27366	−	0.527567i	−0.914075	+	0.405545i	$0.867082\pi$
$678$		0			0
$679$	151956.	−	151956.i	0.329593	−	0.329593i
$680$		0			0
$681$	−106940.	+	106940.i	−0.230593	+	0.230593i
$682$		0			0
$683$	−761421.	−	315391.i	−1.63224	−	0.676095i	−0.636758	−	0.771064i	$-0.719725\pi$
$683$	−761421.	−	315391.i	−1.63224	−	0.676095i	−0.995480	+	0.0949686i	$0.969725\pi$
$684$		0			0
$685$	514636.	−	213169.i	1.09678	−	0.454300i
$686$		0			0
$687$	−87076.2			−0.184496
$688$		0			0
$689$			831227.i			1.75098i
$690$		0			0
$691$	185943.	+	448905.i	0.389424	+	0.940153i	0.990062	+	0.140632i	$0.0449133\pi$
$691$	185943.	+	448905.i	0.389424	+	0.940153i	−0.600638	+	0.799521i	$0.705087\pi$
$692$		0			0
$693$	127246.	−	307200.i	0.264959	−	0.639667i
$694$		0			0
$695$	624775.	+	624775.i	1.29346	+	1.29346i
$696$		0			0
$697$	−325079.	−	325079.i	−0.669151	−	0.669151i
$698$		0			0
$699$	419146.	−	1.01191e6i	0.857850	−	2.07103i
$700$		0			0
$701$	−113206.	−	273303.i	−0.230373	−	0.556171i	0.765848	−	0.643022i	$-0.222320\pi$
$701$	−113206.	−	273303.i	−0.230373	−	0.556171i	−0.996221	+	0.0868511i	$0.972320\pi$
$702$		0			0
$703$		−	269198.i		−	0.544705i
$704$		0			0
$705$	−529162.			−1.06466
$706$		0			0
$707$	−135968.	+	56319.8i	−0.272018	+	0.112674i
$708$		0			0
$709$	97245.4	+	40280.4i	0.193454	+	0.0801311i	0.477307	−	0.878737i	$-0.341613\pi$
$709$	97245.4	+	40280.4i	0.193454	+	0.0801311i	−0.283854	+	0.958868i	$0.591613\pi$
$710$		0			0
$711$	349242.	−	349242.i	0.690856	−	0.690856i
$712$		0			0
$713$	228881.	−	228881.i	0.450226	−	0.450226i
$714$		0			0
$715$	−1.03612e6	−	429175.i	−2.02674	−	0.839502i
$716$		0			0
$717$	−207657.	+	86014.2i	−0.403931	+	0.167314i
$718$		0			0
$719$	−851086.			−1.64632			−0.823162	−	0.567806i	$-0.807792\pi$
$719$	−851086.			−1.64632			−0.823162	+	0.567806i	$0.807792\pi$
$720$		0			0
$721$			184065.i			0.354079i
$722$		0			0
$723$	231105.	+	557936.i	0.442112	+	1.06735i
$724$		0			0
$725$	192440.	−	464590.i	0.366116	−	0.883882i
$726$		0			0
$727$	−365011.	−	365011.i	−0.690617	−	0.690617i	0.271750	−	0.962368i	$-0.412397\pi$
$727$	−365011.	−	365011.i	−0.690617	−	0.690617i	−0.962368	+	0.271750i	$0.912397\pi$
$728$		0			0
$729$	517260.	+	517260.i	0.973316	+	0.973316i
$730$		0			0
$731$	−337451.	+	814679.i	−0.631504	+	1.52459i
$732$		0			0
$733$	145700.	+	351750.i	0.271176	+	0.654676i	0.999534	−	0.0305205i	$-0.00971647\pi$
$733$	145700.	+	351750.i	0.271176	+	0.654676i	−0.728359	+	0.685196i	$0.759716\pi$
$734$		0			0
$735$		−	998064.i		−	1.84750i
$736$		0			0
$737$	21925.4			0.0403656
$738$		0			0
$739$	338957.	−	140401.i	0.620663	−	0.257087i	−0.0501172	−	0.998743i	$-0.515959\pi$
$739$	338957.	−	140401.i	0.620663	−	0.257087i	0.670780	+	0.741656i	$0.265959\pi$
$740$		0			0
$741$	−583951.	−	241880.i	−1.06351	−	0.440518i
$742$		0			0
$743$	−641913.	+	641913.i	−1.16278	+	1.16278i	−0.178918	+	0.983864i	$0.557260\pi$
$743$	−641913.	+	641913.i	−1.16278	+	1.16278i	−0.983864	+	0.178918i	$0.942740\pi$
$744$		0			0
$745$	−868543.	+	868543.i	−1.56487	+	1.56487i
$746$		0			0
$747$	301826.	+	125021.i	0.540899	+	0.224048i
$748$		0			0
$749$	−348830.	+	144490.i	−0.621800	+	0.257558i
$750$		0			0
$751$	−14202.6			−0.0251819			−0.0125910	−	0.999921i	$-0.504008\pi$
$751$	−14202.6			−0.0251819			−0.0125910	+	0.999921i	$0.504008\pi$
$752$		0			0
$753$		−	1.06968e6i		−	1.88653i
$754$		0			0
$755$	6947.91	+	16773.7i	0.0121888	+	0.0294263i
$756$		0			0
$757$	108666.	−	262344.i	0.189628	−	0.457803i	−0.800260	−	0.599653i	$-0.795305\pi$
$757$	108666.	−	262344.i	0.189628	−	0.457803i	0.989888	+	0.141850i	$0.0453051\pi$
$758$		0			0
$759$	−443778.	−	443778.i	−0.770339	−	0.770339i
$760$		0			0
$761$	−152131.	−	152131.i	−0.262693	−	0.262693i	0.563454	−	0.826147i	$-0.309472\pi$
$761$	−152131.	−	152131.i	−0.262693	−	0.262693i	−0.826147	+	0.563454i	$0.809472\pi$
$762$		0			0
$763$	−24307.7	+	58683.9i	−0.0417537	+	0.100802i
$764$		0			0
$765$	628562.	+	1.51748e6i	1.07405	+	2.59299i
$766$		0			0
$767$			316280.i			0.537627i
$768$		0			0
$769$	295109.			0.499033			0.249517	−	0.968370i	$-0.419728\pi$
$769$	295109.			0.499033			0.249517	+	0.968370i	$0.419728\pi$
$770$		0			0
$771$	1.17735e6	−	487673.i	1.98060	−	0.820390i
$772$		0			0
$773$	661480.	+	273994.i	1.10703	+	0.458545i	0.859913	−	0.510441i	$-0.170518\pi$
$773$	661480.	+	273994.i	1.10703	+	0.458545i	0.247114	+	0.968987i	$0.420518\pi$
$774$		0			0
$775$	688258.	−	688258.i	1.14590	−	1.14590i
$776$		0			0
$777$	239916.	−	239916.i	0.397390	−	0.397390i
$778$		0			0
$779$	248989.	+	103135.i	0.410303	+	0.169953i
$780$		0			0
$781$	870197.	−	360447.i	1.42664	−	0.590935i
$782$		0			0
$783$	−122948.			−0.200539
$784$		0			0
$785$		−	386610.i		−	0.627384i
$786$		0			0
$787$	242362.	+	585114.i	0.391305	+	0.944694i	0.989656	+	0.143460i	$0.0458229\pi$
$787$	242362.	+	585114.i	0.391305	+	0.944694i	−0.598351	+	0.801234i	$0.704177\pi$
$788$		0			0
$789$	394023.	−	951256.i	0.632948	−	1.52807i
$790$		0			0
$791$	−12088.2	−	12088.2i	−0.0193201	−	0.0193201i
$792$		0			0
$793$	214960.	+	214960.i	0.341831	+	0.341831i
$794$		0			0
$795$	−882809.	+	2.13129e6i	−1.39680	+	3.37216i
$796$		0			0
$797$	219582.	+	530117.i	0.345684	+	0.834556i	0.997119	+	0.0758511i	$0.0241674\pi$
$797$	219582.	+	530117.i	0.345684	+	0.834556i	−0.651435	+	0.758705i	$0.725833\pi$
$798$		0			0
$799$		−	414478.i		−	0.649244i
$800$		0			0
$801$	−485241.			−0.756297
$802$		0			0
$803$	−920012.	+	381081.i	−1.42680	+	0.590999i
$804$		0			0
$805$	271767.	+	112570.i	0.419377	+	0.173712i
$806$		0			0
$807$	271193.	−	271193.i	0.416419	−	0.416419i
$808$		0			0
$809$	−4276.73	+	4276.73i	−0.00653454	+	0.00653454i	−0.710367	−	0.703832i	$-0.751471\pi$
$809$	−4276.73	+	4276.73i	−0.00653454	+	0.00653454i	0.703832	+	0.710367i	$0.251471\pi$
$810$		0			0
$811$	860159.	+	356289.i	1.30779	+	0.541703i	0.924238	−	0.381818i	$-0.124702\pi$
$811$	860159.	+	356289.i	1.30779	+	0.541703i	0.383549	+	0.923521i	$0.374702\pi$
$812$		0			0
$813$	−1.21889e6	+	504882.i	−1.84410	+	0.763852i
$814$		0			0
$815$	968137.			1.45754
$816$		0			0
$817$		−	516929.i		−	0.774439i
$818$		0			0
$819$	−167341.	−	403997.i	−0.249479	−	0.602297i
$820$		0			0
$821$	−409831.	+	989419.i	−0.608020	+	1.46789i	0.257129	+	0.966377i	$0.417223\pi$
$821$	−409831.	+	989419.i	−0.608020	+	1.46789i	−0.865150	+	0.501514i	$0.832777\pi$
$822$		0			0
$823$	−615366.	−	615366.i	−0.908518	−	0.908518i	0.0876343	−	0.996153i	$-0.472069\pi$
$823$	−615366.	−	615366.i	−0.908518	−	0.908518i	−0.996153	+	0.0876343i	$0.972069\pi$
$824$		0			0
$825$	−1.33446e6	−	1.33446e6i	−1.96064	−	1.96064i
$826$		0			0
$827$	211723.	−	511144.i	0.309568	−	0.747364i	−0.690151	−	0.723665i	$-0.742456\pi$
$827$	211723.	−	511144.i	0.309568	−	0.747364i	0.999719	−	0.0236982i	$-0.00754408\pi$
$828$		0			0
$829$	−228091.	−	550660.i	−0.331894	−	0.801262i	−0.998442	−	0.0558002i	$-0.982229\pi$
$829$	−228091.	−	550660.i	−0.331894	−	0.801262i	0.666548	−	0.745462i	$-0.267771\pi$
$830$		0			0
$831$			1.04282e6i			1.51011i
$832$		0			0
$833$	781756.			1.12663
$834$		0			0
$835$	713467.	−	295528.i	1.02330	−	0.423863i
$836$		0			0
$837$	−219862.	−	91069.6i	−0.313833	−	0.129994i
$838$		0			0
$839$	−718691.	+	718691.i	−1.02098	+	1.02098i	−0.0212071	+	0.999775i	$0.506751\pi$
$839$	−718691.	+	718691.i	−1.02098	+	1.02098i	−0.999775	+	0.0212071i	$0.993249\pi$
$840$		0			0
$841$	307181.	−	307181.i	0.434313	−	0.434313i
$842$		0			0
$843$	−1.37191e6	−	568264.i	−1.93051	−	0.799641i
$844$		0			0
$845$	−311190.	+	128899.i	−0.435825	+	0.180525i
$846$		0			0
$847$	−155908.			−0.217321
$848$		0			0
$849$			1.13349e6i			1.57254i
$850$		0			0
$851$	−134521.	−	324762.i	−0.185751	−	0.448442i
$852$		0			0
$853$	305806.	−	738281.i	0.420289	−	1.01467i	−0.561973	−	0.827155i	$-0.689958\pi$
$853$	305806.	−	738281.i	0.420289	−	1.01467i	0.982262	−	0.187512i	$-0.0600424\pi$
$854$		0			0
$855$	−680854.	−	680854.i	−0.931368	−	0.931368i
$856$		0			0
$857$	−448904.	−	448904.i	−0.611212	−	0.611212i	0.332050	−	0.943262i	$-0.392260\pi$
$857$	−448904.	−	448904.i	−0.611212	−	0.611212i	−0.943262	+	0.332050i	$0.892260\pi$
$858$		0			0
$859$	−103043.	+	248768.i	−0.139647	+	0.337138i	−0.978195	−	0.207691i	$-0.933405\pi$
$859$	−103043.	+	248768.i	−0.139647	+	0.337138i	0.838548	+	0.544828i	$0.183405\pi$
$860$		0			0
$861$	129989.	+	313821.i	0.175347	+	0.423326i
$862$		0			0
$863$		−	830552.i		−	1.11518i	−0.830116	−	0.557591i	$-0.811726\pi$
$863$		−	830552.i		−	1.11518i	0.830116	−	0.557591i	$-0.188274\pi$
$864$		0			0
$865$	956326.			1.27813
$866$		0			0
$867$	−1.13139e6	+	468636.i	−1.50513	+	0.623445i
$868$		0			0
$869$	−677272.	−	280535.i	−0.896857	−	0.371490i
$870$		0			0
$871$	20388.7	−	20388.7i	0.0268753	−	0.0268753i
$872$		0			0
$873$	−649505.	+	649505.i	−0.852225	+	0.852225i
$874$		0			0
$875$	286658.	+	118738.i	0.374411	+	0.155086i
$876$		0			0
$877$	1.24957e6	−	517591.i	1.62466	−	0.672957i	0.630043	−	0.776560i	$-0.283037\pi$
$877$	1.24957e6	−	517591.i	1.62466	−	0.672957i	0.994619	+	0.103603i	$0.0330371\pi$
$878$		0			0
$879$	−1.35532e6			−1.75413
$880$		0			0
$881$		−	285537.i		−	0.367883i	−0.982937	−	0.183942i	$-0.941114\pi$
$881$		−	285537.i		−	0.367883i	0.982937	−	0.183942i	$-0.0588858\pi$
$882$		0			0
$883$	154731.	+	373554.i	0.198452	+	0.479106i	0.991508	−	0.130043i	$-0.0415114\pi$
$883$	154731.	+	373554.i	0.198452	+	0.479106i	−0.793056	+	0.609148i	$0.791511\pi$
$884$		0			0
$885$	−335907.	+	810951.i	−0.428876	+	1.03540i
$886$		0			0
$887$	−724428.	−	724428.i	−0.920764	−	0.920764i	0.0763198	−	0.997083i	$-0.475683\pi$
$887$	−724428.	−	724428.i	−0.920764	−	0.920764i	−0.997083	+	0.0763198i	$0.975683\pi$
$888$		0			0
$889$	−57101.1	−	57101.1i	−0.0722505	−	0.0722505i
$890$		0			0
$891$	270390.	−	652779.i	0.340593	−	0.822263i
$892$		0			0
$893$	92982.5	+	224480.i	0.116600	+	0.281497i
$894$		0			0
$895$			2.38822e6i			2.98146i
$896$		0			0
$897$	−825350.			−1.02578
$898$		0			0
$899$	−487942.	+	202112.i	−0.603739	+	0.250077i
$900$		0			0
$901$	−1.66938e6	−	691480.i	−2.05639	−	0.851785i
$902$		0			0
$903$	460700.	−	460700.i	0.564992	−	0.564992i
$904$		0			0
$905$	−1.31338e6	+	1.31338e6i	−1.60360	+	1.60360i
$906$		0			0
$907$	−1.48223e6	−	613961.i	−1.80178	−	0.746322i	−0.985729	−	0.168342i	$-0.946159\pi$
$907$	−1.48223e6	−	613961.i	−1.80178	−	0.746322i	−0.816051	−	0.577979i	$-0.803841\pi$
$908$		0			0
$909$	581168.	−	240728.i	0.703354	−	0.291339i
$910$		0			0
$911$	1.33057e6			1.60325			0.801627	−	0.597825i	$-0.203968\pi$
$911$	1.33057e6			1.60325			0.801627	+	0.597825i	$0.203968\pi$
$912$		0			0
$913$		−	484895.i		−	0.581709i
$914$		0			0
$915$	322864.	+	779463.i	0.385636	+	0.931008i
$916$		0			0
$917$	201106.	−	485513.i	0.239159	−	0.577381i
$918$		0			0
$919$	−318303.	−	318303.i	−0.376886	−	0.376886i	0.493092	−	0.869977i	$-0.335867\pi$
$919$	−318303.	−	318303.i	−0.376886	−	0.376886i	−0.869977	+	0.493092i	$0.835867\pi$
$920$		0			0
$921$	−446357.	−	446357.i	−0.526214	−	0.526214i
$922$		0			0
$923$	474023.	−	1.14439e6i	0.556412	−	1.34330i
$924$		0			0
$925$	−404511.	−	976576.i	−0.472767	−	1.14136i
$926$		0			0
$927$		−	786748.i		−	0.915537i
$928$		0			0
$929$	244440.			0.283231			0.141616	−	0.989922i	$-0.454770\pi$
$929$	244440.			0.283231			0.141616	+	0.989922i	$0.454770\pi$
$930$		0			0
$931$	−423396.	+	175376.i	−0.488480	+	0.202335i
$932$		0			0
$933$	654805.	+	271229.i	0.752227	+	0.311582i
$934$		0			0
$935$	1.72385e6	−	1.72385e6i	1.97186	−	1.97186i
$936$		0			0
$937$	−900795.	+	900795.i	−1.02600	+	1.02600i	−0.0263453	+	0.999653i	$0.508387\pi$
$937$	−900795.	+	900795.i	−1.02600	+	1.02600i	−0.999653	+	0.0263453i	$0.991613\pi$
$938$		0			0
$939$	320403.	+	132715.i	0.363384	+	0.150519i
$940$		0			0
$941$	932536.	−	386269.i	1.05314	−	0.436225i	0.212128	−	0.977242i	$-0.431960\pi$
$941$	932536.	−	386269.i	1.05314	−	0.436225i	0.841012	+	0.541017i	$0.181960\pi$
$942$		0			0
$943$	351918.			0.395748
$944$		0			0
$945$		−	216267.i		−	0.242173i
$946$		0			0
$947$	−158455.	−	382545.i	−0.176688	−	0.426562i	0.810580	−	0.585628i	$-0.199152\pi$
$947$	−158455.	−	382545.i	−0.176688	−	0.426562i	−0.987268	+	0.159066i	$0.949152\pi$
$948$		0			0
$949$	−501159.	+	1.20990e6i	−0.556472	+	1.34344i
$950$		0			0
$951$	1.45111e6	+	1.45111e6i	1.60449	+	1.60449i
$952$		0			0
$953$	−266623.	−	266623.i	−0.293570	−	0.293570i	0.544919	−	0.838489i	$-0.316560\pi$
$953$	−266623.	−	266623.i	−0.293570	−	0.293570i	−0.838489	+	0.544919i	$0.816560\pi$
$954$		0			0
$955$	−324324.	+	782988.i	−0.355609	+	0.858516i
$956$		0			0
$957$	391876.	+	946072.i	0.427882	+	1.03300i
$958$		0			0
$959$		−	322373.i		−	0.350527i
$960$		0			0
$961$	−98746.2			−0.106924
$962$		0			0
$963$	1.49101e6	−	617595.i	1.60778	−	0.665964i
$964$		0			0
$965$	1.72854e6	+	715984.i	1.85620	+	0.768863i
$966$		0			0
$967$	1.20698e6	−	1.20698e6i	1.29076	−	1.29076i	0.356448	−	0.934315i	$-0.383988\pi$
$967$	1.20698e6	−	1.20698e6i	1.29076	−	1.29076i	0.934315	−	0.356448i	$-0.116012\pi$
$968$		0			0
$969$	971552.	−	971552.i	1.03471	−	1.03471i
$970$		0			0
$971$	1.58951e6	+	658398.i	1.68588	+	0.698312i	0.999579	−	0.0290100i	$-0.00923545\pi$
$971$	1.58951e6	+	658398.i	1.68588	+	0.698312i	0.686296	+	0.727322i	$0.259235\pi$
$972$		0			0
$973$	472420.	−	195683.i	0.499003	−	0.206694i
$974$		0			0
$975$	−2.48187e6			−2.61078
$976$		0			0
$977$			1.11737e6i			1.17060i	0.810817	+	0.585299i	$0.199023\pi$
$977$			1.11737e6i			1.17060i	−0.810817	+	0.585299i	$0.800977\pi$
$978$		0			0
$979$	275615.	+	665394.i	0.287566	+	0.694246i
$980$		0			0
$981$	103898.	−	250833.i	0.107962	−	0.260643i
$982$		0			0
$983$	199468.	+	199468.i	0.206427	+	0.206427i	0.802747	−	0.596320i	$-0.203371\pi$
$983$	199468.	+	199468.i	0.206427	+	0.206427i	−0.596320	+	0.802747i	$0.703371\pi$
$984$		0			0
$985$	1.55638e6	+	1.55638e6i	1.60415	+	1.60415i
$986$		0			0
$987$	−117193.	+	282930.i	−0.120301	+	0.290432i
$988$		0			0
$989$	−258314.	−	623626.i	−0.264092	−	0.637575i
$990$		0			0
$991$			1.65134e6i			1.68147i	0.541444	+	0.840737i	$0.317878\pi$
$991$			1.65134e6i			1.68147i	−0.541444	+	0.840737i	$0.682122\pi$
$992$		0			0
$993$	160104.			0.162369
$994$		0			0
$995$	300219.	−	124355.i	0.303243	−	0.125608i
$996$		0			0
$997$	−337872.	−	139951.i	−0.339908	−	0.140795i	0.206199	−	0.978510i	$-0.433891\pi$
$997$	−337872.	−	139951.i	−0.339908	−	0.140795i	−0.546107	+	0.837716i	$0.683891\pi$
$998$		0			0
$999$	−182744.	+	182744.i	−0.183110	+	0.183110i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	128.5.h.a.15.14		60
4.3	odd	2		32.5.h.a.27.12	yes	60
32.13	even	8		32.5.h.a.19.12	✓	60
32.19	odd	8	inner	128.5.h.a.111.14		60

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
32.5.h.a.19.12	✓	60	32.13	even	8
32.5.h.a.27.12	yes	60	4.3	odd	2
128.5.h.a.15.14		60	1.1	even	1	trivial
128.5.h.a.111.14		60	32.19	odd	8	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 128 = 2^{7} \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	128.h (of order \(8\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(12.3801 - 5.12803i) q^{3} +(-36.8127 - 15.2483i) q^{5} +(-16.3058 + 16.3058i) q^{7} +(69.6958 - 69.6958i) q^{9} +O(q^{10})\)	\(q+(12.3801 - 5.12803i) q^{3} +(-36.8127 - 15.2483i) q^{5} +(-16.3058 + 16.3058i) q^{7} +(69.6958 - 69.6958i) q^{9} +(-135.158 - 55.9844i) q^{11} +(-177.746 + 73.6249i) q^{13} -533.940 q^{15} -418.220i q^{17} +(93.8220 + 226.506i) q^{19} +(-118.251 + 285.484i) q^{21} +(226.375 + 226.375i) q^{23} +(680.721 + 680.721i) q^{25} +(90.0723 - 217.454i) q^{27} +(-199.899 - 482.599i) q^{29} -1011.07i q^{31} -1960.37 q^{33} +(848.895 - 351.624i) q^{35} +(-1014.43 - 420.191i) q^{37} +(-1822.97 + 1822.97i) q^{39} +(777.292 - 777.292i) q^{41} +(-1947.97 - 806.874i) q^{43} +(-3628.43 + 1502.95i) q^{45} +991.052 q^{47} +1869.24i q^{49} +(-2144.64 - 5177.63i) q^{51} +(1653.39 - 3991.63i) q^{53} +(4121.87 + 4121.87i) q^{55} +(2323.06 + 2323.06i) q^{57} +(629.109 - 1518.80i) q^{59} +(-604.682 - 1459.83i) q^{61} +2272.89i q^{63} +7665.97 q^{65} +(-138.463 + 57.3534i) q^{67} +(3963.41 + 1641.70i) q^{69} +(-4552.60 + 4552.60i) q^{71} +(4813.22 - 4813.22i) q^{73} +(11918.2 + 4936.67i) q^{75} +(3116.73 - 1290.99i) q^{77} +5010.95 q^{79} +4829.74i q^{81} +(1268.41 + 3062.22i) q^{83} +(-6377.15 + 15395.8i) q^{85} +(-4949.56 - 4949.56i) q^{87} +(-3481.14 - 3481.14i) q^{89} +(1697.78 - 4098.80i) q^{91} +(-5184.80 - 12517.2i) q^{93} -9768.94i q^{95} -9319.15 q^{97} +(-13321.8 + 5518.09i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9}+O(q^{10}) \) 60 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9	\( 60 q + 4 q^{3} - 4 q^{5} + 4 q^{7} - 4 q^{9} + 4 q^{11} - 4 q^{13} + 8 q^{15} + 4 q^{19} - 4 q^{21} + 1156 q^{23} - 4 q^{25} - 3644 q^{27} - 4 q^{29} - 8 q^{33} + 5188 q^{35} - 4 q^{37} + 2692 q^{39} - 4 q^{41} - 5564 q^{43} - 328 q^{45} + 8 q^{47} - 8384 q^{51} + 956 q^{53} + 11780 q^{55} - 4 q^{57} + 13060 q^{59} + 7548 q^{61} - 8 q^{65} - 18876 q^{67} - 19588 q^{69} - 19964 q^{71} - 4 q^{73} + 200 q^{75} + 9404 q^{77} + 50184 q^{79} - 10556 q^{83} + 2496 q^{85} - 49276 q^{87} - 4 q^{89} - 31868 q^{91} + 320 q^{93} - 8 q^{97} + 46920 q^{99}+O(q^{100}) \) 60 * q + 4 * q^3 - 4 * q^5 + 4 * q^7 - 4 * q^9 + 4 * q^11 - 4 * q^13 + 8 * q^15 + 4 * q^19 - 4 * q^21 + 1156 * q^23 - 4 * q^25 - 3644 * q^27 - 4 * q^29 - 8 * q^33 + 5188 * q^35 - 4 * q^37 + 2692 * q^39 - 4 * q^41 - 5564 * q^43 - 328 * q^45 + 8 * q^47 - 8384 * q^51 + 956 * q^53 + 11780 * q^55 - 4 * q^57 + 13060 * q^59 + 7548 * q^61 - 8 * q^65 - 18876 * q^67 - 19588 * q^69 - 19964 * q^71 - 4 * q^73 + 200 * q^75 + 9404 * q^77 + 50184 * q^79 - 10556 * q^83 + 2496 * q^85 - 49276 * q^87 - 4 * q^89 - 31868 * q^91 + 320 * q^93 - 8 * q^97 + 46920 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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