LMFDB - Embedded newform 152.4.t.a.101.11

Show commands: Magma / Pari/GP / SageMath

Newspace parameters

comment:Compute space of new eigenforms

gp:[N,k,chi] = [152,4,Mod(5,152)] mf = mfinit([N,k,chi],0) lf = mfeigenbasis(mf)

magma://Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code chi := DirichletCharacter("152.5"); S:= CuspForms(chi, 4); N := Newforms(S);

sage:from sage.modular.dirichlet import DirichletCharacter H = DirichletGroup(152, base_ring=CyclotomicField(18)) chi = DirichletCharacter(H, H._module([0, 9, 16])) N = Newforms(chi, 4, names="a")

Level:	$ N $	$=$	$ 152 = 2^{3} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	152.t (of order $18$, degree $6$, minimal)

Newform invariants

comment:select newform

sage:traces = [] f = next(g for g in N if [g.coefficient(i+1).trace() for i in range(0)] == traces)

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

Self dual:	no
Analytic conductor:	$8.96829032087$
Analytic rank:	$0$
Dimension:	$348$
Relative dimension:	$58$ over $\Q(\zeta_{18})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{18}]$

Embedding invariants

Embedding label			101.11
Character	$\chi$	$=$	152.101
Dual form			152.4.t.a.149.11

$q$-expansion

comment:q-expansion

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

gp:mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.43528 - 1.43855i) q^{2} +(-3.10118 + 8.52041i) q^{3} +(3.86117 + 7.00652i) q^{4} +(7.08329 - 1.24898i) q^{5} +(19.8092 - 16.2884i) q^{6} +(11.0229 - 19.0923i) q^{7} +(0.676164 - 22.6173i) q^{8} +(-42.2969 - 35.4913i) q^{9} +(-19.0465 - 7.14804i) q^{10} +(41.6541 - 24.0490i) q^{11} +(-71.6726 + 11.1703i) q^{12} +(11.4841 + 31.5522i) q^{13} +(-54.3090 + 30.6380i) q^{14} +(-11.3248 + 64.2259i) q^{15} +(-34.1827 + 54.1068i) q^{16} +(66.6674 - 55.9406i) q^{17} +(51.9490 + 147.277i) q^{18} +(73.1586 - 38.8177i) q^{19} +(36.1008 + 44.8067i) q^{20} +(128.490 + 153.128i) q^{21} +(-136.035 - 1.35527i) q^{22} +(5.61808 - 31.8617i) q^{23} +(190.612 + 75.9015i) q^{24} +(-68.8485 + 25.0588i) q^{25} +(17.4224 - 93.3588i) q^{26} +(221.555 - 127.915i) q^{27} +(176.332 + 3.51381i) q^{28} +(-166.259 + 198.140i) q^{29} +(119.971 - 140.117i) q^{30} +(82.3992 - 142.720i) q^{31} +(161.079 - 82.5918i) q^{32} +(75.7307 + 429.490i) q^{33} +(-242.827 + 40.3269i) q^{34} +(54.2328 - 149.003i) q^{35} +(85.3551 - 433.393i) q^{36} +2.12984i q^{37} +(-234.003 - 10.7101i) q^{38} -304.452 q^{39} +(-23.4590 - 161.050i) q^{40} +(173.918 + 63.3010i) q^{41} +(-92.6268 - 557.749i) q^{42} +(98.8077 - 17.4225i) q^{43} +(329.333 + 198.993i) q^{44} +(-343.929 - 198.568i) q^{45} +(-59.5162 + 69.5104i) q^{46} +(456.021 + 382.647i) q^{47} +(-355.006 - 459.045i) q^{48} +(-71.5095 - 123.858i) q^{49} +(203.714 + 38.0165i) q^{50} +(269.889 + 741.515i) q^{51} +(-176.729 + 202.292i) q^{52} +(392.632 + 69.2315i) q^{53} +(-723.560 - 7.20857i) q^{54} +(265.011 - 222.371i) q^{55} +(-424.362 - 262.218i) q^{56} +(103.865 + 743.722i) q^{57} +(689.922 - 243.355i) q^{58} +(-455.167 - 542.447i) q^{59} +(-493.727 + 168.640i) q^{60} +(-382.926 - 67.5202i) q^{61} +(-405.974 + 229.027i) q^{62} +(-1143.85 + 416.326i) q^{63} +(-511.086 - 30.5860i) q^{64} +(120.753 + 209.150i) q^{65} +(433.415 - 1154.87i) q^{66} +(-182.336 + 217.300i) q^{67} +(649.363 + 251.110i) q^{68} +(254.053 + 146.677i) q^{69} +(-346.420 + 284.849i) q^{70} +(-6.48653 - 36.7869i) q^{71} +(-831.319 + 932.645i) q^{72} +(-814.882 - 296.593i) q^{73} +(3.06387 - 5.18675i) q^{74} -664.329i q^{75} +(554.455 + 362.706i) q^{76} -1060.36i q^{77} +(741.425 + 437.968i) q^{78} +(-553.469 - 201.446i) q^{79} +(-174.548 + 425.948i) q^{80} +(143.932 + 816.277i) q^{81} +(-332.478 - 404.344i) q^{82} +(1080.09 + 623.592i) q^{83} +(-576.775 + 1491.52i) q^{84} +(402.356 - 479.509i) q^{85} +(-265.687 - 99.7108i) q^{86} +(-1172.64 - 2031.07i) q^{87} +(-515.758 - 958.364i) q^{88} +(1269.82 - 462.178i) q^{89} +(551.916 + 978.326i) q^{90} +(728.991 + 128.541i) q^{91} +(244.932 - 83.6605i) q^{92} +(960.495 + 1144.67i) q^{93} +(-560.084 - 1587.86i) q^{94} +(469.722 - 366.331i) q^{95} +(204.180 + 1628.60i) q^{96} +(121.735 - 102.148i) q^{97} +(-4.02987 + 404.498i) q^{98} +(-2615.37 - 461.160i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 348 q - 6 q^{2} + 12 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 75 q^{10} - 3 q^{12} - 81 q^{14} - 12 q^{15} + 192 q^{16} - 12 q^{17} - 12 q^{18} + 558 q^{20} - 30 q^{22} - 12 q^{23} - 108 q^{24}+ \cdots + 8055 q^{98}+O(q^{100}) $ 348 * q - 6 * q^2 + 12 * q^4 - 24 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 75 * q^10 - 3 * q^12 - 81 * q^14 - 12 * q^15 + 192 * q^16 - 12 * q^17 - 12 * q^18 + 558 * q^20 - 30 * q^22 - 12 * q^23 - 108 * q^24 - 12 * q^25 - 411 * q^26 + 1140 * q^28 - 282 * q^30 - 1122 * q^31 + 39 * q^32 - 174 * q^33 + 1536 * q^34 - 2835 * q^36 + 966 * q^38 - 24 * q^39 - 1068 * q^40 + 48 * q^41 + 3015 * q^42 - 1203 * q^44 - 528 * q^46 - 624 * q^47 + 4755 * q^48 - 6768 * q^49 - 1074 * q^50 - 1089 * q^52 + 615 * q^54 - 762 * q^55 + 2046 * q^56 - 12 * q^57 + 4092 * q^58 + 4050 * q^60 + 3120 * q^62 + 2046 * q^63 + 2355 * q^64 - 6 * q^65 + 1716 * q^66 - 1176 * q^68 - 2973 * q^70 - 12 * q^71 - 7122 * q^72 + 636 * q^73 - 9363 * q^74 - 2454 * q^76 - 6897 * q^78 - 12 * q^79 - 6885 * q^80 + 1206 * q^81 - 7311 * q^82 + 1947 * q^84 + 7452 * q^86 - 6 * q^87 - 1131 * q^88 - 12 * q^89 + 4014 * q^90 + 7656 * q^92 + 11898 * q^94 + 1848 * q^95 - 18966 * q^96 - 12 * q^97 + 8055 * q^98

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/152\mathbb{Z}\right)^\times$.

$n$	$39$	$77$	$97$
$\chi(n)$	$1$	$-1$	$e\left(\frac{7}{9}\right)$

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 $

$2$	−2.43528	−	1.43855i	−0.861001	−	0.508603i
$2$	−2.43528	−	1.43855i	−0.861001	−	0.508603i
$3$	−3.10118	+	8.52041i	−0.596822	+	1.63975i	0.160745	+	0.986996i	$0.448610\pi$
$3$	−3.10118	+	8.52041i	−0.596822	+	1.63975i	−0.757566	+	0.652758i	$0.773612\pi$
$4$	3.86117	+	7.00652i	0.482647	+	0.875815i
$5$	7.08329	−	1.24898i	0.633549	−	0.111712i	0.152355	−	0.988326i	$-0.451314\pi$
$5$	7.08329	−	1.24898i	0.633549	−	0.111712i	0.481194	+	0.876614i	$0.340203\pi$
$6$	19.8092	−	16.2884i	1.34785	−	1.10829i
$7$	11.0229	−	19.0923i	0.595182	−	1.03088i	−0.398340	−	0.917238i	$-0.630413\pi$
$7$	11.0229	−	19.0923i	0.595182	−	1.03088i	0.993521	−	0.113647i	$-0.0362532\pi$
$8$	0.676164	−	22.6173i	0.0298825	−	0.999553i
$9$	−42.2969	−	35.4913i	−1.56655	−	1.31449i
$10$	−19.0465	−	7.14804i	−0.602303	−	0.226041i
$11$	41.6541	−	24.0490i	1.14174	−	0.659185i	0.194881	−	0.980827i	$-0.437568\pi$
$11$	41.6541	−	24.0490i	1.14174	−	0.659185i	0.946862	+	0.321641i	$0.104235\pi$
$12$	−71.6726	+	11.1703i	−1.72418	+	0.268716i
$13$	11.4841	+	31.5522i	0.245008	+	0.673154i	0.999851	+	0.0172489i	$0.00549077\pi$
$13$	11.4841	+	31.5522i	0.245008	+	0.673154i	−0.754843	+	0.655905i	$0.772287\pi$
$14$	−54.3090	+	30.6380i	−1.03676	+	0.584882i
$15$	−11.3248	+	64.2259i	−0.194936	+	1.10554i
$16$	−34.1827	+	54.1068i	−0.534104	+	0.845419i
$17$	66.6674	−	55.9406i	0.951130	−	0.798093i	−0.0283572	−	0.999598i	$-0.509028\pi$
$17$	66.6674	−	55.9406i	0.951130	−	0.798093i	0.979488	+	0.201505i	$0.0645832\pi$
$18$	51.9490	+	147.277i	0.680249	+	1.92853i
$19$	73.1586	−	38.8177i	0.883355	−	0.468705i
$19$	73.1586	−	38.8177i	0.883355	−	0.468705i
$20$	36.1008	+	44.8067i	0.403619	+	0.500955i
$21$	128.490	+	153.128i	1.33518	+	1.59121i
$22$	−136.035	−	1.35527i	−1.31831	−	0.0131338i
$23$	5.61808	−	31.8617i	0.0509327	−	0.288854i	−0.948693	−	0.316197i	$-0.897594\pi$
$23$	5.61808	−	31.8617i	0.0509327	−	0.288854i	0.999626	+	0.0273439i	$0.00870490\pi$
$24$	190.612	+	75.9015i	1.62119	+	0.645555i
$25$	−68.8485	+	25.0588i	−0.550788	+	0.200470i
$26$	17.4224	−	93.3588i	0.131416	−	0.704199i
$27$	221.555	−	127.915i	1.57920	−	0.911749i
$28$	176.332	+	3.51381i	1.19013	+	0.0237160i
$29$	−166.259	+	198.140i	−1.06461	+	1.26875i	−0.102894	+	0.994692i	$0.532810\pi$
$29$	−166.259	+	198.140i	−1.06461	+	1.26875i	−0.961713	+	0.274057i	$0.911634\pi$
$30$	119.971	−	140.117i	0.730119	−	0.852724i
$31$	82.3992	−	142.720i	0.477398	−	0.826877i	−0.522267	−	0.852782i	$-0.674913\pi$
$31$	82.3992	−	142.720i	0.477398	−	0.826877i	0.999664	+	0.0259051i	$0.00824677\pi$
$32$	161.079	−	82.5918i	0.889847	−	0.456260i
$33$	75.7307	+	429.490i	0.399485	+	2.26559i
$34$	−242.827	+	40.3269i	−1.22484	+	0.203412i
$35$	54.2328	−	149.003i	0.261915	−	0.719605i
$36$	85.3551	−	433.393i	0.395162	−	2.00645i
$37$			2.12984i			0.00946332i	0.999989	+	0.00473166i	$0.00150614\pi$
$37$			2.12984i			0.00946332i	−0.999989	+	0.00473166i	$0.998494\pi$
$38$	−234.003	−	10.7101i	−0.998954	−	0.0457211i
$39$	−304.452			−1.25003
$40$	−23.4590	−	161.050i	−0.0927299	−	0.636604i
$41$	173.918	+	63.3010i	0.662474	+	0.241121i	0.651304	−	0.758817i	$-0.274222\pi$
$41$	173.918	+	63.3010i	0.662474	+	0.241121i	0.0111697	+	0.999938i	$0.496445\pi$
$42$	−92.6268	−	557.749i	−0.340301	−	2.04911i
$43$	98.8077	−	17.4225i	0.350419	−	0.0617884i	0.00433189	−	0.999991i	$-0.498621\pi$
$43$	98.8077	−	17.4225i	0.350419	−	0.0617884i	0.346088	+	0.938202i	$0.387510\pi$
$44$	329.333	+	198.993i	1.12838	+	0.681802i
$45$	−343.929	−	198.568i	−1.13933	−	0.657794i
$46$	−59.5162	+	69.5104i	−0.190765	+	0.222799i
$47$	456.021	+	382.647i	1.41527	+	1.18755i	0.953819	+	0.300382i	$0.0971142\pi$
$47$	456.021	+	382.647i	1.41527	+	1.18755i	0.461448	+	0.887168i	$0.347330\pi$
$48$	−355.006	−	459.045i	−1.06751	−	1.38036i
$49$	−71.5095	−	123.858i	−0.208482	−	0.361102i
$50$	203.714	+	38.0165i	0.576189	+	0.107527i
$51$	269.889	+	741.515i	0.741021	+	2.03594i
$52$	−176.729	+	202.292i	−0.471306	+	0.539478i
$53$	392.632	+	69.2315i	1.01759	+	0.179428i	0.657471	−	0.753480i	$-0.271626\pi$
$53$	392.632	+	69.2315i	1.01759	+	0.179428i	0.360116	+	0.932908i	$0.382737\pi$
$54$	−723.560	−	7.20857i	−1.82341	−	0.0181660i
$55$	265.011	−	222.371i	0.649711	−	0.545172i
$56$	−424.362	−	262.218i	−1.01264	−	0.625721i
$57$	103.865	+	743.722i	0.241355	+	1.72822i
$58$	689.922	−	243.355i	1.56192	−	0.550933i
$59$	−455.167	−	542.447i	−1.00437	−	1.19696i	−0.980354	−	0.197248i	$-0.936800\pi$
$59$	−455.167	−	542.447i	−1.00437	−	1.19696i	−0.0240147	−	0.999712i	$-0.507645\pi$
$60$	−493.727	+	168.640i	−1.06233	+	0.362856i
$61$	−382.926	−	67.5202i	−0.803748	−	0.141723i	−0.243342	−	0.969940i	$-0.578244\pi$
$61$	−382.926	−	67.5202i	−0.803748	−	0.141723i	−0.560406	+	0.828218i	$0.689355\pi$
$62$	−405.974	+	229.027i	−0.831592	+	0.469137i
$63$	−1143.85	+	416.326i	−2.28748	+	0.832573i
$64$	−511.086	−	30.5860i	−0.998214	−	0.0597383i
$65$	120.753	+	209.150i	0.230424	+	0.399106i
$66$	433.415	−	1154.87i	0.808330	−	2.15386i
$67$	−182.336	+	217.300i	−0.332477	+	0.396230i	−0.906221	−	0.422804i	$-0.861046\pi$
$67$	−182.336	+	217.300i	−0.332477	+	0.396230i	0.573744	+	0.819034i	$0.305490\pi$
$68$	649.363	+	251.110i	1.15804	+	0.447817i
$69$	254.053	+	146.677i	0.443251	+	0.255911i
$70$	−346.420	+	284.849i	−0.591502	+	0.486370i
$71$	−6.48653	−	36.7869i	−0.0108424	−	0.0614902i	0.978907	−	0.204309i	$-0.0654946\pi$
$71$	−6.48653	−	36.7869i	−0.0108424	−	0.0614902i	−0.989749	+	0.142818i	$0.954383\pi$
$72$	−831.319	+	932.645i	−1.36072	+	1.52657i
$73$	−814.882	−	296.593i	−1.30650	−	0.475528i	−0.407394	−	0.913252i	$-0.633563\pi$
$73$	−814.882	−	296.593i	−1.30650	−	0.475528i	−0.899109	+	0.437724i	$0.855785\pi$
$74$	3.06387	−	5.18675i	0.00481307	−	0.00814793i
$75$		−	664.329i		−	1.02280i
$76$	554.455	+	362.706i	0.836847	+	0.547437i
$77$		−	1060.36i		−	1.56934i
$78$	741.425	+	437.968i	1.07628	+	0.635771i
$79$	−553.469	−	201.446i	−0.788229	−	0.286892i	−0.0836292	−	0.996497i	$-0.526651\pi$
$79$	−553.469	−	201.446i	−0.788229	−	0.286892i	−0.704600	+	0.709605i	$0.748873\pi$
$80$	−174.548	+	425.948i	−0.243938	+	0.595280i
$81$	143.932	+	816.277i	0.197437	+	1.11972i
$82$	−332.478	−	404.344i	−0.447756	−	0.544541i
$83$	1080.09	+	623.592i	1.42838	+	0.824676i	0.996993	−	0.0774902i	$-0.0246906\pi$
$83$	1080.09	+	623.592i	1.42838	+	0.824676i	0.431388	+	0.902166i	$0.358024\pi$
$84$	−576.775	+	1491.52i	−0.749182	+	1.93736i
$85$	402.356	−	479.509i	0.513431	−	0.611884i
$86$	−265.687	−	99.7108i	−0.333137	−	0.125024i
$87$	−1172.64	−	2031.07i	−1.44506	−	2.50291i
$88$	−515.758	−	958.364i	−0.624773	−	1.16093i
$89$	1269.82	−	462.178i	1.51237	−	0.550458i	0.553142	−	0.833087i	$-0.313429\pi$
$89$	1269.82	−	462.178i	1.51237	−	0.550458i	0.959229	+	0.282629i	$0.0912064\pi$
$90$	551.916	+	978.326i	0.646411	+	1.14583i
$91$	728.991	+	128.541i	0.839769	+	0.148074i
$92$	244.932	−	83.6605i	0.277565	−	0.0948066i
$93$	960.495	+	1144.67i	1.07095	+	1.27631i
$94$	−560.084	−	1587.86i	−0.614555	−	1.74229i
$95$	469.722	−	366.331i	0.507289	−	0.395629i
$96$	204.180	+	1628.60i	0.217074	+	1.73144i
$97$	121.735	−	102.148i	0.127426	−	0.106923i	−0.576847	−	0.816852i	$-0.695717\pi$
$97$	121.735	−	102.148i	0.127426	−	0.106923i	0.704274	+	0.709929i	$0.251273\pi$
$98$	−4.02987	+	404.498i	−0.00415387	+	0.416944i
$99$	−2615.37	−	461.160i	−2.65510	−	0.468165i
$100$	−441.411	−	385.632i	−0.441411	−	0.385632i
$101$	58.2210	+	159.961i	0.0573585	+	0.157591i	0.965062	−	0.262020i	$-0.0843887\pi$
$101$	58.2210	+	159.961i	0.0573585	+	0.157591i	−0.907704	+	0.419611i	$0.862166\pi$
$102$	409.447	−	2194.05i	0.397464	−	2.12983i
$103$	−139.425	−	241.492i	−0.133379	−	0.231018i	0.791598	−	0.611042i	$-0.209249\pi$
$103$	−139.425	−	241.492i	−0.133379	−	0.231018i	−0.924977	+	0.380023i	$0.875916\pi$
$104$	721.391	−	238.404i	0.680175	−	0.224783i
$105$	1101.38	+	924.172i	1.02366	+	0.858952i
$106$	−856.575	−	733.417i	−0.784886	−	0.672035i
$107$	108.959	+	62.9076i	0.0984437	+	0.0568365i	0.548414	−	0.836207i	$-0.315232\pi$
$107$	108.959	+	62.9076i	0.0984437	+	0.0568365i	−0.449970	+	0.893044i	$0.648565\pi$
$108$	1751.70	+	1058.43i	1.56072	+	0.943031i
$109$	−939.684	+	165.692i	−0.825738	+	0.145600i	−0.570520	−	0.821284i	$-0.693258\pi$
$109$	−939.684	+	165.692i	−0.825738	+	0.145600i	−0.255218	+	0.966884i	$0.582147\pi$
$110$	−965.267	+	160.304i	−0.836678	+	0.138949i
$111$	−18.1471	−	6.60500i	−0.0155175	−	0.00564791i
$112$	656.228	+	1249.04i	0.553640	+	1.05378i
$113$	984.245			0.819380			0.409690	−	0.912225i	$-0.365637\pi$
$113$	984.245			0.819380			0.409690	+	0.912225i	$0.365637\pi$
$114$	816.938	−	1960.59i	0.671169	−	1.61075i
$115$		−	232.703i		−	0.188693i
$116$	−2030.23	−	399.846i	−1.62502	−	0.320041i
$117$	634.089	−	1742.15i	0.501039	−	1.37659i
$118$	328.125	+	1975.79i	0.255986	+	1.54141i
$119$	−333.163	−	1889.46i	−0.256647	−	1.45552i
$120$	1444.96	+	299.563i	1.09922	+	0.227885i
$121$	491.207	−	850.795i	0.369051	−	0.639215i
$122$	835.401	+	715.287i	0.619948	+	0.530812i
$123$	−1078.70	+	1285.55i	−0.790757	+	0.942388i
$124$	1318.13	+	26.2666i	0.954606	+	0.0190227i
$125$	−1234.99	+	713.024i	−0.883690	+	0.510199i
$126$	3384.49	+	631.604i	2.39297	+	0.446570i
$127$	958.398	−	348.828i	0.669638	−	0.243728i	0.0152462	−	0.999884i	$-0.495147\pi$
$127$	958.398	−	348.828i	0.669638	−	0.243728i	0.654392	+	0.756155i	$0.272925\pi$
$128$	1200.64	+	809.705i	0.829081	+	0.559129i
$129$	−157.974	+	895.913i	−0.107820	+	0.611478i
$130$	6.80496	−	683.048i	0.00459104	−	0.460825i
$131$	577.926	+	688.746i	0.385448	+	0.459359i	0.923526	−	0.383536i	$-0.125294\pi$
$131$	577.926	+	688.746i	0.385448	+	0.459359i	−0.538078	+	0.842895i	$0.680849\pi$
$132$	−2716.82	+	2188.94i	−1.79143	+	1.44336i
$133$	65.3042	−	1824.65i	0.0425759	−	1.18960i
$134$	756.636	−	266.887i	0.487787	−	0.172056i
$135$	1409.58	−	1182.77i	0.898644	−	0.754052i
$136$	−1220.15	−	1545.66i	−0.769315	−	0.974555i
$137$	45.8309	−	259.920i	0.0285810	−	0.162091i	−0.967177	−	0.254105i	$-0.918219\pi$
$137$	45.8309	−	259.920i	0.0285810	−	0.162091i	0.995758	+	0.0920137i	$0.0293303\pi$
$138$	−407.687	−	722.666i	−0.251483	−	0.445779i
$139$	139.341	+	382.835i	0.0850267	+	0.233609i	0.974918	−	0.222563i	$-0.0714424\pi$
$139$	139.341	+	382.835i	0.0850267	+	0.233609i	−0.889892	+	0.456172i	$0.849220\pi$
$140$	1253.40	−	195.345i	0.756653	−	0.117926i
$141$	−4674.51	+	2698.83i	−2.79195	+	1.61193i
$142$	−37.1231	+	98.9176i	−0.0219388	+	0.0584576i
$143$	1237.16	+	1038.10i	0.723470	+	0.607063i
$144$	3366.15	−	1075.36i	1.94800	−	0.622316i
$145$	−930.192	+	1611.14i	−0.532746	+	0.922744i
$146$	1557.80	+	1894.53i	0.883046	+	1.07392i
$147$	1277.08	−	225.185i	0.716545	−	0.126346i
$148$	−14.9227	+	8.22366i	−0.00828812	+	0.00456744i
$149$	−653.104	+	1794.39i	−0.359089	+	0.986590i	0.620257	+	0.784399i	$0.287028\pi$
$149$	−653.104	+	1794.39i	−0.359089	+	0.986590i	−0.979346	+	0.202191i	$0.935194\pi$
$150$	−955.668	+	1617.83i	−0.520200	+	0.880634i
$151$	−56.2650			−0.0303230			−0.0151615	−	0.999885i	$-0.504826\pi$
$151$	−56.2650			−0.0303230			−0.0151615	+	0.999885i	$0.504826\pi$
$152$	−828.485	−	1680.90i	−0.442099	−	0.896966i
$153$	−4805.23			−2.53909
$154$	−1525.38	+	2582.27i	−0.798171	+	1.35120i
$155$	405.404	−	1113.84i	0.210083	−	0.577198i
$156$	−1175.54	−	2133.15i	−0.603325	−	1.09480i
$157$	3015.59	−	531.730i	1.53293	−	0.270297i	0.657431	−	0.753514i	$-0.271643\pi$
$157$	3015.59	−	531.730i	1.53293	−	0.270297i	0.875501	+	0.483217i	$0.160532\pi$
$158$	1058.06	+	1286.77i	0.532752	+	0.647909i
$159$	−1807.50	+	3130.68i	−0.901536	+	1.56151i
$160$	1037.82	−	786.206i	0.512792	−	0.388469i
$161$	−546.385	−	458.471i	−0.267461	−	0.224426i
$162$	823.738	−	2194.91i	0.399500	−	1.06450i
$163$	2322.30	−	1340.78i	1.11593	−	0.644282i	0.175571	−	0.984467i	$-0.443823\pi$
$163$	2322.30	−	1340.78i	1.11593	−	0.644282i	0.940359	+	0.340185i	$0.110490\pi$
$164$	228.008	+	1462.98i	0.108564	+	0.696581i
$165$	1072.84	+	2947.62i	0.506187	+	1.39074i
$166$	−1733.26	−	3072.38i	−0.810406	−	1.43653i
$167$	−176.454	+	1000.72i	−0.0817631	+	0.463702i	0.916245	+	0.400618i	$0.131205\pi$
$167$	−176.454	+	1000.72i	−0.0817631	+	0.463702i	−0.998008	+	0.0630837i	$0.979907\pi$
$168$	3550.23	−	2802.56i	1.63039	−	1.28703i
$169$	819.342	−	687.510i	0.372937	−	0.312931i
$170$	−1669.65	+	588.932i	−0.753271	+	0.265700i
$171$	−4472.08	−	954.628i	−1.99993	−	0.426914i
$172$	503.585	+	625.027i	0.223244	+	0.277081i
$173$	−21.4954	−	25.6173i	−0.00944664	−	0.0112581i	0.761300	−	0.648399i	$-0.224561\pi$
$173$	−21.4954	−	25.6173i	−0.00944664	−	0.0112581i	−0.770747	+	0.637141i	$0.780117\pi$
$174$	−66.0833	+	6633.11i	−0.0287917	+	2.88997i
$175$	−280.482	+	1590.69i	−0.121157	+	0.687115i
$176$	−122.634	+	3075.83i	−0.0525222	+	1.31732i
$177$	6033.43	−	2195.99i	2.56215	−	0.932546i
$178$	−3757.24	−	701.167i	−1.58212	−	0.295251i
$179$	−31.2314	+	18.0314i	−0.0130410	+	0.00752923i	−0.506506	−	0.862236i	$-0.669063\pi$
$179$	−31.2314	+	18.0314i	−0.0130410	+	0.00752923i	0.493465	+	0.869765i	$0.335730\pi$
$180$	63.2980	−	3176.45i	0.0262109	−	1.31533i
$181$	−2623.89	+	3127.04i	−1.07753	+	1.28415i	−0.120954	+	0.992658i	$0.538595\pi$
$181$	−2623.89	+	3127.04i	−1.07753	+	1.28415i	−0.956574	+	0.291489i	$0.905849\pi$
$182$	−1590.38	−	1361.72i	−0.647731	−	0.554601i
$183$	1762.82	−	3053.30i	0.712085	−	1.23337i
$184$	−716.828	−	148.610i	−0.287203	−	0.0595416i
$185$	2.66011	+	15.0863i	0.00105716	+	0.00599548i
$186$	−692.409	−	4169.32i	−0.272957	−	1.64360i
$187$	1431.65	−	3933.43i	0.559855	−	1.53819i
$188$	−920.249	+	4672.59i	−0.357000	+	1.81268i
$189$		−	5639.98i		−	2.17062i
$190$	−1670.89	+	216.401i	−0.637994	+	0.0826284i
$191$	−1968.00			−0.745546			−0.372773	−	0.927923i	$-0.621593\pi$
$191$	−1968.00			−0.745546			−0.372773	+	0.927923i	$0.621593\pi$
$192$	1845.57	−	4259.81i	0.693712	−	1.60117i
$193$	−2992.47	−	1089.17i	−1.11608	−	0.406219i	−0.282857	−	0.959162i	$-0.591282\pi$
$193$	−2992.47	−	1089.17i	−1.11608	−	0.406219i	−0.833219	+	0.552943i	$0.813505\pi$
$194$	−443.404	+	73.6373i	−0.164096	+	0.0272518i
$195$	−2156.52	+	380.253i	−0.791958	+	0.139644i
$196$	591.703	−	979.270i	0.215635	−	0.356877i
$197$	−4007.74	−	2313.87i	−1.44944	−	0.836834i	−0.450991	−	0.892528i	$-0.648930\pi$
$197$	−4007.74	−	2313.87i	−1.44944	−	0.836834i	−0.998448	+	0.0556941i	$0.982263\pi$
$198$	5705.76	+	4885.38i	2.04793	+	1.75348i
$199$	−2716.06	−	2279.05i	−0.967521	−	0.811846i	0.0146395	−	0.999893i	$-0.495340\pi$
$199$	−2716.06	−	2279.05i	−0.967521	−	0.811846i	−0.982160	+	0.188047i	$0.939784\pi$
$200$	520.210	+	1574.11i	0.183922	+	0.556532i
$201$	−1286.03	−	2227.47i	−0.451291	−	0.781659i
$202$	88.3266	−	473.303i	0.0307655	−	0.164859i
$203$	1950.28	+	5358.35i	0.674300	+	1.85262i
$204$	−4153.35	+	4754.11i	−1.42546	+	1.63164i
$205$	1310.97	+	231.160i	0.446646	+	0.0787557i
$206$	−7.85724	+	788.670i	−0.00265747	+	0.266744i
$207$	−1368.44	+	1148.26i	−0.459485	+	0.385554i
$208$	−2099.74	−	457.173i	−0.699957	−	0.152400i
$209$	2113.83	−	3376.31i	0.699601	−	1.11744i
$210$	−1352.72	−	3835.01i	−0.444506	−	1.26019i
$211$	−810.997	−	966.508i	−0.264603	−	0.315342i	0.617341	−	0.786696i	$-0.288210\pi$
$211$	−810.997	−	966.508i	−0.264603	−	0.315342i	−0.881944	+	0.471354i	$0.843766\pi$
$212$	1030.95	+	3018.30i	0.333989	+	0.977818i
$213$	333.556	+	58.8148i	0.107300	+	0.0189198i
$214$	−174.851	−	309.940i	−0.0558530	−	0.0990051i
$215$	678.124	−	246.817i	0.215105	−	0.0782920i
$216$	−2743.28	−	5097.47i	−0.864151	−	1.60574i
$217$	−1816.56	−	3146.37i	−0.568277	−	0.984284i
$218$	2526.75	+	948.273i	0.785014	+	0.294611i
$219$	5054.19	−	6023.35i	1.55950	−	1.85854i
$220$	2581.30	+	998.195i	0.791051	+	0.305901i
$221$	2530.66	+	1461.08i	0.770274	+	0.444718i
$222$	34.6916	+	42.1904i	0.0104881	+	0.0127551i
$223$	586.053	+	3323.67i	0.175987	+	0.998070i	0.936999	+	0.349333i	$0.113592\pi$
$223$	586.053	+	3323.67i	0.175987	+	0.998070i	−0.761012	+	0.648738i	$0.775297\pi$
$224$	198.702	−	3985.77i	0.0592693	−	1.18889i
$225$	3801.45	+	1383.61i	1.12636	+	0.409960i
$226$	−2396.91	−	1415.88i	−0.705487	−	0.416739i
$227$		−	293.124i		−	0.0857063i	−0.999081	−	0.0428531i	$-0.986355\pi$
$227$		−	293.124i		−	0.0857063i	0.999081	−	0.0428531i	$-0.0136448\pi$
$228$	−4809.87	+	3599.37i	−1.39711	+	1.04550i
$229$			3553.94i			1.02555i	0.858523	+	0.512775i	$0.171382\pi$
$229$			3553.94i			1.02555i	−0.858523	+	0.512775i	$0.828618\pi$
$230$	−334.754	+	566.697i	−0.0959696	+	0.162465i
$231$	9034.70	+	3288.36i	2.57333	+	0.936616i
$232$	4368.98	+	3894.32i	1.23637	+	1.10204i
$233$	857.835	+	4865.02i	0.241196	+	1.36789i	0.829164	+	0.559006i	$0.188817\pi$
$233$	857.835	+	4865.02i	0.241196	+	1.36789i	−0.587968	+	0.808884i	$0.700072\pi$
$234$	−4050.34	+	3330.45i	−1.13153	+	0.930419i
$235$	3708.05	+	2140.84i	1.02930	+	0.594269i
$236$	2043.19	−	5283.62i	0.563560	−	1.45735i
$237$	3432.81	−	4091.06i	0.940864	−	1.12128i
$238$	−1906.73	+	5080.63i	−0.519306	+	1.38373i
$239$	−2433.44	−	4214.84i	−0.658602	−	1.14073i	−0.980978	−	0.194121i	$-0.937815\pi$
$239$	−2433.44	−	4214.84i	−0.658602	−	1.14073i	0.322375	−	0.946612i	$-0.395519\pi$
$240$	−3087.95	−	2808.16i	−0.830525	−	0.755274i
$241$	−3128.33	+	1138.62i	−0.836156	+	0.304336i	−0.724383	−	0.689398i	$-0.757875\pi$
$241$	−3128.33	+	1138.62i	−0.836156	+	0.304336i	−0.111773	+	0.993734i	$0.535653\pi$
$242$	−2420.13	+	1365.30i	−0.642860	+	0.362665i
$243$	−598.912	−	105.604i	−0.158108	−	0.0278787i
$244$	−1005.46	−	2943.69i	−0.263804	−	0.772337i
$245$	−661.218	−	788.009i	−0.172423	−	0.205486i
$246$	4476.25	−	1578.90i	1.16014	−	0.409216i
$247$	2064.94	+	1862.53i	0.531940	+	0.479798i
$248$	−3172.22	−	1960.15i	−0.812242	−	0.501894i
$249$	−8662.82	+	7268.97i	−2.20476	+	1.85001i
$250$	4033.27	+	40.1821i	1.02035	+	0.0101653i
$251$	−7405.87	−	1305.85i	−1.86237	−	0.328386i	−0.874665	−	0.484727i	$-0.838919\pi$
$251$	−7405.87	−	1305.85i	−1.86237	−	0.328386i	−0.987703	+	0.156342i	$0.950030\pi$
$252$	−7333.58	−	6406.87i	−1.83322	−	1.60157i
$253$	−532.226	−	1462.28i	−0.132256	−	0.363371i
$254$	−2835.77	−	529.205i	−0.700520	−	0.130729i
$255$	2837.84	+	4915.28i	0.696912	+	1.20709i
$256$	−1759.09	−	3699.03i	−0.429465	−	0.903084i
$257$	−5471.88	−	4591.46i	−1.32812	−	1.11442i	−0.984513	−	0.175311i	$-0.943907\pi$
$257$	−5471.88	−	4591.46i	−1.32812	−	1.11442i	−0.343607	−	0.939114i	$-0.611649\pi$
$258$	1673.52	−	1954.55i	0.403833	−	0.471646i
$259$	40.6634	+	23.4770i	0.00975559	+	0.00563239i
$260$	−999.167	+	1653.62i	−0.238330	+	0.394436i
$261$	14064.5	−	2479.96i	3.33553	−	0.588143i
$262$	−416.620	−	2508.66i	−0.0982399	−	0.591548i
$263$	3048.00	+	1109.38i	0.714629	+	0.260104i	0.673644	−	0.739056i	$-0.264728\pi$
$263$	3048.00	+	1109.38i	0.714629	+	0.260104i	0.0409851	+	0.999160i	$0.486950\pi$
$264$	9765.11	−	1422.42i	2.27652	−	0.331605i
$265$	2867.59			0.664735
$266$	−2783.87	+	4349.58i	−0.641692	+	1.00259i
$267$			12252.7i			2.80844i
$268$	−2226.55	−	438.511i	−0.507493	−	0.0999489i
$269$	1378.88	−	3788.45i	0.312535	−	0.858684i	−0.679608	−	0.733576i	$-0.737850\pi$
$269$	1378.88	−	3788.45i	0.312535	−	0.858684i	0.992143	−	0.125108i	$-0.0399278\pi$
$270$	−5134.19	+	852.648i	−1.15725	+	0.192187i
$271$	1165.82	+	6611.69i	0.261323	+	1.48204i	0.779305	+	0.626644i	$0.215572\pi$
$271$	1165.82	+	6611.69i	0.261323	+	1.48204i	−0.517982	+	0.855391i	$0.673317\pi$
$272$	747.895	+	5519.36i	0.166720	+	1.23037i
$273$	−3355.95	+	5812.67i	−0.743997	+	1.28864i
$274$	−485.518	+	567.048i	−0.107048	+	0.125024i
$275$	−2265.18	+	2699.54i	−0.496711	+	0.591957i
$276$	−46.7568	+	2346.37i	−0.0101972	+	0.511721i
$277$	−5481.64	+	3164.83i	−1.18902	+	0.686484i	−0.958085	−	0.286484i	$-0.907513\pi$
$277$	−5481.64	+	3164.83i	−1.18902	+	0.686484i	−0.230940	+	0.972968i	$0.574180\pi$
$278$	211.392	−	1132.76i	0.0456060	−	0.244382i
$279$	−8550.54	+	3112.14i	−1.83479	+	0.667811i
$280$	−3333.39	−	1327.35i	−0.711457	−	0.283301i
$281$	152.540	−	865.099i	0.0323836	−	0.183656i	−0.964325	−	0.264720i	$-0.914721\pi$
$281$	152.540	−	865.099i	0.0323836	−	0.183656i	0.996709	+	0.0810634i	$0.0258316\pi$
$282$	15266.1	+	152.091i	3.22371	+	0.0321167i
$283$	−1604.60	−	1912.29i	−0.337045	−	0.401675i	0.570726	−	0.821141i	$-0.306662\pi$
$283$	−1604.60	−	1912.29i	−0.337045	−	0.401675i	−0.907771	+	0.419466i	$0.862217\pi$
$284$	232.703	−	187.489i	0.0486210	−	0.0391740i
$285$	1664.60	+	5138.28i	0.345973	+	1.06795i
$286$	−1519.47	−	4307.76i	−0.314154	−	0.890641i
$287$	3125.64	−	2622.72i	0.642860	−	0.539423i
$288$	−9744.46	−	2223.55i	−1.99374	−	0.454944i
$289$	462.058	−	2620.46i	0.0940481	−	0.533373i
$290$	4582.98	−	2585.45i	0.928005	−	0.523528i
$291$	492.821	+	1354.01i	0.0992773	+	0.272762i
$292$	−1068.32	−	6854.69i	−0.214105	−	1.37377i
$293$	−375.687	+	216.903i	−0.0749075	+	0.0432479i	−0.536986	−	0.843591i	$-0.680437\pi$
$293$	−375.687	+	216.903i	−0.0749075	+	0.0432479i	0.462078	+	0.886839i	$0.347104\pi$
$294$	−3434.00	−	1288.76i	−0.681207	−	0.255653i
$295$	−3901.59	−	3273.82i	−0.770031	−	0.646133i
$296$	48.1712	+	1.44012i	0.00945909	+	0.000282788i
$297$	6152.44	−	10656.3i	1.20202	−	2.08197i
$298$	4171.80	−	3430.32i	0.810959	−	0.666822i
$299$	1069.83	−	188.639i	0.206922	−	0.0364859i
$300$	4654.64	−	2565.09i	0.895785	−	0.493652i
$301$	756.515	−	2078.51i	0.144866	−	0.398017i
$302$	137.021	+	80.9397i	0.0261082	+	0.0154224i
$303$	−1543.49			−0.292644
$304$	−400.457	+	5285.27i	−0.0755519	+	0.997142i
$305$	−2796.71			−0.525046
$306$	11702.1	+	6912.55i	2.18616	+	1.29139i
$307$	−343.813	+	944.619i	−0.0639168	+	0.175610i	−0.967540	−	0.252719i	$-0.918675\pi$
$307$	−343.813	+	944.619i	−0.0639168	+	0.175610i	0.903623	+	0.428329i	$0.140897\pi$
$308$	7429.43	−	4094.23i	1.37445	−	0.757437i
$309$	2489.99	−	439.053i	0.458417	−	0.0808312i
$310$	−2589.58	+	2129.32i	−0.474446	+	0.390120i
$311$	1152.30	−	1995.85i	0.210100	−	0.363904i	−0.741646	−	0.670792i	$-0.765954\pi$
$311$	1152.30	−	1995.85i	0.210100	−	0.363904i	0.951746	+	0.306888i	$0.0992878\pi$
$312$	−205.859	+	6885.88i	−0.0373541	+	1.24948i
$313$	1177.67	+	988.181i	0.212670	+	0.178451i	0.742900	−	0.669403i	$-0.233450\pi$
$313$	1177.67	+	988.181i	0.212670	+	0.178451i	−0.530230	+	0.847854i	$0.677894\pi$
$314$	−8108.72	−	3043.15i	−1.45733	−	0.546927i
$315$	−7582.21	+	4377.59i	−1.35622	+	0.783014i
$316$	−725.602	−	4655.71i	−0.129172	−	0.828810i
$317$	−1007.81	−	2768.93i	−0.178562	−	0.490595i	0.817831	−	0.575459i	$-0.195177\pi$
$317$	−1007.81	−	2768.93i	−0.178562	−	0.490595i	−0.996393	+	0.0848643i	$0.972954\pi$
$318$	8905.40	−	5023.92i	1.57041	−	0.885935i
$319$	−2160.31	+	12251.7i	−0.379166	+	2.15036i
$320$	−3658.37	+	421.684i	−0.639091	+	0.0736651i
$321$	−873.900	+	733.289i	−0.151951	+	0.127502i
$322$	671.068	+	1902.51i	0.116140	+	0.329262i
$323$	2705.81	−	6680.41i	0.466115	−	1.15080i
$324$	−5163.52	+	4160.25i	−0.885377	+	0.713348i
$325$	−1581.32	−	1884.54i	−0.269895	−	0.321648i
$326$	−7584.22	−	75.5589i	−1.28850	−	0.0128369i
$327$	1502.37	−	8520.34i	0.254070	−	1.44090i
$328$	1549.29	−	3890.75i	0.260809	−	0.654973i
$329$	12332.3	−	4488.58i	2.06657	−	0.752169i
$330$	1627.60	−	8721.61i	0.271505	−	1.45487i
$331$	−3493.24	+	2016.82i	−0.580079	+	0.334909i	−0.761165	−	0.648559i	$-0.775372\pi$
$331$	−3493.24	+	2016.82i	−0.580079	+	0.334909i	0.181086	+	0.983467i	$0.442039\pi$
$332$	−198.784	+	9975.49i	−0.0328606	+	1.64903i
$333$	75.5907	−	90.0855i	0.0124395	−	0.0148248i
$334$	1869.30	−	2183.20i	0.306238	−	0.357663i
$335$	−1020.14	+	1766.93i	−0.166377	+	0.288173i
$336$	−12677.4	+	1717.84i	−2.05836	+	0.278916i
$337$	1651.88	+	9368.28i	0.267014	+	1.51431i	0.763238	+	0.646117i	$0.223608\pi$
$337$	1651.88	+	9368.28i	0.267014	+	1.51431i	−0.496224	+	0.868194i	$0.665281\pi$
$338$	−2984.34	+	495.617i	−0.480257	+	0.0797575i
$339$	−3052.32	+	8386.17i	−0.489024	+	1.34358i
$340$	4913.26	+	967.648i	0.783703	+	0.154347i
$341$		−	7926.46i		−	1.25877i
$342$	9517.49	+	8758.08i	1.50482	+	1.38474i
$343$	4408.75			0.694024
$344$	−327.239	−	2246.55i	−0.0512894	−	0.352109i
$345$	1982.72	+	721.653i	0.309410	+	0.112616i
$346$	15.4958	+	93.3074i	0.00240769	+	0.0144978i
$347$	11562.2	−	2038.72i	1.78873	−	0.315401i	0.821673	−	0.569960i	$-0.193041\pi$
$347$	11562.2	−	2038.72i	1.78873	−	0.315401i	0.967057	+	0.254558i	$0.0819301\pi$
$348$	9702.96	−	16058.4i	1.49464	−	2.47362i
$349$	−128.403	−	74.1336i	−0.0196942	−	0.0113704i	0.490121	−	0.871655i	$-0.336953\pi$
$349$	−128.403	−	74.1336i	−0.0196942	−	0.0113704i	−0.509815	+	0.860284i	$0.670286\pi$
$350$	2971.34	−	3470.30i	0.453785	−	0.529986i
$351$	6580.34	+	5521.56i	1.00066	+	0.839656i
$352$	4723.36	−	7314.08i	0.715216	−	1.10751i
$353$	1233.91	+	2137.19i	0.186046	+	0.322241i	0.943929	−	0.330150i	$-0.107099\pi$
$353$	1233.91	+	2137.19i	0.186046	+	0.322241i	−0.757882	+	0.652391i	$0.773766\pi$
$354$	−17852.1	−	3331.52i	−2.68031	−	0.500192i
$355$	−91.8919	−	252.471i	−0.0137384	−	0.0377458i
$356$	8141.27	+	7112.50i	1.21204	+	1.05888i
$357$	17132.2	+	3020.86i	2.53986	+	0.447846i
$358$	101.996	+	1.01615i	0.0150577	+	0.000150015i
$359$	447.523	−	375.516i	0.0657921	−	0.0552061i	−0.609299	−	0.792941i	$-0.708549\pi$
$359$	447.523	−	375.516i	0.0657921	−	0.0552061i	0.675091	+	0.737735i	$0.264104\pi$
$360$	−4723.62	+	7644.50i	−0.691546	+	1.11917i
$361$	3845.37	−	5679.70i	0.560632	−	0.828065i
$362$	10888.3	−	3840.61i	1.58087	−	0.557619i
$363$	5725.81	+	6823.75i	0.827898	+	0.986650i
$364$	1914.14	+	5604.01i	0.275626	+	0.806950i
$365$	−6142.49	−	1083.09i	−0.880856	−	0.155319i
$366$	−8685.27	+	4899.73i	−1.24040	+	0.699762i
$367$	−12825.4	+	4668.08i	−1.82420	+	0.663955i	−0.829829	+	0.558017i	$0.811562\pi$
$367$	−12825.4	+	4668.08i	−1.82420	+	0.663955i	−0.994373	+	0.105938i	$0.966216\pi$
$368$	1531.90	+	1393.10i	0.216999	+	0.197337i
$369$	−5109.56	−	8850.02i	−0.720849	−	1.24855i
$370$	15.2241	−	40.5659i	0.00213910	−	0.00569979i
$371$	5649.73	−	6733.09i	0.790619	−	0.942222i
$372$	−4311.54	+	11149.5i	−0.600922	+	1.55397i
$373$	1881.12	+	1086.06i	0.261127	+	0.150762i	0.624849	−	0.780746i	$-0.285161\pi$
$373$	1881.12	+	1086.06i	0.261127	+	0.150762i	−0.363721	+	0.931508i	$0.618494\pi$
$374$	−9144.90	+	7519.51i	−1.26436	+	1.03964i
$375$	−2245.33	−	12733.9i	−0.309195	−	1.75353i
$376$	8962.80	−	10055.2i	1.22931	−	1.37915i
$377$	−8161.10	−	2970.40i	−1.11490	−	0.405791i
$378$	−8113.37	+	13734.9i	−1.10399	+	1.86891i
$379$		−	4437.11i		−	0.601370i	−0.953724	−	0.300685i	$-0.902785\pi$
$379$		−	4437.11i		−	0.601370i	0.953724	−	0.300685i	$-0.0972152\pi$
$380$	4380.38	+	1876.65i	0.591339	+	0.253342i
$381$			9247.73i			1.24350i
$382$	4792.62	+	2831.05i	0.641916	+	0.379187i
$383$	4110.34	+	1496.04i	0.548378	+	0.199593i	0.601326	−	0.799004i	$-0.294639\pi$
$383$	4110.34	+	1496.04i	0.548378	+	0.199593i	−0.0529476	+	0.998597i	$0.516862\pi$
$384$	−10622.4	+	7718.88i	−1.41165	+	1.02579i
$385$	−1324.36	−	7510.84i	−0.175314	−	0.994254i
$386$	5720.68	+	6957.24i	0.754339	+	0.917394i
$387$	−4797.61	−	2769.90i	−0.630171	−	0.363830i
$388$	1185.74	+	458.530i	0.155147	+	0.0599957i
$389$	−8220.63	+	9796.96i	−1.07147	+	1.27693i	−0.112431	+	0.993660i	$0.535864\pi$
$389$	−8220.63	+	9796.96i	−1.07147	+	1.27693i	−0.959040	+	0.283270i	$0.908581\pi$
$390$	5798.75	+	2176.23i	0.752900	+	0.282559i
$391$	−1407.82	−	2438.42i	−0.182088	−	0.315386i
$392$	−2849.69	+	1533.60i	−0.367171	+	0.197599i
$393$	−7660.65	+	2788.25i	−0.983279	+	0.357884i
$394$	6431.36	+	11400.2i	0.822353	+	1.45770i
$395$	−4171.98	−	735.633i	−0.531431	−	0.0937056i
$396$	−6867.27	−	20105.3i	−0.871447	−	2.55133i
$397$	−8968.03	−	10687.7i	−1.13373	−	1.35113i	−0.928025	−	0.372519i	$-0.878494\pi$
$397$	−8968.03	−	10687.7i	−1.13373	−	1.35113i	−0.205710	−	0.978613i	$-0.565950\pi$
$398$	3335.86	+	9457.30i	0.420129	+	1.19108i
$399$	15344.2	+	6214.97i	1.92524	+	0.779794i
$400$	997.575	−	4581.75i	0.124697	−	0.572718i
$401$	−1224.80	+	1027.73i	−0.152528	+	0.127986i	−0.715858	−	0.698246i	$-0.753964\pi$
$401$	−1224.80	+	1027.73i	−0.152528	+	0.127986i	0.563330	+	0.826232i	$0.309520\pi$
$402$	−72.4734	+	7274.52i	−0.00899165	+	0.902537i
$403$	5449.39	+	960.875i	0.673582	+	0.118771i
$404$	−895.968	+	1025.56i	−0.110337	+	0.126296i
$405$	2039.02	+	5602.16i	0.250172	+	0.687342i
$406$	2958.75	−	15854.7i	0.361676	−	1.93806i
$407$	51.2204	+	88.7163i	0.00623808	+	0.0108047i
$408$	16953.6	−	5602.79i	2.05717	−	0.679851i
$409$	−1707.07	−	1432.41i	−0.206380	−	0.173173i	0.533739	−	0.845649i	$-0.320786\pi$
$409$	−1707.07	−	1432.41i	−0.206380	−	0.173173i	−0.740119	+	0.672476i	$0.765231\pi$
$410$	−2860.05	−	2448.83i	−0.344507	−	0.294974i
$411$	2072.50	+	1196.56i	0.248732	+	0.143605i
$412$	1153.67	−	1909.33i	0.137955	−	0.228315i
$413$	−15373.8	+	2710.82i	−1.83171	+	0.322980i
$414$	4984.37	−	827.767i	0.591711	−	0.0982670i
$415$	8429.47	+	3068.08i	0.997076	+	0.362906i
$416$	4455.80	+	4133.92i	0.525153	+	0.487217i
$417$	−3694.03			−0.433807
$418$	−10004.7	+	5181.41i	−1.17069	+	0.606294i
$419$		−	9487.00i		−	1.10613i	−0.833137	−	0.553067i	$-0.813457\pi$
$419$		−	9487.00i		−	1.10613i	0.833137	−	0.553067i	$-0.186543\pi$
$420$	−2222.59	+	11285.3i	−0.258217	+	1.31111i
$421$	856.514	−	2353.25i	0.0991542	−	0.272424i	−0.880191	−	0.474620i	$-0.842586\pi$
$421$	856.514	−	2353.25i	0.0991542	−	0.272424i	0.979345	+	0.202196i	$0.0648078\pi$
$422$	584.637	+	3520.37i	0.0674401	+	0.406088i
$423$	−5707.64	−	32369.6i	−0.656063	−	3.72072i
$424$	1831.31	−	8833.46i	0.209756	−	1.01177i
$425$	−3188.14	+	5522.03i	−0.363877	+	0.630253i
$426$	−727.693	−	623.065i	−0.0827626	−	0.0708630i
$427$	−5510.07	+	6566.65i	−0.624476	+	0.744221i
$428$	−20.0532	+	1006.32i	−0.00226474	+	0.113650i
$429$	−12681.7	+	7321.76i	−1.42722	+	0.824004i
$430$	−2006.48	−	374.444i	−0.225026	−	0.0419937i
$431$	7303.53	−	2658.27i	0.816238	−	0.297086i	0.100040	−	0.994983i	$-0.468103\pi$
$431$	7303.53	−	2658.27i	0.816238	−	0.297086i	0.716198	+	0.697897i	$0.245881\pi$
$432$	−652.283	+	16360.1i	−0.0726458	+	1.82205i
$433$	2374.86	−	13468.5i	0.263576	−	1.49481i	−0.509483	−	0.860481i	$-0.670163\pi$
$433$	2374.86	−	13468.5i	0.263576	−	1.49481i	0.773059	−	0.634334i	$-0.218725\pi$
$434$	−102.371	+	10275.5i	−0.0113225	+	1.13650i
$435$	−10842.9	−	12922.0i	−1.19512	−	1.42429i
$436$	−4789.21	−	5944.15i	−0.526058	−	0.652921i
$437$	−825.788	−	2549.04i	−0.0903954	−	0.279033i
$438$	−20973.2	+	7397.85i	−2.28799	+	0.807039i
$439$	−10046.0	+	8429.63i	−1.09219	+	0.916456i	−0.996875	−	0.0789914i	$-0.974830\pi$
$439$	−10046.0	+	8429.63i	−1.09219	+	0.916456i	−0.0953142	+	0.995447i	$0.530386\pi$
$440$	−4850.24	−	6144.20i	−0.525514	−	0.665712i
$441$	−1371.26	+	7776.78i	−0.148068	+	0.839735i
$442$	−4061.04	−	7198.60i	−0.437023	−	0.774667i
$443$	−4812.28	−	13221.6i	−0.516113	−	1.41801i	−0.874769	−	0.484539i	$-0.838987\pi$
$443$	−4812.28	−	13221.6i	−0.516113	−	1.41801i	0.358656	−	0.933470i	$-0.383235\pi$
$444$	−23.7910	−	152.651i	−0.00254295	−	0.0163164i
$445$	8417.29	−	4859.72i	0.896669	−	0.517692i
$446$	3354.05	−	8937.14i	0.356096	−	0.948847i
$447$	−13263.5	−	11129.4i	−1.40345	−	1.17764i
$448$	−6217.61	+	9420.63i	−0.655702	+	0.993489i
$449$	−4739.42	+	8208.92i	−0.498145	+	0.862813i	−0.999998	−	0.00214024i	$-0.999319\pi$
$449$	−4739.42	+	8208.92i	−0.498145	+	0.862813i	0.501852	+	0.864953i	$0.332652\pi$
$450$	−7267.20	−	8838.05i	−0.761287	−	0.925844i
$451$	8766.71	−	1545.81i	0.915318	−	0.161395i
$452$	3800.34	+	6896.13i	0.395471	+	0.717625i
$453$	174.488	−	479.401i	0.0180975	−	0.0497223i
$454$	−421.672	+	713.839i	−0.0435904	+	0.0737932i
$455$	5324.20			0.548576
$456$	16891.2	−	1846.27i	1.73466	−	0.189604i
$457$	3086.06			0.315886			0.157943	−	0.987448i	$-0.449514\pi$
$457$	3086.06			0.315886			0.157943	+	0.987448i	$0.449514\pi$
$458$	5112.50	−	8654.83i	0.521597	−	0.883000i
$459$	7614.86	−	20921.7i	0.774360	−	2.12754i
$460$	1630.44	−	898.506i	0.165260	−	0.0910719i
$461$	−11271.2	+	1987.42i	−1.13873	+	0.200789i	−0.711050	−	0.703142i	$-0.751780\pi$
$461$	−11271.2	+	1987.42i	−1.13873	+	0.200789i	−0.427679	+	0.903930i	$0.640669\pi$
$462$	−17271.6	−	21004.9i	−1.73928	−	2.11523i
$463$	4658.21	−	8068.25i	0.467571	−	0.809857i	−0.531743	−	0.846906i	$-0.678463\pi$
$463$	4658.21	−	8068.25i	0.467571	−	0.809857i	0.999313	+	0.0370495i	$0.0117959\pi$
$464$	−5037.54	−	15768.7i	−0.504013	−	1.57768i
$465$	8233.14	+	6908.42i	0.821081	+	0.688969i
$466$	4909.49	−	13081.7i	0.488042	−	1.30043i
$467$	−13161.8	+	7599.00i	−1.30419	+	0.752976i	−0.981120	−	0.193399i	$-0.938049\pi$
$467$	−13161.8	+	7599.00i	−1.30419	+	0.752976i	−0.323072	+	0.946374i	$0.604716\pi$
$468$	14654.7	−	2283.97i	1.44747	−	0.225591i
$469$	2138.87	+	5876.49i	0.210584	+	0.578574i
$470$	−5950.44	−	10547.7i	−0.583985	−	1.03517i
$471$	−4821.32	+	27343.1i	−0.471666	+	2.67495i
$472$	−12576.5	+	9927.88i	−1.22644	+	0.968152i
$473$	3696.75	−	3101.94i	0.359359	−	0.301538i
$474$	−14245.0	+	5024.63i	−1.38037	+	0.486896i
$475$	−4064.14	+	4505.81i	−0.392580	+	0.435243i
$476$	11952.1	−	9629.84i	1.15089	−	0.927275i
$477$	−14150.0	−	16863.3i	−1.35825	−	1.61870i
$478$	−137.135	+	13764.9i	−0.0131222	+	1.31714i
$479$	2297.92	−	13032.2i	0.219195	−	1.24312i	−0.654280	−	0.756252i	$-0.727028\pi$
$479$	2297.92	−	13032.2i	0.219195	−	1.24312i	0.873476	−	0.486867i	$-0.161861\pi$
$480$	3480.35	+	11280.8i	0.330949	+	1.07270i
$481$	−67.2010	+	24.4592i	−0.00637027	+	0.00231859i
$482$	9256.32	+	1727.39i	0.874717	+	0.163238i
$483$	5600.80	−	3233.62i	0.527630	−	0.304627i
$484$	7857.75	+	156.583i	0.737955	+	0.0147054i
$485$	734.707	−	875.590i	0.0687862	−	0.0819762i
$486$	1306.60	+	1118.74i	0.121952	+	0.104418i
$487$	−1091.36	+	1890.30i	−0.101549	+	0.175888i	−0.912323	−	0.409471i	$-0.865713\pi$
$487$	−1091.36	+	1890.30i	−0.101549	+	0.175888i	0.810774	+	0.585359i	$0.199047\pi$
$488$	−1786.05	+	8615.10i	−0.165677	+	0.799154i
$489$	4222.14	+	23944.9i	0.390454	+	2.21437i
$490$	476.664	+	2870.21i	0.0439459	+	0.264619i
$491$	1722.76	−	4733.25i	0.158345	−	0.435048i	−0.834997	−	0.550254i	$-0.814531\pi$
$491$	1722.76	−	4733.25i	0.158345	−	0.435048i	0.993342	+	0.115206i	$0.0367529\pi$
$492$	−13172.3	−	2594.23i	−1.20701	−	0.237717i
$493$			22510.1i			2.05640i
$494$	−2349.38	−	7506.30i	−0.213975	−	0.683652i
$495$	−19101.4			−1.73443
$496$	4905.47	+	9336.89i	0.444077	+	0.845240i
$497$	−773.846	−	281.657i	−0.0698425	−	0.0254206i
$498$	31553.1	−	5240.11i	2.83922	−	0.471516i
$499$	7372.95	−	1300.05i	0.661440	−	0.116630i	0.167156	−	0.985930i	$-0.446542\pi$
$499$	7372.95	−	1300.05i	0.661440	−	0.116630i	0.494284	+	0.869301i	$0.335430\pi$
$500$	−9764.34	−	5899.90i	−0.873350	−	0.527703i
$501$	−7979.35	−	4606.88i	−0.711559	−	0.410819i
$502$	16156.8	+	13833.8i	1.43648	+	1.22995i
$503$	7429.60	+	6234.18i	0.658588	+	0.552621i	0.909663	−	0.415347i	$-0.136340\pi$
$503$	7429.60	+	6234.18i	0.658588	+	0.552621i	−0.251076	+	0.967968i	$0.580784\pi$
$504$	8642.74	+	26152.2i	0.763846	+	2.31133i
$505$	612.184	+	1060.33i	0.0539442	+	0.0934341i
$506$	−807.436	+	4326.69i	−0.0709386	+	0.380128i
$507$	3316.94	+	9113.22i	0.290553	+	0.798289i
$508$	6144.61	+	5368.15i	0.536660	+	0.468845i
$509$	−7925.58	−	1397.49i	−0.690167	−	0.121695i	−0.182445	−	0.983216i	$-0.558401\pi$
$509$	−7925.58	−	1397.49i	−0.690167	−	0.121695i	−0.507722	+	0.861521i	$0.669512\pi$
$510$	159.925	−	16052.5i	0.0138855	−	1.39375i
$511$	−14645.0	+	12288.6i	−1.26782	+	1.06383i
$512$	−1037.35	+	11538.7i	−0.0895407	+	0.995983i
$513$	11243.3	−	17958.3i	0.967649	−	1.54557i
$514$	6720.55	+	19053.0i	0.576713	+	1.63501i
$515$	−1289.21	−	1536.42i	−0.110309	−	0.131462i
$516$	−6887.20	+	2352.43i	−0.587581	+	0.200698i
$517$	28197.4	+	4971.96i	2.39869	+	0.422953i
$518$	−65.2539	−	115.669i	−0.00553493	−	0.00981122i
$519$	284.931	−	103.706i	0.0240984	−	0.00877111i
$520$	4812.06	−	2589.69i	0.405813	−	0.218395i
$521$	6161.05	+	10671.2i	0.518081	+	0.897343i	0.999779	+	0.0210059i	$0.00668689\pi$
$521$	6161.05	+	10671.2i	0.518081	+	0.897343i	−0.481698	+	0.876337i	$0.659980\pi$
$522$	−37818.6	−	14193.1i	−3.17102	−	1.19007i
$523$	−11125.4	+	13258.7i	−0.930168	+	1.10853i	0.0637012	+	0.997969i	$0.479710\pi$
$523$	−11125.4	+	13258.7i	−0.930168	+	1.10853i	−0.993869	+	0.110562i	$0.964735\pi$
$524$	−2594.24	+	6708.62i	−0.216278	+	0.559289i
$525$	−12683.5	−	7322.85i	−1.05439	−	0.608753i
$526$	−5826.83	−	7086.33i	−0.483007	−	0.587412i
$527$	−2490.48	−	14124.2i	−0.205857	−	1.16748i
$528$	−25827.0	−	10583.6i	−2.12874	−	0.872331i
$529$	10449.6	+	3803.36i	0.858850	+	0.312596i
$530$	−6983.39	−	4125.16i	−0.572338	−	0.338086i
$531$			39098.4i			3.19534i
$532$	13036.6	−	6587.73i	1.06242	−	0.536869i
$533$			6214.45i			0.505024i
$534$	17626.1	−	29838.8i	1.42838	−	2.41807i
$535$	850.360	+	309.506i	0.0687182	+	0.0250114i
$536$	4791.45	+	4270.89i	0.386118	+	0.344168i
$537$	−56.7813	−	322.023i	−0.00456293	−	0.0258777i
$538$	−8807.83	+	7242.35i	−0.705822	+	0.580372i
$539$	−5957.32	−	3439.46i	−0.476066	−	0.274857i
$540$	13729.8	+	5309.33i	1.09414	+	0.423106i
$541$	−8411.87	+	10024.9i	−0.668493	+	0.796679i	−0.988578	−	0.150710i	$-0.951844\pi$
$541$	−8411.87	+	10024.9i	−0.668493	+	0.796679i	0.320085	+	0.947389i	$0.396288\pi$
$542$	6672.12	−	17778.4i	0.528768	−	1.40894i
$543$	−18506.5	−	32054.2i	−1.46259	−	2.53329i
$544$	6118.51	−	14517.1i	0.482223	−	1.14414i
$545$	−6449.12	+	2347.29i	−0.506880	+	0.184489i
$546$	16534.5	−	9327.80i	1.29599	−	0.731123i
$547$	−752.470	−	132.681i	−0.0588177	−	0.0103711i	0.144162	−	0.989554i	$-0.453951\pi$
$547$	−752.470	−	132.681i	−0.0588177	−	0.0103711i	−0.202980	+	0.979183i	$0.565063\pi$
$548$	1998.10	−	682.481i	0.155756	−	0.0532010i
$549$	13800.2	+	16446.5i	1.07282	+	1.27854i
$550$	9399.75	−	3315.56i	0.728740	−	0.257047i
$551$	−4471.96	+	20949.5i	−0.345757	+	1.61974i
$552$	3489.23	−	5646.81i	0.269042	−	0.435406i
$553$	−9946.90	+	8346.44i	−0.764892	+	0.641820i
$554$	17902.1	+	178.352i	1.37290	+	0.0136777i
$555$	−136.791	−	24.1199i	−0.0104620	−	0.00184474i
$556$	−2144.32	+	2454.48i	−0.163560	+	0.187218i
$557$	356.686	+	979.986i	0.0271333	+	0.0745482i	0.952520	−	0.304477i	$-0.0984816\pi$
$557$	356.686	+	979.986i	0.0271333	+	0.0745482i	−0.925386	+	0.379025i	$0.876259\pi$
$558$	25299.9	+	4721.41i	1.91941	+	0.358196i
$559$	1684.43	+	2917.52i	0.127449	+	0.220748i
$560$	6208.27	+	8027.70i	0.468477	+	0.605772i
$561$	29074.7	+	24396.5i	2.18812	+	1.83605i
$562$	−1615.96	+	1887.32i	−0.121290	+	0.141658i
$563$	−4564.22	−	2635.15i	−0.341668	−	0.197262i	0.319342	−	0.947640i	$-0.396538\pi$
$563$	−4564.22	−	2635.15i	−0.341668	−	0.197262i	−0.661009	+	0.750378i	$0.729872\pi$
$564$	−36958.5	−	22331.4i	−2.75928	−	1.66724i
$565$	6971.69	−	1229.30i	0.519117	−	0.0915344i
$566$	1156.74	+	6965.26i	0.0859035	+	0.517265i
$567$	17171.1	+	6249.77i	1.27181	+	0.462903i
$568$	−836.407	+	121.834i	−0.0617867	+	0.00900006i
$569$	4687.67			0.345373			0.172687	−	0.984977i	$-0.444755\pi$
$569$	4687.67			0.345373			0.172687	+	0.984977i	$0.444755\pi$
$570$	3337.89	−	14907.7i	0.245278	−	1.09547i
$571$		−	3058.58i		−	0.224164i	−0.993699	−	0.112082i	$-0.964248\pi$
$571$		−	3058.58i		−	0.224164i	0.993699	−	0.112082i	$-0.0357519\pi$
$572$	−2496.58	+	12676.4i	−0.182495	+	0.926623i
$573$	6103.11	−	16768.1i	0.444958	−	1.22251i
$574$	−11384.7	+	1890.69i	−0.827855	+	0.137484i
$575$	411.620	+	2334.41i	0.0298535	+	0.169308i
$576$	20531.8	+	19432.8i	1.48523	+	1.40573i
$577$	5649.61	−	9785.42i	0.407620	−	0.706018i	−0.587003	−	0.809585i	$-0.699692\pi$
$577$	5649.61	−	9785.42i	0.407620	−	0.706018i	0.994622	+	0.103567i	$0.0330256\pi$
$578$	−4894.90	+	5716.87i	−0.352251	+	0.411402i
$579$	18560.4	−	22119.4i	1.33220	−	1.58765i
$580$	−14880.1	−	296.520i	−1.06528	−	0.0212281i
$581$	23811.6	−	13747.6i	1.70029	−	0.981664i
$582$	747.655	−	4006.35i	0.0532496	−	0.285341i
$583$	18019.6	−	6558.61i	1.28010	−	0.465918i
$584$	−7259.13	+	18229.9i	−0.514358	+	1.29171i
$585$	2315.54	−	13132.1i	0.163651	−	0.928112i
$586$	1226.93	+	12.2235i	0.0864914	+	0.000861683i
$587$	6278.14	+	7481.99i	0.441442	+	0.526090i	0.940187	−	0.340659i	$-0.110650\pi$
$587$	6278.14	+	7481.99i	0.441442	+	0.526090i	−0.498745	+	0.866749i	$0.666206\pi$
$588$	6508.81	+	8078.45i	0.456494	+	0.566581i
$589$	488.166	−	13639.7i	0.0341503	−	0.954185i
$590$	4791.92	+	13585.3i	0.334373	+	0.947961i
$591$	32143.8	−	26971.9i	2.23726	−	1.87728i
$592$	−115.239	−	72.8035i	−0.00800047	−	0.00505440i
$593$	1513.22	−	8581.92i	0.104790	−	0.594295i	−0.886514	−	0.462703i	$-0.846880\pi$
$593$	1513.22	−	8581.92i	0.104790	−	0.594295i	0.991304	−	0.131593i	$-0.0420091\pi$
$594$	−30312.5	+	17100.6i	−2.09384	+	1.18122i
$595$	−4719.78	−	12967.5i	−0.325197	−	0.893470i
$596$	−15094.2	+	2352.46i	−1.03738	+	0.161678i
$597$	27841.4	−	16074.2i	1.90867	−	1.10197i
$598$	−2876.69	−	1079.60i	−0.196717	−	0.0738266i
$599$	−16329.0	−	13701.6i	−1.11383	−	0.934613i	−0.115552	−	0.993301i	$-0.536864\pi$
$599$	−16329.0	−	13701.6i	−1.11383	−	0.934613i	−0.998276	+	0.0586886i	$0.981308\pi$
$600$	−15025.3	−	449.195i	−1.02234	−	0.0305639i
$601$	2739.75	−	4745.38i	0.185951	−	0.322077i	−0.757946	−	0.652318i	$-0.773797\pi$
$601$	2739.75	−	4745.38i	0.185951	−	0.322077i	0.943897	+	0.330241i	$0.107130\pi$
$602$	−4832.36	+	3973.47i	−0.327163	+	0.269014i
$603$	15424.5	−	2719.76i	1.04168	−	0.183677i
$604$	−217.249	−	394.222i	−0.0146353	−	0.0265574i
$605$	2416.74	−	6639.94i	0.162404	−	0.446201i
$606$	3758.82	+	2220.38i	0.251966	+	0.148839i
$607$	−8039.07			−0.537555			−0.268777	−	0.963202i	$-0.586620\pi$
$607$	−8039.07			−0.537555			−0.268777	+	0.963202i	$0.586620\pi$
$608$	8578.33	−	12295.0i	0.572199	−	0.820115i
$609$	−51703.5			−3.44028
$610$	6810.77	+	4023.19i	0.452065	+	0.267040i
$611$	−6836.39	+	18782.8i	−0.452652	+	1.24365i
$612$	−18553.8	−	33668.0i	−1.22548	−	2.22377i
$613$	−1676.05	+	295.533i	−0.110432	+	0.0194722i	−0.228591	−	0.973523i	$-0.573412\pi$
$613$	−1676.05	+	295.533i	−0.110432	+	0.0194722i	0.118159	+	0.992995i	$0.462301\pi$
$614$	2196.16	−	1805.82i	0.144348	−	0.118692i
$615$	−6035.14	+	10453.2i	−0.395708	+	0.685386i
$616$	−23982.5	−	716.977i	−1.56864	−	0.0468958i
$617$	19783.5	+	16600.3i	1.29085	+	1.08315i	0.991650	+	0.128960i	$0.0411640\pi$
$617$	19783.5	+	16600.3i	1.29085	+	1.08315i	0.299199	+	0.954191i	$0.403280\pi$
$618$	−6695.43	−	2512.75i	−0.435808	−	0.163556i
$619$	−6018.57	+	3474.82i	−0.390802	+	0.225630i	−0.682508	−	0.730878i	$-0.739111\pi$
$619$	−6018.57	+	3474.82i	−0.390802	+	0.225630i	0.291705	+	0.956508i	$0.405777\pi$
$620$	9369.47	−	1460.25i	0.606915	−	0.0945889i
$621$	−2830.87	−	7777.76i	−0.182929	−	0.502594i
$622$	−5677.29	+	3202.80i	−0.365979	+	0.206464i
$623$	5173.14	−	29338.4i	0.332677	−	1.88670i
$624$	10407.0	−	16472.9i	0.667649	−	1.05680i
$625$	−841.551	+	706.145i	−0.0538593	+	0.0451933i
$626$	−1446.41	−	4100.63i	−0.0923484	−	0.261811i
$627$	22212.2	+	28481.2i	1.41478	+	1.81408i
$628$	15369.3	+	19075.7i	0.976595	+	1.21211i
$629$	119.144	+	141.991i	0.00755261	+	0.00900085i
$630$	24762.2	+	246.697i	1.56595	+	0.0156010i
$631$	−672.827	+	3815.79i	−0.0424482	+	0.240736i	−0.998648	−	0.0519784i	$-0.983447\pi$
$631$	−672.827	+	3815.79i	−0.0424482	+	0.240736i	0.956200	+	0.292714i	$0.0945584\pi$
$632$	−4930.40	+	12381.8i	−0.310318	+	0.779304i
$633$	10750.1	−	3912.71i	0.675004	−	0.245682i
$634$	−1528.94	+	8192.89i	−0.0957757	+	0.513220i
$635$	6352.94	−	3667.87i	0.397021	−	0.229220i
$636$	−28914.3	−	576.183i	−1.80271	−	0.0359232i
$637$	3086.77	−	3678.67i	0.191998	−	0.228814i
$638$	22885.6	−	26728.7i	1.42014	−	1.65862i
$639$	−1031.26	+	1786.19i	−0.0638433	+	0.110580i
$640$	9515.77	+	4235.81i	0.587725	+	0.261618i
$641$	−26.7049	−	151.451i	−0.00164552	−	0.00933221i	0.983974	−	0.178312i	$-0.0570637\pi$
$641$	−26.7049	−	151.451i	−0.00164552	−	0.00933221i	−0.985619	+	0.168980i	$0.945953\pi$
$642$	3183.06	−	528.619i	0.195678	−	0.0324968i
$643$	−6219.63	+	17088.3i	−0.381459	+	1.04805i	0.589283	+	0.807927i	$0.299410\pi$
$643$	−6219.63	+	17088.3i	−0.381459	+	1.04805i	−0.970742	+	0.240124i	$0.922812\pi$
$644$	1102.60	−	5598.49i	0.0674668	−	0.342565i
$645$			6543.32i			0.399446i
$646$	−16199.5	+	12376.2i	−0.986625	+	0.753772i
$647$	−16079.7			−0.977061			−0.488530	−	0.872547i	$-0.662467\pi$
$647$	−16079.7			−0.977061			−0.488530	+	0.872547i	$0.662467\pi$
$648$	18559.3	−	2703.41i	1.12512	−	0.163889i
$649$	−32004.9	−	11648.8i	−1.93575	−	0.704555i
$650$	1139.95	+	6864.19i	0.0687888	+	0.414209i
$651$	32441.9	−	5720.38i	1.95314	−	0.344392i
$652$	18361.0	+	11094.3i	1.10287	+	0.666387i
$653$	6386.63	+	3687.32i	0.382739	+	0.220974i	0.679009	−	0.734130i	$-0.262410\pi$
$653$	6386.63	+	3687.32i	0.382739	+	0.220974i	−0.296271	+	0.955104i	$0.595743\pi$
$654$	−15915.6	+	18588.2i	−0.951603	+	1.11140i
$655$	4953.85	+	4156.77i	0.295516	+	0.247967i
$656$	−9369.99	+	7246.34i	−0.557678	+	0.431284i
$657$	23940.6	+	41466.3i	1.42163	+	2.46233i
$658$	−36489.6	−	6809.59i	−2.16187	−	0.403443i
$659$	4065.96	+	11171.1i	0.240345	+	0.660342i	0.999950	+	0.00995779i	$0.00316971\pi$
$659$	4065.96	+	11171.1i	0.240345	+	0.660342i	−0.759606	+	0.650384i	$0.774608\pi$
$660$	−16510.1	+	18898.2i	−0.973719	+	1.11456i
$661$	1851.77	+	326.518i	0.108965	+	0.0192134i	0.227865	−	0.973693i	$-0.426826\pi$
$661$	1851.77	+	326.518i	0.108965	+	0.0192134i	−0.118900	+	0.992906i	$0.537937\pi$
$662$	11408.3	+	113.657i	0.669784	+	0.00667282i
$663$	−20297.0	+	17031.2i	−1.18895	+	0.997643i
$664$	14834.3	−	24007.2i	0.866992	−	1.40310i
$665$	−1816.37	−	13006.1i	−0.105919	−	0.758427i
$666$	−313.677	+	110.643i	−0.0182503	+	0.00643742i
$667$	5379.04	+	6410.48i	0.312259	+	0.372136i
$668$	−7692.90	+	2627.63i	−0.445580	+	0.152195i
$669$	−30136.5	−	5313.88i	−1.74162	−	0.307095i
$670$	5026.14	−	2835.46i	0.289816	−	0.163498i
$671$	−17574.2	+	6396.49i	−1.01110	+	0.368009i
$672$	33344.2	+	14053.6i	1.91411	+	0.806741i
$673$	−735.261	−	1273.51i	−0.0421133	−	0.0729424i	0.844200	−	0.536028i	$-0.180076\pi$
$673$	−735.261	−	1273.51i	−0.0421133	−	0.0729424i	−0.886314	+	0.463085i	$0.846742\pi$
$674$	9453.91	−	25190.7i	0.540283	−	1.43963i
$675$	−12048.3	+	14358.6i	−0.687023	+	0.818762i
$676$	7980.67	+	3086.14i	0.454066	+	0.175588i
$677$	3347.60	+	1932.74i	0.190042	+	0.109721i	0.592002	−	0.805936i	$-0.298338\pi$
$677$	3347.60	+	1932.74i	0.190042	+	0.109721i	−0.401960	+	0.915657i	$0.631671\pi$
$678$	19497.1	−	16031.8i	1.10440	−	0.908107i
$679$	−608.359	−	3450.17i	−0.0343839	−	0.195001i
$680$	−10573.2	−	9424.44i	−0.596268	−	0.531487i
$681$	2497.54	+	909.029i	0.140537	+	0.0511514i
$682$	−11402.6	+	19303.2i	−0.640216	+	1.08381i
$683$		−	28164.0i		−	1.57784i	−0.614495	−	0.788921i	$-0.710640\pi$
$683$		−	28164.0i		−	1.57784i	0.614495	−	0.788921i	$-0.289360\pi$
$684$	−10578.8	−	35019.7i	−0.591363	−	1.95762i
$685$		−	1898.33i		−	0.105885i
$686$	−10736.5	−	6342.19i	−0.597555	−	0.352982i
$687$	−30281.0	−	11021.4i	−1.68165	−	0.612070i
$688$	−2434.84	+	5941.72i	−0.134924	+	0.329253i
$689$	2324.60	+	13183.4i	0.128534	+	0.728954i
$690$	−3790.36	−	4609.67i	−0.209125	−	0.254329i
$691$	−7408.28	−	4277.17i	−0.407850	−	0.235472i	0.282016	−	0.959410i	$-0.408997\pi$
$691$	−7408.28	−	4277.17i	−0.407850	−	0.235472i	−0.689866	+	0.723938i	$0.742330\pi$
$692$	96.4903	−	249.521i	0.00530059	−	0.0137072i
$693$	−37633.6	+	44850.0i	−2.06289	+	2.45846i
$694$	−31089.9	−	11667.8i	−1.70051	−	0.638192i
$695$	1465.14	+	2537.70i	0.0799654	+	0.138504i
$696$	−46730.2	+	25148.6i	−2.54498	+	1.36962i
$697$	15135.7	−	5508.96i	0.822536	−	0.299378i
$698$	206.053	+	365.250i	0.0111737	+	0.0198065i
$699$	−44112.3	−	7778.19i	−2.38695	−	0.420884i
$700$	−12228.2	+	4176.74i	−0.660262	+	0.225523i
$701$	2458.07	+	2929.42i	0.132440	+	0.157835i	0.828188	−	0.560450i	$-0.189372\pi$
$701$	2458.07	+	2929.42i	0.132440	+	0.157835i	−0.695749	+	0.718285i	$0.744927\pi$
$702$	−8081.96	−	22912.7i	−0.434521	−	1.23189i
$703$	82.6753	+	155.816i	0.00443550	+	0.00835947i
$704$	−22024.3	+	11017.1i	−1.17908	+	0.589802i
$705$	−29740.2	+	24955.0i	−1.58877	+	1.33313i
$706$	69.5361	−	6979.69i	0.00370684	−	0.372074i
$707$	3695.78	+	651.666i	0.196597	+	0.0346654i
$708$	38682.4	+	33794.3i	2.05335	+	1.79388i
$709$	9142.68	+	25119.3i	0.484289	+	1.33057i	0.905783	+	0.423741i	$0.139283\pi$
$709$	9142.68	+	25119.3i	0.484289	+	1.33057i	−0.421495	+	0.906831i	$0.638494\pi$
$710$	−139.408	+	747.028i	−0.00736888	+	0.0394866i
$711$	16260.4	+	28163.9i	0.857685	+	1.48555i
$712$	−9594.62	−	29032.5i	−0.505019	−	1.52815i
$713$	−4084.37	−	3427.19i	−0.214531	−	0.180013i
$714$	−37376.0	−	32002.1i	−1.95905	−	1.67738i
$715$	10059.7	+	5807.97i	0.526170	+	0.303784i
$716$	−246.927	−	149.201i	−0.0128884	−	0.00778756i
$717$	43458.7	−	7662.94i	2.26359	−	0.399132i
$718$	−1630.04	+	270.705i	−0.0847251	+	0.0140705i
$719$	24571.3	+	8943.23i	1.27449	+	0.463875i	0.888605	−	0.458673i	$-0.151675\pi$
$719$	24571.3	+	8943.23i	1.27449	+	0.463875i	0.385881	+	0.922548i	$0.373897\pi$
$720$	22500.3	−	11821.3i	1.16463	−	0.611882i
$721$	−6147.50			−0.317538
$722$	−17535.1	+	8299.92i	−0.903861	+	0.427827i
$723$		−	30185.7i		−	1.55272i
$724$	−32040.9	−	6310.35i	−1.64474	−	0.323926i
$725$	6481.55	−	17807.9i	0.332026	−	0.912234i
$726$	−4127.66	−	24854.6i	−0.211008	−	1.27058i
$727$	3807.03	+	21590.7i	0.194216	+	1.10145i	0.913531	+	0.406768i	$0.133344\pi$
$727$	3807.03	+	21590.7i	0.194216	+	1.10145i	−0.719316	+	0.694683i	$0.755544\pi$
$728$	3400.16	−	16400.9i	0.173102	−	0.834969i
$729$	−8432.61	+	14605.7i	−0.428421	+	0.742047i
$730$	13400.6	+	11473.9i	0.679423	+	0.581736i
$731$	5612.63	−	6688.87i	0.283982	−	0.338436i
$732$	28199.5	+	561.940i	1.42389	+	0.0283742i
$733$	12921.1	−	7460.00i	0.651094	−	0.375909i	−0.137781	−	0.990463i	$-0.543997\pi$
$733$	12921.1	−	7460.00i	0.651094	−	0.375909i	0.788875	+	0.614554i	$0.210664\pi$
$734$	37948.8	+	7081.90i	1.90833	+	0.356128i
$735$	8764.72	−	3190.10i	0.439852	−	0.160093i
$736$	−1726.56	−	5596.28i	−0.0864699	−	0.280274i
$737$	−2369.21	+	13436.4i	−0.118414	+	0.671557i
$738$	−287.946	+	28902.6i	−0.0143624	+	1.44163i
$739$	−3789.36	−	4515.98i	−0.188625	−	0.224794i	0.663441	−	0.748228i	$-0.269095\pi$
$739$	−3789.36	−	4515.98i	−0.188625	−	0.224794i	−0.852066	+	0.523434i	$0.824651\pi$
$740$	−95.4310	+	76.8888i	−0.00474069	+	0.00381958i
$741$	−22273.3	+	11818.1i	−1.10422	+	0.585897i
$742$	−23444.5	+	8269.56i	−1.15994	+	0.409144i
$743$	−22407.0	+	18801.7i	−1.10637	+	0.928356i	−0.997837	−	0.0657370i	$-0.979060\pi$
$743$	−22407.0	+	18801.7i	−1.10637	+	0.928356i	−0.108534	+	0.994093i	$0.534616\pi$
$744$	26538.9	−	20949.8i	1.30775	−	1.03234i
$745$	−2384.98	+	13525.9i	−0.117287	+	0.665168i
$746$	−3018.69	−	5350.94i	−0.148153	−	0.262616i
$747$	−23552.5	−	64710.0i	−1.15360	−	3.16950i
$748$	33087.6	−	5156.76i	1.61738	−	0.252072i
$749$	2402.10	−	1386.85i	0.117184	−	0.0676561i
$750$	−12850.3	+	34240.5i	−0.625634	+	1.66705i
$751$	14714.5	+	12347.0i	0.714969	+	0.599930i	0.925988	−	0.377552i	$-0.123234\pi$
$751$	14714.5	+	12347.0i	0.714969	+	0.599930i	−0.211020	+	0.977482i	$0.567678\pi$
$752$	−36291.8	+	11593.9i	−1.75988	+	0.562217i
$753$	34093.3	−	59051.4i	1.64997	−	2.85784i
$754$	15601.5	+	18973.9i	0.753545	+	0.916428i
$755$	−398.541	+	70.2736i	−0.0192111	+	0.00338744i
$756$	39516.6	−	21776.9i	1.90107	−	1.04764i
$757$	−5920.38	+	16266.1i	−0.284253	+	0.780980i	0.712590	+	0.701581i	$0.247522\pi$
$757$	−5920.38	+	16266.1i	−0.284253	+	0.780980i	−0.996843	+	0.0793986i	$0.974700\pi$
$758$	−6382.99	+	10805.6i	−0.305858	+	0.517780i
$759$	14109.8			0.674772
$760$	−7967.80	−	10871.5i	−0.380293	−	0.518885i
$761$	18436.2			0.878200			0.439100	−	0.898438i	$-0.355297\pi$
$761$	18436.2			0.878200			0.439100	+	0.898438i	$0.355297\pi$
$762$	13303.3	−	22520.8i	0.632450	−	1.07066i
$763$	−7194.64	+	19767.1i	−0.341367	+	0.937899i
$764$	−7598.78	−	13788.8i	−0.359835	−	0.652960i
$765$	−34036.9	+	6001.62i	−1.60863	+	0.283646i
$766$	−7857.71	−	9556.20i	−0.370641	−	0.450757i
$767$	11888.2	−	20591.0i	0.559660	−	0.969360i
$768$	36972.5	−	3516.82i	1.73715	−	0.165237i
$769$	−5957.20	−	4998.69i	−0.279353	−	0.234405i	0.492336	−	0.870405i	$-0.336143\pi$
$769$	−5957.20	−	4998.69i	−0.279353	−	0.234405i	−0.771689	+	0.636001i	$0.780588\pi$
$770$	−7579.49	+	20196.2i	−0.354735	+	0.945219i
$771$	56090.4	−	32383.8i	2.62003	−	1.51268i
$772$	−3923.15	−	25172.3i	−0.182898	−	1.17354i
$773$	−2229.81	−	6126.34i	−0.103752	−	0.285057i	0.876944	−	0.480592i	$-0.159578\pi$
$773$	−2229.81	−	6126.34i	−0.103752	−	0.285057i	−0.980697	+	0.195534i	$0.937356\pi$
$774$	7698.89	+	13647.1i	0.357534	+	0.633765i
$775$	−2096.68	+	11890.8i	−0.0971805	+	0.551138i
$776$	−2228.00	−	2822.40i	−0.103068	−	0.130565i
$777$	−326.138	+	273.662i	−0.0150581	+	0.0126352i
$778$	34112.9	−	12032.6i	1.57199	−	0.554485i
$779$	15180.8	−	2120.08i	0.698214	−	0.0975095i
$780$	−10991.0	−	13641.5i	−0.504538	−	0.626210i
$781$	−1154.88	−	1376.33i	−0.0529126	−	0.0630588i
$782$	−79.3370	+	7963.44i	−0.00362798	+	0.364159i
$783$	−11490.5	+	65166.0i	−0.524442	+	2.97426i
$784$	9145.94	+	364.652i	0.416634	+	0.0166113i
$785$	20696.2	−	7532.80i	0.940992	−	0.342493i
$786$	22666.8	+	4230.03i	1.02863	+	0.191959i
$787$	−23909.0	+	13803.9i	−1.08293	+	0.625229i	−0.931685	−	0.363268i	$-0.881661\pi$
$787$	−23909.0	+	13803.9i	−1.08293	+	0.625229i	−0.151243	+	0.988497i	$0.548328\pi$
$788$	737.599	−	37014.6i	0.0333450	−	1.67334i
$789$	−18904.7	+	22529.8i	−0.853012	+	1.01658i
$790$	9101.70	+	7793.06i	0.409904	+	0.350968i
$791$	10849.2	−	18791.4i	0.487680	−	0.844686i
$792$	−12198.6	+	58840.8i	−0.547297	+	2.63992i
$793$	−2267.14	−	12857.6i	−0.101524	−	0.575770i
$794$	6464.94	+	38928.4i	0.288958	+	1.73995i
$795$	−8892.91	+	24433.1i	−0.396728	+	1.09000i
$796$	5481.00	−	27830.0i	0.244057	−	1.23920i
$797$		−	17847.9i		−	0.793232i	−0.917985	−	0.396616i	$-0.870184\pi$
$797$		−	17847.9i		−	0.793232i	0.917985	−	0.396616i	$-0.129816\pi$
$798$	−28427.0	−	37208.6i	−1.26103	−	1.65059i
$799$	51807.2			2.29388
$800$	−9020.42	+	9722.78i	−0.398650	+	0.429690i
$801$	−70113.0	−	25519.0i	−3.09278	−	1.12568i
$802$	4461.18	−	740.879i	0.196421	−	0.0326201i
$803$	−41075.9	+	7242.79i	−1.80515	+	0.318297i
$804$	10641.2	−	17611.2i	0.466775	−	0.772512i
$805$	−4442.82	−	2565.07i	−0.194520	−	0.112306i
$806$	−11888.5	−	10179.2i	−0.519548	−	0.444847i
$807$	28003.0	+	23497.3i	1.22150	+	1.02496i
$808$	3657.25	−	1208.64i	0.159235	−	0.0526237i
$809$	−11680.2	−	20230.8i	−0.507609	−	0.879204i	−0.999961	−	0.00880796i	$-0.997196\pi$
$809$	−11680.2	−	20230.8i	−0.507609	−	0.879204i	0.492353	−	0.870396i	$-0.336137\pi$
$810$	3093.38	−	16576.1i	0.134186	−	0.719041i
$811$	1565.06	+	4299.97i	0.0677641	+	0.186180i	0.968952	−	0.247248i	$-0.0795261\pi$
$811$	1565.06	+	4299.97i	0.0677641	+	0.186180i	−0.901188	+	0.433428i	$0.857304\pi$
$812$	−30013.0	+	34354.2i	−1.29711	+	1.48472i
$813$	−59949.8	−	10570.8i	−2.58614	−	0.456006i
$814$	2.88649	−	289.732i	0.000124289	−	0.0124755i
$815$	14774.9	−	12397.6i	0.635022	−	0.532847i
$816$	−49346.6	−	10744.1i	−2.11700	−	0.460931i
$817$	6552.34	−	5110.09i	0.280584	−	0.218824i
$818$	2096.62	+	5944.01i	0.0896170	+	0.254068i
$819$	−26272.0	−	31309.7i	−1.12090	−	1.33584i
$820$	3442.27	+	10077.9i	0.146597	+	0.429190i
$821$	22330.1	+	3937.40i	0.949241	+	0.167377i	0.626772	−	0.779203i	$-0.284376\pi$
$821$	22330.1	+	3937.40i	0.949241	+	0.167377i	0.322470	+	0.946580i	$0.395487\pi$
$822$	−3325.81	−	5895.33i	−0.141120	−	0.250150i
$823$	−10119.0	+	3683.02i	−0.428586	+	0.155993i	−0.547301	−	0.836936i	$-0.684345\pi$
$823$	−10119.0	+	3683.02i	−0.428586	+	0.155993i	0.118715	+	0.992928i	$0.462123\pi$
$824$	−5556.17	+	2990.14i	−0.234901	+	0.126416i
$825$	−15976.4	−	27672.0i	−0.674216	−	1.16778i
$826$	41339.2	+	15514.3i	1.74137	+	0.653526i
$827$	3488.23	−	4157.11i	0.146672	−	0.174797i	−0.687706	−	0.725989i	$-0.741382\pi$
$827$	3488.23	−	4157.11i	0.146672	−	0.174797i	0.834378	+	0.551192i	$0.185827\pi$
$828$	−13329.1	−	5154.40i	−0.559443	−	0.216338i
$829$	1640.52	+	947.152i	0.0687303	+	0.0396815i	0.533971	−	0.845503i	$-0.320699\pi$
$829$	1640.52	+	947.152i	0.0687303	+	0.0396815i	−0.465241	+	0.885184i	$0.654032\pi$
$830$	−16114.5	−	19597.8i	−0.673909	−	0.819578i
$831$	−9966.10	−	56520.5i	−0.416029	−	2.35942i
$832$	−4904.28	−	16477.1i	−0.204357	−	0.686588i
$833$	−11696.0	−	4257.01i	−0.486487	−	0.177067i
$834$	8996.00	+	5314.03i	0.373508	+	0.220635i
$835$			7308.80i			0.302912i
$836$	31818.0	+	1774.08i	1.31633	+	0.0733945i
$837$		−	42160.3i		−	1.74107i
$838$	−13647.5	+	23103.5i	−0.562583	+	0.952383i
$839$	40414.8	+	14709.8i	1.66302	+	0.605290i	0.990833	−	0.135092i	$-0.0431332\pi$
$839$	40414.8	+	14709.8i	1.66302	+	0.605290i	0.672186	+	0.740382i	$0.265355\pi$
$840$	21647.0	−	24285.5i	0.889158	−	0.997534i
$841$	−7382.27	−	41866.9i	−0.302688	−	1.71663i
$842$	−5471.11	+	4498.69i	−0.223927	+	0.184127i
$843$	6897.94	+	3982.53i	0.281824	+	0.162711i
$844$	3640.46	−	9414.12i	0.148471	−	0.383942i
$845$	4944.96	−	5893.17i	0.201316	−	0.239919i
$846$	−32665.5	+	87039.7i	−1.32750	+	3.53722i
$847$	−10829.1	−	18756.5i	−0.439305	−	0.760898i
$848$	−17167.1	+	18877.5i	−0.695189	+	0.764453i
$849$	21269.7	−	7741.53i	0.859804	−	0.312943i
$850$	15707.7	−	8861.39i	0.633847	−	0.357580i
$851$	67.8603	+	11.9656i	0.00273351	+	0.000481992i
$852$	875.828	+	2564.16i	0.0352176	+	0.103106i
$853$	−67.4544	−	80.3891i	−0.00270762	−	0.00322681i	0.764689	−	0.644400i	$-0.222893\pi$
$853$	−67.4544	−	80.3891i	−0.00270762	−	0.00322681i	−0.767397	+	0.641173i	$0.778448\pi$
$854$	22865.0	−	8065.14i	0.916187	−	0.323165i
$855$	−32869.4	−	1176.39i	−1.31475	−	0.0470548i
$856$	1496.47	−	2421.83i	0.0597529	−	0.0967013i
$857$	−34101.2	+	28614.3i	−1.35925	+	1.14054i	−0.383033	+	0.923735i	$0.625120\pi$
$857$	−34101.2	+	28614.3i	−1.35925	+	1.14054i	−0.976214	+	0.216809i	$0.930435\pi$
$858$	41416.1	+	412.613i	1.64793	+	0.0164177i
$859$	544.845	+	96.0709i	0.0216413	+	0.00381595i	0.184458	−	0.982840i	$-0.440947\pi$
$859$	544.845	+	96.0709i	0.0216413	+	0.00381595i	−0.162817	+	0.986656i	$0.552058\pi$
$860$	4347.68	+	3798.29i	0.172389	+	0.150605i
$861$	12653.5	+	34765.3i	0.500849	+	1.37607i
$862$	−21610.2	−	4032.84i	−0.853881	−	0.159349i
$863$	−11593.9	−	20081.2i	−0.457312	−	0.792087i	0.541506	−	0.840697i	$-0.317854\pi$
$863$	−11593.9	−	20081.2i	−0.457312	−	0.792087i	−0.998818	+	0.0486095i	$0.984521\pi$
$864$	25123.2	−	38903.1i	0.989248	−	1.53184i
$865$	−184.254	−	154.607i	−0.00724257	−	0.00607723i
$866$	−25158.5	+	29383.2i	−0.987206	+	1.15298i
$867$	20894.5	+	12063.4i	0.818471	+	0.472545i
$868$	15031.1	−	24876.4i	0.587774	−	0.972767i
$869$	−27898.8	+	4919.31i	−1.08907	+	0.192032i
$870$	7816.50	+	47066.8i	0.304603	+	1.83415i
$871$	−8950.26	−	3257.63i	−0.348184	−	0.126728i
$872$	3112.12	+	21365.2i	0.120860	+	0.829720i
$873$	−8774.41			−0.340170
$874$	−1655.89	+	7395.57i	−0.0640861	+	0.286223i
$875$			31438.4i			1.21464i
$876$	61717.8	+	12155.1i	2.38042	+	0.468816i
$877$	−8991.63	+	24704.3i	−0.346210	+	0.951203i	0.637343	+	0.770580i	$0.280034\pi$
$877$	−8991.63	+	24704.3i	−0.346210	+	0.951203i	−0.983552	+	0.180623i	$0.942189\pi$
$878$	36591.3	−	6076.81i	1.40649	−	0.233579i
$879$	−683.032	−	3873.67i	−0.0262094	−	0.148641i
$880$	2972.98	+	21940.1i	0.113885	+	0.840457i
$881$	−4689.25	+	8122.02i	−0.179324	+	0.310599i	−0.941649	−	0.336595i	$-0.890725\pi$
$881$	−4689.25	+	8122.02i	−0.179324	+	0.310599i	0.762325	+	0.647195i	$0.224058\pi$
$882$	14526.6	−	16966.0i	0.554578	−	0.647705i
$883$	334.326	−	398.434i	0.0127417	−	0.0151850i	−0.759636	−	0.650349i	$-0.774623\pi$
$883$	334.326	−	398.434i	0.0127417	−	0.0151850i	0.772378	+	0.635164i	$0.219067\pi$
$884$	−465.752	+	23372.6i	−0.0177205	+	0.889260i
$885$	39993.8	−	23090.4i	1.51907	−	0.877036i
$886$	−7300.66	+	39121.0i	−0.276829	+	1.48340i
$887$	−26520.3	+	9652.59i	−1.00390	+	0.365392i	−0.791089	−	0.611701i	$-0.790486\pi$
$887$	−26520.3	+	9652.59i	−1.00390	+	0.365392i	−0.212816	+	0.977092i	$0.568263\pi$
$888$	−161.658	+	405.972i	−0.00610909	+	0.0153418i
$889$	3904.42	−	22143.1i	0.147301	−	0.835383i
$890$	−27489.4	−	273.867i	−1.03533	−	0.0103146i
$891$	25626.0	+	30539.8i	0.963526	+	1.14829i
$892$	−21024.5	+	16939.5i	−0.789186	+	0.635847i
$893$	48215.4	+	10292.3i	1.80679	+	0.385685i
$894$	16290.2	+	46183.5i	0.609426	+	1.72775i
$895$	−198.700	+	166.729i	−0.00742102	+	0.00622697i
$896$	28693.6	−	13997.5i	1.06985	−	0.521903i
$897$	−1710.44	+	9700.37i	−0.0636676	+	0.361077i
$898$	23350.7	−	13173.1i	0.867733	−	0.489525i
$899$	14578.9	+	40055.1i	0.540859	+	1.48600i
$900$	4983.73	+	31977.3i	0.184583	+	1.18435i
$901$	30048.6	−	17348.6i	1.11106	−	0.641470i
$902$	−23573.1	−	8846.84i	−0.870176	−	0.326572i
$903$	15363.7	+	12891.6i	0.566191	+	0.475091i
$904$	665.510	−	22261.0i	0.0244851	−	0.819014i
$905$	−14680.2	+	25426.9i	−0.539212	+	0.933943i
$906$	−1114.57	+	916.467i	−0.0408708	+	0.0336066i
$907$	−14949.7	+	2636.03i	−0.547294	+	0.0965028i	−0.440457	−	0.897774i	$-0.645184\pi$
$907$	−14949.7	+	2636.03i	−0.547294	+	0.0965028i	−0.106837	+	0.994276i	$0.534072\pi$
$908$	2053.78	−	1131.80i	0.0750629	−	0.0413658i
$909$	3214.66	−	8832.20i	0.117298	−	0.322272i
$910$	−12965.9	−	7659.10i	−0.472325	−	0.279007i
$911$	−27459.0			−0.998635			−0.499318	−	0.866419i	$-0.666416\pi$
$911$	−27459.0			−0.998635			−0.499318	+	0.866419i	$0.666416\pi$
$912$	−43790.8	−	19802.6i	−1.58998	−	0.719003i
$913$	59987.0			2.17446
$914$	−7515.42	−	4439.44i	−0.271978	−	0.160660i
$915$	8673.09	−	23829.1i	0.313359	−	0.860946i
$916$	−24900.7	+	13722.4i	−0.898192	+	0.494978i
$917$	19520.1	−	3441.93i	0.702957	−	0.123950i
$918$	−48641.1	+	39995.8i	−1.74880	+	1.43797i
$919$	7651.79	−	13253.3i	0.274656	−	0.475719i	−0.695392	−	0.718631i	$-0.744769\pi$
$919$	7651.79	−	13253.3i	0.274656	−	0.475719i	0.970048	+	0.242912i	$0.0781026\pi$
$920$	−5263.11	−	157.345i	−0.188608	−	0.00563861i
$921$	−6982.32	−	5858.86i	−0.249810	−	0.209616i
$922$	30307.6	+	11374.3i	1.08257	+	0.406281i
$923$	1086.22	−	627.127i	0.0387359	−	0.0223642i
$924$	11844.6	+	75998.8i	0.421707	+	2.70582i
$925$	−53.3711	−	146.636i	−0.00189712	−	0.00521228i
$926$	−22950.6	+	12947.4i	−0.814474	+	0.459480i
$927$	−2673.60	+	15162.8i	−0.0947278	+	0.537228i
$928$	−10416.2	+	45648.0i	−0.368458	+	1.61473i
$929$	20383.2	−	17103.5i	0.719860	−	0.604034i	−0.207486	−	0.978238i	$-0.566528\pi$
$929$	20383.2	−	17103.5i	0.719860	−	0.604034i	0.927347	+	0.374203i	$0.122084\pi$
$930$	−10111.9	−	28667.7i	−0.356541	−	1.01081i
$931$	−10039.4	−	6285.45i	−0.353414	−	0.221265i
$932$	−30774.6	+	24795.1i	−1.08161	+	0.871450i
$933$	13431.9	+	16007.6i	0.471320	+	0.561698i
$934$	42984.3	+	428.237i	1.50588	+	0.0150025i
$935$	5228.05	−	29649.8i	0.182862	−	1.03706i
$936$	−38973.9	−	15519.4i	−1.36101	−	0.541952i
$937$	26136.4	−	9512.86i	0.911246	−	0.331667i	0.156496	−	0.987679i	$-0.449980\pi$
$937$	26136.4	−	9512.86i	0.911246	−	0.331667i	0.754750	+	0.656012i	$0.227758\pi$
$938$	3244.86	−	17387.8i	0.112951	−	0.605256i
$939$	−12071.9	+	6969.69i	−0.419543	+	0.242223i
$940$	−682.443	+	34246.7i	−0.0236796	+	1.18830i
$941$	5261.90	−	6270.88i	0.182288	−	0.217242i	−0.667160	−	0.744914i	$-0.732490\pi$
$941$	5261.90	−	6270.88i	0.182288	−	0.217242i	0.849448	+	0.527672i	$0.176935\pi$
$942$	51075.5	−	59652.3i	1.76659	−	2.06325i
$943$	2993.96	−	5185.70i	0.103390	−	0.179077i
$944$	44908.9	−	6085.34i	1.54837	−	0.209810i
$945$	−7044.20	−	39949.6i	−0.242484	−	1.37520i
$946$	−13464.9	+	2236.15i	−0.462771	+	0.0768537i
$947$	−3801.18	+	10443.7i	−0.130435	+	0.358367i	−0.987668	−	0.156561i	$-0.949959\pi$
$947$	−3801.18	+	10443.7i	−0.130435	+	0.358367i	0.857233	+	0.514928i	$0.172181\pi$
$948$	41918.8	+	8255.74i	1.43614	+	0.282842i
$949$		−	29117.4i		−	0.995987i
$950$	16379.1	−	5126.46i	0.559378	−	0.175078i
$951$	26717.8			0.911024
$952$	−42959.8	+	6257.66i	−1.46254	+	0.213038i
$953$	−42289.2	−	15392.0i	−1.43744	−	0.523185i	−0.498386	−	0.866955i	$-0.666074\pi$
$953$	−42289.2	−	15392.0i	−1.43744	−	0.523185i	−0.939054	+	0.343770i	$0.888296\pi$
$954$	10200.6	+	61422.3i	0.346179	+	2.08451i
$955$	−13939.9	+	2457.98i	−0.472340	+	0.0832863i
$956$	20135.4	−	33324.2i	0.681199	−	1.12739i
$957$	−97690.2	−	56401.5i	−3.29977	−	1.90512i
$958$	−24343.4	+	28431.3i	−0.820981	+	0.958844i
$959$	−4457.27	−	3740.09i	−0.150086	−	0.125937i
$960$	7752.33	−	32478.5i	0.260631	−	1.09192i
$961$	1316.25	+	2279.81i	0.0441828	+	0.0765268i
$962$	198.839	+	37.1068i	0.00666406	+	0.00124363i
$963$	−2375.96	−	6527.91i	−0.0795061	−	0.218441i
$964$	−20056.8	−	17522.3i	−0.670110	−	0.585431i
$965$	−22556.9	−	3977.39i	−0.752468	−	0.132680i
$966$	−18291.2	−	182.229i	−0.609224	−	0.00606949i
$967$	−45069.9	+	37818.1i	−1.49881	+	1.25765i	−0.616161	+	0.787620i	$0.711313\pi$
$967$	−45069.9	+	37818.1i	−1.49881	+	1.25765i	−0.882650	+	0.470031i	$0.844243\pi$
$968$	−18910.6	−	11685.1i	−0.627901	−	0.387987i
$969$	48528.7	+	43771.8i	1.60884	+	1.45114i
$970$	−3048.79	+	1075.40i	−0.100918	+	0.0355968i
$971$	−10009.7	−	11929.1i	−0.330822	−	0.394258i	0.574835	−	0.818269i	$-0.305066\pi$
$971$	−10009.7	−	11929.1i	−0.330822	−	0.394258i	−0.905657	+	0.424011i	$0.860622\pi$
$972$	−1572.58	−	4604.05i	−0.0518937	−	0.151929i
$973$	8845.12	+	1559.63i	0.291430	+	0.0513870i
$974$	5377.06	−	3033.43i	0.176891	−	0.0997919i
$975$	20961.0	−	7629.20i	0.688503	−	0.250595i
$976$	16742.7	−	18410.9i	0.549100	−	0.603809i
$977$	21671.8	+	37536.6i	0.709663	+	1.22917i	0.964982	+	0.262316i	$0.0844863\pi$
$977$	21671.8	+	37536.6i	0.709663	+	1.22917i	−0.255319	+	0.966857i	$0.582180\pi$
$978$	24163.8	−	64386.4i	0.790054	−	2.10516i
$979$	41778.4	−	49789.6i	1.36389	−	1.62541i
$980$	2968.12	−	7675.48i	0.0967482	−	0.250188i
$981$	45626.4	+	26342.4i	1.48495	+	0.857338i
$982$	−11004.4	+	9048.52i	−0.357602	+	0.294043i
$983$	−2965.13	−	16816.1i	−0.0962084	−	0.545625i	−0.994370	−	0.105960i	$-0.966208\pi$
$983$	−2965.13	−	16816.1i	−0.0962084	−	0.545625i	0.898162	−	0.439665i	$-0.144903\pi$
$984$	28346.2	+	25266.5i	0.918337	+	0.818565i
$985$	−31278.0	−	11384.2i	−1.01178	−	0.368256i
$986$	32381.9	−	54818.5i	1.04589	−	1.77056i
$987$			118996.i			3.83757i
$988$	−5076.76	+	21659.6i	−0.163475	+	0.697454i
$989$		−	3246.07i		−	0.104367i
$990$	46517.3	+	27478.2i	1.49335	+	0.882137i
$991$	−11325.3	−	4122.09i	−0.363029	−	0.132132i	0.154064	−	0.988061i	$-0.450764\pi$
$991$	−11325.3	−	4122.09i	−0.363029	−	0.132132i	−0.517093	+	0.855929i	$0.672986\pi$
$992$	1485.35	−	29794.7i	0.0475402	−	0.953611i
$993$	−6351.02	−	36018.4i	−0.202964	−	1.15107i
$994$	1479.35	+	1799.12i	0.0472055	+	0.0574092i
$995$	−22085.1	−	12750.9i	−0.703665	−	0.406261i
$996$	−84378.9	−	32629.5i	−2.68438	−	1.03806i
$997$	15425.8	−	18383.8i	0.490011	−	0.583972i	−0.463209	−	0.886249i	$-0.653302\pi$
$997$	15425.8	−	18383.8i	0.490011	−	0.583972i	0.953220	+	0.302277i	$0.0977467\pi$
$998$	−19825.4	−	7440.34i	−0.628819	−	0.235992i
$999$	272.438	+	471.876i	0.00862817	+	0.0149444i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	152.4.t.a.101.11	✓	348
8.5	even	2	inner	152.4.t.a.101.37	yes	348
19.16	even	9	inner	152.4.t.a.149.37	yes	348
152.149	even	18	inner	152.4.t.a.149.11	yes	348

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
152.4.t.a.101.11	✓	348	1.1	even	1	trivial
152.4.t.a.101.37	yes	348	8.5	even	2	inner
152.4.t.a.149.11	yes	348	152.149	even	18	inner
152.4.t.a.149.37	yes	348	19.16	even	9	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 $\F_{q}$
Belyi maps

Level:	\( N \)	\(=\)	\( 152 = 2^{3} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	152.t (of order \(18\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-2.43528 - 1.43855i) q^{2} +(-3.10118 + 8.52041i) q^{3} +(3.86117 + 7.00652i) q^{4} +(7.08329 - 1.24898i) q^{5} +(19.8092 - 16.2884i) q^{6} +(11.0229 - 19.0923i) q^{7} +(0.676164 - 22.6173i) q^{8} +(-42.2969 - 35.4913i) q^{9} +(-19.0465 - 7.14804i) q^{10} +(41.6541 - 24.0490i) q^{11} +(-71.6726 + 11.1703i) q^{12} +(11.4841 + 31.5522i) q^{13} +(-54.3090 + 30.6380i) q^{14} +(-11.3248 + 64.2259i) q^{15} +(-34.1827 + 54.1068i) q^{16} +(66.6674 - 55.9406i) q^{17} +(51.9490 + 147.277i) q^{18} +(73.1586 - 38.8177i) q^{19} +(36.1008 + 44.8067i) q^{20} +(128.490 + 153.128i) q^{21} +(-136.035 - 1.35527i) q^{22} +(5.61808 - 31.8617i) q^{23} +(190.612 + 75.9015i) q^{24} +(-68.8485 + 25.0588i) q^{25} +(17.4224 - 93.3588i) q^{26} +(221.555 - 127.915i) q^{27} +(176.332 + 3.51381i) q^{28} +(-166.259 + 198.140i) q^{29} +(119.971 - 140.117i) q^{30} +(82.3992 - 142.720i) q^{31} +(161.079 - 82.5918i) q^{32} +(75.7307 + 429.490i) q^{33} +(-242.827 + 40.3269i) q^{34} +(54.2328 - 149.003i) q^{35} +(85.3551 - 433.393i) q^{36} +2.12984i q^{37} +(-234.003 - 10.7101i) q^{38} -304.452 q^{39} +(-23.4590 - 161.050i) q^{40} +(173.918 + 63.3010i) q^{41} +(-92.6268 - 557.749i) q^{42} +(98.8077 - 17.4225i) q^{43} +(329.333 + 198.993i) q^{44} +(-343.929 - 198.568i) q^{45} +(-59.5162 + 69.5104i) q^{46} +(456.021 + 382.647i) q^{47} +(-355.006 - 459.045i) q^{48} +(-71.5095 - 123.858i) q^{49} +(203.714 + 38.0165i) q^{50} +(269.889 + 741.515i) q^{51} +(-176.729 + 202.292i) q^{52} +(392.632 + 69.2315i) q^{53} +(-723.560 - 7.20857i) q^{54} +(265.011 - 222.371i) q^{55} +(-424.362 - 262.218i) q^{56} +(103.865 + 743.722i) q^{57} +(689.922 - 243.355i) q^{58} +(-455.167 - 542.447i) q^{59} +(-493.727 + 168.640i) q^{60} +(-382.926 - 67.5202i) q^{61} +(-405.974 + 229.027i) q^{62} +(-1143.85 + 416.326i) q^{63} +(-511.086 - 30.5860i) q^{64} +(120.753 + 209.150i) q^{65} +(433.415 - 1154.87i) q^{66} +(-182.336 + 217.300i) q^{67} +(649.363 + 251.110i) q^{68} +(254.053 + 146.677i) q^{69} +(-346.420 + 284.849i) q^{70} +(-6.48653 - 36.7869i) q^{71} +(-831.319 + 932.645i) q^{72} +(-814.882 - 296.593i) q^{73} +(3.06387 - 5.18675i) q^{74} -664.329i q^{75} +(554.455 + 362.706i) q^{76} -1060.36i q^{77} +(741.425 + 437.968i) q^{78} +(-553.469 - 201.446i) q^{79} +(-174.548 + 425.948i) q^{80} +(143.932 + 816.277i) q^{81} +(-332.478 - 404.344i) q^{82} +(1080.09 + 623.592i) q^{83} +(-576.775 + 1491.52i) q^{84} +(402.356 - 479.509i) q^{85} +(-265.687 - 99.7108i) q^{86} +(-1172.64 - 2031.07i) q^{87} +(-515.758 - 958.364i) q^{88} +(1269.82 - 462.178i) q^{89} +(551.916 + 978.326i) q^{90} +(728.991 + 128.541i) q^{91} +(244.932 - 83.6605i) q^{92} +(960.495 + 1144.67i) q^{93} +(-560.084 - 1587.86i) q^{94} +(469.722 - 366.331i) q^{95} +(204.180 + 1628.60i) q^{96} +(121.735 - 102.148i) q^{97} +(-4.02987 + 404.498i) q^{98} +(-2615.37 - 461.160i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 348 q - 6 q^{2} + 12 q^{4} - 24 q^{6} - 6 q^{7} - 3 q^{8} - 12 q^{9} + 75 q^{10} - 3 q^{12} - 81 q^{14} - 12 q^{15} + 192 q^{16} - 12 q^{17} - 12 q^{18} + 558 q^{20} - 30 q^{22} - 12 q^{23} - 108 q^{24}+ \cdots + 8055 q^{98}+O(q^{100}) \) 348 * q - 6 * q^2 + 12 * q^4 - 24 * q^6 - 6 * q^7 - 3 * q^8 - 12 * q^9 + 75 * q^10 - 3 * q^12 - 81 * q^14 - 12 * q^15 + 192 * q^16 - 12 * q^17 - 12 * q^18 + 558 * q^20 - 30 * q^22 - 12 * q^23 - 108 * q^24 - 12 * q^25 - 411 * q^26 + 1140 * q^28 - 282 * q^30 - 1122 * q^31 + 39 * q^32 - 174 * q^33 + 1536 * q^34 - 2835 * q^36 + 966 * q^38 - 24 * q^39 - 1068 * q^40 + 48 * q^41 + 3015 * q^42 - 1203 * q^44 - 528 * q^46 - 624 * q^47 + 4755 * q^48 - 6768 * q^49 - 1074 * q^50 - 1089 * q^52 + 615 * q^54 - 762 * q^55 + 2046 * q^56 - 12 * q^57 + 4092 * q^58 + 4050 * q^60 + 3120 * q^62 + 2046 * q^63 + 2355 * q^64 - 6 * q^65 + 1716 * q^66 - 1176 * q^68 - 2973 * q^70 - 12 * q^71 - 7122 * q^72 + 636 * q^73 - 9363 * q^74 - 2454 * q^76 - 6897 * q^78 - 12 * q^79 - 6885 * q^80 + 1206 * q^81 - 7311 * q^82 + 1947 * q^84 + 7452 * q^86 - 6 * q^87 - 1131 * q^88 - 12 * q^89 + 4014 * q^90 + 7656 * q^92 + 11898 * q^94 + 1848 * q^95 - 18966 * q^96 - 12 * q^97 + 8055 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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