LMFDB - Embedded newform 176.5.n.c.129.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [176,5,Mod(17,176)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(176, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 9]))

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

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

chi := DirichletCharacter("176.17");

S:= CuspForms(chi, 5);

N := Newforms(S);

Level:	$ N $	$=$	$ 176 = 2^{4} \cdot 11 $
Weight:	$ k $	$=$	$ 5 $
Character orbit:	$[\chi]$	$=$	176.n (of order $10$, 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:	$18.1931135028$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{10})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 138 x^{14} - 428 x^{13} + 7783 x^{12} - 18620 x^{11} + 235604 x^{10} + \cdots + 1499670491 $ x^16 - 4x^15 + 138x^14 - 428x^13 + 7783x^12 - 18620x^11 + 235604x^10 - 425164x^9 + 4199998x^8 - 5446172x^7 + 45313276x^6 - 38408204x^5 + 290282498x^4 - 132888724x^3 + 1016893202x^2 - 153602264*x + 1499670491
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{12}\cdot 11^{2} $
Twist minimal:	no (minimal twist has level 22)
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			129.3
Root			$-0.309017 - 4.73267i$ of defining polynomial
Character	$\chi$	$=$	176.129
Dual form			176.5.n.c.161.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.309288 - 0.951890i) q^{3} +(35.4031 + 25.7219i) q^{5} +(65.6073 + 21.3171i) q^{7} +(64.7199 - 47.0218i) q^{9} +O(q^{10})$	\(q+(-0.309288 - 0.951890i) q^{3} +(35.4031 + 25.7219i) q^{5} +(65.6073 + 21.3171i) q^{7} +(64.7199 - 47.0218i) q^{9} +(-65.6374 + 101.650i) q^{11} +(-100.269 - 138.009i) q^{13} +(13.5346 - 41.6553i) q^{15} +(-130.596 + 179.749i) q^{17} +(-141.801 + 46.0739i) q^{19} -69.0440i q^{21} +272.896 q^{23} +(398.631 + 1226.86i) q^{25} +(-130.364 - 94.7153i) q^{27} +(571.633 + 185.735i) q^{29} +(714.607 - 519.192i) q^{31} +(117.060 + 31.0405i) q^{33} +(1774.39 + 2442.23i) q^{35} +(440.083 - 1354.44i) q^{37} +(-100.357 + 138.130i) q^{39} +(-1050.88 + 341.452i) q^{41} -1489.14i q^{43} +3500.78 q^{45} +(772.201 + 2376.59i) q^{47} +(1907.45 + 1385.84i) q^{49} +(211.493 + 68.7183i) q^{51} +(-3070.02 + 2230.50i) q^{53} +(-4938.40 + 1910.41i) q^{55} +(87.7146 + 120.729i) q^{57} +(338.601 - 1042.11i) q^{59} +(-1856.32 + 2555.01i) q^{61} +(5248.47 - 1705.33i) q^{63} -7465.07i q^{65} -251.628 q^{67} +(-84.4035 - 259.767i) q^{69} +(-3590.99 - 2609.01i) q^{71} +(3983.96 + 1294.47i) q^{73} +(1044.54 - 758.906i) q^{75} +(-6473.17 + 5269.78i) q^{77} +(3109.83 + 4280.32i) q^{79} +(1952.55 - 6009.32i) q^{81} +(-261.533 + 359.969i) q^{83} +(-9246.98 + 3004.53i) q^{85} -601.577i q^{87} +8935.75 q^{89} +(-3636.45 - 11191.8i) q^{91} +(-715.233 - 519.647i) q^{93} +(-6205.31 - 2016.23i) q^{95} +(1684.12 - 1223.58i) q^{97} +(531.718 + 9665.17i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 2 q^{3} + 30 q^{5} - 150 q^{7} + 110 q^{9}+O(q^{10}) $ 16 * q + 2 * q^3 + 30 * q^5 - 150 * q^7 + 110 * q^9	$ 16 q + 2 q^{3} + 30 q^{5} - 150 q^{7} + 110 q^{9} + 30 q^{11} - 510 q^{13} + 1398 q^{15} + 1770 q^{17} - 1020 q^{19} + 2424 q^{23} - 858 q^{25} - 2224 q^{27} + 4890 q^{29} - 602 q^{31} - 2648 q^{33} + 8670 q^{35} - 4518 q^{37} + 1130 q^{39} + 1290 q^{41} + 12152 q^{45} - 642 q^{47} + 9534 q^{49} + 1500 q^{51} + 2598 q^{53} - 2582 q^{55} + 9140 q^{57} - 6660 q^{59} - 27410 q^{61} + 27260 q^{63} - 21524 q^{67} + 11416 q^{69} + 5562 q^{71} - 7790 q^{73} - 3576 q^{75} - 1110 q^{77} + 2770 q^{79} - 25464 q^{81} + 36900 q^{83} - 24750 q^{85} + 46596 q^{89} - 32370 q^{91} + 20722 q^{93} - 74250 q^{95} - 3732 q^{97} - 45802 q^{99}+O(q^{100}) $ 16 * q + 2 * q^3 + 30 * q^5 - 150 * q^7 + 110 * q^9 + 30 * q^11 - 510 * q^13 + 1398 * q^15 + 1770 * q^17 - 1020 * q^19 + 2424 * q^23 - 858 * q^25 - 2224 * q^27 + 4890 * q^29 - 602 * q^31 - 2648 * q^33 + 8670 * q^35 - 4518 * q^37 + 1130 * q^39 + 1290 * q^41 + 12152 * q^45 - 642 * q^47 + 9534 * q^49 + 1500 * q^51 + 2598 * q^53 - 2582 * q^55 + 9140 * q^57 - 6660 * q^59 - 27410 * q^61 + 27260 * q^63 - 21524 * q^67 + 11416 * q^69 + 5562 * q^71 - 7790 * q^73 - 3576 * q^75 - 1110 * q^77 + 2770 * q^79 - 25464 * q^81 + 36900 * q^83 - 24750 * q^85 + 46596 * q^89 - 32370 * q^91 + 20722 * q^93 - 74250 * q^95 - 3732 * q^97 - 45802 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/176\mathbb{Z}\right)^\times$.

$n$	$111$	$133$	$145$
$\chi(n)$	$1$	$1$	$e\left(\frac{3}{10}\right)$

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 $

$2$		0			0
$2$		0			0
$3$	−0.309288	−	0.951890i	−0.0343653	−	0.105766i	0.932402	−	0.361422i	$-0.117709\pi$
$3$	−0.309288	−	0.951890i	−0.0343653	−	0.105766i	−0.966768	+	0.255656i	$0.917709\pi$
$4$		0			0
$5$	35.4031	+	25.7219i	1.41613	+	1.02888i	0.992396	+	0.123087i	$0.0392793\pi$
$5$	35.4031	+	25.7219i	1.41613	+	1.02888i	0.423730	+	0.905789i	$0.360721\pi$
$6$		0			0
$7$	65.6073	+	21.3171i	1.33892	+	0.435043i	0.888952	−	0.458000i	$-0.151434\pi$
$7$	65.6073	+	21.3171i	1.33892	+	0.435043i	0.449972	+	0.893043i	$0.351434\pi$
$8$		0			0
$9$	64.7199	−	47.0218i	0.799012	−	0.580516i
$10$		0			0
$11$	−65.6374	+	101.650i	−0.542458	+	0.840083i
$11$	−65.6374	+	101.650i	−0.542458	+	0.840083i
$12$		0			0
$13$	−100.269	−	138.009i	−0.593310	−	0.816621i	0.401766	−	0.915743i	$-0.368397\pi$
$13$	−100.269	−	138.009i	−0.593310	−	0.816621i	−0.995075	+	0.0991217i	$0.968397\pi$
$14$		0			0
$15$	13.5346	−	41.6553i	0.0601540	−	0.185135i
$16$		0			0
$17$	−130.596	+	179.749i	−0.451888	+	0.621970i	−0.972802	−	0.231639i	$-0.925591\pi$
$17$	−130.596	+	179.749i	−0.451888	+	0.621970i	0.520914	+	0.853609i	$0.325591\pi$
$18$		0			0
$19$	−141.801	+	46.0739i	−0.392800	+	0.127629i	−0.498756	−	0.866742i	$-0.666210\pi$
$19$	−141.801	+	46.0739i	−0.392800	+	0.127629i	0.105956	+	0.994371i	$0.466210\pi$
$20$		0			0
$21$		−	69.0440i		−	0.156562i
$22$		0			0
$23$	272.896			0.515872			0.257936	−	0.966162i	$-0.416958\pi$
$23$	272.896			0.515872			0.257936	+	0.966162i	$0.416958\pi$
$24$		0			0
$25$	398.631	+	1226.86i	0.637810	+	1.96298i
$26$		0			0
$27$	−130.364	−	94.7153i	−0.178826	−	0.129925i
$28$		0			0
$29$	571.633	+	185.735i	0.679706	+	0.220850i	0.628467	−	0.777837i	$-0.283683\pi$
$29$	571.633	+	185.735i	0.679706	+	0.220850i	0.0512393	+	0.998686i	$0.483683\pi$
$30$		0			0
$31$	714.607	−	519.192i	0.743607	−	0.540262i	−0.150231	−	0.988651i	$-0.548002\pi$
$31$	714.607	−	519.192i	0.743607	−	0.540262i	0.893839	+	0.448388i	$0.148002\pi$
$32$		0			0
$33$	117.060	+	31.0405i	0.107494	+	0.0285036i
$34$		0			0
$35$	1774.39	+	2442.23i	1.44848	+	1.99366i
$36$		0			0
$37$	440.083	−	1354.44i	0.321463	−	0.989363i	−0.651548	−	0.758607i	$-0.725880\pi$
$37$	440.083	−	1354.44i	0.321463	−	0.989363i	0.973012	−	0.230756i	$-0.0741198\pi$
$38$		0			0
$39$	−100.357	+	138.130i	−0.0659811	+	0.0908151i
$40$		0			0
$41$	−1050.88	+	341.452i	−0.625153	+	0.203124i	−0.604427	−	0.796661i	$-0.706598\pi$
$41$	−1050.88	+	341.452i	−0.625153	+	0.203124i	−0.0207260	+	0.999785i	$0.506598\pi$
$42$		0			0
$43$		−	1489.14i		−	0.805374i	−0.915338	−	0.402687i	$-0.868076\pi$
$43$		−	1489.14i		−	0.805374i	0.915338	−	0.402687i	$-0.131924\pi$
$44$		0			0
$45$	3500.78			1.72878
$46$		0			0
$47$	772.201	+	2376.59i	0.349570	+	1.07587i	0.959091	+	0.283097i	$0.0913619\pi$
$47$	772.201	+	2376.59i	0.349570	+	1.07587i	−0.609521	+	0.792770i	$0.708638\pi$
$48$		0			0
$49$	1907.45	+	1385.84i	0.794438	+	0.577193i
$50$		0			0
$51$	211.493	+	68.7183i	0.0813122	+	0.0264199i
$52$		0			0
$53$	−3070.02	+	2230.50i	−1.09292	+	0.794055i	−0.979891	−	0.199536i	$-0.936057\pi$
$53$	−3070.02	+	2230.50i	−1.09292	+	0.794055i	−0.113033	+	0.993591i	$0.536057\pi$
$54$		0			0
$55$	−4938.40	+	1910.41i	−1.63253	+	0.631541i
$56$		0			0
$57$	87.7146	+	120.729i	0.0269974	+	0.0371587i
$58$		0			0
$59$	338.601	−	1042.11i	0.0972711	−	0.299370i	−0.890568	−	0.454851i	$-0.849693\pi$
$59$	338.601	−	1042.11i	0.0972711	−	0.299370i	0.987839	+	0.155481i	$0.0496927\pi$
$60$		0			0
$61$	−1856.32	+	2555.01i	−0.498878	+	0.686646i	−0.981994	−	0.188910i	$-0.939505\pi$
$61$	−1856.32	+	2555.01i	−0.498878	+	0.686646i	0.483117	+	0.875556i	$0.339505\pi$
$62$		0			0
$63$	5248.47	−	1705.33i	1.32236	−	0.429662i
$64$		0			0
$65$		−	7465.07i		−	1.76688i
$66$		0			0
$67$	−251.628			−0.0560544			−0.0280272	−	0.999607i	$-0.508922\pi$
$67$	−251.628			−0.0560544			−0.0280272	+	0.999607i	$0.508922\pi$
$68$		0			0
$69$	−84.4035	−	259.767i	−0.0177281	−	0.0545615i
$70$		0			0
$71$	−3590.99	−	2609.01i	−0.712356	−	0.517557i	0.171577	−	0.985171i	$-0.445114\pi$
$71$	−3590.99	−	2609.01i	−0.712356	−	0.517557i	−0.883933	+	0.467614i	$0.845114\pi$
$72$		0			0
$73$	3983.96	+	1294.47i	0.747599	+	0.242910i	0.657948	−	0.753064i	$-0.271425\pi$
$73$	3983.96	+	1294.47i	0.747599	+	0.242910i	0.0896513	+	0.995973i	$0.471425\pi$
$74$		0			0
$75$	1044.54	−	758.906i	0.185697	−	0.134917i
$76$		0			0
$77$	−6473.17	+	5269.78i	−1.09178	+	0.888815i
$78$		0			0
$79$	3109.83	+	4280.32i	0.498291	+	0.685838i	0.981890	−	0.189451i	$-0.0606709\pi$
$79$	3109.83	+	4280.32i	0.498291	+	0.685838i	−0.483600	+	0.875289i	$0.660671\pi$
$80$		0			0
$81$	1952.55	−	6009.32i	0.297599	−	0.915916i
$82$		0			0
$83$	−261.533	+	359.969i	−0.0379638	+	0.0522527i	−0.827577	−	0.561352i	$-0.810281\pi$
$83$	−261.533	+	359.969i	−0.0379638	+	0.0522527i	0.789613	+	0.613605i	$0.210281\pi$
$84$		0			0
$85$	−9246.98	+	3004.53i	−1.27986	+	0.415852i
$86$		0			0
$87$		−	601.577i		−	0.0794790i
$88$		0			0
$89$	8935.75			1.12811			0.564054	−	0.825738i	$-0.309241\pi$
$89$	8935.75			1.12811			0.564054	+	0.825738i	$0.309241\pi$
$90$		0			0
$91$	−3636.45	−	11191.8i	−0.439132	−	1.35151i
$92$		0			0
$93$	−715.233	−	519.647i	−0.0826954	−	0.0600817i
$94$		0			0
$95$	−6205.31	−	2016.23i	−0.687568	−	0.223405i
$96$		0			0
$97$	1684.12	−	1223.58i	0.178990	−	0.130044i	−0.494683	−	0.869074i	$-0.664716\pi$
$97$	1684.12	−	1223.58i	0.178990	−	0.130044i	0.673673	+	0.739030i	$0.264716\pi$
$98$		0			0
$99$	531.718	+	9665.17i	0.0542514	+	0.986142i
$100$		0			0
$101$	−1308.06	−	1800.39i	−0.128229	−	0.176492i	0.740075	−	0.672524i	$-0.234790\pi$
$101$	−1308.06	−	1800.39i	−0.128229	−	0.176492i	−0.868304	+	0.496032i	$0.834790\pi$
$102$		0			0
$103$	6206.12	−	19100.5i	0.584986	−	1.80040i	−0.0143398	−	0.999897i	$-0.504565\pi$
$103$	6206.12	−	19100.5i	0.584986	−	1.80040i	0.599326	−	0.800505i	$-0.295435\pi$
$104$		0			0
$105$	1775.94	−	2444.37i	0.161083	−	0.221712i
$106$		0			0
$107$	−16829.4	+	5468.19i	−1.46994	+	0.477613i	−0.931090	−	0.364789i	$-0.881141\pi$
$107$	−16829.4	+	5468.19i	−1.46994	+	0.477613i	−0.538851	+	0.842401i	$0.681141\pi$
$108$		0			0
$109$		−	7937.04i		−	0.668045i	−0.942565	−	0.334023i	$-0.891594\pi$
$109$		−	7937.04i		−	0.668045i	0.942565	−	0.334023i	$-0.108406\pi$
$110$		0			0
$111$	−1425.39			−0.115688
$112$		0			0
$113$	−5237.55	−	16119.5i	−0.410177	−	1.26240i	−0.916494	−	0.400048i	$-0.868993\pi$
$113$	−5237.55	−	16119.5i	−0.410177	−	1.26240i	0.506317	−	0.862348i	$-0.331007\pi$
$114$		0			0
$115$	9661.39	+	7019.41i	0.730540	+	0.530768i
$116$		0			0
$117$	−12978.9	−	4217.09i	−0.948123	−	0.308064i
$118$		0			0
$119$	−12399.8	+	9008.95i	−0.875627	+	0.636180i
$120$		0			0
$121$	−6024.46	−	13344.1i	−0.411479	−	0.911419i
$122$		0			0
$123$	650.050	+	894.716i	0.0429671	+	0.0591392i
$124$		0			0
$125$	−8992.63	+	27676.5i	−0.575528	+	1.77129i
$126$		0			0
$127$	−3322.47	+	4572.99i	−0.205994	+	0.283526i	−0.899497	−	0.436928i	$-0.856067\pi$
$127$	−3322.47	+	4572.99i	−0.205994	+	0.283526i	0.693503	+	0.720454i	$0.256067\pi$
$128$		0			0
$129$	−1417.49	+	460.572i	−0.0851808	+	0.0276769i
$130$		0			0
$131$		−	16641.0i		−	0.969699i	−0.874598	−	0.484849i	$-0.838874\pi$
$131$		−	16641.0i		−	0.969699i	0.874598	−	0.484849i	$-0.161126\pi$
$132$		0			0
$133$	−10285.3			−0.581454
$134$		0			0
$135$	−2179.05	−	6706.44i	−0.119564	−	0.367980i
$136$		0			0
$137$	9008.52	+	6545.07i	0.479968	+	0.348717i	0.801313	−	0.598245i	$-0.204135\pi$
$137$	9008.52	+	6545.07i	0.479968	+	0.348717i	−0.321345	+	0.946962i	$0.604135\pi$
$138$		0			0
$139$	−24814.4	−	8062.67i	−1.28432	−	0.417301i	−0.414221	−	0.910177i	$-0.635946\pi$
$139$	−24814.4	−	8062.67i	−1.28432	−	0.417301i	−0.870100	+	0.492876i	$0.835946\pi$
$140$		0			0
$141$	2023.42	−	1470.10i	0.101777	−	0.0739450i
$142$		0			0
$143$	20610.0	−	1133.84i	1.00787	−	0.0554471i
$144$		0			0
$145$	15460.1	+	21279.1i	0.735322	+	1.01208i
$146$		0			0
$147$	729.218	−	2244.30i	0.0337460	−	0.103860i
$148$		0			0
$149$	19071.0	−	26249.0i	0.859016	−	1.18233i	−0.122788	−	0.992433i	$-0.539183\pi$
$149$	19071.0	−	26249.0i	0.859016	−	1.18233i	0.981803	−	0.189901i	$-0.0608166\pi$
$150$		0			0
$151$	8988.06	−	2920.40i	0.394196	−	0.128082i	−0.105210	−	0.994450i	$-0.533552\pi$
$151$	8988.06	−	2920.40i	0.394196	−	0.128082i	0.499406	+	0.866368i	$0.333552\pi$
$152$		0			0
$153$			17774.2i			0.759289i
$154$		0			0
$155$	38653.9			1.60890
$156$		0			0
$157$	1192.27	+	3669.42i	0.0483698	+	0.148867i	0.972324	−	0.233636i	$-0.0750623\pi$
$157$	1192.27	+	3669.42i	0.0483698	+	0.148867i	−0.923954	+	0.382503i	$0.875062\pi$
$158$		0			0
$159$	3072.71	+	2232.46i	0.121542	+	0.0883057i
$160$		0			0
$161$	17904.0	+	5817.36i	0.690714	+	0.224426i
$162$		0			0
$163$	13650.3	−	9917.54i	0.513769	−	0.373275i	−0.300483	−	0.953787i	$-0.597148\pi$
$163$	13650.3	−	9917.54i	0.513769	−	0.373275i	0.814251	+	0.580513i	$0.197148\pi$
$164$		0			0
$165$	3345.89	+	4109.95i	0.122898	+	0.150962i
$166$		0			0
$167$	−8510.67	−	11713.9i	−0.305162	−	0.420020i	0.628703	−	0.777646i	$-0.283586\pi$
$167$	−8510.67	−	11713.9i	−0.305162	−	0.420020i	−0.933865	+	0.357626i	$0.883586\pi$
$168$		0			0
$169$	−166.687	+	513.009i	−0.00583617	+	0.0179619i
$170$		0			0
$171$	−7010.87	+	9649.63i	−0.239762	+	0.330004i
$172$		0			0
$173$	−22622.7	+	7350.55i	−0.755878	+	0.245600i	−0.661509	−	0.749938i	$-0.730084\pi$
$173$	−22622.7	+	7350.55i	−0.755878	+	0.245600i	−0.0943695	+	0.995537i	$0.530084\pi$
$174$		0			0
$175$			88988.6i			2.90575i
$176$		0			0
$177$	−1096.70			−0.0350057
$178$		0			0
$179$	11256.1	+	34642.7i	0.351303	+	1.08120i	0.958122	+	0.286359i	$0.0924450\pi$
$179$	11256.1	+	34642.7i	0.351303	+	1.08120i	−0.606820	+	0.794839i	$0.707555\pi$
$180$		0			0
$181$	−9246.62	−	6718.06i	−0.282245	−	0.205063i	0.437651	−	0.899145i	$-0.355810\pi$
$181$	−9246.62	−	6718.06i	−0.282245	−	0.205063i	−0.719896	+	0.694082i	$0.755810\pi$
$182$		0			0
$183$	3006.23	+	976.782i	0.0897676	+	0.0291672i
$184$		0			0
$185$	50419.0	−	36631.6i	1.47316	−	1.07032i
$186$		0			0
$187$	−9699.58	−	25073.3i	−0.277376	−	0.717016i
$188$		0			0
$189$	−6533.80	−	8993.00i	−0.182912	−	0.251757i
$190$		0			0
$191$	2741.84	−	8438.52i	0.0751581	−	0.231313i	−0.906419	−	0.422380i	$-0.861195\pi$
$191$	2741.84	−	8438.52i	0.0751581	−	0.231313i	0.981577	+	0.191067i	$0.0611948\pi$
$192$		0			0
$193$	−6099.99	+	8395.91i	−0.163762	+	0.225400i	−0.883010	−	0.469354i	$-0.844487\pi$
$193$	−6099.99	+	8395.91i	−0.163762	+	0.225400i	0.719248	+	0.694754i	$0.244487\pi$
$194$		0			0
$195$	−7105.92	+	2308.85i	−0.186875	+	0.0607193i
$196$		0			0
$197$			75824.1i			1.95378i	0.213753	+	0.976888i	$0.431431\pi$
$197$			75824.1i			1.95378i	−0.213753	+	0.976888i	$0.568569\pi$
$198$		0			0
$199$	−65301.9			−1.64900			−0.824498	−	0.565865i	$-0.808542\pi$
$199$	−65301.9			−1.64900			−0.824498	+	0.565865i	$0.808542\pi$
$200$		0			0
$201$	77.8254	+	239.522i	0.00192632	+	0.00592862i
$202$		0			0
$203$	33543.9	+	24371.1i	0.813995	+	0.591402i
$204$		0			0
$205$	−45987.3	−	14942.2i	−1.09428	−	0.355555i
$206$		0			0
$207$	17661.8	−	12832.1i	0.412188	−	0.299472i
$208$		0			0
$209$	4624.03	−	17438.2i	0.105859	−	0.399218i
$210$		0			0
$211$	−23859.2	−	32839.4i	−0.535909	−	0.737615i	0.452108	−	0.891963i	$-0.350672\pi$
$211$	−23859.2	−	32839.4i	−0.535909	−	0.737615i	−0.988016	+	0.154348i	$0.950672\pi$
$212$		0			0
$213$	−1372.84	+	4225.16i	−0.0302594	+	0.0931287i
$214$		0			0
$215$	38303.4	−	52720.1i	0.828630	−	1.14051i
$216$		0			0
$217$	57951.1	−	18829.4i	1.23067	−	0.399869i
$218$		0			0
$219$		−	4192.65i		−	0.0874179i
$220$		0			0
$221$	37901.7			0.776023
$222$		0			0
$223$	2160.07	+	6648.00i	0.0434367	+	0.133685i	0.970423	−	0.241411i	$-0.0776101\pi$
$223$	2160.07	+	6648.00i	0.0434367	+	0.133685i	−0.926986	+	0.375095i	$0.877610\pi$
$224$		0			0
$225$	83488.6	+	60658.0i	1.64916	+	1.19818i
$226$		0			0
$227$	55512.3	+	18037.0i	1.07730	+	0.350036i	0.793327	−	0.608795i	$-0.208347\pi$
$227$	55512.3	+	18037.0i	1.07730	+	0.350036i	0.283974	+	0.958832i	$0.408347\pi$
$228$		0			0
$229$	−64594.9	+	46931.0i	−1.23176	+	0.894929i	−0.997021	−	0.0771287i	$-0.975425\pi$
$229$	−64594.9	+	46931.0i	−1.23176	+	0.894929i	−0.234743	+	0.972058i	$0.575425\pi$
$230$		0			0
$231$	7018.33	+	4531.87i	0.131525	+	0.0849285i
$232$		0			0
$233$	−46025.5	−	63348.7i	−0.847787	−	1.16688i	−0.984346	−	0.176247i	$-0.943604\pi$
$233$	−46025.5	−	63348.7i	−0.847787	−	1.16688i	0.136559	−	0.990632i	$-0.456396\pi$
$234$		0			0
$235$	−33792.1	+	104001.i	−0.611898	+	1.88323i
$236$		0			0
$237$	3112.56	−	4284.06i	0.0554141	−	0.0762710i
$238$		0			0
$239$	70428.8	−	22883.7i	1.23298	−	0.400618i	0.381184	−	0.924499i	$-0.375516\pi$
$239$	70428.8	−	22883.7i	1.23298	−	0.400618i	0.851792	+	0.523881i	$0.175516\pi$
$240$		0			0
$241$		−	12085.3i		−	0.208076i	−0.994573	−	0.104038i	$-0.966824\pi$
$241$		−	12085.3i		−	0.208076i	0.994573	−	0.104038i	$-0.0331764\pi$
$242$		0			0
$243$	−19376.4			−0.328141
$244$		0			0
$245$	31883.1	+	98126.2i	0.531164	+	1.63476i
$246$		0			0
$247$	20576.9	+	14950.0i	0.337276	+	0.245046i
$248$		0			0
$249$	423.540	+	137.616i	0.00683118	+	0.00221958i
$250$		0			0
$251$	5768.29	−	4190.91i	0.0915587	−	0.0665213i	−0.541064	−	0.840981i	$-0.681978\pi$
$251$	5768.29	−	4190.91i	0.0915587	−	0.0665213i	0.632623	+	0.774460i	$0.281978\pi$
$252$		0			0
$253$	−17912.2	+	27739.9i	−0.279839	+	0.433375i
$254$		0			0
$255$	5719.96	+	7872.85i	0.0879655	+	0.121074i
$256$		0			0
$257$	39182.2	−	120591.i	0.593230	−	1.82577i	0.0298821	−	0.999553i	$-0.490487\pi$
$257$	39182.2	−	120591.i	0.593230	−	1.82577i	0.563348	−	0.826220i	$-0.309513\pi$
$258$		0			0
$259$	57745.4	−	79479.7i	0.860830	−	1.18483i
$260$		0			0
$261$	45729.6	−	14858.5i	0.671300	−	0.218119i
$262$		0			0
$263$			16826.9i			0.243272i	0.992575	+	0.121636i	$0.0388140\pi$
$263$			16826.9i			0.243272i	−0.992575	+	0.121636i	$0.961186\pi$
$264$		0			0
$265$	−166061.			−2.36470
$266$		0			0
$267$	−2763.72	−	8505.84i	−0.0387678	−	0.119315i
$268$		0			0
$269$	−19506.7	−	14172.4i	−0.269574	−	0.195857i	0.444783	−	0.895638i	$-0.353281\pi$
$269$	−19506.7	−	14172.4i	−0.269574	−	0.195857i	−0.714357	+	0.699781i	$0.753281\pi$
$270$		0			0
$271$	−130875.	−	42523.8i	−1.78204	−	0.579020i	−0.782967	−	0.622063i	$-0.786295\pi$
$271$	−130875.	−	42523.8i	−1.78204	−	0.579020i	−0.999073	+	0.0430434i	$0.986295\pi$
$272$		0			0
$273$	−9528.69	+	6923.00i	−0.127852	+	0.0928900i
$274$		0			0
$275$	−150876.	−	40007.1i	−1.99505	−	0.529019i
$276$		0			0
$277$	−65996.2	−	90835.9i	−0.860120	−	1.18385i	−0.981541	−	0.191253i	$-0.938745\pi$
$277$	−65996.2	−	90835.9i	−0.860120	−	1.18385i	0.121421	−	0.992601i	$-0.461255\pi$
$278$		0			0
$279$	21836.0	−	67204.2i	0.280520	−	0.863352i
$280$		0			0
$281$	641.902	−	883.502i	0.00812936	−	0.0111891i	−0.804933	−	0.593366i	$-0.797799\pi$
$281$	641.902	−	883.502i	0.00812936	−	0.0111891i	0.813062	+	0.582177i	$0.197799\pi$
$282$		0			0
$283$	−131828.	+	42833.7i	−1.64602	+	0.534826i	−0.977873	−	0.209199i	$-0.932914\pi$
$283$	−131828.	+	42833.7i	−1.64602	+	0.534826i	−0.668152	+	0.744025i	$0.732914\pi$
$284$		0			0
$285$			6530.36i			0.0803984i
$286$		0			0
$287$	−76224.2			−0.925400
$288$		0			0
$289$	10554.8	+	32484.3i	0.126373	+	0.388935i
$290$		0			0
$291$	−1685.59	−	1224.65i	−0.0199052	−	0.0144620i
$292$		0			0
$293$	−29274.9	−	9512.00i	−0.341005	−	0.110799i	0.133508	−	0.991048i	$-0.457376\pi$
$293$	−29274.9	−	9512.00i	−0.341005	−	0.110799i	−0.474513	+	0.880249i	$0.657376\pi$
$294$		0			0
$295$	38792.5	−	28184.4i	0.445762	−	0.323865i
$296$		0			0
$297$	18184.6	−	7034.68i	0.206154	−	0.0797502i
$298$		0			0
$299$	−27363.1	−	37662.1i	−0.306072	−	0.421272i
$300$		0			0
$301$	31744.1	−	97698.2i	0.350372	−	1.07833i
$302$		0			0
$303$	−1309.21	+	1801.97i	−0.0142601	+	0.0196274i
$304$		0			0
$305$	−131439.	+	42707.2i	−1.41295	+	0.459094i
$306$		0			0
$307$		−	47816.2i		−	0.507340i	−0.967291	−	0.253670i	$-0.918362\pi$
$307$		−	47816.2i		−	0.507340i	0.967291	−	0.253670i	$-0.0816376\pi$
$308$		0			0
$309$	−20101.0			−0.210524
$310$		0			0
$311$	33332.0	+	102585.i	0.344620	+	1.06063i	0.961787	+	0.273799i	$0.0882803\pi$
$311$	33332.0	+	102585.i	0.344620	+	1.06063i	−0.617167	+	0.786832i	$0.711720\pi$
$312$		0			0
$313$	16908.4	+	12284.7i	0.172589	+	0.125393i	0.670727	−	0.741705i	$-0.265982\pi$
$313$	16908.4	+	12284.7i	0.172589	+	0.125393i	−0.498137	+	0.867098i	$0.665982\pi$
$314$		0			0
$315$	229677.	+	74626.4i	2.31470	+	0.752093i
$316$		0			0
$317$	72173.0	−	52436.8i	0.718218	−	0.521816i	−0.167596	−	0.985856i	$-0.553601\pi$
$317$	72173.0	−	52436.8i	0.718218	−	0.521816i	0.885814	+	0.464040i	$0.153601\pi$
$318$		0			0
$319$	−56400.4	+	45915.3i	−0.554244	+	0.451208i
$320$		0			0
$321$	10410.2	+	14328.4i	0.101030	+	0.139056i
$322$		0			0
$323$	10236.8	−	31505.7i	0.0981205	−	0.301984i
$324$		0			0
$325$	129347.	−	178031.i	1.22459	−	1.68550i
$326$		0			0
$327$	−7555.19	+	2454.83i	−0.0706561	+	0.0229576i
$328$		0			0
$329$			172383.i			1.59258i
$330$		0			0
$331$	108817.			0.993211			0.496605	−	0.867976i	$-0.334580\pi$
$331$	108817.			0.993211			0.496605	+	0.867976i	$0.334580\pi$
$332$		0			0
$333$	−35205.9	−	108353.i	−0.317488	−	0.977127i
$334$		0			0
$335$	−8908.42	−	6472.35i	−0.0793800	−	0.0576730i
$336$		0			0
$337$	−4809.85	−	1562.81i	−0.0423517	−	0.0137609i	0.287765	−	0.957701i	$-0.407088\pi$
$337$	−4809.85	−	1562.81i	−0.0423517	−	0.0137609i	−0.330116	+	0.943940i	$0.607088\pi$
$338$		0			0
$339$	−13724.1	+	9971.15i	−0.119422	+	0.0867652i
$340$		0			0
$341$	5870.98	+	106718.i	0.0504896	+	0.917762i
$342$		0			0
$343$	−1754.39	−	2414.72i	−0.0149121	−	0.0205247i
$344$		0			0
$345$	3693.55	−	11367.6i	0.0310318	−	0.0955059i
$346$		0			0
$347$	68742.8	−	94616.4i	0.570911	−	0.785791i	−0.421751	−	0.906712i	$-0.638584\pi$
$347$	68742.8	−	94616.4i	0.570911	−	0.785791i	0.992662	+	0.120920i	$0.0385845\pi$
$348$		0			0
$349$	−65879.6	+	21405.6i	−0.540879	+	0.175742i	−0.566700	−	0.823924i	$-0.691780\pi$
$349$	−65879.6	+	21405.6i	−0.540879	+	0.175742i	0.0258206	+	0.999667i	$0.491780\pi$
$350$		0			0
$351$			27488.5i			0.223119i
$352$		0			0
$353$	56886.4			0.456519			0.228259	−	0.973600i	$-0.426697\pi$
$353$	56886.4			0.456519			0.228259	+	0.973600i	$0.426697\pi$
$354$		0			0
$355$	−60023.7	−	184734.i	−0.476284	−	1.46585i
$356$		0			0
$357$	12410.6	+	9016.84i	0.0973771	+	0.0707486i
$358$		0			0
$359$	−141042.	−	45827.4i	−1.09436	−	0.355579i	−0.294431	−	0.955673i	$-0.595130\pi$
$359$	−141042.	−	45827.4i	−1.09436	−	0.355579i	−0.799930	+	0.600093i	$0.795130\pi$
$360$		0			0
$361$	−87447.2	+	63534.1i	−0.671014	+	0.487520i
$362$		0			0
$363$	−10838.8	+	9861.79i	−0.0822561	+	0.0748415i
$364$		0			0
$365$	107748.	+	148303.i	0.808770	+	1.11318i
$366$		0			0
$367$	39191.0	−	120617.i	0.290974	−	0.895525i	−0.693571	−	0.720389i	$-0.743963\pi$
$367$	39191.0	−	120617.i	0.290974	−	0.895525i	0.984544	−	0.175136i	$-0.0560366\pi$
$368$		0			0
$369$	−51957.3	+	71513.1i	−0.381587	+	0.525210i
$370$		0			0
$371$	−248964.	+	80893.2i	−1.80879	+	0.587711i
$372$		0			0
$373$		−	47200.3i		−	0.339256i	−0.985508	−	0.169628i	$-0.945743\pi$
$373$		−	47200.3i		−	0.339256i	0.985508	−	0.169628i	$-0.0542566\pi$
$374$		0			0
$375$	29126.3			0.207120
$376$		0			0
$377$	−31684.2	−	97513.9i	−0.222926	−	0.686094i
$378$		0			0
$379$	222539.	+	161684.i	1.54927	+	1.12561i	0.944168	+	0.329465i	$0.106868\pi$
$379$	222539.	+	161684.i	1.54927	+	1.12561i	0.605103	+	0.796147i	$0.293132\pi$
$380$		0			0
$381$	5380.59	+	1748.26i	0.0370663	+	0.0120436i
$382$		0			0
$383$	45891.7	−	33342.3i	0.312850	−	0.227299i	−0.420268	−	0.907400i	$-0.638064\pi$
$383$	45891.7	−	33342.3i	0.312850	−	0.227299i	0.733119	+	0.680101i	$0.238064\pi$
$384$		0			0
$385$	−364719.	+	20064.6i	−2.46058	+	0.135366i
$386$		0			0
$387$	−70021.9	−	96376.8i	−0.467533	−	0.643503i
$388$		0			0
$389$	29662.0	−	91290.2i	0.196020	−	0.603288i	−0.803943	−	0.594706i	$-0.797268\pi$
$389$	29662.0	−	91290.2i	0.196020	−	0.603288i	0.999963	−	0.00858182i	$-0.00273171\pi$
$390$		0			0
$391$	−35639.1	+	49052.9i	−0.233116	+	0.320857i
$392$		0			0
$393$	−15840.4	+	5146.86i	−0.102561	+	0.0333240i
$394$		0			0
$395$			231527.i			1.48391i
$396$		0			0
$397$	146750.			0.931102			0.465551	−	0.885021i	$-0.345856\pi$
$397$	146750.			0.931102			0.465551	+	0.885021i	$0.345856\pi$
$398$		0			0
$399$	3181.13	+	9790.50i	0.0199818	+	0.0614977i
$400$		0			0
$401$	67876.7	+	49315.3i	0.422116	+	0.306685i	0.778489	−	0.627659i	$-0.215987\pi$
$401$	67876.7	+	49315.3i	0.422116	+	0.306685i	−0.356372	+	0.934344i	$0.615987\pi$
$402$		0			0
$403$	−143306.	−	46563.0i	−0.882379	−	0.286702i
$404$		0			0
$405$	223697.	−	162526.i	1.36380	−	0.990860i
$406$		0			0
$407$	108793.	+	133636.i	0.656767	+	0.806744i
$408$		0			0
$409$	162402.	+	223528.i	0.970836	+	1.33624i	0.941623	+	0.336668i	$0.109300\pi$
$409$	162402.	+	223528.i	0.970836	+	1.33624i	0.0292126	+	0.999573i	$0.490700\pi$
$410$		0			0
$411$	3443.96	−	10599.4i	0.0203880	−	0.0627478i
$412$		0			0
$413$	44429.3	−	61151.8i	0.260477	−	0.358516i
$414$		0			0
$415$	−18518.2	+	6016.92i	−0.107523	+	0.0349364i
$416$		0			0
$417$			26114.2i			0.150177i
$418$		0			0
$419$	245758.			1.39984			0.699922	−	0.714220i	$-0.253218\pi$
$419$	245758.			1.39984			0.699922	+	0.714220i	$0.253218\pi$
$420$		0			0
$421$	18943.8	+	58303.1i	0.106882	+	0.328948i	0.990168	−	0.139887i	$-0.0446739\pi$
$421$	18943.8	+	58303.1i	0.106882	+	0.328948i	−0.883286	+	0.468835i	$0.844674\pi$
$422$		0			0
$423$	161728.	+	117503.i	0.903869	+	0.656699i
$424$		0			0
$425$	−272587.	−	88568.8i	−1.50913	−	0.490347i
$426$		0			0
$427$	−176254.	+	128056.i	−0.966680	+	0.702334i
$428$		0			0
$429$	−7453.72	−	19267.8i	−0.0405003	−	0.104693i
$430$		0			0
$431$	170697.	+	234945.i	0.918908	+	1.26477i	0.964032	+	0.265786i	$0.0856316\pi$
$431$	170697.	+	234945.i	0.918908	+	1.26477i	−0.0451244	+	0.998981i	$0.514368\pi$
$432$		0			0
$433$	−14346.5	+	44154.1i	−0.0765193	+	0.235502i	−0.981999	−	0.188888i	$-0.939512\pi$
$433$	−14346.5	+	44154.1i	−0.0765193	+	0.235502i	0.905479	+	0.424390i	$0.139512\pi$
$434$		0			0
$435$	15473.7	−	21297.7i	0.0817740	−	0.112552i
$436$		0			0
$437$	−38697.0	+	12573.4i	−0.202635	+	0.0658400i
$438$		0			0
$439$			9971.85i			0.0517424i	0.999665	+	0.0258712i	$0.00823598\pi$
$439$			9971.85i			0.0517424i	−0.999665	+	0.0258712i	$0.991764\pi$
$440$		0			0
$441$	188614.			0.969835
$442$		0			0
$443$	70757.7	+	217770.i	0.360551	+	1.10966i	0.952721	+	0.303848i	$0.0982713\pi$
$443$	70757.7	+	217770.i	0.360551	+	1.10966i	−0.592170	+	0.805813i	$0.701729\pi$
$444$		0			0
$445$	316353.	+	229844.i	1.59754	+	1.16068i
$446$		0			0
$447$	−30884.6	−	10035.0i	−0.154570	−	0.0502230i
$448$		0			0
$449$	177611.	−	129042.i	0.881002	−	0.640085i	−0.0525145	−	0.998620i	$-0.516724\pi$
$449$	177611.	−	129042.i	0.881002	−	0.640085i	0.933516	+	0.358535i	$0.116724\pi$
$450$		0			0
$451$	34268.5	−	129234.i	0.168478	−	0.635367i
$452$		0			0
$453$	−5559.79	−	7652.40i	−0.0270933	−	0.0372908i
$454$		0			0
$455$	159134.	−	489763.i	0.768668	−	2.36572i
$456$		0			0
$457$	20840.6	−	28684.6i	0.0997877	−	0.137346i	−0.756203	−	0.654337i	$-0.772948\pi$
$457$	20840.6	−	28684.6i	0.0997877	−	0.137346i	0.855991	+	0.516991i	$0.172948\pi$
$458$		0			0
$459$	34050.0	−	11063.5i	0.161619	−	0.0525132i
$460$		0			0
$461$			112097.i			0.527462i	0.964596	+	0.263731i	$0.0849531\pi$
$461$			112097.i			0.527462i	−0.964596	+	0.263731i	$0.915047\pi$
$462$		0			0
$463$	75195.8			0.350777			0.175389	−	0.984499i	$-0.443882\pi$
$463$	75195.8			0.350777			0.175389	+	0.984499i	$0.443882\pi$
$464$		0			0
$465$	−11955.2	−	36794.3i	−0.0552905	−	0.170167i
$466$		0			0
$467$	8465.10	+	6150.25i	0.0388149	+	0.0282007i	0.607024	−	0.794684i	$-0.292363\pi$
$467$	8465.10	+	6150.25i	0.0388149	+	0.0282007i	−0.568209	+	0.822885i	$0.692363\pi$
$468$		0			0
$469$	−16508.6	−	5363.98i	−0.0750525	−	0.0243860i
$470$		0			0
$471$	3124.13	−	2269.81i	0.0140827	−	0.0102317i
$472$		0			0
$473$	151371.	+	97743.1i	0.676581	+	0.436882i
$474$		0			0
$475$	−113053.	−	155603.i	−0.501064	−	0.689655i
$476$		0			0
$477$	−93809.5	+	288716.i	−0.412297	+	1.26892i
$478$		0			0
$479$	−58592.5	+	80645.7i	−0.255371	+	0.351488i	−0.917383	−	0.398005i	$-0.869703\pi$
$479$	−58592.5	+	80645.7i	−0.255371	+	0.351488i	0.662012	+	0.749493i	$0.269703\pi$
$480$		0			0
$481$	−231051.	+	75073.1i	−0.998662	+	0.324485i
$482$		0			0
$483$		−	18841.9i		−	0.0807662i
$484$		0			0
$485$	91095.8			0.387271
$486$		0			0
$487$	−129497.	−	398552.i	−0.546013	−	1.68045i	−0.718570	−	0.695455i	$-0.755203\pi$
$487$	−129497.	−	398552.i	−0.546013	−	1.68045i	0.172557	−	0.985000i	$-0.444797\pi$
$488$		0			0
$489$	−13662.3	−	9926.22i	−0.0571354	−	0.0415113i
$490$		0			0
$491$	−74522.5	−	24213.8i	−0.309118	−	0.100439i	0.150350	−	0.988633i	$-0.451960\pi$
$491$	−74522.5	−	24213.8i	−0.309118	−	0.100439i	−0.459468	+	0.888194i	$0.651960\pi$
$492$		0			0
$493$	−108038.	+	78494.5i	−0.444513	+	0.322957i
$494$		0			0
$495$	−229782.	+	355854.i	−0.937790	+	1.45232i
$496$		0			0
$497$	−179978.	−	247719.i	−0.728631	−	1.00287i
$498$		0			0
$499$	−119981.	+	369265.i	−0.481851	+	1.48299i	0.354639	+	0.935003i	$0.384604\pi$
$499$	−119981.	+	369265.i	−0.481851	+	1.48299i	−0.836490	+	0.547982i	$0.815396\pi$
$500$		0			0
$501$	−8518.13	+	11724.2i	−0.0339366	+	0.0467098i
$502$		0			0
$503$	−15968.4	+	5188.46i	−0.0631141	+	0.0205070i	−0.340404	−	0.940279i	$-0.610564\pi$
$503$	−15968.4	+	5188.46i	−0.0631141	+	0.0205070i	0.277290	+	0.960786i	$0.410564\pi$
$504$		0			0
$505$		−	97385.4i		−	0.381866i
$506$		0			0
$507$	539.882			0.00210031
$508$		0			0
$509$	−101400.	−	312078.i	−0.391384	−	1.20456i	−0.931742	−	0.363121i	$-0.881711\pi$
$509$	−101400.	−	312078.i	−0.391384	−	1.20456i	0.540358	−	0.841435i	$-0.318289\pi$
$510$		0			0
$511$	233782.	+	169853.i	0.895302	+	0.650475i
$512$		0			0
$513$	22849.7	+	7424.32i	0.0868252	+	0.0282112i
$514$		0			0
$515$	711016.	−	516583.i	2.68080	−	1.94772i
$516$		0			0
$517$	−292266.	−	77499.0i	−1.09345	−	0.289944i
$518$		0			0
$519$	13993.8	+	19260.9i	0.0519520	+	0.0715057i
$520$		0			0
$521$	−57854.4	+	178058.i	−0.213138	+	0.655971i	0.786143	+	0.618045i	$0.212075\pi$
$521$	−57854.4	+	178058.i	−0.213138	+	0.655971i	−0.999281	+	0.0379262i	$0.987925\pi$
$522$		0			0
$523$	−118132.	+	162595.i	−0.431881	+	0.594434i	−0.968384	−	0.249465i	$-0.919745\pi$
$523$	−118132.	+	162595.i	−0.431881	+	0.594434i	0.536502	+	0.843899i	$0.319745\pi$
$524$		0			0
$525$	84707.4	−	27523.1i	0.307328	−	0.0998570i
$526$		0			0
$527$			196254.i			0.706640i
$528$		0			0
$529$	−205369.			−0.733876
$530$		0			0
$531$	−27087.5	−	83366.7i	−0.0960681	−	0.295667i
$532$		0			0
$533$	152495.	+	110794.i	0.536785	+	0.389997i
$534$		0			0
$535$	−736464.	−	239292.i	−2.57303	−	0.836027i
$536$		0			0
$537$	29494.6	−	21429.1i	0.102281	−	0.0743114i
$538$		0			0
$539$	−266071.	+	102929.i	−0.915839	+	0.354291i
$540$		0			0
$541$	−227843.	−	313599.i	−0.778469	−	1.07147i	−0.995449	−	0.0952945i	$-0.969621\pi$
$541$	−227843.	−	313599.i	−0.778469	−	1.07147i	0.216980	−	0.976176i	$-0.430379\pi$
$542$		0			0
$543$	−3534.99	+	10879.6i	−0.0119891	+	0.0368988i
$544$		0			0
$545$	204156.	−	280996.i	0.687335	−	0.946036i
$546$		0			0
$547$	251350.	−	81668.6i	0.840048	−	0.272948i	0.142776	−	0.989755i	$-0.454397\pi$
$547$	251350.	−	81668.6i	0.840048	−	0.272948i	0.697272	+	0.716807i	$0.254397\pi$
$548$		0			0
$549$			252648.i			0.838245i
$550$		0			0
$551$	−89615.6			−0.295175
$552$		0			0
$553$	112784.	+	347112.i	0.368804	+	1.13506i
$554$		0			0
$555$	−50463.2	−	36663.7i	−0.163828	−	0.119028i
$556$		0			0
$557$	138711.	+	45069.9i	0.447095	+	0.145270i	0.523907	−	0.851776i	$-0.324474\pi$
$557$	138711.	+	45069.9i	0.447095	+	0.145270i	−0.0768117	+	0.997046i	$0.524474\pi$
$558$		0			0
$559$	−205514.	+	149315.i	−0.657685	+	0.477836i
$560$		0			0
$561$	−20867.1	+	16987.8i	−0.0663034	+	0.0539773i
$562$		0			0
$563$	−153456.	−	211214.i	−0.484136	−	0.666356i	0.495157	−	0.868803i	$-0.335110\pi$
$563$	−153456.	−	211214.i	−0.484136	−	0.666356i	−0.979293	+	0.202447i	$0.935110\pi$
$564$		0			0
$565$	229199.	−	705402.i	0.717986	−	2.20973i
$566$		0			0
$567$	256203.	−	352633.i	0.796925	−	1.09687i
$568$		0			0
$569$	−231581.	+	75245.2i	−0.715284	+	0.232410i	−0.643977	−	0.765045i	$-0.722717\pi$
$569$	−231581.	+	75245.2i	−0.715284	+	0.232410i	−0.0713065	+	0.997454i	$0.522717\pi$
$570$		0			0
$571$			166213.i			0.509792i	0.966968	+	0.254896i	$0.0820412\pi$
$571$			166213.i			0.509792i	−0.966968	+	0.254896i	$0.917959\pi$
$572$		0			0
$573$	−8880.56			−0.0270477
$574$		0			0
$575$	108785.	+	334806.i	0.329028	+	1.01265i
$576$		0			0
$577$	200993.	+	146030.i	0.603710	+	0.438621i	0.847194	−	0.531284i	$-0.178290\pi$
$577$	200993.	+	146030.i	0.603710	+	0.438621i	−0.243484	+	0.969905i	$0.578290\pi$
$578$		0			0
$579$	9878.63	+	3209.76i	0.0294672	+	0.00957449i
$580$		0			0
$581$	−24831.9	+	18041.5i	−0.0735629	+	0.0534465i
$582$		0			0
$583$	−25222.3	−	458472.i	−0.0742075	−	1.34889i
$584$		0			0
$585$	−351021.	−	483139.i	−1.02570	−	1.41176i
$586$		0			0
$587$	79755.8	−	245463.i	0.231465	−	0.712377i	−0.766105	−	0.642715i	$-0.777808\pi$
$587$	79755.8	−	245463.i	0.231465	−	0.712377i	0.997571	−	0.0696620i	$-0.0221921\pi$
$588$		0			0
$589$	−77410.7	+	106547.i	−0.223136	+	0.307121i
$590$		0			0
$591$	72176.2	−	23451.5i	0.206642	−	0.0671421i
$592$		0			0
$593$			277923.i			0.790342i	0.918608	+	0.395171i	$0.129315\pi$
$593$			277923.i			0.790342i	−0.918608	+	0.395171i	$0.870685\pi$
$594$		0			0
$595$	−670717.			−1.89455
$596$		0			0
$597$	20197.1	+	62160.2i	0.0566682	+	0.174407i
$598$		0			0
$599$	−392348.	−	285058.i	−1.09350	−	0.794472i	−0.113511	−	0.993537i	$-0.536210\pi$
$599$	−392348.	−	285058.i	−1.09350	−	0.794472i	−0.979986	+	0.199064i	$0.936210\pi$
$600$		0			0
$601$	−281101.	−	91335.1i	−0.778239	−	0.252865i	−0.107151	−	0.994243i	$-0.534173\pi$
$601$	−281101.	−	91335.1i	−0.778239	−	0.252865i	−0.671088	+	0.741378i	$0.734173\pi$
$602$		0			0
$603$	−16285.3	+	11832.0i	−0.0447881	+	0.0325404i
$604$		0			0
$605$	129950.	−	627383.i	0.355031	−	1.71404i
$606$		0			0
$607$	387086.	+	532778.i	1.05058	+	1.44600i	0.888303	+	0.459258i	$0.151885\pi$
$607$	387086.	+	532778.i	1.05058	+	1.44600i	0.162279	+	0.986745i	$0.448115\pi$
$608$		0			0
$609$	12823.9	−	39467.8i	0.0345768	−	0.106416i
$610$		0			0
$611$	250563.	−	344870.i	0.671172	−	0.923789i
$612$		0			0
$613$	−195640.	+	63567.3i	−0.520639	+	0.169166i	−0.557535	−	0.830153i	$-0.688253\pi$
$613$	−195640.	+	63567.3i	−0.520639	+	0.169166i	0.0368963	+	0.999319i	$0.488253\pi$
$614$		0			0
$615$			48396.3i			0.127956i
$616$		0			0
$617$	298927.			0.785226			0.392613	−	0.919704i	$-0.371571\pi$
$617$	298927.			0.785226			0.392613	+	0.919704i	$0.371571\pi$
$618$		0			0
$619$	89798.4	+	276371.i	0.234362	+	0.721293i	0.997205	+	0.0747091i	$0.0238028\pi$
$619$	89798.4	+	276371.i	0.234362	+	0.721293i	−0.762843	+	0.646584i	$0.776197\pi$
$620$		0			0
$621$	−35576.0	−	25847.5i	−0.0922515	−	0.0670247i
$622$		0			0
$623$	586250.	+	190484.i	1.51045	+	0.490775i
$624$		0			0
$625$	−377989.	+	274625.i	−0.967653	+	0.703041i
$626$		0			0
$627$	−18029.4	+	991.869i	−0.0458614	+	0.00252301i
$628$		0			0
$629$	185986.	+	255988.i	0.470089	+	0.647022i
$630$		0			0
$631$	37040.0	−	113997.i	0.0930276	−	0.286310i	−0.893707	−	0.448651i	$-0.851905\pi$
$631$	37040.0	−	113997.i	0.0930276	−	0.286310i	0.986735	+	0.162341i	$0.0519046\pi$
$632$		0			0
$633$	−23880.1	+	32868.1i	−0.0595976	+	0.0820290i
$634$		0			0
$635$	−235252.	+	76438.0i	−0.583426	+	0.189567i
$636$		0			0
$637$		−	402202.i		−	0.991209i
$638$		0			0
$639$	−355089.			−0.869631
$640$		0			0
$641$	139619.	+	429704.i	0.339805	+	1.04581i	0.964307	+	0.264788i	$0.0853020\pi$
$641$	139619.	+	429704.i	0.339805	+	1.04581i	−0.624502	+	0.781023i	$0.714698\pi$
$642$		0			0
$643$	−23468.8	−	17051.1i	−0.0567636	−	0.0412412i	0.559042	−	0.829140i	$-0.311169\pi$
$643$	−23468.8	−	17051.1i	−0.0567636	−	0.0412412i	−0.615805	+	0.787898i	$0.711169\pi$
$644$		0			0
$645$	−62030.5	−	20154.9i	−0.149103	−	0.0484464i
$646$		0			0
$647$	−197122.	+	143218.i	−0.470898	+	0.342127i	−0.797791	−	0.602934i	$-0.793998\pi$
$647$	−197122.	+	143218.i	−0.470898	+	0.342127i	0.326893	+	0.945061i	$0.393998\pi$
$648$		0			0
$649$	83705.3	+	102820.i	0.198730	+	0.244111i
$650$		0			0
$651$	−35847.1	−	49339.3i	−0.0845848	−	0.116421i
$652$		0			0
$653$	−29840.9	+	91840.8i	−0.0699819	+	0.215382i	−0.979931	−	0.199339i	$-0.936121\pi$
$653$	−29840.9	+	91840.8i	−0.0699819	+	0.215382i	0.909949	+	0.414721i	$0.136121\pi$
$654$		0			0
$655$	428038.	−	589144.i	0.997699	−	1.37322i
$656$		0			0
$657$	318709.	−	103555.i	0.738353	−	0.239906i
$658$		0			0
$659$			442730.i			1.01946i	0.860336	+	0.509728i	$0.170254\pi$
$659$			442730.i			1.01946i	−0.860336	+	0.509728i	$0.829746\pi$
$660$		0			0
$661$	−666291.			−1.52497			−0.762485	−	0.647006i	$-0.776021\pi$
$661$	−666291.			−1.52497			−0.762485	+	0.647006i	$0.776021\pi$
$662$		0			0
$663$	−11722.5	−	36078.3i	−0.0266683	−	0.0820765i
$664$		0			0
$665$	−364133.	−	264558.i	−0.823411	−	0.598243i
$666$		0			0
$667$	155996.	+	50686.3i	0.350641	+	0.113930i
$668$		0			0
$669$	5660.08	−	4112.29i	0.0126465	−	0.00918822i
$670$		0			0
$671$	−137873.	−	356400.i	−0.306220	−	0.791575i
$672$		0			0
$673$	−111806.	−	153887.i	−0.246850	−	0.339760i	0.667555	−	0.744561i	$-0.267341\pi$
$673$	−111806.	−	153887.i	−0.246850	−	0.339760i	−0.914405	+	0.404801i	$0.867341\pi$
$674$		0			0
$675$	64235.1	−	197695.i	0.140982	−	0.433900i
$676$		0			0
$677$	42042.5	−	57866.5i	0.0917300	−	0.126255i	−0.760685	−	0.649121i	$-0.775137\pi$
$677$	42042.5	−	57866.5i	0.0917300	−	0.126255i	0.852415	+	0.522865i	$0.175137\pi$
$678$		0			0
$679$	136573.	−	44375.4i	0.296228	−	0.0962504i
$680$		0			0
$681$		−	58420.2i		−	0.125970i
$682$		0			0
$683$	−503504.			−1.07935			−0.539674	−	0.841874i	$-0.681453\pi$
$683$	−503504.			−1.07935			−0.539674	+	0.841874i	$0.681453\pi$
$684$		0			0
$685$	150578.	+	463432.i	0.320908	+	0.987654i
$686$		0			0
$687$	64651.5	+	46972.1i	0.136983	+	0.0995236i
$688$		0			0
$689$	615658.	+	200040.i	1.29688	+	0.421383i
$690$		0			0
$691$	−124167.	+	90212.5i	−0.260046	+	0.188934i	−0.710167	−	0.704033i	$-0.751381\pi$
$691$	−124167.	+	90212.5i	−0.260046	+	0.188934i	0.450122	+	0.892967i	$0.351381\pi$
$692$		0			0
$693$	−171149.	+	645440.i	−0.356375	+	1.34397i
$694$		0			0
$695$	−671119.	−	923716.i	−1.38941	−	1.91236i
$696$		0			0
$697$	75864.7	−	233487.i	0.156161	−	0.480616i
$698$		0			0
$699$	−46065.8	+	63404.2i	−0.0942811	+	0.129767i
$700$		0			0
$701$	−624194.	+	202813.i	−1.27023	+	0.412724i	−0.865130	−	0.501548i	$-0.832764\pi$
$701$	−624194.	+	202813.i	−1.27023	+	0.412724i	−0.405103	+	0.914271i	$0.632764\pi$
$702$		0			0
$703$			212337.i			0.429650i
$704$		0			0
$705$	109449.			0.220209
$706$		0			0
$707$	−47439.3	−	146003.i	−0.0949072	−	0.292094i
$708$		0			0
$709$	447847.	+	325380.i	0.890917	+	0.647289i	0.936117	−	0.351689i	$-0.114393\pi$
$709$	447847.	+	325380.i	0.890917	+	0.647289i	−0.0452003	+	0.998978i	$0.514393\pi$
$710$		0			0
$711$	402536.	+	130792.i	0.796280	+	0.258727i
$712$		0			0
$713$	195014.	−	141686.i	0.383606	−	0.278706i
$714$		0			0
$715$	758824.	+	489988.i	1.48433	+	0.958458i
$716$		0			0
$717$	−43565.5	−	59962.8i	−0.0847432	−	0.116639i
$718$		0			0
$719$	−298506.	+	918707.i	−0.577425	+	1.77713i	0.0503452	+	0.998732i	$0.483968\pi$
$719$	−298506.	+	918707.i	−0.577425	+	1.77713i	−0.627770	+	0.778399i	$0.716032\pi$
$720$		0			0
$721$	814333.	−	1.12083e6i	1.56650	−	2.15611i
$722$		0			0
$723$	−11503.9	+	3737.83i	−0.0220073	+	0.00715061i
$724$		0			0
$725$			775353.i			1.47511i
$726$		0			0
$727$	744756.			1.40911			0.704555	−	0.709649i	$-0.251147\pi$
$727$	744756.			1.40911			0.704555	+	0.709649i	$0.251147\pi$
$728$		0			0
$729$	−152163.	−	468311.i	−0.286322	−	0.881210i
$730$		0			0
$731$	267671.	+	194475.i	0.500919	+	0.363939i
$732$		0			0
$733$	417784.	+	135746.i	0.777577	+	0.252650i	0.670805	−	0.741634i	$-0.265949\pi$
$733$	417784.	+	135746.i	0.777577	+	0.252650i	0.106772	+	0.994284i	$0.465949\pi$
$734$		0			0
$735$	83544.2	−	60698.5i	0.154647	−	0.112358i
$736$		0			0
$737$	16516.2	−	25578.0i	0.0304071	−	0.0470903i
$738$		0			0
$739$	237582.	+	327003.i	0.435035	+	0.598774i	0.969100	−	0.246670i	$-0.0793362\pi$
$739$	237582.	+	327003.i	0.435035	+	0.598774i	−0.534065	+	0.845443i	$0.679336\pi$
$740$		0			0
$741$	7866.56	−	24210.8i	0.0143268	−	0.0440933i
$742$		0			0
$743$	−539969.	+	743203.i	−0.978117	+	1.34626i	−0.0402795	+	0.999188i	$0.512825\pi$
$743$	−539969.	+	743203.i	−0.978117	+	1.34626i	−0.937838	+	0.347074i	$0.887175\pi$
$744$		0			0
$745$	1.35035e6	−	438754.i	2.43295	−	0.790513i
$746$		0			0
$747$			35594.9i			0.0637891i
$748$		0			0
$749$	−1.22069e6			−2.17592
$750$		0			0
$751$	182885.	+	562862.i	0.324264	+	0.997981i	0.971772	+	0.235922i	$0.0758111\pi$
$751$	182885.	+	562862.i	0.324264	+	0.997981i	−0.647508	+	0.762058i	$0.724189\pi$
$752$		0			0
$753$	−5773.34	−	4194.58i	−0.0101821	−	0.00739773i
$754$		0			0
$755$	393324.	+	127799.i	0.690012	+	0.224198i
$756$		0			0
$757$	−104124.	+	75650.7i	−0.181702	+	0.132014i	−0.674918	−	0.737892i	$-0.735821\pi$
$757$	−104124.	+	75650.7i	−0.181702	+	0.132014i	0.493216	+	0.869907i	$0.335821\pi$
$758$		0			0
$759$	31945.4	+	8470.83i	0.0554529	+	0.0147042i
$760$		0			0
$761$	506042.	+	696507.i	0.873811	+	1.20270i	0.978097	+	0.208150i	$0.0667443\pi$
$761$	506042.	+	696507.i	0.873811	+	1.20270i	−0.104286	+	0.994547i	$0.533256\pi$
$762$		0			0
$763$	169195.	−	520728.i	0.290628	−	0.894462i
$764$		0			0
$765$	−457186.	+	629263.i	−0.781214	+	1.07525i
$766$		0			0
$767$	−177771.	+	57761.4i	−0.302184	+	0.0981854i
$768$		0			0
$769$			344406.i			0.582395i	0.956663	+	0.291197i	$0.0940537\pi$
$769$			344406.i			0.582395i	−0.956663	+	0.291197i	$0.905946\pi$
$770$		0			0
$771$	−126907.			−0.213490
$772$		0			0
$773$	−164043.	−	504873.i	−0.274536	−	0.844935i	−0.989342	−	0.145612i	$-0.953485\pi$
$773$	−164043.	−	504873.i	−0.274536	−	0.844935i	0.714806	−	0.699323i	$-0.246515\pi$
$774$		0			0
$775$	921841.	+	669757.i	1.53480	+	1.11510i
$776$		0			0
$777$	−93515.8	−	30385.1i	−0.154897	−	0.0503291i
$778$		0			0
$779$	133284.	−	96836.5i	0.219636	−	0.159575i
$780$		0			0
$781$	500909.	−	193776.i	0.821214	−	0.317685i
$782$		0			0
$783$	−56928.6	−	78355.6i	−0.0928554	−	0.127805i
$784$		0			0
$785$	−52174.4	+	160576.i	−0.0846678	+	0.260581i
$786$		0			0
$787$	290841.	−	400308.i	0.469576	−	0.646316i	−0.506884	−	0.862014i	$-0.669203\pi$
$787$	290841.	−	400308.i	0.469576	−	0.646316i	0.976460	+	0.215698i	$0.0692027\pi$
$788$		0			0
$789$	16017.3	−	5204.34i	0.0257297	−	0.00836010i
$790$		0			0
$791$		−	1.16921e6i		−	1.86870i
$792$		0			0
$793$	538747.			0.856719
$794$		0			0
$795$	51360.7	+	158072.i	0.0812637	+	0.250104i
$796$		0			0
$797$	−524007.	−	380713.i	−0.824937	−	0.599351i	0.0931857	−	0.995649i	$-0.470295\pi$
$797$	−524007.	−	380713.i	−0.824937	−	0.599351i	−0.918122	+	0.396297i	$0.870295\pi$
$798$		0			0
$799$	−528037.	−	171570.i	−0.827124	−	0.268749i
$800$		0			0
$801$	578321.	−	420175.i	0.901372	−	0.654885i
$802$		0			0
$803$	−393079.	+	320004.i	−0.609605	+	0.496277i
$804$		0			0
$805$	484224.	+	666477.i	0.747230	+	1.02847i
$806$		0			0
$807$	−7457.41	+	22951.6i	−0.0114509	+	0.0352424i
$808$		0			0
$809$	−152306.	+	209632.i	−0.232713	+	0.320302i	−0.909364	−	0.416002i	$-0.863431\pi$
$809$	−152306.	+	209632.i	−0.232713	+	0.320302i	0.676650	+	0.736305i	$0.263431\pi$
$810$		0			0
$811$	−156597.	+	50881.3i	−0.238090	+	0.0773601i	−0.425632	−	0.904897i	$-0.639948\pi$
$811$	−156597.	+	50881.3i	−0.238090	+	0.0773601i	0.187542	+	0.982257i	$0.439948\pi$
$812$		0			0
$813$			137730.i			0.208377i
$814$		0			0
$815$	738362.			1.11161
$816$		0			0
$817$	68610.4	+	211161.i	0.102789	+	0.316351i
$818$		0			0
$819$	−761611.	−	553343.i	−1.13544	−	0.824948i
$820$		0			0
$821$	−500058.	−	162479.i	−0.741880	−	0.241051i	−0.0863964	−	0.996261i	$-0.527535\pi$
$821$	−500058.	−	162479.i	−0.741880	−	0.241051i	−0.655484	+	0.755209i	$0.727535\pi$
$822$		0			0
$823$	−854678.	+	620960.i	−1.26184	+	0.916778i	−0.998846	−	0.0480208i	$-0.984709\pi$
$823$	−854678.	+	620960.i	−1.26184	+	0.916778i	−0.262990	+	0.964799i	$0.584709\pi$
$824$		0			0
$825$	8581.64	+	155991.i	0.0126085	+	0.229187i
$826$		0			0
$827$	−149221.	−	205385.i	−0.218182	−	0.300302i	0.685870	−	0.727724i	$-0.259422\pi$
$827$	−149221.	−	205385.i	−0.218182	−	0.300302i	−0.904052	+	0.427422i	$0.859422\pi$
$828$		0			0
$829$	−376939.	+	1.16010e6i	−0.548482	+	1.68805i	0.164082	+	0.986447i	$0.447534\pi$
$829$	−376939.	+	1.16010e6i	−0.548482	+	1.68805i	−0.712564	+	0.701607i	$0.752466\pi$
$830$		0			0
$831$	−66054.0	+	90915.5i	−0.0956526	+	0.131655i
$832$		0			0
$833$	−498208.	+	161878.i	−0.717993	+	0.233290i
$834$		0			0
$835$		−	633621.i		−	0.908775i
$836$		0			0
$837$	−142335.			−0.203170
$838$		0			0
$839$	90994.6	+	280053.i	0.129268	+	0.397847i	0.994655	−	0.103259i	$-0.0329269\pi$
$839$	90994.6	+	280053.i	0.129268	+	0.397847i	−0.865386	+	0.501105i	$0.832927\pi$
$840$		0			0
$841$	−279936.	−	203385.i	−0.395792	−	0.287559i
$842$		0			0
$843$	−1039.53	−	337.763i	−0.00146279	−	0.000475289i
$844$		0			0
$845$	−19096.8	+	13874.6i	−0.0267453	+	0.0194316i
$846$		0			0
$847$	−110791.	−	1.00389e6i	−0.154433	−	1.39933i
$848$		0			0
$849$	81545.8	+	112238.i	0.113132	+	0.155713i
$850$		0			0
$851$	120097.	−	369621.i	0.165834	−	0.510385i
$852$		0			0
$853$	−40665.6	+	55971.4i	−0.0558894	+	0.0769251i	−0.836047	−	0.548658i	$-0.815139\pi$
$853$	−40665.6	+	55971.4i	−0.0558894	+	0.0769251i	0.780157	+	0.625583i	$0.215139\pi$
$854$		0			0
$855$	−496414.	+	161295.i	−0.679065	+	0.220642i
$856$		0			0
$857$		−	888080.i		−	1.20918i	−0.796537	−	0.604589i	$-0.793337\pi$
$857$		−	888080.i		−	1.20918i	0.796537	−	0.604589i	$-0.206663\pi$
$858$		0			0
$859$	1.42192e6			1.92703			0.963517	−	0.267648i	$-0.0862466\pi$
$859$	1.42192e6			1.92703			0.963517	+	0.267648i	$0.0862466\pi$
$860$		0			0
$861$	23575.2	+	72557.1i	0.0318016	+	0.0978754i
$862$		0			0
$863$	345303.	+	250878.i	0.463638	+	0.336853i	0.794957	−	0.606666i	$-0.207494\pi$
$863$	345303.	+	250878.i	0.463638	+	0.336853i	−0.331319	+	0.943519i	$0.607494\pi$
$864$		0			0
$865$	−989984.	−	321665.i	−1.32311	−	0.429904i
$866$		0			0
$867$	27657.0	−	20094.0i	0.0367931	−	0.0267318i
$868$		0			0
$869$	−639215.	+	35165.7i	−0.846463	+	0.0465672i
$870$		0			0
$871$	25230.6	+	34726.9i	0.0332576	+	0.0457752i
$872$		0			0
$873$	51460.9	−	158380.i	0.0675225	−	0.207813i
$874$		0			0
$875$	−1.17996e6	+	1.62408e6i	−1.54118	+	2.12125i
$876$		0			0
$877$	1.38361e6	−	449562.i	1.79893	−	0.584509i	0.799072	−	0.601235i	$-0.205324\pi$
$877$	1.38361e6	−	449562.i	1.79893	−	0.584509i	0.999860	+	0.0167265i	$0.00532445\pi$
$878$		0			0
$879$			30808.4i			0.0398742i
$880$		0			0
$881$	−50384.3			−0.0649147			−0.0324574	−	0.999473i	$-0.510333\pi$
$881$	−50384.3			−0.0649147			−0.0324574	+	0.999473i	$0.510333\pi$
$882$		0			0
$883$	−436301.	−	1.34280e6i	−0.559583	−	1.72222i	−0.683522	−	0.729930i	$-0.739552\pi$
$883$	−436301.	−	1.34280e6i	−0.559583	−	1.72222i	0.123938	−	0.992290i	$-0.460448\pi$
$884$		0			0
$885$	−38826.4	−	28209.1i	−0.0495725	−	0.0360166i
$886$		0			0
$887$	109485.	+	35573.8i	0.139158	+	0.0452151i	0.377768	−	0.925900i	$-0.376692\pi$
$887$	109485.	+	35573.8i	0.139158	+	0.0452151i	−0.238610	+	0.971115i	$0.576692\pi$
$888$		0			0
$889$	−315461.	+	229196.i	−0.399156	+	0.290004i
$890$		0			0
$891$	482688.	+	592913.i	0.608010	+	0.746854i
$892$		0			0
$893$	−218998.	−	301424.i	−0.274623	−	0.377986i
$894$		0			0
$895$	−492574.	+	1.51599e6i	−0.614930	+	1.89256i
$896$		0			0
$897$	−27387.1	+	37695.1i	−0.0340378	+	0.0468490i
$898$		0			0
$899$	504925.	−	164060.i	0.624751	−	0.202994i
$900$		0			0
$901$		−	843128.i		−	1.03859i
$902$		0			0
$903$	−102816.			−0.126091
$904$		0			0
$905$	−154558.	−	475681.i	−0.188710	−	0.580789i
$906$		0			0
$907$	−195228.	−	141842.i	−0.237316	−	0.172421i	0.462770	−	0.886478i	$-0.346855\pi$
$907$	−195228.	−	141842.i	−0.237316	−	0.172421i	−0.700087	+	0.714058i	$0.746855\pi$
$908$		0			0
$909$	−169315.	−	55013.9i	−0.204913	−	0.0665802i
$910$		0			0
$911$	160010.	−	116254.i	0.192801	−	0.140078i	−0.487197	−	0.873292i	$-0.661981\pi$
$911$	160010.	−	116254.i	0.192801	−	0.140078i	0.679998	+	0.733214i	$0.261981\pi$
$912$		0			0
$913$	−19424.5	−	50212.3i	−0.0233029	−	0.0602377i
$914$		0			0
$915$	81305.2	+	111907.i	0.0971127	+	0.133664i
$916$		0			0
$917$	354738.	−	1.09177e6i	0.421860	−	1.29835i
$918$		0			0
$919$	754825.	−	1.03893e6i	0.893748	−	1.23014i	−0.0786719	−	0.996901i	$-0.525068\pi$
$919$	754825.	−	1.03893e6i	0.893748	−	1.23014i	0.972420	−	0.233238i	$-0.0749321\pi$
$920$		0			0
$921$	−45515.8	+	14789.0i	−0.0536590	+	0.0174349i
$922$		0			0
$923$			757192.i			0.888797i
$924$		0			0
$925$	1.83714e6			2.14713
$926$		0			0
$927$	−496479.	−	1.52800e6i	−0.577751	−	1.77814i
$928$		0			0
$929$	503249.	+	365632.i	0.583111	+	0.423655i	0.839844	−	0.542827i	$-0.182646\pi$
$929$	503249.	+	365632.i	0.583111	+	0.423655i	−0.256733	+	0.966482i	$0.582646\pi$
$930$		0			0
$931$	−334329.	−	108630.i	−0.385722	−	0.125329i
$932$		0			0
$933$	87340.7	−	63456.8i	0.100335	−	0.0728978i
$934$		0			0
$935$	301538.	−	1.13717e6i	0.344920	−	1.30077i
$936$		0			0
$937$	505212.	+	695365.i	0.575433	+	0.792015i	0.993185	−	0.116545i	$-0.0371821\pi$
$937$	505212.	+	695365.i	0.575433	+	0.792015i	−0.417752	+	0.908561i	$0.637182\pi$
$938$		0			0
$939$	6464.09	−	19894.4i	0.00733122	−	0.0225632i
$940$		0			0
$941$	−619437.	+	852581.i	−0.699548	+	0.962845i	0.300411	+	0.953810i	$0.402876\pi$
$941$	−619437.	+	852581.i	−0.699548	+	0.962845i	−0.999959	+	0.00903557i	$0.997124\pi$
$942$		0			0
$943$	−286782.	+	93181.1i	−0.322499	+	0.104786i
$944$		0			0
$945$		−	486442.i		−	0.544713i
$946$		0			0
$947$	57720.0			0.0643616			0.0321808	−	0.999482i	$-0.489755\pi$
$947$	57720.0			0.0643616			0.0321808	+	0.999482i	$0.489755\pi$
$948$		0			0
$949$	−220821.	−	679617.i	−0.245193	−	0.754626i
$950$		0			0
$951$	−72236.2	−	52482.7i	−0.0798719	−	0.0580303i
$952$		0			0
$953$	311593.	+	101243.i	0.343085	+	0.111475i	0.475491	−	0.879721i	$-0.342270\pi$
$953$	311593.	+	101243.i	0.343085	+	0.111475i	−0.132406	+	0.991196i	$0.542270\pi$
$954$		0			0
$955$	314125.	−	228225.i	0.344425	−	0.250240i
$956$		0			0
$957$	61150.3	+	39485.9i	0.0667690	+	0.0431140i
$958$		0			0
$959$	451502.	+	621440.i	0.490934	+	0.675712i
$960$		0			0
$961$	−44281.4	+	136284.i	−0.0479484	+	0.147570i
$962$		0			0
$963$	−832071.	+	1.14525e6i	−0.897238	+	1.23494i
$964$		0			0
$965$	−431917.	+	140338.i	−0.463816	+	0.150703i
$966$		0			0
$967$		−	1.36682e6i		−	1.46170i	−0.682540	−	0.730848i	$-0.739125\pi$
$967$		−	1.36682e6i		−	1.46170i	0.682540	−	0.730848i	$-0.260875\pi$
$968$		0			0
$969$	−33156.0			−0.0353114
$970$		0			0
$971$	−14536.2	−	44737.9i	−0.0154175	−	0.0474501i	0.943052	−	0.332646i	$-0.107941\pi$
$971$	−14536.2	−	44737.9i	−0.0154175	−	0.0474501i	−0.958469	+	0.285196i	$0.907941\pi$
$972$		0			0
$973$	−1.45613e6	−	1.05794e6i	−1.53806	−	1.11747i
$974$		0			0
$975$	−209472.	−	68061.4i	−0.220351	−	0.0715965i
$976$		0			0
$977$	111116.	−	80730.2i	0.116409	−	0.0845760i	−0.528058	−	0.849209i	$-0.677080\pi$
$977$	111116.	−	80730.2i	0.116409	−	0.0845760i	0.644467	+	0.764633i	$0.277080\pi$
$978$		0			0
$979$	−586519.	+	908319.i	−0.611951	+	0.947705i
$980$		0			0
$981$	−373214.	−	513685.i	−0.387811	−	0.533776i
$982$		0			0
$983$	−136330.	+	419580.i	−0.141086	+	0.434218i	−0.996487	−	0.0837482i	$-0.973311\pi$
$983$	−136330.	+	419580.i	−0.141086	+	0.434218i	0.855401	+	0.517967i	$0.173311\pi$
$984$		0			0
$985$	−1.95034e6	+	2.68441e6i	−2.01019	+	2.76679i
$986$		0			0
$987$	164089.	−	53315.9i	0.168440	−	0.0547296i
$988$		0			0
$989$		−	406380.i		−	0.415470i
$990$		0			0
$991$	−1.11050e6			−1.13076			−0.565379	−	0.824831i	$-0.691270\pi$
$991$	−1.11050e6			−1.13076			−0.565379	+	0.824831i	$0.691270\pi$
$992$		0			0
$993$	−33655.8	−	103582.i	−0.0341320	−	0.105047i
$994$		0			0
$995$	−2.31189e6	−	1.67969e6i	−2.33518	−	1.69661i
$996$		0			0
$997$	−966994.	−	314196.i	−0.972823	−	0.316089i	−0.220868	−	0.975304i	$-0.570889\pi$
$997$	−966994.	−	314196.i	−0.972823	−	0.316089i	−0.751955	+	0.659215i	$0.770889\pi$
$998$		0			0
$999$	−185657.	+	134888.i	−0.186029	+	0.135158i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	176.5.n.c.129.3		16
4.3	odd	2		22.5.d.a.19.3	yes	16
11.7	odd	10	inner	176.5.n.c.161.3		16
12.11	even	2		198.5.j.a.19.1		16
44.7	even	10		22.5.d.a.7.3	✓	16
44.31	odd	10		242.5.b.e.241.4		16
44.35	even	10		242.5.b.e.241.12		16
132.95	odd	10		198.5.j.a.73.1		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
22.5.d.a.7.3	✓	16	44.7	even	10
22.5.d.a.19.3	yes	16	4.3	odd	2
176.5.n.c.129.3		16	1.1	even	1	trivial
176.5.n.c.161.3		16	11.7	odd	10	inner
198.5.j.a.19.1		16	12.11	even	2
198.5.j.a.73.1		16	132.95	odd	10
242.5.b.e.241.4		16	44.31	odd	10
242.5.b.e.241.12		16	44.35	even	10

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:	\( N \)	\(=\)	\( 176 = 2^{4} \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 5 \)
Character orbit:	\([\chi]\)	\(=\)	176.n (of order \(10\), degree \(4\), not minimal)

\(f(q)\)	\(=\)	\(q+(-0.309288 - 0.951890i) q^{3} +(35.4031 + 25.7219i) q^{5} +(65.6073 + 21.3171i) q^{7} +(64.7199 - 47.0218i) q^{9} +O(q^{10})\)	\(q+(-0.309288 - 0.951890i) q^{3} +(35.4031 + 25.7219i) q^{5} +(65.6073 + 21.3171i) q^{7} +(64.7199 - 47.0218i) q^{9} +(-65.6374 + 101.650i) q^{11} +(-100.269 - 138.009i) q^{13} +(13.5346 - 41.6553i) q^{15} +(-130.596 + 179.749i) q^{17} +(-141.801 + 46.0739i) q^{19} -69.0440i q^{21} +272.896 q^{23} +(398.631 + 1226.86i) q^{25} +(-130.364 - 94.7153i) q^{27} +(571.633 + 185.735i) q^{29} +(714.607 - 519.192i) q^{31} +(117.060 + 31.0405i) q^{33} +(1774.39 + 2442.23i) q^{35} +(440.083 - 1354.44i) q^{37} +(-100.357 + 138.130i) q^{39} +(-1050.88 + 341.452i) q^{41} -1489.14i q^{43} +3500.78 q^{45} +(772.201 + 2376.59i) q^{47} +(1907.45 + 1385.84i) q^{49} +(211.493 + 68.7183i) q^{51} +(-3070.02 + 2230.50i) q^{53} +(-4938.40 + 1910.41i) q^{55} +(87.7146 + 120.729i) q^{57} +(338.601 - 1042.11i) q^{59} +(-1856.32 + 2555.01i) q^{61} +(5248.47 - 1705.33i) q^{63} -7465.07i q^{65} -251.628 q^{67} +(-84.4035 - 259.767i) q^{69} +(-3590.99 - 2609.01i) q^{71} +(3983.96 + 1294.47i) q^{73} +(1044.54 - 758.906i) q^{75} +(-6473.17 + 5269.78i) q^{77} +(3109.83 + 4280.32i) q^{79} +(1952.55 - 6009.32i) q^{81} +(-261.533 + 359.969i) q^{83} +(-9246.98 + 3004.53i) q^{85} -601.577i q^{87} +8935.75 q^{89} +(-3636.45 - 11191.8i) q^{91} +(-715.233 - 519.647i) q^{93} +(-6205.31 - 2016.23i) q^{95} +(1684.12 - 1223.58i) q^{97} +(531.718 + 9665.17i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 2 q^{3} + 30 q^{5} - 150 q^{7} + 110 q^{9}+O(q^{10}) \) 16 * q + 2 * q^3 + 30 * q^5 - 150 * q^7 + 110 * q^9	\( 16 q + 2 q^{3} + 30 q^{5} - 150 q^{7} + 110 q^{9} + 30 q^{11} - 510 q^{13} + 1398 q^{15} + 1770 q^{17} - 1020 q^{19} + 2424 q^{23} - 858 q^{25} - 2224 q^{27} + 4890 q^{29} - 602 q^{31} - 2648 q^{33} + 8670 q^{35} - 4518 q^{37} + 1130 q^{39} + 1290 q^{41} + 12152 q^{45} - 642 q^{47} + 9534 q^{49} + 1500 q^{51} + 2598 q^{53} - 2582 q^{55} + 9140 q^{57} - 6660 q^{59} - 27410 q^{61} + 27260 q^{63} - 21524 q^{67} + 11416 q^{69} + 5562 q^{71} - 7790 q^{73} - 3576 q^{75} - 1110 q^{77} + 2770 q^{79} - 25464 q^{81} + 36900 q^{83} - 24750 q^{85} + 46596 q^{89} - 32370 q^{91} + 20722 q^{93} - 74250 q^{95} - 3732 q^{97} - 45802 q^{99}+O(q^{100}) \) 16 * q + 2 * q^3 + 30 * q^5 - 150 * q^7 + 110 * q^9 + 30 * q^11 - 510 * q^13 + 1398 * q^15 + 1770 * q^17 - 1020 * q^19 + 2424 * q^23 - 858 * q^25 - 2224 * q^27 + 4890 * q^29 - 602 * q^31 - 2648 * q^33 + 8670 * q^35 - 4518 * q^37 + 1130 * q^39 + 1290 * q^41 + 12152 * q^45 - 642 * q^47 + 9534 * q^49 + 1500 * q^51 + 2598 * q^53 - 2582 * q^55 + 9140 * q^57 - 6660 * q^59 - 27410 * q^61 + 27260 * q^63 - 21524 * q^67 + 11416 * q^69 + 5562 * q^71 - 7790 * q^73 - 3576 * q^75 - 1110 * q^77 + 2770 * q^79 - 25464 * q^81 + 36900 * q^83 - 24750 * q^85 + 46596 * q^89 - 32370 * q^91 + 20722 * q^93 - 74250 * q^95 - 3732 * q^97 - 45802 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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