LMFDB - Embedded newform 171.4.f.d.64.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [171,4,Mod(64,171)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(171, base_ring=CyclotomicField(6))

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

N = Newforms(chi, 4, names="a")

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

chi := DirichletCharacter("171.64");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 171 = 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	171.f (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

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

Self dual:	no
Analytic conductor:	$10.0893266110$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{73})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 19x^{2} + 18x + 324 $ x^4 - x^3 + 19x^2 + 18x + 324
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 19)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			64.2
Root			$2.38600 + 4.13267i$ of defining polynomial
Character	$\chi$	$=$	171.64
Dual form			171.4.f.d.163.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(2.38600 + 4.13267i) q^{2} +(-7.38600 + 12.7929i) q^{4} +(6.88600 + 11.9269i) q^{5} +27.0880 q^{7} -32.3160 q^{8} +O(q^{10})$	\(q+(2.38600 + 4.13267i) q^{2} +(-7.38600 + 12.7929i) q^{4} +(6.88600 + 11.9269i) q^{5} +27.0880 q^{7} -32.3160 q^{8} +(-32.8600 + 56.9152i) q^{10} +3.68399 q^{11} +(-14.5700 + 25.2360i) q^{13} +(64.6320 + 111.946i) q^{14} +(-18.0180 - 31.2081i) q^{16} +(-63.6060 - 110.169i) q^{17} +(-26.3340 - 78.5208i) q^{19} -203.440 q^{20} +(8.79001 + 15.2248i) q^{22} +(-36.0620 + 62.4612i) q^{23} +(-32.3340 + 56.0042i) q^{25} -139.056 q^{26} +(-200.072 + 346.535i) q^{28} +(66.3260 - 114.880i) q^{29} +36.6320 q^{31} +(-43.2820 + 74.9667i) q^{32} +(303.528 - 525.726i) q^{34} +(186.528 + 323.076i) q^{35} +70.2079 q^{37} +(261.668 - 296.181i) q^{38} +(-222.528 - 385.430i) q^{40} +(26.7280 + 46.2943i) q^{41} +(122.606 + 212.360i) q^{43} +(-27.2100 + 47.1291i) q^{44} -344.176 q^{46} +(19.4460 - 33.6814i) q^{47} +390.760 q^{49} -308.596 q^{50} +(-215.228 - 372.786i) q^{52} +(276.714 - 479.283i) q^{53} +(25.3680 + 43.9386i) q^{55} -875.376 q^{56} +633.016 q^{58} +(-166.872 - 289.031i) q^{59} +(-117.798 + 204.032i) q^{61} +(87.4040 + 151.388i) q^{62} -701.372 q^{64} -401.316 q^{65} +(207.032 - 358.590i) q^{67} +1879.18 q^{68} +(-890.112 + 1541.72i) q^{70} +(384.342 + 665.700i) q^{71} +(246.468 + 426.895i) q^{73} +(167.516 + 290.147i) q^{74} +(1199.01 + 243.066i) q^{76} +99.7921 q^{77} +(16.5340 + 28.6377i) q^{79} +(248.144 - 429.798i) q^{80} +(-127.546 + 220.916i) q^{82} -41.7077 q^{83} +(875.982 - 1517.25i) q^{85} +(-585.076 + 1013.38i) q^{86} -119.052 q^{88} +(318.994 - 552.514i) q^{89} +(-394.672 + 683.592i) q^{91} +(-532.708 - 922.678i) q^{92} +185.592 q^{94} +(755.174 - 854.778i) q^{95} +(666.264 + 1154.00i) q^{97} +(932.354 + 1614.88i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q + q^{2} - 21 q^{4} + 19 q^{5} + 40 q^{7} - 78 q^{8}+O(q^{10}) $ 4 * q + q^2 - 21 * q^4 + 19 * q^5 + 40 * q^7 - 78 * q^8	$ 4 q + q^{2} - 21 q^{4} + 19 q^{5} + 40 q^{7} - 78 q^{8} - 46 q^{10} + 66 q^{11} - 101 q^{13} + 156 q^{14} + 39 q^{16} - 75 q^{17} + 57 q^{19} - 472 q^{20} - 93 q^{22} + q^{23} + 33 q^{25} + 264 q^{26} - 356 q^{28} - 85 q^{29} + 44 q^{31} + 143 q^{32} + 804 q^{34} + 336 q^{35} + 896 q^{37} + 722 q^{38} - 480 q^{40} + 124 q^{41} + 311 q^{43} - 237 q^{44} - 1240 q^{46} + 411 q^{47} + 196 q^{49} - 1354 q^{50} - 878 q^{52} + 261 q^{53} + 204 q^{55} - 1656 q^{56} + 2908 q^{58} + 204 q^{59} - 531 q^{61} + 230 q^{62} - 1934 q^{64} - 1554 q^{65} - 556 q^{67} + 3108 q^{68} - 1920 q^{70} + 1563 q^{71} + 234 q^{73} - 1090 q^{74} + 1387 q^{76} - 216 q^{77} + 331 q^{79} + 104 q^{80} + 11 q^{82} - 2918 q^{83} + 1479 q^{85} - 922 q^{86} - 630 q^{88} + 601 q^{89} - 280 q^{91} - 610 q^{92} - 2436 q^{94} + 1235 q^{95} + 324 q^{97} + 2969 q^{98}+O(q^{100}) $ 4 * q + q^2 - 21 * q^4 + 19 * q^5 + 40 * q^7 - 78 * q^8 - 46 * q^10 + 66 * q^11 - 101 * q^13 + 156 * q^14 + 39 * q^16 - 75 * q^17 + 57 * q^19 - 472 * q^20 - 93 * q^22 + q^23 + 33 * q^25 + 264 * q^26 - 356 * q^28 - 85 * q^29 + 44 * q^31 + 143 * q^32 + 804 * q^34 + 336 * q^35 + 896 * q^37 + 722 * q^38 - 480 * q^40 + 124 * q^41 + 311 * q^43 - 237 * q^44 - 1240 * q^46 + 411 * q^47 + 196 * q^49 - 1354 * q^50 - 878 * q^52 + 261 * q^53 + 204 * q^55 - 1656 * q^56 + 2908 * q^58 + 204 * q^59 - 531 * q^61 + 230 * q^62 - 1934 * q^64 - 1554 * q^65 - 556 * q^67 + 3108 * q^68 - 1920 * q^70 + 1563 * q^71 + 234 * q^73 - 1090 * q^74 + 1387 * q^76 - 216 * q^77 + 331 * q^79 + 104 * q^80 + 11 * q^82 - 2918 * q^83 + 1479 * q^85 - 922 * q^86 - 630 * q^88 + 601 * q^89 - 280 * q^91 - 610 * q^92 - 2436 * q^94 + 1235 * q^95 + 324 * q^97 + 2969 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/171\mathbb{Z}\right)^\times$.

$n$	$20$	$154$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$	2.38600	+	4.13267i	0.843579	+	1.46112i	0.886850	+	0.462058i	$0.152889\pi$
$2$	2.38600	+	4.13267i	0.843579	+	1.46112i	−0.0432711	+	0.999063i	$0.513778\pi$
$3$		0			0
$3$		0			0
$4$	−7.38600	+	12.7929i	−0.923250	+	1.59912i
$5$	6.88600	+	11.9269i	0.615903	+	1.06677i	0.990225	+	0.139476i	$0.0445419\pi$
$5$	6.88600	+	11.9269i	0.615903	+	1.06677i	−0.374323	+	0.927298i	$0.622125\pi$
$6$		0			0
$7$	27.0880			1.46261			0.731307	−	0.682048i	$-0.238910\pi$
$7$	27.0880			1.46261			0.731307	+	0.682048i	$0.238910\pi$
$8$	−32.3160			−1.42818
$9$		0			0
$10$	−32.8600	+	56.9152i	−1.03912	+	1.79982i
$11$	3.68399			0.100979			0.0504894	−	0.998725i	$-0.483922\pi$
$11$	3.68399			0.100979			0.0504894	+	0.998725i	$0.483922\pi$
$12$		0			0
$13$	−14.5700	+	25.2360i	−0.310845	+	0.538400i	−0.978546	−	0.206030i	$-0.933945\pi$
$13$	−14.5700	+	25.2360i	−0.310845	+	0.538400i	0.667700	+	0.744430i	$0.267279\pi$
$14$	64.6320	+	111.946i	1.23383	+	2.13706i
$15$		0			0
$16$	−18.0180	−	31.2081i	−0.281531	−	0.487627i
$17$	−63.6060	−	110.169i	−0.907454	−	1.57176i	−0.817588	−	0.575803i	$-0.804689\pi$
$17$	−63.6060	−	110.169i	−0.907454	−	1.57176i	−0.0898663	−	0.995954i	$-0.528644\pi$
$18$		0			0
$19$	−26.3340	−	78.5208i	−0.317970	−	0.948101i
$19$	−26.3340	−	78.5208i	−0.317970	−	0.948101i
$20$	−203.440			−2.27453
$21$		0			0
$22$	8.79001	+	15.2248i	0.0851835	+	0.147542i
$23$	−36.0620	+	62.4612i	−0.326933	+	0.566264i	−0.981902	−	0.189392i	$-0.939348\pi$
$23$	−36.0620	+	62.4612i	−0.326933	+	0.566264i	0.654969	+	0.755656i	$0.272682\pi$
$24$		0			0
$25$	−32.3340	+	56.0042i	−0.258672	+	0.448033i
$26$	−139.056			−1.04889
$27$		0			0
$28$	−200.072	+	346.535i	−1.35036	+	2.33889i
$29$	66.3260	−	114.880i	0.424705	−	0.735610i	−0.571688	−	0.820471i	$-0.693711\pi$
$29$	66.3260	−	114.880i	0.424705	−	0.735610i	0.996393	+	0.0848609i	$0.0270446\pi$
$30$		0			0
$31$	36.6320			0.212236			0.106118	−	0.994354i	$-0.466158\pi$
$31$	36.6320			0.212236			0.106118	+	0.994354i	$0.466158\pi$
$32$	−43.2820	+	74.9667i	−0.239102	+	0.414136i
$33$		0			0
$34$	303.528	−	525.726i	1.53102	−	2.65180i
$35$	186.528	+	323.076i	0.900828	+	1.56028i
$36$		0			0
$37$	70.2079			0.311949			0.155975	−	0.987761i	$-0.450148\pi$
$37$	70.2079			0.311949			0.155975	+	0.987761i	$0.450148\pi$
$38$	261.668	−	296.181i	1.11706	−	1.26439i
$39$		0			0
$40$	−222.528	−	385.430i	−0.879619	−	1.52355i
$41$	26.7280	+	46.2943i	0.101810	+	0.176340i	0.912430	−	0.409232i	$-0.134203\pi$
$41$	26.7280	+	46.2943i	0.101810	+	0.176340i	−0.810620	+	0.585572i	$0.800870\pi$
$42$		0			0
$43$	122.606	+	212.360i	0.434820	+	0.753130i	0.997281	−	0.0736940i	$-0.0234788\pi$
$43$	122.606	+	212.360i	0.434820	+	0.753130i	−0.562461	+	0.826824i	$0.690145\pi$
$44$	−27.2100	+	47.1291i	−0.0932286	+	0.161477i
$45$		0			0
$46$	−344.176			−1.10317
$47$	19.4460	−	33.6814i	0.0603508	−	0.104531i	−0.834271	−	0.551354i	$-0.814111\pi$
$47$	19.4460	−	33.6814i	0.0603508	−	0.104531i	0.894622	+	0.446823i	$0.147445\pi$
$48$		0			0
$49$	390.760			1.13924
$50$	−308.596			−0.872841
$51$		0			0
$52$	−215.228	−	372.786i	−0.573976	−	0.994156i
$53$	276.714	−	479.283i	0.717162	−	1.24216i	−0.244957	−	0.969534i	$-0.578774\pi$
$53$	276.714	−	479.283i	0.717162	−	1.24216i	0.962120	−	0.272628i	$-0.0878927\pi$
$54$		0			0
$55$	25.3680	+	43.9386i	0.0621931	+	0.107722i
$56$	−875.376			−2.08888
$57$		0			0
$58$	633.016			1.43309
$59$	−166.872	−	289.031i	−0.368219	−	0.637773i	0.621069	−	0.783756i	$-0.286699\pi$
$59$	−166.872	−	289.031i	−0.368219	−	0.637773i	−0.989287	+	0.145983i	$0.953366\pi$
$60$		0			0
$61$	−117.798	+	204.032i	−0.247254	+	0.428256i	−0.962763	−	0.270347i	$-0.912862\pi$
$61$	−117.798	+	204.032i	−0.247254	+	0.428256i	0.715509	+	0.698604i	$0.246195\pi$
$62$	87.4040	+	151.388i	0.179037	+	0.310102i
$63$		0			0
$64$	−701.372			−1.36987
$65$	−401.316			−0.765802
$66$		0			0
$67$	207.032	−	358.590i	0.377508	−	0.653862i	−0.613191	−	0.789934i	$-0.710115\pi$
$67$	207.032	−	358.590i	0.377508	−	0.653862i	0.990699	+	0.136072i	$0.0434479\pi$
$68$	1879.18			3.35123
$69$		0			0
$70$	−890.112	+	1541.72i	−1.51984	+	2.63244i
$71$	384.342	+	665.700i	0.642437	+	1.11273i	0.984887	+	0.173197i	$0.0554098\pi$
$71$	384.342	+	665.700i	0.642437	+	1.11273i	−0.342451	+	0.939536i	$0.611257\pi$
$72$		0			0
$73$	246.468	+	426.895i	0.395163	+	0.684443i	0.993122	−	0.117084i	$-0.0373547\pi$
$73$	246.468	+	426.895i	0.395163	+	0.684443i	−0.597959	+	0.801527i	$0.704021\pi$
$74$	167.516	+	290.147i	0.263154	+	0.455795i
$75$		0			0
$76$	1199.01	+	243.066i	1.80969	+	0.366862i
$77$	99.7921			0.147693
$78$		0			0
$79$	16.5340	+	28.6377i	0.0235471	+	0.0407847i	0.877559	−	0.479469i	$-0.159171\pi$
$79$	16.5340	+	28.6377i	0.0235471	+	0.0407847i	−0.854012	+	0.520254i	$0.825837\pi$
$80$	248.144	−	429.798i	0.346792	−	0.600661i
$81$		0			0
$82$	−127.546	+	220.916i	−0.171770	+	0.297514i
$83$	−41.7077			−0.0551568			−0.0275784	−	0.999620i	$-0.508780\pi$
$83$	−41.7077			−0.0551568			−0.0275784	+	0.999620i	$0.508780\pi$
$84$		0			0
$85$	875.982	−	1517.25i	1.11781	−	1.93610i
$86$	−585.076	+	1013.38i	−0.733609	+	1.27065i
$87$		0			0
$88$	−119.052			−0.144216
$89$	318.994	−	552.514i	0.379925	−	0.658049i	−0.611126	−	0.791533i	$-0.709283\pi$
$89$	318.994	−	552.514i	0.379925	−	0.658049i	0.991051	+	0.133484i	$0.0426165\pi$
$90$		0			0
$91$	−394.672	+	683.592i	−0.454647	+	0.787472i
$92$	−532.708	−	922.678i	−0.603681	−	1.04561i
$93$		0			0
$94$	185.592			0.203642
$95$	755.174	−	854.778i	0.815571	−	0.923140i
$96$		0			0
$97$	666.264	+	1154.00i	0.697411	+	1.20795i	0.969361	+	0.245640i	$0.0789982\pi$
$97$	666.264	+	1154.00i	0.697411	+	1.20795i	−0.271950	+	0.962311i	$0.587668\pi$
$98$	932.354	+	1614.88i	0.961041	+	1.66457i
$99$		0			0
$100$	−477.638	−	827.294i	−0.477638	−	0.827294i
$101$	−175.786	+	304.471i	−0.173182	+	0.299960i	−0.939531	−	0.342465i	$-0.888738\pi$
$101$	−175.786	+	304.471i	−0.173182	+	0.299960i	0.766349	+	0.642425i	$0.222072\pi$
$102$		0			0
$103$	−1591.38			−1.52237			−0.761183	−	0.648537i	$-0.775381\pi$
$103$	−1591.38			−1.52237			−0.761183	+	0.648537i	$0.775381\pi$
$104$	470.844	−	815.526i	0.443943	−	0.768932i
$105$		0			0
$106$	2640.96			2.41993
$107$	−974.672			−0.880609			−0.440304	−	0.897849i	$-0.645129\pi$
$107$	−974.672			−0.880609			−0.440304	+	0.897849i	$0.645129\pi$
$108$		0			0
$109$	−643.774	−	1115.05i	−0.565710	−	0.979839i	−0.996983	−	0.0776171i	$-0.975269\pi$
$109$	−643.774	−	1115.05i	−0.565710	−	0.979839i	0.431273	−	0.902221i	$-0.358065\pi$
$110$	−121.056	+	209.675i	−0.104930	+	0.181743i
$111$		0			0
$112$	−488.072	−	845.366i	−0.411772	−	0.713210i
$113$	305.484			0.254315			0.127157	−	0.991883i	$-0.459415\pi$
$113$	305.484			0.254315			0.127157	+	0.991883i	$0.459415\pi$
$114$		0			0
$115$	−993.292			−0.805435
$116$	979.768	+	1697.01i	0.784217	+	1.35830i
$117$		0			0
$118$	796.314	−	1379.26i	0.621243	−	1.07602i
$119$	−1722.96	−	2984.25i	−1.32726	−	2.29888i
$120$		0			0
$121$	−1317.43			−0.989803
$122$	−1124.26			−0.834312
$123$		0			0
$124$	−270.564	+	468.631i	−0.195947	+	0.339389i
$125$	830.892			0.594538
$126$		0			0
$127$	1298.53	−	2249.11i	0.907288	−	1.57147i	0.0894717	−	0.995989i	$-0.471482\pi$
$127$	1298.53	−	2249.11i	0.907288	−	1.57147i	0.817816	−	0.575479i	$-0.195185\pi$
$128$	−1327.22	−	2298.81i	−0.916489	−	1.58741i
$129$		0			0
$130$	−957.540	−	1658.51i	−0.646014	−	1.11893i
$131$	−94.1083	−	163.000i	−0.0627655	−	0.108713i	0.832935	−	0.553371i	$-0.186659\pi$
$131$	−94.1083	−	163.000i	−0.0627655	−	0.108713i	−0.895701	+	0.444658i	$0.853325\pi$
$132$		0			0
$133$	−713.336	−	2126.97i	−0.465068	−	1.38671i
$134$	1975.92			1.27383
$135$		0			0
$136$	2055.49	+	3560.22i	1.29601	+	2.24475i
$137$	−139.032	+	240.811i	−0.0867031	+	0.150174i	−0.906116	−	0.423030i	$-0.860966\pi$
$137$	−139.032	+	240.811i	−0.0867031	+	0.150174i	0.819413	+	0.573204i	$0.194300\pi$
$138$		0			0
$139$	−719.652	+	1246.47i	−0.439137	+	0.760608i	−0.997623	−	0.0689057i	$-0.978049\pi$
$139$	−719.652	+	1246.47i	−0.439137	+	0.760608i	0.558486	+	0.829514i	$0.311383\pi$
$140$	−5510.79			−3.32676
$141$		0			0
$142$	−1834.08	+	3176.72i	−1.08389	+	1.87736i
$143$	−53.6758	+	92.9692i	−0.0313888	+	0.0543669i
$144$		0			0
$145$	1826.88			1.04631
$146$	−1176.15	+	2037.14i	−0.666702	+	1.15476i
$147$		0			0
$148$	−518.556	+	898.165i	−0.288007	+	0.498843i
$149$	856.722	+	1483.89i	0.471043	+	0.815871i	0.999451	−	0.0331198i	$-0.0105443\pi$
$149$	856.722	+	1483.89i	0.471043	+	0.815871i	−0.528408	+	0.848990i	$0.677211\pi$
$150$		0			0
$151$	407.640			0.219690			0.109845	−	0.993949i	$-0.464964\pi$
$151$	407.640			0.219690			0.109845	+	0.993949i	$0.464964\pi$
$152$	851.010	+	2537.48i	0.454119	+	1.35406i
$153$		0			0
$154$	238.104	+	412.408i	0.124591	+	0.215797i
$155$	252.248	+	436.906i	0.130716	+	0.226408i
$156$		0			0
$157$	−1232.02	−	2133.93i	−0.626281	−	1.08475i	−0.988292	−	0.152576i	$-0.951243\pi$
$157$	−1232.02	−	2133.93i	−0.626281	−	1.08475i	0.362011	−	0.932174i	$-0.382090\pi$
$158$	−78.9001	+	136.659i	−0.0397276	+	0.0688102i
$159$		0			0
$160$	−1192.16			−0.589054
$161$	−976.848	+	1691.95i	−0.478177	+	0.828226i
$162$		0			0
$163$	142.245			0.0683526			0.0341763	−	0.999416i	$-0.489119\pi$
$163$	142.245			0.0683526			0.0341763	+	0.999416i	$0.489119\pi$
$164$	−789.652			−0.375985
$165$		0			0
$166$	−99.5146	−	172.364i	−0.0465291	−	0.0805908i
$167$	1285.97	−	2227.37i	0.595878	−	1.03209i	−0.397544	−	0.917583i	$-0.630137\pi$
$167$	1285.97	−	2227.37i	0.595878	−	1.03209i	0.993422	−	0.114508i	$-0.0365292\pi$
$168$		0			0
$169$	673.930	+	1167.28i	0.306750	+	0.531307i
$170$	8360.38			3.77183
$171$		0			0
$172$	−3622.27			−1.60579
$173$	−564.094	−	977.039i	−0.247903	−	0.429381i	0.715041	−	0.699083i	$-0.246408\pi$
$173$	−564.094	−	977.039i	−0.247903	−	0.429381i	−0.962944	+	0.269702i	$0.913075\pi$
$174$		0			0
$175$	−875.864	+	1517.04i	−0.378338	+	0.655300i
$176$	−66.3783	−	114.971i	−0.0284287	−	0.0492399i
$177$		0			0
$178$	3044.48			1.28199
$179$	−4137.46			−1.72764			−0.863822	−	0.503797i	$-0.831936\pi$
$179$	−4137.46			−1.72764			−0.863822	+	0.503797i	$0.831936\pi$
$180$		0			0
$181$	−897.970	+	1555.33i	−0.368760	+	0.638711i	−0.989372	−	0.145407i	$-0.953551\pi$
$181$	−897.970	+	1555.33i	−0.368760	+	0.638711i	0.620612	+	0.784118i	$0.286884\pi$
$182$	−3766.75			−1.53412
$183$		0			0
$184$	1165.38	−	2018.50i	0.466918	−	0.808726i
$185$	483.452	+	837.363i	0.192130	+	0.332779i
$186$		0			0
$187$	−234.324	−	405.861i	−0.0916336	−	0.158714i
$188$	287.256	+	497.542i	0.111438	+	0.193016i
$189$		0			0
$190$	5334.36	+	1081.39i	2.03682	+	0.412906i
$191$	826.512			0.313111			0.156556	−	0.987669i	$-0.449961\pi$
$191$	826.512			0.313111			0.156556	+	0.987669i	$0.449961\pi$
$192$		0			0
$193$	1990.11	+	3446.97i	0.742235	+	1.28559i	0.951476	+	0.307724i	$0.0995673\pi$
$193$	1990.11	+	3446.97i	0.742235	+	1.28559i	−0.209241	+	0.977864i	$0.567099\pi$
$194$	−3179.41	+	5506.91i	−1.17664	+	2.03800i
$195$		0			0
$196$	−2886.15	+	4998.97i	−1.05181	+	1.82178i
$197$	186.928			0.0676046			0.0338023	−	0.999429i	$-0.489238\pi$
$197$	186.928			0.0676046			0.0338023	+	0.999429i	$0.489238\pi$
$198$		0			0
$199$	175.662	−	304.255i	0.0625745	−	0.108382i	−0.833041	−	0.553211i	$-0.813402\pi$
$199$	175.662	−	304.255i	0.0625745	−	0.108382i	0.895615	+	0.444829i	$0.146736\pi$
$200$	1044.91	−	1809.83i	0.369430	−	0.639872i
$201$		0			0
$202$	−1677.70			−0.584370
$203$	1796.64	−	3111.87i	0.621179	−	1.07591i
$204$		0			0
$205$	−368.098	+	637.565i	−0.125410	+	0.217217i
$206$	−3797.04	−	6576.67i	−1.28424	−	2.22436i
$207$		0			0
$208$	1050.09			0.350051
$209$	−97.0144	−	289.270i	−0.0321083	−	0.0957380i
$210$		0			0
$211$	−2373.51	−	4111.05i	−0.774405	−	1.34131i	−0.935128	−	0.354309i	$-0.884716\pi$
$211$	−2373.51	−	4111.05i	−0.774405	−	1.34131i	0.160723	−	0.987000i	$-0.448617\pi$
$212$	4087.62	+	7079.97i	1.32424	+	2.29365i
$213$		0			0
$214$	−2325.57	−	4028.00i	−0.742863	−	1.28668i
$215$	−1688.53	+	2924.62i	−0.535613	+	0.927709i
$216$		0			0
$217$	992.288			0.310419
$218$	3072.09	−	5321.02i	0.954442	−	1.65314i
$219$		0			0
$220$	−749.472			−0.229679
$221$	3706.96			1.12831
$222$		0			0
$223$	−644.598	−	1116.48i	−0.193567	−	0.335268i	0.752863	−	0.658178i	$-0.228672\pi$
$223$	−644.598	−	1116.48i	−0.193567	−	0.335268i	−0.946430	+	0.322909i	$0.895339\pi$
$224$	−1172.42	+	2030.70i	−0.349714	+	0.605722i
$225$		0			0
$226$	728.886	+	1262.47i	0.214534	+	0.371584i
$227$	−5742.88			−1.67915			−0.839577	−	0.543240i	$-0.817197\pi$
$227$	−5742.88			−1.67915			−0.839577	+	0.543240i	$0.817197\pi$
$228$		0			0
$229$	−3478.14			−1.00368			−0.501838	−	0.864962i	$-0.667343\pi$
$229$	−3478.14			−1.00368			−0.501838	+	0.864962i	$0.667343\pi$
$230$	−2370.00	−	4104.95i	−0.679448	−	1.17684i
$231$		0			0
$232$	−2143.39	+	3712.46i	−0.606554	+	1.05058i
$233$	−637.172	−	1103.61i	−0.179153	−	0.310301i	0.762438	−	0.647061i	$-0.224002\pi$
$233$	−637.172	−	1103.61i	−0.179153	−	0.310301i	−0.941591	+	0.336760i	$0.890669\pi$
$234$		0			0
$235$	535.620			0.148681
$236$	4930.07			1.35983
$237$		0			0
$238$	8221.97	−	14240.9i	2.23929	−	3.87857i
$239$	3154.37			0.853720			0.426860	−	0.904318i	$-0.359620\pi$
$239$	3154.37			0.853720			0.426860	+	0.904318i	$0.359620\pi$
$240$		0			0
$241$	582.303	−	1008.58i	0.155641	−	0.269578i	−0.777651	−	0.628696i	$-0.783589\pi$
$241$	582.303	−	1008.58i	0.155641	−	0.269578i	0.933292	+	0.359118i	$0.116922\pi$
$242$	−3143.38	−	5444.50i	−0.834977	−	1.44622i
$243$		0			0
$244$	−1740.11	−	3013.96i	−0.456554	−	0.790775i
$245$	2690.77	+	4660.56i	0.701662	+	1.21531i
$246$		0			0
$247$	2365.24	+	479.483i	0.609297	+	0.123517i
$248$	−1183.80			−0.303110
$249$		0			0
$250$	1982.51	+	3433.81i	0.501539	+	0.868692i
$251$	299.592	−	518.908i	0.0753389	−	0.130491i	−0.825895	−	0.563824i	$-0.809329\pi$
$251$	299.592	−	518.908i	0.0753389	−	0.130491i	0.901234	+	0.433334i	$0.142663\pi$
$252$		0			0
$253$	−132.852	+	230.107i	−0.0330132	+	0.0571806i
$254$	12393.1			3.06148
$255$		0			0
$256$	3528.00	−	6110.67i	0.861328	−	1.49186i
$257$	2109.96	−	3654.55i	0.512122	−	0.887022i	−0.487779	−	0.872967i	$-0.662193\pi$
$257$	2109.96	−	3654.55i	0.512122	−	0.887022i	0.999901	−	0.0140547i	$-0.00447389\pi$
$258$		0			0
$259$	1901.79			0.456261
$260$	2964.12	−	5134.01i	0.707027	−	1.22461i
$261$		0			0
$262$	449.085	−	777.838i	0.105895	−	0.183416i
$263$	2719.07	+	4709.57i	0.637511	+	1.10420i	0.985977	+	0.166880i	$0.0533691\pi$
$263$	2719.07	+	4709.57i	0.637511	+	1.10420i	−0.348467	+	0.937321i	$0.613298\pi$
$264$		0			0
$265$	7621.81			1.76681
$266$	7088.07	−	8022.94i	1.63382	−	1.84932i
$267$		0			0
$268$	3058.28	+	5297.10i	0.697068	+	1.20736i
$269$	−486.330	−	842.348i	−0.110231	−	0.190925i	0.805633	−	0.592416i	$-0.201826\pi$
$269$	−486.330	−	842.348i	−0.110231	−	0.190925i	−0.915863	+	0.401490i	$0.868492\pi$
$270$		0			0
$271$	1470.31	+	2546.65i	0.329575	+	0.570841i	0.982428	−	0.186644i	$-0.0597611\pi$
$271$	1470.31	+	2546.65i	0.329575	+	0.570841i	−0.652852	+	0.757485i	$0.726428\pi$
$272$	−2292.11	+	3970.05i	−0.510954	+	0.884998i
$273$		0			0
$274$	−1326.92			−0.292563
$275$	−119.118	+	206.319i	−0.0261204	+	0.0452418i
$276$		0			0
$277$	−634.968			−0.137731			−0.0688655	−	0.997626i	$-0.521938\pi$
$277$	−634.968			−0.137731			−0.0688655	+	0.997626i	$0.521938\pi$
$278$	−6868.36			−1.48179
$279$		0			0
$280$	−6027.84	−	10440.5i	−1.28654	−	2.22836i
$281$	−2684.38	+	4649.48i	−0.569882	+	0.987064i	0.426696	+	0.904395i	$0.359678\pi$
$281$	−2684.38	+	4649.48i	−0.569882	+	0.987064i	−0.996577	+	0.0826685i	$0.973656\pi$
$282$		0			0
$283$	−8.02851	−	13.9058i	−0.00168638	−	0.00292090i	0.865181	−	0.501460i	$-0.167203\pi$
$283$	−8.02851	−	13.9058i	−0.00168638	−	0.00292090i	−0.866867	+	0.498539i	$0.833870\pi$
$284$	−11355.0			−2.37252
$285$		0			0
$286$	−512.282			−0.105916
$287$	724.008	+	1254.02i	0.148909	+	0.257918i
$288$		0			0
$289$	−5634.95	+	9760.02i	−1.14695	+	1.98657i
$290$	4358.95	+	7549.92i	0.882642	+	1.52878i
$291$		0			0
$292$	−7281.65			−1.45934
$293$	3611.13			0.720015			0.360007	−	0.932949i	$-0.382774\pi$
$293$	3611.13			0.720015			0.360007	+	0.932949i	$0.382774\pi$
$294$		0			0
$295$	2298.16	−	3980.53i	0.453574	−	0.785613i
$296$	−2268.84			−0.445519
$297$		0			0
$298$	−4088.28	+	7081.11i	−0.794724	+	1.37650i
$299$	−1050.85	−	1820.12i	−0.203251	−	0.352041i
$300$		0			0
$301$	3321.15	+	5752.41i	0.635974	+	1.10154i
$302$	972.629	+	1684.64i	0.185326	+	0.320994i
$303$		0			0
$304$	−1976.00	+	2236.62i	−0.372801	+	0.421971i
$305$	−3244.63			−0.609137
$306$		0			0
$307$	−2316.48	−	4012.25i	−0.430646	−	0.745901i	0.566283	−	0.824211i	$-0.308381\pi$
$307$	−2316.48	−	4012.25i	−0.430646	−	0.745901i	−0.996929	+	0.0783102i	$0.975048\pi$
$308$	−737.064	+	1276.63i	−0.136358	+	0.236178i
$309$		0			0
$310$	−1203.73	+	2084.92i	−0.220539	+	0.381985i
$311$	−5559.42			−1.01365			−0.506826	−	0.862048i	$-0.669181\pi$
$311$	−5559.42			−1.01365			−0.506826	+	0.862048i	$0.669181\pi$
$312$		0			0
$313$	−3178.29	+	5504.96i	−0.573954	+	0.994117i	0.422201	+	0.906502i	$0.361258\pi$
$313$	−3178.29	+	5504.96i	−0.573954	+	0.994117i	−0.996154	+	0.0876147i	$0.972076\pi$
$314$	5879.21	−	10183.1i	1.05663	−	1.83014i
$315$		0			0
$316$	−488.480			−0.0869593
$317$	−3506.82	+	6073.98i	−0.621332	+	1.07618i	0.367905	+	0.929863i	$0.380075\pi$
$317$	−3506.82	+	6073.98i	−0.621332	+	1.07618i	−0.989238	+	0.146316i	$0.953258\pi$
$318$		0			0
$319$	244.345	−	423.218i	0.0428861	−	0.0742810i
$320$	−4829.65	−	8365.20i	−0.843705	−	1.46134i
$321$		0			0
$322$	−9323.04			−1.61352
$323$	−6975.55	+	7895.59i	−1.20164	+	1.36013i
$324$		0			0
$325$	−942.213	−	1631.96i	−0.160814	−	0.278538i
$326$	339.396	+	587.852i	0.0576608	+	0.0998715i
$327$		0			0
$328$	−863.742	−	1496.05i	−0.145403	−	0.251845i
$329$	526.752	−	912.362i	0.0882699	−	0.152888i
$330$		0			0
$331$	8531.43			1.41671			0.708353	−	0.705858i	$-0.249438\pi$
$331$	8531.43			1.41671			0.708353	+	0.705858i	$0.249438\pi$
$332$	308.053	−	533.564i	0.0509235	−	0.0882021i
$333$		0			0
$334$	12273.3			2.01068
$335$	5702.49			0.930031
$336$		0			0
$337$	−3926.57	−	6801.02i	−0.634700	−	1.09933i	−0.986579	−	0.163288i	$-0.947790\pi$
$337$	−3926.57	−	6801.02i	−0.634700	−	1.09933i	0.351878	−	0.936046i	$-0.385543\pi$
$338$	−3216.00	+	5570.27i	−0.517536	+	0.896399i
$339$		0			0
$340$	12940.0	+	22412.8i	2.06403	+	3.57501i
$341$	134.952			0.0214313
$342$		0			0
$343$	1293.73			0.203658
$344$	−3962.14	−	6862.62i	−0.621000	−	1.07560i
$345$		0			0
$346$	2691.86	−	4662.43i	0.418252	−	0.724433i
$347$	5273.78	+	9134.46i	0.815884	+	1.41315i	0.908692	+	0.417468i	$0.137082\pi$
$347$	5273.78	+	9134.46i	0.815884	+	1.41315i	−0.0928082	+	0.995684i	$0.529584\pi$
$348$		0			0
$349$	5781.53			0.886757			0.443379	−	0.896334i	$-0.353780\pi$
$349$	5781.53			0.886757			0.443379	+	0.896334i	$0.353780\pi$
$350$	−8359.25			−1.27663
$351$		0			0
$352$	−159.451	+	276.177i	−0.0241442	+	0.0418190i
$353$	8129.66			1.22577			0.612887	−	0.790171i	$-0.290008\pi$
$353$	8129.66			1.22577			0.612887	+	0.790171i	$0.290008\pi$
$354$		0			0
$355$	−5293.16	+	9168.02i	−0.791357	+	1.37067i
$356$	4712.18	+	8161.74i	0.701531	+	1.21509i
$357$		0			0
$358$	−9871.98	−	17098.8i	−1.45740	−	2.52430i
$359$	−2916.34	−	5051.25i	−0.428742	−	0.742603i	0.568020	−	0.823015i	$-0.307710\pi$
$359$	−2916.34	−	5051.25i	−0.428742	−	0.742603i	−0.996762	+	0.0804118i	$0.974376\pi$
$360$		0			0
$361$	−5472.04	+	4135.54i	−0.797790	+	0.602936i
$362$	−8570.23			−1.24431
$363$		0			0
$364$	−5830.10	−	10098.0i	−0.839506	−	1.45407i
$365$	−3394.36	+	5879.20i	−0.486764	+	0.843100i
$366$		0			0
$367$	−2972.03	+	5147.70i	−0.422721	+	0.732174i	−0.996205	−	0.0870429i	$-0.972258\pi$
$367$	−2972.03	+	5147.70i	−0.422721	+	0.732174i	0.573484	+	0.819217i	$0.305592\pi$
$368$	2599.06			0.368167
$369$		0			0
$370$	−2307.03	+	3995.90i	−0.324154	+	0.561451i
$371$	7495.63	−	12982.8i	1.04893	−	1.81680i
$372$		0			0
$373$	5999.53			0.832825			0.416413	−	0.909176i	$-0.363287\pi$
$373$	5999.53			0.832825			0.416413	+	0.909176i	$0.363287\pi$
$374$	1118.20	−	1936.77i	0.154600	−	0.267776i
$375$		0			0
$376$	−628.416	+	1088.45i	−0.0861917	+	0.149288i
$377$	1932.74	+	3347.60i	0.264035	+	0.457322i
$378$		0			0
$379$	−8786.72			−1.19088			−0.595440	−	0.803400i	$-0.703022\pi$
$379$	−8786.72			−1.19088			−0.595440	+	0.803400i	$0.703022\pi$
$380$	5357.39	+	15974.3i	0.723233	+	2.15648i
$381$		0			0
$382$	1972.06	+	3415.70i	0.264134	+	0.457494i
$383$	−5183.88	−	8978.74i	−0.691603	−	1.19789i	−0.971313	−	0.237807i	$-0.923572\pi$
$383$	−5183.88	−	8978.74i	−0.691603	−	1.19789i	0.279710	−	0.960085i	$-0.409762\pi$
$384$		0			0
$385$	687.168	+	1190.21i	0.0909645	+	0.157555i
$386$	−9496.81	+	16449.0i	−1.25227	+	2.16899i
$387$		0			0
$388$	−19684.1			−2.57554
$389$	2624.21	−	4545.27i	0.342038	−	0.592428i	−0.642773	−	0.766057i	$-0.722216\pi$
$389$	2624.21	−	4545.27i	0.342038	−	0.592428i	0.984811	+	0.173629i	$0.0555493\pi$
$390$		0			0
$391$	9175.05			1.18671
$392$	−12627.8			−1.62704
$393$		0			0
$394$	446.011	+	772.514i	0.0570298	+	0.0987785i
$395$	−227.706	+	394.398i	−0.0290054	+	0.0502388i
$396$		0			0
$397$	−5921.89	−	10257.0i	−0.748643	−	1.29669i	−0.948473	−	0.316857i	$-0.897373\pi$
$397$	−5921.89	−	10257.0i	−0.748643	−	1.29669i	0.199831	−	0.979830i	$-0.435961\pi$
$398$	1676.52			0.211146
$399$		0			0
$400$	2330.38			0.291297
$401$	4101.83	+	7104.57i	0.510812	+	0.884752i	0.999922	+	0.0125294i	$0.00398833\pi$
$401$	4101.83	+	7104.57i	0.510812	+	0.884752i	−0.489110	+	0.872222i	$0.662678\pi$
$402$		0			0
$403$	−533.728	+	924.444i	−0.0659724	+	0.114268i
$404$	−2596.71	−	4497.64i	−0.319780	−	0.553876i
$405$		0			0
$406$	17147.1			2.09605
$407$	258.646			0.0315002
$408$		0			0
$409$	5596.49	−	9693.40i	0.676598	−	1.17190i	−0.299401	−	0.954127i	$-0.596787\pi$
$409$	5596.49	−	9693.40i	0.676598	−	1.17190i	0.975999	−	0.217775i	$-0.0698798\pi$
$410$	−3513.13			−0.423173
$411$		0			0
$412$	11754.0	−	20358.5i	1.40553	−	2.43444i
$413$	−4520.23	−	7829.27i	−0.538562	−	0.932817i
$414$		0			0
$415$	−287.199	−	497.444i	−0.0339712	−	0.0588399i
$416$	−1261.24	−	2184.53i	−0.148647	−	0.257465i
$417$		0			0
$418$	963.984	−	1091.13i	0.112799	−	0.127677i
$419$	−243.522			−0.0283934			−0.0141967	−	0.999899i	$-0.504519\pi$
$419$	−243.522			−0.0283934			−0.0141967	+	0.999899i	$0.504519\pi$
$420$		0			0
$421$	6427.26	+	11132.3i	0.744052	+	1.28874i	0.950637	+	0.310306i	$0.100432\pi$
$421$	6427.26	+	11132.3i	0.744052	+	1.28874i	−0.206585	+	0.978429i	$0.566235\pi$
$422$	11326.4	−	19617.9i	1.30654	−	2.26300i
$423$		0			0
$424$	−8942.29	+	15488.5i	−1.02424	+	1.77403i
$425$	8226.55			0.938933
$426$		0			0
$427$	−3190.91	+	5526.82i	−0.361637	+	0.626374i
$428$	7198.93	−	12468.9i	0.813022	−	1.40820i
$429$		0			0
$430$	−16115.3			−1.80733
$431$	290.227	−	502.688i	0.0324356	−	0.0561801i	−0.849352	−	0.527827i	$-0.823007\pi$
$431$	290.227	−	502.688i	0.0324356	−	0.0561801i	0.881788	+	0.471647i	$0.156340\pi$
$432$		0			0
$433$	4981.09	−	8627.50i	0.552831	−	0.957531i	−0.445238	−	0.895412i	$-0.646881\pi$
$433$	4981.09	−	8627.50i	0.552831	−	0.957531i	0.998069	−	0.0621188i	$-0.0197858\pi$
$434$	2367.60	+	4100.80i	0.261863	+	0.453560i
$435$		0			0
$436$	19019.7			2.08917
$437$	5854.17	+	1186.76i	0.640830	+	0.129910i
$438$		0			0
$439$	−7858.21	−	13610.8i	−0.854332	−	1.47975i	−0.877263	−	0.480009i	$-0.840633\pi$
$439$	−7858.21	−	13610.8i	−0.854332	−	1.47975i	0.0229313	−	0.999737i	$-0.492700\pi$
$440$	−819.792	−	1419.92i	−0.0888228	−	0.153846i
$441$		0			0
$442$	8844.80	+	15319.7i	0.951820	+	1.64860i
$443$	−3492.82	+	6049.73i	−0.374602	+	0.648830i	−0.990267	−	0.139178i	$-0.955554\pi$
$443$	−3492.82	+	6049.73i	−0.374602	+	0.648830i	0.615665	+	0.788008i	$0.288887\pi$
$444$		0			0
$445$	8786.37			0.935987
$446$	3076.02	−	5327.83i	0.326578	−	0.565650i
$447$		0			0
$448$	−18998.8			−2.00359
$449$	−9815.32			−1.03166			−0.515828	−	0.856692i	$-0.672516\pi$
$449$	−9815.32			−1.03166			−0.515828	+	0.856692i	$0.672516\pi$
$450$		0			0
$451$	98.4658	+	170.548i	0.0102807	+	0.0178066i
$452$	−2256.31	+	3908.04i	−0.234796	+	0.406678i
$453$		0			0
$454$	−13702.5	−	23733.4i	−1.41650	−	2.45345i
$455$	−10870.9			−1.12007
$456$		0			0
$457$	2063.17			0.211183			0.105592	−	0.994410i	$-0.466326\pi$
$457$	2063.17			0.211183			0.105592	+	0.994410i	$0.466326\pi$
$458$	−8298.84	−	14374.0i	−0.846680	−	1.46649i
$459$		0			0
$460$	7336.46	−	12707.1i	0.743618	−	1.28798i
$461$	−109.398	−	189.483i	−0.0110524	−	0.0191434i	0.860446	−	0.509541i	$-0.170185\pi$
$461$	−109.398	−	189.483i	−0.0110524	−	0.0191434i	−0.871499	+	0.490398i	$0.836852\pi$
$462$		0			0
$463$	−14716.4			−1.47717			−0.738585	−	0.674160i	$-0.764506\pi$
$463$	−14716.4			−1.47717			−0.738585	+	0.674160i	$0.764506\pi$
$464$	−4780.25			−0.478271
$465$		0			0
$466$	3040.59	−	5266.45i	0.302258	−	0.523527i
$467$	−14620.3			−1.44871			−0.724354	−	0.689428i	$-0.757862\pi$
$467$	−14620.3			−1.44871			−0.724354	+	0.689428i	$0.757862\pi$
$468$		0			0
$469$	5608.09	−	9713.49i	0.552148	−	0.956349i
$470$	1277.99	+	2213.54i	0.125424	+	0.217241i
$471$		0			0
$472$	5392.64	+	9340.33i	0.525882	+	0.910855i
$473$	451.680	+	782.333i	0.0439075	+	0.0760501i
$474$		0			0
$475$	5248.98	+	1064.08i	0.507031	+	0.102786i
$476$	50903.1			4.90156
$477$		0			0
$478$	7526.33	+	13036.0i	0.720180	+	1.24739i
$479$	4162.19	−	7209.13i	0.397026	−	0.687669i	−0.596332	−	0.802738i	$-0.703376\pi$
$479$	4162.19	−	7209.13i	0.397026	−	0.687669i	0.993357	+	0.115069i	$0.0367090\pi$
$480$		0			0
$481$	−1022.93	+	1771.77i	−0.0969679	+	0.167953i
$482$	5557.51			0.525181
$483$		0			0
$484$	9730.53	−	16853.8i	0.913836	−	1.58281i
$485$	−9175.79	+	15892.9i	−0.859075	+	1.48796i
$486$		0			0
$487$	−11866.3			−1.10413			−0.552065	−	0.833801i	$-0.686160\pi$
$487$	−11866.3			−1.10413			−0.552065	+	0.833801i	$0.686160\pi$
$488$	3806.76	−	6593.50i	0.353123	−	0.611627i
$489$		0			0
$490$	−12840.4	+	22240.2i	−1.18381	+	2.05043i
$491$	−5594.08	−	9689.23i	−0.514170	−	0.890568i	−0.999865	−	0.0164397i	$-0.994767\pi$
$491$	−5594.08	−	9689.23i	−0.514170	−	0.890568i	0.485695	−	0.874128i	$-0.338566\pi$
$492$		0			0
$493$	−16874.9			−1.54160
$494$	3661.91	+	10918.8i	0.333516	+	0.994453i
$495$		0			0
$496$	−660.036	−	1143.22i	−0.0597510	−	0.103492i
$497$	10411.1	+	18032.5i	0.939637	+	1.62750i
$498$		0			0
$499$	−2361.67	−	4090.53i	−0.211870	−	0.366969i	0.740430	−	0.672133i	$-0.234622\pi$
$499$	−2361.67	−	4090.53i	−0.211870	−	0.366969i	−0.952300	+	0.305165i	$0.901289\pi$
$500$	−6136.97	+	10629.5i	−0.548907	+	0.950735i
$501$		0			0
$502$	2859.30			0.254217
$503$	−4021.06	+	6964.69i	−0.356442	+	0.617376i	−0.987364	−	0.158471i	$-0.949344\pi$
$503$	−4021.06	+	6964.69i	−0.356442	+	0.617376i	0.630922	+	0.775847i	$0.282677\pi$
$504$		0			0
$505$	−4841.85			−0.426653
$506$	−1267.94			−0.111397
$507$		0			0
$508$	19181.8	+	33223.9i	1.67531	+	2.90172i
$509$	6664.94	−	11544.0i	0.580389	−	1.00526i	−0.415044	−	0.909801i	$-0.636234\pi$
$509$	6664.94	−	11544.0i	0.580389	−	1.00526i	0.995433	−	0.0954622i	$-0.0304329\pi$
$510$		0			0
$511$	6676.33	+	11563.7i	0.577971	+	1.00108i
$512$	12435.7			1.07341
$513$		0			0
$514$	20137.4			1.72806
$515$	−10958.3	−	18980.3i	−0.937630	−	1.62402i
$516$		0			0
$517$	71.6388	−	124.082i	0.00609414	−	0.0105554i
$518$	4537.68	+	7859.49i	0.384892	+	0.666653i
$519$		0			0
$520$	12968.9			1.09370
$521$	11641.5			0.978929			0.489464	−	0.872023i	$-0.337192\pi$
$521$	11641.5			0.978929			0.489464	+	0.872023i	$0.337192\pi$
$522$		0			0
$523$	−6306.19	+	10922.6i	−0.527247	+	0.913219i	0.472248	+	0.881466i	$0.343443\pi$
$523$	−6306.19	+	10922.6i	−0.527247	+	0.913219i	−0.999496	+	0.0317538i	$0.989891\pi$
$524$	2780.34			0.231793
$525$		0			0
$526$	−12975.4	+	22474.1i	−1.07558	+	1.86296i
$527$	−2330.02	−	4035.71i	−0.192594	−	0.333583i
$528$		0			0
$529$	3482.56	+	6031.97i	0.286230	+	0.495765i
$530$	18185.7	+	31498.5i	1.49044	+	2.58152i
$531$		0			0
$532$	32478.9	+	6584.16i	2.64688	+	0.536578i
$533$	−1557.71			−0.126589
$534$		0			0
$535$	−6711.59	−	11624.8i	−0.542369	−	0.939411i
$536$	−6690.45	+	11588.2i	−0.539148	+	0.933832i
$537$		0			0
$538$	2320.77	−	4019.68i	0.185976	−	0.322121i
$539$	1439.56			0.115039
$540$		0			0
$541$	8508.24	−	14736.7i	0.676152	−	1.17113i	−0.299979	−	0.953946i	$-0.596980\pi$
$541$	8508.24	−	14736.7i	0.676152	−	1.17113i	0.976131	−	0.217183i	$-0.0696869\pi$
$542$	−7016.32	+	12152.6i	−0.556046	+	0.963099i
$543$		0			0
$544$	11012.0			0.867896
$545$	8866.06	−	15356.5i	0.696845	−	1.20697i
$546$		0			0
$547$	−140.933	+	244.104i	−0.0110162	+	0.0190807i	−0.871481	−	0.490429i	$-0.836840\pi$
$547$	−140.933	+	244.104i	−0.0110162	+	0.0190807i	0.860465	+	0.509510i	$0.170173\pi$
$548$	−2053.78	−	3557.26i	−0.160097	−	0.277296i
$549$		0			0
$550$	−1136.87			−0.0881384
$551$	−10767.1	−	2182.72i	−0.832476	−	0.168761i
$552$		0			0
$553$	447.872	+	775.738i	0.0344403	+	0.0596523i
$554$	−1515.03	−	2624.11i	−0.116187	−	0.201242i
$555$		0			0
$556$	−10630.7	−	18412.9i	−0.810867	−	1.40446i
$557$	9187.86	−	15913.8i	0.698926	−	1.21058i	−0.269913	−	0.962885i	$-0.586995\pi$
$557$	9187.86	−	15913.8i	0.698926	−	1.21058i	0.968839	−	0.247691i	$-0.0796718\pi$
$558$		0			0
$559$	−7145.48			−0.540647
$560$	6721.73	−	11642.4i	0.507223	−	0.878536i
$561$		0			0
$562$	−25619.7			−1.92296
$563$	8726.37			0.653238			0.326619	−	0.945156i	$-0.394091\pi$
$563$	8726.37			0.653238			0.326619	+	0.945156i	$0.394091\pi$
$564$		0			0
$565$	2103.57	+	3643.48i	0.156633	+	0.271296i
$566$	38.3121	−	66.3585i	0.00284519	−	0.00492801i
$567$		0			0
$568$	−12420.4	−	21512.8i	−0.917515	−	1.58918i
$569$	13771.7			1.01466			0.507328	−	0.861753i	$-0.330633\pi$
$569$	13771.7			1.01466			0.507328	+	0.861753i	$0.330633\pi$
$570$		0			0
$571$	−25213.4			−1.84790			−0.923948	−	0.382517i	$-0.875057\pi$
$571$	−25213.4			−1.84790			−0.923948	+	0.382517i	$0.875057\pi$
$572$	−792.899	−	1373.34i	−0.0579594	−	0.100389i
$573$		0			0
$574$	−3454.97	+	5984.18i	−0.251233	+	0.435148i
$575$	−2332.06	−	4039.25i	−0.169137	−	0.292953i
$576$		0			0
$577$	−8625.99			−0.622365			−0.311182	−	0.950350i	$-0.600725\pi$
$577$	−8625.99			−0.622365			−0.311182	+	0.950350i	$0.600725\pi$
$578$	−53780.0			−3.87016
$579$		0			0
$580$	−13493.4	+	23371.2i	−0.966003	+	1.67317i
$581$	−1129.78			−0.0806732
$582$		0			0
$583$	1019.41	−	1765.68i	0.0724181	−	0.125432i
$584$	−7964.86	−	13795.5i	−0.564364	−	0.977507i
$585$		0			0
$586$	8616.16	+	14923.6i	0.607389	+	1.05203i
$587$	−1422.17	−	2463.26i	−0.0999985	−	0.173202i	0.811685	−	0.584095i	$-0.198550\pi$
$587$	−1422.17	−	2463.26i	−0.0999985	−	0.173202i	−0.911684	+	0.410893i	$0.865217\pi$
$588$		0			0
$589$	−964.668	−	2876.38i	−0.0674846	−	0.201221i
$590$	21933.7			1.53050
$591$		0			0
$592$	−1265.01	−	2191.06i	−0.0878235	−	0.152115i
$593$	−11894.1	+	20601.2i	−0.823663	+	1.42663i	0.0792738	+	0.996853i	$0.474740\pi$
$593$	−11894.1	+	20601.2i	−0.823663	+	1.42663i	−0.902937	+	0.429773i	$0.858593\pi$
$594$		0			0
$595$	23728.6	−	41099.2i	1.63492	−	2.83177i
$596$	−25311.0			−1.73956
$597$		0			0
$598$	5014.64	−	8685.62i	0.342916	−	0.593949i
$599$	−5086.25	+	8809.65i	−0.346943	+	0.600923i	−0.985705	−	0.168482i	$-0.946114\pi$
$599$	−5086.25	+	8809.65i	−0.346943	+	0.600923i	0.638762	+	0.769404i	$0.279447\pi$
$600$		0			0
$601$	4016.48			0.272605			0.136303	−	0.990667i	$-0.456478\pi$
$601$	4016.48			0.272605			0.136303	+	0.990667i	$0.456478\pi$
$602$	−15848.5	+	27450.5i	−1.07299	+	1.85847i
$603$		0			0
$604$	−3010.83	+	5214.91i	−0.202829	+	0.351310i
$605$	−9071.81	−	15712.8i	−0.609622	−	1.05590i
$606$		0			0
$607$	−8338.65			−0.557587			−0.278793	−	0.960351i	$-0.589934\pi$
$607$	−8338.65			−0.557587			−0.278793	+	0.960351i	$0.589934\pi$
$608$	7026.24	+	1424.37i	0.468670	+	0.0950094i
$609$		0			0
$610$	−7741.69	−	13409.0i	−0.513855	−	0.890023i
$611$	566.655	+	981.476i	0.0375195	+	0.0649857i
$612$		0			0
$613$	11257.7	+	19499.0i	0.741754	+	1.28476i	0.951696	+	0.307042i	$0.0993393\pi$
$613$	11257.7	+	19499.0i	0.741754	+	1.28476i	−0.209941	+	0.977714i	$0.567327\pi$
$614$	11054.2	−	19146.5i	0.726567	−	1.25845i
$615$		0			0
$616$	−3224.88			−0.210932
$617$	7338.91	−	12711.4i	0.478855	−	0.829401i	−0.520851	−	0.853647i	$-0.674385\pi$
$617$	7338.91	−	12711.4i	0.478855	−	0.829401i	0.999706	+	0.0242468i	$0.00771876\pi$
$618$		0			0
$619$	22866.5			1.48478			0.742392	−	0.669966i	$-0.233691\pi$
$619$	22866.5			1.48478			0.742392	+	0.669966i	$0.233691\pi$
$620$	−7452.42			−0.482736
$621$		0			0
$622$	−13264.8	−	22975.3i	−0.855095	−	1.48107i
$623$	8640.91	−	14966.5i	0.555684	−	0.962472i
$624$		0			0
$625$	9763.27	+	16910.5i	0.624850	+	1.08227i
$626$	−30333.6			−1.93670
$627$		0			0
$628$	36398.9			2.31286
$629$	−4465.65	−	7734.73i	−0.283080	−	0.490308i
$630$		0			0
$631$	12496.0	−	21643.6i	0.788362	−	1.36548i	−0.138608	−	0.990347i	$-0.544263\pi$
$631$	12496.0	−	21643.6i	0.788362	−	1.36548i	0.926970	−	0.375135i	$-0.122404\pi$
$632$	−534.312	−	925.455i	−0.0336294	−	0.0582478i
$633$		0			0
$634$	−33469.1			−2.09657
$635$	35766.6			2.23520
$636$		0			0
$637$	−5693.37	+	9861.21i	−0.354128	+	0.613368i
$638$	2332.03			0.144711
$639$		0			0
$640$	18278.5	−	31659.2i	1.12894	−	1.95538i
$641$	12426.3	+	21522.9i	0.765692	+	1.32622i	0.939880	+	0.341505i	$0.110937\pi$
$641$	12426.3	+	21522.9i	0.765692	+	1.32622i	−0.174188	+	0.984712i	$0.555730\pi$
$642$		0			0
$643$	−7700.65	−	13337.9i	−0.472292	−	0.818034i	0.527205	−	0.849738i	$-0.323240\pi$
$643$	−7700.65	−	13337.9i	−0.472292	−	0.818034i	−0.999497	+	0.0317041i	$0.989907\pi$
$644$	−14430.0	−	24993.5i	−0.882953	−	1.52932i
$645$		0			0
$646$	−49273.6	−	9988.79i	−3.00099	−	0.608365i
$647$	−18759.3			−1.13989			−0.569943	−	0.821684i	$-0.693035\pi$
$647$	−18759.3			−1.13989			−0.569943	+	0.821684i	$0.693035\pi$
$648$		0			0
$649$	−614.756	−	1064.79i	−0.0371822	−	0.0644015i
$650$	4496.24	−	7787.72i	0.271319	−	0.469938i
$651$		0			0
$652$	−1050.62	+	1819.73i	−0.0631066	+	0.109304i
$653$	−15027.5			−0.900572			−0.450286	−	0.892884i	$-0.648678\pi$
$653$	−15027.5			−0.900572			−0.450286	+	0.892884i	$0.648678\pi$
$654$		0			0
$655$	1296.06	−	2244.84i	0.0773149	−	0.133913i
$656$	963.171	−	1668.26i	0.0573255	−	0.0992906i
$657$		0			0
$658$	5027.33			0.297850
$659$	−4258.33	+	7375.64i	−0.251716	+	0.435985i	−0.963998	−	0.265908i	$-0.914328\pi$
$659$	−4258.33	+	7375.64i	−0.251716	+	0.435985i	0.712282	+	0.701893i	$0.247662\pi$
$660$		0			0
$661$	−266.153	+	460.990i	−0.0156613	+	0.0271262i	−0.873750	−	0.486376i	$-0.838319\pi$
$661$	−266.153	+	460.990i	−0.0156613	+	0.0271262i	0.858089	+	0.513502i	$0.171652\pi$
$662$	20356.0	+	35257.6i	1.19510	+	2.06998i
$663$		0			0
$664$	1347.83			0.0787738
$665$	20456.2	−	23154.2i	1.19287	−	1.35020i
$666$		0			0
$667$	4783.70	+	8285.61i	0.277700	+	0.480990i
$668$	18996.4	+	32902.7i	1.10029	+	1.90576i
$669$		0			0
$670$	13606.2	+	23566.6i	0.784555	+	1.35889i
$671$	−433.967	+	751.653i	−0.0249674	+	0.0432448i
$672$		0			0
$673$	9786.04			0.560511			0.280256	−	0.959925i	$-0.409581\pi$
$673$	9786.04			0.560511			0.280256	+	0.959925i	$0.409581\pi$
$674$	18737.6	−	32454.5i	1.07084	−	1.85475i
$675$		0			0
$676$	−19910.6			−1.13283
$677$	−24769.5			−1.40616			−0.703079	−	0.711111i	$-0.748192\pi$
$677$	−24769.5			−1.40616			−0.703079	+	0.711111i	$0.748192\pi$
$678$		0			0
$679$	18047.8	+	31259.7i	1.02004	+	1.76677i
$680$	−28308.2	+	49031.3i	−1.59643	+	2.76510i
$681$		0			0
$682$	321.996	+	557.713i	0.0180790	+	0.0313137i
$683$	−4542.19			−0.254469			−0.127234	−	0.991873i	$-0.540610\pi$
$683$	−4542.19			−0.254469			−0.127234	+	0.991873i	$0.540610\pi$
$684$		0			0
$685$	−3829.50			−0.213603
$686$	3086.83	+	5346.55i	0.171802	+	0.297569i
$687$		0			0
$688$	4418.23	−	7652.60i	0.244831	−	0.424059i
$689$	8063.45	+	13966.3i	0.445853	+	0.772240i
$690$		0			0
$691$	−770.938			−0.0424427			−0.0212213	−	0.999775i	$-0.506755\pi$
$691$	−770.938			−0.0424427			−0.0212213	+	0.999775i	$0.506755\pi$
$692$	16665.6			0.915507
$693$		0			0
$694$	−25166.5	+	43589.7i	−1.37652	+	2.38421i
$695$	−19822.1			−1.08186
$696$		0			0
$697$	3400.12	−	5889.19i	0.184776	−	0.320041i
$698$	13794.7	+	23893.2i	0.748049	+	1.29566i
$699$		0			0
$700$	−12938.3	−	22409.7i	−0.698601	−	1.21001i
$701$	4998.65	+	8657.92i	0.269325	+	0.466484i	0.968688	−	0.248283i	$-0.0798662\pi$
$701$	4998.65	+	8657.92i	0.269325	+	0.466484i	−0.699363	+	0.714767i	$0.746533\pi$
$702$		0			0
$703$	−1848.86	−	5512.78i	−0.0991906	−	0.295759i
$704$	−2583.85			−0.138327
$705$		0			0
$706$	19397.4	+	33597.2i	1.03404	+	1.79100i
$707$	−4761.70	+	8247.50i	−0.253298	+	0.438726i
$708$		0			0
$709$	927.018	−	1605.64i	0.0491042	−	0.0850510i	−0.840429	−	0.541922i	$-0.817697\pi$
$709$	927.018	−	1605.64i	0.0491042	−	0.0850510i	0.889533	+	0.456871i	$0.151030\pi$
$710$	−50517.9			−2.67029
$711$		0			0
$712$	−10308.6	+	17855.0i	−0.542601	+	0.939812i
$713$	−1321.02	+	2288.08i	−0.0693867	+	0.120181i
$714$		0			0
$715$	−1478.45			−0.0773297
$716$	30559.3	−	52930.2i	1.59505	−	2.76270i
$717$		0			0
$718$	13916.8	−	24104.6i	0.723356	−	1.25289i
$719$	16730.4	+	28977.9i	0.867786	+	1.50305i	0.864254	+	0.503055i	$0.167791\pi$
$719$	16730.4	+	28977.9i	0.867786	+	1.50305i	0.00353117	+	0.999994i	$0.498876\pi$
$720$		0			0
$721$	−43107.4			−2.22664
$722$	−30147.1	−	12746.8i	−1.55396	−	0.657043i
$723$		0			0
$724$	−13264.8	−	22975.3i	−0.680916	−	1.17938i
$725$	4289.17	+	7429.07i	0.219719	+	0.380564i
$726$		0			0
$727$	14367.3	+	24884.8i	0.732947	+	1.26950i	0.955618	+	0.294607i	$0.0951888\pi$
$727$	14367.3	+	24884.8i	0.732947	+	1.26950i	−0.222672	+	0.974893i	$0.571478\pi$
$728$	12754.2	−	22091.0i	0.649317	−	1.12465i
$729$		0			0
$730$	−32395.8			−1.64250
$731$	15597.0	−	27014.7i	0.789158	−	1.36686i
$732$		0			0
$733$	11383.3			0.573606			0.286803	−	0.957990i	$-0.407407\pi$
$733$	11383.3			0.573606			0.286803	+	0.957990i	$0.407407\pi$
$734$	−28365.0			−1.42639
$735$		0			0
$736$	−3121.67	−	5406.90i	−0.156340	−	0.270789i
$737$	762.705	−	1321.04i	0.0381202	−	0.0660262i
$738$		0			0
$739$	12085.7	+	20933.1i	0.601598	+	1.04200i	0.992579	+	0.121600i	$0.0388026\pi$
$739$	12085.7	+	20933.1i	0.601598	+	1.04200i	−0.390981	+	0.920399i	$0.627864\pi$
$740$	−14283.1			−0.709537
$741$		0			0
$742$	71538.4			3.53943
$743$	9127.97	+	15810.1i	0.450704	+	0.780642i	0.998430	−	0.0560160i	$-0.0178398\pi$
$743$	9127.97	+	15810.1i	0.450704	+	0.780642i	−0.547726	+	0.836658i	$0.684506\pi$
$744$		0			0
$745$	−11798.8	+	20436.1i	−0.580233	+	1.00499i
$746$	14314.9	+	24794.1i	0.702554	+	1.21686i
$747$		0			0
$748$	6922.88			0.338403
$749$	−26401.9			−1.28799
$750$		0			0
$751$	8004.44	−	13864.1i	0.388930	−	0.673646i	−0.603376	−	0.797457i	$-0.706178\pi$
$751$	8004.44	−	13864.1i	0.388930	−	0.673646i	0.992306	+	0.123811i	$0.0395116\pi$
$752$	−1401.51			−0.0679625
$753$		0			0
$754$	−9223.04	+	15974.8i	−0.445469	+	0.771574i
$755$	2807.01	+	4861.88i	0.135308	+	0.234360i
$756$		0			0
$757$	17770.8	+	30779.9i	0.853223	+	1.47782i	0.878284	+	0.478139i	$0.158688\pi$
$757$	17770.8	+	30779.9i	0.853223	+	1.47782i	−0.0250617	+	0.999686i	$0.507978\pi$
$758$	−20965.1	−	36312.7i	−1.00460	−	1.74002i
$759$		0			0
$760$	−24404.2	+	27623.0i	−1.16478	+	1.31841i
$761$	−17849.0			−0.850232			−0.425116	−	0.905139i	$-0.639767\pi$
$761$	−17849.0			−0.850232			−0.425116	+	0.905139i	$0.639767\pi$
$762$		0			0
$763$	−17438.6	−	30204.5i	−0.827416	−	1.43313i
$764$	−6104.62	+	10573.5i	−0.289080	+	0.500702i
$765$		0			0
$766$	24737.5	−	42846.6i	1.16684	−	2.02103i
$767$	9725.30			0.457836
$768$		0			0
$769$	16150.3	−	27973.2i	0.757341	−	1.31175i	−0.186861	−	0.982386i	$-0.559831\pi$
$769$	16150.3	−	27973.2i	0.757341	−	1.31175i	0.944202	−	0.329367i	$-0.106835\pi$
$770$	−3279.17	+	5679.69i	−0.153471	+	0.265820i
$771$		0			0
$772$	−58795.8			−2.74107
$773$	−7996.96	+	13851.1i	−0.372097	+	0.644491i	−0.989888	−	0.141852i	$-0.954694\pi$
$773$	−7996.96	+	13851.1i	−0.372097	+	0.644491i	0.617791	+	0.786342i	$0.288028\pi$
$774$		0			0
$775$	−1184.46	+	2051.55i	−0.0548994	+	0.0950886i
$776$	−21531.0	−	37292.8i	−0.996028	−	1.72517i
$777$		0			0
$778$	25045.5			1.15415
$779$	2931.21	−	3317.82i	0.134816	−	0.152597i
$780$		0			0
$781$	1415.91	+	2452.43i	0.0648724	+	0.112362i
$782$	21891.7	+	37917.5i	1.00108	+	1.73392i
$783$		0			0
$784$	−7040.72	−	12194.9i	−0.320733	−	0.555525i
$785$	16967.4	−	29388.4i	0.771456	−	1.33620i
$786$		0			0
$787$	19936.1			0.902978			0.451489	−	0.892277i	$-0.350893\pi$
$787$	19936.1			0.902978			0.451489	+	0.892277i	$0.350893\pi$
$788$	−1380.65	+	2391.36i	−0.0624159	+	0.108108i
$789$		0			0
$790$	−2173.23			−0.0978733
$791$	8274.96			0.371964
$792$		0			0
$793$	−3432.63	−	5945.49i	−0.153715	−	0.266243i
$794$	28259.3	−	48946.5i	1.26308	−	2.18772i
$795$		0			0
$796$	2594.87	+	4494.45i	0.115544	+	0.200128i
$797$	31005.6			1.37801			0.689005	−	0.724756i	$-0.258048\pi$
$797$	31005.6			1.37801			0.689005	+	0.724756i	$0.258048\pi$
$798$		0			0
$799$	−4947.52			−0.219062
$800$	−2798.96	−	4847.95i	−0.123698	−	0.214251i
$801$		0			0
$802$	−19573.9	+	33903.0i	−0.861819	+	1.49272i
$803$	907.987	+	1572.68i	0.0399031	+	0.0691141i
$804$		0			0
$805$	−26906.3			−1.17804
$806$	−5093.90			−0.222612
$807$		0			0
$808$	5680.71	−	9839.27i	0.247335	−	0.428396i
$809$	17553.5			0.762854			0.381427	−	0.924399i	$-0.375433\pi$
$809$	17553.5			0.762854			0.381427	+	0.924399i	$0.375433\pi$
$810$		0			0
$811$	−15567.9	+	26964.3i	−0.674059	+	1.16750i	0.302684	+	0.953091i	$0.402117\pi$
$811$	−15567.9	+	26964.3i	−0.674059	+	1.16750i	−0.976743	+	0.214413i	$0.931216\pi$
$812$	26540.0	+	45968.6i	1.14701	+	1.98668i
$813$		0			0
$814$	617.129	+	1068.90i	0.0265729	+	0.0460256i
$815$	979.498	+	1696.54i	0.0420986	+	0.0729169i
$816$		0			0
$817$	13446.0	−	15219.4i	0.575783	−	0.651726i
$818$	53412.9			2.28305
$819$		0			0
$820$	−5437.54	−	9418.10i	−0.231570	−	0.401091i
$821$	−14772.8	+	25587.3i	−0.627984	+	1.08770i	0.359971	+	0.932963i	$0.382787\pi$
$821$	−14772.8	+	25587.3i	−0.627984	+	1.08770i	−0.987956	+	0.154737i	$0.950547\pi$
$822$		0			0
$823$	−11823.7	+	20479.2i	−0.500786	+	0.867387i	0.499213	+	0.866479i	$0.333622\pi$
$823$	−11823.7	+	20479.2i	−0.500786	+	0.867387i	−1.00000		0.000908092i	$0.999711\pi$
$824$	51427.2			2.17421
$825$		0			0
$826$	21570.6	−	37361.3i	0.908639	−	1.57381i
$827$	10204.6	−	17674.9i	0.429079	−	0.743187i	−0.567713	−	0.823227i	$-0.692171\pi$
$827$	10204.6	−	17674.9i	0.429079	−	0.743187i	0.996792	+	0.0800400i	$0.0255048\pi$
$828$		0			0
$829$	−3542.01			−0.148394			−0.0741972	−	0.997244i	$-0.523639\pi$
$829$	−3542.01			−0.148394			−0.0741972	+	0.997244i	$0.523639\pi$
$830$	1370.52	−	2373.80i	0.0573148	−	0.0992721i
$831$		0			0
$832$	10219.0	−	17699.8i	0.425817	−	0.737537i
$833$	−24854.7	−	43049.6i	−1.03381	−	1.79061i
$834$		0			0
$835$	35420.9			1.46801
$836$	4417.16	+	895.452i	0.182740	+	0.0370453i
$837$		0			0
$838$	−581.044	−	1006.40i	−0.0239521	−	0.0414862i
$839$	−219.487	−	380.163i	−0.00903163	−	0.0156432i	0.861474	−	0.507801i	$-0.169542\pi$
$839$	−219.487	−	380.163i	−0.00903163	−	0.0156432i	−0.870506	+	0.492158i	$0.836208\pi$
$840$		0			0
$841$	3396.21	+	5882.41i	0.139252	+	0.241191i
$842$	−30670.9	+	53123.6i	−1.25533	+	2.17430i
$843$		0			0
$844$	70123.1			2.85988
$845$	−9281.37	+	16075.8i	−0.377857	+	0.654467i
$846$		0			0
$847$	−35686.5			−1.44770
$848$	−19943.4			−0.807615
$849$		0			0
$850$	19628.6	+	33997.7i	0.792064	+	1.37189i
$851$	−2531.84	+	4385.27i	−0.101986	+	0.176645i
$852$		0			0
$853$	−7857.26	−	13609.2i	−0.315390	−	0.546271i	0.664131	−	0.747617i	$-0.268802\pi$
$853$	−7857.26	−	13609.2i	−0.315390	−	0.546271i	−0.979520	+	0.201346i	$0.935469\pi$
$854$	−30454.1			−1.22028
$855$		0			0
$856$	31497.5			1.25767
$857$	−6343.99	−	10988.1i	−0.252867	−	0.437978i	0.711447	−	0.702739i	$-0.248040\pi$
$857$	−6343.99	−	10988.1i	−0.252867	−	0.437978i	−0.964314	+	0.264762i	$0.914707\pi$
$858$		0			0
$859$	−1919.06	+	3323.91i	−0.0762253	+	0.132026i	−0.901618	−	0.432532i	$-0.857620\pi$
$859$	−1919.06	+	3323.91i	−0.0762253	+	0.132026i	0.825393	+	0.564558i	$0.190953\pi$
$860$	−24943.0	−	43202.5i	−0.989010	−	1.71302i
$861$		0			0
$862$	2769.93			0.109448
$863$	9140.17			0.360527			0.180264	−	0.983618i	$-0.442305\pi$
$863$	9140.17			0.360527			0.180264	+	0.983618i	$0.442305\pi$
$864$		0			0
$865$	7768.70	−	13455.8i	0.305369	−	0.528914i
$866$	47539.5			1.86543
$867$		0			0
$868$	−7329.04	+	12694.3i	−0.286594	+	0.496396i
$869$	60.9111	+	105.501i	0.00237775	+	0.00411839i
$870$		0			0
$871$	6032.91	+	10449.3i	0.234693	+	0.406500i
$872$	20804.2	+	36034.0i	0.807935	+	1.39938i
$873$		0			0
$874$	9063.54	+	27025.0i	0.350777	+	1.04592i
$875$	22507.2			0.869580
$876$		0			0
$877$	2506.39	+	4341.19i	0.0965049	+	0.167151i	0.910236	−	0.414091i	$-0.135900\pi$
$877$	2506.39	+	4341.19i	0.0965049	+	0.167151i	−0.813731	+	0.581242i	$0.802567\pi$
$878$	37499.4	−	64950.8i	1.44139	−	2.49657i
$879$		0			0
$880$	914.161	−	1583.37i	0.0350186	−	0.0606540i
$881$	−9010.30			−0.344568			−0.172284	−	0.985047i	$-0.555115\pi$
$881$	−9010.30			−0.344568			−0.172284	+	0.985047i	$0.555115\pi$
$882$		0			0
$883$	−7842.63	+	13583.8i	−0.298896	+	0.517704i	−0.975884	−	0.218291i	$-0.929952\pi$
$883$	−7842.63	+	13583.8i	−0.298896	+	0.517704i	0.676987	+	0.735995i	$0.263285\pi$
$884$	−27379.6	+	47422.8i	−1.04171	+	1.80430i
$885$		0			0
$886$	−33335.4			−1.26403
$887$	138.901	−	240.583i	0.00525798	−	0.00910708i	−0.863384	−	0.504547i	$-0.831660\pi$
$887$	138.901	−	240.583i	0.00525798	−	0.00910708i	0.868642	+	0.495440i	$0.164993\pi$
$888$		0			0
$889$	35174.5	−	60924.0i	1.32701	−	2.29845i
$890$	20964.3	+	36311.2i	0.789578	+	1.36759i
$891$		0			0
$892$	19044.0			0.714844
$893$	−3156.78	−	639.947i	−0.118295	−	0.0239810i
$894$		0			0
$895$	−28490.6	−	49347.1i	−1.06406	−	1.84301i
$896$	−35951.7	−	62270.2i	−1.34047	−	2.32176i
$897$		0			0
$898$	−23419.4	−	40563.5i	−0.870284	−	1.50738i
$899$	2429.66	−	4208.29i	0.0901375	−	0.156123i
$900$		0			0
$901$	−70402.7			−2.60317
$902$	−469.879	+	813.854i	−0.0173451	+	0.0300426i
$903$		0			0
$904$	−9872.03			−0.363207
$905$	−24733.7			−0.908481
$906$		0			0
$907$	21162.2	+	36654.1i	0.774730	+	1.34187i	0.934946	+	0.354790i	$0.115448\pi$
$907$	21162.2	+	36654.1i	0.774730	+	1.34187i	−0.160216	+	0.987082i	$0.551219\pi$
$908$	42416.9	−	73468.2i	1.55028	−	2.68516i
$909$		0			0
$910$	−25937.9	−	44925.7i	−0.944870	−	1.63656i
$911$	−27419.0			−0.997183			−0.498591	−	0.866837i	$-0.666149\pi$
$911$	−27419.0			−0.997183			−0.498591	+	0.866837i	$0.666149\pi$
$912$		0			0
$913$	−153.651			−0.00556966
$914$	4922.72	+	8526.39i	0.178150	+	0.308565i
$915$		0			0
$916$	25689.5	−	44495.6i	0.926644	−	1.60499i
$917$	−2549.21	−	4415.36i	−0.0918018	−	0.159005i
$918$		0			0
$919$	48889.7			1.75487			0.877433	−	0.479699i	$-0.159254\pi$
$919$	48889.7			1.75487			0.877433	+	0.479699i	$0.159254\pi$
$920$	32099.2			1.15030
$921$		0			0
$922$	522.048	−	904.213i	0.0186472	−	0.0322979i
$923$	−22399.4			−0.798794
$924$		0			0
$925$	−2270.10	+	3931.94i	−0.0806925	+	0.139764i
$926$	−35113.4	−	60818.2i	−1.24611	−	2.15832i
$927$		0			0
$928$	5741.45	+	9944.49i	0.203095	+	0.351771i
$929$	25186.1	+	43623.6i	0.889483	+	1.54063i	0.840487	+	0.541831i	$0.182269\pi$
$929$	25186.1	+	43623.6i	0.889483	+	1.54063i	0.0489958	+	0.998799i	$0.484398\pi$
$930$		0			0
$931$	−10290.3	−	30682.8i	−0.362245	−	1.08012i
$932$	18824.6			0.661610
$933$		0			0
$934$	−34884.0	−	60420.9i	−1.22210	−	2.11674i
$935$	3227.11	−	5589.52i	0.112875	−	0.195505i
$936$		0			0
$937$	24039.6	−	41637.8i	0.838142	−	1.45171i	−0.0533035	−	0.998578i	$-0.516975\pi$
$937$	24039.6	−	41637.8i	0.838142	−	1.45171i	0.891446	−	0.453127i	$-0.149692\pi$
$938$	53523.6			1.86312
$939$		0			0
$940$	−3956.09	+	6852.14i	−0.137270	+	0.237758i
$941$	−15714.1	+	27217.6i	−0.544383	+	0.942899i	0.454263	+	0.890868i	$0.349903\pi$
$941$	−15714.1	+	27217.6i	−0.544383	+	0.942899i	−0.998645	+	0.0520309i	$0.983431\pi$
$942$		0			0
$943$	−3855.46			−0.133140
$944$	−6013.41	+	10415.5i	−0.207330	+	0.359106i
$945$		0			0
$946$	−2155.42	+	3733.29i	−0.0740789	+	0.128308i
$947$	5500.93	+	9527.88i	0.188760	+	0.326943i	0.944837	−	0.327540i	$-0.106220\pi$
$947$	5500.93	+	9527.88i	0.188760	+	0.326943i	−0.756077	+	0.654483i	$0.772886\pi$
$948$		0			0
$949$	−14364.2			−0.491338
$950$	8126.57	+	24231.2i	0.277538	+	0.827541i
$951$		0			0
$952$	55679.2	+	96439.2i	1.89556	+	3.28321i
$953$	−25157.4	−	43574.0i	−0.855120	−	1.48111i	−0.876533	−	0.481341i	$-0.840150\pi$
$953$	−25157.4	−	43574.0i	−0.855120	−	1.48111i	0.0214133	−	0.999771i	$-0.493183\pi$
$954$		0			0
$955$	5691.36	+	9857.72i	0.192846	+	0.334019i
$956$	−23298.2	+	40353.6i	−0.788198	+	1.36520i
$957$		0			0
$958$	39724.0			1.33969
$959$	−3766.10	+	6523.08i	−0.126813	+	0.219647i
$960$		0			0
$961$	−28449.1			−0.954956
$962$	−9762.84			−0.327200
$963$		0			0
$964$	8601.79	+	14898.7i	0.287391	+	0.497776i
$965$	−27407.8	+	47471.7i	−0.914289	+	1.58359i
$966$		0			0
$967$	12511.6	+	21670.7i	0.416077	+	0.720666i	0.995541	−	0.0943319i	$-0.0300715\pi$
$967$	12511.6	+	21670.7i	0.416077	+	0.720666i	−0.579464	+	0.814998i	$0.696738\pi$
$968$	42574.0			1.41362
$969$		0			0
$970$	−87573.8			−2.89879
$971$	4319.90	+	7482.28i	0.142772	+	0.247289i	0.928540	−	0.371233i	$-0.121065\pi$
$971$	4319.90	+	7482.28i	0.142772	+	0.247289i	−0.785767	+	0.618522i	$0.787732\pi$
$972$		0			0
$973$	−19493.9	+	33764.5i	−0.642289	+	1.11248i
$974$	−28312.9	−	49039.4i	−0.931421	−	1.61327i
$975$		0			0
$976$	8489.94			0.278439
$977$	−4044.17			−0.132430			−0.0662151	−	0.997805i	$-0.521092\pi$
$977$	−4044.17			−0.132430			−0.0662151	+	0.997805i	$0.521092\pi$
$978$		0			0
$979$	1175.17	−	2035.46i	0.0383643	−	0.0664490i
$980$	−79496.3			−2.59124
$981$		0			0
$982$	26695.0	−	46237.0i	0.867485	−	1.50253i
$983$	17232.1	+	29846.9i	0.559123	+	0.968430i	0.997570	+	0.0696727i	$0.0221955\pi$
$983$	17232.1	+	29846.9i	0.559123	+	0.968430i	−0.438447	+	0.898757i	$0.644471\pi$
$984$		0			0
$985$	1287.19	+	2229.48i	0.0416378	+	0.0721188i
$986$	−40263.6	−	69738.6i	−1.30046	−	2.25247i
$987$		0			0
$988$	−23603.6	+	26716.8i	−0.760052	+	0.860299i
$989$	−17685.7			−0.568627
$990$		0			0
$991$	−4553.29	−	7886.54i	−0.145954	−	0.252799i	0.783775	−	0.621045i	$-0.213292\pi$
$991$	−4553.29	−	7886.54i	−0.145954	−	0.252799i	−0.929728	+	0.368246i	$0.879958\pi$
$992$	−1585.51	+	2746.18i	−0.0507459	+	0.0878945i
$993$		0			0
$994$	−49681.6	+	86051.0i	−1.58532	+	2.74585i
$995$	4838.42			0.154159
$996$		0			0
$997$	−28331.7	+	49072.0i	−0.899975	+	1.55880i	−0.0724517	+	0.997372i	$0.523082\pi$
$997$	−28331.7	+	49072.0i	−0.899975	+	1.55880i	−0.827524	+	0.561431i	$0.810251\pi$
$998$	11269.9	−	19520.0i	0.357457	−	0.619134i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	171.4.f.d.64.2		4
3.2	odd	2		19.4.c.b.7.1	✓	4
12.11	even	2		304.4.i.d.273.1		4
19.11	even	3	inner	171.4.f.d.163.2		4
57.11	odd	6		19.4.c.b.11.1	yes	4
57.26	odd	6		361.4.a.f.1.2		2
57.50	even	6		361.4.a.e.1.1		2
228.11	even	6		304.4.i.d.49.1		4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
19.4.c.b.7.1	✓	4	3.2	odd	2
19.4.c.b.11.1	yes	4	57.11	odd	6
171.4.f.d.64.2		4	1.1	even	1	trivial
171.4.f.d.163.2		4	19.11	even	3	inner
304.4.i.d.49.1		4	228.11	even	6
304.4.i.d.273.1		4	12.11	even	2
361.4.a.e.1.1		2	57.50	even	6
361.4.a.f.1.2		2	57.26	odd	6

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:	\( N \)	\(=\)	\( 171 = 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	171.f (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(2.38600 + 4.13267i) q^{2} +(-7.38600 + 12.7929i) q^{4} +(6.88600 + 11.9269i) q^{5} +27.0880 q^{7} -32.3160 q^{8} +O(q^{10})\)	\(q+(2.38600 + 4.13267i) q^{2} +(-7.38600 + 12.7929i) q^{4} +(6.88600 + 11.9269i) q^{5} +27.0880 q^{7} -32.3160 q^{8} +(-32.8600 + 56.9152i) q^{10} +3.68399 q^{11} +(-14.5700 + 25.2360i) q^{13} +(64.6320 + 111.946i) q^{14} +(-18.0180 - 31.2081i) q^{16} +(-63.6060 - 110.169i) q^{17} +(-26.3340 - 78.5208i) q^{19} -203.440 q^{20} +(8.79001 + 15.2248i) q^{22} +(-36.0620 + 62.4612i) q^{23} +(-32.3340 + 56.0042i) q^{25} -139.056 q^{26} +(-200.072 + 346.535i) q^{28} +(66.3260 - 114.880i) q^{29} +36.6320 q^{31} +(-43.2820 + 74.9667i) q^{32} +(303.528 - 525.726i) q^{34} +(186.528 + 323.076i) q^{35} +70.2079 q^{37} +(261.668 - 296.181i) q^{38} +(-222.528 - 385.430i) q^{40} +(26.7280 + 46.2943i) q^{41} +(122.606 + 212.360i) q^{43} +(-27.2100 + 47.1291i) q^{44} -344.176 q^{46} +(19.4460 - 33.6814i) q^{47} +390.760 q^{49} -308.596 q^{50} +(-215.228 - 372.786i) q^{52} +(276.714 - 479.283i) q^{53} +(25.3680 + 43.9386i) q^{55} -875.376 q^{56} +633.016 q^{58} +(-166.872 - 289.031i) q^{59} +(-117.798 + 204.032i) q^{61} +(87.4040 + 151.388i) q^{62} -701.372 q^{64} -401.316 q^{65} +(207.032 - 358.590i) q^{67} +1879.18 q^{68} +(-890.112 + 1541.72i) q^{70} +(384.342 + 665.700i) q^{71} +(246.468 + 426.895i) q^{73} +(167.516 + 290.147i) q^{74} +(1199.01 + 243.066i) q^{76} +99.7921 q^{77} +(16.5340 + 28.6377i) q^{79} +(248.144 - 429.798i) q^{80} +(-127.546 + 220.916i) q^{82} -41.7077 q^{83} +(875.982 - 1517.25i) q^{85} +(-585.076 + 1013.38i) q^{86} -119.052 q^{88} +(318.994 - 552.514i) q^{89} +(-394.672 + 683.592i) q^{91} +(-532.708 - 922.678i) q^{92} +185.592 q^{94} +(755.174 - 854.778i) q^{95} +(666.264 + 1154.00i) q^{97} +(932.354 + 1614.88i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q + q^{2} - 21 q^{4} + 19 q^{5} + 40 q^{7} - 78 q^{8}+O(q^{10}) \) 4 * q + q^2 - 21 * q^4 + 19 * q^5 + 40 * q^7 - 78 * q^8	\( 4 q + q^{2} - 21 q^{4} + 19 q^{5} + 40 q^{7} - 78 q^{8} - 46 q^{10} + 66 q^{11} - 101 q^{13} + 156 q^{14} + 39 q^{16} - 75 q^{17} + 57 q^{19} - 472 q^{20} - 93 q^{22} + q^{23} + 33 q^{25} + 264 q^{26} - 356 q^{28} - 85 q^{29} + 44 q^{31} + 143 q^{32} + 804 q^{34} + 336 q^{35} + 896 q^{37} + 722 q^{38} - 480 q^{40} + 124 q^{41} + 311 q^{43} - 237 q^{44} - 1240 q^{46} + 411 q^{47} + 196 q^{49} - 1354 q^{50} - 878 q^{52} + 261 q^{53} + 204 q^{55} - 1656 q^{56} + 2908 q^{58} + 204 q^{59} - 531 q^{61} + 230 q^{62} - 1934 q^{64} - 1554 q^{65} - 556 q^{67} + 3108 q^{68} - 1920 q^{70} + 1563 q^{71} + 234 q^{73} - 1090 q^{74} + 1387 q^{76} - 216 q^{77} + 331 q^{79} + 104 q^{80} + 11 q^{82} - 2918 q^{83} + 1479 q^{85} - 922 q^{86} - 630 q^{88} + 601 q^{89} - 280 q^{91} - 610 q^{92} - 2436 q^{94} + 1235 q^{95} + 324 q^{97} + 2969 q^{98}+O(q^{100}) \) 4 * q + q^2 - 21 * q^4 + 19 * q^5 + 40 * q^7 - 78 * q^8 - 46 * q^10 + 66 * q^11 - 101 * q^13 + 156 * q^14 + 39 * q^16 - 75 * q^17 + 57 * q^19 - 472 * q^20 - 93 * q^22 + q^23 + 33 * q^25 + 264 * q^26 - 356 * q^28 - 85 * q^29 + 44 * q^31 + 143 * q^32 + 804 * q^34 + 336 * q^35 + 896 * q^37 + 722 * q^38 - 480 * q^40 + 124 * q^41 + 311 * q^43 - 237 * q^44 - 1240 * q^46 + 411 * q^47 + 196 * q^49 - 1354 * q^50 - 878 * q^52 + 261 * q^53 + 204 * q^55 - 1656 * q^56 + 2908 * q^58 + 204 * q^59 - 531 * q^61 + 230 * q^62 - 1934 * q^64 - 1554 * q^65 - 556 * q^67 + 3108 * q^68 - 1920 * q^70 + 1563 * q^71 + 234 * q^73 - 1090 * q^74 + 1387 * q^76 - 216 * q^77 + 331 * q^79 + 104 * q^80 + 11 * q^82 - 2918 * q^83 + 1479 * q^85 - 922 * q^86 - 630 * q^88 + 601 * q^89 - 280 * q^91 - 610 * q^92 - 2436 * q^94 + 1235 * q^95 + 324 * q^97 + 2969 * q^98

Introduction

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