LMFDB - Embedded newform 126.4.g.a.109.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [126,4,Mod(37,126)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(126, 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("126.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 126 = 2 \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	126.g (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:	$7.43424066072$
Analytic rank:	$0$
Dimension:	$2$
Coefficient field:	$\Q(\zeta_{6})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{2} - x + 1 $ x^2 - x + 1
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 1 $
Twist minimal:	no (minimal twist has level 42)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			109.1
Root			$0.500000 - 0.866025i$ of defining polynomial
Character	$\chi$	$=$	126.109
Dual form			126.4.g.a.37.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.50000 - 12.9904i) q^{5} +(17.5000 - 6.06218i) q^{7} +8.00000 q^{8} +O(q^{10})$	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.50000 - 12.9904i) q^{5} +(17.5000 - 6.06218i) q^{7} +8.00000 q^{8} +(-15.0000 + 25.9808i) q^{10} +(-4.50000 + 7.79423i) q^{11} -88.0000 q^{13} +(-28.0000 - 24.2487i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(-52.0000 - 90.0666i) q^{19} +60.0000 q^{20} +18.0000 q^{22} +(-42.0000 - 72.7461i) q^{23} +(-50.0000 + 86.6025i) q^{25} +(88.0000 + 152.420i) q^{26} +(-14.0000 + 72.7461i) q^{28} -51.0000 q^{29} +(-92.5000 + 160.215i) q^{31} +(-16.0000 + 27.7128i) q^{32} +168.000 q^{34} +(-210.000 - 181.865i) q^{35} +(-22.0000 - 38.1051i) q^{37} +(-104.000 + 180.133i) q^{38} +(-60.0000 - 103.923i) q^{40} +168.000 q^{41} +326.000 q^{43} +(-18.0000 - 31.1769i) q^{44} +(-84.0000 + 145.492i) q^{46} +(-69.0000 - 119.512i) q^{47} +(269.500 - 212.176i) q^{49} +200.000 q^{50} +(176.000 - 304.841i) q^{52} +(319.500 - 553.390i) q^{53} +135.000 q^{55} +(140.000 - 48.4974i) q^{56} +(51.0000 + 88.3346i) q^{58} +(79.5000 - 137.698i) q^{59} +(-361.000 - 625.270i) q^{61} +370.000 q^{62} +64.0000 q^{64} +(660.000 + 1143.15i) q^{65} +(83.0000 - 143.760i) q^{67} +(-168.000 - 290.985i) q^{68} +(-105.000 + 545.596i) q^{70} -1086.00 q^{71} +(-109.000 + 188.794i) q^{73} +(-44.0000 + 76.2102i) q^{74} +416.000 q^{76} +(-31.5000 + 163.679i) q^{77} +(291.500 + 504.893i) q^{79} +(-120.000 + 207.846i) q^{80} +(-168.000 - 290.985i) q^{82} +597.000 q^{83} +1260.00 q^{85} +(-326.000 - 564.649i) q^{86} +(-36.0000 + 62.3538i) q^{88} +(-519.000 - 898.934i) q^{89} +(-1540.00 + 533.472i) q^{91} +336.000 q^{92} +(-138.000 + 239.023i) q^{94} +(-780.000 + 1351.00i) q^{95} -169.000 q^{97} +(-637.000 - 254.611i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 2 q - 2 q^{2} - 4 q^{4} - 15 q^{5} + 35 q^{7} + 16 q^{8}+O(q^{10}) $ 2 * q - 2 * q^2 - 4 * q^4 - 15 * q^5 + 35 * q^7 + 16 * q^8	$ 2 q - 2 q^{2} - 4 q^{4} - 15 q^{5} + 35 q^{7} + 16 q^{8} - 30 q^{10} - 9 q^{11} - 176 q^{13} - 56 q^{14} - 16 q^{16} - 84 q^{17} - 104 q^{19} + 120 q^{20} + 36 q^{22} - 84 q^{23} - 100 q^{25} + 176 q^{26} - 28 q^{28} - 102 q^{29} - 185 q^{31} - 32 q^{32} + 336 q^{34} - 420 q^{35} - 44 q^{37} - 208 q^{38} - 120 q^{40} + 336 q^{41} + 652 q^{43} - 36 q^{44} - 168 q^{46} - 138 q^{47} + 539 q^{49} + 400 q^{50} + 352 q^{52} + 639 q^{53} + 270 q^{55} + 280 q^{56} + 102 q^{58} + 159 q^{59} - 722 q^{61} + 740 q^{62} + 128 q^{64} + 1320 q^{65} + 166 q^{67} - 336 q^{68} - 210 q^{70} - 2172 q^{71} - 218 q^{73} - 88 q^{74} + 832 q^{76} - 63 q^{77} + 583 q^{79} - 240 q^{80} - 336 q^{82} + 1194 q^{83} + 2520 q^{85} - 652 q^{86} - 72 q^{88} - 1038 q^{89} - 3080 q^{91} + 672 q^{92} - 276 q^{94} - 1560 q^{95} - 338 q^{97} - 1274 q^{98}+O(q^{100}) $ 2 * q - 2 * q^2 - 4 * q^4 - 15 * q^5 + 35 * q^7 + 16 * q^8 - 30 * q^10 - 9 * q^11 - 176 * q^13 - 56 * q^14 - 16 * q^16 - 84 * q^17 - 104 * q^19 + 120 * q^20 + 36 * q^22 - 84 * q^23 - 100 * q^25 + 176 * q^26 - 28 * q^28 - 102 * q^29 - 185 * q^31 - 32 * q^32 + 336 * q^34 - 420 * q^35 - 44 * q^37 - 208 * q^38 - 120 * q^40 + 336 * q^41 + 652 * q^43 - 36 * q^44 - 168 * q^46 - 138 * q^47 + 539 * q^49 + 400 * q^50 + 352 * q^52 + 639 * q^53 + 270 * q^55 + 280 * q^56 + 102 * q^58 + 159 * q^59 - 722 * q^61 + 740 * q^62 + 128 * q^64 + 1320 * q^65 + 166 * q^67 - 336 * q^68 - 210 * q^70 - 2172 * q^71 - 218 * q^73 - 88 * q^74 + 832 * q^76 - 63 * q^77 + 583 * q^79 - 240 * q^80 - 336 * q^82 + 1194 * q^83 + 2520 * q^85 - 652 * q^86 - 72 * q^88 - 1038 * q^89 - 3080 * q^91 + 672 * q^92 - 276 * q^94 - 1560 * q^95 - 338 * q^97 - 1274 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/126\mathbb{Z}\right)^\times$.

$n$	$29$	$73$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

Coefficient data

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

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

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

$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$2$	−1.00000	−	1.73205i	−0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	+	3.46410i	−0.250000	+	0.433013i
$5$	−7.50000	−	12.9904i	−0.670820	−	1.16190i	−0.977672	−	0.210138i	$-0.932609\pi$
$5$	−7.50000	−	12.9904i	−0.670820	−	1.16190i	0.306851	−	0.951757i	$-0.400725\pi$
$6$		0			0
$7$	17.5000	−	6.06218i	0.944911	−	0.327327i
$7$	17.5000	−	6.06218i	0.944911	−	0.327327i
$8$	8.00000			0.353553
$9$		0			0
$10$	−15.0000	+	25.9808i	−0.474342	+	0.821584i
$11$	−4.50000	+	7.79423i	−0.123346	+	0.213641i	−0.921085	−	0.389362i	$-0.872696\pi$
$11$	−4.50000	+	7.79423i	−0.123346	+	0.213641i	0.797739	+	0.603002i	$0.206029\pi$
$12$		0			0
$13$	−88.0000			−1.87745			−0.938723	−	0.344671i	$-0.887990\pi$
$13$	−88.0000			−1.87745			−0.938723	+	0.344671i	$0.887990\pi$
$14$	−28.0000	−	24.2487i	−0.534522	−	0.462910i
$15$		0			0
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	−42.0000	+	72.7461i	−0.599206	+	1.03785i	0.393733	+	0.919225i	$0.371183\pi$
$17$	−42.0000	+	72.7461i	−0.599206	+	1.03785i	−0.992939	+	0.118630i	$0.962150\pi$
$18$		0			0
$19$	−52.0000	−	90.0666i	−0.627875	−	1.08751i	−0.987977	−	0.154598i	$-0.950592\pi$
$19$	−52.0000	−	90.0666i	−0.627875	−	1.08751i	0.360103	−	0.932913i	$-0.382742\pi$
$20$	60.0000			0.670820
$21$		0			0
$22$	18.0000			0.174437
$23$	−42.0000	−	72.7461i	−0.380765	−	0.659505i	0.610406	−	0.792088i	$-0.291006\pi$
$23$	−42.0000	−	72.7461i	−0.380765	−	0.659505i	−0.991172	+	0.132583i	$0.957673\pi$
$24$		0			0
$25$	−50.0000	+	86.6025i	−0.400000	+	0.692820i
$26$	88.0000	+	152.420i	0.663778	+	1.14970i
$27$		0			0
$28$	−14.0000	+	72.7461i	−0.0944911	+	0.490990i
$29$	−51.0000			−0.326568			−0.163284	−	0.986579i	$-0.552209\pi$
$29$	−51.0000			−0.326568			−0.163284	+	0.986579i	$0.552209\pi$
$30$		0			0
$31$	−92.5000	+	160.215i	−0.535919	+	0.928239i	0.463199	+	0.886254i	$0.346701\pi$
$31$	−92.5000	+	160.215i	−0.535919	+	0.928239i	−0.999118	+	0.0419848i	$0.986632\pi$
$32$	−16.0000	+	27.7128i	−0.0883883	+	0.153093i
$33$		0			0
$34$	168.000			0.847405
$35$	−210.000	−	181.865i	−1.01419	−	0.878310i
$36$		0			0
$37$	−22.0000	−	38.1051i	−0.0977507	−	0.169309i	0.813003	−	0.582260i	$-0.197831\pi$
$37$	−22.0000	−	38.1051i	−0.0977507	−	0.169309i	−0.910753	+	0.412951i	$0.864498\pi$
$38$	−104.000	+	180.133i	−0.443974	+	0.768986i
$39$		0			0
$40$	−60.0000	−	103.923i	−0.237171	−	0.410792i
$41$	168.000			0.639932			0.319966	−	0.947429i	$-0.396329\pi$
$41$	168.000			0.639932			0.319966	+	0.947429i	$0.396329\pi$
$42$		0			0
$43$	326.000			1.15615			0.578076	−	0.815983i	$-0.303804\pi$
$43$	326.000			1.15615			0.578076	+	0.815983i	$0.303804\pi$
$44$	−18.0000	−	31.1769i	−0.0616728	−	0.106820i
$45$		0			0
$46$	−84.0000	+	145.492i	−0.269242	+	0.466341i
$47$	−69.0000	−	119.512i	−0.214142	−	0.370905i	0.738865	−	0.673854i	$-0.235362\pi$
$47$	−69.0000	−	119.512i	−0.214142	−	0.370905i	−0.953007	+	0.302949i	$0.902029\pi$
$48$		0			0
$49$	269.500	−	212.176i	0.785714	−	0.618590i
$50$	200.000			0.565685
$51$		0			0
$52$	176.000	−	304.841i	0.469362	−	0.812958i
$53$	319.500	−	553.390i	0.828051	−	1.43423i	−0.0715141	−	0.997440i	$-0.522783\pi$
$53$	319.500	−	553.390i	0.828051	−	1.43423i	0.899565	−	0.436787i	$-0.143884\pi$
$54$		0			0
$55$	135.000			0.330971
$56$	140.000	−	48.4974i	0.334077	−	0.115728i
$57$		0			0
$58$	51.0000	+	88.3346i	0.115459	+	0.199981i
$59$	79.5000	−	137.698i	0.175424	−	0.303843i	−0.764884	−	0.644168i	$-0.777204\pi$
$59$	79.5000	−	137.698i	0.175424	−	0.303843i	0.940308	+	0.340325i	$0.110537\pi$
$60$		0			0
$61$	−361.000	−	625.270i	−0.757726	−	1.31242i	−0.944007	−	0.329924i	$-0.892977\pi$
$61$	−361.000	−	625.270i	−0.757726	−	1.31242i	0.186281	−	0.982497i	$-0.440357\pi$
$62$	370.000			0.757904
$63$		0			0
$64$	64.0000			0.125000
$65$	660.000	+	1143.15i	1.25943	+	2.18140i
$66$		0			0
$67$	83.0000	−	143.760i	0.151344	−	0.262136i	−0.780378	−	0.625309i	$-0.784973\pi$
$67$	83.0000	−	143.760i	0.151344	−	0.262136i	0.931722	+	0.363173i	$0.118306\pi$
$68$	−168.000	−	290.985i	−0.299603	−	0.518927i
$69$		0			0
$70$	−105.000	+	545.596i	−0.179284	+	0.931589i
$71$	−1086.00			−1.81527			−0.907637	−	0.419755i	$-0.862116\pi$
$71$	−1086.00			−1.81527			−0.907637	+	0.419755i	$0.862116\pi$
$72$		0			0
$73$	−109.000	+	188.794i	−0.174760	+	0.302693i	−0.940078	−	0.340959i	$-0.889248\pi$
$73$	−109.000	+	188.794i	−0.174760	+	0.302693i	0.765318	+	0.643652i	$0.222582\pi$
$74$	−44.0000	+	76.2102i	−0.0691202	+	0.119720i
$75$		0			0
$76$	416.000			0.627875
$77$	−31.5000	+	163.679i	−0.0466202	+	0.242246i
$78$		0			0
$79$	291.500	+	504.893i	0.415143	+	0.719049i	0.995443	−	0.0953535i	$-0.0303981\pi$
$79$	291.500	+	504.893i	0.415143	+	0.719049i	−0.580300	+	0.814403i	$0.697065\pi$
$80$	−120.000	+	207.846i	−0.167705	+	0.290474i
$81$		0			0
$82$	−168.000	−	290.985i	−0.226250	−	0.391876i
$83$	597.000			0.789509			0.394755	−	0.918787i	$-0.370830\pi$
$83$	597.000			0.789509			0.394755	+	0.918787i	$0.370830\pi$
$84$		0			0
$85$	1260.00			1.60784
$86$	−326.000	−	564.649i	−0.408761	−	0.707996i
$87$		0			0
$88$	−36.0000	+	62.3538i	−0.0436092	+	0.0755334i
$89$	−519.000	−	898.934i	−0.618134	−	1.07064i	−0.989826	−	0.142283i	$-0.954556\pi$
$89$	−519.000	−	898.934i	−0.618134	−	1.07064i	0.371692	−	0.928356i	$-0.378778\pi$
$90$		0			0
$91$	−1540.00	+	533.472i	−1.77402	+	0.614539i
$92$	336.000			0.380765
$93$		0			0
$94$	−138.000	+	239.023i	−0.151421	+	0.262270i
$95$	−780.000	+	1351.00i	−0.842382	+	1.45905i
$96$		0			0
$97$	−169.000			−0.176901			−0.0884503	−	0.996081i	$-0.528191\pi$
$97$	−169.000			−0.176901			−0.0884503	+	0.996081i	$0.528191\pi$
$98$	−637.000	−	254.611i	−0.656599	−	0.262445i
$99$		0			0
$100$	−200.000	−	346.410i	−0.200000	−	0.346410i
$101$	321.000	−	555.988i	0.316244	−	0.547752i	−0.663457	−	0.748215i	$-0.730911\pi$
$101$	321.000	−	555.988i	0.316244	−	0.547752i	0.979701	+	0.200463i	$0.0642447\pi$
$102$		0			0
$103$	−232.000	−	401.836i	−0.221938	−	0.384408i	0.733458	−	0.679735i	$-0.237905\pi$
$103$	−232.000	−	401.836i	−0.221938	−	0.384408i	−0.955396	+	0.295326i	$0.904572\pi$
$104$	−704.000			−0.663778
$105$		0			0
$106$	−1278.00			−1.17104
$107$	196.500	+	340.348i	0.177536	+	0.307502i	0.941036	−	0.338306i	$-0.109854\pi$
$107$	196.500	+	340.348i	0.177536	+	0.307502i	−0.763500	+	0.645808i	$0.776521\pi$
$108$		0			0
$109$	−7.00000	+	12.1244i	−0.00615118	+	0.0106542i	−0.869085	−	0.494663i	$-0.835291\pi$
$109$	−7.00000	+	12.1244i	−0.00615118	+	0.0106542i	0.862933	+	0.505318i	$0.168625\pi$
$110$	−135.000	−	233.827i	−0.117016	−	0.202677i
$111$		0			0
$112$	−224.000	−	193.990i	−0.188982	−	0.163663i
$113$	2184.00			1.81817			0.909086	−	0.416608i	$-0.136781\pi$
$113$	2184.00			1.81817			0.909086	+	0.416608i	$0.136781\pi$
$114$		0			0
$115$	−630.000	+	1091.19i	−0.510850	+	0.884819i
$116$	102.000	−	176.669i	0.0816419	−	0.141408i
$117$		0			0
$118$	−318.000			−0.248087
$119$	−294.000	+	1527.67i	−0.226478	+	1.17682i
$120$		0			0
$121$	625.000	+	1082.53i	0.469572	+	0.813322i
$122$	−722.000	+	1250.54i	−0.535794	+	0.928022i
$123$		0			0
$124$	−370.000	−	640.859i	−0.267960	−	0.464120i
$125$	−375.000			−0.268328
$126$		0			0
$127$	−373.000			−0.260617			−0.130309	−	0.991473i	$-0.541597\pi$
$127$	−373.000			−0.260617			−0.130309	+	0.991473i	$0.541597\pi$
$128$	−64.0000	−	110.851i	−0.0441942	−	0.0765466i
$129$		0			0
$130$	1320.00	−	2286.31i	0.890551	−	1.54248i
$131$	−586.500	−	1015.85i	−0.391166	−	0.677519i	0.601438	−	0.798920i	$-0.294595\pi$
$131$	−586.500	−	1015.85i	−0.391166	−	0.677519i	−0.992604	+	0.121400i	$0.961261\pi$
$132$		0			0
$133$	−1456.00	−	1260.93i	−0.949257	−	0.822081i
$134$	−332.000			−0.214033
$135$		0			0
$136$	−336.000	+	581.969i	−0.211851	+	0.366937i
$137$	15.0000	−	25.9808i	0.00935428	−	0.0162021i	−0.861310	−	0.508079i	$-0.830356\pi$
$137$	15.0000	−	25.9808i	0.00935428	−	0.0162021i	0.870665	+	0.491877i	$0.163689\pi$
$138$		0			0
$139$	−82.0000			−0.0500370			−0.0250185	−	0.999687i	$-0.507964\pi$
$139$	−82.0000			−0.0500370			−0.0250185	+	0.999687i	$0.507964\pi$
$140$	1050.00	−	363.731i	0.633866	−	0.219578i
$141$		0			0
$142$	1086.00	+	1881.01i	0.641796	+	1.11162i
$143$	396.000	−	685.892i	0.231575	−	0.401099i
$144$		0			0
$145$	382.500	+	662.509i	0.219068	+	0.379437i
$146$	436.000			0.247148
$147$		0			0
$148$	176.000			0.0977507
$149$	−717.000	−	1241.88i	−0.394221	−	0.682811i	0.598780	−	0.800913i	$-0.295652\pi$
$149$	−717.000	−	1241.88i	−0.394221	−	0.682811i	−0.993001	+	0.118102i	$0.962319\pi$
$150$		0			0
$151$	1335.50	−	2313.15i	0.719745	−	1.24663i	−0.241356	−	0.970437i	$-0.577592\pi$
$151$	1335.50	−	2313.15i	0.719745	−	1.24663i	0.961101	−	0.276198i	$-0.0890745\pi$
$152$	−416.000	−	720.533i	−0.221987	−	0.384493i
$153$		0			0
$154$	315.000	−	109.119i	0.164827	−	0.0570979i
$155$	2775.00			1.43802
$156$		0			0
$157$	−1126.00	+	1950.29i	−0.572386	+	0.991401i	0.423934	+	0.905693i	$0.360649\pi$
$157$	−1126.00	+	1950.29i	−0.572386	+	0.991401i	−0.996320	+	0.0857085i	$0.972685\pi$
$158$	583.000	−	1009.79i	0.293551	−	0.508444i
$159$		0			0
$160$	480.000			0.237171
$161$	−1176.00	−	1018.45i	−0.575663	−	0.498539i
$162$		0			0
$163$	−838.000	−	1451.46i	−0.402682	−	0.697466i	0.591366	−	0.806403i	$-0.298589\pi$
$163$	−838.000	−	1451.46i	−0.402682	−	0.697466i	−0.994049	+	0.108937i	$0.965255\pi$
$164$	−336.000	+	581.969i	−0.159983	+	0.277098i
$165$		0			0
$166$	−597.000	−	1034.03i	−0.279134	−	0.483474i
$167$	−3030.00			−1.40400			−0.702001	−	0.712176i	$-0.747710\pi$
$167$	−3030.00			−1.40400			−0.702001	+	0.712176i	$0.747710\pi$
$168$		0			0
$169$	5547.00			2.52481
$170$	−1260.00	−	2182.38i	−0.568456	−	0.984595i
$171$		0			0
$172$	−652.000	+	1129.30i	−0.289038	+	0.500628i
$173$	1719.00	+	2977.40i	0.755452	+	1.30848i	0.945149	+	0.326638i	$0.105916\pi$
$173$	1719.00	+	2977.40i	0.755452	+	1.30848i	−0.189698	+	0.981843i	$0.560751\pi$
$174$		0			0
$175$	−350.000	+	1818.65i	−0.151186	+	0.785584i
$176$	144.000			0.0616728
$177$		0			0
$178$	−1038.00	+	1797.87i	−0.437086	+	0.757056i
$179$	−606.000	+	1049.62i	−0.253042	+	0.438282i	−0.964362	−	0.264587i	$-0.914765\pi$
$179$	−606.000	+	1049.62i	−0.253042	+	0.438282i	0.711320	+	0.702869i	$0.248098\pi$
$180$		0			0
$181$	3032.00			1.24512			0.622560	−	0.782572i	$-0.286093\pi$
$181$	3032.00			1.24512			0.622560	+	0.782572i	$0.286093\pi$
$182$	2464.00	+	2133.89i	1.00354	+	0.869089i
$183$		0			0
$184$	−336.000	−	581.969i	−0.134621	−	0.233170i
$185$	−330.000	+	571.577i	−0.131146	+	0.227152i
$186$		0			0
$187$	−378.000	−	654.715i	−0.147819	−	0.256030i
$188$	552.000			0.214142
$189$		0			0
$190$	3120.00			1.19131
$191$	1260.00	+	2182.38i	0.477332	+	0.826763i	0.999662	−	0.0259799i	$-0.00827060\pi$
$191$	1260.00	+	2182.38i	0.477332	+	0.826763i	−0.522331	+	0.852743i	$0.674937\pi$
$192$		0			0
$193$	−182.500	+	316.099i	−0.0680655	+	0.117893i	−0.898050	−	0.439894i	$-0.855016\pi$
$193$	−182.500	+	316.099i	−0.0680655	+	0.117893i	0.829984	+	0.557787i	$0.188349\pi$
$194$	169.000	+	292.717i	0.0625438	+	0.108329i
$195$		0			0
$196$	196.000	+	1357.93i	0.0714286	+	0.494872i
$197$	1590.00			0.575040			0.287520	−	0.957775i	$-0.407169\pi$
$197$	1590.00			0.575040			0.287520	+	0.957775i	$0.407169\pi$
$198$		0			0
$199$	2690.00	−	4659.22i	0.958236	−	1.65971i	0.231455	−	0.972846i	$-0.425652\pi$
$199$	2690.00	−	4659.22i	0.958236	−	1.65971i	0.726782	−	0.686868i	$-0.241015\pi$
$200$	−400.000	+	692.820i	−0.141421	+	0.244949i
$201$		0			0
$202$	−1284.00			−0.447237
$203$	−892.500	+	309.171i	−0.308577	+	0.106894i
$204$		0			0
$205$	−1260.00	−	2182.38i	−0.429279	−	0.743533i
$206$	−464.000	+	803.672i	−0.156934	+	0.271818i
$207$		0			0
$208$	704.000	+	1219.36i	0.234681	+	0.406479i
$209$	936.000			0.309782
$210$		0			0
$211$	−5362.00			−1.74946			−0.874728	−	0.484614i	$-0.838960\pi$
$211$	−5362.00			−1.74946			−0.874728	+	0.484614i	$0.838960\pi$
$212$	1278.00	+	2213.56i	0.414025	+	0.717113i
$213$		0			0
$214$	393.000	−	680.696i	0.125537	−	0.217437i
$215$	−2445.00	−	4234.86i	−0.775570	−	1.34333i
$216$		0			0
$217$	−647.500	+	3364.51i	−0.202558	+	1.05252i
$218$	28.0000			0.00869908
$219$		0			0
$220$	−270.000	+	467.654i	−0.0827427	+	0.143315i
$221$	3696.00	−	6401.66i	1.12498	−	1.94852i
$222$		0			0
$223$	−1573.00			−0.472358			−0.236179	−	0.971710i	$-0.575895\pi$
$223$	−1573.00			−0.472358			−0.236179	+	0.971710i	$0.575895\pi$
$224$	−112.000	+	581.969i	−0.0334077	+	0.173591i
$225$		0			0
$226$	−2184.00	−	3782.80i	−0.642821	−	1.11340i
$227$	460.500	−	797.609i	0.134645	−	0.233212i	−0.790817	−	0.612053i	$-0.790344\pi$
$227$	460.500	−	797.609i	0.134645	−	0.233212i	0.925462	+	0.378841i	$0.123677\pi$
$228$		0			0
$229$	−2026.00	−	3509.13i	−0.584637	−	1.01262i	−0.994921	−	0.100663i	$-0.967904\pi$
$229$	−2026.00	−	3509.13i	−0.584637	−	1.01262i	0.410284	−	0.911958i	$-0.365430\pi$
$230$	2520.00			0.722452
$231$		0			0
$232$	−408.000			−0.115459
$233$	−234.000	−	405.300i	−0.0657933	−	0.113957i	0.831252	−	0.555895i	$-0.187624\pi$
$233$	−234.000	−	405.300i	−0.0657933	−	0.113957i	−0.897046	+	0.441938i	$0.854291\pi$
$234$		0			0
$235$	−1035.00	+	1792.67i	−0.287302	+	0.497622i
$236$	318.000	+	550.792i	0.0877120	+	0.151922i
$237$		0			0
$238$	2940.00	−	1018.45i	0.800722	−	0.277378i
$239$	−4932.00			−1.33483			−0.667415	−	0.744686i	$-0.732599\pi$
$239$	−4932.00			−1.33483			−0.667415	+	0.744686i	$0.732599\pi$
$240$		0			0
$241$	768.500	−	1331.08i	0.205408	−	0.355778i	−0.744854	−	0.667227i	$-0.767481\pi$
$241$	768.500	−	1331.08i	0.205408	−	0.355778i	0.950263	+	0.311449i	$0.100814\pi$
$242$	1250.00	−	2165.06i	0.332037	−	0.575106i
$243$		0			0
$244$	2888.00			0.757726
$245$	−4777.50	−	1909.59i	−1.24581	−	0.497955i
$246$		0			0
$247$	4576.00	+	7925.86i	1.17880	+	2.04174i
$248$	−740.000	+	1281.72i	−0.189476	+	0.328182i
$249$		0			0
$250$	375.000	+	649.519i	0.0948683	+	0.164317i
$251$	−5319.00			−1.33758			−0.668789	−	0.743452i	$-0.733187\pi$
$251$	−5319.00			−1.33758			−0.668789	+	0.743452i	$0.733187\pi$
$252$		0			0
$253$	756.000			0.187863
$254$	373.000	+	646.055i	0.0921421	+	0.159595i
$255$		0			0
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	2673.00	+	4629.77i	0.648783	+	1.12372i	0.983414	+	0.181375i	$0.0580549\pi$
$257$	2673.00	+	4629.77i	0.648783	+	1.12372i	−0.334631	+	0.942349i	$0.608612\pi$
$258$		0			0
$259$	−616.000	−	533.472i	−0.147785	−	0.127986i
$260$	−5280.00			−1.25943
$261$		0			0
$262$	−1173.00	+	2031.70i	−0.276596	+	0.479079i
$263$	387.000	−	670.304i	0.0907355	−	0.157159i	−0.817085	−	0.576517i	$-0.804412\pi$
$263$	387.000	−	670.304i	0.0907355	−	0.157159i	0.907821	+	0.419358i	$0.137745\pi$
$264$		0			0
$265$	−9585.00			−2.22189
$266$	−728.000	+	3782.80i	−0.167807	+	0.871948i
$267$		0			0
$268$	332.000	+	575.041i	0.0756721	+	0.131068i
$269$	1207.50	−	2091.45i	0.273690	−	0.474045i	−0.696114	−	0.717931i	$-0.745089\pi$
$269$	1207.50	−	2091.45i	0.273690	−	0.474045i	0.969804	+	0.243887i	$0.0784225\pi$
$270$		0			0
$271$	237.500	+	411.362i	0.0532365	+	0.0922084i	0.891416	−	0.453187i	$-0.149713\pi$
$271$	237.500	+	411.362i	0.0532365	+	0.0922084i	−0.838179	+	0.545395i	$0.816380\pi$
$272$	1344.00			0.299603
$273$		0			0
$274$	−60.0000			−0.0132290
$275$	−450.000	−	779.423i	−0.0986764	−	0.170913i
$276$		0			0
$277$	−1864.00	+	3228.54i	−0.404321	+	0.700304i	−0.994242	−	0.107156i	$-0.965825\pi$
$277$	−1864.00	+	3228.54i	−0.404321	+	0.700304i	0.589921	+	0.807461i	$0.299159\pi$
$278$	82.0000	+	142.028i	0.0176908	+	0.0306413i
$279$		0			0
$280$	−1680.00	−	1454.92i	−0.358569	−	0.310530i
$281$	−1602.00			−0.340097			−0.170049	−	0.985436i	$-0.554392\pi$
$281$	−1602.00			−0.340097			−0.170049	+	0.985436i	$0.554392\pi$
$282$		0			0
$283$	−343.000	+	594.093i	−0.0720468	+	0.124789i	−0.899798	−	0.436306i	$-0.856286\pi$
$283$	−343.000	+	594.093i	−0.0720468	+	0.124789i	0.827751	+	0.561095i	$0.189620\pi$
$284$	2172.00	−	3762.01i	0.453819	−	0.786037i
$285$		0			0
$286$	−1584.00			−0.327496
$287$	2940.00	−	1018.45i	0.604678	−	0.209467i
$288$		0			0
$289$	−1071.50	−	1855.89i	−0.218095	−	0.377751i
$290$	765.000	−	1325.02i	0.154905	−	0.268303i
$291$		0			0
$292$	−436.000	−	755.174i	−0.0873800	−	0.151347i
$293$	1101.00			0.219526			0.109763	−	0.993958i	$-0.464991\pi$
$293$	1101.00			0.219526			0.109763	+	0.993958i	$0.464991\pi$
$294$		0			0
$295$	−2385.00			−0.470712
$296$	−176.000	−	304.841i	−0.0345601	−	0.0598599i
$297$		0			0
$298$	−1434.00	+	2483.76i	−0.278756	+	0.482820i
$299$	3696.00	+	6401.66i	0.714867	+	1.23819i
$300$		0			0
$301$	5705.00	−	1976.27i	1.09246	−	0.378440i
$302$	−5342.00			−1.01787
$303$		0			0
$304$	−832.000	+	1441.07i	−0.156969	+	0.271878i
$305$	−5415.00	+	9379.06i	−1.01660	+	1.76080i
$306$		0			0
$307$	2780.00			0.516818			0.258409	−	0.966036i	$-0.416802\pi$
$307$	2780.00			0.516818			0.258409	+	0.966036i	$0.416802\pi$
$308$	−504.000	−	436.477i	−0.0932405	−	0.0807486i
$309$		0			0
$310$	−2775.00	−	4806.44i	−0.508417	−	0.880605i
$311$	2148.00	−	3720.45i	0.391646	−	0.678351i	−0.601021	−	0.799233i	$-0.705239\pi$
$311$	2148.00	−	3720.45i	0.391646	−	0.678351i	0.992667	+	0.120883i	$0.0385725\pi$
$312$		0			0
$313$	−2744.50	−	4753.61i	−0.495618	−	0.858435i	0.504370	−	0.863488i	$-0.331725\pi$
$313$	−2744.50	−	4753.61i	−0.495618	−	0.858435i	−0.999987	+	0.00505298i	$0.998392\pi$
$314$	4504.00			0.809476
$315$		0			0
$316$	−2332.00			−0.415143
$317$	2245.50	+	3889.32i	0.397854	+	0.689104i	0.993461	−	0.114172i	$-0.0364216\pi$
$317$	2245.50	+	3889.32i	0.397854	+	0.689104i	−0.595607	+	0.803276i	$0.703088\pi$
$318$		0			0
$319$	229.500	−	397.506i	0.0402807	−	0.0697682i
$320$	−480.000	−	831.384i	−0.0838525	−	0.145237i
$321$		0			0
$322$	−588.000	+	3055.34i	−0.101764	+	0.528780i
$323$	8736.00			1.50490
$324$		0			0
$325$	4400.00	−	7621.02i	0.750979	−	1.30073i
$326$	−1676.00	+	2902.92i	−0.284739	+	0.493183i
$327$		0			0
$328$	1344.00			0.226250
$329$	−1932.00	−	1673.16i	−0.323753	−	0.280378i
$330$		0			0
$331$	1982.00	+	3432.92i	0.329126	+	0.570062i	0.982339	−	0.187112i	$-0.0599127\pi$
$331$	1982.00	+	3432.92i	0.329126	+	0.570062i	−0.653213	+	0.757174i	$0.726579\pi$
$332$	−1194.00	+	2068.07i	−0.197377	+	0.341868i
$333$		0			0
$334$	3030.00	+	5248.11i	0.496390	+	0.859773i
$335$	−2490.00			−0.406099
$336$		0			0
$337$	161.000			0.0260244			0.0130122	−	0.999915i	$-0.495858\pi$
$337$	161.000			0.0260244			0.0130122	+	0.999915i	$0.495858\pi$
$338$	−5547.00	−	9607.69i	−0.892654	−	1.54612i
$339$		0			0
$340$	−2520.00	+	4364.77i	−0.401959	+	0.696214i
$341$	−832.500	−	1441.93i	−0.132206	−	0.228988i
$342$		0			0
$343$	3430.00	−	5346.84i	0.539949	−	0.841698i
$344$	2608.00			0.408761
$345$		0			0
$346$	3438.00	−	5954.79i	0.534185	−	0.925236i
$347$	−2958.00	+	5123.41i	−0.457619	+	0.792619i	−0.998835	−	0.0482646i	$-0.984631\pi$
$347$	−2958.00	+	5123.41i	−0.457619	+	0.792619i	0.541216	+	0.840884i	$0.317964\pi$
$348$		0			0
$349$	−142.000			−0.0217796			−0.0108898	−	0.999941i	$-0.503466\pi$
$349$	−142.000			−0.0217796			−0.0108898	+	0.999941i	$0.503466\pi$
$350$	3500.00	−	1212.44i	0.534522	−	0.185164i
$351$		0			0
$352$	−144.000	−	249.415i	−0.0218046	−	0.0377667i
$353$	−2220.00	+	3845.15i	−0.334727	+	0.579764i	−0.983432	−	0.181275i	$-0.941977\pi$
$353$	−2220.00	+	3845.15i	−0.334727	+	0.579764i	0.648705	+	0.761040i	$0.275311\pi$
$354$		0			0
$355$	8145.00	+	14107.6i	1.21772	+	2.10916i
$356$	4152.00			0.618134
$357$		0			0
$358$	2424.00			0.357856
$359$	1143.00	+	1979.73i	0.168037	+	0.291048i	0.937730	−	0.347366i	$-0.112924\pi$
$359$	1143.00	+	1979.73i	0.168037	+	0.291048i	−0.769693	+	0.638415i	$0.779591\pi$
$360$		0			0
$361$	−1978.50	+	3426.86i	−0.288453	+	0.499615i
$362$	−3032.00	−	5251.58i	−0.440217	−	0.762477i
$363$		0			0
$364$	1232.00	−	6401.66i	0.177402	−	0.921808i
$365$	3270.00			0.468930
$366$		0			0
$367$	1434.50	−	2484.63i	0.204033	−	0.353396i	−0.745791	−	0.666180i	$-0.767928\pi$
$367$	1434.50	−	2484.63i	0.204033	−	0.353396i	0.949824	+	0.312784i	$0.101262\pi$
$368$	−672.000	+	1163.94i	−0.0951914	+	0.164876i
$369$		0			0
$370$	1320.00			0.185469
$371$	2236.50	−	11621.2i	0.312974	−	1.62626i
$372$		0			0
$373$	1532.00	+	2653.50i	0.212665	+	0.368346i	0.952548	−	0.304390i	$-0.0984524\pi$
$373$	1532.00	+	2653.50i	0.212665	+	0.368346i	−0.739883	+	0.672736i	$0.765119\pi$
$374$	−756.000	+	1309.43i	−0.104524	+	0.181040i
$375$		0			0
$376$	−552.000	−	956.092i	−0.0757107	−	0.131135i
$377$	4488.00			0.613113
$378$		0			0
$379$	−6040.00			−0.818612			−0.409306	−	0.912397i	$-0.634229\pi$
$379$	−6040.00			−0.818612			−0.409306	+	0.912397i	$0.634229\pi$
$380$	−3120.00	−	5404.00i	−0.421191	−	0.729524i
$381$		0			0
$382$	2520.00	−	4364.77i	0.337525	−	0.584610i
$383$	921.000	+	1595.22i	0.122874	+	0.212825i	0.920900	−	0.389799i	$-0.127455\pi$
$383$	921.000	+	1595.22i	0.122874	+	0.212825i	−0.798026	+	0.602623i	$0.794122\pi$
$384$		0			0
$385$	2362.50	−	818.394i	0.312738	−	0.108336i
$386$	730.000			0.0962591
$387$		0			0
$388$	338.000	−	585.433i	0.0442251	−	0.0766002i
$389$	3915.00	−	6780.98i	0.510279	−	0.883828i	−0.489650	−	0.871919i	$-0.662876\pi$
$389$	3915.00	−	6780.98i	0.510279	−	0.883828i	0.999929	−	0.0119097i	$-0.00379105\pi$
$390$		0			0
$391$	7056.00			0.912627
$392$	2156.00	−	1697.41i	0.277792	−	0.218704i
$393$		0			0
$394$	−1590.00	−	2753.96i	−0.203307	−	0.352138i
$395$	4372.50	−	7573.39i	0.556973	−	0.964706i
$396$		0			0
$397$	7382.00	+	12786.0i	0.933229	+	1.61640i	0.777762	+	0.628559i	$0.216355\pi$
$397$	7382.00	+	12786.0i	0.933229	+	1.61640i	0.155467	+	0.987841i	$0.450312\pi$
$398$	−10760.0			−1.35515
$399$		0			0
$400$	1600.00			0.200000
$401$	3132.00	+	5424.78i	0.390036	+	0.675563i	0.992454	−	0.122618i	$-0.0391291\pi$
$401$	3132.00	+	5424.78i	0.390036	+	0.675563i	−0.602417	+	0.798181i	$0.705796\pi$
$402$		0			0
$403$	8140.00	−	14098.9i	1.00616	−	1.74272i
$404$	1284.00	+	2223.95i	0.158122	+	0.273876i
$405$		0			0
$406$	1428.00	+	1236.68i	0.174558	+	0.151171i
$407$	396.000			0.0482285
$408$		0			0
$409$	−2375.50	+	4114.49i	−0.287191	+	0.497429i	−0.973138	−	0.230222i	$-0.926055\pi$
$409$	−2375.50	+	4114.49i	−0.287191	+	0.497429i	0.685948	+	0.727651i	$0.259388\pi$
$410$	−2520.00	+	4364.77i	−0.303546	+	0.525757i
$411$		0			0
$412$	1856.00			0.221938
$413$	556.500	−	2891.66i	0.0663041	−	0.344526i
$414$		0			0
$415$	−4477.50	−	7755.26i	−0.529619	−	0.917327i
$416$	1408.00	−	2438.73i	0.165944	−	0.287424i
$417$		0			0
$418$	−936.000	−	1621.20i	−0.109525	−	0.189702i
$419$	4704.00			0.548462			0.274231	−	0.961664i	$-0.411577\pi$
$419$	4704.00			0.548462			0.274231	+	0.961664i	$0.411577\pi$
$420$		0			0
$421$	−4474.00			−0.517932			−0.258966	−	0.965886i	$-0.583382\pi$
$421$	−4474.00			−0.517932			−0.258966	+	0.965886i	$0.583382\pi$
$422$	5362.00	+	9287.26i	0.618526	+	1.07132i
$423$		0			0
$424$	2556.00	−	4427.12i	0.292760	−	0.507076i
$425$	−4200.00	−	7274.61i	−0.479365	−	0.830284i
$426$		0			0
$427$	−10108.0	−	8753.78i	−1.14557	−	0.992097i
$428$	−1572.00			−0.177536
$429$		0			0
$430$	−4890.00	+	8469.73i	−0.548411	+	0.949876i
$431$	−6402.00	+	11088.6i	−0.715484	+	1.23925i	0.247289	+	0.968942i	$0.420460\pi$
$431$	−6402.00	+	11088.6i	−0.715484	+	1.23925i	−0.962773	+	0.270312i	$0.912873\pi$
$432$		0			0
$433$	−5074.00			−0.563143			−0.281571	−	0.959540i	$-0.590856\pi$
$433$	−5074.00			−0.563143			−0.281571	+	0.959540i	$0.590856\pi$
$434$	6475.00	−	2243.01i	0.716152	−	0.248082i
$435$		0			0
$436$	−28.0000	−	48.4974i	−0.00307559	−	0.00532708i
$437$	−4368.00	+	7565.60i	−0.478146	+	0.828173i
$438$		0			0
$439$	633.500	+	1097.25i	0.0688731	+	0.119292i	0.898406	−	0.439167i	$-0.144726\pi$
$439$	633.500	+	1097.25i	0.0688731	+	0.119292i	−0.829532	+	0.558459i	$0.811393\pi$
$440$	1080.00			0.117016
$441$		0			0
$442$	−14784.0			−1.59096
$443$	−3466.50	−	6004.15i	−0.371780	−	0.643941i	0.618060	−	0.786131i	$-0.287919\pi$
$443$	−3466.50	−	6004.15i	−0.371780	−	0.643941i	−0.989839	+	0.142190i	$0.954586\pi$
$444$		0			0
$445$	−7785.00	+	13484.0i	−0.829313	+	1.43641i
$446$	1573.00	+	2724.52i	0.167004	+	0.289259i
$447$		0			0
$448$	1120.00	−	387.979i	0.118114	−	0.0409159i
$449$	−11688.0			−1.22849			−0.614244	−	0.789116i	$-0.710539\pi$
$449$	−11688.0			−1.22849			−0.614244	+	0.789116i	$0.710539\pi$
$450$		0			0
$451$	−756.000	+	1309.43i	−0.0789327	+	0.136715i
$452$	−4368.00	+	7565.60i	−0.454543	+	0.787292i
$453$		0			0
$454$	−1842.00			−0.190417
$455$	18480.0	+	16004.1i	1.90408	+	1.64898i
$456$		0			0
$457$	−275.500	−	477.180i	−0.0281999	−	0.0488436i	0.851581	−	0.524223i	$-0.175644\pi$
$457$	−275.500	−	477.180i	−0.0281999	−	0.0488436i	−0.879781	+	0.475379i	$0.842311\pi$
$458$	−4052.00	+	7018.27i	−0.413401	+	0.716031i
$459$		0			0
$460$	−2520.00	−	4364.77i	−0.255425	−	0.442409i
$461$	−13386.0			−1.35238			−0.676191	−	0.736726i	$-0.736371\pi$
$461$	−13386.0			−1.35238			−0.676191	+	0.736726i	$0.736371\pi$
$462$		0			0
$463$	−6376.00			−0.639995			−0.319998	−	0.947418i	$-0.603682\pi$
$463$	−6376.00			−0.639995			−0.319998	+	0.947418i	$0.603682\pi$
$464$	408.000	+	706.677i	0.0408210	+	0.0707040i
$465$		0			0
$466$	−468.000	+	810.600i	−0.0465229	+	0.0805801i
$467$	2850.00	+	4936.34i	0.282403	+	0.489137i	0.971976	−	0.235080i	$-0.0755351\pi$
$467$	2850.00	+	4936.34i	0.282403	+	0.489137i	−0.689573	+	0.724216i	$0.742202\pi$
$468$		0			0
$469$	581.000	−	3018.96i	0.0572027	−	0.297234i
$470$	4140.00			0.406306
$471$		0			0
$472$	636.000	−	1101.58i	0.0620218	−	0.107425i
$473$	−1467.00	+	2540.92i	−0.142606	+	0.247001i
$474$		0			0
$475$	10400.0			1.00460
$476$	−4704.00	−	4073.78i	−0.452957	−	0.392272i
$477$		0			0
$478$	4932.00	+	8542.47i	0.471934	+	0.817414i
$479$	9897.00	−	17142.1i	0.944062	−	1.63516i	0.186442	−	0.982466i	$-0.440304\pi$
$479$	9897.00	−	17142.1i	0.944062	−	1.63516i	0.757619	−	0.652697i	$-0.226362\pi$
$480$		0			0
$481$	1936.00	+	3353.25i	0.183522	+	0.317869i
$482$	−3074.00			−0.290491
$483$		0			0
$484$	−5000.00			−0.469572
$485$	1267.50	+	2195.37i	0.118668	+	0.205540i
$486$		0			0
$487$	−7967.50	+	13800.1i	−0.741359	+	1.28407i	0.210517	+	0.977590i	$0.432485\pi$
$487$	−7967.50	+	13800.1i	−0.741359	+	1.28407i	−0.951877	+	0.306482i	$0.900848\pi$
$488$	−2888.00	−	5002.16i	−0.267897	−	0.464011i
$489$		0			0
$490$	1470.00	+	10184.5i	0.135526	+	0.938953i
$491$	−9963.00			−0.915731			−0.457865	−	0.889021i	$-0.651386\pi$
$491$	−9963.00			−0.915731			−0.457865	+	0.889021i	$0.651386\pi$
$492$		0			0
$493$	2142.00	−	3710.05i	0.195681	−	0.338930i
$494$	9152.00	−	15851.7i	0.833538	−	1.44373i
$495$		0			0
$496$	2960.00			0.267960
$497$	−19005.0	+	6583.53i	−1.71527	+	0.594188i
$498$		0			0
$499$	−9571.00	−	16577.5i	−0.858631	−	1.48719i	−0.873235	−	0.487299i	$-0.837982\pi$
$499$	−9571.00	−	16577.5i	−0.858631	−	1.48719i	0.0146043	−	0.999893i	$-0.495351\pi$
$500$	750.000	−	1299.04i	0.0670820	−	0.116190i
$501$		0			0
$502$	5319.00	+	9212.78i	0.472906	+	0.819096i
$503$	12192.0			1.08074			0.540372	−	0.841426i	$-0.318283\pi$
$503$	12192.0			1.08074			0.540372	+	0.841426i	$0.318283\pi$
$504$		0			0
$505$	−9630.00			−0.848573
$506$	−756.000	−	1309.43i	−0.0664196	−	0.115042i
$507$		0			0
$508$	746.000	−	1292.11i	0.0651543	−	0.112851i
$509$	−9904.50	−	17155.1i	−0.862494	−	1.49388i	−0.869515	−	0.493907i	$-0.835568\pi$
$509$	−9904.50	−	17155.1i	−0.862494	−	1.49388i	0.00702091	−	0.999975i	$-0.497765\pi$
$510$		0			0
$511$	−763.000	+	3964.66i	−0.0660531	+	0.343222i
$512$	512.000			0.0441942
$513$		0			0
$514$	5346.00	−	9259.54i	0.458759	−	0.794593i
$515$	−3480.00	+	6027.54i	−0.297761	+	0.515738i
$516$		0			0
$517$	1242.00			0.105654
$518$	−308.000	+	1600.41i	−0.0261250	+	0.135749i
$519$		0			0
$520$	5280.00	+	9145.23i	0.445276	+	0.771240i
$521$	−897.000	+	1553.65i	−0.0754286	+	0.130646i	−0.901273	−	0.433253i	$-0.857366\pi$
$521$	−897.000	+	1553.65i	−0.0754286	+	0.130646i	0.825844	+	0.563899i	$0.190699\pi$
$522$		0			0
$523$	3224.00	+	5584.13i	0.269552	+	0.466878i	0.968746	−	0.248054i	$-0.0797911\pi$
$523$	3224.00	+	5584.13i	0.269552	+	0.466878i	−0.699194	+	0.714932i	$0.746458\pi$
$524$	4692.00			0.391166
$525$		0			0
$526$	−1548.00			−0.128319
$527$	−7770.00	−	13458.0i	−0.642251	−	1.11241i
$528$		0			0
$529$	2555.50	−	4426.26i	0.210035	−	0.363792i
$530$	9585.00	+	16601.7i	0.785558	+	1.36063i
$531$		0			0
$532$	7280.00	−	2521.87i	0.593286	−	0.205520i
$533$	−14784.0			−1.20144
$534$		0			0
$535$	2947.50	−	5105.22i	0.238190	−	0.412557i
$536$	664.000	−	1150.08i	0.0535083	−	0.0926790i
$537$		0			0
$538$	−4830.00			−0.387056
$539$	441.000	+	3055.34i	0.0352416	+	0.244161i
$540$		0			0
$541$	−3631.00	−	6289.08i	−0.288556	−	0.499794i	0.684909	−	0.728628i	$-0.259842\pi$
$541$	−3631.00	−	6289.08i	−0.288556	−	0.499794i	−0.973465	+	0.228835i	$0.926509\pi$
$542$	475.000	−	822.724i	0.0376439	−	0.0652012i
$543$		0			0
$544$	−1344.00	−	2327.88i	−0.105926	−	0.183469i
$545$	210.000			0.0165053
$546$		0			0
$547$	14204.0			1.11027			0.555136	−	0.831759i	$-0.312666\pi$
$547$	14204.0			1.11027			0.555136	+	0.831759i	$0.312666\pi$
$548$	60.0000	+	103.923i	0.00467714	+	0.00810104i
$549$		0			0
$550$	−900.000	+	1558.85i	−0.0697748	+	0.120853i
$551$	2652.00	+	4593.40i	0.205044	+	0.355146i
$552$		0			0
$553$	8162.00	+	7068.50i	0.627638	+	0.543550i
$554$	7456.00			0.571796
$555$		0			0
$556$	164.000	−	284.056i	0.0125093	−	0.0216667i
$557$	7912.50	−	13704.9i	0.601909	−	1.04254i	−0.390623	−	0.920551i	$-0.627740\pi$
$557$	7912.50	−	13704.9i	0.601909	−	1.04254i	0.992532	−	0.121986i	$-0.0389264\pi$
$558$		0			0
$559$	−28688.0			−2.17061
$560$	−840.000	+	4364.77i	−0.0633866	+	0.329366i
$561$		0			0
$562$	1602.00	+	2774.75i	0.120243	+	0.208266i
$563$	529.500	−	917.121i	0.0396372	−	0.0686537i	−0.845526	−	0.533934i	$-0.820713\pi$
$563$	529.500	−	917.121i	0.0396372	−	0.0686537i	0.885163	+	0.465280i	$0.154046\pi$
$564$		0			0
$565$	−16380.0	−	28371.0i	−1.21967	−	2.11252i
$566$	1372.00			0.101890
$567$		0			0
$568$	−8688.00			−0.641796
$569$	1980.00	+	3429.46i	0.145880	+	0.252672i	0.929701	−	0.368315i	$-0.120065\pi$
$569$	1980.00	+	3429.46i	0.145880	+	0.252672i	−0.783821	+	0.620987i	$0.786732\pi$
$570$		0			0
$571$	1265.00	−	2191.04i	0.0927121	−	0.160582i	−0.815939	−	0.578138i	$-0.803780\pi$
$571$	1265.00	−	2191.04i	0.0927121	−	0.160582i	0.908651	+	0.417555i	$0.137113\pi$
$572$	1584.00	+	2743.57i	0.115787	+	0.200550i
$573$		0			0
$574$	−4704.00	−	4073.78i	−0.342058	−	0.296231i
$575$	8400.00			0.609225
$576$		0			0
$577$	−5915.50	+	10245.9i	−0.426803	+	0.739245i	−0.996587	−	0.0825498i	$-0.973694\pi$
$577$	−5915.50	+	10245.9i	−0.426803	+	0.739245i	0.569784	+	0.821795i	$0.307027\pi$
$578$	−2143.00	+	3711.78i	−0.154216	+	0.267111i
$579$		0			0
$580$	−3060.00			−0.219068
$581$	10447.5	−	3619.12i	0.746016	−	0.258428i
$582$		0			0
$583$	2875.50	+	4980.51i	0.204273	+	0.353811i
$584$	−872.000	+	1510.35i	−0.0617870	+	0.107018i
$585$		0			0
$586$	−1101.00	−	1906.99i	−0.0776141	−	0.134432i
$587$	−4809.00			−0.338141			−0.169070	−	0.985604i	$-0.554077\pi$
$587$	−4809.00			−0.338141			−0.169070	+	0.985604i	$0.554077\pi$
$588$		0			0
$589$	19240.0			1.34596
$590$	2385.00	+	4130.94i	0.166422	+	0.288251i
$591$		0			0
$592$	−352.000	+	609.682i	−0.0244377	+	0.0423273i
$593$	10902.0	+	18882.8i	0.754960	+	1.30763i	0.945394	+	0.325930i	$0.105677\pi$
$593$	10902.0	+	18882.8i	0.754960	+	1.30763i	−0.190434	+	0.981700i	$0.560989\pi$
$594$		0			0
$595$	22050.0	−	7638.34i	1.51926	−	0.526288i
$596$	5736.00			0.394221
$597$		0			0
$598$	7392.00	−	12803.3i	0.505487	−	0.875530i
$599$	7083.00	−	12268.1i	0.483144	−	0.836831i	−0.516668	−	0.856186i	$-0.672828\pi$
$599$	7083.00	−	12268.1i	0.483144	−	0.836831i	0.999813	+	0.0193549i	$0.00616125\pi$
$600$		0			0
$601$	5891.00			0.399832			0.199916	−	0.979813i	$-0.435933\pi$
$601$	5891.00			0.399832			0.199916	+	0.979813i	$0.435933\pi$
$602$	−9128.00	−	7905.08i	−0.617989	−	0.535194i
$603$		0			0
$604$	5342.00	+	9252.62i	0.359872	+	0.623317i
$605$	9375.00	−	16238.0i	0.629997	−	1.09119i
$606$		0			0
$607$	1368.50	+	2370.31i	0.0915086	+	0.158497i	0.908146	−	0.418653i	$-0.137498\pi$
$607$	1368.50	+	2370.31i	0.0915086	+	0.158497i	−0.816638	+	0.577151i	$0.804164\pi$
$608$	3328.00			0.221987
$609$		0			0
$610$	21660.0			1.43768
$611$	6072.00	+	10517.0i	0.402041	+	0.696355i
$612$		0			0
$613$	13094.0	−	22679.5i	0.862743	−	1.49432i	−0.00652719	−	0.999979i	$-0.502078\pi$
$613$	13094.0	−	22679.5i	0.862743	−	1.49432i	0.869271	−	0.494337i	$-0.164589\pi$
$614$	−2780.00	−	4815.10i	−0.182723	−	0.316485i
$615$		0			0
$616$	−252.000	+	1309.43i	−0.0164827	+	0.0856468i
$617$	2358.00			0.153857			0.0769283	−	0.997037i	$-0.475489\pi$
$617$	2358.00			0.153857			0.0769283	+	0.997037i	$0.475489\pi$
$618$		0			0
$619$	−6883.00	+	11921.7i	−0.446932	+	0.774110i	−0.998185	−	0.0602291i	$-0.980817\pi$
$619$	−6883.00	+	11921.7i	−0.446932	+	0.774110i	0.551252	+	0.834339i	$0.314150\pi$
$620$	−5550.00	+	9612.88i	−0.359505	+	0.622682i
$621$		0			0
$622$	−8592.00			−0.553871
$623$	−14532.0	−	12585.1i	−0.934530	−	0.809327i
$624$		0			0
$625$	9062.50	+	15696.7i	0.580000	+	1.00459i
$626$	−5489.00	+	9507.23i	−0.350455	+	0.607005i
$627$		0			0
$628$	−4504.00	−	7801.16i	−0.286193	−	0.495701i
$629$	3696.00			0.234291
$630$		0			0
$631$	21287.0			1.34298			0.671491	−	0.741012i	$-0.265654\pi$
$631$	21287.0			1.34298			0.671491	+	0.741012i	$0.265654\pi$
$632$	2332.00	+	4039.14i	0.146775	+	0.254222i
$633$		0			0
$634$	4491.00	−	7778.64i	0.281326	−	0.487270i
$635$	2797.50	+	4845.41i	0.174827	+	0.302810i
$636$		0			0
$637$	−23716.0	+	18671.5i	−1.47514	+	1.16137i
$638$	−918.000			−0.0569655
$639$		0			0
$640$	−960.000	+	1662.77i	−0.0592927	+	0.102698i
$641$	10713.0	−	18555.5i	0.660122	−	1.14336i	−0.320462	−	0.947262i	$-0.603838\pi$
$641$	10713.0	−	18555.5i	0.660122	−	1.14336i	0.980583	−	0.196103i	$-0.0628287\pi$
$642$		0			0
$643$	9962.00			0.610984			0.305492	−	0.952195i	$-0.401179\pi$
$643$	9962.00			0.610984			0.305492	+	0.952195i	$0.401179\pi$
$644$	5880.00	−	2036.89i	0.359790	−	0.124635i
$645$		0			0
$646$	−8736.00	−	15131.2i	−0.532064	−	0.921562i
$647$	−9087.00	+	15739.1i	−0.552159	+	0.956367i	0.445960	+	0.895053i	$0.352863\pi$
$647$	−9087.00	+	15739.1i	−0.552159	+	0.956367i	−0.998119	+	0.0613142i	$0.980471\pi$
$648$		0			0
$649$	715.500	+	1239.28i	0.0432755	+	0.0749555i
$650$	−17600.0			−1.06204
$651$		0			0
$652$	6704.00			0.402682
$653$	−9583.50	−	16599.1i	−0.574321	−	0.994752i	−0.996115	−	0.0880610i	$-0.971933\pi$
$653$	−9583.50	−	16599.1i	−0.574321	−	0.994752i	0.421795	−	0.906691i	$-0.361400\pi$
$654$		0			0
$655$	−8797.50	+	15237.7i	−0.524804	+	0.908988i
$656$	−1344.00	−	2327.88i	−0.0799914	−	0.138549i
$657$		0			0
$658$	−966.000	+	5019.48i	−0.0572319	+	0.297386i
$659$	−13080.0			−0.773178			−0.386589	−	0.922252i	$-0.626347\pi$
$659$	−13080.0			−0.773178			−0.386589	+	0.922252i	$0.626347\pi$
$660$		0			0
$661$	7595.00	−	13154.9i	0.446916	−	0.774081i	−0.551268	−	0.834328i	$-0.685856\pi$
$661$	7595.00	−	13154.9i	0.446916	−	0.774081i	0.998183	+	0.0602477i	$0.0191891\pi$
$662$	3964.00	−	6865.85i	0.232727	−	0.403095i
$663$		0			0
$664$	4776.00			0.279134
$665$	−5460.00	+	28371.0i	−0.318391	+	1.65441i
$666$		0			0
$667$	2142.00	+	3710.05i	0.124346	+	0.215373i
$668$	6060.00	−	10496.2i	0.351001	−	0.607951i
$669$		0			0
$670$	2490.00	+	4312.81i	0.143578	+	0.248684i
$671$	6498.00			0.373849
$672$		0			0
$673$	4397.00			0.251845			0.125923	−	0.992040i	$-0.459811\pi$
$673$	4397.00			0.251845			0.125923	+	0.992040i	$0.459811\pi$
$674$	−161.000	−	278.860i	−0.00920102	−	0.0159366i
$675$		0			0
$676$	−11094.0	+	19215.4i	−0.631202	+	1.09327i
$677$	2014.50	+	3489.22i	0.114363	+	0.198082i	0.917525	−	0.397679i	$-0.130184\pi$
$677$	2014.50	+	3489.22i	0.114363	+	0.198082i	−0.803162	+	0.595761i	$0.796851\pi$
$678$		0			0
$679$	−2957.50	+	1024.51i	−0.167155	+	0.0579043i
$680$	10080.0			0.568456
$681$		0			0
$682$	−1665.00	+	2883.86i	−0.0934841	+	0.161919i
$683$	7510.50	−	13008.6i	0.420763	−	0.728783i	−0.575251	−	0.817977i	$-0.695096\pi$
$683$	7510.50	−	13008.6i	0.420763	−	0.728783i	0.996014	+	0.0891936i	$0.0284290\pi$
$684$		0			0
$685$	−450.000			−0.0251002
$686$	−12691.0	−	594.093i	−0.706333	−	0.0330650i
$687$		0			0
$688$	−2608.00	−	4517.19i	−0.144519	−	0.250314i
$689$	−28116.0	+	48698.3i	−1.55462	+	2.69268i
$690$		0			0
$691$	6992.00	+	12110.5i	0.384932	+	0.666722i	0.991760	−	0.128111i	$-0.0408915\pi$
$691$	6992.00	+	12110.5i	0.384932	+	0.666722i	−0.606828	+	0.794834i	$0.707558\pi$
$692$	−13752.0			−0.755452
$693$		0			0
$694$	11832.0			0.647171
$695$	615.000	+	1065.21i	0.0335659	+	0.0581378i
$696$		0			0
$697$	−7056.00	+	12221.4i	−0.383451	+	0.664156i
$698$	142.000	+	245.951i	0.00770026	+	0.0133372i
$699$		0			0
$700$	−5600.00	−	4849.74i	−0.302372	−	0.261861i
$701$	31053.0			1.67312			0.836559	−	0.547877i	$-0.184564\pi$
$701$	31053.0			1.67312			0.836559	+	0.547877i	$0.184564\pi$
$702$		0			0
$703$	−2288.00	+	3962.93i	−0.122750	+	0.212610i
$704$	−288.000	+	498.831i	−0.0154182	+	0.0267051i
$705$		0			0
$706$	8880.00			0.473376
$707$	2247.00	−	11675.8i	0.119529	−	0.621092i
$708$		0			0
$709$	−7543.00	−	13064.9i	−0.399553	−	0.692047i	0.594117	−	0.804378i	$-0.297501\pi$
$709$	−7543.00	−	13064.9i	−0.399553	−	0.692047i	−0.993671	+	0.112332i	$0.964168\pi$
$710$	16290.0	−	28215.1i	0.861060	−	1.49140i
$711$		0			0
$712$	−4152.00	−	7191.47i	−0.218543	−	0.378528i
$713$	15540.0			0.816238
$714$		0			0
$715$	−11880.0			−0.621380
$716$	−2424.00	−	4198.49i	−0.126521	−	0.219141i
$717$		0			0
$718$	2286.00	−	3959.47i	0.118820	−	0.205802i
$719$	−3189.00	−	5523.51i	−0.165410	−	0.286498i	0.771391	−	0.636362i	$-0.219561\pi$
$719$	−3189.00	−	5523.51i	−0.165410	−	0.286498i	−0.936801	+	0.349863i	$0.886228\pi$
$720$		0			0
$721$	−6496.00	−	5625.70i	−0.335539	−	0.290585i
$722$	7914.00			0.407934
$723$		0			0
$724$	−6064.00	+	10503.2i	−0.311280	+	0.539153i
$725$	2550.00	−	4416.73i	0.130627	−	0.226253i
$726$		0			0
$727$	−7363.00			−0.375624			−0.187812	−	0.982205i	$-0.560140\pi$
$727$	−7363.00			−0.375624			−0.187812	+	0.982205i	$0.560140\pi$
$728$	−12320.0	+	4267.77i	−0.627211	+	0.217272i
$729$		0			0
$730$	−3270.00	−	5663.81i	−0.165792	−	0.287160i
$731$	−13692.0	+	23715.2i	−0.692773	+	1.19992i
$732$		0			0
$733$	−16405.0	−	28414.3i	−0.826647	−	1.43180i	−0.900654	−	0.434537i	$-0.856912\pi$
$733$	−16405.0	−	28414.3i	−0.826647	−	1.43180i	0.0740064	−	0.997258i	$-0.476421\pi$
$734$	−5738.00			−0.288547
$735$		0			0
$736$	2688.00			0.134621
$737$	747.000	+	1293.84i	0.0373353	+	0.0646666i
$738$		0			0
$739$	12017.0	−	20814.1i	0.598177	−	1.03607i	−0.394914	−	0.918718i	$-0.629225\pi$
$739$	12017.0	−	20814.1i	0.598177	−	1.03607i	0.993090	−	0.117354i	$-0.0374412\pi$
$740$	−1320.00	−	2286.31i	−0.0655732	−	0.113576i
$741$		0			0
$742$	−22365.0	+	7747.46i	−1.10653	+	0.383313i
$743$	8022.00			0.396095			0.198048	−	0.980192i	$-0.436540\pi$
$743$	8022.00			0.396095			0.198048	+	0.980192i	$0.436540\pi$
$744$		0			0
$745$	−10755.0	+	18628.2i	−0.528903	+	0.916087i
$746$	3064.00	−	5307.00i	0.150377	−	0.260460i
$747$		0			0
$748$	3024.00			0.147819
$749$	5502.00	+	4764.87i	0.268409	+	0.232449i
$750$		0			0
$751$	−14759.5	−	25564.2i	−0.717153	−	1.24215i	−0.962123	−	0.272615i	$-0.912112\pi$
$751$	−14759.5	−	25564.2i	−0.717153	−	1.24215i	0.244970	−	0.969531i	$-0.421222\pi$
$752$	−1104.00	+	1912.18i	−0.0535356	+	0.0927263i
$753$		0			0
$754$	−4488.00	−	7773.44i	−0.216768	−	0.375454i
$755$	−40065.0			−1.93128
$756$		0			0
$757$	−3742.00			−0.179664			−0.0898318	−	0.995957i	$-0.528633\pi$
$757$	−3742.00			−0.179664			−0.0898318	+	0.995957i	$0.528633\pi$
$758$	6040.00	+	10461.6i	0.289423	+	0.501295i
$759$		0			0
$760$	−6240.00	+	10808.0i	−0.297827	+	0.515852i
$761$	−5448.00	−	9436.21i	−0.259514	−	0.449491i	0.706598	−	0.707615i	$-0.250229\pi$
$761$	−5448.00	−	9436.21i	−0.259514	−	0.449491i	−0.966112	+	0.258124i	$0.916896\pi$
$762$		0			0
$763$	−49.0000	+	254.611i	−0.00232493	+	0.0120807i
$764$	−10080.0			−0.477332
$765$		0			0
$766$	1842.00	−	3190.44i	0.0868853	−	0.150490i
$767$	−6996.00	+	12117.4i	−0.329349	+	0.570450i
$768$		0			0
$769$	17285.0			0.810550			0.405275	−	0.914195i	$-0.367176\pi$
$769$	17285.0			0.810550			0.405275	+	0.914195i	$0.367176\pi$
$770$	−3780.00	−	3273.58i	−0.176911	−	0.153210i
$771$		0			0
$772$	−730.000	−	1264.40i	−0.0340327	−	0.0589464i
$773$	5913.00	−	10241.6i	0.275130	−	0.476540i	−0.695038	−	0.718973i	$-0.744612\pi$
$773$	5913.00	−	10241.6i	0.275130	−	0.476540i	0.970168	+	0.242434i	$0.0779456\pi$
$774$		0			0
$775$	−9250.00	−	16021.5i	−0.428735	−	0.742591i
$776$	−1352.00			−0.0625438
$777$		0			0
$778$	−15660.0			−0.721643
$779$	−8736.00	−	15131.2i	−0.401797	−	0.695932i
$780$		0			0
$781$	4887.00	−	8464.53i	0.223906	−	0.387817i
$782$	−7056.00	−	12221.4i	−0.322662	−	0.558868i
$783$		0			0
$784$	−5096.00	−	2036.89i	−0.232143	−	0.0927884i
$785$	33780.0			1.53587
$786$		0			0
$787$	−8857.00	+	15340.8i	−0.401166	+	0.694841i	−0.993867	−	0.110582i	$-0.964728\pi$
$787$	−8857.00	+	15340.8i	−0.401166	+	0.694841i	0.592701	+	0.805423i	$0.298062\pi$
$788$	−3180.00	+	5507.92i	−0.143760	+	0.248999i
$789$		0			0
$790$	−17490.0			−0.787679
$791$	38220.0	−	13239.8i	1.71801	−	0.595136i
$792$		0			0
$793$	31768.0	+	55023.8i	1.42259	+	2.46400i
$794$	14764.0	−	25572.0i	0.659893	−	1.14297i
$795$		0			0
$796$	10760.0	+	18636.9i	0.479118	+	0.829857i
$797$	24939.0			1.10839			0.554194	−	0.832388i	$-0.313027\pi$
$797$	24939.0			1.10839			0.554194	+	0.832388i	$0.313027\pi$
$798$		0			0
$799$	11592.0			0.513261
$800$	−1600.00	−	2771.28i	−0.0707107	−	0.122474i
$801$		0			0
$802$	6264.00	−	10849.6i	0.275797	−	0.477695i
$803$	−981.000	−	1699.14i	−0.0431118	−	0.0746717i
$804$		0			0
$805$	−4410.00	+	22915.0i	−0.193083	+	1.00329i
$806$	−32560.0			−1.42292
$807$		0			0
$808$	2568.00	−	4447.91i	0.111809	−	0.193659i
$809$	−14532.0	+	25170.2i	−0.631543	+	1.09386i	0.355694	+	0.934602i	$0.384245\pi$
$809$	−14532.0	+	25170.2i	−0.631543	+	1.09386i	−0.987236	+	0.159261i	$0.949089\pi$
$810$		0			0
$811$	−15370.0			−0.665492			−0.332746	−	0.943017i	$-0.607975\pi$
$811$	−15370.0			−0.665492			−0.332746	+	0.943017i	$0.607975\pi$
$812$	714.000	−	3710.05i	0.0308577	−	0.160342i
$813$		0			0
$814$	−396.000	−	685.892i	−0.0170513	−	0.0295338i
$815$	−12570.0	+	21771.9i	−0.540255	+	0.935749i
$816$		0			0
$817$	−16952.0	−	29361.7i	−0.725918	−	1.25733i
$818$	9502.00			0.406149
$819$		0			0
$820$	10080.0			0.429279
$821$	22015.5	+	38132.0i	0.935866	+	1.62097i	0.773082	+	0.634306i	$0.218714\pi$
$821$	22015.5	+	38132.0i	0.935866	+	1.62097i	0.162785	+	0.986662i	$0.447952\pi$
$822$		0			0
$823$	2096.00	−	3630.38i	0.0887752	−	0.153763i	−0.818218	−	0.574907i	$-0.805038\pi$
$823$	2096.00	−	3630.38i	0.0887752	−	0.153763i	0.906994	+	0.421144i	$0.138371\pi$
$824$	−1856.00	−	3214.69i	−0.0784670	−	0.135909i
$825$		0			0
$826$	−5565.00	+	1927.77i	−0.234420	+	0.0812056i
$827$	−33195.0			−1.39577			−0.697886	−	0.716209i	$-0.745876\pi$
$827$	−33195.0			−1.39577			−0.697886	+	0.716209i	$0.745876\pi$
$828$		0			0
$829$	−8224.00	+	14244.4i	−0.344549	+	0.596777i	−0.985272	−	0.170996i	$-0.945302\pi$
$829$	−8224.00	+	14244.4i	−0.344549	+	0.596777i	0.640723	+	0.767773i	$0.278635\pi$
$830$	−8955.00	+	15510.5i	−0.374497	+	0.648648i
$831$		0			0
$832$	−5632.00			−0.234681
$833$	4116.00	+	28516.5i	0.171202	+	1.18612i
$834$		0			0
$835$	22725.0	+	39360.9i	0.941834	+	1.63130i
$836$	−1872.00	+	3242.40i	−0.0774455	+	0.134140i
$837$		0			0
$838$	−4704.00	−	8147.57i	−0.193910	−	0.335863i
$839$	−16860.0			−0.693769			−0.346884	−	0.937908i	$-0.612760\pi$
$839$	−16860.0			−0.693769			−0.346884	+	0.937908i	$0.612760\pi$
$840$		0			0
$841$	−21788.0			−0.893354
$842$	4474.00	+	7749.20i	0.183117	+	0.317167i
$843$		0			0
$844$	10724.0	−	18574.5i	0.437364	−	0.757537i
$845$	−41602.5	−	72057.6i	−1.69369	−	2.93356i
$846$		0			0
$847$	17500.0	+	15155.4i	0.709926	+	0.614814i
$848$	−10224.0			−0.414025
$849$		0			0
$850$	−8400.00	+	14549.2i	−0.338962	+	0.587099i
$851$	−1848.00	+	3200.83i	−0.0744402	+	0.128934i
$852$		0			0
$853$	29054.0			1.16623			0.583113	−	0.812391i	$-0.301835\pi$
$853$	29054.0			1.16623			0.583113	+	0.812391i	$0.301835\pi$
$854$	−5054.00	+	26261.4i	−0.202511	+	1.05228i
$855$		0			0
$856$	1572.00	+	2722.78i	0.0627685	+	0.108718i
$857$	20979.0	−	36336.7i	0.836207	−	1.44835i	−0.0568378	−	0.998383i	$-0.518102\pi$
$857$	20979.0	−	36336.7i	0.836207	−	1.44835i	0.893044	−	0.449969i	$-0.148565\pi$
$858$		0			0
$859$	−2773.00	−	4802.98i	−0.110144	−	0.190775i	0.805684	−	0.592345i	$-0.201798\pi$
$859$	−2773.00	−	4802.98i	−0.110144	−	0.190775i	−0.915828	+	0.401570i	$0.868464\pi$
$860$	19560.0			0.775570
$861$		0			0
$862$	25608.0			1.01185
$863$	−16269.0	−	28178.7i	−0.641719	−	1.11149i	−0.985049	−	0.172275i	$-0.944888\pi$
$863$	−16269.0	−	28178.7i	−0.641719	−	1.11149i	0.343330	−	0.939215i	$-0.388445\pi$
$864$		0			0
$865$	25785.0	−	44660.9i	1.01354	−	1.75551i
$866$	5074.00	+	8788.43i	0.199101	+	0.344853i
$867$		0			0
$868$	−10360.0	−	8972.02i	−0.405117	−	0.350841i
$869$	−5247.00			−0.204824
$870$		0			0
$871$	−7304.00	+	12650.9i	−0.284141	+	0.492146i
$872$	−56.0000	+	96.9948i	−0.00217477	+	0.00376681i
$873$		0			0
$874$	17472.0			0.676200
$875$	−6562.50	+	2273.32i	−0.253546	+	0.0878310i
$876$		0			0
$877$	−16048.0	−	27796.0i	−0.617905	−	1.07024i	−0.989867	−	0.141995i	$-0.954648\pi$
$877$	−16048.0	−	27796.0i	−0.617905	−	1.07024i	0.371963	−	0.928248i	$-0.378685\pi$
$878$	1267.00	−	2194.51i	0.0487007	−	0.0843520i
$879$		0			0
$880$	−1080.00	−	1870.61i	−0.0413714	−	0.0716573i
$881$	8490.00			0.324671			0.162336	−	0.986736i	$-0.448097\pi$
$881$	8490.00			0.324671			0.162336	+	0.986736i	$0.448097\pi$
$882$		0			0
$883$	−48352.0			−1.84278			−0.921390	−	0.388640i	$-0.872945\pi$
$883$	−48352.0			−1.84278			−0.921390	+	0.388640i	$0.872945\pi$
$884$	14784.0	+	25606.6i	0.562488	+	0.974258i
$885$		0			0
$886$	−6933.00	+	12008.3i	−0.262888	+	0.455335i
$887$	7746.00	+	13416.5i	0.293219	+	0.507870i	0.974569	−	0.224088i	$-0.0719402\pi$
$887$	7746.00	+	13416.5i	0.293219	+	0.507870i	−0.681350	+	0.731958i	$0.738607\pi$
$888$		0			0
$889$	−6527.50	+	2261.19i	−0.246260	+	0.0853070i
$890$	31140.0			1.17283
$891$		0			0
$892$	3146.00	−	5449.03i	0.118090	−	0.204537i
$893$	−7176.00	+	12429.2i	−0.268909	+	0.465764i
$894$		0			0
$895$	18180.0			0.678984
$896$	−1792.00	−	1551.92i	−0.0668153	−	0.0578638i
$897$		0			0
$898$	11688.0	+	20244.2i	0.434336	+	0.752292i
$899$	4717.50	−	8170.95i	0.175014	−	0.303133i
$900$		0			0
$901$	26838.0	+	46484.8i	0.992346	+	1.71879i
$902$	3024.00			0.111628
$903$		0			0
$904$	17472.0			0.642821
$905$	−22740.0	−	39386.8i	−0.835252	−	1.44670i
$906$		0			0
$907$	4058.00	−	7028.66i	0.148560	−	0.257313i	−0.782136	−	0.623108i	$-0.785870\pi$
$907$	4058.00	−	7028.66i	0.148560	−	0.257313i	0.930695	+	0.365795i	$0.119203\pi$
$908$	1842.00	+	3190.44i	0.0673226	+	0.116606i
$909$		0			0
$910$	9240.00	−	48012.4i	0.336597	−	1.74901i
$911$	4446.00			0.161693			0.0808466	−	0.996727i	$-0.474238\pi$
$911$	4446.00			0.161693			0.0808466	+	0.996727i	$0.474238\pi$
$912$		0			0
$913$	−2686.50	+	4653.15i	−0.0973824	+	0.168671i
$914$	−551.000	+	954.360i	−0.0199403	+	0.0345377i
$915$		0			0
$916$	16208.0			0.584637
$917$	−16422.0	−	14221.9i	−0.591387	−	0.512156i
$918$		0			0
$919$	−13252.0	−	22953.1i	−0.475673	−	0.823889i	0.523939	−	0.851756i	$-0.324462\pi$
$919$	−13252.0	−	22953.1i	−0.475673	−	0.823889i	−0.999612	+	0.0278666i	$0.991129\pi$
$920$	−5040.00	+	8729.54i	−0.180613	+	0.312831i
$921$		0			0
$922$	13386.0	+	23185.2i	0.478139	+	0.828162i
$923$	95568.0			3.40808
$924$		0			0
$925$	4400.00			0.156401
$926$	6376.00	+	11043.6i	0.226273	+	0.391916i
$927$		0			0
$928$	816.000	−	1413.35i	0.0288648	−	0.0499953i
$929$	−2715.00	−	4702.52i	−0.0958840	−	0.166076i	0.814093	−	0.580734i	$-0.197234\pi$
$929$	−2715.00	−	4702.52i	−0.0958840	−	0.166076i	−0.909977	+	0.414658i	$0.863901\pi$
$930$		0			0
$931$	−33124.0	−	13239.8i	−1.16605	−	0.466076i
$932$	1872.00			0.0657933
$933$		0			0
$934$	5700.00	−	9872.69i	0.199689	−	0.345872i
$935$	−5670.00	+	9820.73i	−0.198320	+	0.343500i
$936$		0			0
$937$	33803.0			1.17854			0.589272	−	0.807935i	$-0.299415\pi$
$937$	33803.0			1.17854			0.589272	+	0.807935i	$0.299415\pi$
$938$	−5810.00	+	2012.64i	−0.202242	+	0.0700588i
$939$		0			0
$940$	−4140.00	−	7170.69i	−0.143651	−	0.248811i
$941$	−24241.5	+	41987.5i	−0.839798	+	1.45457i	0.0502645	+	0.998736i	$0.483994\pi$
$941$	−24241.5	+	41987.5i	−0.839798	+	1.45457i	−0.890063	+	0.455838i	$0.849340\pi$
$942$		0			0
$943$	−7056.00	−	12221.4i	−0.243664	−	0.422038i
$944$	−2544.00			−0.0877120
$945$		0			0
$946$	5868.00			0.201676
$947$	18648.0	+	32299.3i	0.639893	+	1.10833i	0.985456	+	0.169931i	$0.0543546\pi$
$947$	18648.0	+	32299.3i	0.639893	+	1.10833i	−0.345563	+	0.938396i	$0.612312\pi$
$948$		0			0
$949$	9592.00	−	16613.8i	0.328103	−	0.568291i
$950$	−10400.0	−	18013.3i	−0.355180	−	0.615189i
$951$		0			0
$952$	−2352.00	+	12221.4i	−0.0800722	+	0.416067i
$953$	38478.0			1.30790			0.653948	−	0.756540i	$-0.273112\pi$
$953$	38478.0			1.30790			0.653948	+	0.756540i	$0.273112\pi$
$954$		0			0
$955$	18900.0	−	32735.8i	0.640408	−	1.10922i
$956$	9864.00	−	17084.9i	0.333708	−	0.577999i
$957$		0			0
$958$	−39588.0			−1.33510
$959$	105.000	−	545.596i	0.00353559	−	0.0183714i
$960$		0			0
$961$	−2217.00	−	3839.96i	−0.0744184	−	0.128897i
$962$	3872.00	−	6706.50i	0.129770	−	0.224767i
$963$		0			0
$964$	3074.00	+	5324.32i	0.102704	+	0.177889i
$965$	5475.00			0.182639
$966$		0			0
$967$	27257.0			0.906438			0.453219	−	0.891399i	$-0.350275\pi$
$967$	27257.0			0.906438			0.453219	+	0.891399i	$0.350275\pi$
$968$	5000.00	+	8660.25i	0.166019	+	0.287553i
$969$		0			0
$970$	2535.00	−	4390.75i	0.0839113	−	0.145339i
$971$	17170.5	+	29740.2i	0.567485	+	0.982912i	0.996814	+	0.0797641i	$0.0254167\pi$
$971$	17170.5	+	29740.2i	0.567485	+	0.982912i	−0.429329	+	0.903148i	$0.641250\pi$
$972$		0			0
$973$	−1435.00	+	497.099i	−0.0472806	+	0.0163785i
$974$	31870.0			1.04844
$975$		0			0
$976$	−5776.00	+	10004.3i	−0.189432	+	0.328105i
$977$	13713.0	−	23751.6i	0.449046	−	0.777770i	−0.549278	−	0.835639i	$-0.685097\pi$
$977$	13713.0	−	23751.6i	0.449046	−	0.777770i	0.998324	+	0.0578693i	$0.0184307\pi$
$978$		0			0
$979$	9342.00			0.304976
$980$	16170.0	−	12730.6i	0.527073	−	0.414963i
$981$		0			0
$982$	9963.00	+	17256.4i	0.323760	+	0.560768i
$983$	6162.00	−	10672.9i	0.199936	−	0.346300i	−0.748571	−	0.663054i	$-0.769260\pi$
$983$	6162.00	−	10672.9i	0.199936	−	0.346300i	0.948508	+	0.316755i	$0.102593\pi$
$984$		0			0
$985$	−11925.0	−	20654.7i	−0.385748	−	0.668136i
$986$	−8568.00			−0.276735
$987$		0			0
$988$	−36608.0			−1.17880
$989$	−13692.0	−	23715.2i	−0.440223	−	0.762488i
$990$		0			0
$991$	−23798.5	+	41220.2i	−0.762850	+	1.32129i	0.178526	+	0.983935i	$0.442867\pi$
$991$	−23798.5	+	41220.2i	−0.762850	+	1.32129i	−0.941376	+	0.337360i	$0.890466\pi$
$992$	−2960.00	−	5126.87i	−0.0947380	−	0.164091i
$993$		0			0
$994$	30408.0	+	26334.1i	0.970305	+	0.840309i
$995$	−80700.0			−2.57122
$996$		0			0
$997$	5621.00	−	9735.86i	0.178555	−	0.309266i	−0.762831	−	0.646598i	$-0.776191\pi$
$997$	5621.00	−	9735.86i	0.178555	−	0.309266i	0.941386	+	0.337332i	$0.109525\pi$
$998$	−19142.0	+	33154.9i	−0.607144	+	1.05160i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	126.4.g.a.109.1		2
3.2	odd	2		42.4.e.b.25.1	✓	2
7.2	even	3	inner	126.4.g.a.37.1		2
7.3	odd	6		882.4.a.h.1.1		1
7.4	even	3		882.4.a.r.1.1		1
7.5	odd	6		882.4.g.l.667.1		2
7.6	odd	2		882.4.g.l.361.1		2
12.11	even	2		336.4.q.d.193.1		2
21.2	odd	6		42.4.e.b.37.1	yes	2
21.5	even	6		294.4.e.e.79.1		2
21.11	odd	6		294.4.a.a.1.1		1
21.17	even	6		294.4.a.g.1.1		1
21.20	even	2		294.4.e.e.67.1		2
84.11	even	6		2352.4.a.u.1.1		1
84.23	even	6		336.4.q.d.289.1		2
84.59	odd	6		2352.4.a.q.1.1		1

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
42.4.e.b.25.1	✓	2	3.2	odd	2
42.4.e.b.37.1	yes	2	21.2	odd	6
126.4.g.a.37.1		2	7.2	even	3	inner
126.4.g.a.109.1		2	1.1	even	1	trivial
294.4.a.a.1.1		1	21.11	odd	6
294.4.a.g.1.1		1	21.17	even	6
294.4.e.e.67.1		2	21.20	even	2
294.4.e.e.79.1		2	21.5	even	6
336.4.q.d.193.1		2	12.11	even	2
336.4.q.d.289.1		2	84.23	even	6
882.4.a.h.1.1		1	7.3	odd	6
882.4.a.r.1.1		1	7.4	even	3
882.4.g.l.361.1		2	7.6	odd	2
882.4.g.l.667.1		2	7.5	odd	6
2352.4.a.q.1.1		1	84.59	odd	6
2352.4.a.u.1.1		1	84.11	even	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:	\( N \)	\(=\)	\( 126 = 2 \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	126.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.50000 - 12.9904i) q^{5} +(17.5000 - 6.06218i) q^{7} +8.00000 q^{8} +O(q^{10})\)	\(q+(-1.00000 - 1.73205i) q^{2} +(-2.00000 + 3.46410i) q^{4} +(-7.50000 - 12.9904i) q^{5} +(17.5000 - 6.06218i) q^{7} +8.00000 q^{8} +(-15.0000 + 25.9808i) q^{10} +(-4.50000 + 7.79423i) q^{11} -88.0000 q^{13} +(-28.0000 - 24.2487i) q^{14} +(-8.00000 - 13.8564i) q^{16} +(-42.0000 + 72.7461i) q^{17} +(-52.0000 - 90.0666i) q^{19} +60.0000 q^{20} +18.0000 q^{22} +(-42.0000 - 72.7461i) q^{23} +(-50.0000 + 86.6025i) q^{25} +(88.0000 + 152.420i) q^{26} +(-14.0000 + 72.7461i) q^{28} -51.0000 q^{29} +(-92.5000 + 160.215i) q^{31} +(-16.0000 + 27.7128i) q^{32} +168.000 q^{34} +(-210.000 - 181.865i) q^{35} +(-22.0000 - 38.1051i) q^{37} +(-104.000 + 180.133i) q^{38} +(-60.0000 - 103.923i) q^{40} +168.000 q^{41} +326.000 q^{43} +(-18.0000 - 31.1769i) q^{44} +(-84.0000 + 145.492i) q^{46} +(-69.0000 - 119.512i) q^{47} +(269.500 - 212.176i) q^{49} +200.000 q^{50} +(176.000 - 304.841i) q^{52} +(319.500 - 553.390i) q^{53} +135.000 q^{55} +(140.000 - 48.4974i) q^{56} +(51.0000 + 88.3346i) q^{58} +(79.5000 - 137.698i) q^{59} +(-361.000 - 625.270i) q^{61} +370.000 q^{62} +64.0000 q^{64} +(660.000 + 1143.15i) q^{65} +(83.0000 - 143.760i) q^{67} +(-168.000 - 290.985i) q^{68} +(-105.000 + 545.596i) q^{70} -1086.00 q^{71} +(-109.000 + 188.794i) q^{73} +(-44.0000 + 76.2102i) q^{74} +416.000 q^{76} +(-31.5000 + 163.679i) q^{77} +(291.500 + 504.893i) q^{79} +(-120.000 + 207.846i) q^{80} +(-168.000 - 290.985i) q^{82} +597.000 q^{83} +1260.00 q^{85} +(-326.000 - 564.649i) q^{86} +(-36.0000 + 62.3538i) q^{88} +(-519.000 - 898.934i) q^{89} +(-1540.00 + 533.472i) q^{91} +336.000 q^{92} +(-138.000 + 239.023i) q^{94} +(-780.000 + 1351.00i) q^{95} -169.000 q^{97} +(-637.000 - 254.611i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 2 q - 2 q^{2} - 4 q^{4} - 15 q^{5} + 35 q^{7} + 16 q^{8}+O(q^{10}) \) 2 * q - 2 * q^2 - 4 * q^4 - 15 * q^5 + 35 * q^7 + 16 * q^8	\( 2 q - 2 q^{2} - 4 q^{4} - 15 q^{5} + 35 q^{7} + 16 q^{8} - 30 q^{10} - 9 q^{11} - 176 q^{13} - 56 q^{14} - 16 q^{16} - 84 q^{17} - 104 q^{19} + 120 q^{20} + 36 q^{22} - 84 q^{23} - 100 q^{25} + 176 q^{26} - 28 q^{28} - 102 q^{29} - 185 q^{31} - 32 q^{32} + 336 q^{34} - 420 q^{35} - 44 q^{37} - 208 q^{38} - 120 q^{40} + 336 q^{41} + 652 q^{43} - 36 q^{44} - 168 q^{46} - 138 q^{47} + 539 q^{49} + 400 q^{50} + 352 q^{52} + 639 q^{53} + 270 q^{55} + 280 q^{56} + 102 q^{58} + 159 q^{59} - 722 q^{61} + 740 q^{62} + 128 q^{64} + 1320 q^{65} + 166 q^{67} - 336 q^{68} - 210 q^{70} - 2172 q^{71} - 218 q^{73} - 88 q^{74} + 832 q^{76} - 63 q^{77} + 583 q^{79} - 240 q^{80} - 336 q^{82} + 1194 q^{83} + 2520 q^{85} - 652 q^{86} - 72 q^{88} - 1038 q^{89} - 3080 q^{91} + 672 q^{92} - 276 q^{94} - 1560 q^{95} - 338 q^{97} - 1274 q^{98}+O(q^{100}) \) 2 * q - 2 * q^2 - 4 * q^4 - 15 * q^5 + 35 * q^7 + 16 * q^8 - 30 * q^10 - 9 * q^11 - 176 * q^13 - 56 * q^14 - 16 * q^16 - 84 * q^17 - 104 * q^19 + 120 * q^20 + 36 * q^22 - 84 * q^23 - 100 * q^25 + 176 * q^26 - 28 * q^28 - 102 * q^29 - 185 * q^31 - 32 * q^32 + 336 * q^34 - 420 * q^35 - 44 * q^37 - 208 * q^38 - 120 * q^40 + 336 * q^41 + 652 * q^43 - 36 * q^44 - 168 * q^46 - 138 * q^47 + 539 * q^49 + 400 * q^50 + 352 * q^52 + 639 * q^53 + 270 * q^55 + 280 * q^56 + 102 * q^58 + 159 * q^59 - 722 * q^61 + 740 * q^62 + 128 * q^64 + 1320 * q^65 + 166 * q^67 - 336 * q^68 - 210 * q^70 - 2172 * q^71 - 218 * q^73 - 88 * q^74 + 832 * q^76 - 63 * q^77 + 583 * q^79 - 240 * q^80 - 336 * q^82 + 1194 * q^83 + 2520 * q^85 - 652 * q^86 - 72 * q^88 - 1038 * q^89 - 3080 * q^91 + 672 * q^92 - 276 * q^94 - 1560 * q^95 - 338 * q^97 - 1274 * q^98

Introduction

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