LMFDB - Embedded newform 378.4.e.a.235.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [378,4,Mod(37,378)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(378, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("378.37");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 378 = 2 \cdot 3^{3} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	378.e (of order $3$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$22.3027219822$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{3})$
Twist minimal:	no (minimal twist has level 126)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			235.9
Character	$\chi$	$=$	378.235
Dual form			378.4.e.a.37.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-2.00000 q^{2} +4.00000 q^{4} +(5.06718 - 8.77661i) q^{5} +(14.4394 - 11.5975i) q^{7} -8.00000 q^{8} +O(q^{10})$	\(q-2.00000 q^{2} +4.00000 q^{4} +(5.06718 - 8.77661i) q^{5} +(14.4394 - 11.5975i) q^{7} -8.00000 q^{8} +(-10.1344 + 17.5532i) q^{10} +(-19.0546 - 33.0036i) q^{11} +(-1.46126 - 2.53098i) q^{13} +(-28.8789 + 23.1951i) q^{14} +16.0000 q^{16} +(56.0159 - 97.0224i) q^{17} +(-39.2887 - 68.0500i) q^{19} +(20.2687 - 35.1064i) q^{20} +(38.1092 + 66.0071i) q^{22} +(-73.5122 + 127.327i) q^{23} +(11.1475 + 19.3080i) q^{25} +(2.92253 + 5.06197i) q^{26} +(57.7577 - 46.3901i) q^{28} +(-137.710 + 238.521i) q^{29} +102.334 q^{31} -32.0000 q^{32} +(-112.032 + 194.045i) q^{34} +(-28.6198 - 185.496i) q^{35} +(-25.1233 - 43.5149i) q^{37} +(78.5773 + 136.100i) q^{38} +(-40.5374 + 70.2128i) q^{40} +(-1.16281 - 2.01405i) q^{41} +(184.064 - 318.808i) q^{43} +(-76.2185 - 132.014i) q^{44} +(147.024 - 254.654i) q^{46} -399.584 q^{47} +(73.9944 - 334.924i) q^{49} +(-22.2949 - 38.6159i) q^{50} +(-5.84506 - 10.1239i) q^{52} +(50.8233 - 88.0285i) q^{53} -386.212 q^{55} +(-115.515 + 92.7803i) q^{56} +(275.420 - 477.042i) q^{58} -27.4171 q^{59} -612.693 q^{61} -204.669 q^{62} +64.0000 q^{64} -29.6179 q^{65} -624.291 q^{67} +(224.064 - 388.090i) q^{68} +(57.2397 + 370.992i) q^{70} +514.486 q^{71} +(590.915 - 1023.49i) q^{73} +(50.2467 + 87.0298i) q^{74} +(-157.155 - 272.200i) q^{76} +(-657.898 - 255.566i) q^{77} -340.185 q^{79} +(81.0748 - 140.426i) q^{80} +(2.32563 + 4.02810i) q^{82} +(312.272 - 540.871i) q^{83} +(-567.685 - 983.259i) q^{85} +(-368.127 + 637.615i) q^{86} +(152.437 + 264.028i) q^{88} +(-349.147 - 604.740i) q^{89} +(-50.4530 - 19.5989i) q^{91} +(-294.049 + 509.308i) q^{92} +799.167 q^{94} -796.330 q^{95} +(-345.941 + 599.187i) q^{97} +(-147.989 + 669.847i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 48 q^{2} + 96 q^{4} - 10 q^{5} + 17 q^{7} - 192 q^{8}+O(q^{10}) $ 24 * q - 48 * q^2 + 96 * q^4 - 10 * q^5 + 17 * q^7 - 192 * q^8	$ 24 q - 48 q^{2} + 96 q^{4} - 10 q^{5} + 17 q^{7} - 192 q^{8} + 20 q^{10} + 4 q^{11} + 80 q^{13} - 34 q^{14} + 384 q^{16} - 92 q^{17} + 54 q^{19} - 40 q^{20} - 8 q^{22} - 131 q^{23} - 178 q^{25} - 160 q^{26} + 68 q^{28} + 278 q^{29} - 220 q^{31} - 768 q^{32} + 184 q^{34} + 493 q^{35} - 21 q^{37} - 108 q^{38} + 80 q^{40} - 465 q^{41} + 159 q^{43} + 16 q^{44} + 262 q^{46} + 678 q^{47} - 207 q^{49} + 356 q^{50} + 320 q^{52} + 78 q^{53} - 1532 q^{55} - 136 q^{56} - 556 q^{58} + 1622 q^{59} - 1978 q^{61} + 440 q^{62} + 1536 q^{64} + 624 q^{65} - 80 q^{67} - 368 q^{68} - 986 q^{70} - 980 q^{71} + 1510 q^{73} + 42 q^{74} + 216 q^{76} + 350 q^{77} + 812 q^{79} - 160 q^{80} + 930 q^{82} + 7 q^{83} - 581 q^{85} - 318 q^{86} - 32 q^{88} - 675 q^{89} - 232 q^{91} - 524 q^{92} - 1356 q^{94} - 2438 q^{95} + 2836 q^{97} + 414 q^{98}+O(q^{100}) $ 24 * q - 48 * q^2 + 96 * q^4 - 10 * q^5 + 17 * q^7 - 192 * q^8 + 20 * q^10 + 4 * q^11 + 80 * q^13 - 34 * q^14 + 384 * q^16 - 92 * q^17 + 54 * q^19 - 40 * q^20 - 8 * q^22 - 131 * q^23 - 178 * q^25 - 160 * q^26 + 68 * q^28 + 278 * q^29 - 220 * q^31 - 768 * q^32 + 184 * q^34 + 493 * q^35 - 21 * q^37 - 108 * q^38 + 80 * q^40 - 465 * q^41 + 159 * q^43 + 16 * q^44 + 262 * q^46 + 678 * q^47 - 207 * q^49 + 356 * q^50 + 320 * q^52 + 78 * q^53 - 1532 * q^55 - 136 * q^56 - 556 * q^58 + 1622 * q^59 - 1978 * q^61 + 440 * q^62 + 1536 * q^64 + 624 * q^65 - 80 * q^67 - 368 * q^68 - 986 * q^70 - 980 * q^71 + 1510 * q^73 + 42 * q^74 + 216 * q^76 + 350 * q^77 + 812 * q^79 - 160 * q^80 + 930 * q^82 + 7 * q^83 - 581 * q^85 - 318 * q^86 - 32 * q^88 - 675 * q^89 - 232 * q^91 - 524 * q^92 - 1356 * q^94 - 2438 * q^95 + 2836 * q^97 + 414 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/378\mathbb{Z}\right)^\times$.

$n$	$29$	$325$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$

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 $

$2$	−2.00000			−0.707107
$2$	−2.00000			−0.707107
$3$		0			0
$3$		0			0
$4$	4.00000			0.500000
$5$	5.06718	−	8.77661i	0.453222	−	0.785004i	−0.545362	−	0.838201i	$-0.683608\pi$
$5$	5.06718	−	8.77661i	0.453222	−	0.785004i	0.998584	+	0.0531971i	$0.0169412\pi$
$6$		0			0
$7$	14.4394	−	11.5975i	0.779656	−	0.626208i
$7$	14.4394	−	11.5975i	0.779656	−	0.626208i
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−10.1344	+	17.5532i	−0.320476	+	0.555081i
$11$	−19.0546	−	33.0036i	−0.522289	−	0.904632i	−0.999664	−	0.0259317i	$-0.991745\pi$
$11$	−19.0546	−	33.0036i	−0.522289	−	0.904632i	0.477374	−	0.878700i	$-0.341589\pi$
$12$		0			0
$13$	−1.46126	−	2.53098i	−0.0311755	−	0.0539976i	0.850017	−	0.526756i	$-0.176592\pi$
$13$	−1.46126	−	2.53098i	−0.0311755	−	0.0539976i	−0.881192	+	0.472758i	$0.843258\pi$
$14$	−28.8789	+	23.1951i	−0.551300	+	0.442796i
$15$		0			0
$16$	16.0000			0.250000
$17$	56.0159	−	97.0224i	0.799168	−	1.38420i	−0.120991	−	0.992654i	$-0.538607\pi$
$17$	56.0159	−	97.0224i	0.799168	−	1.38420i	0.920159	−	0.391546i	$-0.128060\pi$
$18$		0			0
$19$	−39.2887	−	68.0500i	−0.474391	−	0.821670i	0.525179	−	0.850992i	$-0.323999\pi$
$19$	−39.2887	−	68.0500i	−0.474391	−	0.821670i	−0.999570	+	0.0293220i	$0.990665\pi$
$20$	20.2687	−	35.1064i	0.226611	−	0.392502i
$21$		0			0
$22$	38.1092	+	66.0071i	0.369314	+	0.639671i
$23$	−73.5122	+	127.327i	−0.666450	+	1.15433i	0.312440	+	0.949938i	$0.398854\pi$
$23$	−73.5122	+	127.327i	−0.666450	+	1.15433i	−0.978890	+	0.204388i	$0.934480\pi$
$24$		0			0
$25$	11.1475	+	19.3080i	0.0891796	+	0.154464i
$26$	2.92253	+	5.06197i	0.0220444	+	0.0381821i
$27$		0			0
$28$	57.7577	−	46.3901i	0.389828	−	0.313104i
$29$	−137.710	+	238.521i	−0.881798	+	1.52732i	−0.0324583	+	0.999473i	$0.510334\pi$
$29$	−137.710	+	238.521i	−0.881798	+	1.52732i	−0.849340	+	0.527846i	$0.823000\pi$
$30$		0			0
$31$	102.334			0.592897			0.296448	−	0.955049i	$-0.404198\pi$
$31$	102.334			0.592897			0.296448	+	0.955049i	$0.404198\pi$
$32$	−32.0000			−0.176777
$33$		0			0
$34$	−112.032	+	194.045i	−0.565097	+	0.978777i
$35$	−28.6198	−	185.496i	−0.138218	−	0.895844i
$36$		0			0
$37$	−25.1233	−	43.5149i	−0.111628	−	0.193346i	0.804799	−	0.593548i	$-0.202273\pi$
$37$	−25.1233	−	43.5149i	−0.111628	−	0.193346i	−0.916427	+	0.400202i	$0.868940\pi$
$38$	78.5773	+	136.100i	0.335445	+	0.581008i
$39$		0			0
$40$	−40.5374	+	70.2128i	−0.160238	+	0.277541i
$41$	−1.16281	−	2.01405i	−0.00442929	−	0.00767176i	0.863802	−	0.503831i	$-0.168077\pi$
$41$	−1.16281	−	2.01405i	−0.00442929	−	0.00767176i	−0.868232	+	0.496159i	$0.834743\pi$
$42$		0			0
$43$	184.064	−	318.808i	0.652778	−	1.13064i	−0.329668	−	0.944097i	$-0.606937\pi$
$43$	184.064	−	318.808i	0.652778	−	1.13064i	0.982446	−	0.186547i	$-0.0597297\pi$
$44$	−76.2185	−	132.014i	−0.261145	−	0.452316i
$45$		0			0
$46$	147.024	−	254.654i	0.471252	−	0.816232i
$47$	−399.584			−1.24011			−0.620056	−	0.784558i	$-0.712890\pi$
$47$	−399.584			−1.24011			−0.620056	+	0.784558i	$0.712890\pi$
$48$		0			0
$49$	73.9944	−	334.924i	0.215727	−	0.976454i
$50$	−22.2949	−	38.6159i	−0.0630595	−	0.109222i
$51$		0			0
$52$	−5.84506	−	10.1239i	−0.0155878	−	0.0269988i
$53$	50.8233	−	88.0285i	0.131719	−	0.228144i	−0.792620	−	0.609716i	$-0.791284\pi$
$53$	50.8233	−	88.0285i	0.131719	−	0.228144i	0.924339	+	0.381571i	$0.124617\pi$
$54$		0			0
$55$	−386.212			−0.946852
$56$	−115.515	+	92.7803i	−0.275650	+	0.221398i
$57$		0			0
$58$	275.420	−	477.042i	0.623526	−	1.07998i
$59$	−27.4171			−0.0604984			−0.0302492	−	0.999542i	$-0.509630\pi$
$59$	−27.4171			−0.0604984			−0.0302492	+	0.999542i	$0.509630\pi$
$60$		0			0
$61$	−612.693			−1.28602			−0.643011	−	0.765857i	$-0.722315\pi$
$61$	−612.693			−1.28602			−0.643011	+	0.765857i	$0.722315\pi$
$62$	−204.669			−0.419241
$63$		0			0
$64$	64.0000			0.125000
$65$	−29.6179			−0.0565177
$66$		0			0
$67$	−624.291			−1.13835			−0.569173	−	0.822217i	$-0.692737\pi$
$67$	−624.291			−1.13835			−0.569173	+	0.822217i	$0.692737\pi$
$68$	224.064	−	388.090i	0.399584	−	0.692100i
$69$		0			0
$70$	57.2397	+	370.992i	0.0977350	+	0.633457i
$71$	514.486			0.859975			0.429988	−	0.902835i	$-0.358518\pi$
$71$	514.486			0.859975			0.429988	+	0.902835i	$0.358518\pi$
$72$		0			0
$73$	590.915	−	1023.49i	0.947416	−	1.64097i	0.196575	−	0.980489i	$-0.437018\pi$
$73$	590.915	−	1023.49i	0.947416	−	1.64097i	0.750841	−	0.660483i	$-0.229649\pi$
$74$	50.2467	+	87.0298i	0.0789332	+	0.136716i
$75$		0			0
$76$	−157.155	−	272.200i	−0.237196	−	0.410835i
$77$	−657.898	−	255.566i	−0.973694	−	0.378240i
$78$		0			0
$79$	−340.185			−0.484479			−0.242239	−	0.970217i	$-0.577882\pi$
$79$	−340.185			−0.484479			−0.242239	+	0.970217i	$0.577882\pi$
$80$	81.0748	−	140.426i	0.113305	−	0.196251i
$81$		0			0
$82$	2.32563	+	4.02810i	0.00313198	+	0.00542475i
$83$	312.272	−	540.871i	0.412967	−	0.715280i	−0.582245	−	0.813013i	$-0.697826\pi$
$83$	312.272	−	540.871i	0.412967	−	0.715280i	0.995213	+	0.0977327i	$0.0311590\pi$
$84$		0			0
$85$	−567.685	−	983.259i	−0.724401	−	1.25470i
$86$	−368.127	+	637.615i	−0.461583	+	0.799486i
$87$		0			0
$88$	152.437	+	264.028i	0.184657	+	0.319836i
$89$	−349.147	−	604.740i	−0.415837	−	0.720251i	0.579679	−	0.814845i	$-0.303178\pi$
$89$	−349.147	−	604.740i	−0.415837	−	0.720251i	−0.995516	+	0.0945943i	$0.969845\pi$
$90$		0			0
$91$	−50.4530	−	19.5989i	−0.0581199	−	0.0225772i
$92$	−294.049	+	509.308i	−0.333225	+	0.577163i
$93$		0			0
$94$	799.167			0.876892
$95$	−796.330			−0.860019
$96$		0			0
$97$	−345.941	+	599.187i	−0.362113	+	0.627198i	−0.988308	−	0.152468i	$-0.951278\pi$
$97$	−345.941	+	599.187i	−0.362113	+	0.627198i	0.626195	+	0.779666i	$0.284611\pi$
$98$	−147.989	+	669.847i	−0.152542	+	0.690457i
$99$		0			0
$100$	44.5898	+	77.2318i	0.0445898	+	0.0772318i
$101$	−226.151	−	391.704i	−0.222800	−	0.385901i	0.732857	−	0.680383i	$-0.238186\pi$
$101$	−226.151	−	391.704i	−0.222800	−	0.385901i	−0.955657	+	0.294481i	$0.904853\pi$
$102$		0			0
$103$	−121.582	+	210.587i	−0.116309	+	0.201454i	−0.918302	−	0.395880i	$-0.870440\pi$
$103$	−121.582	+	210.587i	−0.116309	+	0.201454i	0.801993	+	0.597333i	$0.203773\pi$
$104$	11.6901	+	20.2479i	0.0110222	+	0.0190910i
$105$		0			0
$106$	−101.647	+	176.057i	−0.0931395	+	0.161322i
$107$	−994.029	−	1721.71i	−0.898097	−	1.55555i	−0.829924	−	0.557876i	$-0.811616\pi$
$107$	−994.029	−	1721.71i	−0.898097	−	1.55555i	−0.0681728	−	0.997674i	$-0.521717\pi$
$108$		0			0
$109$	−720.516	+	1247.97i	−0.633146	+	1.09664i	0.353759	+	0.935337i	$0.384903\pi$
$109$	−720.516	+	1247.97i	−0.633146	+	1.09664i	−0.986905	+	0.161304i	$0.948430\pi$
$110$	772.425			0.669526
$111$		0			0
$112$	231.031	−	185.561i	0.194914	−	0.156552i
$113$	267.691	+	463.654i	0.222852	+	0.385990i	0.955673	−	0.294431i	$-0.0951301\pi$
$113$	267.691	+	463.654i	0.222852	+	0.385990i	−0.732821	+	0.680421i	$0.761797\pi$
$114$		0			0
$115$	744.999	+	1290.38i	0.604100	+	1.04633i
$116$	−550.841	+	954.085i	−0.440899	+	0.763660i
$117$		0			0
$118$	54.8343			0.0427789
$119$	−316.383	−	2050.60i	−0.243721	−	1.57964i
$120$		0			0
$121$	−60.6567	+	105.061i	−0.0455723	+	0.0789336i
$122$	1225.39			0.909355
$123$		0			0
$124$	409.338			0.296448
$125$	1492.74			1.06812
$126$		0			0
$127$	1820.07			1.27170			0.635848	−	0.771815i	$-0.280651\pi$
$127$	1820.07			1.27170			0.635848	+	0.771815i	$0.280651\pi$
$128$	−128.000			−0.0883883
$129$		0			0
$130$	59.2359			0.0399641
$131$	904.614	−	1566.84i	0.603332	−	1.04500i	−0.388981	−	0.921246i	$-0.627173\pi$
$131$	904.614	−	1566.84i	0.603332	−	1.04500i	0.992313	−	0.123755i	$-0.0394938\pi$
$132$		0			0
$133$	−1356.52	−	526.951i	−0.884399	−	0.343552i
$134$	1248.58			0.804933
$135$		0			0
$136$	−448.127	+	776.179i	−0.282549	+	0.489388i
$137$	1365.54	+	2365.19i	0.851578	+	1.47498i	0.879784	+	0.475374i	$0.157687\pi$
$137$	1365.54	+	2365.19i	0.851578	+	1.47498i	−0.0282055	+	0.999602i	$0.508979\pi$
$138$		0			0
$139$	−157.186	−	272.253i	−0.0959159	−	0.166131i	0.814075	−	0.580760i	$-0.197245\pi$
$139$	−157.186	−	272.253i	−0.0959159	−	0.166131i	−0.909990	+	0.414629i	$0.863911\pi$
$140$	−114.479	−	741.984i	−0.0691091	−	0.447922i
$141$		0			0
$142$	−1028.97			−0.608094
$143$	−55.6877	+	96.4538i	−0.0325653	+	0.0564047i
$144$		0			0
$145$	1395.60	+	2417.26i	0.799301	+	1.38443i
$146$	−1181.83	+	2046.99i	−0.669924	+	1.16034i
$147$		0			0
$148$	−100.493	−	174.060i	−0.0558142	−	0.0966730i
$149$	−901.626	+	1561.66i	−0.495732	+	0.858633i	−0.999988	−	0.00492109i	$-0.998434\pi$
$149$	−901.626	+	1561.66i	−0.495732	+	0.858633i	0.504256	+	0.863554i	$0.331767\pi$
$150$		0			0
$151$	237.232	+	410.898i	0.127852	+	0.221446i	0.922844	−	0.385173i	$-0.125858\pi$
$151$	237.232	+	410.898i	0.127852	+	0.221446i	−0.794992	+	0.606620i	$0.792525\pi$
$152$	314.309	+	544.400i	0.167723	+	0.290504i
$153$		0			0
$154$	1315.80	+	511.132i	0.688505	+	0.267456i
$155$	518.546	−	898.149i	0.268714	−	0.465426i
$156$		0			0
$157$	−1470.11			−0.747308			−0.373654	−	0.927568i	$-0.621895\pi$
$157$	−1470.11			−0.747308			−0.373654	+	0.927568i	$0.621895\pi$
$158$	680.370			0.342578
$159$		0			0
$160$	−162.150	+	280.851i	−0.0801191	+	0.138770i
$161$	415.203	+	2691.09i	0.203246	+	1.31731i
$162$		0			0
$163$	648.995	+	1124.09i	0.311860	+	0.540158i	0.978765	−	0.204985i	$-0.0657146\pi$
$163$	648.995	+	1124.09i	0.311860	+	0.540158i	−0.666905	+	0.745143i	$0.732381\pi$
$164$	−4.65125	−	8.05621i	−0.00221465	−	0.00383588i
$165$		0			0
$166$	−624.544	+	1081.74i	−0.292012	+	0.505780i
$167$	217.257	+	376.300i	0.100670	+	0.174365i	0.911961	−	0.410277i	$-0.134568\pi$
$167$	217.257	+	376.300i	0.100670	+	0.174365i	−0.811291	+	0.584642i	$0.801235\pi$
$168$		0			0
$169$	1094.23	−	1895.26i	0.498056	−	0.862659i
$170$	1135.37	+	1966.52i	0.512229	+	0.887206i
$171$		0			0
$172$	736.254	−	1275.23i	0.326389	−	0.565322i
$173$	3054.22			1.34224			0.671122	−	0.741347i	$-0.265813\pi$
$173$	3054.22			1.34224			0.671122	+	0.741347i	$0.265813\pi$
$174$		0			0
$175$	384.888	+	149.513i	0.166256	+	0.0645835i
$176$	−304.874	−	528.057i	−0.130572	−	0.226158i
$177$		0			0
$178$	698.294	+	1209.48i	0.294041	+	0.509294i
$179$	−9.92535	+	17.1912i	−0.00414445	+	0.00717839i	−0.868090	−	0.496407i	$-0.834653\pi$
$179$	−9.92535	+	17.1912i	−0.00414445	+	0.00717839i	0.863946	+	0.503585i	$0.167986\pi$
$180$		0			0
$181$	2851.14			1.17085			0.585423	−	0.810728i	$-0.300928\pi$
$181$	2851.14			1.17085			0.585423	+	0.810728i	$0.300928\pi$
$182$	100.906	+	39.1978i	0.0410970	+	0.0159645i
$183$		0			0
$184$	588.098	−	1018.62i	0.235626	−	0.408116i
$185$	−509.217			−0.202370
$186$		0			0
$187$	−4269.45			−1.66959
$188$	−1598.33			−0.620056
$189$		0			0
$190$	1592.66			0.608125
$191$	1924.67			0.729133			0.364567	−	0.931177i	$-0.381217\pi$
$191$	1924.67			0.729133			0.364567	+	0.931177i	$0.381217\pi$
$192$		0			0
$193$	−2069.91			−0.771996			−0.385998	−	0.922500i	$-0.626143\pi$
$193$	−2069.91			−0.771996			−0.385998	+	0.922500i	$0.626143\pi$
$194$	691.881	−	1198.37i	0.256053	−	0.443496i
$195$		0			0
$196$	295.978	−	1339.69i	0.107864	−	0.488227i
$197$	332.446			0.120232			0.0601162	−	0.998191i	$-0.480853\pi$
$197$	332.446			0.120232			0.0601162	+	0.998191i	$0.480853\pi$
$198$		0			0
$199$	370.864	−	642.355i	0.132110	−	0.228821i	−0.792380	−	0.610028i	$-0.791158\pi$
$199$	370.864	−	642.355i	0.132110	−	0.228821i	0.924490	+	0.381207i	$0.124492\pi$
$200$	−89.1796	−	154.464i	−0.0315298	−	0.0546112i
$201$		0			0
$202$	452.301	+	783.409i	0.157544	+	0.272873i
$203$	777.799	+	5041.21i	0.268920	+	1.74297i
$204$		0			0
$205$	−23.5687			−0.00802981
$206$	243.165	−	421.174i	0.0822432	−	0.142449i
$207$		0			0
$208$	−23.3802	−	40.4957i	−0.00779388	−	0.0134994i
$209$	−1497.26	+	2593.33i	−0.495539	+	0.858299i
$210$		0			0
$211$	−1964.14	−	3402.00i	−0.640840	−	1.10997i	−0.985246	−	0.171146i	$-0.945253\pi$
$211$	−1964.14	−	3402.00i	−0.640840	−	1.10997i	0.344406	−	0.938821i	$-0.388080\pi$
$212$	203.293	−	352.114i	0.0658596	−	0.114072i
$213$		0			0
$214$	1988.06	+	3443.42i	0.635051	+	1.09994i
$215$	−1865.37	−	3230.91i	−0.591706	−	1.02487i
$216$		0			0
$217$	1477.65	−	1186.83i	0.462256	−	0.371277i
$218$	1441.03	−	2495.94i	0.447702	−	0.775442i
$219$		0			0
$220$	−1544.85			−0.473426
$221$	−327.416			−0.0996579
$222$		0			0
$223$	−1109.99	+	1922.55i	−0.333319	+	0.577325i	−0.983160	−	0.182745i	$-0.941502\pi$
$223$	−1109.99	+	1922.55i	−0.333319	+	0.577325i	0.649842	+	0.760070i	$0.274835\pi$
$224$	−462.062	+	371.121i	−0.137825	+	0.110699i
$225$		0			0
$226$	−535.382	−	927.308i	−0.157580	−	0.272936i
$227$	2342.95	+	4058.12i	0.685054	+	1.18655i	0.973420	+	0.229029i	$0.0735549\pi$
$227$	2342.95	+	4058.12i	0.685054	+	1.18655i	−0.288365	+	0.957520i	$0.593112\pi$
$228$		0			0
$229$	334.061	−	578.610i	0.0963989	−	0.166968i	−0.813793	−	0.581155i	$-0.802601\pi$
$229$	334.061	−	578.610i	0.0963989	−	0.166968i	0.910192	+	0.414187i	$0.135934\pi$
$230$	−1490.00	−	2580.75i	−0.427163	−	0.739868i
$231$		0			0
$232$	1101.68	−	1908.17i	0.311763	−	0.539989i
$233$	398.140	+	689.598i	0.111944	+	0.193893i	0.916554	−	0.399911i	$-0.130959\pi$
$233$	398.140	+	689.598i	0.111944	+	0.193893i	−0.804610	+	0.593804i	$0.797626\pi$
$234$		0			0
$235$	−2024.76	+	3506.99i	−0.562046	+	0.973492i
$236$	−109.669			−0.0302492
$237$		0			0
$238$	632.766	+	4101.19i	0.172337	+	1.11698i
$239$	−1775.21	−	3074.76i	−0.480456	−	0.832175i	0.519292	−	0.854597i	$-0.326196\pi$
$239$	−1775.21	−	3074.76i	−0.480456	−	0.832175i	−0.999749	+	0.0224219i	$0.992862\pi$
$240$		0			0
$241$	3023.59	+	5237.02i	0.808161	+	1.39978i	0.914136	+	0.405407i	$0.132870\pi$
$241$	3023.59	+	5237.02i	0.808161	+	1.39978i	−0.105975	+	0.994369i	$0.533796\pi$
$242$	121.313	−	210.121i	0.0322245	−	0.0558145i
$243$		0			0
$244$	−2450.77			−0.643011
$245$	−2564.55	−	2346.54i	−0.668747	−	0.611897i
$246$		0			0
$247$	−114.822	+	198.878i	−0.0295788	+	0.0512320i
$248$	−818.675			−0.209621
$249$		0			0
$250$	−2985.48			−0.755273
$251$	489.857			0.123185			0.0615926	−	0.998101i	$-0.480382\pi$
$251$	489.857			0.123185			0.0615926	+	0.998101i	$0.480382\pi$
$252$		0			0
$253$	5602.99			1.39232
$254$	−3640.14			−0.899224
$255$		0			0
$256$	256.000			0.0625000
$257$	814.873	−	1411.40i	0.197783	−	0.342571i	−0.750026	−	0.661408i	$-0.769959\pi$
$257$	814.873	−	1411.40i	0.197783	−	0.342571i	0.947809	+	0.318837i	$0.103292\pi$
$258$		0			0
$259$	−867.432	−	336.961i	−0.208107	−	0.0808408i
$260$	−118.472			−0.0282589
$261$		0			0
$262$	−1809.23	+	3133.67i	−0.426620	+	0.738927i
$263$	−3266.87	−	5658.39i	−0.765946	−	1.32666i	−0.939745	−	0.341877i	$-0.888937\pi$
$263$	−3266.87	−	5658.39i	−0.765946	−	1.32666i	0.173798	−	0.984781i	$-0.444396\pi$
$264$		0			0
$265$	−515.061	−	892.112i	−0.119396	−	0.206800i
$266$	2713.04	+	1053.90i	0.625364	+	0.242928i
$267$		0			0
$268$	−2497.16			−0.569173
$269$	345.254	−	597.998i	0.0782547	−	0.135541i	−0.824242	−	0.566237i	$-0.808399\pi$
$269$	345.254	−	597.998i	0.0782547	−	0.135541i	0.902497	+	0.430696i	$0.141732\pi$
$270$		0			0
$271$	−1984.68	−	3437.56i	−0.444873	−	0.770543i	0.553170	−	0.833068i	$-0.313418\pi$
$271$	−1984.68	−	3437.56i	−0.444873	−	0.770543i	−0.998043	+	0.0625254i	$0.980085\pi$
$272$	896.255	−	1552.36i	0.199792	−	0.346050i
$273$		0			0
$274$	−2731.09	−	4730.38i	−0.602157	−	1.04297i
$275$	424.821	−	735.811i	0.0931552	−	0.161349i
$276$		0			0
$277$	2680.37	+	4642.54i	0.581400	+	1.00701i	0.995314	+	0.0966983i	$0.0308282\pi$
$277$	2680.37	+	4642.54i	0.581400	+	1.00701i	−0.413914	+	0.910316i	$0.635838\pi$
$278$	314.371	+	544.507i	0.0678228	+	0.117472i
$279$		0			0
$280$	228.959	+	1483.97i	0.0488675	+	0.316729i
$281$	2307.16	−	3996.11i	0.489799	−	0.848356i	−0.510132	−	0.860096i	$-0.670404\pi$
$281$	2307.16	−	3996.11i	0.489799	−	0.848356i	0.999931	+	0.0117398i	$0.00373697\pi$
$282$		0			0
$283$	287.292			0.0603453			0.0301726	−	0.999545i	$-0.490394\pi$
$283$	287.292			0.0603453			0.0301726	+	0.999545i	$0.490394\pi$
$284$	2057.94			0.429988
$285$		0			0
$286$	111.375	−	192.908i	0.0230271	−	0.0398842i
$287$	−40.1484	−	15.5960i	−0.00825744	−	0.00320767i
$288$		0			0
$289$	−3819.07	−	6614.82i	−0.777339	−	1.34639i
$290$	−2791.21	−	4834.51i	−0.565191	−	0.978939i
$291$		0			0
$292$	2363.66	−	4093.98i	0.473708	−	0.820486i
$293$	1261.49	+	2184.97i	0.251526	+	0.435656i	0.963946	−	0.266097i	$-0.0857343\pi$
$293$	1261.49	+	2184.97i	0.251526	+	0.435656i	−0.712420	+	0.701753i	$0.752401\pi$
$294$		0			0
$295$	−138.927	+	240.629i	−0.0274192	+	0.0474915i
$296$	200.987	+	348.119i	0.0394666	+	0.0683581i
$297$		0			0
$298$	1803.25	−	3123.32i	0.350536	−	0.607145i
$299$	429.683			0.0831077
$300$		0			0
$301$	−1039.61	−	6738.08i	−0.199076	−	1.29029i
$302$	−474.464	−	821.796i	−0.0904051	−	0.156586i
$303$		0			0
$304$	−628.619	−	1088.80i	−0.118598	−	0.205418i
$305$	−3104.62	+	5377.37i	−0.582853	+	1.00953i
$306$		0			0
$307$	−7744.02			−1.43966			−0.719828	−	0.694152i	$-0.755779\pi$
$307$	−7744.02			−1.43966			−0.719828	+	0.694152i	$0.755779\pi$
$308$	−2631.59	−	1022.26i	−0.486847	−	0.189120i
$309$		0			0
$310$	−1037.09	+	1796.30i	−0.190009	+	0.329106i
$311$	6952.86			1.26772			0.633860	−	0.773448i	$-0.281470\pi$
$311$	6952.86			1.26772			0.633860	+	0.773448i	$0.281470\pi$
$312$		0			0
$313$	9577.44			1.72955			0.864775	−	0.502160i	$-0.167461\pi$
$313$	9577.44			1.72955			0.864775	+	0.502160i	$0.167461\pi$
$314$	2940.22			0.528427
$315$		0			0
$316$	−1360.74			−0.242239
$317$	−1953.00			−0.346030			−0.173015	−	0.984919i	$-0.555351\pi$
$317$	−1953.00			−0.346030			−0.173015	+	0.984919i	$0.555351\pi$
$318$		0			0
$319$	10496.1			1.84222
$320$	324.299	−	561.703i	0.0566527	−	0.0981254i
$321$		0			0
$322$	−830.407	−	5382.18i	−0.143717	−	0.931481i
$323$	−8803.16			−1.51647
$324$		0			0
$325$	32.5788	−	56.4281i	0.00556044	−	0.00963097i
$326$	−1297.99	−	2248.19i	−0.220519	−	0.381949i
$327$		0			0
$328$	9.30251	+	16.1124i	0.00156599	+	0.00271238i
$329$	−5769.76	+	4634.18i	−0.966861	+	0.776568i
$330$		0			0
$331$	−11066.3			−1.83764			−0.918822	−	0.394673i	$-0.870858\pi$
$331$	−11066.3			−1.83764			−0.918822	+	0.394673i	$0.870858\pi$
$332$	1249.09	−	2163.48i	0.206484	−	0.357640i
$333$		0			0
$334$	−434.514	−	752.600i	−0.0711842	−	0.123295i
$335$	−3163.39	+	5479.15i	−0.515924	+	0.893606i
$336$		0			0
$337$	3991.30	+	6913.13i	0.645163	+	1.11746i	0.984264	+	0.176705i	$0.0565439\pi$
$337$	3991.30	+	6913.13i	0.645163	+	1.11746i	−0.339101	+	0.940750i	$0.610123\pi$
$338$	−2188.46	+	3790.52i	−0.352179	+	0.609992i
$339$		0			0
$340$	−2270.74	−	3933.04i	−0.362201	−	0.627350i
$341$	−1949.94	−	3377.40i	−0.309664	−	0.536353i
$342$		0			0
$343$	−2815.85	−	5694.26i	−0.443270	−	0.896388i
$344$	−1472.51	+	2550.46i	−0.230792	+	0.399743i
$345$		0			0
$346$	−6108.45			−0.949110
$347$	5190.20			0.802953			0.401476	−	0.915869i	$-0.368497\pi$
$347$	5190.20			0.802953			0.401476	+	0.915869i	$0.368497\pi$
$348$		0			0
$349$	2454.68	−	4251.64i	0.376494	−	0.652106i	−0.614056	−	0.789263i	$-0.710463\pi$
$349$	2454.68	−	4251.64i	0.376494	−	0.652106i	0.990549	+	0.137157i	$0.0437963\pi$
$350$	−769.775	−	299.026i	−0.117561	−	0.0456675i
$351$		0			0
$352$	609.748	+	1056.11i	0.0923286	+	0.159918i
$353$	2683.78	+	4648.44i	0.404655	+	0.700883i	0.994281	−	0.106793i	$-0.0340583\pi$
$353$	2683.78	+	4648.44i	0.404655	+	0.700883i	−0.589626	+	0.807676i	$0.700725\pi$
$354$		0			0
$355$	2606.99	−	4515.44i	0.389760	−	0.675084i
$356$	−1396.59	−	2418.96i	−0.207918	−	0.360125i
$357$		0			0
$358$	19.8507	−	34.3824i	0.00293057	−	0.00507589i
$359$	−4518.15	−	7825.66i	−0.664230	−	1.15048i	−0.979493	−	0.201476i	$-0.935426\pi$
$359$	−4518.15	−	7825.66i	−0.664230	−	1.15048i	0.315263	−	0.949004i	$-0.397907\pi$
$360$		0			0
$361$	342.302	−	592.884i	0.0499055	−	0.0864389i
$362$	−5702.27			−0.827914
$363$		0			0
$364$	−201.812	−	78.3956i	−0.0290600	−	0.0112886i
$365$	−5988.54	−	10372.5i	−0.858779	−	1.48745i
$366$		0			0
$367$	−4559.69	−	7897.61i	−0.648539	−	1.12330i	−0.983472	−	0.181060i	$-0.942047\pi$
$367$	−4559.69	−	7897.61i	−0.648539	−	1.12330i	0.334933	−	0.942242i	$-0.391286\pi$
$368$	−1176.20	+	2037.23i	−0.166613	+	0.288581i
$369$		0			0
$370$	1018.43			0.143097
$371$	−287.054	−	1860.51i	−0.0401701	−	0.260358i
$372$		0			0
$373$	−364.638	+	631.572i	−0.0506173	+	0.0876718i	−0.890224	−	0.455523i	$-0.849452\pi$
$373$	−364.638	+	631.572i	−0.0506173	+	0.0876718i	0.839607	+	0.543195i	$0.182786\pi$
$374$	8538.89			1.18058
$375$		0			0
$376$	3196.67			0.438446
$377$	804.924			0.109962
$378$		0			0
$379$	12023.6			1.62957			0.814787	−	0.579760i	$-0.196854\pi$
$379$	12023.6			1.62957			0.814787	+	0.579760i	$0.196854\pi$
$380$	−3185.32			−0.430009
$381$		0			0
$382$	−3849.35			−0.515575
$383$	−5253.43	+	9099.22i	−0.700882	+	1.21396i	0.267275	+	0.963620i	$0.413877\pi$
$383$	−5253.43	+	9099.22i	−0.700882	+	1.21396i	−0.968157	+	0.250344i	$0.919456\pi$
$384$		0			0
$385$	−5576.69	+	4479.11i	−0.738219	+	0.592926i
$386$	4139.82			0.545884
$387$		0			0
$388$	−1383.76	+	2396.75i	−0.181056	+	0.313599i
$389$	4080.46	+	7067.57i	0.531845	+	0.921183i	0.999309	+	0.0371706i	$0.0118345\pi$
$389$	4080.46	+	7067.57i	0.531845	+	0.921183i	−0.467464	+	0.884012i	$0.654832\pi$
$390$		0			0
$391$	8235.71	+	14264.7i	1.06521	+	1.84500i
$392$	−591.955	+	2679.39i	−0.0762710	+	0.345229i
$393$		0			0
$394$	−664.892			−0.0850172
$395$	−1723.78	+	2985.67i	−0.219576	+	0.380318i
$396$		0			0
$397$	5248.40	+	9090.49i	0.663500	+	1.14922i	0.979690	+	0.200519i	$0.0642630\pi$
$397$	5248.40	+	9090.49i	0.663500	+	1.14922i	−0.316190	+	0.948696i	$0.602404\pi$
$398$	−741.728	+	1284.71i	−0.0934157	+	0.161801i
$399$		0			0
$400$	178.359	+	308.927i	0.0222949	+	0.0386159i
$401$	−4981.66	+	8628.49i	−0.620380	+	1.07453i	0.369035	+	0.929415i	$0.379688\pi$
$401$	−4981.66	+	8628.49i	−0.620380	+	1.07453i	−0.989415	+	0.145114i	$0.953645\pi$
$402$		0			0
$403$	−149.538	−	259.007i	−0.0184839	−	0.0320150i
$404$	−904.602	−	1566.82i	−0.111400	−	0.192951i
$405$		0			0
$406$	−1555.60	−	10082.4i	−0.190155	−	1.23247i
$407$	−957.431	+	1658.32i	−0.116605	+	0.201965i
$408$		0			0
$409$	12811.2			1.54883			0.774415	−	0.632678i	$-0.218044\pi$
$409$	12811.2			1.54883			0.774415	+	0.632678i	$0.218044\pi$
$410$	47.1374			0.00567793
$411$		0			0
$412$	−486.330	+	842.348i	−0.0581547	+	0.100727i
$413$	−395.888	+	317.971i	−0.0471680	+	0.0378846i
$414$		0			0
$415$	−3164.67	−	5481.37i	−0.374332	−	0.648362i
$416$	46.7605	+	80.9915i	0.00551111	+	0.00954551i
$417$		0			0
$418$	2994.52	−	5186.66i	0.350399	−	0.606909i
$419$	2431.12	+	4210.82i	0.283456	+	0.490960i	0.972234	−	0.234013i	$-0.0751857\pi$
$419$	2431.12	+	4210.82i	0.283456	+	0.490960i	−0.688778	+	0.724973i	$0.741852\pi$
$420$		0			0
$421$	5744.98	−	9950.59i	0.665067	−	1.15193i	−0.314200	−	0.949357i	$-0.601736\pi$
$421$	5744.98	−	9950.59i	0.665067	−	1.15193i	0.979267	−	0.202573i	$-0.0649303\pi$
$422$	3928.29	+	6803.99i	0.453142	+	0.784866i
$423$		0			0
$424$	−406.586	+	704.228i	−0.0465698	+	0.0806612i
$425$	2497.74			0.285078
$426$		0			0
$427$	−8846.94	+	7105.73i	−1.00265	+	0.805317i
$428$	−3976.11	−	6886.83i	−0.449049	−	0.777775i
$429$		0			0
$430$	3730.73	+	6461.82i	0.418400	+	0.724689i
$431$	5074.40	−	8789.12i	0.567112	−	0.982266i	−0.429738	−	0.902954i	$-0.641394\pi$
$431$	5074.40	−	8789.12i	0.567112	−	0.982266i	0.996850	−	0.0793128i	$-0.0252726\pi$
$432$		0			0
$433$	−16331.5			−1.81257			−0.906285	−	0.422667i	$-0.861094\pi$
$433$	−16331.5			−1.81257			−0.906285	+	0.422667i	$0.861094\pi$
$434$	−2955.30	+	2373.65i	−0.326864	+	0.262532i
$435$		0			0
$436$	−2882.06	+	4991.88i	−0.316573	+	0.548321i
$437$	11552.8			1.26463
$438$		0			0
$439$	9655.66			1.04975			0.524874	−	0.851180i	$-0.324112\pi$
$439$	9655.66			1.04975			0.524874	+	0.851180i	$0.324112\pi$
$440$	3089.70			0.334763
$441$		0			0
$442$	654.832			0.0704688
$443$	6311.51			0.676905			0.338453	−	0.940983i	$-0.390096\pi$
$443$	6311.51			0.676905			0.338453	+	0.940983i	$0.390096\pi$
$444$		0			0
$445$	−7076.75			−0.753866
$446$	2219.97	−	3845.10i	0.235692	−	0.408231i
$447$		0			0
$448$	924.124	−	742.242i	0.0974570	−	0.0782760i
$449$	15208.5			1.59852			0.799259	−	0.600987i	$-0.205226\pi$
$449$	15208.5			1.59852			0.799259	+	0.600987i	$0.205226\pi$
$450$		0			0
$451$	−44.3139	+	76.7540i	−0.00462674	+	0.00801376i
$452$	1070.76	+	1854.62i	0.111426	+	0.192995i
$453$		0			0
$454$	−4685.91	−	8116.23i	−0.484407	−	0.839017i
$455$	−427.666	+	343.495i	−0.0440644	+	0.0353919i
$456$		0			0
$457$	685.689			0.0701863			0.0350932	−	0.999384i	$-0.488827\pi$
$457$	685.689			0.0701863			0.0350932	+	0.999384i	$0.488827\pi$
$458$	−668.122	+	1157.22i	−0.0681643	+	0.118064i
$459$		0			0
$460$	2979.99	+	5161.50i	0.302050	+	0.523166i
$461$	1170.39	−	2027.18i	0.118245	−	0.204806i	−0.800828	−	0.598895i	$-0.795607\pi$
$461$	1170.39	−	2027.18i	0.118245	−	0.204806i	0.919072	+	0.394089i	$0.128940\pi$
$462$		0			0
$463$	−1600.72	−	2772.53i	−0.160673	−	0.278294i	0.774437	−	0.632651i	$-0.218033\pi$
$463$	−1600.72	−	2772.53i	−0.160673	−	0.278294i	−0.935110	+	0.354357i	$0.884700\pi$
$464$	−2203.36	+	3816.34i	−0.220450	+	0.381830i
$465$		0			0
$466$	−796.279	−	1379.20i	−0.0791565	−	0.137103i
$467$	−2890.53	−	5006.54i	−0.286419	−	0.496093i	0.686533	−	0.727099i	$-0.259132\pi$
$467$	−2890.53	−	5006.54i	−0.286419	−	0.496093i	−0.972952	+	0.231006i	$0.925798\pi$
$468$		0			0
$469$	−9014.40	+	7240.23i	−0.887519	+	0.712842i
$470$	4049.52	−	7013.98i	0.397427	−	0.688363i
$471$		0			0
$472$	219.337			0.0213894
$473$	−14029.0			−1.36376
$474$		0			0
$475$	875.937	−	1517.17i	0.0846121	−	0.146552i
$476$	−1265.53	−	8202.38i	−0.121860	−	0.789822i
$477$		0			0
$478$	3550.43	+	6149.52i	0.339734	+	0.588436i
$479$	6033.42	+	10450.2i	0.575520	+	0.996830i	0.995985	+	0.0895214i	$0.0285337\pi$
$479$	6033.42	+	10450.2i	0.575520	+	0.996830i	−0.420465	+	0.907309i	$0.638133\pi$
$480$		0			0
$481$	−73.4236	+	127.173i	−0.00696014	+	0.0120553i
$482$	−6047.19	−	10474.0i	−0.571456	−	0.989791i
$483$		0			0
$484$	−242.627	+	420.242i	−0.0227862	+	0.0394668i
$485$	3505.89	+	6072.37i	0.328235	+	0.568520i
$486$		0			0
$487$	−324.153	+	561.449i	−0.0301617	+	0.0522416i	−0.880712	−	0.473652i	$-0.842936\pi$
$487$	−324.153	+	561.449i	−0.0301617	+	0.0522416i	0.850551	+	0.525893i	$0.176269\pi$
$488$	4901.55			0.454677
$489$		0			0
$490$	5129.10	+	4693.07i	0.472876	+	0.432676i
$491$	−10750.9	−	18621.2i	−0.988152	−	1.71153i	−0.626990	−	0.779027i	$-0.715713\pi$
$491$	−10750.9	−	18621.2i	−0.988152	−	1.71153i	−0.361162	−	0.932503i	$-0.617620\pi$
$492$		0			0
$493$	15427.9	+	26722.0i	1.40941	+	2.44117i
$494$	229.644	−	397.756i	0.0209154	−	0.0362265i
$495$		0			0
$496$	1637.35			0.148224
$497$	7428.88	−	5966.77i	0.670485	−	0.538523i
$498$		0			0
$499$	1815.80	−	3145.07i	0.162899	−	0.282149i	−0.773008	−	0.634396i	$-0.781249\pi$
$499$	1815.80	−	3145.07i	0.162899	−	0.282149i	0.935907	+	0.352247i	$0.114582\pi$
$500$	5970.95			0.534058
$501$		0			0
$502$	−979.714			−0.0871051
$503$	−685.011			−0.0607219			−0.0303610	−	0.999539i	$-0.509666\pi$
$503$	−685.011			−0.0607219			−0.0303610	+	0.999539i	$0.509666\pi$
$504$		0			0
$505$	−4583.78			−0.403912
$506$	−11206.0			−0.984519
$507$		0			0
$508$	7280.29			0.635848
$509$	−9836.86	+	17037.9i	−0.856604	+	1.48368i	0.0185452	+	0.999828i	$0.494097\pi$
$509$	−9836.86	+	17037.9i	−0.856604	+	1.48368i	−0.875149	+	0.483853i	$0.839237\pi$
$510$		0			0
$511$	−3337.54	−	21631.8i	−0.288931	−	1.87267i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	−1629.75	+	2822.80i	−0.139854	+	0.242234i
$515$	1232.16	+	2134.16i	0.105428	+	0.182607i
$516$		0			0
$517$	7613.91	+	13187.7i	0.647697	+	1.12184i
$518$	1734.86	+	673.923i	0.147154	+	0.0571631i
$519$		0			0
$520$	236.943			0.0199820
$521$	1428.20	−	2473.71i	0.120097	−	0.208014i	−0.799709	−	0.600388i	$-0.795013\pi$
$521$	1428.20	−	2473.71i	0.120097	−	0.208014i	0.919806	+	0.392374i	$0.128346\pi$
$522$		0			0
$523$	508.387	+	880.552i	0.0425052	+	0.0736211i	0.886495	−	0.462738i	$-0.153133\pi$
$523$	508.387	+	880.552i	0.0425052	+	0.0736211i	−0.843990	+	0.536359i	$0.819799\pi$
$524$	3618.45	−	6267.35i	0.301666	−	0.522501i
$525$		0			0
$526$	6533.74	+	11316.8i	0.541606	+	0.938089i
$527$	5732.36	−	9928.73i	0.473824	−	0.820688i
$528$		0			0
$529$	−4724.59	−	8183.24i	−0.388312	−	0.672576i
$530$	1030.12	+	1784.22i	0.0844258	+	0.146230i
$531$		0			0
$532$	−5426.07	−	2107.80i	−0.442199	−	0.171776i
$533$	−3.39836	+	5.88612i	−0.000276171	+	0.000478342i
$534$		0			0
$535$	−20147.7			−1.62815
$536$	4994.33			0.402466
$537$		0			0
$538$	−690.508	+	1196.00i	−0.0553344	+	0.0958420i
$539$	−12463.6	+	3939.76i	−0.996003	+	0.314838i
$540$		0			0
$541$	9526.57	+	16500.5i	0.757078	+	1.31130i	0.944335	+	0.328986i	$0.106707\pi$
$541$	9526.57	+	16500.5i	0.757078	+	1.31130i	−0.187257	+	0.982311i	$0.559960\pi$
$542$	3969.36	+	6875.13i	0.314573	+	0.544856i
$543$		0			0
$544$	−1792.51	+	3104.72i	−0.141274	+	0.244694i
$545$	7301.96	+	12647.4i	0.573911	+	0.994044i
$546$		0			0
$547$	−1969.20	+	3410.76i	−0.153925	+	0.266606i	−0.932667	−	0.360738i	$-0.882525\pi$
$547$	−1969.20	+	3410.76i	−0.153925	+	0.266606i	0.778742	+	0.627344i	$0.215858\pi$
$548$	5462.17	+	9460.76i	0.425789	+	0.737488i
$549$		0			0
$550$	−849.642	+	1471.62i	−0.0658706	+	0.114091i
$551$	21641.8			1.67327
$552$		0			0
$553$	−4912.08	+	3945.31i	−0.377727	+	0.303384i
$554$	−5360.74	−	9285.07i	−0.411112	−	0.712067i
$555$		0			0
$556$	−628.742	−	1089.01i	−0.0479579	−	0.0830656i
$557$	7987.80	−	13835.3i	0.607637	−	1.05246i	−0.383991	−	0.923337i	$-0.625451\pi$
$557$	7987.80	−	13835.3i	0.607637	−	1.05246i	0.991629	−	0.129122i	$-0.0412159\pi$
$558$		0			0
$559$	−1075.86			−0.0814027
$560$	−457.918	−	2967.94i	−0.0345546	−	0.223961i
$561$		0			0
$562$	−4614.31	+	7992.22i	−0.346340	+	0.599878i
$563$	6038.96			0.452064			0.226032	−	0.974120i	$-0.427425\pi$
$563$	6038.96			0.452064			0.226032	+	0.974120i	$0.427425\pi$
$564$		0			0
$565$	5425.75			0.404005
$566$	−574.583			−0.0426705
$567$		0			0
$568$	−4115.89			−0.304047
$569$	−9396.43			−0.692300			−0.346150	−	0.938179i	$-0.612511\pi$
$569$	−9396.43			−0.692300			−0.346150	+	0.938179i	$0.612511\pi$
$570$		0			0
$571$	−129.814			−0.00951410			−0.00475705	−	0.999989i	$-0.501514\pi$
$571$	−129.814			−0.00951410			−0.00475705	+	0.999989i	$0.501514\pi$
$572$	−222.751	+	385.815i	−0.0162826	+	0.0282024i
$573$		0			0
$574$	80.2968	+	31.1920i	0.00583889	+	0.00226817i
$575$	−3277.90			−0.237735
$576$		0			0
$577$	3571.96	−	6186.82i	0.257717	−	0.446379i	−0.707913	−	0.706300i	$-0.750363\pi$
$577$	3571.96	−	6186.82i	0.257717	−	0.446379i	0.965630	+	0.259921i	$0.0836965\pi$
$578$	7638.13	+	13229.6i	0.549662	+	0.952042i
$579$		0			0
$580$	5582.42	+	9669.03i	0.399650	+	0.692215i
$581$	−1763.74	−	11431.4i	−0.125942	−	0.816276i
$582$		0			0
$583$	−3873.67			−0.275182
$584$	−4727.32	+	8187.96i	−0.334962	+	0.580171i
$585$		0			0
$586$	−2522.98	−	4369.93i	−0.177856	−	0.308055i
$587$	2440.05	−	4226.29i	0.171570	−	0.297168i	−0.767399	−	0.641170i	$-0.778449\pi$
$587$	2440.05	−	4226.29i	0.171570	−	0.297168i	0.938969	+	0.344002i	$0.111783\pi$
$588$		0			0
$589$	−4020.58	−	6963.85i	−0.281265	−	0.487166i
$590$	277.855	−	481.259i	0.0193883	−	0.0335816i
$591$		0			0
$592$	−401.973	−	696.238i	−0.0279071	−	0.0483365i
$593$	11169.5	+	19346.2i	0.773485	+	1.33972i	0.935642	+	0.352951i	$0.114822\pi$
$593$	11169.5	+	19346.2i	0.773485	+	1.33972i	−0.162157	+	0.986765i	$0.551845\pi$
$594$		0			0
$595$	−19600.4	−	7613.96i	−1.35049	−	0.524608i
$596$	−3606.50	+	6246.65i	−0.247866	+	0.429317i
$597$		0			0
$598$	−859.366			−0.0587660
$599$	−15642.0			−1.06697			−0.533484	−	0.845810i	$-0.679117\pi$
$599$	−15642.0			−1.06697			−0.533484	+	0.845810i	$0.679117\pi$
$600$		0			0
$601$	12769.4	−	22117.2i	0.866678	−	1.50113i	0.00130757	−	0.999999i	$-0.499584\pi$
$601$	12769.4	−	22117.2i	0.866678	−	1.50113i	0.865371	−	0.501132i	$-0.167083\pi$
$602$	2079.21	+	13476.2i	0.140768	+	0.912371i
$603$		0			0
$604$	948.928	+	1643.59i	0.0639261	+	0.110723i
$605$	614.717	+	1064.72i	0.0413087	+	0.0715488i
$606$		0			0
$607$	−10188.0	+	17646.1i	−0.681246	+	1.17995i	0.293355	+	0.956004i	$0.405228\pi$
$607$	−10188.0	+	17646.1i	−0.681246	+	1.17995i	−0.974601	+	0.223949i	$0.928105\pi$
$608$	1257.24	+	2177.60i	0.0838614	+	0.145252i
$609$		0			0
$610$	6209.25	−	10754.7i	0.412140	−	0.713847i
$611$	583.897	+	1011.34i	0.0386611	+	0.0669631i
$612$		0			0
$613$	−9378.35	+	16243.8i	−0.617925	+	1.07028i	0.371939	+	0.928257i	$0.378693\pi$
$613$	−9378.35	+	16243.8i	−0.617925	+	1.07028i	−0.989864	+	0.142020i	$0.954640\pi$
$614$	15488.0			1.01799
$615$		0			0
$616$	5263.18	+	2044.53i	0.344253	+	0.133728i
$617$	4934.80	+	8547.32i	0.321989	+	0.557702i	0.980898	−	0.194521i	$-0.0623152\pi$
$617$	4934.80	+	8547.32i	0.321989	+	0.557702i	−0.658909	+	0.752223i	$0.728982\pi$
$618$		0			0
$619$	−28.4617	−	49.2970i	−0.00184809	−	0.00320099i	0.865100	−	0.501600i	$-0.167255\pi$
$619$	−28.4617	−	49.2970i	−0.00184809	−	0.00320099i	−0.866948	+	0.498399i	$0.833922\pi$
$620$	2074.19	−	3592.60i	0.134357	−	0.232713i
$621$		0			0
$622$	−13905.7			−0.896413
$623$	−12055.0	−	4682.86i	−0.775237	−	0.301147i
$624$		0			0
$625$	6170.54	−	10687.7i	0.394914	−	0.684012i
$626$	−19154.9			−1.22298
$627$		0			0
$628$	−5880.43			−0.373654
$629$	−5629.22			−0.356839
$630$		0			0
$631$	16197.8			1.02191			0.510953	−	0.859608i	$-0.329292\pi$
$631$	16197.8			1.02191			0.510953	+	0.859608i	$0.329292\pi$
$632$	2721.48			0.171289
$633$		0			0
$634$	3906.00			0.244680
$635$	9222.63	−	15974.1i	0.576360	−	0.998285i
$636$		0			0
$637$	−955.812	+	302.133i	−0.0594515	+	0.0187927i
$638$	−20992.1			−1.30264
$639$		0			0
$640$	−648.599	+	1123.41i	−0.0400595	+	0.0693852i
$641$	−4859.04	−	8416.10i	−0.299408	−	0.518590i	0.676593	−	0.736357i	$-0.263456\pi$
$641$	−4859.04	−	8416.10i	−0.299408	−	0.518590i	−0.976001	+	0.217768i	$0.930122\pi$
$642$		0			0
$643$	−2191.82	−	3796.34i	−0.134427	−	0.232835i	0.790951	−	0.611879i	$-0.209586\pi$
$643$	−2191.82	−	3796.34i	−0.134427	−	0.232835i	−0.925379	+	0.379044i	$0.876253\pi$
$644$	1660.81	+	10764.4i	0.101623	+	0.658657i
$645$		0			0
$646$	17606.3			1.07231
$647$	7211.34	−	12490.4i	0.438187	−	0.758962i	−0.559363	−	0.828923i	$-0.688954\pi$
$647$	7211.34	−	12490.4i	0.438187	−	0.758962i	0.997550	+	0.0699608i	$0.0222874\pi$
$648$		0			0
$649$	522.423	+	904.863i	0.0315977	+	0.0547288i
$650$	−65.1575	+	112.856i	−0.00393183	+	0.00681012i
$651$		0			0
$652$	2595.98	+	4496.37i	0.155930	+	0.270079i
$653$	7683.72	−	13308.6i	0.460470	−	0.797558i	−0.538514	−	0.842616i	$-0.681014\pi$
$653$	7683.72	−	13308.6i	0.460470	−	0.797558i	0.998984	+	0.0450586i	$0.0143475\pi$
$654$		0			0
$655$	−9167.67	−	15878.9i	−0.546886	−	0.947235i
$656$	−18.6050	−	32.2248i	−0.00110732	−	0.00191794i
$657$		0			0
$658$	11539.5	−	9268.37i	0.683674	−	0.549117i
$659$	2981.41	−	5163.96i	0.176236	−	0.305249i	−0.764352	−	0.644799i	$-0.776941\pi$
$659$	2981.41	−	5163.96i	0.176236	−	0.305249i	0.940588	+	0.339549i	$0.110275\pi$
$660$		0			0
$661$	1913.38			0.112590			0.0562948	−	0.998414i	$-0.482071\pi$
$661$	1913.38			0.112590			0.0562948	+	0.998414i	$0.482071\pi$
$662$	22132.6			1.29941
$663$		0			0
$664$	−2498.17	+	4326.97i	−0.146006	+	0.252890i
$665$	−11498.6	+	9235.47i	−0.670519	+	0.538550i
$666$		0			0
$667$	−20246.8	−	35068.4i	−1.17535	−	2.03576i
$668$	869.027	+	1505.20i	0.0503348	+	0.0871825i
$669$		0			0
$670$	6326.78	−	10958.3i	0.364813	−	0.631875i
$671$	11674.6	+	20221.1i	0.671675	+	1.16338i
$672$		0			0
$673$	4203.83	−	7281.25i	0.240781	−	0.417045i	−0.720156	−	0.693812i	$-0.755930\pi$
$673$	4203.83	−	7281.25i	0.240781	−	0.417045i	0.960937	+	0.276767i	$0.0892631\pi$
$674$	−7982.60	−	13826.3i	−0.456199	−	0.790160i
$675$		0			0
$676$	4376.92	−	7581.04i	0.249028	−	0.431329i
$677$	2955.73			0.167796			0.0838980	−	0.996474i	$-0.473263\pi$
$677$	2955.73			0.167796			0.0838980	+	0.996474i	$0.473263\pi$
$678$		0			0
$679$	1953.90	+	12664.0i	0.110433	+	0.715757i
$680$	4541.48	+	7866.07i	0.256114	+	0.443603i
$681$		0			0
$682$	3899.89	+	6754.80i	0.218965	+	0.379259i
$683$	7452.33	−	12907.8i	0.417504	−	0.723139i	−0.578183	−	0.815907i	$-0.696238\pi$
$683$	7452.33	−	12907.8i	0.417504	−	0.723139i	0.995688	+	0.0927680i	$0.0295715\pi$
$684$		0			0
$685$	27677.8			1.54382
$686$	5631.70	+	11388.5i	0.313439	+	0.633842i
$687$		0			0
$688$	2945.02	−	5100.92i	0.163194	−	0.282661i
$689$	−297.065			−0.0164257
$690$		0			0
$691$	13014.3			0.716482			0.358241	−	0.933629i	$-0.383377\pi$
$691$	13014.3			0.716482			0.358241	+	0.933629i	$0.383377\pi$
$692$	12216.9			0.671122
$693$		0			0
$694$	−10380.4			−0.567773
$695$	−3185.95			−0.173885
$696$		0			0
$697$	−260.544			−0.0141590
$698$	−4909.37	+	8503.28i	−0.266221	+	0.461109i
$699$		0			0
$700$	1539.55	+	598.052i	0.0831279	+	0.0322918i
$701$	498.114			0.0268381			0.0134190	−	0.999910i	$-0.495728\pi$
$701$	498.114			0.0268381			0.0134190	+	0.999910i	$0.495728\pi$
$702$		0			0
$703$	−1974.12	+	3419.28i	−0.105911	+	0.183443i
$704$	−1219.50	−	2112.23i	−0.0652862	−	0.113079i
$705$		0			0
$706$	−5367.56	−	9296.88i	−0.286134	−	0.495599i
$707$	−7808.29	−	3033.20i	−0.415362	−	0.161351i
$708$		0			0
$709$	−30008.1			−1.58953			−0.794765	−	0.606917i	$-0.792406\pi$
$709$	−30008.1			−1.58953			−0.794765	+	0.606917i	$0.792406\pi$
$710$	−5213.98	+	9030.88i	−0.275602	+	0.477356i
$711$		0			0
$712$	2793.17	+	4837.92i	0.147021	+	0.254647i
$713$	−7522.83	+	13029.9i	−0.395136	+	0.684396i
$714$		0			0
$715$	564.358	+	977.497i	0.0295186	+	0.0511277i
$716$	−39.7014	+	68.7649i	−0.00207222	+	0.00358919i
$717$		0			0
$718$	9036.29	+	15651.3i	0.469682	+	0.813512i
$719$	−4836.60	−	8377.24i	−0.250869	−	0.434518i	0.712896	−	0.701269i	$-0.247383\pi$
$719$	−4836.60	−	8377.24i	−0.250869	−	0.434518i	−0.963765	+	0.266752i	$0.914050\pi$
$720$		0			0
$721$	686.708	+	4450.81i	0.0354707	+	0.229899i
$722$	−684.604	+	1185.77i	−0.0352885	+	0.0611215i
$723$		0			0
$724$	11404.5			0.585423
$725$	−6140.47			−0.314554
$726$		0			0
$727$	−4048.68	+	7012.51i	−0.206544	+	0.357744i	−0.950623	−	0.310347i	$-0.899555\pi$
$727$	−4048.68	+	7012.51i	−0.206544	+	0.357744i	0.744080	+	0.668091i	$0.232888\pi$
$728$	403.624	+	156.791i	0.0205485	+	0.00798224i
$729$		0			0
$730$	11977.1	+	20744.9i	0.607249	+	1.05179i
$731$	−20621.0	−	35716.6i	−1.04336	−	1.80715i
$732$		0			0
$733$	−14017.2	+	24278.4i	−0.706325	+	1.22339i	0.259887	+	0.965639i	$0.416315\pi$
$733$	−14017.2	+	24278.4i	−0.706325	+	1.22339i	−0.966211	+	0.257751i	$0.917019\pi$
$734$	9119.37	+	15795.2i	0.458586	+	0.794294i
$735$		0			0
$736$	2352.39	−	4074.46i	0.117813	−	0.204058i
$737$	11895.6	+	20603.8i	0.594546	+	1.02978i
$738$		0			0
$739$	−8095.53	+	14021.9i	−0.402975	+	0.697974i	−0.994084	−	0.108618i	$-0.965357\pi$
$739$	−8095.53	+	14021.9i	−0.402975	+	0.697974i	0.591108	+	0.806592i	$0.298691\pi$
$740$	−2036.87			−0.101185
$741$		0			0
$742$	574.109	+	3721.01i	0.0284046	+	0.184101i
$743$	7441.12	+	12888.4i	0.367414	+	0.636379i	0.989160	−	0.146839i	$-0.0469100\pi$
$743$	7441.12	+	12888.4i	0.367414	+	0.636379i	−0.621747	+	0.783218i	$0.713577\pi$
$744$		0			0
$745$	9137.40	+	15826.4i	0.449353	+	0.778303i
$746$	729.277	−	1263.14i	0.0357918	−	0.0619933i
$747$		0			0
$748$	−17077.8			−0.834794
$749$	−34320.8	−	13332.2i	−1.67430	−	0.650398i
$750$		0			0
$751$	18099.6	−	31349.4i	0.879444	−	1.52324i	0.0274919	−	0.999622i	$-0.491248\pi$
$751$	18099.6	−	31349.4i	0.879444	−	1.52324i	0.851952	−	0.523620i	$-0.175419\pi$
$752$	−6393.34			−0.310028
$753$		0			0
$754$	−1609.85			−0.0777549
$755$	4808.39			0.231782
$756$		0			0
$757$	−14141.6			−0.678979			−0.339489	−	0.940610i	$-0.610254\pi$
$757$	−14141.6			−0.678979			−0.339489	+	0.940610i	$0.610254\pi$
$758$	−24047.1			−1.15228
$759$		0			0
$760$	6370.64			0.304062
$761$	8160.06	−	14133.6i	0.388702	−	0.673251i	−0.603574	−	0.797307i	$-0.706257\pi$
$761$	8160.06	−	14133.6i	0.388702	−	0.673251i	0.992275	+	0.124056i	$0.0395904\pi$
$762$		0			0
$763$	4069.54	+	26376.2i	0.193089	+	1.25148i
$764$	7698.69			0.364567
$765$		0			0
$766$	10506.9	−	18198.4i	0.495599	−	0.858402i
$767$	40.0637	+	69.3924i	0.00188607	+	0.00326677i
$768$		0			0
$769$	1035.13	+	1792.89i	0.0485404	+	0.0840745i	0.889275	−	0.457373i	$-0.151210\pi$
$769$	1035.13	+	1792.89i	0.0485404	+	0.0840745i	−0.840734	+	0.541448i	$0.817876\pi$
$770$	11153.4	−	8958.22i	0.522000	−	0.419262i
$771$		0			0
$772$	−8279.64			−0.385998
$773$	−6449.50	+	11170.9i	−0.300094	+	0.519778i	−0.976157	−	0.217066i	$-0.930351\pi$
$773$	−6449.50	+	11170.9i	−0.300094	+	0.519778i	0.676063	+	0.736844i	$0.263685\pi$
$774$		0			0
$775$	1140.77	+	1975.87i	0.0528743	+	0.0915810i
$776$	2767.53	−	4793.50i	0.128026	−	0.221748i
$777$		0			0
$778$	−8160.93	−	14135.1i	−0.376071	−	0.651375i
$779$	−91.3708	+	158.259i	−0.00420244	+	0.00727883i
$780$		0			0
$781$	−9803.33	−	16979.9i	−0.449156	−	0.777961i
$782$	−16471.4	−	28529.3i	−0.753218	−	1.30461i
$783$		0			0
$784$	1183.91	−	5358.78i	0.0539318	−	0.244113i
$785$	−7449.30	+	12902.6i	−0.338697	+	0.586640i
$786$		0			0
$787$	−18231.3			−0.825764			−0.412882	−	0.910785i	$-0.635478\pi$
$787$	−18231.3			−0.825764			−0.412882	+	0.910785i	$0.635478\pi$
$788$	1329.78			0.0601162
$789$		0			0
$790$	3447.56	−	5971.34i	0.155264	−	0.268925i
$791$	9242.55	+	3590.35i	0.415458	+	0.161388i
$792$		0			0
$793$	895.307	+	1550.72i	0.0400924	+	0.0694421i
$794$	−10496.8	−	18181.0i	−0.469165	−	0.812618i
$795$		0			0
$796$	1483.46	−	2569.42i	0.0660549	−	0.114410i
$797$	−3102.97	−	5374.51i	−0.137908	−	0.238864i	0.788796	−	0.614655i	$-0.210705\pi$
$797$	−3102.97	−	5374.51i	−0.137908	−	0.238864i	−0.926705	+	0.375790i	$0.877371\pi$
$798$		0			0
$799$	−22383.0	+	38768.6i	−0.991058	+	1.71656i
$800$	−356.719	−	617.855i	−0.0157649	−	0.0273056i
$801$		0			0
$802$	9963.32	−	17257.0i	0.438675	−	0.759807i
$803$	−45038.6			−1.97930
$804$		0			0
$805$	25722.5	+	9992.14i	1.12621	+	0.437487i
$806$	299.075	+	518.014i	0.0130701	+	0.0226380i
$807$		0			0
$808$	1809.20	+	3133.63i	0.0787718	+	0.136437i
$809$	3193.05	−	5530.52i	0.138766	−	0.240350i	−0.788264	−	0.615337i	$-0.789020\pi$
$809$	3193.05	−	5530.52i	0.138766	−	0.240350i	0.927030	+	0.374988i	$0.122353\pi$
$810$		0			0
$811$	41701.4			1.80559			0.902795	−	0.430071i	$-0.141512\pi$
$811$	41701.4			1.80559			0.902795	+	0.430071i	$0.141512\pi$
$812$	3111.20	+	20164.8i	0.134460	+	0.871486i
$813$		0			0
$814$	1914.86	−	3316.64i	0.0824519	−	0.142811i
$815$	13154.3			0.565368
$816$		0			0
$817$	−28926.5			−1.23869
$818$	−25622.3			−1.09519
$819$		0			0
$820$	−94.2749			−0.00401490
$821$	8758.22			0.372307			0.186153	−	0.982521i	$-0.440398\pi$
$821$	8758.22			0.372307			0.186153	+	0.982521i	$0.440398\pi$
$822$		0			0
$823$	3758.20			0.159177			0.0795885	−	0.996828i	$-0.474639\pi$
$823$	3758.20			0.159177			0.0795885	+	0.996828i	$0.474639\pi$
$824$	972.660	−	1684.70i	0.0411216	−	0.0712247i
$825$		0			0
$826$	791.776	−	635.943i	0.0333528	−	0.0267885i
$827$	−5909.53			−0.248482			−0.124241	−	0.992252i	$-0.539650\pi$
$827$	−5909.53			−0.248482			−0.124241	+	0.992252i	$0.539650\pi$
$828$		0			0
$829$	11329.0	−	19622.4i	0.474634	−	0.822090i	−0.524944	−	0.851137i	$-0.675914\pi$
$829$	11329.0	−	19622.4i	0.474634	−	0.822090i	0.999578	+	0.0290467i	$0.00924715\pi$
$830$	6329.35	+	10962.7i	0.264693	+	0.458461i
$831$		0			0
$832$	−93.5209	−	161.983i	−0.00389694	−	0.00674970i
$833$	−28350.2	−	25940.2i	−1.17920	−	1.07896i
$834$		0			0
$835$	4403.51			0.182503
$836$	−5989.04	+	10373.3i	−0.247770	+	0.429150i
$837$		0			0
$838$	−4862.24	−	8421.65i	−0.200434	−	0.347161i
$839$	4336.21	−	7510.53i	0.178430	−	0.309049i	−0.762913	−	0.646501i	$-0.776232\pi$
$839$	4336.21	−	7510.53i	0.178430	−	0.309049i	0.941343	+	0.337452i	$0.109565\pi$
$840$		0			0
$841$	−25733.7	−	44572.1i	−1.05514	−	1.82755i
$842$	−11490.0	+	19901.2i	−0.470273	+	0.814537i
$843$		0			0
$844$	−7856.58	−	13608.0i	−0.320420	−	0.554984i
$845$	−11089.3	−	19207.2i	−0.451460	−	0.781952i
$846$		0			0
$847$	342.595	+	2220.48i	0.0138981	+	0.0900788i
$848$	813.173	−	1408.46i	0.0329298	−	0.0570361i
$849$		0			0
$850$	−4995.48			−0.201581
$851$	7387.49			0.297579
$852$		0			0
$853$	7818.47	−	13542.0i	0.313833	−	0.543574i	−0.665356	−	0.746526i	$-0.731720\pi$
$853$	7818.47	−	13542.0i	0.313833	−	0.543574i	0.979189	+	0.202952i	$0.0650536\pi$
$854$	17693.9	−	14211.5i	0.708984	−	0.569445i
$855$		0			0
$856$	7952.23	+	13773.7i	0.317525	+	0.549970i
$857$	−11054.8	−	19147.4i	−0.440635	−	0.763202i	0.557102	−	0.830444i	$-0.311913\pi$
$857$	−11054.8	−	19147.4i	−0.440635	−	0.763202i	−0.997737	+	0.0672422i	$0.978580\pi$
$858$		0			0
$859$	20755.8	−	35950.1i	0.824421	−	1.42794i	−0.0779396	−	0.996958i	$-0.524834\pi$
$859$	20755.8	−	35950.1i	0.824421	−	1.42794i	0.902361	−	0.430981i	$-0.141833\pi$
$860$	−7461.46	−	12923.6i	−0.295853	−	0.512433i
$861$		0			0
$862$	−10148.8	+	17578.2i	−0.401009	+	0.694567i
$863$	−13658.8	−	23657.7i	−0.538760	−	0.933161i	−0.998971	−	0.0453508i	$-0.985559\pi$
$863$	−13658.8	−	23657.7i	−0.538760	−	0.933161i	0.460211	−	0.887810i	$-0.347774\pi$
$864$		0			0
$865$	15476.3	−	26805.7i	0.608335	−	1.05367i
$866$	32663.0			1.28168
$867$		0			0
$868$	5910.60	−	4747.31i	0.231128	−	0.185638i
$869$	6482.10	+	11227.3i	0.253038	+	0.438275i
$870$		0			0
$871$	912.254	+	1580.07i	0.0354886	+	0.0614680i
$872$	5764.13	−	9983.76i	0.223851	−	0.387721i
$873$		0			0
$874$	−23105.6			−0.894231
$875$	21554.3	−	17312.1i	0.832764	−	0.668863i
$876$		0			0
$877$	23992.7	−	41556.6i	0.923805	−	1.60008i	0.130333	−	0.991470i	$-0.458395\pi$
$877$	23992.7	−	41556.6i	0.923805	−	1.60008i	0.793472	−	0.608607i	$-0.208271\pi$
$878$	−19311.3			−0.742284
$879$		0			0
$880$	−6179.40			−0.236713
$881$	−10139.6			−0.387754			−0.193877	−	0.981026i	$-0.562106\pi$
$881$	−10139.6			−0.387754			−0.193877	+	0.981026i	$0.562106\pi$
$882$		0			0
$883$	−27045.7			−1.03076			−0.515380	−	0.856962i	$-0.672349\pi$
$883$	−27045.7			−1.03076			−0.515380	+	0.856962i	$0.672349\pi$
$884$	−1309.66			−0.0498290
$885$		0			0
$886$	−12623.0			−0.478644
$887$	−24472.7	+	42387.9i	−0.926394	+	1.60456i	−0.137090	+	0.990559i	$0.543775\pi$
$887$	−24472.7	+	42387.9i	−0.926394	+	1.60456i	−0.789304	+	0.614003i	$0.789558\pi$
$888$		0			0
$889$	26280.8	−	21108.3i	0.991485	−	0.796346i
$890$	14153.5			0.533064
$891$		0			0
$892$	−4439.94	+	7690.20i	−0.166659	+	0.288663i
$893$	15699.1	+	27191.6i	0.588298	+	1.01896i
$894$		0			0
$895$	100.587	+	174.222i	0.00375671	+	0.00650681i
$896$	−1848.25	+	1484.48i	−0.0689125	+	0.0553495i
$897$		0			0
$898$	−30417.0			−1.13032
$899$	−14092.5	+	24408.9i	−0.522815	+	0.905543i
$900$		0			0
$901$	−5693.83	−	9862.00i	−0.210532	−	0.364651i
$902$	88.6279	−	153.508i	0.00327160	−	0.00566658i
$903$		0			0
$904$	−2141.53	−	3709.23i	−0.0787900	−	0.136468i
$905$	14447.2	−	25023.3i	0.530654	−	0.919119i
$906$		0			0
$907$	−5737.04	−	9936.84i	−0.210028	−	0.363779i	0.741695	−	0.670737i	$-0.234022\pi$
$907$	−5737.04	−	9936.84i	−0.210028	−	0.363779i	−0.951723	+	0.306958i	$0.900689\pi$
$908$	9371.82	+	16232.5i	0.342527	+	0.593275i
$909$		0			0
$910$	855.332	−	686.990i	0.0311582	−	0.0250258i
$911$	−8714.62	+	15094.2i	−0.316935	+	0.548948i	−0.979847	−	0.199750i	$-0.935987\pi$
$911$	−8714.62	+	15094.2i	−0.316935	+	0.548948i	0.662912	+	0.748698i	$0.269320\pi$
$912$		0			0
$913$	−23800.9			−0.862754
$914$	−1371.38			−0.0496292
$915$		0			0
$916$	1336.24	−	2314.44i	0.0481995	−	0.0834839i
$917$	−5109.34	−	33115.5i	−0.183997	−	1.19255i
$918$		0			0
$919$	10899.4	+	18878.3i	0.391226	+	0.677624i	0.992612	−	0.121335i	$-0.0387176\pi$
$919$	10899.4	+	18878.3i	0.391226	+	0.677624i	−0.601385	+	0.798959i	$0.705384\pi$
$920$	−5959.99	−	10323.0i	−0.213582	−	0.369934i
$921$		0			0
$922$	−2340.79	+	4054.37i	−0.0836115	+	0.144819i
$923$	−751.800	−	1302.16i	−0.0268102	−	0.0464366i
$924$		0			0
$925$	560.122	−	970.160i	0.0199100	−	0.0344851i
$926$	3201.44	+	5545.06i	0.113613	+	0.196784i
$927$		0			0
$928$	4406.73	−	7632.68i	0.155881	−	0.269994i
$929$	33606.1			1.18685			0.593424	−	0.804890i	$-0.297776\pi$
$929$	33606.1			1.18685			0.593424	+	0.804890i	$0.297776\pi$
$930$		0			0
$931$	−25698.7	+	8123.39i	−0.904662	+	0.285965i
$932$	1592.56	+	2758.39i	0.0559721	+	0.0969465i
$933$		0			0
$934$	5781.06	+	10013.1i	0.202529	+	0.350790i
$935$	−21634.0	+	37471.3i	−0.756694	+	1.31063i
$936$		0			0
$937$	−46831.2			−1.63277			−0.816386	−	0.577506i	$-0.804026\pi$
$937$	−46831.2			−1.63277			−0.816386	+	0.577506i	$0.804026\pi$
$938$	18028.8	−	14480.5i	0.627571	−	0.504055i
$939$		0			0
$940$	−8099.04	+	14028.0i	−0.281023	+	0.486746i
$941$	−3329.38			−0.115340			−0.0576698	−	0.998336i	$-0.518367\pi$
$941$	−3329.38			−0.115340			−0.0576698	+	0.998336i	$0.518367\pi$
$942$		0			0
$943$	341.924			0.0118076
$944$	−438.674			−0.0151246
$945$		0			0
$946$	28058.1			0.964321
$947$	17566.0			0.602764			0.301382	−	0.953503i	$-0.402552\pi$
$947$	17566.0			0.602764			0.301382	+	0.953503i	$0.402552\pi$
$948$		0			0
$949$	−3453.93			−0.118145
$950$	−1751.87	+	3034.34i	−0.0598298	+	0.103628i
$951$		0			0
$952$	2531.06	+	16404.8i	0.0861683	+	0.558489i
$953$	43035.4			1.46280			0.731402	−	0.681946i	$-0.238866\pi$
$953$	43035.4			1.46280			0.731402	+	0.681946i	$0.238866\pi$
$954$		0			0
$955$	9752.66	−	16892.1i	0.330459	−	0.572372i
$956$	−7100.86	−	12299.0i	−0.240228	−	0.416087i
$957$		0			0
$958$	−12066.8	−	20900.4i	−0.406954	−	0.704865i
$959$	47148.0	+	18315.1i	1.58758	+	0.616709i
$960$		0			0
$961$	−19318.7			−0.648473
$962$	146.847	−	254.347i	0.00492157	−	0.00852440i
$963$		0			0
$964$	12094.4	+	20948.1i	0.404081	+	0.699888i
$965$	−10488.6	+	18166.8i	−0.349886	+	0.606020i
$966$		0			0
$967$	13509.5	+	23399.1i	0.449261	+	0.778143i	0.998338	−	0.0576288i	$-0.0183540\pi$
$967$	13509.5	+	23399.1i	0.449261	+	0.778143i	−0.549077	+	0.835772i	$0.685021\pi$
$968$	485.254	−	840.485i	0.0161122	−	0.0279072i
$969$		0			0
$970$	−7011.77	−	12144.7i	−0.232097	−	0.402004i
$971$	−2542.74	−	4404.15i	−0.0840374	−	0.145557i	0.820943	−	0.571010i	$-0.193448\pi$
$971$	−2542.74	−	4404.15i	−0.0840374	−	0.145557i	−0.904981	+	0.425453i	$0.860115\pi$
$972$		0			0
$973$	−5427.14	−	2108.22i	−0.178814	−	0.0694619i
$974$	648.305	−	1122.90i	0.0213276	−	0.0369404i
$975$		0			0
$976$	−9803.09			−0.321505
$977$	4907.06			0.160687			0.0803433	−	0.996767i	$-0.474398\pi$
$977$	4907.06			0.160687			0.0803433	+	0.996767i	$0.474398\pi$
$978$		0			0
$979$	−13305.7	+	23046.2i	−0.434374	+	0.752359i
$980$	−10258.2	−	9386.15i	−0.334374	−	0.305948i
$981$		0			0
$982$	21501.9	+	37242.3i	0.698729	+	1.21023i
$983$	7473.15	+	12943.9i	0.242479	+	0.419985i	0.961420	−	0.275086i	$-0.0887063\pi$
$983$	7473.15	+	12943.9i	0.242479	+	0.419985i	−0.718941	+	0.695071i	$0.755373\pi$
$984$		0			0
$985$	1684.56	−	2917.75i	0.0544920	−	0.0943829i
$986$	−30855.9	−	53443.9i	−0.996603	−	1.72617i
$987$		0			0
$988$	−459.289	+	795.512i	−0.0147894	+	0.0256160i
$989$	27061.8	+	46872.5i	0.870088	+	1.50704i
$990$		0			0
$991$	−19418.8	+	33634.4i	−0.622462	+	1.07814i	0.366564	+	0.930393i	$0.380534\pi$
$991$	−19418.8	+	33634.4i	−0.622462	+	1.07814i	−0.989026	+	0.147742i	$0.952799\pi$
$992$	−3274.70			−0.104810
$993$		0			0
$994$	−14857.8	+	11933.5i	−0.474104	+	0.380794i
$995$	−3758.46	−	6509.85i	−0.119750	−	0.207413i
$996$		0			0
$997$	−7806.47	−	13521.2i	−0.247977	−	0.429509i	0.714987	−	0.699138i	$-0.246433\pi$
$997$	−7806.47	−	13521.2i	−0.247977	−	0.429509i	−0.962965	+	0.269628i	$0.913099\pi$
$998$	−3631.61	+	6290.13i	−0.115187	+	0.199510i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	378.4.e.a.235.9		24
3.2	odd	2		126.4.e.b.25.8	✓	24
7.2	even	3		378.4.h.b.289.4		24
9.4	even	3		378.4.h.b.361.4		24
9.5	odd	6		126.4.h.a.67.1	yes	24
21.2	odd	6		126.4.h.a.79.1	yes	24
63.23	odd	6		126.4.e.b.121.8	yes	24
63.58	even	3	inner	378.4.e.a.37.9		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
126.4.e.b.25.8	✓	24	3.2	odd	2
126.4.e.b.121.8	yes	24	63.23	odd	6
126.4.h.a.67.1	yes	24	9.5	odd	6
126.4.h.a.79.1	yes	24	21.2	odd	6
378.4.e.a.37.9		24	63.58	even	3	inner
378.4.e.a.235.9		24	1.1	even	1	trivial
378.4.h.b.289.4		24	7.2	even	3
378.4.h.b.361.4		24	9.4	even	3

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:	\( N \)	\(=\)	\( 378 = 2 \cdot 3^{3} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	378.e (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q-2.00000 q^{2} +4.00000 q^{4} +(5.06718 - 8.77661i) q^{5} +(14.4394 - 11.5975i) q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q-2.00000 q^{2} +4.00000 q^{4} +(5.06718 - 8.77661i) q^{5} +(14.4394 - 11.5975i) q^{7} -8.00000 q^{8} +(-10.1344 + 17.5532i) q^{10} +(-19.0546 - 33.0036i) q^{11} +(-1.46126 - 2.53098i) q^{13} +(-28.8789 + 23.1951i) q^{14} +16.0000 q^{16} +(56.0159 - 97.0224i) q^{17} +(-39.2887 - 68.0500i) q^{19} +(20.2687 - 35.1064i) q^{20} +(38.1092 + 66.0071i) q^{22} +(-73.5122 + 127.327i) q^{23} +(11.1475 + 19.3080i) q^{25} +(2.92253 + 5.06197i) q^{26} +(57.7577 - 46.3901i) q^{28} +(-137.710 + 238.521i) q^{29} +102.334 q^{31} -32.0000 q^{32} +(-112.032 + 194.045i) q^{34} +(-28.6198 - 185.496i) q^{35} +(-25.1233 - 43.5149i) q^{37} +(78.5773 + 136.100i) q^{38} +(-40.5374 + 70.2128i) q^{40} +(-1.16281 - 2.01405i) q^{41} +(184.064 - 318.808i) q^{43} +(-76.2185 - 132.014i) q^{44} +(147.024 - 254.654i) q^{46} -399.584 q^{47} +(73.9944 - 334.924i) q^{49} +(-22.2949 - 38.6159i) q^{50} +(-5.84506 - 10.1239i) q^{52} +(50.8233 - 88.0285i) q^{53} -386.212 q^{55} +(-115.515 + 92.7803i) q^{56} +(275.420 - 477.042i) q^{58} -27.4171 q^{59} -612.693 q^{61} -204.669 q^{62} +64.0000 q^{64} -29.6179 q^{65} -624.291 q^{67} +(224.064 - 388.090i) q^{68} +(57.2397 + 370.992i) q^{70} +514.486 q^{71} +(590.915 - 1023.49i) q^{73} +(50.2467 + 87.0298i) q^{74} +(-157.155 - 272.200i) q^{76} +(-657.898 - 255.566i) q^{77} -340.185 q^{79} +(81.0748 - 140.426i) q^{80} +(2.32563 + 4.02810i) q^{82} +(312.272 - 540.871i) q^{83} +(-567.685 - 983.259i) q^{85} +(-368.127 + 637.615i) q^{86} +(152.437 + 264.028i) q^{88} +(-349.147 - 604.740i) q^{89} +(-50.4530 - 19.5989i) q^{91} +(-294.049 + 509.308i) q^{92} +799.167 q^{94} -796.330 q^{95} +(-345.941 + 599.187i) q^{97} +(-147.989 + 669.847i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 48 q^{2} + 96 q^{4} - 10 q^{5} + 17 q^{7} - 192 q^{8}+O(q^{10}) \) 24 * q - 48 * q^2 + 96 * q^4 - 10 * q^5 + 17 * q^7 - 192 * q^8	\( 24 q - 48 q^{2} + 96 q^{4} - 10 q^{5} + 17 q^{7} - 192 q^{8} + 20 q^{10} + 4 q^{11} + 80 q^{13} - 34 q^{14} + 384 q^{16} - 92 q^{17} + 54 q^{19} - 40 q^{20} - 8 q^{22} - 131 q^{23} - 178 q^{25} - 160 q^{26} + 68 q^{28} + 278 q^{29} - 220 q^{31} - 768 q^{32} + 184 q^{34} + 493 q^{35} - 21 q^{37} - 108 q^{38} + 80 q^{40} - 465 q^{41} + 159 q^{43} + 16 q^{44} + 262 q^{46} + 678 q^{47} - 207 q^{49} + 356 q^{50} + 320 q^{52} + 78 q^{53} - 1532 q^{55} - 136 q^{56} - 556 q^{58} + 1622 q^{59} - 1978 q^{61} + 440 q^{62} + 1536 q^{64} + 624 q^{65} - 80 q^{67} - 368 q^{68} - 986 q^{70} - 980 q^{71} + 1510 q^{73} + 42 q^{74} + 216 q^{76} + 350 q^{77} + 812 q^{79} - 160 q^{80} + 930 q^{82} + 7 q^{83} - 581 q^{85} - 318 q^{86} - 32 q^{88} - 675 q^{89} - 232 q^{91} - 524 q^{92} - 1356 q^{94} - 2438 q^{95} + 2836 q^{97} + 414 q^{98}+O(q^{100}) \) 24 * q - 48 * q^2 + 96 * q^4 - 10 * q^5 + 17 * q^7 - 192 * q^8 + 20 * q^10 + 4 * q^11 + 80 * q^13 - 34 * q^14 + 384 * q^16 - 92 * q^17 + 54 * q^19 - 40 * q^20 - 8 * q^22 - 131 * q^23 - 178 * q^25 - 160 * q^26 + 68 * q^28 + 278 * q^29 - 220 * q^31 - 768 * q^32 + 184 * q^34 + 493 * q^35 - 21 * q^37 - 108 * q^38 + 80 * q^40 - 465 * q^41 + 159 * q^43 + 16 * q^44 + 262 * q^46 + 678 * q^47 - 207 * q^49 + 356 * q^50 + 320 * q^52 + 78 * q^53 - 1532 * q^55 - 136 * q^56 - 556 * q^58 + 1622 * q^59 - 1978 * q^61 + 440 * q^62 + 1536 * q^64 + 624 * q^65 - 80 * q^67 - 368 * q^68 - 986 * q^70 - 980 * q^71 + 1510 * q^73 + 42 * q^74 + 216 * q^76 + 350 * q^77 + 812 * q^79 - 160 * q^80 + 930 * q^82 + 7 * q^83 - 581 * q^85 - 318 * q^86 - 32 * q^88 - 675 * q^89 - 232 * q^91 - 524 * q^92 - 1356 * q^94 - 2438 * q^95 + 2836 * q^97 + 414 * q^98

Introduction

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