LMFDB - Embedded newform 230.3.d.a.91.5

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [230,3,Mod(91,230)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(230, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("230.91");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 230 = 2 \cdot 5 \cdot 23 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	230.d (of order $2$, degree $1$, 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:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} + 78x^{14} + 2165x^{12} + 28310x^{10} + 184804x^{8} + 569634x^{6} + 696037x^{4} + 285578x^{2} + 529 $ x^16 + 78x^14 + 2165x^12 + 28310x^10 + 184804x^8 + 569634x^6 + 696037x^4 + 285578*x^2 + 529
Coefficient ring:	$\Z[a_1, \ldots, a_{23}]$
Coefficient ring index:	$ 2^{7} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			91.5
Root			$-1.01877i$ of defining polynomial
Character	$\chi$	$=$	230.91
Dual form			230.3.d.a.91.6

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-1.41421 q^{2} +2.34854 q^{3} +2.00000 q^{4} -2.23607i q^{5} -3.32134 q^{6} -7.61815i q^{7} -2.82843 q^{8} -3.48436 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +2.34854 q^{3} +2.00000 q^{4} -2.23607i q^{5} -3.32134 q^{6} -7.61815i q^{7} -2.82843 q^{8} -3.48436 q^{9} +3.16228i q^{10} -12.3764i q^{11} +4.69708 q^{12} -13.0302 q^{13} +10.7737i q^{14} -5.25149i q^{15} +4.00000 q^{16} +9.13040i q^{17} +4.92764 q^{18} -14.4549i q^{19} -4.47214i q^{20} -17.8915i q^{21} +17.5029i q^{22} +(22.5529 + 4.51289i) q^{23} -6.64267 q^{24} -5.00000 q^{25} +18.4275 q^{26} -29.3200 q^{27} -15.2363i q^{28} -21.2813 q^{29} +7.42673i q^{30} +36.8428 q^{31} -5.65685 q^{32} -29.0666i q^{33} -12.9123i q^{34} -17.0347 q^{35} -6.96873 q^{36} -56.9603i q^{37} +20.4424i q^{38} -30.6019 q^{39} +6.32456i q^{40} +70.7680 q^{41} +25.3024i q^{42} -70.0086i q^{43} -24.7529i q^{44} +7.79128i q^{45} +(-31.8946 - 6.38219i) q^{46} -66.2614 q^{47} +9.39416 q^{48} -9.03623 q^{49} +7.07107 q^{50} +21.4431i q^{51} -26.0604 q^{52} +77.4364i q^{53} +41.4648 q^{54} -27.6746 q^{55} +21.5474i q^{56} -33.9480i q^{57} +30.0963 q^{58} +82.7923 q^{59} -10.5030i q^{60} -23.9941i q^{61} -52.1036 q^{62} +26.5444i q^{63} +8.00000 q^{64} +29.1364i q^{65} +41.1063i q^{66} +118.512i q^{67} +18.2608i q^{68} +(52.9664 + 10.5987i) q^{69} +24.0907 q^{70} +69.0263 q^{71} +9.85527 q^{72} +25.9840 q^{73} +80.5540i q^{74} -11.7427 q^{75} -28.9099i q^{76} -94.2857 q^{77} +43.2777 q^{78} +28.8543i q^{79} -8.94427i q^{80} -37.4999 q^{81} -100.081 q^{82} +69.3871i q^{83} -35.7831i q^{84} +20.4162 q^{85} +99.0071i q^{86} -49.9800 q^{87} +35.0059i q^{88} +45.4428i q^{89} -11.0185i q^{90} +99.2661i q^{91} +(45.1058 + 9.02579i) q^{92} +86.5269 q^{93} +93.7077 q^{94} -32.3222 q^{95} -13.2853 q^{96} +74.4458i q^{97} +12.7792 q^{98} +43.1241i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	$ 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) $ 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/230\mathbb{Z}\right)^\times$.

$n$	$47$	$51$
$\chi(n)$	$1$	$-1$

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 $

$2$	−1.41421			−0.707107
$2$	−1.41421			−0.707107
$3$	2.34854			0.782846			0.391423	−	0.920211i	$-0.371983\pi$
$3$	2.34854			0.782846			0.391423	+	0.920211i	$0.371983\pi$
$4$	2.00000			0.500000
$5$		−	2.23607i		−	0.447214i
$5$		−	2.23607i		−	0.447214i
$6$	−3.32134			−0.553556
$7$		−	7.61815i		−	1.08831i	−0.838986	−	0.544154i	$-0.816851\pi$
$7$		−	7.61815i		−	1.08831i	0.838986	−	0.544154i	$-0.183149\pi$
$8$	−2.82843			−0.353553
$9$	−3.48436			−0.387152
$10$			3.16228i			0.316228i
$11$		−	12.3764i		−	1.12513i	−0.826752	−	0.562566i	$-0.809814\pi$
$11$		−	12.3764i		−	1.12513i	0.826752	−	0.562566i	$-0.190186\pi$
$12$	4.69708			0.391423
$13$	−13.0302			−1.00232			−0.501162	−	0.865354i	$-0.667094\pi$
$13$	−13.0302			−1.00232			−0.501162	+	0.865354i	$0.667094\pi$
$14$			10.7737i			0.769549i
$15$		−	5.25149i		−	0.350100i
$16$	4.00000			0.250000
$17$			9.13040i			0.537083i	0.963268	+	0.268541i	$0.0865416\pi$
$17$			9.13040i			0.537083i	−0.963268	+	0.268541i	$0.913458\pi$
$18$	4.92764			0.273758
$19$		−	14.4549i		−	0.760787i	−0.924825	−	0.380393i	$-0.875789\pi$
$19$		−	14.4549i		−	0.760787i	0.924825	−	0.380393i	$-0.124211\pi$
$20$		−	4.47214i		−	0.223607i
$21$		−	17.8915i		−	0.851977i
$22$			17.5029i			0.795588i
$23$	22.5529	+	4.51289i	0.980561	+	0.196213i
$23$	22.5529	+	4.51289i	0.980561	+	0.196213i
$24$	−6.64267			−0.276778
$25$	−5.00000			−0.200000
$26$	18.4275			0.708750
$27$	−29.3200			−1.08593
$28$		−	15.2363i		−	0.544154i
$29$	−21.2813			−0.733839			−0.366919	−	0.930253i	$-0.619588\pi$
$29$	−21.2813			−0.733839			−0.366919	+	0.930253i	$0.619588\pi$
$30$			7.42673i			0.247558i
$31$	36.8428			1.18848			0.594239	−	0.804288i	$-0.297453\pi$
$31$	36.8428			1.18848			0.594239	+	0.804288i	$0.297453\pi$
$32$	−5.65685			−0.176777
$33$		−	29.0666i		−	0.880805i
$34$		−	12.9123i		−	0.379775i
$35$	−17.0347			−0.486706
$36$	−6.96873			−0.193576
$37$		−	56.9603i		−	1.53947i	−0.638365	−	0.769734i	$-0.720389\pi$
$37$		−	56.9603i		−	1.53947i	0.638365	−	0.769734i	$-0.279611\pi$
$38$			20.4424i			0.537957i
$39$	−30.6019			−0.784665
$40$			6.32456i			0.158114i
$41$	70.7680			1.72605			0.863024	−	0.505163i	$-0.168567\pi$
$41$	70.7680			1.72605			0.863024	+	0.505163i	$0.168567\pi$
$42$			25.3024i			0.602439i
$43$		−	70.0086i		−	1.62811i	−0.580790	−	0.814053i	$-0.697256\pi$
$43$		−	70.0086i		−	1.62811i	0.580790	−	0.814053i	$-0.302744\pi$
$44$		−	24.7529i		−	0.562566i
$45$			7.79128i			0.173139i
$46$	−31.8946	−	6.38219i	−0.693362	−	0.138743i
$47$	−66.2614			−1.40982			−0.704908	−	0.709299i	$-0.749012\pi$
$47$	−66.2614			−1.40982			−0.704908	+	0.709299i	$0.749012\pi$
$48$	9.39416			0.195712
$49$	−9.03623			−0.184413
$50$	7.07107			0.141421
$51$			21.4431i			0.420453i
$52$	−26.0604			−0.501162
$53$			77.4364i			1.46106i	0.682879	+	0.730532i	$0.260728\pi$
$53$			77.4364i			1.46106i	−0.682879	+	0.730532i	$0.739272\pi$
$54$	41.4648			0.767866
$55$	−27.6746			−0.503174
$56$			21.5474i			0.384775i
$57$		−	33.9480i		−	0.595579i
$58$	30.0963			0.518902
$59$	82.7923			1.40326			0.701630	−	0.712541i	$-0.252456\pi$
$59$	82.7923			1.40326			0.701630	+	0.712541i	$0.252456\pi$
$60$		−	10.5030i		−	0.175050i
$61$		−	23.9941i		−	0.393346i	−0.980469	−	0.196673i	$-0.936986\pi$
$61$		−	23.9941i		−	0.393346i	0.980469	−	0.196673i	$-0.0630137\pi$
$62$	−52.1036			−0.840381
$63$			26.5444i			0.421340i
$64$	8.00000			0.125000
$65$			29.1364i			0.448253i
$66$			41.1063i			0.622823i
$67$			118.512i			1.76884i	0.466695	+	0.884418i	$0.345445\pi$
$67$			118.512i			1.76884i	−0.466695	+	0.884418i	$0.654555\pi$
$68$			18.2608i			0.268541i
$69$	52.9664	+	10.5987i	0.767629	+	0.153604i
$70$	24.0907			0.344153
$71$	69.0263			0.972202			0.486101	−	0.873903i	$-0.338419\pi$
$71$	69.0263			0.972202			0.486101	+	0.873903i	$0.338419\pi$
$72$	9.85527			0.136879
$73$	25.9840			0.355945			0.177973	−	0.984035i	$-0.443046\pi$
$73$	25.9840			0.355945			0.177973	+	0.984035i	$0.443046\pi$
$74$			80.5540i			1.08857i
$75$	−11.7427			−0.156569
$76$		−	28.9099i		−	0.380393i
$77$	−94.2857			−1.22449
$78$	43.2777			0.554842
$79$			28.8543i			0.365244i	0.983183	+	0.182622i	$0.0584585\pi$
$79$			28.8543i			0.365244i	−0.983183	+	0.182622i	$0.941541\pi$
$80$		−	8.94427i		−	0.111803i
$81$	−37.4999			−0.462962
$82$	−100.081			−1.22050
$83$			69.3871i			0.835989i	0.908449	+	0.417995i	$0.137267\pi$
$83$			69.3871i			0.835989i	−0.908449	+	0.417995i	$0.862733\pi$
$84$		−	35.7831i		−	0.425989i
$85$	20.4162			0.240191
$86$			99.0071i			1.15125i
$87$	−49.9800			−0.574483
$88$			35.0059i			0.397794i
$89$			45.4428i			0.510594i	0.966863	+	0.255297i	$0.0821732\pi$
$89$			45.4428i			0.510594i	−0.966863	+	0.255297i	$0.917827\pi$
$90$		−	11.0185i		−	0.122428i
$91$			99.2661i			1.09084i
$92$	45.1058	+	9.02579i	0.490281	+	0.0981064i
$93$	86.5269			0.930396
$94$	93.7077			0.996891
$95$	−32.3222			−0.340234
$96$	−13.2853			−0.138389
$97$			74.4458i			0.767482i	0.923441	+	0.383741i	$0.125364\pi$
$97$			74.4458i			0.767482i	−0.923441	+	0.383741i	$0.874636\pi$
$98$	12.7792			0.130400
$99$			43.1241i			0.435597i
$100$	−10.0000			−0.100000
$101$	−17.0563			−0.168874			−0.0844372	−	0.996429i	$-0.526909\pi$
$101$	−17.0563			−0.168874			−0.0844372	+	0.996429i	$0.526909\pi$
$102$		−	30.3251i		−	0.297305i
$103$		−	153.952i		−	1.49468i	−0.664442	−	0.747340i	$-0.731331\pi$
$103$		−	153.952i		−	1.49468i	0.664442	−	0.747340i	$-0.268669\pi$
$104$	36.8550			0.354375
$105$	−40.0067			−0.381016
$106$		−	109.512i		−	1.03313i
$107$			112.821i			1.05441i	0.849740	+	0.527203i	$0.176759\pi$
$107$			112.821i			1.05441i	−0.849740	+	0.527203i	$0.823241\pi$
$108$	−58.6400			−0.542963
$109$		−	97.6061i		−	0.895468i	−0.894167	−	0.447734i	$-0.852231\pi$
$109$		−	97.6061i		−	0.895468i	0.894167	−	0.447734i	$-0.147769\pi$
$110$	39.1378			0.355798
$111$		−	133.773i		−	1.20517i
$112$		−	30.4726i		−	0.272077i
$113$		−	57.0620i		−	0.504974i	−0.967600	−	0.252487i	$-0.918752\pi$
$113$		−	57.0620i		−	0.504974i	0.967600	−	0.252487i	$-0.0812485\pi$
$114$			48.0097i			0.421138i
$115$	10.0911	−	50.4298i	0.0877490	−	0.438520i
$116$	−42.5627			−0.366919
$117$	45.4020			0.388051
$118$	−117.086			−0.992255
$119$	69.5568			0.584511
$120$			14.8535i			0.123779i
$121$	−32.1765			−0.265921
$122$			33.9328i			0.278137i
$123$	166.201			1.35123
$124$	73.6857			0.594239
$125$			11.1803i			0.0894427i
$126$		−	37.5395i		−	0.297932i
$127$	−151.376			−1.19194			−0.595969	−	0.803007i	$-0.703232\pi$
$127$	−151.376			−1.19194			−0.595969	+	0.803007i	$0.703232\pi$
$128$	−11.3137			−0.0883883
$129$		−	164.418i		−	1.27456i
$130$		−	41.2051i		−	0.316962i
$131$	46.7334			0.356743			0.178372	−	0.983963i	$-0.442917\pi$
$131$	46.7334			0.356743			0.178372	+	0.983963i	$0.442917\pi$
$132$		−	58.1331i		−	0.440403i
$133$	−110.120			−0.827970
$134$		−	167.601i		−	1.25076i
$135$			65.5616i			0.485641i
$136$		−	25.8247i		−	0.189887i
$137$			31.1949i			0.227700i	0.993498	+	0.113850i	$0.0363183\pi$
$137$			31.1949i			0.227700i	−0.993498	+	0.113850i	$0.963682\pi$
$138$	−74.9058	−	14.9888i	−0.542796	−	0.108615i
$139$	36.5517			0.262962			0.131481	−	0.991319i	$-0.458027\pi$
$139$	36.5517			0.262962			0.131481	+	0.991319i	$0.458027\pi$
$140$	−34.0694			−0.243353
$141$	−155.617			−1.10367
$142$	−97.6180			−0.687451
$143$			161.268i			1.12775i
$144$	−13.9375			−0.0967879
$145$			47.5865i			0.328183i
$146$	−36.7470			−0.251691
$147$	−21.2219			−0.144367
$148$		−	113.921i		−	0.769734i
$149$		−	182.281i		−	1.22336i	−0.791104	−	0.611681i	$-0.790494\pi$
$149$		−	182.281i		−	1.22336i	0.791104	−	0.611681i	$-0.209506\pi$
$150$	16.6067			0.110711
$151$	40.9462			0.271167			0.135584	−	0.990766i	$-0.456709\pi$
$151$	40.9462			0.271167			0.135584	+	0.990766i	$0.456709\pi$
$152$			40.8848i			0.268979i
$153$		−	31.8136i		−	0.207932i
$154$	133.340			0.865845
$155$		−	82.3831i		−	0.531504i
$156$	−61.2039			−0.392333
$157$		−	252.396i		−	1.60762i	−0.594887	−	0.803810i	$-0.702803\pi$
$157$		−	252.396i		−	1.60762i	0.594887	−	0.803810i	$-0.297197\pi$
$158$		−	40.8062i		−	0.258267i
$159$			181.862i			1.14379i
$160$			12.6491i			0.0790569i
$161$	34.3799	−	171.811i	0.213540	−	1.06715i
$162$	53.0329			0.327364
$163$	−46.9686			−0.288151			−0.144076	−	0.989567i	$-0.546021\pi$
$163$	−46.9686			−0.288151			−0.144076	+	0.989567i	$0.546021\pi$
$164$	141.536			0.863024
$165$	−64.9948			−0.393908
$166$		−	98.1282i		−	0.591134i
$167$	78.4530			0.469778			0.234889	−	0.972022i	$-0.424527\pi$
$167$	78.4530			0.469778			0.234889	+	0.972022i	$0.424527\pi$
$168$			50.6049i			0.301220i
$169$	0.786229			0.00465224
$170$	−28.8729			−0.169840
$171$			50.3663i			0.294540i
$172$		−	140.017i		−	0.814053i
$173$	137.080			0.792369			0.396184	−	0.918171i	$-0.370334\pi$
$173$	137.080			0.792369			0.396184	+	0.918171i	$0.370334\pi$
$174$	70.6824			0.406221
$175$			38.0908i			0.217661i
$176$		−	49.5058i		−	0.281283i
$177$	194.441			1.09854
$178$		−	64.2659i		−	0.361044i
$179$	−55.6699			−0.311005			−0.155503	−	0.987835i	$-0.549700\pi$
$179$	−55.6699			−0.311005			−0.155503	+	0.987835i	$0.549700\pi$
$180$			15.5826i			0.0865697i
$181$			23.7317i			0.131114i	0.997849	+	0.0655572i	$0.0208825\pi$
$181$			23.7317i			0.131114i	−0.997849	+	0.0655572i	$0.979118\pi$
$182$		−	140.383i		−	0.771337i
$183$		−	56.3511i		−	0.307929i
$184$	−63.7893	−	12.7644i	−0.346681	−	0.0693717i
$185$	−127.367			−0.688471
$186$	−122.367			−0.657890
$187$	113.002			0.604289
$188$	−132.523			−0.704908
$189$			223.364i			1.18182i
$190$	45.7105			0.240582
$191$			351.658i			1.84114i	0.390576	+	0.920571i	$0.372276\pi$
$191$			351.658i			1.84114i	−0.390576	+	0.920571i	$0.627724\pi$
$192$	18.7883			0.0978558
$193$	−39.4808			−0.204564			−0.102282	−	0.994755i	$-0.532614\pi$
$193$	−39.4808			−0.204564			−0.102282	+	0.994755i	$0.532614\pi$
$194$		−	105.282i		−	0.542692i
$195$			68.4280i			0.350913i
$196$	−18.0725			−0.0922064
$197$	−225.017			−1.14222			−0.571108	−	0.820875i	$-0.693486\pi$
$197$	−225.017			−1.14222			−0.571108	+	0.820875i	$0.693486\pi$
$198$		−	60.9866i		−	0.308013i
$199$			37.0872i			0.186368i	0.995649	+	0.0931840i	$0.0297045\pi$
$199$			37.0872i			0.186368i	−0.995649	+	0.0931840i	$0.970296\pi$
$200$	14.1421			0.0707107
$201$			278.330i			1.38473i
$202$	24.1213			0.119412
$203$			162.124i			0.798642i
$204$			42.8862i			0.210227i
$205$		−	158.242i		−	0.771912i
$206$			217.721i			1.05690i
$207$	−78.5826	−	15.7246i	−0.379626	−	0.0759641i
$208$	−52.1208			−0.250581
$209$	−178.901			−0.855985
$210$	56.5780			0.269419
$211$	217.064			1.02874			0.514369	−	0.857569i	$-0.328026\pi$
$211$	217.064			1.02874			0.514369	+	0.857569i	$0.328026\pi$
$212$			154.873i			0.730532i
$213$	162.111			0.761085
$214$		−	159.554i		−	0.745577i
$215$	−156.544			−0.728111
$216$	82.9295			0.383933
$217$		−	280.674i		−	1.29343i
$218$			138.036i			0.633192i
$219$	61.0245			0.278651
$220$	−55.3492			−0.251587
$221$		−	118.971i		−	0.538330i
$222$			189.184i			0.852181i
$223$	269.398			1.20806			0.604030	−	0.796961i	$-0.293561\pi$
$223$	269.398			1.20806			0.604030	+	0.796961i	$0.293561\pi$
$224$			43.0948i			0.192387i
$225$	17.4218			0.0774303
$226$			80.6979i			0.357070i
$227$			175.997i			0.775319i	0.921803	+	0.387659i	$0.126716\pi$
$227$			175.997i			0.775319i	−0.921803	+	0.387659i	$0.873284\pi$
$228$		−	67.8960i		−	0.297789i
$229$			63.0669i			0.275401i	0.990474	+	0.137701i	$0.0439712\pi$
$229$			63.0669i			0.275401i	−0.990474	+	0.137701i	$0.956029\pi$
$230$	−14.2710	+	71.3186i	−0.0620479	+	0.310081i
$231$	−221.434			−0.958587
$232$	60.1927			0.259451
$233$	4.48041			0.0192292			0.00961461	−	0.999954i	$-0.496940\pi$
$233$	4.48041			0.0192292			0.00961461	+	0.999954i	$0.496940\pi$
$234$	−64.2081			−0.274394
$235$			148.165i			0.630489i
$236$	165.585			0.701630
$237$			67.7655i			0.285930i
$238$	−98.3682			−0.413312
$239$	85.5205			0.357826			0.178913	−	0.983865i	$-0.442742\pi$
$239$	85.5205			0.357826			0.178913	+	0.983865i	$0.442742\pi$
$240$		−	21.0060i		−	0.0875249i
$241$		−	257.515i		−	1.06853i	−0.845318	−	0.534263i	$-0.820589\pi$
$241$		−	257.515i		−	1.06853i	0.845318	−	0.534263i	$-0.179411\pi$
$242$	45.5044			0.188035
$243$	175.810			0.723498
$244$		−	47.9882i		−	0.196673i
$245$			20.2056i			0.0824719i
$246$	−235.044			−0.955464
$247$			188.351i			0.762554i
$248$	−104.207			−0.420191
$249$			162.958i			0.654451i
$250$		−	15.8114i		−	0.0632456i
$251$		−	121.438i		−	0.483816i	−0.970299	−	0.241908i	$-0.922227\pi$
$251$		−	121.438i		−	0.483816i	0.970299	−	0.241908i	$-0.0777733\pi$
$252$			53.0888i			0.210670i
$253$	55.8536	−	279.125i	0.220765	−	1.10326i
$254$	214.078			0.842827
$255$	47.9482			0.188032
$256$	16.0000			0.0625000
$257$	192.295			0.748230			0.374115	−	0.927382i	$-0.377947\pi$
$257$	192.295			0.748230			0.374115	+	0.927382i	$0.377947\pi$
$258$			232.522i			0.901248i
$259$	−433.932			−1.67541
$260$			58.2728i			0.224126i
$261$	74.1519			0.284107
$262$	−66.0910			−0.252256
$263$		−	417.798i		−	1.58858i	−0.607536	−	0.794292i	$-0.707842\pi$
$263$		−	417.798i		−	1.58858i	0.607536	−	0.794292i	$-0.292158\pi$
$264$			82.2127i			0.311412i
$265$	173.153			0.653407
$266$	155.733			0.585463
$267$			106.724i			0.399716i
$268$			237.024i			0.884418i
$269$	−474.878			−1.76534			−0.882672	−	0.469989i	$-0.844258\pi$
$269$	−474.878			−1.76534			−0.882672	+	0.469989i	$0.844258\pi$
$270$		−	92.7180i		−	0.343400i
$271$	−32.0762			−0.118362			−0.0591812	−	0.998247i	$-0.518849\pi$
$271$	−32.0762			−0.118362			−0.0591812	+	0.998247i	$0.518849\pi$
$272$			36.5216i			0.134271i
$273$			233.130i			0.853957i
$274$		−	44.1162i		−	0.161008i
$275$			61.8822i			0.225026i
$276$	105.933	+	21.1974i	0.383814	+	0.0768022i
$277$	459.038			1.65718			0.828589	−	0.559858i	$-0.189144\pi$
$277$	459.038			1.65718			0.828589	+	0.559858i	$0.189144\pi$
$278$	−51.6919			−0.185942
$279$	−128.374			−0.460121
$280$	48.1814			0.172076
$281$		−	321.543i		−	1.14428i	−0.820156	−	0.572140i	$-0.806113\pi$
$281$		−	321.543i		−	1.14428i	0.820156	−	0.572140i	$-0.193887\pi$
$282$	220.076			0.780412
$283$			428.712i			1.51488i	0.652904	+	0.757441i	$0.273551\pi$
$283$			428.712i			1.51488i	−0.652904	+	0.757441i	$0.726449\pi$
$284$	138.053			0.486101
$285$	−75.9100			−0.266351
$286$		−	228.067i		−	0.797437i
$287$		−	539.121i		−	1.87847i
$288$	19.7105			0.0684394
$289$	205.636			0.711542
$290$		−	67.2975i		−	0.232060i
$291$			174.839i			0.600821i
$292$	51.9680			0.177973
$293$		−	359.840i		−	1.22812i	−0.789258	−	0.614062i	$-0.789534\pi$
$293$		−	359.840i		−	1.22812i	0.789258	−	0.614062i	$-0.210466\pi$
$294$	30.0123			0.102083
$295$		−	185.129i		−	0.627557i
$296$			161.108i			0.544284i
$297$			362.878i			1.22181i
$298$			257.784i			0.865048i
$299$	−293.869	−	58.8039i	−0.982840	−	0.196669i
$300$	−23.4854			−0.0782846
$301$	−533.336			−1.77188
$302$	−57.9067			−0.191744
$303$	−40.0574			−0.132203
$304$		−	57.8198i		−	0.190197i
$305$	−53.6524			−0.175910
$306$			44.9913i			0.147030i
$307$	−448.843			−1.46203			−0.731014	−	0.682362i	$-0.760953\pi$
$307$	−448.843			−1.46203			−0.731014	+	0.682362i	$0.760953\pi$
$308$	−188.571			−0.612245
$309$		−	361.562i		−	1.17010i
$310$			116.507i			0.375830i
$311$	187.562			0.603094			0.301547	−	0.953451i	$-0.402497\pi$
$311$	187.562			0.603094			0.301547	+	0.953451i	$0.402497\pi$
$312$	86.5554			0.277421
$313$			93.4265i			0.298487i	0.988800	+	0.149244i	$0.0476839\pi$
$313$			93.4265i			0.298487i	−0.988800	+	0.149244i	$0.952316\pi$
$314$			356.942i			1.13676i
$315$	59.3551			0.188429
$316$			57.7086i			0.182622i
$317$	453.069			1.42924			0.714620	−	0.699513i	$-0.246600\pi$
$317$	453.069			1.42924			0.714620	+	0.699513i	$0.246600\pi$
$318$		−	257.192i		−	0.808780i
$319$			263.387i			0.825665i
$320$		−	17.8885i		−	0.0559017i
$321$			264.965i			0.825437i
$322$	−48.6205	+	242.978i	−0.150995	+	0.754590i
$323$	131.979			0.408605
$324$	−74.9999			−0.231481
$325$	65.1510			0.200465
$326$	66.4237			0.203754
$327$		−	229.232i		−	0.701014i
$328$	−200.162			−0.610250
$329$			504.789i			1.53431i
$330$	91.9166			0.278535
$331$	−178.326			−0.538749			−0.269374	−	0.963036i	$-0.586817\pi$
$331$	−178.326			−0.538749			−0.269374	+	0.963036i	$0.586817\pi$
$332$			138.774i			0.417995i
$333$			198.470i			0.596007i
$334$	−110.949			−0.332183
$335$	265.001			0.791048
$336$		−	71.5661i		−	0.212994i
$337$		−	85.7271i		−	0.254383i	−0.991878	−	0.127192i	$-0.959404\pi$
$337$		−	85.7271i		−	0.254383i	0.991878	−	0.127192i	$-0.0405963\pi$
$338$	−1.11190			−0.00328963
$339$		−	134.012i		−	0.395317i
$340$	40.8324			0.120095
$341$		−	455.984i		−	1.33720i
$342$		−	71.2287i		−	0.208271i
$343$		−	304.450i		−	0.887610i
$344$			198.014i			0.575623i
$345$	23.6994	−	118.436i	0.0686940	−	0.343294i
$346$	−193.860			−0.560289
$347$	216.730			0.624582			0.312291	−	0.949986i	$-0.398904\pi$
$347$	216.730			0.624582			0.312291	+	0.949986i	$0.398904\pi$
$348$	−99.9601			−0.287242
$349$	−528.822			−1.51525			−0.757624	−	0.652691i	$-0.773640\pi$
$349$	−528.822			−1.51525			−0.757624	+	0.652691i	$0.773640\pi$
$350$		−	53.8685i		−	0.153910i
$351$	382.046			1.08845
$352$			70.0118i			0.198897i
$353$	−28.7915			−0.0815623			−0.0407811	−	0.999168i	$-0.512985\pi$
$353$	−28.7915			−0.0815623			−0.0407811	+	0.999168i	$0.512985\pi$
$354$	−274.981			−0.776783
$355$		−	154.348i		−	0.434782i
$356$			90.8857i			0.255297i
$357$	163.357			0.457582
$358$	78.7292			0.219914
$359$			55.5671i			0.154783i	0.997001	+	0.0773914i	$0.0246591\pi$
$359$			55.5671i			0.154783i	−0.997001	+	0.0773914i	$0.975341\pi$
$360$		−	22.0371i		−	0.0612140i
$361$	152.055			0.421204
$362$		−	33.5617i		−	0.0927119i
$363$	−75.5677			−0.208176
$364$			198.532i			0.545418i
$365$		−	58.1020i		−	0.159184i
$366$			79.6924i			0.217739i
$367$		−	164.288i		−	0.447652i	−0.974629	−	0.223826i	$-0.928145\pi$
$367$		−	164.288i		−	0.447652i	0.974629	−	0.223826i	$-0.0718547\pi$
$368$	90.2116	+	18.0516i	0.245140	+	0.0490532i
$369$	−246.581			−0.668242
$370$	180.124			0.486822
$371$	589.922			1.59009
$372$	173.054			0.465198
$373$		−	25.1481i		−	0.0674212i	−0.999432	−	0.0337106i	$-0.989268\pi$
$373$		−	25.1481i		−	0.0674212i	0.999432	−	0.0337106i	$-0.0107325\pi$
$374$	−159.809			−0.427297
$375$			26.2575i			0.0700199i
$376$	187.415			0.498445
$377$	277.300			0.735544
$378$		−	315.885i		−	0.835674i
$379$		−	456.740i		−	1.20512i	−0.798074	−	0.602560i	$-0.794148\pi$
$379$		−	456.740i		−	1.20512i	0.798074	−	0.602560i	$-0.205852\pi$
$380$	−64.6445			−0.170117
$381$	−355.513			−0.933104
$382$		−	497.319i		−	1.30188i
$383$			371.017i			0.968712i	0.874871	+	0.484356i	$0.160946\pi$
$383$			371.017i			0.968712i	−0.874871	+	0.484356i	$0.839054\pi$
$384$	−26.5707			−0.0691945
$385$			210.829i			0.547608i
$386$	55.8343			0.144648
$387$			243.935i			0.630324i
$388$			148.892i			0.383741i
$389$		−	400.013i		−	1.02831i	−0.857697	−	0.514155i	$-0.828105\pi$
$389$		−	400.013i		−	1.02831i	0.857697	−	0.514155i	$-0.171895\pi$
$390$		−	96.7718i		−	0.248133i
$391$	−41.2045	+	205.917i	−0.105382	+	0.526642i
$392$	25.5583			0.0651998
$393$	109.755			0.279275
$394$	318.222			0.807669
$395$	64.5202			0.163342
$396$			86.2481i			0.217798i
$397$	264.267			0.665659			0.332830	−	0.942987i	$-0.391997\pi$
$397$	264.267			0.665659			0.332830	+	0.942987i	$0.391997\pi$
$398$		−	52.4493i		−	0.131782i
$399$	−258.621			−0.648173
$400$	−20.0000			−0.0500000
$401$			425.319i			1.06065i	0.847796	+	0.530323i	$0.177929\pi$
$401$			425.319i			1.06065i	−0.847796	+	0.530323i	$0.822071\pi$
$402$		−	393.618i		−	0.979150i
$403$	−480.070			−1.19124
$404$	−34.1126			−0.0844372
$405$			83.8524i			0.207043i
$406$		−	229.278i		−	0.564725i
$407$	−704.966			−1.73210
$408$		−	60.6503i		−	0.148653i
$409$	−241.558			−0.590607			−0.295304	−	0.955403i	$-0.595421\pi$
$409$	−241.558			−0.590607			−0.295304	+	0.955403i	$0.595421\pi$
$410$			223.788i			0.545824i
$411$			73.2624i			0.178254i
$412$		−	307.904i		−	0.747340i
$413$		−	630.725i		−	1.52718i
$414$	111.133	+	22.2379i	0.268436	+	0.0537147i
$415$	155.154			0.373866
$416$	73.7100			0.177187
$417$	85.8431			0.205859
$418$	253.004			0.605273
$419$		−	358.352i		−	0.855256i	−0.903955	−	0.427628i	$-0.859349\pi$
$419$		−	358.352i		−	0.855256i	0.903955	−	0.427628i	$-0.140651\pi$
$420$	−80.0133			−0.190508
$421$			672.051i			1.59632i	0.602446	+	0.798160i	$0.294193\pi$
$421$			672.051i			1.59632i	−0.602446	+	0.798160i	$0.705807\pi$
$422$	−306.975			−0.727428
$423$	230.879			0.545813
$424$		−	219.023i		−	0.516564i
$425$		−	45.6520i		−	0.107417i
$426$	−229.260			−0.538168
$427$	−182.791			−0.428081
$428$			225.643i			0.527203i
$429$			378.743i			0.882852i
$430$	221.387			0.514852
$431$		−	819.926i		−	1.90238i	−0.308604	−	0.951191i	$-0.599862\pi$
$431$		−	819.926i		−	1.90238i	0.308604	−	0.951191i	$-0.400138\pi$
$432$	−117.280			−0.271482
$433$			316.231i			0.730326i	0.930944	+	0.365163i	$0.118987\pi$
$433$			316.231i			0.730326i	−0.930944	+	0.365163i	$0.881013\pi$
$434$			396.933i			0.914593i
$435$			111.759i			0.256917i
$436$		−	195.212i		−	0.447734i
$437$	65.2336	−	326.001i	0.149276	−	0.745998i
$438$	−86.3017			−0.197036
$439$	208.878			0.475805			0.237903	−	0.971289i	$-0.423540\pi$
$439$	208.878			0.475805			0.237903	+	0.971289i	$0.423540\pi$
$440$	78.2755			0.177899
$441$	31.4855			0.0713957
$442$			168.250i			0.380657i
$443$	−706.981			−1.59589			−0.797947	−	0.602728i	$-0.794081\pi$
$443$	−706.981			−1.59589			−0.797947	+	0.602728i	$0.794081\pi$
$444$		−	267.547i		−	0.602583i
$445$	101.613			0.228344
$446$	−380.986			−0.854228
$447$		−	428.094i		−	0.957705i
$448$		−	60.9452i		−	0.136038i
$449$	−524.552			−1.16827			−0.584134	−	0.811658i	$-0.698566\pi$
$449$	−524.552			−1.16827			−0.584134	+	0.811658i	$0.698566\pi$
$450$	−24.6382			−0.0547515
$451$		−	875.856i		−	1.94203i
$452$		−	114.124i		−	0.252487i
$453$	96.1639			0.212282
$454$		−	248.898i		−	0.548233i
$455$	221.966			0.487837
$456$			96.0194i			0.210569i
$457$			786.926i			1.72194i	0.508657	+	0.860969i	$0.330142\pi$
$457$			786.926i			1.72194i	−0.508657	+	0.860969i	$0.669858\pi$
$458$		−	89.1901i		−	0.194738i
$459$		−	267.704i		−	0.583232i
$460$	20.1823	−	100.860i	0.0438745	−	0.219260i
$461$	−38.2459			−0.0829629			−0.0414814	−	0.999139i	$-0.513208\pi$
$461$	−38.2459			−0.0829629			−0.0414814	+	0.999139i	$0.513208\pi$
$462$	313.154			0.677823
$463$	−525.945			−1.13595			−0.567976	−	0.823045i	$-0.692273\pi$
$463$	−525.945			−1.13595			−0.567976	+	0.823045i	$0.692273\pi$
$464$	−85.1253			−0.183460
$465$		−	193.480i		−	0.416086i
$466$	−6.33625			−0.0135971
$467$			166.631i			0.356812i	0.983957	+	0.178406i	$0.0570941\pi$
$467$			166.631i			0.356812i	−0.983957	+	0.178406i	$0.942906\pi$
$468$	90.8040			0.194026
$469$	902.843			1.92504
$470$		−	209.537i		−	0.445823i
$471$		−	592.762i		−	1.25852i
$472$	−234.172			−0.496127
$473$	−866.458			−1.83183
$474$		−	95.8349i		−	0.202183i
$475$			72.2747i			0.152157i
$476$	139.114			0.292255
$477$		−	269.817i		−	0.565653i
$478$	−120.944			−0.253021
$479$			32.0653i			0.0669422i	0.999440	+	0.0334711i	$0.0106562\pi$
$479$			32.0653i			0.0669422i	−0.999440	+	0.0334711i	$0.989344\pi$
$480$			29.7069i			0.0618894i
$481$			742.204i			1.54304i
$482$			364.181i			0.755562i
$483$	80.7425	−	403.506i	0.167169	−	0.835416i
$484$	−64.3530			−0.132961
$485$	166.466			0.343228
$486$	−248.633			−0.511591
$487$	685.808			1.40823			0.704115	−	0.710085i	$-0.251344\pi$
$487$	685.808			1.40823			0.704115	+	0.710085i	$0.251344\pi$
$488$			67.8655i			0.139069i
$489$	−110.308			−0.225578
$490$		−	28.5751i		−	0.0583165i
$491$	775.805			1.58005			0.790026	−	0.613074i	$-0.210067\pi$
$491$	775.805			1.58005			0.790026	+	0.613074i	$0.210067\pi$
$492$	332.403			0.675615
$493$		−	194.307i		−	0.394132i
$494$		−	266.368i		−	0.539207i
$495$	96.4283			0.194805
$496$	147.371			0.297120
$497$		−	525.853i		−	1.05805i
$498$		−	230.458i		−	0.462767i
$499$	392.467			0.786507			0.393253	−	0.919430i	$-0.371350\pi$
$499$	392.467			0.786507			0.393253	+	0.919430i	$0.371350\pi$
$500$			22.3607i			0.0447214i
$501$	184.250			0.367764
$502$			171.739i			0.342110i
$503$			633.449i			1.25934i	0.776862	+	0.629671i	$0.216810\pi$
$503$			633.449i			1.25934i	−0.776862	+	0.629671i	$0.783190\pi$
$504$		−	75.0789i		−	0.148966i
$505$			38.1391i			0.0755229i
$506$	−78.9889	+	394.742i	−0.156105	+	0.780123i
$507$	1.84649			0.00364199
$508$	−302.752			−0.595969
$509$	540.009			1.06092			0.530460	−	0.847710i	$-0.322019\pi$
$509$	540.009			1.06092			0.530460	+	0.847710i	$0.322019\pi$
$510$	−67.8091			−0.132959
$511$		−	197.950i		−	0.387378i
$512$	−22.6274			−0.0441942
$513$			423.819i			0.826158i
$514$	−271.946			−0.529078
$515$	−344.247			−0.668441
$516$		−	328.836i		−	0.637279i
$517$			820.080i			1.58623i
$518$	613.673			1.18470
$519$	321.937			0.620303
$520$		−	82.4102i		−	0.158481i
$521$			396.259i			0.760574i	0.924869	+	0.380287i	$0.124175\pi$
$521$			396.259i			0.760574i	−0.924869	+	0.380287i	$0.875825\pi$
$522$	−104.867			−0.200894
$523$		−	27.4737i		−	0.0525309i	−0.999655	−	0.0262655i	$-0.991638\pi$
$523$		−	27.4737i		−	0.0525309i	0.999655	−	0.0262655i	$-0.00836152\pi$
$524$	93.4668			0.178372
$525$			89.4576i			0.170395i
$526$			590.855i			1.12330i
$527$			336.390i			0.638311i
$528$		−	116.266i		−	0.220201i
$529$	488.268	+	203.558i	0.923001	+	0.384797i
$530$	−244.875			−0.462029
$531$	−288.479			−0.543274
$532$	−220.240			−0.413985
$533$	−922.121			−1.73006
$534$		−	150.931i		−	0.282642i
$535$	252.276			0.471544
$536$		−	335.203i		−	0.625378i
$537$	−130.743			−0.243469
$538$	671.578			1.24829
$539$			111.836i			0.207489i
$540$			131.123i			0.242821i
$541$	−802.725			−1.48378			−0.741890	−	0.670522i	$-0.766070\pi$
$541$	−802.725			−1.48378			−0.741890	+	0.670522i	$0.766070\pi$
$542$	45.3626			0.0836948
$543$			55.7349i			0.102643i
$544$		−	51.6494i		−	0.0949437i
$545$	−218.254			−0.400466
$546$		−	329.696i		−	0.603839i
$547$	−439.126			−0.802790			−0.401395	−	0.915905i	$-0.631475\pi$
$547$	−439.126			−0.802790			−0.401395	+	0.915905i	$0.631475\pi$
$548$			62.3897i			0.113850i
$549$			83.6042i			0.152284i
$550$		−	87.5147i		−	0.159118i
$551$			307.620i			0.558295i
$552$	−149.812	−	29.9777i	−0.271398	−	0.0543074i
$553$	219.817			0.397498
$554$	−649.178			−1.17180
$555$	−299.127			−0.538967
$556$	73.1034			0.131481
$557$		−	795.405i		−	1.42802i	−0.700137	−	0.714008i	$-0.746878\pi$
$557$		−	795.405i		−	1.42802i	0.700137	−	0.714008i	$-0.253122\pi$
$558$	181.548			0.325355
$559$			912.226i			1.63189i
$560$	−68.1388			−0.121676
$561$	265.390			0.473065
$562$			454.730i			0.809128i
$563$		−	214.573i		−	0.381124i	−0.981675	−	0.190562i	$-0.938969\pi$
$563$		−	214.573i		−	0.381124i	0.981675	−	0.190562i	$-0.0610309\pi$
$564$	−311.235			−0.551835
$565$	−127.595			−0.225831
$566$		−	606.290i		−	1.07118i
$567$			285.680i			0.503845i
$568$	−195.236			−0.343725
$569$			1101.54i			1.93592i	0.251114	+	0.967958i	$0.419203\pi$
$569$			1101.54i			1.93592i	−0.251114	+	0.967958i	$0.580797\pi$
$570$	107.353			0.188339
$571$			560.543i			0.981686i	0.871248	+	0.490843i	$0.163311\pi$
$571$			560.543i			0.981686i	−0.871248	+	0.490843i	$0.836689\pi$
$572$			322.535i			0.563873i
$573$			825.882i			1.44133i
$574$			762.433i			1.32828i
$575$	−112.765	−	22.5645i	−0.196112	−	0.0392425i
$576$	−27.8749			−0.0483939
$577$	795.419			1.37854			0.689271	−	0.724504i	$-0.257931\pi$
$577$	795.419			1.37854			0.689271	+	0.724504i	$0.257931\pi$
$578$	−290.813			−0.503136
$579$	−92.7222			−0.160142
$580$			95.1730i			0.164091i
$581$	528.602			0.909813
$582$		−	247.259i		−	0.424844i
$583$	958.387			1.64389
$584$	−73.4939			−0.125846
$585$		−	101.522i		−	0.173542i
$586$			508.891i			0.868415i
$587$	579.454			0.987144			0.493572	−	0.869705i	$-0.335691\pi$
$587$	579.454			0.987144			0.493572	+	0.869705i	$0.335691\pi$
$588$	−42.4439			−0.0721834
$589$		−	532.561i		−	0.904179i
$590$			261.812i			0.443750i
$591$	−528.460			−0.894180
$592$		−	227.841i		−	0.384867i
$593$	−175.139			−0.295344			−0.147672	−	0.989036i	$-0.547178\pi$
$593$	−175.139			−0.295344			−0.147672	+	0.989036i	$0.547178\pi$
$594$		−	513.187i		−	0.863950i
$595$		−	155.534i		−	0.261401i
$596$		−	364.562i		−	0.611681i
$597$			87.1009i			0.145898i
$598$	415.594	+	83.1613i	0.694973	+	0.139066i
$599$	−512.672			−0.855879			−0.427940	−	0.903807i	$-0.640760\pi$
$599$	−512.672			−0.855879			−0.427940	+	0.903807i	$0.640760\pi$
$600$	33.2134			0.0553556
$601$	−175.570			−0.292130			−0.146065	−	0.989275i	$-0.546661\pi$
$601$	−175.570			−0.292130			−0.146065	+	0.989275i	$0.546661\pi$
$602$	754.251			1.25291
$603$		−	412.939i		−	0.684808i
$604$	81.8925			0.135584
$605$			71.9488i			0.118924i
$606$	56.6497			0.0934814
$607$	−173.873			−0.286447			−0.143223	−	0.989690i	$-0.545747\pi$
$607$	−173.873			−0.286447			−0.143223	+	0.989690i	$0.545747\pi$
$608$			81.7695i			0.134489i
$609$			380.755i			0.625214i
$610$	75.8760			0.124387
$611$	863.399			1.41309
$612$		−	63.6273i		−	0.103966i
$613$			560.182i			0.913837i	0.889509	+	0.456919i	$0.151047\pi$
$613$			560.182i			0.913837i	−0.889509	+	0.456919i	$0.848953\pi$
$614$	634.760			1.03381
$615$		−	371.638i		−	0.604289i
$616$	266.680			0.432922
$617$			308.240i			0.499578i	0.968300	+	0.249789i	$0.0803613\pi$
$617$			308.240i			0.499578i	−0.968300	+	0.249789i	$0.919639\pi$
$618$			511.326i			0.827389i
$619$			424.114i			0.685161i	0.939489	+	0.342580i	$0.111301\pi$
$619$			424.114i			0.685161i	−0.939489	+	0.342580i	$0.888699\pi$
$620$		−	164.766i		−	0.265752i
$621$	−661.252	−	132.318i	−1.06482	−	0.213073i
$622$	−265.253			−0.426452
$623$	346.190			0.555683
$624$	−122.408			−0.196166
$625$	25.0000			0.0400000
$626$		−	132.125i		−	0.211062i
$627$	−420.156			−0.670105
$628$		−	504.792i		−	0.803810i
$629$	520.070			0.826821
$630$	−83.9408			−0.133239
$631$		−	172.251i		−	0.272981i	−0.990641	−	0.136491i	$-0.956418\pi$
$631$		−	172.251i		−	0.272981i	0.990641	−	0.136491i	$-0.0435823\pi$
$632$		−	81.6123i		−	0.129133i
$633$	509.783			0.805344
$634$	−640.737			−1.01063
$635$			338.487i			0.533051i
$636$			363.725i			0.571894i
$637$	117.744			0.184841
$638$		−	372.486i		−	0.583834i
$639$	−240.513			−0.376390
$640$			25.2982i			0.0395285i
$641$			365.954i			0.570912i	0.958392	+	0.285456i	$0.0921450\pi$
$641$			365.954i			0.570912i	−0.958392	+	0.285456i	$0.907855\pi$
$642$		−	374.718i		−	0.583672i
$643$			823.317i			1.28043i	0.768195	+	0.640215i	$0.221155\pi$
$643$			823.317i			1.28043i	−0.768195	+	0.640215i	$0.778845\pi$
$644$	68.7598	−	343.623i	0.106770	−	0.533576i
$645$	−367.650			−0.569999
$646$	−186.647			−0.288927
$647$	−828.654			−1.28076			−0.640381	−	0.768057i	$-0.721224\pi$
$647$	−828.654			−1.28076			−0.640381	+	0.768057i	$0.721224\pi$
$648$	106.066			0.163682
$649$		−	1024.68i		−	1.57885i
$650$	−92.1375			−0.141750
$651$		−	659.175i		−	1.01256i
$652$	−93.9372			−0.144076
$653$	−912.811			−1.39787			−0.698937	−	0.715183i	$-0.746343\pi$
$653$	−912.811			−1.39787			−0.698937	+	0.715183i	$0.746343\pi$
$654$			324.182i			0.495692i
$655$		−	104.499i		−	0.159541i
$656$	283.072			0.431512
$657$	−90.5378			−0.137805
$658$		−	713.880i		−	1.08492i
$659$		−	247.106i		−	0.374971i	−0.982267	−	0.187486i	$-0.939966\pi$
$659$		−	247.106i		−	0.374971i	0.982267	−	0.187486i	$-0.0600338\pi$
$660$	−129.990			−0.196954
$661$			937.016i			1.41757i	0.705423	+	0.708787i	$0.250757\pi$
$661$			937.016i			1.41757i	−0.705423	+	0.708787i	$0.749243\pi$
$662$	252.191			0.380953
$663$		−	279.408i		−	0.421430i
$664$		−	196.256i		−	0.295567i
$665$			246.236i			0.370279i
$666$		−	280.680i		−	0.421441i
$667$	−479.956	−	96.0404i	−0.719574	−	0.143989i
$668$	156.906			0.234889
$669$	632.691			0.945726
$670$	−374.768			−0.559355
$671$	−296.962			−0.442566
$672$			101.210i			0.150610i
$673$	1174.75			1.74554			0.872769	−	0.488134i	$-0.162322\pi$
$673$	1174.75			1.74554			0.872769	+	0.488134i	$0.162322\pi$
$674$			121.236i			0.179876i
$675$	146.600			0.217185
$676$	1.57246			0.00232612
$677$		−	266.022i		−	0.392943i	−0.980510	−	0.196471i	$-0.937052\pi$
$677$		−	266.022i		−	0.392943i	0.980510	−	0.196471i	$-0.0629483\pi$
$678$			189.522i			0.279531i
$679$	567.139			0.835256
$680$	−57.7457			−0.0849202
$681$			413.337i			0.606955i
$682$			644.858i			0.945540i
$683$	−214.808			−0.314507			−0.157254	−	0.987558i	$-0.550264\pi$
$683$	−214.808			−0.314507			−0.157254	+	0.987558i	$0.550264\pi$
$684$			100.733i			0.147270i
$685$	69.7539			0.101830
$686$			430.557i			0.627635i
$687$			148.115i			0.215597i
$688$		−	280.034i		−	0.407027i
$689$		−	1009.01i		−	1.46446i
$690$	−33.5161	+	167.494i	−0.0485740	+	0.242746i
$691$	−998.531			−1.44505			−0.722526	−	0.691344i	$-0.757019\pi$
$691$	−998.531			−1.44505			−0.722526	+	0.691344i	$0.757019\pi$
$692$	274.160			0.396184
$693$	328.526			0.474063
$694$	−306.502			−0.441646
$695$		−	81.7321i		−	0.117600i
$696$	141.365			0.203110
$697$			646.140i			0.927030i
$698$	747.867			1.07144
$699$	10.5224			0.0150535
$700$			76.1815i			0.108831i
$701$		−	1089.04i		−	1.55356i	−0.629773	−	0.776779i	$-0.716852\pi$
$701$		−	1089.04i		−	1.55356i	0.629773	−	0.776779i	$-0.283148\pi$
$702$	−540.294			−0.769650
$703$	−823.358			−1.17121
$704$		−	99.0116i		−	0.140641i
$705$			347.971i			0.493576i
$706$	40.7173			0.0576732
$707$			129.938i			0.183787i
$708$	388.882			0.549268
$709$			779.102i			1.09887i	0.835535	+	0.549437i	$0.185158\pi$
$709$			779.102i			1.09887i	−0.835535	+	0.549437i	$0.814842\pi$
$710$			218.280i			0.307437i
$711$		−	100.539i		−	0.141405i
$712$		−	128.532i		−	0.180522i
$713$	830.913	+	166.268i	1.16538	+	0.233195i
$714$	−231.021			−0.323559
$715$	360.605			0.504343
$716$	−111.340			−0.155503
$717$	200.848			0.280123
$718$		−	78.5837i		−	0.109448i
$719$	−802.454			−1.11607			−0.558035	−	0.829817i	$-0.688445\pi$
$719$	−802.454			−1.11607			−0.558035	+	0.829817i	$0.688445\pi$
$720$			31.1651i			0.0432849i
$721$	−1172.83			−1.62667
$722$	−215.038			−0.297836
$723$		−	604.784i		−	0.836492i
$724$			47.4634i			0.0655572i
$725$	106.407			0.146768
$726$	106.869			0.147202
$727$		−	19.7852i		−	0.0272149i	−0.999907	−	0.0136075i	$-0.995668\pi$
$727$		−	19.7852i		−	0.0272149i	0.999907	−	0.0136075i	$-0.00433152\pi$
$728$		−	280.767i		−	0.385669i
$729$	750.396			1.02935
$730$			82.1687i			0.112560i
$731$	639.207			0.874428
$732$		−	112.702i		−	0.153965i
$733$		−	609.029i		−	0.830871i	−0.909623	−	0.415436i	$-0.863629\pi$
$733$		−	609.029i		−	0.830871i	0.909623	−	0.415436i	$-0.136371\pi$
$734$			232.339i			0.316538i
$735$			47.4537i			0.0645628i
$736$	−127.579	−	25.5288i	−0.173340	−	0.0346858i
$737$	1466.76			1.99017
$738$	348.719			0.472519
$739$	780.692			1.05642			0.528209	−	0.849115i	$-0.322864\pi$
$739$	780.692			1.05642			0.528209	+	0.849115i	$0.322864\pi$
$740$	−254.734			−0.344235
$741$			442.349i			0.596963i
$742$	−834.276			−1.12436
$743$		−	46.4819i		−	0.0625598i	−0.999511	−	0.0312799i	$-0.990042\pi$
$743$		−	46.4819i		−	0.0625598i	0.999511	−	0.0312799i	$-0.00995832\pi$
$744$	−244.735			−0.328945
$745$	−407.593			−0.547104
$746$			35.5648i			0.0476740i
$747$		−	241.770i		−	0.323655i
$748$	226.004			0.302144
$749$	859.490			1.14752
$750$		−	37.1337i		−	0.0495116i
$751$			1258.62i			1.67592i	0.545728	+	0.837962i	$0.316253\pi$
$751$			1258.62i			1.67592i	−0.545728	+	0.837962i	$0.683747\pi$
$752$	−265.045			−0.352454
$753$		−	285.202i		−	0.378754i
$754$	−392.161			−0.520108
$755$		−	91.5586i		−	0.121270i
$756$			446.729i			0.590911i
$757$		−	615.435i		−	0.812992i	−0.913653	−	0.406496i	$-0.866751\pi$
$757$		−	615.435i		−	0.812992i	0.913653	−	0.406496i	$-0.133249\pi$
$758$			645.928i			0.852148i
$759$	131.174	−	655.536i	0.172825	−	0.863684i
$760$	91.4211			0.120291
$761$	−795.461			−1.04528			−0.522642	−	0.852552i	$-0.675053\pi$
$761$	−795.461			−1.04528			−0.522642	+	0.852552i	$0.675053\pi$
$762$	502.771			0.659804
$763$	−743.578			−0.974545
$764$			703.316i			0.920571i
$765$	−71.1375			−0.0929902
$766$		−	524.697i		−	0.684983i
$767$	−1078.80			−1.40652
$768$	37.5766			0.0489279
$769$		−	1031.00i		−	1.34070i	−0.742046	−	0.670349i	$-0.766145\pi$
$769$		−	1031.00i		−	1.34070i	0.742046	−	0.670349i	$-0.233855\pi$
$770$		−	298.157i		−	0.387217i
$771$	451.613			0.585749
$772$	−78.9616			−0.102282
$773$		−	1281.23i		−	1.65747i	−0.559638	−	0.828737i	$-0.689060\pi$
$773$		−	1281.23i		−	1.65747i	0.559638	−	0.828737i	$-0.310940\pi$
$774$		−	344.977i		−	0.445706i
$775$	−184.214			−0.237696
$776$		−	210.564i		−	0.271346i
$777$	−1019.11			−1.31159
$778$			565.704i			0.727126i
$779$		−	1022.95i		−	1.31315i
$780$			136.856i			0.175456i
$781$		−	854.301i		−	1.09386i
$782$	58.2720	−	291.211i	0.0745166	−	0.372392i
$783$	623.969			0.796895
$784$	−36.1449			−0.0461032
$785$	−564.375			−0.718949
$786$	−155.217			−0.197477
$787$		−	1496.92i		−	1.90206i	−0.309096	−	0.951031i	$-0.600027\pi$
$787$		−	1496.92i		−	1.90206i	0.309096	−	0.951031i	$-0.399973\pi$
$788$	−450.033			−0.571108
$789$		−	981.215i		−	1.24362i
$790$	−91.2453			−0.115500
$791$	−434.707			−0.549567
$792$		−	121.973i		−	0.154007i
$793$			312.648i			0.394260i
$794$	−373.730			−0.470692
$795$	406.657			0.511518
$796$			74.1745i			0.0931840i
$797$			87.1739i			0.109378i	0.998503	+	0.0546888i	$0.0174167\pi$
$797$			87.1739i			0.109378i	−0.998503	+	0.0546888i	$0.982583\pi$
$798$	365.745			0.458327
$799$		−	604.993i		−	0.757188i
$800$	28.2843			0.0353553
$801$		−	158.339i		−	0.197677i
$802$		−	601.492i		−	0.749990i
$803$		−	321.590i		−	0.400486i
$804$			556.660i			0.692364i
$805$	−384.182	−	76.8758i	−0.477245	−	0.0954979i
$806$	678.921			0.842334
$807$	−1115.27			−1.38199
$808$	48.2425			0.0597061
$809$	602.054			0.744196			0.372098	−	0.928194i	$-0.378639\pi$
$809$	602.054			0.744196			0.372098	+	0.928194i	$0.378639\pi$
$810$		−	118.585i		−	0.146401i
$811$	1198.57			1.47790			0.738948	−	0.673763i	$-0.235323\pi$
$811$	1198.57			1.47790			0.738948	+	0.673763i	$0.235323\pi$
$812$			324.249i			0.399321i
$813$	−75.3322			−0.0926595
$814$	996.973			1.22478
$815$			105.025i			0.128865i
$816$			85.7724i			0.105113i
$817$	−1011.97			−1.23864
$818$	341.615			0.417622
$819$		−	345.879i		−	0.422319i
$820$		−	316.484i		−	0.385956i
$821$	−816.712			−0.994777			−0.497388	−	0.867528i	$-0.665708\pi$
$821$	−816.712			−0.994777			−0.497388	+	0.867528i	$0.665708\pi$
$822$		−	103.609i		−	0.126045i
$823$	143.774			0.174694			0.0873472	−	0.996178i	$-0.472161\pi$
$823$	143.774			0.174694			0.0873472	+	0.996178i	$0.472161\pi$
$824$			435.442i			0.528449i
$825$			145.333i			0.176161i
$826$			891.979i			1.07988i
$827$			523.617i			0.633153i	0.948567	+	0.316576i	$0.102533\pi$
$827$			523.617i			0.633153i	−0.948567	+	0.316576i	$0.897467\pi$
$828$	−157.165	−	31.4491i	−0.189813	−	0.0379820i
$829$	735.461			0.887167			0.443583	−	0.896233i	$-0.353707\pi$
$829$	735.461			0.887167			0.443583	+	0.896233i	$0.353707\pi$
$830$	−219.421			−0.264363
$831$	1078.07			1.29732
$832$	−104.242			−0.125290
$833$		−	82.5044i		−	0.0990449i
$834$	−121.400			−0.145564
$835$		−	175.426i		−	0.210091i
$836$	−357.802			−0.427993
$837$	−1080.23			−1.29060
$838$			506.786i			0.604757i
$839$			752.262i			0.896617i	0.893879	+	0.448309i	$0.147973\pi$
$839$			752.262i			0.896617i	−0.893879	+	0.448309i	$0.852027\pi$
$840$	113.156			0.134709
$841$	−388.105			−0.461481
$842$		−	950.423i		−	1.12877i
$843$		−	755.156i		−	0.895796i
$844$	434.128			0.514369
$845$		−	1.75806i		−	0.00208055i
$846$	−326.512			−0.385948
$847$			245.125i			0.289404i
$848$			309.745i			0.365266i
$849$			1006.85i			1.18592i
$850$			64.5617i			0.0759549i
$851$	257.056	−	1284.62i	0.302063	−	1.50954i
$852$	324.222			0.380542
$853$	−463.137			−0.542951			−0.271475	−	0.962445i	$-0.587512\pi$
$853$	−463.137			−0.542951			−0.271475	+	0.962445i	$0.587512\pi$
$854$	258.505			0.302699
$855$	112.622			0.131722
$856$		−	319.107i		−	0.372789i
$857$	−284.684			−0.332186			−0.166093	−	0.986110i	$-0.553115\pi$
$857$	−284.684			−0.332186			−0.166093	+	0.986110i	$0.553115\pi$
$858$		−	535.624i		−	0.624270i
$859$	625.746			0.728459			0.364230	−	0.931309i	$-0.381332\pi$
$859$	625.746			0.728459			0.364230	+	0.931309i	$0.381332\pi$
$860$	−313.088			−0.364056
$861$		−	1266.15i		−	1.47055i
$862$			1159.55i			1.34519i
$863$	110.774			0.128359			0.0641793	−	0.997938i	$-0.479557\pi$
$863$	110.774			0.128359			0.0641793	+	0.997938i	$0.479557\pi$
$864$	165.859			0.191967
$865$		−	306.520i		−	0.354358i
$866$		−	447.219i		−	0.516419i
$867$	482.944			0.557028
$868$		−	561.349i		−	0.646715i
$869$	357.114			0.410948
$870$		−	158.051i		−	0.181668i
$871$		−	1544.24i		−	1.77295i
$872$			276.072i			0.316596i
$873$		−	259.396i		−	0.297132i
$874$	−92.2543	+	461.035i	−0.105554	+	0.527500i
$875$	85.1735			0.0973412
$876$	122.049			0.139325
$877$	−336.486			−0.383678			−0.191839	−	0.981426i	$-0.561445\pi$
$877$	−336.486			−0.383678			−0.191839	+	0.981426i	$0.561445\pi$
$878$	−295.399			−0.336445
$879$		−	845.099i		−	0.961433i
$880$	−110.698			−0.125794
$881$		−	508.337i		−	0.577000i	−0.957480	−	0.288500i	$-0.906843\pi$
$881$		−	508.337i		−	0.577000i	0.957480	−	0.288500i	$-0.0931565\pi$
$882$	−44.5272			−0.0504844
$883$	−334.663			−0.379006			−0.189503	−	0.981880i	$-0.560688\pi$
$883$	−334.663			−0.379006			−0.189503	+	0.981880i	$0.560688\pi$
$884$		−	237.942i		−	0.269165i
$885$		−	434.783i		−	0.491281i
$886$	999.822			1.12847
$887$	−278.810			−0.314330			−0.157165	−	0.987572i	$-0.550235\pi$
$887$	−278.810			−0.314330			−0.157165	+	0.987572i	$0.550235\pi$
$888$			378.369i			0.426091i
$889$			1153.21i			1.29719i
$890$	−143.703			−0.161464
$891$			464.116i			0.520893i
$892$	538.795			0.604030
$893$			957.804i			1.07257i
$894$			605.416i			0.677200i
$895$			124.482i			0.139086i
$896$			86.1895i			0.0961937i
$897$	−690.163	−	138.103i	−0.769412	−	0.153961i
$898$	741.828			0.826090
$899$	−784.065			−0.872152
$900$	34.8436			0.0387152
$901$	−707.025			−0.784712
$902$			1238.65i			1.37322i
$903$	−1252.56			−1.38711
$904$			161.396i			0.178535i
$905$	53.0657			0.0586362
$906$	−135.996			−0.150106
$907$			547.165i			0.603269i	0.953424	+	0.301634i	$0.0975322\pi$
$907$			547.165i			0.603269i	−0.953424	+	0.301634i	$0.902468\pi$
$908$			351.995i			0.387659i
$909$	59.4304			0.0653800
$910$	−313.907			−0.344953
$911$			1702.27i			1.86857i	0.356527	+	0.934285i	$0.383961\pi$
$911$			1702.27i			1.86857i	−0.356527	+	0.934285i	$0.616039\pi$
$912$		−	135.792i		−	0.148895i
$913$	858.766			0.940598
$914$		−	1112.88i		−	1.21759i
$915$	−126.005			−0.137710
$916$			126.134i			0.137701i
$917$		−	356.022i		−	0.388247i
$918$			378.590i			0.412407i
$919$			230.872i			0.251220i	0.992080	+	0.125610i	$0.0400889\pi$
$919$			230.872i			0.251220i	−0.992080	+	0.125610i	$0.959911\pi$
$920$	−28.5420	+	142.637i	−0.0310240	+	0.155040i
$921$	−1054.12			−1.14454
$922$	54.0879			0.0586636
$923$	−899.427			−0.974461
$924$	−442.867			−0.479293
$925$			284.801i			0.307893i
$926$	743.799			0.803239
$927$			536.425i			0.578668i
$928$	120.385			0.129726
$929$	1312.19			1.41247			0.706237	−	0.707975i	$-0.250391\pi$
$929$	1312.19			1.41247			0.706237	+	0.707975i	$0.250391\pi$
$930$			273.622i			0.294217i
$931$			130.618i			0.140299i
$932$	8.96082			0.00961461
$933$	440.497			0.472130
$934$		−	235.652i		−	0.252304i
$935$		−	252.680i		−	0.270246i
$936$	−128.416			−0.137197
$937$			933.379i			0.996136i	0.867138	+	0.498068i	$0.165957\pi$
$937$			933.379i			0.996136i	−0.867138	+	0.498068i	$0.834043\pi$
$938$	−1276.81			−1.36121
$939$			219.416i			0.233670i
$940$			296.330i			0.315244i
$941$		−	58.6896i		−	0.0623694i	−0.999514	−	0.0311847i	$-0.990072\pi$
$941$		−	58.6896i		−	0.0623694i	0.999514	−	0.0311847i	$-0.00992801\pi$
$942$			838.293i			0.889907i
$943$	1596.02	+	319.368i	1.69250	+	0.338673i
$944$	331.169			0.350815
$945$	499.458			0.528527
$946$	1225.36			1.29530
$947$	1070.42			1.13033			0.565165	−	0.824978i	$-0.308812\pi$
$947$	1070.42			1.13033			0.565165	+	0.824978i	$0.308812\pi$
$948$			135.531i			0.142965i
$949$	−338.577			−0.356772
$950$		−	102.212i		−	0.107591i
$951$	1064.05			1.11888
$952$	−196.736			−0.206656
$953$			1370.22i			1.43780i	0.695114	+	0.718899i	$0.255354\pi$
$953$			1370.22i			1.43780i	−0.695114	+	0.718899i	$0.744646\pi$
$954$			381.578i			0.399977i
$955$	786.331			0.823383
$956$	171.041			0.178913
$957$			618.575i			0.646369i
$958$		−	45.3472i		−	0.0473353i
$959$	237.647			0.247807
$960$		−	42.0119i		−	0.0437624i
$961$	396.395			0.412482
$962$		−	1049.64i		−	1.09110i
$963$		−	393.111i		−	0.408215i
$964$		−	515.030i		−	0.534263i
$965$			88.2817i			0.0914837i
$966$	−114.187	+	570.644i	−0.118206	+	0.590728i
$967$	145.068			0.150019			0.0750094	−	0.997183i	$-0.476101\pi$
$967$	145.068			0.150019			0.0750094	+	0.997183i	$0.476101\pi$
$968$	91.0088			0.0940174
$969$	309.959			0.319875
$970$	−235.418			−0.242699
$971$			996.133i			1.02588i	0.858423	+	0.512942i	$0.171444\pi$
$971$			996.133i			1.02588i	−0.858423	+	0.512942i	$0.828556\pi$
$972$	351.620			0.361749
$973$		−	278.456i		−	0.286183i
$974$	−969.880			−0.995770
$975$	153.010			0.156933
$976$		−	95.9764i		−	0.0983365i
$977$			161.683i			0.165489i	0.996571	+	0.0827444i	$0.0263685\pi$
$977$			161.683i			0.165489i	−0.996571	+	0.0827444i	$0.973631\pi$
$978$	155.999			0.159508
$979$	562.421			0.574485
$980$			40.4112i			0.0412360i
$981$			340.095i			0.346682i
$982$	−1097.15			−1.11727
$983$			1023.25i			1.04095i	0.853878	+	0.520474i	$0.174245\pi$
$983$			1023.25i			1.04095i	−0.853878	+	0.520474i	$0.825755\pi$
$984$	−470.088			−0.477732
$985$			503.153i			0.510815i
$986$			274.792i			0.278693i
$987$			1185.52i			1.20113i
$988$			376.702i			0.381277i
$989$	315.941	−	1578.90i	0.319455	−	1.59646i
$990$	−136.370			−0.137748
$991$	−518.210			−0.522917			−0.261458	−	0.965215i	$-0.584203\pi$
$991$	−518.210			−0.522917			−0.261458	+	0.965215i	$0.584203\pi$
$992$	−208.415			−0.210095
$993$	−418.805			−0.421757
$994$			743.669i			0.748158i
$995$	82.9296			0.0833463
$996$			325.917i			0.327226i
$997$	−1927.76			−1.93356			−0.966780	−	0.255611i	$-0.917723\pi$
$997$	−1927.76			−1.93356			−0.966780	+	0.255611i	$0.917723\pi$
$998$	−555.032			−0.556144
$999$			1670.08i			1.67175i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	230.3.d.a.91.5	✓	16
3.2	odd	2		2070.3.c.a.91.13		16
4.3	odd	2		1840.3.k.d.321.5		16
5.2	odd	4		1150.3.c.c.1149.11		32
5.3	odd	4		1150.3.c.c.1149.22		32
5.4	even	2		1150.3.d.b.551.12		16
23.22	odd	2	inner	230.3.d.a.91.6	yes	16
69.68	even	2		2070.3.c.a.91.12		16
92.91	even	2		1840.3.k.d.321.6		16
115.22	even	4		1150.3.c.c.1149.21		32
115.68	even	4		1150.3.c.c.1149.12		32
115.114	odd	2		1150.3.d.b.551.11		16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
230.3.d.a.91.5	✓	16	1.1	even	1	trivial
230.3.d.a.91.6	yes	16	23.22	odd	2	inner
1150.3.c.c.1149.11		32	5.2	odd	4
1150.3.c.c.1149.12		32	115.68	even	4
1150.3.c.c.1149.21		32	115.22	even	4
1150.3.c.c.1149.22		32	5.3	odd	4
1150.3.d.b.551.11		16	115.114	odd	2
1150.3.d.b.551.12		16	5.4	even	2
1840.3.k.d.321.5		16	4.3	odd	2
1840.3.k.d.321.6		16	92.91	even	2
2070.3.c.a.91.12		16	69.68	even	2
2070.3.c.a.91.13		16	3.2	odd	2

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:	\( N \)	\(=\)	\( 230 = 2 \cdot 5 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	230.d (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-1.41421 q^{2} +2.34854 q^{3} +2.00000 q^{4} -2.23607i q^{5} -3.32134 q^{6} -7.61815i q^{7} -2.82843 q^{8} -3.48436 q^{9} +O(q^{10})\)	\(q-1.41421 q^{2} +2.34854 q^{3} +2.00000 q^{4} -2.23607i q^{5} -3.32134 q^{6} -7.61815i q^{7} -2.82843 q^{8} -3.48436 q^{9} +3.16228i q^{10} -12.3764i q^{11} +4.69708 q^{12} -13.0302 q^{13} +10.7737i q^{14} -5.25149i q^{15} +4.00000 q^{16} +9.13040i q^{17} +4.92764 q^{18} -14.4549i q^{19} -4.47214i q^{20} -17.8915i q^{21} +17.5029i q^{22} +(22.5529 + 4.51289i) q^{23} -6.64267 q^{24} -5.00000 q^{25} +18.4275 q^{26} -29.3200 q^{27} -15.2363i q^{28} -21.2813 q^{29} +7.42673i q^{30} +36.8428 q^{31} -5.65685 q^{32} -29.0666i q^{33} -12.9123i q^{34} -17.0347 q^{35} -6.96873 q^{36} -56.9603i q^{37} +20.4424i q^{38} -30.6019 q^{39} +6.32456i q^{40} +70.7680 q^{41} +25.3024i q^{42} -70.0086i q^{43} -24.7529i q^{44} +7.79128i q^{45} +(-31.8946 - 6.38219i) q^{46} -66.2614 q^{47} +9.39416 q^{48} -9.03623 q^{49} +7.07107 q^{50} +21.4431i q^{51} -26.0604 q^{52} +77.4364i q^{53} +41.4648 q^{54} -27.6746 q^{55} +21.5474i q^{56} -33.9480i q^{57} +30.0963 q^{58} +82.7923 q^{59} -10.5030i q^{60} -23.9941i q^{61} -52.1036 q^{62} +26.5444i q^{63} +8.00000 q^{64} +29.1364i q^{65} +41.1063i q^{66} +118.512i q^{67} +18.2608i q^{68} +(52.9664 + 10.5987i) q^{69} +24.0907 q^{70} +69.0263 q^{71} +9.85527 q^{72} +25.9840 q^{73} +80.5540i q^{74} -11.7427 q^{75} -28.9099i q^{76} -94.2857 q^{77} +43.2777 q^{78} +28.8543i q^{79} -8.94427i q^{80} -37.4999 q^{81} -100.081 q^{82} +69.3871i q^{83} -35.7831i q^{84} +20.4162 q^{85} +99.0071i q^{86} -49.9800 q^{87} +35.0059i q^{88} +45.4428i q^{89} -11.0185i q^{90} +99.2661i q^{91} +(45.1058 + 9.02579i) q^{92} +86.5269 q^{93} +93.7077 q^{94} -32.3222 q^{95} -13.2853 q^{96} +74.4458i q^{97} +12.7792 q^{98} +43.1241i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9}+O(q^{10}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9	\( 16 q + 32 q^{4} - 8 q^{6} + 64 q^{9} + 24 q^{13} + 64 q^{16} - 32 q^{18} + 4 q^{23} - 16 q^{24} - 80 q^{25} + 96 q^{26} - 96 q^{27} - 108 q^{29} - 116 q^{31} + 60 q^{35} + 128 q^{36} + 248 q^{39} - 156 q^{41} - 124 q^{46} - 128 q^{47} - 28 q^{49} + 48 q^{52} + 224 q^{54} + 160 q^{58} + 204 q^{59} + 64 q^{62} + 128 q^{64} - 268 q^{69} - 120 q^{70} + 236 q^{71} - 64 q^{72} - 112 q^{73} - 936 q^{77} - 432 q^{78} - 136 q^{81} - 64 q^{82} + 60 q^{85} - 152 q^{87} + 8 q^{92} + 856 q^{93} - 216 q^{94} - 160 q^{95} - 32 q^{96} + 256 q^{98}+O(q^{100}) \) 16 * q + 32 * q^4 - 8 * q^6 + 64 * q^9 + 24 * q^13 + 64 * q^16 - 32 * q^18 + 4 * q^23 - 16 * q^24 - 80 * q^25 + 96 * q^26 - 96 * q^27 - 108 * q^29 - 116 * q^31 + 60 * q^35 + 128 * q^36 + 248 * q^39 - 156 * q^41 - 124 * q^46 - 128 * q^47 - 28 * q^49 + 48 * q^52 + 224 * q^54 + 160 * q^58 + 204 * q^59 + 64 * q^62 + 128 * q^64 - 268 * q^69 - 120 * q^70 + 236 * q^71 - 64 * q^72 - 112 * q^73 - 936 * q^77 - 432 * q^78 - 136 * q^81 - 64 * q^82 + 60 * q^85 - 152 * q^87 + 8 * q^92 + 856 * q^93 - 216 * q^94 - 160 * q^95 - 32 * q^96 + 256 * q^98

Introduction

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