LMFDB - Embedded newform 230.3.d.a.91.6

Newspace parameters

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

Newform invariants

Self dual:	no
Analytic conductor:	$6.26704608029$
Analytic rank:	$0$
Dimension:	$16$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} + \cdots)$
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			91.6
Root			$1.01877i$ of defining polynomial
Character	$\chi$	$=$	230.91
Dual form			230.3.d.a.91.5

$q$-expansion

$f(q)$	$=$	$q-1.41421 q^{2} +2.34854 q^{3} +2.00000 q^{4} +2.23607i q^{5} -3.32134 q^{6} +7.61815i q^{7} -2.82843 q^{8} -3.48436 q^{9} +O(q^{10})$	\(q-1.41421 q^{2} +2.34854 q^{3} +2.00000 q^{4} +2.23607i q^{5} -3.32134 q^{6} +7.61815i q^{7} -2.82843 q^{8} -3.48436 q^{9} -3.16228i q^{10} +12.3764i q^{11} +4.69708 q^{12} -13.0302 q^{13} -10.7737i q^{14} +5.25149i q^{15} +4.00000 q^{16} -9.13040i q^{17} +4.92764 q^{18} +14.4549i q^{19} +4.47214i q^{20} +17.8915i q^{21} -17.5029i q^{22} +(22.5529 - 4.51289i) q^{23} -6.64267 q^{24} -5.00000 q^{25} +18.4275 q^{26} -29.3200 q^{27} +15.2363i q^{28} -21.2813 q^{29} -7.42673i q^{30} +36.8428 q^{31} -5.65685 q^{32} +29.0666i q^{33} +12.9123i q^{34} -17.0347 q^{35} -6.96873 q^{36} +56.9603i q^{37} -20.4424i q^{38} -30.6019 q^{39} -6.32456i q^{40} +70.7680 q^{41} -25.3024i q^{42} +70.0086i q^{43} +24.7529i q^{44} -7.79128i q^{45} +(-31.8946 + 6.38219i) q^{46} -66.2614 q^{47} +9.39416 q^{48} -9.03623 q^{49} +7.07107 q^{50} -21.4431i q^{51} -26.0604 q^{52} -77.4364i q^{53} +41.4648 q^{54} -27.6746 q^{55} -21.5474i q^{56} +33.9480i q^{57} +30.0963 q^{58} +82.7923 q^{59} +10.5030i q^{60} +23.9941i q^{61} -52.1036 q^{62} -26.5444i q^{63} +8.00000 q^{64} -29.1364i q^{65} -41.1063i q^{66} -118.512i q^{67} -18.2608i q^{68} +(52.9664 - 10.5987i) q^{69} +24.0907 q^{70} +69.0263 q^{71} +9.85527 q^{72} +25.9840 q^{73} -80.5540i q^{74} -11.7427 q^{75} +28.9099i q^{76} -94.2857 q^{77} +43.2777 q^{78} -28.8543i q^{79} +8.94427i q^{80} -37.4999 q^{81} -100.081 q^{82} -69.3871i q^{83} +35.7831i q^{84} +20.4162 q^{85} -99.0071i q^{86} -49.9800 q^{87} -35.0059i q^{88} -45.4428i q^{89} +11.0185i q^{90} -99.2661i q^{91} +(45.1058 - 9.02579i) q^{92} +86.5269 q^{93} +93.7077 q^{94} -32.3222 q^{95} -13.2853 q^{96} -74.4458i q^{97} +12.7792 q^{98} -43.1241i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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	$0.183149\pi$
$7$			7.61815i			1.08831i	−0.838986	+	0.544154i	$0.816851\pi$
$8$	−2.82843			−0.353553
$9$	−3.48436			−0.387152
$10$		−	3.16228i		−	0.316228i
$11$			12.3764i			1.12513i	0.826752	+	0.562566i	$0.190186\pi$
$11$			12.3764i			1.12513i	−0.826752	+	0.562566i	$0.809814\pi$
$12$	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	$-0.913458\pi$
$17$		−	9.13040i		−	0.537083i	0.963268	−	0.268541i	$-0.0865416\pi$
$18$	4.92764			0.273758
$19$			14.4549i			0.760787i	0.924825	+	0.380393i	$0.124211\pi$
$19$			14.4549i			0.760787i	−0.924825	+	0.380393i	$0.875789\pi$
$20$			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	$0.279611\pi$
$37$			56.9603i			1.53947i	−0.638365	+	0.769734i	$0.720389\pi$
$38$		−	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	$0.302744\pi$
$43$			70.0086i			1.62811i	−0.580790	+	0.814053i	$0.697256\pi$
$44$			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	$-0.739272\pi$
$53$		−	77.4364i		−	1.46106i	0.682879	−	0.730532i	$-0.260728\pi$
$54$	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	$0.0630137\pi$
$61$			23.9941i			0.393346i	−0.980469	+	0.196673i	$0.936986\pi$
$62$	−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	$-0.654555\pi$
$67$		−	118.512i		−	1.76884i	0.466695	−	0.884418i	$-0.345445\pi$
$68$		−	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	$-0.941541\pi$
$79$		−	28.8543i		−	0.365244i	0.983183	−	0.182622i	$-0.0584585\pi$
$80$			8.94427i			0.111803i
$81$	−37.4999			−0.462962
$82$	−100.081			−1.22050
$83$		−	69.3871i		−	0.835989i	−0.908449	−	0.417995i	$-0.862733\pi$
$83$		−	69.3871i		−	0.835989i	0.908449	−	0.417995i	$-0.137267\pi$
$84$			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	$-0.917827\pi$
$89$		−	45.4428i		−	0.510594i	0.966863	−	0.255297i	$-0.0821732\pi$
$90$			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	$-0.874636\pi$
$97$		−	74.4458i		−	0.767482i	0.923441	−	0.383741i	$-0.125364\pi$
$98$	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	$0.268669\pi$
$103$			153.952i			1.49468i	−0.664442	+	0.747340i	$0.731331\pi$
$104$	36.8550			0.354375
$105$	−40.0067			−0.381016
$106$			109.512i			1.03313i
$107$		−	112.821i		−	1.05441i	−0.849740	−	0.527203i	$-0.823241\pi$
$107$		−	112.821i		−	1.05441i	0.849740	−	0.527203i	$-0.176759\pi$
$108$	−58.6400			−0.542963
$109$			97.6061i			0.895468i	0.894167	+	0.447734i	$0.147769\pi$
$109$			97.6061i			0.895468i	−0.894167	+	0.447734i	$0.852231\pi$
$110$	39.1378			0.355798
$111$			133.773i			1.20517i
$112$			30.4726i			0.272077i
$113$			57.0620i			0.504974i	0.967600	+	0.252487i	$0.0812485\pi$
$113$			57.0620i			0.504974i	−0.967600	+	0.252487i	$0.918752\pi$
$114$		−	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	$-0.963682\pi$
$137$		−	31.1949i		−	0.227700i	0.993498	−	0.113850i	$-0.0363183\pi$
$138$	−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	$0.209506\pi$
$149$			182.281i			1.22336i	−0.791104	+	0.611681i	$0.790494\pi$
$150$	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	$0.297197\pi$
$157$			252.396i			1.60762i	−0.594887	+	0.803810i	$0.702803\pi$
$158$			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	$-0.979118\pi$
$181$		−	23.7317i		−	0.131114i	0.997849	−	0.0655572i	$-0.0208825\pi$
$182$			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	$-0.627724\pi$
$191$		−	351.658i		−	1.84114i	0.390576	−	0.920571i	$-0.372276\pi$
$192$	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	$-0.970296\pi$
$199$		−	37.0872i		−	0.186368i	0.995649	−	0.0931840i	$-0.0297045\pi$
$200$	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	$-0.873284\pi$
$227$		−	175.997i		−	0.775319i	0.921803	−	0.387659i	$-0.126716\pi$
$228$			67.8960i			0.297789i
$229$		−	63.0669i		−	0.275401i	−0.990474	−	0.137701i	$-0.956029\pi$
$229$		−	63.0669i		−	0.275401i	0.990474	−	0.137701i	$-0.0439712\pi$
$230$	−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	$0.179411\pi$
$241$			257.515i			1.06853i	−0.845318	+	0.534263i	$0.820589\pi$
$242$	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	$0.0777733\pi$
$251$			121.438i			0.483816i	−0.970299	+	0.241908i	$0.922227\pi$
$252$		−	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	$0.292158\pi$
$263$			417.798i			1.58858i	−0.607536	+	0.794292i	$0.707842\pi$
$264$		−	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	$0.193887\pi$
$281$			321.543i			1.14428i	−0.820156	+	0.572140i	$0.806113\pi$
$282$	220.076			0.780412
$283$		−	428.712i		−	1.51488i	−0.652904	−	0.757441i	$-0.726449\pi$
$283$		−	428.712i		−	1.51488i	0.652904	−	0.757441i	$-0.273551\pi$
$284$	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	$0.210466\pi$
$293$			359.840i			1.22812i	−0.789258	+	0.614062i	$0.789534\pi$
$294$	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	$-0.952316\pi$
$313$		−	93.4265i		−	0.298487i	0.988800	−	0.149244i	$-0.0476839\pi$
$314$		−	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	$0.0405963\pi$
$337$			85.7271i			0.254383i	−0.991878	+	0.127192i	$0.959404\pi$
$338$	−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	$-0.975341\pi$
$359$		−	55.5671i		−	0.154783i	0.997001	−	0.0773914i	$-0.0246591\pi$
$360$			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	$0.0718547\pi$
$367$			164.288i			0.447652i	−0.974629	+	0.223826i	$0.928145\pi$
$368$	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	$0.0107325\pi$
$373$			25.1481i			0.0674212i	−0.999432	+	0.0337106i	$0.989268\pi$
$374$	−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	$0.205852\pi$
$379$			456.740i			1.20512i	−0.798074	+	0.602560i	$0.794148\pi$
$380$	−64.6445			−0.170117
$381$	−355.513			−0.933104
$382$			497.319i			1.30188i
$383$		−	371.017i		−	0.968712i	−0.874871	−	0.484356i	$-0.839054\pi$
$383$		−	371.017i		−	0.968712i	0.874871	−	0.484356i	$-0.160946\pi$
$384$	−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	$0.171895\pi$
$389$			400.013i			1.02831i	−0.857697	+	0.514155i	$0.828105\pi$
$390$			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	$-0.822071\pi$
$401$		−	425.319i		−	1.06065i	0.847796	−	0.530323i	$-0.177929\pi$
$402$			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	$0.140651\pi$
$419$			358.352i			0.855256i	−0.903955	+	0.427628i	$0.859349\pi$
$420$	−80.0133			−0.190508
$421$		−	672.051i		−	1.59632i	−0.602446	−	0.798160i	$-0.705807\pi$
$421$		−	672.051i		−	1.59632i	0.602446	−	0.798160i	$-0.294193\pi$
$422$	−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	$0.400138\pi$
$431$			819.926i			1.90238i	−0.308604	+	0.951191i	$0.599862\pi$
$432$	−117.280			−0.271482
$433$		−	316.231i		−	0.730326i	−0.930944	−	0.365163i	$-0.881013\pi$
$433$		−	316.231i		−	0.730326i	0.930944	−	0.365163i	$-0.118987\pi$
$434$		−	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	$-0.669858\pi$
$457$		−	786.926i		−	1.72194i	0.508657	−	0.860969i	$-0.330142\pi$
$458$			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	$-0.942906\pi$
$467$		−	166.631i		−	0.356812i	0.983957	−	0.178406i	$-0.0570941\pi$
$468$	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	$-0.989344\pi$
$479$		−	32.0653i		−	0.0669422i	0.999440	−	0.0334711i	$-0.0106562\pi$
$480$		−	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	$-0.783190\pi$
$503$		−	633.449i		−	1.25934i	0.776862	−	0.629671i	$-0.216810\pi$
$504$			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	$-0.875825\pi$
$521$		−	396.259i		−	0.760574i	0.924869	−	0.380287i	$-0.124175\pi$
$522$	−104.867			−0.200894
$523$			27.4737i			0.0525309i	0.999655	+	0.0262655i	$0.00836152\pi$
$523$			27.4737i			0.0525309i	−0.999655	+	0.0262655i	$0.991638\pi$
$524$	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	$0.253122\pi$
$557$			795.405i			1.42802i	−0.700137	+	0.714008i	$0.746878\pi$
$558$	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	$0.0610309\pi$
$563$			214.573i			0.381124i	−0.981675	+	0.190562i	$0.938969\pi$
$564$	−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	$-0.580797\pi$
$569$		−	1101.54i		−	1.93592i	0.251114	−	0.967958i	$-0.419203\pi$
$570$	107.353			0.188339
$571$		−	560.543i		−	0.981686i	−0.871248	−	0.490843i	$-0.836689\pi$
$571$		−	560.543i		−	0.981686i	0.871248	−	0.490843i	$-0.163311\pi$
$572$		−	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	$-0.848953\pi$
$613$		−	560.182i		−	0.913837i	0.889509	−	0.456919i	$-0.151047\pi$
$614$	634.760			1.03381
$615$			371.638i			0.604289i
$616$	266.680			0.432922
$617$		−	308.240i		−	0.499578i	−0.968300	−	0.249789i	$-0.919639\pi$
$617$		−	308.240i		−	0.499578i	0.968300	−	0.249789i	$-0.0803613\pi$
$618$		−	511.326i		−	0.827389i
$619$		−	424.114i		−	0.685161i	−0.939489	−	0.342580i	$-0.888699\pi$
$619$		−	424.114i		−	0.685161i	0.939489	−	0.342580i	$-0.111301\pi$
$620$			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	$0.0435823\pi$
$631$			172.251i			0.272981i	−0.990641	+	0.136491i	$0.956418\pi$
$632$			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	$-0.907855\pi$
$641$		−	365.954i		−	0.570912i	0.958392	−	0.285456i	$-0.0921450\pi$
$642$			374.718i			0.583672i
$643$		−	823.317i		−	1.28043i	−0.768195	−	0.640215i	$-0.778845\pi$
$643$		−	823.317i		−	1.28043i	0.768195	−	0.640215i	$-0.221155\pi$
$644$	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	$0.0600338\pi$
$659$			247.106i			0.374971i	−0.982267	+	0.187486i	$0.939966\pi$
$660$	−129.990			−0.196954
$661$		−	937.016i		−	1.41757i	−0.705423	−	0.708787i	$-0.749243\pi$
$661$		−	937.016i		−	1.41757i	0.705423	−	0.708787i	$-0.250757\pi$
$662$	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	$0.0629483\pi$
$677$			266.022i			0.392943i	−0.980510	+	0.196471i	$0.937052\pi$
$678$		−	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	$0.283148\pi$
$701$			1089.04i			1.55356i	−0.629773	+	0.776779i	$0.716852\pi$
$702$	−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	$-0.814842\pi$
$709$		−	779.102i		−	1.09887i	0.835535	−	0.549437i	$-0.185158\pi$
$710$		−	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	$0.00433152\pi$
$727$			19.7852i			0.0272149i	−0.999907	+	0.0136075i	$0.995668\pi$
$728$			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	$0.136371\pi$
$733$			609.029i			0.830871i	−0.909623	+	0.415436i	$0.863629\pi$
$734$		−	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	$0.00995832\pi$
$743$			46.4819i			0.0625598i	−0.999511	+	0.0312799i	$0.990042\pi$
$744$	−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	$-0.683747\pi$
$751$		−	1258.62i		−	1.67592i	0.545728	−	0.837962i	$-0.316253\pi$
$752$	−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	$0.133249\pi$
$757$			615.435i			0.812992i	−0.913653	+	0.406496i	$0.866751\pi$
$758$		−	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	$0.233855\pi$
$769$			1031.00i			1.34070i	−0.742046	+	0.670349i	$0.766145\pi$
$770$			298.157i			0.387217i
$771$	451.613			0.585749
$772$	−78.9616			−0.102282
$773$			1281.23i			1.65747i	0.559638	+	0.828737i	$0.310940\pi$
$773$			1281.23i			1.65747i	−0.559638	+	0.828737i	$0.689060\pi$
$774$			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	$0.399973\pi$
$787$			1496.92i			1.90206i	−0.309096	+

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

L-functions

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