LMFDB - Embedded newform 336.4.h.a.239.7

Newspace parameters

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.h (of order $2$, degree $1$, minimal)

Newform invariants

Self dual:	no
Analytic conductor:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$12$
Coefficient field:	$\mathbb{Q}[x]/(x^{12} + \cdots)$
Defining polynomial:	$ x^{12} + 152x^{10} + 8222x^{8} + 194132x^{6} + 1882697x^{4} + 5152508x^{2} + 4008004 $ x^12 + 152x^10 + 8222x^8 + 194132x^6 + 1882697x^4 + 5152508*x^2 + 4008004
Coefficient ring:	$\Z[a_1, \ldots, a_{11}]$
Coefficient ring index:	$ 2^{7}\cdot 3^{2}\cdot 7^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			239.7
Root			$-5.90052i$ of defining polynomial
Character	$\chi$	$=$	336.239
Dual form			336.4.h.a.239.8

$q$-expansion

$f(q)$	$=$	$q+(2.18705 - 4.71347i) q^{3} -14.5852i q^{5} +7.00000i q^{7} +(-17.4336 - 20.6172i) q^{9} +O(q^{10})$	\(q+(2.18705 - 4.71347i) q^{3} -14.5852i q^{5} +7.00000i q^{7} +(-17.4336 - 20.6172i) q^{9} -31.0233 q^{11} -55.7458 q^{13} +(-68.7469 - 31.8986i) q^{15} +86.4384i q^{17} -96.8558i q^{19} +(32.9943 + 15.3094i) q^{21} +115.219 q^{23} -87.7283 q^{25} +(-135.307 + 37.0818i) q^{27} +49.1735i q^{29} +12.5750i q^{31} +(-67.8496 + 146.228i) q^{33} +102.096 q^{35} -296.822 q^{37} +(-121.919 + 262.756i) q^{39} +213.956i q^{41} -165.680i q^{43} +(-300.706 + 254.273i) q^{45} +426.135 q^{47} -49.0000 q^{49} +(407.425 + 189.045i) q^{51} -460.767i q^{53} +452.482i q^{55} +(-456.527 - 211.829i) q^{57} -686.382 q^{59} -583.424 q^{61} +(144.320 - 122.035i) q^{63} +813.064i q^{65} -589.155i q^{67} +(251.989 - 543.080i) q^{69} +766.330 q^{71} -904.778 q^{73} +(-191.866 + 413.505i) q^{75} -217.163i q^{77} -459.440i q^{79} +(-121.139 + 718.865i) q^{81} -1115.25 q^{83} +1260.72 q^{85} +(231.778 + 107.545i) q^{87} -119.900i q^{89} -390.221i q^{91} +(59.2717 + 27.5021i) q^{93} -1412.66 q^{95} -331.017 q^{97} +(540.848 + 639.614i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 12 q + 76 q^{9}+O(q^{10}) $ 12 * q + 76 * q^9	$ 12 q + 76 q^{9} - 96 q^{13} + 112 q^{21} - 1068 q^{25} - 832 q^{33} - 720 q^{37} + 392 q^{45} - 588 q^{49} - 2336 q^{57} + 432 q^{61} - 424 q^{69} + 1656 q^{73} - 868 q^{81} - 1464 q^{85} + 696 q^{93} - 6264 q^{97}+O(q^{100}) $ 12 * q + 76 * q^9 - 96 * q^13 + 112 * q^21 - 1068 * q^25 - 832 * q^33 - 720 * q^37 + 392 * q^45 - 588 * q^49 - 2336 * q^57 + 432 * q^61 - 424 * q^69 + 1656 * q^73 - 868 * q^81 - 1464 * q^85 + 696 * q^93 - 6264 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$-1$	$-1$	$1$

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 $

$2$		0			0
$2$		0			0
$3$	2.18705	−	4.71347i	0.420898	−	0.907108i
$3$	2.18705	−	4.71347i	0.420898	−	0.907108i
$4$		0			0
$5$		−	14.5852i		−	1.30454i	−0.757986	−	0.652270i	$-0.773817\pi$
$5$		−	14.5852i		−	1.30454i	0.757986	−	0.652270i	$-0.226183\pi$
$6$		0			0
$7$			7.00000i			0.377964i
$7$			7.00000i			0.377964i
$8$		0			0
$9$	−17.4336	−	20.6172i	−0.645689	−	0.763600i
$10$		0			0
$11$	−31.0233			−0.850353			−0.425177	−	0.905110i	$-0.639788\pi$
$11$	−31.0233			−0.850353			−0.425177	+	0.905110i	$0.639788\pi$
$12$		0			0
$13$	−55.7458			−1.18932			−0.594658	−	0.803979i	$-0.702713\pi$
$13$	−55.7458			−1.18932			−0.594658	+	0.803979i	$0.702713\pi$
$14$		0			0
$15$	−68.7469	−	31.8986i	−1.18336	−	0.549079i
$16$		0			0
$17$			86.4384i			1.23320i	0.787277	+	0.616600i	$0.211490\pi$
$17$			86.4384i			1.23320i	−0.787277	+	0.616600i	$0.788510\pi$
$18$		0			0
$19$		−	96.8558i		−	1.16949i	−0.811218	−	0.584743i	$-0.801195\pi$
$19$		−	96.8558i		−	1.16949i	0.811218	−	0.584743i	$-0.198805\pi$
$20$		0			0
$21$	32.9943	+	15.3094i	0.342855	+	0.159085i
$22$		0			0
$23$	115.219			1.04456			0.522278	−	0.852775i	$-0.325082\pi$
$23$	115.219			1.04456			0.522278	+	0.852775i	$0.325082\pi$
$24$		0			0
$25$	−87.7283			−0.701826
$26$		0			0
$27$	−135.307	+	37.0818i	−0.964437	+	0.264311i
$28$		0			0
$29$			49.1735i			0.314872i	0.987529	+	0.157436i	$0.0503228\pi$
$29$			49.1735i			0.314872i	−0.987529	+	0.157436i	$0.949677\pi$
$30$		0			0
$31$			12.5750i			0.0728558i	0.999336	+	0.0364279i	$0.0115979\pi$
$31$			12.5750i			0.0728558i	−0.999336	+	0.0364279i	$0.988402\pi$
$32$		0			0
$33$	−67.8496	+	146.228i	−0.357912	+	0.771362i
$34$		0			0
$35$	102.096			0.493070
$36$		0			0
$37$	−296.822			−1.31884			−0.659421	−	0.751774i	$-0.729199\pi$
$37$	−296.822			−1.31884			−0.659421	+	0.751774i	$0.729199\pi$
$38$		0			0
$39$	−121.919	+	262.756i	−0.500581	+	1.07884i
$40$		0			0
$41$			213.956i			0.814982i	0.913209	+	0.407491i	$0.133596\pi$
$41$			213.956i			0.814982i	−0.913209	+	0.407491i	$0.866404\pi$
$42$		0			0
$43$		−	165.680i		−	0.587581i	−0.955870	−	0.293790i	$-0.905083\pi$
$43$		−	165.680i		−	0.587581i	0.955870	−	0.293790i	$-0.0949168\pi$
$44$		0			0
$45$	−300.706	+	254.273i	−0.996148	+	0.842328i
$46$		0			0
$47$	426.135			1.32251			0.661257	−	0.750159i	$-0.270023\pi$
$47$	426.135			1.32251			0.661257	+	0.750159i	$0.270023\pi$
$48$		0			0
$49$	−49.0000			−0.142857
$50$		0			0
$51$	407.425	+	189.045i	1.11864	+	0.519052i
$52$		0			0
$53$		−	460.767i		−	1.19417i	−0.802177	−	0.597087i	$-0.796325\pi$
$53$		−	460.767i		−	1.19417i	0.802177	−	0.597087i	$-0.203675\pi$
$54$		0			0
$55$			452.482i			1.10932i
$56$		0			0
$57$	−456.527	−	211.829i	−1.06085	−	0.492235i
$58$		0			0
$59$	−686.382			−1.51456			−0.757282	−	0.653088i	$-0.773473\pi$
$59$	−686.382			−1.51456			−0.757282	+	0.653088i	$0.773473\pi$
$60$		0			0
$61$	−583.424			−1.22459			−0.612293	−	0.790631i	$-0.709753\pi$
$61$	−583.424			−1.22459			−0.612293	+	0.790631i	$0.709753\pi$
$62$		0			0
$63$	144.320	−	122.035i	0.288614	−	0.244048i
$64$		0			0
$65$			813.064i			1.55151i
$66$		0			0
$67$		−	589.155i		−	1.07428i	−0.843493	−	0.537140i	$-0.819505\pi$
$67$		−	589.155i		−	1.07428i	0.843493	−	0.537140i	$-0.180495\pi$
$68$		0			0
$69$	251.989	−	543.080i	0.439652	−	0.947524i
$70$		0			0
$71$	766.330			1.28094			0.640469	−	0.767984i	$-0.278740\pi$
$71$	766.330			1.28094			0.640469	+	0.767984i	$0.278740\pi$
$72$		0			0
$73$	−904.778			−1.45063			−0.725317	−	0.688415i	$-0.758307\pi$
$73$	−904.778			−1.45063			−0.725317	+	0.688415i	$0.758307\pi$
$74$		0			0
$75$	−191.866	+	413.505i	−0.295397	+	0.636632i
$76$		0			0
$77$		−	217.163i		−	0.321403i
$78$		0			0
$79$		−	459.440i		−	0.654317i	−0.944969	−	0.327159i	$-0.893909\pi$
$79$		−	459.440i		−	0.654317i	0.944969	−	0.327159i	$-0.106091\pi$
$80$		0			0
$81$	−121.139	+	718.865i	−0.166171	+	0.986097i
$82$		0			0
$83$	−1115.25			−1.47487			−0.737436	−	0.675417i	$-0.763964\pi$
$83$	−1115.25			−1.47487			−0.737436	+	0.675417i	$0.763964\pi$
$84$		0			0
$85$	1260.72			1.60876
$86$		0			0
$87$	231.778	+	107.545i	0.285623	+	0.132529i
$88$		0			0
$89$		−	119.900i		−	0.142802i	−0.997448	−	0.0714011i	$-0.977253\pi$
$89$		−	119.900i		−	0.142802i	0.997448	−	0.0714011i	$-0.0227470\pi$
$90$		0			0
$91$		−	390.221i		−	0.449519i
$92$		0			0
$93$	59.2717	+	27.5021i	0.0660881	+	0.0306649i
$94$		0			0
$95$	−1412.66			−1.52564
$96$		0			0
$97$	−331.017			−0.346491			−0.173246	−	0.984879i	$-0.555425\pi$
$97$	−331.017			−0.346491			−0.173246	+	0.984879i	$0.555425\pi$
$98$		0			0
$99$	540.848	+	639.614i	0.549064	+	0.649330i
$100$		0			0
$101$			1609.16i			1.58532i	0.609662	+	0.792661i	$0.291305\pi$
$101$			1609.16i			1.58532i	−0.609662	+	0.792661i	$0.708695\pi$
$102$		0			0
$103$		−	1388.96i		−	1.32872i	−0.747411	−	0.664362i	$-0.768703\pi$
$103$		−	1388.96i		−	1.32872i	0.747411	−	0.664362i	$-0.231297\pi$
$104$		0			0
$105$	223.290	−	481.229i	0.207532	−	0.447268i
$106$		0			0
$107$	502.365			0.453883			0.226941	−	0.973908i	$-0.427127\pi$
$107$	502.365			0.453883			0.226941	+	0.973908i	$0.427127\pi$
$108$		0			0
$109$	1599.88			1.40588			0.702938	−	0.711251i	$-0.251871\pi$
$109$	1599.88			1.40588			0.702938	+	0.711251i	$0.251871\pi$
$110$		0			0
$111$	−649.164	+	1399.06i	−0.555099	+	1.19633i
$112$		0			0
$113$		−	934.016i		−	0.777565i	−0.921330	−	0.388782i	$-0.872896\pi$
$113$		−	934.016i		−	0.777565i	0.921330	−	0.388782i	$-0.127104\pi$
$114$		0			0
$115$		−	1680.49i		−	1.36266i
$116$		0			0
$117$	971.851	+	1149.32i	0.767928	+	0.908162i
$118$		0			0
$119$	−605.069			−0.466105
$120$		0			0
$121$	−368.553			−0.276900
$122$		0			0
$123$	1008.47	+	467.932i	0.739277	+	0.343025i
$124$		0			0
$125$		−	543.616i		−	0.388980i
$126$		0			0
$127$		−	301.355i		−	0.210558i	−0.994443	−	0.105279i	$-0.966426\pi$
$127$		−	301.355i		−	0.210558i	0.994443	−	0.105279i	$-0.0335736\pi$
$128$		0			0
$129$	−780.928	−	362.351i	−0.532999	−	0.247312i
$130$		0			0
$131$	−389.347			−0.259675			−0.129837	−	0.991535i	$-0.541445\pi$
$131$	−389.347			−0.259675			−0.129837	+	0.991535i	$0.541445\pi$
$132$		0			0
$133$	677.991			0.442024
$134$		0			0
$135$	540.846	+	1973.48i	0.344805	+	1.25815i
$136$		0			0
$137$		−	3037.04i		−	1.89395i	−0.321302	−	0.946977i	$-0.604120\pi$
$137$		−	3037.04i		−	1.89395i	0.321302	−	0.946977i	$-0.395880\pi$
$138$		0			0
$139$		−	1287.18i		−	0.785445i	−0.919657	−	0.392723i	$-0.871533\pi$
$139$		−	1287.18i		−	0.785445i	0.919657	−	0.392723i	$-0.128467\pi$
$140$		0			0
$141$	931.979	−	2008.57i	0.556644	−	1.19966i
$142$		0			0
$143$	1729.42			1.01134
$144$		0			0
$145$	717.205			0.410763
$146$		0			0
$147$	−107.166	+	230.960i	−0.0601283	+	0.129587i
$148$		0			0
$149$		−	2051.44i		−	1.12792i	−0.825801	−	0.563961i	$-0.809277\pi$
$149$		−	2051.44i		−	1.12792i	0.825801	−	0.563961i	$-0.190723\pi$
$150$		0			0
$151$		−	473.535i		−	0.255204i	−0.991825	−	0.127602i	$-0.959272\pi$
$151$		−	473.535i		−	0.255204i	0.991825	−	0.127602i	$-0.0407280\pi$
$152$		0			0
$153$	1782.12	−	1506.93i	0.941671	−	0.796263i
$154$		0			0
$155$	183.409			0.0950434
$156$		0			0
$157$	1184.81			0.602280			0.301140	−	0.953580i	$-0.402633\pi$
$157$	1184.81			0.602280			0.301140	+	0.953580i	$0.402633\pi$
$158$		0			0
$159$	−2171.81	−	1007.72i	−1.08324	−	0.502626i
$160$		0			0
$161$			806.531i			0.394805i
$162$		0			0
$163$			4055.24i			1.94866i	0.225132	+	0.974328i	$0.427719\pi$
$163$			4055.24i			1.94866i	−0.225132	+	0.974328i	$0.572281\pi$
$164$		0			0
$165$	2132.76	+	989.601i	1.00627	+	0.466911i
$166$		0			0
$167$	3681.23			1.70576			0.852881	−	0.522105i	$-0.174853\pi$
$167$	3681.23			1.70576			0.852881	+	0.522105i	$0.174853\pi$
$168$		0			0
$169$	910.598			0.414473
$170$		0			0
$171$	−1996.90	+	1688.55i	−0.893020	+	0.755125i
$172$		0			0
$173$		−	1069.27i		−	0.469914i	−0.972006	−	0.234957i	$-0.924505\pi$
$173$		−	1069.27i		−	0.469914i	0.972006	−	0.234957i	$-0.0754949\pi$
$174$		0			0
$175$		−	614.098i		−	0.265265i
$176$		0			0
$177$	−1501.15	+	3235.24i	−0.637478	+	1.37387i
$178$		0			0
$179$	2666.57			1.11346			0.556728	−	0.830695i	$-0.312056\pi$
$179$	2666.57			1.11346			0.556728	+	0.830695i	$0.312056\pi$
$180$		0			0
$181$	2648.47			1.08762			0.543810	−	0.839208i	$-0.316981\pi$
$181$	2648.47			1.08762			0.543810	+	0.839208i	$0.316981\pi$
$182$		0			0
$183$	−1275.98	+	2749.95i	−0.515427	+	1.11083i
$184$		0			0
$185$			4329.20i			1.72048i
$186$		0			0
$187$		−	2681.61i		−	1.04865i
$188$		0			0
$189$	−259.573	−	947.148i	−0.0999003	−	0.364523i
$190$		0			0
$191$	864.174			0.327379			0.163690	−	0.986512i	$-0.447660\pi$
$191$	864.174			0.327379			0.163690	+	0.986512i	$0.447660\pi$
$192$		0			0
$193$	−1133.69			−0.422822			−0.211411	−	0.977397i	$-0.567806\pi$
$193$	−1133.69			−0.422822			−0.211411	+	0.977397i	$0.567806\pi$
$194$		0			0
$195$	3832.36	+	1778.21i	1.40739	+	0.653029i
$196$		0			0
$197$			1642.58i			0.594056i	0.954869	+	0.297028i	$0.0959955\pi$
$197$			1642.58i			0.594056i	−0.954869	+	0.297028i	$0.904004\pi$
$198$		0			0
$199$		−	4912.39i		−	1.74990i	−0.484213	−	0.874950i	$-0.660894\pi$
$199$		−	4912.39i		−	1.74990i	0.484213	−	0.874950i	$-0.339106\pi$
$200$		0			0
$201$	−2776.96	−	1288.51i	−0.974487	−	0.452162i
$202$		0			0
$203$	−344.214			−0.119010
$204$		0			0
$205$	3120.59			1.06318
$206$		0			0
$207$	−2008.68	−	2375.49i	−0.674458	−	0.797623i
$208$		0			0
$209$			3004.79i			0.994476i
$210$		0			0
$211$		−	928.566i		−	0.302963i	−0.988460	−	0.151481i	$-0.951596\pi$
$211$		−	928.566i		−	0.302963i	0.988460	−	0.151481i	$-0.0484043\pi$
$212$		0			0
$213$	1676.00	−	3612.07i	0.539145	−	1.16195i
$214$		0			0
$215$	−2416.48			−0.766523
$216$		0			0
$217$	−88.0248			−0.0275369
$218$		0			0
$219$	−1978.80	+	4264.64i	−0.610569	+	1.31588i
$220$		0			0
$221$		−	4818.58i		−	1.46666i
$222$		0			0
$223$			208.318i			0.0625561i	0.999511	+	0.0312781i	$0.00995774\pi$
$223$			208.318i			0.0625561i	−0.999511	+	0.0312781i	$0.990042\pi$
$224$		0			0
$225$	1529.42	+	1808.71i	0.453161	+	0.535915i
$226$		0			0
$227$	−6151.95			−1.79876			−0.899382	−	0.437165i	$-0.855983\pi$
$227$	−6151.95			−1.79876			−0.899382	+	0.437165i	$0.855983\pi$
$228$		0			0
$229$	1493.71			0.431035			0.215518	−	0.976500i	$-0.430856\pi$
$229$	1493.71			0.431035			0.215518	+	0.976500i	$0.430856\pi$
$230$		0			0
$231$	−1023.59	−	474.947i	−0.291547	−	0.135278i
$232$		0			0
$233$		−	1003.48i		−	0.282146i	−0.989999	−	0.141073i	$-0.954945\pi$
$233$		−	1003.48i		−	0.282146i	0.989999	−	0.141073i	$-0.0450552\pi$
$234$		0			0
$235$		−	6215.27i		−	1.72527i
$236$		0			0
$237$	−2165.56	−	1004.82i	−0.593536	−	0.275401i
$238$		0			0
$239$	−6048.49			−1.63701			−0.818503	−	0.574502i	$-0.805196\pi$
$239$	−6048.49			−1.63701			−0.818503	+	0.574502i	$0.805196\pi$
$240$		0			0
$241$	−5619.61			−1.50204			−0.751018	−	0.660282i	$-0.770437\pi$
$241$	−5619.61			−1.50204			−0.751018	+	0.660282i	$0.770437\pi$
$242$		0			0
$243$	3123.41	+	2143.18i	0.824555	+	0.565782i
$244$		0			0
$245$			714.675i			0.186363i
$246$		0			0
$247$			5399.31i			1.39089i
$248$		0			0
$249$	−2439.11	+	5256.69i	−0.620771	+	1.33787i
$250$		0			0
$251$	6402.41			1.61003			0.805013	−	0.593257i	$-0.202158\pi$
$251$	6402.41			1.61003			0.805013	+	0.593257i	$0.202158\pi$
$252$		0			0
$253$	−3574.47			−0.888241
$254$		0			0
$255$	2757.26	−	5942.37i	0.677124	−	1.45932i
$256$		0			0
$257$		−	1609.20i		−	0.390580i	−0.980746	−	0.195290i	$-0.937435\pi$
$257$		−	1609.20i		−	0.390580i	0.980746	−	0.195290i	$-0.0625648\pi$
$258$		0			0
$259$		−	2077.75i		−	0.498475i
$260$		0			0
$261$	1013.82	−	857.271i	0.240436	−	0.203309i
$262$		0			0
$263$	−1897.73			−0.444940			−0.222470	−	0.974940i	$-0.571412\pi$
$263$	−1897.73			−0.444940			−0.222470	+	0.974940i	$0.571412\pi$
$264$		0			0
$265$	−6720.38			−1.55785
$266$		0			0
$267$	−565.146	−	262.228i	−0.129537	−	0.0601053i
$268$		0			0
$269$		−	3874.72i		−	0.878238i	−0.898429	−	0.439119i	$-0.855291\pi$
$269$		−	3874.72i		−	0.878238i	0.898429	−	0.439119i	$-0.144709\pi$
$270$		0			0
$271$		−	1292.92i		−	0.289813i	−0.989445	−	0.144906i	$-0.953712\pi$
$271$		−	1292.92i		−	0.289813i	0.989445	−	0.144906i	$-0.0462881\pi$
$272$		0			0
$273$	−1839.29	−	853.433i	−0.407762	−	0.189202i
$274$		0			0
$275$	2721.62			0.596800
$276$		0			0
$277$	−5644.74			−1.22440			−0.612202	−	0.790702i	$-0.709716\pi$
$277$	−5644.74			−1.22440			−0.612202	+	0.790702i	$0.709716\pi$
$278$		0			0
$279$	259.261	−	219.227i	0.0556328	−	0.0470422i
$280$		0			0
$281$			1146.55i			0.243407i	0.992566	+	0.121704i	$0.0388357\pi$
$281$			1146.55i			0.243407i	−0.992566	+	0.121704i	$0.961164\pi$
$282$		0			0
$283$		−	5222.40i		−	1.09696i	−0.836164	−	0.548479i	$-0.815207\pi$
$283$		−	5222.40i		−	1.09696i	0.836164	−	0.548479i	$-0.184793\pi$
$284$		0			0
$285$	−3089.57	+	6658.54i	−0.642141	+	1.38392i
$286$		0			0
$287$	−1497.69			−0.308034
$288$		0			0
$289$	−2558.59			−0.520780
$290$		0			0
$291$	−723.951	+	1560.24i	−0.145838	+	0.314305i
$292$		0			0
$293$			4783.47i			0.953765i	0.878967	+	0.476883i	$0.158233\pi$
$293$			4783.47i			0.953765i	−0.878967	+	0.476883i	$0.841767\pi$
$294$		0			0
$295$			10011.0i			1.97581i
$296$		0			0
$297$	4197.67	−	1150.40i	0.820112	−	0.224758i
$298$		0			0
$299$	−6422.97			−1.24231
$300$		0			0
$301$	1159.76			0.222085
$302$		0			0
$303$	7584.74	+	3519.32i	1.43806	+	0.667260i
$304$		0			0
$305$			8509.36i			1.59752i
$306$		0			0
$307$			9710.23i			1.80519i	0.430494	+	0.902593i	$0.358339\pi$
$307$			9710.23i			1.80519i	−0.430494	+	0.902593i	$0.641661\pi$
$308$		0			0
$309$	−6546.84	−	3037.74i	−1.20530	−	0.559258i
$310$		0			0
$311$	3463.09			0.631427			0.315713	−	0.948855i	$-0.397756\pi$
$311$	3463.09			0.631427			0.315713	+	0.948855i	$0.397756\pi$
$312$		0			0
$313$	2972.44			0.536780			0.268390	−	0.963310i	$-0.413508\pi$
$313$	2972.44			0.536780			0.268390	+	0.963310i	$0.413508\pi$
$314$		0			0
$315$	−1779.91	−	2104.94i	−0.318370	−	0.376508i
$316$		0			0
$317$			1056.65i			0.187217i	0.995609	+	0.0936083i	$0.0298401\pi$
$317$			1056.65i			0.187217i	−0.995609	+	0.0936083i	$0.970160\pi$
$318$		0			0
$319$		−	1525.52i		−	0.267752i
$320$		0			0
$321$	1098.70	−	2367.88i	0.191038	−	0.411720i
$322$		0			0
$323$	8372.06			1.44221
$324$		0			0
$325$	4890.48			0.834693
$326$		0			0
$327$	3499.02	−	7540.97i	0.591731	−	1.27528i
$328$		0			0
$329$			2982.94i			0.499863i
$330$		0			0
$331$			11409.6i			1.89465i	0.320279	+	0.947323i	$0.396223\pi$
$331$			11409.6i			1.89465i	−0.320279	+	0.947323i	$0.603777\pi$
$332$		0			0
$333$	5174.67	+	6119.63i	0.851562	+	1.00707i
$334$		0			0
$335$	−8592.94			−1.40144
$336$		0			0
$337$	−6052.69			−0.978371			−0.489185	−	0.872180i	$-0.662706\pi$
$337$	−6052.69			−0.978371			−0.489185	+	0.872180i	$0.662706\pi$
$338$		0			0
$339$	−4402.45	−	2042.74i	−0.705335	−	0.327276i
$340$		0			0
$341$		−	390.117i		−	0.0619532i
$342$		0			0
$343$		−	343.000i		−	0.0539949i
$344$		0			0
$345$	−7920.94	−	3675.32i	−1.23608	−	0.573543i
$346$		0			0
$347$	−1661.68			−0.257071			−0.128535	−	0.991705i	$-0.541028\pi$
$347$	−1661.68			−0.257071			−0.128535	+	0.991705i	$0.541028\pi$
$348$		0			0
$349$	−5890.92			−0.903535			−0.451768	−	0.892136i	$-0.649206\pi$
$349$	−5890.92			−0.903535			−0.451768	+	0.892136i	$0.649206\pi$
$350$		0			0
$351$	7542.79	−	2067.16i	1.14702	−	0.314350i
$352$		0			0
$353$		−	4847.63i		−	0.730916i	−0.930828	−	0.365458i	$-0.880912\pi$
$353$		−	4847.63i		−	0.730916i	0.930828	−	0.365458i	$-0.119088\pi$
$354$		0			0
$355$		−	11177.1i		−	1.67104i
$356$		0			0
$357$	−1323.32	+	2851.97i	−0.196183	+	0.422808i
$358$		0			0
$359$	9508.69			1.39791			0.698954	−	0.715166i	$-0.253649\pi$
$359$	9508.69			1.39791			0.698954	+	0.715166i	$0.253649\pi$
$360$		0			0
$361$	−2522.04			−0.367699
$362$		0			0
$363$	−806.046	+	1737.17i	−0.116547	+	0.251178i
$364$		0			0
$365$			13196.4i			1.89241i
$366$		0			0
$367$			3663.26i			0.521037i	0.965469	+	0.260518i	$0.0838935\pi$
$367$			3663.26i			0.521037i	−0.965469	+	0.260518i	$0.916106\pi$
$368$		0			0
$369$	4411.17	−	3730.02i	0.622321	−	0.526225i
$370$		0			0
$371$	3225.37			0.451355
$372$		0			0
$373$	6227.72			0.864502			0.432251	−	0.901753i	$-0.357720\pi$
$373$	6227.72			0.864502			0.432251	+	0.901753i	$0.357720\pi$
$374$		0			0
$375$	−2562.32	−	1188.92i	−0.352847	−	0.163721i
$376$		0			0
$377$		−	2741.22i		−	0.374482i
$378$		0			0
$379$		−	5881.91i		−	0.797186i	−0.917128	−	0.398593i	$-0.869499\pi$
$379$		−	5881.91i		−	0.797186i	0.917128	−	0.398593i	$-0.130501\pi$
$380$		0			0
$381$	−1420.43	−	659.079i	−0.190999	−	0.0886237i
$382$		0			0
$383$	−3238.56			−0.432069			−0.216035	−	0.976386i	$-0.569312\pi$
$383$	−3238.56			−0.432069			−0.216035	+	0.976386i	$0.569312\pi$
$384$		0			0
$385$	−3167.37			−0.419284
$386$		0			0
$387$	−3415.86	+	2888.40i	−0.448677	+	0.379395i
$388$		0			0
$389$		−	7962.71i		−	1.03785i	−0.854818	−	0.518927i	$-0.826332\pi$
$389$		−	7962.71i		−	1.03785i	0.854818	−	0.518927i	$-0.173668\pi$
$390$		0			0
$391$			9959.32i			1.28814i
$392$		0			0
$393$	−851.521	+	1835.17i	−0.109297	+	0.235553i
$394$		0			0
$395$	−6701.03			−0.853583
$396$		0			0
$397$	−5784.53			−0.731277			−0.365639	−	0.930757i	$-0.619149\pi$
$397$	−5784.53			−0.731277			−0.365639	+	0.930757i	$0.619149\pi$
$398$		0			0
$399$	1482.80	−	3195.69i	0.186047	−	0.400964i
$400$		0			0
$401$		−	2460.74i		−	0.306443i	−0.988192	−	0.153221i	$-0.951035\pi$
$401$		−	2460.74i		−	0.306443i	0.988192	−	0.153221i	$-0.0489647\pi$
$402$		0			0
$403$		−	701.002i		−	0.0866486i
$404$		0			0
$405$	10484.8	+	1766.84i	1.28640	+	0.216777i
$406$		0			0
$407$	9208.39			1.12148
$408$		0			0
$409$	12763.1			1.54301			0.771507	−	0.636221i	$-0.219503\pi$
$409$	12763.1			1.54301			0.771507	+	0.636221i	$0.219503\pi$
$410$		0			0
$411$	−14315.0	−	6642.16i	−1.71802	−	0.797162i
$412$		0			0
$413$		−	4804.67i		−	0.572452i
$414$		0			0
$415$			16266.1i			1.92403i
$416$		0			0
$417$	−6067.07	−	2815.12i	−0.712483	−	0.330593i
$418$		0			0
$419$	−7332.36			−0.854915			−0.427457	−	0.904035i	$-0.640591\pi$
$419$	−7332.36			−0.854915			−0.427457	+	0.904035i	$0.640591\pi$
$420$		0			0
$421$	11584.3			1.34106			0.670528	−	0.741885i	$-0.266068\pi$
$421$	11584.3			1.34106			0.670528	+	0.741885i	$0.266068\pi$
$422$		0			0
$423$	−7429.07	−	8785.71i	−0.853933	−	1.00987i
$424$		0			0
$425$		−	7583.09i		−	0.865491i
$426$		0			0
$427$		−	4083.97i		−	0.462850i
$428$		0			0
$429$	3782.33	−	8151.57i	0.425671	−	0.917393i
$430$		0			0
$431$	−973.251			−0.108770			−0.0543850	−	0.998520i	$-0.517320\pi$
$431$	−973.251			−0.108770			−0.0543850	+	0.998520i	$0.517320\pi$
$432$		0			0
$433$	−6021.08			−0.668256			−0.334128	−	0.942528i	$-0.608442\pi$
$433$	−6021.08			−0.668256			−0.334128	+	0.942528i	$0.608442\pi$
$434$		0			0
$435$	1568.56	−	3380.52i	0.172890	−	0.372606i
$436$		0			0
$437$		−	11159.6i		−	1.22159i
$438$		0			0
$439$		−	4643.72i		−	0.504858i	−0.967615	−	0.252429i	$-0.918771\pi$
$439$		−	4643.72i		−	0.504858i	0.967615	−	0.252429i	$-0.0812295\pi$
$440$		0			0
$441$	854.247	+	1010.24i	0.0922413	+	0.109086i
$442$		0			0
$443$	14381.2			1.54238			0.771189	−	0.636606i	$-0.219662\pi$
$443$	14381.2			1.54238			0.771189	+	0.636606i	$0.219662\pi$
$444$		0			0
$445$	−1748.77			−0.186291
$446$		0			0
$447$	−9669.40	−	4486.61i	−1.02315	−	0.474741i
$448$		0			0
$449$		−	10241.0i		−	1.07639i	−0.842819	−	0.538197i	$-0.819106\pi$
$449$		−	10241.0i		−	1.07639i	0.842819	−	0.538197i	$-0.180894\pi$
$450$		0			0
$451$		−	6637.62i		−	0.693023i
$452$		0			0
$453$	−2231.99	−	1035.65i	−0.231497	−	0.107415i
$454$		0			0
$455$	−5691.45			−0.586416
$456$		0			0
$457$	18144.7			1.85728			0.928638	−	0.370988i	$-0.120981\pi$
$457$	18144.7			1.85728			0.928638	+	0.370988i	$0.120981\pi$
$458$		0			0
$459$	−3205.29	−	11695.7i	−0.325948	−	1.18934i
$460$		0			0
$461$			10005.2i			1.01083i	0.862877	+	0.505413i	$0.168660\pi$
$461$			10005.2i			1.01083i	−0.862877	+	0.505413i	$0.831340\pi$
$462$		0			0
$463$			13659.6i			1.37109i	0.728031	+	0.685544i	$0.240436\pi$
$463$			13659.6i			1.37109i	−0.728031	+	0.685544i	$0.759564\pi$
$464$		0			0
$465$	401.124	−	864.491i	0.0400036	−	0.0862146i
$466$		0			0
$467$	11500.9			1.13961			0.569804	−	0.821781i	$-0.307019\pi$
$467$	11500.9			1.13961			0.569804	+	0.821781i	$0.307019\pi$
$468$		0			0
$469$	4124.08			0.406039
$470$		0			0
$471$	2591.24	−	5584.56i	0.253499	−	0.546333i
$472$		0			0
$473$			5139.95i			0.499651i
$474$		0			0
$475$			8496.99i			0.820776i
$476$		0			0
$477$	−9499.73	+	8032.83i	−0.911871	+	0.771065i
$478$		0			0
$479$	−3223.54			−0.307489			−0.153745	−	0.988111i	$-0.549133\pi$
$479$	−3223.54			−0.307489			−0.153745	+	0.988111i	$0.549133\pi$
$480$		0			0
$481$	16546.6			1.56852
$482$		0			0
$483$	3801.56	+	1763.93i	0.358131	+	0.166173i
$484$		0			0
$485$			4827.95i			0.452012i
$486$		0			0
$487$			13316.6i			1.23908i	0.784964	+	0.619542i	$0.212682\pi$
$487$			13316.6i			1.23908i	−0.784964	+	0.619542i	$0.787318\pi$
$488$		0			0
$489$	19114.3	+	8869.03i	1.76764	+	0.820187i
$490$		0			0
$491$	−4229.41			−0.388739			−0.194369	−	0.980928i	$-0.562266\pi$
$491$	−4229.41			−0.388739			−0.194369	+	0.980928i	$0.562266\pi$
$492$		0			0
$493$	−4250.47			−0.388300
$494$		0			0
$495$	9328.91	−	7888.38i	0.847077	−	0.716276i
$496$		0			0
$497$			5364.31i			0.484149i
$498$		0			0
$499$			2412.58i			0.216437i	0.994127	+	0.108219i	$0.0345146\pi$
$499$			2412.58i			0.216437i	−0.994127	+	0.108219i	$0.965485\pi$
$500$		0			0
$501$	8051.05	−	17351.4i	0.717953	−	1.54731i
$502$		0			0
$503$	6942.70			0.615427			0.307714	−	0.951479i	$-0.400436\pi$
$503$	6942.70			0.615427			0.307714	+	0.951479i	$0.400436\pi$
$504$		0			0
$505$	23470.0			2.06812
$506$		0			0
$507$	1991.52	−	4292.07i	0.174451	−	0.375972i
$508$		0			0
$509$			5335.45i			0.464616i	0.972642	+	0.232308i	$0.0746278\pi$
$509$			5335.45i			0.464616i	−0.972642	+	0.232308i	$0.925372\pi$
$510$		0			0
$511$		−	6333.44i		−	0.548288i
$512$		0			0
$513$	3591.59	+	13105.2i	0.309108	+	1.12790i
$514$		0			0
$515$	−20258.3			−1.73337
$516$		0			0
$517$	−13220.1			−1.12460
$518$		0			0
$519$	−5039.97	−	2338.55i	−0.426262	−	0.197786i
$520$		0			0
$521$			4804.38i			0.404000i	0.979386	+	0.202000i	$0.0647440\pi$
$521$			4804.38i			0.404000i	−0.979386	+	0.202000i	$0.935256\pi$
$522$		0			0
$523$			20692.5i			1.73006i	0.501722	+	0.865029i	$0.332700\pi$
$523$			20692.5i			1.73006i	−0.501722	+	0.865029i	$0.667300\pi$
$524$		0			0
$525$	−2894.53	−	1343.06i	−0.240624	−	0.111650i
$526$		0			0
$527$	−1086.96			−0.0898458
$528$		0			0
$529$	1108.36			0.0910959
$530$		0			0
$531$	11966.1	+	14151.3i	0.977938	+	1.15652i
$532$		0			0
$533$		−	11927.1i		−	0.969271i
$534$		0			0
$535$		−	7327.09i		−	0.592108i
$536$		0			0
$537$	5831.93	−	12568.8i	0.468652	−	1.01003i
$538$		0			0
$539$	1520.14			0.121479
$540$		0			0
$541$	−5176.25			−0.411357			−0.205679	−	0.978620i	$-0.565940\pi$
$541$	−5176.25			−0.411357			−0.205679	+	0.978620i	$0.565940\pi$
$542$		0			0
$543$	5792.34	−	12483.5i	0.457777	−	0.986588i
$544$		0			0
$545$		−	23334.5i		−	1.83402i
$546$		0			0
$547$		−	439.585i		−	0.0343607i	−0.999852	−	0.0171804i	$-0.994531\pi$
$547$		−	439.585i		−	0.0343607i	0.999852	−	0.0171804i	$-0.00546895\pi$
$548$		0			0
$549$	10171.2	+	12028.6i	0.790702	+	0.935095i
$550$		0			0
$551$	4762.73			0.368238
$552$		0			0
$553$	3216.08			0.247309
$554$		0			0
$555$	20405.6	+	9468.20i	1.56066	+	0.724149i
$556$		0			0
$557$			19663.7i			1.49583i	0.663795	+	0.747914i	$0.268945\pi$
$557$			19663.7i			1.49583i	−0.663795	+	0.747914i	$0.731055\pi$
$558$		0			0
$559$			9235.97i			0.698819i
$560$		0			0
$561$	−12639.7	−	5864.81i	−0.951243	−	0.441377i
$562$		0			0
$563$	3268.52			0.244675			0.122337	−	0.992489i	$-0.460961\pi$
$563$	3268.52			0.244675			0.122337	+	0.992489i	$0.460961\pi$
$564$		0			0
$565$	−13622.8			−1.01436
$566$		0			0
$567$	−5032.05	−	847.973i	−0.372710	−	0.0628069i
$568$		0			0
$569$		−	12364.5i		−	0.910980i	−0.890241	−	0.455490i	$-0.849464\pi$
$569$		−	12364.5i		−	0.910980i	0.890241	−	0.455490i	$-0.150536\pi$
$570$		0			0
$571$		−	12593.6i		−	0.922990i	−0.887143	−	0.461495i	$-0.847313\pi$
$571$		−	12593.6i		−	0.922990i	0.887143	−	0.461495i	$-0.152687\pi$
$572$		0			0
$573$	1889.99	−	4073.26i	0.137793	−	0.296968i
$574$		0			0
$575$	−10107.9			−0.733096
$576$		0			0
$577$	−13016.7			−0.939156			−0.469578	−	0.882891i	$-0.655594\pi$
$577$	−13016.7			−0.939156			−0.469578	+	0.882891i	$0.655594\pi$
$578$		0			0
$579$	−2479.43	+	5343.60i	−0.177965	+	0.383545i
$580$		0			0
$581$		−	7806.74i		−	0.557449i
$582$		0			0
$583$			14294.5i			1.01547i
$584$		0			0
$585$	16763.1	−	14174.6i	1.18473	−	1.00179i
$586$		0			0
$587$	16247.0			1.14240			0.571199	−	0.820812i	$-0.306479\pi$
$587$	16247.0			1.14240			0.571199	+	0.820812i	$0.306479\pi$
$588$		0			0
$589$	1217.96			0.0852039
$590$		0			0
$591$	7742.26	+	3592.41i	0.538873	+	0.250037i
$592$		0			0
$593$			17711.4i			1.22651i	0.789885	+	0.613256i	$0.210140\pi$
$593$			17711.4i			1.22651i	−0.789885	+	0.613256i	$0.789860\pi$
$594$		0			0
$595$			8825.05i			0.608053i
$596$		0			0
$597$	−23154.4	−	10743.7i	−1.58735	−	0.736530i
$598$		0			0
$599$	8240.46			0.562097			0.281048	−	0.959694i	$-0.409318\pi$
$599$	8240.46			0.562097			0.281048	+	0.959694i	$0.409318\pi$
$600$		0			0
$601$	5366.47			0.364231			0.182116	−	0.983277i	$-0.441706\pi$
$601$	5366.47			0.364231			0.182116	+	0.983277i	$0.441706\pi$
$602$		0			0
$603$	−12146.7	+	10271.1i	−0.820320	+	0.693650i
$604$		0			0
$605$			5375.43i			0.361227i
$606$		0			0
$607$		−	7742.72i		−	0.517739i	−0.965912	−	0.258869i	$-0.916650\pi$
$607$		−	7742.72i		−	0.517739i	0.965912	−	0.258869i	$-0.0833499\pi$
$608$		0			0
$609$	−752.814	+	1622.44i	−0.0500913	+	0.107955i
$610$		0			0
$611$	−23755.2			−1.57289
$612$		0			0
$613$	2581.09			0.170064			0.0850320	−	0.996378i	$-0.472901\pi$
$613$	2581.09			0.170064			0.0850320	+	0.996378i	$0.472901\pi$
$614$		0			0
$615$	6824.89	−	14708.8i	0.447490	−	0.964416i
$616$		0			0
$617$		−	5974.41i		−	0.389823i	−0.980821	−	0.194911i	$-0.937558\pi$
$617$		−	5974.41i		−	0.389823i	0.980821	−	0.194911i	$-0.0624419\pi$
$618$		0			0
$619$		−	6142.33i		−	0.398839i	−0.979914	−	0.199419i	$-0.936094\pi$
$619$		−	6142.33i		−	0.398839i	0.979914	−	0.199419i	$-0.0639056\pi$
$620$		0			0
$621$	−15589.9	+	4272.52i	−1.00741	+	0.276088i
$622$		0			0
$623$	839.302			0.0539742
$624$		0			0
$625$	−18894.8			−1.20927
$626$		0			0
$627$	14163.0	+	6571.63i	0.902097	+	0.418574i
$628$		0			0
$629$		−	25656.8i		−	1.62639i
$630$		0			0
$631$			4185.65i			0.264070i	0.991245	+	0.132035i	$0.0421511\pi$
$631$			4185.65i			0.264070i	−0.991245	+	0.132035i	$0.957849\pi$
$632$		0			0
$633$	−4376.77	−	2030.82i	−0.274820	−	0.127517i
$634$		0			0
$635$	−4395.32			−0.274682
$636$		0			0
$637$	2731.55			0.169902
$638$		0			0
$639$	−13359.9	−	15799.6i	−0.827088	−	0.978125i
$640$		0			0
$641$			11627.2i			0.716452i	0.933635	+	0.358226i	$0.116618\pi$
$641$			11627.2i			0.716452i	−0.933635	+	0.358226i	$0.883382\pi$
$642$		0			0
$643$		−	30093.1i		−	1.84565i	−0.385215	−	0.922827i	$-0.625873\pi$
$643$		−	30093.1i		−	1.84565i	0.385215	−	0.922827i	$-0.374127\pi$
$644$		0			0
$645$	−5284.96	+	11390.0i	−0.322628	+	0.695319i
$646$		0			0
$647$	−23676.7			−1.43868			−0.719340	−	0.694659i	$-0.755555\pi$
$647$	−23676.7			−1.43868			−0.719340	+	0.694659i	$0.755555\pi$
$648$		0			0
$649$	21293.8			1.28791
$650$		0			0
$651$	−192.515	+	414.902i	−0.0115902	+	0.0249790i
$652$		0			0
$653$			13535.0i			0.811126i	0.914067	+	0.405563i	$0.132924\pi$
$653$			13535.0i			0.811126i	−0.914067	+	0.405563i	$0.867076\pi$
$654$		0			0
$655$			5678.70i			0.338756i
$656$		0			0
$657$	15773.5	+	18654.0i	0.936658	+	1.10770i
$658$		0			0
$659$	−4587.12			−0.271152			−0.135576	−	0.990767i	$-0.543288\pi$
$659$	−4587.12			−0.271152			−0.135576	+	0.990767i	$0.543288\pi$
$660$		0			0
$661$	−22014.3			−1.29540			−0.647698	−	0.761897i	$-0.724268\pi$
$661$	−22014.3			−1.29540			−0.647698	+	0.761897i	$0.724268\pi$
$662$		0			0
$663$	−22712.2	−	10538.5i	−1.33042	−	0.617316i
$664$		0			0
$665$		−	9888.63i		−	0.576639i
$666$		0			0
$667$			5665.70i			0.328901i
$668$		0			0
$669$	981.902	+	455.603i	0.0567452	+	0.0263298i
$670$		0			0
$671$	18099.8			1.04133
$672$		0			0
$673$	5312.83			0.304301			0.152150	−	0.988357i	$-0.451380\pi$
$673$	5312.83			0.304301			0.152150	+	0.988357i	$0.451380\pi$
$674$		0			0
$675$	11870.2	−	3253.13i	0.676867	−	0.185501i
$676$		0			0
$677$			31630.1i			1.79563i	0.440372	+	0.897815i	$0.354846\pi$
$677$			31630.1i			1.79563i	−0.440372	+	0.897815i	$0.645154\pi$
$678$		0			0
$679$		−	2317.12i		−	0.130961i
$680$		0			0
$681$	−13454.6	+	28997.0i	−0.757097	+	1.63167i
$682$		0			0
$683$	16304.5			0.913435			0.456718	−	0.889612i	$-0.349025\pi$
$683$	16304.5			0.913435			0.456718	+	0.889612i	$0.349025\pi$
$684$		0			0
$685$	−44295.8			−2.47074
$686$		0			0
$687$	3266.82	−	7040.55i	0.181422	−	0.390995i
$688$		0			0
$689$			25685.8i			1.42025i
$690$		0			0
$691$		−	9225.62i		−	0.507900i	−0.967217	−	0.253950i	$-0.918270\pi$
$691$		−	9225.62i		−	0.507900i	0.967217	−	0.253950i	$-0.0817299\pi$
$692$		0			0
$693$	−4477.30	+	3785.94i	−0.245424	+	0.207527i
$694$		0			0
$695$	−18773.7			−1.02464
$696$		0			0
$697$	−18494.0			−1.00504
$698$		0			0
$699$	−4729.86	−	2194.66i	−0.255937	−	0.118755i
$700$		0			0
$701$		−	4759.97i		−	0.256464i	−0.991744	−	0.128232i	$-0.959070\pi$
$701$		−	4759.97i		−	0.256464i	0.991744	−	0.128232i	$-0.0409303\pi$
$702$		0			0
$703$			28748.9i			1.54237i
$704$		0			0
$705$	−29295.5	−	13593.1i	−1.56501	−	0.726165i
$706$		0			0
$707$	−11264.1			−0.599196
$708$		0			0
$709$	29605.9			1.56823			0.784114	−	0.620617i	$-0.213118\pi$
$709$	29605.9			1.56823			0.784114	+	0.620617i	$0.213118\pi$
$710$		0			0
$711$	−9472.38	+	8009.70i	−0.499637	+	0.422485i
$712$		0			0
$713$			1448.87i			0.0761020i
$714$		0			0
$715$		−	25224.0i		−	1.31933i
$716$		0			0
$717$	−13228.4	+	28509.4i	−0.689013	+	1.48494i
$718$		0			0
$719$	−34086.2			−1.76801			−0.884007	−	0.467474i	$-0.845164\pi$
$719$	−34086.2			−1.76801			−0.884007	+	0.467474i	$0.845164\pi$
$720$		0			0
$721$	9722.74			0.502211
$722$		0			0
$723$	−12290.4	+	26487.8i	−0.632204	+	1.36251i
$724$		0			0
$725$		−	4313.90i		−	0.220985i
$726$		0			0
$727$		−	15552.2i		−	0.793396i	−0.917949	−	0.396698i	$-0.870156\pi$
$727$		−	15552.2i		−	0.793396i	0.917949	−	0.396698i	$-0.129844\pi$
$728$		0			0
$729$	16932.9	−	10034.9i	0.860279	−	0.509823i
$730$		0			0
$731$	14321.1			0.724604
$732$		0			0
$733$	−1511.48			−0.0761636			−0.0380818	−	0.999275i	$-0.512125\pi$
$733$	−1511.48			−0.0761636			−0.0380818	+	0.999275i	$0.512125\pi$
$734$		0			0
$735$	3368.60	+	1563.03i	0.169051	+	0.0784399i
$736$		0			0
$737$			18277.5i			0.913517i
$738$		0			0
$739$		−	6749.94i		−	0.335995i	−0.985787	−	0.167998i	$-0.946270\pi$
$739$		−	6749.94i		−	0.335995i	0.985787	−	0.167998i	$-0.0537301\pi$
$740$		0			0
$741$	25449.5	+	11808.6i	1.26169	+	0.585423i
$742$		0			0
$743$	24008.4			1.18544			0.592719	−	0.805409i	$-0.298054\pi$
$743$	24008.4			1.18544			0.592719	+	0.805409i	$0.298054\pi$
$744$		0			0
$745$	−29920.7			−1.47142
$746$		0			0
$747$	19442.8	+	22993.3i	0.952309	+	1.12621i
$748$		0			0
$749$			3516.55i			0.171552i
$750$		0			0
$751$		−	35758.5i		−	1.73748i	−0.495272	−	0.868738i	$-0.664931\pi$
$751$		−	35758.5i		−	1.73748i	0.495272	−	0.868738i	$-0.335069\pi$
$752$		0			0
$753$	14002.4	−	30177.6i	0.677658	−	1.46047i
$754$		0			0
$755$	−6906.61			−0.332924
$756$		0			0
$757$	−12640.7			−0.606916			−0.303458	−	0.952845i	$-0.598141\pi$
$757$	−12640.7			−0.606916			−0.303458	+	0.952845i	$0.598141\pi$
$758$		0			0
$759$	−7817.55	+	16848.2i	−0.373859	+	0.805730i
$760$		0			0
$761$		−	28346.1i		−	1.35026i	−0.737699	−	0.675129i	$-0.764088\pi$
$761$		−	28346.1i		−	1.35026i	0.737699	−	0.675129i	$-0.235912\pi$
$762$		0			0
$763$			11199.1i			0.531371i
$764$		0			0
$765$	−21978.9	−	25992.6i	−1.03876	−	1.22845i
$766$		0			0
$767$	38262.9			1.80130
$768$		0			0
$769$	−15226.0			−0.713999			−0.356999	−	0.934105i	$-0.616200\pi$
$769$	−15226.0			−0.713999			−0.356999	+	0.934105i	$0.616200\pi$
$770$		0			0
$771$	−7584.91	−	3519.40i	−0.354298	−	0.164395i
$772$		0			0
$773$		−	20084.4i		−	0.934522i	−0.884119	−	0.467261i	$-0.845241\pi$
$773$		−	20084.4i		−	0.934522i	0.884119	−	0.467261i	$-0.154759\pi$
$774$		0			0
$775$		−	1103.18i		−	0.0511321i
$776$		0			0
$777$	−9793.42	−	4544.15i	−0.452171	−	0.209808i
$778$		0			0
$779$	20722.8			0.953110
$780$		0			0
$781$	−23774.1			−1.08925
$782$		0			0
$783$	−1823.44	−	6653.50i	−0.0832242	−	0.303674i
$784$		0			0
$785$		−	17280.7i		−	0.785699i
$786$		0			0
$787$		−	18800.0i		−	0.851522i	−0.904836	−	0.425761i	$-0.860006\pi$
$787$		−	18800.0i		−	0.851522i	0.904836	−	0.425761i	$-0.139994\pi$
$788$		0			0
$789$	−4150.44	+	8944.91i	−0.187275	+	0.403609i
$790$		0			0
$791$	6538.11			0.293892
$792$		0			0
$793$	32523.5			1.45642
$794$		0			0
$795$	−14697.8	+	31676.3i	−0.655696	+	1.41314i
$796$		0

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:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(2.18705 - 4.71347i) q^{3} -14.5852i q^{5} +7.00000i q^{7} +(-17.4336 - 20.6172i) q^{9} +O(q^{10})\)	\(q+(2.18705 - 4.71347i) q^{3} -14.5852i q^{5} +7.00000i q^{7} +(-17.4336 - 20.6172i) q^{9} -31.0233 q^{11} -55.7458 q^{13} +(-68.7469 - 31.8986i) q^{15} +86.4384i q^{17} -96.8558i q^{19} +(32.9943 + 15.3094i) q^{21} +115.219 q^{23} -87.7283 q^{25} +(-135.307 + 37.0818i) q^{27} +49.1735i q^{29} +12.5750i q^{31} +(-67.8496 + 146.228i) q^{33} +102.096 q^{35} -296.822 q^{37} +(-121.919 + 262.756i) q^{39} +213.956i q^{41} -165.680i q^{43} +(-300.706 + 254.273i) q^{45} +426.135 q^{47} -49.0000 q^{49} +(407.425 + 189.045i) q^{51} -460.767i q^{53} +452.482i q^{55} +(-456.527 - 211.829i) q^{57} -686.382 q^{59} -583.424 q^{61} +(144.320 - 122.035i) q^{63} +813.064i q^{65} -589.155i q^{67} +(251.989 - 543.080i) q^{69} +766.330 q^{71} -904.778 q^{73} +(-191.866 + 413.505i) q^{75} -217.163i q^{77} -459.440i q^{79} +(-121.139 + 718.865i) q^{81} -1115.25 q^{83} +1260.72 q^{85} +(231.778 + 107.545i) q^{87} -119.900i q^{89} -390.221i q^{91} +(59.2717 + 27.5021i) q^{93} -1412.66 q^{95} -331.017 q^{97} +(540.848 + 639.614i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 12 q + 76 q^{9}+O(q^{10}) \) 12 * q + 76 * q^9	\( 12 q + 76 q^{9} - 96 q^{13} + 112 q^{21} - 1068 q^{25} - 832 q^{33} - 720 q^{37} + 392 q^{45} - 588 q^{49} - 2336 q^{57} + 432 q^{61} - 424 q^{69} + 1656 q^{73} - 868 q^{81} - 1464 q^{85} + 696 q^{93} - 6264 q^{97}+O(q^{100}) \) 12 * q + 76 * q^9 - 96 * q^13 + 112 * q^21 - 1068 * q^25 - 832 * q^33 - 720 * q^37 + 392 * q^45 - 588 * q^49 - 2336 * q^57 + 432 * q^61 - 424 * q^69 + 1656 * q^73 - 868 * q^81 - 1464 * q^85 + 696 * q^93 - 6264 * q^97

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