LMFDB - Embedded newform 338.4.e.i.23.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [338,4,Mod(23,338)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(338, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([5]))

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

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

chi := DirichletCharacter("338.23");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 338 = 2 \cdot 13^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	338.e (of order $6$, degree $2$, not minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$19.9426455819$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			23.9
Character	$\chi$	$=$	338.23
Dual form			338.4.e.i.147.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(1.73205 - 1.00000i) q^{2} +(-1.67908 - 2.90825i) q^{3} +(2.00000 - 3.46410i) q^{4} +6.80407i q^{5} +(-5.81649 - 3.35815i) q^{6} +(13.4563 + 7.76902i) q^{7} -8.00000i q^{8} +(7.86140 - 13.6163i) q^{9} +(6.80407 + 11.7850i) q^{10} +(-16.9750 + 9.80052i) q^{11} -13.4326 q^{12} +31.0761 q^{14} +(19.7879 - 11.4246i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(62.9859 - 109.095i) q^{17} -31.4456i q^{18} +(84.1839 + 48.6036i) q^{19} +(23.5700 + 13.6081i) q^{20} -52.1791i q^{21} +(-19.6010 + 33.9500i) q^{22} +(64.9251 + 112.454i) q^{23} +(-23.2660 + 13.4326i) q^{24} +78.7047 q^{25} -143.470 q^{27} +(53.8253 - 31.0761i) q^{28} +(-73.9704 - 128.121i) q^{29} +(22.8491 - 39.5758i) q^{30} -172.602i q^{31} +(-27.7128 - 16.0000i) q^{32} +(57.0047 + 32.9117i) q^{33} -251.944i q^{34} +(-52.8609 + 91.5578i) q^{35} +(-31.4456 - 54.4654i) q^{36} +(191.625 - 110.635i) q^{37} +194.414 q^{38} +54.4325 q^{40} +(-24.3297 + 14.0468i) q^{41} +(-52.1791 - 90.3769i) q^{42} +(180.884 - 313.301i) q^{43} +78.4042i q^{44} +(92.6465 + 53.4895i) q^{45} +(224.907 + 129.850i) q^{46} -456.486i q^{47} +(-26.8652 + 46.5319i) q^{48} +(-50.7848 - 87.9618i) q^{49} +(136.321 - 78.7047i) q^{50} -423.033 q^{51} -643.067 q^{53} +(-248.497 + 143.470i) q^{54} +(-66.6834 - 115.499i) q^{55} +(62.1521 - 107.651i) q^{56} -326.437i q^{57} +(-256.241 - 147.941i) q^{58} +(269.267 + 155.461i) q^{59} -91.3964i q^{60} +(-405.728 + 702.742i) q^{61} +(-172.602 - 298.956i) q^{62} +(211.571 - 122.151i) q^{63} -64.0000 q^{64} +131.647 q^{66} +(6.06611 - 3.50227i) q^{67} +(-251.944 - 436.379i) q^{68} +(218.028 - 377.636i) q^{69} +211.444i q^{70} +(736.799 + 425.391i) q^{71} +(-108.931 - 62.8912i) q^{72} +1127.56i q^{73} +(221.269 - 383.249i) q^{74} +(-132.151 - 228.893i) q^{75} +(336.735 - 194.414i) q^{76} -304.562 q^{77} +278.080 q^{79} +(94.2799 - 54.4325i) q^{80} +(28.6389 + 49.6041i) q^{81} +(-28.0935 + 48.6594i) q^{82} -417.276i q^{83} +(-180.754 - 104.358i) q^{84} +(742.288 + 428.560i) q^{85} -723.537i q^{86} +(-248.404 + 430.249i) q^{87} +(78.4042 + 135.800i) q^{88} +(280.827 - 162.136i) q^{89} +213.958 q^{90} +519.401 q^{92} +(-501.970 + 289.812i) q^{93} +(-456.486 - 790.657i) q^{94} +(-330.702 + 572.793i) q^{95} +107.461i q^{96} +(71.0986 + 41.0488i) q^{97} +(-175.924 - 101.570i) q^{98} +308.183i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 18 q^{3} + 48 q^{4} - 226 q^{9} + 72 q^{10} - 144 q^{12} + 200 q^{14} - 192 q^{16} + 198 q^{17} - 148 q^{22} + 534 q^{23} - 1472 q^{25} + 2676 q^{27} + 238 q^{29} + 472 q^{30} - 1228 q^{35} + 904 q^{36}+ \cdots - 8186 q^{95}+O(q^{100}) $ 24 * q - 18 * q^3 + 48 * q^4 - 226 * q^9 + 72 * q^10 - 144 * q^12 + 200 * q^14 - 192 * q^16 + 198 * q^17 - 148 * q^22 + 534 * q^23 - 1472 * q^25 + 2676 * q^27 + 238 * q^29 + 472 * q^30 - 1228 * q^35 + 904 * q^36 + 648 * q^38 + 576 * q^40 + 104 * q^42 + 856 * q^43 - 288 * q^48 + 1798 * q^49 - 1156 * q^51 + 356 * q^53 - 2252 * q^55 + 400 * q^56 - 3408 * q^61 - 2500 * q^62 - 1536 * q^64 + 6096 * q^66 - 792 * q^68 + 2336 * q^69 - 1096 * q^74 + 3596 * q^75 - 11160 * q^77 - 3500 * q^79 - 6676 * q^81 + 4560 * q^82 - 3204 * q^87 + 592 * q^88 + 9720 * q^90 + 4272 * q^92 + 3944 * q^94 - 8186 * q^95

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/338\mathbb{Z}\right)^\times$.

$n$	$171$
$\chi(n)$	$e\left(\frac{5}{6}\right)$

Coefficient data

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

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

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

$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$2$	1.73205	−	1.00000i	0.612372	−	0.353553i
$3$	−1.67908	−	2.90825i	−0.323139	−	0.559692i	0.657995	−	0.753022i	$-0.271405\pi$
$3$	−1.67908	−	2.90825i	−0.323139	−	0.559692i	−0.981134	+	0.193330i	$0.938071\pi$
$4$	2.00000	−	3.46410i	0.250000	−	0.433013i
$5$			6.80407i			0.608574i	0.952580	+	0.304287i	$0.0984182\pi$
$5$			6.80407i			0.608574i	−0.952580	+	0.304287i	$0.901582\pi$
$6$	−5.81649	−	3.35815i	−0.395762	−	0.228493i
$7$	13.4563	+	7.76902i	0.726574	+	0.419487i	0.817167	−	0.576400i	$-0.195543\pi$
$7$	13.4563	+	7.76902i	0.726574	+	0.419487i	−0.0905938	+	0.995888i	$0.528876\pi$
$8$		−	8.00000i		−	0.353553i
$9$	7.86140	−	13.6163i	0.291163	−	0.504309i
$10$	6.80407	+	11.7850i	0.215163	+	0.372674i
$11$	−16.9750	+	9.80052i	−0.465287	+	0.268633i	−0.714265	−	0.699876i	$-0.753239\pi$
$11$	−16.9750	+	9.80052i	−0.465287	+	0.268633i	0.248978	+	0.968509i	$0.419905\pi$
$12$	−13.4326			−0.323139
$13$		0			0
$13$		0			0
$14$	31.0761			0.593245
$15$	19.7879	−	11.4246i	0.340614	−	0.196654i
$16$	−8.00000	−	13.8564i	−0.125000	−	0.216506i
$17$	62.9859	−	109.095i	0.898607	−	1.55643i	0.0693317	−	0.997594i	$-0.477913\pi$
$17$	62.9859	−	109.095i	0.898607	−	1.55643i	0.829276	−	0.558840i	$-0.188753\pi$
$18$		−	31.4456i		−	0.411767i
$19$	84.1839	+	48.6036i	1.01648	+	0.586865i	0.913082	−	0.407776i	$-0.133695\pi$
$19$	84.1839	+	48.6036i	1.01648	+	0.586865i	0.103397	+	0.994640i	$0.467029\pi$
$20$	23.5700	+	13.6081i	0.263520	+	0.152144i
$21$		−	52.1791i		−	0.542210i
$22$	−19.6010	+	33.9500i	−0.189953	+	0.329007i
$23$	64.9251	+	112.454i	0.588600	+	1.01949i	0.994416	+	0.105531i	$0.0336542\pi$
$23$	64.9251	+	112.454i	0.588600	+	1.01949i	−0.405816	+	0.913955i	$0.633012\pi$
$24$	−23.2660	+	13.4326i	−0.197881	+	0.114247i
$25$	78.7047			0.629637
$26$		0			0
$27$	−143.470			−1.02262
$28$	53.8253	−	31.0761i	0.363287	−	0.209744i
$29$	−73.9704	−	128.121i	−0.473654	−	0.820393i	0.525891	−	0.850552i	$-0.323732\pi$
$29$	−73.9704	−	128.121i	−0.473654	−	0.820393i	−0.999545	+	0.0301591i	$0.990399\pi$
$30$	22.8491	−	39.5758i	0.139055	−	0.240851i
$31$		−	172.602i		−	1.00001i	−0.866023	−	0.500004i	$-0.833332\pi$
$31$		−	172.602i		−	1.00001i	0.866023	−	0.500004i	$-0.166668\pi$
$32$	−27.7128	−	16.0000i	−0.153093	−	0.0883883i
$33$	57.0047	+	32.9117i	0.300704	+	0.173612i
$34$		−	251.944i		−	1.27082i
$35$	−52.8609	+	91.5578i	−0.255289	+	0.442174i
$36$	−31.4456	−	54.4654i	−0.145581	−	0.252155i
$37$	191.625	−	110.635i	0.851430	−	0.491573i	−0.00970317	−	0.999953i	$-0.503089\pi$
$37$	191.625	−	110.635i	0.851430	−	0.491573i	0.861133	+	0.508380i	$0.169755\pi$
$38$	194.414			0.829952
$39$		0			0
$40$	54.4325			0.215163
$41$	−24.3297	+	14.0468i	−0.0926746	+	0.0535057i	−0.545621	−	0.838032i	$-0.683706\pi$
$41$	−24.3297	+	14.0468i	−0.0926746	+	0.0535057i	0.452946	+	0.891538i	$0.350373\pi$
$42$	−52.1791	−	90.3769i	−0.191700	−	0.332035i
$43$	180.884	−	313.301i	0.641502	−	1.11111i	−0.343596	−	0.939118i	$-0.611645\pi$
$43$	180.884	−	313.301i	0.641502	−	1.11111i	0.985098	−	0.171996i	$-0.0550217\pi$
$44$			78.4042i			0.268633i
$45$	92.6465	+	53.4895i	0.306910	+	0.177194i
$46$	224.907	+	129.850i	0.720885	+	0.416203i
$47$		−	456.486i		−	1.41671i	−0.705857	−	0.708354i	$-0.749438\pi$
$47$		−	456.486i		−	1.41671i	0.705857	−	0.708354i	$-0.250562\pi$
$48$	−26.8652	+	46.5319i	−0.0807846	+	0.139923i
$49$	−50.7848	−	87.9618i	−0.148061	−	0.256448i
$50$	136.321	−	78.7047i	0.385573	−	0.222610i
$51$	−423.033			−1.16150
$52$		0			0
$53$	−643.067			−1.66664			−0.833321	−	0.552789i	$-0.813563\pi$
$53$	−643.067			−1.66664			−0.833321	+	0.552789i	$0.813563\pi$
$54$	−248.497	+	143.470i	−0.626225	+	0.361551i
$55$	−66.6834	−	115.499i	−0.163483	−	0.283162i
$56$	62.1521	−	107.651i	0.148311	−	0.256883i
$57$		−	326.437i		−	0.758554i
$58$	−256.241	−	147.941i	−0.580105	−	0.334924i
$59$	269.267	+	155.461i	0.594163	+	0.343040i	0.766742	−	0.641956i	$-0.221877\pi$
$59$	269.267	+	155.461i	0.594163	+	0.343040i	−0.172579	+	0.984996i	$0.555210\pi$
$60$		−	91.3964i		−	0.196654i
$61$	−405.728	+	702.742i	−0.851610	+	1.47503i	0.0281456	+	0.999604i	$0.491040\pi$
$61$	−405.728	+	702.742i	−0.851610	+	1.47503i	−0.879755	+	0.475427i	$0.842294\pi$
$62$	−172.602	−	298.956i	−0.353556	−	0.612378i
$63$	211.571	−	122.151i	0.423103	−	0.244278i
$64$	−64.0000			−0.125000
$65$		0			0
$66$	131.647			0.245524
$67$	6.06611	−	3.50227i	0.0110611	−	0.00638612i	−0.494459	−	0.869201i	$-0.664634\pi$
$67$	6.06611	−	3.50227i	0.0110611	−	0.00638612i	0.505520	+	0.862815i	$0.331301\pi$
$68$	−251.944	−	436.379i	−0.449304	−	0.778217i
$69$	218.028	−	377.636i	0.380399	−	0.658870i
$70$			211.444i			0.361034i
$71$	736.799	+	425.391i	1.23158	+	0.711051i	0.967358	−	0.253412i	$-0.0815528\pi$
$71$	736.799	+	425.391i	1.23158	+	0.711051i	0.264218	+	0.964463i	$0.414886\pi$
$72$	−108.931	−	62.8912i	−0.178300	−	0.102942i
$73$			1127.56i			1.80782i	0.427728	+	0.903908i	$0.359314\pi$
$73$			1127.56i			1.80782i	−0.427728	+	0.903908i	$0.640686\pi$
$74$	221.269	−	383.249i	0.347595	−	0.602052i
$75$	−132.151	−	228.893i	−0.203460	−	0.352403i
$76$	336.735	−	194.414i	0.508240	−	0.293432i
$77$	−304.562			−0.450754
$78$		0			0
$79$	278.080			0.396031			0.198015	−	0.980199i	$-0.436550\pi$
$79$	278.080			0.396031			0.198015	+	0.980199i	$0.436550\pi$
$80$	94.2799	−	54.4325i	0.131760	−	0.0760718i
$81$	28.6389	+	49.6041i	0.0392852	+	0.0680440i
$82$	−28.0935	+	48.6594i	−0.0378343	+	0.0655309i
$83$		−	417.276i		−	0.551832i	−0.961182	−	0.275916i	$-0.911019\pi$
$83$		−	417.276i		−	0.551832i	0.961182	−	0.275916i	$-0.0889811\pi$
$84$	−180.754	−	104.358i	−0.234784	−	0.135553i
$85$	742.288	+	428.560i	0.947205	+	0.546869i
$86$		−	723.537i		−	0.907221i
$87$	−248.404	+	430.249i	−0.306112	+	0.530201i
$88$	78.4042	+	135.800i	0.0949763	+	0.164504i
$89$	280.827	−	162.136i	0.334467	−	0.193105i	−0.323355	−	0.946278i	$-0.604811\pi$
$89$	280.827	−	162.136i	0.334467	−	0.193105i	0.657823	+	0.753173i	$0.271478\pi$
$90$	213.958			0.250591
$91$		0			0
$92$	519.401			0.588600
$93$	−501.970	+	289.812i	−0.559697	+	0.323141i
$94$	−456.486	−	790.657i	−0.500882	−	0.867553i
$95$	−330.702	+	572.793i	−0.357151	+	0.618603i
$96$			107.461i			0.114247i
$97$	71.0986	+	41.0488i	0.0744224	+	0.0429678i	0.536749	−	0.843742i	$-0.319652\pi$
$97$	71.0986	+	41.0488i	0.0744224	+	0.0429678i	−0.462327	+	0.886709i	$0.652985\pi$
$98$	−175.924	−	101.570i	−0.181336	−	0.104695i
$99$			308.183i			0.312865i
$100$	157.409	−	272.641i	0.157409	−	0.272641i
$101$	358.261	+	620.526i	0.352953	+	0.611333i	0.986765	−	0.162154i	$-0.0518442\pi$
$101$	358.261	+	620.526i	0.352953	+	0.611333i	−0.633812	+	0.773487i	$0.718511\pi$
$102$	−732.714	+	423.033i	−0.711270	+	0.410652i
$103$	935.493			0.894921			0.447460	−	0.894304i	$-0.352329\pi$
$103$	935.493			0.894921			0.447460	+	0.894304i	$0.352329\pi$
$104$		0			0
$105$	355.030			0.329975
$106$	−1113.82	+	643.067i	−1.02061	+	0.589247i
$107$	599.382	+	1038.16i	0.541536	+	0.937969i	0.998816	+	0.0486457i	$0.0154905\pi$
$107$	599.382	+	1038.16i	0.541536	+	0.937969i	−0.457280	+	0.889323i	$0.651176\pi$
$108$	−286.939	+	496.994i	−0.255655	+	0.442808i
$109$			119.517i			0.105024i	0.998620	+	0.0525120i	$0.0167228\pi$
$109$			119.517i			0.105024i	−0.998620	+	0.0525120i	$0.983277\pi$
$110$	−230.998	−	133.367i	−0.200225	−	0.115600i
$111$	−643.505	−	371.528i	−0.550260	−	0.317693i
$112$		−	248.609i		−	0.209744i
$113$	303.346	−	525.410i	0.252534	−	0.437402i	−0.711689	−	0.702495i	$-0.752069\pi$
$113$	303.346	−	525.410i	0.252534	−	0.437402i	0.964223	+	0.265093i	$0.0854026\pi$
$114$	−326.437	−	565.405i	−0.268189	−	0.464518i
$115$	−765.141	+	441.754i	−0.620433	+	0.358207i
$116$	−591.764			−0.473654
$117$		0			0
$118$	621.846			0.485132
$119$	1695.12	−	978.677i	1.30581	−	0.753909i
$120$	−91.3964	−	158.303i	−0.0695276	−	0.120425i
$121$	−473.400	+	819.952i	−0.355672	+	0.616042i
$122$			1622.91i			1.20436i
$123$	81.7029	+	47.1712i	0.0598935	+	0.0345795i
$124$	−597.911	−	345.204i	−0.433016	−	0.250002i
$125$			1386.02i			0.991755i
$126$	244.301	−	423.142i	0.172731	−	0.299179i
$127$	928.966	+	1609.02i	0.649074	+	1.12423i	0.983344	+	0.181752i	$0.0581769\pi$
$127$	928.966	+	1609.02i	0.649074	+	1.12423i	−0.334270	+	0.942477i	$0.608490\pi$
$128$	−110.851	+	64.0000i	−0.0765466	+	0.0441942i
$129$	−1214.87			−0.829176
$130$		0			0
$131$	−1867.72			−1.24568			−0.622838	−	0.782351i	$-0.714020\pi$
$131$	−1867.72			−1.24568			−0.622838	+	0.782351i	$0.714020\pi$
$132$	228.019	−	131.647i	0.150352	−	0.0868058i
$133$	755.204	+	1308.05i	0.492365	+	0.852801i
$134$	7.00454	−	12.1322i	0.00451567	−	0.00782137i
$135$		−	976.178i		−	0.622341i
$136$	−872.758	−	503.887i	−0.550282	−	0.317706i
$137$	−456.522	−	263.573i	−0.284695	−	0.164369i	0.350852	−	0.936431i	$-0.385892\pi$
$137$	−456.522	−	263.573i	−0.284695	−	0.164369i	−0.635547	+	0.772062i	$0.719225\pi$
$138$		−	872.113i		−	0.537965i
$139$	747.477	−	1294.67i	0.456116	−	0.790017i	−0.542635	−	0.839969i	$-0.682573\pi$
$139$	747.477	−	1294.67i	0.456116	−	0.790017i	0.998752	+	0.0499516i	$0.0159067\pi$
$140$	211.444	+	366.231i	0.127645	+	0.221087i
$141$	−1327.57	+	766.475i	−0.792921	+	0.457793i
$142$	1701.56			1.00558
$143$		0			0
$144$	−251.565			−0.145581
$145$	871.741	−	503.300i	0.499270	−	0.288254i
$146$	1127.56	+	1952.99i	0.639159	+	1.10706i
$147$	−170.543	+	295.389i	−0.0956881	+	0.165737i
$148$		−	885.077i		−	0.491573i
$149$	−1505.71	−	869.319i	−0.827867	−	0.477969i	0.0252549	−	0.999681i	$-0.491960\pi$
$149$	−1505.71	−	869.319i	−0.827867	−	0.477969i	−0.853122	+	0.521712i	$0.825294\pi$
$150$	−457.785	−	264.302i	−0.249187	−	0.143868i
$151$			1923.77i			1.03678i	0.855144	+	0.518391i	$0.173469\pi$
$151$			1923.77i			1.03678i	−0.855144	+	0.518391i	$0.826531\pi$
$152$	388.829	−	673.471i	0.207488	−	0.359380i
$153$	−990.315	−	1715.28i	−0.523282	−	0.906352i
$154$	−527.516	+	304.562i	−0.276029	+	0.159365i
$155$	1174.40			0.608579
$156$		0			0
$157$	275.052			0.139819			0.0699093	−	0.997553i	$-0.477729\pi$
$157$	275.052			0.139819			0.0699093	+	0.997553i	$0.477729\pi$
$158$	481.649	−	278.080i	0.242518	−	0.140018i
$159$	1079.76	+	1870.20i	0.538556	+	0.932807i
$160$	108.865	−	188.560i	0.0537909	−	0.0931685i
$161$			2017.62i			0.987642i
$162$	99.2082	+	57.2779i	0.0481144	+	0.0277788i
$163$	−3353.63	−	1936.22i	−1.61151	−	0.930407i	−0.989020	−	0.147780i	$-0.952787\pi$
$163$	−3353.63	−	1936.22i	−1.61151	−	0.930407i	−0.622491	−	0.782627i	$-0.713879\pi$
$164$			112.374i			0.0535057i
$165$	−223.933	+	387.864i	−0.105656	+	0.183001i
$166$	−417.276	−	722.744i	−0.195102	−	0.337926i
$167$	616.965	−	356.205i	0.285881	−	0.165054i	−0.350202	−	0.936674i	$-0.613887\pi$
$167$	616.965	−	356.205i	0.285881	−	0.165054i	0.636083	+	0.771621i	$0.280554\pi$
$168$	−417.433			−0.191700
$169$		0			0
$170$	1714.24			0.773390
$171$	1323.61	−	764.184i	0.591922	−	0.341746i
$172$	−723.537	−	1253.20i	−0.320751	−	0.555557i
$173$	−405.847	+	702.947i	−0.178358	+	0.308925i	−0.941318	−	0.337520i	$-0.890412\pi$
$173$	−405.847	+	702.947i	−0.178358	+	0.308925i	0.762960	+	0.646446i	$0.223745\pi$
$174$			993.617i			0.432907i
$175$	1059.08	+	611.458i	0.457478	+	0.264125i
$176$	271.600	+	156.808i	0.116322	+	0.0671584i
$177$		−	1044.13i		−	0.443398i
$178$	324.271	−	561.654i	0.136546	−	0.236504i
$179$	431.918	+	748.105i	0.180353	+	0.312380i	0.942001	−	0.335611i	$-0.108943\pi$
$179$	431.918	+	748.105i	0.180353	+	0.312380i	−0.761648	+	0.647991i	$0.775609\pi$
$180$	370.586	−	213.958i	0.153455	−	0.0885971i
$181$	−1426.89			−0.585965			−0.292982	−	0.956118i	$-0.594648\pi$
$181$	−1426.89			−0.585965			−0.292982	+	0.956118i	$0.594648\pi$
$182$		0			0
$183$	2725.00			1.10075
$184$	899.628	−	519.401i	0.360443	−	0.208102i
$185$	752.765	+	1303.83i	0.299159	+	0.518158i
$186$	−579.625	+	1003.94i	−0.228495	+	0.395766i
$187$			2469.18i			0.965584i
$188$	−1581.31	−	912.972i	−0.613453	−	0.354177i
$189$	−1930.58	−	1114.62i	−0.743009	−	0.428977i
$190$			1322.81i			0.505087i
$191$	392.215	−	679.337i	0.148585	−	0.257357i	−0.782120	−	0.623128i	$-0.785862\pi$
$191$	392.215	−	679.337i	0.148585	−	0.257357i	0.930705	+	0.365772i	$0.119195\pi$
$192$	107.461	+	186.128i	0.0403923	+	0.0699615i
$193$	−2609.25	+	1506.45i	−0.973149	+	0.561848i	−0.900195	−	0.435487i	$-0.856576\pi$
$193$	−2609.25	+	1506.45i	−0.973149	+	0.561848i	−0.0729543	+	0.997335i	$0.523243\pi$
$194$	164.195			0.0607656
$195$		0			0
$196$	−406.278			−0.148061
$197$	−2363.64	+	1364.65i	−0.854836	+	0.493540i	−0.862280	−	0.506433i	$-0.830964\pi$
$197$	−2363.64	+	1364.65i	−0.854836	+	0.493540i	0.00744371	+	0.999972i	$0.497631\pi$
$198$	308.183	+	533.789i	0.110614	+	0.191590i
$199$	−480.802	+	832.774i	−0.171272	+	0.296652i	−0.938865	−	0.344286i	$-0.888121\pi$
$199$	−480.802	+	832.774i	−0.171272	+	0.296652i	0.767593	+	0.640938i	$0.221454\pi$
$200$		−	629.637i		−	0.222610i
$201$	−20.3709	−	11.7612i	−0.00714853	−	0.00412720i
$202$	1241.05	+	716.521i	0.432277	+	0.249576i
$203$		−	2298.71i		−	0.794768i
$204$	−846.065	+	1465.43i	−0.290375	+	0.502944i
$205$	−95.5751	−	165.541i	−0.0325622	−	0.0563994i
$206$	1620.32	−	935.493i	0.548025	−	0.316402i
$207$	2041.61			0.685515
$208$		0			0
$209$	−1905.36			−0.630606
$210$	614.930	−	355.030i	0.202068	−	0.116664i
$211$	−1888.57	−	3271.10i	−0.616183	−	1.06726i	−0.990176	−	0.139829i	$-0.955345\pi$
$211$	−1888.57	−	3271.10i	−0.616183	−	1.06726i	0.373992	−	0.927432i	$-0.377989\pi$
$212$	−1286.13	+	2227.65i	−0.416661	+	0.721677i
$213$		−	2857.06i		−	0.919072i
$214$	2076.32	+	1198.76i	0.663244	+	0.382924i
$215$	2131.72	+	1230.75i	0.676195	+	0.390401i
$216$			1147.76i			0.361551i
$217$	1340.95	−	2322.59i	0.419491	−	0.726580i
$218$	119.517	+	207.009i	0.0371316	+	0.0643139i
$219$	3279.21	−	1893.25i	1.01182	−	0.584175i
$220$	−533.467			−0.163483
$221$		0			0
$222$	−1486.11			−0.449285
$223$	−3781.34	+	2183.15i	−1.13550	+	0.655582i	−0.945313	−	0.326165i	$-0.894243\pi$
$223$	−3781.34	+	2183.15i	−1.13550	+	0.655582i	−0.190189	+	0.981747i	$0.560910\pi$
$224$	−248.609	−	430.603i	−0.0741556	−	0.128441i
$225$	618.729	−	1071.67i	0.183327	−	0.317532i
$226$		−	1213.38i		−	0.357137i
$227$	1582.22	+	913.495i	0.462624	+	0.267096i	0.713147	−	0.701015i	$-0.247269\pi$
$227$	1582.22	+	913.495i	0.462624	+	0.267096i	−0.250523	+	0.968111i	$0.580603\pi$
$228$	−1130.81	−	652.873i	−0.328464	−	0.189639i
$229$			4376.52i			1.26292i	0.775409	+	0.631459i	$0.217544\pi$
$229$			4376.52i			1.26292i	−0.775409	+	0.631459i	$0.782456\pi$
$230$	−883.509	+	1530.28i	−0.253291	+	0.438712i
$231$	511.382	+	885.740i	0.145656	+	0.252283i
$232$	−1024.96	+	591.764i	−0.290053	+	0.167462i
$233$	−4723.89			−1.32821			−0.664104	−	0.747641i	$-0.731187\pi$
$233$	−4723.89			−1.32821			−0.664104	+	0.747641i	$0.731187\pi$
$234$		0			0
$235$	3105.96			0.862172
$236$	1077.07	−	621.846i	0.297081	−	0.171520i
$237$	−466.918	−	808.725i	−0.127973	−	0.221655i
$238$	1957.35	−	3390.24i	0.533094	−	0.923346i
$239$			2312.19i			0.625788i	0.949788	+	0.312894i	$0.101298\pi$
$239$			2312.19i			0.625788i	−0.949788	+	0.312894i	$0.898702\pi$
$240$	−316.606	−	182.793i	−0.0851536	−	0.0491634i
$241$	6190.00	+	3573.80i	1.65449	+	0.955223i	0.975191	+	0.221364i	$0.0710510\pi$
$241$	6190.00	+	3573.80i	1.65449	+	0.955223i	0.679303	+	0.733858i	$0.262282\pi$
$242$			1893.60i			0.502996i
$243$	−1840.67	+	3188.13i	−0.485921	+	0.841640i
$244$	1622.91	+	2810.97i	0.425805	+	0.737515i
$245$	598.498	−	345.543i	0.156068	−	0.0901058i
$246$	188.685			0.0489028
$247$		0			0
$248$	−1380.82			−0.353556
$249$	−1213.54	+	700.639i	−0.308856	+	0.178318i
$250$	1386.02	+	2400.66i	0.350638	+	0.607324i
$251$	−1369.27	+	2371.64i	−0.344332	+	0.596401i	−0.985232	−	0.171224i	$-0.945228\pi$
$251$	−1369.27	+	2371.64i	−0.344332	+	0.596401i	0.640900	+	0.767624i	$0.278561\pi$
$252$		−	977.206i		−	0.244278i
$253$	−2204.21	−	1272.60i	−0.547736	−	0.316236i
$254$	3218.03	+	1857.93i	0.794950	+	0.458965i
$255$		−	2878.34i		−	0.706858i
$256$	−128.000	+	221.703i	−0.0312500	+	0.0541266i
$257$	−3028.18	−	5244.96i	−0.734991	−	1.27304i	−0.954727	−	0.297483i	$-0.903853\pi$
$257$	−3028.18	−	5244.96i	−0.734991	−	1.27304i	0.219736	−	0.975559i	$-0.429481\pi$
$258$	−2104.22	+	1214.87i	−0.507764	+	0.293158i
$259$	3438.09			0.824835
$260$		0			0
$261$	−2326.05			−0.551642
$262$	−3234.99	+	1867.72i	−0.762817	+	0.440413i
$263$	−2667.09	−	4619.54i	−0.625323	−	1.08309i	−0.988478	−	0.151362i	$-0.951634\pi$
$263$	−2667.09	−	4619.54i	−0.625323	−	1.08309i	0.363156	−	0.931728i	$-0.381699\pi$
$264$	263.293	−	456.037i	0.0613810	−	0.106315i
$265$		−	4375.47i		−	1.01428i
$266$	2616.10	+	1510.41i	0.603021	+	0.348154i
$267$	−943.060	−	544.476i	−0.216159	−	0.124799i
$268$		−	28.0181i		−	0.00638612i
$269$	−309.630	+	536.295i	−0.0701803	+	0.121556i	−0.898980	−	0.437989i	$-0.855691\pi$
$269$	−309.630	+	536.295i	−0.0701803	+	0.121556i	0.828800	+	0.559545i	$0.189024\pi$
$270$	−976.178	−	1690.79i	−0.220031	−	0.381104i
$271$	−1134.37	+	654.928i	−0.254273	+	0.146805i	−0.621719	−	0.783240i	$-0.713566\pi$
$271$	−1134.37	+	654.928i	−0.254273	+	0.146805i	0.367446	+	0.930045i	$0.380232\pi$
$272$	−2015.55			−0.449304
$273$		0			0
$274$	−1054.29			−0.232453
$275$	−1336.01	+	771.347i	−0.292962	+	0.169142i
$276$	−872.113	−	1510.54i	−0.190199	−	0.329435i
$277$	3291.31	−	5700.72i	0.713920	−	1.23655i	−0.249454	−	0.968387i	$-0.580251\pi$
$277$	3291.31	−	5700.72i	0.713920	−	1.23655i	0.963375	−	0.268159i	$-0.0864154\pi$
$278$		−	2989.91i		−	0.645046i
$279$	−2350.21	−	1356.89i	−0.504313	−	0.291165i
$280$	732.462	+	422.887i	0.156332	+	0.0902584i
$281$		−	7406.25i		−	1.57231i	−0.618028	−	0.786156i	$-0.712068\pi$
$281$		−	7406.25i		−	1.57231i	0.618028	−	0.786156i	$-0.287932\pi$
$282$	−1532.95	+	2655.15i	−0.323709	+	0.560680i
$283$	1109.97	+	1922.53i	0.233149	+	0.403825i	0.958733	−	0.284308i	$-0.0917638\pi$
$283$	1109.97	+	1922.53i	0.233149	+	0.403825i	−0.725584	+	0.688133i	$0.758430\pi$
$284$	2947.20	−	1701.56i	0.615788	−	0.355526i
$285$	2221.10			0.461637
$286$		0			0
$287$	−436.518			−0.0897799
$288$	−435.723	+	251.565i	−0.0891501	+	0.0514708i
$289$	−5477.95	−	9488.08i	−1.11499	−	1.93122i
$290$	1006.60	−	1743.48i	0.203826	−	0.353037i
$291$		−	275.696i		−	0.0555382i
$292$	3905.97	+	2255.11i	0.782807	+	0.451954i
$293$	1951.28	+	1126.57i	0.389062	+	0.224625i	0.681754	−	0.731582i	$-0.261218\pi$
$293$	1951.28	+	1126.57i	0.389062	+	0.224625i	−0.292691	+	0.956207i	$0.594551\pi$
$294$			682.172i			0.135323i
$295$	−1057.77	+	1832.11i	−0.208765	+	0.361592i
$296$	−885.077	−	1533.00i	−0.173797	−	0.301026i
$297$	2435.40	−	1406.08i	0.475812	−	0.274710i
$298$	−3477.28			−0.675950
$299$		0			0
$300$	−1057.21			−0.203460
$301$	4868.07	−	2810.58i	0.932197	−	0.538204i
$302$	1923.77	+	3332.06i	0.366558	+	0.634897i
$303$	1203.09	−	2083.82i	0.228105	−	0.395090i
$304$		−	1555.31i		−	0.293432i
$305$	−4781.50	−	2760.60i	−0.897666	−	0.518268i
$306$	−3430.55	−	1980.63i	−0.640887	−	0.370017i
$307$		−	6633.50i		−	1.23321i	−0.787274	−	0.616603i	$-0.788509\pi$
$307$		−	6633.50i		−	1.23321i	0.787274	−	0.616603i	$-0.211491\pi$
$308$	−609.123	+	1055.03i	−0.112688	+	0.195182i
$309$	−1570.76	−	2720.64i	−0.289183	−	0.500880i
$310$	2034.11	−	1174.40i	0.372677	−	0.215165i
$311$	−815.823			−0.148749			−0.0743747	−	0.997230i	$-0.523696\pi$
$311$	−815.823			−0.148749			−0.0743747	+	0.997230i	$0.523696\pi$
$312$		0			0
$313$	6169.43			1.11411			0.557055	−	0.830475i	$-0.311931\pi$
$313$	6169.43			1.11411			0.557055	+	0.830475i	$0.311931\pi$
$314$	476.403	−	275.052i	0.0856210	−	0.0494333i
$315$	831.122	+	1439.54i	0.148662	+	0.257489i
$316$	556.160	−	963.297i	0.0990077	−	0.171486i
$317$			8846.56i			1.56742i	0.621126	+	0.783711i	$0.286676\pi$
$317$			8846.56i			1.56742i	−0.621126	+	0.783711i	$0.713324\pi$
$318$	3740.39	+	2159.52i	0.659594	+	0.380817i
$319$	2511.30	+	1449.90i	0.440770	+	0.254479i
$320$		−	435.460i		−	0.0760718i
$321$	2012.82	−	3486.30i	0.349983	−	0.606188i
$322$	2017.62	+	3494.61i	0.349184	+	0.604805i
$323$	10604.8	−	6122.68i	1.82683	−	1.05472i
$324$	229.111			0.0392852
$325$		0			0
$326$	−7744.87			−1.31579
$327$	347.584	−	200.678i	0.0587812	−	0.0339373i
$328$	112.374	+	194.638i	0.0189171	+	0.0327654i
$329$	3546.45	−	6142.63i	0.594292	−	1.02934i
$330$			895.732i			0.149420i
$331$	8236.93	+	4755.60i	1.36780	+	0.789701i	0.990647	−	0.136449i	$-0.0435688\pi$
$331$	8236.93	+	4755.60i	1.36780	+	0.789701i	0.377156	+	0.926150i	$0.376902\pi$
$332$	−1445.49	−	834.553i	−0.238950	−	0.137958i
$333$		−	3478.97i		−	0.572512i
$334$	712.409	−	1233.93i	0.116710	−	0.202148i
$335$	23.8297	+	41.2742i	0.00388643	+	0.00673149i
$336$	−723.015	+	417.433i	−0.117392	+	0.0677763i
$337$	4745.81			0.767124			0.383562	−	0.923515i	$-0.374697\pi$
$337$	4745.81			0.767124			0.383562	+	0.923515i	$0.374697\pi$
$338$		0			0
$339$	−2037.36			−0.326414
$340$	2969.15	−	1714.24i	0.473603	−	0.273435i
$341$	1691.59	+	2929.92i	0.268636	+	0.465291i
$342$	1528.37	−	2647.21i	0.241651	−	0.418552i
$343$		−	6907.74i		−	1.08741i
$344$	−2506.40	−	1447.07i	−0.392838	−	0.226805i
$345$	2569.46	+	1483.48i	0.400972	+	0.231501i
$346$			1623.39i			0.252237i
$347$	−4692.18	+	8127.10i	−0.725906	+	1.25731i	0.232693	+	0.972550i	$0.425246\pi$
$347$	−4692.18	+	8127.10i	−0.725906	+	1.25731i	−0.958600	+	0.284757i	$0.908087\pi$
$348$	993.617	+	1720.99i	0.153056	+	0.265101i
$349$	−8063.42	+	4655.42i	−1.23675	+	0.714036i	−0.968428	−	0.249294i	$-0.919802\pi$
$349$	−8063.42	+	4655.42i	−1.23675	+	0.714036i	−0.268319	+	0.963330i	$0.586468\pi$
$350$	2445.83			0.373529
$351$		0			0
$352$	627.233			0.0949763
$353$	1066.95	−	616.005i	0.160873	−	0.0928800i	−0.417402	−	0.908722i	$-0.637059\pi$
$353$	1066.95	−	616.005i	0.160873	−	0.0928800i	0.578275	+	0.815842i	$0.303726\pi$
$354$	−1044.13	−	1808.48i	−0.156765	−	0.271525i
$355$	−2894.39	+	5013.23i	−0.432727	+	0.749506i
$356$		−	1297.08i		−	0.193105i
$357$	−5692.47	−	3286.55i	−0.843914	−	0.487234i
$358$	1496.21	+	863.837i	0.220886	+	0.127528i
$359$		−	6179.13i		−	0.908417i	−0.890895	−	0.454209i	$-0.849922\pi$
$359$		−	6179.13i		−	0.908417i	0.890895	−	0.454209i	$-0.150078\pi$
$360$	427.916	−	741.172i	0.0626476	−	0.108509i
$361$	1295.12	+	2243.21i	0.188820	+	0.327046i
$362$	−2471.44	+	1426.89i	−0.358829	+	0.207170i
$363$	3179.50			0.459725
$364$		0			0
$365$	−7671.97			−1.10019
$366$	4719.83	−	2725.00i	0.674070	−	0.389174i
$367$	235.037	+	407.095i	0.0334300	+	0.0579025i	0.882256	−	0.470769i	$-0.156024\pi$
$367$	235.037	+	407.095i	0.0334300	+	0.0579025i	−0.848826	+	0.528672i	$0.822690\pi$
$368$	1038.80	−	1799.26i	0.147150	−	0.254871i
$369$			441.709i			0.0623156i
$370$	2607.65	+	1505.53i	0.366393	+	0.211537i
$371$	−8653.32	−	4996.00i	−1.21094	−	0.699135i
$372$			2318.50i			0.323141i
$373$	2559.15	−	4432.59i	0.355249	−	0.615310i	−0.631911	−	0.775041i	$-0.717729\pi$
$373$	2559.15	−	4432.59i	0.355249	−	0.615310i	0.987161	+	0.159731i	$0.0510626\pi$
$374$	2469.18	+	4276.74i	0.341386	+	0.591297i
$375$	4030.89	−	2327.23i	0.555078	−	0.320474i
$376$	−3651.89			−0.500882
$377$		0			0
$378$	−4458.48			−0.606665
$379$	−428.638	+	247.474i	−0.0580940	+	0.0335406i	−0.528766	−	0.848768i	$-0.677345\pi$
$379$	−428.638	+	247.474i	−0.0580940	+	0.0335406i	0.470672	+	0.882308i	$0.344012\pi$
$380$	1322.81	+	2291.17i	0.178575	+	0.309302i
$381$	3119.61	−	5403.33i	0.419482	−	0.726564i
$382$		−	1568.86i		−	0.210131i
$383$	3727.82	+	2152.26i	0.497343	+	0.287141i	0.727616	−	0.685985i	$-0.240628\pi$
$383$	3727.82	+	2152.26i	0.497343	+	0.287141i	−0.230272	+	0.973126i	$0.573962\pi$
$384$	372.256	+	214.922i	0.0494703	+	0.0285617i
$385$		−	2072.26i		−	0.274317i
$386$	−3012.90	+	5218.50i	−0.397286	+	0.688120i
$387$	−2844.01	−	4925.96i	−0.373563	−	0.647030i
$388$	284.394	−	164.195i	0.0372112	−	0.0214839i
$389$	−5599.48			−0.729832			−0.364916	−	0.931040i	$-0.618902\pi$
$389$	−5599.48			−0.729832			−0.364916	+	0.931040i	$0.618902\pi$
$390$		0			0
$391$	16357.5			2.11568
$392$	−703.694	+	406.278i	−0.0906682	+	0.0523473i
$393$	3136.05	+	5431.79i	0.402526	+	0.697195i
$394$	−2729.30	+	4727.29i	−0.348985	+	0.604460i
$395$			1892.07i			0.241014i
$396$	1067.58	+	616.367i	0.135474	+	0.0782161i
$397$	8493.19	+	4903.55i	1.07371	+	0.619904i	0.929192	−	0.369598i	$-0.120505\pi$
$397$	8493.19	+	4903.55i	1.07371	+	0.619904i	0.144514	+	0.989503i	$0.453838\pi$
$398$			1923.21i			0.242215i
$399$	2536.09	−	4392.64i	0.318204	−	0.551145i
$400$	−629.637	−	1090.56i	−0.0787047	−	0.136321i
$401$	−12694.6	+	7329.22i	−1.58089	+	0.912728i	−0.586161	+	0.810194i	$0.699362\pi$
$401$	−12694.6	+	7329.22i	−1.58089	+	0.912728i	−0.994730	+	0.102534i	$0.967305\pi$
$402$	−47.0446			−0.00583675
$403$		0			0
$404$	2866.08			0.352953
$405$	−337.509	+	194.861i	−0.0414098	+	0.0239080i
$406$	−2298.71	−	3981.48i	−0.280993	−	0.486694i
$407$	−2168.55	+	3756.04i	−0.264106	+	0.457445i
$408$			3384.26i			0.410652i
$409$	−9253.81	−	5342.69i	−1.11876	−	0.645914i	−0.177673	−	0.984090i	$-0.556857\pi$
$409$	−9253.81	−	5342.69i	−1.11876	−	0.645914i	−0.941083	+	0.338175i	$0.890190\pi$
$410$	−331.082	−	191.150i	−0.0398804	−	0.0230250i
$411$			1770.24i			0.212456i
$412$	1870.99	−	3240.64i	0.223730	−	0.387512i
$413$	2415.57	+	4183.88i	0.287802	+	0.498488i
$414$	3536.17	−	2041.61i	0.419790	−	0.242366i
$415$	2839.18			0.335830
$416$		0			0
$417$	−5020.29			−0.589555
$418$	−3300.18	+	1905.36i	−0.386166	+	0.222953i
$419$	−3205.07	−	5551.34i	−0.373694	−	0.647257i	0.616437	−	0.787405i	$-0.288576\pi$
$419$	−3205.07	−	5551.34i	−0.373694	−	0.647257i	−0.990131	+	0.140147i	$0.955242\pi$
$420$	710.060	−	1229.86i	0.0824938	−	0.142883i
$421$		−	2672.97i		−	0.309436i	−0.987959	−	0.154718i	$-0.950553\pi$
$421$		−	2672.97i		−	0.309436i	0.987959	−	0.154718i	$-0.0494469\pi$
$422$	−6542.21	−	3777.14i	−0.754667	−	0.435707i
$423$	−6215.67	−	3588.62i	−0.714459	−	0.412493i
$424$			5144.53i			0.589247i
$425$	4957.28	−	8586.27i	0.565797	−	0.979989i
$426$	−2857.06	−	4948.57i	−0.324941	−	0.562814i
$427$	−10919.2	+	6304.22i	−1.23751	+	0.714479i
$428$	4795.05			0.541536
$429$		0			0
$430$	4922.99			0.552111
$431$	−4482.32	+	2587.87i	−0.500941	+	0.289218i	−0.729102	−	0.684405i	$-0.760062\pi$
$431$	−4482.32	+	2587.87i	−0.500941	+	0.289218i	0.228161	+	0.973623i	$0.426729\pi$
$432$	1147.76	+	1987.98i	0.127828	+	0.221404i
$433$	−2085.98	+	3613.02i	−0.231515	+	0.400995i	−0.958254	−	0.285918i	$-0.907701\pi$
$433$	−2085.98	+	3613.02i	−0.231515	+	0.400995i	0.726739	+	0.686913i	$0.241035\pi$
$434$		−	5363.80i		−	0.593250i
$435$	−2927.44	−	1690.16i	−0.322667	−	0.186292i
$436$	414.018	+	239.033i	0.0454768	+	0.0262560i
$437$			12622.4i			1.38172i
$438$	3786.51	−	6558.43i	0.413074	−	0.715465i
$439$	5332.27	+	9235.77i	0.579717	+	1.00410i	0.995512	+	0.0946401i	$0.0301700\pi$
$439$	5332.27	+	9235.77i	0.579717	+	1.00410i	−0.415795	+	0.909458i	$0.636497\pi$
$440$	−923.992	+	533.467i	−0.100113	+	0.0578001i
$441$	−1596.96			−0.172439
$442$		0			0
$443$	2122.16			0.227600			0.113800	−	0.993504i	$-0.463698\pi$
$443$	2122.16			0.227600			0.113800	+	0.993504i	$0.463698\pi$
$444$	−2574.02	+	1486.11i	−0.275130	+	0.158846i
$445$	1103.18	+	1910.77i	0.117519	+	0.203548i
$446$	−4366.31	+	7562.67i	−0.463567	+	0.802921i
$447$			5838.62i			0.617801i
$448$	−861.205	−	497.217i	−0.0908217	−	0.0524359i
$449$	−13237.6	−	7642.71i	−1.39136	−	0.803300i	−0.397891	−	0.917433i	$-0.630258\pi$
$449$	−13237.6	−	7642.71i	−1.39136	−	0.803300i	−0.993466	+	0.114132i	$0.963591\pi$
$450$		−	2474.92i		−	0.259264i
$451$	275.331	−	476.887i	0.0287469	−	0.0497910i
$452$	−1213.38	−	2101.64i	−0.126267	−	0.218701i
$453$	5594.79	−	3230.16i	0.580279	−	0.335024i
$454$	3653.98			0.377731
$455$		0			0
$456$	−2611.49			−0.268189
$457$	−7390.60	+	4266.96i	−0.756494	+	0.436762i	−0.828035	−	0.560676i	$-0.810541\pi$
$457$	−7390.60	+	4266.96i	−0.756494	+	0.436762i	0.0715418	+	0.997438i	$0.477208\pi$
$458$	4376.52	+	7580.35i	0.446509	+	0.773376i
$459$	−9036.57	+	15651.8i	−0.918935	+	1.59164i
$460$			3534.04i			0.358207i
$461$	5375.22	+	3103.39i	0.543057	+	0.313534i	0.746317	−	0.665591i	$-0.231820\pi$
$461$	5375.22	+	3103.39i	0.543057	+	0.313534i	−0.203260	+	0.979125i	$0.565154\pi$
$462$	1771.48	+	1022.76i	0.178391	+	0.102994i
$463$			14278.3i			1.43319i	0.697487	+	0.716597i	$0.254302\pi$
$463$			14278.3i			1.43319i	−0.697487	+	0.716597i	$0.745698\pi$
$464$	−1183.53	+	2049.93i	−0.118414	+	0.205098i
$465$	−1971.90	−	3415.43i	−0.196655	−	0.340617i
$466$	−8182.02	+	4723.89i	−0.813357	+	0.469592i
$467$	1787.57			0.177129			0.0885643	−	0.996070i	$-0.471772\pi$
$467$	1787.57			0.177129			0.0885643	+	0.996070i	$0.471772\pi$
$468$		0			0
$469$	108.837			0.0107156
$470$	5379.68	−	3105.96i	0.527971	−	0.304824i
$471$	−461.833	−	799.918i	−0.0451807	−	0.0782553i
$472$	1243.69	−	2154.14i	0.121283	−	0.210068i
$473$			7091.04i			0.689315i
$474$	−1617.45	−	933.835i	−0.156734	−	0.0904905i
$475$	6625.66	+	3825.33i	0.640013	+	0.369512i
$476$		−	7829.42i		−	0.753909i
$477$	−5055.41	+	8756.22i	−0.485264	+	0.840503i
$478$	2312.19	+	4004.83i	0.221249	+	0.383215i
$479$	11895.4	−	6867.79i	1.13468	−	0.655109i	0.189574	−	0.981866i	$-0.439289\pi$
$479$	11895.4	−	6867.79i	1.13468	−	0.655109i	0.945108	+	0.326757i	$0.105956\pi$
$480$	−731.171			−0.0695276
$481$		0			0
$482$	14295.2			1.35089
$483$	5867.72	−	3387.73i	0.552776	−	0.319145i
$484$	1893.60	+	3279.81i	0.177836	+	0.308021i
$485$	−279.299	+	483.760i	−0.0261491	+	0.0452915i
$486$			7362.67i			0.687197i
$487$	14738.9	+	8509.51i	1.37142	+	0.791792i	0.991107	−	0.133064i	$-0.0424816\pi$
$487$	14738.9	+	8509.51i	1.37142	+	0.791792i	0.380317	+	0.924856i	$0.375815\pi$
$488$	5621.94	+	3245.83i	0.521502	+	0.301089i
$489$			13004.2i			1.20260i
$490$	691.086	−	1197.00i	0.0637144	−	0.110357i
$491$	−6821.33	−	11814.9i	−0.626970	−	1.08594i	−0.988156	−	0.153451i	$-0.950961\pi$
$491$	−6821.33	−	11814.9i	−0.626970	−	1.08594i	0.361186	−	0.932494i	$-0.382372\pi$
$492$	326.811	−	188.685i	0.0299467	−	0.0172898i
$493$	−18636.4			−1.70252
$494$		0			0
$495$	−2096.90			−0.190401
$496$	−2391.65	+	1380.82i	−0.216508	+	0.125001i
$497$	6609.74	+	11448.4i	0.596554	+	1.03326i
$498$	−1401.28	+	2427.08i	−0.126090	+	0.218394i
$499$			4507.63i			0.404387i	0.979346	+	0.202194i	$0.0648070\pi$
$499$			4507.63i			0.404387i	−0.979346	+	0.202194i	$0.935193\pi$
$500$	4801.31	+	2772.04i	0.429443	+	0.247939i
$501$	−2071.86	−	1196.19i	−0.184758	−	0.106670i
$502$			5477.07i			0.486959i
$503$	4794.70	−	8304.67i	0.425020	−	0.736157i	−0.571402	−	0.820670i	$-0.693600\pi$
$503$	4794.70	−	8304.67i	0.425020	−	0.736157i	0.996422	+	0.0845135i	$0.0269336\pi$
$504$	−977.206	−	1692.57i	−0.0863655	−	0.149589i
$505$	−4222.10	+	2437.63i	−0.372041	+	0.214798i
$506$	−5090.40			−0.447225
$507$		0			0
$508$	7431.73			0.649074
$509$	8997.81	−	5194.89i	0.783539	−	0.452376i	−0.0541444	−	0.998533i	$-0.517243\pi$
$509$	8997.81	−	5194.89i	0.783539	−	0.452376i	0.837683	+	0.546157i	$0.183910\pi$
$510$	−2878.34	−	4985.44i	−0.249912	−	0.432860i
$511$	−8760.01	+	15172.8i	−0.758356	+	1.31351i
$512$			512.000i			0.0441942i
$513$	−12077.8	−	6973.14i	−1.03947	−	0.600140i
$514$	−10489.9	−	6056.36i	−0.900177	−	0.519717i
$515$			6365.15i			0.544626i
$516$	−2429.75	+	4208.45i	−0.207294	+	0.359044i
$517$	4473.80	+	7748.85i	0.380575	+	0.659176i
$518$	5954.94	−	3438.09i	0.505106	−	0.291623i
$519$	2725.79			0.230538
$520$		0			0
$521$	−3202.79			−0.269322			−0.134661	−	0.990892i	$-0.542995\pi$
$521$	−3202.79			−0.269322			−0.134661	+	0.990892i	$0.542995\pi$
$522$	−4028.83	+	2326.05i	−0.337810	+	0.195035i
$523$	3828.77	+	6631.62i	0.320115	+	0.554456i	0.980512	−	0.196461i	$-0.0629450\pi$
$523$	3828.77	+	6631.62i	0.320115	+	0.554456i	−0.660396	+	0.750917i	$0.729612\pi$
$524$	−3735.44	+	6469.97i	−0.311419	+	0.539393i
$525$		−	4106.74i		−	0.341396i
$526$	−9239.07	−	5334.18i	−0.765861	−	0.442170i
$527$	−18830.0	−	10871.5i	−1.55645	−	0.898615i
$528$		−	1053.17i		−	0.0868058i
$529$	−2347.03	+	4065.17i	−0.192901	+	0.334114i
$530$	−4375.47	−	7578.54i	−0.358600	−	0.621114i
$531$	4233.63	−	2444.29i	0.345996	−	0.199761i
$532$	6041.63			0.492365
$533$		0			0
$534$	−2177.90			−0.176493
$535$	−7063.70	+	4078.23i	−0.570823	+	0.329565i
$536$	−28.0181	−	48.5288i	−0.00225783	−	0.00391068i
$537$	1450.45	−	2512.25i	0.116558	−	0.201884i
$538$			1238.52i			0.0992499i
$539$	1724.14	+	995.434i	0.137781	+	0.0795480i
$540$	−3381.58	−	1952.36i	−0.269481	−	0.155585i
$541$			6536.41i			0.519450i	0.965683	+	0.259725i	$0.0836319\pi$
$541$			6536.41i			0.519450i	−0.965683	+	0.259725i	$0.916368\pi$
$542$	−1309.86	+	2268.74i	−0.103807	+	0.179798i
$543$	2395.85	+	4149.74i	0.189348	+	0.327960i
$544$	−3491.03	+	2015.55i	−0.275141	+	0.158853i
$545$	−813.200			−0.0639149
$546$		0			0
$547$	−2020.69			−0.157950			−0.0789748	−	0.996877i	$-0.525165\pi$
$547$	−2020.69			−0.157950			−0.0789748	+	0.996877i	$0.525165\pi$
$548$	−1826.09	+	1054.29i	−0.142348	+	0.0821845i
$549$	6379.19	+	11049.1i	0.495914	+	0.858949i
$550$	−1542.69	+	2672.02i	−0.119601	+	0.207155i
$551$		−	14380.9i		−	1.11188i
$552$	−3021.09	−	1744.23i	−0.232946	−	0.134491i
$553$	3741.94	+	2160.41i	0.287746	+	0.166130i
$554$		−	13165.3i		−	1.00964i
$555$	2527.90	−	4378.45i	0.193339	−	0.334874i
$556$	−2989.91	−	5178.67i	−0.228058	−	0.395008i
$557$	−8698.31	+	5021.97i	−0.661686	+	0.382025i	−0.792919	−	0.609327i	$-0.791440\pi$
$557$	−8698.31	+	5021.97i	−0.661686	+	0.382025i	0.131233	+	0.991352i	$0.458106\pi$
$558$	−5427.58			−0.411770
$559$		0			0
$560$	1691.55			0.127645
$561$	7180.98	−	4145.94i	0.540430	−	0.312017i
$562$	−7406.25	−	12828.0i	−0.555896	−	0.962841i
$563$	4184.05	−	7246.99i	0.313209	−	0.542494i	−0.665846	−	0.746089i	$-0.731929\pi$
$563$	4184.05	−	7246.99i	0.313209	−	0.542494i	0.979055	+	0.203595i	$0.0652626\pi$
$564$			6131.80i			0.457793i
$565$	3574.93	+	2063.98i	0.266192	+	0.153686i
$566$	3845.06	+	2219.95i	0.285548	+	0.164861i
$567$			889.985i			0.0659186i
$568$	3403.13	−	5894.39i	0.251395	−	0.435428i
$569$	−7049.80	−	12210.6i	−0.519408	−	0.899640i	−0.999746	−	0.0225569i	$-0.992819\pi$
$569$	−7049.80	−	12210.6i	−0.519408	−	0.899640i	0.480338	−	0.877084i	$-0.340514\pi$
$570$	3847.05	−	2221.10i	0.282693	−	0.163213i
$571$	7703.05			0.564558			0.282279	−	0.959332i	$-0.408910\pi$
$571$	7703.05			0.564558			0.282279	+	0.959332i	$0.408910\pi$
$572$		0			0
$573$	−2634.24			−0.192054
$574$	−756.071	+	436.518i	−0.0549788	+	0.0317420i
$575$	5109.91	+	8850.62i	0.370605	+	0.641907i
$576$	−503.130	+	871.446i	−0.0363954	+	0.0630386i
$577$			14074.3i			1.01546i	0.861517	+	0.507729i	$0.169515\pi$
$577$			14074.3i			1.01546i	−0.861517	+	0.507729i	$0.830485\pi$
$578$	−18976.2	−	10955.9i	−1.36558	−	0.788417i
$579$	8762.26	+	5058.89i	0.628924	+	0.363109i
$580$		−	4026.40i		−	0.288254i
$581$	3241.83	−	5615.01i	0.231486	−	0.400946i
$582$	−275.696	−	477.520i	−0.0196357	−	0.0340100i
$583$	10916.1	−	6302.39i	0.775467	−	0.447716i
$584$	9020.45			0.639159
$585$		0			0
$586$	4506.30			0.317668
$587$	3806.69	−	2197.79i	0.267664	−	0.154536i	−0.360162	−	0.932890i	$-0.617278\pi$
$587$	3806.69	−	2197.79i	0.267664	−	0.154536i	0.627826	+	0.778354i	$0.283945\pi$
$588$	682.172	+	1181.56i	0.0478441	+	0.0828684i
$589$	8389.08	−	14530.3i	0.586869	−	1.01649i
$590$			4231.08i			0.295239i
$591$	7937.48	+	4582.71i	0.552461	+	0.318963i
$592$	−3066.00	−	1770.15i	−0.212857	−	0.122893i
$593$		−	9239.06i		−	0.639802i	−0.947451	−	0.319901i	$-0.896350\pi$
$593$		−	9239.06i		−	0.639802i	0.947451	−	0.319901i	$-0.103650\pi$
$594$	2812.16	−	4870.80i	0.194249	−	0.336450i
$595$	6658.98	+	11533.7i	0.458810	+	0.794681i
$596$	−6022.82	+	3477.28i	−0.413933	+	0.238985i
$597$	3229.21			0.221378
$598$		0			0
$599$	−15261.0			−1.04098			−0.520492	−	0.853867i	$-0.674251\pi$
$599$	−15261.0			−1.04098			−0.520492	+	0.853867i	$0.674251\pi$
$600$	−1831.14	+	1057.21i	−0.124593	+	0.0719340i
$601$	−8195.48	−	14195.0i	−0.556241	−	0.963437i	−0.997806	−	0.0662077i	$-0.978910\pi$
$601$	−8195.48	−	14195.0i	−0.556241	−	0.963437i	0.441565	−	0.897229i	$-0.354423\pi$
$602$	5621.17	−	9736.15i	0.380568	−	0.659162i
$603$		−	110.131i		−	0.00743761i
$604$	6664.13	+	3847.54i	0.448940	+	0.259195i
$605$	−5579.01	−	3221.04i	−0.374907	−	0.216453i
$606$		−	4812.38i		−	0.322590i
$607$	−7031.79	+	12179.4i	−0.470200	+	0.814411i	−0.999419	−	0.0340744i	$-0.989152\pi$
$607$	−7031.79	+	12179.4i	−0.470200	+	0.814411i	0.529219	+	0.848485i	$0.322485\pi$
$608$	−1555.31	−	2693.88i	−0.103744	−	0.179690i
$609$	−6685.22	+	3859.71i	−0.444825	+	0.256820i
$610$	−11042.4			−0.732941
$611$		0			0
$612$	−7922.52			−0.523282
$613$	−6391.17	+	3689.94i	−0.421104	+	0.243125i	−0.695550	−	0.718478i	$-0.744839\pi$
$613$	−6391.17	+	3689.94i	−0.421104	+	0.243125i	0.274445	+	0.961603i	$0.411506\pi$
$614$	−6633.50	−	11489.6i	−0.436004	−	0.755181i
$615$	−320.956	+	555.912i	−0.0210442	+	0.0364496i
$616$			2436.49i			0.159365i
$617$	−9868.51	−	5697.59i	−0.643908	−	0.371761i	0.142210	−	0.989836i	$-0.454579\pi$
$617$	−9868.51	−	5697.59i	−0.643908	−	0.371761i	−0.786118	+	0.618076i	$0.787912\pi$
$618$	−5441.29	−	3141.53i	−0.354176	−	0.204483i
$619$			5223.75i			0.339192i	0.985514	+	0.169596i	$0.0542464\pi$
$619$			5223.75i			0.339192i	−0.985514	+	0.169596i	$0.945754\pi$
$620$	2348.79	−	4068.23i	0.152145	−	0.263523i
$621$	−9314.78	−	16133.7i	−0.601915	−	1.04255i
$622$	−1413.05	+	815.823i	−0.0910901	+	0.0525909i
$623$	5038.53			0.324020
$624$		0			0
$625$	407.511			0.0260807
$626$	10685.8	−	6169.43i	0.682251	−	0.393898i
$627$	3199.25	+	5541.26i	0.203773	+	0.352945i
$628$	550.103	−	952.807i	0.0349546	−	0.0605432i
$629$		−	27873.7i		−	1.76693i
$630$	2879.09	+	1662.24i	0.182072	+	0.105120i
$631$	16565.8	+	9564.25i	1.04512	+	0.603402i	0.921280	−	0.388900i	$-0.127145\pi$
$631$	16565.8	+	9564.25i	1.04512	+	0.603402i	0.123843	+	0.992302i	$0.460478\pi$
$632$		−	2224.64i		−	0.140018i
$633$	−6342.12	+	10984.9i	−0.398225	+	0.689746i
$634$	8846.56	+	15322.7i	0.554167	+	0.959846i
$635$	−10947.9	+	6320.75i	−0.684177	+	0.395010i
$636$	8638.07			0.538556
$637$		0			0
$638$	5799.59			0.359887
$639$	11584.5	−	6688.34i	0.717179	−	0.414064i
$640$	−435.460	−	754.239i	−0.0268954	−	0.0465843i
$641$	930.204	−	1611.16i	0.0573180	−	0.0992777i	−0.835943	−	0.548817i	$-0.815078\pi$
$641$	930.204	−	1611.16i	0.0573180	−	0.0992777i	0.893261	+	0.449539i	$0.148412\pi$
$642$		−	8051.26i		−	0.494950i
$643$	8284.94	+	4783.31i	0.508128	+	0.293368i	0.732064	−	0.681236i	$-0.238557\pi$
$643$	8284.94	+	4783.31i	0.508128	+	0.293368i	−0.223936	+	0.974604i	$0.571891\pi$
$644$	6989.23	+	4035.23i	0.427662	+	0.246911i
$645$		−	8266.08i		−	0.504615i
$646$	12245.4	−	21209.6i	0.745801	−	1.29176i
$647$	11478.5	+	19881.3i	0.697473	+	1.20806i	0.969340	+	0.245724i	$0.0790256\pi$
$647$	11478.5	+	19881.3i	0.697473	+	1.20806i	−0.271867	+	0.962335i	$0.587641\pi$
$648$	396.833	−	229.111i	0.0240572	−	0.0138894i
$649$	−6094.41			−0.368608
$650$		0			0
$651$	−9006.22			−0.542215
$652$	−13414.5	+	7744.87i	−0.805756	+	0.465203i
$653$	2049.77	+	3550.30i	0.122838	+	0.212763i	0.920886	−	0.389832i	$-0.127467\pi$
$653$	2049.77	+	3550.30i	0.122838	+	0.212763i	−0.798047	+	0.602595i	$0.794134\pi$
$654$	401.356	−	695.168i	0.0239973	−	0.0415646i
$655$		−	12708.1i		−	0.758086i
$656$	389.275	+	224.748i	0.0231687	+	0.0133764i
$657$	15353.2	+	8864.17i	0.911698	+	0.526369i
$658$		−	14185.8i		−	0.840455i
$659$	−14231.6	+	24649.9i	−0.841252	+	1.45709i	0.0475845	+	0.998867i	$0.484848\pi$
$659$	−14231.6	+	24649.9i	−0.841252	+	1.45709i	−0.888837	+	0.458224i	$0.848486\pi$
$660$	895.732	+	1551.45i	0.0528278	+	0.0915004i
$661$	−7094.82	+	4096.20i	−0.417483	+	0.241034i	−0.694000	−	0.719975i	$-0.744153\pi$
$661$	−7094.82	+	4096.20i	−0.417483	+	0.241034i	0.276517	+	0.961009i	$0.410820\pi$
$662$	19022.4			1.11681
$663$		0			0
$664$	−3338.21			−0.195102
$665$	−8900.07	+	5138.46i	−0.518992	+	0.299640i
$666$	−3478.97	−	6025.75i	−0.202413	−	0.350590i
$667$	9605.07	−	16636.5i	0.557586	−	0.965767i
$668$		−	2849.64i		−	0.165054i
$669$	12698.3	+	7331.37i	0.733849	+	0.423688i
$670$	82.5484	+	47.6593i	0.00475988	+	0.00274812i
$671$		−	15905.4i		−	0.915083i
$672$	−834.866	+	1446.03i	−0.0479251	+	0.0830086i
$673$	17137.1	+	29682.2i	0.981553	+	1.70010i	0.656354	+	0.754453i	$0.272098\pi$
$673$	17137.1	+	29682.2i	0.981553	+	1.70010i	0.325199	+	0.945646i	$0.394569\pi$
$674$	8219.99	−	4745.81i	0.469766	−	0.271219i
$675$	−11291.7			−0.643880
$676$		0			0
$677$	−11531.2			−0.654623			−0.327311	−	0.944917i	$-0.606143\pi$
$677$	−11531.2			−0.654623			−0.327311	+	0.944917i	$0.606143\pi$
$678$	−3528.82	+	2037.36i	−0.199887	+	0.115405i
$679$	637.817	+	1104.73i	0.0360489	+	0.0624385i
$680$	3428.48	−	5938.30i	0.193347	−	0.334888i
$681$		−	6135.32i		−	0.345236i
$682$	5859.84	+	3383.18i	0.329010	+	0.189954i
$683$	−6534.72	−	3772.82i	−0.366097	−	0.211366i	0.305655	−	0.952142i	$-0.401125\pi$
$683$	−6534.72	−	3772.82i	−0.366097	−	0.211366i	−0.671752	+	0.740776i	$0.734458\pi$
$684$		−	6113.48i		−	0.341746i
$685$	1793.37	−	3106.20i	0.100031	−	0.173258i
$686$	−6907.74	−	11964.5i	−0.384459	−	0.665902i
$687$	12728.0	−	7348.51i	0.706846	−	0.408098i
$688$	−5788.29			−0.320751
$689$		0			0
$690$	5933.92			0.327392
$691$	29859.0	−	17239.1i	1.64384	−	0.949069i	0.664383	−	0.747392i	$-0.268694\pi$
$691$	29859.0	−	17239.1i	1.64384	−	0.949069i	0.979452	−	0.201677i	$-0.0646391\pi$
$692$	1623.39	+	2811.79i	0.0891791	+	0.154463i
$693$	−2394.28	+	4147.02i	−0.131243	+	0.227319i
$694$			18768.7i			1.02659i
$695$	8809.01	+	5085.88i	0.480784	+	0.277581i
$696$	3441.99	+	1987.23i	0.187454	+	0.108227i
$697$			3538.99i			0.192323i
$698$	−9310.83	+	16126.8i	−0.504900	+	0.874512i
$699$	7931.77	+	13738.2i	0.429195	+	0.743387i
$700$	4236.30	−	2445.83i	0.228739	−	0.132063i
$701$	−1042.89			−0.0561905			−0.0280952	−	0.999605i	$-0.508944\pi$
$701$	−1042.89			−0.0561905			−0.0280952	+	0.999605i	$0.508944\pi$
$702$		0			0
$703$	21508.9			1.15395
$704$	1086.40	−	627.233i	0.0581609	−	0.0335792i
$705$	−5215.15	−	9032.90i	−0.278601	−	0.482551i
$706$	1232.01	−	2133.91i	0.0656761	−	0.113754i
$707$			11133.3i			0.592238i
$708$	−3616.96	−	2088.25i	−0.191997	−	0.110849i
$709$	16263.8	+	9389.88i	0.861492	+	0.497383i	0.864512	−	0.502613i	$-0.167628\pi$
$709$	16263.8	+	9389.88i	0.861492	+	0.497383i	−0.00301951	+	0.999995i	$0.500961\pi$
$710$			11577.6i			0.611969i
$711$	2186.10	−	3786.43i	0.115310	−	0.199722i
$712$	−1297.08	−	2246.62i	−0.0682729	−	0.118252i
$713$	19409.7	−	11206.2i	1.01949	−	0.588605i
$714$	−13146.2			−0.689053
$715$		0			0
$716$	3455.35			0.180353
$717$	6724.42	−	3882.35i	0.350249	−	0.202216i
$718$	−6179.13	−	10702.6i	−0.321174	−	0.556290i
$719$	17256.2	−	29888.6i	0.895059	−	1.55029i	0.0613275	−	0.998118i	$-0.480467\pi$
$719$	17256.2	−	29888.6i	0.895059	−	1.55029i	0.833732	−	0.552170i	$-0.186200\pi$
$720$		−	1711.66i		−	0.0885971i
$721$	12588.3	+	7267.86i	0.650226	+	0.375408i
$722$	4486.41	+	2590.23i	0.231256	+	0.133516i
$723$		−	24002.7i		−	1.23468i
$724$	−2853.77	+	4942.88i	−0.146491	+	0.253730i
$725$	−5821.82	−	10083.7i	−0.298230	−	0.516550i
$726$	5507.05	−	3179.50i	0.281523	−	0.162537i
$727$	6114.86			0.311950			0.155975	−	0.987761i	$-0.450148\pi$
$727$	6114.86			0.311950			0.155975	+	0.987761i	$0.450148\pi$
$728$		0			0
$729$	13909.0			0.706650
$730$	−13288.2	+	7671.97i	−0.673726	+	0.388976i
$731$	−22786.3	−	39467.0i	−1.15292	−	1.99691i
$732$	5449.99	−	9439.66i	0.275188	−	0.476639i
$733$		−	20350.9i		−	1.02548i	−0.858543	−	0.512742i	$-0.828630\pi$
$733$		−	20350.9i		−	1.02548i	0.858543	−	0.512742i	$-0.171370\pi$
$734$	814.191	+	470.073i	0.0409432	+	0.0236386i
$735$	−2009.85	−	1160.39i	−0.100863	−	0.0582333i
$736$		−	4155.20i		−	0.208102i
$737$	−68.6481	+	118.902i	−0.00343105	+	0.00594276i
$738$	441.709	+	765.062i	0.0220319	+	0.0381603i
$739$	−9284.97	+	5360.68i	−0.462183	+	0.266841i	−0.712962	−	0.701203i	$-0.752647\pi$
$739$	−9284.97	+	5360.68i	−0.462183	+	0.266841i	0.250779	+	0.968044i	$0.419313\pi$
$740$	6022.12			0.299159
$741$		0			0
$742$	−19984.0			−0.988727
$743$	−24012.1	+	13863.4i	−1.18562	+	0.684519i	−0.957308	−	0.289069i	$-0.906654\pi$
$743$	−24012.1	+	13863.4i	−1.18562	+	0.684519i	−0.228313	+	0.973588i	$0.573321\pi$
$744$	2318.50	+	4015.76i	0.114248	+	0.197883i
$745$	5914.91	−	10244.9i	0.290880	−	0.503818i
$746$		−	10236.6i		−	0.502398i
$747$	−5681.78	−	3280.38i	−0.278294	−	0.160673i
$748$	8553.49	+	4938.36i	0.418110	+	0.241396i
$749$			18626.4i			0.908671i
$750$	4654.47	−	8061.78i	0.226610	−	0.392499i
$751$	−15684.0	−	27165.5i	−0.762075	−	1.31995i	−0.941779	−	0.336232i	$-0.890847\pi$
$751$	−15684.0	−	27165.5i	−0.762075	−	1.31995i	0.179704	−	0.983721i	$-0.442486\pi$
$752$	−6325.25	+	3651.89i	−0.306726	+	0.177089i
$753$	9196.41			0.445068
$754$		0			0
$755$	−13089.4			−0.630959
$756$	−7722.31	+	4458.48i	−0.371505	+	0.214488i
$757$	−4458.12	−	7721.68i	−0.214046	−	0.370739i	0.738931	−	0.673781i	$-0.235331\pi$
$757$	−4458.12	−	7721.68i	−0.214046	−	0.370739i	−0.952977	+	0.303042i	$0.901998\pi$
$758$	−494.948	+	857.275i	−0.0237168	+	0.0410787i
$759$			8547.17i			0.408752i
$760$	4582.34	+	2645.62i	0.218709	+	0.126272i
$761$	9762.51	+	5636.39i	0.465034	+	0.268487i	0.714158	−	0.699984i	$-0.246810\pi$
$761$	9762.51	+	5636.39i	0.465034	+	0.268487i	−0.249125	+	0.968471i	$0.580143\pi$
$762$		−	12478.4i		−	0.593237i
$763$	−928.527	+	1608.26i	−0.0440563	+	0.0763077i
$764$	−1568.86	−	2717.35i	−0.0742924	−	0.128678i
$765$	11670.8	−	6738.17i	0.551582	−	0.318456i
$766$	8609.02			0.406079
$767$		0			0
$768$	859.687			0.0403923
$769$	−8009.36	+	4624.21i	−0.375585	+	0.216844i	−0.675896	−	0.736997i	$-0.736243\pi$
$769$	−8009.36	+	4624.21i	−0.375585	+	0.216844i	0.300311	+	0.953841i	$0.402910\pi$
$770$	−2072.26	−	3589.26i	−0.0969857	−	0.167984i
$771$	−10169.1	+	17613.4i	−0.475008	+	0.822738i
$772$			12051.6i			0.561848i
$773$	11568.3	+	6678.95i	0.538269	+	0.310770i	0.744377	−	0.667759i	$-0.232746\pi$
$773$	11568.3	+	6678.95i	0.538269	+	0.310770i	−0.206108	+	0.978529i	$0.566080\pi$
$774$	−9851.93	−	5688.01i	−0.457520	−	0.264149i
$775$		−	13584.6i		−	0.629643i
$776$	328.390	−	568.789i	0.0151914	−	0.0263123i
$777$	−5772.81	−	9998.81i	−0.266536	−	0.461654i
$778$	−9698.58	+	5599.48i	−0.446929	+	0.258035i
$779$	−2730.89			−0.125602
$780$		0			0
$781$	−16676.2			−0.764049
$782$	28331.9	−	16357.5i	1.29559	−	0.748007i
$783$	10612.5	+	18381.4i	0.484369	+	0.838951i
$784$	−812.556	+	1407.39i	−0.0370151	+	0.0641121i
$785$			1871.47i			0.0850899i
$786$	10863.6	+	6272.09i	0.492991	+	0.284629i
$787$	43.1767	+	24.9281i	0.00195563	+	0.00112909i	0.500977	−	0.865460i	$-0.332974\pi$
$787$	43.1767	+	24.9281i	0.00195563	+	0.00112909i	−0.499022	+	0.866589i	$0.666307\pi$
$788$			10917.2i			0.493540i
$789$	−8956.50	+	15513.1i	−0.404132	+	0.699977i
$790$	1892.07	+	3277.17i	0.0852114	+	0.147590i
$791$	8163.84	−	4713.40i	0.366969	−	0.211870i
$792$	2465.47			0.110614
$793$		0			0
$794$	19614.2			0.876677
$795$	−12724.9	+	7346.75i	−0.567682	+	0.327751i
$796$	1923.21	+	3331.09i	0.0856361	+	0.148326i
$797$	−5756.94	+	9971.31i	−0.255861	+	0.443164i	−0.965129	−	0.261775i	$-0.915692\pi$
$797$	−5756.94	+	9971.31i	−0.255861	+	0.443164i	0.709268	+	0.704939i	$0.249026\pi$
$798$		−	10144.4i		−	0.450008i
$799$	−49800.2	−	28752.2i	−2.20501	−	1.27306i
$800$	−2181.13	−	1259.27i	−0.0963932	−	0.0556526i
$801$		−	5098.45i		−	0.224900i
$802$	−14658.4	+	25389.2i	−0.645396	+	1.11786i
$803$	−11050.6	−	19140.3i	−0.485640	−	0.841153i
$804$	−81.4837	+	47.0446i	−0.00357426	+	0.00206360i
$805$	−13728.0			−0.601054
$806$		0			0
$807$	2079.57			0.0907118
$808$	4964.20	−	2866.08i	0.216139	−	0.124788i
$809$	−6503.80	−	11264.9i	−0.282647	−	0.489559i	0.689389	−	0.724391i	$-0.257879\pi$
$809$	−6503.80	−	11264.9i	−0.282647	−	0.489559i	−0.972036	+	0.234833i	$0.924546\pi$
$810$	−389.722	+	675.019i	−0.0169055	+	0.0292812i
$811$			1032.74i			0.0447156i	0.999750	+	0.0223578i	$0.00711731\pi$
$811$			1032.74i			0.0447156i	−0.999750	+	0.0223578i	$0.992883\pi$
$812$	−7962.97	−	4597.42i	−0.344145	−	0.198692i
$813$	3809.39	+	2199.35i	0.164331	+	0.0948765i
$814$			8674.21i			0.373502i
$815$	13174.2	−	22818.3i	0.566222	−	0.980724i
$816$	3384.26	+	5861.71i	0.145187	+	0.251472i
$817$	30455.1	−	17583.2i	1.30415	−	0.752949i
$818$	−21370.8			−0.913461
$819$		0			0
$820$	−764.601			−0.0325622
$821$	−4408.83	+	2545.44i	−0.187417	+	0.108205i	−0.590773	−	0.806838i	$-0.701177\pi$
$821$	−4408.83	+	2545.44i	−0.187417	+	0.108205i	0.403356	+	0.915043i	$0.367844\pi$
$822$	1770.24	+	3066.14i	0.0751145	+	0.130102i
$823$	10894.9	−	18870.5i	0.461447	−	0.799250i	−0.537586	−	0.843209i	$-0.680664\pi$
$823$	10894.9	−	18870.5i	0.461447	−	0.799250i	0.999033	+	0.0439588i	$0.0139970\pi$
$824$		−	7483.94i		−	0.316402i
$825$	4486.53	+	2590.30i	0.189335	+	0.109312i
$826$	8367.77	+	4831.13i	0.352484	+	0.203507i
$827$			22544.8i			0.947955i	0.880537	+	0.473977i	$0.157182\pi$
$827$			22544.8i			0.947955i	−0.880537	+	0.473977i	$0.842818\pi$
$828$	4083.22	−	7072.34i	0.171379	−	0.296837i
$829$	−5248.91	−	9091.38i	−0.219906	−	0.380888i	0.734873	−	0.678205i	$-0.237242\pi$
$829$	−5248.91	−	9091.38i	−0.219906	−	0.380888i	−0.954779	+	0.297316i	$0.903908\pi$
$830$	4917.60	−	2839.18i	0.205653	−	0.118734i
$831$	−22105.5			−0.922780
$832$		0			0
$833$	−12794.9			−0.532193
$834$	−8695.39	+	5020.29i	−0.361027	+	0.208439i
$835$	2423.64	+	4197.87i	0.100447	+	0.173980i
$836$	−3810.72	+	6600.37i	−0.157651	+	0.273060i
$837$			24763.2i			1.02263i
$838$	−11102.7	−	6410.14i	−0.457680	−	0.264242i
$839$	−12499.5	−	7216.59i	−0.514340	−	0.296954i	0.220276	−	0.975438i	$-0.429304\pi$
$839$	−12499.5	−	7216.59i	−0.514340	−	0.296954i	−0.734616	+	0.678483i	$0.762637\pi$
$840$		−	2840.24i		−	0.116664i
$841$	1251.25	−	2167.22i	0.0513037	−	0.0888607i
$842$	−2672.97	−	4629.72i	−0.109402	−	0.189490i
$843$	−21539.2	+	12435.7i	−0.880011	+	0.508075i
$844$	−15108.6			−0.616183
$845$		0			0
$846$	−14354.5			−0.583353
$847$	−12740.4	+	7355.70i	−0.516844	+	0.298400i
$848$	5144.53	+	8910.60i	0.208330	+	0.360839i
$849$	3727.46	−	6456.15i	0.150679	−	0.260983i
$850$		−	19829.1i		−	0.800158i
$851$	24882.5	+	14365.9i	1.00230	+	0.578681i
$852$	−9897.14	−	5714.11i	−0.397970	−	0.229768i
$853$			4097.21i			0.164462i	0.996613	+	0.0822309i	$0.0262045\pi$
$853$			4097.21i			0.164462i	−0.996613	+	0.0822309i	$0.973796\pi$
$854$	−12608.4	+	21838.5i	−0.505213	+	0.875055i
$855$	5199.56	+	9005.91i	0.207978	+	0.360229i
$856$	8305.27	−	4795.05i	0.331622	−	0.191462i
$857$	5188.52			0.206810			0.103405	−	0.994639i	$-0.467026\pi$
$857$	5188.52			0.206810			0.103405	+	0.994639i	$0.467026\pi$
$858$		0			0
$859$	6351.40			0.252278			0.126139	−	0.992013i	$-0.459741\pi$
$859$	6351.40			0.252278			0.126139	+	0.992013i	$0.459741\pi$
$860$	8526.87	−	4922.99i	0.338098	−	0.195201i
$861$	732.947	+	1269.50i	0.0290114	+	0.0502491i
$862$	−5175.73	+	8964.63i	−0.204508	+	0.354219i
$863$		−	19337.4i		−	0.762751i	−0.924420	−	0.381376i	$-0.875450\pi$
$863$		−	19337.4i		−	0.762751i	0.924420	−	0.381376i	$-0.124550\pi$
$864$	3975.95	+	2295.52i	0.156556	+	0.0903878i
$865$	−4782.90	−	2761.41i	−0.188004	−	0.108544i
$866$			8343.92i			0.327411i
$867$	−18395.8	+	31862.4i	−0.720593	+	1.24810i
$868$	−5363.80	−	9290.37i	−0.209745	−	0.363290i
$869$	−4720.41	+	2725.33i	−0.184268	+	0.106387i
$870$	−6760.63			−0.263456
$871$		0			0
$872$	956.134			0.0371316
$873$	1117.87	−	645.402i	0.0433381	−	0.0250212i
$874$	12622.4	+	21862.6i	0.488510	+	0.846124i
$875$	−10768.0	+	18650.7i	−0.416029	+	0.720583i
$876$		−	15146.0i		−	0.584175i
$877$	−14740.2	−	8510.28i	−0.567552	−	0.327676i	0.188619	−	0.982050i	$-0.439599\pi$
$877$	−14740.2	−	8510.28i	−0.567552	−	0.327676i	−0.756171	+	0.654374i	$0.772932\pi$
$878$	18471.5	+	10664.5i	0.710005	+	0.409921i
$879$		−	7566.42i		−	0.290340i
$880$	−1066.93	+	1847.98i	−0.0408709	+	0.0707904i
$881$	−7506.10	−	13000.9i	−0.287045	−	0.497177i	0.686058	−	0.727547i	$-0.259340\pi$
$881$	−7506.10	−	13000.9i	−0.287045	−	0.497177i	−0.973103	+	0.230370i	$0.926006\pi$
$882$	−2766.01	+	1596.96i	−0.105597	+	0.0609664i
$883$	46753.9			1.78187			0.890936	−	0.454129i	$-0.150049\pi$
$883$	46753.9			1.78187			0.890936	+	0.454129i	$0.150049\pi$
$884$		0			0
$885$	7104.31			0.269840
$886$	3675.69	−	2122.16i	0.139376	−	0.0804688i
$887$	5953.40	+	10311.6i	0.225361	+	0.390337i	0.956428	−	0.291969i	$-0.0943104\pi$
$887$	5953.40	+	10311.6i	0.225361	+	0.390337i	−0.731066	+	0.682306i	$0.760977\pi$
$888$	−2972.22	+	5148.04i	−0.112321	+	0.194546i
$889$			28868.6i			1.08911i
$890$	3821.53	+	2206.36i	0.143930	+	0.0830982i
$891$	−972.292	−	561.353i	−0.0365578	−	0.0211067i
$892$			17465.2i			0.655582i
$893$	22186.8	−	38428.8i	0.831416	−	1.44006i
$894$	5838.62	+	10112.8i	0.218426	+	0.378324i
$895$	−5090.15	+	2938.80i	−0.190106	+	0.109758i
$896$	−1988.87			−0.0741556
$897$		0			0
$898$	−30570.8			−1.13604
$899$	−22113.9	+	12767.5i	−0.820400	+	0.473658i
$900$	−2474.92	−	4286.68i	−0.0916636	−	0.158766i
$901$	−40504.1	+	70155.2i	−1.49766	+	2.59402i
$902$		−	1101.32i		−	0.0406542i
$903$	−16347.7	−	9438.37i	−0.602457	−	0.347829i
$904$	−4203.28	−	2426.77i	−0.154645	−	0.0892843i
$905$		−	9708.63i		−	0.356603i
$906$	6460.31	−	11189.6i	0.236898	−	0.410319i
$907$	14577.2	+	25248.5i	0.533660	+	0.924326i	0.999227	+	0.0393134i	$0.0125171\pi$
$907$	14577.2	+	25248.5i	0.533660	+	0.924326i	−0.465567	+	0.885013i	$0.654150\pi$
$908$	6328.88	−	3653.98i	0.231312	−	0.133548i
$909$	11265.7			0.411068
$910$		0			0
$911$	−6426.94			−0.233737			−0.116868	−	0.993147i	$-0.537286\pi$
$911$	−6426.94			−0.233737			−0.116868	+	0.993147i	$0.537286\pi$
$912$	−4523.24	+	2611.49i	−0.164232	+	0.0948193i
$913$	4089.52	+	7083.26i	0.148240	+	0.256760i
$914$	−8533.93	+	14781.2i	−0.308837	+	0.534922i
$915$			18541.1i			0.669889i
$916$	15160.7	+	8753.03i	0.546860	+	0.315730i
$917$	−25132.7	−	14510.4i	−0.905075	−	0.522545i
$918$			36146.3i			1.29957i
$919$	13666.7	−	23671.5i	0.490560	−	0.849674i	−0.509381	−	0.860541i	$-0.670126\pi$
$919$	13666.7	−	23671.5i	0.490560	−	0.849674i	0.999941	+	0.0108669i	$0.00345909\pi$
$920$	3534.04	+	6121.13i	0.126645	+	0.219356i
$921$	−19291.9	+	11138.2i	−0.690216	+	0.398496i
$922$	12413.5			0.443404
$923$		0			0
$924$	4091.06			0.145656
$925$	15081.8	−	8707.46i	0.536092	−	0.309513i
$926$	14278.3	+	24730.8i	0.506711	+	0.877649i
$927$	7354.28	−	12738.0i	0.260568	−	0.451317i
$928$			4734.11i			0.167462i
$929$	−7564.48	−	4367.36i	−0.267150	−	0.154239i	0.360442	−	0.932782i	$-0.382626\pi$
$929$	−7564.48	−	4367.36i	−0.267150	−	0.154239i	−0.627592	+	0.778542i	$0.715959\pi$
$930$	−6830.87	−	3943.80i	−0.240853	−	0.139056i
$931$		−	9873.29i		−	0.347566i
$932$	−9447.78	+	16364.0i	−0.332052	+	0.575131i
$933$	1369.83	+	2372.61i	0.0480667	+	0.0832539i
$934$	3096.17	−	1787.57i	0.108469	−	0.0626244i
$935$	−16800.5			−0.587630
$936$		0			0
$937$	38518.8			1.34296			0.671480	−	0.741023i	$-0.265659\pi$
$937$	38518.8			1.34296			0.671480	+	0.741023i	$0.265659\pi$
$938$	188.511	−	108.837i	0.00656193	−	0.00378853i
$939$	−10358.9	−	17942.2i	−0.360012	−	0.623559i
$940$	6211.92	−	10759.4i	0.215543	−	0.373332i
$941$			33183.6i			1.14958i	0.818301	+	0.574790i	$0.194916\pi$
$941$			33183.6i			1.14958i	−0.818301	+	0.574790i	$0.805084\pi$
$942$	−1599.84	−	923.666i	−0.0553349	−	0.0319476i
$943$	−3159.21	−	1823.97i	−0.109097	−	0.0629870i
$944$		−	4974.77i		−	0.171520i
$945$	7583.94	−	13135.8i	0.261064	−	0.452176i
$946$	7091.04	+	12282.0i	0.243710	+	0.422118i
$947$	−24763.2	+	14297.1i	−0.849733	+	0.490594i	−0.860561	−	0.509348i	$-0.829887\pi$
$947$	−24763.2	+	14297.1i	−0.849733	+	0.490594i	0.0108276	+	0.999941i	$0.496553\pi$
$948$	−3735.34			−0.127973
$949$		0			0
$950$	15301.3			0.522569
$951$	25728.0	−	14854.1i	0.877274	−	0.506494i
$952$	−7829.42	−	13560.9i	−0.266547	−	0.461673i
$953$	−4792.89	+	8301.53i	−0.162914	+	0.282175i	−0.935913	−	0.352232i	$-0.885423\pi$
$953$	−4792.89	+	8301.53i	−0.162914	+	0.282175i	0.772999	+	0.634408i	$0.218756\pi$
$954$			20221.6i			0.686268i
$955$	4622.25	+	2668.66i	0.156621	+	0.0904249i
$956$	8009.67	+	4624.38i	0.270974	+	0.156447i
$957$		−	9737.96i		−	0.328927i
$958$	13735.6	−	23790.7i	0.463232	−	0.802342i
$959$	−4095.40	−	7093.45i	−0.137901	−	0.238852i
$960$	−1266.43	+	731.171i	−0.0425768	+	0.0245817i
$961$	−0.495919			−1.66466e−5
$962$		0			0
$963$	18847.9			0.630701
$964$	24760.0	−	14295.2i	0.827247	−	0.477611i
$965$	−10250.0	−	17753.5i	−0.341926	−	0.592233i
$966$	6775.46	−	11735.4i	0.225670	−	0.390871i
$967$			5738.23i			0.190826i	0.995438	+	0.0954132i	$0.0304172\pi$
$967$			5738.23i			0.190826i	−0.995438	+	0.0954132i	$0.969583\pi$
$968$	6559.62	+	3787.20i	0.217804	+	0.125749i
$969$	−35612.5	−	20560.9i	−1.18064	−	0.681642i
$970$			1117.19i			0.0369804i
$971$	23508.0	−	40717.0i	0.776938	−	1.34570i	−0.156760	−	0.987637i	$-0.550105\pi$
$971$	23508.0	−	40717.0i	0.776938	−	1.34570i	0.933699	−	0.358060i	$-0.116562\pi$
$972$	7362.67	+	12752.5i	0.242961	+	0.420820i
$973$	20116.6	−	11614.3i	0.662804	−	0.382670i
$974$	34038.1			1.11976
$975$		0			0
$976$	12983.3			0.425805
$977$	−31456.5	+	18161.4i	−1.03007	+	0.594713i	−0.917006	−	0.398874i	$-0.869401\pi$
$977$	−31456.5	+	18161.4i	−1.03007	+	0.594713i	−0.113068	+	0.993587i	$0.536068\pi$
$978$	13004.2	+	22524.0i	0.425184	+	0.736440i
$979$	−3178.03	+	5504.50i	−0.103749	+	0.179698i
$980$		−	2764.34i		−	0.0901058i
$981$	1627.38	+	939.569i	0.0529646	+	0.0305791i
$982$	−23629.8	−	13642.7i	−0.767879	−	0.443335i
$983$			33276.4i			1.07971i	0.841759	+	0.539854i	$0.181520\pi$
$983$			33276.4i			1.07971i	−0.841759	+	0.539854i	$0.818480\pi$
$984$	377.369	−	653.623i	0.0122257	−	0.0211755i
$985$	−9285.17	−	16082.4i	−0.300356	−	0.520231i
$986$	−32279.2	+	18636.4i	−1.04257	+	0.601930i
$987$	−23819.0			−0.768154
$988$		0			0
$989$	46975.7			1.51035
$990$	−3631.94	+	2096.90i	−0.116596	+	0.0673170i
$991$	23175.4	+	40141.0i	0.742877	+	1.28670i	0.951180	+	0.308636i	$0.0998725\pi$
$991$	23175.4	+	40141.0i	0.742877	+	1.28670i	−0.208303	+	0.978064i	$0.566794\pi$
$992$	−2761.63	+	4783.29i	−0.0883891	+	0.153094i
$993$		−	31940.0i		−	1.02073i
$994$	22896.8	+	13219.5i	0.730627	+	0.421827i
$995$	−5666.25	−	3271.41i	−0.180535	−	0.104232i
$996$			5605.11i			0.178318i
$997$	−9198.72	+	15932.6i	−0.292203	+	0.506110i	−0.974330	−	0.225123i	$-0.927722\pi$
$997$	−9198.72	+	15932.6i	−0.292203	+	0.506110i	0.682127	+	0.731233i	$0.261055\pi$
$998$	4507.63	+	7807.44i	0.142972	+	0.247636i
$999$	−27492.3	+	15872.7i	−0.870690	+	0.502693i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	338.4.e.i.23.9		24
13.2	odd	12		338.4.a.o.1.4	yes	6
13.3	even	3		338.4.b.h.337.10		12
13.4	even	6	inner	338.4.e.i.147.9		24
13.5	odd	4		338.4.c.o.315.3		12
13.6	odd	12		338.4.c.o.191.3		12
13.7	odd	12		338.4.c.p.191.3		12
13.8	odd	4		338.4.c.p.315.3		12
13.9	even	3	inner	338.4.e.i.147.6		24
13.10	even	6		338.4.b.h.337.4		12
13.11	odd	12		338.4.a.n.1.4	✓	6
13.12	even	2	inner	338.4.e.i.23.6		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
338.4.a.n.1.4	✓	6	13.11	odd	12
338.4.a.o.1.4	yes	6	13.2	odd	12
338.4.b.h.337.4		12	13.10	even	6
338.4.b.h.337.10		12	13.3	even	3
338.4.c.o.191.3		12	13.6	odd	12
338.4.c.o.315.3		12	13.5	odd	4
338.4.c.p.191.3		12	13.7	odd	12
338.4.c.p.315.3		12	13.8	odd	4
338.4.e.i.23.6		24	13.12	even	2	inner
338.4.e.i.23.9		24	1.1	even	1	trivial
338.4.e.i.147.6		24	13.9	even	3	inner
338.4.e.i.147.9		24	13.4	even	6	inner

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:	\( N \)	\(=\)	\( 338 = 2 \cdot 13^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	338.e (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.73205 - 1.00000i) q^{2} +(-1.67908 - 2.90825i) q^{3} +(2.00000 - 3.46410i) q^{4} +6.80407i q^{5} +(-5.81649 - 3.35815i) q^{6} +(13.4563 + 7.76902i) q^{7} -8.00000i q^{8} +(7.86140 - 13.6163i) q^{9} +(6.80407 + 11.7850i) q^{10} +(-16.9750 + 9.80052i) q^{11} -13.4326 q^{12} +31.0761 q^{14} +(19.7879 - 11.4246i) q^{15} +(-8.00000 - 13.8564i) q^{16} +(62.9859 - 109.095i) q^{17} -31.4456i q^{18} +(84.1839 + 48.6036i) q^{19} +(23.5700 + 13.6081i) q^{20} -52.1791i q^{21} +(-19.6010 + 33.9500i) q^{22} +(64.9251 + 112.454i) q^{23} +(-23.2660 + 13.4326i) q^{24} +78.7047 q^{25} -143.470 q^{27} +(53.8253 - 31.0761i) q^{28} +(-73.9704 - 128.121i) q^{29} +(22.8491 - 39.5758i) q^{30} -172.602i q^{31} +(-27.7128 - 16.0000i) q^{32} +(57.0047 + 32.9117i) q^{33} -251.944i q^{34} +(-52.8609 + 91.5578i) q^{35} +(-31.4456 - 54.4654i) q^{36} +(191.625 - 110.635i) q^{37} +194.414 q^{38} +54.4325 q^{40} +(-24.3297 + 14.0468i) q^{41} +(-52.1791 - 90.3769i) q^{42} +(180.884 - 313.301i) q^{43} +78.4042i q^{44} +(92.6465 + 53.4895i) q^{45} +(224.907 + 129.850i) q^{46} -456.486i q^{47} +(-26.8652 + 46.5319i) q^{48} +(-50.7848 - 87.9618i) q^{49} +(136.321 - 78.7047i) q^{50} -423.033 q^{51} -643.067 q^{53} +(-248.497 + 143.470i) q^{54} +(-66.6834 - 115.499i) q^{55} +(62.1521 - 107.651i) q^{56} -326.437i q^{57} +(-256.241 - 147.941i) q^{58} +(269.267 + 155.461i) q^{59} -91.3964i q^{60} +(-405.728 + 702.742i) q^{61} +(-172.602 - 298.956i) q^{62} +(211.571 - 122.151i) q^{63} -64.0000 q^{64} +131.647 q^{66} +(6.06611 - 3.50227i) q^{67} +(-251.944 - 436.379i) q^{68} +(218.028 - 377.636i) q^{69} +211.444i q^{70} +(736.799 + 425.391i) q^{71} +(-108.931 - 62.8912i) q^{72} +1127.56i q^{73} +(221.269 - 383.249i) q^{74} +(-132.151 - 228.893i) q^{75} +(336.735 - 194.414i) q^{76} -304.562 q^{77} +278.080 q^{79} +(94.2799 - 54.4325i) q^{80} +(28.6389 + 49.6041i) q^{81} +(-28.0935 + 48.6594i) q^{82} -417.276i q^{83} +(-180.754 - 104.358i) q^{84} +(742.288 + 428.560i) q^{85} -723.537i q^{86} +(-248.404 + 430.249i) q^{87} +(78.4042 + 135.800i) q^{88} +(280.827 - 162.136i) q^{89} +213.958 q^{90} +519.401 q^{92} +(-501.970 + 289.812i) q^{93} +(-456.486 - 790.657i) q^{94} +(-330.702 + 572.793i) q^{95} +107.461i q^{96} +(71.0986 + 41.0488i) q^{97} +(-175.924 - 101.570i) q^{98} +308.183i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 18 q^{3} + 48 q^{4} - 226 q^{9} + 72 q^{10} - 144 q^{12} + 200 q^{14} - 192 q^{16} + 198 q^{17} - 148 q^{22} + 534 q^{23} - 1472 q^{25} + 2676 q^{27} + 238 q^{29} + 472 q^{30} - 1228 q^{35} + 904 q^{36}+ \cdots - 8186 q^{95}+O(q^{100}) \) 24 * q - 18 * q^3 + 48 * q^4 - 226 * q^9 + 72 * q^10 - 144 * q^12 + 200 * q^14 - 192 * q^16 + 198 * q^17 - 148 * q^22 + 534 * q^23 - 1472 * q^25 + 2676 * q^27 + 238 * q^29 + 472 * q^30 - 1228 * q^35 + 904 * q^36 + 648 * q^38 + 576 * q^40 + 104 * q^42 + 856 * q^43 - 288 * q^48 + 1798 * q^49 - 1156 * q^51 + 356 * q^53 - 2252 * q^55 + 400 * q^56 - 3408 * q^61 - 2500 * q^62 - 1536 * q^64 + 6096 * q^66 - 792 * q^68 + 2336 * q^69 - 1096 * q^74 + 3596 * q^75 - 11160 * q^77 - 3500 * q^79 - 6676 * q^81 + 4560 * q^82 - 3204 * q^87 + 592 * q^88 + 9720 * q^90 + 4272 * q^92 + 3944 * q^94 - 8186 * q^95

Introduction

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