LMFDB - Embedded newform 224.4.t.a.177.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [224,4,Mod(81,224)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(224, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 3, 4]))

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

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

chi := DirichletCharacter("224.81");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 224 = 2^{5} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	224.t (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:	$13.2164278413$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{6})$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			177.8
Character	$\chi$	$=$	224.177
Dual form			224.4.t.a.81.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-2.65541 + 1.53310i) q^{3} +(-7.57927 - 4.37589i) q^{5} +(-17.7736 + 5.20552i) q^{7} +(-8.79921 + 15.2407i) q^{9} +(46.4189 - 26.8000i) q^{11} -32.2514i q^{13} +26.8347 q^{15} +(31.9026 + 55.2570i) q^{17} +(74.9753 + 43.2870i) q^{19} +(39.2157 - 41.0716i) q^{21} +(64.1008 - 111.026i) q^{23} +(-24.2031 - 41.9211i) q^{25} -136.748i q^{27} -82.8256i q^{29} +(118.872 + 205.892i) q^{31} +(-82.1740 + 142.330i) q^{33} +(157.490 + 38.3215i) q^{35} +(183.998 + 106.231i) q^{37} +(49.4447 + 85.6407i) q^{39} +348.562 q^{41} -221.770i q^{43} +(133.383 - 77.0088i) q^{45} +(-123.164 + 213.326i) q^{47} +(288.805 - 185.042i) q^{49} +(-169.429 - 97.8198i) q^{51} +(403.213 - 232.795i) q^{53} -469.095 q^{55} -265.453 q^{57} +(-163.759 + 94.5465i) q^{59} +(-162.805 - 93.9955i) q^{61} +(77.0584 - 316.687i) q^{63} +(-141.129 + 244.442i) q^{65} +(-155.578 + 89.8230i) q^{67} +393.092i q^{69} +394.379 q^{71} +(-428.204 - 741.671i) q^{73} +(128.538 + 74.2116i) q^{75} +(-685.525 + 717.967i) q^{77} +(44.9579 - 77.8694i) q^{79} +(-27.9308 - 48.3776i) q^{81} -199.293i q^{83} -558.410i q^{85} +(126.980 + 219.936i) q^{87} +(-508.742 + 881.168i) q^{89} +(167.886 + 573.225i) q^{91} +(-631.306 - 364.485i) q^{93} +(-378.839 - 656.168i) q^{95} +196.625 q^{97} +943.274i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 4 q^{7} + 160 q^{9} + 116 q^{15} - 2 q^{17} - 162 q^{23} + 348 q^{25} + 374 q^{31} - 110 q^{33} - 52 q^{39} - 8 q^{41} + 738 q^{47} + 356 q^{49} + 2268 q^{55} - 452 q^{57} - 668 q^{63} + 248 q^{65}+ \cdots + 1672 q^{97}+O(q^{100}) $ 44 * q + 4 * q^7 + 160 * q^9 + 116 * q^15 - 2 * q^17 - 162 * q^23 + 348 * q^25 + 374 * q^31 - 110 * q^33 - 52 * q^39 - 8 * q^41 + 738 * q^47 + 356 * q^49 + 2268 * q^55 - 452 * q^57 - 668 * q^63 + 248 * q^65 - 1248 * q^71 - 218 * q^73 - 298 * q^79 - 1050 * q^81 - 2140 * q^87 + 422 * q^89 + 2434 * q^95 + 1672 * q^97

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/224\mathbb{Z}\right)^\times$.

$n$	$127$	$129$	$197$
$\chi(n)$	$1$	$e\left(\frac{1}{3}\right)$	$-1$

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
$3$	−2.65541	+	1.53310i	−0.511033	+	0.295045i	−0.733258	−	0.679950i	$-0.762001\pi$
$3$	−2.65541	+	1.53310i	−0.511033	+	0.295045i	0.222225	+	0.974995i	$0.428668\pi$
$4$		0			0
$5$	−7.57927	−	4.37589i	−0.677910	−	0.391392i	0.121157	−	0.992633i	$-0.461340\pi$
$5$	−7.57927	−	4.37589i	−0.677910	−	0.391392i	−0.799067	+	0.601242i	$0.794673\pi$
$6$		0			0
$7$	−17.7736	+	5.20552i	−0.959687	+	0.281072i
$7$	−17.7736	+	5.20552i	−0.959687	+	0.281072i
$8$		0			0
$9$	−8.79921	+	15.2407i	−0.325897	+	0.564470i
$10$		0			0
$11$	46.4189	−	26.8000i	1.27235	−	0.734590i	0.296918	−	0.954903i	$-0.404041\pi$
$11$	46.4189	−	26.8000i	1.27235	−	0.734590i	0.975429	+	0.220313i	$0.0707079\pi$
$12$		0			0
$13$		−	32.2514i		−	0.688072i	−0.938956	−	0.344036i	$-0.888206\pi$
$13$		−	32.2514i		−	0.688072i	0.938956	−	0.344036i	$-0.111794\pi$
$14$		0			0
$15$	26.8347			0.461913
$16$		0			0
$17$	31.9026	+	55.2570i	0.455149	+	0.788340i	0.998697	−	0.0510376i	$-0.0162528\pi$
$17$	31.9026	+	55.2570i	0.455149	+	0.788340i	−0.543548	+	0.839378i	$0.682920\pi$
$18$		0			0
$19$	74.9753	+	43.2870i	0.905291	+	0.522670i	0.878913	−	0.476982i	$-0.158269\pi$
$19$	74.9753	+	43.2870i	0.905291	+	0.522670i	0.0263778	+	0.999652i	$0.491603\pi$
$20$		0			0
$21$	39.2157	−	41.0716i	0.407503	−	0.426788i
$22$		0			0
$23$	64.1008	−	111.026i	0.581128	−	1.00654i	−0.414218	−	0.910178i	$-0.635945\pi$
$23$	64.1008	−	111.026i	0.581128	−	1.00654i	0.995346	−	0.0963651i	$-0.0307216\pi$
$24$		0			0
$25$	−24.2031	−	41.9211i	−0.193625	−	0.335368i
$26$		0			0
$27$		−	136.748i		−	0.974707i
$28$		0			0
$29$		−	82.8256i		−	0.530356i	−0.964199	−	0.265178i	$-0.914569\pi$
$29$		−	82.8256i		−	0.530356i	0.964199	−	0.265178i	$-0.0854307\pi$
$30$		0			0
$31$	118.872	+	205.892i	0.688710	+	1.19288i	0.972255	+	0.233922i	$0.0751559\pi$
$31$	118.872	+	205.892i	0.688710	+	1.19288i	−0.283546	+	0.958959i	$0.591511\pi$
$32$		0			0
$33$	−82.1740	+	142.330i	−0.433474	+	0.750800i
$34$		0			0
$35$	157.490	+	38.3215i	0.760591	+	0.185072i
$36$		0			0
$37$	183.998	+	106.231i	0.817542	+	0.472008i	0.849568	−	0.527479i	$-0.176863\pi$
$37$	183.998	+	106.231i	0.817542	+	0.472008i	−0.0320263	+	0.999487i	$0.510196\pi$
$38$		0			0
$39$	49.4447	+	85.6407i	0.203012	+	0.351628i
$40$		0			0
$41$	348.562			1.32771			0.663856	−	0.747860i	$-0.268919\pi$
$41$	348.562			1.32771			0.663856	+	0.747860i	$0.268919\pi$
$42$		0			0
$43$		−	221.770i		−	0.786504i	−0.919431	−	0.393252i	$-0.871350\pi$
$43$		−	221.770i		−	0.786504i	0.919431	−	0.393252i	$-0.128650\pi$
$44$		0			0
$45$	133.383	−	77.0088i	0.441857	−	0.255106i
$46$		0			0
$47$	−123.164	+	213.326i	−0.382239	+	0.662058i	−0.991382	−	0.131003i	$-0.958180\pi$
$47$	−123.164	+	213.326i	−0.382239	+	0.662058i	0.609143	+	0.793061i	$0.291514\pi$
$48$		0			0
$49$	288.805	−	185.042i	0.841997	−	0.539482i
$50$		0			0
$51$	−169.429	−	97.8198i	−0.465192	−	0.268579i
$52$		0			0
$53$	403.213	−	232.795i	1.04501	−	0.603338i	0.123763	−	0.992312i	$-0.460504\pi$
$53$	403.213	−	232.795i	1.04501	−	0.603338i	0.921249	+	0.388974i	$0.127171\pi$
$54$		0			0
$55$	−469.095			−1.15005
$56$		0			0
$57$	−265.453			−0.616845
$58$		0			0
$59$	−163.759	+	94.5465i	−0.361350	+	0.208626i	−0.669673	−	0.742656i	$-0.733566\pi$
$59$	−163.759	+	94.5465i	−0.361350	+	0.208626i	0.308323	+	0.951282i	$0.400232\pi$
$60$		0			0
$61$	−162.805	−	93.9955i	−0.341722	−	0.197293i	0.319311	−	0.947650i	$-0.396548\pi$
$61$	−162.805	−	93.9955i	−0.341722	−	0.197293i	−0.661033	+	0.750357i	$0.729882\pi$
$62$		0			0
$63$	77.0584	−	316.687i	0.154102	−	0.633314i
$64$		0			0
$65$	−141.129	+	244.442i	−0.269306	+	0.466451i
$66$		0			0
$67$	−155.578	+	89.8230i	−0.283685	+	0.163786i	−0.635090	−	0.772438i	$-0.719037\pi$
$67$	−155.578	+	89.8230i	−0.283685	+	0.163786i	0.351406	+	0.936223i	$0.385704\pi$
$68$		0			0
$69$			393.092i			0.685836i
$70$		0			0
$71$	394.379			0.659214			0.329607	−	0.944118i	$-0.393084\pi$
$71$	394.379			0.659214			0.329607	+	0.944118i	$0.393084\pi$
$72$		0			0
$73$	−428.204	−	741.671i	−0.686541	−	1.18912i	−0.972950	−	0.231016i	$-0.925795\pi$
$73$	−428.204	−	741.671i	−0.686541	−	1.18912i	0.286409	−	0.958107i	$-0.407538\pi$
$74$		0			0
$75$	128.538	+	74.2116i	0.197898	+	0.114256i
$76$		0			0
$77$	−685.525	+	717.967i	−1.01458	+	1.06260i
$78$		0			0
$79$	44.9579	−	77.8694i	0.0640273	−	0.110899i	−0.832235	−	0.554423i	$-0.812939\pi$
$79$	44.9579	−	77.8694i	0.0640273	−	0.110899i	0.896262	+	0.443525i	$0.146272\pi$
$80$		0			0
$81$	−27.9308	−	48.3776i	−0.0383139	−	0.0663616i
$82$		0			0
$83$		−	199.293i		−	0.263557i	−0.991279	−	0.131778i	$-0.957931\pi$
$83$		−	199.293i		−	0.263557i	0.991279	−	0.131778i	$-0.0420688\pi$
$84$		0			0
$85$		−	558.410i		−	0.712565i
$86$		0			0
$87$	126.980	+	219.936i	0.156479	+	0.271030i
$88$		0			0
$89$	−508.742	+	881.168i	−0.605917	+	1.04948i	0.385989	+	0.922503i	$0.373860\pi$
$89$	−508.742	+	881.168i	−0.605917	+	1.04948i	−0.991906	+	0.126975i	$0.959473\pi$
$90$		0			0
$91$	167.886	+	573.225i	0.193398	+	0.660334i
$92$		0			0
$93$	−631.306	−	364.485i	−0.703907	−	0.406401i
$94$		0			0
$95$	−378.839	−	656.168i	−0.409137	−	0.708647i
$96$		0			0
$97$	196.625			0.205816			0.102908	−	0.994691i	$-0.467185\pi$
$97$	196.625			0.205816			0.102908	+	0.994691i	$0.467185\pi$
$98$		0			0
$99$			943.274i			0.957602i
$100$		0			0
$101$	−1741.62	+	1005.52i	−1.71582	+	0.990627i	−0.789609	+	0.613610i	$0.789717\pi$
$101$	−1741.62	+	1005.52i	−1.71582	+	0.990627i	−0.926207	+	0.377017i	$0.876950\pi$
$102$		0			0
$103$	298.306	−	516.681i	0.285369	−	0.494273i	−0.687330	−	0.726345i	$-0.741217\pi$
$103$	298.306	−	516.681i	0.285369	−	0.494273i	0.972698	+	0.232073i	$0.0745507\pi$
$104$		0			0
$105$	−476.951	+	139.689i	−0.443292	+	0.129831i
$106$		0			0
$107$	−355.200	−	205.075i	−0.320920	−	0.185283i	0.330882	−	0.943672i	$-0.392654\pi$
$107$	−355.200	−	205.075i	−0.320920	−	0.185283i	−0.651803	+	0.758389i	$0.725987\pi$
$108$		0			0
$109$	755.806	−	436.365i	0.664156	−	0.383451i	−0.129702	−	0.991553i	$-0.541402\pi$
$109$	755.806	−	436.365i	0.664156	−	0.383451i	0.793859	+	0.608102i	$0.208069\pi$
$110$		0			0
$111$	−651.452			−0.557055
$112$		0			0
$113$	1088.92			0.906521			0.453261	−	0.891378i	$-0.350261\pi$
$113$	1088.92			0.906521			0.453261	+	0.891378i	$0.350261\pi$
$114$		0			0
$115$	−971.674	+	560.996i	−0.787905	+	0.454897i
$116$		0			0
$117$	491.534	+	283.787i	0.388396	+	0.224240i
$118$		0			0
$119$	−854.668	−	816.048i	−0.658380	−	0.628630i
$120$		0			0
$121$	770.975	−	1335.37i	0.579245	−	1.00328i
$122$		0			0
$123$	−925.573	+	534.380i	−0.678505	+	0.391735i
$124$		0			0
$125$			1517.61i			1.08592i
$126$		0			0
$127$	1223.26			0.854699			0.427349	−	0.904087i	$-0.359447\pi$
$127$	1223.26			0.854699			0.427349	+	0.904087i	$0.359447\pi$
$128$		0			0
$129$	339.996	+	588.891i	0.232054	+	0.401930i
$130$		0			0
$131$	2126.40	+	1227.68i	1.41820	+	0.818798i	0.996141	−	0.0877697i	$-0.0279740\pi$
$131$	2126.40	+	1227.68i	1.41820	+	0.818798i	0.422060	+	0.906568i	$0.361307\pi$
$132$		0			0
$133$	−1557.92	−	379.083i	−1.01570	−	0.247148i
$134$		0			0
$135$	−598.393	+	1036.45i	−0.381492	+	0.660764i
$136$		0			0
$137$	−1219.84	−	2112.83i	−0.760716	−	1.31760i	−0.942482	−	0.334257i	$-0.891515\pi$
$137$	−1219.84	−	2112.83i	−0.760716	−	1.31760i	0.181766	−	0.983342i	$-0.441819\pi$
$138$		0			0
$139$		−	2783.96i		−	1.69879i	−0.527756	−	0.849396i	$-0.676967\pi$
$139$		−	2783.96i		−	1.69879i	0.527756	−	0.849396i	$-0.323033\pi$
$140$		0			0
$141$		−	755.288i		−	0.451112i
$142$		0			0
$143$	−864.337	−	1497.07i	−0.505451	−	0.875466i
$144$		0			0
$145$	−362.436	+	627.757i	−0.207577	+	0.359534i
$146$		0			0
$147$	−483.207	+	934.129i	−0.271117	+	0.524120i
$148$		0			0
$149$	1086.95	+	627.552i	0.597628	+	0.345041i	0.768108	−	0.640320i	$-0.221198\pi$
$149$	1086.95	+	627.552i	0.597628	+	0.345041i	−0.170480	+	0.985361i	$0.554532\pi$
$150$		0			0
$151$	1374.36	+	2380.46i	0.740689	+	1.28291i	0.952182	+	0.305531i	$0.0988340\pi$
$151$	1374.36	+	2380.46i	0.740689	+	1.28291i	−0.211493	+	0.977379i	$0.567833\pi$
$152$		0			0
$153$	−1122.87			−0.593325
$154$		0			0
$155$		−	2080.68i		−	1.07822i
$156$		0			0
$157$	2173.05	−	1254.61i	1.10464	−	0.637764i	0.167204	−	0.985922i	$-0.446526\pi$
$157$	2173.05	−	1254.61i	1.10464	−	0.637764i	0.937436	+	0.348158i	$0.113193\pi$
$158$		0			0
$159$	−713.797	+	1236.33i	−0.356024	+	0.616651i
$160$		0			0
$161$	−561.357	+	2307.01i	−0.274790	+	1.12930i
$162$		0			0
$163$	−2259.90	−	1304.75i	−1.08594	−	0.626971i	−0.153451	−	0.988156i	$-0.549039\pi$
$163$	−2259.90	−	1304.75i	−1.08594	−	0.626971i	−0.932494	+	0.361186i	$0.882372\pi$
$164$		0			0
$165$	1245.64	−	719.169i	0.587714	−	0.339317i
$166$		0			0
$167$	695.155			0.322112			0.161056	−	0.986945i	$-0.448510\pi$
$167$	695.155			0.322112			0.161056	+	0.986945i	$0.448510\pi$
$168$		0			0
$169$	1156.85			0.526557
$170$		0			0
$171$	−1319.45	+	761.783i	−0.590062	+	0.340673i
$172$		0			0
$173$	1543.24	+	890.989i	0.678209	+	0.391564i	0.799180	−	0.601092i	$-0.205267\pi$
$173$	1543.24	+	890.989i	0.678209	+	0.391564i	−0.120971	+	0.992656i	$0.538601\pi$
$174$		0			0
$175$	648.399	+	619.100i	0.280082	+	0.267426i
$176$		0			0
$177$	289.899	−	502.119i	0.123108	−	0.213229i
$178$		0			0
$179$	2087.67	−	1205.32i	0.871730	−	0.503293i	0.00380701	−	0.999993i	$-0.498788\pi$
$179$	2087.67	−	1205.32i	0.871730	−	0.503293i	0.867923	+	0.496699i	$0.165455\pi$
$180$		0			0
$181$		−	2234.05i		−	0.917435i	−0.888582	−	0.458717i	$-0.848309\pi$
$181$		−	2234.05i		−	0.917435i	0.888582	−	0.458717i	$-0.151691\pi$
$182$		0			0
$183$	576.418			0.232842
$184$		0			0
$185$	−929.712	−	1610.31i	−0.369480	−	0.639958i
$186$		0			0
$187$	2961.77	+	1709.98i	1.15821	+	0.668695i
$188$		0			0
$189$	711.843	+	2430.50i	0.273963	+	0.935414i
$190$		0			0
$191$	−364.827	+	631.899i	−0.138209	+	0.239385i	−0.926819	−	0.375509i	$-0.877468\pi$
$191$	−364.827	+	631.899i	−0.138209	+	0.239385i	0.788610	+	0.614894i	$0.210801\pi$
$192$		0			0
$193$	2388.81	+	4137.54i	0.890934	+	1.54314i	0.838757	+	0.544506i	$0.183283\pi$
$193$	2388.81	+	4137.54i	0.890934	+	1.54314i	0.0521772	+	0.998638i	$0.483384\pi$
$194$		0			0
$195$		−	865.458i		−	0.317829i
$196$		0			0
$197$		−	2330.88i		−	0.842987i	−0.906832	−	0.421493i	$-0.861506\pi$
$197$		−	2330.88i		−	0.842987i	0.906832	−	0.421493i	$-0.138494\pi$
$198$		0			0
$199$	−1720.27	−	2979.60i	−0.612799	−	1.06140i	−0.990766	−	0.135580i	$-0.956710\pi$
$199$	−1720.27	−	2979.60i	−0.612799	−	1.06140i	0.377967	−	0.925819i	$-0.376623\pi$
$200$		0			0
$201$	275.415	−	477.033i	0.0966483	−	0.167400i
$202$		0			0
$203$	431.150	+	1472.11i	0.149068	+	0.508976i
$204$		0			0
$205$	−2641.84	−	1525.27i	−0.900070	−	0.519656i
$206$		0			0
$207$	1128.07	+	1953.88i	0.378775	+	0.656058i
$208$		0			0
$209$	4640.36			1.53579
$210$		0			0
$211$		−	4280.43i		−	1.39657i	−0.715818	−	0.698287i	$-0.753946\pi$
$211$		−	4280.43i		−	1.39657i	0.715818	−	0.698287i	$-0.246054\pi$
$212$		0			0
$213$	−1047.24	+	604.623i	−0.336880	+	0.194498i
$214$		0			0
$215$	−970.443	+	1680.86i	−0.307831	+	0.533179i
$216$		0			0
$217$	−3184.56	−	3040.66i	−0.996231	−	0.951215i
$218$		0			0
$219$	2274.11	+	1312.96i	0.701690	+	0.405121i
$220$		0			0
$221$	1782.12	−	1028.91i	0.542435	−	0.313175i
$222$		0			0
$223$	3964.54			1.19052			0.595258	−	0.803535i	$-0.297050\pi$
$223$	3964.54			1.19052			0.595258	+	0.803535i	$0.297050\pi$
$224$		0			0
$225$	851.874			0.252407
$226$		0			0
$227$	1560.76	−	901.104i	0.456349	−	0.263473i	−0.254159	−	0.967162i	$-0.581799\pi$
$227$	1560.76	−	901.104i	0.456349	−	0.263473i	0.710508	+	0.703689i	$0.248465\pi$
$228$		0			0
$229$	3326.21	+	1920.39i	0.959835	+	0.554161i	0.896122	−	0.443807i	$-0.146373\pi$
$229$	3326.21	+	1920.39i	0.959835	+	0.554161i	0.0637125	+	0.997968i	$0.479706\pi$
$230$		0			0
$231$	719.632	−	2957.47i	0.204971	−	0.842370i
$232$		0			0
$233$	−282.326	+	489.004i	−0.0793812	+	0.137492i	−0.902983	−	0.429676i	$-0.858628\pi$
$233$	−282.326	+	489.004i	−0.0793812	+	0.137492i	0.823602	+	0.567168i	$0.191961\pi$
$234$		0			0
$235$	1866.98	−	1077.90i	0.518248	−	0.299211i
$236$		0			0
$237$			275.700i			0.0755638i
$238$		0			0
$239$	−1560.15			−0.422250			−0.211125	−	0.977459i	$-0.567713\pi$
$239$	−1560.15			−0.422250			−0.211125	+	0.977459i	$0.567713\pi$
$240$		0			0
$241$	2108.53	+	3652.08i	0.563578	+	0.976147i	0.997180	+	0.0750420i	$0.0239091\pi$
$241$	2108.53	+	3652.08i	0.563578	+	0.976147i	−0.433602	+	0.901105i	$0.642758\pi$
$242$		0			0
$243$	3345.86	+	1931.73i	0.883281	+	0.509962i
$244$		0			0
$245$	−2998.66	+	138.705i	−0.781947	+	0.0361695i
$246$		0			0
$247$	1396.07	−	2418.06i	0.359634	−	0.622905i
$248$		0			0
$249$	305.536	+	529.204i	0.0777612	+	0.134686i
$250$		0			0
$251$			6029.33i			1.51621i	0.652134	+	0.758104i	$0.273874\pi$
$251$			6029.33i			1.51621i	−0.652134	+	0.758104i	$0.726126\pi$
$252$		0			0
$253$		−	6871.59i		−	1.70756i
$254$		0			0
$255$	856.098	+	1482.81i	0.210239	+	0.364145i
$256$		0			0
$257$	−1537.80	+	2663.55i	−0.373250	+	0.646489i	−0.990064	−	0.140621i	$-0.955090\pi$
$257$	−1537.80	+	2663.55i	−0.373250	+	0.646489i	0.616813	+	0.787110i	$0.288423\pi$
$258$		0			0
$259$	−3823.30	−	930.311i	−0.917252	−	0.223192i
$260$		0			0
$261$	1262.32	+	728.800i	0.299370	+	0.172841i
$262$		0			0
$263$	208.250	+	360.700i	0.0488260	+	0.0845691i	0.889406	−	0.457119i	$-0.151119\pi$
$263$	208.250	+	360.700i	0.0488260	+	0.0845691i	−0.840579	+	0.541688i	$0.817785\pi$
$264$		0			0
$265$	−4074.75			−0.944565
$266$		0			0
$267$		−	3119.81i		−	0.715091i
$268$		0			0
$269$	−6849.24	+	3954.41i	−1.55244	+	0.896300i	−0.554495	+	0.832187i	$0.687089\pi$
$269$	−6849.24	+	3954.41i	−1.55244	+	0.896300i	−0.997943	+	0.0641134i	$0.979578\pi$
$270$		0			0
$271$	100.871	−	174.714i	0.0226107	−	0.0391629i	−0.854499	−	0.519454i	$-0.826136\pi$
$271$	100.871	−	174.714i	0.0226107	−	0.0391629i	0.877109	+	0.480291i	$0.159469\pi$
$272$		0			0
$273$	−1324.62	−	1264.76i	−0.293661	−	0.280391i
$274$		0			0
$275$	−2246.96	−	1297.29i	−0.492717	−	0.284470i
$276$		0			0
$277$	−2478.67	+	1431.06i	−0.537650	+	0.310413i	−0.744126	−	0.668039i	$-0.767134\pi$
$277$	−2478.67	+	1431.06i	−0.537650	+	0.310413i	0.206476	+	0.978452i	$0.433801\pi$
$278$		0			0
$279$	−4183.91			−0.897793
$280$		0			0
$281$	−3676.81			−0.780569			−0.390284	−	0.920694i	$-0.627623\pi$
$281$	−3676.81			−0.780569			−0.390284	+	0.920694i	$0.627623\pi$
$282$		0			0
$283$	−5065.23	+	2924.41i	−1.06395	+	0.614270i	−0.926521	−	0.376243i	$-0.877216\pi$
$283$	−5065.23	+	2924.41i	−1.06395	+	0.614270i	−0.137425	+	0.990512i	$0.543883\pi$
$284$		0			0
$285$	2011.94	+	1161.60i	0.418166	+	0.241428i
$286$		0			0
$287$	−6195.21	+	1814.45i	−1.27419	+	0.373182i
$288$		0			0
$289$	420.944	−	729.097i	0.0856797	−	0.148402i
$290$		0			0
$291$	−522.118	+	301.445i	−0.105179	+	0.0607252i
$292$		0			0
$293$		−	1025.09i		−	0.204391i	−0.994764	−	0.102196i	$-0.967413\pi$
$293$		−	1025.09i		−	0.204391i	0.994764	−	0.102196i	$-0.0325867\pi$
$294$		0			0
$295$	1654.90			0.326617
$296$		0			0
$297$	−3664.83	−	6347.67i	−0.716010	−	1.24017i
$298$		0			0
$299$	−3580.74	−	2067.34i	−0.692574	−	0.399858i
$300$		0			0
$301$	1154.43	+	3941.67i	0.221064	+	0.754797i
$302$		0			0
$303$	3083.13	−	5340.15i	0.584559	−	1.01249i
$304$		0			0
$305$	822.628	+	1424.83i	0.154438	+	0.267494i
$306$		0			0
$307$		−	2028.66i		−	0.377140i	−0.982060	−	0.188570i	$-0.939615\pi$
$307$		−	2028.66i		−	0.377140i	0.982060	−	0.188570i	$-0.0603852\pi$
$308$		0			0
$309$			1829.33i			0.336787i
$310$		0			0
$311$	1802.47	+	3121.96i	0.328644	+	0.569229i	0.982243	−	0.187612i	$-0.0600749\pi$
$311$	1802.47	+	3121.96i	0.328644	+	0.569229i	−0.653599	+	0.756841i	$0.726742\pi$
$312$		0			0
$313$	1447.00	−	2506.27i	0.261307	−	0.452597i	−0.705283	−	0.708926i	$-0.749180\pi$
$313$	1447.00	−	2506.27i	0.261307	−	0.452597i	0.966589	+	0.256330i	$0.0825132\pi$
$314$		0			0
$315$	−1969.83	+	2063.06i	−0.352341	+	0.369016i
$316$		0			0
$317$	−1058.34	−	611.032i	−0.187515	−	0.108262i	0.403304	−	0.915066i	$-0.367862\pi$
$317$	−1058.34	−	611.032i	−0.187515	−	0.108262i	−0.590819	+	0.806804i	$0.701195\pi$
$318$		0			0
$319$	−2219.72	−	3844.67i	−0.389594	−	0.674797i
$320$		0			0
$321$	1257.60			0.218668
$322$		0			0
$323$			5523.88i			0.951570i
$324$		0			0
$325$	−1352.01	+	780.586i	−0.230758	+	0.133228i
$326$		0			0
$327$	−1337.98	+	2317.45i	−0.226271	+	0.391912i
$328$		0			0
$329$	1078.59	−	4432.70i	0.180744	−	0.742805i
$330$		0			0
$331$	332.286	+	191.845i	0.0551785	+	0.0318573i	0.527335	−	0.849657i	$-0.323191\pi$
$331$	332.286	+	191.845i	0.0551785	+	0.0318573i	−0.472157	+	0.881514i	$0.656524\pi$
$332$		0			0
$333$	−3238.07	+	1869.50i	−0.532868	+	0.307652i
$334$		0			0
$335$	1572.22			0.256417
$336$		0			0
$337$	7826.94			1.26517			0.632583	−	0.774493i	$-0.281995\pi$
$337$	7826.94			1.26517			0.632583	+	0.774493i	$0.281995\pi$
$338$		0			0
$339$	−2891.52	+	1669.42i	−0.463263	+	0.267465i
$340$		0			0
$341$	11035.8	+	6371.52i	1.75256	+	1.01184i
$342$		0			0
$343$	−4169.88	+	4792.26i	−0.656421	+	0.754395i
$344$		0			0
$345$	1720.13	−	2979.35i	0.268430	−	0.464935i
$346$		0			0
$347$	584.362	−	337.382i	0.0904040	−	0.0521948i	−0.454116	−	0.890942i	$-0.650045\pi$
$347$	584.362	−	337.382i	0.0904040	−	0.0521948i	0.544520	+	0.838748i	$0.316712\pi$
$348$		0			0
$349$		−	7024.54i		−	1.07741i	−0.842496	−	0.538703i	$-0.818914\pi$
$349$		−	7024.54i		−	1.07741i	0.842496	−	0.538703i	$-0.181086\pi$
$350$		0			0
$351$	−4410.31			−0.670669
$352$		0			0
$353$	−1569.65	−	2718.71i	−0.236668	−	0.409921i	0.723088	−	0.690756i	$-0.242722\pi$
$353$	−1569.65	−	2718.71i	−0.236668	−	0.409921i	−0.959756	+	0.280835i	$0.909389\pi$
$354$		0			0
$355$	−2989.11	−	1725.76i	−0.446888	−	0.258011i
$356$		0			0
$357$	3520.57	+	856.649i	0.521929	+	0.126999i
$358$		0			0
$359$	535.877	−	928.166i	0.0787814	−	0.136453i	−0.823943	−	0.566673i	$-0.808230\pi$
$359$	535.877	−	928.166i	0.0787814	−	0.136453i	0.902724	+	0.430219i	$0.141564\pi$
$360$		0			0
$361$	318.035	+	550.853i	0.0463676	+	0.0803110i
$362$		0			0
$363$			4727.92i			0.683614i
$364$		0			0
$365$			7495.09i			1.07483i
$366$		0			0
$367$	−885.623	−	1533.94i	−0.125965	−	0.218178i	0.796145	−	0.605106i	$-0.206869\pi$
$367$	−885.623	−	1533.94i	−0.125965	−	0.218178i	−0.922110	+	0.386928i	$0.873536\pi$
$368$		0			0
$369$	−3067.07	+	5312.32i	−0.432697	+	0.749453i
$370$		0			0
$371$	−5954.75	+	6236.56i	−0.833302	+	0.872738i
$372$		0			0
$373$	−9657.76	−	5575.91i	−1.34064	−	0.774021i	−0.353741	−	0.935343i	$-0.615091\pi$
$373$	−9657.76	−	5575.91i	−1.34064	−	0.774021i	−0.986902	+	0.161323i	$0.948424\pi$
$374$		0			0
$375$	−2326.65	−	4029.88i	−0.320394	−	0.554939i
$376$		0			0
$377$	−2671.24			−0.364923
$378$		0			0
$379$		−	11982.3i		−	1.62399i	−0.583667	−	0.811993i	$-0.698383\pi$
$379$		−	11982.3i		−	1.62399i	0.583667	−	0.811993i	$-0.301617\pi$
$380$		0			0
$381$	−3248.25	+	1875.38i	−0.436780	+	0.252175i
$382$		0			0
$383$	−168.027	+	291.031i	−0.0224172	+	0.0388277i	−0.877016	−	0.480460i	$-0.840470\pi$
$383$	−168.027	+	291.031i	−0.0224172	+	0.0388277i	0.854599	+	0.519288i	$0.173803\pi$
$384$		0			0
$385$	8337.53	−	2441.88i	1.10369	−	0.323246i
$386$		0			0
$387$	3379.93	+	1951.40i	0.443957	+	0.256319i
$388$		0			0
$389$	−3352.87	+	1935.78i	−0.437010	+	0.252308i	−0.702329	−	0.711853i	$-0.747856\pi$
$389$	−3352.87	+	1935.78i	−0.437010	+	0.252308i	0.265318	+	0.964161i	$0.414523\pi$
$390$		0			0
$391$	8179.93			1.05800
$392$		0			0
$393$	−7528.60			−0.966330
$394$		0			0
$395$	−681.496	+	393.462i	−0.0868096	+	0.0501195i
$396$		0			0
$397$	−5876.75	−	3392.94i	−0.742936	−	0.428934i	0.0801996	−	0.996779i	$-0.474444\pi$
$397$	−5876.75	−	3392.94i	−0.742936	−	0.428934i	−0.823136	+	0.567844i	$0.807778\pi$
$398$		0			0
$399$	4718.08	−	1381.82i	0.591978	−	0.173378i
$400$		0			0
$401$	−6141.21	+	10636.9i	−0.764782	+	1.32464i	0.175581	+	0.984465i	$0.443820\pi$
$401$	−6141.21	+	10636.9i	−0.764782	+	1.32464i	−0.940362	+	0.340175i	$0.889514\pi$
$402$		0			0
$403$	6640.31	−	3833.78i	0.820788	−	0.473882i
$404$		0			0
$405$			488.889i			0.0599830i
$406$		0			0
$407$	11388.0			1.38693
$408$		0			0
$409$	−1572.28	−	2723.27i	−0.190084	−	0.329234i	0.755194	−	0.655501i	$-0.227543\pi$
$409$	−1572.28	−	2723.27i	−0.190084	−	0.329234i	−0.945278	+	0.326267i	$0.894209\pi$
$410$		0			0
$411$	6478.35	+	3740.28i	0.777502	+	0.448891i
$412$		0			0
$413$	2418.44	−	2532.89i	0.288144	−	0.301781i
$414$		0			0
$415$	−872.084	+	1510.49i	−0.103154	+	0.178668i
$416$		0			0
$417$	4268.08	+	7392.53i	0.501220	+	0.868139i
$418$		0			0
$419$			2133.06i			0.248704i	0.992238	+	0.124352i	$0.0396852\pi$
$419$			2133.06i			0.248704i	−0.992238	+	0.124352i	$0.960315\pi$
$420$		0			0
$421$		−	4230.88i		−	0.489787i	−0.969550	−	0.244893i	$-0.921247\pi$
$421$		−	4230.88i		−	0.489787i	0.969550	−	0.244893i	$-0.0787530\pi$
$422$		0			0
$423$	−2167.48	−	3754.19i	−0.249141	−	0.431525i
$424$		0			0
$425$	1544.29	−	2674.78i	0.176256	−	0.305285i
$426$		0			0
$427$	3382.93	+	823.158i	0.383400	+	0.0932913i
$428$		0			0
$429$	4590.33	+	2650.23i	0.516604	+	0.298262i
$430$		0			0
$431$	92.2433	+	159.770i	0.0103091	+	0.0178558i	0.871134	−	0.491046i	$-0.163385\pi$
$431$	92.2433	+	159.770i	0.0103091	+	0.0178558i	−0.860825	+	0.508901i	$0.830052\pi$
$432$		0			0
$433$	−5972.94			−0.662912			−0.331456	−	0.943471i	$-0.607540\pi$
$433$	−5972.94			−0.662912			−0.331456	+	0.943471i	$0.607540\pi$
$434$		0			0
$435$		−	2222.60i		−	0.244978i
$436$		0			0
$437$	9611.96	−	5549.47i	1.05218	−	0.607476i
$438$		0			0
$439$	−5535.24	+	9587.32i	−0.601783	+	1.04232i	0.390768	+	0.920489i	$0.372209\pi$
$439$	−5535.24	+	9587.32i	−0.601783	+	1.04232i	−0.992551	+	0.121829i	$0.961124\pi$
$440$		0			0
$441$	278.913	+	6029.81i	0.0301169	+	0.651097i
$442$		0			0
$443$	−1854.17	−	1070.51i	−0.198858	−	0.114811i	0.397264	−	0.917704i	$-0.369960\pi$
$443$	−1854.17	−	1070.51i	−0.198858	−	0.114811i	−0.596123	+	0.802893i	$0.703293\pi$
$444$		0			0
$445$	7711.79	−	4452.40i	0.821514	−	0.474302i
$446$		0			0
$447$	−3848.40			−0.407211
$448$		0			0
$449$	5106.95			0.536775			0.268387	−	0.963311i	$-0.413509\pi$
$449$	5106.95			0.536775			0.268387	+	0.963311i	$0.413509\pi$
$450$		0			0
$451$	16179.8	−	9341.44i	1.68931	−	0.975324i
$452$		0			0
$453$	−7298.98	−	4214.07i	−0.757033	−	0.437073i
$454$		0			0
$455$	1235.92	−	5079.28i	0.127343	−	0.523341i
$456$		0			0
$457$	−3095.20	+	5361.05i	−0.316822	+	0.548751i	−0.979823	−	0.199867i	$-0.935949\pi$
$457$	−3095.20	+	5361.05i	−0.316822	+	0.548751i	0.663001	+	0.748618i	$0.269282\pi$
$458$		0			0
$459$	7556.26	−	4362.61i	0.768401	−	0.443637i
$460$		0			0
$461$		−	10592.5i		−	1.07016i	−0.844803	−	0.535078i	$-0.820282\pi$
$461$		−	10592.5i		−	1.07016i	0.844803	−	0.535078i	$-0.179718\pi$
$462$		0			0
$463$	4511.99			0.452894			0.226447	−	0.974023i	$-0.427289\pi$
$463$	4511.99			0.452894			0.226447	+	0.974023i	$0.427289\pi$
$464$		0			0
$465$	3189.89	+	5525.05i	0.318124	+	0.551007i
$466$		0			0
$467$	3025.77	+	1746.93i	0.299820	+	0.173101i	0.642362	−	0.766401i	$-0.277955\pi$
$467$	3025.77	+	1746.93i	0.299820	+	0.173101i	−0.342542	+	0.939502i	$0.611288\pi$
$468$		0			0
$469$	2297.61	−	2406.35i	0.226213	−	0.236919i
$470$		0			0
$471$	−3846.89	+	6663.01i	−0.376338	+	0.651837i
$472$		0			0
$473$	−5943.44	−	10294.3i	−0.577758	−	1.00071i
$474$		0			0
$475$		−	4190.73i		−	0.404808i
$476$		0			0
$477$			8193.66i			0.786503i
$478$		0			0
$479$	1024.99	+	1775.34i	0.0977729	+	0.169348i	0.910762	−	0.412931i	$-0.135495\pi$
$479$	1024.99	+	1775.34i	0.0977729	+	0.169348i	−0.812990	+	0.582278i	$0.802161\pi$
$480$		0			0
$481$	3426.11	−	5934.19i	0.324775	−	0.562528i
$482$		0			0
$483$	−2046.25	−	6986.67i	−0.192769	−	0.658187i
$484$		0			0
$485$	−1490.27	−	860.408i	−0.139525	−	0.0805549i
$486$		0			0
$487$	−3873.91	−	6709.80i	−0.360459	−	0.624333i	0.627577	−	0.778554i	$-0.284047\pi$
$487$	−3873.91	−	6709.80i	−0.360459	−	0.624333i	−0.988036	+	0.154221i	$0.950713\pi$
$488$		0			0
$489$	8001.27			0.739939
$490$		0			0
$491$			10491.3i			0.964291i	0.876091	+	0.482146i	$0.160142\pi$
$491$			10491.3i			0.964291i	−0.876091	+	0.482146i	$0.839858\pi$
$492$		0			0
$493$	4576.69	−	2642.35i	0.418101	−	0.241391i
$494$		0			0
$495$	4127.66	−	7149.32i	0.374797	−	0.649168i
$496$		0			0
$497$	−7009.56	+	2052.95i	−0.632639	+	0.185286i
$498$		0			0
$499$	−1725.97	−	996.491i	−0.154840	−	0.0893969i	0.420578	−	0.907256i	$-0.361827\pi$
$499$	−1725.97	−	996.491i	−0.154840	−	0.0893969i	−0.575418	+	0.817859i	$0.695161\pi$
$500$		0			0
$501$	−1845.92	+	1065.74i	−0.164610	+	0.0950377i
$502$		0			0
$503$	−3940.26			−0.349279			−0.174640	−	0.984632i	$-0.555876\pi$
$503$	−3940.26			−0.349279			−0.174640	+	0.984632i	$0.555876\pi$
$504$		0			0
$505$	17600.2			1.55089
$506$		0			0
$507$	−3071.90	+	1773.56i	−0.269088	+	0.155358i
$508$		0			0
$509$	5019.62	+	2898.08i	0.437114	+	0.252368i	0.702373	−	0.711810i	$-0.252124\pi$
$509$	5019.62	+	2898.08i	0.437114	+	0.252368i	−0.265259	+	0.964177i	$0.585457\pi$
$510$		0			0
$511$	11471.5	+	10953.2i	0.993093	+	0.948219i
$512$		0			0
$513$	5919.40	−	10252.7i	0.509450	−	0.882394i
$514$		0			0
$515$	−4521.88	+	2610.71i	−0.386909	+	0.223382i
$516$		0			0
$517$			13203.1i			1.12316i
$518$		0			0
$519$	−5463.90			−0.462117
$520$		0			0
$521$	7361.53	+	12750.5i	0.619030	+	1.07219i	0.989663	+	0.143412i	$0.0458074\pi$
$521$	7361.53	+	12750.5i	0.619030	+	1.07219i	−0.370633	+	0.928779i	$0.620859\pi$
$522$		0			0
$523$	−14898.2	−	8601.49i	−1.24561	−	0.719153i	−0.275379	−	0.961336i	$-0.588803\pi$
$523$	−14898.2	−	8601.49i	−1.24561	−	0.719153i	−0.970231	+	0.242183i	$0.922137\pi$
$524$		0			0
$525$	−2670.91	−	649.902i	−0.222034	−	0.0540268i
$526$		0			0
$527$	−7584.65	+	13137.0i	−0.626931	+	1.08588i
$528$		0			0
$529$	−2134.32	−	3696.75i	−0.175419	−	0.303834i
$530$		0			0
$531$		−	3327.74i		−	0.271962i
$532$		0			0
$533$		−	11241.6i		−	0.913562i
$534$		0			0
$535$	1794.77	+	3108.63i	0.145037	+	0.251211i
$536$		0			0
$537$	−3695.74	+	6401.21i	−0.296989	+	0.514399i
$538$		0			0
$539$	8446.88	−	16329.4i	0.675015	−	1.30493i
$540$		0			0
$541$	12396.0	+	7156.85i	0.985114	+	0.568756i	0.903810	−	0.427934i	$-0.140758\pi$
$541$	12396.0	+	7156.85i	0.985114	+	0.568756i	0.0813037	+	0.996689i	$0.474092\pi$
$542$		0			0
$543$	3425.02	+	5932.31i	0.270685	+	0.468840i
$544$		0			0
$545$	−7637.94			−0.600318
$546$		0			0
$547$			18243.6i			1.42604i	0.701145	+	0.713018i	$0.252672\pi$
$547$			18243.6i			1.42604i	−0.701145	+	0.713018i	$0.747328\pi$
$548$		0			0
$549$	2865.11	−	1654.17i	0.222732	−	0.128594i
$550$		0			0
$551$	3585.27	−	6209.88i	0.277201	−	0.480126i
$552$		0			0
$553$	−393.715	+	1618.05i	−0.0302757	+	0.124424i
$554$		0			0
$555$	4937.53	+	2850.68i	0.377633	+	0.218027i
$556$		0			0
$557$	16086.0	−	9287.24i	1.22367	−	0.706486i	0.257972	−	0.966152i	$-0.416946\pi$
$557$	16086.0	−	9287.24i	1.22367	−	0.706486i	0.965698	+	0.259666i	$0.0836125\pi$
$558$		0			0
$559$	−7152.41			−0.541171
$560$		0			0
$561$	−10486.3			−0.789181
$562$		0			0
$563$	−4972.40	+	2870.82i	−0.372224	+	0.214903i	−0.674429	−	0.738339i	$-0.735610\pi$
$563$	−4972.40	+	2870.82i	−0.372224	+	0.214903i	0.302206	+	0.953243i	$0.402277\pi$
$564$		0			0
$565$	−8253.21	−	4764.99i	−0.614540	−	0.354805i
$566$		0			0
$567$	748.264	+	714.452i	0.0554217	+	0.0529174i
$568$		0			0
$569$	3623.14	−	6275.46i	0.266942	−	0.462356i	−0.701129	−	0.713035i	$-0.747320\pi$
$569$	3623.14	−	6275.46i	0.266942	−	0.462356i	0.968070	+	0.250678i	$0.0806536\pi$
$570$		0			0
$571$	−7153.20	+	4129.90i	−0.524259	+	0.302681i	−0.738676	−	0.674061i	$-0.764548\pi$
$571$	−7153.20	+	4129.90i	−0.524259	+	0.302681i	0.214416	+	0.976742i	$0.431215\pi$
$572$		0			0
$573$		−	2237.26i		−	0.163112i
$574$		0			0
$575$	−6205.76			−0.450084
$576$		0			0
$577$	1280.85	+	2218.49i	0.0924132	+	0.160064i	0.908526	−	0.417828i	$-0.137209\pi$
$577$	1280.85	+	2218.49i	0.0924132	+	0.160064i	−0.816113	+	0.577893i	$0.803875\pi$
$578$		0			0
$579$	−12686.5	−	7324.57i	−0.910594	−	0.525732i
$580$		0			0
$581$	1037.42	+	3542.16i	0.0740784	+	0.252932i
$582$		0			0
$583$	12477.8	−	21612.2i	0.886411	−	1.53531i
$584$		0			0
$585$	−2483.64	−	4301.80i	−0.175532	−	0.304030i
$586$		0			0
$587$		−	2146.44i		−	0.150925i	−0.997149	−	0.0754624i	$-0.975957\pi$
$587$		−	2146.44i		−	0.150925i	0.997149	−	0.0754624i	$-0.0240433\pi$
$588$		0			0
$589$			20582.4i			1.43987i
$590$		0			0
$591$	3573.47	+	6189.44i	0.248719	+	0.430794i
$592$		0			0
$593$	7900.80	−	13684.6i	0.547128	−	0.947653i	−0.451342	−	0.892351i	$-0.649055\pi$
$593$	7900.80	−	13684.6i	0.547128	−	0.947653i	0.998470	−	0.0553020i	$-0.0176122\pi$
$594$		0			0
$595$	2906.82	+	9924.98i	0.200282	+	0.683840i
$596$		0			0
$597$	9136.06	+	5274.70i	0.626321	+	0.361607i
$598$		0			0
$599$	11161.4	+	19332.1i	0.761339	+	1.31868i	0.942160	+	0.335162i	$0.108791\pi$
$599$	11161.4	+	19332.1i	0.761339	+	1.31868i	−0.180821	+	0.983516i	$0.557876\pi$
$600$		0			0
$601$	−12041.0			−0.817242			−0.408621	−	0.912704i	$-0.633990\pi$
$601$	−12041.0			−0.817242			−0.408621	+	0.912704i	$0.633990\pi$
$602$		0			0
$603$		−	3161.49i		−	0.213509i
$604$		0			0
$605$	−11686.8	+	6747.40i	−0.785352	+	0.453423i
$606$		0			0
$607$	3607.64	−	6248.62i	0.241235	−	0.417832i	−0.719831	−	0.694149i	$-0.755781\pi$
$607$	3607.64	−	6248.62i	0.241235	−	0.417832i	0.961066	+	0.276318i	$0.0891141\pi$
$608$		0			0
$609$	−3401.78	−	3248.06i	−0.226350	−	0.216122i
$610$		0			0
$611$	6880.05	+	3972.20i	0.455544	+	0.263008i
$612$		0			0
$613$	−24381.6	+	14076.7i	−1.60646	+	0.927493i	−0.616312	+	0.787502i	$0.711374\pi$
$613$	−24381.6	+	14076.7i	−1.60646	+	0.927493i	−0.990153	+	0.139991i	$0.955293\pi$
$614$		0			0
$615$	9353.56			0.613288
$616$		0			0
$617$	−8547.35			−0.557704			−0.278852	−	0.960334i	$-0.589954\pi$
$617$	−8547.35			−0.557704			−0.278852	+	0.960334i	$0.589954\pi$
$618$		0			0
$619$	4572.60	−	2639.99i	0.296912	−	0.171422i	−0.344143	−	0.938917i	$-0.611830\pi$
$619$	4572.60	−	2639.99i	0.296912	−	0.171422i	0.641055	+	0.767495i	$0.278497\pi$
$620$		0			0
$621$	−15182.5	−	8765.63i	−0.981085	−	0.566429i
$622$		0			0
$623$	4455.27	−	18309.8i	0.286511	−	1.17748i
$624$		0			0
$625$	3615.52	−	6262.27i	0.231394	−	0.400785i
$626$		0			0
$627$	−12322.0	+	7114.14i	−0.784841	+	0.453128i
$628$		0			0
$629$			13556.2i			0.859335i
$630$		0			0
$631$	−26983.8			−1.70239			−0.851194	−	0.524852i	$-0.824121\pi$
$631$	−26983.8			−1.70239			−0.851194	+	0.524852i	$0.824121\pi$
$632$		0			0
$633$	6562.33	+	11366.3i	0.412053	+	0.713696i
$634$		0			0
$635$	−9271.41	−	5352.85i	−0.579409	−	0.334522i
$636$		0			0
$637$	−5967.88	−	9314.38i	−0.371202	−	0.579355i
$638$		0			0
$639$	−3470.22	+	6010.61i	−0.214836	+	0.372106i
$640$		0			0
$641$	−11038.3	−	19118.9i	−0.680166	−	1.17808i	−0.974930	−	0.222512i	$-0.928574\pi$
$641$	−11038.3	−	19118.9i	−0.680166	−	1.17808i	0.294764	−	0.955570i	$-0.404759\pi$
$642$		0			0
$643$			7248.12i			0.444538i	0.974985	+	0.222269i	$0.0713464\pi$
$643$			7248.12i			0.444538i	−0.974985	+	0.222269i	$0.928654\pi$
$644$		0			0
$645$		−	5951.15i		−	0.363296i
$646$		0			0
$647$	−13986.9	−	24226.0i	−0.849893	−	1.47206i	−0.881303	−	0.472551i	$-0.843333\pi$
$647$	−13986.9	−	24226.0i	−0.849893	−	1.47206i	0.0314105	−	0.999507i	$-0.490000\pi$
$648$		0			0
$649$	−5067.69	+	8777.49i	−0.306509	+	0.530888i
$650$		0			0
$651$	13117.9	+	3191.94i	0.789758	+	0.192169i
$652$		0			0
$653$	−16345.2	−	9436.90i	−0.979536	−	0.565535i	−0.0774060	−	0.997000i	$-0.524664\pi$
$653$	−16345.2	−	9436.90i	−0.979536	−	0.565535i	−0.902130	+	0.431464i	$0.857997\pi$
$654$		0			0
$655$	−10744.4	−	18609.8i	−0.640942	−	1.11014i
$656$		0			0
$657$	15071.4			0.894965
$658$		0			0
$659$			12594.1i			0.744455i	0.928141	+	0.372228i	$0.121406\pi$
$659$			12594.1i			0.744455i	−0.928141	+	0.372228i	$0.878594\pi$
$660$		0			0
$661$	16194.5	−	9349.92i	0.952941	−	0.550181i	0.0589480	−	0.998261i	$-0.481225\pi$
$661$	16194.5	−	9349.92i	0.952941	−	0.550181i	0.893993	+	0.448080i	$0.147892\pi$
$662$		0			0
$663$	−3154.83	+	5464.32i	−0.184802	+	0.320086i
$664$		0			0
$665$	10149.0	+	9690.45i	0.591824	+	0.565082i
$666$		0			0
$667$	−9195.78	−	5309.18i	−0.533826	−	0.308205i
$668$		0			0
$669$	−10527.5	+	6078.03i	−0.608393	+	0.351256i
$670$		0			0
$671$	−10076.3			−0.579719
$672$		0			0
$673$	−26792.3			−1.53457			−0.767286	−	0.641305i	$-0.778393\pi$
$673$	−26792.3			−1.53457			−0.767286	+	0.641305i	$0.778393\pi$
$674$		0			0
$675$	−5732.61	+	3309.72i	−0.326886	+	0.188728i
$676$		0			0
$677$	−9315.61	−	5378.37i	−0.528845	−	0.305329i	0.211701	−	0.977334i	$-0.432100\pi$
$677$	−9315.61	−	5378.37i	−0.528845	−	0.305329i	−0.740546	+	0.672006i	$0.765433\pi$
$678$		0			0
$679$	−3494.74	+	1023.53i	−0.197519	+	0.0578492i
$680$		0			0
$681$	−2762.96	+	4785.59i	−0.155473	+	0.269287i
$682$		0			0
$683$	−27340.4	+	15785.0i	−1.53170	+	0.884328i	−0.532417	+	0.846482i	$0.678716\pi$
$683$	−27340.4	+	15785.0i	−1.53170	+	0.884328i	−0.999284	+	0.0378455i	$0.987951\pi$
$684$		0			0
$685$			21351.6i			1.19095i
$686$		0			0
$687$	−11776.6			−0.654010
$688$		0			0
$689$	−7507.98	−	13004.2i	−0.415140	−	0.719043i
$690$		0			0
$691$	24576.0	+	14189.0i	1.35299	+	0.781149i	0.988667	−	0.150123i	$-0.0479671\pi$
$691$	24576.0	+	14189.0i	1.35299	+	0.781149i	0.364323	+	0.931273i	$0.381300\pi$
$692$		0			0
$693$	−4910.23	−	16765.4i	−0.269155	−	0.918998i
$694$		0			0
$695$	−12182.3	+	21100.3i	−0.664893	+	1.15163i
$696$		0			0
$697$	11120.0	+	19260.5i	0.604306	+	1.04669i
$698$		0			0
$699$		−	1731.34i		−	0.0936841i
$700$		0			0
$701$			3313.45i			0.178527i	0.996008	+	0.0892634i	$0.0284513\pi$
$701$			3313.45i			0.178527i	−0.996008	+	0.0892634i	$0.971549\pi$
$702$		0			0
$703$	9196.86	+	15929.4i	0.493409	+	0.854609i
$704$		0			0
$705$	−3305.06	+	5724.53i	−0.176561	+	0.305813i
$706$		0			0
$707$	25720.6	−	26937.8i	1.36821	−	1.43296i
$708$		0			0
$709$	11822.5	+	6825.73i	0.626239	+	0.361559i	0.779294	−	0.626658i	$-0.215578\pi$
$709$	11822.5	+	6825.73i	0.626239	+	0.361559i	−0.153055	+	0.988218i	$0.548911\pi$
$710$		0			0
$711$	791.188	+	1370.38i	0.0417326	+	0.0722830i
$712$		0			0
$713$	30479.1			1.60091
$714$		0			0
$715$			15129.0i			0.791317i
$716$		0			0
$717$	4142.84	−	2391.87i	0.215784	−	0.124583i
$718$		0			0
$719$	17155.5	−	29714.1i	0.889834	−	1.54124i	0.0497630	−	0.998761i	$-0.484153\pi$
$719$	17155.5	−	29714.1i	0.889834	−	1.54124i	0.840071	−	0.542477i	$-0.182513\pi$
$720$		0			0
$721$	−2612.39	+	10736.1i	−0.134938	+	0.554556i
$722$		0			0
$723$	−11198.0	−	6465.18i	−0.576015	−	0.332562i
$724$		0			0
$725$	−3472.14	+	2004.64i	−0.177865	+	0.102690i
$726$		0			0
$727$	5988.54			0.305506			0.152753	−	0.988264i	$-0.451186\pi$
$727$	5988.54			0.305506			0.152753	+	0.988264i	$0.451186\pi$
$728$		0			0
$729$	−10337.9			−0.525220
$730$		0			0
$731$	12254.4	−	7075.06i	0.620033	−	0.357976i
$732$		0			0
$733$	−30860.2	−	17817.1i	−1.55504	−	0.897804i	−0.997719	−	0.0675083i	$-0.978495\pi$
$733$	−30860.2	−	17817.1i	−1.55504	−	0.897804i	−0.557323	−	0.830296i	$-0.688172\pi$
$734$		0			0
$735$	7750.00	−	4965.56i	0.388929	−	0.249194i
$736$		0			0
$737$	−4814.51	+	8338.97i	−0.240630	+	0.416784i
$738$		0			0
$739$	−16663.6	+	9620.75i	−0.829474	+	0.478897i	−0.853673	−	0.520810i	$-0.825630\pi$
$739$	−16663.6	+	9620.75i	−0.829474	+	0.478897i	0.0241983	+	0.999707i	$0.492297\pi$
$740$		0			0
$741$			8561.25i			0.424434i
$742$		0			0
$743$	33062.3			1.63249			0.816244	−	0.577707i	$-0.196052\pi$
$743$	33062.3			1.63249			0.816244	+	0.577707i	$0.196052\pi$
$744$		0			0
$745$	−5492.20	−	9512.77i	−0.270092	−	0.467814i
$746$		0			0
$747$	3037.36	+	1753.62i	0.148770	+	0.0858923i
$748$		0			0
$749$	7380.72	+	1795.92i	0.360061	+	0.0876124i
$750$		0			0
$751$	−653.983	+	1132.73i	−0.0317765	+	0.0550386i	−0.881476	−	0.472228i	$-0.843450\pi$
$751$	−653.983	+	1132.73i	−0.0317765	+	0.0550386i	0.849700	+	0.527267i	$0.176783\pi$
$752$		0			0
$753$	−9243.57	−	16010.3i	−0.447350	−	0.774833i
$754$		0			0
$755$		−	24056.2i		−	1.15960i
$756$		0			0
$757$			22928.8i			1.10087i	0.834877	+	0.550437i	$0.185539\pi$
$757$			22928.8i			1.10087i	−0.834877	+	0.550437i	$0.814461\pi$
$758$		0			0
$759$	10534.8	+	18246.9i	0.503808	+	0.872621i
$760$		0			0
$761$	12998.0	−	22513.1i	0.619154	−	1.07241i	−0.370487	−	0.928838i	$-0.620809\pi$
$761$	12998.0	−	22513.1i	0.619154	−	1.07241i	0.989640	−	0.143568i	$-0.0458576\pi$
$762$		0			0
$763$	−11161.9	+	11690.2i	−0.529605	+	0.554668i
$764$		0			0
$765$	8510.55	+	4913.57i	0.402221	+	0.232223i
$766$		0			0
$767$	3049.26	+	5281.47i	0.143549	+	0.248635i
$768$		0			0
$769$	−7834.78			−0.367398			−0.183699	−	0.982982i	$-0.558807\pi$
$769$	−7834.78			−0.367398			−0.183699	+	0.982982i	$0.558807\pi$
$770$		0			0
$771$		−	9430.41i		−	0.440503i
$772$		0			0
$773$	5328.06	−	3076.15i	0.247913	−	0.143133i	−0.370895	−	0.928675i	$-0.620949\pi$
$773$	5328.06	−	3076.15i	0.247913	−	0.143133i	0.618808	+	0.785542i	$0.287616\pi$
$774$		0			0
$775$	5754.14	−	9966.46i	0.266703	−	0.461943i
$776$		0			0
$777$	11578.7	−	3391.15i	0.534598	−	0.156572i
$778$		0			0
$779$	26133.5	+	15088.2i	1.20197	+	0.693955i
$780$		0			0
$781$	18306.6	−	10569.3i	0.838749	−	0.484252i
$782$		0			0
$783$	−11326.2			−0.516942
$784$		0			0
$785$	−21960.2			−0.998462
$786$		0			0
$787$	9159.31	−	5288.13i	0.414859	−	0.239519i	−0.278016	−	0.960576i	$-0.589677\pi$
$787$	9159.31	−	5288.13i	0.414859	−	0.239519i	0.692875	+	0.721057i	$0.256344\pi$
$788$		0			0
$789$	−1105.98	−	638.536i	−0.0499034	−	0.0288118i
$790$		0			0
$791$	−19354.1	+	5668.39i	−0.869977	+	0.254798i
$792$		0			0
$793$	−3031.49	+	5250.69i	−0.135752	+	0.235129i
$794$		0			0
$795$	10820.1	−	6247.00i	0.482704	−	0.278689i
$796$		0			0
$797$			11570.5i			0.514241i	0.966379	+	0.257120i	$0.0827737\pi$
$797$			11570.5i			0.514241i	−0.966379	+	0.257120i	$0.917226\pi$
$798$		0			0
$799$	−15717.0			−0.695903
$800$		0			0
$801$	−8953.06	−	15507.2i	−0.394933	−	0.684043i
$802$		0			0
$803$	−39753.5	−	22951.7i	−1.74704	−	1.00865i
$804$		0			0
$805$	14349.9	−	15029.0i	0.628283	−	0.658017i
$806$		0			0
$807$	12125.0	−	21001.1i	0.528898	−	0.916079i
$808$		0			0
$809$	20835.6	+	36088.3i	0.905488	+	1.56835i	0.820261	+	0.571989i	$0.193828\pi$
$809$	20835.6	+	36088.3i	0.905488	+	1.56835i	0.0852262	+	0.996362i	$0.472839\pi$
$810$		0			0
$811$			4576.16i			0.198139i	0.995081	+	0.0990696i	$0.0315866\pi$
$811$			4576.16i			0.198139i	−0.995081	+	0.0990696i	$0.968413\pi$
$812$		0			0
$813$			618.583i			0.0266847i
$814$		0			0
$815$	11418.9	+	19778.2i	0.490782	+	0.850060i
$816$		0			0
$817$	9599.78	−	16627.3i	0.411082	−	0.712015i
$818$		0			0
$819$	−10213.6	−	2485.24i	−0.435766	−	0.106033i
$820$		0			0
$821$	16660.8	+	9619.13i	0.708242	+	0.408904i	0.810410	−	0.585863i	$-0.199244\pi$
$821$	16660.8	+	9619.13i	0.708242	+	0.408904i	−0.102168	+	0.994767i	$0.532578\pi$
$822$		0			0
$823$	5624.38	+	9741.71i	0.238218	+	0.412606i	0.960203	−	0.279303i	$-0.0901033\pi$
$823$	5624.38	+	9741.71i	0.238218	+	0.412606i	−0.721985	+	0.691909i	$0.756770\pi$
$824$		0			0
$825$	7955.47			0.335726
$826$		0			0
$827$			17626.7i			0.741163i	0.928800	+	0.370582i	$0.120842\pi$
$827$			17626.7i			0.741163i	−0.928800	+	0.370582i	$0.879158\pi$
$828$		0			0
$829$	28478.1	−	16441.8i	1.19310	−	0.688839i	0.234095	−	0.972214i	$-0.424787\pi$
$829$	28478.1	−	16441.8i	1.19310	−	0.688839i	0.959009	+	0.283374i	$0.0914539\pi$
$830$		0			0
$831$	4387.93	−	7600.11i	0.183171	−	0.317262i
$832$		0			0
$833$	19438.5	+	10055.2i	0.808529	+	0.418236i
$834$		0			0
$835$	−5268.77	−	3041.92i	−0.218363	−	0.126072i
$836$		0			0
$837$	28155.2	−	16255.4i	1.16271	−	0.671291i
$838$		0			0
$839$	−8483.06			−0.349068			−0.174534	−	0.984651i	$-0.555842\pi$
$839$	−8483.06			−0.349068			−0.174534	+	0.984651i	$0.555842\pi$
$840$		0			0
$841$	17528.9			0.718723
$842$		0			0
$843$	9763.41	−	5636.91i	0.398897	−	0.230303i
$844$		0			0
$845$	−8768.04	−	5062.23i	−0.356958	−	0.206090i
$846$		0			0
$847$	−6751.75	+	27747.7i	−0.273899	+	1.12565i
$848$		0			0
$849$	8966.83	−	15531.0i	0.362475	−	0.627824i
$850$		0			0
$851$	23588.8	−	13619.0i	0.950192	−	0.548594i
$852$		0			0
$853$		−	1148.92i		−	0.0461176i	−0.999734	−	0.0230588i	$-0.992660\pi$
$853$		−	1148.92i		−	0.0461176i	0.999734	−	0.0230588i	$-0.00734049\pi$
$854$		0			0
$855$	13333.9			0.533346
$856$		0			0
$857$	19525.6	+	33819.3i	0.778275	+	1.34801i	0.932935	+	0.360044i	$0.117238\pi$
$857$	19525.6	+	33819.3i	0.778275	+	1.34801i	−0.154661	+	0.987968i	$0.549428\pi$
$858$		0			0
$859$	12358.3	+	7135.08i	0.490874	+	0.283406i	0.724937	−	0.688815i	$-0.241869\pi$
$859$	12358.3	+	7135.08i	0.490874	+	0.283406i	−0.234063	+	0.972221i	$0.575202\pi$
$860$		0			0
$861$	13669.1	−	14316.0i	0.541047	−	0.566652i
$862$		0			0
$863$	3995.09	−	6919.69i	0.157583	−	0.272942i	−0.776413	−	0.630224i	$-0.782963\pi$
$863$	3995.09	−	6919.69i	0.157583	−	0.272942i	0.933997	+	0.357282i	$0.116296\pi$
$864$		0			0
$865$	−7797.74	−	13506.1i	−0.306510	−	0.530891i
$866$		0			0
$867$			2581.40i			0.101118i
$868$		0			0
$869$		−	4819.48i		−	0.188135i
$870$		0			0
$871$	2896.92	+	5017.61i	0.112696	+	0.195196i
$872$		0			0
$873$	−1730.14	+	2996.69i	−0.0670749	+	0.116177i
$874$		0			0
$875$	−7899.97	−	26973.5i	−0.305220	−	1.04214i
$876$		0			0
$877$	9621.74	+	5555.12i	0.370471	+	0.213892i	0.673664	−	0.739038i	$-0.264719\pi$
$877$	9621.74	+	5555.12i	0.370471	+	0.213892i	−0.303193	+	0.952929i	$0.598053\pi$
$878$		0			0
$879$	1571.57	+	2722.04i	0.0603046	+	0.104451i
$880$		0			0
$881$	−17590.4			−0.672683			−0.336342	−	0.941740i	$-0.609190\pi$
$881$	−17590.4			−0.672683			−0.336342	+	0.941740i	$0.609190\pi$
$882$		0			0
$883$		−	22009.6i		−	0.838826i	−0.907796	−	0.419413i	$-0.862236\pi$
$883$		−	22009.6i		−	0.838826i	0.907796	−	0.419413i	$-0.137764\pi$
$884$		0			0
$885$	−4394.44	+	2537.13i	−0.166912	+	0.0963669i
$886$		0			0
$887$	−22650.3	+	39231.5i	−0.857410	+	1.48508i	0.0169818	+	0.999856i	$0.494594\pi$
$887$	−22650.3	+	39231.5i	−0.857410	+	1.48508i	−0.874391	+	0.485221i	$0.838739\pi$
$888$		0			0
$889$	−21741.8	+	6367.71i	−0.820243	+	0.240232i
$890$		0			0
$891$	−2593.04	−	1497.09i	−0.0974972	−	0.0562900i
$892$		0			0
$893$	−18468.5	+	10662.8i	−0.692075	+	0.399570i
$894$		0			0
$895$	−21097.3			−0.787939
$896$		0			0
$897$	12677.8			0.471904
$898$		0			0
$899$	17053.1	−	9845.63i	0.632651	−	0.365261i
$900$		0			0
$901$	25727.1	+	14853.6i	0.951271	+	0.549216i
$902$		0			0
$903$	−9108.45	−	8696.88i	−0.335670	−	0.320503i
$904$		0			0
$905$	−9775.97	+	16932.5i	−0.359076	+	0.621938i
$906$		0			0
$907$	−9627.87	+	5558.65i	−0.352468	+	0.203497i	−0.665772	−	0.746156i	$-0.731897\pi$
$907$	−9627.87	+	5558.65i	−0.352468	+	0.203497i	0.313304	+	0.949653i	$0.398564\pi$
$908$		0			0
$909$		−	35391.2i		−	1.29137i
$910$		0			0
$911$	−4926.27			−0.179160			−0.0895800	−	0.995980i	$-0.528552\pi$
$911$	−4926.27			−0.179160			−0.0895800	+	0.995980i	$0.528552\pi$
$912$		0			0
$913$	−5341.04	−	9250.95i	−0.193606	−	0.335336i
$914$		0			0
$915$	−4368.83	−	2522.34i	−0.157846	−	0.0911323i
$916$		0			0
$917$	−44184.5	−	10751.3i	−1.59117	−	0.387174i
$918$		0			0
$919$	−12450.7	+	21565.2i	−0.446910	+	0.774070i	−0.998183	−	0.0602546i	$-0.980809\pi$
$919$	−12450.7	+	21565.2i	−0.446910	+	0.774070i	0.551274	+	0.834325i	$0.314142\pi$
$920$		0			0
$921$	3110.14	+	5386.93i	0.111273	+	0.192731i
$922$		0			0
$923$		−	12719.3i		−	0.453587i
$924$		0			0
$925$		−	10284.5i		−	0.365570i
$926$		0			0
$927$	5249.71	+	9092.77i	0.186001	+	0.322164i
$928$		0			0
$929$	−5730.85	+	9926.12i	−0.202393	+	0.350555i	−0.949299	−	0.314375i	$-0.898205\pi$
$929$	−5730.85	+	9926.12i	−0.202393	+	0.350555i	0.746906	+	0.664930i	$0.231538\pi$
$930$		0			0
$931$	29663.2	−	1372.09i	1.04422	−	0.0483012i
$932$		0			0
$933$	−9572.56	−	5526.72i	−0.335896	−	0.193930i
$934$		0			0
$935$	−14965.4	−	25920.8i	−0.523443	−	0.906630i
$936$		0			0
$937$	−5527.69			−0.192723			−0.0963617	−	0.995346i	$-0.530721\pi$
$937$	−5527.69			−0.192723			−0.0963617	+	0.995346i	$0.530721\pi$
$938$		0			0
$939$			8873.55i			0.308389i
$940$		0			0
$941$	−1517.92	+	876.373i	−0.0525854	+	0.0303602i	−0.526062	−	0.850446i	$-0.676332\pi$
$941$	−1517.92	+	876.373i	−0.0525854	+	0.0303602i	0.473477	+	0.880806i	$0.342999\pi$
$942$		0			0
$943$	22343.1	−	38699.4i	0.771570	−	1.33640i
$944$		0			0
$945$	5240.38	−	21536.4i	0.180391	−	0.741353i
$946$		0			0
$947$	17093.0	+	9868.64i	0.586533	+	0.338635i	0.763726	−	0.645541i	$-0.223368\pi$
$947$	17093.0	+	9868.64i	0.586533	+	0.338635i	−0.177192	+	0.984176i	$0.556701\pi$
$948$		0			0
$949$	−23919.9	+	13810.2i	−0.818202	+	0.472389i
$950$		0			0
$951$	3747.09			0.127768
$952$		0			0
$953$	17751.6			0.603389			0.301694	−	0.953405i	$-0.402448\pi$
$953$	17751.6			0.603389			0.301694	+	0.953405i	$0.402448\pi$
$954$		0			0
$955$	5530.24	−	3192.89i	0.187387	−	0.108188i
$956$		0			0
$957$	11788.5	+	6806.11i	0.398191	+	0.229896i
$958$		0			0
$959$	32679.4	+	31202.7i	1.10039	+	1.05067i
$960$		0			0
$961$	−13365.5	+	23149.7i	−0.448642	+	0.777072i
$962$		0			0
$963$	6250.96	−	3608.99i	0.209174	−	0.120766i
$964$		0			0
$965$		−	41812.7i		−	1.39482i
$966$		0			0
$967$	31083.0			1.03367			0.516836	−	0.856085i	$-0.327110\pi$
$967$	31083.0			1.03367			0.516836	+	0.856085i	$0.327110\pi$
$968$		0			0
$969$	−8468.66	−	14668.2i	−0.280756	−	0.486284i
$970$		0			0
$971$	−10899.2	−	6292.63i	−0.360217	−	0.207971i	0.308959	−	0.951075i	$-0.400019\pi$
$971$	−10899.2	−	6292.63i	−0.360217	−	0.207971i	−0.669176	+	0.743104i	$0.733353\pi$
$972$		0			0
$973$	14491.9	+	49481.0i	0.477482	+	1.63031i
$974$		0			0
$975$	2393.43	−	4145.54i	0.0786166	−	0.136168i
$976$		0			0
$977$	−10203.6	−	17673.1i	−0.334126	−	0.578722i	0.649191	−	0.760625i	$-0.275108\pi$
$977$	−10203.6	−	17673.1i	−0.334126	−	0.578722i	−0.983316	+	0.181903i	$0.941774\pi$
$978$		0			0
$979$			54537.1i			1.78040i
$980$		0			0
$981$			15358.7i			0.499861i
$982$		0			0
$983$	−23381.3	−	40497.5i	−0.758643	−	1.31401i	−0.943543	−	0.331251i	$-0.892529\pi$
$983$	−23381.3	−	40497.5i	−0.758643	−	1.31401i	0.184900	−	0.982757i	$-0.440804\pi$
$984$		0			0
$985$	−10199.7	+	17666.4i	−0.329938	+	0.571469i
$986$		0			0
$987$	3931.67	+	13424.2i	0.126795	+	0.432926i
$988$		0			0
$989$	−24622.2	−	14215.7i	−0.791650	−	0.457059i
$990$		0			0
$991$	−3271.64	−	5666.64i	−0.104871	−	0.181641i	0.808815	−	0.588064i	$-0.200110\pi$
$991$	−3271.64	−	5666.64i	−0.104871	−	0.181641i	−0.913685	+	0.406422i	$0.866776\pi$
$992$		0			0
$993$	−1176.47			−0.0375974
$994$		0			0
$995$			30110.9i			0.959378i
$996$		0			0
$997$	−11066.6	+	6389.30i	−0.351537	+	0.202960i	−0.665362	−	0.746521i	$-0.731723\pi$
$997$	−11066.6	+	6389.30i	−0.351537	+	0.202960i	0.313825	+	0.949481i	$0.398389\pi$
$998$		0			0
$999$	14526.9	−	25161.3i	0.460070	−	0.796864i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	224.4.t.a.177.8		44
4.3	odd	2		56.4.p.a.37.22	yes	44
7.4	even	3	inner	224.4.t.a.81.15		44
8.3	odd	2		56.4.p.a.37.8	✓	44
8.5	even	2	inner	224.4.t.a.177.15		44
28.11	odd	6		56.4.p.a.53.8	yes	44
56.11	odd	6		56.4.p.a.53.22	yes	44
56.53	even	6	inner	224.4.t.a.81.8		44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.4.p.a.37.8	✓	44	8.3	odd	2
56.4.p.a.37.22	yes	44	4.3	odd	2
56.4.p.a.53.8	yes	44	28.11	odd	6
56.4.p.a.53.22	yes	44	56.11	odd	6
224.4.t.a.81.8		44	56.53	even	6	inner
224.4.t.a.81.15		44	7.4	even	3	inner
224.4.t.a.177.8		44	1.1	even	1	trivial
224.4.t.a.177.15		44	8.5	even	2	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:	\( N \)	\(=\)	\( 224 = 2^{5} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	224.t (of order \(6\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(-2.65541 + 1.53310i) q^{3} +(-7.57927 - 4.37589i) q^{5} +(-17.7736 + 5.20552i) q^{7} +(-8.79921 + 15.2407i) q^{9} +(46.4189 - 26.8000i) q^{11} -32.2514i q^{13} +26.8347 q^{15} +(31.9026 + 55.2570i) q^{17} +(74.9753 + 43.2870i) q^{19} +(39.2157 - 41.0716i) q^{21} +(64.1008 - 111.026i) q^{23} +(-24.2031 - 41.9211i) q^{25} -136.748i q^{27} -82.8256i q^{29} +(118.872 + 205.892i) q^{31} +(-82.1740 + 142.330i) q^{33} +(157.490 + 38.3215i) q^{35} +(183.998 + 106.231i) q^{37} +(49.4447 + 85.6407i) q^{39} +348.562 q^{41} -221.770i q^{43} +(133.383 - 77.0088i) q^{45} +(-123.164 + 213.326i) q^{47} +(288.805 - 185.042i) q^{49} +(-169.429 - 97.8198i) q^{51} +(403.213 - 232.795i) q^{53} -469.095 q^{55} -265.453 q^{57} +(-163.759 + 94.5465i) q^{59} +(-162.805 - 93.9955i) q^{61} +(77.0584 - 316.687i) q^{63} +(-141.129 + 244.442i) q^{65} +(-155.578 + 89.8230i) q^{67} +393.092i q^{69} +394.379 q^{71} +(-428.204 - 741.671i) q^{73} +(128.538 + 74.2116i) q^{75} +(-685.525 + 717.967i) q^{77} +(44.9579 - 77.8694i) q^{79} +(-27.9308 - 48.3776i) q^{81} -199.293i q^{83} -558.410i q^{85} +(126.980 + 219.936i) q^{87} +(-508.742 + 881.168i) q^{89} +(167.886 + 573.225i) q^{91} +(-631.306 - 364.485i) q^{93} +(-378.839 - 656.168i) q^{95} +196.625 q^{97} +943.274i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 4 q^{7} + 160 q^{9} + 116 q^{15} - 2 q^{17} - 162 q^{23} + 348 q^{25} + 374 q^{31} - 110 q^{33} - 52 q^{39} - 8 q^{41} + 738 q^{47} + 356 q^{49} + 2268 q^{55} - 452 q^{57} - 668 q^{63} + 248 q^{65}+ \cdots + 1672 q^{97}+O(q^{100}) \) 44 * q + 4 * q^7 + 160 * q^9 + 116 * q^15 - 2 * q^17 - 162 * q^23 + 348 * q^25 + 374 * q^31 - 110 * q^33 - 52 * q^39 - 8 * q^41 + 738 * q^47 + 356 * q^49 + 2268 * q^55 - 452 * q^57 - 668 * q^63 + 248 * q^65 - 1248 * q^71 - 218 * q^73 - 298 * q^79 - 1050 * q^81 - 2140 * q^87 + 422 * q^89 + 2434 * q^95 + 1672 * q^97

Introduction

L-functions

Modular forms

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Database

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