LMFDB - Embedded newform 644.4.i.b.93.10

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [644,4,Mod(93,644)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(644, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([0, 2, 0]))

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

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

chi := DirichletCharacter("644.93");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 644 = 2^{2} \cdot 7 \cdot 23 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	644.i (of order $3$, degree $2$, 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:	$37.9972300437$
Analytic rank:	$0$
Dimension:	$44$
Relative dimension:	$22$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			93.10
Character	$\chi$	$=$	644.93
Dual form			644.4.i.b.277.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.439555 - 0.761331i) q^{3} +(5.30456 - 9.18776i) q^{5} +(-16.9718 + 7.41335i) q^{7} +(13.1136 - 22.7134i) q^{9} +O(q^{10})$	\(q+(-0.439555 - 0.761331i) q^{3} +(5.30456 - 9.18776i) q^{5} +(-16.9718 + 7.41335i) q^{7} +(13.1136 - 22.7134i) q^{9} +(29.3313 + 50.8033i) q^{11} +39.3034 q^{13} -9.32657 q^{15} +(-12.9581 - 22.4441i) q^{17} +(-67.1347 + 116.281i) q^{19} +(13.1041 + 9.66259i) q^{21} +(11.5000 - 19.9186i) q^{23} +(6.22333 + 10.7791i) q^{25} -46.7925 q^{27} -21.6803 q^{29} +(39.7437 + 68.8381i) q^{31} +(25.7854 - 44.6617i) q^{33} +(-21.9159 + 195.257i) q^{35} +(129.331 - 224.007i) q^{37} +(-17.2760 - 29.9229i) q^{39} +397.769 q^{41} +259.970 q^{43} +(-139.124 - 240.969i) q^{45} +(-133.817 + 231.777i) q^{47} +(233.085 - 251.636i) q^{49} +(-11.3916 + 19.7308i) q^{51} +(66.3148 + 114.861i) q^{53} +622.359 q^{55} +118.038 q^{57} +(-159.655 - 276.531i) q^{59} +(197.037 - 341.278i) q^{61} +(-54.1789 + 482.703i) q^{63} +(208.487 - 361.110i) q^{65} +(-92.7140 - 160.585i) q^{67} -20.2195 q^{69} -326.312 q^{71} +(466.189 + 807.463i) q^{73} +(5.47099 - 9.47604i) q^{75} +(-874.429 - 644.781i) q^{77} +(9.85342 - 17.0666i) q^{79} +(-333.499 - 577.637i) q^{81} +1187.58 q^{83} -274.948 q^{85} +(9.52966 + 16.5059i) q^{87} +(-466.516 + 808.029i) q^{89} +(-667.049 + 291.370i) q^{91} +(34.9391 - 60.5163i) q^{93} +(712.240 + 1233.64i) q^{95} +1402.60 q^{97} +1538.56 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	$ 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) $ 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/644\mathbb{Z}\right)^\times$.

$n$	$185$	$281$	$323$
$\chi(n)$	$e\left(\frac{1}{3}\right)$	$1$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.439555	−	0.761331i	−0.0845923	−	0.146518i	0.820625	−	0.571467i	$-0.193625\pi$
$3$	−0.439555	−	0.761331i	−0.0845923	−	0.146518i	−0.905217	+	0.424949i	$0.860292\pi$
$4$		0			0
$5$	5.30456	−	9.18776i	0.474454	−	0.821779i	−0.525118	−	0.851029i	$-0.675979\pi$
$5$	5.30456	−	9.18776i	0.474454	−	0.821779i	0.999572	+	0.0292509i	$0.00931216\pi$
$6$		0			0
$7$	−16.9718	+	7.41335i	−0.916392	+	0.400283i
$7$	−16.9718	+	7.41335i	−0.916392	+	0.400283i
$8$		0			0
$9$	13.1136	−	22.7134i	0.485688	−	0.841237i
$10$		0			0
$11$	29.3313	+	50.8033i	0.803975	+	1.39253i	0.916981	+	0.398932i	$0.130619\pi$
$11$	29.3313	+	50.8033i	0.803975	+	1.39253i	−0.113005	+	0.993594i	$0.536048\pi$
$12$		0			0
$13$	39.3034			0.838523			0.419261	−	0.907866i	$-0.362289\pi$
$13$	39.3034			0.838523			0.419261	+	0.907866i	$0.362289\pi$
$14$		0			0
$15$	−9.32657			−0.160541
$16$		0			0
$17$	−12.9581	−	22.4441i	−0.184871	−	0.320206i	0.758662	−	0.651484i	$-0.225853\pi$
$17$	−12.9581	−	22.4441i	−0.184871	−	0.320206i	−0.943533	+	0.331278i	$0.892520\pi$
$18$		0			0
$19$	−67.1347	+	116.281i	−0.810619	+	1.40403i	0.101812	+	0.994804i	$0.467536\pi$
$19$	−67.1347	+	116.281i	−0.810619	+	1.40403i	−0.912431	+	0.409230i	$0.865797\pi$
$20$		0			0
$21$	13.1041	+	9.66259i	0.136168	+	0.100407i
$22$		0			0
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$23$	11.5000	−	19.9186i	0.104257	−	0.180579i
$24$		0			0
$25$	6.22333	+	10.7791i	0.0497867	+	0.0862331i
$26$		0			0
$27$	−46.7925			−0.333527
$28$		0			0
$29$	−21.6803			−0.138825			−0.0694125	−	0.997588i	$-0.522112\pi$
$29$	−21.6803			−0.138825			−0.0694125	+	0.997588i	$0.522112\pi$
$30$		0			0
$31$	39.7437	+	68.8381i	0.230264	+	0.398829i	0.957886	−	0.287150i	$-0.0927077\pi$
$31$	39.7437	+	68.8381i	0.230264	+	0.398829i	−0.727622	+	0.685979i	$0.759374\pi$
$32$		0			0
$33$	25.7854	−	44.6617i	0.136020	−	0.235594i
$34$		0			0
$35$	−21.9159	+	195.257i	−0.105842	+	0.942987i
$36$		0			0
$37$	129.331	−	224.007i	0.574643	−	0.995312i	−0.421437	−	0.906858i	$-0.638474\pi$
$37$	129.331	−	224.007i	0.574643	−	0.995312i	0.996080	−	0.0884538i	$-0.0281926\pi$
$38$		0			0
$39$	−17.2760	−	29.9229i	−0.0709326	−	0.122859i
$40$		0			0
$41$	397.769			1.51515			0.757574	−	0.652749i	$-0.226385\pi$
$41$	397.769			1.51515			0.757574	+	0.652749i	$0.226385\pi$
$42$		0			0
$43$	259.970			0.921976			0.460988	−	0.887406i	$-0.347495\pi$
$43$	259.970			0.921976			0.460988	+	0.887406i	$0.347495\pi$
$44$		0			0
$45$	−139.124	−	240.969i	−0.460874	−	0.798256i
$46$		0			0
$47$	−133.817	+	231.777i	−0.415301	+	0.719323i	−0.995460	−	0.0951805i	$-0.969657\pi$
$47$	−133.817	+	231.777i	−0.415301	+	0.719323i	0.580159	+	0.814503i	$0.302991\pi$
$48$		0			0
$49$	233.085	−	251.636i	0.679547	−	0.733632i
$50$		0			0
$51$	−11.3916	+	19.7308i	−0.0312773	+	0.0541739i
$52$		0			0
$53$	66.3148	+	114.861i	0.171869	+	0.297685i	0.939073	−	0.343717i	$-0.111686\pi$
$53$	66.3148	+	114.861i	0.171869	+	0.297685i	−0.767205	+	0.641402i	$0.778353\pi$
$54$		0			0
$55$	622.359			1.52580
$56$		0			0
$57$	118.038			0.274289
$58$		0			0
$59$	−159.655	−	276.531i	−0.352294	−	0.610191i	0.634357	−	0.773040i	$-0.281265\pi$
$59$	−159.655	−	276.531i	−0.352294	−	0.610191i	−0.986651	+	0.162849i	$0.947932\pi$
$60$		0			0
$61$	197.037	−	341.278i	0.413574	−	0.716330i	−0.581704	−	0.813401i	$-0.697614\pi$
$61$	197.037	−	341.278i	0.413574	−	0.716330i	0.995278	+	0.0970701i	$0.0309471\pi$
$62$		0			0
$63$	−54.1789	+	482.703i	−0.108348	+	0.965315i
$64$		0			0
$65$	208.487	−	361.110i	0.397841	−	0.689080i
$66$		0			0
$67$	−92.7140	−	160.585i	−0.169057	−	0.292815i	0.769032	−	0.639211i	$-0.220739\pi$
$67$	−92.7140	−	160.585i	−0.169057	−	0.292815i	−0.938089	+	0.346395i	$0.887406\pi$
$68$		0			0
$69$	−20.2195			−0.0352774
$70$		0			0
$71$	−326.312			−0.545439			−0.272719	−	0.962094i	$-0.587923\pi$
$71$	−326.312			−0.545439			−0.272719	+	0.962094i	$0.587923\pi$
$72$		0			0
$73$	466.189	+	807.463i	0.747442	+	1.29461i	0.949045	+	0.315140i	$0.102052\pi$
$73$	466.189	+	807.463i	0.747442	+	1.29461i	−0.201603	+	0.979467i	$0.564615\pi$
$74$		0			0
$75$	5.47099	−	9.47604i	0.00842314	−	0.0145893i
$76$		0			0
$77$	−874.429	−	644.781i	−1.29416	−	0.954281i
$78$		0			0
$79$	9.85342	−	17.0666i	0.0140329	−	0.0243056i	−0.858924	−	0.512104i	$-0.828866\pi$
$79$	9.85342	−	17.0666i	0.0140329	−	0.0243056i	0.872957	+	0.487798i	$0.162200\pi$
$80$		0			0
$81$	−333.499	−	577.637i	−0.457474	−	0.792369i
$82$		0			0
$83$	1187.58			1.57053			0.785266	−	0.619159i	$-0.212526\pi$
$83$	1187.58			1.57053			0.785266	+	0.619159i	$0.212526\pi$
$84$		0			0
$85$	−274.948			−0.350851
$86$		0			0
$87$	9.52966	+	16.5059i	0.0117435	+	0.0203404i
$88$		0			0
$89$	−466.516	+	808.029i	−0.555624	+	0.962369i	0.442230	+	0.896901i	$0.354187\pi$
$89$	−466.516	+	808.029i	−0.555624	+	0.962369i	−0.997855	+	0.0654680i	$0.979146\pi$
$90$		0			0
$91$	−667.049	+	291.370i	−0.768415	+	0.335647i
$92$		0			0
$93$	34.9391	−	60.5163i	0.0389571	−	0.0674757i
$94$		0			0
$95$	712.240	+	1233.64i	0.769203	+	1.33230i
$96$		0			0
$97$	1402.60			1.46817			0.734086	−	0.679056i	$-0.237611\pi$
$97$	1402.60			1.46817			0.734086	+	0.679056i	$0.237611\pi$
$98$		0			0
$99$	1538.56			1.56193
$100$		0			0
$101$	375.965	+	651.190i	0.370395	+	0.641543i	0.989626	−	0.143666i	$-0.0458891\pi$
$101$	375.965	+	651.190i	0.370395	+	0.641543i	−0.619231	+	0.785208i	$0.712556\pi$
$102$		0			0
$103$	632.709	−	1095.88i	0.605268	−	1.04836i	−0.386741	−	0.922189i	$-0.626399\pi$
$103$	632.709	−	1095.88i	0.605268	−	1.04836i	0.992009	−	0.126167i	$-0.0402675\pi$
$104$		0			0
$105$	158.289	−	69.1411i	0.147118	−	0.0642618i
$106$		0			0
$107$	378.847	−	656.183i	0.342286	−	0.592856i	−0.642571	−	0.766226i	$-0.722132\pi$
$107$	378.847	−	656.183i	0.342286	−	0.592856i	0.984857	+	0.173370i	$0.0554657\pi$
$108$		0			0
$109$	−492.933	−	853.786i	−0.433160	−	0.750255i	0.563983	−	0.825786i	$-0.309268\pi$
$109$	−492.933	−	853.786i	−0.433160	−	0.750255i	−0.997143	+	0.0755308i	$0.975935\pi$
$110$		0			0
$111$	−227.391			−0.194442
$112$		0			0
$113$	1387.71			1.15527			0.577633	−	0.816297i	$-0.303977\pi$
$113$	1387.71			1.15527			0.577633	+	0.816297i	$0.303977\pi$
$114$		0			0
$115$	−122.005	−	211.319i	−0.0989305	−	0.171353i
$116$		0			0
$117$	515.408	−	892.713i	0.407261	−	0.705396i
$118$		0			0
$119$	386.309	+	284.854i	0.297587	+	0.219433i
$120$		0			0
$121$	−1055.15	+	1827.58i	−0.792752	+	1.37309i
$122$		0			0
$123$	−174.841	−	302.834i	−0.128170	−	0.221997i
$124$		0			0
$125$	1458.19			1.04339
$126$		0			0
$127$	2455.64			1.71577			0.857886	−	0.513839i	$-0.171777\pi$
$127$	2455.64			1.71577			0.857886	+	0.513839i	$0.171777\pi$
$128$		0			0
$129$	−114.271	−	197.923i	−0.0779921	−	0.135086i
$130$		0			0
$131$	−104.992	+	181.851i	−0.0700242	+	0.121286i	−0.898912	−	0.438130i	$-0.855641\pi$
$131$	−104.992	+	181.851i	−0.0700242	+	0.121286i	0.828887	+	0.559415i	$0.188974\pi$
$132$		0			0
$133$	277.368	−	2471.19i	0.180834	−	1.61112i
$134$		0			0
$135$	−248.214	+	429.918i	−0.158243	+	0.274085i
$136$		0			0
$137$	−284.725	−	493.158i	−0.177560	−	0.307543i	0.763484	−	0.645826i	$-0.223487\pi$
$137$	−284.725	−	493.158i	−0.177560	−	0.307543i	−0.941044	+	0.338284i	$0.890154\pi$
$138$		0			0
$139$	509.273			0.310762			0.155381	−	0.987855i	$-0.450339\pi$
$139$	509.273			0.310762			0.155381	+	0.987855i	$0.450339\pi$
$140$		0			0
$141$	235.279			0.140525
$142$		0			0
$143$	1152.82	+	1996.74i	0.674152	+	1.16766i
$144$		0			0
$145$	−115.004	+	199.193i	−0.0658660	+	0.114083i
$146$		0			0
$147$	−294.032	−	66.8468i	−0.164975	−	0.0375063i
$148$		0			0
$149$	−1125.16	+	1948.83i	−0.618633	+	1.07150i	0.371102	+	0.928592i	$0.378980\pi$
$149$	−1125.16	+	1948.83i	−0.618633	+	1.07150i	−0.989735	+	0.142912i	$0.954353\pi$
$150$		0			0
$151$	97.1244	+	168.224i	0.0523435	+	0.0906616i	0.891010	−	0.453984i	$-0.149998\pi$
$151$	97.1244	+	168.224i	0.0523435	+	0.0906616i	−0.838666	+	0.544645i	$0.816664\pi$
$152$		0			0
$153$	−679.710			−0.359159
$154$		0			0
$155$	843.291			0.436999
$156$		0			0
$157$	763.186	+	1321.88i	0.387955	+	0.671957i	0.992174	−	0.124861i	$-0.0398484\pi$
$157$	763.186	+	1321.88i	0.387955	+	0.671957i	−0.604220	+	0.796818i	$0.706515\pi$
$158$		0			0
$159$	58.2979	−	100.975i	0.0290775	−	0.0503638i
$160$		0			0
$161$	−47.5124	+	423.308i	−0.0232578	+	0.207213i
$162$		0			0
$163$	−87.2232	+	151.075i	−0.0419132	+	0.0725957i	−0.886221	−	0.463263i	$-0.846679\pi$
$163$	−87.2232	+	151.075i	−0.0419132	+	0.0725957i	0.844308	+	0.535858i	$0.180012\pi$
$164$		0			0
$165$	−273.561	−	473.821i	−0.129071	−	0.223557i
$166$		0			0
$167$	−3719.21			−1.72336			−0.861679	−	0.507453i	$-0.830587\pi$
$167$	−3719.21			−1.72336			−0.861679	+	0.507453i	$0.830587\pi$
$168$		0			0
$169$	−652.244			−0.296879
$170$		0			0
$171$	1760.75	+	3049.72i	0.787417	+	1.36385i
$172$		0			0
$173$	−97.5873	+	169.026i	−0.0428869	+	0.0742822i	−0.886672	−	0.462399i	$-0.846989\pi$
$173$	−97.5873	+	169.026i	−0.0428869	+	0.0742822i	0.843785	+	0.536681i	$0.180322\pi$
$174$		0			0
$175$	−185.531	−	136.806i	−0.0801417	−	0.0590945i
$176$		0			0
$177$	−140.354	+	243.101i	−0.0596027	+	0.103235i
$178$		0			0
$179$	−2012.50	−	3485.75i	−0.840341	−	1.45551i	−0.889606	−	0.456728i	$-0.849021\pi$
$179$	−2012.50	−	3485.75i	−0.840341	−	1.45551i	0.0492649	−	0.998786i	$-0.484312\pi$
$180$		0			0
$181$	1044.53			0.428948			0.214474	−	0.976730i	$-0.431196\pi$
$181$	1044.53			0.428948			0.214474	+	0.976730i	$0.431196\pi$
$182$		0			0
$183$	−346.434			−0.139941
$184$		0			0
$185$	−1372.08	−	2376.52i	−0.545284	−	0.944459i
$186$		0			0
$187$	760.158	−	1316.63i	0.297263	−	0.514875i
$188$		0			0
$189$	794.153	−	346.889i	0.305641	−	0.133505i
$190$		0			0
$191$	1656.82	−	2869.70i	0.627661	−	1.08714i	−0.360358	−	0.932814i	$-0.617346\pi$
$191$	1656.82	−	2869.70i	0.627661	−	1.08714i	0.988020	−	0.154328i	$-0.0493211\pi$
$192$		0			0
$193$	2519.65	+	4364.16i	0.939731	+	1.62766i	0.765972	+	0.642874i	$0.222258\pi$
$193$	2519.65	+	4364.16i	0.939731	+	1.62766i	0.173759	+	0.984788i	$0.444408\pi$
$194$		0			0
$195$	−366.566			−0.134617
$196$		0			0
$197$	−5383.62			−1.94704			−0.973521	−	0.228597i	$-0.926586\pi$
$197$	−5383.62			−1.94704			−0.973521	+	0.228597i	$0.926586\pi$
$198$		0			0
$199$	−874.722	−	1515.06i	−0.311595	−	0.539698i	0.667113	−	0.744957i	$-0.267530\pi$
$199$	−874.722	−	1515.06i	−0.311595	−	0.539698i	−0.978708	+	0.205258i	$0.934197\pi$
$200$		0			0
$201$	−81.5058	+	141.172i	−0.0286019	+	0.0495399i
$202$		0			0
$203$	367.953	−	160.723i	0.127218	−	0.0555693i
$204$		0			0
$205$	2109.99	−	3654.61i	0.718868	−	1.24512i
$206$		0			0
$207$	−301.612	−	522.408i	−0.101273	−	0.175410i
$208$		0			0
$209$	−7876.60			−2.60687
$210$		0			0
$211$	−5111.43			−1.66770			−0.833851	−	0.551990i	$-0.813869\pi$
$211$	−5111.43			−1.66770			−0.833851	+	0.551990i	$0.813869\pi$
$212$		0			0
$213$	143.432	+	248.432i	0.0461399	+	0.0799167i
$214$		0			0
$215$	1379.02	−	2388.54i	0.437435	−	0.757660i
$216$		0			0
$217$	−1184.84	−	873.674i	−0.370656	−	0.273313i
$218$		0			0
$219$	409.831	−	709.848i	0.126456	−	0.219028i
$220$		0			0
$221$	−509.298	−	882.130i	−0.155019	−	0.268500i
$222$		0			0
$223$	−3217.18			−0.966092			−0.483046	−	0.875595i	$-0.660470\pi$
$223$	−3217.18			−0.966092			−0.483046	+	0.875595i	$0.660470\pi$
$224$		0			0
$225$	326.441			0.0967232
$226$		0			0
$227$	1614.23	+	2795.93i	0.471983	+	0.817498i	0.999486	−	0.0320547i	$-0.0102051\pi$
$227$	1614.23	+	2795.93i	0.471983	+	0.817498i	−0.527503	+	0.849553i	$0.676872\pi$
$228$		0			0
$229$	2393.08	−	4144.94i	0.690564	−	1.19609i	−0.281089	−	0.959682i	$-0.590696\pi$
$229$	2393.08	−	4144.94i	0.690564	−	1.19609i	0.971653	−	0.236410i	$-0.0759710\pi$
$230$		0			0
$231$	−106.533	+	949.146i	−0.0303435	+	0.270343i
$232$		0			0
$233$	−470.729	+	815.327i	−0.132354	+	0.229244i	−0.924584	−	0.380979i	$-0.875587\pi$
$233$	−470.729	+	815.327i	−0.132354	+	0.229244i	0.792230	+	0.610223i	$0.208920\pi$
$234$		0			0
$235$	1419.68	+	2458.95i	0.394083	+	0.682571i
$236$		0			0
$237$	−17.3245			−0.00474829
$238$		0			0
$239$	5485.87			1.48473			0.742367	−	0.669994i	$-0.233703\pi$
$239$	5485.87			1.48473			0.742367	+	0.669994i	$0.233703\pi$
$240$		0			0
$241$	1057.09	+	1830.93i	0.282544	+	0.489380i	0.972011	−	0.234937i	$-0.0754884\pi$
$241$	1057.09	+	1830.93i	0.282544	+	0.489380i	−0.689467	+	0.724317i	$0.742155\pi$
$242$		0			0
$243$	−924.881	+	1601.94i	−0.244161	+	0.422899i
$244$		0			0
$245$	−1075.56	−	3476.34i	−0.280469	−	0.906512i
$246$		0			0
$247$	−2638.62	+	4570.23i	−0.679723	+	1.17731i
$248$		0			0
$249$	−522.007	−	904.143i	−0.132855	−	0.230111i
$250$		0			0
$251$	158.941			0.0399692			0.0199846	−	0.999800i	$-0.493638\pi$
$251$	158.941			0.0399692			0.0199846	+	0.999800i	$0.493638\pi$
$252$		0			0
$253$	1349.24			0.335281
$254$		0			0
$255$	120.855	+	209.327i	0.0296793	+	0.0514061i
$256$		0			0
$257$	−3246.36	+	5622.86i	−0.787947	+	1.36476i	0.139276	+	0.990254i	$0.455522\pi$
$257$	−3246.36	+	5622.86i	−0.787947	+	1.36476i	−0.927223	+	0.374510i	$0.877811\pi$
$258$		0			0
$259$	−534.331	+	4760.58i	−0.128192	+	1.14212i
$260$		0			0
$261$	−284.306	+	492.432i	−0.0674256	+	0.116785i
$262$		0			0
$263$	−929.421	−	1609.80i	−0.217911	−	0.377433i	0.736258	−	0.676701i	$-0.236591\pi$
$263$	−929.421	−	1609.80i	−0.217911	−	0.377433i	−0.954169	+	0.299268i	$0.903258\pi$
$264$		0			0
$265$	1407.08			0.326175
$266$		0			0
$267$	820.237			0.188006
$268$		0			0
$269$	−332.597	−	576.075i	−0.0753858	−	0.130572i	0.825868	−	0.563863i	$-0.190686\pi$
$269$	−332.597	−	576.075i	−0.0753858	−	0.130572i	−0.901254	+	0.433291i	$0.857352\pi$
$270$		0			0
$271$	−1116.82	+	1934.39i	−0.250339	+	0.433601i	−0.963619	−	0.267279i	$-0.913876\pi$
$271$	−1116.82	+	1934.39i	−0.250339	+	0.433601i	0.713280	+	0.700879i	$0.247209\pi$
$272$		0			0
$273$	515.034	+	379.773i	0.114180	+	0.0841937i
$274$		0			0
$275$	−365.077	+	632.332i	−0.0800545	+	0.138658i
$276$		0			0
$277$	2469.78	+	4277.78i	0.535720	+	0.927894i	0.999128	+	0.0417493i	$0.0132931\pi$
$277$	2469.78	+	4277.78i	0.535720	+	0.927894i	−0.463408	+	0.886145i	$0.653374\pi$
$278$		0			0
$279$	2084.73			0.447346
$280$		0			0
$281$	−6636.34			−1.40886			−0.704432	−	0.709772i	$-0.748798\pi$
$281$	−6636.34			−1.40886			−0.704432	+	0.709772i	$0.748798\pi$
$282$		0			0
$283$	3373.87	+	5843.71i	0.708678	+	1.22747i	0.965348	+	0.260967i	$0.0840412\pi$
$283$	3373.87	+	5843.71i	0.708678	+	1.22747i	−0.256670	+	0.966499i	$0.582625\pi$
$284$		0			0
$285$	626.137	−	1084.50i	0.130137	−	0.225405i
$286$		0			0
$287$	−6750.86	+	2948.80i	−1.38847	+	0.606488i
$288$		0			0
$289$	2120.67	−	3673.12i	0.431645	−	0.747632i
$290$		0			0
$291$	−616.521	−	1067.85i	−0.124196	−	0.215114i
$292$		0			0
$293$	1713.95			0.341740			0.170870	−	0.985294i	$-0.445342\pi$
$293$	1713.95			0.341740			0.170870	+	0.985294i	$0.445342\pi$
$294$		0			0
$295$	−3387.60			−0.668589
$296$		0			0
$297$	−1372.49	−	2377.22i	−0.268147	−	0.464445i
$298$		0			0
$299$	451.989	−	782.868i	0.0874221	−	0.151419i
$300$		0			0
$301$	−4412.15	+	1927.24i	−0.844891	+	0.369052i
$302$		0			0
$303$	330.514	−	572.467i	0.0626651	−	0.108539i
$304$		0			0
$305$	−2090.39	−	3620.66i	−0.392443	−	0.679732i
$306$		0			0
$307$	−1262.72			−0.234747			−0.117374	−	0.993088i	$-0.537448\pi$
$307$	−1262.72			−0.234747			−0.117374	+	0.993088i	$0.537448\pi$
$308$		0			0
$309$	−1112.44			−0.204804
$310$		0			0
$311$	29.5734	+	51.2225i	0.00539213	+	0.00933943i	0.868709	−	0.495323i	$-0.164950\pi$
$311$	29.5734	+	51.2225i	0.00539213	+	0.00933943i	−0.863317	+	0.504662i	$0.831617\pi$
$312$		0			0
$313$	2243.90	−	3886.54i	0.405216	−	0.701854i	−0.589131	−	0.808038i	$-0.700530\pi$
$313$	2243.90	−	3886.54i	0.405216	−	0.701854i	0.994347	+	0.106184i	$0.0338631\pi$
$314$		0			0
$315$	4147.56	+	3058.31i	0.741869	+	0.547035i
$316$		0			0
$317$	282.452	−	489.222i	0.0500445	−	0.0866796i	−0.839918	−	0.542713i	$-0.817397\pi$
$317$	282.452	−	489.222i	0.0500445	−	0.0866796i	0.889963	+	0.456034i	$0.150730\pi$
$318$		0			0
$319$	−635.911	−	1101.43i	−0.111612	−	0.193317i
$320$		0			0
$321$	−666.097			−0.115819
$322$		0			0
$323$	3479.76			0.599440
$324$		0			0
$325$	244.598	+	423.656i	0.0417473	+	0.0723084i
$326$		0			0
$327$	−433.342	+	750.571i	−0.0732841	+	0.126932i
$328$		0			0
$329$	552.865	−	4925.71i	0.0926457	−	0.825420i
$330$		0			0
$331$	−685.820	+	1187.87i	−0.113885	+	0.197255i	−0.917334	−	0.398119i	$-0.869663\pi$
$331$	−685.820	+	1187.87i	−0.113885	+	0.197255i	0.803448	+	0.595375i	$0.202996\pi$
$332$		0			0
$333$	−3391.97	−	5875.07i	−0.558195	−	0.966822i
$334$		0			0
$335$	−1967.23			−0.320839
$336$		0			0
$337$	−11620.8			−1.87841			−0.939206	−	0.343355i	$-0.888437\pi$
$337$	−11620.8			−1.87841			−0.939206	+	0.343355i	$0.888437\pi$
$338$		0			0
$339$	−609.976	−	1056.51i	−0.0977266	−	0.169268i
$340$		0			0
$341$	−2331.47	+	4038.23i	−0.370253	+	0.641297i
$342$		0			0
$343$	−2090.40	+	5998.65i	−0.329070	+	0.944305i
$344$		0			0
$345$	−107.256	+	185.772i	−0.0167375	+	0.0289902i
$346$		0			0
$347$	−331.851	−	574.783i	−0.0513392	−	0.0889221i	0.839214	−	0.543802i	$-0.183016\pi$
$347$	−331.851	−	574.783i	−0.0513392	−	0.0889221i	−0.890553	+	0.454880i	$0.849682\pi$
$348$		0			0
$349$	−10070.1			−1.54453			−0.772267	−	0.635298i	$-0.780877\pi$
$349$	−10070.1			−1.54453			−0.772267	+	0.635298i	$0.780877\pi$
$350$		0			0
$351$	−1839.10			−0.279670
$352$		0			0
$353$	−2422.02	−	4195.06i	−0.365187	−	0.632523i	0.623619	−	0.781729i	$-0.285662\pi$
$353$	−2422.02	−	4195.06i	−0.365187	−	0.632523i	−0.988806	+	0.149206i	$0.952328\pi$
$354$		0			0
$355$	−1730.94	+	2998.08i	−0.258786	+	0.448230i
$356$		0			0
$357$	47.0646	−	419.318i	0.00697737	−	0.0621643i
$358$		0			0
$359$	5923.14	−	10259.2i	0.870784	−	1.50824i	0.00959665	−	0.999954i	$-0.496945\pi$
$359$	5923.14	−	10259.2i	0.870784	−	1.50824i	0.861187	−	0.508288i	$-0.169721\pi$
$360$		0			0
$361$	−5584.65	−	9672.89i	−0.814207	−	1.41025i
$362$		0			0
$363$	1855.19			0.268243
$364$		0			0
$365$	9891.70			1.41851
$366$		0			0
$367$	−333.259	−	577.222i	−0.0474005	−	0.0821001i	0.841352	−	0.540488i	$-0.181760\pi$
$367$	−333.259	−	577.222i	−0.0474005	−	0.0821001i	−0.888752	+	0.458388i	$0.848427\pi$
$368$		0			0
$369$	5216.17	−	9034.68i	0.735889	−	1.27460i
$370$		0			0
$371$	−1976.98	−	1457.78i	−0.276657	−	0.204000i
$372$		0			0
$373$	−481.219	+	833.497i	−0.0668005	+	0.115702i	−0.897491	−	0.441032i	$-0.854612\pi$
$373$	−481.219	+	833.497i	−0.0668005	+	0.115702i	0.830691	+	0.556734i	$0.187946\pi$
$374$		0			0
$375$	−640.953	−	1110.16i	−0.0882632	−	0.152876i
$376$		0			0
$377$	−852.107			−0.116408
$378$		0			0
$379$	−5218.91			−0.707328			−0.353664	−	0.935373i	$-0.615064\pi$
$379$	−5218.91			−0.707328			−0.353664	+	0.935373i	$0.615064\pi$
$380$		0			0
$381$	−1079.39	−	1869.56i	−0.145141	−	0.251392i
$382$		0			0
$383$	−2707.29	+	4689.16i	−0.361191	+	0.625601i	−0.988157	−	0.153446i	$-0.950963\pi$
$383$	−2707.29	+	4689.16i	−0.361191	+	0.625601i	0.626966	+	0.779046i	$0.284296\pi$
$384$		0			0
$385$	−10562.6	+	4613.76i	−1.39823	+	0.610751i
$386$		0			0
$387$	3409.13	−	5904.79i	0.447793	−	0.775600i
$388$		0			0
$389$	−2209.70	−	3827.31i	−0.288011	−	0.498850i	0.685324	−	0.728238i	$-0.259661\pi$
$389$	−2209.70	−	3827.31i	−0.288011	−	0.498850i	−0.973335	+	0.229389i	$0.926327\pi$
$390$		0			0
$391$	−596.074			−0.0770965
$392$		0			0
$393$	184.599			0.0236941
$394$		0			0
$395$	−104.536	−	181.062i	−0.0133159	−	0.0230638i
$396$		0			0
$397$	−5102.28	+	8837.40i	−0.645028	+	1.11722i	0.339268	+	0.940690i	$0.389821\pi$
$397$	−5102.28	+	8837.40i	−0.645028	+	1.11722i	−0.984295	+	0.176531i	$0.943513\pi$
$398$		0			0
$399$	−2003.31	+	875.054i	−0.251356	+	0.109793i
$400$		0			0
$401$	846.115	−	1465.51i	0.105369	−	0.182504i	−0.808520	−	0.588469i	$-0.799731\pi$
$401$	846.115	−	1465.51i	0.105369	−	0.182504i	0.913889	+	0.405964i	$0.133064\pi$
$402$		0			0
$403$	1562.06	+	2705.57i	0.193082	+	0.334427i
$404$		0			0
$405$	−7076.26			−0.868202
$406$		0			0
$407$	15173.7			1.84800
$408$		0			0
$409$	979.605	+	1696.73i	0.118431	+	0.205129i	0.919146	−	0.393917i	$-0.128880\pi$
$409$	979.605	+	1696.73i	0.118431	+	0.205129i	−0.800715	+	0.599046i	$0.795547\pi$
$410$		0			0
$411$	−250.304	+	433.540i	−0.0300404	+	0.0520315i
$412$		0			0
$413$	4759.66	+	3509.65i	0.567088	+	0.418156i
$414$		0			0
$415$	6299.60	−	10911.2i	0.745145	−	1.29063i
$416$		0			0
$417$	−223.853	−	387.725i	−0.0262881	−	0.0455323i
$418$		0			0
$419$	413.665			0.0482312			0.0241156	−	0.999709i	$-0.492323\pi$
$419$	413.665			0.0482312			0.0241156	+	0.999709i	$0.492323\pi$
$420$		0			0
$421$	−3390.35			−0.392483			−0.196242	−	0.980556i	$-0.562874\pi$
$421$	−3390.35			−0.392483			−0.196242	+	0.980556i	$0.562874\pi$
$422$		0			0
$423$	3509.63	+	6078.86i	0.403414	+	0.698733i
$424$		0			0
$425$	161.285	−	279.355i	0.0184082	−	0.0318840i
$426$		0			0
$427$	−814.061	+	7252.81i	−0.0922603	+	0.821986i
$428$		0			0
$429$	1013.46	−	1755.36i	0.114056	−	0.197551i
$430$		0			0
$431$	5147.76	+	8916.18i	0.575310	+	0.996467i	0.996008	+	0.0892658i	$0.0284521\pi$
$431$	5147.76	+	8916.18i	0.575310	+	0.996467i	−0.420697	+	0.907201i	$0.638215\pi$
$432$		0			0
$433$	−554.125			−0.0615001			−0.0307501	−	0.999527i	$-0.509790\pi$
$433$	−554.125			−0.0615001			−0.0307501	+	0.999527i	$0.509790\pi$
$434$		0			0
$435$	202.203			0.0222871
$436$		0			0
$437$	1544.10	+	2674.46i	0.169026	+	0.292761i
$438$		0			0
$439$	−7793.75	+	13499.2i	−0.847325	+	1.46761i	0.0362624	+	0.999342i	$0.488455\pi$
$439$	−7793.75	+	13499.2i	−0.847325	+	1.46761i	−0.883587	+	0.468267i	$0.844879\pi$
$440$		0			0
$441$	−2658.93	−	8593.99i	−0.287110	−	0.927976i
$442$		0			0
$443$	4405.46	−	7630.48i	0.472482	−	0.818363i	−0.527022	−	0.849852i	$-0.676691\pi$
$443$	4405.46	−	7630.48i	0.472482	−	0.818363i	0.999504	+	0.0314885i	$0.0100247\pi$
$444$		0			0
$445$	4949.32	+	8572.47i	0.527236	+	0.913200i
$446$		0			0
$447$	1978.27			0.209327
$448$		0			0
$449$	14021.1			1.47371			0.736856	−	0.676050i	$-0.236309\pi$
$449$	14021.1			1.47371			0.736856	+	0.676050i	$0.236309\pi$
$450$		0			0
$451$	11667.1	+	20208.0i	1.21814	+	2.10988i
$452$		0			0
$453$	85.3830	−	147.888i	0.00885572	−	0.0153386i
$454$		0			0
$455$	−861.367	+	7674.28i	−0.0887506	+	0.790716i
$456$		0			0
$457$	3388.09	−	5868.34i	0.346801	−	0.600677i	−0.638878	−	0.769308i	$-0.720601\pi$
$457$	3388.09	−	5868.34i	0.346801	−	0.600677i	0.985679	+	0.168631i	$0.0539345\pi$
$458$		0			0
$459$	606.343	+	1050.22i	0.0616594	+	0.106797i
$460$		0			0
$461$	7296.11			0.737123			0.368561	−	0.929603i	$-0.379850\pi$
$461$	7296.11			0.737123			0.368561	+	0.929603i	$0.379850\pi$
$462$		0			0
$463$	−7792.58			−0.782186			−0.391093	−	0.920351i	$-0.627903\pi$
$463$	−7792.58			−0.782186			−0.391093	+	0.920351i	$0.627903\pi$
$464$		0			0
$465$	−370.673	−	642.024i	−0.0369667	−	0.0640283i
$466$		0			0
$467$	−4766.78	+	8256.30i	−0.472335	+	0.818107i	−0.999499	−	0.0316560i	$-0.989922\pi$
$467$	−4766.78	+	8256.30i	−0.472335	+	0.818107i	0.527164	+	0.849763i	$0.323255\pi$
$468$		0			0
$469$	2764.00	+	2038.10i	0.272131	+	0.200663i
$470$		0			0
$471$	670.924	−	1162.07i	0.0656360	−	0.113685i
$472$		0			0
$473$	7625.25	+	13207.3i	0.741246	+	1.28388i
$474$		0			0
$475$	−1671.21			−0.161432
$476$		0			0
$477$	3478.50			0.333898
$478$		0			0
$479$	−3243.38	−	5617.70i	−0.309382	−	0.535865i	0.668845	−	0.743401i	$-0.266789\pi$
$479$	−3243.38	−	5617.70i	−0.309382	−	0.535865i	−0.978227	+	0.207536i	$0.933455\pi$
$480$		0			0
$481$	5083.13	−	8804.23i	0.481852	−	0.834592i
$482$		0			0
$483$	343.162	−	149.894i	0.0323280	−	0.0141210i
$484$		0			0
$485$	7440.19	−	12886.8i	0.696580	−	1.20651i
$486$		0			0
$487$	1159.86	+	2008.93i	0.107922	+	0.186927i	0.914928	−	0.403616i	$-0.132247\pi$
$487$	1159.86	+	2008.93i	0.107922	+	0.186927i	−0.807006	+	0.590543i	$0.798914\pi$
$488$		0			0
$489$	153.357			0.0141821
$490$		0			0
$491$	19306.5			1.77452			0.887262	−	0.461265i	$-0.152604\pi$
$491$	19306.5			1.77452			0.887262	+	0.461265i	$0.152604\pi$
$492$		0			0
$493$	280.935	+	486.594i	0.0256647	+	0.0444526i
$494$		0			0
$495$	8161.35	−	14135.9i	0.741062	−	1.28356i
$496$		0			0
$497$	5538.11	−	2419.07i	0.499835	−	0.218330i
$498$		0			0
$499$	−7314.25	+	12668.6i	−0.656174	+	1.13653i	0.325424	+	0.945568i	$0.394493\pi$
$499$	−7314.25	+	12668.6i	−0.656174	+	1.13653i	−0.981598	+	0.190958i	$0.938841\pi$
$500$		0			0
$501$	1634.79	+	2831.55i	0.145783	+	0.252503i
$502$		0			0
$503$	−13377.0			−1.18579			−0.592894	−	0.805280i	$-0.702015\pi$
$503$	−13377.0			−1.18579			−0.592894	+	0.805280i	$0.702015\pi$
$504$		0			0
$505$	7977.30			0.702941
$506$		0			0
$507$	286.697	+	496.574i	0.0251137	+	0.0434982i
$508$		0			0
$509$	639.421	−	1107.51i	0.0556814	−	0.0964430i	−0.836841	−	0.547446i	$-0.815600\pi$
$509$	639.421	−	1107.51i	0.0556814	−	0.0964430i	0.892523	+	0.451003i	$0.148934\pi$
$510$		0			0
$511$	−13898.1	−	10248.1i	−1.20316	−	0.887179i
$512$		0			0
$513$	3141.40	−	5441.07i	0.270363	−	0.468283i
$514$		0			0
$515$	−6712.48	−	11626.4i	−0.574344	−	0.994793i
$516$		0			0
$517$	−15700.1			−1.33557
$518$		0			0
$519$	171.580			0.0145116
$520$		0			0
$521$	4023.66	+	6969.18i	0.338348	+	0.586037i	0.984122	−	0.177492i	$-0.0567984\pi$
$521$	4023.66	+	6969.18i	0.338348	+	0.586037i	−0.645774	+	0.763529i	$0.723465\pi$
$522$		0			0
$523$	−1082.44	+	1874.83i	−0.0905002	+	0.156751i	−0.907722	−	0.419573i	$-0.862180\pi$
$523$	−1082.44	+	1874.83i	−0.0905002	+	0.156751i	0.817221	+	0.576324i	$0.195513\pi$
$524$		0			0
$525$	−22.6035	+	201.384i	−0.00187904	+	0.0167412i
$526$		0			0
$527$	1030.01	−	1784.03i	0.0851382	−	0.147464i
$528$		0			0
$529$	−264.500	−	458.127i	−0.0217391	−	0.0376533i
$530$		0			0
$531$	−8374.61			−0.684420
$532$		0			0
$533$	15633.7			1.27049
$534$		0			0
$535$	−4019.23	−	6961.52i	−0.324798	−	0.562566i
$536$		0			0
$537$	−1769.21	+	3064.35i	−0.142173	+	0.246251i
$538$		0			0
$539$	19620.6	+	4460.66i	1.56794	+	0.356464i
$540$		0			0
$541$	9370.81	−	16230.7i	0.744700	−	1.28986i	−0.205635	−	0.978629i	$-0.565926\pi$
$541$	9370.81	−	16230.7i	0.744700	−	1.28986i	0.950335	−	0.311230i	$-0.100741\pi$
$542$		0			0
$543$	−459.130	−	795.236i	−0.0362857	−	0.0628487i
$544$		0			0
$545$	−10459.2			−0.822058
$546$		0			0
$547$	8830.82			0.690271			0.345136	−	0.938553i	$-0.387833\pi$
$547$	8830.82			0.690271			0.345136	+	0.938553i	$0.387833\pi$
$548$		0			0
$549$	−5167.72	−	8950.75i	−0.401736	−	0.695827i
$550$		0			0
$551$	1455.50	−	2521.00i	0.112534	−	0.194915i
$552$		0			0
$553$	−40.7095	+	362.698i	−0.00313046	+	0.0278906i
$554$		0			0
$555$	−1206.21	+	2089.22i	−0.0922537	+	0.159788i
$556$		0			0
$557$	−2222.22	−	3848.99i	−0.169045	−	0.292795i	0.769039	−	0.639202i	$-0.220735\pi$
$557$	−2222.22	−	3848.99i	−0.169045	−	0.292795i	−0.938084	+	0.346407i	$0.887402\pi$
$558$		0			0
$559$	10217.7			0.773098
$560$		0			0
$561$	−1336.52			−0.100585
$562$		0			0
$563$	2742.23	+	4749.68i	0.205277	+	0.355551i	0.950221	−	0.311576i	$-0.100857\pi$
$563$	2742.23	+	4749.68i	0.205277	+	0.355551i	−0.744944	+	0.667127i	$0.767524\pi$
$564$		0			0
$565$	7361.20	−	12750.0i	0.548121	−	0.949373i
$566$		0			0
$567$	9942.30	+	7331.20i	0.736398	+	0.543001i
$568$		0			0
$569$	8195.86	−	14195.6i	0.603846	−	1.04589i	−0.388387	−	0.921496i	$-0.626968\pi$
$569$	8195.86	−	14195.6i	0.603846	−	1.04589i	0.992233	−	0.124395i	$-0.0396991\pi$
$570$		0			0
$571$	−6684.89	−	11578.6i	−0.489937	−	0.848595i	0.509996	−	0.860177i	$-0.329647\pi$
$571$	−6684.89	−	11578.6i	−0.489937	−	0.848595i	−0.999933	+	0.0115815i	$0.996313\pi$
$572$		0			0
$573$	−2913.05			−0.212381
$574$		0			0
$575$	286.273			0.0207625
$576$		0			0
$577$	13098.6	+	22687.4i	0.945061	+	1.63689i	0.755630	+	0.654999i	$0.227331\pi$
$577$	13098.6	+	22687.4i	0.945061	+	1.63689i	0.189431	+	0.981894i	$0.439336\pi$
$578$		0			0
$579$	2215.05	−	3836.57i	0.158988	−	0.275376i
$580$		0			0
$581$	−20155.4	+	8803.96i	−1.43922	+	0.628657i
$582$		0			0
$583$	−3890.20	+	6738.02i	−0.276356	+	0.478663i
$584$		0			0
$585$	−5468.03	−	9470.90i	−0.386453	−	0.669356i
$586$		0			0
$587$	−922.522			−0.0648664			−0.0324332	−	0.999474i	$-0.510326\pi$
$587$	−922.522			−0.0648664			−0.0324332	+	0.999474i	$0.510326\pi$
$588$		0			0
$589$	−10672.7			−0.746626
$590$		0			0
$591$	2366.40	+	4098.72i	0.164705	+	0.285277i
$592$		0			0
$593$	−7031.20	+	12178.4i	−0.486908	+	0.843350i	−0.999887	−	0.0150514i	$-0.995209\pi$
$593$	−7031.20	+	12178.4i	−0.486908	+	0.843350i	0.512978	+	0.858402i	$0.328542\pi$
$594$		0			0
$595$	4666.37	−	2038.29i	0.321517	−	0.140440i
$596$		0			0
$597$	−768.976	+	1331.91i	−0.0527171	+	0.0913087i
$598$		0			0
$599$	7173.29	+	12424.5i	0.489304	+	0.847499i	0.999924	−	0.0123074i	$-0.00391766\pi$
$599$	7173.29	+	12424.5i	0.489304	+	0.847499i	−0.510621	+	0.859806i	$0.670584\pi$
$600$		0			0
$601$	−1762.16			−0.119601			−0.0598004	−	0.998210i	$-0.519046\pi$
$601$	−1762.16			−0.119601			−0.0598004	+	0.998210i	$0.519046\pi$
$602$		0			0
$603$	−4863.25			−0.328436
$604$		0			0
$605$	11194.2	+	19389.0i	0.752249	+	1.30293i
$606$		0			0
$607$	5833.08	−	10103.2i	0.390045	−	0.675578i	−0.602410	−	0.798187i	$-0.705793\pi$
$607$	5833.08	−	10103.2i	0.390045	−	0.675578i	0.992455	+	0.122609i	$0.0391260\pi$
$608$		0			0
$609$	−284.099	−	209.488i	−0.0189036	−	0.0139390i
$610$		0			0
$611$	−5259.45	+	9109.63i	−0.348240	+	0.603169i
$612$		0			0
$613$	11344.4	+	19649.1i	0.747467	+	1.29465i	0.949033	+	0.315175i	$0.102063\pi$
$613$	11344.4	+	19649.1i	0.747467	+	1.29465i	−0.201567	+	0.979475i	$0.564603\pi$
$614$		0			0
$615$	−3709.82			−0.243243
$616$		0			0
$617$	13761.3			0.897910			0.448955	−	0.893554i	$-0.351796\pi$
$617$	13761.3			0.897910			0.448955	+	0.893554i	$0.351796\pi$
$618$		0			0
$619$	14883.5	+	25779.1i	0.966430	+	1.67391i	0.705723	+	0.708488i	$0.250622\pi$
$619$	14883.5	+	25779.1i	0.966430	+	1.67391i	0.260707	+	0.965418i	$0.416044\pi$
$620$		0			0
$621$	−538.114	+	932.040i	−0.0347726	+	0.0602279i
$622$		0			0
$623$	1927.42	−	17172.2i	0.123949	−	1.10431i
$624$		0			0
$625$	6957.12	−	12050.1i	0.445256	−	0.771206i
$626$		0			0
$627$	3462.20	+	5996.70i	0.220521	+	0.381954i
$628$		0			0
$629$	−6703.52			−0.424939
$630$		0			0
$631$	16571.8			1.04550			0.522752	−	0.852485i	$-0.324905\pi$
$631$	16571.8			1.04550			0.522752	+	0.852485i	$0.324905\pi$
$632$		0			0
$633$	2246.75	+	3891.49i	0.141075	+	0.244349i
$634$		0			0
$635$	13026.1	−	22561.9i	0.814055	−	1.40999i
$636$		0			0
$637$	9161.01	−	9890.14i	0.569816	−	0.615167i
$638$		0			0
$639$	−4279.12	+	7411.66i	−0.264913	+	0.458843i
$640$		0			0
$641$	−7907.29	−	13695.8i	−0.487238	−	0.843920i	0.512655	−	0.858595i	$-0.328662\pi$
$641$	−7907.29	−	13695.8i	−0.487238	−	0.843920i	−0.999892	+	0.0146747i	$0.995329\pi$
$642$		0			0
$643$	−23333.2			−1.43106			−0.715530	−	0.698583i	$-0.753815\pi$
$643$	−23333.2			−1.43106			−0.715530	+	0.698583i	$0.753815\pi$
$644$		0			0
$645$	−2424.62			−0.148015
$646$		0			0
$647$	−5785.68	−	10021.1i	−0.351559	−	0.608918i	0.634964	−	0.772542i	$-0.281015\pi$
$647$	−5785.68	−	10021.1i	−0.351559	−	0.608918i	−0.986523	+	0.163624i	$0.947682\pi$
$648$		0			0
$649$	9365.80	−	16222.0i	0.566471	−	0.981157i
$650$		0			0
$651$	−144.351	+	1286.09i	−0.00869059	+	0.0774281i
$652$		0			0
$653$	638.473	−	1105.87i	0.0382625	−	0.0662725i	−0.846260	−	0.532770i	$-0.821151\pi$
$653$	638.473	−	1105.87i	0.0382625	−	0.0662725i	0.884522	+	0.466498i	$0.154484\pi$
$654$		0			0
$655$	1113.87	+	1929.28i	0.0664466	+	0.115089i
$656$		0			0
$657$	24453.6			1.45210
$658$		0			0
$659$	17871.7			1.05642			0.528210	−	0.849114i	$-0.322863\pi$
$659$	17871.7			1.05642			0.528210	+	0.849114i	$0.322863\pi$
$660$		0			0
$661$	1989.27	+	3445.52i	0.117055	+	0.202746i	0.918600	−	0.395190i	$-0.129321\pi$
$661$	1989.27	+	3445.52i	0.117055	+	0.202746i	−0.801544	+	0.597936i	$0.795988\pi$
$662$		0			0
$663$	−447.729	+	775.489i	−0.0262268	+	0.0454261i
$664$		0			0
$665$	−21233.4	−	15657.0i	−1.23819	−	0.913008i
$666$		0			0
$667$	−249.323	+	431.840i	−0.0144735	+	0.0250688i
$668$		0			0
$669$	1414.13	+	2449.34i	0.0817240	+	0.141550i
$670$		0			0
$671$	23117.4			1.33001
$672$		0			0
$673$	−16363.4			−0.937243			−0.468621	−	0.883399i	$-0.655249\pi$
$673$	−16363.4			−0.937243			−0.468621	+	0.883399i	$0.655249\pi$
$674$		0			0
$675$	−291.205	−	504.383i	−0.0166052	−	0.0287610i
$676$		0			0
$677$	5717.85	−	9903.60i	0.324601	−	0.562225i	−0.656831	−	0.754038i	$-0.728103\pi$
$677$	5717.85	−	9903.60i	0.324601	−	0.562225i	0.981431	+	0.191813i	$0.0614367\pi$
$678$		0			0
$679$	−23804.7	+	10398.0i	−1.34542	+	0.587685i
$680$		0			0
$681$	1419.08	−	2457.92i	0.0798523	−	0.138308i
$682$		0			0
$683$	−10677.9	−	18494.6i	−0.598210	−	1.03613i	−0.993085	−	0.117396i	$-0.962545\pi$
$683$	−10677.9	−	18494.6i	−0.598210	−	1.03613i	0.394875	−	0.918735i	$-0.370788\pi$
$684$		0			0
$685$	−6041.36			−0.336976
$686$		0			0
$687$	−4207.56			−0.233666
$688$		0			0
$689$	2606.39	+	4514.41i	0.144116	+	0.249616i
$690$		0			0
$691$	7530.27	−	13042.8i	0.414566	−	0.718049i	−0.580817	−	0.814034i	$-0.697267\pi$
$691$	7530.27	−	13042.8i	0.414566	−	0.718049i	0.995383	+	0.0959852i	$0.0306002\pi$
$692$		0			0
$693$	−26112.1	+	11405.8i	−1.43134	+	0.625212i
$694$		0			0
$695$	2701.47	−	4679.08i	0.147442	−	0.255378i
$696$		0			0
$697$	−5154.34	−	8927.57i	−0.280107	−	0.485159i
$698$		0			0
$699$	827.645			0.0447845
$700$		0			0
$701$	−326.311			−0.0175815			−0.00879073	−	0.999961i	$-0.502798\pi$
$701$	−326.311			−0.0175815			−0.00879073	+	0.999961i	$0.502798\pi$
$702$		0			0
$703$	17365.1	+	30077.3i	0.931634	+	1.61364i
$704$		0			0
$705$	1248.05	−	2161.69i	0.0666728	−	0.115481i
$706$		0			0
$707$	−11208.3	−	8264.71i	−0.596225	−	0.439641i
$708$		0			0
$709$	−6774.52	+	11733.8i	−0.358847	+	0.621541i	−0.987768	−	0.155928i	$-0.950163\pi$
$709$	−6774.52	+	11733.8i	−0.358847	+	0.621541i	0.628922	+	0.777469i	$0.283497\pi$
$710$		0			0
$711$	−258.427	−	447.609i	−0.0136312	−	0.0236099i
$712$		0			0
$713$	1828.21			0.0960267
$714$		0			0
$715$	24460.8			1.27942
$716$		0			0
$717$	−2411.34	−	4176.56i	−0.125597	−	0.217540i
$718$		0			0
$719$	16923.7	−	29312.6i	0.877810	−	1.52041i	0.0240720	−	0.999710i	$-0.492337\pi$
$719$	16923.7	−	29312.6i	0.877810	−	1.52041i	0.853738	−	0.520702i	$-0.174330\pi$
$720$		0			0
$721$	−2614.04	+	23289.6i	−0.135024	+	1.20298i
$722$		0			0
$723$	929.297	−	1609.59i	0.0478021	−	0.0827957i
$724$		0			0
$725$	−134.923	−	233.694i	−0.00691163	−	0.0119713i
$726$		0			0
$727$	30076.9			1.53437			0.767187	−	0.641424i	$-0.221656\pi$
$727$	30076.9			1.53437			0.767187	+	0.641424i	$0.221656\pi$
$728$		0			0
$729$	−16382.8			−0.832332
$730$		0			0
$731$	−3368.72	−	5834.79i	−0.170447	−	0.295222i
$732$		0			0
$733$	−8267.21	+	14319.2i	−0.416585	+	0.721546i	−0.995593	−	0.0937756i	$-0.970106\pi$
$733$	−8267.21	+	14319.2i	−0.416585	+	0.721546i	0.579009	+	0.815321i	$0.303440\pi$
$734$		0			0
$735$	−2173.88	+	2346.90i	−0.109095	+	0.117778i
$736$		0			0
$737$	5438.85	−	9420.37i	0.271835	−	0.470833i
$738$		0			0
$739$	−1858.20	−	3218.49i	−0.0924964	−	0.160208i	0.816065	−	0.577961i	$-0.196151\pi$
$739$	−1858.20	−	3218.49i	−0.0924964	−	0.160208i	−0.908561	+	0.417752i	$0.862818\pi$
$740$		0			0
$741$	4639.28			0.229997
$742$		0			0
$743$	−2452.50			−0.121095			−0.0605474	−	0.998165i	$-0.519285\pi$
$743$	−2452.50			−0.121095			−0.0605474	+	0.998165i	$0.519285\pi$
$744$		0			0
$745$	11936.9	+	20675.3i	0.587026	+	1.01676i
$746$		0			0
$747$	15573.5	−	26974.0i	0.762788	−	1.32119i
$748$		0			0
$749$	−1565.21	+	13945.1i	−0.0763573	+	0.680299i
$750$		0			0
$751$	807.401	−	1398.46i	0.0392310	−	0.0679500i	−0.845743	−	0.533590i	$-0.820843\pi$
$751$	807.401	−	1398.46i	0.0392310	−	0.0679500i	0.884974	+	0.465640i	$0.154176\pi$
$752$		0			0
$753$	−69.8634	−	121.007i	−0.00338109	−	0.00585622i
$754$		0			0
$755$	2060.81			0.0993384
$756$		0			0
$757$	−4499.48			−0.216032			−0.108016	−	0.994149i	$-0.534450\pi$
$757$	−4499.48			−0.216032			−0.108016	+	0.994149i	$0.534450\pi$
$758$		0			0
$759$	−593.065	−	1027.22i	−0.0283622	−	0.0491248i
$760$		0			0
$761$	−9528.49	+	16503.8i	−0.453886	+	0.786154i	−0.998623	−	0.0524529i	$-0.983296\pi$
$761$	−9528.49	+	16503.8i	−0.453886	+	0.786154i	0.544737	+	0.838607i	$0.316629\pi$
$762$		0			0
$763$	14695.4	+	10836.0i	0.697259	+	0.514141i
$764$		0			0
$765$	−3605.56	+	6245.01i	−0.170404	+	0.295149i
$766$		0			0
$767$	−6274.99	−	10868.6i	−0.295407	−	0.511659i
$768$		0			0
$769$	−23811.3			−1.11659			−0.558295	−	0.829642i	$-0.688544\pi$
$769$	−23811.3			−1.11659			−0.558295	+	0.829642i	$0.688544\pi$
$770$		0			0
$771$	5707.81			0.266617
$772$		0			0
$773$	−9264.23	−	16046.1i	−0.431062	−	0.746622i	0.565903	−	0.824472i	$-0.308528\pi$
$773$	−9264.23	−	16046.1i	−0.431062	−	0.746622i	−0.996965	+	0.0778502i	$0.975194\pi$
$774$		0			0
$775$	−494.677	+	856.805i	−0.0229282	+	0.0397127i
$776$		0			0
$777$	3859.24	−	1685.73i	0.178185	−	0.0778318i
$778$		0			0
$779$	−26704.1	+	46252.9i	−1.22821	+	2.12732i
$780$		0			0
$781$	−9571.17	−	16577.8i	−0.438519	−	0.759537i
$782$		0			0
$783$	1014.47			0.0463018
$784$		0			0
$785$	16193.5			0.736267
$786$		0			0
$787$	−9819.10	−	17007.2i	−0.444744	−	0.770319i	0.553291	−	0.832988i	$-0.313372\pi$
$787$	−9819.10	−	17007.2i	−0.444744	−	0.770319i	−0.998034	+	0.0626697i	$0.980039\pi$
$788$		0			0
$789$	−817.063	+	1415.19i	−0.0368672	+	0.0638558i
$790$		0			0
$791$	−23552.0	+	10287.6i	−1.05868	+	0.462433i
$792$		0			0
$793$	7744.22	−	13413.4i	0.346791	−	0.600659i
$794$		0			0
$795$	−618.489	−	1071.26i	−0.0275919	−	0.0477906i
$796$		0			0
$797$	−7938.89			−0.352836			−0.176418	−	0.984315i	$-0.556451\pi$
$797$	−7938.89			−0.352836			−0.176418	+	0.984315i	$0.556451\pi$
$798$		0			0
$799$	6936.05			0.307109
$800$		0			0
$801$	12235.4	+	21192.3i	0.539720	+	0.934823i
$802$		0			0
$803$	−27347.9	+	47367.9i	−1.20185	+	2.08167i
$804$		0			0
$805$	3637.22	+	2681.99i	0.159249	+	0.117426i
$806$		0			0
$807$	−292.389	+	506.433i	−0.0127541	+	0.0220908i
$808$		0			0
$809$	−13827.3	−	23949.6i	−0.600917	−	1.04082i	−0.992683	−	0.120754i	$-0.961469\pi$
$809$	−13827.3	−	23949.6i	−0.600917	−	1.04082i	0.391766	−	0.920065i	$-0.371864\pi$
$810$		0			0
$811$	−19937.0			−0.863233			−0.431616	−	0.902057i	$-0.642057\pi$
$811$	−19937.0			−0.863233			−0.431616	+	0.902057i	$0.642057\pi$
$812$		0			0
$813$	1963.61			0.0847072
$814$		0			0
$815$	925.361	+	1602.77i	0.0397717	+	0.0688867i
$816$		0			0
$817$	−17453.0	+	30229.5i	−0.747372	+	1.29449i
$818$		0			0
$819$	−2129.42	+	18971.9i	−0.0908520	+	0.809439i
$820$		0			0
$821$	19919.4	−	34501.4i	0.846762	−	1.46663i	−0.0373201	−	0.999303i	$-0.511882\pi$
$821$	19919.4	−	34501.4i	0.846762	−	1.46663i	0.884082	−	0.467332i	$-0.154785\pi$
$822$		0			0
$823$	8523.04	+	14762.3i	0.360990	+	0.625252i	0.988124	−	0.153659i	$-0.0491056\pi$
$823$	8523.04	+	14762.3i	0.360990	+	0.625252i	−0.627134	+	0.778911i	$0.715772\pi$
$824$		0			0
$825$	641.886			0.0270880
$826$		0			0
$827$	−38961.5			−1.63824			−0.819119	−	0.573624i	$-0.805537\pi$
$827$	−38961.5			−1.63824			−0.819119	+	0.573624i	$0.805537\pi$
$828$		0			0
$829$	−709.128	−	1228.25i	−0.0297093	−	0.0514581i	0.850788	−	0.525508i	$-0.176125\pi$
$829$	−709.128	−	1228.25i	−0.0297093	−	0.0514581i	−0.880498	+	0.474050i	$0.842791\pi$
$830$		0			0
$831$	2171.20	−	3760.63i	0.0906356	−	0.156986i
$832$		0			0
$833$	−8668.08	−	1970.65i	−0.360542	−	0.0819676i
$834$		0			0
$835$	−19728.7	+	34171.2i	−0.817654	+	1.41622i
$836$		0			0
$837$	−1859.71	−	3221.11i	−0.0767992	−	0.133020i
$838$		0			0
$839$	−14367.2			−0.591194			−0.295597	−	0.955313i	$-0.595518\pi$
$839$	−14367.2			−0.591194			−0.295597	+	0.955313i	$0.595518\pi$
$840$		0			0
$841$	−23919.0			−0.980728
$842$		0			0
$843$	2917.03	+	5052.45i	0.119179	+	0.206424i
$844$		0			0
$845$	−3459.87	+	5992.66i	−0.140856	+	0.243969i
$846$		0			0
$847$	4359.38	−	38839.5i	0.176848	−	1.57561i
$848$		0			0
$849$	2966.00	−	5137.26i	0.119897	−	0.207668i
$850$		0			0
$851$	−2974.60	−	5152.16i	−0.119821	−	0.207537i
$852$		0			0
$853$	12725.7			0.510807			0.255404	−	0.966835i	$-0.417792\pi$
$853$	12725.7			0.510807			0.255404	+	0.966835i	$0.417792\pi$
$854$		0			0
$855$	37360.1			1.49437
$856$		0			0
$857$	16359.8	+	28336.0i	0.652089	+	1.12945i	0.982615	+	0.185655i	$0.0594406\pi$
$857$	16359.8	+	28336.0i	0.652089	+	1.12945i	−0.330526	+	0.943797i	$0.607226\pi$
$858$		0			0
$859$	−14843.8	+	25710.3i	−0.589599	+	1.02122i	0.404686	+	0.914456i	$0.367381\pi$
$859$	−14843.8	+	25710.3i	−0.589599	+	1.02122i	−0.994285	+	0.106760i	$0.965952\pi$
$860$		0			0
$861$	5212.38	+	3843.48i	0.206315	+	0.152132i
$862$		0			0
$863$	16815.9	−	29125.9i	0.663289	−	1.14885i	−0.316457	−	0.948607i	$-0.602493\pi$
$863$	16815.9	−	29125.9i	0.663289	−	1.14885i	0.979746	−	0.200244i	$-0.0641734\pi$
$864$		0			0
$865$	1035.32	+	1793.22i	0.0406957	+	0.0704870i
$866$		0			0
$867$	−3728.61			−0.146056
$868$		0			0
$869$	1156.06			0.0451283
$870$		0			0
$871$	−3643.97	−	6311.55i	−0.141758	−	0.245532i
$872$		0			0
$873$	18393.1	−	31857.9i	0.713074	−	1.23508i
$874$		0			0
$875$	−24748.1	+	10810.1i	−0.956157	+	0.417653i
$876$		0			0
$877$	−14203.1	+	24600.6i	−0.546871	+	0.947208i	0.451616	+	0.892213i	$0.350848\pi$
$877$	−14203.1	+	24600.6i	−0.546871	+	0.947208i	−0.998487	+	0.0549958i	$0.982485\pi$
$878$		0			0
$879$	−753.374	−	1304.88i	−0.0289086	−	0.0500712i
$880$		0			0
$881$	−18458.9			−0.705900			−0.352950	−	0.935642i	$-0.614821\pi$
$881$	−18458.9			−0.705900			−0.352950	+	0.935642i	$0.614821\pi$
$882$		0			0
$883$	−44131.3			−1.68192			−0.840961	−	0.541095i	$-0.818010\pi$
$883$	−44131.3			−1.68192			−0.840961	+	0.541095i	$0.818010\pi$
$884$		0			0
$885$	1489.04	+	2579.09i	0.0565575	+	0.0979605i
$886$		0			0
$887$	22396.9	−	38792.6i	0.847819	−	1.46846i	−0.0353323	−	0.999376i	$-0.511249\pi$
$887$	22396.9	−	38792.6i	0.847819	−	1.46846i	0.883151	−	0.469089i	$-0.155418\pi$
$888$		0			0
$889$	−41676.7	+	18204.5i	−1.57232	+	0.686795i
$890$		0			0
$891$	19563.9	−	33885.7i	0.735596	−	1.27409i
$892$		0			0
$893$	−17967.5	−	31120.6i	−0.673303	−	1.16619i
$894$		0			0
$895$	−42701.6			−1.59481
$896$		0			0
$897$	−794.695			−0.0295809
$898$		0			0
$899$	−861.654	−	1492.43i	−0.0319664	−	0.0553674i
$900$		0			0
$901$	1718.63	−	2976.75i	0.0635470	−	0.110067i
$902$		0			0
$903$	3406.65	+	2511.98i	0.125544	+	0.0925730i
$904$		0			0
$905$	5540.79	−	9596.93i	0.203516	−	0.352500i
$906$		0			0
$907$	−17036.3	−	29507.7i	−0.623682	−	1.08025i	−0.988794	−	0.149286i	$-0.952303\pi$
$907$	−17036.3	−	29507.7i	−0.623682	−	1.08025i	0.365112	−	0.930964i	$-0.381031\pi$
$908$		0			0
$909$	19721.0			0.719586
$910$		0			0
$911$	−9304.82			−0.338400			−0.169200	−	0.985582i	$-0.554118\pi$
$911$	−9304.82			−0.338400			−0.169200	+	0.985582i	$0.554118\pi$
$912$		0			0
$913$	34833.4	+	60333.1i	1.26267	+	2.18701i
$914$		0			0
$915$	−1837.68	+	3182.95i	−0.0663954	+	0.115000i
$916$		0			0
$917$	433.775	−	3864.68i	0.0156211	−	0.139175i
$918$		0			0
$919$	3494.30	−	6052.31i	0.125426	−	0.217244i	−0.796473	−	0.604674i	$-0.793304\pi$
$919$	3494.30	−	6052.31i	0.125426	−	0.217244i	0.921899	+	0.387429i	$0.126637\pi$
$920$		0			0
$921$	555.036	+	961.351i	0.0198578	+	0.0343948i
$922$		0			0
$923$	−12825.2			−0.457363
$924$		0			0
$925$	3219.47			0.114438
$926$		0			0
$927$	−16594.2	−	28741.9i	−0.587943	−	1.01835i
$928$		0			0
$929$	−18166.3	+	31464.9i	−0.641568	+	1.11123i	0.343515	+	0.939147i	$0.388382\pi$
$929$	−18166.3	+	31464.9i	−0.641568	+	1.11123i	−0.985083	+	0.172081i	$0.944951\pi$
$930$		0			0
$931$	13612.3	+	43996.8i	0.479191	+	1.54880i
$932$		0			0
$933$	25.9982	−	45.0302i	0.000912265	−	0.00158009i
$934$		0			0
$935$	−8064.60	−	13968.3i	−0.282076	−	0.488569i
$936$		0			0
$937$	19262.9			0.671602			0.335801	−	0.941933i	$-0.390993\pi$
$937$	19262.9			0.671602			0.335801	+	0.941933i	$0.390993\pi$
$938$		0			0
$939$	−3945.26			−0.137113
$940$		0			0
$941$	−1928.66	−	3340.53i	−0.0668145	−	0.115726i	0.830683	−	0.556746i	$-0.187950\pi$
$941$	−1928.66	−	3340.53i	−0.0668145	−	0.115726i	−0.897497	+	0.441020i	$0.854617\pi$
$942$		0			0
$943$	4574.34	−	7922.99i	0.157965	−	0.273604i
$944$		0			0
$945$	1025.50	−	9136.59i	0.0353010	−	0.314511i
$946$		0			0
$947$	1878.00	−	3252.80i	0.0644423	−	0.111617i	−0.832004	−	0.554769i	$-0.812806\pi$
$947$	1878.00	−	3252.80i	0.0644423	−	0.111617i	0.896446	+	0.443152i	$0.146140\pi$
$948$		0			0
$949$	18322.8	+	31736.0i	0.626747	+	1.08556i
$950$		0			0
$951$	−496.613			−0.0169335
$952$		0			0
$953$	20977.5			0.713040			0.356520	−	0.934288i	$-0.383963\pi$
$953$	20977.5			0.713040			0.356520	+	0.934288i	$0.383963\pi$
$954$		0			0
$955$	−17577.4	−	30445.0i	−0.595593	−	1.03160i
$956$		0			0
$957$	−559.035	+	968.277i	−0.0188830	+	0.0327063i
$958$		0			0
$959$	8488.25	+	6259.02i	0.285818	+	0.210755i
$960$		0			0
$961$	11736.4	−	20328.0i	0.393957	−	0.682354i
$962$		0			0
$963$	−9936.09	−	17209.8i	−0.332488	−	0.575886i
$964$		0			0
$965$	53462.4			1.78344
$966$		0			0
$967$	931.211			0.0309676			0.0154838	−	0.999880i	$-0.495071\pi$
$967$	931.211			0.0309676			0.0154838	+	0.999880i	$0.495071\pi$
$968$		0			0
$969$	−1529.55	−	2649.25i	−0.0507080	−	0.0878289i
$970$		0			0
$971$	19982.1	−	34610.0i	0.660408	−	1.14386i	−0.320100	−	0.947384i	$-0.603717\pi$
$971$	19982.1	−	34610.0i	0.660408	−	1.14386i	0.980508	−	0.196477i	$-0.0629501\pi$
$972$		0			0
$973$	−8643.28	+	3775.41i	−0.284780	+	0.124393i
$974$		0			0
$975$	215.029	−	372.440i	0.00706300	−	0.0122335i
$976$		0			0
$977$	1217.21	+	2108.27i	0.0398588	+	0.0690374i	0.885267	−	0.465084i	$-0.153976\pi$
$977$	1217.21	+	2108.27i	0.0398588	+	0.0690374i	−0.845408	+	0.534121i	$0.820643\pi$
$978$		0			0
$979$	−54734.1			−1.78683
$980$		0			0
$981$	−25856.5			−0.841523
$982$		0			0
$983$	5022.39	+	8699.03i	0.162960	+	0.282254i	0.935929	−	0.352189i	$-0.114563\pi$
$983$	5022.39	+	8699.03i	0.162960	+	0.282254i	−0.772969	+	0.634444i	$0.781229\pi$
$984$		0			0
$985$	−28557.7	+	49463.5i	−0.923782	+	1.60004i
$986$		0			0
$987$	−3993.11	+	1744.20i	−0.128776	+	0.0562499i
$988$		0			0
$989$	2989.65	−	5178.22i	0.0961227	−	0.166489i
$990$		0			0
$991$	−24494.6	−	42425.8i	−0.785162	−	1.35994i	−0.928902	−	0.370325i	$-0.879246\pi$
$991$	−24494.6	−	42425.8i	−0.785162	−	1.35994i	0.143740	−	0.989615i	$-0.454087\pi$
$992$		0			0
$993$	1205.82			0.0385353
$994$		0			0
$995$	−18560.1			−0.591350
$996$		0			0
$997$	−22044.0	−	38181.4i	−0.700242	−	1.21285i	−0.968381	−	0.249474i	$-0.919742\pi$
$997$	−22044.0	−	38181.4i	−0.700242	−	1.21285i	0.268139	−	0.963380i	$-0.413591\pi$
$998$		0			0
$999$	−6051.70	+	10481.8i	−0.191659	+	0.331963i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	644.4.i.b.93.10	✓	44
7.4	even	3	inner	644.4.i.b.277.10	yes	44

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
644.4.i.b.93.10	✓	44	1.1	even	1	trivial
644.4.i.b.277.10	yes	44	7.4	even	3	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:	\( N \)	\(=\)	\( 644 = 2^{2} \cdot 7 \cdot 23 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	644.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.439555 - 0.761331i) q^{3} +(5.30456 - 9.18776i) q^{5} +(-16.9718 + 7.41335i) q^{7} +(13.1136 - 22.7134i) q^{9} +O(q^{10})\)	\(q+(-0.439555 - 0.761331i) q^{3} +(5.30456 - 9.18776i) q^{5} +(-16.9718 + 7.41335i) q^{7} +(13.1136 - 22.7134i) q^{9} +(29.3313 + 50.8033i) q^{11} +39.3034 q^{13} -9.32657 q^{15} +(-12.9581 - 22.4441i) q^{17} +(-67.1347 + 116.281i) q^{19} +(13.1041 + 9.66259i) q^{21} +(11.5000 - 19.9186i) q^{23} +(6.22333 + 10.7791i) q^{25} -46.7925 q^{27} -21.6803 q^{29} +(39.7437 + 68.8381i) q^{31} +(25.7854 - 44.6617i) q^{33} +(-21.9159 + 195.257i) q^{35} +(129.331 - 224.007i) q^{37} +(-17.2760 - 29.9229i) q^{39} +397.769 q^{41} +259.970 q^{43} +(-139.124 - 240.969i) q^{45} +(-133.817 + 231.777i) q^{47} +(233.085 - 251.636i) q^{49} +(-11.3916 + 19.7308i) q^{51} +(66.3148 + 114.861i) q^{53} +622.359 q^{55} +118.038 q^{57} +(-159.655 - 276.531i) q^{59} +(197.037 - 341.278i) q^{61} +(-54.1789 + 482.703i) q^{63} +(208.487 - 361.110i) q^{65} +(-92.7140 - 160.585i) q^{67} -20.2195 q^{69} -326.312 q^{71} +(466.189 + 807.463i) q^{73} +(5.47099 - 9.47604i) q^{75} +(-874.429 - 644.781i) q^{77} +(9.85342 - 17.0666i) q^{79} +(-333.499 - 577.637i) q^{81} +1187.58 q^{83} -274.948 q^{85} +(9.52966 + 16.5059i) q^{87} +(-466.516 + 808.029i) q^{89} +(-667.049 + 291.370i) q^{91} +(34.9391 - 60.5163i) q^{93} +(712.240 + 1233.64i) q^{95} +1402.60 q^{97} +1538.56 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9}+O(q^{10}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9	\( 44 q + 12 q^{3} + 10 q^{5} - 6 q^{7} - 238 q^{9} + 28 q^{11} - 152 q^{13} + 208 q^{15} - 52 q^{17} + 38 q^{19} - 10 q^{21} + 506 q^{23} - 516 q^{25} - 876 q^{27} - 100 q^{29} + 230 q^{31} + 424 q^{33} + 98 q^{35} + 18 q^{37} - 350 q^{39} + 784 q^{41} - 336 q^{43} + 1156 q^{45} + 452 q^{47} + 546 q^{49} - 498 q^{51} - 508 q^{53} - 3084 q^{55} - 1916 q^{57} + 508 q^{59} + 1386 q^{61} + 1290 q^{63} + 360 q^{65} - 1896 q^{67} + 552 q^{69} - 3352 q^{71} + 990 q^{73} + 3328 q^{75} + 1328 q^{77} + 524 q^{79} - 4486 q^{81} - 1120 q^{83} - 5296 q^{85} + 3700 q^{87} + 1216 q^{89} + 1438 q^{91} + 366 q^{93} + 90 q^{95} + 716 q^{97} + 5716 q^{99}+O(q^{100}) \) 44 * q + 12 * q^3 + 10 * q^5 - 6 * q^7 - 238 * q^9 + 28 * q^11 - 152 * q^13 + 208 * q^15 - 52 * q^17 + 38 * q^19 - 10 * q^21 + 506 * q^23 - 516 * q^25 - 876 * q^27 - 100 * q^29 + 230 * q^31 + 424 * q^33 + 98 * q^35 + 18 * q^37 - 350 * q^39 + 784 * q^41 - 336 * q^43 + 1156 * q^45 + 452 * q^47 + 546 * q^49 - 498 * q^51 - 508 * q^53 - 3084 * q^55 - 1916 * q^57 + 508 * q^59 + 1386 * q^61 + 1290 * q^63 + 360 * q^65 - 1896 * q^67 + 552 * q^69 - 3352 * q^71 + 990 * q^73 + 3328 * q^75 + 1328 * q^77 + 524 * q^79 - 4486 * q^81 - 1120 * q^83 - 5296 * q^85 + 3700 * q^87 + 1216 * q^89 + 1438 * q^91 + 366 * q^93 + 90 * q^95 + 716 * q^97 + 5716 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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