LMFDB - Embedded newform 672.4.q.c.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [672,4,Mod(193,672)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(672, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("672.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 672 = 2^{5} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	672.q (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:	$39.6492835239$
Analytic rank:	$0$
Dimension:	$4$
Relative dimension:	$2$ over $\Q(\zeta_{3})$
Coefficient field:	$\Q(\sqrt{-3}, \sqrt{37})$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{4} - x^{3} + 10x^{2} + 9x + 81 $ x^4 - x^3 + 10x^2 + 9x + 81
Coefficient ring:	$\Z[a_1, \ldots, a_{5}]$
Coefficient ring index:	$ 2^{2} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.2
Root			$1.77069 + 3.06693i$ of defining polynomial
Character	$\chi$	$=$	672.289
Dual form			672.4.q.c.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.50000 - 2.59808i) q^{3} +(6.04138 - 10.4640i) q^{5} +(-12.0414 + 14.0714i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(-1.50000 - 2.59808i) q^{3} +(6.04138 - 10.4640i) q^{5} +(-12.0414 + 14.0714i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-0.665525 - 1.15272i) q^{11} +34.1655 q^{13} -36.2483 q^{15} +(27.4138 + 47.4821i) q^{17} +(14.9172 - 25.8374i) q^{19} +(54.6207 + 10.1773i) q^{21} +(-29.9104 + 51.8063i) q^{23} +(-10.4966 - 18.1806i) q^{25} +27.0000 q^{27} +114.069 q^{29} +(56.2897 + 97.4966i) q^{31} +(-1.99658 + 3.45817i) q^{33} +(74.4966 + 211.012i) q^{35} +(144.586 - 250.431i) q^{37} +(-51.2483 - 88.7646i) q^{39} +91.3105 q^{41} +198.331 q^{43} +(54.3724 + 94.1758i) q^{45} +(-80.4275 + 139.305i) q^{47} +(-53.0103 - 338.879i) q^{49} +(82.2414 - 142.446i) q^{51} +(-39.7103 - 68.7803i) q^{53} -16.0828 q^{55} -89.5034 q^{57} +(268.976 + 465.880i) q^{59} +(60.2346 - 104.329i) q^{61} +(-55.4897 - 157.175i) q^{63} +(206.407 - 357.507i) q^{65} +(-300.083 - 519.759i) q^{67} +179.462 q^{69} -156.800 q^{71} +(-285.179 - 493.945i) q^{73} +(-31.4897 + 54.5418i) q^{75} +(24.2343 + 4.51549i) q^{77} +(235.269 - 407.498i) q^{79} +(-40.5000 - 70.1481i) q^{81} -476.959 q^{83} +662.469 q^{85} +(-171.104 - 296.360i) q^{87} +(508.869 - 881.387i) q^{89} +(-411.400 + 480.758i) q^{91} +(168.869 - 292.490i) q^{93} +(-180.241 - 312.187i) q^{95} +1235.22 q^{97} +11.9795 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 4 q - 6 q^{3} + 12 q^{5} - 36 q^{7} - 18 q^{9}+O(q^{10}) $ 4 * q - 6 * q^3 + 12 * q^5 - 36 * q^7 - 18 * q^9	$ 4 q - 6 q^{3} + 12 q^{5} - 36 q^{7} - 18 q^{9} + 46 q^{11} + 88 q^{13} - 72 q^{15} - 12 q^{17} + 84 q^{19} + 36 q^{21} + 148 q^{23} + 104 q^{25} + 108 q^{27} - 152 q^{29} + 140 q^{31} + 138 q^{33} + 152 q^{35} + 700 q^{37} - 132 q^{39} - 608 q^{41} + 696 q^{43} + 108 q^{45} - 784 q^{47} - 650 q^{49} - 36 q^{51} - 244 q^{53} - 40 q^{55} - 504 q^{57} + 54 q^{59} - 416 q^{61} + 216 q^{63} + 412 q^{65} - 1176 q^{67} - 888 q^{69} + 784 q^{71} - 1676 q^{73} + 312 q^{75} + 1204 q^{77} - 20 q^{79} - 162 q^{81} - 156 q^{83} + 1336 q^{85} + 228 q^{87} + 16 q^{89} - 940 q^{91} + 420 q^{93} - 356 q^{95} + 172 q^{97} - 828 q^{99}+O(q^{100}) $ 4 * q - 6 * q^3 + 12 * q^5 - 36 * q^7 - 18 * q^9 + 46 * q^11 + 88 * q^13 - 72 * q^15 - 12 * q^17 + 84 * q^19 + 36 * q^21 + 148 * q^23 + 104 * q^25 + 108 * q^27 - 152 * q^29 + 140 * q^31 + 138 * q^33 + 152 * q^35 + 700 * q^37 - 132 * q^39 - 608 * q^41 + 696 * q^43 + 108 * q^45 - 784 * q^47 - 650 * q^49 - 36 * q^51 - 244 * q^53 - 40 * q^55 - 504 * q^57 + 54 * q^59 - 416 * q^61 + 216 * q^63 + 412 * q^65 - 1176 * q^67 - 888 * q^69 + 784 * q^71 - 1676 * q^73 + 312 * q^75 + 1204 * q^77 - 20 * q^79 - 162 * q^81 - 156 * q^83 + 1336 * q^85 + 228 * q^87 + 16 * q^89 - 940 * q^91 + 420 * q^93 - 356 * q^95 + 172 * q^97 - 828 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/672\mathbb{Z}\right)^\times$.

$n$	$127$	$421$	$449$	$577$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$3$	−1.50000	−	2.59808i	−0.288675	−	0.500000i
$4$		0			0
$5$	6.04138	−	10.4640i	0.540358	−	0.935927i	−0.458526	−	0.888681i	$-0.651622\pi$
$5$	6.04138	−	10.4640i	0.540358	−	0.935927i	0.998883	−	0.0472456i	$-0.0150444\pi$
$6$		0			0
$7$	−12.0414	+	14.0714i	−0.650173	+	0.759786i
$7$	−12.0414	+	14.0714i	−0.650173	+	0.759786i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	−0.665525	−	1.15272i	−0.0182421	−	0.0315963i	0.856760	−	0.515715i	$-0.172474\pi$
$11$	−0.665525	−	1.15272i	−0.0182421	−	0.0315963i	−0.875002	+	0.484119i	$0.839140\pi$
$12$		0			0
$13$	34.1655			0.728909			0.364454	−	0.931221i	$-0.381256\pi$
$13$	34.1655			0.728909			0.364454	+	0.931221i	$0.381256\pi$
$14$		0			0
$15$	−36.2483			−0.623951
$16$		0			0
$17$	27.4138	+	47.4821i	0.391107	+	0.677418i	0.992596	−	0.121464i	$-0.0387588\pi$
$17$	27.4138	+	47.4821i	0.391107	+	0.677418i	−0.601488	+	0.798881i	$0.705425\pi$
$18$		0			0
$19$	14.9172	−	25.8374i	0.180118	−	0.311974i	−0.761802	−	0.647810i	$-0.775685\pi$
$19$	14.9172	−	25.8374i	0.180118	−	0.311974i	0.941921	+	0.335835i	$0.109019\pi$
$20$		0			0
$21$	54.6207	+	10.1773i	0.567582	+	0.105755i
$22$		0			0
$23$	−29.9104	+	51.8063i	−0.271163	+	0.469668i	−0.969160	−	0.246433i	$-0.920742\pi$
$23$	−29.9104	+	51.8063i	−0.271163	+	0.469668i	0.697997	+	0.716101i	$0.254075\pi$
$24$		0			0
$25$	−10.4966	−	18.1806i	−0.0839726	−	0.145445i
$26$		0			0
$27$	27.0000			0.192450
$28$		0			0
$29$	114.069			0.730417			0.365209	−	0.930926i	$-0.380998\pi$
$29$	114.069			0.730417			0.365209	+	0.930926i	$0.380998\pi$
$30$		0			0
$31$	56.2897	+	97.4966i	0.326127	+	0.564868i	0.981740	−	0.190229i	$-0.0609231\pi$
$31$	56.2897	+	97.4966i	0.326127	+	0.564868i	−0.655613	+	0.755097i	$0.727590\pi$
$32$		0			0
$33$	−1.99658	+	3.45817i	−0.0105321	+	0.0182421i
$34$		0			0
$35$	74.4966	+	211.012i	0.359778	+	1.01907i
$36$		0			0
$37$	144.586	−	250.431i	0.642428	−	1.11272i	−0.342462	−	0.939532i	$-0.611261\pi$
$37$	144.586	−	250.431i	0.642428	−	1.11272i	0.984889	−	0.173185i	$-0.0554060\pi$
$38$		0			0
$39$	−51.2483	−	88.7646i	−0.210418	−	0.364454i
$40$		0			0
$41$	91.3105			0.347812			0.173906	−	0.984762i	$-0.444361\pi$
$41$	91.3105			0.347812			0.173906	+	0.984762i	$0.444361\pi$
$42$		0			0
$43$	198.331			0.703377			0.351688	−	0.936117i	$-0.385608\pi$
$43$	198.331			0.703377			0.351688	+	0.936117i	$0.385608\pi$
$44$		0			0
$45$	54.3724	+	94.1758i	0.180119	+	0.311976i
$46$		0			0
$47$	−80.4275	+	139.305i	−0.249608	+	0.432333i	−0.963417	−	0.268007i	$-0.913635\pi$
$47$	−80.4275	+	139.305i	−0.249608	+	0.432333i	0.713809	+	0.700340i	$0.246968\pi$
$48$		0			0
$49$	−53.0103	−	338.879i	−0.154549	−	0.987985i
$50$		0			0
$51$	82.2414	−	142.446i	0.225806	−	0.391107i
$52$		0			0
$53$	−39.7103	−	68.7803i	−0.102918	−	0.178259i	0.809968	−	0.586474i	$-0.199484\pi$
$53$	−39.7103	−	68.7803i	−0.102918	−	0.178259i	−0.912886	+	0.408216i	$0.866151\pi$
$54$		0			0
$55$	−16.0828			−0.0394291
$56$		0			0
$57$	−89.5034			−0.207983
$58$		0			0
$59$	268.976	+	465.880i	0.593520	+	1.02801i	0.993754	+	0.111594i	$0.0355957\pi$
$59$	268.976	+	465.880i	0.593520	+	1.02801i	−0.400234	+	0.916413i	$0.631071\pi$
$60$		0			0
$61$	60.2346	−	104.329i	0.126430	−	0.218984i	−0.795861	−	0.605480i	$-0.792981\pi$
$61$	60.2346	−	104.329i	0.126430	−	0.218984i	0.922291	+	0.386496i	$0.126315\pi$
$62$		0			0
$63$	−55.4897	−	157.175i	−0.110969	−	0.314320i
$64$		0			0
$65$	206.407	−	357.507i	0.393871	−	0.682205i
$66$		0			0
$67$	−300.083	−	519.759i	−0.547178	−	0.947741i	−0.998466	−	0.0553622i	$-0.982369\pi$
$67$	−300.083	−	519.759i	−0.547178	−	0.947741i	0.451288	−	0.892378i	$-0.350965\pi$
$68$		0			0
$69$	179.462			0.313112
$70$		0			0
$71$	−156.800			−0.262095			−0.131048	−	0.991376i	$-0.541834\pi$
$71$	−156.800			−0.262095			−0.131048	+	0.991376i	$0.541834\pi$
$72$		0			0
$73$	−285.179	−	493.945i	−0.457229	−	0.791944i	0.541584	−	0.840646i	$-0.317825\pi$
$73$	−285.179	−	493.945i	−0.457229	−	0.791944i	−0.998813	+	0.0487028i	$0.984491\pi$
$74$		0			0
$75$	−31.4897	+	54.5418i	−0.0484816	+	0.0839726i
$76$		0			0
$77$	24.2343	+	4.51549i	0.0358670	+	0.00668296i
$78$		0			0
$79$	235.269	−	407.498i	0.335061	−	0.580343i	−0.648435	−	0.761270i	$-0.724576\pi$
$79$	235.269	−	407.498i	0.335061	−	0.580343i	0.983497	+	0.180927i	$0.0579096\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	−476.959			−0.630760			−0.315380	−	0.948966i	$-0.602132\pi$
$83$	−476.959			−0.630760			−0.315380	+	0.948966i	$0.602132\pi$
$84$		0			0
$85$	662.469			0.845351
$86$		0			0
$87$	−171.104	−	296.360i	−0.210853	−	0.365209i
$88$		0			0
$89$	508.869	−	881.387i	0.606068	−	1.04974i	−0.385814	−	0.922577i	$-0.626079\pi$
$89$	508.869	−	881.387i	0.606068	−	1.04974i	0.991882	−	0.127164i	$-0.0405873\pi$
$90$		0			0
$91$	−411.400	+	480.758i	−0.473917	+	0.553814i
$92$		0			0
$93$	168.869	−	292.490i	0.188289	−	0.326127i
$94$		0			0
$95$	−180.241	−	312.187i	−0.194657	−	0.337155i
$96$		0			0
$97$	1235.22			1.29297			0.646483	−	0.762928i	$-0.276239\pi$
$97$	1235.22			1.29297			0.646483	+	0.762928i	$0.276239\pi$
$98$		0			0
$99$	11.9795			0.0121614
$100$		0			0
$101$	−101.765	−	176.263i	−0.100258	−	0.173652i	0.811533	−	0.584307i	$-0.198633\pi$
$101$	−101.765	−	176.263i	−0.100258	−	0.173652i	−0.911791	+	0.410655i	$0.865300\pi$
$102$		0			0
$103$	140.193	−	242.821i	0.134113	−	0.232290i	−0.791145	−	0.611628i	$-0.790515\pi$
$103$	140.193	−	242.821i	0.134113	−	0.232290i	0.925258	+	0.379338i	$0.123848\pi$
$104$		0			0
$105$	436.479	−	510.065i	0.405677	−	0.474069i
$106$		0			0
$107$	457.135	−	791.781i	0.413018	−	0.715367i	−0.582201	−	0.813045i	$-0.697808\pi$
$107$	457.135	−	791.781i	0.413018	−	0.715367i	0.995218	+	0.0976778i	$0.0311415\pi$
$108$		0			0
$109$	796.587	+	1379.73i	0.699992	+	1.21242i	0.968468	+	0.249136i	$0.0801466\pi$
$109$	796.587	+	1379.73i	0.699992	+	1.21242i	−0.268476	+	0.963286i	$0.586520\pi$
$110$		0			0
$111$	−867.517			−0.741812
$112$		0			0
$113$	2306.48			1.92014			0.960070	−	0.279761i	$-0.0902551\pi$
$113$	2306.48			1.92014			0.960070	+	0.279761i	$0.0902551\pi$
$114$		0			0
$115$	361.400	+	625.963i	0.293050	+	0.507577i
$116$		0			0
$117$	−153.745	+	266.294i	−0.121485	+	0.210418i
$118$		0			0
$119$	−998.241	−	185.999i	−0.768980	−	0.143281i
$120$		0			0
$121$	664.614	−	1151.15i	0.499334	−	0.864873i
$122$		0			0
$123$	−136.966	−	237.232i	−0.100405	−	0.173906i
$124$		0			0
$125$	1256.69			0.899214
$126$		0			0
$127$	2846.40			1.98880			0.994399	−	0.105694i	$-0.0337064\pi$
$127$	2846.40			1.98880			0.994399	+	0.105694i	$0.0337064\pi$
$128$		0			0
$129$	−297.497	−	515.279i	−0.203047	−	0.351688i
$130$		0			0
$131$	443.611	−	768.356i	0.295866	−	0.512455i	−0.679320	−	0.733842i	$-0.737725\pi$
$131$	443.611	−	768.356i	0.295866	−	0.512455i	0.975186	+	0.221387i	$0.0710585\pi$
$132$		0			0
$133$	183.945	+	521.025i	0.119925	+	0.339689i
$134$		0			0
$135$	163.117	−	282.527i	0.103992	−	0.180119i
$136$		0			0
$137$	−866.193	−	1500.29i	−0.540174	−	0.935610i	−0.998894	−	0.0470283i	$-0.985025\pi$
$137$	−866.193	−	1500.29i	−0.540174	−	0.935610i	0.458719	−	0.888581i	$-0.348308\pi$
$138$		0			0
$139$	624.745			0.381225			0.190612	−	0.981665i	$-0.438953\pi$
$139$	624.745			0.381225			0.190612	+	0.981665i	$0.438953\pi$
$140$		0			0
$141$	482.565			0.288222
$142$		0			0
$143$	−22.7380	−	39.3834i	−0.0132968	−	0.0230308i
$144$		0			0
$145$	689.135	−	1193.62i	0.394686	−	0.683617i
$146$		0			0
$147$	−800.918	+	646.043i	−0.449378	+	0.362481i
$148$		0			0
$149$	−497.366	+	861.463i	−0.273462	+	0.473650i	−0.969746	−	0.244117i	$-0.921502\pi$
$149$	−497.366	+	861.463i	−0.273462	+	0.473650i	0.696284	+	0.717766i	$0.254835\pi$
$150$		0			0
$151$	1287.55	+	2230.09i	0.693900	+	1.20187i	0.970550	+	0.240900i	$0.0774425\pi$
$151$	1287.55	+	2230.09i	0.693900	+	1.20187i	−0.276650	+	0.960971i	$0.589224\pi$
$152$		0			0
$153$	−493.449			−0.260738
$154$		0			0
$155$	1360.27			0.704900
$156$		0			0
$157$	525.642	+	910.438i	0.267202	+	0.462808i	0.968138	−	0.250416i	$-0.0805675\pi$
$157$	525.642	+	910.438i	0.267202	+	0.462808i	−0.700936	+	0.713224i	$0.747234\pi$
$158$		0			0
$159$	−119.131	+	206.341i	−0.0594195	+	0.102918i
$160$		0			0
$161$	−368.826	−	1044.70i	−0.180544	−	0.511391i
$162$		0			0
$163$	−258.214	+	447.240i	−0.124079	+	0.214911i	−0.921373	−	0.388681i	$-0.872931\pi$
$163$	−258.214	+	447.240i	−0.124079	+	0.214911i	0.797294	+	0.603592i	$0.206264\pi$
$164$		0			0
$165$	24.1241	+	41.7842i	0.0113822	+	0.0197145i
$166$		0			0
$167$	−3740.04			−1.73301			−0.866507	−	0.499165i	$-0.833640\pi$
$167$	−3740.04			−1.73301			−0.866507	+	0.499165i	$0.833640\pi$
$168$		0			0
$169$	−1029.72			−0.468692
$170$		0			0
$171$	134.255	+	232.537i	0.0600395	+	0.103991i
$172$		0			0
$173$	−1121.52	+	1942.53i	−0.492875	+	0.853685i	−0.999966	−	0.00820755i	$-0.997387\pi$
$173$	−1121.52	+	1942.53i	−0.492875	+	0.853685i	0.507091	+	0.861892i	$0.330721\pi$
$174$		0			0
$175$	382.220	+	71.2177i	0.165104	+	0.0307632i
$176$		0			0
$177$	806.928	−	1397.64i	0.342669	−	0.593520i
$178$		0			0
$179$	−1543.81	−	2673.95i	−0.644634	−	1.11654i	−0.984386	−	0.176024i	$-0.943676\pi$
$179$	−1543.81	−	2673.95i	−0.644634	−	1.11654i	0.339751	−	0.940515i	$-0.389657\pi$
$180$		0			0
$181$	−1620.17			−0.665337			−0.332669	−	0.943044i	$-0.607949\pi$
$181$	−1620.17			−0.665337			−0.332669	+	0.943044i	$0.607949\pi$
$182$		0			0
$183$	−361.408			−0.145989
$184$		0			0
$185$	−1747.00	−	3025.89i	−0.694281	−	1.20253i
$186$		0			0
$187$	36.4892	−	63.2011i	0.0142693	−	0.0247151i
$188$		0			0
$189$	−325.117	+	379.929i	−0.125126	+	0.146221i
$190$		0			0
$191$	−287.462	+	497.899i	−0.108901	+	0.188622i	−0.915325	−	0.402715i	$-0.868066\pi$
$191$	−287.462	+	497.899i	−0.108901	+	0.188622i	0.806424	+	0.591337i	$0.201400\pi$
$192$		0			0
$193$	−103.604	−	179.447i	−0.0386403	−	0.0669269i	0.846059	−	0.533090i	$-0.178969\pi$
$193$	−103.604	−	179.447i	−0.0386403	−	0.0669269i	−0.884699	+	0.466163i	$0.845636\pi$
$194$		0			0
$195$	−1238.44			−0.454803
$196$		0			0
$197$	2035.53			0.736170			0.368085	−	0.929792i	$-0.380013\pi$
$197$	2035.53			0.736170			0.368085	+	0.929792i	$0.380013\pi$
$198$		0			0
$199$	2691.24	+	4661.37i	0.958679	+	1.66048i	0.725715	+	0.687996i	$0.241509\pi$
$199$	2691.24	+	4661.37i	0.958679	+	1.66048i	0.232965	+	0.972485i	$0.425157\pi$
$200$		0			0
$201$	−900.248	+	1559.28i	−0.315914	+	0.547178i
$202$		0			0
$203$	−1373.55	+	1605.11i	−0.474898	+	0.554960i
$204$		0			0
$205$	551.642	−	955.471i	0.187943	−	0.325527i
$206$		0			0
$207$	−269.193	−	466.257i	−0.0903876	−	0.156556i
$208$		0			0
$209$	−39.7112			−0.0131430
$210$		0			0
$211$	1318.85			0.430302			0.215151	−	0.976581i	$-0.430976\pi$
$211$	1318.85			0.430302			0.215151	+	0.976581i	$0.430976\pi$
$212$		0			0
$213$	235.200	+	407.379i	0.0756604	+	0.131048i
$214$		0			0
$215$	1198.19	−	2075.33i	0.380075	−	0.658309i
$216$		0			0
$217$	−2049.72	−	381.917i	−0.641217	−	0.119476i
$218$		0			0
$219$	−855.538	+	1481.83i	−0.263981	+	0.457229i
$220$		0			0
$221$	936.607	+	1622.25i	0.285082	+	0.493776i
$222$		0			0
$223$	350.814			0.105347			0.0526733	−	0.998612i	$-0.483226\pi$
$223$	350.814			0.105347			0.0526733	+	0.998612i	$0.483226\pi$
$224$		0			0
$225$	188.938			0.0559817
$226$		0			0
$227$	−2196.91	−	3805.16i	−0.642352	−	1.11259i	−0.984906	−	0.173088i	$-0.944625\pi$
$227$	−2196.91	−	3805.16i	−0.642352	−	1.11259i	0.342554	−	0.939498i	$-0.388708\pi$
$228$		0			0
$229$	−1808.51	+	3132.43i	−0.521877	+	0.903917i	0.477799	+	0.878469i	$0.341435\pi$
$229$	−1808.51	+	3132.43i	−0.521877	+	0.903917i	−0.999676	+	0.0254482i	$0.991899\pi$
$230$		0			0
$231$	−24.6199	−	69.7358i	−0.00701242	−	0.0198627i
$232$		0			0
$233$	−1837.70	+	3183.00i	−0.516704	+	0.894957i	0.483108	+	0.875561i	$0.339508\pi$
$233$	−1837.70	+	3183.00i	−0.516704	+	0.894957i	−0.999812	+	0.0193965i	$0.993826\pi$
$234$		0			0
$235$	971.787	+	1683.18i	0.269755	+	0.467229i
$236$		0			0
$237$	−1411.61			−0.386895
$238$		0			0
$239$	−604.124			−0.163504			−0.0817522	−	0.996653i	$-0.526052\pi$
$239$	−604.124			−0.163504			−0.0817522	+	0.996653i	$0.526052\pi$
$240$		0			0
$241$	−1793.54	−	3106.51i	−0.479387	−	0.830322i	0.520334	−	0.853963i	$-0.325808\pi$
$241$	−1793.54	−	3106.51i	−0.479387	−	0.830322i	−0.999721	+	0.0236408i	$0.992474\pi$
$242$		0			0
$243$	−121.500	+	210.444i	−0.0320750	+	0.0555556i
$244$		0			0
$245$	−3866.28	−	1492.60i	−1.00819	−	0.389219i
$246$		0			0
$247$	509.655	−	882.749i	0.131290	−	0.227401i
$248$		0			0
$249$	715.438	+	1239.18i	0.182085	+	0.315380i
$250$		0			0
$251$	1554.90			0.391015			0.195507	−	0.980702i	$-0.437365\pi$
$251$	1554.90			0.391015			0.195507	+	0.980702i	$0.437365\pi$
$252$		0			0
$253$	79.6245			0.0197863
$254$		0			0
$255$	−993.704	−	1721.15i	−0.244032	−	0.422676i
$256$		0			0
$257$	−1441.78	+	2497.23i	−0.349944	+	0.606121i	−0.986239	−	0.165324i	$-0.947133\pi$
$257$	−1441.78	+	2497.23i	−0.349944	+	0.606121i	0.636295	+	0.771446i	$0.280466\pi$
$258$		0			0
$259$	1782.90	+	5050.06i	0.427737	+	1.21157i
$260$		0			0
$261$	−513.311	+	889.080i	−0.121736	+	0.210853i
$262$		0			0
$263$	1315.78	+	2279.00i	0.308496	+	0.534331i	0.978034	−	0.208448i	$-0.0668411\pi$
$263$	1315.78	+	2279.00i	0.308496	+	0.534331i	−0.669538	+	0.742778i	$0.733508\pi$
$264$		0			0
$265$	−959.621			−0.222449
$266$		0			0
$267$	−3053.22			−0.699827
$268$		0			0
$269$	4190.58	+	7258.30i	0.949830	+	1.64515i	0.745780	+	0.666193i	$0.232077\pi$
$269$	4190.58	+	7258.30i	0.949830	+	1.64515i	0.204050	+	0.978961i	$0.434590\pi$
$270$		0			0
$271$	2588.23	−	4482.95i	0.580163	−	1.00487i	−0.415297	−	0.909686i	$-0.636322\pi$
$271$	2588.23	−	4482.95i	0.580163	−	1.00487i	0.995460	−	0.0951852i	$-0.0303443\pi$
$272$		0			0
$273$	1866.15	+	347.712i	0.413715	+	0.0770861i
$274$		0			0
$275$	−13.9715	+	24.1993i	−0.00306368	+	0.00530644i
$276$		0			0
$277$	1098.88	+	1903.32i	0.238359	+	0.412850i	0.960244	−	0.279164i	$-0.0900572\pi$
$277$	1098.88	+	1903.32i	0.238359	+	0.412850i	−0.721885	+	0.692014i	$0.756724\pi$
$278$		0			0
$279$	−1013.21			−0.217418
$280$		0			0
$281$	−5024.94			−1.06677			−0.533386	−	0.845872i	$-0.679081\pi$
$281$	−5024.94			−1.06677			−0.533386	+	0.845872i	$0.679081\pi$
$282$		0			0
$283$	−543.275	−	940.980i	−0.114114	−	0.197652i	0.803311	−	0.595560i	$-0.203070\pi$
$283$	−543.275	−	940.980i	−0.114114	−	0.197652i	−0.917425	+	0.397908i	$0.869736\pi$
$284$		0			0
$285$	−540.724	+	936.562i	−0.112385	+	0.194657i
$286$		0			0
$287$	−1099.50	+	1284.87i	−0.226138	+	0.264263i
$288$		0			0
$289$	953.466	−	1651.45i	0.194070	−	0.336139i
$290$		0			0
$291$	−1852.83	−	3209.20i	−0.373247	−	0.646483i
$292$		0			0
$293$	3778.59			0.753406			0.376703	−	0.926334i	$-0.377058\pi$
$293$	3778.59			0.753406			0.376703	+	0.926334i	$0.377058\pi$
$294$		0			0
$295$	6499.95			1.28285
$296$		0			0
$297$	−17.9692	−	31.1235i	−0.00351070	−	0.00608071i
$298$		0			0
$299$	−1021.90	+	1769.99i	−0.197653	+	0.342345i
$300$		0			0
$301$	−2388.18	+	2790.80i	−0.457317	+	0.534416i
$302$		0			0
$303$	−305.296	+	528.789i	−0.0578839	+	0.100258i
$304$		0			0
$305$	−727.800	−	1260.59i	−0.136635	−	0.236659i
$306$		0			0
$307$	9599.11			1.78453			0.892264	−	0.451515i	$-0.149116\pi$
$307$	9599.11			1.78453			0.892264	+	0.451515i	$0.149116\pi$
$308$		0			0
$309$	−841.158			−0.154860
$310$		0			0
$311$	−2671.35	−	4626.92i	−0.487069	−	0.843629i	0.512820	−	0.858496i	$-0.328601\pi$
$311$	−2671.35	−	4626.92i	−0.487069	−	0.843629i	−0.999889	+	0.0148674i	$0.995267\pi$
$312$		0			0
$313$	−2452.60	+	4248.02i	−0.442904	+	0.767132i	−0.997904	−	0.0647185i	$-0.979385\pi$
$313$	−2452.60	+	4248.02i	−0.442904	+	0.767132i	0.555000	+	0.831851i	$0.312718\pi$
$314$		0			0
$315$	−1979.91	−	368.909i	−0.354143	−	0.0659863i
$316$		0			0
$317$	−3450.57	+	5976.56i	−0.611367	+	1.05892i	0.379644	+	0.925133i	$0.376047\pi$
$317$	−3450.57	+	5976.56i	−0.611367	+	1.05892i	−0.991010	+	0.133785i	$0.957287\pi$
$318$		0			0
$319$	−75.9158	−	131.490i	−0.0133244	−	0.0230785i
$320$		0			0
$321$	−2742.81			−0.476912
$322$		0			0
$323$	1635.75			0.281783
$324$		0			0
$325$	−358.621	−	621.150i	−0.0612084	−	0.106016i
$326$		0			0
$327$	2389.76	−	4139.19i	0.404141	−	0.699992i
$328$		0			0
$329$	−991.756	−	2809.15i	−0.166192	−	0.470740i
$330$		0			0
$331$	−1237.12	+	2142.75i	−0.205433	+	0.355820i	−0.950270	−	0.311426i	$-0.899193\pi$
$331$	−1237.12	+	2142.75i	−0.205433	+	0.355820i	0.744838	+	0.667245i	$0.232527\pi$
$332$		0			0
$333$	1301.28	+	2253.88i	0.214143	+	0.370906i
$334$		0			0
$335$	−7251.66			−1.18269
$336$		0			0
$337$	−1172.77			−0.189569			−0.0947844	−	0.995498i	$-0.530216\pi$
$337$	−1172.77			−0.189569			−0.0947844	+	0.995498i	$0.530216\pi$
$338$		0			0
$339$	−3459.73	−	5992.42i	−0.554297	−	0.960070i
$340$		0			0
$341$	74.9244	−	129.773i	0.0118985	−	0.0206088i
$342$		0			0
$343$	5406.83	+	3334.64i	0.851141	+	0.524938i
$344$		0			0
$345$	1084.20	−	1877.89i	0.169192	−	0.293050i
$346$		0			0
$347$	−3257.88	−	5642.81i	−0.504011	−	0.872973i	−0.999989	−	0.00463807i	$-0.998524\pi$
$347$	−3257.88	−	5642.81i	−0.504011	−	0.872973i	0.495978	−	0.868335i	$-0.334810\pi$
$348$		0			0
$349$	−9451.71			−1.44968			−0.724841	−	0.688917i	$-0.758087\pi$
$349$	−9451.71			−1.44968			−0.724841	+	0.688917i	$0.758087\pi$
$350$		0			0
$351$	922.469			0.140279
$352$		0			0
$353$	−1742.84	−	3018.69i	−0.262782	−	0.455152i	0.704198	−	0.710003i	$-0.251307\pi$
$353$	−1742.84	−	3018.69i	−0.262782	−	0.455152i	−0.966980	+	0.254852i	$0.917973\pi$
$354$		0			0
$355$	−947.290	+	1640.75i	−0.141625	+	0.245302i
$356$		0			0
$357$	1014.12	+	2872.51i	0.150345	+	0.425852i
$358$		0			0
$359$	−6228.35	+	10787.8i	−0.915654	+	1.58596i	−0.109714	+	0.993963i	$0.534993\pi$
$359$	−6228.35	+	10787.8i	−0.915654	+	1.58596i	−0.805941	+	0.591996i	$0.798340\pi$
$360$		0			0
$361$	2984.45	+	5169.22i	0.435115	+	0.753641i
$362$		0			0
$363$	−3987.68			−0.576582
$364$		0			0
$365$	−6891.51			−0.988268
$366$		0			0
$367$	−6908.94	−	11966.6i	−0.982680	−	1.70205i	−0.651822	−	0.758372i	$-0.725995\pi$
$367$	−6908.94	−	11966.6i	−0.982680	−	1.70205i	−0.330858	−	0.943681i	$-0.607338\pi$
$368$		0			0
$369$	−410.897	+	711.695i	−0.0579687	+	0.100405i
$370$		0			0
$371$	1446.00	+	269.429i	0.202353	+	0.0377036i
$372$		0			0
$373$	196.344	−	340.077i	0.0272555	−	0.0472078i	−0.852076	−	0.523418i	$-0.824657\pi$
$373$	196.344	−	340.077i	0.0272555	−	0.0472078i	0.879331	+	0.476210i	$0.157990\pi$
$374$		0			0
$375$	−1885.04	−	3264.98i	−0.259581	−	0.449607i
$376$		0			0
$377$	3897.23			0.532407
$378$		0			0
$379$	13599.9			1.84322			0.921611	−	0.388115i	$-0.126874\pi$
$379$	13599.9			1.84322			0.921611	+	0.388115i	$0.126874\pi$
$380$		0			0
$381$	−4269.60	−	7395.17i	−0.574116	−	0.994399i
$382$		0			0
$383$	−3710.81	+	6427.31i	−0.495074	+	0.857494i	−0.999984	−	0.00567845i	$-0.998192\pi$
$383$	−3710.81	+	6427.31i	−0.495074	+	0.857494i	0.504910	+	0.863172i	$0.331526\pi$
$384$		0			0
$385$	193.659	−	226.307i	0.0256357	−	0.0299577i
$386$		0			0
$387$	−892.490	+	1545.84i	−0.117229	+	0.203047i
$388$		0			0
$389$	−3235.92	−	5604.78i	−0.421768	−	0.730523i	0.574345	−	0.818613i	$-0.305257\pi$
$389$	−3235.92	−	5604.78i	−0.421768	−	0.730523i	−0.996112	+	0.0880904i	$0.971924\pi$
$390$		0			0
$391$	−3279.83			−0.424215
$392$		0			0
$393$	−2661.66			−0.341637
$394$		0			0
$395$	−2842.70	−	4923.70i	−0.362106	−	0.627186i
$396$		0			0
$397$	−5572.58	+	9651.99i	−0.704483	+	1.22020i	0.262395	+	0.964961i	$0.415488\pi$
$397$	−5572.58	+	9651.99i	−0.704483	+	1.22020i	−0.966878	+	0.255240i	$0.917846\pi$
$398$		0			0
$399$	1077.74	−	1259.44i	0.135225	−	0.158022i
$400$		0			0
$401$	−4060.08	+	7032.27i	−0.505613	+	0.875747i	0.494366	+	0.869254i	$0.335400\pi$
$401$	−4060.08	+	7032.27i	−0.505613	+	0.875747i	−0.999979	+	0.00649355i	$0.997933\pi$
$402$		0			0
$403$	1923.17	+	3331.02i	0.237716	+	0.411737i
$404$		0			0
$405$	−978.704			−0.120079
$406$		0			0
$407$	−384.903			−0.0468770
$408$		0			0
$409$	527.121	+	913.000i	0.0637273	+	0.110379i	0.896129	−	0.443794i	$-0.146368\pi$
$409$	527.121	+	913.000i	0.0637273	+	0.110379i	−0.832401	+	0.554173i	$0.813035\pi$
$410$		0			0
$411$	−2598.58	+	4500.87i	−0.311870	+	0.540174i
$412$		0			0
$413$	−9794.44	−	1824.96i	−1.16696	−	0.217435i
$414$		0			0
$415$	−2881.49	+	4990.89i	−0.340836	+	0.590345i
$416$		0			0
$417$	−937.118	−	1623.14i	−0.110050	−	0.190612i
$418$		0			0
$419$	13665.7			1.59335			0.796675	−	0.604407i	$-0.206590\pi$
$419$	13665.7			1.59335			0.796675	+	0.604407i	$0.206590\pi$
$420$		0			0
$421$	10996.4			1.27299			0.636497	−	0.771280i	$-0.280383\pi$
$421$	10996.4			1.27299			0.636497	+	0.771280i	$0.280383\pi$
$422$		0			0
$423$	−723.848	−	1253.74i	−0.0832025	−	0.144111i
$424$		0			0
$425$	575.502	−	996.799i	0.0656846	−	0.113769i
$426$		0			0
$427$	742.756	+	2103.86i	0.0841791	+	0.238437i
$428$		0			0
$429$	−68.2140	+	118.150i	−0.00767693	+	0.0132968i
$430$		0			0
$431$	2250.62	+	3898.19i	0.251528	+	0.435659i	0.963947	−	0.266095i	$-0.0857336\pi$
$431$	2250.62	+	3898.19i	0.251528	+	0.435659i	−0.712419	+	0.701755i	$0.752400\pi$
$432$		0			0
$433$	−837.365			−0.0929358			−0.0464679	−	0.998920i	$-0.514797\pi$
$433$	−837.365			−0.0929358			−0.0464679	+	0.998920i	$0.514797\pi$
$434$		0			0
$435$	−4134.81			−0.455745
$436$		0			0
$437$	892.361	+	1545.61i	0.0976828	+	0.169192i
$438$		0			0
$439$	1768.11	−	3062.45i	0.192226	−	0.332945i	−0.753762	−	0.657148i	$-0.771763\pi$
$439$	1768.11	−	3062.45i	0.192226	−	0.332945i	0.945988	+	0.324203i	$0.105096\pi$
$440$		0			0
$441$	2879.85	+	1111.78i	0.310965	+	0.120050i
$442$		0			0
$443$	−3444.28	+	5965.67i	−0.369396	+	0.639813i	−0.989471	−	0.144729i	$-0.953769\pi$
$443$	−3444.28	+	5965.67i	−0.369396	+	0.639813i	0.620075	+	0.784543i	$0.287102\pi$
$444$		0			0
$445$	−6148.55	−	10649.6i	−0.654987	−	1.13447i
$446$		0			0
$447$	2984.20			0.315766
$448$		0			0
$449$	12248.7			1.28742			0.643712	−	0.765268i	$-0.277393\pi$
$449$	12248.7			1.28742			0.643712	+	0.765268i	$0.277393\pi$
$450$		0			0
$451$	−60.7694	−	105.256i	−0.00634483	−	0.0109896i
$452$		0			0
$453$	3862.64	−	6690.28i	0.400624	−	0.693900i
$454$		0			0
$455$	2545.21	+	7209.32i	0.262245	+	0.742809i
$456$		0			0
$457$	−2413.74	+	4180.72i	−0.247068	+	0.427934i	−0.962711	−	0.270532i	$-0.912800\pi$
$457$	−2413.74	+	4180.72i	−0.247068	+	0.427934i	0.715643	+	0.698466i	$0.246134\pi$
$458$		0			0
$459$	740.173	+	1282.02i	0.0752687	+	0.130369i
$460$		0			0
$461$	1105.41			0.111679			0.0558393	−	0.998440i	$-0.482217\pi$
$461$	1105.41			0.111679			0.0558393	+	0.998440i	$0.482217\pi$
$462$		0			0
$463$	7974.37			0.800433			0.400217	−	0.916421i	$-0.368935\pi$
$463$	7974.37			0.800433			0.400217	+	0.916421i	$0.368935\pi$
$464$		0			0
$465$	−2040.40	−	3534.08i	−0.203487	−	0.352450i
$466$		0			0
$467$	7172.21	−	12422.6i	0.710686	−	1.23094i	−0.253914	−	0.967227i	$-0.581718\pi$
$467$	7172.21	−	12422.6i	0.710686	−	1.23094i	0.964600	−	0.263717i	$-0.0849485\pi$
$468$		0			0
$469$	10927.2	+	2036.02i	1.07584	+	0.200458i
$470$		0			0
$471$	1576.92	−	2731.31i	0.154269	−	0.267202i
$472$		0			0
$473$	−131.994	−	228.621i	−0.0128311	−	0.0222241i
$474$		0			0
$475$	−626.320			−0.0605000
$476$		0			0
$477$	714.786			0.0686117
$478$		0			0
$479$	−6141.22	−	10636.9i	−0.585802	−	1.01464i	−0.994775	−	0.102093i	$-0.967446\pi$
$479$	−6141.22	−	10636.9i	−0.585802	−	1.01464i	0.408973	−	0.912547i	$-0.365887\pi$
$480$		0			0
$481$	4939.86	−	8556.09i	0.468271	−	0.811069i
$482$		0			0
$483$	−2160.97	+	2525.29i	−0.203577	+	0.237898i
$484$		0			0
$485$	7462.44	−	12925.3i	0.698664	−	1.21012i
$486$		0			0
$487$	6865.42	+	11891.3i	0.638813	+	1.10646i	0.985694	+	0.168548i	$0.0539077\pi$
$487$	6865.42	+	11891.3i	0.638813	+	1.10646i	−0.346880	+	0.937909i	$0.612759\pi$
$488$		0			0
$489$	1549.28			0.143274
$490$		0			0
$491$	15077.1			1.38578			0.692891	−	0.721042i	$-0.256337\pi$
$491$	15077.1			1.38578			0.692891	+	0.721042i	$0.256337\pi$
$492$		0			0
$493$	3127.07	+	5416.24i	0.285672	+	0.494798i
$494$		0			0
$495$	72.3724	−	125.353i	0.00657151	−	0.0113822i
$496$		0			0
$497$	1888.09	−	2206.40i	0.170407	−	0.199136i
$498$		0			0
$499$	−10814.8	+	18731.8i	−0.970216	+	1.68046i	−0.275319	+	0.961353i	$0.588784\pi$
$499$	−10814.8	+	18731.8i	−0.970216	+	1.68046i	−0.694896	+	0.719110i	$0.744550\pi$
$500$		0			0
$501$	5610.07	+	9716.92i	0.500278	+	0.866507i
$502$		0			0
$503$	−18037.6			−1.59892			−0.799461	−	0.600718i	$-0.794881\pi$
$503$	−18037.6			−1.59892			−0.799461	+	0.600718i	$0.794881\pi$
$504$		0			0
$505$	−2459.21			−0.216700
$506$		0			0
$507$	1544.58	+	2675.28i	0.135300	+	0.234346i
$508$		0			0
$509$	5725.90	−	9917.56i	0.498617	−	0.863631i	−0.501381	−	0.865226i	$-0.667175\pi$
$509$	5725.90	−	9917.56i	0.498617	−	0.863631i	0.999999	+	0.00159571i	$0.000507931\pi$
$510$		0			0
$511$	10384.5	+	1934.90i	0.898985	+	0.167505i
$512$		0			0
$513$	402.765	−	697.610i	0.0346638	−	0.0600395i
$514$		0			0
$515$	−1693.92	−	2933.95i	−0.144938	−	0.251040i
$516$		0			0
$517$	214.106			0.0182135
$518$		0			0
$519$	6729.11			0.569123
$520$		0			0
$521$	6600.53	+	11432.5i	0.555038	+	0.961353i	0.997901	+	0.0647640i	$0.0206294\pi$
$521$	6600.53	+	11432.5i	0.555038	+	0.961353i	−0.442863	+	0.896589i	$0.646037\pi$
$522$		0			0
$523$	970.862	−	1681.58i	0.0811718	−	0.140594i	−0.822582	−	0.568647i	$-0.807467\pi$
$523$	970.862	−	1681.58i	0.0811718	−	0.140594i	0.903754	+	0.428053i	$0.140800\pi$
$524$		0			0
$525$	−388.301	−	1099.86i	−0.0322797	−	0.0914324i
$526$		0			0
$527$	−3086.23	+	5345.51i	−0.255101	+	0.441848i
$528$		0			0
$529$	4294.24	+	7437.84i	0.352941	+	0.611312i
$530$		0			0
$531$	−4841.57			−0.395680
$532$		0			0
$533$	3119.67			0.253523
$534$		0			0
$535$	−5523.45	−	9566.90i	−0.446354	−	0.773108i
$536$		0			0
$537$	−4631.42	+	8021.86i	−0.372180	+	0.644634i
$538$		0			0
$539$	−355.354	+	286.639i	−0.0283974	+	0.0229061i
$540$		0			0
$541$	11042.4	−	19125.9i	0.877537	−	1.51994i	0.0235025	−	0.999724i	$-0.492518\pi$
$541$	11042.4	−	19125.9i	0.877537	−	1.51994i	0.854035	−	0.520216i	$-0.174148\pi$
$542$		0			0
$543$	2430.25	+	4209.32i	0.192066	+	0.332669i
$544$		0			0
$545$	19249.9			1.51298
$546$		0			0
$547$	−1937.59			−0.151454			−0.0757272	−	0.997129i	$-0.524128\pi$
$547$	−1937.59			−0.151454			−0.0757272	+	0.997129i	$0.524128\pi$
$548$		0			0
$549$	542.111	+	938.964i	0.0421434	+	0.0729946i
$550$		0			0
$551$	1701.60	−	2947.25i	0.131562	−	0.227871i
$552$		0			0
$553$	2901.12	+	8217.41i	0.223089	+	0.631899i
$554$		0			0
$555$	−5241.00	+	9077.68i	−0.400843	+	0.694281i
$556$		0			0
$557$	−1123.32	−	1945.65i	−0.0854519	−	0.148007i	0.820132	−	0.572175i	$-0.193900\pi$
$557$	−1123.32	−	1945.65i	−0.0854519	−	0.148007i	−0.905584	+	0.424168i	$0.860567\pi$
$558$		0			0
$559$	6776.08			0.512697
$560$		0			0
$561$	−218.935			−0.0164767
$562$		0			0
$563$	−6492.51	−	11245.4i	−0.486016	−	0.841804i	0.513855	−	0.857877i	$-0.328217\pi$
$563$	−6492.51	−	11245.4i	−0.486016	−	0.841804i	−0.999871	+	0.0160732i	$0.994884\pi$
$564$		0			0
$565$	13934.3	−	24135.0i	1.03756	−	1.79711i
$566$		0			0
$567$	1474.76	+	274.787i	0.109231	+	0.0203526i
$568$		0			0
$569$	−10185.7	+	17642.2i	−0.750452	+	1.29982i	0.197152	+	0.980373i	$0.436831\pi$
$569$	−10185.7	+	17642.2i	−0.750452	+	1.29982i	−0.947604	+	0.319448i	$0.896503\pi$
$570$		0			0
$571$	−8116.06	−	14057.4i	−0.594828	−	1.03027i	−0.993571	−	0.113209i	$-0.963887\pi$
$571$	−8116.06	−	14057.4i	−0.594828	−	1.03027i	0.398743	−	0.917063i	$-0.369446\pi$
$572$		0			0
$573$	1724.77			0.125748
$574$		0			0
$575$	1255.83			0.0910810
$576$		0			0
$577$	2302.85	+	3988.65i	0.166150	+	0.287781i	0.937063	−	0.349160i	$-0.113533\pi$
$577$	2302.85	+	3988.65i	0.166150	+	0.287781i	−0.770913	+	0.636941i	$0.780200\pi$
$578$		0			0
$579$	−310.812	+	538.342i	−0.0223090	+	0.0386403i
$580$		0			0
$581$	5743.24	−	6711.49i	0.410103	−	0.479242i
$582$		0			0
$583$	−52.8564	+	91.5500i	−0.00375487	+	0.00650363i
$584$		0			0
$585$	1857.66	+	3217.57i	0.131290	+	0.227402i
$586$		0			0
$587$	−12173.8			−0.855992			−0.427996	−	0.903781i	$-0.640780\pi$
$587$	−12173.8			−0.855992			−0.427996	+	0.903781i	$0.640780\pi$
$588$		0			0
$589$	3358.75			0.234966
$590$		0			0
$591$	−3053.30	−	5288.46i	−0.212514	−	0.368085i
$592$		0			0
$593$	3388.27	−	5868.66i	0.234637	−	0.406403i	−0.724530	−	0.689243i	$-0.757943\pi$
$593$	3388.27	−	5868.66i	0.234637	−	0.406403i	0.959167	+	0.282840i	$0.0912766\pi$
$594$		0			0
$595$	−7977.04	+	9321.89i	−0.549625	+	0.642286i
$596$		0			0
$597$	8073.73	−	13984.1i	0.553494	−	0.958679i
$598$		0			0
$599$	−7593.94	−	13153.1i	−0.517997	−	0.897197i	−0.999781	−	0.0209071i	$-0.993345\pi$
$599$	−7593.94	−	13153.1i	−0.517997	−	0.897197i	0.481785	−	0.876290i	$-0.339989\pi$
$600$		0			0
$601$	−5667.91			−0.384690			−0.192345	−	0.981327i	$-0.561609\pi$
$601$	−5667.91			−0.384690			−0.192345	+	0.981327i	$0.561609\pi$
$602$		0			0
$603$	5401.49			0.364786
$604$		0			0
$605$	−8030.37	−	13909.0i	−0.539638	−	0.934681i
$606$		0			0
$607$	2214.19	−	3835.10i	0.148058	−	0.256444i	−0.782451	−	0.622712i	$-0.786031\pi$
$607$	2214.19	−	3835.10i	0.148058	−	0.256444i	0.930510	+	0.366267i	$0.119364\pi$
$608$		0			0
$609$	6230.53	+	1160.91i	0.414571	+	0.0772456i
$610$		0			0
$611$	−2747.85	+	4759.41i	−0.181941	+	0.315131i
$612$		0			0
$613$	−12976.2	−	22475.5i	−0.854984	−	1.48087i	−0.876660	−	0.481110i	$-0.840234\pi$
$613$	−12976.2	−	22475.5i	−0.854984	−	1.48087i	0.0216768	−	0.999765i	$-0.493100\pi$
$614$		0			0
$615$	−3309.85			−0.217018
$616$		0			0
$617$	−4712.95			−0.307514			−0.153757	−	0.988109i	$-0.549137\pi$
$617$	−4712.95			−0.307514			−0.153757	+	0.988109i	$0.549137\pi$
$618$		0			0
$619$	−1456.11	−	2522.05i	−0.0945490	−	0.163764i	0.814871	−	0.579642i	$-0.196808\pi$
$619$	−1456.11	−	2522.05i	−0.0945490	−	0.163764i	−0.909420	+	0.415878i	$0.863474\pi$
$620$		0			0
$621$	−807.580	+	1398.77i	−0.0521853	+	0.0903876i
$622$		0			0
$623$	6274.89	+	17773.6i	0.403529	+	1.14300i
$624$		0			0
$625$	8904.22	−	15422.6i	0.569870	−	0.987043i
$626$		0			0
$627$	59.5668	+	103.173i	0.00379405	+	0.00657148i
$628$		0			0
$629$	15854.6			1.00503
$630$		0			0
$631$	23349.3			1.47309			0.736544	−	0.676389i	$-0.236456\pi$
$631$	23349.3			1.47309			0.736544	+	0.676389i	$0.236456\pi$
$632$		0			0
$633$	−1978.28	−	3426.48i	−0.124217	−	0.215151i
$634$		0			0
$635$	17196.2	−	29784.7i	1.07466	−	1.86137i
$636$		0			0
$637$	−1811.12	−	11578.0i	−0.112652	−	0.720151i
$638$		0			0
$639$	705.601	−	1222.14i	0.0436825	−	0.0756604i
$640$		0			0
$641$	−695.908	−	1205.35i	−0.0428810	−	0.0742720i	0.843788	−	0.536676i	$-0.180320\pi$
$641$	−695.908	−	1205.35i	−0.0428810	−	0.0742720i	−0.886669	+	0.462404i	$0.846987\pi$
$642$		0			0
$643$	−22821.0			−1.39964			−0.699821	−	0.714318i	$-0.746737\pi$
$643$	−22821.0			−1.39964			−0.699821	+	0.714318i	$0.746737\pi$
$644$		0			0
$645$	−7189.16			−0.438873
$646$		0			0
$647$	−5850.52	−	10133.4i	−0.355499	−	0.615742i	0.631704	−	0.775209i	$-0.282356\pi$
$647$	−5850.52	−	10133.4i	−0.355499	−	0.615742i	−0.987203	+	0.159467i	$0.949022\pi$
$648$		0			0
$649$	358.021	−	620.110i	0.0216541	−	0.0375061i
$650$		0			0
$651$	2082.33	+	5898.21i	0.125366	+	0.355098i
$652$		0			0
$653$	−4638.16	+	8033.53i	−0.277956	+	0.481434i	−0.970877	−	0.239580i	$-0.922990\pi$
$653$	−4638.16	+	8033.53i	−0.277956	+	0.481434i	0.692921	+	0.721014i	$0.256324\pi$
$654$		0			0
$655$	−5360.04	−	9283.87i	−0.319747	−	0.553818i
$656$		0			0
$657$	5133.23			0.304819
$658$		0			0
$659$	19472.7			1.15106			0.575531	−	0.817780i	$-0.304796\pi$
$659$	19472.7			1.15106			0.575531	+	0.817780i	$0.304796\pi$
$660$		0			0
$661$	6374.73	+	11041.4i	0.375111	+	0.649711i	0.990344	−	0.138634i	$-0.0442713\pi$
$661$	6374.73	+	11041.4i	0.375111	+	0.649711i	−0.615233	+	0.788346i	$0.710938\pi$
$662$		0			0
$663$	2809.82	−	4866.75i	0.164592	−	0.285082i
$664$		0			0
$665$	6563.28	+	1222.91i	0.382726	+	0.0713120i
$666$		0			0
$667$	−3411.85	+	5909.50i	−0.198062	+	0.343053i
$668$		0			0
$669$	−526.222	−	911.443i	−0.0304109	−	0.0526733i
$670$		0			0
$671$	−160.351			−0.00922543
$672$		0			0
$673$	−8082.06			−0.462913			−0.231457	−	0.972845i	$-0.574349\pi$
$673$	−8082.06			−0.462913			−0.231457	+	0.972845i	$0.574349\pi$
$674$		0			0
$675$	−283.408	−	490.876i	−0.0161605	−	0.0279909i
$676$		0			0
$677$	13208.3	−	22877.4i	0.749831	−	1.29875i	−0.198072	−	0.980187i	$-0.563468\pi$
$677$	13208.3	−	22877.4i	0.749831	−	1.29875i	0.947903	−	0.318558i	$-0.103199\pi$
$678$		0			0
$679$	−14873.8	+	17381.3i	−0.840652	+	0.982377i
$680$		0			0
$681$	−6590.72	+	11415.5i	−0.370862	+	0.642352i
$682$		0			0
$683$	−457.115	−	791.747i	−0.0256091	−	0.0443563i	0.852937	−	0.522014i	$-0.174819\pi$
$683$	−457.115	−	791.747i	−0.0256091	−	0.0443563i	−0.878546	+	0.477658i	$0.841486\pi$
$684$		0			0
$685$	−20932.0			−1.16755
$686$		0			0
$687$	10851.1			0.602611
$688$		0			0
$689$	−1356.72	−	2349.92i	−0.0750175	−	0.129934i
$690$		0			0
$691$	5516.31	−	9554.52i	0.303691	−	0.526007i	−0.673278	−	0.739389i	$-0.735114\pi$
$691$	5516.31	−	9554.52i	0.303691	−	0.526007i	0.976969	+	0.213382i	$0.0684478\pi$
$692$		0			0
$693$	−144.249	+	168.568i	−0.00790703	+	0.00924007i
$694$		0			0
$695$	3774.33	−	6537.32i	0.205998	−	0.356798i
$696$		0			0
$697$	2503.17	+	4335.62i	0.136032	+	0.235614i
$698$		0			0
$699$	11026.2			0.596638
$700$		0			0
$701$	−11973.6			−0.645129			−0.322565	−	0.946547i	$-0.604545\pi$
$701$	−11973.6			−0.645129			−0.322565	+	0.946547i	$0.604545\pi$
$702$		0			0
$703$	−4313.65	−	7471.47i	−0.231426	−	0.400842i
$704$		0			0
$705$	2915.36	−	5049.55i	0.155743	−	0.269755i
$706$		0			0
$707$	3705.67	+	690.463i	0.197123	+	0.0367292i
$708$		0			0
$709$	5056.56	−	8758.21i	0.267846	−	0.463923i	−0.700459	−	0.713692i	$-0.747021\pi$
$709$	5056.56	−	8758.21i	0.267846	−	0.463923i	0.968305	+	0.249769i	$0.0803547\pi$
$710$		0			0
$711$	2117.42	+	3667.48i	0.111687	+	0.193448i
$712$		0			0
$713$	−6734.58			−0.353734
$714$		0			0
$715$	−549.476			−0.0287402
$716$		0			0
$717$	906.187	+	1569.56i	0.0471997	+	0.0817522i
$718$		0			0
$719$	−12188.9	+	21111.9i	−0.632226	+	1.09505i	0.354869	+	0.934916i	$0.384525\pi$
$719$	−12188.9	+	21111.9i	−0.632226	+	1.09505i	−0.987096	+	0.160132i	$0.948808\pi$
$720$		0			0
$721$	1728.73	+	4896.62i	0.0892942	+	0.252926i
$722$		0			0
$723$	−5380.63	+	9319.52i	−0.276774	+	0.479387i
$724$		0			0
$725$	−1197.33	−	2073.84i	−0.0613350	−	0.106235i
$726$		0			0
$727$	−8265.40			−0.421660			−0.210830	−	0.977523i	$-0.567617\pi$
$727$	−8265.40			−0.421660			−0.210830	+	0.977523i	$0.567617\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	5437.01	+	9417.18i	0.275096	+	0.476480i
$732$		0			0
$733$	−9544.62	+	16531.8i	−0.480953	+	0.833035i	−0.999761	−	0.0218554i	$-0.993043\pi$
$733$	−9544.62	+	16531.8i	−0.480953	+	0.833035i	0.518808	+	0.854891i	$0.326376\pi$
$734$		0			0
$735$	1921.53	+	12283.8i	0.0964310	+	0.616454i
$736$		0			0
$737$	−399.425	+	691.825i	−0.0199634	+	0.0345776i
$738$		0			0
$739$	−7939.11	−	13750.9i	−0.395189	−	0.684488i	0.597936	−	0.801544i	$-0.295988\pi$
$739$	−7939.11	−	13750.9i	−0.395189	−	0.684488i	−0.993125	+	0.117056i	$0.962654\pi$
$740$		0			0
$741$	−3057.93			−0.151600
$742$		0			0
$743$	17150.0			0.846799			0.423399	−	0.905943i	$-0.360837\pi$
$743$	17150.0			0.846799			0.423399	+	0.905943i	$0.360837\pi$
$744$		0			0
$745$	6009.55	+	10408.9i	0.295534	+	0.511880i
$746$		0			0
$747$	2146.32	−	3717.53i	0.105127	−	0.182085i
$748$		0			0
$749$	5636.95	+	15966.7i	0.274993	+	0.778918i
$750$		0			0
$751$	10773.7	−	18660.5i	0.523484	−	0.906701i	−0.476142	−	0.879368i	$-0.657965\pi$
$751$	10773.7	−	18660.5i	0.523484	−	0.906701i	0.999626	−	0.0273326i	$-0.00870133\pi$
$752$		0			0
$753$	−2332.36	−	4039.76i	−0.112876	−	0.195507i
$754$		0			0
$755$	31114.2			1.49982
$756$		0			0
$757$	12318.5			0.591444			0.295722	−	0.955274i	$-0.404440\pi$
$757$	12318.5			0.591444			0.295722	+	0.955274i	$0.404440\pi$
$758$		0			0
$759$	−119.437	−	206.870i	−0.00571183	−	0.00989317i
$760$		0			0
$761$	−4889.93	+	8469.61i	−0.232930	+	0.403447i	−0.958669	−	0.284523i	$-0.908165\pi$
$761$	−4889.93	+	8469.61i	−0.232930	+	0.403447i	0.725739	+	0.687970i	$0.241498\pi$
$762$		0			0
$763$	−29006.8	−	5404.73i	−1.37630	−	0.256441i
$764$		0			0
$765$	−2981.11	+	5163.44i	−0.140892	+	0.244032i
$766$		0			0
$767$	9189.71	+	15917.0i	0.432622	+	0.749323i
$768$		0			0
$769$	32018.7			1.50146			0.750731	−	0.660608i	$-0.229701\pi$
$769$	32018.7			1.50146			0.750731	+	0.660608i	$0.229701\pi$
$770$		0			0
$771$	8650.67			0.404081
$772$		0			0
$773$	−3809.37	−	6598.02i	−0.177249	−	0.307004i	0.763688	−	0.645585i	$-0.223386\pi$
$773$	−3809.37	−	6598.02i	−0.177249	−	0.307004i	−0.940937	+	0.338581i	$0.890053\pi$
$774$		0			0
$775$	1181.70	−	2046.76i	0.0547714	−	0.0948668i
$776$		0			0
$777$	10446.1	−	12207.2i	0.482306	−	0.563618i
$778$		0			0
$779$	1362.10	−	2359.23i	0.0626474	−	0.108508i
$780$		0			0
$781$	104.354	+	180.747i	0.00478117	+	0.00828124i
$782$		0			0
$783$	3079.86			0.140569
$784$		0			0
$785$	12702.4			0.577539
$786$		0			0
$787$	−13641.8	−	23628.3i	−0.617887	−	1.07021i	−0.989871	−	0.141973i	$-0.954655\pi$
$787$	−13641.8	−	23628.3i	−0.617887	−	1.07021i	0.371983	−	0.928239i	$-0.378678\pi$
$788$		0			0
$789$	3947.34	−	6836.99i	0.178110	−	0.308496i
$790$		0			0
$791$	−27773.3	+	32455.5i	−1.24842	+	1.45889i
$792$		0			0
$793$	2057.95	−	3564.47i	0.0921561	−	0.159619i
$794$		0			0
$795$	1439.43	+	2493.17i	0.0642156	+	0.111225i
$796$		0			0
$797$	−359.790			−0.0159905			−0.00799525	−	0.999968i	$-0.502545\pi$
$797$	−359.790			−0.0159905			−0.00799525	+	0.999968i	$0.502545\pi$
$798$		0			0
$799$	−8819.30			−0.390494
$800$		0			0
$801$	4579.82	+	7932.49i	0.202023	+	0.349913i
$802$		0			0
$803$	−379.588	+	657.465i	−0.0166816	+	0.0288935i
$804$		0			0
$805$	−13160.0	−	2452.05i	−0.576183	−	0.107358i
$806$		0			0
$807$	12571.7	−	21774.9i	0.548384	−	0.949830i
$808$		0			0
$809$	−1769.09	−	3064.16i	−0.0768826	−	0.133165i	0.825021	−	0.565102i	$-0.191163\pi$
$809$	−1769.09	−	3064.16i	−0.0768826	−	0.133165i	−0.901903	+	0.431938i	$0.857830\pi$
$810$		0			0
$811$	−28330.1			−1.22664			−0.613319	−	0.789835i	$-0.710166\pi$
$811$	−28330.1			−1.22664			−0.613319	+	0.789835i	$0.710166\pi$
$812$		0			0
$813$	−15529.4			−0.669914
$814$		0			0
$815$	3119.94	+	5403.89i	0.134094	+	0.232258i
$816$		0			0
$817$	2958.55	−	5124.36i	0.126691	−	0.219435i
$818$		0			0
$819$	−1895.84	−	5369.96i	−0.0808863	−	0.229110i
$820$		0			0
$821$	−5221.03	+	9043.10i	−0.221943	+	0.384417i	−0.955398	−	0.295321i	$-0.904573\pi$
$821$	−5221.03	+	9043.10i	−0.221943	+	0.384417i	0.733455	+	0.679738i	$0.237907\pi$
$822$		0			0
$823$	−8992.92	−	15576.2i	−0.380891	−	0.659723i	0.610299	−	0.792171i	$-0.291049\pi$
$823$	−8992.92	−	15576.2i	−0.380891	−	0.659723i	−0.991190	+	0.132449i	$0.957716\pi$
$824$		0			0
$825$	83.8288			0.00353763
$826$		0			0
$827$	42470.5			1.78579			0.892893	−	0.450269i	$-0.148672\pi$
$827$	42470.5			1.78579			0.892893	+	0.450269i	$0.148672\pi$
$828$		0			0
$829$	14519.9	+	25149.1i	0.608318	+	1.05364i	0.991518	+	0.129972i	$0.0414888\pi$
$829$	14519.9	+	25149.1i	0.608318	+	1.05364i	−0.383200	+	0.923666i	$0.625178\pi$
$830$		0			0
$831$	3296.65	−	5709.96i	0.137617	−	0.238359i
$832$		0			0
$833$	14637.5	−	11807.0i	0.608834	−	0.491103i
$834$		0			0
$835$	−22595.0	+	39135.7i	−0.936447	+	1.62197i
$836$		0			0
$837$	1519.82	+	2632.41i	0.0627631	+	0.108709i
$838$		0			0
$839$	−25352.1			−1.04321			−0.521603	−	0.853188i	$-0.674666\pi$
$839$	−25352.1			−1.04321			−0.521603	+	0.853188i	$0.674666\pi$
$840$		0			0
$841$	−11377.2			−0.466491
$842$		0			0
$843$	7537.41	+	13055.2i	0.307951	+	0.533386i
$844$		0			0
$845$	−6220.91	+	10774.9i	−0.253261	+	0.438662i
$846$		0			0
$847$	8195.39	+	23213.5i	0.332464	+	0.941704i
$848$		0			0
$849$	−1629.83	+	2822.94i	−0.0658839	+	0.114114i
$850$		0			0
$851$	8649.26	+	14981.0i	0.348405	+	0.603455i
$852$		0			0
$853$	−10921.7			−0.438396			−0.219198	−	0.975680i	$-0.570344\pi$
$853$	−10921.7			−0.438396			−0.219198	+	0.975680i	$0.570344\pi$
$854$		0			0
$855$	3244.35			0.129771
$856$		0			0
$857$	−265.387	−	459.664i	−0.0105781	−	0.0183218i	0.860688	−	0.509133i	$-0.170034\pi$
$857$	−265.387	−	459.664i	−0.0105781	−	0.0183218i	−0.871266	+	0.490811i	$0.836701\pi$
$858$		0			0
$859$	8019.76	−	13890.6i	0.318545	−	0.551737i	−0.661639	−	0.749822i	$-0.730139\pi$
$859$	8019.76	−	13890.6i	0.318545	−	0.551737i	0.980185	+	0.198085i	$0.0634723\pi$
$860$		0			0
$861$	4987.45	+	929.293i	0.197412	+	0.0367831i
$862$		0			0
$863$	−5626.93	+	9746.14i	−0.221950	+	0.384429i	−0.955400	−	0.295314i	$-0.904576\pi$
$863$	−5626.93	+	9746.14i	−0.221950	+	0.384429i	0.733450	+	0.679744i	$0.237909\pi$
$864$		0			0
$865$	13551.0	+	23471.1i	0.532658	+	0.922590i
$866$		0			0
$867$	−5720.79			−0.224093
$868$		0			0
$869$	−626.310			−0.0244489
$870$		0			0
$871$	−10252.5	−	17757.8i	−0.398843	−	0.690816i
$872$		0			0
$873$	−5558.50	+	9627.60i	−0.215494	+	0.373247i
$874$		0			0
$875$	−15132.3	+	17683.4i	−0.584645	+	0.683210i
$876$		0			0
$877$	−17716.3	+	30685.5i	−0.682139	+	1.18150i	0.292188	+	0.956361i	$0.405617\pi$
$877$	−17716.3	+	30685.5i	−0.682139	+	1.18150i	−0.974327	+	0.225138i	$0.927717\pi$
$878$		0			0
$879$	−5667.89	−	9817.08i	−0.217489	−	0.376703i
$880$		0			0
$881$	−36249.0			−1.38622			−0.693111	−	0.720831i	$-0.743760\pi$
$881$	−36249.0			−1.38622			−0.693111	+	0.720831i	$0.743760\pi$
$882$		0			0
$883$	15102.7			0.575590			0.287795	−	0.957692i	$-0.407078\pi$
$883$	15102.7			0.575590			0.287795	+	0.957692i	$0.407078\pi$
$884$		0			0
$885$	−9749.92	−	16887.4i	−0.370328	−	0.641426i
$886$		0			0
$887$	−5045.72	+	8739.44i	−0.191002	+	0.330825i	−0.945583	−	0.325382i	$-0.894507\pi$
$887$	−5045.72	+	8739.44i	−0.191002	+	0.330825i	0.754581	+	0.656207i	$0.227840\pi$
$888$		0			0
$889$	−34274.6	+	40052.9i	−1.29306	+	1.51106i
$890$		0			0
$891$	−53.9075	+	93.3706i	−0.00202690	+	0.00351070i
$892$		0			0
$893$	2399.51	+	4156.08i	0.0899178	+	0.155742i
$894$		0			0
$895$	−37306.9			−1.39333
$896$		0			0
$897$	6131.42			0.228230
$898$		0			0
$899$	6420.91	+	11121.3i	0.238208	+	0.412589i
$900$		0			0
$901$	2177.22	−	3771.06i	0.0805037	−	0.139436i
$902$		0			0
$903$	10833.0	+	2018.47i	0.399224	+	0.0743859i
$904$		0			0
$905$	−9788.04	+	16953.4i	−0.359520	+	0.622707i
$906$		0			0
$907$	−8273.26	−	14329.7i	−0.302877	−	0.524598i	0.673910	−	0.738814i	$-0.264614\pi$
$907$	−8273.26	−	14329.7i	−0.302877	−	0.524598i	−0.976786	+	0.214216i	$0.931280\pi$
$908$		0			0
$909$	1831.78			0.0668385
$910$		0			0
$911$	11427.4			0.415596			0.207798	−	0.978172i	$-0.433370\pi$
$911$	11427.4			0.415596			0.207798	+	0.978172i	$0.433370\pi$
$912$		0			0
$913$	317.428	+	549.802i	0.0115064	+	0.0199297i
$914$		0			0
$915$	−2183.40	+	3781.76i	−0.0788863	+	0.136635i
$916$		0			0
$917$	5470.19	+	15494.3i	0.196992	+	0.557979i
$918$		0			0
$919$	19812.2	−	34315.8i	0.711149	−	1.23175i	−0.253277	−	0.967394i	$-0.581509\pi$
$919$	19812.2	−	34315.8i	0.711149	−	1.23175i	0.964426	−	0.264352i	$-0.0851581\pi$
$920$		0			0
$921$	−14398.7	−	24939.2i	−0.515149	−	0.892264i
$922$		0			0
$923$	−5357.16			−0.191043
$924$		0			0
$925$	−6070.64			−0.215785
$926$		0			0
$927$	1261.74	+	2185.39i	0.0447043	+	0.0774301i
$928$		0			0
$929$	−2046.32	+	3544.33i	−0.0722686	+	0.125173i	−0.899895	−	0.436106i	$-0.856357\pi$
$929$	−2046.32	+	3544.33i	−0.0722686	+	0.125173i	0.827627	+	0.561279i	$0.189691\pi$
$930$		0			0
$931$	−9546.52	−	3685.49i	−0.336063	−	0.129739i
$932$		0			0
$933$	−8014.06	+	13880.8i	−0.281210	+	0.487069i
$934$		0			0
$935$	−440.890	−	763.644i	−0.0154210	−	0.0267100i
$936$		0			0
$937$	−54276.2			−1.89234			−0.946172	−	0.323665i	$-0.895085\pi$
$937$	−54276.2			−1.89234			−0.946172	+	0.323665i	$0.895085\pi$
$938$		0			0
$939$	14715.6			0.511421
$940$		0			0
$941$	−9333.73	−	16166.5i	−0.323348	−	0.560056i	0.657828	−	0.753168i	$-0.271475\pi$
$941$	−9333.73	−	16166.5i	−0.323348	−	0.560056i	−0.981177	+	0.193112i	$0.938142\pi$
$942$		0			0
$943$	−2731.13	+	4730.46i	−0.0943138	+	0.163356i
$944$		0			0
$945$	2011.41	+	5697.31i	0.0692393	+	0.196120i
$946$		0			0
$947$	−22458.3	+	38898.9i	−0.770639	+	1.33479i	0.166574	+	0.986029i	$0.446730\pi$
$947$	−22458.3	+	38898.9i	−0.770639	+	1.33479i	−0.937213	+	0.348758i	$0.886604\pi$
$948$		0			0
$949$	−9743.30	−	16875.9i	−0.333278	−	0.577254i
$950$		0			0
$951$	20703.4			0.705945
$952$		0			0
$953$	−54279.0			−1.84499			−0.922493	−	0.386015i	$-0.873851\pi$
$953$	−54279.0			−1.84499			−0.922493	+	0.386015i	$0.873851\pi$
$954$		0			0
$955$	3473.34	+	6016.00i	0.117691	+	0.203846i
$956$		0			0
$957$	−227.747	+	394.470i	−0.00769282	+	0.0133244i
$958$		0			0
$959$	31541.4	+	5877.00i	1.06207	+	0.197892i
$960$		0			0
$961$	8558.45	−	14823.7i	0.287283	−	0.497589i
$962$		0			0
$963$	4114.21	+	7126.02i	0.137673	+	0.238456i
$964$		0			0
$965$	−2503.64			−0.0835182
$966$		0			0
$967$	−3150.59			−0.104774			−0.0523869	−	0.998627i	$-0.516683\pi$
$967$	−3150.59			−0.104774			−0.0523869	+	0.998627i	$0.516683\pi$
$968$		0			0
$969$	−2453.63	−	4249.81i	−0.0813436	−	0.140891i
$970$		0			0
$971$	14441.4	−	25013.2i	0.477287	−	0.826686i	−0.522374	−	0.852716i	$-0.674954\pi$
$971$	14441.4	−	25013.2i	0.477287	−	0.826686i	0.999661	+	0.0260309i	$0.00828684\pi$
$972$		0			0
$973$	−7522.80	+	8791.06i	−0.247862	+	0.289649i
$974$		0			0
$975$	−1075.86	+	1863.45i	−0.0353387	+	0.0612084i
$976$		0			0
$977$	−3102.09	−	5372.99i	−0.101581	−	0.175944i	0.810755	−	0.585386i	$-0.199057\pi$
$977$	−3102.09	−	5372.99i	−0.101581	−	0.175944i	−0.912336	+	0.409442i	$0.865723\pi$
$978$		0			0
$979$	−1354.66			−0.0442239
$980$		0			0
$981$	−14338.6			−0.466662
$982$		0			0
$983$	1210.15	+	2096.04i	0.0392653	+	0.0680095i	0.884990	−	0.465610i	$-0.154165\pi$
$983$	1210.15	+	2096.04i	0.0392653	+	0.0680095i	−0.845725	+	0.533619i	$0.820832\pi$
$984$		0			0
$985$	12297.4	−	21299.8i	0.397795	−	0.689002i
$986$		0			0
$987$	−5810.75	+	6790.38i	−0.187394	+	0.218987i
$988$		0			0
$989$	−5932.16	+	10274.8i	−0.190730	+	0.330354i
$990$		0			0
$991$	−9255.87	−	16031.6i	−0.296693	−	0.513887i	0.678685	−	0.734430i	$-0.262550\pi$
$991$	−9255.87	−	16031.6i	−0.296693	−	0.513887i	−0.975377	+	0.220543i	$0.929217\pi$
$992$		0			0
$993$	7422.71			0.237213
$994$		0			0
$995$	65035.3			2.07212
$996$		0			0
$997$	10751.8	+	18622.7i	0.341537	+	0.591560i	0.984718	−	0.174154i	$-0.0557190\pi$
$997$	10751.8	+	18622.7i	0.341537	+	0.591560i	−0.643181	+	0.765714i	$0.722386\pi$
$998$		0			0
$999$	3903.83	−	6761.63i	0.123635	−	0.214143i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	672.4.q.c.289.2	yes	4
4.3	odd	2		672.4.q.d.289.2	yes	4
7.4	even	3	inner	672.4.q.c.193.2	✓	4
28.11	odd	6		672.4.q.d.193.2	yes	4

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
672.4.q.c.193.2	✓	4	7.4	even	3	inner
672.4.q.c.289.2	yes	4	1.1	even	1	trivial
672.4.q.d.193.2	yes	4	28.11	odd	6
672.4.q.d.289.2	yes	4	4.3	odd	2

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:	\( N \)	\(=\)	\( 672 = 2^{5} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	672.q (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.50000 - 2.59808i) q^{3} +(6.04138 - 10.4640i) q^{5} +(-12.0414 + 14.0714i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(-1.50000 - 2.59808i) q^{3} +(6.04138 - 10.4640i) q^{5} +(-12.0414 + 14.0714i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(-0.665525 - 1.15272i) q^{11} +34.1655 q^{13} -36.2483 q^{15} +(27.4138 + 47.4821i) q^{17} +(14.9172 - 25.8374i) q^{19} +(54.6207 + 10.1773i) q^{21} +(-29.9104 + 51.8063i) q^{23} +(-10.4966 - 18.1806i) q^{25} +27.0000 q^{27} +114.069 q^{29} +(56.2897 + 97.4966i) q^{31} +(-1.99658 + 3.45817i) q^{33} +(74.4966 + 211.012i) q^{35} +(144.586 - 250.431i) q^{37} +(-51.2483 - 88.7646i) q^{39} +91.3105 q^{41} +198.331 q^{43} +(54.3724 + 94.1758i) q^{45} +(-80.4275 + 139.305i) q^{47} +(-53.0103 - 338.879i) q^{49} +(82.2414 - 142.446i) q^{51} +(-39.7103 - 68.7803i) q^{53} -16.0828 q^{55} -89.5034 q^{57} +(268.976 + 465.880i) q^{59} +(60.2346 - 104.329i) q^{61} +(-55.4897 - 157.175i) q^{63} +(206.407 - 357.507i) q^{65} +(-300.083 - 519.759i) q^{67} +179.462 q^{69} -156.800 q^{71} +(-285.179 - 493.945i) q^{73} +(-31.4897 + 54.5418i) q^{75} +(24.2343 + 4.51549i) q^{77} +(235.269 - 407.498i) q^{79} +(-40.5000 - 70.1481i) q^{81} -476.959 q^{83} +662.469 q^{85} +(-171.104 - 296.360i) q^{87} +(508.869 - 881.387i) q^{89} +(-411.400 + 480.758i) q^{91} +(168.869 - 292.490i) q^{93} +(-180.241 - 312.187i) q^{95} +1235.22 q^{97} +11.9795 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 4 q - 6 q^{3} + 12 q^{5} - 36 q^{7} - 18 q^{9}+O(q^{10}) \) 4 * q - 6 * q^3 + 12 * q^5 - 36 * q^7 - 18 * q^9	\( 4 q - 6 q^{3} + 12 q^{5} - 36 q^{7} - 18 q^{9} + 46 q^{11} + 88 q^{13} - 72 q^{15} - 12 q^{17} + 84 q^{19} + 36 q^{21} + 148 q^{23} + 104 q^{25} + 108 q^{27} - 152 q^{29} + 140 q^{31} + 138 q^{33} + 152 q^{35} + 700 q^{37} - 132 q^{39} - 608 q^{41} + 696 q^{43} + 108 q^{45} - 784 q^{47} - 650 q^{49} - 36 q^{51} - 244 q^{53} - 40 q^{55} - 504 q^{57} + 54 q^{59} - 416 q^{61} + 216 q^{63} + 412 q^{65} - 1176 q^{67} - 888 q^{69} + 784 q^{71} - 1676 q^{73} + 312 q^{75} + 1204 q^{77} - 20 q^{79} - 162 q^{81} - 156 q^{83} + 1336 q^{85} + 228 q^{87} + 16 q^{89} - 940 q^{91} + 420 q^{93} - 356 q^{95} + 172 q^{97} - 828 q^{99}+O(q^{100}) \) 4 * q - 6 * q^3 + 12 * q^5 - 36 * q^7 - 18 * q^9 + 46 * q^11 + 88 * q^13 - 72 * q^15 - 12 * q^17 + 84 * q^19 + 36 * q^21 + 148 * q^23 + 104 * q^25 + 108 * q^27 - 152 * q^29 + 140 * q^31 + 138 * q^33 + 152 * q^35 + 700 * q^37 - 132 * q^39 - 608 * q^41 + 696 * q^43 + 108 * q^45 - 784 * q^47 - 650 * q^49 - 36 * q^51 - 244 * q^53 - 40 * q^55 - 504 * q^57 + 54 * q^59 - 416 * q^61 + 216 * q^63 + 412 * q^65 - 1176 * q^67 - 888 * q^69 + 784 * q^71 - 1676 * q^73 + 312 * q^75 + 1204 * q^77 - 20 * q^79 - 162 * q^81 - 156 * q^83 + 1336 * q^85 + 228 * q^87 + 16 * q^89 - 940 * q^91 + 420 * q^93 - 356 * q^95 + 172 * q^97 - 828 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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