LMFDB - Embedded newform 252.4.i.a.25.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [252,4,Mod(25,252)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(252, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("252.25");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 252 = 2^{2} \cdot 3^{2} \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	252.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:	$14.8684813214$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$24$ over $\Q(\zeta_{3})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			25.9
Character	$\chi$	$=$	252.25
Dual form			252.4.i.a.121.9

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.93223 + 4.82354i) q^{3} +(-7.79077 + 13.4940i) q^{5} +(0.496367 + 18.5136i) q^{7} +(-19.5330 - 18.6403i) q^{9} +O(q^{10})$	\(q+(-1.93223 + 4.82354i) q^{3} +(-7.79077 + 13.4940i) q^{5} +(0.496367 + 18.5136i) q^{7} +(-19.5330 - 18.6403i) q^{9} +(20.8381 + 36.0927i) q^{11} +(15.8378 + 27.4318i) q^{13} +(-50.0353 - 63.6526i) q^{15} +(-18.7824 + 32.5321i) q^{17} +(-45.8855 - 79.4760i) q^{19} +(-90.2601 - 33.3783i) q^{21} +(23.6712 - 40.9997i) q^{23} +(-58.8922 - 102.004i) q^{25} +(127.655 - 58.2007i) q^{27} +(1.84457 - 3.19489i) q^{29} +124.177 q^{31} +(-214.358 + 30.7741i) q^{33} +(-253.690 - 137.537i) q^{35} +(-202.205 - 350.230i) q^{37} +(-162.921 + 23.3895i) q^{39} +(189.575 + 328.354i) q^{41} +(-10.1455 + 17.5725i) q^{43} +(403.710 - 118.356i) q^{45} -500.974 q^{47} +(-342.507 + 18.3791i) q^{49} +(-120.628 - 153.457i) q^{51} +(36.0419 - 62.4263i) q^{53} -649.380 q^{55} +(472.016 - 67.7645i) q^{57} +588.033 q^{59} +893.353 q^{61} +(335.404 - 370.879i) q^{63} -493.554 q^{65} -787.490 q^{67} +(152.025 + 193.399i) q^{69} -132.781 q^{71} +(-252.320 + 437.031i) q^{73} +(605.815 - 86.9732i) q^{75} +(-657.863 + 403.704i) q^{77} -413.941 q^{79} +(34.0756 + 728.203i) q^{81} +(225.944 - 391.347i) q^{83} +(-292.659 - 506.901i) q^{85} +(11.8465 + 15.0706i) q^{87} +(583.982 + 1011.49i) q^{89} +(-500.001 + 306.831i) q^{91} +(-239.938 + 598.972i) q^{93} +1429.93 q^{95} +(-303.395 + 525.495i) q^{97} +(265.749 - 1093.43i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	$ 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) $ 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/252\mathbb{Z}\right)^\times$.

$n$	$29$	$73$	$127$
$\chi(n)$	$e\left(\frac{2}{3}\right)$	$e\left(\frac{2}{3}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−1.93223	+	4.82354i	−0.371857	+	0.928290i
$3$	−1.93223	+	4.82354i	−0.371857	+	0.928290i
$4$		0			0
$5$	−7.79077	+	13.4940i	−0.696828	+	1.20694i	0.272733	+	0.962090i	$0.412072\pi$
$5$	−7.79077	+	13.4940i	−0.696828	+	1.20694i	−0.969561	+	0.244851i	$0.921261\pi$
$6$		0			0
$7$	0.496367	+	18.5136i	0.0268013	+	0.999641i
$7$	0.496367	+	18.5136i	0.0268013	+	0.999641i
$8$		0			0
$9$	−19.5330	−	18.6403i	−0.723444	−	0.690383i
$10$		0			0
$11$	20.8381	+	36.0927i	0.571176	+	0.989305i	0.996446	+	0.0842386i	$0.0268458\pi$
$11$	20.8381	+	36.0927i	0.571176	+	0.989305i	−0.425270	+	0.905067i	$0.639821\pi$
$12$		0			0
$13$	15.8378	+	27.4318i	0.337893	+	0.585248i	0.984036	−	0.177968i	$-0.0569524\pi$
$13$	15.8378	+	27.4318i	0.337893	+	0.585248i	−0.646143	+	0.763216i	$0.723619\pi$
$14$		0			0
$15$	−50.0353	−	63.6526i	−0.861271	−	1.09567i
$16$		0			0
$17$	−18.7824	+	32.5321i	−0.267965	+	0.464129i	−0.968336	−	0.249650i	$-0.919685\pi$
$17$	−18.7824	+	32.5321i	−0.267965	+	0.464129i	0.700371	+	0.713779i	$0.253018\pi$
$18$		0			0
$19$	−45.8855	−	79.4760i	−0.554045	−	0.959633i	−0.997977	−	0.0635732i	$-0.979750\pi$
$19$	−45.8855	−	79.4760i	−0.554045	−	0.959633i	0.443933	−	0.896060i	$-0.353583\pi$
$20$		0			0
$21$	−90.2601	−	33.3783i	−0.937923	−	0.346844i
$22$		0			0
$23$	23.6712	−	40.9997i	0.214599	−	0.371697i	−0.738549	−	0.674199i	$-0.764489\pi$
$23$	23.6712	−	40.9997i	0.214599	−	0.371697i	0.953148	+	0.302503i	$0.0978222\pi$
$24$		0			0
$25$	−58.8922	−	102.004i	−0.471138	−	0.816035i
$26$		0			0
$27$	127.655	−	58.2007i	0.909893	−	0.414842i
$28$		0			0
$29$	1.84457	−	3.19489i	0.0118113	−	0.0204578i	−0.860059	−	0.510194i	$-0.829574\pi$
$29$	1.84457	−	3.19489i	0.0118113	−	0.0204578i	0.871871	+	0.489736i	$0.162907\pi$
$30$		0			0
$31$	124.177			0.719446			0.359723	−	0.933059i	$-0.382871\pi$
$31$	124.177			0.719446			0.359723	+	0.933059i	$0.382871\pi$
$32$		0			0
$33$	−214.358	+	30.7741i	−1.13076	+	0.162336i
$34$		0			0
$35$	−253.690	−	137.537i	−1.22518	−	0.664230i
$36$		0			0
$37$	−202.205	−	350.230i	−0.898442	−	1.55615i	−0.829485	−	0.558528i	$-0.811366\pi$
$37$	−202.205	−	350.230i	−0.898442	−	1.55615i	−0.0689570	−	0.997620i	$-0.521967\pi$
$38$		0			0
$39$	−162.921	+	23.3895i	−0.668928	+	0.0960339i
$40$		0			0
$41$	189.575	+	328.354i	0.722113	+	1.25074i	0.960151	+	0.279481i	$0.0901624\pi$
$41$	189.575	+	328.354i	0.722113	+	1.25074i	−0.238038	+	0.971256i	$0.576504\pi$
$42$		0			0
$43$	−10.1455	+	17.5725i	−0.0359808	+	0.0623207i	−0.883455	−	0.468516i	$-0.844789\pi$
$43$	−10.1455	+	17.5725i	−0.0359808	+	0.0623207i	0.847474	+	0.530837i	$0.178122\pi$
$44$		0			0
$45$	403.710	−	118.356i	1.33737	−	0.392077i
$46$		0			0
$47$	−500.974			−1.55478			−0.777388	−	0.629021i	$-0.783456\pi$
$47$	−500.974			−1.55478			−0.777388	+	0.629021i	$0.783456\pi$
$48$		0			0
$49$	−342.507	+	18.3791i	−0.998563	+	0.0535834i
$50$		0			0
$51$	−120.628	−	153.457i	−0.331202	−	0.421339i
$52$		0			0
$53$	36.0419	−	62.4263i	0.0934100	−	0.161791i	−0.815534	−	0.578709i	$-0.803557\pi$
$53$	36.0419	−	62.4263i	0.0934100	−	0.161791i	0.908944	+	0.416918i	$0.136890\pi$
$54$		0			0
$55$	−649.380			−1.59204
$56$		0			0
$57$	472.016	−	67.7645i	1.09684	−	0.157467i
$58$		0			0
$59$	588.033			1.29755			0.648774	−	0.760981i	$-0.275282\pi$
$59$	588.033			1.29755			0.648774	+	0.760981i	$0.275282\pi$
$60$		0			0
$61$	893.353			1.87512			0.937558	−	0.347829i	$-0.113081\pi$
$61$	893.353			1.87512			0.937558	+	0.347829i	$0.113081\pi$
$62$		0			0
$63$	335.404	−	370.879i	0.670746	−	0.741687i
$64$		0			0
$65$	−493.554			−0.941813
$66$		0			0
$67$	−787.490			−1.43593			−0.717965	−	0.696079i	$-0.754926\pi$
$67$	−787.490			−1.43593			−0.717965	+	0.696079i	$0.754926\pi$
$68$		0			0
$69$	152.025	+	193.399i	0.265242	+	0.337428i
$70$		0			0
$71$	−132.781			−0.221946			−0.110973	−	0.993823i	$-0.535397\pi$
$71$	−132.781			−0.221946			−0.110973	+	0.993823i	$0.535397\pi$
$72$		0			0
$73$	−252.320	+	437.031i	−0.404545	+	0.700693i	−0.994268	−	0.106913i	$-0.965903\pi$
$73$	−252.320	+	437.031i	−0.404545	+	0.700693i	0.589723	+	0.807605i	$0.299237\pi$
$74$		0			0
$75$	605.815	−	86.9732i	0.932713	−	0.133904i
$76$		0			0
$77$	−657.863	+	403.704i	−0.973641	+	0.597485i
$78$		0			0
$79$	−413.941			−0.589519			−0.294760	−	0.955571i	$-0.595240\pi$
$79$	−413.941			−0.589519			−0.294760	+	0.955571i	$0.595240\pi$
$80$		0			0
$81$	34.0756	+	728.203i	0.0467430	+	0.998907i
$82$		0			0
$83$	225.944	−	391.347i	0.298803	−	0.517541i	−0.677060	−	0.735928i	$-0.736746\pi$
$83$	225.944	−	391.347i	0.298803	−	0.517541i	0.975862	+	0.218387i	$0.0700794\pi$
$84$		0			0
$85$	−292.659	−	506.901i	−0.373451	−	0.646837i
$86$		0			0
$87$	11.8465	+	15.0706i	0.0145986	+	0.0185717i
$88$		0			0
$89$	583.982	+	1011.49i	0.695528	+	1.20469i	0.970002	+	0.243095i	$0.0781628\pi$
$89$	583.982	+	1011.49i	0.695528	+	1.20469i	−0.274474	+	0.961594i	$0.588504\pi$
$90$		0			0
$91$	−500.001	+	306.831i	−0.575982	+	0.353457i
$92$		0			0
$93$	−239.938	+	598.972i	−0.267531	+	0.667855i
$94$		0			0
$95$	1429.93			1.54429
$96$		0			0
$97$	−303.395	+	525.495i	−0.317578	+	0.550061i	−0.979982	−	0.199085i	$-0.936203\pi$
$97$	−303.395	+	525.495i	−0.317578	+	0.550061i	0.662404	+	0.749147i	$0.269536\pi$
$98$		0			0
$99$	265.749	−	1093.43i	0.269786	−	1.11004i
$100$		0			0
$101$	828.368	+	1434.78i	0.816096	+	1.41352i	0.908538	+	0.417802i	$0.137199\pi$
$101$	828.368	+	1434.78i	0.816096	+	1.41352i	−0.0924424	+	0.995718i	$0.529467\pi$
$102$		0			0
$103$	193.273	−	334.759i	0.184891	−	0.320241i	−0.758649	−	0.651500i	$-0.774140\pi$
$103$	193.273	−	334.759i	0.184891	−	0.320241i	0.943540	+	0.331259i	$0.107473\pi$
$104$		0			0
$105$	1153.60	−	957.929i	1.07219	−	0.890327i
$106$		0			0
$107$	62.8449	+	108.850i	0.0567798	+	0.0983455i	0.893018	−	0.450021i	$-0.148583\pi$
$107$	62.8449	+	108.850i	0.0567798	+	0.0983455i	−0.836238	+	0.548366i	$0.815250\pi$
$108$		0			0
$109$	576.216	−	998.035i	0.506344	−	0.877013i	−0.493629	−	0.869672i	$-0.664330\pi$
$109$	576.216	−	998.035i	0.506344	−	0.877013i	0.999973	−	0.00734084i	$-0.00233668\pi$
$110$		0			0
$111$	2080.05	−	298.621i	1.77865	−	0.255350i
$112$		0			0
$113$	874.797	+	1515.19i	0.728265	+	1.26139i	0.957616	+	0.288048i	$0.0930063\pi$
$113$	874.797	+	1515.19i	0.728265	+	1.26139i	−0.229351	+	0.973344i	$0.573660\pi$
$114$		0			0
$115$	368.833	+	638.838i	0.299077	+	0.518017i
$116$		0			0
$117$	201.980	−	831.047i	0.159598	−	0.656670i
$118$		0			0
$119$	−611.610	−	331.583i	−0.471145	−	0.255430i
$120$		0			0
$121$	−202.955	+	351.528i	−0.152483	+	0.264108i
$122$		0			0
$123$	−1950.13	+	279.968i	−1.42957	+	0.205235i
$124$		0			0
$125$	−112.429			−0.0804478
$126$		0			0
$127$	−824.473			−0.576064			−0.288032	−	0.957621i	$-0.593001\pi$
$127$	−824.473			−0.576064			−0.288032	+	0.957621i	$0.593001\pi$
$128$		0			0
$129$	−65.1584	−	82.8914i	−0.0444719	−	0.0565750i
$130$		0			0
$131$	−362.156	+	627.273i	−0.241540	+	0.418360i	−0.961153	−	0.276016i	$-0.910986\pi$
$131$	−362.156	+	627.273i	−0.241540	+	0.418360i	0.719613	+	0.694375i	$0.244319\pi$
$132$		0			0
$133$	1448.61	−	888.955i	0.944440	−	0.579565i
$134$		0			0
$135$	−209.166	+	2176.00i	−0.133349	+	1.38726i
$136$		0			0
$137$	912.003	+	1579.64i	0.568742	+	0.985090i	0.996691	+	0.0812872i	$0.0259031\pi$
$137$	912.003	+	1579.64i	0.568742	+	0.985090i	−0.427949	+	0.903803i	$0.640764\pi$
$138$		0			0
$139$	−1464.48	−	2536.55i	−0.893635	−	1.54782i	−0.835485	−	0.549514i	$-0.814813\pi$
$139$	−1464.48	−	2536.55i	−0.893635	−	1.54782i	−0.0581507	−	0.998308i	$-0.518520\pi$
$140$		0			0
$141$	967.995	−	2416.46i	0.578155	−	1.44328i
$142$		0			0
$143$	−660.059	+	1143.26i	−0.385993	+	0.668559i
$144$		0			0
$145$	28.7412	+	49.7813i	0.0164609	+	0.0285111i
$146$		0			0
$147$	573.150	−	1687.61i	0.321582	−	0.946882i
$148$		0			0
$149$	−507.264	+	878.607i	−0.278904	+	0.483076i	−0.971113	−	0.238622i	$-0.923304\pi$
$149$	−507.264	+	878.607i	−0.278904	+	0.483076i	0.692209	+	0.721697i	$0.256638\pi$
$150$		0			0
$151$	−244.878	−	424.140i	−0.131973	−	0.228583i	0.792464	−	0.609918i	$-0.208798\pi$
$151$	−244.878	−	424.140i	−0.131973	−	0.228583i	−0.924437	+	0.381335i	$0.875464\pi$
$152$		0			0
$153$	973.287	−	285.339i	0.514285	−	0.150773i
$154$		0			0
$155$	−967.434	+	1675.64i	−0.501330	+	0.868329i
$156$		0			0
$157$	2335.30			1.18711			0.593557	−	0.804792i	$-0.297723\pi$
$157$	2335.30			1.18711			0.593557	+	0.804792i	$0.297723\pi$
$158$		0			0
$159$	231.475	+	294.471i	0.115454	+	0.146875i
$160$		0			0
$161$	770.801	+	417.888i	0.377315	+	0.204560i
$162$		0			0
$163$	759.334	+	1315.20i	0.364881	+	0.631993i	0.988757	−	0.149531i	$-0.0477763\pi$
$163$	759.334	+	1315.20i	0.364881	+	0.631993i	−0.623876	+	0.781523i	$0.714443\pi$
$164$		0			0
$165$	1254.75	−	3132.31i	0.592013	−	1.47788i
$166$		0			0
$167$	−1501.21	−	2600.16i	−0.695609	−	1.20483i	−0.969975	−	0.243205i	$-0.921801\pi$
$167$	−1501.21	−	2600.16i	−0.695609	−	1.20483i	0.274365	−	0.961625i	$-0.411532\pi$
$168$		0			0
$169$	596.829	−	1033.74i	0.271657	−	0.470523i
$170$		0			0
$171$	−585.178	+	2407.72i	−0.261694	+	1.07674i
$172$		0			0
$173$	−3912.14			−1.71928			−0.859638	−	0.510903i	$-0.829311\pi$
$173$	−3912.14			−1.71928			−0.859638	+	0.510903i	$0.829311\pi$
$174$		0			0
$175$	1859.24	−	1140.94i	0.803114	−	0.492839i
$176$		0			0
$177$	−1136.21	+	2836.40i	−0.482503	+	1.20450i
$178$		0			0
$179$	−284.594	+	492.932i	−0.118836	+	0.205829i	−0.919306	−	0.393542i	$-0.871249\pi$
$179$	−284.594	+	492.932i	−0.118836	+	0.205829i	0.800471	+	0.599372i	$0.204583\pi$
$180$		0			0
$181$	−3759.52			−1.54388			−0.771941	−	0.635694i	$-0.780714\pi$
$181$	−3759.52			−1.54388			−0.771941	+	0.635694i	$0.780714\pi$
$182$		0			0
$183$	−1726.16	+	4309.12i	−0.697276	+	1.74065i
$184$		0			0
$185$	6301.35			2.50424
$186$		0			0
$187$	−1565.56			−0.612221
$188$		0			0
$189$	1140.87	+	2334.46i	0.439079	+	0.898448i
$190$		0			0
$191$	−1140.15			−0.431930			−0.215965	−	0.976401i	$-0.569290\pi$
$191$	−1140.15			−0.431930			−0.215965	+	0.976401i	$0.569290\pi$
$192$		0			0
$193$	−2753.15			−1.02682			−0.513410	−	0.858143i	$-0.671618\pi$
$193$	−2753.15			−1.02682			−0.513410	+	0.858143i	$0.671618\pi$
$194$		0			0
$195$	953.659	−	2380.68i	0.350220	−	0.874275i
$196$		0			0
$197$	−602.619			−0.217943			−0.108972	−	0.994045i	$-0.534756\pi$
$197$	−602.619			−0.217943			−0.108972	+	0.994045i	$0.534756\pi$
$198$		0			0
$199$	−1578.43	+	2733.91i	−0.562270	+	0.973880i	0.435028	+	0.900417i	$0.356738\pi$
$199$	−1578.43	+	2733.91i	−0.562270	+	0.973880i	−0.997298	+	0.0734628i	$0.976595\pi$
$200$		0			0
$201$	1521.61	−	3798.49i	0.533961	−	1.33296i
$202$		0			0
$203$	60.0645	+	32.5638i	0.0207670	+	0.0112588i
$204$		0			0
$205$	−5907.74			−2.01275
$206$		0			0
$207$	−1226.62	+	359.608i	−0.411863	+	0.120746i
$208$		0			0
$209$	1912.33	−	3312.26i	0.632913	−	1.09624i
$210$		0			0
$211$	172.298	+	298.429i	0.0562156	+	0.0973682i	0.892764	−	0.450525i	$-0.148763\pi$
$211$	172.298	+	298.429i	0.0562156	+	0.0973682i	−0.836548	+	0.547893i	$0.815430\pi$
$212$		0			0
$213$	256.563	−	640.473i	0.0825324	−	0.206031i
$214$		0			0
$215$	−158.083	−	273.807i	−0.0501449	−	0.0868535i
$216$		0			0
$217$	61.6374	+	2298.96i	0.0192821	+	0.719188i
$218$		0			0
$219$	−1620.49	−	2061.52i	−0.500013	−	0.636093i
$220$		0			0
$221$	−1189.89			−0.362174
$222$		0			0
$223$	−2351.80	+	4073.44i	−0.706226	+	1.22322i	0.260022	+	0.965603i	$0.416270\pi$
$223$	−2351.80	+	4073.44i	−0.706226	+	1.22322i	−0.966247	+	0.257616i	$0.917063\pi$
$224$		0			0
$225$	−751.054	+	3090.22i	−0.222534	+	0.915621i
$226$		0			0
$227$	−2918.23	−	5054.52i	−0.853259	−	1.47789i	−0.878251	−	0.478200i	$-0.841289\pi$
$227$	−2918.23	−	5054.52i	−0.853259	−	1.47789i	0.0249920	−	0.999688i	$-0.492044\pi$
$228$		0			0
$229$	−1387.76	+	2403.68i	−0.400463	+	0.693623i	−0.993782	−	0.111345i	$-0.964484\pi$
$229$	−1387.76	+	2403.68i	−0.400463	+	0.693623i	0.593319	+	0.804968i	$0.297817\pi$
$230$		0			0
$231$	−676.141	−	3953.27i	−0.192584	−	1.12600i
$232$		0			0
$233$	−1956.77	−	3389.23i	−0.550182	−	0.952942i	−0.998261	−	0.0589487i	$-0.981225\pi$
$233$	−1956.77	−	3389.23i	−0.550182	−	0.952942i	0.448079	−	0.893994i	$-0.352108\pi$
$234$		0			0
$235$	3902.97	−	6760.14i	1.08341	−	1.87652i
$236$		0			0
$237$	799.828	−	1996.66i	0.219217	−	0.547245i
$238$		0			0
$239$	1676.30	+	2903.44i	0.453686	+	0.785808i	0.998612	−	0.0526770i	$-0.0167754\pi$
$239$	1676.30	+	2903.44i	0.453686	+	0.785808i	−0.544925	+	0.838485i	$0.683442\pi$
$240$		0			0
$241$	−1046.49	−	1812.58i	−0.279711	−	0.484474i	0.691602	−	0.722279i	$-0.256905\pi$
$241$	−1046.49	−	1812.58i	−0.279711	−	0.484474i	−0.971313	+	0.237805i	$0.923572\pi$
$242$		0			0
$243$	−3578.36	−	1242.69i	−0.944657	−	0.328060i
$244$		0			0
$245$	2420.39	−	4764.98i	0.631155	−	1.24255i
$246$		0			0
$247$	1453.45	−	2517.45i	0.374416	−	0.648507i
$248$		0			0
$249$	1451.10	+	1846.02i	0.369316	+	0.469827i
$250$		0			0
$251$	739.593			0.185987			0.0929934	−	0.995667i	$-0.470356\pi$
$251$	739.593			0.185987			0.0929934	+	0.995667i	$0.470356\pi$
$252$		0			0
$253$	1973.05			0.490295
$254$		0			0
$255$	3010.54	−	432.205i	0.739322	−	0.106140i
$256$		0			0
$257$	994.012	−	1721.68i	0.241264	−	0.417881i	−0.719811	−	0.694170i	$-0.755771\pi$
$257$	994.012	−	1721.68i	0.241264	−	0.417881i	0.961075	+	0.276289i	$0.0891048\pi$
$258$		0			0
$259$	6383.65	−	3917.39i	1.53151	−	0.939827i
$260$		0			0
$261$	−95.5838	+	28.0223i	−0.0226685	+	0.00664574i
$262$		0			0
$263$	−3458.98	−	5991.13i	−0.810988	−	1.40467i	−0.912173	−	0.409805i	$-0.865597\pi$
$263$	−3458.98	−	5991.13i	−0.810988	−	1.40467i	0.101185	−	0.994868i	$-0.467737\pi$
$264$		0			0
$265$	561.588	+	972.698i	0.130181	+	0.225481i
$266$		0			0
$267$	−6007.33	+	862.436i	−1.37694	+	0.197679i
$268$		0			0
$269$	−1850.32	+	3204.85i	−0.419391	+	0.726406i	−0.995878	−	0.0906996i	$-0.971090\pi$
$269$	−1850.32	+	3204.85i	−0.419391	+	0.726406i	0.576487	+	0.817106i	$0.304423\pi$
$270$		0			0
$271$	1011.65	+	1752.23i	0.226765	+	0.392769i	0.956848	−	0.290590i	$-0.0938517\pi$
$271$	1011.65	+	1752.23i	0.226765	+	0.392769i	−0.730082	+	0.683359i	$0.760518\pi$
$272$		0			0
$273$	−513.893	−	3004.64i	−0.113928	−	0.666114i
$274$		0			0
$275$	2454.41	−	4251.16i	0.538205	−	0.932198i
$276$		0			0
$277$	−341.254	−	591.069i	−0.0740214	−	0.128209i	0.826639	−	0.562733i	$-0.190250\pi$
$277$	−341.254	−	591.069i	−0.0740214	−	0.128209i	−0.900660	+	0.434524i	$0.856917\pi$
$278$		0			0
$279$	−2425.55	−	2314.70i	−0.520479	−	0.496693i
$280$		0			0
$281$	−1537.13	+	2662.39i	−0.326326	+	0.565213i	−0.981780	−	0.190022i	$-0.939144\pi$
$281$	−1537.13	+	2662.39i	−0.326326	+	0.565213i	0.655454	+	0.755235i	$0.272477\pi$
$282$		0			0
$283$	4234.89			0.889534			0.444767	−	0.895646i	$-0.353287\pi$
$283$	4234.89			0.889534			0.444767	+	0.895646i	$0.353287\pi$
$284$		0			0
$285$	−2762.96	+	6897.33i	−0.574257	+	1.43355i
$286$		0			0
$287$	−5984.91	+	3672.70i	−1.23093	+	0.755375i
$288$		0			0
$289$	1750.94	+	3032.72i	0.356389	+	0.617284i
$290$		0			0
$291$	−1948.52	−	2478.81i	−0.392523	−	0.499349i
$292$		0			0
$293$	1358.57	+	2353.12i	0.270883	+	0.469183i	0.969088	−	0.246714i	$-0.0793510\pi$
$293$	1358.57	+	2353.12i	0.270883	+	0.469183i	−0.698205	+	0.715898i	$0.746018\pi$
$294$		0			0
$295$	−4581.23	+	7934.92i	−0.904168	+	1.56606i
$296$		0			0
$297$	4760.70	+	3394.60i	0.930114	+	0.663215i
$298$		0			0
$299$	1499.59			0.290046
$300$		0			0
$301$	−330.367	−	179.108i	−0.0632626	−	0.0342976i
$302$		0			0
$303$	−8521.28	+	1223.35i	−1.61563	+	0.231946i
$304$		0			0
$305$	−6959.91	+	12054.9i	−1.30663	+	2.26315i
$306$		0			0
$307$	10078.0			1.87357			0.936783	−	0.349912i	$-0.113789\pi$
$307$	10078.0			1.87357			0.936783	+	0.349912i	$0.113789\pi$
$308$		0			0
$309$	1241.27	+	1579.09i	0.228523	+	0.290716i
$310$		0			0
$311$	4547.78			0.829198			0.414599	−	0.910004i	$-0.363922\pi$
$311$	4547.78			0.829198			0.414599	+	0.910004i	$0.363922\pi$
$312$		0			0
$313$	−3115.84			−0.562676			−0.281338	−	0.959609i	$-0.590778\pi$
$313$	−3115.84			−0.562676			−0.281338	+	0.959609i	$0.590778\pi$
$314$		0			0
$315$	2391.58	+	7415.38i	0.427779	+	1.32638i
$316$		0			0
$317$	630.080			0.111637			0.0558183	−	0.998441i	$-0.482223\pi$
$317$	630.080			0.111637			0.0558183	+	0.998441i	$0.482223\pi$
$318$		0			0
$319$	153.749			0.0269853
$320$		0			0
$321$	−646.475	+	92.8105i	−0.112407	+	0.0161376i
$322$		0			0
$323$	3447.36			0.593859
$324$		0			0
$325$	1865.44	−	3231.04i	0.318388	−	0.551465i
$326$		0			0
$327$	3700.68	+	4707.83i	0.625835	+	0.796158i
$328$		0			0
$329$	−248.667	−	9274.83i	−0.0416701	−	1.55422i
$330$		0			0
$331$	10565.2			1.75442			0.877211	−	0.480105i	$-0.159401\pi$
$331$	10565.2			1.75442			0.877211	+	0.480105i	$0.159401\pi$
$332$		0			0
$333$	−2578.73	+	10610.2i	−0.424365	+	1.74606i
$334$		0			0
$335$	6135.16	−	10626.4i	1.00060	−	1.73308i
$336$		0			0
$337$	4946.97	+	8568.39i	0.799639	+	1.38502i	0.919851	+	0.392267i	$0.128309\pi$
$337$	4946.97	+	8568.39i	0.799639	+	1.38502i	−0.120212	+	0.992748i	$0.538358\pi$
$338$		0			0
$339$	−8998.89	+	1291.92i	−1.44175	+	0.206983i
$340$		0			0
$341$	2587.61	+	4481.88i	0.410930	+	0.711752i
$342$		0			0
$343$	−510.273	−	6331.92i	−0.0803270	−	0.996769i
$344$		0			0
$345$	−3794.13	+	544.700i	−0.592084	+	0.0850019i
$346$		0			0
$347$	−1466.34			−0.226852			−0.113426	−	0.993546i	$-0.536182\pi$
$347$	−1466.34			−0.226852			−0.113426	+	0.993546i	$0.536182\pi$
$348$		0			0
$349$	4181.77	−	7243.04i	0.641390	−	1.11092i	−0.343732	−	0.939068i	$-0.611691\pi$
$349$	4181.77	−	7243.04i	0.641390	−	1.11092i	0.985123	−	0.171853i	$-0.0549754\pi$
$350$		0			0
$351$	3618.32	+	2580.03i	0.550232	+	0.392341i
$352$		0			0
$353$	3333.43	+	5773.67i	0.502608	+	0.870543i	0.999995	+	0.00301425i	$0.000959466\pi$
$353$	3333.43	+	5773.67i	0.502608	+	0.870543i	−0.497387	+	0.867529i	$0.665707\pi$
$354$		0			0
$355$	1034.47	−	1791.75i	0.154658	−	0.267876i
$356$		0			0
$357$	2781.17	−	2309.43i	0.412311	−	0.342375i
$358$		0			0
$359$	1417.66	+	2455.45i	0.208415	+	0.360986i	0.951215	−	0.308527i	$-0.0998361\pi$
$359$	1417.66	+	2455.45i	0.208415	+	0.360986i	−0.742800	+	0.669513i	$0.766503\pi$
$360$		0			0
$361$	−781.452	+	1353.51i	−0.113931	+	0.197334i
$362$		0			0
$363$	−1303.45	−	1658.19i	−0.188467	−	0.239759i
$364$		0			0
$365$	−3931.53	−	6809.61i	−0.563797	−	0.976524i
$366$		0			0
$367$	5946.13	+	10299.0i	0.845738	+	1.46486i	0.884979	+	0.465631i	$0.154172\pi$
$367$	5946.13	+	10299.0i	0.845738	+	1.46486i	−0.0392416	+	0.999230i	$0.512494\pi$
$368$		0			0
$369$	2417.65	−	9947.47i	0.341079	−	1.40337i
$370$		0			0
$371$	1173.63	+	636.278i	0.164236	+	0.0890402i
$372$		0			0
$373$	−6249.39	+	10824.3i	−0.867509	+	1.50257i	−0.00297519	+	0.999996i	$0.500947\pi$
$373$	−6249.39	+	10824.3i	−0.867509	+	1.50257i	−0.864534	+	0.502574i	$0.832386\pi$
$374$		0			0
$375$	217.239	−	542.307i	0.0299151	−	0.0746789i
$376$		0			0
$377$	116.856			0.0159638
$378$		0			0
$379$	1433.99			0.194351			0.0971757	−	0.995267i	$-0.469019\pi$
$379$	1433.99			0.194351			0.0971757	+	0.995267i	$0.469019\pi$
$380$		0			0
$381$	1593.07	−	3976.87i	0.214214	−	0.534754i
$382$		0			0
$383$	−2441.09	+	4228.10i	−0.325676	+	0.564088i	−0.981649	−	0.190697i	$-0.938925\pi$
$383$	−2441.09	+	4228.10i	−0.325676	+	0.564088i	0.655973	+	0.754785i	$0.272259\pi$
$384$		0			0
$385$	−322.331	−	12022.4i	−0.0426689	−	1.59147i
$386$		0			0
$387$	525.730	−	154.129i	0.0690552	−	0.0202450i
$388$		0			0
$389$	−6968.04	−	12069.0i	−0.908210	−	1.57307i	−0.816549	−	0.577275i	$-0.804116\pi$
$389$	−6968.04	−	12069.0i	−0.908210	−	1.57307i	−0.0916605	−	0.995790i	$-0.529217\pi$
$390$		0			0
$391$	889.204	+	1540.15i	0.115010	+	0.199204i
$392$		0			0
$393$	−2325.91	−	2958.91i	−0.298541	−	0.379789i
$394$		0			0
$395$	3224.92	−	5585.73i	0.410793	−	0.711515i
$396$		0			0
$397$	93.8893	+	162.621i	0.0118694	+	0.0205585i	0.871899	−	0.489686i	$-0.162888\pi$
$397$	93.8893	+	162.621i	0.0118694	+	0.0205585i	−0.860030	+	0.510244i	$0.829555\pi$
$398$		0			0
$399$	1488.86	+	8705.09i	0.186808	+	1.09223i
$400$		0			0
$401$	4335.33	−	7509.01i	0.539890	−	0.935117i	−0.459019	−	0.888426i	$-0.651799\pi$
$401$	4335.33	−	7509.01i	0.539890	−	0.935117i	0.998909	−	0.0466906i	$-0.0148675\pi$
$402$		0			0
$403$	1966.69	+	3406.40i	0.243096	+	0.421054i
$404$		0			0
$405$	−10091.9	−	5213.45i	−1.23819	−	0.639650i
$406$		0			0
$407$	8427.16	−	14596.3i	1.02634	−	1.77767i
$408$		0			0
$409$	6406.87			0.774570			0.387285	−	0.921960i	$-0.373413\pi$
$409$	6406.87			0.774570			0.387285	+	0.921960i	$0.373413\pi$
$410$		0			0
$411$	−9381.63	+	1346.86i	−1.12594	+	0.161644i
$412$		0			0
$413$	291.880	+	10886.6i	0.0347760	+	1.29708i
$414$		0			0
$415$	3520.56	+	6097.79i	0.416428	+	0.721274i
$416$		0			0
$417$	15064.8	−	2162.77i	1.76913	−	0.253984i
$418$		0			0
$419$	6958.80	+	12053.0i	0.811359	+	1.40532i	0.911913	+	0.410384i	$0.134605\pi$
$419$	6958.80	+	12053.0i	0.811359	+	1.40532i	−0.100554	+	0.994932i	$0.532061\pi$
$420$		0			0
$421$	3815.65	−	6608.90i	0.441718	−	0.765079i	−0.556099	−	0.831116i	$-0.687702\pi$
$421$	3815.65	−	6608.90i	0.441718	−	0.765079i	0.997817	+	0.0660375i	$0.0210357\pi$
$422$		0			0
$423$	9785.51	+	9338.32i	1.12479	+	1.07339i
$424$		0			0
$425$	4424.56			0.504994
$426$		0			0
$427$	443.431	+	16539.2i	0.0502556	+	1.87444i
$428$		0			0
$429$	−4239.15	−	5392.85i	−0.477082	−	0.606921i
$430$		0			0
$431$	5430.30	−	9405.55i	0.606887	−	1.05116i	−0.384863	−	0.922974i	$-0.625751\pi$
$431$	5430.30	−	9405.55i	0.606887	−	1.05116i	0.991750	−	0.128185i	$-0.0409152\pi$
$432$		0			0
$433$	−2992.12			−0.332083			−0.166042	−	0.986119i	$-0.553099\pi$
$433$	−2992.12			−0.332083			−0.166042	+	0.986119i	$0.553099\pi$
$434$		0			0
$435$	−295.656	+	42.4456i	−0.0325877	+	0.00467842i
$436$		0			0
$437$	−4344.65			−0.475590
$438$		0			0
$439$	−7384.89			−0.802874			−0.401437	−	0.915887i	$-0.631489\pi$
$439$	−7384.89			−0.802874			−0.401437	+	0.915887i	$0.631489\pi$
$440$		0			0
$441$	7032.78	+	6025.45i	0.759398	+	0.650626i
$442$		0			0
$443$	−17026.9			−1.82612			−0.913061	−	0.407823i	$-0.866288\pi$
$443$	−17026.9			−1.82612			−0.913061	+	0.407823i	$0.866288\pi$
$444$		0			0
$445$	−18198.7			−1.93865
$446$		0			0
$447$	−3257.84	−	4144.47i	−0.344722	−	0.438539i
$448$		0			0
$449$	−4674.47			−0.491318			−0.245659	−	0.969356i	$-0.579004\pi$
$449$	−4674.47			−0.491318			−0.245659	+	0.969356i	$0.579004\pi$
$450$		0			0
$451$	−7900.78	+	13684.5i	−0.824907	+	1.42878i
$452$		0			0
$453$	2519.02	−	361.640i	0.261266	−	0.0375084i
$454$		0			0
$455$	−244.984	−	9137.47i	−0.0252418	−	0.941475i
$456$		0			0
$457$	8324.40			0.852077			0.426039	−	0.904705i	$-0.359909\pi$
$457$	8324.40			0.852077			0.426039	+	0.904705i	$0.359909\pi$
$458$		0			0
$459$	−504.270	+	5246.02i	−0.0512795	+	0.533472i
$460$		0			0
$461$	−4159.68	+	7204.77i	−0.420250	+	0.727895i	−0.995964	−	0.0897567i	$-0.971391\pi$
$461$	−4159.68	+	7204.77i	−0.420250	+	0.727895i	0.575713	+	0.817652i	$0.304724\pi$
$462$		0			0
$463$	4411.93	+	7641.69i	0.442851	+	0.767040i	0.997900	−	0.0647777i	$-0.0206338\pi$
$463$	4411.93	+	7641.69i	0.442851	+	0.767040i	−0.555049	+	0.831818i	$0.687300\pi$
$464$		0			0
$465$	−6213.23	−	7904.18i	−0.619638	−	0.788274i
$466$		0			0
$467$	277.317	+	480.328i	0.0274790	+	0.0475951i	0.879438	−	0.476014i	$-0.157919\pi$
$467$	277.317	+	480.328i	0.0274790	+	0.0475951i	−0.851959	+	0.523609i	$0.824585\pi$
$468$		0			0
$469$	−390.885	−	14579.3i	−0.0384848	−	1.43541i
$470$		0			0
$471$	−4512.32	+	11264.4i	−0.441437	+	1.10199i
$472$		0			0
$473$	−845.654			−0.0822055
$474$		0			0
$475$	−5404.59	+	9361.03i	−0.522063	+	0.904239i
$476$		0			0
$477$	−1867.65	+	547.541i	−0.179275	+	0.0525580i
$478$		0			0
$479$	−2147.38	−	3719.38i	−0.204836	−	0.354787i	0.745244	−	0.666791i	$-0.232333\pi$
$479$	−2147.38	−	3719.38i	−0.204836	−	0.354787i	−0.950081	+	0.312005i	$0.898999\pi$
$480$		0			0
$481$	6404.97	−	11093.7i	0.607155	−	1.05162i
$482$		0			0
$483$	−3505.06	+	2910.53i	−0.330198	+	0.274190i
$484$		0			0
$485$	−4727.36	−	8188.02i	−0.442594	−	0.766596i
$486$		0			0
$487$	8302.90	−	14381.0i	0.772567	−	1.33813i	−0.163585	−	0.986529i	$-0.552306\pi$
$487$	8302.90	−	14381.0i	0.772567	−	1.33813i	0.936152	−	0.351596i	$-0.114361\pi$
$488$		0			0
$489$	−7811.14	+	1121.40i	−0.722356	+	0.103704i
$490$		0			0
$491$	92.6197	+	160.422i	0.00851297	+	0.0147449i	0.870251	−	0.492609i	$-0.163957\pi$
$491$	92.6197	+	160.422i	0.00851297	+	0.0147449i	−0.861738	+	0.507354i	$0.830624\pi$
$492$		0			0
$493$	69.2910	+	120.016i	0.00633004	+	0.0109640i
$494$		0			0
$495$	12684.3	+	12104.7i	1.15175	+	1.09912i
$496$		0			0
$497$	−65.9081	−	2458.25i	−0.00594846	−	0.221867i
$498$		0			0
$499$	1698.88	−	2942.55i	0.152410	−	0.263981i	−0.779703	−	0.626149i	$-0.784630\pi$
$499$	1698.88	−	2942.55i	0.152410	−	0.263981i	0.932113	+	0.362168i	$0.117963\pi$
$500$		0			0
$501$	15442.7	−	2217.01i	1.37710	−	0.197702i
$502$		0			0
$503$	2837.00			0.251482			0.125741	−	0.992063i	$-0.459869\pi$
$503$	2837.00			0.251482			0.125741	+	0.992063i	$0.459869\pi$
$504$		0			0
$505$	−25814.5			−2.27471
$506$		0			0
$507$	3833.07	+	4876.25i	0.335764	+	0.427143i
$508$		0			0
$509$	5331.96	−	9235.23i	0.464313	−	0.804213i	−0.534858	−	0.844942i	$-0.679635\pi$
$509$	5331.96	−	9235.23i	0.464313	−	0.804213i	0.999170	+	0.0407292i	$0.0129681\pi$
$510$		0			0
$511$	−8216.26	−	4454.42i	−0.711283	−	0.385620i
$512$		0			0
$513$	−10483.0	−	7474.90i	−0.902218	−	0.643323i
$514$		0			0
$515$	3011.50	+	5216.06i	0.257675	+	0.446305i
$516$		0			0
$517$	−10439.3	−	18081.5i	−0.888050	−	1.53815i
$518$		0			0
$519$	7559.15	−	18870.4i	0.639326	−	1.59599i
$520$		0			0
$521$	−4807.12	+	8326.17i	−0.404229	+	0.700146i	−0.994231	−	0.107256i	$-0.965794\pi$
$521$	−4807.12	+	8326.17i	−0.404229	+	0.700146i	0.590002	+	0.807402i	$0.299127\pi$
$522$		0			0
$523$	−4160.08	−	7205.47i	−0.347816	−	0.602434i	0.638046	−	0.769999i	$-0.279743\pi$
$523$	−4160.08	−	7205.47i	−0.347816	−	0.602434i	−0.985861	+	0.167564i	$0.946410\pi$
$524$		0			0
$525$	1910.89	+	11172.6i	0.158854	+	0.928789i
$526$		0			0
$527$	−2332.34	+	4039.74i	−0.192787	+	0.333916i
$528$		0			0
$529$	4962.85	+	8595.91i	0.407894	+	0.706494i
$530$		0			0
$531$	−11486.0	−	10961.1i	−0.938704	−	0.895805i
$532$		0			0
$533$	−6004.90	+	10400.8i	−0.487994	+	0.845231i
$534$		0			0
$535$	−1958.44			−0.158263
$536$		0			0
$537$	−1827.77	−	2325.21i	−0.146879	−	0.186853i
$538$		0			0
$539$	−7800.56	−	11979.0i	−0.623365	−	0.957278i
$540$		0			0
$541$	9635.79	+	16689.7i	0.765758	+	1.32633i	0.939845	+	0.341601i	$0.110969\pi$
$541$	9635.79	+	16689.7i	0.765758	+	1.32633i	−0.174087	+	0.984730i	$0.555697\pi$
$542$		0			0
$543$	7264.24	−	18134.2i	0.574104	−	1.43317i
$544$		0			0
$545$	8978.33	+	15550.9i	0.705669	+	1.22225i
$546$		0			0
$547$	7601.01	−	13165.3i	0.594142	−	1.02908i	−0.399525	−	0.916722i	$-0.630825\pi$
$547$	7601.01	−	13165.3i	0.594142	−	1.02908i	0.993667	−	0.112362i	$-0.0358417\pi$
$548$		0			0
$549$	−17449.9	−	16652.4i	−1.35654	−	1.29455i
$550$		0			0
$551$	−338.556			−0.0261760
$552$		0			0
$553$	−205.467	−	7663.54i	−0.0157999	−	0.589307i
$554$		0			0
$555$	−12175.6	+	30394.8i	−0.931220	+	2.32466i
$556$		0			0
$557$	−9936.29	+	17210.2i	−0.755861	+	1.30919i	0.189085	+	0.981961i	$0.439448\pi$
$557$	−9936.29	+	17210.2i	−0.755861	+	1.30919i	−0.944945	+	0.327228i	$0.893885\pi$
$558$		0			0
$559$	−642.730			−0.0486307
$560$		0			0
$561$	3025.02	−	7551.55i	0.227659	−	0.568318i
$562$		0			0
$563$	15444.7			1.15616			0.578079	−	0.815981i	$-0.303803\pi$
$563$	15444.7			1.15616			0.578079	+	0.815981i	$0.303803\pi$
$564$		0			0
$565$	−27261.4			−2.02990
$566$		0			0
$567$	−13464.8	+	992.319i	−0.997295	+	0.0734982i
$568$		0			0
$569$	−4002.87			−0.294919			−0.147460	−	0.989068i	$-0.547110\pi$
$569$	−4002.87			−0.294919			−0.147460	+	0.989068i	$0.547110\pi$
$570$		0			0
$571$	13724.2			1.00585			0.502923	−	0.864331i	$-0.332258\pi$
$571$	13724.2			1.00585			0.502923	+	0.864331i	$0.332258\pi$
$572$		0			0
$573$	2203.04	−	5499.57i	0.160616	−	0.400956i
$574$		0			0
$575$	−5576.19			−0.404423
$576$		0			0
$577$	3846.21	−	6661.83i	0.277504	−	0.480651i	−0.693260	−	0.720688i	$-0.743826\pi$
$577$	3846.21	−	6661.83i	0.277504	−	0.480651i	0.970764	+	0.240037i	$0.0771595\pi$
$578$		0			0
$579$	5319.72	−	13279.9i	0.381831	−	0.953187i
$580$		0			0
$581$	7357.40	+	3988.79i	0.525364	+	0.284825i
$582$		0			0
$583$	3004.18			0.213414
$584$		0			0
$585$	9640.59	+	9200.01i	0.681349	+	0.650212i
$586$		0			0
$587$	−11898.0	+	20608.0i	−0.836601	+	1.44904i	0.0561195	+	0.998424i	$0.482127\pi$
$587$	−11898.0	+	20608.0i	−0.836601	+	1.44904i	−0.892720	+	0.450611i	$0.851206\pi$
$588$		0			0
$589$	−5697.92	−	9869.08i	−0.398605	−	0.690405i
$590$		0			0
$591$	1164.40	−	2906.75i	0.0810438	−	0.202314i
$592$		0			0
$593$	8813.97	+	15266.3i	0.610365	+	1.05718i	0.991179	+	0.132532i	$0.0423106\pi$
$593$	8813.97	+	15266.3i	0.610365	+	1.05718i	−0.380814	+	0.924652i	$0.624356\pi$
$594$		0			0
$595$	9239.29	−	5669.79i	0.636595	−	0.390653i
$596$		0			0
$597$	−10137.3	−	12896.1i	−0.694958	−	0.884093i
$598$		0			0
$599$	−27641.2			−1.88545			−0.942727	−	0.333565i	$-0.891748\pi$
$599$	−27641.2			−1.88545			−0.942727	+	0.333565i	$0.891748\pi$
$600$		0			0
$601$	−11722.3	+	20303.7i	−0.795614	+	1.37804i	0.126834	+	0.991924i	$0.459518\pi$
$601$	−11722.3	+	20303.7i	−0.795614	+	1.37804i	−0.922448	+	0.386121i	$0.873815\pi$
$602$		0			0
$603$	15382.0	+	14679.1i	1.03881	+	0.991341i
$604$		0			0
$605$	−3162.35	−	5477.35i	−0.212509	−	0.368076i
$606$		0			0
$607$	8067.06	−	13972.6i	0.539427	−	0.934314i	−0.459508	−	0.888174i	$-0.651974\pi$
$607$	8067.06	−	13972.6i	0.539427	−	0.934314i	0.998935	−	0.0461410i	$-0.0146923\pi$
$608$		0			0
$609$	−273.131	+	226.803i	−0.0181738	+	0.0150911i
$610$		0			0
$611$	−7934.31	−	13742.6i	−0.525348	−	0.909930i
$612$		0			0
$613$	3733.05	−	6465.83i	0.245965	−	0.426023i	−0.716438	−	0.697651i	$-0.754229\pi$
$613$	3733.05	−	6465.83i	0.245965	−	0.426023i	0.962402	+	0.271628i	$0.0875619\pi$
$614$		0			0
$615$	11415.1	−	28496.2i	0.748458	−	1.86842i
$616$		0			0
$617$	9868.66	+	17093.0i	0.643918	+	1.11530i	0.984550	+	0.175102i	$0.0560255\pi$
$617$	9868.66	+	17093.0i	0.643918	+	1.11530i	−0.340632	+	0.940197i	$0.610641\pi$
$618$		0			0
$619$	2941.22	+	5094.34i	0.190982	+	0.330790i	0.945576	−	0.325402i	$-0.105500\pi$
$619$	2941.22	+	5094.34i	0.190982	+	0.330790i	−0.754594	+	0.656192i	$0.772166\pi$
$620$		0			0
$621$	635.522	−	6611.47i	0.0410670	−	0.427229i
$622$		0			0
$623$	−18436.4	+	11313.7i	−1.18562	+	0.727565i
$624$		0			0
$625$	8237.44	−	14267.7i	0.527196	−	0.913130i
$626$		0			0
$627$	12281.7	+	15624.3i	0.782273	+	0.995171i
$628$		0			0
$629$	15191.6			0.963005
$630$		0			0
$631$	−13597.2			−0.857838			−0.428919	−	0.903343i	$-0.641105\pi$
$631$	−13597.2			−0.857838			−0.428919	+	0.903343i	$0.641105\pi$
$632$		0			0
$633$	−1772.40	+	254.453i	−0.111290	+	0.0159772i
$634$		0			0
$635$	6423.28	−	11125.4i	0.401417	−	0.695275i
$636$		0			0
$637$	−5928.73	−	9104.52i	−0.368767	−	0.566302i
$638$		0			0
$639$	2593.61	+	2475.08i	0.160566	+	0.153228i
$640$		0			0
$641$	7866.64	+	13625.4i	0.484733	+	0.839582i	0.999846	−	0.0175403i	$-0.00558354\pi$
$641$	7866.64	+	13625.4i	0.484733	+	0.839582i	−0.515113	+	0.857122i	$0.672250\pi$
$642$		0			0
$643$	6237.64	+	10803.9i	0.382564	+	0.662620i	0.991428	−	0.130655i	$-0.0417079\pi$
$643$	6237.64	+	10803.9i	0.382564	+	0.662620i	−0.608864	+	0.793274i	$0.708375\pi$
$644$		0			0
$645$	1626.17	−	233.460i	0.0992720	−	0.0142519i
$646$		0			0
$647$	12902.0	−	22347.0i	0.783975	−	1.35788i	−0.145634	−	0.989338i	$-0.546522\pi$
$647$	12902.0	−	22347.0i	0.783975	−	1.35788i	0.929609	−	0.368546i	$-0.120144\pi$
$648$		0			0
$649$	12253.5	+	21223.7i	0.741128	+	1.28367i
$650$		0			0
$651$	−11208.2	−	4144.81i	−0.674785	−	0.249536i
$652$		0			0
$653$	7006.63	−	12135.8i	0.419894	−	0.727277i	−0.576035	−	0.817425i	$-0.695401\pi$
$653$	7006.63	−	12135.8i	0.419894	−	0.727277i	0.995928	+	0.0901482i	$0.0287341\pi$
$654$		0			0
$655$	−5642.96	−	9773.89i	−0.336624	−	0.583049i
$656$		0			0
$657$	13075.0	−	3833.19i	0.776412	−	0.227621i
$658$		0			0
$659$	12259.2	−	21233.6i	0.724660	−	1.25515i	−0.234454	−	0.972127i	$-0.575330\pi$
$659$	12259.2	−	21233.6i	0.724660	−	1.25515i	0.959114	−	0.283021i	$-0.0913365\pi$
$660$		0			0
$661$	−18581.1			−1.09338			−0.546689	−	0.837336i	$-0.684112\pi$
$661$	−18581.1			−1.09338			−0.546689	+	0.837336i	$0.684112\pi$
$662$		0			0
$663$	2299.13	−	5739.47i	0.134677	−	0.336203i
$664$		0			0
$665$	709.772	+	26473.2i	0.0413891	+	1.54374i
$666$		0			0
$667$	−87.3262	−	151.253i	−0.00506939	−	0.00878044i
$668$		0			0
$669$	−15104.2	−	19214.8i	−0.872886	−	1.11044i
$670$		0			0
$671$	18615.8	+	32243.5i	1.07102	+	1.85506i
$672$		0			0
$673$	−1730.90	+	2998.01i	−0.0991401	+	0.171716i	−0.911329	−	0.411679i	$-0.864943\pi$
$673$	−1730.90	+	2998.01i	−0.0991401	+	0.171716i	0.812189	+	0.583395i	$0.198276\pi$
$674$		0			0
$675$	−13454.6	−	9593.74i	−0.767211	−	0.547057i
$676$		0			0
$677$	−6873.88			−0.390228			−0.195114	−	0.980781i	$-0.562508\pi$
$677$	−6873.88			−0.390228			−0.195114	+	0.980781i	$0.562508\pi$
$678$		0			0
$679$	−9879.41	−	5356.09i	−0.558375	−	0.302722i
$680$		0			0
$681$	30019.4	−	4309.70i	1.68920	−	0.242508i
$682$		0			0
$683$	−5529.81	+	9577.92i	−0.309799	+	0.536587i	−0.978318	−	0.207108i	$-0.933595\pi$
$683$	−5529.81	+	9577.92i	−0.309799	+	0.536587i	0.668520	+	0.743695i	$0.266928\pi$
$684$		0			0
$685$	−28420.8			−1.58526
$686$		0			0
$687$	−8912.75	−	11338.4i	−0.494968	−	0.629675i
$688$		0			0
$689$	2283.29			0.126250
$690$		0			0
$691$	−10961.1			−0.603446			−0.301723	−	0.953396i	$-0.597562\pi$
$691$	−10961.1			−0.603446			−0.301723	+	0.953396i	$0.597562\pi$
$692$		0			0
$693$	20375.2	+	4377.23i	1.11687	+	0.239938i
$694$		0			0
$695$	45637.6			2.49084
$696$		0			0
$697$	−14242.7			−0.774005
$698$		0			0
$699$	20129.0	−	2889.80i	1.08920	−	0.156369i
$700$		0			0
$701$	8928.81			0.481079			0.240540	−	0.970639i	$-0.422676\pi$
$701$	8928.81			0.481079			0.240540	+	0.970639i	$0.422676\pi$
$702$		0			0
$703$	−18556.6	+	32140.9i	−0.995554	+	1.72435i
$704$		0			0
$705$	25066.4	+	31888.2i	1.33908	+	1.70352i
$706$		0			0
$707$	−26151.7	+	16048.3i	−1.39114	+	0.853687i
$708$		0			0
$709$	33964.5			1.79910			0.899552	−	0.436813i	$-0.143893\pi$
$709$	33964.5			1.79910			0.899552	+	0.436813i	$0.143893\pi$
$710$		0			0
$711$	8085.51	+	7716.00i	0.426484	+	0.406994i
$712$		0			0
$713$	2939.41	−	5091.21i	0.154393	−	0.267416i
$714$		0			0
$715$	−10284.7	−	17813.7i	−0.537941	−	0.931740i
$716$		0			0
$717$	−17243.9	+	2475.60i	−0.898164	+	0.128944i
$718$		0			0
$719$	−261.492	−	452.917i	−0.0135633	−	0.0234923i	0.859164	−	0.511700i	$-0.170984\pi$
$719$	−261.492	−	452.917i	−0.0135633	−	0.0234923i	−0.872727	+	0.488208i	$0.837651\pi$
$720$		0			0
$721$	6293.53	+	3412.02i	0.325081	+	0.176242i
$722$		0			0
$723$	10765.1	−	1545.48i	0.553745	−	0.0794979i
$724$		0			0
$725$	−434.523			−0.0222590
$726$		0			0
$727$	−6918.42	+	11983.1i	−0.352944	+	0.611316i	−0.986764	−	0.162164i	$-0.948153\pi$
$727$	−6918.42	+	11983.1i	−0.352944	+	0.611316i	0.633820	+	0.773480i	$0.281486\pi$
$728$		0			0
$729$	12908.4	−	14859.2i	0.655812	−	0.754924i
$730$		0			0
$731$	−381.115	−	660.110i	−0.0192832	−	0.0333995i
$732$		0			0
$733$	−2757.57	+	4776.26i	−0.138954	+	0.240675i	−0.927101	−	0.374812i	$-0.877707\pi$
$733$	−2757.57	+	4776.26i	−0.138954	+	0.240675i	0.788147	+	0.615487i	$0.211041\pi$
$734$		0			0
$735$	18307.3	+	20881.9i	0.918743	+	1.04794i
$736$		0			0
$737$	−16409.8	−	28422.7i	−0.820168	−	1.42057i
$738$		0			0
$739$	−12392.7	+	21464.8i	−0.616880	+	1.06847i	0.373172	+	0.927762i	$0.378270\pi$
$739$	−12392.7	+	21464.8i	−0.616880	+	1.06847i	−0.990052	+	0.140705i	$0.955063\pi$
$740$		0			0
$741$	9334.60	+	11875.0i	0.462773	+	0.588718i
$742$		0			0
$743$	7857.64	+	13609.8i	0.387980	+	0.672000i	0.992178	−	0.124834i	$-0.0398398\pi$
$743$	7857.64	+	13609.8i	0.387980	+	0.672000i	−0.604198	+	0.796834i	$0.706506\pi$
$744$		0			0
$745$	−7903.95	−	13690.1i	−0.388696	−	0.673241i
$746$		0			0
$747$	−11708.2	+	3432.50i	−0.573469	+	0.168124i
$748$		0			0
$749$	−1984.02	+	1217.51i	−0.0967884	+	0.0593952i
$750$		0			0
$751$	12593.8	−	21813.1i	0.611923	−	1.05988i	−0.378993	−	0.925400i	$-0.623729\pi$
$751$	12593.8	−	21813.1i	0.611923	−	1.05988i	0.990916	−	0.134482i	$-0.0429372\pi$
$752$		0			0
$753$	−1429.06	+	3567.45i	−0.0691606	+	0.172650i
$754$		0			0
$755$	7631.14			0.367848
$756$		0			0
$757$	4679.88			0.224694			0.112347	−	0.993669i	$-0.464163\pi$
$757$	4679.88			0.224694			0.112347	+	0.993669i	$0.464163\pi$
$758$		0			0
$759$	−3812.38	+	9517.08i	−0.182320	+	0.455136i
$760$		0			0
$761$	−16366.6	+	28347.8i	−0.779617	+	1.35034i	0.152546	+	0.988296i	$0.451253\pi$
$761$	−16366.6	+	28347.8i	−0.779617	+	1.35034i	−0.932163	+	0.362040i	$0.882081\pi$
$762$		0			0
$763$	18763.2	+	10172.4i	0.890269	+	0.482657i
$764$		0			0
$765$	−3732.29	+	15356.6i	−0.176394	+	0.725775i
$766$		0			0
$767$	9313.13	+	16130.8i	0.438433	+	0.759387i
$768$		0			0
$769$	6390.68	+	11069.0i	0.299680	+	0.519061i	0.976063	−	0.217489i	$-0.0697867\pi$
$769$	6390.68	+	11069.0i	0.299680	+	0.519061i	−0.676383	+	0.736550i	$0.736453\pi$
$770$		0			0
$771$	6383.92	+	8121.33i	0.298199	+	0.379355i
$772$		0			0
$773$	10243.6	−	17742.4i	0.476630	−	0.825548i	−0.523011	−	0.852326i	$-0.675191\pi$
$773$	10243.6	−	17742.4i	0.476630	−	0.825548i	0.999641	+	0.0267781i	$0.00852475\pi$
$774$		0			0
$775$	−7313.06	−	12666.6i	−0.338958	−	0.587093i
$776$		0			0
$777$	6561.02	+	38361.1i	0.302928	+	1.77117i
$778$		0			0
$779$	17397.5	−	30133.3i	0.800166	−	1.38593i
$780$		0			0
$781$	−2766.91	−	4792.42i	−0.126770	−	0.219573i
$782$		0			0
$783$	49.5229	−	515.197i	0.00226029	−	0.0235142i
$784$		0			0
$785$	−18193.8	+	31512.5i	−0.827214	+	1.43278i
$786$		0			0
$787$	−20512.6			−0.929091			−0.464545	−	0.885549i	$-0.653782\pi$
$787$	−20512.6			−0.929091			−0.464545	+	0.885549i	$0.653782\pi$
$788$		0			0
$789$	35582.0	−	5108.29i	1.60552	−	0.230494i
$790$		0			0
$791$	−27617.4	+	16947.7i	−1.24142	+	0.761810i
$792$		0			0
$793$	14148.7	+	24506.3i	0.633589	+	1.09741i
$794$		0			0
$795$	−5776.96	+	829.363i	−0.257720	+	0.0369994i
$796$		0			0
$797$	−1250.13	−	2165.28i	−0.0555605	−	0.0962337i	0.836907	−	0.547344i	$-0.184361\pi$
$797$	−1250.13	−	2165.28i	−0.0555605	−	0.0962337i	−0.892468	+	0.451111i	$0.851028\pi$
$798$		0			0
$799$	9409.50	−	16297.7i	0.416626	−	0.721618i
$800$		0			0
$801$	7447.54	−	30643.0i	0.328522	−	1.35171i
$802$		0			0
$803$	−21031.5			−0.924265
$804$		0			0
$805$	−11644.1	+	7145.53i	−0.509815	+	0.312853i
$806$		0			0
$807$	−11883.5	−	15117.6i	−0.518362	−	0.659436i
$808$		0			0
$809$	8583.75	−	14867.5i	0.373039	−	0.646122i	−0.616993	−	0.786969i	$-0.711649\pi$
$809$	8583.75	−	14867.5i	0.373039	−	0.646122i	0.990031	+	0.140847i	$0.0449825\pi$
$810$		0			0
$811$	−20249.0			−0.876744			−0.438372	−	0.898794i	$-0.644445\pi$
$811$	−20249.0			−0.876744			−0.438372	+	0.898794i	$0.644445\pi$
$812$		0			0
$813$	−10406.7	+	1494.02i	−0.448927	+	0.0644498i
$814$		0			0
$815$	−23663.2			−1.01704
$816$		0			0
$817$	1862.13			0.0797400
$818$		0			0
$819$	15485.9	+	3326.86i	0.660711	+	0.141941i
$820$		0			0
$821$	−14662.1			−0.623278			−0.311639	−	0.950201i	$-0.600878\pi$
$821$	−14662.1			−0.623278			−0.311639	+	0.950201i	$0.600878\pi$
$822$		0			0
$823$	16747.5			0.709332			0.354666	−	0.934993i	$-0.384595\pi$
$823$	16747.5			0.709332			0.354666	+	0.934993i	$0.384595\pi$
$824$		0			0
$825$	15763.1	+	20053.1i	0.665215	+	0.846255i
$826$		0			0
$827$	32996.7			1.38743			0.693717	−	0.720248i	$-0.255972\pi$
$827$	32996.7			1.38743			0.693717	+	0.720248i	$0.255972\pi$
$828$		0			0
$829$	11282.1	−	19541.2i	0.472671	−	0.818690i	−0.526840	−	0.849965i	$-0.676623\pi$
$829$	11282.1	−	19541.2i	0.472671	−	0.818690i	0.999511	+	0.0312742i	$0.00995652\pi$
$830$		0			0
$831$	3510.42	−	503.970i	0.146540	−	0.0210379i
$832$		0			0
$833$	5835.21	−	11487.7i	0.242711	−	0.477821i
$834$		0			0
$835$	46782.2			1.93888
$836$		0			0
$837$	15851.7	−	7227.19i	0.654619	−	0.298456i
$838$		0			0
$839$	3321.03	−	5752.20i	0.136657	−	0.236696i	−0.789573	−	0.613657i	$-0.789698\pi$
$839$	3321.03	−	5752.20i	0.136657	−	0.236696i	0.926229	+	0.376961i	$0.123031\pi$
$840$		0			0
$841$	12187.7	+	21109.7i	0.499721	+	0.865542i
$842$		0			0
$843$	−9872.04	−	12558.8i	−0.403335	−	0.513104i
$844$		0			0
$845$	9299.52	+	16107.2i	0.378596	+	0.655747i
$846$		0			0
$847$	−6608.80	−	3582.94i	−0.268100	−	0.145350i
$848$		0			0
$849$	−8182.77	+	20427.1i	−0.330780	+	0.825745i
$850$		0			0
$851$	−19145.8			−0.771220
$852$		0			0
$853$	−12850.8	+	22258.2i	−0.515828	+	0.893441i	0.484003	+	0.875066i	$0.339182\pi$
$853$	−12850.8	+	22258.2i	−0.515828	+	0.893441i	−0.999831	+	0.0183746i	$0.994151\pi$
$854$		0			0
$855$	−27930.9	−	26654.4i	−1.11721	−	1.06615i
$856$		0			0
$857$	−1250.79	−	2166.43i	−0.0498555	−	0.0863523i	0.840021	−	0.542554i	$-0.182543\pi$
$857$	−1250.79	−	2166.43i	−0.0498555	−	0.0863523i	−0.889876	+	0.456202i	$0.849209\pi$
$858$		0			0
$859$	4093.73	−	7090.54i	0.162603	−	0.281637i	−0.773198	−	0.634164i	$-0.781344\pi$
$859$	4093.73	−	7090.54i	0.162603	−	0.281637i	0.935802	+	0.352527i	$0.114678\pi$
$860$		0			0
$861$	−6151.20	−	35964.9i	−0.243475	−	1.42356i
$862$		0			0
$863$	−6423.90	−	11126.5i	−0.253386	−	0.438877i	0.711070	−	0.703121i	$-0.248211\pi$
$863$	−6423.90	−	11126.5i	−0.253386	−	0.438877i	−0.964456	+	0.264244i	$0.914878\pi$
$864$		0			0
$865$	30478.6	−	52790.5i	1.19804	−	2.07507i
$866$		0			0
$867$	−18011.6	+	2585.82i	−0.705545	+	0.101291i
$868$		0			0
$869$	−8625.76	−	14940.2i	−0.336719	−	0.583214i
$870$		0			0
$871$	−12472.1	−	21602.3i	−0.485191	−	0.840375i
$872$		0			0
$873$	15721.6	−	4609.11i	0.609503	−	0.178688i
$874$		0			0
$875$	−55.8062	−	2081.47i	−0.00215611	−	0.0804189i
$876$		0			0
$877$	−4984.36	+	8633.17i	−0.191916	+	0.332407i	−0.945885	−	0.324502i	$-0.894803\pi$
$877$	−4984.36	+	8633.17i	−0.191916	+	0.332407i	0.753969	+	0.656909i	$0.228137\pi$
$878$		0			0
$879$	−13975.4	+	2006.37i	−0.536268	+	0.0769888i
$880$		0			0
$881$	14050.2			0.537302			0.268651	−	0.963238i	$-0.413422\pi$
$881$	14050.2			0.537302			0.268651	+	0.963238i	$0.413422\pi$
$882$		0			0
$883$	−1281.24			−0.0488305			−0.0244152	−	0.999702i	$-0.507772\pi$
$883$	−1281.24			−0.0488305			−0.0244152	+	0.999702i	$0.507772\pi$
$884$		0			0
$885$	−29422.4	−	37429.8i	−1.11754	−	1.42168i
$886$		0			0
$887$	−14254.6	+	24689.7i	−0.539597	+	0.934609i	0.459329	+	0.888266i	$0.348090\pi$
$887$	−14254.6	+	24689.7i	−0.539597	+	0.934609i	−0.998926	+	0.0463428i	$0.985243\pi$
$888$		0			0
$889$	−409.241	−	15264.0i	−0.0154393	−	0.575857i
$890$		0			0
$891$	−25572.7	+	16404.3i	−0.961525	+	0.616794i
$892$		0			0
$893$	22987.4	+	39815.3i	0.861416	+	1.49202i
$894$		0			0
$895$	−4434.42	−	7680.64i	−0.165616	−	0.286855i
$896$		0			0
$897$	−2897.56	+	7233.35i	−0.107856	+	0.269247i
$898$		0			0
$899$	229.053	−	396.731i	0.00849760	−	0.0147183i
$900$		0			0
$901$	1353.91	+	2345.04i	0.0500613	+	0.0867086i
$902$		0			0
$903$	1502.28	−	1247.46i	0.0553628	−	0.0459722i
$904$		0			0
$905$	29289.5	−	50731.0i	1.07582	−	1.86338i
$906$		0			0
$907$	−15707.8	−	27206.6i	−0.575047	−	0.996010i	−0.996037	−	0.0889449i	$-0.971651\pi$
$907$	−15707.8	−	27206.6i	−0.575047	−	0.996010i	0.420990	−	0.907065i	$-0.361683\pi$
$908$		0			0
$909$	10564.2	−	43466.5i	0.385470	−	1.58602i
$910$		0			0
$911$	−5631.68	+	9754.36i	−0.204814	+	0.354749i	−0.950074	−	0.312026i	$-0.898992\pi$
$911$	−5631.68	+	9754.36i	−0.204814	+	0.354749i	0.745259	+	0.666775i	$0.232326\pi$
$912$		0			0
$913$	18833.0			0.682675
$914$		0			0
$915$	−44699.2	−	56864.2i	−1.61498	−	2.05451i
$916$		0			0
$917$	−11792.9	−	6393.46i	−0.424683	−	0.230241i
$918$		0			0
$919$	−10371.8	−	17964.4i	−0.372288	−	0.644822i	0.617629	−	0.786470i	$-0.288093\pi$
$919$	−10371.8	−	17964.4i	−0.372288	−	0.644822i	−0.989917	+	0.141648i	$0.954760\pi$
$920$		0			0
$921$	−19473.1	+	48611.8i	−0.696699	+	1.73921i
$922$		0			0
$923$	−2102.95	−	3642.42i	−0.0749941	−	0.129894i
$924$		0			0
$925$	−23816.7	+	41251.7i	−0.846580	+	1.46632i
$926$		0			0
$927$	−10015.2	+	2936.17i	−0.354847	+	0.104031i
$928$		0			0
$929$	6715.88			0.237181			0.118590	−	0.992943i	$-0.462162\pi$
$929$	6715.88			0.237181			0.118590	+	0.992943i	$0.462162\pi$
$930$		0			0
$931$	17176.8	+	26377.8i	0.604669	+	0.928567i
$932$		0			0
$933$	−8787.34	+	21936.4i	−0.308344	+	0.769737i
$934$		0			0
$935$	12196.9	−	21125.7i	0.426612	−	0.738914i
$936$		0			0
$937$	−36371.2			−1.26809			−0.634043	−	0.773298i	$-0.718606\pi$
$937$	−36371.2			−1.26809			−0.634043	+	0.773298i	$0.718606\pi$
$938$		0			0
$939$	6020.51	−	15029.4i	0.209235	−	0.522327i
$940$		0			0
$941$	−28733.5			−0.995414			−0.497707	−	0.867345i	$-0.665824\pi$
$941$	−28733.5			−0.995414			−0.497707	+	0.867345i	$0.665824\pi$
$942$		0			0
$943$	17949.8			0.619859
$944$		0			0
$945$	−40389.4	−	2792.32i	−1.39034	−	0.0961209i
$946$		0			0
$947$	52586.9			1.80448			0.902240	−	0.431233i	$-0.141921\pi$
$947$	52586.9			1.80448			0.902240	+	0.431233i	$0.141921\pi$
$948$		0			0
$949$	−15984.7			−0.546772
$950$		0			0
$951$	−1217.46	+	3039.21i	−0.0415129	+	0.103631i
$952$		0			0
$953$	−2772.66			−0.0942447			−0.0471224	−	0.998889i	$-0.515005\pi$
$953$	−2772.66			−0.0942447			−0.0471224	+	0.998889i	$0.515005\pi$
$954$		0			0
$955$	8882.67	−	15385.2i	0.300981	−	0.521314i
$956$		0			0
$957$	−297.079	+	741.616i	−0.0100347	+	0.0250502i
$958$		0			0
$959$	−28792.1	+	17668.5i	−0.969493	+	0.594940i
$960$		0			0
$961$	−14371.1			−0.482397
$962$		0			0
$963$	801.462	−	3297.63i	0.0268190	−	0.110347i
$964$		0			0
$965$	21449.2	−	37151.1i	0.715517	−	1.23931i
$966$		0			0
$967$	21929.0	+	37982.1i	0.729254	+	1.26311i	0.957199	+	0.289432i	$0.0934663\pi$
$967$	21929.0	+	37982.1i	0.729254	+	1.26311i	−0.227944	+	0.973674i	$0.573200\pi$
$968$		0			0
$969$	−6661.09	+	16628.5i	−0.220831	+	0.551273i
$970$		0			0
$971$	−15901.2	−	27541.6i	−0.525533	−	0.910251i	−0.999558	−	0.0297389i	$-0.990532\pi$
$971$	−15901.2	−	27541.6i	−0.525533	−	0.910251i	0.474024	−	0.880512i	$-0.342801\pi$
$972$		0			0
$973$	46233.7	−	28371.8i	1.52332	−	0.934798i
$974$		0			0
$975$	11980.6	+	15241.1i	0.393524	+	0.500623i
$976$		0			0
$977$	−24751.4			−0.810509			−0.405255	−	0.914204i	$-0.632817\pi$
$977$	−24751.4			−0.810509			−0.405255	+	0.914204i	$0.632817\pi$
$978$		0			0
$979$	−24338.2	+	42155.0i	−0.794537	+	1.37618i
$980$		0			0
$981$	−29858.9	+	8753.76i	−0.971787	+	0.284899i
$982$		0			0
$983$	10174.1	+	17622.0i	0.330114	+	0.571774i	0.982534	−	0.186084i	$-0.0595795\pi$
$983$	10174.1	+	17622.0i	0.330114	+	0.571774i	−0.652420	+	0.757857i	$0.726246\pi$
$984$		0			0
$985$	4694.86	−	8131.74i	0.151869	−	0.263045i
$986$		0			0
$987$	45217.9	+	16721.6i	1.45826	+	0.539266i
$988$		0			0
$989$	480.312	+	831.925i	0.0154429	+	0.0267479i
$990$		0			0
$991$	18916.8	−	32764.8i	0.606369	−	1.05026i	−0.385464	−	0.922723i	$-0.625959\pi$
$991$	18916.8	−	32764.8i	0.606369	−	1.05026i	0.991834	−	0.127539i	$-0.0407079\pi$
$992$		0			0
$993$	−20414.3	+	50961.4i	−0.652395	+	1.62861i
$994$		0			0
$995$	−24594.3	−	42598.6i	−0.783610	−	1.35725i
$996$		0			0
$997$	5431.33	+	9407.34i	0.172530	+	0.298830i	0.939304	−	0.343087i	$-0.111473\pi$
$997$	5431.33	+	9407.34i	0.172530	+	0.298830i	−0.766774	+	0.641917i	$0.778139\pi$
$998$		0			0
$999$	−46196.1	−	32940.0i	−1.46304	−	1.04322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	252.4.i.a.25.9	✓	48
3.2	odd	2		756.4.i.a.613.23		48
7.2	even	3		252.4.l.a.205.7	yes	48
9.4	even	3		252.4.l.a.193.7	yes	48
9.5	odd	6		756.4.l.a.361.2		48
21.2	odd	6		756.4.l.a.289.2		48
63.23	odd	6		756.4.i.a.37.23		48
63.58	even	3	inner	252.4.i.a.121.9	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
252.4.i.a.25.9	✓	48	1.1	even	1	trivial
252.4.i.a.121.9	yes	48	63.58	even	3	inner
252.4.l.a.193.7	yes	48	9.4	even	3
252.4.l.a.205.7	yes	48	7.2	even	3
756.4.i.a.37.23		48	63.23	odd	6
756.4.i.a.613.23		48	3.2	odd	2
756.4.l.a.289.2		48	21.2	odd	6
756.4.l.a.361.2		48	9.5	odd	6

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:	\( N \)	\(=\)	\( 252 = 2^{2} \cdot 3^{2} \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	252.i (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.93223 + 4.82354i) q^{3} +(-7.79077 + 13.4940i) q^{5} +(0.496367 + 18.5136i) q^{7} +(-19.5330 - 18.6403i) q^{9} +O(q^{10})\)	\(q+(-1.93223 + 4.82354i) q^{3} +(-7.79077 + 13.4940i) q^{5} +(0.496367 + 18.5136i) q^{7} +(-19.5330 - 18.6403i) q^{9} +(20.8381 + 36.0927i) q^{11} +(15.8378 + 27.4318i) q^{13} +(-50.0353 - 63.6526i) q^{15} +(-18.7824 + 32.5321i) q^{17} +(-45.8855 - 79.4760i) q^{19} +(-90.2601 - 33.3783i) q^{21} +(23.6712 - 40.9997i) q^{23} +(-58.8922 - 102.004i) q^{25} +(127.655 - 58.2007i) q^{27} +(1.84457 - 3.19489i) q^{29} +124.177 q^{31} +(-214.358 + 30.7741i) q^{33} +(-253.690 - 137.537i) q^{35} +(-202.205 - 350.230i) q^{37} +(-162.921 + 23.3895i) q^{39} +(189.575 + 328.354i) q^{41} +(-10.1455 + 17.5725i) q^{43} +(403.710 - 118.356i) q^{45} -500.974 q^{47} +(-342.507 + 18.3791i) q^{49} +(-120.628 - 153.457i) q^{51} +(36.0419 - 62.4263i) q^{53} -649.380 q^{55} +(472.016 - 67.7645i) q^{57} +588.033 q^{59} +893.353 q^{61} +(335.404 - 370.879i) q^{63} -493.554 q^{65} -787.490 q^{67} +(152.025 + 193.399i) q^{69} -132.781 q^{71} +(-252.320 + 437.031i) q^{73} +(605.815 - 86.9732i) q^{75} +(-657.863 + 403.704i) q^{77} -413.941 q^{79} +(34.0756 + 728.203i) q^{81} +(225.944 - 391.347i) q^{83} +(-292.659 - 506.901i) q^{85} +(11.8465 + 15.0706i) q^{87} +(583.982 + 1011.49i) q^{89} +(-500.001 + 306.831i) q^{91} +(-239.938 + 598.972i) q^{93} +1429.93 q^{95} +(-303.395 + 525.495i) q^{97} +(265.749 - 1093.43i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9}+O(q^{10}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9	\( 48 q + 20 q^{5} - 6 q^{7} - 44 q^{9} + 4 q^{11} - 12 q^{13} - 26 q^{15} + 112 q^{17} + 60 q^{19} - 80 q^{21} + 10 q^{23} - 600 q^{25} + 194 q^{29} + 60 q^{31} - 472 q^{33} + 394 q^{35} - 84 q^{37} + 604 q^{39} + 210 q^{41} + 42 q^{43} + 254 q^{45} - 132 q^{47} - 78 q^{49} - 58 q^{51} - 468 q^{53} + 612 q^{55} + 1476 q^{57} - 916 q^{59} - 804 q^{61} - 444 q^{63} + 1656 q^{65} - 588 q^{67} - 28 q^{69} - 2228 q^{71} - 336 q^{73} - 668 q^{75} - 1216 q^{77} - 768 q^{79} - 104 q^{81} + 1024 q^{83} + 360 q^{85} + 2188 q^{87} + 2922 q^{89} - 120 q^{91} - 1292 q^{93} + 2428 q^{95} - 264 q^{97} - 2246 q^{99}+O(q^{100}) \) 48 * q + 20 * q^5 - 6 * q^7 - 44 * q^9 + 4 * q^11 - 12 * q^13 - 26 * q^15 + 112 * q^17 + 60 * q^19 - 80 * q^21 + 10 * q^23 - 600 * q^25 + 194 * q^29 + 60 * q^31 - 472 * q^33 + 394 * q^35 - 84 * q^37 + 604 * q^39 + 210 * q^41 + 42 * q^43 + 254 * q^45 - 132 * q^47 - 78 * q^49 - 58 * q^51 - 468 * q^53 + 612 * q^55 + 1476 * q^57 - 916 * q^59 - 804 * q^61 - 444 * q^63 + 1656 * q^65 - 588 * q^67 - 28 * q^69 - 2228 * q^71 - 336 * q^73 - 668 * q^75 - 1216 * q^77 - 768 * q^79 - 104 * q^81 + 1024 * q^83 + 360 * q^85 + 2188 * q^87 + 2922 * q^89 - 120 * q^91 - 1292 * q^93 + 2428 * q^95 - 264 * q^97 - 2246 * q^99

Introduction

L-functions

Modular forms

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Database

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