LMFDB - Embedded newform 684.3.g.d.343.9

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [684,3,Mod(343,684)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(684, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([1, 0, 0]))

N = Newforms(chi, 3, names="a")

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

chi := DirichletCharacter("684.343");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 684 = 2^{2} \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	684.g (of order $2$, degree $1$, 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:	$18.6376500822$
Analytic rank:	$0$
Dimension:	$36$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.9
Character	$\chi$	$=$	684.343
Dual form			684.3.g.d.343.10

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.42379 - 1.40457i) q^{2} +(0.0543607 + 3.99963i) q^{4} +5.95758 q^{5} -3.23592i q^{7} +(5.54037 - 5.77099i) q^{8} +O(q^{10})$	\(q+(-1.42379 - 1.40457i) q^{2} +(0.0543607 + 3.99963i) q^{4} +5.95758 q^{5} -3.23592i q^{7} +(5.54037 - 5.77099i) q^{8} +(-8.48235 - 8.36785i) q^{10} +19.4200i q^{11} +24.4099 q^{13} +(-4.54508 + 4.60727i) q^{14} +(-15.9941 + 0.434846i) q^{16} +0.948997 q^{17} -4.35890i q^{19} +(0.323858 + 23.8281i) q^{20} +(27.2768 - 27.6501i) q^{22} +11.5855i q^{23} +10.4928 q^{25} +(-34.7545 - 34.2854i) q^{26} +(12.9425 - 0.175907i) q^{28} -37.6641 q^{29} +24.2906i q^{31} +(23.3830 + 21.8457i) q^{32} +(-1.35117 - 1.33293i) q^{34} -19.2783i q^{35} +25.7227 q^{37} +(-6.12238 + 6.20616i) q^{38} +(33.0072 - 34.3812i) q^{40} -24.1340 q^{41} +13.1022i q^{43} +(-77.6730 + 1.05569i) q^{44} +(16.2727 - 16.4954i) q^{46} +32.7988i q^{47} +38.5288 q^{49} +(-14.9395 - 14.7379i) q^{50} +(1.32694 + 97.6304i) q^{52} +16.3022 q^{53} +115.696i q^{55} +(-18.6745 - 17.9282i) q^{56} +(53.6257 + 52.9019i) q^{58} +58.8822i q^{59} -25.0420 q^{61} +(34.1179 - 34.5848i) q^{62} +(-2.60867 - 63.9468i) q^{64} +145.424 q^{65} -91.2524i q^{67} +(0.0515881 + 3.79564i) q^{68} +(-27.0777 + 27.4482i) q^{70} +90.9890i q^{71} +35.7111 q^{73} +(-36.6238 - 36.1294i) q^{74} +(17.4340 - 0.236953i) q^{76} +62.8417 q^{77} -86.9891i q^{79} +(-95.2861 + 2.59063i) q^{80} +(34.3617 + 33.8979i) q^{82} +8.80707i q^{83} +5.65373 q^{85} +(18.4030 - 18.6548i) q^{86} +(112.073 + 107.594i) q^{88} +148.890 q^{89} -78.9883i q^{91} +(-46.3378 + 0.629798i) q^{92} +(46.0683 - 46.6987i) q^{94} -25.9685i q^{95} +192.306 q^{97} +(-54.8570 - 54.1165i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 12 q^{4}+O(q^{10}) $ 36 * q - 12 * q^4	$ 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) $ 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/684\mathbb{Z}\right)^\times$.

$n$	$325$	$343$	$533$
$\chi(n)$	$1$	$-1$	$1$

Coefficient data

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

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

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

$2$	−1.42379	−	1.40457i	−0.711895	−	0.702285i
$2$	−1.42379	−	1.40457i	−0.711895	−	0.702285i
$3$		0			0
$3$		0			0
$4$	0.0543607	+	3.99963i	0.0135902	+	0.999908i
$5$	5.95758			1.19152			0.595758	−	0.803164i	$-0.296852\pi$
$5$	5.95758			1.19152			0.595758	+	0.803164i	$0.296852\pi$
$6$		0			0
$7$		−	3.23592i		−	0.462274i	−0.972921	−	0.231137i	$-0.925755\pi$
$7$		−	3.23592i		−	0.462274i	0.972921	−	0.231137i	$-0.0742446\pi$
$8$	5.54037	−	5.77099i	0.692546	−	0.721374i
$9$		0			0
$10$	−8.48235	−	8.36785i	−0.848235	−	0.836785i
$11$			19.4200i			1.76546i	0.469882	+	0.882729i	$0.344296\pi$
$11$			19.4200i			1.76546i	−0.469882	+	0.882729i	$0.655704\pi$
$12$		0			0
$13$	24.4099			1.87768			0.938841	−	0.344352i	$-0.111901\pi$
$13$	24.4099			1.87768			0.938841	+	0.344352i	$0.111901\pi$
$14$	−4.54508	+	4.60727i	−0.324649	+	0.329091i
$15$		0			0
$16$	−15.9941	+	0.434846i	−0.999631	+	0.0271778i
$17$	0.948997			0.0558233			0.0279117	−	0.999610i	$-0.491114\pi$
$17$	0.948997			0.0558233			0.0279117	+	0.999610i	$0.491114\pi$
$18$		0			0
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	0.323858	+	23.8281i	0.0161929	+	1.19141i
$21$		0			0
$22$	27.2768	−	27.6501i	1.23986	−	1.25682i
$23$			11.5855i			0.503719i	0.967764	+	0.251859i	$0.0810420\pi$
$23$			11.5855i			0.503719i	−0.967764	+	0.251859i	$0.918958\pi$
$24$		0			0
$25$	10.4928			0.419711
$26$	−34.7545	−	34.2854i	−1.33671	−	1.31867i
$27$		0			0
$28$	12.9425	−	0.175907i	0.462232	−	0.00628239i
$29$	−37.6641			−1.29876			−0.649380	−	0.760464i	$-0.724972\pi$
$29$	−37.6641			−1.29876			−0.649380	+	0.760464i	$0.724972\pi$
$30$		0			0
$31$			24.2906i			0.783568i	0.920057	+	0.391784i	$0.128142\pi$
$31$			24.2906i			0.783568i	−0.920057	+	0.391784i	$0.871858\pi$
$32$	23.3830	+	21.8457i	0.730719	+	0.682678i
$33$		0			0
$34$	−1.35117	−	1.33293i	−0.0397404	−	0.0392039i
$35$		−	19.2783i		−	0.550807i
$36$		0			0
$37$	25.7227			0.695209			0.347605	−	0.937641i	$-0.386995\pi$
$37$	25.7227			0.695209			0.347605	+	0.937641i	$0.386995\pi$
$38$	−6.12238	+	6.20616i	−0.161115	+	0.163320i
$39$		0			0
$40$	33.0072	−	34.3812i	0.825180	−	0.859529i
$41$	−24.1340			−0.588633			−0.294317	−	0.955708i	$-0.595092\pi$
$41$	−24.1340			−0.588633			−0.294317	+	0.955708i	$0.595092\pi$
$42$		0			0
$43$			13.1022i			0.304702i	0.988326	+	0.152351i	$0.0486844\pi$
$43$			13.1022i			0.304702i	−0.988326	+	0.152351i	$0.951316\pi$
$44$	−77.6730	+	1.05569i	−1.76530	+	0.0239929i
$45$		0			0
$46$	16.2727	−	16.4954i	0.353754	−	0.358595i
$47$			32.7988i			0.697847i	0.937151	+	0.348924i	$0.113453\pi$
$47$			32.7988i			0.697847i	−0.937151	+	0.348924i	$0.886547\pi$
$48$		0			0
$49$	38.5288			0.786303
$50$	−14.9395	−	14.7379i	−0.298791	−	0.294757i
$51$		0			0
$52$	1.32694	+	97.6304i	0.0255180	+	1.87751i
$53$	16.3022			0.307590			0.153795	−	0.988103i	$-0.450851\pi$
$53$	16.3022			0.307590			0.153795	+	0.988103i	$0.450851\pi$
$54$		0			0
$55$			115.696i			2.10357i
$56$	−18.6745	−	17.9282i	−0.333473	−	0.320146i
$57$		0			0
$58$	53.6257	+	52.9019i	0.924582	+	0.912101i
$59$			58.8822i			0.998004i	0.866601	+	0.499002i	$0.166300\pi$
$59$			58.8822i			0.998004i	−0.866601	+	0.499002i	$0.833700\pi$
$60$		0			0
$61$	−25.0420			−0.410524			−0.205262	−	0.978707i	$-0.565805\pi$
$61$	−25.0420			−0.410524			−0.205262	+	0.978707i	$0.565805\pi$
$62$	34.1179	−	34.5848i	0.550289	−	0.557819i
$63$		0			0
$64$	−2.60867	−	63.9468i	−0.0407605	−	0.999169i
$65$	145.424			2.23729
$66$		0			0
$67$		−	91.2524i		−	1.36198i	−0.732295	−	0.680988i	$-0.761551\pi$
$67$		−	91.2524i		−	1.36198i	0.732295	−	0.680988i	$-0.238449\pi$
$68$	0.0515881	+	3.79564i	0.000758649	+	0.0558182i
$69$		0			0
$70$	−27.0777	+	27.4482i	−0.386824	+	0.392117i
$71$			90.9890i			1.28154i	0.767735	+	0.640768i	$0.221384\pi$
$71$			90.9890i			1.28154i	−0.767735	+	0.640768i	$0.778616\pi$
$72$		0			0
$73$	35.7111			0.489193			0.244597	−	0.969625i	$-0.421344\pi$
$73$	35.7111			0.489193			0.244597	+	0.969625i	$0.421344\pi$
$74$	−36.6238	−	36.1294i	−0.494916	−	0.488235i
$75$		0			0
$76$	17.4340	−	0.236953i	0.229395	−	0.00311780i
$77$	62.8417			0.816126
$78$		0			0
$79$		−	86.9891i		−	1.10113i	−0.834793	−	0.550564i	$-0.814413\pi$
$79$		−	86.9891i		−	1.10113i	0.834793	−	0.550564i	$-0.185587\pi$
$80$	−95.2861	+	2.59063i	−1.19108	+	0.0323828i
$81$		0			0
$82$	34.3617	+	33.8979i	0.419045	+	0.413389i
$83$			8.80707i			0.106109i	0.998592	+	0.0530546i	$0.0168957\pi$
$83$			8.80707i			0.106109i	−0.998592	+	0.0530546i	$0.983104\pi$
$84$		0			0
$85$	5.65373			0.0665144
$86$	18.4030	−	18.6548i	0.213988	−	0.216916i
$87$		0			0
$88$	112.073	+	107.594i	1.27356	+	1.22266i
$89$	148.890			1.67292			0.836458	−	0.548030i	$-0.184622\pi$
$89$	148.890			1.67292			0.836458	+	0.548030i	$0.184622\pi$
$90$		0			0
$91$		−	78.9883i		−	0.868004i
$92$	−46.3378	+	0.629798i	−0.503672	+	0.00684563i
$93$		0			0
$94$	46.0683	−	46.6987i	0.490088	−	0.496794i
$95$		−	25.9685i		−	0.273353i
$96$		0			0
$97$	192.306			1.98254			0.991270	−	0.131845i	$-0.0420903\pi$
$97$	192.306			1.98254			0.991270	+	0.131845i	$0.0420903\pi$
$98$	−54.8570	−	54.1165i	−0.559765	−	0.552209i
$99$		0			0
$100$	0.570395	+	41.9673i	0.00570395	+	0.419673i
$101$	−48.9633			−0.484785			−0.242393	−	0.970178i	$-0.577932\pi$
$101$	−48.9633			−0.484785			−0.242393	+	0.970178i	$0.577932\pi$
$102$		0			0
$103$		−	148.215i		−	1.43898i	−0.694502	−	0.719491i	$-0.744375\pi$
$103$		−	148.215i		−	1.43898i	0.694502	−	0.719491i	$-0.255625\pi$
$104$	135.240	−	140.869i	1.30038	−	1.35451i
$105$		0			0
$106$	−23.2110	−	22.8977i	−0.218972	−	0.216016i
$107$		−	49.4191i		−	0.461860i	−0.972970	−	0.230930i	$-0.925823\pi$
$107$		−	49.4191i		−	0.461860i	0.972970	−	0.230930i	$-0.0741769\pi$
$108$		0			0
$109$	8.02569			0.0736301			0.0368151	−	0.999322i	$-0.488279\pi$
$109$	8.02569			0.0736301			0.0368151	+	0.999322i	$0.488279\pi$
$110$	162.504	−	164.728i	1.47731	−	1.49752i
$111$		0			0
$112$	1.40713	+	51.7556i	0.0125636	+	0.462104i
$113$	190.703			1.68764			0.843819	−	0.536628i	$-0.180302\pi$
$113$	190.703			1.68764			0.843819	+	0.536628i	$0.180302\pi$
$114$		0			0
$115$			69.0217i			0.600189i
$116$	−2.04745	−	150.642i	−0.0176504	−	1.29864i
$117$		0			0
$118$	82.7043	−	83.8360i	0.700884	−	0.710475i
$119$		−	3.07088i		−	0.0258057i
$120$		0			0
$121$	−256.138			−2.11684
$122$	35.6545	+	35.1732i	0.292250	+	0.288305i
$123$		0			0
$124$	−97.1535	+	1.32046i	−0.783496	+	0.0106488i
$125$	−86.4279			−0.691424
$126$		0			0
$127$			138.269i			1.08873i	0.838848	+	0.544366i	$0.183230\pi$
$127$			138.269i			1.08873i	−0.838848	+	0.544366i	$0.816770\pi$
$128$	−86.1036	+	94.7110i	−0.672685	+	0.739929i
$129$		0			0
$130$	−207.053	−	204.258i	−1.59272	−	1.57121i
$131$		−	227.357i		−	1.73555i	−0.496955	−	0.867776i	$-0.665549\pi$
$131$		−	227.357i		−	1.73555i	0.496955	−	0.867776i	$-0.334451\pi$
$132$		0			0
$133$	−14.1050			−0.106053
$134$	−128.170	+	129.924i	−0.956496	+	0.969584i
$135$		0			0
$136$	5.25779	−	5.47665i	0.0386602	−	0.0402695i
$137$	−120.809			−0.881816			−0.440908	−	0.897552i	$-0.645344\pi$
$137$	−120.809			−0.881816			−0.440908	+	0.897552i	$0.645344\pi$
$138$		0			0
$139$		−	128.261i		−	0.922745i	−0.887207	−	0.461372i	$-0.847357\pi$
$139$		−	128.261i		−	0.922745i	0.887207	−	0.461372i	$-0.152643\pi$
$140$	77.1059	−	1.04798i	0.550756	−	0.00748557i
$141$		0			0
$142$	127.801	−	129.549i	0.900004	−	0.912319i
$143$			474.040i			3.31497i
$144$		0			0
$145$	−224.387			−1.54749
$146$	−50.8451	−	50.1588i	−0.348254	−	0.343553i
$147$		0			0
$148$	1.39831	+	102.881i	0.00944802	+	0.695145i
$149$	248.099			1.66509			0.832546	−	0.553957i	$-0.186883\pi$
$149$	248.099			1.66509			0.832546	+	0.553957i	$0.186883\pi$
$150$		0			0
$151$			109.223i			0.723330i	0.932308	+	0.361665i	$0.117792\pi$
$151$			109.223i			0.723330i	−0.932308	+	0.361665i	$0.882208\pi$
$152$	−25.1552	−	24.1499i	−0.165495	−	0.158881i
$153$		0			0
$154$	−89.4734	−	88.2656i	−0.580996	−	0.573153i
$155$			144.713i			0.933635i
$156$		0			0
$157$	−129.337			−0.823802			−0.411901	−	0.911229i	$-0.635135\pi$
$157$	−129.337			−0.823802			−0.411901	+	0.911229i	$0.635135\pi$
$158$	−122.182	+	123.854i	−0.773306	+	0.783888i
$159$		0			0
$160$	139.306	+	130.148i	0.870664	+	0.813422i
$161$	37.4898			0.232856
$162$		0			0
$163$			246.799i			1.51410i	0.653356	+	0.757051i	$0.273360\pi$
$163$			246.799i			1.51410i	−0.653356	+	0.757051i	$0.726640\pi$
$164$	−1.31194	−	96.5270i	−0.00799963	−	0.588579i
$165$		0			0
$166$	12.3702	−	12.5394i	0.0745190	−	0.0755387i
$167$			20.5836i			0.123255i	0.998099	+	0.0616275i	$0.0196291\pi$
$167$			20.5836i			0.123255i	−0.998099	+	0.0616275i	$0.980371\pi$
$168$		0			0
$169$	426.841			2.52569
$170$	−8.04972	−	7.94106i	−0.0473513	−	0.0467121i
$171$		0			0
$172$	−52.4039	+	0.712244i	−0.304674	+	0.00414096i
$173$	−171.756			−0.992807			−0.496403	−	0.868092i	$-0.665346\pi$
$173$	−171.756			−0.992807			−0.496403	+	0.868092i	$0.665346\pi$
$174$		0			0
$175$		−	33.9538i		−	0.194022i
$176$	−8.44472	−	310.606i	−0.0479814	−	1.76481i
$177$		0			0
$178$	−211.988	−	209.126i	−1.19094	−	1.17487i
$179$			2.82747i			0.0157959i	0.999969	+	0.00789795i	$0.00251402\pi$
$179$			2.82747i			0.0157959i	−0.999969	+	0.00789795i	$0.997486\pi$
$180$		0			0
$181$	24.4632			0.135156			0.0675779	−	0.997714i	$-0.478473\pi$
$181$	24.4632			0.135156			0.0675779	+	0.997714i	$0.478473\pi$
$182$	−110.945	+	112.463i	−0.609586	+	0.617928i
$183$		0			0
$184$	66.8600	+	64.1881i	0.363369	+	0.348848i
$185$	153.245			0.828353
$186$		0			0
$187$			18.4296i			0.0985538i
$188$	−131.183	+	1.78297i	−0.697783	+	0.00948387i
$189$		0			0
$190$	−36.4746	+	36.9737i	−0.191972	+	0.194598i
$191$			37.3053i			0.195316i	0.995220	+	0.0976580i	$0.0311351\pi$
$191$			37.3053i			0.195316i	−0.995220	+	0.0976580i	$0.968865\pi$
$192$		0			0
$193$	−17.7882			−0.0921669			−0.0460834	−	0.998938i	$-0.514674\pi$
$193$	−17.7882			−0.0921669			−0.0460834	+	0.998938i	$0.514674\pi$
$194$	−273.804	−	270.108i	−1.41136	−	1.39231i
$195$		0			0
$196$	2.09445	+	154.101i	0.0106860	+	0.786230i
$197$	74.8343			0.379869			0.189935	−	0.981797i	$-0.439172\pi$
$197$	74.8343			0.379869			0.189935	+	0.981797i	$0.439172\pi$
$198$		0			0
$199$			26.4456i			0.132892i	0.997790	+	0.0664462i	$0.0211661\pi$
$199$			26.4456i			0.132892i	−0.997790	+	0.0664462i	$0.978834\pi$
$200$	58.1339	−	60.5538i	0.290669	−	0.302769i
$201$		0			0
$202$	69.7135	+	68.7724i	0.345116	+	0.340458i
$203$			121.878i			0.600384i
$204$		0			0
$205$	−143.780			−0.701366
$206$	−208.179	+	211.027i	−1.01058	+	1.02440i
$207$		0			0
$208$	−390.413	+	10.6145i	−1.87699	+	0.0510313i
$209$	84.6500			0.405024
$210$		0			0
$211$			350.716i			1.66216i	0.556153	+	0.831080i	$0.312277\pi$
$211$			350.716i			1.66216i	−0.556153	+	0.831080i	$0.687723\pi$
$212$	0.886202	+	65.2030i	0.00418020	+	0.307561i
$213$		0			0
$214$	−69.4126	+	70.3624i	−0.324358	+	0.328796i
$215$			78.0574i			0.363057i
$216$		0			0
$217$	78.6025			0.362224
$218$	−11.4269	−	11.2726i	−0.0524170	−	0.0517094i
$219$		0			0
$220$	−462.743	+	6.28934i	−2.10338	+	0.0285879i
$221$	23.1649			0.104818
$222$		0			0
$223$		−	375.549i		−	1.68408i	−0.539419	−	0.842038i	$-0.681356\pi$
$223$		−	375.549i		−	1.68408i	0.539419	−	0.842038i	$-0.318644\pi$
$224$	70.6910	−	75.6655i	0.315585	−	0.337793i
$225$		0			0
$226$	−271.521	−	267.856i	−1.20142	−	1.18520i
$227$		−	217.094i		−	0.956361i	−0.878262	−	0.478180i	$-0.841296\pi$
$227$		−	217.094i		−	0.956361i	0.878262	−	0.478180i	$-0.158704\pi$
$228$		0			0
$229$	−134.179			−0.585936			−0.292968	−	0.956122i	$-0.594643\pi$
$229$	−134.179			−0.585936			−0.292968	+	0.956122i	$0.594643\pi$
$230$	96.9459	−	98.2725i	0.421504	−	0.427272i
$231$		0			0
$232$	−208.673	+	217.359i	−0.899451	+	0.936892i
$233$	−347.312			−1.49061			−0.745305	−	0.666724i	$-0.767696\pi$
$233$	−347.312			−1.49061			−0.745305	+	0.666724i	$0.767696\pi$
$234$		0			0
$235$			195.402i			0.831497i
$236$	−235.507	+	3.20088i	−0.997912	+	0.0135631i
$237$		0			0
$238$	−4.31327	+	4.37229i	−0.0181230	+	0.0183710i
$239$			253.050i			1.05879i	0.848377	+	0.529393i	$0.177580\pi$
$239$			253.050i			1.05879i	−0.848377	+	0.529393i	$0.822420\pi$
$240$		0			0
$241$	−345.448			−1.43339			−0.716697	−	0.697384i	$-0.754347\pi$
$241$	−345.448			−1.43339			−0.716697	+	0.697384i	$0.754347\pi$
$242$	364.687	+	359.764i	1.50697	+	1.48663i
$243$		0			0
$244$	−1.36130	−	100.159i	−0.00557910	−	0.410486i
$245$	229.539			0.936892
$246$		0			0
$247$		−	106.400i		−	0.430770i
$248$	140.181	+	134.579i	0.565246	+	0.542657i
$249$		0			0
$250$	123.055	+	121.394i	0.492221	+	0.485577i
$251$		−	290.826i		−	1.15867i	−0.815090	−	0.579334i	$-0.803313\pi$
$251$		−	290.826i		−	1.15867i	0.815090	−	0.579334i	$-0.196687\pi$
$252$		0			0
$253$	−224.991			−0.889294
$254$	194.209	−	196.866i	0.764601	−	0.775064i
$255$		0			0
$256$	255.622	−	13.9099i	0.998523	−	0.0543356i
$257$	−207.990			−0.809298			−0.404649	−	0.914472i	$-0.632606\pi$
$257$	−207.990			−0.809298			−0.404649	+	0.914472i	$0.632606\pi$
$258$		0			0
$259$		−	83.2367i		−	0.321377i
$260$	7.90534	+	581.641i	0.0304051	+	2.23708i
$261$		0			0
$262$	−319.340	+	323.709i	−1.21885	+	1.23553i
$263$		−	261.957i		−	0.996035i	−0.867167	−	0.498017i	$-0.834062\pi$
$263$		−	261.957i		−	0.996035i	0.867167	−	0.498017i	$-0.165938\pi$
$264$		0			0
$265$	97.1220			0.366498
$266$	20.0826	+	19.8115i	0.0754986	+	0.0744795i
$267$		0			0
$268$	364.976	−	4.96054i	1.36185	−	0.0185095i
$269$	92.1520			0.342572			0.171286	−	0.985221i	$-0.445208\pi$
$269$	92.1520			0.342572			0.171286	+	0.985221i	$0.445208\pi$
$270$		0			0
$271$		−	359.236i		−	1.32559i	−0.748799	−	0.662797i	$-0.769369\pi$
$271$		−	359.236i		−	1.32559i	0.748799	−	0.662797i	$-0.230631\pi$
$272$	−15.1783	+	0.412667i	−0.0558027	+	0.00151716i
$273$		0			0
$274$	172.006	+	169.685i	0.627761	+	0.619287i
$275$			203.770i			0.740983i
$276$		0			0
$277$	186.783			0.674306			0.337153	−	0.941450i	$-0.390536\pi$
$277$	186.783			0.674306			0.337153	+	0.941450i	$0.390536\pi$
$278$	−180.152	+	182.618i	−0.648030	+	0.656898i
$279$		0			0
$280$	−111.255	−	106.809i	−0.397338	−	0.381459i
$281$	−399.281			−1.42093			−0.710465	−	0.703733i	$-0.751515\pi$
$281$	−399.281			−1.42093			−0.710465	+	0.703733i	$0.751515\pi$
$282$		0			0
$283$		−	246.911i		−	0.872476i	−0.899831	−	0.436238i	$-0.856311\pi$
$283$		−	246.911i		−	0.872476i	0.899831	−	0.436238i	$-0.143689\pi$
$284$	−363.922	+	4.94623i	−1.28142	+	0.0174163i
$285$		0			0
$286$	665.823	−	674.934i	2.32805	−	2.35991i
$287$			78.0956i			0.272110i
$288$		0			0
$289$	−288.099			−0.996884
$290$	319.480	+	315.167i	1.10165	+	1.08678i
$291$		0			0
$292$	1.94128	+	142.831i	0.00664822	+	0.489148i
$293$	160.112			0.546456			0.273228	−	0.961949i	$-0.411909\pi$
$293$	160.112			0.546456			0.273228	+	0.961949i	$0.411909\pi$
$294$		0			0
$295$			350.796i			1.18914i
$296$	142.513	−	148.446i	0.481464	−	0.501506i
$297$		0			0
$298$	−353.240	−	348.472i	−1.18537	−	1.16937i
$299$			282.801i			0.945823i
$300$		0			0
$301$	42.3976			0.140856
$302$	153.411	−	155.511i	0.507984	−	0.514936i
$303$		0			0
$304$	1.89545	+	69.7166i	0.00623503	+	0.229331i
$305$	−149.190			−0.489146
$306$		0			0
$307$			162.736i			0.530085i	0.964237	+	0.265043i	$0.0853860\pi$
$307$			162.736i			0.530085i	−0.964237	+	0.265043i	$0.914614\pi$
$308$	3.41612	+	251.344i	0.0110913	+	0.816051i
$309$		0			0
$310$	203.260	−	206.042i	0.655678	−	0.664650i
$311$			32.2385i			0.103661i	0.998656	+	0.0518303i	$0.0165055\pi$
$311$			32.2385i			0.103661i	−0.998656	+	0.0518303i	$0.983494\pi$
$312$		0			0
$313$	−343.053			−1.09602			−0.548009	−	0.836473i	$-0.684614\pi$
$313$	−343.053			−1.09602			−0.548009	+	0.836473i	$0.684614\pi$
$314$	184.149	+	181.663i	0.586461	+	0.578544i
$315$		0			0
$316$	347.924	−	4.72879i	1.10103	−	0.0149645i
$317$	−98.3227			−0.310166			−0.155083	−	0.987901i	$-0.549565\pi$
$317$	−98.3227			−0.310166			−0.155083	+	0.987901i	$0.549565\pi$
$318$		0			0
$319$		−	731.438i		−	2.29291i
$320$	−15.5414	−	380.968i	−0.0485668	−	1.19053i
$321$		0			0
$322$	−53.3777	−	52.6571i	−0.165769	−	0.163532i
$323$		−	4.13658i		−	0.0128068i
$324$		0			0
$325$	256.127			0.788084
$326$	346.646	−	351.390i	1.06333	−	1.07788i
$327$		0			0
$328$	−133.711	+	139.277i	−0.407656	+	0.424625i
$329$	106.134			0.322597
$330$		0			0
$331$			509.436i			1.53908i	0.638597	+	0.769542i	$0.279515\pi$
$331$			509.436i			1.53908i	−0.638597	+	0.769542i	$0.720485\pi$
$332$	−35.2250	+	0.478759i	−0.106099	+	0.00144204i
$333$		0			0
$334$	28.9111	−	29.3067i	0.0865601	−	0.0877446i
$335$		−	543.643i		−	1.62282i
$336$		0			0
$337$	−178.023			−0.528257			−0.264128	−	0.964488i	$-0.585084\pi$
$337$	−178.023			−0.528257			−0.264128	+	0.964488i	$0.585084\pi$
$338$	−607.732	−	599.529i	−1.79802	−	1.77375i
$339$		0			0
$340$	0.307341	+	22.6128i	0.000903943	+	0.0665083i
$341$	−471.725			−1.38336
$342$		0			0
$343$		−	283.236i		−	0.825762i
$344$	75.6126	+	72.5909i	0.219804	+	0.211020i
$345$		0			0
$346$	244.544	+	241.243i	0.706775	+	0.697234i
$347$		−	332.419i		−	0.957981i	−0.877820	−	0.478990i	$-0.841003\pi$
$347$		−	332.419i		−	0.957981i	0.877820	−	0.478990i	$-0.158997\pi$
$348$		0			0
$349$	−346.039			−0.991515			−0.495758	−	0.868461i	$-0.665110\pi$
$349$	−346.039			−0.991515			−0.495758	+	0.868461i	$0.665110\pi$
$350$	−47.6905	+	48.3431i	−0.136259	+	0.138123i
$351$		0			0
$352$	−424.245	+	454.099i	−1.20524	+	1.29005i
$353$	316.212			0.895785			0.447893	−	0.894087i	$-0.352175\pi$
$353$	316.212			0.895785			0.447893	+	0.894087i	$0.352175\pi$
$354$		0			0
$355$			542.074i			1.52697i
$356$	8.09375	+	595.503i	0.0227352	+	1.67276i
$357$		0			0
$358$	3.97138	−	4.02572i	0.0110932	−	0.0112450i
$359$		−	407.303i		−	1.13455i	−0.823529	−	0.567274i	$-0.807998\pi$
$359$		−	407.303i		−	1.13455i	0.823529	−	0.567274i	$-0.192002\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−34.8305	−	34.3603i	−0.0962169	−	0.0949180i
$363$		0			0
$364$	315.924	−	4.29386i	0.867924	−	0.0117963i
$365$	212.752			0.582882
$366$		0			0
$367$		−	460.918i		−	1.25591i	−0.778251	−	0.627954i	$-0.783893\pi$
$367$		−	460.918i		−	1.25591i	0.778251	−	0.627954i	$-0.216107\pi$
$368$	−5.03792	−	185.300i	−0.0136900	−	0.503533i
$369$		0			0
$370$	−218.189	−	215.244i	−0.589701	−	0.581741i
$371$		−	52.7528i		−	0.142191i
$372$		0			0
$373$	−456.921			−1.22499			−0.612495	−	0.790474i	$-0.709834\pi$
$373$	−456.921			−1.22499			−0.612495	+	0.790474i	$0.709834\pi$
$374$	25.8856	−	26.2398i	0.0692129	−	0.0701600i
$375$		0			0
$376$	189.282	+	181.718i	0.503409	+	0.483291i
$377$	−919.374			−2.43866
$378$		0			0
$379$		−	339.563i		−	0.895946i	−0.894047	−	0.447973i	$-0.852146\pi$
$379$		−	339.563i		−	0.895946i	0.894047	−	0.447973i	$-0.147854\pi$
$380$	103.864	−	1.41167i	0.273327	−	0.00371491i
$381$		0			0
$382$	52.3980	−	53.1150i	0.137168	−	0.139045i
$383$			128.846i			0.336414i	0.985752	+	0.168207i	$0.0537977\pi$
$383$			128.846i			0.336414i	−0.985752	+	0.168207i	$0.946202\pi$
$384$		0			0
$385$	374.385			0.972428
$386$	25.3267	+	24.9848i	0.0656132	+	0.0647275i
$387$		0			0
$388$	10.4539	+	769.155i	0.0269431	+	1.98236i
$389$	−10.6346			−0.0273383			−0.0136692	−	0.999907i	$-0.504351\pi$
$389$	−10.6346			−0.0273383			−0.0136692	+	0.999907i	$0.504351\pi$
$390$		0			0
$391$			10.9946i			0.0281193i
$392$	213.464	−	222.349i	0.544551	−	0.567218i
$393$		0			0
$394$	−106.548	−	105.110i	−0.270427	−	0.266777i
$395$		−	518.245i		−	1.31201i
$396$		0			0
$397$	535.363			1.34852			0.674260	−	0.738494i	$-0.264463\pi$
$397$	535.363			1.34852			0.674260	+	0.738494i	$0.264463\pi$
$398$	37.1447	−	37.6530i	0.0933283	−	0.0946054i
$399$		0			0
$400$	−167.822	+	4.56274i	−0.419556	+	0.0114068i
$401$	75.3930			0.188012			0.0940062	−	0.995572i	$-0.470033\pi$
$401$	75.3930			0.188012			0.0940062	+	0.995572i	$0.470033\pi$
$402$		0			0
$403$			592.931i			1.47129i
$404$	−2.66168	−	195.835i	−0.00658832	−	0.484740i
$405$		0			0
$406$	171.186	−	173.529i	0.421641	−	0.427410i
$407$			499.537i			1.22736i
$408$		0			0
$409$	183.655			0.449035			0.224518	−	0.974470i	$-0.427919\pi$
$409$	183.655			0.449035			0.224518	+	0.974470i	$0.427919\pi$
$410$	204.713	+	201.949i	0.499300	+	0.492559i
$411$		0			0
$412$	592.806	−	8.05708i	1.43885	−	0.0195560i
$413$	190.538			0.461352
$414$		0			0
$415$			52.4688i			0.126431i
$416$	570.776	+	533.251i	1.37206	+	1.28185i
$417$		0			0
$418$	−120.524	−	118.897i	−0.288335	−	0.284442i
$419$		−	339.012i		−	0.809098i	−0.914516	−	0.404549i	$-0.867429\pi$
$419$		−	339.012i		−	0.809098i	0.914516	−	0.404549i	$-0.132571\pi$
$420$		0			0
$421$	767.739			1.82361			0.911804	−	0.410626i	$-0.134690\pi$
$421$	767.739			1.82361			0.911804	+	0.410626i	$0.134690\pi$
$422$	492.605	−	499.346i	1.16731	−	1.18328i
$423$		0			0
$424$	90.3204	−	94.0801i	0.213020	−	0.221887i
$425$	9.95762			0.0234297
$426$		0			0
$427$			81.0338i			0.189775i
$428$	197.658	−	2.68645i	0.461818	−	0.00627676i
$429$		0			0
$430$	109.637	−	111.137i	0.254970	−	0.258459i
$431$			297.068i			0.689253i	0.938740	+	0.344626i	$0.111994\pi$
$431$			297.068i			0.689253i	−0.938740	+	0.344626i	$0.888006\pi$
$432$		0			0
$433$	671.091			1.54986			0.774932	−	0.632045i	$-0.217784\pi$
$433$	671.091			1.54986			0.774932	+	0.632045i	$0.217784\pi$
$434$	−111.914	−	110.403i	−0.257865	−	0.254384i
$435$		0			0
$436$	0.436282	+	32.0998i	0.00100065	+	0.0736233i
$437$	50.5002			0.115561
$438$		0			0
$439$		−	319.050i		−	0.726765i	−0.931640	−	0.363382i	$-0.881622\pi$
$439$		−	319.050i		−	0.726765i	0.931640	−	0.363382i	$-0.118378\pi$
$440$	667.683	+	641.001i	1.51746	+	1.45682i
$441$		0			0
$442$	−32.9819	−	32.5367i	−0.0746198	−	0.0736125i
$443$		−	585.719i		−	1.32217i	−0.750313	−	0.661083i	$-0.770097\pi$
$443$		−	585.719i		−	1.32217i	0.750313	−	0.661083i	$-0.229903\pi$
$444$		0			0
$445$	887.022			1.99331
$446$	−527.485	+	534.703i	−1.18270	+	1.19889i
$447$		0			0
$448$	−206.927	+	8.44145i	−0.461890	+	0.0188425i
$449$	−98.6722			−0.219760			−0.109880	−	0.993945i	$-0.535047\pi$
$449$	−98.6722			−0.219760			−0.109880	+	0.993945i	$0.535047\pi$
$450$		0			0
$451$		−	468.683i		−	1.03921i
$452$	10.3668	+	762.742i	0.0229353	+	1.68748i
$453$		0			0
$454$	−304.924	+	309.096i	−0.671638	+	0.680829i
$455$		−	470.579i		−	1.03424i
$456$		0			0
$457$	53.7548			0.117625			0.0588127	−	0.998269i	$-0.481269\pi$
$457$	53.7548			0.117625			0.0588127	+	0.998269i	$0.481269\pi$
$458$	191.043	+	188.465i	0.417125	+	0.411495i
$459$		0			0
$460$	−276.061	+	3.75207i	−0.600134	+	0.00815668i
$461$	−336.038			−0.728934			−0.364467	−	0.931216i	$-0.618749\pi$
$461$	−336.038			−0.728934			−0.364467	+	0.931216i	$0.618749\pi$
$462$		0			0
$463$			725.299i			1.56652i	0.621694	+	0.783261i	$0.286445\pi$
$463$			725.299i			1.56652i	−0.621694	+	0.783261i	$0.713555\pi$
$464$	602.402	−	16.3780i	1.29828	−	0.0352975i
$465$		0			0
$466$	494.500	+	487.824i	1.06116	+	1.04683i
$467$		−	445.818i		−	0.954643i	−0.878729	−	0.477322i	$-0.841608\pi$
$467$		−	445.818i		−	0.954643i	0.878729	−	0.477322i	$-0.158392\pi$
$468$		0			0
$469$	−295.285			−0.629606
$470$	274.456	−	278.211i	0.583948	−	0.591939i
$471$		0			0
$472$	339.809	+	326.229i	0.719934	+	0.691164i
$473$	−254.445			−0.537939
$474$		0			0
$475$		−	45.7370i		−	0.0962884i
$476$	12.2824	−	0.166935i	0.0258033	−	0.000350704i
$477$		0			0
$478$	355.426	−	360.290i	0.743570	−	0.753745i
$479$		−	619.711i		−	1.29376i	−0.762592	−	0.646880i	$-0.776074\pi$
$479$		−	619.711i		−	1.29376i	0.762592	−	0.646880i	$-0.223926\pi$
$480$		0			0
$481$	627.889			1.30538
$482$	491.846	+	485.206i	1.02043	+	1.00665i
$483$		0			0
$484$	−13.9238	−	1024.46i	−0.0287683	−	2.11665i
$485$	1145.68			2.36223
$486$		0			0
$487$			774.007i			1.58934i	0.607044	+	0.794669i	$0.292355\pi$
$487$			774.007i			1.58934i	−0.607044	+	0.794669i	$0.707645\pi$
$488$	−138.742	+	144.517i	−0.284307	+	0.296141i
$489$		0			0
$490$	−326.815	−	322.403i	−0.666969	−	0.657966i
$491$			714.862i			1.45593i	0.685614	+	0.727965i	$0.259534\pi$
$491$			714.862i			1.45593i	−0.685614	+	0.727965i	$0.740466\pi$
$492$		0			0
$493$	−35.7431			−0.0725012
$494$	−149.446	+	151.491i	−0.302523	+	0.306663i
$495$		0			0
$496$	−10.5627	−	388.506i	−0.0212957	−	0.783279i
$497$	294.433			0.592421
$498$		0			0
$499$			501.079i			1.00417i	0.864820	+	0.502083i	$0.167433\pi$
$499$			501.079i			1.00417i	−0.864820	+	0.502083i	$0.832567\pi$
$500$	−4.69828	−	345.680i	−0.00939657	−	0.691360i
$501$		0			0
$502$	−408.485	+	414.075i	−0.813716	+	0.824850i
$503$		−	732.396i		−	1.45605i	−0.685548	−	0.728027i	$-0.740437\pi$
$503$		−	732.396i		−	1.45605i	0.685548	−	0.728027i	$-0.259563\pi$
$504$		0			0
$505$	−291.703			−0.577630
$506$	320.341	+	316.017i	0.633085	+	0.624539i
$507$		0			0
$508$	−553.025	+	7.51641i	−1.08863	+	0.0147961i
$509$	−879.418			−1.72774			−0.863869	−	0.503717i	$-0.831965\pi$
$509$	−879.418			−1.72774			−0.863869	+	0.503717i	$0.831965\pi$
$510$		0			0
$511$		−	115.558i		−	0.226141i
$512$	−383.489	−	339.234i	−0.749003	−	0.662567i
$513$		0			0
$514$	296.134	+	292.136i	0.576135	+	0.568358i
$515$		−	883.003i		−	1.71457i
$516$		0			0
$517$	−636.955			−1.23202
$518$	−116.912	+	118.512i	−0.225699	+	0.228787i
$519$		0			0
$520$	805.701	−	839.239i	1.54942	−	1.61392i
$521$	−441.154			−0.846744			−0.423372	−	0.905956i	$-0.639154\pi$
$521$	−441.154			−0.846744			−0.423372	+	0.905956i	$0.639154\pi$
$522$		0			0
$523$		−	567.571i		−	1.08522i	−0.839984	−	0.542611i	$-0.817436\pi$
$523$		−	567.571i		−	1.08522i	0.839984	−	0.542611i	$-0.182564\pi$
$524$	909.345	−	12.3593i	1.73539	−	0.0235865i
$525$		0			0
$526$	−367.937	+	372.972i	−0.699501	+	0.709072i
$527$			23.0517i			0.0437414i
$528$		0			0
$529$	394.776			0.746267
$530$	−138.281	−	136.415i	−0.260908	−	0.257386i
$531$		0			0
$532$	−0.766760	−	56.4150i	−0.00144128	−	0.106043i
$533$	−589.107			−1.10527
$534$		0			0
$535$		−	294.418i		−	0.550314i
$536$	−526.617	−	505.572i	−0.982494	−	0.943231i
$537$		0			0
$538$	−131.205	−	129.434i	−0.243876	−	0.240584i
$539$			748.231i			1.38818i
$540$		0			0
$541$	−404.864			−0.748363			−0.374182	−	0.927355i	$-0.622076\pi$
$541$	−404.864			−0.748363			−0.374182	+	0.927355i	$0.622076\pi$
$542$	−504.573	+	511.477i	−0.930946	+	0.943685i
$543$		0			0
$544$	22.1904	+	20.7315i	0.0407912	+	0.0381094i
$545$	47.8137			0.0877315
$546$		0			0
$547$		−	16.7796i		−	0.0306757i	−0.999882	−	0.0153378i	$-0.995118\pi$
$547$		−	16.7796i		−	0.0306757i	0.999882	−	0.0153378i	$-0.00488238\pi$
$548$	−6.56725	−	483.191i	−0.0119840	−	0.881735i
$549$		0			0
$550$	286.210	−	290.126i	0.520382	−	0.527502i
$551$			164.174i			0.297956i
$552$		0			0
$553$	−281.490			−0.509023
$554$	−265.940	−	262.350i	−0.480035	−	0.473555i
$555$		0			0
$556$	512.999	−	6.97239i	0.922659	−	0.0125403i
$557$	−494.207			−0.887266			−0.443633	−	0.896209i	$-0.646311\pi$
$557$	−494.207			−0.887266			−0.443633	+	0.896209i	$0.646311\pi$
$558$		0			0
$559$			319.823i			0.572133i
$560$	8.38306	+	308.338i	0.0149698	+	0.550604i
$561$		0			0
$562$	568.493	+	560.819i	1.01155	+	0.997898i
$563$			441.524i			0.784235i	0.919915	+	0.392118i	$0.128257\pi$
$563$			441.524i			0.784235i	−0.919915	+	0.392118i	$0.871743\pi$
$564$		0			0
$565$	1136.13			2.01085
$566$	−346.804	+	351.549i	−0.612727	+	0.621112i
$567$		0			0
$568$	525.097	+	504.112i	0.924466	+	0.887522i
$569$	843.702			1.48278			0.741390	−	0.671074i	$-0.234167\pi$
$569$	843.702			1.48278			0.741390	+	0.671074i	$0.234167\pi$
$570$		0			0
$571$			930.360i			1.62935i	0.579916	+	0.814676i	$0.303085\pi$
$571$			930.360i			1.62935i	−0.579916	+	0.814676i	$0.696915\pi$
$572$	−1895.99	+	25.7692i	−3.31466	+	0.0450510i
$573$		0			0
$574$	109.691	−	111.192i	0.191099	−	0.193714i
$575$			121.564i			0.211416i
$576$		0			0
$577$	−437.513			−0.758255			−0.379127	−	0.925345i	$-0.623776\pi$
$577$	−437.513			−0.758255			−0.379127	+	0.925345i	$0.623776\pi$
$578$	410.193	+	404.656i	0.709677	+	0.700097i
$579$		0			0
$580$	−12.1978	−	897.464i	−0.0210307	−	1.54735i
$581$	28.4990			0.0490516
$582$		0			0
$583$			316.590i			0.543037i
$584$	197.853	−	206.088i	0.338789	−	0.352891i
$585$		0			0
$586$	−227.965	−	224.888i	−0.389019	−	0.383768i
$587$			807.351i			1.37538i	0.726002	+	0.687692i	$0.241376\pi$
$587$			807.351i			1.37538i	−0.726002	+	0.687692i	$0.758624\pi$
$588$		0			0
$589$	105.880			0.179763
$590$	492.718	−	499.460i	0.835114	−	0.846542i
$591$		0			0
$592$	−411.412	+	11.1854i	−0.694953	+	0.0188943i
$593$	−881.434			−1.48640			−0.743199	−	0.669070i	$-0.766693\pi$
$593$	−881.434			−1.48640			−0.743199	+	0.669070i	$0.766693\pi$
$594$		0			0
$595$		−	18.2950i		−	0.0307479i
$596$	13.4868	+	992.303i	0.0226289	+	1.66494i
$597$		0			0
$598$	397.214	−	402.650i	0.664238	−	0.673327i
$599$		−	293.198i		−	0.489480i	−0.969589	−	0.244740i	$-0.921297\pi$
$599$		−	293.198i		−	0.489480i	0.969589	−	0.244740i	$-0.0787025\pi$
$600$		0			0
$601$	705.067			1.17316			0.586578	−	0.809892i	$-0.300475\pi$
$601$	705.067			1.17316			0.586578	+	0.809892i	$0.300475\pi$
$602$	−60.3654	−	59.5505i	−0.100275	−	0.0989211i
$603$		0			0
$604$	−436.851	+	5.93743i	−0.723264	+	0.00983019i
$605$	−1525.96			−2.52225
$606$		0			0
$607$		−	753.115i		−	1.24072i	−0.784318	−	0.620359i	$-0.786987\pi$
$607$		−	753.115i		−	1.24072i	0.784318	−	0.620359i	$-0.213013\pi$
$608$	95.2232	−	101.924i	0.156617	−	0.167638i
$609$		0			0
$610$	212.415	+	209.547i	0.348221	+	0.343520i
$611$			800.615i			1.31033i
$612$		0			0
$613$	−389.239			−0.634974			−0.317487	−	0.948263i	$-0.602839\pi$
$613$	−389.239			−0.634974			−0.317487	+	0.948263i	$0.602839\pi$
$614$	228.574	−	231.702i	0.372271	−	0.377365i
$615$		0			0
$616$	348.166	−	362.659i	0.565205	−	0.588732i
$617$	489.497			0.793350			0.396675	−	0.917959i	$-0.370164\pi$
$617$	489.497			0.793350			0.396675	+	0.917959i	$0.370164\pi$
$618$		0			0
$619$		−	50.9447i		−	0.0823016i	−0.999153	−	0.0411508i	$-0.986898\pi$
$619$		−	50.9447i		−	0.0823016i	0.999153	−	0.0411508i	$-0.0131024\pi$
$620$	−578.800	+	7.86672i	−0.933548	+	0.0126883i
$621$		0			0
$622$	45.2812	−	45.9008i	0.0727994	−	0.0737955i
$623$		−	481.795i		−	0.773346i
$624$		0			0
$625$	−777.221			−1.24355
$626$	488.436	+	481.843i	0.780250	+	0.769717i
$627$		0			0
$628$	−7.03084	−	517.300i	−0.0111956	−	0.823726i
$629$	24.4108			0.0388089
$630$		0			0
$631$		−	45.2806i		−	0.0717600i	−0.999356	−	0.0358800i	$-0.988577\pi$
$631$		−	45.2806i		−	0.0717600i	0.999356	−	0.0358800i	$-0.0114234\pi$
$632$	−502.013	−	481.952i	−0.794325	−	0.762582i
$633$		0			0
$634$	139.991	+	138.101i	0.220806	+	0.217825i
$635$			823.749i			1.29724i
$636$		0			0
$637$	940.483			1.47643
$638$	−1027.36	+	1041.41i	−1.61028	+	1.63231i
$639$		0			0
$640$	−512.969	+	564.248i	−0.801515	+	0.881638i
$641$	144.569			0.225537			0.112769	−	0.993621i	$-0.464028\pi$
$641$	144.569			0.225537			0.112769	+	0.993621i	$0.464028\pi$
$642$		0			0
$643$		−	1175.05i		−	1.82745i	−0.406329	−	0.913727i	$-0.633191\pi$
$643$		−	1175.05i		−	1.82745i	0.406329	−	0.913727i	$-0.366809\pi$
$644$	2.03797	+	149.946i	0.00316456	+	0.232835i
$645$		0			0
$646$	−5.81012	+	5.88963i	−0.00899400	+	0.00911707i
$647$			537.844i			0.831288i	0.909527	+	0.415644i	$0.136444\pi$
$647$			537.844i			0.831288i	−0.909527	+	0.415644i	$0.863556\pi$
$648$		0			0
$649$	−1143.50			−1.76193
$650$	−364.672	−	359.749i	−0.561033	−	0.553460i
$651$		0			0
$652$	−987.103	+	13.4161i	−1.51396	+	0.0205769i
$653$	23.5689			0.0360932			0.0180466	−	0.999837i	$-0.494255\pi$
$653$	23.5689			0.0360932			0.0180466	+	0.999837i	$0.494255\pi$
$654$		0			0
$655$		−	1354.50i		−	2.06794i
$656$	386.001	−	10.4945i	0.588416	−	0.0159978i
$657$		0			0
$658$	−151.113	−	149.073i	−0.229655	−	0.226555i
$659$		−	941.065i		−	1.42802i	−0.700136	−	0.714010i	$-0.746877\pi$
$659$		−	941.065i		−	1.42802i	0.700136	−	0.714010i	$-0.253123\pi$
$660$		0			0
$661$	562.343			0.850745			0.425373	−	0.905018i	$-0.360143\pi$
$661$	562.343			0.850745			0.425373	+	0.905018i	$0.360143\pi$
$662$	715.540	−	725.331i	1.08088	−	1.09567i
$663$		0			0
$664$	50.8255	+	48.7944i	0.0765445	+	0.0734855i
$665$	−84.0320			−0.126364
$666$		0			0
$667$		−	436.358i		−	0.654210i
$668$	−82.3267	+	1.11894i	−0.123244	+	0.00167506i
$669$		0			0
$670$	−763.586	+	774.035i	−1.13968	+	1.15528i
$671$		−	486.316i		−	0.724763i
$672$		0			0
$673$	−732.788			−1.08884			−0.544419	−	0.838813i	$-0.683250\pi$
$673$	−732.788			−1.08884			−0.544419	+	0.838813i	$0.683250\pi$
$674$	253.467	+	250.045i	0.376064	+	0.370987i
$675$		0			0
$676$	23.2034	+	1707.21i	0.0343245	+	2.52545i
$677$	−215.961			−0.318998			−0.159499	−	0.987198i	$-0.550988\pi$
$677$	−215.961			−0.318998			−0.159499	+	0.987198i	$0.550988\pi$
$678$		0			0
$679$		−	622.288i		−	0.916477i
$680$	31.3237	−	32.6276i	0.0460643	−	0.0479818i
$681$		0			0
$682$	671.638	+	662.571i	0.984806	+	0.971512i
$683$			615.156i			0.900668i	0.892860	+	0.450334i	$0.148695\pi$
$683$			615.156i			0.900668i	−0.892860	+	0.450334i	$0.851305\pi$
$684$		0			0
$685$	−719.728			−1.05070
$686$	−397.825	+	403.269i	−0.579920	+	0.587856i
$687$		0			0
$688$	−5.69743	−	209.558i	−0.00828115	−	0.304590i
$689$	397.936			0.577555
$690$		0			0
$691$		−	698.251i		−	1.01049i	−0.862975	−	0.505247i	$-0.831402\pi$
$691$		−	698.251i		−	1.01049i	0.862975	−	0.505247i	$-0.168598\pi$
$692$	−9.33675	−	686.959i	−0.0134924	−	0.992715i
$693$		0			0
$694$	−466.907	+	473.296i	−0.672776	+	0.681982i
$695$		−	764.128i		−	1.09947i
$696$		0			0
$697$	−22.9031			−0.0328595
$698$	492.687	+	486.036i	0.705855	+	0.696327i
$699$		0			0
$700$	135.803	−	1.84575i	0.194004	−	0.00263679i
$701$	−54.6385			−0.0779436			−0.0389718	−	0.999240i	$-0.512408\pi$
$701$	−54.6385			−0.0779436			−0.0389718	+	0.999240i	$0.512408\pi$
$702$		0			0
$703$		−	112.123i		−	0.159492i
$704$	1241.85	−	50.6605i	1.76399	−	0.0719610i
$705$		0			0
$706$	−450.220	−	444.143i	−0.637705	−	0.629097i
$707$			158.441i			0.224104i
$708$		0			0
$709$	195.286			0.275439			0.137719	−	0.990471i	$-0.456023\pi$
$709$	195.286			0.275439			0.137719	+	0.990471i	$0.456023\pi$
$710$	761.382	−	771.801i	1.07237	−	1.08704i
$711$		0			0
$712$	824.903	−	859.241i	1.15857	−	1.20680i
$713$	−281.420			−0.394698
$714$		0			0
$715$			2824.13i			3.94984i
$716$	−11.3088	+	0.153703i	−0.0157944	+	0.000214669i
$717$		0			0
$718$	−572.086	+	579.914i	−0.796777	+	0.807680i
$719$		−	333.639i		−	0.464031i	−0.972712	−	0.232016i	$-0.925468\pi$
$719$		−	333.639i		−	0.464031i	0.972712	−	0.232016i	$-0.0745321\pi$
$720$		0			0
$721$	−479.612			−0.665204
$722$	27.0520	+	26.6868i	0.0374682	+	0.0369624i
$723$		0			0
$724$	1.32984	+	97.8438i	0.00183679	+	0.135143i
$725$	−395.201			−0.545105
$726$		0			0
$727$			645.513i			0.887914i	0.896048	+	0.443957i	$0.146426\pi$
$727$			645.513i			0.887914i	−0.896048	+	0.443957i	$0.853574\pi$
$728$	−455.841	−	437.624i	−0.626155	−	0.601132i
$729$		0			0
$730$	−302.914	−	298.825i	−0.414951	−	0.409349i
$731$			12.4339i			0.0170095i
$732$		0			0
$733$	−493.265			−0.672941			−0.336470	−	0.941694i	$-0.609233\pi$
$733$	−493.265			−0.672941			−0.336470	+	0.941694i	$0.609233\pi$
$734$	−647.392	+	656.251i	−0.882005	+	0.894074i
$735$		0			0
$736$	−253.094	+	270.905i	−0.343878	+	0.368077i
$737$	1772.13			2.40451
$738$		0			0
$739$		−	55.3844i		−	0.0749450i	−0.999298	−	0.0374725i	$-0.988069\pi$
$739$		−	55.3844i		−	0.0749450i	0.999298	−	0.0374725i	$-0.0119307\pi$
$740$	8.33053	+	612.925i	0.0112575	+	0.828277i
$741$		0			0
$742$	−74.0950	+	75.1089i	−0.0998585	+	0.101225i
$743$		−	640.483i		−	0.862022i	−0.902347	−	0.431011i	$-0.858157\pi$
$743$		−	640.483i		−	0.862022i	0.902347	−	0.431011i	$-0.141843\pi$
$744$		0			0
$745$	1478.07			1.98398
$746$	650.560	+	641.778i	0.872065	+	0.860293i
$747$		0			0
$748$	−73.7114	+	1.00184i	−0.0985447	+	0.00133936i
$749$	−159.916			−0.213506
$750$		0			0
$751$		−	1112.92i		−	1.48192i	−0.671552	−	0.740958i	$-0.734372\pi$
$751$		−	1112.92i		−	1.48192i	0.671552	−	0.740958i	$-0.265628\pi$
$752$	−14.2624	−	524.587i	−0.0189660	−	0.697590i
$753$		0			0
$754$	1309.00	+	1291.33i	1.73607	+	1.71263i
$755$			650.704i			0.861860i
$756$		0			0
$757$	−1365.36			−1.80364			−0.901821	−	0.432110i	$-0.857769\pi$
$757$	−1365.36			−1.80364			−0.901821	+	0.432110i	$0.857769\pi$
$758$	−476.941	+	483.467i	−0.629210	+	0.637820i
$759$		0			0
$760$	−149.864	−	143.875i	−0.197189	−	0.189309i
$761$	788.208			1.03575			0.517877	−	0.855455i	$-0.326723\pi$
$761$	788.208			1.03575			0.517877	+	0.855455i	$0.326723\pi$
$762$		0			0
$763$		−	25.9705i		−	0.0340373i
$764$	−149.208	+	2.02795i	−0.195298	+	0.00265438i
$765$		0			0
$766$	180.974	−	183.450i	0.236258	−	0.239491i
$767$			1437.31i			1.87393i
$768$		0			0
$769$	−183.013			−0.237988			−0.118994	−	0.992895i	$-0.537967\pi$
$769$	−183.013			−0.237988			−0.118994	+	0.992895i	$0.537967\pi$
$770$	−533.045	−	525.850i	−0.692267	−	0.682922i
$771$		0			0
$772$	−0.966980	−	71.1463i	−0.00125256	−	0.0921584i
$773$	262.180			0.339171			0.169586	−	0.985515i	$-0.445757\pi$
$773$	262.180			0.339171			0.169586	+	0.985515i	$0.445757\pi$
$774$		0			0
$775$			254.876i			0.328873i
$776$	1065.45	−	1109.80i	1.37300	−	1.43015i
$777$		0			0
$778$	15.1415	+	14.9371i	0.0194620	+	0.0191993i
$779$			105.198i			0.135042i
$780$		0			0
$781$	−1767.01			−2.26250
$782$	15.4427	−	15.6541i	0.0197477	−	0.0200180i
$783$		0			0
$784$	−616.233	+	16.7541i	−0.786012	+	0.0213700i
$785$	−770.535			−0.981573
$786$		0			0
$787$			945.850i			1.20184i	0.799308	+	0.600921i	$0.205199\pi$
$787$			945.850i			1.20184i	−0.799308	+	0.600921i	$0.794801\pi$
$788$	4.06804	+	299.309i	0.00516249	+	0.379834i
$789$		0			0
$790$	−727.911	+	737.872i	−0.921407	+	0.934015i
$791$		−	617.100i		−	0.780151i
$792$		0			0
$793$	−611.271			−0.770833
$794$	−762.245	−	751.955i	−0.960006	−	0.947047i
$795$		0			0
$796$	−105.773	+	1.43760i	−0.132880	+	0.00180603i
$797$	1178.02			1.47806			0.739032	−	0.673671i	$-0.235283\pi$
$797$	1178.02			1.47806			0.739032	+	0.673671i	$0.235283\pi$
$798$		0			0
$799$			31.1260i			0.0389562i
$800$	245.353	+	229.222i	0.306691	+	0.286528i
$801$		0			0
$802$	−107.344	−	105.895i	−0.133845	−	0.132038i
$803$			693.511i			0.863650i
$804$		0			0
$805$	223.349			0.277452
$806$	832.813	−	844.209i	1.03327	−	1.04741i
$807$		0			0
$808$	−271.275	+	282.567i	−0.335736	+	0.349711i
$809$	887.826			1.09744			0.548718	−	0.836007i	$-0.315116\pi$
$809$	887.826			1.09744			0.548718	+	0.836007i	$0.315116\pi$
$810$		0			0
$811$			1294.73i			1.59646i	0.602354	+	0.798229i	$0.294230\pi$
$811$			1294.73i			1.59646i	−0.602354	+	0.798229i	$0.705770\pi$
$812$	−487.467	+	6.62537i	−0.600328	+	0.00815932i
$813$		0			0
$814$	701.635	−	711.236i	0.861959	−	0.873754i
$815$			1470.32i			1.80408i
$816$		0			0
$817$	57.1111			0.0699034
$818$	−261.487	−	257.957i	−0.319666	−	0.315351i
$819$		0			0
$820$	−7.81599	−	575.067i	−0.00953169	−	0.701302i
$821$	−623.409			−0.759329			−0.379664	−	0.925124i	$-0.623961\pi$
$821$	−623.409			−0.759329			−0.379664	+	0.925124i	$0.623961\pi$
$822$		0			0
$823$		−	551.433i		−	0.670028i	−0.942213	−	0.335014i	$-0.891259\pi$
$823$		−	551.433i		−	0.670028i	0.942213	−	0.335014i	$-0.108741\pi$
$824$	−855.348	−	821.166i	−1.03804	−	0.996561i
$825$		0			0
$826$	−271.287	−	267.624i	−0.328434	−	0.324001i
$827$		−	1369.70i		−	1.65623i	−0.560557	−	0.828116i	$-0.689413\pi$
$827$		−	1369.70i		−	1.65623i	0.560557	−	0.828116i	$-0.310587\pi$
$828$		0			0
$829$	211.957			0.255679			0.127839	−	0.991795i	$-0.459196\pi$
$829$	211.957			0.255679			0.127839	+	0.991795i	$0.459196\pi$
$830$	73.6962	−	74.7047i	0.0887906	−	0.0900056i
$831$		0			0
$832$	−63.6773	−	1560.93i	−0.0765352	−	1.87612i
$833$	36.5637			0.0438940
$834$		0			0
$835$			122.628i			0.146860i
$836$	4.60163	+	338.569i	0.00550435	+	0.404987i
$837$		0			0
$838$	−476.166	+	482.682i	−0.568218	+	0.575993i
$839$		−	782.828i		−	0.933049i	−0.884508	−	0.466525i	$-0.845506\pi$
$839$		−	782.828i		−	0.933049i	0.884508	−	0.466525i	$-0.154494\pi$
$840$		0			0
$841$	577.582			0.686780
$842$	−1093.10	−	1078.34i	−1.29822	−	1.28069i
$843$		0			0
$844$	−1402.73	+	19.0652i	−1.66201	+	0.0225890i
$845$	2542.94			3.00940
$846$		0			0
$847$			828.842i			0.978562i
$848$	−260.740	+	7.08896i	−0.307476	+	0.00835962i
$849$		0			0
$850$	−14.1776	−	13.9862i	−0.0166795	−	0.0164543i
$851$			298.012i			0.350190i
$852$		0			0
$853$	−814.796			−0.955212			−0.477606	−	0.878574i	$-0.658495\pi$
$853$	−814.796			−0.955212			−0.477606	+	0.878574i	$0.658495\pi$
$854$	113.818	−	115.375i	0.133276	−	0.135100i
$855$		0			0
$856$	−285.197	−	273.800i	−0.333174	−	0.319859i
$857$	533.483			0.622501			0.311250	−	0.950328i	$-0.399252\pi$
$857$	533.483			0.622501			0.311250	+	0.950328i	$0.399252\pi$
$858$		0			0
$859$			1150.42i			1.33926i	0.742696	+	0.669629i	$0.233547\pi$
$859$			1150.42i			1.33926i	−0.742696	+	0.669629i	$0.766453\pi$
$860$	−312.201	+	4.24325i	−0.363024	+	0.00493402i
$861$		0			0
$862$	417.253	−	422.963i	0.484052	−	0.490676i
$863$			1164.39i			1.34924i	0.738167	+	0.674618i	$0.235692\pi$
$863$			1164.39i			1.34924i	−0.738167	+	0.674618i	$0.764308\pi$
$864$		0			0
$865$	−1023.25			−1.18295
$866$	−955.493	−	942.595i	−1.10334	−	1.08845i
$867$		0			0
$868$	4.27289	+	314.381i	0.00492268	+	0.362190i
$869$	1689.33			1.94400
$870$		0			0
$871$		−	2227.46i		−	2.55736i
$872$	44.4652	−	46.3162i	0.0509922	−	0.0531149i
$873$		0			0
$874$	−71.9017	−	70.9310i	−0.0822673	−	0.0811568i
$875$			279.674i			0.319627i
$876$		0			0
$877$	−123.293			−0.140585			−0.0702927	−	0.997526i	$-0.522393\pi$
$877$	−123.293			−0.140585			−0.0702927	+	0.997526i	$0.522393\pi$
$878$	−448.128	+	454.260i	−0.510396	+	0.517381i
$879$		0			0
$880$	−50.3101	−	1850.46i	−0.0571706	−	2.10280i
$881$	−702.214			−0.797064			−0.398532	−	0.917154i	$-0.630480\pi$
$881$	−702.214			−0.797064			−0.398532	+	0.917154i	$0.630480\pi$
$882$		0			0
$883$			185.366i			0.209928i	0.994476	+	0.104964i	$0.0334727\pi$
$883$			185.366i			0.209928i	−0.994476	+	0.104964i	$0.966527\pi$
$884$	1.25926	+	92.6509i	0.00142450	+	0.104809i
$885$		0			0
$886$	−822.685	+	833.942i	−0.928538	+	0.941244i
$887$		−	90.6065i		−	0.102149i	−0.998695	−	0.0510747i	$-0.983735\pi$
$887$		−	90.6065i		−	0.102149i	0.998695	−	0.0510747i	$-0.0162647\pi$
$888$		0			0
$889$	447.428			0.503293
$890$	−1262.93	−	1245.89i	−1.41903	−	1.39987i
$891$		0			0
$892$	1502.06	−	20.4151i	1.68392	−	0.0228869i
$893$	142.967			0.160097
$894$		0			0
$895$			16.8449i			0.0188211i
$896$	306.477	+	278.624i	0.342050	+	0.310965i
$897$		0			0
$898$	140.489	+	138.592i	0.156446	+	0.154334i
$899$		−	914.883i		−	1.01767i
$900$		0			0
$901$	15.4708			0.0171707
$902$	−658.298	+	667.306i	−0.729821	+	0.739807i
$903$		0			0
$904$	1056.56	−	1100.55i	1.16877	−	1.21742i
$905$	145.742			0.161040
$906$		0			0
$907$			306.895i			0.338363i	0.985585	+	0.169181i	$0.0541123\pi$
$907$			306.895i			0.338363i	−0.985585	+	0.169181i	$0.945888\pi$
$908$	868.295	−	11.8014i	0.956273	−	0.0129971i
$909$		0			0
$910$	−660.962	+	670.007i	−0.726332	+	0.736271i
$911$		−	1120.43i		−	1.22989i	−0.788571	−	0.614944i	$-0.789179\pi$
$911$		−	1120.43i		−	1.22989i	0.788571	−	0.614944i	$-0.210821\pi$
$912$		0			0
$913$	−171.034			−0.187332
$914$	−76.5356	−	75.5024i	−0.0837369	−	0.0826066i
$915$		0			0
$916$	−7.29409	−	536.668i	−0.00796298	−	0.585882i
$917$	−735.710			−0.802301
$918$		0			0
$919$		−	1117.64i		−	1.21615i	−0.793881	−	0.608073i	$-0.791943\pi$
$919$		−	1117.64i		−	1.21615i	0.793881	−	0.608073i	$-0.208057\pi$
$920$	398.324	+	382.406i	0.432961	+	0.415658i
$921$		0			0
$922$	478.449	+	471.990i	0.518925	+	0.511920i
$923$			2221.03i			2.40631i
$924$		0			0
$925$	269.903			0.291787
$926$	1018.73	−	1032.67i	1.10015	−	1.11520i
$927$		0			0
$928$	−880.699	−	822.798i	−0.949029	−	0.886636i
$929$	−747.184			−0.804288			−0.402144	−	0.915576i	$-0.631735\pi$
$929$	−747.184			−0.804288			−0.402144	+	0.915576i	$0.631735\pi$
$930$		0			0
$931$		−	167.943i		−	0.180390i
$932$	−18.8801	−	1389.12i	−0.0202577	−	1.49047i
$933$		0			0
$934$	−626.184	+	634.752i	−0.670432	+	0.679606i
$935$			109.796i			0.117428i
$936$		0			0
$937$	750.568			0.801033			0.400516	−	0.916290i	$-0.368831\pi$
$937$	750.568			0.801033			0.400516	+	0.916290i	$0.368831\pi$
$938$	420.425	+	414.749i	0.448214	+	0.442163i
$939$		0			0
$940$	−781.535	+	10.6222i	−0.831420	+	0.0113002i
$941$	−470.304			−0.499792			−0.249896	−	0.968273i	$-0.580396\pi$
$941$	−470.304			−0.499792			−0.249896	+	0.968273i	$0.580396\pi$
$942$		0			0
$943$		−	279.605i		−	0.296506i
$944$	−25.6047	−	941.768i	−0.0271236	−	0.997635i
$945$		0			0
$946$	362.277	+	357.386i	0.382956	+	0.377787i
$947$			542.946i			0.573333i	0.958031	+	0.286666i	$0.0925471\pi$
$947$			542.946i			0.573333i	−0.958031	+	0.286666i	$0.907453\pi$
$948$		0			0
$949$	871.703			0.918549
$950$	−64.2408	+	65.1199i	−0.0676219	+	0.0685473i
$951$		0			0
$952$	−17.7220	−	17.0138i	−0.0186156	−	0.0178716i
$953$	−237.146			−0.248842			−0.124421	−	0.992230i	$-0.539707\pi$
$953$	−237.146			−0.248842			−0.124421	+	0.992230i	$0.539707\pi$
$954$		0			0
$955$			222.250i			0.232722i
$956$	−1012.11	+	13.7560i	−1.05869	+	0.0143891i
$957$		0			0
$958$	−870.428	+	882.338i	−0.908588	+	0.921021i
$959$			390.928i			0.407641i
$960$		0			0
$961$	370.966			0.386021
$962$	−893.982	−	881.914i	−0.929295	−	0.916751i
$963$		0			0
$964$	−18.7788	−	1381.66i	−0.0194801	−	1.43326i
$965$	−105.975			−0.109818
$966$		0			0
$967$		−	1673.70i		−	1.73081i	−0.501070	−	0.865407i	$-0.667060\pi$
$967$		−	1673.70i		−	1.73081i	0.501070	−	0.865407i	$-0.332940\pi$
$968$	−1419.10	+	1478.17i	−1.46601	+	1.52704i
$969$		0			0
$970$	−1631.21	−	1609.19i	−1.68166	−	1.65896i
$971$		−	553.943i		−	0.570487i	−0.958455	−	0.285244i	$-0.907926\pi$
$971$		−	553.943i		−	0.570487i	0.958455	−	0.285244i	$-0.0920745\pi$
$972$		0			0
$973$	−415.044			−0.426561
$974$	1087.15	−	1102.02i	1.11617	−	1.13144i
$975$		0			0
$976$	400.524	−	10.8894i	0.410372	−	0.0111572i
$977$	1319.85			1.35092			0.675460	−	0.737396i	$-0.263945\pi$
$977$	1319.85			1.35092			0.675460	+	0.737396i	$0.263945\pi$
$978$		0			0
$979$			2891.44i			2.95347i
$980$	12.4779	+	918.070i	0.0127325	+	0.936806i
$981$		0			0
$982$	1004.07	−	1017.81i	1.02248	−	1.03647i
$983$		−	1598.94i		−	1.62659i	−0.581851	−	0.813296i	$-0.697671\pi$
$983$		−	1598.94i		−	1.62659i	0.581851	−	0.813296i	$-0.302329\pi$
$984$		0			0
$985$	445.831			0.452621
$986$	50.8907	+	50.2037i	0.0516132	+	0.0509165i
$987$		0			0
$988$	425.561	−	5.78399i	0.430730	−	0.00585424i
$989$	−151.796			−0.153484
$990$		0			0
$991$		−	1227.92i		−	1.23907i	−0.784970	−	0.619533i	$-0.787322\pi$
$991$		−	1227.92i		−	1.23907i	0.784970	−	0.619533i	$-0.212678\pi$
$992$	−530.646	+	567.988i	−0.534925	+	0.572568i
$993$		0			0
$994$	−419.211	−	413.552i	−0.421742	−	0.416049i
$995$			157.552i			0.158343i
$996$		0			0
$997$	570.772			0.572489			0.286245	−	0.958157i	$-0.407593\pi$
$997$	570.772			0.572489			0.286245	+	0.958157i	$0.407593\pi$
$998$	703.800	−	713.431i	0.705211	−	0.714861i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.d.343.9	✓	36
3.2	odd	2	inner	684.3.g.d.343.28	yes	36
4.3	odd	2	inner	684.3.g.d.343.10	yes	36
12.11	even	2	inner	684.3.g.d.343.27	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
684.3.g.d.343.9	✓	36	1.1	even	1	trivial
684.3.g.d.343.10	yes	36	4.3	odd	2	inner
684.3.g.d.343.27	yes	36	12.11	even	2	inner
684.3.g.d.343.28	yes	36	3.2	odd	2	inner

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 684 = 2^{2} \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	684.g (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.42379 - 1.40457i) q^{2} +(0.0543607 + 3.99963i) q^{4} +5.95758 q^{5} -3.23592i q^{7} +(5.54037 - 5.77099i) q^{8} +O(q^{10})\)	\(q+(-1.42379 - 1.40457i) q^{2} +(0.0543607 + 3.99963i) q^{4} +5.95758 q^{5} -3.23592i q^{7} +(5.54037 - 5.77099i) q^{8} +(-8.48235 - 8.36785i) q^{10} +19.4200i q^{11} +24.4099 q^{13} +(-4.54508 + 4.60727i) q^{14} +(-15.9941 + 0.434846i) q^{16} +0.948997 q^{17} -4.35890i q^{19} +(0.323858 + 23.8281i) q^{20} +(27.2768 - 27.6501i) q^{22} +11.5855i q^{23} +10.4928 q^{25} +(-34.7545 - 34.2854i) q^{26} +(12.9425 - 0.175907i) q^{28} -37.6641 q^{29} +24.2906i q^{31} +(23.3830 + 21.8457i) q^{32} +(-1.35117 - 1.33293i) q^{34} -19.2783i q^{35} +25.7227 q^{37} +(-6.12238 + 6.20616i) q^{38} +(33.0072 - 34.3812i) q^{40} -24.1340 q^{41} +13.1022i q^{43} +(-77.6730 + 1.05569i) q^{44} +(16.2727 - 16.4954i) q^{46} +32.7988i q^{47} +38.5288 q^{49} +(-14.9395 - 14.7379i) q^{50} +(1.32694 + 97.6304i) q^{52} +16.3022 q^{53} +115.696i q^{55} +(-18.6745 - 17.9282i) q^{56} +(53.6257 + 52.9019i) q^{58} +58.8822i q^{59} -25.0420 q^{61} +(34.1179 - 34.5848i) q^{62} +(-2.60867 - 63.9468i) q^{64} +145.424 q^{65} -91.2524i q^{67} +(0.0515881 + 3.79564i) q^{68} +(-27.0777 + 27.4482i) q^{70} +90.9890i q^{71} +35.7111 q^{73} +(-36.6238 - 36.1294i) q^{74} +(17.4340 - 0.236953i) q^{76} +62.8417 q^{77} -86.9891i q^{79} +(-95.2861 + 2.59063i) q^{80} +(34.3617 + 33.8979i) q^{82} +8.80707i q^{83} +5.65373 q^{85} +(18.4030 - 18.6548i) q^{86} +(112.073 + 107.594i) q^{88} +148.890 q^{89} -78.9883i q^{91} +(-46.3378 + 0.629798i) q^{92} +(46.0683 - 46.6987i) q^{94} -25.9685i q^{95} +192.306 q^{97} +(-54.8570 - 54.1165i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 12 q^{4}+O(q^{10}) \) 36 * q - 12 * q^4	\( 36 q - 12 q^{4} + 8 q^{10} + 24 q^{13} - 92 q^{16} - 60 q^{22} + 44 q^{25} - 48 q^{28} - 148 q^{34} + 200 q^{37} + 180 q^{40} + 140 q^{46} - 332 q^{49} + 60 q^{52} - 64 q^{58} + 40 q^{61} + 60 q^{64} + 36 q^{70} - 200 q^{73} + 312 q^{82} + 16 q^{85} + 104 q^{88} + 184 q^{94} + 280 q^{97}+O(q^{100}) \) 36 * q - 12 * q^4 + 8 * q^10 + 24 * q^13 - 92 * q^16 - 60 * q^22 + 44 * q^25 - 48 * q^28 - 148 * q^34 + 200 * q^37 + 180 * q^40 + 140 * q^46 - 332 * q^49 + 60 * q^52 - 64 * q^58 + 40 * q^61 + 60 * q^64 + 36 * q^70 - 200 * q^73 + 312 * q^82 + 16 * q^85 + 104 * q^88 + 184 * q^94 + 280 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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