LMFDB - Embedded newform 684.3.g.c.343.6

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:	no (minimal twist has level 228)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			343.6
Character	$\chi$	$=$	684.343
Dual form			684.3.g.c.343.5

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.79512 + 0.881776i) q^{2} +(2.44494 - 3.16579i) q^{4} +9.55892 q^{5} -12.8591i q^{7} +(-1.59745 + 7.83889i) q^{8} +O(q^{10})$	\(q+(-1.79512 + 0.881776i) q^{2} +(2.44494 - 3.16579i) q^{4} +9.55892 q^{5} -12.8591i q^{7} +(-1.59745 + 7.83889i) q^{8} +(-17.1594 + 8.42882i) q^{10} -1.12979i q^{11} +7.90255 q^{13} +(11.3388 + 23.0836i) q^{14} +(-4.04452 - 15.4804i) q^{16} +24.0897 q^{17} -4.35890i q^{19} +(23.3710 - 30.2616i) q^{20} +(0.996226 + 2.02812i) q^{22} +11.4459i q^{23} +66.3729 q^{25} +(-14.1861 + 6.96828i) q^{26} +(-40.7091 - 31.4396i) q^{28} -27.7128 q^{29} +2.59314i q^{31} +(20.9106 + 24.2228i) q^{32} +(-43.2441 + 21.2417i) q^{34} -122.919i q^{35} -27.2994 q^{37} +(3.84357 + 7.82477i) q^{38} +(-15.2699 + 74.9313i) q^{40} -39.4375 q^{41} +3.30095i q^{43} +(-3.57670 - 2.76228i) q^{44} +(-10.0928 - 20.5469i) q^{46} -20.9106i q^{47} -116.355 q^{49} +(-119.148 + 58.5260i) q^{50} +(19.3213 - 25.0179i) q^{52} -19.2748 q^{53} -10.7996i q^{55} +(100.801 + 20.5417i) q^{56} +(49.7479 - 24.4365i) q^{58} -25.7718i q^{59} +104.935 q^{61} +(-2.28657 - 4.65501i) q^{62} +(-58.8963 - 25.0445i) q^{64} +75.5398 q^{65} +28.7262i q^{67} +(58.8980 - 76.2631i) q^{68} +(108.387 + 220.654i) q^{70} +89.0283i q^{71} -38.3163 q^{73} +(49.0058 - 24.0719i) q^{74} +(-13.7994 - 10.6573i) q^{76} -14.5281 q^{77} -141.038i q^{79} +(-38.6612 - 147.976i) q^{80} +(70.7953 - 34.7751i) q^{82} -37.7772i q^{83} +230.272 q^{85} +(-2.91070 - 5.92561i) q^{86} +(8.85633 + 1.80479i) q^{88} +71.6321 q^{89} -101.619i q^{91} +(36.2355 + 27.9847i) q^{92} +(18.4385 + 37.5372i) q^{94} -41.6664i q^{95} -30.5172 q^{97} +(208.872 - 102.599i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8}+O(q^{10}) $ 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8	$ 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8} + 8 q^{10} - 24 q^{13} + 12 q^{14} + 4 q^{16} + 40 q^{17} + 80 q^{20} + 12 q^{22} + 284 q^{25} + 112 q^{26} - 48 q^{28} - 104 q^{29} - 44 q^{32} + 140 q^{34} - 184 q^{37} + 180 q^{40} + 200 q^{41} - 96 q^{44} - 28 q^{46} - 332 q^{49} - 176 q^{50} + 276 q^{52} - 264 q^{53} + 192 q^{56} - 184 q^{58} + 40 q^{61} + 240 q^{62} - 372 q^{64} - 176 q^{65} + 104 q^{68} - 60 q^{70} + 424 q^{73} + 104 q^{74} + 400 q^{77} - 704 q^{80} + 528 q^{82} - 128 q^{85} - 668 q^{86} - 496 q^{88} + 520 q^{89} + 456 q^{92} - 32 q^{94} - 440 q^{97} + 472 q^{98}+O(q^{100}) $ 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8 + 8 * q^10 - 24 * q^13 + 12 * q^14 + 4 * q^16 + 40 * q^17 + 80 * q^20 + 12 * q^22 + 284 * q^25 + 112 * q^26 - 48 * q^28 - 104 * q^29 - 44 * q^32 + 140 * q^34 - 184 * q^37 + 180 * q^40 + 200 * q^41 - 96 * q^44 - 28 * q^46 - 332 * q^49 - 176 * q^50 + 276 * q^52 - 264 * q^53 + 192 * q^56 - 184 * q^58 + 40 * q^61 + 240 * q^62 - 372 * q^64 - 176 * q^65 + 104 * q^68 - 60 * q^70 + 424 * q^73 + 104 * q^74 + 400 * q^77 - 704 * q^80 + 528 * q^82 - 128 * q^85 - 668 * q^86 - 496 * q^88 + 520 * q^89 + 456 * q^92 - 32 * q^94 - 440 * q^97 + 472 * q^98

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 $

$2$	−1.79512	+	0.881776i	−0.897562	+	0.440888i
$2$	−1.79512	+	0.881776i	−0.897562	+	0.440888i
$3$		0			0
$3$		0			0
$4$	2.44494	−	3.16579i	0.611236	−	0.791449i
$5$	9.55892			1.91178			0.955892	−	0.293719i	$-0.0948931\pi$
$5$	9.55892			1.91178			0.955892	+	0.293719i	$0.0948931\pi$
$6$		0			0
$7$		−	12.8591i		−	1.83701i	−0.395412	−	0.918504i	$-0.629398\pi$
$7$		−	12.8591i		−	1.83701i	0.395412	−	0.918504i	$-0.370602\pi$
$8$	−1.59745	+	7.83889i	−0.199682	+	0.979861i
$9$		0			0
$10$	−17.1594	+	8.42882i	−1.71594	+	0.842882i
$11$		−	1.12979i		−	0.102709i	−0.998680	−	0.0513543i	$-0.983646\pi$
$11$		−	1.12979i		−	0.102709i	0.998680	−	0.0513543i	$-0.0163538\pi$
$12$		0			0
$13$	7.90255			0.607888			0.303944	−	0.952690i	$-0.401696\pi$
$13$	7.90255			0.607888			0.303944	+	0.952690i	$0.401696\pi$
$14$	11.3388	+	23.0836i	0.809915	+	1.64883i
$15$		0			0
$16$	−4.04452	−	15.4804i	−0.252782	−	0.967523i
$17$	24.0897			1.41704			0.708521	−	0.705689i	$-0.249363\pi$
$17$	24.0897			1.41704			0.708521	+	0.705689i	$0.249363\pi$
$18$		0			0
$19$		−	4.35890i		−	0.229416i
$19$		−	4.35890i		−	0.229416i
$20$	23.3710	−	30.2616i	1.16855	−	1.51308i
$21$		0			0
$22$	0.996226	+	2.02812i	0.0452830	+	0.0921874i
$23$			11.4459i			0.497650i	0.968548	+	0.248825i	$0.0800444\pi$
$23$			11.4459i			0.497650i	−0.968548	+	0.248825i	$0.919956\pi$
$24$		0			0
$25$	66.3729			2.65492
$26$	−14.1861	+	6.96828i	−0.545618	+	0.268011i
$27$		0			0
$28$	−40.7091	−	31.4396i	−1.45390	−	1.12284i
$29$	−27.7128			−0.955614			−0.477807	−	0.878465i	$-0.658568\pi$
$29$	−27.7128			−0.955614			−0.477807	+	0.878465i	$0.658568\pi$
$30$		0			0
$31$			2.59314i			0.0836497i	0.999125	+	0.0418248i	$0.0133171\pi$
$31$			2.59314i			0.0836497i	−0.999125	+	0.0418248i	$0.986683\pi$
$32$	20.9106	+	24.2228i	0.653457	+	0.756964i
$33$		0			0
$34$	−43.2441	+	21.2417i	−1.27188	+	0.624757i
$35$		−	122.919i		−	3.51196i
$36$		0			0
$37$	−27.2994			−0.737821			−0.368911	−	0.929465i	$-0.620269\pi$
$37$	−27.2994			−0.737821			−0.368911	+	0.929465i	$0.620269\pi$
$38$	3.84357	+	7.82477i	0.101147	+	0.205915i
$39$		0			0
$40$	−15.2699	+	74.9313i	−0.381748	+	1.87328i
$41$	−39.4375			−0.961891			−0.480945	−	0.876751i	$-0.659707\pi$
$41$	−39.4375			−0.961891			−0.480945	+	0.876751i	$0.659707\pi$
$42$		0			0
$43$			3.30095i			0.0767662i	0.999263	+	0.0383831i	$0.0122207\pi$
$43$			3.30095i			0.0767662i	−0.999263	+	0.0383831i	$0.987779\pi$
$44$	−3.57670	−	2.76228i	−0.0812886	−	0.0627792i
$45$		0			0
$46$	−10.0928	−	20.5469i	−0.219408	−	0.446672i
$47$		−	20.9106i		−	0.444907i	−0.974943	−	0.222453i	$-0.928593\pi$
$47$		−	20.9106i		−	0.444907i	0.974943	−	0.222453i	$-0.0714065\pi$
$48$		0			0
$49$	−116.355			−2.37460
$50$	−119.148	+	58.5260i	−2.38295	+	1.17052i
$51$		0			0
$52$	19.3213	−	25.0179i	0.371563	−	0.481113i
$53$	−19.2748			−0.363676			−0.181838	−	0.983329i	$-0.558205\pi$
$53$	−19.2748			−0.363676			−0.181838	+	0.983329i	$0.558205\pi$
$54$		0			0
$55$		−	10.7996i		−	0.196357i
$56$	100.801	+	20.5417i	1.80001	+	0.366817i
$57$		0			0
$58$	49.7479	−	24.4365i	0.857723	−	0.421319i
$59$		−	25.7718i		−	0.436810i	−0.975858	−	0.218405i	$-0.929915\pi$
$59$		−	25.7718i		−	0.436810i	0.975858	−	0.218405i	$-0.0700853\pi$
$60$		0			0
$61$	104.935			1.72025			0.860123	−	0.510087i	$-0.170387\pi$
$61$	104.935			1.72025			0.860123	+	0.510087i	$0.170387\pi$
$62$	−2.28657	−	4.65501i	−0.0368801	−	0.0750808i
$63$		0			0
$64$	−58.8963	−	25.0445i	−0.920255	−	0.391320i
$65$	75.5398			1.16215
$66$		0			0
$67$			28.7262i			0.428750i	0.976751	+	0.214375i	$0.0687714\pi$
$67$			28.7262i			0.428750i	−0.976751	+	0.214375i	$0.931229\pi$
$68$	58.8980	−	76.2631i	0.866147	−	1.12152i
$69$		0			0
$70$	108.387	+	220.654i	1.54838	+	3.15220i
$71$			89.0283i			1.25392i	0.779051	+	0.626960i	$0.215701\pi$
$71$			89.0283i			1.25392i	−0.779051	+	0.626960i	$0.784299\pi$
$72$		0			0
$73$	−38.3163			−0.524881			−0.262441	−	0.964948i	$-0.584527\pi$
$73$	−38.3163			−0.524881			−0.262441	+	0.964948i	$0.584527\pi$
$74$	49.0058	−	24.0719i	0.662241	−	0.325297i
$75$		0			0
$76$	−13.7994	−	10.6573i	−0.181571	−	0.140227i
$77$	−14.5281			−0.188677
$78$		0			0
$79$		−	141.038i		−	1.78529i	−0.450765	−	0.892643i	$-0.648849\pi$
$79$		−	141.038i		−	1.78529i	0.450765	−	0.892643i	$-0.351151\pi$
$80$	−38.6612	−	147.976i	−0.483265	−	1.84969i
$81$		0			0
$82$	70.7953	−	34.7751i	0.863357	−	0.424086i
$83$		−	37.7772i		−	0.455147i	−0.973761	−	0.227573i	$-0.926921\pi$
$83$		−	37.7772i		−	0.455147i	0.973761	−	0.227573i	$-0.0730792\pi$
$84$		0			0
$85$	230.272			2.70908
$86$	−2.91070	−	5.92561i	−0.0338453	−	0.0689025i
$87$		0			0
$88$	8.85633	+	1.80479i	0.100640	+	0.0205090i
$89$	71.6321			0.804855			0.402427	−	0.915452i	$-0.368167\pi$
$89$	71.6321			0.804855			0.402427	+	0.915452i	$0.368167\pi$
$90$		0			0
$91$		−	101.619i		−	1.11670i
$92$	36.2355	+	27.9847i	0.393864	+	0.304181i
$93$		0			0
$94$	18.4385	+	37.5372i	0.196154	+	0.399332i
$95$		−	41.6664i		−	0.438593i
$96$		0			0
$97$	−30.5172			−0.314610			−0.157305	−	0.987550i	$-0.550281\pi$
$97$	−30.5172			−0.314610			−0.157305	+	0.987550i	$0.550281\pi$
$98$	208.872	−	102.599i	2.13135	−	1.04693i
$99$		0			0
$100$	162.278	−	210.123i	1.62278	−	2.10123i
$101$	−65.6550			−0.650050			−0.325025	−	0.945706i	$-0.605373\pi$
$101$	−65.6550			−0.650050			−0.325025	+	0.945706i	$0.605373\pi$
$102$		0			0
$103$		−	98.4912i		−	0.956225i	−0.878299	−	0.478113i	$-0.841321\pi$
$103$		−	98.4912i		−	0.956225i	0.878299	−	0.478113i	$-0.158679\pi$
$104$	−12.6240	+	61.9472i	−0.121384	+	0.595646i
$105$		0			0
$106$	34.6007	−	16.9961i	0.326422	−	0.160340i
$107$			161.334i			1.50779i	0.656993	+	0.753896i	$0.271828\pi$
$107$			161.334i			1.50779i	−0.656993	+	0.753896i	$0.728172\pi$
$108$		0			0
$109$	155.521			1.42679			0.713397	−	0.700760i	$-0.247156\pi$
$109$	155.521			1.42679			0.713397	+	0.700760i	$0.247156\pi$
$110$	9.52284	+	19.3867i	0.0865713	+	0.176242i
$111$		0			0
$112$	−199.063	+	52.0087i	−1.77735	+	0.464363i
$113$	−141.007			−1.24785			−0.623926	−	0.781484i	$-0.714463\pi$
$113$	−141.007			−1.24785			−0.623926	+	0.781484i	$0.714463\pi$
$114$		0			0
$115$			109.411i			0.951399i
$116$	−67.7562	+	87.7330i	−0.584105	+	0.756319i
$117$		0			0
$118$	22.7249	+	46.2635i	0.192584	+	0.392064i
$119$		−	309.771i		−	2.60312i
$120$		0			0
$121$	119.724			0.989451
$122$	−188.371	+	92.5291i	−1.54403	+	0.758436i
$123$		0			0
$124$	8.20935	+	6.34008i	0.0662044	+	0.0511297i
$125$	395.480			3.16384
$126$		0			0
$127$			57.3067i			0.451234i	0.974216	+	0.225617i	$0.0724398\pi$
$127$			57.3067i			0.451234i	−0.974216	+	0.225617i	$0.927560\pi$
$128$	127.810	−	6.97534i	0.998514	−	0.0544948i
$129$		0			0
$130$	−135.603	+	66.6092i	−1.04310	+	0.512378i
$131$			212.454i			1.62179i	0.585194	+	0.810894i	$0.301018\pi$
$131$			212.454i			1.62179i	−0.585194	+	0.810894i	$0.698982\pi$
$132$		0			0
$133$	−56.0513			−0.421439
$134$	−25.3301	−	51.5672i	−0.189031	−	0.384830i
$135$		0			0
$136$	−38.4822	+	188.837i	−0.282957	+	1.38850i
$137$	117.655			0.858792			0.429396	−	0.903116i	$-0.358726\pi$
$137$	117.655			0.858792			0.429396	+	0.903116i	$0.358726\pi$
$138$		0			0
$139$			30.9322i			0.222533i	0.993791	+	0.111267i	$0.0354908\pi$
$139$			30.9322i			0.222533i	−0.993791	+	0.111267i	$0.964509\pi$
$140$	−389.135	−	300.529i	−2.77954	−	2.14664i
$141$		0			0
$142$	−78.5030	−	159.817i	−0.552838	−	1.12547i
$143$		−	8.92826i		−	0.0624354i
$144$		0			0
$145$	−264.904			−1.82693
$146$	68.7826	−	33.7864i	0.471113	−	0.231414i
$147$		0			0
$148$	−66.7454	+	86.4243i	−0.450983	+	0.583948i
$149$	24.2929			0.163040			0.0815199	−	0.996672i	$-0.474023\pi$
$149$	24.2929			0.163040			0.0815199	+	0.996672i	$0.474023\pi$
$150$		0			0
$151$		−	129.438i		−	0.857203i	−0.903494	−	0.428602i	$-0.859006\pi$
$151$		−	129.438i		−	0.857203i	0.903494	−	0.428602i	$-0.140994\pi$
$152$	34.1689	+	6.96314i	0.224795	+	0.0458101i
$153$		0			0
$154$	26.0797	−	12.8105i	0.169349	−	0.0831852i
$155$			24.7876i			0.159920i
$156$		0			0
$157$	−88.2876			−0.562341			−0.281171	−	0.959658i	$-0.590723\pi$
$157$	−88.2876			−0.562341			−0.281171	+	0.959658i	$0.590723\pi$
$158$	124.364	+	253.180i	0.787111	+	1.60240i
$159$		0			0
$160$	199.883	+	231.544i	1.24927	+	1.44715i
$161$	147.184			0.914187
$162$		0			0
$163$			115.881i			0.710928i	0.934690	+	0.355464i	$0.115677\pi$
$163$			115.881i			0.710928i	−0.934690	+	0.355464i	$0.884323\pi$
$164$	−96.4225	+	124.851i	−0.587942	+	0.761287i
$165$		0			0
$166$	33.3110	+	67.8147i	0.200669	+	0.408522i
$167$			11.6133i			0.0695407i	0.999395	+	0.0347703i	$0.0110700\pi$
$167$			11.6133i			0.0695407i	−0.999395	+	0.0347703i	$0.988930\pi$
$168$		0			0
$169$	−106.550			−0.630472
$170$	−413.366	+	203.048i	−2.43157	+	1.19440i
$171$		0			0
$172$	10.4501	+	8.07063i	0.0607565	+	0.0469222i
$173$	141.667			0.818882			0.409441	−	0.912337i	$-0.365724\pi$
$173$	141.667			0.818882			0.409441	+	0.912337i	$0.365724\pi$
$174$		0			0
$175$		−	853.493i		−	4.87710i
$176$	−17.4896	+	4.56947i	−0.0993730	+	0.0259629i
$177$		0			0
$178$	−128.588	+	63.1634i	−0.722407	+	0.354851i
$179$		−	91.6386i		−	0.511948i	−0.966684	−	0.255974i	$-0.917604\pi$
$179$		−	91.6386i		−	0.511948i	0.966684	−	0.255974i	$-0.0823961\pi$
$180$		0			0
$181$	119.350			0.659391			0.329695	−	0.944087i	$-0.393054\pi$
$181$	119.350			0.659391			0.329695	+	0.944087i	$0.393054\pi$
$182$	89.6055	+	182.419i	0.492338	+	1.00230i
$183$		0			0
$184$	−89.7235	−	18.2844i	−0.487628	−	0.0993715i
$185$	−260.953			−1.41055
$186$		0			0
$187$		−	27.2165i		−	0.145543i
$188$	−66.1987	−	51.1253i	−0.352121	−	0.271943i
$189$		0			0
$190$	36.7404	+	74.7963i	0.193370	+	0.393665i
$191$			0.567840i			0.00297299i	0.999999	+	0.00148649i	$0.000473166\pi$
$191$			0.567840i			0.00297299i	−0.999999	+	0.00148649i	$0.999527\pi$
$192$		0			0
$193$	3.60632			0.0186856			0.00934279	−	0.999956i	$-0.497026\pi$
$193$	3.60632			0.0186856			0.00934279	+	0.999956i	$0.497026\pi$
$194$	54.7821	−	26.9093i	0.282382	−	0.138708i
$195$		0			0
$196$	−284.482	+	368.357i	−1.45144	+	1.87937i
$197$	−61.1615			−0.310465			−0.155232	−	0.987878i	$-0.549613\pi$
$197$	−61.1615			−0.310465			−0.155232	+	0.987878i	$0.549613\pi$
$198$		0			0
$199$			208.457i			1.04752i	0.851866	+	0.523760i	$0.175471\pi$
$199$			208.457i			1.04752i	−0.851866	+	0.523760i	$0.824529\pi$
$200$	−106.028	+	520.290i	−0.530138	+	2.60145i
$201$		0			0
$202$	117.859	−	57.8930i	0.583460	−	0.286599i
$203$			356.360i			1.75547i
$204$		0			0
$205$	−376.980			−1.83893
$206$	86.8472	+	176.804i	0.421588	+	0.858271i
$207$		0			0
$208$	−31.9620	−	122.334i	−0.153663	−	0.588146i
$209$	−4.92466			−0.0235630
$210$		0			0
$211$			75.2285i			0.356533i	0.983982	+	0.178267i	$0.0570489\pi$
$211$			75.2285i			0.356533i	−0.983982	+	0.178267i	$0.942951\pi$
$212$	−47.1258	+	61.0201i	−0.222292	+	0.287831i
$213$		0			0
$214$	−142.260	−	289.614i	−0.664768	−	1.35334i
$215$			31.5535i			0.146760i
$216$		0			0
$217$	33.3453			0.153665
$218$	−279.179	+	137.134i	−1.28064	+	0.629056i
$219$		0			0
$220$	−34.1894	−	26.4044i	−0.155406	−	0.120020i
$221$	190.370			0.861404
$222$		0			0
$223$			321.739i			1.44277i	0.692532	+	0.721387i	$0.256495\pi$
$223$			321.739i			1.44277i	−0.692532	+	0.721387i	$0.743505\pi$
$224$	311.483	−	268.891i	1.39055	−	1.20041i
$225$		0			0
$226$	253.126	−	124.337i	1.12002	−	0.550163i
$227$		−	434.273i		−	1.91310i	−0.291573	−	0.956549i	$-0.594179\pi$
$227$		−	434.273i		−	1.91310i	0.291573	−	0.956549i	$-0.405821\pi$
$228$		0			0
$229$	−105.105			−0.458974			−0.229487	−	0.973312i	$-0.573705\pi$
$229$	−105.105			−0.458974			−0.229487	+	0.973312i	$0.573705\pi$
$230$	−96.4759	−	196.406i	−0.419460	−	0.853940i
$231$		0			0
$232$	44.2699	−	217.237i	0.190818	−	0.936368i
$233$	−255.387			−1.09608			−0.548040	−	0.836452i	$-0.684626\pi$
$233$	−255.387			−1.09608			−0.548040	+	0.836452i	$0.684626\pi$
$234$		0			0
$235$		−	199.883i		−	0.850566i
$236$	−81.5882	−	63.0105i	−0.345713	−	0.266994i
$237$		0			0
$238$	273.149	+	556.078i	1.14768	+	2.33646i
$239$		−	318.980i		−	1.33464i	−0.744770	−	0.667321i	$-0.767441\pi$
$239$		−	318.980i		−	1.33464i	0.744770	−	0.667321i	$-0.232559\pi$
$240$		0			0
$241$	201.257			0.835091			0.417545	−	0.908656i	$-0.362891\pi$
$241$	201.257			0.835091			0.417545	+	0.908656i	$0.362891\pi$
$242$	−214.919	+	105.569i	−0.888094	+	0.436237i
$243$		0			0
$244$	256.560	−	332.203i	1.05148	−	1.36149i
$245$	−1112.23			−4.53972
$246$		0			0
$247$		−	34.4464i		−	0.139459i
$248$	−20.3273	−	4.14242i	−0.0819651	−	0.0167033i
$249$		0			0
$250$	−709.936	+	348.725i	−2.83974	+	1.39490i
$251$		−	236.952i		−	0.944032i	−0.881590	−	0.472016i	$-0.843526\pi$
$251$		−	236.952i		−	0.944032i	0.881590	−	0.472016i	$-0.156474\pi$
$252$		0			0
$253$	12.9316			0.0511129
$254$	−50.5317	−	102.873i	−0.198944	−	0.405010i
$255$		0			0
$256$	−223.284	+	125.221i	−0.872202	+	0.489145i
$257$	−179.367			−0.697928			−0.348964	−	0.937136i	$-0.613466\pi$
$257$	−179.367			−0.697928			−0.348964	+	0.937136i	$0.613466\pi$
$258$		0			0
$259$			351.044i			1.35538i
$260$	184.690	−	239.144i	0.710348	−	0.919783i
$261$		0			0
$262$	−187.337	−	381.382i	−0.715026	−	1.45565i
$263$			128.740i			0.489505i	0.969586	+	0.244753i	$0.0787067\pi$
$263$			128.740i			0.489505i	−0.969586	+	0.244753i	$0.921293\pi$
$264$		0			0
$265$	−184.246			−0.695270
$266$	100.619	−	49.4247i	0.378267	−	0.185807i
$267$		0			0
$268$	90.9414	+	70.2340i	0.339334	+	0.262067i
$269$	99.5423			0.370046			0.185023	−	0.982734i	$-0.440764\pi$
$269$	99.5423			0.370046			0.185023	+	0.982734i	$0.440764\pi$
$270$		0			0
$271$			460.189i			1.69811i	0.528301	+	0.849057i	$0.322829\pi$
$271$			460.189i			1.69811i	−0.528301	+	0.849057i	$0.677171\pi$
$272$	−97.4313	−	372.918i	−0.358203	−	1.37102i
$273$		0			0
$274$	−211.204	+	103.745i	−0.770819	+	0.378631i
$275$		−	74.9878i		−	0.272683i
$276$		0			0
$277$	172.050			0.621119			0.310559	−	0.950554i	$-0.399484\pi$
$277$	172.050			0.621119			0.310559	+	0.950554i	$0.399484\pi$
$278$	−27.2752	−	55.5271i	−0.0981123	−	0.199738i
$279$		0			0
$280$	963.545	+	196.357i	3.44123	+	0.701274i
$281$	−225.184			−0.801368			−0.400684	−	0.916216i	$-0.631227\pi$
$281$	−225.184			−0.801368			−0.400684	+	0.916216i	$0.631227\pi$
$282$		0			0
$283$		−	432.083i		−	1.52679i	−0.645930	−	0.763397i	$-0.723530\pi$
$283$		−	432.083i		−	1.52679i	0.645930	−	0.763397i	$-0.276470\pi$
$284$	281.845	+	217.669i	0.992413	+	0.766441i
$285$		0			0
$286$	7.87273	+	16.0273i	0.0275270	+	0.0560396i
$287$			507.129i			1.76700i
$288$		0			0
$289$	291.315			1.00801
$290$	475.536	−	233.586i	1.63978	−	0.805470i
$291$		0			0
$292$	−93.6812	+	121.302i	−0.320826	+	0.415416i
$293$	−49.9896			−0.170613			−0.0853064	−	0.996355i	$-0.527187\pi$
$293$	−49.9896			−0.170613			−0.0853064	+	0.996355i	$0.527187\pi$
$294$		0			0
$295$		−	246.350i		−	0.835086i
$296$	43.6095	−	213.997i	0.147329	−	0.722962i
$297$		0			0
$298$	−43.6089	+	21.4209i	−0.146338	+	0.0718823i
$299$			90.4522i			0.302516i
$300$		0			0
$301$	42.4471			0.141020
$302$	114.135	+	232.357i	0.377931	+	0.769393i
$303$		0			0
$304$	−67.4774	+	17.6296i	−0.221965	+	0.0579922i
$305$	1003.06			3.28874
$306$		0			0
$307$			144.627i			0.471099i	0.971862	+	0.235550i	$0.0756890\pi$
$307$			144.627i			0.471099i	−0.971862	+	0.235550i	$0.924311\pi$
$308$	−35.5204	+	45.9930i	−0.115326	+	0.149328i
$309$		0			0
$310$	−21.8571	−	44.4968i	−0.0705068	−	0.143538i
$311$			396.625i			1.27532i	0.770318	+	0.637660i	$0.220098\pi$
$311$			396.625i			1.27532i	−0.770318	+	0.637660i	$0.779902\pi$
$312$		0			0
$313$	−420.706			−1.34411			−0.672055	−	0.740501i	$-0.734588\pi$
$313$	−420.706			−1.34411			−0.672055	+	0.740501i	$0.734588\pi$
$314$	158.487	−	77.8499i	0.504736	−	0.247930i
$315$		0			0
$316$	−446.496	−	344.829i	−1.41296	−	1.09123i
$317$	201.579			0.635897			0.317949	−	0.948108i	$-0.397006\pi$
$317$	201.579			0.635897			0.317949	+	0.948108i	$0.397006\pi$
$318$		0			0
$319$			31.3098i			0.0981498i
$320$	−562.985	−	239.398i	−1.75933	−	0.748120i
$321$		0			0
$322$	−264.214	+	129.783i	−0.820540	+	0.403054i
$323$		−	105.005i		−	0.325092i
$324$		0			0
$325$	524.515			1.61389
$326$	−102.181	−	208.021i	−0.313440	−	0.638102i
$327$		0			0
$328$	62.9996	−	309.146i	0.192072	−	0.942519i
$329$	−268.891			−0.817297
$330$		0			0
$331$			461.393i			1.39394i	0.717102	+	0.696969i	$0.245468\pi$
$331$			461.393i			1.39394i	−0.717102	+	0.696969i	$0.754532\pi$
$332$	−119.595	−	92.3630i	−0.360225	−	0.278202i
$333$		0			0
$334$	−10.2403	−	20.8473i	−0.0306596	−	0.0624171i
$335$			274.592i			0.819677i
$336$		0			0
$337$	−74.5735			−0.221286			−0.110643	−	0.993860i	$-0.535291\pi$
$337$	−74.5735			−0.221286			−0.110643	+	0.993860i	$0.535291\pi$
$338$	191.270	−	93.9530i	0.565887	−	0.277967i
$339$		0			0
$340$	563.001	−	728.993i	1.65589	−	2.14410i
$341$	2.92972			0.00859154
$342$		0			0
$343$			866.126i			2.52515i
$344$	−25.8758	−	5.27311i	−0.0752202	−	0.0153288i
$345$		0			0
$346$	−254.309	+	124.918i	−0.734997	+	0.361035i
$347$			344.595i			0.993068i	0.868017	+	0.496534i	$0.165394\pi$
$347$			344.595i			0.993068i	−0.868017	+	0.496534i	$0.834606\pi$
$348$		0			0
$349$	166.528			0.477157			0.238579	−	0.971123i	$-0.423319\pi$
$349$	166.528			0.477157			0.238579	+	0.971123i	$0.423319\pi$
$350$	752.589	+	1532.13i	2.15026	+	4.37750i
$351$		0			0
$352$	27.3668	−	23.6247i	0.0777467	−	0.0671157i
$353$	−534.558			−1.51433			−0.757164	−	0.653224i	$-0.773416\pi$
$353$	−534.558			−1.51433			−0.757164	+	0.653224i	$0.773416\pi$
$354$		0			0
$355$			851.014i			2.39722i
$356$	175.136	−	226.772i	0.491956	−	0.637001i
$357$		0			0
$358$	80.8048	+	164.503i	0.225712	+	0.459505i
$359$			271.901i			0.757384i	0.925523	+	0.378692i	$0.123626\pi$
$359$			271.901i			0.757384i	−0.925523	+	0.378692i	$0.876374\pi$
$360$		0			0
$361$	−19.0000			−0.0526316
$362$	−214.248	+	105.240i	−0.591844	+	0.290717i
$363$		0			0
$364$	−321.706	−	248.453i	−0.883808	−	0.682564i
$365$	−366.263			−1.00346
$366$		0			0
$367$		−	53.9677i		−	0.147051i	−0.997293	−	0.0735255i	$-0.976575\pi$
$367$		−	53.9677i		−	0.147051i	0.997293	−	0.0735255i	$-0.0234250\pi$
$368$	177.188	−	46.2933i	0.481488	−	0.125797i
$369$		0			0
$370$	468.442	−	230.102i	1.26606	−	0.621897i
$371$			247.856i			0.668076i
$372$		0			0
$373$	310.654			0.832853			0.416427	−	0.909169i	$-0.363282\pi$
$373$	310.654			0.832853			0.416427	+	0.909169i	$0.363282\pi$
$374$	23.9988	+	48.8569i	0.0641680	+	0.130633i
$375$		0			0
$376$	163.916	+	33.4037i	0.435947	+	0.0888397i
$377$	−219.002			−0.580907
$378$		0			0
$379$		−	116.334i		−	0.306950i	−0.988153	−	0.153475i	$-0.950954\pi$
$379$		−	116.334i		−	0.306950i	0.988153	−	0.153475i	$-0.0490464\pi$
$380$	−131.907	−	101.872i	−0.347124	−	0.268084i
$381$		0			0
$382$	−0.500708	−	1.01934i	−0.00131075	−	0.00266844i
$383$			311.066i			0.812183i	0.913833	+	0.406091i	$0.133109\pi$
$383$			311.066i			0.812183i	−0.913833	+	0.406091i	$0.866891\pi$
$384$		0			0
$385$	−138.873			−0.360709
$386$	−6.47379	+	3.17996i	−0.0167715	+	0.00823825i
$387$		0			0
$388$	−74.6127	+	96.6111i	−0.192301	+	0.248998i
$389$	32.4592			0.0834426			0.0417213	−	0.999129i	$-0.486716\pi$
$389$	32.4592			0.0834426			0.0417213	+	0.999129i	$0.486716\pi$
$390$		0			0
$391$			275.730i			0.705191i
$392$	185.872	−	912.096i	0.474164	−	2.32678i
$393$		0			0
$394$	109.793	−	53.9308i	0.278661	−	0.136880i
$395$		−	1348.17i		−	3.41308i
$396$		0			0
$397$	−721.562			−1.81754			−0.908769	−	0.417300i	$-0.862976\pi$
$397$	−721.562			−1.81754			−0.908769	+	0.417300i	$0.862976\pi$
$398$	−183.812	−	374.206i	−0.461839	−	0.940215i
$399$		0			0
$400$	−268.446	−	1027.48i	−0.671116	−	2.56869i
$401$	377.180			0.940599			0.470299	−	0.882507i	$-0.344146\pi$
$401$	377.180			0.940599			0.470299	+	0.882507i	$0.344146\pi$
$402$		0			0
$403$			20.4924i			0.0508497i
$404$	−160.523	+	207.850i	−0.397333	+	0.514481i
$405$		0			0
$406$	−314.230	−	639.711i	−0.773966	−	1.57564i
$407$			30.8427i			0.0757806i
$408$		0			0
$409$	687.913			1.68194			0.840970	−	0.541082i	$-0.181985\pi$
$409$	687.913			1.68194			0.840970	+	0.541082i	$0.181985\pi$
$410$	676.726	−	332.412i	1.65055	−	0.810761i
$411$		0			0
$412$	−311.803	−	240.805i	−0.756803	−	0.584479i
$413$	−331.401			−0.802423
$414$		0			0
$415$		−	361.109i		−	0.870142i
$416$	165.247	+	191.422i	0.397229	+	0.460149i
$417$		0			0
$418$	8.84038	−	4.34245i	0.0211492	−	0.0103886i
$419$			436.231i			1.04113i	0.853824	+	0.520563i	$0.174278\pi$
$419$			436.231i			1.04113i	−0.853824	+	0.520563i	$0.825722\pi$
$420$		0			0
$421$	176.033			0.418132			0.209066	−	0.977902i	$-0.432958\pi$
$421$	176.033			0.418132			0.209066	+	0.977902i	$0.432958\pi$
$422$	−66.3347	−	135.045i	−0.157191	−	0.320011i
$423$		0			0
$424$	30.7906	−	151.093i	0.0726194	−	0.356352i
$425$	1598.90			3.76213
$426$		0			0
$427$		−	1349.36i		−	3.16010i
$428$	510.750	+	394.452i	1.19334	+	0.921616i
$429$		0			0
$430$	−27.8231	−	56.6424i	−0.0647049	−	0.131727i
$431$		−	736.013i		−	1.70769i	−0.520531	−	0.853843i	$-0.674266\pi$
$431$		−	736.013i		−	1.70769i	0.520531	−	0.853843i	$-0.325734\pi$
$432$		0			0
$433$	−390.416			−0.901652			−0.450826	−	0.892612i	$-0.648871\pi$
$433$	−390.416			−0.901652			−0.450826	+	0.892612i	$0.648871\pi$
$434$	−59.8590	+	29.4031i	−0.137924	+	0.0677491i
$435$		0			0
$436$	380.239	−	492.346i	0.872107	−	1.12923i
$437$	49.8917			0.114169
$438$		0			0
$439$		−	523.530i		−	1.19255i	−0.802780	−	0.596275i	$-0.796647\pi$
$439$		−	523.530i		−	1.19255i	0.802780	−	0.596275i	$-0.203353\pi$
$440$	84.6570	+	17.2519i	0.192402	+	0.0392088i
$441$		0			0
$442$	−341.738	+	167.864i	−0.773164	+	0.379783i
$443$		−	6.89254i		−	0.0155588i	−0.999970	−	0.00777939i	$-0.997524\pi$
$443$		−	6.89254i		−	0.0155588i	0.999970	−	0.00777939i	$-0.00247628\pi$
$444$		0			0
$445$	684.725			1.53871
$446$	−283.701	−	577.561i	−0.636102	−	1.29498i
$447$		0			0
$448$	−322.049	+	757.351i	−0.718859	+	1.69051i
$449$	294.620			0.656169			0.328084	−	0.944648i	$-0.393597\pi$
$449$	294.620			0.656169			0.328084	+	0.944648i	$0.393597\pi$
$450$		0			0
$451$			44.5563i			0.0987945i
$452$	−344.755	+	446.400i	−0.762731	+	0.987611i
$453$		0			0
$454$	382.932	+	779.574i	0.843462	+	1.71712i
$455$		−	971.371i		−	2.13488i
$456$		0			0
$457$	−743.227			−1.62632			−0.813159	−	0.582042i	$-0.802254\pi$
$457$	−743.227			−1.62632			−0.813159	+	0.582042i	$0.802254\pi$
$458$	188.677	−	92.6792i	0.411958	−	0.202356i
$459$		0			0
$460$	346.372	+	267.503i	0.752983	+	0.581529i
$461$	−66.9190			−0.145161			−0.0725803	−	0.997363i	$-0.523123\pi$
$461$	−66.9190			−0.145161			−0.0725803	+	0.997363i	$0.523123\pi$
$462$		0			0
$463$			186.893i			0.403657i	0.979421	+	0.201828i	$0.0646883\pi$
$463$			186.893i			0.403657i	−0.979421	+	0.201828i	$0.935312\pi$
$464$	112.085	+	429.004i	0.241562	+	0.924578i
$465$		0			0
$466$	458.451	−	225.194i	0.983800	−	0.483249i
$467$			756.684i			1.62031i	0.586218	+	0.810154i	$0.300616\pi$
$467$			756.684i			1.62031i	−0.586218	+	0.810154i	$0.699384\pi$
$468$		0			0
$469$	369.392			0.787617
$470$	176.252	+	358.815i	0.375004	+	0.763435i
$471$		0			0
$472$	202.022	+	41.1692i	0.428013	+	0.0872229i
$473$	3.72939			0.00788455
$474$		0			0
$475$		−	289.313i		−	0.609079i
$476$	−980.672	−	757.373i	−2.06024	−	1.59112i
$477$		0			0
$478$	281.268	+	572.608i	0.588428	+	1.19792i
$479$			635.260i			1.32622i	0.748521	+	0.663111i	$0.230764\pi$
$479$			635.260i			1.32622i	−0.748521	+	0.663111i	$0.769236\pi$
$480$		0			0
$481$	−215.735			−0.448513
$482$	−361.281	+	177.463i	−0.749546	+	0.368181i
$483$		0			0
$484$	292.717	−	379.020i	0.604788	−	0.783100i
$485$	−291.711			−0.601466
$486$		0			0
$487$		−	639.103i		−	1.31233i	−0.754619	−	0.656163i	$-0.772178\pi$
$487$		−	639.103i		−	1.31233i	0.754619	−	0.656163i	$-0.227822\pi$
$488$	−167.629	+	822.573i	−0.343501	+	1.68560i
$489$		0			0
$490$	1996.59	−	980.738i	4.07468	−	2.00151i
$491$		−	653.912i		−	1.33180i	−0.746042	−	0.665899i	$-0.768048\pi$
$491$		−	653.912i		−	1.33180i	0.746042	−	0.665899i	$-0.231952\pi$
$492$		0			0
$493$	−667.594			−1.35415
$494$	30.3740	+	61.8356i	0.0614859	+	0.125173i
$495$		0			0
$496$	40.1428	−	10.4880i	0.0809330	−	0.0211452i
$497$	1144.82			2.30346
$498$		0			0
$499$			95.3010i			0.190984i	0.995430	+	0.0954919i	$0.0304424\pi$
$499$			95.3010i			0.190984i	−0.995430	+	0.0954919i	$0.969558\pi$
$500$	966.926	−	1252.01i	1.93385	−	2.50402i
$501$		0			0
$502$	208.939	+	425.358i	0.416212	+	0.847327i
$503$			96.7545i			0.192355i	0.995364	+	0.0961775i	$0.0306616\pi$
$503$			96.7545i			0.192355i	−0.995364	+	0.0961775i	$0.969338\pi$
$504$		0			0
$505$	−627.591			−1.24275
$506$	−23.2138	+	11.4028i	−0.0458770	+	0.0225351i
$507$		0			0
$508$	181.421	+	140.112i	0.357128	+	0.275810i
$509$	−478.766			−0.940600			−0.470300	−	0.882507i	$-0.655854\pi$
$509$	−478.766			−0.940600			−0.470300	+	0.882507i	$0.655854\pi$
$510$		0			0
$511$			492.712i			0.964211i
$512$	290.405	−	421.674i	0.567197	−	0.823582i
$513$		0			0
$514$	321.987	−	158.162i	0.626434	−	0.307708i
$515$		−	941.469i		−	1.82810i
$516$		0			0
$517$	−23.6247			−0.0456958
$518$	−309.543	−	630.168i	−0.597572	−	1.21654i
$519$		0			0
$520$	−120.671	+	592.148i	−0.232060	+	1.13875i
$521$	−541.859			−1.04004			−0.520018	−	0.854155i	$-0.674075\pi$
$521$	−541.859			−1.04004			−0.520018	+	0.854155i	$0.674075\pi$
$522$		0			0
$523$		−	84.4204i		−	0.161416i	−0.996738	−	0.0807079i	$-0.974282\pi$
$523$		−	84.4204i		−	0.161416i	0.996738	−	0.0807079i	$-0.0257181\pi$
$524$	672.586	+	519.438i	1.28356	+	0.991294i
$525$		0			0
$526$	−113.520	−	231.104i	−0.215817	−	0.439361i
$527$			62.4680i			0.118535i
$528$		0			0
$529$	397.990			0.752345
$530$	330.745	−	162.464i	0.624048	−	0.306536i
$531$		0			0
$532$	−137.042	+	177.447i	−0.257598	+	0.333547i
$533$	−311.657			−0.584722
$534$		0			0
$535$			1542.18i			2.88257i
$536$	−225.182	−	45.8888i	−0.420115	−	0.0856135i
$537$		0			0
$538$	−178.691	+	87.7740i	−0.332139	+	0.163149i
$539$			131.458i			0.243892i
$540$		0			0
$541$	677.152			1.25167			0.625834	−	0.779956i	$-0.284759\pi$
$541$	677.152			1.25167			0.625834	+	0.779956i	$0.284759\pi$
$542$	−405.784	−	826.096i	−0.748678	−	1.52416i
$543$		0			0
$544$	503.731	+	583.521i	0.925977	+	1.07265i
$545$	1486.61			2.72772
$546$		0			0
$547$			475.148i			0.868643i	0.900758	+	0.434321i	$0.143012\pi$
$547$			475.148i			0.868643i	−0.900758	+	0.434321i	$0.856988\pi$
$548$	287.659	−	372.470i	0.524924	−	0.679690i
$549$		0			0
$550$	66.1224	+	134.612i	0.120223	+	0.244750i
$551$			120.797i			0.219233i
$552$		0			0
$553$	−1813.61			−3.27958
$554$	−308.851	+	151.709i	−0.557492	+	0.273844i
$555$		0			0
$556$	97.9249	+	75.6273i	0.176124	+	0.136020i
$557$	−554.385			−0.995306			−0.497653	−	0.867376i	$-0.665805\pi$
$557$	−554.385			−0.995306			−0.497653	+	0.867376i	$0.665805\pi$
$558$		0			0
$559$			26.0859i			0.0466653i
$560$	−1902.83	+	497.146i	−3.39790	+	0.887761i
$561$		0			0
$562$	404.234	−	198.562i	0.719278	−	0.353314i
$563$			337.935i			0.600239i	0.953902	+	0.300119i	$0.0970266\pi$
$563$			337.935i			0.600239i	−0.953902	+	0.300119i	$0.902973\pi$
$564$		0			0
$565$	−1347.88			−2.38562
$566$	381.000	+	775.642i	0.673145	+	1.37039i
$567$		0			0
$568$	−697.883	−	142.219i	−1.22867	−	0.250385i
$569$	670.695			1.17873			0.589363	−	0.807869i	$-0.299379\pi$
$569$	670.695			1.17873			0.589363	+	0.807869i	$0.299379\pi$
$570$		0			0
$571$			937.861i			1.64249i	0.570577	+	0.821244i	$0.306720\pi$
$571$			937.861i			1.64249i	−0.570577	+	0.821244i	$0.693280\pi$
$572$	−28.2650	−	21.8291i	−0.0494144	−	0.0381627i
$573$		0			0
$574$	−447.175	−	910.360i	−0.779050	−	1.58599i
$575$			759.701i			1.32122i
$576$		0			0
$577$	575.702			0.997750			0.498875	−	0.866674i	$-0.333747\pi$
$577$	575.702			0.997750			0.498875	+	0.866674i	$0.333747\pi$
$578$	−522.947	+	256.875i	−0.904752	+	0.444420i
$579$		0			0
$580$	−647.676	+	838.633i	−1.11668	+	1.44592i
$581$	−485.779			−0.836108
$582$		0			0
$583$			21.7766i			0.0373527i
$584$	61.2085	−	300.357i	0.104809	−	0.514310i
$585$		0			0
$586$	89.7375	−	44.0796i	0.153136	−	0.0752212i
$587$		−	87.9756i		−	0.149873i	−0.997188	−	0.0749366i	$-0.976125\pi$
$587$		−	87.9756i		−	0.149873i	0.997188	−	0.0749366i	$-0.0238754\pi$
$588$		0			0
$589$	11.3032			0.0191906
$590$	217.226	+	442.229i	0.368179	+	0.749541i
$591$		0			0
$592$	110.413	+	422.605i	0.186508	+	0.713859i
$593$	−78.7171			−0.132744			−0.0663719	−	0.997795i	$-0.521142\pi$
$593$	−78.7171			−0.132744			−0.0663719	+	0.997795i	$0.521142\pi$
$594$		0			0
$595$		−	2961.08i		−	4.97660i
$596$	59.3948	−	76.9065i	0.0996558	−	0.129038i
$597$		0			0
$598$	−79.7586	−	162.373i	−0.133376	−	0.271527i
$599$			530.191i			0.885126i	0.896737	+	0.442563i	$0.145931\pi$
$599$			530.191i			0.885126i	−0.896737	+	0.442563i	$0.854069\pi$
$600$		0			0
$601$	992.809			1.65193			0.825964	−	0.563723i	$-0.190631\pi$
$601$	992.809			1.65193			0.825964	+	0.563723i	$0.190631\pi$
$602$	−76.1978	+	37.4288i	−0.126574	+	0.0621741i
$603$		0			0
$604$	−409.773	−	316.468i	−0.678432	−	0.523953i
$605$	1144.43			1.89162
$606$		0			0
$607$			910.285i			1.49965i	0.661638	+	0.749823i	$0.269861\pi$
$607$			910.285i			1.49965i	−0.661638	+	0.749823i	$0.730139\pi$
$608$	105.585	−	91.1473i	0.173659	−	0.149913i
$609$		0			0
$610$	−1800.63	+	884.478i	−2.95185	+	1.44996i
$611$		−	165.247i		−	0.270454i
$612$		0			0
$613$	253.955			0.414282			0.207141	−	0.978311i	$-0.433584\pi$
$613$	253.955			0.414282			0.207141	+	0.978311i	$0.433584\pi$
$614$	−127.529	−	259.624i	−0.207702	−	0.422841i
$615$		0			0
$616$	23.2079	−	113.884i	0.0376752	−	0.184877i
$617$	−319.178			−0.517306			−0.258653	−	0.965970i	$-0.583279\pi$
$617$	−319.178			−0.517306			−0.258653	+	0.965970i	$0.583279\pi$
$618$		0			0
$619$			336.279i			0.543262i	0.962401	+	0.271631i	$0.0875630\pi$
$619$			336.279i			0.543262i	−0.962401	+	0.271631i	$0.912437\pi$
$620$	78.4725	+	60.6043i	0.126569	+	0.0977488i
$621$		0			0
$622$	−349.734	−	711.990i	−0.562273	−	1.14468i
$623$		−	921.121i		−	1.47852i
$624$		0			0
$625$	2121.04			3.39366
$626$	755.220	−	370.969i	1.20642	−	0.592602i
$627$		0			0
$628$	−215.858	+	279.500i	−0.343723	+	0.445064i
$629$	−657.635			−1.04552
$630$		0			0
$631$		−	27.6999i		−	0.0438983i	−0.999759	−	0.0219492i	$-0.993013\pi$
$631$		−	27.6999i		−	0.0438983i	0.999759	−	0.0219492i	$-0.00698720\pi$
$632$	1105.58	+	225.301i	1.74933	+	0.356489i
$633$		0			0
$634$	−361.860	+	177.748i	−0.570757	+	0.280359i
$635$			547.790i			0.862661i
$636$		0			0
$637$	−919.504			−1.44349
$638$	−27.6082	−	56.2049i	−0.0432731	−	0.0880955i
$639$		0			0
$640$	1221.72	−	66.6767i	1.90894	−	0.104182i
$641$	−1178.70			−1.83884			−0.919422	−	0.393272i	$-0.871343\pi$
$641$	−1178.70			−1.83884			−0.919422	+	0.393272i	$0.871343\pi$
$642$		0			0
$643$		−	834.938i		−	1.29850i	−0.760573	−	0.649252i	$-0.775082\pi$
$643$		−	834.938i		−	1.29850i	0.760573	−	0.649252i	$-0.224918\pi$
$644$	359.857	−	465.955i	0.558784	−	0.723532i
$645$		0			0
$646$	92.5906	+	188.496i	0.143329	+	0.291790i
$647$			820.328i			1.26789i	0.773376	+	0.633947i	$0.218566\pi$
$647$			820.328i			1.26789i	−0.773376	+	0.633947i	$0.781434\pi$
$648$		0			0
$649$	−29.1168			−0.0448641
$650$	−941.570	+	462.505i	−1.44857	+	0.711546i
$651$		0			0
$652$	366.857	+	283.323i	0.562663	+	0.434545i
$653$	−304.280			−0.465972			−0.232986	−	0.972480i	$-0.574850\pi$
$653$	−304.280			−0.465972			−0.232986	+	0.972480i	$0.574850\pi$
$654$		0			0
$655$			2030.83i			3.10051i
$656$	159.506	+	610.508i	0.243149	+	0.930652i
$657$		0			0
$658$	482.693	−	237.102i	0.733575	−	0.360337i
$659$			251.488i			0.381621i	0.981627	+	0.190810i	$0.0611116\pi$
$659$			251.488i			0.381621i	−0.981627	+	0.190810i	$0.938888\pi$
$660$		0			0
$661$	−1130.70			−1.71058			−0.855292	−	0.518146i	$-0.826622\pi$
$661$	−1130.70			−1.71058			−0.855292	+	0.518146i	$0.826622\pi$
$662$	−406.845	−	828.258i	−0.614570	−	1.25115i
$663$		0			0
$664$	296.131	+	60.3473i	0.445980	+	0.0908844i
$665$	−535.790			−0.805699
$666$		0			0
$667$		−	317.199i		−	0.475561i
$668$	36.7653	+	28.3938i	0.0550379	+	0.0425057i
$669$		0			0
$670$	−242.128	−	492.926i	−0.361386	−	0.735711i
$671$		−	118.555i		−	0.176684i
$672$		0			0
$673$	−375.280			−0.557622			−0.278811	−	0.960346i	$-0.589940\pi$
$673$	−375.280			−0.557622			−0.278811	+	0.960346i	$0.589940\pi$
$674$	133.869	−	65.7571i	0.198618	−	0.0975625i
$675$		0			0
$676$	−260.508	+	337.315i	−0.385367	+	0.498986i
$677$	139.858			0.206585			0.103293	−	0.994651i	$-0.467062\pi$
$677$	139.858			0.206585			0.103293	+	0.994651i	$0.467062\pi$
$678$		0			0
$679$			392.422i			0.577941i
$680$	−367.848	+	1805.07i	−0.540953	+	2.65452i
$681$		0			0
$682$	−5.25921	+	2.58335i	−0.00771145	+	0.00378791i
$683$		−	1016.92i		−	1.48891i	−0.667673	−	0.744455i	$-0.732710\pi$
$683$		−	1016.92i		−	1.48891i	0.667673	−	0.744455i	$-0.267290\pi$
$684$		0			0
$685$	1124.65			1.64182
$686$	−763.729	−	1554.80i	−1.11331	−	2.26648i
$687$		0			0
$688$	51.0999	−	13.3507i	0.0742731	−	0.0194051i
$689$	−152.320			−0.221074
$690$		0			0
$691$			1104.69i			1.59869i	0.600873	+	0.799345i	$0.294820\pi$
$691$			1104.69i			1.59869i	−0.600873	+	0.799345i	$0.705180\pi$
$692$	346.367	−	448.487i	0.500530	−	0.648103i
$693$		0			0
$694$	−303.855	−	618.590i	−0.437832	−	0.891340i
$695$			295.678i			0.425436i
$696$		0			0
$697$	−950.039			−1.36304
$698$	−298.938	+	146.840i	−0.428278	+	0.210373i
$699$		0			0
$700$	−2701.98	−	2086.74i	−3.85998	−	2.98106i
$701$	808.397			1.15320			0.576602	−	0.817025i	$-0.304378\pi$
$701$	808.397			1.15320			0.576602	+	0.817025i	$0.304378\pi$
$702$		0			0
$703$			118.995i			0.169268i
$704$	−28.2952	+	66.5407i	−0.0401920	+	0.0945181i
$705$		0			0
$706$	959.598	−	471.361i	1.35920	−	0.667649i
$707$			844.261i			1.19415i
$708$		0			0
$709$	−326.875			−0.461037			−0.230519	−	0.973068i	$-0.574042\pi$
$709$	−326.875			−0.461037			−0.230519	+	0.973068i	$0.574042\pi$
$710$	−750.404	−	1527.68i	−1.05691	−	2.15166i
$711$		0			0
$712$	−114.429	+	561.516i	−0.160715	+	0.788646i
$713$	−29.6810			−0.0416283
$714$		0			0
$715$		−	85.3445i		−	0.119363i
$716$	−290.109	−	224.051i	−0.405180	−	0.312921i
$717$		0			0
$718$	−239.756	−	488.096i	−0.333921	−	0.679799i
$719$		−	197.399i		−	0.274547i	−0.990533	−	0.137273i	$-0.956166\pi$
$719$		−	197.399i		−	0.274547i	0.990533	−	0.137273i	$-0.0438339\pi$
$720$		0			0
$721$	−1266.50			−1.75659
$722$	34.1074	−	16.7537i	0.0472401	−	0.0232046i
$723$		0			0
$724$	291.803	−	377.837i	0.403043	−	0.521874i
$725$	−1839.38			−2.53707
$726$		0			0
$727$		−	423.612i		−	0.582685i	−0.956619	−	0.291342i	$-0.905898\pi$
$727$		−	423.612i		−	0.582685i	0.956619	−	0.291342i	$-0.0941019\pi$
$728$	796.582	+	162.332i	1.09421	+	0.222984i
$729$		0			0
$730$	657.487	−	322.962i	0.900667	−	0.442413i
$731$			79.5189i			0.108781i
$732$		0			0
$733$	129.420			0.176561			0.0882807	−	0.996096i	$-0.471863\pi$
$733$	129.420			0.176561			0.0882807	+	0.996096i	$0.471863\pi$
$734$	47.5875	+	96.8788i	0.0648331	+	0.131987i
$735$		0			0
$736$	−277.253	+	239.342i	−0.376703	+	0.325193i
$737$	32.4548			0.0440363
$738$		0			0
$739$			265.338i			0.359049i	0.983753	+	0.179525i	$0.0574560\pi$
$739$			265.338i			0.359049i	−0.983753	+	0.179525i	$0.942544\pi$
$740$	−638.014	+	826.122i	−0.862181	+	1.11638i
$741$		0			0
$742$	−218.554	−	444.932i	−0.294547	−	0.599639i
$743$			1180.75i			1.58916i	0.607159	+	0.794581i	$0.292309\pi$
$743$			1180.75i			1.58916i	−0.607159	+	0.794581i	$0.707691\pi$
$744$		0			0
$745$	232.214			0.311697
$746$	−557.663	+	273.928i	−0.747538	+	0.367195i
$747$		0			0
$748$	−86.1617	−	66.5427i	−0.115189	−	0.0889608i
$749$	2074.60			2.76983
$750$		0			0
$751$		−	772.516i		−	1.02865i	−0.857595	−	0.514325i	$-0.828042\pi$
$751$		−	772.516i		−	1.02865i	0.857595	−	0.514325i	$-0.171958\pi$
$752$	−323.704	+	84.5734i	−0.430458	+	0.112465i
$753$		0			0
$754$	393.135	−	193.110i	0.521400	−	0.256115i
$755$		−	1237.28i		−	1.63879i
$756$		0			0
$757$	578.181			0.763780			0.381890	−	0.924208i	$-0.375273\pi$
$757$	578.181			0.763780			0.381890	+	0.924208i	$0.375273\pi$
$758$	102.580	+	208.834i	0.135330	+	0.275506i
$759$		0			0
$760$	326.618	+	66.5600i	0.429760	+	0.0875790i
$761$	−8.24240			−0.0108310			−0.00541551	−	0.999985i	$-0.501724\pi$
$761$	−8.24240			−0.0108310			−0.00541551	+	0.999985i	$0.501724\pi$
$762$		0			0
$763$		−	1999.85i		−	2.62103i
$764$	1.79767	+	1.38834i	0.00235297	+	0.00181719i
$765$		0			0
$766$	−274.290	−	558.402i	−0.358082	−	0.728984i
$767$		−	203.663i		−	0.265532i
$768$		0			0
$769$	451.396			0.586992			0.293496	−	0.955960i	$-0.405181\pi$
$769$	451.396			0.586992			0.293496	+	0.955960i	$0.405181\pi$
$770$	249.294	−	122.455i	0.323759	−	0.159032i
$771$		0			0
$772$	8.81723	−	11.4169i	0.0114213	−	0.0147887i
$773$	−640.940			−0.829159			−0.414580	−	0.910013i	$-0.636071\pi$
$773$	−640.940			−0.829159			−0.414580	+	0.910013i	$0.636071\pi$
$774$		0			0
$775$			172.114i			0.222083i
$776$	48.7497	−	239.221i	0.0628218	−	0.308274i
$777$		0			0
$778$	−58.2682	+	28.6217i	−0.0748949	+	0.0367888i
$779$			171.904i			0.220673i
$780$		0			0
$781$	100.584			0.128788
$782$	−243.132	−	494.969i	−0.310910	−	0.632953i
$783$		0			0
$784$	470.601	+	1801.22i	0.600256	+	2.29748i
$785$	−843.934			−1.07507
$786$		0			0
$787$			967.945i			1.22992i	0.788559	+	0.614959i	$0.210827\pi$
$787$			967.945i			1.22992i	−0.788559	+	0.614959i	$0.789173\pi$
$788$	−149.536	+	193.625i	−0.189767	+	0.245717i
$789$		0			0
$790$	1188.78	+	2420.13i	1.50479	+	3.06345i
$791$			1813.22i			2.29231i
$792$		0			0
$793$	829.254			1.04572
$794$	1295.29	−	636.256i	1.63135	−	0.801331i
$795$		0			0
$796$	659.931	+	509.664i	0.829059	+	0.640282i
$797$	1120.25			1.40558			0.702792	−	0.711396i	$-0.251937\pi$
$797$	1120.25			1.40558			0.702792	+	0.711396i	$0.251937\pi$
$798$		0			0
$799$		−	503.731i		−	0.630452i
$800$	1387.90	+	1607.74i	1.73487	+	2.00967i
$801$		0			0
$802$	−677.085	+	332.588i	−0.844246	+	0.414699i
$803$			43.2896i			0.0539098i
$804$		0			0
$805$	1406.92			1.74773
$806$	−18.0697	−	36.7864i	−0.0224190	−	0.0456407i
$807$		0			0
$808$	104.881	−	514.662i	0.129803	−	0.636958i
$809$	−274.505			−0.339313			−0.169657	−	0.985503i	$-0.554266\pi$
$809$	−274.505			−0.339313			−0.169657	+	0.985503i	$0.554266\pi$
$810$		0			0
$811$		−	520.272i		−	0.641519i	−0.947161	−	0.320759i	$-0.896062\pi$
$811$		−	520.272i		−	0.641519i	0.947161	−	0.320759i	$-0.103938\pi$
$812$	1128.16	+	871.281i	1.38936	+	1.07301i
$813$		0			0
$814$	−27.1964	−	55.3665i	−0.0334108	−	0.0680178i
$815$			1107.70i			1.35914i
$816$		0			0
$817$	14.3885			0.0176114
$818$	−1234.89	+	606.585i	−1.50965	+	0.741547i
$819$		0			0
$820$	−921.694	+	1193.44i	−1.12402	+	1.45542i
$821$	696.715			0.848617			0.424309	−	0.905518i	$-0.360517\pi$
$821$	696.715			0.848617			0.424309	+	0.905518i	$0.360517\pi$
$822$		0			0
$823$			392.242i			0.476601i	0.971191	+	0.238300i	$0.0765903\pi$
$823$			392.242i			0.476601i	−0.971191	+	0.238300i	$0.923410\pi$
$824$	772.061	+	157.335i	0.936967	+	0.190941i
$825$		0			0
$826$	594.905	−	292.221i	0.720225	−	0.353779i
$827$		−	1195.11i		−	1.44511i	−0.691313	−	0.722556i	$-0.742967\pi$
$827$		−	1195.11i		−	1.44511i	0.691313	−	0.722556i	$-0.257033\pi$
$828$		0			0
$829$	401.086			0.483819			0.241910	−	0.970299i	$-0.422226\pi$
$829$	401.086			0.483819			0.241910	+	0.970299i	$0.422226\pi$
$830$	318.417	+	648.235i	0.383635	+	0.781006i
$831$		0			0
$832$	−465.431	−	197.915i	−0.559412	−	0.237879i
$833$	−2802.97			−3.36491
$834$		0			0
$835$			111.010i			0.132947i
$836$	−12.0405	+	15.5905i	−0.0144025	+	0.0186489i
$837$		0			0
$838$	−384.658	−	783.090i	−0.459020	−	0.934474i
$839$			50.4781i			0.0601646i	0.999547	+	0.0300823i	$0.00957694\pi$
$839$			50.4781i			0.0601646i	−0.999547	+	0.0300823i	$0.990423\pi$
$840$		0			0
$841$	−73.0009			−0.0868025
$842$	−316.002	+	155.222i	−0.375299	+	0.184349i
$843$		0			0
$844$	238.158	+	183.929i	0.282178	+	0.217926i
$845$	−1018.50			−1.20533
$846$		0			0
$847$		−	1539.53i		−	1.81763i
$848$	77.9573	+	298.381i	0.0919308	+	0.351865i
$849$		0			0
$850$	−2870.23	+	1409.88i	−3.37674	+	1.65868i
$851$		−	312.467i		−	0.367177i
$852$		0			0
$853$	−887.671			−1.04065			−0.520323	−	0.853970i	$-0.674188\pi$
$853$	−887.671			−1.04065			−0.520323	+	0.853970i	$0.674188\pi$
$854$	1189.84	+	2422.28i	1.39325	+	2.83639i
$855$		0			0
$856$	−1264.68	−	257.723i	−1.47743	−	0.301078i
$857$	−606.425			−0.707614			−0.353807	−	0.935319i	$-0.615113\pi$
$857$	−606.425			−0.707614			−0.353807	+	0.935319i	$0.615113\pi$
$858$		0			0
$859$		−	470.482i		−	0.547709i	−0.961771	−	0.273854i	$-0.911701\pi$
$859$		−	470.482i		−	0.547709i	0.961771	−	0.273854i	$-0.0882986\pi$
$860$	99.8919	+	77.1464i	0.116153	+	0.0897052i
$861$		0			0
$862$	648.998	+	1321.23i	0.752898	+	1.53275i
$863$		−	136.781i		−	0.158494i	−0.996855	−	0.0792472i	$-0.974748\pi$
$863$		−	136.781i		−	0.158494i	0.996855	−	0.0792472i	$-0.0252516\pi$
$864$		0			0
$865$	1354.18			1.56552
$866$	700.844	−	344.259i	0.809289	−	0.397528i
$867$		0			0
$868$	81.5274	−	105.564i	0.0939256	−	0.121618i
$869$	−159.343			−0.183364
$870$		0			0
$871$			227.011i			0.260632i
$872$	−248.437	+	1219.11i	−0.284904	+	1.39806i
$873$		0			0
$874$	−89.5619	+	43.9933i	−0.102474	+	0.0503356i
$875$		−	5085.50i		−	5.81200i
$876$		0			0
$877$	564.591			0.643775			0.321888	−	0.946778i	$-0.395683\pi$
$877$	564.591			0.643775			0.321888	+	0.946778i	$0.395683\pi$
$878$	461.636	+	939.801i	0.525781	+	1.07039i
$879$		0			0
$880$	−167.182	+	43.6792i	−0.189980	+	0.0496355i
$881$	108.605			0.123275			0.0616376	−	0.998099i	$-0.480368\pi$
$881$	108.605			0.123275			0.0616376	+	0.998099i	$0.480368\pi$
$882$		0			0
$883$		−	378.797i		−	0.428988i	−0.976725	−	0.214494i	$-0.931190\pi$
$883$		−	378.797i		−	0.428988i	0.976725	−	0.214494i	$-0.0688103\pi$
$884$	465.444	−	602.673i	0.526521	−	0.681757i
$885$		0			0
$886$	6.07767	+	12.3730i	0.00685968	+	0.0139650i
$887$			1220.79i			1.37631i	0.725563	+	0.688155i	$0.241579\pi$
$887$			1220.79i			1.37631i	−0.725563	+	0.688155i	$0.758421\pi$
$888$		0			0
$889$	736.910			0.828920
$890$	−1229.17	+	603.774i	−1.38109	+	0.678398i
$891$		0			0
$892$	1018.56	+	786.633i	1.14188	+	0.881875i
$893$	−91.1473			−0.102069
$894$		0			0
$895$		−	875.966i		−	0.978733i
$896$	−89.6963	−	1643.51i	−0.100107	−	1.83428i
$897$		0			0
$898$	−528.879	+	259.789i	−0.588952	+	0.289297i
$899$		−	71.8632i		−	0.0799368i
$900$		0			0
$901$	−464.325			−0.515344
$902$	−39.2887	−	79.9841i	−0.0435573	−	0.0886742i
$903$		0			0
$904$	225.252	−	1105.34i	0.249173	−	1.22272i
$905$	1140.85			1.26061
$906$		0			0
$907$		−	39.4352i		−	0.0434787i	−0.999764	−	0.0217393i	$-0.993080\pi$
$907$		−	39.4352i		−	0.0434787i	0.999764	−	0.0217393i	$-0.00692039\pi$
$908$	−1374.82	−	1061.77i	−1.51412	−	1.16935i
$909$		0			0
$910$	856.531	+	1743.73i	0.941243	+	1.91619i
$911$			283.204i			0.310871i	0.987846	+	0.155436i	$0.0496781\pi$
$911$			283.204i			0.310871i	−0.987846	+	0.155436i	$0.950322\pi$
$912$		0			0
$913$	−42.6805			−0.0467475
$914$	1334.19	−	655.360i	1.45972	−	0.717024i
$915$		0			0
$916$	−256.976	+	332.741i	−0.280542	+	0.363255i
$917$	2731.96			2.97924
$918$		0			0
$919$			380.395i			0.413923i	0.978349	+	0.206962i	$0.0663575\pi$
$919$			380.395i			0.413923i	−0.978349	+	0.206962i	$0.933642\pi$
$920$	−857.659	−	174.779i	−0.932239	−	0.189977i
$921$		0			0
$922$	120.128	−	59.0076i	0.130291	−	0.0639995i
$923$			703.551i			0.762244i
$924$		0			0
$925$	−1811.94			−1.95885
$926$	−164.798	−	335.496i	−0.177967	−	0.362307i
$927$		0			0
$928$	−579.492	−	671.282i	−0.624453	−	0.723365i
$929$	−1276.35			−1.37389			−0.686946	−	0.726708i	$-0.741049\pi$
$929$	−1276.35			−1.37389			−0.686946	+	0.726708i	$0.741049\pi$
$930$		0			0
$931$			507.181i			0.544770i
$932$	−624.406	+	808.502i	−0.669963	+	0.867491i
$933$		0			0
$934$	−667.225	−	1358.34i	−0.714374	−	1.45433i
$935$		−	260.160i		−	0.278246i
$936$		0			0
$937$	468.427			0.499922			0.249961	−	0.968256i	$-0.419582\pi$
$937$	468.427			0.499922			0.249961	+	0.968256i	$0.419582\pi$
$938$	−663.105	+	325.721i	−0.706935	+	0.347251i
$939$		0			0
$940$	−632.788	−	488.702i	−0.673179	−	0.519896i
$941$	−167.876			−0.178402			−0.0892008	−	0.996014i	$-0.528431\pi$
$941$	−167.876			−0.178402			−0.0892008	+	0.996014i	$0.528431\pi$
$942$		0			0
$943$		−	451.400i		−	0.478685i
$944$	−398.957	+	104.234i	−0.422624	+	0.110418i
$945$		0			0
$946$	−6.69473	+	3.28849i	−0.00707688	+	0.00347621i
$947$		−	1044.57i		−	1.10303i	−0.834166	−	0.551513i	$-0.814051\pi$
$947$		−	1044.57i		−	1.10303i	0.834166	−	0.551513i	$-0.185949\pi$
$948$		0			0
$949$	−302.797			−0.319069
$950$	255.109	+	519.352i	0.268536	+	0.546687i
$951$		0			0
$952$	2428.26	+	494.845i	2.55069	+	0.519795i
$953$	131.011			0.137472			0.0687362	−	0.997635i	$-0.478103\pi$
$953$	131.011			0.137472			0.0687362	+	0.997635i	$0.478103\pi$
$954$		0			0
$955$			5.42794i			0.00568371i
$956$	−1009.82	−	779.886i	−1.05630	−	0.815781i
$957$		0			0
$958$	−560.157	−	1140.37i	−0.584715	−	1.19037i
$959$		−	1512.93i		−	1.57761i
$960$		0			0
$961$	954.276			0.993003
$962$	387.271	−	190.230i	0.402568	−	0.197744i
$963$		0			0
$964$	492.061	−	637.138i	0.510437	−	0.660931i
$965$	34.4725			0.0357228
$966$		0			0
$967$		−	1330.66i		−	1.37607i	−0.725679	−	0.688034i	$-0.758474\pi$
$967$		−	1330.66i		−	1.37607i	0.725679	−	0.688034i	$-0.241526\pi$
$968$	−191.253	+	938.499i	−0.197575	+	0.969524i
$969$		0			0
$970$	523.658	−	257.224i	0.539853	−	0.265179i
$971$		−	1472.05i		−	1.51601i	−0.652247	−	0.758007i	$-0.726173\pi$
$971$		−	1472.05i		−	1.51601i	0.652247	−	0.758007i	$-0.273827\pi$
$972$		0			0
$973$	397.758			0.408796
$974$	563.546	+	1147.27i	0.578589	+	1.17789i
$975$		0			0
$976$	−424.411	−	1624.43i	−0.434848	−	1.66438i
$977$	884.608			0.905433			0.452717	−	0.891654i	$-0.350455\pi$
$977$	884.608			0.905433			0.452717	+	0.891654i	$0.350455\pi$
$978$		0			0
$979$		−	80.9296i		−	0.0826655i
$980$	−2719.34	+	3521.09i	−2.77484	+	3.59295i
$981$		0			0
$982$	576.604	+	1173.85i	0.587173	+	1.19537i
$983$			859.121i			0.873978i	0.899467	+	0.436989i	$0.143955\pi$
$983$			859.121i			0.873978i	−0.899467	+	0.436989i	$0.856045\pi$
$984$		0			0
$985$	−584.638			−0.593541
$986$	1198.41	−	588.668i	1.21543	−	0.597026i
$987$		0			0
$988$	−109.050	−	84.2195i	−0.110375	−	0.0852424i
$989$	−37.7825			−0.0382027
$990$		0			0
$991$		−	434.553i		−	0.438499i	−0.975669	−	0.219250i	$-0.929639\pi$
$991$		−	434.553i		−	0.438499i	0.975669	−	0.219250i	$-0.0703609\pi$
$992$	−62.8132	+	54.2242i	−0.0633198	+	0.0546615i
$993$		0			0
$994$	−2055.09	+	1009.47i	−2.06750	+	1.01557i
$995$			1992.62i			2.00263i
$996$		0			0
$997$	−451.031			−0.452388			−0.226194	−	0.974082i	$-0.572628\pi$
$997$	−451.031			−0.452388			−0.226194	+	0.974082i	$0.572628\pi$
$998$	−84.0341	−	171.077i	−0.0842025	−	0.171420i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	684.3.g.c.343.6		36
3.2	odd	2		228.3.g.a.115.31	✓	36
4.3	odd	2	inner	684.3.g.c.343.5		36
12.11	even	2		228.3.g.a.115.32	yes	36

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
228.3.g.a.115.31	✓	36	3.2	odd	2
228.3.g.a.115.32	yes	36	12.11	even	2
684.3.g.c.343.5		36	4.3	odd	2	inner
684.3.g.c.343.6		36	1.1	even	1	trivial

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)

\(f(q)\)	\(=\)	\(q+(-1.79512 + 0.881776i) q^{2} +(2.44494 - 3.16579i) q^{4} +9.55892 q^{5} -12.8591i q^{7} +(-1.59745 + 7.83889i) q^{8} +O(q^{10})\)	\(q+(-1.79512 + 0.881776i) q^{2} +(2.44494 - 3.16579i) q^{4} +9.55892 q^{5} -12.8591i q^{7} +(-1.59745 + 7.83889i) q^{8} +(-17.1594 + 8.42882i) q^{10} -1.12979i q^{11} +7.90255 q^{13} +(11.3388 + 23.0836i) q^{14} +(-4.04452 - 15.4804i) q^{16} +24.0897 q^{17} -4.35890i q^{19} +(23.3710 - 30.2616i) q^{20} +(0.996226 + 2.02812i) q^{22} +11.4459i q^{23} +66.3729 q^{25} +(-14.1861 + 6.96828i) q^{26} +(-40.7091 - 31.4396i) q^{28} -27.7128 q^{29} +2.59314i q^{31} +(20.9106 + 24.2228i) q^{32} +(-43.2441 + 21.2417i) q^{34} -122.919i q^{35} -27.2994 q^{37} +(3.84357 + 7.82477i) q^{38} +(-15.2699 + 74.9313i) q^{40} -39.4375 q^{41} +3.30095i q^{43} +(-3.57670 - 2.76228i) q^{44} +(-10.0928 - 20.5469i) q^{46} -20.9106i q^{47} -116.355 q^{49} +(-119.148 + 58.5260i) q^{50} +(19.3213 - 25.0179i) q^{52} -19.2748 q^{53} -10.7996i q^{55} +(100.801 + 20.5417i) q^{56} +(49.7479 - 24.4365i) q^{58} -25.7718i q^{59} +104.935 q^{61} +(-2.28657 - 4.65501i) q^{62} +(-58.8963 - 25.0445i) q^{64} +75.5398 q^{65} +28.7262i q^{67} +(58.8980 - 76.2631i) q^{68} +(108.387 + 220.654i) q^{70} +89.0283i q^{71} -38.3163 q^{73} +(49.0058 - 24.0719i) q^{74} +(-13.7994 - 10.6573i) q^{76} -14.5281 q^{77} -141.038i q^{79} +(-38.6612 - 147.976i) q^{80} +(70.7953 - 34.7751i) q^{82} -37.7772i q^{83} +230.272 q^{85} +(-2.91070 - 5.92561i) q^{86} +(8.85633 + 1.80479i) q^{88} +71.6321 q^{89} -101.619i q^{91} +(36.2355 + 27.9847i) q^{92} +(18.4385 + 37.5372i) q^{94} -41.6664i q^{95} -30.5172 q^{97} +(208.872 - 102.599i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8}+O(q^{10}) \) 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8	\( 36 q - 4 q^{2} + 12 q^{4} - 8 q^{5} + 20 q^{8} + 8 q^{10} - 24 q^{13} + 12 q^{14} + 4 q^{16} + 40 q^{17} + 80 q^{20} + 12 q^{22} + 284 q^{25} + 112 q^{26} - 48 q^{28} - 104 q^{29} - 44 q^{32} + 140 q^{34} - 184 q^{37} + 180 q^{40} + 200 q^{41} - 96 q^{44} - 28 q^{46} - 332 q^{49} - 176 q^{50} + 276 q^{52} - 264 q^{53} + 192 q^{56} - 184 q^{58} + 40 q^{61} + 240 q^{62} - 372 q^{64} - 176 q^{65} + 104 q^{68} - 60 q^{70} + 424 q^{73} + 104 q^{74} + 400 q^{77} - 704 q^{80} + 528 q^{82} - 128 q^{85} - 668 q^{86} - 496 q^{88} + 520 q^{89} + 456 q^{92} - 32 q^{94} - 440 q^{97} + 472 q^{98}+O(q^{100}) \) 36 * q - 4 * q^2 + 12 * q^4 - 8 * q^5 + 20 * q^8 + 8 * q^10 - 24 * q^13 + 12 * q^14 + 4 * q^16 + 40 * q^17 + 80 * q^20 + 12 * q^22 + 284 * q^25 + 112 * q^26 - 48 * q^28 - 104 * q^29 - 44 * q^32 + 140 * q^34 - 184 * q^37 + 180 * q^40 + 200 * q^41 - 96 * q^44 - 28 * q^46 - 332 * q^49 - 176 * q^50 + 276 * q^52 - 264 * q^53 + 192 * q^56 - 184 * q^58 + 40 * q^61 + 240 * q^62 - 372 * q^64 - 176 * q^65 + 104 * q^68 - 60 * q^70 + 424 * q^73 + 104 * q^74 + 400 * q^77 - 704 * q^80 + 528 * q^82 - 128 * q^85 - 668 * q^86 - 496 * q^88 + 520 * q^89 + 456 * q^92 - 32 * q^94 - 440 * q^97 + 472 * q^98

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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