LMFDB - Embedded newform 308.3.r.a.57.7

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [308,3,Mod(29,308)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(308, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 0, 7]))

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

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

chi := DirichletCharacter("308.29");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 308 = 2^{2} \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	308.r (of order $10$, degree $4$, 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:	$8.39239214230$
Analytic rank:	$0$
Dimension:	$48$
Relative dimension:	$12$ over $\Q(\zeta_{10})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{10}]$

Embedding invariants

Embedding label			57.7
Character	$\chi$	$=$	308.57
Dual form			308.3.r.a.281.7

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.251197 - 0.182505i) q^{3} +(2.69700 + 8.30052i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.75136 + 8.46782i) q^{9} +O(q^{10})$	\(q+(0.251197 - 0.182505i) q^{3} +(2.69700 + 8.30052i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.75136 + 8.46782i) q^{9} +(-7.36521 - 8.17029i) q^{11} +(-4.10300 - 1.33315i) q^{13} +(2.19237 + 1.59285i) q^{15} +(-21.4513 + 6.96994i) q^{17} +(-12.2753 - 16.8956i) q^{19} +0.821498i q^{21} +29.3769 q^{23} +(-41.3993 + 30.0784i) q^{25} +(1.71783 + 5.28693i) q^{27} +(8.91872 - 12.2756i) q^{29} +(-9.46221 + 29.1217i) q^{31} +(-3.34124 - 0.708163i) q^{33} +(-21.9611 - 7.13559i) q^{35} +(49.0892 + 35.6654i) q^{37} +(-1.27397 + 0.413937i) q^{39} +(21.9890 + 30.2652i) q^{41} +42.9288i q^{43} -77.7077 q^{45} +(-19.3327 + 14.0460i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(-4.11645 + 5.66581i) q^{51} +(14.9001 - 45.8578i) q^{53} +(47.9536 - 83.1703i) q^{55} +(-6.16706 - 2.00380i) q^{57} +(79.3047 + 57.6182i) q^{59} +(-77.7564 + 25.2646i) q^{61} +(-13.8463 - 19.0578i) q^{63} -37.6525i q^{65} +45.5769 q^{67} +(7.37941 - 5.36145i) q^{69} +(-11.9202 - 36.6865i) q^{71} +(22.8473 - 31.4466i) q^{73} +(-4.90993 + 15.1112i) q^{75} +(28.9421 - 3.05903i) q^{77} +(16.7576 + 5.44489i) q^{79} +(-63.4320 - 46.0860i) q^{81} +(-49.3657 + 16.0399i) q^{83} +(-115.708 - 159.259i) q^{85} -4.71130i q^{87} +117.237 q^{89} +(9.23425 - 6.70908i) q^{91} +(2.93799 + 9.04220i) q^{93} +(107.135 - 147.459i) q^{95} +(-10.3629 + 31.8938i) q^{97} +(89.4489 - 39.8879i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	$ 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) $ 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/308\mathbb{Z}\right)^\times$.

$n$	$45$	$57$	$155$
$\chi(n)$	$1$	$e\left(\frac{1}{10}\right)$	$1$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	0.251197	−	0.182505i	0.0837324	−	0.0608352i	−0.545131	−	0.838351i	$-0.683520\pi$
$3$	0.251197	−	0.182505i	0.0837324	−	0.0608352i	0.628864	+	0.777515i	$0.283520\pi$
$4$		0			0
$5$	2.69700	+	8.30052i	0.539400	+	1.66010i	0.733945	+	0.679209i	$0.237677\pi$
$5$	2.69700	+	8.30052i	0.539400	+	1.66010i	−0.194544	+	0.980894i	$0.562323\pi$
$6$		0			0
$7$	−1.55513	+	2.14046i	−0.222162	+	0.305780i
$7$	−1.55513	+	2.14046i	−0.222162	+	0.305780i
$8$		0			0
$9$	−2.75136	+	8.46782i	−0.305707	+	0.940869i
$10$		0			0
$11$	−7.36521	−	8.17029i	−0.669565	−	0.742754i
$11$	−7.36521	−	8.17029i	−0.669565	−	0.742754i
$12$		0			0
$13$	−4.10300	−	1.33315i	−0.315615	−	0.102550i	0.146926	−	0.989148i	$-0.453062\pi$
$13$	−4.10300	−	1.33315i	−0.315615	−	0.102550i	−0.462541	+	0.886598i	$0.653062\pi$
$14$		0			0
$15$	2.19237	+	1.59285i	0.146158	+	0.106190i
$16$		0			0
$17$	−21.4513	+	6.96994i	−1.26184	+	0.409997i	−0.862150	−	0.506654i	$-0.830882\pi$
$17$	−21.4513	+	6.96994i	−1.26184	+	0.409997i	−0.399690	+	0.916650i	$0.630882\pi$
$18$		0			0
$19$	−12.2753	−	16.8956i	−0.646070	−	0.889240i	0.352851	−	0.935680i	$-0.385212\pi$
$19$	−12.2753	−	16.8956i	−0.646070	−	0.889240i	−0.998921	+	0.0464399i	$0.985212\pi$
$20$		0			0
$21$			0.821498i			0.0391189i
$22$		0			0
$23$	29.3769			1.27726			0.638629	−	0.769515i	$-0.279502\pi$
$23$	29.3769			1.27726			0.638629	+	0.769515i	$0.279502\pi$
$24$		0			0
$25$	−41.3993	+	30.0784i	−1.65597	+	1.20313i
$26$		0			0
$27$	1.71783	+	5.28693i	0.0636233	+	0.195812i
$28$		0			0
$29$	8.91872	−	12.2756i	0.307542	−	0.423295i	−0.627071	−	0.778962i	$-0.715746\pi$
$29$	8.91872	−	12.2756i	0.307542	−	0.423295i	0.934613	+	0.355667i	$0.115746\pi$
$30$		0			0
$31$	−9.46221	+	29.1217i	−0.305233	+	0.939410i	0.674358	+	0.738405i	$0.264421\pi$
$31$	−9.46221	+	29.1217i	−0.305233	+	0.939410i	−0.979590	+	0.201005i	$0.935579\pi$
$32$		0			0
$33$	−3.34124	−	0.708163i	−0.101250	−	0.0214595i
$34$		0			0
$35$	−21.9611	−	7.13559i	−0.627460	−	0.203874i
$36$		0			0
$37$	49.0892	+	35.6654i	1.32673	+	0.963929i	0.999822	+	0.0188738i	$0.00600808\pi$
$37$	49.0892	+	35.6654i	1.32673	+	0.963929i	0.326912	+	0.945055i	$0.393992\pi$
$38$		0			0
$39$	−1.27397	+	0.413937i	−0.0326659	+	0.0106138i
$40$		0			0
$41$	21.9890	+	30.2652i	0.536317	+	0.738176i	0.988077	−	0.153963i	$-0.0492037\pi$
$41$	21.9890	+	30.2652i	0.536317	+	0.738176i	−0.451760	+	0.892139i	$0.649204\pi$
$42$		0			0
$43$			42.9288i			0.998345i	0.866503	+	0.499172i	$0.166363\pi$
$43$			42.9288i			0.998345i	−0.866503	+	0.499172i	$0.833637\pi$
$44$		0			0
$45$	−77.7077			−1.72684
$46$		0			0
$47$	−19.3327	+	14.0460i	−0.411335	+	0.298852i	−0.774142	−	0.633012i	$-0.781818\pi$
$47$	−19.3327	+	14.0460i	−0.411335	+	0.298852i	0.362807	+	0.931864i	$0.381818\pi$
$48$		0			0
$49$	−2.16312	−	6.65740i	−0.0441453	−	0.135865i
$50$		0			0
$51$	−4.11645	+	5.66581i	−0.0807147	+	0.111094i
$52$		0			0
$53$	14.9001	−	45.8578i	0.281134	−	0.865242i	−0.706397	−	0.707816i	$-0.749681\pi$
$53$	14.9001	−	45.8578i	0.281134	−	0.865242i	0.987531	−	0.157426i	$-0.0503194\pi$
$54$		0			0
$55$	47.9536	−	83.1703i	0.871884	−	1.51219i
$56$		0			0
$57$	−6.16706	−	2.00380i	−0.108194	−	0.0351544i
$58$		0			0
$59$	79.3047	+	57.6182i	1.34415	+	0.976580i	0.999280	+	0.0379287i	$0.0120760\pi$
$59$	79.3047	+	57.6182i	1.34415	+	0.976580i	0.344867	+	0.938652i	$0.387924\pi$
$60$		0			0
$61$	−77.7564	+	25.2646i	−1.27470	+	0.414174i	−0.866709	−	0.498814i	$-0.833769\pi$
$61$	−77.7564	+	25.2646i	−1.27470	+	0.414174i	−0.407986	+	0.912988i	$0.633769\pi$
$62$		0			0
$63$	−13.8463	−	19.0578i	−0.219782	−	0.302504i
$64$		0			0
$65$		−	37.6525i		−	0.579269i
$66$		0			0
$67$	45.5769			0.680252			0.340126	−	0.940380i	$-0.389530\pi$
$67$	45.5769			0.680252			0.340126	+	0.940380i	$0.389530\pi$
$68$		0			0
$69$	7.37941	−	5.36145i	0.106948	−	0.0777022i
$70$		0			0
$71$	−11.9202	−	36.6865i	−0.167890	−	0.516711i	0.831348	−	0.555752i	$-0.187570\pi$
$71$	−11.9202	−	36.6865i	−0.167890	−	0.516711i	−0.999238	+	0.0390412i	$0.987570\pi$
$72$		0			0
$73$	22.8473	−	31.4466i	0.312977	−	0.430775i	−0.623330	−	0.781959i	$-0.714221\pi$
$73$	22.8473	−	31.4466i	0.312977	−	0.430775i	0.936307	+	0.351184i	$0.114221\pi$
$74$		0			0
$75$	−4.90993	+	15.1112i	−0.0654657	+	0.201483i
$76$		0			0
$77$	28.9421	−	3.05903i	0.375871	−	0.0397277i
$78$		0			0
$79$	16.7576	+	5.44489i	0.212122	+	0.0689226i	0.413150	−	0.910663i	$-0.364428\pi$
$79$	16.7576	+	5.44489i	0.212122	+	0.0689226i	−0.201028	+	0.979585i	$0.564428\pi$
$80$		0			0
$81$	−63.4320	−	46.0860i	−0.783111	−	0.568964i
$82$		0			0
$83$	−49.3657	+	16.0399i	−0.594767	+	0.193252i	−0.590905	−	0.806741i	$-0.701229\pi$
$83$	−49.3657	+	16.0399i	−0.594767	+	0.193252i	−0.00386189	+	0.999993i	$0.501229\pi$
$84$		0			0
$85$	−115.708	−	159.259i	−1.36127	−	1.87363i
$86$		0			0
$87$		−	4.71130i		−	0.0541529i
$88$		0			0
$89$	117.237			1.31727			0.658633	−	0.752464i	$-0.271135\pi$
$89$	117.237			1.31727			0.658633	+	0.752464i	$0.271135\pi$
$90$		0			0
$91$	9.23425	−	6.70908i	0.101475	−	0.0737261i
$92$		0			0
$93$	2.93799	+	9.04220i	0.0315913	+	0.0972279i
$94$		0			0
$95$	107.135	−	147.459i	1.12774	−	1.55220i
$96$		0			0
$97$	−10.3629	+	31.8938i	−0.106834	+	0.328802i	−0.990157	−	0.139964i	$-0.955301\pi$
$97$	−10.3629	+	31.8938i	−0.106834	+	0.328802i	0.883322	+	0.468766i	$0.155301\pi$
$98$		0			0
$99$	89.4489	−	39.8879i	0.903524	−	0.402908i
$100$		0			0
$101$	130.437	+	42.3816i	1.29146	+	0.419620i	0.872601	−	0.488434i	$-0.162432\pi$
$101$	130.437	+	42.3816i	1.29146	+	0.419620i	0.418855	+	0.908053i	$0.362432\pi$
$102$		0			0
$103$	42.0100	+	30.5220i	0.407864	+	0.296330i	0.772736	−	0.634727i	$-0.218888\pi$
$103$	42.0100	+	30.5220i	0.407864	+	0.296330i	−0.364873	+	0.931057i	$0.618888\pi$
$104$		0			0
$105$	−6.81885	+	2.21558i	−0.0649415	+	0.0211008i
$106$		0			0
$107$	−30.1636	−	41.5166i	−0.281902	−	0.388005i	0.644460	−	0.764638i	$-0.277082\pi$
$107$	−30.1636	−	41.5166i	−0.281902	−	0.388005i	−0.926363	+	0.376632i	$0.877082\pi$
$108$		0			0
$109$			112.885i			1.03564i	0.855490	+	0.517820i	$0.173256\pi$
$109$			112.885i			1.03564i	−0.855490	+	0.517820i	$0.826744\pi$
$110$		0			0
$111$	18.8402			0.169731
$112$		0			0
$113$	−50.4550	+	36.6577i	−0.446505	+	0.324405i	−0.788214	−	0.615401i	$-0.788994\pi$
$113$	−50.4550	+	36.6577i	−0.446505	+	0.324405i	0.341710	+	0.939806i	$0.388994\pi$
$114$		0			0
$115$	79.2296	+	243.844i	0.688953	+	2.12038i
$116$		0			0
$117$	22.5777	−	31.0755i	0.192972	−	0.265602i
$118$		0			0
$119$	18.4407	−	56.7547i	0.154964	−	0.476931i
$120$		0			0
$121$	−12.5073	+	120.352i	−0.103366	+	0.994643i
$122$		0			0
$123$	11.0471	+	3.58943i	0.0898142	+	0.0291824i
$124$		0			0
$125$	−184.799	−	134.264i	−1.47839	−	1.07411i
$126$		0			0
$127$	220.407	−	71.6147i	1.73549	−	0.563895i	0.741267	−	0.671211i	$-0.234225\pi$
$127$	220.407	−	71.6147i	1.73549	−	0.563895i	0.994225	+	0.107315i	$0.0342254\pi$
$128$		0			0
$129$	7.83474	+	10.7836i	0.0607345	+	0.0835938i
$130$		0			0
$131$		−	92.0417i		−	0.702609i	−0.936261	−	0.351304i	$-0.885738\pi$
$131$		−	92.0417i		−	0.702609i	0.936261	−	0.351304i	$-0.114262\pi$
$132$		0			0
$133$	55.2540			0.415444
$134$		0			0
$135$	−39.2513	+	28.5177i	−0.290750	+	0.211242i
$136$		0			0
$137$	−70.6563	−	217.458i	−0.515739	−	1.58728i	−0.781933	−	0.623363i	$-0.785766\pi$
$137$	−70.6563	−	217.458i	−0.515739	−	1.58728i	0.266193	−	0.963920i	$-0.414234\pi$
$138$		0			0
$139$	70.1526	−	96.5568i	0.504695	−	0.694653i	−0.478319	−	0.878186i	$-0.658754\pi$
$139$	70.1526	−	96.5568i	0.504695	−	0.694653i	0.983013	+	0.183534i	$0.0587536\pi$
$140$		0			0
$141$	−2.29285	+	7.05666i	−0.0162613	+	0.0500472i
$142$		0			0
$143$	19.3273	+	43.3416i	0.135156	+	0.303088i
$144$		0			0
$145$	125.947	+	40.9228i	0.868602	+	0.282226i
$146$		0			0
$147$	−1.75838	−	1.27754i	−0.0119618	−	0.00869074i
$148$		0			0
$149$	−176.943	+	57.4923i	−1.18754	+	0.385854i	−0.835162	−	0.550004i	$-0.814626\pi$
$149$	−176.943	+	57.4923i	−1.18754	+	0.385854i	−0.352376	+	0.935859i	$0.614626\pi$
$150$		0			0
$151$	−19.0585	−	26.2318i	−0.126215	−	0.173720i	0.741233	−	0.671248i	$-0.234241\pi$
$151$	−19.0585	−	26.2318i	−0.126215	−	0.173720i	−0.867448	+	0.497527i	$0.834241\pi$
$152$		0			0
$153$		−	200.822i		−	1.31256i
$154$		0			0
$155$	−267.245			−1.72416
$156$		0			0
$157$	−60.7878	+	44.1649i	−0.387183	+	0.281305i	−0.764300	−	0.644861i	$-0.776915\pi$
$157$	−60.7878	+	44.1649i	−0.387183	+	0.281305i	0.377117	+	0.926166i	$0.376915\pi$
$158$		0			0
$159$	−4.62644	−	14.2387i	−0.0290971	−	0.0895516i
$160$		0			0
$161$	−45.6851	+	62.8801i	−0.283758	+	0.390560i
$162$		0			0
$163$	−37.0816	+	114.125i	−0.227494	+	0.700156i	0.770534	+	0.637398i	$0.219989\pi$
$163$	−37.0816	+	114.125i	−0.227494	+	0.700156i	−0.998029	+	0.0627574i	$0.980011\pi$
$164$		0			0
$165$	−3.13322	−	29.6440i	−0.0189892	−	0.179660i
$166$		0			0
$167$	−198.544	−	64.5107i	−1.18888	−	0.386292i	−0.353224	−	0.935539i	$-0.614915\pi$
$167$	−198.544	−	64.5107i	−1.18888	−	0.386292i	−0.835660	+	0.549247i	$0.814915\pi$
$168$		0			0
$169$	−121.667	−	88.3959i	−0.719920	−	0.523053i
$170$		0			0
$171$	176.842	−	57.4596i	1.03417	−	0.336021i
$172$		0			0
$173$	113.888	+	156.753i	0.658310	+	0.906086i	0.999424	−	0.0339360i	$-0.0108042\pi$
$173$	113.888	+	156.753i	0.658310	+	0.906086i	−0.341114	+	0.940022i	$0.610804\pi$
$174$		0			0
$175$		−	135.389i		−	0.773654i
$176$		0			0
$177$	30.4368			0.171959
$178$		0			0
$179$	57.3723	−	41.6834i	0.320516	−	0.232868i	−0.415880	−	0.909420i	$-0.636526\pi$
$179$	57.3723	−	41.6834i	0.320516	−	0.232868i	0.736395	+	0.676551i	$0.236526\pi$
$180$		0			0
$181$	57.3996	+	176.658i	0.317125	+	0.976009i	0.974871	+	0.222770i	$0.0715098\pi$
$181$	57.3996	+	176.658i	0.317125	+	0.976009i	−0.657746	+	0.753239i	$0.728490\pi$
$182$		0			0
$183$	−14.9213	+	20.5374i	−0.0815370	+	0.112226i
$184$		0			0
$185$	−163.647	+	503.655i	−0.884580	+	2.72246i
$186$		0			0
$187$	214.940	+	123.928i	1.14941	+	0.662717i
$188$		0			0
$189$	−13.9879	−	4.54495i	−0.0740101	−	0.0240473i
$190$		0			0
$191$	−179.811	−	130.640i	−0.941417	−	0.683980i	0.00734414	−	0.999973i	$-0.497662\pi$
$191$	−179.811	−	130.640i	−0.941417	−	0.683980i	−0.948761	+	0.315993i	$0.897662\pi$
$192$		0			0
$193$	−84.8948	+	27.5840i	−0.439869	+	0.142922i	−0.520575	−	0.853816i	$-0.674283\pi$
$193$	−84.8948	+	27.5840i	−0.439869	+	0.142922i	0.0807060	+	0.996738i	$0.474283\pi$
$194$		0			0
$195$	−6.87179	−	9.45821i	−0.0352399	−	0.0485036i
$196$		0			0
$197$		−	41.5270i		−	0.210797i	−0.994430	−	0.105398i	$-0.966388\pi$
$197$		−	41.5270i		−	0.210797i	0.994430	−	0.105398i	$-0.0336118\pi$
$198$		0			0
$199$	203.602			1.02312			0.511562	−	0.859246i	$-0.329067\pi$
$199$	203.602			1.02312			0.511562	+	0.859246i	$0.329067\pi$
$200$		0			0
$201$	11.4488	−	8.31803i	0.0569592	−	0.0413833i
$202$		0			0
$203$	12.4055	+	38.1803i	0.0611110	+	0.188080i
$204$		0			0
$205$	−191.913	+	264.145i	−0.936160	+	1.28851i
$206$		0			0
$207$	−80.8266	+	248.759i	−0.390466	+	1.20173i
$208$		0			0
$209$	−47.6311	+	224.732i	−0.227900	+	1.07527i
$210$		0			0
$211$	332.903	+	108.167i	1.57774	+	0.512639i	0.961474	−	0.274898i	$-0.0886439\pi$
$211$	332.903	+	108.167i	1.57774	+	0.512639i	0.616268	+	0.787537i	$0.288644\pi$
$212$		0			0
$213$	−9.68979	−	7.04005i	−0.0454920	−	0.0330519i
$214$		0			0
$215$	−356.331	+	115.779i	−1.65736	+	0.538507i
$216$		0			0
$217$	−47.6188	−	65.5416i	−0.219441	−	0.302035i
$218$		0			0
$219$		−	12.0691i		−	0.0551098i
$220$		0			0
$221$	97.3065			0.440301
$222$		0			0
$223$	36.5671	−	26.5675i	0.163978	−	0.119137i	−0.502770	−	0.864420i	$-0.667686\pi$
$223$	36.5671	−	26.5675i	0.163978	−	0.119137i	0.666748	+	0.745283i	$0.267686\pi$
$224$		0			0
$225$	−140.794	−	433.318i	−0.625750	−	1.92586i
$226$		0			0
$227$	−79.7176	+	109.722i	−0.351179	+	0.483356i	−0.947665	−	0.319267i	$-0.896563\pi$
$227$	−79.7176	+	109.722i	−0.351179	+	0.483356i	0.596486	+	0.802624i	$0.296563\pi$
$228$		0			0
$229$	−4.90207	+	15.0870i	−0.0214064	+	0.0658822i	−0.961189	−	0.275890i	$-0.911027\pi$
$229$	−4.90207	+	15.0870i	−0.0214064	+	0.0658822i	0.939783	+	0.341773i	$0.111027\pi$
$230$		0			0
$231$	6.71187	−	6.05050i	0.0290557	−	0.0261927i
$232$		0			0
$233$	356.456	+	115.820i	1.52985	+	0.497079i	0.948555	−	0.316611i	$-0.102545\pi$
$233$	356.456	+	115.820i	1.52985	+	0.497079i	0.581298	+	0.813691i	$0.302545\pi$
$234$		0			0
$235$	−168.730	−	122.589i	−0.717999	−	0.521657i
$236$		0			0
$237$	5.20320	−	1.69062i	0.0219544	−	0.00713342i
$238$		0			0
$239$	−159.162	−	219.067i	−0.665948	−	0.916599i	0.333712	−	0.942675i	$-0.391699\pi$
$239$	−159.162	−	219.067i	−0.665948	−	0.916599i	−0.999660	+	0.0260762i	$0.991699\pi$
$240$		0			0
$241$			457.471i			1.89822i	0.314943	+	0.949110i	$0.398014\pi$
$241$			457.471i			1.89822i	−0.314943	+	0.949110i	$0.601986\pi$
$242$		0			0
$243$	−74.3760			−0.306074
$244$		0			0
$245$	49.4259	−	35.9100i	0.201738	−	0.146571i
$246$		0			0
$247$	27.8415	+	85.6873i	0.112719	+	0.346912i
$248$		0			0
$249$	−9.47315	+	13.0387i	−0.0380448	+	0.0523642i
$250$		0			0
$251$	−69.6372	+	214.321i	−0.277439	+	0.853869i	0.711125	+	0.703066i	$0.248186\pi$
$251$	−69.6372	+	214.321i	−0.277439	+	0.853869i	−0.988564	+	0.150803i	$0.951814\pi$
$252$		0			0
$253$	−216.367	−	240.018i	−0.855207	−	0.948688i
$254$		0			0
$255$	−58.1312	−	18.8880i	−0.227965	−	0.0740705i
$256$		0			0
$257$	−321.367	−	233.487i	−1.25046	−	0.908509i	−0.252207	−	0.967673i	$-0.581156\pi$
$257$	−321.367	−	233.487i	−1.25046	−	0.908509i	−0.998248	+	0.0591644i	$0.981156\pi$
$258$		0			0
$259$	−152.680	+	49.6089i	−0.589500	+	0.191540i
$260$		0			0
$261$	79.4086	+	109.297i	0.304248	+	0.418761i
$262$		0			0
$263$		−	450.540i		−	1.71308i	−0.516082	−	0.856539i	$-0.672610\pi$
$263$		−	450.540i		−	1.71308i	0.516082	−	0.856539i	$-0.327390\pi$
$264$		0			0
$265$	420.829			1.58803
$266$		0			0
$267$	29.4496	−	21.3964i	0.110298	−	0.0801361i
$268$		0			0
$269$	−76.6639	−	235.947i	−0.284996	−	0.877127i	−0.986400	−	0.164363i	$-0.947443\pi$
$269$	−76.6639	−	235.947i	−0.284996	−	0.877127i	0.701404	−	0.712764i	$-0.252557\pi$
$270$		0			0
$271$	−263.755	+	363.028i	−0.973267	+	1.33959i	−0.0328884	+	0.999459i	$0.510471\pi$
$271$	−263.755	+	363.028i	−0.973267	+	1.33959i	−0.940379	+	0.340129i	$0.889529\pi$
$272$		0			0
$273$	1.09518	−	3.37060i	0.00401163	−	0.0123465i
$274$		0			0
$275$	550.664	+	116.711i	2.00241	+	0.424403i
$276$		0			0
$277$	288.817	+	93.8422i	1.04266	+	0.338781i	0.779784	−	0.626049i	$-0.215329\pi$
$277$	288.817	+	93.8422i	1.04266	+	0.338781i	0.262876	+	0.964830i	$0.415329\pi$
$278$		0			0
$279$	−220.563	−	160.249i	−0.790549	−	0.574368i
$280$		0			0
$281$	224.220	−	72.8536i	0.797937	−	0.259266i	0.118457	−	0.992959i	$-0.462205\pi$
$281$	224.220	−	72.8536i	0.797937	−	0.259266i	0.679480	+	0.733694i	$0.262205\pi$
$282$		0			0
$283$	−31.1045	−	42.8117i	−0.109910	−	0.151278i	0.750518	−	0.660850i	$-0.229804\pi$
$283$	−31.1045	−	42.8117i	−0.109910	−	0.151278i	−0.860428	+	0.509572i	$0.829804\pi$
$284$		0			0
$285$		−	56.5941i		−	0.198576i
$286$		0			0
$287$	−98.9772			−0.344868
$288$		0			0
$289$	177.771	−	129.158i	0.615126	−	0.446915i
$290$		0			0
$291$	3.21766	+	9.90293i	0.0110572	+	0.0340307i
$292$		0			0
$293$	299.360	−	412.034i	1.02171	−	1.40626i	0.110709	−	0.993853i	$-0.464688\pi$
$293$	299.360	−	412.034i	1.02171	−	1.40626i	0.910999	−	0.412408i	$-0.135312\pi$
$294$		0			0
$295$	−264.376	+	813.666i	−0.896191	+	2.75819i
$296$		0			0
$297$	30.5436	−	52.9745i	0.102840	−	0.178365i
$298$		0			0
$299$	−120.534	−	39.1637i	−0.403122	−	0.130982i
$300$		0			0
$301$	−91.8873	−	66.7600i	−0.305273	−	0.221794i
$302$		0			0
$303$	40.5003	−	13.1593i	0.133664	−	0.0434302i
$304$		0			0
$305$	−419.418	−	577.280i	−1.37514	−	1.89272i
$306$		0			0
$307$		−	407.324i		−	1.32679i	−0.748270	−	0.663394i	$-0.769115\pi$
$307$		−	407.324i		−	1.32679i	0.748270	−	0.663394i	$-0.230885\pi$
$308$		0			0
$309$	16.1232			0.0521787
$310$		0			0
$311$	−431.141	+	313.243i	−1.38631	+	1.00721i	−0.390048	+	0.920795i	$0.627541\pi$
$311$	−431.141	+	313.243i	−1.38631	+	1.00721i	−0.996259	+	0.0864162i	$0.972459\pi$
$312$		0			0
$313$	55.4289	+	170.592i	0.177089	+	0.545024i	0.999723	−	0.0235478i	$-0.00749618\pi$
$313$	55.4289	+	170.592i	0.177089	+	0.545024i	−0.822634	+	0.568572i	$0.807496\pi$
$314$		0			0
$315$	120.846	−	166.330i	0.383638	−	0.528032i
$316$		0			0
$317$	38.1094	−	117.289i	0.120219	−	0.369996i	−0.872781	−	0.488112i	$-0.837686\pi$
$317$	38.1094	−	117.289i	0.120219	−	0.369996i	0.993000	+	0.118117i	$0.0376857\pi$
$318$		0			0
$319$	−165.983	+	17.5436i	−0.520323	+	0.0549957i
$320$		0			0
$321$	−15.1540	−	4.92384i	−0.0472088	−	0.0153391i
$322$		0			0
$323$	381.083	+	276.873i	1.17982	+	0.857191i
$324$		0			0
$325$	209.960	−	68.2202i	0.646032	−	0.209908i
$326$		0			0
$327$	20.6021	+	28.3563i	0.0630033	+	0.0867167i
$328$		0			0
$329$		−	63.2244i		−	0.192171i
$330$		0			0
$331$	422.529			1.27652			0.638261	−	0.769820i	$-0.279654\pi$
$331$	422.529			1.27652			0.638261	+	0.769820i	$0.279654\pi$
$332$		0			0
$333$	−437.070	+	317.550i	−1.31252	+	0.953603i
$334$		0			0
$335$	122.921	+	378.312i	0.366928	+	1.12929i
$336$		0			0
$337$	218.012	−	300.067i	0.646919	−	0.890408i	−0.352042	−	0.935984i	$-0.614513\pi$
$337$	218.012	−	300.067i	0.646919	−	0.890408i	0.998961	+	0.0455767i	$0.0145125\pi$
$338$		0			0
$339$	−5.98393	+	18.4166i	−0.0176517	+	0.0543264i
$340$		0			0
$341$	307.624	−	137.178i	0.902123	−	0.402283i
$342$		0			0
$343$	17.6138	+	5.72307i	0.0513522	+	0.0166853i
$344$		0			0
$345$	64.4051	+	46.7930i	0.186681	+	0.135632i
$346$		0			0
$347$	620.177	−	201.508i	1.78725	−	0.580714i	0.787872	−	0.615839i	$-0.211183\pi$
$347$	620.177	−	201.508i	1.78725	−	0.580714i	0.999383	+	0.0351253i	$0.0111830\pi$
$348$		0			0
$349$	44.3315	+	61.0171i	0.127024	+	0.174834i	0.867792	−	0.496927i	$-0.165538\pi$
$349$	44.3315	+	61.0171i	0.127024	+	0.174834i	−0.740768	+	0.671761i	$0.765538\pi$
$350$		0			0
$351$		−	23.9824i		−	0.0683259i
$352$		0			0
$353$	183.717			0.520446			0.260223	−	0.965549i	$-0.416204\pi$
$353$	183.717			0.520446			0.260223	+	0.965549i	$0.416204\pi$
$354$		0			0
$355$	272.368	−	197.887i	0.767234	−	0.557428i
$356$		0			0
$357$	−5.72579	−	17.6222i	−0.0160386	−	0.0493618i
$358$		0			0
$359$	135.688	−	186.758i	0.377960	−	0.520218i	−0.577082	−	0.816686i	$-0.695809\pi$
$359$	135.688	−	186.758i	0.377960	−	0.520218i	0.955043	+	0.296468i	$0.0958089\pi$
$360$		0			0
$361$	−23.2207	+	71.4659i	−0.0643232	+	0.197967i
$362$		0			0
$363$	18.8231	+	32.5147i	0.0518542	+	0.0895722i
$364$		0			0
$365$	322.642	+	104.833i	0.883951	+	0.287213i
$366$		0			0
$367$	−223.216	−	162.176i	−0.608219	−	0.441897i	0.240568	−	0.970632i	$-0.422666\pi$
$367$	−223.216	−	162.176i	−0.608219	−	0.441897i	−0.848787	+	0.528735i	$0.822666\pi$
$368$		0			0
$369$	−316.780	+	102.928i	−0.858483	+	0.278938i
$370$		0			0
$371$	74.9850	+	103.208i	0.202116	+	0.278189i
$372$		0			0
$373$			65.4078i			0.175356i	0.996149	+	0.0876780i	$0.0279446\pi$
$373$			65.4078i			0.175356i	−0.996149	+	0.0876780i	$0.972055\pi$
$374$		0			0
$375$	−70.9250			−0.189133
$376$		0			0
$377$	−52.9586	+	38.4767i	−0.140474	+	0.102060i
$378$		0			0
$379$	−205.669	−	632.983i	−0.542661	−	1.67014i	−0.726487	−	0.687180i	$-0.758848\pi$
$379$	−205.669	−	632.983i	−0.542661	−	1.67014i	0.183826	−	0.982959i	$-0.441152\pi$
$380$		0			0
$381$	42.2957	−	58.2150i	0.111012	−	0.152795i
$382$		0			0
$383$	52.0712	−	160.259i	0.135956	−	0.418430i	−0.859781	−	0.510662i	$-0.829400\pi$
$383$	52.0712	−	160.259i	0.135956	−	0.418430i	0.995738	+	0.0922324i	$0.0294003\pi$
$384$		0			0
$385$	103.448	+	231.984i	0.268697	+	0.602555i
$386$		0			0
$387$	−363.513	−	118.113i	−0.939311	−	0.305201i
$388$		0			0
$389$	319.769	+	232.326i	0.822028	+	0.597239i	0.917293	−	0.398213i	$-0.130370\pi$
$389$	319.769	+	232.326i	0.822028	+	0.597239i	−0.0952645	+	0.995452i	$0.530370\pi$
$390$		0			0
$391$	−630.173	+	204.756i	−1.61170	+	0.523672i
$392$		0			0
$393$	−16.7981	−	23.1206i	−0.0427433	−	0.0588311i
$394$		0			0
$395$			153.782i			0.389321i
$396$		0			0
$397$	82.3882			0.207527			0.103763	−	0.994602i	$-0.466911\pi$
$397$	82.3882			0.207527			0.103763	+	0.994602i	$0.466911\pi$
$398$		0			0
$399$	13.8797	−	10.0842i	0.0347861	−	0.0252736i
$400$		0			0
$401$	52.7052	+	162.210i	0.131434	+	0.404513i	0.995018	−	0.0996915i	$-0.0317856\pi$
$401$	52.7052	+	162.210i	0.131434	+	0.404513i	−0.863584	+	0.504205i	$0.831786\pi$
$402$		0			0
$403$	77.6469	−	106.872i	0.192672	−	0.265191i
$404$		0			0
$405$	211.462	−	650.812i	0.522128	−	1.60694i
$406$		0			0
$407$	−70.1557	−	663.756i	−0.172373	−	1.63085i
$408$		0			0
$409$	590.881	+	191.989i	1.44470	+	0.469410i	0.923358	−	0.383940i	$-0.125433\pi$
$409$	590.881	+	191.989i	1.44470	+	0.469410i	0.521338	+	0.853350i	$0.325433\pi$
$410$		0			0
$411$	−57.4359	−	41.7296i	−0.139747	−	0.101532i
$412$		0			0
$413$	−246.659	+	80.1443i	−0.597237	+	0.194054i
$414$		0			0
$415$	−266.279	−	366.501i	−0.641635	−	0.883135i
$416$		0			0
$417$		−	37.0580i		−	0.0888682i
$418$		0			0
$419$	−45.3925			−0.108335			−0.0541677	−	0.998532i	$-0.517251\pi$
$419$	−45.3925			−0.108335			−0.0541677	+	0.998532i	$0.517251\pi$
$420$		0			0
$421$	183.882	−	133.598i	0.436774	−	0.317335i	−0.347578	−	0.937651i	$-0.612996\pi$
$421$	183.882	−	133.598i	0.436774	−	0.317335i	0.784352	+	0.620316i	$0.212996\pi$
$422$		0			0
$423$	−65.7481	−	202.352i	−0.155433	−	0.478373i
$424$		0			0
$425$	678.424	−	933.770i	1.59629	−	2.19711i
$426$		0			0
$427$	66.8438	−	205.724i	0.156543	−	0.481790i
$428$		0			0
$429$	12.7650	+	7.35996i	0.0297553	+	0.0171561i
$430$		0			0
$431$	−503.555	−	163.615i	−1.16834	−	0.379617i	−0.340318	−	0.940311i	$-0.610535\pi$
$431$	−503.555	−	163.615i	−1.16834	−	0.379617i	−0.828023	+	0.560694i	$0.810535\pi$
$432$		0			0
$433$	−216.378	−	157.208i	−0.499718	−	0.363066i	0.309191	−	0.951000i	$-0.399942\pi$
$433$	−216.378	−	157.208i	−0.499718	−	0.363066i	−0.808909	+	0.587933i	$0.799942\pi$
$434$		0			0
$435$	39.1062	−	12.7064i	0.0898994	−	0.0292101i
$436$		0			0
$437$	−360.612	−	496.340i	−0.825199	−	1.13579i
$438$		0			0
$439$			426.656i			0.971881i	0.873992	+	0.485941i	$0.161523\pi$
$439$			426.656i			0.971881i	−0.873992	+	0.485941i	$0.838477\pi$
$440$		0			0
$441$	62.3251			0.141327
$442$		0			0
$443$	−404.167	+	293.645i	−0.912342	+	0.662855i	−0.941606	−	0.336717i	$-0.890684\pi$
$443$	−404.167	+	293.645i	−0.912342	+	0.662855i	0.0292642	+	0.999572i	$0.490684\pi$
$444$		0			0
$445$	316.188	+	973.126i	0.710534	+	2.18680i
$446$		0			0
$447$	−33.9550	+	46.7350i	−0.0759619	+	0.104553i
$448$		0			0
$449$	−213.987	+	658.583i	−0.476585	+	1.46678i	0.367224	+	0.930133i	$0.380308\pi$
$449$	−213.987	+	658.583i	−0.476585	+	1.46678i	−0.843809	+	0.536644i	$0.819692\pi$
$450$		0			0
$451$	85.3222	−	402.566i	0.189185	−	0.892608i
$452$		0			0
$453$	−9.57489	−	3.11107i	−0.0211366	−	0.00686771i
$454$		0			0
$455$	80.5936	+	58.5547i	0.177129	+	0.128692i
$456$		0			0
$457$	−769.506	+	250.028i	−1.68382	+	0.547106i	−0.985647	−	0.168822i	$-0.946004\pi$
$457$	−769.506	+	250.028i	−1.68382	+	0.547106i	−0.698174	+	0.715928i	$0.746004\pi$
$458$		0			0
$459$	−73.6992	−	101.438i	−0.160565	−	0.220998i
$460$		0			0
$461$			231.256i			0.501640i	0.968034	+	0.250820i	$0.0807002\pi$
$461$			231.256i			0.501640i	−0.968034	+	0.250820i	$0.919300\pi$
$462$		0			0
$463$	−606.956			−1.31092			−0.655461	−	0.755229i	$-0.727525\pi$
$463$	−606.956			−1.31092			−0.655461	+	0.755229i	$0.727525\pi$
$464$		0			0
$465$	−67.1311	+	48.7736i	−0.144368	+	0.104890i
$466$		0			0
$467$	140.548	+	432.563i	0.300960	+	0.926259i	0.981154	+	0.193227i	$0.0618955\pi$
$467$	140.548	+	432.563i	0.300960	+	0.926259i	−0.680194	+	0.733032i	$0.738105\pi$
$468$		0			0
$469$	−70.8782	+	97.5554i	−0.151126	+	0.208007i
$470$		0			0
$471$	−7.20938	+	22.1882i	−0.0153065	+	0.0471087i
$472$		0			0
$473$	350.741	−	316.180i	0.741524	−	0.668456i
$474$		0			0
$475$	1016.38	+	330.242i	2.13975	+	0.695247i
$476$		0			0
$477$	347.320	+	252.343i	0.728134	+	0.529021i
$478$		0			0
$479$	111.211	−	36.1347i	0.232174	−	0.0754378i	−0.190620	−	0.981664i	$-0.561050\pi$
$479$	111.211	−	36.1347i	0.232174	−	0.0754378i	0.422793	+	0.906226i	$0.361050\pi$
$480$		0			0
$481$	−153.866	−	211.778i	−0.319887	−	0.440287i
$482$		0			0
$483$			24.1331i			0.0499650i
$484$		0			0
$485$	−292.684			−0.603472
$486$		0			0
$487$	176.862	−	128.498i	0.363166	−	0.263856i	−0.391205	−	0.920303i	$-0.627942\pi$
$487$	176.862	−	128.498i	0.363166	−	0.263856i	0.754371	+	0.656448i	$0.227942\pi$
$488$		0			0
$489$	11.5137	+	35.4356i	0.0235454	+	0.0724654i
$490$		0			0
$491$	−173.055	+	238.190i	−0.352454	+	0.485112i	−0.948027	−	0.318190i	$-0.896925\pi$
$491$	−173.055	+	238.190i	−0.352454	+	0.485112i	0.595573	+	0.803301i	$0.296925\pi$
$492$		0			0
$493$	−105.758	+	325.489i	−0.214519	+	0.660222i
$494$		0			0
$495$	572.334	+	634.894i	1.15623	+	1.28261i
$496$		0			0
$497$	97.0633	+	31.5378i	0.195298	+	0.0634563i
$498$		0			0
$499$	−133.181	−	96.7613i	−0.266895	−	0.193910i	0.446286	−	0.894890i	$-0.352746\pi$
$499$	−133.181	−	96.7613i	−0.266895	−	0.193910i	−0.713181	+	0.700980i	$0.752746\pi$
$500$		0			0
$501$	−61.6472	+	20.0304i	−0.123048	+	0.0399808i
$502$		0			0
$503$	−8.06997	−	11.1074i	−0.0160437	−	0.0220822i	0.800920	−	0.598772i	$-0.204344\pi$
$503$	−8.06997	−	11.1074i	−0.0160437	−	0.0220822i	−0.816963	+	0.576689i	$0.804344\pi$
$504$		0			0
$505$			1197.00i			2.37029i
$506$		0			0
$507$	−46.6950			−0.0921007
$508$		0			0
$509$	345.151	−	250.767i	0.678096	−	0.492666i	−0.194629	−	0.980877i	$-0.562350\pi$
$509$	345.151	−	250.767i	0.678096	−	0.492666i	0.872726	+	0.488211i	$0.162350\pi$
$510$		0			0
$511$	31.7795	+	97.8073i	0.0621908	+	0.191404i
$512$		0			0
$513$	68.2387	−	93.9226i	0.133019	−	0.183085i
$514$		0			0
$515$	−140.048	+	431.022i	−0.271937	+	0.836936i
$516$		0			0
$517$	257.150	+	54.5019i	0.497389	+	0.105419i
$518$		0			0
$519$	57.2165	+	18.5908i	0.110244	+	0.0358204i
$520$		0			0
$521$	659.927	+	479.465i	1.26665	+	0.920278i	0.999064	−	0.0432546i	$-0.0137727\pi$
$521$	659.927	+	479.465i	1.26665	+	0.920278i	0.267590	+	0.963533i	$0.413773\pi$
$522$		0			0
$523$	−691.946	+	224.827i	−1.32303	+	0.429879i	−0.883535	−	0.468365i	$-0.844843\pi$
$523$	−691.946	+	224.827i	−1.32303	+	0.429879i	−0.439497	+	0.898244i	$0.644843\pi$
$524$		0			0
$525$	−24.7093	−	34.0094i	−0.0470653	−	0.0647799i
$526$		0			0
$527$		−	690.649i		−	1.31053i
$528$		0			0
$529$	334.004			0.631388
$530$		0			0
$531$	−706.097	+	513.009i	−1.32975	+	0.966119i
$532$		0			0
$533$	−49.8728	−	153.493i	−0.0935700	−	0.287979i
$534$		0			0
$535$	263.258	−	362.343i	0.492071	−	0.677277i
$536$		0			0
$537$	6.80431	−	20.9415i	0.0126710	−	0.0389973i
$538$		0			0
$539$	−38.4610	+	66.7064i	−0.0713563	+	0.123760i
$540$		0			0
$541$	−686.838	−	223.167i	−1.26957	−	0.412509i	−0.404676	−	0.914460i	$-0.632616\pi$
$541$	−686.838	−	223.167i	−1.26957	−	0.412509i	−0.864896	+	0.501952i	$0.832616\pi$
$542$		0			0
$543$	46.6596	+	33.9002i	0.0859293	+	0.0624313i
$544$		0			0
$545$	−937.002	+	304.450i	−1.71927	+	0.558625i
$546$		0			0
$547$	−238.615	−	328.426i	−0.436225	−	0.600413i	0.533143	−	0.846025i	$-0.321011\pi$
$547$	−238.615	−	328.426i	−0.436225	−	0.600413i	−0.969368	+	0.245613i	$0.921011\pi$
$548$		0			0
$549$		−	727.939i		−	1.32594i
$550$		0			0
$551$	−316.883			−0.575105
$552$		0			0
$553$	−37.7149	+	27.4015i	−0.0682006	+	0.0495506i
$554$		0			0
$555$	50.8120	+	156.383i	0.0915532	+	0.281772i
$556$		0			0
$557$	−368.122	+	506.677i	−0.660901	+	0.909653i	−0.999511	−	0.0312743i	$-0.990043\pi$
$557$	−368.122	+	506.677i	−0.660901	+	0.909653i	0.338609	+	0.940927i	$0.390043\pi$
$558$		0			0
$559$	57.2304	−	176.137i	0.102380	−	0.315093i
$560$		0			0
$561$	76.6098	−	8.09728i	0.136559	−	0.0144337i
$562$		0			0
$563$	−86.0684	−	27.9653i	−0.152875	−	0.0496720i	0.231580	−	0.972816i	$-0.425610\pi$
$563$	−86.0684	−	27.9653i	−0.152875	−	0.0496720i	−0.384455	+	0.923144i	$0.625610\pi$
$564$		0			0
$565$	−440.355	−	319.937i	−0.779390	−	0.566260i
$566$		0			0
$567$	197.290	−	64.1036i	0.347955	−	0.113057i
$568$		0			0
$569$	−272.849	−	375.544i	−0.479523	−	0.660007i	0.498890	−	0.866665i	$-0.333741\pi$
$569$	−272.849	−	375.544i	−0.479523	−	0.660007i	−0.978413	+	0.206658i	$0.933741\pi$
$570$		0			0
$571$			612.506i			1.07269i	0.843999	+	0.536345i	$0.180195\pi$
$571$			612.506i			1.07269i	−0.843999	+	0.536345i	$0.819805\pi$
$572$		0			0
$573$	−69.0105			−0.120437
$574$		0			0
$575$	−1216.19	+	883.610i	−2.11510	+	1.53671i
$576$		0			0
$577$	−115.123	−	354.314i	−0.199521	−	0.614062i	−0.999894	−	0.0145597i	$-0.995365\pi$
$577$	−115.123	−	354.314i	−0.199521	−	0.614062i	0.800373	−	0.599502i	$-0.204635\pi$
$578$		0			0
$579$	−16.2911	+	22.4228i	−0.0281366	+	0.0387268i
$580$		0			0
$581$	42.4375	−	130.609i	0.0730422	−	0.224801i
$582$		0			0
$583$	−484.414	+	216.014i	−0.830899	+	0.370522i
$584$		0			0
$585$	318.835	+	103.596i	0.545016	+	0.177087i
$586$		0			0
$587$	393.456	+	285.862i	0.670282	+	0.486989i	0.870120	−	0.492841i	$-0.164041\pi$
$587$	393.456	+	285.862i	0.670282	+	0.486989i	−0.199837	+	0.979829i	$0.564041\pi$
$588$		0			0
$589$	608.179	−	197.609i	1.03256	−	0.335500i
$590$		0			0
$591$	−7.57890	−	10.4315i	−0.0128239	−	0.0176505i
$592$		0			0
$593$		−	1060.60i		−	1.78854i	−0.447531	−	0.894269i	$-0.647696\pi$
$593$		−	1060.60i		−	1.78854i	0.447531	−	0.894269i	$-0.352304\pi$
$594$		0			0
$595$	520.828			0.875342
$596$		0			0
$597$	51.1442	−	37.1584i	0.0856686	−	0.0622419i
$598$		0			0
$599$	−172.929	−	532.220i	−0.288696	−	0.888515i	−0.985266	−	0.171026i	$-0.945292\pi$
$599$	−172.929	−	532.220i	−0.288696	−	0.888515i	0.696571	−	0.717488i	$-0.254708\pi$
$600$		0			0
$601$	−343.902	+	473.340i	−0.572216	+	0.787588i	−0.992815	−	0.119659i	$-0.961820\pi$
$601$	−343.902	+	473.340i	−0.572216	+	0.787588i	0.420599	+	0.907247i	$0.361820\pi$
$602$		0			0
$603$	−125.399	+	385.937i	−0.207958	+	0.640028i
$604$		0			0
$605$	−1032.71	+	220.772i	−1.70697	+	0.364913i
$606$		0			0
$607$	−606.433	−	197.042i	−0.999065	−	0.324616i	−0.236573	−	0.971614i	$-0.576024\pi$
$607$	−606.433	−	197.042i	−0.999065	−	0.324616i	−0.762492	+	0.646998i	$0.776024\pi$
$608$		0			0
$609$	10.0843	+	7.32671i	0.0165589	+	0.0120307i
$610$		0			0
$611$	98.0476	−	31.8576i	0.160471	−	0.0521401i
$612$		0			0
$613$	362.845	+	499.413i	0.591917	+	0.814703i	0.994938	−	0.100487i	$-0.0320401\pi$
$613$	362.845	+	499.413i	0.591917	+	0.814703i	−0.403022	+	0.915190i	$0.632040\pi$
$614$		0			0
$615$			101.378i			0.164842i
$616$		0			0
$617$	790.755			1.28161			0.640806	−	0.767703i	$-0.278600\pi$
$617$	790.755			1.28161			0.640806	+	0.767703i	$0.278600\pi$
$618$		0			0
$619$	265.880	−	193.173i	0.429531	−	0.312072i	−0.351931	−	0.936026i	$-0.614475\pi$
$619$	265.880	−	193.173i	0.429531	−	0.312072i	0.781461	+	0.623954i	$0.214475\pi$
$620$		0			0
$621$	50.4645	+	155.314i	0.0812633	+	0.250103i
$622$		0			0
$623$	−182.319	+	250.940i	−0.292647	+	0.402793i
$624$		0			0
$625$	220.732	−	679.342i	0.353171	−	1.08695i
$626$		0			0
$627$	29.0501	+	65.1451i	0.0463319	+	0.103900i
$628$		0			0
$629$	−1301.61	−	422.919i	−2.06933	−	0.672367i
$630$		0			0
$631$	−5.25753	−	3.81982i	−0.00833206	−	0.00605359i	0.583611	−	0.812033i	$-0.301639\pi$
$631$	−5.25753	−	3.81982i	−0.00833206	−	0.00605359i	−0.591943	+	0.805979i	$0.701639\pi$
$632$		0			0
$633$	103.365	−	33.5855i	0.163295	−	0.0530576i
$634$		0			0
$635$	1188.88	+	1636.35i	1.87225	+	2.57693i
$636$		0			0
$637$			30.1990i			0.0474082i
$638$		0			0
$639$	343.451			0.537482
$640$		0			0
$641$	−388.531	+	282.284i	−0.606133	+	0.440381i	−0.848050	−	0.529915i	$-0.822224\pi$
$641$	−388.531	+	282.284i	−0.606133	+	0.440381i	0.241918	+	0.970297i	$0.422224\pi$
$642$		0			0
$643$	−86.4289	−	266.001i	−0.134415	−	0.413687i	0.861083	−	0.508464i	$-0.169786\pi$
$643$	−86.4289	−	266.001i	−0.134415	−	0.413687i	−0.995499	+	0.0947764i	$0.969786\pi$
$644$		0			0
$645$	−68.3791	+	94.1158i	−0.106014	+	0.145916i
$646$		0			0
$647$	320.623	−	986.777i	0.495554	−	1.52516i	−0.320539	−	0.947235i	$-0.603864\pi$
$647$	320.623	−	986.777i	0.495554	−	1.52516i	0.816092	−	0.577922i	$-0.196136\pi$
$648$		0			0
$649$	−113.338	−	1072.31i	−0.174635	−	1.65225i
$650$		0			0
$651$	−23.9234	−	7.77319i	−0.0367487	−	0.0119404i
$652$		0			0
$653$	54.5949	+	39.6655i	0.0836063	+	0.0607435i	0.628803	−	0.777564i	$-0.283545\pi$
$653$	54.5949	+	39.6655i	0.0836063	+	0.0607435i	−0.545197	+	0.838308i	$0.683545\pi$
$654$		0			0
$655$	763.994	−	248.237i	1.16640	−	0.378987i
$656$		0			0
$657$	203.423	+	279.988i	0.309624	+	0.426161i
$658$		0			0
$659$			510.554i			0.774741i	0.921924	+	0.387370i	$0.126617\pi$
$659$			510.554i			0.774741i	−0.921924	+	0.387370i	$0.873383\pi$
$660$		0			0
$661$	−417.267			−0.631267			−0.315633	−	0.948881i	$-0.602217\pi$
$661$	−417.267			−0.631267			−0.315633	+	0.948881i	$0.602217\pi$
$662$		0			0
$663$	24.4431	−	17.7590i	0.0368675	−	0.0267858i
$664$		0			0
$665$	149.020	+	458.637i	0.224090	+	0.689679i
$666$		0			0
$667$	262.005	−	360.618i	0.392811	−	0.540657i
$668$		0			0
$669$	4.33683	−	13.3474i	0.00648256	−	0.0199513i
$670$		0			0
$671$	779.112	+	449.213i	1.16112	+	0.669468i
$672$		0			0
$673$	142.382	+	46.2626i	0.211562	+	0.0687408i	0.412881	−	0.910785i	$-0.364523\pi$
$673$	142.382	+	46.2626i	0.211562	+	0.0687408i	−0.201318	+	0.979526i	$0.564523\pi$
$674$		0			0
$675$	−230.139	−	167.206i	−0.340947	−	0.247713i
$676$		0			0
$677$	−352.781	+	114.626i	−0.521095	+	0.169314i	−0.557742	−	0.830014i	$-0.688332\pi$
$677$	−352.781	+	114.626i	−0.521095	+	0.169314i	0.0366472	+	0.999328i	$0.488332\pi$
$678$		0			0
$679$	−52.1516	−	71.7805i	−0.0768065	−	0.105715i
$680$		0			0
$681$			42.1107i			0.0618366i
$682$		0			0
$683$	83.4982			0.122252			0.0611260	−	0.998130i	$-0.480531\pi$
$683$	83.4982			0.122252			0.0611260	+	0.998130i	$0.480531\pi$
$684$		0			0
$685$	1614.45	−	1172.97i	2.35686	−	1.71236i
$686$		0			0
$687$	1.52208	+	4.68447i	0.00221554	+	0.00681874i
$688$		0			0
$689$	−122.270	+	168.291i	−0.177460	+	0.244253i
$690$		0			0
$691$	−249.534	+	767.988i	−0.361121	+	1.11142i	0.591254	+	0.806485i	$0.298633\pi$
$691$	−249.534	+	767.988i	−0.361121	+	1.11142i	−0.952375	+	0.304930i	$0.901367\pi$
$692$		0			0
$693$	−53.7267	+	253.493i	−0.0775277	+	0.365790i
$694$		0			0
$695$	990.672	+	321.889i	1.42543	+	0.463150i
$696$		0			0
$697$	−682.639	−	495.966i	−0.979395	−	0.711572i
$698$		0			0
$699$	110.678	−	35.9616i	0.158338	−	0.0514472i
$700$		0			0
$701$	373.396	+	513.935i	0.532661	+	0.733145i	0.987533	−	0.157412i	$-0.0503149\pi$
$701$	373.396	+	513.935i	0.532661	+	0.733145i	−0.454872	+	0.890557i	$0.650315\pi$
$702$		0			0
$703$		−	1267.19i		−	1.80255i
$704$		0			0
$705$	−64.7577			−0.0918549
$706$		0			0
$707$	−293.563	+	213.286i	−0.415224	+	0.301678i
$708$		0			0
$709$	336.839	+	1036.69i	0.475091	+	1.46218i	0.845835	+	0.533444i	$0.179103\pi$
$709$	336.839	+	1036.69i	0.475091	+	1.46218i	−0.370744	+	0.928735i	$0.620897\pi$
$710$		0			0
$711$	−92.2126	+	126.920i	−0.129694	+	0.178509i
$712$		0			0
$713$	−277.971	+	855.506i	−0.389861	+	1.19987i
$714$		0			0
$715$	−307.632	+	277.319i	−0.430254	+	0.387858i
$716$		0			0
$717$	−79.9619	−	25.9812i	−0.111523	−	0.0362360i
$718$		0			0
$719$	−258.798	−	188.028i	−0.359942	−	0.261513i	0.393086	−	0.919502i	$-0.371408\pi$
$719$	−258.798	−	188.028i	−0.359942	−	0.261513i	−0.753028	+	0.657988i	$0.771408\pi$
$720$		0			0
$721$	−130.662	+	42.4547i	−0.181224	+	0.0588831i
$722$		0			0
$723$	83.4910	+	114.916i	0.115479	+	0.158943i
$724$		0			0
$725$			776.460i			1.07098i
$726$		0			0
$727$	−14.0045			−0.0192634			−0.00963168	−	0.999954i	$-0.503066\pi$
$727$	−14.0045			−0.0192634			−0.00963168	+	0.999954i	$0.503066\pi$
$728$		0			0
$729$	552.205	−	401.200i	0.757483	−	0.550344i
$730$		0			0
$731$	−299.211	−	920.878i	−0.409318	−	1.25975i
$732$		0			0
$733$	−249.687	+	343.664i	−0.340637	+	0.468846i	−0.944627	−	0.328145i	$-0.893576\pi$
$733$	−249.687	+	343.664i	−0.340637	+	0.468846i	0.603991	+	0.796991i	$0.293576\pi$
$734$		0			0
$735$	5.86187	−	18.0410i	0.00797534	−	0.0245456i
$736$		0			0
$737$	−335.684	−	372.376i	−0.455473	−	0.505260i
$738$		0			0
$739$	−65.3797	−	21.2432i	−0.0884706	−	0.0287458i	0.264447	−	0.964400i	$-0.414810\pi$
$739$	−65.3797	−	21.2432i	−0.0884706	−	0.0287458i	−0.352918	+	0.935654i	$0.614810\pi$
$740$		0			0
$741$	22.6321	+	16.4432i	0.0305426	+	0.0221905i
$742$		0			0
$743$	1102.87	−	358.345i	1.48435	−	0.482295i	0.548941	−	0.835861i	$-0.315031\pi$
$743$	1102.87	−	358.345i	1.48435	−	0.482295i	0.935409	+	0.353567i	$0.115031\pi$
$744$		0			0
$745$	−954.431	−	1313.66i	−1.28112	−	1.76330i
$746$		0			0
$747$		−	462.151i		−	0.618676i
$748$		0			0
$749$	135.773			0.181272
$750$		0			0
$751$	382.587	−	277.966i	0.509437	−	0.370128i	−0.303173	−	0.952936i	$-0.598046\pi$
$751$	382.587	−	277.966i	0.509437	−	0.370128i	0.812610	+	0.582808i	$0.198046\pi$
$752$		0			0
$753$	21.6221	+	66.5460i	0.0287146	+	0.0883746i
$754$		0			0
$755$	166.337	−	228.943i	0.220313	−	0.303235i
$756$		0			0
$757$	53.0468	−	163.261i	0.0700750	−	0.215669i	−0.909886	−	0.414859i	$-0.863831\pi$
$757$	53.0468	−	163.261i	0.0700750	−	0.215669i	0.979961	+	0.199190i	$0.0638311\pi$
$758$		0			0
$759$	−98.1555	−	20.8037i	−0.129322	−	0.0274093i
$760$		0			0
$761$	296.335	+	96.2850i	0.389402	+	0.126524i	0.497173	−	0.867651i	$-0.334371\pi$
$761$	296.335	+	96.2850i	0.389402	+	0.126524i	−0.107771	+	0.994176i	$0.534371\pi$
$762$		0			0
$763$	−241.625	−	175.551i	−0.316678	−	0.230080i
$764$		0			0
$765$	1666.93	−	541.618i	2.17899	−	0.707998i
$766$		0			0
$767$	−248.574	−	342.132i	−0.324086	−	0.446066i
$768$		0			0
$769$			410.795i			0.534194i	0.963670	+	0.267097i	$0.0860645\pi$
$769$			410.795i			0.534194i	−0.963670	+	0.267097i	$0.913936\pi$
$770$		0			0
$771$	−123.339			−0.159973
$772$		0			0
$773$	820.271	−	595.962i	1.06115	−	0.770972i	0.0868513	−	0.996221i	$-0.472320\pi$
$773$	820.271	−	595.962i	1.06115	−	0.770972i	0.974301	+	0.225249i	$0.0723195\pi$
$774$		0			0
$775$	−484.204	−	1490.23i	−0.624779	−	1.92287i
$776$		0			0
$777$	−29.2990	+	40.3266i	−0.0377079	+	0.0519004i
$778$		0			0
$779$	241.426	−	743.032i	0.309917	−	0.953828i
$780$		0			0
$781$	−211.945	+	367.595i	−0.271376	+	0.470672i
$782$		0			0
$783$	80.2209	+	26.0653i	0.102453	+	0.0332891i
$784$		0			0
$785$	−530.536	−	385.457i	−0.675842	−	0.491028i
$786$		0			0
$787$	52.0081	−	16.8985i	0.0660840	−	0.0214720i	−0.275788	−	0.961218i	$-0.588939\pi$
$787$	52.0081	−	16.8985i	0.0660840	−	0.0214720i	0.341872	+	0.939746i	$0.388939\pi$
$788$		0			0
$789$	−82.2259	−	113.174i	−0.104215	−	0.143440i
$790$		0			0
$791$		−	165.005i		−	0.208602i
$792$		0			0
$793$	352.716			0.444787
$794$		0			0
$795$	105.711	−	76.8036i	0.132970	−	0.0966083i
$796$		0			0
$797$	−177.211	−	545.400i	−0.222348	−	0.684316i	−0.998550	−	0.0538321i	$-0.982856\pi$
$797$	−177.211	−	545.400i	−0.222348	−	0.684316i	0.776202	−	0.630484i	$-0.217144\pi$
$798$		0			0
$799$	316.812	−	436.054i	0.396510	−	0.545749i
$800$		0			0
$801$	−322.561	+	992.740i	−0.402697	+	1.23938i
$802$		0			0
$803$	−425.203	+	44.9419i	−0.529518	+	0.0559675i
$804$		0			0
$805$	−645.150	−	209.622i	−0.801428	−	0.260400i
$806$		0			0
$807$	−62.3194	−	45.2777i	−0.0772236	−	0.0561062i
$808$		0			0
$809$	−540.930	+	175.759i	−0.668640	+	0.217254i	−0.623615	−	0.781732i	$-0.714337\pi$
$809$	−540.930	+	175.759i	−0.668640	+	0.217254i	−0.0450249	+	0.998986i	$0.514337\pi$
$810$		0			0
$811$	930.144	+	1280.23i	1.14691	+	1.57859i	0.751007	+	0.660294i	$0.229568\pi$
$811$	930.144	+	1280.23i	1.14691	+	1.57859i	0.395903	+	0.918292i	$0.370432\pi$
$812$		0			0
$813$			139.329i			0.171376i
$814$		0			0
$815$	−1047.31			−1.28504
$816$		0			0
$817$	725.306	−	526.966i	0.887768	−	0.645001i
$818$		0			0
$819$	31.4045	+	96.6531i	0.0383449	+	0.118014i
$820$		0			0
$821$	−453.017	+	623.524i	−0.551786	+	0.759469i	−0.990253	−	0.139279i	$-0.955522\pi$
$821$	−453.017	+	623.524i	−0.551786	+	0.759469i	0.438467	+	0.898747i	$0.355522\pi$
$822$		0			0
$823$	286.874	−	882.907i	0.348571	−	1.07279i	−0.611073	−	0.791574i	$-0.709262\pi$
$823$	286.874	−	882.907i	0.348571	−	1.07279i	0.959644	−	0.281217i	$-0.0907380\pi$
$824$		0			0
$825$	159.626	−	71.1817i	0.193486	−	0.0862809i
$826$		0			0
$827$	529.991	+	172.204i	0.640859	+	0.208228i	0.611379	−	0.791338i	$-0.290615\pi$
$827$	529.991	+	172.204i	0.640859	+	0.208228i	0.0294799	+	0.999565i	$0.490615\pi$
$828$		0			0
$829$	−674.137	−	489.790i	−0.813194	−	0.590820i	0.101561	−	0.994829i	$-0.467616\pi$
$829$	−674.137	−	489.790i	−0.813194	−	0.590820i	−0.914755	+	0.404010i	$0.867616\pi$
$830$		0			0
$831$	89.6767	−	29.1377i	0.107914	−	0.0350634i
$832$		0			0
$833$	92.8033	+	127.733i	0.111409	+	0.153341i
$834$		0			0
$835$		−	1822.00i		−	2.18204i
$836$		0			0
$837$	−170.219			−0.203368
$838$		0			0
$839$	533.557	−	387.652i	0.635944	−	0.462040i	−0.222510	−	0.974930i	$-0.571425\pi$
$839$	533.557	−	387.652i	0.635944	−	0.462040i	0.858454	+	0.512890i	$0.171425\pi$
$840$		0			0
$841$	188.737	+	580.874i	0.224420	+	0.690694i
$842$		0			0
$843$	43.0274	−	59.2221i	0.0510408	−	0.0702516i
$844$		0			0
$845$	405.597	−	1248.30i	0.479996	−	1.47728i
$846$		0			0
$847$	−238.158	−	213.935i	−0.281178	−	0.252579i
$848$		0			0
$849$	−15.6268	−	5.07744i	−0.0184061	−	0.00598049i
$850$		0			0
$851$	1442.09	+	1047.74i	1.69458	+	1.23119i
$852$		0			0
$853$	869.829	−	282.624i	1.01973	−	0.331330i	0.249007	−	0.968502i	$-0.419896\pi$
$853$	869.829	−	282.624i	1.01973	−	0.331330i	0.770722	+	0.637172i	$0.219896\pi$
$854$		0			0
$855$	953.888	+	1312.91i	1.11566	+	1.53557i
$856$		0			0
$857$			212.124i			0.247519i	0.992312	+	0.123760i	$0.0394951\pi$
$857$			212.124i			0.247519i	−0.992312	+	0.123760i	$0.960505\pi$
$858$		0			0
$859$	−167.659			−0.195180			−0.0975898	−	0.995227i	$-0.531113\pi$
$859$	−167.659			−0.195180			−0.0975898	+	0.995227i	$0.531113\pi$
$860$		0			0
$861$	−24.8628	+	18.0639i	−0.0288767	+	0.0209801i
$862$		0			0
$863$	−274.919	−	846.115i	−0.318563	−	0.980435i	−0.974263	−	0.225414i	$-0.927627\pi$
$863$	−274.919	−	846.115i	−0.318563	−	0.980435i	0.655701	−	0.755021i	$-0.272373\pi$
$864$		0			0
$865$	−993.975	+	1368.09i	−1.14910	+	1.58161i
$866$		0			0
$867$	21.0835	−	64.8885i	0.0243178	−	0.0748425i
$868$		0			0
$869$	−78.9373	−	177.018i	−0.0908369	−	0.203703i
$870$		0			0
$871$	−187.002	−	60.7606i	−0.214698	−	0.0697596i
$872$		0			0
$873$	−241.559	−	175.503i	−0.276700	−	0.201034i
$874$		0			0
$875$	574.774	−	186.755i	0.656885	−	0.213435i
$876$		0			0
$877$	−181.737	−	250.139i	−0.207225	−	0.285221i	0.692736	−	0.721192i	$-0.256405\pi$
$877$	−181.737	−	250.139i	−0.207225	−	0.285221i	−0.899961	+	0.435970i	$0.856405\pi$
$878$		0			0
$879$		−	158.137i		−	0.179905i
$880$		0			0
$881$	−359.931			−0.408549			−0.204274	−	0.978914i	$-0.565483\pi$
$881$	−359.931			−0.408549			−0.204274	+	0.978914i	$0.565483\pi$
$882$		0			0
$883$	180.528	−	131.162i	0.204449	−	0.148541i	−0.480850	−	0.876803i	$-0.659672\pi$
$883$	180.528	−	131.162i	0.204449	−	0.148541i	0.685299	+	0.728262i	$0.259672\pi$
$884$		0			0
$885$	82.0880	+	252.641i	0.0927548	+	0.285470i
$886$		0			0
$887$	191.853	−	264.062i	0.216294	−	0.297703i	−0.687059	−	0.726602i	$-0.741098\pi$
$887$	191.853	−	264.062i	0.216294	−	0.297703i	0.903352	+	0.428899i	$0.141098\pi$
$888$		0			0
$889$	−189.475	+	583.143i	−0.213132	+	0.655954i
$890$		0			0
$891$	90.6538	+	857.691i	0.101744	+	0.962617i
$892$		0			0
$893$	474.632	+	154.217i	0.531502	+	0.172696i
$894$		0			0
$895$	500.727	+	363.800i	0.559472	+	0.406480i
$896$		0			0
$897$	−37.4253	+	12.1602i	−0.0417227	+	0.0135565i
$898$		0			0
$899$	273.094	+	375.882i	0.303776	+	0.418111i
$900$		0			0
$901$			1087.56i			1.20706i
$902$		0			0
$903$	−35.2659			−0.0390542
$904$		0			0
$905$	−1311.54	+	952.892i	−1.44922	+	1.05292i
$906$		0			0
$907$	−455.295	−	1401.25i	−0.501979	−	1.54493i	−0.805790	−	0.592201i	$-0.798259\pi$
$907$	−455.295	−	1401.25i	−0.501979	−	1.54493i	0.303811	−	0.952732i	$-0.401741\pi$
$908$		0			0
$909$	−717.759	+	987.910i	−0.789614	+	1.08681i
$910$		0			0
$911$	96.1136	−	295.807i	0.105503	−	0.324706i	−0.884345	−	0.466834i	$-0.845394\pi$
$911$	96.1136	−	295.807i	0.105503	−	0.324706i	0.989848	+	0.142128i	$0.0453945\pi$
$912$		0			0
$913$	494.639	+	285.195i	0.541773	+	0.312371i
$914$		0			0
$915$	−210.713	−	68.4649i	−0.230288	−	0.0748251i
$916$		0			0
$917$	197.011	+	143.137i	0.214843	+	0.156093i
$918$		0			0
$919$	−640.580	+	208.137i	−0.697040	+	0.226482i	−0.636041	−	0.771656i	$-0.719429\pi$
$919$	−640.580	+	208.137i	−0.697040	+	0.226482i	−0.0609998	+	0.998138i	$0.519429\pi$
$920$		0			0
$921$	−74.3389	−	102.319i	−0.0807154	−	0.111095i
$922$		0			0
$923$			166.416i			0.180299i
$924$		0			0
$925$	−3105.01			−3.35677
$926$		0			0
$927$	−374.039	+	271.756i	−0.403495	+	0.293156i
$928$		0			0
$929$	−65.9923	−	203.103i	−0.0710358	−	0.218626i	0.909236	−	0.416282i	$-0.136667\pi$
$929$	−65.9923	−	203.103i	−0.0710358	−	0.218626i	−0.980271	+	0.197656i	$0.936667\pi$
$930$		0			0
$931$	−85.9274	+	118.269i	−0.0922958	+	0.127034i
$932$		0			0
$933$	−51.1331	+	157.371i	−0.0548050	+	0.168672i
$934$		0			0
$935$	−448.974	+	2118.34i	−0.480186	+	2.26561i
$936$		0			0
$937$	463.188	+	150.499i	0.494331	+	0.160618i	0.545565	−	0.838069i	$-0.316315\pi$
$937$	463.188	+	150.499i	0.494331	+	0.160618i	−0.0512334	+	0.998687i	$0.516315\pi$
$938$		0			0
$939$	45.0576	+	32.7363i	0.0479847	+	0.0348629i
$940$		0			0
$941$	1358.23	−	441.316i	1.44339	−	0.468986i	0.520438	−	0.853900i	$-0.325769\pi$
$941$	1358.23	−	441.316i	1.44339	−	0.468986i	0.922953	+	0.384914i	$0.125769\pi$
$942$		0			0
$943$	645.969	+	889.100i	0.685015	+	0.942842i
$944$		0			0
$945$		−	128.365i		−	0.135836i
$946$		0			0
$947$	1415.04			1.49424			0.747119	−	0.664691i	$-0.231437\pi$
$947$	1415.04			1.49424			0.747119	+	0.664691i	$0.231437\pi$
$948$		0			0
$949$	−135.665	+	98.5666i	−0.142956	+	0.103864i
$950$		0			0
$951$	−11.8328	−	36.4177i	−0.0124425	−	0.0382942i
$952$		0			0
$953$	464.267	−	639.008i	0.487163	−	0.670523i	−0.492698	−	0.870200i	$-0.663989\pi$
$953$	464.267	−	639.008i	0.487163	−	0.670523i	0.979862	+	0.199677i	$0.0639894\pi$
$954$		0			0
$955$	599.431	−	1844.86i	0.627676	−	1.93179i
$956$		0			0
$957$	−38.4927	+	34.6997i	−0.0402223	+	0.0362589i
$958$		0			0
$959$	575.339	+	186.939i	0.599936	+	0.194931i
$960$		0			0
$961$	18.9255	+	13.7502i	0.0196935	+	0.0143082i
$962$		0			0
$963$	434.546	−	141.192i	0.451242	−	0.146617i
$964$		0			0
$965$	−457.923	−	630.277i	−0.474531	−	0.653136i
$966$		0			0
$967$			577.174i			0.596871i	0.954430	+	0.298436i	$0.0964648\pi$
$967$			577.174i			0.596871i	−0.954430	+	0.298436i	$0.903535\pi$
$968$		0			0
$969$	146.258			0.150937
$970$		0			0
$971$	−234.900	+	170.665i	−0.241915	+	0.175762i	−0.702136	−	0.712043i	$-0.747770\pi$
$971$	−234.900	+	170.665i	−0.241915	+	0.175762i	0.460221	+	0.887804i	$0.347770\pi$
$972$		0			0
$973$	97.5790	+	300.317i	0.100287	+	0.308651i
$974$		0			0
$975$	40.2909	−	55.4556i	0.0413240	−	0.0568776i
$976$		0			0
$977$	322.723	−	993.239i	0.330320	−	1.01662i	−0.638661	−	0.769488i	$-0.720511\pi$
$977$	322.723	−	993.239i	0.330320	−	1.01662i	0.968981	−	0.247134i	$-0.0794886\pi$
$978$		0			0
$979$	−863.474	−	957.858i	−0.881996	−	0.978405i
$980$		0			0
$981$	−955.888	−	310.587i	−0.974401	−	0.316602i
$982$		0			0
$983$	626.292	+	455.028i	0.637123	+	0.462897i	0.858861	−	0.512209i	$-0.171173\pi$
$983$	626.292	+	455.028i	0.637123	+	0.462897i	−0.221738	+	0.975106i	$0.571173\pi$
$984$		0			0
$985$	344.695	−	111.998i	0.349944	−	0.113704i
$986$		0			0
$987$	−11.5388	−	15.8818i	−0.0116908	−	0.0160910i
$988$		0			0
$989$			1261.12i			1.27514i
$990$		0			0
$991$	1383.91			1.39648			0.698240	−	0.715864i	$-0.253967\pi$
$991$	1383.91			1.39648			0.698240	+	0.715864i	$0.253967\pi$
$992$		0			0
$993$	106.138	−	77.1139i	0.106886	−	0.0776575i
$994$		0			0
$995$	549.114	+	1690.00i	0.551873	+	1.69849i
$996$		0			0
$997$	−232.348	+	319.800i	−0.233047	+	0.320762i	−0.909484	−	0.415739i	$-0.863523\pi$
$997$	−232.348	+	319.800i	−0.233047	+	0.320762i	0.676437	+	0.736501i	$0.263523\pi$
$998$		0			0
$999$	−104.234	+	320.798i	−0.104338	+	0.321119i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	308.3.r.a.57.7	✓	48
11.6	odd	10	inner	308.3.r.a.281.7	yes	48

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
308.3.r.a.57.7	✓	48	1.1	even	1	trivial
308.3.r.a.281.7	yes	48	11.6	odd	10	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:	\( N \)	\(=\)	\( 308 = 2^{2} \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	308.r (of order \(10\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(0.251197 - 0.182505i) q^{3} +(2.69700 + 8.30052i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.75136 + 8.46782i) q^{9} +O(q^{10})\)	\(q+(0.251197 - 0.182505i) q^{3} +(2.69700 + 8.30052i) q^{5} +(-1.55513 + 2.14046i) q^{7} +(-2.75136 + 8.46782i) q^{9} +(-7.36521 - 8.17029i) q^{11} +(-4.10300 - 1.33315i) q^{13} +(2.19237 + 1.59285i) q^{15} +(-21.4513 + 6.96994i) q^{17} +(-12.2753 - 16.8956i) q^{19} +0.821498i q^{21} +29.3769 q^{23} +(-41.3993 + 30.0784i) q^{25} +(1.71783 + 5.28693i) q^{27} +(8.91872 - 12.2756i) q^{29} +(-9.46221 + 29.1217i) q^{31} +(-3.34124 - 0.708163i) q^{33} +(-21.9611 - 7.13559i) q^{35} +(49.0892 + 35.6654i) q^{37} +(-1.27397 + 0.413937i) q^{39} +(21.9890 + 30.2652i) q^{41} +42.9288i q^{43} -77.7077 q^{45} +(-19.3327 + 14.0460i) q^{47} +(-2.16312 - 6.65740i) q^{49} +(-4.11645 + 5.66581i) q^{51} +(14.9001 - 45.8578i) q^{53} +(47.9536 - 83.1703i) q^{55} +(-6.16706 - 2.00380i) q^{57} +(79.3047 + 57.6182i) q^{59} +(-77.7564 + 25.2646i) q^{61} +(-13.8463 - 19.0578i) q^{63} -37.6525i q^{65} +45.5769 q^{67} +(7.37941 - 5.36145i) q^{69} +(-11.9202 - 36.6865i) q^{71} +(22.8473 - 31.4466i) q^{73} +(-4.90993 + 15.1112i) q^{75} +(28.9421 - 3.05903i) q^{77} +(16.7576 + 5.44489i) q^{79} +(-63.4320 - 46.0860i) q^{81} +(-49.3657 + 16.0399i) q^{83} +(-115.708 - 159.259i) q^{85} -4.71130i q^{87} +117.237 q^{89} +(9.23425 - 6.70908i) q^{91} +(2.93799 + 9.04220i) q^{93} +(107.135 - 147.459i) q^{95} +(-10.3629 + 31.8938i) q^{97} +(89.4489 - 39.8879i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9}+O(q^{10}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9	\( 48 q + 10 q^{3} + 6 q^{5} - 40 q^{9} - 10 q^{11} + 30 q^{13} + 24 q^{15} + 60 q^{19} - 132 q^{23} - 186 q^{25} - 110 q^{27} - 90 q^{29} - 26 q^{31} + 46 q^{33} + 82 q^{37} + 290 q^{39} - 336 q^{45} + 84 q^{47} + 84 q^{49} - 20 q^{51} + 58 q^{53} + 370 q^{55} - 20 q^{57} + 436 q^{59} + 160 q^{61} + 276 q^{67} - 118 q^{69} - 150 q^{71} - 320 q^{73} - 692 q^{75} + 28 q^{77} - 560 q^{79} + 122 q^{81} - 630 q^{83} + 220 q^{85} - 444 q^{89} - 126 q^{91} + 500 q^{93} + 440 q^{95} - 80 q^{97} + 1034 q^{99}+O(q^{100}) \) 48 * q + 10 * q^3 + 6 * q^5 - 40 * q^9 - 10 * q^11 + 30 * q^13 + 24 * q^15 + 60 * q^19 - 132 * q^23 - 186 * q^25 - 110 * q^27 - 90 * q^29 - 26 * q^31 + 46 * q^33 + 82 * q^37 + 290 * q^39 - 336 * q^45 + 84 * q^47 + 84 * q^49 - 20 * q^51 + 58 * q^53 + 370 * q^55 - 20 * q^57 + 436 * q^59 + 160 * q^61 + 276 * q^67 - 118 * q^69 - 150 * q^71 - 320 * q^73 - 692 * q^75 + 28 * q^77 - 560 * q^79 + 122 * q^81 - 630 * q^83 + 220 * q^85 - 444 * q^89 - 126 * q^91 + 500 * q^93 + 440 * q^95 - 80 * q^97 + 1034 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

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