LMFDB - Embedded newform 336.4.q.l.289.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [336,4,Mod(193,336)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(336, base_ring=CyclotomicField(6))

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

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

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

chi := DirichletCharacter("336.193");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 336 = 2^{4} \cdot 3 \cdot 7 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	336.q (of order $3$, degree $2$, not 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:	$19.8246417619$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.10253065563.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 3x^{5} + 58x^{4} - 111x^{3} + 802x^{2} - 747x + 189 $ x^6 - 3x^5 + 58x^4 - 111x^3 + 802x^2 - 747*x + 189
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 2^{4}\cdot 3 $
Twist minimal:	no (minimal twist has level 168)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			289.2
Root			$0.500000 + 5.58188i$ of defining polynomial
Character	$\chi$	$=$	336.289
Dual form			336.4.q.l.193.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.50000 + 2.59808i) q^{3} +(-0.119644 + 0.207230i) q^{5} +(-12.9074 - 13.2815i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})$	\(q+(1.50000 + 2.59808i) q^{3} +(-0.119644 + 0.207230i) q^{5} +(-12.9074 - 13.2815i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(4.04846 + 7.01213i) q^{11} +43.7693 q^{13} -0.717867 q^{15} +(30.4074 + 52.6671i) q^{17} +(-49.4430 + 85.6378i) q^{19} +(15.1454 - 53.4567i) q^{21} +(-106.937 + 185.221i) q^{23} +(62.4714 + 108.204i) q^{25} -27.0000 q^{27} +110.313 q^{29} +(-40.0069 - 69.2940i) q^{31} +(-12.1454 + 21.0364i) q^{33} +(4.29663 - 1.08574i) q^{35} +(1.44032 - 2.49471i) q^{37} +(65.6540 + 113.716i) q^{39} -242.307 q^{41} -367.006 q^{43} +(-1.07680 - 1.86507i) q^{45} +(44.6955 - 77.4149i) q^{47} +(-9.79860 + 342.860i) q^{49} +(-91.2222 + 158.001i) q^{51} +(-5.70636 - 9.88370i) q^{53} -1.93750 q^{55} -296.658 q^{57} +(200.049 + 346.494i) q^{59} +(-240.191 + 416.022i) q^{61} +(161.603 - 40.8362i) q^{63} +(-5.23675 + 9.07033i) q^{65} +(-120.500 - 208.712i) q^{67} -641.624 q^{69} +978.496 q^{71} +(311.108 + 538.854i) q^{73} +(-187.414 + 324.611i) q^{75} +(40.8769 - 144.278i) q^{77} +(-272.978 + 472.813i) q^{79} +(-40.5000 - 70.1481i) q^{81} +845.995 q^{83} -14.5523 q^{85} +(165.470 + 286.602i) q^{87} +(101.659 - 176.079i) q^{89} +(-564.948 - 581.324i) q^{91} +(120.021 - 207.882i) q^{93} +(-11.8312 - 20.4922i) q^{95} -1199.17 q^{97} -72.8722 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 9 q^{3} + 11 q^{5} + q^{7} - 27 q^{9}+O(q^{10}) $ 6 * q + 9 * q^3 + 11 * q^5 + q^7 - 27 * q^9	$ 6 q + 9 q^{3} + 11 q^{5} + q^{7} - 27 q^{9} - 19 q^{11} - 44 q^{13} + 66 q^{15} + 104 q^{17} + 202 q^{19} - 39 q^{21} - 280 q^{23} - 186 q^{25} - 162 q^{27} - 146 q^{29} - 131 q^{31} + 57 q^{33} + 252 q^{35} + 326 q^{37} - 66 q^{39} - 1032 q^{41} - 72 q^{43} + 99 q^{45} - 126 q^{47} + 33 q^{49} - 312 q^{51} + 385 q^{53} + 1222 q^{55} + 1212 q^{57} + 285 q^{59} + 34 q^{61} - 126 q^{63} + 920 q^{65} - 100 q^{67} - 1680 q^{69} - 68 q^{71} + 108 q^{73} + 558 q^{75} + 1571 q^{77} - 2463 q^{79} - 243 q^{81} + 230 q^{83} - 1000 q^{85} - 219 q^{87} + 110 q^{89} - 110 q^{91} + 393 q^{93} - 2064 q^{95} - 5882 q^{97} + 342 q^{99}+O(q^{100}) $ 6 * q + 9 * q^3 + 11 * q^5 + q^7 - 27 * q^9 - 19 * q^11 - 44 * q^13 + 66 * q^15 + 104 * q^17 + 202 * q^19 - 39 * q^21 - 280 * q^23 - 186 * q^25 - 162 * q^27 - 146 * q^29 - 131 * q^31 + 57 * q^33 + 252 * q^35 + 326 * q^37 - 66 * q^39 - 1032 * q^41 - 72 * q^43 + 99 * q^45 - 126 * q^47 + 33 * q^49 - 312 * q^51 + 385 * q^53 + 1222 * q^55 + 1212 * q^57 + 285 * q^59 + 34 * q^61 - 126 * q^63 + 920 * q^65 - 100 * q^67 - 1680 * q^69 - 68 * q^71 + 108 * q^73 + 558 * q^75 + 1571 * q^77 - 2463 * q^79 - 243 * q^81 + 230 * q^83 - 1000 * q^85 - 219 * q^87 + 110 * q^89 - 110 * q^91 + 393 * q^93 - 2064 * q^95 - 5882 * q^97 + 342 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/336\mathbb{Z}\right)^\times$.

$n$	$85$	$113$	$127$	$241$
$\chi(n)$	$1$	$1$	$1$	$e\left(\frac{1}{3}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$3$	1.50000	+	2.59808i	0.288675	+	0.500000i
$4$		0			0
$5$	−0.119644	+	0.207230i	−0.0107013	+	0.0185352i	−0.871326	−	0.490704i	$-0.836740\pi$
$5$	−0.119644	+	0.207230i	−0.0107013	+	0.0185352i	0.860625	+	0.509239i	$0.170073\pi$
$6$		0			0
$7$	−12.9074	−	13.2815i	−0.696934	−	0.717136i
$7$	−12.9074	−	13.2815i	−0.696934	−	0.717136i
$8$		0			0
$9$	−4.50000	+	7.79423i	−0.166667	+	0.288675i
$10$		0			0
$11$	4.04846	+	7.01213i	0.110969	+	0.192203i	0.916161	−	0.400810i	$-0.131271\pi$
$11$	4.04846	+	7.01213i	0.110969	+	0.192203i	−0.805192	+	0.593014i	$0.797938\pi$
$12$		0			0
$13$	43.7693			0.933802			0.466901	−	0.884310i	$-0.345370\pi$
$13$	43.7693			0.933802			0.466901	+	0.884310i	$0.345370\pi$
$14$		0			0
$15$	−0.717867			−0.0123568
$16$		0			0
$17$	30.4074	+	52.6671i	0.433816	+	0.751392i	0.997198	−	0.0748049i	$-0.0238334\pi$
$17$	30.4074	+	52.6671i	0.433816	+	0.751392i	−0.563382	+	0.826197i	$0.690500\pi$
$18$		0			0
$19$	−49.4430	+	85.6378i	−0.597000	+	1.03404i	0.396261	+	0.918138i	$0.370308\pi$
$19$	−49.4430	+	85.6378i	−0.597000	+	1.03404i	−0.993261	+	0.115897i	$0.963026\pi$
$20$		0			0
$21$	15.1454	−	53.4567i	0.157380	−	0.555486i
$22$		0			0
$23$	−106.937	+	185.221i	−0.969478	+	1.67919i	−0.272408	+	0.962182i	$0.587820\pi$
$23$	−106.937	+	185.221i	−0.969478	+	1.67919i	−0.697070	+	0.717003i	$0.745513\pi$
$24$		0			0
$25$	62.4714	+	108.204i	0.499771	+	0.865629i
$26$		0			0
$27$	−27.0000			−0.192450
$28$		0			0
$29$	110.313			0.706367			0.353184	−	0.935554i	$-0.385099\pi$
$29$	110.313			0.706367			0.353184	+	0.935554i	$0.385099\pi$
$30$		0			0
$31$	−40.0069	−	69.2940i	−0.231789	−	0.401470i	0.726546	−	0.687118i	$-0.241125\pi$
$31$	−40.0069	−	69.2940i	−0.231789	−	0.401470i	−0.958335	+	0.285648i	$0.907791\pi$
$32$		0			0
$33$	−12.1454	+	21.0364i	−0.0640678	+	0.110969i
$34$		0			0
$35$	4.29663	−	1.08574i	0.0207504	−	0.00524353i
$36$		0			0
$37$	1.44032	−	2.49471i	0.00639966	−	0.0110845i	−0.862808	−	0.505532i	$-0.831296\pi$
$37$	1.44032	−	2.49471i	0.00639966	−	0.0110845i	0.869207	+	0.494447i	$0.164630\pi$
$38$		0			0
$39$	65.6540	+	113.716i	0.269565	+	0.466901i
$40$		0			0
$41$	−242.307			−0.922976			−0.461488	−	0.887146i	$-0.652684\pi$
$41$	−242.307			−0.922976			−0.461488	+	0.887146i	$0.652684\pi$
$42$		0			0
$43$	−367.006			−1.30158			−0.650790	−	0.759258i	$-0.725562\pi$
$43$	−367.006			−1.30158			−0.650790	+	0.759258i	$0.725562\pi$
$44$		0			0
$45$	−1.07680	−	1.86507i	−0.00356711	−	0.00617841i
$46$		0			0
$47$	44.6955	−	77.4149i	0.138713	−	0.240258i	−0.788297	−	0.615295i	$-0.789037\pi$
$47$	44.6955	−	77.4149i	0.138713	−	0.240258i	0.927010	+	0.375037i	$0.122370\pi$
$48$		0			0
$49$	−9.79860	+	342.860i	−0.0285673	+	0.999592i
$50$		0			0
$51$	−91.2222	+	158.001i	−0.250464	+	0.433816i
$52$		0			0
$53$	−5.70636	−	9.88370i	−0.0147892	−	0.0256157i	0.858536	−	0.512753i	$-0.171374\pi$
$53$	−5.70636	−	9.88370i	−0.0147892	−	0.0256157i	−0.873325	+	0.487137i	$0.838041\pi$
$54$		0			0
$55$	−1.93750			−0.00475005
$56$		0			0
$57$	−296.658			−0.689357
$58$		0			0
$59$	200.049	+	346.494i	0.441425	+	0.764571i	0.997796	−	0.0663633i	$-0.0211396\pi$
$59$	200.049	+	346.494i	0.441425	+	0.764571i	−0.556370	+	0.830935i	$0.687806\pi$
$60$		0			0
$61$	−240.191	+	416.022i	−0.504152	+	0.873217i	0.495837	+	0.868416i	$0.334861\pi$
$61$	−240.191	+	416.022i	−0.504152	+	0.873217i	−0.999988	+	0.00480073i	$0.998472\pi$
$62$		0			0
$63$	161.603	−	40.8362i	0.323175	−	0.0816648i
$64$		0			0
$65$	−5.23675	+	9.07033i	−0.00999292	+	0.0173082i
$66$		0			0
$67$	−120.500	−	208.712i	−0.219722	−	0.380570i	0.735001	−	0.678066i	$-0.237182\pi$
$67$	−120.500	−	208.712i	−0.219722	−	0.380570i	−0.954723	+	0.297496i	$0.903848\pi$
$68$		0			0
$69$	−641.624			−1.11946
$70$		0			0
$71$	978.496			1.63558			0.817790	−	0.575517i	$-0.195199\pi$
$71$	978.496			1.63558			0.817790	+	0.575517i	$0.195199\pi$
$72$		0			0
$73$	311.108	+	538.854i	0.498800	+	0.863947i	0.999999	−	0.00138514i	$-0.000440903\pi$
$73$	311.108	+	538.854i	0.498800	+	0.863947i	−0.501199	+	0.865332i	$0.667108\pi$
$74$		0			0
$75$	−187.414	+	324.611i	−0.288543	+	0.499771i
$76$		0			0
$77$	40.8769	−	144.278i	0.0604981	−	0.213533i
$78$		0			0
$79$	−272.978	+	472.813i	−0.388766	+	0.673362i	−0.992284	−	0.123987i	$-0.960432\pi$
$79$	−272.978	+	472.813i	−0.388766	+	0.673362i	0.603518	+	0.797349i	$0.293765\pi$
$80$		0			0
$81$	−40.5000	−	70.1481i	−0.0555556	−	0.0962250i
$82$		0			0
$83$	845.995			1.11879			0.559397	−	0.828900i	$-0.311033\pi$
$83$	845.995			1.11879			0.559397	+	0.828900i	$0.311033\pi$
$84$		0			0
$85$	−14.5523			−0.0185696
$86$		0			0
$87$	165.470	+	286.602i	0.203911	+	0.353184i
$88$		0			0
$89$	101.659	−	176.079i	0.121077	−	0.209712i	−0.799116	−	0.601177i	$-0.794698\pi$
$89$	101.659	−	176.079i	0.121077	−	0.209712i	0.920193	+	0.391466i	$0.128032\pi$
$90$		0			0
$91$	−564.948	−	581.324i	−0.650798	−	0.669663i
$92$		0			0
$93$	120.021	−	207.882i	0.133823	−	0.231789i
$94$		0			0
$95$	−11.8312	−	20.4922i	−0.0127774	−	0.0221311i
$96$		0			0
$97$	−1199.17			−1.25523			−0.627617	−	0.778522i	$-0.715970\pi$
$97$	−1199.17			−1.25523			−0.627617	+	0.778522i	$0.715970\pi$
$98$		0			0
$99$	−72.8722			−0.0739791
$100$		0			0
$101$	−183.793	−	318.338i	−0.181070	−	0.313622i	0.761175	−	0.648546i	$-0.224623\pi$
$101$	−183.793	−	318.338i	−0.181070	−	0.313622i	−0.942245	+	0.334924i	$0.891289\pi$
$102$		0			0
$103$	472.614	−	818.591i	0.452117	−	0.783089i	−0.546401	−	0.837524i	$-0.684002\pi$
$103$	472.614	−	818.591i	0.452117	−	0.783089i	0.998517	+	0.0544348i	$0.0173357\pi$
$104$		0			0
$105$	9.26578	+	9.53437i	0.00861189	+	0.00886152i
$106$		0			0
$107$	−356.578	+	617.612i	−0.322166	+	0.558007i	−0.980935	−	0.194338i	$-0.937744\pi$
$107$	−356.578	+	617.612i	−0.322166	+	0.558007i	0.658769	+	0.752345i	$0.271078\pi$
$108$		0			0
$109$	466.811	+	808.540i	0.410205	+	0.710496i	0.994912	−	0.100748i	$-0.0321237\pi$
$109$	466.811	+	808.540i	0.410205	+	0.710496i	−0.584707	+	0.811245i	$0.698790\pi$
$110$		0			0
$111$	8.64192			0.00738969
$112$		0			0
$113$	1191.38			0.991822			0.495911	−	0.868373i	$-0.334834\pi$
$113$	1191.38			0.991822			0.495911	+	0.868373i	$0.334834\pi$
$114$		0			0
$115$	−25.5889	−	44.3213i	−0.0207494	−	0.0359390i
$116$		0			0
$117$	−196.962	+	341.148i	−0.155634	+	0.269565i
$118$		0			0
$119$	307.021	−	1083.65i	0.236509	−	0.834775i
$120$		0			0
$121$	632.720	−	1095.90i	0.475372	−	0.823368i
$122$		0			0
$123$	−363.461	−	629.533i	−0.266440	−	0.461488i
$124$		0			0
$125$	−59.8085			−0.0427955
$126$		0			0
$127$	1196.63			0.836090			0.418045	−	0.908426i	$-0.362715\pi$
$127$	1196.63			0.836090			0.418045	+	0.908426i	$0.362715\pi$
$128$		0			0
$129$	−550.509	−	953.510i	−0.375734	−	0.650790i
$130$		0			0
$131$	252.754	−	437.783i	0.168574	−	0.291979i	−0.769345	−	0.638834i	$-0.779417\pi$
$131$	252.754	−	437.783i	0.168574	−	0.291979i	0.937919	+	0.346855i	$0.112750\pi$
$132$		0			0
$133$	1775.58	−	448.681i	1.15761	−	0.292523i
$134$		0			0
$135$	3.23040	−	5.59522i	0.00205947	−	0.00356711i
$136$		0			0
$137$	369.771	+	640.462i	0.230596	+	0.399404i	0.957984	−	0.286823i	$-0.0925990\pi$
$137$	369.771	+	640.462i	0.230596	+	0.399404i	−0.727388	+	0.686227i	$0.759266\pi$
$138$		0			0
$139$	−3095.88			−1.88913			−0.944566	−	0.328322i	$-0.893517\pi$
$139$	−3095.88			−1.88913			−0.944566	+	0.328322i	$0.893517\pi$
$140$		0			0
$141$	268.173			0.160172
$142$		0			0
$143$	177.198	+	306.916i	0.103623	+	0.179480i
$144$		0			0
$145$	−13.1984	+	22.8602i	−0.00755906	+	0.0130927i
$146$		0			0
$147$	−905.474	+	488.833i	−0.508043	+	0.274274i
$148$		0			0
$149$	1494.58	−	2588.69i	0.821751	−	1.42331i	−0.0826265	−	0.996581i	$-0.526331\pi$
$149$	1494.58	−	2588.69i	0.821751	−	1.42331i	0.904377	−	0.426734i	$-0.140336\pi$
$150$		0			0
$151$	−884.842	−	1532.59i	−0.476871	−	0.825964i	0.522778	−	0.852469i	$-0.324896\pi$
$151$	−884.842	−	1532.59i	−0.476871	−	0.825964i	−0.999649	+	0.0265047i	$0.991562\pi$
$152$		0			0
$153$	−547.333			−0.289211
$154$		0			0
$155$	19.1464			0.00992179
$156$		0			0
$157$	−1164.01	−	2016.12i	−0.591707	−	1.02487i	−0.994003	−	0.109357i	$-0.965121\pi$
$157$	−1164.01	−	2016.12i	−0.591707	−	1.02487i	0.402296	−	0.915510i	$-0.368212\pi$
$158$		0			0
$159$	17.1191	−	29.6511i	0.00853856	−	0.0147892i
$160$		0			0
$161$	3840.30	−	970.427i	1.87987	−	0.475033i
$162$		0			0
$163$	−1298.68	+	2249.38i	−0.624051	+	1.08089i	0.364672	+	0.931136i	$0.381181\pi$
$163$	−1298.68	+	2249.38i	−0.624051	+	1.08089i	−0.988724	+	0.149752i	$0.952152\pi$
$164$		0			0
$165$	−2.90625	−	5.03378i	−0.00137122	−	0.00237502i
$166$		0			0
$167$	3276.61			1.51827			0.759137	−	0.650931i	$-0.225621\pi$
$167$	3276.61			1.51827			0.759137	+	0.650931i	$0.225621\pi$
$168$		0			0
$169$	−281.247			−0.128014
$170$		0			0
$171$	−444.987	−	770.741i	−0.199000	−	0.344678i
$172$		0			0
$173$	115.018	−	199.217i	0.0505471	−	0.0875501i	−0.839645	−	0.543136i	$-0.817237\pi$
$173$	115.018	−	199.217i	0.0505471	−	0.0875501i	0.890192	+	0.455586i	$0.150570\pi$
$174$		0			0
$175$	630.768	−	2226.34i	0.272466	−	0.961689i
$176$		0			0
$177$	−600.146	+	1039.48i	−0.254857	+	0.441425i
$178$		0			0
$179$	−1865.28	−	3230.76i	−0.778869	−	1.34904i	−0.932594	−	0.360927i	$-0.882460\pi$
$179$	−1865.28	−	3230.76i	−0.778869	−	1.34904i	0.153725	−	0.988114i	$-0.450873\pi$
$180$		0			0
$181$	−1649.91			−0.677550			−0.338775	−	0.940867i	$-0.610013\pi$
$181$	−1649.91			−0.677550			−0.338775	+	0.940867i	$0.610013\pi$
$182$		0			0
$183$	−1441.14			−0.582144
$184$		0			0
$185$	0.344653	+	0.596956i	0.000136970	+	0.000237238i
$186$		0			0
$187$	−246.206	+	426.441i	−0.0962800	+	0.166762i
$188$		0			0
$189$	348.500	+	358.602i	0.134125	+	0.138013i
$190$		0			0
$191$	904.827	−	1567.21i	0.342780	−	0.593712i	−0.642168	−	0.766564i	$-0.721965\pi$
$191$	904.827	−	1567.21i	0.342780	−	0.593712i	0.984948	+	0.172852i	$0.0552982\pi$
$192$		0			0
$193$	−2183.61	−	3782.13i	−0.814404	−	1.41059i	−0.909755	−	0.415146i	$-0.863731\pi$
$193$	−2183.61	−	3782.13i	−0.814404	−	1.41059i	0.0953506	−	0.995444i	$-0.469603\pi$
$194$		0			0
$195$	−31.4205			−0.0115388
$196$		0			0
$197$	398.287			0.144044			0.0720222	−	0.997403i	$-0.477055\pi$
$197$	398.287			0.144044			0.0720222	+	0.997403i	$0.477055\pi$
$198$		0			0
$199$	2171.67	+	3761.45i	0.773598	+	1.33991i	0.935579	+	0.353117i	$0.114878\pi$
$199$	2171.67	+	3761.45i	0.773598	+	1.33991i	−0.161981	+	0.986794i	$0.551788\pi$
$200$		0			0
$201$	361.499	−	626.135i	0.126857	−	0.219722i
$202$		0			0
$203$	−1423.86	−	1465.13i	−0.492291	−	0.506561i
$204$		0			0
$205$	28.9907	−	50.2134i	0.00987707	−	0.0171076i
$206$		0			0
$207$	−962.437	−	1666.99i	−0.323159	−	0.559728i
$208$		0			0
$209$	−800.672			−0.264993
$210$		0			0
$211$	2723.91			0.888728			0.444364	−	0.895846i	$-0.353430\pi$
$211$	2723.91			0.888728			0.444364	+	0.895846i	$0.353430\pi$
$212$		0			0
$213$	1467.74	+	2542.21i	0.472151	+	0.817790i
$214$		0			0
$215$	43.9102	−	76.0548i	0.0139286	−	0.0241251i
$216$		0			0
$217$	−403.946	+	1425.76i	−0.126367	+	0.446022i
$218$		0			0
$219$	−933.323	+	1616.56i	−0.287982	+	0.498800i
$220$		0			0
$221$	1330.91	+	2305.20i	0.405098	+	0.701651i
$222$		0			0
$223$	4896.87			1.47049			0.735243	−	0.677803i	$-0.237068\pi$
$223$	4896.87			1.47049			0.735243	+	0.677803i	$0.237068\pi$
$224$		0			0
$225$	−1124.48			−0.333181
$226$		0			0
$227$	1615.77	+	2798.60i	0.472434	+	0.818280i	0.999502	−	0.0315427i	$-0.0100420\pi$
$227$	1615.77	+	2798.60i	0.472434	+	0.818280i	−0.527068	+	0.849823i	$0.676709\pi$
$228$		0			0
$229$	−2959.27	+	5125.60i	−0.853947	+	1.47908i	0.0236721	+	0.999720i	$0.492464\pi$
$229$	−2959.27	+	5125.60i	−0.853947	+	1.47908i	−0.877619	+	0.479359i	$0.840869\pi$
$230$		0			0
$231$	436.161	−	110.216i	0.124231	−	0.0313925i
$232$		0			0
$233$	260.972	−	452.017i	0.0733771	−	0.127093i	−0.827002	−	0.562199i	$-0.809956\pi$
$233$	260.972	−	452.017i	0.0733771	−	0.127093i	0.900379	+	0.435106i	$0.143289\pi$
$234$		0			0
$235$	10.6951	+	18.5245i	0.00296882	+	0.00514216i
$236$		0			0
$237$	−1637.87			−0.448908
$238$		0			0
$239$	6626.70			1.79350			0.896748	−	0.442542i	$-0.145923\pi$
$239$	6626.70			1.79350			0.896748	+	0.442542i	$0.145923\pi$
$240$		0			0
$241$	−1012.70	−	1754.04i	−0.270678	−	0.468829i	0.698357	−	0.715749i	$-0.253915\pi$
$241$	−1012.70	−	1754.04i	−0.270678	−	0.468829i	−0.969036	+	0.246921i	$0.920581\pi$
$242$		0			0
$243$	121.500	−	210.444i	0.0320750	−	0.0555556i
$244$		0			0
$245$	−69.8786	−	43.0519i	−0.0182220	−	0.0112265i
$246$		0			0
$247$	−2164.09	+	3748.31i	−0.557480	+	0.965584i
$248$		0			0
$249$	1268.99	+	2197.96i	0.322968	+	0.559397i
$250$		0			0
$251$	−3352.64			−0.843096			−0.421548	−	0.906806i	$-0.638513\pi$
$251$	−3352.64			−0.843096			−0.421548	+	0.906806i	$0.638513\pi$
$252$		0			0
$253$	−1731.73			−0.430327
$254$		0			0
$255$	−21.8284	−	37.8080i	−0.00536059	−	0.00928481i
$256$		0			0
$257$	−3413.37	+	5912.12i	−0.828482	+	1.43497i	0.0707462	+	0.997494i	$0.477462\pi$
$257$	−3413.37	+	5912.12i	−0.828482	+	1.43497i	−0.899229	+	0.437479i	$0.855871\pi$
$258$		0			0
$259$	−51.7244	+	13.0705i	−0.0124092	+	0.00313576i
$260$		0			0
$261$	−496.409	+	859.806i	−0.117728	+	0.203911i
$262$		0			0
$263$	−897.082	−	1553.79i	−0.210329	−	0.364300i	0.741489	−	0.670965i	$-0.234120\pi$
$263$	−897.082	−	1553.79i	−0.210329	−	0.364300i	−0.951817	+	0.306665i	$0.900787\pi$
$264$		0			0
$265$	2.73094			0.000633057
$266$		0			0
$267$	609.956			0.139808
$268$		0			0
$269$	733.331	+	1270.17i	0.166216	+	0.287894i	0.937086	−	0.349098i	$-0.113512\pi$
$269$	733.331	+	1270.17i	0.166216	+	0.287894i	−0.770871	+	0.636992i	$0.780179\pi$
$270$		0			0
$271$	−878.257	+	1521.19i	−0.196865	+	0.340979i	−0.947510	−	0.319726i	$-0.896409\pi$
$271$	−878.257	+	1521.19i	−0.196865	+	0.340979i	0.750646	+	0.660705i	$0.229743\pi$
$272$		0			0
$273$	662.902	−	2339.76i	0.146962	−	0.518714i
$274$		0			0
$275$	−505.825	+	876.115i	−0.110918	+	0.192115i
$276$		0			0
$277$	−3854.00	−	6675.32i	−0.835972	−	1.44795i	−0.893236	−	0.449588i	$-0.851571\pi$
$277$	−3854.00	−	6675.32i	−0.835972	−	1.44795i	0.0572638	−	0.998359i	$-0.481762\pi$
$278$		0			0
$279$	720.125			0.154526
$280$		0			0
$281$	6837.65			1.45160			0.725800	−	0.687905i	$-0.241470\pi$
$281$	6837.65			1.45160			0.725800	+	0.687905i	$0.241470\pi$
$282$		0			0
$283$	1624.30	+	2813.37i	0.341182	+	0.590945i	0.984653	−	0.174526i	$-0.0558393\pi$
$283$	1624.30	+	2813.37i	0.341182	+	0.590945i	−0.643470	+	0.765471i	$0.722506\pi$
$284$		0			0
$285$	35.4935	−	61.4765i	0.00737703	−	0.0127774i
$286$		0			0
$287$	3127.55	+	3218.21i	0.643253	+	0.661899i
$288$		0			0
$289$	607.281	−	1051.84i	0.123607	−	0.214094i
$290$		0			0
$291$	−1798.76	−	3115.55i	−0.362355	−	0.627617i
$292$		0			0
$293$	−9674.19			−1.92892			−0.964458	−	0.264237i	$-0.914880\pi$
$293$	−9674.19			−1.92892			−0.964458	+	0.264237i	$0.914880\pi$
$294$		0			0
$295$	−95.7388			−0.0188953
$296$		0			0
$297$	−109.308	−	189.328i	−0.0213559	−	0.0369896i
$298$		0			0
$299$	−4680.58	+	8107.00i	−0.905300	+	1.56803i
$300$		0			0
$301$	4737.09	+	4874.41i	0.907114	+	0.933409i
$302$		0			0
$303$	551.378	−	955.014i	0.104541	−	0.181070i
$304$		0			0
$305$	−57.4749	−	99.5495i	−0.0107902	−	0.0186891i
$306$		0			0
$307$	−4959.70			−0.922035			−0.461018	−	0.887391i	$-0.652516\pi$
$307$	−4959.70			−0.922035			−0.461018	+	0.887391i	$0.652516\pi$
$308$		0			0
$309$	2835.68			0.522059
$310$		0			0
$311$	−3378.87	−	5852.38i	−0.616071	−	1.06707i	−0.990196	−	0.139688i	$-0.955390\pi$
$311$	−3378.87	−	5852.38i	−0.616071	−	1.06707i	0.374124	−	0.927379i	$-0.377943\pi$
$312$		0			0
$313$	−1691.01	+	2928.91i	−0.305372	+	0.528920i	−0.977344	−	0.211657i	$-0.932114\pi$
$313$	−1691.01	+	2928.91i	−0.305372	+	0.528920i	0.671972	+	0.740576i	$0.265447\pi$
$314$		0			0
$315$	−10.8724	+	38.3748i	−0.00194472	+	0.00686404i
$316$		0			0
$317$	−433.504	+	750.852i	−0.0768077	+	0.133035i	−0.901871	−	0.432006i	$-0.857806\pi$
$317$	−433.504	+	750.852i	−0.0768077	+	0.133035i	0.825063	+	0.565040i	$0.191139\pi$
$318$		0			0
$319$	446.598	+	773.531i	0.0783846	+	0.135766i
$320$		0			0
$321$	−2139.47			−0.372005
$322$		0			0
$323$	−6013.73			−1.03595
$324$		0			0
$325$	2734.33	+	4736.00i	0.466687	+	0.808326i
$326$		0			0
$327$	−1400.43	+	2425.62i	−0.236832	+	0.410205i
$328$		0			0
$329$	−1605.09	+	405.599i	−0.268971	+	0.0679678i
$330$		0			0
$331$	−689.605	+	1194.43i	−0.114514	+	0.198344i	−0.917585	−	0.397539i	$-0.869864\pi$
$331$	−689.605	+	1194.43i	−0.114514	+	0.198344i	0.803071	+	0.595883i	$0.203198\pi$
$332$		0			0
$333$	12.9629	+	22.4524i	0.00213322	+	0.00369484i
$334$		0			0
$335$	57.6685			0.00940527
$336$		0			0
$337$	−2109.75			−0.341025			−0.170513	−	0.985355i	$-0.554542\pi$
$337$	−2109.75			−0.341025			−0.170513	+	0.985355i	$0.554542\pi$
$338$		0			0
$339$	1787.08	+	3095.31i	0.286314	+	0.495911i
$340$		0			0
$341$	323.933	−	561.068i	0.0514426	−	0.0891012i
$342$		0			0
$343$	4680.18	−	4295.29i	0.736753	−	0.676162i
$344$		0			0
$345$	76.7668	−	132.964i	0.0119797	−	0.0207494i
$346$		0			0
$347$	−2094.15	−	3627.17i	−0.323976	−	0.561143i	0.657328	−	0.753604i	$-0.271686\pi$
$347$	−2094.15	−	3627.17i	−0.323976	−	0.561143i	−0.981305	+	0.192461i	$0.938353\pi$
$348$		0			0
$349$	10456.8			1.60385			0.801923	−	0.597428i	$-0.203810\pi$
$349$	10456.8			1.60385			0.801923	+	0.597428i	$0.203810\pi$
$350$		0			0
$351$	−1181.77			−0.179710
$352$		0			0
$353$	2290.62	+	3967.47i	0.345375	+	0.598207i	0.985422	−	0.170129i	$-0.0544185\pi$
$353$	2290.62	+	3967.47i	0.345375	+	0.598207i	−0.640047	+	0.768336i	$0.721085\pi$
$354$		0			0
$355$	−117.072	+	202.774i	−0.0175029	+	0.0303159i
$356$		0			0
$357$	3275.94	−	827.815i	0.485662	−	0.122724i
$358$		0			0
$359$	−3890.34	+	6738.27i	−0.571934	+	0.990619i	0.424433	+	0.905459i	$0.360473\pi$
$359$	−3890.34	+	6738.27i	−0.571934	+	0.990619i	−0.996367	+	0.0851595i	$0.972860\pi$
$360$		0			0
$361$	−1459.73	−	2528.32i	−0.212819	−	0.368613i
$362$		0			0
$363$	3796.32			0.548912
$364$		0			0
$365$	−148.889			−0.0213513
$366$		0			0
$367$	−2063.30	−	3573.73i	−0.293469	−	0.508303i	0.681158	−	0.732136i	$-0.261476\pi$
$367$	−2063.30	−	3573.73i	−0.293469	−	0.508303i	−0.974628	+	0.223833i	$0.928143\pi$
$368$		0			0
$369$	1090.38	−	1888.60i	0.153829	−	0.266440i
$370$		0			0
$371$	−57.6166	+	203.362i	−0.00806282	+	0.0284583i
$372$		0			0
$373$	2564.91	−	4442.56i	0.356048	−	0.616694i	−0.631248	−	0.775581i	$-0.717457\pi$
$373$	2564.91	−	4442.56i	0.356048	−	0.616694i	0.987297	+	0.158887i	$0.0507905\pi$
$374$		0			0
$375$	−89.7128	−	155.387i	−0.0123540	−	0.0213977i
$376$		0			0
$377$	4828.33			0.659607
$378$		0			0
$379$	1017.94			0.137963			0.0689815	−	0.997618i	$-0.478025\pi$
$379$	1017.94			0.137963			0.0689815	+	0.997618i	$0.478025\pi$
$380$		0			0
$381$	1794.94	+	3108.93i	0.241359	+	0.418045i
$382$		0			0
$383$	−5183.30	+	8977.74i	−0.691525	+	1.19776i	0.279813	+	0.960055i	$0.409728\pi$
$383$	−5183.30	+	8977.74i	−0.691525	+	1.19776i	−0.971338	+	0.237702i	$0.923606\pi$
$384$		0			0
$385$	25.0081	+	25.7330i	0.00331047	+	0.00340643i
$386$		0			0
$387$	1651.53	−	2860.53i	0.216930	−	0.375734i
$388$		0			0
$389$	−6503.31	−	11264.1i	−0.847637	−	1.46815i	−0.883311	−	0.468788i	$-0.844691\pi$
$389$	−6503.31	−	11264.1i	−0.847637	−	1.46815i	0.0356736	−	0.999363i	$-0.488642\pi$
$390$		0			0
$391$	−13006.8			−1.68230
$392$		0			0
$393$	1516.52			0.194653
$394$		0			0
$395$	−65.3207	−	113.139i	−0.00832061	−	0.0144117i
$396$		0			0
$397$	−977.246	+	1692.64i	−0.123543	+	0.213983i	−0.921162	−	0.389178i	$-0.872759\pi$
$397$	−977.246	+	1692.64i	−0.123543	+	0.213983i	0.797619	+	0.603161i	$0.206092\pi$
$398$		0			0
$399$	3829.08	+	3940.08i	0.480436	+	0.494362i
$400$		0			0
$401$	−5423.03	+	9392.97i	−0.675345	+	1.16973i	0.301023	+	0.953617i	$0.402672\pi$
$401$	−5423.03	+	9392.97i	−0.675345	+	1.16973i	−0.976368	+	0.216115i	$0.930661\pi$
$402$		0			0
$403$	−1751.08	−	3032.95i	−0.216445	−	0.374894i
$404$		0			0
$405$	19.3824			0.00237807
$406$		0			0
$407$	23.3243			0.00284065
$408$		0			0
$409$	2950.18	+	5109.86i	0.356667	+	0.617766i	0.987402	−	0.158233i	$-0.0505796\pi$
$409$	2950.18	+	5109.86i	0.356667	+	0.617766i	−0.630734	+	0.775999i	$0.717246\pi$
$410$		0			0
$411$	−1109.31	+	1921.39i	−0.133135	+	0.230596i
$412$		0			0
$413$	2019.87	−	7129.29i	0.240657	−	0.849417i
$414$		0			0
$415$	−101.219	+	175.316i	−0.0119726	+	0.0207371i
$416$		0			0
$417$	−4643.82	−	8043.34i	−0.545345	−	0.944566i
$418$		0			0
$419$	8994.03			1.04866			0.524328	−	0.851516i	$-0.324316\pi$
$419$	8994.03			1.04866			0.524328	+	0.851516i	$0.324316\pi$
$420$		0			0
$421$	8032.54			0.929886			0.464943	−	0.885341i	$-0.346075\pi$
$421$	8032.54			0.929886			0.464943	+	0.885341i	$0.346075\pi$
$422$		0			0
$423$	402.260	+	696.734i	0.0462377	+	0.0800860i
$424$		0			0
$425$	−3799.18	+	6580.38i	−0.433617	+	0.751047i
$426$		0			0
$427$	8625.65	−	2179.66i	0.977575	−	0.247029i
$428$		0			0
$429$	−531.594	+	920.749i	−0.0598266	+	0.103623i
$430$		0			0
$431$	−3642.97	−	6309.80i	−0.407136	−	0.705180i	0.587432	−	0.809274i	$-0.300139\pi$
$431$	−3642.97	−	6309.80i	−0.407136	−	0.705180i	−0.994567	+	0.104094i	$0.966806\pi$
$432$		0			0
$433$	11152.5			1.23777			0.618887	−	0.785480i	$-0.287584\pi$
$433$	11152.5			1.23777			0.618887	+	0.785480i	$0.287584\pi$
$434$		0			0
$435$	−79.1902			−0.00872845
$436$		0			0
$437$	−10574.6	−	18315.8i	−1.15756	−	2.00495i
$438$		0			0
$439$	5449.46	−	9438.74i	0.592457	−	1.02616i	−0.401444	−	0.915884i	$-0.631492\pi$
$439$	5449.46	−	9438.74i	0.592457	−	1.02616i	0.993900	−	0.110281i	$-0.0351752\pi$
$440$		0			0
$441$	−2628.24	−	1619.24i	−0.283796	−	0.174845i
$442$		0			0
$443$	8592.22	−	14882.2i	0.921509	−	1.59610i	0.124428	−	0.992229i	$-0.460290\pi$
$443$	8592.22	−	14882.2i	0.921509	−	1.59610i	0.797081	−	0.603872i	$-0.206376\pi$
$444$		0			0
$445$	24.3259	+	42.1338i	0.00259137	+	0.00448839i
$446$		0			0
$447$	8967.49			0.948876
$448$		0			0
$449$	5273.80			0.554312			0.277156	−	0.960825i	$-0.410608\pi$
$449$	5273.80			0.554312			0.277156	+	0.960825i	$0.410608\pi$
$450$		0			0
$451$	−980.970	−	1699.09i	−0.102421	−	0.177399i
$452$		0			0
$453$	2654.53	−	4597.78i	0.275321	−	0.476871i
$454$		0			0
$455$	188.061	−	47.5221i	0.0193768	−	0.00489641i
$456$		0			0
$457$	−2472.53	+	4282.54i	−0.253085	+	0.438356i	−0.964374	−	0.264544i	$-0.914779\pi$
$457$	−2472.53	+	4282.54i	−0.253085	+	0.438356i	0.711289	+	0.702900i	$0.248112\pi$
$458$		0			0
$459$	−821.000	−	1422.01i	−0.0834880	−	0.144605i
$460$		0			0
$461$	−6611.17			−0.667924			−0.333962	−	0.942587i	$-0.608386\pi$
$461$	−6611.17			−0.667924			−0.333962	+	0.942587i	$0.608386\pi$
$462$		0			0
$463$	4339.15			0.435545			0.217772	−	0.976000i	$-0.430121\pi$
$463$	4339.15			0.435545			0.217772	+	0.976000i	$0.430121\pi$
$464$		0			0
$465$	28.7196	+	49.7439i	0.00286417	+	0.00496090i
$466$		0			0
$467$	−6148.23	+	10649.0i	−0.609221	+	1.05520i	0.382148	+	0.924101i	$0.375184\pi$
$467$	−6148.23	+	10649.0i	−0.609221	+	1.05520i	−0.991369	+	0.131100i	$0.958149\pi$
$468$		0			0
$469$	−1216.68	+	4294.34i	−0.119789	+	0.422803i
$470$		0			0
$471$	3492.03	−	6048.36i	0.341622	−	0.591707i
$472$		0			0
$473$	−1485.81	−	2573.50i	−0.144435	−	0.250168i
$474$		0			0
$475$	−12355.1			−1.19345
$476$		0			0
$477$	102.714			0.00985948
$478$		0			0
$479$	−1949.86	−	3377.25i	−0.185994	−	0.322151i	0.757917	−	0.652351i	$-0.226217\pi$
$479$	−1949.86	−	3377.25i	−0.185994	−	0.322151i	−0.943911	+	0.330200i	$0.892884\pi$
$480$		0			0
$481$	63.0418	−	109.192i	0.00597601	−	0.0103508i
$482$		0			0
$483$	8281.70	+	8521.76i	0.780187	+	0.802802i
$484$		0			0
$485$	143.475	−	248.505i	0.0134327	−	0.0232661i
$486$		0			0
$487$	4996.22	+	8653.71i	0.464888	+	0.805210i	0.999196	−	0.0400800i	$-0.0127613\pi$
$487$	4996.22	+	8653.71i	0.464888	+	0.805210i	−0.534309	+	0.845290i	$0.679428\pi$
$488$		0			0
$489$	−7792.07			−0.720592
$490$		0			0
$491$	18654.9			1.71463			0.857317	−	0.514788i	$-0.172130\pi$
$491$	18654.9			1.71463			0.857317	+	0.514788i	$0.172130\pi$
$492$		0			0
$493$	3354.34	+	5809.88i	0.306433	+	0.530758i
$494$		0			0
$495$	8.71875	−	15.1013i	0.000791674	−	0.00137122i
$496$		0			0
$497$	−12629.8	−	12995.9i	−1.13989	−	1.17293i
$498$		0			0
$499$	8834.50	−	15301.8i	0.792558	−	1.37275i	−0.131820	−	0.991274i	$-0.542082\pi$
$499$	8834.50	−	15301.8i	0.792558	−	1.37275i	0.924378	−	0.381477i	$-0.124585\pi$
$500$		0			0
$501$	4914.92	+	8512.89i	0.438288	+	0.759137i
$502$		0			0
$503$	−11137.5			−0.987270			−0.493635	−	0.869669i	$-0.664332\pi$
$503$	−11137.5			−0.987270			−0.493635	+	0.869669i	$0.664332\pi$
$504$		0			0
$505$	87.9590			0.00775074
$506$		0			0
$507$	−421.871	−	730.701i	−0.0369545	−	0.0640071i
$508$		0			0
$509$	−5436.24	+	9415.84i	−0.473393	+	0.819941i	−0.999536	−	0.0304552i	$-0.990304\pi$
$509$	−5436.24	+	9415.84i	−0.473393	+	0.819941i	0.526143	+	0.850396i	$0.323638\pi$
$510$		0			0
$511$	3141.23	−	11087.2i	0.271937	−	0.959821i
$512$		0			0
$513$	1334.96	−	2312.22i	0.114893	−	0.199000i
$514$		0			0
$515$	113.091	+	195.880i	0.00967650	+	0.0167602i
$516$		0			0
$517$	723.791			0.0615712
$518$		0			0
$519$	690.107			0.0583667
$520$		0			0
$521$	10228.6	+	17716.5i	0.860123	+	1.48978i	0.871809	+	0.489845i	$0.162947\pi$
$521$	10228.6	+	17716.5i	0.860123	+	1.48978i	−0.0116862	+	0.999932i	$0.503720\pi$
$522$		0			0
$523$	7457.07	−	12916.0i	0.623470	−	1.07988i	−0.365365	−	0.930864i	$-0.619056\pi$
$523$	7457.07	−	12916.0i	0.623470	−	1.07988i	0.988835	−	0.149017i	$-0.0476110\pi$
$524$		0			0
$525$	6730.36	−	1700.73i	0.559499	−	0.141383i
$526$		0			0
$527$	2433.01	−	4214.10i	0.201108	−	0.348328i
$528$		0			0
$529$	−16787.7	−	29077.2i	−1.37977	−	2.38984i
$530$		0			0
$531$	−3600.87			−0.294284
$532$		0			0
$533$	−10605.6			−0.861877
$534$		0			0
$535$	−85.3252	−	147.788i	−0.00689520	−	0.0119428i
$536$		0			0
$537$	5595.84	−	9692.28i	0.449680	−	0.778869i
$538$		0			0
$539$	−2443.85	+	1319.34i	−0.195295	+	0.105433i
$540$		0			0
$541$	−1807.94	+	3131.45i	−0.143677	+	0.248857i	−0.928879	−	0.370384i	$-0.879226\pi$
$541$	−1807.94	+	3131.45i	−0.143677	+	0.248857i	0.785201	+	0.619241i	$0.212559\pi$
$542$		0			0
$543$	−2474.86	−	4286.58i	−0.195592	−	0.338775i
$544$		0			0
$545$	−223.405			−0.0175590
$546$		0			0
$547$	13365.1			1.04470			0.522350	−	0.852731i	$-0.325055\pi$
$547$	13365.1			1.04470			0.522350	+	0.852731i	$0.325055\pi$
$548$		0			0
$549$	−2161.72	−	3744.20i	−0.168051	−	0.291072i
$550$		0			0
$551$	−5454.22	+	9446.98i	−0.421701	+	0.730408i
$552$		0			0
$553$	9803.12	−	2477.20i	0.753836	−	0.190491i
$554$		0			0
$555$	−1.03396	+	1.79087i	−7.90794e−5	+	0.000136970i
$556$		0			0
$557$	−1466.97	−	2540.88i	−0.111594	−	0.193286i	0.804819	−	0.593520i	$-0.202262\pi$
$557$	−1466.97	−	2540.88i	−0.111594	−	0.193286i	−0.916413	+	0.400234i	$0.868929\pi$
$558$		0			0
$559$	−16063.6			−1.21542
$560$		0			0
$561$	−1477.24			−0.111175
$562$		0			0
$563$	477.124	+	826.402i	0.0357164	+	0.0618627i	0.883331	−	0.468750i	$-0.155295\pi$
$563$	477.124	+	826.402i	0.0357164	+	0.0618627i	−0.847615	+	0.530612i	$0.821962\pi$
$564$		0			0
$565$	−142.542	+	246.891i	−0.0106138	+	0.0183837i
$566$		0			0
$567$	−408.925	+	1443.33i	−0.0302879	+	0.106903i
$568$		0			0
$569$	−6629.30	+	11482.3i	−0.488426	+	0.845979i	−0.999911	−	0.0133129i	$-0.995762\pi$
$569$	−6629.30	+	11482.3i	−0.488426	+	0.845979i	0.511485	+	0.859292i	$0.329096\pi$
$570$		0			0
$571$	1386.87	+	2402.13i	0.101644	+	0.176053i	0.912362	−	0.409384i	$-0.134256\pi$
$571$	1386.87	+	2402.13i	0.101644	+	0.176053i	−0.810718	+	0.585437i	$0.800923\pi$
$572$		0			0
$573$	5428.96			0.395808
$574$		0			0
$575$	−26722.1			−1.93807
$576$		0			0
$577$	−5180.50	−	8972.89i	−0.373773	−	0.647394i	0.616369	−	0.787457i	$-0.288603\pi$
$577$	−5180.50	−	8972.89i	−0.373773	−	0.647394i	−0.990143	+	0.140063i	$0.955269\pi$
$578$		0			0
$579$	6550.84	−	11346.4i	0.470197	−	0.814404i
$580$		0			0
$581$	−10919.6	−	11236.1i	−0.779726	−	0.802328i
$582$		0			0
$583$	46.2039	−	80.0275i	0.00328228	−	0.00568508i
$584$		0			0
$585$	−47.1308	−	81.6329i	−0.00333097	−	0.00576941i
$586$		0			0
$587$	−4373.97			−0.307552			−0.153776	−	0.988106i	$-0.549143\pi$
$587$	−4373.97			−0.307552			−0.153776	+	0.988106i	$0.549143\pi$
$588$		0			0
$589$	7912.25			0.553512
$590$		0			0
$591$	597.430	+	1034.78i	0.0415820	+	0.0720222i
$592$		0			0
$593$	10551.1	−	18275.1i	0.730662	−	1.26554i	−0.225939	−	0.974141i	$-0.572545\pi$
$593$	10551.1	−	18275.1i	0.730662	−	1.26554i	0.956601	−	0.291402i	$-0.0941216\pi$
$594$		0			0
$595$	187.832	+	193.277i	0.0129418	+	0.0133169i
$596$		0			0
$597$	−6515.02	+	11284.4i	−0.446637	+	0.773598i
$598$		0			0
$599$	2690.71	+	4660.44i	0.183538	+	0.317897i	0.943083	−	0.332558i	$-0.107912\pi$
$599$	2690.71	+	4660.44i	0.183538	+	0.317897i	−0.759545	+	0.650455i	$0.774578\pi$
$600$		0			0
$601$	26223.5			1.77983			0.889915	−	0.456126i	$-0.150763\pi$
$601$	26223.5			1.77983			0.889915	+	0.456126i	$0.150763\pi$
$602$		0			0
$603$	2168.99			0.146481
$604$		0			0
$605$	151.403	+	262.237i	0.0101742	+	0.0176223i
$606$		0			0
$607$	−9511.10	+	16473.7i	−0.635986	+	1.10156i	0.350319	+	0.936631i	$0.386073\pi$
$607$	−9511.10	+	16473.7i	−0.635986	+	1.10156i	−0.986305	+	0.164930i	$0.947260\pi$
$608$		0			0
$609$	1670.73	−	5896.98i	0.111168	−	0.392377i
$610$		0			0
$611$	1956.29	−	3388.40i	0.129530	−	0.224353i
$612$		0			0
$613$	−133.927	−	231.969i	−0.00882426	−	0.0152841i	0.861580	−	0.507623i	$-0.169476\pi$
$613$	−133.927	−	231.969i	−0.00882426	−	0.0152841i	−0.870404	+	0.492338i	$0.836142\pi$
$614$		0			0
$615$	173.944			0.0114051
$616$		0			0
$617$	18568.5			1.21157			0.605785	−	0.795628i	$-0.292859\pi$
$617$	18568.5			1.21157			0.605785	+	0.795628i	$0.292859\pi$
$618$		0			0
$619$	11436.9	+	19809.3i	0.742630	+	1.28627i	0.951294	+	0.308285i	$0.0997551\pi$
$619$	11436.9	+	19809.3i	0.742630	+	1.28627i	−0.208664	+	0.977987i	$0.566912\pi$
$620$		0			0
$621$	2887.31	−	5000.97i	0.186576	−	0.323159i
$622$		0			0
$623$	−3650.76	+	922.529i	−0.234774	+	0.0593264i
$624$		0			0
$625$	−7801.77	+	13513.1i	−0.499313	+	0.864835i
$626$		0			0
$627$	−1201.01	−	2080.21i	−0.0764970	−	0.132497i
$628$		0			0
$629$	175.186			0.0111051
$630$		0			0
$631$	−16406.4			−1.03507			−0.517535	−	0.855662i	$-0.673150\pi$
$631$	−16406.4			−1.03507			−0.517535	+	0.855662i	$0.673150\pi$
$632$		0			0
$633$	4085.86	+	7076.92i	0.256554	+	0.444364i
$634$		0			0
$635$	−143.170	+	247.977i	−0.00894727	+	0.0154971i
$636$		0			0
$637$	−428.878	+	15006.7i	−0.0266762	+	0.933421i
$638$		0			0
$639$	−4403.23	+	7626.62i	−0.272597	+	0.472151i
$640$		0			0
$641$	13077.9	+	22651.7i	0.805847	+	1.39577i	0.915718	+	0.401822i	$0.131623\pi$
$641$	13077.9	+	22651.7i	0.805847	+	1.39577i	−0.109871	+	0.993946i	$0.535044\pi$
$642$		0			0
$643$	−4898.20			−0.300414			−0.150207	−	0.988655i	$-0.547994\pi$
$643$	−4898.20			−0.300414			−0.150207	+	0.988655i	$0.547994\pi$
$644$		0			0
$645$	263.461			0.0160834
$646$		0			0
$647$	−5964.62	−	10331.0i	−0.362432	−	0.627750i	0.625929	−	0.779880i	$-0.284720\pi$
$647$	−5964.62	−	10331.0i	−0.362432	−	0.627750i	−0.988360	+	0.152130i	$0.951387\pi$
$648$		0			0
$649$	−1619.78	+	2805.53i	−0.0979688	+	0.169687i
$650$		0			0
$651$	−4310.15	+	1089.15i	−0.259490	+	0.0655719i
$652$		0			0
$653$	−3624.93	+	6278.57i	−0.217235	+	0.376262i	−0.953962	−	0.299928i	$-0.903037\pi$
$653$	−3624.93	+	6278.57i	−0.217235	+	0.376262i	0.736726	+	0.676191i	$0.236371\pi$
$654$		0			0
$655$	60.4812	+	104.757i	0.00360793	+	0.00624912i
$656$		0			0
$657$	−5599.94			−0.332533
$658$		0			0
$659$	12078.7			0.713992			0.356996	−	0.934106i	$-0.383801\pi$
$659$	12078.7			0.713992			0.356996	+	0.934106i	$0.383801\pi$
$660$		0			0
$661$	908.319	+	1573.25i	0.0534486	+	0.0925756i	0.891512	−	0.452997i	$-0.149645\pi$
$661$	908.319	+	1573.25i	0.0534486	+	0.0925756i	−0.838063	+	0.545573i	$0.816312\pi$
$662$		0			0
$663$	−3992.73	+	6915.61i	−0.233884	+	0.405098i
$664$		0			0
$665$	−119.458	+	421.637i	−0.00696600	+	0.0245870i
$666$		0			0
$667$	−11796.6	+	20432.3i	−0.684807	+	1.18612i
$668$		0			0
$669$	7345.30	+	12722.4i	0.424493	+	0.735243i
$670$		0			0
$671$	−3889.60			−0.223780
$672$		0			0
$673$	−21386.6			−1.22495			−0.612477	−	0.790488i	$-0.709827\pi$
$673$	−21386.6			−1.22495			−0.612477	+	0.790488i	$0.709827\pi$
$674$		0			0
$675$	−1686.73	−	2921.50i	−0.0961810	−	0.166590i
$676$		0			0
$677$	−7014.73	+	12149.9i	−0.398225	+	0.689745i	−0.993507	−	0.113771i	$-0.963707\pi$
$677$	−7014.73	+	12149.9i	−0.398225	+	0.689745i	0.595282	+	0.803517i	$0.297040\pi$
$678$		0			0
$679$	15478.2	+	15926.9i	0.874815	+	0.900173i
$680$		0			0
$681$	−4847.32	+	8395.80i	−0.272760	+	0.472434i
$682$		0			0
$683$	6016.30	+	10420.5i	0.337053	+	0.583793i	0.983877	−	0.178846i	$-0.0572364\pi$
$683$	6016.30	+	10420.5i	0.337053	+	0.583793i	−0.646824	+	0.762639i	$0.723903\pi$
$684$		0			0
$685$	−176.964			−0.00987074
$686$		0			0
$687$	−17755.6			−0.986053
$688$		0			0
$689$	−249.763	−	432.603i	−0.0138102	−	0.0239200i
$690$		0			0
$691$	5437.55	−	9418.12i	0.299355	−	0.518498i	−0.676634	−	0.736320i	$-0.736562\pi$
$691$	5437.55	−	9418.12i	0.299355	−	0.518498i	0.975989	+	0.217822i	$0.0698952\pi$
$692$		0			0
$693$	940.590	+	967.855i	0.0515585	+	0.0530531i
$694$		0			0
$695$	370.405	−	641.561i	0.0202162	−	0.0350155i
$696$		0			0
$697$	−7367.93	−	12761.6i	−0.400402	−	0.693517i
$698$		0			0
$699$	1565.83			0.0847285
$700$		0			0
$701$	31811.2			1.71397			0.856984	−	0.515343i	$-0.172335\pi$
$701$	31811.2			1.71397			0.856984	+	0.515343i	$0.172335\pi$
$702$		0			0
$703$	142.428	+	246.692i	0.00764119	+	0.0132349i
$704$		0			0
$705$	−32.0854	+	55.5736i	−0.00171405	+	0.00296882i
$706$		0			0
$707$	−1855.74	+	6549.96i	−0.0987159	+	0.348425i
$708$		0			0
$709$	13463.8	−	23320.0i	0.713180	−	1.23526i	−0.250477	−	0.968123i	$-0.580587\pi$
$709$	13463.8	−	23320.0i	0.713180	−	1.23526i	0.963657	−	0.267142i	$-0.0860792\pi$
$710$		0			0
$711$	−2456.81	−	4255.31i	−0.129589	−	0.224454i
$712$		0			0
$713$	17112.9			0.898857
$714$		0			0
$715$	−84.8031			−0.00443560
$716$		0			0
$717$	9940.05	+	17216.7i	0.517738	+	0.896748i
$718$		0			0
$719$	−7274.71	+	12600.2i	−0.377331	+	0.653556i	−0.990673	−	0.136261i	$-0.956491\pi$
$719$	−7274.71	+	12600.2i	−0.377331	+	0.653556i	0.613342	+	0.789817i	$0.289825\pi$
$720$		0			0
$721$	−16972.4	+	4288.84i	−0.876677	+	0.221532i
$722$		0			0
$723$	3038.09	−	5262.12i	0.156276	−	0.270678i
$724$		0			0
$725$	6891.42	+	11936.3i	0.353022	+	0.611452i
$726$		0			0
$727$	−8370.11			−0.427001			−0.213501	−	0.976943i	$-0.568487\pi$
$727$	−8370.11			−0.427001			−0.213501	+	0.976943i	$0.568487\pi$
$728$		0			0
$729$	729.000			0.0370370
$730$		0			0
$731$	−11159.7	−	19329.2i	−0.564646	−	0.977996i
$732$		0			0
$733$	−3833.83	+	6640.39i	−0.193187	+	0.334609i	−0.946305	−	0.323277i	$-0.895216\pi$
$733$	−3833.83	+	6640.39i	−0.193187	+	0.334609i	0.753118	+	0.657886i	$0.228549\pi$
$734$		0			0
$735$	7.03409	−	246.128i	0.000353002	−	0.0123518i
$736$		0			0
$737$	975.676	−	1689.92i	0.0487645	−	0.0844627i
$738$		0			0
$739$	18962.3	+	32843.7i	0.943899	+	1.63488i	0.757942	+	0.652322i	$0.226205\pi$
$739$	18962.3	+	32843.7i	0.943899	+	1.63488i	0.185957	+	0.982558i	$0.440462\pi$
$740$		0			0
$741$	−12984.5			−0.643723
$742$		0			0
$743$	27008.1			1.33356			0.666778	−	0.745256i	$-0.267673\pi$
$743$	27008.1			1.33356			0.666778	+	0.745256i	$0.267673\pi$
$744$		0			0
$745$	357.637	+	619.445i	0.0175876	+	0.0304627i
$746$		0			0
$747$	−3806.98	+	6593.87i	−0.186466	+	0.322968i
$748$		0			0
$749$	12805.3	−	3235.85i	0.624695	−	0.157858i
$750$		0			0
$751$	−8846.54	+	15322.7i	−0.429847	+	0.744516i	−0.996859	−	0.0791929i	$-0.974766\pi$
$751$	−8846.54	+	15322.7i	−0.429847	+	0.744516i	0.567013	+	0.823709i	$0.308099\pi$
$752$		0			0
$753$	−5028.97	−	8710.42i	−0.243381	−	0.421548i
$754$		0			0
$755$	423.466			0.0204126
$756$		0			0
$757$	−39291.5			−1.88649			−0.943247	−	0.332093i	$-0.892245\pi$
$757$	−39291.5			−1.88649			−0.943247	+	0.332093i	$0.892245\pi$
$758$		0			0
$759$	−2597.59	−	4499.16i	−0.124225	−	0.215163i
$760$		0			0
$761$	−10667.5	+	18476.7i	−0.508143	+	0.880129i	0.491813	+	0.870701i	$0.336334\pi$
$761$	−10667.5	+	18476.7i	−0.508143	+	0.880129i	−0.999956	+	0.00942822i	$0.996999\pi$
$762$		0			0
$763$	4713.35	−	16636.1i	0.223637	−	0.789342i
$764$		0			0
$765$	65.4853	−	113.424i	0.00309494	−	0.00536059i
$766$		0			0
$767$	8755.99	+	15165.8i	0.412204	+	0.713958i
$768$		0			0
$769$	−17085.6			−0.801201			−0.400600	−	0.916253i	$-0.631198\pi$
$769$	−17085.6			−0.801201			−0.400600	+	0.916253i	$0.631198\pi$
$770$		0			0
$771$	−20480.2			−0.956649
$772$		0			0
$773$	−16368.0	−	28350.3i	−0.761601	−	1.31913i	−0.942025	−	0.335542i	$-0.891080\pi$
$773$	−16368.0	−	28350.3i	−0.761601	−	1.31913i	0.180424	−	0.983589i	$-0.442253\pi$
$774$		0			0
$775$	4998.57	−	8657.78i	0.231683	−	0.401286i
$776$		0			0
$777$	−111.545	−	114.778i	−0.00515012	−	0.00529941i
$778$		0			0
$779$	11980.4	−	20750.7i	0.551017	−	0.954390i
$780$		0			0
$781$	3961.40	+	6861.34i	0.181498	+	0.314364i
$782$		0			0
$783$	−2978.46			−0.135940
$784$		0			0
$785$	557.069			0.0253282
$786$		0			0
$787$	5237.31	+	9071.29i	0.237217	+	0.410872i	0.959915	−	0.280292i	$-0.0904313\pi$
$787$	5237.31	+	9071.29i	0.237217	+	0.410872i	−0.722697	+	0.691164i	$0.757098\pi$
$788$		0			0
$789$	2691.24	−	4661.37i	0.121433	−	0.210329i
$790$		0			0
$791$	−15377.7	−	15823.4i	−0.691234	−	0.711271i
$792$		0			0
$793$	−10513.0	+	18209.0i	−0.470778	+	0.815411i
$794$		0			0
$795$	4.09640	+	7.09518i	0.000182748	+	0.000316528i
$796$		0			0
$797$	−41837.3			−1.85941			−0.929706	−	0.368302i	$-0.879939\pi$
$797$	−41837.3			−1.85941			−0.929706	+	0.368302i	$0.879939\pi$
$798$		0			0
$799$	5436.29			0.240704
$800$		0			0
$801$	914.934	+	1584.71i	0.0403590	+	0.0699039i
$802$		0			0
$803$	−2519.01	+	4363.06i	−0.110702	+	0.191742i
$804$		0			0
$805$	−258.369	+	911.933i	−0.0113122	+	0.0399272i
$806$		0			0
$807$	−2199.99	+	3810.50i	−0.0959646	+	0.166216i
$808$		0			0
$809$	18864.9	+	32675.0i	0.819846	+	1.42001i	0.905795	+	0.423715i	$0.139274\pi$
$809$	18864.9	+	32675.0i	0.819846	+	1.42001i	−0.0859494	+	0.996300i	$0.527392\pi$
$810$		0			0
$811$	9550.14			0.413503			0.206751	−	0.978394i	$-0.433711\pi$
$811$	9550.14			0.413503			0.206751	+	0.978394i	$0.433711\pi$
$812$		0			0
$813$	−5269.54			−0.227320
$814$		0			0
$815$	−310.759	−	538.251i	−0.0133563	−	0.0231339i
$816$		0			0
$817$	18145.9	−	31429.6i	0.777043	−	1.34588i
$818$		0			0
$819$	7073.24	−	1787.37i	0.301781	−	0.0762587i
$820$		0			0
$821$	20639.9	−	35749.3i	0.877389	−	1.51968i	0.0231934	−	0.999731i	$-0.492617\pi$
$821$	20639.9	−	35749.3i	0.877389	−	1.51968i	0.854196	−	0.519952i	$-0.174050\pi$
$822$		0			0
$823$	5239.86	+	9075.71i	0.221932	+	0.384398i	0.955395	−	0.295332i	$-0.0954303\pi$
$823$	5239.86	+	9075.71i	0.221932	+	0.384398i	−0.733462	+	0.679730i	$0.762097\pi$
$824$		0			0
$825$	−3034.95			−0.128077
$826$		0			0
$827$	−2353.89			−0.0989757			−0.0494879	−	0.998775i	$-0.515759\pi$
$827$	−2353.89			−0.0989757			−0.0494879	+	0.998775i	$0.515759\pi$
$828$		0			0
$829$	6214.40	+	10763.7i	0.260356	+	0.450950i	0.966337	−	0.257281i	$-0.0828268\pi$
$829$	6214.40	+	10763.7i	0.260356	+	0.450950i	−0.705981	+	0.708231i	$0.749493\pi$
$830$		0			0
$831$	11562.0	−	20026.0i	0.482649	−	0.835972i
$832$		0			0
$833$	−18355.4	+	9909.41i	−0.763478	+	0.412174i
$834$		0			0
$835$	−392.028	+	679.013i	−0.0162475	+	0.0281416i
$836$		0			0
$837$	1080.19	+	1870.94i	0.0446078	+	0.0772630i
$838$		0			0
$839$	44513.6			1.83168			0.915840	−	0.401544i	$-0.131526\pi$
$839$	44513.6			1.83168			0.915840	+	0.401544i	$0.131526\pi$
$840$		0			0
$841$	−12220.0			−0.501046
$842$		0			0
$843$	10256.5	+	17764.7i	0.419041	+	0.725800i
$844$		0			0
$845$	33.6497	−	58.2829i	0.00136992	−	0.00237277i
$846$		0			0
$847$	−22722.0	+	5741.75i	−0.921769	+	0.232927i
$848$		0			0
$849$	−4872.90	+	8440.11i	−0.196982	+	0.341182i
$850$		0			0
$851$	308.048	+	533.555i	0.0124086	+	0.0214924i
$852$		0			0
$853$	−17576.4			−0.705516			−0.352758	−	0.935715i	$-0.614756\pi$
$853$	−17576.4			−0.705516			−0.352758	+	0.935715i	$0.614756\pi$
$854$		0			0
$855$	212.961			0.00851826
$856$		0			0
$857$	−390.599	−	676.537i	−0.0155690	−	0.0269662i	0.858136	−	0.513423i	$-0.171623\pi$
$857$	−390.599	−	676.537i	−0.0155690	−	0.0269662i	−0.873705	+	0.486456i	$0.838289\pi$
$858$		0			0
$859$	17633.2	−	30541.6i	0.700391	−	1.21311i	−0.267938	−	0.963436i	$-0.586342\pi$
$859$	17633.2	−	30541.6i	0.700391	−	1.21311i	0.968329	−	0.249677i	$-0.0803245\pi$
$860$		0			0
$861$	−3669.83	+	12952.9i	−0.145258	+	0.512700i
$862$		0			0
$863$	−1988.90	+	3444.87i	−0.0784506	+	0.135880i	−0.902582	−	0.430519i	$-0.858331\pi$
$863$	−1988.90	+	3444.87i	−0.0784506	+	0.135880i	0.824131	+	0.566399i	$0.191664\pi$
$864$		0			0
$865$	27.5225	+	47.6703i	0.00108184	+	0.00187380i
$866$		0			0
$867$	3643.69			0.142729
$868$		0			0
$869$	−4420.57			−0.172563
$870$		0			0
$871$	−5274.19	−	9135.16i	−0.205177	−	0.355377i
$872$		0			0
$873$	5396.28	−	9346.64i	0.209206	−	0.362355i
$874$		0			0
$875$	771.972	+	794.349i	0.0298256	+	0.0306902i
$876$		0			0
$877$	7810.15	−	13527.6i	0.300718	−	0.520859i	−0.675581	−	0.737286i	$-0.736107\pi$
$877$	7810.15	−	13527.6i	0.300718	−	0.520859i	0.976299	+	0.216427i	$0.0694403\pi$
$878$		0			0
$879$	−14511.3	−	25134.3i	−0.556830	−	0.964458i
$880$		0			0
$881$	30711.6			1.17446			0.587231	−	0.809419i	$-0.300218\pi$
$881$	30711.6			1.17446			0.587231	+	0.809419i	$0.300218\pi$
$882$		0			0
$883$	−15042.1			−0.573279			−0.286640	−	0.958038i	$-0.592538\pi$
$883$	−15042.1			−0.573279			−0.286640	+	0.958038i	$0.592538\pi$
$884$		0			0
$885$	−143.608	−	248.737i	−0.00545462	−	0.00944767i
$886$		0			0
$887$	8136.35	−	14092.6i	0.307995	−	0.533463i	−0.669928	−	0.742426i	$-0.733675\pi$
$887$	8136.35	−	14092.6i	0.307995	−	0.533463i	0.977924	+	0.208962i	$0.0670086\pi$
$888$		0			0
$889$	−15445.3	−	15893.1i	−0.582699	−	0.599590i
$890$		0			0
$891$	327.925	−	567.983i	0.0123299	−	0.0213559i
$892$		0			0
$893$	4419.76	+	7655.25i	0.165623	+	0.286868i
$894$		0			0
$895$	892.682			0.0333397
$896$		0			0
$897$	−28083.5			−1.04535
$898$		0			0
$899$	−4413.29	−	7644.04i	−0.163728	−	0.283585i
$900$		0			0
$901$	347.031	−	601.075i	0.0128316	−	0.0222250i
$902$		0			0
$903$	−5558.44	+	19618.9i	−0.204843	+	0.723009i
$904$		0			0
$905$	197.402	−	341.910i	0.00725068	−	0.0125585i
$906$		0			0
$907$	−6363.48	−	11021.9i	−0.232961	−	0.403501i	0.725717	−	0.687994i	$-0.241508\pi$
$907$	−6363.48	−	11021.9i	−0.232961	−	0.403501i	−0.958678	+	0.284492i	$0.908175\pi$
$908$		0			0
$909$	3308.27			0.120713
$910$		0			0
$911$	23984.8			0.872283			0.436142	−	0.899878i	$-0.356345\pi$
$911$	23984.8			0.872283			0.436142	+	0.899878i	$0.356345\pi$
$912$		0			0
$913$	3424.97	+	5932.23i	0.124151	+	0.215036i
$914$		0			0
$915$	172.425	−	298.649i	0.00622972	−	0.0107902i
$916$		0			0
$917$	−9076.82	+	2293.67i	−0.326874	+	0.0825994i
$918$		0			0
$919$	−4806.83	+	8325.67i	−0.172538	+	0.298845i	−0.939307	−	0.343079i	$-0.888530\pi$
$919$	−4806.83	+	8325.67i	−0.172538	+	0.298845i	0.766768	+	0.641924i	$0.221863\pi$
$920$		0			0
$921$	−7439.55	−	12885.7i	−0.266169	−	0.461018i
$922$		0			0
$923$	42828.1			1.52731
$924$		0			0
$925$	359.915			0.0127934
$926$		0			0
$927$	4253.52	+	7367.32i	0.150706	+	0.261030i
$928$		0			0
$929$	9348.98	−	16192.9i	0.330172	−	0.571875i	−0.652373	−	0.757898i	$-0.726227\pi$
$929$	9348.98	−	16192.9i	0.330172	−	0.571875i	0.982545	+	0.186023i	$0.0595598\pi$
$930$		0			0
$931$	−28877.3	−	17791.2i	−1.01656	−	0.626296i
$932$		0			0
$933$	10136.6	−	17557.1i	0.355689	−	0.616071i
$934$		0			0
$935$	−58.9143	−	102.043i	−0.00206065	−	0.00356915i
$936$		0			0
$937$	6833.17			0.238239			0.119120	−	0.992880i	$-0.461993\pi$
$937$	6833.17			0.238239			0.119120	+	0.992880i	$0.461993\pi$
$938$		0			0
$939$	−10146.1			−0.352613
$940$		0			0
$941$	3444.32	+	5965.74i	0.119322	+	0.206671i	0.919499	−	0.393092i	$-0.128595\pi$
$941$	3444.32	+	5965.74i	0.119322	+	0.206671i	−0.800177	+	0.599763i	$0.795261\pi$
$942$		0			0
$943$	25911.7	−	44880.4i	0.894805	−	1.54985i
$944$		0			0
$945$	−116.009	+	29.3150i	−0.00399341	+	0.00100912i
$946$		0			0
$947$	−10585.9	+	18335.2i	−0.363246	+	0.629161i	−0.988493	−	0.151266i	$-0.951665\pi$
$947$	−10585.9	+	18335.2i	−0.363246	+	0.629161i	0.625247	+	0.780427i	$0.284998\pi$
$948$		0			0
$949$	13617.0	+	23585.3i	0.465780	+	0.806755i
$950$		0			0
$951$	−2601.03			−0.0886899
$952$		0			0
$953$	50173.4			1.70543			0.852715	−	0.522376i	$-0.174954\pi$
$953$	50173.4			1.70543			0.852715	+	0.522376i	$0.174954\pi$
$954$		0			0
$955$	216.515	+	375.015i	0.00733640	+	0.0127070i
$956$		0			0
$957$	−1339.79	+	2320.59i	−0.0452554	+	0.0783846i
$958$		0			0
$959$	3733.55	−	13177.8i	0.125717	−	0.443727i
$960$		0			0
$961$	11694.4	−	20255.3i	0.392548	−	0.679913i
$962$		0			0
$963$	−3209.21	−	5558.51i	−0.107389	−	0.186002i
$964$		0			0
$965$	1045.03			0.0348608
$966$		0			0
$967$	−30613.9			−1.01807			−0.509036	−	0.860745i	$-0.669998\pi$
$967$	−30613.9			−1.01807			−0.509036	+	0.860745i	$0.669998\pi$
$968$		0			0
$969$	−9020.60	−	15624.1i	−0.299054	−	0.517977i
$970$		0			0
$971$	−3028.39	+	5245.33i	−0.100088	+	0.173358i	−0.911721	−	0.410810i	$-0.865246\pi$
$971$	−3028.39	+	5245.33i	−0.100088	+	0.173358i	0.811633	+	0.584168i	$0.198579\pi$
$972$		0			0
$973$	39959.8	+	41118.1i	1.31660	+	1.35476i
$974$		0			0
$975$	−8202.99	+	14208.0i	−0.269442	+	0.466687i
$976$		0			0
$977$	−12960.0	−	22447.5i	−0.424389	−	0.735064i	0.571974	−	0.820272i	$-0.306178\pi$
$977$	−12960.0	−	22447.5i	−0.424389	−	0.735064i	−0.996363	+	0.0852079i	$0.972845\pi$
$978$		0			0
$979$	1646.25			0.0537431
$980$		0			0
$981$	−8402.60			−0.273470
$982$		0			0
$983$	−1677.22	−	2905.03i	−0.0544201	−	0.0942584i	0.837532	−	0.546388i	$-0.183998\pi$
$983$	−1677.22	−	2905.03i	−0.0544201	−	0.0942584i	−0.891952	+	0.452130i	$0.850664\pi$
$984$		0			0
$985$	−47.6528	+	82.5370i	−0.00154147	+	0.00266990i
$986$		0			0
$987$	−3461.41	−	3561.75i	−0.111629	−	0.114865i
$988$		0			0
$989$	39246.7	−	67977.3i	1.26185	−	2.18559i
$990$		0			0
$991$	−4312.76	−	7469.93i	−0.138244	−	0.239445i	0.788588	−	0.614922i	$-0.210812\pi$
$991$	−4312.76	−	7469.93i	−0.138244	−	0.239445i	−0.926832	+	0.375477i	$0.877479\pi$
$992$		0			0
$993$	−4137.63			−0.132229
$994$		0			0
$995$	−1039.32			−0.0331141
$996$		0			0
$997$	−31100.6	−	53867.7i	−0.987928	−	1.71114i	−0.628123	−	0.778114i	$-0.716176\pi$
$997$	−31100.6	−	53867.7i	−0.987928	−	1.71114i	−0.359805	−	0.933027i	$-0.617157\pi$
$998$		0			0
$999$	−38.8887	+	67.3571i	−0.00123161	+	0.00213322i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	336.4.q.l.289.2		6
4.3	odd	2		168.4.q.e.121.2	yes	6
7.2	even	3		2352.4.a.ch.1.2		3
7.4	even	3	inner	336.4.q.l.193.2		6
7.5	odd	6		2352.4.a.cj.1.2		3
12.11	even	2		504.4.s.g.289.2		6
28.11	odd	6		168.4.q.e.25.2	✓	6
28.19	even	6		1176.4.a.x.1.2		3
28.23	odd	6		1176.4.a.y.1.2		3
84.11	even	6		504.4.s.g.361.2		6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
168.4.q.e.25.2	✓	6	28.11	odd	6
168.4.q.e.121.2	yes	6	4.3	odd	2
336.4.q.l.193.2		6	7.4	even	3	inner
336.4.q.l.289.2		6	1.1	even	1	trivial
504.4.s.g.289.2		6	12.11	even	2
504.4.s.g.361.2		6	84.11	even	6
1176.4.a.x.1.2		3	28.19	even	6
1176.4.a.y.1.2		3	28.23	odd	6
2352.4.a.ch.1.2		3	7.2	even	3
2352.4.a.cj.1.2		3	7.5	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

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

Level:	\( N \)	\(=\)	\( 336 = 2^{4} \cdot 3 \cdot 7 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	336.q (of order \(3\), degree \(2\), not minimal)

\(f(q)\)	\(=\)	\(q+(1.50000 + 2.59808i) q^{3} +(-0.119644 + 0.207230i) q^{5} +(-12.9074 - 13.2815i) q^{7} +(-4.50000 + 7.79423i) q^{9} +O(q^{10})\)	\(q+(1.50000 + 2.59808i) q^{3} +(-0.119644 + 0.207230i) q^{5} +(-12.9074 - 13.2815i) q^{7} +(-4.50000 + 7.79423i) q^{9} +(4.04846 + 7.01213i) q^{11} +43.7693 q^{13} -0.717867 q^{15} +(30.4074 + 52.6671i) q^{17} +(-49.4430 + 85.6378i) q^{19} +(15.1454 - 53.4567i) q^{21} +(-106.937 + 185.221i) q^{23} +(62.4714 + 108.204i) q^{25} -27.0000 q^{27} +110.313 q^{29} +(-40.0069 - 69.2940i) q^{31} +(-12.1454 + 21.0364i) q^{33} +(4.29663 - 1.08574i) q^{35} +(1.44032 - 2.49471i) q^{37} +(65.6540 + 113.716i) q^{39} -242.307 q^{41} -367.006 q^{43} +(-1.07680 - 1.86507i) q^{45} +(44.6955 - 77.4149i) q^{47} +(-9.79860 + 342.860i) q^{49} +(-91.2222 + 158.001i) q^{51} +(-5.70636 - 9.88370i) q^{53} -1.93750 q^{55} -296.658 q^{57} +(200.049 + 346.494i) q^{59} +(-240.191 + 416.022i) q^{61} +(161.603 - 40.8362i) q^{63} +(-5.23675 + 9.07033i) q^{65} +(-120.500 - 208.712i) q^{67} -641.624 q^{69} +978.496 q^{71} +(311.108 + 538.854i) q^{73} +(-187.414 + 324.611i) q^{75} +(40.8769 - 144.278i) q^{77} +(-272.978 + 472.813i) q^{79} +(-40.5000 - 70.1481i) q^{81} +845.995 q^{83} -14.5523 q^{85} +(165.470 + 286.602i) q^{87} +(101.659 - 176.079i) q^{89} +(-564.948 - 581.324i) q^{91} +(120.021 - 207.882i) q^{93} +(-11.8312 - 20.4922i) q^{95} -1199.17 q^{97} -72.8722 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 9 q^{3} + 11 q^{5} + q^{7} - 27 q^{9}+O(q^{10}) \) 6 * q + 9 * q^3 + 11 * q^5 + q^7 - 27 * q^9	\( 6 q + 9 q^{3} + 11 q^{5} + q^{7} - 27 q^{9} - 19 q^{11} - 44 q^{13} + 66 q^{15} + 104 q^{17} + 202 q^{19} - 39 q^{21} - 280 q^{23} - 186 q^{25} - 162 q^{27} - 146 q^{29} - 131 q^{31} + 57 q^{33} + 252 q^{35} + 326 q^{37} - 66 q^{39} - 1032 q^{41} - 72 q^{43} + 99 q^{45} - 126 q^{47} + 33 q^{49} - 312 q^{51} + 385 q^{53} + 1222 q^{55} + 1212 q^{57} + 285 q^{59} + 34 q^{61} - 126 q^{63} + 920 q^{65} - 100 q^{67} - 1680 q^{69} - 68 q^{71} + 108 q^{73} + 558 q^{75} + 1571 q^{77} - 2463 q^{79} - 243 q^{81} + 230 q^{83} - 1000 q^{85} - 219 q^{87} + 110 q^{89} - 110 q^{91} + 393 q^{93} - 2064 q^{95} - 5882 q^{97} + 342 q^{99}+O(q^{100}) \) 6 * q + 9 * q^3 + 11 * q^5 + q^7 - 27 * q^9 - 19 * q^11 - 44 * q^13 + 66 * q^15 + 104 * q^17 + 202 * q^19 - 39 * q^21 - 280 * q^23 - 186 * q^25 - 162 * q^27 - 146 * q^29 - 131 * q^31 + 57 * q^33 + 252 * q^35 + 326 * q^37 - 66 * q^39 - 1032 * q^41 - 72 * q^43 + 99 * q^45 - 126 * q^47 + 33 * q^49 - 312 * q^51 + 385 * q^53 + 1222 * q^55 + 1212 * q^57 + 285 * q^59 + 34 * q^61 - 126 * q^63 + 920 * q^65 - 100 * q^67 - 1680 * q^69 - 68 * q^71 + 108 * q^73 + 558 * q^75 + 1571 * q^77 - 2463 * q^79 - 243 * q^81 + 230 * q^83 - 1000 * q^85 - 219 * q^87 + 110 * q^89 - 110 * q^91 + 393 * q^93 - 2064 * q^95 - 5882 * q^97 + 342 * q^99

Introduction

L-functions

Modular forms

Varieties

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Representations

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Database

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