LMFDB - Embedded newform 342.4.g.h.163.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [342,4,Mod(163,342)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(342, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([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("342.163");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 342 = 2 \cdot 3^{2} \cdot 19 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	342.g (of order $3$, degree $2$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$20.1786532220$
Analytic rank:	$0$
Dimension:	$6$
Relative dimension:	$3$ over $\Q(\zeta_{3})$
Coefficient field:	6.0.627014547.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} + 26x^{4} + 169x^{2} + 147 $ x^6 + 26x^4 + 169x^2 + 147
Coefficient ring:	$\Z[a_1, \ldots, a_{13}]$
Coefficient ring index:	$ 2^{6}\cdot 3^{3} $
Twist minimal:	no (minimal twist has level 114)
Sato-Tate group:	$\mathrm{SU}(2)[C_{3}]$

Embedding invariants

Embedding label			163.2
Root			$4.00355i$ of defining polynomial
Character	$\chi$	$=$	342.163
Dual form			342.4.g.h.235.2

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.09405 - 3.62701i) q^{5} +3.18810 q^{7} -8.00000 q^{8} +O(q^{10})$	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.09405 - 3.62701i) q^{5} +3.18810 q^{7} -8.00000 q^{8} +(-4.18810 - 7.25401i) q^{10} -69.4003 q^{11} +(4.06431 + 7.03960i) q^{13} +(3.18810 - 5.52196i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-53.0418 + 91.8711i) q^{17} +(42.6656 - 70.9834i) q^{19} -16.7524 q^{20} +(-69.4003 + 120.205i) q^{22} +(-88.2468 - 152.848i) q^{23} +(53.7299 + 93.0629i) q^{25} +16.2573 q^{26} +(-6.37621 - 11.0439i) q^{28} +(-33.1109 - 57.3498i) q^{29} -140.915 q^{31} +(16.0000 + 27.7128i) q^{32} +(106.084 + 183.742i) q^{34} +(6.67606 - 11.5633i) q^{35} -156.003 q^{37} +(-80.2814 - 144.882i) q^{38} +(-16.7524 + 29.0160i) q^{40} +(-207.281 + 359.022i) q^{41} +(-57.9252 + 100.329i) q^{43} +(138.801 + 240.410i) q^{44} -352.987 q^{46} +(310.141 + 537.181i) q^{47} -332.836 q^{49} +214.920 q^{50} +(16.2573 - 28.1584i) q^{52} +(-185.993 - 322.149i) q^{53} +(-145.328 + 251.715i) q^{55} -25.5048 q^{56} -132.444 q^{58} +(45.8465 - 79.4084i) q^{59} +(-109.310 - 189.331i) q^{61} +(-140.915 + 244.072i) q^{62} +64.0000 q^{64} +34.0436 q^{65} +(72.6712 + 125.870i) q^{67} +424.334 q^{68} +(-13.3521 - 23.1265i) q^{70} +(443.915 - 768.883i) q^{71} +(-99.5081 + 172.353i) q^{73} +(-156.003 + 270.205i) q^{74} +(-331.225 - 5.83100i) q^{76} -221.255 q^{77} +(194.779 - 337.367i) q^{79} +(33.5048 + 58.0321i) q^{80} +(414.563 + 718.044i) q^{82} -380.039 q^{83} +(222.145 + 384.766i) q^{85} +(115.850 + 200.659i) q^{86} +555.202 q^{88} +(-212.899 - 368.753i) q^{89} +(12.9575 + 22.4430i) q^{91} +(-352.987 + 611.392i) q^{92} +1240.57 q^{94} +(-168.113 - 303.391i) q^{95} +(-209.923 + 363.597i) q^{97} +(-332.836 + 576.489i) q^{98} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8}+O(q^{10}) $ 6 * q + 6 * q^2 - 12 * q^4 + 10 * q^5 + 14 * q^7 - 48 * q^8	$ 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8} - 20 q^{10} + 88 q^{11} + 9 q^{13} + 14 q^{14} - 48 q^{16} - 84 q^{17} + 32 q^{19} - 80 q^{20} + 88 q^{22} - 2 q^{23} + 83 q^{25} + 36 q^{26} - 28 q^{28} + 92 q^{29} - 218 q^{31} + 96 q^{32} + 168 q^{34} + 282 q^{35} + 490 q^{37} + 74 q^{38} - 80 q^{40} - 688 q^{41} + 103 q^{43} - 176 q^{44} - 8 q^{46} + 322 q^{47} - 1508 q^{49} + 332 q^{50} + 36 q^{52} - 1322 q^{53} + 248 q^{55} - 112 q^{56} + 368 q^{58} + 252 q^{59} + 435 q^{61} - 218 q^{62} + 384 q^{64} + 3164 q^{65} + 719 q^{67} + 672 q^{68} - 564 q^{70} - 62 q^{71} + 581 q^{73} + 490 q^{74} + 20 q^{76} + 408 q^{77} + 489 q^{79} + 160 q^{80} + 1376 q^{82} - 4992 q^{83} - 1632 q^{85} - 206 q^{86} - 704 q^{88} + 1584 q^{89} + 1573 q^{91} - 8 q^{92} + 1288 q^{94} - 2362 q^{95} - 974 q^{97} - 1508 q^{98}+O(q^{100}) $ 6 * q + 6 * q^2 - 12 * q^4 + 10 * q^5 + 14 * q^7 - 48 * q^8 - 20 * q^10 + 88 * q^11 + 9 * q^13 + 14 * q^14 - 48 * q^16 - 84 * q^17 + 32 * q^19 - 80 * q^20 + 88 * q^22 - 2 * q^23 + 83 * q^25 + 36 * q^26 - 28 * q^28 + 92 * q^29 - 218 * q^31 + 96 * q^32 + 168 * q^34 + 282 * q^35 + 490 * q^37 + 74 * q^38 - 80 * q^40 - 688 * q^41 + 103 * q^43 - 176 * q^44 - 8 * q^46 + 322 * q^47 - 1508 * q^49 + 332 * q^50 + 36 * q^52 - 1322 * q^53 + 248 * q^55 - 112 * q^56 + 368 * q^58 + 252 * q^59 + 435 * q^61 - 218 * q^62 + 384 * q^64 + 3164 * q^65 + 719 * q^67 + 672 * q^68 - 564 * q^70 - 62 * q^71 + 581 * q^73 + 490 * q^74 + 20 * q^76 + 408 * q^77 + 489 * q^79 + 160 * q^80 + 1376 * q^82 - 4992 * q^83 - 1632 * q^85 - 206 * q^86 - 704 * q^88 + 1584 * q^89 + 1573 * q^91 - 8 * q^92 + 1288 * q^94 - 2362 * q^95 - 974 * q^97 - 1508 * q^98

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/342\mathbb{Z}\right)^\times$.

$n$	$191$	$325$
$\chi(n)$	$1$	$e\left(\frac{2}{3}\right)$

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 $

$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$2$	1.00000	−	1.73205i	0.353553	−	0.612372i
$3$		0			0
$3$		0			0
$4$	−2.00000	−	3.46410i	−0.250000	−	0.433013i
$5$	2.09405	−	3.62701i	0.187298	−	0.324409i	−0.757051	−	0.653356i	$-0.773360\pi$
$5$	2.09405	−	3.62701i	0.187298	−	0.324409i	0.944348	+	0.328947i	$0.106694\pi$
$6$		0			0
$7$	3.18810			0.172141			0.0860707	−	0.996289i	$-0.472569\pi$
$7$	3.18810			0.172141			0.0860707	+	0.996289i	$0.472569\pi$
$8$	−8.00000			−0.353553
$9$		0			0
$10$	−4.18810	−	7.25401i	−0.132440	−	0.229392i
$11$	−69.4003			−1.90227			−0.951135	−	0.308774i	$-0.900081\pi$
$11$	−69.4003			−1.90227			−0.951135	+	0.308774i	$0.900081\pi$
$12$		0			0
$13$	4.06431	+	7.03960i	0.0867106	+	0.150187i	0.906119	−	0.423023i	$-0.139031\pi$
$13$	4.06431	+	7.03960i	0.0867106	+	0.150187i	−0.819408	+	0.573210i	$0.805698\pi$
$14$	3.18810	−	5.52196i	0.0608612	−	0.105415i
$15$		0			0
$16$	−8.00000	+	13.8564i	−0.125000	+	0.216506i
$17$	−53.0418	+	91.8711i	−0.756737	+	1.31071i	0.187770	+	0.982213i	$0.439874\pi$
$17$	−53.0418	+	91.8711i	−0.756737	+	1.31071i	−0.944506	+	0.328493i	$0.893459\pi$
$18$		0			0
$19$	42.6656	−	70.9834i	0.515166	−	0.857090i
$19$	42.6656	−	70.9834i	0.515166	−	0.857090i
$20$	−16.7524			−0.187298
$21$		0			0
$22$	−69.4003	+	120.205i	−0.672554	+	1.16490i
$23$	−88.2468	−	152.848i	−0.800031	−	1.38570i	−0.919595	−	0.392869i	$-0.871483\pi$
$23$	−88.2468	−	152.848i	−0.800031	−	1.38570i	0.119563	−	0.992827i	$-0.461851\pi$
$24$		0			0
$25$	53.7299	+	93.0629i	0.429839	+	0.744503i
$26$	16.2573			0.122627
$27$		0			0
$28$	−6.37621	−	11.0439i	−0.0430354	−	0.0745394i
$29$	−33.1109	−	57.3498i	−0.212019	−	0.367227i	0.740327	−	0.672247i	$-0.234670\pi$
$29$	−33.1109	−	57.3498i	−0.212019	−	0.367227i	−0.952346	+	0.305019i	$0.901337\pi$
$30$		0			0
$31$	−140.915			−0.816421			−0.408210	−	0.912888i	$-0.633847\pi$
$31$	−140.915			−0.816421			−0.408210	+	0.912888i	$0.633847\pi$
$32$	16.0000	+	27.7128i	0.0883883	+	0.153093i
$33$		0			0
$34$	106.084	+	183.742i	0.535094	+	0.926809i
$35$	6.67606	−	11.5633i	0.0322417	−	0.0558443i
$36$		0			0
$37$	−156.003			−0.693156			−0.346578	−	0.938021i	$-0.612656\pi$
$37$	−156.003			−0.693156			−0.346578	+	0.938021i	$0.612656\pi$
$38$	−80.2814	−	144.882i	−0.342720	−	0.618501i
$39$		0			0
$40$	−16.7524	+	29.0160i	−0.0662198	+	0.114696i
$41$	−207.281	+	359.022i	−0.789559	+	1.36756i	0.136679	+	0.990615i	$0.456357\pi$
$41$	−207.281	+	359.022i	−0.789559	+	1.36756i	−0.926238	+	0.376940i	$0.876976\pi$
$42$		0			0
$43$	−57.9252	+	100.329i	−0.205430	+	0.355816i	−0.950270	−	0.311428i	$-0.899193\pi$
$43$	−57.9252	+	100.329i	−0.205430	+	0.355816i	0.744839	+	0.667244i	$0.232526\pi$
$44$	138.801	+	240.410i	0.475568	+	0.823707i
$45$		0			0
$46$	−352.987			−1.13142
$47$	310.141	+	537.181i	0.962527	+	1.66715i	0.716117	+	0.697980i	$0.245918\pi$
$47$	310.141	+	537.181i	0.962527	+	1.66715i	0.246410	+	0.969166i	$0.420749\pi$
$48$		0			0
$49$	−332.836			−0.970367
$50$	214.920			0.607884
$51$		0			0
$52$	16.2573	−	28.1584i	0.0433553	−	0.0750936i
$53$	−185.993	−	322.149i	−0.482039	−	0.834916i	0.517748	−	0.855533i	$-0.326770\pi$
$53$	−185.993	−	322.149i	−0.482039	−	0.834916i	−0.999787	+	0.0206167i	$0.993437\pi$
$54$		0			0
$55$	−145.328	+	251.715i	−0.356291	+	0.617114i
$56$	−25.5048			−0.0608612
$57$		0			0
$58$	−132.444			−0.299840
$59$	45.8465	−	79.4084i	0.101164	−	0.175222i	−0.811000	−	0.585046i	$-0.801077\pi$
$59$	45.8465	−	79.4084i	0.101164	−	0.175222i	0.912165	+	0.409824i	$0.134410\pi$
$60$		0			0
$61$	−109.310	−	189.331i	−0.229438	−	0.397399i	0.728203	−	0.685361i	$-0.240356\pi$
$61$	−109.310	−	189.331i	−0.229438	−	0.397399i	−0.957642	+	0.287962i	$0.907022\pi$
$62$	−140.915	+	244.072i	−0.288648	+	0.499954i
$63$		0			0
$64$	64.0000			0.125000
$65$	34.0436			0.0649628
$66$		0			0
$67$	72.6712	+	125.870i	0.132510	+	0.229515i	0.924644	−	0.380833i	$-0.124363\pi$
$67$	72.6712	+	125.870i	0.132510	+	0.229515i	−0.792133	+	0.610348i	$0.791030\pi$
$68$	424.334			0.756737
$69$		0			0
$70$	−13.3521	−	23.1265i	−0.0227983	−	0.0394879i
$71$	443.915	−	768.883i	0.742014	−	1.28521i	−0.209563	−	0.977795i	$-0.567204\pi$
$71$	443.915	−	768.883i	0.742014	−	1.28521i	0.951577	−	0.307410i	$-0.0994625\pi$
$72$		0			0
$73$	−99.5081	+	172.353i	−0.159542	+	0.276334i	−0.934703	−	0.355429i	$-0.884335\pi$
$73$	−99.5081	+	172.353i	−0.159542	+	0.276334i	0.775162	+	0.631763i	$0.217668\pi$
$74$	−156.003	+	270.205i	−0.245067	+	0.424469i
$75$		0			0
$76$	−331.225	−	5.83100i	−0.499923	−	0.00880082i
$77$	−221.255			−0.327460
$78$		0			0
$79$	194.779	−	337.367i	0.277397	−	0.480465i	−0.693340	−	0.720610i	$-0.743862\pi$
$79$	194.779	−	337.367i	0.277397	−	0.480465i	0.970737	+	0.240145i	$0.0771951\pi$
$80$	33.5048	+	58.0321i	0.0468244	+	0.0811023i
$81$		0			0
$82$	414.563	+	718.044i	0.558302	+	0.967008i
$83$	−380.039			−0.502586			−0.251293	−	0.967911i	$-0.580856\pi$
$83$	−380.039			−0.502586			−0.251293	+	0.967911i	$0.580856\pi$
$84$		0			0
$85$	222.145	+	384.766i	0.283470	+	0.490985i
$86$	115.850	+	200.659i	0.145261	+	0.251600i
$87$		0			0
$88$	555.202			0.672554
$89$	−212.899	−	368.753i	−0.253565	−	0.439188i	0.710940	−	0.703253i	$-0.248270\pi$
$89$	−212.899	−	368.753i	−0.253565	−	0.439188i	−0.964505	+	0.264065i	$0.914937\pi$
$90$		0			0
$91$	12.9575	+	22.4430i	0.0149265	+	0.0258534i
$92$	−352.987	+	611.392i	−0.400016	+	0.692848i
$93$		0			0
$94$	1240.57			1.36122
$95$	−168.113	−	303.391i	−0.181559	−	0.327656i
$96$		0			0
$97$	−209.923	+	363.597i	−0.219736	+	0.380595i	−0.954727	−	0.297482i	$-0.903853\pi$
$97$	−209.923	+	363.597i	−0.219736	+	0.380595i	0.734991	+	0.678077i	$0.237186\pi$
$98$	−332.836	+	576.489i	−0.343077	+	0.594226i
$99$		0			0
$100$	214.920	−	372.252i	0.214920	−	0.372252i
$101$	−620.855	−	1075.35i	−0.611657	−	1.05942i	−0.990961	−	0.134150i	$-0.957170\pi$
$101$	−620.855	−	1075.35i	−0.611657	−	1.05942i	0.379304	−	0.925272i	$-0.376164\pi$
$102$		0			0
$103$	−593.606			−0.567862			−0.283931	−	0.958845i	$-0.591639\pi$
$103$	−593.606			−0.567862			−0.283931	+	0.958845i	$0.591639\pi$
$104$	−32.5145	−	56.3168i	−0.0306568	−	0.0530992i
$105$		0			0
$106$	−743.971			−0.681706
$107$	1778.56			1.60691			0.803457	−	0.595363i	$-0.202992\pi$
$107$	1778.56			1.60691			0.803457	+	0.595363i	$0.202992\pi$
$108$		0			0
$109$	534.995	−	926.639i	0.470121	−	0.814274i	−0.529295	−	0.848438i	$-0.677543\pi$
$109$	534.995	−	926.639i	0.470121	−	0.814274i	0.999416	+	0.0341638i	$0.0108768\pi$
$110$	290.656	+	503.431i	0.251936	+	0.436366i
$111$		0			0
$112$	−25.5048	+	44.1757i	−0.0215177	+	0.0372697i
$113$	−583.197			−0.485510			−0.242755	−	0.970088i	$-0.578051\pi$
$113$	−583.197			−0.485510			−0.242755	+	0.970088i	$0.578051\pi$
$114$		0			0
$115$	−739.173			−0.599376
$116$	−132.444	+	229.399i	−0.106009	+	0.183614i
$117$		0			0
$118$	−91.6929	−	158.817i	−0.0715341	−	0.123901i
$119$	−169.103	+	292.895i	−0.130266	+	0.225627i
$120$		0			0
$121$	3485.40			2.61863
$122$	−437.241			−0.324475
$123$		0			0
$124$	281.830	+	488.143i	0.204105	+	0.353521i
$125$	973.566			0.696627
$126$		0			0
$127$	−829.677	−	1437.04i	−0.579700	−	1.00407i	−0.995513	−	0.0946199i	$-0.969836\pi$
$127$	−829.677	−	1437.04i	−0.579700	−	1.00407i	0.415814	−	0.909450i	$-0.363497\pi$
$128$	64.0000	−	110.851i	0.0441942	−	0.0765466i
$129$		0			0
$130$	34.0436	−	58.9652i	0.0229678	−	0.0397814i
$131$	298.773	−	517.490i	0.199267	−	0.345140i	−0.749024	−	0.662543i	$-0.769477\pi$
$131$	298.773	−	517.490i	0.199267	−	0.345140i	0.948291	+	0.317403i	$0.102811\pi$
$132$		0			0
$133$	136.022	−	226.303i	0.0886814	−	0.147541i
$134$	290.685			0.187398
$135$		0			0
$136$	424.334	−	734.969i	0.267547	−	0.463405i
$137$	−888.654	−	1539.19i	−0.554182	−	0.959871i	−0.997967	−	0.0637373i	$-0.979698\pi$
$137$	−888.654	−	1539.19i	−0.554182	−	0.959871i	0.443785	−	0.896133i	$-0.353635\pi$
$138$		0			0
$139$	−81.7836	−	141.653i	−0.0499050	−	0.0864379i	0.839994	−	0.542596i	$-0.182559\pi$
$139$	−81.7836	−	141.653i	−0.0499050	−	0.0864379i	−0.889899	+	0.456158i	$0.849225\pi$
$140$	−53.4085			−0.0322417
$141$		0			0
$142$	−887.829	−	1537.77i	−0.524683	−	0.908778i
$143$	−282.065	−	488.550i	−0.164947	−	0.285697i
$144$		0			0
$145$	−277.344			−0.158843
$146$	199.016	+	344.706i	0.112813	+	0.195398i
$147$		0			0
$148$	312.006	+	540.411i	0.173289	+	0.300145i
$149$	−559.899	+	969.774i	−0.307844	+	0.533201i	−0.977890	−	0.209118i	$-0.932941\pi$
$149$	−559.899	+	969.774i	−0.307844	+	0.533201i	0.670047	+	0.742319i	$0.266274\pi$
$150$		0			0
$151$	−2807.15			−1.51286			−0.756432	−	0.654073i	$-0.773059\pi$
$151$	−2807.15			−1.51286			−0.756432	+	0.654073i	$0.773059\pi$
$152$	−341.325	+	567.868i	−0.182139	+	0.303027i
$153$		0			0
$154$	−221.255	+	383.226i	−0.115774	+	0.200527i
$155$	−295.083	+	511.099i	−0.152914	+	0.264854i
$156$		0			0
$157$	−501.971	+	869.439i	−0.255170	+	0.441967i	−0.964942	−	0.262465i	$-0.915465\pi$
$157$	−501.971	+	869.439i	−0.255170	+	0.441967i	0.709772	+	0.704432i	$0.248798\pi$
$158$	−389.558	−	674.734i	−0.196149	−	0.339740i
$159$		0			0
$160$	134.019			0.0662198
$161$	−281.340	−	487.295i	−0.137719	−	0.238536i
$162$		0			0
$163$	1271.99			0.611225			0.305612	−	0.952156i	$-0.401139\pi$
$163$	1271.99			0.611225			0.305612	+	0.952156i	$0.401139\pi$
$164$	1658.25			0.789559
$165$		0			0
$166$	−380.039	+	658.246i	−0.177691	+	0.307770i
$167$	−1492.49	−	2585.07i	−0.691572	−	1.19784i	−0.971323	−	0.237765i	$-0.923585\pi$
$167$	−1492.49	−	2585.07i	−0.691572	−	1.19784i	0.279751	−	0.960073i	$-0.409748\pi$
$168$		0			0
$169$	1065.46	−	1845.44i	0.484963	−	0.839980i
$170$	888.578			0.400887
$171$		0			0
$172$	463.402			0.205430
$173$	28.3873	−	49.1683i	0.0124754	−	0.0216081i	−0.859720	−	0.510765i	$-0.829362\pi$
$173$	28.3873	−	49.1683i	0.0124754	−	0.0216081i	0.872196	+	0.489157i	$0.162696\pi$
$174$		0			0
$175$	171.297	+	296.694i	0.0739931	+	0.128160i
$176$	555.202	−	961.639i	0.237784	−	0.411854i
$177$		0			0
$178$	−851.598			−0.358595
$179$	4640.98			1.93790			0.968948	−	0.247266i	$-0.0795323\pi$
$179$	4640.98			1.93790			0.968948	+	0.247266i	$0.0795323\pi$
$180$		0			0
$181$	−1887.70	−	3269.60i	−0.775204	−	1.34269i	−0.934680	−	0.355491i	$-0.884314\pi$
$181$	−1887.70	−	3269.60i	−0.775204	−	1.34269i	0.159476	−	0.987202i	$-0.449020\pi$
$182$	51.8298			0.0211093
$183$		0			0
$184$	705.974	+	1222.78i	0.282854	+	0.489917i
$185$	−326.679	+	565.824i	−0.129826	+	0.224866i
$186$		0			0
$187$	3681.12	−	6375.88i	1.43952	−	2.49332i
$188$	1240.57	−	2148.72i	0.481264	−	0.833573i
$189$		0			0
$190$	−693.603	−	12.2104i	−0.264838	−	0.00466230i
$191$	2762.53			1.04654			0.523271	−	0.852166i	$-0.324712\pi$
$191$	2762.53			1.04654			0.523271	+	0.852166i	$0.324712\pi$
$192$		0			0
$193$	−1030.76	+	1785.32i	−0.384433	+	0.665857i	−0.991690	−	0.128648i	$-0.958936\pi$
$193$	−1030.76	+	1785.32i	−0.384433	+	0.665857i	0.607258	+	0.794505i	$0.292270\pi$
$194$	419.846	+	727.194i	0.155377	+	0.269121i
$195$		0			0
$196$	665.672	+	1152.98i	0.242592	+	0.420181i
$197$	−2094.82			−0.757614			−0.378807	−	0.925476i	$-0.623666\pi$
$197$	−2094.82			−0.757614			−0.378807	+	0.925476i	$0.623666\pi$
$198$		0			0
$199$	858.681	+	1487.28i	0.305881	+	0.529801i	0.977457	−	0.211134i	$-0.0677158\pi$
$199$	858.681	+	1487.28i	0.305881	+	0.529801i	−0.671576	+	0.740935i	$0.734382\pi$
$200$	−429.839	−	744.503i	−0.151971	−	0.263222i
$201$		0			0
$202$	−2483.42			−0.865014
$203$	−105.561	−	182.837i	−0.0364972	−	0.0632151i
$204$		0			0
$205$	868.116	+	1503.62i	0.295765	+	0.512280i
$206$	−593.606	+	1028.16i	−0.200769	+	0.347743i
$207$		0			0
$208$	−130.058			−0.0433553
$209$	−2961.00	+	4926.27i	−0.979985	+	1.63042i
$210$		0			0
$211$	1145.53	−	1984.11i	0.373750	−	0.647354i	−0.616389	−	0.787442i	$-0.711405\pi$
$211$	1145.53	−	1984.11i	0.373750	−	0.647354i	0.990139	+	0.140088i	$0.0447384\pi$
$212$	−743.971	+	1288.60i	−0.241020	+	0.417458i
$213$		0			0
$214$	1778.56	−	3080.55i	0.568130	−	0.984030i
$215$	242.597	+	420.190i	0.0769533	+	0.133287i
$216$		0			0
$217$	−449.251			−0.140540
$218$	−1069.99	−	1853.28i	−0.332426	−	0.575779i
$219$		0			0
$220$	1162.62			0.356291
$221$	−862.314			−0.262468
$222$		0			0
$223$	−1628.09	+	2819.94i	−0.488902	+	0.846804i	−0.999918	−	0.0127673i	$-0.995936\pi$
$223$	−1628.09	+	2819.94i	−0.488902	+	0.846804i	0.511016	+	0.859571i	$0.329269\pi$
$224$	51.0097	+	88.3514i	0.0152153	+	0.0263537i
$225$		0			0
$226$	−583.197	+	1010.13i	−0.171654	+	0.297313i
$227$	998.044			0.291817			0.145909	−	0.989298i	$-0.453389\pi$
$227$	998.044			0.291817			0.145909	+	0.989298i	$0.453389\pi$
$228$		0			0
$229$	−1028.59			−0.296816			−0.148408	−	0.988926i	$-0.547415\pi$
$229$	−1028.59			−0.296816			−0.148408	+	0.988926i	$0.547415\pi$
$230$	−739.173	+	1280.29i	−0.211912	+	0.367042i
$231$		0			0
$232$	264.887	+	458.799i	0.0749600	+	0.129835i
$233$	−62.7431	+	108.674i	−0.0176414	+	0.0305557i	−0.874711	−	0.484644i	$-0.838949\pi$
$233$	−62.7431	+	108.674i	−0.0176414	+	0.0305557i	0.857070	+	0.515200i	$0.172282\pi$
$234$		0			0
$235$	2597.81			0.721117
$236$	−366.772			−0.101164
$237$		0			0
$238$	338.206	+	585.789i	0.0921118	+	0.159542i
$239$	−3591.03			−0.971901			−0.485950	−	0.873986i	$-0.661526\pi$
$239$	−3591.03			−0.971901			−0.485950	+	0.873986i	$0.661526\pi$
$240$		0			0
$241$	1845.92	+	3197.23i	0.493386	+	0.854570i	0.999971	−	0.00762002i	$-0.00242555\pi$
$241$	1845.92	+	3197.23i	0.493386	+	0.854570i	−0.506585	+	0.862190i	$0.669092\pi$
$242$	3485.40	−	6036.89i	0.925827	−	1.60358i
$243$		0			0
$244$	−437.241	+	757.324i	−0.114719	+	0.198700i
$245$	−696.976	+	1207.20i	−0.181748	+	0.314796i
$246$		0			0
$247$	673.101	+	11.8495i	0.173394	+	0.00305250i
$248$	1127.32			0.288648
$249$		0			0
$250$	973.566	−	1686.27i	0.246295	−	0.426595i
$251$	3647.44	+	6317.55i	0.917228	+	1.58869i	0.803606	+	0.595162i	$0.202912\pi$
$251$	3647.44	+	6317.55i	0.917228	+	1.58869i	0.113622	+	0.993524i	$0.463755\pi$
$252$		0			0
$253$	6124.35	+	10607.7i	1.52188	+	2.63597i
$254$	−3318.71			−0.819820
$255$		0			0
$256$	−128.000	−	221.703i	−0.0312500	−	0.0541266i
$257$	1151.60	+	1994.63i	0.279513	+	0.484131i	0.971264	−	0.238006i	$-0.0764937\pi$
$257$	1151.60	+	1994.63i	0.279513	+	0.484131i	−0.691751	+	0.722136i	$0.743160\pi$
$258$		0			0
$259$	−497.354			−0.119321
$260$	−68.0871	−	117.930i	−0.0162407	−	0.0281297i
$261$		0			0
$262$	−597.546	−	1034.98i	−0.140903	−	0.244051i
$263$	3569.19	−	6182.01i	0.836827	−	1.44943i	−0.0557070	−	0.998447i	$-0.517741\pi$
$263$	3569.19	−	6182.01i	0.836827	−	1.44943i	0.892534	−	0.450980i	$-0.148925\pi$
$264$		0			0
$265$	−1557.91			−0.361139
$266$	−255.945	−	461.900i	−0.0589963	−	0.106470i
$267$		0			0
$268$	290.685	−	503.481i	0.0662552	−	0.114757i
$269$	−2723.33	+	4716.95i	−0.617265	+	1.06913i	0.372717	+	0.927945i	$0.378426\pi$
$269$	−2723.33	+	4716.95i	−0.617265	+	1.06913i	−0.989983	+	0.141190i	$0.954907\pi$
$270$		0			0
$271$	1701.84	−	2947.67i	0.381474	−	0.660732i	−0.609799	−	0.792556i	$-0.708750\pi$
$271$	1701.84	−	2947.67i	0.381474	−	0.660732i	0.991273	+	0.131824i	$0.0420834\pi$
$272$	−848.669	−	1469.94i	−0.189184	−	0.327677i
$273$		0			0
$274$	−3554.62			−0.783731
$275$	−3728.87	−	6458.59i	−0.817670	−	1.41625i
$276$		0			0
$277$	−5131.93			−1.11317			−0.556584	−	0.830791i	$-0.687888\pi$
$277$	−5131.93			−1.11317			−0.556584	+	0.830791i	$0.687888\pi$
$278$	−327.134			−0.0705763
$279$		0			0
$280$	−53.4085	+	92.5062i	−0.0113992	+	0.0197439i
$281$	1683.34	+	2915.63i	0.357365	+	0.618975i	0.987520	−	0.157495i	$-0.0503417\pi$
$281$	1683.34	+	2915.63i	0.357365	+	0.618975i	−0.630154	+	0.776470i	$0.717008\pi$
$282$		0			0
$283$	−3342.88	+	5790.04i	−0.702168	+	1.21619i	0.265535	+	0.964101i	$0.414451\pi$
$283$	−3342.88	+	5790.04i	−0.702168	+	1.21619i	−0.967704	+	0.252090i	$0.918882\pi$
$284$	−3551.32			−0.742014
$285$		0			0
$286$	−1128.26			−0.233270
$287$	−660.835	+	1144.60i	−0.135916	+	0.235413i
$288$		0			0
$289$	−3170.36	−	5491.23i	−0.645301	−	1.11769i
$290$	−277.344	+	480.374i	−0.0561593	+	0.0972708i
$291$		0			0
$292$	796.065			0.159542
$293$	5625.93			1.12174			0.560871	−	0.827903i	$-0.310466\pi$
$293$	5625.93			1.12174			0.560871	+	0.827903i	$0.310466\pi$
$294$		0			0
$295$	−192.010	−	332.571i	−0.0378957	−	0.0656374i
$296$	1248.02			0.245067
$297$		0			0
$298$	1119.80	+	1939.55i	0.217678	+	0.377030i
$299$	717.325	−	1242.44i	0.138742	−	0.240309i
$300$		0			0
$301$	−184.672	+	319.861i	−0.0353631	+	0.0612507i
$302$	−2807.15	+	4862.12i	−0.534878	+	0.926436i
$303$		0			0
$304$	642.251	+	1159.06i	0.121170	+	0.218673i
$305$	−915.606			−0.171893
$306$		0			0
$307$	−2801.77	+	4852.81i	−0.520865	+	0.902164i	0.478841	+	0.877902i	$0.341057\pi$
$307$	−2801.77	+	4852.81i	−0.520865	+	0.902164i	−0.999706	+	0.0242627i	$0.992276\pi$
$308$	442.511	+	766.451i	0.0818649	+	0.141794i
$309$		0			0
$310$	590.166	+	1022.20i	0.108126	+	0.187280i
$311$	−6668.20			−1.21582			−0.607908	−	0.794008i	$-0.707991\pi$
$311$	−6668.20			−1.21582			−0.607908	+	0.794008i	$0.707991\pi$
$312$		0			0
$313$	−2245.70	−	3889.67i	−0.405541	−	0.702418i	0.588843	−	0.808247i	$-0.299584\pi$
$313$	−2245.70	−	3889.67i	−0.405541	−	0.702418i	−0.994384	+	0.105829i	$0.966250\pi$
$314$	1003.94	+	1738.88i	0.180432	+	0.312518i
$315$		0			0
$316$	−1558.23			−0.277397
$317$	−633.023	−	1096.43i	−0.112158	−	0.194264i	0.804482	−	0.593977i	$-0.202443\pi$
$317$	−633.023	−	1096.43i	−0.112158	−	0.194264i	−0.916640	+	0.399713i	$0.869110\pi$
$318$		0			0
$319$	2297.91	+	3980.10i	0.403317	+	0.698566i
$320$	134.019	−	232.128i	0.0234122	−	0.0405512i
$321$		0			0
$322$	−1125.36			−0.194764
$323$	4258.27	+	7684.82i	0.733549	+	1.32382i
$324$		0			0
$325$	−436.750	+	756.474i	−0.0745432	+	0.129113i
$326$	1271.99	−	2203.14i	0.216101	−	0.374297i
$327$		0			0
$328$	1658.25	−	2872.17i	0.279151	−	0.483504i
$329$	988.763	+	1712.59i	0.165691	+	0.286985i
$330$		0			0
$331$	−5068.09			−0.841594			−0.420797	−	0.907155i	$-0.638249\pi$
$331$	−5068.09			−0.841594			−0.420797	+	0.907155i	$0.638249\pi$
$332$	760.077	+	1316.49i	0.125647	+	0.217626i
$333$		0			0
$334$	−5969.97			−0.978031
$335$	608.709			0.0992757
$336$		0			0
$337$	−5372.06	+	9304.68i	−0.868352	+	1.50403i	−0.00467268	+	0.999989i	$0.501487\pi$
$337$	−5372.06	+	9304.68i	−0.868352	+	1.50403i	−0.863680	+	0.504041i	$0.831846\pi$
$338$	−2130.93	−	3690.87i	−0.342920	−	0.593955i
$339$		0			0
$340$	888.578	−	1539.06i	0.141735	−	0.245492i
$341$	9779.53			1.55305
$342$		0			0
$343$	−2154.64			−0.339182
$344$	463.402	−	802.635i	0.0726306	−	0.125800i
$345$		0			0
$346$	−56.7747	−	98.3367i	−0.00882146	−	0.0152792i
$347$	−2425.67	+	4201.38i	−0.375264	+	0.649977i	−0.990367	−	0.138471i	$-0.955781\pi$
$347$	−2425.67	+	4201.38i	−0.375264	+	0.649977i	0.615102	+	0.788447i	$0.289115\pi$
$348$		0			0
$349$	−7611.35			−1.16741			−0.583705	−	0.811966i	$-0.698398\pi$
$349$	−7611.35			−1.16741			−0.583705	+	0.811966i	$0.698398\pi$
$350$	685.186			0.104642
$351$		0			0
$352$	−1110.40	−	1923.28i	−0.168139	−	0.291225i
$353$	−5567.64			−0.839477			−0.419739	−	0.907645i	$-0.637878\pi$
$353$	−5567.64			−0.839477			−0.419739	+	0.907645i	$0.637878\pi$
$354$		0			0
$355$	−1859.16	−	3220.16i	−0.277955	−	0.481432i
$356$	−851.598	+	1475.01i	−0.126783	+	0.219594i
$357$		0			0
$358$	4640.98	−	8038.42i	0.685149	−	1.18671i
$359$	2170.66	−	3759.69i	0.319116	−	0.552726i	−0.661187	−	0.750221i	$-0.729947\pi$
$359$	2170.66	−	3759.69i	0.319116	−	0.552726i	0.980304	+	0.197495i	$0.0632805\pi$
$360$		0			0
$361$	−3218.30	−	6057.10i	−0.469208	−	0.883088i
$362$	−7550.82			−1.09630
$363$		0			0
$364$	51.8298	−	89.7719i	0.00746325	−	0.0129267i
$365$	416.750	+	721.833i	0.0597636	+	0.103514i
$366$		0			0
$367$	4482.24	+	7763.47i	0.637524	+	1.10422i	0.985974	+	0.166896i	$0.0533745\pi$
$367$	4482.24	+	7763.47i	0.637524	+	1.10422i	−0.348451	+	0.937327i	$0.613292\pi$
$368$	2823.90			0.400016
$369$		0			0
$370$	653.357	+	1131.65i	0.0918012	+	0.159004i
$371$	−592.965	−	1027.04i	−0.0829789	−	0.143724i
$372$		0			0
$373$	5048.11			0.700755			0.350377	−	0.936609i	$-0.386053\pi$
$373$	5048.11			0.700755			0.350377	+	0.936609i	$0.386053\pi$
$374$	−7362.23	−	12751.8i	−1.01789	−	1.76304i
$375$		0			0
$376$	−2481.13	−	4297.45i	−0.340305	−	0.589425i
$377$	269.147	−	466.175i	0.0367686	−	0.0636850i
$378$		0			0
$379$	−9290.41			−1.25915			−0.629573	−	0.776941i	$-0.716770\pi$
$379$	−9290.41			−1.25915			−0.629573	+	0.776941i	$0.716770\pi$
$380$	−714.752	+	1189.14i	−0.0964894	+	0.160531i
$381$		0			0
$382$	2762.53	−	4784.84i	0.370009	−	0.640874i
$383$	2081.13	−	3604.62i	0.277652	−	0.480907i	−0.693149	−	0.720794i	$-0.743777\pi$
$383$	2081.13	−	3604.62i	0.277652	−	0.480907i	0.970801	+	0.239887i	$0.0771105\pi$
$384$		0			0
$385$	−463.320	+	802.495i	−0.0613325	+	0.106231i
$386$	2061.51	+	3570.65i	0.271835	+	0.470832i
$387$		0			0
$388$	1679.38			0.219736
$389$	2092.61	+	3624.51i	0.272750	+	0.472417i	0.969565	−	0.244834i	$-0.0787335\pi$
$389$	2092.61	+	3624.51i	0.272750	+	0.472417i	−0.696815	+	0.717251i	$0.745400\pi$
$390$		0			0
$391$	18723.1			2.42165
$392$	2662.69			0.343077
$393$		0			0
$394$	−2094.82	+	3628.34i	−0.267857	+	0.463942i
$395$	−815.754	−	1412.93i	−0.103912	−	0.179980i
$396$		0			0
$397$	2264.88	−	3922.89i	0.286325	−	0.495930i	−0.686605	−	0.727031i	$-0.740900\pi$
$397$	2264.88	−	3922.89i	0.286325	−	0.495930i	0.972930	+	0.231101i	$0.0742329\pi$
$398$	3434.72			0.432581
$399$		0			0
$400$	−1719.36			−0.214920
$401$	−4748.53	+	8224.69i	−0.591347	+	1.02424i	0.402704	+	0.915330i	$0.368070\pi$
$401$	−4748.53	+	8224.69i	−0.591347	+	1.02424i	−0.994051	+	0.108913i	$0.965263\pi$
$402$		0			0
$403$	−572.722	−	991.984i	−0.0707924	−	0.122616i
$404$	−2483.42	+	4301.41i	−0.305829	+	0.529711i
$405$		0			0
$406$	−422.245			−0.0516149
$407$	10826.7			1.31857
$408$		0			0
$409$	2677.22	+	4637.08i	0.323667	+	0.560608i	0.981242	−	0.192781i	$-0.0617508\pi$
$409$	2677.22	+	4637.08i	0.323667	+	0.560608i	−0.657574	+	0.753390i	$0.728417\pi$
$410$	3472.46			0.418275
$411$		0			0
$412$	1187.21	+	2056.31i	0.141965	+	0.245891i
$413$	146.163	−	253.162i	0.0174146	−	0.0301630i
$414$		0			0
$415$	−795.821	+	1378.40i	−0.0941333	+	0.163044i
$416$	−130.058	+	225.267i	−0.0153284	+	0.0265496i
$417$		0			0
$418$	5571.55	+	10054.9i	0.651946	+	1.17656i
$419$	−14506.1			−1.69134			−0.845668	−	0.533709i	$-0.820798\pi$
$419$	−14506.1			−1.69134			−0.845668	+	0.533709i	$0.820798\pi$
$420$		0			0
$421$	631.724	−	1094.18i	0.0731315	−	0.126667i	−0.827141	−	0.561995i	$-0.810034\pi$
$421$	631.724	−	1094.18i	0.0731315	−	0.126667i	0.900272	+	0.435327i	$0.143367\pi$
$422$	−2291.05	−	3968.22i	−0.264281	−	0.457749i
$423$		0			0
$424$	1487.94	+	2577.19i	0.170427	+	0.295187i
$425$	−11399.7			−1.30110
$426$		0			0
$427$	−348.493	−	603.607i	−0.0394959	−	0.0684089i
$428$	−3557.12	−	6161.11i	−0.401729	−	0.695814i
$429$		0			0
$430$	970.387			0.108828
$431$	−4093.81	−	7090.69i	−0.457522	−	0.792451i	0.541308	−	0.840825i	$-0.317929\pi$
$431$	−4093.81	−	7090.69i	−0.457522	−	0.792451i	−0.998829	+	0.0483738i	$0.984596\pi$
$432$		0			0
$433$	4621.47	+	8004.63i	0.512919	+	0.888401i	0.999888	+	0.0149820i	$0.00476910\pi$
$433$	4621.47	+	8004.63i	0.512919	+	0.888401i	−0.486969	+	0.873419i	$0.661898\pi$
$434$	−449.251	+	778.126i	−0.0496884	+	0.0860628i
$435$		0			0
$436$	−4279.96			−0.470121
$437$	−14614.8	−	257.284i	−1.59982	−	0.0281637i
$438$		0			0
$439$	1021.52	−	1769.33i	0.111059	−	0.192359i	−0.805139	−	0.593086i	$-0.797909\pi$
$439$	1021.52	−	1769.33i	0.111059	−	0.192359i	0.916197	+	0.400727i	$0.131243\pi$
$440$	1162.62	−	2013.72i	0.125968	−	0.218183i
$441$		0			0
$442$	−862.314	+	1493.57i	−0.0927966	+	0.160728i
$443$	−4834.57	−	8373.71i	−0.518504	−	0.898075i	−0.999769	−	0.0214998i	$-0.993156\pi$
$443$	−4834.57	−	8373.71i	−0.518504	−	0.898075i	0.481265	−	0.876575i	$-0.340177\pi$
$444$		0			0
$445$	−1783.29			−0.189969
$446$	3256.19	+	5639.88i	0.345706	+	0.598781i
$447$		0			0
$448$	204.039			0.0215177
$449$	13227.2			1.39027			0.695134	−	0.718881i	$-0.255345\pi$
$449$	13227.2			1.39027			0.695134	+	0.718881i	$0.255345\pi$
$450$		0			0
$451$	14385.4	−	24916.2i	1.50195	−	2.60146i
$452$	1166.39	+	2020.26i	0.121377	+	0.210232i
$453$		0			0
$454$	998.044	−	1728.66i	0.103173	−	0.178701i
$455$	108.534			0.0111828
$456$		0			0
$457$	−5380.98			−0.550791			−0.275396	−	0.961331i	$-0.588809\pi$
$457$	−5380.98			−0.550791			−0.275396	+	0.961331i	$0.588809\pi$
$458$	−1028.59	+	1781.56i	−0.104940	+	0.181762i
$459$		0			0
$460$	1478.35	+	2560.57i	0.149844	+	0.259538i
$461$	−1422.33	+	2463.55i	−0.143698	+	0.248892i	−0.928886	−	0.370365i	$-0.879233\pi$
$461$	−1422.33	+	2463.55i	−0.143698	+	0.248892i	0.785189	+	0.619257i	$0.212566\pi$
$462$		0			0
$463$	6625.39			0.665028			0.332514	−	0.943098i	$-0.392103\pi$
$463$	6625.39			0.665028			0.332514	+	0.943098i	$0.392103\pi$
$464$	1059.55			0.106009
$465$		0			0
$466$	125.486	+	217.348i	0.0124743	+	0.0216062i
$467$	18635.1			1.84653			0.923264	−	0.384167i	$-0.125511\pi$
$467$	18635.1			1.84653			0.923264	+	0.384167i	$0.125511\pi$
$468$		0			0
$469$	231.683	+	401.288i	0.0228106	+	0.0395090i
$470$	2597.81	−	4499.54i	0.254953	−	0.441592i
$471$		0			0
$472$	−366.772	+	635.267i	−0.0357670	+	0.0619503i
$473$	4020.03	−	6962.89i	0.390784	−	0.676858i
$474$		0			0
$475$	8898.34	+	156.650i	0.859545	+	0.0151317i
$476$	1352.82			0.130266
$477$		0			0
$478$	−3591.03	+	6219.84i	−0.343619	+	0.595165i
$479$	778.310	+	1348.07i	0.0742420	+	0.128591i	0.900756	−	0.434325i	$-0.143013\pi$
$479$	778.310	+	1348.07i	0.0742420	+	0.128591i	−0.826514	+	0.562916i	$0.809680\pi$
$480$		0			0
$481$	−634.046	−	1098.20i	−0.0601039	−	0.104103i
$482$	7383.68			0.697754
$483$		0			0
$484$	−6970.80	−	12073.8i	−0.654659	−	1.13390i
$485$	879.179	+	1522.78i	0.0823123	+	0.142569i
$486$		0			0
$487$	19339.5			1.79950			0.899751	−	0.436405i	$-0.143748\pi$
$487$	19339.5			1.79950			0.899751	+	0.436405i	$0.143748\pi$
$488$	874.482	+	1514.65i	0.0811188	+	0.140502i
$489$		0			0
$490$	1393.95	+	2414.40i	0.128515	+	0.222594i
$491$	−3419.12	+	5922.10i	−0.314262	+	0.544319i	−0.979280	−	0.202509i	$-0.935091\pi$
$491$	−3419.12	+	5922.10i	−0.314262	+	0.544319i	0.665018	+	0.746827i	$0.268424\pi$
$492$		0			0
$493$	7025.05			0.641770
$494$	693.625	−	1154.00i	0.0631734	−	0.105103i
$495$		0			0
$496$	1127.32	−	1952.57i	0.102053	−	0.176760i
$497$	1415.25	−	2451.28i	0.127731	−	0.221237i
$498$		0			0
$499$	9057.49	−	15688.0i	0.812563	−	1.40740i	−0.0985021	−	0.995137i	$-0.531405\pi$
$499$	9057.49	−	15688.0i	0.812563	−	1.40740i	0.911065	−	0.412263i	$-0.135262\pi$
$500$	−1947.13	−	3372.53i	−0.174157	−	0.301648i
$501$		0			0
$502$	14589.8			1.29716
$503$	−2915.92	−	5050.53i	−0.258478	−	0.447698i	0.707356	−	0.706857i	$-0.249888\pi$
$503$	−2915.92	−	5050.53i	−0.258478	−	0.447698i	−0.965834	+	0.259160i	$0.916554\pi$
$504$		0			0
$505$	−5200.41			−0.458248
$506$	24497.4			2.15226
$507$		0			0
$508$	−3318.71	+	5748.17i	−0.289850	+	0.502035i
$509$	4957.32	+	8586.34i	0.431689	+	0.747707i	0.997019	−	0.0771579i	$-0.0245846\pi$
$509$	4957.32	+	8586.34i	0.431689	+	0.747707i	−0.565330	+	0.824865i	$0.691251\pi$
$510$		0			0
$511$	−317.242	+	549.480i	−0.0274637	+	0.0475686i
$512$	−512.000			−0.0441942
$513$		0			0
$514$	4606.40			0.395291
$515$	−1243.04	+	2153.01i	−0.106359	+	0.184220i
$516$		0			0
$517$	−21523.9	−	37280.5i	−1.83099	−	3.17136i
$518$	−497.354	+	861.443i	−0.0421863	+	0.0730688i
$519$		0			0
$520$	−272.348			−0.0229678
$521$	5851.91			0.492086			0.246043	−	0.969259i	$-0.420869\pi$
$521$	5851.91			0.492086			0.246043	+	0.969259i	$0.420869\pi$
$522$		0			0
$523$	−3447.05	−	5970.46i	−0.288200	−	0.499178i	0.685180	−	0.728374i	$-0.259724\pi$
$523$	−3447.05	−	5970.46i	−0.288200	−	0.499178i	−0.973380	+	0.229196i	$0.926390\pi$
$524$	−2390.19			−0.199267
$525$		0			0
$526$	−7138.38	−	12364.0i	−0.591726	−	1.02490i
$527$	7474.37	−	12946.0i	0.617816	−	1.07009i
$528$		0			0
$529$	−9491.49	+	16439.7i	−0.780101	+	1.35117i
$530$	−1557.91	+	2698.39i	−0.127682	+	0.221152i
$531$		0			0
$532$	−1055.98	−	18.5899i	−0.0860574	−	0.00151499i
$533$	−3369.83			−0.273853
$534$		0			0
$535$	3724.40	−	6450.84i	0.300971	−	0.521298i
$536$	−581.370	−	1006.96i	−0.0468495	−	0.0811458i
$537$		0			0
$538$	5446.66	+	9433.89i	0.436472	+	0.755992i
$539$	23098.9			1.84590
$540$		0			0
$541$	2812.50	+	4871.39i	0.223509	+	0.387130i	0.955871	−	0.293786i	$-0.0949153\pi$
$541$	2812.50	+	4871.39i	0.223509	+	0.387130i	−0.732362	+	0.680916i	$0.761582\pi$
$542$	−3403.68	−	5895.34i	−0.269743	−	0.467208i
$543$		0			0
$544$	−3394.67			−0.267547
$545$	−2240.62	−	3880.86i	−0.176105	−	0.305023i
$546$		0			0
$547$	−1798.07	−	3114.35i	−0.140548	−	0.243437i	0.787155	−	0.616755i	$-0.211553\pi$
$547$	−1798.07	−	3114.35i	−0.140548	−	0.243437i	−0.927703	+	0.373319i	$0.878220\pi$
$548$	−3554.62	+	6156.78i	−0.277091	+	0.479935i
$549$		0			0
$550$	−14915.5			−1.15636
$551$	−5483.59	−	96.5350i	−0.423972	−	0.00746376i
$552$		0			0
$553$	620.975	−	1075.56i	0.0477515	−	0.0827080i
$554$	−5131.93	+	8888.76i	−0.393564	+	0.681674i
$555$		0			0
$556$	−327.134	+	566.613i	−0.0249525	+	0.0432190i
$557$	9190.73	+	15918.8i	0.699145	+	1.21095i	0.968763	+	0.247987i	$0.0797692\pi$
$557$	9190.73	+	15918.8i	0.699145	+	1.21095i	−0.269618	+	0.962967i	$0.586897\pi$
$558$		0			0
$559$	−941.705			−0.0712520
$560$	106.817	+	185.012i	0.00806043	+	0.0139611i
$561$		0			0
$562$	6733.36			0.505391
$563$	−5578.33			−0.417582			−0.208791	−	0.977960i	$-0.566953\pi$
$563$	−5578.33			−0.417582			−0.208791	+	0.977960i	$0.566953\pi$
$564$		0			0
$565$	−1221.25	+	2115.26i	−0.0909349	+	0.157504i
$566$	6685.76	+	11580.1i	0.496508	+	0.859977i
$567$		0			0
$568$	−3551.32	+	6151.06i	−0.262341	+	0.454389i
$569$	−16981.3			−1.25113			−0.625564	−	0.780173i	$-0.715131\pi$
$569$	−16981.3			−1.25113			−0.625564	+	0.780173i	$0.715131\pi$
$570$		0			0
$571$	−19520.5			−1.43066			−0.715332	−	0.698785i	$-0.753724\pi$
$571$	−19520.5			−1.43066			−0.715332	+	0.698785i	$0.753724\pi$
$572$	−1128.26	+	1954.20i	−0.0824735	+	0.142848i
$573$		0			0
$574$	1321.67	+	2289.20i	0.0961070	+	0.166462i
$575$	9482.98	−	16425.0i	0.687770	−	1.19125i
$576$		0			0
$577$	6371.35			0.459693			0.229846	−	0.973227i	$-0.426178\pi$
$577$	6371.35			0.459693			0.229846	+	0.973227i	$0.426178\pi$
$578$	−12681.4			−0.912593
$579$		0			0
$580$	554.688	+	960.748i	0.0397107	+	0.0687809i
$581$	−1211.60			−0.0865159
$582$		0			0
$583$	12908.0	+	22357.2i	0.916969	+	1.58824i
$584$	796.065	−	1378.82i	0.0564065	−	0.0976989i
$585$		0			0
$586$	5625.93	−	9744.39i	0.396596	−	0.686924i
$587$	5379.52	−	9317.61i	0.378257	−	0.655160i	−0.612552	−	0.790430i	$-0.709857\pi$
$587$	5379.52	−	9317.61i	0.378257	−	0.655160i	0.990809	+	0.135271i	$0.0431904\pi$
$588$		0			0
$589$	−6012.21	+	10002.6i	−0.420592	+	0.699747i
$590$	−768.039			−0.0535927
$591$		0			0
$592$	1248.02	−	2161.64i	0.0866444	−	0.150073i
$593$	1805.88	+	3127.87i	0.125057	+	0.216604i	0.921755	−	0.387773i	$-0.126755\pi$
$593$	1805.88	+	3127.87i	0.125057	+	0.216604i	−0.796698	+	0.604377i	$0.793422\pi$
$594$		0			0
$595$	708.220	+	1226.67i	0.0487970	+	0.0845188i
$596$	4479.19			0.307844
$597$		0			0
$598$	−1434.65	−	2484.89i	−0.0981057	−	0.169924i
$599$	−4590.12	−	7950.31i	−0.313100	−	0.542306i	0.665932	−	0.746013i	$-0.268034\pi$
$599$	−4590.12	−	7950.31i	−0.313100	−	0.542306i	−0.979032	+	0.203707i	$0.934701\pi$
$600$		0			0
$601$	12700.4			0.862000			0.431000	−	0.902352i	$-0.358161\pi$
$601$	12700.4			0.862000			0.431000	+	0.902352i	$0.358161\pi$
$602$	369.343	+	639.721i	0.0250055	+	0.0433108i
$603$		0			0
$604$	5614.29	+	9724.24i	0.378216	+	0.655089i
$605$	7298.61	−	12641.6i	0.490464	−	0.849509i
$606$		0			0
$607$	−24227.5			−1.62004			−0.810019	−	0.586404i	$-0.800543\pi$
$607$	−24227.5			−1.62004			−0.810019	+	0.586404i	$0.800543\pi$
$608$	2649.80	+	46.6480i	0.176749	+	0.00311156i
$609$		0			0
$610$	−915.606	+	1585.88i	−0.0607734	+	0.105263i
$611$	−2521.02	+	4366.54i	−0.166923	+	0.289119i
$612$		0			0
$613$	8106.74	−	14041.3i	0.534141	−	0.925159i	−0.465064	−	0.885277i	$-0.653969\pi$
$613$	8106.74	−	14041.3i	0.534141	−	0.925159i	0.999204	−	0.0398814i	$-0.0126980\pi$
$614$	5603.54	+	9705.62i	0.368307	+	0.637927i
$615$		0			0
$616$	1770.04			0.115774
$617$	−10757.7	−	18632.8i	−0.701924	−	1.21577i	−0.967790	−	0.251758i	$-0.918991\pi$
$617$	−10757.7	−	18632.8i	−0.701924	−	1.21577i	0.265866	−	0.964010i	$-0.414342\pi$
$618$		0			0
$619$	−15878.5			−1.03103			−0.515516	−	0.856880i	$-0.672400\pi$
$619$	−15878.5			−1.03103			−0.515516	+	0.856880i	$0.672400\pi$
$620$	2360.66			0.152914
$621$		0			0
$622$	−6668.20	+	11549.7i	−0.429856	+	0.744532i
$623$	−678.746	−	1175.62i	−0.0436491	−	0.0756024i
$624$		0			0
$625$	−4677.54	+	8101.73i	−0.299362	+	0.518511i
$626$	−8982.80			−0.573522
$627$		0			0
$628$	4015.77			0.255170
$629$	8274.68	−	14332.2i	0.524536	−	0.908523i
$630$		0			0
$631$	−2779.87	−	4814.88i	−0.175380	−	0.303768i	0.764912	−	0.644134i	$-0.222782\pi$
$631$	−2779.87	−	4814.88i	−0.175380	−	0.303768i	−0.940293	+	0.340366i	$0.889449\pi$
$632$	−1558.23	+	2698.94i	−0.0980745	+	0.169870i
$633$		0			0
$634$	−2532.09			−0.158616
$635$	−6949.55			−0.434306
$636$		0			0
$637$	−1352.75	−	2343.03i	−0.0841412	−	0.145737i
$638$	9191.64			0.570377
$639$		0			0
$640$	−268.039	−	464.257i	−0.0165549	−	0.0286740i
$641$	−10243.5	+	17742.2i	−0.631190	+	1.09325i	0.356119	+	0.934441i	$0.384100\pi$
$641$	−10243.5	+	17742.2i	−0.631190	+	1.09325i	−0.987309	+	0.158812i	$0.949234\pi$
$642$		0			0
$643$	2051.15	−	3552.69i	0.125800	−	0.217892i	−0.796245	−	0.604974i	$-0.793184\pi$
$643$	2051.15	−	3552.69i	0.125800	−	0.217892i	0.922045	+	0.387082i	$0.126517\pi$
$644$	−1125.36	+	1949.18i	−0.0688593	+	0.119268i
$645$		0			0
$646$	17568.8	+	309.287i	1.07002	+	0.0188370i
$647$	−22860.4			−1.38908			−0.694539	−	0.719455i	$-0.744392\pi$
$647$	−22860.4			−1.38908			−0.694539	+	0.719455i	$0.744392\pi$
$648$		0			0
$649$	−3181.76	+	5510.97i	−0.192442	+	0.333320i
$650$	873.501	+	1512.95i	0.0527100	+	0.0912964i
$651$		0			0
$652$	−2543.97	−	4406.29i	−0.152806	−	0.264668i
$653$	−26388.5			−1.58141			−0.790706	−	0.612197i	$-0.790286\pi$
$653$	−26388.5			−1.58141			−0.790706	+	0.612197i	$0.790286\pi$
$654$		0			0
$655$	−1251.29	−	2167.30i	−0.0746444	−	0.129288i
$656$	−3316.50	−	5744.35i	−0.197390	−	0.341889i
$657$		0			0
$658$	3955.05			0.234322
$659$	1611.65	+	2791.45i	0.0952668	+	0.165007i	0.909720	−	0.415222i	$-0.136296\pi$
$659$	1611.65	+	2791.45i	0.0952668	+	0.165007i	−0.814453	+	0.580229i	$0.802963\pi$
$660$		0			0
$661$	13740.1	+	23798.5i	0.808513	+	1.40039i	0.913894	+	0.405953i	$0.133060\pi$
$661$	13740.1	+	23798.5i	0.808513	+	1.40039i	−0.105381	+	0.994432i	$0.533606\pi$
$662$	−5068.09	+	8778.19i	−0.297548	+	0.515369i
$663$		0			0
$664$	3040.31			0.177691
$665$	−535.963	−	967.243i	−0.0312538	−	0.0564031i
$666$		0			0
$667$	−5843.87	+	10121.9i	−0.339244	+	0.587587i
$668$	−5969.97	+	10340.3i	−0.345786	+	0.598919i
$669$		0			0
$670$	608.709	−	1054.32i	0.0350992	−	0.0607937i
$671$	7586.17	+	13139.6i	0.436454	+	0.755961i
$672$		0			0
$673$	−2165.00			−0.124004			−0.0620020	−	0.998076i	$-0.519749\pi$
$673$	−2165.00			−0.124004			−0.0620020	+	0.998076i	$0.519749\pi$
$674$	10744.1	+	18609.4i	0.614018	+	1.06351i
$675$		0			0
$676$	−8523.70			−0.484963
$677$	−11999.0			−0.681179			−0.340589	−	0.940212i	$-0.610627\pi$
$677$	−11999.0			−0.681179			−0.340589	+	0.940212i	$0.610627\pi$
$678$		0			0
$679$	−669.256	+	1159.19i	−0.0378258	+	0.0655161i
$680$	−1777.16	−	3078.13i	−0.100222	−	0.173589i
$681$		0			0
$682$	9779.53	−	16938.6i	0.549087	−	0.951047i
$683$	−5234.35			−0.293246			−0.146623	−	0.989192i	$-0.546840\pi$
$683$	−5234.35			−0.293246			−0.146623	+	0.989192i	$0.546840\pi$
$684$		0			0
$685$	−7443.56			−0.415188
$686$	−2154.64	+	3731.94i	−0.119919	+	0.207706i
$687$		0			0
$688$	−926.803	−	1605.27i	−0.0513576	−	0.0889540i
$689$	1511.87	−	2618.63i	0.0835958	−	0.144792i
$690$		0			0
$691$	−5160.63			−0.284109			−0.142055	−	0.989859i	$-0.545371\pi$
$691$	−5160.63			−0.284109			−0.142055	+	0.989859i	$0.545371\pi$
$692$	−227.099			−0.0124754
$693$		0			0
$694$	4851.34	+	8402.76i	0.265352	+	0.459603i
$695$	−685.036			−0.0373884
$696$		0			0
$697$	−21989.1	−	38086.3i	−1.19498	−	2.06976i
$698$	−7611.35	+	13183.2i	−0.412742	+	0.714890i
$699$		0			0
$700$	685.186	−	1186.78i	0.0369966	−	0.0640799i
$701$	−1657.51	+	2870.90i	−0.0893059	+	0.154682i	−0.907218	−	0.420661i	$-0.861798\pi$
$701$	−1657.51	+	2870.90i	−0.0893059	+	0.154682i	0.817912	+	0.575343i	$0.195132\pi$
$702$		0			0
$703$	−6655.96	+	11073.6i	−0.357090	+	0.594097i
$704$	−4441.62			−0.237784
$705$		0			0
$706$	−5567.64	+	9643.43i	−0.296800	+	0.514073i
$707$	−1979.35	−	3428.34i	−0.105292	−	0.182370i
$708$		0			0
$709$	9166.60	+	15877.0i	0.485555	+	0.841007i	0.999862	−	0.0165995i	$-0.00528404\pi$
$709$	9166.60	+	15877.0i	0.485555	+	0.841007i	−0.514307	+	0.857606i	$0.671951\pi$
$710$	−7436.64			−0.393088
$711$		0			0
$712$	1703.20	+	2950.02i	0.0896488	+	0.155276i
$713$	12435.3	+	21538.5i	0.653162	+	1.13131i
$714$		0			0
$715$	−2362.63			−0.123577
$716$	−9281.96	−	16076.8i	−0.484474	−	0.839133i
$717$		0			0
$718$	−4341.31	−	7519.37i	−0.225649	−	0.390836i
$719$	4873.50	−	8441.15i	0.252783	−	0.437833i	−0.711508	−	0.702678i	$-0.751987\pi$
$719$	4873.50	−	8441.15i	0.252783	−	0.437833i	0.964291	+	0.264845i	$0.0853208\pi$
$720$		0			0
$721$	−1892.48			−0.0977526
$722$	−13709.5	−	482.844i	−0.706669	−	0.0248886i
$723$		0			0
$724$	−7550.82	+	13078.4i	−0.387602	+	0.671346i
$725$	3558.09	−	6162.80i	0.182268	−	0.315697i
$726$		0			0
$727$	−16361.8	+	28339.4i	−0.834697	+	1.44574i	0.0595791	+	0.998224i	$0.481024\pi$
$727$	−16361.8	+	28339.4i	−0.834697	+	1.44574i	−0.894277	+	0.447515i	$0.852309\pi$
$728$	−103.660	−	179.544i	−0.00527731	−	0.00914057i
$729$		0			0
$730$	1667.00			0.0845185
$731$	−6144.91	−	10643.3i	−0.310914	−	0.538518i
$732$		0			0
$733$	36938.2			1.86131			0.930657	−	0.365894i	$-0.119237\pi$
$733$	36938.2			1.86131			0.930657	+	0.365894i	$0.119237\pi$
$734$	17929.0			0.901594
$735$		0			0
$736$	2823.90	−	4891.13i	0.141427	−	0.244959i
$737$	−5043.40	−	8735.43i	−0.252071	−	0.436599i
$738$		0			0
$739$	4993.60	−	8649.16i	0.248569	−	0.430534i	−0.714560	−	0.699574i	$-0.753373\pi$
$739$	4993.60	−	8649.16i	0.248569	−	0.430534i	0.963129	+	0.269040i	$0.0867064\pi$
$740$	2613.43			0.129826
$741$		0			0
$742$	−2371.86			−0.117350
$743$	10869.9	−	18827.2i	0.536713	−	0.929615i	−0.462365	−	0.886690i	$-0.652999\pi$
$743$	10869.9	−	18827.2i	0.536713	−	0.929615i	0.999078	−	0.0429249i	$-0.0136676\pi$
$744$		0			0
$745$	2344.92	+	4061.51i	0.115317	+	0.199735i
$746$	5048.11	−	8743.59i	0.247754	−	0.429123i
$747$		0			0
$748$	−29448.9			−1.43952
$749$	5670.23			0.276617
$750$		0			0
$751$	19033.7	+	32967.3i	0.924833	+	1.60186i	0.791830	+	0.610742i	$0.209129\pi$
$751$	19033.7	+	32967.3i	0.924833	+	1.60186i	0.133003	+	0.991116i	$0.457538\pi$
$752$	−9924.53			−0.481264
$753$		0			0
$754$	−538.293	−	932.351i	−0.0259993	−	0.0450321i
$755$	−5878.31	+	10181.5i	−0.283356	+	0.490787i
$756$		0			0
$757$	5682.61	−	9842.58i	0.272838	−	0.472569i	−0.696750	−	0.717314i	$-0.745371\pi$
$757$	5682.61	−	9842.58i	0.272838	−	0.472569i	0.969587	+	0.244746i	$0.0787045\pi$
$758$	−9290.41	+	16091.5i	−0.445176	+	0.771067i
$759$		0			0
$760$	1344.91	+	2427.13i	0.0641907	+	0.115844i
$761$	−24549.3			−1.16940			−0.584699	−	0.811250i	$-0.698787\pi$
$761$	−24549.3			−1.16940			−0.584699	+	0.811250i	$0.698787\pi$
$762$		0			0
$763$	1705.62	−	2954.22i	0.0809274	−	0.140170i
$764$	−5525.06	−	9569.68i	−0.261636	−	0.453166i
$765$		0			0
$766$	−4162.26	−	7209.24i	−0.196330	−	0.340053i
$767$	745.338			0.0350881
$768$		0			0
$769$	−7111.27	−	12317.1i	−0.333471	−	0.577588i	0.649719	−	0.760174i	$-0.274886\pi$
$769$	−7111.27	−	12317.1i	−0.333471	−	0.577588i	−0.983190	+	0.182586i	$0.941553\pi$
$770$	926.641	+	1604.99i	0.0433686	+	0.0751166i
$771$		0			0
$772$	8246.06			0.384433
$773$	8041.29	+	13927.9i	0.374159	+	0.648063i	0.990201	−	0.139651i	$-0.0445980\pi$
$773$	8041.29	+	13927.9i	0.374159	+	0.648063i	−0.616041	+	0.787714i	$0.711265\pi$
$774$		0			0
$775$	−7571.34	−	13113.9i	−0.350930	−	0.607828i
$776$	1679.38	−	2908.78i	0.0776886	−	0.134561i
$777$		0			0
$778$	8370.46			0.385727
$779$	16640.8	+	30031.4i	0.765365	+	1.38124i
$780$		0			0
$781$	−30807.8	+	53360.7i	−1.41151	+	2.44481i
$782$	18723.1	−	32429.3i	0.856183	−	1.48295i
$783$		0			0
$784$	2662.69	−	4611.91i	0.121296	−	0.210091i
$785$	2102.31	+	3641.30i	0.0955854	+	0.165559i
$786$		0			0
$787$	30058.0			1.36144			0.680720	−	0.732544i	$-0.261667\pi$
$787$	30058.0			1.36144			0.680720	+	0.732544i	$0.261667\pi$
$788$	4189.64	+	7256.68i	0.189403	+	0.328056i
$789$		0			0
$790$	−3263.02			−0.146953
$791$	−1859.29			−0.0835764
$792$		0			0
$793$	888.543	−	1539.00i	0.0397895	−	0.0689174i
$794$	−4529.76	−	7845.77i	−0.202462	−	0.350675i
$795$		0			0
$796$	3434.72	−	5949.12i	0.152940	−	0.264901i
$797$	20008.2			0.889243			0.444621	−	0.895719i	$-0.353338\pi$
$797$	20008.2			0.889243			0.444621	+	0.895719i	$0.353338\pi$
$798$		0			0
$799$	−65801.8			−2.91352
$800$	−1719.36	+	2978.01i	−0.0759855	+	0.131611i
$801$		0			0
$802$	9497.05	+	16449.4i	0.418145	+	0.724249i
$803$	6905.89	−	11961.4i	0.303491	−	0.525662i
$804$		0			0
$805$	−2356.56			−0.103178
$806$	−2290.89			−0.100116
$807$		0			0
$808$	4966.84	+	8602.82i	0.216254	+	0.374562i
$809$	−35302.3			−1.53419			−0.767097	−	0.641532i	$-0.778299\pi$
$809$	−35302.3			−1.53419			−0.767097	+	0.641532i	$0.778299\pi$
$810$		0			0
$811$	−5490.38	−	9509.61i	−0.237723	−	0.411748i	0.722338	−	0.691540i	$-0.243068\pi$
$811$	−5490.38	−	9509.61i	−0.237723	−	0.411748i	−0.960060	+	0.279793i	$0.909734\pi$
$812$	−422.245	+	731.349i	−0.0182486	+	0.0316075i
$813$		0			0
$814$	10826.7	−	18752.3i	0.466185	−	0.807456i
$815$	2663.60	−	4613.50i	0.114481	−	0.198287i
$816$		0			0
$817$	4650.31	+	8392.34i	0.199136	+	0.359377i
$818$	10708.9			0.457735
$819$		0			0
$820$	3472.46	−	6014.48i	0.147883	−	0.256140i
$821$	−2813.34	−	4872.85i	−0.119594	−	0.207142i	0.800013	−	0.599983i	$-0.204826\pi$
$821$	−2813.34	−	4872.85i	−0.119594	−	0.207142i	−0.919607	+	0.392840i	$0.871492\pi$
$822$		0			0
$823$	−14383.1	−	24912.3i	−0.609191	−	1.05515i	−0.991374	−	0.131063i	$-0.958161\pi$
$823$	−14383.1	−	24912.3i	−0.609191	−	1.05515i	0.382183	−	0.924087i	$-0.375172\pi$
$824$	4748.85			0.200769
$825$		0			0
$826$	−292.327	−	506.325i	−0.0123140	−	0.0213284i
$827$	22241.2	+	38522.9i	0.935191	+	1.61980i	0.774294	+	0.632827i	$0.218105\pi$
$827$	22241.2	+	38522.9i	0.935191	+	1.61980i	0.160897	+	0.986971i	$0.448561\pi$
$828$		0			0
$829$	23302.5			0.976271			0.488136	−	0.872768i	$-0.337677\pi$
$829$	23302.5			0.976271			0.488136	+	0.872768i	$0.337677\pi$
$830$	1591.64	+	2756.80i	0.0665623	+	0.115289i
$831$		0			0
$832$	260.116	+	450.534i	0.0108388	+	0.0187734i
$833$	17654.2	−	30578.0i	0.734312	−	1.27187i
$834$		0			0
$835$	−12501.4			−0.518120
$836$	22987.1	+	404.673i	0.950988	+	0.0167415i
$837$		0			0
$838$	−14506.1	+	25125.3i	−0.597978	+	1.03573i
$839$	−13841.8	+	23974.8i	−0.569575	+	0.986533i	0.427033	+	0.904236i	$0.359559\pi$
$839$	−13841.8	+	23974.8i	−0.569575	+	0.986533i	−0.996608	+	0.0822969i	$0.973774\pi$
$840$		0			0
$841$	10001.8	−	17323.7i	0.410096	−	0.710307i
$842$	−1263.45	−	2188.36i	−0.0517118	−	0.0895674i
$843$		0			0
$844$	−9164.21			−0.373750
$845$	−4462.27	−	7728.88i	−0.181665	−	0.314653i
$846$		0			0
$847$	11111.8			0.450776
$848$	5951.77			0.241020
$849$		0			0
$850$	−11399.7	+	19744.9i	−0.460008	+	0.796758i
$851$	13766.8	+	23844.7i	0.554546	+	0.960502i
$852$		0			0
$853$	15304.7	−	26508.6i	0.614331	−	1.06405i	−0.376171	−	0.926550i	$-0.622759\pi$
$853$	15304.7	−	26508.6i	0.614331	−	1.06405i	0.990502	−	0.137502i	$-0.0439072\pi$
$854$	−1393.97			−0.0558556
$855$		0			0
$856$	−14228.5			−0.568130
$857$	5459.14	−	9455.50i	0.217597	−	0.376889i	−0.736476	−	0.676464i	$-0.763512\pi$
$857$	5459.14	−	9455.50i	0.217597	−	0.376889i	0.954073	+	0.299575i	$0.0968449\pi$
$858$		0			0
$859$	−7319.75	−	12678.2i	−0.290741	−	0.503578i	0.683244	−	0.730190i	$-0.260569\pi$
$859$	−7319.75	−	12678.2i	−0.290741	−	0.503578i	−0.973985	+	0.226612i	$0.927235\pi$
$860$	970.387	−	1680.76i	0.0384767	−	0.0666435i
$861$		0			0
$862$	−16375.2			−0.647033
$863$	22775.2			0.898353			0.449176	−	0.893443i	$-0.351717\pi$
$863$	22775.2			0.898353			0.449176	+	0.893443i	$0.351717\pi$
$864$		0			0
$865$	−118.889	−	205.922i	−0.00467324	−	0.00809429i
$866$	18485.9			0.725377
$867$		0			0
$868$	898.502	+	1556.25i	0.0351350	+	0.0608556i
$869$	−13517.7	+	23413.4i	−0.527684	+	0.913975i
$870$		0			0
$871$	−590.717	+	1023.15i	−0.0229801	+	0.0398028i
$872$	−4279.96	+	7413.11i	−0.166213	+	0.287889i
$873$		0			0
$874$	−15060.4	+	25056.2i	−0.582867	+	0.969725i
$875$	3103.83			0.119918
$876$		0			0
$877$	−402.954	+	697.937i	−0.0155152	+	0.0268730i	−0.873679	−	0.486503i	$-0.838272\pi$
$877$	−402.954	+	697.937i	−0.0155152	+	0.0268730i	0.858164	+	0.513376i	$0.171605\pi$
$878$	−2043.05	−	3538.67i	−0.0785303	−	0.136018i
$879$		0			0
$880$	−2325.25	−	4027.44i	−0.0890728	−	0.154279i
$881$	901.690			0.0344821			0.0172410	−	0.999851i	$-0.494512\pi$
$881$	901.690			0.0344821			0.0172410	+	0.999851i	$0.494512\pi$
$882$		0			0
$883$	12703.2	+	22002.5i	0.484140	+	0.838554i	0.999834	−	0.0182183i	$-0.00579938\pi$
$883$	12703.2	+	22002.5i	0.484140	+	0.838554i	−0.515695	+	0.856773i	$0.672466\pi$
$884$	1724.63	+	2987.14i	0.0656171	+	0.113652i
$885$		0			0
$886$	−19338.3			−0.733275
$887$	14280.2	+	24734.1i	0.540568	+	0.936291i	0.998871	+	0.0474953i	$0.0151239\pi$
$887$	14280.2	+	24734.1i	0.540568	+	0.936291i	−0.458304	+	0.888796i	$0.651543\pi$
$888$		0			0
$889$	−2645.10	−	4581.44i	−0.0997904	−	0.172842i
$890$	−1783.29	+	3088.75i	−0.0671641	+	0.116332i
$891$		0			0
$892$	13024.8			0.488902
$893$	51363.3	+	904.218i	1.92476	+	0.0338841i
$894$		0			0
$895$	9718.46	−	16832.9i	0.362963	−	0.628671i
$896$	204.039	−	353.405i	0.00760765	−	0.0131768i
$897$		0			0
$898$	13227.2	−	22910.2i	0.491534	−	0.851361i
$899$	4665.82	+	8081.44i	0.173097	+	0.299812i
$900$		0			0
$901$	39461.6			1.45911
$902$	−28770.8	−	49832.4i	−1.06204	−	1.83951i
$903$		0			0
$904$	4665.58			0.171654
$905$	−15811.8			−0.580776
$906$		0			0
$907$	20452.7	−	35425.1i	0.748755	−	1.29688i	−0.199665	−	0.979864i	$-0.563985\pi$
$907$	20452.7	−	35425.1i	0.748755	−	1.29688i	0.948420	−	0.317017i	$-0.102681\pi$
$908$	−1996.09	−	3457.33i	−0.0729543	−	0.126361i
$909$		0			0
$910$	108.534	−	187.987i	0.00395372	−	0.00684804i
$911$	−30047.9			−1.09279			−0.546395	−	0.837527i	$-0.684000\pi$
$911$	−30047.9			−1.09279			−0.546395	+	0.837527i	$0.684000\pi$
$912$		0			0
$913$	26374.8			0.956055
$914$	−5380.98	+	9320.13i	−0.194734	+	0.337289i
$915$		0			0
$916$	2057.17	+	3563.12i	0.0742040	+	0.128525i
$917$	952.520	−	1649.81i	0.0343021	−	0.0594129i
$918$		0			0
$919$	−49600.1			−1.78036			−0.890182	−	0.455605i	$-0.849423\pi$
$919$	−49600.1			−1.78036			−0.890182	+	0.455605i	$0.849423\pi$
$920$	5913.39			0.211912
$921$		0			0
$922$	2844.67	+	4927.11i	0.101610	+	0.175993i
$923$	7216.84			0.257362
$924$		0			0
$925$	−8382.03	−	14518.1i	−0.297945	−	0.516057i
$926$	6625.39	−	11475.5i	0.235123	−	0.407245i
$927$		0			0
$928$	1059.55	−	1835.19i	0.0374800	−	0.0649173i
$929$	13778.4	−	23864.8i	0.486603	−	0.842821i	−0.513279	−	0.858222i	$-0.671569\pi$
$929$	13778.4	−	23864.8i	0.486603	−	0.842821i	0.999881	+	0.0154015i	$0.00490263\pi$
$930$		0			0
$931$	−14200.6	+	23625.8i	−0.499900	+	0.831693i
$932$	501.945			0.0176414
$933$		0			0
$934$	18635.1	−	32276.9i	0.652846	−	1.13076i
$935$	−15416.9	−	26702.9i	−0.539237	−	0.933986i
$936$		0			0
$937$	13440.4	+	23279.5i	0.468601	+	0.811641i	0.999356	−	0.0358846i	$-0.0114249\pi$
$937$	13440.4	+	23279.5i	0.468601	+	0.811641i	−0.530755	+	0.847525i	$0.678092\pi$
$938$	926.734			0.0322590
$939$		0			0
$940$	−5195.62	−	8999.08i	−0.180279	−	0.312253i
$941$	−3205.67	−	5552.38i	−0.111054	−	0.192351i	0.805142	−	0.593083i	$-0.202089\pi$
$941$	−3205.67	−	5552.38i	−0.111054	−	0.192351i	−0.916195	+	0.400732i	$0.868756\pi$
$942$		0			0
$943$	73167.6			2.52669
$944$	733.544	+	1270.53i	0.0252911	+	0.0438055i
$945$		0			0
$946$	−8040.05	−	13925.8i	−0.276326	−	0.478611i
$947$	−994.915	+	1723.24i	−0.0341398	+	0.0591319i	−0.882590	−	0.470143i	$-0.844202\pi$
$947$	−994.915	+	1723.24i	−0.0341398	+	0.0591319i	0.848451	+	0.529274i	$0.177536\pi$
$948$		0			0
$949$	−1617.73			−0.0553358
$950$	9169.67	−	15255.7i	0.313161	−	0.521012i
$951$		0			0
$952$	1352.82	−	2343.16i	0.0460559	−	0.0797712i
$953$	−19133.2	+	33139.7i	−0.650351	+	1.12644i	0.332686	+	0.943038i	$0.392045\pi$
$953$	−19133.2	+	33139.7i	−0.650351	+	1.12644i	−0.983038	+	0.183404i	$0.941288\pi$
$954$		0			0
$955$	5784.88	−	10019.7i	0.196015	−	0.339508i
$956$	7182.05	+	12439.7i	0.242975	+	0.420845i
$957$		0			0
$958$	3113.24			0.104994
$959$	−2833.12	−	4907.11i	−0.0953976	−	0.165234i
$960$		0			0
$961$	−9934.01			−0.333457
$962$	−2536.18			−0.0849998
$963$		0			0
$964$	7383.68	−	12788.9i	0.246693	−	0.427285i
$965$	4316.92	+	7477.12i	0.144007	+	0.249427i
$966$		0			0
$967$	−110.058	+	190.626i	−0.00366001	+	0.00633932i	−0.867850	−	0.496827i	$-0.834498\pi$
$967$	−110.058	+	190.626i	−0.00366001	+	0.00633932i	0.864190	+	0.503166i	$0.167832\pi$
$968$	−27883.2			−0.925827
$969$		0			0
$970$	3516.72			0.116407
$971$	1087.68	−	1883.91i	0.0359478	−	0.0622633i	−0.847492	−	0.530809i	$-0.821888\pi$
$971$	1087.68	−	1883.91i	0.0359478	−	0.0622633i	0.883440	+	0.468545i	$0.155222\pi$
$972$		0			0
$973$	−260.735	−	451.606i	−0.00859072	−	0.0148796i
$974$	19339.5	−	33497.0i	0.636220	−	1.10196i
$975$		0			0
$976$	3497.93			0.114719
$977$	−13707.7			−0.448872			−0.224436	−	0.974489i	$-0.572054\pi$
$977$	−13707.7			−0.448872			−0.224436	+	0.974489i	$0.572054\pi$
$978$		0			0
$979$	14775.3	+	25591.5i	0.482350	+	0.835454i
$980$	5575.81			0.181748
$981$		0			0
$982$	6838.25	+	11844.2i	0.222217	+	0.384891i
$983$	−9442.87	+	16355.5i	−0.306389	+	0.530682i	−0.977570	−	0.210612i	$-0.932454\pi$
$983$	−9442.87	+	16355.5i	−0.306389	+	0.530682i	0.671180	+	0.741294i	$0.265788\pi$
$984$		0			0
$985$	−4386.67	+	7597.93i	−0.141899	+	0.245777i
$986$	7025.05	−	12167.7i	0.226900	−	0.393002i
$987$		0			0
$988$	−1305.15	−	2355.39i	−0.0420268	−	0.0758451i
$989$	20446.8			0.657403
$990$		0			0
$991$	20327.5	−	35208.3i	0.651589	−	1.12858i	−0.331149	−	0.943579i	$-0.607436\pi$
$991$	20327.5	−	35208.3i	0.651589	−	1.12858i	0.982737	−	0.185006i	$-0.0592305\pi$
$992$	−2254.64	−	3905.15i	−0.0721621	−	0.124988i
$993$		0			0
$994$	−2830.49	−	4902.56i	−0.0903197	−	0.156438i
$995$	7192.49			0.229163
$996$		0			0
$997$	8216.65	+	14231.7i	0.261007	+	0.452077i	0.966510	−	0.256630i	$-0.0826121\pi$
$997$	8216.65	+	14231.7i	0.261007	+	0.452077i	−0.705503	+	0.708707i	$0.749279\pi$
$998$	−18115.0	−	31376.1i	−0.574569	−	0.995182i
$999$		0			0

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	342.4.g.h.163.2		6
3.2	odd	2		114.4.e.d.49.2	yes	6
19.7	even	3	inner	342.4.g.h.235.2		6
57.8	even	6		2166.4.a.t.1.2		3
57.11	odd	6		2166.4.a.u.1.2		3
57.26	odd	6		114.4.e.d.7.2	✓	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
114.4.e.d.7.2	✓	6	57.26	odd	6
114.4.e.d.49.2	yes	6	3.2	odd	2
342.4.g.h.163.2		6	1.1	even	1	trivial
342.4.g.h.235.2		6	19.7	even	3	inner
2166.4.a.t.1.2		3	57.8	even	6
2166.4.a.u.1.2		3	57.11	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:	\( N \)	\(=\)	\( 342 = 2 \cdot 3^{2} \cdot 19 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	342.g (of order \(3\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.09405 - 3.62701i) q^{5} +3.18810 q^{7} -8.00000 q^{8} +O(q^{10})\)	\(q+(1.00000 - 1.73205i) q^{2} +(-2.00000 - 3.46410i) q^{4} +(2.09405 - 3.62701i) q^{5} +3.18810 q^{7} -8.00000 q^{8} +(-4.18810 - 7.25401i) q^{10} -69.4003 q^{11} +(4.06431 + 7.03960i) q^{13} +(3.18810 - 5.52196i) q^{14} +(-8.00000 + 13.8564i) q^{16} +(-53.0418 + 91.8711i) q^{17} +(42.6656 - 70.9834i) q^{19} -16.7524 q^{20} +(-69.4003 + 120.205i) q^{22} +(-88.2468 - 152.848i) q^{23} +(53.7299 + 93.0629i) q^{25} +16.2573 q^{26} +(-6.37621 - 11.0439i) q^{28} +(-33.1109 - 57.3498i) q^{29} -140.915 q^{31} +(16.0000 + 27.7128i) q^{32} +(106.084 + 183.742i) q^{34} +(6.67606 - 11.5633i) q^{35} -156.003 q^{37} +(-80.2814 - 144.882i) q^{38} +(-16.7524 + 29.0160i) q^{40} +(-207.281 + 359.022i) q^{41} +(-57.9252 + 100.329i) q^{43} +(138.801 + 240.410i) q^{44} -352.987 q^{46} +(310.141 + 537.181i) q^{47} -332.836 q^{49} +214.920 q^{50} +(16.2573 - 28.1584i) q^{52} +(-185.993 - 322.149i) q^{53} +(-145.328 + 251.715i) q^{55} -25.5048 q^{56} -132.444 q^{58} +(45.8465 - 79.4084i) q^{59} +(-109.310 - 189.331i) q^{61} +(-140.915 + 244.072i) q^{62} +64.0000 q^{64} +34.0436 q^{65} +(72.6712 + 125.870i) q^{67} +424.334 q^{68} +(-13.3521 - 23.1265i) q^{70} +(443.915 - 768.883i) q^{71} +(-99.5081 + 172.353i) q^{73} +(-156.003 + 270.205i) q^{74} +(-331.225 - 5.83100i) q^{76} -221.255 q^{77} +(194.779 - 337.367i) q^{79} +(33.5048 + 58.0321i) q^{80} +(414.563 + 718.044i) q^{82} -380.039 q^{83} +(222.145 + 384.766i) q^{85} +(115.850 + 200.659i) q^{86} +555.202 q^{88} +(-212.899 - 368.753i) q^{89} +(12.9575 + 22.4430i) q^{91} +(-352.987 + 611.392i) q^{92} +1240.57 q^{94} +(-168.113 - 303.391i) q^{95} +(-209.923 + 363.597i) q^{97} +(-332.836 + 576.489i) q^{98} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8}+O(q^{10}) \) 6 * q + 6 * q^2 - 12 * q^4 + 10 * q^5 + 14 * q^7 - 48 * q^8	\( 6 q + 6 q^{2} - 12 q^{4} + 10 q^{5} + 14 q^{7} - 48 q^{8} - 20 q^{10} + 88 q^{11} + 9 q^{13} + 14 q^{14} - 48 q^{16} - 84 q^{17} + 32 q^{19} - 80 q^{20} + 88 q^{22} - 2 q^{23} + 83 q^{25} + 36 q^{26} - 28 q^{28} + 92 q^{29} - 218 q^{31} + 96 q^{32} + 168 q^{34} + 282 q^{35} + 490 q^{37} + 74 q^{38} - 80 q^{40} - 688 q^{41} + 103 q^{43} - 176 q^{44} - 8 q^{46} + 322 q^{47} - 1508 q^{49} + 332 q^{50} + 36 q^{52} - 1322 q^{53} + 248 q^{55} - 112 q^{56} + 368 q^{58} + 252 q^{59} + 435 q^{61} - 218 q^{62} + 384 q^{64} + 3164 q^{65} + 719 q^{67} + 672 q^{68} - 564 q^{70} - 62 q^{71} + 581 q^{73} + 490 q^{74} + 20 q^{76} + 408 q^{77} + 489 q^{79} + 160 q^{80} + 1376 q^{82} - 4992 q^{83} - 1632 q^{85} - 206 q^{86} - 704 q^{88} + 1584 q^{89} + 1573 q^{91} - 8 q^{92} + 1288 q^{94} - 2362 q^{95} - 974 q^{97} - 1508 q^{98}+O(q^{100}) \) 6 * q + 6 * q^2 - 12 * q^4 + 10 * q^5 + 14 * q^7 - 48 * q^8 - 20 * q^10 + 88 * q^11 + 9 * q^13 + 14 * q^14 - 48 * q^16 - 84 * q^17 + 32 * q^19 - 80 * q^20 + 88 * q^22 - 2 * q^23 + 83 * q^25 + 36 * q^26 - 28 * q^28 + 92 * q^29 - 218 * q^31 + 96 * q^32 + 168 * q^34 + 282 * q^35 + 490 * q^37 + 74 * q^38 - 80 * q^40 - 688 * q^41 + 103 * q^43 - 176 * q^44 - 8 * q^46 + 322 * q^47 - 1508 * q^49 + 332 * q^50 + 36 * q^52 - 1322 * q^53 + 248 * q^55 - 112 * q^56 + 368 * q^58 + 252 * q^59 + 435 * q^61 - 218 * q^62 + 384 * q^64 + 3164 * q^65 + 719 * q^67 + 672 * q^68 - 564 * q^70 - 62 * q^71 + 581 * q^73 + 490 * q^74 + 20 * q^76 + 408 * q^77 + 489 * q^79 + 160 * q^80 + 1376 * q^82 - 4992 * q^83 - 1632 * q^85 - 206 * q^86 - 704 * q^88 + 1584 * q^89 + 1573 * q^91 - 8 * q^92 + 1288 * q^94 - 2362 * q^95 - 974 * q^97 - 1508 * q^98

Introduction

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