LMFDB - Embedded newform 392.3.h.a.293.2

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [392,3,Mod(293,392)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(392, base_ring=CyclotomicField(2))

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

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

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

chi := DirichletCharacter("392.293");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 392 = 2^{3} \cdot 7^{2} $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	392.h (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$10.6812263629$
Analytic rank:	$0$
Dimension:	$28$
Twist minimal:	no (minimal twist has level 56)
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			293.2
Character	$\chi$	$=$	392.293
Dual form			392.3.h.a.293.4

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-1.95479 - 0.422821i) q^{2} +3.86988 q^{3} +(3.64244 + 1.65306i) q^{4} +4.67764 q^{5} +(-7.56482 - 1.63627i) q^{6} +(-6.42128 - 4.77149i) q^{8} +5.97596 q^{9} +O(q^{10})$	\(q+(-1.95479 - 0.422821i) q^{2} +3.86988 q^{3} +(3.64244 + 1.65306i) q^{4} +4.67764 q^{5} +(-7.56482 - 1.63627i) q^{6} +(-6.42128 - 4.77149i) q^{8} +5.97596 q^{9} +(-9.14383 - 1.97781i) q^{10} +14.5934i q^{11} +(14.0958 + 6.39713i) q^{12} +12.7102 q^{13} +18.1019 q^{15} +(10.5348 + 12.0423i) q^{16} -19.5223i q^{17} +(-11.6818 - 2.52677i) q^{18} +17.7247 q^{19} +(17.0380 + 7.73241i) q^{20} +(6.17041 - 28.5271i) q^{22} +8.86075 q^{23} +(-24.8496 - 18.4651i) q^{24} -3.11968 q^{25} +(-24.8458 - 5.37413i) q^{26} -11.7027 q^{27} +35.4981i q^{29} +(-35.3855 - 7.65387i) q^{30} +29.0213i q^{31} +(-15.5016 - 27.9946i) q^{32} +56.4747i q^{33} +(-8.25445 + 38.1621i) q^{34} +(21.7671 + 9.87861i) q^{36} -12.2169i q^{37} +(-34.6481 - 7.49437i) q^{38} +49.1868 q^{39} +(-30.0364 - 22.3193i) q^{40} -22.0903i q^{41} -79.8001i q^{43} +(-24.1238 + 53.1557i) q^{44} +27.9534 q^{45} +(-17.3210 - 3.74652i) q^{46} +42.1513i q^{47} +(40.7684 + 46.6024i) q^{48} +(6.09833 + 1.31907i) q^{50} -75.5490i q^{51} +(46.2961 + 21.0106i) q^{52} -36.1532i q^{53} +(22.8763 + 4.94813i) q^{54} +68.2627i q^{55} +68.5923 q^{57} +(15.0093 - 69.3915i) q^{58} -2.40696 q^{59} +(65.9352 + 29.9235i) q^{60} +29.2449 q^{61} +(12.2708 - 56.7306i) q^{62} +(18.4657 + 61.2782i) q^{64} +59.4536 q^{65} +(23.8787 - 110.397i) q^{66} -40.6804i q^{67} +(32.2715 - 71.1089i) q^{68} +34.2900 q^{69} -22.6174 q^{71} +(-38.3733 - 28.5143i) q^{72} +76.3935i q^{73} +(-5.16559 + 23.8816i) q^{74} -12.0728 q^{75} +(64.5611 + 29.2999i) q^{76} +(-96.1501 - 20.7972i) q^{78} +136.803 q^{79} +(49.2780 + 56.3298i) q^{80} -99.0715 q^{81} +(-9.34025 + 43.1820i) q^{82} -49.9942 q^{83} -91.3184i q^{85} +(-33.7412 + 155.993i) q^{86} +137.373i q^{87} +(69.6324 - 93.7084i) q^{88} -1.12009i q^{89} +(-54.6432 - 11.8193i) q^{90} +(32.2748 + 14.6473i) q^{92} +112.309i q^{93} +(17.8225 - 82.3971i) q^{94} +82.9096 q^{95} +(-59.9893 - 108.336i) q^{96} -158.827i q^{97} +87.2097i q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9}+O(q^{10}) $ 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9	$ 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9} + 28 q^{15} - 32 q^{16} + 84 q^{18} - 92 q^{22} - 60 q^{23} + 64 q^{25} - 44 q^{30} - 176 q^{32} + 256 q^{36} + 40 q^{39} + 84 q^{44} - 136 q^{46} + 400 q^{50} + 124 q^{57} + 44 q^{58} + 124 q^{60} - 520 q^{64} + 104 q^{65} - 136 q^{71} - 192 q^{72} + 276 q^{74} - 956 q^{78} + 324 q^{79} + 36 q^{81} - 336 q^{86} - 100 q^{88} + 1020 q^{92} - 580 q^{95}+O(q^{100}) $ 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9 + 28 * q^15 - 32 * q^16 + 84 * q^18 - 92 * q^22 - 60 * q^23 + 64 * q^25 - 44 * q^30 - 176 * q^32 + 256 * q^36 + 40 * q^39 + 84 * q^44 - 136 * q^46 + 400 * q^50 + 124 * q^57 + 44 * q^58 + 124 * q^60 - 520 * q^64 + 104 * q^65 - 136 * q^71 - 192 * q^72 + 276 * q^74 - 956 * q^78 + 324 * q^79 + 36 * q^81 - 336 * q^86 - 100 * q^88 + 1020 * q^92 - 580 * q^95

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/392\mathbb{Z}\right)^\times$.

$n$	$197$	$295$	$297$
$\chi(n)$	$-1$	$1$	$-1$

Coefficient data

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

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

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

$2$	−1.95479	−	0.422821i	−0.977397	−	0.211411i
$2$	−1.95479	−	0.422821i	−0.977397	−	0.211411i
$3$	3.86988			1.28996			0.644980	−	0.764200i	$-0.276866\pi$
$3$	3.86988			1.28996			0.644980	+	0.764200i	$0.276866\pi$
$4$	3.64244	+	1.65306i	0.910611	+	0.413265i
$5$	4.67764			0.935528			0.467764	−	0.883853i	$-0.345060\pi$
$5$	4.67764			0.935528			0.467764	+	0.883853i	$0.345060\pi$
$6$	−7.56482	−	1.63627i	−1.26080	−	0.272711i
$7$		0			0
$7$		0			0
$8$	−6.42128	−	4.77149i	−0.802660	−	0.596437i
$9$	5.97596			0.663996
$10$	−9.14383	−	1.97781i	−0.914383	−	0.197781i
$11$			14.5934i			1.32667i	0.748321	+	0.663337i	$0.230860\pi$
$11$			14.5934i			1.32667i	−0.748321	+	0.663337i	$0.769140\pi$
$12$	14.0958	+	6.39713i	1.17465	+	0.533095i
$13$	12.7102			0.977705			0.488853	−	0.872366i	$-0.337416\pi$
$13$	12.7102			0.977705			0.488853	+	0.872366i	$0.337416\pi$
$14$		0			0
$15$	18.1019			1.20679
$16$	10.5348	+	12.0423i	0.658425	+	0.752646i
$17$		−	19.5223i		−	1.14837i	−0.818725	−	0.574186i	$-0.805319\pi$
$17$		−	19.5223i		−	1.14837i	0.818725	−	0.574186i	$-0.194681\pi$
$18$	−11.6818	−	2.52677i	−0.648988	−	0.140376i
$19$	17.7247			0.932877			0.466439	−	0.884554i	$-0.345537\pi$
$19$	17.7247			0.932877			0.466439	+	0.884554i	$0.345537\pi$
$20$	17.0380	+	7.73241i	0.851902	+	0.386621i
$21$		0			0
$22$	6.17041	−	28.5271i	0.280473	−	1.29669i
$23$	8.86075			0.385250			0.192625	−	0.981272i	$-0.438300\pi$
$23$	8.86075			0.385250			0.192625	+	0.981272i	$0.438300\pi$
$24$	−24.8496	−	18.4651i	−1.03540	−	0.769379i
$25$	−3.11968			−0.124787
$26$	−24.8458	−	5.37413i	−0.955606	−	0.206697i
$27$	−11.7027			−0.433432
$28$		0			0
$29$			35.4981i			1.22407i	0.790830	+	0.612036i	$0.209649\pi$
$29$			35.4981i			1.22407i	−0.790830	+	0.612036i	$0.790351\pi$
$30$	−35.3855	−	7.65387i	−1.17952	−	0.255129i
$31$			29.0213i			0.936170i	0.883684	+	0.468085i	$0.155056\pi$
$31$			29.0213i			0.936170i	−0.883684	+	0.468085i	$0.844944\pi$
$32$	−15.5016	−	27.9946i	−0.484425	−	0.874833i
$33$			56.4747i			1.71136i
$34$	−8.25445	+	38.1621i	−0.242778	+	1.12242i
$35$		0			0
$36$	21.7671	+	9.87861i	0.604642	+	0.274406i
$37$		−	12.2169i		−	0.330188i	−0.986278	−	0.165094i	$-0.947207\pi$
$37$		−	12.2169i		−	0.330188i	0.986278	−	0.165094i	$-0.0527927\pi$
$38$	−34.6481	−	7.49437i	−0.911792	−	0.197220i
$39$	49.1868			1.26120
$40$	−30.0364	−	22.3193i	−0.750911	−	0.557983i
$41$		−	22.0903i		−	0.538788i	−0.963030	−	0.269394i	$-0.913177\pi$
$41$		−	22.0903i		−	0.538788i	0.963030	−	0.269394i	$-0.0868233\pi$
$42$		0			0
$43$		−	79.8001i		−	1.85582i	−0.372809	−	0.927908i	$-0.621605\pi$
$43$		−	79.8001i		−	1.85582i	0.372809	−	0.927908i	$-0.378395\pi$
$44$	−24.1238	+	53.1557i	−0.548267	+	1.20808i
$45$	27.9534			0.621187
$46$	−17.3210	−	3.74652i	−0.376542	−	0.0814460i
$47$			42.1513i			0.896836i	0.893824	+	0.448418i	$0.148012\pi$
$47$			42.1513i			0.896836i	−0.893824	+	0.448418i	$0.851988\pi$
$48$	40.7684	+	46.6024i	0.849342	+	0.970884i
$49$		0			0
$50$	6.09833	+	1.31907i	0.121967	+	0.0263813i
$51$		−	75.5490i		−	1.48135i
$52$	46.2961	+	21.0106i	0.890309	+	0.404051i
$53$		−	36.1532i		−	0.682137i	−0.940039	−	0.341068i	$-0.889211\pi$
$53$		−	36.1532i		−	0.682137i	0.940039	−	0.341068i	$-0.110789\pi$
$54$	22.8763	+	4.94813i	0.423635	+	0.0916321i
$55$			68.2627i			1.24114i
$56$		0			0
$57$	68.5923			1.20337
$58$	15.0093	−	69.3915i	0.258782	−	1.19640i
$59$	−2.40696			−0.0407959			−0.0203979	−	0.999792i	$-0.506493\pi$
$59$	−2.40696			−0.0407959			−0.0203979	+	0.999792i	$0.506493\pi$
$60$	65.9352	+	29.9235i	1.09892	+	0.498725i
$61$	29.2449			0.479424			0.239712	−	0.970844i	$-0.422947\pi$
$61$	29.2449			0.479424			0.239712	+	0.970844i	$0.422947\pi$
$62$	12.2708	−	56.7306i	0.197916	−	0.915010i
$63$		0			0
$64$	18.4657	+	61.2782i	0.288527	+	0.957472i
$65$	59.4536			0.914671
$66$	23.8787	−	110.397i	0.361799	−	1.67267i
$67$		−	40.6804i		−	0.607170i	−0.952804	−	0.303585i	$-0.901816\pi$
$67$		−	40.6804i		−	0.607170i	0.952804	−	0.303585i	$-0.0981837\pi$
$68$	32.2715	−	71.1089i	0.474581	−	1.04572i
$69$	34.2900			0.496957
$70$		0			0
$71$	−22.6174			−0.318554			−0.159277	−	0.987234i	$-0.550916\pi$
$71$	−22.6174			−0.318554			−0.159277	+	0.987234i	$0.550916\pi$
$72$	−38.3733	−	28.5143i	−0.532963	−	0.396031i
$73$			76.3935i			1.04649i	0.852184	+	0.523243i	$0.175278\pi$
$73$			76.3935i			1.04649i	−0.852184	+	0.523243i	$0.824722\pi$
$74$	−5.16559	+	23.8816i	−0.0698052	+	0.322725i
$75$	−12.0728			−0.160970
$76$	64.5611	+	29.2999i	0.849488	+	0.385525i
$77$		0			0
$78$	−96.1501	−	20.7972i	−1.23269	−	0.266631i
$79$	136.803			1.73168			0.865840	−	0.500321i	$-0.166785\pi$
$79$	136.803			1.73168			0.865840	+	0.500321i	$0.166785\pi$
$80$	49.2780	+	56.3298i	0.615975	+	0.704122i
$81$	−99.0715			−1.22311
$82$	−9.34025	+	43.1820i	−0.113906	+	0.526610i
$83$	−49.9942			−0.602340			−0.301170	−	0.953571i	$-0.597377\pi$
$83$	−49.9942			−0.602340			−0.301170	+	0.953571i	$0.597377\pi$
$84$		0			0
$85$		−	91.3184i		−	1.07433i
$86$	−33.7412	+	155.993i	−0.392339	+	1.81387i
$87$			137.373i			1.57900i
$88$	69.6324	−	93.7084i	0.791277	−	1.06487i
$89$		−	1.12009i		−	0.0125852i	−0.999980	−	0.00629262i	$-0.997997\pi$
$89$		−	1.12009i		−	0.0125852i	0.999980	−	0.00629262i	$-0.00200302\pi$
$90$	−54.6432	−	11.8193i	−0.607146	−	0.131326i
$91$		0			0
$92$	32.2748	+	14.6473i	0.350813	+	0.159210i
$93$			112.309i			1.20762i
$94$	17.8225	−	82.3971i	0.189601	−	0.876565i
$95$	82.9096			0.872733
$96$	−59.9893	−	108.336i	−0.624889	−	1.12850i
$97$		−	158.827i		−	1.63740i	−0.574225	−	0.818698i	$-0.694696\pi$
$97$		−	158.827i		−	1.63740i	0.574225	−	0.818698i	$-0.305304\pi$
$98$		0			0
$99$			87.2097i			0.880906i
$100$	−11.3633	−	5.15701i	−0.113633	−	0.0515701i
$101$	−69.6244			−0.689350			−0.344675	−	0.938722i	$-0.612011\pi$
$101$	−69.6244			−0.689350			−0.344675	+	0.938722i	$0.612011\pi$
$102$	−31.9437	+	147.683i	−0.313174	+	1.44787i
$103$		−	19.6197i		−	0.190482i	−0.995454	−	0.0952411i	$-0.969638\pi$
$103$		−	19.6197i		−	0.190482i	0.995454	−	0.0952411i	$-0.0303622\pi$
$104$	−81.6156	−	60.6465i	−0.784765	−	0.583139i
$105$		0			0
$106$	−15.2864	+	70.6722i	−0.144211	+	0.666718i
$107$			44.7493i			0.418218i	0.977892	+	0.209109i	$0.0670563\pi$
$107$			44.7493i			0.418218i	−0.977892	+	0.209109i	$0.932944\pi$
$108$	−42.6263	−	19.3452i	−0.394688	−	0.179122i
$109$			56.6045i			0.519308i	0.965702	+	0.259654i	$0.0836084\pi$
$109$			56.6045i			0.519308i	−0.965702	+	0.259654i	$0.916392\pi$
$110$	28.8629	−	133.440i	0.262390	−	1.21309i
$111$		−	47.2781i		−	0.425929i
$112$		0			0
$113$	−188.632			−1.66931			−0.834657	−	0.550770i	$-0.814334\pi$
$113$	−188.632			−1.66931			−0.834657	+	0.550770i	$0.814334\pi$
$114$	−134.084	−	29.0023i	−1.17617	−	0.254406i
$115$	41.4474			0.360412
$116$	−58.6804	+	129.300i	−0.505865	+	1.11465i
$117$	75.9555			0.649192
$118$	4.70511	+	1.01771i	0.0398738	+	0.00862469i
$119$		0			0
$120$	−116.237	−	86.3731i	−0.968645	−	0.719776i
$121$	−91.9677			−0.760063
$122$	−57.1678	−	12.3654i	−0.468588	−	0.101355i
$123$		−	85.4868i		−	0.695014i
$124$	−47.9738	+	105.708i	−0.386886	+	0.852486i
$125$	−131.534			−1.05227
$126$		0			0
$127$	45.8547			0.361060			0.180530	−	0.983569i	$-0.442219\pi$
$127$	45.8547			0.361060			0.180530	+	0.983569i	$0.442219\pi$
$128$	−10.1870	−	127.594i	−0.0795856	−	0.996828i
$129$		−	308.817i		−	2.39393i
$130$	−116.220	−	25.1383i	−0.893997	−	0.193371i
$131$	−120.996			−0.923637			−0.461818	−	0.886975i	$-0.652803\pi$
$131$	−120.996			−0.923637			−0.461818	+	0.886975i	$0.652803\pi$
$132$	−93.3560	+	205.706i	−0.707243	+	1.55838i
$133$		0			0
$134$	−17.2006	+	79.5219i	−0.128362	+	0.593447i
$135$	−54.7408			−0.405488
$136$	−93.1506	+	125.358i	−0.684931	+	0.921752i
$137$	−145.241			−1.06016			−0.530078	−	0.847949i	$-0.677837\pi$
$137$	−145.241			−1.06016			−0.530078	+	0.847949i	$0.677837\pi$
$138$	−67.0300	−	14.4986i	−0.485725	−	0.105062i
$139$	86.3503			0.621225			0.310613	−	0.950537i	$-0.399466\pi$
$139$	86.3503			0.621225			0.310613	+	0.950537i	$0.399466\pi$
$140$		0			0
$141$			163.120i			1.15688i
$142$	44.2123	+	9.56311i	0.311354	+	0.0673458i
$143$			185.485i			1.29710i
$144$	62.9556	+	71.9646i	0.437191	+	0.499754i
$145$			166.047i			1.14515i
$146$	32.3008	−	149.334i	0.221238	−	1.02283i
$147$		0			0
$148$	20.1953	−	44.4996i	0.136455	−	0.300673i
$149$		−	218.857i		−	1.46884i	−0.678695	−	0.734421i	$-0.737454\pi$
$149$		−	218.857i		−	1.46884i	0.678695	−	0.734421i	$-0.262546\pi$
$150$	23.5998	+	5.10463i	0.157332	+	0.0340309i
$151$	83.3104			0.551725			0.275862	−	0.961197i	$-0.411037\pi$
$151$	83.3104			0.551725			0.275862	+	0.961197i	$0.411037\pi$
$152$	−113.815	−	84.5731i	−0.748783	−	0.556402i
$153$		−	116.665i		−	0.762514i
$154$		0			0
$155$			135.751i			0.875813i
$156$	179.160	+	81.3087i	1.14846	+	0.521209i
$157$	35.4415			0.225742			0.112871	−	0.993610i	$-0.463995\pi$
$157$	35.4415			0.225742			0.112871	+	0.993610i	$0.463995\pi$
$158$	−267.421	−	57.8431i	−1.69254	−	0.366096i
$159$		−	139.909i		−	0.879929i
$160$	−72.5109	−	130.949i	−0.453193	−	0.818431i
$161$		0			0
$162$	193.664	+	41.8896i	1.19546	+	0.258578i
$163$			10.4548i			0.0641399i	0.999486	+	0.0320699i	$0.0102099\pi$
$163$			10.4548i			0.0641399i	−0.999486	+	0.0320699i	$0.989790\pi$
$164$	36.5165	−	80.4627i	0.222662	−	0.490626i
$165$			264.169i			1.60102i
$166$	97.7284	+	21.1386i	0.588725	+	0.127341i
$167$			78.8843i			0.472361i	0.971709	+	0.236181i	$0.0758957\pi$
$167$			78.8843i			0.472361i	−0.971709	+	0.236181i	$0.924104\pi$
$168$		0			0
$169$	−7.45163			−0.0440925
$170$	−38.6114	+	178.509i	−0.227126	+	1.05005i
$171$	105.922			0.619427
$172$	131.914	−	290.667i	0.766943	−	1.68993i
$173$	−191.842			−1.10891			−0.554456	−	0.832213i	$-0.687073\pi$
$173$	−191.842			−1.10891			−0.554456	+	0.832213i	$0.687073\pi$
$174$	58.0844	−	268.537i	0.333818	−	1.54331i
$175$		0			0
$176$	−175.739	+	153.739i	−0.998516	+	0.873515i
$177$	−9.31463			−0.0526250
$178$	−0.473596	+	2.18954i	−0.00266065	+	0.0123008i
$179$			69.9086i			0.390551i	0.980748	+	0.195275i	$0.0625601\pi$
$179$			69.9086i			0.390551i	−0.980748	+	0.195275i	$0.937440\pi$
$180$	101.819	+	46.2086i	0.565660	+	0.256714i
$181$	−343.635			−1.89853			−0.949267	−	0.314472i	$-0.898173\pi$
$181$	−343.635			−1.89853			−0.949267	+	0.314472i	$0.898173\pi$
$182$		0			0
$183$	113.174			0.618438
$184$	−56.8974	−	42.2790i	−0.309225	−	0.229777i
$185$		−	57.1465i		−	0.308900i
$186$	47.4865	−	219.541i	0.255304	−	1.18033i
$187$	284.897			1.52351
$188$	−69.6785	+	153.534i	−0.370630	+	0.816668i
$189$		0			0
$190$	−162.071	−	35.0560i	−0.853007	−	0.184505i
$191$	−139.779			−0.731827			−0.365913	−	0.930649i	$-0.619243\pi$
$191$	−139.779			−0.731827			−0.365913	+	0.930649i	$0.619243\pi$
$192$	71.4601	+	237.139i	0.372188	+	1.23510i
$193$	22.9233			0.118773			0.0593867	−	0.998235i	$-0.481086\pi$
$193$	22.9233			0.118773			0.0593867	+	0.998235i	$0.481086\pi$
$194$	−67.1556	+	310.475i	−0.346163	+	1.60039i
$195$	230.078			1.17989
$196$		0			0
$197$		−	287.788i		−	1.46085i	−0.682992	−	0.730426i	$-0.739322\pi$
$197$		−	287.788i		−	1.46085i	0.682992	−	0.730426i	$-0.260678\pi$
$198$	36.8741	−	170.477i	0.186233	−	0.860995i
$199$		−	65.4821i		−	0.329056i	−0.986372	−	0.164528i	$-0.947390\pi$
$199$		−	65.4821i		−	0.329056i	0.986372	−	0.164528i	$-0.0526100\pi$
$200$	20.0323	+	14.8855i	0.100162	+	0.0744276i
$201$		−	157.428i		−	0.783225i
$202$	136.101	+	29.4387i	0.673769	+	0.145736i
$203$		0			0
$204$	124.887	−	275.183i	0.612191	−	1.34894i
$205$		−	103.330i		−	0.504051i
$206$	−8.29561	+	38.3524i	−0.0402700	+	0.186177i
$207$	52.9515			0.255805
$208$	133.899	+	153.060i	0.643745	+	0.735866i
$209$			258.663i			1.23762i
$210$		0			0
$211$		−	17.8985i		−	0.0848270i	−0.999100	−	0.0424135i	$-0.986495\pi$
$211$		−	17.8985i		−	0.0848270i	0.999100	−	0.0424135i	$-0.0135047\pi$
$212$	59.7634	−	131.686i	0.281903	−	0.621161i
$213$	−87.5265			−0.410922
$214$	18.9210	−	87.4757i	0.0884158	−	0.408765i
$215$		−	373.276i		−	1.73617i
$216$	75.1461	+	55.8391i	0.347898	+	0.258515i
$217$		0			0
$218$	23.9336	−	110.650i	0.109787	−	0.507570i
$219$			295.633i			1.34992i
$220$	−112.842	+	248.643i	−0.512919	+	1.13020i
$221$		−	248.132i		−	1.12277i
$222$	−19.9902	+	92.4190i	−0.0900459	+	0.416302i
$223$			258.973i			1.16132i	0.814148	+	0.580658i	$0.197205\pi$
$223$			258.973i			1.16132i	−0.814148	+	0.580658i	$0.802795\pi$
$224$		0			0
$225$	−18.6431			−0.0828581
$226$	368.738	+	79.7578i	1.63158	+	0.352911i
$227$	117.344			0.516935			0.258468	−	0.966020i	$-0.416782\pi$
$227$	117.344			0.516935			0.258468	+	0.966020i	$0.416782\pi$
$228$	249.844	+	113.387i	1.09581	+	0.497312i
$229$	−87.0949			−0.380327			−0.190164	−	0.981752i	$-0.560902\pi$
$229$	−87.0949			−0.380327			−0.190164	+	0.981752i	$0.560902\pi$
$230$	−81.0212	−	17.5249i	−0.352266	−	0.0761950i
$231$		0			0
$232$	169.379	−	227.943i	0.730081	−	0.982514i
$233$	−311.651			−1.33756			−0.668778	−	0.743462i	$-0.733183\pi$
$233$	−311.651			−1.33756			−0.668778	+	0.743462i	$0.733183\pi$
$234$	−148.477	−	32.1156i	−0.634519	−	0.137246i
$235$			197.169i			0.839015i
$236$	−8.76721	−	3.97884i	−0.0371492	−	0.0168595i
$237$	529.410			2.23380
$238$		0			0
$239$	−140.823			−0.589218			−0.294609	−	0.955618i	$-0.595189\pi$
$239$	−140.823			−0.589218			−0.294609	+	0.955618i	$0.595189\pi$
$240$	190.700	+	217.989i	0.794583	+	0.908289i
$241$		−	48.0871i		−	0.199532i	−0.995011	−	0.0997658i	$-0.968191\pi$
$241$		−	48.0871i		−	0.199532i	0.995011	−	0.0997658i	$-0.0318094\pi$
$242$	179.778	+	38.8859i	0.742884	+	0.160686i
$243$	−278.071			−1.14432
$244$	106.523	+	48.3435i	0.436569	+	0.198129i
$245$		0			0
$246$	−36.1456	+	167.109i	−0.146934	+	0.679305i
$247$	225.283			0.912079
$248$	138.475	−	186.354i	0.558366	−	0.751426i
$249$	−193.471			−0.776994
$250$	257.121	+	55.6153i	1.02849	+	0.222461i
$251$	152.080			0.605895			0.302947	−	0.953007i	$-0.402029\pi$
$251$	152.080			0.605895			0.302947	+	0.953007i	$0.402029\pi$
$252$		0			0
$253$			129.309i			0.511101i
$254$	−89.6364	−	19.3883i	−0.352899	−	0.0763320i
$255$		−	353.391i		−	1.38585i
$256$	−34.0361	+	253.727i	−0.132953	+	0.991122i
$257$		−	145.669i		−	0.566807i	−0.959001	−	0.283403i	$-0.908536\pi$
$257$		−	145.669i		−	0.566807i	0.959001	−	0.283403i	$-0.0914635\pi$
$258$	−130.574	+	603.673i	−0.506102	+	2.33982i
$259$		0			0
$260$	216.556	+	98.2803i	0.832909	+	0.378001i
$261$			212.135i			0.812779i
$262$	236.523	+	51.1599i	0.902760	+	0.195267i
$263$	353.393			1.34370			0.671850	−	0.740688i	$-0.265500\pi$
$263$	353.393			1.34370			0.671850	+	0.740688i	$0.265500\pi$
$264$	269.469	−	362.640i	1.02072	−	1.37364i
$265$		−	169.112i		−	0.638158i
$266$		0			0
$267$		−	4.33460i		−	0.0162345i
$268$	67.2471	−	148.176i	0.250922	−	0.552896i
$269$	−133.298			−0.495532			−0.247766	−	0.968820i	$-0.579696\pi$
$269$	−133.298			−0.495532			−0.247766	+	0.968820i	$0.579696\pi$
$270$	107.007	+	23.1456i	0.396322	+	0.0857244i
$271$			376.827i			1.39051i	0.718765	+	0.695253i	$0.244708\pi$
$271$			376.827i			1.39051i	−0.718765	+	0.695253i	$0.755292\pi$
$272$	235.094	−	205.664i	0.864318	−	0.756116i
$273$		0			0
$274$	283.917	+	61.4112i	1.03619	+	0.224128i
$275$		−	45.5267i		−	0.165552i
$276$	124.900	+	56.6834i	0.452535	+	0.205375i
$277$		−	77.9178i		−	0.281292i	−0.990060	−	0.140646i	$-0.955082\pi$
$277$		−	77.9178i		−	0.281292i	0.990060	−	0.140646i	$-0.0449179\pi$
$278$	−168.797	−	36.5108i	−0.607184	−	0.131334i
$279$			173.430i			0.621613i
$280$		0			0
$281$	324.564			1.15503			0.577516	−	0.816380i	$-0.304022\pi$
$281$	324.564			1.15503			0.577516	+	0.816380i	$0.304022\pi$
$282$	68.9708	−	318.867i	0.244577	−	1.13073i
$283$	−299.482			−1.05824			−0.529119	−	0.848547i	$-0.677478\pi$
$283$	−299.482			−1.05824			−0.529119	+	0.848547i	$0.677478\pi$
$284$	−82.3825	−	37.3878i	−0.290079	−	0.131647i
$285$	320.850			1.12579
$286$	78.4269	−	362.585i	0.274220	−	1.26778i
$287$		0			0
$288$	−92.6370	−	167.295i	−0.321656	−	0.580885i
$289$	−92.1208			−0.318757
$290$	70.2083	−	324.588i	0.242098	−	1.11927i
$291$		−	614.643i		−	2.11217i
$292$	−126.283	+	278.259i	−0.432475	+	0.952941i
$293$	−81.7250			−0.278925			−0.139463	−	0.990227i	$-0.544537\pi$
$293$	−81.7250			−0.278925			−0.139463	+	0.990227i	$0.544537\pi$
$294$		0			0
$295$	−11.2589			−0.0381657
$296$	−58.2931	+	78.4485i	−0.196936	+	0.265029i
$297$		−	170.782i		−	0.575022i
$298$	−92.5376	+	427.821i	−0.310529	+	1.43564i
$299$	112.622			0.376661
$300$	−43.9744	−	19.9570i	−0.146581	−	0.0665233i
$301$		0			0
$302$	−162.855	−	35.2254i	−0.539254	−	0.116641i
$303$	−269.438			−0.889234
$304$	186.726	+	213.447i	0.614230	+	0.702127i
$305$	136.797			0.448515
$306$	−49.3283	+	228.055i	−0.161204	+	0.745279i
$307$	−361.930			−1.17892			−0.589462	−	0.807796i	$-0.700660\pi$
$307$	−361.930			−1.17892			−0.589462	+	0.807796i	$0.700660\pi$
$308$		0			0
$309$		−	75.9257i		−	0.245714i
$310$	57.3984	−	265.365i	0.185156	−	0.856017i
$311$			188.803i			0.607085i	0.952818	+	0.303542i	$0.0981694\pi$
$311$			188.803i			0.607085i	−0.952818	+	0.303542i	$0.901831\pi$
$312$	−315.842	−	234.694i	−1.01232	−	0.752226i
$313$			25.6878i			0.0820697i	0.999158	+	0.0410349i	$0.0130655\pi$
$313$			25.6878i			0.0820697i	−0.999158	+	0.0410349i	$0.986935\pi$
$314$	−69.2808	−	14.9854i	−0.220639	−	0.0477242i
$315$		0			0
$316$	498.296	+	226.143i	1.57689	+	0.715642i
$317$			499.128i			1.57454i	0.616611	+	0.787268i	$0.288505\pi$
$317$			499.128i			1.57454i	−0.616611	+	0.787268i	$0.711495\pi$
$318$	−59.1564	+	273.493i	−0.186026	+	0.860040i
$319$	−518.038			−1.62394
$320$	86.3760	+	286.637i	0.269925	+	0.895742i
$321$			173.174i			0.539484i
$322$		0			0
$323$		−	346.027i		−	1.07129i
$324$	−360.863	−	163.771i	−1.11377	−	0.505466i
$325$	−39.6516			−0.122005
$326$	4.42051	−	20.4370i	0.0135599	−	0.0626901i
$327$			219.053i			0.669886i
$328$	−105.404	+	141.848i	−0.321353	+	0.432464i
$329$		0			0
$330$	111.696	−	516.395i	0.338473	−	1.56483i
$331$		−	249.859i		−	0.754861i	−0.926038	−	0.377431i	$-0.876808\pi$
$331$		−	249.859i		−	0.754861i	0.926038	−	0.377431i	$-0.123192\pi$
$332$	−182.101	−	82.6433i	−0.548497	−	0.248926i
$333$		−	73.0080i		−	0.219243i
$334$	33.3540	−	154.203i	0.0998622	−	0.461685i
$335$		−	190.288i		−	0.568025i
$336$		0			0
$337$	−84.4039			−0.250457			−0.125228	−	0.992128i	$-0.539966\pi$
$337$	−84.4039			−0.250457			−0.125228	+	0.992128i	$0.539966\pi$
$338$	14.5664	+	3.15071i	0.0430959	+	0.00932163i
$339$	−729.985			−2.15335
$340$	150.955	−	332.622i	0.443984	−	0.978300i
$341$	−423.519			−1.24199
$342$	−207.056	−	44.7861i	−0.605426	−	0.130953i
$343$		0			0
$344$	−380.766	+	512.419i	−1.10688	+	1.48959i
$345$	160.396			0.464917
$346$	375.011	+	81.1148i	1.08385	+	0.234436i
$347$			377.249i			1.08717i	0.839354	+	0.543586i	$0.182934\pi$
$347$			377.249i			1.08717i	−0.839354	+	0.543586i	$0.817066\pi$
$348$	−227.086	+	500.374i	−0.652546	+	1.43786i
$349$	400.193			1.14668			0.573342	−	0.819316i	$-0.305647\pi$
$349$	400.193			1.14668			0.573342	+	0.819316i	$0.305647\pi$
$350$		0			0
$351$	−148.743			−0.423768
$352$	408.537	−	226.221i	1.16062	−	0.642674i
$353$			295.942i			0.838363i	0.907903	+	0.419181i	$0.137683\pi$
$353$			295.942i			0.838363i	−0.907903	+	0.419181i	$0.862317\pi$
$354$	18.2082	+	3.93843i	0.0514356	+	0.0111255i
$355$	−105.796			−0.298017
$356$	1.85157	−	4.07985i	0.00520103	−	0.0114603i
$357$		0			0
$358$	29.5588	−	136.657i	0.0825666	−	0.381723i
$359$	−205.174			−0.571515			−0.285757	−	0.958302i	$-0.592245\pi$
$359$	−205.174			−0.571515			−0.285757	+	0.958302i	$0.592245\pi$
$360$	−179.497	−	133.379i	−0.498602	−	0.370499i
$361$	−46.8362			−0.129740
$362$	671.735	+	145.296i	1.85562	+	0.401370i
$363$	−355.904			−0.980451
$364$		0			0
$365$			357.341i			0.979017i
$366$	−221.232	−	47.8525i	−0.604460	−	0.130744i
$367$		−	353.588i		−	0.963456i	−0.876321	−	0.481728i	$-0.840009\pi$
$367$		−	353.588i		−	0.963456i	0.876321	−	0.481728i	$-0.159991\pi$
$368$	93.3462	+	106.704i	0.253658	+	0.289957i
$369$		−	132.011i		−	0.357753i
$370$	−24.1628	+	111.710i	−0.0653048	+	0.301918i
$371$		0			0
$372$	−185.653	+	409.078i	−0.499067	+	1.09967i
$373$		−	358.028i		−	0.959862i	−0.877306	−	0.479931i	$-0.840662\pi$
$373$		−	358.028i		−	0.959862i	0.877306	−	0.479931i	$-0.159338\pi$
$374$	−556.915	−	120.461i	−1.48908	−	0.322087i
$375$	−509.020			−1.35739
$376$	201.124	−	270.665i	0.534906	−	0.719854i
$377$			451.187i			1.19678i
$378$		0			0
$379$		−	514.679i		−	1.35799i	−0.734142	−	0.678996i	$-0.762415\pi$
$379$		−	514.679i		−	1.35799i	0.734142	−	0.678996i	$-0.237585\pi$
$380$	301.994	+	137.054i	0.794720	+	0.360670i
$381$	177.452			0.465753
$382$	273.239	+	59.1015i	0.715286	+	0.154716i
$383$		−	519.838i		−	1.35728i	−0.734472	−	0.678639i	$-0.762570\pi$
$383$		−	519.838i		−	1.35728i	0.734472	−	0.678639i	$-0.237430\pi$
$384$	−39.4223	−	493.773i	−0.102662	−	1.28587i
$385$		0			0
$386$	−44.8103	−	9.69244i	−0.116089	−	0.0251100i
$387$		−	476.882i		−	1.23225i
$388$	262.551	−	578.520i	0.676677	−	1.49103i
$389$			105.456i			0.271096i	0.990771	+	0.135548i	$0.0432795\pi$
$389$			105.456i			0.271096i	−0.990771	+	0.135548i	$0.956721\pi$
$390$	−449.756	−	97.2820i	−1.15322	−	0.249441i
$391$		−	172.982i		−	0.442410i
$392$		0			0
$393$	−468.241			−1.19145
$394$	−121.683	+	562.566i	−0.308840	+	1.42783i
$395$	639.914			1.62004
$396$	−144.163	+	317.656i	−0.364047	+	0.802163i
$397$	371.524			0.935828			0.467914	−	0.883774i	$-0.345006\pi$
$397$	371.524			0.935828			0.467914	+	0.883774i	$0.345006\pi$
$398$	−27.6872	+	128.004i	−0.0695659	+	0.321618i
$399$		0			0
$400$	−32.8652	−	37.5682i	−0.0821629	−	0.0939206i
$401$	299.272			0.746314			0.373157	−	0.927768i	$-0.378275\pi$
$401$	299.272			0.746314			0.373157	+	0.927768i	$0.378275\pi$
$402$	−66.5640	+	307.740i	−0.165582	+	0.765522i
$403$			368.865i			0.915298i
$404$	−253.603	−	115.093i	−0.627730	−	0.284884i
$405$	−463.421			−1.14425
$406$		0			0
$407$	178.287			0.438052
$408$	−360.481	+	485.121i	−0.883533	+	1.18902i
$409$		−	20.3701i		−	0.0498046i	−0.999690	−	0.0249023i	$-0.992073\pi$
$409$		−	20.3701i		−	0.0498046i	0.999690	−	0.0249023i	$-0.00792747\pi$
$410$	−43.6903	+	201.990i	−0.106562	+	0.492658i
$411$	−562.067			−1.36756
$412$	32.4324	−	71.4635i	0.0787195	−	0.173455i
$413$		0			0
$414$	−103.509	−	22.3890i	−0.250023	−	0.0540798i
$415$	−233.855			−0.563506
$416$	−197.028	−	355.817i	−0.473625	−	0.855328i
$417$	334.165			0.801355
$418$	109.368	−	505.634i	0.261647	−	1.20965i
$419$	−183.085			−0.436956			−0.218478	−	0.975842i	$-0.570109\pi$
$419$	−183.085			−0.436956			−0.218478	+	0.975842i	$0.570109\pi$
$420$		0			0
$421$			293.022i			0.696014i	0.937492	+	0.348007i	$0.113141\pi$
$421$			293.022i			0.696014i	−0.937492	+	0.348007i	$0.886859\pi$
$422$	−7.56787	+	34.9879i	−0.0179333	+	0.0829097i
$423$			251.894i			0.595495i
$424$	−172.505	+	232.150i	−0.406851	+	0.547524i
$425$			60.9033i			0.143302i
$426$	171.096	+	37.0081i	0.401634	+	0.0868734i
$427$		0			0
$428$	−73.9732	+	162.997i	−0.172835	+	0.380834i
$429$			717.803i			1.67320i
$430$	−157.829	+	729.678i	−0.367045	+	1.69693i
$431$	−75.2217			−0.174528			−0.0872641	−	0.996185i	$-0.527812\pi$
$431$	−75.2217			−0.174528			−0.0872641	+	0.996185i	$0.527812\pi$
$432$	−123.285	−	140.927i	−0.285382	−	0.326221i
$433$		−	506.209i		−	1.16907i	−0.811367	−	0.584536i	$-0.801276\pi$
$433$		−	506.209i		−	1.16907i	0.811367	−	0.584536i	$-0.198724\pi$
$434$		0			0
$435$			642.583i			1.47720i
$436$	−93.5706	+	206.179i	−0.214611	+	0.472887i
$437$	157.054			0.359391
$438$	125.000	−	577.903i	0.285388	−	1.31941i
$439$			163.226i			0.371813i	0.982567	+	0.185907i	$0.0595222\pi$
$439$			163.226i			0.371813i	−0.982567	+	0.185907i	$0.940478\pi$
$440$	325.715	−	438.334i	0.740262	−	0.996214i
$441$		0			0
$442$	−104.915	+	485.047i	−0.237365	+	1.09739i
$443$			113.707i			0.256675i	0.991731	+	0.128338i	$0.0409641\pi$
$443$			113.707i			0.256675i	−0.991731	+	0.128338i	$0.959036\pi$
$444$	78.1535	−	172.208i	0.176021	−	0.387856i
$445$		−	5.23936i		−	0.0117738i
$446$	109.499	−	506.240i	0.245514	−	1.13507i
$447$		−	846.952i		−	1.89475i
$448$		0			0
$449$	391.120			0.871091			0.435546	−	0.900167i	$-0.356555\pi$
$449$	391.120			0.871091			0.435546	+	0.900167i	$0.356555\pi$
$450$	36.4434	+	7.88269i	0.0809853	+	0.0175171i
$451$	322.373			0.714796
$452$	−687.083	−	311.820i	−1.52010	−	0.689868i
$453$	322.401			0.711703
$454$	−229.384	−	49.6157i	−0.505251	−	0.109286i
$455$		0			0
$456$	−440.451	−	327.288i	−0.965900	−	0.717736i
$457$	573.786			1.25555			0.627774	−	0.778396i	$-0.283966\pi$
$457$	573.786			1.25555			0.627774	+	0.778396i	$0.283966\pi$
$458$	170.253	+	36.8256i	0.371731	+	0.0804053i
$459$			228.463i			0.497741i
$460$	150.970	+	68.5150i	0.328195	+	0.148946i
$461$	847.131			1.83759			0.918797	−	0.394729i	$-0.129162\pi$
$461$	847.131			1.83759			0.918797	+	0.394729i	$0.129162\pi$
$462$		0			0
$463$	109.055			0.235539			0.117770	−	0.993041i	$-0.462426\pi$
$463$	109.055			0.235539			0.117770	+	0.993041i	$0.462426\pi$
$464$	−427.480	+	373.965i	−0.921293	+	0.805959i
$465$			525.340i			1.12976i
$466$	609.213	+	131.773i	1.30732	+	0.282774i
$467$	642.410			1.37561			0.687805	−	0.725895i	$-0.258574\pi$
$467$	642.410			1.37561			0.687805	+	0.725895i	$0.258574\pi$
$468$	276.664	+	125.559i	0.591162	+	0.268288i
$469$		0			0
$470$	83.3671	−	385.424i	0.177377	−	0.820051i
$471$	137.154			0.291198
$472$	15.4557	+	11.4848i	0.0327452	+	0.0243322i
$473$	1164.56			2.46206
$474$	−1034.89	−	223.846i	−2.18331	−	0.472249i
$475$	−55.2952			−0.116411
$476$		0			0
$477$		−	216.050i		−	0.452936i
$478$	275.280	+	59.5430i	0.575900	+	0.124567i
$479$		−	424.825i		−	0.886899i	−0.896299	−	0.443449i	$-0.853755\pi$
$479$		−	424.825i		−	0.886899i	0.896299	−	0.443449i	$-0.146245\pi$
$480$	−280.609	−	506.756i	−0.584601	−	1.05574i
$481$		−	155.279i		−	0.322826i
$482$	−20.3323	+	94.0004i	−0.0421831	+	0.195022i
$483$		0			0
$484$	−334.987	−	152.028i	−0.692122	−	0.314107i
$485$		−	742.937i		−	1.53183i
$486$	543.572	+	117.574i	1.11846	+	0.241923i
$487$	777.233			1.59596			0.797980	−	0.602684i	$-0.205902\pi$
$487$	777.233			1.59596			0.797980	+	0.602684i	$0.205902\pi$
$488$	−187.790	−	139.542i	−0.384815	−	0.285946i
$489$			40.4588i			0.0827379i
$490$		0			0
$491$			476.370i			0.970203i	0.874458	+	0.485102i	$0.161217\pi$
$491$			476.370i			0.970203i	−0.874458	+	0.485102i	$0.838783\pi$
$492$	141.315	−	311.381i	0.287225	−	0.632888i
$493$	693.005			1.40569
$494$	−440.383	−	95.2547i	−0.891463	−	0.192823i
$495$			407.936i			0.824112i
$496$	−349.484	+	305.733i	−0.704605	+	0.616397i
$497$		0			0
$498$	378.197	+	81.8039i	0.759432	+	0.164265i
$499$			435.397i			0.872539i	0.899816	+	0.436269i	$0.143701\pi$
$499$			435.397i			0.872539i	−0.899816	+	0.436269i	$0.856299\pi$
$500$	−479.104	−	217.433i	−0.958209	−	0.434866i
$501$			305.273i			0.609327i
$502$	−297.284	−	64.3025i	−0.592200	−	0.128093i
$503$			375.404i			0.746329i	0.927765	+	0.373165i	$0.121727\pi$
$503$			375.404i			0.746329i	−0.927765	+	0.373165i	$0.878273\pi$
$504$		0			0
$505$	−325.678			−0.644907
$506$	54.6745	−	252.772i	0.108052	−	0.499549i
$507$	−28.8369			−0.0568776
$508$	167.023	+	75.8004i	0.328786	+	0.149213i
$509$	−147.823			−0.290419			−0.145210	−	0.989401i	$-0.546386\pi$
$509$	−147.823			−0.290419			−0.145210	+	0.989401i	$0.546386\pi$
$510$	−149.421	+	690.807i	−0.292983	+	1.35452i
$511$		0			0
$512$	173.815	−	481.594i	0.339482	−	0.940613i
$513$	−207.426			−0.404339
$514$	−61.5921	+	284.754i	−0.119829	+	0.553995i
$515$		−	91.7737i		−	0.178201i
$516$	510.492	−	1124.85i	0.989325	−	2.17994i
$517$	−615.131			−1.18981
$518$		0			0
$519$	−742.404			−1.43045
$520$	−381.768	−	283.682i	−0.734170	−	0.545543i
$521$			872.148i			1.67399i	0.547212	+	0.836994i	$0.315689\pi$
$521$			872.148i			1.67399i	−0.547212	+	0.836994i	$0.684311\pi$
$522$	89.6953	−	414.681i	0.171830	−	0.794408i
$523$	357.200			0.682982			0.341491	−	0.939885i	$-0.389068\pi$
$523$	357.200			0.682982			0.341491	+	0.939885i	$0.389068\pi$
$524$	−440.723	−	200.014i	−0.841074	−	0.381706i
$525$		0			0
$526$	−690.811	−	149.422i	−1.31333	−	0.284072i
$527$	566.562			1.07507
$528$	−680.088	+	594.950i	−1.28805	+	1.12680i
$529$	−450.487			−0.851582
$530$	−71.5041	+	330.579i	−0.134913	+	0.623734i
$531$	−14.3839			−0.0270883
$532$		0			0
$533$		−	280.771i		−	0.526776i
$534$	−1.83276	+	8.47325i	−0.00343214	+	0.0158675i
$535$			209.321i			0.391255i
$536$	−194.106	+	261.220i	−0.362139	+	0.487352i
$537$			270.538i			0.503795i
$538$	260.570	+	56.3613i	0.484331	+	0.104761i
$539$		0			0
$540$	−199.390	−	90.4898i	−0.369241	−	0.167574i
$541$		−	932.072i		−	1.72287i	−0.507869	−	0.861434i	$-0.669567\pi$
$541$		−	932.072i		−	1.72287i	0.507869	−	0.861434i	$-0.330433\pi$
$542$	159.331	−	736.620i	0.293968	−	1.35908i
$543$	−1329.82			−2.44903
$544$	−546.520	+	302.627i	−1.00463	+	0.556300i
$545$			264.776i			0.485827i
$546$		0			0
$547$			151.397i			0.276778i	0.990378	+	0.138389i	$0.0441924\pi$
$547$			151.397i			0.276778i	−0.990378	+	0.138389i	$0.955808\pi$
$548$	−529.034	−	240.093i	−0.965390	−	0.438125i
$549$	174.766			0.318336
$550$	−19.2497	+	88.9954i	−0.0349994	+	0.161810i
$551$			629.192i			1.14191i
$552$	−220.186	−	163.615i	−0.398888	−	0.296403i
$553$		0			0
$554$	−32.9453	+	152.313i	−0.0594681	+	0.274934i
$555$		−	221.150i		−	0.398469i
$556$	314.526	+	142.742i	0.565695	+	0.256730i
$557$		−	895.577i		−	1.60786i	−0.594725	−	0.803929i	$-0.702739\pi$
$557$		−	895.577i		−	1.60786i	0.594725	−	0.803929i	$-0.297261\pi$
$558$	73.3299	−	339.020i	0.131416	−	0.607563i
$559$		−	1014.27i		−	1.81444i
$560$		0			0
$561$	1102.52			1.96527
$562$	−634.456	−	137.233i	−1.12892	−	0.244186i
$563$	279.915			0.497185			0.248592	−	0.968608i	$-0.420032\pi$
$563$	279.915			0.497185			0.248592	+	0.968608i	$0.420032\pi$
$564$	−269.647	+	594.157i	−0.478098	+	1.05347i
$565$	−882.355			−1.56169
$566$	585.425	+	126.627i	1.03432	+	0.223723i
$567$		0			0
$568$	145.232	+	107.919i	0.255691	+	0.189998i
$569$	321.926			0.565775			0.282887	−	0.959153i	$-0.408708\pi$
$569$	321.926			0.565775			0.282887	+	0.959153i	$0.408708\pi$
$570$	−627.196	−	135.662i	−1.10034	−	0.238004i
$571$		−	822.820i		−	1.44102i	−0.693446	−	0.720508i	$-0.743909\pi$
$571$		−	822.820i		−	1.44102i	0.693446	−	0.720508i	$-0.256091\pi$
$572$	−306.617	+	675.618i	−0.536044	+	1.18115i
$573$	−540.928			−0.944027
$574$		0			0
$575$	−27.6427			−0.0480742
$576$	110.350	+	366.196i	0.191581	+	0.635757i
$577$			962.053i			1.66734i	0.552266	+	0.833668i	$0.313763\pi$
$577$			962.053i			1.66734i	−0.552266	+	0.833668i	$0.686237\pi$
$578$	180.077	+	38.9506i	0.311552	+	0.0673886i
$579$	88.7102			0.153213
$580$	−274.486	+	604.818i	−0.473251	+	1.04279i
$581$		0			0
$582$	−259.884	+	1201.50i	−0.446536	+	2.06443i
$583$	527.599			0.904973
$584$	364.511	−	490.544i	0.624162	−	0.839972i
$585$	355.293			0.607338
$586$	159.756	+	34.5551i	0.272621	+	0.0589677i
$587$	885.638			1.50875			0.754377	−	0.656442i	$-0.227939\pi$
$587$	885.638			1.50875			0.754377	+	0.656442i	$0.227939\pi$
$588$		0			0
$589$			514.392i			0.873331i
$590$	22.0088	+	4.76050i	0.0373030	+	0.00806864i
$591$		−	1113.70i		−	1.88444i
$592$	147.121	−	128.703i	0.248515	−	0.217404i
$593$		−	335.808i		−	0.566286i	−0.959078	−	0.283143i	$-0.908623\pi$
$593$		−	335.808i		−	0.566286i	0.959078	−	0.283143i	$-0.0913772\pi$
$594$	−72.2102	+	333.843i	−0.121566	+	0.562025i
$595$		0			0
$596$	361.784	−	797.176i	0.607020	−	1.33754i
$597$		−	253.408i		−	0.424468i
$598$	−220.152	−	47.6189i	−0.368148	−	0.0796302i
$599$	−60.3064			−0.100679			−0.0503393	−	0.998732i	$-0.516030\pi$
$599$	−60.3064			−0.100679			−0.0503393	+	0.998732i	$0.516030\pi$
$600$	77.5227	+	57.6052i	0.129204	+	0.0960086i
$601$			509.153i			0.847176i	0.905855	+	0.423588i	$0.139230\pi$
$601$			509.153i			0.847176i	−0.905855	+	0.423588i	$0.860770\pi$
$602$		0			0
$603$		−	243.105i		−	0.403159i
$604$	303.454	+	137.717i	0.502407	+	0.228008i
$605$	−430.192			−0.711061
$606$	526.696	+	113.924i	0.869135	+	0.187994i
$607$			1039.65i			1.71277i	0.516340	+	0.856384i	$0.327294\pi$
$607$			1039.65i			1.71277i	−0.516340	+	0.856384i	$0.672706\pi$
$608$	−274.761	−	496.196i	−0.451909	−	0.816111i
$609$		0			0
$610$	−267.410	−	57.8407i	−0.438377	−	0.0948209i
$611$			535.750i			0.876841i
$612$	192.853	−	424.944i	0.315120	−	0.694354i
$613$		−	198.928i		−	0.324516i	−0.986748	−	0.162258i	$-0.948122\pi$
$613$		−	198.928i		−	0.324516i	0.986748	−	0.162258i	$-0.0518777\pi$
$614$	707.498	+	153.032i	1.15228	+	0.249237i
$615$		−	399.876i		−	0.650206i
$616$		0			0
$617$	136.689			0.221538			0.110769	−	0.993846i	$-0.464669\pi$
$617$	136.689			0.221538			0.110769	+	0.993846i	$0.464669\pi$
$618$	−32.1030	+	148.419i	−0.0519466	+	0.240160i
$619$	−461.877			−0.746166			−0.373083	−	0.927798i	$-0.621699\pi$
$619$	−461.877			−0.746166			−0.373083	+	0.927798i	$0.621699\pi$
$620$	−224.404	+	494.465i	−0.361942	+	0.797525i
$621$	−103.694			−0.166980
$622$	79.8301	−	369.072i	0.128344	−	0.593363i
$623$		0			0
$624$	518.173	+	592.324i	0.830406	+	0.949238i
$625$	−537.276			−0.859641
$626$	10.8614	−	50.2144i	0.0173504	−	0.0802148i
$627$			1001.00i			1.59648i
$628$	129.094	+	58.5868i	0.205563	+	0.0932911i
$629$	−238.503			−0.379178
$630$		0			0
$631$	1042.33			1.65187			0.825933	−	0.563768i	$-0.190649\pi$
$631$	1042.33			1.65187			0.825933	+	0.563768i	$0.190649\pi$
$632$	−878.449	−	652.753i	−1.38995	−	1.03284i
$633$		−	69.2650i		−	0.109423i
$634$	211.042	−	975.692i	0.332874	−	1.53895i
$635$	214.492			0.337782
$636$	231.277	−	509.609i	0.363643	−	0.801273i
$637$		0			0
$638$	1012.66	+	219.038i	1.58724	+	0.343319i
$639$	−135.161			−0.211519
$640$	−47.6509	−	596.839i	−0.0744546	−	0.932561i
$641$	122.667			0.191368			0.0956840	−	0.995412i	$-0.469496\pi$
$641$	122.667			0.191368			0.0956840	+	0.995412i	$0.469496\pi$
$642$	73.2219	−	338.520i	0.114053	−	0.527290i
$643$	720.813			1.12102			0.560508	−	0.828149i	$-0.310606\pi$
$643$	720.813			1.12102			0.560508	+	0.828149i	$0.310606\pi$
$644$		0			0
$645$		−	1444.53i		−	2.23959i
$646$	−146.307	+	676.411i	−0.226482	+	1.04708i
$647$			589.850i			0.911669i	0.890065	+	0.455834i	$0.150659\pi$
$647$			589.850i			0.911669i	−0.890065	+	0.455834i	$0.849341\pi$
$648$	636.166	+	472.719i	0.981738	+	0.729505i
$649$		−	35.1257i		−	0.0541228i
$650$	77.5108	+	16.7656i	0.119247	+	0.0257932i
$651$		0			0
$652$	−17.2824	+	38.0810i	−0.0265067	+	0.0584065i
$653$			248.600i			0.380705i	0.981716	+	0.190352i	$0.0609631\pi$
$653$			248.600i			0.380705i	−0.981716	+	0.190352i	$0.939037\pi$
$654$	92.6202	−	428.203i	0.141621	−	0.654745i
$655$	−565.978			−0.864088
$656$	266.019	−	232.717i	0.405517	−	0.354751i
$657$			456.524i			0.694862i
$658$		0			0
$659$		−	640.918i		−	0.972562i	−0.873802	−	0.486281i	$-0.838353\pi$
$659$		−	640.918i		−	0.972562i	0.873802	−	0.486281i	$-0.161647\pi$
$660$	−436.686	+	962.219i	−0.661645	+	1.45791i
$661$	−966.642			−1.46239			−0.731197	−	0.682167i	$-0.761038\pi$
$661$	−966.642			−1.46239			−0.731197	+	0.682167i	$0.761038\pi$
$662$	−105.646	+	488.423i	−0.159586	+	0.737799i
$663$		−	960.240i		−	1.44833i
$664$	321.027	+	238.547i	0.483474	+	0.359257i
$665$		0			0
$666$	−30.8694	+	142.716i	−0.0463504	+	0.214288i
$667$			314.540i			0.471574i
$668$	−130.400	+	287.332i	−0.195210	+	0.430137i
$669$			1002.20i			1.49805i
$670$	−80.4580	+	371.975i	−0.120087	+	0.555186i
$671$			426.783i			0.636040i
$672$		0			0
$673$	−754.537			−1.12115			−0.560577	−	0.828102i	$-0.689421\pi$
$673$	−754.537			−1.12115			−0.560577	+	0.828102i	$0.689421\pi$
$674$	164.992	+	35.6878i	0.244796	+	0.0529492i
$675$	36.5085			0.0540867
$676$	−27.1422	−	12.3180i	−0.0401511	−	0.0182219i
$677$	761.957			1.12549			0.562745	−	0.826631i	$-0.309745\pi$
$677$	761.957			1.12549			0.562745	+	0.826631i	$0.309745\pi$
$678$	1426.97	+	308.653i	2.10468	+	0.455241i
$679$		0			0
$680$	−435.725	+	586.381i	−0.640772	+	0.862325i
$681$	454.108			0.666825
$682$	827.893	+	179.073i	1.21392	+	0.262570i
$683$		−	759.336i		−	1.11177i	−0.831261	−	0.555883i	$-0.812380\pi$
$683$		−	759.336i		−	1.11177i	0.831261	−	0.555883i	$-0.187620\pi$
$684$	385.815	+	175.095i	0.564057	+	0.255987i
$685$	−679.387			−0.991806
$686$		0			0
$687$	−337.047			−0.490607
$688$	960.980	−	840.678i	1.39677	−	1.22192i
$689$		−	459.514i		−	0.666928i
$690$	−313.542	−	67.8191i	−0.454409	−	0.0982885i
$691$	490.152			0.709337			0.354669	−	0.934992i	$-0.384594\pi$
$691$	490.152			0.709337			0.354669	+	0.934992i	$0.384594\pi$
$692$	−698.773	−	317.125i	−1.00979	−	0.458274i
$693$		0			0
$694$	159.509	−	737.443i	0.229840	−	1.06260i
$695$	403.916			0.581174
$696$	655.476	−	882.113i	0.941775	−	1.26740i
$697$	−431.254			−0.618728
$698$	−782.294	−	169.210i	−1.12077	−	0.242421i
$699$	−1206.05			−1.72539
$700$		0			0
$701$		−	577.533i		−	0.823870i	−0.911213	−	0.411935i	$-0.864853\pi$
$701$		−	577.533i		−	0.823870i	0.911213	−	0.411935i	$-0.135147\pi$
$702$	290.761	+	62.8916i	0.414190	+	0.0895892i
$703$		−	216.541i		−	0.308025i
$704$	−894.258	+	269.478i	−1.27025	+	0.382781i
$705$			763.018i			1.08230i
$706$	125.131	−	578.506i	0.177239	−	0.819413i
$707$		0			0
$708$	−33.9280	−	15.3976i	−0.0479209	−	0.0217481i
$709$			711.080i			1.00293i	0.865177	+	0.501467i	$0.167206\pi$
$709$			711.080i			1.00293i	−0.865177	+	0.501467i	$0.832794\pi$
$710$	206.809	+	44.7328i	0.291281	+	0.0630039i
$711$	817.528			1.14983
$712$	−5.34448	+	7.19239i	−0.00750630	+	0.0101017i
$713$			257.150i			0.360659i
$714$		0			0
$715$			867.631i			1.21347i
$716$	−115.563	+	254.638i	−0.161401	+	0.355640i
$717$	−544.968			−0.760068
$718$	401.073	+	86.7519i	0.558597	+	0.120824i
$719$			173.713i			0.241603i	0.992677	+	0.120802i	$0.0385465\pi$
$719$			173.713i			0.241603i	−0.992677	+	0.120802i	$0.961453\pi$
$720$	294.484	+	336.625i	0.409005	+	0.467534i
$721$		0			0
$722$	91.5551	+	19.8033i	0.126808	+	0.0274285i
$723$		−	186.091i		−	0.257388i
$724$	−1251.67	−	568.048i	−1.72883	−	0.784597i
$725$		−	110.743i		−	0.152748i
$726$	695.719	+	150.484i	0.958290	+	0.207278i
$727$			1056.57i			1.45333i	0.686993	+	0.726664i	$0.258930\pi$
$727$			1056.57i			1.45333i	−0.686993	+	0.726664i	$0.741070\pi$
$728$		0			0
$729$	−184.457			−0.253028
$730$	151.091	−	698.529i	0.206975	−	0.956888i
$731$	−1557.88			−2.13117
$732$	412.231	+	187.084i	0.563157	+	0.255579i
$733$	−230.597			−0.314594			−0.157297	−	0.987551i	$-0.550278\pi$
$733$	−230.597			−0.314594			−0.157297	+	0.987551i	$0.550278\pi$
$734$	−149.505	+	691.192i	−0.203685	+	0.941679i
$735$		0			0
$736$	−137.356	−	248.054i	−0.186625	−	0.337029i
$737$	593.666			0.805517
$738$	−55.8170	+	258.054i	−0.0756328	+	0.349667i
$739$			89.4860i			0.121091i	0.998165	+	0.0605453i	$0.0192840\pi$
$739$			89.4860i			0.121091i	−0.998165	+	0.0605453i	$0.980716\pi$
$740$	94.4665	−	208.153i	0.127657	−	0.281288i
$741$	871.820			1.17654
$742$		0			0
$743$	−236.120			−0.317793			−0.158897	−	0.987295i	$-0.550794\pi$
$743$	−236.120			−0.317793			−0.158897	+	0.987295i	$0.550794\pi$
$744$	535.880	−	721.166i	0.720269	−	0.969309i
$745$		−	1023.74i		−	1.37414i
$746$	−151.382	+	699.872i	−0.202925	+	0.938166i
$747$	−298.763			−0.399951
$748$	1037.72	+	470.952i	1.38733	+	0.629614i
$749$		0			0
$750$	995.029	+	215.224i	1.32671	+	0.286966i
$751$	−1435.38			−1.91130			−0.955649	−	0.294510i	$-0.904844\pi$
$751$	−1435.38			−1.91130			−0.955649	+	0.294510i	$0.904844\pi$
$752$	−507.600	+	444.055i	−0.675000	+	0.590499i
$753$	588.530			0.781580
$754$	190.771	−	881.977i	0.253012	−	1.16973i
$755$	389.696			0.516154
$756$		0			0
$757$		−	692.645i		−	0.914987i	−0.889213	−	0.457494i	$-0.848747\pi$
$757$		−	692.645i		−	0.914987i	0.889213	−	0.457494i	$-0.151253\pi$
$758$	−217.617	+	1006.09i	−0.287094	+	1.32730i
$759$			500.409i			0.659300i
$760$	−532.386	−	395.603i	−0.700508	−	0.520530i
$761$			1154.48i			1.51706i	0.651639	+	0.758529i	$0.274082\pi$
$761$			1154.48i			1.51706i	−0.651639	+	0.758529i	$0.725918\pi$
$762$	−346.882	−	75.0305i	−0.455226	−	0.0984652i
$763$		0			0
$764$	−509.137	−	231.063i	−0.666410	−	0.302438i
$765$		−	545.715i		−	0.713353i
$766$	−219.798	+	1016.18i	−0.286943	+	1.32660i
$767$	−30.5928			−0.0398863
$768$	−131.715	+	981.894i	−0.171504	+	1.27851i
$769$		−	894.095i		−	1.16267i	−0.813663	−	0.581336i	$-0.802530\pi$
$769$		−	894.095i		−	1.16267i	0.813663	−	0.581336i	$-0.197470\pi$
$770$		0			0
$771$		−	563.723i		−	0.731158i
$772$	83.4967	+	37.8935i	0.108156	+	0.0490848i
$773$	929.076			1.20191			0.600954	−	0.799283i	$-0.294787\pi$
$773$	929.076			1.20191			0.600954	+	0.799283i	$0.294787\pi$
$774$	−201.636	+	932.207i	−0.260512	+	1.20440i
$775$		−	90.5370i		−	0.116822i
$776$	−757.844	+	1019.88i	−0.976603	+	1.31427i
$777$		0			0
$778$	44.5892	−	206.145i	0.0573126	−	0.264968i
$779$		−	391.543i		−	0.502623i
$780$	838.047	+	380.333i	1.07442	+	0.487606i
$781$		−	330.065i		−	0.422618i
$782$	−73.1407	+	338.145i	−0.0935303	+	0.432411i
$783$		−	415.422i		−	0.530552i
$784$		0			0
$785$	165.782			0.211188
$786$	915.316	+	197.982i	1.16452	+	0.251886i
$787$	1386.03			1.76115			0.880576	−	0.473905i	$-0.157156\pi$
$787$	1386.03			1.76115			0.880576	+	0.473905i	$0.157156\pi$
$788$	475.730	−	1048.25i	0.603718	−	1.33027i
$789$	1367.59			1.73332
$790$	−1250.90	−	270.569i	−1.58342	−	0.342493i
$791$		0			0
$792$	416.120	−	559.998i	0.525405	−	0.707068i
$793$	371.708			0.468736
$794$	−726.252	−	157.088i	−0.914675	−	0.197844i
$795$		−	654.442i		−	0.823198i
$796$	108.246	−	238.515i	0.135987	−	0.299642i
$797$	388.524			0.487484			0.243742	−	0.969840i	$-0.421625\pi$
$797$	388.524			0.487484			0.243742	+	0.969840i	$0.421625\pi$
$798$		0			0
$799$	822.890			1.02990
$800$	48.3600	+	87.3343i	0.0604500	+	0.109168i
$801$		−	6.69359i		−	0.00835655i
$802$	−585.015	−	126.539i	−0.729445	−	0.157779i
$803$	−1114.84			−1.38835
$804$	260.238	−	573.424i	0.323679	−	0.713214i
$805$		0			0
$806$	155.964	−	721.055i	0.193504	−	0.894610i
$807$	−515.847			−0.639216
$808$	447.078	+	332.212i	0.553314	+	0.411154i
$809$	510.224			0.630685			0.315342	−	0.948978i	$-0.397881\pi$
$809$	510.224			0.630685			0.315342	+	0.948978i	$0.397881\pi$
$810$	905.893	+	195.944i	1.11839	+	0.241907i
$811$	54.8689			0.0676558			0.0338279	−	0.999428i	$-0.489230\pi$
$811$	54.8689			0.0676558			0.0338279	+	0.999428i	$0.489230\pi$
$812$		0			0
$813$			1458.28i			1.79370i
$814$	−348.514	−	75.3835i	−0.428150	−	0.0926088i
$815$			48.9038i			0.0600047i
$816$	909.787	−	795.893i	1.11493	−	0.975360i
$817$		−	1414.43i		−	1.73125i
$818$	−8.61291	+	39.8193i	−0.0105292	+	0.0486789i
$819$		0			0
$820$	170.811	−	376.375i	0.208306	−	0.458995i
$821$		−	192.888i		−	0.234942i	−0.993076	−	0.117471i	$-0.962521\pi$
$821$		−	192.888i		−	0.234942i	0.993076	−	0.117471i	$-0.0374787\pi$
$822$	1098.73	+	237.654i	1.33665	+	0.289117i
$823$	142.648			0.173327			0.0866636	−	0.996238i	$-0.472379\pi$
$823$	142.648			0.173327			0.0866636	+	0.996238i	$0.472379\pi$
$824$	−93.6150	+	125.983i	−0.113610	+	0.152892i
$825$		−	176.183i		−	0.213555i
$826$		0			0
$827$		−	91.3639i		−	0.110476i	−0.998473	−	0.0552382i	$-0.982408\pi$
$827$		−	91.3639i		−	0.110476i	0.998473	−	0.0552382i	$-0.0175918\pi$
$828$	192.873	+	87.5320i	0.232938	+	0.105715i
$829$	465.999			0.562122			0.281061	−	0.959690i	$-0.409314\pi$
$829$	465.999			0.562122			0.281061	+	0.959690i	$0.409314\pi$
$830$	457.138	+	98.8788i	0.550769	+	0.119131i
$831$		−	301.533i		−	0.362855i
$832$	234.702	+	778.856i	0.282094	+	0.936125i
$833$		0			0
$834$	−653.224	−	141.292i	−0.783243	−	0.169415i
$835$			368.993i			0.441907i
$836$	−427.586	+	942.167i	−0.511466	+	1.12699i
$837$		−	339.626i		−	0.405766i
$838$	357.893	+	77.4121i	0.427080	+	0.0923773i
$839$			24.9426i			0.0297289i	0.999890	+	0.0148645i	$0.00473168\pi$
$839$			24.9426i			0.0297289i	−0.999890	+	0.0148645i	$0.995268\pi$
$840$		0			0
$841$	−419.114			−0.498352
$842$	123.896	−	572.798i	0.147145	−	0.680282i
$843$	1256.02			1.48994
$844$	29.5873	−	65.1943i	0.0350560	−	0.0772444i
$845$	−34.8561			−0.0412498
$846$	106.506	−	492.402i	0.125894	−	0.582035i
$847$		0			0
$848$	435.370	−	380.867i	0.513408	−	0.449136i
$849$	−1158.96			−1.36509
$850$	25.7512	−	119.053i	0.0302956	−	0.140063i
$851$		−	108.251i		−	0.127205i
$852$	−318.810	−	144.686i	−0.374190	−	0.169820i
$853$	1642.90			1.92603			0.963016	−	0.269445i	$-0.0868403\pi$
$853$	1642.90			1.92603			0.963016	+	0.269445i	$0.0868403\pi$
$854$		0			0
$855$	495.465			0.579491
$856$	213.521	−	287.348i	0.249440	−	0.335687i
$857$		−	151.136i		−	0.176355i	−0.996105	−	0.0881775i	$-0.971896\pi$
$857$		−	151.136i		−	0.176355i	0.996105	−	0.0881775i	$-0.0281043\pi$
$858$	303.503	−	1403.16i	0.353733	−	1.63538i
$859$	−900.014			−1.04775			−0.523873	−	0.851796i	$-0.675513\pi$
$859$	−900.014			−1.04775			−0.523873	+	0.851796i	$0.675513\pi$
$860$	617.047	−	1359.64i	0.717497	−	1.58097i
$861$		0			0
$862$	147.043	+	31.8053i	0.170583	+	0.0368971i
$863$	415.864			0.481882			0.240941	−	0.970540i	$-0.422544\pi$
$863$	415.864			0.481882			0.240941	+	0.970540i	$0.422544\pi$
$864$	181.410	+	327.612i	0.209965	+	0.379180i
$865$	−897.366			−1.03742
$866$	−214.036	+	989.534i	−0.247155	+	1.14265i
$867$	−356.496			−0.411184
$868$		0			0
$869$			1996.42i			2.29737i
$870$	271.698	−	1256.12i	0.312296	−	1.44381i
$871$		−	517.055i		−	0.593634i
$872$	270.088	−	363.474i	0.309734	−	0.416828i
$873$		−	949.146i		−	1.08722i
$874$	−307.008	−	66.4058i	−0.351268	−	0.0759791i
$875$		0			0
$876$	−488.699	+	1076.83i	−0.557876	+	1.22926i
$877$			1718.84i			1.95991i	0.199226	+	0.979954i	$0.436157\pi$
$877$			1718.84i			1.95991i	−0.199226	+	0.979954i	$0.563843\pi$
$878$	69.0155	−	319.073i	0.0786053	−	0.363409i
$879$	−316.266			−0.359802
$880$	−822.043	+	719.134i	−0.934140	+	0.817198i
$881$			1094.47i			1.24231i	0.783689	+	0.621153i	$0.213336\pi$
$881$			1094.47i			1.24231i	−0.783689	+	0.621153i	$0.786664\pi$
$882$		0			0
$883$			527.301i			0.597170i	0.954383	+	0.298585i	$0.0965146\pi$
$883$			527.301i			0.597170i	−0.954383	+	0.298585i	$0.903485\pi$
$884$	410.176	−	903.807i	0.464000	−	1.02241i
$885$	−43.5705			−0.0492322
$886$	48.0778	−	222.274i	0.0542639	−	0.250874i
$887$		−	1685.85i		−	1.90062i	−0.311304	−	0.950310i	$-0.600766\pi$
$887$		−	1685.85i		−	1.90062i	0.311304	−	0.950310i	$-0.399234\pi$
$888$	−225.587	+	303.586i	−0.254040	+	0.341876i
$889$		0			0
$890$	−2.21531	+	10.2419i	−0.00248912	+	0.0115077i
$891$		−	1445.79i		−	1.62266i
$892$	−428.098	+	943.296i	−0.479930	+	1.05751i
$893$			747.117i			0.836637i
$894$	−358.109	+	1655.62i	−0.400570	+	1.85192i
$895$			327.007i			0.365371i
$896$		0			0
$897$	435.832			0.485878
$898$	−764.559	−	165.374i	−0.851402	−	0.184158i
$899$	−1030.20			−1.14594
$900$	−67.9064	−	30.8181i	−0.0754515	−	0.0342423i
$901$	−705.795			−0.783346
$902$	−630.173	−	136.306i	−0.698639	−	0.151115i
$903$		0			0
$904$	1211.26	+	900.058i	1.33989	+	0.995640i
$905$	−1607.40			−1.77613
$906$	−630.228	−	136.318i	−0.695616	−	0.150462i
$907$			1662.05i			1.83247i	0.400644	+	0.916234i	$0.368786\pi$
$907$			1662.05i			1.83247i	−0.400644	+	0.916234i	$0.631214\pi$
$908$	427.420	+	193.977i	0.470727	+	0.213631i
$909$	−416.073			−0.457726
$910$		0			0
$911$	−1220.19			−1.33940			−0.669698	−	0.742633i	$-0.733577\pi$
$911$	−1220.19			−1.33940			−0.669698	+	0.742633i	$0.733577\pi$
$912$	722.606	+	826.012i	0.792331	+	0.905715i
$913$		−	729.586i		−	0.799108i
$914$	−1121.63	−	242.609i	−1.22717	−	0.265436i
$915$	529.388			0.578566
$916$	−317.238	−	143.973i	−0.346330	−	0.157176i
$917$		0			0
$918$	96.5990	−	446.598i	0.105228	−	0.486490i
$919$	−76.2434			−0.0829635			−0.0414817	−	0.999139i	$-0.513208\pi$
$919$	−76.2434			−0.0829635			−0.0414817	+	0.999139i	$0.513208\pi$
$920$	−266.146	−	197.766i	−0.289289	−	0.214963i
$921$	−1400.62			−1.52076
$922$	−1655.97	−	358.185i	−1.79606	−	0.388487i
$923$	−287.471			−0.311452
$924$		0			0
$925$			38.1129i			0.0412032i
$926$	−213.180	−	46.1107i	−0.230216	−	0.0497955i
$927$		−	117.246i		−	0.126479i
$928$	993.756	−	550.277i	1.07086	−	0.592971i
$929$		−	231.821i		−	0.249538i	−0.992186	−	0.124769i	$-0.960181\pi$
$929$		−	231.821i		−	0.249538i	0.992186	−	0.124769i	$-0.0398189\pi$
$930$	222.125	−	1026.93i	0.238844	−	1.10423i
$931$		0			0
$932$	−1135.17	−	515.177i	−1.21799	−	0.552765i
$933$			730.646i			0.783115i
$934$	−1255.78	−	271.625i	−1.34452	−	0.290819i
$935$	1332.65			1.42529
$936$	−487.732	−	362.421i	−0.521081	−	0.387202i
$937$		−	985.061i		−	1.05129i	−0.850703	−	0.525646i	$-0.823824\pi$
$937$		−	985.061i		−	1.05129i	0.850703	−	0.525646i	$-0.176176\pi$
$938$		0			0
$939$			99.4088i			0.105867i
$940$	−325.931	+	718.175i	−0.346735	+	0.764016i
$941$	1408.48			1.49679			0.748394	−	0.663254i	$-0.230825\pi$
$941$	1408.48			1.49679			0.748394	+	0.663254i	$0.230825\pi$
$942$	−268.108	−	57.9917i	−0.284616	−	0.0615623i
$943$		−	195.737i		−	0.207568i
$944$	−25.3568	−	28.9854i	−0.0268610	−	0.0307049i
$945$		0			0
$946$	−2276.47	−	492.399i	−2.40641	−	0.520506i
$947$		−	166.417i		−	0.175731i	−0.996132	−	0.0878654i	$-0.971995\pi$
$947$		−	166.417i		−	0.175731i	0.996132	−	0.0878654i	$-0.0280045\pi$
$948$	1928.35	+	875.145i	2.03412	+	0.923149i
$949$			970.974i			1.02315i
$950$	108.091	+	23.3800i	0.113780	+	0.0246105i
$951$			1931.56i			2.03109i
$952$		0			0
$953$	815.618			0.855843			0.427921	−	0.903816i	$-0.359246\pi$
$953$	815.618			0.855843			0.427921	+	0.903816i	$0.359246\pi$
$954$	−91.3507	+	422.334i	−0.0957555	+	0.442698i
$955$	−653.836			−0.684645
$956$	−512.940	−	232.789i	−0.536548	−	0.243503i
$957$	−2004.74			−2.09482
$958$	−179.625	+	830.445i	−0.187500	+	0.866853i
$959$		0			0
$960$	334.265	+	1109.25i	0.348192	+	1.15547i
$961$	118.767			0.123587
$962$	−65.6555	+	303.539i	−0.0682489	+	0.315530i
$963$			267.420i			0.277695i
$964$	79.4908	−	175.155i	0.0824593	−	0.181696i
$965$	107.227			0.111116
$966$		0			0
$967$	−86.3395			−0.0892860			−0.0446430	−	0.999003i	$-0.514215\pi$
$967$	−86.3395			−0.0892860			−0.0446430	+	0.999003i	$0.514215\pi$
$968$	590.550	+	438.823i	0.610073	+	0.453330i
$969$		−	1339.08i		−	1.38192i
$970$	−314.130	+	1452.29i	−0.323845	+	1.49721i
$971$	−679.301			−0.699589			−0.349795	−	0.936826i	$-0.613749\pi$
$971$	−679.301			−0.699589			−0.349795	+	0.936826i	$0.613749\pi$
$972$	−1012.86	−	459.667i	−1.04203	−	0.472909i
$973$		0			0
$974$	−1519.33	−	328.631i	−1.55989	−	0.337403i
$975$	−153.447			−0.157382
$976$	308.089	+	352.177i	0.315665	+	0.360837i
$977$	−214.057			−0.219096			−0.109548	−	0.993981i	$-0.534940\pi$
$977$	−214.057			−0.219096			−0.109548	+	0.993981i	$0.534940\pi$
$978$	17.1069	−	79.0887i	0.0174917	−	0.0808678i
$979$	16.3459			0.0166965
$980$		0			0
$981$			338.267i			0.344818i
$982$	201.419	−	931.205i	0.205111	−	0.948274i
$983$			1800.29i			1.83143i	0.401833	+	0.915713i	$0.368373\pi$
$983$			1800.29i			1.83143i	−0.401833	+	0.915713i	$0.631627\pi$
$984$	−407.900	+	548.935i	−0.414532	+	0.557860i
$985$		−	1346.17i		−	1.36667i
$986$	−1354.68	−	293.017i	−1.37392	−	0.297178i
$987$		0			0
$988$	820.583	+	372.407i	0.830549	+	0.376930i
$989$		−	707.089i		−	0.714953i
$990$	172.484	−	797.430i	0.174226	−	0.805485i
$991$	411.427			0.415163			0.207582	−	0.978218i	$-0.433441\pi$
$991$	411.427			0.415163			0.207582	+	0.978218i	$0.433441\pi$
$992$	812.440	−	449.876i	0.818992	−	0.453504i
$993$		−	966.925i		−	0.973741i
$994$		0			0
$995$		−	306.302i		−	0.307841i
$996$	−704.709	−	319.820i	−0.707539	−	0.321104i
$997$	−1612.00			−1.61685			−0.808425	−	0.588599i	$-0.799680\pi$
$997$	−1612.00			−1.61685			−0.808425	+	0.588599i	$0.799680\pi$
$998$	184.095	−	851.111i	0.184464	−	0.852817i
$999$			142.971i			0.143114i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	392.3.h.a.293.2		28
4.3	odd	2		1568.3.h.a.881.6		28
7.2	even	3		392.3.j.e.325.9		28
7.3	odd	6		392.3.j.e.117.11		28
7.4	even	3		56.3.j.a.5.11	yes	28
7.5	odd	6		56.3.j.a.45.9	yes	28
7.6	odd	2	inner	392.3.h.a.293.1		28
8.3	odd	2		1568.3.h.a.881.23		28
8.5	even	2	inner	392.3.h.a.293.3		28
28.11	odd	6		224.3.n.a.145.12		28
28.19	even	6		224.3.n.a.17.3		28
28.27	even	2		1568.3.h.a.881.24		28
56.5	odd	6		56.3.j.a.45.11	yes	28
56.11	odd	6		224.3.n.a.145.3		28
56.13	odd	2	inner	392.3.h.a.293.4		28
56.19	even	6		224.3.n.a.17.12		28
56.27	even	2		1568.3.h.a.881.5		28
56.37	even	6		392.3.j.e.325.11		28
56.45	odd	6		392.3.j.e.117.9		28
56.53	even	6		56.3.j.a.5.9	✓	28

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
56.3.j.a.5.9	✓	28	56.53	even	6
56.3.j.a.5.11	yes	28	7.4	even	3
56.3.j.a.45.9	yes	28	7.5	odd	6
56.3.j.a.45.11	yes	28	56.5	odd	6
224.3.n.a.17.3		28	28.19	even	6
224.3.n.a.17.12		28	56.19	even	6
224.3.n.a.145.3		28	56.11	odd	6
224.3.n.a.145.12		28	28.11	odd	6
392.3.h.a.293.1		28	7.6	odd	2	inner
392.3.h.a.293.2		28	1.1	even	1	trivial
392.3.h.a.293.3		28	8.5	even	2	inner
392.3.h.a.293.4		28	56.13	odd	2	inner
392.3.j.e.117.9		28	56.45	odd	6
392.3.j.e.117.11		28	7.3	odd	6
392.3.j.e.325.9		28	7.2	even	3
392.3.j.e.325.11		28	56.37	even	6
1568.3.h.a.881.5		28	56.27	even	2
1568.3.h.a.881.6		28	4.3	odd	2
1568.3.h.a.881.23		28	8.3	odd	2
1568.3.h.a.881.24		28	28.27	even	2

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:	\( N \)	\(=\)	\( 392 = 2^{3} \cdot 7^{2} \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	392.h (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.95479 - 0.422821i) q^{2} +3.86988 q^{3} +(3.64244 + 1.65306i) q^{4} +4.67764 q^{5} +(-7.56482 - 1.63627i) q^{6} +(-6.42128 - 4.77149i) q^{8} +5.97596 q^{9} +O(q^{10})\)	\(q+(-1.95479 - 0.422821i) q^{2} +3.86988 q^{3} +(3.64244 + 1.65306i) q^{4} +4.67764 q^{5} +(-7.56482 - 1.63627i) q^{6} +(-6.42128 - 4.77149i) q^{8} +5.97596 q^{9} +(-9.14383 - 1.97781i) q^{10} +14.5934i q^{11} +(14.0958 + 6.39713i) q^{12} +12.7102 q^{13} +18.1019 q^{15} +(10.5348 + 12.0423i) q^{16} -19.5223i q^{17} +(-11.6818 - 2.52677i) q^{18} +17.7247 q^{19} +(17.0380 + 7.73241i) q^{20} +(6.17041 - 28.5271i) q^{22} +8.86075 q^{23} +(-24.8496 - 18.4651i) q^{24} -3.11968 q^{25} +(-24.8458 - 5.37413i) q^{26} -11.7027 q^{27} +35.4981i q^{29} +(-35.3855 - 7.65387i) q^{30} +29.0213i q^{31} +(-15.5016 - 27.9946i) q^{32} +56.4747i q^{33} +(-8.25445 + 38.1621i) q^{34} +(21.7671 + 9.87861i) q^{36} -12.2169i q^{37} +(-34.6481 - 7.49437i) q^{38} +49.1868 q^{39} +(-30.0364 - 22.3193i) q^{40} -22.0903i q^{41} -79.8001i q^{43} +(-24.1238 + 53.1557i) q^{44} +27.9534 q^{45} +(-17.3210 - 3.74652i) q^{46} +42.1513i q^{47} +(40.7684 + 46.6024i) q^{48} +(6.09833 + 1.31907i) q^{50} -75.5490i q^{51} +(46.2961 + 21.0106i) q^{52} -36.1532i q^{53} +(22.8763 + 4.94813i) q^{54} +68.2627i q^{55} +68.5923 q^{57} +(15.0093 - 69.3915i) q^{58} -2.40696 q^{59} +(65.9352 + 29.9235i) q^{60} +29.2449 q^{61} +(12.2708 - 56.7306i) q^{62} +(18.4657 + 61.2782i) q^{64} +59.4536 q^{65} +(23.8787 - 110.397i) q^{66} -40.6804i q^{67} +(32.2715 - 71.1089i) q^{68} +34.2900 q^{69} -22.6174 q^{71} +(-38.3733 - 28.5143i) q^{72} +76.3935i q^{73} +(-5.16559 + 23.8816i) q^{74} -12.0728 q^{75} +(64.5611 + 29.2999i) q^{76} +(-96.1501 - 20.7972i) q^{78} +136.803 q^{79} +(49.2780 + 56.3298i) q^{80} -99.0715 q^{81} +(-9.34025 + 43.1820i) q^{82} -49.9942 q^{83} -91.3184i q^{85} +(-33.7412 + 155.993i) q^{86} +137.373i q^{87} +(69.6324 - 93.7084i) q^{88} -1.12009i q^{89} +(-54.6432 - 11.8193i) q^{90} +(32.2748 + 14.6473i) q^{92} +112.309i q^{93} +(17.8225 - 82.3971i) q^{94} +82.9096 q^{95} +(-59.9893 - 108.336i) q^{96} -158.827i q^{97} +87.2097i q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9}+O(q^{10}) \) 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9	\( 28 q + 4 q^{2} + 8 q^{4} - 20 q^{8} + 64 q^{9} + 28 q^{15} - 32 q^{16} + 84 q^{18} - 92 q^{22} - 60 q^{23} + 64 q^{25} - 44 q^{30} - 176 q^{32} + 256 q^{36} + 40 q^{39} + 84 q^{44} - 136 q^{46} + 400 q^{50} + 124 q^{57} + 44 q^{58} + 124 q^{60} - 520 q^{64} + 104 q^{65} - 136 q^{71} - 192 q^{72} + 276 q^{74} - 956 q^{78} + 324 q^{79} + 36 q^{81} - 336 q^{86} - 100 q^{88} + 1020 q^{92} - 580 q^{95}+O(q^{100}) \) 28 * q + 4 * q^2 + 8 * q^4 - 20 * q^8 + 64 * q^9 + 28 * q^15 - 32 * q^16 + 84 * q^18 - 92 * q^22 - 60 * q^23 + 64 * q^25 - 44 * q^30 - 176 * q^32 + 256 * q^36 + 40 * q^39 + 84 * q^44 - 136 * q^46 + 400 * q^50 + 124 * q^57 + 44 * q^58 + 124 * q^60 - 520 * q^64 + 104 * q^65 - 136 * q^71 - 192 * q^72 + 276 * q^74 - 956 * q^78 + 324 * q^79 + 36 * q^81 - 336 * q^86 - 100 * q^88 + 1020 * q^92 - 580 * q^95

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

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