LMFDB - Embedded newform 136.3.t.b.73.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [136,3,Mod(41,136)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(136, base_ring=CyclotomicField(16))

chi = DirichletCharacter(H, H._module([0, 0, 11]))

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

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

chi := DirichletCharacter("136.41");

S:= CuspForms(chi, 3);

N := Newforms(S);

Level:	$ N $	$=$	$ 136 = 2^{3} \cdot 17 $
Weight:	$ k $	$=$	$ 3 $
Character orbit:	$[\chi]$	$=$	136.t (of order $16$, degree $8$, 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:	$3.70573159530$
Analytic rank:	$0$
Dimension:	$40$
Relative dimension:	$5$ over $\Q(\zeta_{16})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{16}]$

Embedding invariants

Embedding label			73.3
Character	$\chi$	$=$	136.73
Dual form			136.3.t.b.41.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.708293 - 1.06004i) q^{3} +(-0.482121 + 2.42379i) q^{5} +(2.22606 + 11.1911i) q^{7} +(2.82215 - 6.81328i) q^{9} +O(q^{10})$	\(q+(-0.708293 - 1.06004i) q^{3} +(-0.482121 + 2.42379i) q^{5} +(2.22606 + 11.1911i) q^{7} +(2.82215 - 6.81328i) q^{9} +(14.2613 + 9.52909i) q^{11} +(0.0771647 + 0.0771647i) q^{13} +(2.91078 - 1.20569i) q^{15} +(16.9800 - 0.824179i) q^{17} +(-3.70126 - 8.93564i) q^{19} +(10.2863 - 10.2863i) q^{21} +(-25.4008 + 38.0150i) q^{23} +(17.4547 + 7.22997i) q^{25} +(-20.4748 + 4.07269i) q^{27} +(-39.7529 - 7.90735i) q^{29} +(27.3712 - 18.2889i) q^{31} -21.8669i q^{33} -28.1982 q^{35} +(-8.58062 - 12.8418i) q^{37} +(0.0271421 - 0.136453i) q^{39} +(-5.22473 - 26.2665i) q^{41} +(9.37842 - 22.6415i) q^{43} +(15.1533 + 10.1251i) q^{45} +(5.26803 + 5.26803i) q^{47} +(-75.0164 + 31.0728i) q^{49} +(-12.9005 - 17.4157i) q^{51} +(-22.6332 - 54.6413i) q^{53} +(-29.9722 + 29.9722i) q^{55} +(-6.85052 + 10.2525i) q^{57} +(-40.3308 - 16.7056i) q^{59} +(93.4459 - 18.5875i) q^{61} +(82.5307 + 16.4164i) q^{63} +(-0.224234 + 0.149828i) q^{65} -68.2478i q^{67} +58.2885 q^{69} +(-6.98793 - 10.4582i) q^{71} +(-10.6730 + 53.6570i) q^{73} +(-4.69901 - 23.6235i) q^{75} +(-74.8950 + 180.813i) q^{77} +(17.6840 + 11.8161i) q^{79} +(-28.1126 - 28.1126i) q^{81} +(2.41901 - 1.00199i) q^{83} +(-6.18879 + 41.5533i) q^{85} +(19.7747 + 47.7402i) q^{87} +(12.1775 - 12.1775i) q^{89} +(-0.691789 + 1.03534i) q^{91} +(-38.7737 - 16.0606i) q^{93} +(23.4425 - 4.66301i) q^{95} +(160.989 + 32.0227i) q^{97} +(105.172 - 70.2737i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	$ 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) $ 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{5}{16}\right)$

Coefficient data

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

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

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

$2$		0			0
$2$		0			0
$3$	−0.708293	−	1.06004i	−0.236098	−	0.353345i	0.694434	−	0.719556i	$-0.255655\pi$
$3$	−0.708293	−	1.06004i	−0.236098	−	0.353345i	−0.930532	+	0.366211i	$0.880655\pi$
$4$		0			0
$5$	−0.482121	+	2.42379i	−0.0964242	+	0.484757i	0.902152	+	0.431418i	$0.141987\pi$
$5$	−0.482121	+	2.42379i	−0.0964242	+	0.484757i	−0.998576	+	0.0533395i	$0.983013\pi$
$6$		0			0
$7$	2.22606	+	11.1911i	0.318008	+	1.59874i	0.727292	+	0.686328i	$0.240779\pi$
$7$	2.22606	+	11.1911i	0.318008	+	1.59874i	−0.409284	+	0.912407i	$0.634221\pi$
$8$		0			0
$9$	2.82215	−	6.81328i	0.313573	−	0.757031i
$10$		0			0
$11$	14.2613	+	9.52909i	1.29648	+	0.866281i	0.996160	−	0.0875568i	$-0.0279059\pi$
$11$	14.2613	+	9.52909i	1.29648	+	0.866281i	0.300322	+	0.953838i	$0.402906\pi$
$12$		0			0
$13$	0.0771647	+	0.0771647i	0.00593575	+	0.00593575i	0.710068	−	0.704133i	$-0.248664\pi$
$13$	0.0771647	+	0.0771647i	0.00593575	+	0.00593575i	−0.704133	+	0.710068i	$0.748664\pi$
$14$		0			0
$15$	2.91078	−	1.20569i	0.194052	−	0.0803791i
$16$		0			0
$17$	16.9800	−	0.824179i	0.998824	−	0.0484811i
$17$	16.9800	−	0.824179i	0.998824	−	0.0484811i
$18$		0			0
$19$	−3.70126	−	8.93564i	−0.194803	−	0.470297i	0.796051	−	0.605229i	$-0.206918\pi$
$19$	−3.70126	−	8.93564i	−0.194803	−	0.470297i	−0.990855	+	0.134932i	$0.956918\pi$
$20$		0			0
$21$	10.2863	−	10.2863i	0.489825	−	0.489825i
$22$		0			0
$23$	−25.4008	+	38.0150i	−1.10438	+	1.65283i	−0.460627	+	0.887594i	$0.652375\pi$
$23$	−25.4008	+	38.0150i	−1.10438	+	1.65283i	−0.643756	+	0.765231i	$0.722625\pi$
$24$		0			0
$25$	17.4547	+	7.22997i	0.698187	+	0.289199i
$26$		0			0
$27$	−20.4748	+	4.07269i	−0.758327	+	0.150841i
$28$		0			0
$29$	−39.7529	−	7.90735i	−1.37079	−	0.272667i	−0.545848	−	0.837884i	$-0.683792\pi$
$29$	−39.7529	−	7.90735i	−1.37079	−	0.272667i	−0.824942	+	0.565217i	$0.808792\pi$
$30$		0			0
$31$	27.3712	−	18.2889i	0.882943	−	0.589964i	−0.0293190	−	0.999570i	$-0.509334\pi$
$31$	27.3712	−	18.2889i	0.882943	−	0.589964i	0.912262	+	0.409606i	$0.134334\pi$
$32$		0			0
$33$		−	21.8669i		−	0.662633i
$34$		0			0
$35$	−28.1982			−0.805662
$36$		0			0
$37$	−8.58062	−	12.8418i	−0.231909	−	0.347076i	0.697204	−	0.716873i	$-0.254427\pi$
$37$	−8.58062	−	12.8418i	−0.231909	−	0.347076i	−0.929113	+	0.369797i	$0.879427\pi$
$38$		0			0
$39$	0.0271421	−	0.136453i	0.000695952	−	0.00349879i
$40$		0			0
$41$	−5.22473	−	26.2665i	−0.127432	−	0.640646i	−0.990718	−	0.135931i	$-0.956598\pi$
$41$	−5.22473	−	26.2665i	−0.127432	−	0.640646i	0.863286	−	0.504715i	$-0.168402\pi$
$42$		0			0
$43$	9.37842	−	22.6415i	0.218103	−	0.526547i	−0.776522	−	0.630090i	$-0.783018\pi$
$43$	9.37842	−	22.6415i	0.218103	−	0.526547i	0.994625	+	0.103543i	$0.0330180\pi$
$44$		0			0
$45$	15.1533	+	10.1251i	0.336741	+	0.225003i
$46$		0			0
$47$	5.26803	+	5.26803i	0.112086	+	0.112086i	0.760925	−	0.648840i	$-0.224745\pi$
$47$	5.26803	+	5.26803i	0.112086	+	0.112086i	−0.648840	+	0.760925i	$0.724745\pi$
$48$		0			0
$49$	−75.0164	+	31.0728i	−1.53095	+	0.634139i
$50$		0			0
$51$	−12.9005	−	17.4157i	−0.252951	−	0.341484i
$52$		0			0
$53$	−22.6332	−	54.6413i	−0.427041	−	1.03097i	−0.980221	−	0.197906i	$-0.936586\pi$
$53$	−22.6332	−	54.6413i	−0.427041	−	1.03097i	0.553180	−	0.833062i	$-0.313414\pi$
$54$		0			0
$55$	−29.9722	+	29.9722i	−0.544948	+	0.544948i
$56$		0			0
$57$	−6.85052	+	10.2525i	−0.120185	+	0.179869i
$58$		0			0
$59$	−40.3308	−	16.7056i	−0.683574	−	0.283145i	0.0137463	−	0.999906i	$-0.495624\pi$
$59$	−40.3308	−	16.7056i	−0.683574	−	0.283145i	−0.697320	+	0.716760i	$0.745624\pi$
$60$		0			0
$61$	93.4459	−	18.5875i	1.53190	−	0.304714i	0.644099	−	0.764942i	$-0.277232\pi$
$61$	93.4459	−	18.5875i	1.53190	−	0.304714i	0.887801	+	0.460228i	$0.152232\pi$
$62$		0			0
$63$	82.5307	+	16.4164i	1.31001	+	0.260578i
$64$		0			0
$65$	−0.224234	+	0.149828i	−0.00344975	+	0.00230505i
$66$		0			0
$67$		−	68.2478i		−	1.01862i	−0.860582	−	0.509312i	$-0.829900\pi$
$67$		−	68.2478i		−	1.01862i	0.860582	−	0.509312i	$-0.170100\pi$
$68$		0			0
$69$	58.2885			0.844760
$70$		0			0
$71$	−6.98793	−	10.4582i	−0.0984215	−	0.147298i	0.778991	−	0.627036i	$-0.215732\pi$
$71$	−6.98793	−	10.4582i	−0.0984215	−	0.147298i	−0.877412	+	0.479737i	$0.840732\pi$
$72$		0			0
$73$	−10.6730	+	53.6570i	−0.146206	+	0.735027i	0.836223	+	0.548390i	$0.184759\pi$
$73$	−10.6730	+	53.6570i	−0.146206	+	0.735027i	−0.982429	+	0.186637i	$0.940241\pi$
$74$		0			0
$75$	−4.69901	−	23.6235i	−0.0626535	−	0.314980i
$76$		0			0
$77$	−74.8950	+	180.813i	−0.972663	+	2.34822i
$78$		0			0
$79$	17.6840	+	11.8161i	0.223848	+	0.149571i	0.662438	−	0.749117i	$-0.269522\pi$
$79$	17.6840	+	11.8161i	0.223848	+	0.149571i	−0.438590	+	0.898687i	$0.644522\pi$
$80$		0			0
$81$	−28.1126	−	28.1126i	−0.347069	−	0.347069i
$82$		0			0
$83$	2.41901	−	1.00199i	0.0291447	−	0.0120721i	−0.368063	−	0.929801i	$-0.619979\pi$
$83$	2.41901	−	1.00199i	0.0291447	−	0.0120721i	0.397208	+	0.917729i	$0.369979\pi$
$84$		0			0
$85$	−6.18879	+	41.5533i	−0.0728093	+	0.488862i
$86$		0			0
$87$	19.7747	+	47.7402i	0.227295	+	0.548738i
$88$		0			0
$89$	12.1775	−	12.1775i	0.136826	−	0.136826i	−0.635376	−	0.772203i	$-0.719155\pi$
$89$	12.1775	−	12.1775i	0.136826	−	0.136826i	0.772203	+	0.635376i	$0.219155\pi$
$90$		0			0
$91$	−0.691789	+	1.03534i	−0.00760207	+	0.0113773i
$92$		0			0
$93$	−38.7737	−	16.0606i	−0.416922	−	0.172695i
$94$		0			0
$95$	23.4425	−	4.66301i	0.246764	−	0.0490843i
$96$		0			0
$97$	160.989	+	32.0227i	1.65968	+	0.330130i	0.933828	−	0.357722i	$-0.116447\pi$
$97$	160.989	+	32.0227i	1.65968	+	0.330130i	0.725850	+	0.687853i	$0.241447\pi$
$98$		0			0
$99$	105.172	−	70.2737i	1.06234	−	0.709835i
$100$		0			0
$101$			123.412i			1.22190i	0.791670	+	0.610950i	$0.209212\pi$
$101$			123.412i			1.22190i	−0.791670	+	0.610950i	$0.790788\pi$
$102$		0			0
$103$	130.705			1.26898			0.634490	−	0.772931i	$-0.281210\pi$
$103$	130.705			1.26898			0.634490	+	0.772931i	$0.281210\pi$
$104$		0			0
$105$	19.9726	+	29.8911i	0.190215	+	0.284677i
$106$		0			0
$107$	8.65839	−	43.5287i	0.0809195	−	0.406810i	−0.919002	−	0.394254i	$-0.871003\pi$
$107$	8.65839	−	43.5287i	0.0809195	−	0.406810i	0.999921	−	0.0125562i	$-0.00399687\pi$
$108$		0			0
$109$	−36.5333	−	183.665i	−0.335168	−	1.68500i	−0.669711	−	0.742622i	$-0.733582\pi$
$109$	−36.5333	−	183.665i	−0.335168	−	1.68500i	0.334543	−	0.942381i	$-0.391418\pi$
$110$		0			0
$111$	−7.53518	+	18.1915i	−0.0678845	+	0.163888i
$112$		0			0
$113$	−23.5114	−	15.7098i	−0.208065	−	0.139025i	0.447172	−	0.894448i	$-0.352431\pi$
$113$	−23.5114	−	15.7098i	−0.208065	−	0.139025i	−0.655237	+	0.755423i	$0.727431\pi$
$114$		0			0
$115$	−79.8939	−	79.8939i	−0.694730	−	0.694730i
$116$		0			0
$117$	0.743516	−	0.307974i	0.00635484	−	0.00263226i
$118$		0			0
$119$	47.0220	+	188.191i	0.395143	+	1.58144i
$120$		0			0
$121$	66.2762	+	160.005i	0.547737	+	1.32236i
$122$		0			0
$123$	−24.1428	+	24.1428i	−0.196283	+	0.196283i
$124$		0			0
$125$	−60.2633	+	90.1904i	−0.482106	+	0.721523i
$126$		0			0
$127$	−119.259	−	49.3988i	−0.939050	−	0.388967i	−0.139945	−	0.990159i	$-0.544693\pi$
$127$	−119.259	−	49.3988i	−0.939050	−	0.388967i	−0.799105	+	0.601192i	$0.794693\pi$
$128$		0			0
$129$	−30.6435	+	6.09537i	−0.237546	+	0.0472509i
$130$		0			0
$131$	−96.2685	−	19.1490i	−0.734874	−	0.146176i	−0.186555	−	0.982445i	$-0.559732\pi$
$131$	−96.2685	−	19.1490i	−0.734874	−	0.146176i	−0.548319	+	0.836269i	$0.684732\pi$
$132$		0			0
$133$	91.7609	−	61.3126i	0.689931	−	0.460997i
$134$		0			0
$135$		−	51.5901i		−	0.382149i
$136$		0			0
$137$	−32.1029			−0.234328			−0.117164	−	0.993113i	$-0.537380\pi$
$137$	−32.1029			−0.234328			−0.117164	+	0.993113i	$0.537380\pi$
$138$		0			0
$139$	−128.501	−	192.316i	−0.924469	−	1.38357i	−0.923513	−	0.383566i	$-0.874696\pi$
$139$	−128.501	−	192.316i	−0.924469	−	1.38357i	−0.000955713	−	1.00000i	$-0.500304\pi$
$140$		0			0
$141$	1.85299	−	9.31561i	0.0131418	−	0.0660682i
$142$		0			0
$143$	0.365159	+	1.83578i	0.00255356	+	0.0128376i
$144$		0			0
$145$	38.3315	−	92.5403i	0.264355	−	0.638209i
$146$		0			0
$147$	86.0719	+	57.5114i	0.585523	+	0.391234i
$148$		0			0
$149$	−52.9745	−	52.9745i	−0.355534	−	0.355534i	0.506630	−	0.862164i	$-0.330891\pi$
$149$	−52.9745	−	52.9745i	−0.355534	−	0.355534i	−0.862164	+	0.506630i	$0.830891\pi$
$150$		0			0
$151$	−37.1788	+	15.4000i	−0.246217	+	0.101986i	−0.502379	−	0.864647i	$-0.667542\pi$
$151$	−37.1788	+	15.4000i	−0.246217	+	0.101986i	0.256162	+	0.966634i	$0.417542\pi$
$152$		0			0
$153$	42.3048	−	118.016i	0.276502	−	0.771344i
$154$		0			0
$155$	31.1321	+	75.1595i	0.200852	+	0.484900i
$156$		0			0
$157$	48.5156	−	48.5156i	0.309016	−	0.309016i	−0.535512	−	0.844528i	$-0.679881\pi$
$157$	48.5156	−	48.5156i	0.309016	−	0.309016i	0.844528	+	0.535512i	$0.179881\pi$
$158$		0			0
$159$	−41.8908	+	62.6940i	−0.263464	+	0.394302i
$160$		0			0
$161$	−481.975	−	199.641i	−2.99363	−	1.24000i
$162$		0			0
$163$	−39.9839	+	7.95328i	−0.245300	+	0.0487932i	−0.316209	−	0.948690i	$-0.602410\pi$
$163$	−39.9839	+	7.95328i	−0.245300	+	0.0487932i	0.0709090	+	0.997483i	$0.477410\pi$
$164$		0			0
$165$	53.0006	+	10.5425i	0.321216	+	0.0638938i
$166$		0			0
$167$	92.9523	−	62.1088i	0.556601	−	0.371909i	−0.245225	−	0.969466i	$-0.578862\pi$
$167$	92.9523	−	62.1088i	0.556601	−	0.371909i	0.801826	+	0.597557i	$0.203862\pi$
$168$		0			0
$169$		−	168.988i		−	0.999930i
$170$		0			0
$171$	−71.3266			−0.417115
$172$		0			0
$173$	−76.6097	−	114.655i	−0.442831	−	0.662743i	0.541169	−	0.840914i	$-0.317982\pi$
$173$	−76.6097	−	114.655i	−0.442831	−	0.662743i	−0.984000	+	0.178171i	$0.942982\pi$
$174$		0			0
$175$	−42.0565	+	211.432i	−0.240323	+	1.20818i
$176$		0			0
$177$	10.8576	+	54.5846i	0.0613421	+	0.308388i
$178$		0			0
$179$	−103.478	+	249.818i	−0.578090	+	1.39563i	0.316436	+	0.948614i	$0.397514\pi$
$179$	−103.478	+	249.818i	−0.578090	+	1.39563i	−0.894525	+	0.447018i	$0.852486\pi$
$180$		0			0
$181$	173.744	+	116.092i	0.959911	+	0.641392i	0.933621	−	0.358263i	$-0.116631\pi$
$181$	173.744	+	116.092i	0.959911	+	0.641392i	0.0262897	+	0.999654i	$0.491631\pi$
$182$		0			0
$183$	−85.8906	−	85.8906i	−0.469347	−	0.469347i
$184$		0			0
$185$	35.2627	−	14.6063i	0.190609	−	0.0789529i
$186$		0			0
$187$	250.011	+	150.050i	1.33696	+	0.802408i
$188$		0			0
$189$	−91.1562	−	220.071i	−0.482308	−	1.16439i
$190$		0			0
$191$	45.4459	−	45.4459i	0.237937	−	0.237937i	−0.578059	−	0.815995i	$-0.696189\pi$
$191$	45.4459	−	45.4459i	0.237937	−	0.237937i	0.815995	+	0.578059i	$0.196189\pi$
$192$		0			0
$193$	−129.323	+	193.546i	−0.670068	+	1.00283i	0.328235	+	0.944596i	$0.393546\pi$
$193$	−129.323	+	193.546i	−0.670068	+	1.00283i	−0.998303	+	0.0582320i	$0.981454\pi$
$194$		0			0
$195$	0.317646	+	0.131573i	0.00162896	+	0.000674735i
$196$		0			0
$197$	185.960	−	36.9898i	0.943961	−	0.187766i	0.300965	−	0.953635i	$-0.402691\pi$
$197$	185.960	−	36.9898i	0.943961	−	0.187766i	0.642996	+	0.765870i	$0.277691\pi$
$198$		0			0
$199$	−269.016	−	53.5107i	−1.35184	−	0.268898i	−0.534556	−	0.845133i	$-0.679521\pi$
$199$	−269.016	−	53.5107i	−1.35184	−	0.268898i	−0.817284	+	0.576235i	$0.804521\pi$
$200$		0			0
$201$	−72.3451	+	48.3394i	−0.359926	+	0.240495i
$202$		0			0
$203$		−	462.483i		−	2.27824i
$204$		0			0
$205$	66.1833			0.322845
$206$		0			0
$207$	187.322	+	280.347i	0.904936	+	1.35433i
$208$		0			0
$209$	32.3637	−	162.704i	0.154850	−	0.778486i
$210$		0			0
$211$	−15.5812	−	78.3322i	−0.0738447	−	0.371243i	0.926138	−	0.377186i	$-0.123108\pi$
$211$	−15.5812	−	78.3322i	−0.0738447	−	0.371243i	−0.999982	+	0.00594327i	$0.998108\pi$
$212$		0			0
$213$	−6.13654	+	14.8149i	−0.0288100	+	0.0695536i
$214$		0			0
$215$	50.3566	+	33.6472i	0.234217	+	0.156499i
$216$		0			0
$217$	265.604	+	265.604i	1.22398	+	1.22398i
$218$		0			0
$219$	64.4380	−	26.6911i	0.294237	−	0.121877i
$220$		0			0
$221$	1.37386	+	1.24666i	0.00621654	+	0.00564100i
$222$		0			0
$223$	16.2361	+	39.1974i	0.0728075	+	0.175773i	0.956094	−	0.293062i	$-0.0946741\pi$
$223$	16.2361	+	39.1974i	0.0728075	+	0.175773i	−0.883286	+	0.468834i	$0.844674\pi$
$224$		0			0
$225$	98.5196	−	98.5196i	0.437865	−	0.437865i
$226$		0			0
$227$	−197.549	+	295.653i	−0.870259	+	1.30243i	0.0818400	+	0.996645i	$0.473920\pi$
$227$	−197.549	+	295.653i	−0.870259	+	1.30243i	−0.952099	+	0.305789i	$0.901080\pi$
$228$		0			0
$229$	187.619	+	77.7142i	0.819295	+	0.339363i	0.752656	−	0.658414i	$-0.228772\pi$
$229$	187.619	+	77.7142i	0.819295	+	0.339363i	0.0666394	+	0.997777i	$0.478772\pi$
$230$		0			0
$231$	244.715	−	48.6769i	1.05937	−	0.210723i
$232$		0			0
$233$	438.723	+	87.2675i	1.88293	+	0.374539i	0.996151	−	0.0876494i	$-0.0279355\pi$
$233$	438.723	+	87.2675i	1.88293	+	0.374539i	0.886782	+	0.462188i	$0.152936\pi$
$234$		0			0
$235$	−15.3084	+	10.2288i	−0.0651422	+	0.0435266i
$236$		0			0
$237$		−	27.1149i		−	0.114409i
$238$		0			0
$239$	−260.199			−1.08870			−0.544349	−	0.838859i	$-0.683223\pi$
$239$	−260.199			−1.08870			−0.544349	+	0.838859i	$0.683223\pi$
$240$		0			0
$241$	−130.656	−	195.541i	−0.542142	−	0.811373i	0.454711	−	0.890639i	$-0.349742\pi$
$241$	−130.656	−	195.541i	−0.542142	−	0.811373i	−0.996854	+	0.0792658i	$0.974742\pi$
$242$		0			0
$243$	−46.5426	+	233.986i	−0.191533	+	0.962904i
$244$		0			0
$245$	−39.1468	−	196.804i	−0.159783	−	0.803284i
$246$		0			0
$247$	0.403909	−	0.975123i	0.00163526	−	0.00394787i
$248$		0			0
$249$	−2.77551	−	1.85453i	−0.0111466	−	0.00744793i
$250$		0			0
$251$	259.360	+	259.360i	1.03331	+	1.03331i	0.999426	+	0.0338805i	$0.0107866\pi$
$251$	259.360	+	259.360i	1.03331	+	1.03331i	0.0338805	+	0.999426i	$0.489213\pi$
$252$		0			0
$253$	−724.496	+	300.096i	−2.86362	+	1.18615i
$254$		0			0
$255$	48.4314	−	22.8716i	0.189927	−	0.0896924i
$256$		0			0
$257$	153.628	+	370.890i	0.597773	+	1.44315i	0.875846	+	0.482591i	$0.160304\pi$
$257$	153.628	+	370.890i	0.597773	+	1.44315i	−0.278073	+	0.960560i	$0.589696\pi$
$258$		0			0
$259$	124.614	−	124.614i	0.481133	−	0.481133i
$260$		0			0
$261$	−166.064	+	248.532i	−0.636260	+	0.952231i
$262$		0			0
$263$	−111.688	−	46.2627i	−0.424670	−	0.175904i	0.160104	−	0.987100i	$-0.448817\pi$
$263$	−111.688	−	46.2627i	−0.424670	−	0.175904i	−0.584774	+	0.811196i	$0.698817\pi$
$264$		0			0
$265$	143.351	−	28.5142i	0.540946	−	0.107601i
$266$		0			0
$267$	−21.5339	−	4.28335i	−0.0806511	−	0.0160425i
$268$		0			0
$269$	151.153	−	100.997i	0.561906	−	0.375454i	−0.241940	−	0.970291i	$-0.577784\pi$
$269$	151.153	−	100.997i	0.561906	−	0.375454i	0.803846	+	0.594838i	$0.202784\pi$
$270$		0			0
$271$		−	378.602i		−	1.39705i	−0.715584	−	0.698527i	$-0.753839\pi$
$271$		−	378.602i		−	1.39705i	0.715584	−	0.698527i	$-0.246161\pi$
$272$		0			0
$273$	1.58748			0.00581495
$274$		0			0
$275$	180.031	+	269.436i	0.654660	+	0.979767i
$276$		0			0
$277$	−24.8846	+	125.103i	−0.0898360	+	0.451636i	0.909517	+	0.415667i	$0.136452\pi$
$277$	−24.8846	+	125.103i	−0.0898360	+	0.451636i	−0.999353	+	0.0359691i	$0.988548\pi$
$278$		0			0
$279$	−47.3615	−	238.102i	−0.169754	−	0.853413i
$280$		0			0
$281$	35.5452	−	85.8138i	0.126495	−	0.305387i	−0.847926	−	0.530114i	$-0.822149\pi$
$281$	35.5452	−	85.8138i	0.126495	−	0.305387i	0.974422	+	0.224727i	$0.0721491\pi$
$282$		0			0
$283$	166.689	+	111.378i	0.589007	+	0.393562i	0.814057	−	0.580785i	$-0.197254\pi$
$283$	166.689	+	111.378i	0.589007	+	0.393562i	−0.225049	+	0.974347i	$0.572254\pi$
$284$		0			0
$285$	−21.5472	−	21.5472i	−0.0756041	−	0.0756041i
$286$		0			0
$287$	282.322	−	116.941i	0.983699	−	0.407461i
$288$		0			0
$289$	287.641	−	27.9891i	0.995299	−	0.0968482i
$290$		0			0
$291$	−80.0821	−	193.335i	−0.275196	−	0.664383i
$292$		0			0
$293$	−151.840	+	151.840i	−0.518224	+	0.518224i	−0.917034	−	0.398810i	$-0.869423\pi$
$293$	−151.840	+	151.840i	−0.518224	+	0.518224i	0.398810	+	0.917034i	$0.369423\pi$
$294$		0			0
$295$	59.9351	−	89.6993i	0.203170	−	0.304065i
$296$		0			0
$297$	−330.806	−	137.025i	−1.11383	−	0.461362i
$298$		0			0
$299$	−4.89346	+	0.973370i	−0.0163661	+	0.00325542i
$300$		0			0
$301$	274.261	+	54.5540i	0.911167	+	0.181242i
$302$		0			0
$303$	130.821	−	87.4118i	0.431752	−	0.288488i
$304$		0			0
$305$			235.454i			0.771982i
$306$		0			0
$307$	18.0902			0.0589257			0.0294628	−	0.999566i	$-0.490620\pi$
$307$	18.0902			0.0589257			0.0294628	+	0.999566i	$0.490620\pi$
$308$		0			0
$309$	−92.5775	−	138.552i	−0.299604	−	0.448388i
$310$		0			0
$311$	13.4086	−	67.4095i	0.0431144	−	0.216751i	−0.953222	−	0.302271i	$-0.902255\pi$
$311$	13.4086	−	67.4095i	0.0431144	−	0.216751i	0.996336	+	0.0855203i	$0.0272552\pi$
$312$		0			0
$313$	−42.0205	−	211.251i	−0.134251	−	0.674924i	−0.988027	−	0.154283i	$-0.950693\pi$
$313$	−42.0205	−	211.251i	−0.134251	−	0.674924i	0.853776	−	0.520640i	$-0.174307\pi$
$314$		0			0
$315$	−79.5796	+	192.122i	−0.252634	+	0.609912i
$316$		0			0
$317$	−251.081	−	167.767i	−0.792054	−	0.529233i	0.0924774	−	0.995715i	$-0.470521\pi$
$317$	−251.081	−	167.767i	−0.792054	−	0.529233i	−0.884531	+	0.466482i	$0.845521\pi$
$318$		0			0
$319$	−491.578	−	491.578i	−1.54100	−	1.54100i
$320$		0			0
$321$	−52.2746	+	21.6529i	−0.162849	+	0.0674544i
$322$		0			0
$323$	−70.2121	−	148.677i	−0.217375	−	0.460300i
$324$		0			0
$325$	0.788988	+	1.90478i	0.00242765	+	0.00586088i
$326$		0			0
$327$	−168.816	+	168.816i	−0.516255	+	0.516255i
$328$		0			0
$329$	−47.2284	+	70.6822i	−0.143551	+	0.214840i
$330$		0			0
$331$	−228.839	−	94.7881i	−0.691356	−	0.286369i	0.00920905	−	0.999958i	$-0.497069\pi$
$331$	−228.839	−	94.7881i	−0.691356	−	0.286369i	−0.700565	+	0.713589i	$0.747069\pi$
$332$		0			0
$333$	−111.711	+	22.2206i	−0.335467	+	0.0667286i
$334$		0			0
$335$	165.418	+	32.9037i	0.493785	+	0.0982200i
$336$		0			0
$337$	−515.915	+	344.724i	−1.53091	+	1.02292i	−0.548503	+	0.836149i	$0.684802\pi$
$337$	−515.915	+	344.724i	−1.53091	+	1.02292i	−0.982404	+	0.186770i	$0.940198\pi$
$338$		0			0
$339$			36.0500i			0.106342i
$340$		0			0
$341$	564.626			1.65579
$342$		0			0
$343$	−204.106	−	305.467i	−0.595062	−	0.890574i
$344$		0			0
$345$	−28.1021	+	141.279i	−0.0814554	+	0.409504i
$346$		0			0
$347$	23.8769	+	120.037i	0.0688095	+	0.345929i	0.999818	−	0.0190684i	$-0.00607002\pi$
$347$	23.8769	+	120.037i	0.0688095	+	0.345929i	−0.931009	+	0.364997i	$0.881070\pi$
$348$		0			0
$349$	−128.144	+	309.368i	−0.367176	+	0.886441i	0.627034	+	0.778992i	$0.284269\pi$
$349$	−128.144	+	309.368i	−0.367176	+	0.886441i	−0.994211	+	0.107450i	$0.965731\pi$
$350$		0			0
$351$	−1.89420	−	1.26567i	−0.00539659	−	0.00360588i
$352$		0			0
$353$	−264.793	−	264.793i	−0.750122	−	0.750122i	0.224380	−	0.974502i	$-0.427964\pi$
$353$	−264.793	−	264.793i	−0.750122	−	0.750122i	−0.974502	+	0.224380i	$0.927964\pi$
$354$		0			0
$355$	28.7174	−	11.8951i	0.0808941	−	0.0335074i
$356$		0			0
$357$	166.184	−	183.140i	0.465501	−	0.512996i
$358$		0			0
$359$	−67.0648	−	161.909i	−0.186810	−	0.450999i	0.802532	−	0.596609i	$-0.203486\pi$
$359$	−67.0648	−	161.909i	−0.186810	−	0.450999i	−0.989342	+	0.145610i	$0.953486\pi$
$360$		0			0
$361$	189.119	−	189.119i	0.523876	−	0.523876i
$362$		0			0
$363$	122.668	−	183.586i	0.337928	−	0.505746i
$364$		0			0
$365$	−124.907	−	51.7383i	−0.342212	−	0.141749i
$366$		0			0
$367$	−423.014	+	84.1428i	−1.15263	+	0.229272i	−0.734171	−	0.678965i	$-0.762429\pi$
$367$	−423.014	+	84.1428i	−1.15263	+	0.229272i	−0.418457	+	0.908237i	$0.637429\pi$
$368$		0			0
$369$	−193.706	−	38.5305i	−0.524948	−	0.104419i
$370$		0			0
$371$	561.116	−	374.926i	1.51244	−	1.01058i
$372$		0			0
$373$			256.163i			0.686763i	0.939196	+	0.343382i	$0.111572\pi$
$373$			256.163i			0.686763i	−0.939196	+	0.343382i	$0.888428\pi$
$374$		0			0
$375$	138.289			0.368771
$376$		0			0
$377$	−2.45736	−	3.67769i	−0.00651818	−	0.00975515i
$378$		0			0
$379$	−65.2602	+	328.085i	−0.172190	+	0.865660i	0.794017	+	0.607895i	$0.207986\pi$
$379$	−65.2602	+	328.085i	−0.172190	+	0.865660i	−0.966208	+	0.257765i	$0.917014\pi$
$380$		0			0
$381$	32.1061	+	161.408i	0.0842679	+	0.423643i
$382$		0			0
$383$	185.672	−	448.251i	0.484782	−	1.17037i	−0.472531	−	0.881314i	$-0.656659\pi$
$383$	185.672	−	448.251i	0.484782	−	1.17037i	0.957313	−	0.289054i	$-0.0933406\pi$
$384$		0			0
$385$	−402.143	−	268.703i	−1.04453	−	0.697930i
$386$		0			0
$387$	−127.796	−	127.796i	−0.330221	−	0.330221i
$388$		0			0
$389$	113.757	−	47.1196i	0.292434	−	0.121130i	−0.231643	−	0.972801i	$-0.574410\pi$
$389$	113.757	−	47.1196i	0.292434	−	0.121130i	0.524077	+	0.851671i	$0.324410\pi$
$390$		0			0
$391$	−399.975	+	666.429i	−1.02295	+	1.70442i
$392$		0			0
$393$	47.8877	+	115.611i	0.121852	+	0.294176i
$394$		0			0
$395$	−37.1655	+	37.1655i	−0.0940899	+	0.0940899i
$396$		0			0
$397$	104.914	−	157.015i	0.264267	−	0.395504i	−0.675478	−	0.737380i	$-0.736063\pi$
$397$	104.914	−	157.015i	0.264267	−	0.395504i	0.939745	+	0.341877i	$0.111063\pi$
$398$		0			0
$399$	−129.987	−	53.8425i	−0.325783	−	0.134944i
$400$		0			0
$401$	−401.869	+	79.9368i	−1.00217	+	0.199344i	−0.668791	−	0.743450i	$-0.733188\pi$
$401$	−401.869	+	79.9368i	−1.00217	+	0.199344i	−0.333376	+	0.942794i	$0.608188\pi$
$402$		0			0
$403$	3.52335	+	0.700838i	0.00874281	+	0.00173905i
$404$		0			0
$405$	81.6925	−	54.5852i	0.201710	−	0.134778i
$406$		0			0
$407$		−	264.906i		−	0.650875i
$408$		0			0
$409$	389.614			0.952602			0.476301	−	0.879282i	$-0.341977\pi$
$409$	389.614			0.952602			0.476301	+	0.879282i	$0.341977\pi$
$410$		0			0
$411$	22.7383	+	34.0302i	0.0553243	+	0.0827987i
$412$		0			0
$413$	97.1759	−	488.536i	0.235293	−	1.18290i
$414$		0			0
$415$	1.26234	+	6.34624i	0.00304180	+	0.0152921i
$416$		0			0
$417$	−112.845	+	272.432i	−0.270611	+	0.653314i
$418$		0			0
$419$	403.250	+	269.443i	0.962411	+	0.643062i	0.934279	−	0.356542i	$-0.116044\pi$
$419$	403.250	+	269.443i	0.962411	+	0.643062i	0.0281315	+	0.999604i	$0.491044\pi$
$420$		0			0
$421$	33.5905	+	33.5905i	0.0797874	+	0.0797874i	0.745874	−	0.666087i	$-0.232032\pi$
$421$	33.5905	+	33.5905i	0.0797874	+	0.0797874i	−0.666087	+	0.745874i	$0.732032\pi$
$422$		0			0
$423$	50.7598	−	21.0254i	0.119999	−	0.0497054i
$424$		0			0
$425$	302.340	+	108.379i	0.711387	+	0.255010i
$426$		0			0
$427$	416.032	+	1004.39i	0.974314	+	2.35220i
$428$		0			0
$429$	1.68735	−	1.68735i	0.00393322	−	0.00393322i
$430$		0			0
$431$	36.0635	−	53.9729i	0.0836741	−	0.125227i	−0.787272	−	0.616606i	$-0.788507\pi$
$431$	36.0635	−	53.9729i	0.0836741	−	0.125227i	0.870946	+	0.491379i	$0.163507\pi$
$432$		0			0
$433$	461.541	+	191.176i	1.06591	+	0.441516i	0.845547	−	0.533901i	$-0.179274\pi$
$433$	461.541	+	191.176i	1.06591	+	0.441516i	0.220367	+	0.975417i	$0.429274\pi$
$434$		0			0
$435$	−125.246	+	24.9130i	−0.287922	+	0.0572712i
$436$		0			0
$437$	433.703	+	86.2689i	0.992456	+	0.197412i
$438$		0			0
$439$	85.4602	−	57.1027i	0.194670	−	0.130074i	−0.454415	−	0.890790i	$-0.650152\pi$
$439$	85.4602	−	57.1027i	0.194670	−	0.130074i	0.649085	+	0.760716i	$0.275152\pi$
$440$		0			0
$441$			598.800i			1.35782i
$442$		0			0
$443$	−373.795			−0.843780			−0.421890	−	0.906647i	$-0.638633\pi$
$443$	−373.795			−0.843780			−0.421890	+	0.906647i	$0.638633\pi$
$444$		0			0
$445$	23.6447	+	35.3867i	0.0531341	+	0.0795208i
$446$		0			0
$447$	−18.6334	+	93.6764i	−0.0416854	+	0.209567i
$448$		0			0
$449$	−99.1328	−	498.374i	−0.220786	−	1.10996i	−0.919055	−	0.394130i	$-0.871046\pi$
$449$	−99.1328	−	498.374i	−0.220786	−	1.10996i	0.698269	−	0.715835i	$-0.253954\pi$
$450$		0			0
$451$	175.784	−	424.381i	0.389766	−	0.940978i
$452$		0			0
$453$	42.6580	+	28.5032i	0.0941677	+	0.0629209i
$454$		0			0
$455$	−2.17591	−	2.17591i	−0.00478221	−	0.00478221i
$456$		0			0
$457$	256.637	−	106.303i	0.561570	−	0.232610i	−0.0837966	−	0.996483i	$-0.526705\pi$
$457$	256.637	−	106.303i	0.561570	−	0.232610i	0.645367	+	0.763873i	$0.276705\pi$
$458$		0			0
$459$	−344.306	+	86.0293i	−0.750122	+	0.187428i
$460$		0			0
$461$	−167.201	−	403.660i	−0.362693	−	0.875618i	−0.994904	−	0.100822i	$-0.967853\pi$
$461$	−167.201	−	403.660i	−0.362693	−	0.875618i	0.632212	−	0.774796i	$-0.282147\pi$
$462$		0			0
$463$	−234.702	+	234.702i	−0.506916	+	0.506916i	−0.913578	−	0.406662i	$-0.866693\pi$
$463$	−234.702	+	234.702i	−0.506916	+	0.506916i	0.406662	+	0.913578i	$0.366693\pi$
$464$		0			0
$465$	57.6211	−	86.2361i	0.123916	−	0.185454i
$466$		0			0
$467$	516.595	+	213.981i	1.10620	+	0.458203i	0.859627	−	0.510922i	$-0.170696\pi$
$467$	516.595	+	213.981i	1.10620	+	0.458203i	0.246572	+	0.969124i	$0.420696\pi$
$468$		0			0
$469$	763.771	−	151.923i	1.62851	−	0.323931i
$470$		0			0
$471$	−85.7915	−	17.0650i	−0.182148	−	0.0362314i
$472$		0			0
$473$	349.501	−	233.529i	0.738903	−	0.493719i
$474$		0			0
$475$		−	182.729i		−	0.384692i
$476$		0			0
$477$	−436.161			−0.914383
$478$		0			0
$479$	228.980	+	342.693i	0.478037	+	0.715434i	0.989605	−	0.143809i	$-0.0459352\pi$
$479$	228.980	+	342.693i	0.478037	+	0.715434i	−0.511568	+	0.859243i	$0.670935\pi$
$480$		0			0
$481$	0.328813	−	1.65306i	0.000683603	−	0.00343670i
$482$		0			0
$483$	129.753	+	652.315i	0.268641	+	1.35055i
$484$		0			0
$485$	−155.232	+	374.764i	−0.320066	+	0.772709i
$486$		0			0
$487$	435.159	+	290.764i	0.893550	+	0.597051i	0.915327	−	0.402712i	$-0.131932\pi$
$487$	435.159	+	290.764i	0.893550	+	0.597051i	−0.0217769	+	0.999763i	$0.506932\pi$
$488$		0			0
$489$	36.7511	+	36.7511i	0.0751556	+	0.0751556i
$490$		0			0
$491$	−92.8703	+	38.4682i	−0.189145	+	0.0783465i	−0.475246	−	0.879853i	$-0.657641\pi$
$491$	−92.8703	+	38.4682i	−0.189145	+	0.0783465i	0.286101	+	0.958200i	$0.407641\pi$
$492$		0			0
$493$	−681.522	−	101.503i	−1.38240	−	0.205889i
$494$		0			0
$495$	119.623	+	288.795i	0.241662	+	0.583424i
$496$		0			0
$497$	101.483	−	101.483i	0.204192	−	0.204192i
$498$		0			0
$499$	175.827	−	263.144i	0.352360	−	0.527343i	−0.612375	−	0.790567i	$-0.709786\pi$
$499$	175.827	−	263.144i	0.352360	−	0.527343i	0.964735	+	0.263224i	$0.0847858\pi$
$500$		0			0
$501$	−131.675	−	54.5416i	−0.262824	−	0.108865i
$502$		0			0
$503$	296.099	−	58.8978i	0.588667	−	0.117093i	0.108235	−	0.994125i	$-0.465480\pi$
$503$	296.099	−	58.8978i	0.588667	−	0.117093i	0.480432	+	0.877032i	$0.340480\pi$
$504$		0			0
$505$	−299.124	−	59.4994i	−0.592325	−	0.117821i
$506$		0			0
$507$	−179.133	+	119.693i	−0.353320	+	0.236081i
$508$		0			0
$509$			176.920i			0.347584i	0.984782	+	0.173792i	$0.0556020\pi$
$509$			176.920i			0.347584i	−0.984782	+	0.173792i	$0.944398\pi$
$510$		0			0
$511$	−624.242			−1.22161
$512$		0			0
$513$	112.175	+	167.882i	0.218664	+	0.327254i
$514$		0			0
$515$	−63.0156	+	316.801i	−0.122360	+	0.615148i
$516$		0			0
$517$	24.9294	+	125.328i	0.0482193	+	0.242415i
$518$		0			0
$519$	−67.2758	+	162.418i	−0.129626	+	0.312944i
$520$		0			0
$521$	−340.712	−	227.657i	−0.653958	−	0.436961i	0.183829	−	0.982958i	$-0.441151\pi$
$521$	−340.712	−	227.657i	−0.653958	−	0.436961i	−0.837787	+	0.545997i	$0.816151\pi$
$522$		0			0
$523$	556.260	+	556.260i	1.06359	+	1.06359i	0.997836	+	0.0657587i	$0.0209468\pi$
$523$	556.260	+	556.260i	1.06359	+	1.06359i	0.0657587	+	0.997836i	$0.479053\pi$
$524$		0			0
$525$	253.914	−	105.175i	0.483646	−	0.200333i
$526$		0			0
$527$	449.691	−	333.104i	0.853303	−	0.632076i
$528$		0			0
$529$	−597.499	−	1442.49i	−1.12949	−	2.72682i
$530$		0			0
$531$	−227.640	+	227.640i	−0.428700	+	0.428700i
$532$		0			0
$533$	1.62368	−	2.43001i	0.00304631	−	0.00455912i
$534$		0			0
$535$	101.330	+	41.9722i	0.189401	+	0.0784527i
$536$		0			0
$537$	338.109	−	67.2540i	0.629625	−	0.125240i
$538$		0			0
$539$	−1365.93	−	271.700i	−2.53419	−	0.504081i
$540$		0			0
$541$	−477.231	+	318.876i	−0.882128	+	0.589419i	−0.912025	−	0.410134i	$-0.865482\pi$
$541$	−477.231	+	318.876i	−0.882128	+	0.589419i	0.0298972	+	0.999553i	$0.490482\pi$
$542$		0			0
$543$		−	266.402i		−	0.490611i
$544$		0			0
$545$	462.779			0.849136
$546$		0			0
$547$	−132.750	−	198.674i	−0.242686	−	0.363206i	0.690052	−	0.723760i	$-0.257588\pi$
$547$	−132.750	−	198.674i	−0.242686	−	0.363206i	−0.932738	+	0.360554i	$0.882588\pi$
$548$		0			0
$549$	137.077	−	689.130i	0.249684	−	1.25525i
$550$		0			0
$551$	76.4788	+	384.485i	0.138800	+	0.697795i
$552$		0			0
$553$	−92.8699	+	224.208i	−0.167938	+	0.405439i
$554$		0			0
$555$	−40.4595	−	27.0342i	−0.0729000	−	0.0487102i
$556$		0			0
$557$	557.539	+	557.539i	1.00097	+	1.00097i	1.00000		0.000968143i	$0.000308169\pi$
$557$	557.539	+	557.539i	1.00097	+	1.00097i	0.000968143		1.00000i	$0.499692\pi$
$558$		0			0
$559$	2.47081	−	1.02344i	0.00442005	−	0.00183084i
$560$		0			0
$561$	−18.0222	−	371.300i	−0.0321252	−	0.661853i
$562$		0			0
$563$	−376.606	−	909.207i	−0.668927	−	1.61493i	−0.783408	−	0.621507i	$-0.786521\pi$
$563$	−376.606	−	909.207i	−0.668927	−	1.61493i	0.114481	−	0.993425i	$-0.463479\pi$
$564$		0			0
$565$	49.4125	−	49.4125i	0.0874557	−	0.0874557i
$566$		0			0
$567$	252.032	−	377.192i	0.444500	−	0.665242i
$568$		0			0
$569$	937.566	+	388.353i	1.64774	+	0.682518i	0.997045	−	0.0768183i	$-0.0244761\pi$
$569$	937.566	+	388.353i	1.64774	+	0.682518i	0.650699	+	0.759336i	$0.274476\pi$
$570$		0			0
$571$	7.25641	−	1.44339i	0.0127083	−	0.00252783i	−0.188732	−	0.982029i	$-0.560438\pi$
$571$	7.25641	−	1.44339i	0.0127083	−	0.00252783i	0.201440	+	0.979501i	$0.435438\pi$
$572$		0			0
$573$	−80.3634	−	15.9853i	−0.140250	−	0.0278975i
$574$		0			0
$575$	−718.210	+	479.893i	−1.24906	+	0.834596i
$576$		0			0
$577$			64.9096i			0.112495i	0.998417	+	0.0562475i	$0.0179136\pi$
$577$			64.9096i			0.112495i	−0.998417	+	0.0562475i	$0.982086\pi$
$578$		0			0
$579$	296.764			0.512546
$580$		0			0
$581$	16.5982	+	24.8410i	0.0285684	+	0.0427556i
$582$		0			0
$583$	197.904	−	994.929i	0.339457	−	1.70657i
$584$		0			0
$585$	0.387999	+	1.95060i	0.000663247	+	0.00333437i
$586$		0			0
$587$	228.376	−	551.348i	0.389056	−	0.939264i	−0.601084	−	0.799185i	$-0.705264\pi$
$587$	228.376	−	551.348i	0.389056	−	0.939264i	0.990140	−	0.140079i	$-0.0447355\pi$
$588$		0			0
$589$	−264.731	−	176.888i	−0.449459	−	0.300319i
$590$		0			0
$591$	−170.925	−	170.925i	−0.289213	−	0.289213i
$592$		0			0
$593$	−484.559	+	200.711i	−0.817132	+	0.338467i	−0.751796	−	0.659396i	$-0.770812\pi$
$593$	−484.559	+	200.711i	−0.817132	+	0.338467i	−0.0653365	+	0.997863i	$0.520812\pi$
$594$		0			0
$595$	−478.805	+	23.2403i	−0.804715	+	0.0390594i
$596$		0			0
$597$	133.819	+	323.068i	0.224153	+	0.541153i
$598$		0			0
$599$	−103.792	+	103.792i	−0.173276	+	0.173276i	−0.788417	−	0.615141i	$-0.789099\pi$
$599$	−103.792	+	103.792i	−0.173276	+	0.173276i	0.615141	+	0.788417i	$0.289099\pi$
$600$		0			0
$601$	−369.890	+	553.579i	−0.615457	+	0.921097i	−0.999998	−	0.00201122i	$-0.999360\pi$
$601$	−369.890	+	553.579i	−0.615457	+	0.921097i	0.384541	+	0.923108i	$0.374360\pi$
$602$		0			0
$603$	−464.991	−	192.606i	−0.771130	−	0.319412i
$604$		0			0
$605$	−419.771	+	83.4977i	−0.693837	+	0.138013i
$606$		0			0
$607$	71.3521	+	14.1928i	0.117549	+	0.0233819i	0.253514	−	0.967332i	$-0.418414\pi$
$607$	71.3521	+	14.1928i	0.117549	+	0.0233819i	−0.135965	+	0.990714i	$0.543414\pi$
$608$		0			0
$609$	−490.249	+	327.574i	−0.805006	+	0.537888i
$610$		0			0
$611$			0.813012i			0.00133063i
$612$		0			0
$613$	−878.977			−1.43389			−0.716947	−	0.697128i	$-0.754461\pi$
$613$	−878.977			−1.43389			−0.716947	+	0.697128i	$0.754461\pi$
$614$		0			0
$615$	−46.8772	−	70.1567i	−0.0762231	−	0.114076i
$616$		0			0
$617$	−23.6766	+	119.030i	−0.0383737	+	0.192918i	−0.995217	−	0.0976857i	$-0.968856\pi$
$617$	−23.6766	+	119.030i	−0.0383737	+	0.192918i	0.956844	+	0.290603i	$0.0938560\pi$
$618$		0			0
$619$	135.112	+	679.255i	0.218275	+	1.09734i	0.922095	+	0.386964i	$0.126476\pi$
$619$	135.112	+	679.255i	0.218275	+	1.09734i	−0.703820	+	0.710378i	$0.748524\pi$
$620$		0			0
$621$	365.253	−	881.799i	0.588169	−	1.41997i
$622$		0			0
$623$	163.388	+	109.173i	0.262260	+	0.175237i
$624$		0			0
$625$	144.433	+	144.433i	0.231093	+	0.231093i
$626$		0			0
$627$	−195.395	+	80.9351i	−0.311634	+	0.129083i
$628$		0			0
$629$	−156.283	−	210.982i	−0.248462	−	0.335424i
$630$		0			0
$631$	9.68876	+	23.3907i	0.0153546	+	0.0370693i	0.931371	−	0.364072i	$-0.118614\pi$
$631$	9.68876	+	23.3907i	0.0153546	+	0.0370693i	−0.916016	+	0.401141i	$0.868614\pi$
$632$		0			0
$633$	−71.9988	+	71.9988i	−0.113742	+	0.113742i
$634$		0			0
$635$	177.230	−	265.243i	0.279102	−	0.417706i
$636$		0			0
$637$	−8.18634	−	3.39089i	−0.0128514	−	0.00532322i
$638$		0			0
$639$	−90.9755	+	18.0962i	−0.142372	+	0.0283195i
$640$		0			0
$641$	5.61666	+	1.11722i	0.00876234	+	0.00174294i	0.199470	−	0.979904i	$-0.436078\pi$
$641$	5.61666	+	1.11722i	0.00876234	+	0.00174294i	−0.190707	+	0.981647i	$0.561078\pi$
$642$		0			0
$643$	831.365	−	555.500i	1.29295	−	0.863920i	0.297090	−	0.954849i	$-0.403984\pi$
$643$	831.365	−	555.500i	1.29295	−	0.863920i	0.995857	+	0.0909296i	$0.0289838\pi$
$644$		0			0
$645$		−	77.2119i		−	0.119708i
$646$		0			0
$647$	−622.118			−0.961542			−0.480771	−	0.876846i	$-0.659643\pi$
$647$	−622.118			−0.961542			−0.480771	+	0.876846i	$0.659643\pi$
$648$		0			0
$649$	−415.981	−	622.560i	−0.640957	−	0.959260i
$650$		0			0
$651$	93.4241	−	469.675i	0.143509	−	0.721466i
$652$		0			0
$653$	−32.2737	−	162.251i	−0.0494238	−	0.248470i	0.948173	−	0.317754i	$-0.102929\pi$
$653$	−32.2737	−	162.251i	−0.0494238	−	0.248470i	−0.997597	+	0.0692838i	$0.977929\pi$
$654$		0			0
$655$	92.8262	−	224.102i	0.141719	−	0.342141i
$656$		0			0
$657$	335.459	+	224.147i	0.510593	+	0.341167i
$658$		0			0
$659$	−141.629	−	141.629i	−0.214915	−	0.214915i	0.591437	−	0.806351i	$-0.298561\pi$
$659$	−141.629	−	141.629i	−0.214915	−	0.214915i	−0.806351	+	0.591437i	$0.798561\pi$
$660$		0			0
$661$	55.0897	−	22.8189i	0.0833429	−	0.0345218i	−0.340623	−	0.940200i	$-0.610638\pi$
$661$	55.0897	−	22.8189i	0.0833429	−	0.0345218i	0.423965	+	0.905678i	$0.360638\pi$
$662$		0			0
$663$	0.348412	−	2.33934i	0.000525508	−	0.00352841i
$664$		0			0
$665$	104.369	+	251.969i	0.156946	+	0.378901i
$666$		0			0
$667$	1310.35	−	1310.35i	1.96455	−	1.96455i
$668$		0			0
$669$	30.0507	−	44.9741i	0.0449188	−	0.0672258i
$670$		0			0
$671$	1509.78	+	625.372i	2.25005	+	0.932000i
$672$		0			0
$673$	−386.820	+	76.9432i	−0.574769	+	0.114329i	−0.473912	−	0.880572i	$-0.657159\pi$
$673$	−386.820	+	76.9432i	−0.574769	+	0.114329i	−0.100857	+	0.994901i	$0.532159\pi$
$674$		0			0
$675$	−386.827	−	76.9447i	−0.573077	−	0.113992i
$676$		0			0
$677$	−826.962	+	552.558i	−1.22151	+	0.816186i	−0.987740	−	0.156106i	$-0.950106\pi$
$677$	−826.962	+	552.558i	−1.22151	+	0.816186i	−0.233769	+	0.972292i	$0.575106\pi$
$678$		0			0
$679$			1872.93i			2.75837i
$680$		0			0
$681$	453.325			0.665675
$682$		0			0
$683$	42.9330	+	64.2537i	0.0628594	+	0.0940757i	0.861568	−	0.507643i	$-0.169483\pi$
$683$	42.9330	+	64.2537i	0.0628594	+	0.0940757i	−0.798708	+	0.601718i	$0.794483\pi$
$684$		0			0
$685$	15.4775	−	77.8106i	0.0225949	−	0.113592i
$686$		0			0
$687$	−50.5092	−	253.927i	−0.0735214	−	0.369617i
$688$		0			0
$689$	2.46990	−	5.96286i	0.00358476	−	0.00865437i
$690$		0			0
$691$	−975.457	−	651.780i	−1.41166	−	0.943241i	−0.999483	−	0.0321374i	$-0.989769\pi$
$691$	−975.457	−	651.780i	−1.41166	−	0.943241i	−0.412177	−	0.911104i	$-0.635231\pi$
$692$		0			0
$693$	1020.56	+	1020.56i	1.47267	+	1.47267i
$694$		0			0
$695$	528.085	−	218.740i	0.759835	−	0.314734i
$696$		0			0
$697$	−110.364	−	441.699i	−0.158342	−	0.633715i
$698$		0			0
$699$	−218.238	−	526.874i	−0.312215	−	0.753753i
$700$		0			0
$701$	−365.359	+	365.359i	−0.521197	+	0.521197i	−0.917933	−	0.396736i	$-0.870143\pi$
$701$	−365.359	+	365.359i	−0.521197	+	0.521197i	0.396736	+	0.917933i	$0.370143\pi$
$702$		0			0
$703$	−82.9906	+	124.204i	−0.118052	+	0.176677i
$704$		0			0
$705$	21.6857	+	8.98251i	0.0307598	+	0.0127411i
$706$		0			0
$707$	−1381.12	+	274.722i	−1.95349	+	0.388574i
$708$		0			0
$709$	734.297	+	146.061i	1.03568	+	0.206010i	0.683521	−	0.729931i	$-0.260448\pi$
$709$	734.297	+	146.061i	1.03568	+	0.206010i	0.352159	+	0.935940i	$0.385448\pi$
$710$		0			0
$711$	130.413	−	87.1394i	0.183422	−	0.122559i
$712$		0			0
$713$			1505.07i			2.11090i
$714$		0			0
$715$	−4.62559			−0.00646935
$716$		0			0
$717$	184.297	+	275.820i	0.257039	+	0.384686i
$718$		0			0
$719$	−100.953	+	507.524i	−0.140407	+	0.705875i	0.844878	+	0.534959i	$0.179673\pi$
$719$	−100.953	+	507.524i	−0.140407	+	0.705875i	−0.985286	+	0.170916i	$0.945327\pi$
$720$		0			0
$721$	290.957	+	1462.74i	0.403546	+	2.02876i
$722$		0			0
$723$	−114.737	+	277.001i	−0.158696	+	0.383127i
$724$		0			0
$725$	−636.705	−	425.433i	−0.878214	−	0.586804i
$726$		0			0
$727$	−711.060	−	711.060i	−0.978075	−	0.978075i	0.0216900	−	0.999765i	$-0.493095\pi$
$727$	−711.060	−	711.060i	−0.978075	−	0.978075i	−0.999765	+	0.0216900i	$0.993095\pi$
$728$		0			0
$729$	−49.5786	+	20.5361i	−0.0680091	+	0.0281703i
$730$		0			0
$731$	140.585	−	392.182i	0.192319	−	0.536501i
$732$		0			0
$733$	392.009	+	946.394i	0.534801	+	1.29112i	0.928311	+	0.371803i	$0.121260\pi$
$733$	392.009	+	946.394i	0.534801	+	1.29112i	−0.393511	+	0.919320i	$0.628740\pi$
$734$		0			0
$735$	−180.892	+	180.892i	−0.246112	+	0.246112i
$736$		0			0
$737$	650.339	−	973.301i	0.882414	−	1.32063i
$738$		0			0
$739$	906.748	+	375.587i	1.22699	+	0.508237i	0.899626	−	0.436660i	$-0.143839\pi$
$739$	906.748	+	375.587i	1.22699	+	0.508237i	0.327366	+	0.944897i	$0.393839\pi$
$740$		0			0
$741$	−1.31975	+	0.262515i	−0.00178104	+	0.000354271i
$742$		0			0
$743$	−507.459	−	100.940i	−0.682986	−	0.135854i	−0.158610	−	0.987341i	$-0.550701\pi$
$743$	−507.459	−	100.940i	−0.682986	−	0.135854i	−0.524376	+	0.851487i	$0.675701\pi$
$744$		0			0
$745$	153.939	−	102.859i	0.206630	−	0.138065i
$746$		0			0
$747$		−	19.3091i		−	0.0258489i
$748$		0			0
$749$	506.410			0.676114
$750$		0			0
$751$	570.781	+	854.235i	0.760028	+	1.13746i	0.986550	+	0.163457i	$0.0522645\pi$
$751$	570.781	+	854.235i	0.760028	+	1.13746i	−0.226522	+	0.974006i	$0.572736\pi$
$752$		0			0
$753$	91.2279	−	458.634i	0.121153	−	0.609075i
$754$		0			0
$755$	−19.4015	−	97.5381i	−0.0256974	−	0.129189i
$756$		0			0
$757$	421.645	−	1017.94i	0.556995	−	1.34470i	−0.355140	−	0.934813i	$-0.615567\pi$
$757$	421.645	−	1017.94i	0.556995	−	1.34470i	0.912134	−	0.409891i	$-0.134433\pi$
$758$		0			0
$759$	831.269	+	555.436i	1.09522	+	0.731800i
$760$		0			0
$761$	−423.085	−	423.085i	−0.555960	−	0.555960i	0.372195	−	0.928155i	$-0.378605\pi$
$761$	−423.085	−	423.085i	−0.555960	−	0.555960i	−0.928155	+	0.372195i	$0.878605\pi$
$762$		0			0
$763$	1974.10	−	817.699i	2.58729	−	1.07169i
$764$		0			0
$765$	265.649	+	159.436i	0.347253	+	0.208413i
$766$		0			0
$767$	−1.82304	−	4.40120i	−0.00237684	−	0.00573820i
$768$		0			0
$769$	−272.887	+	272.887i	−0.354860	+	0.354860i	−0.861914	−	0.507054i	$-0.830734\pi$
$769$	−272.887	+	272.887i	−0.354860	+	0.354860i	0.507054	+	0.861914i	$0.330734\pi$
$770$		0			0
$771$	284.343	−	425.549i	0.368798	−	0.551945i
$772$		0			0
$773$	54.1983	+	22.4497i	0.0701143	+	0.0290423i	0.417465	−	0.908693i	$-0.362919\pi$
$773$	54.1983	+	22.4497i	0.0701143	+	0.0290423i	−0.347351	+	0.937735i	$0.612919\pi$
$774$		0			0
$775$	609.985	−	121.333i	0.787077	−	0.156559i
$776$		0			0
$777$	−220.358	−	43.8319i	−0.283601	−	0.0564117i
$778$		0			0
$779$	−215.370	+	143.906i	−0.276470	+	0.184731i
$780$		0			0
$781$		−	215.736i		−	0.276230i
$782$		0			0
$783$	846.138			1.08064
$784$		0			0
$785$	94.2010	+	140.982i	0.120001	+	0.179595i
$786$		0			0
$787$	−199.923	+	1005.08i	−0.254031	+	1.27710i	0.617426	+	0.786629i	$0.288176\pi$
$787$	−199.923	+	1005.08i	−0.254031	+	1.27710i	−0.871457	+	0.490472i	$0.836824\pi$
$788$		0			0
$789$	30.0678	+	151.161i	0.0381087	+	0.191586i
$790$		0			0
$791$	123.473	−	298.090i	0.156097	−	0.376852i
$792$		0			0
$793$	8.64503	+	5.77643i	0.0109017	+	0.00728427i
$794$		0			0
$795$	−131.761	−	131.761i	−0.165737	−	0.165737i
$796$		0			0
$797$	−300.327	+	124.400i	−0.376822	+	0.156085i	−0.563052	−	0.826421i	$-0.690373\pi$
$797$	−300.327	+	124.400i	−0.376822	+	0.156085i	0.186230	+	0.982506i	$0.440373\pi$
$798$		0			0
$799$	93.7930	+	85.1094i	0.117388	+	0.106520i
$800$		0			0
$801$	−48.6020	−	117.336i	−0.0606767	−	0.146486i
$802$		0			0
$803$	−663.514	+	663.514i	−0.826294	+	0.826294i
$804$		0			0
$805$	716.256	−	1071.95i	0.889759	−	1.33162i
$806$		0			0
$807$	−214.121	−	88.6918i	−0.265330	−	0.109903i
$808$		0			0
$809$	−250.751	+	49.8775i	−0.309952	+	0.0616533i	−0.347616	−	0.937637i	$-0.613009\pi$
$809$	−250.751	+	49.8775i	−0.309952	+	0.0616533i	0.0376633	+	0.999290i	$0.488009\pi$
$810$		0			0
$811$	57.3241	+	11.4025i	0.0706832	+	0.0140598i	0.230305	−	0.973118i	$-0.426028\pi$
$811$	57.3241	+	11.4025i	0.0706832	+	0.0140598i	−0.159622	+	0.987178i	$0.551028\pi$
$812$		0			0
$813$	−401.331	+	268.161i	−0.493642	+	0.329841i
$814$		0			0
$815$		−	100.747i		−	0.123616i
$816$		0			0
$817$	−237.028			−0.290120
$818$		0			0
$819$	5.10170	+	7.63523i	0.00622918	+	0.00932262i
$820$		0			0
$821$	−174.747	+	878.512i	−0.212846	+	1.07005i	0.715579	+	0.698532i	$0.246163\pi$
$821$	−174.747	+	878.512i	−0.212846	+	1.07005i	−0.928425	+	0.371519i	$0.878837\pi$
$822$		0			0
$823$	97.0117	+	487.711i	0.117876	+	0.592601i	0.993895	+	0.110326i	$0.0351894\pi$
$823$	97.0117	+	487.711i	0.117876	+	0.592601i	−0.876020	+	0.482275i	$0.839811\pi$
$824$		0			0
$825$	158.097	−	381.680i	0.191633	−	0.462642i
$826$		0			0
$827$	−1333.07	−	890.728i	−1.61193	−	1.07706i	−0.942509	−	0.334180i	$-0.891541\pi$
$827$	−1333.07	−	890.728i	−1.61193	−	1.07706i	−0.669424	−	0.742880i	$-0.733459\pi$
$828$		0			0
$829$	−756.440	−	756.440i	−0.912473	−	0.912473i	0.0839934	−	0.996466i	$-0.473233\pi$
$829$	−756.440	−	756.440i	−0.912473	−	0.912473i	−0.996466	+	0.0839934i	$0.973233\pi$
$830$		0			0
$831$	150.239	−	62.2312i	0.180794	−	0.0748871i
$832$		0			0
$833$	−1248.17	+	589.443i	−1.49840	+	0.707615i
$834$		0			0
$835$	105.724	+	255.241i	0.126616	+	0.305677i
$836$		0			0
$837$	−485.936	+	485.936i	−0.580569	+	0.580569i
$838$		0			0
$839$	350.486	−	524.539i	0.417742	−	0.625196i	−0.561599	−	0.827410i	$-0.689814\pi$
$839$	350.486	−	524.539i	0.417742	−	0.625196i	0.979341	+	0.202214i	$0.0648136\pi$
$840$		0			0
$841$	740.786	+	306.844i	0.880840	+	0.364856i
$842$		0			0
$843$	−116.142	+	23.1021i	−0.137772	+	0.0274046i
$844$		0			0
$845$	409.591	+	81.4727i	0.484723	+	0.0964174i
$846$		0			0
$847$	−1643.10	+	1097.89i	−1.93991	+	1.29621i
$848$		0			0
$849$		−	255.585i		−	0.301042i
$850$		0			0
$851$	706.135			0.829771
$852$		0			0
$853$	205.723	+	307.886i	0.241176	+	0.360945i	0.932235	−	0.361853i	$-0.117856\pi$
$853$	205.723	+	307.886i	0.241176	+	0.360945i	−0.691059	+	0.722798i	$0.742856\pi$
$854$		0			0
$855$	34.3881	−	172.880i	0.0402200	−	0.202199i
$856$		0			0
$857$	−40.7239	−	204.733i	−0.0475192	−	0.238895i	0.949725	−	0.313086i	$-0.101363\pi$
$857$	−40.7239	−	204.733i	−0.0475192	−	0.238895i	−0.997244	+	0.0741905i	$0.976363\pi$
$858$		0			0
$859$	−527.928	+	1274.53i	−0.614584	+	1.48374i	0.243330	+	0.969944i	$0.421760\pi$
$859$	−527.928	+	1274.53i	−0.614584	+	1.48374i	−0.857914	+	0.513793i	$0.828240\pi$
$860$		0			0
$861$	−323.929	−	216.442i	−0.376224	−	0.251385i
$862$		0			0
$863$	262.271	+	262.271i	0.303906	+	0.303906i	0.842540	−	0.538634i	$-0.181059\pi$
$863$	262.271	+	262.271i	0.303906	+	0.303906i	−0.538634	+	0.842540i	$0.681059\pi$
$864$		0			0
$865$	314.833	−	130.408i	0.363969	−	0.150761i
$866$		0			0
$867$	−233.404	−	285.086i	−0.269209	−	0.328819i
$868$		0			0
$869$	139.600	+	337.025i	0.160645	+	0.387831i
$870$		0			0
$871$	5.26632	−	5.26632i	0.00604629	−	0.00604629i
$872$		0			0
$873$	672.515	−	1006.49i	0.770349	−	1.15291i
$874$		0			0
$875$	−1143.48	−	473.646i	−1.30684	−	0.541310i
$876$		0			0
$877$	−1186.53	+	236.016i	−1.35295	+	0.269118i	−0.817732	−	0.575599i	$-0.804769\pi$
$877$	−1186.53	+	236.016i	−1.35295	+	0.269118i	−0.535214	+	0.844716i	$0.679769\pi$
$878$		0			0
$879$	268.503	+	53.4085i	0.305464	+	0.0607605i
$880$		0			0
$881$	1063.73	−	710.762i	1.20741	−	0.806768i	0.221686	−	0.975118i	$-0.428844\pi$
$881$	1063.73	−	710.762i	1.20741	−	0.806768i	0.985727	+	0.168350i	$0.0538440\pi$
$882$		0			0
$883$		−	990.015i		−	1.12120i	−0.828088	−	0.560598i	$-0.810571\pi$
$883$		−	990.015i		−	1.12120i	0.828088	−	0.560598i	$-0.189429\pi$
$884$		0			0
$885$	−137.536			−0.155408
$886$		0			0
$887$	527.272	+	789.119i	0.594444	+	0.889649i	0.999698	−	0.0245552i	$-0.00781695\pi$
$887$	527.272	+	789.119i	0.594444	+	0.889649i	−0.405254	+	0.914204i	$0.632817\pi$
$888$		0			0
$889$	287.352	−	1444.61i	0.323230	−	1.62499i
$890$		0			0
$891$	−133.034	−	668.809i	−0.149309	−	0.750627i
$892$		0			0
$893$	27.5749	−	66.5716i	0.0308789	−	0.0745483i
$894$		0			0
$895$	−555.617	−	371.251i	−0.620801	−	0.414806i
$896$		0			0
$897$	4.49781	+	4.49781i	0.00501428	+	0.00501428i
$898$		0			0
$899$	−1232.70	+	510.603i	−1.37119	+	0.567967i
$900$		0			0
$901$	−429.346	−	909.156i	−0.476521	−	1.00905i
$902$		0			0
$903$	−136.428	−	329.367i	−0.151083	−	0.364747i
$904$		0			0
$905$	−365.148	+	365.148i	−0.403478	+	0.403478i
$906$		0			0
$907$	208.028	−	311.335i	0.229358	−	0.343258i	−0.698884	−	0.715235i	$-0.746320\pi$
$907$	208.028	−	311.335i	0.229358	−	0.343258i	0.928242	+	0.371976i	$0.121320\pi$
$908$		0			0
$909$	840.840	+	348.287i	0.925016	+	0.383154i
$910$		0			0
$911$	−797.107	+	158.555i	−0.874981	+	0.174044i	−0.612097	−	0.790783i	$-0.709674\pi$
$911$	−797.107	+	158.555i	−0.874981	+	0.174044i	−0.262884	+	0.964827i	$0.584674\pi$
$912$		0			0
$913$	44.0462	+	8.76133i	0.0482434	+	0.00959620i
$914$		0			0
$915$	249.590	−	166.771i	0.272776	−	0.182263i
$916$		0			0
$917$		−	1119.98i		−	1.22135i
$918$		0			0
$919$	−1570.14			−1.70853			−0.854267	−	0.519834i	$-0.825994\pi$
$919$	−1570.14			−1.70853			−0.854267	+	0.519834i	$0.825994\pi$
$920$		0			0
$921$	−12.8132	−	19.1762i	−0.0139122	−	0.0208211i
$922$		0			0
$923$	0.267781	−	1.34622i	0.000290120	−	0.00145853i
$924$		0			0
$925$	−56.9262	−	286.187i	−0.0615418	−	0.309392i
$926$		0			0
$927$	368.870	−	890.530i	0.397918	−	0.960658i
$928$		0			0
$929$	691.212	+	461.853i	0.744039	+	0.497151i	0.868878	−	0.495026i	$-0.164841\pi$
$929$	691.212	+	461.853i	0.744039	+	0.497151i	−0.124839	+	0.992177i	$0.539841\pi$
$930$		0			0
$931$	555.311	+	555.311i	0.596467	+	0.596467i
$932$		0			0
$933$	−80.9537	+	33.5321i	−0.0867670	+	0.0359401i
$934$		0			0
$935$	−484.225	+	533.630i	−0.517888	+	0.570727i
$936$		0			0
$937$	−207.722	−	501.485i	−0.221688	−	0.535203i	0.773431	−	0.633880i	$-0.218539\pi$
$937$	−207.722	−	501.485i	−0.221688	−	0.535203i	−0.995119	+	0.0986776i	$0.968539\pi$
$938$		0			0
$939$	−194.171	+	194.171i	−0.206785	+	0.206785i
$940$		0			0
$941$	264.703	−	396.155i	0.281299	−	0.420994i	−0.663734	−	0.747969i	$-0.731029\pi$
$941$	264.703	−	396.155i	0.281299	−	0.420994i	0.945033	+	0.326975i	$0.106029\pi$
$942$		0			0
$943$	1131.23	+	468.572i	1.19961	+	0.496895i
$944$		0			0
$945$	577.353	−	114.843i	0.610955	−	0.121527i
$946$		0			0
$947$	−137.534	−	27.3572i	−0.145231	−	0.0288883i	0.121939	−	0.992538i	$-0.461089\pi$
$947$	−137.534	−	27.3572i	−0.145231	−	0.0288883i	−0.267171	+	0.963649i	$0.586089\pi$
$948$		0			0
$949$	−4.96401	+	3.31685i	−0.00523078	+	0.00349509i
$950$		0			0
$951$			384.983i			0.404819i
$952$		0			0
$953$	−1602.19			−1.68121			−0.840605	−	0.541649i	$-0.817800\pi$
$953$	−1602.19			−1.68121			−0.840605	+	0.541649i	$0.817800\pi$
$954$		0			0
$955$	88.2408	+	132.062i	0.0923987	+	0.138284i
$956$		0			0
$957$	−172.909	+	869.272i	−0.180678	+	0.908331i
$958$		0			0
$959$	−71.4629	−	359.269i	−0.0745182	−	0.374628i
$960$		0			0
$961$	46.9432	−	113.331i	0.0488483	−	0.117930i
$962$		0			0
$963$	−272.138	−	181.837i	−0.282594	−	0.188823i
$964$		0			0
$965$	−406.764	−	406.764i	−0.421518	−	0.421518i
$966$		0			0
$967$	1099.19	−	455.299i	1.13670	−	0.470837i	0.266647	−	0.963794i	$-0.414084\pi$
$967$	1099.19	−	455.299i	1.13670	−	0.470837i	0.870054	+	0.492957i	$0.164084\pi$
$968$		0			0
$969$	−107.872	+	179.734i	−0.111323	+	0.185484i
$970$		0			0
$971$	343.816	+	830.046i	0.354085	+	0.854836i	0.996107	+	0.0881503i	$0.0280956\pi$
$971$	343.816	+	830.046i	0.354085	+	0.854836i	−0.642022	+	0.766686i	$0.721904\pi$
$972$		0			0
$973$	1866.18	−	1866.18i	1.91797	−	1.91797i
$974$		0			0
$975$	1.46031	−	2.18550i	0.00149775	−	0.00224154i
$976$		0			0
$977$	−791.203	−	327.727i	−0.809829	−	0.335442i	−0.0609434	−	0.998141i	$-0.519411\pi$
$977$	−791.203	−	327.727i	−0.809829	−	0.335442i	−0.748886	+	0.662699i	$0.769411\pi$
$978$		0			0
$979$	289.708	−	57.6265i	0.295922	−	0.0588626i
$980$		0			0
$981$	−1354.47	−	269.420i	−1.38070	−	0.274638i
$982$		0			0
$983$	−1003.02	+	670.198i	−1.02037	+	0.681789i	−0.948875	−	0.315652i	$-0.897777\pi$
$983$	−1003.02	+	670.198i	−1.02037	+	0.681789i	−0.0714939	+	0.997441i	$0.522777\pi$
$984$		0			0
$985$			468.562i			0.475697i
$986$		0			0
$987$	108.377			0.109805
$988$		0			0
$989$	622.497	+	931.632i	0.629420	+	0.941994i
$990$		0			0
$991$	−7.67485	+	38.5841i	−0.00774455	+	0.0389345i	−0.984464	−	0.175585i	$-0.943818\pi$
$991$	−7.67485	+	38.5841i	−0.00774455	+	0.0389345i	0.976720	+	0.214519i	$0.0688184\pi$
$992$		0			0
$993$	61.6062	+	309.715i	0.0620405	+	0.311898i
$994$		0			0
$995$	259.397	−	626.239i	0.260700	−	0.629386i
$996$		0			0
$997$	−1123.88	−	750.953i	−1.12726	−	0.753213i	−0.155188	−	0.987885i	$-0.549598\pi$
$997$	−1123.88	−	750.953i	−1.12726	−	0.753213i	−0.972074	+	0.234672i	$0.924598\pi$
$998$		0			0
$999$	227.987	+	227.987i	0.228215	+	0.228215i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.73.3	yes	40
4.3	odd	2		272.3.bh.g.209.3		40
17.7	odd	16	inner	136.3.t.b.41.3	✓	40
68.7	even	16		272.3.bh.g.177.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.41.3	✓	40	17.7	odd	16	inner
136.3.t.b.73.3	yes	40	1.1	even	1	trivial
272.3.bh.g.177.3		40	68.7	even	16
272.3.bh.g.209.3		40	4.3	odd	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:	\( N \)	\(=\)	\( 136 = 2^{3} \cdot 17 \)
Weight:	\( k \)	\(=\)	\( 3 \)
Character orbit:	\([\chi]\)	\(=\)	136.t (of order \(16\), degree \(8\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.708293 - 1.06004i) q^{3} +(-0.482121 + 2.42379i) q^{5} +(2.22606 + 11.1911i) q^{7} +(2.82215 - 6.81328i) q^{9} +O(q^{10})\)	\(q+(-0.708293 - 1.06004i) q^{3} +(-0.482121 + 2.42379i) q^{5} +(2.22606 + 11.1911i) q^{7} +(2.82215 - 6.81328i) q^{9} +(14.2613 + 9.52909i) q^{11} +(0.0771647 + 0.0771647i) q^{13} +(2.91078 - 1.20569i) q^{15} +(16.9800 - 0.824179i) q^{17} +(-3.70126 - 8.93564i) q^{19} +(10.2863 - 10.2863i) q^{21} +(-25.4008 + 38.0150i) q^{23} +(17.4547 + 7.22997i) q^{25} +(-20.4748 + 4.07269i) q^{27} +(-39.7529 - 7.90735i) q^{29} +(27.3712 - 18.2889i) q^{31} -21.8669i q^{33} -28.1982 q^{35} +(-8.58062 - 12.8418i) q^{37} +(0.0271421 - 0.136453i) q^{39} +(-5.22473 - 26.2665i) q^{41} +(9.37842 - 22.6415i) q^{43} +(15.1533 + 10.1251i) q^{45} +(5.26803 + 5.26803i) q^{47} +(-75.0164 + 31.0728i) q^{49} +(-12.9005 - 17.4157i) q^{51} +(-22.6332 - 54.6413i) q^{53} +(-29.9722 + 29.9722i) q^{55} +(-6.85052 + 10.2525i) q^{57} +(-40.3308 - 16.7056i) q^{59} +(93.4459 - 18.5875i) q^{61} +(82.5307 + 16.4164i) q^{63} +(-0.224234 + 0.149828i) q^{65} -68.2478i q^{67} +58.2885 q^{69} +(-6.98793 - 10.4582i) q^{71} +(-10.6730 + 53.6570i) q^{73} +(-4.69901 - 23.6235i) q^{75} +(-74.8950 + 180.813i) q^{77} +(17.6840 + 11.8161i) q^{79} +(-28.1126 - 28.1126i) q^{81} +(2.41901 - 1.00199i) q^{83} +(-6.18879 + 41.5533i) q^{85} +(19.7747 + 47.7402i) q^{87} +(12.1775 - 12.1775i) q^{89} +(-0.691789 + 1.03534i) q^{91} +(-38.7737 - 16.0606i) q^{93} +(23.4425 - 4.66301i) q^{95} +(160.989 + 32.0227i) q^{97} +(105.172 - 70.2737i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9} + 24 q^{11} - 48 q^{13} - 96 q^{15} - 40 q^{19} + 80 q^{21} + 48 q^{23} + 48 q^{25} + 224 q^{27} + 24 q^{29} + 88 q^{31} + 32 q^{35} - 176 q^{37} - 120 q^{39} - 352 q^{43} + 264 q^{45} - 48 q^{47} - 208 q^{49} + 400 q^{51} - 472 q^{53} - 208 q^{55} + 24 q^{57} - 576 q^{59} - 632 q^{63} - 32 q^{65} + 160 q^{69} - 160 q^{71} + 256 q^{73} + 1128 q^{75} - 208 q^{77} + 1000 q^{79} + 24 q^{81} + 312 q^{83} + 1240 q^{85} - 664 q^{87} + 720 q^{89} + 664 q^{91} - 432 q^{93} + 736 q^{95} - 288 q^{97} + 16 q^{99}+O(q^{100}) \) 40 * q + 8 * q^3 - 8 * q^7 - 16 * q^9 + 24 * q^11 - 48 * q^13 - 96 * q^15 - 40 * q^19 + 80 * q^21 + 48 * q^23 + 48 * q^25 + 224 * q^27 + 24 * q^29 + 88 * q^31 + 32 * q^35 - 176 * q^37 - 120 * q^39 - 352 * q^43 + 264 * q^45 - 48 * q^47 - 208 * q^49 + 400 * q^51 - 472 * q^53 - 208 * q^55 + 24 * q^57 - 576 * q^59 - 632 * q^63 - 32 * q^65 + 160 * q^69 - 160 * q^71 + 256 * q^73 + 1128 * q^75 - 208 * q^77 + 1000 * q^79 + 24 * q^81 + 312 * q^83 + 1240 * q^85 - 664 * q^87 + 720 * q^89 + 664 * q^91 - 432 * q^93 + 736 * q^95 - 288 * q^97 + 16 * q^99

Introduction

L-functions

Modular forms

Varieties

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Database

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