LMFDB - Embedded newform 136.3.t.b.65.3

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			65.3
Character	$\chi$	$=$	136.65
Dual form			136.3.t.b.113.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.0253220 + 0.127302i) q^{3} +(-2.11962 + 1.41628i) q^{5} +(5.83745 + 3.90046i) q^{7} +(8.29935 + 3.43770i) q^{9} +O(q^{10})$	\(q+(-0.0253220 + 0.127302i) q^{3} +(-2.11962 + 1.41628i) q^{5} +(5.83745 + 3.90046i) q^{7} +(8.29935 + 3.43770i) q^{9} +(-6.06896 + 1.20719i) q^{11} +(15.1916 + 15.1916i) q^{13} +(-0.126623 - 0.305695i) q^{15} +(14.8358 - 8.30058i) q^{17} +(-15.6237 + 6.47155i) q^{19} +(-0.644354 + 0.644354i) q^{21} +(-4.90727 - 24.6705i) q^{23} +(-7.08017 + 17.0930i) q^{25} +(-1.29678 + 1.94077i) q^{27} +(3.88272 + 5.81090i) q^{29} +(11.8786 + 2.36280i) q^{31} -0.803161i q^{33} -17.8973 q^{35} +(9.88982 - 49.7195i) q^{37} +(-2.31862 + 1.54925i) q^{39} +(-13.2705 - 8.86709i) q^{41} +(-60.9212 - 25.2344i) q^{43} +(-22.4602 + 4.46761i) q^{45} +(-19.8590 - 19.8590i) q^{47} +(0.110741 + 0.267352i) q^{49} +(0.681012 + 2.09882i) q^{51} +(3.12825 - 1.29576i) q^{53} +(11.1541 - 11.1541i) q^{55} +(-0.428220 - 2.15281i) q^{57} +(24.9315 - 60.1899i) q^{59} +(0.934584 - 1.39870i) q^{61} +(35.0384 + 52.4387i) q^{63} +(-53.7161 - 10.6848i) q^{65} +107.662i q^{67} +3.26488 q^{69} +(8.16946 - 41.0707i) q^{71} +(-19.3601 + 12.9360i) q^{73} +(-1.99670 - 1.33415i) q^{75} +(-40.1358 - 16.6248i) q^{77} +(147.773 - 29.3939i) q^{79} +(56.9542 + 56.9542i) q^{81} +(13.1847 + 31.8307i) q^{83} +(-19.6902 + 38.6057i) q^{85} +(-0.838059 + 0.347135i) q^{87} +(23.1807 - 23.1807i) q^{89} +(29.4261 + 147.935i) q^{91} +(-0.601580 + 1.45234i) q^{93} +(23.9507 - 35.8448i) q^{95} +(-50.3961 - 75.4231i) q^{97} +(-54.5184 - 10.8444i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 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 $\left(\mathbb{Z}/136\mathbb{Z}\right)^\times$.

$n$	$69$	$103$	$105$
$\chi(n)$	$1$	$1$	$e\left(\frac{9}{16}\right)$

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
$3$	−0.0253220	+	0.127302i	−0.00844067	+	0.0424341i	−0.984776	−	0.173828i	$-0.944386\pi$
$3$	−0.0253220	+	0.127302i	−0.00844067	+	0.0424341i	0.976335	+	0.216262i	$0.0693864\pi$
$4$		0			0
$5$	−2.11962	+	1.41628i	−0.423923	+	0.283257i	−0.749176	−	0.662370i	$-0.769551\pi$
$5$	−2.11962	+	1.41628i	−0.423923	+	0.283257i	0.325253	+	0.945627i	$0.394551\pi$
$6$		0			0
$7$	5.83745	+	3.90046i	0.833921	+	0.557208i	0.897625	−	0.440761i	$-0.145291\pi$
$7$	5.83745	+	3.90046i	0.833921	+	0.557208i	−0.0637035	+	0.997969i	$0.520291\pi$
$8$		0			0
$9$	8.29935	+	3.43770i	0.922150	+	0.381967i
$10$		0			0
$11$	−6.06896	+	1.20719i	−0.551723	+	0.109745i	−0.463076	−	0.886318i	$-0.653254\pi$
$11$	−6.06896	+	1.20719i	−0.551723	+	0.109745i	−0.0886473	+	0.996063i	$0.528254\pi$
$12$		0			0
$13$	15.1916	+	15.1916i	1.16859	+	1.16859i	0.982541	+	0.186047i	$0.0595677\pi$
$13$	15.1916	+	15.1916i	1.16859	+	1.16859i	0.186047	+	0.982541i	$0.440432\pi$
$14$		0			0
$15$	−0.126623	−	0.305695i	−0.00844155	−	0.0203797i
$16$		0			0
$17$	14.8358	−	8.30058i	0.872693	−	0.488269i
$17$	14.8358	−	8.30058i	0.872693	−	0.488269i
$18$		0			0
$19$	−15.6237	+	6.47155i	−0.822300	+	0.340608i	−0.753850	−	0.657047i	$-0.771805\pi$
$19$	−15.6237	+	6.47155i	−0.822300	+	0.340608i	−0.0684502	+	0.997655i	$0.521805\pi$
$20$		0			0
$21$	−0.644354	+	0.644354i	−0.0306835	+	0.0306835i
$22$		0			0
$23$	−4.90727	−	24.6705i	−0.213360	−	1.07263i	−0.927841	−	0.372977i	$-0.878337\pi$
$23$	−4.90727	−	24.6705i	−0.213360	−	1.07263i	0.714481	−	0.699655i	$-0.246663\pi$
$24$		0			0
$25$	−7.08017	+	17.0930i	−0.283207	+	0.683721i
$26$		0			0
$27$	−1.29678	+	1.94077i	−0.0480290	+	0.0718805i
$28$		0			0
$29$	3.88272	+	5.81090i	0.133887	+	0.200376i	0.892355	−	0.451334i	$-0.149052\pi$
$29$	3.88272	+	5.81090i	0.133887	+	0.200376i	−0.758468	+	0.651710i	$0.774052\pi$
$30$		0			0
$31$	11.8786	+	2.36280i	0.383181	+	0.0762193i	0.382922	−	0.923781i	$-0.374918\pi$
$31$	11.8786	+	2.36280i	0.383181	+	0.0762193i	0.000258391		1.00000i	$0.499918\pi$
$32$		0			0
$33$		−	0.803161i		−	0.0243382i
$34$		0			0
$35$	−17.8973			−0.511352
$36$		0			0
$37$	9.88982	−	49.7195i	0.267292	−	1.34377i	−0.580854	−	0.814008i	$-0.697281\pi$
$37$	9.88982	−	49.7195i	0.267292	−	1.34377i	0.848146	−	0.529762i	$-0.177719\pi$
$38$		0			0
$39$	−2.31862	+	1.54925i	−0.0594517	+	0.0397243i
$40$		0			0
$41$	−13.2705	−	8.86709i	−0.323672	−	0.216271i	0.383109	−	0.923703i	$-0.374853\pi$
$41$	−13.2705	−	8.86709i	−0.323672	−	0.216271i	−0.706781	+	0.707433i	$0.749853\pi$
$42$		0			0
$43$	−60.9212	−	25.2344i	−1.41677	−	0.586846i	−0.462725	−	0.886502i	$-0.653128\pi$
$43$	−60.9212	−	25.2344i	−1.41677	−	0.586846i	−0.954047	+	0.299656i	$0.903128\pi$
$44$		0			0
$45$	−22.4602	+	4.46761i	−0.499116	+	0.0992803i
$46$		0			0
$47$	−19.8590	−	19.8590i	−0.422532	−	0.422532i	0.463542	−	0.886075i	$-0.346578\pi$
$47$	−19.8590	−	19.8590i	−0.422532	−	0.422532i	−0.886075	+	0.463542i	$0.846578\pi$
$48$		0			0
$49$	0.110741	+	0.267352i	0.00226001	+	0.00545615i
$50$		0			0
$51$	0.681012	+	2.09882i	0.0133532	+	0.0411533i
$52$		0			0
$53$	3.12825	−	1.29576i	0.0590235	−	0.0244483i	−0.352976	−	0.935632i	$-0.614830\pi$
$53$	3.12825	−	1.29576i	0.0590235	−	0.0244483i	0.412000	+	0.911184i	$0.364830\pi$
$54$		0			0
$55$	11.1541	−	11.1541i	0.202803	−	0.202803i
$56$		0			0
$57$	−0.428220	−	2.15281i	−0.00751263	−	0.0377685i
$58$		0			0
$59$	24.9315	−	60.1899i	0.422567	−	1.02017i	−0.559020	−	0.829154i	$-0.688822\pi$
$59$	24.9315	−	60.1899i	0.422567	−	1.02017i	0.981587	−	0.191014i	$-0.0611775\pi$
$60$		0			0
$61$	0.934584	−	1.39870i	0.0153211	−	0.0229296i	−0.823730	−	0.566982i	$-0.808111\pi$
$61$	0.934584	−	1.39870i	0.0153211	−	0.0229296i	0.839051	+	0.544053i	$0.183111\pi$
$62$		0			0
$63$	35.0384	+	52.4387i	0.556165	+	0.832360i
$64$		0			0
$65$	−53.7161	−	10.6848i	−0.826402	−	0.164382i
$66$		0			0
$67$			107.662i			1.60690i	0.595374	+	0.803448i	$0.297004\pi$
$67$			107.662i			1.60690i	−0.595374	+	0.803448i	$0.702996\pi$
$68$		0			0
$69$	3.26488			0.0473171
$70$		0			0
$71$	8.16946	−	41.0707i	0.115063	−	0.578460i	−0.879638	−	0.475644i	$-0.842215\pi$
$71$	8.16946	−	41.0707i	0.115063	−	0.578460i	0.994700	−	0.102815i	$-0.0327851\pi$
$72$		0			0
$73$	−19.3601	+	12.9360i	−0.265207	+	0.177206i	−0.681063	−	0.732225i	$-0.738482\pi$
$73$	−19.3601	+	12.9360i	−0.265207	+	0.177206i	0.415856	+	0.909430i	$0.363482\pi$
$74$		0			0
$75$	−1.99670	−	1.33415i	−0.0266227	−	0.0177887i
$76$		0			0
$77$	−40.1358	−	16.6248i	−0.521245	−	0.215907i
$78$		0			0
$79$	147.773	−	29.3939i	1.87054	−	0.372074i	0.876532	−	0.481343i	$-0.159851\pi$
$79$	147.773	−	29.3939i	1.87054	−	0.372074i	0.994012	+	0.109269i	$0.0348509\pi$
$80$		0			0
$81$	56.9542	+	56.9542i	0.703138	+	0.703138i
$82$		0			0
$83$	13.1847	+	31.8307i	0.158852	+	0.383502i	0.983187	−	0.182599i	$-0.0584511\pi$
$83$	13.1847	+	31.8307i	0.158852	+	0.383502i	−0.824336	+	0.566101i	$0.808451\pi$
$84$		0			0
$85$	−19.6902	+	38.6057i	−0.231649	+	0.454185i
$86$		0			0
$87$	−0.838059	+	0.347135i	−0.00963286	+	0.00399006i
$88$		0			0
$89$	23.1807	−	23.1807i	0.260458	−	0.260458i	−0.564782	−	0.825240i	$-0.691040\pi$
$89$	23.1807	−	23.1807i	0.260458	−	0.260458i	0.825240	+	0.564782i	$0.191040\pi$
$90$		0			0
$91$	29.4261	+	147.935i	0.323363	+	1.62566i
$92$		0			0
$93$	−0.601580	+	1.45234i	−0.00646860	+	0.0156166i
$94$		0			0
$95$	23.9507	−	35.8448i	0.252113	−	0.377314i
$96$		0			0
$97$	−50.3961	−	75.4231i	−0.519548	−	0.777558i	0.475204	−	0.879876i	$-0.342374\pi$
$97$	−50.3961	−	75.4231i	−0.519548	−	0.777558i	−0.994752	+	0.102318i	$0.967374\pi$
$98$		0			0
$99$	−54.5184	−	10.8444i	−0.550691	−	0.109539i
$100$		0			0
$101$			5.62455i			0.0556886i	0.999612	+	0.0278443i	$0.00886426\pi$
$101$			5.62455i			0.0556886i	−0.999612	+	0.0278443i	$0.991136\pi$
$102$		0			0
$103$	158.767			1.54143			0.770713	−	0.637182i	$-0.219900\pi$
$103$	158.767			1.54143			0.770713	+	0.637182i	$0.219900\pi$
$104$		0			0
$105$	0.453196	−	2.27837i	0.00431615	−	0.0216988i
$106$		0			0
$107$	−116.202	+	77.6434i	−1.08600	+	0.725639i	−0.963736	−	0.266859i	$-0.914014\pi$
$107$	−116.202	+	77.6434i	−1.08600	+	0.725639i	−0.122260	+	0.992498i	$0.539014\pi$
$108$		0			0
$109$	−19.3101	−	12.9026i	−0.177157	−	0.118372i	0.463830	−	0.885924i	$-0.346475\pi$
$109$	−19.3101	−	12.9026i	−0.177157	−	0.118372i	−0.640987	+	0.767552i	$0.721475\pi$
$110$		0			0
$111$	6.07898	+	2.51800i	0.0547656	+	0.0226846i
$112$		0			0
$113$	137.048	−	27.2605i	1.21281	−	0.241243i	0.453074	−	0.891473i	$-0.350327\pi$
$113$	137.048	−	27.2605i	1.21281	−	0.241243i	0.759738	+	0.650230i	$0.225327\pi$
$114$		0			0
$115$	45.3420	+	45.3420i	0.394278	+	0.394278i
$116$		0			0
$117$	73.8564	+	178.305i	0.631251	+	1.52398i
$118$		0			0
$119$	118.979	+	9.41213i	0.999825	+	0.0790935i
$120$		0			0
$121$	−76.4145	+	31.6519i	−0.631525	+	0.261586i
$122$		0			0
$123$	1.46484	−	1.46484i	0.0119093	−	0.0119093i
$124$		0			0
$125$	−21.6346	−	108.765i	−0.173077	−	0.870117i
$126$		0			0
$127$	−28.1517	+	67.9641i	−0.221667	+	0.535151i	−0.995117	−	0.0987068i	$-0.968529\pi$
$127$	−28.1517	+	67.9641i	−0.221667	+	0.535151i	0.773450	+	0.633857i	$0.218529\pi$
$128$		0			0
$129$	4.75505	−	7.11643i	0.0368608	−	0.0551661i
$130$		0			0
$131$	−133.185	−	199.326i	−1.01668	−	1.52157i	−0.843820	−	0.536626i	$-0.819699\pi$
$131$	−133.185	−	199.326i	−1.01668	−	1.52157i	−0.172861	−	0.984946i	$-0.555301\pi$
$132$		0			0
$133$	−116.445	−	23.1623i	−0.875523	−	0.174152i
$134$		0			0
$135$		−	5.95031i		−	0.0440764i
$136$		0			0
$137$	−225.761			−1.64789			−0.823945	−	0.566669i	$-0.808232\pi$
$137$	−225.761			−1.64789			−0.823945	+	0.566669i	$0.808232\pi$
$138$		0			0
$139$	21.8004	−	109.598i	0.156837	−	0.788475i	−0.819644	−	0.572873i	$-0.805829\pi$
$139$	21.8004	−	109.598i	0.156837	−	0.788475i	0.976481	−	0.215602i	$-0.0691713\pi$
$140$		0			0
$141$	3.03097	−	2.02523i	0.0214962	−	0.0143633i
$142$		0			0
$143$	−110.537	−	73.8582i	−0.772984	−	0.516491i
$144$		0			0
$145$	−16.4597	−	6.81785i	−0.113515	−	0.0470197i
$146$		0			0
$147$	−0.0368387	+	0.00732766i	−0.000250603	+	4.98481e-5i
$148$		0			0
$149$	54.8267	+	54.8267i	0.367965	+	0.367965i	0.866735	−	0.498770i	$-0.166215\pi$
$149$	54.8267	+	54.8267i	0.367965	+	0.367965i	−0.498770	+	0.866735i	$0.666215\pi$
$150$		0			0
$151$	−12.3137	−	29.7279i	−0.0815477	−	0.196874i	0.877847	−	0.478942i	$-0.158980\pi$
$151$	−12.3137	−	29.7279i	−0.0815477	−	0.196874i	−0.959394	+	0.282068i	$0.908980\pi$
$152$		0			0
$153$	151.662	−	17.8884i	0.991257	−	0.116918i
$154$		0			0
$155$	−28.5245	+	11.8152i	−0.184029	+	0.0762272i
$156$		0			0
$157$	89.9563	−	89.9563i	0.572970	−	0.572970i	−0.359987	−	0.932957i	$-0.617219\pi$
$157$	89.9563	−	89.9563i	0.572970	−	0.572970i	0.932957	+	0.359987i	$0.117219\pi$
$158$		0			0
$159$	0.0857401	+	0.431044i	0.000539246	+	0.00271097i
$160$		0			0
$161$	67.5804	−	163.154i	0.419754	−	1.01338i
$162$		0			0
$163$	16.3088	−	24.4079i	0.100054	−	0.149742i	−0.778065	−	0.628184i	$-0.783798\pi$
$163$	16.3088	−	24.4079i	0.100054	−	0.149742i	0.878119	+	0.478442i	$0.158798\pi$
$164$		0			0
$165$	1.13750	+	1.70239i	0.00689396	+	0.0103175i
$166$		0			0
$167$	−229.275	−	45.6057i	−1.37291	−	0.273088i	−0.547112	−	0.837059i	$-0.684273\pi$
$167$	−229.275	−	45.6057i	−1.37291	−	0.273088i	−0.825794	+	0.563971i	$0.809273\pi$
$168$		0			0
$169$			292.572i			1.73120i
$170$		0			0
$171$	−151.914			−0.888385
$172$		0			0
$173$	54.1035	−	271.997i	0.312737	−	1.57223i	−0.430112	−	0.902775i	$-0.641526\pi$
$173$	54.1035	−	271.997i	0.312737	−	1.57223i	0.742849	−	0.669459i	$-0.233474\pi$
$174$		0			0
$175$	−108.001	+	72.1638i	−0.617147	+	0.412365i
$176$		0			0
$177$	7.03100	+	4.69797i	0.0397232	+	0.0265422i
$178$		0			0
$179$	−161.940	−	67.0779i	−0.904695	−	0.374737i	−0.118671	−	0.992934i	$-0.537864\pi$
$179$	−161.940	−	67.0779i	−0.904695	−	0.374737i	−0.786023	+	0.618197i	$0.787864\pi$
$180$		0			0
$181$	34.4129	−	6.84516i	0.190127	−	0.0378185i	−0.0991084	−	0.995077i	$-0.531599\pi$
$181$	34.4129	−	6.84516i	0.190127	−	0.0378185i	0.289235	+	0.957258i	$0.406599\pi$
$182$		0			0
$183$	0.154393	+	0.154393i	0.000843676	+	0.000843676i
$184$		0			0
$185$	49.4542	+	119.393i	0.267320	+	0.645368i
$186$		0			0
$187$	−80.0173	+	68.2855i	−0.427900	+	0.365163i
$188$		0			0
$189$	−15.1398	+	6.27111i	−0.0801048	+	0.0331805i
$190$		0			0
$191$	195.426	−	195.426i	1.02317	−	1.02317i	0.0234464	−	0.999725i	$-0.492536\pi$
$191$	195.426	−	195.426i	1.02317	−	1.02317i	0.999725	−	0.0234464i	$-0.00746389\pi$
$192$		0			0
$193$	−39.2432	−	197.289i	−0.203332	−	1.02222i	−0.938748	−	0.344605i	$-0.888013\pi$
$193$	−39.2432	−	197.289i	−0.203332	−	1.02222i	0.735415	−	0.677617i	$-0.236987\pi$
$194$		0			0
$195$	2.72040	−	6.56763i	0.0139508	−	0.0336802i
$196$		0			0
$197$	−216.080	+	323.387i	−1.09685	+	1.64156i	−0.415523	+	0.909583i	$0.636401\pi$
$197$	−216.080	+	323.387i	−1.09685	+	1.64156i	−0.681331	+	0.731975i	$0.738599\pi$
$198$		0			0
$199$	101.987	+	152.635i	0.512500	+	0.767010i	0.993993	−	0.109440i	$-0.0349056\pi$
$199$	101.987	+	152.635i	0.512500	+	0.767010i	−0.481494	+	0.876449i	$0.659906\pi$
$200$		0			0
$201$	−13.7056	−	2.72622i	−0.0681873	−	0.0135633i
$202$		0			0
$203$			49.0652i			0.241700i
$204$		0			0
$205$	40.6868			0.198472
$206$		0			0
$207$	44.0828	−	221.619i	0.212960	−	1.07062i
$208$		0			0
$209$	87.0072	−	58.1364i	0.416302	−	0.278164i
$210$		0			0
$211$	68.4830	+	45.7589i	0.324564	+	0.216867i	0.707168	−	0.707046i	$-0.249973\pi$
$211$	68.4830	+	45.7589i	0.324564	+	0.216867i	−0.382604	+	0.923913i	$0.624973\pi$
$212$		0			0
$213$	5.02152	+	2.07998i	0.0235752	+	0.00976518i
$214$		0			0
$215$	164.869	−	32.7944i	0.766831	−	0.152532i
$216$		0			0
$217$	60.1247	+	60.1247i	0.277072	+	0.277072i
$218$		0			0
$219$	−1.15655	−	2.79215i	−0.00528104	−	0.0127496i
$220$		0			0
$221$	351.479	+	99.2804i	1.59040	+	0.449233i
$222$		0			0
$223$	−239.624	+	99.2556i	−1.07455	+	0.445092i	−0.848593	−	0.529046i	$-0.822550\pi$
$223$	−239.624	+	99.2556i	−1.07455	+	0.445092i	−0.225954	+	0.974138i	$0.572550\pi$
$224$		0			0
$225$	−117.522	+	117.522i	−0.522318	+	0.522318i
$226$		0			0
$227$	37.3158	+	187.599i	0.164387	+	0.826428i	0.971684	+	0.236283i	$0.0759294\pi$
$227$	37.3158	+	187.599i	0.164387	+	0.826428i	−0.807297	+	0.590145i	$0.799071\pi$
$228$		0			0
$229$	83.0715	−	200.552i	0.362758	−	0.875775i	−0.632137	−	0.774857i	$-0.717822\pi$
$229$	83.0715	−	200.552i	0.362758	−	0.875775i	0.994895	−	0.100918i	$-0.0321780\pi$
$230$		0			0
$231$	3.13270	−	4.68841i	0.0135615	−	0.0202962i
$232$		0			0
$233$	186.948	+	279.787i	0.802350	+	1.20080i	0.976380	+	0.216061i	$0.0693210\pi$
$233$	186.948	+	279.787i	0.802350	+	1.20080i	−0.174030	+	0.984740i	$0.555679\pi$
$234$		0			0
$235$	70.2195	+	13.9675i	0.298806	+	0.0594363i
$236$		0			0
$237$			19.5562i			0.0825155i
$238$		0			0
$239$	83.2750			0.348431			0.174215	−	0.984708i	$-0.444261\pi$
$239$	83.2750			0.348431			0.174215	+	0.984708i	$0.444261\pi$
$240$		0			0
$241$	31.6516	−	159.123i	0.131334	−	0.660262i	−0.857887	−	0.513838i	$-0.828223\pi$
$241$	31.6516	−	159.123i	0.131334	−	0.660262i	0.989222	−	0.146425i	$-0.0467766\pi$
$242$		0			0
$243$	−26.1596	+	17.4793i	−0.107653	+	0.0719311i
$244$		0			0
$245$	−0.613373	−	0.409843i	−0.00250356	−	0.00167283i
$246$		0			0
$247$	−335.663	−	139.036i	−1.35896	−	0.562900i
$248$		0			0
$249$	−4.38599	+	0.872427i	−0.0176144	+	0.00350372i
$250$		0			0
$251$	195.351	+	195.351i	0.778290	+	0.778290i	0.979540	−	0.201250i	$-0.0645004\pi$
$251$	195.351	+	195.351i	0.778290	+	0.778290i	−0.201250	+	0.979540i	$0.564500\pi$
$252$		0			0
$253$	59.5641	+	143.800i	0.235431	+	0.568381i
$254$		0			0
$255$	−4.41600	−	3.48418i	−0.0173177	−	0.0136635i
$256$		0			0
$257$	−27.0176	+	11.1911i	−0.105127	+	0.0435450i	−0.434627	−	0.900611i	$-0.643120\pi$
$257$	−27.0176	+	11.1911i	−0.105127	+	0.0435450i	0.329500	+	0.944156i	$0.393120\pi$
$258$		0			0
$259$	251.660	−	251.660i	0.971661	−	0.971661i
$260$		0			0
$261$	12.2479	+	61.5743i	0.0469268	+	0.235917i
$262$		0			0
$263$	−137.265	+	331.387i	−0.521920	+	1.26003i	0.414790	+	0.909917i	$0.363855\pi$
$263$	−137.265	+	331.387i	−0.521920	+	1.26003i	−0.936709	+	0.350108i	$0.886145\pi$
$264$		0			0
$265$	−4.79552	+	7.17700i	−0.0180963	+	0.0270830i
$266$		0			0
$267$	2.36398	+	3.53795i	0.00885386	+	0.0132507i
$268$		0			0
$269$	−23.6126	−	4.69684i	−0.0877792	−	0.0174604i	0.151005	−	0.988533i	$-0.451749\pi$
$269$	−23.6126	−	4.69684i	−0.0877792	−	0.0174604i	−0.238784	+	0.971073i	$0.576749\pi$
$270$		0			0
$271$			379.339i			1.39977i	0.714253	+	0.699887i	$0.246766\pi$
$271$			379.339i			1.39977i	−0.714253	+	0.699887i	$0.753234\pi$
$272$		0			0
$273$	−19.5776			−0.0717127
$274$		0			0
$275$	22.3347	−	112.284i	0.0812170	−	0.408306i
$276$		0			0
$277$	−184.859	+	123.519i	−0.667360	+	0.445916i	−0.842549	−	0.538619i	$-0.818946\pi$
$277$	−184.859	+	123.519i	−0.667360	+	0.445916i	0.175189	+	0.984535i	$0.443946\pi$
$278$		0			0
$279$	90.4620	+	60.4448i	0.324237	+	0.216648i
$280$		0			0
$281$	−126.721	−	52.4894i	−0.450963	−	0.186795i	0.145630	−	0.989339i	$-0.453479\pi$
$281$	−126.721	−	52.4894i	−0.450963	−	0.186795i	−0.596593	+	0.802544i	$0.703479\pi$
$282$		0			0
$283$	468.724	−	93.2351i	1.65627	−	0.329453i	0.723610	−	0.690209i	$-0.242481\pi$
$283$	468.724	−	93.2351i	1.65627	−	0.329453i	0.932660	+	0.360757i	$0.117481\pi$
$284$		0			0
$285$	3.95665	+	3.95665i	0.0138830	+	0.0138830i
$286$		0			0
$287$	−42.8804	−	103.522i	−0.149409	−	0.360705i
$288$		0			0
$289$	151.201	−	246.291i	0.523186	−	0.852219i
$290$		0			0
$291$	10.8777	−	4.50568i	0.0373803	−	0.0154834i
$292$		0			0
$293$	−78.8751	+	78.8751i	−0.269198	+	0.269198i	−0.828777	−	0.559579i	$-0.810963\pi$
$293$	−78.8751	+	78.8751i	−0.269198	+	0.269198i	0.559579	+	0.828777i	$0.310963\pi$
$294$		0			0
$295$	32.4008	+	162.890i	0.109833	+	0.552168i
$296$		0			0
$297$	5.52724	−	13.3439i	0.0186102	−	0.0449291i
$298$		0			0
$299$	300.236	−	449.335i	1.00413	−	1.50279i
$300$		0			0
$301$	−257.199	−	384.925i	−0.854481	−	1.27882i
$302$		0			0
$303$	−0.716018	−	0.142425i	−0.00236310	−	0.000470049i
$304$		0			0
$305$			4.28835i			0.0140602i
$306$		0			0
$307$	393.661			1.28228			0.641141	−	0.767423i	$-0.278461\pi$
$307$	393.661			1.28228			0.641141	+	0.767423i	$0.278461\pi$
$308$		0			0
$309$	−4.02030	+	20.2114i	−0.0130107	+	0.0654091i
$310$		0			0
$311$	−484.323	+	323.614i	−1.55731	+	1.04056i	−0.583801	+	0.811896i	$0.698435\pi$
$311$	−484.323	+	323.614i	−1.55731	+	1.04056i	−0.973506	+	0.228663i	$0.926565\pi$
$312$		0			0
$313$	−293.613	−	196.186i	−0.938060	−	0.626792i	−0.0102913	−	0.999947i	$-0.503276\pi$
$313$	−293.613	−	196.186i	−0.938060	−	0.626792i	−0.927769	+	0.373155i	$0.878276\pi$
$314$		0			0
$315$	−148.536	−	61.5256i	−0.471543	−	0.195319i
$316$		0			0
$317$	−365.733	+	72.7488i	−1.15373	+	0.229492i	−0.734643	−	0.678454i	$-0.762650\pi$
$317$	−365.733	+	72.7488i	−1.15373	+	0.229492i	−0.419089	+	0.907945i	$0.637650\pi$
$318$		0			0
$319$	−30.5789	−	30.5789i	−0.0958586	−	0.0958586i
$320$		0			0
$321$	−6.94173	−	16.7588i	−0.0216253	−	0.0522082i
$322$		0			0
$323$	−178.072	+	225.696i	−0.551307	+	0.698750i
$324$		0			0
$325$	−367.231	+	152.112i	−1.12994	+	0.468037i
$326$		0			0
$327$	2.13150	−	2.13150i	0.00651835	−	0.00651835i
$328$		0			0
$329$	−38.4667	−	193.385i	−0.116920	−	0.587797i
$330$		0			0
$331$	48.2700	−	116.534i	0.145831	−	0.352067i	−0.834039	−	0.551706i	$-0.813977\pi$
$331$	48.2700	−	116.534i	0.145831	−	0.352067i	0.979869	+	0.199639i	$0.0639771\pi$
$332$		0			0
$333$	253.000	−	378.641i	0.759760	−	1.13706i
$334$		0			0
$335$	−152.480	−	228.202i	−0.455164	−	0.681201i
$336$		0			0
$337$	−440.635	−	87.6477i	−1.30752	−	0.260082i	−0.508332	−	0.861161i	$-0.669738\pi$
$337$	−440.635	−	87.6477i	−1.30752	−	0.260082i	−0.799190	+	0.601079i	$0.794738\pi$
$338$		0			0
$339$			18.1368i			0.0535009i
$340$		0			0
$341$	−74.9431			−0.219774
$342$		0			0
$343$	66.7169	−	335.409i	0.194510	−	0.977868i
$344$		0			0
$345$	−6.92029	+	4.62399i	−0.0200588	+	0.0134029i
$346$		0			0
$347$	19.7197	+	13.1763i	0.0568291	+	0.0379720i	0.583660	−	0.811998i	$-0.301620\pi$
$347$	19.7197	+	13.1763i	0.0568291	+	0.0379720i	−0.526831	+	0.849970i	$0.676620\pi$
$348$		0			0
$349$	152.886	+	63.3276i	0.438070	+	0.181455i	0.590808	−	0.806812i	$-0.298809\pi$
$349$	152.886	+	63.3276i	0.438070	+	0.181455i	−0.152738	+	0.988267i	$0.548809\pi$
$350$		0			0
$351$	−49.1838	+	9.78327i	−0.140125	+	0.0278726i
$352$		0			0
$353$	320.540	+	320.540i	0.908044	+	0.908044i	0.996114	−	0.0880701i	$-0.0280700\pi$
$353$	320.540	+	320.540i	0.908044	+	0.908044i	−0.0880701	+	0.996114i	$0.528070\pi$
$354$		0			0
$355$	40.8515	+	98.6243i	0.115075	+	0.277815i
$356$		0			0
$357$	−4.21098	+	14.9080i	−0.0117955	+	0.0417591i
$358$		0			0
$359$	436.810	−	180.932i	1.21674	−	0.503990i	0.320368	−	0.947293i	$-0.396193\pi$
$359$	436.810	−	180.932i	1.21674	−	0.503990i	0.896372	+	0.443303i	$0.146193\pi$
$360$		0			0
$361$	−53.0464	+	53.0464i	−0.146943	+	0.146943i
$362$		0			0
$363$	−2.09439	−	10.5292i	−0.00576968	−	0.0290062i
$364$		0			0
$365$	22.7150	−	54.8388i	0.0622328	−	0.150243i
$366$		0			0
$367$	−230.743	+	345.332i	−0.628728	+	0.940958i	0.371195	+	0.928555i	$0.378948\pi$
$367$	−230.743	+	345.332i	−0.628728	+	0.940958i	−0.999923	+	0.0124031i	$0.996052\pi$
$368$		0			0
$369$	−79.6544	−	119.211i	−0.215866	−	0.323066i
$370$		0			0
$371$	23.3150	+	4.63765i	0.0628438	+	0.0125004i
$372$		0			0
$373$		−	340.654i		−	0.913282i	−0.889651	−	0.456641i	$-0.849052\pi$
$373$		−	340.654i		−	0.913282i	0.889651	−	0.456641i	$-0.150948\pi$
$374$		0			0
$375$	14.3938			0.0383836
$376$		0			0
$377$	−29.2922	+	147.262i	−0.0776982	+	0.390615i
$378$		0			0
$379$	34.7384	−	23.2114i	0.0916580	−	0.0612439i	−0.508897	−	0.860828i	$-0.669946\pi$
$379$	34.7384	−	23.2114i	0.0916580	−	0.0612439i	0.600555	+	0.799584i	$0.294946\pi$
$380$		0			0
$381$	−7.93914	−	5.30476i	−0.0208376	−	0.0139233i
$382$		0			0
$383$	−2.68019	−	1.11017i	−0.00699787	−	0.00289861i	0.379182	−	0.925322i	$-0.376206\pi$
$383$	−2.68019	−	1.11017i	−0.00699787	−	0.00289861i	−0.386180	+	0.922424i	$0.626206\pi$
$384$		0			0
$385$	108.618	−	21.6055i	0.282125	−	0.0561181i
$386$		0			0
$387$	−418.858	−	418.858i	−1.08232	−	1.08232i
$388$		0			0
$389$	159.461	+	384.973i	0.409926	+	0.989648i	0.985157	+	0.171657i	$0.0549121\pi$
$389$	159.461	+	384.973i	0.409926	+	0.989648i	−0.575231	+	0.817991i	$0.695088\pi$
$390$		0			0
$391$	−277.583	−	325.273i	−0.709931	−	0.831901i
$392$		0			0
$393$	28.7472	−	11.9075i	0.0731480	−	0.0302989i
$394$		0			0
$395$	−271.592	+	271.592i	−0.687575	+	0.687575i
$396$		0			0
$397$	−108.991	−	547.933i	−0.274536	−	1.38018i	−0.834199	−	0.551463i	$-0.814070\pi$
$397$	−108.991	−	547.933i	−0.274536	−	1.38018i	0.559664	−	0.828720i	$-0.310930\pi$
$398$		0			0
$399$	5.89722	−	14.2372i	0.0147800	−	0.0356821i
$400$		0			0
$401$	−84.6011	+	126.614i	−0.210975	+	0.315747i	−0.921832	−	0.387590i	$-0.873308\pi$
$401$	−84.6011	+	126.614i	−0.210975	+	0.315747i	0.710856	+	0.703337i	$0.248308\pi$
$402$		0			0
$403$	144.561	+	216.350i	0.358711	+	0.536849i
$404$		0			0
$405$	−201.384	−	40.0578i	−0.497245	−	0.0989083i
$406$		0			0
$407$			313.684i			0.770723i
$408$		0			0
$409$	−449.002			−1.09780			−0.548902	−	0.835887i	$-0.684954\pi$
$409$	−449.002			−1.09780			−0.548902	+	0.835887i	$0.684954\pi$
$410$		0			0
$411$	5.71672	−	28.7399i	0.0139093	−	0.0699268i
$412$		0			0
$413$	380.304	−	254.111i	0.920834	−	0.615282i
$414$		0			0
$415$	−73.0278	−	48.7956i	−0.175971	−	0.117580i
$416$		0			0
$417$	13.4001	+	5.55049i	0.0321344	+	0.0133105i
$418$		0			0
$419$	808.799	−	160.880i	1.93031	−	0.383962i	0.930463	−	0.366386i	$-0.119405\pi$
$419$	808.799	−	160.880i	1.93031	−	0.383962i	0.999846	−	0.0175764i	$-0.00559502\pi$
$420$		0			0
$421$	409.126	+	409.126i	0.971796	+	0.971796i	0.999613	−	0.0278172i	$-0.00885563\pi$
$421$	409.126	+	409.126i	0.971796	+	0.971796i	−0.0278172	+	0.999613i	$0.508856\pi$
$422$		0			0
$423$	−96.5475	−	233.086i	−0.228245	−	0.551032i
$424$		0			0
$425$	36.8423	+	312.358i	0.0866878	+	0.734960i
$426$		0			0
$427$	10.9112	−	4.51956i	0.0255531	−	0.0105844i
$428$		0			0
$429$	12.2013	−	12.2013i	0.0284414	−	0.0284414i
$430$		0			0
$431$	140.354	+	705.608i	0.325648	+	1.63714i	0.703084	+	0.711107i	$0.251806\pi$
$431$	140.354	+	705.608i	0.325648	+	1.63714i	−0.377436	+	0.926036i	$0.623194\pi$
$432$		0			0
$433$	104.530	−	252.357i	0.241409	−	0.582812i	−0.756015	−	0.654555i	$-0.772856\pi$
$433$	104.530	−	252.357i	0.241409	−	0.582812i	0.997423	+	0.0717430i	$0.0228561\pi$
$434$		0			0
$435$	1.28472	−	1.92272i	0.00295338	−	0.00442005i
$436$		0			0
$437$	236.326	+	353.687i	0.540792	+	0.809353i
$438$		0			0
$439$	223.001	+	44.3576i	0.507974	+	0.101042i	0.442422	−	0.896807i	$-0.354119\pi$
$439$	223.001	+	44.3576i	0.507974	+	0.101042i	0.0655518	+	0.997849i	$0.479119\pi$
$440$		0			0
$441$			2.59954i			0.00589464i
$442$		0			0
$443$	57.3827			0.129532			0.0647660	−	0.997900i	$-0.479370\pi$
$443$	57.3827			0.129532			0.0647660	+	0.997900i	$0.479370\pi$
$444$		0			0
$445$	−16.3038	+	81.9648i	−0.0366378	+	0.184190i
$446$		0			0
$447$	−8.36790	+	5.59125i	−0.0187201	+	0.0125084i
$448$		0			0
$449$	150.819	+	100.774i	0.335900	+	0.224441i	0.712068	−	0.702110i	$-0.247759\pi$
$449$	150.819	+	100.774i	0.335900	+	0.224441i	−0.376169	+	0.926551i	$0.622759\pi$
$450$		0			0
$451$	91.2426	+	37.7939i	0.202312	+	0.0838003i
$452$		0			0
$453$	4.09624	−	0.814793i	0.00904247	−	0.00179866i
$454$		0			0
$455$	−271.890	−	271.890i	−0.597559	−	0.597559i
$456$		0			0
$457$	271.196	+	654.724i	0.593426	+	1.43266i	0.880174	+	0.474651i	$0.157426\pi$
$457$	271.196	+	654.724i	0.593426	+	1.43266i	−0.286748	+	0.958006i	$0.592574\pi$
$458$		0			0
$459$	−3.12924	+	39.5569i	−0.00681753	+	0.0861807i
$460$		0			0
$461$	348.801	−	144.478i	0.756618	−	0.313401i	0.0291791	−	0.999574i	$-0.490711\pi$
$461$	348.801	−	144.478i	0.756618	−	0.313401i	0.727438	+	0.686173i	$0.240711\pi$
$462$		0			0
$463$	−182.721	+	182.721i	−0.394645	+	0.394645i	−0.876339	−	0.481694i	$-0.840022\pi$
$463$	−182.721	+	182.721i	−0.394645	+	0.394645i	0.481694	+	0.876339i	$0.340022\pi$
$464$		0			0
$465$	−0.781809	−	3.93042i	−0.00168131	−	0.00845251i
$466$		0			0
$467$	−45.7719	+	110.503i	−0.0980127	+	0.236623i	−0.965279	−	0.261221i	$-0.915875\pi$
$467$	−45.7719	+	110.503i	−0.0980127	+	0.236623i	0.867266	+	0.497844i	$0.165875\pi$
$468$		0			0
$469$	−419.932	+	628.472i	−0.895376	+	1.34003i
$470$		0			0
$471$	9.17377	+	13.7295i	0.0194772	+	0.0291497i
$472$		0			0
$473$	400.191	+	79.6029i	0.846070	+	0.168294i
$474$		0			0
$475$		−	312.876i		−	0.658687i
$476$		0			0
$477$	30.4169			0.0637670
$478$		0			0
$479$	−80.7855	+	406.136i	−0.168654	+	0.847883i	0.800101	+	0.599865i	$0.204779\pi$
$479$	−80.7855	+	406.136i	−0.168654	+	0.847883i	−0.968755	+	0.248018i	$0.920221\pi$
$480$		0			0
$481$	905.563	−	605.078i	1.88267	−	1.25796i
$482$		0			0
$483$	19.0586	+	12.7345i	0.0394587	+	0.0263655i
$484$		0			0
$485$	213.641	+	88.4930i	0.440497	+	0.182460i
$486$		0			0
$487$	−748.638	+	148.913i	−1.53725	+	0.305777i	−0.889806	−	0.456340i	$-0.849160\pi$
$487$	−748.638	+	148.913i	−1.53725	+	0.305777i	−0.647439	+	0.762117i	$0.724160\pi$
$488$		0			0
$489$	2.69421	+	2.69421i	0.00550963	+	0.00550963i
$490$		0			0
$491$	−37.0187	−	89.3710i	−0.0753945	−	0.182018i	0.881689	−	0.471831i	$-0.156407\pi$
$491$	−37.0187	−	89.3710i	−0.0753945	−	0.182018i	−0.957083	+	0.289813i	$0.906407\pi$
$492$		0			0
$493$	105.837	+	53.9804i	0.214679	+	0.109494i
$494$		0			0
$495$	130.917	−	54.2275i	0.264478	−	0.109551i
$496$		0			0
$497$	207.883	−	207.883i	0.418276	−	0.418276i
$498$		0			0
$499$	−57.8167	−	290.664i	−0.115865	−	0.582493i	−0.994477	−	0.104956i	$-0.966530\pi$
$499$	−57.8167	−	290.664i	−0.115865	−	0.582493i	0.878612	−	0.477537i	$-0.158470\pi$
$500$		0			0
$501$	11.6114	−	28.0325i	0.0231765	−	0.0559530i
$502$		0			0
$503$	67.2065	−	100.582i	0.133611	−	0.199964i	−0.758631	−	0.651521i	$-0.774131\pi$
$503$	67.2065	−	100.582i	0.133611	−	0.199964i	0.892242	+	0.451557i	$0.149131\pi$
$504$		0			0
$505$	−7.96595	−	11.9219i	−0.0157742	−	0.0236077i
$506$		0			0
$507$	−37.2451	−	7.40852i	−0.0734618	−	0.0146125i
$508$		0			0
$509$			229.001i			0.449905i	0.974370	+	0.224952i	$0.0722226\pi$
$509$			229.001i			0.449905i	−0.974370	+	0.224952i	$0.927777\pi$
$510$		0			0
$511$	−163.470			−0.319902
$512$		0			0
$513$	7.70074	−	38.7143i	0.0150112	−	0.0754664i
$514$		0			0
$515$	−336.525	+	224.859i	−0.653447	+	0.436619i
$516$		0			0
$517$	144.497	+	96.5499i	0.279492	+	0.186750i
$518$		0			0
$519$	33.2558	+	13.7750i	0.0640767	+	0.0265414i
$520$		0			0
$521$	−928.474	+	184.685i	−1.78210	+	0.354482i	−0.972572	−	0.232601i	$-0.925276\pi$
$521$	−928.474	+	184.685i	−1.78210	+	0.354482i	−0.809527	+	0.587083i	$0.800276\pi$
$522$		0			0
$523$	−159.639	−	159.639i	−0.305238	−	0.305238i	0.537821	−	0.843059i	$-0.319248\pi$
$523$	−159.639	−	159.639i	−0.305238	−	0.305238i	−0.843059	+	0.537821i	$0.819248\pi$
$524$		0			0
$525$	−6.45183	−	15.5761i	−0.0122892	−	0.0296687i
$526$		0			0
$527$	195.841	−	63.5453i	0.371615	−	0.120579i
$528$		0			0
$529$	−95.8213	+	39.6905i	−0.181137	+	0.0750293i
$530$		0			0
$531$	413.830	−	413.830i	0.779341	−	0.779341i
$532$		0			0
$533$	−66.8956	−	336.307i	−0.125508	−	0.630970i
$534$		0			0
$535$	136.338	−	329.149i	0.254837	−	0.615231i
$536$		0			0
$537$	12.6398	−	18.9168i	0.0235379	−	0.0352269i
$538$		0			0
$539$	−0.994825	−	1.48886i	−0.00184569	−	0.00276226i
$540$		0			0
$541$	106.918	+	21.2673i	0.197630	+	0.0393110i	0.292913	−	0.956139i	$-0.405376\pi$
$541$	106.918	+	21.2673i	0.197630	+	0.0393110i	−0.0952828	+	0.995450i	$0.530376\pi$
$542$		0			0
$543$			4.55418i			0.00838707i
$544$		0			0
$545$	59.2037			0.108631
$546$		0			0
$547$	−164.534	+	827.168i	−0.300793	+	1.51219i	0.474312	+	0.880357i	$0.342697\pi$
$547$	−164.534	+	827.168i	−0.300793	+	1.51219i	−0.775105	+	0.631832i	$0.782303\pi$
$548$		0			0
$549$	12.5648	−	8.39551i	0.0228867	−	0.0152924i
$550$		0			0
$551$	−98.2679	−	65.6605i	−0.178345	−	0.119166i
$552$		0			0
$553$	977.267	+	404.797i	1.76721	+	0.732002i
$554$		0			0
$555$	−16.4513	+	3.27237i	−0.0296420	+	0.00589616i
$556$		0			0
$557$	−437.546	−	437.546i	−0.785540	−	0.785540i	0.195220	−	0.980760i	$-0.437458\pi$
$557$	−437.546	−	437.546i	−0.785540	−	0.785540i	−0.980760	+	0.195220i	$0.937458\pi$
$558$		0			0
$559$	−542.141	−	1308.85i	−0.969841	−	2.34140i
$560$		0			0
$561$	−6.66671	−	11.9155i	−0.0118836	−	0.0212398i
$562$		0			0
$563$	−455.754	+	188.780i	−0.809510	+	0.335310i	−0.748759	−	0.662843i	$-0.769350\pi$
$563$	−455.754	+	188.780i	−0.809510	+	0.335310i	−0.0607518	+	0.998153i	$0.519350\pi$
$564$		0			0
$565$	−251.880	+	251.880i	−0.445806	+	0.445806i
$566$		0			0
$567$	110.320	+	554.615i	0.194567	+	0.978157i
$568$		0			0
$569$	−200.946	+	485.128i	−0.353157	+	0.852597i	0.643070	+	0.765808i	$0.277661\pi$
$569$	−200.946	+	485.128i	−0.353157	+	0.852597i	−0.996227	+	0.0867890i	$0.972339\pi$
$570$		0			0
$571$	350.122	−	523.994i	0.613173	−	0.917678i	−0.386817	−	0.922156i	$-0.626426\pi$
$571$	350.122	−	523.994i	0.613173	−	0.917678i	0.999990	+	0.00447841i	$0.00142553\pi$
$572$		0			0
$573$	19.9296	+	29.8267i	0.0347811	+	0.0520536i
$574$		0			0
$575$	456.438	+	90.7913i	0.793806	+	0.157898i
$576$		0			0
$577$		−	907.982i		−	1.57363i	−0.617191	−	0.786813i	$-0.711730\pi$
$577$		−	907.982i		−	1.57363i	0.617191	−	0.786813i	$-0.288270\pi$
$578$		0			0
$579$	26.1090			0.0450933
$580$		0			0
$581$	−47.1892	+	237.236i	−0.0812207	+	0.408324i
$582$		0			0
$583$	−17.4210	+	11.6403i	−0.0298816	+	0.0199662i
$584$		0			0
$585$	−409.078	−	273.337i	−0.699278	−	0.467243i
$586$		0			0
$587$	−550.480	−	228.016i	−0.937785	−	0.388443i	−0.139158	−	0.990270i	$-0.544440\pi$
$587$	−550.480	−	228.016i	−0.937785	−	0.388443i	−0.798626	+	0.601827i	$0.794440\pi$
$588$		0			0
$589$	−200.879	+	39.9572i	−0.341050	+	0.0678391i
$590$		0			0
$591$	−35.6963	−	35.6963i	−0.0603999	−	0.0603999i
$592$		0			0
$593$	−418.341	−	1009.97i	−0.705466	−	1.70315i	−0.711030	−	0.703161i	$-0.751771\pi$
$593$	−418.341	−	1009.97i	−0.705466	−	1.70315i	0.00556444	−	0.999985i	$-0.498229\pi$
$594$		0			0
$595$	−265.520	+	148.558i	−0.446253	+	0.249677i
$596$		0			0
$597$	−22.0133	+	9.11822i	−0.0368732	+	0.0152734i
$598$		0			0
$599$	17.0281	−	17.0281i	0.0284275	−	0.0284275i	−0.692750	−	0.721178i	$-0.743601\pi$
$599$	17.0281	−	17.0281i	0.0284275	−	0.0284275i	0.721178	+	0.692750i	$0.243601\pi$
$600$		0			0
$601$	28.3388	+	142.469i	0.0471527	+	0.237053i	0.997173	−	0.0751342i	$-0.0239385\pi$
$601$	28.3388	+	142.469i	0.0471527	+	0.237053i	−0.950021	+	0.312187i	$0.898939\pi$
$602$		0			0
$603$	−370.110	+	893.526i	−0.613782	+	1.48180i
$604$		0			0
$605$	117.141	−	175.314i	0.193622	−	0.289776i
$606$		0			0
$607$	−180.389	−	269.972i	−0.297182	−	0.444764i	0.652588	−	0.757713i	$-0.273683\pi$
$607$	−180.389	−	269.972i	−0.297182	−	0.444764i	−0.949770	+	0.312949i	$0.898683\pi$
$608$		0			0
$609$	−6.24611	−	1.24243i	−0.0102563	−	0.00204011i
$610$		0			0
$611$		−	603.382i		−	0.987532i
$612$		0			0
$613$	−455.956			−0.743811			−0.371906	−	0.928271i	$-0.621295\pi$
$613$	−455.956			−0.743811			−0.371906	+	0.928271i	$0.621295\pi$
$614$		0			0
$615$	−1.03027	+	5.17952i	−0.00167524	+	0.00842199i
$616$		0			0
$617$	−427.496	+	285.644i	−0.692862	+	0.462956i	−0.851482	−	0.524384i	$-0.824296\pi$
$617$	−427.496	+	285.644i	−0.692862	+	0.462956i	0.158620	+	0.987340i	$0.449296\pi$
$618$		0			0
$619$	803.573	+	536.930i	1.29818	+	0.867415i	0.996301	−	0.0859315i	$-0.0273866\pi$
$619$	803.573	+	536.930i	1.29818	+	0.867415i	0.301878	+	0.953347i	$0.402387\pi$
$620$		0			0
$621$	54.2436	+	22.4684i	0.0873487	+	0.0361810i
$622$		0			0
$623$	225.732	−	44.9009i	0.362330	−	0.0720720i
$624$		0			0
$625$	−127.162	−	127.162i	−0.203460	−	0.203460i
$626$		0			0
$627$	5.19770	+	12.5484i	0.00828979	+	0.0200133i
$628$		0			0
$629$	−265.977	−	819.719i	−0.422858	−	1.30321i
$630$		0			0
$631$	−262.743	+	108.832i	−0.416392	+	0.172475i	−0.581036	−	0.813878i	$-0.697352\pi$
$631$	−262.743	+	108.832i	−0.416392	+	0.172475i	0.164644	+	0.986353i	$0.447352\pi$
$632$		0			0
$633$	−7.55934	+	7.55934i	−0.0119421	+	0.0119421i
$634$		0			0
$635$	−36.5857	−	183.929i	−0.0576152	−	0.289651i
$636$		0			0
$637$	−2.37918	+	5.74384i	−0.00373497	+	0.00901702i
$638$		0			0
$639$	208.990	−	312.776i	0.327058	−	0.489477i
$640$		0			0
$641$	−131.190	−	196.340i	−0.204665	−	0.306303i	0.714911	−	0.699216i	$-0.246467\pi$
$641$	−131.190	−	196.340i	−0.204665	−	0.306303i	−0.919576	+	0.392913i	$0.871467\pi$
$642$		0			0
$643$	−365.607	−	72.7237i	−0.568595	−	0.113101i	−0.0975831	−	0.995227i	$-0.531111\pi$
$643$	−365.607	−	72.7237i	−0.568595	−	0.113101i	−0.471012	+	0.882127i	$0.656111\pi$
$644$		0			0
$645$			21.8186i			0.0338273i
$646$		0			0
$647$	1181.95			1.82682			0.913409	−	0.407044i	$-0.133440\pi$
$647$	1181.95			1.82682			0.913409	+	0.407044i	$0.133440\pi$
$648$		0			0
$649$	−78.6474	+	395.387i	−0.121182	+	0.609225i
$650$		0			0
$651$	−9.17649	+	6.13154i	−0.0140960	+	0.00941864i
$652$		0			0
$653$	−152.652	−	101.999i	−0.233770	−	0.156200i	0.433168	−	0.901313i	$-0.357396\pi$
$653$	−152.652	−	101.999i	−0.233770	−	0.156200i	−0.666938	+	0.745113i	$0.732396\pi$
$654$		0			0
$655$	564.604	+	233.867i	0.861990	+	0.357048i
$656$		0			0
$657$	−205.147	+	40.8062i	−0.312247	+	0.0621099i
$658$		0			0
$659$	−121.390	−	121.390i	−0.184204	−	0.184204i	0.608981	−	0.793185i	$-0.291579\pi$
$659$	−121.390	−	121.390i	−0.184204	−	0.184204i	−0.793185	+	0.608981i	$0.791579\pi$
$660$		0			0
$661$	−274.007	−	661.510i	−0.414533	−	1.00077i	−0.983905	−	0.178692i	$-0.942813\pi$
$661$	−274.007	−	661.510i	−0.414533	−	1.00077i	0.569372	−	0.822080i	$-0.307187\pi$
$662$		0			0
$663$	−21.5388	+	42.2302i	−0.0324869	+	0.0636956i
$664$		0			0
$665$	279.622	−	115.823i	0.420484	−	0.174170i
$666$		0			0
$667$	124.304	−	124.304i	0.186363	−	0.186363i
$668$		0			0
$669$	−6.56770	−	33.0181i	−0.00981720	−	0.0493544i
$670$		0			0
$671$	−3.98345	+	9.61690i	−0.00593659	+	0.0143322i
$672$		0			0
$673$	−635.145	+	950.561i	−0.943752	+	1.41242i	−0.0330066	+	0.999455i	$0.510508\pi$
$673$	−635.145	+	950.561i	−0.943752	+	1.41242i	−0.910745	+	0.412969i	$0.864492\pi$
$674$		0			0
$675$	−23.9923	−	35.9070i	−0.0355441	−	0.0531955i
$676$		0			0
$677$	923.536	+	183.703i	1.36416	+	0.271348i	0.822268	−	0.569100i	$-0.192708\pi$
$677$	923.536	+	183.703i	1.36416	+	0.271348i	0.541892	+	0.840448i	$0.317708\pi$
$678$		0			0
$679$		−	636.847i		−	0.937918i
$680$		0			0
$681$	−24.8267			−0.0364563
$682$		0			0
$683$	−181.538	+	912.655i	−0.265796	+	1.33624i	0.585122	+	0.810945i	$0.301047\pi$
$683$	−181.538	+	912.655i	−0.265796	+	1.33624i	−0.850918	+	0.525299i	$0.823953\pi$
$684$		0			0
$685$	478.527	−	319.741i	0.698579	−	0.466776i
$686$		0			0
$687$	23.4273	+	15.6536i	0.0341008	+	0.0227854i
$688$		0			0
$689$	67.2080	+	27.8384i	0.0975442	+	0.0404041i
$690$		0			0
$691$	−459.738	+	91.4476i	−0.665323	+	0.132341i	−0.516187	−	0.856476i	$-0.672649\pi$
$691$	−459.738	+	91.4476i	−0.665323	+	0.132341i	−0.149136	+	0.988817i	$0.547649\pi$
$692$		0			0
$693$	−275.950	−	275.950i	−0.398197	−	0.398197i
$694$		0			0
$695$	109.013	+	263.181i	0.156854	+	0.378678i
$696$		0			0
$697$	−270.481	−	21.3970i	−0.388064	−	0.0306987i
$698$		0			0
$699$	−40.3514	+	16.7141i	−0.0577273	+	0.0239114i
$700$		0			0
$701$	−637.951	+	637.951i	−0.910058	+	0.910058i	−0.996276	−	0.0862183i	$-0.972522\pi$
$701$	−637.951	+	637.951i	−0.910058	+	0.910058i	0.0862183	+	0.996276i	$0.472522\pi$
$702$		0			0
$703$	167.246	+	840.805i	0.237904	+	1.19602i
$704$		0			0
$705$	−3.55620	+	8.58542i	−0.00504425	+	0.0121779i
$706$		0			0
$707$	−21.9383	+	32.8330i	−0.0310301	+	0.0464399i
$708$		0			0
$709$	391.661	+	586.162i	0.552413	+	0.826745i	0.997639	−	0.0686736i	$-0.0218767\pi$
$709$	391.661	+	586.162i	0.552413	+	0.826745i	−0.445226	+	0.895418i	$0.646877\pi$
$710$		0			0
$711$	1327.47	+	264.050i	1.86704	+	0.371378i
$712$		0			0
$713$		−	304.646i		−	0.427274i
$714$		0			0
$715$	338.900			0.473985
$716$		0			0
$717$	−2.10869	+	10.6011i	−0.00294099	+	0.0147854i
$718$		0			0
$719$	658.320	−	439.875i	0.915605	−	0.611788i	−0.00597248	−	0.999982i	$-0.501901\pi$
$719$	658.320	−	439.875i	0.915605	−	0.611788i	0.921577	+	0.388194i	$0.126901\pi$
$720$		0			0
$721$	926.793	+	619.264i	1.28543	+	0.858895i
$722$		0			0
$723$	19.4553	+	8.05864i	0.0269091	+	0.0111461i
$724$		0			0
$725$	−126.816	+	25.2253i	−0.174919	+	0.0347935i
$726$		0			0
$727$	187.419	+	187.419i	0.257797	+	0.257797i	0.824158	−	0.566360i	$-0.191649\pi$
$727$	187.419	+	187.419i	0.257797	+	0.257797i	−0.566360	+	0.824158i	$0.691649\pi$
$728$		0			0
$729$	275.848	+	665.956i	0.378392	+	0.913519i
$730$		0			0
$731$	−1113.27	+	131.310i	−1.52295	+	0.179630i
$732$		0			0
$733$	903.383	−	374.194i	1.23245	−	0.510496i	0.331100	−	0.943596i	$-0.392580\pi$
$733$	903.383	−	374.194i	1.23245	−	0.510496i	0.901346	+	0.433099i	$0.142580\pi$
$734$		0			0
$735$	0.0677058	−	0.0677058i	9.21167e−5	−	9.21167e-5i
$736$		0			0
$737$	−129.969	−	653.397i	−0.176348	−	0.886563i
$738$		0			0
$739$	−91.0141	+	219.727i	−0.123158	+	0.297331i	−0.973419	−	0.229031i	$-0.926444\pi$
$739$	−91.0141	+	219.727i	−0.123158	+	0.297331i	0.850261	+	0.526362i	$0.176444\pi$
$740$		0			0
$741$	26.1993	−	39.2100i	0.0353567	−	0.0529150i
$742$		0			0
$743$	274.650	+	411.043i	0.369651	+	0.553221i	0.968935	−	0.247315i	$-0.0795482\pi$
$743$	274.650	+	411.043i	0.369651	+	0.553221i	−0.599285	+	0.800536i	$0.704548\pi$
$744$		0			0
$745$	−193.862	−	38.5615i	−0.260217	−	0.0517604i
$746$		0			0
$747$			309.499i			0.414323i
$748$		0			0
$749$	−981.166			−1.30997
$750$		0			0
$751$	76.2428	−	383.298i	0.101522	−	0.510384i	−0.896243	−	0.443563i	$-0.853714\pi$
$751$	76.2428	−	383.298i	0.101522	−	0.510384i	0.997765	−	0.0668212i	$-0.0212857\pi$
$752$		0			0
$753$	−29.8153	+	19.9219i	−0.0395953	+	0.0264568i
$754$		0			0
$755$	68.2034	+	45.5721i	0.0903357	+	0.0603604i
$756$		0			0
$757$	328.729	+	136.164i	0.434253	+	0.179873i	0.589091	−	0.808066i	$-0.299486\pi$
$757$	328.729	+	136.164i	0.434253	+	0.179873i	−0.154839	+	0.987940i	$0.549486\pi$
$758$		0			0
$759$	−19.8144	+	3.94133i	−0.0261059	+	0.00519280i
$760$		0			0
$761$	−529.945	−	529.945i	−0.696380	−	0.696380i	0.267248	−	0.963628i	$-0.413886\pi$
$761$	−529.945	−	529.945i	−0.696380	−	0.696380i	−0.963628	+	0.267248i	$0.913886\pi$
$762$		0			0
$763$	−62.3957	−	150.636i	−0.0817768	−	0.197427i
$764$		0			0
$765$	−296.131	+	252.713i	−0.387099	+	0.330344i
$766$		0			0
$767$	1293.13	−	535.634i	1.68596	−	0.698349i
$768$		0			0
$769$	−638.491	+	638.491i	−0.830288	+	0.830288i	−0.987556	−	0.157268i	$-0.949731\pi$
$769$	−638.491	+	638.491i	−0.830288	+	0.830288i	0.157268	+	0.987556i	$0.449731\pi$
$770$		0			0
$771$	−0.740508	−	3.72279i	−0.000960451	−	0.00482852i
$772$		0			0
$773$	3.70426	−	8.94288i	0.00479206	−	0.0115691i	−0.921465	−	0.388460i	$-0.873007\pi$
$773$	3.70426	−	8.94288i	0.00479206	−	0.0115691i	0.926257	+	0.376891i	$0.123007\pi$
$774$		0			0
$775$	−124.490	+	186.312i	−0.160632	+	0.240403i
$776$		0			0
$777$	25.6644	+	38.4095i	0.0330301	+	0.0494330i
$778$		0			0
$779$	264.719	+	52.6558i	0.339819	+	0.0675942i
$780$		0			0
$781$			259.118i			0.331777i
$782$		0			0
$783$	−16.3127			−0.0208336
$784$		0			0
$785$	−63.2693	+	318.076i	−0.0805979	+	0.405193i
$786$		0			0
$787$	432.484	−	288.977i	0.549535	−	0.367188i	−0.249591	−	0.968351i	$-0.580296\pi$
$787$	432.484	−	288.977i	0.549535	−	0.367188i	0.799126	+	0.601164i	$0.205296\pi$
$788$		0			0
$789$	−38.7105	−	25.8655i	−0.0490627	−	0.0327827i
$790$		0			0
$791$	906.337	+	375.417i	1.14581	+	0.474611i
$792$		0			0
$793$	35.4465	−	7.05074i	0.0446992	−	0.00889123i
$794$		0			0
$795$	−0.792217	−	0.792217i	−0.000996499	−	0.000996499i
$796$		0			0
$797$	29.1906	+	70.4723i	0.0366256	+	0.0884220i	0.941134	−	0.338034i	$-0.109762\pi$
$797$	29.1906	+	70.4723i	0.0366256	+	0.0884220i	−0.904508	+	0.426456i	$0.859762\pi$
$798$		0			0
$799$	−459.465	−	129.783i	−0.575050	−	0.162431i
$800$		0			0
$801$	272.074	−	112.697i	0.339667	−	0.140695i
$802$		0			0
$803$	101.880	−	101.880i	0.126874	−	0.126874i
$804$		0			0
$805$	87.8270	+	441.536i	0.109102	+	0.548492i
$806$		0			0
$807$	1.19584	−	2.88701i	0.00148183	−	0.00357745i
$808$		0			0
$809$	728.283	−	1089.95i	0.900226	−	1.34728i	−0.0372760	−	0.999305i	$-0.511868\pi$
$809$	728.283	−	1089.95i	0.900226	−	1.34728i	0.937502	−	0.347979i	$-0.113132\pi$
$810$		0			0
$811$	526.425	+	787.851i	0.649106	+	0.971456i	0.999394	+	0.0348141i	$0.0110839\pi$
$811$	526.425	+	787.851i	0.649106	+	0.971456i	−0.350287	+	0.936642i	$0.613916\pi$
$812$		0			0
$813$	−48.2907	−	9.60562i	−0.0593982	−	0.0118150i
$814$		0			0
$815$			74.8333i			0.0918200i
$816$		0			0
$817$	1115.12			1.36490
$818$		0			0
$819$	−264.339	+	1328.92i	−0.322758	+	1.62261i
$820$		0			0
$821$	483.151	−	322.831i	0.588491	−	0.393217i	−0.225373	−	0.974273i	$-0.572360\pi$
$821$	483.151	−	322.831i	0.588491	−	0.393217i	0.813864	+	0.581055i	$0.197360\pi$
$822$		0			0
$823$	−940.709	−	628.562i	−1.14302	−	0.763745i	−0.167988	−	0.985789i	$-0.553727\pi$
$823$	−940.709	−	628.562i	−1.14302	−	0.763745i	−0.975037	+	0.222044i	$0.928727\pi$
$824$		0			0
$825$	13.7285	+	5.68652i	0.0166406	+	0.00689275i
$826$		0			0
$827$	−1406.43	+	279.756i	−1.70064	+	0.338278i	−0.947542	−	0.319633i	$-0.896441\pi$
$827$	−1406.43	+	279.756i	−1.70064	+	0.338278i	−0.753096	+	0.657910i	$0.771441\pi$
$828$		0			0
$829$	153.806	+	153.806i	0.185532	+	0.185532i	0.793761	−	0.608230i	$-0.208120\pi$
$829$	153.806	+	153.806i	0.185532	+	0.185532i	−0.608230	+	0.793761i	$0.708120\pi$
$830$		0			0
$831$	−11.0432	−	26.6607i	−0.0132891	−	0.0320827i
$832$		0			0
$833$	3.86210	+	3.04716i	0.00463637	+	0.00365805i
$834$		0			0
$835$	550.567	−	228.052i	0.659361	−	0.273116i
$836$		0			0
$837$	−19.9896	+	19.9896i	−0.0238825	+	0.0238825i
$838$		0			0
$839$	−144.613	−	727.019i	−0.172364	−	0.866530i	−0.966080	−	0.258242i	$-0.916857\pi$
$839$	−144.613	−	727.019i	−0.172364	−	0.866530i	0.793717	−	0.608288i	$-0.208143\pi$
$840$		0			0
$841$	303.146	−	731.859i	0.360459	−	0.870224i
$842$		0			0
$843$	9.89084	−	14.8027i	0.0117329	−	0.0175595i
$844$		0			0
$845$	−414.365	−	620.141i	−0.490373	−	0.733894i
$846$		0			0
$847$	−569.523	−	113.285i	−0.672400	−	0.133749i
$848$		0			0
$849$			62.0306i			0.0730632i
$850$		0			0
$851$	−1275.14			−1.49840
$852$		0			0
$853$	−224.458	+	1128.43i	−0.263139	+	1.32289i	0.592606	+	0.805492i	$0.298099\pi$
$853$	−224.458	+	1128.43i	−0.263139	+	1.32289i	−0.855745	+	0.517398i	$0.826901\pi$
$854$		0			0
$855$	321.999	−	215.153i	0.376607	−	0.251641i
$856$		0			0
$857$	−6.11980	−	4.08912i	−0.00714096	−	0.00477143i	0.551995	−	0.833848i	$-0.313867\pi$
$857$	−6.11980	−	4.08912i	−0.00714096	−	0.00477143i	−0.559136	+	0.829076i	$0.688867\pi$
$858$		0			0
$859$	−820.092	−	339.693i	−0.954706	−	0.395452i	−0.149708	−	0.988730i	$-0.547833\pi$
$859$	−820.092	−	339.693i	−0.954706	−	0.395452i	−0.804998	+	0.593278i	$0.797833\pi$
$860$		0			0
$861$	14.2645	−	2.83738i	0.0165673	−	0.00329544i
$862$		0			0
$863$	−674.651	−	674.651i	−0.781751	−	0.781751i	0.198375	−	0.980126i	$-0.436434\pi$
$863$	−674.651	−	674.651i	−0.781751	−	0.781751i	−0.980126	+	0.198375i	$0.936434\pi$
$864$		0			0
$865$	270.545	+	653.154i	0.312769	+	0.755092i
$866$		0			0
$867$	27.5247	+	25.4848i	0.0317471	+	0.0293942i
$868$		0			0
$869$	−861.344	+	356.780i	−0.991190	+	0.410564i
$870$		0			0
$871$	−1635.56	+	1635.56i	−1.87780	+	1.87780i
$872$		0			0
$873$	−158.973	−	799.210i	−0.182099	−	0.915475i
$874$		0			0
$875$	297.941	−	719.293i	0.340504	−	0.822049i
$876$		0			0
$877$	133.642	−	200.009i	0.152385	−	0.228060i	−0.747421	−	0.664351i	$-0.768708\pi$
$877$	133.642	−	200.009i	0.152385	−	0.228060i	0.899806	+	0.436291i	$0.143708\pi$
$878$		0			0
$879$	−8.04371	−	12.0383i	−0.00915098	−	0.0136954i
$880$		0			0
$881$	802.517	+	159.631i	0.910916	+	0.181193i	0.628237	−	0.778022i	$-0.283777\pi$
$881$	802.517	+	159.631i	0.910916	+	0.181193i	0.282679	+	0.959215i	$0.408777\pi$
$882$		0			0
$883$		−	1134.33i		−	1.28463i	−0.766442	−	0.642314i	$-0.777975\pi$
$883$		−	1134.33i		−	1.28463i	0.766442	−	0.642314i	$-0.222025\pi$
$884$		0			0
$885$	−21.5567			−0.0243578
$886$		0			0
$887$	268.710	−	1350.90i	0.302943	−	1.52300i	−0.466639	−	0.884448i	$-0.654535\pi$
$887$	268.710	−	1350.90i	0.302943	−	1.52300i	0.769582	−	0.638548i	$-0.220465\pi$
$888$		0			0
$889$	−429.425	+	286.933i	−0.483043	+	0.322759i
$890$		0			0
$891$	−414.407	−	276.898i	−0.465104	−	0.310772i
$892$		0			0
$893$	438.790	+	181.753i	0.491366	+	0.203531i
$894$		0			0
$895$	438.253	−	87.1739i	0.489668	−	0.0974010i
$896$		0			0
$897$	49.5989	+	49.5989i	0.0552942	+	0.0552942i
$898$		0			0
$899$	32.3912	+	78.1994i	0.0360303	+	0.0869848i
$900$		0			0
$901$	35.6544	−	45.1899i	0.0395720	−	0.0501553i
$902$		0			0
$903$	55.5147	−	22.9949i	0.0614780	−	0.0254650i
$904$		0			0
$905$	−63.2475	+	63.2475i	−0.0698868	+	0.0698868i
$906$		0			0
$907$	−96.2074	−	483.667i	−0.106072	−	0.533260i	−0.996884	−	0.0788872i	$-0.974863\pi$
$907$	−96.2074	−	483.667i	−0.106072	−	0.533260i	0.890811	−	0.454373i	$-0.150137\pi$
$908$		0			0
$909$	−19.3355	+	46.6801i	−0.0212712	+	0.0513532i
$910$		0			0
$911$	−406.461	+	608.311i	−0.446170	+	0.667740i	−0.984578	−	0.174944i	$-0.944026\pi$
$911$	−406.461	+	608.311i	−0.446170	+	0.667740i	0.538409	+	0.842684i	$0.319026\pi$
$912$		0			0
$913$	−118.443	−	177.263i	−0.129730	−	0.194154i
$914$		0			0
$915$	−0.545917	−	0.108590i	−0.000596631	−	0.000118677i
$916$		0			0
$917$		−	1683.04i		−	1.83537i
$918$		0			0
$919$	415.884			0.452540			0.226270	−	0.974065i	$-0.427347\pi$
$919$	415.884			0.452540			0.226270	+	0.974065i	$0.427347\pi$
$920$		0			0
$921$	−9.96828	+	50.1139i	−0.0108233	+	0.0544125i
$922$		0			0
$923$	748.038	−	499.823i	0.810442	−	0.541520i
$924$		0			0
$925$	779.835	+	521.069i	0.843065	+	0.563318i
$926$		0			0
$927$	1317.66	+	545.793i	1.42143	+	0.588774i
$928$		0			0
$929$	−1305.29	+	259.639i	−1.40505	+	0.279482i	−0.838660	−	0.544655i	$-0.816660\pi$
$929$	−1305.29	+	259.639i	−1.40505	+	0.279482i	−0.566390	+	0.824137i	$0.691660\pi$
$930$		0			0
$931$	−3.46036	−	3.46036i	−0.00371682	−	0.00371682i
$932$		0			0
$933$	−28.9328	−	69.8500i	−0.0310105	−	0.0748660i
$934$		0			0
$935$	72.8945	−	258.066i	0.0779621	−	0.276007i
$936$		0			0
$937$	−456.676	+	189.162i	−0.487381	+	0.201880i	−0.612822	−	0.790221i	$-0.709966\pi$
$937$	−456.676	+	189.162i	−0.487381	+	0.201880i	0.125440	+	0.992101i	$0.459966\pi$
$938$		0			0
$939$	32.4098	−	32.4098i	0.0345152	−	0.0345152i
$940$		0			0
$941$	−36.9169	−	185.594i	−0.0392315	−	0.197230i	0.956199	−	0.292717i	$-0.0945593\pi$
$941$	−36.9169	−	185.594i	−0.0392315	−	0.197230i	−0.995431	+	0.0954865i	$0.969559\pi$
$942$		0			0
$943$	−153.634	+	370.904i	−0.162920	+	0.393324i
$944$		0			0
$945$	23.2089	−	34.7346i	0.0245597	−	0.0367562i
$946$		0			0
$947$	−585.715	−	876.584i	−0.618495	−	0.925643i	−0.999999	−	0.00127603i	$-0.999594\pi$
$947$	−585.715	−	876.584i	−0.618495	−	0.925643i	0.381504	−	0.924367i	$-0.375406\pi$
$948$		0			0
$949$	−490.631	−	97.5926i	−0.516998	−	0.102837i
$950$		0			0
$951$		−	48.4008i		−	0.0508947i
$952$		0			0
$953$	975.466			1.02357			0.511787	−	0.859113i	$-0.328984\pi$
$953$	975.466			1.02357			0.511787	+	0.859113i	$0.328984\pi$
$954$		0			0
$955$	−137.450	+	691.006i	−0.143926	+	0.723566i
$956$		0			0
$957$	4.66709	−	3.11845i	0.00487679	−	0.00325857i
$958$		0			0
$959$	−1317.87	−	880.572i	−1.37421	−	0.918218i
$960$		0			0
$961$	−752.330	−	311.625i	−0.782862	−	0.324272i
$962$		0			0
$963$	−1231.31	+	244.923i	−1.27862	+	0.254334i
$964$		0			0
$965$	362.597	+	362.597i	0.375748	+	0.375748i
$966$		0			0
$967$	−378.755	−	914.396i	−0.391681	−	0.945601i	−0.989574	−	0.144025i	$-0.953995\pi$
$967$	−378.755	−	914.396i	−0.391681	−	0.945601i	0.597893	−	0.801576i	$-0.296005\pi$
$968$		0			0
$969$	−24.2225	−	28.3841i	−0.0249974	−	0.0292922i
$970$		0			0
$971$	−598.021	+	247.709i	−0.615882	+	0.255107i	−0.668741	−	0.743495i	$-0.733167\pi$
$971$	−598.021	+	247.709i	−0.615882	+	0.255107i	0.0528592	+	0.998602i	$0.483167\pi$
$972$		0			0
$973$	554.741	−	554.741i	0.570135	−	0.570135i
$974$		0			0
$975$	−10.0652	−	50.6011i	−0.0103233	−	0.0518986i
$976$		0			0
$977$	−249.451	+	602.228i	−0.255324	+	0.616406i	−0.998618	−	0.0525589i	$-0.983262\pi$
$977$	−249.451	+	602.228i	−0.255324	+	0.616406i	0.743294	+	0.668965i	$0.233262\pi$
$978$		0			0
$979$	−112.699	+	168.667i	−0.115117	+	0.172284i
$980$		0			0
$981$	−115.906	−	173.466i	−0.118151	−	0.176825i
$982$		0			0
$983$	−445.712	−	88.6576i	−0.453420	−	0.0901908i	−0.0369032	−	0.999319i	$-0.511749\pi$
$983$	−445.712	−	88.6576i	−0.453420	−	0.0901908i	−0.416517	+	0.909128i	$0.636749\pi$
$984$		0			0
$985$		−	991.487i		−	1.00659i
$986$		0			0
$987$	25.5925			0.0259295
$988$		0			0
$989$	−323.589	+	1626.79i	−0.327188	+	1.64488i
$990$		0			0
$991$	−785.080	+	524.574i	−0.792210	+	0.529338i	−0.884581	−	0.466387i	$-0.845555\pi$
$991$	−785.080	+	524.574i	−0.792210	+	0.529338i	0.0923710	+	0.995725i	$0.470555\pi$
$992$		0			0
$993$	13.6128	+	9.09576i	0.0137087	+	0.00915988i
$994$		0			0
$995$	−432.349	−	179.085i	−0.434521	−	0.179985i
$996$		0			0
$997$	1267.38	−	252.097i	1.27119	−	0.252855i	0.487014	−	0.873394i	$-0.338086\pi$
$997$	1267.38	−	252.097i	1.27119	−	0.252855i	0.784175	+	0.620539i	$0.213086\pi$
$998$		0			0
$999$	83.6693	+	83.6693i	0.0837530	+	0.0837530i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	136.3.t.b.65.3	✓	40
4.3	odd	2		272.3.bh.g.65.3		40
17.11	odd	16	inner	136.3.t.b.113.3	yes	40
68.11	even	16		272.3.bh.g.113.3		40

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
136.3.t.b.65.3	✓	40	1.1	even	1	trivial
136.3.t.b.113.3	yes	40	17.11	odd	16	inner
272.3.bh.g.65.3		40	4.3	odd	2
272.3.bh.g.113.3		40	68.11	even	16

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)

\(f(q)\)	\(=\)	\(q+(-0.0253220 + 0.127302i) q^{3} +(-2.11962 + 1.41628i) q^{5} +(5.83745 + 3.90046i) q^{7} +(8.29935 + 3.43770i) q^{9} +O(q^{10})\)	\(q+(-0.0253220 + 0.127302i) q^{3} +(-2.11962 + 1.41628i) q^{5} +(5.83745 + 3.90046i) q^{7} +(8.29935 + 3.43770i) q^{9} +(-6.06896 + 1.20719i) q^{11} +(15.1916 + 15.1916i) q^{13} +(-0.126623 - 0.305695i) q^{15} +(14.8358 - 8.30058i) q^{17} +(-15.6237 + 6.47155i) q^{19} +(-0.644354 + 0.644354i) q^{21} +(-4.90727 - 24.6705i) q^{23} +(-7.08017 + 17.0930i) q^{25} +(-1.29678 + 1.94077i) q^{27} +(3.88272 + 5.81090i) q^{29} +(11.8786 + 2.36280i) q^{31} -0.803161i q^{33} -17.8973 q^{35} +(9.88982 - 49.7195i) q^{37} +(-2.31862 + 1.54925i) q^{39} +(-13.2705 - 8.86709i) q^{41} +(-60.9212 - 25.2344i) q^{43} +(-22.4602 + 4.46761i) q^{45} +(-19.8590 - 19.8590i) q^{47} +(0.110741 + 0.267352i) q^{49} +(0.681012 + 2.09882i) q^{51} +(3.12825 - 1.29576i) q^{53} +(11.1541 - 11.1541i) q^{55} +(-0.428220 - 2.15281i) q^{57} +(24.9315 - 60.1899i) q^{59} +(0.934584 - 1.39870i) q^{61} +(35.0384 + 52.4387i) q^{63} +(-53.7161 - 10.6848i) q^{65} +107.662i q^{67} +3.26488 q^{69} +(8.16946 - 41.0707i) q^{71} +(-19.3601 + 12.9360i) q^{73} +(-1.99670 - 1.33415i) q^{75} +(-40.1358 - 16.6248i) q^{77} +(147.773 - 29.3939i) q^{79} +(56.9542 + 56.9542i) q^{81} +(13.1847 + 31.8307i) q^{83} +(-19.6902 + 38.6057i) q^{85} +(-0.838059 + 0.347135i) q^{87} +(23.1807 - 23.1807i) q^{89} +(29.4261 + 147.935i) q^{91} +(-0.601580 + 1.45234i) q^{93} +(23.9507 - 35.8448i) q^{95} +(-50.3961 - 75.4231i) q^{97} +(-54.5184 - 10.8444i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 40 q + 8 q^{3} - 8 q^{7} - 16 q^{9}+O(q^{10}) \) 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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