LMFDB - Embedded newform 197.4.e.a.33.20

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [197,4,Mod(6,197)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(197, base_ring=CyclotomicField(14))

chi = DirichletCharacter(H, H._module([13]))

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

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

chi := DirichletCharacter("197.6");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 197 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	197.e (of order $14$, degree $6$, 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:	$11.6233762711$
Analytic rank:	$0$
Dimension:	$288$
Relative dimension:	$48$ over $\Q(\zeta_{14})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{14}]$

Embedding invariants

Embedding label			33.20
Character	$\chi$	$=$	197.33
Dual form			197.4.e.a.6.20

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.38176 - 0.315378i) q^{2} +(-3.51241 + 0.801685i) q^{3} +(-5.39795 - 2.59951i) q^{4} +(-1.22448 - 2.54267i) q^{5} +5.10615 q^{6} +(5.06822 + 22.2053i) q^{7} +(15.5035 + 12.3637i) q^{8} +(-12.6318 + 6.08317i) q^{9} +(0.890043 + 3.89953i) q^{10} +(30.6850 + 7.00365i) q^{11} +(21.0438 + 4.80311i) q^{12} +(-10.9076 + 8.69855i) q^{13} -32.2809i q^{14} +(6.33930 + 7.94923i) q^{15} +(12.3610 + 15.5002i) q^{16} +(-52.8307 - 109.704i) q^{17} +(19.3727 - 4.42169i) q^{18} -62.9013 q^{19} +16.9082i q^{20} +(-35.6033 - 73.9310i) q^{21} +(-40.1906 - 19.3548i) q^{22} +(-18.1483 + 79.5131i) q^{23} +(-64.3666 - 30.9973i) q^{24} +(72.9704 - 91.5020i) q^{25} +(17.8151 - 8.57929i) q^{26} +(115.543 - 92.1426i) q^{27} +(30.3651 - 133.038i) q^{28} +(41.2557 - 180.753i) q^{29} +(-6.25239 - 12.9832i) q^{30} +(-92.2103 - 21.0464i) q^{31} +(-81.0221 - 168.244i) q^{32} -113.393 q^{33} +(38.4012 + 168.247i) q^{34} +(50.2547 - 40.0768i) q^{35} +83.9993 q^{36} +(-39.0619 + 48.9821i) q^{37} +(86.9146 + 19.8377i) q^{38} +(31.3386 - 39.2973i) q^{39} +(12.4528 - 54.5594i) q^{40} +(396.630 - 191.007i) q^{41} +(25.8791 + 113.384i) q^{42} +(0.493990 - 2.16431i) q^{43} +(-147.430 - 117.571i) q^{44} +(30.9349 + 24.6698i) q^{45} +(50.1534 - 104.145i) q^{46} +(-77.0092 + 96.5665i) q^{47} +(-55.8431 - 44.5334i) q^{48} +(-158.356 + 76.2605i) q^{49} +(-129.686 + 103.421i) q^{50} +(273.511 + 342.972i) q^{51} +(81.4909 - 18.5998i) q^{52} +(-535.563 - 257.914i) q^{53} +(-188.713 + 90.8794i) q^{54} +(-19.7653 - 86.5976i) q^{55} +(-195.964 + 406.923i) q^{56} +(220.935 - 50.4270i) q^{57} +(-114.011 + 236.747i) q^{58} +(-1.31030 + 5.74079i) q^{59} +(-13.5551 - 59.3887i) q^{60} +(147.661 - 646.946i) q^{61} +(120.775 + 58.1623i) q^{62} +(-199.100 - 249.663i) q^{63} +(23.6000 + 103.398i) q^{64} +(35.4737 + 17.0832i) q^{65} +(156.682 + 35.7617i) q^{66} +(-523.274 - 417.297i) q^{67} +729.511i q^{68} -293.832i q^{69} +(-82.0794 + 39.5274i) q^{70} +(92.0348 + 191.112i) q^{71} +(-271.049 - 61.8651i) q^{72} +(808.193 + 644.513i) q^{73} +(69.4221 - 55.3623i) q^{74} +(-182.946 + 379.892i) q^{75} +(339.538 + 163.513i) q^{76} +716.866i q^{77} +(-55.6960 + 44.4161i) q^{78} +(345.573 - 717.591i) q^{79} +(24.2760 - 50.4096i) q^{80} +(-95.9452 + 120.311i) q^{81} +(-608.287 + 138.838i) q^{82} +1171.77 q^{83} +491.627i q^{84} +(-214.250 + 268.661i) q^{85} +(-1.36515 + 2.83477i) q^{86} +667.953i q^{87} +(389.136 + 487.961i) q^{88} +(-372.090 + 84.9272i) q^{89} +(-34.9644 - 43.8440i) q^{90} +(-248.436 - 198.121i) q^{91} +(304.659 - 382.031i) q^{92} +340.753 q^{93} +(136.863 - 109.145i) q^{94} +(77.0216 + 159.937i) q^{95} +(419.461 + 525.988i) q^{96} +(-1208.57 + 582.014i) q^{97} +(242.862 - 55.4316i) q^{98} +(-430.212 + 98.1932i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9} + 149 q^{10} + 91 q^{11} - 63 q^{12} - 7 q^{13} - 473 q^{15} - 1113 q^{16} - 7 q^{17} - 196 q^{18} + 464 q^{19}+ \cdots + 2464 q^{99}+O(q^{100}) $ 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9 + 149 * q^10 + 91 * q^11 - 63 * q^12 - 7 * q^13 - 473 * q^15 - 1113 * q^16 - 7 * q^17 - 196 * q^18 + 464 * q^19 - 7 * q^21 + 807 * q^22 + 413 * q^23 - 1425 * q^24 + 1195 * q^25 - 543 * q^26 + 455 * q^27 + 174 * q^28 - 906 * q^29 + 798 * q^30 + 917 * q^31 + 945 * q^32 + 894 * q^33 - 219 * q^34 - 7 * q^35 + 3250 * q^36 + 1734 * q^37 - 63 * q^38 - 825 * q^39 + 141 * q^40 + 563 * q^41 + 432 * q^42 - 423 * q^43 + 2149 * q^44 - 3808 * q^45 - 2569 * q^46 - 289 * q^47 - 3703 * q^48 - 3747 * q^49 - 4963 * q^50 - 87 * q^51 + 3654 * q^52 - 1573 * q^53 - 1228 * q^54 + 2825 * q^55 + 98 * q^56 - 518 * q^57 - 5103 * q^58 + 2045 * q^59 + 3375 * q^60 + 287 * q^61 - 2547 * q^62 + 1453 * q^63 + 6475 * q^64 + 1268 * q^65 + 4634 * q^66 - 3577 * q^67 - 814 * q^70 - 273 * q^71 - 1008 * q^72 - 679 * q^73 - 315 * q^74 - 1281 * q^75 + 6078 * q^76 + 4739 * q^78 + 1463 * q^79 + 441 * q^80 - 4427 * q^81 - 7 * q^82 + 4900 * q^83 - 3351 * q^85 + 3472 * q^86 + 3738 * q^88 + 147 * q^89 + 7133 * q^90 - 14133 * q^91 - 803 * q^92 - 4894 * q^93 - 7833 * q^94 - 7700 * q^95 - 16450 * q^96 + 1233 * q^97 - 2030 * q^98 + 2464 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/197\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{1}{14}\right)$

Coefficient data

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

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

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

$2$	−1.38176	−	0.315378i	−0.488527	−	0.111503i	−0.0288397	−	0.999584i	$-0.509181\pi$
$2$	−1.38176	−	0.315378i	−0.488527	−	0.111503i	−0.459687	+	0.888081i	$0.652038\pi$
$3$	−3.51241	+	0.801685i	−0.675964	+	0.154284i	−0.546703	−	0.837326i	$-0.684117\pi$
$3$	−3.51241	+	0.801685i	−0.675964	+	0.154284i	−0.129260	+	0.991611i	$0.541260\pi$
$4$	−5.39795	−	2.59951i	−0.674744	−	0.324939i
$5$	−1.22448	−	2.54267i	−0.109521	−	0.227423i	0.839004	−	0.544126i	$-0.183139\pi$
$5$	−1.22448	−	2.54267i	−0.109521	−	0.227423i	−0.948525	+	0.316703i	$0.897424\pi$
$6$	5.10615			0.347429
$7$	5.06822	+	22.2053i	0.273658	+	1.19897i	0.905659	+	0.424006i	$0.139377\pi$
$7$	5.06822	+	22.2053i	0.273658	+	1.19897i	−0.632001	+	0.774967i	$0.717766\pi$
$8$	15.5035	+	12.3637i	0.685166	+	0.546402i
$9$	−12.6318	+	6.08317i	−0.467846	+	0.225303i
$10$	0.890043	+	3.89953i	0.0281456	+	0.123314i
$11$	30.6850	+	7.00365i	0.841080	+	0.191971i	0.621294	−	0.783577i	$-0.286607\pi$
$11$	30.6850	+	7.00365i	0.841080	+	0.191971i	0.219785	+	0.975548i	$0.429464\pi$
$12$	21.0438	+	4.80311i	0.506235	+	0.115545i
$13$	−10.9076	+	8.69855i	−0.232710	+	0.185580i	−0.732902	−	0.680335i	$-0.761834\pi$
$13$	−10.9076	+	8.69855i	−0.232710	+	0.185580i	0.500191	+	0.865915i	$0.333263\pi$
$14$		−	32.2809i		−	0.616244i
$15$	6.33930	+	7.94923i	0.109120	+	0.136832i
$16$	12.3610	+	15.5002i	0.193140	+	0.242190i
$17$	−52.8307	−	109.704i	−0.753725	−	1.56513i	−0.823338	−	0.567552i	$-0.807891\pi$
$17$	−52.8307	−	109.704i	−0.753725	−	1.56513i	0.0696128	−	0.997574i	$-0.477824\pi$
$18$	19.3727	−	4.42169i	0.253677	−	0.0579001i
$19$	−62.9013			−0.759502			−0.379751	−	0.925089i	$-0.623990\pi$
$19$	−62.9013			−0.759502			−0.379751	+	0.925089i	$0.623990\pi$
$20$			16.9082i			0.189040i
$21$	−35.6033	−	73.9310i	−0.369966	−	0.768241i
$22$	−40.1906	−	19.3548i	−0.389485	−	0.187566i
$23$	−18.1483	+	79.5131i	−0.164530	+	0.720853i	0.823592	+	0.567183i	$0.191967\pi$
$23$	−18.1483	+	79.5131i	−0.164530	+	0.720853i	−0.988122	+	0.153671i	$0.950890\pi$
$24$	−64.3666	−	30.9973i	−0.547449	−	0.263637i
$25$	72.9704	−	91.5020i	0.583764	−	0.732016i
$26$	17.8151	−	8.57929i	0.134378	−	0.0647130i
$27$	115.543	−	92.1426i	0.823567	−	0.656773i
$28$	30.3651	−	133.038i	0.204945	−	0.897922i
$29$	41.2557	−	180.753i	0.264172	−	1.15741i	−0.652505	−	0.757785i	$-0.726282\pi$
$29$	41.2557	−	180.753i	0.264172	−	1.15741i	0.916677	−	0.399629i	$-0.130861\pi$
$30$	−6.25239	−	12.9832i	−0.0380508	−	0.0790134i
$31$	−92.2103	−	21.0464i	−0.534241	−	0.121937i	−0.0531148	−	0.998588i	$-0.516915\pi$
$31$	−92.2103	−	21.0464i	−0.534241	−	0.121937i	−0.481126	+	0.876651i	$0.659772\pi$
$32$	−81.0221	−	168.244i	−0.447588	−	0.929426i
$33$	−113.393			−0.598157
$34$	38.4012	+	168.247i	0.193698	+	0.848648i
$35$	50.2547	−	40.0768i	0.242703	−	0.193549i
$36$	83.9993			0.388886
$37$	−39.0619	+	48.9821i	−0.173561	+	0.217638i	−0.861002	−	0.508602i	$-0.830162\pi$
$37$	−39.0619	+	48.9821i	−0.173561	+	0.217638i	0.687441	+	0.726240i	$0.258734\pi$
$38$	86.9146	+	19.8377i	0.371037	+	0.0846868i
$39$	31.3386	−	39.2973i	0.128672	−	0.161349i
$40$	12.4528	−	54.5594i	0.0492241	−	0.215665i
$41$	396.630	−	191.007i	1.51081	−	0.727567i	0.518937	−	0.854812i	$-0.326328\pi$
$41$	396.630	−	191.007i	1.51081	−	0.727567i	0.991871	+	0.127245i	$0.0406135\pi$
$42$	25.8791	+	113.384i	0.0950768	+	0.416559i
$43$	0.493990	−	2.16431i	0.00175193	−	0.00767569i	−0.974044	−	0.226357i	$-0.927318\pi$
$43$	0.493990	−	2.16431i	0.00175193	−	0.00767569i	0.975796	+	0.218681i	$0.0701755\pi$
$44$	−147.430	−	117.571i	−0.505134	−	0.402831i
$45$	30.9349	+	24.6698i	0.102478	+	0.0817234i
$46$	50.1534	−	104.145i	0.160755	−	0.333810i
$47$	−77.0092	+	96.5665i	−0.238999	+	0.299695i	−0.886837	−	0.462083i	$-0.847102\pi$
$47$	−77.0092	+	96.5665i	−0.238999	+	0.299695i	0.647838	+	0.761778i	$0.275674\pi$
$48$	−55.8431	−	44.5334i	−0.167922	−	0.133913i
$49$	−158.356	+	76.2605i	−0.461681	+	0.222334i
$50$	−129.686	+	103.421i	−0.366806	+	0.292518i
$51$	273.511	+	342.972i	0.750965	+	0.941680i
$52$	81.4909	−	18.5998i	0.217322	−	0.0496023i
$53$	−535.563	−	257.914i	−1.38802	−	0.668437i	−0.417330	−	0.908755i	$-0.637034\pi$
$53$	−535.563	−	257.914i	−1.38802	−	0.668437i	−0.970694	+	0.240318i	$0.922748\pi$
$54$	−188.713	+	90.8794i	−0.475566	+	0.229021i
$55$	−19.7653	−	86.5976i	−0.0484574	−	0.212306i
$56$	−195.964	+	406.923i	−0.467620	+	0.971024i
$57$	220.935	−	50.4270i	0.513396	−	0.117179i
$58$	−114.011	+	236.747i	−0.258110	+	0.535972i
$59$	−1.31030	+	5.74079i	−0.00289129	+	0.0126676i	−0.976353	−	0.216182i	$-0.930639\pi$
$59$	−1.31030	+	5.74079i	−0.00289129	+	0.0126676i	0.973462	+	0.228850i	$0.0734965\pi$
$60$	−13.5551	−	59.3887i	−0.0291659	−	0.127784i
$61$	147.661	−	646.946i	0.309936	−	1.35792i	−0.544675	−	0.838647i	$-0.683347\pi$
$61$	147.661	−	646.946i	0.309936	−	1.35792i	0.854611	−	0.519270i	$-0.173796\pi$
$62$	120.775	+	58.1623i	0.247395	+	0.119139i
$63$	−199.100	−	249.663i	−0.398162	−	0.499279i
$64$	23.6000	+	103.398i	0.0460938	+	0.201950i
$65$	35.4737	+	17.0832i	0.0676919	+	0.0325987i
$66$	156.682	+	35.7617i	0.292216	+	0.0666964i
$67$	−523.274	−	417.297i	−0.954151	−	0.760910i	0.0168816	−	0.999857i	$-0.494626\pi$
$67$	−523.274	−	417.297i	−0.954151	−	0.760910i	−0.971032	+	0.238948i	$0.923198\pi$
$68$			729.511i			1.30097i
$69$		−	293.832i		−	0.512655i
$70$	−82.0794	+	39.5274i	−0.140148	+	0.0674917i
$71$	92.0348	+	191.112i	0.153838	+	0.319449i	0.963617	−	0.267287i	$-0.0861271\pi$
$71$	92.0348	+	191.112i	0.153838	+	0.319449i	−0.809779	+	0.586735i	$0.800413\pi$
$72$	−271.049	−	61.8651i	−0.443658	−	0.101262i
$73$	808.193	+	644.513i	1.29578	+	1.03335i	0.996869	+	0.0790679i	$0.0251944\pi$
$73$	808.193	+	644.513i	1.29578	+	1.03335i	0.298910	+	0.954281i	$0.403377\pi$
$74$	69.4221	−	55.3623i	0.109056	−	0.0869694i
$75$	−182.946	+	379.892i	−0.281664	+	0.584882i
$76$	339.538	+	163.513i	0.512469	+	0.246792i
$77$			716.866i			1.06097i
$78$	−55.6960	+	44.4161i	−0.0808504	+	0.0644760i
$79$	345.573	−	717.591i	0.492153	−	1.02197i	−0.495976	−	0.868336i	$-0.665190\pi$
$79$	345.573	−	717.591i	0.492153	−	1.02197i	0.988129	−	0.153629i	$-0.0490961\pi$
$80$	24.2760	−	50.4096i	0.0339267	−	0.0704495i
$81$	−95.9452	+	120.311i	−0.131612	+	0.165036i
$82$	−608.287	+	138.838i	−0.819196	+	0.186976i
$83$	1171.77			1.54962			0.774808	−	0.632197i	$-0.217847\pi$
$83$	1171.77			1.54962			0.774808	+	0.632197i	$0.217847\pi$
$84$			491.627i			0.638582i
$85$	−214.250	+	268.661i	−0.273397	+	0.342829i
$86$	−1.36515	+	2.83477i	−0.00171173	+	0.00355443i
$87$			667.953i			0.823127i
$88$	389.136	+	487.961i	0.471386	+	0.591100i
$89$	−372.090	+	84.9272i	−0.443163	+	0.101149i	−0.438279	−	0.898839i	$-0.644412\pi$
$89$	−372.090	+	84.9272i	−0.443163	+	0.101149i	−0.00488406	+	0.999988i	$0.501555\pi$
$90$	−34.9644	−	43.8440i	−0.0409508	−	0.0513507i
$91$	−248.436	−	198.121i	−0.286189	−	0.228228i
$92$	304.659	−	382.031i	0.345249	−	0.432929i
$93$	340.753			0.379940
$94$	136.863	−	109.145i	0.150174	−	0.119760i
$95$	77.0216	+	159.937i	0.0831815	+	0.172728i
$96$	419.461	+	525.988i	0.445949	+	0.559202i
$97$	−1208.57	+	582.014i	−1.26506	+	0.609223i	−0.941509	−	0.336987i	$-0.890592\pi$
$97$	−1208.57	+	582.014i	−1.26506	+	0.609223i	−0.323555	+	0.946210i	$0.604878\pi$
$98$	242.862	−	55.4316i	0.250334	−	0.0571371i
$99$	−430.212	+	98.1932i	−0.436747	+	0.0996847i
$100$	−631.752	+	304.236i	−0.631752	+	0.304236i
$101$	402.931	+	505.260i	0.396962	+	0.497775i	0.939639	−	0.342167i	$-0.111161\pi$
$101$	402.931	+	505.260i	0.396962	+	0.497775i	−0.542677	+	0.839941i	$0.682589\pi$
$102$	−269.761	−	560.165i	−0.261866	−	0.543771i
$103$	1020.97	−	814.193i	0.976687	−	0.778882i	0.00143974	−	0.999999i	$-0.499542\pi$
$103$	1020.97	−	814.193i	0.976687	−	0.778882i	0.975247	+	0.221117i	$0.0709703\pi$
$104$	−276.653			−0.260847
$105$	−144.386	+	181.055i	−0.134197	+	0.168277i
$106$	658.681	+	525.280i	0.603554	+	0.481318i
$107$	588.181	+	737.556i	0.531417	+	0.666376i	0.972989	−	0.230850i	$-0.0741506\pi$
$107$	588.181	+	737.556i	0.531417	+	0.666376i	−0.441573	+	0.897226i	$0.645579\pi$
$108$	−863.222	+	197.025i	−0.769108	+	0.175544i
$109$	−799.949	−	1003.10i	−0.702947	−	0.881467i	0.294293	−	0.955715i	$-0.404916\pi$
$109$	−799.949	−	1003.10i	−0.702947	−	0.881467i	−0.997240	+	0.0742478i	$0.976344\pi$
$110$			125.891i			0.109120i
$111$	97.9332	−	203.360i	0.0837425	−	0.173893i
$112$	−281.538	+	353.038i	−0.237526	+	0.297848i
$113$		−	1209.42i		−	1.00684i	−0.864042	−	0.503420i	$-0.832075\pi$
$113$		−	1209.42i		−	1.00684i	0.864042	−	0.503420i	$-0.167925\pi$
$114$	−321.183			−0.263873
$115$	224.398	−	51.2173i	0.181958	−	0.0415307i
$116$	−692.567	+	868.451i	−0.554338	+	0.695118i
$117$	84.8687	−	176.232i	0.0670608	−	0.139253i
$118$	3.62104	−	7.51917i	0.00282495	−	0.00586606i
$119$	2168.25	−	1729.13i	1.67028	−	1.33201i
$120$			201.618i			0.153376i
$121$	−306.671	−	147.685i	−0.230406	−	0.110958i
$122$	−408.065	+	847.356i	−0.302824	+	0.628820i
$123$	−1240.00	+	988.866i	−0.908999	+	0.724903i
$124$	443.036	+	353.310i	0.320853	+	0.255872i
$125$	−665.934	−	151.995i	−0.476503	−	0.108759i
$126$	196.370	+	407.766i	0.138841	+	0.288307i
$127$	−383.441	+	184.655i	−0.267912	+	0.129020i	−0.563017	−	0.826445i	$-0.690360\pi$
$127$	−383.441	+	184.655i	−0.267912	+	0.129020i	0.295105	+	0.955465i	$0.404645\pi$
$128$			1343.58i			0.927787i
$129$			7.99798i			0.00545878i
$130$	−43.6285	−	34.7926i	−0.0294344	−	0.0234732i
$131$	1353.00	+	308.814i	0.902384	+	0.205963i	0.648449	−	0.761258i	$-0.275418\pi$
$131$	1353.00	+	308.814i	0.902384	+	0.205963i	0.253935	+	0.967221i	$0.418275\pi$
$132$	612.090	+	294.767i	0.403603	+	0.194365i
$133$	−318.797	−	1396.74i	−0.207844	−	0.910623i
$134$	591.434	+	741.635i	0.381284	+	0.478115i
$135$	−375.769	−	180.961i	−0.239563	−	0.115367i
$136$	537.281	−	2353.98i	0.338761	−	1.48421i
$137$	144.263	+	632.057i	0.0899651	+	0.394163i	0.999783	−	0.0208455i	$-0.00663580\pi$
$137$	144.263	+	632.057i	0.0899651	+	0.394163i	−0.909818	+	0.415008i	$0.863779\pi$
$138$	−92.6681	+	406.006i	−0.0571626	+	0.250446i
$139$	506.307	−	1051.36i	0.308952	−	0.641546i	−0.687456	−	0.726226i	$-0.741272\pi$
$139$	506.307	−	1051.36i	0.308952	−	0.641546i	0.996408	+	0.0846800i	$0.0269868\pi$
$140$	−375.453	+	85.6946i	−0.226654	+	0.0517323i
$141$	193.072	−	400.918i	0.115316	−	0.239457i
$142$	−66.8976	−	293.097i	−0.0395346	−	0.173213i
$143$	−395.623	+	190.522i	−0.231354	+	0.111414i
$144$	−250.432	−	120.602i	−0.144926	−	0.0697927i
$145$	−510.112	+	116.430i	−0.292155	+	0.0666824i
$146$	−913.466	−	1145.45i	−0.517801	−	0.649302i
$147$	495.076	−	394.810i	0.277777	−	0.221520i
$148$	338.184	−	162.861i	0.187828	−	0.0904532i
$149$	−1801.99	−	1437.04i	−0.990770	−	0.790113i	−0.0130266	−	0.999915i	$-0.504147\pi$
$149$	−1801.99	−	1437.04i	−0.990770	−	0.790113i	−0.977744	+	0.209802i	$0.932718\pi$
$150$	372.598	−	467.223i	0.202817	−	0.254324i
$151$	948.063	−	1968.67i	0.510942	−	1.06098i	−0.472762	−	0.881190i	$-0.656743\pi$
$151$	948.063	−	1968.67i	0.510942	−	1.06098i	0.983705	−	0.179793i	$-0.0575427\pi$
$152$	−975.193	−	777.690i	−0.520385	−	0.414994i
$153$	1334.70	+	1064.39i	0.705254	+	0.562421i
$154$	226.084	−	990.538i	0.118301	−	0.518311i
$155$	59.3960	+	260.231i	0.0307794	+	0.134853i
$156$	−271.318	+	130.660i	−0.139249	+	0.0670588i
$157$	106.903	−	468.373i	0.0543427	−	0.238091i	−0.940461	−	0.339901i	$-0.889606\pi$
$157$	106.903	−	468.373i	0.0543427	−	0.238091i	0.994804	+	0.101810i	$0.0324635\pi$
$158$	−703.813	+	882.553i	−0.354382	+	0.444381i
$159$	2087.88	+	476.546i	1.04138	+	0.237689i
$160$	−328.578	+	412.024i	−0.162352	+	0.203583i
$161$	−1857.59			−0.909309
$162$	170.517	−	135.983i	0.0826980	−	0.0659495i
$163$	−769.017	−	3369.28i	−0.369534	−	1.61903i	−0.728059	−	0.685514i	$-0.759577\pi$
$163$	−769.017	−	3369.28i	−0.369534	−	1.61903i	0.358525	−	0.933520i	$-0.383280\pi$
$164$	−2637.51			−1.25582
$165$	138.848	+	288.321i	0.0655109	+	0.136035i
$166$	−1619.10	−	369.550i	−0.757029	−	0.172787i
$167$	−940.742	−	1953.47i	−0.435909	−	0.905174i	−0.996999	−	0.0774192i	$-0.975332\pi$
$167$	−940.742	−	1953.47i	−0.435909	−	0.905174i	0.561090	−	0.827755i	$-0.310382\pi$
$168$	362.081	−	1586.38i	0.166281	−	0.728523i
$169$	−445.567	+	1952.16i	−0.202807	+	0.888555i
$170$	380.773	−	303.656i	0.171788	−	0.136996i
$171$	794.559	−	382.639i	0.355330	−	0.171118i
$172$	−8.29270	+	10.3987i	−0.00367624	+	0.00460985i
$173$	1547.77	+	745.367i	0.680202	+	0.327568i	0.741884	−	0.670528i	$-0.233932\pi$
$173$	1547.77	+	745.367i	0.680202	+	0.327568i	−0.0616826	+	0.998096i	$0.519647\pi$
$174$	210.658	−	922.952i	0.0917812	−	0.402120i
$175$	2401.66	+	1156.58i	1.03742	+	0.499595i
$176$	270.739	+	562.196i	0.115953	+	0.240779i
$177$		−	21.2145i		−	0.00900891i
$178$	540.925			0.227775
$179$	1297.31	−	296.102i	0.541705	−	0.123641i	0.0570914	−	0.998369i	$-0.481817\pi$
$179$	1297.31	−	296.102i	0.541705	−	0.123641i	0.484614	+	0.874728i	$0.338960\pi$
$180$	−102.856	−	213.582i	−0.0425912	−	0.0884415i
$181$	406.147	+	509.293i	0.166788	+	0.209146i	0.858201	−	0.513315i	$-0.171583\pi$
$181$	406.147	+	509.293i	0.166788	+	0.209146i	−0.691412	+	0.722460i	$0.743011\pi$
$182$	280.797	+	352.108i	0.114363	+	0.143406i
$183$			2390.72i			0.965720i
$184$	−1264.44	+	1008.35i	−0.506606	+	0.404005i
$185$	172.376	+	39.3436i	0.0685044	+	0.0156357i
$186$	−470.840	−	107.466i	−0.185611	−	0.0423645i
$187$	−852.781	−	3736.28i	−0.333484	−	1.46109i
$188$	666.718	−	321.074i	0.258646	−	0.124557i
$189$	2631.65	+	2098.67i	1.01283	+	0.807704i
$190$	−55.9848	−	245.286i	−0.0213767	−	0.0936573i
$191$	140.837			0.0533539			0.0266770	−	0.999644i	$-0.491507\pi$
$191$	140.837			0.0533539			0.0266770	+	0.999644i	$0.491507\pi$
$192$	−165.786	−	344.258i	−0.0623154	−	0.129399i
$193$	−2901.18	−	1397.14i	−1.08203	−	0.521078i	−0.194065	−	0.980989i	$-0.562167\pi$
$193$	−2901.18	−	1397.14i	−1.08203	−	0.521078i	−0.887965	+	0.459910i	$0.847882\pi$
$194$	1853.50	−	423.050i	0.685948	−	0.156563i
$195$	−138.294	−	31.5646i	−0.0507867	−	0.0115917i
$196$	1053.04			0.383761
$197$	−2353.77	+	1450.91i	−0.851266	+	0.524735i
$197$	−2353.77	+	1450.91i	−0.851266	+	0.524735i
$198$	625.419			0.224478
$199$	−4331.08	−	988.541i	−1.54282	−	0.352140i	−0.635342	−	0.772231i	$-0.719141\pi$
$199$	−4331.08	−	988.541i	−1.54282	−	0.352140i	−0.907482	+	0.420091i	$0.861998\pi$
$200$	2262.60	−	516.424i	0.799950	−	0.182583i
$201$	2172.49	+	1046.22i	0.762368	+	0.367137i
$202$	−397.407	−	825.225i	−0.138423	−	0.287439i
$203$	4222.77			1.46000
$204$	−584.838	−	2562.34i	−0.200720	−	0.879411i
$205$	−971.333	−	774.612i	−0.330931	−	0.263909i
$206$	−1667.51	+	803.031i	−0.563985	+	0.271601i
$207$	−254.445	−	1114.80i	−0.0854355	−	0.374317i
$208$	−269.658	−	61.5478i	−0.0898915	−	0.0205172i
$209$	−1930.13	−	440.539i	−0.638802	−	0.145802i
$210$	256.608	−	204.638i	0.0843221	−	0.0672446i
$211$			65.6005i			0.0214034i	0.999943	+	0.0107017i	$0.00340653\pi$
$211$			65.6005i			0.0214034i	−0.999943	+	0.0107017i	$0.996593\pi$
$212$	2220.49	+	2784.41i	0.719359	+	0.902047i
$213$	−476.476	−	597.481i	−0.153275	−	0.192201i
$214$	−580.117	−	1204.63i	−0.185308	−	0.384797i
$215$	−6.10801	+	1.39411i	−0.00193750	+	0.000442222i
$216$	2930.55			0.923142
$217$		−	2154.23i		−	0.673910i
$218$	788.982	+	1638.34i	0.245122	+	0.509001i
$219$	−3355.40	−	1615.88i	−1.03533	−	0.498588i
$220$	−118.419	+	518.829i	−0.0362902	+	0.158998i
$221$	1530.52	+	737.061i	0.465856	+	0.224344i
$222$	−199.456	+	250.110i	−0.0603000	+	0.0756138i
$223$	−3619.84	+	1743.22i	−1.08701	+	0.523474i	−0.889550	−	0.456838i	$-0.848982\pi$
$223$	−3619.84	+	1743.22i	−1.08701	+	0.523474i	−0.197455	+	0.980312i	$0.563268\pi$
$224$	3325.27	−	2651.82i	0.991871	−	0.790991i
$225$	−365.128	+	1599.73i	−0.108186	+	0.473994i
$226$	−381.425	+	1671.13i	−0.112266	+	0.491868i
$227$	1484.99	+	3083.61i	0.434195	+	0.901615i	0.997173	+	0.0751431i	$0.0239414\pi$
$227$	1484.99	+	3083.61i	0.434195	+	0.901615i	−0.562978	+	0.826472i	$0.690344\pi$
$228$	−1323.68	−	302.122i	−0.384487	−	0.0877566i
$229$	357.455	+	742.263i	0.103150	+	0.214193i	0.946156	−	0.323711i	$-0.104931\pi$
$229$	357.455	+	742.263i	0.103150	+	0.214193i	−0.843006	+	0.537904i	$0.819216\pi$
$230$	−326.217			−0.0935222
$231$	−574.700	−	2517.93i	−0.163691	−	0.717175i
$232$	2874.38	−	2292.24i	0.813415	−	0.648677i
$233$	6614.67			1.85984			0.929918	−	0.367768i	$-0.119878\pi$
$233$	6614.67			1.85984			0.929918	+	0.367768i	$0.119878\pi$
$234$	−172.848	+	216.744i	−0.0482881	+	0.0605514i
$235$	339.833	+	77.5646i	0.0943330	+	0.0215309i
$236$	21.9962	−	27.5824i	0.00606708	−	0.00760788i
$237$	−638.514	+	2797.51i	−0.175004	+	0.766743i
$238$	−3541.34	+	1705.42i	−0.964500	+	0.464479i
$239$	303.302	+	1328.85i	0.0820876	+	0.359649i	0.999244	−	0.0388782i	$-0.0123784\pi$
$239$	303.302	+	1328.85i	0.0820876	+	0.359649i	−0.917156	+	0.398528i	$0.869521\pi$
$240$	−44.8546	+	196.521i	−0.0120640	+	0.0528557i
$241$	−3112.92	−	2482.47i	−0.832037	−	0.663527i	0.111876	−	0.993722i	$-0.464314\pi$
$241$	−3112.92	−	2482.47i	−0.832037	−	0.663527i	−0.943913	+	0.330195i	$0.892885\pi$
$242$	377.170	+	300.783i	0.100188	+	0.0798969i
$243$	−1490.74	+	3095.55i	−0.393543	+	0.817200i
$244$	−2478.81	+	3108.33i	−0.650368	+	0.815535i
$245$	387.810	+	309.268i	0.101128	+	0.0806465i
$246$	2025.25	−	975.309i	0.524899	−	0.252778i
$247$	686.104	−	547.150i	0.176744	−	0.140949i
$248$	−1169.38	−	1466.35i	−0.299417	−	0.375457i
$249$	−4115.72	+	939.387i	−1.04748	+	0.239081i
$250$	872.226	+	420.042i	0.220658	+	0.106263i
$251$	−6471.91	+	3116.71i	−1.62750	+	0.783764i	−0.627515	+	0.778604i	$0.715928\pi$
$251$	−6471.91	+	3116.71i	−1.62750	+	0.783764i	−0.999987	+	0.00515967i	$0.998358\pi$
$252$	425.727	+	1865.23i	0.106422	+	0.466264i
$253$	−1113.76	+	2312.76i	−0.276766	+	0.574710i
$254$	588.060	−	134.221i	0.145268	−	0.0331566i
$255$	537.153	−	1115.41i	0.131913	−	0.273920i
$256$	612.536	−	2683.69i	0.149545	−	0.655199i
$257$	1511.25	+	6621.20i	0.366805	+	1.60708i	0.735498	+	0.677527i	$0.236948\pi$
$257$	1511.25	+	6621.20i	0.366805	+	1.60708i	−0.368693	+	0.929551i	$0.620195\pi$
$258$	2.52239	−	11.0513i	0.000608671	−	0.00266676i
$259$	−1285.64	−	619.130i	−0.308438	−	0.148536i
$260$	−147.077	−	184.429i	−0.0350821	−	0.0439915i
$261$	578.417	+	2534.21i	0.137177	+	0.601010i
$262$	−1772.13	−	853.414i	−0.417873	−	0.201237i
$263$	59.7292	+	13.6328i	0.0140040	+	0.00319633i	0.229517	−	0.973305i	$-0.426285\pi$
$263$	59.7292	+	13.6328i	0.0140040	+	0.00319633i	−0.215513	+	0.976501i	$0.569142\pi$
$264$	−1757.99	−	1401.95i	−0.409837	−	0.326834i
$265$			1677.57i			0.388876i
$266$			2030.51i			0.468039i
$267$	1238.85	−	596.598i	0.283956	−	0.136746i
$268$	1739.84	+	3612.81i	0.396558	+	0.823460i
$269$	−5479.76	−	1250.72i	−1.24203	−	0.283486i	−0.449481	−	0.893290i	$-0.648391\pi$
$269$	−5479.76	−	1250.72i	−1.24203	−	0.283486i	−0.792552	+	0.609804i	$0.791248\pi$
$270$	462.152	+	368.554i	0.104169	+	0.0830721i
$271$	4653.93	−	3711.38i	1.04319	−	0.831920i	0.0571443	−	0.998366i	$-0.481800\pi$
$271$	4653.93	−	3711.38i	1.04319	−	0.831920i	0.986051	+	0.166446i	$0.0532290\pi$
$272$	1047.39	−	2174.94i	0.233484	−	0.484834i
$273$	1031.44	+	496.716i	0.228665	+	0.110119i
$274$		−	918.850i		−	0.202590i
$275$	2879.95	−	2296.68i	0.631518	−	0.503618i
$276$	−763.820	+	1586.09i	−0.166582	+	0.345911i
$277$	1992.87	−	4138.25i	0.432275	−	0.897629i	−0.565086	−	0.825032i	$-0.691157\pi$
$277$	1992.87	−	4138.25i	0.432275	−	0.897629i	0.997361	−	0.0725969i	$-0.0231286\pi$
$278$	−1031.17	+	1293.05i	−0.222466	+	0.278963i
$279$	1292.81	−	295.077i	0.277415	−	0.0633182i
$280$	1274.62			0.272047
$281$			3085.01i			0.654933i	0.944863	+	0.327466i	$0.106195\pi$
$281$			3085.01i			0.654933i	−0.944863	+	0.327466i	$0.893805\pi$
$282$	−393.221	+	493.083i	−0.0830352	+	0.104123i
$283$	849.594	−	1764.20i	0.178456	−	0.370568i	−0.792483	−	0.609894i	$-0.791212\pi$
$283$	849.594	−	1764.20i	0.178456	−	0.370568i	0.970939	+	0.239326i	$0.0769264\pi$
$284$		−	1270.86i		−	0.265534i
$285$	−398.750	−	500.017i	−0.0828769	−	0.103924i
$286$	606.743	−	138.485i	0.125446	−	0.0286321i
$287$	6251.57	+	7839.22i	1.28578	+	1.61232i
$288$	2046.92	+	1632.36i	0.418804	+	0.333985i
$289$	−6180.69	+	7750.34i	−1.25803	+	1.57752i
$290$	741.572			0.150161
$291$	3778.38	−	3013.16i	0.761144	−	0.606992i
$292$	−2687.17	−	5579.96i	−0.538543	−	1.11830i
$293$	2331.18	+	2923.20i	0.464808	+	0.582851i	0.957891	−	0.287131i	$-0.0927017\pi$
$293$	2331.18	+	2923.20i	0.464808	+	0.582851i	−0.493083	+	0.869982i	$0.664130\pi$
$294$	−808.591	+	389.397i	−0.160401	+	0.0772452i
$295$	16.2014	−	3.69785i	0.00319756	−	0.000729821i
$296$	−1211.20	+	276.448i	−0.237836	+	0.0542844i
$297$	4190.78	−	2018.17i	0.818767	−	0.394297i
$298$	2036.71	+	2553.95i	0.395918	+	0.496465i
$299$	−493.693	−	1025.16i	−0.0954883	−	0.198284i
$300$	1975.07	−	1575.07i	0.380102	−	0.303121i
$301$	50.5629			0.00968238
$302$	−1930.87	+	2421.24i	−0.367912	+	0.461347i
$303$	−1820.32	−	1451.66i	−0.345131	−	0.275233i
$304$	−777.522	−	974.982i	−0.146691	−	0.183944i
$305$	−1825.78	+	416.721i	−0.342766	+	0.0782341i
$306$	−1508.55	−	1891.66i	−0.281824	−	0.353396i
$307$		−	733.933i		−	0.136442i	−0.997670	−	0.0682211i	$-0.978268\pi$
$307$		−	733.933i		−	0.136442i	0.997670	−	0.0682211i	$-0.0217323\pi$
$308$	1863.50	−	3869.61i	0.344750	−	0.715881i
$309$	−2933.32	+	3678.27i	−0.540036	+	0.677183i
$310$		−	378.309i		−	0.0693114i
$311$	−7781.77			−1.41885			−0.709427	−	0.704779i	$-0.751046\pi$
$311$	−7781.77			−1.41885			−0.709427	+	0.704779i	$0.751046\pi$
$312$	971.718	−	221.788i	0.176323	−	0.0402445i
$313$	−3050.04	+	3824.63i	−0.550793	+	0.690673i	−0.976826	−	0.214035i	$-0.931339\pi$
$313$	−3050.04	+	3824.63i	−0.550793	+	0.690673i	0.426033	+	0.904708i	$0.359911\pi$
$314$	−295.429	+	613.466i	−0.0530957	+	0.110254i
$315$	−391.015	+	811.952i	−0.0699404	+	0.145233i
$316$	−3730.78	+	2975.19i	−0.664154	+	0.529645i
$317$		−	7428.16i		−	1.31611i	−0.752970	−	0.658055i	$-0.771379\pi$
$317$		−	7428.16i		−	1.31611i	0.752970	−	0.658055i	$-0.228621\pi$
$318$	−2734.66	−	1316.95i	−0.482240	−	0.232235i
$319$	2531.86	−	5257.47i	0.444380	−	0.922764i
$320$	234.010	−	186.617i	0.0408798	−	0.0326006i
$321$	−2657.22	−	2119.06i	−0.462030	−	0.368456i
$322$	2566.75	+	585.844i	0.444222	+	0.101391i
$323$	3323.12	+	6900.53i	0.572456	+	1.18872i
$324$	830.659	−	400.024i	0.142431	−	0.0685912i
$325$			1632.81i			0.278683i
$326$			4898.08i			0.832146i
$327$	3613.92	+	2882.01i	0.611163	+	0.487386i
$328$	8510.71	+	1942.51i	1.43270	+	0.327004i
$329$	−2534.59	−	1220.59i	−0.424731	−	0.204540i
$330$	−100.925	−	442.180i	−0.0168355	−	0.0737612i
$331$	−2408.17	−	3019.74i	−0.399894	−	0.501451i	0.540592	−	0.841285i	$-0.318200\pi$
$331$	−2408.17	−	3019.74i	−0.399894	−	0.501451i	−0.940485	+	0.339834i	$0.889629\pi$
$332$	−6325.14	−	3046.03i	−1.04559	−	0.503531i
$333$	195.457	−	856.354i	0.0321651	−	0.140925i
$334$	683.799	+	2995.92i	0.112023	+	0.490807i
$335$	−420.307	+	1841.48i	−0.0685487	+	0.300331i
$336$	705.853	−	1465.72i	0.114605	−	0.237981i
$337$	8115.49	−	1852.31i	1.31181	−	0.299411i	0.491271	−	0.871007i	$-0.336532\pi$
$337$	8115.49	−	1852.31i	1.31181	−	0.299411i	0.820536	+	0.571595i	$0.193675\pi$
$338$	1231.33	−	2556.89i	0.198153	−	0.411469i
$339$	969.575	+	4247.99i	0.155340	+	0.680587i
$340$	1854.90	−	893.274i	0.295871	−	0.142484i
$341$	−2682.07	−	1291.62i	−0.425931	−	0.205117i
$342$	−1218.57	+	278.130i	−0.192668	+	0.0439753i
$343$	2374.91	+	2978.05i	0.373858	+	0.468803i
$344$	34.4174	−	27.4470i	0.00539437	−	0.00430187i
$345$	−747.116	+	359.792i	−0.116589	+	0.0561465i
$346$	−1903.58	−	1518.05i	−0.295772	−	0.235870i
$347$	1370.10	−	1718.05i	0.211961	−	0.265791i	−0.664473	−	0.747312i	$-0.731344\pi$
$347$	1370.10	−	1718.05i	0.211961	−	0.265791i	0.876435	+	0.481521i	$0.159915\pi$
$348$	1736.35	−	3605.58i	0.267466	−	0.555400i
$349$	1969.62	+	1570.72i	0.302096	+	0.240913i	0.762791	−	0.646645i	$-0.223828\pi$
$349$	1969.62	+	1570.72i	0.302096	+	0.240913i	−0.460695	+	0.887558i	$0.652400\pi$
$350$	−2953.76	−	2355.55i	−0.451101	−	0.359741i
$351$	−458.796	+	2010.12i	−0.0697684	+	0.305675i
$352$	−1307.84	−	5730.02i	−0.198034	−	0.867645i
$353$	9123.48	−	4393.64i	1.37562	−	0.662464i	0.407559	−	0.913179i	$-0.366380\pi$
$353$	9123.48	−	4393.64i	1.37562	−	0.662464i	0.968061	+	0.250715i	$0.0806658\pi$
$354$	−6.69058	+	29.3133i	−0.00100452	+	0.00440109i
$355$	373.239	−	468.027i	0.0558014	−	0.0699727i
$356$	2229.29	+	508.822i	0.331889	+	0.0757514i
$357$	−6229.59	+	7811.65i	−0.923542	+	1.15809i
$358$	−1885.95			−0.278424
$359$	−6609.01	+	5270.51i	−0.971616	+	0.774838i	−0.974322	−	0.225159i	$-0.927710\pi$
$359$	−6609.01	+	5270.51i	−0.971616	+	0.774838i	0.00270626	+	0.999996i	$0.499139\pi$
$360$	174.592	+	764.938i	0.0255606	+	0.111988i
$361$	−2902.43			−0.423156
$362$	−400.579	−	831.811i	−0.0581601	−	0.120771i
$363$	1195.55	+	272.877i	0.172865	+	0.0394554i
$364$	826.027	+	1715.26i	0.118944	+	0.246989i
$365$	649.161	−	2844.16i	0.0930921	−	0.407863i
$366$	753.980	−	3303.40i	0.107681	−	0.471780i
$367$	−5937.55	+	4735.04i	−0.844517	+	0.673480i	−0.946993	−	0.321256i	$-0.895895\pi$
$367$	−5937.55	+	4735.04i	−0.844517	+	0.673480i	0.102475	+	0.994736i	$0.467324\pi$
$368$	−1456.80	+	701.558i	−0.206361	+	0.0993783i
$369$	−3848.23	+	4825.53i	−0.542903	+	0.680778i
$370$	−225.774	−	108.727i	−0.0317228	−	0.0152769i
$371$	3012.70	−	13199.5i	0.421595	−	1.84713i
$372$	−1839.37	−	885.793i	−0.256362	−	0.123458i
$373$	−1975.98	−	4103.16i	−0.274296	−	0.569581i	0.717626	−	0.696428i	$-0.245229\pi$
$373$	−1975.98	−	4103.16i	−0.274296	−	0.569581i	−0.991922	+	0.126847i	$0.959514\pi$
$374$			5431.59i			0.750965i
$375$	2460.88			0.338879
$376$	−2387.83	+	545.007i	−0.327508	+	0.0747516i
$377$	1122.29	+	2330.45i	0.153318	+	0.318367i
$378$	−2974.44	−	3729.83i	−0.404732	−	0.507518i
$379$	−2268.28	−	2844.33i	−0.307424	−	0.385497i	0.603988	−	0.796994i	$-0.293578\pi$
$379$	−2268.28	−	2844.33i	−0.307424	−	0.385497i	−0.911411	+	0.411496i	$0.865006\pi$
$380$		−	1063.55i		−	0.143576i
$381$	1198.77	−	955.984i	0.161193	−	0.128547i
$382$	−194.603	−	44.4169i	−0.0260648	−	0.00594913i
$383$	1846.00	+	421.337i	0.246282	+	0.0562123i	0.343880	−	0.939014i	$-0.388259\pi$
$383$	1846.00	+	421.337i	0.246282	+	0.0562123i	−0.0975976	+	0.995226i	$0.531116\pi$
$384$	−1077.13	−	4719.20i	−0.143143	−	0.627150i
$385$	1822.75	−	877.790i	0.241288	−	0.116198i
$386$	3568.12	+	2845.48i	0.470499	+	0.375210i
$387$	6.92588	+	30.3443i	0.000909722	+	0.00398575i
$388$	8036.73			1.05155
$389$	−5126.68	−	10645.7i	−0.668209	−	1.38755i	−0.908927	−	0.416954i	$-0.863097\pi$
$389$	−5126.68	−	10645.7i	−0.668209	−	1.38755i	0.240719	−	0.970595i	$-0.422617\pi$
$390$	181.134	+	87.2295i	0.0235181	+	0.0113257i
$391$	9681.70	−	2209.78i	1.25224	−	0.285815i
$392$	−3397.95	−	775.559i	−0.437812	−	0.0999276i
$393$	−4999.87			−0.641755
$394$	3709.94	−	1262.48i	0.474375	−	0.161428i
$395$	−2247.74			−0.286319
$396$	2577.52	+	588.302i	0.327084	+	0.0746548i
$397$	6700.18	−	1529.27i	0.847033	−	0.193330i	0.223088	−	0.974798i	$-0.428386\pi$
$397$	6700.18	−	1529.27i	0.847033	−	0.193330i	0.623945	+	0.781468i	$0.285529\pi$
$398$	5672.76	+	2731.86i	0.714446	+	0.344059i
$399$	2239.49	+	4650.36i	0.280990	+	0.583481i
$400$	2320.29			0.290036
$401$	1728.33	+	7572.29i	0.215233	+	0.942997i	0.960947	+	0.276732i	$0.0892513\pi$
$401$	1728.33	+	7572.29i	0.215233	+	0.942997i	−0.745714	+	0.666266i	$0.767892\pi$
$402$	−2671.91	−	2130.78i	−0.331500	−	0.264362i
$403$	1188.87	−	572.530i	0.146952	−	0.0707686i
$404$	−861.572	−	3774.79i	−0.106101	−	0.464859i
$405$	423.395	+	96.6371i	0.0519473	+	0.0118566i
$406$	−5834.86	−	1331.77i	−0.713250	−	0.162795i
$407$	−1541.67	+	1229.44i	−0.187758	+	0.149732i
$408$			8698.88i			1.05554i
$409$	−4408.84	−	5528.51i	−0.533015	−	0.668380i	0.440301	−	0.897850i	$-0.354872\pi$
$409$	−4408.84	−	5528.51i	−0.533015	−	0.668380i	−0.973316	+	0.229471i	$0.926300\pi$
$410$	1097.85	+	1376.67i	0.132242	+	0.165826i
$411$	−1013.42	−	2104.39i	−0.121626	−	0.252560i
$412$	−7627.63	+	1740.96i	−0.912103	+	0.208181i
$413$	−134.117			−0.0159793
$414$			1620.63i			0.192390i
$415$	−1434.81	−	2979.41i	−0.169716	−	0.352418i
$416$	2347.24	+	1130.37i	0.276641	+	0.133223i
$417$	−935.500	+	4098.69i	−0.109860	+	0.481328i
$418$	2528.04	+	1217.44i	0.295814	+	0.142457i
$419$	3201.83	−	4014.97i	0.373316	−	0.468124i	−0.559315	−	0.828955i	$-0.688936\pi$
$419$	3201.83	−	4014.97i	0.373316	−	0.468124i	0.932631	+	0.360831i	$0.117507\pi$
$420$	1250.04	−	601.989i	0.145228	−	0.0699382i
$421$	129.063	−	102.924i	0.0149409	−	0.0119150i	−0.615991	−	0.787753i	$-0.711244\pi$
$421$	129.063	−	102.924i	0.0149409	−	0.0119150i	0.630932	+	0.775838i	$0.282673\pi$
$422$	20.6890	−	90.6443i	0.00238655	−	0.0104561i
$423$	385.337	−	1688.27i	0.0442925	−	0.194058i
$424$	−5114.37	−	10620.1i	−0.585792	−	1.21641i
$425$	−13893.2	−	3171.04i	−1.58569	−	0.361924i
$426$	469.943	+	975.847i	0.0534479	+	0.110986i
$427$	15114.0			1.71292
$428$	−1257.68	−	5510.27i	−0.142038	−	0.622311i
$429$	1236.85	−	986.355i	0.139197	−	0.111006i
$430$	8.87948			0.000995830
$431$	−1929.73	+	2419.81i	−0.215666	+	0.270436i	−0.877883	−	0.478876i	$-0.841044\pi$
$431$	−1929.73	+	2419.81i	−0.215666	+	0.270436i	0.662217	+	0.749312i	$0.269616\pi$
$432$	2856.46	+	651.968i	0.318128	+	0.0726107i
$433$	−7895.81	+	9901.04i	−0.876324	+	1.09888i	0.118056	+	0.993007i	$0.462334\pi$
$433$	−7895.81	+	9901.04i	−0.876324	+	1.09888i	−0.994380	+	0.105869i	$0.966238\pi$
$434$	−679.396	+	2976.63i	−0.0751430	+	0.329223i
$435$	1698.38	−	817.897i	0.187198	−	0.0901498i
$436$	1710.50	+	7494.18i	0.187885	+	0.823180i
$437$	1141.55	−	5001.48i	0.124961	−	0.547490i
$438$	4126.75	+	3290.98i	0.450192	+	0.359016i
$439$	−3603.99	−	2874.09i	−0.391820	−	0.312466i	0.407688	−	0.913121i	$-0.366335\pi$
$439$	−3603.99	−	2874.09i	−0.391820	−	0.312466i	−0.799508	+	0.600655i	$0.794907\pi$
$440$	764.231	−	1586.94i	0.0828029	−	0.171942i
$441$	1536.43	−	1926.62i	0.165903	−	0.208036i
$442$	−1882.37	−	1501.14i	−0.202568	−	0.161543i
$443$	−4869.64	+	2345.10i	−0.522265	+	0.251510i	−0.676393	−	0.736541i	$-0.736458\pi$
$443$	−4869.64	+	2345.10i	−0.522265	+	0.251510i	0.154127	+	0.988051i	$0.450743\pi$
$444$	−1057.28	+	843.150i	−0.113009	+	0.0901220i
$445$	671.560	+	842.109i	0.0715393	+	0.0897075i
$446$	5551.53	−	1267.10i	0.589400	−	0.134527i
$447$	7481.38	+	3602.84i	0.791627	+	0.381227i
$448$	−2176.38	+	1048.09i	−0.229519	+	0.110531i
$449$	−1702.02	−	7457.03i	−0.178893	−	0.783784i	−0.982142	−	0.188140i	$-0.939754\pi$
$449$	−1702.02	−	7457.03i	−0.178893	−	0.783784i	0.803249	−	0.595644i	$-0.203103\pi$
$450$	1009.04	−	2095.29i	0.105704	−	0.219496i
$451$	13508.3	−	3083.19i	1.41038	−	0.321911i
$452$	−3143.91	+	6528.40i	−0.327162	+	0.679359i
$453$	−1751.73	+	7674.83i	−0.181685	+	0.796016i
$454$	−1079.40	−	4729.15i	−0.111583	−	0.488877i
$455$	−199.550	+	874.286i	−0.0205606	+	0.0900817i
$456$	4048.74	+	1949.77i	0.415789	+	0.200233i
$457$	−8056.61	−	10102.7i	−0.824666	−	1.03410i	−0.998780	−	0.0493733i	$-0.984278\pi$
$457$	−8056.61	−	10102.7i	−0.824666	−	1.03410i	0.174114	−	0.984725i	$-0.444294\pi$
$458$	−259.824	−	1138.36i	−0.0265083	−	0.116140i
$459$	−16212.6	−	7807.60i	−1.64867	−	0.793960i
$460$	−1344.43	−	306.857i	−0.136270	−	0.0311027i
$461$	424.611	+	338.616i	0.0428983	+	0.0342103i	0.644704	−	0.764432i	$-0.276981\pi$
$461$	424.611	+	338.616i	0.0428983	+	0.0342103i	−0.601806	+	0.798642i	$0.705552\pi$
$462$			3660.42i			0.368611i
$463$		−	2495.66i		−	0.250503i	−0.992125	−	0.125252i	$-0.960026\pi$
$463$		−	2495.66i		−	0.250503i	0.992125	−	0.125252i	$-0.0399738\pi$
$464$	3311.67	−	1594.82i	0.331337	−	0.159564i
$465$	−417.246	−	866.421i	−0.0416115	−	0.0864071i
$466$	−9139.90	−	2086.12i	−0.908579	−	0.207377i
$467$	−8654.36	−	6901.62i	−0.857550	−	0.683873i	0.0925876	−	0.995705i	$-0.470486\pi$
$467$	−8654.36	−	6901.62i	−0.857550	−	0.683873i	−0.950137	+	0.311831i	$0.899058\pi$
$468$	−916.234	+	730.672i	−0.0904977	+	0.0721695i
$469$	6614.15	−	13734.4i	0.651200	−	1.35223i
$470$	−445.106	−	214.352i	−0.0436834	−	0.0210368i
$471$			1730.82i			0.169325i
$472$	−91.2915	+	72.8025i	−0.00890261	+	0.00709960i
$473$	30.3162	−	62.9522i	0.00294702	−	0.00611955i
$474$	1764.55	−	3664.12i	0.170988	−	0.355061i
$475$	−4589.93	+	5755.60i	−0.443370	+	0.555968i
$476$	−16199.0	+	3697.32i	−1.55983	+	0.356022i
$477$	8334.08			0.799982
$478$		−	1931.81i		−	0.184851i
$479$	7013.47	−	8794.62i	0.669006	−	0.838907i	−0.325284	−	0.945616i	$-0.605460\pi$
$479$	7013.47	−	8794.62i	0.669006	−	0.838907i	0.994290	+	0.106709i	$0.0340315\pi$
$480$	823.788	−	1710.61i	0.0783346	−	0.162663i
$481$		−	874.061i		−	0.0828560i
$482$	3518.40	+	4411.93i	0.332487	+	0.416925i
$483$	6524.63	−	1489.20i	0.614660	−	0.140292i
$484$	1271.48	+	1594.39i	0.119411	+	0.149736i
$485$	2959.73	+	2360.31i	0.277102	+	0.220982i
$486$	3036.11	−	3807.16i	0.283376	−	0.355343i
$487$	5744.46			0.534510			0.267255	−	0.963626i	$-0.413883\pi$
$487$	5744.46			0.534510			0.267255	+	0.963626i	$0.413883\pi$
$488$	10287.9	−	8204.32i	0.954326	−	0.761050i
$489$	5402.20	+	11217.8i	0.499583	+	1.03739i
$490$	−438.324	−	549.641i	−0.0404112	−	0.0506740i
$491$	2536.85	−	1221.68i	0.233169	−	0.112289i	−0.313651	−	0.949538i	$-0.601552\pi$
$491$	2536.85	−	1221.68i	0.233169	−	0.112289i	0.546821	+	0.837250i	$0.315838\pi$
$492$	9264.02	−	2114.45i	0.848891	−	0.193754i
$493$	−22008.9	+	5023.39i	−2.01061	+	0.458909i
$494$	−1120.59	+	539.649i	−0.102060	+	0.0491497i
$495$	776.460	+	973.650i	0.0705036	+	0.0884087i
$496$	−813.588	−	1689.43i	−0.0736516	−	0.152939i
$497$	−3777.25	+	3012.26i	−0.340911	+	0.271868i
$498$	5983.21			0.538382
$499$	5922.47	−	7426.54i	0.531315	−	0.666248i	−0.441654	−	0.897186i	$-0.645608\pi$
$499$	5922.47	−	7426.54i	0.531315	−	0.666248i	0.972969	+	0.230938i	$0.0741794\pi$
$500$	3199.56	+	2551.57i	0.286178	+	0.228219i
$501$	4870.34	+	6107.21i	0.434313	+	0.544611i
$502$	9925.57	−	2265.45i	0.882470	−	0.201418i
$503$	−11692.8	−	14662.3i	−1.03649	−	1.29972i	−0.952921	−	0.303218i	$-0.901939\pi$
$503$	−11692.8	−	14662.3i	−1.03649	−	1.29972i	−0.0835708	−	0.996502i	$-0.526632\pi$
$504$		−	6332.26i		−	0.559646i
$505$	791.324	−	1643.20i	0.0697296	−	0.144795i
$506$	2268.35	−	2844.42i	0.199289	−	0.249901i
$507$		−	7213.97i		−	0.631921i
$508$	2549.81			0.222696
$509$	9043.63	−	2064.15i	0.787528	−	0.179748i	0.190200	−	0.981745i	$-0.439086\pi$
$509$	9043.63	−	2064.15i	0.787528	−	0.179748i	0.597328	+	0.801997i	$0.296229\pi$
$510$	−1093.99	+	1371.83i	−0.0949860	+	0.119109i
$511$	−10215.5	+	21212.7i	−0.884359	+	1.83639i
$512$	2970.90	−	6169.14i	0.256439	−	0.532500i
$513$	−7267.82	+	5795.89i	−0.625501	+	0.498820i
$514$		−	9625.53i		−	0.826000i
$515$	−3320.38	−	1599.01i	−0.284103	−	0.136817i
$516$	20.7909	−	43.1727i	0.00177377	−	0.00368328i
$517$	−3039.35	+	2423.80i	−0.258550	+	0.206187i
$518$	1581.18	+	1260.95i	0.134118	+	0.106956i
$519$	−6033.96	−	1377.21i	−0.510330	−	0.116480i
$520$	338.757	+	703.436i	0.0285682	+	0.0593225i
$521$	−1041.79	+	501.699i	−0.0876038	+	0.0421878i	−0.477173	−	0.878810i	$-0.658338\pi$
$521$	−1041.79	+	501.699i	−0.0876038	+	0.0421878i	0.389569	+	0.920997i	$0.372624\pi$
$522$		−	3684.09i		−	0.308905i
$523$			10908.6i			0.912049i	0.889967	+	0.456025i	$0.150727\pi$
$523$			10908.6i			0.912049i	−0.889967	+	0.456025i	$0.849273\pi$
$524$	−6500.66	−	5184.11i	−0.541952	−	0.432192i
$525$	−9362.83	−	2137.00i	−0.778338	−	0.177650i
$526$	−78.2320	−	37.6746i	−0.00648494	−	0.00312298i
$527$	2562.66	+	11227.7i	0.211824	+	0.928061i
$528$	−1401.65	−	1757.61i	−0.115528	−	0.144868i
$529$	4969.12	+	2393.00i	0.408409	+	0.196680i
$530$	529.069	−	2318.00i	0.0433609	−	0.189976i
$531$	−18.3708	−	80.4875i	−0.00150136	−	0.00657789i
$532$	−1910.00	+	8368.26i	−0.155656	+	0.681974i
$533$	−2664.81	+	5533.53i	−0.216559	+	0.449689i
$534$	−1899.95	+	433.651i	−0.153968	+	0.0351422i
$535$	1155.14	−	2398.67i	0.0933477	−	0.193839i
$536$	−2953.28	−	12939.2i	−0.237989	−	1.04270i
$537$	−4319.29	+	2080.06i	−0.347097	+	0.167153i
$538$	7177.28	+	3456.39i	0.575157	+	0.276981i
$539$	−5393.27	+	1230.98i	−0.430992	+	0.0983711i
$540$	1557.97	+	1953.63i	0.124156	+	0.155687i
$541$	7255.15	−	5785.79i	0.576568	−	0.459797i	−0.291273	−	0.956640i	$-0.594079\pi$
$541$	7255.15	−	5785.79i	0.576568	−	0.459797i	0.867841	+	0.496843i	$0.165507\pi$
$542$	−7601.11	+	3660.50i	−0.602390	+	0.290096i
$543$	−1834.85	−	1463.24i	−0.145011	−	0.115642i
$544$	−14176.6	+	17776.9i	−1.11731	+	1.40106i
$545$	−1571.03	+	3262.29i	−0.123478	+	0.256405i
$546$	−1268.55	−	1011.64i	−0.0994304	−	0.0792931i
$547$	12404.1	+	9891.95i	0.969582	+	0.773216i	0.973947	−	0.226775i	$-0.0728181\pi$
$547$	12404.1	+	9891.95i	0.969582	+	0.773216i	−0.00436517	+	0.999990i	$0.501389\pi$
$548$	864.319	−	3786.83i	0.0673757	−	0.295192i
$549$	2070.25	+	9070.36i	0.160940	+	0.705125i
$550$	−4703.72	+	2265.19i	−0.364668	+	0.175615i
$551$	−2595.04	+	11369.6i	−0.200639	+	0.879059i
$552$	3632.84	−	4555.44i	0.280116	−	0.351254i
$553$	17685.8	+	4036.66i	1.35999	+	0.310409i
$554$	−4058.79	+	5089.56i	−0.311266	+	0.390316i
$555$	−636.995			−0.0487188
$556$	−5466.04	+	4359.02i	−0.416927	+	0.332488i
$557$	−840.666	−	3683.20i	−0.0639501	−	0.280183i	0.932835	−	0.360303i	$-0.117327\pi$
$557$	−840.666	−	3683.20i	−0.0639501	−	0.280183i	−0.996785	+	0.0801199i	$0.974470\pi$
$558$	−1879.42			−0.142585
$559$	13.4381	+	27.9045i	0.00101677	+	0.00211134i
$560$	1242.40	+	283.569i	0.0937515	+	0.0213982i
$561$	5990.63	+	12439.7i	0.450846	+	0.936192i
$562$	972.944	−	4262.75i	0.0730270	−	0.319952i
$563$	−193.143	+	846.215i	−0.0144583	+	0.0633459i	−0.981642	−	0.190731i	$-0.938914\pi$
$563$	−193.143	+	846.215i	−0.0144583	+	0.0633459i	0.967184	+	0.254076i	$0.0817715\pi$
$564$	−2084.39	+	1662.24i	−0.155618	+	0.124101i
$565$	−3075.16	+	1480.92i	−0.228978	+	0.110270i
$566$	−1730.33	+	2169.76i	−0.128500	+	0.161134i
$567$	−3157.82	−	1520.73i	−0.233891	−	0.112636i
$568$	−935.982	+	4100.80i	−0.0691425	+	0.302933i
$569$	−6404.08	−	3084.04i	−0.471833	−	0.227223i	0.182829	−	0.983145i	$-0.441475\pi$
$569$	−6404.08	−	3084.04i	−0.471833	−	0.227223i	−0.654662	+	0.755922i	$0.727189\pi$
$570$	393.283	+	816.661i	0.0288997	+	0.0600108i
$571$			24907.2i			1.82546i	0.408568	+	0.912728i	$0.366028\pi$
$571$			24907.2i			1.82546i	−0.408568	+	0.912728i	$0.633972\pi$
$572$	2630.81			0.192307
$573$	−494.677	+	112.907i	−0.0360653	+	0.00823167i
$574$	−6165.86	−	12803.5i	−0.448359	−	0.931027i
$575$	5951.32	+	7462.72i	0.431630	+	0.541247i
$576$	−927.102	−	1162.55i	−0.0670647	−	0.0840965i
$577$			24668.6i			1.77984i	0.456118	+	0.889919i	$0.349239\pi$
$577$			24668.6i			1.77984i	−0.456118	+	0.889919i	$0.650761\pi$
$578$	10984.5	−	8759.87i	0.790478	−	0.630385i
$579$	11310.2	+	2581.48i	0.811807	+	0.185290i
$580$	3056.22	+	697.561i	0.218797	+	0.0499391i
$581$	5938.77	+	26019.4i	0.424065	+	1.85795i
$582$	−6171.11	+	2971.85i	−0.439520	+	0.211662i
$583$	−14627.4	−	11665.0i	−1.03912	−	0.828669i
$584$	4561.32	+	19984.5i	0.323200	+	1.41603i
$585$	−552.018			−0.0390139
$586$	−2299.22	−	4774.37i	−0.162081	−	0.336566i
$587$	20360.9	+	9805.29i	1.43166	+	0.689451i	0.979305	−	0.202388i	$-0.0648703\pi$
$587$	20360.9	+	9805.29i	1.43166	+	0.689451i	0.452353	+	0.891839i	$0.350585\pi$
$588$	−3698.71	+	844.206i	−0.259408	+	0.0592083i
$589$	5800.15	+	1323.85i	0.405757	+	0.0926114i
$590$	−23.5526			−0.00164347
$591$	7104.24	−	6983.16i	0.494466	−	0.486039i
$592$	−1242.08			−0.0862314
$593$	−2304.83	−	526.063i	−0.159609	−	0.0364297i	0.141970	−	0.989871i	$-0.454656\pi$
$593$	−2304.83	−	526.063i	−0.159609	−	0.0364297i	−0.301579	+	0.953441i	$0.597514\pi$
$594$	−6427.15	+	1466.95i	−0.443955	+	0.101330i
$595$	−7051.58	−	3395.86i	−0.485860	−	0.233978i
$596$	5991.45	+	12441.4i	0.411777	+	0.855064i
$597$	16005.0			1.09722
$598$	358.852	+	1572.23i	0.0245394	+	0.107514i
$599$	−18946.1	−	15109.0i	−1.29235	−	1.03061i	−0.997171	−	0.0751729i	$-0.976049\pi$
$599$	−18946.1	−	15109.0i	−1.29235	−	1.03061i	−0.295179	−	0.955442i	$-0.595379\pi$
$600$	−7533.17	+	3627.78i	−0.512567	+	0.246839i
$601$	−5172.25	−	22661.1i	−0.351049	−	1.53805i	−0.774764	−	0.632251i	$-0.782131\pi$
$601$	−5172.25	−	22661.1i	−0.351049	−	1.53805i	0.423715	−	0.905796i	$-0.360726\pi$
$602$	−69.8659	−	15.9464i	−0.00473010	−	0.00107961i
$603$	9148.40	+	2088.06i	0.617831	+	0.141016i
$604$	−10235.2	+	8162.29i	−0.689510	+	0.549866i
$605$			960.599i			0.0645519i
$606$	2057.43	+	2579.93i	0.137916	+	0.172942i
$607$	5780.40	+	7248.40i	0.386523	+	0.484684i	0.936586	−	0.350439i	$-0.113968\pi$
$607$	5780.40	+	7248.40i	0.386523	+	0.484684i	−0.550063	+	0.835123i	$0.685396\pi$
$608$	5096.39	+	10582.8i	0.339944	+	0.705901i
$609$	−14832.1	+	3385.33i	−0.986908	+	0.225255i
$610$	2654.21			0.176174
$611$		−	1723.18i		−	0.114096i
$612$	−4437.74	−	9215.06i	−0.293113	−	0.608655i
$613$	4588.30	+	2209.61i	0.302316	+	0.145588i	0.578892	−	0.815404i	$-0.303485\pi$
$613$	4588.30	+	2209.61i	0.302316	+	0.145588i	−0.276576	+	0.960992i	$0.589200\pi$
$614$	−231.466	+	1014.12i	−0.0152137	+	0.0666557i
$615$	4032.71	+	1942.05i	0.264414	+	0.127335i
$616$	−8863.09	+	11114.0i	−0.579715	+	0.726939i
$617$	−2414.24	+	1162.63i	−0.157526	+	0.0758604i	−0.510986	−	0.859589i	$-0.670719\pi$
$617$	−2414.24	+	1162.63i	−0.157526	+	0.0758604i	0.353460	+	0.935450i	$0.385005\pi$
$618$	5213.20	−	4157.39i	0.339330	−	0.270606i
$619$	−1504.55	+	6591.87i	−0.0976946	+	0.428028i	−0.999995	−	0.00307921i	$-0.999020\pi$
$619$	−1504.55	+	6591.87i	−0.0976946	+	0.428028i	0.902301	+	0.431107i	$0.141877\pi$
$620$	355.858	−	1559.11i	0.0230509	−	0.100993i
$621$	5229.63	+	10859.4i	0.337935	+	0.701730i
$622$	10752.5	+	2454.20i	0.693148	+	0.158206i
$623$	−3771.67	−	7831.95i	−0.242550	−	0.503661i
$624$	996.492			0.0639289
$625$	−2826.40	−	12383.3i	−0.180890	−	0.792530i
$626$	5420.63	−	4322.81i	0.346089	−	0.275997i
$627$	7132.57			0.454302
$628$	−1794.60	+	2250.36i	−0.114032	+	0.142992i
$629$	7437.20	+	1697.49i	0.471448	+	0.107605i
$630$	796.362	−	998.606i	0.0503616	−	0.0631515i
$631$	3878.01	−	16990.7i	0.244661	−	1.07193i	−0.692056	−	0.721844i	$-0.743295\pi$
$631$	3878.01	−	16990.7i	0.244661	−	1.07193i	0.936717	−	0.350087i	$-0.113848\pi$
$632$	14229.7	−	6852.65i	0.895610	−	0.431303i
$633$	−52.5909	−	230.416i	−0.00330221	−	0.0144679i
$634$	−2342.68	+	10263.9i	−0.146750	+	0.642955i
$635$	939.034	+	748.854i	0.0586841	+	0.0467990i
$636$	−10031.5	−	7999.85i	−0.625432	−	0.498765i
$637$	1063.94	−	2209.29i	0.0661771	−	0.137418i
$638$	−5156.52	+	6466.08i	−0.319982	+	0.401245i
$639$	−2325.14	−	1854.23i	−0.143945	−	0.114792i
$640$	3416.27	−	1645.19i	0.211000	−	0.101612i
$641$	−9048.11	+	7215.63i	−0.557533	+	0.444618i	−0.861277	−	0.508136i	$-0.830335\pi$
$641$	−9048.11	+	7215.63i	−0.557533	+	0.444618i	0.303744	+	0.952754i	$0.401763\pi$
$642$	3003.34	+	3766.07i	0.184630	+	0.231518i
$643$	−8117.79	+	1852.83i	−0.497876	+	0.113637i	−0.464083	−	0.885792i	$-0.653616\pi$
$643$	−8117.79	+	1852.83i	−0.497876	+	0.113637i	−0.0337933	+	0.999429i	$0.510759\pi$
$644$	10027.2	+	4828.84i	0.613551	+	0.295470i
$645$	20.3362	−	9.79339i	0.00124145	−	0.000597852i
$646$	−2415.48	−	10582.9i	−0.147114	−	0.644550i
$647$	4380.12	−	9095.41i	0.266152	−	0.552670i	−0.724469	−	0.689307i	$-0.757915\pi$
$647$	4380.12	−	9095.41i	0.266152	−	0.552670i	0.990621	+	0.136637i	$0.0436295\pi$
$648$	−2974.98	+	679.020i	−0.180352	+	0.0411642i
$649$	−80.4130	+	166.979i	−0.00486362	+	0.0100994i
$650$	514.952	−	2256.15i	0.0310740	−	0.136144i
$651$	1727.01	+	7566.53i	0.103974	+	0.455538i
$652$	−4607.39	+	20186.3i	−0.276747	+	1.21251i
$653$	5624.81	+	2708.77i	0.337084	+	0.162331i	0.594766	−	0.803899i	$-0.297245\pi$
$653$	5624.81	+	2708.77i	0.337084	+	0.162331i	−0.257682	+	0.966230i	$0.582959\pi$
$654$	−4084.66	−	5122.00i	−0.244224	−	0.306248i
$655$	−871.517	−	3818.37i	−0.0519893	−	0.227780i
$656$	7863.38	+	3786.80i	0.468008	+	0.225381i
$657$	−14129.6	−	3225.00i	−0.839041	−	0.191506i
$658$	3117.25	+	2485.92i	0.184685	+	0.147282i
$659$		−	23029.3i		−	1.36130i	−0.732609	−	0.680649i	$-0.761698\pi$
$659$		−	23029.3i		−	1.36130i	0.732609	−	0.680649i	$-0.238302\pi$
$660$		−	1917.28i		−	0.113076i
$661$	8528.08	−	4106.91i	0.501821	−	0.241664i	−0.165808	−	0.986158i	$-0.553023\pi$
$661$	8528.08	−	4106.91i	0.501821	−	0.241664i	0.667630	+	0.744494i	$0.267309\pi$
$662$	2375.15	+	4932.05i	0.139445	+	0.289561i
$663$	−5966.72	−	1361.86i	−0.349514	−	0.0797744i
$664$	18166.5	+	14487.3i	1.06174	+	0.846713i
$665$	−3161.09	+	2520.88i	−0.184333	+	0.147001i
$666$	−540.151	+	1121.63i	−0.0314270	+	0.0652589i
$667$	13623.5	+	6560.74i	0.790862	+	0.380859i
$668$			12990.2i			0.752404i
$669$	11316.8	−	9024.87i	0.654012	−	0.521557i
$670$	1161.53	−	2411.94i	0.0669757	−	0.139077i
$671$	9061.97	−	18817.4i	0.521361	−	1.08262i
$672$	−9553.80	+	11980.1i	−0.548431	+	0.687711i
$673$	−15017.0	+	3427.54i	−0.860124	+	0.196318i	−0.629763	−	0.776787i	$-0.716848\pi$
$673$	−15017.0	+	3427.54i	−0.860124	+	0.196318i	−0.230361	+	0.973105i	$0.573991\pi$
$674$	−11797.9			−0.674238
$675$		−	17296.1i		−	0.986264i
$676$	7479.80	−	9379.38i	0.425569	−	0.533647i
$677$	−2731.67	+	5672.38i	−0.155076	+	0.322019i	−0.964004	−	0.265889i	$-0.914334\pi$
$677$	−2731.67	+	5672.38i	−0.155076	+	0.322019i	0.808927	+	0.587909i	$0.200049\pi$
$678$		−	6175.49i		−	0.349806i
$679$	−19049.1	−	23886.8i	−1.07664	−	1.35006i
$680$	−6643.28	+	1516.29i	−0.374644	+	0.0855101i
$681$	−7687.98	−	9640.42i	−0.432605	−	0.542469i
$682$	3298.64	+	2630.58i	0.185207	+	0.147698i
$683$	19391.8	−	24316.5i	1.08639	−	1.36229i	0.159400	−	0.987214i	$-0.449044\pi$
$683$	19391.8	−	24316.5i	1.08639	−	1.36229i	0.926993	−	0.375079i	$-0.122384\pi$
$684$	−5283.66			−0.295360
$685$	1430.46	−	1140.76i	0.0797886	−	0.0636293i
$686$	−2342.35	−	4863.94i	−0.130367	−	0.270709i
$687$	−1850.59	−	2320.57i	−0.102772	−	0.128872i
$688$	39.6535	−	19.0961i	0.00219735	−	0.00105819i
$689$	8085.20	−	1845.39i	0.447056	−	0.102038i
$690$	1145.81	−	261.523i	0.0632176	−	0.0144290i
$691$	21073.8	−	10148.6i	1.16018	−	0.558713i	0.248104	−	0.968734i	$-0.420193\pi$
$691$	21073.8	−	10148.6i	1.16018	−	0.558713i	0.912076	+	0.410020i	$0.134478\pi$
$692$	−6417.20	−	8046.91i	−0.352522	−	0.442049i
$693$	−4360.82	−	9055.33i	−0.239039	−	0.496369i
$694$	−2434.98	+	1941.83i	−0.133185	+	0.106212i
$695$	−3293.21			−0.179739
$696$	−8258.35	+	10355.6i	−0.449758	+	0.563979i
$697$	−41908.4	−	33420.9i	−2.27747	−	1.81622i
$698$	−2226.18	−	2791.54i	−0.120719	−	0.151377i
$699$	−23233.4	+	5302.88i	−1.25718	+	0.286943i
$700$	−9957.50	−	12486.3i	−0.537654	−	0.674197i
$701$			7248.67i			0.390554i	0.980748	+	0.195277i	$0.0625606\pi$
$701$			7248.67i			0.390554i	−0.980748	+	0.195277i	$0.937439\pi$
$702$	1267.89	−	2632.81i	0.0681675	−	0.141551i
$703$	2457.04	−	3081.04i	0.131820	−	0.165297i
$704$			3338.07i			0.178705i
$705$	−1255.81			−0.0670875
$706$	−13992.1	+	3193.61i	−0.745894	+	0.170245i
$707$	−9177.31	+	11508.0i	−0.488187	+	0.612167i
$708$	−55.1473	+	114.515i	−0.00292735	+	0.00607870i
$709$	13005.6	−	27006.4i	0.688907	−	1.43053i	−0.203398	−	0.979096i	$-0.565199\pi$
$709$	13005.6	−	27006.4i	0.688907	−	1.43053i	0.892305	−	0.451433i	$-0.149087\pi$
$710$	−663.333	+	528.991i	−0.0350626	+	0.0279615i
$711$			11166.7i			0.589005i
$712$	−6818.73	−	3283.73i	−0.358908	−	0.172841i
$713$	3346.93	−	6949.97i	0.175797	−	0.365047i
$714$	11071.4	−	8829.17i	0.580305	−	0.462778i
$715$	968.866	+	772.645i	0.0506763	+	0.0404130i
$716$	−7772.51	−	1774.03i	−0.405688	−	0.0925956i
$717$	−2130.64	−	4424.32i	−0.110977	−	0.230445i
$718$	10794.3	−	5198.25i	0.561057	−	0.270191i
$719$		−	14556.8i		−	0.755046i	−0.926000	−	0.377523i	$-0.876776\pi$
$719$		−	14556.8i		−	0.755046i	0.926000	−	0.377523i	$-0.123224\pi$
$720$			784.441i			0.0406033i
$721$	23253.9	+	18544.4i	1.20114	+	0.957875i
$722$	4010.46	+	915.362i	0.206723	+	0.0471832i
$723$	12924.0	+	6223.88i	0.664798	+	0.320150i
$724$	−868.448	−	3804.92i	−0.0445796	−	0.195316i
$725$	−13528.8	−	16964.6i	−0.693032	−	0.869035i
$726$	−1565.91	−	754.101i	−0.0800499	−	0.0385500i
$727$	−5546.05	+	24298.8i	−0.282932	+	1.23961i	0.611082	+	0.791567i	$0.290734\pi$
$727$	−5546.05	+	24298.8i	−0.282932	+	1.23961i	−0.894014	+	0.448039i	$0.852123\pi$
$728$	−1402.14	−	6143.16i	−0.0713828	−	0.312748i
$729$	3678.97	−	16118.6i	0.186911	−	0.818911i
$730$	−1793.97	+	3725.22i	−0.0909560	+	0.188872i
$731$	−263.532	+	60.1494i	−0.0133339	+	0.00304337i
$732$	6214.70	−	12905.0i	0.313801	−	0.651614i
$733$	−75.8609	−	332.368i	−0.00382263	−	0.0167480i	0.972981	−	0.230887i	$-0.0741627\pi$
$733$	−75.8609	−	332.368i	−0.00382263	−	0.0167480i	−0.976803	+	0.214139i	$0.931306\pi$
$734$	9697.61	−	4670.12i	0.487664	−	0.234847i
$735$	−1610.08	−	775.374i	−0.0808010	−	0.0389117i
$736$	14848.0	−	3388.96i	0.743622	−	0.169727i
$737$	−13134.1	−	16469.6i	−0.656444	−	0.823155i
$738$	6839.21	−	5454.09i	0.341131	−	0.272043i
$739$	12298.1	−	5922.47i	0.612171	−	0.294806i	−0.101992	−	0.994785i	$-0.532522\pi$
$739$	12298.1	−	5922.47i	0.612171	−	0.294806i	0.714163	+	0.699979i	$0.246807\pi$
$740$	−828.201	−	660.468i	−0.0411423	−	0.0328098i
$741$	−1971.24	+	2471.85i	−0.0977263	+	0.122545i
$742$	−8325.67	+	17288.4i	−0.411921	+	0.855362i
$743$	5028.41	+	4010.02i	0.248283	+	0.197999i	0.739722	−	0.672913i	$-0.234957\pi$
$743$	5028.41	+	4010.02i	0.248283	+	0.197999i	−0.491438	+	0.870912i	$0.663529\pi$
$744$	5282.88	+	4212.96i	0.260322	+	0.207600i
$745$	−1447.40	+	6341.49i	−0.0711795	+	0.311858i
$746$	1436.29	+	6292.78i	0.0704908	+	0.308840i
$747$	−14801.6	+	7128.06i	−0.724981	+	0.349133i
$748$	−5109.24	+	22385.1i	−0.249749	+	1.09422i
$749$	−13396.6	+	16798.8i	−0.653541	+	0.819514i
$750$	−3400.36	−	776.109i	−0.165551	−	0.0377860i
$751$	−1487.72	+	1865.55i	−0.0722874	+	0.0906456i	−0.816660	−	0.577119i	$-0.804177\pi$
$751$	−1487.72	+	1865.55i	−0.0722874	+	0.0906456i	0.744373	+	0.667764i	$0.232748\pi$
$752$	−2448.71			−0.118744
$753$	20233.4	−	16135.6i	0.979210	−	0.780894i
$754$	−815.760	−	3574.08i	−0.0394008	−	0.172626i
$755$	−6166.56			−0.297251
$756$	−8750.00	−	18169.6i	−0.420945	−	0.874101i
$757$	39391.3	+	8990.80i	1.89128	+	0.431673i	0.999772	−	0.0213314i	$-0.00679051\pi$
$757$	39391.3	+	8990.80i	1.89128	+	0.431673i	0.891509	+	0.453004i	$0.149648\pi$
$758$	2237.18	+	4645.55i	0.107201	+	0.222604i
$759$	2057.90	−	9016.23i	0.0984149	−	0.431184i
$760$	−783.299	+	3431.86i	−0.0373859	+	0.163798i
$761$	16643.0	−	13272.3i	0.792782	−	0.632223i	−0.141022	−	0.990006i	$-0.545039\pi$
$761$	16643.0	−	13272.3i	0.792782	−	0.632223i	0.933805	+	0.357784i	$0.116467\pi$
$762$	−1957.91	+	942.878i	−0.0930806	+	0.0448253i
$763$	18219.9	−	22847.1i	0.864489	−	1.08404i
$764$	−760.231	−	366.108i	−0.0360002	−	0.0173368i
$765$	1072.06	−	4697.01i	0.0506673	−	0.221988i
$766$	−2417.85	−	1164.38i	−0.114048	−	0.0549224i
$767$	−35.6443	−	74.0162i	−0.00167802	−	0.00348444i
$768$			9917.30i			0.465963i
$769$	−15200.1			−0.712783			−0.356391	−	0.934337i	$-0.615993\pi$
$769$	−15200.1			−0.712783			−0.356391	+	0.934337i	$0.615993\pi$
$770$	−2795.44	+	638.042i	−0.130832	+	0.0298616i
$771$	−10616.2	−	22044.8i	−0.495894	−	1.02973i
$772$	12028.6	+	15083.3i	0.560774	+	0.703188i
$773$	13047.8	+	16361.4i	0.607109	+	0.761291i	0.986467	−	0.163959i	$-0.0524266\pi$
$773$	13047.8	+	16361.4i	0.607109	+	0.761291i	−0.379358	+	0.925250i	$0.623855\pi$
$774$		−	44.1128i		−	0.00204858i
$775$	−8654.42	+	6901.67i	−0.401130	+	0.319891i
$776$	−25932.9	−	5919.01i	−1.19966	−	0.273814i
$777$	5012.03	+	1143.96i	0.231410	+	0.0528178i
$778$	3726.44	+	16326.6i	0.171722	+	0.752362i
$779$	−24948.5	+	12014.6i	−1.14746	+	0.552589i
$780$	664.449	+	529.880i	0.0305014	+	0.0243240i
$781$	1485.60	+	6508.86i	0.0680654	+	0.298214i
$782$	−14074.7			−0.643620
$783$	−11888.3	−	24686.2i	−0.542594	−	1.12671i
$784$	−3139.49	−	1511.90i	−0.143016	−	0.0688730i
$785$	−1321.82	+	301.696i	−0.0600990	+	0.0137172i
$786$	6908.62	+	1576.85i	0.313515	+	0.0715577i
$787$	−1366.91			−0.0619125			−0.0309563	−	0.999521i	$-0.509855\pi$
$787$	−1366.91			−0.0619125			−0.0309563	+	0.999521i	$0.509855\pi$
$788$	16477.2	−	1713.25i	0.744893	−	0.0774518i
$789$	−220.723			−0.00995936
$790$	3105.84	+	708.889i	0.139875	+	0.0319255i
$791$	26855.6	−	6129.62i	1.20717	−	0.275530i
$792$	−7883.85	−	3796.66i	−0.353712	−	0.170339i
$793$	4016.86	+	8341.09i	0.179877	+	0.373519i
$794$	−9740.35			−0.435355
$795$	−1344.88	−	5892.31i	−0.0599975	−	0.262866i
$796$	20809.2	+	16594.8i	0.926587	+	0.738928i
$797$	18762.0	−	9035.30i	0.833857	−	0.401564i	0.0322969	−	0.999478i	$-0.489718\pi$
$797$	18762.0	−	9035.30i	0.833857	−	0.401564i	0.801560	+	0.597914i	$0.204004\pi$
$798$	−1627.83	−	7131.97i	−0.0722111	−	0.316377i
$799$	14662.2	+	3346.55i	0.649200	+	0.148176i
$800$	−21306.9	−	4863.16i	−0.941640	−	0.214923i
$801$	4183.56	−	3336.28i	0.184543	−	0.147168i
$802$		−	11008.2i		−	0.484678i
$803$	20285.5	+	25437.2i	0.891481	+	1.11788i
$804$	−9007.35	−	11294.9i	−0.395105	−	0.495447i
$805$	2274.59	+	4723.24i	0.0995885	+	0.206798i
$806$	−1823.30	+	416.156i	−0.0796811	+	0.0181867i
$807$	20249.8			0.883307
$808$			12815.0i			0.557959i
$809$	−2248.37	−	4668.78i	−0.0977112	−	0.202899i	0.846383	−	0.532574i	$-0.178775\pi$
$809$	−2248.37	−	4668.78i	−0.0977112	−	0.202899i	−0.944095	+	0.329675i	$0.893061\pi$
$810$	−554.554	−	267.059i	−0.0240556	−	0.0115846i
$811$	9314.18	−	40808.1i	0.403286	−	1.76691i	−0.210656	−	0.977560i	$-0.567560\pi$
$811$	9314.18	−	40808.1i	0.403286	−	1.76691i	0.613942	−	0.789351i	$-0.289583\pi$
$812$	−22794.3	−	10977.2i	−0.985127	−	0.474412i
$813$	−13371.1	+	16766.9i	−0.576810	+	0.723296i
$814$	2517.96	−	1212.58i	0.108421	−	0.0522126i
$815$	−7625.31	+	6080.98i	−0.327734	+	0.261359i
$816$	−1935.26	+	8478.95i	−0.0830243	+	0.363753i
$817$	−31.0726	+	136.138i	−0.00133059	+	0.00582971i
$818$	4348.40	+	9029.54i	0.185866	+	0.385954i
$819$	4343.41	+	991.355i	0.185313	+	0.0422964i
$820$	3229.59	+	6706.31i	0.137539	+	0.285603i
$821$	−6332.88			−0.269207			−0.134603	−	0.990900i	$-0.542976\pi$
$821$	−6332.88			−0.269207			−0.134603	+	0.990900i	$0.542976\pi$
$822$	736.628	+	3227.38i	0.0312565	+	0.136944i
$823$	8226.74	−	6560.60i	0.348440	−	0.277871i	−0.433593	−	0.901109i	$-0.642754\pi$
$823$	8226.74	−	6560.60i	0.348440	−	0.277871i	0.782033	+	0.623237i	$0.214183\pi$
$824$	25895.0			1.09478
$825$	−8274.34	+	10375.7i	−0.349182	+	0.437861i
$826$	185.318	+	42.2975i	0.00780633	+	0.00178174i
$827$	−16749.7	+	21003.4i	−0.704284	+	0.883145i	−0.997335	−	0.0729522i	$-0.976758\pi$
$827$	−16749.7	+	21003.4i	−0.704284	+	0.883145i	0.293051	+	0.956097i	$0.405329\pi$
$828$	−1524.45	+	6679.04i	−0.0639834	+	0.280330i
$829$	−14889.2	+	7170.25i	−0.623791	+	0.300402i	−0.718952	−	0.695060i	$-0.755378\pi$
$829$	−14889.2	+	7170.25i	−0.623791	+	0.300402i	0.0951610	+	0.995462i	$0.469663\pi$
$830$	1042.92	+	4569.34i	0.0436149	+	0.191089i
$831$	−3682.22	+	16132.9i	−0.153712	+	0.673458i
$832$	−1156.84	−	922.547i	−0.0482045	−	0.0384418i
$833$	16732.2	+	13343.5i	0.695960	+	0.555010i
$834$	2585.28	−	5368.38i	0.107339	−	0.222892i
$835$	−3815.10	+	4783.98i	−0.158116	+	0.198271i
$836$	9273.54	+	7395.40i	0.383651	+	0.305951i
$837$	−12593.6	+	6064.73i	−0.520068	+	0.250451i
$838$	−5690.40	+	4537.94i	−0.234572	+	0.187065i
$839$	−1998.31	−	2505.81i	−0.0822282	−	0.103111i	0.739016	−	0.673688i	$-0.235291\pi$
$839$	−1998.31	−	2505.81i	−0.0822282	−	0.103111i	−0.821244	+	0.570577i	$0.806719\pi$
$840$	−4477.00	+	1021.85i	−0.183894	+	0.0419726i
$841$	−8995.93	−	4332.21i	−0.368852	−	0.177630i
$842$	−210.794	+	101.513i	−0.00862760	+	0.00415484i
$843$	−2473.20	−	10835.8i	−0.101046	−	0.442711i
$844$	170.529	−	354.108i	0.00695482	−	0.0144418i
$845$	5509.27	−	1257.45i	0.224289	−	0.0511926i
$846$	−1064.89	+	2211.26i	−0.0432762	+	0.0898639i
$847$	1725.11	−	7558.22i	0.0699830	−	0.306616i
$848$	−2622.38	−	11489.4i	−0.106194	−	0.465268i
$849$	−1569.79	+	6877.70i	−0.0634571	+	0.278024i
$850$	18197.0	+	8763.24i	0.734298	+	0.353619i
$851$	−3185.81	−	3994.88i	−0.128329	−	0.160920i
$852$	1018.83	+	4463.78i	0.0409677	+	0.179491i
$853$	−44537.4	−	21448.1i	−1.78773	−	0.860925i	−0.948244	−	0.317542i	$-0.897142\pi$
$853$	−44537.4	−	21448.1i	−1.78773	−	0.860925i	−0.839485	−	0.543383i	$-0.817143\pi$
$854$	−20884.0	−	4766.63i	−0.836809	−	0.190996i
$855$	−1945.85	−	1551.76i	−0.0778323	−	0.0620692i
$856$			18706.8i			0.746945i
$857$		−	7451.77i		−	0.297022i	−0.988911	−	0.148511i	$-0.952552\pi$
$857$		−	7451.77i		−	0.297022i	0.988911	−	0.148511i	$-0.0474480\pi$
$858$	−2020.11	+	972.832i	−0.0803792	+	0.0387086i
$859$	5794.91	+	12033.3i	0.230174	+	0.477962i	0.983783	−	0.179361i	$-0.0574030\pi$
$859$	5794.91	+	12033.3i	0.230174	+	0.477962i	−0.753609	+	0.657323i	$0.771689\pi$
$860$	36.5947	+	8.35251i	0.00145101	+	0.000331184i
$861$	−28242.7	−	22522.8i	−1.11789	−	0.891491i
$862$	3429.58	−	2735.00i	0.135513	−	0.108068i
$863$	6368.17	−	13223.6i	0.251188	−	0.521596i	−0.736804	−	0.676107i	$-0.763666\pi$
$863$	6368.17	−	13223.6i	0.251188	−	0.521596i	0.987991	+	0.154510i	$0.0493800\pi$
$864$	−24864.0	−	11973.9i	−0.979040	−	0.471481i
$865$		−	4848.15i		−	0.190569i
$866$	14032.7	−	11190.7i	0.550636	−	0.439117i
$867$	15495.8	−	32177.3i	0.606995	−	1.26044i
$868$	−5599.94	+	11628.4i	−0.218980	+	0.454716i
$869$	15629.7	−	19599.0i	0.610127	−	0.765075i
$870$	−2604.70	+	594.507i	−0.101503	+	0.0231674i
$871$	9337.56			0.363251
$872$		−	25442.0i		−	0.988043i
$873$	11725.9	−	14703.8i	0.454595	−	0.570045i
$874$	−3154.71	+	6550.83i	−0.122094	+	0.253530i
$875$		−	15557.6i		−	0.601078i
$876$	13911.8	+	17444.8i	0.536571	+	0.672838i
$877$	−49432.7	+	11282.7i	−1.90333	+	0.434423i	−0.903349	+	0.428907i	$0.858899\pi$
$877$	−49432.7	+	11282.7i	−1.90333	+	0.434423i	−0.999985	+	0.00551654i	$0.998244\pi$
$878$	4073.43	+	5107.92i	0.156574	+	0.196337i
$879$	−10531.5	−	8398.61i	−0.404118	−	0.322273i
$880$	1097.96	−	1376.80i	0.0420593	−	0.0527407i
$881$	−4102.96			−0.156904			−0.0784518	−	0.996918i	$-0.524998\pi$
$881$	−4102.96			−0.156904			−0.0784518	+	0.996918i	$0.524998\pi$
$882$	−2730.59	+	2177.57i	−0.104245	+	0.0831323i
$883$	19150.1	+	39765.7i	0.729845	+	1.51554i	0.852293	+	0.523064i	$0.175211\pi$
$883$	19150.1	+	39765.7i	0.729845	+	1.51554i	−0.122448	+	0.992475i	$0.539075\pi$
$884$	−6345.69	−	7957.24i	−0.241435	−	0.302750i
$885$	−53.9413	+	25.9767i	−0.00204883	+	0.000986665i
$886$	7468.27	−	1704.58i	0.283185	−	0.0646350i
$887$	26355.8	−	6015.55i	0.997681	−	0.227714i	0.307654	−	0.951498i	$-0.400456\pi$
$887$	26355.8	−	6015.55i	0.997681	−	0.227714i	0.690027	+	0.723784i	$0.257599\pi$
$888$	4032.59	−	1941.99i	0.152393	−	0.0733886i
$889$	−6043.69	−	7578.55i	−0.228008	−	0.285913i
$890$	−662.353	−	1375.39i	−0.0249462	−	0.0518013i
$891$	−3786.70	+	3019.79i	−0.142378	+	0.113543i
$892$	24071.2			0.903547
$893$	4843.98	−	6074.16i	0.181520	−	0.227619i
$894$	−9201.23	−	7337.73i	−0.344223	−	0.274508i
$895$	−2341.42	−	2936.04i	−0.0874468	−	0.109655i
$896$	−29834.6	+	6809.55i	−1.11239	+	0.253896i
$897$	2555.91	+	3205.01i	0.0951386	+	0.119300i
$898$			10840.6i			0.402846i
$899$	−7608.41	+	15799.0i	−0.282263	+	0.586126i
$900$	6129.47	−	7686.11i	0.227017	−	0.284671i
$901$			72379.2i			2.67625i
$902$	−19637.7			−0.724903
$903$	−177.598	+	40.5355i	−0.00654494	+	0.00149384i
$904$	14952.9	−	18750.3i	0.550139	−	0.689853i
$905$	797.640	−	1656.32i	0.0292977	−	0.0608374i
$906$	4840.95	−	10052.3i	0.177516	−	0.368616i
$907$	12594.3	−	10043.7i	0.461068	−	0.367689i	−0.365235	−	0.930915i	$-0.619011\pi$
$907$	12594.3	−	10043.7i	0.461068	−	0.367689i	0.826303	+	0.563226i	$0.190440\pi$
$908$		−	20505.4i		−	0.749446i
$909$	−8163.35	−	3931.26i	−0.297867	−	0.143445i
$910$	551.461	−	1145.12i	0.0200888	−	0.0417147i
$911$	−27964.7	+	22301.1i	−1.01703	+	0.811051i	−0.982104	−	0.188339i	$-0.939690\pi$
$911$	−27964.7	+	22301.1i	−1.01703	+	0.811051i	−0.0349217	+	0.999390i	$0.511118\pi$
$912$	3512.60	+	2801.21i	0.127537	+	0.101708i
$913$	35955.7	+	8206.65i	1.30335	+	0.297481i
$914$	7946.16	+	16500.4i	0.287566	+	0.597138i
$915$	6078.79	−	2927.39i	0.219627	−	0.105767i
$916$		−	4935.91i		−	0.178043i
$917$			31608.9i			1.13830i
$918$	19939.7	+	15901.4i	0.716892	+	0.571703i
$919$	32850.5	+	7497.91i	1.17915	+	0.269133i	0.766796	−	0.641891i	$-0.221850\pi$
$919$	32850.5	+	7497.91i	1.17915	+	0.269133i	0.412353	+	0.911024i	$0.364707\pi$
$920$	4112.19	+	1980.33i	0.147364	+	0.0709668i
$921$	588.383	+	2577.87i	0.0210509	+	0.0922300i
$922$	−479.920	−	601.800i	−0.0171424	−	0.0214959i
$923$	−2666.28	−	1284.01i	−0.0950831	−	0.0457896i
$924$	−3443.19	+	15085.6i	−0.122589	+	0.537099i
$925$	1631.60	+	7148.49i	0.0579963	+	0.254098i
$926$	−787.075	+	3448.40i	−0.0279319	+	0.122377i
$927$	−7943.80	+	16495.5i	−0.281455	+	0.584447i
$928$	−33753.3	+	7703.96i	−1.19397	+	0.272516i
$929$	8626.87	−	17913.9i	0.304670	−	0.632654i	−0.691278	−	0.722589i	$-0.742952\pi$
$929$	8626.87	−	17913.9i	0.304670	−	0.632654i	0.995948	+	0.0899355i	$0.0286661\pi$
$930$	303.285	+	1328.78i	0.0106937	+	0.0468520i
$931$	9960.83	−	4796.88i	0.350648	−	0.168863i
$932$	−35705.7	−	17194.9i	−1.25491	−	0.604334i
$933$	27332.8	−	6238.52i	0.959093	−	0.218907i
$934$	9781.64	+	12265.8i	0.342682	+	0.429710i
$935$	−8455.89	+	6743.34i	−0.295762	+	0.235862i
$936$	3494.63	−	1682.93i	0.122036	−	0.0587695i
$937$	−9229.81	−	7360.53i	−0.321798	−	0.256625i	0.449245	−	0.893409i	$-0.351693\pi$
$937$	−9229.81	−	7360.53i	−0.321798	−	0.256625i	−0.771043	+	0.636783i	$0.780265\pi$
$938$	−13470.7	+	16891.7i	−0.468906	+	0.587990i
$939$	7646.84	−	15878.8i	0.265756	−	0.551848i
$940$	−1632.77	−	1302.09i	−0.0566543	−	0.0451803i
$941$	30979.6	+	24705.4i	1.07322	+	0.855868i	0.990057	−	0.140667i	$-0.0449248\pi$
$941$	30979.6	+	24705.4i	1.07322	+	0.855868i	0.0831678	+	0.996536i	$0.473496\pi$
$942$	545.863	−	2391.58i	0.0188802	−	0.0827198i
$943$	7989.37	+	35003.7i	0.275896	+	1.20878i
$944$	−105.180	+	50.6520i	−0.00362639	+	0.00174638i
$945$	2113.81	−	9261.20i	0.0727643	−	0.318801i
$946$	−61.7435	+	77.4239i	−0.00212205	+	0.00266096i
$947$	50081.1	+	11430.7i	1.71850	+	0.392236i	0.964383	−	0.264509i	$-0.0852097\pi$
$947$	50081.1	+	11430.7i	1.71850	+	0.392236i	0.754113	+	0.656744i	$0.228067\pi$
$948$	10718.8	−	13441.0i	0.367228	−	0.460489i
$949$	−14421.8			−0.493310
$950$	8157.39	−	6505.30i	0.278590	−	0.222168i
$951$	5955.04	+	26090.7i	0.203055	+	0.889642i
$952$	54994.0			1.87223
$953$	18826.2	+	39093.1i	0.639918	+	1.32880i	0.928494	+	0.371347i	$0.121104\pi$
$953$	18826.2	+	39093.1i	0.639918	+	1.32880i	−0.288576	+	0.957457i	$0.593182\pi$
$954$	−11515.7	−	2628.39i	−0.390812	−	0.0892004i
$955$	−172.452	−	358.101i	−0.00584338	−	0.0121339i
$956$	1817.16	−	7961.51i	0.0614762	−	0.269345i
$957$	−4678.11	+	20496.1i	−0.158017	+	0.692316i
$958$	−12464.6	+	9940.17i	−0.420368	+	0.335232i
$959$	−13303.9	+	6406.81i	−0.447971	+	0.215732i
$960$	−672.331	+	843.076i	−0.0226035	+	0.0283439i
$961$	−18781.0	−	9044.44i	−0.630424	−	0.303596i
$962$	−275.660	+	1207.74i	−0.00923869	+	0.0404774i
$963$	−11916.5	−	5738.68i	−0.398757	−	0.192031i
$964$	10350.2	+	21492.3i	0.345805	+	0.718072i
$965$			9087.51i			0.303148i
$966$	−9485.14			−0.315921
$967$	−45971.6	+	10492.7i	−1.52880	+	0.348938i	−0.902515	−	0.430658i	$-0.858282\pi$
$967$	−45971.6	+	10492.7i	−1.52880	+	0.348938i	−0.626283	+	0.779596i	$0.715425\pi$
$968$	−2928.56	−	6081.22i	−0.0972391	−	0.201919i
$969$	−17204.2	−	21573.4i	−0.570360	−	0.715208i
$970$	−3345.26	−	4194.82i	−0.110732	−	0.138853i
$971$			3571.00i			0.118022i	0.998257	+	0.0590108i	$0.0187946\pi$
$971$			3571.00i			0.118022i	−0.998257	+	0.0590108i	$0.981205\pi$
$972$	16093.8	−	12834.4i	0.531081	−	0.423523i
$973$	25911.8	+	5914.19i	0.853744	+	0.194862i
$974$	−7937.47	−	1811.68i	−0.261122	−	0.0595994i
$975$	−1309.00	−	5735.09i	−0.0429964	−	0.188379i
$976$	11853.0	−	5708.12i	0.388736	−	0.187205i
$977$	−27018.6	−	21546.6i	−0.884750	−	0.705564i	0.0717109	−	0.997425i	$-0.477154\pi$
$977$	−27018.6	−	21546.6i	−0.884750	−	0.705564i	−0.956461	+	0.291861i	$0.905726\pi$
$978$	−3926.71	−	17204.1i	−0.128387	−	0.562500i
$979$	−12012.4			−0.392153
$980$	−1289.43	−	2677.53i	−0.0420299	−	0.0872760i
$981$	16206.9	+	7804.82i	0.527468	+	0.254015i
$982$	−3890.61	+	888.006i	−0.126430	+	0.0288568i
$983$	−56384.0	−	12869.3i	−1.82947	−	0.417565i	−0.837760	−	0.546039i	$-0.816135\pi$
$983$	−56384.0	−	12869.3i	−1.82947	−	0.417565i	−0.991713	+	0.128474i	$0.958992\pi$
$984$	−31450.4			−1.01890
$985$	6571.32	+	4208.24i	0.212568	+	0.136128i
$986$	31995.4			1.03341
$987$	9881.04	+	2255.28i	0.318660	+	0.0727320i
$988$	−5125.88	+	1169.95i	−0.165057	+	0.0376731i
$989$	163.126	+	78.5574i	0.00524480	+	0.00252576i
$990$	−765.815	−	1590.23i	−0.0245851	−	0.0510514i
$991$	−18972.6			−0.608159			−0.304080	−	0.952647i	$-0.598349\pi$
$991$	−18972.6			−0.608159			−0.304080	+	0.952647i	$0.598349\pi$
$992$	3930.14	+	17219.1i	0.125788	+	0.551115i
$993$	10879.3	+	8675.99i	0.347679	+	0.277265i
$994$	6169.26	−	2970.96i	0.196858	−	0.0948020i
$995$	2789.81	+	12222.9i	0.0888872	+	0.389440i
$996$	24658.4	+	5628.12i	0.784470	+	0.179050i
$997$	−57383.4	−	13097.4i	−1.82282	−	0.416047i	−0.832404	−	0.554169i	$-0.813036\pi$
$997$	−57383.4	−	13097.4i	−1.82282	−	0.416047i	−0.990415	+	0.138123i	$0.955893\pi$
$998$	−10525.6	+	8393.90i	−0.333850	+	0.266237i
$999$			9258.82i			0.293229i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	197.4.e.a.33.20	yes	288
197.6	even	14	inner	197.4.e.a.6.20	✓	288

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
197.4.e.a.6.20	✓	288	197.6	even	14	inner
197.4.e.a.33.20	yes	288	1.1	even	1	trivial

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:	\( N \)	\(=\)	\( 197 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	197.e (of order \(14\), degree \(6\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.38176 - 0.315378i) q^{2} +(-3.51241 + 0.801685i) q^{3} +(-5.39795 - 2.59951i) q^{4} +(-1.22448 - 2.54267i) q^{5} +5.10615 q^{6} +(5.06822 + 22.2053i) q^{7} +(15.5035 + 12.3637i) q^{8} +(-12.6318 + 6.08317i) q^{9} +(0.890043 + 3.89953i) q^{10} +(30.6850 + 7.00365i) q^{11} +(21.0438 + 4.80311i) q^{12} +(-10.9076 + 8.69855i) q^{13} -32.2809i q^{14} +(6.33930 + 7.94923i) q^{15} +(12.3610 + 15.5002i) q^{16} +(-52.8307 - 109.704i) q^{17} +(19.3727 - 4.42169i) q^{18} -62.9013 q^{19} +16.9082i q^{20} +(-35.6033 - 73.9310i) q^{21} +(-40.1906 - 19.3548i) q^{22} +(-18.1483 + 79.5131i) q^{23} +(-64.3666 - 30.9973i) q^{24} +(72.9704 - 91.5020i) q^{25} +(17.8151 - 8.57929i) q^{26} +(115.543 - 92.1426i) q^{27} +(30.3651 - 133.038i) q^{28} +(41.2557 - 180.753i) q^{29} +(-6.25239 - 12.9832i) q^{30} +(-92.2103 - 21.0464i) q^{31} +(-81.0221 - 168.244i) q^{32} -113.393 q^{33} +(38.4012 + 168.247i) q^{34} +(50.2547 - 40.0768i) q^{35} +83.9993 q^{36} +(-39.0619 + 48.9821i) q^{37} +(86.9146 + 19.8377i) q^{38} +(31.3386 - 39.2973i) q^{39} +(12.4528 - 54.5594i) q^{40} +(396.630 - 191.007i) q^{41} +(25.8791 + 113.384i) q^{42} +(0.493990 - 2.16431i) q^{43} +(-147.430 - 117.571i) q^{44} +(30.9349 + 24.6698i) q^{45} +(50.1534 - 104.145i) q^{46} +(-77.0092 + 96.5665i) q^{47} +(-55.8431 - 44.5334i) q^{48} +(-158.356 + 76.2605i) q^{49} +(-129.686 + 103.421i) q^{50} +(273.511 + 342.972i) q^{51} +(81.4909 - 18.5998i) q^{52} +(-535.563 - 257.914i) q^{53} +(-188.713 + 90.8794i) q^{54} +(-19.7653 - 86.5976i) q^{55} +(-195.964 + 406.923i) q^{56} +(220.935 - 50.4270i) q^{57} +(-114.011 + 236.747i) q^{58} +(-1.31030 + 5.74079i) q^{59} +(-13.5551 - 59.3887i) q^{60} +(147.661 - 646.946i) q^{61} +(120.775 + 58.1623i) q^{62} +(-199.100 - 249.663i) q^{63} +(23.6000 + 103.398i) q^{64} +(35.4737 + 17.0832i) q^{65} +(156.682 + 35.7617i) q^{66} +(-523.274 - 417.297i) q^{67} +729.511i q^{68} -293.832i q^{69} +(-82.0794 + 39.5274i) q^{70} +(92.0348 + 191.112i) q^{71} +(-271.049 - 61.8651i) q^{72} +(808.193 + 644.513i) q^{73} +(69.4221 - 55.3623i) q^{74} +(-182.946 + 379.892i) q^{75} +(339.538 + 163.513i) q^{76} +716.866i q^{77} +(-55.6960 + 44.4161i) q^{78} +(345.573 - 717.591i) q^{79} +(24.2760 - 50.4096i) q^{80} +(-95.9452 + 120.311i) q^{81} +(-608.287 + 138.838i) q^{82} +1171.77 q^{83} +491.627i q^{84} +(-214.250 + 268.661i) q^{85} +(-1.36515 + 2.83477i) q^{86} +667.953i q^{87} +(389.136 + 487.961i) q^{88} +(-372.090 + 84.9272i) q^{89} +(-34.9644 - 43.8440i) q^{90} +(-248.436 - 198.121i) q^{91} +(304.659 - 382.031i) q^{92} +340.753 q^{93} +(136.863 - 109.145i) q^{94} +(77.0216 + 159.937i) q^{95} +(419.461 + 525.988i) q^{96} +(-1208.57 + 582.014i) q^{97} +(242.862 - 55.4316i) q^{98} +(-430.212 + 98.1932i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 288 q - 7 q^{2} - 7 q^{3} + 159 q^{4} - 7 q^{5} + 26 q^{6} - 53 q^{7} + 49 q^{8} + 391 q^{9} + 149 q^{10} + 91 q^{11} - 63 q^{12} - 7 q^{13} - 473 q^{15} - 1113 q^{16} - 7 q^{17} - 196 q^{18} + 464 q^{19}+ \cdots + 2464 q^{99}+O(q^{100}) \) 288 * q - 7 * q^2 - 7 * q^3 + 159 * q^4 - 7 * q^5 + 26 * q^6 - 53 * q^7 + 49 * q^8 + 391 * q^9 + 149 * q^10 + 91 * q^11 - 63 * q^12 - 7 * q^13 - 473 * q^15 - 1113 * q^16 - 7 * q^17 - 196 * q^18 + 464 * q^19 - 7 * q^21 + 807 * q^22 + 413 * q^23 - 1425 * q^24 + 1195 * q^25 - 543 * q^26 + 455 * q^27 + 174 * q^28 - 906 * q^29 + 798 * q^30 + 917 * q^31 + 945 * q^32 + 894 * q^33 - 219 * q^34 - 7 * q^35 + 3250 * q^36 + 1734 * q^37 - 63 * q^38 - 825 * q^39 + 141 * q^40 + 563 * q^41 + 432 * q^42 - 423 * q^43 + 2149 * q^44 - 3808 * q^45 - 2569 * q^46 - 289 * q^47 - 3703 * q^48 - 3747 * q^49 - 4963 * q^50 - 87 * q^51 + 3654 * q^52 - 1573 * q^53 - 1228 * q^54 + 2825 * q^55 + 98 * q^56 - 518 * q^57 - 5103 * q^58 + 2045 * q^59 + 3375 * q^60 + 287 * q^61 - 2547 * q^62 + 1453 * q^63 + 6475 * q^64 + 1268 * q^65 + 4634 * q^66 - 3577 * q^67 - 814 * q^70 - 273 * q^71 - 1008 * q^72 - 679 * q^73 - 315 * q^74 - 1281 * q^75 + 6078 * q^76 + 4739 * q^78 + 1463 * q^79 + 441 * q^80 - 4427 * q^81 - 7 * q^82 + 4900 * q^83 - 3351 * q^85 + 3472 * q^86 + 3738 * q^88 + 147 * q^89 + 7133 * q^90 - 14133 * q^91 - 803 * q^92 - 4894 * q^93 - 7833 * q^94 - 7700 * q^95 - 16450 * q^96 + 1233 * q^97 - 2030 * q^98 + 2464 * q^99

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more