LMFDB - Embedded newform 36.4.h.b.11.8

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [36,4,Mod(11,36)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(36, base_ring=CyclotomicField(6))

chi = DirichletCharacter(H, H._module([3, 1]))

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

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

chi := DirichletCharacter("36.11");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 36 = 2^{2} \cdot 3^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	36.h (of order $6$, degree $2$, minimal)

Newform invariants

comment: select newform

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

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

Self dual:	no
Analytic conductor:	$2.12406876021$
Analytic rank:	$0$
Dimension:	$24$
Relative dimension:	$12$ over $\Q(\zeta_{6})$
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{6}]$

Embedding invariants

Embedding label			11.8
Character	$\chi$	$=$	36.11
Dual form			36.4.h.b.23.8

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(0.823719 - 2.70582i) q^{2} +(2.72340 - 4.42528i) q^{3} +(-6.64298 - 4.45768i) q^{4} +(-4.71466 + 2.72201i) q^{5} +(-9.73072 - 11.0142i) q^{6} +(20.9358 + 12.0873i) q^{7} +(-17.5336 + 14.3029i) q^{8} +(-12.1662 - 24.1036i) q^{9} +O(q^{10})$	\(q+(0.823719 - 2.70582i) q^{2} +(2.72340 - 4.42528i) q^{3} +(-6.64298 - 4.45768i) q^{4} +(-4.71466 + 2.72201i) q^{5} +(-9.73072 - 11.0142i) q^{6} +(20.9358 + 12.0873i) q^{7} +(-17.5336 + 14.3029i) q^{8} +(-12.1662 - 24.1036i) q^{9} +(3.48173 + 14.9992i) q^{10} +(25.3999 - 43.9939i) q^{11} +(-37.8179 + 17.2570i) q^{12} +(25.0883 + 43.4542i) q^{13} +(49.9512 - 46.6920i) q^{14} +(-0.794244 + 28.2768i) q^{15} +(24.2582 + 59.2245i) q^{16} +51.7146i q^{17} +(-75.2416 + 13.0650i) q^{18} +27.9305i q^{19} +(43.4533 + 2.93419i) q^{20} +(110.506 - 59.7282i) q^{21} +(-98.1174 - 104.966i) q^{22} +(-3.93548 - 6.81645i) q^{23} +(15.5431 + 116.544i) q^{24} +(-47.6813 + 82.5864i) q^{25} +(138.245 - 32.0905i) q^{26} +(-139.799 - 11.8049i) q^{27} +(-85.1946 - 173.620i) q^{28} +(-212.788 - 122.853i) q^{29} +(75.8579 + 25.4412i) q^{30} +(-51.4009 + 29.6763i) q^{31} +(180.233 - 16.8542i) q^{32} +(-125.511 - 232.215i) q^{33} +(139.931 + 42.5982i) q^{34} -131.607 q^{35} +(-26.6263 + 214.353i) q^{36} +295.334 q^{37} +(75.5750 + 23.0069i) q^{38} +(260.622 + 7.32039i) q^{39} +(43.7327 - 115.160i) q^{40} +(-146.833 + 84.7741i) q^{41} +(-70.5881 - 348.209i) q^{42} +(-284.968 - 164.526i) q^{43} +(-364.841 + 179.026i) q^{44} +(122.970 + 80.5238i) q^{45} +(-21.6859 + 5.03388i) q^{46} +(-47.9742 + 83.0938i) q^{47} +(328.150 + 53.9424i) q^{48} +(120.704 + 209.066i) q^{49} +(184.188 + 197.045i) q^{50} +(228.851 + 140.839i) q^{51} +(27.0439 - 400.500i) q^{52} +300.751i q^{53} +(-147.097 + 368.547i) q^{54} +276.555i q^{55} +(-539.963 + 87.5075i) q^{56} +(123.600 + 76.0659i) q^{57} +(-507.697 + 474.571i) q^{58} +(113.273 + 196.195i) q^{59} +(131.325 - 184.302i) q^{60} +(173.722 - 300.896i) q^{61} +(37.9590 + 163.527i) q^{62} +(36.6381 - 651.684i) q^{63} +(102.857 - 501.562i) q^{64} +(-236.566 - 136.581i) q^{65} +(-731.718 + 148.332i) q^{66} +(904.675 - 522.314i) q^{67} +(230.527 - 343.538i) q^{68} +(-40.8826 - 1.14832i) q^{69} +(-108.407 + 356.105i) q^{70} +243.524 q^{71} +(558.068 + 248.612i) q^{72} -1094.68 q^{73} +(243.272 - 799.122i) q^{74} +(235.613 + 435.919i) q^{75} +(124.505 - 185.542i) q^{76} +(1063.53 - 614.031i) q^{77} +(234.487 - 699.168i) q^{78} +(-530.679 - 306.388i) q^{79} +(-275.579 - 213.192i) q^{80} +(-432.967 + 586.498i) q^{81} +(108.435 + 467.135i) q^{82} +(283.063 - 490.280i) q^{83} +(-1000.34 - 95.8273i) q^{84} +(-140.768 - 243.817i) q^{85} +(-679.912 + 635.549i) q^{86} +(-1123.17 + 607.068i) q^{87} +(183.886 + 1134.66i) q^{88} -212.529i q^{89} +(319.176 - 266.406i) q^{90} +1213.00i q^{91} +(-4.24224 + 62.8246i) q^{92} +(-8.65911 + 308.284i) q^{93} +(185.320 + 198.256i) q^{94} +(-76.0272 - 131.683i) q^{95} +(416.262 - 843.482i) q^{96} +(234.298 - 405.817i) q^{97} +(665.122 - 154.393i) q^{98} +(-1369.43 - 76.9903i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	$ 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) $ 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/36\mathbb{Z}\right)^\times$.

$n$	$19$	$29$
$\chi(n)$	$-1$	$e\left(\frac{1}{6}\right)$

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 $

$2$	0.823719	−	2.70582i	0.291229	−	0.956654i
$2$	0.823719	−	2.70582i	0.291229	−	0.956654i
$3$	2.72340	−	4.42528i	0.524118	−	0.851645i
$3$	2.72340	−	4.42528i	0.524118	−	0.851645i
$4$	−6.64298	−	4.45768i	−0.830372	−	0.557210i
$5$	−4.71466	+	2.72201i	−0.421692	+	0.243464i	−0.695801	−	0.718234i	$-0.744951\pi$
$5$	−4.71466	+	2.72201i	−0.421692	+	0.243464i	0.274109	+	0.961699i	$0.411617\pi$
$6$	−9.73072	−	11.0142i	−0.662091	−	0.749423i
$7$	20.9358	+	12.0873i	1.13043	+	0.652651i	0.944042	−	0.329826i	$-0.106990\pi$
$7$	20.9358	+	12.0873i	1.13043	+	0.652651i	0.186383	+	0.982477i	$0.440323\pi$
$8$	−17.5336	+	14.3029i	−0.774885	+	0.632103i
$9$	−12.1662	−	24.1036i	−0.450600	−	0.892726i
$10$	3.48173	+	14.9992i	0.110102	+	0.474317i
$11$	25.3999	−	43.9939i	0.696214	−	1.20588i	−0.273556	−	0.961856i	$-0.588200\pi$
$11$	25.3999	−	43.9939i	0.696214	−	1.20588i	0.969770	−	0.244022i	$-0.0784669\pi$
$12$	−37.8179	+	17.2570i	−0.909758	+	0.415139i
$13$	25.0883	+	43.4542i	0.535249	+	0.927078i	0.999151	+	0.0411921i	$0.0131156\pi$
$13$	25.0883	+	43.4542i	0.535249	+	0.927078i	−0.463902	+	0.885886i	$0.653551\pi$
$14$	49.9512	−	46.6920i	0.953573	−	0.891355i
$15$	−0.794244	+	28.2768i	−0.0136715	+	0.486736i
$16$	24.2582	+	59.2245i	0.379035	+	0.925382i
$17$			51.7146i			0.737801i	0.929469	+	0.368901i	$0.120266\pi$
$17$			51.7146i			0.737801i	−0.929469	+	0.368901i	$0.879734\pi$
$18$	−75.2416	+	13.0650i	−0.985257	+	0.171081i
$19$			27.9305i			0.337247i	0.985681	+	0.168624i	$0.0539322\pi$
$19$			27.9305i			0.337247i	−0.985681	+	0.168624i	$0.946068\pi$
$20$	43.4533	+	2.93419i	0.485822	+	0.0328052i
$21$	110.506	−	59.7282i	1.14830	−	0.620655i
$22$	−98.1174	−	104.966i	−0.950850	−	1.01722i
$23$	−3.93548	−	6.81645i	−0.0356785	−	0.0617969i	0.847635	−	0.530580i	$-0.178026\pi$
$23$	−3.93548	−	6.81645i	−0.0356785	−	0.0617969i	−0.883313	+	0.468783i	$0.844693\pi$
$24$	15.5431	+	116.544i	0.132196	+	0.991224i
$25$	−47.6813	+	82.5864i	−0.381450	+	0.660691i
$26$	138.245	−	32.0905i	1.04277	−	0.242056i
$27$	−139.799	−	11.8049i	−0.996454	−	0.0841427i
$28$	−85.1946	−	173.620i	−0.575010	−	1.17183i
$29$	−212.788	−	122.853i	−1.36254	−	0.786665i	−0.372581	−	0.928000i	$-0.621527\pi$
$29$	−212.788	−	122.853i	−1.36254	−	0.786665i	−0.989962	+	0.141335i	$0.954861\pi$
$30$	75.8579	+	25.4412i	0.461657	+	0.154830i
$31$	−51.4009	+	29.6763i	−0.297802	+	0.171936i	−0.641455	−	0.767161i	$-0.721669\pi$
$31$	−51.4009	+	29.6763i	−0.297802	+	0.171936i	0.343653	+	0.939097i	$0.388336\pi$
$32$	180.233	−	16.8542i	0.995656	−	0.0931073i
$33$	−125.511	−	232.215i	−0.662082	−	1.22495i
$34$	139.931	+	42.5982i	0.705820	+	0.214869i
$35$	−131.607			−0.635589
$36$	−26.6263	+	214.353i	−0.123270	+	0.992373i
$37$	295.334			1.31223			0.656116	−	0.754660i	$-0.272198\pi$
$37$	295.334			1.31223			0.656116	+	0.754660i	$0.272198\pi$
$38$	75.5750	+	23.0069i	0.322629	+	0.0982160i
$39$	260.622	+	7.32039i	1.07008	+	0.0300564i
$40$	43.7327	−	115.160i	0.172868	−	0.455210i
$41$	−146.833	+	84.7741i	−0.559304	+	0.322915i	−0.752866	−	0.658173i	$-0.771329\pi$
$41$	−146.833	+	84.7741i	−0.559304	+	0.322915i	0.193562	+	0.981088i	$0.437996\pi$
$42$	−70.5881	−	348.209i	−0.259333	−	1.27928i
$43$	−284.968	−	164.526i	−1.01063	−	0.583488i	−0.0992550	−	0.995062i	$-0.531646\pi$
$43$	−284.968	−	164.526i	−1.01063	−	0.583488i	−0.911376	+	0.411574i	$0.864979\pi$
$44$	−364.841	+	179.026i	−1.25004	+	0.613390i
$45$	122.970	+	80.5238i	0.407361	+	0.266751i
$46$	−21.6859	+	5.03388i	−0.0695088	+	0.0161349i
$47$	−47.9742	+	83.0938i	−0.148888	+	0.257882i	−0.930817	−	0.365486i	$-0.880903\pi$
$47$	−47.9742	+	83.0938i	−0.148888	+	0.257882i	0.781928	+	0.623368i	$0.214236\pi$
$48$	328.150	+	53.9424i	0.986757	+	0.162206i
$49$	120.704	+	209.066i	0.351908	+	0.609522i
$50$	184.188	+	197.045i	0.520964	+	0.557328i
$51$	228.851	+	140.839i	0.628345	+	0.386695i
$52$	27.0439	−	400.500i	0.0721213	−	1.06807i
$53$			300.751i			0.779459i	0.920929	+	0.389729i	$0.127431\pi$
$53$			300.751i			0.779459i	−0.920929	+	0.389729i	$0.872569\pi$
$54$	−147.097	+	368.547i	−0.370691	+	0.928756i
$55$			276.555i			0.678013i
$56$	−539.963	+	87.5075i	−1.28849	+	0.208816i
$57$	123.600	+	76.0659i	0.287215	+	0.176757i
$58$	−507.697	+	474.571i	−1.14938	+	1.07438i
$59$	113.273	+	196.195i	0.249947	+	0.432921i	0.963511	−	0.267669i	$-0.0862534\pi$
$59$	113.273	+	196.195i	0.249947	+	0.432921i	−0.713564	+	0.700590i	$0.752920\pi$
$60$	131.325	−	184.302i	0.282567	−	0.396554i
$61$	173.722	−	300.896i	0.364637	−	0.631570i	−0.624081	−	0.781360i	$-0.714526\pi$
$61$	173.722	−	300.896i	0.364637	−	0.631570i	0.988718	+	0.149790i	$0.0478597\pi$
$62$	37.9590	+	163.527i	0.0777548	+	0.334966i
$63$	36.6381	−	651.684i	0.0732692	−	1.30324i
$64$	102.857	−	501.562i	0.200892	−	0.979613i
$65$	−236.566	−	136.581i	−0.451421	−	0.260628i
$66$	−731.718	+	148.332i	−1.36467	+	0.276643i
$67$	904.675	−	522.314i	1.64961	−	0.952401i	0.672378	−	0.740208i	$-0.265273\pi$
$67$	904.675	−	522.314i	1.64961	−	0.952401i	0.977228	−	0.212193i	$-0.0680605\pi$
$68$	230.527	−	343.538i	0.411110	−	0.612649i
$69$	−40.8826	−	1.14832i	−0.0713288	−	0.00200349i
$70$	−108.407	+	356.105i	−0.185102	+	0.608038i
$71$	243.524			0.407057			0.203528	−	0.979069i	$-0.434759\pi$
$71$	243.524			0.407057			0.203528	+	0.979069i	$0.434759\pi$
$72$	558.068	+	248.612i	0.913458	+	0.406934i
$73$	−1094.68			−1.75510			−0.877552	−	0.479481i	$-0.840825\pi$
$73$	−1094.68			−1.75510			−0.877552	+	0.479481i	$0.840825\pi$
$74$	243.272	−	799.122i	0.382159	−	1.25535i
$75$	235.613	+	435.919i	0.362750	+	0.671141i
$76$	124.505	−	185.542i	0.187917	−	0.280041i
$77$	1063.53	−	614.031i	1.57404	−	0.908770i
$78$	234.487	−	699.168i	0.340390	−	1.01494i
$79$	−530.679	−	306.388i	−0.755773	−	0.436346i	0.0720031	−	0.997404i	$-0.477061\pi$
$79$	−530.679	−	306.388i	−0.755773	−	0.436346i	−0.827776	+	0.561059i	$0.810394\pi$
$80$	−275.579	−	213.192i	−0.385134	−	0.297945i
$81$	−432.967	+	586.498i	−0.593919	+	0.804525i
$82$	108.435	+	467.135i	0.146032	+	0.629103i
$83$	283.063	−	490.280i	0.374340	−	0.648376i	−0.615888	−	0.787834i	$-0.711203\pi$
$83$	283.063	−	490.280i	0.374340	−	0.648376i	0.990228	+	0.139458i	$0.0445360\pi$
$84$	−1000.34	−	95.8273i	−1.29935	−	0.124472i
$85$	−140.768	−	243.817i	−0.179628	−	0.311125i
$86$	−679.912	+	635.549i	−0.852521	+	0.796896i
$87$	−1123.17	+	607.068i	−1.38409	+	0.748098i
$88$	183.886	+	1134.66i	0.222754	+	1.37450i
$89$		−	212.529i		−	0.253124i	−0.991959	−	0.126562i	$-0.959606\pi$
$89$		−	212.529i		−	0.253124i	0.991959	−	0.126562i	$-0.0403943\pi$
$90$	319.176	−	266.406i	0.373823	−	0.312018i
$91$			1213.00i			1.39732i
$92$	−4.24224	+	62.8246i	−0.00480744	+	0.0711948i
$93$	−8.65911	+	308.284i	−0.00965493	+	0.343737i
$94$	185.320	+	198.256i	0.203343	+	0.217537i
$95$	−76.0272	−	131.683i	−0.0821076	−	0.142215i
$96$	416.262	−	843.482i	0.442547	−	0.896745i
$97$	234.298	−	405.817i	0.245252	−	0.424788i	−0.716951	−	0.697124i	$-0.754463\pi$
$97$	234.298	−	405.817i	0.245252	−	0.424788i	0.962202	+	0.272336i	$0.0877961\pi$
$98$	665.122	−	154.393i	0.685587	−	0.159143i
$99$	−1369.43	−	76.9903i	−1.39023	−	0.0781598i
$100$	684.889	−	336.072i	0.684889	−	0.336072i
$101$	1552.98	+	896.613i	1.52997	+	0.883330i	0.999362	+	0.0357140i	$0.0113705\pi$
$101$	1552.98	+	896.613i	1.52997	+	0.883330i	0.530610	+	0.847616i	$0.321963\pi$
$102$	569.596	−	503.220i	0.552925	−	0.488492i
$103$	119.871	−	69.2074i	0.114672	−	0.0662059i	−0.441567	−	0.897228i	$-0.645577\pi$
$103$	119.871	−	69.2074i	0.114672	−	0.0662059i	0.556239	+	0.831022i	$0.312244\pi$
$104$	−1061.41	−	403.076i	−1.00077	−	0.380046i
$105$	−358.418	+	582.397i	−0.333124	+	0.541297i
$106$	813.779	+	247.734i	0.745672	+	0.227001i
$107$	−771.292			−0.696857			−0.348428	−	0.937335i	$-0.613285\pi$
$107$	−771.292			−0.696857			−0.348428	+	0.937335i	$0.613285\pi$
$108$	876.056	+	701.596i	0.780542	+	0.625103i
$109$	−275.772			−0.242332			−0.121166	−	0.992632i	$-0.538663\pi$
$109$	−275.772			−0.242332			−0.121166	+	0.992632i	$0.538663\pi$
$110$	748.310	+	227.804i	0.648623	+	0.197457i
$111$	804.312	−	1306.93i	0.687765	−	1.11756i
$112$	−207.998	+	1533.13i	−0.175481	+	1.29345i
$113$	−542.916	+	313.453i	−0.451976	+	0.260948i	−0.708664	−	0.705546i	$-0.750702\pi$
$113$	−542.916	+	313.453i	−0.451976	+	0.260948i	0.256689	+	0.966494i	$0.417369\pi$
$114$	307.633	−	271.784i	0.252741	−	0.223288i
$115$	37.1089	+	21.4249i	0.0300907	+	0.0173729i
$116$	865.906	+	1764.65i	0.693080	+	1.41245i
$117$	742.173	−	1133.39i	0.586444	−	0.895572i
$118$	624.173	−	144.888i	0.486947	−	0.113034i
$119$	−625.088	+	1082.68i	−0.481527	+	0.834029i
$120$	−390.513	−	507.156i	−0.297074	−	0.385806i
$121$	−624.809	−	1082.20i	−0.469428	−	0.813073i
$122$	−671.073	−	717.916i	−0.498001	−	0.532762i
$123$	−24.7359	+	880.651i	−0.0181330	+	0.645575i
$124$	473.742	+	31.9895i	0.343091	+	0.0231673i
$125$		−	1199.66i		−	0.858406i
$126$	−1733.16	−	635.940i	−1.22542	−	0.449635i
$127$			71.3408i			0.0498463i	0.999689	+	0.0249231i	$0.00793410\pi$
$127$			71.3408i			0.0498463i	−0.999689	+	0.0249231i	$0.992066\pi$
$128$	−1272.41	−	691.458i	−0.878645	−	0.477475i
$129$	−1504.15	+	812.991i	−1.02662	+	0.554883i
$130$	−564.428	+	527.601i	−0.380797	+	0.355951i
$131$	−358.903	−	621.638i	−0.239370	−	0.414601i	0.721164	−	0.692765i	$-0.243608\pi$
$131$	−358.903	−	621.638i	−0.239370	−	0.414601i	−0.960534	+	0.278164i	$0.910274\pi$
$132$	−201.369	+	2102.08i	−0.132780	+	1.38608i
$133$	−337.604	+	584.747i	−0.220105	+	0.381233i
$134$	−668.093	−	2878.13i	−0.430705	−	1.85547i
$135$	691.236	−	324.877i	0.440683	−	0.207119i
$136$	−739.666	−	906.744i	−0.466366	−	0.571711i
$137$	190.925	+	110.231i	0.119065	+	0.0687420i	0.558350	−	0.829606i	$-0.311435\pi$
$137$	190.925	+	110.231i	0.119065	+	0.0687420i	−0.439285	+	0.898348i	$0.644768\pi$
$138$	−36.7829	+	109.675i	−0.0226896	+	0.0676534i
$139$	1214.70	−	701.309i	0.741222	−	0.427945i	−0.0812916	−	0.996690i	$-0.525905\pi$
$139$	1214.70	−	701.309i	0.741222	−	0.427945i	0.822513	+	0.568746i	$0.192571\pi$
$140$	874.261	+	586.661i	0.527775	+	0.354156i
$141$	237.060	+	438.597i	0.141589	+	0.261961i
$142$	200.596	−	658.934i	0.118547	−	0.389412i
$143$	2548.96			1.49059
$144$	1132.39	−	1305.25i	0.655320	−	0.755352i
$145$	1337.63			0.766099
$146$	−901.708	+	2962.01i	−0.511136	+	1.67903i
$147$	1253.90	+	35.2198i	0.703538	+	0.0197611i
$148$	−1961.90	−	1316.50i	−1.08964	−	0.731188i
$149$	−1289.36	+	744.413i	−0.708917	+	0.409293i	−0.810660	−	0.585517i	$-0.800891\pi$
$149$	−1289.36	+	744.413i	−0.708917	+	0.409293i	0.101743	+	0.994811i	$0.467558\pi$
$150$	1373.60	−	278.453i	0.747692	−	0.151570i
$151$	−1704.17	−	983.903i	−0.918433	−	0.530257i	−0.0352979	−	0.999377i	$-0.511238\pi$
$151$	−1704.17	−	983.903i	−0.918433	−	0.530257i	−0.883135	+	0.469120i	$0.844571\pi$
$152$	−399.486	−	489.723i	−0.213175	−	0.261328i
$153$	1246.51	−	629.169i	0.658654	−	0.332453i
$154$	−785.408	−	3383.52i	−0.410974	−	1.77047i
$155$	161.559	−	279.828i	0.0837206	−	0.145008i
$156$	−1698.68	−	1210.40i	−0.871813	−	0.621215i
$157$	564.122	+	977.088i	0.286763	+	0.496689i	0.973035	−	0.230656i	$-0.0740874\pi$
$157$	564.122	+	977.088i	0.286763	+	0.496689i	−0.686272	+	0.727345i	$0.740754\pi$
$158$	−1266.16	+	1183.55i	−0.637534	+	0.595937i
$159$	1330.91	+	819.065i	0.663823	+	0.408529i
$160$	−803.861	+	570.059i	−0.397192	+	0.281669i
$161$		−	190.277i		−	0.0931424i
$162$	1230.32	+	1654.64i	0.596685	+	0.802476i
$163$		−	1940.05i		−	0.932250i	−0.884719	−	0.466125i	$-0.845650\pi$
$163$		−	1940.05i		−	0.932250i	0.884719	−	0.466125i	$-0.154350\pi$
$164$	1353.30	+	91.3821i	0.644362	+	0.0435106i
$165$	1223.83	+	753.170i	0.577427	+	0.355359i
$166$	−1093.45	−	1169.77i	−0.511252	−	0.546939i
$167$	1242.52	+	2152.11i	0.575743	+	0.997217i	0.995960	+	0.0897933i	$0.0286206\pi$
$167$	1242.52	+	2152.11i	0.575743	+	0.997217i	−0.420217	+	0.907424i	$0.638046\pi$
$168$	−1083.29	+	2627.80i	−0.497485	+	1.20678i
$169$	−160.344	+	277.723i	−0.0729830	+	0.126410i
$170$	−775.678	+	180.056i	−0.349952	+	0.0812334i
$171$	673.226	−	339.808i	0.301069	−	0.151964i
$172$	1159.63	+	2363.24i	0.514075	+	1.04765i
$173$	−2492.67	−	1439.15i	−1.09546	−	0.632464i	−0.160435	−	0.987046i	$-0.551290\pi$
$173$	−2492.67	−	1439.15i	−1.09546	−	0.632464i	−0.935025	+	0.354583i	$0.884623\pi$
$174$	717.447	+	3539.15i	0.312583	+	1.54197i
$175$	−1996.49	+	1152.67i	−0.862402	+	0.497908i
$176$	3221.67	+	437.081i	1.37979	+	0.187194i
$177$	1176.70	+	33.0514i	0.499697	+	0.0140356i
$178$	−575.067	−	175.064i	−0.242152	−	0.0737170i
$179$	−2965.78			−1.23840			−0.619198	−	0.785235i	$-0.712542\pi$
$179$	−2965.78			−1.23840			−0.619198	+	0.785235i	$0.712542\pi$
$180$	−457.936	−	1083.08i	−0.189625	−	0.448488i
$181$	1250.55			0.513551			0.256776	−	0.966471i	$-0.417340\pi$
$181$	1250.55			0.513551			0.256776	+	0.966471i	$0.417340\pi$
$182$	3282.15	+	999.167i	1.33675	+	0.406941i
$183$	−858.433	−	1588.23i	−0.346761	−	0.641559i
$184$	166.498	+	63.2286i	0.0667087	+	0.0253330i
$185$	−1392.40	+	803.902i	−0.553358	+	0.319482i
$186$	827.029	+	277.369i	0.326025	+	0.109342i
$187$	2275.12	+	1313.54i	0.889698	+	0.513668i
$188$	689.097	−	338.136i	0.267327	−	0.131176i
$189$	−2784.10	−	1936.93i	−1.07150	−	0.745454i
$190$	−418.936	+	97.2465i	−0.159962	+	0.0371316i
$191$	−387.763	+	671.626i	−0.146898	+	0.254435i	−0.930080	−	0.367358i	$-0.880262\pi$
$191$	−387.763	+	671.626i	−0.146898	+	0.254435i	0.783181	+	0.621793i	$0.213596\pi$
$192$	−1939.43	−	1821.12i	−0.728992	−	0.684522i
$193$	2185.71	+	3785.76i	0.815185	+	1.41194i	0.909195	+	0.416370i	$0.136698\pi$
$193$	2185.71	+	3785.76i	0.815185	+	1.41194i	−0.0940101	+	0.995571i	$0.529969\pi$
$194$	−905.073	−	968.249i	−0.334951	−	0.358331i
$195$	−1248.67	+	674.904i	−0.458561	+	0.247851i
$196$	130.113	−	1926.88i	0.0474173	−	0.702216i
$197$			1648.60i			0.596233i	0.954530	+	0.298116i	$0.0963584\pi$
$197$			1648.60i			0.596233i	−0.954530	+	0.298116i	$0.903642\pi$
$198$	−1336.35	+	3642.02i	−0.479647	+	1.30721i
$199$			2946.42i			1.04958i	0.851232	+	0.524790i	$0.175856\pi$
$199$			2946.42i			1.04958i	−0.851232	+	0.524790i	$0.824144\pi$
$200$	−345.195	−	2130.02i	−0.122045	−	0.753075i
$201$	152.404	−	5425.91i	0.0534812	−	1.90405i
$202$	3705.30	−	3463.53i	1.29061	−	1.20640i
$203$	−2969.92	−	5144.05i	−1.02684	−	1.77853i
$204$	−892.437	−	1955.74i	−0.306290	−	0.671221i
$205$	461.513	−	799.363i	0.157236	−	0.272341i
$206$	−88.5233	−	381.356i	−0.0299403	−	0.128982i
$207$	−116.421	+	177.790i	−0.0390910	+	0.0596968i
$208$	−1964.95	+	2539.96i	−0.655024	+	0.846705i
$209$	1228.77	+	709.432i	0.406679	+	0.234796i
$210$	1280.63	+	1449.55i	0.420818	+	0.476325i
$211$	−477.089	+	275.447i	−0.155659	+	0.0898700i	−0.575806	−	0.817586i	$-0.695312\pi$
$211$	−477.089	+	275.447i	−0.155659	+	0.0898700i	0.420147	+	0.907456i	$0.361979\pi$
$212$	1340.65	−	1997.88i	0.434322	−	0.647241i
$213$	663.214	−	1077.66i	0.213346	−	0.346668i
$214$	−635.328	+	2086.98i	−0.202945	+	0.666650i
$215$	1791.37			0.568234
$216$	2620.02	−	1792.54i	0.825323	−	0.564660i
$217$	−1434.82			−0.448857
$218$	−227.159	+	746.192i	−0.0705741	+	0.231828i
$219$	−2981.25	+	4844.27i	−0.919882	+	1.49473i
$220$	1232.79	−	1837.15i	0.377795	−	0.563003i
$221$	−2247.21	+	1297.43i	−0.684000	+	0.394907i
$222$	−2873.81	−	3252.87i	−0.868818	−	0.983417i
$223$	−1564.82	−	903.449i	−0.469902	−	0.271298i	0.246297	−	0.969194i	$-0.420786\pi$
$223$	−1564.82	−	903.449i	−0.469902	−	0.271298i	−0.716199	+	0.697897i	$0.754120\pi$
$224$	3977.04	+	1825.67i	1.18628	+	0.544565i
$225$	2570.73	+	144.528i	0.761698	+	0.0428231i
$226$	400.938	+	1727.23i	0.118009	+	0.508380i
$227$	752.796	−	1303.88i	0.220109	−	0.381241i	−0.734732	−	0.678358i	$-0.762692\pi$
$227$	752.796	−	1303.88i	0.220109	−	0.381241i	0.954841	+	0.297117i	$0.0960252\pi$
$228$	−481.996	−	1056.27i	−0.140004	−	0.306813i
$229$	−767.015	−	1328.51i	−0.221335	−	0.383364i	0.733878	−	0.679281i	$-0.237708\pi$
$229$	−767.015	−	1328.51i	−0.221335	−	0.383364i	−0.955214	+	0.295917i	$0.904375\pi$
$230$	88.5392	−	82.7622i	0.0253831	−	0.0237269i
$231$	179.165	−	6378.68i	0.0510312	−	1.81682i
$232$	5488.10	−	889.413i	1.55307	−	0.251693i
$233$		−	1257.04i		−	0.353440i	−0.984261	−	0.176720i	$-0.943451\pi$
$233$		−	1257.04i		−	0.353440i	0.984261	−	0.176720i	$-0.0565487\pi$
$234$	−2455.41	−	2941.79i	−0.685963	−	0.821840i
$235$		−	522.346i		−	0.144996i
$236$	122.102	−	1808.25i	0.0336787	−	0.498759i
$237$	−2801.10	+	1513.99i	−0.767726	+	0.414954i
$238$	2414.66	+	2583.21i	0.657643	+	0.703548i
$239$	916.982	+	1588.26i	0.248178	+	0.429858i	0.963020	−	0.269428i	$-0.0868347\pi$
$239$	916.982	+	1588.26i	0.248178	+	0.429858i	−0.714842	+	0.699286i	$0.753501\pi$
$240$	−1693.95	+	638.907i	−0.455599	+	0.171839i
$241$	−358.771	+	621.410i	−0.0958941	+	0.166094i	−0.909981	−	0.414649i	$-0.863904\pi$
$241$	−358.771	+	621.410i	−0.0958941	+	0.166094i	0.814087	+	0.580743i	$0.197238\pi$
$242$	−3442.91	+	799.194i	−0.914540	+	0.212290i
$243$	1416.28	+	3513.27i	0.373886	+	0.927475i
$244$	−2495.33	+	1224.45i	−0.654701	+	0.321259i
$245$	−1138.16	−	657.117i	−0.296794	−	0.171354i
$246$	2362.51	+	792.340i	0.612310	+	0.205357i
$247$	−1213.70	+	700.728i	−0.312655	+	0.180511i
$248$	476.788	−	1255.51i	0.122081	−	0.321472i
$249$	−1398.73	−	2587.86i	−0.355988	−	0.658630i
$250$	−3246.07	−	988.182i	−0.821198	−	0.249992i
$251$	1053.84			0.265010			0.132505	−	0.991182i	$-0.457698\pi$
$251$	1053.84			0.265010			0.132505	+	0.991182i	$0.457698\pi$
$252$	−3148.38	+	4165.80i	−0.787021	+	1.04135i
$253$	−399.843			−0.0993594
$254$	193.036	+	58.7648i	0.0476856	+	0.0145167i
$255$	−1462.32	−	41.0740i	−0.359115	−	0.0100869i
$256$	−2919.08	+	2873.36i	−0.712665	+	0.701504i
$257$	5985.55	−	3455.76i	1.45280	−	0.838772i	0.454157	−	0.890922i	$-0.349941\pi$
$257$	5985.55	−	3455.76i	1.45280	−	0.838772i	0.998639	+	0.0521496i	$0.0166073\pi$
$258$	960.811	+	4739.65i	0.231851	+	1.14371i
$259$	6183.04	+	3569.78i	1.48338	+	0.856430i
$260$	962.665	+	1961.84i	0.229623	+	0.467954i
$261$	−372.384	+	6623.62i	−0.0883141	+	1.57085i
$262$	−1977.68	+	459.073i	−0.466341	+	0.108251i
$263$	1325.23	−	2295.36i	0.310712	−	0.538168i	−0.667805	−	0.744336i	$-0.732766\pi$
$263$	1325.23	−	2295.36i	0.310712	−	0.538168i	0.978517	+	0.206168i	$0.0660993\pi$
$264$	5522.00	+	2276.40i	1.28733	+	0.530691i
$265$	−818.648	−	1417.94i	−0.189770	−	0.328692i
$266$	1304.13	+	1395.16i	0.300607	+	0.321590i
$267$	−940.502	−	578.802i	−0.215572	−	0.132667i
$268$	−8338.04	−	563.027i	−1.90047	−	0.128330i
$269$			2386.16i			0.540843i	0.962742	+	0.270422i	$0.0871631\pi$
$269$			2386.16i			0.540843i	−0.962742	+	0.270422i	$0.912837\pi$
$270$	−309.677	−	2137.97i	−0.0698013	−	0.481899i
$271$		−	4287.45i		−	0.961048i	−0.876982	−	0.480524i	$-0.840446\pi$
$271$		−	4287.45i		−	0.961048i	0.876982	−	0.480524i	$-0.159554\pi$
$272$	−3062.77	+	1254.50i	−0.682748	+	0.279652i
$273$	5367.84	+	3303.47i	1.19002	+	0.732363i
$274$	455.534	−	425.811i	0.100437	−	0.0938839i
$275$	2422.20	+	4195.37i	0.531142	+	0.919965i
$276$	266.463	+	189.870i	0.0581130	+	0.0414087i
$277$	−2416.58	+	4185.64i	−0.524181	+	0.907909i	0.475422	+	0.879758i	$0.342295\pi$
$277$	−2416.58	+	4185.64i	−0.524181	+	0.907909i	−0.999604	+	0.0281511i	$0.991038\pi$
$278$	−897.046	−	3864.46i	−0.193530	−	0.833722i
$279$	1340.66	+	877.898i	0.287682	+	0.188381i
$280$	2307.55	−	1882.35i	0.492508	−	0.401758i
$281$	1501.29	+	866.770i	0.318717	+	0.184011i	0.650821	−	0.759232i	$-0.274425\pi$
$281$	1501.29	+	866.770i	0.318717	+	0.184011i	−0.332104	+	0.943243i	$0.607758\pi$
$282$	1382.04	−	280.163i	0.291841	−	0.0591612i
$283$	3227.63	−	1863.47i	0.677960	−	0.391420i	−0.121126	−	0.992637i	$-0.538650\pi$
$283$	3227.63	−	1863.47i	0.677960	−	0.391420i	0.799086	+	0.601217i	$0.205317\pi$
$284$	−1617.73	−	1085.55i	−0.338009	−	0.226816i
$285$	−789.786	−	22.1836i	−0.164150	−	0.00461068i
$286$	2099.62	−	6897.03i	0.434103	−	1.42598i
$287$	−4098.75			−0.843003
$288$	−2599.00	−	4139.21i	−0.531762	−	0.846894i
$289$	2238.61			0.455649
$290$	1101.83	−	3619.40i	0.223110	−	0.732891i
$291$	−1157.76	−	2142.04i	−0.233228	−	0.431507i
$292$	7271.93	+	4879.73i	1.45739	+	0.977961i
$293$	5604.61	−	3235.82i	1.11749	−	0.645183i	0.176731	−	0.984259i	$-0.443448\pi$
$293$	5604.61	−	3235.82i	1.11749	−	0.645183i	0.940759	+	0.339076i	$0.110114\pi$
$294$	1128.16	−	3363.83i	0.223795	−	0.667287i
$295$	−1068.09	−	616.661i	−0.210802	−	0.121706i
$296$	−5178.28	+	4224.12i	−1.01683	+	0.829466i
$297$	−4070.21	+	5850.44i	−0.795211	+	1.14302i
$298$	952.180	+	4101.97i	0.185095	+	0.797386i
$299$	197.469	−	342.026i	0.0381937	−	0.0661534i
$300$	378.015	−	3946.08i	0.0727490	−	0.759424i
$301$	−3977.34	−	6888.96i	−0.761629	−	1.31918i
$302$	−4066.02	+	3800.72i	−0.774746	+	0.724196i
$303$	8197.14	−	4430.53i	1.55417	−	0.840025i
$304$	−1654.17	+	677.545i	−0.312083	+	0.127828i
$305$			1891.50i			0.355104i
$306$	−675.651	−	3891.09i	−0.126224	−	0.726924i
$307$		−	7858.86i		−	1.46101i	−0.682909	−	0.730503i	$-0.739285\pi$
$307$		−	7858.86i		−	1.46101i	0.682909	−	0.730503i	$-0.260715\pi$
$308$	−9802.17	−	661.893i	−1.81341	−	0.122451i
$309$	20.1937	−	718.940i	0.00371773	−	0.132360i
$310$	−624.086	−	667.648i	−0.114341	−	0.122322i
$311$	3745.08	+	6486.66i	0.682842	+	1.18272i	0.974110	+	0.226075i	$0.0725896\pi$
$311$	3745.08	+	6486.66i	0.682842	+	1.18272i	−0.291268	+	0.956642i	$0.594077\pi$
$312$	−4674.36	+	3599.29i	−0.848184	+	0.653108i
$313$	4304.38	−	7455.41i	0.777310	−	1.34634i	−0.156176	−	0.987729i	$-0.549917\pi$
$313$	4304.38	−	7455.41i	0.777310	−	1.34634i	0.933487	−	0.358612i	$-0.116750\pi$
$314$	3108.51	−	721.570i	0.558672	−	0.129683i
$315$	1601.15	+	3172.20i	0.286396	+	0.567407i
$316$	2159.51	+	4400.92i	0.384437	+	0.783453i
$317$	−4705.42	−	2716.67i	−0.833699	−	0.481336i	0.0214185	−	0.999771i	$-0.493182\pi$
$317$	−4705.42	−	2716.67i	−0.833699	−	0.481336i	−0.855117	+	0.518434i	$0.826515\pi$
$318$	3312.54	−	2926.52i	0.584144	−	0.516073i
$319$	−10809.6	+	6240.92i	−1.89724	+	1.09537i
$320$	880.323	+	2644.67i	0.153786	+	0.462006i
$321$	−2100.54	+	3413.18i	−0.365235	+	0.593475i
$322$	−514.856	−	156.735i	−0.0891050	−	0.0271257i
$323$	−1444.41			−0.248821
$324$	5490.61	−	1966.07i	0.941463	−	0.337117i
$325$	−4784.97			−0.816684
$326$	−5249.44	−	1598.06i	−0.891840	−	0.271498i
$327$	−751.038	+	1220.37i	−0.127011	+	0.206381i
$328$	1362.01	−	3586.53i	0.229281	−	0.603759i
$329$	−2008.75	+	1159.75i	−0.336615	+	0.194344i
$330$	3046.04	−	2691.08i	0.508119	−	0.448907i
$331$	1367.21	+	789.359i	0.227035	+	0.131079i	0.609204	−	0.793014i	$-0.291489\pi$
$331$	1367.21	+	789.359i	0.227035	+	0.131079i	−0.382168	+	0.924093i	$0.624823\pi$
$332$	−4065.89	+	1995.11i	−0.672122	+	0.329807i
$333$	−3593.09	−	7118.61i	−0.591292	−	1.17146i
$334$	6846.72	−	1589.31i	1.12166	−	0.260369i
$335$	−2843.49	+	4925.07i	−0.463751	+	0.803240i
$336$	6218.05	+	5095.76i	1.00959	+	0.827371i
$337$	−3400.38	−	5889.62i	−0.549645	−	0.952013i	−0.998299	−	0.0583070i	$-0.981430\pi$
$337$	−3400.38	−	5889.62i	−0.549645	−	0.952013i	0.448654	−	0.893706i	$-0.351904\pi$
$338$	619.393	+	662.628i	0.0996761	+	0.106634i
$339$	−91.4609	+	3256.21i	−0.0146533	+	0.521691i
$340$	−151.740	+	2247.17i	−0.0242037	+	0.358440i
$341$			3015.10i			0.478818i
$342$	−364.912	−	2101.54i	−0.0576965	−	0.332275i
$343$		−	2455.93i		−	0.386611i
$344$	7349.71	−	1191.11i	1.15195	−	0.186687i
$345$	195.873	−	105.869i	0.0305666	−	0.0165211i
$346$	−5947.34	+	5559.29i	−0.924078	+	0.863784i
$347$	−6228.10	−	10787.4i	−0.963522	−	1.66887i	−0.713535	−	0.700620i	$-0.752907\pi$
$347$	−6228.10	−	10787.4i	−0.963522	−	1.66887i	−0.249987	−	0.968249i	$-0.580427\pi$
$348$	10167.3	+	973.975i	1.56616	+	0.150030i
$349$	−910.729	+	1577.43i	−0.139685	+	0.241942i	−0.927378	−	0.374127i	$-0.877942\pi$
$349$	−910.729	+	1577.43i	−0.139685	+	0.241942i	0.787692	+	0.616069i	$0.211276\pi$
$350$	1474.39	+	6351.63i	0.225169	+	0.970025i
$351$	−2994.33	−	6371.00i	−0.455344	−	0.968828i
$352$	3836.42	−	8357.25i	0.580914	−	1.26546i
$353$	6019.52	+	3475.37i	0.907611	+	0.524010i	0.879662	−	0.475600i	$-0.157769\pi$
$353$	6019.52	+	3475.37i	0.907611	+	0.524010i	0.0279495	+	0.999609i	$0.491102\pi$
$354$	1058.70	−	3156.73i	0.158953	−	0.473950i
$355$	−1148.14	+	662.877i	−0.171653	+	0.0991038i
$356$	−947.387	+	1411.83i	−0.141043	+	0.210187i
$357$	3088.82	+	5714.77i	0.457920	+	0.847220i
$358$	−2442.97	+	8024.88i	−0.360656	+	1.18472i
$359$	−318.743			−0.0468597			−0.0234298	−	0.999725i	$-0.507459\pi$
$359$	−318.743			−0.0468597			−0.0234298	+	0.999725i	$0.507459\pi$
$360$	−3307.83	+	346.944i	−0.484272	+	0.0507932i
$361$	6078.89			0.886264
$362$	1030.10	−	3383.77i	0.149561	−	0.491290i
$363$	−6490.64	−	182.310i	−0.938486	−	0.0263603i
$364$	5407.14	−	8057.90i	0.778602	−	1.16030i
$365$	5161.05	−	2979.73i	0.740114	−	0.427305i
$366$	−5004.58	+	1014.52i	−0.714736	+	0.144890i
$367$	5425.21	+	3132.25i	0.771645	+	0.445510i	0.833461	−	0.552578i	$-0.186356\pi$
$367$	5425.21	+	3132.25i	0.771645	+	0.445510i	−0.0618160	+	0.998088i	$0.519689\pi$
$368$	308.233	−	398.432i	0.0436624	−	0.0564394i
$369$	3829.76	+	2507.83i	0.540297	+	0.353800i
$370$	1028.27	+	4429.78i	0.144479	+	0.622414i
$371$	−3635.26	+	6296.45i	−0.508715	+	0.881120i
$372$	1431.75	−	2009.32i	0.199551	−	0.280050i
$373$	6066.19	+	10506.9i	0.842078	+	1.45852i	0.888135	+	0.459583i	$0.152001\pi$
$373$	6066.19	+	10506.9i	0.842078	+	1.45852i	−0.0460564	+	0.998939i	$0.514665\pi$
$374$	5428.28	−	5074.10i	0.750508	−	0.701538i
$375$	−5308.83	−	3267.15i	−0.731058	−	0.449907i
$376$	−347.316	−	2143.10i	−0.0476368	−	0.293942i
$377$		−	12328.7i		−	1.68425i
$378$	−7534.30	+	5937.81i	−1.02519	+	0.807957i
$379$			1928.72i			0.261402i	0.991422	+	0.130701i	$0.0417229\pi$
$379$			1928.72i			0.261402i	−0.991422	+	0.130701i	$0.958277\pi$
$380$	−81.9533	+	1213.67i	−0.0110635	+	0.163842i
$381$	315.703	+	194.290i	0.0424513	+	0.0261253i
$382$	1497.89	+	1602.45i	0.200625	+	0.214630i
$383$	2974.93	+	5152.73i	0.396898	+	0.687448i	0.993341	−	0.115208i	$-0.0367533\pi$
$383$	2974.93	+	5152.73i	0.396898	+	0.687448i	−0.596443	+	0.802655i	$0.703420\pi$
$384$	−6525.19	+	3747.67i	−0.867154	+	0.498040i
$385$	−3342.80	+	5789.90i	−0.442506	+	0.766443i
$386$	12044.0	−	2795.74i	1.58814	−	0.368652i
$387$	−498.700	+	8870.40i	−0.0655047	+	1.16514i
$388$	−3365.44	+	1651.40i	−0.440346	+	0.216076i
$389$	2023.11	+	1168.05i	0.263691	+	0.152242i	0.626017	−	0.779809i	$-0.284684\pi$
$389$	2023.11	+	1168.05i	0.263691	+	0.152242i	−0.362326	+	0.932051i	$0.618017\pi$
$390$	797.617	+	3934.62i	0.103561	+	0.510865i
$391$	352.510	−	203.522i	0.0455938	−	0.0263236i
$392$	−5106.63	−	1939.27i	−0.657968	−	0.249867i
$393$	−3728.36	−	104.723i	−0.478551	−	0.0134416i
$394$	4460.82	+	1357.98i	0.570388	+	0.173640i
$395$	3335.97			0.424938
$396$	8753.90	+	6615.93i	1.11086	+	0.839553i
$397$	−6080.16			−0.768652			−0.384326	−	0.923198i	$-0.625566\pi$
$397$	−6080.16			−0.768652			−0.384326	+	0.923198i	$0.625566\pi$
$398$	7972.51	+	2427.02i	1.00408	+	0.305668i
$399$	1668.24	+	3086.49i	0.209314	+	0.387262i
$400$	−6047.80	−	820.499i	−0.755975	−	0.102562i
$401$	−11997.7	+	6926.90i	−1.49411	+	0.862626i	−0.999977	−	0.00675957i	$-0.997848\pi$
$401$	−11997.7	+	6926.90i	−1.49411	+	0.862626i	−0.494135	+	0.869385i	$0.664515\pi$
$402$	−14556.0	−	4881.80i	−1.80594	−	0.605677i
$403$	−2579.12	−	1489.05i	−0.318797	−	0.184057i
$404$	−6319.59	−	12878.9i	−0.778246	−	1.58601i
$405$	444.839	−	3943.69i	0.0545783	−	0.483860i
$406$	−16365.3	+	3798.83i	−2.00048	+	0.464367i
$407$	7501.45	−	12992.9i	0.913594	−	1.58239i
$408$	−6027.00	+	803.802i	−0.731326	+	0.0975346i
$409$	135.435	+	234.581i	0.0163737	+	0.0283601i	0.874096	−	0.485753i	$-0.161455\pi$
$409$	135.435	+	234.581i	0.0163737	+	0.0283601i	−0.857722	+	0.514113i	$0.828121\pi$
$410$	−1782.78	−	1907.22i	−0.214745	−	0.229734i
$411$	1007.77	−	544.695i	0.120948	−	0.0653719i
$412$	−1104.80	−	74.6019i	−0.132111	−	0.00892081i
$413$			5476.64i			0.652513i
$414$	385.169	+	461.464i	0.0457247	+	0.0547819i
$415$			3082.01i			0.364553i
$416$	5254.12	+	7409.03i	0.619242	+	0.873216i
$417$	204.632	−	7285.35i	0.0240309	−	0.855552i
$418$	2931.76	−	2740.47i	0.343055	−	0.320672i
$419$	−3950.75	−	6842.90i	−0.460637	−	0.797846i	0.538356	−	0.842718i	$-0.319046\pi$
$419$	−3950.75	−	6842.90i	−0.460637	−	0.797846i	−0.998993	+	0.0448712i	$0.985712\pi$
$420$	4977.10	−	2271.14i	0.578232	−	0.263858i
$421$	3331.91	−	5771.04i	0.385718	−	0.668083i	−0.606150	−	0.795350i	$-0.707287\pi$
$421$	3331.91	−	5771.04i	0.385718	−	0.668083i	0.991869	+	0.127267i	$0.0406204\pi$
$422$	352.325	+	1517.81i	0.0406420	+	0.175085i
$423$	2586.52	+	145.416i	0.297307	+	0.0167148i
$424$	−4301.60	−	5273.26i	−0.492698	−	0.603991i
$425$	−4270.92	−	2465.82i	−0.487459	−	0.281435i
$426$	−2369.67	−	2682.23i	−0.269509	−	0.305058i
$427$	7274.02	−	4199.66i	0.824390	−	0.475962i
$428$	5123.68	+	3438.17i	0.578650	+	0.388295i
$429$	6941.83	−	11279.9i	0.781246	−	1.26946i
$430$	1475.58	−	4847.13i	0.165486	−	0.543603i
$431$	14773.0			1.65102			0.825509	−	0.564388i	$-0.190888\pi$
$431$	14773.0			1.65102			0.825509	+	0.564388i	$0.190888\pi$
$432$	−2692.13	−	8565.86i	−0.299827	−	0.953994i
$433$	−2372.81			−0.263349			−0.131674	−	0.991293i	$-0.542035\pi$
$433$	−2372.81			−0.263349			−0.131674	+	0.991293i	$0.542035\pi$
$434$	−1181.89	+	3882.38i	−0.130720	+	0.429401i
$435$	3642.91	−	5919.40i	0.401526	−	0.652445i
$436$	1831.95	+	1229.30i	0.201226	+	0.135030i
$437$	190.387	−	109.920i	0.0208408	−	0.0120325i
$438$	10652.0	+	12057.1i	1.16204	+	1.31532i
$439$	2509.56	+	1448.89i	0.272835	+	0.157522i	0.630175	−	0.776453i	$-0.282983\pi$
$439$	2509.56	+	1448.89i	0.272835	+	0.157522i	−0.357340	+	0.933974i	$0.616316\pi$
$440$	−3955.53	−	4849.02i	−0.428574	−	0.525382i
$441$	3570.73	−	5452.95i	0.385566	−	0.588808i
$442$	1659.54	+	7149.28i	0.178589	+	0.769359i
$443$	3932.06	−	6810.53i	0.421711	−	0.730425i	−0.574396	−	0.818578i	$-0.694763\pi$
$443$	3932.06	−	6810.53i	0.421711	−	0.730425i	0.996107	+	0.0881526i	$0.0280963\pi$
$444$	−11168.9	+	5096.57i	−1.19381	+	0.544758i
$445$	578.508	+	1002.00i	0.0616267	+	0.106741i
$446$	−3733.55	+	3489.94i	−0.396387	+	0.370523i
$447$	−217.209	+	7733.12i	−0.0229835	+	0.818264i
$448$	8215.90	−	9257.33i	0.866439	−	0.976267i
$449$			1335.91i			0.140413i	0.997532	+	0.0702064i	$0.0223658\pi$
$449$			1335.91i			0.140413i	−0.997532	+	0.0702064i	$0.977634\pi$
$450$	2508.63	−	6836.90i	0.262795	−	0.716210i
$451$			8613.02i			0.899271i
$452$	5003.85	+	337.886i	0.520711	+	0.0351611i
$453$	−8995.18	+	4861.87i	−0.932959	+	0.504261i
$454$	−2907.98	−	3110.97i	−0.300613	−	0.321597i
$455$	−3301.79	−	5718.87i	−0.340198	−	0.589241i
$456$	−3255.12	+	434.125i	−0.334287	+	0.0445828i
$457$	−8696.49	+	15062.8i	−0.890164	+	1.54181i	−0.0504849	+	0.998725i	$0.516077\pi$
$457$	−8696.49	+	15062.8i	−0.890164	+	1.54181i	−0.839679	+	0.543084i	$0.817257\pi$
$458$	−4226.52	+	981.091i	−0.431206	+	0.100095i
$459$	610.484	−	7229.62i	0.0620806	−	0.735185i
$460$	−151.009	−	307.744i	−0.0153061	−	0.0311927i
$461$	−1933.14	−	1116.10i	−0.195304	−	0.112759i	0.399159	−	0.916882i	$-0.369302\pi$
$461$	−1933.14	−	1116.10i	−0.195304	−	0.112759i	−0.594463	+	0.804123i	$0.702635\pi$
$462$	−17112.0	−	5739.03i	−1.72321	−	0.577930i
$463$	3435.96	−	1983.75i	0.344887	−	0.199121i	−0.317544	−	0.948244i	$-0.602858\pi$
$463$	3435.96	−	1983.75i	0.344887	−	0.199121i	0.662431	+	0.749123i	$0.269525\pi$
$464$	2114.06	−	15582.5i	0.211514	−	1.55905i
$465$	−798.327	−	1477.02i	−0.0796162	−	0.147302i
$466$	−3401.33	−	1035.45i	−0.338120	−	0.102932i
$467$	−8810.21			−0.872993			−0.436497	−	0.899706i	$-0.643781\pi$
$467$	−8810.21			−0.872993			−0.436497	+	0.899706i	$0.643781\pi$
$468$	−9982.52	+	4220.71i	−0.985988	+	0.416886i
$469$	25253.4			2.48634
$470$	−1413.38	−	430.266i	−0.138711	−	0.0422270i
$471$	5860.22	+	164.603i	0.573300	+	0.0161029i
$472$	−4792.23	−	1819.88i	−0.467331	−	0.177472i
$473$	−14476.3	+	8357.89i	−1.40723	+	0.812466i
$474$	1789.26	+	8826.39i	0.173383	+	0.855294i
$475$	−2306.68	−	1331.76i	−0.222816	−	0.128643i
$476$	8978.70	−	4405.80i	0.864576	−	0.424243i
$477$	7249.18	−	3659.00i	0.695843	−	0.351224i
$478$	5052.89	−	1172.91i	0.483502	−	0.112234i
$479$	−9734.00	+	16859.8i	−0.928513	+	1.60823i	−0.142702	+	0.989766i	$0.545579\pi$
$479$	−9734.00	+	16859.8i	−0.928513	+	1.60823i	−0.785811	+	0.618466i	$0.787754\pi$
$480$	333.435	+	5109.81i	0.0317066	+	0.485895i
$481$	7409.42	+	12833.5i	0.702371	+	1.21654i
$482$	1385.90	+	1482.64i	0.130967	+	0.140109i
$483$	−842.028	−	518.200i	−0.0793243	−	0.0488176i
$484$	−673.511	+	9974.23i	−0.0632524	+	0.936723i
$485$			2551.05i			0.238840i
$486$	10672.9	−	938.251i	0.996158	−	0.0875719i
$487$			5226.26i			0.486293i	0.969990	+	0.243146i	$0.0781795\pi$
$487$			5226.26i			0.486293i	−0.969990	+	0.243146i	$0.921820\pi$
$488$	1257.69	+	7760.52i	0.116666	+	0.719882i
$489$	−8585.28	−	5283.54i	−0.793946	−	0.488609i
$490$	−2715.57	+	2538.38i	−0.250361	+	0.234025i
$491$	4793.56	+	8302.69i	0.440591	+	0.763127i	0.997733	−	0.0672904i	$-0.0214354\pi$
$491$	4793.56	+	8302.69i	0.440591	+	0.763127i	−0.557142	+	0.830417i	$0.688102\pi$
$492$	4089.98	−	5739.88i	0.374777	−	0.525963i
$493$	6353.30	−	11004.2i	0.580402	−	1.00529i
$494$	896.303	+	3861.25i	0.0816327	+	0.351672i
$495$	6665.98	−	3364.63i	0.605280	−	0.305513i
$496$	−3004.46	−	2324.29i	−0.271984	−	0.210411i
$497$	5098.37	+	2943.55i	0.460147	+	0.265666i
$498$	−8154.46	+	1653.05i	−0.733755	+	0.148745i
$499$	2085.65	−	1204.15i	0.187108	−	0.108027i	−0.403520	−	0.914971i	$-0.632213\pi$
$499$	2085.65	−	1204.15i	0.187108	−	0.108027i	0.590628	+	0.806944i	$0.298880\pi$
$500$	−5347.69	+	7969.31i	−0.478312	+	0.712797i
$501$	12907.6	+	362.550i	1.15103	+	0.0323304i
$502$	868.064	−	2851.49i	0.0771785	−	0.253523i
$503$	−17192.1			−1.52397			−0.761985	−	0.647595i	$-0.775775\pi$
$503$	−17192.1			−1.52397			−0.761985	+	0.647595i	$0.775775\pi$
$504$	8678.54	+	11950.4i	0.767010	+	1.05618i
$505$	−9762.37			−0.860237
$506$	−329.358	+	1081.91i	−0.0289363	+	0.0950525i
$507$	792.324	+	1465.92i	0.0694050	+	0.128410i
$508$	318.014	−	473.915i	0.0277748	−	0.0413909i
$509$	−2562.66	+	1479.55i	−0.223159	+	0.128841i	−0.607412	−	0.794387i	$-0.707792\pi$
$509$	−2562.66	+	1479.55i	−0.223159	+	0.128841i	0.384253	+	0.923228i	$0.374459\pi$
$510$	−1315.68	+	3922.96i	−0.114234	+	0.340611i
$511$	−22918.0	−	13231.7i	−1.98401	−	1.14547i
$512$	5370.32	+	10265.4i	0.463548	+	0.886072i
$513$	329.716	−	3904.64i	0.0283769	−	0.336051i
$514$	−4420.27	−	19042.4i	−0.379319	−	1.63410i
$515$	−376.767	+	652.579i	−0.0322375	+	0.0558370i
$516$	13616.1	+	1304.36i	1.16166	+	0.111281i
$517$	2437.08	+	4221.14i	0.207316	+	0.359083i
$518$	14752.3	−	13789.7i	1.25131	−	1.16966i
$519$	−13157.2	+	7111.41i	−1.11279	+	0.601457i
$520$	6101.36	−	988.798i	0.514543	−	0.0833878i
$521$		−	12490.4i		−	1.05032i	−0.851004	−	0.525159i	$-0.824006\pi$
$521$		−	12490.4i		−	1.05032i	0.851004	−	0.525159i	$-0.175994\pi$
$522$	17615.6	+	6463.60i	1.47704	+	0.541962i
$523$			13273.1i			1.10974i	0.831939	+	0.554868i	$0.187231\pi$
$523$			13273.1i			1.10974i	−0.831939	+	0.554868i	$0.812769\pi$
$524$	−386.878	+	5729.40i	−0.0322535	+	0.477652i
$525$	−336.333	+	11974.2i	−0.0279596	+	0.995424i
$526$	−5119.24	−	5476.57i	−0.424352	−	0.453973i
$527$	−1534.70	−	2658.17i	−0.126855	−	0.219719i
$528$	10708.1	−	13066.5i	0.882595	−	1.07698i
$529$	6052.52	−	10483.3i	0.497454	−	0.861616i
$530$	−4511.03	+	1047.13i	−0.369711	+	0.0858200i
$531$	3350.89	−	5117.23i	0.273854	−	0.418209i
$532$	4849.30	−	2379.53i	0.395195	−	0.193920i
$533$	−7367.58	−	4253.68i	−0.598734	−	0.345679i
$534$	−2340.85	+	2068.06i	−0.189697	+	0.167591i
$535$	3636.38	−	2099.47i	0.293859	−	0.169660i
$536$	−8391.65	+	22097.5i	−0.676239	+	1.78072i
$537$	−8077.00	+	13124.4i	−0.649066	+	1.05467i
$538$	6456.53	+	1965.53i	0.517400	+	0.157509i
$539$	12263.5			0.980012
$540$	−6040.07	−	923.156i	−0.481339	−	0.0735672i
$541$	−12385.8			−0.984302			−0.492151	−	0.870510i	$-0.663789\pi$
$541$	−12385.8			−0.984302			−0.492151	+	0.870510i	$0.663789\pi$
$542$	−11601.1	−	3531.65i	−0.919390	−	0.279885i
$543$	3405.75	−	5534.04i	0.269162	−	0.437363i
$544$	871.609	+	9320.67i	0.0686947	+	0.734596i
$545$	1300.17	−	750.656i	0.102190	−	0.0589992i
$546$	13360.2	−	11803.3i	1.04719	−	0.925156i
$547$	−15941.6	−	9203.89i	−1.24609	−	0.719433i	−0.275766	−	0.961225i	$-0.588932\pi$
$547$	−15941.6	−	9203.89i	−1.24609	−	0.719433i	−0.970328	+	0.241792i	$0.922265\pi$
$548$	−776.939	−	1583.34i	−0.0605642	−	0.123425i
$549$	−9366.21	−	526.574i	−0.728124	−	0.0409356i
$550$	13347.2	−	3098.24i	1.03477	−	0.240199i
$551$	3431.35	−	5943.28i	0.265300	−	0.459514i
$552$	733.245	−	564.604i	0.0565380	−	0.0435346i
$553$	−7406.78	−	12828.9i	−0.569563	−	0.986512i
$554$	9335.03	+	9986.63i	0.715898	+	0.765869i
$555$	−234.567	+	8351.11i	−0.0179402	+	0.638711i
$556$	−11195.5	−	755.975i	−0.853944	−	0.0576627i
$557$		−	13864.9i		−	1.05472i	−0.849643	−	0.527358i	$-0.823183\pi$
$557$		−	13864.9i		−	1.05472i	0.849643	−	0.527358i	$-0.176817\pi$
$558$	3479.76	−	2904.45i	0.263997	−	0.220350i
$559$		−	16510.7i		−	1.24925i
$560$	−3192.55	−	7794.35i	−0.240910	−	0.588163i
$561$	12008.9	−	6490.76i	0.903770	−	0.488485i
$562$	3581.97	−	3348.25i	0.268854	−	0.251312i
$563$	7442.77	+	12891.3i	0.557150	+	0.965012i	0.997733	+	0.0672999i	$0.0214384\pi$
$563$	7442.77	+	12891.3i	0.557150	+	0.965012i	−0.440583	+	0.897712i	$0.645228\pi$
$564$	380.337	−	3970.32i	0.0283955	−	0.296420i
$565$	1706.44	−	2955.65i	0.127063	−	0.220080i
$566$	−2383.57	−	10268.4i	−0.177012	−	0.762566i
$567$	−16153.7	+	7045.40i	−1.19646	+	0.521833i
$568$	−4269.87	+	3483.09i	−0.315422	+	0.257302i
$569$	5893.56	+	3402.65i	0.434219	+	0.250697i	0.701142	−	0.713021i	$-0.252674\pi$
$569$	5893.56	+	3402.65i	0.434219	+	0.250697i	−0.266923	+	0.963718i	$0.586007\pi$
$570$	−710.587	+	2118.75i	−0.0522161	+	0.155692i
$571$	−7163.27	+	4135.72i	−0.524998	+	0.303108i	−0.738977	−	0.673731i	$-0.764691\pi$
$571$	−7163.27	+	4135.72i	−0.524998	+	0.303108i	0.213979	+	0.976838i	$0.431357\pi$
$572$	−16932.7	−	11362.4i	−1.23775	−	0.830572i
$573$	1916.10	+	3545.07i	0.139697	+	0.258459i
$574$	−3376.22	+	11090.5i	−0.245506	+	0.806461i
$575$	750.595			0.0544382
$576$	−13340.8	+	3622.89i	−0.965048	+	0.262072i
$577$	−12153.3			−0.876863			−0.438432	−	0.898765i	$-0.644466\pi$
$577$	−12153.3			−0.876863			−0.438432	+	0.898765i	$0.644466\pi$
$578$	1843.98	−	6057.27i	0.132698	−	0.435899i
$579$	22705.6	+	637.758i	1.62973	+	0.0457760i
$580$	−8885.86	−	5962.73i	−0.636147	−	0.426878i
$581$	11852.3	−	6842.92i	0.846327	−	0.488627i
$582$	−6749.65	+	1368.27i	−0.480725	+	0.0974514i
$583$	13231.2	+	7639.04i	0.939932	+	0.542670i
$584$	19193.7	−	15657.0i	1.36000	−	1.10941i
$585$	−413.995	+	7363.76i	−0.0292591	+	0.520434i
$586$	−4138.95	−	17830.5i	−0.291772	−	1.25695i
$587$	−7165.79	+	12411.5i	−0.503856	+	0.872705i	0.496134	+	0.868246i	$0.334753\pi$
$587$	−7165.79	+	12411.5i	−0.503856	+	0.872705i	−0.999990	+	0.00445871i	$0.998581\pi$
$588$	−8172.64	−	5823.45i	−0.573187	−	0.408427i
$589$	−828.874	−	1435.65i	−0.0579850	−	0.100433i
$590$	−2548.38	+	2382.10i	−0.177822	+	0.166220i
$591$	7295.51	+	4489.79i	0.507779	+	0.312497i
$592$	7164.28	+	17491.0i	0.497382	+	1.21432i
$593$			17892.9i			1.23908i	0.784966	+	0.619539i	$0.212681\pi$
$593$			17892.9i			1.23908i	−0.784966	+	0.619539i	$0.787319\pi$
$594$	12477.6	+	15832.4i	0.861886	+	1.09362i
$595$		−	6805.99i		−	0.468938i
$596$	11883.5	+	802.438i	0.816727	+	0.0551496i
$597$	13038.8	+	8024.29i	0.893870	+	0.550104i
$598$	−762.804	−	816.049i	−0.0521628	−	0.0558039i
$599$	−5989.96	−	10374.9i	−0.408586	−	0.707692i	0.586145	−	0.810206i	$-0.300645\pi$
$599$	−5989.96	−	10374.9i	−0.408586	−	0.707692i	−0.994732	+	0.102514i	$0.967311\pi$
$600$	−10366.0	−	4273.31i	−0.705319	−	0.290762i
$601$	−1473.48	+	2552.14i	−0.100007	+	0.173218i	−0.911687	−	0.410885i	$-0.865220\pi$
$601$	−1473.48	+	2552.14i	−0.100007	+	0.173218i	0.811680	+	0.584102i	$0.198553\pi$
$602$	−21916.5	+	5087.43i	−1.48381	+	0.344432i
$603$	−23596.1	−	15451.3i	−1.59355	−	1.04349i
$604$	6934.83	+	14132.7i	0.467176	+	0.952070i
$605$	5891.53	+	3401.48i	0.395909	+	0.228578i
$606$	−5236.10	−	25829.5i	−0.350994	−	1.73144i
$607$	22272.8	−	12859.2i	1.48933	−	0.859866i	0.489406	−	0.872056i	$-0.337214\pi$
$607$	22272.8	−	12859.2i	1.48933	−	0.859866i	0.999926	+	0.0121903i	$0.00388040\pi$
$608$	470.747	+	5034.00i	0.0314002	+	0.335782i
$609$	−30852.2	−	866.580i	−2.05286	−	0.0576611i
$610$	5118.06	+	1558.06i	0.339712	+	0.103417i
$611$	−4814.36			−0.318770
$612$	−11085.1	−	1376.97i	−0.732174	−	0.0909487i
$613$	−1851.43			−0.121988			−0.0609938	−	0.998138i	$-0.519427\pi$
$613$	−1851.43			−0.121988			−0.0609938	+	0.998138i	$0.519427\pi$
$614$	−21264.7	−	6473.49i	−1.39768	−	0.425487i
$615$	−2280.52	−	4219.31i	−0.149528	−	0.276649i
$616$	−9865.20	+	25977.7i	−0.645260	+	1.69914i
$617$	17363.4	−	10024.8i	1.13294	−	0.654103i	0.188267	−	0.982118i	$-0.439713\pi$
$617$	17363.4	−	10024.8i	1.13294	−	0.654103i	0.944673	+	0.328015i	$0.106379\pi$
$618$	−1928.69	−	646.845i	−0.125539	−	0.0421035i
$619$	19210.5	+	11091.2i	1.24739	+	0.720183i	0.970589	−	0.240743i	$-0.0773911\pi$
$619$	19210.5	+	11091.2i	1.24739	+	0.720183i	0.276805	+	0.960926i	$0.410724\pi$
$620$	−2320.61	+	1138.71i	−0.150319	+	0.0737609i
$621$	469.707	+	999.388i	0.0303522	+	0.0645798i
$622$	20636.7	−	4790.34i	1.33031	−	0.308802i
$623$	2568.90	−	4449.46i	0.165202	−	0.286138i
$624$	5888.69	+	15612.8i	0.377782	+	1.00162i
$625$	−2694.67	−	4667.31i	−0.172459	−	0.298708i
$626$	−16627.4	−	17788.1i	−1.06161	−	1.13571i
$627$	6485.87	−	3505.59i	0.413111	−	0.223285i
$628$	608.094	−	9005.44i	0.0386395	−	0.572223i
$629$			15273.1i			0.968166i
$630$	9902.32	−	1719.45i	0.626219	−	0.108737i
$631$			28148.1i			1.77584i	0.459994	+	0.887922i	$0.347851\pi$
$631$			28148.1i			1.77584i	−0.459994	+	0.887922i	$0.652149\pi$
$632$	13687.0	−	2218.14i	0.861452	−	0.139609i
$633$	−80.3715	+	2861.40i	−0.00504657	+	0.179669i
$634$	−11226.8	+	10494.3i	−0.703269	+	0.657382i
$635$	−194.191	−	336.348i	−0.0121358	−	0.0210198i
$636$	−5190.06	−	11373.8i	−0.323584	−	0.709119i
$637$	−6056.53	+	10490.2i	−0.376716	+	0.652492i
$638$	7982.77	+	34389.6i	0.495362	+	2.13401i
$639$	−2962.77	−	5869.82i	−0.183420	−	0.363390i
$640$	7881.16	−	203.534i	0.486766	−	0.0125709i
$641$	6980.56	+	4030.23i	0.430134	+	0.248338i	0.699404	−	0.714727i	$-0.253449\pi$
$641$	6980.56	+	4030.23i	0.430134	+	0.248338i	−0.269270	+	0.963065i	$0.586782\pi$
$642$	7505.23	+	8495.19i	0.461383	+	0.522240i
$643$	−666.166	+	384.611i	−0.0408570	+	0.0235888i	−0.520289	−	0.853990i	$-0.674176\pi$
$643$	−666.166	+	384.611i	−0.0408570	+	0.0235888i	0.479432	+	0.877579i	$0.340843\pi$
$644$	−848.193	+	1264.00i	−0.0518998	+	0.0773428i
$645$	4878.61	−	7927.31i	0.297822	−	0.483934i
$646$	−1189.79	+	3908.33i	−0.0724639	+	0.238036i
$647$	25155.2			1.52852			0.764259	−	0.644909i	$-0.223105\pi$
$647$	25155.2			1.52852			0.764259	+	0.644909i	$0.223105\pi$
$648$	−797.112	−	16476.1i	−0.0483233	−	0.998832i
$649$	11508.5			0.696067
$650$	−3941.47	+	12947.3i	−0.237842	+	0.781283i
$651$	−3907.59	+	6349.49i	−0.235254	+	0.382267i
$652$	−8648.13	+	12887.7i	−0.519458	+	0.774114i
$653$	17852.0	−	10306.9i	1.06984	−	0.617671i	0.141701	−	0.989910i	$-0.454743\pi$
$653$	17852.0	−	10306.9i	1.06984	−	0.617671i	0.928137	+	0.372238i	$0.121410\pi$
$654$	2683.46	+	3037.42i	0.160446	+	0.181609i
$655$	3384.21	+	1953.88i	0.201881	+	0.116556i
$656$	−8582.62	−	6639.64i	−0.510815	−	0.395175i
$657$	13318.1	+	26385.7i	0.790850	+	1.56683i
$658$	1483.44	+	6390.65i	0.0878886	+	0.378622i
$659$	12082.8	−	20928.0i	0.714231	−	1.23708i	−0.249024	−	0.968497i	$-0.580110\pi$
$659$	12082.8	−	20928.0i	0.714231	−	1.23708i	0.963255	−	0.268587i	$-0.0865568\pi$
$660$	−4772.51	−	10458.8i	−0.281469	−	0.616828i
$661$	−9976.53	−	17279.9i	−0.587053	−	1.01681i	−0.994616	−	0.103629i	$-0.966955\pi$
$661$	−9976.53	−	17279.9i	−0.587053	−	1.01681i	0.407563	−	0.913177i	$-0.366379\pi$
$662$	3262.06	−	3049.22i	0.191516	−	0.179020i
$663$	−378.571	+	13478.0i	−0.0221757	+	0.789503i
$664$	2049.27	+	12645.0i	0.119770	+	0.739038i
$665$		−	3675.84i		−	0.214351i
$666$	−22221.4	+	3858.54i	−1.29289	+	0.224498i
$667$			1933.95i			0.112268i
$668$	1339.37	−	19835.2i	0.0775777	−	1.14887i
$669$	−8259.64	+	4464.31i	−0.477334	+	0.257997i
$670$	10984.1	+	11750.9i	0.633365	+	0.677575i
$671$	−8825.05	−	15285.4i	−0.507731	−	0.879416i
$672$	18910.2	−	12627.5i	1.08553	−	0.724875i
$673$	3449.60	−	5974.88i	0.197581	−	0.342221i	−0.750162	−	0.661254i	$-0.770025\pi$
$673$	3449.60	−	5974.88i	0.197581	−	0.342221i	0.947744	+	0.319033i	$0.103358\pi$
$674$	−18737.2	+	4349.43i	−1.07082	+	0.248566i
$675$	7640.70	−	10982.6i	0.435690	−	0.626252i
$676$	2303.16	−	1130.15i	0.131040	−	0.0643007i
$677$	−7812.18	−	4510.37i	−0.443496	−	0.256052i	0.261584	−	0.965181i	$-0.415755\pi$
$677$	−7812.18	−	4510.37i	−0.443496	−	0.256052i	−0.705079	+	0.709128i	$0.749089\pi$
$678$	8735.40	+	2929.68i	0.494810	+	0.165949i
$679$	9810.44	−	5664.06i	0.554477	−	0.320128i
$680$	5955.44	+	2261.61i	0.335854	+	0.127543i
$681$	−3719.88	−	6882.32i	−0.209319	−	0.387271i
$682$	8158.33	+	2483.59i	0.458062	+	0.139445i
$683$	−7388.19			−0.413911			−0.206956	−	0.978350i	$-0.566356\pi$
$683$	−7388.19			−0.413911			−0.206956	+	0.978350i	$0.566356\pi$
$684$	−5986.98	−	743.686i	−0.334675	−	0.0415724i
$685$	−1200.20			−0.0669448
$686$	−6645.30	−	2022.99i	−0.369853	−	0.112592i
$687$	−7967.91	−	223.804i	−0.442496	−	0.0124289i
$688$	2831.16	−	20868.2i	0.156885	−	1.15638i
$689$	−13068.9	+	7545.32i	−0.722620	+	0.417205i
$690$	−125.118	−	617.205i	−0.00690315	−	0.0340531i
$691$	−25972.9	−	14995.5i	−1.42989	−	0.825549i	−0.432781	−	0.901499i	$-0.642468\pi$
$691$	−25972.9	−	14995.5i	−1.42989	−	0.825549i	−0.997112	+	0.0759500i	$0.975801\pi$
$692$	10143.5	+	20671.7i	0.557224	+	1.13558i
$693$	−27739.5	−	18164.5i	−1.52054	−	0.995691i
$694$	−34319.0	+	7966.38i	−1.87713	+	0.435734i
$695$	−3817.95	+	6612.88i	−0.208378	+	0.360922i
$696$	11010.4	−	26708.6i	0.599637	−	1.45458i
$697$	−4384.06	−	7593.41i	−0.238247	−	0.412656i
$698$	3518.06	+	3763.63i	0.190775	+	0.204091i
$699$	−5562.76	−	3423.43i	−0.301006	−	0.185244i
$700$	18400.9	+	1242.52i	0.993554	+	0.0670899i
$701$			23559.3i			1.26936i	0.772774	+	0.634681i	$0.218869\pi$
$701$			23559.3i			1.26936i	−0.772774	+	0.634681i	$0.781131\pi$
$702$	−19705.3	+	2854.24i	−1.05944	+	0.153456i
$703$			8248.82i			0.442547i
$704$	−19453.1	−	17264.7i	−1.04143	−	0.924272i
$705$	−2311.53	−	1422.56i	−0.123485	−	0.0759951i
$706$	14362.1	−	13425.0i	0.765618	−	0.715663i
$707$	21675.2	+	37542.6i	1.15301	+	1.99708i
$708$	−7669.48	−	5464.92i	−0.407114	−	0.290091i
$709$	−6114.96	+	10591.4i	−0.323910	+	0.561028i	−0.981291	−	0.192530i	$-0.938331\pi$
$709$	−6114.96	+	10591.4i	−0.323910	+	0.561028i	0.657381	+	0.753558i	$0.271664\pi$
$710$	847.887	+	3652.68i	0.0448178	+	0.193074i
$711$	−928.700	+	16518.9i	−0.0489859	+	0.871315i
$712$	3039.78	+	3726.41i	0.160001	+	0.196142i
$713$	404.574	+	233.581i	0.0212502	+	0.0122688i
$714$	18007.5	−	3650.43i	0.943856	−	0.191336i
$715$	−12017.5	+	6938.30i	−0.628571	+	0.362906i
$716$	19701.6	+	13220.5i	1.02833	+	0.690046i
$717$	9525.80	+	267.562i	0.496161	+	0.0139362i
$718$	−262.555	+	862.464i	−0.0136469	+	0.0448285i
$719$	−37718.6			−1.95642			−0.978211	−	0.207613i	$-0.933431\pi$
$719$	−37718.6			−1.95642			−0.978211	+	0.207613i	$0.933431\pi$
$720$	−1785.95	+	9236.19i	−0.0924423	+	0.478073i
$721$	3346.11			0.172837
$722$	5007.29	−	16448.4i	0.258105	−	0.847848i
$723$	1772.84	+	3280.01i	0.0911929	+	0.168720i
$724$	−8307.38	−	5574.55i	−0.426438	−	0.286156i
$725$	20292.0	−	11715.6i	1.03949	−	0.600147i
$726$	−5839.76	+	17412.4i	−0.298532	+	0.890129i
$727$	7555.48	+	4362.16i	0.385443	+	0.222536i	0.680184	−	0.733041i	$-0.261900\pi$
$727$	7555.48	+	4362.16i	0.385443	+	0.222536i	−0.294741	+	0.955577i	$0.595233\pi$
$728$	−17349.3	−	21268.2i	−0.883252	−	1.08276i
$729$	19404.3	+	3300.61i	0.985840	+	0.167689i
$730$	−3811.38	−	16419.4i	−0.193241	−	0.832476i
$731$	8508.39	−	14737.0i	0.430498	−	0.745645i
$732$	−1377.26	+	14377.2i	−0.0695424	+	0.725951i
$733$	7960.97	+	13788.8i	0.401153	+	0.694817i	0.993865	−	0.110597i	$-0.0352762\pi$
$733$	7960.97	+	13788.8i	0.401153	+	0.694817i	−0.592712	+	0.805414i	$0.701943\pi$
$734$	12944.2	−	12099.6i	0.650923	−	0.608452i
$735$	−6007.59	+	3247.09i	−0.301488	+	0.162953i
$736$	−824.189	−	1162.22i	−0.0412772	−	0.0582065i
$737$		−	53066.9i		−	2.65230i
$738$	9940.39	−	8296.92i	0.495814	−	0.413840i
$739$		−	21026.0i		−	1.04662i	−0.852141	−	0.523312i	$-0.824696\pi$
$739$		−	21026.0i		−	1.04662i	0.852141	−	0.523312i	$-0.175304\pi$
$740$	12833.2	+	866.565i	0.637511	+	0.0430480i
$741$	−204.462	+	7279.31i	−0.0101364	+	0.360880i
$742$	14042.7	+	15022.9i	0.694774	+	0.743271i
$743$	−5813.11	−	10068.6i	−0.287029	−	0.497148i	0.686071	−	0.727535i	$-0.259334\pi$
$743$	−5813.11	−	10068.6i	−0.287029	−	0.497148i	−0.973099	+	0.230387i	$0.926001\pi$
$744$	−4257.51	−	5529.18i	−0.209796	−	0.272459i
$745$	4052.60	−	7019.32i	0.199297	−	0.345192i
$746$	33426.8	−	7759.27i	1.64054	−	0.380814i
$747$	−15261.3	−	858.000i	−0.747499	−	0.0420249i
$748$	−9258.24	−	18867.6i	−0.452560	−	0.922284i
$749$	−16147.6	−	9322.82i	−0.787744	−	0.454804i
$750$	−13213.3	+	11673.5i	−0.643310	+	0.568344i
$751$	6096.06	−	3519.56i	0.296203	−	0.171013i	−0.344533	−	0.938774i	$-0.611963\pi$
$751$	6096.06	−	3519.56i	0.296203	−	0.171013i	0.640736	+	0.767761i	$0.278629\pi$
$752$	−6084.95	−	825.539i	−0.295074	−	0.0400323i
$753$	2870.01	−	4663.52i	0.138897	−	0.225695i
$754$	−33359.3	−	10155.4i	−1.61124	−	0.490500i
$755$	10712.8			0.516395
$756$	9860.52	+	25277.6i	0.474370	+	1.21605i
$757$	−28354.3			−1.36137			−0.680685	−	0.732577i	$-0.738318\pi$
$757$	−28354.3			−1.36137			−0.680685	+	0.732577i	$0.738318\pi$
$758$	5218.77	+	1588.72i	0.250072	+	0.0761279i
$759$	−1088.93	+	1769.42i	−0.0520761	+	0.0846190i
$760$	3216.47	+	1221.47i	0.153518	+	0.0582994i
$761$	−20274.5	+	11705.5i	−0.965771	+	0.557588i	−0.897944	−	0.440109i	$-0.854940\pi$
$761$	−20274.5	+	11705.5i	−0.965771	+	0.557588i	−0.0678265	+	0.997697i	$0.521606\pi$
$762$	785.764	−	694.197i	0.0373559	−	0.0330028i
$763$	−5773.51	−	3333.34i	−0.273939	−	0.158158i
$764$	5569.79	−	2733.07i	0.263754	−	0.129423i
$765$	−4164.25	+	6359.33i	−0.196809	+	0.300552i
$766$	16392.9	−	3805.24i	0.773237	−	0.179490i
$767$	−5683.65	+	9844.37i	−0.267568	+	0.463441i
$768$	4765.62	+	20743.0i	0.223912	+	0.974609i
$769$	12632.8	+	21880.6i	0.592392	+	1.02605i	0.993909	+	0.110202i	$0.0351498\pi$
$769$	12632.8	+	21880.6i	0.592392	+	1.02605i	−0.401517	+	0.915852i	$0.631517\pi$
$770$	12912.9	+	13814.3i	0.604350	+	0.646535i
$771$	1008.34	−	35899.2i	0.0471005	−	1.67688i
$772$	2356.08	−	34891.9i	0.109841	−	1.62667i
$773$			31081.3i			1.44621i	0.690740	+	0.723103i	$0.257285\pi$
$773$			31081.3i			1.44621i	−0.690740	+	0.723103i	$0.742715\pi$
$774$	23591.0	+	8656.11i	1.09556	+	0.401986i
$775$		−	5660.02i		−	0.262340i
$776$	1696.24	+	10466.6i	0.0784682	+	0.484186i
$777$	32636.2	−	17639.8i	1.50684	−	0.814443i
$778$	4827.00	−	4512.05i	0.222438	−	0.207924i
$779$	−2367.78	−	4101.12i	−0.108902	−	0.188624i
$780$	11303.4	+	1082.81i	0.518881	+	0.0497062i
$781$	6185.49	−	10713.6i	0.283399	−	0.490861i
$782$	−260.325	−	1121.47i	−0.0119043	−	0.0512837i
$783$	28297.2	+	19686.6i	1.29152	+	0.898523i
$784$	−9453.75	+	12220.2i	−0.430656	+	0.556679i
$785$	−5319.29	−	3071.09i	−0.241852	−	0.139633i
$786$	−3354.48	+	10002.0i	−0.152227	+	0.453893i
$787$	−29654.1	+	17120.8i	−1.34314	+	0.775463i	−0.987267	−	0.159070i	$-0.949150\pi$
$787$	−29654.1	+	17120.8i	−1.34314	+	0.775463i	−0.355875	+	0.934534i	$0.615817\pi$
$788$	7348.92	−	10951.6i	0.332227	−	0.495095i
$789$	−6548.50	−	12115.7i	−0.295479	−	0.546680i
$790$	2747.90	−	9026.54i	0.123754	−	0.406519i
$791$	−15155.2			−0.681233
$792$	25112.3	−	18236.9i	1.12667	−	0.818205i
$793$	17433.6			0.780686
$794$	−5008.34	+	16451.9i	−0.223853	+	0.735333i
$795$	−8504.28	−	238.870i	−0.379391	−	0.0106564i
$796$	13134.2	−	19573.0i	0.584836	−	0.871542i
$797$	−15734.1	+	9084.08i	−0.699285	+	0.403732i	−0.807081	−	0.590441i	$-0.798954\pi$
$797$	−15734.1	+	9084.08i	−0.699285	+	0.403732i	0.107796	+	0.994173i	$0.465621\pi$
$798$	9725.65	−	1971.56i	0.431434	−	0.0874593i
$799$	−4297.16	−	2480.96i	−0.190266	−	0.109850i
$800$	−7201.81	+	15688.4i	−0.318278	+	0.693337i
$801$	−5122.72	+	2585.67i	−0.225971	+	0.114058i
$802$	8860.21	+	38169.6i	0.390106	+	1.68057i
$803$	−27804.8	+	48159.2i	−1.22193	+	2.11644i
$804$	−25199.4	+	35364.8i	−1.10536	+	1.55127i
$805$	517.936	+	897.092i	0.0226768	+	0.0392774i
$806$	−6153.59	+	5752.08i	−0.268922	+	0.251375i
$807$	10559.4	+	6498.47i	0.460607	+	0.283466i
$808$	−40053.5	+	6491.15i	−1.74391	+	0.282621i
$809$			24608.1i			1.06944i	0.845029	+	0.534720i	$0.179583\pi$
$809$			24608.1i			1.06944i	−0.845029	+	0.534720i	$0.820417\pi$
$810$	−10304.5	−	4452.14i	−0.446992	−	0.193126i
$811$			3293.86i			0.142618i	0.997454	+	0.0713089i	$0.0227176\pi$
$811$			3293.86i			0.142618i	−0.997454	+	0.0713089i	$0.977282\pi$
$812$	−3201.42	+	47410.8i	−0.138359	+	2.04900i
$813$	−18973.2	−	11676.4i	−0.818472	−	0.503703i
$814$	−28977.4	−	31000.1i	−1.24774	−	1.33483i
$815$	5280.85	+	9146.70i	0.226969	+	0.393123i
$816$	−2789.61	+	16970.1i	−0.119676	+	0.728030i
$817$	4595.30	−	7959.29i	0.196780	−	0.340833i
$818$	746.295	−	173.236i	0.0318993	−	0.00740470i
$819$	29237.6	−	14757.5i	1.24743	−	0.629634i
$820$	−6629.12	+	3252.88i	−0.282316	+	0.138531i
$821$	−33264.9	−	19205.5i	−1.41407	−	0.816414i	−0.418301	−	0.908308i	$-0.637374\pi$
$821$	−33264.9	−	19205.5i	−1.41407	−	0.816414i	−0.995769	+	0.0918946i	$0.970708\pi$
$822$	−643.733	−	3175.52i	−0.0273148	−	0.134743i
$823$	−531.302	+	306.747i	−0.0225031	+	0.0129922i	−0.511209	−	0.859456i	$-0.670802\pi$
$823$	−531.302	+	306.747i	−0.0225031	+	0.0129922i	0.488706	+	0.872448i	$0.337469\pi$
$824$	−1111.91	+	2927.95i	−0.0470086	+	0.123786i
$825$	25162.3	+	706.762i	1.06187	+	0.0298258i
$826$	14818.8	+	4511.21i	0.624229	+	0.190031i
$827$	19933.1			0.838140			0.419070	−	0.907954i	$-0.362356\pi$
$827$	19933.1			0.838140			0.419070	+	0.907954i	$0.362356\pi$
$828$	1565.91	−	662.083i	0.0657237	−	0.0277886i
$829$	32209.0			1.34941			0.674707	−	0.738086i	$-0.264270\pi$
$829$	32209.0			1.34941			0.674707	+	0.738086i	$0.264270\pi$
$830$	8339.37	+	2538.71i	0.348751	+	0.106168i
$831$	11941.3	+	22093.2i	0.498483	+	0.922268i
$832$	24375.5	−	8113.78i	1.01571	−	0.338094i
$833$	−10811.8	+	6242.17i	−0.449706	+	0.259638i
$834$	−19544.3	−	6554.78i	−0.811468	−	0.272150i
$835$	−11716.1	−	6764.32i	−0.485573	−	0.280346i
$836$	−5000.28	−	10190.2i	−0.206864	−	0.421574i
$837$	7536.09	−	3541.92i	0.311213	−	0.146269i
$838$	−21770.0	+	5053.41i	−0.897413	+	0.208314i
$839$	21916.3	−	37960.1i	0.901828	−	1.56201i	0.0767097	−	0.997053i	$-0.475559\pi$
$839$	21916.3	−	37960.1i	0.901828	−	1.56201i	0.825119	−	0.564959i	$-0.191108\pi$
$840$	−2045.57	−	15337.9i	−0.0840225	−	0.630011i
$841$	17991.3	+	31161.9i	0.737682	+	1.27770i
$842$	−12870.9	−	13769.3i	−0.526792	−	0.563564i
$843$	7924.31	−	4283.07i	0.323758	−	0.174990i
$844$	4397.14	+	296.918i	0.179332	+	0.0121094i
$845$		−	1745.83i		−	0.0710750i
$846$	2524.04	−	6878.89i	0.102575	−	0.279552i
$847$		−	30208.9i		−	1.22549i
$848$	−17811.8	+	7295.69i	−0.721297	+	0.295442i
$849$	543.734	−	19358.1i	0.0219799	−	0.782532i
$850$	−10190.1	+	9525.22i	−0.411197	+	0.384368i
$851$	−1162.28	−	2013.13i	−0.0468184	−	0.0810919i
$852$	−9209.59	+	4202.50i	−0.370323	+	0.168985i
$853$	−6391.08	+	11069.7i	−0.256537	+	0.444336i	−0.965312	−	0.261099i	$-0.915915\pi$
$853$	−6391.08	+	11069.7i	−0.256537	+	0.444336i	0.708775	+	0.705435i	$0.249248\pi$
$854$	−5371.79	−	23141.6i	−0.215245	−	0.927269i
$855$	−2249.07	+	3434.61i	−0.0899609	+	0.137381i
$856$	13523.6	−	11031.7i	0.539983	−	0.440485i
$857$	32179.0	+	18578.6i	1.28263	+	0.740527i	0.977329	−	0.211728i	$-0.0679092\pi$
$857$	32179.0	+	18578.6i	1.28263	+	0.740527i	0.305302	+	0.952256i	$0.401243\pi$
$858$	−24803.2	−	28074.8i	−0.986908	−	1.11708i
$859$	−7232.93	+	4175.93i	−0.287293	+	0.165869i	−0.636720	−	0.771095i	$-0.719709\pi$
$859$	−7232.93	+	4175.93i	−0.287293	+	0.165869i	0.349428	+	0.936963i	$0.386376\pi$
$860$	−11900.0	−	7985.34i	−0.471846	−	0.316626i
$861$	−11162.5	+	18138.1i	−0.441833	+	0.717939i
$862$	12168.8	−	39973.1i	0.480824	−	1.57945i
$863$	11795.5			0.465265			0.232633	−	0.972565i	$-0.425266\pi$
$863$	11795.5			0.465265			0.232633	+	0.972565i	$0.425266\pi$
$864$	−25395.3	+	228.567i	−0.999959	+	0.00900000i
$865$	15669.5			0.615929
$866$	−1954.53	+	6420.41i	−0.0766947	+	0.251934i
$867$	6096.61	−	9906.45i	0.238814	−	0.388052i
$868$	9531.49	+	6395.97i	0.372719	+	0.250108i
$869$	−26958.4	+	15564.4i	−1.05236	+	0.607580i
$870$	−13016.1	−	14733.0i	−0.507227	−	0.574132i
$871$	45393.5	+	26207.9i	1.76590	+	1.01954i
$872$	4835.29	−	3944.33i	0.187780	−	0.153179i
$873$	−12632.2	−	710.188i	−0.489730	−	0.0275329i
$874$	−140.599	−	605.697i	−0.00544145	−	0.0234416i
$875$	14500.6	−	25115.8i	0.560240	−	0.970364i
$876$	41398.5	−	18890.9i	1.59672	−	0.728612i
$877$	7828.97	+	13560.2i	0.301443	+	0.522114i	0.976463	−	0.215685i	$-0.0691984\pi$
$877$	7828.97	+	13560.2i	0.301443	+	0.522114i	−0.675020	+	0.737799i	$0.735865\pi$
$878$	5987.63	−	5596.95i	0.230151	−	0.215134i
$879$	944.166	−	33614.4i	0.0362297	−	1.28986i
$880$	−16378.8	+	6708.74i	−0.627421	+	0.256991i
$881$		−	39103.2i		−	1.49537i	−0.664054	−	0.747684i	$-0.731166\pi$
$881$		−	39103.2i		−	1.49537i	0.664054	−	0.747684i	$-0.268834\pi$
$882$	−11813.4	−	14153.5i	−0.450997	−	0.540331i
$883$			23664.8i			0.901907i	0.892547	+	0.450953i	$0.148916\pi$
$883$			23664.8i			0.901907i	−0.892547	+	0.450953i	$0.851084\pi$
$884$	20711.7	+	1398.56i	0.788020	+	0.0532112i
$885$	−5637.73	+	3047.17i	−0.214136	+	0.115740i
$886$	−15189.2	−	16249.4i	−0.575949	−	0.616152i
$887$	−22019.4	−	38138.8i	−0.833529	−	1.44371i	−0.895223	−	0.445619i	$-0.852984\pi$
$887$	−22019.4	−	38138.8i	−0.833529	−	1.44371i	0.0616939	−	0.998095i	$-0.480350\pi$
$888$	4590.39	+	34419.3i	0.173472	+	1.30072i
$889$	−862.316	+	1493.58i	−0.0325322	+	0.0563475i
$890$	3187.78	−	739.970i	0.120061	−	0.0278695i
$891$	14805.0	+	33944.9i	0.556664	+	1.27632i
$892$	6367.77	+	12977.1i	0.239023	+	0.487112i
$893$	−2320.85	−	1339.94i	−0.0869701	−	0.0502122i
$894$	20745.5	+	6957.64i	0.776101	+	0.260289i
$895$	13982.7	−	8072.89i	0.522222	−	0.301505i
$896$	−18281.1	−	29856.2i	−0.681618	−	1.11320i
$897$	−975.775	−	1805.33i	−0.0363213	−	0.0671997i
$898$	3614.73	+	1100.41i	0.134326	+	0.0408922i
$899$	14583.3			0.541024
$900$	−16433.0	−	12419.6i	−0.608631	−	0.459984i
$901$	−15553.2			−0.575086
$902$	23305.3	+	7094.70i	0.860291	+	0.261893i
$903$	−41317.5	−	1160.53i	−1.52266	−	0.0427686i
$904$	5036.02	−	13261.2i	0.185283	−	0.487900i
$905$	−5895.93	+	3404.02i	−0.216561	+	0.125031i
$906$	5745.86	+	28344.2i	0.210699	+	1.03937i
$907$	28310.7	+	16345.2i	1.03643	+	0.598384i	0.918820	−	0.394676i	$-0.129143\pi$
$907$	28310.7	+	16345.2i	1.03643	+	0.598384i	0.117610	+	0.993060i	$0.462477\pi$
$908$	−10813.1	+	5305.93i	−0.395204	+	0.193925i
$909$	2717.75	−	48340.8i	0.0991661	−	1.76387i
$910$	−18194.0	+	4223.33i	−0.662775	+	0.153848i
$911$	−12749.9	+	22083.5i	−0.463693	+	0.803140i	−0.999141	−	0.0414281i	$-0.986809\pi$
$911$	−12749.9	+	22083.5i	−0.463693	+	0.803140i	0.535448	+	0.844568i	$0.320143\pi$
$912$	−1506.64	+	9165.38i	−0.0547037	+	0.332781i
$913$	−14379.5	−	24906.1i	−0.521241	−	0.902817i
$914$	33593.7	+	35938.7i	1.21574	+	1.30060i
$915$	8370.40	+	5151.30i	0.302423	+	0.186117i
$916$	−826.802	+	12244.4i	−0.0298235	+	0.441665i
$917$		−	17352.6i		−	0.624901i
$918$	−19059.2	−	7607.04i	−0.685237	−	0.273496i
$919$		−	20221.1i		−	0.725825i	−0.931823	−	0.362912i	$-0.881782\pi$
$919$		−	20221.1i		−	0.725825i	0.931823	−	0.362912i	$-0.118218\pi$
$920$	−957.091	+	155.108i	−0.0342982	+	0.00555844i
$921$	−34777.7	−	21402.8i	−1.24426	−	0.765740i
$922$	−4612.33	+	4311.38i	−0.164749	+	0.154000i
$923$	6109.61	+	10582.2i	0.217877	+	0.377374i
$924$	−29624.3	+	41574.7i	−1.05473	+	1.48020i
$925$	−14081.9	+	24390.6i	−0.500551	+	0.866980i
$926$	−2537.42	−	10931.2i	−0.0900485	−	0.387927i
$927$	−3126.52	−	2047.32i	−0.110775	−	0.0725382i
$928$	−40422.0	−	18555.8i	−1.42987	−	0.656385i
$929$	32318.8	+	18659.3i	1.14139	+	0.658979i	0.946773	−	0.321901i	$-0.104322\pi$
$929$	32318.8	+	18659.3i	1.14139	+	0.658979i	0.194612	+	0.980880i	$0.437655\pi$
$930$	−4654.16	+	943.481i	−0.164103	+	0.0332666i
$931$	−5839.32	+	3371.33i	−0.205560	+	0.118680i
$932$	−5603.49	+	8350.50i	−0.196940	+	0.293487i
$933$	38904.6	+	1092.76i	1.36515	+	0.0383444i
$934$	−7257.13	+	23838.9i	−0.254241	+	0.835152i
$935$	−14301.9			−0.500239
$936$	3197.72	+	30487.6i	0.111667	+	1.06466i
$937$	−16237.5			−0.566121			−0.283060	−	0.959102i	$-0.591350\pi$
$937$	−16237.5			−0.566121			−0.283060	+	0.959102i	$0.591350\pi$
$938$	20801.7	−	68331.3i	0.724094	−	2.37857i
$939$	−21269.7	−	39352.2i	−0.739203	−	1.36763i
$940$	−2328.45	+	3469.93i	−0.0807932	+	0.120401i
$941$	−1785.15	+	1030.66i	−0.0618429	+	0.0357050i	−0.530603	−	0.847621i	$-0.678034\pi$
$941$	−1785.15	+	1030.66i	−0.0618429	+	0.0357050i	0.468760	+	0.883326i	$0.344701\pi$
$942$	5272.56	−	15721.1i	0.182366	−	0.543760i
$943$	1155.72	+	667.254i	0.0399102	+	0.0230422i
$944$	−8871.72	+	11467.9i	−0.305879	+	0.395389i
$945$	18398.5	+	1553.60i	0.633335	+	0.0534802i
$946$	10690.6	+	46054.9i	0.367422	+	1.58285i
$947$	−8954.48	+	15509.6i	−0.307267	+	0.532202i	−0.977763	−	0.209711i	$-0.932748\pi$
$947$	−8954.48	+	15509.6i	−0.307267	+	0.532202i	0.670497	+	0.741913i	$0.266081\pi$
$948$	25356.5	+	2429.03i	0.868715	+	0.0832185i
$949$	−27463.6	−	47568.4i	−0.939418	−	1.62712i
$950$	−5503.57	+	5144.47i	−0.187957	+	0.175693i
$951$	−24836.8	+	13424.2i	−0.846885	+	0.457739i
$952$	−4525.41	−	27923.9i	−0.154064	−	0.950651i
$953$			10905.6i			0.370689i	0.982674	+	0.185344i	$0.0593400\pi$
$953$			10905.6i			0.370689i	−0.982674	+	0.185344i	$0.940660\pi$
$954$	−3929.32	−	22629.0i	−0.133350	−	0.767967i
$955$		−	4221.99i		−	0.143058i
$956$	988.459	−	14638.4i	0.0334404	−	0.495229i
$957$	−1821.01	+	64831.9i	−0.0615098	+	2.18988i
$958$	37601.5	+	40226.2i	1.26811	+	1.35663i
$959$	2664.78	+	4615.53i	0.0897291	+	0.155415i
$960$	14100.9	+	3306.82i	0.474067	+	0.111174i
$961$	−13134.1	+	22749.0i	−0.440876	+	0.763619i
$962$	40828.4	−	9477.40i	1.36836	−	0.317634i
$963$	9383.70	+	18590.9i	0.314004	+	0.622102i
$964$	5153.35	−	2528.72i	0.172177	−	0.0844862i
$965$	−20609.8	−	11899.0i	−0.687515	−	0.396937i
$966$	−2095.75	+	1851.53i	−0.0698030	+	0.0616688i
$967$	−42102.8	+	24308.1i	−1.40014	+	0.808370i	−0.994406	−	0.105622i	$-0.966317\pi$
$967$	−42102.8	+	24308.1i	−1.40014	+	0.808370i	−0.405732	+	0.913992i	$0.632983\pi$
$968$	26433.7	+	10038.4i	0.877699	+	0.333311i
$969$	−3933.71	+	6391.93i	−0.130412	+	0.211908i
$970$	6902.70	+	2101.35i	0.228487	+	0.0695570i
$971$	24102.8			0.796596			0.398298	−	0.917256i	$-0.369601\pi$
$971$	24102.8			0.796596			0.398298	+	0.917256i	$0.369601\pi$
$972$	6252.73	−	29651.9i	0.206334	−	0.978482i
$973$	33907.7			1.11719
$974$	14141.3	+	4304.97i	0.465213	+	0.141622i
$975$	−13031.4	+	21174.8i	−0.428039	+	0.695525i
$976$	22034.6	+	2989.41i	0.722654	+	0.0980417i
$977$	21356.3	−	12330.1i	0.699333	−	0.403760i	−0.107766	−	0.994176i	$-0.534370\pi$
$977$	21356.3	−	12330.1i	0.699333	−	0.403760i	0.807099	+	0.590416i	$0.201036\pi$
$978$	−21368.2	+	18878.1i	−0.698649	+	0.617234i
$979$	−9349.99	−	5398.22i	−0.305237	−	0.176229i
$980$	4631.56	+	9438.77i	0.150969	+	0.307664i
$981$	3355.10	+	6647.11i	0.109195	+	0.216336i
$982$	26414.2	−	6131.46i	0.858361	−	0.199249i
$983$	11000.9	−	19054.2i	0.356943	−	0.618244i	−0.630505	−	0.776185i	$-0.717152\pi$
$983$	11000.9	−	19054.2i	0.356943	−	0.618244i	0.987449	+	0.157941i	$0.0504856\pi$
$984$	−12162.1	−	15794.8i	−0.394019	−	0.511708i
$985$	−4487.51	−	7772.59i	−0.145161	−	0.251427i
$986$	−24542.2	−	26255.3i	−0.792681	−	0.848012i
$987$	−338.399	+	12047.8i	−0.0109132	+	0.388536i
$988$	11186.2	+	755.348i	0.360202	+	0.0243227i
$989$			2589.96i			0.0832718i
$990$	−3613.20	−	20808.5i	−0.115995	−	0.668017i
$991$		−	21100.2i		−	0.676358i	−0.941082	−	0.338179i	$-0.890189\pi$
$991$		−	21100.2i		−	0.676358i	0.941082	−	0.338179i	$-0.109811\pi$
$992$	−8763.96	+	6214.97i	−0.280500	+	0.198917i
$993$	7216.59	−	3900.55i	0.230626	−	0.124653i
$994$	12164.3	−	11370.6i	0.388159	−	0.362832i
$995$	−8020.20	−	13891.4i	−0.255535	−	0.442600i
$996$	−2244.11	+	23426.2i	−0.0713929	+	0.745268i
$997$	−4141.70	+	7173.64i	−0.131564	+	0.227875i	−0.924280	−	0.381716i	$-0.875333\pi$
$997$	−4141.70	+	7173.64i	−0.131564	+	0.227875i	0.792716	+	0.609591i	$0.208666\pi$
$998$	−1540.23	−	6635.30i	−0.0488530	−	0.210458i
$999$	−41287.3	−	3486.38i	−1.30758	−	0.110415i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	36.4.h.b.11.8	yes	24
3.2	odd	2		108.4.h.b.35.5		24
4.3	odd	2	inner	36.4.h.b.11.3	✓	24
9.2	odd	6		324.4.b.c.323.21		24
9.4	even	3		108.4.h.b.71.10		24
9.5	odd	6	inner	36.4.h.b.23.3	yes	24
9.7	even	3		324.4.b.c.323.4		24
12.11	even	2		108.4.h.b.35.10		24
36.7	odd	6		324.4.b.c.323.22		24
36.11	even	6		324.4.b.c.323.3		24
36.23	even	6	inner	36.4.h.b.23.8	yes	24
36.31	odd	6		108.4.h.b.71.5		24

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
36.4.h.b.11.3	✓	24	4.3	odd	2	inner
36.4.h.b.11.8	yes	24	1.1	even	1	trivial
36.4.h.b.23.3	yes	24	9.5	odd	6	inner
36.4.h.b.23.8	yes	24	36.23	even	6	inner
108.4.h.b.35.5		24	3.2	odd	2
108.4.h.b.35.10		24	12.11	even	2
108.4.h.b.71.5		24	36.31	odd	6
108.4.h.b.71.10		24	9.4	even	3
324.4.b.c.323.3		24	36.11	even	6
324.4.b.c.323.4		24	9.7	even	3
324.4.b.c.323.21		24	9.2	odd	6
324.4.b.c.323.22		24	36.7	odd	6

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 36 = 2^{2} \cdot 3^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	36.h (of order \(6\), degree \(2\), minimal)

\(f(q)\)	\(=\)	\(q+(0.823719 - 2.70582i) q^{2} +(2.72340 - 4.42528i) q^{3} +(-6.64298 - 4.45768i) q^{4} +(-4.71466 + 2.72201i) q^{5} +(-9.73072 - 11.0142i) q^{6} +(20.9358 + 12.0873i) q^{7} +(-17.5336 + 14.3029i) q^{8} +(-12.1662 - 24.1036i) q^{9} +O(q^{10})\)	\(q+(0.823719 - 2.70582i) q^{2} +(2.72340 - 4.42528i) q^{3} +(-6.64298 - 4.45768i) q^{4} +(-4.71466 + 2.72201i) q^{5} +(-9.73072 - 11.0142i) q^{6} +(20.9358 + 12.0873i) q^{7} +(-17.5336 + 14.3029i) q^{8} +(-12.1662 - 24.1036i) q^{9} +(3.48173 + 14.9992i) q^{10} +(25.3999 - 43.9939i) q^{11} +(-37.8179 + 17.2570i) q^{12} +(25.0883 + 43.4542i) q^{13} +(49.9512 - 46.6920i) q^{14} +(-0.794244 + 28.2768i) q^{15} +(24.2582 + 59.2245i) q^{16} +51.7146i q^{17} +(-75.2416 + 13.0650i) q^{18} +27.9305i q^{19} +(43.4533 + 2.93419i) q^{20} +(110.506 - 59.7282i) q^{21} +(-98.1174 - 104.966i) q^{22} +(-3.93548 - 6.81645i) q^{23} +(15.5431 + 116.544i) q^{24} +(-47.6813 + 82.5864i) q^{25} +(138.245 - 32.0905i) q^{26} +(-139.799 - 11.8049i) q^{27} +(-85.1946 - 173.620i) q^{28} +(-212.788 - 122.853i) q^{29} +(75.8579 + 25.4412i) q^{30} +(-51.4009 + 29.6763i) q^{31} +(180.233 - 16.8542i) q^{32} +(-125.511 - 232.215i) q^{33} +(139.931 + 42.5982i) q^{34} -131.607 q^{35} +(-26.6263 + 214.353i) q^{36} +295.334 q^{37} +(75.5750 + 23.0069i) q^{38} +(260.622 + 7.32039i) q^{39} +(43.7327 - 115.160i) q^{40} +(-146.833 + 84.7741i) q^{41} +(-70.5881 - 348.209i) q^{42} +(-284.968 - 164.526i) q^{43} +(-364.841 + 179.026i) q^{44} +(122.970 + 80.5238i) q^{45} +(-21.6859 + 5.03388i) q^{46} +(-47.9742 + 83.0938i) q^{47} +(328.150 + 53.9424i) q^{48} +(120.704 + 209.066i) q^{49} +(184.188 + 197.045i) q^{50} +(228.851 + 140.839i) q^{51} +(27.0439 - 400.500i) q^{52} +300.751i q^{53} +(-147.097 + 368.547i) q^{54} +276.555i q^{55} +(-539.963 + 87.5075i) q^{56} +(123.600 + 76.0659i) q^{57} +(-507.697 + 474.571i) q^{58} +(113.273 + 196.195i) q^{59} +(131.325 - 184.302i) q^{60} +(173.722 - 300.896i) q^{61} +(37.9590 + 163.527i) q^{62} +(36.6381 - 651.684i) q^{63} +(102.857 - 501.562i) q^{64} +(-236.566 - 136.581i) q^{65} +(-731.718 + 148.332i) q^{66} +(904.675 - 522.314i) q^{67} +(230.527 - 343.538i) q^{68} +(-40.8826 - 1.14832i) q^{69} +(-108.407 + 356.105i) q^{70} +243.524 q^{71} +(558.068 + 248.612i) q^{72} -1094.68 q^{73} +(243.272 - 799.122i) q^{74} +(235.613 + 435.919i) q^{75} +(124.505 - 185.542i) q^{76} +(1063.53 - 614.031i) q^{77} +(234.487 - 699.168i) q^{78} +(-530.679 - 306.388i) q^{79} +(-275.579 - 213.192i) q^{80} +(-432.967 + 586.498i) q^{81} +(108.435 + 467.135i) q^{82} +(283.063 - 490.280i) q^{83} +(-1000.34 - 95.8273i) q^{84} +(-140.768 - 243.817i) q^{85} +(-679.912 + 635.549i) q^{86} +(-1123.17 + 607.068i) q^{87} +(183.886 + 1134.66i) q^{88} -212.529i q^{89} +(319.176 - 266.406i) q^{90} +1213.00i q^{91} +(-4.24224 + 62.8246i) q^{92} +(-8.65911 + 308.284i) q^{93} +(185.320 + 198.256i) q^{94} +(-76.0272 - 131.683i) q^{95} +(416.262 - 843.482i) q^{96} +(234.298 - 405.817i) q^{97} +(665.122 - 154.393i) q^{98} +(-1369.43 - 76.9903i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9}+O(q^{10}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9	\( 24 q - 12 q^{4} - 72 q^{5} + 60 q^{6} - 84 q^{9} + 96 q^{10} + 216 q^{12} - 216 q^{13} - 36 q^{14} - 72 q^{16} + 276 q^{18} - 540 q^{20} + 384 q^{21} - 192 q^{22} - 168 q^{24} + 252 q^{25} - 672 q^{28} + 576 q^{29} + 660 q^{30} + 360 q^{32} - 1236 q^{33} - 660 q^{34} + 276 q^{36} + 1248 q^{37} - 144 q^{38} + 636 q^{40} + 1116 q^{41} - 288 q^{42} - 1296 q^{45} + 960 q^{46} - 288 q^{48} + 348 q^{49} - 648 q^{50} + 132 q^{52} - 2616 q^{54} - 1692 q^{56} - 1668 q^{57} + 516 q^{58} - 192 q^{60} - 264 q^{61} + 960 q^{64} - 2592 q^{65} + 1068 q^{66} + 5688 q^{68} + 1608 q^{69} + 564 q^{70} + 4224 q^{72} - 4776 q^{73} + 5652 q^{74} - 600 q^{76} + 648 q^{77} + 3660 q^{78} + 3948 q^{81} - 4104 q^{82} - 4872 q^{84} + 720 q^{85} - 9540 q^{86} + 1956 q^{88} - 7656 q^{90} - 7416 q^{92} + 5400 q^{93} - 1188 q^{94} - 5640 q^{96} + 588 q^{97}+O(q^{100}) \) 24 * q - 12 * q^4 - 72 * q^5 + 60 * q^6 - 84 * q^9 + 96 * q^10 + 216 * q^12 - 216 * q^13 - 36 * q^14 - 72 * q^16 + 276 * q^18 - 540 * q^20 + 384 * q^21 - 192 * q^22 - 168 * q^24 + 252 * q^25 - 672 * q^28 + 576 * q^29 + 660 * q^30 + 360 * q^32 - 1236 * q^33 - 660 * q^34 + 276 * q^36 + 1248 * q^37 - 144 * q^38 + 636 * q^40 + 1116 * q^41 - 288 * q^42 - 1296 * q^45 + 960 * q^46 - 288 * q^48 + 348 * q^49 - 648 * q^50 + 132 * q^52 - 2616 * q^54 - 1692 * q^56 - 1668 * q^57 + 516 * q^58 - 192 * q^60 - 264 * q^61 + 960 * q^64 - 2592 * q^65 + 1068 * q^66 + 5688 * q^68 + 1608 * q^69 + 564 * q^70 + 4224 * q^72 - 4776 * q^73 + 5652 * q^74 - 600 * q^76 + 648 * q^77 + 3660 * q^78 + 3948 * q^81 - 4104 * q^82 - 4872 * q^84 + 720 * q^85 - 9540 * q^86 + 1956 * q^88 - 7656 * q^90 - 7416 * q^92 + 5400 * q^93 - 1188 * q^94 - 5640 * q^96 + 588 * q^97

Introduction

L-functions

Modular forms

Varieties

Fields

Representations

Groups

Database

Properties

Related objects

Downloads

Learn more