LMFDB - Embedded newform 11.4.c.a.5.1

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [11,4,Mod(3,11)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(11, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([8]))

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

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

chi := DirichletCharacter("11.3");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 11 $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	11.c (of order $5$, degree $4$, 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:	$0.649021010063$
Analytic rank:	$0$
Dimension:	$8$
Relative dimension:	$2$ over $\Q(\zeta_{5})$
Coefficient field:	8.0.29283765625.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{8} - x^{7} + 10x^{6} - 19x^{5} + 109x^{4} + 171x^{3} + 810x^{2} + 729x + 6561 $ x^8 - x^7 + 10x^6 - 19x^5 + 109x^4 + 171x^3 + 810x^2 + 729x + 6561
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 1 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			5.1
Root			$-1.09435 - 3.36805i$ of defining polynomial
Character	$\chi$	$=$	11.5
Dual form			11.4.c.a.9.1

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q+(-0.976313 - 3.00478i) q^{2} +(1.24700 + 0.906001i) q^{3} +(-1.60339 + 1.16493i) q^{4} +(-5.33576 + 16.4218i) q^{5} +(1.50487 - 4.63152i) q^{6} +(7.73807 - 5.62204i) q^{7} +(-15.3824 - 11.1760i) q^{8} +(-7.60928 - 23.4190i) q^{9} +O(q^{10})$	\(q+(-0.976313 - 3.00478i) q^{2} +(1.24700 + 0.906001i) q^{3} +(-1.60339 + 1.16493i) q^{4} +(-5.33576 + 16.4218i) q^{5} +(1.50487 - 4.63152i) q^{6} +(7.73807 - 5.62204i) q^{7} +(-15.3824 - 11.1760i) q^{8} +(-7.60928 - 23.4190i) q^{9} +54.5532 q^{10} +(-8.01537 + 35.5915i) q^{11} -3.05487 q^{12} +(-2.00292 - 6.16434i) q^{13} +(-24.4478 - 17.7624i) q^{14} +(-21.5319 + 15.6438i) q^{15} +(-23.4628 + 72.2111i) q^{16} +(29.2135 - 89.9099i) q^{17} +(-62.9398 + 45.7285i) q^{18} +(42.5672 + 30.9269i) q^{19} +(-10.5750 - 32.5464i) q^{20} +14.7430 q^{21} +(114.770 - 10.6640i) q^{22} +82.2579 q^{23} +(-9.05645 - 27.8729i) q^{24} +(-140.077 - 101.772i) q^{25} +(-16.5670 + 12.0367i) q^{26} +(24.5893 - 75.6779i) q^{27} +(-5.85788 + 18.0287i) q^{28} +(-121.265 + 88.1041i) q^{29} +(68.0281 + 49.4253i) q^{30} +(40.6007 + 124.956i) q^{31} +87.7765 q^{32} +(-42.2411 + 37.1208i) q^{33} -298.681 q^{34} +(51.0354 + 157.071i) q^{35} +(39.4822 + 28.6855i) q^{36} +(99.3085 - 72.1518i) q^{37} +(51.3696 - 158.099i) q^{38} +(3.08726 - 9.50160i) q^{39} +(265.606 - 192.974i) q^{40} +(-153.793 - 111.737i) q^{41} +(-14.3938 - 44.2994i) q^{42} -320.348 q^{43} +(-28.6099 - 66.4046i) q^{44} +425.182 q^{45} +(-80.3094 - 247.167i) q^{46} +(356.916 + 259.314i) q^{47} +(-94.6816 + 68.7902i) q^{48} +(-77.7224 + 239.205i) q^{49} +(-169.044 + 520.263i) q^{50} +(117.888 - 85.6505i) q^{51} +(10.3925 + 7.55060i) q^{52} +(-38.1858 - 117.524i) q^{53} -251.403 q^{54} +(-541.707 - 321.534i) q^{55} -181.862 q^{56} +(25.0617 + 77.1318i) q^{57} +(383.126 + 278.358i) q^{58} +(58.6475 - 42.6099i) q^{59} +(16.3001 - 50.1664i) q^{60} +(76.8425 - 236.497i) q^{61} +(335.827 - 243.993i) q^{62} +(-190.543 - 138.438i) q^{63} +(102.005 + 313.940i) q^{64} +111.916 q^{65} +(152.780 + 90.6839i) q^{66} -128.926 q^{67} +(57.8984 + 178.193i) q^{68} +(102.576 + 74.5257i) q^{69} +(422.137 - 306.700i) q^{70} +(306.810 - 944.264i) q^{71} +(-144.680 + 445.280i) q^{72} +(-418.233 + 303.864i) q^{73} +(-313.757 - 227.958i) q^{74} +(-82.4713 - 253.820i) q^{75} -104.280 q^{76} +(138.073 + 320.472i) q^{77} -31.5644 q^{78} +(177.589 + 546.562i) q^{79} +(-1060.64 - 770.603i) q^{80} +(-438.649 + 318.697i) q^{81} +(-185.596 + 571.204i) q^{82} +(58.1187 - 178.871i) q^{83} +(-23.6388 + 17.1746i) q^{84} +(1320.60 + 959.475i) q^{85} +(312.760 + 962.577i) q^{86} -231.040 q^{87} +(521.064 - 457.902i) q^{88} -42.1254 q^{89} +(-415.111 - 1277.58i) q^{90} +(-50.1549 - 36.4396i) q^{91} +(-131.892 + 95.8250i) q^{92} +(-62.5812 + 192.605i) q^{93} +(430.722 - 1325.63i) q^{94} +(-735.003 + 534.011i) q^{95} +(109.458 + 79.5257i) q^{96} +(-397.278 - 1222.70i) q^{97} +794.640 q^{98} +(894.506 - 83.1140i) q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9}+O(q^{10}) $ 8 * q - 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - 29 * q^6 - 35 * q^7 + 47 * q^8 + 31 * q^9	\( 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9} + 40 q^{10} + 67 q^{11} + 190 q^{12} - 65 q^{13} - 196 q^{14} - 121 q^{15} - 377 q^{16} - 31 q^{17} - 102 q^{18} + 148 q^{19} + 342 q^{20} + 334 q^{21} + 647 q^{22} - 12 q^{23} - 447 q^{24} - 201 q^{25} - 140 q^{26} + 72 q^{27} - 42 q^{28} - 199 q^{29} - 114 q^{30} - 361 q^{31} + 324 q^{32} - 232 q^{33} - 298 q^{34} + 237 q^{35} + 120 q^{36} + 81 q^{37} - 52 q^{38} + 365 q^{39} + 532 q^{40} - 31 q^{41} + 170 q^{42} - 650 q^{43} - 1208 q^{44} + 452 q^{45} + 1204 q^{46} + 857 q^{47} + 644 q^{48} + 1375 q^{49} - 147 q^{50} - 246 q^{51} - 590 q^{52} - 1493 q^{53} - 3100 q^{54} - 1583 q^{55} - 1560 q^{56} + 102 q^{57} + 1392 q^{58} + 676 q^{59} + 1068 q^{60} - 525 q^{61} + 2456 q^{62} - 68 q^{63} + 471 q^{64} + 1790 q^{65} + 1014 q^{66} + 86 q^{67} + 710 q^{68} - 42 q^{69} - 144 q^{70} + 1143 q^{71} + 919 q^{72} - 2155 q^{73} - 1476 q^{74} - 160 q^{75} - 242 q^{76} - 2015 q^{77} - 1340 q^{78} - 861 q^{79} - 1916 q^{80} - 26 q^{81} - 3497 q^{82} + 52 q^{83} - 84 q^{84} + 2383 q^{85} + 1061 q^{86} + 2310 q^{87} + 4543 q^{88} + 3782 q^{89} - 1682 q^{90} + 135 q^{91} - 2450 q^{92} - 2077 q^{93} + 702 q^{94} - 1317 q^{95} + 1252 q^{96} - 1344 q^{97} + 2740 q^{98} + 2099 q^{99}+O(q^{100}) \) 8 * q - 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - 29 * q^6 - 35 * q^7 + 47 * q^8 + 31 * q^9 + 40 * q^10 + 67 * q^11 + 190 * q^12 - 65 * q^13 - 196 * q^14 - 121 * q^15 - 377 * q^16 - 31 * q^17 - 102 * q^18 + 148 * q^19 + 342 * q^20 + 334 * q^21 + 647 * q^22 - 12 * q^23 - 447 * q^24 - 201 * q^25 - 140 * q^26 + 72 * q^27 - 42 * q^28 - 199 * q^29 - 114 * q^30 - 361 * q^31 + 324 * q^32 - 232 * q^33 - 298 * q^34 + 237 * q^35 + 120 * q^36 + 81 * q^37 - 52 * q^38 + 365 * q^39 + 532 * q^40 - 31 * q^41 + 170 * q^42 - 650 * q^43 - 1208 * q^44 + 452 * q^45 + 1204 * q^46 + 857 * q^47 + 644 * q^48 + 1375 * q^49 - 147 * q^50 - 246 * q^51 - 590 * q^52 - 1493 * q^53 - 3100 * q^54 - 1583 * q^55 - 1560 * q^56 + 102 * q^57 + 1392 * q^58 + 676 * q^59 + 1068 * q^60 - 525 * q^61 + 2456 * q^62 - 68 * q^63 + 471 * q^64 + 1790 * q^65 + 1014 * q^66 + 86 * q^67 + 710 * q^68 - 42 * q^69 - 144 * q^70 + 1143 * q^71 + 919 * q^72 - 2155 * q^73 - 1476 * q^74 - 160 * q^75 - 242 * q^76 - 2015 * q^77 - 1340 * q^78 - 861 * q^79 - 1916 * q^80 - 26 * q^81 - 3497 * q^82 + 52 * q^83 - 84 * q^84 + 2383 * q^85 + 1061 * q^86 + 2310 * q^87 + 4543 * q^88 + 3782 * q^89 - 1682 * q^90 + 135 * q^91 - 2450 * q^92 - 2077 * q^93 + 702 * q^94 - 1317 * q^95 + 1252 * q^96 - 1344 * q^97 + 2740 * q^98 + 2099 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/11\mathbb{Z}\right)^\times$.

$n$	$2$
$\chi(n)$	$e\left(\frac{2}{5}\right)$

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 $

$2$	−0.976313	−	3.00478i	−0.345179	−	1.06235i	−0.961488	−	0.274847i	$-0.911373\pi$
$2$	−0.976313	−	3.00478i	−0.345179	−	1.06235i	0.616309	−	0.787504i	$-0.288627\pi$
$3$	1.24700	+	0.906001i	0.239986	+	0.174360i	0.701277	−	0.712889i	$-0.252614\pi$
$3$	1.24700	+	0.906001i	0.239986	+	0.174360i	−0.461291	+	0.887249i	$0.652614\pi$
$4$	−1.60339	+	1.16493i	−0.200424	+	0.145617i
$5$	−5.33576	+	16.4218i	−0.477245	+	1.46881i	0.365661	+	0.930748i	$0.380843\pi$
$5$	−5.33576	+	16.4218i	−0.477245	+	1.46881i	−0.842906	+	0.538060i	$0.819157\pi$
$6$	1.50487	−	4.63152i	0.102393	−	0.315135i
$7$	7.73807	−	5.62204i	0.417817	−	0.303562i	−0.358942	−	0.933360i	$-0.616862\pi$
$7$	7.73807	−	5.62204i	0.417817	−	0.303562i	0.776759	+	0.629798i	$0.216862\pi$
$8$	−15.3824	−	11.1760i	−0.679811	−	0.493912i
$9$	−7.60928	−	23.4190i	−0.281825	−	0.867369i
$10$	54.5532			1.72512
$11$	−8.01537	+	35.5915i	−0.219702	+	0.975567i
$11$	−8.01537	+	35.5915i	−0.219702	+	0.975567i
$12$	−3.05487			−0.0734888
$13$	−2.00292	−	6.16434i	−0.0427314	−	0.131514i	0.927415	−	0.374034i	$-0.122026\pi$
$13$	−2.00292	−	6.16434i	−0.0427314	−	0.131514i	−0.970146	+	0.242521i	$0.922026\pi$
$14$	−24.4478	−	17.7624i	−0.466710	−	0.339085i
$15$	−21.5319	+	15.6438i	−0.370633	+	0.269281i
$16$	−23.4628	+	72.2111i	−0.366607	+	1.12830i
$17$	29.2135	−	89.9099i	0.416783	−	1.28273i	−0.493863	−	0.869540i	$-0.664415\pi$
$17$	29.2135	−	89.9099i	0.416783	−	1.28273i	0.910646	−	0.413187i	$-0.135585\pi$
$18$	−62.9398	+	45.7285i	−0.824170	+	0.598794i
$19$	42.5672	+	30.9269i	0.513978	+	0.373427i	0.814331	−	0.580401i	$-0.197104\pi$
$19$	42.5672	+	30.9269i	0.513978	+	0.373427i	−0.300353	+	0.953828i	$0.597104\pi$
$20$	−10.5750	−	32.5464i	−0.118232	−	0.363880i
$21$	14.7430			0.153199
$22$	114.770	−	10.6640i	1.11223	−	0.103344i
$23$	82.2579			0.745737			0.372868	−	0.927884i	$-0.378374\pi$
$23$	82.2579			0.745737			0.372868	+	0.927884i	$0.378374\pi$
$24$	−9.05645	−	27.8729i	−0.0770267	−	0.237064i
$25$	−140.077	−	101.772i	−1.12062	−	0.814177i
$26$	−16.5670	+	12.0367i	−0.124964	+	0.0907916i
$27$	24.5893	−	75.6779i	0.175267	−	0.539416i
$28$	−5.85788	+	18.0287i	−0.0395370	+	0.121682i
$29$	−121.265	+	88.1041i	−0.776494	+	0.564156i	−0.903925	−	0.427691i	$-0.859327\pi$
$29$	−121.265	+	88.1041i	−0.776494	+	0.564156i	0.127430	+	0.991848i	$0.459327\pi$
$30$	68.0281	+	49.4253i	0.414006	+	0.300793i
$31$	40.6007	+	124.956i	0.235229	+	0.723961i	0.997091	+	0.0762213i	$0.0242855\pi$
$31$	40.6007	+	124.956i	0.235229	+	0.723961i	−0.761862	+	0.647740i	$0.775714\pi$
$32$	87.7765			0.484902
$33$	−42.2411	+	37.1208i	−0.222825	+	0.195815i
$34$	−298.681			−1.50657
$35$	51.0354	+	157.071i	0.246473	+	0.758566i
$36$	39.4822	+	28.6855i	0.182788	+	0.132803i
$37$	99.3085	−	72.1518i	0.441249	−	0.320586i	−0.344882	−	0.938646i	$-0.612081\pi$
$37$	99.3085	−	72.1518i	0.441249	−	0.320586i	0.786131	+	0.618060i	$0.212081\pi$
$38$	51.3696	−	158.099i	0.219296	−	0.674924i
$39$	3.08726	−	9.50160i	0.0126758	−	0.0390121i
$40$	265.606	−	192.974i	1.04990	−	0.762796i
$41$	−153.793	−	111.737i	−0.585815	−	0.425619i	0.255001	−	0.966941i	$-0.417924\pi$
$41$	−153.793	−	111.737i	−0.585815	−	0.425619i	−0.840816	+	0.541321i	$0.817924\pi$
$42$	−14.3938	−	44.2994i	−0.0528811	−	0.162751i
$43$	−320.348			−1.13611			−0.568054	−	0.822991i	$-0.692304\pi$
$43$	−320.348			−1.13611			−0.568054	+	0.822991i	$0.692304\pi$
$44$	−28.6099	−	66.4046i	−0.0980253	−	0.227520i
$45$	425.182			1.40850
$46$	−80.3094	−	247.167i	−0.257413	−	0.792234i
$47$	356.916	+	259.314i	1.10769	+	0.804785i	0.982299	−	0.187322i	$-0.0599808\pi$
$47$	356.916	+	259.314i	1.10769	+	0.804785i	0.125393	+	0.992107i	$0.459981\pi$
$48$	−94.6816	+	68.7902i	−0.284711	+	0.206854i
$49$	−77.7224	+	239.205i	−0.226596	+	0.697390i
$50$	−169.044	+	520.263i	−0.478128	+	1.47153i
$51$	117.888	−	85.6505i	0.323678	−	0.235166i
$52$	10.3925	+	7.55060i	0.0277151	+	0.0201362i
$53$	−38.1858	−	117.524i	−0.0989665	−	0.304588i	0.889301	−	0.457323i	$-0.151192\pi$
$53$	−38.1858	−	117.524i	−0.0989665	−	0.304588i	−0.988267	+	0.152736i	$0.951192\pi$
$54$	−251.403			−0.633547
$55$	−541.707	−	321.534i	−1.32807	−	0.788285i
$56$	−181.862			−0.433969
$57$	25.0617	+	77.1318i	0.0582368	+	0.179234i
$58$	383.126	+	278.358i	0.867361	+	0.630175i
$59$	58.6475	−	42.6099i	0.129411	−	0.0940227i	−0.521197	−	0.853437i	$-0.674514\pi$
$59$	58.6475	−	42.6099i	0.129411	−	0.0940227i	0.650608	+	0.759414i	$0.274514\pi$
$60$	16.3001	−	50.1664i	0.0350721	−	0.107941i
$61$	76.8425	−	236.497i	0.161290	−	0.496399i	−0.837454	−	0.546508i	$-0.815957\pi$
$61$	76.8425	−	236.497i	0.161290	−	0.496399i	0.998744	+	0.0501090i	$0.0159569\pi$
$62$	335.827	−	243.993i	0.687905	−	0.499792i
$63$	−190.543	−	138.438i	−0.381051	−	0.276850i
$64$	102.005	+	313.940i	0.199229	+	0.613164i
$65$	111.916			0.213562
$66$	152.780	+	90.6839i	0.284939	+	0.169127i
$67$	−128.926			−0.235086			−0.117543	−	0.993068i	$-0.537502\pi$
$67$	−128.926			−0.235086			−0.117543	+	0.993068i	$0.537502\pi$
$68$	57.8984	+	178.193i	0.103253	+	0.317780i
$69$	102.576	+	74.5257i	0.178966	+	0.130027i
$70$	422.137	−	306.700i	0.720786	−	0.523682i
$71$	306.810	−	944.264i	0.512840	−	1.57836i	−0.274338	−	0.961633i	$-0.588459\pi$
$71$	306.810	−	944.264i	0.512840	−	1.57836i	0.787178	−	0.616726i	$-0.211541\pi$
$72$	−144.680	+	445.280i	−0.236816	+	0.728844i
$73$	−418.233	+	303.864i	−0.670554	+	0.487186i	−0.870211	−	0.492680i	$-0.836017\pi$
$73$	−418.233	+	303.864i	−0.670554	+	0.487186i	0.199657	+	0.979866i	$0.436017\pi$
$74$	−313.757	−	227.958i	−0.492885	−	0.358102i
$75$	−82.4713	−	253.820i	−0.126973	−	0.390782i
$76$	−104.280			−0.157391
$77$	138.073	+	320.472i	0.204349	+	0.474301i
$78$	−31.5644			−0.0458200
$79$	177.589	+	546.562i	0.252915	+	0.778392i	0.994233	+	0.107239i	$0.0342009\pi$
$79$	177.589	+	546.562i	0.252915	+	0.778392i	−0.741318	+	0.671154i	$0.765799\pi$
$80$	−1060.64	−	770.603i	−1.48229	−	1.07695i
$81$	−438.649	+	318.697i	−0.601714	+	0.437171i
$82$	−185.596	+	571.204i	−0.249946	+	0.769256i
$83$	58.1187	−	178.871i	0.0768597	−	0.236550i	−0.905244	−	0.424893i	$-0.860312\pi$
$83$	58.1187	−	178.871i	0.0768597	−	0.236550i	0.982103	+	0.188343i	$0.0603117\pi$
$84$	−23.6388	+	17.1746i	−0.0307048	+	0.0223084i
$85$	1320.60	+	959.475i	1.68517	+	1.22435i
$86$	312.760	+	962.577i	0.392160	+	1.20695i
$87$	−231.040			−0.284714
$88$	521.064	−	457.902i	0.631200	−	0.554688i
$89$	−42.1254			−0.0501717			−0.0250859	−	0.999685i	$-0.507986\pi$
$89$	−42.1254			−0.0501717			−0.0250859	+	0.999685i	$0.507986\pi$
$90$	−415.111	−	1277.58i	−0.486184	−	1.49632i
$91$	−50.1549	−	36.4396i	−0.0577765	−	0.0419771i
$92$	−131.892	+	95.8250i	−0.149464	+	0.108592i
$93$	−62.5812	+	192.605i	−0.0697781	+	0.214755i
$94$	430.722	−	1325.63i	0.472613	−	1.45455i
$95$	−735.003	+	534.011i	−0.793786	+	0.576719i
$96$	109.458	+	79.5257i	0.116370	+	0.0845474i
$97$	−397.278	−	1222.70i	−0.415850	−	1.27985i	−0.911488	−	0.411326i	$-0.865066\pi$
$97$	−397.278	−	1222.70i	−0.415850	−	1.27985i	0.495638	−	0.868529i	$-0.334934\pi$
$98$	794.640			0.819089
$99$	894.506	−	83.1140i	0.908094	−	0.0843765i
$100$	343.157			0.343157
$101$	81.1583	+	249.780i	0.0799560	+	0.246079i	0.983042	−	0.183380i	$-0.0587040\pi$
$101$	81.1583	+	249.780i	0.0799560	+	0.246079i	−0.903086	+	0.429460i	$0.858704\pi$
$102$	−372.457	−	270.606i	−0.361556	−	0.262686i
$103$	−309.719	+	225.024i	−0.296286	+	0.215265i	−0.725990	−	0.687705i	$-0.758618\pi$
$103$	−309.719	+	225.024i	−0.296286	+	0.215265i	0.429704	+	0.902970i	$0.358618\pi$
$104$	−38.0828	+	117.207i	−0.0359069	+	0.110510i
$105$	−78.6650	+	242.106i	−0.0731135	+	0.225020i
$106$	−315.852	+	229.480i	−0.289418	+	0.210274i
$107$	−917.382	−	666.517i	−0.828848	−	0.602193i	0.0903854	−	0.995907i	$-0.471190\pi$
$107$	−917.382	−	666.517i	−0.828848	−	0.602193i	−0.919233	+	0.393714i	$0.871190\pi$
$108$	48.7336	+	149.986i	0.0434203	+	0.133634i
$109$	1031.11			0.906078			0.453039	−	0.891491i	$-0.350340\pi$
$109$	1031.11			0.906078			0.453039	+	0.891491i	$0.350340\pi$
$110$	−437.264	+	1941.63i	−0.379014	+	1.68297i
$111$	189.208			0.161791
$112$	224.417	+	690.684i	0.189334	+	0.582710i
$113$	−251.235	−	182.533i	−0.209153	−	0.151958i	0.478278	−	0.878209i	$-0.341261\pi$
$113$	−251.235	−	182.533i	−0.209153	−	0.151958i	−0.687430	+	0.726250i	$0.741261\pi$
$114$	207.296	−	150.610i	0.170308	−	0.123736i
$115$	−438.908	+	1350.82i	−0.355899	+	1.09534i
$116$	91.8000	−	282.531i	0.0734777	−	0.226141i
$117$	−129.122	+	93.8124i	−0.102028	+	0.0741278i
$118$	−185.292	−	134.622i	−0.144555	−	0.105025i
$119$	−279.421	−	859.969i	−0.215248	−	0.662464i
$120$	506.046			0.384962
$121$	−1202.51	−	570.558i	−0.903462	−	0.428669i
$122$	−785.644			−0.583024
$123$	−90.5463	−	278.673i	−0.0663763	−	0.204285i
$124$	−210.665	−	153.057i	−0.152567	−	0.110846i
$125$	672.548	−	488.635i	0.481236	−	0.349639i
$126$	−229.946	+	707.700i	−0.162581	+	0.500373i
$127$	207.464	−	638.507i	0.144956	−	0.446129i	−0.852049	−	0.523462i	$-0.824640\pi$
$127$	207.464	−	638.507i	0.144956	−	0.446129i	0.997005	+	0.0773327i	$0.0246404\pi$
$128$	1411.83	−	1025.76i	0.974919	−	0.708320i
$129$	−399.475	−	290.236i	−0.272650	−	0.198092i
$130$	−109.266	−	336.285i	−0.0737171	−	0.226878i
$131$	2235.09			1.49069			0.745346	−	0.666677i	$-0.232284\pi$
$131$	2235.09			1.49069			0.745346	+	0.666677i	$0.232284\pi$
$132$	24.4859	−	108.727i	0.0161456	−	0.0716932i
$133$	503.260			0.328107
$134$	125.872	+	387.394i	0.0811468	+	0.249744i
$135$	1111.56	+	807.598i	0.708653	+	0.514867i
$136$	−1454.20	+	1056.54i	−0.916888	+	0.666158i
$137$	116.249	−	357.776i	0.0724948	−	0.223116i	−0.908244	−	0.418442i	$-0.862576\pi$
$137$	116.249	−	357.776i	0.0724948	−	0.223116i	0.980738	+	0.195326i	$0.0625764\pi$
$138$	123.787	−	380.979i	0.0763586	−	0.235008i
$139$	225.847	−	164.088i	0.137814	−	0.100127i	−0.516742	−	0.856141i	$-0.672856\pi$
$139$	225.847	−	164.088i	0.137814	−	0.100127i	0.654556	+	0.756013i	$0.272856\pi$
$140$	−264.807	−	192.394i	−0.159859	−	0.116144i
$141$	210.136	+	646.732i	0.125508	+	0.386274i
$142$	−3136.85			−1.85379
$143$	235.452	−	21.8773i	0.137689	−	0.0127935i
$144$	1869.64			1.08197
$145$	−799.786	−	2461.49i	−0.458059	−	1.40976i
$146$	1321.37	+	960.032i	0.749024	+	0.544198i
$147$	−313.640	+	227.873i	−0.175977	+	0.127855i
$148$	−75.1785	+	231.376i	−0.0417543	+	0.128507i
$149$	−788.246	+	2425.97i	−0.433394	+	1.33385i	0.461330	+	0.887229i	$0.347372\pi$
$149$	−788.246	+	2425.97i	−0.433394	+	1.33385i	−0.894724	+	0.446620i	$0.852628\pi$
$150$	−682.157	+	495.616i	−0.371319	+	0.269779i
$151$	436.880	+	317.412i	0.235449	+	0.171064i	0.699253	−	0.714874i	$-0.253516\pi$
$151$	436.880	+	317.412i	0.235449	+	0.171064i	−0.463804	+	0.885938i	$0.653516\pi$
$152$	−309.147	−	951.458i	−0.164968	−	0.507720i
$153$	−2327.89			−1.23006
$154$	828.147	−	727.761i	0.433337	−	0.380810i
$155$	−2268.64			−1.17562
$156$	6.11865	+	18.8313i	0.00314028	+	0.00966479i
$157$	−533.257	−	387.434i	−0.271074	−	0.196947i	0.443941	−	0.896056i	$-0.353580\pi$
$157$	−533.257	−	387.434i	−0.271074	−	0.196947i	−0.715015	+	0.699109i	$0.753580\pi$
$158$	1468.92	−	1067.23i	0.739625	−	0.537369i
$159$	58.8589	−	181.149i	0.0293573	−	0.0903526i
$160$	−468.354	+	1441.45i	−0.231417	+	0.712227i
$161$	636.517	−	462.457i	0.311581	−	0.226377i
$162$	1385.88	+	1006.90i	0.672127	+	0.488329i
$163$	883.474	+	2719.05i	0.424534	+	1.30658i	0.903440	+	0.428715i	$0.141034\pi$
$163$	883.474	+	2719.05i	0.424534	+	1.30658i	−0.478906	+	0.877866i	$0.658966\pi$
$164$	376.757			0.179389
$165$	−384.201	−	891.742i	−0.181273	−	0.420739i
$166$	−594.210			−0.277829
$167$	1199.61	+	3692.01i	0.555859	+	1.71076i	0.693664	+	0.720298i	$0.255995\pi$
$167$	1199.61	+	3692.01i	0.555859	+	1.71076i	−0.137805	+	0.990459i	$0.544005\pi$
$168$	−226.782	−	164.767i	−0.104147	−	0.0756669i
$169$	1743.42	−	1266.67i	0.793547	−	0.576546i
$170$	1593.69	−	4904.88i	0.719003	−	2.21286i
$171$	400.369	−	1232.21i	0.179047	−	0.551050i
$172$	513.645	−	373.185i	0.227704	−	0.165436i
$173$	14.4973	+	10.5329i	0.00637116	+	0.00462892i	0.590966	−	0.806696i	$-0.298747\pi$
$173$	14.4973	+	10.5329i	0.00637116	+	0.00462892i	−0.584595	+	0.811325i	$0.698747\pi$
$174$	225.568	+	694.226i	0.0982772	+	0.302466i
$175$	−1656.10			−0.715366
$176$	−2382.04	−	1413.88i	−1.02019	−	0.605539i
$177$	111.738			0.0474506
$178$	41.1276	+	126.578i	0.0173182	+	0.0533000i
$179$	−1160.36	−	843.048i	−0.484520	−	0.352025i	0.318553	−	0.947905i	$-0.396803\pi$
$179$	−1160.36	−	843.048i	−0.484520	−	0.352025i	−0.803073	+	0.595881i	$0.796803\pi$
$180$	−681.735	+	495.309i	−0.282297	+	0.205101i
$181$	1004.49	−	3091.51i	0.412504	−	1.26956i	−0.501960	−	0.864891i	$-0.667388\pi$
$181$	1004.49	−	3091.51i	0.412504	−	1.26956i	0.914464	−	0.404667i	$-0.132612\pi$
$182$	−60.5264	+	186.281i	−0.0246512	+	0.0758685i
$183$	310.089	−	225.293i	0.125259	−	0.0910063i
$184$	−1265.32	−	919.310i	−0.506960	−	0.368328i
$185$	654.975	+	2015.81i	0.260296	+	0.801108i
$186$	639.835			0.252231
$187$	2965.87	+	1760.41i	1.15982	+	0.688418i
$188$	−874.361			−0.339199
$189$	−235.191	−	723.843i	−0.0905165	−	0.278581i
$190$	2322.18	+	1687.16i	0.886676	+	0.644208i
$191$	−1238.45	+	899.788i	−0.469169	+	0.340871i	−0.797117	−	0.603825i	$-0.793643\pi$
$191$	−1238.45	+	899.788i	−0.469169	+	0.340871i	0.327949	+	0.944696i	$0.393643\pi$
$192$	−157.229	+	483.901i	−0.0590991	+	0.181888i
$193$	−1070.17	+	3293.64i	−0.399132	+	1.22840i	0.526564	+	0.850135i	$0.323480\pi$
$193$	−1070.17	+	3293.64i	−0.399132	+	1.22840i	−0.925697	+	0.378267i	$0.876520\pi$
$194$	−3286.07	+	2387.47i	−1.21611	+	0.883557i
$195$	139.560	+	101.396i	0.0512519	+	0.0372367i
$196$	−154.038	−	474.081i	−0.0561364	−	0.172770i
$197$	−2587.46			−0.935783			−0.467891	−	0.883786i	$-0.654986\pi$
$197$	−2587.46			−0.935783			−0.467891	+	0.883786i	$0.654986\pi$
$198$	−1123.06	−	2606.65i	−0.403092	−	0.935589i
$199$	1552.28			0.552955			0.276477	−	0.961020i	$-0.410833\pi$
$199$	1552.28			0.552955			0.276477	+	0.961020i	$0.410833\pi$
$200$	1017.32	+	3130.99i	0.359678	+	1.10697i
$201$	−160.771	−	116.807i	−0.0564174	−	0.0409897i
$202$	671.297	−	487.726i	0.233823	−	0.169883i
$203$	−443.032	+	1363.51i	−0.153176	+	0.471428i
$204$	−89.2435	+	274.663i	−0.0306289	+	0.0942660i
$205$	2655.52	−	1929.35i	0.904730	−	0.657325i
$206$	978.530	+	710.944i	0.330958	+	0.240455i
$207$	−625.923	−	1926.39i	−0.210167	−	0.646829i
$208$	492.128			0.164053
$209$	−1441.93	+	1267.14i	−0.477225	+	0.419377i
$210$	804.277			0.264288
$211$	−1868.93	−	5751.97i	−0.609774	−	1.87669i	−0.459855	−	0.887994i	$-0.652099\pi$
$211$	−1868.93	−	5751.97i	−0.609774	−	1.87669i	−0.149919	−	0.988698i	$-0.547901\pi$
$212$	198.135	+	143.953i	0.0641884	+	0.0466356i
$213$	1238.10	−	899.530i	0.398277	−	0.289365i
$214$	−1107.09	+	3407.26i	−0.353640	+	1.08839i
$215$	1709.30	−	5260.69i	0.542202	−	1.66872i
$216$	−1224.01	+	889.298i	−0.385572	+	0.280135i
$217$	1016.68	+	738.661i	0.318049	+	0.231076i
$218$	−1006.69	−	3098.26i	−0.312759	−	0.962572i
$219$	−796.839			−0.245869
$220$	1243.14	−	115.507i	0.380965	−	0.0353977i
$221$	−612.748			−0.186506
$222$	−184.726	−	568.528i	−0.0558468	−	0.171879i
$223$	977.315	+	710.061i	0.293479	+	0.213225i	0.724775	−	0.688985i	$-0.241944\pi$
$223$	977.315	+	710.061i	0.293479	+	0.213225i	−0.431296	+	0.902210i	$0.641944\pi$
$224$	679.221	−	493.483i	0.202600	−	0.147197i
$225$	−1317.51	+	4054.88i	−0.390373	+	1.20144i
$226$	−303.188	+	933.117i	−0.0892379	+	0.274646i
$227$	4189.33	−	3043.73i	1.22492	−	0.889953i	0.228417	−	0.973563i	$-0.426645\pi$
$227$	4189.33	−	3043.73i	1.22492	−	0.889953i	0.996499	+	0.0836105i	$0.0266452\pi$
$228$	−130.037	−	94.4776i	−0.0377716	−	0.0274427i
$229$	195.138	+	600.573i	0.0563104	+	0.173306i	0.975256	−	0.221079i	$-0.0709578\pi$
$229$	195.138	+	600.573i	0.0563104	+	0.173306i	−0.918946	+	0.394384i	$0.870958\pi$
$230$	4487.43			1.28649
$231$	−118.170	+	524.725i	−0.0336582	+	0.149456i
$232$	2849.99			0.806513
$233$	169.314	+	521.096i	0.0476058	+	0.146516i	0.972034	−	0.234841i	$-0.0754570\pi$
$233$	169.314	+	521.096i	0.0476058	+	0.146516i	−0.924428	+	0.381357i	$0.875457\pi$
$234$	407.949	+	296.392i	0.113968	+	0.0828024i
$235$	−6162.82	+	4477.55i	−1.71072	+	1.24291i
$236$	−44.3973	+	136.641i	−0.0122459	+	0.0376889i
$237$	−273.732	+	842.460i	−0.0750245	+	0.230902i
$238$	−2311.22	+	1679.20i	−0.629471	+	0.457337i
$239$	−5405.89	−	3927.61i	−1.46309	−	1.06300i	−0.982545	−	0.186024i	$-0.940440\pi$
$239$	−5405.89	−	3927.61i	−1.46309	−	1.06300i	−0.480542	−	0.876972i	$-0.659560\pi$
$240$	−624.459	−	1921.89i	−0.167953	−	0.516906i
$241$	6150.04			1.64381			0.821907	−	0.569622i	$-0.192911\pi$
$241$	6150.04			1.64381			0.821907	+	0.569622i	$0.192911\pi$
$242$	−540.378	+	4170.32i	−0.143541	+	1.10776i
$243$	−2984.19			−0.787803
$244$	152.295	+	468.714i	0.0399576	+	0.122977i
$245$	−3513.46	−	2552.68i	−0.916191	−	0.665652i
$246$	−748.950	+	544.144i	−0.194111	+	0.141030i
$247$	105.385	−	324.343i	0.0271478	−	0.0835523i
$248$	771.968	−	2375.87i	0.197661	−	0.608339i
$249$	234.531	−	170.397i	0.0596900	−	0.0433674i
$250$	−2124.86	−	1543.80i	−0.537552	−	0.390554i
$251$	1629.63	+	5015.50i	0.409807	+	1.26126i	0.916814	+	0.399315i	$0.130752\pi$
$251$	1629.63	+	5015.50i	0.409807	+	1.26126i	−0.507007	+	0.861942i	$0.669248\pi$
$252$	466.787			0.116686
$253$	−659.327	+	2927.68i	−0.163840	+	0.727516i
$254$	−2121.13			−0.523981
$255$	777.513	+	2392.94i	0.190940	+	0.587653i
$256$	−2324.14	−	1688.59i	−0.567418	−	0.412253i
$257$	4945.78	−	3593.32i	1.20043	−	0.872161i	0.206100	−	0.978531i	$-0.433923\pi$
$257$	4945.78	−	3593.32i	1.20043	−	0.872161i	0.994327	+	0.106370i	$0.0339229\pi$
$258$	−482.083	+	1483.70i	−0.116330	+	0.358027i
$259$	362.816	−	1116.63i	0.0870436	−	0.267893i
$260$	−179.446	+	130.375i	−0.0428030	+	0.0310982i
$261$	2986.05	+	2169.49i	0.708167	+	0.514513i
$262$	−2182.15	−	6715.96i	−0.514556	−	1.58364i
$263$	2730.09			0.640092			0.320046	−	0.947402i	$-0.396302\pi$
$263$	2730.09			0.640092			0.320046	+	0.947402i	$0.396302\pi$
$264$	1064.63	−	98.9211i	0.248195	−	0.0230613i
$265$	2133.70			0.494612
$266$	−491.339	−	1512.19i	−0.113255	−	0.348564i
$267$	−52.5305	−	38.1657i	−0.0120405	−	0.00874794i
$268$	206.719	−	150.190i	0.0471170	−	0.0342325i
$269$	−1377.27	+	4238.79i	−0.312169	+	0.960756i	0.664736	+	0.747079i	$0.268544\pi$
$269$	−1377.27	+	4238.79i	−0.312169	+	0.960756i	−0.976904	+	0.213678i	$0.931456\pi$
$270$	1341.42	−	4128.48i	0.302357	−	0.930560i
$271$	−4848.39	+	3522.56i	−1.08678	+	0.789595i	−0.978853	−	0.204563i	$-0.934423\pi$
$271$	−4848.39	+	3522.56i	−1.08678	+	0.789595i	−0.107931	+	0.994158i	$0.534423\pi$
$272$	5807.07	+	4219.08i	1.29450	+	0.940512i
$273$	−29.5289	−	90.8807i	−0.00654642	−	0.0201478i
$274$	−1188.54			−0.262051
$275$	4744.99	−	4169.82i	1.04049	−	0.914362i
$276$	−251.287			−0.0548033
$277$	−349.755	−	1076.44i	−0.0758655	−	0.233490i	0.905931	−	0.423425i	$-0.139172\pi$
$277$	−349.755	−	1076.44i	−0.0758655	−	0.233490i	−0.981797	+	0.189935i	$0.939172\pi$
$278$	−713.545	−	518.421i	−0.153941	−	0.111845i
$279$	2617.40	−	1901.65i	0.561647	−	0.408061i
$280$	970.370	−	2986.49i	0.207110	−	0.637418i
$281$	−663.771	+	2042.88i	−0.140916	+	0.433693i	−0.996463	−	0.0840307i	$-0.973221\pi$
$281$	−663.771	+	2042.88i	−0.140916	+	0.433693i	0.855548	+	0.517724i	$0.173221\pi$
$282$	1738.13	−	1262.83i	0.367036	−	0.266667i
$283$	−2104.36	−	1528.91i	−0.442019	−	0.321146i	0.344417	−	0.938817i	$-0.388076\pi$
$283$	−2104.36	−	1528.91i	−0.442019	−	0.321146i	−0.786437	+	0.617671i	$0.788076\pi$
$284$	608.068	+	1871.44i	0.127050	+	0.391020i
$285$	−1400.37			−0.291054
$286$	−295.611	−	686.123i	−0.0611184	−	0.141858i
$287$	−1818.25			−0.373965
$288$	−667.916	−	2055.63i	−0.136657	−	0.420588i
$289$	−3255.67	−	2365.38i	−0.662663	−	0.481453i
$290$	−6615.40	+	4806.37i	−1.33955	+	0.973240i
$291$	612.357	−	1884.64i	0.123357	−	0.379655i
$292$	316.611	−	974.428i	0.0634529	−	0.195288i
$293$	−5211.58	+	3786.43i	−1.03913	+	0.754969i	−0.970115	−	0.242647i	$-0.921984\pi$
$293$	−5211.58	+	3786.43i	−1.03913	+	0.754969i	−0.0690105	+	0.997616i	$0.521984\pi$
$294$	990.919	+	719.945i	0.196570	+	0.142816i
$295$	386.801	+	1190.45i	0.0763405	+	0.234952i
$296$	−2333.97			−0.458307
$297$	2496.40	+	1481.75i	0.487730	+	0.289495i
$298$	8059.10			1.56661
$299$	−164.756	−	507.065i	−0.0318664	−	0.0980747i
$300$	427.918	+	310.901i	0.0823529	+	0.0598329i
$301$	−2478.88	+	1801.01i	−0.474685	+	0.344879i
$302$	527.222	−	1622.62i	0.100458	−	0.309177i
$303$	−125.096	+	385.006i	−0.0237181	+	0.0729967i
$304$	−3232.01	+	2348.19i	−0.609765	+	0.443020i
$305$	3473.69	+	2523.78i	0.652140	+	0.473808i
$306$	2272.75	+	6994.80i	0.424590	+	1.30675i
$307$	−6003.78			−1.11614			−0.558068	−	0.829795i	$-0.688457\pi$
$307$	−6003.78			−1.11614			−0.558068	+	0.829795i	$0.688457\pi$
$308$	−594.715	−	352.997i	−0.110023	−	0.0653048i
$309$	−590.092			−0.108638
$310$	2214.90	+	6816.76i	0.405800	+	1.24892i
$311$	4219.87	+	3065.92i	0.769412	+	0.559010i	0.901783	−	0.432190i	$-0.142259\pi$
$311$	4219.87	+	3065.92i	0.769412	+	0.559010i	−0.132371	+	0.991200i	$0.542259\pi$
$312$	−153.679	+	111.654i	−0.0278857	+	0.0202602i
$313$	1793.46	−	5519.69i	0.323873	−	0.996778i	−0.648074	−	0.761577i	$-0.724425\pi$
$313$	1793.46	−	5519.69i	0.323873	−	0.996778i	0.971947	−	0.235201i	$-0.0755747\pi$
$314$	−643.529	+	1980.58i	−0.115657	+	0.355957i
$315$	3290.09	−	2390.39i	0.588494	−	0.427566i
$316$	−921.453	−	669.475i	−0.164037	−	0.119180i
$317$	−2350.18	−	7233.12i	−0.416402	−	1.28155i	−0.910991	−	0.412427i	$-0.864681\pi$
$317$	−2350.18	−	7233.12i	−0.416402	−	1.28155i	0.494589	−	0.869127i	$-0.335319\pi$
$318$	−601.778			−0.106120
$319$	−2163.77	−	5022.19i	−0.379775	−	0.881469i
$320$	−5699.72			−0.995701
$321$	−540.114	−	1662.30i	−0.0939134	−	0.289036i
$322$	−2011.02	−	1461.09i	−0.348043	−	0.252868i
$323$	4024.17	−	2923.73i	0.693222	−	0.503655i
$324$	332.066	−	1022.00i	0.0569387	−	0.175239i
$325$	−346.795	+	1067.33i	−0.0591899	+	0.182168i
$326$	7307.62	−	5309.30i	1.24151	−	0.902008i
$327$	1285.80	+	934.187i	0.217446	+	0.157984i
$328$	1116.93	+	3437.56i	0.188025	+	0.578682i
$329$	4219.72			0.707114
$330$	−2304.39	+	2025.06i	−0.384402	+	0.337805i
$331$	−2597.13			−0.431272			−0.215636	−	0.976474i	$-0.569182\pi$
$331$	−2597.13			−0.431272			−0.215636	+	0.976474i	$0.569182\pi$
$332$	115.186	+	354.505i	0.0190411	+	0.0586024i
$333$	−2445.39	−	1776.68i	−0.402421	−	0.292376i
$334$	9922.50	−	7209.12i	1.62555	−	1.18103i
$335$	687.917	−	2117.19i	0.112194	−	0.345297i
$336$	−345.912	+	1064.61i	−0.0561638	+	0.172854i
$337$	2398.78	−	1742.81i	0.387744	−	0.281712i	−0.376787	−	0.926300i	$-0.622971\pi$
$337$	2398.78	−	1742.81i	0.387744	−	0.281712i	0.764530	+	0.644588i	$0.222971\pi$
$338$	−5508.20	−	4001.94i	−0.886410	−	0.644014i
$339$	−147.916	−	455.239i	−0.0236982	−	0.0729357i
$340$	−3235.18			−0.516035
$341$	−4772.81	+	443.470i	−0.757953	+	0.0704260i
$342$	−4093.41			−0.647211
$343$	1757.20	+	5408.09i	0.276617	+	0.851340i
$344$	4927.72	+	3580.20i	0.772339	+	0.561137i
$345$	−1771.16	+	1286.83i	−0.276395	+	0.200813i
$346$	17.4952	−	53.8447i	0.00271835	−	0.00836621i
$347$	−2050.00	+	6309.26i	−0.317147	+	0.976077i	0.657715	+	0.753267i	$0.271523\pi$
$347$	−2050.00	+	6309.26i	−0.317147	+	0.976077i	−0.974862	+	0.222810i	$0.928477\pi$
$348$	370.449	−	269.147i	0.0570636	−	0.0414591i
$349$	−1044.20	−	758.653i	−0.160156	−	0.116360i	0.504821	−	0.863224i	$-0.331559\pi$
$349$	−1044.20	−	758.653i	−0.160156	−	0.116360i	−0.664977	+	0.746864i	$0.731559\pi$
$350$	1616.87	+	4976.21i	0.246929	+	0.759970i
$351$	−515.755			−0.0784301
$352$	−703.561	+	3124.10i	−0.106534	+	0.473054i
$353$	4378.37			0.660161			0.330081	−	0.943953i	$-0.392924\pi$
$353$	4378.37			0.660161			0.330081	+	0.943953i	$0.392924\pi$
$354$	−109.092	−	335.749i	−0.0163790	−	0.0504092i
$355$	13869.4	+	10076.7i	2.07356	+	1.50653i
$356$	67.5436	−	49.0733i	0.0100556	−	0.00730585i
$357$	430.694	−	1325.54i	0.0638508	−	0.196513i
$358$	−1400.31	+	4309.70i	−0.206728	+	0.636242i
$359$	−196.692	+	142.905i	−0.0289165	+	0.0210091i	−0.602150	−	0.798383i	$-0.705689\pi$
$359$	−196.692	+	142.905i	−0.0289165	+	0.0210091i	0.573233	+	0.819392i	$0.305689\pi$
$360$	−6540.31	−	4751.81i	−0.957513	−	0.695674i
$361$	−1264.05	−	3890.36i	−0.184291	−	0.567190i
$362$	−10270.0			−1.49110
$363$	−982.605	−	1800.96i	−0.142076	−	0.260402i
$364$	122.868			0.0176924
$365$	−2758.40	−	8489.47i	−0.395565	−	1.21742i
$366$	−979.701	−	711.795i	−0.139917	−	0.101656i
$367$	−10044.2	+	7297.57i	−1.42862	+	1.03796i	−0.438354	+	0.898803i	$0.644438\pi$
$367$	−10044.2	+	7297.57i	−1.42862	+	1.03796i	−0.990271	+	0.139154i	$0.955562\pi$
$368$	−1930.00	+	5939.93i	−0.273392	+	0.841414i
$369$	−1446.51	+	4451.91i	−0.204072	+	0.628068i
$370$	5417.60	−	3936.12i	0.761210	−	0.553051i
$371$	−956.208	−	694.726i	−0.133811	−	0.0972194i
$372$	−124.030	−	381.725i	−0.0172867	−	0.0532030i
$373$	5566.76			0.772750			0.386375	−	0.922342i	$-0.373727\pi$
$373$	5566.76			0.772750			0.386375	+	0.922342i	$0.373727\pi$
$374$	2394.04	−	10630.5i	0.330997	−	1.46976i
$375$	1281.37			0.176453
$376$	−2592.13	−	7977.74i	−0.355528	−	1.09420i
$377$	785.987	+	571.053i	0.107375	+	0.0780126i
$378$	−1945.37	+	1413.39i	−0.264707	+	0.192321i
$379$	−927.871	+	2855.69i	−0.125756	+	0.387037i	−0.994038	−	0.109034i	$-0.965224\pi$
$379$	−927.871	+	2855.69i	−0.125756	+	0.387037i	0.868282	+	0.496071i	$0.165224\pi$
$380$	556.412	−	1712.46i	0.0751140	−	0.231177i
$381$	837.196	−	608.259i	0.112574	−	0.0817901i
$382$	3912.78	+	2842.80i	0.524072	+	0.380760i
$383$	−598.200	−	1841.07i	−0.0798083	−	0.245625i	0.903189	−	0.429242i	$-0.141219\pi$
$383$	−598.200	−	1841.07i	−0.0798083	−	0.245625i	−0.982998	+	0.183617i	$0.941219\pi$
$384$	2689.90			0.357470
$385$	−5999.45	+	557.445i	−0.794182	+	0.0737923i
$386$	10941.5			1.44277
$387$	2437.62	+	7502.22i	0.320184	+	0.985424i
$388$	2061.35	+	1497.66i	0.269715	+	0.195959i
$389$	4396.01	−	3193.89i	0.572974	−	0.416290i	−0.263211	−	0.964738i	$-0.584781\pi$
$389$	4396.01	−	3193.89i	0.572974	−	0.416290i	0.836184	+	0.548449i	$0.184781\pi$
$390$	168.420	−	518.343i	0.0218674	−	0.0673008i
$391$	2403.04	−	7395.80i	0.310811	−	0.956577i
$392$	3868.90	−	2810.92i	0.498492	−	0.362176i
$393$	2787.17	+	2024.99i	0.357745	+	0.259917i
$394$	2526.18	+	7774.77i	0.323012	+	0.994130i
$395$	−9923.09			−1.26401
$396$	−1337.42	+	1175.31i	−0.169717	+	0.149145i
$397$	−8136.70			−1.02864			−0.514319	−	0.857599i	$-0.671955\pi$
$397$	−8136.70			−1.02864			−0.514319	+	0.857599i	$0.671955\pi$
$398$	−1515.51	−	4664.25i	−0.190868	−	0.587432i
$399$	627.567	+	455.954i	0.0787410	+	0.0572087i
$400$	10635.7	−	7727.28i	1.32946	−	0.965910i
$401$	−1350.78	+	4157.27i	−0.168216	+	0.517716i	−0.999259	−	0.0384926i	$-0.987744\pi$
$401$	−1350.78	+	4157.27i	−0.168216	+	0.517716i	0.831043	+	0.556208i	$0.187744\pi$
$402$	−194.017	+	597.122i	−0.0240713	+	0.0740839i
$403$	688.952	−	500.553i	0.0851592	−	0.0618718i
$404$	−421.106	−	305.951i	−0.0518584	−	0.0376773i
$405$	−2893.05	−	8903.89i	−0.354955	−	1.09244i
$406$	4529.60			0.553695
$407$	1772.00	+	4112.86i	0.215810	+	0.500902i
$408$	−2770.62			−0.336192
$409$	2734.38	+	8415.56i	0.330578	+	1.01742i	0.968859	+	0.247612i	$0.0796458\pi$
$409$	2734.38	+	8415.56i	0.330578	+	1.01742i	−0.638281	+	0.769803i	$0.720354\pi$
$410$	−8389.90	−	6095.62i	−1.01060	−	0.734246i
$411$	469.108	−	340.827i	0.0563003	−	0.0409045i
$412$	234.463	−	721.604i	0.0280368	−	0.0862885i
$413$	214.264	−	659.437i	0.0255284	−	0.0785685i
$414$	−5177.29	+	3761.52i	−0.614614	+	0.446543i
$415$	2627.27	+	1908.82i	0.310765	+	0.225784i
$416$	−175.809	−	541.084i	−0.0207205	−	0.0637713i
$417$	430.296			0.0505316
$418$	5215.25	+	3095.55i	0.610254	+	0.362220i
$419$	10035.1			1.17005			0.585023	−	0.811017i	$-0.301086\pi$
$419$	10035.1			1.17005			0.585023	+	0.811017i	$0.301086\pi$
$420$	−155.907	−	479.831i	−0.0181130	−	0.0557461i
$421$	−6437.19	−	4676.89i	−0.745201	−	0.541420i	0.149135	−	0.988817i	$-0.452351\pi$
$421$	−6437.19	−	4676.89i	−0.745201	−	0.541420i	−0.894336	+	0.447397i	$0.852351\pi$
$422$	−15458.8	+	11231.4i	−1.78322	+	1.29559i
$423$	3357.00	−	10331.8i	0.385870	−	1.18759i
$424$	−726.052	+	2234.56i	−0.0831609	+	0.255943i
$425$	−13242.5	+	9621.22i	−1.51142	+	1.09811i
$426$	−3911.66	−	2841.99i	−0.444884	−	0.323227i
$427$	−734.982	−	2262.04i	−0.0832981	−	0.256365i
$428$	2247.37			0.253811
$429$	313.431	+	186.039i	0.0352740	+	0.0209372i
$430$	−17476.0			−1.95993
$431$	2181.64	+	6714.41i	0.243819	+	0.750398i	0.995828	+	0.0912457i	$0.0290849\pi$
$431$	2181.64	+	6714.41i	0.243819	+	0.750398i	−0.752009	+	0.659153i	$0.770915\pi$
$432$	4887.86	+	3551.24i	0.544368	+	0.395507i
$433$	4666.53	−	3390.43i	0.517919	−	0.376290i	−0.297900	−	0.954597i	$-0.596286\pi$
$433$	4666.53	−	3390.43i	0.517919	−	0.376290i	0.815820	+	0.578307i	$0.196286\pi$
$434$	1226.92	−	3776.07i	0.135700	−	0.417643i
$435$	1232.78	−	3794.09i	0.135878	−	0.418190i
$436$	−1653.28	+	1201.18i	−0.181600	+	0.131940i
$437$	3501.49	+	2543.98i	0.383292	+	0.278478i
$438$	777.964	+	2394.33i	0.0848689	+	0.261200i
$439$	7816.65			0.849814			0.424907	−	0.905237i	$-0.360307\pi$
$439$	7816.65			0.849814			0.424907	+	0.905237i	$0.360307\pi$
$440$	4739.30	+	11000.1i	0.513493	+	1.19183i
$441$	6193.34			0.668755
$442$	598.233	+	1841.17i	0.0643780	+	0.198135i
$443$	−5372.04	−	3903.01i	−0.576147	−	0.418595i	0.261186	−	0.965289i	$-0.415886\pi$
$443$	−5372.04	−	3903.01i	−0.576147	−	0.418595i	−0.837333	+	0.546693i	$0.815886\pi$
$444$	−303.375	+	220.415i	−0.0324269	+	0.0235595i
$445$	224.771	−	691.774i	0.0239442	−	0.0736926i
$446$	1179.41	−	3629.86i	0.125217	−	0.385379i
$447$	−3180.88	+	2311.04i	−0.336578	+	0.244538i
$448$	2554.31	+	1855.81i	0.269374	+	0.195712i
$449$	3052.77	+	9395.45i	0.320866	+	0.987525i	0.973272	+	0.229655i	$0.0737597\pi$
$449$	3052.77	+	9395.45i	0.320866	+	0.987525i	−0.652406	+	0.757870i	$0.726240\pi$
$450$	13470.3			1.41110
$451$	5209.59	−	4578.10i	0.543925	−	0.477992i
$452$	615.469			0.0640469
$453$	257.215	+	791.627i	0.0266778	+	0.0821057i
$454$	−13235.8	−	9616.40i	−1.36826	−	0.994097i
$455$	866.018	−	629.199i	0.0892298	−	0.0648292i
$456$	476.514	−	1466.56i	0.0489360	−	0.150609i
$457$	4410.00	−	13572.6i	0.451403	−	1.38927i	−0.423904	−	0.905707i	$-0.639341\pi$
$457$	4410.00	−	13572.6i	0.451403	−	1.38927i	0.875307	−	0.483568i	$-0.160659\pi$
$458$	1614.07	−	1172.69i	0.164674	−	0.119643i
$459$	−6085.86	−	4421.64i	−0.618875	−	0.449639i
$460$	−869.874	−	2677.20i	−0.0881698	−	0.271359i
$461$	−3196.86			−0.322977			−0.161489	−	0.986875i	$-0.551629\pi$
$461$	−3196.86			−0.322977			−0.161489	+	0.986875i	$0.551629\pi$
$462$	1692.05	−	157.219i	0.170393	−	0.0158322i
$463$	−7931.12			−0.796091			−0.398046	−	0.917366i	$-0.630311\pi$
$463$	−7931.12			−0.796091			−0.398046	+	0.917366i	$0.630311\pi$
$464$	−3516.88	−	10823.9i	−0.351869	−	1.08294i
$465$	−2829.00	−	2055.39i	−0.282133	−	0.204981i
$466$	1400.48	−	1017.51i	0.139219	−	0.101148i
$467$	−1822.79	+	5609.99i	−0.180619	+	0.555887i	−0.999845	−	0.0175828i	$-0.994403\pi$
$467$	−1822.79	+	5609.99i	−0.180619	+	0.555887i	0.819227	+	0.573470i	$0.194403\pi$
$468$	97.7477	−	300.836i	0.00965468	−	0.0297140i
$469$	−997.637	+	724.826i	−0.0982230	+	0.0713632i
$470$	19470.9	+	14146.4i	1.91091	+	1.38835i
$471$	−313.958	−	966.263i	−0.0307143	−	0.0945288i
$472$	−1378.34			−0.134414
$473$	2567.71	−	11401.7i	0.249605	−	1.10835i
$474$	2798.66			0.271195
$475$	−2815.20	−	8664.31i	−0.271938	−	0.836938i
$476$	1449.83	+	1053.36i	0.139607	+	0.101430i
$477$	−2461.72	+	1788.54i	−0.236299	+	0.171681i
$478$	−6523.77	+	20078.1i	−0.624247	+	1.92124i
$479$	2256.18	−	6943.81i	0.215214	−	0.662361i	−0.783924	−	0.620856i	$-0.786785\pi$
$479$	2256.18	−	6943.81i	0.215214	−	0.662361i	0.999138	−	0.0415042i	$-0.0132150\pi$
$480$	−1889.99	+	1373.16i	−0.179721	+	0.130575i
$481$	−643.675	−	467.657i	−0.0610167	−	0.0443313i
$482$	−6004.36	−	18479.5i	−0.567409	−	1.74631i
$483$	1212.73			0.114246
$484$	2592.76	−	486.013i	0.243497	−	0.0456436i
$485$	22198.6			2.07832
$486$	2913.51	+	8966.86i	0.271933	+	0.836924i
$487$	−6663.47	−	4841.30i	−0.620022	−	0.450472i	0.232907	−	0.972499i	$-0.425176\pi$
$487$	−6663.47	−	4841.30i	−0.620022	−	0.450472i	−0.852929	+	0.522027i	$0.825176\pi$
$488$	−3825.10	+	2779.10i	−0.354824	+	0.257795i
$489$	−1361.77	+	4191.10i	−0.125933	+	0.387583i
$490$	−4240.01	+	13049.4i	−0.390906	+	1.20309i
$491$	−12015.7	+	8729.95i	−1.10441	+	0.802397i	−0.981773	−	0.190055i	$-0.939133\pi$
$491$	−12015.7	+	8729.95i	−1.10441	+	0.802397i	−0.122632	+	0.992452i	$0.539133\pi$
$492$	469.817	+	341.342i	0.0430508	+	0.0312782i
$493$	4378.86	+	13476.8i	0.400029	+	1.23116i
$494$	−1077.47			−0.0981327
$495$	−3407.99	+	15132.9i	−0.309450	+	1.37408i
$496$	−9975.83			−0.903081
$497$	−2934.57	−	9031.68i	−0.264856	−	0.815143i
$498$	−740.982	−	538.355i	−0.0666751	−	0.0484423i
$499$	−4584.66	+	3330.95i	−0.411298	+	0.298825i	−0.774127	−	0.633030i	$-0.781811\pi$
$499$	−4584.66	+	3330.95i	−0.411298	+	0.298825i	0.362829	+	0.931856i	$0.381811\pi$
$500$	−509.133	+	1566.95i	−0.0455382	+	0.140152i
$501$	−1849.05	+	5690.80i	−0.164889	+	0.507477i
$502$	13479.5	−	9793.39i	1.19844	−	0.870718i
$503$	−11318.9	−	8223.65i	−1.00335	−	0.728975i	−0.0405442	−	0.999178i	$-0.512909\pi$
$503$	−11318.9	−	8223.65i	−1.00335	−	0.728975i	−0.962803	+	0.270203i	$0.912909\pi$
$504$	1383.84	+	4259.01i	0.122303	+	0.376411i
$505$	−4534.87			−0.399602
$506$	9440.75	−	877.197i	0.829432	−	0.0770675i
$507$	3321.66			0.290967
$508$	411.173	+	1265.46i	0.0359111	+	0.110523i
$509$	17391.7	+	12635.8i	1.51449	+	1.10034i	0.964138	+	0.265403i	$0.0855050\pi$
$509$	17391.7	+	12635.8i	1.51449	+	1.10034i	0.550348	+	0.834935i	$0.314495\pi$
$510$	6431.16	−	4672.51i	0.558386	−	0.405691i
$511$	−1527.98	+	4702.64i	−0.132278	+	0.407109i
$512$	1509.43	−	4645.54i	0.130289	−	0.400988i
$513$	3387.18	−	2460.93i	0.291516	−	0.211799i
$514$	−15625.8	−	11352.8i	−1.34090	−	0.974223i
$515$	−2042.71	−	6286.80i	−0.174781	−	0.537922i
$516$	978.622			0.0834912
$517$	−12090.2	+	10624.7i	−1.02848	+	0.903814i
$518$	−3709.46			−0.314641
$519$	8.53537	+	26.2692i	0.000721891	+	0.00222175i
$520$	−1721.54	−	1250.77i	−0.145182	−	0.105481i
$521$	−575.141	+	417.864i	−0.0483635	+	0.0351381i	−0.611704	−	0.791086i	$-0.709516\pi$
$521$	−575.141	+	417.864i	−0.0483635	+	0.0351381i	0.563341	+	0.826225i	$0.309516\pi$
$522$	3603.53	−	11090.5i	0.302150	−	0.929921i
$523$	4533.60	−	13953.0i	0.379045	−	1.16658i	−0.561664	−	0.827366i	$-0.689839\pi$
$523$	4533.60	−	13953.0i	0.379045	−	1.16658i	0.940709	−	0.339215i	$-0.110161\pi$
$524$	−3583.73	+	2603.73i	−0.298771	+	0.217070i
$525$	−2065.16	−	1500.42i	−0.171678	−	0.124731i
$526$	−2665.42	−	8203.31i	−0.220946	−	0.680003i
$527$	12420.9			1.02668
$528$	−1689.44	−	3921.24i	−0.139249	−	0.323201i
$529$	−5400.65			−0.443876
$530$	−2083.16	−	6411.31i	−0.170730	−	0.525452i
$531$	−1444.14	−	1049.23i	−0.118024	−	0.0857492i
$532$	−806.925	+	586.265i	−0.0657606	+	0.0477778i
$533$	−380.751	+	1171.83i	−0.0309421	+	0.0952301i
$534$	−63.3933	+	195.104i	−0.00513726	+	0.0158109i
$535$	15840.3	−	11508.7i	1.28007	−	0.930025i
$536$	1983.18	+	1440.87i	0.159814	+	0.116112i
$537$	−683.166	−	2102.57i	−0.0548991	−	0.168962i
$538$	14081.3			1.12841
$539$	−7890.68	−	4683.57i	−0.630567	−	0.374278i
$540$	−2723.07			−0.217005
$541$	6894.88	+	21220.2i	0.547937	+	1.68638i	0.713903	+	0.700245i	$0.246926\pi$
$541$	6894.88	+	21220.2i	0.547937	+	1.68638i	−0.165966	+	0.986132i	$0.553074\pi$
$542$	15318.1	+	11129.2i	1.21396	+	0.881995i
$543$	4053.51	−	2945.05i	0.320355	−	0.232752i
$544$	2564.26	−	7891.98i	0.202099	−	0.621996i
$545$	−5501.76	+	16932.7i	−0.432421	+	1.33085i
$546$	−244.247	+	177.456i	−0.0191444	+	0.0139092i
$547$	17291.6	+	12563.0i	1.35162	+	0.982006i	0.998929	+	0.0462641i	$0.0147316\pi$
$547$	17291.6	+	12563.0i	1.35162	+	0.982006i	0.352686	+	0.935742i	$0.385268\pi$
$548$	230.394	+	709.079i	0.0179597	+	0.0552743i
$549$	−6123.23			−0.476016
$550$	−17162.0	−	10186.6i	−1.33053	−	0.789744i
$551$	−7886.69			−0.609772
$552$	−744.965	−	2292.77i	−0.0574417	−	0.176787i
$553$	4446.99	+	3230.92i	0.341962	+	0.248450i
$554$	−2892.98	+	2101.88i	−0.221861	+	0.161192i
$555$	−1009.57	+	3107.13i	−0.0772139	+	0.237640i
$556$	−170.971	+	526.194i	−0.0130410	+	0.0401360i
$557$	16403.8	−	11918.0i	1.24785	−	0.906613i	0.249750	−	0.968310i	$-0.419651\pi$
$557$	16403.8	−	11918.0i	1.24785	−	0.906613i	0.998095	+	0.0616977i	$0.0196515\pi$
$558$	−8269.45	−	6008.11i	−0.627373	−	0.455813i
$559$	641.630	+	1974.74i	0.0485475	+	0.149414i
$560$	−12539.7			−0.946248
$561$	2103.52	+	4882.32i	0.158307	+	0.367437i
$562$	6786.45			0.509376
$563$	−679.485	−	2091.24i	−0.0508648	−	0.156546i	0.922398	−	0.386242i	$-0.126227\pi$
$563$	−679.485	−	2091.24i	−0.0508648	−	0.156546i	−0.973262	+	0.229696i	$0.926227\pi$
$564$	−1090.33	−	792.172i	−0.0814029	−	0.0591427i
$565$	4338.05	−	3151.78i	0.323014	−	0.234684i
$566$	−2539.53	+	7815.85i	−0.188594	+	0.580433i
$567$	−1602.57	+	4932.21i	−0.118698	+	0.365314i
$568$	−15272.5	+	11096.1i	−1.12820	+	0.819689i
$569$	−11678.1	−	8484.62i	−0.860405	−	0.625121i	0.0675901	−	0.997713i	$-0.478469\pi$
$569$	−11678.1	−	8484.62i	−0.860405	−	0.625121i	−0.927995	+	0.372592i	$0.878469\pi$
$570$	1367.19	+	4207.79i	0.100466	+	0.309202i
$571$	−11848.7			−0.868396			−0.434198	−	0.900817i	$-0.642968\pi$
$571$	−11848.7			−0.868396			−0.434198	+	0.900817i	$0.642968\pi$
$572$	−352.037	+	309.364i	−0.0257332	+	0.0226139i
$573$	−2359.56			−0.172028
$574$	1775.18	+	5463.45i	0.129085	+	0.397282i
$575$	−11522.5	−	8371.56i	−0.835687	−	0.607162i
$576$	6575.95	−	4777.71i	0.475691	−	0.345610i
$577$	6355.12	−	19559.0i	0.458522	−	1.41119i	−0.408428	−	0.912790i	$-0.633923\pi$
$577$	6355.12	−	19559.0i	0.458522	−	1.41119i	0.866950	−	0.498395i	$-0.166077\pi$
$578$	−3928.90	+	12091.9i	−0.282735	+	0.870169i
$579$	−4318.55	+	3137.61i	−0.309970	+	0.225207i
$580$	4149.85	+	3015.04i	0.297091	+	0.215849i
$581$	−555.892	−	1710.86i	−0.0396942	−	0.122166i
$582$	−6260.79			−0.445907
$583$	4488.92	−	417.093i	0.318889	−	0.0296299i
$584$	9829.38			0.696477
$585$	−851.604	−	2620.97i	−0.0601872	−	0.185237i
$586$	16465.5	+	11962.9i	1.16073	+	0.843316i
$587$	−6626.00	+	4814.07i	−0.465901	+	0.338497i	−0.795842	−	0.605505i	$-0.792971\pi$
$587$	−6626.00	+	4814.07i	−0.465901	+	0.338497i	0.329940	+	0.944002i	$0.392971\pi$
$588$	237.432	−	730.740i	0.0166523	−	0.0512504i
$589$	−2136.24	+	6574.69i	−0.149444	+	0.459941i
$590$	3199.41	−	2324.51i	0.223250	−	0.162201i
$591$	−3226.58	−	2344.25i	−0.224575	−	0.163163i
$592$	2880.11	+	8864.07i	0.199952	+	0.615390i
$593$	−27583.5			−1.91015			−0.955074	−	0.296367i	$-0.904225\pi$
$593$	−27583.5			−1.91015			−0.955074	+	0.296367i	$0.904225\pi$
$594$	2015.08	−	8947.79i	0.139192	−	0.618068i
$595$	15613.1			1.07576
$596$	−1562.23	−	4808.05i	−0.107368	−	0.330445i
$597$	1935.69	+	1406.36i	0.132701	+	0.0964132i
$598$	−1362.77	+	990.109i	−0.0931902	+	0.0677066i
$599$	−278.766	+	857.954i	−0.0190152	+	0.0585227i	−0.960114	−	0.279609i	$-0.909795\pi$
$599$	−278.766	+	857.954i	−0.0190152	+	0.0585227i	0.941099	+	0.338132i	$0.109795\pi$
$600$	−1568.08	+	4826.06i	−0.106694	+	0.328372i
$601$	1476.81	−	1072.96i	0.100233	−	0.0728238i	−0.536540	−	0.843875i	$-0.680269\pi$
$601$	1476.81	−	1072.96i	0.100233	−	0.0728238i	0.636773	+	0.771051i	$0.280269\pi$
$602$	7831.80	+	5690.14i	0.530233	+	0.385237i
$603$	981.032	+	3019.31i	0.0662533	+	0.203907i
$604$	−1070.25			−0.0720994
$605$	15785.9	−	16703.0i	1.06080	−	1.12243i
$606$	1278.99			0.0857351
$607$	−2484.52	−	7646.55i	−0.166134	−	0.511308i	0.832984	−	0.553297i	$-0.186631\pi$
$607$	−2484.52	−	7646.55i	−0.166134	−	0.511308i	−0.999118	+	0.0419890i	$0.986631\pi$
$608$	3736.40	+	2714.65i	0.249229	+	0.181075i
$609$	−1787.81	+	1298.92i	−0.118958	+	0.0864282i
$610$	4192.01	−	12901.7i	0.278245	−	0.856350i
$611$	883.630	−	2719.53i	0.0585071	−	0.180066i
$612$	3732.53	−	2711.84i	0.246533	−	0.179117i
$613$	12370.6	+	8987.76i	0.815079	+	0.592190i	0.915299	−	0.402776i	$-0.131955\pi$
$613$	12370.6	+	8987.76i	0.815079	+	0.592190i	−0.100219	+	0.994965i	$0.531955\pi$
$614$	5861.57	+	18040.0i	0.385266	+	1.18573i
$615$	5059.44			0.331734
$616$	1457.69	−	6472.72i	0.0953440	−	0.423366i
$617$	−16580.7			−1.08187			−0.540936	−	0.841064i	$-0.681930\pi$
$617$	−16580.7			−1.08187			−0.540936	+	0.841064i	$0.681930\pi$
$618$	576.115	+	1773.10i	0.0374996	+	0.115412i
$619$	3520.04	+	2557.46i	0.228566	+	0.166063i	0.696174	−	0.717873i	$-0.254884\pi$
$619$	3520.04	+	2557.46i	0.228566	+	0.166063i	−0.467608	+	0.883936i	$0.654884\pi$
$620$	3637.52	−	2642.81i	0.235623	−	0.171190i
$621$	2022.66	−	6225.10i	0.130703	−	0.402262i
$622$	5092.50	−	15673.1i	0.328281	−	1.01034i
$623$	−325.969	+	236.831i	−0.0209626	+	0.0152302i
$624$	613.686	+	445.869i	0.0393703	+	0.0286042i
$625$	−2252.40	−	6932.17i	−0.144153	−	0.443659i
$626$	−18336.5			−1.17072
$627$	−2946.12	+	273.741i	−0.187650	+	0.0174357i
$628$	1306.36			0.0830085
$629$	−3586.02	−	11036.6i	−0.227319	−	0.699617i
$630$	−10394.8	−	7552.24i	−0.657361	−	0.477600i
$631$	19712.4	−	14321.9i	1.24364	−	0.903561i	0.245809	−	0.969318i	$-0.420946\pi$
$631$	19712.4	−	14321.9i	1.24364	−	0.903561i	0.997836	+	0.0657575i	$0.0209464\pi$
$632$	3376.61	−	10392.1i	0.212523	−	0.654078i
$633$	2880.73	−	8865.98i	0.180883	−	0.556700i
$634$	−19439.4	+	14123.6i	−1.21773	+	0.884730i
$635$	9378.45	+	6813.84i	0.586098	+	0.425825i
$636$	116.653	+	359.020i	0.00727293	+	0.0223838i
$637$	1630.21			0.101399
$638$	−12978.1	+	11404.9i	−0.805339	+	0.707718i
$639$	−24448.3			−1.51355
$640$	9311.55	+	28658.0i	0.575111	+	1.77001i
$641$	−10915.3	−	7930.41i	−0.672586	−	0.488662i	0.198304	−	0.980141i	$-0.436457\pi$
$641$	−10915.3	−	7930.41i	−0.672586	−	0.488662i	−0.870890	+	0.491478i	$0.836457\pi$
$642$	−4467.53	+	3245.85i	−0.274641	+	0.199538i
$643$	2155.57	−	6634.16i	0.132204	−	0.406883i	−0.862940	−	0.505306i	$-0.831380\pi$
$643$	2155.57	−	6634.16i	0.132204	−	0.406883i	0.995145	+	0.0984228i	$0.0313798\pi$
$644$	−481.856	+	1483.00i	−0.0294842	+	0.0907429i
$645$	6897.69	−	5011.47i	0.421080	−	0.305932i
$646$	−12714.0	−	9237.28i	−0.774345	−	0.562594i
$647$	9152.86	+	28169.6i	0.556161	+	1.71169i	0.692859	+	0.721073i	$0.256351\pi$
$647$	9152.86	+	28169.6i	0.556161	+	1.71169i	−0.136698	+	0.990613i	$0.543649\pi$
$648$	10309.2			0.624976
$649$	1046.47	+	2428.89i	0.0632935	+	0.146906i
$650$	3545.66			0.213957
$651$	598.576	+	1842.23i	0.0360369	+	0.110910i
$652$	−4584.08	−	3330.53i	−0.275347	−	0.200051i
$653$	−6641.57	+	4825.38i	−0.398017	+	0.289176i	−0.768733	−	0.639570i	$-0.779112\pi$
$653$	−6641.57	+	4825.38i	−0.398017	+	0.289176i	0.370716	+	0.928746i	$0.379112\pi$
$654$	1551.69	−	4775.60i	0.0927764	−	0.285536i
$655$	−11925.9	+	36704.2i	−0.711425	+	2.18954i
$656$	11677.1	−	8483.89i	0.694989	−	0.504939i
$657$	10298.6	+	7482.39i	0.611549	+	0.444316i
$658$	−4119.76	−	12679.3i	−0.244081	−	0.751203i
$659$	25825.3			1.52657			0.763286	−	0.646061i	$-0.223585\pi$
$659$	25825.3			1.52657			0.763286	+	0.646061i	$0.223585\pi$
$660$	1654.85	+	982.245i	0.0975982	+	0.0579301i
$661$	−8681.63			−0.510857			−0.255428	−	0.966828i	$-0.582216\pi$
$661$	−8681.63			−0.510857			−0.255428	+	0.966828i	$0.582216\pi$
$662$	2535.61	+	7803.81i	0.148866	+	0.458162i
$663$	−764.098	−	555.150i	−0.0447589	−	0.0325192i
$664$	−2893.05	+	2101.93i	−0.169085	+	0.122847i
$665$	−2685.27	+	8264.43i	−0.156587	+	0.481926i
$666$	−2951.07	+	9082.45i	−0.171699	+	0.528435i
$667$	−9975.00	+	7247.26i	−0.579060	+	0.420712i
$668$	−6224.40	−	4522.29i	−0.360523	−	0.261935i
$669$	575.399	+	1770.90i	0.0332529	+	0.102342i
$670$	−7033.32			−0.405553
$671$	7801.36	+	4630.55i	0.448835	+	0.266409i
$672$	1294.09			0.0742865
$673$	−3581.43	−	11022.5i	−0.205132	−	0.631332i	−0.999708	−	0.0241669i	$-0.992307\pi$
$673$	−3581.43	−	11022.5i	−0.205132	−	0.631332i	0.794576	−	0.607165i	$-0.207693\pi$
$674$	−7578.73	−	5506.27i	−0.433118	−	0.314679i
$675$	−11146.3	+	8098.26i	−0.635587	+	0.461781i
$676$	−1319.81	+	4061.95i	−0.0750914	+	0.231108i
$677$	3450.21	−	10618.7i	0.195868	−	0.602819i	−0.804098	−	0.594497i	$-0.797351\pi$
$677$	3450.21	−	10618.7i	0.195868	−	0.602819i	0.999965	−	0.00832169i	$-0.00264891\pi$
$678$	−1223.48	+	888.912i	−0.0693032	+	0.0503517i
$679$	−9948.21	−	7227.80i	−0.562264	−	0.408509i
$680$	−9590.99	−	29518.0i	−0.540879	−	1.66465i
$681$	7981.73			0.449135
$682$	5992.28	+	13908.3i	0.336446	+	0.780902i
$683$	16099.5			0.901948			0.450974	−	0.892537i	$-0.351077\pi$
$683$	16099.5			0.901948			0.450974	+	0.892537i	$0.351077\pi$
$684$	793.494	+	2442.12i	0.0443567	+	0.136516i
$685$	5255.05	+	3818.02i	0.293117	+	0.212962i
$686$	14534.6	−	10560.0i	0.808940	−	0.587729i
$687$	−300.782	+	925.712i	−0.0167039	+	0.0514092i
$688$	7516.27	−	23132.7i	0.416505	−	1.28187i
$689$	−647.974	+	470.781i	−0.0358285	+	0.0260309i
$690$	5595.84	+	4065.62i	0.308739	+	0.224312i
$691$	−6881.07	−	21177.8i	−0.378825	−	1.16590i	−0.940861	−	0.338792i	$-0.889982\pi$
$691$	−6881.07	−	21177.8i	−0.378825	−	1.16590i	0.562036	−	0.827113i	$-0.310018\pi$
$692$	−35.5151			−0.00195098
$693$	6454.49	−	5672.09i	0.353803	−	0.310916i
$694$	20959.4			1.14641
$695$	1489.54	+	4584.34i	0.0812972	+	0.250207i
$696$	3553.95	+	2582.09i	0.193552	+	0.140624i
$697$	−14539.1	+	10563.3i	−0.790111	+	0.574049i
$698$	−1260.12	+	3878.27i	−0.0683330	+	0.210307i
$699$	−260.978	+	803.208i	−0.0141217	+	0.0434622i
$700$	2655.37	−	1929.24i	0.143377	−	0.104169i
$701$	−17265.4	−	12544.1i	−0.930250	−	0.675866i	0.0158040	−	0.999875i	$-0.494969\pi$
$701$	−17265.4	−	12544.1i	−0.930250	−	0.675866i	−0.946054	+	0.324009i	$0.894969\pi$
$702$	503.538	+	1549.73i	0.0270724	+	0.0833203i
$703$	6458.71			0.346508
$704$	−11991.2	+	1114.17i	−0.641953	+	0.0596477i
$705$	−11741.7			−0.627261
$706$	−4274.66	−	13156.0i	−0.227874	−	0.701323i
$707$	2032.28	+	1476.54i	0.108107	+	0.0785444i
$708$	−179.161	+	130.168i	−0.00951026	+	0.00690961i
$709$	−7923.60	+	24386.3i	−0.419714	+	1.29175i	0.488252	+	0.872703i	$0.337635\pi$
$709$	−7923.60	+	24386.3i	−0.419714	+	1.29175i	−0.907966	+	0.419044i	$0.862365\pi$
$710$	16737.5	−	51512.7i	0.884713	−	2.72287i
$711$	11448.6	−	8317.88i	0.603875	−	0.438741i
$712$	647.989	+	470.791i	0.0341073	+	0.0247804i
$713$	3339.73	+	10278.6i	0.175419	+	0.539884i
$714$	−4403.45			−0.230805
$715$	−897.052	+	3983.27i	−0.0469201	+	0.208344i
$716$	2842.61			0.148370
$717$	−3182.75	−	9795.48i	−0.165777	−	0.510208i
$718$	621.433	+	451.498i	0.0323004	+	0.0234676i
$719$	18706.6	−	13591.2i	0.970292	−	0.704958i	0.0147738	−	0.999891i	$-0.495297\pi$
$719$	18706.6	−	13591.2i	0.970292	−	0.704958i	0.955518	+	0.294933i	$0.0952972\pi$
$720$	−9975.97	+	30702.9i	−0.516365	+	1.58921i
$721$	−1131.53	+	3482.50i	−0.0584473	+	0.179882i
$722$	−10455.6	+	7596.41i	−0.538941	+	0.391564i
$723$	7669.12	+	5571.94i	0.394492	+	0.286615i
$724$	1990.81	+	6127.07i	0.102193	+	0.314518i
$725$	25953.0			1.32948
$726$	−4452.17	+	4710.82i	−0.227597	+	0.240819i
$727$	−1183.00			−0.0603507			−0.0301753	−	0.999545i	$-0.509607\pi$
$727$	−1183.00			−0.0603507			−0.0301753	+	0.999545i	$0.509607\pi$
$728$	364.253	+	1121.06i	0.0185441	+	0.0570730i
$729$	8122.23	+	5901.14i	0.412652	+	0.299809i
$730$	−22816.0	+	16576.8i	−1.15679	+	0.840457i
$731$	−9358.49	+	28802.5i	−0.473511	+	1.45732i
$732$	−234.744	+	722.468i	−0.0118530	+	0.0364797i
$733$	−9593.61	+	6970.17i	−0.483422	+	0.351226i	−0.802649	−	0.596452i	$-0.796577\pi$
$733$	−9593.61	+	6970.17i	−0.483422	+	0.351226i	0.319227	+	0.947678i	$0.396577\pi$
$734$	31733.9	+	23056.1i	1.59580	+	1.15942i
$735$	−2068.57	−	6366.40i	−0.103810	−	0.319494i
$736$	7220.31			0.361609
$737$	1033.39	−	4588.66i	0.0516490	−	0.229343i
$738$	14789.3			0.737669
$739$	−10324.9	−	31776.8i	−0.513949	−	1.58177i	−0.785187	−	0.619259i	$-0.787433\pi$
$739$	−10324.9	−	31776.8i	−0.513949	−	1.58177i	0.271238	−	0.962512i	$-0.412567\pi$
$740$	−3398.47	−	2469.13i	−0.168824	−	0.122658i
$741$	425.271	−	308.977i	0.0210833	−	0.0153179i
$742$	−1153.94	+	3551.47i	−0.0570924	+	0.175712i
$743$	−9851.15	+	30318.7i	−0.486411	+	1.49702i	0.343515	+	0.939147i	$0.388382\pi$
$743$	−9851.15	+	30318.7i	−0.486411	+	1.49702i	−0.829926	+	0.557873i	$0.811618\pi$
$744$	3115.19	−	2263.32i	0.153506	−	0.111529i
$745$	−35632.9	−	25888.8i	−1.75233	−	1.27314i
$746$	−5434.90	−	16726.9i	−0.266737	−	0.820932i
$747$	−4631.21			−0.226837
$748$	−6806.23	+	632.408i	−0.332701	+	0.0309133i
$749$	−10846.0			−0.529109
$750$	−1251.02	−	3850.25i	−0.0609078	−	0.187455i
$751$	−12957.4	−	9414.13i	−0.629592	−	0.457425i	0.226667	−	0.973972i	$-0.427217\pi$
$751$	−12957.4	−	9414.13i	−0.629592	−	0.457425i	−0.856259	+	0.516547i	$0.827217\pi$
$752$	−27099.6	+	19689.0i	−1.31413	+	0.954768i
$753$	−2511.89	+	7730.80i	−0.121565	+	0.374138i
$754$	948.521	−	2919.25i	0.0458131	−	0.140998i
$755$	−7543.55	+	5480.71i	−0.363626	+	0.264190i
$756$	1220.33	+	886.624i	0.0587078	+	0.0426537i
$757$	−2806.24	−	8636.71i	−0.134735	−	0.414672i	0.860814	−	0.508920i	$-0.169955\pi$
$757$	−2806.24	−	8636.71i	−0.134735	−	0.414672i	−0.995549	+	0.0942484i	$0.969955\pi$
$758$	9486.63			0.454578
$759$	−3474.66	+	3053.48i	−0.166169	+	0.146027i
$760$	17274.2			0.824473
$761$	6751.26	+	20778.2i	0.321594	+	0.989765i	0.972955	+	0.230996i	$0.0741985\pi$
$761$	6751.26	+	20778.2i	0.321594	+	0.989765i	−0.651361	+	0.758768i	$0.725801\pi$
$762$	−2645.05	−	1921.74i	−0.125748	−	0.0913614i
$763$	7978.81	−	5796.94i	0.378574	−	0.275050i
$764$	937.533	−	2885.43i	0.0443963	−	0.136638i
$765$	12421.1	−	38228.1i	0.587038	−	1.80672i
$766$	−4947.98	+	3594.92i	−0.233392	+	0.169569i
$767$	−380.128	−	276.179i	−0.0178952	−	0.0130016i
$768$	−1368.35	−	4211.35i	−0.0642918	−	0.197870i
$769$	21420.5			1.00448			0.502239	−	0.864729i	$-0.332510\pi$
$769$	21420.5			1.00448			0.502239	+	0.864729i	$0.332510\pi$
$770$	7532.34	+	17482.8i	0.352528	+	0.818229i
$771$	9422.97			0.440155
$772$	−2120.97	−	6527.69i	−0.0988802	−	0.304322i
$773$	1982.31	+	1440.23i	0.0922362	+	0.0670136i	0.632948	−	0.774195i	$-0.281845\pi$
$773$	1982.31	+	1440.23i	0.0922362	+	0.0670136i	−0.540711	+	0.841208i	$0.681845\pi$
$774$	20162.7	−	14649.0i	0.936346	−	0.680295i
$775$	7029.81	−	21635.5i	0.325830	−	1.00280i
$776$	−7553.71	+	23247.9i	−0.349436	+	1.07545i
$777$	1464.10	−	1063.73i	0.0675990	−	0.0491135i
$778$	−13888.8	−	10090.8i	−0.640024	−	0.465005i
$779$	−3090.85	−	9512.66i	−0.142158	−	0.437518i
$780$	−341.890			−0.0156944
$781$	31148.6	+	18488.4i	1.42712	+	0.847079i
$782$	−24568.9			−1.12351
$783$	3685.73	+	11343.5i	0.168221	+	0.517731i
$784$	−15449.7	−	11224.8i	−0.703793	−	0.511336i
$785$	9207.69	−	6689.78i	0.418645	−	0.304164i
$786$	3363.52	−	10351.9i	0.152637	−	0.469769i
$787$	−3823.42	+	11767.3i	−0.173177	+	0.532983i	−0.999546	−	0.0301460i	$-0.990403\pi$
$787$	−3823.42	+	11767.3i	−0.173177	+	0.532983i	0.826369	+	0.563129i	$0.190403\pi$
$788$	4148.73	−	3014.23i	0.187554	−	0.136266i
$789$	3404.43	+	2473.46i	0.153613	+	0.111606i
$790$	9688.04	+	29816.7i	0.436310	+	1.34282i
$791$	−2970.29			−0.133516
$792$	−14688.5	−	8718.47i	−0.659007	−	0.391158i
$793$	−1611.76			−0.0721755
$794$	7943.96	+	24449.0i	0.355064	+	1.09277i
$795$	2660.73	+	1933.14i	0.118700	+	0.0862406i
$796$	−2488.91	+	1808.30i	−0.110826	+	0.0805195i
$797$	6072.41	−	18688.9i	0.269882	−	0.830610i	−0.720647	−	0.693302i	$-0.756155\pi$
$797$	6072.41	−	18688.9i	0.269882	−	0.830610i	0.990528	−	0.137308i	$-0.0438450\pi$
$798$	757.341	−	2330.86i	0.0335960	−	0.103398i
$799$	33741.7	−	24514.8i	1.49399	−	1.08545i
$800$	−12295.5	−	8933.21i	−0.543390	−	0.394796i
$801$	320.544	+	986.533i	0.0141397	+	0.0435174i
$802$	13810.5			0.608061
$803$	−7462.68	−	17321.1i	−0.327960	−	0.761206i
$804$	393.852			0.0172762
$805$	4198.06	+	12920.3i	0.183804	+	0.565691i
$806$	−2176.69	−	1581.46i	−0.0951247	−	0.0691122i
$807$	−5557.80	+	4037.98i	−0.242434	+	0.176138i
$808$	1543.12	−	4749.22i	0.0671864	−	0.206779i
$809$	8460.25	−	26038.0i	0.367672	−	1.13158i	−0.580619	−	0.814175i	$-0.697189\pi$
$809$	8460.25	−	26038.0i	0.367672	−	1.13158i	0.948291	−	0.317402i	$-0.102811\pi$
$810$	−23929.7	+	17386.0i	−1.03803	+	0.754174i
$811$	29480.3	+	21418.7i	1.27644	+	0.927389i	0.999439	−	0.0334808i	$-0.0106593\pi$
$811$	29480.3	+	21418.7i	1.27644	+	0.927389i	0.277002	+	0.960869i	$0.410659\pi$
$812$	−878.047	−	2702.35i	−0.0379476	−	0.116791i
$813$	−9237.40			−0.398487
$814$	10628.2	−	9339.90i	0.457640	−	0.402166i
$815$	−49365.7			−2.12172
$816$	3418.94	+	10522.4i	0.146675	+	0.451420i
$817$	−13636.3	−	9907.37i	−0.583935	−	0.424253i
$818$	22617.3	−	16432.4i	0.966744	−	0.702380i
$819$	−471.736	+	1451.85i	−0.0201267	+	0.0619437i
$820$	−2010.28	+	6187.02i	−0.0856124	+	0.263488i
$821$	−14383.8	+	10450.4i	−0.611447	+	0.444242i	−0.849924	−	0.526906i	$-0.823352\pi$
$821$	−14383.8	+	10450.4i	−0.611447	+	0.444242i	0.238477	+	0.971148i	$0.423352\pi$
$822$	−1482.11	−	1076.81i	−0.0628886	−	0.0456913i
$823$	3000.47	+	9234.48i	0.127083	+	0.391123i	0.994275	−	0.106852i	$-0.0340772\pi$
$823$	3000.47	+	9234.48i	0.127083	+	0.391123i	−0.867191	+	0.497975i	$0.834077\pi$
$824$	7279.06			0.307740
$825$	9694.88	−	900.810i	0.409130	−	0.0380148i
$826$	−2190.65			−0.0922792
$827$	−5509.99	−	16958.0i	−0.231682	−	0.713044i	−0.997544	−	0.0700392i	$-0.977688\pi$
$827$	−5509.99	−	16958.0i	−0.231682	−	0.713044i	0.765862	−	0.643005i	$-0.222312\pi$
$828$	3247.72	+	2359.61i	0.136312	+	0.0990363i
$829$	−32366.3	+	23515.5i	−1.35600	+	0.985195i	−0.357317	+	0.933983i	$0.616308\pi$
$829$	−32366.3	+	23515.5i	−1.35600	+	0.985195i	−0.998688	+	0.0512121i	$0.983692\pi$
$830$	3170.56	−	9757.98i	0.132593	−	0.408078i
$831$	539.106	−	1659.20i	0.0225047	−	0.0692622i
$832$	1730.92	−	1257.59i	0.0721262	−	0.0524027i
$833$	19236.4	+	13976.0i	0.800120	+	0.581321i
$834$	−420.103	−	1292.94i	−0.0174424	−	0.0536823i
$835$	−67030.2			−2.77806
$836$	835.841	−	3711.47i	0.0345791	−	0.153545i
$837$	10454.8			0.431744
$838$	−9797.45	−	30153.4i	−0.403875	−	1.24300i
$839$	−7702.06	−	5595.88i	−0.316931	−	0.230264i	0.417934	−	0.908477i	$-0.362754\pi$
$839$	−7702.06	−	5595.88i	−0.316931	−	0.230264i	−0.734865	+	0.678214i	$0.762754\pi$
$840$	3915.82	−	2845.01i	0.160844	−	0.116860i
$841$	−593.767	+	1827.43i	−0.0243457	+	0.0749283i
$842$	−7768.34	+	23908.5i	−0.317951	+	0.978552i
$843$	−2678.57	+	1946.10i	−0.109437	+	0.0795103i
$844$	9697.30	+	7045.50i	0.395491	+	0.287341i
$845$	11498.5	+	35388.8i	0.468119	+	1.44072i
$846$	−34322.3			−1.39483
$847$	−12512.8	+	2345.53i	−0.507609	+	0.0951515i
$848$	9382.48			0.379948
$849$	−1238.96	−	3813.11i	−0.0500835	−	0.154141i
$850$	41838.5	+	30397.4i	1.68829	+	1.22662i
$851$	8168.90	−	5935.06i	0.329056	−	0.239073i
$852$	−937.265	+	2884.60i	−0.0376880	+	0.115992i
$853$	−8753.99	+	26942.0i	−0.351384	+	1.08145i	0.606692	+	0.794937i	$0.292496\pi$
$853$	−8753.99	+	26942.0i	−0.351384	+	1.08145i	−0.958076	+	0.286513i	$0.907504\pi$
$854$	−6079.37	+	4416.92i	−0.243597	+	0.176984i
$855$	18098.8	+	13149.6i	0.723937	+	0.525971i
$856$	6662.56	+	20505.2i	0.266030	+	0.818755i
$857$	9537.44			0.380155			0.190078	−	0.981769i	$-0.439126\pi$
$857$	9537.44			0.380155			0.190078	+	0.981769i	$0.439126\pi$
$858$	253.000	−	1123.42i	0.0100668	−	0.0447005i
$859$	47932.8			1.90390			0.951948	−	0.306258i	$-0.0990771\pi$
$859$	47932.8			1.90390			0.951948	+	0.306258i	$0.0990771\pi$
$860$	3387.67	+	10426.2i	0.134324	+	0.413407i
$861$	−2267.36	−	1647.34i	−0.0897463	−	0.0652045i
$862$	18045.4	−	13110.7i	0.713025	−	0.518043i
$863$	14732.9	−	45343.2i	0.581128	−	1.78853i	−0.0331644	−	0.999450i	$-0.510558\pi$
$863$	14732.9	−	45343.2i	0.581128	−	1.78853i	0.614292	−	0.789078i	$-0.289442\pi$
$864$	2158.36	−	6642.75i	0.0849871	−	0.261564i
$865$	−250.323	+	181.871i	−0.00983960	+	0.00714888i
$866$	−14743.5	−	10711.8i	−0.578527	−	0.420325i
$867$	−1916.79	−	5899.27i	−0.0750837	−	0.231084i
$868$	−2490.63			−0.0973934
$869$	−20876.4	+	1939.75i	−0.814940	+	0.0757210i
$870$	−12604.0			−0.491167
$871$	258.227	+	794.742i	0.0100456	+	0.0309171i
$872$	−15860.9	−	11523.6i	−0.615962	−	0.447522i
$873$	−25611.3	+	18607.7i	−0.992909	+	0.721391i
$874$	4225.56	−	13004.9i	0.163537	−	0.503316i
$875$	2457.10	−	7562.19i	0.0949317	−	0.292170i
$876$	1277.65	−	928.265i	0.0492782	−	0.0358027i
$877$	−6049.13	−	4394.95i	−0.232913	−	0.169221i	0.465207	−	0.885202i	$-0.345980\pi$
$877$	−6049.13	−	4394.95i	−0.232913	−	0.169221i	−0.698120	+	0.715981i	$0.745980\pi$
$878$	−7631.50	−	23487.3i	−0.293338	−	0.902801i
$879$	−9929.37			−0.381012
$880$	35928.3	−	31573.2i	1.37630	−	1.20947i
$881$	24097.1			0.921510			0.460755	−	0.887527i	$-0.347579\pi$
$881$	24097.1			0.921510			0.460755	+	0.887527i	$0.347579\pi$
$882$	−6046.64	−	18609.6i	−0.230840	−	0.710452i
$883$	−1138.85	−	827.423i	−0.0434036	−	0.0315345i	0.565872	−	0.824493i	$-0.308540\pi$
$883$	−1138.85	−	827.423i	−0.0434036	−	0.0315345i	−0.609276	+	0.792959i	$0.708540\pi$
$884$	982.476	−	713.811i	0.0373804	−	0.0271584i
$885$	−596.208	+	1834.94i	−0.0226456	+	0.0696959i
$886$	−6482.92	+	19952.4i	−0.245822	+	0.756561i
$887$	2656.82	−	1930.29i	0.100572	−	0.0730698i	−0.536363	−	0.843988i	$-0.680202\pi$
$887$	2656.82	−	1930.29i	0.100572	−	0.0730698i	0.636935	+	0.770918i	$0.280202\pi$
$888$	−2910.46	−	2114.58i	−0.109987	−	0.0799105i
$889$	−1984.34	−	6107.19i	−0.0748625	−	0.230403i
$890$	−2298.08			−0.0865525
$891$	−7826.98	−	18166.7i	−0.294291	−	0.683059i
$892$	−2394.20			−0.0898695
$893$	7173.11	+	22076.6i	0.268801	+	0.827284i
$894$	10049.7	+	7301.55i	0.375965	+	0.273155i
$895$	20035.7	−	14556.8i	0.748291	−	0.543666i
$896$	5158.02	−	15874.8i	0.192319	−	0.591896i
$897$	253.951	−	781.581i	0.00945282	−	0.0290928i
$898$	25250.8	−	18345.8i	0.938341	−	0.681745i
$899$	−15932.6	−	11575.7i	−0.591081	−	0.429446i
$900$	−2611.18	−	8036.38i	−0.0967103	−	0.297644i
$901$	−11682.1			−0.431950
$902$	−18842.4	−	11184.0i	−0.695547	−	0.412847i
$903$	−4722.89			−0.174051
$904$	1824.61	+	5615.59i	0.0671303	+	0.206606i
$905$	45408.3	+	32991.1i	1.66787	+	1.21178i
$906$	2127.54	−	1545.75i	0.0780165	−	0.0566823i
$907$	−8038.55	+	24740.1i	−0.294284	+	0.905713i	0.689177	+	0.724593i	$0.257972\pi$
$907$	−8038.55	+	24740.1i	−0.294284	+	0.905713i	−0.983461	+	0.181120i	$0.942028\pi$
$908$	−3171.41	+	9760.59i	−0.115911	+	0.356736i
$909$	5232.02	−	3801.28i	0.190908	−	0.138703i
$910$	−2736.11	−	1987.90i	−0.0996716	−	0.0724157i
$911$	2322.93	+	7149.24i	0.0844809	+	0.260006i	0.984370	−	0.176114i	$-0.0563526\pi$
$911$	2322.93	+	7149.24i	0.0844809	+	0.260006i	−0.899889	+	0.436119i	$0.856353\pi$
$912$	−6157.80			−0.223580
$913$	5900.44	+	3502.25i	0.213884	+	0.126952i
$914$	−45088.2			−1.63171
$915$	2045.15	+	6294.33i	0.0738914	+	0.227414i
$916$	−1012.51	−	735.632i	−0.0365222	−	0.0265349i
$917$	17295.3	−	12565.8i	0.622836	−	0.452517i
$918$	−7344.35	+	22603.6i	−0.264052	+	0.812668i
$919$	−3323.73	+	10229.4i	−0.119303	+	0.367178i	−0.992820	−	0.119616i	$-0.961834\pi$
$919$	−3323.73	+	10229.4i	−0.119303	+	0.367178i	0.873517	+	0.486794i	$0.161834\pi$
$920$	21848.1	−	15873.6i	0.782948	−	0.568845i
$921$	−7486.73	−	5439.43i	−0.267857	−	0.194609i
$922$	3121.13	+	9605.86i	0.111485	+	0.343115i
$923$	−6435.28			−0.229491
$924$	−421.796	−	979.001i	−0.0150174	−	0.0348558i
$925$	−21253.9			−0.755486
$926$	7743.25	+	23831.3i	0.274794	+	0.845728i
$927$	7626.56	+	5541.02i	0.270215	+	0.196322i
$928$	−10644.2	+	7733.48i	−0.376523	+	0.273560i
$929$	−1209.48	+	3722.41i	−0.0427146	+	0.131462i	−0.970140	−	0.242547i	$-0.922017\pi$
$929$	−1209.48	+	3722.41i	−0.0427146	+	0.131462i	0.927425	+	0.374009i	$0.122017\pi$
$930$	−3414.01	+	10507.2i	−0.120376	+	0.370479i
$931$	−10706.3	+	7778.57i	−0.376890	+	0.273826i
$932$	−878.520	−	638.282i	−0.0308765	−	0.0224331i
$933$	2484.47	+	7646.42i	0.0871790	+	0.268309i
$934$	18636.4			0.652893
$935$	−44734.3	+	39311.7i	−1.56467	+	1.37501i
$936$	3034.64			0.105973
$937$	7568.24	+	23292.7i	0.263867	+	0.812100i	0.991952	+	0.126613i	$0.0404107\pi$
$937$	7568.24	+	23292.7i	0.263867	+	0.812100i	−0.728085	+	0.685487i	$0.759589\pi$
$938$	3151.95	+	2290.03i	0.109717	+	0.0797143i
$939$	7237.30	−	5258.20i	0.251523	−	0.182742i
$940$	4665.38	−	14358.6i	0.161881	−	0.498218i
$941$	12094.9	−	37224.2i	0.419002	−	1.28956i	−0.489619	−	0.871936i	$-0.662864\pi$
$941$	12094.9	−	37224.2i	0.419002	−	1.28956i	0.908622	−	0.417620i	$-0.137136\pi$
$942$	−2596.89	+	1886.75i	−0.0898209	+	0.0652587i
$943$	−12650.7	−	9191.25i	−0.436864	−	0.317400i
$944$	1700.87	+	5234.75i	0.0586427	+	0.180484i
$945$	13141.7			0.452381
$946$	−36766.4	+	3416.19i	−1.26361	+	0.117410i
$947$	29856.8			1.02451			0.512257	−	0.858832i	$-0.328809\pi$
$947$	29856.8			1.02451			0.512257	+	0.858832i	$0.328809\pi$
$948$	−542.511	−	1669.68i	−0.0185864	−	0.0572031i
$949$	2710.81	+	1969.52i	0.0927255	+	0.0673690i
$950$	−23285.8	+	16918.2i	−0.795255	+	0.577787i
$951$	3622.53	−	11149.0i	0.123521	−	0.380159i
$952$	−5312.81	+	16351.2i	−0.180871	+	0.556664i
$953$	21099.4	−	15329.6i	0.717186	−	0.521066i	−0.168298	−	0.985736i	$-0.553827\pi$
$953$	21099.4	−	15329.6i	0.717186	−	0.521066i	0.885484	+	0.464670i	$0.153827\pi$
$954$	7777.59	+	5650.75i	0.263951	+	0.191771i
$955$	−8168.03	−	25138.6i	−0.276766	−	0.851798i
$956$	13243.2			0.448028
$957$	1851.87	−	8223.07i	0.0625523	−	0.277758i
$958$	−23067.4			−0.777947
$959$	−1111.89	−	3422.05i	−0.0374399	−	0.115228i
$960$	−7107.58	−	5163.96i	−0.238954	−	0.173610i
$961$	10135.8	−	7364.09i	0.340230	−	0.247192i
$962$	−776.780	+	2390.68i	−0.0260337	+	0.0801234i
$963$	−8628.52	+	26555.9i	−0.288733	+	0.888630i
$964$	−9860.94	+	7164.39i	−0.329460	+	0.239367i
$965$	−48377.3	−	35148.2i	−1.61380	−	1.17250i
$966$	−1184.00	−	3643.98i	−0.0394354	−	0.121370i
$967$	23639.7			0.786145			0.393073	−	0.919507i	$-0.371412\pi$
$967$	23639.7			0.786145			0.393073	+	0.919507i	$0.371412\pi$
$968$	12120.9	+	22215.7i	0.402459	+	0.737644i
$969$	7667.06			0.254181
$970$	−21672.8	−	66702.0i	−0.717393	−	2.20791i
$971$	−16299.7	−	11842.4i	−0.538706	−	0.391393i	0.284898	−	0.958558i	$-0.408040\pi$
$971$	−16299.7	−	11842.4i	−0.538706	−	0.391393i	−0.823604	+	0.567165i	$0.808040\pi$
$972$	4784.84	−	3476.39i	0.157895	−	0.114717i
$973$	825.115	−	2539.44i	0.0271860	−	0.0836699i
$974$	−8041.41	+	24748.9i	−0.264541	+	0.814175i
$975$	−1399.45	+	1016.76i	−0.0459675	+	0.0333974i
$976$	15274.8	+	11097.8i	0.500957	+	0.363966i
$977$	−1892.05	−	5823.14i	−0.0619571	−	0.190684i	0.915287	−	0.402802i	$-0.131964\pi$
$977$	−1892.05	−	5823.14i	−0.0619571	−	0.190684i	−0.977244	+	0.212118i	$0.931964\pi$
$978$	13922.9			0.455219
$979$	337.651	−	1499.31i	0.0110228	−	0.0489459i
$980$	8607.17			0.280557
$981$	−7846.01	−	24147.5i	−0.255355	−	0.785903i
$982$	37962.7	+	27581.5i	1.23364	+	0.896296i
$983$	6443.34	−	4681.36i	0.209065	−	0.151895i	−0.478326	−	0.878183i	$-0.658756\pi$
$983$	6443.34	−	4681.36i	0.209065	−	0.151895i	0.687390	+	0.726288i	$0.258756\pi$
$984$	−1721.62	+	5298.59i	−0.0557756	+	0.171660i
$985$	13806.1	−	42490.8i	0.446597	−	1.37449i
$986$	36219.6	−	26315.1i	1.16984	−	0.849941i
$987$	5262.00	+	3823.07i	0.169697	+	0.123292i
$988$	208.864	+	642.816i	0.00672554	+	0.0206991i
$989$	−26351.2			−0.847238
$990$	48798.2	−	4534.14i	1.56658	−	0.145560i
$991$	34996.8			1.12181			0.560904	−	0.827881i	$-0.310454\pi$
$991$	34996.8			1.12181			0.560904	+	0.827881i	$0.310454\pi$
$992$	3563.79	+	10968.2i	0.114063	+	0.351050i
$993$	−3238.63	−	2353.00i	−0.103499	−	0.0751966i
$994$	−24273.2	+	17635.5i	−0.774546	+	0.562740i
$995$	−8282.58	+	25491.1i	−0.263895	+	0.812185i
$996$	−177.545	+	546.427i	−0.00564832	+	0.0173837i
$997$	−18737.1	+	13613.3i	−0.595197	+	0.432436i	−0.844171	−	0.536074i	$-0.819907\pi$
$997$	−18737.1	+	13613.3i	−0.595197	+	0.432436i	0.248974	+	0.968510i	$0.419907\pi$
$998$	14484.8	+	10523.9i	0.459429	+	0.333794i
$999$	−3018.38	−	9289.62i	−0.0955929	−	0.294205i

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	11.4.c.a.5.1	✓	8
3.2	odd	2		99.4.f.c.82.2		8
4.3	odd	2		176.4.m.c.49.1		8
11.2	odd	10		121.4.c.i.9.2		8
11.3	even	5		121.4.a.g.1.1		4
11.4	even	5		121.4.c.h.3.2		8
11.5	even	5		121.4.c.h.81.2		8
11.6	odd	10		121.4.c.b.81.1		8
11.7	odd	10		121.4.c.b.3.1		8
11.8	odd	10		121.4.a.f.1.4		4
11.9	even	5	inner	11.4.c.a.9.1	yes	8
11.10	odd	2		121.4.c.i.27.2		8
33.8	even	10		1089.4.a.bh.1.1		4
33.14	odd	10		1089.4.a.y.1.4		4
33.20	odd	10		99.4.f.c.64.2		8
44.3	odd	10		1936.4.a.bk.1.3		4
44.19	even	10		1936.4.a.bl.1.3		4
44.31	odd	10		176.4.m.c.97.1		8

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
11.4.c.a.5.1	✓	8	1.1	even	1	trivial
11.4.c.a.9.1	yes	8	11.9	even	5	inner
99.4.f.c.64.2		8	33.20	odd	10
99.4.f.c.82.2		8	3.2	odd	2
121.4.a.f.1.4		4	11.8	odd	10
121.4.a.g.1.1		4	11.3	even	5
121.4.c.b.3.1		8	11.7	odd	10
121.4.c.b.81.1		8	11.6	odd	10
121.4.c.h.3.2		8	11.4	even	5
121.4.c.h.81.2		8	11.5	even	5
121.4.c.i.9.2		8	11.2	odd	10
121.4.c.i.27.2		8	11.10	odd	2
176.4.m.c.49.1		8	4.3	odd	2
176.4.m.c.97.1		8	44.31	odd	10
1089.4.a.y.1.4		4	33.14	odd	10
1089.4.a.bh.1.1		4	33.8	even	10
1936.4.a.bk.1.3		4	44.3	odd	10
1936.4.a.bl.1.3		4	44.19	even	10

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:	\( N \)	\(=\)	\( 11 \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	11.c (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-0.976313 - 3.00478i) q^{2} +(1.24700 + 0.906001i) q^{3} +(-1.60339 + 1.16493i) q^{4} +(-5.33576 + 16.4218i) q^{5} +(1.50487 - 4.63152i) q^{6} +(7.73807 - 5.62204i) q^{7} +(-15.3824 - 11.1760i) q^{8} +(-7.60928 - 23.4190i) q^{9} +O(q^{10})\)	\(q+(-0.976313 - 3.00478i) q^{2} +(1.24700 + 0.906001i) q^{3} +(-1.60339 + 1.16493i) q^{4} +(-5.33576 + 16.4218i) q^{5} +(1.50487 - 4.63152i) q^{6} +(7.73807 - 5.62204i) q^{7} +(-15.3824 - 11.1760i) q^{8} +(-7.60928 - 23.4190i) q^{9} +54.5532 q^{10} +(-8.01537 + 35.5915i) q^{11} -3.05487 q^{12} +(-2.00292 - 6.16434i) q^{13} +(-24.4478 - 17.7624i) q^{14} +(-21.5319 + 15.6438i) q^{15} +(-23.4628 + 72.2111i) q^{16} +(29.2135 - 89.9099i) q^{17} +(-62.9398 + 45.7285i) q^{18} +(42.5672 + 30.9269i) q^{19} +(-10.5750 - 32.5464i) q^{20} +14.7430 q^{21} +(114.770 - 10.6640i) q^{22} +82.2579 q^{23} +(-9.05645 - 27.8729i) q^{24} +(-140.077 - 101.772i) q^{25} +(-16.5670 + 12.0367i) q^{26} +(24.5893 - 75.6779i) q^{27} +(-5.85788 + 18.0287i) q^{28} +(-121.265 + 88.1041i) q^{29} +(68.0281 + 49.4253i) q^{30} +(40.6007 + 124.956i) q^{31} +87.7765 q^{32} +(-42.2411 + 37.1208i) q^{33} -298.681 q^{34} +(51.0354 + 157.071i) q^{35} +(39.4822 + 28.6855i) q^{36} +(99.3085 - 72.1518i) q^{37} +(51.3696 - 158.099i) q^{38} +(3.08726 - 9.50160i) q^{39} +(265.606 - 192.974i) q^{40} +(-153.793 - 111.737i) q^{41} +(-14.3938 - 44.2994i) q^{42} -320.348 q^{43} +(-28.6099 - 66.4046i) q^{44} +425.182 q^{45} +(-80.3094 - 247.167i) q^{46} +(356.916 + 259.314i) q^{47} +(-94.6816 + 68.7902i) q^{48} +(-77.7224 + 239.205i) q^{49} +(-169.044 + 520.263i) q^{50} +(117.888 - 85.6505i) q^{51} +(10.3925 + 7.55060i) q^{52} +(-38.1858 - 117.524i) q^{53} -251.403 q^{54} +(-541.707 - 321.534i) q^{55} -181.862 q^{56} +(25.0617 + 77.1318i) q^{57} +(383.126 + 278.358i) q^{58} +(58.6475 - 42.6099i) q^{59} +(16.3001 - 50.1664i) q^{60} +(76.8425 - 236.497i) q^{61} +(335.827 - 243.993i) q^{62} +(-190.543 - 138.438i) q^{63} +(102.005 + 313.940i) q^{64} +111.916 q^{65} +(152.780 + 90.6839i) q^{66} -128.926 q^{67} +(57.8984 + 178.193i) q^{68} +(102.576 + 74.5257i) q^{69} +(422.137 - 306.700i) q^{70} +(306.810 - 944.264i) q^{71} +(-144.680 + 445.280i) q^{72} +(-418.233 + 303.864i) q^{73} +(-313.757 - 227.958i) q^{74} +(-82.4713 - 253.820i) q^{75} -104.280 q^{76} +(138.073 + 320.472i) q^{77} -31.5644 q^{78} +(177.589 + 546.562i) q^{79} +(-1060.64 - 770.603i) q^{80} +(-438.649 + 318.697i) q^{81} +(-185.596 + 571.204i) q^{82} +(58.1187 - 178.871i) q^{83} +(-23.6388 + 17.1746i) q^{84} +(1320.60 + 959.475i) q^{85} +(312.760 + 962.577i) q^{86} -231.040 q^{87} +(521.064 - 457.902i) q^{88} -42.1254 q^{89} +(-415.111 - 1277.58i) q^{90} +(-50.1549 - 36.4396i) q^{91} +(-131.892 + 95.8250i) q^{92} +(-62.5812 + 192.605i) q^{93} +(430.722 - 1325.63i) q^{94} +(-735.003 + 534.011i) q^{95} +(109.458 + 79.5257i) q^{96} +(-397.278 - 1222.70i) q^{97} +794.640 q^{98} +(894.506 - 83.1140i) q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9}+O(q^{10}) \) 8 * q - 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - 29 * q^6 - 35 * q^7 + 47 * q^8 + 31 * q^9	\( 8 q - 7 q^{2} - 3 q^{3} + 3 q^{4} - 7 q^{5} - 29 q^{6} - 35 q^{7} + 47 q^{8} + 31 q^{9} + 40 q^{10} + 67 q^{11} + 190 q^{12} - 65 q^{13} - 196 q^{14} - 121 q^{15} - 377 q^{16} - 31 q^{17} - 102 q^{18} + 148 q^{19} + 342 q^{20} + 334 q^{21} + 647 q^{22} - 12 q^{23} - 447 q^{24} - 201 q^{25} - 140 q^{26} + 72 q^{27} - 42 q^{28} - 199 q^{29} - 114 q^{30} - 361 q^{31} + 324 q^{32} - 232 q^{33} - 298 q^{34} + 237 q^{35} + 120 q^{36} + 81 q^{37} - 52 q^{38} + 365 q^{39} + 532 q^{40} - 31 q^{41} + 170 q^{42} - 650 q^{43} - 1208 q^{44} + 452 q^{45} + 1204 q^{46} + 857 q^{47} + 644 q^{48} + 1375 q^{49} - 147 q^{50} - 246 q^{51} - 590 q^{52} - 1493 q^{53} - 3100 q^{54} - 1583 q^{55} - 1560 q^{56} + 102 q^{57} + 1392 q^{58} + 676 q^{59} + 1068 q^{60} - 525 q^{61} + 2456 q^{62} - 68 q^{63} + 471 q^{64} + 1790 q^{65} + 1014 q^{66} + 86 q^{67} + 710 q^{68} - 42 q^{69} - 144 q^{70} + 1143 q^{71} + 919 q^{72} - 2155 q^{73} - 1476 q^{74} - 160 q^{75} - 242 q^{76} - 2015 q^{77} - 1340 q^{78} - 861 q^{79} - 1916 q^{80} - 26 q^{81} - 3497 q^{82} + 52 q^{83} - 84 q^{84} + 2383 q^{85} + 1061 q^{86} + 2310 q^{87} + 4543 q^{88} + 3782 q^{89} - 1682 q^{90} + 135 q^{91} - 2450 q^{92} - 2077 q^{93} + 702 q^{94} - 1317 q^{95} + 1252 q^{96} - 1344 q^{97} + 2740 q^{98} + 2099 q^{99}+O(q^{100}) \) 8 * q - 7 * q^2 - 3 * q^3 + 3 * q^4 - 7 * q^5 - 29 * q^6 - 35 * q^7 + 47 * q^8 + 31 * q^9 + 40 * q^10 + 67 * q^11 + 190 * q^12 - 65 * q^13 - 196 * q^14 - 121 * q^15 - 377 * q^16 - 31 * q^17 - 102 * q^18 + 148 * q^19 + 342 * q^20 + 334 * q^21 + 647 * q^22 - 12 * q^23 - 447 * q^24 - 201 * q^25 - 140 * q^26 + 72 * q^27 - 42 * q^28 - 199 * q^29 - 114 * q^30 - 361 * q^31 + 324 * q^32 - 232 * q^33 - 298 * q^34 + 237 * q^35 + 120 * q^36 + 81 * q^37 - 52 * q^38 + 365 * q^39 + 532 * q^40 - 31 * q^41 + 170 * q^42 - 650 * q^43 - 1208 * q^44 + 452 * q^45 + 1204 * q^46 + 857 * q^47 + 644 * q^48 + 1375 * q^49 - 147 * q^50 - 246 * q^51 - 590 * q^52 - 1493 * q^53 - 3100 * q^54 - 1583 * q^55 - 1560 * q^56 + 102 * q^57 + 1392 * q^58 + 676 * q^59 + 1068 * q^60 - 525 * q^61 + 2456 * q^62 - 68 * q^63 + 471 * q^64 + 1790 * q^65 + 1014 * q^66 + 86 * q^67 + 710 * q^68 - 42 * q^69 - 144 * q^70 + 1143 * q^71 + 919 * q^72 - 2155 * q^73 - 1476 * q^74 - 160 * q^75 - 242 * q^76 - 2015 * q^77 - 1340 * q^78 - 861 * q^79 - 1916 * q^80 - 26 * q^81 - 3497 * q^82 + 52 * q^83 - 84 * q^84 + 2383 * q^85 + 1061 * q^86 + 2310 * q^87 + 4543 * q^88 + 3782 * q^89 - 1682 * q^90 + 135 * q^91 - 2450 * q^92 - 2077 * q^93 + 702 * q^94 - 1317 * q^95 + 1252 * q^96 - 1344 * q^97 + 2740 * q^98 + 2099 * q^99

Introduction

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