LMFDB - Embedded newform 150.4.g.b.61.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [150,4,Mod(31,150)]

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

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(150, base_ring=CyclotomicField(10))

chi = DirichletCharacter(H, H._module([0, 4]))

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

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

chi := DirichletCharacter("150.31");

S:= CuspForms(chi, 4);

N := Newforms(S);

Level:	$ N $	$=$	$ 150 = 2 \cdot 3 \cdot 5^{2} $
Weight:	$ k $	$=$	$ 4 $
Character orbit:	$[\chi]$	$=$	150.g (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:	$8.85028650086$
Analytic rank:	$0$
Dimension:	$16$
Relative dimension:	$4$ over $\Q(\zeta_{5})$
Coefficient field:	$\mathbb{Q}[x]/(x^{16} - \cdots)$
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{16} - 4 x^{15} + 66 x^{14} + 116 x^{13} - 15174 x^{12} + 66830 x^{11} - 253085 x^{10} + \cdots + 48733788520125 $ x^16 - 4x^15 + 66x^14 + 116x^13 - 15174x^12 + 66830x^11 - 253085x^10 - 2763760x^9 + 83790040x^8 - 245751650x^7 + 550471825x^6 + 10129042700x^5 - 118334390050x^4 + 286942998000x^3 + 664960189500x^2 - 7593598503000*x + 48733788520125
Coefficient ring:	$\Z[a_1, \ldots, a_{7}]$
Coefficient ring index:	$ 5^{4} $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{5}]$

Embedding invariants

Embedding label			61.3
Root			$1.36008 + 4.54276i$ of defining polynomial
Character	$\chi$	$=$	150.61
Dual form			150.4.g.b.91.3

$q$-expansion

comment: q-expansion

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

gp: mfcoefs(f, 20)

$f(q)$	$=$	\(q+(-1.61803 + 1.17557i) q^{2} +(0.927051 - 2.85317i) q^{3} +(1.23607 - 3.80423i) q^{4} +(0.900748 - 11.1440i) q^{5} +(1.85410 + 5.70634i) q^{6} -31.6588 q^{7} +(2.47214 + 7.60845i) q^{8} +(-7.28115 - 5.29007i) q^{9} +(11.6431 + 19.0903i) q^{10} +(-32.3404 + 23.4967i) q^{11} +(-9.70820 - 7.05342i) q^{12} +(57.7437 + 41.9533i) q^{13} +(51.2251 - 37.2172i) q^{14} +(-30.9607 - 12.9010i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(38.0021 + 116.958i) q^{17} +18.0000 q^{18} +(-5.21701 - 16.0563i) q^{19} +(-41.2809 - 17.2014i) q^{20} +(-29.3493 + 90.3280i) q^{21} +(24.7059 - 76.0368i) q^{22} +(-37.8694 + 27.5138i) q^{23} +24.0000 q^{24} +(-123.377 - 20.0759i) q^{25} -142.750 q^{26} +(-21.8435 + 15.8702i) q^{27} +(-39.1325 + 120.437i) q^{28} +(-56.3174 + 173.327i) q^{29} +(65.2615 - 15.5221i) q^{30} +(-89.9717 - 276.905i) q^{31} +32.0000 q^{32} +(37.0588 + 114.055i) q^{33} +(-198.982 - 144.569i) q^{34} +(-28.5166 + 352.806i) q^{35} +(-29.1246 + 21.1603i) q^{36} +(-200.744 - 145.849i) q^{37} +(27.3166 + 19.8467i) q^{38} +(173.231 - 125.860i) q^{39} +(87.0153 - 20.6962i) q^{40} +(-149.266 - 108.448i) q^{41} +(-58.6987 - 180.656i) q^{42} -113.319 q^{43} +(49.4117 + 152.074i) q^{44} +(-65.5110 + 76.3761i) q^{45} +(28.9297 - 89.0364i) q^{46} +(-68.2785 + 210.140i) q^{47} +(-38.8328 + 28.2137i) q^{48} +659.281 q^{49} +(223.229 - 112.555i) q^{50} +368.932 q^{51} +(230.975 - 167.813i) q^{52} +(10.8048 - 33.2538i) q^{53} +(16.6869 - 51.3571i) q^{54} +(232.716 + 381.566i) q^{55} +(-78.2649 - 240.875i) q^{56} -50.6478 q^{57} +(-112.635 - 346.654i) q^{58} +(-528.425 - 383.923i) q^{59} +(-87.3480 + 101.835i) q^{60} +(-295.442 + 214.651i) q^{61} +(471.098 + 342.273i) q^{62} +(230.513 + 167.477i) q^{63} +(-51.7771 + 37.6183i) q^{64} +(519.540 - 605.707i) q^{65} +(-194.042 - 140.980i) q^{66} +(-24.7441 - 76.1546i) q^{67} +491.910 q^{68} +(43.3945 + 133.555i) q^{69} +(-368.607 - 604.375i) q^{70} +(-114.809 + 353.346i) q^{71} +(22.2492 - 68.4761i) q^{72} +(-138.114 + 100.345i) q^{73} +496.267 q^{74} +(-171.657 + 333.405i) q^{75} -67.5304 q^{76} +(1023.86 - 743.877i) q^{77} +(-132.337 + 407.291i) q^{78} +(409.357 - 1259.87i) q^{79} +(-116.464 + 135.780i) q^{80} +(25.0304 + 77.0356i) q^{81} +369.006 q^{82} +(312.670 + 962.298i) q^{83} +(307.350 + 223.303i) q^{84} +(1337.62 - 318.145i) q^{85} +(183.354 - 133.215i) q^{86} +(442.323 + 321.366i) q^{87} +(-258.723 - 187.973i) q^{88} +(284.301 - 206.557i) q^{89} +(16.2135 - 200.592i) q^{90} +(-1828.10 - 1328.19i) q^{91} +(57.8594 + 178.073i) q^{92} -873.464 q^{93} +(-136.557 - 420.279i) q^{94} +(-183.631 + 43.6756i) q^{95} +(29.6656 - 91.3014i) q^{96} +(-463.412 + 1426.24i) q^{97} +(-1066.74 + 775.031i) q^{98} +359.774 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 16 q - 8 q^{2} - 12 q^{3} - 16 q^{4} + 15 q^{5} - 24 q^{6} + 46 q^{7} - 32 q^{8} - 36 q^{9} + 50 q^{10} - 83 q^{11} - 48 q^{12} + 22 q^{13} + 2 q^{14} - 60 q^{15} - 64 q^{16} - 79 q^{17} + 288 q^{18} - 15 q^{19}+ \cdots + 1368 q^{99}+O(q^{100}) $ 16 * q - 8 * q^2 - 12 * q^3 - 16 * q^4 + 15 * q^5 - 24 * q^6 + 46 * q^7 - 32 * q^8 - 36 * q^9 + 50 * q^10 - 83 * q^11 - 48 * q^12 + 22 * q^13 + 2 * q^14 - 60 * q^15 - 64 * q^16 - 79 * q^17 + 288 * q^18 - 15 * q^19 - 80 * q^20 - 72 * q^21 + 14 * q^22 - 143 * q^23 + 384 * q^24 - 205 * q^25 + 144 * q^26 - 108 * q^27 - 96 * q^28 + 255 * q^29 - 378 * q^31 + 512 * q^32 + 21 * q^33 - 248 * q^34 - 610 * q^35 - 144 * q^36 - 514 * q^37 - 160 * q^38 + 66 * q^39 - 918 * q^41 - 144 * q^42 + 1012 * q^43 + 28 * q^44 - 180 * q^45 - 36 * q^46 - 209 * q^47 - 192 * q^48 + 1478 * q^49 + 620 * q^50 + 1218 * q^51 + 88 * q^52 - 1738 * q^53 - 216 * q^54 + 265 * q^55 - 192 * q^56 + 570 * q^57 + 510 * q^58 + 695 * q^59 - 240 * q^60 + 352 * q^61 + 384 * q^62 + 9 * q^63 - 256 * q^64 + 1150 * q^65 - 498 * q^66 - 1554 * q^67 + 1624 * q^68 - 54 * q^69 + 200 * q^70 - 1543 * q^71 - 288 * q^72 - 778 * q^73 + 1332 * q^74 + 165 * q^75 + 760 * q^76 + 2622 * q^77 - 348 * q^78 + 920 * q^79 - 320 * q^80 - 324 * q^81 + 2044 * q^82 + 2967 * q^83 + 12 * q^84 - 2215 * q^85 + 164 * q^86 - 720 * q^87 - 664 * q^88 - 2605 * q^89 + 270 * q^90 - 5683 * q^91 - 72 * q^92 + 1116 * q^93 - 418 * q^94 - 1865 * q^95 - 384 * q^96 + 1251 * q^97 - 464 * q^98 + 1368 * q^99

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/150\mathbb{Z}\right)^\times$.

$n$	$101$	$127$
$\chi(n)$	$1$	$e\left(\frac{4}{5}\right)$

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 $

$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$2$	−1.61803	+	1.17557i	−0.572061	+	0.415627i
$3$	0.927051	−	2.85317i	0.178411	−	0.549093i
$3$	0.927051	−	2.85317i	0.178411	−	0.549093i
$4$	1.23607	−	3.80423i	0.154508	−	0.475528i
$5$	0.900748	−	11.1440i	0.0805654	−	0.996749i
$5$	0.900748	−	11.1440i	0.0805654	−	0.996749i
$6$	1.85410	+	5.70634i	0.126156	+	0.388267i
$7$	−31.6588			−1.70942			−0.854708	−	0.519109i	$-0.826264\pi$
$7$	−31.6588			−1.70942			−0.854708	+	0.519109i	$0.826264\pi$
$8$	2.47214	+	7.60845i	0.109254	+	0.336249i
$9$	−7.28115	−	5.29007i	−0.269672	−	0.195928i
$10$	11.6431	+	19.0903i	0.368188	+	0.603687i
$11$	−32.3404	+	23.4967i	−0.886454	+	0.644047i	−0.934951	−	0.354777i	$-0.884557\pi$
$11$	−32.3404	+	23.4967i	−0.886454	+	0.644047i	0.0484970	+	0.998823i	$0.484557\pi$
$12$	−9.70820	−	7.05342i	−0.233543	−	0.169679i
$13$	57.7437	+	41.9533i	1.23194	+	0.895058i	0.997034	−	0.0769602i	$-0.0245215\pi$
$13$	57.7437	+	41.9533i	1.23194	+	0.895058i	0.234907	+	0.972018i	$0.424521\pi$
$14$	51.2251	−	37.2172i	0.977891	−	0.710479i
$15$	−30.9607	−	12.9010i	−0.532934	−	0.222069i
$16$	−12.9443	−	9.40456i	−0.202254	−	0.146946i
$17$	38.0021	+	116.958i	0.542169	+	1.66862i	0.727628	+	0.685972i	$0.240623\pi$
$17$	38.0021	+	116.958i	0.542169	+	1.66862i	−0.185460	+	0.982652i	$0.559377\pi$
$18$	18.0000			0.235702
$19$	−5.21701	−	16.0563i	−0.0629928	−	0.193872i	0.914607	−	0.404344i	$-0.132500\pi$
$19$	−5.21701	−	16.0563i	−0.0629928	−	0.193872i	−0.977600	+	0.210472i	$0.932500\pi$
$20$	−41.2809	−	17.2014i	−0.461534	−	0.192317i
$21$	−29.3493	+	90.3280i	−0.304979	+	0.938628i
$22$	24.7059	−	76.0368i	0.239423	−	0.736868i
$23$	−37.8694	+	27.5138i	−0.343318	+	0.249435i	−0.746061	−	0.665878i	$-0.768057\pi$
$23$	−37.8694	+	27.5138i	−0.343318	+	0.249435i	0.402742	+	0.915313i	$0.368057\pi$
$24$	24.0000			0.204124
$25$	−123.377	−	20.0759i	−0.987018	−	0.160607i
$26$	−142.750			−1.07676
$27$	−21.8435	+	15.8702i	−0.155695	+	0.113119i
$28$	−39.1325	+	120.437i	−0.264119	+	0.812876i
$29$	−56.3174	+	173.327i	−0.360617	+	1.10986i	0.592064	+	0.805891i	$0.298313\pi$
$29$	−56.3174	+	173.327i	−0.360617	+	1.10986i	−0.952681	+	0.303973i	$0.901687\pi$
$30$	65.2615	−	15.5221i	0.397169	−	0.0944647i
$31$	−89.9717	−	276.905i	−0.521271	−	1.60431i	−0.771574	−	0.636140i	$-0.780530\pi$
$31$	−89.9717	−	276.905i	−0.521271	−	1.60431i	0.250303	−	0.968168i	$-0.419470\pi$
$32$	32.0000			0.176777
$33$	37.0588	+	114.055i	0.195488	+	0.601650i
$34$	−198.982	−	144.569i	−1.00368	−	0.729215i
$35$	−28.5166	+	352.806i	−0.137720	+	1.70386i
$36$	−29.1246	+	21.1603i	−0.134836	+	0.0979642i
$37$	−200.744	−	145.849i	−0.891950	−	0.648040i	0.0444355	−	0.999012i	$-0.485851\pi$
$37$	−200.744	−	145.849i	−0.891950	−	0.648040i	−0.936386	+	0.350972i	$0.885851\pi$
$38$	27.3166	+	19.8467i	0.116614	+	0.0847252i
$39$	173.231	−	125.860i	0.711262	−	0.516762i
$40$	87.0153	−	20.6962i	0.343958	−	0.0818088i
$41$	−149.266	−	108.448i	−0.568572	−	0.413092i	0.266014	−	0.963969i	$-0.414293\pi$
$41$	−149.266	−	108.448i	−0.568572	−	0.413092i	−0.834586	+	0.550877i	$0.814293\pi$
$42$	−58.6987	−	180.656i	−0.215652	−	0.663710i
$43$	−113.319			−0.401884			−0.200942	−	0.979603i	$-0.564400\pi$
$43$	−113.319			−0.401884			−0.200942	+	0.979603i	$0.564400\pi$
$44$	49.4117	+	152.074i	0.169298	+	0.521045i
$45$	−65.5110	+	76.3761i	−0.217018	+	0.253011i
$46$	28.9297	−	89.0364i	0.0927271	−	0.285385i
$47$	−68.2785	+	210.140i	−0.211903	+	0.652171i	0.787456	+	0.616371i	$0.211398\pi$
$47$	−68.2785	+	210.140i	−0.211903	+	0.652171i	−0.999359	+	0.0357997i	$0.988602\pi$
$48$	−38.8328	+	28.2137i	−0.116772	+	0.0848395i
$49$	659.281			1.92210
$50$	223.229	−	112.555i	0.631388	−	0.318354i
$51$	368.932			1.01296
$52$	230.975	−	167.813i	0.615971	−	0.447529i
$53$	10.8048	−	33.2538i	0.0280030	−	0.0861843i	−0.936078	−	0.351792i	$-0.885573\pi$
$53$	10.8048	−	33.2538i	0.0280030	−	0.0861843i	0.964081	+	0.265607i	$0.0855725\pi$
$54$	16.6869	−	51.3571i	0.0420519	−	0.129422i
$55$	232.716	+	381.566i	0.570535	+	0.935460i
$56$	−78.2649	−	240.875i	−0.186761	−	0.574790i
$57$	−50.6478			−0.117692
$58$	−112.635	−	346.654i	−0.254994	−	0.784792i
$59$	−528.425	−	383.923i	−1.16602	−	0.847161i	−0.175491	−	0.984481i	$-0.556151\pi$
$59$	−528.425	−	383.923i	−1.16602	−	0.847161i	−0.990527	+	0.137320i	$0.956151\pi$
$60$	−87.3480	+	101.835i	−0.187943	+	0.219114i
$61$	−295.442	+	214.651i	−0.620122	+	0.450545i	−0.852964	−	0.521970i	$-0.825197\pi$
$61$	−295.442	+	214.651i	−0.620122	+	0.450545i	0.232842	+	0.972514i	$0.425197\pi$
$62$	471.098	+	342.273i	0.964992	+	0.701108i
$63$	230.513	+	167.477i	0.460982	+	0.334923i
$64$	−51.7771	+	37.6183i	−0.101127	+	0.0734732i
$65$	519.540	−	605.707i	0.991400	−	1.15583i
$66$	−194.042	−	140.980i	−0.361893	−	0.262931i
$67$	−24.7441	−	76.1546i	−0.0451191	−	0.138862i	0.925959	−	0.377624i	$-0.123259\pi$
$67$	−24.7441	−	76.1546i	−0.0451191	−	0.138862i	−0.971078	+	0.238761i	$0.923259\pi$
$68$	491.910			0.877247
$69$	43.3945	+	133.555i	0.0757114	+	0.233016i
$70$	−368.607	−	604.375i	−0.629386	−	1.03195i
$71$	−114.809	+	353.346i	−0.191906	+	0.590627i	0.808092	+	0.589056i	$0.200500\pi$
$71$	−114.809	+	353.346i	−0.191906	+	0.590627i	−0.999999	+	0.00157116i	$0.999500\pi$
$72$	22.2492	−	68.4761i	0.0364180	−	0.112083i
$73$	−138.114	+	100.345i	−0.221438	+	0.160884i	−0.692974	−	0.720963i	$-0.743700\pi$
$73$	−138.114	+	100.345i	−0.221438	+	0.160884i	0.471536	+	0.881847i	$0.343700\pi$
$74$	496.267			0.779593
$75$	−171.657	+	333.405i	−0.264283	+	0.513311i
$76$	−67.5304			−0.101925
$77$	1023.86	−	743.877i	1.51532	−	1.10094i
$78$	−132.337	+	407.291i	−0.192105	+	0.591239i
$79$	409.357	−	1259.87i	0.582991	−	1.79426i	−0.0242022	−	0.999707i	$-0.507705\pi$
$79$	409.357	−	1259.87i	0.582991	−	1.79426i	0.607193	−	0.794554i	$-0.292295\pi$
$80$	−116.464	+	135.780i	−0.162763	+	0.189758i
$81$	25.0304	+	77.0356i	0.0343352	+	0.105673i
$82$	369.006			0.496950
$83$	312.670	+	962.298i	0.413493	+	1.27260i	0.913592	+	0.406633i	$0.133297\pi$
$83$	312.670	+	962.298i	0.413493	+	1.27260i	−0.500098	+	0.865969i	$0.666703\pi$
$84$	307.350	+	223.303i	0.399222	+	0.290052i
$85$	1337.62	−	318.145i	1.70688	−	0.405973i
$86$	183.354	−	133.215i	0.229903	−	0.167034i
$87$	442.323	+	321.366i	0.545080	+	0.396024i
$88$	−258.723	−	187.973i	−0.313409	−	0.227705i
$89$	284.301	−	206.557i	0.338605	−	0.246011i	−0.405468	−	0.914109i	$-0.632891\pi$
$89$	284.301	−	206.557i	0.338605	−	0.246011i	0.744073	+	0.668098i	$0.232891\pi$
$90$	16.2135	−	200.592i	0.0189894	−	0.234936i
$91$	−1828.10	−	1328.19i	−2.10590	−	1.53003i
$92$	57.8594	+	178.073i	0.0655680	+	0.201798i
$93$	−873.464			−0.973914
$94$	−136.557	−	420.279i	−0.149838	−	0.461154i
$95$	−183.631	+	43.6756i	−0.198317	+	0.0471687i
$96$	29.6656	−	91.3014i	0.0315389	−	0.0970668i
$97$	−463.412	+	1426.24i	−0.485076	+	1.49291i	0.346795	+	0.937941i	$0.387270\pi$
$97$	−463.412	+	1426.24i	−0.485076	+	1.49291i	−0.831871	+	0.554969i	$0.812730\pi$
$98$	−1066.74	+	775.031i	−1.09956	+	0.798878i
$99$	359.774			0.365239
$100$	−228.876	+	444.540i	−0.228876	+	0.444540i
$101$	−1102.06			−1.08573			−0.542864	−	0.839820i	$-0.682660\pi$
$101$	−1102.06			−1.08573			−0.542864	+	0.839820i	$0.682660\pi$
$102$	−596.945	+	433.706i	−0.579474	+	0.421013i
$103$	−114.795	+	353.303i	−0.109817	+	0.337981i	−0.990831	−	0.135109i	$-0.956861\pi$
$103$	−114.795	+	353.303i	−0.109817	+	0.337981i	0.881014	+	0.473090i	$0.156861\pi$
$104$	−176.449	+	543.055i	−0.166368	+	0.512028i
$105$	980.178	+	408.432i	0.911006	+	0.379608i
$106$	21.6097	+	66.5077i	0.0198011	+	0.0609415i
$107$	116.046			0.104847			0.0524233	−	0.998625i	$-0.483305\pi$
$107$	116.046			0.104847			0.0524233	+	0.998625i	$0.483305\pi$
$108$	33.3738	+	102.714i	0.0297352	+	0.0915155i
$109$	−895.234	−	650.425i	−0.786677	−	0.571555i	0.120298	−	0.992738i	$-0.461615\pi$
$109$	−895.234	−	650.425i	−0.786677	−	0.571555i	−0.906976	+	0.421183i	$0.861615\pi$
$110$	−825.100	−	343.812i	−0.715184	−	0.298011i
$111$	−602.233	+	437.548i	−0.514968	+	0.374146i
$112$	409.800	+	297.737i	0.345737	+	0.251192i
$113$	−674.299	−	489.907i	−0.561352	−	0.407846i	0.270602	−	0.962691i	$-0.412777\pi$
$113$	−674.299	−	489.907i	−0.561352	−	0.407846i	−0.831953	+	0.554845i	$0.812777\pi$
$114$	81.9498	−	59.5400i	0.0673272	−	0.0489161i
$115$	272.502	+	446.800i	0.220965	+	0.362298i
$116$	589.764	+	428.488i	0.472053	+	0.342967i
$117$	−198.505	−	610.937i	−0.156853	−	0.482745i
$118$	1306.34			1.01914
$119$	−1203.10	−	3702.77i	−0.926792	−	2.85237i
$120$	21.6180	−	267.456i	0.0164453	−	0.203461i
$121$	82.5058	−	253.927i	0.0619878	−	0.190779i
$122$	225.697	−	694.625i	0.167489	−	0.515478i
$123$	−447.799	+	325.345i	−0.328265	+	0.238499i
$124$	−1164.62			−0.843434
$125$	−334.857	+	1356.83i	−0.239604	+	0.970871i
$126$	−569.859			−0.402913
$127$	140.782	−	102.284i	0.0983652	−	0.0714665i	−0.537516	−	0.843254i	$-0.680637\pi$
$127$	140.782	−	102.284i	0.0983652	−	0.0714665i	0.635881	+	0.771787i	$0.280637\pi$
$128$	39.5542	−	121.735i	0.0273135	−	0.0840623i
$129$	−105.053	+	323.319i	−0.0717006	+	0.220672i
$130$	−128.582	+	1590.81i	−0.0867492	+	1.07326i
$131$	534.656	+	1645.50i	0.356588	+	1.09747i	0.955083	+	0.296339i	$0.0957659\pi$
$131$	534.656	+	1645.50i	0.356588	+	1.09747i	−0.598494	+	0.801127i	$0.704234\pi$
$132$	479.699			0.316306
$133$	165.164	+	508.324i	0.107681	+	0.331408i
$134$	129.562	+	94.1323i	0.0835258	+	0.0606850i
$135$	157.182	+	257.718i	0.100208	+	0.164303i
$136$	−795.927	+	578.275i	−0.501839	+	0.364608i
$137$	466.355	+	338.827i	0.290828	+	0.211299i	0.723626	−	0.690192i	$-0.242474\pi$
$137$	466.355	+	338.827i	0.290828	+	0.211299i	−0.432799	+	0.901491i	$0.642474\pi$
$138$	−227.217	−	165.083i	−0.140159	−	0.101832i
$139$	−1512.78	+	1099.10i	−0.923110	+	0.670679i	−0.944296	−	0.329097i	$-0.893256\pi$
$139$	−1512.78	+	1099.10i	−0.923110	+	0.670679i	0.0211858	+	0.999776i	$0.493256\pi$
$140$	1306.90	+	544.576i	0.788954	+	0.328750i
$141$	536.266	+	389.620i	0.320296	+	0.232709i
$142$	−229.618	−	706.693i	−0.135698	−	0.417636i
$143$	−2853.22			−1.66852
$144$	44.4984	+	136.952i	0.0257514	+	0.0792547i
$145$	1880.83	+	783.725i	1.07720	+	0.448861i
$146$	105.509	−	324.725i	0.0598084	−	0.184071i
$147$	611.187	−	1881.04i	0.342924	−	1.05541i
$148$	−802.977	+	583.397i	−0.445975	+	0.324020i
$149$	1643.52			0.903640			0.451820	−	0.892109i	$-0.350775\pi$
$149$	1643.52			0.903640			0.451820	+	0.892109i	$0.350775\pi$
$150$	−114.194	−	741.255i	−0.0621596	−	0.403488i
$151$	2760.47			1.48771			0.743854	−	0.668342i	$-0.232996\pi$
$151$	2760.47			1.48771			0.743854	+	0.668342i	$0.232996\pi$
$152$	109.266	−	79.3867i	0.0583071	−	0.0423626i
$153$	342.019	−	1052.63i	0.180723	−	0.556208i
$154$	−782.158	+	2407.24i	−0.409274	+	1.25961i
$155$	−3166.87	+	753.224i	−1.64109	+	0.390325i
$156$	−264.674	−	814.582i	−0.135839	−	0.418069i
$157$	2389.36			1.21460			0.607299	−	0.794474i	$-0.292253\pi$
$157$	2389.36			1.21460			0.607299	+	0.794474i	$0.292253\pi$
$158$	818.714	+	2519.74i	0.412237	+	1.26873i
$159$	−84.8622	−	61.6560i	−0.0423271	−	0.0307525i
$160$	28.8239	−	356.608i	0.0142421	−	0.176202i
$161$	1198.90	−	871.053i	0.586874	−	0.426389i
$162$	−131.061	−	95.2212i	−0.0635624	−	0.0461808i
$163$	−1873.71	−	1361.33i	−0.900371	−	0.654158i	0.0381900	−	0.999270i	$-0.487841\pi$
$163$	−1873.71	−	1361.33i	−0.900371	−	0.654158i	−0.938561	+	0.345112i	$0.887841\pi$
$164$	−597.065	+	433.793i	−0.284286	+	0.206546i
$165$	1304.41	−	310.248i	0.615444	−	0.146380i
$166$	−1637.16	−	1189.47i	−0.765471	−	0.556147i
$167$	−650.608	−	2002.37i	−0.301470	−	0.927831i	−0.980971	−	0.194155i	$-0.937803\pi$
$167$	−650.608	−	2002.37i	−0.301470	−	0.927831i	0.679500	−	0.733675i	$-0.262197\pi$
$168$	−759.812			−0.348933
$169$	895.352	+	2755.61i	0.407534	+	1.25426i
$170$	−1790.30	+	2087.23i	−0.807707	+	0.941667i
$171$	−46.9531	+	144.507i	−0.0209976	+	0.0646240i
$172$	−140.070	+	431.092i	−0.0620946	+	0.191107i
$173$	1011.72	−	735.056i	0.444621	−	0.323036i	−0.342847	−	0.939391i	$-0.611391\pi$
$173$	1011.72	−	735.056i	0.444621	−	0.323036i	0.787468	+	0.616355i	$0.211391\pi$
$174$	−1093.48			−0.476417
$175$	3905.98	+	635.578i	1.68722	+	0.274544i
$176$	639.599			0.273929
$177$	−1585.27	+	1151.77i	−0.673201	+	0.489109i
$178$	−217.187	+	668.432i	−0.0914541	+	0.281467i
$179$	1234.17	−	3798.37i	0.515340	−	1.58605i	−0.267322	−	0.963607i	$-0.586139\pi$
$179$	1234.17	−	3798.37i	0.515340	−	1.58605i	0.782662	−	0.622447i	$-0.213861\pi$
$180$	209.576	+	343.625i	0.0867826	+	0.142290i
$181$	−463.477	−	1426.43i	−0.190331	−	0.585779i	0.809668	−	0.586888i	$-0.199647\pi$
$181$	−463.477	−	1426.43i	−0.190331	−	0.585779i	−0.999999	+	0.00110861i	$0.999647\pi$
$182$	4519.31			1.84062
$183$	338.546	+	1041.94i	0.136754	+	0.420886i
$184$	−302.956	−	220.110i	−0.121381	−	0.0881887i
$185$	−1806.16	+	2105.72i	−0.717794	+	0.836841i
$186$	1413.29	−	1026.82i	0.557139	−	0.404785i
$187$	−3977.14	−	2889.56i	−1.55528	−	1.12998i
$188$	715.022	+	519.494i	0.277385	+	0.201532i
$189$	691.538	−	502.432i	0.266148	−	0.193368i
$190$	245.777	−	286.539i	0.0938448	−	0.109409i
$191$	1260.46	+	915.775i	0.477505	+	0.346927i	0.800359	−	0.599521i	$-0.204642\pi$
$191$	1260.46	+	915.775i	0.477505	+	0.346927i	−0.322854	+	0.946449i	$0.604642\pi$
$192$	59.3313	+	182.603i	0.0223014	+	0.0686366i
$193$	−1078.98			−0.402416			−0.201208	−	0.979548i	$-0.564487\pi$
$193$	−1078.98			−0.402416			−0.201208	+	0.979548i	$0.564487\pi$
$194$	−926.824	−	2852.47i	−0.343000	−	1.05565i
$195$	−1246.54	−	2043.86i	−0.457779	−	0.750583i
$196$	814.916	−	2508.05i	0.296981	−	0.914014i
$197$	419.638	−	1291.51i	0.151766	−	0.467089i	−0.846052	−	0.533100i	$-0.821027\pi$
$197$	419.638	−	1291.51i	0.151766	−	0.467089i	0.997819	+	0.0660104i	$0.0210271\pi$
$198$	−582.127	+	422.940i	−0.208939	+	0.151803i
$199$	1305.02			0.464875			0.232437	−	0.972611i	$-0.425330\pi$
$199$	1305.02			0.464875			0.232437	+	0.972611i	$0.425330\pi$
$200$	−152.259	−	988.341i	−0.0538318	−	0.349431i
$201$	−240.221			−0.0842980
$202$	1783.16	−	1295.54i	0.621103	−	0.451258i
$203$	1782.94	−	5487.33i	0.616444	−	1.89722i
$204$	456.025	−	1403.50i	0.156511	−	0.481690i
$205$	−1343.00	+	1565.74i	−0.457556	+	0.533443i
$206$	−229.590	−	706.606i	−0.0776520	−	0.238988i
$207$	421.283			0.141455
$208$	−352.898	−	1086.11i	−0.117640	−	0.362058i
$209$	545.990	+	396.685i	0.180703	+	0.131288i
$210$	−2066.10	+	491.412i	−0.678927	+	0.161479i
$211$	−2445.36	+	1776.66i	−0.797845	+	0.579668i	−0.910281	−	0.413990i	$-0.864135\pi$
$211$	−2445.36	+	1776.66i	−0.797845	+	0.579668i	0.112436	+	0.993659i	$0.464135\pi$
$212$	−113.150	−	82.2080i	−0.0366564	−	0.0266324i
$213$	901.723	+	655.140i	0.290071	+	0.210749i
$214$	−187.766	+	136.420i	−0.0599787	+	0.0435771i
$215$	−102.072	+	1262.83i	−0.0323780	+	0.400578i
$216$	−174.748	−	126.962i	−0.0550466	−	0.0399937i
$217$	2848.40	+	8766.47i	0.891069	+	2.74243i
$218$	2213.14			0.687581
$219$	158.264	+	487.087i	0.0488333	+	0.150294i
$220$	1739.22	−	413.664i	0.532990	−	0.126769i
$221$	−2712.41	+	8347.94i	−0.825594	+	2.54092i
$222$	460.065	−	1415.93i	0.139088	−	0.428069i
$223$	508.197	−	369.227i	0.152607	−	0.110876i	−0.508861	−	0.860848i	$-0.669933\pi$
$223$	508.197	−	369.227i	0.152607	−	0.110876i	0.661469	+	0.749973i	$0.269933\pi$
$224$	−1013.08			−0.302185
$225$	792.126	+	798.850i	0.234704	+	0.236696i
$226$	1666.96			0.490639
$227$	−2471.67	+	1795.77i	−0.722690	+	0.525065i	−0.887242	−	0.461303i	$-0.847382\pi$
$227$	−2471.67	+	1795.77i	−0.722690	+	0.525065i	0.164553	+	0.986368i	$0.447382\pi$
$228$	−62.6041	+	192.676i	−0.0181845	+	0.0559660i
$229$	1614.10	−	4967.70i	0.465777	−	1.43351i	−0.392226	−	0.919869i	$-0.628295\pi$
$229$	1614.10	−	4967.70i	0.465777	−	1.43351i	0.858003	−	0.513645i	$-0.171705\pi$
$230$	−966.163	−	402.592i	−0.276986	−	0.115418i
$231$	−1173.24	−	3610.85i	−0.334170	−	1.02847i
$232$	−1457.98			−0.412590
$233$	−1382.61	−	4255.23i	−0.388746	−	1.19644i	−0.933726	−	0.357988i	$-0.883463\pi$
$233$	−1382.61	−	4255.23i	−0.388746	−	1.19644i	0.544981	−	0.838449i	$-0.316537\pi$
$234$	1039.39	+	755.159i	0.290371	+	0.210967i
$235$	2280.29	+	950.179i	0.632979	+	0.263757i
$236$	−2113.70	+	1535.69i	−0.583009	+	0.423581i
$237$	−3215.13	−	2335.93i	−0.881204	−	0.640232i
$238$	6299.53	+	4576.87i	1.71570	+	1.24653i
$239$	−4597.61	+	3340.36i	−1.24433	+	0.904059i	−0.997879	−	0.0650967i	$-0.979264\pi$
$239$	−4597.61	+	3340.36i	−1.24433	+	0.904059i	−0.246451	+	0.969155i	$0.579264\pi$
$240$	279.435	+	458.166i	0.0751560	+	0.123227i
$241$	172.186	+	125.100i	0.0460226	+	0.0334374i	0.610559	−	0.791971i	$-0.290945\pi$
$241$	172.186	+	125.100i	0.0460226	+	0.0334374i	−0.564536	+	0.825408i	$0.690945\pi$
$242$	165.012	+	507.853i	0.0438320	+	0.134901i
$243$	243.000			0.0641500
$244$	451.395	+	1389.25i	0.118433	+	0.364498i
$245$	593.846	−	7347.03i	0.154855	−	1.91585i
$246$	342.088	−	1052.84i	0.0886614	−	0.272872i
$247$	372.365	−	1146.02i	0.0959232	−	0.295221i
$248$	1884.39	−	1369.09i	0.482496	−	0.350554i
$249$	3035.46			0.772548
$250$	−1053.24	−	2589.05i	−0.266452	−	0.654984i
$251$	−800.033			−0.201186			−0.100593	−	0.994928i	$-0.532074\pi$
$251$	−800.033			−0.201186			−0.100593	+	0.994928i	$0.532074\pi$
$252$	922.051	−	669.909i	0.230491	−	0.167462i
$253$	578.231	−	1779.61i	0.143688	−	0.442226i
$254$	−107.548	+	330.998i	−0.0265675	+	0.0817664i
$255$	332.315	−	4111.38i	0.0816093	−	1.00967i
$256$	79.1084	+	243.470i	0.0193136	+	0.0594410i
$257$	735.879			0.178610			0.0893052	−	0.996004i	$-0.471535\pi$
$257$	735.879			0.178610			0.0893052	+	0.996004i	$0.471535\pi$
$258$	−210.106	−	646.638i	−0.0507000	−	0.156039i
$259$	6355.33	+	4617.42i	1.52471	+	1.10777i
$260$	−1662.06	−	2725.14i	−0.396448	−	0.650024i
$261$	1326.97	−	964.099i	0.314702	−	0.228644i
$262$	−2799.49	−	2033.95i	−0.660127	−	0.479610i
$263$	3190.24	+	2317.85i	0.747980	+	0.543440i	0.895200	−	0.445664i	$-0.147032\pi$
$263$	3190.24	+	2317.85i	0.747980	+	0.543440i	−0.147220	+	0.989104i	$0.547032\pi$
$264$	−776.169	+	563.920i	−0.180947	+	0.131465i
$265$	−360.848	−	150.362i	−0.0836481	−	0.0348554i
$266$	−864.812	−	628.323i	−0.199342	−	0.144831i
$267$	−325.780	−	1002.65i	−0.0746719	−	0.229817i
$268$	−320.295			−0.0730042
$269$	1250.24	+	3847.85i	0.283378	+	0.872147i	0.986880	+	0.161454i	$0.0516184\pi$
$269$	1250.24	+	3847.85i	0.283378	+	0.872147i	−0.703502	+	0.710693i	$0.748382\pi$
$270$	−557.292	−	232.219i	−0.125614	−	0.0523422i
$271$	−249.532	+	767.981i	−0.0559336	+	0.172146i	−0.975120	−	0.221676i	$-0.928847\pi$
$271$	−249.532	+	767.981i	−0.0559336	+	0.172146i	0.919187	+	0.393822i	$0.128847\pi$
$272$	608.034	−	1871.34i	0.135542	−	0.417156i
$273$	−5484.30	+	3984.58i	−1.21584	+	0.883361i
$274$	−1152.89			−0.254193
$275$	4461.79	−	2249.69i	0.978385	−	0.493315i
$276$	561.710			0.122504
$277$	−1830.01	+	1329.58i	−0.396948	+	0.288400i	−0.768297	−	0.640094i	$-0.778896\pi$
$277$	−1830.01	+	1329.58i	−0.396948	+	0.288400i	0.371349	+	0.928494i	$0.378896\pi$
$278$	1155.66	−	3556.76i	0.249324	−	0.767339i
$279$	−809.746	+	2492.14i	−0.173757	+	0.534769i
$280$	−2754.80	+	655.217i	−0.587968	+	0.139845i
$281$	−229.564	−	706.524i	−0.0487353	−	0.149992i	0.923727	−	0.383051i	$-0.125127\pi$
$281$	−229.564	−	706.524i	−0.0487353	−	0.149992i	−0.972463	+	0.233059i	$0.925127\pi$
$282$	−1325.72			−0.279949
$283$	−746.749	−	2298.26i	−0.156854	−	0.482746i	0.841490	−	0.540272i	$-0.181679\pi$
$283$	−746.749	−	2298.26i	−0.156854	−	0.482746i	−0.998344	+	0.0575261i	$0.981679\pi$
$284$	1202.30	+	873.520i	0.251209	+	0.182514i
$285$	−45.6209	+	564.419i	−0.00948192	+	0.117310i
$286$	4616.60	−	3354.16i	0.954495	−	0.693481i
$287$	4725.59	+	3433.34i	0.971926	+	0.706146i
$288$	−232.997	−	169.282i	−0.0476718	−	0.0346356i
$289$	−8260.43	+	6001.55i	−1.68134	+	1.22157i
$290$	−3964.57	+	942.954i	−0.802785	+	0.190938i
$291$	3639.69	+	2644.39i	0.733203	+	0.532703i
$292$	211.019	+	649.449i	0.0422909	+	0.130158i
$293$	1883.68			0.375583			0.187792	−	0.982209i	$-0.439867\pi$
$293$	1883.68			0.375583			0.187792	+	0.982209i	$0.439867\pi$
$294$	1222.37	+	3762.08i	0.242484	+	0.746289i
$295$	−4754.41	+	5542.95i	−0.938348	+	1.09398i
$296$	613.420	−	1887.91i	0.120454	−	0.370719i
$297$	333.529	−	1026.50i	0.0651627	−	0.200550i
$298$	−2659.27	+	1932.07i	−0.516938	+	0.375577i
$299$	−3341.02			−0.646207
$300$	1056.17	+	1065.13i	0.203260	+	0.204985i
$301$	3587.56			0.686988
$302$	−4466.54	+	3245.13i	−0.851061	+	0.618332i
$303$	−1021.66	+	3144.35i	−0.193706	+	0.596166i
$304$	−83.4721	+	256.901i	−0.0157482	+	0.0484680i
$305$	2125.95	+	3485.75i	0.399120	+	0.654404i
$306$	684.038	+	2105.25i	0.127790	+	0.393298i
$307$	−5535.95			−1.02916			−0.514582	−	0.857441i	$-0.672053\pi$
$307$	−5535.95			−1.02916			−0.514582	+	0.857441i	$0.672053\pi$
$308$	−1564.32	−	4814.47i	−0.289400	−	0.890682i
$309$	901.613	+	655.060i	0.165990	+	0.120599i
$310$	4238.63	−	4941.61i	0.776574	−	0.905370i
$311$	−6658.53	+	4837.70i	−1.21405	+	0.882061i	−0.995592	−	0.0937850i	$-0.970103\pi$
$311$	−6658.53	+	4837.70i	−1.21405	+	0.882061i	−0.218460	+	0.975846i	$0.570103\pi$
$312$	1385.85	+	1006.88i	0.251469	+	0.182703i
$313$	4303.66	+	3126.79i	0.777180	+	0.564654i	0.904131	−	0.427255i	$-0.140519\pi$
$313$	4303.66	+	3126.79i	0.777180	+	0.564654i	−0.126951	+	0.991909i	$0.540519\pi$
$314$	−3866.07	+	2808.86i	−0.694824	+	0.504819i
$315$	2074.00	−	2417.98i	0.370974	−	0.432500i
$316$	−4286.84	−	3114.57i	−0.763145	−	0.554457i
$317$	−142.032	−	437.130i	−0.0251650	−	0.0774500i	0.937685	−	0.347486i	$-0.112964\pi$
$317$	−142.032	−	437.130i	−0.0251650	−	0.0774500i	−0.962850	+	0.270036i	$0.912964\pi$
$318$	209.791			0.0369953
$319$	−2251.28	−	6928.74i	−0.395134	−	1.21610i
$320$	372.580	+	610.888i	0.0650870	+	0.106718i
$321$	107.581	−	331.099i	0.0187058	−	0.0575705i
$322$	−915.880	+	2818.79i	−0.158509	+	0.487841i
$323$	1679.66	−	1220.35i	0.289347	−	0.210223i
$324$	324.000			0.0555556
$325$	−6282.02	−	6335.34i	−1.07220	−	1.08130i
$326$	4632.07			0.786953
$327$	−2685.70	+	1951.28i	−0.454188	+	0.329987i
$328$	456.117	−	1403.78i	0.0767831	−	0.236314i
$329$	2161.62	−	6652.78i	0.362231	−	1.11483i
$330$	−1745.86	+	2035.42i	−0.291232	+	0.339534i
$331$	849.074	+	2613.18i	0.140995	+	0.433938i	0.996474	−	0.0838991i	$-0.0267373\pi$
$331$	849.074	+	2613.18i	0.140995	+	0.433938i	−0.855479	+	0.517837i	$0.826737\pi$
$332$	4047.28			0.669046
$333$	690.098	+	2123.90i	0.113565	+	0.349517i
$334$	3406.63	+	2475.06i	0.558091	+	0.405477i
$335$	−870.955	+	207.152i	−0.142046	+	0.0337849i
$336$	1229.40	−	893.212i	0.199611	−	0.145026i
$337$	−8890.91	−	6459.63i	−1.43715	−	1.04415i	−0.988629	−	0.150376i	$-0.951952\pi$
$337$	−8890.91	−	6459.63i	−1.43715	−	1.04415i	−0.448519	−	0.893773i	$-0.648048\pi$
$338$	−4688.12	−	3406.12i	−0.754439	−	0.548132i
$339$	−2022.90	+	1469.72i	−0.324097	+	0.235470i
$340$	443.087	−	5481.84i	0.0706757	−	0.874396i
$341$	9416.06	+	6841.17i	1.49533	+	1.08642i
$342$	−93.9062	−	289.013i	−0.0148476	−	0.0456961i
$343$	−10013.1			−1.57626
$344$	−280.141	−	862.185i	−0.0439075	−	0.135133i
$345$	1527.42	−	363.289i	0.238358	−	0.0566923i
$346$	−772.883	+	2378.69i	−0.120088	+	0.369593i
$347$	−2020.14	+	6217.34i	−0.312526	+	0.961856i	0.664235	+	0.747524i	$0.268758\pi$
$347$	−2020.14	+	6217.34i	−0.312526	+	0.961856i	−0.976761	+	0.214332i	$0.931242\pi$
$348$	1769.29	−	1285.46i	0.272540	−	0.198012i
$349$	12038.3			1.84641			0.923206	−	0.384306i	$-0.125559\pi$
$349$	12038.3			1.84641			0.923206	+	0.384306i	$0.125559\pi$
$350$	−7067.18	+	3563.37i	−1.07930	+	0.544200i
$351$	−1927.13			−0.293056
$352$	−1034.89	+	751.893i	−0.156704	+	0.113852i
$353$	3348.42	−	10305.4i	0.504868	−	1.55382i	−0.296124	−	0.955149i	$-0.595694\pi$
$353$	3348.42	−	10305.4i	0.504868	−	1.55382i	0.800992	−	0.598675i	$-0.204306\pi$
$354$	1211.04	−	3727.20i	0.181825	−	0.559601i
$355$	3834.28	+	1597.71i	0.573246	+	0.238867i
$356$	−434.373	−	1336.86i	−0.0646678	−	0.199027i
$357$	−11680.0			−1.73157
$358$	2468.33	+	7596.74i	0.364401	+	1.12151i
$359$	−4947.25	−	3594.38i	−0.727314	−	0.528424i	0.161399	−	0.986889i	$-0.448400\pi$
$359$	−4947.25	−	3594.38i	−0.727314	−	0.528424i	−0.888713	+	0.458465i	$0.848400\pi$
$360$	−743.056	−	309.625i	−0.108785	−	0.0453296i
$361$	5318.46	−	3864.09i	0.775399	−	0.563360i
$362$	2426.80	+	1763.17i	0.352347	+	0.255995i
$363$	−648.009	−	470.806i	−0.0936960	−	0.0680741i
$364$	−7312.40	+	5312.77i	−1.05295	+	0.765013i
$365$	993.843	+	1629.52i	0.142521	+	0.233680i
$366$	−1772.65	−	1287.91i	−0.253164	−	0.183934i
$367$	885.966	+	2726.72i	0.126014	+	0.387831i	0.994084	−	0.108610i	$-0.0346400\pi$
$367$	885.966	+	2726.72i	0.126014	+	0.387831i	−0.868071	+	0.496441i	$0.834640\pi$
$368$	748.947			0.106091
$369$	513.132	+	1579.26i	0.0723918	+	0.222799i
$370$	447.012	−	5530.40i	0.0628082	−	0.777059i
$371$	−342.068	+	1052.78i	−0.0478687	+	0.147325i
$372$	−1079.66	+	3322.85i	−0.150478	+	0.463124i
$373$	−5763.16	+	4187.18i	−0.800013	+	0.581244i	−0.910918	−	0.412587i	$-0.864625\pi$
$373$	−5763.16	+	4187.18i	−0.800013	+	0.581244i	0.110905	+	0.993831i	$0.464625\pi$
$374$	9832.03			1.35936
$375$	3560.84	+	2213.26i	0.490350	+	0.304779i
$376$	−1767.63			−0.242443
$377$	−10523.6	+	7645.86i	−1.43765	+	1.04451i
$378$	−528.288	+	1625.90i	−0.0718842	+	0.221237i
$379$	−1860.73	+	5726.74i	−0.252188	+	0.776155i	0.742182	+	0.670198i	$0.233791\pi$
$379$	−1860.73	+	5726.74i	−0.252188	+	0.776155i	−0.994371	+	0.105958i	$0.966209\pi$
$380$	−60.8279	+	752.558i	−0.00821159	+	0.101593i
$381$	−161.322	−	496.497i	−0.0216923	−	0.0667620i
$382$	−3116.02			−0.417354
$383$	−379.391	−	1167.65i	−0.0506161	−	0.155780i	0.922554	−	0.385869i	$-0.126098\pi$
$383$	−379.391	−	1167.65i	−0.0506161	−	0.155780i	−0.973170	+	0.230089i	$0.926098\pi$
$384$	−310.663	−	225.710i	−0.0412850	−	0.0299953i
$385$	−7367.52	−	12079.9i	−0.975282	−	1.59909i
$386$	1745.82	−	1268.41i	0.230207	−	0.167255i
$387$	825.095	+	599.467i	0.108377	+	0.0787406i
$388$	4852.91	+	3525.85i	0.634973	+	0.461335i
$389$	7823.02	−	5683.76i	1.01965	−	0.740817i	0.0534368	−	0.998571i	$-0.482982\pi$
$389$	7823.02	−	5683.76i	1.01965	−	0.740817i	0.966211	+	0.257754i	$0.0829824\pi$
$390$	4419.65	+	1841.63i	0.573840	+	0.239114i
$391$	−4657.09	−	3383.57i	−0.602350	−	0.437633i
$392$	1629.83	+	5016.11i	0.209997	+	0.646305i
$393$	5190.55			0.666230
$394$	839.277	+	2583.03i	0.107315	+	0.330282i
$395$	−13671.3	−	5696.70i	−1.74146	−	0.725651i
$396$	444.705	−	1368.66i	0.0564326	−	0.173682i
$397$	−227.645	+	700.620i	−0.0287788	+	0.0885720i	−0.964414	−	0.264396i	$-0.914827\pi$
$397$	−227.645	+	700.620i	−0.0287788	+	0.0885720i	0.935635	+	0.352968i	$0.114827\pi$
$398$	−2111.56	+	1534.14i	−0.265937	+	0.193215i
$399$	1603.45			0.201185
$400$	1408.22	+	1420.18i	0.176028	+	0.177522i
$401$	407.905			0.0507975			0.0253987	−	0.999677i	$-0.491914\pi$
$401$	407.905			0.0507975			0.0253987	+	0.999677i	$0.491914\pi$
$402$	388.686	−	282.397i	0.0482236	−	0.0350365i
$403$	6421.75	−	19764.1i	0.793772	−	2.44298i
$404$	−1362.21	+	4192.47i	−0.167754	+	0.516295i
$405$	881.030	−	209.549i	0.108096	−	0.0257100i
$406$	3565.89	+	10974.7i	0.435891	+	1.34154i
$407$	9919.12			1.20804
$408$	912.051	+	2807.00i	0.110670	+	0.340606i
$409$	−1623.89	−	1179.83i	−0.196323	−	0.142637i	0.485281	−	0.874358i	$-0.338717\pi$
$409$	−1623.89	−	1179.83i	−0.196323	−	0.142637i	−0.681604	+	0.731721i	$0.738717\pi$
$410$	332.382	−	4112.21i	0.0400370	−	0.495335i
$411$	1399.06	−	1016.48i	0.167909	−	0.121993i
$412$	1202.15	+	873.414i	0.143752	+	0.104442i
$413$	16729.3	+	12154.6i	1.99321	+	1.44815i
$414$	−681.650	+	495.248i	−0.0809209	+	0.0587925i
$415$	11005.5	−	2617.60i	1.30178	−	0.309622i
$416$	1847.80	+	1342.51i	0.217778	+	0.158225i
$417$	1733.49	+	5335.14i	0.203572	+	0.626530i
$418$	−1349.76			−0.157940
$419$	817.215	+	2515.13i	0.0952830	+	0.293251i	0.987327	−	0.158697i	$-0.0507293\pi$
$419$	817.215	+	2515.13i	0.0952830	+	0.293251i	−0.892044	+	0.451948i	$0.850729\pi$
$420$	2765.33	−	3223.97i	0.321273	−	0.374556i
$421$	3648.20	−	11228.0i	0.422333	−	1.29981i	−0.483192	−	0.875515i	$-0.660523\pi$
$421$	3648.20	−	11228.0i	0.422333	−	1.29981i	0.905525	−	0.424293i	$-0.139477\pi$
$422$	1868.09	−	5749.38i	0.215491	−	0.663212i
$423$	1608.80	−	1168.86i	0.184923	−	0.134355i
$424$	279.721			0.0320388
$425$	−2340.56	−	15192.9i	−0.267138	−	1.73404i
$426$	−2229.18			−0.253531
$427$	9353.33	−	6795.59i	1.06005	−	0.770168i
$428$	143.441	−	441.465i	0.0161997	−	0.0498576i
$429$	−2645.08	+	8140.71i	−0.297682	+	0.916171i
$430$	−1319.39	−	2163.29i	−0.147969	−	0.242612i
$431$	4044.97	+	12449.1i	0.452064	+	1.39131i	0.874548	+	0.484939i	$0.161158\pi$
$431$	4044.97	+	12449.1i	0.452064	+	1.39131i	−0.422484	+	0.906370i	$0.638842\pi$
$432$	432.000			0.0481125
$433$	−281.343	−	865.884i	−0.0312251	−	0.0961010i	0.934229	−	0.356673i	$-0.116089\pi$
$433$	−281.343	−	865.884i	−0.0312251	−	0.0961010i	−0.965454	+	0.260572i	$0.916089\pi$
$434$	−14914.4	−	10836.0i	−1.64957	−	1.19849i
$435$	3979.73	−	4639.77i	0.438651	−	0.511402i
$436$	−3580.94	+	2601.70i	−0.393339	+	0.285777i
$437$	639.334	+	464.504i	0.0699852	+	0.0508472i
$438$	−828.682	−	602.072i	−0.0904017	−	0.0656807i
$439$	9917.61	−	7205.56i	1.07823	−	0.783378i	0.100854	−	0.994901i	$-0.467843\pi$
$439$	9917.61	−	7205.56i	1.07823	−	0.783378i	0.977373	+	0.211524i	$0.0678425\pi$
$440$	−2327.82	+	2713.89i	−0.252215	+	0.294045i
$441$	−4800.33	−	3487.64i	−0.518338	−	0.376594i
$442$	−5424.82	−	16695.9i	−0.583783	−	1.79670i
$443$	9116.14			0.977699			0.488850	−	0.872368i	$-0.337417\pi$
$443$	9116.14			0.977699			0.488850	+	0.872368i	$0.337417\pi$
$444$	920.130	+	2831.87i	0.0983501	+	0.302690i
$445$	−2045.78	−	3354.30i	−0.217931	−	0.357324i
$446$	−388.228	+	1194.84i	−0.0412178	+	0.126855i
$447$	1523.63	−	4689.24i	0.161219	−	0.496182i
$448$	1639.20	−	1190.95i	0.172868	−	0.125596i
$449$	−6134.16			−0.644741			−0.322371	−	0.946613i	$-0.604480\pi$
$449$	−6134.16			−0.644741			−0.322371	+	0.946613i	$0.604480\pi$
$450$	−2220.79	−	361.366i	−0.232642	−	0.0378554i
$451$	7375.50			0.770064
$452$	−2697.20	+	1959.63i	−0.280676	+	0.203923i
$453$	2559.10	−	7876.09i	0.265424	−	0.816890i
$454$	1888.19	−	5811.25i	0.195192	−	0.600739i
$455$	−16448.0	+	19176.0i	−1.69471	+	1.97579i
$456$	−125.208	−	385.351i	−0.0128584	−	0.0395740i
$457$	−17434.5			−1.78458			−0.892291	−	0.451461i	$-0.850903\pi$
$457$	−17434.5			−1.78458			−0.892291	+	0.451461i	$0.850903\pi$
$458$	3228.21	+	9935.40i	0.329354	+	1.01365i
$459$	−2686.25	−	1951.68i	−0.273167	−	0.198467i
$460$	2036.56	−	484.386i	0.206424	−	0.0490970i
$461$	12039.0	−	8746.83i	1.21629	−	0.883689i	0.220506	−	0.975386i	$-0.429229\pi$
$461$	12039.0	−	8746.83i	1.21629	−	0.883689i	0.995787	+	0.0916970i	$0.0292291\pi$
$462$	6143.15	+	4463.26i	0.618626	+	0.449458i
$463$	408.667	+	296.914i	0.0410202	+	0.0298029i	0.608106	−	0.793856i	$-0.291929\pi$
$463$	408.667	+	296.914i	0.0410202	+	0.0298029i	−0.567086	+	0.823658i	$0.691929\pi$
$464$	2359.05	−	1713.95i	0.236027	−	0.171483i
$465$	−786.771	+	9733.88i	−0.0784637	+	0.970748i
$466$	7239.44	+	5259.76i	0.719658	+	0.522862i
$467$	675.779	+	2079.83i	0.0669622	+	0.206088i	0.978939	−	0.204154i	$-0.0654442\pi$
$467$	675.779	+	2079.83i	0.0669622	+	0.206088i	−0.911977	+	0.410242i	$0.865444\pi$
$468$	−2569.51			−0.253794
$469$	783.370	+	2410.97i	0.0771273	+	0.237373i
$470$	−4806.60	+	1143.23i	−0.471727	+	0.112198i
$471$	2215.06	−	6817.25i	0.216698	−	0.666927i
$472$	1614.72	−	4969.60i	0.157465	−	0.484628i
$473$	3664.79	−	2662.63i	0.356252	−	0.258832i
$474$	7948.25			0.770200
$475$	321.316	+	2085.72i	0.0310379	+	0.201472i
$476$	−15573.3			−1.49958
$477$	−254.587	+	184.968i	−0.0244376	+	0.0177549i
$478$	3512.26	−	10809.6i	0.336082	−	1.03435i
$479$	−895.817	+	2757.04i	−0.0854508	+	0.262990i	−0.984648	−	0.174554i	$-0.944152\pi$
$479$	−895.817	+	2757.04i	−0.0854508	+	0.262990i	0.899197	+	0.437544i	$0.144152\pi$
$480$	−990.741	−	412.833i	−0.0942103	−	0.0392566i
$481$	−5472.87	−	16843.8i	−0.518797	−	1.59669i
$482$	−425.667			−0.0402253
$483$	−1373.82	−	4228.18i	−0.129422	−	0.398321i
$484$	−864.012	−	627.741i	−0.0811431	−	0.0589539i
$485$	15476.5	+	6448.94i	1.44898	+	0.603776i
$486$	−393.182	+	285.664i	−0.0366978	+	0.0266625i
$487$	7555.31	+	5489.25i	0.703005	+	0.510763i	0.880910	−	0.473284i	$-0.156932\pi$
$487$	7555.31	+	5489.25i	0.703005	+	0.510763i	−0.177904	+	0.984048i	$0.556932\pi$
$488$	−2363.53	−	1717.21i	−0.219246	−	0.159292i
$489$	−5621.14	+	4084.00i	−0.519830	+	0.377678i
$490$	7676.08	+	12585.8i	0.707694	+	1.16035i
$491$	6285.56	+	4566.73i	0.577726	+	0.419743i	0.837904	−	0.545818i	$-0.183781\pi$
$491$	6285.56	+	4566.73i	0.577726	+	0.419743i	−0.260177	+	0.965561i	$0.583781\pi$
$492$	684.175	+	2105.68i	0.0626931	+	0.192950i
$493$	−22412.3			−2.04746
$494$	744.730	+	2292.04i	0.0678279	+	0.208753i
$495$	324.066	−	4009.32i	0.0294256	−	0.364052i
$496$	−1439.55	+	4430.47i	−0.130318	+	0.401077i
$497$	3634.72	−	11186.5i	0.328048	−	1.00963i
$498$	−4911.48	+	3568.40i	−0.441945	+	0.321092i
$499$	12594.6			1.12988			0.564941	−	0.825131i	$-0.308899\pi$
$499$	12594.6			1.12988			0.564941	+	0.825131i	$0.308899\pi$
$500$	4747.79	+	2951.01i	0.424656	+	0.263946i
$501$	−6316.24			−0.563251
$502$	1294.48	−	940.495i	0.115091	−	0.0836182i
$503$	−2084.82	+	6416.41i	−0.184806	+	0.568774i	−0.999945	−	0.0104911i	$-0.996661\pi$
$503$	−2084.82	+	6416.41i	−0.184806	+	0.568774i	0.815139	+	0.579265i	$0.196661\pi$
$504$	−704.384	+	2167.87i	−0.0622535	+	0.191597i
$505$	−992.674	+	12281.3i	−0.0874721	+	1.08220i
$506$	1156.46	+	3559.22i	0.101603	+	0.312701i
$507$	8692.26			0.761414
$508$	−215.096	−	661.996i	−0.0187861	−	0.0578176i
$509$	−9024.77	−	6556.88i	−0.785886	−	0.570980i	0.120854	−	0.992670i	$-0.461437\pi$
$509$	−9024.77	−	6556.88i	−0.785886	−	0.570980i	−0.906740	+	0.421691i	$0.861437\pi$
$510$	4295.52	+	7043.01i	0.372958	+	0.611509i
$511$	4372.51	−	3176.82i	0.378530	−	0.275018i
$512$	−414.217	−	300.946i	−0.0357538	−	0.0259767i
$513$	368.774	+	267.930i	0.0317384	+	0.0230593i
$514$	−1190.68	+	865.078i	−0.102176	+	0.0742353i
$515$	3833.81	+	1597.51i	0.328035	+	0.136689i
$516$	1100.13	+	799.289i	0.0938573	+	0.0681914i
$517$	−2729.43	−	8400.32i	−0.232186	−	0.714595i
$518$	−15711.2			−1.33265
$519$	−1159.33	−	3568.04i	−0.0980515	−	0.301771i
$520$	5892.86	+	2455.50i	0.496960	+	0.207079i
$521$	−4300.78	+	13236.4i	−0.361651	+	1.11305i	0.590400	+	0.807111i	$0.298970\pi$
$521$	−4300.78	+	13236.4i	−0.361651	+	1.11305i	−0.952051	+	0.305938i	$0.901030\pi$
$522$	−1013.71	+	3119.89i	−0.0849981	+	0.261597i
$523$	555.823	−	403.829i	0.0464712	−	0.0337633i	−0.564307	−	0.825565i	$-0.690857\pi$
$523$	555.823	−	403.829i	0.0464712	−	0.0337633i	0.610778	+	0.791802i	$0.290857\pi$
$524$	6920.73			0.576972
$525$	5434.46	−	10555.2i	0.451770	−	0.877461i
$526$	−7886.72			−0.653759
$527$	28967.2	−	21045.9i	2.39437	−	1.73961i
$528$	592.941	−	1824.88i	0.0488720	−	0.150413i
$529$	−3082.72	+	9487.64i	−0.253367	+	0.779785i
$530$	760.626	−	180.911i	0.0623387	−	0.0148270i
$531$	1816.56	+	5590.81i	0.148460	+	0.456912i
$532$	2137.93			0.174231
$533$	−4069.43	−	12524.4i	−0.330706	−	1.01781i
$534$	1705.81	+	1239.34i	0.138235	+	0.100434i
$535$	104.528	−	1293.22i	0.00844701	−	0.104506i
$536$	518.248	−	376.529i	0.0417629	−	0.0303425i
$537$	−9693.27	−	7042.57i	−0.778948	−	0.565939i
$538$	−6546.35	−	4756.20i	−0.524597	−	0.381142i
$539$	−21321.4	+	15490.9i	−1.70386	+	1.23792i
$540$	1174.71	−	279.398i	0.0936136	−	0.0222655i
$541$	−383.278	−	278.468i	−0.0304592	−	0.0221299i	0.572451	−	0.819939i	$-0.305992\pi$
$541$	−383.278	−	278.468i	−0.0304592	−	0.0221299i	−0.602911	+	0.797809i	$0.705992\pi$
$542$	−499.064	−	1535.96i	−0.0395510	−	0.121725i
$543$	−4499.53			−0.355604
$544$	1216.07	+	3742.67i	0.0958428	+	0.294974i
$545$	−8054.72	+	9390.61i	−0.633076	+	0.738073i
$546$	4189.63	−	12894.4i	0.328388	−	1.01067i
$547$	−2896.51	+	8914.55i	−0.226409	+	0.696817i	0.771736	+	0.635943i	$0.219389\pi$
$547$	−2896.51	+	8914.55i	−0.226409	+	0.696817i	−0.998145	+	0.0608736i	$0.980611\pi$
$548$	1865.42	−	1355.31i	0.145414	−	0.105649i
$549$	3286.67			0.255504
$550$	−4574.65	+	8885.23i	−0.354661	+	0.688850i
$551$	3076.80			0.237888
$552$	−908.867	+	660.330i	−0.0700796	+	0.0509158i
$553$	−12959.8	+	39886.1i	−0.996574	+	3.06714i
$554$	1398.00	−	4302.61i	0.107212	−	0.329965i
$555$	4333.57	+	7105.40i	0.331441	+	0.543437i
$556$	2311.32	+	7113.52i	0.176298	+	0.542591i
$557$	−3423.24			−0.260408			−0.130204	−	0.991487i	$-0.541563\pi$
$557$	−3423.24			−0.260408			−0.130204	+	0.991487i	$0.541563\pi$
$558$	−1619.49	−	4984.28i	−0.122865	−	0.378139i
$559$	−6543.48	−	4754.12i	−0.495098	−	0.359710i
$560$	3687.11	−	4298.63i	0.278230	−	0.324375i
$561$	−11931.4	+	8668.68i	−0.897941	+	0.652392i
$562$	1202.01	+	873.312i	0.0902202	+	0.0655488i
$563$	2088.92	+	1517.69i	0.156372	+	0.113611i	0.663220	−	0.748424i	$-0.269189\pi$
$563$	2088.92	+	1517.69i	0.156372	+	0.113611i	−0.506848	+	0.862036i	$0.669189\pi$
$564$	2145.07	−	1558.48i	0.160148	−	0.116354i
$565$	−6066.90	+	7073.11i	−0.451746	+	0.526669i
$566$	3910.03	+	2840.80i	0.290372	+	0.210968i
$567$	−792.432	−	2438.86i	−0.0586932	−	0.180639i
$568$	−2972.24			−0.219564
$569$	4215.80	+	12974.9i	0.310607	+	0.955951i	0.977525	+	0.210820i	$0.0676134\pi$
$569$	4215.80	+	12974.9i	0.310607	+	0.955951i	−0.666917	+	0.745132i	$0.732387\pi$
$570$	−589.698	−	966.879i	−0.0433328	−	0.0710493i
$571$	−5608.22	+	17260.3i	−0.411027	+	1.26501i	0.504729	+	0.863278i	$0.331592\pi$
$571$	−5608.22	+	17260.3i	−0.411027	+	1.26501i	−0.915756	+	0.401734i	$0.868408\pi$
$572$	−3526.77	+	10854.3i	−0.257800	+	0.793427i
$573$	3781.37	−	2747.32i	0.275687	−	0.200299i
$574$	−11682.3			−0.849495
$575$	5224.59	−	2634.31i	0.378923	−	0.191058i
$576$	576.000			0.0416667
$577$	7634.57	−	5546.84i	0.550834	−	0.400204i	−0.277259	−	0.960795i	$-0.589426\pi$
$577$	7634.57	−	5546.84i	0.550834	−	0.400204i	0.828093	+	0.560591i	$0.189426\pi$
$578$	6310.40	−	19421.4i	0.454115	−	1.39762i
$579$	−1000.27	+	3078.50i	−0.0717955	+	0.220964i
$580$	5306.30	−	6186.36i	0.379883	−	0.442887i
$581$	−9898.75	−	30465.2i	−0.706832	−	2.17541i
$582$	−8997.80			−0.640843
$583$	431.922	+	1329.32i	0.0306833	+	0.0944336i
$584$	−1104.91	−	802.763i	−0.0782902	−	0.0568811i
$585$	−6987.08	+	1661.84i	−0.493812	+	0.117451i
$586$	−3047.86	+	2214.40i	−0.214857	+	0.156102i
$587$	−7358.97	−	5346.61i	−0.517440	−	0.375942i	0.298199	−	0.954504i	$-0.403614\pi$
$587$	−7358.97	−	5346.61i	−0.517440	−	0.375942i	−0.815639	+	0.578562i	$0.803614\pi$
$588$	−6400.44	−	4650.19i	−0.448894	−	0.326140i
$589$	−3976.68	+	2889.23i	−0.278194	+	0.202120i
$590$	1176.68	−	14557.8i	0.0821071	−	1.01582i
$591$	−3295.88	−	2394.60i	−0.229398	−	0.166668i
$592$	1226.84	+	3775.83i	0.0851737	+	0.262138i
$593$	−13517.8			−0.936106			−0.468053	−	0.883700i	$-0.655044\pi$
$593$	−13517.8			−0.936106			−0.468053	+	0.883700i	$0.655044\pi$
$594$	667.058	+	2052.99i	0.0460770	+	0.141810i
$595$	−42347.3	+	10072.1i	−2.91777	+	0.693977i
$596$	2031.50	−	6252.32i	0.139620	−	0.429706i
$597$	1209.82	−	3723.43i	0.0829388	−	0.255259i
$598$	5405.88	−	3927.60i	0.369670	−	0.268581i
$599$	−17686.4			−1.20642			−0.603211	−	0.797582i	$-0.706112\pi$
$599$	−17686.4			−1.20642			−0.603211	+	0.797582i	$0.706112\pi$
$600$	−2961.06	−	481.821i	−0.201474	−	0.0327838i
$601$	−12937.2			−0.878070			−0.439035	−	0.898470i	$-0.644680\pi$
$601$	−12937.2			−0.878070			−0.439035	+	0.898470i	$0.644680\pi$
$602$	−5804.79	+	4217.43i	−0.392999	+	0.285531i
$603$	−222.697	+	685.392i	−0.0150397	+	0.0462874i
$604$	3412.13	−	10501.5i	0.229864	−	0.707447i
$605$	−2755.44	−	1148.17i	−0.185165	−	0.0771565i
$606$	−2043.32	−	6288.70i	−0.136971	−	0.421553i
$607$	19817.6			1.32516			0.662580	−	0.748991i	$-0.269461\pi$
$607$	19817.6			1.32516			0.662580	+	0.748991i	$0.269461\pi$
$608$	−166.944	−	513.802i	−0.0111357	−	0.0342721i
$609$	−14003.4	−	10174.1i	−0.931768	−	0.676969i
$610$	−7537.60	−	3140.85i	−0.500309	−	0.208474i
$611$	−12758.7	+	9269.74i	−0.844783	+	0.613770i
$612$	−3581.67	−	2602.24i	−0.236569	−	0.171878i
$613$	21978.5	+	15968.3i	1.44813	+	1.05213i	0.986265	+	0.165173i	$0.0528183\pi$
$613$	21978.5	+	15968.3i	1.44813	+	1.05213i	0.461862	+	0.886952i	$0.347182\pi$
$614$	8957.35	−	6507.90i	0.588745	−	0.427748i
$615$	3222.29	+	5283.32i	0.211277	+	0.346413i
$616$	8190.87	+	5951.02i	0.535746	+	0.389242i
$617$	4086.06	+	12575.6i	0.266610	+	0.820542i	0.991318	+	0.131486i	$0.0419748\pi$
$617$	4086.06	+	12575.6i	0.266610	+	0.820542i	−0.724708	+	0.689056i	$0.758025\pi$
$618$	−2228.91			−0.145081
$619$	1550.65	+	4772.40i	0.100688	+	0.309885i	0.988694	−	0.149946i	$-0.0479100\pi$
$619$	1550.65	+	4772.40i	0.100688	+	0.309885i	−0.888006	+	0.459831i	$0.847910\pi$
$620$	−1049.03	+	12978.5i	−0.0679516	+	0.840693i
$621$	390.551	−	1201.99i	0.0252371	−	0.0776719i
$622$	5086.66	−	15655.1i	0.327904	−	1.00919i
$623$	−9000.63	+	6539.34i	−0.578817	+	0.420535i
$624$	−3426.01			−0.219792
$625$	14818.9	+	4953.81i	0.948411	+	0.317044i
$626$	−10639.2			−0.679280
$627$	1637.97	−	1190.05i	0.104329	−	0.0757993i
$628$	2953.41	−	9089.67i	0.187666	−	0.577575i
$629$	9429.60	−	29021.3i	0.597747	−	1.83968i
$630$	−513.299	+	6350.50i	−0.0324608	+	0.401603i
$631$	−2862.66	−	8810.36i	−0.180603	−	0.555840i	0.819242	−	0.573448i	$-0.194395\pi$
$631$	−2862.66	−	8810.36i	−0.180603	−	0.555840i	−0.999845	+	0.0176086i	$0.994395\pi$
$632$	10597.7			0.667013
$633$	2802.13	+	8624.07i	0.175947	+	0.541510i
$634$	743.689	+	540.322i	0.0465862	+	0.0338469i
$635$	−1013.04	−	1661.01i	−0.0633093	−	0.103803i
$636$	−339.449	+	246.624i	−0.0211636	+	0.0153762i
$637$	38069.4	+	27659.0i	2.36792	+	1.72039i
$638$	11787.9	+	8564.39i	0.731483	+	0.531454i
$639$	2705.17	−	1965.42i	0.167472	−	0.121676i
$640$	−1320.99	−	550.444i	−0.0815885	−	0.0339972i
$641$	−14484.6	−	10523.7i	−0.892524	−	0.648456i	0.0440111	−	0.999031i	$-0.485986\pi$
$641$	−14484.6	−	10523.7i	−0.892524	−	0.648456i	−0.936535	+	0.350575i	$0.885986\pi$
$642$	215.161	+	662.198i	0.0132270	+	0.0407085i
$643$	−2202.25			−0.135068			−0.0675338	−	0.997717i	$-0.521513\pi$
$643$	−2202.25			−0.135068			−0.0675338	+	0.997717i	$0.521513\pi$
$644$	−1831.76	−	5637.57i	−0.112083	−	0.344956i
$645$	3508.44	+	1461.94i	0.214178	+	0.0892461i
$646$	−1283.15	+	3949.13i	−0.0781499	+	0.240521i
$647$	−6966.93	+	21442.0i	−0.423336	+	1.30289i	0.481244	+	0.876587i	$0.340185\pi$
$647$	−6966.93	+	21442.0i	−0.423336	+	1.30289i	−0.904579	+	0.426306i	$0.859815\pi$
$648$	−524.243	+	380.885i	−0.0317812	+	0.0230904i
$649$	26110.4			1.57923
$650$	17612.2	+	2865.84i	1.06278	+	0.172934i
$651$	27652.8			1.66482
$652$	−7494.85	+	5445.33i	−0.450186	+	0.327079i
$653$	1687.69	−	5194.17i	0.101140	−	0.311277i	−0.887665	−	0.460489i	$-0.847674\pi$
$653$	1687.69	−	5194.17i	0.101140	−	0.311277i	0.988805	+	0.149213i	$0.0476740\pi$
$654$	2051.69	−	6314.46i	0.122672	−	0.377546i
$655$	18819.0	−	4476.02i	1.12263	−	0.267012i
$656$	912.234	+	2807.57i	0.0542938	+	0.167099i
$657$	1536.46			0.0912375
$658$	4323.24	+	13305.6i	0.256136	+	0.788305i
$659$	−3842.68	−	2791.87i	−0.227146	−	0.165031i	0.468391	−	0.883521i	$-0.344834\pi$
$659$	−3842.68	−	2791.87i	−0.227146	−	0.165031i	−0.695538	+	0.718490i	$0.744834\pi$
$660$	432.088	−	5345.76i	0.0254833	−	0.315278i
$661$	−11307.5	+	8215.36i	−0.665370	+	0.483420i	−0.868472	−	0.495738i	$-0.834898\pi$
$661$	−11307.5	+	8215.36i	−0.665370	+	0.483420i	0.203102	+	0.979158i	$0.434898\pi$
$662$	−4445.81	−	3230.07i	−0.261014	−	0.189638i
$663$	21303.5	+	15477.9i	1.24790	+	0.906656i
$664$	−6548.64	+	4757.86i	−0.382736	+	0.278074i
$665$	5813.53	−	1382.72i	0.339006	−	0.0806309i
$666$	−3613.40	−	2625.29i	−0.210235	−	0.152744i
$667$	−2636.17	−	8113.31i	−0.153033	−	0.470987i
$668$	−8421.65			−0.487789
$669$	−582.342	−	1792.26i	−0.0336542	−	0.103577i
$670$	1165.71	−	1359.05i	0.0672170	−	0.0783651i
$671$	4511.11	−	13883.8i	0.259537	−	0.798774i
$672$	−939.179	+	2890.50i	−0.0539131	+	0.165928i
$673$	−21746.8	+	15800.0i	−1.24558	+	0.904968i	−0.997957	−	0.0638876i	$-0.979650\pi$
$673$	−21746.8	+	15800.0i	−1.24558	+	0.904968i	−0.247625	+	0.968856i	$0.579650\pi$
$674$	21979.5			1.25611
$675$	3013.60	−	1519.50i	0.171842	−	0.0866451i
$676$	11589.7			0.659404
$677$	4083.45	−	2966.80i	0.231816	−	0.168424i	−0.465813	−	0.884883i	$-0.654238\pi$
$677$	4083.45	−	2966.80i	0.231816	−	0.168424i	0.697630	+	0.716459i	$0.254238\pi$
$678$	1545.36	−	4756.12i	0.0875355	−	0.269407i
$679$	14671.1	−	45152.9i	0.829196	−	2.55200i
$680$	5727.36	+	9390.68i	0.322992	+	0.529583i
$681$	2832.28	+	8716.87i	0.159373	+	0.490501i
$682$	−23277.8			−1.30697
$683$	−1625.36	−	5002.34i	−0.0910581	−	0.280248i	0.895148	−	0.445769i	$-0.147070\pi$
$683$	−1625.36	−	5002.34i	−0.0910581	−	0.280248i	−0.986206	+	0.165521i	$0.947070\pi$
$684$	491.699	+	357.240i	0.0274862	+	0.0199699i
$685$	4195.95	−	4891.86i	0.234042	−	0.272859i
$686$	16201.5	−	11771.1i	0.901715	−	0.655135i
$687$	−12677.3	−	9210.62i	−0.704033	−	0.511510i
$688$	1466.84	+	1065.72i	0.0812828	+	0.0590554i
$689$	2019.02	−	1466.90i	0.111638	−	0.0811097i
$690$	−2044.34	+	2383.40i	−0.112793	+	0.131499i
$691$	−4360.09	−	3167.79i	−0.240037	−	0.174397i	0.461263	−	0.887264i	$-0.347397\pi$
$691$	−4360.09	−	3167.79i	−0.240037	−	0.174397i	−0.701300	+	0.712867i	$0.747397\pi$
$692$	−1545.77	−	4757.38i	−0.0849151	−	0.261342i
$693$	−11390.0			−0.624346
$694$	−4040.27	−	12434.7i	−0.220989	−	0.680135i
$695$	10885.7	+	17848.4i	0.594128	+	0.974143i
$696$	−1351.62	+	4159.85i	−0.0736105	+	0.226550i
$697$	7011.51	−	21579.2i	0.381033	−	1.17270i
$698$	−19478.4	+	14151.9i	−1.05626	+	0.767418i
$699$	−13422.7			−0.726311
$700$	7245.94	−	14073.6i	0.391244	−	0.759904i
$701$	−28818.6			−1.55273			−0.776364	−	0.630285i	$-0.782938\pi$
$701$	−28818.6			−1.55273			−0.776364	+	0.630285i	$0.782938\pi$
$702$	3118.16	−	2265.48i	0.167646	−	0.121802i
$703$	−1294.52	+	3984.11i	−0.0694503	+	0.213746i
$704$	790.588	−	2433.18i	0.0423244	−	0.130261i
$705$	4824.97	−	5625.20i	0.257757	−	0.300507i
$706$	6696.84	+	20610.8i	0.356996	+	1.09872i
$707$	34889.8			1.85596
$708$	2422.08	+	7454.41i	0.128570	+	0.395697i
$709$	20746.6	+	15073.3i	1.09895	+	0.798434i	0.980888	−	0.194572i	$-0.0623317\pi$
$709$	20746.6	+	15073.3i	1.09895	+	0.798434i	0.118062	+	0.993006i	$0.462332\pi$
$710$	−8082.21	+	1922.31i	−0.427211	+	0.101610i
$711$	−9645.40	+	7007.79i	−0.508763	+	0.369638i
$712$	2274.41	+	1652.45i	0.119715	+	0.0869780i
$713$	11025.9	+	8010.76i	0.579133	+	0.420765i
$714$	18898.6	−	13730.6i	0.990562	−	0.719686i
$715$	−2570.03	+	31796.3i	−0.134425	+	1.66309i
$716$	−12924.4	−	9390.09i	−0.674589	−	0.490118i
$717$	5268.40	+	16214.5i	0.274410	+	0.844547i
$718$	12230.3			0.635696
$719$	2906.15	+	8944.21i	0.150739	+	0.463926i	0.997704	−	0.0677219i	$-0.0215731\pi$
$719$	2906.15	+	8944.21i	0.150739	+	0.463926i	−0.846966	+	0.531648i	$0.821573\pi$
$720$	1566.28	−	372.531i	0.0810718	−	0.0192825i
$721$	3634.28	−	11185.2i	0.187722	−	0.577749i
$722$	−4062.94	+	12504.4i	−0.209428	+	0.644553i
$723$	516.557	−	375.301i	0.0265712	−	0.0193051i
$724$	−5999.37			−0.307962
$725$	10428.0	−	20254.0i	0.534187	−	1.03754i
$726$	1601.97			0.0818933
$727$	−13886.5	+	10089.1i	−0.708421	+	0.514698i	−0.882664	−	0.470005i	$-0.844252\pi$
$727$	−13886.5	+	10089.1i	−0.708421	+	0.514698i	0.174243	+	0.984703i	$0.444252\pi$
$728$	5586.17	−	17192.5i	0.284392	−	0.875269i
$729$	225.273	−	693.320i	0.0114451	−	0.0352243i
$730$	−3523.69	−	1468.29i	−0.178654	−	0.0744437i
$731$	−4306.37	−	13253.7i	−0.217889	−	0.670594i
$732$	4382.23			0.221273
$733$	−6671.26	−	20532.0i	−0.336164	−	1.03461i	−0.966146	−	0.257997i	$-0.916937\pi$
$733$	−6671.26	−	20532.0i	−0.336164	−	1.03461i	0.629981	−	0.776610i	$-0.283063\pi$
$734$	−4638.98	−	3370.42i	−0.233280	−	0.169488i
$735$	−20411.8	−	8505.41i	−1.02435	−	0.426839i
$736$	−1211.82	+	880.440i	−0.0606907	+	0.0440944i
$737$	2589.62	+	1881.47i	0.129430	+	0.0940362i
$738$	−2686.79	−	1952.07i	−0.134014	−	0.0973667i
$739$	−16172.4	+	11750.0i	−0.805024	+	0.584884i	−0.912384	−	0.409336i	$-0.865760\pi$
$739$	−16172.4	+	11750.0i	−0.805024	+	0.584884i	0.107360	+	0.994220i	$0.465760\pi$
$740$	5778.10	+	9473.87i	0.287036	+	0.470630i
$741$	−2924.59	−	2124.84i	−0.144990	−	0.105341i
$742$	−684.136	−	2105.56i	−0.0338483	−	0.104174i
$743$	−6008.86			−0.296694			−0.148347	−	0.988935i	$-0.547395\pi$
$743$	−6008.86			−0.296694			−0.148347	+	0.988935i	$0.547395\pi$
$744$	−2159.32	−	6645.71i	−0.106404	−	0.327478i
$745$	1480.40	−	18315.4i	0.0728021	−	0.900703i
$746$	4402.66	−	13550.0i	0.216076	−	0.665014i
$747$	2814.03	−	8660.68i	0.137831	−	0.424201i
$748$	−15908.6	+	11558.2i	−0.777639	+	0.564988i
$749$	−3673.88			−0.179227
$750$	−8363.41	+	604.898i	−0.407185	+	0.0294503i
$751$	15433.5			0.749900			0.374950	−	0.927045i	$-0.377660\pi$
$751$	15433.5			0.749900			0.374950	+	0.927045i	$0.377660\pi$
$752$	2860.09	−	2077.98i	0.138692	−	0.100766i
$753$	−741.671	+	2282.63i	−0.0358938	+	0.110470i
$754$	8039.33	−	24742.5i	0.388296	−	1.19505i
$755$	2486.49	−	30762.7i	0.119858	−	1.48287i
$756$	−1056.58	−	3251.81i	−0.0508298	−	0.156438i
$757$	−2125.51			−0.102051			−0.0510257	−	0.998697i	$-0.516249\pi$
$757$	−2125.51			−0.102051			−0.0510257	+	0.998697i	$0.516249\pi$
$758$	−3721.46	−	11453.5i	−0.178324	−	0.548825i
$759$	−4541.48	−	3299.58i	−0.217188	−	0.157796i
$760$	−786.264	−	1289.17i	−0.0375273	−	0.0615305i
$761$	−4185.75	+	3041.12i	−0.199387	+	0.144863i	−0.682999	−	0.730420i	$-0.739325\pi$
$761$	−4185.75	+	3041.12i	−0.199387	+	0.144863i	0.483612	+	0.875282i	$0.339325\pi$
$762$	844.691	+	613.704i	0.0401574	+	0.0291761i
$763$	28342.0	+	20591.7i	1.34476	+	0.977025i
$764$	5041.82	−	3663.10i	0.238752	−	0.173464i
$765$	−11422.4	−	4759.61i	−0.539840	−	0.224946i
$766$	1986.52	+	1443.29i	0.0937021	+	0.0680786i
$767$	−14406.4	−	44338.3i	−0.678207	−	2.08731i
$768$	768.000			0.0360844
$769$	4046.85	+	12454.9i	0.189770	+	0.584053i	0.999998	−	0.00206263i	$-0.000656557\pi$
$769$	4046.85	+	12454.9i	0.189770	+	0.584053i	−0.810228	+	0.586115i	$0.800657\pi$
$770$	26121.7	+	10884.7i	1.22255	+	0.509424i
$771$	682.197	−	2099.59i	0.0318661	−	0.0980737i
$772$	−1333.69	+	4104.67i	−0.0621768	+	0.191360i
$773$	−13928.3	+	10119.5i	−0.648082	+	0.470859i	−0.862617	−	0.505857i	$-0.831176\pi$
$773$	−13928.3	+	10119.5i	−0.648082	+	0.470859i	0.214535	+	0.976716i	$0.431176\pi$
$774$	−2039.75			−0.0947251
$775$	5541.37	+	35970.0i	0.256841	+	1.66720i
$776$	−11997.1			−0.554986
$777$	19066.0	−	13852.3i	0.880294	−	0.639571i
$778$	−5976.26	+	18393.0i	−0.275397	+	0.847586i
$779$	−962.555	+	2962.44i	−0.0442710	+	0.136252i
$780$	−9316.11	+	2215.79i	−0.427654	+	0.101715i
$781$	−4589.49	−	14125.0i	−0.210275	−	0.647160i
$782$	11513.0			0.526474
$783$	−1520.57	−	4679.83i	−0.0694007	−	0.213593i
$784$	−8533.91	−	6200.25i	−0.388753	−	0.282446i
$785$	2152.21	−	26627.0i	0.0978545	−	1.21065i
$786$	−8398.48	+	6101.85i	−0.381125	+	0.276903i
$787$	12195.0	+	8860.20i	0.552358	+	0.401311i	0.828654	−	0.559761i	$-0.189107\pi$
$787$	12195.0	+	8860.20i	0.552358	+	0.401311i	−0.276296	+	0.961072i	$0.589107\pi$
$788$	−4394.51	−	3192.80i	−0.198665	−	0.144339i
$789$	9570.73	−	6953.54i	0.431847	−	0.313755i
$790$	28817.5	−	6854.10i	1.29782	−	0.308681i
$791$	21347.5	+	15509.9i	0.959584	+	0.697178i
$792$	889.411	+	2737.33i	0.0399038	+	0.122811i
$793$	−26065.2			−1.16722
$794$	−455.290	−	1401.24i	−0.0203497	−	0.0626299i
$795$	−763.534	+	890.168i	−0.0340626	+	0.0397120i
$796$	1613.09	−	4964.57i	0.0718271	−	0.221061i
$797$	1178.23	−	3626.21i	0.0523650	−	0.161163i	−0.921454	−	0.388487i	$-0.872998\pi$
$797$	1178.23	−	3626.21i	0.0523650	−	0.161163i	0.973819	+	0.227324i	$0.0729977\pi$
$798$	−2594.44	+	1884.97i	−0.115090	+	0.0836180i
$799$	−27172.3			−1.20311
$800$	−3948.07	−	642.428i	−0.174482	−	0.0283916i
$801$	−3162.74			−0.139513
$802$	−660.004	+	479.521i	−0.0290593	+	0.0211128i
$803$	2108.87	−	6490.42i	0.0926778	−	0.285233i
$804$	−296.930	+	913.856i	−0.0130248	+	0.0400861i
$805$	−8627.11	−	14145.2i	−0.377721	−	0.619318i
$806$	12843.5	+	39528.2i	0.561282	+	1.72745i
$807$	12137.6			0.529447
$808$	−2724.43	−	8384.93i	−0.118620	−	0.365075i
$809$	−9077.48	−	6595.17i	−0.394496	−	0.286618i	0.372799	−	0.927912i	$-0.378398\pi$
$809$	−9077.48	−	6595.17i	−0.394496	−	0.286618i	−0.767295	+	0.641294i	$0.778398\pi$
$810$	−1179.20	+	1374.77i	−0.0511516	+	0.0596352i
$811$	30244.2	−	21973.7i	1.30952	−	0.951419i	0.309516	−	0.950894i	$-0.399833\pi$
$811$	30244.2	−	21973.7i	1.30952	−	0.951419i	1.00000		0.000525238i	$-0.000167189\pi$
$812$	−18671.2	−	13565.4i	−0.806935	−	0.586273i
$813$	1959.85	+	1423.91i	0.0845449	+	0.0614254i
$814$	−16049.5	+	11660.6i	−0.691074	+	0.502094i
$815$	−16858.4	+	19654.4i	−0.724570	+	0.844742i
$816$	−4775.56	−	3469.65i	−0.204875	−	0.148850i
$817$	591.188	+	1819.49i	0.0253158	+	0.0779142i
$818$	4014.48			0.171593
$819$	6284.45	+	19341.5i	0.268127	+	0.825211i
$820$	4296.38	+	7044.43i	0.182971	+	0.300002i
$821$	3213.89	−	9891.35i	0.136621	−	0.420476i	−0.859218	−	0.511610i	$-0.829049\pi$
$821$	3213.89	−	9891.35i	0.136621	−	0.420476i	0.995839	+	0.0911344i	$0.0290493\pi$
$822$	−1068.79	+	3289.40i	−0.0453508	+	0.139575i
$823$	11065.3	−	8039.42i	0.468666	−	0.340506i	−0.328255	−	0.944589i	$-0.606461\pi$
$823$	11065.3	−	8039.42i	0.468666	−	0.340506i	0.796921	+	0.604083i	$0.206461\pi$
$824$	−2971.88			−0.125644
$825$	−2282.46	−	14815.8i	−0.0963211	−	0.625237i
$826$	−41357.1			−1.74213
$827$	−37636.3	+	27344.4i	−1.58252	+	1.14977i	−0.668782	+	0.743458i	$0.733184\pi$
$827$	−37636.3	+	27344.4i	−1.58252	+	1.14977i	−0.913736	+	0.406309i	$0.866816\pi$
$828$	520.734	−	1602.66i	0.0218560	−	0.0672658i
$829$	3673.62	−	11306.2i	0.153908	−	0.473681i	−0.844140	−	0.536122i	$-0.819889\pi$
$829$	3673.62	−	11306.2i	0.153908	−	0.473681i	0.998049	+	0.0624412i	$0.0198886\pi$
$830$	−14730.1	+	17173.1i	−0.616010	+	0.718177i
$831$	2097.01	+	6453.92i	0.0875383	+	0.269415i
$832$	−4568.01			−0.190345
$833$	25054.1	+	77108.5i	1.04210	+	3.20727i
$834$	−9076.68	−	6594.60i	−0.376858	−	0.273804i
$835$	−22900.4	+	5446.75i	−0.949103	+	0.225739i
$836$	2183.96	−	1586.74i	0.0903514	−	0.0656442i
$837$	6359.83	+	4620.68i	0.262638	+	0.190817i
$838$	−4278.99	−	3108.87i	−0.176391	−	0.128155i
$839$	12352.6	−	8974.69i	0.508294	−	0.369297i	−0.303882	−	0.952710i	$-0.598283\pi$
$839$	12352.6	−	8974.69i	0.508294	−	0.369297i	0.812176	+	0.583412i	$0.198283\pi$
$840$	−684.399	+	8467.34i	−0.0281119	+	0.347799i
$841$	−7139.54	−	5187.18i	−0.292736	−	0.212685i
$842$	7296.39	+	22456.0i	0.298635	+	0.919103i
$843$	−2228.65			−0.0910543
$844$	3736.17	+	11498.8i	0.152375	+	0.468962i
$845$	31515.0	−	7495.69i	1.28302	−	0.305159i
$846$	−1229.01	+	3782.51i	−0.0499460	+	0.153718i
$847$	−2612.04	+	8039.02i	−0.105963	+	0.326120i
$848$	−452.599	+	328.832i	−0.0183282	+	0.0133162i
$849$	−7249.59			−0.293057
$850$	21647.5	+	21831.2i	0.873532	+	0.880947i
$851$	11614.9			0.467867
$852$	3606.89	−	2620.56i	0.145035	−	0.105374i
$853$	15098.7	−	46469.0i	0.606060	−	1.86526i	0.116724	−	0.993164i	$-0.462761\pi$
$853$	15098.7	−	46469.0i	0.606060	−	1.86526i	0.489336	−	0.872095i	$-0.337239\pi$
$854$	−7145.31	+	21991.0i	−0.286309	+	0.881167i
$855$	1568.09	+	653.409i	0.0627223	+	0.0261358i
$856$	286.882	+	882.931i	0.0114549	+	0.0352546i
$857$	−32642.9			−1.30112			−0.650560	−	0.759455i	$-0.725466\pi$
$857$	−32642.9			−1.30112			−0.650560	+	0.759455i	$0.725466\pi$
$858$	−5290.16	−	16281.4i	−0.210493	−	0.647831i
$859$	−14096.8	−	10241.9i	−0.559926	−	0.406810i	0.271506	−	0.962437i	$-0.412478\pi$
$859$	−14096.8	−	10241.9i	−0.559926	−	0.406810i	−0.831432	+	0.555627i	$0.812478\pi$
$860$	4677.92	+	1949.25i	0.185484	+	0.0772894i
$861$	14176.8	−	10300.0i	0.561142	−	0.407694i
$862$	−21179.7	−	15388.0i	−0.836874	−	0.608024i
$863$	−6414.16	−	4660.16i	−0.253002	−	0.183817i	0.454054	−	0.890974i	$-0.349977\pi$
$863$	−6414.16	−	4660.16i	−0.253002	−	0.183817i	−0.707056	+	0.707157i	$0.749977\pi$
$864$	−698.991	+	507.846i	−0.0275233	+	0.0199969i
$865$	−7280.16	−	11936.7i	−0.286165	−	0.469201i
$866$	1473.13	+	1070.29i	0.0578048	+	0.0419977i
$867$	9465.61	+	29132.1i	0.370783	+	1.14115i
$868$	36870.5			1.44178
$869$	16364.0	+	50363.3i	0.638793	+	1.96600i
$870$	−984.952	+	12185.8i	−0.0383827	+	0.474869i
$871$	1766.12	−	5435.55i	0.0687057	−	0.211454i
$872$	2735.59	−	8419.28i	0.106237	−	0.326964i
$873$	10919.1	−	7933.16i	0.423315	−	0.307556i
$874$	−1580.52			−0.0611693
$875$	10601.2	−	42955.7i	0.409583	−	1.65962i
$876$	2048.61			0.0790140
$877$	−13027.7	+	9465.18i	−0.501613	+	0.364443i	−0.809633	−	0.586937i	$-0.800334\pi$
$877$	−13027.7	+	9465.18i	−0.501613	+	0.364443i	0.308020	+	0.951380i	$0.400334\pi$
$878$	−7576.38	+	23317.7i	−0.291219	+	0.896280i
$879$	1746.27	−	5374.46i	0.0670082	−	0.206230i
$880$	576.117	−	7127.69i	0.0220692	−	0.273039i
$881$	−3618.93	−	11137.9i	−0.138394	−	0.425932i	0.857709	−	0.514136i	$-0.171887\pi$
$881$	−3618.93	−	11137.9i	−0.138394	−	0.425932i	−0.996102	+	0.0882037i	$0.971887\pi$
$882$	11867.1			0.453044
$883$	−7787.89	−	23968.7i	−0.296810	−	0.913488i	−0.982607	−	0.185695i	$-0.940546\pi$
$883$	−7787.89	−	23968.7i	−0.296810	−	0.913488i	0.685797	−	0.727793i	$-0.259454\pi$
$884$	28404.7	+	20637.2i	1.08072	+	0.785187i
$885$	11407.4	+	18703.7i	0.433282	+	0.710418i
$886$	−14750.2	+	10716.7i	−0.559304	+	0.406358i
$887$	−22937.3	−	16664.9i	−0.868273	−	0.630837i	0.0618503	−	0.998085i	$-0.480300\pi$
$887$	−22937.3	−	16664.9i	−0.868273	−	0.630837i	−0.930123	+	0.367248i	$0.880300\pi$
$888$	−4817.86	−	3500.38i	−0.182069	−	0.132281i
$889$	−4456.99	+	3238.19i	−0.168147	+	0.122166i
$890$	7253.37	+	3022.42i	0.273184	+	0.113833i
$891$	−2619.57	−	1903.23i	−0.0984949	−	0.0715607i
$892$	−776.456	−	2389.69i	−0.0291454	−	0.0897002i
$893$	3730.28			0.139786
$894$	3047.25	+	9378.48i	0.113999	+	0.350854i
$895$	−41217.4	−	17174.9i	−1.53938	−	0.641446i
$896$	−1252.24	+	3853.99i	−0.0466901	+	0.143697i
$897$	−3097.29	+	9532.49i	−0.115291	+	0.354828i
$898$	9925.28	−	7211.14i	0.368832	−	0.267972i
$899$	53062.1			1.96854
$900$	4018.13	−	2026.00i	0.148820	−	0.0750369i
$901$	4299.93			0.158991
$902$	−11933.8	+	8670.42i	−0.440524	+	0.320059i
$903$	3325.85	−	10235.9i	0.122566	−	0.377220i
$904$	2060.48	−	6341.49i	0.0758080	−	0.233313i
$905$	−16313.7	+	3880.13i	−0.599209	+	0.142519i
$906$	5118.20	+	15752.2i	0.187683	+	0.577628i
$907$	24333.2			0.890818			0.445409	−	0.895327i	$-0.353058\pi$
$907$	24333.2			0.890818			0.445409	+	0.895327i	$0.353058\pi$
$908$	3776.38	+	11622.5i	0.138021	+	0.424786i
$909$	8024.23	+	5829.95i	0.292791	+	0.212725i
$910$	4070.76	−	50363.2i	0.148291	−	1.83464i
$911$	−28880.4	+	20982.8i	−1.05033	+	0.763109i	−0.972275	−	0.233840i	$-0.924871\pi$
$911$	−28880.4	+	20982.8i	−1.05033	+	0.763109i	−0.0780549	+	0.996949i	$0.524871\pi$
$912$	655.599	+	476.320i	0.0238038	+	0.0172945i
$913$	−32722.7	−	23774.4i	−1.18616	−	0.861794i
$914$	28209.7	−	20495.5i	1.02089	−	0.741720i
$915$	11916.3	−	2834.23i	0.430536	−	0.102401i
$916$	−16903.1	−	12280.8i	−0.609710	−	0.442980i
$917$	−16926.6	−	52094.6i	−0.609558	−	1.87603i
$918$	6640.78			0.238756
$919$	−3839.75	−	11817.5i	−0.137825	−	0.424183i	0.858193	−	0.513327i	$-0.171587\pi$
$919$	−3839.75	−	11817.5i	−0.137825	−	0.424183i	−0.996019	+	0.0891434i	$0.971587\pi$
$920$	−2725.79	+	3177.87i	−0.0976812	+	0.113882i
$921$	−5132.10	+	15795.0i	−0.183614	+	0.565106i
$922$	−9196.96	+	28305.3i	−0.328509	+	1.01105i
$923$	−21453.6	+	15586.9i	−0.765062	+	0.555850i
$924$	−15186.7			−0.540699
$925$	21839.2	+	22024.6i	0.776292	+	0.782881i
$926$	−1010.28			−0.0358530
$927$	2704.84	−	1965.18i	0.0958345	−	0.0696278i
$928$	−1802.16	+	5546.47i	−0.0637486	+	0.196198i
$929$	−9452.18	+	29090.8i	−0.333817	+	1.02738i	0.633485	+	0.773755i	$0.281624\pi$
$929$	−9452.18	+	29090.8i	−0.333817	+	1.02738i	−0.967302	+	0.253628i	$0.918376\pi$
$930$	−10169.8	−	16674.7i	−0.358583	−	0.587939i
$931$	−3439.48	−	10585.6i	−0.121079	−	0.372642i
$932$	−17896.9			−0.629004
$933$	7629.99	+	23482.7i	0.267733	+	0.823997i
$934$	−3538.43	−	2570.82i	−0.123962	−	0.0900639i
$935$	−35783.6	+	41718.4i	−1.25160	+	1.45919i
$936$	4157.55	−	3020.64i	0.145186	−	0.105484i
$937$	46198.0	+	33564.8i	1.61070	+	1.17024i	0.861256	+	0.508172i	$0.169678\pi$
$937$	46198.0	+	33564.8i	1.61070	+	1.17024i	0.749443	+	0.662069i	$0.230322\pi$
$938$	−4101.78	−	2980.12i	−0.142780	−	0.103736i
$939$	12911.0	−	9380.38i	0.448705	−	0.326003i
$940$	6433.29	−	7500.27i	0.223224	−	0.260247i
$941$	−33984.4	−	24691.1i	−1.17732	−	0.855374i	−0.185455	−	0.982653i	$-0.559376\pi$
$941$	−33984.4	−	24691.1i	−1.17732	−	0.855374i	−0.991867	+	0.127278i	$0.959376\pi$
$942$	4430.12	+	13634.5i	0.153228	+	0.471588i
$943$	8636.45			0.298241
$944$	3229.44	+	9939.21i	0.111345	+	0.342684i
$945$	−4976.20	−	8159.06i	−0.171297	−	0.280862i
$946$	−2799.65	+	8616.44i	−0.0962204	+	0.296136i
$947$	−2840.88	+	8743.31i	−0.0974826	+	0.300021i	−0.987893	−	0.155138i	$-0.950418\pi$
$947$	−2840.88	+	8743.31i	−0.0974826	+	0.300021i	0.890410	+	0.455159i	$0.150418\pi$
$948$	−12860.5	+	9343.72i	−0.440602	+	0.320116i
$949$	−12185.0			−0.416799
$950$	−2971.81	−	2997.03i	−0.101493	−	0.102354i
$951$	−1378.88			−0.0470169
$952$	25198.1	−	18307.5i	0.857852	−	0.623266i
$953$	−5075.36	+	15620.4i	−0.172515	+	0.530948i	−0.999511	−	0.0312602i	$-0.990048\pi$
$953$	−5075.36	+	15620.4i	−0.172515	+	0.530948i	0.826996	+	0.562208i	$0.190048\pi$
$954$	194.487	−	598.569i	0.00660036	−	0.0203138i
$955$	11340.7	−	13221.6i	0.384270	−	0.448002i
$956$	7024.53	+	21619.3i	0.237646	+	0.731399i
$957$	−21855.9			−0.738246
$958$	−1791.63	−	5514.08i	−0.0604228	−	0.185962i
$959$	−14764.2	−	10726.9i	−0.497145	−	0.361197i
$960$	2088.37	−	496.708i	0.0702102	−	0.0166992i
$961$	−44479.8	+	32316.5i	−1.49306	+	1.08477i
$962$	28656.3	+	20820.0i	0.960413	+	0.697781i
$963$	−844.949	−	613.891i	−0.0282742	−	0.0205424i
$964$	688.743	−	500.401i	0.0230113	−	0.0167187i
$965$	−971.885	+	12024.1i	−0.0324208	+	0.401108i
$966$	7193.41	+	5226.32i	0.239590	+	0.174073i
$967$	11097.4	+	34154.3i	0.369047	+	1.13581i	0.947408	+	0.320030i	$0.103693\pi$
$967$	11097.4	+	34154.3i	0.369047	+	1.13581i	−0.578360	+	0.815782i	$0.696307\pi$
$968$	2135.95			0.0709217
$969$	−1924.72	−	5923.69i	−0.0638091	−	0.196384i
$970$	−32622.8	+	7759.17i	−1.07985	+	0.256837i
$971$	−4470.21	+	13757.9i	−0.147740	+	0.454698i	−0.997353	−	0.0727087i	$-0.976836\pi$
$971$	−4470.21	+	13757.9i	−0.147740	+	0.454698i	0.849613	+	0.527407i	$0.176836\pi$
$972$	300.365	−	924.427i	0.00991172	−	0.0305052i
$973$	47892.8	−	34796.2i	1.57798	−	1.14647i
$974$	−18677.7			−0.614449
$975$	−23899.6	+	12050.5i	−0.785024	+	0.395820i
$976$	5842.97			0.191628
$977$	−10234.9	+	7436.07i	−0.335151	+	0.243502i	−0.742613	−	0.669721i	$-0.766414\pi$
$977$	−10234.9	+	7436.07i	−0.335151	+	0.243502i	0.407462	+	0.913222i	$0.366414\pi$
$978$	4294.17	−	13216.1i	0.140401	−	0.432110i
$979$	−4341.01	+	13360.3i	−0.141715	+	0.436155i
$980$	−27215.7	−	11340.5i	−0.887116	−	0.369654i
$981$	3077.54	+	9471.69i	0.100161	+	0.308265i
$982$	−15538.8			−0.504951
$983$	−12226.7	−	37629.8i	−0.396714	−	1.22096i	−0.927619	−	0.373529i	$-0.878148\pi$
$983$	−12226.7	−	37629.8i	−0.396714	−	1.22096i	0.530904	−	0.847432i	$-0.321852\pi$
$984$	−3582.39	−	2602.76i	−0.116059	−	0.0843220i
$985$	−14014.6	−	5839.78i	−0.453344	−	0.188904i
$986$	36263.8	−	26347.2i	1.17127	−	0.850979i
$987$	−16977.6	−	12334.9i	−0.547520	−	0.397796i
$988$	−3899.46	−	2833.12i	−0.125565	−	0.0912283i
$989$	4291.34	−	3117.84i	0.137974	−	0.100244i
$990$	4188.89	+	6868.18i	0.134477	+	0.220490i
$991$	−8535.14	−	6201.14i	−0.273590	−	0.198775i	0.442527	−	0.896755i	$-0.354082\pi$
$991$	−8535.14	−	6201.14i	−0.273590	−	0.198775i	−0.716117	+	0.697981i	$0.754082\pi$
$992$	−2879.10	−	8860.95i	−0.0921486	−	0.283604i
$993$	8242.99			0.263427
$994$	7269.45	+	22373.1i	0.231965	+	0.713914i
$995$	1175.49	−	14543.1i	0.0374528	−	0.463364i
$996$	3752.03	−	11547.6i	0.119365	−	0.367368i
$997$	−7766.64	+	23903.3i	−0.246712	+	0.759301i	0.748638	+	0.662979i	$0.230708\pi$
$997$	−7766.64	+	23903.3i	−0.246712	+	0.759301i	−0.995350	+	0.0963227i	$0.969292\pi$
$998$	−20378.5	+	14805.8i	−0.646362	+	0.469610i
$999$	6699.61			0.212178

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	150.4.g.b.61.3	✓	16
25.16	even	5	inner	150.4.g.b.91.3	yes	16

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
150.4.g.b.61.3	✓	16	1.1	even	1	trivial
150.4.g.b.91.3	yes	16	25.16	even	5	inner

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:	\( N \)	\(=\)	\( 150 = 2 \cdot 3 \cdot 5^{2} \)
Weight:	\( k \)	\(=\)	\( 4 \)
Character orbit:	\([\chi]\)	\(=\)	150.g (of order \(5\), degree \(4\), minimal)

\(f(q)\)	\(=\)	\(q+(-1.61803 + 1.17557i) q^{2} +(0.927051 - 2.85317i) q^{3} +(1.23607 - 3.80423i) q^{4} +(0.900748 - 11.1440i) q^{5} +(1.85410 + 5.70634i) q^{6} -31.6588 q^{7} +(2.47214 + 7.60845i) q^{8} +(-7.28115 - 5.29007i) q^{9} +(11.6431 + 19.0903i) q^{10} +(-32.3404 + 23.4967i) q^{11} +(-9.70820 - 7.05342i) q^{12} +(57.7437 + 41.9533i) q^{13} +(51.2251 - 37.2172i) q^{14} +(-30.9607 - 12.9010i) q^{15} +(-12.9443 - 9.40456i) q^{16} +(38.0021 + 116.958i) q^{17} +18.0000 q^{18} +(-5.21701 - 16.0563i) q^{19} +(-41.2809 - 17.2014i) q^{20} +(-29.3493 + 90.3280i) q^{21} +(24.7059 - 76.0368i) q^{22} +(-37.8694 + 27.5138i) q^{23} +24.0000 q^{24} +(-123.377 - 20.0759i) q^{25} -142.750 q^{26} +(-21.8435 + 15.8702i) q^{27} +(-39.1325 + 120.437i) q^{28} +(-56.3174 + 173.327i) q^{29} +(65.2615 - 15.5221i) q^{30} +(-89.9717 - 276.905i) q^{31} +32.0000 q^{32} +(37.0588 + 114.055i) q^{33} +(-198.982 - 144.569i) q^{34} +(-28.5166 + 352.806i) q^{35} +(-29.1246 + 21.1603i) q^{36} +(-200.744 - 145.849i) q^{37} +(27.3166 + 19.8467i) q^{38} +(173.231 - 125.860i) q^{39} +(87.0153 - 20.6962i) q^{40} +(-149.266 - 108.448i) q^{41} +(-58.6987 - 180.656i) q^{42} -113.319 q^{43} +(49.4117 + 152.074i) q^{44} +(-65.5110 + 76.3761i) q^{45} +(28.9297 - 89.0364i) q^{46} +(-68.2785 + 210.140i) q^{47} +(-38.8328 + 28.2137i) q^{48} +659.281 q^{49} +(223.229 - 112.555i) q^{50} +368.932 q^{51} +(230.975 - 167.813i) q^{52} +(10.8048 - 33.2538i) q^{53} +(16.6869 - 51.3571i) q^{54} +(232.716 + 381.566i) q^{55} +(-78.2649 - 240.875i) q^{56} -50.6478 q^{57} +(-112.635 - 346.654i) q^{58} +(-528.425 - 383.923i) q^{59} +(-87.3480 + 101.835i) q^{60} +(-295.442 + 214.651i) q^{61} +(471.098 + 342.273i) q^{62} +(230.513 + 167.477i) q^{63} +(-51.7771 + 37.6183i) q^{64} +(519.540 - 605.707i) q^{65} +(-194.042 - 140.980i) q^{66} +(-24.7441 - 76.1546i) q^{67} +491.910 q^{68} +(43.3945 + 133.555i) q^{69} +(-368.607 - 604.375i) q^{70} +(-114.809 + 353.346i) q^{71} +(22.2492 - 68.4761i) q^{72} +(-138.114 + 100.345i) q^{73} +496.267 q^{74} +(-171.657 + 333.405i) q^{75} -67.5304 q^{76} +(1023.86 - 743.877i) q^{77} +(-132.337 + 407.291i) q^{78} +(409.357 - 1259.87i) q^{79} +(-116.464 + 135.780i) q^{80} +(25.0304 + 77.0356i) q^{81} +369.006 q^{82} +(312.670 + 962.298i) q^{83} +(307.350 + 223.303i) q^{84} +(1337.62 - 318.145i) q^{85} +(183.354 - 133.215i) q^{86} +(442.323 + 321.366i) q^{87} +(-258.723 - 187.973i) q^{88} +(284.301 - 206.557i) q^{89} +(16.2135 - 200.592i) q^{90} +(-1828.10 - 1328.19i) q^{91} +(57.8594 + 178.073i) q^{92} -873.464 q^{93} +(-136.557 - 420.279i) q^{94} +(-183.631 + 43.6756i) q^{95} +(29.6656 - 91.3014i) q^{96} +(-463.412 + 1426.24i) q^{97} +(-1066.74 + 775.031i) q^{98} +359.774 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 16 q - 8 q^{2} - 12 q^{3} - 16 q^{4} + 15 q^{5} - 24 q^{6} + 46 q^{7} - 32 q^{8} - 36 q^{9} + 50 q^{10} - 83 q^{11} - 48 q^{12} + 22 q^{13} + 2 q^{14} - 60 q^{15} - 64 q^{16} - 79 q^{17} + 288 q^{18} - 15 q^{19}+ \cdots + 1368 q^{99}+O(q^{100}) \) 16 * q - 8 * q^2 - 12 * q^3 - 16 * q^4 + 15 * q^5 - 24 * q^6 + 46 * q^7 - 32 * q^8 - 36 * q^9 + 50 * q^10 - 83 * q^11 - 48 * q^12 + 22 * q^13 + 2 * q^14 - 60 * q^15 - 64 * q^16 - 79 * q^17 + 288 * q^18 - 15 * q^19 - 80 * q^20 - 72 * q^21 + 14 * q^22 - 143 * q^23 + 384 * q^24 - 205 * q^25 + 144 * q^26 - 108 * q^27 - 96 * q^28 + 255 * q^29 - 378 * q^31 + 512 * q^32 + 21 * q^33 - 248 * q^34 - 610 * q^35 - 144 * q^36 - 514 * q^37 - 160 * q^38 + 66 * q^39 - 918 * q^41 - 144 * q^42 + 1012 * q^43 + 28 * q^44 - 180 * q^45 - 36 * q^46 - 209 * q^47 - 192 * q^48 + 1478 * q^49 + 620 * q^50 + 1218 * q^51 + 88 * q^52 - 1738 * q^53 - 216 * q^54 + 265 * q^55 - 192 * q^56 + 570 * q^57 + 510 * q^58 + 695 * q^59 - 240 * q^60 + 352 * q^61 + 384 * q^62 + 9 * q^63 - 256 * q^64 + 1150 * q^65 - 498 * q^66 - 1554 * q^67 + 1624 * q^68 - 54 * q^69 + 200 * q^70 - 1543 * q^71 - 288 * q^72 - 778 * q^73 + 1332 * q^74 + 165 * q^75 + 760 * q^76 + 2622 * q^77 - 348 * q^78 + 920 * q^79 - 320 * q^80 - 324 * q^81 + 2044 * q^82 + 2967 * q^83 + 12 * q^84 - 2215 * q^85 + 164 * q^86 - 720 * q^87 - 664 * q^88 - 2605 * q^89 + 270 * q^90 - 5683 * q^91 - 72 * q^92 + 1116 * q^93 - 418 * q^94 - 1865 * q^95 - 384 * q^96 + 1251 * q^97 - 464 * q^98 + 1368 * q^99

Introduction

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